List of top Questions asked in JEE Main

Two wires as shown in the figure below, made of steel and have breaking stress of $12 \times 10^8 \text{ N/m}^2$. Area of cross-section of upper wire is $0.008 \text{ cm}^2$ and of lower wire is $0.004 \text{ cm}^2$. The maximum mass that can be added to pan without breaking any wire is _________ kg. (take $g = 10 \text{ m/s}^2$)}

Three masses $m_1 = 4$ kg, $m_2 = 4$ kg and $m_3 = 6$ kg are suspended from a fixed smooth frictionless pulley as shown in the figure below. The value of $T_1/T_2$ is: (take $g = 10 \text{ m/s}^2$)}

Refer to the figure given below, current between terminals $A$ and $B$ is _____}

A wedge $Y$ with mass of 10 kg and all frictionless surfaces and the inclined surface making $37^\circ$ with horizontal. A block $X$ with mass 2 kg is placed at the highest point of the wedge as shown in figure is at rest. At $t = 0$ wedge ($Y$) is pulled toward right with constant force ($f$) of 24 N. Taking the block $X$ at rest at $t = 0$, the time taken by it to slide down 8.8 m on the slope, while $Y$ is on the move, is ________s.

(take $\tan (37^\circ) = 3/4$ and $g = 10 \text{ m/s}^2$)

From \(18 \text{ m}\) height above the ground a ball is dropped from rest. The height above the ground at which the magnitude of velocity equal to the magnitude of acceleration (in the same set of units) due to gravity is ____ \text{m}. (Take \(g = 10 \text{ m/s}^2\) and neglect air resistance)}

In a Vernier calipers, when both jaws touch each other, zero of the Vernier scale is shifted to the right of zero of the main scale and $7^{th}$ Vernier division coincides with a main scale reading. If the value of 1 main scale division is 1 mm and there are 10 Vernier scale divisions, then the Vernier caliper has:

A cube has side length \(5 \text{ cm}\) and modulus of rigidity \(10^5 \text{ N/m}^2\). The displacement produced by a force of \(10 \text{ N}\) in the upper face of the cube is ____ \text{mm}.

A ray of light passing through an equilateral prism is having velocity $2.12 \times 10^8 \text{ m/s}$ in the prism material, then the minimum angle of deviation is _______ degrees.

$L, C$ and $R$ represents physical quantities inductance, capacitance and resistance respectively. The dimensional formula $M L^2 T^{-4} A^{-2}$ corresponds to _________.

Light source having wavelength 331 nm is used to generate photo-electrons whose stopping potential is 0.2 V. The work function of the used metal in the experiment is $\alpha \times 10^{-19} \text{ J}$. The value of $\alpha$ is ______. ($h = 6.62 \times 10^{-34} \text{ Js}, e = 1.6 \times 10^{-19} \text{ C and } c = 3 \times 10^8 \text{ m/s}$)

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R}
Statement I: Change in internal energy of a system containing $n$ mole of ideal gas can be written as $\Delta U = n C_v (T_f - T_i) = \frac{nR}{\gamma - 1}(T_f - T_i)$, where $\gamma = \frac{C_p}{C_v}, T_i = \text{initial temperature}, T_f = \text{final temperature}$.
Statement II: Relation between degree of freedom $f$ and $\gamma (= C_p/C_v)$ is $\gamma = 1 + \frac{2}{f}$}
Choose the correct answer from the options given below

An a.c. source of angular frequency $\omega$ is connected across a resistor $R$ and a capacitor $C$ in series. The current is observed as $I$. Now the frequency of the source is changed to $\omega/4$, (keeping the voltage unchanged) the current is found to be $I/3$. The ratio of resistance to reactance at frequency $\omega$ is:

Let the midpoints of the sides of a triangle \(ABC\) be \( \left(\frac{5}{2},7\right), \left(\frac{5}{2},3\right)\) and \( (4,5) \). If its incentre is \((h,k)\), then \(3h+k\) is equal to:

If the point of intersection of the lines \[ \frac{x+1}{3}=\frac{y+a}{5}=\frac{z+b+1}{7} \] \[ \frac{x-2}{1}=\frac{y-b}{4}=\frac{z-2a}{7} \] lies on the \(xy\)-plane, then the value of \(a+b\) is:

Let \[ A= \begin{bmatrix} 1 & 2\\ 1 & \alpha \end{bmatrix} \quad \text{and} \quad B= \begin{bmatrix} 3 & 3\\ \beta & 2 \end{bmatrix}. \] If \(A^2-4A+I=O\) and \(B^2-5B-6I=O\), then among the following statements: (S1): \[ [(B-A)(B+A)]^T= \begin{bmatrix} 13 & 15\\ 7 & 10 \end{bmatrix} \] (S2): \[ \det(\operatorname{adj}(A+B))=-5 \] Choose the correct option:

Let a line \(L\) passing through the point \((1,1,1)\) be perpendicular to both the vectors \(2\hat{i}+2\hat{j}+\hat{k}\) and \(\hat{i}+2\hat{j}+2\hat{k}\). If \((a,b,c)\) is the foot of perpendicular from the origin on the line \(L\), then the value of \(34(a+b+c)\) is:

If \(|\vec a|=2\) and \(|\vec b|=3\), then the maximum value of \[ 3\left|\left(\vec a+2\vec b\right)\right| + 4\left|\left(3\vec a-2\vec b\right)\right| \] is:

If the domain of the function} \[ f(x)=\sqrt{\log_{0.6}\left(\left|\frac{2x-5}{x^2-4}\right|\right)} \] is \((-\infty,a] \cup \{b\} \cup [c,d) \cup (e,\infty)\), then the value of \(a+b+c+d+e\) is _______.}

If \[ \sin\left(\frac{\pi}{18}\right)\sin\left(\frac{5\pi}{18}\right)\sin\left(\frac{7\pi}{18}\right)=K, \] then the value of \[ \sin\left(\frac{10K\pi}{3}\right) \] is:

If the mean of the following grouped data is \(21\): then \(k\) is one of the roots of the equation:

The number of elements in the set} \[ S=\left\{(r,k): k\in \mathbb{Z} \text{ and } {^{36}C_{r+1}}=\frac{6\left({^{35}C_r}\right)}{k^2-3}\right\} \] is:

The number of seven-digit numbers that can be formed by using the digits \(1,2,3,5,7\) such that each digit is used at least once, is:

Let \( \alpha, \beta \in \mathbb{R} \) be such that the system of linear equations} \[ x + 2y + z = 5 \] \[ 2x + y + \alpha z = 5 \] \[ 8x + 4y + \beta z = 18 \] has no solution. Then \( \frac{\beta}{\alpha} \) is equal to:

If \[ \alpha=\int_{0}^{2\sqrt{3}} \log_2(x^2+4)\,dx + \int_{2}^{4} \sqrt{2^x-4}\,dx, \] then \(\alpha^2\) is equal to _____.

The number of critical points of the function} \[ f(x)= \begin{cases} \dfrac{|\sin x|}{x}, & x\neq0\\ 1, & x=0 \end{cases} \] in the interval \((-2\pi,2\pi)\) is equal to: