List of top Questions asked in JEE Main

The negation of the Boolean expression \(x\leftrightarrow\ \sim y\) is equivalent to :

Let \(f(x)=x\cdot\left[\frac{x}{2}\right]\), for \(-10\lt x\lt 10\), where \([t]\) denotes the greatest integer function. Then the number of points of discontinuity of \(f\) is equal to ______.

If \(2^{10}+2^{9}\cdot 3^{1}+2^{8}\cdot 3^{2}+\ldots+2\cdot 3^{9}+3^{10}=S-2^{11}\), then \(S\) is equal to :

If the point \(P\) on the curve, \(4x^2+5y^2=20\) is farthest from the point \(Q(0,-4)\), then \(PQ^2\) is equal to:

A survey shows that \(73\%\) of the persons working in an office like coffee, whereas \(65\%\) like tea. If \(x\) denotes the percentage of them, who like both coffee and tea, then \(x\) cannot be :

The value of \(\displaystyle\int_{-\pi/2}^{\pi/2}\frac{1}{1+e^{\sin x}}\,dx\) is:

If \((a,\ b,\ c)\) is the image of the point \((1,\ 2,\ -3)\) in the line \(\frac{x+1}{2}=\frac{y-3}{-2}=\frac{z}{-1}\), then \(a+b+c\) is :

If the four complex numbers \(z,\ \overline{z},\ \overline{z}-2\,\mathrm{Re}(z)\) and \(z-2\,\mathrm{Re}(z)\) represent the vertices of a square of side 4 units in the Argand plane, then \(|z|\) is equal to :

The product of the roots of the equation \(9x^2-18|x|+5=0\) is :

If \(3^{2\sin2\alpha-1}\), \(14\) and \(3^{4-2\sin2\alpha}\) are the first three terms of an A.P. for some \(\alpha\), then the sixth term of this A.P. is:

If the co-ordinates of two points \(A\) and \(B\) are \(\left(\sqrt7,0\right)\) and \(\left(-\sqrt7,0\right)\) respectively and \(P\) is any point on the conic, \(9x^2+16y^2=144\), then \(PA+PB\) is equal to :

If \(\alpha\) is positive root of the equation, \(p(x)=x^2-x-2=0\), then
\( \lim_{x\to\alpha^+}\frac{\sqrt{1-\cos\left(p(x)\right)}}{x+\alpha-4} \)
is equal to :

If
\( \int\left(e^{2x}+2e^x-e^{-x}-1\right)e^{\left(e^x+e^{-x}\right)}dx = g(x)\,e^{\left(e^x+e^{-x}\right)}+c \)
where \(c\) is a constant of integration, then \(g(0)\) is equal to :

If \(S\) is the sum of the first 10 terms of the series
\( \tan^{-1}\left(\frac{1}{3}\right)+\tan^{-1}\left(\frac{1}{7}\right)+\tan^{-1}\left(\frac{1}{13}\right)+\tan^{-1}\left(\frac{1}{21}\right)+\dots \)
then \(\tan(S)\) is equal to :

If the minimum and the maximum values of the function \( f:\left[\frac{\pi}{4},\frac{\pi}{2}\right]\to R \), defined by
\( f(\theta)=\begin{vmatrix} -\sin^2\theta & -1-\sin^2\theta & 1 \\ -\cos^2\theta & -1-\cos^2\theta & 1 \\ 12 & 10 & -2 \end{vmatrix} \)
are \(m\) and \(M\) respectively, then the ordered pair \((m, M)\) is equal to :

Let \(\lambda\in R\). The system of linear equations
\(2x_1-4x_2+\lambda x_3=1\)
\(x_1-6x_2+x_3=2\)
\(\lambda x_1-10x_2+4x_3=3\)
is inconsistent for:

If \(y=y(x)\) is the solution of the differential equation
\( \frac{5+e^x}{2+y}\cdot\frac{dy}{dx}+e^x=0 \)
satisfying \(y(0)=1\), then a value of \(y(\log_e 13)\) is :

If the function
\( f(x)=\begin{cases} k_1(x-\pi)^2-1, & x \le \pi \\ k_2\cos x, & x \gt \pi \end{cases} \)
is twice differentiable, then the ordered pair \((k_1, k_2)\) is equal to :

A 100 mL solution was made by adding 1.43 g of \(\mathrm{Na_2CO_3 \cdot xH_2O}\). The normality of the solution is 0.1 N. The value of x is ______.
(The atomic mass of Na is 23 g/mol)

Consider the following equations :
\(\mathrm{2Fe^{2+} + H_2O_2 \to xA + yB}\) (in basic medium)
\(\mathrm{2MnO_4^- + 6H^+ + 5H_2O_2 \to x'C + y'D + z'E}\) (in acidic medium)
The sum of the stoichiometric coefficients x, y, x', y', and z' for products A, B, C, D and E, respectively, is ______.

The processes of calcination and roasting in metallurgical industries, respectively, can lead to :

The number of molecules with energy greater than the threshold energy for a reaction increases five fold by a rise of temperature from \(27^\circ\mathrm{C}\) to \(42^\circ\mathrm{C}\). Its energy of activation in J/mol is ______.
(Take \(\ln 5 = 1.6094\); \(R = 8.314\ \mathrm{J\,mol^{-1}\,K^{-1}}\))

The osmotic pressure of a solution of NaCl is 0.10 atm and that of a glucose solution is 0.20 atm. The osmotic pressure of a solution formed by mixing 1 L of the sodium chloride solution with 2 L of the glucose solution is \(x \times 10^{-3}\) atm. x is ______. (nearest integer)

An alkaline earth metal 'M' readily forms water soluble sulphate and water insoluble hydroxide. Its oxide MO is very stable to heat and does not have rock-salt structure. M is :

The number of chiral centres present in threonine is ________.