Commerce (English Medium) कक्षा ११ - CBSE Question Bank Solutions for Mathematics

Evaluate the

(v)  \[\left( 3 + \sqrt{2} \right)^5 - \left( 3 - \sqrt{2} \right)^5\]

Evaluate the

(vi)  \[\left( 2 + \sqrt{3} \right)^7 + \left( 2 - \sqrt{3} \right)^7\]

Evaluate the

(vii) \[\left( \sqrt{3} + 1 \right)^5 - \left( \sqrt{3} - 1 \right)^5\]

Evaluate the

(viii)  \[\left( 0 . 99 \right)^5 + \left( 1 . 01 \right)^5\]

Evaluate the

(ix) \[\left( \sqrt{3} + \sqrt{2} \right)^6 - \left( \sqrt{3} - \sqrt{2} \right)^6\]

Evaluate the

(x) \[\left\{ a^2 + \sqrt{a^2 - 1} \right\}^4 + \left\{ a^2 - \sqrt{a^2 - 1} \right\}^4\]

Find  \[\left( a + b \right)^4 - \left( a - b \right)^4\] . Hence, evaluate \[\left( \sqrt{3} + \sqrt{2} \right)^4 - \left( \sqrt{3} - \sqrt{2} \right)^4\] .

Find \[\left( x + 1 \right)^6 + \left( x - 1 \right)^6\] . Hence, or otherwise evaluate \[\left( \sqrt{2} + 1 \right)^6 + \sqrt{2} - 1^6\] .

Using binomial theorem evaluate :

(i) (96)³

Using binomial theorem evaluate  .

(ii) (102)⁵

Using binomial theorem evaluate .

(iii) (101)⁴

Using binomial theorem evaluate .

Using binomial theorem, prove that \[2^{3n} - 7n - 1\] is divisible by 49, where \[n \in N\] .

Using binomial theorem, prove that  \[3^{2n + 2} - 8n - 9\]  is divisible by 64, \[n \in N\] .

Find the coefficient of: 

(i) x¹⁰ in the expansion of  \[\left( 2 x^2 - \frac{1}{x} \right)^{20}\]

Name the octants in which the following points lie: (5, 2, 3)

Find the coefficient of: 

(ii) x⁷ in the expansion of  \[\left( x - \frac{1}{x^2} \right)^{40}\]

Find the coefficient of: 

(iii)  \[x^{- 15}\]  in the expansion of  \[\left( 3 x^2 - \frac{a}{3 x^3} \right)^{10}\]

Find the coefficient of: 

(iv)  \[x^9\]  in the expansion of  \[\left( x^2 - \frac{1}{3x} \right)^9\]

Find the coefficient of: 

(v)  \[x^m\]  in the expansion of  \[\left( x + \frac{1}{x} \right)^n\]