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

Differentiate the following function with respect to x: `(log x)^x+x^(logx)`

If `y=log[x+sqrt(x^2+a^2)]` show that `(x^2+a^2)(d^2y)/(dx^2)+xdy/dx=0`

Evaluate: `int(5x-2)/(1+2x+3x^2)dx`

Evaluate : ` int x^2/((x^2+4)(x^2+9))dx`

find : `int(3x+1)sqrt(4-3x-2x^2)dx`

Find:

`int(x^3-1)/(x^3+x)dx`

Matrix A = `[(0,2b,-2),(3,1,3),(3a,3,-1)]`is given to be symmetric, find values of a and b

if x^x+x^y+y^x=a^b, then find `dy/dx`.

Evaluate:

`int((x+3)e^x)/((x+5)^3)dx`

If A= `((3,5),(7,9))`is written as A = P + Q, where P is a symmetric matrix and Q is skew symmetric matrix, then write the matrix P.

If A is a skew symmetric matric of order 3, then prove that det A  = 0

If A = `[(-1, 2, 3),(5, 7, 9),(-2, 1, 1)]` and B = `[(-4, 1, -5),(1, 2, 0),(1, 3, 1)]`, then verify that (A + B)' = A' + B'

If A = `[(-1, 2, 3),(5, 7, 9),(-2, 1, 1)]` and B = `[(-4, 1, -5),(1, 2, 0),(1, 3, 1)]`, then verify that (A – B)' = A' – B'

If  A' = `[(3, 4),(-1, 2),(0, 1)]` and B = `[(-1, 2, 1),(1, 2, 3)]`, then verify that (A + B)' = A' + B'

If A' = `[(3, 4),(-1, 2),(0, 1)]` and B = `[(-1, 2, 1),(1, 2, 3)]`, then verify that (A – B)' = A' – B'

If A' = `[(-2, 3),(1, 2)]` and B = `[(-1, 0),(1, 2)]`, then find (A + 2B)'

For the matrices A and B, verify that (AB)′ = B'A', where A = `[(1),(-4),(3)]`, B = `[(-1, 2, 1)]`

For the matrices A and B, verify that (AB)′ = B'A' where A = `[(0),(1),(2)]`, B = `[(1, 5, 7)]`

If A = `[(cos α, sin α), (-sin α, cos α)]`, then verify that  A' A = I

If A = `[(sin α, cos α), (-cos α, sin α)]`, then verify that A'A = I