SSC CGL Tier-2 18-February-2018 Maths

What is the value of $$\left[(\sec 2\theta + 1)\sqrt{\sec^2 \theta -1}\right] \times \frac{1}{2} (\cot \theta - \tan \theta)$$

What is the value of sin $$(630$$° + $$A) + \cos A$$?

What is the value of $$[(\sin 59$$° $$\cos 31$$° + $$\cos 59$$° $$\sin 31$$°) $$\div$$ ($$\cos 20$$° $$\cos 25$$° - $$\sin 20$$° $$\sin 25$$°$$)]$$?

What is the value of $$\cos (90 - B) \sin (C - A) + \sin (90 + A) \cos (B + C) - \sin (90 - C) \cos (A + B)$$?

Two trees are standing along the opposite sides of a road. Distance between the two trees is 400 metres. There is a point on the road between the trees. The angle of depressions of the point from the top of the trees are 45° and 60°. If the height of the tree which makes 45°angle is 200 metres, then what will be the height (in metres) of the other tree?

A tower stands on the top of a building which is 40 metres high. The angle of depression of a point situated on the ground from the top and bottom of the tower are found to be 60° and 45° respectively. What is the height (in metres) of tower?

From a point P, the angle of elevation of a tower is such that its tangent is $$\frac{3}{4}$$. On walking 560 metres towards the tower the tangent of the angle of elevation of the tower becomes $$\frac{4}{3}$$. What is the height (in metres) of the tower?

What are the average sales of milk (in litres) by the salesmen A in all the given states?

What is the respective ratio of sales of milk in state P and Q by salesmen B and the sales of milk in state R and T by salesmen A?

What will be the central angle (in degrees) formed by the average sale of milk in state Q, T and S together?