List of top Questions asked in JEE Main- 2022

Let a function ƒ : N →N be defined by
\(f(n) = \left\{ \begin{array}{ll} 2n & n = 2,4,6,8,\ldots \\ n - 1 & n = 3,7,11,15,\ldots \\ \frac{n+1}{2} & n = 1,5,9,13 \end{array} \right.\)
then, ƒ is

Let f(x) be a quadratic polynomial such that f(–2) + f(3) = 0. If one of the roots of f(x) = 0 is –1, then the sum of the roots of f(x) = 0 is equal to:

Let f,g : R → R be functions defined by*
\(f(x) = \begin{cases} [x], & x < 0 \\ |1 - x|, & x \geq 0 \end{cases}\)
and \(g(x) = \begin{cases} e^x - x, & x < 0 \\ {(x - 1)^2 - 1}, & x \geq 0 \end{cases}\)
Where [x] denotes the greatest integer less than or equal to x. Then, the function fog is discontinuous at exactly:

If
\(f(x) = \begin{cases} x + a, & x \leq 0 \\ |x - 4|, & x > 0 \end{cases}\) and \(g(x) = \begin{cases} x + 1, & x < 0 \\ (x - 4)^2 + b, & x \geq 0 \end{cases}\)
are continuous on R, then (gof) (2) + (fog) (–2) is equal to

Let
\(f(x) = \begin{cases} x^3 - x^2 + 10x - 7, & x \leq 1 \\ -2x + \log_2(b^2 - 4), & x > 1 \end{cases}\)
Then the set of all values of b, for which f(x) has maximum value at x = 1, is

Let a function f: ℝ → ℝ be defined as :
\(\begin{array}{l}f(x) = \left\{\begin{matrix}\int_{0}^{x}(5-|t-3|)dt, & x>4 \\x^2 + bx, & x \le4 \\\end{matrix}\right.\end{array}\)
where b ∈ ℝ. If f is continuous at x = 4 then which of the following statements is NOT true?

Let A and B be two events such that

\(\begin{array}{l} P\left(B/A\right)\frac{2}{5},\ P\left(A/B\right)=\frac{1}{7}\ \text{and}\ P\left(A\cap B\right)=\frac{1}{9}.\end{array} Consider \begin{array}{l} \left(S1\right)P\left(A’\cup B\right)=\frac{5}{6},\end{array}\)

\(\begin{array}{l} \left(S2\right)P\left(A’\cap B’\right)=\frac{1}{18}.\end{array}\)Then

A six faced die is biased such that
3 × P (a prime number) = 6 × P (a composite number) = 2 × P (1).
Let X be a random variable that counts the number of times one gets a perfect square on some
throws of this die. If the die is thrown twice, then the mean of X is :

Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be black in colour. Then the probability, that the transferred ball is red, is :

Match List-I with List-II.

List-I	List-II
(A) N₂(g) + 3H₂(g) → 2NH₃(g)	(I) Cu
(B) CO(g) + 3H₂(g) → CH₄(g) + H₂O(g)	(II) Cu/ZnO – Cr₂O₃
(C) CO(g) + H₂(g) → HCHO(g)	(III) Fe_xO_y + K₂O + Al₂O₃
(D) CO(g) + 2H₂(g) → CH₃OH(g)	(IV) Ni