List of top Questions asked in JEE Main

Two wires of cross sectional area $1 \text{ cm}^2$ and $2 \text{ cm}^2$ and lengths 20 cm and 30 cm are connected to the same load. If their extensions are same, find the ratio of their Young's modulus :

10kg ice at $-10^\circ C$ & 100kg water at $25^\circ C$ are mixed together. Find final temperature. (Given $S_{ice} = \frac{1}{2}$ cal/g$^\circ C$, $L_{fusion} = 80$cal/g and $S_{water} = 1$cal/g$^\circ C$)

An atom ${}_3^8 X$ is bombarded with electrons, neutrons and protons and in 10 sec, 10 electrons, 10 protons and 9 neutrons are absorbed. If final surface area is x% of initial area, find x : -

In the system of two discs and a rod of mass 600 g each, a torque of magnitude $43 \times 10^5$ dyne-cm is applied along the axis of rotation as shown in figure. Find the approx angular acceleration about given axis :

Find external force F so that block can move on inclined plane with constant velocity.

As shown in the figure, radius of gyration about the axis shown in $\sqrt{n}$ cm for a solid sphere. Find 'n'.

Consider the following changes : $\text{SnO}_2 \rightarrow \text{SnO}$ $\Delta G_1^o$ and $\text{PbO}_2 \rightarrow \text{PbO}$ $\Delta G_2^o$. Select the correct option

If sum of first 4 terms of an A.P. is 6 and sum of first 6 terms is 4, then sum of first 12 terms of an A.P. is

Area bounded by $\{(x, y) : xy \le 8 ; y \le x^2, y \ge 1\}$ is :

Value of : $\sum_{k=1}^{\infty} \frac{(-1)^k \cdot k(k+1)}{k!}$

In $\Delta ABC$ if $\frac{\tan(A-B)}{\tan A} + \frac{\sin^2 C}{\sin^2 A} = 1$ where $A, B, C \in (0, \frac{\pi}{2})$ then

Let x be the number of 9 digit numbers formed by taking digits from first 9 natural numbers, where only one digit is repeated twice & y be the number of 9 digit numbers formed from first 9 natural numbers, such that exactly 2 digits repeated twice then

Consider the 10 observations 2, 3, 5, 10, 11, 13, 15, 21, a and b such that mean of observation is a and variance is 34.2. Then the mean deviation about median, is :

Let $\tan \left( \frac{\pi}{4} + \frac{1}{2} \cos^{-1} \frac{2}{3} \right) + \tan \left( \frac{\pi}{4} - \frac{1}{2} \sin^{-1} \frac{2}{3} \right) = k$. Then number of solution of the equation $\sin^{-1}(kx - 1) = \sin x - \cos^{-1} x$ is/are :

If $f(x^2 + 1) = x^4 + 5x^2 + 1$, then find $\int_{0}^{3} f(x) dx$ :

The value of $\lim_{x \to 0} \frac{\ln(\sec(ex) \cdot \sec(e^2x) \dots \sec(e^{10}x))}{e^2 - e^{2\cos x}}$ is :

Let $x \frac{dy}{dx} - \sin 2y = x^3(2 - x^3) \cos^2 y ; y(2) = 0$, then find $\tan(y(1))$ :

Given $\frac{1}{\alpha} - \frac{1}{\beta} = \frac{1}{3}$ such that roots of the quadratic equation $\lambda x^2 + (\lambda+1)x + 3 = 0$ are $\alpha$ & $\beta$, then sum of values of $\lambda$ is equal to :

The value of $S = \sum_{r=1}^{20} \sqrt{\pi \int_{0}^{r} x |\sin \pi x| dx}$ is :

Let $\int \frac{1 - 5 \cos^2 x}{\sin^5 x \cos^2 x} dx = f(x) + c$ then find $f\left(\frac{\pi}{4}\right) - f\left(\frac{\pi}{6}\right)$ :

If $\vec{a}, \vec{b} \& \vec{c}$ are unit vectors such that $(\vec{a}-\vec{b})^2 + (\vec{b}-\vec{c})^2 + (\vec{c}-\vec{a})^2 = 9$. Find positive k if $|2\vec{a} + k\vec{b} + k\vec{c}| = 3$ :

Product of first 3 terms of a G.P. is 27 and sum is $R - \{a,b\}$, then $a^2 + b^2$ is equal to :

If $g(x) = 3x^2 + 2x - 3, f(0) = -3, 4g(f(x)) = 3x^2 - 32x + 72$ then find $f(g(2))$ where $f(x)>0$ for all valid x:

Find possible no. of triplets (b, c, d), such that $x^2 + 2$ is divisor of $x^3 + bx^2 + cx + d$ & b, c, d $ \le $ 20 & b, c, d $ \in $ N :

Maximum value of $n$ for which $40^n$ divides $60!$ is