SSC CGL Tier-2 11th September 2019 Maths

If $$5\sin\theta-4\cos\theta=0,0^{\circ}<\theta<90^{\circ}$$, then the value of $$\frac{5\sin\theta-2\cos\theta}{5\sin\theta+3\cos\theta}$$is:

If the radius of the base of a cone is doubled, and the volume of the new cone is three times the volume of the original cone, then what will be the ratio of the height of the original cone to that of the new cone?

Abhi rows upstream a distance of 28 km in 4 h and rows downstream a distance of 50 km in 2 h. To row a distance of 44.8 km in still water, he will take:

A sum of ₹8,400 amounts to ₹11,046 at 8.75% p.a. simple interest in certain time. What is the simple interest on the sum of ₹9,600 at the same rate for the same time?

If the diameter of the base of a cone is 42 cm andits curved surface area is 2310 $$cm^2$$, then what will be its volume (in $$cm^3$$) ?

If a cuboid of dimensions 32 cm $$\times$$ 12 cm $$\times$$ 9 cm is cut into two cubes of same size, what will be the ratio of the surface area of the cuboid to the total surface area of the two cubes?

When x is added to each of 2, 3, 30 and 35, then the numbers obtained in this order, are in proportion. What is the mean proportional between (x + 7) and (x - 2)?

The ratio of investment by A to that by B in a business is 14 : 15 and the ratio of their respective profits at the end of a year is 2 : 5. IfA invested the money for 3 months, then for how much time (in months) B invested his money?

In $$\triangle ABC,AB=7cm,BC=10cm,$$ and $$AC = 8 cm$$. If $$AD$$ is the angle bisector of $$\angle BAC$$, where $$D$$ is a point on $$BC$$, then $$BD$$ is equal to:

The base of right prism is a trapezium whose parallel sides are 11 cm and 15 cm and the distance between them is 9 cm. If the volume of the prism is 1731.6 cm$$^3$$, then the height(in cm) of the prism will be: