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

If A = {1, 2, 3} and f, g are relations corresponding to the subset of A × A indicated against them, which of f, g is a function? Why?
f = {(1, 3), (2, 3), (3, 2)}
g = {(1, 2), (1, 3), (3, 1)}

Let f: R → R be defined by f(x) = sin x and g: R → R be defined by g(x) = x 2 , then f o g is ______.

Let f, g: R → R be defined by f(x) = 2x + 1 and g(x) = x² – 2, ∀ x ∈ R, respectively. Then, find gof

If A = {a, b, c, d} and the function f = {(a, b), (b, d), (c, a), (d, c)}, write f^–1 

If the mappings f and g are given by f = {(1, 2), (3, 5), (4, 1)} and g = {(2, 3), (5, 1), (1, 3)}, write f o g.

If functions f: A → B and g: B → A satisfy gof = I_A, then show that f is one-one and g is onto

Functions f , g: R → R are defined, respectively, by f(x) = x 2 + 3x + 1, g(x) = 2x – 3, find f o g

Functions f , g: R → R are defined, respectively, by f(x) = x 2 + 3x + 1, g(x) = 2x – 3, find g o f

Functions f , g: R → R are defined, respectively, by f(x) = x 2 + 3x + 1, g(x) = 2x – 3, find f o f

Functions f , g: R → R are defined, respectively, by f(x) = x 2 + 3x + 1, g(x) = 2x – 3, find g o g

Let f: R → R be defined by f(x) = `{{:(2x",", x > 3),(x^2",", 1 < x ≤ 3),(3x",", x ≤ 1):}`. Then f(–1) + f(2) + f(4) is ______.

Let f: R → R be defined by f(x) = `x/sqrt(1 + x^2)`. Then (f o f o f) (x) = ______.

Show that a matrix which is both symmetric and skew symmetric is a zero matrix.

Express the matrix A as the sum of a symmetric and a skew-symmetric matrix, where A = `[(2, 4, -6),(7, 3, 5),(1, -2, 4)]`

Let A = `[(2, 3),(-1, 2)]`. Then show that A² – 4A + 7I = O. Using this result calculate A⁵ also.

If A and B are symmetric matrices of the same order, then (AB′ –BA′) is a ______.

If A and B are two skew-symmetric matrices of same order, then AB is symmetric matrix if ______.

If A = `[(0, 1),(1, 1)]` and B = `[(0, -1),(1, 0)]`, show that (A + B)(A – B) ≠ A² – B² 

Show that A′A and AA′ are both symmetric matrices for any matrix A.

If A = `[(cosalpha, sinalpha),(-sinalpha, cosalpha)]`, and A^–1 = A′, find value of α