List of top Questions asked in JEE Main- 2025

Let the points \( \left( \frac{11}{2}, \alpha \right) \) lie on or inside the triangle with sides \( x + y = 11 \), \( x + 2y = 16 \), and \( 2x + 3y = 29 \). Then the product of the smallest and the largest values of \( \alpha \) is equal to:
The system of equations \[ x + y + z = 6, \] \[ x + 2y + 5z = 9, \] \[ x + 5y + \lambda z = \mu, \] has no solution if:
The number of ways, 5 boys and 4 girls can sit in a row so that either all the boys sit together or no two boys sit together is:

The correct stability order of the following species/molecules is:
 


 

The successive 5 ionisation energies of an element are 800, 2427, 3658, 25024 and 32824 kJ/mol, respectively. By using the above values, predict the group in which the above element is present:
Which one of the following reactions will not lead to the desired ether formation in major proportion?
(iso-Bu = isobutyl, sec-Bu = sec-butyl, nPr = n-propyl, tBu = tert-butyl, Et = ethyl)

Match List-I with List-II

Choose the correct answer from the options given below :

Propane molecule on chlorination under photochemical condition gives two di-chloro products, "x" and "y". Amongst "x" and "y", "x" is an optically active molecule. How many tri-chloro products (consider only structural isomers) will be obtained from "x" when it is further treated with chlorine under the photochemical condition?
Let \( y = y(x) \) be the solution of the differential equation \( \frac{dy}{dx} + 3(\tan^2 x) y + 3y = \sec^2 x \), with \( y(0) = \frac{1}{3} + e^3 \). Then \( y\left(\frac{\pi}{4}\right) \) is equal to
If for the solution curve \( y = f(x) \) of the differential equation \[ \frac{dy}{dx} + (\tan x) y = 2 + \sec^2 x, \quad y(\frac{\pi}{3}) = \sqrt{3}, \] \(\text{then}\) \( y(\frac{\pi}{4}) \) is equal to:
A gas is kept in a container having walls which are thermally non-conducting. Initially the gas has a volume of 800 $ cm^3 $ and temperature 27°C. The change in temperature when the gas is adiabatically compressed to 200 $ cm^3 $ is: (Take $ \gamma $ = 1.5 : $ \gamma $ is the ratio of specific heats at constant pressure and at constant volume)
If the sum of the first 20 terms of the series $$ \frac{4.1}{4 + 3.1^2 + 1^4} + \frac{4.2}{4 + 3.2^2 + 2^4} + \frac{4.3}{4 + 3.3^2 + 3^4} + \frac{4.4}{4 + 3.4^2 + 4^4} + ... $$ is $ \frac{m}{n} $, where $ m $ and $ n $ are coprime, then $ m + n $ is equal to:
Visualize a vibrant street food festival set in an urban environment. Consider street food stalls, chefs preparing dishes, people standing in line and a variety of cuisines. Include street decorations and seating arrangements capturing the lively and diverse scene. Use suitable colours of your choice.
Sketch a unique treehouse that reconnects with nature. Include features such as wooden decks, ladder using natural materials. The structure should blend harmoniously with the surrounding. Depict natural light, shadow and textures effectively. Colour it as per your choice.
Using black and white medium only, draw a proportionate sketch of the image given below in detail with proper light and shade.
Let the lines \[ 3x - 4y - \alpha = 0, \quad 8x - 11y - 33 = 0, \quad 2x - 3y + \lambda = 0 \] be concurrent. If the image of the point \( (1, 2) \) in the line \[ 2x - 3y + \lambda = 0 \text{ is } \left( \frac{57}{13}, \frac{-40}{13} \right), \text{ then } |\alpha \lambda| \text{ is equal to:} \]
The perpendicular distance of the line \( \frac{x - 1}{2} = \frac{y + 2}{-1} = \frac{z + 3}{2} \) from the point \( P(2, -10, 1) \) is:
Let \( x = x(y) \) be the solution of the differential equation \( y^2 dx + \left( x - \frac{1}{y} \right) dy = 0 \). If \( x(1) = 1 \), then \( x\left( \frac{1}{2} \right) \) is :

The integral $ \int_{0}^{\pi} \frac{8x dx}{4 \cos^2 x + \sin^2 x} $ is equal to

The mean and standard deviation of 100 observations are 40 and 5.1, respectively. By mistake one observation is taken as 50 instead of 40. If the correct mean and the correct standard deviation are $ \mu $ and $ \sigma $ respectively, then $ 10(\mu + \sigma) $ is equal to:
For the function \( f(x) = \ln(x^2 + 1) \), what is the second derivative of \( f(x) \)?
The interior angles of a polygon with \( n \) sides, are in an A.P. with common difference 6°. If the largest interior angle of the polygon is 219°, then \( n \) is equal to:
Let \( T_r \) be the \( r^{th} \) term of an A.P. If for some \( m \), \( T_m = \frac{1}{25} \), \( T_{25} = \frac{1}{20} \), and \( \sum_{r=1}^{25} T_r = 13 \), then

\[ 5m \sum_{r=m}^{2m} T_r \text{ is equal to:} \]

Let the length of a latus rectum of an ellipse $ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 $ be 10. If its eccentricity is $ e $, and the minimum value of the function $ f(t) = t^2 + t + \frac{11}{12} $, where $ t \in \mathbb{R} $, then $ a^2 + b^2 $ is equal to:
Let \( \langle a_n \rangle \) be a sequence such that \( a_0 = 0 \), \( a_1 = \frac{1}{2} \), and \( 2a_{n+2} = 5a_{n+1} - 3a_n \).n= 0,1,2,3.... Then \( \sum_{k=1}^{100} a_k \) is equal to: