# SSC CHSL 2021 12th August Shift 1 - QA

**1. SSC CHSL 2021 12th August Shift 1 - QA | Number Theory - SSC**

A sum of ₹ x is divided among A, B and C such that the ratio of the shares of A and C is 8 : 7 and that of B and is 3 : 2. If the difference between the shares of A and B is ₹240, then what is the value of ?

- A.
2544

- B.
2580

- C.
2490

- D.
2448

Answer: Option D

**Explanation** :

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**2. SSC CHSL 2021 12th August Shift 1 - QA | Percentage, Profit & Loss - SSC**

If a pair of shoes marked at ₹350 is offered at ₹308, then what will be the discount percentage?

- A.
42%

- B.
13.6%

- C.
12%

- D.
14%

Answer: Option C

**Explanation** :

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**3. SSC CHSL 2021 12th August Shift 1 - QA | Triangles - SSC**

In △ABC, AD is the bisector of ∠A meeting BC at D. If AB = 15 cm, BC = 10 cm and the length of BD is 2 cm less than that of DC, then the length of AC is:

- A.
18.5 cm

- B.
18 cm

- C.
16 cm

- D.
22.5 cm

Answer: Option D

**Explanation** :

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**4. SSC CHSL 2021 12th August Shift 1 - QA | Simple Equation - SSC**

Simplify the following expression.

$\frac{13{\displaystyle \frac{7}{9}}\xf7{\displaystyle \frac{2}{3}}\mathrm{of}{\displaystyle \frac{1}{3}}+{\displaystyle \frac{2}{3}}\times 3}{{\displaystyle \frac{7}{5}}\mathrm{of}325-20+7}$

- A.
$\frac{40}{1989}$

- B.
$\frac{31}{2210}$

- C.
$\frac{32}{221}$

- D.
$\frac{33}{217}$

Answer: Option C

**Explanation** :

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**5. SSC CHSL 2021 12th August Shift 1 - QA | Trigonometry - SSC**

The value of cosec(58° + θ) - sec(32° - θ) + sin 15° sin 35° sec 55° sin 30° sec 75° is:

- A.
1

- B.
2

- C.
$\frac{1}{2}$

- D.
0

Answer: Option C

**Explanation** :

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**6. SSC CHSL 2021 12th August Shift 1 - QA | Tables & Graphs - SSC**

Some persons went on an outstation tour.

The histogram shows their ages.

How many persons are less than 20 years of age?

- A.
22

- B.
31

- C.
25

- D.
18

Answer: Option A

**Explanation** :

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**7. SSC CHSL 2021 12th August Shift 1 - QA | Tables & Graphs - SSC**

Study the given graph and answer the question that follow

The total production of paper by company B in 2015 and 2017 to 2019 was what percentage less than 90% of the total production of paper by company A in 2014 to 2019 (correct to one decimal place)?

- A.
22.4%

- B.
19.6%

- C.
21.2%

- D.
17.5%

Answer: Option D

**Explanation** :

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**8. SSC CHSL 2021 12th August Shift 1 - QA | Triangles - SSC**

In △ABC, D and E are points on AB and BC, respectively, such that DE is parallel to AC. If DE = 3 cm, AC = 5 cm and the area of trapezium ACED = 32 cm^{2}, then what will be the area of △BDE?

- A.
$\frac{144}{17}$ cm

^{2} - B.
$\frac{48}{5}$ cm

^{2} - C.
16 cm

^{2} - D.
18 cm

^{2}

Answer: Option D

**Explanation** :

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**9. SSC CHSL 2021 12th August Shift 1 - QA | Tables & Graphs - SSC**

**Study the given pie chart and answer the question that follows.**

Total number of students admitted in a college = 700.

Distribution of the percentage of students in various courses.

Percentage-wise distribution of the number of boys

The ratio of the total number of girls admitted in B.Sc. Maths to the total number of students admitted in B.Sc. Maths is:

- A.
3 : 7

- B.
4 : 7

- C.
3 : 5

- D.
2 : 5

Answer: Option C

**Explanation** :

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**10. SSC CHSL 2021 12th August Shift 1 - QA | Circles - SSC**

In a circle with centre O and radius 6.5 cm, a chord AB is at a distance 2.5 cm from the centre. If tangents at A and B intersect at P, then find the distance of P from the centre.

- A.
16.9 cm

- B.
18 cm

- C.
15 cm

- D.
17 cm

Answer: Option A

**Explanation** :

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**11. SSC CHSL 2021 12th August Shift 1 - QA | Simple & Compound Interest - SSC**

What is the compound interest(₹) on a sum of ₹46,000 for years at 15% per annum, interest being compounded annually (nearst to a ₹)?

- A.
18,458

- B.
18,485

- C.
19,485

- D.
19,458

Answer: Option B

**Explanation** :

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**12. SSC CHSL 2021 12th August Shift 1 - QA | Simple Equation - SSC**

If $\sqrt{x}$ + $\frac{1}{\sqrt{x}}$ = 2$\sqrt{3}$, then what will be the value of x^{4} + $\frac{1}{{x}^{4}}$?

- A.
10402

- B.
9606

- C.
9602

- D.
10406

Answer: Option C

**Explanation** :

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**13. SSC CHSL 2021 12th August Shift 1 - QA | Simple Equation - SSC**

If 3x - 2y + 3 = 0, then what will be the value of 27x^{3} + 54xy + 30 - 8y^{3}?

- A.
-27

- B.
57

- C.
-57

- D.
3

Answer: Option D

**Explanation** :

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**14. SSC CHSL 2021 12th August Shift 1 - QA | Circles - SSC**

Chords AB and CD of a circle meet at point P (outside the circle), when produced. If AB = 9cm, PB = $\frac{1}{3}$ AB and CD = 5 cm, then the length of PD (in cm) is:

- A.
7

- B.
6

- C.
5

- D.
4

Answer: Option D

**Explanation** :

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**15. SSC CHSL 2021 12th August Shift 1 - QA | Percentage, Profit & Loss - SSC**

By selling an article for ₹3,150, a shopkeeper earns 5% profit. For how much money should he sell the article in order to gain 8%?

- A.
₹3,240

- B.
₹3,180

- C.
₹3,200

- D.
₹3,250

Answer: Option A

**Explanation** :

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**16. SSC CHSL 2021 12th August Shift 1 - QA | Simple Equation - SSC**

Given that 3$\sqrt{3}$x^{3} - 8y^{3} = ($\sqrt{3}$x + Ay)(3x^{2} + By^{2} + Cxy), the value of (A^{2} + B^{2} + C^{2}) is:

- A.
4

- B.
8

- C.
12

- D.
0

Answer: Option B

**Explanation** :

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**17. SSC CHSL 2021 12th August Shift 1 - QA | Circles - SSC**

A solid metallic sphere of radius 12 cm is melted and recast in the form of small spheres of radius 2 cm. How many small spheres are formed?

- A.
24

- B.
96

- C.
864

- D.
216

Answer: Option D

**Explanation** :

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**18. SSC CHSL 2021 12th August Shift 1 - QA | Time & Work - SSC**

A tap can fill a tank in 4 hours. Another tap can fill the same tank in 6 hours. If both the taps are opened at the same time, then in how much time will the empty tank be filled completely?

- A.
2h 30 min

- B.
2h 24 min

- C.
3 h

- D.
2 h

Answer: Option B

**Explanation** :

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**19. SSC CHSL 2021 12th August Shift 1 - QA | Trigonometry - SSC**

If tan 30θ = sin 45°. cos 45° + cos 60° and 3θ is an acute angle, then what will be the value of sin 4θ?

- A.
$\frac{\sqrt{3}}{2}$

- B.
$\frac{1}{\sqrt{2}}$

- C.
$\frac{1}{2}$

- D.
1

Answer: Option A

**Explanation** :

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**20. SSC CHSL 2021 12th August Shift 1 - QA | Time, Speed & Distance - SSC**

A boat can go 15 km downstream and 8 km upstream in 2h. It can go 20 km downstream and 12 km upstream in 2h 50 min. What is the speed (in km/h of the boat while going downstream?

- A.
16

- B.
15

- C.
20

- D.
18

Answer: Option B

**Explanation** :

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**21. SSC CHSL 2021 12th August Shift 1 - QA | Tables & Graphs - SSC**

**Study the given pie chart and answer the question that follows.**

The pie chart shows the distribution (degree wise) of the number of computers sold by a shopkeeper during five months.

If the difference between the number of computers sold in May and the number of computers sold in February is x, then the value of x will be:

- A.
450

- B.
480

- C.
540

- D.
420

Answer: Option B

**Explanation** :

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**22. SSC CHSL 2021 12th August Shift 1 - QA | Average, Mixture & Alligation - SSC**

The average of 40 numbers is 48.2. The average of the first 15 numbers is 45 and that of the next 22 numbers is 50.5. The 38th number is 1 more than the 39th number, and the 39th number is 3 less than the 40th number. What is the average of the 39th and 40th numbers?

- A.
48

- B.
49

- C.
47.5

- D.
48.5

Answer: Option C

**Explanation** :

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**23. SSC CHSL 2021 12th August Shift 1 - QA | Number Theory - SSC**

If the five-digit number 457 ab is divisible by 3, 7 and 11, then whatis the value of a^{2} + b^{2} - ab ?

- A.
49

- B.
36

- C.
24

- D.
33

Answer: Option A

**Explanation** :

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**24. SSC CHSL 2021 12th August Shift 1 - QA | Percentage, Profit & Loss - SSC**

Renu spends 68% of her income. When her income increases by 40%, she increases her expenditure by 30%. Her savings are increased by:

- A.
62.5%

- B.
37.98%

- C.
61.25%

- D.
51.6%

Answer: Option C

**Explanation** :

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**25. SSC CHSL 2021 12th August Shift 1 - QA | Trigonometry - SSC**

If tan θ + cot θ = 3, then what will be the value of tan^{2} θ + cot^{2} θ?

- A.
1

- B.
7

- C.
11

- D.
-1

Answer: Option B

**Explanation** :

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