List of top Questions asked in JEE Main

The sum of all rational numbers in $ (2 + \sqrt{3})^8 $ is:

At 715 mm pressure, 300 K, volume of N$_2$ (g) evolved was 80 mL by a 0.4 g sample of organic compound. Find the percentage of N in the organic compound. Given aqueous tension at 300 K = 15 mm.

$ x $ is a peptide which is hydrolyzed to 2 amino acids $ y $ and $ z $. $ y $ when reacted with HNO$_2$ gives lactic acid. $ z $ when heated gives a cyclic structure as below:

Let $ I_1 = \int_{\frac{1}{2}}^{1} 2x \cdot f(2x(1 - 2x)) \, dx $
and $ I_2 = \int_{-1}^{1} f(x(1 - x)) \, dx \; \text{then} \frac{I_2}{I_1} \text{ equals to:} $

From the combination of resistors with resistance values $ R_1 = R_2 = R_3 = 5 \, \Omega $ and $ R_4 = 10 \, \Omega $, which of the following combination is the best circuit to get an equivalent resistance of 6 $ \Omega $?

An object is kept at rest at a distance of 3R above the earth’s surface where $ R $ is earth’s radius. The minimum speed with which it must be projected so that it does not return to earth is: (Assume $ M $ = mass of earth, $ G $ = Universal gravitational constant)

Displacement of a wave is expressed as $$ x(t) = 5 \cos \left( 628t + \frac{\pi}{2} \right) \, \text{m}. $$ The wavelength of the wave when its velocity is 300 m/s is:

A particle of charge 1.6 $\mu$C and mass 16 $\mu$g is present in a strong magnetic field of 6.28 T. The particle is then fired perpendicular to magnetic field. The time required for the particle to return to original location for the first time is _______ s. (Take $ \pi = 3.14 $)

Let the set of all values of $ p \in \mathbb{R} $, for which both the roots of the equation $ x^2 - (p + 2)x + (2p + 9) = 0 $ are negative real numbers, be the interval $ (\alpha, \beta) $. Then $ \beta - 2\alpha $ is equal to:

The number of singular matrices of order 2, whose elements are from the set $ \{2, 3, 6, 9\} $ is:

Given below are two statements:
Statement I: D-(+)-glucose + D-(+)-fructose $\xrightarrow{H_2O}$ sucrose sucrose $\xrightarrow{\text{Hydrolysis}}$ D-(+)-glucose + D-(+)-fructose
Statement II: Invert sugar is formed during sucrose hydrolysis.
In the light of the above statements, choose the correct answer from the options given below -

Let $ f(x) = \begin{cases} (1+ax)^{1/x} & , x<0 \\1+b & , x = 0 \\\frac{(x+4)^{1/2} - 2}{(x+c)^{1/3} - 2} & , x>0 \end{cases} $ be continuous at x = 0. Then $ e^a bc $ is equal to

Let the product of the focal distances of the point P(4, $ 2\sqrt{3} $) on the hyperbola H: $ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 $ be 32. Let the length of the conjugate axis of H be p and the length of its latus rectum be q. Then $ p^2 + q^2 $ is equal to .....

The probability of forming a 12 persons committee from 4 engineers, 2 doctors, and 10 professors containing at least 3 engineers and at least 1 doctor is:

For $\mathrm{A}_{2}+\mathrm{B}_{2} \rightleftharpoons 2 \mathrm{AB}$ $\mathrm{E}_{\mathrm{a}}$ for forward and backward reaction are 180 and $200 \mathrm{~kJ} \mathrm{~mol}^{-1}$ respectively. If catalyst lowers $\mathrm{E}_{\mathrm{a}}$ for both reaction by $100 \mathrm{~kJ} \mathrm{~mol}^{-1}$. Which of the following statement is correct?

Fortification of food with iron is done using $\mathrm{FeSO}_{4} .7 \mathrm{H}_{2} \mathrm{O}$. The mass in grams of the $\mathrm{FeSO}_{4} .7 \mathrm{H}_{2} \mathrm{O}$ required to achieve 12 ppm of iron in 150 kg of wheat is _______ (Nearest integer).} (Given : Molar mass of $\mathrm{Fe}, \mathrm{S}$ and O respectively are 56,32 and $16 \mathrm{~g} \mathrm{~mol}^{-1}$ )

If the domain of the function $ f(x) = \log_7(1 - \log_4(x^2 - 9x + 18)) $ is $ (\alpha, \beta) \cup (\gamma, \delta) $, then $ \alpha + \beta + \gamma + \delta $ is equal to

The number of real roots of the equation $ x|x-2| + 3|x-3| + 1 = 0 $ is:

Let $ e_1 $ and $ e_2 $ be the eccentricities of the ellipse $ \frac{x^2}{b^2} + \frac{y^2}{25} = 1 $ and the hyperbola $ \frac{x^2}{16} - \frac{y^2}{b^2} = 1, $ respectively. If $ b<5 $ and $ e_1 e_2 = 1 $, then the eccentricity of the ellipse having its axes along the coordinate axes and passing through all four foci (two of the ellipse and two of the hyperbola) is:

Given below are two statements :
Statement (I) : On hydrolysis, oligo peptides give rise to fewer number of $ \alpha $-amino acids while proteins give rise to a large number of $ \beta $-amino acids.
Statement (II) : Natural proteins are denatured by acids which convert the water soluble form of fibrous proteins to their water insoluble form.
In the light of the above statements, choose the most appropriate answer from the options given below :

The hydration energies of $ K^+ $ and $ Cl^- $ are $ -x $ and $ -y $ kJ/mol respectively. If lattice energy of KCl is $ -z $ kJ/mol, then the heat of solution of KCl is :

Only litre buffer solution was prepared by adding 0.10 mol each of $ NH_3 $ and $ NH_4Cl $ in deionised water. The change in pH on addition of 0.05 mol of HCl to the above solution is _____ $ \times 10^{-2} $, (Nearest integer) (Given : $ pK_b $ of $ NH_3 = 4.745 $ and $ \log_{10}3 = 0.477 $)

Consider the following molecules:

The order of rate of hydrolysis is:

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Net dipole moment of a polar linear isotropic dielectric substance is not zero even in the absence of an external electric field. Reason
(R): In absence of an external electric field, the different permanent dipoles of a polar dielectric substance are oriented in random directions.
In the light of the above statements, choose the most appropriate answer from the options given below:

The molarity of a 70%(mass/mass) aqueous solution of a monobasic acid (X) is: