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

`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 ____________.

Let R be a relation on the set N of natural numbers denoted by nRm ⇔ n is a factor of m (i.e. n | m). Then, R is ____________.

Let S = {1, 2, 3, 4, 5} and let A = S x S. Define the relation R on A as follows:
(a, b) R (c, d) iff ad = cb. Then, R is ____________.

Let R be the relation “is congruent to” on the set of all triangles in a plane is ____________.

Total number of equivalence relations defined in the set S = {a, b, c} is ____________.

The relation R is defined on the set of natural numbers as {(a, b) : a = 2b}. Then, R^-1 is given by ____________.

Let A = {x : -1 ≤ x ≤ 1} and f : A → A is a function defined by f(x) = x |x| then f is ____________.

Find the position vector of a point A in space such that `vec"OA"` is inclined at 60º to OX and at 45° to OY and `|vec"OA"|` = 10 units.

Let `"f" ("x") = ("In" (1 + "ax") - "In" (1 - "bx"))/"x", "x" ne 0` If f (x) is continuous at x = 0, then f(0) = ____________.