List of top Questions asked in JEE Main- 2021

A fair coin is tossed \(n\)-times such that the probability of getting at least one head is at least 0.9. Then the minimum value of \(n\) is ______________.

If a tangent to the ellipse \(x^2+4y^2=4\) meets the tangents at the extremities of it major axis at B and C, then the circle with BC as diameter passes through the point :

Consider the function \(f(x)=\begin{cases}\dfrac{P(x)}{\sin(x-2)}, & x\ne 2\\ 7, & x=2\end{cases}\) where \(P(x)\) is a polynomial such that \(P''(x)\) is always a constant and \(P(3)=9\). If \(f(x)\) is continuous at \(x=2\), then \(P(5)\) is equal to _____________.

The equation of a circle is \(\mathrm{Re}(z^2)+2(\mathrm{Im}(z))^2+2\,\mathrm{Re}(z)=0\), where \(z=x+iy\). A line which passes through the center of the given circle and the vertex of the parabola, \(x^2-6x-y+13=0\), has y-intercept equal to ______________.

Consider the statement "The match will be played only if the weather is good and ground is not wet". Select the correct negation from the following :

Let \(y=y(x)\) be the solution of the differential equation \(x\,dy=(y+x^3\cos x)\,dx\) with \(y(\pi)=0\), then \(y\left(\frac\pi2\right)\) is equal to :

If \(P=\begin{bmatrix}1&0\\ \frac12&1\end{bmatrix}\), then \(P^{50}\) is :

If \({}^nP_r={}^nP_{r+1}\) and \({}^nC_r={}^nC_{r-1}\), then the value of \(r\) is equal to :

Let \(X\) be a random variable such that the probability function of a distribution is given by \(P(X=0)=\frac12,\ P(X=j)=\frac{1}{3^j}\ (j=1,2,3,\dots,\infty)\). Then the mean of the distribution and \(P(X\) is positive and even\()\) respectively are :

Consider function \(f:A\to B\) and \(g:B\to C\) (\(A,B,C\subseteq\mathbb{R}\)) such that \((gof)^{-1}\) exists, then :

If \(|\vec a|=2,\ |\vec b|=5\) and \(|\vec a\times\vec b|=8\), then \(|\vec a\cdot\vec b|\) is equal to :

The number of distinct real roots of \(\begin{vmatrix}\sin x&\cos x&\cos x\\ \cos x&\sin x&\cos x\\ \cos x&\cos x&\sin x\end{vmatrix}=0\) in the interval \(-\frac{\pi}{4}\le x\le\frac{\pi}{4}\) is :

If \([x]\) be the greatest integer less than or equal to \(x\), then \(\sum_{n=8}^{100}\left[\frac{(-1)^n n}{2}\right]\) is equal to :

The lowest integer which is greater than \(\left(1+\frac{1}{10^{100}}\right)^{10^{100}}\) is ______________.

The value of \(\cot\frac{\pi}{24}\) is :

The value of the integral \(\int_{-1}^{1}\log\left(x+\sqrt{x^2+1}\right)dx\) is :

If \(f(x)=\begin{cases}\int_0^x (5+|1-t|)\,dt, & x\gt 2\\ 5x+1, & x\le 2\end{cases}\), then

The first of the two samples in a group has 100 items with mean 15 and standard deviation 3. If the whole group has 250 items with mean 15.6 and standard deviation \(\sqrt{13.44}\), then the standard deviation of the second sample is :

If the greatest value of the term independent of 'x' in the expansion of \(\left(x\sin\alpha+a\frac{\cos\alpha}{x}\right)^{10}\) is \(\frac{10!}{(5!)^2}\), then the value of 'a' is equal to :

The sum of all those terms which are rational numbers in the expansion of \((2^{1/3}+3^{1/4})^{12}\) is :

Number of electrons that Vanadium (Z = 23) has in p-orbitals is equal to _____________

If the standard molar enthalpy change for combustion of graphite powder is \(-2.48\times 10^{2}\) kJ \(\mathrm{mol^{-1}}\), the amount of heat generated on combustion of 1 g of graphite powder is ___________ kJ. (Nearest integer)

\(\mathrm{N_2O_{5(g)} \rightarrow 2NO_{2(g)} + \frac{1}{2}O_{2(g)}}\)

In the above first order reaction the initial concentration of \(\mathrm{N_2O_5}\) is \(2.40\times 10^{-2}\) mol \(\mathrm{L^{-1}}\) at 318 K. The concentration of \(\mathrm{N_2O_5}\) after 1 hour was \(1.60\times 10^{-2}\) mol \(\mathrm{L^{-1}}\). The rate constant of the reaction at 318 K is ______________ \(\times 10^{-3}\) \(\mathrm{min^{-1}}\). (Nearest integer)

[Given : log 3 = 0.477, log 5 = 0.699]

A copper complex crystallising in a CCP lattice with a cell edge of 0.4518 nm has been revealed by employing X-ray diffraction studies. The density of a copper complex is found to be 7.62 g \(\mathrm{cm^{-3}}\). The molar mass of copper complex is ____________ g \(\mathrm{mol^{-1}}\). (Nearest integer)

[Given : \(N_A = 6.022\times 10^{23}\ \mathrm{mol^{-1}}\)]

Methylation of 10 g of benzene gave 9.2 g of toluene. Calculate the percentage yield of toluene ________. (Nearest integer)