WB JEE 2017

In a GP series consisting of positive terms, each term is equal to the sum of next two terms. Then, the common ratio of this GP series is

On R, the relation \(\rho\) be defined by 'x\(\rho\)y holds if and only if x \(-\) y is zero or irrational'. Then,

On set A = {1, 2, 3}, relations R and S are given byR = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)},S = {(1, 1), (2, 2), (3, 3), (1, 3), (3, 1)}. Then,

On the set R of real numbers we define xPy if and only if xy \(\ge\) 0. Then, the relation P is

On R, the set of real numbers, a relation \(\rho\) is defined as 'a\(\rho\)b if and only if 1 + ab > 0'. Then,

Mean of n observations x1, x2, ...., xn is \(\overline x\). If an observation xq is replaced by xq' then the new mean is

The point P(3, 6) is first reflected on the line y = x and then the image point Q is again reflected on the line y = \(-\) x to get the image point Q'. Then, the circumcentre of the \(\Delta\)PQQ' is

Let d1 and d2 be the lengths of the perpendiculars drawn from any point of the line \(7x - 9y + 10 = 0\) upon the lines 3x + 4y = 5 and 12x + 5y = 7, respectively. Then,

Let A(2, \(-\)3) and B(\(-\) 2, 1) be two angular points of \(\Delta\)ABC. If the centroid of the triangle moves on the line 2x + 3y = 1, then the locus of the angular point C is given by

Transforming to parallel axes through a point (p, q), the equation \(2{x^2} + 3xy + 4{y^2} + x + 18y + 25 = 0\) becomes \(2{x^2} + 3xy + 4{y^2} = 1\). Then,

Three lines are drawn from the origin O with direction cosines proportional to (1, \(-\)1, 1), (2, \(-\)3, 0) and (1, 0, 3). The three lines are

The equation of the plane through (1, 2, \(-\)3) and (2, \(-\)2, 1) and parallel to X-axis is

The equation \(\sin x(\sin x + \cos x) = k\) has real solutions, where k is a real number. Then,

For any vector x, where \(\widehat i\), \(\widehat j\), \(\widehat k\) have their usual meanings the value of \({(x \times \widehat i)^2} + {(x \times \widehat j)^2} + {(x \times \widehat k)^2}\) where \(\widehat i\), \(\widehat j\), $$\wid...

If the sum of two unit vectors is a unit vector, then the magnitude of their difference is

When the frequency of the AC voltage applied to a series LCR circuit is gradually increased from a low value, the impedance of the circuit

The de-Broglie wavelength of an electron is \(0.4 \times {10^{ - 10}}\) m when its kinetic energy is 1.0 keV. Its wavelength will be \(1.0 \times {10^{ - 10}}\) m, when its kinetic energy is

Let vn and En be the respective speed and energy of an electron in the nth orbit of radius rn, in a hydrogen atom, as predicted by Bohr's model. Then

Radon-222 has a half-life of 3.8 days. If one starts with 0.064 kg of radon-222 left after 19 days will be

Three capacitors of capacitance 1.0, 2.0 and 5.0 \(\mu\)F are connected in series to a 10 V source. The potential difference across the 2.0\(\mu\)F capacitor is

A small steel ball bounces on a steel plate held horizontally. On each bounce the speed of the ball arriving at the plate is reduced by a factor e (coefficient of restitution) in the rebound, so that Vupward = eVdownward. If the ball is ini...

Two particles A and B (both initially at rest) start moving towards each other under a mutual force of attraction. At the instant, when the speed of A is v and the speed of B is 2v, the speed of the centre of mass is

Consider the circuit shown in the figure.The value of the resistance X for which the thermal power generated in it is practically independent of small variation of its resistance is

Six wires, each of resistance r, are connected so as to form a tetrahedron. The equivalent resistance of the combination when current enters through one corner and leaves through some other corner is

Consider the circuit shown in the figure where all the resistances are of magnitude 1 k\(\Omega\). If the current in the extreme right resistance X is 1 mA, the potential difference between A and B is

Consider the circuit given here. The potential difference VBC between the points B and C is

When light of frequency v1 is incident on a metal with work function W (where hv1 > W), then photocurrent falls to zero at a stopping potential of V1. If the frequency of light is increased to v2, the stopping potential changes to V2. There...

In the given circuit, the binary inputs at A and B are both 1 in one case and both 0 in the next case. The respective outputs at Y in these two cases will be

When a semiconducting device is connected in series with a battery and a resistance, a current is found to flow in the circuit. If however, the polarity of the battery is reversed, practically no current flows in the circuit. The device may...

A positive charge Q is situated at the centre of a cube. The electric flux through any face of the cube is (in SI units)

A particle with charge Q coulomb, tied at the end of an inextensible string of length R metre, revolves in a vertical plane. At the centre of the circular trajectory, there is a fixed charge of magnitude Q coulomb. The mass of the moving ch...

A charge of 0.8 coulomb is divided into two charges Q1 and Q2. These are kept at a separation of 30 cm. The force on Q1 is maximum when

A unit negative charge with mass M resides at the mid-point of the straight line of length 2a adjoining two fixed charges of magnitude +Q each. If it is given a very small displacement x(x << a) in a direction perpendicular to the straight ...

A point object is held above a thin equiconvex lens at its focus. The focal length is 0.1 m and the lens rests on a horizontal thin plane mirror. The final image will be formed at

The ratio of the diameter of the sun to the distance between the earth and the sun is approximately 0.009. The approximate diameter of the image of the sun formed by concave spherical mirror of radius of curvature 0.4 m is

A parallel beam of light is incident on a glass prism in the shape of a quarter cylinder of radius R = 0.05 m and refractive index n = 1.5, placed on a horizontal table as shown in the figure. Beyond the cylinder, a patch of light is found ...

If the pressure, temperature and density of an ideal gas are denoted by p, T and \(\rho\), respectively, the velocity of sound in the gas is

Temperature of an ideal gas, initially at 27\(^\circ\)C, is raised by 6\(^\circ\)C. The rms velocity of the gas molecules will

2 moles of an ideal monoatomic gas is carried from a state (p0, V0) to state (2p0, 2V0) along a straight line path in a p-V diagram. The amount of heat absorbed by the gas in the process is given by

A block of mass 1 kg starts from rest at x = 0 and moves along the X-axis under the action of a force F = kt, where t is time and k = 1 Ns\(-\)1. The distance the block will travel in 6 seconds is

If \(\chi\) stands for the magnetic susceptibility of a substance, \(\mu\) for its magnetic permeability and \(\mu\)0 for the permeability of free space, then

Two long parallel wires separated by 0.1 m carry currents of 1A and 2A, respectively in opposite directions. A third current-carrying wire parallel to both of them is placed in the same plane such that it feels no net magnetic force. It is ...

The magnetic field due to a current in a straight wire segment of length L at a point on its perpendicular bisector at a distance r(r >> L)

A proton is moving with a uniform velocity of \({{{10}^6}}\) ms\(-\)1 along the Y-axis, under the joint action of a magnetic field along Z-axis and an electric field of magnitude 2 \(\times\) 104 Vm\(-\)1 along the negative X-axis. If the...

A particle with charge e and mass m, moving along the X-axis with a uniform speed u, enters a region where a uniform electric field E is acting along the Y-axis. The particle starts to move in a parabola. Its focal length (neglecting any ef...

The magnets of two suspended coil galvanometers are of the same strength so that they produce identical uniform magnetic fields in the region of the coils. The coil of the first one is in the shape of a square of side a and that of the seco...

A solid rectangular sheet has two different coefficients of linear expansion \(\alpha\)1 and \(\alpha\)2 along its length and breadth respectively. The coefficient of surface expansion is (for \(\alpha\)1 t << 1, \(\alpha\)2t < <1)

A uniform capillary tube of length l and inner radius r with its upper end sealed is submerged vertically into water. The outside pressure is p0 and surface tension of water is \(\gamma\). When a length x of the capillary is submerged into ...

A liquid of bulk modulus k is compressed by applying an external pressure such that its density increases by 0.01%. The pressure applied on the liquid is

The velocity of a particle executing a simple harmonic motion is 13 ms\(-\)1, when its distance from the equilibrium position (Q) is 3 m and its velocity is 12 ms\(-\)1, when it is 5 m away from Q. The frequency of the simple harmonic motio...