**Section 3: Mathematics : SSC CHSL Tier 1 Practice Set**

**Q.1:** If 71^{83}+73^{83} is divided by 36, the remainder is:

(A) 0

(B) 8

(C) 9

(D) 13

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**Q.2:** A shopkeeper marks his goods at a price such that after giving a discount of 20%, he gains 25%. If the cost price of the article is ₹560, what will be its marked price (in₹)?

(A) 914

(B) 875

(C) 856

(D) 765

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**Q.3:** If $latex \frac{cot\theta+cos\theta}{cot\theta-cos\theta}=\frac{K+1}{1-K},K\neq1$, then K is equal to:

(A) sin$latex \theta$

(B) cosec$latex \theta$

(C) cos$latex \theta$

(D) sec$latex \theta$

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**Q.4:**

(A) 35 : 61

(B) 33 : 56

(C) 37 : 59

(D) 31 : 56

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**Q.5:** 40 persons take 6 days to complete a certain task, working 10 hours a day. How many hours a day will be sufficient for 30 persons to complete the same task in 10 days?

(A) 9

(B) 8

(C) 10

(D) 6

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**Q.6:** If $latex \sqrt{13} sin\theta=2$, then the value of $latex \frac{3tan\theta+\sqrt{13}sin\theta}{\sqrt{13}cos\theta-3 tan\theta}$ is:

(A) 5

(B) 4

(C) 3

(D) $latex \frac12$

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**Q.7:** If $latex cos^2\theta-sin^2\theta-3cos\theta+2=0,0^o<\theta<90^o$, then what will be the value of $latex sec\theta-cos\theta$?

(A) $latex \frac43$

(B) $latex \frac12$

(C) $latex \frac32$

(D) $latex \frac23$

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**Q.8:** If X+2y=19 and x^{3}+8y^{3}=361, then xy is equal to:

(A) 57

(B) 56

(C) 55

(D) 58

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**Q.9:** The perimeter of a right-angled triangle whose sides that make right angles are 15cm and 20cm is:

(A) 60 cm

(B) 50 cm

(C) 70 cm

(D) 40 cm

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**Q.10:** The compound interest on a certain sum of money for 3 years, compounded annually, at a rate of interest of 10% per annum is ₹1,324. The sum is:

(A) ₹5,500

(B) ₹4,500

(C) ₹4,000

(D) ₹5,000

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**Q.11:** The value of cosec $latex (58^o + \theta)-sec(32^o – \theta)$ + sin15^{o}sin35^{o}sec55^{o}sin30^{o}sec75^{o} is :

(A) 1

(B) 2

(C) $latex \frac12$

(D) 0

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**Q.12:** Study the given bar graph and answer the question that follows.

(A) 2002

(B) 2005

(C) 2007

(D) 2008

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**Q.13:** X sells an article to Y at 12% loss. Y sells it to Z at 9% profit. If Z Pays ₹21,582 for it, then at what price (in₹) was the article purchased by X?

(A) 19,800

(B) 23,275

(C) 22,500

(D) 21,000

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**Q.14:** If (3x+2y)^{3}+(3x-2y)^{3}=3kx(3x^{2}+4y^{2}), then the value of K will be:

(A) 18

(B) 9

(C) 3

(D) 6

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**Q.15:** The value of $latex 42\div10-(\frac74\times\frac13)of \frac65+\frac{16}{3}\times\frac{9}{10}-(\frac16\div\frac{1}{36})$ is:

(A) 1.7

(B) 2.9

(C) 1.5

(D) 2.3

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**Q.16:** A solid cube having volume 46656 cm^{3} is cut into 27 cubes of equal volume. The surface area :in cm^{2} ) of the smaller cubes is:

(A) 864

(B) 756

(C) 936

(D) 921

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**Q.17:** If 27x^{3}-64y^{3}=(Ax+By)(Cx2+Dy2-Exy), then value of (A-B+C-D+E) will be:

(A) -12

(B) 18

(C) 15

(D) -20

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**Q.18:** A circle touches the side BC of $latex \triangle\text{ABC}$ at P and also touches AB and AC produced at Q perimeter of $latex \triangle\text{ABC}=14.1$cm, then the length (in cm ) of AQ will be:

(A) 10.3

(B) 7.05

(C) 6.25

(D) 9.15

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**Q.19:** Study the given graph and answer the question that follows.

(A) 2018

(B) 2017

(C) 2019

(D) 2015

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**Q.20:** In a proportion, the product of the first and fourth terms is 70 and that of the second and third terms is 3.5y. The value of y is:

(A) 17

(B) 20

(C) 15

(D) 22

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**Q.21:** Two circles touch each other extremally. The distance between their centers is 14 cm. If the radius of one circle is 8 cm, then the radius of the other circle is:

(A) 7 cm

(B) 6 cm

(C) 5 cm

(D) 8 cm

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**Q.22:** The average of 42 numbers is 37. The average of the first 26 number is 32, and the average of the last 17 numbers is 44. The 26^{th} number is:

(A) 28

(B) 27

(C) 26

(D) 25

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**Q.23:** Dimple is travelling at a speed of 90 km per hour on a highway, while Sachin is travelling at a speed of 108 km per hour. What is the difference in their speeds, in metres per second?

(A) 5

(B) 3

(C) 4

(D) 6

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**Q.24:** In $latex \triangle\text{ABC}$, D and E are the points on the sides AB and AC, respectively such that $latex \angle\text{AED}=\angle\text{ABC}$. If AE=6 cm, BD=2 cm, DE=3 cm and BC=5cm, then (AB+AC) is equal to:

(A) $latex \frac{86}{3}$ cm

(B) $latex \frac{49}{3}$ cm

(C) $latex \frac{50}{3}$ cm

(D) $latex \frac{70}{3}$ cm

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**Q.25:** Gaurav earns 800 per day. After some weeks, he earns 960 per day. What is the percentage increase in his daily earnings?

(A) 18%

(B) 20%

(C) 16%

(D) 14%

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SSC CHSL Tier 1 Practice Set

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