SSC CGL Tier-2 19-February-2018 Maths

The height of a cone is 45 cm. It is cut at a height of 15 cm from its base by a plane parallel to its base. If the volume of the smaller cone is 2310 $$cm^3$$, then what is the volume (in $$cm^3$$) of the original cone?

The ratio of the curved surface area and total surface area of a right circular cylinder is 2 : 5. If the total surface area is 3080 $$cm^2$$, then what is the volume (in $$cm^3$$) of the cylinder?

The radius and height of a solid cylinder are increased by 2% each. What will be the approximate percentage increase in volume?6.76

A sphere of radius 21 cm is cut into 8 identical parts by 3 cuts (1 cut along each axis). What will be the total surface area (in $$cm^2$$) of each part?

Two identical hemispheres of maximum possible size are cut from a solid cube of side 14 $$cm$$. The bases of the hemispheres are part of the two opposite faces of cube. What is the total volume (in $$cm^3$$) of the remaining part of the cube?

Identical cubes of largest possible size are cut from a solid cuboid of size $$65 cm \times 26 cm \times 3.9 cm$$. What is the total surface area (in $$cm^2$$) of all the small cubes taken together?

A regular triangular pyramid is cut by 2 planes which are parallel to its base. The planes trisects the altitude of the pyramid. Volume of top, middle and bottom part is $$V_1, V_2$$ and $$V_3$$ respectively. What is the value of $$V_1 : V_2 : V_3$$?

What is the value of $$[(\cos 7A + \cos 5A)÷(\sin 7A - \sin 5A)]$$?

What is the value of $$\frac{[1 - \sin (90 - 2A)]}{[1 + \sin (90 + 2A)]}$$?

What is the value of $$\sin$$ 75° + $$\sin$$ 15°?