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

Find the intervals in which the function `f("x") = (4sin"x")/(2+cos"x") -"x";0≤"x"≤2pi` is strictly increasing or strictly decreasing. 

Using integration find the area of the triangle formed by negative x-axis and tangent and normal to the circle `"x"^2 + "y"^2 = 9  "at" (-1,2sqrt2)`.

If A and B are square matrices of the same order 3, such that ∣A∣ = 2 and AB = 2I, write the value of ∣B∣.

If f(x) = x + 1, find `d/dx (fof) (x)`

if  `vec"a"= 2hat"i" + 3hat"j"+ hat"k", vec"b" = hat"i" -2hat"j" + hat"k" and vec"c" = -3hat"i" + hat"j" + 2hat"k", "find" [vec"a" vec"b" vec"c"]`

Choose the correct option from the given alternatives :

Let f(x) = x³ – 6x² + 9x + 18, then f(x) is strictly decreasing in ______.

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.