The shape of a pencil with one end sharpened is the combination of a and a _____.

Find the ratio of the volumes of a solid right circular cylinder and a solid right circular cone of equal radii and equal heights.

The radius of a right circular cylinder and a hemisphere is equal and their volumes are also equal. The height of the hemisphere is greater than the height of the cylinder by (a) 25% (b) 50% (c) 100% (d) 200%

If the height and base area of a solid hemisphere and a solid cylinder are same, then the ratio of their volume is (a) 1 : 3 (b) 1 : 2 (c) 2 : 3 (d) 3 : 4

The lower part of an ice-cream is conical and upper part is hemispheric with same circular base. If the height of the cone is 9cm and radius of the base 2.5 cm. Find the volume of the ice-cream.

If A = and B = , then the order of AB is: (a) 2 × 2 (b) 2 × 1 (c) 1 × 2 (d) AB is not possible

Statement 1: The point which is equidistant from three non-collinear points D, E and F is the circumcentre of △DEF. Statement 2: The incentre of a triangle is the point where the bisectors of the angles intersect. (a) Both statements are true. (b) Both statements are false. (c) Statement 1 is true and Statement 2 is false. (d) Statement 1 is false and Statement 2 is true.

If A = , then A² is equal to: (a) (b) (c) (d)

Assertion (A): The probability of getting a number greater than 6 on throwing a die is . Reason (R): The possible outcomes on throwing a die are 1, 2, 3, 4, 5 and 6. (a) A is true and R is false. (b) A is false and R is true. (c) Both A and R are true and R is the correct explanation of A. (d) Both A and R are true but R is not the correct explanation of A.

(x + 3), 1, (3x − 7) and −5 are in proportion. The value of x is : (a) −1 (b) 1 (c) −5 (d) 5

The marked price of a refrigerator is ₹ 12,000 and GST paid by the customer is ₹ 2,160. The rate of GST is: (a) 5% (b) 12% (c) 18% (d) 28%

Mr Anuj deposits ₹500 per month for 18 months in a recurring deposit account at a certain rate. If he earns ₹570 as interest at the time of maturity, then his matured amount is: (a) ₹(500 × 18 + 570) (b) ₹(500 × 19 + 570) (c) ₹(500 × 18 × 19 + 570) (d) ₹(500 × 9 × 19 + 570)

A and B opened a recurring deposit account in a bank which is paying simple interest at 9% per annum. A deposited ₹ 1,500 for one year and B deposited ₹ 1,200 for 15 months. The amount invested by : (a) A is ₹ 27 more than B (b) A is ₹ 300 more than B (c) A is ₹ 300 less than B (d) Both A and B are same (₹ 18,000)