List of top Questions asked in JEE Main

A Copper (Cu) rod of length 25 cm and cross-sectional area 3 mm\(^2\) is joined with a similar Aluminium (Al) rod as shown in figure. Find the resistance of the combination between the ends A and B.
(Take Resistivity of Copper \(= 1.7 \times 10^{-8}\ \Omega\)m and Resistivity of Aluminium \(= 2.6 \times 10^{-8}\ \Omega\)m)

Consider a situation in which a ring, a solid cylinder and a solid sphere roll down on the same inclined plane without slipping. Assume that they start rolling from rest and having identical diameter.

The correct statement for this situation is

Intensity of sunlight is observed as \(0.092\ \mathrm{Wm^{-2}}\) at a point in free space. What will be the peak value of magnetic field at the point?

(\(\varepsilon_0 = 8.85 \times 10^{-12}\ \mathrm{C^2N^{-1}m^{-2}}\))

A porter lifts a heavy suitcase of mass 80 kg and at the destination lowers it down by a distance of 80 cm with a constant velocity. Calculate the work done by the porter in lowering the suitcase.

(take \(g = 9.8\ \mathrm{ms^{-2}}\))

In a circuit consisting of a capacitance and a generator with alternating emf \(E_g = E_{g_0}\sin\omega t\), \(V_C\) and \(I_C\) are the voltage and current. Correct phasor diagram for such circuit is

Let \(f : \mathbb{R} \to \mathbb{R}\) be a function defined as
\(f(x) = \begin{cases} 3\left(1 - \frac{|x|}{2}\right) & \text{if } |x| \le 2 \\ 0 & \text{if } |x| \gt 2 \end{cases}\)
Let \(g : \mathbb{R} \to \mathbb{R}\) be given by
\(g(x) = f(x + 2) - f(x - 2)\).
If \(n\) and \(m\) denote the number of points in \(\mathbb{R}\) where \(g\) is not continuous and not differentiable, respectively, then \(n + m\) is equal to ______________.

If the constant term, in binomial expansion of \(\left(2x^r + \frac{1}{x^2}\right)^{10}\) is 180, then \(r\) is equal to __________________.

What will be the projection of vector
\(\vec{A} = \hat{i} + \hat{j} + \hat{k}\)
on vector
\(\vec{B} = \hat{i} + \hat{j}\) ?

The area (in sq. units) of the region bounded by the curves \(x^2 + 2y - 1 = 0\), \(y^2 + 4x - 4 = 0\) and \(y^2 - 4x - 4 = 0\), in the upper half plane is _______________.

The number of elements in the set \(\{n \in \{1, 2, 3, \ldots\ldots, 100\} \mid (11)^n \gt (10)^n + (9)^n\}\) is ______________.

Let \(y = y(x)\) be the solution of the differential equation
\(\left((x + 2)e^{\left(\frac{y + 1}{x + 2}\right)} + (y + 1)\right)dx = (x + 2)\,dy\), \(y(1) = 1\).
If the domain of \(y = y(x)\) is an open interval \((\alpha, \beta)\), then \(|\alpha + \beta|\) is equal to _____________.

Consider the following frequency distribution :

Class :	0-6	6-12	12-18	18-24	24-30
Frequency :	\(a\)	\(b\)	12	9	5

If mean \(= \frac{309}{22}\) and median \(= 14\), then the value \((a - b)^2\) is equal to _____________.

Let \(A = \{0, 1, 2, 3, 4, 5, 6, 7\}\). Then the number of bijective functions \(f : A \to A\) such that \(f(1) + f(2) = 3 - f(3)\) is equal to

If the digits are not allowed to repeat in any number formed by using the digits 0, 2, 4, 6, 8, then the number of all numbers greater than 10,000 is equal to _____________.

Let a line \(L : 2x + y = k,\ k \gt 0\) be a tangent to the hyperbola \(x^2 - y^2 = 3\). If \(L\) is also a tangent to the parabola \(y^2 = \alpha x\), then \(\alpha\) is equal to :

The number of solutions of \(\sin^7 x + \cos^7 x = 1\), \(x \in [0, 4\pi]\) is equal to

Let \(A = \begin{bmatrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{bmatrix}\). Then the number of \(3 \times 3\) matrices \(B\) with entries from the set \(\{1, 2, 3, 4, 5\}\) and satisfying \(AB = BA\) is ____________.

Let three vectors \(\vec{a}\), \(\vec{b}\) and \(\vec{c}\) be such that \(\vec{a}\times\vec{b} = \vec{c}\), \(\vec{b}\times\vec{c} = \vec{a}\) and \(|\vec{a}| = 2\). Then which one of the following is not true?

Which of the following Boolean expressions is not a tautology?

Let L be the line of intersection of planes \(\vec{r}\cdot(\hat{i} - \hat{j} + 2\hat{k}) = 2\) and \(\vec{r}\cdot(2\hat{i} + \hat{j} - \hat{k}) = 2\). If \(P(\alpha, \beta, \gamma)\) is the foot of perpendicular on L from the point \((1, 2, 0)\), then the value of \(35(\alpha + \beta + \gamma)\) is equal to :

Let \(E_1 : \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1,\ a \gt b\). Let \(E_2\) be another ellipse such that it touches the end points of major axis of \(E_1\) and the foci of \(E_2\) are the end points of minor axis of \(E_1\). If \(E_1\) and \(E_2\) have same eccentricities, then its value is :

Let n denote the number of solutions of the equation \(z^2 + 3\overline{z} = 0\), where z is a complex number. Then the value of \(\sum_{k=0}^{\infty}\frac{1}{n^k}\) is equal to :

Let the circle \(S : 36x^2 + 36y^2 - 108x + 120y + C = 0\) be such that it neither intersects nor touches the co-ordinate axes. If the point of intersection of the lines, \(x - 2y = 4\) and \(2x - y = 5\) lies inside the circle S, then :

Let \(f : R \to R\) be defined as \(f(x) = \begin{cases} \frac{x^3}{(1 - \cos 2x)^2}\log_e\left(\frac{1 + 2xe^{-2x}}{(1 - xe^{-x})^2}\right), & x \ne 0 \\ \alpha, & x = 0 \end{cases}\)
If f is continuous at \(x = 0\), then \(\alpha\) is equal to :

Let \([x]\) denote the greatest integer less than or equal to x. Then, the values of \(x \in R\) satisfying the equation \([e^x]^2 + [e^x + 1] - 3 = 0\) lie in the interval :