List of top Questions asked in JEE Main

The value of the integral $\int_{\pi/6}^{\pi/3} \left( \frac{4 - \csc^2 x}{\cos^4 x} \right) dx$ is:

Consider the system of linear equations in x, y, z:
x+2y+tz = 0,
6x + y + 5t z = 0,
3x + y + f(t) z = 0,
where f: R$\rightarrow$ R is a differentiable function. If this system has infinitely many solutions for all t $\in$ R, then f

Let $A = \{1, 2, 3, 4, 5, 6\}$. The number of one-one functions $f: A \to A$ such that $f(1) \ge 3, f(3) \le 4$ and $f(2) + f(3) = 5$, is _________.

The product of all possible values of $\alpha$, for which $\lim_{x \to 0} \frac{1-\cos(\alpha x)\cos((\alpha+1)x)\cos((\alpha+2)x)}{\sin^2((\alpha+1)x)} = 2$, is:

If $\frac{\pi}{4} + \sum_{p=1}^{11} \tan^{-1} \left( \frac{2^{p-1}}{1 + 2^{2p-1}} \right) = \alpha$, then $\tan \alpha$ is equal to _________.

Let tan A, tan B, where A, B $\in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$, be the roots of the quadratic equation $x^2 - 2x - 5 = 0$. Then $20 \sin^2\left(\frac{A+B}{2}\right)$ is equal to:

Let the sum of the first n terms of an A.P. be $3n^2 + 5n$. Then the sum of squares of the first 10 terms of the A.P. is:

The mean deviation about the mean for the data

56 is equal to:

The sum of all the integral values of p such that the equation $3\sin^2x + 12\cos x - 3 = p, x \in \mathbb{R}$, has at least one solution, is:

The square of the distance of the point of intersection of the lines $\vec{r} = (\hat{i} + \hat{j} - \hat{k}) + \lambda(a\hat{i} - \hat{j})$, $a \neq 0$ and $\vec{r} = (4\hat{i} - \hat{k}) + \mu(2\hat{i} + a\hat{k})$ from the origin is:

Let a, b $\in$ C. Let $\alpha, \beta$ be the roots of the equation $x^2 + ax + b = 0$. If $\beta-\alpha =\sqrt{11}$ and $\beta^2-\alpha^2 = 3i\sqrt{11}$, then $(\beta^3 - \alpha^3)^2$ is equal to:

Let a focus of the ellipse E: $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ be S(4, 0) and its eccentricity be $\frac{4}{5}$. If the point P(3, $\alpha$) lies on E and O is the origin, then the area of $\Delta$POS is equal to:

If minimum deviation for an equilateral prism is \(30^\circ\), then refractive index of the prism is:

Match List-I with List-II.

Given below are two statements for catalytic properties of transition metals.
Statement I: First row transition metals which act as catalyst utilise their 3d electrons only for formation of bonds between reactant molecules and atoms on the surface of catalyst.
Statement II: There is increase in the concentration of reactants on the surface of catalyst which strengthens the bonds in reacting molecules.

‘x’ is the product which is obtained from benzene by reacting it with carbon monoxide and hydrogen chloride in the presence of cuprous chloride. ‘y’ is the major product obtained from the benzene by reacting it with ethanoyl chloride in the presence of anhydrous AlCl$_3$. Product (major) obtained by heating x and y in the presence of alkali is z. Total number of $\pi$ (pi) electrons in z is _______.

Match List-I with List-II.

Which of the following statements are not correct?
A. For water, magnitude of \(K_b\) is more than the magnitude of \(K_f\).
B. The elevation in boiling point of water when a non-volatile solute is added to it is larger in magnitude than its depression in freezing point.
C. Osmotic pressure measurement is preferred over any other colligative property to determine molar mass of proteins and polymers.
D. The dimerised form of benzoic acid in benzene is C₆H₅-C-OH ⋯ O=C-C₆H₅

n-Butane on monochlorination under photochemical condition gives an optically active compound "P". "P" on further chlorination gives dichloro compounds. The number of dichloro compounds obtained (ignore stereoisomers) is:

Consider the following reaction.
[The structure of a piperidine derivative reacting with $NaBH_4/MeOH$, $NaOH(aq)$, \(\Delta\), $H_3O_+$]
The major product (P) formed is:}

Which of the following amino acid will give violet coloured complex with neutral ferric chloride solution?

Consider the reaction} \[ 2\text{H}_2\text{S (g)} + 3\text{O}_2\text{(g)} \rightarrow 2\text{H}_2\text{O (l)} + 2\text{SO}_2\text{(g)} \] The magnitude of enthalpy change for the reaction in kJ mol\(^{-1}\) is _______ (Nearest integer).

The total number of aromatic compounds/species from the following is ________.
[Six structures shown]}

Which statements are True?
A. In Hoffmann bromamide degradation, 4 moles of NaOH and 2 moles of Br₂ are consumed per mole of an amide.
B. Hoffmann bromamide reaction is not given by alkyl amides.
C. Primary amines can be synthesized by Hoffmann bromamide degradation.
D. Secondary amide on reaction with $Br_2$ and NaOH will give secondary amine.
E. The by-products of Hoffmann degradation are $Na_2CO_3$, $NaBr$ and $H_2O$.

The major product of which of the following reaction is not obtained by rearrangement reaction?}