List of top Questions asked in JEE Main- 2026

A particle is rotating in a circular path and at any instant its motion can be described as} \[ \theta=\frac{5t^4}{40}-\frac{t^3}{3}. \] The angular acceleration of the particle after \(10\) seconds is ____ rad/s\(^2\).

A parallel plate air capacitor has a capacitance \(C\). When it is half filled as shown in the figure with a dielectric constant \(K=5\), the percentage increase in the capacitance is:

The position of an object having mass \(0.1\) kg as a function of time \(t\) is given as} \[ \vec r = (10t^2\hat{i}+5t^3\hat{j})\ \text{m}. \] At \(t=1\) s, which of the following statements are correct?} A.} Linear momentum \( \vec p = (2\hat{i}+1.5\hat{j})\) kg m/s. B.} Force acting on the object \( \vec F = (2\hat{i}+3\hat{j})\) N. C.} Angular momentum about origin \( \vec L = 15\hat{k}\) J s. D.} Torque about origin \( \vec \tau = 20\hat{k}\) N m. Choose the correct answer.

A planet \(P_1\) is moving around a star of mass \(2M\) in an orbit of radius \(R\). Another planet \(P_2\) is moving around another star of mass \(4M\) in an orbit of radius \(2R\). The ratio of time periods of revolution of \(P_2\) and \(P_1\) is:

Heat is supplied to a diatomic gas at constant pressure. Then the ratio of \( \Delta Q : \Delta U : \Delta W \) is:

The diameter of a wire measured by a screw gauge of least count \(0.001\) cm is \(0.08\) cm. The length measured by a scale of least count \(0.1\) cm is \(150\) cm. When a weight of \(100\) N is applied to the wire, the extension in length is \(0.5\) cm measured by a micrometer of least count \(0.001\) cm. The error in the measured Young’s modulus is \(\alpha \times 10^9\) N/m\(^2\). The value of \(\alpha\) is:

Let a circle \(C\) have its centre in the first quadrant, intersect the coordinate axes at exactly three points and cut off equal intercepts from the coordinate axes. If the length of the chord of \(C\) on the line \(x+y=1\) is \(\sqrt{14}\), then the square of the radius of \(C\) is _____.}

Let \(a,b,c \in \{1,2,3,4\}\). If the probability that \[ ax^2 + 2\sqrt{2}\,bx + c>0 \quad \text{for all } x \in \mathbb{R} \] is \( \frac{m}{n} \), where \(\gcd(m,n)=1\), then \(m+n\) 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 _____.

Let \([\,]\) denote the greatest integer function. Then the value of} \[ \int_{0}^{3}\left(\frac{e^x+e^{-x}}{[x]!}\right)dx \] is:

If the curve \(y=f(x)\) passes through the point \((1,e)\) and satisfies the differential equation} \[ dy=y(2+\log_e x)\,dx,\quad x>0, \] then \(f(e)\) is equal to:

Let \(y=y(x)\) be the solution curve of the differential equation} \[ (1+\sin x)\frac{dy}{dx}+(y+1)\cos x=0,\qquad y(0)=0. \] If the curve passes through the point \( \left(\alpha,-\frac12\right) \), then a value of \( \alpha \) 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 \[ \sum_{k=1}^{n} a_k = 6n^3, \] then} \[ \sum_{k=1}^{6}\left(\frac{a_{k+1}-a_k}{36}\right)^2 \] is equal to _______.

If \[ \lim_{x\to 2}\frac{\sin(x^3-5x^2+ax+b)}{(\sqrt{x-1}-1)\log_e(x-1)}=m, \] then \(a+b+m\) is equal to:

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 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 \[ S=\{x\in[-\pi,\pi]:\sin x(\sin x+\cos x)=a,\; a\in\mathbb{Z}\}. \] Then \(n(S)\) is equal to:

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:

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 an ellipse \[ \frac{x^2}{a^2}+\frac{y^2}{b^2}=1,\quad a<b \] pass through the point \((4,3)\) and have eccentricity \( \frac{\sqrt5}{3} \). Then the length of its latus rectum 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:

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:

Let \(A\) be the set of first \(101\) terms of an A.P., whose first term is \(1\) and the common difference is \(5\), and let \(B\) be the set of first \(71\) terms of an A.P., whose first term is \(9\) and the common difference is \(7\). Then the number of elements in \(A \cap B\), which are divisible by \(3\), 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: