(English Medium) ICSE Class 9 - CISCE Question Bank Solutions

Evaluate the following:

`7^-4 xx (343)^(2/3) ÷ (49)^(-1/2)`

Evaluate the following:

`(64/216)^(2/3) xx (16/36)^(-3/2)`

State true or false in the following:
If log ₂ 8 = 3, then log ₈ 2 = `(1)/(3)`

Construct an isosceles triangle in which: Base BC = 6.4 cm and side AB = 7.2 cm

Construct an isosceles triangle in which: Base QR = 5.2 cm and the altitude PM = 4.8 cm

Construct an isosceles triangle in which: Base DE = 6 cm and ∠F = 45°

Construct an isosceles triangle using the given data: Altitude RM = 5cm and vertex ∠R = 120°

Construct an isosceles triangle using the given data: Altitude AD = 4cm and vertex ∠A = 90°

Construct an isosceles triangle using the given data: Altitude XT = 6.8cm and vertex ∠X = 30°

Construct an isosceles right-angled triangle whose hypotenuse is of length 6 cm.

M and N divide the side AB of ΔABC into three equal parts. Line segments MP and NQ are both parallel to BC, and meet AC in P and Q respectively. Prove that P and Q divide AC into three equal parts.

In the given figure, the lines l, m and n are parallel to each other. D is the midpoint of CE. Find: a. BC, b. EF, c. CG and d. BD.

Find the length of the perpendicular of a triangle whose base is 5cm and the hypotenuse is 13cm. Also, find its area.

Find the length of the hypotenuse of a triangle whose other two sides are 24cm and 7cm.

Calculate the area of a right-angled triangle whose hypotenuse is 65cm and one side is 16cm.

A man goes 10 m due east and then 24 m due north. Find the distance from the straight point.

A ladder 25m long reaches a window of a building 20m above the ground. Determine the distance of the foot of the ladder from the building.

A right triangle has hypotenuse p cm and one side q cm. If p - q = 1, find the length of third side of the triangle.

A ladder 15m long reaches a window which is 9m above the ground on one side of a street. Keeping its foot at the same point, the ladder is turned to other side of the street to reach a window 12m high. Find the width of the street.

The foot of a ladder is 6m away from a wall and its top reaches a window 8m above the ground. If the ladder is shifted in such a way that its foot is 8m away from the wall to what height does its tip reach?