SSC CGL Tier-2 21-February-2018 Maths

The height of a cone is $$24 cm$$ and the area of the base is $$154 cm^2$$. What is the curved surface area (in $$cm^2$$) of the cone?

A right circular solid cylinder has radius of base $$7 cm$$ and height is $$28 cm$$. It is melted to form a cuboid such that the ratio of its side is 2 : 3 : 6. What is the total surface area (in $$cm^2$$) cuboid?

A right circular cylinder is formed. A = sum of total surface area and the area of the two bases. B = the curved surface area of this cylinder. If A : B = 3 : 2 and the volume of cylinder is 4312 $$cm^3$$, then what is the sum of area (in $$cm^2$$) of the two bases of this cylinder?

A solid sphere has a radius 21 cm. It is melted to form a cube. 20% material is wasted in this process. The cube is melted to form hemisphere. In this process 20% material is wasted. The hemisphere is melted to form two spheres of equal radius. 20% material was also wasted in this process. What is the radius (in cm) of each new sphere?

A solid hemisphere has radius 14 cm. It is melted to form a cylinder such that the ratio of its curved surface area and total surface area is 2 : 3. What is the radius (in cm) of its base?

A cuboid has dimensions $$8 cm \times 10 cm \times 12 cm$$. It is cut into small cubes of side $$2 cm$$. What is the percentage increase in the total surface area?

A pyramid has a square base. The side of square is $$12 cm$$ and height of pyramid is $$21 cm$$. The pyramid is cut into 3 parts by 2 cuts parallel to its base. The cuts are at height of $$7 cm$$ and $$14 cm$$ respectively from the base. What is the difference (in $$cm^3$$) in the volume of top most and bottom most part?

What is the value of $$\frac{\left\{(\sin 4x + \sin 4y) [(\tan 2x - 2y)]\right\}}{(\sin 4x - \sin 4y)}$$?

What is the value of $$\frac{(32 \cos^6 x - 48 \cos^4 x + 18 \cos^2 x - 1)}{[4 \sin x \cos x \sin (60 - x) \cos (60 - x) \sin (60 + x) \cos (60 + x)]}$$?

What is the value of $$\frac{\left[2 \cot \times \frac{(p - A)}{2}\right]}{\left[1 + \tan^2 \times \frac{(2p - A)}{2}\right]}$$?