List of top Questions asked in JEE Main- 2019

Let S be the set of all real values of \(\lambda\) such that a plane passing through the points \((-\lambda^2,1,1)\), \((1,-\lambda^2,1)\) and \((1,1,-\lambda^2)\) also passes through the point \((-1,-1,1)\). Then S is equal to :

If the sum of the first 15 terms of the series \(\left(\frac{3}{4}\right)^3+\left(1\frac{1}{2}\right)^3+\left(2\frac{1}{4}\right)^3+3^3+\left(3\frac{3}{4}\right)^3+\ldots\) is equal to 225 k, then k is equal to :

\(\lim_{x\to\infty}\left(\dfrac{n}{n^2+1^2}+\dfrac{n}{n^2+2^2}+\dfrac{n}{n^2+3^2}+\ldots+\dfrac{1}{5n}\right)\) is equal to :

Let f be a differentiable function such that \(f(1)=2\) and \(f'(x)=f(x)\) for all \(x\in R\). If \(h(x)=f(f(x))\), then \(h'(1)\) is equal to :

The mean and the variance of five observations are 4 and 5.20, respectively. If three of the observations are 3, 4 and 4 ; then the absolute value of the difference of the other two observations, is :

The tangent to the curve \(y=x^2-5x+5\), parallel to the line \(2y=4x+1\), also passes through the point :

\(\lim_{x\to1^-}\dfrac{\sqrt\pi-\sqrt{2\sin^{-1}x}}{\sqrt{1-x}}\) is equal to :

If \(\sin^4\alpha+4\cos^4\beta+2=4\sqrt2\,\sin\alpha\cos\beta;\ \alpha,\beta\in[0,\pi]\), then \(\cos(\alpha+\beta)-\cos(\alpha-\beta)\) is equal to :

If \(^nC_4,\ ^nC_5\) and \(^nC_6\) are in A.P., then n can be :

If \(A=\begin{bmatrix}1&\sin\theta&1\\-\sin\theta&1&\sin\theta\\-1&-\sin\theta&1\end{bmatrix}\); then for all \(\theta\in\left(\frac{3\pi}{4},\frac{5\pi}{4}\right)\), \(\det(A)\) lies in the interval :

The number of integral values of m for which the quadratic expression, \((1+2m)x^2-2(1+3m)x+4(1+m)\), \(x\in R\), is always positive, is :

If the function f given by \(f(x)=x^3-3(a-2)x^2+3ax+7\), for some \(a\in R\) is increasing in (0, 1] and decreasing in [1, 5), then a root of the equation, \(\frac{f(x)-14}{(x-1)^2}=0\ (x\ne1)\) is :

In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 opted for both NCC and NSS. If one of these students is selected at random, then the probability that the students selected has opted neither for NCC nor for NSS is :

Let \(z_1\) and \(z_2\) be two complex numbers satisfying \(|z_1|=9\) and \(|z_2-3-4i|=4\). Then the minimum value of \(|z_1-z_2|\) is :

The integral \(\int_1^e \left\{\left(\frac{x}{e}\right)^{2x}-\left(\frac{e}{x}\right)^{x}\right\}\log_e x\,dx\) is equal to :

The molecule that has minimum /no role in the formation of photochemical smog, is :

A metal on combustion in excess air forms X. X upon hydrolysis with water yields \(\mathrm{H_2O_2}\) and \(\mathrm{O_2}\) along with another product. The metal is :

Water samples with BOD values of 4 ppm and 18 ppm, respectively are :

The correct order for acid strength of compounds :
\(\mathrm{CH\equiv CH}\), \(\mathrm{CH_3{-}C\equiv CH}\) and \(\mathrm{CH_2{=}CH_2}\) is as follows

The major product of the following reaction is

The volume of gas A is twice than that of gas B. The compressibility factor of gas A is thrice than that of gas B at same temperature. The pressures of the gases for equal number of moles are -

The standard electrode potential \(E^\circ\) and its temperature coefficient \(\left(\frac{dE^\circ}{dT}\right)\) for a cell are 2 V and \(-5\times10^{-4}\ \mathrm{VK^{-1}}\) at 300 K respectively. The cell reaction is
\(\mathrm{Zn(s) + Cu^{2+}(aq) \rightarrow Zn^{2+}(aq) + Cu(s)}\)
The standard reaction enthalpy \((\Delta_rH^\circ)\) at 300 K in \(\mathrm{kJ\ mol^{-1}}\) is, [Use \(R = 8\ \mathrm{JK^{-1}mol^{-1}}\) and \(F = 96{,}000\ \mathrm{C\ mol^{-1}}\)]

The major product of the following reaction is \(-\)

Among the following four aromatic compounds, which one will have the lowest melting point ?

What is the work function of the metal if the light of wavelength \(4000\ \mathrm{\AA}\) generates photoelectrons of velocity \(6\times 10^{5}\ \mathrm{ms^{-1}}\) from it ?
(Mass of electron = \(9\times 10^{-31}\) kg;
Velocity of light = \(3\times 10^{8}\ \mathrm{ms^{-1}}\)
Plank's constant = \(6.626\times 10^{-34}\) Js;
Charge of electron = \(1.6\times 10^{-19}\ \mathrm{JeV^{-1}}\))