WB JEE 2016

Let S be the set of points, whose abscissae and ordinates are natural numbers. Let P \(\in\) S, such that the sum of the distance of P from (8, 0) and (0, 12) is minimum among all elements in S. Then, the number of such points P and S is

The smallest positive root of the equation tan x \(-\) x = 0 lies in

If the parabola x2 = ay makes an intercept of length \(\sqrt {40}\) units on the line y \(-\) 2x = 1, then, a is equal to

The points (\(-\)a, \(-\)b), (a, b), (0, 0) and (a2, ab), a \(\ne\) 0, b \(\ne\) 0 are always

The number of ways in which the letters of the word ARRANGE can be permuted such that the R's occur together, is

The locus of the point of intersection of the straight lines \({x \over a} + {y \over b} = K\) and \({x \over a} - {y \over b} = {1 \over K}\), where K is a non-zero real variable, is given by

The number of points at which the function f(x) = max {a \(-\) x, a + x, b}, \(-\) \(\infty\) < x < \(\infty\), 0 < a < b cannot be differentiable, is

The order of the differential equation of all parabolas whose axis of symmetry along X-axis is

\(\int {{{\log \sqrt x } \over {3x}}} dx\) is equal to

If the function f : R \(\to\) R is defined by f(x) = (x2 + 1)35, \(\forall\) x\(\in\)R, then f is

If f(x) is an odd differentiable function defined on (\(-\)\(\infty\), \(\infty\)) such that f'(3) = 2, then f'(\(-\)3) is equal to

The value of \(\cos 15^\circ \cos 7{{1^\circ } \over 2}\sin 7{{1^\circ } \over 2}\) is

For non-zero vectors a and b, if | a + b | < | a \(-\) b |, then a and b are

If the first and (2n \(-\) 1)th terms of an AP, GP and HP are equal and their nth terms are respectively a, b, c, then always

If the matrix \(A = \left[ {\matrix{ 2 & 0 & 0 \cr 0 & 2 & 0 \cr 2 & 0 & 2 \cr } } \right]\), then \({A^n} = \left[ {\matrix{ a & 0 & 0 \cr 0 & a & 0 \cr b & 0 & a \cr } } \right],n \in N\), where

The wavelength of second Balmer line in hydrogen spectrum is 600 nm. The wavelength for its third line in Lyman series is

Equivalent capacitance between A and B in the figure is

A 1 \(\mu\)F capacitor C is connected to a battery of 10 V through a resistance 1 M\(\Omega\). The voltage across C after 1 s is approximately

A current I = I0e\(-\)\(\lambda\)t is flowing in a circuit consisting of a parallel combination of resistance R and capacitance C. The total charge over the entire pulse period is

Two bodies of masses m1 and m2 are separated by a distance R. The distance of the centre of mass of the bodies from the mass m1 is

The effective resistance between A and B in the figure is \({7 \over {12}}\Omega\) if each side of the cube has 1\(\Omega\) resistance. The effective resistance between the same two points, when the link AB is removed, is

Two equal resistances, 400 \(\Omega\) each, are connected in series with a 8 V battery. If the resistance of first one increases by 0.5%, the change required in the resistance of the second one in order to keep the potential difference acro...

Two wires of same radius having lengths l1 and l2 and resistivities \({{\rho _1}}\) and \({{\rho _2}}\) are connected in series. The equivalent resistivity will be

The potential difference V required for accelerating an electron to have the de-Broglie wavelength of 1 \(\mathop A\limits^o\) is

The distance between a light source and photoelectric cell is d. If the distance is decreased to \({d \over 2}\), then

The number of de-Broglie wavelengths contained in the second Bohr orbit of hydrogen atom is

The work function of Cesium is 2.27 eV. The cut-off voltage which stops the emission of electrons from a cesium cathode irradiated with light of 600 nm wavelength is

Two coils of self-inductances 6 mH and 8 mH are connected in series and are adjusted for highest coefficient of coupling. Equivalent self-inductance L for the assembly is approximately

A Zener diode having break-down voltage 5.6 V is connected in reverse bias with a battery of emf 10 V and a resistance of 100 \(\Omega\) in series. The current flowing through the Zener diode is

In case of a bipolar transistor \(\beta\) = 45. The potential drop across the collector resistance of 1 k\(\Omega\) is 5V. The base current is approximately

A hollow metal sphere of radius R is charged with a charge Q. The electric potential and intensity inside the sphere are respectively

Angle between an equipotential surface and electric lines of force is

A charged particle of mass m1 and charge q1 is revolving in a circle of radius r. Another charged particle of charge q2 and mass m2 is situated at the centre of the circle. If the velocity and time period of the revolving particle be v and ...

Light travels through a glass plate of thickness t and having refractive index \(\mu\). If c be the velocity of light in vacuum, time taken by the light to travel through this thickness of glass is

A ray of light strikes a glass plate at an angle of 60\(^\circ\). If the reflected and refracted rays are perpendicular to each other, the refractive index of glass is

The temperature of the water of a pond is 0\(^\circ\)C while that of the surrounding atmosphere is \(-\)20\(^\circ\)C. If the density of ice is \(\rho\), coefficient of thermal conductivity is k and latent heat of melting is L, then the thi...

The perfect gas equation for 4g of hydrogen gas is

The temperature of a blackbody radiation enclosed in a container of volume V is increased from 100\(^\circ\)C to 1000\(^\circ\)C. The heat required in the process is

If the rms velocity of hydrogen gas at a certain temperature is c, then the rms velocity of oxygen gas at the same temperature is

If the temperature of the Sun gets doubled, the rate of energy received on the Earth will increase by a factor of

A mass of 1 kg is suspended by means of a thread. The system is (i) lifted up with an acceleration of 4.9 ms\(-\)2. (ii) lowered with an acceleration of 4.9 ms\(-\)2. The ratio of tension in the first and second case is

A rectangular coil carrying-current is placed in a non-uniform magnetic field. On that coil, the total

An electron enters an electric field having intensity \(E = 3\widehat i + 6\widehat j + 2\widehat k\) Vm\(-\)1 and magnetic field having induction \(B = 2\widehat i + 3\widehat j\) T with a velocity \(v = 2\widehat i + 3\widehat j\) ms\(-\)...

A train moves from rest with acceleration \(\alpha\) and in time t1 covers a distance x. It then decelerates to rest at constant retardation \(\beta\) for distance y in time t2. Then,

At a particular height, the velocity of an ascending body is u. The velocity at the same height while the body falls freely is

A drop of water detaches itself from the exit of a tap when (\(\sigma\) = surface tension of water, \(\rho\) = density of water, R = radius of the tap exit, r = radius of the drop)

A gas bubble of 2 cm diameter rises through a liquid of density 1.75 g cm\(-\)3 with a fixed speed of 0.35 cms\(-\)1. Neglect the density of the gas. The coefficient of viscosity of the liquid is

1000 droplets of water having 2 mm diameter each coalesce to form a single drop. Given the surface tension of water is 0.072 Nm\(-\)1. The energy loss in the process is

A particle vibrating simple harmonically has an acceleration of 16 cms\(-\)2 when it is at a distance of 4 cm from the mean position. Its time period is

If x = at + bt2, where x is in metre (m) and t is in hour (h), then unit of b will be