SSC CGL Tier-2 29th January 2022 Maths

$$\frac{1+\cos\theta-\sin^{2}\theta}{\sin\theta\left(1+\cos\theta\right)}\times\frac{\sqrt{\sec^{2}\theta+\csc^{2}\theta}}{\tan\theta+\cot\theta}, 0^\circ < \theta < 90^\circ$$ is equal to:

If a + b = 8, ab = 10, then the value of $$a^{3}+b^{3}$$ is:

If $$x=\sqrt{1+\frac{\sqrt{3}}{2}}-\sqrt{1-\frac{\sqrt{3}}{2}}$$, then the value of $$\frac{\sqrt{3}-x}{\sqrt{3}+x}$$ (corrected to two decimal place) is:

A circle is inscribed in $$\triangle$$ PQR touching the sides QR, PR and PQ at the points S , U and T, respectively. PQ = (QR + 5) cm, PQ = (PR + 2) cm . If the perimeter of $$\triangle$$ PQR is 32 cm ,then PR is equal to:

Let x=$$\frac{5\frac{3}{4}-\frac{3}{7}\times15\frac{3}{4}+2\frac{2}{35}\div1\frac{11}{25}}{\frac{3}{4}\div5\frac{1}{4}+5\frac{3}{5}\div3\frac{4}{15}}$$. When y is added to  x, the result is $$\frac{7}{13}$$. What is the value of y?

The value of $$\frac{1}{4-\sqrt{15}}-\frac{1}{\sqrt{15}-\sqrt{14}}+\frac{1}{\sqrt{14}-\sqrt{13}}-\frac{1}{\sqrt{13}-\sqrt{12}}+\frac{1}{\sqrt{12}-\sqrt{11}}-\frac{1}{\sqrt{11}-\sqrt{10}}+\frac{1}{\sqrt{10}-3}-\frac{1}{3-\sqrt{3}}$$

If $$\sin A=\frac{5}{13}$$ and 7 $$\cot$$ B = 24 , then the value of $$\left(\sec A \cos B\right) \left(\csc B \tan A\right)$$ is:

The sum of and different between the LCM and HCF of two numbers are 512 and 496, respectively. If one number is 72, then the other number is:

The angle of elevation of the top of a tower 25 $$\sqrt{3}$$ m high from two points on the level ground on its opposite sides are $$4545^{\circ}$$ and $$60^{\circ}$$. What is the distance (in m) between the two points (correct to one decimal place)?

ABCD is a cyclic quadrilateral and BC is a diameter of the circle. If $$\angle DBC = 29^{\circ}$$ , then $$\angle$$ BAD = ?