Science (English Medium) Class 11 - CBSE Question Bank Solutions

If a, b, c and d in any binomial expansion be the 6th, 7th, 8th and 9th terms respectively, then prove that \[\frac{b^2 - ac}{c^2 - bd} = \frac{4a}{3c}\].

If the sum of first n even natural numbers is equal to k times the sum of first n odd natural numbers, then k =

If the coefficients of three consecutive terms in the expansion of (1 + x)ⁿ be 76, 95 and 76, find n.

If the first, second and last term of an A.P are a, b and 2a respectively, then its sum is

If, S₁ is the sum of an arithmetic progression of 'n' odd number of terms and S₂ the sum of the terms of the series in odd places, then \[\frac{S_1}{S_2}\] = 

If in an A.P., S_n = n²p and S_m = m²p, where S_r denotes the sum of r terms of the A.P., then S_p is equal to

If the 6th, 7th and 8th terms in the expansion of (x + a)ⁿ are respectively 112, 7 and 1/4, find x, a, n.

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If in an A.P., the pth term is q and (p + q)th term is zero, then the qth term is

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The 10th common term between the A.P.s 3, 7, 11, 15, ... and 1, 6, 11, 16, ... is

If the 2nd, 3rd and 4th terms in the expansion of (x + a)ⁿ are 240, 720 and 1080 respectively, find x, a, n.

Find a, b and n in the expansion of (a + b)ⁿ, if the first three terms in the expansion are 729, 7290 and 30375 respectively.

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\[\text { If in an A . P } . S_n = n^2 q \text { and } S_m = m^2 q, \text { where } S_r \text{ denotes the sum of r terms of the A . P  . , then }S_q \text { equals }\]

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Let S_n denote the sum of first n terms of an A.P. If S_2n = 3S_n, then S_3n : S_n is equal to

If the term free from x in the expansion of  \[\left( \sqrt{x} - \frac{k}{x^2} \right)^{10}\]  is 405, find the value of k.

If p is a real number and if the middle term in the expansion of  \[\left( \frac{p}{2} + 2 \right)^8\] is 1120, find p.

Write the middle term in the expansion of `((2x^2)/3 + 3/(2x)^2)^10`.

Write the middle term in the expansion of  \[\left( x + \frac{1}{x} \right)^{10}\]

Write the coefficient of the middle term in the expansion of \[\left( 1 + x \right)^{2n}\] . 

Find the sum of the coefficients of two middle terms in the binomial expansion of  \[\left( 1 + x \right)^{2n - 1}\]

Write the total number of terms in the expansion of  \[\left( x + a \right)^{100} + \left( x - a \right)^{100}\] .