# SSC CHSL Tier 1 Practice Paper

### Section 3: Mathematics

Q.1: A solid metallic sphere of radius 10cm is melted and recast into spheres of radius 2cm each. How many such spheres can be made ?
(A) 64
(B) 216
(C) 100
(D) 125

Ans : (D) 125

Q.2: There are 3 groups of persons-male, female and children. There are 20 males and the number of females and children taken together is 4 more than that of the males. The average weight of males is 54 kg, that of females is 49 kg and that of children is 30 kg. If the average weight of the whole group is 48.25 kg. then what is the difference between the number of females and the number of children?
(A) 17
(B) 10
(C) 7
(D) 14

Ans : (B) 10

Q.3: If $x+\frac{1}{15x}=3$, then the value of $9x^3+\frac{1}{375x^3}$ will be:
(A) 237.6
(B) 376.2
(C) 273.6
(D) 367.2

Ans : (A) 237.6

Q.4: Simplify the given expression. $(x-\frac2x)^3-(x+\frac2x)^3$
(A) $-4 (3x+\frac{4}{x^3})$
(B) $4 (3x-\frac{4}{x^3})$
(C) $-4 (x+\frac{4}{x^3})$
(D) $2 (x-\frac{4}{x^3})$

Ans : (A) $-4 (3x+\frac{4}{x^3})$

Q.5: Study the given graph and answer the question that follows. By what percentage is the average expenditure of the company in 2014, 2016 and 2018 less than the revenue in 2017?

(A) 37.5%
(B) 56.25%
(C) 63.27%
(D) 38.75%

Ans : (D) 38.75%

Q.6: Evaluate the following expression. $\frac {3(cot^246^o-sec^244^o)}{2(sin^228^o+sin^262^o)}+\frac {2cos^260^otan^233^otan^257^o}{sec^2(90^o-\theta)-cot^2\theta}$
(A) -1
(B) 1
(C) -2
(D) 2

Ans : (A) -1

Q.7: Nalini’s younger brother is 12 years old. If the ratio of the age of Nalini to that of her brother is 7 : 6, then what will be ratio in their ages 6 years hence?
(A) 10 : 9
(B) 13 : 12
(C) 17 : 15
(D) 10 : 6

Ans : (A) 10 : 9

Q.8: $16\frac14\div[2\frac16+{4\frac13-(2\frac12+\frac34)}]$ is equal to:
(A) 6
(B) 4
(C) 5
(D) 3

Ans : (C) 5

Q.9: The number of students enrolled in different streams at senior secondary level in five schools is shown in the bar graph.
What is the ratio of the number of students of science stream of schools A, B and D taken together to the number of students of vocational stream in schools B, D and E taken together?

(A) 94 : 65
(B) 178 : 125
(C) 7 : 5
(D) 89 : 65

Ans : (D) 89 : 65

Q.10: ABC is a triangle inscribed in a circle and $\angle\text{ACB}$ is equal to 35o . P is a point on the circle on the side AB, opposite to C. What is the value of $\angle\text{APB}$ in degrees?
(A) 72.5
(B) 145
(C) 175
(D) 70

Ans : (B) 145

Q.11: Let 0 be the centre of a circle and AC be the diameter. BD is a chord intersecting AC at E, AD and AB are joined. If $\angle\text{BOC}=40^o$ and $\angle\text{AOD}=120^o$, then $\angle\text{BEC}$ is equal to:
(A) 55o
(B) 80o
(C) 90o
(D) 70o

Ans : (B) 80o

Q.12: The simple interest on a sum of ₹12,000 at the end of 5 years is ₹6,000. What would have been the compound interest on the same sum at the same rate for 3 years when compounded annually?
(A) ₹3,970
(B) ₹3,972
(C) ₹3,600
(D) ₹2,520

Ans : (B) ₹3,972

Q.13: 10 men or 15 women can complete a work in 30 days. In how many days can 15 men and 27 women complete the work?
(A) $6\frac{1}{11}$
(B) $5\frac{1}{11}$
(C) $11\frac{1}{11}$
(D) $9\frac{1}{11}$

Ans : (D) $9\frac{1}{11}$

Q.14: A person saves 25% of his income. If his income increases by 20% and his saving remains the same, then what will be the increased percentage of his expenditure?
(A) 20
(B) 26
(C) 30
(D) $26\frac{2}{3}$

Ans : (D) $26\frac{2}{3}$

Q.15: Study the given bar graph and answer the question that follows.
The bar graph shows the exports of cars of types A and B (in ₹million). What is the ratio of the total exports of cars of type A in 2016 and 2018 to the total exports of cars of type B in 2015 and 2017?

(A) 23 : 21
(B) 15 : 29
(C) 18 : 23
(D) 21 : 23

Ans : (A) 23 : 21

Q.16: If $x^6-6\sqrt6y^6=(x^2+Ay^2)(x^4+Bx^2y^2+Cy^4)$. then what will be the value of (A2-B2+C2)?
(A) 27
(B) 42
(C) 36
(D) 18

Ans : (C) 36

Q.17: Students of Primary, Middle, Secondary and Sr. Secondary classes collected donation for a Relief Fund as shown in the given pie chart. If the donation collected from Middle classes was ₹6,750, then how much money was collected by Middle classes as compared to Secondary classes?

(A) ₹6,075
(B) ₹1,125
(C) ₹675
(D) ₹2,025

Ans : (C) ₹675

Q.18: For $\theta : 0^o <\theta<90^o$ $3 sec \theta+4cos\theta=4\sqrt3,$ find the value of $(1-sin\theta+cos\theta)$.
(A) $\frac{1+2\sqrt3}{2}$
(B) $\frac{1+\sqrt3}{2}$
(C) $\frac{1-\sqrt3}{2}$
(D) $\frac{1-2\sqrt3}{2}$

Ans : (B) $\frac{1+\sqrt3}{2}$

Q.19: An article is sold at a certain price. If it is sold at $33\frac13$%. What is the percentage profit or percentage loss when it is sold at 40% of the original selling price ?
(A) Loss 12%
(B) Profit 18%
(C) Loss 20%
(D) Profit 15%

Ans : (C) Loss 20%

Q.20: In triangle ABC, AD is the internal bisector of $\angle{A}$ meeting BC at D. If BD=3.6 cm and BC=8cm, then the ratio of AB to AC will be:
(A) 11 : 9
(B) 7 : 13
(C) 13 : 7
(D) 9 : 11

Ans : (D) 9 : 11

Q.21: In $\triangle\text{ABC}$, points D and E are on AB and AC, respectively, such that DE is Parallel to BC. If AD=3cm, BD=6 cm and AE=2cm, then find the length of CE.
(A) 6 cm
(B) 16 cm
(C) 8 cm
(D) 4 cm

Ans : (D) 4 cm

Q.22: After allowing a discount of 15% on the market price of an article, it was sold for ₹425. Had the discount not been given, the profit would have been 25% What was the cost price (in₹) of the article?
(A) 325
(B) 450
(C) 500
(D) 400

Ans : (D) 400

Q.23: What is the sum of all the possible values of K for which a seven-digit number 23k567k is divisible by 3?
(A) 15
(B) 3
(C) 109
(D) 16

Ans : (A) 15

Q.24: Sunil can row a boat 20 km upstream in 1 hour 15 minutes. If the speed of the current of the river is 2 km/h, then how much time will he take to row the boat 30 km downstream?
(A) 1 h 10 m
(B) 1 h 45 m
(C) 1 h 30 m
(D) 1 h 20 m

Ans : (C) 1 h 30 m

Q.25: If $tan\theta =\frac43$, then the value of $\frac{9sin\theta+12cos\theta}{27cos\theta-20sin\theta}$ will be equal to:
(A) 72
(B) 36
(C) 18
(D) 100