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

A matrix denotes a number.

Two matrices are equal if they have same number of rows and same number of columns.

If (AB)′ = B′ A′, where A and B are not square matrices, then number of rows in A is equal to number of columns in B and number of columns in A is equal to number of rows in B.

If A = `[(2, 3, -1),(1, 4, 2)]` and B = `[(2, 3),(4, 5),(2, 1)]`, then AB and BA are defined and equal.

The function f(x) = cot x is discontinuous on the set ______.

Trigonometric and inverse-trigonometric functions are differentiable in their respective domain.

f(x) = x^x has a stationary point at ______.

Solve the differential equation `"dy"/"dx" + y/x` = x².

If A = `[(0,0,0,0),(0,0,0,0),(1,0,0,0),(0,1,0,0)],` then ____________.

`abs((1,1,1),("e",0,sqrt2),(2,2,2))` is equal to ____________.

`("e"^(-2sqrt(x))/sqrt(x) - y/sqrt(x))("d"x)/("d"y) = 1(x ≠ 0)` when written in the form `"dy"/"dx" + "P"y` = Q, then P = ______.

`"dy"/"dx" + y` = 5 is a differential equation of the type `"dy"/"dx" + "P"y` = Q but it can be solved using variable separable method also.

`lim_("h" -> 0) (1/("h"^2 sqrt(8 + "h")) - 1/(2"h"))` is equal to ____________.

`lim_("x" -> -3) sqrt("x"^2 + 7 - 4)/("x" + 3)` is equal to ____________.

`lim_("x"-> 0) ("cosec x - cot x")/"x"`  is equal to ____________.

If f : R → R and g : R → R defined by f(x) = 2x + 3 and g(x) = x² + 7, then the value of x for which f(g(x)) = 25 is ____________.

`("d"y)/("d"x) + y/(xlogx) = 1/x` is an equation of the type ______.

Integrating factor of the differential equation of the form `("d"x)/("d"y) + "P"_1x = "Q"_1` is given by `"e"^(int P_1dy)`.

Solution of the differential equation of the type `("d"x)/("d"y) + "p"_1x = "Q"_1` is given by x.I.F. = `("I"."F") xx "Q"_1"d"y`.

Correct substitution for the solution of the differential equation of the type `("d"y)/("d"x) = "f"(x, y)`, where f(x, y) is a homogeneous function of zero degree is y = vx.