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

Find the inverse of each of the matrices, if it exists.

`[(2,0,-1),(5,1,0),(0,1,3)]`

Find the inverse of each of the matrices, if it exists.

`[(1,3,-2),(-3,0,-5),(2,5,0)]`

Find the inverse of each of the matrices, if it exists.

`[(2,0,-1),(5,1,0),(0,1,3)]`

If x and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.

x = 2at², y = at⁴

If x and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.

x = a cos θ, y = b cos θ

If x and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.

x = sin t, y = cos 2t

If x and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.

x = 4t, y = `4/y`

If x and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.

x = cos θ – cos 2θ, y = sin θ – sin 2θ

If x and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.

x = a (θ – sin θ), y = a (1 + cos θ)

If x and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.

`x = (sin^3t)/sqrt(cos 2t), y = (cos^3t)/sqrt(cos 2t)`

If x and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.

x = `a(cos t + log tan  t/2)`, y = a sin t

If x and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.

x = a sec θ, y = b tan θ

If x and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.

x = a (cos θ + θ sin θ), y = a (sin θ – θ cos θ)

If x = `sqrt(a^(sin^(-1)t))`, y = `sqrt(a^(cos^(-1)t))` show that `dy/dx = - y/x`.

If A is a 3 × 3 invertible matrix, then what will be the value of k if det(A^–1) = (det A)^k

if `A = ((2,3,1),(1,2,2),(-3,1,-1))`, Find `A^(-1)` and hence solve the system of equations 2x + y – 3z = 13, 3x + 2y + z = 4, x + 2y – z = 8

If x = a (2θ – sin 2θ) and y = a (1 – cos 2θ), find `dy/dx` when `theta = pi/3`