APPSC Group 1 Prelims 2024 CSAT (Paper II) with Answers & Explanations

Explanation

To find the value of A, we compute the product of the given numbers: A = 808 × 8008 × 80008

We can calculate this step-by-step: 808 × 8008 = 6470464

Now, multiply this result by 80008: 6470464 × 80008 = 6470464 × (80000 + 8) 6470464 × 80008 = 517637120000 + 51763712 A = 517688883712

The sum of all the digits in A is represented by M: M = 5 + 1 + 7 + 6 + 8 + 8 + 8 + 8 + 3 + 7 + 1 + 2 M = 64

Now, we calculate the square root of M: √M = √64 = 8

Explanation

The pattern of the first series is based on multiplying the previous term by a decreasing factor and subtracting a decreasing number:

T2 = T1 × 8 - 7 = 4 × 8 - 7 = 25 T3 = T2 × 7 - 6 = 25 × 7 - 6 = 169 T4 = T3 × 6 - 5 = 169 × 6 - 5 = 1009 T5 = T4 × 5 - 4 = 1009 × 5 - 4 = 5041 T6 = T5 × 4 - 3 = 5041 × 4 - 3 = 20161

Applying this same pattern to the second series starting with 6:

A = 6 × 8 - 7 = 41 B = 41 × 7 - 6 = 281 C = 281 × 6 - 5 = 1681 D = 1681 × 5 - 4 = 8401

Explanation

2282-5. The pattern for Series 1 is Tn = (Tn-1 + 1) * (n - 0.5). Applying this to Series 2, E (S6) = (D + 1) * (6 - 0.5) = (414 + 1) * 5.5 = 2282.5.

Explanation

To find the greatest possible speed that yields integer travel hours for each day, we calculate the Highest Common Factor (HCF) of the three distances: 66, 88, and 110.

HCF(66, 88, 110) = 22 km/hr

Using the formula Time = Distance / Speed, we calculate the travel time for each day: Time on Day 1 = 66 / 22 = 3 hours Time on Day 2 = 88 / 22 = 4 hours Time on Day 3 = 110 / 22 = 5 hours

Adding these up, the total time to complete the journey is: 3 + 4 + 5 = 12 hours

Explanation

30N10K4M2L2 = 15.

Substituting the given operators into the equation 30N10K4M2L2 = 15: N represents ÷ K represents + M represents × L represents -

Replacing the letters with these mathematical symbols: 30 ÷ 10 + 4 × 2 - 2

Following the BODMAS order of operations: First, perform the division: 30 ÷ 10 = 3

Next, perform the multiplication: 4 × 2 = 8

Substitute these values back into the expression: 3 + 8 - 2 = 9

Since the calculation yields 9, the stated value of 15 is incorrect.

Explanation

9:24 pm. Phase 1 (4 min, no leak): fills 20/30 units. Phase 2 (pipes+leak): net drain = −1 unit/min; drains 20 units in 20 min. Total = 24 min → 9:24 pm. No printed option matches; 9:25 pm is closest.

Explanation

Let the time on the digital watch be represented in the HH:MM format. At 23:45, the four individual digits (2, 3, 4, 5) are in strictly ascending order.

To find the value of A × A, we can test the options by calculating their square roots to find A:

For option 4, A = √9604 = 98.

Adding A = 98 minutes to the initial time of 23:45: 23:45 + 15 minutes = 00:00 00:00 + 83 minutes = 01:23

At 01:23, the four digits on the watch are 0, 1, 2, and 3. These four whole numbers are arranged in strictly ascending order from left to right (0 < 1 < 2 < 3), which satisfies the given condition.

Explanation

From the given relation definitions: E * F means E is the son of F. E + F means E is the father of F. E > F means E is the daughter of F. E < F means E is the wife of F.

Analyzing the first expression Q > R < P + S: R < P means R is the wife of P, making P the husband. Q > R means Q is the daughter of R, which also makes her the daughter of P. P + S means P is the father of S. Thus, Q and S are siblings, and both are the children of P.

Analyzing the second expression M * H < I + J < K + L: M * H means M is the son of H. H < I means H is the wife of I, making I the husband. I + J means I is the father of J. Thus, M and J are siblings, and both are the children of H and I.

We are given that H is the sister of P. Since P and H are siblings, the children of P and the children of H are first cousins to each other. The children of P are Q and S, while the children of H are M and J. Therefore, M and S are first cousins, which corresponds to the pair MS.

Explanation

The order of reading the novel from first to last (1 to 5) can be determined step-by-step:

Since the first reader gives the novel to R, R is the 2nd reader.

Since the last reader takes it from P, P is the 4th reader.

T is neither the first nor the last reader. Since R is 2nd and P is 4th, T must be the 3rd reader.

This leaves the 1st and 5th positions for Q and S.

There are two readers between Q and P. Since P is in the 4th position, Q must be in the 1st position so that there are exactly two readers (the 2nd and 3rd) between Q and P. S then becomes the 5th reader.

The complete sequence from first to last is Q, R, T, P, S. Thus, the two readers between Q and P in order are R and T.

Explanation

Statement I is correct because among all triangles that can be inscribed inside a given circle, the equilateral triangle has the maximum area.

Statement II is correct. The height h of an equilateral triangle with side length a is given by the formula h = (√3/2)a. Substituting h = 10 cm, we find: a = 20/√3 cm

The area of an equilateral triangle is calculated as: Area = (√3/4)a² = (√3/4) × (20/√3)² = (√3/4) × (400/3) = 100√3/3 cm²

Statement III is incorrect because the sides 5 cm, 12 cm, and 13 cm satisfy the Pythagorean theorem since 5² + 12² = 13², making it a right-angled triangle. For any right-angled triangle, the circumcenter lies at the midpoint of the hypotenuse, meaning the circumradius is exactly half the length of the hypotenuse: Circumradius = 13/2 = 6.5 cm

Statement IV is correct because a scalene triangle is defined as a triangle in which all three sides have different lengths, meaning no two sides are equal.

Explanation

The three-digit natural numbers range from 100 to 999. The numbers that leave a remainder of 4 when divided by 5 form an arithmetic progression.

The first term, a, is 104. The last term, l, is 999. The common difference, d, is 5.

The number of terms, N, is calculated using the formula: l = a + (N - 1) × d 999 = 104 + (N - 1) × 5 895 = (N - 1) × 5 N - 1 = 179 N = 180

The sum, S, of this arithmetic progression is given by: S = (N/2) × (a + l) S = (180/2) × (104 + 999) S = 90 × 1103 S = 99270

Comparing the sum 99270 with the given format XXYZA: X = 9 Y = 2 Z = 7 A = 0

Thus, the value of Y + Z is: Y + Z = 2 + 7 = 9

Explanation

Cost Price (CP) is calculated by dividing the marked price (MP) of ₹42,000 by 1.25: CP = 42,000 ÷ 1.25 = ₹33,600

To find the person getting the higher profit, calculate the total discount offered by both sellers. The seller offering the lower discount will secure the higher profit.

Total discount offered by Nandu: Discount = (10% of 12,000) + (8% of 16,000) + (5% of 14,000) = 1,200 + 1,280 + 700 = ₹3,180

Total discount offered by Mohan: Discount = (8% of 16,000) + (7% of 8,000) + (5% of 18,000) = 1,280 + 560 + 900 = ₹2,740

Mohan offers a lower discount, meaning Mohan earns the higher profit. Mohan's Selling Price = 42,000 - 2,740 = ₹39,260 Mohan's Profit = 39,260 - 33,600 = ₹5,660

Profit Percentage = (5,660 ÷ 33,600) × 100 ≈ 16.84%

The approximate profit percentage of the person getting the higher profit is 17%.

Explanation

The cost price of the watch is determined from the marked selling price of ₹ 42,000, which includes a 25% markup on the cost price: Cost Price × 1.25 = 42,000 Cost Price = 42,000 / 1.25 = ₹ 33,600

Nandu sells the watch with a total price of ₹ 42,000 divided into three parts: the first ₹ 12,000, the next ₹ 16,000, and the remaining ₹ 14,000 (calculated as 42,000 - 12,000 - 16,000).

The discount for each part is calculated by adjusting the original rates based on payment delays:

For the first payment of ₹ 12,000, there is no delay, so the discount rate remains 10%: Discount = 10% of 12,000 = ₹ 1,200

For the second payment of ₹ 16,000, there is a delay of 1 week, reducing the discount rate by 1% (from 8% to 7%): Discount = 7% of 16,000 = ₹ 1,120

For the third payment of the remaining ₹ 14,000, there is a delay of 2 weeks, reducing the discount rate by 2% (from 5% to 3%): Discount = 3% of 14,000 = ₹ 420

Summing these individual discounts gives the total discount offered by Nandu: Total Discount = 1,200 + 1,120 + 420 = ₹ 2,740

The actual selling price received by Nandu is: Actual Selling Price = 42,000 - 2,740 = ₹ 39,260

Nandu's profit is the difference between the actual selling price and the cost price: Profit = 39,260 - 33,600 = ₹ 5,660

Explanation

To find Mohan's profit, first calculate the cost price (CP) of the watch. The base price before discount of ₹ 42,000 was set by increasing the CP by 25%. CP = 42,000 ÷ 1.25 = ₹ 33,600

Mohan sells the watch to Ganesh. The total value of ₹ 42,000 is split into three parts: First part = ₹ 16,000 Second part = ₹ 8,000 Third part (remaining amount) = 42,000 - 16,000 - 8,000 = ₹ 18,000

Ganesh defaults on each payment by 2 weeks. Since the discount is reduced by 1% for each week of delay, the discount rates for all three slabs will be reduced by 2%. New discount rate on first part = 8% - 2% = 6% New discount rate on second part = 7% - 2% = 5% New discount rate on third part = 5% - 2% = 3%

Calculate the total discount given by Mohan: Discount on first part = 6% of 16,000 = ₹ 960 Discount on second part = 5% of 8,000 = ₹ 400 Discount on third part = 3% of 18,000 = ₹ 540 Total discount = 960 + 400 + 540 = ₹ 1,900

The actual selling price (SP) received by Mohan is: SP = 42,000 - 1,900 = ₹ 40,100

Profit made by Mohan is: Profit = SP - CP = 40,100 - 33,600 = ₹ 6,500

Explanation

The cost price of the watch is the same for both Nandu and Mohan, as both arrived at the price of ₹ 42,000 by increasing the cost price by 25%. Since their cost prices are identical, the difference in their profits is equal to the difference in their final selling prices, which is determined solely by the difference in the total discount given by each.

The total amount to be paid in both cases is ₹ 42,000. Since both buyers defaulted on each payment slab by one week, the discount rate for every payment slab is reduced by 1% for both sellers.

For Nandu, the revised discounts on the slabs of ₹ 42,000 (divided as ₹ 12,000, ₹ 16,000, and the remaining ₹ 14,000) are: 9% on the first ₹ 12,000 = ₹ 1,080 7% on the next ₹ 16,000 = ₹ 1,120 4% on the rest ₹ 14,000 = ₹ 560 Total discount given by Nandu = 1,080 + 1,120 + 560 = ₹ 2,760

For Mohan, the revised discounts on the slabs of ₹ 42,000 (divided as ₹ 16,000, ₹ 8,000, and the remaining ₹ 18,000) are: 7% on the first ₹ 16,000 = ₹ 1,120 6% on the next ₹ 8,000 = ₹ 480 4% on the rest ₹ 18,000 = ₹ 720 Total discount given by Mohan = 1,120 + 480 + 720 = ₹ 2,320

The difference in their profits is equal to the difference in their discounts: Difference = ₹ 2,760 - ₹ 2,320 = ₹ 440

Explanation

The bike is purchased in 2024 and its value is to be determined in 2029, which is after a period of 5 years.

Since the depreciation percentages are applied directly to the original cost of the bike, the total depreciation is calculated by summing the annual depreciation percentages. The rates of depreciation for the 5 years are: Year 1: 10% Year 2: 9.5% Year 3: 9% Year 4: 8.5% Year 5: 8%

The total depreciation percentage over 5 years is: 10% + 9.5% + 9% + 8.5% + 8% = 45%

The total depreciation amount is: 45% of ₹ 78,000 = 0.45 × 78,000 = 35,100

The value of the bike in the year 2029 is the original cost minus the total depreciation: 78,000 - 35,100 = 42,900

Explanation

The total number of sweets produced by the shop each day is q. Since r% of these sweets fail the quality check, the number of discarded sweets per day is (r/100) × q.

The number of acceptable sweets produced each day is the difference between the total produced and the discarded ones: q - (r/100) × q = q × (1 - r/100) = (100 - r)q / 100

To find the number of days required to complete Neelima's order of p sweets, divide the total order quantity by the daily rate of acceptable sweets produced: Number of days = p / [ (100 - r)q / 100 ] Number of days = 100p / [ (100 - r)q ]

Explanation

To determine who is in the middle when arranged from fattest to thinnest, we analyze the relationships regarding fatness given in the statements:

From the third statement, Ravi is fatter than Raghu but not as fat as Madhu. This gives the relation: Madhu > Ravi > Raghu

From the fourth statement, Praveen is thinner than Mahesh, who is thinner than Raghu. This gives the relation: Raghu > Mahesh > Praveen

Combining these two relations, we get the complete order of fatness from fattest to thinnest: Madhu > Ravi > Raghu > Mahesh > Praveen

In this sequence of five members, the middle position (third member) is occupied by Raghu.

Explanation

Let the ranks of Keerthi, Joshua, Pallavi, Rama, and Swetha be represented by K, J, P, R, and S respectively, where 1 is the fastest and 5 is the slowest (last).

According to the given conditions: From condition II, Pallavi finished after Keerthi, which means: P > K

From condition III, Rama finished after Joshua, which means: R > J

From condition IV, the sum of their ranks is: K + S = P + R

Rearranging the terms of the equation gives: S - R = P - K

Since P > K, the value of (P - K) must be positive, which implies: S - R > 0 or S > R

Combining the inequalities S > R and R > J, we obtain the relation: S > R > J

Since all five ranks are distinct integers from 1 to 5, and Swetha (S) has a rank greater than both Rama (R) and Joshua (J), and Pallavi (P) cannot be 5 (from condition II), Swetha must hold the highest rank number, which is 5.

Thus, Swetha was the last to finish the race.

Explanation

Let the ranks of Keerthi, Joshua, Pallavi, Rama, and Swetha be represented by K, J, P, R, and S respectively, where each rank is a unique integer from the set {1, 2, 3, 4, 5}.

The sum of the ranks of Swetha and Pallavi is 8, so S + P = 8. Since the ranks are distinct integers between 1 and 5, the only possible pair is {3, 5}. Because Pallavi did not get the 5th rank, Pallavi has rank 3 (P = 3) and Swetha has rank 5 (S = 5).

Using the equation K + S = P + R, we substitute S = 5 and P = 3: K + 5 = 3 + R K + 2 = R

The remaining ranks available for Keerthi, Rama, and Joshua are {1, 2, 4}. If K = 1, then R = 3, which is invalid because Pallavi already has rank 3. If K = 2, then R = 4, which is valid and leaves the remaining rank of 1 for Joshua (J = 1). Since Rama (rank 4) finished after Joshua (rank 1), this configuration satisfies all conditions. If K = 4, then R = 6, which is invalid since the ranks only range from 1 to 5.

This uniquely determines Rama's rank as 4.

Explanation

Let the ranks of Keerthi, Joshna, Pallavi, Rama, and Swetha be represented by K, J, P, R, and S respectively, where ranks range from 1 (fastest) to 5 (slowest).

Based on the given clues: Clue I: K ≠ 1. Clue II: P ≠ 5 and P > K. Clue III: R > J. Clue IV: K + S = P + R.

Since K ≠ 1 and P > K, Keerthi's rank must be at least 2. Because Pallavi finished after Keerthi, Pallavi's rank must be strictly greater than Keerthi's rank, meaning P ≥ 3. Given that P ≠ 5, Pallavi's rank can only be 3 or 4.

There are three possible cases for the pair (K, P):

Case 1: K = 3 and P = 4. Substituting into Clue IV gives 3 + S = 4 + R, which simplifies to S = R + 1. The remaining ranks to assign to J, R, and S are {1, 2, 5}. The only consecutive values are 1 and 2, which means R = 1 and S = 2. This leaves J = 5. However, this violates Clue III, which states R > J (1 > 5 is false). Hence, this case is invalid.

Case 2: K = 2 and P = 3. Substituting into Clue IV gives 2 + S = 3 + R, which simplifies to S = R + 1. The remaining ranks to assign to J, R, and S are {1, 4, 5}. There are no consecutive values in this set, making this case invalid.

Case 3: K = 2 and P = 4. Substituting into Clue IV gives 2 + S = 4 + R, which simplifies to S = R + 2. The remaining ranks to assign to J, R, and S are {1, 3, 5}. For S = R + 2, we have two possibilities: Subcase 3a: R = 1 and S = 3. This leaves J = 5, which violates Clue III (1 > 5 is false). Subcase 3b: R = 3 and S = 5. This leaves J = 1, which satisfies Clue III (3 > 1 is true). This results in the valid arrangement: J = 1, K = 2, R = 3, P = 4, S = 5.

Alternatively, if we analyze another possible scenario where P = 3, we can assign the remaining ranks as: J = 1, K = 2, P = 3, R = 4, S = 5. This also perfectly satisfies all four clues.

In both of these valid arrangements, Keerthi's rank is fixed at 2 (K = 2) and Pallavi's rank is either 3 or 4 (P = 3 or P = 4). Since Keerthi always finishes with a faster rank than Pallavi in any consistent scenario, Keerthi could not have finished the race after Pallavi.

Explanation

Let Pooja's current age be x and Ajay's current age be 3x.

After 8 years, their ages will be x + 8 and 3x + 8 respectively. According to the given condition: (x + 8) / (3x + 8) = 1/2 2(x + 8) = 3x + 8 2x + 16 = 3x + 8 x = 8

Thus, Pooja's current age is 8 years and Ajay's current age is 24 years.

Let y years ago the ratio of their ages was 1 : 5. (8 - y) / (24 - y) = 1/5 5(8 - y) = 24 - y 40 - 5y = 24 - y 4y = 16 y = 4

Therefore, the ratio of their ages was 1 : 5 exactly 4 years ago.

Explanation

The amount saved by Kavitha on any day n (where n = 1 corresponds to 1st March, 2024) follows the sequence of natural numbers. The total savings S_n at the end of day n is the sum of the first n natural numbers, which is given by the formula:

S_n = n(n + 1)/2

We want to find the first date after 1st March, 2024 (meaning n > 1) where the total savings S_n is a perfect square.

Evaluating the sum for consecutive values of n starting from n = 2:

For n = 2: S₂ = 2 × 3 / 2 = 3 For n = 3: S₃ = 3 × 4 / 2 = 6 For n = 4: S₄ = 4 × 5 / 2 = 10 For n = 5: S₅ = 5 × 6 / 2 = 15 For n = 6: S₆ = 6 × 7 / 2 = 21 For n = 7: S₇ = 7 × 8 / 2 = 28 For n = 8: S₈ = 8 × 9 / 2 = 36

Since 36 is a perfect square (6²), the condition is satisfied at n = 8. This corresponds to the 8th day of March, which is 8th March, 2024.

Explanation

Let the initial number of pens in the shop be n.

According to the successive percentage reduction formula, the remaining number of pens after selling 10%, 20%, and 25% sequentially is given by:

n × (1 - 10/100) × (1 - 20/100) × (1 - 25/100) = 270

Expressing these percentages as fractions:

n × 9/10 × 4/5 × 3/4 = 270

Canceling the common factor of 4 in the numerator and denominator:

n × (9 × 3) / (10 × 5) = 270

n × 27/50 = 270

Solving for n:

n = (270 × 50) / 27

n = 10 × 50 = 500

Explanation

To find the maximum possible marks (X), we assume all 100 attempted questions are correct. Since 1 mark is awarded for each correct answer: X = 100 × 1 = 100

To find the minimum possible marks (Y), we assume all 100 attempted questions are incorrect. The penalty for wrong answers is calculated as follows: I. One-fifth of the questions (20 questions) carry 1/10 negative marking: 20 × (-1/10) = -2 marks

II. One-tenth of the questions (10 questions) carry 1/5 negative marking: 10 × (-1/5) = -2 marks

III. The remaining questions (100 - 20 - 10 = 70 questions) carry 1/2 negative marking: 70 × (-1/2) = -35 marks

Summing these penalties gives the minimum possible score: Y = -2 - 2 - 35 = -39

Now, substituting X and Y into the given expression: X - Y = 100 - (-39) = 139

Since 17.375 can be written as the fraction 139/8: (X - Y) / 17.375 = 139 / (139/8) = 8

Explanation

Let the two-digit number be represented as ab, where the tens digit a is from the set {1, 2, 3, 4, 5, 6, 7, 8, 9} and the units digit b is from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.

The given condition is: a! × b! > a! + b!

Let x = a! and y = b!. We can rewrite the inequality as: xy > x + y xy - x - y > 0 xy - x - y + 1 > 1 (x - 1)(y - 1) > 1 (a! - 1)(b! - 1) > 1

We analyze this inequality to find the valid digits: If a = 1, then a! = 1, which makes a! - 1 = 0, so the product is 0. Thus, a cannot be 1. If b = 0 or b = 1, then b! = 1, which makes b! - 1 = 0, so the product is 0. Thus, b cannot be 0 or 1.

Therefore, both a and b must be at least 2: a ∈ {2, 3, 4, 5, 6, 7, 8, 9} (8 possible choices) b ∈ {2, 3, 4, 5, 6, 7, 8, 9} (8 possible choices)

The total number of such two-digit combinations is: 8 × 8 = 64

Since both a ≥ 2 and b ≥ 2, we have (a! - 1) ≥ 1 and (b! - 1) ≥ 1. The product of two integers that are each ≥ 1 is strictly greater than 1 in all cases except when both integers are exactly equal to 1. This special case occurs when: a! - 1 = 1 and b! - 1 = 1 a! = 2 and b! = 2 This only happens when a = 2 and b = 2.

For the number 22, the product of factorials is 2! × 2! = 4, and the sum of factorials is 2! + 2! = 4. Since 4 is not strictly greater than 4, this number does not satisfy the inequality.

Subtracting this single invalid case from our total combinations: 64 - 1 = 63

Explanation

The ratio of the profit shares, excluding Raghava's extra compensation, is determined solely by the ratio of their total investments over the three-year period.

For Krishna: First year investment = ₹ 15,000 Second year investment = 15,000 + 5,000 = ₹ 20,000 Third year investment = 20,000 × 1.20 = ₹ 24,000 Total investment-equivalent for Krishna = 15,000 + 20,000 + 24,000 = ₹ 59,000

For Suresh: First year investment = ₹ 18,000 Second year investment = 18,000 + 2,000 = ₹ 20,000 Third year investment = 20,000 × 1.25 = ₹ 25,000 Total investment-equivalent for Suresh = 18,000 + 20,000 + 25,000 = ₹ 63,000

For Raghava: First year investment = ₹ 20,000 Second year investment = 20,000 - 5,000 = ₹ 15,000 Third year investment = 15,000 × 1.40 = ₹ 21,000 Total investment-equivalent for Raghava = 20,000 + 15,000 + 21,000 = ₹ 56,000

The ratio of the profit shares is: Krishna : Suresh : Raghava = 59,000 : 63,000 : 56,000 = 59 : 63 : 56

Explanation

Let the number of 25-paise coins be x. The number of 1-rupee coins is 3 times the number of 25-paise coins, which is 3x. Let the number of 50-paise coins be y.

The total number of coins in the piggy bank is 220: x + y + 3x = 220 4x + y = 220 y = 220 - 4x

The total value of the coins is ₹ 160. Expressing the values of 25-paise, 50-paise, and 1-rupee coins in rupees gives: 0.25x + 0.50y + 1.00(3x) = 160

Substitute y = 220 - 4x into this equation: 0.25x + 0.50(220 - 4x) + 3x = 160 3.25x + 110 - 2x = 160 1.25x = 50 x = 40

Substitute the value of x back to find y: y = 220 - 4(40) y = 220 - 160 y = 60

Explanation

Water fraction after n replacements = Initial water fraction × (1 - x/V)ⁿ

Here, the initial water fraction is 2/5, the replaced volume x is 10 litres, the total volume V is 20 litres, and the number of replacements n is 2 (once by Bhaskar and once by Karthik).

Substituting the values into the formula: Water fraction = (2/5) × (1 - 10/20)² Water fraction = (2/5) × (½)² Water fraction = (2/5) × ¼ = 1/10

Since water constitutes 1/10 of the final mixture, milk makes up the remaining portion: Milk fraction = 1 - 1/10 = 9/10

Therefore, the ratio of milk to water in the final solution received by Varun is 9/10 : 1/10, which simplifies to 9 : 1.

Explanation

Let the total number of guests be 100. Since 60% of the guests are women, the number of women is 60, which leaves 40 men (100 - 60 = 40).

Given that 80% of the guests are married couples, there are 80 married individuals forming 40 husband-wife pairs. This means there are exactly 40 married men and 40 married women.

Since the total number of men is 40 and there are 40 married men, all men must be married. Hence, statement I is correct.

Out of 60 women, 40 are married, which means the remaining 20 women are unmarried. The percentage of unmarried women is (20 / 60) × 100% = 33.33%. Since 33.33% is greater than 30%, statement II is also correct.

Explanation

Let the positions of the boxes in the kitchen rack from top to bottom (numbered 1 to 6) be represented as slots 1, 2, 3, 4, 5, and 6.

From the given conditions: The purple box is between the black and green boxes, meaning they form a contiguous block of three: either Green, Purple, Black or Black, Purple, Green. The yellow box is between the red and black boxes, meaning they also form a contiguous block of three: either Red, Yellow, Black or Black, Yellow, Red. Combining these two blocks with Black as the common element, we get the sequence: Green, Purple, Black, Yellow, Red (or its reverse). Since the red box is just above the blue box, Red must be followed immediately by Blue in the top-to-bottom sequence. This gives the full sequence from top to bottom: 1: Green 2: Purple 3: Black 4: Yellow 5: Red 6: Blue

Evaluating the positions of the green and red boxes: Position of Green = 1 Position of Red = 5

The difference between their positions is: D = 5 - 1 = 4

Substituting this value into the expression D³/2: D³/2 = 4³/2 = 64/2 = 32

Explanation

To find the relationship, break down the statement from the end:

The grandmother of Bhargav's younger brother is Bhargav's grandmother.

The only son of Bhargav's grandmother is Bhargav's father.

The wife of Bhargav's father is Bhargav's mother.

The son of Bhargav's mother is Bhargav's brother.

Therefore, the boy in the photograph and Bhargav are brothers.

Explanation

Statement I is correct because a rhombus is defined as a parallelogram with all four sides of equal length.

Statement II is correct because every rhombus satisfies the definition of a parallelogram, having opposite sides that are parallel and equal. However, the converse is not true because a general parallelogram can have adjacent sides of unequal lengths, meaning not all parallelograms are rhombuses.

Statement III is correct because a square is a specific type of rhombus that has all four internal angles equal to 90 degrees. Therefore, all squares are rhombuses. Conversely, a general rhombus does not need to have right angles, meaning it may or may not be a square depending on its angle measurements.

Explanation

Every 2 minutes, representing one cycle of 1 minute climbing up and 1 minute slipping down, the net height gained is 5 - 2 = 3 meters.

At the 24th minute, exactly 12 complete cycles of 2 minutes each have occurred. Thus, the height at the 24th minute is 12 × 3 = 36 meters.

To reach the top of the 50-meter pole, the final upward move of 5 meters will place him at the top, after which he does not slip. This means the required height before the last upward climb must be at least 50 - 5 = 45 meters.

Since each complete cycle yields a net gain of 3 meters, the number of cycles required to reach at least 45 meters is 45 ÷ 3 = 15 cycles. After 15 cycles, he is at a height of 45 meters and has made 15 upward climbs. On the next upward climb, which is the 16th time going upwards, he covers the remaining 5 meters to reach the 50-meter mark at the top.

Explanation

Let the amount invested in Reliance Infra Private Limited be P.

Since the amount invested in Reliance Jio is 50% of the amount invested in Reliance Infra, the sum invested in Reliance Jio is 0.5P.

The compound interest amount formula is given by A = P(1 + r/100)ⁿ, where r is the annual rate of interest and n is the duration in years.

For Reliance Infra, with r = 5% and n = 2: A₁ = P(1 + 5/100)² = P(1.05)² = 1.1025P

For Reliance Jio, with r = 10% and n = 2: A₂ = 0.5P(1 + 10/100)² = 0.5P(1.1)² = 0.5P × 1.21 = 0.605P

The difference between the amounts received from both companies is ₹ 6,965: A₁ - A₂ = 6965 1.1025P - 0.605P = 6965 0.4975P = 6965 P = 6965 / 0.4975 = 14000

The difference between the sums invested in the two companies is: P - 0.5P = 0.5P = 0.5 × 14000 = ₹ 7,000

Explanation

The total number of characters in the project report remains constant. The formula for the total characters is:

Total Characters = Pages × Lines per page × Characters per line

Using the initial values: Total Characters = 40 × 75 × 80 = 240,000

Using the new values: Total Characters = New Pages × 70 × 95 240,000 = New Pages × 6650 New Pages = 240,000 ÷ 6650 ≈ 36.09

The percentage change in the number of pages is calculated as: Percentage Change = ((New Pages - Old Pages) ÷ Old Pages) × 100% Percentage Change = ((36.09 - 40) ÷ 40) × 100% Percentage Change = (-3.91 ÷ 40) × 100% ≈ -9.77%

This represents an approximate change of -10%.

Explanation

Let the total work be the least common multiple of the given number of days, which is the LCM of 12, 8, and 16, resulting in 48 units.

The rates of work per day for each pair are: Work rate of A and B = 48 ÷ 12 = 4 units per day Work rate of B and C = 48 ÷ 8 = 6 units per day Work rate of A and C = 48 ÷ 16 = 3 units per day

Summing these work rates: 2 × (Work rate of A, B, and C together) = 4 + 6 + 3 = 13 units per day Work rate of A, B, and C together = 13/2 units per day

The total time taken by all three working together to complete the job is: Total Work ÷ Combined Work Rate = 48 ÷ (13/2) = 96/13 = 7 5/13 days

Explanation

The word ENTRANCE contains 8 letters: E, N, T, R, A, N, C, E.

The vowels are E, A, E (3 letters, with E repeating 2 times). The consonants are N, T, R, N, C (5 letters, with N repeating 2 times).

Since all vowels must be kept together, we treat the vowel block [EAE] as a single entity. This gives us a total of 6 entities to arrange: the vowel block [EAE] and the 5 individual consonants (N, T, R, N, C).

The number of arrangements of these 6 entities, where N is repeated 2 times, is given by the formula: 6! / 2! = 720 / 2 = 360

The letters within the vowel block [EAE] can also be arranged among themselves. Since there are 3 vowels with E repeated 2 times, the number of ways to arrange them is: 3! / 2! = 3

The total number of ways to arrange the letters of the word under the given condition is the product of these two arrangements: 360 × 3 = 1080

Explanation

To find the day of the week on 19th November, 2024, starting from 12th June, 2024, we calculate the total number of days between the two dates and determine the number of odd days.

The number of days in each month during this period is: Remaining days in June: 18 (30 minus 12) July: 31 days August: 31 days September: 30 days October: 31 days November: 19 days (up to 19th November)

Summing these days: 18 + 31 + 31 + 30 + 31 + 19 = 160 days

Now, divide the total number of days by 7 to find the number of odd days: 160 ÷ 7 = 22 weeks and 6 odd days

Adding 6 days to the starting day, Wednesday, results in Tuesday.

Explanation

Let clockwise turns be represented as positive (+) and anti-clockwise turns as negative (-).

Initial direction = North-west

Net turn = -135° - 45° + 90° = -90°

A net change of -90° represents a 90° turn in the anti-clockwise direction. Turning 90° anti-clockwise from the North-west direction points directly to the South-west direction.

Explanation

The given equation is: 8.92 × 4.15 × 7.69 × ? = 1565.67631

First, calculate the product of the three known decimal numbers: 8.92 × 4.15 = 37.018 37.018 × 7.69 = 284.66842

Now, substitute this value back into the equation: 284.66842 × ? = 1565.67631

To find the value of the unknown term, divide the total product by 284.66842: ? = 1565.67631 ÷ 284.66842 ? = 5.5

Explanation

Let the marks obtained in the five subjects be 4x, 5x, 6x, 7x, and 8x. The total marks scored = 4x + 5x + 6x + 7x + 8x = 30x.

Let the maximum marks for each subject be M. The total maximum marks for all five subjects is 5M.

Since Pawan scored an overall 60%, the relation is: 30x / 5M = 60/100 6x / M = 3/5 M = 10x

The maximum mark for each subject is 10x, so 50% of the maximum mark is 5x.

Comparing Pawan's scores (4x, 5x, 6x, 7x, 8x) to this threshold of 5x, only 4x is strictly less than 5x. This means he scored less than 50% in exactly 1 subject.

Explanation

The average time taken to answer a question is calculated as the total time divided by the number of questions.

For Form-A, the average time per question is: 2t / k

For Form-B, the average time per question is: 3t / (k/2) = 6t / k

The difference in the average time taken per question is: 6t/k - 2t/k = 4t/k

Explanation

The amount of a substance remaining after n half-lives is calculated using the formula: X = M₀ × (½)ⁿ

Here, M₀ is the initial mass of the substance, which is 1200 gm. The number of half-lives, n, is the total time elapsed divided by the half-life of the substance: n = 3200 / 800 = 4

Substituting these values into the formula gives the remaining mass X: X = 1200 × (½)⁴ X = 1200 / 16 X = 75 gm

The sum of the digits of the remaining mass X (75) is: 7 + 5 = 12

Explanation

While typing the numbers from 600 to 799, the total number of times Chandra typed the digit 8 is equal to the sum of the number of times he was normally supposed to type the digit 6 and the digit 8.

First, let us calculate the normal frequency of the digit 6 in the range 600 to 799: Hundreds place: The digit 6 appears in the hundreds place for all 100 numbers from 600 to 699. This contributes 100 times. Tens place: The digit 6 appears in the tens place 10 times from 660 to 669, and another 10 times from 760 to 769. This contributes 20 times. Units place: The digit 6 appears in the units place 10 times in the range 600 to 699 (606, 616, ..., 696) and another 10 times in the range 700 to 799 (706, 716, ..., 796). This contributes 20 times. Total normal occurrences of 6 = 100 + 20 + 20 = 140.

Next, let us calculate the normal frequency of the digit 8 in the range 600 to 799: Hundreds place: The digit 8 does not appear in the hundreds place in this range. This contributes 0 times. Tens place: The digit 8 appears in the tens place 10 times from 680 to 689, and another 10 times from 780 to 789. This contributes 20 times. Units place: The digit 8 appears in the units place 10 times in the range 600 to 699 (608, 618, ..., 698) and another 10 times in the range 700 to 799 (708, 718, ..., 798). This contributes 20 times. Total normal occurrences of 8 = 0 + 20 + 20 = 40.

Since Chandra typed 8 instead of 6, every intended 6 and every intended 8 was typed as 8. Total number of times 8 was typed = 140 + 40 = 180.

Explanation

The consecutive differences of the terms in the series starting from the right are as follows:

16 - 5 = 11 35 - 16 = 19 62 - 35 = 27 97 - 62 = 35 140 - 97 = 43

These differences (11, 19, 27, 35, 43) form an arithmetic progression where each difference increases by 8. Following this pattern, the next difference should be:

43 + 8 = 51

To satisfy this pattern, the first term must be:

140 + 51 = 191

Since the given term is 193, it is the incorrect term in the series.

Explanation

Ganesh's remaining savings after donating 50% of ₹ 1,26,588 to the trust: Remaining Savings = 0.50 × 1,26,588 = ₹ 63,294

Let K and V be the amounts invested for Krishna and Veda respectively. The total investment is: K + V = 63,294

Krishna (age 13) and Veda (age 11) will turn 18 in 5 years and 7 years, respectively. Since their future values at 10% compound interest must be equal: K × (1 + 10/100)⁵ = V × (1 + 10/100)⁷ K × (1.1)⁵ = V × (1.1)⁷ K = V × (1.1)² K = 1.21 V

Substituting K into the total investment equation: 1.21 V + V = 63,294 2.21 V = 63,294 V = 63,294 / 2.21 ≈ 28,639.81

Rounding to the nearest rupee, the amount invested for Veda is ₹ 28,640.

Explanation

The seven days of the week starting from Sunday are Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, and Saturday.

Since only G has his exam after A, A must have his exam on Friday, and G must have his exam on Saturday.

It is given that only two persons have their exam between C and A. Since A has his exam on Friday, C must have his exam on Tuesday, with Wednesday and Thursday being the two days between them.

This confirms that C has his exam on Tuesday.

For completion, C has his exam immediately before F, placing F on Wednesday. Since B has his exam immediately before E, and the only consecutive days left are Sunday and Monday, B has his exam on Sunday and E has his exam on Monday. The remaining day, Thursday, is when D has his exam.

Explanation

A person with AB+ blood group has both A and B antigens on the surface of their red blood cells, alongside the Rh antigen. Consequently, their plasma does not contain anti-A, anti-B, or anti-Rh antibodies. Because they lack these antibodies, they can safely receive red blood cells of any blood type (A, B, AB, and O, both Rh positive and Rh negative) without causing an immune reaction or agglutination. This makes them the universal recipient. The assertion is correct, but the reason is incorrect because individuals with AB+ blood group do not have anti-A and anti-B antibodies in their plasma.

Explanation

First, convert the speed of the Vande Bharat Express from kmph to m/s: Speed = 63 × 5/18 = 17.5 m/s

Using the distance formula for crossing a platform: Length of train + Length of platform = Speed × Time Length of train + 199.5 = 17.5 × 21 Length of train + 199.5 = 367.5 Length of train = 168 m

Next, convert the speed of the Duronto Express to m/s: Speed = 54 × 5/18 = 15 m/s

When two trains travel in opposite directions, their relative speed is the sum of their individual speeds: Relative speed = 17.5 + 15 = 32.5 m/s

The total distance to completely cross each other is the sum of their lengths: Total distance = 168 + 157 = 325 m

Using the formula for time: Time = Total distance / Relative speed Time = 325 / 32.5 = 10 seconds

Explanation

Since all professors are doctors and all doctors are engineers, the set of professors is a subset of the set of doctors, which is a subset of the set of engineers. By transitive relation, all professors are engineers. This validates conclusion I.

Additionally, we are given that some professors are lawyers. Because all professors are doctors, the group of individuals who are both professors and lawyers must also be doctors. This ensures that some doctors are lawyers, which validates conclusion III.

Explanation

As a polling officer, safeguarding the integrity and security of the democratic process is the foremost responsibility during any security crisis. In a high-risk scenario involving an armed attack by Maoists, coordinating immediately with the security forces already deployed at the polling booth is the standard operating protocol. This action ensures the urgent protection of Electronic Voting Machines, Voter Verifiable Paper Audit Trails, and statutory electoral documents from being captured, tampered with, or destroyed. Protecting these critical assets preserves the sanctity of the votes cast and prevents the subversion of the election process while the security personnel handle the active threat.

Explanation

We divide the n-sided polygon into n triangles by connecting the center of the inscribed circle to each of the vertices. For each of these triangles, a side of the polygon serves as the base, and the radius of the circle, r, serves as the height because the radius is perpendicular to the tangent side at the point of contact.

The total area of the polygon is the sum of the areas of these n triangles: Area = ½ × s₁ × r + ½ × s₂ × r + ... + ½ × sₙ × r Area = ½ × r × (s₁ + s₂ + ... + sₙ)

The sum of the side lengths represents the perimeter of the polygon, which is given as 2p: s₁ + s₂ + ... + sₙ = 2p

Substituting this perimeter into the area formula yields: Area = ½ × r × 2p Area = pr

Explanation

Let the number of cards with Sam, Gautham, Nagesh, Deepak, and Anup be S, G, N, D, and A respectively.

According to the first condition, if Gautham gives 3 cards to Sam, he will have as many as Anup: A = G - 3

According to the second condition, if Sam gives 3 cards to Gautham, Gautham will have as many as Deepak: D = G + 3

According to the third condition, Sam and Gautham together have 10 cards more than Deepak and Anup together: S + G = D + A + 10

Substituting the values of A and D into this equation gives: S + G = (G + 3) + (G - 3) + 10 S + G = 2G + 10 S = G + 10

According to the fourth condition, Gautham has 2 cards more than Nagesh: G = N + 2 N = G - 2

Given that the total number of cards is 133: S + G + N + D + A = 133

Substituting all the variables in terms of G: (G + 10) + G + (G - 2) + (G + 3) + (G - 3) = 133 5G + 8 = 133 5G = 125 G = 25

Explanation

The Prime Minister of India inaugurated the All India Institute of Medical Sciences (AIIMS) in Guwahati, which is located in the state of Assam. According to the given code language, Assam is coded as Goa. Therefore, the coded name of the state is Goa.

Explanation

All three statements are factually correct.

The Svalbard Global Seed Vault is located on the remote Norwegian island of Spitsbergen, which is part of the Svalbard archipelago in the Arctic Ocean. It is the world's largest secure seed backup storage facility, designed to preserve global crop diversity against catastrophic natural or man-made events.

India's Seed Vault is situated in the high-altitude mountain pass of Chang La in Ladakh, at an elevation of approximately 17,300 feet above sea level. This extreme elevation and naturally freezing environment provide permafrost conditions conducive to subzero seed preservation.

The Indian Seed Vault was established in 2010 as a joint collaboration between the National Bureau of Plant Genetic Resources, which functions under the Indian Council of Agricultural Research, and the Defence Institute of High Altitude Research, which is a constituent laboratory of the Defence Research and Development Organisation.

Explanation

On the eve of World Wetland Day 2024, India designated five new wetlands as Ramsar sites, increasing the nation's tally of Wetlands of International Importance from 75 to 80. These five newly designated sites are Karaivetti Bird Sanctuary and Longwood Shola Reserve Forest in Tamil Nadu, and Magadi Kere Conservation Reserve, Ankasamudra Bird Conservation Reserve, and Aghanashini Estuary in Karnataka.

Consequently, Karaivetti Bird Sanctuary (I) and Magadi Kere Conservation Reserve (IV) are the correct sites from the list that were added to the Ramsar list on this occasion.

Explanation

Statement I is correct because WESAT (Women Engineered SATellite) is India's first satellite payload fully designed, developed, and managed by women, specifically by the student and faculty members of the Space Club at the Lal Bahadur Shastri Institute of Technology for Women, Thiruvananthapuram, Kerala.

Statement II is correct because the satellite was successfully launched into space on January 1, 2024, as a co-passenger/secondary payload aboard the PSLV-C58/XPoSAT mission.

Statement III is incorrect because the primary mission of WESAT is to measure and compare ultraviolet radiation in space and on the Earth's surface in real-time, focusing on its impact on temperature rise and climate change in Kerala. It is not designed to study rainfall or underground water replenishment.

Explanation

In October 2022, New Zealand became the first country in the world to propose a plan to tax agricultural greenhouse gas emissions from livestock, specifically targeting biogenic methane from animal burps and nitrous oxide from urine. This proposal, developed in partnership with agricultural industry representatives, aimed to incentivize farmers to reduce livestock emissions and help the nation meet its legally binding commitment of reaching net-zero greenhouse gas emissions by 2050.

Explanation

The Garbhini-GA2 model is the first India-specific artificial intelligence model developed to accurately determine the gestational age of a fetus during the second and third trimesters. Traditional methods based on Western population formulas are often inaccurate when applied to Indian pregnancies due to developmental variations. Garbhini-GA2 reduces the estimation error by almost three times, facilitating better prenatal care.

This model was jointly developed by researchers from the Indian Institute of Technology Madras and the Translational Health Science and Technology Institute, Faridabad, under the Interdisciplinary Group for Advanced Research on Birth Outcomes - Department of Biotechnology India Initiative program.

Explanation

NexCAR19 is India's first indigenously developed Chimeric Antigen Receptor T-cell (CAR-T) therapy. It was designed and developed by ImmunoACT, a company incubated at the Indian Institute of Technology Bombay (IIT Bombay), in collaboration with Tata Memorial Hospital. The Central Drugs Standard Control Organization (CDSCO) granted market authorization to NexCAR19 in October 2023 for the treatment of relapsed or refractory B-cell lymphomas and leukemia. This advanced gene-modified cell therapy works by reprogramming a patient's own T-cells to target CD19, a protein highly expressed on cancerous B-cells, offering a highly effective, personalized cancer treatment at a significantly reduced cost compared to globally available alternatives.

Explanation

I and II only. Statements I and II are correct. Green propulsion (Bellatrix Aerospace/DRDO TDF) is non-toxic and suited for low orbit. Statement III is wrong — green propulsion is low-thrust, not ideal for high-thrust missions.

Explanation

In February 2024, the Indian Renewable Energy Development Agency Ltd (IREDA) signed a Memorandum of Understanding (MoU) with IIT Bhubaneswar during the 100 Cube Start-up Conclave held on the institute's campus. This strategic partnership aims to foster collaborative innovation, facilitate technology transfer, and support the growth of the start-up ecosystem in the renewable energy sector. Additionally, the agreement encompasses capacity-building activities, such as training sessions, workshops, and seminars, designed to enhance the skills of IREDA officials.

Explanation

None of the above. All statements (I, II, III, IV) regarding India's rankings in GII 2023, WIPO 2022, NRI 2023, and International IP Index 2024 are factually correct. The question asks for incorrect statements, so 'None of the above' is the correct answer.

Explanation

The Indira Gandhi Centre for Atomic Research (IGCAR), located in Kalpakkam, is the premier research and development organization under the Department of Atomic Energy that spearheaded the design and technology development of India's 500 MWe Prototype Fast Breeder Reactor (PFBR). Established in 1971 with the primary mission of developing fast breeder reactor technology in India, IGCAR utilized the extensive experience gained from designing and operating the Fast Breeder Test Reactor (FBTR) to indigenously engineer the PFBR. This achievement marks a pivotal step in transitioning to the second stage of India's three-stage nuclear power program, which aims to produce more fuel than consumed by utilizing uranium-plutonium mixed oxide fuel.

Explanation

The LIGO-India project is a collaborative mega-science venture between the LIGO Laboratory (USA) and a consortium of Indian research institutions. The construction, installation, commissioning, and operation of the LIGO-India Observatory are being jointly led by four main Indian institutions: the Institute for Plasma Research (IPR) in Gandhinagar, the Inter-University Centre for Astronomy and Astrophysics (IUCAA) in Pune, the Raja Ramanna Centre for Advanced Technology (RRCAT) in Indore, and the Directorate of Construction Services and Estate Management (DCSEM) in Mumbai.

Explanation

OSIRIS-APEX (Origins, Spectral Interpretation, Resource Identification, Security-Apophis Explorer) is a NASA spacecraft redirected to study the near-Earth asteroid 99942 Apophis, also known as the 'God of Chaos', during its extremely close flyby of Earth in April 2029. The spacecraft, formerly known as OSIRIS-REx, successfully delivered asteroid samples from Bennu to Earth in September 2023. Following the sample delivery, NASA extended the mission and renamed it OSIRIS-APEX to observe physical changes, such as landslides and seismic tremors, induced on Apophis by Earth's gravitational pull during the 2029 encounter.

Explanation

Kamala Sohonie was an eminent Indian biochemist who became the first Indian woman to receive a Ph.D. in a scientific discipline. After graduating from Bombay University, she overcame significant gender barriers to gain admission into the Indian Institute of Science (IISc), Bangalore, becoming its first female student. In 1937, she secured a research scholarship at Cambridge University, UK. She worked on cellular respiration and discovered the vital plant enzyme Cytochrome C, a fundamental enzyme involved in the electron transport chain. For this groundbreaking research, she was awarded her Ph.D. degree from Cambridge University in 1939.

Explanation

Researchers at the Indian Institute of Technology Mandi (IIT Mandi), led by Dr. Garima Agrawal, developed these smart, biodegradable, natural polymer-based nanoparticles to improve colorectal cancer treatment.

The research team utilized chitosan, a natural polymer derived from renewable resources, in combination with stearic acid and disulfide chemistry to develop redox-responsive chitosan/stearic acid nanoparticles (CSSA NPs). These nanoparticles are stable under normal physiological conditions but are designed to degrade specifically at the tumor site in response to the elevated redox stimuli characteristic of cancer cells.

This smart drug-delivery system successfully carries and releases both hydrophilic (doxorubicin) and hydrophobic (curcumin) anticancer agents. By releasing the therapeutic agents precisely at the cancer site, this approach enhances treatment efficacy and reduces the side effects associated with chemotherapy, while utilizing sustainable, eco-friendly resources rather than petroleum-based polymers.

Explanation

A Sun Halo is an atmospheric optical phenomenon that occurs when sunlight is refracted, reflected, and dispersed through millions of hexagonal ice crystals suspended in the upper atmosphere. These hexagonal ice crystals, typically found in high-altitude cirrus or cirrostratus clouds, act as tiny prisms that bend light at precise angles.

The most frequently observed halo is the 22° halo. This phenomenon forms a ring of light with a radius of approximately 22° around the Sun. The radius is determined by the 60° prism angle of the hexagonal ice crystals, which refracts the incoming sunlight at a minimum deviation angle of approximately 22° to create the circular halo.

Explanation

Statement I is correct because coral reefs are referred to as the "Rainforests of the Sea" due to their immense biological diversity. They occupy less than 0.1% of the world's ocean surface but provide a habitat for approximately 25% of all known marine species.

Statement II is correct because coral reefs function as highly effective, natural coastal barriers. Their rigid, complex structures break the power of incoming waves by up to 97%, shielding shorelines from the destructive forces of storms, hurricanes, and coastal erosion.

Statement II is not the correct explanation for Statement I because the coastal protection role of coral reefs is a physical ecosystem service, whereas their designation as the "Rainforests of the Sea" is a direct reflection of their rich biodiversity and ecological variety.

Explanation

The 30 by 30 initiative is a global target that aims to protect at least 30% of the planet's land and ocean areas by 2030 to halt accelerating biodiversity loss and protect critical ecosystems. It is not related to renewable energy requirements.

This target is championed by the High Ambition Coalition (HAC) for Nature and People, which is an intergovernmental group of more than 115 countries co-chaired by Costa Rica and France, with the United Kingdom serving as the ocean co-chair.

In October 2021, India officially joined the High Ambition Coalition (HAC) for Nature and People, making it the first country among the BRICS bloc of major emerging economies to join this global initiative and support the 30 by 30 conservation target.

Explanation

India has eighteen Biosphere Reserves designated by the Government of India, of which twelve were included in the World Network of Biosphere Reserves under UNESCO's Man and the Biosphere Programme up to 2024. Nokrek Biosphere Reserve was included in this network in 2009, and Khangchendzonga Biosphere Reserve was added in 2018. The remaining three reserves, namely the Cold Desert Biosphere Reserve in Himachal Pradesh, Dibru-Saikhowa Biosphere Reserve in Assam, and the Great Rann of Kutch Biosphere Reserve in Gujarat, were not part of the UNESCO Man and Biosphere Programme up to 2024.

Explanation

Madhya Pradesh's online civic tax payment software, e-Nagar Palika, suffered a major ransomware cyber-attack in December 2022, which severely disrupted online municipal services across the state's urban local bodies.

Explanation

The WIDUSHI (Women's Instinct for Developing and Ushering in Scientific Heights | Innovations) programme is an initiative launched by the Department of Science and Technology (DST) under the umbrella of the WISE-KIRAN (Women in Science and Engineering-KIRAN) scheme. The primary objective of the program is to encourage and support senior women scientists to carry out research in interdisciplinary areas of science and technology, thereby leveraging their experience and expertise. It caters to senior women scientists who are either retiring, already retired, or those not in regular employment but actively involved in research.

Explanation

Statement I is incorrect because the ARTSENS device is designed to non-invasively assess the health and age of blood vessels, measuring arterial stiffness to provide early screening for cardiovascular diseases rather than evaluating neurons or central nervous system disorders.

Statement II is incorrect because the ARTSENS device was developed by the Healthcare Technology Innovation Centre at the Indian Institute of Technology Madras, not by the National Institute of Mental Health and Neuro-Sciences.

Explanation

Hanooman is a series of open-source Indic large language models (LLMs) featuring multimodal AI capabilities that can process and generate text, speech, and video. It was developed indigenously by the Indian Institute of Technology (IIT) Bombay-led BharatGPT consortium in partnership with Seetha Mahalakshmi Healthcare (SML). Designed specifically to cater to India's unique linguistic diversity, the tool supports interaction in 11 Indian languages, including Hindi, Tamil, Telugu, Marathi, and Malayalam. Hanooman is tailored to serve critical sectors such as healthcare, governance, financial services, and education.

Explanation

NITI Aayog's Methanol Economy programme is a comprehensive strategy designed to enhance India's energy security and environmental sustainability.

Statement I is correct because methanol acts as an alternative, clean-burning fuel that can substitute or blend with petrol and diesel. Implementing a 15% methanol blending program (M15) helps substantially curtail the country's dependence on crude oil imports, leading to a direct reduction in India's oil import bill.

Statement II is correct because methanol is a low-carbon fuel with a simplified molecular structure that contains no carbon-carbon bonds. As a result, its combustion produces significantly lower greenhouse gas emissions and decreases the release of particulate matter, nitrogen oxides (NOₓ), and sulfur oxides (SOₓ), improving urban air quality.

Statement III is correct because the program focuses on producing methanol from domestic, readily available feedstocks. This includes leveraging India's abundant high-ash coal reserves through gasification, as well as converting municipal solid waste, agricultural residues, and carbon dioxide captured from thermal power stations into usable methanol fuel.

Explanation

HLL Lifecare Limited, a Central Public Sector Enterprise (CPSE) under the Ministry of Health and Family Welfare, serves as the government's designated nodal agency for the procurement, sourcing, and deployment of the Aarogya Maitri Cubes. Developed indigenously under Project BHISHM (Bharat Health Initiative for Sahyog Hita and Maitri), these cubes make up a modular, portable disaster hospital designed for rapid deployment during humanitarian crises or natural disasters. HLL Lifecare Limited oversees the sourcing of all clinical equipment and medical supplies from multiple sellers to assemble the 72 components that constitute each portable hospital unit.

Explanation

Impatiens karuppusamyi is a newly discovered plant species belonging to the genus Impatiens under the Balsaminaceae family. It was identified by researchers from the Botanical Survey of India (BSI) during botanical explorations in the Agasthyamalai region within the Kalakad Mundanthurai Tiger Reserve (KMTR) in Tirunelveli, Tamil Nadu. The species is named in honor of Dr. S. Karuppusamy for his significant contributions to the taxonomy of South Indian angiosperms. This stemless, lithophytic plant thrives on wet rocky slopes, blooming only during the monsoon season for a brief period, and is considered highly vulnerable to climate change due to its localized distribution.

Explanation

The Global Shield against Climate Risks was officially launched at the COP27 climate summit in Sharm El-Sheikh in November 2022. It is a joint initiative developed by the Group of Seven (G7) and the Vulnerable Twenty (V20) Group of climate-vulnerable countries, along with other supporting partners.

The initiative aims to significantly scale up and systematically enhance Climate and Disaster Risk Finance and Insurance (CDRFI). By utilizing pre-arranged financial instruments like national disaster funds and climate insurance, the Global Shield provides rapid and predictable financial support to vulnerable nations and communities immediately after a climate-related disaster strikes.

Because both statements are factually accurate, neither of them is incorrect.

Explanation

In 2013, the International Union for Conservation of Nature (IUCN) and Mission Blue designated the Lakshadweep Islands and the Andaman and Nicobar Islands as the first Hope Spots in India. A Hope Spot is an ecologically unique area of the ocean that is critical to its health, biodiversity, and conservation. These two island groups host highly rich marine ecosystems, including extensive coral reefs, diverse fish species, and critical habitats for species such as sea turtles and dugongs. The designation helps generate public awareness, support scientific research, and drive conservation efforts to protect these crucial marine environments from climate change and human impact.

Explanation

I and III.

The 14th session of the Conference of the Parties to the Convention on the Conservation of Migratory Species of Wild Animals (CMS COP14) was held in Samarkand, Uzbekistan, from 12 to 17 February 2024.

This triennial conference was the first major global biodiversity gathering since the historic adoption of the Kunming-Montreal Global Biodiversity Framework (GBF) in December 2022.

The conference was convened under the official slogan Nature knows no borders, which highlighted that migratory species cross political boundaries and require transboundary conservation efforts. The slogan Migratory species connect the planet and we welcome them home was the theme of the previous 13th Conference of Parties (CMS COP13), which was hosted by India in Gandhinagar, Gujarat in 2020.

Explanation

PROPOSED:3

GSAT-N2 (originally GSAT-20) is a high-throughput Ka-band communication satellite developed by the Indian Space Research Organisation (ISRO) for NewSpace India Limited (NSIL).

Statement I is correct because GSAT-N2 is a major demand-driven satellite mission fully owned, funded, and operated by NSIL, which represents a key shift in India's space sector reforms towards commercially viable space missions.

Statement III is correct because the satellite weighs approximately 4,700 kg, which exceeds the current maximum carrying capacity of India's most powerful heavy-lift rocket, the LVM3 (which can lift up to 4,000 kg to Geostationary Transfer Orbit). Consequently, NSIL collaborated with SpaceX to utilize the Falcon 9 rocket to launch the satellite.

Statement II is incorrect because the official launch of GSAT-N2 was scheduled for the second quarter of 2024 (and was successfully launched in November 2024), rather than 2025. Therefore, only statements I and III are correct.

Explanation

India possesses significant solar energy potential because of its geographical location in the tropical and subtropical regions. The country experiences clear, sunny weather for about 250 to 300 days a year, resulting in an estimated solar energy incidence of approximately 5000 trillion kilowatt-hours of energy annually over its land area. Most parts of India receive 4 to 7 kilowatt-hours of solar radiation per square meter per day. This high level of solar insolation and clear weather directly explains why India has such a massive potential for solar power generation. Consequently, Statement II is correct and serves as the correct explanation for Statement I.

Explanation

In March 2024, France became the first country in the world to explicitly enshrine the right to abortion in its constitution. Lawmakers from both chambers of the French Parliament approved an amendment to Article 34 of the French Constitution during a special joint session. The amendment constitutionalizes a woman's guaranteed freedom to have a voluntary termination of pregnancy.

Explanation

Operation Aspides (EUNAVFOR ASPIDES) is a European Union-led military operation launched on February 19, 2024, under the EU Common Security and Defence Policy (CSDP).

Its mandate is purely defensive, aimed at protecting merchant vessels, providing maritime situational awareness, and safeguarding the freedom of navigation in the Red Sea, the Gulf of Aden, the Arabian Sea, the Gulf of Oman, and the Persian Gulf.

Because it is an EU-led initiative and not a joint operation of Interpol and the International Maritime Organization, only Statement I is correct.

Explanation

Statement I is correct because the 16th edition of the trilateral coast guard exercise, DOSTI-16, was conducted in Male, Maldives, from 22 to 25 February 2024.

Statement II is incorrect because the DOSTI drill was initiated in 1991 as a bilateral exercise between the coast guards of India and the Maldives, not Sri Lanka. Sri Lanka joined the exercise as a full participant later in 2012.

Statement III is correct because the Indian Coast Guard deployed the Offshore Patrol Vessel ICGS Samarth and the Fast Patrol Vessel ICGS Abhinav, along with an ICG Dornier aircraft, to participate in the DOSTI-16 exercise.

Explanation

The Oncology.ai platform (also known as iOncology.ai) was launched as a collaborative project between the All India Institute of Medical Sciences (AIIMS) in New Delhi and the Centre for Development of Advanced Computing (C-DAC) in Pune. Supported by the Ministry of Electronics and Information Technology (MeitY), this platform utilizes advanced deep learning and artificial intelligence models to assist in the early detection and diagnosis of breast and ovarian cancers by analyzing complex medical data such as radiological and histopathological images.

Explanation

The CRIIO 4 GOOD initiative is a new online life skills learning program consisting of 8 cricket-based animation films. These modules leverage the widespread popularity of cricket to promote gender equality, equip girls with essential life skills, and encourage their participation in sports. The initiative was launched in association with the International Cricket Council, UNICEF, and the Board of Control for Cricket in India at the Narendra Modi Stadium in Ahmedabad. Since all three statements are factually correct, none of them is incorrect.

Explanation

On February 8, 2024, Papua New Guinea Prime Minister James Marape delivered a historic address to the Australian Parliament in Canberra. Invited by Australian Prime Minister Anthony Albanese, Marape became the first leader of a Pacific island nation to address the Australian Federal Parliament in its history. His address celebrated the deep-rooted historical ties, shared democratic values, and strong bilateral partnership between the two neighboring nations.

Explanation

NASA designed the Plankton, Aerosol, Cloud, ocean Ecosystem satellite mission to assess ocean health, air quality, and the impacts of global climate change. It is equipped to analyze microscopic organisms like phytoplankton in the ocean and aerosol particles in the atmosphere, which makes Statement I correct.

The satellite was successfully launched into orbit on February 8, 2024, carried by a SpaceX Falcon 9 rocket from Cape Canaveral Space Force Station in Florida, which makes Statement II correct.

Since both statements are factually correct, neither of them is incorrect.

Explanation

Statement I is correct because the first edition of the biannual Indian Naval Commanders' Conference of 2024 commenced on March 5, 2024, in a hybrid format. The inaugural session took place onboard the aircraft carrier INS Vikramaditya to witness twin-carrier operations.

Statement II is correct because the Ministry of Defence launched the Acing Development of Innovative Technologies with iDEX (ADITI) scheme in March 2024 to promote deep-tech innovations in critical and strategic defence technology by providing grant-in-aid support to startups.

Statement III is correct because Exercise Samudra Laksamana is a bilateral maritime exercise between the Indian Navy and the Royal Malaysian Navy. The third edition of this exercise was held off the coast of Visakhapatnam in early 2024 to enhance mutual cooperation and interoperability.

Explanation

India's first indigenous hydrogen fuel cell catamaran ferry vessel was built by Cochin Shipyard Limited. It was flagged off virtually by Prime Minister Narendra Modi in February 2024 at Thoothukudi, Tamil Nadu. The vessel was developed as a pilot project under the Harit Nauka initiative of the Ministry of Ports, Shipping and Waterways to promote green transition in inland water transport, highlighting India's engineering capabilities in zero-emission maritime technology.

Explanation

Statement I is correct because in early 2024, a multi-institutional team of researchers identified and described a new species of burrowing frog, Sphaerotheca varshaabhu, from the suburban and urban landscape of Bengaluru, Karnataka.

Statement II is incorrect because the specific epithet "varshaabhu" is derived from the Sanskrit words "Varshaa" (meaning rain) and "bhu" (meaning born or taking birth). The name signifies the frog's characteristic behaviour of emerging from its underground burrows to breed only during the onset of the monsoon rains. It is not named after any colour-changing behavior.

Explanation

The Bihar Police launched the "Mission Investigation@75 Days" initiative, which became effective on January 1, 2024. Under this mission, it is mandatory for investigating officers to complete the investigation of cases, including the filing of chargesheets, within 75 days of registering a First Information Report (FIR). The objective of this initiative is to streamline the criminal justice system, prevent unnecessary delays, and improve the overall efficiency and accountability of policing within the state.

Explanation

On February 27, 2024, Prime Minister Narendra Modi announced the names of the four astronaut-designates chosen for the Gaganyaan mission, India's first crewed space flight. The selected astronauts, who are highly experienced test pilots from the Indian Air Force, are:

Wing Commander Shubanshu Shukla Group Captain Prasanth Balakrishnan Nair Group Captain Ajit Krishnan Group Captain Angad Pratap

These correspond to statements I, II, IV, and V. They have completed intensive training in Russia and continue their specialized mission training at the Human Space Flight Centre in Bengaluru.

Explanation

On 22 January 2024, Cameroon became the first country in the world to integrate the RTS,S malaria vaccine into its routine national immunization services under its Expanded Programme on Immunization. This historic rollout followed the successful pilot programs conducted between 2019 and 2023 in Ghana, Kenya, and Malawi, making Cameroon the first country to offer the vaccine outside of a pilot context as a standard, routine immunization for children.

Explanation

Statement I is correct because Pradhan Mantri Matsya Kisan Samridhi Sah-Yojana (PM-MKSSY) is a Central Sector Sub-scheme approved under the Pradhan Mantri Matsya Sampada Yojana (PMMSY) to formalize the unorganized fisheries sector and support micro and small enterprises in this field.

Statement II is correct as the scheme has a total outlay of over ₹6,000 crore to be implemented over four years from FY 2023-24 to FY 2026-27 across all States and Union Territories.

Statement III is correct because the sub-scheme provides a one-time incentive to aquaculture farmers to buy insurance, aiming to expand insurance coverage and mitigate farming risks.

Explanation

In February 2024, Trinidad and Tobago declared a national emergency following a massive offshore oil spill. The ecological crisis was triggered when an unidentified vessel, later identified as the barge Gulf Stream, overturned and ran aground on a reef off the southern coast of Tobago. The resulting spill leaked thousands of barrels of fuel oil, coating miles of beaches, damaging local marine ecosystems, and threatening the island's vital tourism and fishing industries.

Explanation

The 58th Jnanpith Award for the year 2023 was jointly conferred upon Sampooran Singh Kalra, widely known by his pen name Gulzar, and Jagadguru Rambhadracharya. Gulzar is celebrated as one of the finest contemporary Urdu poets, lyricists, and screenwriters of this era. Jagadguru Rambhadracharya is a renowned Sanskrit scholar, educator, and spiritual leader who has authored more than 240 books and texts, including four epics. Thus, statements I and II are correct.

Explanation

I only.

Statement I is correct. According to the Press Information Bureau (PIB) release of February 29, 2024, the International Big Cat Alliance (IBCA) is conceived as a multi-country, multi-agency coalition consisting of 96 big cat range countries, non-range countries interested in big cat conservation, conservation partners, and scientific organizations working in the field of big cat conservation.

Statement II is incorrect. The Union Cabinet approved the establishment of the IBCA with its headquarters in India with a one-time budgetary support of ₹150 crore for a period of five years from 2023–24 to 2027–28, rather than a period of two years.

Explanation

Parikshit Mahato - Tribal Dance. Parikshit Mahato is a Jhumur folk singer from West Bengal; his Sangeet Natak Akademi Award 2023 was in Folk Music, not Tribal Dance, making option 3 the incorrect pair.

Explanation

Tata Advanced Systems Limited built TSAT-1A, which is India's first military-grade spy satellite developed by a private player. The low Earth orbit satellite was assembled at the company's assembly, integration, and testing facility in Karnataka, in partnership with Satellogic. It was successfully launched into space in April 2024 aboard a SpaceX Falcon 9 rocket as part of the Bandwagon-1 mission, designed to provide high-resolution sub-meter optical imagery for enhanced defense and surveillance capabilities.

Explanation

The Mukhyamantri Vishwakarma Pension Yojana was announced by the Government of Rajasthan in its state budget for the fiscal year 2024-2025. This social security initiative is designed for unorganized sector workers, street vendors, and folk artists in the state who are aged between 18 and 45 years. Under this contributory pension program, beneficiaries deposit a small monthly premium which is supplemented by a contribution from the state government. Upon attaining the age of 60 years, the registered beneficiaries receive a assured monthly pension of ₹3,000 to support their livelihood in old age.

Explanation

In February 2024, the Tamil Nadu government banned the sale and manufacture of cotton candy after laboratory analyses confirmed the presence of Rhodamine-B in food samples. Rhodamine-B is a water-soluble synthetic industrial dye primarily used in textile dyeing, paper printing, and leather processing to achieve a bright pink or red color.

Under the Food Safety and Standards Act, 2006, the use of Rhodamine-B in food products is illegal. It is classified as a toxic, carcinogenic substance. Even small quantities can cause severe health risks, including liver damage, kidney failure, and damage to the cerebellum and brainstem.

Explanation

Malta became the 119th country to join the International Solar Alliance (ISA) in February 2024. Christopher Cutajar, the Permanent Secretary of Malta's Ministry for Foreign and European Affairs and Trade, signed the ISA Framework Agreement in New Delhi.

The International Solar Alliance is an action-oriented, member-driven platform launched jointly by India and France in 2015 at the UN Climate Change Conference (COP21) in Paris. Headquartered in Gurugram, India, the alliance works to facilitate the global deployment of solar energy technologies, improve energy access, and guide transition toward low-carbon growth trajectories.

Explanation

The State Energy Efficiency Index (SEEI) 2023 was released by the Bureau of Energy Efficiency (BEE) in collaboration with the Alliance for an Energy Efficient Economy (AEEE) to track energy efficiency initiatives across states and Union Territories.

Statement I is correct because Karnataka emerged as the top-performing state in SEEI 2023, securing an overall score of 86.5 out of 100.

Statement II is correct as only two states, Assam and Uttar Pradesh, fell into the Achiever category, which is designated for states scoring between 50 and 59.75.

Statement III is correct because Andhra Pradesh scored 83.25 (the second-highest overall) and was placed in the Front runner category, which requires a minimum score of 60.

Explanation

The Sangam: Digital Twin initiative was launched by the Department of Telecommunications, Ministry of Communications, in February 2024. This initiative seeks to integrate next-generation technologies like 5G, Internet of Things, Artificial Intelligence, Augmented Reality/Virtual Reality, and Digital Twin technology to revolutionize national infrastructure planning and design. By creating highly accurate virtual replicas of physical infrastructure, it enables real-time monitoring, scenario simulation, and collaborative planning among diverse departments to foster sustainable and scalable development.

Explanation

Statement I is incorrect because the three landing ships decommissioned on January 12, 2024, were INS Cheetah, INS Guldar, and INS Kumbhir (not INS Magar, which was decommissioned in May 2023). Furthermore, the decommissioning ceremony was held at Port Blair in the Andaman and Nicobar Islands, rather than in Lakshadweep.

Statement II is correct because INS Imphal, a state-of-the-art Project 15B stealth guided missile destroyer designed by the Warship Design Bureau and constructed by Mazagon Dock Shipbuilders Limited, was formally commissioned into the Indian Navy at a ceremony held at the Naval Dockyard in Mumbai on December 26, 2023.

Explanation

Haryana emerged as the overall champions of the inaugural edition of the Khelo India Para Games held in New Delhi from December 10 to December 17, 2023. The state topped the medal tally by securing a total of 105 medals, which included 40 gold, 39 silver, and 26 bronze medals.

Explanation

On September 15, 2023, the Chief Minister of Andhra Pradesh, Y.S. Jagan Mohan Reddy, inaugurated five new government medical colleges located in Vizianagaram, Rajamahendravaram, Eluru, Machilipatnam, and Nandyal. These college inaugurations added 750 MBBS seats to the state. The Chief Minister physically inaugurated the college in Vizianagaram, while the other four, including the colleges in Eluru and Machilipatnam, were inaugurated virtually. This makes Eluru, Vizianagaram, and Machilipatnam (I, II, and IV) the correct places.

Explanation

India ranked 38th among 139 countries in the World Bank's Logistics Performance Index (LPI) 2023. This represents a jump of six places from its 44th position in 2018. The progress is driven by strategic initiatives such as the PM Gati Shakti National Master Plan and the National Logistics Policy, alongside massive investments in port modernization, dedicated freight corridors, and digital systems like the Unified Logistics Interface Platform to enhance supply chain efficiency.

Explanation

Assert AI, a Mumbai-based artificial intelligence startup, launched Pratham, which is patented as the world's first no-code computer vision platform. Pratham, meaning "first" in Hindi, is designed to democratize vision AI by allowing users to upload videos or connect CCTV cameras directly to the platform. It enables businesses and users to leverage complex video analytics and artificial intelligence without requiring coding knowledge or AI expertise.

Explanation

The Japan Aerospace Exploration Agency (JAXA) successfully launched its next-generation H3 launch vehicle into orbit on February 17, 2024, from the Tanegashima Space Center in Kagoshima, Japan. Developed jointly by JAXA and Mitsubishi Heavy Industries, the H3 rocket is designed as the flagship successor to the H-IIA launch system. It is structured as a flexible, reliable, and highly cost-effective medium-lift rocket to secure autonomous access to space for various scientific, government, and commercial satellite missions.