Commerce (English Medium) कक्षा १२ - CBSE Question Bank Solutions for Mathematics

Evaluate the following integrals: `int(x - 2)/sqrt(x + 5).dx`

Integrate the following functions w.r.t. x : `(e^(2x) + 1)/(e^(2x) - 1)`

Let the function f: R → R be defined by f(x) = 4x – 1, ∀ x ∈ R. Then, show that f is one-one.

Let f: R → R be the function defined by f(x) = 4x – 3 ∀ x ∈ R. Then write f^–1 

If A = {a, b, c, d} and f = {a, b), (b, d), (c, a), (d, c)}, show that f is one-one from A onto A. Find f^–1

Show that the function f: R → R defined by f(x) = `x/(x^2 + 1)`, ∀ ∈ + R , is neither one-one nor onto

Let f, g: R → R be two functions defined as f(x) = |x| + x and g(x) = x – x ∀ x ∈ R. Then, find f o g and g o f

Let R be the set of real numbers and f: R → R be the function defined by f(x) = 4x + 5. Show that f is invertible and find f^–1.

Let N be the set of natural numbers and the function f: N → N be defined by f(n) = 2n + 3 ∀ n ∈ N. Then f is ______.

Set A has 3 elements and the set B has 4 elements. Then the number of injective mappings that can be defined from A to B is ______.

Let f: R → R be defined by f(x) = 3x – 4. Then f^–1(x) is given by ______.

Let f: R → R be defined by f(x) = x² + 1. Then, pre-images of 17 and – 3, respectively, are ______.

The domain of the function f: R → R defined by f(x) = `sqrt(x^2 - 3x + 2)` is ______

Consider the set A containing n elements. Then, the total number of injective functions from A onto itself is ______

Let A be a finite set. Then, each injective function from A into itself is not surjective.

For sets A, B and C, let f: A → B, g: B → C be functions such that g o f is injective. Then both f and g are injective functions.

For sets A, B and C, let f: A → B, g: B → C be functions such that g o f is surjective. Then g is surjective.

Let D be the domain of the real valued function f defined by f(x) = `sqrt(25 - x^2)`. Then, write D

Let f: R → R be the function defined by f(x) = 2x – 3 ∀ x ∈ R. write f^–1 

If f: R → R is defined by f(x) = x² – 3x + 2, write f(f (x))