SSC CGL Tier-2 20-February-2018 Maths

If $$\sec \theta (\cos \theta + \sin \theta) = \surd2$$, then what is the value of $$\frac{(2 \sin \theta)}{(\cos \theta - \sin \theta)}$$?

What is the value of $$\frac{1}{\sin^4 (90 - \theta)}+\frac{1}{[\cos^2 (90 - \theta)] - 1}?$$

What is the value of $$\frac{[\tan (90 - A) + \cot (90 - A)]^2}{[2 \sec^2 (90 - 2A)]}$$?

What is the value of 

$$ \left\{ \sin (90 + x) \cos [\pi - (x - y)] \right\}$$ $$+ \left\{  \cos (90 + x) \sin [\pi - (x - y)] \right\}$$?

The angle of elevation of an aeroplane from a point on the ground is 60°. After flying for 30 seconds, the angle of elevation changes to 30°. If the aeroplane is flying at a height of 4500 m, then what is the speed (in m/s) of aeroplane?

A kite is flying in the sky. The length of string between a point on the ground and kite is 420 m. The angle of elevation of string with the ground is 30°. Assuming that there is no slack in the string, then what is the height (in metres) of the kite?

A balloon leaves from a point P rises at a uniform speed. After 6 minutes, an observer situated at a distance of $$450\surd3$$ metres from point P observes that angle of elevation of the balloon is 60°. Assume that point of observation and point P are on the same level. What is the speed (in m/s) of the balloon?

What is the total number of wooden bats of brand A manufactured by company T?

N = Wooden bats of Brand B manufactured by U.
M = Total wooden bats manufactured by R and W together.
What is the value of $$\frac{N}{M}$$?

P = Sum of wooden bats of Brand B manufactured by S and wooden bats of Brand A manufactured by W.
Q = Difference of Brand B wooden bats and Brand A wooden bats manufactured by U.

What is the value P - Q?