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

If log ₁₀ x = p, express the following in terms of x : 10^p 

If log ₁₀ x = p, express the following in terms of x: 10^p+1 

If log ₁₀ x = p, express the following in terms of x: 10^2p-3 

If log ₁₀ x = p, express the following in terms of x: 10^2-p 

If log ₁₀ x = a, log ₁₀ y = b and log ₁₀ z = 2a - 3b, express z in terms of x and y.

If Iog ₁₀ a = x, log ₁₀ b = y and log ₁₀ c = z, find 
10^2x-3 in term of a

If Iog ₁₀ a = x, log ₁₀ b = y and log ₁₀ c = z, find 
10^{3y -1} in terms of b

If log ₁₀ a = x,  and log ₁₀ c = z, find
`10^(x-y+z)` in terms of a, b and c

State true or false in the following:
If log ₁₀ 100 = 2, then 10² = 100

State true or false in the following:
If log ₁₀ p = q, then 10^p = q

In the given figure, ∠Q: ∠R = 1: 2. Find:
a. ∠Q
b. ∠R

The exterior angles, obtained on producing the side of a triangle both ways, are 100° and 120°. Find all the angles of the triangle.

Use the given figure to find the value of x in terms of y. Calculate x, if y = 15°.

In a triangle PQR, ∠P + ∠Q = 130° and ∠P + ∠R = 120°. Calculate each angle of the triangle.

The angles of a triangle are (x + 10)°, (x + 30)° and (x - 10)°. Find the value of 'x'. Also, find the measure of each angle of the triangle.

Use the given figure to find the value of y in terms of p, q and r.

In the figure given below, if RS is parallel to PQ, then find the value of ∠y.

In a triangle PQR, the internal bisectors of angles Q and R meet at A and the external bisectors of the angles Q and R meet at B. Prove that: ∠QAR + ∠QBR = 180°.

Use the given figure to show that: ∠p + ∠q + ∠r = 360°.

In a triangle ABC. If D is a point on BC such that ∠CAD = ∠B, then prove that: ∠ADC = ∠BAC.