Arts (English Medium) Class 12 - CBSE Question Bank Solutions

If cos^–1α + cos^–1β + cos^–1γ = 3π, then α(β + γ) + β(γ + α) + γ(α + β) equals ______.

The number of real solutions of the equation `sqrt(1 + cos 2x) = sqrt(2) cos^-1 (cos x)` in `[pi/2, pi]` is ______.

If cos^–1x > sin^–1x, then ______.

If y = `2 tan^-1x + sin^-1 ((2x)/(1 + x^2))` for all x, then ______ < y < ______.

The value of cot^–1(–x) for all x ∈ R in terms of cot^–1x is ______.

The matrix A = `[(0, 0, 5),(0, 5, 0),(5, 0, 0)]` is a ______.

If A and B are matrices of same order, then (3A –2B)′ is equal to______.

If two matrices A and B are of the same order, then 2A + B = B + 2A.

For the non singular matrix A, (A′)^–1 = (A^–1)′.

AB = AC ⇒ B = C for any three matrices of same order.

If A = `[(3, -4),(1, 1),(2, 0)]` and B = `[(2, 1, 2),(1, 2, 4)]`, then verify (BA)² ≠ B²A² 

Show by an example that for A ≠ O, B ≠ O, AB = O

Given A = `[(2, 4, 0),(3, 9, 6)]` and B = `[(1, 4),(2, 8),(1, 3)]` is (AB)′ = B′A′? 

If X and Y are 2 × 2 matrices, then solve the following matrix equations for X and Y.

2X + 3Y = `[(2, 3),(4, 0)]`, 3Y + 2Y = `[(-2, 2),(1, -5)]`

Find A^–1 if A = `[(0, 1, 1),(1, 0, 1),(1, 1, 0)]` and show that A^–1 = `("A"^2 - 3"I")/2`.

If A = `[(1, 2, 0),(-2, -1, -2),(0, -1, 1)]`, find A^–1. Using A^–1, solve the system of linear equations x – 2y = 10, 2x – y – z = 8, –2y + z = 7.

Using matrix method, solve the system of equations
3x + 2y – 2z = 3, x + 2y + 3z = 6, 2x – y + z = 2.

Given A = `[(2, 2, -4),(-4, 2, -4),(2, -1, 5)]`, B = `[(1, -1, 0),(2, 3, 4),(0, 1, 2)]`, find BA and use this to solve the system of equations y + 2z = 7, x – y = 3, 2x + 3y + 4z = 17.

If A is a matrix of order 3 × 3, then number of minors in determinant of A are ______.

The sum of the products of elements of any row with the co-factors of corresponding elements is equal to ______.