List of top Questions asked in JEE Main

Match List - I with List - II. 

The variance of the numbers 8, 21, 34, 47, \dots, 320, is:
The value of \( (\sin 70^\circ)(\cot 10^\circ \cot 70^\circ - 1) \) is:
Let A and B be the two points of intersection of the line \( y + 5 = 0 \) and the mirror image of the parabola \( y^2 = 4x \) with respect to the line \( x + y + 4 = 0 \). If \( d \) denotes the distance between A and B, and \( a \) denotes the area of \( \Delta SAB \), where \( S \) is the focus of the parabola \( y^2 = 4x \), then the value of \( (a + d) \) is:
The Young's double slit interference experiment is performed using light consisting of 480 nm and 600 nm wavelengths to form interference patterns. The least number of the bright fringes of 480 nm light that are required for the first coincidence with the bright fringes formed by 600 nm light is:
Let $ x_1, x_2, x_3, x_4 $ be in a geometric progression. If 2, 7, 9, 5 are subtracted respectively from $ x_1, x_2, x_3, x_4 $, then the resulting numbers are in an arithmetic progression. Then the value of $ \frac{1}{24} (x_1 x_2 x_3 x_4) $ is:
Which of the following electronegativity order is incorrect?
Two iron solid discs of negligible thickness have radii \( R_1 \) and \( R_2 \) and moment of inertia \( I_1 \) and \( I_2 \), respectively. For \( R_2 = 2R_1 \), the ratio of \( I_1 \) and \( I_2 \) would be \( \frac{1}{x} \), where \( x \) is:
Let the area of a triangle \( \triangle PQR \) with vertices \( P(5, 4) \), \( Q(-2, 4) \), and \( R(a, b) \) be 35 square units. If its orthocenter and centroid are \( O(2, \frac{14}{5}) \) and \( C(c, d) \) respectively, then \( c + 2d \) is equal to:
A force \( \mathbf{F} = 2\hat{i} + b\hat{j} + \hat{k} \) is applied on a particle and it undergoes a displacement \( \mathbf{r} = \hat{i} - 2\hat{j} - \hat{k} \). What will be the value of \( b \), if the work done on the particle is zero?
If \[ \sum_{r=1}^{13} \frac{1}{\sin \frac{\pi}{4} + (r-1) \frac{\pi}{6}} \sin \frac{\pi}{4} + \frac{\pi}{6} = a \sqrt{3} + b, \quad a, b \in \mathbb{Z}, { then } a^2 + b^2 { is equal to:} \]
A bar magnet has total length \( 2l = 20 \) units and the field point \( P \) is at a distance \( d = 10 \) units from the centre of the magnet. If the relative uncertainty of length measurement is 1%, then the uncertainty of the magnetic field at point P is:
bar magnet has total length 2l = 20 units
If the equation of the parabola with vertex $\left(\frac{3}{2},\, 3\right)$ and the directrix $x + 2y = 0$ is
$$ ax^2 + by^2 - cxy - 30x - 60y + 225 = 0, $$ then $\alpha + \beta + \gamma$ is equal to: 
When sec-butylcyclohexane reacts with bromine in the presence of sunlight, the major product is:
Let \( A(6,8) \), \( B(10\cos\alpha, -10\sin\alpha) \), and \( C(-10\sin\alpha, 10\cos\alpha) \) be the vertices of a triangle. If \( L(a,9) \) and \( G(h,k) \) be its orthocenter and centroid respectively, then \( 5a - 3h + 6k + 100\sin2\alpha \) is equal to _________.
A body of mass \(4\) kg is placed at a point \(P\) having coordinates \( (3,4) \) m. Under the action of force \( \mathbf{F} = (2\hat{i} + 3\hat{j}) \) N, it moves to a new point \(Q\) having coordinates \( (6,10) \) m in \(4\) sec. The average power and instantaneous power at the end of \(4\) sec are in the ratio:
An AC current is represented as: $ i = 5\sqrt{2} + 10 \cos\left(650\pi t + \frac{\pi}{6}\right) \text{ Amp} $ The RMS value of the current is:
HA $ (aq) \rightleftharpoons H^+ (aq) + A^- (aq) $ The freezing point depression of a 0.1 m aqueous solution of a monobasic weak acid HA is 0.20 °C. The dissociation constant for the acid is Given: $ K_f(H_2O) = 1.8 \, \text{K kg mol}^{-1} $, molality ≡ molarity

Let a line passing through the point $ (4,1,0) $ intersect the line $ L_1: \frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{4} $ at the point $ A(\alpha, \beta, \gamma) $ and the line $ L_2: x - 6 = y = -z + 4 $ at the point $ B(a, b, c) $. Then $ \begin{vmatrix} 1 & 0 & 1 \\ \alpha & \beta & \gamma \\ a & b & c \end{vmatrix} \text{ is equal to} $

If $ \frac{1}{1^4} + \frac{1}{2^4} + \frac{1}{3^4} + ... \infty = \frac{\pi^4}{90}, $ $ \frac{1}{1^4} + \frac{1}{3^4} + \frac{1}{5^4} + ... \infty = \alpha, $ $ \frac{1}{2^4} + \frac{1}{4^4} + \frac{1}{6^4} + ... \infty = \beta, $ then $ \frac{\alpha}{\beta} $ is equal to:

Let the ellipse $ 3x^2 + py^2 = 4 $ pass through the centre $ C $ of the circle $ x^2 + y^2 - 2x - 4y - 11 = 0 $ of radius $ r $. Let $ f_1, f_2 $ be the focal distances of the point $ C $ on the ellipse. Then $ 6f_1 f_2 - r $ is equal to
Let $ f(x) $ be a positive function and $I_1 = \int_{-\frac{1}{2}}^1 2x \, f\left(2x(1-2x)\right) dx$ and $I_2 = \int_{-1}^2 f\left(x(1-x)\right) dx.$ Then the value of $\frac{I_2}{I_1}$ is equal to ____

Let $\alpha$ be a solution of $x^2 + x + 1 = 0$, and for some $a$ and $b$ in $\mathbb{R}$, $ \begin{bmatrix} 1 & 16 & 13 \\-1 & -1 & 2 \\-2 & -14 & -8 \end{bmatrix} \begin{bmatrix} 4 \\a \\b \end{bmatrix} = \begin{bmatrix} 0 \\0 \\0 \end{bmatrix}. $ If $\frac{4}{\alpha^4} + \frac{m} {\alpha^a} + \frac{n}{\alpha^b} = 3$, then $m + n$ is equal to _____.

Let $ A = \begin{bmatrix} 2 & 2 + p & 2 + p + q \\4 & 6 + 2p & 8 + 3p + 2q \\6 & 12 + 3p & 20 + 6p + 3q \end{bmatrix} $ If $ \text{det}(\text{adj}(\text{adj}(3A))) = 2^m \cdot 3^n, \, m, n \in \mathbb{N}, $ then $ m + n $ is equal to:

The number of integral terms in the expansion of $ \left( 5^{\frac{1}{2}} + 7^{\frac{1}{8}} \right)^{1016} $ is: