List of top Questions asked in JEE Main

Given below are two statement: one is labelled as Assertion A and the other is labelled as Reason R.  
Assertion A : If an electric dipole of dipole moment 30 x 10-5 Cm is enclosed by a closed surface, the net flux coming out of the surface will by zero.
Reason R : Electric dipole consists of two equal and opposite charges. 
In the light of above, statements, choose the correct answer from the options given below:
In an n-p-n common emitter (CE) transistor the collector current changes from 5 mA to 16 mA for the change in base current from 100 μA and 200 μA, respectively. The current gain of transistor is______.
Let S = {1, 2, 3, 4, 5, 6}. Then the number of one-one functions \(f : S → P(S)\), where \(P(S)\) denotes the power set of S, such that \(f(n) ⊂ f(m)\) where \(n < m,\) is:
A fish rising vertically upward with a uniform velocity of 8 ms-1, observes that a bird is diving vertically downward towards the fish with the velocity of 12 ms-1. If the refractive index of water is \(\frac{4}{3}\) , then the actual velocity of the diving bird to pick the fish, will be _______ ms-1
Let \(f(x)\) be a quadratic polynomial with leading coefficient 1 such that \(f(0) = p, p≠0\) and \(f(1)=\frac{1}{3}\). If the equation \(f(x) = 0\) and \(fofofof(x) = 0\) have a common real root, then \(f(–3)\) is equal to.......................
Let \(𝑎_1=𝑏_1=1\)and \(𝑎_𝑛=𝑎_{𝑛−1}+(𝑛−1)\), \(𝑏_𝑛=𝑏_{𝑛−1}+𝑎_{𝑛−1}\), \(∀𝑛≥2\). If \(𝑆= \displaystyle\sum_{ 𝑛=1}^{10}\frac {𝑏_𝑛}{2^𝑛}\) and \(𝑇= \displaystyle\sum_{𝑛=1}^{8} \frac {𝑛}{2^{𝑛−1}}\), then \(2^7(2𝑆−𝑇)\)  is equal to ____ .
Let \(\sum_{n=0}^{\infty }\frac{n^{3}((2n)!+(2n-1)(n!))}{(n!)((2n)!)}=ae+\frac{b}{e}+c\), where $a, b, c \in Z$ and $e=\displaystyle\sum_{n=0}^{\infty} \frac{1}{n !}$ Then $a^2-b+c$ is equal to _______
Let sets A and B have 5 elements each. Let mean of the elements in sets A and B be 5 and 8 respectively and the variance of the elements in sets A and B be 12 and 20 respectively. A new set C of 10 elements is formed by subtracting 3 from each element of A and adding 2 to each element of B. Then the sum of the mean and variance of the elements of C is:
$Ka _1, Ka _2$ and $Ka _3$ are the respective ionization constants for the following reactions (a), (b) and (c)
(a) $H _2 C _2 O _4 \rightleftharpoons H ^{+}+ HC _2 O _4^{-}$
(b) $HC _2 O _4^{-} \rightleftharpoons H ^{+}+ HC _2 O _4^{2-}$
(c) $H _2 C _2 O _4 \rightleftharpoons 2 H ^{+}+ C _2 O _4^{2-}$
The relationship between $K _{ a _1}, K _{ a _2}$ and $K _{ a _3}$ is given as
The range of the function $f(x)=\sqrt{3-x}+\sqrt{2+x}$ is:
Let \( S = \{ M = [a_{ij}], a_{ij} \in \{0, 1, 2\}, 1 \leq i, j \leq 2 \} \) be a sample space and \( A = \{ M \in S : M \text{ is invertible} \} \) be an event. Then \( P(A) \) is equal to:
The foci of a hyperbola are (±2,0) and its eccentricity is \(\frac{3}{2}\) . A tangent, perpendicular to the line 2x + 3y = 6, is drawn at a point in the first quadrant on the hyperbola. If the intercepts made by the tangent on the x- and y-axes are a and b respectively, then |6a| + |5b| is equal to_____.
If y=y(x) is the solution of the differential equation \(\frac{dy}{dx}+\frac{4x}{(x^2-1)}y=\frac{x+2}{(x^2-1)^{\frac{5}{2}}},x>1\) such that \(y(2)=\frac{2}{9}\log_e(2+\sqrt3)\ \text{and}\ y(\sqrt2)=\alpha\log_e(\sqrt{\alpha}+\beta)+\beta-\sqrt{\gamma}∈\N,\) then αβγ is equal to
Let f(x) = \(\displaystyle\sum_{k=1}^{10} kx^k\) , x ∈ R. If 2f(2) + f(2) = 190(2)n + 1 then n is equal to____. 

If the x-intercept of a focal chord of the parabola \(y^2=8 x+4 y+4\) is 3 , then the length of this chord is equal to ___

The total number of monobromo derivatives formed by the alkanes with molecular formula $C _5 H _{12}$ is (excluding stereo isomers) _______

Let $\vec{a}=\hat{i}+2 \hat{j}+\lambda \hat{k}, \vec{b}=3 \hat{i}-5 \hat{j}-\lambda \hat{k}, \vec{a} \cdot \vec{c}=7,2 \vec{b} \cdot \vec{c}+43=0, \vec{a} \times \vec{c}=\vec{b} \times \vec{c}$. Then $|\vec{a} \cdot \vec{b}|$ is equal to

Let $A$ be the area bounded by the curve $y=x|x-3|$, the $x$-axis and the ordinates $x=-1$ and $x=2$ Then $12 A$ is equal to _____

“A” obtained by Ostwald’s method involving air oxidation of\( NH_3\), upon further air oxidation produces “B”. “B” on hydration forms an oxoacid of Nitrogen along with evolution of “A”. The oxoacid also produces “A” and gives positive brown ring test. 

The reaction representing the Mond process for metal refining is _________.
Find out the correct statement from the options given below for the above 2 reactions.
nucleophile
In the above reaction 'A' and 'B' are:
A’ and ‘B’ in the above reactions are

For 1 mol of gas, the plot of pV vs. p is shown below. p is the pressure and V is the volume of the gas. What is the value of compressibility factor at point A?
Pv vs V graph

A solution is prepared by adding 2 g of X” to 1 moIe of water. Mass percent of “X” in the solution is
One mole of P4 reacts with 8 moles of SOCI2 to give 4 moles of A. x mole of SO2 and 2 moles of B. A, B and x respectively are