List of top Questions asked in JEE Main

Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in $s m$) of the flower-bed, is :

Let $a, b, c \, \in \, R$. If $f(x) = ax^2 + bx + c$ is such that $a + b + c = 3$ and $f (x + y) = f (x) + f (y) + xy, \forall \, x, y \, \in \, R,$ then $\displaystyle\sum^{10}_{n = 1} f(n)$ is equal to :

If for $x \epsilon \left(0, \frac{1}{4}\right) ,$ the derivative of $ \tan^{-1} \left(\frac{6x \sqrt{x}}{1-9x^{3}}\right) $ is $\sqrt{x} . g(x)$, then $g(x)$ equals :

The integral $\int \sqrt{ 1 + 2 \cot \, x (cosec \, x + \cot \, x) } dx \, \left( 0 < x < \frac{\pi}{2} \right)$ is equal to : (where $C$ is a constant of integration)

Which of the following species is not paramagnetic?

A car is standing $200\, m$ behind a bus, which is also at rest. The two start moving at the same instant but with different forward accelerations. The bus has acceleration $2 \, m/s^2$ and the car has acceleration $4 \, m/s^2$. The car will catch up with the bus after a time of :

If $(2 + \sin \, x ) \frac{dy}{dx} + (y + 1) \cos \, x = 0$ and $y(0) = 1,$ then $y \left( \frac{\pi}{2} \right)$ is equal to :

The normal to the curve $y(x-2)(x-3)=x+6$ at the point where the curve intersects the y-axis passes through the point :

Let a vertical tower $AB$ have its end $A$ on the level ground. Let $C$ be the mid-point of $AB$ and $P$ be a point on the ground such that $AP = 2AB$. If $\angle BPC = \beta $, then tan $\beta$ is equal to :

Let $\omega$ be a complex number such that $2 \omega + 1 = z$ where $z = \sqrt{-3}$ ,If $\begin{vmatrix}1&1&1\\ 1&-\omega^{2} - 1 &\omega^{2}\\ 1&\omega^{2}& \omega^{7}\end{vmatrix} = 3 k , $ then $k$ is equal to :

If, for a positive integer n, the quadratic equation, $x(x+1)+(x+1)(x+2)+....+(x + \overline{ n - 1}) (x+ n)=10n$ has two consecutive integral solutions, then $n$ is equal to :

A box contains $15$ green and $10$ yellow balls. If $10$ balls are randomly drawn, one-by-one, with replacement, then the variance of the number of green balls drawn is :

$3$-Methylpent-$2$-ene on reaction with $HBr$ in presence of peroxide forms an addition product. The number of possible stereoisomers for the product is :

Which of the following ions does not liberate hydrogen gas on reaction with dilute acids?

Among the following, the essential amino acid is :

Which of the following compounds will show highest dipole moment ?

Which of the following molecules is least resonance stabilized?

Addition of sodium hydroxide solution to a weak acid (HA) results in a buffer of pH 6. If ionisation constant of HA is $10^{-5}$, the ratio of salt to acid concentration in the buffer solution will be :

$pK_a$ of a weak acid (HA) and $pK_b$ of a weak base (BOH) are $3.2$ and $3.4,$ respectively. .The pH of their salt (AB) solution is :

What quantity (in mL) of a $45\%$ acid solution of a monoprotic strong acid must be mixed with a $20\%$ solution of the same acid to produce $800\ mL$ of a $29.875\%$ acid solution ?

An ideal gas undergoes isothermal expansion at constant pressure. During the process :

If the shortest wavelength in Lyman series of hydrogen atom is $A$, then the longest wavelength in Paschen series of $He^{+}$ is :

For any three positive real numbers a, b and c, $9(25a^2 + b^2) + 25 (c^2 - 3ac) = 15b (3a + c)$. Then :

$\Delta U $ is equal to :

The temperature of an open room of volume $30 \, m^3$ increases from $17^{\circ}C$ to $27^{\circ}C$ due to the sunshine. The atmospheric pressure in the room remains $1 \times 10^5 \, Pa$. If $n_i$ and $n_f$ are the number of molecules in the room before and after heating, then $n_f-n_i$ will be :