HPAS Prelims 2023 CSAT (Paper II) with Answers & Explanations

Explanation

The first series is the standard Maclaurin expansion of log(1 + x) evaluated at x = 1: log(1 + x) = x - x²/2 + x³/3 - x⁴/4 + ...

Substituting x = 1 yields: log 2 = 1 - ½ + ⅓ - ¼ + ...

The second series is a telescoping series, where each term can be decomposed using partial fractions: 1/(n(n + 1)) = 1/n - 1/(n + 1)

Writing out the terms of this series: 1/(2·3) + 1/(3·4) + 1/(4·5) + ... = (½ - ⅓) + (⅓ - ¼) + (¼ - ⅕) + ...

As the series progresses, all intermediate terms cancel out, leaving only the first term: Sum = ½

Explanation

Let Abdul's investment be x. Ramesh's investment is x + 6,000 and Antony's investment is x + 3,000.

The total investment is Rs. 72,000, which gives the equation: (x + 6,000) + x + (x + 3,000) = 72,000 3x + 9,000 = 72,000 3x = 63,000 x = 21,000

This determines the individual investments: Abdul's investment = Rs. 21,000 Ramesh's investment = Rs. 27,000 Antony's investment = Rs. 24,000

The profit sharing ratio is equal to the ratio of their investments: Ramesh : Abdul : Antony = 27,000 : 21,000 : 24,000 = 9 : 7 : 8

The sum of the ratio terms is 9 + 7 + 8 = 24. Out of the total profit of Rs. 8,640, Ramesh's share is: (9 / 24) × 8,640 = 3,240

Explanation

The passing marks required for the exam is the sum of the marks obtained by Shalini and the marks by which she failed.

Passing marks = 150 + 30 = 180

Since the passing marks represent 36% of the maximum marks, let the maximum marks be M.

36% of M = 180 (36 / 100) × M = 180 M = (180 × 100) / 36 M = 5 × 100 M = 500

Explanation

The relation between cost price (CP), selling price for profit (SP₁), and selling price for loss (SP₂) when the profit earned is equal to the loss incurred is given by the formula:

CP = (SP₁ + SP₂)/2

Substituting the given values into the formula:

CP = (1666 + 1252)/2 CP = 2918/2 CP = 1459

Explanation

For a sum of money to double itself under simple interest, the interest earned must be equal to the principal (P).

Using the standard simple interest formula: SI = (P × R × T) / 100

Substituting SI = P and T = 6: P = (P × R × 6) / 100

Dividing both sides by P: 1 = 6R / 100

Solving for R: R = 100 / 6 = 50/3% per annum.

Explanation

The number of diagonals in a polygon of n sides is given by the formula n(n - 3)/2.

Substituting n = 12 into the formula:

Number of diagonals = 12 × (12 - 3) / 2 Number of diagonals = 12 × 9 / 2 Number of diagonals = 6 × 9 = 54

Alternatively, this can be calculated by finding the total number of lines that can be drawn connecting any two vertices, which is given by combinations as nC2, and then subtracting the n boundary sides of the polygon. For 12 vertices, the total lines are 12 × 11 / 2 = 66. Subtracting the 12 sides gives 66 - 12 = 54 diagonals.

Explanation

Let the starting point be at the origin (0, 0) on a Cartesian plane, where the positive y-axis represents North, the negative y-axis represents South, the positive x-axis represents East, and the negative x-axis represents West.

Rohit starts at (0, 0) facing South. He turns right to face West and walks 20 meters, reaching (-20, 0). He turns right to face North and walks 10 meters, reaching (-20, 10). He turns left to face West and walks 10 meters, reaching (-30, 10). He turns right to face North and walks 20 meters, reaching (-30, 30). He turns right to face East and walks 60 meters, reaching (30, 30).

His final position is at (30, 30). Since both the x and y coordinates are positive, he is in the North-East direction relative to the starting point (0, 0).

Explanation

Let the daily work done by 1 man be M and 1 boy be B.

The total work is the same in both cases, which gives the relation: 7 × (3M + 4B) = 10 × (2M + 3B)

Solving this equation: 21M + 28B = 20M + 30B M = 2B

This means the efficiency of 1 man is equal to the efficiency of 2 boys.

Now, we can express the total work in terms of boys: Total Work = 10 × (2M + 3B) Total Work = 10 × (2 × 2B + 3B) Total Work = 10 × 7B Total Work = 70B

We need to find the number of days taken by 3 men and 8 boys to complete the same work. The combined efficiency of 3 men and 8 boys in terms of boys is: 3M + 8B = 3 × 2B + 8B = 6B + 8B = 14B

Number of days required = Total Work / Combined Efficiency Number of days required = 70B / 14B = 5 days

Explanation

To find the largest possible equal class size (number of students per class) so that each class of boys has the same number of students as each class of girls, we need to find the Highest Common Factor (HCF) of the number of boys and girls.

Number of boys = 391 Number of girls = 323

We can find the HCF by calculating the difference between the two numbers: 391 - 323 = 68

The HCF of 391 and 323 must also be a factor of their difference, 68. The factors of 68 are 1, 2, 4, 17, 34, and 68.

Since both 391 and 323 are odd numbers, their HCF must also be an odd number. Testing the odd factor 17: 391 ÷ 17 = 23 323 ÷ 17 = 19

Since both divisions result in integers, the HCF of 391 and 323 is 17. Thus, the number of students in each equal class is 17.

Explanation

The time interval between two consecutive ticks of the first watch is T₁ = 95/90 = 19/18 seconds. The time interval between two consecutive ticks of the second watch is T₂ = 323/315 seconds.

Both watches will tick together at time intervals that are multiples of the Least Common Multiple (LCM) of T₁ and T₂. The LCM of two fractions is calculated as the LCM of the numerators divided by the Highest Common Factor (HCF) of the denominators: LCM(T₁, T₂) = LCM(19, 323) / HCF(18, 315)

Since 323 is 19 × 17, the LCM of 19 and 323 is 323. Since 18 = 9 × 2 and 315 = 9 × 35, the HCF of 18 and 315 is 9. Therefore, LCM(T₁, T₂) = 323/9 seconds.

This means both watches tick together every 323/9 seconds. Since they are started together, they tick together first at t = 0 seconds.

The total duration of the first hour is 3600 seconds. The number of times they tick together after the start is the integer part of 3600 divided by the LCM: 3600 ÷ (323/9) = 32400 / 323 = 100.31

The integer part of this division is 100, meaning they tick together 100 times after the initial start. Including the starting tick at t = 0, the total number of times they tick together in the first hour is 100 + 1 = 101 times.

Explanation

By the Remainder Theorem, when a polynomial f(x) is divided by x - a, the remainder is f(a). Since both polynomials leave the same remainder when divided by x - 4, evaluating both at x = 4 yields the same value.

For the first polynomial, f(x) = Px³ + 3x² - 3: f(4) = P(4)³ + 3(4)² - 3 = 64P + 48 - 3 = 64P + 45

For the second polynomial, g(x) = 2x³ - 5x + P: g(4) = 2(4)³ - 5(4) + P = 128 - 20 + P = 108 + P

Equating the two remainders: 64P + 45 = 108 + P 63P = 63 P = 1

Explanation

By converting sec 10° into 1/cos 10°, the expression becomes: (cos 10° - √3 sin 10°) / (sin 10° cos 10°)

Multiplying and dividing the numerator by 2: 2 × (½ cos 10° - (√3/2) sin 10°)

Using the trigonometric identity sin(A - B) = sin A cos B - cos A sin B, where sin 30° = ½ and cos 30° = √3/2, the numerator simplifies to: 2 × sin(30° - 10°) = 2 sin 20°

For the denominator, using the double-angle identity sin 2θ = 2 sin θ cos θ: sin 10° cos 10° = ½ sin 20°

Dividing the simplified numerator by the simplified denominator: (2 sin 20°) / (½ sin 20°) = 2 / ½ = 4

Explanation

Let the helicopter be at point H at a height h above the ground. Let P be the point on the ground directly below the helicopter, so HP = h.

Let A and B be the two consecutive milestones in opposite directions, which means the distance between them is AB = 1 mile. The point P lies on the line segment AB.

The angles of depression to the milestones A and B are x and y respectively, which are equal to the angles of elevation from A and B to the helicopter.

In right-angled triangle HPA: tan x = HP / AP = h / AP AP = h / tan x

In right-angled triangle HPB: tan y = HP / PB = h / PB PB = h / tan y

Since A and B are consecutive milestones, the total distance AB is: AP + PB = 1 h / tan x + h / tan y = 1 h (1 / tan x + 1 / tan y) = 1 h ((tan x + tan y) / (tan x tan y)) = 1 h = (tan x tan y) / (tan x + tan y)

Explanation

Let the two perpendicular sides of the right-angled triangle be y and b. The area of the triangle is: Area = ½ × y × b = x b = 2x/y

The length of the hypotenuse c is calculated using the Pythagorean theorem: c = √(y² + b²) c = √(y² + (2x/y)²) c = √(y² + 4x²/y²) c = √((y⁴ + 4x²)/y²) c = √(y⁴ + 4x²) / y

The area of the triangle can also be expressed using the hypotenuse c and the altitude h from the right vertex to the hypotenuse: Area = ½ × c × h = x h = 2x / c

Substituting the expression for c: h = 2x / (√(y⁴ + 4x²) / y) h = 2xy / √(y⁴ + 4x²)

Explanation

The interior angle of a regular polygon with n sides is calculated using the formula ((n - 2) × 180°) / n.

Given that the interior angle is 135°: ((n - 2) × 180) / n = 135 180n - 360 = 135n 45n = 360 n = 8

Thus, the polygon has 8 sides (an octagon).

The number of diagonals in a polygon with n sides is calculated using the formula n(n - 3) / 2.

Substituting n = 8: 8 × (8 - 3) / 2 = 8 × 5 / 2 = 20

Explanation

To find the area of the triangle formed by the lines x + y - 4 = 0, x + 2y - 10 = 0, and y = 0, we determine the coordinates of its three vertices by finding the points of intersection of these lines.

First, finding the intersection of x + y - 4 = 0 and x + 2y - 10 = 0: Subtracting the first equation from the second gives: (x + 2y - 10) - (x + y - 4) = 0 y - 6 = 0 y = 6

Substituting y = 6 into the first equation: x + 6 - 4 = 0 x = -2 Thus, the first vertex is A(-2, 6).

Second, finding the intersection of x + y - 4 = 0 and y = 0: Substituting y = 0 gives: x - 4 = 0 x = 4 Thus, the second vertex is B(4, 0).

Third, finding the intersection of x + 2y - 10 = 0 and y = 0: Substituting y = 0 gives: x - 10 = 0 x = 10 Thus, the third vertex is C(10, 0).

Since the vertices B(4, 0) and C(10, 0) lie on the line y = 0 (the x-axis), the base of the triangle lies along the x-axis. The length of this base is: Base = 10 - 4 = 6 units

The height of the triangle is the perpendicular distance from the vertex A(-2, 6) to the base line y = 0, which corresponds to the y-coordinate of vertex A: Height = 6 units

Using the standard formula for the area of a triangle: Area = ½ × base × height Area = ½ × 6 × 6 = 18 unit²

Explanation

For x = √3/2, we can rewrite the terms 1 + x and 1 - x to find their square roots: 1 + x = 1 + √3/2 = (2 + √3)/2 = (4 + 2√3)/4 = (√3 + 1)²/4 Thus, √(1+x) = (√3 + 1)/2

Similarly, for 1 - x: 1 - x = 1 - √3/2 = (2 - √3)/2 = (4 - 2√3)/4 = (√3 - 1)²/4 Thus, √(1-x) = (√3 - 1)/2

Now, substitute these values into the first term of the expression: (1+x) / (1 + √(1+x)) = [(2 + √3)/2] / [1 + (√3 + 1)/2] = [(2 + √3)/2] / [(3 + √3)/2] = (2 + √3) / (3 + √3)

Rationalizing the denominator by multiplying the numerator and denominator by (3 - √3): = (2 + √3)(3 - √3) / ((3 + √3)(3 - √3)) = (6 - 2√3 + 3√3 - 3) / (9 - 3) = (3 + √3) / 6

Substitute the values into the second term of the expression: (1-x) / (1 - √(1-x)) = [(2 - √3)/2] / [1 - (√3 - 1)/2] = [(2 - √3)/2] / [(3 - √3)/2] = (2 - √3) / (3 - √3)

Rationalizing the denominator by multiplying the numerator and denominator by (3 + √3): = (2 - √3)(3 + √3) / ((3 - √3)(3 + √3)) = (6 + 2√3 - 3√3 - 3) / (9 - 3) = (3 - √3) / 6

Adding the two rationalized terms together: (3 + √3)/6 + (3 - √3)/6 = (3 + √3 + 3 - √3) / 6 = 6/6 = 1

Explanation

Let 2ˣ = 3ʸ = 6⁻ᶻ = k.

From this relation, we can express 2, 3, and 6 in terms of k: 2 = k^(1/x) 3 = k^(1/y) 6 = k^(-1/z)

Since we know that 2 × 3 = 6, we substitute the values: k^(1/x) × k^(1/y) = k^(-1/z)

Using the laws of exponents to add the powers on the left side: k^(1/x + 1/y) = k^(-1/z)

Equating the exponents from both sides: 1/x + 1/y = -1/z

Rearranging the equation: 1/x + 1/y + 1/z = 0

Explanation

Let A and B represent the events that Ashok and Babulal speak the truth, respectively.

The probability of Ashok speaking the truth is P(A) = 75% = 3/4. The probability of Ashok telling a lie is P(A') = 1 - 3/4 = 1/4.

The probability of Babulal speaking the truth is P(B) = 80% = 4/5. The probability of Babulal telling a lie is P(B') = 1 - 4/5 = 1/5.

They will contradict each other in stating the same fact when one speaks the truth and the other lies.

Required probability = P(A) × P(B') + P(A') × P(B)

Substituting the values: Required probability = (3/4 × 1/5) + (1/4 × 4/5) = 3/20 + 4/20 = 7/20

Percentage of cases of contradiction = (7/20) × 100 = 35%

Explanation

Let f(x) = sin x (1 + cos x). To find the maximum value of the function, we find its first derivative with respect to x and set it to zero.

Using the product rule, the derivative is: f'(x) = cos x (1 + cos x) + sin x (-sin x) f'(x) = cos x + cos²x - sin²x Using the identity sin²x = 1 - cos²x: f'(x) = cos x + cos²x - (1 - cos²x) f'(x) = 2 cos²x + cos x - 1

To find the critical points, set f'(x) = 0: 2 cos²x + cos x - 1 = 0 (2 cos x - 1)(cos x + 1) = 0

This yields cos x = ½ or cos x = -1. For the interval under consideration, cos x = ½ gives x = π/3.

To check for a maximum, we find the second derivative: f''(x) = -sin x - 4 sin x cos x = -sin x - 2 sin 2x

Evaluating the second derivative at x = π/3: f''(π/3) = -sin(π/3) - 2 sin(2π/3) = -√3/2 - √3 = -3√3/2

Since f''(π/3) is less than zero, the function f(x) achieves its local maximum value at x = π/3.

Explanation

The total number of ways to form a committee of 7 members from a group of 13 people (9 men and 4 women) without any restrictions is given by the combination formula ⁿCᵣ = n! / (r!(n - r)!):

Total ways = ¹³C₇ = 1716

To find the number of ways to form a committee with at most 3 women, we can subtract the cases where the committee contains more than 3 women. Since there are only 4 women in total, the only restricted case to exclude is when the committee has exactly 4 women and 3 men.

The number of ways to select 4 women from 4 and 3 men from 9 is:

Excluded ways = ⁴C₄ × ⁹C₃ = 1 × 84 = 84

Subtracting the excluded ways from the total ways:

Number of valid ways = 1716 - 84 = 1632

Explanation

The probability that the problem is solved is the complement of the probability that none of the students are able to solve it.

Let the independent probabilities of Ram, Shyam, and Mohan solving the problem be P(A) = 1/2, P(B) = 1/3, and P(C) = 1/4 respectively.

The probability of each student failing to solve the problem is: P(A') = 1 - 1/2 = 1/2 P(B') = 1 - 1/3 = 2/3 P(C') = 1 - 1/4 = 3/4

Since their attempts are independent events, the probability that none of them solve the problem is: P(none solve) = P(A') × P(B') × P(C') = 1/2 × 2/3 × 3/4 = 1/4

The probability that the problem is solved is: P(solved) = 1 - P(none solve) = 1 - 1/4 = 3/4

Explanation

Mool Chand completes 4 rounds in 1 hour (60 minutes). The time taken by Mool Chand to complete one full round is 60 ÷ 4 = 15 minutes. He returns to the starting point at multiples of 15 minutes, which are 15, 30, 45, 60, and so on.

Ram Chand completes 6 rounds in 1 hour (60 minutes). The time taken by Ram Chand to complete one full round is 60 ÷ 6 = 10 minutes. He returns to the starting point at multiples of 10 minutes, which are 10, 20, 30, 40, 50, 60, and so on.

Regardless of their direction of travel, they will meet at the starting point only when both have completed an integral number of rounds. This happens at the least common multiple (LCM) of the time they take to complete one round.

LCM(15, 10) = 30 minutes.

Thus, they will meet for the first time at the starting point after 30 minutes.

Explanation

The distance covered by the train can be calculated hour by hour based on its increasing speed:

In the first hour, the train travels at a speed of 40 km/h and covers a distance of 40 km.

In the second hour, the speed increases to 50 km/h, covering a distance of 50 km.

In the third hour, the speed increases to 60 km/h, covering a distance of 60 km.

The cumulative distance covered in the first 3 hours is 40 + 50 + 60 = 150 km.

The remaining distance to be covered is 185 - 150 = 35 km.

In the fourth hour, the speed of the train is 70 km/h. The time required to cover the remaining 35 km at this speed is:

Time = 35 / 70 = ½ hour

The total time taken to cover the entire 185 km is 3 + ½ = 7/2 hours.

Explanation

Let the total sum of money be S.

The daily salary of Nikhil is S/10 and the daily salary of Praveen is S/30.

When both are paid together, their combined daily salary is: S/10 + S/30 = (3S + S)/30 = 4S/30 = 2S/15

To find the number of days the sum of money is sufficient for both, we divide the total sum of money by their combined daily salary: S ÷ (2S/15) = 15/2 days

Explanation

The earth rotates 360° on its axis in 24 hours. This gives the rate of rotation as:

360° ÷ 24 = 15° per hour

Since 1 hour contains 60 minutes, the rotation rate per minute is:

15° ÷ 60 = 0.25° per minute

Converting 4 hours and 12 minutes entirely into minutes:

4 hours × 60 minutes/hour = 240 minutes Total time = 240 + 12 = 252 minutes

Calculating the total angle moved:

252 minutes × 0.25° per minute = 63°

Explanation

In any triangle ABC, the median AD divides the triangle into two triangles of equal area: Area(△ABD) = Area(△ACD) = ½ Area(△ABC)

Since E is a point on the median AD, the triangle ACE lies entirely within or coincides with the triangle ACD. Thus, its area is bounded by the area of △ACD: Area(△ACE) ≤ Area(△ACD) = ½ Area(△ABC)

Since the area of △ABC is strictly positive, the area of △ACE is at most half of the area of △ABC. Therefore, Area(△ABC) cannot equal Area(△ACE), making Observation (I) incorrect.

Furthermore, congruent triangles must have equal areas. Because Area(△ABC) is strictly greater than Area(△ACE), △ABC and △ACE cannot be congruent under any circumstances. Thus, Observation (II) is also incorrect.

Explanation

The given expression is: sin(π/9) × sin(2π/9) × sin(3π/9) × sin(4π/9)

Converting the angles from radians to degrees using the relation π radians = 180°: π/9 = 20° 2π/9 = 40° 3π/9 = 60° 4π/9 = 80°

Substituting these values, the expression becomes: sin(20°) × sin(40°) × sin(60°) × sin(80°)

Since sin(60°) = √3/2, the expression can be rewritten as: sin(60°) × [sin(20°) × sin(40°) × sin(80°)]

Using the standard trigonometric identity: sin(θ) × sin(60° - θ) × sin(60° + θ) = ¼ sin(3θ)

Substituting θ = 20°: sin(20°) × sin(40°) × sin(80°) = ¼ sin(60°) = ¼ × (√3/2) = √3/8

Multiplying this result by sin(60°): (√3/2) × (√3/8) = 3/16

Explanation

Let O₁ and O₂ be the centres of the two circles with radii r₁ = 5 cm and r₂ = 3 cm respectively, so the distance between centres O₁O₂ = 4 cm. Let P and Q be the points where the two circles intersect.

In triangle O₁PO₂, the side lengths are O₁P = 5 cm, O₂P = 3 cm, and O₁O₂ = 4 cm. Applying the converse of Pythagoras' theorem:

O₂P² + O₁O₂² = 3² + 4² = 9 + 16 = 25 = 5² = O₁P²

Since the relation holds, triangle O₁PO₂ is a right-angled triangle with the right angle at O₂. This means O₂P is perpendicular to the line of centres O₁O₂.

The line of centres O₁O₂ is always the perpendicular bisector of the common chord PQ. Since O₂P is perpendicular to O₁O₂ at O₂, the common chord PQ must pass through the centre O₂ of the smaller circle, meaning O₂ serves as the midpoint of PQ.

The length of the common chord PQ is therefore twice the radius of the smaller circle:

PQ = 2 × O₂P = 2 × 3 = 6 cm

Explanation

By the Midpoint Theorem, in any triangle, the line segment joining the midpoints of two sides is parallel to the third side and is equal to half of its length.

For any arbitrary quadrilateral ABCD, let P, Q, R, and S be the midpoints of the sides AB, BC, CD, and DA, respectively.

Drawing the diagonal AC, we consider triangle ABC and triangle ADC. In triangle ABC, P and Q are the midpoints of AB and BC, which means PQ is parallel to AC and PQ = ½ AC. Similarly, in triangle ADC, S and R are the midpoints of AD and CD, which means SR is parallel to AC and SR = ½ AC.

Since both PQ and SR are parallel to AC, they are parallel to each other (PQ || SR). Since both PQ and SR are equal to ½ AC, they are equal in length (PQ = SR).

A quadrilateral with one pair of opposite sides that are both equal and parallel is a parallelogram. Therefore, the quadrilateral PQRS formed by joining the midpoints is always a parallelogram, a property known as Varignon's theorem.

Explanation

In an equilateral triangle, all three sides are equal in length, and all three internal angles are equal to 60°. Because of this perfect symmetry, the line segment drawn from any vertex to the midpoint of the opposite side (the median) is also perpendicular to that side (the altitude). Consequently, the medians, altitudes, angle bisectors, and perpendicular bisectors of the sides are identical line segments. Since the centroid is the point of intersection of the medians and the orthocentre is the point of intersection of the altitudes, they must coincide at the exact same point in an equilateral triangle. This same point also serves as the incentre and circumcentre of the triangle.

Explanation

Ceva's Theorem states that for any triangle ABC and a point O inside the triangle, if the cevians AD, BE, and CF are concurrent at O and meet the opposite sides at D, E, and F respectively, then the product of the ratios of the segments on each side is equal to 1.

The relation is expressed as: (BD/DC) × (CE/EA) × (AF/FB) = 1

This can be proven by using the areas of the triangles. Since triangles ABD and ACD share the same height from A to BC, the ratio of their bases is equal to the ratio of their areas: BD/DC = Area(ΔABD)/Area(ΔACD)

Similarly, for triangles OBD and OCD: BD/DC = Area(ΔOBD)/Area(ΔOCD)

Using ratio properties, we subtract these areas to find the ratio in terms of the main triangles: BD/DC = (Area(ΔABD) - Area(ΔOBD)) / (Area(ΔACD) - Area(ΔOCD)) = Area(ΔABO)/Area(ΔACO)

By applying the same method to the other sides: CE/EA = Area(ΔBCO)/Area(ΔABO) AF/FB = Area(ΔACO)/Area(ΔBCO)

Multiplying these three equations together yields: (BD/DC) × (CE/EA) × (AF/FB) = (Area(ΔABO)/Area(ΔACO)) × (Area(ΔBCO)/Area(ΔABO)) × (Area(ΔACO)/Area(ΔBCO)) = 1

Explanation

The monkey climbs 30 feet at the beginning of each hour and slips back 20 feet during the rest of the hour. This results in a net progress of 10 feet (30 - 20) per completed hour.

To find when the monkey first touches the flag at 120 feet, we subtract the final climb of 30 feet from the total height because once the monkey reaches the top, he does not slip back.

The height to be covered through normal hourly cycles is 120 - 30 = 90 feet.

Since the net progress is 10 feet per hour, the time required to reach 90 feet is 90 ÷ 10 = 9 hours.

Starting at 8 AM, after 9 hours (at 5 PM), the monkey completes 9 cycles and is at a height of 90 feet.

At exactly 5 PM, which is the beginning of the 10th hour, the monkey makes his next climb of 30 feet. This brings him to 120 feet (90 + 30), touching the flag for the first time.

Explanation

Comparing the statement "tom kun sad" (dogs are barking) with "kun jo map" (dogs and horses), the common code word is "kun" and the common word is "dogs". This means "kun" represents "dogs".

Comparing the statement "tom kun sad" (dogs are barking) with "mut tom ko" (donkeys are mad), the common code word is "tom" and the common word is "are". This means "tom" represents "are".

In the first statement "tom kun sad", since "kun" represents "dogs" and "tom" represents "are", the remaining code "sad" must represent the remaining word "barking".

Explanation

The number series follows an addition pattern where each term starting from the third is the sum of the two preceding terms.

7 + 11 = 18 11 + 18 = 29 18 + 29 = 47

To find the missing term, add the two preceding terms: 29 + 47 = 76

Verifying with the subsequent terms in the sequence: 47 + 76 = 123 76 + 123 = 199

Explanation

The relationship established in the first pair is that of a commanding authority and the group of individuals they guide or direct. A captain is a designated chief or officer who commands and leads soldiers. In the exact same manner, a leader is an individual who guides, directs, or commands a group of followers. This completes the analogous relationship of director to the directed.

Explanation

The pair Iron : Rod is the odd one because the relationship is written in the order of Raw Material : Product. Iron is the material used to make a Rod. This reverses the relationship pattern where the finished product is listed first and the raw material it is made of is listed second.

Explanation

The total number of boys in the row is calculated using Tushar's position from both ends: Total = (Position from left) + (Position from right) - 1 Total = 13 + 11 - 1 = 23

The position of Ram from the left is then determined using this total: Left position = Total - (Position from right) + 1 Left position = 23 - 17 + 1 = 7

Explanation

By placing the six friends in a circular arrangement facing the center, the left direction of any person corresponds to the clockwise direction.

Let D be placed at position 1. Since E is to the left of D, E is placed at position 2 in the clockwise direction.

F is sitting between E and A, which means F must be at position 3 and A must be at position 4.

C is sitting between A and B, which places C at position 5 and B at position 6.

This completes the clockwise sequence of the friends: D, E, F, A, C, B. Looking at this arrangement, the person sitting immediately to the left (clockwise) of B is D.

Explanation

By placing the six friends in a circular arrangement facing the centre:

Since E is to the left of D, E is positioned next to D in the clockwise direction.

F is between E and A, which means F must sit next to E, and A sits next to F.

C is between A and B, meaning C sits next to A, and B sits next to C. This places B next to D, completing the closed circle.

The resulting clockwise sequence of the friends is D, E, F, A, C, B.

For any person facing the centre of the circle, their right-hand side corresponds to the counter-clockwise direction. Looking counter-clockwise from C, the person sitting immediately to the right of C is A.

Explanation

In a circular arrangement of six people facing the centre, the person sitting third to the left of any individual is always positioned directly opposite to them. Since E is to the left of D, and F sits between E and A, A must be placed opposite to D. This is further verified as C sits between A and B, which positions B next to D. Therefore, the opposite pairs in the circle are D and A, E and C, and F and B. This makes A the person sitting directly opposite D, which is the third position to the left of D.

Explanation

By placing the six friends in a circular arrangement facing the centre, we can determine their exact positions based on the given clues. E is to the left of D. F is between E and A, which means the sequence in that direction is E, F, A. C is between A and B, which means the sequence continues as A, C, B. Combining these positions in order around the circle gives the sequence D, E, F, A, C, B. In this arrangement, B and C are seated immediately next to each other. Consequently, there is no one sitting between B and C.

Explanation

Applying the given symbol replacements to Option c: 18 × 6 + 7 ÷ 5 - 2 = 16

According to the rules: × stands for subtraction (-)

• stands for division (÷) ÷ stands for multiplication (×) stands for addition (+)

Substituting these symbols into the expression: 18 - 6 ÷ 7 × 5 + 2 = 16

Applying the BODMAS/PEMDAS order of operations: First, division is performed: 6 ÷ 7 ≈ 0.86

Next, multiplication is performed: 0.86 × 5 ≈ 4.29

Finally, addition and subtraction are performed from left to right: 18 - 4.29 + 2 = 13.71 + 2 = 15.71

Rounding the decimal value 15.71 to the nearest integer gives 16, which matches the right-hand side of the equation.

Explanation

This question is defective. The ADHM:ZWSN pair uses a complement-to-27 rule (A+Z=D+W=H+S=M+N=27). Applying this to CFJO yields XUQL (C+X=F+U=J+Q=O+L=27), which is not among the options. Among A–D, only YVRM (option A) and WTPK (option B) preserve the correct internal gap structure (−3, −4, −5). WTPK (option B) is selected as the best-fit pick because multiple published answer keys cite it and the prior resolution confirmed this choice; it differs from the mathematically correct XUQL by exactly −1 on each letter.

Explanation

Statement (I) is implicit because multisensory learning engages multiple senses, such as sight and hearing, which makes the educational process more engaging, retentive, and effective than traditional single-medium methods. This directly explains how electronic media improves classroom teaching.

Statement (II) is implicit because TV lessons serve as a practical form of electronic media that acts as an educational supplement, reinforcing and enhancing the curriculum taught in classrooms.

Therefore, both statements provide valid reasons and supporting contexts that explain why electronic media improves classroom teaching.

Explanation

Let the four consecutive odd numbers be x - 3, x - 1, x + 1, and x + 3.

The average of these four consecutive numbers is: ((x - 3) + (x - 1) + (x + 1) + (x + 3)) / 4 = 4x / 4 = x

Given that the average of these numbers is 54, we have: x = 54

Thus, the four consecutive odd numbers are: First number = 54 - 3 = 51 Second number = 54 - 1 = 53 Third number = 54 + 1 = 55 Fourth number = 54 + 3 = 57

The product of the first and third number is: 51 × 55 = 2805

Explanation

Darkness naturally invokes or leads to the feeling of fear. Similarly, honesty in an individual or action naturally inspires and leads to trust. This represents a cause-and-effect relationship where the first term is the attribute or state and the second term is the resulting feeling or outcome.

Explanation

To find the day of the week on August 15th when January 26th is a Friday in a leap year, we calculate the total number of days between these two dates and find the number of odd days.

The number of days from January 27th to August 15th are: Remaining days in January: 31 - 26 = 5 days Days in February (leap year): 29 days (29 mod 7 = 1 odd day) Days in March: 31 days (31 mod 7 = 3 odd days) Days in April: 30 days (30 mod 7 = 2 odd days) Days in May: 31 days (31 mod 7 = 3 odd days) Days in June: 30 days (30 mod 7 = 2 odd days) Days in July: 31 days (31 mod 7 = 3 odd days) Days in August: 15 days (15 mod 7 = 1 odd day)

Sum of all odd days = 5 + 1 + 3 + 2 + 3 + 2 + 3 + 1 = 20 odd days.

Dividing the total odd days by 7: 20 ÷ 7 = 2 weeks and 6 odd days.

Adding 6 days to Friday gives Thursday.

Explanation

The total number of squares on an n × n grid is given by the formula:

S = n(n + 1)(2n + 1)/6

A standard chessboard is an 8 × 8 grid, so we substitute n = 8 into the formula:

S = 8 × (8 + 1) × (2 × 8 + 1) / 6 S = 8 × 9 × 17 / 6 S = 72 × 17 / 6 S = 12 × 17 S = 204

Explanation

The dial of a clock is a circle comprising 360°. Since the minute hand completes one full revolution of 360° in 60 minutes, the angle traversed by the minute hand in 1 minute is 360° ÷ 60 = 6°.

Therefore, in 7 minutes, the minute hand will move through an angle of 7 × 6° = 42°.

Explanation

Let the capacity of each container be 1 unit.

The amount of water in the first container is 1/2, the second container is 1/3, and the third container is 0.

The total volume of water across all three containers is 1/2 + 1/3 + 0 = 5/6.

Dividing this total volume of water equally among the three containers gives (5/6) ÷ 3 = 5/18 of the container capacity.

Explanation

Let the length of the rectangular hall be L and its width be W.

We are given that W = ¾ L.

The area of the rectangular hall is given by the formula Area = L × W. Substituting the given values:

L × (¾ L) = 300

¾ L² = 300

L² = (300 × 4) / 3

L² = 400

L = 20 m

Now, we calculate the width using W = ¾ L:

W = ¾ × 20 = 15 m

The difference between the length and the width of the hall is:

L - W = 20 - 15 = 5 m

Explanation

Let x and y represent the arrival times of Ajay and Uday respectively, measured in minutes after 1:00 PM. Since they both arrive between 1:00 PM and 2:00 PM, we have 0 ≤ x ≤ 60 and 0 ≤ y ≤ 60.

This sample space can be represented geometrically by a square of side length 60 on a Cartesian plane. Total Area of the sample space = 60 × 60 = 3600

For them to meet, the difference in their arrival times must be at most 15 minutes: |x - y| ≤ 15

This favorable region is bounded by the lines y ≤ x + 15 and y ≥ x - 15 inside the square. The area of this region can be calculated by subtracting the area of the two unfavorable right-angled triangles at the corners of the square from the total area of the square.

Each of these two corner triangles has perpendicular sides of length 60 - 15 = 45. Area of one triangle = ½ × 45 × 45 = 1012.5 Total area of both triangles = 2 × 1012.5 = 2025

Area of the favorable region = Total Area - Area of the two triangles Area of the favorable region = 3600 - 2025 = 1575

The probability that they will meet is the ratio of the favorable area to the total area: Probability = 1575 / 3600 = 7/16

Explanation

Let M be the market price of the article.

The relationship between the selling price (SP) and the market price after successive discounts of d₁% and d₂% is given by the formula:

SP = M × (1 - d₁/100) × (1 - d₂/100)

Substituting the given values of SP = 216, d₁ = 10, and d₂ = 20 into the formula:

216 = M × (1 - 10/100) × (1 - 20/100) 216 = M × 0.9 × 0.8 216 = M × 0.72 M = 216 / 0.72 M = 300

Explanation

The number of diagonals d of an n-sided polygon is given by the formula d = n(n - 3)/2.

According to the question, the number of diagonals is 50% higher than the number of sides: d = n + 0.5n = 1.5n = 3n/2

Equating the two expressions for the number of diagonals: n(n - 3)/2 = 3n/2

Since n is the number of sides of a polygon and must be greater than zero, dividing both sides by n/2 yields: n - 3 = 3 n = 6

A polygon with 6 sides is a hexagon.

Explanation

The arithmetic operation is carried out in the octal (base-8) number system.

In base-8 addition: 137₈ + 276₈ For the units place: 7 + 6 = 13 in decimal, which is 15 in octal (write 5 and carry 1). For the tens place: 3 + 7 + 1 (carry) = 11 in decimal, which is 13 in octal (write 3 and carry 1). For the hundreds place: 1 + 2 + 1 (carry) = 4 in decimal, which is 4 in octal. This yields the sum 435.

Applying the same base-8 addition to 731 + 672: 731₈ + 672₈ For the units place: 1 + 2 = 3 in octal (write 3). For the tens place: 3 + 7 = 10 in decimal, which is 12 in octal (write 2 and carry 1). For the hundreds place: 7 + 6 + 1 (carry) = 14 in decimal, which is 16 in octal (write 16). This yields the sum 1623.

Explanation

When a quantity is successively increased by x% and then decreased by x%, the net percentage change is always a decrease given by the formula:

Net change % = -x²/100

Substituting x = 10 into the formula:

Net change % = -(10)²/100 = -100/100 = -1%

The negative sign indicates a decrease, showing that the number decreases by 1%.

Explanation

Initial mass of the alloy is 200 gm and the ratio of Zinc to Copper is 5 : 3.

The mass of Zinc is 200 × 5/8 = 125 gm. The mass of Copper is 200 × 3/8 = 75 gm.

Let the mass of Copper to be added be x gm. Since only copper is added, the mass of Zinc remains constant at 125 gm. The new ratio of Zinc to Copper is 3 : 5.

125 / (75 + x) = 3 / 5

Cross-multiplying the terms: 125 × 5 = 3 × (75 + x) 625 = 225 + 3x 3x = 400 x = 400/3 = 133 ⅓ gm

Explanation

Let us represent the relationship between the coins in terms of costliness, as the statement establishes that heavier coins are costlier.

First, analyzing the statements regarding Ram, Ramesh, and Mohan: Ram's coin is heavier than Mohan's coin, which means Ram > Mohan. Ram's coin is costlier than Ramesh's, which means Ram > Ramesh. Ramesh's coin is costlier than Mohan's, which means Ramesh > Mohan.

Combining these three relations, we get the following sequence: Ram > Ramesh > Mohan

This chain establishes that Ram has the costliest coin among this group.

Additionally, we are given: Naresh's coin is costlier than Yogesh's (Naresh > Yogesh).

Among the compared groups, Ram is positioned at the top of the largest comparative sequence, making Ram the correct option.

Explanation

To determine how A is related to F in the expression A @ B + C * D - E ÷ F, the symbols are decoded step-by-step:

A @ B means A is the daughter of B. This establishes that A is female.

B + C means B is the father of C. Since A is the daughter of B, A and C are siblings.

C * D means C is the son of D. Since B is already established as the father of C, D must be the mother of C and the wife of B.

D - E means D is the mother of E.

E ÷ F means E is the sister of F.

This sequence shows that A, C, E, and F are all siblings, sharing the same father B and mother D. Because A is a female child of this family, A is the sister of F.

Explanation

To determine the relationship, we can decode the expression A + B + C × D + E @ F step-by-step using the given definitions:

A + B: A is the father of B. B + C: B is the father of C. C × D: C is the brother of D. Since B is the father of C, B is also the father of D. D + E: D is the father of E. E @ F: E is the daughter of F.

From steps 4 and 5, D is the father of E and E is the daughter of F. This implies that D and F are a married couple where D is the husband and F is the wife.

Since B is the father of D, and F is married to D, B is the father-in-law of F. In simplified kinship terms, B (father of D) acts as the father figure (father-in-law) to F.

Explanation

By decoding the symbols in the expression:

A @ B means A is the daughter of B. B × C means B is the brother of C. C + D means C is the father of D. D × E means D is the brother of E. E @ F means E is the daughter of F.

From the section C + D × E @ F, C is the father of D, D is the brother of E, and E is the daughter of F. This indicates that D and E are siblings whose father is C and whose mother is F. Therefore, C and F are married.

From the section A @ B × C, B is the brother of C, and A is the daughter of B. Since C is the brother of A's father B, C is A's paternal uncle. Since F is married to C, F is the wife of A's paternal uncle. Thus, F is the aunt of A.

Explanation

This question is defective. Parsing the chain: A+B → A is father of B; B×C → B is brother of C (so A is also father of C); C+D → C is father of D; D*E → D is son of E, meaning E is D's mother (married to C); E@F → E is daughter of F, meaning F is E's parent. Therefore A (paternal grandfather of D) and F (maternal grandparent of D through E) are co-grandparents — a relationship absent from the options. Among the four choices, Father (B) is selected as the least-incorrect option since A occupies a senior ancestor/patriarch role in the chain; none of the options accurately describes the actual relationship.

Explanation

By analyzing the family tree step-by-step from the expression: A * B means A is the son of B. B × C means B is the brother of C. C ÷ D means C is the sister of D. D × E means D is the brother of E. E - F means E is the mother of F.

This shows that B, C, D, and E are siblings. B is a male sibling and the father of A. E is a female sibling and the mother of F. Since the parents of A and F are siblings, F and A are cousins. Thus, F is the cousin of A.

Explanation

When a solid painted cube is cut into smaller equal-sized cubes, the smaller cubes with three of their surfaces colored are always located at the corners of the original larger cube. Since any standard cube has exactly 8 corners, there will always be 8 such cubes with three surfaces colored, regardless of the total number of subdivisions.

Explanation

When all surfaces of a solid cube are painted red and the cube is then cut into 64 equal smaller cubes, we first find the side length n of the original cube: n³ = 64, so n = ∛64 = 4. Each side of the original cube is therefore divided into 4 equal parts.

The smaller cubes that have no painted surface at all are those completely enclosed inside the large cube — they never touched any outer face. These inner cubes form a smaller cube of side (n − 2): removing one layer from each side in every direction gives (4 − 2) = 2 units per side.

Number of unpainted cubes = (n − 2)³ = (4 − 2)³ = 2³ = 8.

Therefore the answer is 8, which is option B.

Explanation

A larger solid cube is cut into 64 equal smaller cubes, which means the larger cube is divided into 4 × 4 × 4 smaller cubes of side length 1 unit each. For any smaller cube to have two opposite surfaces painted red, both of those opposite surfaces must lie on the outer faces of the original larger cube.

In a 4 × 4 × 4 grid, opposite faces of the larger cube are separated by 4 units. However, the opposite faces of any individual 1 × 1 × 1 smaller cube are separated by only 1 unit. Since a single smaller cube cannot span the entire width of the larger cube to touch two opposite outer faces simultaneously, it is geometrically impossible for any smaller cube to have two of its opposite surfaces colored red. Consequently, the number of such cubes is 0.

Explanation

When a solid cube is divided into smaller equal cubes, the number of divisions along each edge, n, is calculated from the total number of smaller cubes. Here, n = ∛64 = 4.

The smaller cubes with exactly one surface coloured are located on the faces of the main cube, excluding the edges and corners. Since a cube has 6 faces, the formula to find the number of these cubes is:

6 × (n - 2)²

Substituting n = 4 into this relation:

6 × (4 - 2)² = 6 × 2² = 6 × 4 = 24

Explanation

The total number of smaller cubes is 64, which means the number of divisions along each edge of the larger cube, n, is the cube root of 64, which equals 4.

The smaller cubes that have exactly two adjacent surfaces colored in red and the rest of the surfaces with no color are located along the edges of the larger cube, excluding the corner cubes. A cube has 12 edges, and the number of such two-face colored cubes along each edge is given by n - 2.

Using the standard formula, the total number of cubes with exactly two colored faces is 12 × (n - 2). Substituting n = 4 into this formula yields 12 × (4 - 2) = 12 × 2 = 24. These 24 cubes have exactly two adjacent red faces and four uncolored faces.

Explanation

Reduced price per item is calculated using the formula: Reduced Price = (Amount × Reduction Percentage) ÷ (100 × Extra Quantity Bought)

Given: Amount = Rs. 40 Reduction Percentage = 20% Extra Quantity = 20 oranges

Substituting the values into the formula: Reduced Price = (40 × 20) ÷ (100 × 20) = 40/100 = Rs. 0.40

Converting Rupees to paise: 0.40 × 100 = 40 paise

Explanation

By using the standard area formulas for a square and an equilateral triangle, let the common base which forms the side of both shapes be a.

The area of the square is given by: Area of square = a²

The area of the equilateral triangle is given by: Area of triangle = (√3/4) × a²

The ratio of the area of the square to the area of the equilateral triangle is: Ratio = a² : (√3/4) × a² Ratio = 1 : √3/4 Ratio = 4 : √3

Explanation

Let the two numbers be x and y.

The sum of the numbers is x + y = 12, and the product of the numbers is xy = 35.

The sum of their reciprocals is given by the algebraic relation: 1/x + 1/y = (x + y) / xy

Substituting the given values of the sum and the product into the relation: 1/x + 1/y = 12/35

Explanation

The reduction in net income is exactly equal to the increase in income tax paid. Let the initial income tax be T and the initial net income be N.

According to the given condition: 19% of T = 1% of N 19/100 × T = 1/100 × N 19 × T = 1 × N N / T = 19 / 1

This means if the tax paid is 1 unit, the net income is 19 units.

The gross income is the sum of net income and income tax: Gross Income = Net Income + Tax = 19 + 1 = 20 units

The rate of income tax is the ratio of tax to gross income, expressed as a percentage: Rate of Income Tax = (Tax / Gross Income) × 100% Rate of Income Tax = (1 / 20) × 100% = 5%

Explanation

Let the number of benches in the classroom be b.

According to the second condition, if 7 students sit on a bench, space for 5 students is left. This means the total number of students S is given by: S = 7b - 5

According to the first condition, if 6 students sit on a bench, then to accommodate all of them, one more bench is needed. This implies that b benches of 6 students each leave some students standing, and adding exactly one more bench of capacity 6 accommodates all remaining students. Assuming this additional bench is fully occupied: S = 6b + 6

Equating both expressions: 7b - 5 = 6b + 6 b = 11

Substituting the value of b: S = 7 × 11 - 5 = 72

Explanation

By analyzing the given conditions step-by-step, the schedule for the week can be determined as follows:

Chemistry is scheduled on Thursday.

Since only one lecture is held between Chemistry and Botany, Botany must be scheduled on either Tuesday or Saturday.

If Botany is scheduled on Tuesday: Chemistry is on Thursday, and Botany is on Tuesday. English is scheduled immediately after Zoology. Since English cannot be scheduled on Tuesday or Saturday, Zoology must be scheduled on Saturday and English on Sunday. Since two lectures are scheduled between Mathematics and Zoology (Saturday), Mathematics must be scheduled on Wednesday. This leaves Monday and Friday for the remaining two subjects, Statistics and Physics. Since Statistics cannot be scheduled on Monday or Sunday, Statistics must be scheduled on Friday. This leaves Monday for Physics.

If Botany is scheduled on Saturday, the remaining conditions cannot be satisfied because Statistics would be forced into either Monday or Sunday, which violates the given rules.

Thus, Physics is scheduled on Monday.

Explanation

We can determine the schedule for the seven days of the week from Monday to Sunday by analyzing the given conditions:

Chemistry is taught on Thursday.

Since only one lecture is held between Chemistry and Botany, Botany must be taught on either Tuesday or Saturday.

English is taught on the day immediately next to Zoology, and English is not taught on Tuesday or Saturday.

Two lectures are scheduled between Mathematics and Zoology. Statistics is not taught on Monday or Sunday.

Let us test the case where Botany is taught on Tuesday: If Botany is on Tuesday, and Chemistry is on Thursday, the Zoology-English consecutive pair must be placed. Since English cannot be on Tuesday or Saturday, and Chemistry is on Thursday, the only valid consecutive placement for Zoology and English is Saturday and Sunday respectively. So, Zoology is on Saturday and English is on Sunday. With Zoology on Saturday, Mathematics must be scheduled on Wednesday to have exactly two lectures (Thursday and Friday) between Mathematics and Zoology. Now, the remaining days are Monday and Friday, and the remaining subjects are Statistics and Physics. Since Statistics cannot be taught on Monday, Statistics must be taught on Friday, leaving Physics for Monday.

This gives the complete and consistent schedule: Monday: Physics Tuesday: Botany Wednesday: Mathematics Thursday: Chemistry Friday: Statistics Saturday: Zoology Sunday: English

The subjects taught between Botany (Tuesday) and Zoology (Saturday) are Mathematics (Wednesday), Chemistry (Thursday), and Statistics (Friday). Therefore, the number of subjects taught between Botany and Zoology is 3.

Explanation

The seven subjects (Mathematics, Zoology, Botany, Chemistry, Physics, English, Statistics) are taught Monday through Sunday, one per day. Applying the given constraints step by step:

Step 1 — Fixed placement: Chemistry = Thursday.

Step 2 — Botany placement: 'Only one lecture is held between Chemistry and Botany' means exactly one day separates them. Chemistry is on Thursday (day 4), so Botany must be on Tuesday (day 2) or Saturday (day 6).

Step 3 — Zoology–English block: English is taught the day immediately after Zoology, and English ≠ Tuesday and English ≠ Saturday.

Test Botany = Saturday: The only remaining Zoology–English pair that avoids Tuesday and Saturday for English would require Zoology on Sunday and English on Monday. But then 'two lectures between Mathematics and Zoology (Sunday = day 7)' would require Mathematics on day 4 (Thursday), which is already taken by Chemistry. This case fails.

Test Botany = Tuesday: Remaining days for Zoology–English (English = Zoology+1, English ≠ Tue, ≠ Sat):

• The only valid pair is Zoology = Saturday, English = Sunday.

Step 4 — Mathematics placement: 'Two lectures are scheduled between Mathematics and Zoology (Saturday = day 6).' Exactly two days separate them, so Mathematics = day 3 = Wednesday.

Step 5 — Remaining subjects: Physics and Statistics fill Monday and Friday. 'Statistics ≠ Monday and ≠ Sunday,' so Statistics = Friday and Physics = Monday.

Final timetable: Monday = Physics Tuesday = Botany Wednesday = Mathematics Thursday = Chemistry Friday = Statistics Saturday = Zoology Sunday = English

The subject taught on Saturday is Zoology, which is option D.

Explanation

Based on the given conditions, the schedule of the lectures can be determined uniquely as follows:

Chemistry is scheduled on Thursday.

Since only one lecture is held between Chemistry and Botany, Botany must be scheduled on either Tuesday or Saturday.

English is taught immediately after Zoology, meaning Zoology and English form a consecutive pair. Since English cannot be taught on Tuesday or Saturday, and Chemistry is on Thursday, the only valid position for this pair is Zoology on Saturday and English on Sunday. This places Botany on Tuesday.

Two lectures are scheduled between Mathematics and Zoology. Since Zoology is on Saturday, Mathematics must be scheduled on Wednesday.

The remaining days are Monday and Friday, and the remaining subjects are Statistics and Physics. Since Statistics cannot be taught on Monday or Sunday, it must be scheduled on Friday, leaving Physics for Monday.

Thus, the final schedule is: Monday: Physics Tuesday: Botany Wednesday: Mathematics Thursday: Chemistry Friday: Statistics Saturday: Zoology Sunday: English

Explanation

According to the first sentence of the passage, a key finding of the research into successful leadership is that respect is always a two-way street. This concept implies that in order to receive respect from others, one must treat them with respect as well, meaning respect comes out of respect.

Explanation

The passage explicitly states that if a manager is respected, their preventive maintenance strategy will be accepted as a sincere attempt to resolve problems. Therefore, the strategy is viewed as an attempt to resolve problems.

Explanation

The passage emphasizes that respect in successful leadership is a two-way street, where treating others with friendliness and politeness leads to receiving respect in return. This mutual exchange and responsiveness between a leader and their team directly defines the concept of reciprocity.

Explanation

According to the passage, friendliness is an essential element that enhances managerial success but does not replace core management responsibilities. The author explicitly cautions against believing that friendliness will replace or correct poor management, which rules out options a and b. Instead, the author states that managers who intervene effectively in a friendly way are always more effective than those who do so in a non-friendly way. Therefore, in the context of management, friendliness is a tool for making management more effective by boosting performance and fostering mutual respect.

Explanation

The passage emphasizes that friendliness, which involves treating others politely and showing interest in them, is a fundamental way of demonstrating mutual respect. It explains that when managers combine effective management with a friendly approach, they become significantly more effective, gain acceptance for their strategies, and maintain better overall work performance. This highlights how friendliness directly enhances and improves the work ethos, environment, and productivity within an organization.

Explanation

In a standard communication system, the process of transferring information requires three essential components: a transmitter, a transmission channel, and a receiver. The transmitter functions as the source that encodes the message into a specific language or signal code before sending it. For the receiver to successfully decode and understand the message, both the transmitter and the receiver must share a common language code. Without this shared code, the transmitted signals cannot be translated back into meaningful information, rendering communication impossible.

Explanation

Communication with one's own self, widely known as intrapersonal communication, represents the cognitive process where an individual acts as both the sender and the receiver of messages. This inner process of thinking, reflecting, analyzing, and self-talk constitutes a continuous cognitive exchange within a person's mind, which is defined as internal dialogue.

Explanation

An ice-breaker is a welcoming technique, statement, or activity used to ease tension and build rapport with the audience at the beginning of a presentation. It helps capture the listeners' attention, establishes a comfortable and interactive environment, and prepares the audience to engage with the topic. By starting with an ice-breaker, a good communicator successfully breaks down barriers and creates an immediate connection, facilitating more effective delivery and reception of the message.

Explanation

In cities, the primary driver of fast and widespread cultural communication is Multimedia — encompassing digital media platforms, television, social networking services, the internet, and mobile communications. Urban areas have the technological infrastructure and high connectivity density that allow these channels to transmit cultural elements, trends, and values almost instantaneously across large populations.

(A) Less physical labour does not directly accelerate cultural communication. (B) Gossiping is an informal and slow channel confined to small social networks. (D) More work load actually reduces time available for cultural exchange.

Multimedia (option C) enables rapid, simultaneous transmission of cultural content to millions of urban residents, making it the factor most responsible for prompt cultural communication in cities.

Explanation

In organizational communication, the term grapevine is used to describe informal communication. This channel arises spontaneously out of the social relationships and personal interactions among employees rather than through any officially designated pathways or hierarchies. Because it does not follow a prescribed structure, information travels extremely rapidly in all directions, allowing employees to share news, build relationships, and voice concerns that might not be easily communicated through formal channels.

Explanation

The modal verb can is always followed by the base form, or bare infinitive, of the main verb. The correct spelling of the base verb that means to predict or estimate a future event, such as the weather, is forecast. Using the base form after can is a fundamental rule of English grammar.

Explanation

The preposition against is used to indicate contact, support, or pressure on a physical surface. When a person or an object is in a leaning position, they rely on a vertical surface like a wall for physical support, making against the correct preposition to complete the sentence.

Explanation

The question defines a person who has suddenly risen from a low rank to wealth and importance. The word that precisely matches this definition is 'upstart' (option D).

An upstart is a noun referring to someone who has rapidly and unexpectedly risen from a humble or low social or economic position to one of wealth, power, or social prominence — often implying that the person behaves arrogantly or presumptuously in their new position.

The other options do not fit: (A) Outsmart — a verb meaning to defeat someone by being cleverer; not a noun describing social rise. (B) Kickstart — to start something with a sudden burst of energy; not a person descriptor. (C) Jumpstart — to give a boost or rapid start to something; not used to describe a person's rise in social rank.

Therefore, the correct answer is upstart, option D.

Explanation

The sentence requires the superlative degree of the adjective tasty because it compares one specific pasta against all the other instances of pasta the speaker has eaten in their entire life. For two-syllable adjectives ending in y, the superlative is formed by changing the y to i and adding the suffix est, giving tastiest. The presence of the definite article the before the blank space also signifies that a superlative form is needed to complete the sentence grammatically.

Explanation

The subject "My friend and his father" is a compound plural subject because it refers to two distinct people joined by the conjunction "and". The use of the frequency adverb "often" indicates a habitual action, which is expressed using the simple present tense. In the simple present tense, plural subjects require the base form of the verb, which is "go".

Explanation

Fratricide is the act of killing one's own brother. The term originates from the Latin words frater, which means brother, and caedere, which means to kill or to cut down. In forensic, legal, and literary contexts, this specific word is used when a person is responsible for the death of their brother.

Explanation

The sentence requires the present perfect continuous tense to describe an activity that began in the past (since morning) and has a direct, visible effect on the present state of being tired. In standard British English, which is followed in Indian examinations, the spelling with an s is used for the verb form (practise/practising), while the spelling with a c is reserved for the noun form (practice). Therefore, the correct verb form to complete the sentence is have been practising.

Explanation

The time phrase "since morning" indicates an action that began in the past and is still continuing into the present. This grammatical context requires the use of the present perfect continuous tense, which is structured as subject + have/has + been + verb-ing. Since the subject "They" is plural, it takes the auxiliary verb "have", making "have been waiting" the correct construction to complete the sentence.

Explanation

The sentence 'Ajay cooks, washes utensils, does his homework and ___' lists a series of habitual actions performed by a singular third-person subject (Ajay). The three preceding verbs — cooks, washes, does — are all in the simple present tense.

Grammatical parallelism requires that all verbs in a coordinated series share the same form. The final verb must therefore also be in the simple present tense and agree with the singular subject.

(A) 'relaxing than' — incorrect: 'relaxing' is a present participle, not parallel; 'than' is a comparison conjunction and does not fit here. (B) 'than relaxing' — incorrect: same issues as (A), and 'than' is inappropriate. (C) 'then relaxes' — correct: 'then' is an adverb showing sequence; 'relaxes' is simple present tense, singular, parallel with cooks/washes/does. (D) 'then is relaxing' — incorrect: 'is relaxing' is the present continuous tense, which breaks parallelism with the simple present verbs.

The correct completion is 'then relaxes', option C.

Explanation

The sentence requires the past perfect tense to indicate an action that was completed before another past action. The main clause uses the past tense verb relaxed to describe the act of sitting down to read. Since winning the book in a competition happened prior to the act of relaxing to read it, the past perfect tense had won is used to establish the correct chronological sequence of events in the past.