List of top Questions asked in JEE Main

The number of real solutions of x7 + 5x3 + 3x + 1 = 0 is equal to ______.
The number of real solutions of the equation e4x + 4e3x - 58e2x + 4ex + 1 = 0 is _____.

g :R→R be two real valued functions defined as
\(f(x) = \begin{cases}        -|x + 3| &  x < 0 \\       e^x, & x \geq 0  \end{cases}\)
and
\(g(x) = \begin{cases}        x^2 + k_1x ,&  x < 0 \\       4x + k_2 ,&  x \geq 0  \end{cases}\)
where k1 and k2 are real constants. If (goƒ) is differentiable at x = 0, then (goƒ) (–4) + (goƒ) (4) is
equal to:

\(\alpha = \sin 36^\circ\)  is a root of which of the following equation?
Let \(\alpha, \beta\) be the roots of the equation \(x^2 - 4\lambda x + 5 = 0\) and α, γ be the roots of the equation \(x^2 - (3\sqrt{2} + 2\sqrt{3})x + 7 + 3\lambda\sqrt{3} = 0\). If \(\beta + \gamma = 3\sqrt{2}\) then \((\alpha + 2\beta + \gamma)^2\) is equal to _______.

Let 
\(f(x)=max\left\{|x+1|,|x+2|,……,|x+5|\right\} \)
Then \(\int_{-6}^{0} f(x) \, dx\)
is equal to_______

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

The number of functions f, from the set
\(A = {x∈N: x^2-10x+9≤0} \)to the set \(B = {n62:n∈N}\)
such that
\(f(x)≤(x-3)^2+1\), for every \(x∈A,\)
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?
The probability that a randomly chosen one-one function from the set {a, b, c, d} to the set {1, 2, 3, 4, 5} satisfies f(a) + 2f(b) – f(c) = f(d) is :
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

Let E1, E2, E3 be three mutually exclusive events such that
\(P(E_1)=\frac{2+3p}{6}, P(E_2)=\frac{2−p}{8} and\ P(E_3)=\frac{1−p}{2}.\)
If the maximum and minimum values of p are p1 and p2, then (p1 + p2) is equal to :

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 :

Let S = {1, 2, 3, …, 2022}. Then the probability that a randomly chosen number n from the set S such that HCF (n, 2022) = 1, 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-IList-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) FexOy + K2O + Al2O3
(D) CO(g) + 2H2(g) → CH3OH(g)(IV) Ni

Choose the correct answer from the options given below :

Consider the following reactions. 

\(PCl_3+H_2→A+HCL\)

\(A+H_2o→B+HCL\)

The number of ionisable protons present in the product B is

Amongst FeCl3.3H2O, K3[Fe(CN)6)] and [Co(NH3)6]Cl3, the spin-only magnetic moment value of the inner-orbital complex that absorbs light at shortest wavelength is_______B.M. [nearest integer]
The neutralization occurs when 10 mL of 0.1M acid ‘A’ is allowed to react with 30 mL of 0.05 M base M(OH)2. The basicity of the acid ‘A’ is____[M is a metal]
20 mL of 0.02 M K2Cr2O7 solution is used for the titration of 10 mL of Fe2+ solution in the acidic medium. The molarity of Fe2+ solution is ______×10–2 M. (Nearest integer)
2NO + 2H2 → N2 + 2H2O
The above reaction has been studied at 800 °C. The related data is given in the table below.
The order of the reaction with respect to NO is ___.
Amongst the following, the number of oxide(s) which are paramagnetic in nature is
Na2O, KO2, NO2, N2O, ClO2, NO, SO2, Cl2O