SSC CGL Tier-2 9-March-2018 Maths-shift-1

If $$P + Q + R = 60$$°, then what is the value of $$\cos Q \cos R (\cos P - \sin P) + \sin Q \sin R (\sin P - \cos P)$$?

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

What is the value of $$\frac{[1 +2 \cot^2(90 - x) - 2\cosec(90 - x) \cot(90 - x)]}{[\cosec(90 - x) - \cot(90 - x)]}$$?

What is the value of $$\sin(180 - \theta) \sin(90 - \theta) - \left[\frac{\cot(90 - \theta)}{1 + \tan^2 \theta}\right]$$

A pole is standing on the top of a house. Height of house is 25 metres. The angle of elevation of the top of house from point P is 45° and the angle of elevation of the top of pole from P is 60°. Point P is on the ground level. What is the height (in metres) of pole?

A ladder is placed against a wall such that it just reaches the top of the wall. The foot of the ladder is at a distance of 5 metres from the wall. The angle of elevation of the top of the wall from the base of the ladder is 15°. What is the length (in metres) of the ladder?

An aeroplane is flying horizontally at a height of 1.8 km above the ground. The angle of elevation of plane from point X is 60° and after 20 seconds, its angle of elevation from X is become 30°. If point X is on ground, then what is the speed (in m/s) of aeroplane?

What is the difference between the R1 type of rice produced by state X and the R2 type of rice produced by state H?

What is the sum of the total production of maize by state X and T and total production of R2 type of Rice by state S and R?

Production of R3 type of rice by state X is what percentage of production of R1 type of rice by state S?