List of top Questions asked in JEE Main

Compare boiling point of given solutions:
(i) \( 10^{-4} \) NaCl
(ii) \( 10^{-3} \) NaCl
(iii) \( 10^{-2} \) NaCl
(iv) \( 10^{-4} \) urea

Let {an}ⁿ⁼⁰_∞ be a sequence such that a₀=a₁=0 and a_n+2=3a_n+1−2a_n+1,∀ n≥0. Then a₂₅a₂₃−2a₂₅a₂₂−2a₂₃a₂₄+4a₂₂a₂₄  is equal to

The sum of the cubes of all the roots of the equation x⁴ – 3x³ –2x² + 3x +1 = 0 is

N>40000, where N is divisible by 5. How many such 5 digit numbers can be formed using 0,1,3,5,7,9 without repetition.

Let $A$ be the area of the region
$\left\{(x, y): y \geq x^2, y \geq(1-x)^2, y \leq 2 x(1-x)\right\}$. 
Then $540 A$ is equal to ______.

Let \( f: (0, \pi) \to \mathbb{R} \) be a function given by
\[ f(x) = \begin{cases} \left(\frac{8}{7}\right)^{\tan 8x / \tan 7x}, & 0 < x < \frac{\pi}{2} \\ a - 8, & x = \frac{\pi}{2} \\ \left(1 + |\cot x|\right)^{b^{\lfloor \tan x \rfloor}}, & \frac{\pi}{2} < x < \pi \end{cases} \]
Where \( a, b \in \mathbb{Z} \). If \( f \) is continuous at \( x = \frac{\pi}{2} \), then \( a^2 + b^2 \) is equal to __________.

Let \( y = \log_e \left( \frac{1 - x^2}{1 + x^2} \right), -1 < x < 1 \). Then at \( x = \frac{1}{2} \), the value of \( 225(y' - y'') \) is equal to

A hydrogen atom in ground state is given an energy of 10.2 eV. How many spectral lines will be emitted due to transition of electrons ?

The correct nomenclature for the following compound is:

In a single slit experiment, a parallel beam of green light of wavelength 550 nm passes through a slit of width 0.20 mm. The transmitted light is collected on a screen 100 cm away. The distance of first order minima from the central maximum will be\(x \times 10^{–5}\)m. The value of x is :

A satellite of \( 10^3 \, \text{kg} \) mass is revolving in a circular orbit of radius \( 2R \). If \[ \frac{10^4 R}{6} \, \text{J} \] energy is supplied to the satellite, it would revolve in a new circular orbit of radius: \[ \text{(use } g = 10 \, \text{m/s}^2, \, R = \text{radius of earth)}. \]