List of top Questions asked in JEE Main

A modulating signal 2sin (6.28 × 106) t is added to the carrier signal 4sin(12.56 × 109) t for amplitude modulation. The combined signal is passed through a non-linear square law device. The output is then passed through a band pass filter. The bandwidth of the output signal of band pass filter will be ______MHz.
The speed of a transverse wave passing through a string of length 50 cm and mass 10 g is 60 ms–1. The area of cross-section of the wire is 2.0 mm2 and its Young’s modulus is 1.2 × 1011 Nm–2. The extension of the wire over its natural length due to its tension will be x × 10–5 m. The value of x is _____.
The metallic bob of simple pendulum has the relative density 5. The time period of this pendulum is 10 s. If the metallic bob is immersed in water, then the new time period becomes 5√x s. The value of x will be _____.
Two radioactive materials A and B have decay constants 25λ and 16λ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of B to that of A will be ‘e’ after a time \(\frac{1}{(aλ)}\). The value of a is _____.
A capacitor of capacitance 500 μF is charged completely using a dc supply of 100 V. It is now connected to an inductor of inductance 50 mH to form an LC circuit. The maximum current in the LC circuit will be ______A.
Two identical thin metal plates has charge q1 and q2 respectively such that q1 > q2. The plates were brought close to each other to form a parallel plate capacitor of capacitance C. The potential difference between them is
An unpolarised light beam of intensity 2I0 is passed through a polaroid P and then through another polaroid Q which is oriented in such a way that its passing axis makes an angle of 30° relative to that of P. The intensity of the emergent light is

A thermodynamic system is taken from an original state D to an intermediate state E by the linear process shown in the figure. Its volume is then reduced to the original volume from E to F by an isobaric process. The total work done by the gas from D to E to F will be

A thermodynamic system is taken from an original state D to an intermediate state

A tube of length 50 cm is filled completely with an incompressible liquid of mass 250 g and closed at both ends. The tube is then rotated in horizontal plane about one of its ends with a uniform angular velocity x√F rad s−1. If F be the force exerted by the liquid at the other end then the value of x will be______.

A 8 V Zener diode along with a series resistance R is connected across a 20 V supply (as shown in the figure). If the maximum Zener current is 25 mA, then the minimum value of R will be ____ Ω.

A 8 V Zener diode along with a series resistance R is connected across a

The acute angle between the pair of tangents drawn to the ellipse 2x2 + 3y2 = 5 from the point (1, 3) is

The vapour pressures of two volatile liquids A and B at 25°C are 50 Torr and 100 Torr, respectively. If the liquid mixture, contains 0.3 mole fraction of A, then the mole fraction of liquid B in the vapour phase is \(\frac {x}{17}\). The value of x is _____.
Let the circumcentre of a triangle with vertices A(a, 3), B(b, 5) and C(a, b), ab > 0 be P(1, 1). If the line AP intersects the line BC at the point Q(k1, k2), then k1 + k2 is equal to :
\(250\) \(g\) solution of \(D-glucose\) in water contains 10.8% of carbon by weight. The molality of the solution is nearest to (Given: Atomic Weights are, \(H, 1 u; C, 12 u; O, 16 u\))

If the line x – 1 = 0 is a directrix of the hyperbola kx2 – y2 = 6, then the hyperbola passes through the point

The equations of the sides AB, BC and CA of a triangle ABC are 2x + y = 0, x + py = 15a and x – y = 3, respectively. If its orthocentre is
\((2, a),−\frac{1}{2}<a<2 \)
then p is equal to _______.

If\(\begin{array}{l}1 + \left(2 + ^{49}C_1 + ^{49}C_2 + … ^{49}C_{49}\right) \left(^{50}C_2 + ^{50}C_4 + … ^{50}C_{50}\right) \end{array}\)is equal to 2n. m, where m is odd, then n + m is equal to ______.
Let m1, m2 be the slopes of two adjacent sides of a square of side a such that \(a^2 + 11a + 3(m_1^2 + m_2^2) = 220\). If one vertex of the square is \((10(\cos \alpha - \sin \alpha), 10(\sin \alpha + \cos \alpha))\), where \(\alpha \in \left(0, \frac{\pi}{2}\right)\)and the equation of one diagonal is \((\cos \alpha - \sin \alpha)x + (\sin \alpha + \cos \alpha)y = 10\), then \(72(\sin^4 \alpha + \cos^4 \alpha) + a^2 - 3a + 13\) is equal to :
Let R be a relation from the set \(\{1, 2, 3, ….., 60\}\) to itself such that \(R = \{(a, b) : b = pq,\) where \(p, q≥ 3\) are prime numbers\(\}\). Then, the number of elements in R is :
A particle executes simple harmonic motion. Its amplitude is 8 cm and time period is 6s. The time it will take to travel from its position of maximum displacement to the point corresponding to half of its amplitude, is _________s.
The limiting molar conductivities of \(NaI\), \(NaNO_3\) and \(AgNO_3\) are \(12.7\), \(12.0\) and \(13.3\) mS m2 mol–1, respectively (all at 25°C). The limiting molar conductivity of \(AgI\) at this temperature is ____ mS m2 mol–1.

Let Q and R be two points on the line 
\(\frac{x+1}{2}=\frac{y+2}{3}=\frac{z−1}{2}\) at a distance \(\sqrt{26}\) 
from the point P(4, 2, 7). Then the square of the area of the triangle PQR is _______ .

A rigid nitrogen tank stored inside a laboratory has a pressure of 30 atm at 06:00 am when the temperature is 27°C. At 03:00 pm, when the temperature is 45°C, the pressure in the tank will be _______ atm. [nearest integer]
Given below are two statements :
Statement-I : For KI, molar conductivity increases steeply with dilution.
Statement-II : For carbonic acid, molar conductivity increases slowly with dilution.
In the light of the above statements, choose the correct answer from the options given below :
If the solubility product of PbS is 8 × 10–28, then the solubility of PbS in pure water at 298 K is x × 10–16 mol L–1. The value of x is ________. (Nearest integer)
[given : \(\sqrt2=1.41\)]