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

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 ____________.

Let f : R `->` R be a function defined by f(x) = x³ + 4, then f is ______.

Let f : R → R, g : R → R be two functions such that f(x) = 2x – 3, g(x) = x³ + 5. The function (fog)^-1 (x) is equal to ____________.

The domain of the function `"f"("x") = 1/(sqrt ({"sin x"} + {"sin" ( pi + "x")}))` where {.} denotes fractional part, is

Range of `"f"("x") = sqrt((1 - "cos x") sqrt ((1 - "cos x")sqrt ((1 - "cos x")....infty))`

If `"A" = [("a","b"),("b","a")]` and `"A"^2 = [(alpha,beta),(beta, alpha)]` then ____________.

If matrix A `= [("a","b","c"),("b","c","a"),("c","a","b")]` where a, b, c are real positive numbers, abc = 1 and A^TA = I, then the value of a³ + b³ + c³ is ____________.

Find the values of x, y, z respectively if the matrix A `= [(0,2"y","z"),("x","y","-z"),("x","-y","z")]` satisfy the equation A^TA = I₃.

If `vec"a", vec"b", vec"c"` are three vectors such that `vec"a" + vec"b" + vec"a" = vec0` and `|vec"a"|` = 2, `|vec"b"|` = 3, `|vec"c"|` = 5, then value of `vec"a"*vec"b" + vec"b"*vec"c" + vec"c"*vec"a"` is ______.

If A `= [(0,1,1),(1,0,1),(1,1,0)] "then"  ("A"^2 - 3"I")/2 =` ____________.

If `|vec"a"| = |vec"b"|`, then necessarily it implies `vec"a" = +- vec"b"`.