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

If x^p occurs in the expansion of `(x^2 + 1/x)^(2n)`, prove that its coefficient is `(2n!)/(((4n - p)/3)!((2n + p)/3)!)`

Find the term independent of x in the expansion of (1 + x + 2x³) `(3/2 x^2 - 1/(3x))^9`

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 ______.