JEE Main 2016 (Online) 9th April Morning Slot

If the four letter words (need not be meaningful ) are to be formed using the
letters from the word “MEDITERRANEAN” such that the first letter is R and the fourth letter is E, then the total number of all such words is :

If A and B are any two events such that P(A) = \({2 \over 5}\) and P (A \(\cap\) B) = \({3 \over {20}}\), hen the conditional probability, P(A \(\left| {} \right.\)(A' \(\cup\) B')), where A' denotes the complement of A, is equal to :

If the equations x2 + bx−1 = 0 and x2 + x + b = 0 have a common root different from −1, then \(\left| b \right|\) is equal to :

Let x, y, z be positive real numbers such that x + y + z = 12 and x3y4z5 = (0.1) (600)3. Then x3 + y3 + z3is equal to :

If the mean deviation of the numbers 1, 1 + d, ..., 1 +100d from their mean is 255, then a value of d is :

If a variable line drawn through the intersection of the lines \({x \over 3} + {y \over 4} = 1\) and \({x \over 4} + {y \over 3} = 1,\) meets the coordinate axes at A and B, (A \(\ne\) B), then the locus of the midpoint of AB is :

The point (2, 1) is translated parallel to the line L : x− y = 4 by \(2\sqrt 3\) units. If the newpoint Q lies in the third quadrant, then the equation of the line passing through Q and perpendicular to L is :

The number of x \(\in\) [0,   2\(\pi\) ] for which
\(\left| {\sqrt {2{{\sin }^4}x + 18{{\cos }^2}x} - \sqrt {2{{\cos }^4}x + 18{{\sin }^2}x} } \right| = 1\) is :

If  m and M are the minimum and the maximum values of
4 + \({1 \over 2}\) sin2 2x \(-\) 2cos4 x, x \(\in\) R, then M \(-\) m is equal to :

In a triangle ABC, right angled at the vertex A, if the position vectors of A, B and C are respectively 3\(\widehat i\) + \(\widehat j\) \(-\) \(\widehat k\),   \(-\)\(\widehat i\) + 3\(\widehat j\) + p\(\widehat k\) and 5\(\widehat i\) + q...

A series LR circuit is connected to a voltage source with
V(t) = V0 sin\(\Omega\)t. After very large time, current I(t) behaves as
(t0 >> \({L \over R}\)) :

A hydrogen atom makes a transition from n = 2 to n = 1 and emits a photon. This photon strikes a doubly ionized lithium atom (z = 3) in excited state and completely removes the orbiting electron. The least quantum number for the excited sta...

Three capacitors each of 4 \(\mu\)F are to be connected in such a way that the effective capacitance is 6 \(\mu\)F. This can be done by connecting them :

An audio signal consists of two distinct sounds : one a human speech signal in the frequency band of 200 Hz to 2700 Hz, while the other is a high frequency music signal in the frequency band of 10200 Hz to 15200 Hz. The ratio of the AM sign...

A 50 \(\Omega\) resistance is connected to a battery of 5 V. A galvanometer of resistance 100 \(\Omega\) is to be used as an ammeter to measure current through the resistance, for this a resistance rs is connected to the galvanometer. Whi...

In the circuit shown, the resistance r is a variable resistance. If for r = fR, the heat generation in r is maximum then the value of f is :

When photons of wavelength \({\lambda _1}\) are incident on an isolated sphere, the corresponding stopping potential is found to be V. When photons of wavelength \({\lambda _2}\) are used, the corresponding stopping potential was thrice tha...

Microwave oven acts on the principle of :

An unknown transistor needs to be identified as a npn or pnp type. A multimeter, with + ve and − ve terminals, is used to measure resistance between different terminals of transistor. If terminal 2 is the base of the transistor then which o...

The truth table given in fig. represents :

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An experiment is performed to determine the I - V characteristics of a Zener diode, which has a protective resistance of R = 100 \(\Omega\), and a maximum power of dissipation rating of 1 W. The minimum voltage range of the DC source in th...

The potential (in volts) of a charge distribution is given by.
V(z) = 30 \(-\) 5x2 for \(\left| z \right|\) \(\le\) 1 m.
V(z) = 35 \(-\) 10 \(\left| z \right|\) for \(\left| z \right|\) \(\ge\)1 m.
V(z) does not depend on x and y. If t...

A convex lens, of focal length 30 cm, a concave lens of focal length 120 cm, and aplane mirror are arranged as shown. For an object kept at a distance of 60 cm from the convex lens, the final image, formed by the combination, is a real imag...

To find the focal length of a convex mirror, a student records the following data :

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Figure shows elliptical path abcd of a planet around the sun S such that the area of triangle csa is \({1 \over 4}\) the area of the ellipse. (See figure) With db as the semimajor axis, and ca as the semiminor axis. If t1 is the time taken...

The ratio of work done by an ideal monoatomic gas to the heat supplied to it
in an isobaric process is :

200 g water is heated from 40oC to 60oC. Ignoring the slight expansion of water, the change in its internal energy is close to (Given specific heat of water = 4184 J/kg/K) :

A simple pendulum made of a bob of mass m and a metallic wire of negligible mass has time period 2 s at T=0oC. If the temperature of the wire is increased and the corresponding change in its time period is
plotted against its temperature, t...

A rocket is fired vertically from the earth with an acceleration of 2g, where g is the
gravitational acceleration. On an inclined plane inside the rocket, making an angle \(\theta\) with the horizontal, a point object of mass m is kept. Th...

A magnetic dipole is acted upon by two magnetic fields which are inclined to each other at an angle of 75o. One of the fields has a magnitude of 15 mT. The dipole attains stable equilibrium at an angle of 30o with this field. The magnitude ...

To know the resistance G of a galvanometer by half deflection method, a battery of emf VE and resistance R is used to deflect the galvanometer by angle \(\theta\). If a shunt of resistance S is needed to get half deflection then G, R and S...

Which of the following option correctly describes the variation of the speed v and acceleration ‘a’ of a point mass falling vertically in a viscous medium that applies a force F = − kv, where ‘k’ is a constant, on the body ? (Graphs are sch...

Consider a water jar of radius R that has water filled up to height H and is kept on astand of height h (see figure). Through a hole of radius r (r << R) at its bottom, the water leaks out and the stream of water
coming down towards the gro...

A uniformly tapering conical wire is made from a material of Young’s modulus
Y and has a normal, unextended length L. The radii, at the upper and lower ends of this conical wire, have values R and 3 R, respectively. The upper end of the wir...

A cubical block of side 30 cm is moving with velocity 2 ms−1 on a smooth horizontal surface. The surface has a bump at a point O as shown in figure. The angular
velocity (in rad/s) of the block immediately after it hits the bump, is :

Two particles are performing simple harmonic motion in a straight line about
the same equilibrium point. The amplitude and time period for both particles are same and equal to A and I, respectively. At time t = 0 one particle has
displacem...

In the following ‘I’ refers to current and other symbols have their usual meaning.
Choose the option that corresponds to the dimensions of electrical conductivity :

In Young’s double slit experiment, the distance between slits and the screen is
1.0 m and monochromatic light of 600 nm is being used. A person standing near the slits is looking at the fringe pattern. When the separation between the slits ...

Two engines pass each other moving in opposite directions with uniform speed of 30 m/s. One of them is blowing a whistle of frequency 540 Hz. Calculate the
frequency heard by driver of second engine before they pass each other. Speed of sou...

A car of weight W is on an inclined road that rises by 100 m over a distance of 1 km
and applies a constant frictional force \({W \over 20}\) on the car. While moving uphill on the road at a speed of 10 ms−1, the car needs power P. If it ne...