JEE Main 2015 (Offline)

Let \(O\) be the vertex and \(Q\) be any point on the parabola, \({{x^2} = 8y}\). If the point \(P\) divides the line segment \(OQ\) internally in the ratio \(1:3\), then locus of \(P\) is :

The number of integers greater than 6,000 that can be formed, using the digits 3, 5, 6, 7 and 8, without repetition, is:

If \(12\) different balls are to be placed in \(3\) identical boxes, then the probability that one of the boxes contains exactly \(3\) balls is :

Let \(\alpha\) and \(\beta\) be the roots of equation \({x^2} - 6x - 2 = 0\). If \({a_n} = {\alpha ^n} - {\beta ^n},\) for \(n \ge 1,\) then the value of \({{{a_{10}} - 2{a_8}} \over {2{a_9}}}\) is equal to :

If m is the A.M. of two distinct real numbers l and n \((l,n > 1)\) and \({G_1},{G_2}\) and \({G_3}\) are three geometric means between \(l\) and n, then \(G_1^4\, + 2G_2^4\, + G_3^4\) equals:

The sum of first 9 terms of the series.
\({{{1^3}} \over 1} + {{{1^3} + {2^3}} \over {1 + 3}} + {{{1^3} + {2^3} + {3^3}} \over {1 + 3 + 5}} + ......\)

Let A and B be two sets containing four and
two elements respectively. Then, the number
of subsets of the set A $\times$ B , each having atleast
three elements are

The mean of the data set comprising of 16 observations is 16. If one of the observation valued 16 is deleted
and three new observations valued 3, 4 and 5 are added to the data, then the mean of the resultant data, is :

The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices \((0, 0)\) \((0, 41)\) and \((41, 0)\) is :

Let \(\overrightarrow a ,\overrightarrow b\) and \(\overrightarrow c\) be three non-zero vectors such that no two of them are collinear and $$\left( {\overrightarrow a \times \overrightarrow b } \right) \times \overrightarrow c = {1 \ov...

An \(LCR\) circuit is equivalent to a damped pendulum. In an \(LCR\) circuit the capacitor is charged to \({Q_0}\) and then connected to the \(L\) and \(R\) as shown below :

If a student plots graphs of the square of maximum charge $$\lef...

An inductor \((L=0.03\) \(H)\) and a resistor \(\left( {R = 0.15\,k\Omega } \right)\) are connected in series to a battery of \(15V\) \(EMF\) in a circuit shown below. The key \({K_1}\) has been kept closed for a long time. Then at \(t=0\),...

As an electron makes a transition from an excited state to the ground state of a hydrogen - like atom/ion :

In the given circuit, charges \({Q_2}\) on the \(2\mu F\) capacitor changes as \(C\) is varied from \(1\,\mu F\) to \(3\mu F.\) \({Q_2}\) as a function of \('C'\) is given properly by:
$$\left( {figures\,\,are\,\,drawn\,\,schematically\,\,...

Distance of the center of mass of a solid uniform cone from its vertex is \(z{}_0\). If the radius of its base is \(R\) and its height is \(h\) then \(z{}_0\) is equal to :

A particle of mass \(m\) moving in the \(x\) direction with speed \(2v\) is hit by another particle of mass \(2m\) moving in the \(y\) direction with speed \(v.\) If the collision is perfectly inelastic, the percentage loss in the energy ...

A signal of \(5\) \(kHz\) frequency is amplitude modulated on a carrier wave of frequency \(2\) \(MHz.\) The frequencies of the resultant signal is/are :

In the circuit shown, the current in the \(1\Omega\) resistor is :

When \(5V\) potential difference is applied across a wire of length \(0.1\) \(m,\) the drift speed of electrons is \(2.5 \times {10^{ - 4}}\,\,m{s^{ - 1}}.\) If the electron density in the wire is \(8 \times {10^{28}}\,\,{m^{ - 3}},\) the r...

Match List - \({\rm I}\) (Fundamental Experiment) with List - \({\rm II}\) (its conclusion) and select the correct option from the choices given below the list:

Two coaxial solenoids of different radius carry current \(I\) in the same direction. \(\overrightarrow {{F_1}}\) be the magnetic force on the inner solenoid due to the outer one and \(\overrightarrow {{F_2}}\) be the magnetic force on the...

A red \(LED\) emits light at \(0.1\) watt uniformly around it. The amplitude of the electric field of the light at a distance of \(1\) \(m\) from the diode is :

A long cylindrical shell carries positives surfaces change \(\sigma\) in the upper half and negative surface charge - \(\sigma\) in the lower half. The electric field lines around the cylinder will look like figure given in :
(figures ar...

A uniformly charged solid sphere of radius \(R\) has potential \({V_0}\) (measured with respect to \(\infty\)) on its surface. For this sphere the equipotential surfaces with potentials $${{3{V_0}} \over 2},\,{{5{V_0}} \over 4},\,{{3{V_0}}...

Monochromatic light is incident on a glass prism of angle \(A\). If the refractive index of the material of the prism is \(\mu\), a ray, incident at an angle \(\theta\). on the face \(AB\) would get transmitted through the face \(AC\) of ...

From a solid sphere of mass \(M\) and radius \(R,\) a spherical portion of radius \(R/2\) is removed, as shown in the figure. Taking gravitational potential \(V=0\) at \(r = \infty ,\) the potential at the center of the cavity thus formed i...

A solid body of constant heat capacity \(1\) \(J/{}^ \circ C\) is being heated by keeping it in contact with reservoirs in two ways:
\((i)\) Sequentially keeping in contact with \(2\) reservoirs such that each reservoir
$$\,\,\,\,\,\,\,\,...

Consider a spherical shell of radius \(R\) at temperature \(T\). The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume \(u = {U \over V}\, \propto \,{T^4}\) and pressure $$p = {...

Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as \({V^q},\) where \(V\) is the volume of the gas. The value of \(q\) is: ...

Given in the figure are two blocks \(A\) and \(B\) of weight 20 N and 100 N, respectively. These are being pressed against a wall by a force \(F\) as shown. If the coefficient of friction between the blocks is 0.1 and between block \(B\) an...

A rectangular loop of sides \(10\) \(cm\) and \(5\) \(cm\) carrying a current \(1\) of \(12A\) is placed in different orientations as shown in the figures below :

If there is a uniform magnetic field of \(0.3\) \(T\) in the positive \(z\) ...

Two long current carrying thin wires, both with current \(I,\) are held by insulating threads of length \(L\) and are in equilibrium as shown in the figure, with threads making an angle \('\theta '\) with the vertical. If wires have mass $$...

Two stones are thrown up simultaneously from the edge of a cliff \(240\) \(m\) high with initial speed of \(10\) \(m/s\) and \(40\) \(m/s\) respectively. Which of the following graph best represents the time variation of relative position o...

From a solid sphere of mass \(M\) and radius \(R\) a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its center and perpendicular to one of its face is:

The period of oscillation of a simple pendulum is \(T = 2\pi \sqrt {{L \over g}}\). Measured value of L is 20.0 cm known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using wrist watch of 1 s resolutio...

A pendulum made of a uniform wire of cross sectional area \(A\) has time period \(T.\) When an additional mass \(M\) is added to its bob, the time period changes to \({T_{M.}}\) If the Young's modulus of the material of the wire is \(Y\) th...

For a simple pendulum, a graph is plotted between its kinetic energy \((KE)\) and potential energy \((PE)\) against its displacement \(d.\) Which one of the following represents these correctly?
\((graphs\) \(are\) \(schematic\) \(and\) $...

Assuming human pupil to have a radius of \(0.25\) \(cm\) and a comfortable viewing distance of \(25\) \(cm\), the minimum separation between two objects that human eye can resolve at \(500\) \(nm\) wavelength is :

On a hot summer night, the refractive index of air is smallest near the ground and increases with height from the ground. When a light beam is directed horizontally, the Huygens' principle leads us to conclude that as it travels, the ligh...

A train is moving on a straight track with speed \(20\,m{s^{ - 1}}.\) It is blowing its whistle at the frequency of \(1000\) \(Hz\). The percentage change in the frequency heard by a person standing near the track as the train passes him is...