List of top Questions asked in JEE Main

Match List I with List II

List I	List II
A. \( \oint \vec{B} \cdot d\vec{l} = \mu_0 i_c + \mu_0 \epsilon_0 \frac{d\phi_E}{dt} \)	I. Gauss' law for electricity
B. \( \oint \vec{E} \cdot d\vec{l} = -\frac{d\phi_B}{dt} \)	II. Gauss' law for magnetism
C. \( \oint \vec{E} \cdot d\vec{A} = \frac{Q}{\epsilon_0} \)	III. Faraday law
D. \( \oint \vec{B} \cdot d\vec{A} = 0 \)	IV. Ampere – Maxwell law

Choose the correct answer from the options given below

The potential energy function (in joules) of a particle in a region of space is given as\[U = (2x^2 + 3y^3 + 2z).\]Here \( x \), \( y \), and \( z \) are in meters. The magnitude of the \( x \)-component of force (in newtons) acting on the particle at point \( P (1, 2, 3) \) m is:

A line with direction ratios \( 2, 1, 2 \) meets the lines \(x = y + 2 = z\) and \(x + 2 = 2y = 2z\) respectively at the points \( P \) and \( Q \). If the length of the perpendicular from the point \( (1, 2, 12) \) to the line \( PQ \) is \( l \), then \( l^2 \) is

If the mean and variance of the data \( 65, 68, 58, 44, 48, 45, 60, \alpha, \beta, 60 \) where \( \alpha > \beta \) are \( 56 \) and \( 66.2 \) respectively, then \( \alpha^2 + \beta^2 \) is equal to

If the solution curve \( y = y \, x \) of the differential equation \((1 + y^2) \left(1 + \log_e x\right) dx + x \, dy = 0, \quad x > 0\) passes through the point \( (1, 1) \) and\[y(e) = \frac{\alpha - \tan\left(\frac{3}{2}\right)}{\beta + \tan\left(\frac{3}{2}\right)},\]then \( \alpha + 2\beta \) is

If the points of intersection of two distinct conics \(x^2 + y^2 = 4b\) and \(\frac{x^2}{16} + \frac{y^2}{b^2} = 1\) lie on the curve \(y^2 = 3x^2\) then \( 3\sqrt{3} \) times the area of the rectangle formed by the intersection points is __.

Let \( f(x) = 2^x - x^2, \, x \in \mathbb{R} \). If \( m \) and \( n \) are respectively the number of points at which the curves \( y = f(x) \) and \( y = f'(x) \) intersect the x-axis, then the value of \( m + n \) is

Equation of two diameters of a circle are \(2x-3y=5\) and \(3x-4y=7\).The line joining the points \((-\frac{22}{7},-4)\) and \((-\frac{1}{7},3)\) intersects the circle at only one point \(P(\alpha,\beta)\).Then \(17\beta-\alpha\) is equal to.

Suppose\(f(x)=\frac{(2^x+2^{-x})tanx\sqrt{tan^{-1}(x^2-x+1)}}{(7x^2+3x+1)^{3}}\) then the value of \(f'(0)\) is equal to

Let PQR be a triangle with R (-1,4, 2). Suppose M(2, 1, 2) is the mid point of PQ. The distance of the centroid of \(\triangle PQR\) from the point of intersection of the line\(\frac{x-2}{0}=\frac{y}{2}=\frac{z+3}{-1}\) and \(\frac{x-1}{1}=\frac{y+3}{-3}=\frac{z+1}{1}\) is

A function \(y=f(x)\) satisfies\(f (x)sin2x+sinx-(1+cos^2x) f'(x)=0\) with condition\(f(0)=0\).Then\(f(\frac{\pi}{2})\) equals to

If\(\alpha,-\frac{\pi}{2}<\alpha<\frac{\pi}{2}\)is the solution of\( 4cos\theta+ 5sin\theta=1\)then the value of \(tan\alpha\) is

Let\((5,\frac{a}{4})\),be the circumcenter of a triangle with vertices A (a, -2),B (a, 6)and C \((\frac{a}{4},-2)\).Let \(\alpha\) denote the circumradius, \(\beta\) denote the area and \(\gamma\) denote the perimeter of the triangle. Then \(\alpha+\beta+\gamma\) is

In an A.P., the sixth term a_6​=2. If the product a₁​a₄​a₅ is the greatest, then the common difference of the A.P. is equal to:

Total number of compounds with Chiral carbon atoms from following is ________.

$\text{CH}_3 - \text{CH}_2 - \text{CH(NO}_2\text{) - COOH} \\ \text{CH}_3 - \text{CH}_2 - \text{CHBr - CH}_2 - \text{CH}_3 \\ \text{CH}_3 - \text{CH(I) - CH}_2 - \text{NO}_2 \\ \text{CH}_3 - \text{CH}_2 - \text{CH(OH) - CH}_2\text{OH} \\$

$9.3 \, \text{g of aniline is subjected to reaction with excess of acetic anhydride to prepare acetanilide. The mass of acetanilide produced if the reaction is 100\% completed is } \_\_\_\_\_ \times 10^{-1} \, \text{g.} \\ \text{(Given molar mass in g mol}^{-1}\text{) N: 14, O: 16, C: 12, H: 1}$

$\text{For a certain thermochemical reaction } \text{M} \rightarrow \text{N at } T = 400 \, \text{K}, \, \Delta H^\circ = 77.2 \, \text{kJ mol}^{-1}, \, \Delta S = 122 \, \text{JK}^{-1}, \\ \text{log equilibrium constant (log K) is } - \_\_\_\_\_ \times 10^{-1}.$

$\text{The Spin only magnetic moment value of square planar complex } [\text{Pt(NH}_3\text{)}_2\text{Cl(NH}_2\text{CH}_3\text{)}]\text{Cl is } \_\_\_\_\_\_ \text{ B.M. (Nearest integer)} \\ \text{(Given atomic number for Pt = 78)}$

Identity the incorrect pair from the following:

The incorrect statement regarding conformations of ethane is:

Identify B formed in the reaction.
\[ \text{Cl} - \text{(CH}_2\text{)}_4 - \text{Cl} \xrightarrow{\text{excess NH}_3} A \xrightarrow{\text{NaOH}} B + \text{H}_2\text{O} + \text{NaCl} \]

Given below are two statements:
Statement (I) : Oxygen being the first member of group 16 exhibits only –2 oxidation state.
Statement (II) : Down the group 16 stability of +4 oxidation state decreases and +6 oxidation state increases.
In the light of the above statements, choose the most appropriate answer from the options given below:

Bond line formula of HOCH(CN)$_2$ is:

Match List-I with List-II.

Choose the correct answer from the options given below:

The final product A, formed in the following reaction sequence is: