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

Solve :
`4x + [ x - y ]/8 = 17`

`2y + x - [ 5y + 2 ]/3 = 2`

Evaluate : `(64)^(2/3) - root(3)(125) - 1/2^(-5) + (27)^(-2/3) xx (25/9)^(-1/2)`

If `[ 9^n. 3^2 . 3^n - (27)^n]/[ (3^m . 2 )^3 ] = 3^-3`

Show that : m - n = 1.

Solve for x : (13)^√x = 4⁴ - 3⁴ - 6

If 3^4x = ( 81 )^-1 and `10^(1/y) = 0.0001, "Find the value of " 2^(- x ) xx 16^y `

Solve : 3(2^x + 1) - 2^x+2 + 5 = 0.

If (a^m)ⁿ = a^m .aⁿ, find the value of : m(n - 1) - (n - 1)

Evaluate :
`[ 2^n xx 6^(m + 1 ) xx 10^( m - n ) xx 15^(m + n - 2)]/[4^m xx 3^(2m + n) xx 25^(m - 1)]`

Prove that : `( a + b + c )/( a^-1b^-1 + b^-1c^-1 + c^-1a^-1 ) = abc`

Prove that: `a^-1/(a^-1+b^-1) + a^-1/(a^-1 - b^-1) = (2b^2)/(b^2 - a^2 )`

Evaluate : `((x^q)/(x^r))^(1/(qr)) xx ((x^r)/(x^p))^(1/(rp)) xx ((x^p)/(x^q))^(1/(pq))`

An isosceles triangle ABC has AC = BC. CD bisects AB at D and ∠CAB = 55°.

Find: 

1. ∠DCB 
2. ∠CBD

In the figure given below, LM = LN; angle PLN = 110^o.

calculate: (i) ∠LMN
                 (ii) ∠MLN

In the figure, given below, AB = AC.

Prove that: ∠BOC = ∠ACD.

Calculate x :

Calculate x :

In the given figure; AB = BC and AD = EC.
Prove that: BD = BE.

Prove that a triangle ABC is isosceles, if: altitude AD bisects angles BAC.

Prove that a triangle ABC is isosceles, if: bisector of angle BAC is perpendicular to base BC.

In the given figure, AD = AB = AC, BD is parallel to CA and angle ACB = 65°. Find angle DAC.