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

If the function f : R → R be given by f[x] = x² + 2 and g : R ​→ R be given by  `g(x)=x/(x−1)` , x≠1, find fog and gof and hence find fog (2) and gof (−3).

Solve the differential equation ` (1 + x2) dy/dx+y=e^(tan^(−1))x.`

If the sum of the lengths of the hypotenuse and a side of a right triangle is given, show that the area of the triangle is maximum, when the angle between them is 60º.

Find the distance between the planes 2x - y +  2z = 5 and 5x - 2.5y + 5z = 20

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 alpha, sin alpha), (-sin alpha, cos alpha)]` then verify that  A' A = I

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

Show that the matrix  A = `[(1,-1,5),(-1,2,1),(5,1,3)]` is a symmetric matrix.

Show that the matrix  A = `[(0,1,-1),(-1,0,1),(1,-1,0)]` is a skew symmetric matrix.

For the matrix A = `[(1,5),(6,7)]` verify that (A + A') is a symmetric matrix.

For the matrix A = `[(1,5),(6,7)]` verify that (A - A') is a skew symmetric matrix.

Find `1/2` (A + A')  and  `1/2` (A -A') When `A = [(0, a, b),(-a,0,c),(-b,-c,0)]`

Express the following matrices as the sum of a symmetric and a skew symmetric matrix:

`[(3,5),(1,-1)]`