Arts (English Medium) कक्षा १२ - CBSE Important Questions

If for any 2 x 2 square matrix A, `A("adj"  "A") = [(8,0), (0,8)]`, then write the value of |A|

If A is a skew symmetric matric of order 3, then prove that det A  = 0

If A is a square matrix of order 3 with |A| = 4 , then the write the value of |-2A| . 

If `[(2, 0),(5, 4)]` = P + Q, where P is symmetric, and Q is a skew-symmetric matrix, then Q is equal to ______.

If `[(1, 2, 1),(2, 3, 1),(3, a, 1)]` is non-singular matrix and a ∈ A, then the set A is ______.

If | A | = | kA |, where A is a square matrix of order 2, then sum of all possible values of k is ______.

If \[\begin{vmatrix}2x & 5 \\ 8 & x\end{vmatrix} = \begin{vmatrix}6 & - 2 \\ 7 & 3\end{vmatrix}\] , write the value of x.

Find the inverse of the following matrix, using elementary transformations: 

`A= [[2 , 3 , 1 ],[2 , 4 , 1],[3 , 7 ,2]]`

If `"A" = [(1,1,1),(1,0,2),(3,1,1)]`, find A^-1. Hence, solve the system of equations x + y + z = 6, x + 2z = 7, 3x + y + z = 12.

Using the matrix method, solve the following system of linear equations:

`2/x + 3/y + 10/z` = 4, `4/x - 6/y + 5/z` = 1, `6/x + 9/y - 20/z` = 2.

 If x=a sin 2t(1+cos 2t) and y=b cos 2t(1−cos 2t), find `dy/dx `

if x^x+x^y+y^x=a^b, then find `dy/dx`.

If e^y (x + 1) = 1, show that `(d^2y)/(dx^2) = (dy/dx)^2`.

If sin y = xsin(a + y) prove that `(dy)/(dx) = sin^2(a + y)/sin a`

If x^y - y^x = a^b, find `(dy)/(dx)`.

If f(x) = x + 1, find `d/dx (fof) (x)`

If x = `e^(x/y)`, then prove that `dy/dx = (x - y)/(xlogx)`.

The function f(x) = x |x| is ______.

If y = `sqrt(ax + b)`, prove that `y((d^2y)/dx^2) + (dy/dx)^2` = 0.

If f(x) = `{{:(ax + b; 0 < x ≤ 1),(2x^2 - x; 1 < x < 2):}` is a differentiable function in (0, 2), then find the values of a and b.