List of top Questions asked in JEE Main

Given below are two statements :

Statement I : A second's pendulum has a time period of 1 second.

Statement II : It takes precisely one second to move between the two extreme positions.

In the light of the above statements, choose the correct answer from the options given below :

Two masses A and B, each of mass M are fixed together by a massless spring. A force acts on the mass B as shown in the figure. If the mass A starts moving away from mass B with acceleration 'a', then the acceleration of mass B will be :

A wire of 1\(\Omega\) has a length of 1 m. It is stretched till its length increases by 25%. The percentage change in resistance to the nearest integer is :

The trajectory of a projectile in a vertical plane is \(y = \alpha x - \beta x^2\), where \(\alpha\) and \(\beta\) are constants and x & y are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection \(\theta\) and the maximum height attained H are respectively given by :

The incident ray, reflected ray and the outward drawn normal are denoted by the unit vectors \(\vec{a}\), \(\vec{b}\) and \(\vec{c}\) respectively. Then choose the correct relation for these vectors.

The internal energy (U), pressure (P) and volume (V) of an ideal gas are related as U = 3PV + 4. The gas is :

The length of metallic wire is \(l_1\) when tension in it is \(T_1\). It is \(l_2\) when the tension is \(T_2\). The original length of the wire will be :

If 'C' and 'V' represent capacity and voltage respectively then what are the dimensions of \(\lambda\) where C/V = \(\lambda\) ?

The recoil speed of a hydrogen atom after it emits a photon in going from n = 5 state to n = 1 state will be :

A scooter accelerates from rest for time \(t_1\) at constant rate \(a_1\) and then retards at constant rate \(a_2\) for time \(t_2\) and comes to rest. The correct value of \(\frac{t_1}{t_2}\) wil be :

Given below are two statements:

Statement I : An electric dipole is placed at the center of a hollow sphere. The flux of the electric field through the sphere is zero but the electric field is not zero anywhere in the sphere.

Statement II : If R is the radius of a solid metallic sphere and Q be the total charge on it. The electric field at any point on the spherical surface of radius r (< R) is zero but the electric flux passing through this closed spherical surface of radius r is not zero..

In the light of the above statements, choose the correct answer from the options given below :

Find the peak current and resonant frequency of the following circuit (as shown in figure).

An aeroplane, with its wings spread 10 m, is flying at a speed of 180 km/h in a horizontal direction. The total intensity of earth's field at that part is \(2.5 \times 10^{-4}\) Wb/m\(^2\) and the angle of dip is \(60^\circ\). The emf induced between the tips of the plane wings will be __________.

Let \(X_1,X_2,\dots,X_{18}\) be eighteen observations such that
\(\sum_{i=1}^{18}(X_i-\alpha)=36\)
and
\(\sum_{i=1}^{18}(X_i-\beta)^2=90\)
, where \(\alpha\) and \(\beta\) are distinct real numbers. If the standard deviation of these observations is 1, then the value of \(|\alpha-\beta|\) is ____________.

Let the normals at all the points on a given curve pass through a fixed point \((a,b)\). If the curve passes through \((3,-3)\) and \((4,-2\sqrt2)\), and given that \(a-2\sqrt2\,b=3\), then \((a^2+b^2+ab)\) is equal to __________.

Draw the output signal Y in the given combination of gates.

Let \(L\) be a common tangent line to the curves
\(4x^2+9y^2=36\) and \((2x)^2+(2y)^2=31\). Then the square of the slope of the line \(L\) is __________.

If \(I_{m,n}=\int_0^1x^{m-1}(1-x)^{n-1}dx\), for \(m,n\ge1\), and
\(\int_0^1\frac{x^{m-1}+x^{n-1}}{(1+x)^{m+1}}dx=\alpha I_{m,n}\), \(\alpha\in R\), then \(\alpha\) equals ___________.

Let \(a\) be an integer such that all the real roots of the polynomial \(2x^5+5x^4+10x^3+10x^2+10x+10\) lie in the interval \((a,a+1)\). Then, \(|a|\) is equal to ___________.

Let \(z\) be those complex numbers which satisfy
\(|z+5|\le4\) and \(z(1+i)+\overline{z}(1-i)\ge-10\), \(i=\sqrt{-1}\).
If the maximum value of \(|z+1|^2\) is \(\alpha+\beta\sqrt2\), then the value of \((\alpha+\beta)\) is ____________.

Let \(\alpha\) and \(\beta\) be two real numbers such that \(\alpha+\beta=1\) and \(\alpha\beta=-1\). Let \(p_n=(\alpha)^n+(\beta)^n\), \(p_{n-1}=11\) and \(p_{n+1}=29\) for some integer \(n\ge1\). Then, the value of \(p_n^2\) is ___________.

If the arithmetic mean and geometric mean of the \(p^{th}\) and \(q^{th}\) terms of the sequence \(-16,8,-4,2,\dots\) satisfy the equation \(4x^2-9x+5=0\), then \(p+q\) is equal to __________.

If the matrix \(A=\begin{bmatrix}1&0&0\\0&2&0\\3&0&-1\end{bmatrix}\) satisfies the equation
\(A^{20}+\alpha A^{19}+\beta A=\begin{bmatrix}1&0&0\\0&4&0\\0&0&1\end{bmatrix}\)
for some real numbers \(\alpha\) and \(\beta\), then \(\beta-\alpha\) is equal to ___________.

The total number of 4-digit numbers whose greatest common divisor with 18 is 3, is _________.

Let slope of the tangent line to a curve at any point \(P(x,y)\) be given by \(\frac{xy^2+y}{x}\). If the curve intersects the line \(x+2y=4\) at \(x=-2\), then the value of \(y\), for which the point \((3,y)\) lies on the curve, is :