Science (English Medium) कक्षा १२ - CBSE Question Bank Solutions

Matrix multiplication is commutative.

If A and B are two square matrices of the same order, then A + B = B + A.

(AB)^–1 = A^–1. B^–1, where A and B are invertible matrices satisfying commutative property with respect to multiplication.

Find A^–1 if A = `[(0, 1, 1),(1, 0, 1),(1, 1, 0)]` and show that A^–1 = `("A"^2 - 3"I")/2`.

If A = `[(1, 2, 0),(-2, -1, -2),(0, -1, 1)]`, find A^–1. Using A^–1, solve the system of linear equations x – 2y = 10, 2x – y – z = 8, –2y + z = 7.

Using matrix method, solve the system of equations
3x + 2y – 2z = 3, x + 2y + 3z = 6, 2x – y + z = 2.

Given A = `[(2, 2, -4),(-4, 2, -4),(2, -1, 5)]`, B = `[(1, -1, 0),(2, 3, 4),(0, 1, 2)]`, find BA and use this to solve the system of equations y + 2z = 7, x – y = 3, 2x + 3y + 4z = 17.

If A is a matrix of order 3 × 3, then number of minors in determinant of A are ______.

The sum of the products of elements of any row with the co-factors of corresponding elements is equal to ______.

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 ______.

The maximum value of sinx + cosx is ______.

At what point, the slope of the curve y = – x³ + 3x² + 9x – 27 is maximum? Also find the maximum slope.

Prove that f(x) = sinx + `sqrt(3)` cosx has maximum value at x = `pi/6`