SSC CGL Tier-2 13th September 2019 Maths

A circle touches the side BC of $$\triangle$$ABC at D and AB and AC are produced to E and F, respectively. If AB = 10 em, AC = 8.6 cm and BC = 6.4 cm, then BE =?

If the measure of each exterior angle of a regular polygon is $$\left(51\frac{3}{7}\right)^\circ$$ then the ratio of the number of its diagonals to the number of its sides is:

Two numbers are in the ratio 3 : 5. If 13 is subtracted from each, the new numbers are in the ratio 10 : 21, If 15 is added to each ofthe original numbers, then the ratio becomes:

Pipes A and B are filling pipes while pipe C is an emptying pipe. A and B can fill a tank in 72 and 90 minutes respectively. When all the three pipes are opened together, the tank gets filled in 2 hours. A and B are opened together for 12 minutes, then closed and C is opened, The tank will be empty after:

The LCM of two numbers x and yis 204 times their HCF. If their HCF is 12 and the difference between the numbers is 60, then x + y = ?

In $$\triangle ABC, BE \perp AC, CD \perp AB$$ and $$BE$$ and $$CD$$ intersect each other at O. The bisectors of $$\angle OBC$$ and $$\angle OCB$$ meet at P. If $$\angle BPC = 148^\circ$$, then what is the measure of $$\angle A$$?

The value of $$\frac{2(\sin^6 \theta + \cos^6 \theta) - 3(\sin^4 \theta + \cos^4 \theta)}{\cos^4 \theta - \sin^4 \theta - 2 \cos^2 \theta}$$ is:

The value of $$24 \times 2 \div 12 + 12 \div 6  of  2 \div (15 \div 8 \times 4)  of  (28 \div 7  of  5)$$ is:

A person covers 40% of the distance from A to B at 8 km/h, 40% of the remaining distance at 9 km/h and the rest at 12 km/h. His average speed (in km/h) for the journey is:

A 15 m deep well with radius 2.8 m is dug and the earth taken out from it is spread evenly to form platform of breadth 8 m and height 1.5 m. What will be the length of the platform? (Take $$\pi = \frac{22}{7}$$)