List of top Questions asked in JEE Main

The area (in sq. units) of the region, given by the set $\{(x, y) \in R \times R \mid x \ge 0, 2x^2 \le y \le 4 - 2x\}$ is :
If \( y = f(x) \) passes through \( (1, 2) \) and \( x \frac{dy}{dx} + y = b x^4 \), then for what value of \( b \), \( \displaystyle \int_{1}^{2} f(x)\,dx = \frac{62}{5} \) ?
The value of \(2 \sin(\frac{\pi}{8}) \sin(\frac{2\pi}{8}) \sin(\frac{3\pi}{8}) \sin(\frac{5\pi}{8}) \sin(\frac{6\pi}{8}) \sin(\frac{7\pi}{8})\) is :
The value of the integral \( \int_{0}^{1} \frac{\sqrt{x} dx}{(1+x)(1+3x)(3+x)} \) is :
Three numbers are in an increasing geometric progression with common ratio \( r \). If the middle number is doubled, then the new numbers are in an arithmetic progression with common difference \( d \). If the fourth term of GP is \( 3 r^2 \), then \( r^2 - d \) is equal to :
A hyperbola passes through the foci of the ellipse $\frac{x^2}{25} + \frac{y^2}{16} = 1$ and its transverse and conjugate axes coincide with major and minor axes of the ellipse, respectively. If the product of their eccentricities is one, then the equation of the hyperbola is:
The value of the integral, \[ \int_{1}^{3} \left[ x^{2} - 2x - 2 \right] \, dx, \] where \( [x] \) denotes the greatest integer less than or equal to \( x \), is:
The angle between the straight lines, whose direction cosines are given by the equations 2l + 2m - n = 0 and mn + nl + lm = 0, is :
Let \( f \) be any continuous function on \( [0, 2] \) and twice differentiable on \( (0, 2) \). If \( f(0) = 0, f(1) = 1 \) and \( f(2) = 2 \), then :
The function \( f(x) = \dfrac{4x^3 - 3x^2}{6} - 2 \sin x + (2x - 1)\cos x \) :
Let the foot of perpendicular from a point $P(1, 2, -1)$ to the straight line $L: \frac{x}{1} = \frac{y}{0} = \frac{z}{-1}$ be $N$. Let a line be drawn from $P$ parallel to the plane $x + y + 2z = 0$ which meets $L$ at point $Q$. If $\alpha$ is the acute angle between the lines $PN$ and $PQ$, then $\cos \alpha$ is equal to ________.
The equation of one of the straight lines which passes through the point (1, 3) and makes an angle tan⁻¹(√2) with the straight line, y + 1 = 3√2 x is :
Which one of the following is correct for the adsorption of a gas at a given temperature on a solid surface ?
Which one of the following complexes is violet in colour ?
Which one of the following lanthanides exhibits +2 oxidation state with diamagnetic nature ? (Given Z for Nd=60, Yb=70, La=57, Ce=58)
Which one of the following correctly represents the order of stability of oxides, \( X_2O \); (X = halogen) ?

The major product of the following reaction is : 

The correct structures of A and B formed in the following reactions are : 

 

Which one of the following is the correct PV vs P plot at constant temperature for an ideal gas ? (P and V stand for pressure and volume of the gas respectively) 

The water soluble protein is :

Match List - I with List - II : 

Choose the most appropriate answer from the options given below : 
 

The \( \text{Eu}^{2+} \) ion is a strong reducing agent in spite of its ground state electronic configuration (outermost) : [Atomic number of Eu = 63]

Given below are two statements : 
Statement I : Penicillin is a bacteriostatic type antibiotic. 
Statement II : The general structure of Penicillin is : 
Choose the correct option : 

 

Tyndall effect is more effectively shown by:
Potassium permanganate on heating at 513 K gives a product which is :