List of top Questions asked in JEE Main, KCET

Consider the differential equation \[ \sin\left(\frac{y}{x}\right)\frac{dy}{dx} + 1 = \frac{y}{x}\sin\left(\frac{y}{x}\right) \] with $ y(1) = \frac{\pi}{2} $. Let \[ \alpha = \cos\left(\frac{y(e^{12})}{e^{12}}\right). \] If $ r $ is the radius of the circle \[ x^2 + y^2 - 2px + 2py + \alpha + 2 = 0, \] then the number of integral values of $ p $ is:

In a period, ionisation energy of the extreme left and electronegativity of the extreme right element is respectively ______. (Don’t consider Noble gases).

Given below are two statements:

Thin symmetric prism of $\mu = 1.5$. Find ratio of incident angle and minimum deviation.

0.2 g of an organic compound is subjected to estimation of $S$ by Carius method, giving $0.6$ g $BaSO_4$. Find \% of $S$. (Nearest integer)

Sum of $ 1 + \dfrac{1}{2}(1^2 + 2^2) + \dfrac{1}{3}(1^2 + 2^2 + 3^2) + \dots $ up to 10 terms is

The sum of all possible values of $ \theta \in [0, 2\pi] $, for which the system of equations:
$ x \cos 3\theta - 8y - 12z = 0 $
$ x \cos 2\theta + 3y + 3z = 0 $
$ x \sin \theta + y + 3z = 0 $
has a non-trivial solution, is equal to:

\[ \int_{-1}^{1} \frac{x^3 + |x| + 1}{x^2 + |x| + 1} \, dx \]

The area (in square units) of the region $\{(x,y): x^2 - 8x \leq y \leq -x\}$ is:

Compare the bond length x, y, and z in the following compound.

Given the nuclear reaction: \[ \text{H}_2^2 + \text{H}_1^2 \rightarrow \text{He}_4 \] Binding energy per nucleon of H$_1^2$ and H$_2^4$ are 1.1 MeV and 7 MeV respectively. Find energy released in the nuclear reaction given above.

The compound

is treated sequentially with: (A) Excess HI/Red P
(B) $ \text{V}_2\text{O}_5 $, 773 K
(C) Benzyl chloride/AlCl$_3$
Find the number of π-bonds in the final product.

The hybridisation states of Ni in the 3 complexes Ni(CO)$_4$, [Ni(NH$_3$)$_6$]$^{2+}$, [Ni(CN)$_4$]$^{2-}$ are

Find the electric field for the given electrostatic potential field at point $P(2,3)$: \[ V = 5(x^2 - y^2) \]

If the percentage change in the radius of a sphere is $2\%$, then find the percentage change in the volume of the sphere.

Minimum deviation for an equilateral prism is $30^\circ$. The refractive index of the prism material is:

If the system shown in the figure is released from rest, find the speed of the $6\,\text{kg}$ block just before hitting the ground. $(g = 10\,\text{m/s}^2)$

Find the voltage $V_{AB}$ and the current $i_{BA}$ in the given circuit.

For the circuit shown below, find the current across $ AB $, $ (I_{AB}) $.

If moment of inertia of rod about axis AB is equal to moment of inertia of solid sphere about an axis parallel to AB which is at 9m from AB axis as shown in the figure. If $ R = \frac{\alpha}{2} $, then find $ \alpha $.

Find the work done in expanding a soap bubble from radius $1\,\text{cm}$ to $2\,\text{cm}$. Surface tension is $ \gamma = 7.2 \times 10^{-2}\,\text{N/m} $.

P is a point on \[ \frac{x^2}{9}+\frac{y^2}{4}=1 \] as $P(3\cos\alpha,2\sin\alpha)$. Q is a point on \[ x^2+y^2-14x+14y+82=0 \] R is a point on line \[ x+y=5 \] If the centroid of triangle $PQR$ is \[ \left(\cos\alpha+2,\;\frac{2\sin\alpha}{3}+3\right) \] find the sum of possible ordinates of $R$.

If $\left(2\alpha+1,\;\alpha^2-3\alpha,\;\frac{\alpha-1}{2}\right)$ is the image of $(\alpha,2\alpha,1)$ in the line \[ \frac{x-2}{3}=\frac{y-1}{2}=\frac{z}{1}, \] then the value of $\alpha$ is:

For tetrahedral complex, the correct order of energy of $d$-orbitals is:

The value of $ \sum_{n=1}^{10} \frac{528}{n(n+1)(n+2)} $ is equal to: