List of top Questions asked in JEE Main

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : At 10°C, the density of a 5 M solution of KCl [atomic masses of K & Cl are 39 & 35.5 g \(mol^{–1}\) respectively], is ‘x’ g \(ml^{–1}\). The solution is cooled to –21°C. The molality of the solution will remain unchanged.
Reason (R) : The molality of a solution does not change with temperature as mass remains unaffected with temperature.
In the light of the above statements, choose the correct answer from the options given below.
Nitrogen gas is obtained by thermal decomposition of
Numbers are to be formed between 1000 and 3000, which are divisible by 4, using the digits 1, 2, 3, 4, 5 and 6 without repetition of digits. Then the total number of such numbers is ______________.
Given below are two statements:
Statement I: In ‘Lassaigne’s Test’, when both nitrogen and sulphur are present in an organic compound, sodium thiocyanate is formed.
Statement II: If both nitrogen and sulphur are present in an organic compound, then the excess of
sodium used in sodium fusion will decompose the sodium thiocyanate formed to give NaCN and Na2S.
In the light of the above statements, choose the most appropriate answer from the options given below:
Optical activity of an enantiomeric mixture is +12.6° and the specific rotation of (+) isomer is +30°. The optical purity is _______%.
Resistance of a conductivity cell (cell constant 129 m–1) filled with 74.5 ppm solution of KCI is 100 Ω (labelled as solution 1). When the same cell is filled with KCl solution of 149 ppm, the resistance is 50 Ω (labelled as solution 2). The ratio of molar conductivity of solution 1 and solution 2 is \(\frac{\Lambda_1}{\Lambda_2} = x \times 10^{-3}\). The value of x is _________. (Nearest integer)
(Given : molar mass of KCl is 74.5 g mol–1).
The area of the region 
\(\begin{array}{l} \left\{\left(x,y\right);\left|x-1\right|\leq y \leq \sqrt{5-x^2} \right\}\end{array}\)
is equal to
An evacuated glass vessel weighs 40.0 g when empty, 135.0 g when filled with a liquid of density 0.95 g mL–1 and 40.5 g when filled with an ideal gas at 0.82 atm at 250 K. The molar mass of the gas in g mol–1 is: (Given : R = 0.082 L atm K–1 mol–1)
The current in a coil of self inductance \(2.0\ H\) is increasing according to \(I = 2\ sin(t^2)\ A\). The amount of energy spent during the period when current changes from 0 to \(2\ A\) is _______ \(J\).

An organic compound ‘A’ on reaction with NH3 followed by heating gives compound B. Which on further strong heating gives compound C(C8H5NO2). Compound C on sequential reaction with ethanolic KOH, alkyl chloride and hydrolysis with alkali gives a primary amine. The compound A is :

The sum of the infinite series
\(1 + \frac{5}{6} + \frac{12}{6^2} + \frac{22}{6^3} + \frac{35}{6^4} +\frac{51}{6^5} + \frac{70}{6^6}+…..\)
is equal to

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 :
If the length of the latus rectum of the ellipse x2 + 4y2 + 2x + 8y – λ = 0 is 4, and l is the length of its major axis, then λ + l is equal to ________.
Two isomers ‘A’ and ‘B’ with molecular formula C4H8 give different products on oxidation with KMnO4/H+ results in effervescence of a gas and gives ketone. The compound ‘A’ is
The polymer, which can be stretched and retains its original status on releasing the force is
Which of the following pairs is not isoelectronic species? 
(At. no. Sm, 62; Er, 68; Yb, 70; Lu, 71; Eu, 63; Tb, 65; Tm, 69)
In the above reaction, 5 g of toluene is converted into benzaldehyde with 92% yield. The amount of benzaldehyde produced is______ × 10–2 g. (Nearest integer).

In the following reaction,
the % yield for reaction I is 60% and that of reaction II is 50%. The overall yield of the complete reaction is _______%. [Nearest integer].

the % yield for reaction I is 60% and that of reaction II is 50%.

In the given reaction,

Fig. 

The number of π electrons present in the product ‘P’ is_____.

Two coils of self-inductance L1 and L2 are connected in series combination having mutual inductance of the coils as M. The equivalent self-inductance of the combination will be:
Two coils of self-inductance L1 and L2 are connected in series combination having mutual inductance of the coils as M
Let A be a matrix of order 2 × 2, whose entries are from the set {0, 1, 3, 4, 5}. If the sum of all the entries of A is a prime number p, \(2 < p < 8\), then the number of such matrices A is ___________.
Let α and β be the roots of the equation x2 + (2i – 1) = 0. Then, the value of |α2 + β2| is equal to
A steam engine intakes \(50\ g\) of steam at \(100°C\) per minute and cools it down to \(20°C\). If latent heat of vaporization of steam is \(540\ cal\ g^{–1}\), then the heat rejected by the steam engine per minute is ______ \(× 10^3\) \(cal.\)
(Given : specific heat capacity of water : \(1\ cal \ g^{–1} °C^{–1}\))

Let f(x) and g(x) be two real polynomials of degree 2 and 1 respectively. If f(g(x)) = 8x2 – 2x and g(f(x)) = 4x2 + 6x + 1, then the value of f(2) + g(2) is ____________ .

Let
\(f(x) = \begin{vmatrix} a & -1 & 0\\ ax & a & -1\\ ax^2 & ax & a \end{vmatrix}\)
a ∈ R. Then the sum of the square of all the values of a, for which 2f′(10) –f′(5) + 100 = 0, is