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

If A and B are any two matrices of the same order, then (AB)′ = A′B′.

AA′ is always a symmetric matrix for any matrix A.

If A is skew-symmetric matrix, then A² is a symmetric matrix.

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

If P is of order 2 x 3 and Q is of order 3 x 2, then PQ is of order ____________.

If A and B are symmetric matrices of the same order, then ____________.

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

`("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.

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.

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

Let f : R → R be given by f(x) = tan x. Then f^-1(1) is ____________.

If f : `(1, infty) → (2, infty)  "is given by f"("x") = "x" + 1/"x"`, then f^-1 equals to ____________.

Let f(x) = x² – x + 1, x ≥ `1/2`, then the solution of the equation f(x) = f^-1(x) is ____________.

If A and B are symmetric matrices of the same order, then ____________.

If A = `[(3, "x" - 1),(2"x" + 3, "x" + 2)]` is a symmetric matrix, then x = ____________.