List of top Questions asked in JEE Main

If both the mean and the standard deviation of 50 observations \(x_1,x_2,\ldots,x_{50}\) are equal to 16, then the mean of \((x_1-4)^2,(x_2-4)^2,\ldots,(x_{50}-4)^2\) is :

Let \(\lambda\) be a real number for which the system of linear equations \(x+y+z=6,\; 4x+\lambda y-\lambda z=\lambda-2,\; 3x+2y-4z=-5\) has infinitely many solutions. Then \(\lambda\) is a root of the quadratic equation :

If \(\displaystyle\lim_{x\to 1}\frac{x^2-ax+b}{x-1}=5\), then \(a+b\) is equal to :

If \(\displaystyle\int x^5e^{-x^2}\,dx=g(x)e^{-x^2}+c\), where \(c\) is a constant of integration, then \(g(-1)\) is equal to :

The distance of the point having position vector \(-\hat{i}+2\hat{j}+6\hat{k}\) from the straight line passing through the point \((2,3,-4)\) and parallel to the vector \(6\hat{i}+3\hat{j}-4\hat{k}\) is :

Let \(f(x)=\log_e(\sin x)\), \((0\lt x\lt\pi)\) and \(g(x)=\sin^{-1}(e^{-x})\), \((x\ge 0)\). If \(\alpha\) is a positive real number such that \(a=(f\circ g)^{\prime}(\alpha)\) and \(b=(f\circ g)(\alpha)\), then :

A spherical iron ball of radius 10 cm is coated with a layer of ice of uniform thickness that melts at a rate of 50 cm\(^3\)/min. When the thickness of the ice is 5 cm, then the rate at which the thickness (in cm/min) of the ice decreases, is :

Minimum number of times a fair coin must be tossed so that the probability of getting at least one head is more than 99% is :

The sum of the real roots of the equation
\(\begin{vmatrix} x & -6 & -1 \\ 2 & -3x & x-3 \\ -3 & 2x & x+2 \end{vmatrix}=0\)
is equal to :

The correct order of catenation is :

Consider the following table :

Gas	\(a/(\mathrm{kPa\ dm^6\ mol^{-1}})\)	\(b/(\mathrm{dm^3\ mol^{-1}})\)
A	642.32	0.05196
B	155.21	0.04136
C	431.91	0.05196
D	155.21	0.4382

\(a\) and \(b\) are van der Waals constants. The correct statement about the gases is :

The regions of the atmosphere, where clouds form and where we live, respectively, are :

The synonym for water gas when used in the production of methanol is :

Match the refining methods (Column I) with metals (Column II).

Column I (Refining Methods)	Column II (Metals)
(I) Liquation	(a) Zr
(II) Zone Refining	(b) Ni
(III) Mond Process	(c) Sn
(IV) Van Arkel Method	(d) Ga

Consider the statements S1 and S2
S1 : Conductivity always increases with decrease in the concentration of electrolyte.
S2 : Molar conductivity always increases with decrease in the concentration of electrolyte.
The correct option among the following is :

The alloy used in the construction of aircrafts is :

A gas undergoes physical adsorption on a surface and follows the given Freundlich adsorption isotherm equation
\(\frac{x}{m} = kp^{0.5}\)
Adsorption of the gas increase with :

Consider the hydrated ions of \(\mathrm{Ti^{2+}}\), \(\mathrm{V^{2+}}\), \(\mathrm{Ti^{3+}}\), and \(\mathrm{Sc^{3+}}\). The correct order of their spin-only magnetic moments is :

Increasing rate of \(\mathrm{S_N1}\) reaction in the following compounds is :

Major products of the following reaction are :

A bacterial infection in an internal wound grows as \(N'(t) = N_0\exp(t)\), where the time \(t\) is in hours. A dose of antibiotic, taken orally, needs 1 hour to reach the wound. Once it reaches there, the bacterial population goes down as \(\frac{dN}{dt} = -5N^2\). What will be the plot of \(\frac{N_0}{N}\) vs. \(t\) after 1 hour?

At 300 K and 1 atmospheric pressure, 10 mL of a hydrocarbon required 55 mL of \(\mathrm{O_2}\) for complete combustion, and 40 mL of \(\mathrm{CO_2}\) is formed. The formula of the hydrocarbon is :

During the change of \(\mathrm{O_2}\) to \(\mathrm{O_2^-}\), the incoming electron goes to the orbital :

A process will be spontaneous at all temperatures if :

The major product of the following reaction is :