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

Find the middle terms(s) in the expansion of:

(ix)  \[\left( \frac{p}{x} + \frac{x}{p} \right)^9\]

Find the middle terms(s) in the expansion of:

(x)  \[\left( \frac{x}{a} - \frac{a}{x} \right)^{10}\]

Write the common difference of an A.P. whose nth term is xn + y.

Write the common difference of an A.P. the sum of whose first n terms is

Find the term independent of x in the expansion of the expression: 

(i) \[\left( \frac{3}{2} x^2 - \frac{1}{3x} \right)^9\]

Find the term independent of x in the expansion of the expression:

(ii)  \[\left( 2x + \frac{1}{3 x^2} \right)^9\]

If the sum of n terms of an AP is 2n² + 3n, then write its nth term.

Find the term independent of x in the expansion of the expression: 

(iii)  \[\left( 2 x^2 - \frac{3}{x^3} \right)^{25}\]

Find the term independent of x in the expansion of the expression: 

(iv) \[\left( 3x - \frac{2}{x^2} \right)^{15}\]

Find the term independent of x in the expansion of the expression: 

(v)  \[\left( \frac{\sqrt{x}}{3} + \frac{3}{2 x^2} \right)^{10}\]

Find the term independent of x in the expansion of the expression: 

(vi)  \[\left( x - \frac{1}{x^2} \right)^{3n}\]

Find the term independent of x in the expansion of the expression: 

(vii)  \[\left( \frac{1}{2} x^{1/3} + x^{- 1/5} \right)^8\]

If log 2, log (2^x − 1) and log (2^x + 3) are in A.P., write the value of x.

If the sums of n terms of two arithmetic progressions are in the ratio 2n + 5 : 3n + 4, then write the ratio of their m th terms.

Find the term independent of x in the expansion of the expression: 

(ix) \[\left( \sqrt[3]{x} + \frac{1}{2 \sqrt[3]{x}} \right)^{18} , x > 0\]

Find the term independent of x in the expansion of the expression: 

(x) \[\left( \frac{3}{2} x^2 - \frac{1}{3x} \right)^6\]

Write the value of n for which n th terms of the A.P.s 3, 10, 17, ... and 63, 65, 67, .... are equal.

If the coefficients of \[\left( 2r + 4 \right)\text{ th and } \left( r - 2 \right)\] th terms in the expansion of  \[\left( 1 + x \right)^{18}\]  are equal, find r.