List of top Questions asked in JEE Main

The number of points of non-differentiability of the function f(x) = [4 + 13sinx] in (0, 2𝜋) is ____.

Solid Lead nitrate is dissolved in 1 litre of water. The solution was found to boil at $100.15\degree C$. When 0.2 mol of NaCl is added to the resulting solution, it was observed that the solution froze at $–0.8\degree C$. The solubility product of PbCl₂ formed is ________ $\times 10^{–6}$ at 298 K. (Nearest integer) Given: $Kb = 0.5 K \text{ kg mol}^{–1}$ and $Kf = 1.8 K \text{ kg mol}^{–1}$.
Assume molality to be equal to molarity in all cases.

$0.3\, g$ of ethane undergoes combustion at $27^{\circ} C$ in a bomb calorimeter The temperature of calorimeter system (including the water) is found to rise by $05^{\circ} C$ The heat evolved during combustion of ethane at constant pressure is ___$kJ \, mol ^{-1}$ (Nearest integer) [Given : The heat capacity of the calorimeter system is $20 \, kJ\, K ^{-1}, R =83 \, JK ^{-1}\, mol ^{-1}$ Assume ideal gas behaviour Atomic mass of $C$ and $H$ are 12 and $1\, g\, mol ^{-1}$ respectively]

The number of possible isomeric products formed when 3-chioro-1-butene reacts with HCl through carbocation formation is __________

In an Isothermal change, the change in pressure and volume of a gas can be represented for three different temperature $T3 > T2 > T1$ as :

$\lim\limits_{x\rightarrow0}\left(\left(\frac{1-cos^2(3x)}{cos^3(4x)}\right)\left(\frac{sin^3(4x)}{(log_e(2x+1))^5}\right)\right)$is equal to

$\displaystyle\lim _{x \rightarrow \infty} \frac{(\sqrt{3 x+1}+\sqrt{3 x-1})^6+(\sqrt{3 x+1}-\sqrt{3 x-1})^6}{\left(x+\sqrt{x^2-1}\right)^6+\left(x-\sqrt{x^2-1}\right)^6} x^3$

Let f_n = $\int\limits_0^{\pi/2}$ $\left(\displaystyle\sum_{k=1}^{n}\,sin^{k-1}x\right)\left(\displaystyle\sum_{k=1}^{n}\,(2k-1)sin^{k-1}x\right)$ cosx dx, n ∈ N. Then f₂₁ – f₂₀ is equal to____.

Let $f: R -\{2,6\} \rightarrow R$ be real valued function defined as $f(x)=\frac{x^2+2 x+1}{x^2-8 x+12}$ Then range of $f$ is

The ratio of powers of two motors is $\frac{3\sqrt x}{\sqrt x+1}$, that are capable of raising 300 kg water in 5 minutes and 50 kg water in 2 minutes respectively from a well of 100 m deep. The value of x will be

The sum $\displaystyle\sum_{n=1}^{21} \frac{3}{(4 n-1)(4 n+3)}$ is equal to

Let $S =\{1,2,3,5,7,10,11\}$ The number of non-empty subsets of $S$ that have the sum of all elements a multiple of 3 , is _____

A hypothetical gas expands adiabatically such that its volume changes from 08 litres to 27 litres. If the ratio of final pressure of the gas to initial pressure of the gas is $\frac{16}{B 1}$. Then the ratio of $\frac{C p}{C v}$ will be

If the number of words, with or without meaning, which can be made using all the letters of the word MATHEMATICS in which C and S do not come together, is (6!)k , is equal to

When 0.01 mol of an organic compound containing 60% carbon was burnt completely, 4.4 g of $CO_2$ was produced. The molar mass of compound is _______ $gmol^{−1}$. (Nearest integer).

Find out the rank of MONDAY in English dictionary if all alphabets are arranged in order?

The vapour pressure vs. temperature curve for a solution solvent system is shown below.

The boiling point of the solvent is _____°C.

A drop of liquid of density ρ is floating half immersed in a liquid of density σ and surface tension 7.5×10⁻⁴Ncm⁻¹. The radius of drop in cm will be : ( Take : g=10 m/s²)

Let the area enclosed by the lines $ x + y = 2 $, $ y = 0 $, $ x = 0 $, and the curve $ f(x) = \min \left\{ x^2 + \frac{3}{4}, 1 + [x] \right\} $, where $ [x] $ denotes the greatest integer less than or equal to $ x $, be $ A $. Then the value of $ 12A $ is ____________.

Let $ S = \{ M = [a_{ij}], a_{ij} \in \{0, 1, 2\}, 1 \leq i, j \leq 2 \} $ be a sample space and $ A = \{ M \in S : M \text{ is invertible} \} $ be an event. Then $ P(A) $ is equal to:

If $\int \sqrt{\sec 2 x-1} d x=\alpha \log _e\left|\cos 2 x+\beta+\sqrt{\cos 2 x\left(1+\cos \frac{1}{\beta} x\right)}\right|+$ constant, then $\beta-\alpha$ is equal to_______

A small block of mass 100 g is tied to a spring of spring constant 7.5 N/m and length 20 cm. The other end of spring is fixed at a particular point A. If the block moves in a circular path on a smooth horizontal surface with constant angular velocity 5 rad/s about point A, then tension in the spring is-

Which of the following correctly represents the variation of electric potential (V) of a charged spherical conductor of radius (R) with radial distance (r) from the center?

The rms value of conduction current in a parallel plate capacitor is $69\, \mu A$ The capacity of this capacitor, if it is connected to $230 \, V$ ac supply with an angular frequency of $600\, rad / s$, will be :

The number of bijective functions $f :\{1,3,5$, $7, \ldots \ldots 99\} \rightarrow\{2,4,6,8, \ldots \ldots , 100\}$, such that $f (3) \geq f (9) \geq f (15) \geq f (21) \geq \ldots f (99), $ is _____