List of top Questions asked in JEE Main

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 ___.
A 2.0 g sample containing MnO2 is treated with HCl liberating Cl2. The Cl2 gas is passed into a solution of KI and 60.0 mL of 0.1 M Na2S2O3 is required to titrate the liberated iodine. The percentage of MnO2 in the sample is ______. (Nearest integer)
[Atomic masses (in u) Mn = 55; Cl = 35.5; O = 16, I = 127, Na = 23, K = 39, S = 32]

For real number a, b (a > b > 0), let
\(\text{{Area}} \left\{ (x, y) : x^2 + y^2 \leq a^2 \text{{ and }} \frac{x^2}{a^2} + \frac{y^2}{b^2} \geq 1 \right\} = 30\pi\)
and 
\(\text{{Area}} \left\{ (x, y) : x^2 + y^2 \geq b^2 \text{{ and }} \frac{x^2}{a^2} + \frac{y^2}{b^2} \leq 1 \right\} = 18\pi\)
Then the value of (a – b)2 is equal to _____.

Ka1, Ka2 and Ka3 are the respective ionization constants for the following reactions (a),(b), and (c).
(a) H2C2O4⇌H++HC2O4−
(b) HC2O4−⇌H++HC2O42−
(c) H2C2O4⇌2H++C2O42−
The relationship between Ka1,Ka2 and Ka3 is given as
If the solution curve of the differential equation \(\frac{dy}{dx} = \frac{x + y - 2}{x - y}\) passes through the points \((2, 1)\) and (k + 1, 2), k > 0, then
A point P moves so that the sum of squares of its distances from the points (1, 2) and (–2, 1) is 14. Let f(x, y) = 0 be the locus of P, which intersects the x-axis at the points A, B and the y-axis at the points C, D. Then the area of the quadrilateral ACBD is equal to
If \(a_1, a_2, a_3\) ….. and \(b_1, b_2, b_3\) ….. are A.P., and \(a_1 = 2, a_{10} = 3, a_1b_1 = 1 = a_{10}b_{10}\), then \(a_4b_4\) is equal to
At 310 K, the solubility of CaF2 in water is 2.34 ×10–3 g/100 mL. The solubility product of CaF2 is _____ × 10–8 (mol/L)3.
(Given molar mass : CaF2 = 78 g mol–1).
If \(\begin{array}{l} \frac{6}{3^{12}}+\frac{10}{3^{11}}+\frac{20}{3^{10}}+\frac{40}{3^9}+\cdots +\frac{10240}{3}=2^n\cdot m, \end{array}\)where m is odd, then m⋅n is equal to ________.
Let
\(\begin{array}{l}f\left(x\right) = min \{\left[x – 1\right], \left[x – 2\right], …., \left[x – 10\right]\}\end{array}\)
where [t] denotes the greatest integer ≤t. Then
\(\begin{array}{l} \displaystyle\int\limits_{0}^{10}f\left(x\right)dx+\displaystyle\int\limits_{0}^{10}\left(f\left(x\right)\right)^2dx+\displaystyle\int\limits_{0}^{10}\left|f\left(x\right)\right|dx\end{array}\)
is equal to ________.

Let y = y(x) be the solution curve of the differential equation
\(\sin(2x^2) \log_e(\tan(x^2)) \,dy + (4xy - 4\sqrt{2}x\sin(x^2 - \frac{\pi}{4})) \,dx = 0, \quad 0 < x < \sqrt{\frac{\pi}{2}}\)
which passes through the point \((\sqrt{\frac{π}{6}},1)\). Then \(|y(\sqrt{\frac{π}{3}})|\)
is equal to _______.

The value of \(\cot\left(\sum_{n=1}^{50} \tan^{-1}\left(\frac{1}{1+n+n^2}\right)\right)\) is
The locus of the mid-point of the line segment joining the point (4, 3) and the points on the ellipse x2 + 2y2 = 4 is an ellipse with eccentricity:
The remainder when (2021)2023 is divided by 7 is
A flask is filled with equal moles of A and B. The half lives of A and B are 100 s and 50 s respectively and are independent of the initial concentration. The time required for the concentration of A to be four times that of B is ________s.
(Given : In 2 = 0.693)
The value of the integral \(∫^2_{-2}\frac{ |x^3+x|}{(e^x|x|+1)}dx\) is equal to:
Number of electron deficient molecules among the following
\(PH_3, B_2H_6, CCl_4, NH_3, LiH \) and \(BCl_3\) is
A \(100\) \(mL\) solution of \(CH_3CH_2MgBr\) on treatment with methanol produces \(2.24\) \(mL\) of a gas at STP. The weight of gas produced is_____ mg. [nearest integer]

Let f : R → R be a continuous function satisfying f(x) + f(x + k) = n, for all x ∈ R where k > 0 and n is a positive integer. If
 \(l_1 = \int_{0}^{4nk} f(x) \, dx\) and \(l_2 = \int_{-k}^{3k} f(x) \, dx\), then

Let for n = 1, 2, …, 50, Sn be the sum of the infinite geometric progression whose first term is n2 and whose common ratio is 
\(\frac{1}{(n+1)^2}\) . Then the value of 
\(\frac{1}{26} + \sum_{n=1}^{50} \left(S_n+\frac{2}{n+1}-n-1  \right)\)
 is equal to ________.

A silver wire has a mass \((0.6  \overset{+}{-}  0.006)\) g, radius \((0.5 \overset{+}{-} 0.005)\) mm and length \((4 \overset{+}{-} 0.04)\) cm. The maximum percentage error in the measurement of its density will be

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

A body of mass M at rest explodes into three pieces, in the ratio of masses 1 : 1 : 2. Two smaller pieces fly off perpendicular to each other with velocities of 30 ms–1 and 40 ms–1 respectively. The velocity of the third piece will be
A solid cylinder and a solid sphere, having same mass M and radius R, roll down the same inclined plane from top without slipping They start from rest The ratio of velocity of the solid cylinder to that of the solid sphere, with which they reach the ground, will be :
Let S = {4, 6, 9} and T = {9, 10, 11, …,1000}. If A = {a1 + a2 + … +ak :k∈N, a1, a2, a3, …, ak∈S}, then the sum of all the elements in the set T – A is equal to ____________.