List of top Questions asked in JEE Main

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 \(a_1, a_2, a_3\) ….. 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
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 ________.
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:
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 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 :
A small toy starts moving from the position of rest under a constant acceleration. If it travels a distance of 10 m in t s, the distance travelled by the toy in the next t s will be :
Water is being filled at the rate of 1 cm3/sec in a right circular conical vessel (vertex downwards) of height 35 cm and diameter 14 cm. When the height of the water level is 10 cm, the rate (in cm2/sec) at which the wet conical surface area of the vessel increase, is
What will be the effect on the root mean square velocity of oxygen molecules if the temperature is doubled and oxygen molecule dissociates into atomic oxygen?
A coil is placed in a time varying magnetic field. If the number of turns in the coil were to be halved and the radius of wire doubled, the electrical power dissipated due to the current induced in the coil would be: (Assume the coil to be short circuited.)
L-isomer of a compound ‘A’ \((C_4H_8O_4)\) gives a positive test with \([Ag(NH_3)^2]^+\). Treatment of ‘A’ with acetic anhydride yields triacetate derivative. Compound ‘A’ produces an optically active compound (B) and an optically inactive compound (C) on treatment with bromine water and \(HNO_3\) respectively. Compound (A) is:
In isolation of which one of the following metals from their ores, the use of cyanide salt is not commonly involved?
Which of the following compound does not contain sulphur atom?
A wire of length 22 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into an equilateral triangle. Then, the length of the side of the equilateral triangle, so that the combined area of the square and the equilateral triangle is minimum, is

If A =\(\sum_{n=1}^{\infty}\)\(\frac{1}{( 3 + (-1)^n)^n}\) and B = \(\sum_{n=1}^{\infty}\) \(\frac{(-1)^n}{( 3 + (-1)^n)^n}\) , 
then A/B is equal to :

The area of the region bounded by y2 = 8x and y2 = 16(3 – x) is equal to

If the lines
\(\stackrel{→}{r}= ( \hat{i} - \hat{j} + \hat{k} ) + λ (\hat{3j} - \hat{k} )= ( \hat{i} - \hat{j} + \hat{k} ) + λ (\hat{3j} - \hat{k} )\)
and
\(\stackrel{→}{r} = ( \alpha \hat{i} - \hat{j} ) + μ( \hat{2j} - \hat{3k} )\)
are co-planer , then the distance of the plane containing these two lines from the point \(( α , 0 , 0 )\) is :

Let \(y = y(x)\) be the solution of the differential equation \((x + 1)y' – y = e^{3x}(x + 1)^2\), with \(y(0)=\frac 13\). Then, the point \(x=−\frac 43\) for the curve \(y = y(x)\) is :