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

Find the value of the following:

If sin⁻¹ x = y, then

`tan^(-1) sqrt3 - sec^(-1)(-2)` is equal to ______.

Find the value of the following:

`cos^(-1) (cos  (13pi)/6)`

Find the value of the following:

`tan^(-1) (tan  (7x)/6)`

Prove that:

`tan^-1  ((sqrt(1 + x) - sqrt(1 - x))/(sqrt(1 + x) + sqrt(1 - x))) = pi/4 - 1/2 cos^-1 x`, for `- 1/sqrt2 <= x <= 1`

[Hint: put x =  cos 2θ]

The bookshop of a particular school has 10 dozen chemistry books, 8 dozen physics books, 10 dozen economics books. Their selling prices are Rs 80, Rs 60 and Rs 40 each respectively. Find the total amount the bookshop will receive from selling all the books using matrix algebra.

Evaluate the determinant.

`|(2,4),(-5, -1)|`

Which of the following is correct?

A. Determinant is a square matrix.

B. Determinant is a number associated to a matrix.

C. Determinant is a number associated to a square matrix.

D. None of these

Prove that the function f (x) = 5x – 3 is continuous at x = 0, at x = – 3 and at x = 5.

Examine the continuity of the function f(x) = 2x² – 1 at x = 3.

Prove that the function `f(x) = x^n` is continuous at x = n, where n is a positive integer.

Is the function f defined by f(x)= `{(x, if x<=1),(5, if x > 1):}`  continuous at x = 0? At x = 1? At x = 2?

Find all point of discontinuity of f, where f is defined by `f (x) = {(2x + 3, if x<=2),(2x - 3, if x > 2):}`

Find all points of discontinuity of f, where f is defined by `f(x) = {(|x|+3, if x<= -3),(-2x, if -3 < x < 3),(6x + 2, if x >= 3):}`

Find all points of discontinuity of f, where f is defined by `f(x) = {(|x|/x , if x != 0),(0, if x = 0):}`

Find all points of discontinuity of f, where f is defined by `f (x) = {(x/|x|, if x<0),(-1, if x >= 0):}`

Find all points of discontinuity of f, where f is defined by `f (x) = {(x+1, if x>=1),(x^2+1, if x < 1):}`

Find all points of discontinuity of f, where f is defined by `f(x) = {(x^3 - 3, if x <= 2),(x^2 + 1, if x > 2):}`

Find all points of discontinuity of f, where f is defined by `f (x) = {(x^10 - 1, if x<=1),(x^2, if x > 1):}`

Is the function defined by `f(x) = {(x+5, if x <= 1),(x -5, if x > 1):}` a continuous function?