WB JEE 2020

If P(x) = ax2 + bx + c and Q(x) = \(-\)ax2 + dx + c, where ac \(\ne\) 0 [a, b, c, d are all real], then P(x).Q(x) = 0 has

In a certain test, there are n questions. In this test 2n-i students gave wrong answers to at least i questions, where i = 1, 2, ..., n. If the total number of wrong answers given is 2047, then n is equal to

If a and b are arbitrary positive real numbers, then the least possible value of \({{6a} \over {5b}} + {{10b} \over {3a}}\) is

Let I(n) = nn, J(n) = 13.5 ......... (2n \(-\) 1) for all (n > 1), n \(\in\) N, then

Let the relation p be defined on R by a p b holds if and only if a \(-\) b is zero or irrational, then

Let p1 and p2 be two equivalence relations defined on a non-void set S. Then

A straight line through the origin O meets the parallel lines 4x + 2y = 9 and 2x + y + 6 = 0 at P and Q respectively. The point O divides the segment PQ in the ratio

The equation \(r\,\cos \left( {\theta - {\pi \over 3}} \right) = 2\) represents

Let each of the equations x2 + 2xy + ay2 = 0 and ax2 + 2xy + y2 = 0 represent two straight lines passing through the origin. If they have a common line, then the other two lines are given by

A line cuts the X-axis at A(7, 0) and the Y-axis at B(0, \(-\)5). A variable line PQ is drawn perpendicular to AB cutting the X-axis at P(a, 0) and the Y-axis at Q(0, b). If AQ and BP intersect at R, the locus of R is

The equation of the straight line passing through the point (4, 3) and making intercepts on the coordinate axes whose sum is \(- 1\) is

The sine of the angle between the straight line \({{x - 2} \over 3} = {{y - 3} \over 4} = {{z - 4} \over 5}\) and the plane \(2x - 2y + z = 5\) is

The equation of the plane through the point \((2, - 1, - 3)\) and parallel to the lines\({{x - 1} \over 2} = {{y + 2} \over 3} = {z \over { - 4}}\) and \({x \over 2} = {{y - 1} \over { - 3}} = {{z - 2} \over 2}\) is

Let f(x) = sin x + cos ax be periodic function. Then,

\(\cos (2x + 7) = a(2 - \sin x)\) can have a real solution for

The unit vector in ZOX plane, making angles \(45^\circ\) and \(60^\circ\) respectively with \(\alpha = 2\widehat i + 2\widehat j - \widehat k\) and \(\beta = \widehat j - \widehat k\) is

When a DC voltage is applied at the two ends of a circuit kept in a closed box, it is observed that the current gradually increases from zero to a certain value and then remains constant. What do you think that the circuit contains?

A 400\(\Omega\) resistor, a 250 mH inductor and a 2.5 \(\mu\)F capacitor are connected in series with an AC source of peak voltage 5 V and angular frequency 2kHZ. What is the peak value of the electrostatic energy of the capacitor?

A nucleus X emits a \(\beta\)-particle to produce a nucleus Y. If their atomic masses are Mx and My respectively, then the maximum energy of the \(\beta\)-particle emitted is (where, me is the mass of an electron and c is the velocity of ...

For nuclei with mass number close to 119 and 238, the binding energies per nucleon are approximately 7.6 MeV and 8.6 MeV, respectively. If a nucleus of mass number 238 breaks into two nuclei of nearly equal masses, what will be the approxim...

If R is the Rydberg constant in cm-1, then hydrogen atom does not emit any radiation of wavelength in the range of

A galvanometer can be converted to a voltmeter of full scale deflection V0 by connecting a series resistance R1 and can be converted to an ammeter of full scale deflection I0 by connecting a shunt resistance R2. What is the current flowing ...

What will be the equivalent resistance between the terminals A and B of the infinite resistive network shown in the figure?

Consider the circuit shown.If all the cells have negligible internal resistance, what will be the current through the 2\(\Omega\)
resistor when steady state is reached?

A point source of light is used in an experiment of photoelectric effects. If the distance between the source and the photoelectric surface is doubled, which of the following may result?

Consider a conducting wire of length L bent in the form of a circle of radius R and another conductor of length a (a < < R) is bent in the form of a square. The two loops are then placed in same plane such that the square loop is exactly at...

A conducting circular loop of resistance 20\(\Omega\)
and cross-sectional area 20 \(\times\) 10-2 m2 is placed perpendicular to a spatially uniform magnetic field B, which varies with time t as B = 2sin(50\(\pi\)t) T. Find the net char...

In the circuit shown, the value of \(\beta\) of the transistor is 48. If the supplied base current is 200 \(\mu\)A, what is the voltage at the terminal Y?

A common emitter transistor amplifier is connected with a load resistance of 6 k\(\Omega\)
. When a small AC signal of 15 mV is added to the base-emitter voltage, the alternating base current is 20\(\mu\)A and the alternating collector cu...

A pair of parallel metal plates are kept with a separation d. One plate is at a potential + V and the other is at ground potential. A narrow beam of electrons enters the space between the plates with a velocity v0 and in a direction paralle...

A very long charged solid cylinder of radius a contains a uniform charge density p. Dielectric constant of the material of the cylinder is K. What will be the magnitude of electric field at a radial distance x (x < a) from the axis of the c...

Two pith balls, each carrying charge + q are hung from a hook by two springs. It is found that when each charge is tripled, angle between the strings double. What was the initial angle between the strings?

As shown in the figure, a point charge q1 = + 1 \(\times\) 10-6 C is placed at the origin in xy-plane and another point charge q2 = + 3 \(\times\) 10-6 C is placed at the coordinate (10, 0).In that case, which of the following graph(s) ...

Four identical point masses, each of mass m and carrying charge + q are placed at the corners of a square of sides a on a frictionless plane surface. If the particles are released simultaneously, the kinetic energy of the system when they a...

An object, is placed 60 cm in front of a convex mirror of focal length 30 cm. A plane mirror is now placed facing the object in between the object and the convex mirror such that it covers lower half of the convex mirror. What should be the...

A tennis ball hits the floor with a speed v at an angle \(\theta\) with the normal to the floor. If the collision is inelastic and the coefficient of restitution is \(\varepsilon\), what will be the angle of reflection?

A thin convex lens is placed just above an empty vessel of depth 80 cm. The image of a coin kept at the bottom of the vessel is thus formed 20 cm above the lens. If now water is poured in the vessel upto a height of 64 cm, what will be the ...

An ideal gas undergoes the cyclic process abca as shown in the given p - V diagramIt rejects 50J of heat during ab and absorbs 80J of heat during ca. During bc, there is no transfer of heat and 40J of work is done by the gas. What should be...

A metallic block of mass 20 kg is dragged with a uniform velocity of 0.5 ms-1 on a horizontal table for 2.1 s. The coefficient of static friction between the block and the table is 0.10. What will be the maximum possible rise in temperature...

A container AB in the shape of a rectangular parallelopiped of length 5 m is divided internally by a movable partition P as shown in the figure.The left compartment is filled with a given mass of an ideal gas of molar mass 32 while the righ...

When 100 g of boiling water at 100\(^\circ\)
C is added into a calorimeter containing 300 g of cold water at 10\(^\circ\)
C, temperature of the mixture becomes 20\(^\circ\)
C. Then, a metallic block of mass 1 kg at 10\(^\circ\)
C is dip...

A block of mass m rests on a horizontal table with a coefficient of static friction \(\mu\). What minimum force must be applied on the block to drag it on the table?

As shown in the figure, a single conducting wire is bent to form a loop in the form of a circle of radius r concentrically inside a square of side a, where a : r = 8 : \(\pi\). A battery B drives a current through the wire. If the battery ...

As shown in the figure, a wire is bent to form a D-shaped closed loop, carrying current I, where the curved part is a semi-circle of radius R. The loop is placed in a uniform magnetic field B, which is directed into the plane of the paper. ...

A charged particle moves with constant velocity in a region, where no effect of gravity is felt but an electrostatic field E together with a magnetic field B may be present. Then, which of the following cases are possible?

A fighter plane, flying horizontally with a speed 360 km/h at an altitude of 500 m drops a bomb for a target straight ahead of it on the ground. The bomb should be dropped at what approximate distance ahead of the target? Assume that accele...

Which of the following diagrams correctly shows the relation between the terminal velocity vT of a spherical body falling in a liquid and viscosity \(\eta\)
of the liquid?

A steel and a brass wire, each of length 50 cm and cross-sectional area 0.005 cm2 hang from a ceiling and are 15 cm apart. Lower ends of the wires are attached to a light horizontal bar. A suitable downward load is applied to the bar, so th...

Two metallic spheres of equal outer radii are found to have same moment of inertia about their respective diameters. Then, which of the following statement(s) is/are true?

A simple pendulum of length l is displaced, so that its taught string is horizontal and then released. A uniform bar pivoted at one end is simultaneously released from its horizontal position. If their motions are synchronous, what is the l...