JEE Main 2017 (Online) 8th April Morning Slot

The number of real values of \(\lambda\) for which the system of linear equations
2x + 4y \(-\) \(\lambda\)z = 0
4x + \(\lambda\)y + 2z = 0
\(\lambda\)x + 2y + 2z = 0
has infinitely many solutions, is :

If the common tangents to the parabola, x2 = 4y and the circle, x2 + y2 = 4 intersect at the point P, then the distance of P from the origin, is :

If all the words, with or without meaning, are written using the letters of the word QUEEN and are arranged as in English dictionary, then the position of the word QUEEN is :

An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is :

Three persons P, Q and R independently try to hit a target. I the probabilities of their hitting the target are \({3 \over 4},{1 \over 2}\) and \({5 \over 8}\) respectively, then the probability that the target is hit by P or Q but not by R...

Let p(x) be a quadratic polynomial such that p(0)=1. If p(x) leaves remainder 4 when divided by x\(-\) 1 and it leaves remainder 6 when divided by x + 1; then :

If the sum of the first n terms of the series \(\,\sqrt 3 + \sqrt {75} + \sqrt {243} + \sqrt {507} + ......\) is \(435\sqrt 3 ,\) then n equals :

If the arithmetic mean of two numbers a and b, a > b > 0, is five times their geometric mean, then \({{a + b} \over {a - b}}\) is equal to :

The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place. If now the mean age of the teachers in this school is 39 years, then the age (in years) of the newly...

The area (in sq. units) of the parallelogram whose diagonals are along the vectors \(8\widehat i - 6\widehat j\) and \(3\widehat i + 4\widehat j - 12\widehat k,\) is :

Two deuterons undergo nuclear fusion to form a Helium nucleus. Energy released in this process is : (given binding energy per nucleon for deuteron = 1.1 MeV and for helium = 7.0 MeV)

According to Bohr’s theory, the time averaged magnetic field at the centre (i.e. nucleus) of a hydrogen atom due to the motion of electrons in the nth orbit is proportional to : (n = principal quantum number)

The energy stored in the electric field produced by a metal sphere is 4.5 J. If the sphere contains 4 \(\mu\)C charge, its radius will be :
[ Take : \({1 \over {4\,\pi { \in _0}}} =\) 9 \(\times\) 109 N \(-\) m2/C2 ]

A signal of frequency 20 kHz and peak voltage of 5 Volt is used to modulate a carrier wave of frequency 1.2 MHz and peak voltage 25 Volts. Choose the correct statement.

A potentiometer PQ is set up to compare two resistances as shown in the figure. The ammeter A in the circuit reads 1.0 A when two way key K3 is open. The balance point is at a length \(\ell\)1 cm from P when two way key K3 is plugged in...

A 9 V battery with internal resistance of 0.5 \(\Omega\) is connected across an infinite network as shown in the figure. All ammeters A1, A2,
3 and voltmeter V are ideal.
Choose correct statement.

The maximum velocity of the photoelectrons emitted from the surface is v when light of frequency n falls on a metal surface. If the incident frequency is increased to 3n, the maximum velocity of the ejected photoelectrons will be :

A small circular loop of wire of radius a is located at the centre of a much larger circular wire loop of radius b. The two loops are in the same plane. The outer loop of radius b carries an alternating current I = Io cos (\(\omega\)t). Th...

Magnetic field in a plane electromagnetic wave is given by
\(\overrightarrow B\) = B0 sin (k x + \(\omega\)t) \(\widehat j\,T\)
Expression for corresponding electric field will be :
Where c is speed of light.

The V-I characteristic of a diode is shown in the figure. The ratio of forward to reverse bias
resistance is :

What is the conductivity of a semiconductor sale having electron concentration of \(5 \times {10^{18}}\,\,{m^{ - 3}},\) hole concentration of \(5 \times {10^{19}}\,\,{m^{ - 3}},\) electron mobility of 2.0 m2 V\(-\)1 s-1 and hole mobility o...

There is a uniform electrostatic field in a region. The potential at various points on a small sphere centred at \(P,\) in the region, is found to vary between the limits 589.0 V to 589.8 V. What is the potential at a point on the sphere wh...

Let the refractive index of a denser medium with respect to a rarer medium be n12 and its critical angle be θC . At an angle of incidence A when light is travelling from
denser medium to rarer medium, a part of the light is reflected and th...

If the Earth has no rotational motion, the weight of a person on the equator is W. Determine the speed with which the earth would have to rotate about its axis so that the person at the equator will weigh \({3 \over 4}\) W. Radius of the E...

An ideal gas has molecules with 5 degrees of freedom. The ratio of specific heats at constant pressure (Cp ) and at constant volume (Cv) is :

In an experiment, a sphere of aluminium of mass 0.20 kg is heated upto 150oC. Immediately, it is put into water of volume 150 cc at 27oC kept in a calorimeter of water equivalent to 0.025 kg. Final temperature of the system is 40oC. The spe...

An engine operates by taking n moles of an ideal gas through the cycle ABCDA shown in figure. The thermal efficiency of the engine is :
(Take Cv = 1.5 R, where R is gas constant)

A compressive force, F is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its temperature increases by \(\Delta\)T. The net change in its length is zero. Let \(\ell\) be the length of the rod, A i...

A magnetic dipole in a constant magnetic field has :

In a certain region static electric and magnetic fields exist. The magnetic field is given by \(\overrightarrow B = {B_0}\left( {\widehat i + 2\widehat j - 4\widehat k} \right)\) . If a test charge moving with a velocity $$\overrightarrow ...

Which graph corresponds to an object moving with a constant negative
acceleration and a positive velocity ?

In a physical balance working on the principle of moments, when 5 mg weight is placed on the left pan, the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct ?

Moment of inertia of an equilateral triangular lamina ABC, about the axis
passing through its centre O and perpendicular to its plane is Io as shown in the figure. A cavity DEF is cut out from the lamina, where D, E, F are the mid points o...

A uniform disc of radius R and mass M is free to rotate only about its axis. A string is wrapped over its rim and a body of mass m is tied to the free end of the string as shown in the figure. The body is released from rest. Then the accele...

A 1 kg block attached to a spring vibrates with a frequency of 1 Hz on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to an 8 kg block placed on the same table. So, the frequency of vi...

The ratio of maximum acceleration to maximum velocity in a simple harmonic motion is 10 s−1 . At, t = 0 the displacement is 5 m. What is the maximum acceleration ? The initial phase is \({\pi \over 4}\).

Time (T), velocity (C) and angular momentum (h) are chosen as fundamentalquantities instead of mass, length and time. In terms of these, the dimensions of mass would be :

A single slit of width b is illuminated by a coherent monochromatic light of wavelength \(\lambda\). If the second and fourthminima in the diffraction pattern at a distance 1 m from the slit are at 3 cm and 6 cm respectively from the cent...

Two wires W1 and W2 have the same radius r and respective densities \(\rho\)1 and \(\rho\)2 such that ρ2 = 4\(\rho\)1 . They are joined together at the point O, as shown in the figure. The combination is used as a sonometer wire and k...

An object is dropped from a height h from the ground. Every time it hits the ground it looses 50% of its kinetic energy. The total distance covered as t \(\to\) \(\infty\) is :