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

Find the values of m and n if : 
`4^(2m) = ( root(3)(16))^(-6/n) = (sqrt8)^2`

Solve x and y if : ( √32 )^x ÷ 2^{y + 1} = 1 and 8^y - 16^{4 - x/2} = 0

Evaluate : `[(-2/3)^-2]^3 xx (1/3)^-4 xx 3^-1 xx 1/6`

Simplify : `[ 3 xx 9^( n + 1 ) - 9 xx 3^(2n)]/[3 xx 3^(2n + 3) - 9^(n + 1 )]`

Solve : 3^x-1× 5^2y-3 = 225.

If `((a^-1b^2 )/(a^2b^-4))^7 ÷ (( a^3b^-5)/(a^-2b^3))^-5 = a^x . b^y` , find x + y.

If 3^{x + 1} = 9^{x - 3} , find the value of 2^{1 + x}.

If 2^x = 4^y = 8^z and `1/(2x) + 1/(4y) + 1/(8z) = 4` , find the value of x.

If m = `root(3)(15) and n = root(3)(14), "find the value of " m - n - 1/[ m^2 + mn + n^2 ]`

Evaluate : `4/(216)^(-2/3) + 1/(256)^(-3/4) + 2/(243)^(-1/5)`

If the following pair of the triangle is congruent? state the condition of congruency : 
In  ΔABC and ΔDEF,  ∠B = ∠E = 90^o; AC = DF and BC = EF.

If the following pair of the triangle is congruent? state the condition of congruency: 

In ΔABC and ΔPQR, BC = QR, ∠A = 90°, ∠C = ∠R = 40° and ∠Q = 50°.

On the sides AB and AC of triangle ABC, equilateral triangle ABD and ACE are drawn. Prove that: 

1. ∠CAD = ∠BAE
2. CD = BE

In the following diagram, ABCD is a square and APB is an equilateral triangle.

(i) Prove that: ΔAPD≅ ΔBPC
(ii) Find the angles of ΔDPC.

In the following diagram, AP and BQ are equal and parallel to each other. 

Prove that:  

1. ΔAOP ≅ ΔBOQ.
2. AB and PQ bisect each other.

In the following figure, OA = OC and AB = BC.

Prove that:
(i) ∠AOB = 90o
(ii) ΔAOD ≅ ΔCOD
(iii) AD = CD

In the following figure, OA = OC and AB = BC. 

Prove that: AD = CD

The following figure has shown a triangle ABC in which AB = AC. M is a point on AB and N is a point on AC such that BM = CN.
Prove that:  (i) AM = AN  (ii) ΔAMC ≅ ΔANB

The following figure shown a triangle ABC in which AB = AC. M is a point on AB and N is a point on AC such that BM = CN.

Prove that:  ΔAMC≅ ΔANB

The following figure has shown a triangle ABC in which AB = AC. M is a point on AB and N is a point on AC such that BM = CN.

Prove that: (i) BN = CM (ii) ΔBMC ≅ ΔCNB