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

Write the integrating factor of the following differential equation:

(1+y²) dx−(tan⁻¹ y−x) dy=0

If `veca=4hati-hatj+hatk` then find a unit vector parallel to the vector `veca+vecb`

Find:

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

Find the differential equation of the family of lines passing through the origin.

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.

Find the differential equation representing the family of curves v=A/r+ B, where A and B are arbitrary constants.

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.