Arts (English Medium) इयत्ता १२ - CBSE Question Bank Solutions for Mathematics

If the set A contains 5 elements and the set B contains 6 elements, then the number of one-one and onto mappings from A to B is ______.

Let A = {1, 2, 3, ...n} and B = {a, b}. Then the number of surjections from A into B is ______.

Let f: R → R be defined by f(x) = `1/x` ∀ x ∈ R. Then f is ______.

Which of the following functions from Z into Z are bijections?

Let f: R → R be the functions defined by f(x) = x³ + 5. Then f^–1(x) is ______.

Let f: R – `{3/5}` → R be defined by f(x) = `(3x + 2)/(5x - 3)`. Then ______.

Let f: `[2, oo)` → R be the function defined by f(x) = x² – 4x + 5, then the range of f is ______.

Let f: R → R be given by f(x) = tan x. Then f^–1(1) is ______.

If f(x) = (4 – (x – 7)³}, then f^–1(x) = ______.

Let A = {0, 1} and N be the set of natural numbers. Then the mapping f: N → A defined by f(2n – 1) = 0, f(2n) = 1, ∀ n ∈ N, is onto.

If A is square matrix such that A² = A, show that (I + A)³ = 7A + I..

If A is a square matrix such that A² = I, then (A – I)³ + (A + I)³ –7A is equal to ______.

Matrix addition is associative as well as commutative.

Matrix multiplication is commutative.

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

(AB)^–1 = A^–1. B^–1, where A and B are invertible matrices satisfying commutative property with respect to multiplication.

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.