SSC CGL Tier-2-17-February-2018 Maths

What is the value of $$\sin (B - C) \cos (A - D) + \sin (A - B) \cos (C - D) + \sin (C - A) \cos (B - D)?$$

What is the value of $$\frac{\left\{[4 \cos (90 - A) \sin^3(90 + A)] - [4 \sin (90 + A) \cos^3(90 - A)]\right\}}{\cos\left[\frac{180 + 8A}{2}\right]}$$?

What is the value of 

$$\cos [\frac{(180 - \theta)}{2}] \cos [\frac{(180 - 9\theta)}{2}] + \sin [\frac{(180 - 3\theta)}{2}] \sin [\frac{(180 - 13\theta)}{2}]?$$

What is the value of 

$$[\tan^2 (90 - \theta) - \sin^2 (90 - \theta)] \cosec^2 (90 - \theta) \cot^2 (90 - \theta)?$$

Two points P and Q are at the distance of x and y (where y > x) respectively from the base of a building and on a straight line. If the angles of elevation of the top of the building from points P and Q are complementary, then what is the height of the building?

The tops of two poles of height 60 metres and 35 metres are connected by a rope. If the rope makes an angle with the horizontal whose tangent is 5/9 metres, then what is the distance (in metres) between the two poles?

A Navy captain going away from a lighthouse at the speed of $$4[(\surd3) - 1]$$ m/s. He observes that it takes him 1 minute to change the angle of elevation of the top of the lighthouse from $$60^\circ$$ to $$45^\circ$$. What is the height (in metres) of the lighthouse?

If A equals to 15% of total applicants who are present at exam centre F and B equals to present applicants at exam centre K, then A is what percent of B?

Total number of offline applicants from exam centre H, K and F are how much less than the total number of present applicants from exam centre G and J?

What are the total number of offline applicants from the exam centre F, H, J and G?