Real Numbers — Maths STD 10 — Question

Ayush starts walking from his house to office. Instead of going to the office directly, he goes to a bank first, from there to his daughter’s school and then reaches the office. What is the extra distance travelled by Ayush in reaching the office? (Assume that all distance covered are in straight lines). If the house is situated at (2, 4), bank at (5, 8), school at (13, 14) and office at (13, 26) and coordinates are in kilometers.

A cylinder and a cone are of the same base radius and of same height. Find the ratio of the value of the cylinder to that of the cone.

A spherical cannon ball 28cm in diameter is melted and recast into a right circular conical mould, base of which is 35cm in diameter. Find the height of the cone.

If R(x, y) is a point on the line segment joining the points P(a, b) and Q(b, a), then prove that x + y = a + b.

For what value of k(k > 0) is the area of the triangle with vertices (-2, 5), (k, -4) and (2k + 1, 10) equal to 53 square units?

Three different coins are tossed together. Find the probability of getting
(i) Exactly two heads
(ii) At least two heads
(iii) at least two tails

Find the area of an isoscale triangle each of whose equal sides is 13cm and whose base is 24cm.

All kings, queens and aces are removed from a pack of 52 cards. The remaining cards are well shuffled and then a card is drawn from it. Find the probability that the drawn card is
(i) A black face card
(ii) A red card