SSC CHSL 2017 PYQs

Question 1

Which of the following equations has the sum of its roots as 5?

Accepted Answer

For a quadratic equation ax²+bx+c=0, the sum of roots is -b/a. In option 1, a=1, b=-5, so sum = -(-5)/1 = 5.

Question 2

Given: 6x + 2(6-x) > 2x -2 < 5x/2 - 3x/4; then x can take which of the following values?

Accepted Answer

Solve the two inequalities separately: 6x + 12 - 2x > 2x - 2 gives x > -7. And 2x - 2 < 10x/4 - 3x/4 simplifies to 2x - 2 < 7x/4, which gives x < 8. So, -7 < x < 8. The only option in this range is 5.

Question 3

If(36−16x)−(4x−8)=4, then the value of x is

Accepted Answer

Simplify the equation: 36 - 16x - 4x + 8 = 4. Combine like terms: 44 - 20x = 4. Subtract 44 from both sides: -20x = -40. Divide by -20 to get x = 2.

Question 4

What is the value of cosec3π4?

Accepted Answer

Convert 3π/4 to degrees (135°). cosec(135°) = cosec(180°-45°) = cosec(45°) = √2. The value is positive in the second quadrant.

Question 5

Improve the bracketed part of the sentence.When I last saw Ravi, he (had been running) to catch his  bus.

Accepted Answer

The action of running was ongoing when the speaker saw Ravi. The past continuous tense (was running) correctly describes an action in progress at a specific point in the past.

Question 6

The base angle of an isosceles trapezium is 45°. If the shorter side and both the equal sides are 10 cm each, what is the area of the trapezium?

Accepted Answer

Draw perpendiculars from the shorter base to the longer base. This forms two right-angled triangles and a rectangle. Calculate height and the extra length of the longer base using trigonometry (sin 45°, cos 45°). Then apply the trapezium area formula.

Question 7

A cone of height 12 cm and diameter 10 cm is mounted on a hemisphere of the same diameter. What is the volume of the solid thus formed?

Accepted Answer

Calculate the volume of the cone (1/3πr²h) and the hemisphere (2/3πr³). Sum these volumes. Given diameter 10 cm, radius is 5 cm. Cone height is 12 cm. Total volume is (1/3 * π * 5² * 12) + (2/3 * π * 5³) = 100π + 250π/3 = 550π/3 ≈ 576.19 cm³.

Question 8

At least one pair of opposite angles is congruent in a ...................

Accepted Answer

A kite is a quadrilateral where at least one pair of opposite angles is congruent. Specifically, the angles between the unequal sides are equal.

Question 9

What is the length of the arc whose central angle is 30° and radius of the circle is 21 cm?

Accepted Answer

The arc length formula is (θ/360) * 2πr. Substitute θ=30° and r=21 cm: (30/360) * 2 * (22/7) * 21 = (1/12) * 2 * 22 * 3 = 11 cm.

Question 10

Marked price of an item is Rs 400. On purchase of 1 item discount is 6% and on purchase of 4 items discount is 24%. Rachita buys 5 items, what is the effective discount?

Accepted Answer

Rachita buys 5 items. She gets 24% discount on 4 items and 6% on 1 item. Calculate total discount amount and then effective discount percentage on total marked price.

Question 11

What is the value of 2 consecutive natural numbers, sum  of whose squares is 145?

Accepted Answer

Let the numbers be x and x+1. So, x^2 + (x+1)^2 = 145. This simplifies to 2x^2 + 2x - 144 = 0, or x^2 + x - 72 = 0. Factoring gives (x+9)(x-8)=0. Since x is natural, x=8. The numbers are 8 and 9.

Question 12

The average weight of Shivshankar, Gopesh and Reena is 97 kg. If the average weight of Shivshankar and Gopesh is 93 kg and that of Gopesh and Reena is 82 kg, then the weight of Gopesh is

Accepted Answer

Calculate total weights: S+G+R = 97*3 = 291. S+G = 93*2 = 186. G+R = 82*2 = 164. Add (S+G) and (G+R) to get S+2G+R = 186+164 = 350. Subtract (S+G+R) from this: 350 - 291 = 59 kg.

Question 13

Select the antonym of mishmash

Accepted Answer

Mishmash means a confused mixture. Therefore, its antonym is 'organized', which implies order and structure.

Question 14

Rahul sells a machine for Rs 50 lakhs at a loss. Had he  sold it for Rs 60 lakh, his gain would have been 7 times the earlier loss. What is the cost price of the  machine?

Accepted Answer

Let CP be x. Loss = x - 50. Gain = 60 - x. Given 60 - x = 7(x - 50). Solve for x: 60 - x = 7x - 350 => 8x = 410 => x = 51.25 lakhs.

Question 15

The length of the diagonal of a rectangle is 26 cm and that of one side is 10 cm. What is the area of this rectangle?

Accepted Answer

Use Pythagoras theorem to find the other side: √(26² - 10²) = √(676 - 100) = √576 = 24 cm. Area = length × width = 24 × 10 = 240 sq cm.

Question 16

A rice trader buys 25 quintals of rice for Rs 1,825. 27% rice is lost in transportation. At what rate should he sell to earn 20% profit?

Accepted Answer

Cost price of 25 quintals is Rs 1825. After 27% loss, remaining rice is 25 * (1-0.27) = 18.25 quintals. To earn 20% profit, total selling price should be 1825 * 1.20 = Rs 2190. Rate per quintal = 2190 / 18.25 = Rs 120.

Question 17

A solid copper sphere of radius 9 cm is melted and reformed into a wire of radius 1 mm. What will be the length of this wire? (Take π = 22/7)

Accepted Answer

Equate the volume of the sphere (4/3πR³) to the volume of the wire (πr²h). Convert all units to cm. Solve for h, then convert h to meters.

Question 18

In a triangle the length of the side opposite the angle which measures 60° is 6√3 cm. What is the length of the side opposite to the angle which measures 90°?

Accepted Answer

This is a 30-60-90 triangle. The sides are in ratio 1:√3:2. Since the side opposite 60° is 6√3, the side opposite 30° is 6. Thus, the hypotenuse (opposite 90°) is 2 * 6 = 12 cm.

Question 19

Ifcosec4A−cosec2A=x, then value of x is?

Accepted Answer

Factor out cosec²A from the expression. Use the identity cosec²A = 1 + cot²A. Substitute and expand to get cot⁴A + cot²A.

Question 20

If the radius of a circle is increased by 27%, then its area will increase by

Accepted Answer

Area of a circle is πr². If radius increases by 27%, new radius is 1.27r. New area is π(1.27r)² = π(1.6129r²). Percentage increase is (1.6129 - 1) * 100 = 61.29%.