List of top Questions asked in JEE Main

If $∫^{0.15}_{-0.15 }|100x^2-1|dx=\frac{k}{3000,}$ then k is equal to____.

Two circles in the first quadrant of radii r₁ and r₂ touch the coordinate axes. Each of them cuts off an intercept of 2 units with the line x + y = 2. Then $r^2_1+r_2^2– r_1r_2$ is equal to_____.

Let the plane x + 3y – 2z + 6 = 0 meet the co-ordinate axes at the points A,B,C. If the orthocentre of the triangle ABC is $(α,β,\frac{6}{7}),$ then 98(α + β)² is equal to___.

Values of work function (Wo) for a few metals are given below

Metal	Li	Na	K	Mg	Cu	Ag
W_o/eV	2.42	2.3	2.25	3.7	4.8	4.3

The number of metals which will show photoelectric effect when light of wavelength 400nm falls on it is____

Given: h = 6.6 × 10^-34 J s
c = 3 x 10⁸ m s^-1
e = 1.6 x 10^-19 C

In an oligopeptide named Alanylglycylphenyl alanyl isoleucine, the number of sp² hybridised carbons is_____.

The mass of NH3 produced when 131.8 kg of cyclohexanecarbaldehyde undergoes Tollen's test is ___ kg. (Nearest Integer)
Molar Mass of C = 12g/mol
N = 14g/mol
0 = 16g/mol

What weight of glucose must be dissolved in 100 g of water to lower the vapour pressure by 0.20 mm Hg?
(Assume dilute solution is being formed)
Given : Vapour pressure of pure water is 54.2 mm Hg at room temperature. Molar mass of glucose is 180 g mol^–1 .

A body cools from $60\degree C$ to $40\degree C$ in 6 minutes. If, temperature of surroundings is $10\degree C$. Then, after the next 6 minutes, its temperature will be ______$\degree C$.

Cobalt chloride when dissolved in water forms pink colored complex $X$ which has octahedral geometry. This solution on treating with cone $HCl$ forms deep blue complex, $\underline{Y}$ which has a $\underline{Z}$ geometry $X, Y$ and $Z$, respectively, are

$I _{ CM }$ is the moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc $I_{A B}$ is it's moment of inertia about an axis $AB$ perpendicular to plane and parallel to axis $CM$ at a distance $\frac{2}{3} R$ from center Where $R$ is the radius of the dise The ratio of $I _{ AB }$ and $I _{ CM }$ is $x: 9$ The value of $x$ is______

Five digit numbers are formed using the digits 1, 2, 3, 5, 7 with repetitions and are written in descending order with serial number. For example, the number 77777 has serial number 1. Then the serial number of 35337 is _________

Two simple harmonic waves having equal amplitudes of 8 cm and equal frequency of 10 Hz are moving along the same direction. The resultant amplitude is also 8 cm. The phase difference between the individual waves is _____ degree.

If the constant term in the binomial expansion of $\left(\frac{x^{\frac{3}{2}}}{2}-\frac{4}{x^l}\right)^9$ is $-84$ and the coefficient of $x^{-3 l}$ is $2^\alpha \beta$, where $\beta<0$ is an odd number, then $|\alpha l-\beta|$ is equal to_____

The force required to stretch a wire of cross-section $1 cm ^2$ to double its length will be: (Given Yong's modulus of the wire $=2 \times 10^{11} N / m ^2$ )

Let the solution curve y = y(x) of the differential equation (4 + x²)dy – 2x(x² + 3y + 4)dx = 0 pass through the origin. Then y(2) is equal to _______.

If the function
$f(x) = \begin{cases} \frac {log_e(1−x+x^2)+log_e(1+x+x_2)}{sec⁡\ x−cos⁡\ x}, & \quad x∈(−\frac \pi2,\frac \pi2)−{0}\\ k, & \quad x=0 \end{cases}$
is continuous at $x = 0$, then k is equal to

NCC parade is going at a uniform speed of $9\, km / h$ under a mango tree on which a monkey is sitting at a height of $196\, m$ At any particular instant, the monkey drops a mango A cadet will receive the mango whose distance from the tree at time of drop is : (Given g= 9.8 m/s²)

Only 2% of the optical source frequency is the available channel bandwidth for an optical communicating system operating at 1000 nm. If an audio signal requires a bandwidth of 8 kHz, how many channels can be accommodated for transmission?

A sample of 0.125 g of an organic compound when analysed by Duma’s method yields 22.78 mL of nitrogen gas collected over KOH solution at 280 K and 759 mm Hg. The percentage of nitrogen in the given organic compound is____.(Nearest integer)

Given : 1. The vapour pressure of water of 280 K is 14.2 mm Hg.

2. R = 0.082 L atm K^–1 mol^–1

If the function $f(x)= \begin{cases} \frac{\log _e\left(1-x+x^2\right)+\log_e\left(1+x+x^2\right)}{\sec x-\cos x}, x \in\left(\frac{-\pi}{2}, \frac{\pi}{2}\right)-\{0\} \\k, \,\,\,\,\, x=0\end{cases}$ is continuous at $x=0$, then $k$ is equal to :

A vessel contains $14 g$ of nitrogen gas at a temperature of $27°C$. The amount of heat to be transferred to the gas to double the r.m.s speed of its molecules will be:

Take $R=8.32 J-mol^{-1}K^{-1}$

Hydrolysis of which compound will give carbolic acid?

The sum of all real value of $x$ for which $\frac{3x^2-9x+17}{x^2+3x+10}=\frac {5x^2-7x+19}{3x^2+5x+12}$ is equal to________.

While estimating the nitrogen present in an organic compound by Kjeldahl’s method, the ammonia evolved from 0.25g of the compound neutralized 2.5mL of 2M H₂SO₄. The percentage of nitrogen present in organic compound is ________