SSC CHSL Tier 1 2016 Quantitative Aptitude Questions with Solutions

Explanation

To find the ratio A : B : C from the equation 7A = 5B = 2C, we express each variable in terms of a constant k:

7A = 5B = 2C = k

This gives: A = k/7 B = k/5 C = k/2

Thus, the ratio A : B : C is: A : B : C = 1/7 : 1/5 : 1/2

To express this ratio in integers, we multiply each term by the Least Common Multiple (LCM) of the denominators (7, 5, and 2), which is 70:

A : B : C = (1/7 × 70) : (1/5 × 70) : (1/2 × 70) A : B : C = 10 : 14 : 35

Explanation

To determine if a number N is prime, we test its divisibility by prime numbers less than or equal to √N.

For N = 731, √731 is approximately 27.04. The prime numbers less than or equal to 27 are 2, 3, 5, 7, 11, 13, 17, 19, and 23.

Testing these primes for divisibility: 731 ÷ 17 = 43

Since 731 is divisible by 17 and 43, it has factors other than 1 and itself, making it a composite number rather than a prime number.

Explanation

Average Cost = (Total Cost of All Machines) / (Total Number of Machines)

The factory buys a total of 7 machines, consisting of: 2 of Machine A at ₹95,000 each 2 of Machine B at ₹75,000 each 3 of Machine C (7 - 2 - 2 = 3) at ₹43,000 each

Total Cost = (2 × 95000) + (2 × 75000) + (3 × 43000) Total Cost = 190000 + 150000 + 129000 Total Cost = ₹469000

Average Cost = 469000 / 7 = ₹67000

Explanation

Set the two expressions equal to each other to find the value of x: 7x + 13 = 13x - 7

Rearranging the terms to isolate the variable x on one side and the constants on the other side: 13 + 7 = 13x - 7x 20 = 6x

Solving for x by dividing both sides by 6: x = 20/6

Simplifying the fraction by dividing the numerator and the denominator by their greatest common divisor, 2, yields: x = 10/3

Explanation

A can complete the work in 15 days, so A's one-day work rate is 1/15. B can complete the work in 9 days, so B's one-day work rate is 1/9.

When working together, their combined rate of work per day is: 1/15 + 1/9 = 3/45 + 5/45 = 8/45

In 5 days, the total work completed by them together is: 5 × 8/45 = 40/45 = 8/9

The fraction of work remaining is the total work minus the completed work: 1 - 8/9 = 1/9

Explanation

To divide 256a²b²c² by 64a², we divide the numerical coefficients and the algebraic variables separately:

(256a²b²c²) / (64a²) = (256/64) × (a²/a²) × b² × c²

Dividing the coefficients, 256 ÷ 64 = 4. Dividing the variable terms, a² / a² = 1, leaving the remaining variables b² and c² unchanged.

Multiplying these simplified parts together yields 4 × 1 × b² × c² = 4b²c².

Explanation

When two objects move towards each other, their relative speed is the sum of their individual speeds.

Relative speed = 8 km/hr + 13 km/hr = 21 km/hr

The time taken by Rehman and Roma to meet is 36 minutes. Converting this time into hours:

Time = 36/60 hours = 0.6 hours

The initial distance between them is the product of their relative speed and the time taken to meet:

Distance = Relative speed × Time = 21 km/hr × 0.6 hours = 12.6 km

Explanation

The Simple Interest (SI) for two years is ₹4800. Since Simple Interest is equal for every year, the interest earned in the first year is: First year interest = 4800 / 2 = ₹2400

For the first year, both Simple Interest and Compound Interest (CI) are equal. The difference between the Compound Interest and Simple Interest over the two-year period is: Difference = CI - SI = 5088 - 4800 = ₹288

This difference of ₹288 is the interest earned in the second year on the interest accumulated in the first year (₹2400).

Using the interest formula to find the rate of interest (R): Interest = (Principal × Rate × Time) / 100 288 = (2400 × R × 1) / 100 288 = 24 × R R = 288 / 24 = 12%

Explanation

Let the marks obtained by the two students be x and y, with x being the higher score.

Based on the given conditions, the difference between their marks is 24: x - y = 24

The higher score, x, is 65% of the sum of their marks: x = 0.65 × (x + y) x = 0.65x + 0.65y 0.35x = 0.65y 7x = 13y x = 13y / 7

Substituting the value of x into the first equation: (13y / 7) - y = 24 6y / 7 = 24 y = 28

Substituting y = 28 back into the first equation: x = 28 + 24 = 52

The marks obtained by the two students are 52 and 28.

Explanation

Solving the first inequality: 3x - 4 > 2 - x/3

Multiplying the entire inequality by 3 to clear the fraction: 9x - 12 > 6 - x 10x > 18 x > 1.8

Solving the second inequality: 3x + 5 > 4x - 5 10 > x x < 10

Combining both results gives the range for x as: 1.8 < x < 10

The value 7 is the only option that lies strictly between 1.8 and 10, satisfying both inequalities simultaneously.

Explanation

The relation between the Marked Price (MP) and the Cost Price (CP) when a discount of D% yields a profit of P% is given by the formula:

MP/CP = (100 + P) / (100 - D)

In the first scenario, a discount of 25% yields a profit of 32%:

MP/CP = (100 + 32) / (100 - 25) = 132 / 75 = 44 / 25

In the second scenario, with a discount of 17%, let the new profit percentage be P:

MP/CP = (100 + P) / (100 - 17)

Substituting the ratio MP/CP = 44/25:

44 / 25 = (100 + P) / 83

100 + P = (44 × 83) / 25

100 + P = 3652 / 25

100 + P = 146.08

P = 46.08

Explanation

To find the value of x - y, solve the given system of linear equations.

From the second equation, express y in terms of x: y = 4x - 24

Substitute this expression for y into the first equation: 3x + 2(4x - 24) = 7 3x + 8x - 48 = 7 11x = 55 x = 5

Substitute the value of x back to find y: y = 4(5) - 24 y = -4

Now, calculate the value of x - y: x - y = 5 - (-4) = 5 + 4 = 9

Explanation

The slope m of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:

m = (y₂ - y₁) / (x₂ - x₁)

Substituting the given points (4, -2) and (-3, 5) into the formula:

m = (5 - (-2)) / (-3 - 4) m = 7 / -7 m = -1

Parallel lines always have identical slopes. Therefore, any line parallel to the line passing through these two points must also have a slope of -1.

Explanation

Let the marked price of the washing machine be MP.

At a 24% discount, the selling price is 76% of the marked price: 76% of MP = 38000 MP = 38000 × 100 / 76 = 50000

At a 40% discount, the new selling price is 60% of the marked price: New Selling Price = 60% of 50000 = 50000 × 60 / 100 = 30000

Explanation

According to Euler's formula for any convex polyhedron: F + V - E = 2

where F is the number of faces, V is the number of vertices, and E is the number of edges.

A regular dodecahedron has 12 pentagonal faces, so F = 12. Given that the number of vertices V = 20, we can substitute these values into the formula to find the number of edges:

12 + 20 - E = 2 32 - E = 2 E = 30

Explanation

Let x be the side of the square. The area of the square is given by x² = 15√3.

The diagonal d of a square is related to its side by the formula d = √2 x. Squaring both sides gives d² = 2x². Substituting the value of x²: d² = 2 × 15√3 = 30√3

Since the diagonal of the square is equal to the side s of the equilateral triangle, we have s = d, which means s² = d² = 30√3.

The area of an equilateral triangle with side s is given by: Area = (√3/4) s²

Substituting the value of s²: Area = (√3/4) × 30√3 = (30 × 3) / 4 = 90/4 = 45/2 sq cm

Explanation

The curved surface area (CSA) of a right circular cone is given by the formula: CSA = π × r × l

where r is the radius of the base and l is the slant height.

Substituting the given values: 3080 = (22/7) × r × 35 3080 = 110 × r r = 28 cm

The total surface area (TSA) of the cone is given by: TSA = CSA + π × r²

Substituting the values: TSA = 3080 + (22/7) × 28 × 28 TSA = 3080 + 22 × 4 × 28 TSA = 3080 + 2464 TSA = 5544 sq cm

Explanation

The angle 11π/6 can be written as 2π - π/6, which lies in the fourth quadrant. In the fourth quadrant, the cosecant function is negative. Using the trigonometric identity cosec(2π - θ) = -cosec θ, we have:

cosec(11π/6) = cosec(2π - π/6) = -cosec(π/6)

Since sin(π/6) = ½, the cosecant value is cosec(π/6) = 1/sin(π/6) = 2. Substituting this value gives:

-cosec(π/6) = -2

Explanation

By the standard trigonometric sum and difference identities:

cos(A + B) = cos A cos B - sin A sin B cos(A - B) = cos A cos B + sin A sin B

Adding these two equations:

cos(A + B) + cos(A - B) = (cos A cos B - sin A sin B) + (cos A cos B + sin A sin B)

The term sin A sin B cancels out, leaving:

cos(A + B) + cos(A - B) = 2 cos A cos B

Explanation

We start by simplifying the given expression:

1 / (tanA + cotA)

Using the basic trigonometric relations tanA = sinA/cosA and cotA = cosA/sinA, we get:

tanA + cotA = sinA/cosA + cosA/sinA = (sin²A + cos²A) / (sinA cosA)

Since sin²A + cos²A = 1, this simplifies to:

tanA + cotA = 1 / (sinA cosA)

Therefore, the reciprocal of the expression is:

1 / (tanA + cotA) = sinA cosA

Now, we evaluate the expression:

(cosecA - sinA)(secA - cosA)

Using the relations cosecA = 1/sinA and secA = 1/cosA, we can rewrite the terms as:

cosecA - sinA = 1/sinA - sinA = (1 - sin²A) / sinA = cos²A / sinA

secA - cosA = 1/cosA - cosA = (1 - cos²A) / cosA = sin²A / cosA

Multiplying these two simplified terms together gives:

(cosecA - sinA)(secA - cosA) = (cos²A / sinA) × (sin²A / cosA) = sinA cosA

Since both expressions simplify to sinA cosA, they are equal.

Explanation

The weight-to-height ratio is calculated as weight divided by height.

For Arushi, the ratio is 52 ÷ 1.68 ≈ 30.95.

For the others, the ratios are: Aruna: 79 ÷ 1.61 ≈ 49.07 Arya: 52 ÷ 1.5 ≈ 34.67 Asha: 53 ÷ 1.63 ≈ 32.52

Comparing these values, Arushi has the lowest ratio.

Explanation

Based on the given table, the least percent profit is 5%, which occurred in the year 2012.

The standard formula relating Revenue, Expenditure, and Profit Percentage is:

Revenue = Expenditure × (1 + Profit Percentage/100)

Substituting the given values into the formula:

Expenditure = 575 Profit Percentage = 5

Revenue = 575 × (1 + 5/100) Revenue = 575 × 1.05 Revenue = 603.75

The revenue of the company in that year was Rs 603.75 crore.

Explanation

The average number of children per house is calculated using the formula for the weighted mean:

Mean = Σ(f × x) / Σf

where x represents the number of children and f represents the number of houses.

Calculating the total number of children, Σ(f × x): Total children = (0 × 4) + (1 × 13) + (2 × 17) + (3 × 5) = 0 + 13 + 34 + 15 = 62

Calculating the total number of houses, Σf: Total houses = 4 + 13 + 17 + 5 = 39

Calculating the average: Average = 62 / 39 ≈ 1.59

Explanation

Total shares issued by the company is 6,00,000 (six lakhs).

Dhiraj's present share is 5% of the total shares.

Dhiraj's current number of shares = 5% of 6,00,000 = (5 ÷ 100) × 6,00,000 = 30,000 shares.

When Chinmay sells 15,000 shares to Dhiraj, the total number of shares held by Dhiraj becomes: 30,000 + 15,000 = 45,000 shares.

Explanation

The given sequence 91 + 92 + 93 + ... + 140 is an arithmetic progression (AP) with the first term a = 91, the last term l = 140, and the common difference d = 1.

The number of terms (n) in this progression is: n = (140 - 91) + 1 = 50

The sum of an arithmetic progression (Sₙ) is given by the formula: Sₙ = n/2 × (a + l)

Substituting the values into the formula: S₅₀ = 50/2 × (91 + 140) S₅₀ = 25 × 231 S₅₀ = 5775

Explanation

The total revenue for the 9 consecutive years is: 9 × 80 = 720 lakhs

The total revenue for the first 5 years is: 5 × 75 = 375 lakhs

The total revenue for the last 5 years is: 5 × 87 = 435 lakhs

Since the 5th year is common to both the first 5 years and the last 5 years, its revenue is included twice when these two sums are added together.

The revenue of the 5th year is: (Total of first 5 years + Total of last 5 years) - Total of 9 years = (375 + 435) - 720 = 810 - 720 = 90 lakhs

Explanation

Let the number of selected candidates be 3x and the number of unselected candidates be x. The total number of candidates who originally applied is 3x + x = 4x.

If 60 fewer candidates had applied, the new total number of applicants would be 4x - 60.

If 30 fewer candidates were selected, the new number of selected candidates would be 3x - 30.

The new number of unselected candidates is the difference between the new total applied and the new selected: (4x - 60) - (3x - 30) = x - 30

The new ratio of selected to unselected candidates is 5:1. This relationship is represented by the equation: (3x - 30) / (x - 30) = 5 / 1

Cross-multiplying to solve for x: 3x - 30 = 5(x - 30) 3x - 30 = 5x - 150 2x = 120 x = 60

The total number of candidates who originally applied is: 4 × 60 = 240

Explanation

Using the half-angle trigonometric identities: cos A = 2 cos²(A/2) - 1 cos A = 1 - 2 sin²(A/2)

These can be rearranged to express the half-angle terms: 1 + cos A = 2 cos²(A/2) 1 - cos A = 2 sin²(A/2)

Dividing the first equation by the second equation: (1 + cos A) / (1 - cos A) = [2 cos²(A/2)] / [2 sin²(A/2)] (1 + cos A) / (1 - cos A) = cot²(A/2)

Taking the square root of both sides gives: cot(A/2) = √[(1 + cos A) / (1 - cos A)]

Substituting cot(A/2) = x yields: x = √[(1 + cos A) / (1 - cos A)]

Explanation

To find the value of x, we can simplify the given expression by multiplying both the numerator and the denominator by (1 - cos A):

x = (1 - cos A) / (1 + cos A)

Multiplying the numerator and denominator by (1 - cos A):

x = ((1 - cos A)(1 - cos A)) / ((1 + cos A)(1 - cos A))

x = (1 - cos A)² / (1 - cos² A)

Using the trigonometric identity 1 - cos² A = sin² A:

x = (1 - cos A)² / sin² A

x = ((1 - cos A) / sin A)²

x = (1/sin A - cos A/sin A)²

Using the relations cosec A = 1/sin A and cot A = cos A/sin A:

x = (cosec A - cot A)²

Since (cosec A - cot A)² is equivalent to (cot A - cosec A)², we get:

x = (cot A - cosec A)²

Explanation

Let Manjeet's efficiency be 1 unit per hour. Since he completes the work in 18 hours, the total work is 18 units. Jaya is 100% more efficient than Manjeet, which means her efficiency is 1 + (100% of 1) = 2 units per hour. When they work together, their combined efficiency is 1 + 2 = 3 units per hour. The time taken to complete the total work of 18 units with a combined efficiency of 3 units per hour is calculated as 18 ÷ 3 = 6 hours.

Explanation

Let the distance between City A and City B be d. The relation between distance, speeds, and the difference in time Δt is given by the formula:

d = (s₁ × s₂ × Δt) / (s₂ - s₁)

Substituting the given values, speed s₁ = 30 km/hr, speed s₂ = 36 km/hr, and time difference Δt = 3 hours:

d = (30 × 36 × 3) / (36 - 30) d = 3240 / 6 d = 540 km

Explanation

By applying the rule of alligation, the ratio of the quantities sold at 13% profit and 23% profit is determined by the differences in their respective profit percentages relative to the overall average profit:

Ratio = (23 - 17) : (17 - 13) = 6 : 4 = 3 : 2

The total quantity of wheat is 12 quintals. Since 1 quintal is equal to 100 kg, the total weight is 1200 kg.

The quantity of wheat sold at 23% profit is given by:

(2 / (3 + 2)) × 1200 = 2/5 × 1200 = 480 kg

Explanation

To find the percentage error, we use the standard formula:

Percentage Error = (|Correct Value - Incorrect Value| ÷ Correct Value) × 100

Let the number be x.

The correct calculation should have been: Correct Value = (13/6)x

The actual calculation done by the student is: Incorrect Value = (6/13)x

The absolute error in the calculation is: Error = (13/6)x - (6/13)x Error = (169 - 36)x ÷ 78 Error = 133x ÷ 78

Now, substituting these values into the percentage error formula: Percentage Error = ((133x ÷ 78) ÷ (13x ÷ 6)) × 100 Percentage Error = (133 ÷ 78) × (6 ÷ 13) × 100 Percentage Error = (133 ÷ 169) × 100 Percentage Error = 13300 ÷ 169 Percentage Error ≈ 78.7%

Explanation

First, calculate the compound interest on Rs. 10000 for 2 years at 10% per annum. The effective compound interest rate for 2 years at 10% is calculated using the successive percentage formula:

Effective rate = 10 + 10 + (10 × 10) / 100 = 21%

Compound Interest (CI) = 21% of Rs. 10000 = (21 / 100) × 10000 = Rs. 2100

According to the question, the simple interest (SI) on the sum is half of this compound interest:

SI = 2100 / 2 = Rs. 1050

The formula for simple interest is:

SI = (P × R × T) / 100

where P is the principal sum, R is the rate of interest (14% per annum), and T is the time period (3 years). Substituting the known values into the formula:

1050 = (P × 14 × 3) / 100

1050 = 42 × P / 100

P = (1050 × 100) / 42

P = 25 × 100 = Rs. 2500

Explanation

Discount = Marked Price - Selling Price

Given that the Marked Price is Rs 1250 and the Selling Price is Rs 1000:

Discount = 1250 - 1000 = Rs 250

Discount Percentage = (Discount / Marked Price) × 100

Discount Percentage = (250 / 1250) × 100 = (1/5) × 100 = 20%

Explanation

When a solid is melted and recast into another solid shape, its total volume remains unchanged.

The volume of a cylinder of radius r and height h₁ is given by the formula: V_cylinder = π × r² × h₁

The volume of a cone of the same radius r and height h₂ is given by the formula: V_cone = ⅓ × π × r² × h₂

Equating the two volumes because the cylinder is melted and recast into the cone: π × r² × h₁ = ⅓ × π × r² × h₂

Cancelling π × r² from both sides gives: h₁ = ⅓ × h₂

Rearranging this relation to find the height of the cone: h₂ = 3 × h₁

Substituting the given height of the cylinder, h₁ = 9 cm, into the equation: h₂ = 3 × 9 = 27 cm

Explanation

Since PQ is parallel to BC, triangle APQ is similar to triangle ABC by Angle-Angle similarity.

The ratio of the corresponding sides of these similar triangles is AP/AB. Given the ratio AP:PB is 2:5, we find AB by adding AP and PB: AB = AP + PB = 2 + 5 = 7

This gives the side ratio: AP/AB = 2/7

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides: Area(ΔAPQ) / Area(ΔABC) = (AP/AB)² Area(ΔAPQ) / Area(ΔABC) = (2/7)² = 4/49

Given that the area of ΔAPQ is 4 sq cm, we can substitute this value into the ratio: 4 / Area(ΔABC) = 4/49 Area(ΔABC) = 49 sq cm

The area of trapezium PQCB is found by subtracting the area of the smaller triangle APQ from the area of the larger triangle ABC: Area(PQCB) = Area(ΔABC) - Area(ΔAPQ) = 49 - 4 = 45 sq cm

Explanation

The perpendicular bisector of a segment joining two points passes through their midpoint and is perpendicular to the line segment.

First, calculate the midpoint of the segment joining (2, -6) and (4, 0): Midpoint = ((2 + 4)/2, (-6 + 0)/2) = (3, -3)

Next, find the slope of the line segment joining (2, -6) and (4, 0): Slope of segment = (0 - (-6)) / (4 - 2) = 6 / 2 = 3

Since the perpendicular bisector is perpendicular to this segment, its slope is the negative reciprocal of 3: Slope of perpendicular bisector = -1/3

Using the point-slope form with the midpoint (3, -3) and slope -1/3, the equation of the perpendicular bisector is: y - (-3) = -1/3 × (x - 3)

Multiplying both sides by 3: 3(y + 3) = -(x - 3) 3y + 9 = -x + 3 x + 3y = -6

Explanation

The measure of each interior angle of a regular polygon with n sides is given by the formula:

Interior angle = (n - 2) × 180° / n

A regular dodecagon has 12 sides, so n = 12. Substituting this value into the formula:

Interior angle = (12 - 2) × 180° / 12 Interior angle = 10 × 15° Interior angle = 150°

Alternatively, the exterior angle of a regular polygon is given by 360° / n. For a dodecagon, the exterior angle is 360° / 12 = 30°. Since the interior and exterior angles are supplementary, the interior angle is 180° - 30° = 150°.

Explanation

The radius r of the circle is half of its diameter: r = 28/2 = 14 cm

The formula for the area of a circle is: Area = πr²

Using π = 22/7: Area = (22/7) × 14² Area = (22/7) × 196 Area = 22 × 28 Area = 616 sq cm

Explanation

Expanding the product of the two binomials (x + 8)(6 - 3x) gives:

(x + 8)(6 - 3x) = x(6) + x(-3x) + 8(6) + 8(-3x) = 6x - 3x² + 48 - 24x

Grouping the terms of x together:

-3x² + (6 - 24)x + 48 = -3x² - 18x + 48

The coefficient of the term containing x is -18.

Explanation

Using the standard algebraic identity: (x + y)² = x² + y² + 2xy

Substitute the given values x + y = 10 and x² + y² = 68 into the formula: 10² = 68 + 2xy 100 = 68 + 2xy

Subtract 68 from both sides of the equation: 2xy = 100 - 68 2xy = 32

Divide by 2 to solve for xy: xy = 16

Explanation

Let the two-digit number be 89.

The sum of its digits is 8 + 9 = 17, which satisfies the first condition.

When we add 9 to the number, we get: 89 + 9 = 98

The digits of 89 are 8 and 9. Interchanging these digits yields 98. Since this matches the result obtained by adding 9, the number is 89.

Explanation

To find the possible values of x, we solve the system of inequalities by breaking it into two separate inequalities.

First, solve the left-hand inequality: 5x + 4(1 - x) > 3x - 4 5x + 4 - 4x > 3x - 4 x + 4 > 3x - 4 8 > 2x x < 4

Second, solve the right-hand inequality: 3x - 4 > 5x/3 - x/3 3x - 4 > 4x/3 9x - 12 > 4x 5x > 12 x > 12/5 x > 2.4

Combining both solutions gives the range: 2.4 < x < 4

Only the value 3 lies within this interval.

Explanation

To find the average bonus per employee, we first calculate the total bonus paid to each category of employees.

For managers, the total bonus is 3 × 36,00,000 × 50% = 54,00,000 rupees. For executives, the total bonus is 4 × 12,00,000 × 30% = 14,40,000 rupees. For trainees, the total bonus is 3 × 4,00,000 × 10% = 1,20,000 rupees.

Summing these amounts gives the total bonus paid by the company: Total bonus = 54,00,000 + 14,40,000 + 1,20,000 = 69,60,000 rupees.

The total number of employees is 3 + 4 + 3 = 10.

The average bonus per employee is calculated by dividing the total bonus by the total number of employees: Average bonus = 69,60,000 ÷ 10 = 6,96,000 rupees.

Explanation

Correct Answer: C

The total exports from the three companies (Company A, Company B, and Company C) for each year are calculated by summing their respective export figures:

Total exports in 2011 = 2000 + 2000 + 3000 = 7000 lakh rupees.

Total exports in 2012 = 2000 + 3000 + 2000 = 7000 lakh rupees.

Total exports in 2013 = 5000 + 1000 + 5000 = 11000 lakh rupees.

Total exports in 2014 = 2000 + 5000 + 3000 = 10000 lakh rupees.

Total exports in 2015 = 1000 + 2000 + 3000 = 6000 lakh rupees.

Comparing these totals, the exports for the years 2011 and 2012 are equal, with both years amounting to 7000 lakh rupees.

Explanation

To find the total profit or loss of the company over the last five years, we sum the profit or loss values for each year from 2011 to 2015 as shown in the table.

Total profit or loss = 10 + 10 + 25 + 15 + 5 = 65 crore

Since the resulting sum is positive, it represents a net profit. Therefore, the total profit of the company in the last five years is Rs 65 crores.

Explanation

To find the percentage of Jewellery in the total exports, we first calculate the total value of India's exports in 2015 by summing the export values of all categories:

Total exports = 825 + 750 + 875 + 875 + 975 = 4300 million USThe export value of Jewellery is 825 million US.

Percentage of Jewellery = (Value of Jewellery / Total exports) × 100 Percentage of Jewellery = (825 / 4300) × 100 = 825 / 43 ≈ 19.19%

Explanation

The given expression represents cosec(-11π/6), where the symbol n stands for the mathematical constant π.

Using the negative angle identity cosec(-θ) = -cosec(θ), we have: cosec(-11π/6) = -cosec(11π/6)

We can rewrite 11π/6 as 2π - π/6. Since cosec(2π - θ) = -cosec(θ) in the fourth quadrant: cosec(2π - π/6) = -cosec(π/6)

Substituting this back into the expression: -cosec(11π/6) = -(-cosec(π/6)) = cosec(π/6)

Since sin(π/6) = ½, the value of its reciprocal cosec(π/6) is 2.

Explanation

Using the half-angle trigonometric identities, we have: sin A = 2 sin(A/2) cos(A/2) 1 - cos A = 2 sin²(A/2)

Substituting these identities into the expression gives: sin A / (1 - cos A) = 2 sin(A/2) cos(A/2) / (2 sin²(A/2))

By canceling out the common term 2 sin(A/2) from both the numerator and the denominator, we get: sin A / (1 - cos A) = cos(A/2) / sin(A/2) = cot(A/2)

Since cot(A/2) = x, it follows that x = sin A / (1 - cos A).