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

Find the value of the following:

`cos^(-1) (1/2) + 2 sin^(-1)(1/2)`

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  (7pi)/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 following determinant.

`|(cos theta, -sin theta),(sin theta, cos theta)|`

Evaluate the following determinant.

`|(x^2-x+1, x -1),(x+1, x+1)|`

If A = `[(1,2),(4,2)]` then show that |2A| = 4|A|.

If A = `[(1,0,1),(0,1,2),(0,0,4)]`, then show that |3A| = 27|A|.

Evaluate the determinant.

`|(3,-1,-2),(0,0,-1),(3,-5,0)|`

Evaluate the determinant.

`|(3,-4,5),(1,1,-2),(2,3,1)|`

Evaluate the determinant.

`|(0,1,2),(-1,0,-3),(-2,3,0)|`

Evaluate the determinant.

`|(2,-1,-2),(0,2,-1),(3,-5,0)|`

If `|(x, 2),(18, x)| = |(6,2),(18,6)|`, then x is equal to ______.

Prove that the determinant `|(x,sin theta, cos theta),(-sin theta, -x, 1),(cos theta, 1, x)|` is independent of θ.

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.

Evaluate `|(cos alpha cos beta, cos alpha sin beta, -sin alpha),(-sin beta, cos beta, 0),(sin alpha cos beta, sin alpha sin beta,cos alpha )|`