SSC CGL Tier-2 9-March-2018 Maths-shift-1

A cone of radius 90 cm and height 120 cm stands on its base. It is cut into 3 parts by 2 cuts parallel to its base such that the height of the three parts (from top to bottom) are in ratio of 1 : 2 : 3. What is the total surface area (in cm$$^2$$) of the middle part?

The curved surface area of a cylinder is 594 cm$$^2$$ and its volume is 1336.5 cm$$^3$$. What is the height (in cm) of the cylinder?

A hollow cylinder is made up of metal. The difference between outer and inner curved surface area of this cylinder is 352 cm$$^2$$. Height of the cylinder is 28 cm. If the total surface area of this hollow cylinder is 2640 cm$$^2$$, then what are the inner and outer radius (in cm)?

A solid metal sphere has radius 14 cm. It is melted to form small cones of radius 1.75 cm and height 3.5 cm. How many small cones will be obtained from the sphere?

A metallic hemispherical bowl is made up of steel. The total steel used in making the bowl is $$486\pi cm^3$$. The bowl can hold $$144\pi cm^3$$ water. What is the thickness (in $$cm$$) of bowl and the curved surface area (in $$cm^2$$) of outer side?

There is a box of cuboid shape. The smallest side of the box is 20 cm and largest side is 40 cm. Which of the following can be volume (in cm$$^3$$) of the box?

A pyramid has a square base, whose side is 8 cm. If the height of pyramid is 16 cm, then what is the total surface area (in cm$$^2$$) of the pyramid?

What is the value of $$\frac{2(1 - \sin^2 \theta)\cosec^2 \theta}{\cot^2 \theta(1 + \tan^2 \theta)} - 1$$?

What is the value of $$\frac{\cos 2A + 2\cos^2 A - 2\cos 2A \cos A}{\sin 2A - 2\sin^2 A \sin 2A }$$?

What is the value of cos 15° - cos 165°?