JEE Main 2017 (Offline)

If \(A = \left[ {\matrix{ 2 & { - 3} \cr { - 4} & 1 \cr } } \right]\),
then adj(3A2 + 12A) is equal to

A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are
ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X
and Y together can throw a party i...

For three events A, B and C, P(Exactly one of A or B occurs) = P(Exactly one of B or C occurs) = P
(Exactly one of C or A occurs) = \({1 \over 4}\)
and P(All the three events occur simultaneously) = \({1 \over {16}}\).
Then the
probabilit...

If two different numbers are taken from the set {0, 1, 2, 3, ........, 10}; then the probability that their sum as
well as absolute difference are both multiple of 4, is :

A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one-by-one, with
replacement, then the variance of the number of green balls drawn is :

If for a positive integer n, the quadratic equation
\(x\left( {x + 1} \right) + \left( {x + 1} \right)\left( {x + 2} \right)\)\(+ .... + \left( {x + \overline {n - 1} } \right)\left( {x + n} \right)\)\(= 10n\)
has two consecutive integral...

For any three positive real numbers a, b and c,
9(25\({a^2}\) + b2) + 25(c2 - 3\(a\)c) = 15b(3\(a\) + c).
Then

Let k be an integer such that the triangle with vertices (k, – 3k), (5, k) and (–k, 2) has area 28 sq. units. Then the orthocentre of this triangle is at the point :

If \(5\left( {{{\tan }^2}x - {{\cos }^2}x} \right) = 2\cos 2x + 9\),
then the value of \(\cos 4x\) is :

Let \(\overrightarrow a = 2\widehat i + \widehat j -2 \widehat k\) and \(\overrightarrow b = \widehat i + \widehat j\).
Let \(\overrightarrow c\) be a vector such that \(\left| {\overrightarrow c - \overrightarrow a } \right| = 3\),
$$\...

Some energy levels of a molecule are shown in the figure. The
ratio of the wavelengths r = \({{\lambda _1}}\)/\({{\lambda _2}}\), is given by:

A radioactive nucleus A with a half life T, decays into a nucleus B. At t = 0, there is no nucleus B. At
sometime t, the ratio of the number of B to that of A is 0.3. Then, t is given by :

A capacitance of 2 \(\mu\)F is required in an electrical circuit across a potential difference of 1.0 kV. A large
number of 1 \(\mu\)F capacitors are available which can withstand a potential difference of not more than 300 V.
The minimum...

In the given circuit diagram when the current reaches steady state in the
circuit, the charge on the capacitor of capacitance C will be:

In amplitude modulation, sinusoidal carrier frequency used is denoted by \({\omega _c}\) and the signal frequency is
denoted by \({\omega _m}\). The bandwidth (\(\Delta {\omega _m}\)) of the signal is such that \(\Delta {\omega _m}\) < < $$...

When a current of 5 mA is passed through a galvanometer having a coil of resistance 15\(\Omega\), it shows full
scale deflection. The value of the resistance to be put in series with the galvanometer to convert it into a
voltmeter of range...

Which of the following statements is false?

In the given circuit, the current in each resistance is:

An electron beam is accelerated by a potential difference V to hit a metallic target to produce X–rays. It
produces continuous as well as characteristic X-rays. If \(\lambda\)min is the smallest possible wavelength of X-ray in the spectrum...

A particle A of mass m and initial velocity v collides with a particle B of mass m/2 which is at rest. The
collision is head on, and elastic. The ratio of the de-Broglie wavelengths \({\lambda _A}\) to \({\lambda _B}\) after the collision i...

In a coil of resistance 100 \(\Omega\), a current is induced by changing
the magnetic flux through it as shown in the figure. The
magnitude of change in flux through the coil is:

In a common emitter amplifier circuit using an n-p-n transistor, the phase difference between the input and
the output voltages will be:

An electric dipole has a fixed dipole moment \(\overrightarrow p\), which makes angle \(\theta\) with respect to x-axis. When
subjected to an electric field \(\mathop {{E_1}}\limits^ \to = E\widehat i\) , it experiences a torque $$\over...

A diverging lens with magnitude of focal length 25 cm is placed at a distance of 15cm from a converging
lens of magnitude of focal length 20cm. A beam of parallel light falls on the diverging lens. The final
image formed is:

The variation of acceleration due to gravity \(g\) with distance d from centre of the earth is best represented by
(R = Earth’s radius):

The temperature of an open room of volume 30 m3 increases from 17oC to 27oC due to the sunshine. The atmospheric pressure in the room remains 1 \(\times\) 105 Pa. If Ni
and Nf are the number of molecules in the room
before and after heat...

CP and Cv are specific heats at constant pressure and constant volume respectively. It is observed that CP – Cv = a for hydrogen gas CP – Cv = b for nitrogen gas The correct relation between a and b is

An external pressure P is applied on a cube at 0oC so that it is equally compressed from all sides. K is the
bulk modulus of the material of the cube and \(\alpha\) is its coefficient of linear expansion. Suppose we want to
bring the cube t...

A copper ball of mass 100 gm is at a temperature T. It is dropped in a copper calorimeter of mass 100 gm,
filled with 170 gm of water at room temperature. Subsequently, the temperature of the system is found to
be 75oC. T is given by: (Give...

A magnetic needle of magnetic moment 6.7 \(\times\) 10-2 A m2 and moment of inertia 7.5 \(\times\) 10-6 kg m2 is
performing simple harmonic oscillations in a magnetic field of 0.01 T. Time taken for 10 complete oscillations is:

A body is thrown vertically upwards. Which one of the following graphs correctly represent the velocity vs
time?

A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his
density remains same, the stress in the leg will change by a factor of :

A slender uniform rod of mass M and length \(l\) is pivoted at one end so that it
can rotate in a vertical plane (see figure). There is negligible friction at the
pivot. The free end is held vertically above the pivot and then released. The...

The moment of inertia of a uniform cylinder of length \(l\) and radius R about its perpendicular bisector is \(I\).
What is the ratio \({l \over R}\) such that the moment of inertia is minimum?

A particle is executing simple harmonic motion with a time period T. At time t = 0, it is at its position of
equilibrium. The kinetic energy – time graph of the particle will look like:

The following observations were taken for determining surface tension T of water by capillary method:
diameter of capillary, D = 1.25 \(\times\) 10-2 m
rise of water, h = 1.45 \(\times\) 10-2m
Using g = 9.80 m/s2 and the simplified relation...

In a Young’s double slit experiment, slits are separated by 0.5 mm, and the screen is placed 150 cm away.
A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes
on the screen. The least dist...

An observer is moving with half the speed of light towards a stationary microwave source emitting waves
at frequency 10 GHz. What is the frequency of the microwave measured by the observer? (speed of light =
3 ×108 ms–1)

A time dependent force F = 6t acts on a particle of mass 1 kg. If the particle starts from rest, the work done
by the force during the first 1 sec. will be:

A body of mass m = 10–2 kg is moving in a medium and experiences a frictional force F = –kv2. Its initial speed is v0 = 10 ms–1. If, after 10 s, its energy is \({1 \over 8}mv_0^2\), the value of k will be: