SSC CHSL 2020 PYQs

Question 1

The given bar graph represents the pass percentage of10thand12thclasses of a school during the consecutive four years period 2016-2019.What is the average percentage of the failed students of the 12th class for all four years?

Accepted Answer

Calculate the failure percentage for 12th class each year (100 - pass%). Sum these failure percentages and divide by 4 to find the average. (20+25+20+30)/4 = 23.75%.

Question 2

The area of the largest triangle that can be inscribed in a semi-circle of radius4‌cm(incm2)

Accepted Answer

The largest triangle inscribed in a semicircle has its base as the diameter and height as the radius. Area = 0.5 * diameter * radius = 0.5 * (2r) * r = r². For r=4cm, Area = 4² = 16cm².

Question 3

Ifcos(x−y)=√32andsin(x+y)=12, then the value ofx(0<x<90)is

Accepted Answer

From cos(x-y) = √3/2, we get x-y = 30°. From sin(x+y) = 1/2, we get x+y = 30° or 150°. Solving x-y=30° and x+y=30° gives x=30°, y=0°. Solving x-y=30° and x+y=150° gives x=90°, y=60°. Since 0<x<90, x=30° is the correct answer.

Question 4

When an integernis divided by 5 , the remainder is 3 . What is the remainder if8nis divided by 5 ?

Accepted Answer

If n leaves a remainder of 3 when divided by 5, then 8n will leave a remainder of (8 * 3) mod 5. This is 24 mod 5, which equals 4.

Question 5

Ifsin‌x−cos‌x=0,0°<x<90°, then the value of(sec‌x+cosec‌x)2is

Accepted Answer

From sin x - cos x = 0, we get sin x = cos x, which implies tan x = 1. For 0° < x < 90°, x = 45°. Substitute x = 45° into (sec x + cosec x)² to get (√2 + √2)² = (2√2)² = 8.

Question 6

InΔ‌XYZ, if G is the centroid and XL is the medians with length 18cm, then the length of XG is

Accepted Answer

The centroid divides the median in a 2:1 ratio. So, XG is 2/3 of XL. Calculate (2/3) * 18 cm to get 12 cm.

Question 7

Ifcot‌A=k, thensin‌Ais equal to (presume that A is an acute angle)

Accepted Answer

Given cot A = k. We know that cosec²A - cot²A = 1. So, cosec²A = 1 + cot²A = 1 + k². Thus, cosec A = √(1 + k²). Since sin A = 1/cosec A, sin A = 1/√(1 + k²).

Question 8

The following graph shows the performance in aggregate marks of 2 board examinations of a group of friends. On the basis of the graph, identify the girl who has shown the maximum improvement from Class X to Class XII.

Accepted Answer

Calculate the difference between Class XII and Class X marks for each girl. Alka's improvement (90-60=30) is the highest among all, indicating maximum improvement.

Question 9

What is the value ofsin245°+cos245°?

Accepted Answer

The fundamental trigonometric identity states that sin²θ + cos²θ = 1 for any angle θ. Here, θ is 45°, so the value is 1.

Question 10

In aΔ‌ABC,∠ABC=2∠CAB, if the side BC is extended to D and∠ACD=126°, then∠CABis

Accepted Answer

By the exterior angle theorem, ∠ACD = ∠CAB + ∠ABC. Given ∠ACD = 126° and ∠ABC = 2∠CAB. Substitute these values to find ∠CAB = 42°.

Question 11

Rakesh walking at the speed of8‌km∕hcrosses a bridge in30‌min. What is the length of the bridge (inkm)?

Accepted Answer

Distance = Speed × Time. Convert 30 minutes to hours (0.5 hours). Distance = 8 km/h × 0.5 h = 4 km. So, the bridge length is 4 km.

Question 12

If the sum of two numbers is 11 and the sum of their squares is 65 , then the sum of their cubes will be

Accepted Answer

Let the numbers be x and y. Given x+y=11 and x^2+y^2=65. We know (x+y)^2 = x^2+y^2+2xy, so 11^2 = 65+2xy, which gives 2xy = 121-65 = 56, so xy=28. Now, x^3+y^3 = (x+y)(x^2-xy+y^2) = (11)(65-28) = 11 * 37 = 407.

Question 13

Study the given pie-chart and table carefully and answer the question that follows. The percentage-wise distribution of lecturers in the five different subjects in a university is shown in the pie-chart. The total number of lecturers is 500 .Ratio of male to female lecturers.LecturesMales: FemalesMathematics7 : 3Physics2 : 3Chemistry4 : 1Botany3 : 5Zoology2 : 5Find the number of male lecturers in Physics.

Accepted Answer

First, calculate the total number of Physics lecturers using the pie chart percentage. Then, apply the male-to-female ratio for Physics to find the number of male lecturers.

Question 14

In how many years will a sum of ₹ 5000 yield a simple interest of₹2000at an interset rate of10%p.a.?

Accepted Answer

Use the simple interest formula: SI = (P * R * T) / 100. Substitute the given values: 2000 = (5000 * 10 * T) / 100. Solve for T to get 4 years.

Question 15

Ifcos‌θ+sin‌θcos‌θ−sin‌θ=8, then the value ofcot‌θis equal to

Accepted Answer

Divide numerator and denominator by sinθ. This transforms the expression into (cotθ+1)/(cotθ-1) = 8. Solve for cotθ to get 9/7.

Question 16

Ifa+b=11andab=15, thena2+b2is equal to

Accepted Answer

Use the identity (a+b)² = a² + b² + 2ab. Substitute the given values: 11² = a² + b² + 2(15). Simplify to find a² + b² = 121 - 30 = 91.

Question 17

The value of27+[3(50−20)+168÷4+2−11×2]is

Accepted Answer

First, solve inside the brackets: 3(30) + 42 + 2 - 22. This simplifies to 90 + 42 + 2 - 22 = 112. Finally, add 27 to 112, resulting in 139.

Question 18

In the given figureXYZ is a secant and ZT is a tangent. What is the value ofx?

Accepted Answer

Apply the tangent-secant theorem: ZT² = ZY × ZX. Substitute the given values (ZT=6, ZY=4, ZX=4+x) to get 36 = 4(4+x). Solve for x: 36 = 16 + 4x, so 20 = 4x, which means x = 5.

Question 19

List the price of a bike is15%more than it's cost price. It is sold at a discount of20%. Find the dealer's loss or profit percentage.

Accepted Answer

Assume CP is 100. Marked Price = 100 + 15% of 100 = 115. Selling Price = 115 - 20% of 115 = 115 - 23 = 92. Loss = 100 - 92 = 8. Loss percentage = 8%.

Question 20

XYZ is a triangle. If the medians ZL and YM intersect each other at G, then Area ofΔ‌GLM: Area ofΔ‌XYZis

Accepted Answer

The centroid (G) divides a triangle into 6 smaller triangles of equal area. Also, the triangle formed by joining the midpoints of the sides (ΔLMN) has 1/4th the area of the original triangle. The centroid divides this smaller triangle into 3 equal parts. Thus, Area(ΔGLM) is 1/3 of Area(ΔLMN), which is 1/3 of (1/4 Area(ΔXYZ)), resulting in a 1:12 ratio.