WB JEE 2019

Let x1, x2 be the roots of \({x^2} - 3x + a = 0\) and x3, x4 be the roots of \({x^2} - 12x + b = 0\). If \({x_1} < {x_2} < {x_3} < {x_4}\) and \({x_1},{x_2},{x_3},{x_4}\) are in GP, then ab equals

Let f : X \(\to\) Y and A, B are non-void subsets of Y, then (where the symbols have their usual interpretation)

Let S, T, U be three non-void sets and f : S \(\to\) T, g : T \(\to\) U be so that gof : s \(\to\) U is surjective. Then,

Let the relation \(\rho\) be defined on R as a\(\rho\)b if 1 + ab > 0. Then,

A variable line passes through a fixed point \(({x_1},{y_1})\) and meets the axes at A and B. If the rectangle OAPB be completed, the locus of P is, (O being the origin of the system of axes).

If the point of intersection of the lines 2ax + 4ay + c = 0 and 7bx + 3by \(-\) d = 0 lies in the 4th quadrant and is equidistant from the two axes, where a, b, c and d are non-zero numbers, then ad : bc equals to

A straight line through the point (3, \(-\)2) is inclined at an angle 60\(^\circ\) to the line \(\sqrt 3 x + y = 1\). If it intersects the X-axis, then its equation will be

A variable line passes through the fixed point \((\alpha ,\beta )\). The locus of the foot of the perpendicular from the origin on the line is

Straight lines x \(-\) y = 7 and x + 4y = 2 intersect at B. Points A and C are so chosen on these two lines such that AB = AC. The equation of line AC passing through (2, \(-\)7) is

The direction ratios of the normal to the plane passing through the points (1, 2, \(-\)3), (\(-\)1, \(-\)2, 1) and parallel to \({{x - 2} \over 2} = {{y + 1} \over 3} = {z \over 4}\) is

The equation of the plane, which bisects the line joining the points (1, 2, 3) and (3, 4, 5) at right angles is

The graphs of the polynomial x2 \(-\) 1 and cos x intersect

If \({e^{\sin x}} - {e^{-\sin x}} - 4 = 0\), then the number of real values of x is

Let \(\widehat \alpha\), \(\widehat \beta\), \(\widehat \gamma\) be three unit vectors such that \(\widehat \alpha \, \times \,(\widehat \beta \times \widehat \gamma ) = {1 \over 2}(\widehat \beta + \widehat \gamma )\) where $$\widehat...

The position vectors of the points A, B, C and D are \(3\widehat i - 2\widehat j - \widehat k\), \(2\widehat i - 3\widehat j + 2\widehat k\), \(5\widehat i - \widehat j + 2\widehat k\) and \(4\widehat i - \widehat j - \lambda \widehat k\), ...

A parallel plate capacitor in series with a resistance of 100\(\Omega\), an inductor of 20 mH and an AC voltage source of variable frequency shows resonance at a frequency of \({{1250} \over \pi }\) Hz. If this capacitor is charged by a DC...

When a 60 mH inductor and a resistor are connected in series with an AC voltage source, the voltage leads the current by 60\(^\circ\). If the inductor is replaced by a 0.5 \(\mu\)F capacitor, the voltage lags behind the current by 30$$^\cir...

To which of the following the angular velocity of the electron in the n-th Bohr orbit is proportional?

A parent nucleus X undergoes \(\alpha\)-decay with a half-life of 75000 yrs. The daughter nucleus Y undergoes \(\beta\)-decay with a half-life of 9 months. In a particular sample, it is found that the rate of emission of \(\beta\)-particles...

A proton and an electron initially at rest are accelerated by the same potential difference. Assuming that a proton is 2000 times heavier than an electron, what will be the relation between the de Broglie wavelength of the proton ($$\lambda...

A capacitor of capacitance C is connected in series with a resistance R and DC source of emf E through a key. The capacitor starts charging when the key is closed. By the time the capacitor has been fully charged, what amount of energy is d...

What is the current I shown in the given circuit?

In the circuit shown in the figure all the resistance are identical and each has the value r\(\Omega\). The equivalent resistance of the combination between the points A and B will remain unchanged even when the following pairs of points m...

When the value of R in the balanced Wheatstone bridge, shown in the figure, is increased from 5\(\Omega\) to 7\(\Omega\), the value of S has to be increased by 3\(\Omega\) in order to maintain the balance. What is the initial values of S...

Five identical capacitors, of capacitance 20\(\mu\)F each, are connected to a battery of 150V, in a combination as shown in the diagram. What is the total amount of charge stored?

Electrons are emitted with kinetic energy T from a metal plate by an irradiation of light of intensity J and frequency v. Then, which of the following will be true?

Each of the two inputs A and B can assume values either 0 or 1. Then which of the following will be equal to \(\overline {A\,}\) . \(\overline {B\,}\)?

In the circuit shown, what will be the current through the 6V zener?

A negative charge is placed at the midpoint between two fixed equal positive charges, separated by a distance 2d. If the negative charge is given a small displacement x(x < < d) perpendicular to the line joining the positive charges, how th...

Eleven equal point charges, all of them having a charge +Q, are placed at all the hour positions of a circular clock of radius r, except at the 10 h position. What is the electric field strength at the centre of the clock?

A point object is placed on the axis of a thin convex lens of focal length 0.05 m at a distance of 0.2 m from the lens and its image is formed on the axis. If the object is now made to oscillate along the axis with a small amplitude of A cm...

A ray of light is reflected by a plane mirror. \({\widehat e_0}\), \(\widehat e\) and \(\widehat n\) be the unit vectors along the incident ray, reflected ray and the normal to the reflecting surface respectively.Which of the following give...

Assume that the earth moves around the sun in a circular orbit of radius R and there exists a planet which also move around the sun in a circular orbit with an angular speed twice as large as that of the earth. The earth of the orbit of the...

Two identical blocks of ice move in opposite directions with equal speed and collide with each other. What will be the minimum speed required to make both the blocks melt completely, if the initial temperatures of the blocks were \(-\)8$$^\...

Consider the given diagram. An ideal gas is contained in a chamber (left) of volume V and is at an absolute temperature T. It is allowed to rush freely into the right chamber of volume V which is initially vacuum. The whole system is therma...

The initial pressure and volume of a given mass of an ideal gas with \(\left( {{{{C_p}} \over {{C_V}}} = \gamma } \right)\), taken in a cylinder fitted with a piston, are p0 and V0 respectively. At this stage the gas has the same temperatur...

Two black bodies A and B have equal surface areas are maintained at temperatures 27\(^\circ\)C and 177\(^\circ\)C respectively. What will be the ratio of the thermal energy radiated per second by A to that by B?

A horizontal fire hose with a nozzle of cross-sectional area \({5 \over {\sqrt {21} }} \times {10^{ - 3}}{m^2}\) delivers a cubic metre of water in 10s. What will be the maximum possible increase in the temperature of water while it hits a ...

What will be the molar specific heat at constant volume of an ideal gas consisting of rigid diatomic molecules?

Two weights of the mass m1 and m2 (> m1) are joined by an inextensible string of negligible mass passing over a fixed frictionless pulley. The magnitude of the acceleration of the loads is

A current 'I' is flowing along an infinite, straight wire, in the positive Z-direction and the same current is flowing along a similar parallel wire 5 m apart, in the negative Z-direction. A point P is at a perpendicular distance 3m from th...

To which of the following quantities, the radius of the circular path of a charged particle moving at right angles to a uniform magnetic field is directly proportional?

A particle with charge q moves with a velocity v in a direction perpendicular to the directions of uniform electric and magnetic fields, E and B respectively, which are mutually perpendicular to each other. Which one of the following gives ...

A metallic loop is placed in a uniform magnetic field B with the plane of the loop perpendicular to B. Under which condition(s) given an emf will be induced in the loop? "If the loop is ............"

An electric current 'I' enters and leaves a uniform circular wire of radius r through diametrically opposite points. A particle carrying a charge q moves along the axis of the circular wire with speed v. What is the magnetic force experienc...

A square conducting loop is placed near an infinitely long current carrying wire with one edge parallel to the wire as shown in the figure. If the current in the straight wire is suddenly halved, which of the following statements will be tr...

A projectile thrown with an initial velocity of 10 ms\(-\)1 at an angle \(\alpha\) with the horizontal, has a range of 5 m. Taking g = 10 ms\(-\)2 and neglecting air resistance, what will be the estimated value of \(\alpha\)?

Two particles are simultaneously projected in the horizontal direction from a point P at a certain height. The initial velocities of the particles are oppositely directed to each other and have magnitude v each. The separation between the p...

A compressive force is applied to a uniform rod of rectangular cross-section so that its length decreases by 1%. If the Poisson's ratio for the material of the rod be 0.2, which of the following statements is correct?"The volume approximate...

A small spherical body of radius r and density \(\rho\) moves with the terminal velocity v in a fluid of coefficient of viscosity \(\eta\) and density \(\sigma\). What will be the net force on the body?