SSC CGL 12th April 2022 Shift-3

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

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.

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:

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

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.

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 ₹)?

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?

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:

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

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?