SSC CHSL 2017 PYQs

Question 1

(1 + sinA)/(1 - sinA) is equal to?

Accepted Answer

Multiply numerator and denominator by (1 + sinA). This simplifies to (1 + sinA)^2 / cos^2A, which is (1/cosA + sinA/cosA)^2 = (secA + tanA)^2. This is not among options. Convert sinA to 1/cosecA. Then simplify the expression.

Question 2

The simplified form of(4x+3)2(3x−5)−(4x2−12x2+9x−20)is

Accepted Answer

First, expand (4x+3)(3x-5) to 12x^2 - 20x + 9x - 15 = 12x^2 - 11x - 15. Simplify the second expression to -8x^2 + 9x - 20. Subtracting the second from the first gives (12x^2 - 11x - 15) - (-8x^2 + 9x - 20) = 20x^2 - 20x + 5.

Question 3

What is the value of cot210°?

Accepted Answer

cot210° is in the third quadrant, where cotangent is positive. cot(180° + 30°) = cot30° = √3.

Question 4

If in a two digit number, the digit at unit place is z and the digit at tens place is 8, then the number is

Accepted Answer

A two-digit number is formed by (tens digit × 10) + (units digit). Here, tens digit is 8 and units digit is z, so the number is (8 × 10) + z = 80 + z.

Question 5

What is the measure of an interior angle of a regular Octagon?

Accepted Answer

For a regular polygon with 'n' sides, the interior angle is given by the formula (n-2) * 180 / n. For an octagon, n=8. So, (8-2) * 180 / 8 = 6 * 180 / 8 = 1080 / 8 = 135°.

Question 6

Select the antonym of amusement

Accepted Answer

Amusement means the state of being entertained or amused. Melancholy means a feeling of pensive sadness, typically with no obvious cause. Thus, melancholy is the antonym.

Question 7

Improve the bracketed part of the sentence.I would love (to availing) a short holiday, and go for an  overnight trek.

Accepted Answer

The verb 'avail' is typically used with a reflexive pronoun (myself, yourself, etc.) when it means to take advantage of an opportunity. Thus, 'to avail myself' is correct.

Question 8

If Girilal's salary is 11/7 times of Hariram's and Shekhar's is 3/4 times of Hariram's, what is the ratio of Girilal's salary to Shekhar's salary.

Accepted Answer

Let Hariram's salary be H. Girilal's salary is (11/7)H and Shekhar's is (3/4)H. The ratio of Girilal's to Shekhar's salary is (11/7)H : (3/4)H = 11/7 : 3/4 = 44:21.

Question 9

If a merchant offers a discount of 25% on the list price, then he makes a loss of 5%. What % profit or % loss will he make if he sells at a discount of 10% of the list price?

Accepted Answer

Let list price be 100. Selling price at 25% discount is 75. If 75 is 95% of cost price (100-5% loss), then CP = 75/0.95. At 10% discount, SP = 90. Calculate profit percentage on CP.

Question 10

Expanded and simplification of (x + 3)(x - 1) will be equal to

Accepted Answer

Multiply each term in the first binomial by each term in the second: `x*x + x*(-1) + 3*x + 3*(-1)`. Simplify to `x^2 - x + 3x - 3`, which is `x^2 + 2x - 3`.

Question 11

The sum of a non-zero number and its reciprocal is 2.  What is the number?

Accepted Answer

Let the number be x. The equation is x + 1/x = 2. Multiplying by x gives x^2 + 1 = 2x, which simplifies to (x-1)^2 = 0. Thus, x = 1.

Question 12

199994 x 200006 = ?

Accepted Answer

Recognize the pattern (a-b)(a+b) = a^2 - b^2. Here, a=200000 and b=6. So, (200000-6)(200000+6) = 200000^2 - 6^2 = 40000000000 - 36 = 39999999964.

Question 13

A shopkeeper by selling 17 Omega watches, earns a profit  equal to the selling price of 7 Omega watches.What is his profit percentage?

Accepted Answer

Let SP of one watch be Re 1. Profit = 7. SP of 17 watches = 17. CP = SP - Profit = 17 - 7 = 10. Profit percentage = (Profit/CP) * 100 = (7/10) * 100 = 70%. (Note: The provided correct answer 58.82% is incorrect based on the question. If the profit was 7 watches' CP, then 7/17 * 100 = 41.17%. If the profit was 7 watches' SP, then 7/10 * 100 = 70%. Assuming the question implies profit is 7 watches' SP, and the options are for a different question or calculation error.)

Question 14

If 4(2x -4) - 2 > 3x - 1 ≥ 4x -7, then x can take which of the following values?

Accepted Answer

Solve the two inequalities separately: 8x - 18 > 3x - 1 gives x > 17/5 (3.4). And 3x - 1 ≥ 4x - 7 gives x ≤ 6. So, 3.4 < x ≤ 6. Only 6 satisfies this range.

Question 15

Rearrange the parts of the sentence in correct order.This aloneP-should alert us to whatQ-is actually aboutR-the demand for a Uniform Civil Code

Accepted Answer

The sentence starts with 'This alone'. P ('should alert us to what') logically follows. Q ('is actually about') then connects 'what' to R ('the demand for a Uniform Civil Code'), forming a coherent statement.

Question 16

(cosA+sinA)2+(cosA−sinA)2is equals to

Accepted Answer

Expand both squares: (cos²A + sin²A + 2sinAcosA) + (cos²A + sin²A - 2sinAcosA). The 2sinAcosA terms cancel out. Using the identity cos²A + sin²A = 1, the expression simplifies to 1 + 1 = 2.

Question 17

P(3,1) and R(-7,5) are vertices of a rhombus PQRS. What is the equation of diagonal QS?

Accepted Answer

Diagonals of a rhombus bisect each other at right angles. Find the midpoint of PR, which is also the midpoint of QS. Calculate the slope of PR. The slope of QS will be its negative reciprocal. Use the midpoint and perpendicular slope to find the equation of QS.

Question 18

If 4/5th of 6/7th of a number is 216, then 8/9th of that number will be

Accepted Answer

Let the number be x. (4/5) * (6/7) * x = 216. Solve for x: x = 216 * (5/4) * (7/6) = 315. Then calculate (8/9) * 315 = 280.

Question 19

What is the value of cosec -150°?

Accepted Answer

Use the identity cosec(-θ) = -cosec(θ). So, cosec(-150°) = -cosec(150°). Since cosec(150°) = cosec(180°-30°) = cosec(30°) = 2, the value is -2.

Question 20

A missile travels at 1260 km/h. How many metres does it travel in one second?

Accepted Answer

To convert km/h to m/s, multiply by 5/18. So, 1260 * (5/18) = 70 * 5 = 350 metres. The missile travels 350 metres in one second.