List of top Questions asked in JEE Main- 2019

A transformer consisting of 300 turns in the primary and 150 turns in the secondary gives output power of 2.2 kW. If the current in the secondary coil is 10A, then the input voltage and current in the primary coil are :

A ray of light AO in vacuum is incident on a glass slab at angle \(60^\circ\) and refracted at angle \(30^\circ\) along OB as shown in the figure. The optical path length of light ray from A to B is:

A proton, an electron, and a Helium nucleus, have the same energy. They are in circular orbits in a plane due to magnetic field perpendicualr to the plane. Let \(r_p\), \(r_e\) and \(r_{He}\) be their respective radii, then

A particle of mass m is moving along a trajectory given by
\(x = x_0 + a\cos\omega_1 t\)
\(y = y_0 + b\sin\omega_2 t\)
The torque, acting on the particle about the origin, at \(t = 0\) is :

A moving coil galvanometer allows a full scale current of \(10^{-4}\) A. A series resistance of 2 M\(\Omega\) is required to convert the above galvanometer into a voltmeter of range 0-5 V. Therefore the value of shunt resistance required to convert the above galvanometer into an ammeter of range 0.10 mA is :

A ball is thrown upward with an initial velocity \(V_0\) from the surface of the earth. The motion of the ball is affected by a drag force equal to \(m\gamma u^2\) (where m is mass of the ball, u is its instantaneous velocity and \(\gamma\) is a constant). Time taken by the ball to rise to its zenith is :

In an experiment, the resistance of a material is plotted as a function of temperature (in some range). As shown in the figure, it is a straight line. One may conclude that :

In a photoelectric effect experiment the threshold wavelength of the light is 380 nm. If the wavelentgh of incident light is 260 nm, the maximum kinetic energy of emitted electrons will be:
Given E (in eV) = 1237/\(\lambda\) (in nm)

In a meter bridge experiment, the circuit diagram and the corresponding observation table are shown in figure

Sl. No.	\(R\,(\Omega)\)	\(l\,(\mathrm{cm})\)
1.	1000	60
2.	100	13
3.	10	1.5
4.	1	1.0

Which of the readings is inconsistent?

The electric field of a plane electromagnetic wave is given by
\(\vec{E} = E_0\hat{i}\cos(kz)\cos(\omega t)\)
The corresponding magnetic field \(\vec{B}\) is then given by

Two coaxial discs, having moments of inertia \(I_1\) and \(I_1/2\), are rotating with respective angular velocities \(\omega_1\) and \(\omega_1/2\), about their common axis. They are brought in contact with each other and thereafter they rotate with a common angular velocity. If \(E_f\) and \(E_i\) are the final and initial total energies, then \((E_f - E_i)\) is:

Figure shows charge (q) versus voltage (V) graph for series and parallel combination of two given capacitors. The capacitances are :

A \(25\times 10^{-3}\,\mathrm{m^3}\) volume cylinder is filled with 1 mol of \(\mathrm{O_2}\) gas at room temperature (300 K). The molecular diameter of \(\mathrm{O_2}\), and its root mean square speed, are found to be 0.3 nm, and 200 m/s, respectively. What is the average collision rate (per second) for an \(\mathrm{O_2}\) molecule ?

The ratio of surface tensions of mercury and water is given to be 7.5 while the ratio of their densities is 13.6. Their contact angles, with glass, are close to \(135^\circ\) and \(0^\circ\), respectively. It is observed that mercury gets depressed by an amount \(h\) in a capillary tube of radius \(r_1\), while water rises by the same amount \(h\) in a capillary tube of radius \(r_2\). The ratio, \((r_1/r_2)\), is then close to :

The line \(x = y\) touches a circle at the point \((1, 1)\). If the circle also passes through the point \((1, -3)\), then its radius is :

Which one of the following Boolean expressions is a tautology?

If the line \(x - 2y = 12\) is tangent to the ellipse \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\) at the point \(\left(3, -\frac{9}{2}\right)\), then the length of the latus rectum of the ellipse is :

The sum
\(\frac{3\times 1^3}{1^3} + \frac{5\times(1^3 + 2^3)}{1^2 + 2^2} + \frac{7\times(1^3 + 2^3 + 3^3)}{1^2 + 2^2 + 3^2} + \dots\)
upto 10 terms is:

If the circles \(x^2 + y^2 + 5Kx + 2y + K = 0\) and \(2(x^2 + y^2) + 2Kx + 3y - 1 = 0\), \((K \in \mathbb{R})\), intersect at the points \(P\) and \(Q\), then the line \(4x + 5y - K = 0\) passes through \(P\) and \(Q\), for :

If \(y = y(x)\) is the solution of the differential equation
\(\frac{dy}{dx} = (\tan x - y)\sec^2 x\), \(x \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\),
such that \(y(0) = 0\), then \(y\left(-\frac{\pi}{4}\right)\) is equal to :

Let \(A(3, 0, -1)\), \(B(2, 10, 6)\) and \(C(1, 2, 1)\) be the vertices of a triangle and \(M\) be the midpoint of \(AC\). If \(G\) divides \(BM\) in the ratio \(2 : 1\), then \(\cos(\angle GOA)\) (\(O\) being the origin) is equal to :

If the system of linear equations
\(x + y + z = 5\)
\(x + 2y + 2z = 6\)
\(x + 3y + \lambda z = \mu\), \((\lambda, \mu \in \mathbb{R})\), has infinitely many solutions, then the value of \(\lambda + \mu\) is :

If \(\int \frac{dx}{(x^2 - 2x + 10)^2} = A\left(\tan^{-1}\left(\frac{x-1}{3}\right) + \frac{f(x)}{x^2 - 2x + 10}\right) + C\)
where \(C\) is a constant of integration then :

If the coefficients of \(x^2\) and \(x^3\) are both zero, in the expansion of the expression \((1 + ax + bx^2)(1 - 3x)^{15}\) in powers of \(x\), then the ordered pair \((a, b)\) is equal to :

All the pairs \((x, y)\) that satisfy the inequality
\(2^{\sqrt{\sin^2 x - 2\sin x + 5}} \cdot \frac{1}{4^{\sin^2 y}} \le 1\)
also satisfy the equation