Science (English Medium) इयत्ता ११ - CBSE Question Bank Solutions

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.

Find the distance between the following pairs of points: 

P(1, –1, 0) and Q(2, 1, 2)

Find the distance between the following pairs of point: 

A(3, 2, –1) and B(–1, –1, –1).

If \[\frac{3 + 5 + 7 + . . . + \text { upto n terms }}{5 + 8 + 11 + . . . . \text { upto 10 terms }}\] 7, then find the value of n.

Find the distance between the points P and Q having coordinates (–2, 3, 1) and (2, 1, 2).

If the coefficients of (2r + 1)th term and (r + 2)th term in the expansion of (1 + x)⁴³ are equal, find r.

If m th term of an A.P. is n and nth term is m, then write its pth term.

Prove that the coefficient of (r + 1)th term in the expansion of (1 + x)^{n + 1} is equal to the sum of the coefficients of rth and (r + 1)th terms in the expansion of (1 + x)ⁿ.

Using distance formula prove that the following points are collinear:

A(4, –3, –1), B(5, –7, 6) and C(3, 1, –8)

If the sums of n terms of two AP.'s are in the ratio (3n + 2) : (2n + 3), then find the ratio of their 12th terms.