SSC CGL 12th April 2022 Shift-3

Instructions

For the following questions answer them individually

Question 51

$$\tan^{2} A + 5\sec A = 13$$, where $$0 < A < 90^{\circ}$$. Solve for A (in degrees).

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Question 52

In $$\triangle$$ ABC, AD is perpendicular to B and AE is the bisector of $$\angle$$ BAC . If $$\angle ABC = 58^{\circ}$$ and $$\angle ACB = 34^{\circ}$$, then find the measure of $$\angle$$ DAE.

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Question 53

In a circle with centre O, AC and BD are two chords. AC and BD meet at E, when produced. If AB is a diameter and $$\angle AEB = 36^{\circ}$$. then the measure of $$\angle$$ DOC is:

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Question 54

If $$8k^{6} + 15k^{3} - 2 = 0$$, then the positive value of $$\left(k + \frac{1}{k}\right)$$ is:

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Question 55

If $$2k \sin 30^{\circ} \cos 30^{\circ} \cot 60^{\circ} = \frac{\cot^{2}30^{\circ}\sec 60^{\circ}\tan 45^{\circ}}{\cosec^{2}45^{\circ}\cosec^{2}30^{\circ}}$$, then find the value of k.

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Question 56

A, B and C invested ₹40,000, 48,000 and ₹80,000, respectively, for a business at the start of a year. After six months, for the remaining time of the year. A added ₹4,000, B added ₹4,000 while C withdrew ₹4,000 every month. If the total profit is ₹6,72,000, then what is C's share (in ₹)?

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Question 57

The average of 15 numbers is 30, while the average of 13 of these numbers is 31. If the remaining two numbers are equal, then what is each of the two numbers?

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Question 58

A certain sum on simple interest becomes ₹49,600 in 3 years and ₹56,000 in 5 years. If the rate of interest had been 2%, more, then in how many years would the sum have doubled:

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Question 59

In a circle, ABCD is a cyclic quadrilateral. AC and BD intersect each other at P. If AB = AC and $$\angle BAC = 48^{\circ}$$, then the measure of $$\angle$$ ADC is

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Question 60

Five men and 2 boys can do in 30 days as much work as 7 men and 10 boys can do in 15 days. How many boys should join 40 men to do the same work in 4 days?

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