List of top Questions asked in JEE Main

Match List-I with List-II

Choose the correct answer from the options given below :

The descending order of basicity of following amines is :

Choose the correct answer from the options given below :

Let $ A $ be the set of all functions $ f: \mathbb{Z} \to \mathbb{Z} $ and $ R $ be a relation on $ A $ such that $$ R = \{ (f, g) : f(0) = g(1) \text{ and } f(1) = g(0) \} $$ Then $ R $ is:

Let $ A $ be a $ 3 \times 3 $ real matrix such that \[ A^{2}(A - 2I) - 4(A - I) = O, \] where $ I $ and $ O $ are the identity and null matrices, respectively.
If \[ A^{5} = \alpha A^{2} + \beta A + \gamma I, \] where $ \alpha, \beta, \gamma $ are real constants, then $ \alpha + \beta + \gamma $ is equal to:

Two identical objects are placed in front of convex mirror and concave mirror having same radii of curvature of 12 cm, at same distance of 18 cm from the respective mirrors. The ratio of sizes of the images formed by convex mirror and by concave mirror is:

A mass of 100 g is projected with an initial velocity of 12 m/s at an angle of 60° with the horizontal. Find the difference between the kinetic energy at the point of projection and the kinetic energy at the highest point.

From the English alphabets, 5 letters are chosen and arranged in alphabetical order. The total number of ways in which the middle letter is M is:

The total number of ways the word 'DAUGHTER' can be arranged so that all vowels don't occur together:

Let for some function $ y = f(x) $, $\int_0^x t f(t) \, dt = x^2 f(x), x>0$ and $ f(2) = 3 $. Then $ f(6) $ is equal to:

If \[ \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{96x^2 \cos^2 x}{1 + e^x} dx = \pi(a\pi^2 + \beta), \quad a, \beta \in \mathbb{Z}, \] then $ (a + \beta)^2 $ equals:

The compounds that produce CO$_2$ with aqueous NaHCO$_3$ solution are:

Define a relation $ R $ on the interval $ \left[ 0, \frac{\pi}{2} \right] $ by $ x \, R \, y $ if and only if $ \sec^2 x - \tan^2 y = 1 $. Then $ R $ is:

Let the line $ x + y = 1 $ meet the circle $ x^2 + y^2 = 4 $ at the points A and B. If the line perpendicular to $ AB $ and passing through the mid point of the chord AB intersects the circle at C and D, then the area of the quadrilateral ABCD is equal to:

If $ \lambda $ and $ K $ are de Broglie wavelength and kinetic energy, respectively, of a particle with constant mass. The correct graphical representation for the particle will be:

Match List - I with List - II.

\[ \begin{array}{|c|c|} \hline \text{List - I} & \text{List - II} \\ \hline \text{(A) } \text{Ti}^{3+} & \text{(I) } 3.87 \\ \text{(B) } \text{V}^{2+} & \text{(II) } 0.00 \\ \text{(C) } \text{Ni}^{2+} & \text{(III) } 1.73 \\ \text{(D) } \text{Sc}^{3+} & \text{(IV) } 2.84 \\ \hline \end{array} \]

If \[ \lim_{x \to \infty} \left( \frac{e}{1 - e} \left( \frac{1}{e} - \frac{x}{1 + x} \right) \right)^x = \alpha, \] then the value of \[ \frac{\log_e \alpha}{1 + \log_e \alpha} \] equals:

Let $ y = f(x) $ be the solution of the differential equation\[\frac{dy}{dx} + \frac{xy}{x^2 - 1} = \frac{x^6 + 4x}{\sqrt{1 - x^2}}, \quad -1 < x < 1\] such that $ f(0) = 0 $. If \[6 \int_{-1/2}^{1/2} f(x)dx = 2\pi - \alpha\] then $ \alpha^2 $ is equal to __________.

The torque due to the force $ \left( 2\hat{i} + \hat{j} + 2\hat{k} \right) $ about the origin, acting on a particle whose position vector is $ \hat{i} + \hat{j} + \hat{k} $, would be:

Consider the following cases of standard enthalpy of reaction ($ \Delta H_f^\circ $ in kJ mol$^{-1}$): \[ \text{C}_2\text{H}_6(g) + 7 \text{O}_2(g) \rightarrow 2 \text{CO}_2(g) + 3 \text{H}_2\text{O}(l) \quad \Delta H_1^\circ = -1550 \] \[ \text{C(graphite)} + \text{O}_2(g) \rightarrow \text{CO}_2(g) \quad \Delta H_2^\circ = -393.5 \] \[ \text{H}_2(g) + \frac{1}{2} \text{O}_2(g) \rightarrow \text{H}_2\text{O}(g) \quad \Delta H_3^\circ = -286 \] The magnitude of $ \Delta H_f^\circ $ of $ \text{C}_2\text{H}_6(g) $ is $\_\_\_\_\_$ kJ mol$^{-1}$ (Nearest integer).

In an oxidation-reduction reaction, what happens to the oxidation state of the central atom in $ \text{MnO}_4^- $ when it is reduced to $ \text{Mn}^{2+} $?

If the midpoint of a chord of the ellipse $ \frac{x^2}{9} + \frac{y^2}{4} = 1 $ is $ \left( \sqrt{2}, \frac{4}{3} \right) $, and the length of the chord is $ \frac{2\sqrt{\alpha}}{3} $, then $ \alpha $ is:

The ratio of vapour densities of two gases at the same temperature is $ \frac{4}{25} $, then the ratio of r.m.s. velocities will be:

The volume contraction of a solid copper cube of edge length 10 cm, when subjected to a hydraulic pressure of $ 7 \times 10^6 $ Pa, would be ________________________ mm$^3$. (Given bulk modulus of copper = $ 1.4 \times 10^{11} $ N m$^{-2}$)

The major product of the following reaction is: