SSC CGL Tier-2 18-February-2018 Maths

A cube is placed inside a cone of radius 20 cm and height 10 cm, one of its face being on the base of the cone and vertices of opposite face touching the cone. What is the length (in cm) of side of the cube?

A cylinder of radius 4.5 cm and height 12 cm just fits in another cylinder completely with their axis perpendicular. What is the radius (in cm) of second cylinder?

A right circular cylinder has height 28 cm and radius of base 14 cm. Two hemispheres of radius 7 cm each are cut from each of the two bases of the cylinder. What is the total surface area (in $$cm^2$$) of the remaining part?

Two spheres of equal radius are taken out by cutting from a solid cube of side $$(12 + 4\surd3)$$ cm. What is the maximum volume (in $$cm^3$$) of each sphere?

Three toys are in a shape of cylinder, hemisphere and cone. The three toys have same base. Height of each toy is $$2\surd2$$ cm. What is the ratio of the total surface areas of cylinder, hemisphere and cone respectively?

A solid cube is cut into 27 identical cubes. What is the percentage increase in the total surface area?

A regular square pyramid has side of its base 20 cm and height 45 cm is melted and recast into regular triangular pyramids of equilateral base of side 10 cm and height $$10\surd3$$ cm. What are the total numbers of regular triangular pyramid?

What is the value of $$[(\sin 7x - \sin 5x) \div (\cos 7x + \cos 5x)] - [(\cos 6x - \cos 4x) \div (\sin 6x + \sin 4x)]$$?

What is the value of $$[(\cos^3 2\theta + 3 \cos 2\theta) \div (\cos^6 \theta - \sin^6 \theta)]$$?

What is the value of $$\tan \left(\frac{\pi}{4} + A\right) \times \tan \left(\frac{3\pi}{4} + A\right)?$$