List of top Questions asked in JEE Main

A string is clamped at both the ends and it is vibrating in its 4th harmonic. The equation of the stationary wave is \(Y = 0.3\sin(0.157x)\cos(200\pi t)\). The length of the string is : (All quantities are in SI units.)

The pressure wave, \(P = 0.01\sin[1000t - 3x]\ \mathrm{Nm^{-2}}\), corresponds to the sound produced by a vibrating blade on a day when atmospheric temperature is \(0^\circ\mathrm{C}\). On some other day, when temperature is T, the speed of sound produced by the same blade and at the same frequency is found to be \(336\ \mathrm{ms^{-1}}\). Approximate value of T is

Taking the wavelength of first Balmer line in hydrogen spectrum (n = 3 to n = 2) as 660 nm, the wavelength of the 2nd Balmer line (n = 4 to n = 2) will be :

For a given gas at 1 atm pressure, rms speed of the molecule is 200 m/s at \(127^\circ\mathrm{C}\). At 2 atm pressure and at \(227^\circ\mathrm{C}\), the rms speed of the molecules will be :

Following figure shows two processes A and B for a gas. If \(\Delta Q_A\) and \(\Delta Q_B\) are the amount of heat absorbed by the system in two cases, and \(\Delta U_A\) and \(\Delta U_B\) are changes in internal energies, respectively, then :

A plane passing through the points \((0, -1, 0)\) and \((0, 0, 1)\) and making an angle \(\frac{\pi}{4}\) with the plane \(y - z + 5 = 0\), also passes through the point

Let \(S = \{\theta \in [-2\pi, 2\pi] : 2\cos^2\theta + 3\sin\theta = 0\}\). Then the sum of the elements of S is

If the line \(y = mx + 7\sqrt{3}\) is normal to the hyperbola \(\frac{x^2}{24} - \frac{y^2}{18} = 1\), then a value of \(m\) is :

If the tangent to the curve, \(y = x^3 + ax - b\) at the point \((1, -5)\) is perpendicular to the line, \(-x + y + 4 = 0\), then which one of the following points lies on the curve ?

Let S be the set of all values of x for which the tangent to the curve \(y = f(x) = x^3 - x^2 - 2x\) at \((x, y)\) is parallel to the line segment joining the points \((1, f(1))\) and \((-1, f(-1))\), then S is equal to :

If the line, \(\frac{x-1}{2} = \frac{y+1}{3} = \frac{z-2}{4}\) meets the plane, \(x + 2y + 3z = 15\) at a point P, then the distance of P from the origin is :

Let the sum of the first \(n\) terms of a non-constant A.P., \(a_1,a_2,a_3,\dots\) be \(50n+\frac{n(n-7)}{2}A\), where \(A\) is a constant. If \(d\) is the common difference of this A.P., then the ordered pair \((d,a_{50})\) is equal to

The value of \(\int_0^{\pi/2}\frac{\sin^3x}{\sin x+\cos x}\,dx\) is

Let \(p,q\in R\). If \(2-\sqrt3\) is a root of the quadratic equation, \(x^2+px+q=0\), then :

If the function \(f:R-\{1,-1\}\to A\) defined by \(f(x)=\frac{x^2}{1-x^2}\), is surjective, then \(A\) is equal to

If the function \(f\) defined on \(\left(\frac{\pi}{6},\frac{\pi}{3}\right)\) by \(f(x)=\begin{cases}\dfrac{\sqrt2\cos x-1}{\cot x-1},&x\ne\dfrac{\pi}{4}\\ k,&x=\dfrac{\pi}{4}\end{cases}\) is continuous, then \(k\) is equal to

Let \(\sum_{k=1}^{10}f(a+k)=16\left(2^{10}-1\right)\) where the function \(f\) satisfies \(f(x+y)=f(x)f(y)\) for all natural numbers \(x,y\) and \(f(1)=2\). then the natural number '\(a\)' is

If the standard deviation of the numbers \(-1,0,1,k\) is \(\sqrt5\) where \(k\gt0\), then \(k\) is equal to

Let \(\alpha\) and \(\beta\) be the roots of the equation \(x^2+x+1=0\). Then for \(y\ne0\) in \(R\), \(\begin{vmatrix}y+1&\alpha&\beta\\ \alpha&y+\beta&1\\ \beta&1&y+\alpha\end{vmatrix}\) is equal to

The area (in sq. units) of the region \(A=\{(x,y):x^2\le y\le x+2\}\) is

If \(f(x)\) is a non-zero polynomial of degree four, having local extreme points at \(x=-1,0,1\); then the set \(S=\{x\in R:f(x)=f(0)\}\) Contains exactly :

If the fourth term in the binomial expansion of \(\left(\frac{2}{x}+x^{\log_8 x}\right)^6\) (\(x\gt0\)) is \(20\times8^7\), then a value of \(x\) is :

Let \(\vec{\alpha}=3\hat{i}+\hat{j}\) and \(\vec{\beta}=2\hat{i}-\hat{j}+3\hat{k}\). If \(\vec{\beta}=\vec{\beta}_1-\vec{\beta}_2\), where \(\vec{\beta}_1\) is parallel to \(\vec{\alpha}\) and \(\vec{\beta}_2\) is perpendicular to \(\vec{\alpha}\), then \(\vec{\beta}_1\times\vec{\beta}_2\) is equal to

The solution of the differential equation \(x\frac{dy}{dx}+2y=x^2\) (\(x\ne0\)) with \(y(1)=1\), is :

All the points in the set \(S=\left\{\frac{\alpha+i}{\alpha-i}:\alpha\in R\right\}\) (\(i=\sqrt{-1}\)) lie on a :