List of top Questions asked in JEE Main

A particle 'P' is formed due to a completely inelastic collision of particles 'x' and 'y' having de-Broglie wavelengths '\(\lambda_x\)' and '\(\lambda_y\)' respectively. If x and y were moving in opposite directions, then the de-Broglie wavelength of 'P' is :-

The position of a particle as a function of time t, is given by
\(x(t)=at+bt^2-ct^3\)
where a, b and c are constants. When the particle attains zero acceleration, then its velocity will be :

The area of a square is 5.29 cm². The area of 7 such squares taking into account the significant figures is :-

The resistance of a galvanometer is 50 ohm and the maximum current which can be passed through it is 0.002 A. What resistance must be connected to it in order to convert it into an ammeter of range 0 - 0.5 A ?

A thin convex lens L (refractive index = 1.5) is placed on a plane mirror M. When a pin is placed at A, such that OA = 18 cm, its real inverted image is formed at A itself, as shown in figure. When a liquid of refractive index \(\mu_1\) is put between the lens and the mirror, The pin has to be moved to A', such that OA' = 27 cm, to get its inverted real image at A' itself. The value of \(\mu_1\) will be :-

A wedge of mass \(M=4m\) lies on a frictionless plane. A particle of mass m approaches the wedge with speed v. There is no friction between the particle and the plane or between the particle and the wedge. The maximum height climbed by the particle on the wedge is given by :-

The specific heats, \(C_P\) and \(C_V\) of a gas of diatomic molecules, A, are given (in units of \(\mathrm{J\ mol^{-1}\ K^{-1}}\)) by 29 and 22, respectively. Another gas of diatomic molecules, B, has the corresponding values 30 and 21. If they are treated as ideal gases, then :-

A massless spring \((k=800\ \mathrm{N/m})\), attached with a mass \((500\ \mathrm{g})\) is completely immersed in \(1\) kg of water. The spring is stretched by \(2\) cm and released so that it starts vibrating. What would be the order of magnitude of the change in the temperature of water when the vibrations stop completely ? (Assume that the water container and spring receive negligible heat and specific heat of mass \(=400\ \mathrm{J/kg\,K}\), specific heat of water \(=4184\ \mathrm{J/kg\,K}\))

The position vector of a particle changes with time according to the relation \(\vec r(t)=15t^2\hat i+(4-20t^2)\hat j\). What is the magnitude of the acceleration at \(t=1\) ?

A moving coil galvanometer has a coil with 175 turns and area 1 cm². It uses a torsion band of torsion constant \(10^{-6}\) N-m/rad. The coil is placed in a maganetic field B parallel to its plane. The coil deflects by \(1^\circ\) for a current of 1 mA. The value of B (in Tesla) is approximately :-

A thin smooth rod of length L and mass M is rotating freely with angular speed \(\omega_0\) about an axis perpendicular to the rod and passing through its center. Two beads of mass m and negligible size are at the center of the rod initially. The beads are free to slide along the rod. The angular speed of the system , when the beads reach the opposite ends of the rod, will be :-

Moment of inertia of a body about a given axis is \(1.5\ \mathrm{kg\,m^2}\). Initially the body is at rest. In order to produce a rotational kinetic energy of \(1200\) J, the angular accleration of \(20\ \mathrm{rad/s^2}\) must be applied about the axis for a duration of :-

Two coils 'P' and 'Q' are separated by some distance. When a current of 3 A flows through coil 'P', a magnetic flux of \(10^{-3}\) Wb passes through 'Q'. No current is passed through 'Q'. When no current passes through 'P' and a current of 2 A passes through 'Q', the flux through 'P' is :-

A very long solenoid of radius R is carrying current \(I(t)=kte^{-a t}\ (k\gt 0)\), as a function of time \((t\ge0)\). counter clockwise current is taken to be positive. A circular conducting coil of radius 2R is placed in the equatorial plane of the solenoid and concentric with the solenoid. The current induced in the outer coil is correctly depicted, as a function of time, by :-

Two poles standing on a horizontal ground are of heights \(5\) m and \(10\) m respectively. The line joining their tops makes an angle of \(15^\circ\) with ground. Then the distance (in m) between the poles, is :-

A particle of mass 'm' is moving with speed '2v' and collides with a mass '2m' moving with speed 'v' in the same direction. After collision, the first mass is stopped completely while the second one splits into two particles each of mass 'm', which move at angle \(45^\circ\) with respect to the origianl direction. The speed of each of the moving particle will be :-

The common tangent to the circles \(x^2+y^2=4\) and \(x^2+y^2+6x+8y-24=0\) also passes through the point :

Let P be the plane, which contains the line of intersection of the planes, \(x+y+z-6=0\) and \(2x+3y+z+5=0\) and it is perpendicular to the xy-plane. Then the distance of the point \((0,0,256)\) from P is equal to :

In a conductor, if the number of conduction electrons per unit volume is \(8.5\times10^{28}\ \mathrm{m^{-3}}\) and mean free time is \(25\ \mathrm{fs}\) (femto second), it's approximate resistivity is :- \((m_e=9.1\times10^{-31}\ \mathrm{kg})\)

If the two lines x + (a - 1) y = 1 and 2x + a²y = 1 \((a \in R - \{0, 1\})\) are perpendicular, then the distance of their point of intersection from the origin is :

If the system of equations 2x + 3y - z = 0, x + ky - 2z = 0 and 2x - y + z = 0 has a non-trival solution (x, y, z), then \(\frac{x}{y} + \frac{y}{z} + \frac{z}{x} + k\) is equal to :-

The value of the integral \(\int_0^1 x\cot^{-1}(1-x^2+x^4)\,dx\) is :-

If the tangent to the parabola \(y^2=x\) at a point \((\alpha,\beta)\), \((\beta\gt 0)\) is also a tangent to the ellipse, \(x^2+2y^2=1\), then \(\alpha\) is equal to :

The sum of the series \(1+2\times 3+3\times 5+4\times 7+\ldots\) upto 11th term is :-

Let z \(\in\) C be such that |z| \(\lt\) 1. If \(\omega = \frac{5 + 3z}{5(1 - z)}\), then :