# SSC CGL 13th April Shift 1 - QA

**1. SSC CGL 13th April Shift 1 - QA | Lines & Angles - SSC**

A kite flying at a height of 120 m is attached to a string which makes an angle of 60° with the horizontal. What is the length (in m) of the string?

- A.
90$\sqrt{3}$

- B.
75$\sqrt{3}$

- C.
84$\sqrt{3}$

- D.
80$\sqrt{3}$

Answer: Option D

**Explanation** :

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**2. SSC CGL 13th April Shift 1 - QA | Tables & Graphs - SSC**

The following histogram shows the marks scored by 40 students in a test of 30 marks. A student has to score a minimum of 10 marks to pass the test.

How many students have passed the test and obtained less than 50% marks?

- A.
17

- B.
15

- C.
10

- D.
7

Answer: Option D

**Explanation** :

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**3. SSC CGL 13th April Shift 1 - QA | Percentage, Profit & Loss - SSC**

A, B and C start a business. A invests 33$\frac{1}{3}$% of the total capital, B invests 25% of the remaining and C, the rest. If the total profit at the end of the year is ₹2,19,000, then A's share (in ₹) is:

- A.
79,000

- B.
73,000

- C.
65,000

- D.
71,000

Answer: Option B

**Explanation** :

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**4. SSC CGL 13th April Shift 1 - QA | Number Theory - SSC**

If the 9-digit number 7x79251y8 is divisible by 36, What is the value of (10x^{2} - 3y^{2}) for the largest possible value of y?

- A.
490

- B.
289

- C.
298

- D.
192

Answer: Option C

**Explanation** :

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**5. SSC CGL 13th April Shift 1 - QA | Simplification - SSC**

What is the value of x, if

5(1 - $\frac{x}{5}$) - (5 - x) - $\frac{1}{200}$ of (20 - x) = 0.08?

- A.
18

- B.
24

- C.
9

- D.
36

Answer: Option D

**Explanation** :

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**6. SSC CGL 13th April Shift 1 - QA | Time & Work - SSC**

If 4 men and 6 boys can do a work in 8 days and 6 men and 4 boys can do the same work in 7 days, then how many days will 5 men and 4 boys take to do the same work?

- A.
5

- B.
8

- C.
6

- D.
7

Answer: Option B

**Explanation** :

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**7. SSC CGL 13th April Shift 1 - QA | Simplification - SSC**

If 5 sin θ − 4 cos θ = 0, 0° < θ < 90°, then the value of $\frac{5\mathrm{sin}\theta +2\mathrm{cos}\theta}{5\mathrm{sin}\theta +3\mathrm{cos}\theta}$

- A.
$\frac{4}{7}$

- B.
$\frac{6}{7}$

- C.
$\frac{3}{7}$

- D.
$\frac{2}{7}$

Answer: Option B

**Explanation** :

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**8. SSC CGL 13th April Shift 1 - QA | Simplification - SSC**

If x + y + z = 18, xyz = 81 and xy + yz + zx = 90, then find the value of $\sqrt{{x}^{3}+{y}^{3}+{z}^{3}+xyz}$.

- A.
1321

- B.
1225

- C.
1250

- D.
1296

Answer: Option D

**Explanation** :

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**9. SSC CGL 13th April Shift 1 - QA | Coordinate Geometry - SSC**

Chords AB and CD of a circle, when produced, meet at the point P. If AB = 6.3 cm, BP= 4.5 cm, and CD= 3.6 cm, then the length (in cm) of PD is

- A.
4.8cm

- B.
3.5 cm

- C.
3.1 cm

- D.
5.4 cm

Answer: Option D

**Explanation** :

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**10. SSC CGL 13th April Shift 1 - QA | Percentage, Profit & Loss - SSC**

A shopkeeper allows 28% discount on the marked price of an article and still makes a profit of 20%. If he gains ₹3,080 on the sale of one article, then what is the selling price (in ₹) of the article?

- A.
18,480

- B.
14,880

- C.
10,884

- D.
18,840

Answer: Option A

**Explanation** :

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**11. SSC CGL 13th April Shift 1 - QA | Coordinate Geometry - SSC**

A cylindrical vessel of diameter 32 cm is partially filled with water. A solid metallic sphere of radius 12 cm is dropped into it. What will be the increase in the level of water in the vessel (in cm)?

- A.
27

- B.
9

- C.
72

- D.
2.25

Answer: Option B

**Explanation** :

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**12. SSC CGL 13th April Shift 1 - QA | Number Theory - SSC**

13, a, b, c are four distinct numbers and the HCF of each pair of numbers ( 13, a); (13, b); ( 13, c) is 13, where a, b, c are each less than 60 and a< b < c. What is the value of $\frac{a+c}{b}$?

- A.
5

- B.
2

- C.
3.5

- D.
4.5

Answer: Option B

**Explanation** :

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**13. SSC CGL 13th April Shift 1 - QA | Triangles - SSC**

In △ABC , D is a point on side BC such that ∠ADC = ∠BAC. If CA = 12 cm and CD = 8 cm, then CB (in cm) =?

- A.
18

- B.
10

- C.
12

- D.
15

Answer: Option A

**Explanation** :

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**14. SSC CGL 13th April Shift 1 - QA | Coordinate Geometry - SSC**

If the length of a diagonal of a square is ( a+b ), then the area of the square is:

- A.
${a}^{2}$ + ${b}^{2}$

- B.
$\frac{1}{2}$(a² + b²)

- C.
$\frac{1}{2}$(a² + b²) + ab

- D.
a² + b² + 2ab

Answer: Option C

**Explanation** :

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**15. SSC CGL 13th April Shift 1 - QA | Time, Speed & Distance - SSC**

A train covers a distance of 225 km in 2$\frac{1}{2}$ hours with a uniform speed. The time taken, in hours, to cover a distance of 450 km with the same speed is:

- A.
5

- B.
4

- C.
6

- D.
3

Answer: Option A

**Explanation** :

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**16. SSC CGL 13th April Shift 1 - QA | Time, Speed & Distance - SSC**

Simple interest on a certain sum is one-fourth of the sum and the interest rate percentage per annum is 4 times the number of years. If the rate of interest increases by 2%, then what will be the simple interest (in ₹) on ₹5,000 for 3 years?

- A.
1,500

- B.
2,000

- C.
1,800

- D.
300

Answer: Option C

**Explanation** :

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**17. SSC CGL 13th April Shift 1 - QA | Percentage, Profit & Loss - SSC**

A tea seller used to make 50% of profit by selling tea at ₹9 per cup. When the cost of ingredients increased by 25%, be started selling tea at ₹10 per cup.What is his profit percentage now?

- A.
33$\frac{1}{3}$

- B.
25

- C.
33$\frac{2}{3}$

- D.
30

Answer: Option A

**Explanation** :

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**18. SSC CGL 13th April Shift 1 - QA | Average, Mixture & Alligation - SSC**

The average of five numbers is 30. If one number is excluded, the average becomes 31. What is the excluded number?

- A.
24

- B.
26

- C.
31

- D.
30

Answer: Option B

**Explanation** :

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**19. SSC CGL 13th April Shift 1 - QA | Tables & Graphs - SSC**

The given pie chart represents the percentage-wise distribution of the total number of vanilla cakes and chocolate cakes sold every day. The total number of cakes sold in a week = 10500. Study the pie chart and answer the question that follows.

The ratio of vanilla cakes sold to chocolate cakes sold on Friday is 4:3. If the price of one vanilla cake is ₹9 and that of one chocolate cake is ₹10, then the total amount earned (in ₹) by selling all vanilla cakes and chocolate cakes on Friday is:

- A.
9,900

- B.
10,000

- C.
11,000

- D.
8,900

Answer: Option A

**Explanation** :

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**20. SSC CGL 13th April Shift 1 - QA | Tables & Graphs - SSC**

The given pie charts show the monthly household expenditure of Family A and Family B under various heads. The monthly expenditures incurred for Family A and Family B are ₹50,000 and ₹75,000, respectively.

Study the charts carefully and answer the question that follows.

Monthly Household Expenditure of ₹50,000 under various heads of Family A

Monthly household expenditure on ₹75,000 under various heads for Family B

If the monthly expenditures of both families are combined together then the expenditures on Entertainment of both families together will be what percentage of the total monthly expenditures of both families? Express your answer to the nearest integer.

- A.
10%

- B.
23%

- C.
11%

- D.
22%

Answer: Option C

**Explanation** :

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**21. SSC CGL 13th April Shift 1 - QA | Circles - SSC**

In a circle of diameter 20 cm, chords AB and CD are parallel to each other. BC is diameter. If AB is 6 cm from the centre of the circle, what is the length (in cm) of the chord CD?

- A.
12

- B.
16

- C.
8

- D.
20

Answer: Option B

**Explanation** :

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**22. SSC CGL 13th April Shift 1 - QA | Triangles - SSC**

In a triangle ABC, D and E are points on BC such that AD = AE and ∠BAD - ∠CAE. If AB = (2p + 3), BD = 2p. AC = (3q - 1) and CE = q, then find the value of (p + q).

- A.
3

- B.
3.6

- C.
4.5

- D.
2

Answer: Option A

**Explanation** :

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**23. SSC CGL 13th April Shift 1 - QA | Percentage, Profit & Loss - SSC**

In a factory with 400 employees, the ratio of the number of male employees to that of female employees is 5: 3. There are 87.5% regular employees in the factory. If 92% of male employees are regular employees, then what is the percentage of regular female employees?

- A.
80%

- B.
78%

- C.
87.5%

- D.
85%

Answer: Option A

**Explanation** :

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**24. SSC CGL 13th April Shift 1 - QA | Trigonometry - SSC**

Find the value of the following expression:

$\frac{{\mathrm{tan}}^{3}45\xb0+4{\mathrm{cos}}^{3}60\xb0}{2\mathrm{cos}e{c}^{2}45\xb0-3se{c}^{2}30\xb0+\mathrm{sin}30\xb0}$

- A.
1 + $\sqrt{2}$

- B.
$\frac{4}{3}$

- C.
$\frac{3}{4}$

- D.
3

Answer: Option D

**Explanation** :

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**25. SSC CGL 13th April Shift 1 - QA | Tables & Graphs - SSC**

The given bar graph shows the income and expenditure (in crores ₹) of a company over 5 years, from 2014 to 2018.

Study the bar graph and answer the question that follows.

In which of the following years is the ratio of expenditure to income the minimum?

- A.
2016

- B.
2017

- C.
2014

- D.
2018

Answer: Option C

**Explanation** :

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