Science (English Medium) इयत्ता १२ - CBSE Question Bank Solutions

Integrate the function:

`sqrt(x^2 + 3x)`

Integrate the function:

`sqrt(1+ x^2/9)`

`int sqrt(1+ x^2)  dx` is equal to ______.

`int sqrt(x^2 - 8x + 7) dx` is equal to ______.

Consider `f:R - {-4/3} -> R - {4/3}` given by f(x) = `(4x + 3)/(3x + 4)`. Show that f is bijective. Find the inverse of f and hence find `f^(-1) (0)` and X such that `f^(-1) (x) = 2`

Find `int dx/(5 - 8x - x^2)`

Evaluate : `int_2^3 3^x dx`

Show that all the diagonal elements of a skew symmetric matrix are zero.

Find `int (2x)/(x^2 + 1)(x^2 + 2)^2 dx`

Find the shortest distance between the lines `vecr = (4hati - hatj) + lambda(hati+2hatj-3hatk)` and `vecr = (hati - hatj + 2hatk) + mu(2hati + 4hatj - 5hatk)`

If \[A = \begin{bmatrix}1 & 2 \\ 0 & 3\end{bmatrix}\] is written as B + C, where B is a symmetric matrix and C is a skew-symmetric matrix, then B is equal to.

For what value of x, is the matrix \[A = \begin{bmatrix}0 & 1 & - 2 \\ - 1 & 0 & 3 \\ x & - 3 & 0\end{bmatrix}\] a skew-symmetric matrix?

If a matrix A is both symmetric and skew-symmetric, then

The matrix \[\begin{bmatrix}0 & 5 & - 7 \\ - 5 & 0 & 11 \\ 7 & - 11 & 0\end{bmatrix}\] is

If A is a square matrix, then AA is a

If A and B are symmetric matrices, then ABA is

If A = [a_ij] is a square matrix of even order such that a_ij = i² − j², then 

If \[A = \begin{bmatrix}2 & 0 & - 3 \\ 4 & 3 & 1 \\ - 5 & 7 & 2\end{bmatrix}\]  is expressed as the sum of a symmetric and skew-symmetric matrix, then the symmetric matrix is