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

If A = `[(2, lambda, -3),(0, 2, 5),(1, 1, 3)]`, then A^–1 exists if ______.

If x, y, z are all different from zero and `|(1 + x, 1, 1),(1, 1 + y, 1),(1, 1, 1 + z)|` = 0, then value of x^–1 + y^–1 + z^–1 is ______.

There are two values of a which makes determinant, ∆ = `|(1, -2, 5),(2, "a", -1),(0, 4, 2"a")|` = 86, then sum of these number is ______.

If A is a matrix of order 3 × 3, then |3A| = ______.

If A is invertible matrix of order 3 × 3, then |A^–1| ______.

If A is a matrix of order 3 × 3, then (A²)^–1 = ______.

`|(0, xyz, x - z),(y - x, 0, y  z),(z - x, z - y, 0)|` = ______.

If f(x) = `|((1 + x)^17, (1 + x)^19, (1 + x)^23),((1 + x)^23, (1 + x)^29, (1 + x)^34),((1 +x)^41, (1 +x)^43, (1 + x)^47)|` = A + Bx + Cx² + ..., then A = ______.

If A and B are matrices of order 3 and |A| = 5, |B| = 3, then |3AB| = 27 × 5 × 3 = 405.

The maximum value of `|(1, 1, 1),(1, (1 + sintheta), 1),(1, 1, 1 + costheta)|` is `1/2`

If f(x) = 2x and g(x) = `x^2/2 + 1`, then which of the following can be a discontinuous function ______.

The function f(x) = `(4 - x^2)/(4x - x^3)` is ______.

The function f(x) = `"e"^|x|` is ______.

Let f(x) = |sin x|. Then ______.

If f.g is continuous at x = a, then f and g are separately continuous at x = a.

For the curve y = 5x – 2x³, if x increases at the rate of 2 units/sec, then how fast is the slope of curve changing when x = 3?

Water is dripping out from a conical funnel of semi-vertical angle `pi/4` at the uniform rate of 2cm²/sec in the surface area, through a tiny hole at the vertex of the bottom. When the slant height of cone is 4 cm, find the rate of decrease of the slant height of water.

Water is dripping out at a steady rate of 1 cu cm/sec through a tiny hole at the vertex of the conical vessel, whose axis is vertical. When the slant height of water in the vessel is 4 cm, find the rate of decrease of slant height, where the vertical angle of the conical vessel is `pi/6`

The rate of change of volume of a sphere with respect to its surface area, when the radius is 2 cm, is ______.

A spherical ball of salt is dissolving in water in such a manner that the rate of decrease of the volume at any instant is proportional to the surface. Prove that the radius is decreasing at a constant rate