List of top Questions asked in JEE Main

The number of words (with or without meaning) that can be formed from all the letters of the word “LETTER” in which vowels never come together is ________ .

Suppose that a function \(f : R \to R\) satisfies \(f(x + y) = f(x)f(y)\) for all \(x, y \in R\) and \(f(1) = 3\). If \(\sum_{i=1}^{n} f(i) = 363\) then n is equal to ________ .

Two planets have masses M and 16 M and their radii are \(a\) and \(2a\), respectively. The separation between the centres of the planets is \(10a\). A body of mass m is fired from the surface of the larger planet towards the smaller planet along the line joining their centres. For the body to be able to reach at the surface of smaller planet, the minimum firing speed needed is :

Consider the data on x taking the values \(0, 2, 4, 8, \ldots, 2^n\) with frequencies \({}^nC_0, {}^nC_1, {}^nC_2, \ldots, {}^nC_n\) respectively. If the mean of this data is \(\frac{728}{2^n}\), then n is equal to ________ .

The sum of distinct values of \(\lambda\) for which the system of equations
\((\lambda - 1)x + (3\lambda + 1)y + 2\lambda z = 0\)
\((\lambda - 1)x + (4\lambda - 2)y + (\lambda + 3)z = 0\)
\(2x + (3\lambda + 1)y + 3(\lambda - 1)z = 0\)
has non-zero solutions, is ________ .

The angle of elevation of the summit of a mountain from a point on the ground is \(45^\circ\). After climbing up one km towards the summit at an inclination of \(30^\circ\) from the ground, the angle of elevation of the summit is found to be \(60^\circ\). Then the height (in km) of the summit from the ground is :

A plane P meets the coordinate axes at A, B and C respectively. The centroid of \(\Delta ABC\) is given to be \((1, 1, 2)\). Then the equation of the line through this centroid and perpendicular to the plane P is :

Consider the statement :
“For an integer n, if \(n^3 - 1\) is even, then n is odd.”
The contrapositive statement of this statement is :

If \(y = \left(\frac{2}{\pi}x - 1\right)\mathrm{cosec}\,x\) is the solution of the differential equation,
\(\frac{dy}{dx} + p(x)\,y = \frac{2}{\pi}\mathrm{cosec}\,x\), \(0 \lt x \lt \frac{\pi}{2}\),
then the function \(p(x)\) is equal to :

If the normal at an end of a latus rectum of an ellipse passes through an extremity of the minor axis, then the eccentricity \(e\) of the ellipse satisfies :

If \(\alpha\) and \(\beta\) are the roots of the equation \(2x(2x+1)=1\), then \(\beta\) is equal to :

If the tangent to the curve, \(y = f(x) = x\log_e x\), \((x \gt 0)\) at a point \((c, f(c))\) is parallel to the line-segment joining the points \((1, 0)\) and \((e, e)\), then \(c\) is equal to :

The probabilities of three events A, B and C are given by \(P(A)=0.6\), \(P(B)=0.4\) and \(P(C)=0.5\). If \(P(A\cup B)=0.8\), \(P(A\cap C)=0.3\), \(P(A\cap B\cap C)=0.2\), \(P(B\cap C)=\beta\) and \(P(A\cup B\cup C)=\alpha\), where \(0.85\le\alpha\le0.95\), then \(\beta\) lies in the interval :

Let \(z=x+iy\) be a non-zero complex number such that \(z^2=i|z|^2\), where \(i=\sqrt{-1}\), then z lies on the :

The common difference of the A.P. \(b_1,b_2,\ldots,b_m\) is 2 more than the common difference of A.P. \(a_1,a_2,\ldots,a_n\). If \(a_{40}=-159\), \(a_{100}=-399\) and \(b_{100}=a_{70}\), then \(b_1\) is equal to :

Let \(\theta=\frac{\pi}{5}\) and \(A=\begin{bmatrix}\cos\theta & \sin\theta\\ -\sin\theta & \cos\theta\end{bmatrix}\). If \(B=A+A^4\), then det (B) :

Let \(f:\mathbb{R}\to\mathbb{R}\) be a function defined by \(f(x)=\max\{x,x^2\}\). Let S denote the set of all points in \(\mathbb{R}\), where f is not differentiable. Then :

If the constant term in the binomial expansion of \(\left(\sqrt{x}-\frac{k}{x^2}\right)^{10}\) is 405, then \(|k|\) equals :

For all twice differentiable functions \(f:\mathbb{R}\to\mathbb{R}\), with \(f(0)=f(1)=f'(0)=0\)

For a suitably chosen real constant a, let a function, \(f:\mathbb{R}-\{-a\}\to\mathbb{R}\) be defined by \(f(x)=\frac{a-x}{a+x}\). Further suppose that for any real number \(x\ne -a\) and \(f(x)\ne -a\), \((f\circ f)(x)=x\). Then \(f\left(-\frac12\right)\) is equal to :

The area (in sq. units) of the region enclosed by the curves \(y=x^2-1\) and \(y=1-x^2\) is equal to :

Let L denote the line in the xy-plane with x and y intercepts as 3 and 1 respectively. Then the image of the point \((-1,-4)\) in this line is :

The integral
\(\int_1^2 e^x \cdot x^x\,(2+\log_e x)\,dx\)
equals :

The elevation of boiling point of 0.10 m aqueous \(\mathrm{CrCl_3 \cdot xNH_3}\) solution is two times that of 0.05 m aqueous \(\mathrm{CaCl_2}\) solution. The value of x is ______.

[Assume 100% ionisation of the complex and \(\mathrm{CaCl_2}\), coordination number of Cr as 6, and that all \(\mathrm{NH_3}\) molecules are present inside the coordination sphere]

In an estimation of bromine by Carius method, 1.6 g of an organic compound gave 1.88 g of AgBr. The mass percentage of bromine in the compound is ______.
(Atomic mass, Ag = 108, Br = 80 g \(\mathrm{mol^{-1}}\))