JEE Main 2013 (Offline)

Let A and B be two sets containing 2 elements and
4 elements respectively. The number of subsets of
A \(\times\) B having 3 or more elements is :

Let \({T_n}\) be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If \({T_{n + 1}} - {T_n}\) = 10, then the value of n is :

A multiple choice examination has \(5\) questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get \(4\) or more correct answers just by guessing is :

If the equations \({x^2} + 2x + 3 = 0\) and \(a{x^2} + bx + c = 0,\) \(a,\,b,\,c\, \in \,R,\) have a common root, then \(a\,:b\,:c\,\) is

The sum of first 20 terms of the sequence 0.7, 0.77, 0.777,........,is

All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10
to each of the students. Which of the following statistical measures will not change even after the grace
marks were given?

The \(x\)-coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as \((0, 1) (1, 1)\) and \((1, 0)\) is :

A ray of light along \(x + \sqrt 3 y = \sqrt 3\) gets reflected upon reaching \(X\)-axis, the equation of the reflected ray is :

The expression \({{\tan {\rm A}} \over {1 - \cot {\rm A}}} + {{\cot {\rm A}} \over {1 - \tan {\rm A}}}\) can be written as:

If the vectors \(\overrightarrow {AB} = 3\widehat i + 4\widehat k\) and \(\overrightarrow {AC} = 5\widehat i - 2\widehat j + 4\widehat k\) are the sides of a triangle \(ABC,\) then the length of the median through \(A\) is :

In an \(LCR\) circuit as shown below both switches are open initially. Now switch \({S_1}\) is closed, \({S_2}\) kept open. (\(q\) is charge on the capacitor and \(\tau\) \(=RC\) is Capacitance time constant). Which of the following statem...

In a hydrogen like atom electron make transition from an energy level with quantum number \(n\) to another with quantum number \(\left( {n - 1} \right)\). If \(n > > 1,\) the frequency of radiation emitted is proportional to :

Two capacitors \({C_1}\) and \({C_2}\) are charged to \(120\) \(V\) and \(200\) \(V\) respectively. It is found that connecting them together the potential on each one can be made zero. Then

This question has statement \({\rm I}\) and statement \({\rm I}\)\({\rm I}\). Of the four choices given after the statements, choose the one that best describes the two statements.
Statement - \({\rm I}\): A point particle of mass \(m\) mov...

This questions has Statement - \({\rm I}\) and Statement - \({\rm I}\)\({\rm I}\). Of the four choices given after the Statements, choose the one that best describes into two Statements.
Statement - \({\rm I}\) : Higher the range, greater ...

The supply voltage to room is \(120V.\) The resistance of the lead wires is \(6\Omega\). A \(60\) \(W\) bulb is already switched on. What is the decrease of voltage across the bulb, when a \(240\) \(W\) heater is switched on in parallel t...

The anode voltage of a photocell is kept fixed. The wavelength \(\lambda\) of the light falling on the cathode is gradually changed. The plate current \(I\) of the photocell varies as follows :

A circular loop of radius \(0.3\) \(cm\) lies center of the small loop is on the axis of the bigger loop. The distance between their centers is \(15\) \(cm.\) If a current of \(2.0\) \(A\) flows through the smaller loop, than the flux linke...

A metallic rod of length \('\ell '\) is tied to a string of length \(2\)\(\ell\) and made to rotate with angular speed \(w\) on a horizontal table with one end of the string fixed. If there is a vertical magnetic field \('B'\) in the regi...

The magnetic field in a travelling electromagnetic wave has a peak value of \(20\) \(n\)\(T\). The peak value of electric field strength is :

The \({\rm I}\)-\(V\) characteristic of an \(LED\) is

A diode detector is used to detect an amplitude modulated wave of \(60\%\) modulation by using a condenser of capacity \(250\) picofarad in parallel with a load resistance \(100\) kilo \(ohm.\) Find the maximum modulated frequency which co...

A charge \(Q\) is uniformly distributed over a long rod \(AB\) of length \(L\) as shown in the figure. The electric potential at the point \(O\) lying at distance \(L\) from the end \(A\) is

Two charges, each equals to \(q,\) are kept at \(x=-a\) and \(x=a\) on the \(x\)-axis. A particle of mass \(m\) and charge \({q_0} = {q \over 2}\) is placed at the origin. If charge \({q_0}\) is given a small displacement $$\left( {y < < ...

The graph between angle of deviation \(\left( \delta \right)\) and angle of incidence \((i)\) for a triangular prism is represented by

Diameter of a plano-convex lens is \(6\) \(cm\) and thickness at the center is \(3mm\). If speed of light in material of lens is \(2 \times {10^8}\,m/s,\) the focal length of the lens is

What is the minimum energy required to launch a satellite of mass \(m\) from the surface of a planet of mass \(M\) and radius \(R\) in a circular orbit at an altitude of \(2R\)?

The above \(p\)-\(v\) diagram represents the thermodynamic cycle of an engine, operating with an ideal monatomic gas. The amount of heat, extracted from the source in a single cycle is

Assume that a drop of liquid evaporates by decreases in its surface energy, so that its temperature remains unchanged. What should be the minimum radius of the drop for this to be possible ? The surface tension is \(T,\) density of liquid i...

Two short bar magnets of length \(1\) \(cm\) each have magnetic moments \(1.20\) \(A{m^2}\) and \(1.00\) \(A{m^2}\) respectively. They are placed on a horizontal table parallel to each other with their \(N\) poles pointing towards the Sout...

A projectile is given an initial velocity of \(\left( {\widehat i + 2\widehat j} \right)\) m/s, where \({\widehat i}\) is along the ground and \({\widehat j}\) is along the
vertical. If g = 10 m/s2, the equation of its trajectory is:

A uniform cylinder of length \(L\) and mass \(M\) having cross-sectional area \(A\) is suspended, with its length vertical, from a fixed point by a mass-less spring such that it is half submerged in a liquid of density \(\sigma\) at equili...

If a piece of metal is heated to temperature \(\theta\) and then allowed to cool in a room which is at temperature \({\theta _0},\) the graph between the temperature \(T\) of the metal and time \(t\) will be closest to

A hoop of radius \(r\) and mass \(m\) rotating with an angular velocity \({\omega _0}\) is placed on a rough horizontal surface. The initial velocity of the center of the hoop is zero. What will be the velocity of the center of the hoop whe...

An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass \(M.\) The piston and the cylinder have equal cross sectional area \(A\). When the piston is in equilibrium, the volume of the gas is $${V_0}$...

The amplitude of a damped oscillator decreases to \(0.9\) times its original magnitude in \(5s\). In another \(10s\) it will decrease to \(\alpha\) times its original magnitude, where \(\alpha\) equals

Let [\({\varepsilon _0}\)] denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = time
and A = electric current, then:

Two coherent point sources \({S_1}\) and \({S_2}\) are separated by a small distance \('d'\) as shown. The fringes obtained on the screen will be

A beam of unpolarised light of intensity \({{\rm I}_0}\) is passed through a polaroid \(A\) and then through another polaroid \(B\) which is oriented so that its principal plane makes an angle of \({45^ \circ }\) relative to that of \(A\). ...

A sonometer wire of length \(1.5\) \(m\) is made of steel. The tension in it produces an elastic strain of \(1\%\). What is the fundamental frequency of steel if density and elasticity of steel are \(7.7 \times {10^3}\,kg/{m^3}\) and $$2....