JEE Main 2018 (Online) 15th April Evening Slot

The number of four letter words that can be formed using the letters of the word BARRACK is :

A player X has a biased coin whose probability of showing heads is p and a player Y has a fair coin. They start playing a game with their own coins and play alternately. The player who throws a head first is a winner. If X starts the game, ...

If f(x) is a quadratic expression such that f (1) + f (2) = 0, and \(-\) 1 is a root of f (x) = 0, then the other root of f(x) = 0 is :

If  a,   b,   c  are in A.P. and  a2,  b2,  c2 are in G.P. such that
a < b < c and   a + b + c = \({3 \over 4},\) then the value of a is :

Let    An = \(\left( {{3 \over 4}} \right) - {\left( {{3 \over 4}} \right)^2} + {\left( {{3 \over 4}} \right)^3}\) \(-\). . . . . + (\(-\)1)n-1 \({\left( {{3 \over 4}} \right)^n}\)    and    Bn = 1 \(-\) An.
Then, the least dd natural numb...

If the mean of the data : 7, 8, 9, 7, 8, 7, \(\lambda\), 8 is 8, then the variance of this data is :

The foot of the perpendicular drawn from the origin, on the line, 3x + y = \(\lambda\) (\(\lambda\) \(\ne\) 0) is P. If the line meets x-axis at A and y-axis at B, then the ratio BP : PA is :

The sides of a rhombus ABCD are parallel to the lines, x \(-\) y + 2 = 0 and 7x \(-\) y + 3 = 0. If the diagonals of the rhombus intersect P(1, 2) and the vertex A (different from the origin) is on the y-axis, then the coordinate of A is :

The number of solutions of sin3x = cos 2x, in the interval \(\left( {{\pi \over 2},\pi } \right)\) is :

If the position vectors of the vertices A, B and C of a \(\Delta\) ABC are respectively \(4\widehat i + 7\widehat j + 8\widehat k,\)    \(2\widehat i + 3\widehat j + 4\widehat k,\) and \(2\widehat i + 5\widehat j + 7\widehat k,\) then the ...

An unstable heavy nucleus at rest breaks into two nuclei which move away with velocities in the ratio of 8 : 27. The ratio of the radii of the nuclei (assumed to be spherical) is :

Muon (\(\mu\)\(-\)) is a negatively charged (|q| = |e|) particle with a mass m\(\mu\) = 200 me, where me is the mass of the electron and e is the electronic charge. If \(\mu\)\(-\) is bond to a proton to form a hydrogen like atom, ident...

A capacitor C1 = 1.0 \(\mu\)F is charged up to a voltage V = 60 V by connecting it to battery B through switch (1). Now C1 is disconnected from battery and connected to a circuit consisting of two uncharged capacitors \({C_2} = 3.0\mu F\) ...

A parallel plate capacitor with area 200 cm2 and separation between the plates 1.5 cm, is connected across a battery of emf V. If the force of attraction between the plates is \(25 \times {10^{ - 6}}N,\) the value of V is approximately : $...

A proton of mass m collides elastically with a particle of unknown mass at rest. After the collision, the proton and the unknown particle are seen moving at an angle of 90o with respect to each other. The mass of unknown particle is :

A disc rotates about its axis of symmetry in a horizontal plane at a steady rate of \(3.5\) revolutions per second. A coin placed at a distnce of 1.25 cm from the axis of rotation remains at rest on the disc. The coefficient of friction bet...

The carrier frequency of a transmitter is provided by a tank circuit of a coil of inductance 49 \(\mu\)H and a capacitance of 2.5 nF. It is modulated by an audio signal of \(12\) \(kHz.\) The frequency range occupied by the side bands is :...

A constant voltages is applied between two ends of a metallic wire. If the length is halved and the radius of the wire is doubled, the rate of heat developed in the wire will be :

A copper rod of cross-sectional area A carries a uniform current I through it. At temperature T, if the volume charge density of the rod is \(\rho\), how long will the changes take to travel a distance d ?

If the de Broglie wavelengths associated with a proton and an \(\alpha\)-particle are equal, then the ratio of velocities of the proton and the \(\alpha\)-particle will be :

At the center of a fixed large circular coil of radius R, a much smaller circular coil of radius r is placed. The two coils are concentric and are in the same plane. The larger coil carries a current I. The smaller coil is set to rotate wit...

A copper rod of mass m slides under gravity on two smooth parallel rails, with separation l and set at an angle of \(\theta\) with the horizontal. At the bottom rails are joined by a resistance R. There is a uniform magnetic field B normal...

A plane polarized monochromatic EM wave is traveling in vacuum along z direction such that at t = t1 it is found that the electric field is zero at a spatial point z1. The next zero that occurs in its neighbourhood is at z2. The frequency o...

Truth table for the following digital circuit will be :

A solid ball of radius R has a charge density \(\rho\)
given by \(\rho\) = \(\rho\)o (1 \(-\) \({\raise0.5ex\hbox{$\scriptstyle r$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle R$}}\)) for 0 \(\le\) r \(\le\) R. The ele...

A convergent doublet of separated lenses, corrected for spherical aberration, has resultant focal length of 10 cm. The separation between the two lenses is \(2\) cm. The focal lengths of the component lenses are :

The value closest to the thermal velocity of a Helium atom at room temperature (300 K) in ms-1 is :
[kB =1.4 \(\times\) 10-23 J/K; mHe = 7 \(\times\) 10 -27 kg ]

Two Carnot engines A and B are operated in series. Engine A receives heat from a reservoir at 600 K and rejects heat to a reservoir at temperature T. Engine B receives heat rejected by engine A and in turn rejects it to a reservoir at 100 K...

A body of mass 2 kg slides down with an acceleration of 3 m/s2 on a rough inclined plane having a slope of \({30^o}\). The external force required to take the same body up the plane with the same acceleration will be : (g = 10 m/s2)

A current of 1 A is flowing on the sides of an equilateral triangle of side 4.5 \(\times\) 10-2 m. The magnetic field at the center of the triangle will be :

A man in a car at location Q on a straight highway is moving with speed \(\upsilon\). He decides to reach a point P in a field at a distance d from the highway (point M) as shown in the figure. Speed of the car in the field is half to that...

When an air bubble of radius r rises from the bottom to the surface of a lake its radius becomes \({{5r} \over 4}.\) Taking the atmospheric pressure to be equal to 10 m height of water column, the depth of the lake would approximately be (i...

As shown in the figure, forces of 105 N each are applied in opposite directions, on the upper and lower faces of a cube of side 10 cm, shifting the upper face parallel to itself by 0.5 cm. If the side of another cube of the same material i...

A body takes 10 minutes to cool from 60oC to 50oC. The tempertature of surroundings is constant at 25oC. Then, the temperature of the body after next 10 minutes will be approximately :

A thin uniform bar of length \(L\) and mass \(8\) m lies on a smooth horizontal table. Two point masses m and 2 m are moving in the same horizontal plane from opposite sides of the bar with speeds 2\(\upsilon\) and \(\upsilon\) respective...

A thin rod MN, free to rotate in the vertical plane aboutthe fixed end N, is held horizontal. When the end M is released the speed of this end, when the rod makes an angle \(\alpha\) with the horizontal, will be proportional to : (see figu...

Two simple harmonic motions, as shown below, are at right angles. They are combined to form Lissajous figures.
x(t) = A sin (at + \(\delta\))
y(t) = B sin (bt)
Identify the correct match below.

The characteristic distance at which quantum gravitational effects are significant, the Planck length, can be determined from a suitable combination of the fundamental physical constants G, h and c. Which of the following correctly gives th...

A plane polarized light is incident on a polariser with its pass axis aking angle \(\theta\) with x-axis, as shown in the figure. At four different values of \(\theta ,\,\theta\) = 8o, 38o, 188o and 218o, the observed intensities are sam...

5 beats / econd are heard when a tuning fork is sounded with a sonometer wire under tension, when the length of the sonometer wire is either 0.95 m or 1 m. The frequency of the fork will be :