List of top Questions asked in JEE Main- 2019

A 200 \(\Omega\) resistor has a certain color code. If one replaces the red color by green in the code, the new resistance will be :

In SI units, the dimensions of \(\sqrt{\dfrac{\in_0}{\mu_0}}\) is :

The wavelength of the carrier waves in a modern optical fiber communication network is close to :

A particle moves in one dimension from rest under the influence of a force that varies with the distance travelled by the particle as shown in the figure. The kinetic energy of the particle after it has travelled 3m is :

In figure, the optical fiber is \(l\) = 2m long and has a diameter of d = 20 \(\mu\)m. If a ray of light is incident on one end of the fiber at angle \(\theta_1\) = 40°, the number of reflection it makes before emerging from the other end is close to: (refractive index of fibre is 1.31 and sin 40° = 0.64)

The reverse breakdown voltage of a Zener diode is 5.6 V in the given circuit.

The current \(I_Z\) through the Zener is :

Radiation coming from transitions \(n = 2\) to \(n = 1\) of hydrogen atoms fall on \(\mathrm{He^+}\) ions in \(n = 1\) and \(n = 2\) states. The possible transition of helium ions as they absorb energy from the radiation is :

Water from a pipe is coming at a rate of 100 litres per minute. If the radius of the pipe is 5 cm, the Reynolds number for the flow is of the order of : (density of water = 1000 kg/m³, coefficient of viscosity of water = 1mPas)

Ship A is sailing towards north-east with velocity \(\vec{v} = 30\hat{i} + 50\hat{j}\) km/hr where \(\hat{i}\) points east and \(\hat{j}\), north. Ship B is at a distance of 80 km east and 150 km north of Ship A and is sailing towards west at 10 km/hr. A will be at minimum distance from B in :

An upright object is placed at a distance of 40 cm in front of a convergent lens of focal length 20 cm. A convergent mirror of focal length 10 cm is placed at a distance of 60 cm on the other side of the lens. The position and size of the final image will be :

Two particles move at right angle to each other. Their de-Broglie wavelengths are \(\lambda_1\) and \(\lambda_2\) respectively. The particles suffer perfectly inelastic collision. The de-Broglie wavelength \(\lambda_2\) of the final particle, is given by :

The bob of a simple pendulum has mass 2g and a charge of \(5.0\ \mu\mathrm{C}\). It is at rest in a uniform horizontal electric field of intensity 2000 V/m. At equilibrium, the angle that the pendulum makes with the vertical is : (take \(g = 10\ \mathrm{m/s^2}\))

Four particles A, B, C and D with masses \(m_A = m\), \(m_B = 2m\), \(m_C = 3m\) and \(m_D = 4m\) are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles is :

A wire of length \(2L\), is made by joining two wires A and B of same length but different radii \(r\) and \(2r\) and made of the same material. It is vibrating at a frequency such that the joint of the two wires forms a node. If the number of antinodes in wire A is \(p\) and that in B is \(q\) then the ratio \(p : q\) is :

A thin strip 10 cm long is on a U shaped wire of negligible resistance and it is connected to a spring of spring constant \(0.5\ \mathrm{N\,m^{-1}}\) (see figure). The assembly is kept in a uniform magnetic field of 0.1 T. If the strip is pulled from its equilibrium position and released, the number of oscillation it performs before its amplitude decreases by a factor of \(e\) is \(N\). If the mass of the strip is 50 grams, its resistance \(10\ \Omega\) and air drag negligible, \(N\) will be close to :

The shortest distance between the line \(y = x\) and the curve \(y^2 = x - 2\) is :

If \(2y = \left(\cot^{-1}\left(\frac{\sqrt{3}\cos x + \sin x}{\cos x - \sqrt{3}\sin x}\right)\right)^2,\ x \in \left(0, \frac{\pi}{2}\right)\), then \(\frac{dy}{dx}\) is equal to :

The equation of a plane containing the line of intersection of the planes \(2x - y - 4 = 0\) and \(y + 2z - 4 = 0\) and passing through the point \((1, 1, 0)\) is :

If the tangents on the ellipse \(4x^2 + y^2 = 8\) at the points \((1, 2)\) and \((a, b)\) are perpendicular to each other, then \(a^2\) is equal to :

If \(S_1\) and \(S_2\) are respectively the sets of local minimum and local maximum points of the function \(f(x) = 9x^4 + 12x^3 - 36x^2 + 25,\ x \in R\), then :

The magnitude of the projection of the vector \(2\hat{i} + 3\hat{j} + \hat{k}\) on the vector perpendicular to the plane containing the vectors \(\hat{i} + \hat{j} + \hat{k}\) and \(\hat{i} + 2\hat{j} + 3\hat{k}\), is :

The length of the perpendicular from the point \((2, -1, 4)\) on the straight line,
\(\frac{x + 3}{10} = \frac{y - 2}{-7} = \frac{z}{1}\) is :

Let A and B be two non-null events such that \(A \subset B\). Then, which of the following statements is always correct?

If \(\alpha = \cos^{-1}\left(\frac{3}{5}\right)\), \(\beta = \tan^{-1}\left(\frac{1}{3}\right)\), where \(0 \lt \alpha, \beta \lt \frac{\pi}{2}\), then \(\alpha - \beta\) is equal to :

The area (in sq. units) of the region \(A = \{(x, y) \in R \times R \mid 0 \le x \le 3,\ 0 \le y \le 4,\ y \le x^2 + 3x\}\) is :