Science (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

The maximum value of sinx + cosx is ______.

At what point, the slope of the curve y = – x³ + 3x² + 9x – 27 is maximum? Also find the maximum slope.

Prove that f(x) = sinx + `sqrt(3)` cosx has maximum value at x = `pi/6`

At x = `(5pi)/6`, f(x) = 2 sin3x + 3 cos3x is ______.

The least value of the function f(x) = `"a"x + "b"/x` (where a > 0, b > 0, x > 0) is ______.

If the graph of a differentiable function y = f (x) meets the lines y = – 1 and y = 1, then the graph ____________.

The function f : A → B defined by f(x) = 4x + 7, x ∈ R is ____________.

The smallest integer function f(x) = [x] is ____________.

The function f : R → R defined by f(x) = 3 – 4x is ____________.

The number of bijective functions from set A to itself when A contains 106 elements is ____________.

Let f : R → R be defind by f(x) = `1/"x"  AA  "x" in "R".` Then f is ____________.

Which of the following functions from Z into Z is bijective?

Let X = {-1, 0, 1}, Y = {0, 2} and a function f : X → Y defiend by y = 2x⁴, is ____________.

Let f : R → R be a function defined by f(x) `= ("e"^abs"x" - "e"^-"x")/("e"^"x" + "e"^-"x")` then f(x) is

Let g(x) = x² – 4x – 5, then ____________.

Let A = R – {3}, B = R – {1}. Let f : A → B be defined by `"f"("x") = ("x" - 2)/("x" - 3)` Then, ____________.

The mapping f : N → N is given by f(n) = 1 + n², n ∈ N when N is the set of natural numbers is ____________.

The function f : R → R given by f(x) = x³ – 1 is ____________.

Let f : [0, ∞) → [0, 2] be defined by `"f" ("x") = (2"x")/(1 + "x"),` then f is ____________.

If N be the set of all-natural numbers, consider f: N → N such that f(x) = 2x, ∀ x ∈ N, then f is ____________.