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

The degree of the differential equation `(("d"^2y)/("d"x^2))^2 + (("d"y)/("d"x))^2 = xsin(("d"y)/("d"x))` is ______.

The degree of the differential equation `[1 + (("d"y)/("d"x))^2]^(3/2) = ("d"^2y)/("d"x^2)` is ______.

The order and degree of the differential equation `("d"^2y)/("d"x^2) + (("d"y)/("d"x))^(1/4) + x^(1/5)` = 0, respectively, are ______.

The degree of the differential equation `("d"^2y)/("d"x^2) + (("d"y)/("d"x))^3 + 6y^5` = 0 is ______.

The instantaneous rate of change at t = 1 for the function f (t) = te^-t + 9 is ____________.

The order and degree of the differential equation `(("d"^3y)/("d"x^3))^2 - 3 ("d"^2y)/("d"x^2) + 2(("d"y)/("d"x))^4` = y⁴ are ______.

The order and degree of the differential equation `[1 + ((dy)/(dx))^2] = (d^2y)/(dx^2)` are ______.

`lim_("x"-> pi) (1 + "cos"^2 "x")/("x" - pi)^2` is equal to ____________.

`lim_("x" -> 0) ("x cos x" - "log" (1 + "x"))/"x"^2` is equal to ____________.

`lim_("x" -> 0) (1 - "cos" 4 "x")/"x"^2` is equal to ____________.

`lim_("x" -> 0) (1 - "cos x")/"x sin x"` is equal to ____________.

Let `"f"("x") = ("x" - 1)/("x" + 1),` then f(f(x)) is ____________.

If f(x) = `1 - 1/"x", "then f"("f"(1/"x"))` ____________.

The degree of the differential equation `("d"^2y)/("d"x^2) + "e"^((dy)/(dx))` = 0 is ______.

The degree of the differential equation `sqrt(1 + (("d"y)/("d"x))^2)` = x is ______.

Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as aRb if a is congruent to b ∀ a, b ∈ T. Then R is ____________.

Let us define a relation R in R as aRb if a ≥ b. Then R is ____________.

Let A = {1, 2, 3} and consider the relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)}. Then R is ____________.

Let A = {1, 2, 3, …. n} and B = {a, b}. Then the number of surjections from A into B is ____________.