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

If the middle term of `(1/x + x sin x)^10` is equal to `7 7/8`, then value of x is ______.

In the expansion of `(x^2 - 1/x^2)^16`, the value of constant term is ______.

Middle term in the expansion of (a³ + ba)²⁸ is ______.

The position of the term independent of x in the expansion of `(sqrt(x/3) + 3/(2x^2))^10` is ______.

The number of terms in the expansion of [(2x + y³)⁴]⁷ is 8.

The sum of coefficients of the two middle terms in the expansion of (1 + x)^2n–1 is equal to ^2n–1C_n. 

The last two digits of the numbers 3⁴⁰⁰ are 01.

If the expansion of `(x - 1/x^2)^(2n)` contains a term independent of x, then n is a multiple of 2.

The first term of an A.P. is a, the second term is b and the last term is c. Show that the sum of the A.P. is `((b + c - 2a)(c + a))/(2(b - a))`.

The p^th term of an A.P. is a and q^th term is b. Prove that the sum of its (p + q) terms is `(p + q)/2[a + b + (a - b)/(p - q)]`.

If there are (2n + 1) terms in an A.P., then prove that the ratio of the sum of odd terms and the sum of even terms is (n + 1) : n

Find the sum of first 24 terms of the A.P. a₁, a₂, a₃, ... if it is known that a₁ + a₅ + a₁₀ + a₁₅ + a₂₀ + a₂₄ = 225.

The product of three numbers in A.P. is 224, and the largest number is 7 times the smallest. Find the numbers

Show that (x² + xy + y²), (z² + xz + x²) and (y² + yz + z²) are consecutive terms of an A.P., if x, y and z are in A.P.

If the sum of m terms of an A.P. is equal to the sum of either the next n terms or the next p terms, then prove that `(m + n) (1/m - 1/p) = (m + p) (1/m - 1/n)`

If a₁, a₂, ..., an are in A.P. with common difference d (where d ≠ 0); then the sum of the series sin d (cosec a1 cosec a₂ + cosec a₂ cosec a₃ + ...+ cosec a_n–1 cosec a_n) is equal to cot a₁ – cot a_n 

If a, b, c, d are four distinct positive quantities in A.P., then show that bc > ad

In an A.P. the p^th term is q and the (p + q)^th term is 0. Then the q^th term is ______.

The first term of an A.P.is a, and the sum of the first p terms is zero, show that the sum of its next q terms is `(-a(p + q)q)/(p - 1)`

A man saved Rs 66000 in 20 years. In each succeeding year after the first year he saved Rs 200 more than what he saved in the previous year. How much did he save in the first year?