# SSC CGL 17th August Shift 2 - QA

**1. SSC CGL 17th August Shift 2 - QA | Lines & Angles - SSC**

Points P, Q, R, S and lie in this order on a circle with centre O. If chord TS is parallel to diameter PR and ∠RQT = 58° then find the measure (in degrees) of ∠RTS.

- A.
23

- B.
32

- C.
45

- D.
58

Answer: Option B

**Explanation** :

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**2. SSC CGL 17th August Shift 2 - QA | Trigonometry - SSC**

If sin A = $\frac{1}{2}$, A is an acute angle, then find the value of $\frac{\mathrm{tan}A-cotA}{\sqrt{3}(1+\mathrm{cos}ecA)}$

- A.
$\frac{4\sqrt{3}}{9}$

- B.
$\frac{2}{9}$

- C.
-$\frac{2}{9}$

- D.
-$\frac{4\sqrt{3}}{9}$

Answer: Option C

**Explanation** :

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**3. SSC CGL 17th August Shift 2 - QA | Triangles - SSC**

In △ABC, AD is the bisector of ∠A meeting BC at D. If AC = 21 cm, BC = 11 cm and the length of BD is 3 cm less than DC, then the length(in cm) of side AB is:

- A.
10

- B.
15

- C.
18

- D.
12

Answer: Option D

**Explanation** :

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**4. SSC CGL 17th August Shift 2 - QA | Lines & Angles - SSC**

In △ABC, AD ⊥ BC at D and AE is the bisector of ∠A. If ∠B = 62° and ∠C = 36°, then what is the measure of ∠DAE?

- A.
23°

- B.
27°

- C.
54°

- D.
13°

Answer: Option D

**Explanation** :

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**5. SSC CGL 17th August Shift 2 - QA | Trigonometry - SSC**

For 0° < θ < 90°, $\frac{1}{\mathrm{cos}\theta}$ + $\frac{1}{\mathrm{tan}\theta -sec\theta}$ is equal to:

- A.
sec θ

- B.
-sec θ

- C.
-tan θ

- D.
tan θ

Answer: Option C

**Explanation** :

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**6. SSC CGL 17th August Shift 2 - QA | Circles - SSC**

What is the volume(in cm^{3}) ofa spherical shell whose inner and outerradii are respectively 2 cm and 3 cm?

- A.
$\frac{86\pi}{3}$

- B.
$\frac{56\pi}{3}$

- C.
$\frac{106\pi}{3}$

- D.
$\frac{76\pi}{3}$

Answer: Option D

**Explanation** :

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**7. SSC CGL 17th August Shift 2 - QA | Tables & Graphs - SSC**

Table shows District-wise data of the number of primary school teachers posted in schools of a city.

Study the table and answer the question:

What is the average number of female teachers in the five districts?

- A.
1690

- B.
2871

- C.
1698

- D.
1173

Answer: Option C

**Explanation** :

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**8. SSC CGL 17th August Shift 2 - QA | Number Theory - SSC**

Find the smallest value of a so that 42a48b (a > b)is divisible by 11.

- A.
9

- B.
4

- C.
5

- D.
0

Answer: Option C

**Explanation** :

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**9. SSC CGL 17th August Shift 2 - QA | Tables & Graphs - SSC**

Pie-chart shows the distribution of percentage of students in various courses. Total number of students is 1400

What is the ratio of number of girls in B.Sc. Maths to number of boys in B.Sc. C. Sci.?

- A.
2 : 7

- B.
5 : 3

- C.
3 : 5

- D.
7 : 2

Answer: Option C

**Explanation** :

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**10. SSC CGL 17th August Shift 2 - QA | Ratio, Proportion & Variation - SSC**

In a class the ratio of rural to urban students is 4 : 7. In an examination the average percentage marks of the rural and the urban studentsare respectively 65 and 63. Whatis the overall average percentage marks of the class (correct to two decimal places)?

- A.
63.73%

- B.
65.87%

- C.
64.37%

- D.
73.63%

Answer: Option A

**Explanation** :

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**11. SSC CGL 17th August Shift 2 - QA | Simple Equation - SSC**

If x^{2} - $\sqrt{11}$x + 1 = 0, then (x^{3} + x^{3}) =

- A.
8$\sqrt{11}$

- B.
10$\sqrt{11}$

- C.
4$\sqrt{11}$

- D.
7$\sqrt{11}$

Answer: Option A

**Explanation** :

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**12. SSC CGL 17th August Shift 2 - QA | Percentage, Profit & Loss - SSC**

Rajan spent 10% of his salary on rent. He spent 20%ofthe remaining part of the salary on transport. After which he spent 40°ofthe balance ofthe salary on food. Further, he spent 80% of the balance on variousbills. He deposits ₹5000 in the bank andkept the remaining ₹1480 for his own petty expenditure. Find his monthly salary (in ₹).

- A.
75000

- B.
80000

- C.
64800

- D.
82500

Answer: Option A

**Explanation** :

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**13. SSC CGL 17th August Shift 2 - QA | Simplification - SSC**

If (x + y)^{3} + 27(x - y)^{3} = (Ax - 2y)(Bx^{2} + Cxy + 13y^{2}), then the value of A - B - C is:

- A.
27

- B.
13

- C.
15

- D.
20

Answer: Option B

**Explanation** :

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**14. SSC CGL 17th August Shift 2 - QA | Simple Equation - SSC**

5$\frac{1}{5}$ ÷ $\left[3\frac{1}{2}-\left\{\frac{5}{6}-\left(\frac{3}{5}+\frac{1}{101}-\frac{4}{15}\right)\right\}\right]$ is equal to:

- A.
$\frac{22}{31}$

- B.
$\frac{52}{31}$

- C.
$\frac{12}{31}$

- D.
$\frac{72}{31}$

Answer: Option B

**Explanation** :

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**15. SSC CGL 17th August Shift 2 - QA | Tables & Graphs - SSC**

In the table, production and sale (in 1000 tonnes) of a certain product of a company over5 years is given. Study the table and answerthe question:

In which year(s) the sale increases by more than 25% of the previous year?

- A.
2018

- B.
2017 and 2019

- C.
2016 and 2018

- D.
2017

Answer: Option C

**Explanation** :

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**16. SSC CGL 17th August Shift 2 - QA | Simple & Compound Interest - SSC**

A borrowed a sum of ₹160000 from B at 10% per annum simple interest. At the same time helent the same sum to C at the same rate on compound interest, compounded semi-annually for 2 years. Find the amount (in ₹) earned by A in the whole transaction.

- A.
4281

- B.
4280

- C.
2481

- D.
2840

Answer: Option C

**Explanation** :

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**17. SSC CGL 17th August Shift 2 - QA | Time, Speed & Distance - SSC**

A train running at 72 km/h crosses a pole in 12 seconds. How much time(in seconds)will it take to cross a bridge 360 m long?

- A.
40

- B.
75

- C.
60

- D.
30

Answer: Option D

**Explanation** :

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**18. SSC CGL 17th August Shift 2 - QA | Percentage, Profit & Loss - SSC**

The marked price of an article is ₹2720. If a shopkeeper sold the article at 15% loss after giving 25% discount, then the cost price (in ₹) of the article is:

- A.
2000

- B.
2400

- C.
1800

- D.
1200

Answer: Option B

**Explanation** :

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**19. SSC CGL 17th August Shift 2 - QA | Trigonometry - SSC**

If cos θ − sin θ = $\sqrt{3}$cos (90° - θ), 0° < θ < 90° then find the value of tan θ - cot θ.

- A.
$\frac{3-2\sqrt{3}}{(1+\sqrt{3})}$

- B.
-$\frac{3+2\sqrt{3}}{(1+\sqrt{3})}$

- C.
-$\frac{3+2\sqrt{3}}{(1-\sqrt{3})}$

- D.
$\frac{3+2\sqrt{3}}{(1+\sqrt{3})}$

Answer: Option B

**Explanation** :

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**20. SSC CGL 17th August Shift 2 - QA | Simplification - SSC**

If x^{8} - 433x^{4} + 16 = 0, x > 0, then what is the value of $\left(x+\frac{2}{x}\right)$?

- A.
7

- B.
4

- C.
5

- D.
9

Answer: Option C

**Explanation** :

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**21. SSC CGL 17th August Shift 2 - QA | Time & Work - SSC**

There are two water taps in a tank which can fill the empty tank in 12 hours and 18 hours respectively. It is seen that there is a leakage point at the bottom of the tank which can empty the completely filled tank in 36 hours. If both the water taps are openedat the same timetofill the empty tank and the leakage point was repaired after 1 hour, then in how muchtime the empty tank will be completely filled?

- A.
7 hours

- B.
8 hours 24 minutes

- C.
7 hours 24 minutes

- D.
7 hours 12 minutes

Answer: Option C

**Explanation** :

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**22. SSC CGL 17th August Shift 2 - QA | Tables & Graphs - SSC**

The given Pie-Chart shows the degree wise breakup of expenditure of a family in a month. Total income of a family is ₹43200.

The amount spent on food is what percent of the savings and miscellaneous expenses?

- A.
84%

- B.
60%

- C.
75%

- D.
90%

Answer: Option A

**Explanation** :

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**23. SSC CGL 17th August Shift 2 - QA | Ratio, Proportion & Variation - SSC**

What is the difference in the mean proportional between 1.8 and 3.2 and the third proportional to 5 and 3?

- A.
0.7

- B.
0.4

- C.
0.5

- D.
0.6

Answer: Option D

**Explanation** :

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**24. SSC CGL 17th August Shift 2 - QA | Percentage, Profit & Loss - SSC**

A shopkeeper bought 20 kg of sugar at ₹45 per Kg, 25 kg of sugar at ₹50 per kg and 35 kg of sugar at ₹40 per kg. He spent a sum of ₹450 ontransportation and other expenses. He mixed all the three types of sugar andsold all the stock at ₹52.50 per kg. His profit percentin the entire transaction is:

- A.
5%

- B.
4.25%

- C.
6.5%

- D.
7.25%

Answer: Option A

**Explanation** :

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**25. SSC CGL 17th August Shift 2 - QA | Coordinate Geometry - SSC**

ABCD is a cyclic quadrilateral such that AB is the diameter ofthe circle and ∠ADC = 145°, then what is the measure of ∠BAC?

- A.
65°

- B.
45°

- C.
55°

- D.
35°

Answer: Option C

**Explanation** :

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