List of top Questions asked in JEE Main

If the system of linear equations \(x - 2y + z = -4\); \(2x + αy + 3z = 5\) and \(3x - y + βz = 3\) has infinitely many solutions then \(12α + 13β\) is equal to

Consider the following redox reaction:\[\text{MnO}_4^- + \text{H}^+ + \text{H}_2 \text{C}_2 \text{O}_4 \rightleftharpoons \text{Mn}^{2+} + \text{H}_2 \text{O} + \text{CO}_2\]The standard reduction potentials are given as below (E\(_\text{red}\)):\[E^\circ_{\text{MnO}_4^-/\text{Mn}^{2+}} = +1.51 \, \text{V}\]\[E^\circ_{\text{CO}_2/\text{H}_2 \text{C}_2 \text{O}_4} = -0.49 \, \text{V}\]If the equilibrium constant of the above reaction is given as \(K_\text{eq} = 10^x\), then the value of (x = ________ ) (nearest integer).

An urn contains 6 white and 9 black balls. Two successive draws of 4 balls are made without replacement. The probability that the first draw gives all white balls, and the second draw gives all black balls, is:

Consider the following reaction
\[A + B \rightarrow C\]
The time taken for A to become 1/4th of its initial concentration is twice the time taken to become 1/2 of the same. Also, when the change of concentration of B is plotted against time, the resulting graph gives a straight line with a negative slope and a positive intercept on the concentration axis.
The overall order of the reaction is ____.

A parallel plate capacitor with plate separation 5mm is charged up by a battery. It is found that on introducing a dielectric sheet of thickness 2 mm, while keeping the battery connections intact, the capacitor draws 25% more charge from the battery than before. The dielectric constant of the sheet is ____.

Considering only the principal values of inverse trigonometric functions, the number of positive real values of \( x \) satisfying \[ \tan^{-1}(x) + \tan^{-1}(2x) = \frac{\pi}{4} \] is:

Let the positive integers be written in the form :

If the $k^\text{th}$ row contains exactly $k$ numbers for every natural number $k$, then the row in which the number $5310$ will be, is _____

Let the range of the function \[ f(x) = \frac{1}{2 + \sin 3x + \cos 3x}, \, x \in \mathbb{R} \, \text{be } [a, b]. \] If \( \alpha \) and \( \beta \) are respectively the arithmetic mean (A.M.) and the geometric mean (G.M.) of \( a \) and \( b \), then \( \frac{\alpha}{\beta} \) is equal to:

Let $A = \{1, 2, 3, 4, 5\}$. Let $R$ be a relation on $A$ defined by $xRy$ if and only if $4x \leq 5y$. Let $m$ be the number of elements in $R$ and $n$ be the minimum number of elements from $A \times A$ that are required to be added to $R$ to make it a symmetric relation. Then $m + n$ is equal to:

Let A= {2, 3, 6, 8, 9, 11} and B = {1, 4, 5, 10, 15} Let R be a relation on A × B define by (a, b)R(c, d) if and only if 3ad – 7bc is an even integer. Then the relation R is

Distance between virtual image, which is twice the size of object placed in front of mirror and object is 45 cm. The magnitude of focal length of the mirror is _____cm.

The total kinetic energy of 1 mole of oxygen at 27°C is :
[Use universal gas constant (R)= 8.31 J/mole K]

If the distance between object and its two times magnified virtual image produced by a curved mirror is 15 cm, the focal length of the mirror must be :

Force between two point charges \( q_1 \) and \( q_2 \) placed in vacuum at \( r \) cm apart is \( F \). Force between them when placed in a medium having dielectric \( K = 5 \) at \( r/5 \) cm apart will be:

Let \( S = (-1, \infty) \) and \( f : S \rightarrow \mathbb{R} \) be defined as \[ f(x) = \int_{-1}^{x} (e^t - 1)^{11} (2t - 1)^5 (t - 2)^7 (t - 3)^{12} (2t - 10)^{61} \, dt \] Let \( p = \) Sum of squares of the values of \( x \), where \( f(x) \) attains local maxima on \( S \). And \( q = \) Sum of the values of \( x \), where \( f(x) \) attains local minima on \( S \). Then, the value of \( p^2 + 2q \) is ______

A square is inscribed in the circle \( x^2 + y^2 - 10x - 6y + 30 = 0 \). One side of this square is parallel to \( y = x + 3 \). If \( (x_i, y_i) \) are the vertices of the square, then \( \sum (x_i^2 + y_i^2) \) is equal to:

Ratio of radius of gyration of a hollow sphere to that of a solid cylinder of equal mass, for moment of Inertia about their diameter axis AB as shown in figure is \(\sqrt\frac{8} {x }\). The value of x is:

$\text{2-chlorobutane} + \text{Cl}_2 \rightarrow \text{C}_4\text{H}_8\text{Cl}_2 \, (\text{isomers})$
$\text{Total number of optically active isomers shown by} \, \text{C}_4\text{H}_8\text{Cl}_2, \, \text{obtained in the above reaction is} \, \_\_\_\_\_\_.$

In photoelectric experiment energy of 2.48 eV irradiates a photo sensitive material. The stopping potential was measured to be 0.5 V. Work function of the photo sensitive material is :

If $\sin x = -\frac{3}{5}$, where $\pi<x<\frac{3\pi}{2}$, then $80(\tan^2 x - \cos x)$ is equal to:

Let $A = I_2 - MM^T$, where $M$ is a real matrix of order $2 \times 1$ such that the relation $M^T M = I_1$ holds. If $\lambda$ is a real number such that the relation $AX = \lambda X$ holds for some non-zero real matrix $X$ of order $2 \times 1$, then the sum of squares of all possible values of $\lambda$ is equal to:

Let \( R \) be the interior region between the lines \( 3x - y + 1 = 0 \) and \( x + 2y - 5 = 0 \) containing the origin. The set of all values of \( a \), for which the points \( (a^2, a + 1) \) lie in \( R \), is:

Number of geometrical isomers possible for the given structure is/are ___________.