List of top Questions asked in JEE Main- 2017

$C_p$ and $C_v$ are specific heats at constant pressure and constant volume respectively. It is observed that $C_p-C_v$ = a for hydrogen gas $C_p-C_v$ = b for nitrogen gas The correct relation between $a$ and $b$ is :

$sp^3d^2$ hybridization is not displayed by :

$\displaystyle\lim_{x \to \frac{\pi}{2}} \frac{\cot x - \cos x}{\left(\pi - 2x\right)^{3}} $ equals :

A sinusoidal voltage of peak value $283\, V$ and angular frequency $320/s$ is applied to a series $LCR$ circuit. Given that $R = 5 \, \Omega , L = 25 \, mH $ and $C=1000 \, \mu F$. The total impedance, and phase difference between the voltage across the source and the current will respectively be :

A physical quantity $P$ is described by the relation $P = a^{1/2} b^2 c^3 d^{-4} $ If the relative errors in the measurement of $a, b, c$ and $d$ respectively, are $2\%, 1\%, 3\%$ and $5\%$, then the relative error in $P$ will be :

The current gain of a common emitter amplifier is $69$ . If the emitter current is $7.0 \,mA$, collector current is :

The energy stored in the electric field produced by a metal sphere is $4.5\, J$. If the sphere contains $ 4 \, \mu C$ charge, its radius will be : [Take : $\frac{1}{4 \pi \epsilon_o } = 9 \times 10^{9} \, N - m^2 / C^2$ ]

$2$ moles of an ideal monatomic gas is carried from a state $(P_0, V_0)$ to a state $(2P_0, 2V_0)$ along a straight line path in a P-V diagram. The amount of heat absorbed by the gas in the process is given by

The group having triangular planar structures is :

The electron in the hydrogen atom undergoes transition from higher orbitals to orbital of radius $211.6\, pm$. This transition is associated with

The area (in s units) of the region $\{ (x , y) : x \geq 0 , x + y \leq 3, x^2 \leq 4 y$ and $y \leq 1 + \sqrt{x} \}$ is

If two different numbers are taken from the set $\{0,1,2,3, \ldots \ldots, 10\}$then the probability that their sum as well as absolute difference are both multiple of $4$, is :

Let $S_{n} = \frac{1}{1^{3}} + \frac{1+2}{1^{3} + 2^{3}} + \frac{1+2+3}{1^{3} + 2^{3} + 3^{3}} + ...... + \frac{1+2+...+n}{1^{3} + 2^{3} +.... +n^{3}} . $ . If $100 \, S_n = n , $ then $n$ is equal to :

Let $z \in C$, the set of complex numbers. Then the equation, $2 | z + 3i| - | z - i| = 0 $ represents :

An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is :

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 :