JEE Main 2016 (Offline)

Let \(P\) be the point on the parabola, \({{y^2} = 8x}\) which is at a minimum distance from the centre \(C\) of the circle, \({x^2} + {\left( {y + 6} \right)^2} = 1\). Then the equation of the circle, passing through \(C\) and having its c...

If all the words (with or without meaning) having five letters,formed using the letters of the word SMALL and arranged as in a dictionary, then the position of the word SMALL is :

Let two fair six-faced dice \(A\) and \(B\) be thrown simultaneously. If \({E_1}\) is the event that die \(A\) shows up four, \({E_2}\) is the event that die \(B\) shows up two and \({E_3}\) is the event that the sum of numbers on both dice...

The sum of all real values of \(x\) satisfying the equation \({\left( {{x^2} - 5x + 5} \right)^{{x^2} + 4x - 60}}\, = 1\) is :

If the sum of the first ten terms of the series \({\left( {1{3 \over 5}} \right)^2} + {\left( {2{2 \over 5}} \right)^2} + {\left( {3{1 \over 5}} \right)^2} + {4^2} + {\left( {4{4 \over 5}} \right)^2} + .......is\,{{16} \over 5}m,\) then m i...

If the \({2^{nd}},{5^{th}}\,and\,{9^{th}}\) terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is :

If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true?

Two sides of a rhombus are along the lines, \(x - y + 1 = 0\) and \(7x - y - 5 = 0\). If its diagonals intersect at \((-1, -2)\), then which one of the following is a vertex of this rhombus?

If \(0 \le x < 2\pi\), then the number of real values of \(x\), which satisfy the equation \(\,\cos x + \cos 2x + \cos 3x + \cos 4x = 0\) is:

Let \(\overrightarrow a ,\overrightarrow b\) and \(\overrightarrow c\) be three unit vectors such that $$\overrightarrow a \times \left( {\overrightarrow b \times \overrightarrow c } \right) = {{\sqrt 3 } \over 2}\left( {\overrightarrow...

An arc lamp requires a direct current of
10 A at 80 V to function. If it is connected
to a 220 V (rms), 50 Hz AC supply, the
series inductor needed for it to work is
close to :

Half-lives of two radioactive elements \(A\) and \(B\) are \(20\) minutes and \(40\) minutes, respectively. Initially, the samples have equal number of nuclei. After \(80\) minutes, the ratio of decayed number of \(A\) and \(B\) nuclei will...

A combination of capacitors is set up as shown in the figure. The magnitude of the electric field, due to a point charge \(Q\) (having a charge equal to the sum of the charges on the \(4\) \(\mu \,F\) and \(9\) \(\mu \,F\) capacitors), at a...

Choose the correct statement :

A galvanometer having a coil resistance of \(100\,\Omega\) gives a full scale deflection, when a currect of \(1\) \(mA\) is passed through it. The value of the resistance, which can convert this galvanometer into ammeter giving a full scal...

Radiation of wavelength \(\lambda ,\) is incident on a photocell. The fastest emitted electron has speed \(v.\) If the wavelength is changed to \({{3\lambda } \over 4},\) the speed of the fastest emitted electron will be:

Arrange the following electromagnetic
radiations per quantum in the order of
increasing energy :
A : Blue light           B : Yellow light
C : X-ray                 D : Radiowave.

If \(a, b, c, d\) are inputs to a gate and \(x\) is its output, then, as per the following time graph, the gate is :

The temperature dependence of resistance of \(Cu\) and undoped \(Si\) in the temperature range \(300-400\) \(K,\) is best described by :

For a common emitter configuration, if \(\alpha\) and \(\beta\) have their usual meanings, the incorrect relationship between \(\alpha\) and \(\beta\) is :

Identify the semiconductor devices whose characteristics are given below, in the order \((a), (b), (c), (d)\) :

The region between two concentric spheres of radii \('a'\) and \('b',\) respectively (see figure), have volume charge density \(\rho = {A \over r},\) where \(A\) is a constant and \(r\) is the distance from the center. A such that the elec...

An observer looks at a distant tree of height \(10\) \(m\) with a telescope of magnifying power of \(20.\) To the observer the tree appears:

In an experiment for determination of refractive index of glass of a prism by \(i - \delta ,\) plot it was found thata ray incident at angle \({35^ \circ }\), suffers a deviation of \({40^ \circ }\) and that it emerges at angle $${79^ \circ...

A satellite is revolving in a circular orbit at a height \('h'\) from the earth's surface (radius of earth \(R;h < < R\)). The minimum increase in its orbital velocity required, so that the satellite could escape from the earth's gravitat...

A pendulum clock loses \(12\) \(s\) a day if the temperature is \({40^ \circ }C\) and gains \(4\) \(s\) a day if the temperature is \({20^ \circ }C.\) The temperature at which the clock will show correct time, and the co-efficient of linear...

An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity \(C\) remains constant. If during this process the relation of pressure \(P\) and volume \(V\) is given by \(P{V^n} =\) constant, then \(n\) is give...

\('n'\) moles of an ideal gas undergoes a process \(A\) \(\to\) \(B\) as shown in the figure. The maximum temperature of the gas during the process will be :

Hysteresis loops for two magnetic materials \(A\) and \(B\) are given below :

These materials are used to make magnets for electric generators, transformer core and electromagnet core. Then it is proper to use :

Two identical wires \(A\) and \(B,\) each of length \('l'\), carry the same current \(I\). Wire \(A\) is bent into a circle of radius \(R\) and wire \(B\) is bent to form a square of side \('a'\). If \({B_A}\) and \({B_B}\) are the values o...

A particle of mass m is moving along the
side of a square of side ‘a’, with a uniform
speed v in the x-y plane as shown in the
figure :

Which of the following statements is false
for the angular momentum \(\overrightarrow L\) about the
or...

A roller is made by joining together two cones at their vertices \(0\). It is kept on two rails \(AB\) and \(CD\), which are placed asymmetrically (see figure), with its axis perpendicular to \(CD\) and its center \(O\) at the center of lin...

A particle performs simple harmonic motion with amplitude \(A.\) Its speed is trebled at the instant that it is at a distance \({{2A} \over 3}\) from equilibrium position. The new amplitude of the motion is:

A screw gauge with a pitch of 0.5 mm and a circular scale with 50 divisions is used to measure the
thickness of a thin sheet of Aluminium. Before starting the measurement, it is found that when the two jaws of the screw gauge are brought in...

A student measures the time period of 100 oscillations of a simple pendulum four times. The data set is 90 s, 91 s, 95 s and 92 s. If the minimum division in the measuring clock is 1 s, then the reported mean time should be :

The box of a pin hole camera, of length \(L,\) has a hole of radius a. It is assumed that when the hole is illuminated by a parallel beam of light of wavelength \(\lambda\) the spread of the spot (obtained on the opposite wall of the camer...

A uniform string of length \(20\) \(m\) is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the supports is :
(take \({\,\,g = 10m{s^{ - 2}}}\) )

A pipe open at both ends has a fundamental frequency \(f\) in air. The pipe is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now :

A person trying to lose weight by burning fat lifts a mass of \(10\) \(kg\) upto a height of \(1\) \(m\) \(1000\) times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up conside...

A point particle of mass \(m,\) moves long the uniformly rough track \(PQR\) as shown in the figure. The coefficient of friction, between the particle and the rough track equals \(\mu .\) The particle is released, from rest from the point $...