SSC CGL Tier-2 9-March-2018 Maths Shift-2

Four identical cones each of radius 10.5 cm and height 14 cm are cut from a cuboid of dimensions $$30 cm \times 32 cm \times 40 cm$$ (base of each cone lies on the surface of cuboid). What is the total surface area (in cm$$^2$$) of the remaining solid?

A hollow cylinder of thickness 0.7 cm and height 15 cm is made of iron. If inner radius of cylinder is 3.5 cm, then what is the total surface area (in cm$$^2$$) of the hollow cylinder?

A hollow cylinder has height 90 cm and the outer curved surface area is 11880 cm$$^2$$. It can hold 55440 cm$$^3$$ of air inside it. What is the thickness (in cm) of this cylinder?

A hollow sphere is melted to form small identical! hollow spheres. Inner and outer radius of the bigger sphere are 4 cm and 6 cm respectively. If inner and outer radii of the smaller sphere are 2 cm and 3 cm respectively, then how many smaller spheres can be formed?

A hemispherical dome is open from its base and is made of iron. Thickness of dome is 3.5 meter. Total cost of painting domes outer curved surface is Rs 2464. If the rate of painting is Rs 8 per meter$$^2$$, then what is the volume (in meter$$^3$$) of iron used in making dome?

A solid cuboid has dimensions $$14 cm \times 18 cm \times 24 cm$$. A hemisphere of radius 3.5 cm is cut from the centre of each face of cuboid. What is the total surface area (in $$cm^2$$)of the remaining solid?

A right pyramid with square base has side of base 12 cm and height 40 cm. It is kept on its base. It is cut into 4 parts of equal heights by 3 cuts parallel to its base. What is the ratio of volume of the four parts?

What is the value of $$2 \sin 15$$° $$\cos 15$$° - $$4 \sin^3 15$$° $$\cos 15$$°?

If $$\sin x = \frac{1}{2}$$ and $$\sin y = \frac{2}{3}$$, then what is the value of $$\left[\frac{(6 \cos^2 x - 4 \cos^4 x)}{(18 \cos^2 y - 27 \cos^4 y)}\right]$$

What is the value of $$\cos 15$$° + $$\cos 105$$°?