Arts (English Medium) Class 12 - CBSE Important Questions

A function f : [– 4, 4] `rightarrow` [0, 4] is given by f(x) = `sqrt(16 - x^2)`. Show that f is an onto function but not a one-one function. Further, find all possible values of 'a' for which f(a) = `sqrt(7)`.

Let A = {3, 5}. Then number of reflexive relations on A is ______.

If `sin (sin^(−1)(1/5)+cos^(−1) x)=1`, then find the value of x.

Prove that `2tan^(-1)(1/5)+sec^(-1)((5sqrt2)/7)+2tan^(-1)(1/8)=pi/4`

Prove that `tan {pi/4 + 1/2 cos^(-1)  a/b} + tan {pi/4 - 1/2 cos^(-1)  a/b} = (2b)/a`

Solve: tan^-1 4 x + tan^-1 6x `= π/(4)`.

Evaluate `sin^-1 (sin  (3π)/4) + cos^-1 (cos π) + tan^-1 (1)`.

Draw the graph of cos^–1 x, where x ∈ [–1, 0]. Also, write its range.

`sin[π/3 + sin^-1 (1/2)]` is equal to ______.

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.

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 ______.