PUC Science इयत्ता ११ - Karnataka Board PUC Question Bank Solutions

If the sum of n terms of an A.P. be 3 n² − n and its common difference is 6, then its first term is

Determine the points in xy-plan are equidistant from the points A(1, –1, 0), B(2, 1, 2) and C(3, 2, –1).

Sum of all two digit numbers which when divided by 4 yield unity as remainder is

If the coefficients of 2nd, 3rd and 4th terms in the expansion of (1 + x)²ⁿ are in A.P., show that  \[2 n^2 - 9n + 7 = 0\]

Determine the points in yz-plane and are equidistant from the points A(1, –1, 0), B(2, 1, 2) and C(3, 2, –1).

If the coefficients of 2nd, 3rd and 4th terms in the expansion of (1 + x)ⁿ are in A.P., then find the value of n.

In n A.M.'s are introduced between 3 and 17 such that the ratio of the last mean to the first mean is 3 : 1, then the value of n is

If in the expansion of (1 + x)ⁿ, the coefficients of pth and qth terms are equal, prove that p + q = n + 2, where  \[p \neq q\]

If S_n denotes the sum of first n terms of an A.P. < a_n > such that

The first and last terms of an A.P. are 1 and 11. If the sum of its terms is 36, then the number of terms will be

If the sum of n terms of an A.P., is 3 n² + 5 n then which of its terms is 164?

If the sum of n terms of an A.P. is 2 n² + 5 n, then its nth term is

In the expansion of (1 + x)ⁿ the binomial coefficients of three consecutive terms are respectively 220, 495 and 792, find the value of n.

If a₁, a₂, a₃, .... a_n are in A.P. with common difference d, then the sum of the series sin d [cosec a₁cosec a₂ + cosec a₁ cosec a₃ + .... + cosec a_{n − 1} cosec a_n] is

Show that the points (0, 7, 10), (–1, 6, 6) and (–4, 9, 6) are the vertices of an isosceles right-angled triangle. 

In the arithmetic progression whose common difference is non-zero, the sum of first 3 n terms is equal to the sum of next n terms. Then the ratio of the sum of the first 2 n terms to the next 2 nterms is

If in the expansion of (1 + x)ⁿ, the coefficients of three consecutive terms are 56, 70 and 56, then find n and the position of the terms of these coefficients.

If a₁, a₂, a₃, .... a_n are in A.P. with common difference d, then the sum of the series sin d [sec a₁ sec a₂ + sec a₂ sec a₃ + .... + sec a_{n − 1} sec a_n], is