SSC CHSL 2nd June 2022 Shift-2

Which among the below option can be a square root of?
$$\left(x^{2}-14x+49\right)\left(x^{2}+6x+9\right)$$

Find $$\theta$$, if $$\cos \theta = -\frac{\sqrt{3}}{2}$$.

Ruksana travelled at 60 km/h while going from point A to point B, and returned via the same route at a different speed. If Ruksana’s overall average speed during the two-way journey was 48 km/h, what was her speed while travelling from B to A?

If $$\left(x^{3}+y^{3}\right)^{\frac{2}{3}}=\left(x^{2}+y^{2}\right)$$, then the value of $$\frac{x^{2}+y^{2}}{xy} x \neq 0, y \neq 0$$, is:

An arc on a circle that is 15 cm long subtends a 24° angle at the centre. What is the circumference of the circle?

In an election between two candidates, one of the candidates secured 35% of the votes cast and was defeated by the other candidate by 1296 votes. If there were no invalid votes, then the total number of votes polled was:

The lengths of a pair of parallel sides of a trapezium are 20 cm and 25 cm, respectively, and the perpendicular distance between these two sides is 14 cm. What is the area (in $$cm^{2}$$ ) of the trapezium?

The ratio of the radii of two right circular cylinders is 2 : 3. If their heights are in the ratio 5 : 3, find the ratio of their volumes.

Find the $$4^{th}$$ proportional to 5, 10 and 12.

If $$\left(x-\frac{1}{x}\right)=7.5$$, what is the value of $$\left(x^{2}+\frac{1}{x^{2}}\right)$$