Science (English Medium) इयत्ता १२ - CBSE Important Questions for Mathematics

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.

If A = [a_ij] is a square matrix of order 2 such that a_ij = `{(1","  "when i" ≠ "j"),(0","  "when"  "i" = "j"):},` then A² is ______.

If `|(α, 3, 4),(1, 2, 1),(1, 4, 1)|` = 0, then the value of α is ______.

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 y = e^ax. cos bx, then prove that

`(d^2y)/(dx^2) - 2ady/dx + (a^2 + b^2)y` = 0

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 `log (x^2 + y^2) = 2 tan^-1 (y/x)`, show that `(dy)/(dx) = (x + y)/(x - y)`

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)`.

If `d/dx` [f(x)] = ax+ b and f(0) = 0, then f(x) is equal to ______.

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