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

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 ______.

Let f(x) = x|x|, for all x ∈ R. Discuss the derivability of f(x) at x = 0

If y = tan(x + y), find `("d"y)/("d"x)`

If y = tanx + secx, prove that `("d"^2y)/("d"x^2) = cosx/(1 - sinx)^2`

Differentiate `tan^-1 (sqrt(1 - x^2)/x)` with respect to`cos^-1(2xsqrt(1 - x^2))`, where `x ∈ (1/sqrt(2), 1)`

Let f(x)= |cosx|. Then, ______.

Differential coefficient of sec (tan^–1x) w.r.t. x is ______.

If u = `sin^-1 ((2x)/(1 + x^2))` and v = `tan^-1 ((2x)/(1 - x^2))`, then `"du"/"dv"` is ______.