Science (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

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) = ______.

If a matrix has 28 elements, what are the possible orders it can have? What if it has 13 elements?

In the matrix A = `[("a", 1, x),(2, sqrt(3), x^2 - y),(0, 5, (-2)/5)]`, write: The number of elements

In the matrix A = `[("a", 1, x),(2, sqrt(3), x^2 - y),(0, 5, (-2)/5)]`, write: elements a₂₃, a₃₁, a₁₂ 

Construct a 3 × 2 matrix whose elements are given by a_ij = e^i.x sinjx.

Find the values of a and b if A = B, where A = `[("a" + 4, 3"b"),(8, -6)]`, B = `[(2"a" + 2, "b"^2 + 2),(8, "b"^2 - 5"b")]`

Find non-zero values of x satisfying the matrix equation:

`x[(2x, 2),(3, x)] + 2[(8, 5x),(4, 4x)] = 2[(x^2 + 8, 24),(10, 6x)]`

Find the matrix A satisfying the matrix equation:

`[(2, 1),(3, 2)] "A" [(-3, 2),(5, -3)] = [(1, 0),(0, 1)]`

Find A, if `[(4),(1),(3)]` A = `[(-4, 8,4),(-1, 2, 1),(-3, 6, 3)]`