Arts (English Medium) Class 12 - CBSE Question Bank Solutions

If A = `[(1, 0, -1),(2, 1, 3 ),(0, 1, 1)]`, then verify that A² + A = A(A + I), where I is 3 × 3 unit matrix.

If A = `[(1, 2),(4, 1),(5, 6)]` B = `[(1, 2),(6, 4),(7, 3)]`, then verify that: (2A + B)′ = 2A′ + B′

Let A = `[(1, 2),(-1, 3)]`, B = `[(4, 0),(1, 5)]`, C = `[(2, 0),(1, -2)]` and a = 4, b = –2. Show that: A + (B + C) = (A + B) + C

Let A = `[(1, 2),(-1, 3)]`, B = `[(4, 0),(1, 5)]`, C = `[(2, 0),(1, -2)]` and a = 4, b = –2. Show that: (a + b)B = aB + bB

If A = `[(0, -x),(x, 0)]`, B = `[(0, 1),(1, 0)]` and x² = –1, then show that (A + B)² = A² + B². 

If A = `[(1, 2),(4, 1)]`, find A² + 2A + 7I.

Matrix multiplication is ______ over addition.

Matrices of any order can be added.

If `|(2x, 5),(8, x)| = |(6, 5),(8, 3)|`, then find x

Prove that (A^–1)′ = (A′)^–1, where A is an invertible matrix.

Show that if the determinant ∆ = `|(3, -2, sin3theta),(-7, 8, cos2theta),(-11, 14, 2)|` = 0, then sinθ = 0 or `1/2`.

If `|(2x, 5),(8, x)| = |(6, -2),(7, 3)|`, then value of x is ______.

Show that the local maximum value of `x + 1/x` is less than local minimum value.

Find the maximum and minimum values of f(x) = secx + log cos²x, 0 < x < 2π

Find the area of greatest rectangle that can be inscribed in an ellipse `x^2/"a"^2 + y^2/"b"^2` = 1

Find the difference between the greatest and least values of the function f(x) = sin2x – x, on `[- pi/2, pi/2]`

An isosceles triangle of vertical angle 2θ is inscribed in a circle of radius a. Show that the area of triangle is maximum when θ = `pi/6`

The values of a for which y = x² + ax + 25 touches the axis of x are ______.

If f(x) = `1/(4x^2 + 2x + 1)`, then its maximum value is ______.

Minimum value of f if f(x) = sinx in `[(-pi)/2, pi/2]` is ______.