List of top Questions asked in JEE Main

Let \(X\) be a random variable having binomial distribution \(B(7, p)\). If \(P(X = 3) = 5P(X = 4)\), then the sum of the mean and the variance of \(X\) is:

Which of the following can be used to prevent the decomposition of \(H_2O_2\)?

Five numbers, \(x_1, x_2, x_3, x_4, x_5\) are randomly selected from the numbers \(1, 2, 3\),….., \(18\) and are arranged in the increasing order \((x_1<x_2<x_3<x_4<x_5)\). The probability that \(x_2 = 7\) and \(x_4 = 11\) is:

Borazine, also known as inorganic benzene, can be prepared by the reaction of 3-equivalents of “X” with 6-equivalents of “Y”. “X” and “Y”, respectively are:

Which of the given reactions is not an example of a disproportionation reaction?

An expression for a dimensionless quantity P is given by \(P=\frac{α}{β} log_e(\frac{kt}{βx})\); where α and β are constants, x is distance; k is Boltzmann constant and t is the temperature. Then the dimensions of α will be

The dark purple colour of \(KMnO_4\) disappears in the titration with oxalic acid in acidic medium. The overall change in the oxidation number of manganese in the reaction is :

\(\dot Cl + CH_4 → A + B\)
A and B in the above atmospheric reaction step are:

Which technique among the following, is most appropriate in separation of a mixture of 100 mg of p-nitrophenol and picric acid?

The products formed in the following reaction, A and B are

Which reactant will give the following alcohol on reaction with one mole of phenyl magnesium bromide (PhMgBr) followed by acidic hydrolysis?

Stearic acid and polyethylene glycol react to form which one of the following soap/s detergents?

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Experimental reaction of \(CH_3Cl\) with aniline and anhydrous \(AlCl_3\) does not give o and p-methylaniline.
Reason (R): The \(–NH_2\)group of aniline becomes deactivating because of salt formation with anhydrous \(AlCl_3\) and hence yields m-methyl aniline as the product.
In the light of the above statements, choose the most appropriate answer from the options given below :

Match List-I with List-II

List-I (Processes/ Reactions)	List-II (Catalyst)
(A) \(2SO_2(g) + O_2(g)\)	(I) \(\underrightarrow {Fe(s)}\ \  2SO_3(g)\)
(B) \(4NH_3(g) + 5O_2(g)\)	(II) \(\underrightarrow {Pt(s) – Rh(s)}\ \  4NO(g) + 6H_2O(g)\)
(C) \(N_2(g) + 3H_2(g)\)	(III) \(\underrightarrow {V_2O_5}\ \  2NH_3(g)\)
(D) Vegetable oil \((l)+ H_2\)	(IV) \(\underrightarrow {Ni(s)}\)  Vegetable ghee(s)

Choose the correct answer from the options given below:

Let \(f :R→R\) and \(g : R→R\) be two functions defined by \(f(x) = log_e(x^2 + 1) – e^{–x} + 1\) and \(g(x)=\frac {1−2e^{2x}}{e^x}\). Then, for which of the following range of α, the inequality \(f(g((\frac {α−1)^2}{3}))>f(g(α−\frac 53))\) holds?

The sum of diameters of the circles that touch (i) the parabola \(75x^2 \)= \(64(5y – 3)\) at the point (\(\frac{8}{5}\), \(\frac{6}{5}\)) and (ii) the y-axis is equal to _______.
 

Let \(\vec a=a_1\hat i+a_2\hat j+a_3\hat k\), \(a_i>0,\ i=1, 2, 3\) be a vector which makes equal angles with the coordinate axes OX, OY and OZ. Also, let the projection of \(\vec a\) on the vector \(3\hat i+4\hat j\) be 7. Let \(\vec b\) be a vector obtained by rotating \(\vec a\) with 90°. If \(\vec a,\vec b\) and x-axis are co-planar, then projection of a vector \(\vec b\) on \(3\hat i+4\hat j\) is equal to :

A uniform chain of 6 m length is placed on a table such that a part of its length is hanging over the edge of the table. The system is at rest. The co-efficient of static friction between the chain and the surface of the table is 0.5, the maximum length of the chain hanging from the table is ____m.

A \(0.5\ kg\) block moving at a speed of \(12\ ms^{–1}\) compresses a spring through a distance 30 cm when its speed is halved. The spring constant of the spring will be _____ \(Nm^{–1}\).

The velocity of upper layer of water in a river is \(36\ kmh^{–1}\). Shearing stress between horizontal layers of water is \(10^{–3} Nm^{–2}\). Depth of the river is ______ m. (Co-efficient of viscosity of water is \(10^{–2} Pa.s\))

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 : \(1\ cal \ g^{–1} °C^{–1}\))

The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is 20 cm. The length of the open organ pipe is ______ cm.

The equivalent capacitance between points A and B in below shown figure will be ______ μF.

A resistor develops 300 J of thermal energy in 15 s, when a current of 2 A is passed through it. If the current increases to 3 A, the energy developed in 10 s is ______ J.

The total current supplied to the circuit as shown in figure by the 5 V battery is _______ A.