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

Evaluate the following:

`int_"0"^pi  (x"d"x)/(1 + sin x)`

Evaluate the following:

`int (2x - 1)/((x - 1)(x + 2)(x - 3)) "d"x`

Evaluate the following:

`int "e"^(-3x) cos^3x  "d"x`

Evaluate the following:

`int sqrt(tanx)  "d"x`  (Hint: Put tanx = t²)

If `int "dx"/((x + 2)(x^2 + 1)) = "a"log|1 + x^2| + "b" tan^-1x + 1/5 log|x + 2| + "C"`, then ______.

If f(x) = (ax² + b)³, then the function g such that f(g(x)) = g(f(x)) is given by ____________.

If f : R → R, g : R → R and h : R → R is such that f(x) = x², g(x) = tanx and h(x) = logx, then the value of [ho(gof)](x), if x = `sqrtpi/2` will be ____________.

Let f : N → R : f(x) = `((2"x"−1))/2` and g : Q → R : g(x) = x + 2 be two functions. Then, (gof) `(3/2)` is ____________.

If f : R → R, g : R → R and h : R → R are such that f(x) = x², g(x) = tan x and h(x) = log x, then the value of (go(foh)) (x), if x = 1 will be ____________.

If f(x) = `(3"x" + 2)/(5"x" - 3)` then (fof)(x) is ____________.

Let f : R → R be the functions defined by f(x) = x³ + 5. Then f^-1(x) is ____________.

Let f : R – `{3/5}`→ R be defined by f(x) = `(3"x" + 2)/(5"x" - 3)` Then ____________.

If f(x) = (ax² – b)³, then the function g such that f{g(x)} = g{f(x)} is given by ____________.

Which one of the following functions is not invertible?

The inverse of the function `"y" = (10^"x" - 10^-"x")/(10^"x" + 10^-"x")` is ____________.

If f : R → R defind by f(x) = `(2"x" - 7)/4` is an invertible function, then find f^-1.

Consider the function f in `"A = R" - {2/3}` defiend as `"f"("x") = (4"x" + 3)/(6"x" - 4)` Find f^-1.

If f is an invertible function defined as f(x) `= (3"x" - 4)/5,` then f^-1(x) is ____________.

If f : R → R defined by f(x) `= (3"x" + 5)/2` is an invertible function, then find f^-1.

A general election of Lok Sabha is a gigantic exercise. About 911 million people were eligible to vote and voter turnout was about 67%, the highest ever

Let I be the set of all citizens of India who were eligible to exercise their voting right in the general election held in 2019. A relation ‘R’ is defined on I as follows:

R = {(V1, V2) ∶ V1, V2 ∈ I and both use their voting right in the general election - 2019}

• Two neighbors X and Y ∈ I. X exercised his voting right while Y did not cast her vote in a general election - 2019. Which of the following is true?