WB JEE 2018

If \({b_1}{b_2} = 2({c_1} + {c_2})\) and b1, b2, c1, c2 are all real numbers, then at least one of the equations \({x^2} + {b_1}x + {c_1} = 0\) and \({x^2} + {b_2}x + {c_2} = 0\) has

Given that n numbers of arithmetic means are inserted between two sets of numbers a, 2b and 2a, b where a, b \(\in\) R. Suppose further that the mth means between these sets of numbers are same, then the ratio a : b equals

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

Let \(\rho\) be a relation defined on N, the set of natural numbers, as\(\rho\) = {(x, y) \(\in\) N \(\times\) N : 2x + y = 41}. Then

On the set R of real numbers, the relation \(\rho\) is defined by x\(\rho\)y, (x, y) \(\in\) R.

The angular points of a triangle are A(\(-\) 1, \(-\) 7), B(5, 1) and C(1, 4). The equation of the bisector of the angle \(\angle\)ABC is

The area of the triangle formed by the intersection of a line parallel to X-axis and passing through P(h, k), with the lines y = x and x + y = 2 is h2. The locus of the point P is

The point Q is the image of the point P(1, 5) about the line y = x and R is the image of the point Q about the line y = \(-\) X. The circumcentre of the \(\Delta\)PQR is

A line cuts the X-axis at A(5, 0) and the Y-axis at B(0, \(-\)3). A variable line PQ is drawn perpendicular to AB cutting the X-axis at P and the Y-axis at Q. If AQ and BP meet at R, then the locus of R is

The foot of the perpendicular drawn from the point (1, 8, 4) on the line joining the point (0, \(-\)11, 4) and (2, \(-\)3, 1) is

A point P lies on a line through Q(1, \(-\)2, 3) and is parallel to the line \({x \over 1} = {y \over 4} = {z \over 5}\). If P lies on the plane 2x + 3y \(-\) 4z + 22 = 0, then segment PQ equals

If sin6\(\theta\) + sin4\(\theta\) + sin2\(\theta\) = 0, then general value of \(\theta\) is

The approximate value of sin31\(^\circ\) is

Let \(\overrightarrow \alpha\), \({\overrightarrow \beta }\), \({\overrightarrow \gamma }\) be the three unit vectors such that \(\overrightarrow \alpha .\overrightarrow \beta = \overrightarrow \alpha .\overrightarrow \gamma = 0\)...

Let \(\overrightarrow \alpha\) = \(\widehat i + \widehat j + \widehat k\), \(\overrightarrow \beta\) = \(\widehat i - \widehat j - \widehat k\) and \({\overrightarrow \gamma }\) = \(- \widehat i - \widehat j - \widehat k\) be three ve...

An alternating current is flowing through a series L-C-R circuit. It is found that the current reaches a value of 1 mA at both 200 Hz and 800 Hz frequency. What is the resonance frequency of the circuit?

How the linear velocity v of an electron in the Bohr orbit is related to its quantum number n?

An electron accelerated through a potential of 10000 V from rest has a de-Broglie wave length \(\lambda\). What should be the accelerating potential, so that the wavelength is doubled?

If the half-life of a radioactive nucleus is 3 days, nearly what fraction of the initial number of nuclei will decay on the third day? (Given, \(\root 3 \of {0.25} \approx 0.63\))

The insulated plates of a charged parallel plate capacitor (with small separation between the plates) are approaching each other due to electrostatic attraction. Assuming no other force to be operative and no radiation taking place, which o...

A solid spherical ball and a hollow spherical ball of two different materials of densities \(\rho\)1 and \(\rho\)2 respectively have same outer radii and same mass. What will be the ratio, the moment of inertia (about an axis passing thro...

A non-zero current passes through the galvanometer G shown in the circuit when the key K is closed and its value does not change when the key is opened. Then, which of the following statement(s) is/are true?

Four resistors, 100\(\Omega\), 200\(\Omega\), 300\(\Omega\) and 400\(\Omega\) are connected to form four sides of a square. The resistors can be connected in any order. What is the maximum possible equivalent resistance across the diago...

An electric bulb, a capacitor, a battery and a switch are all in series in a circuit. How does the intensity of light vary when the switch is turn on?

What will be current through the 200\(\Omega\) resistor in the given circuit, a long time after the switch K is made on?

As shown in the figure, a rectangular loop of conducting wire is moving away with a constant velocity v in a perpendicular direction from a very long straight conductor carrying a steady current I. When the breadth of the rectangular loop i...

What will be the current flowing through the 6k\(\Omega\) resistor in the circuit shown, where the breakdown voltage of the Zener is 6V?

In the circuit shown, inputs A and B are in states 1 and 0 respectively. What is the only possible stable state of the outputs X and Y?

Consider a region in free space bounded by the surfaces of an imaginary cube having sides of length a as shown in the figure. A charge + Q is placed at the centre O of the cube. P is such a point outside the cube that the line OP perpendicu...

Four equal charges of value + Q are placed at any four vertices of a regular hexagon of side 'a'. By suitably choosing the vertices, what can be maximum possible magnitude of electric field at the centre of the hexagon?

Two positive charges Q and 4Q are placed at points A and B respectively, where B is at a distance d units to the right of A. The total electric potential due to these charges is minimum at P on the line through A and B. What is (are) the di...

The bob of a pendulum of mass m, suspended by an inextensible string of length L as shown in the figure carries a small charge q. An infinite horizontal plane conductor with uniform surface charge density \(\sigma\) is placed below it. What...

A point charge \(-\) q is carried from a point A to another point B on the axis of a charged ring of radius r carrying a charge + q. If the point A is at a distance \({4 \over 3}r\) from the centre of the ring and the point B is $${3 \over ...

There is a small air bubble at the centre of a solid glass sphere of radius r and refractive index \(\mu\). What will be the apparent distance of the bubble from the centre of the sphere, when viewed from outside?

Two identical equiconvex lenses, each of focal length f are placed side by side in contact with each other with a layer of water in between them as shown in the figure. If refractive index of the material of the lenses is greater than that ...

A point source is placed at coordinates (0, 1) in xy-plane. A ray of light from the source is reflected on a plane mirror placed along the X-axis and perpendicular to the xy-plane. The reflected ray passes through the point (3, 3). What is ...

A ray of light is incident on a right angled isosceles prism parallel to its base as shown in the figure. Refractive index of the material of the prism is \(\sqrt 2\). Then, which of the following statement(s) is/are true?

The ratio of accelerations due to gravity g1 : g2 on the surfaces of two planets is 5 : 2 and the ratio of their respective average densities \({{\rho _1}}\) : \({{\rho _2}}\) is 2 : 1. What is the ratio of respective escape velocities v1 :...

The water equivalent of a calorimeter is 10 g and it contains 50 g of water at 15\(^\circ\)C. Some amount of ice, initially at \(-\) 10\(^\circ\)C is dropped in it and half of the ice melts till equilibrium is reached. What was the initial ...

One mole of a monoatomic ideal gas undergoes a quasistatic process, which is depicted by a straight line joining points \(({V_0},{T_0})\) and \(({2V_0},{3T_0})\) in a V-T diagram. What is the value of the heat capacity of the gas at the poi...

Which of the following statement(s) is/are true?"Internal energy of an ideal gas .............."

For an ideal gas with initial pressure and volume pi and Vi respectively, a reversible isothermal expansion happens, when its volume becomes V0. Then, it is compressed to its original volume Vi by a reversible adiabatic process. If the fina...

A block of mass m2 is placed on a horizontal table and another block of mass m1 is placed on top of it. An increasing horizontal force F = at is exerted on the upper block but the lower block never moves as a result. If the coefficient of f...

The velocity (v) of a particle (under a force F) depends on its distance (x) from the origin (with x > 0) \(v \propto {1 \over {\sqrt x }}\). Find how the magnitude of the force (F) on the particle depends on x?

A uniform current is flowing along the length of an infinite, straight, thin, hollow cylinder of radius R. The magnetic field B produced at a perpendicular distance d from the axis of the cylinder is plotted in a graph. Which of the followi...

A light charged particle is revolving in a circle of radius r in electrostatic attraction of a static heavy particle with opposite charge. How does the magnetic field B at the centre of the circle due to the moving charge depend on r?

A circular loop of radius r of conducting wire connected with a voltage source of zero internal resistance produces a magnetic field B at its centre. If instead, a circular loop of radius 2r, made of same material, having the same cross-sec...

A proton of mass m moving with a speed v (< < c, velocity of light in vacuum) completes a circular orbit in time T in a uniform magnetic field. If the speed of the proton is increased to \(\sqrt 2\) v, what will be time needed to complete ...

What will be the approximate terminal velocity of a rain drop of diameter \({1.8 \times {{10}^{ - 3}}}\) m, when density of rain water \(\approx\) \({1.8 \times {{10}^{ - 5}}}\) N-sm\(-\)2 (Neglect buoyancy of air)

The stress along the length of a rod (with rectangular cross-section) is 1% of the Young's modulus of its material. What is the approximate percentage of change of its volume? (Poisson's ratio of the material of the rod is 0.3).