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

The function f (x) = x², for all real x, is ____________.

The function f(x) = mx + c where m, c are constants, is a strict decreasing function for all `"x" in "R"` , if ____________.

The function f(x) = tan^-1 x is ____________.

The interval in which the function f is given by f(x) = x² e^-x is strictly increasing, is: ____________.

Let `"f (x) = x – cos x, x" in "R"`, then f is ____________.

In `(0, pi/2),`  the function f (x) = `"x"/"sin x"` is ____________.

Let f (x) = tan x – 4x, then in the interval `[- pi/3, pi/3], "f"("x")` 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 ____________.