List of practice Questions

Heat energy of 184 kJ is given to ice of mass $600 g$ at −12°C. Specific heat of ice is $ 2222.3 J kg^{−1}C^{−1}$ and latent heat of ice in $ 336 kJkg^{−1} $
A. Final temperature of system will be 0°C.
B. Final temperature of the system will be greater than 0°C.
C. The final system will have a mixture of ice and water in the ratio of 5:1.
D. The final system will have a mixture of ice and water in the ratio of 1:5.
E. The final system will have water only.
Choose the correct answer from the options given below:

If $\int \limits_0^\pi \frac{5^{\cos x}\left(1+\cos x \cos 3 x+\cos ^2 x+\cos ^3 x \cos 3 x\right) d x}{1+5^{\cos x}}=\frac{ k \pi}{16}$, then $k$ is equal to

Given below are two statements:
Statement I: Electromagnetic waves are not deflected by electric and magnetic field.
Statement II: The amplitude of electric field and the magnetic field in electromagnetic waves are related to each other as $E_0 = \sqrt{\frac{\mu_0}{E_0}}B_0$.
In the light of the above statements, choose the correct answer from the options given below:

A scientist is observing a bacteria through a compound microscope. For better analysis and to improve its resolving power he should. (Select the best option)

With the help of potentiometer, we can determine the value of emf of a given cell. The sensitivity of the potentiometer is
(A) directly proportional to the length of the potentiometer wire
(B) directly proportional to the potential gradient of the wire
(C) inversely proportional to the potential gradient of the wire
(D) inversely proportional to the length of the potentiometer wire
Choose the correct option for the above statements:

The electric current in a circular coil of four turns produces a magnetic induction 32 T at its centre. The coil is unwound and is rewound into a circular coil of single turn, the magnetic induction at the centre of the coil by the same current will be :

An alternating voltage source $V =260 \sin (628 t )$ is connected across a pure inductor of $5 mH$ Inductive reactance in the circuit is :

The modulation index for an A.M. wave having maximum and minimum peak-to-peak voltages of 14 mV and 6 mV respectively is:

A point charge $2×10^{−2}C$ is moved from P to S in a uniform electric field of $30NC^{−1}$ directed along positive x-axis. If coordinates of P and S are $(1,2,0) m $ and $(0,0,0) m$ respectively, the work done by electric field will be

A body weight W, is projected vertically upwards from earth's surface to reach a height above the earth which is equal to nine times the radius of earth The weight of the body at that height will be :

An object moves at a constant speed along a circular path in a horizontal plane with center at the origin. When the object is at =+2 m, its velocity is $−4\hat{j}m/s$. The object's velocity (v) and acceleration (𝑎) at 𝑥=−2 m will be

Identify the correct statements from the following:
A. Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket is negative.
B. Work done by gravitational force in lifting a bucket out of a well by a rope tied to the bucket is negative.
C. Work done by friction on a body sliding down an inclined plane is positive.
D. Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity in zero.
E. Work done by the air resistance on an oscillating pendulum in negative.
Choose the correct answer from the options given below:

A fully loaded boeing aircraft has a mass of $5.4×10^5 $ kg. Its total wing area is $500 m^2$. It is in level flight with a speed of 1080 km/h. If the density of air 𝜌 is $1.2 kg m^{−3}$, the fractional increase in the speed of the air on the upper surface of the wing relative to the lower surface in percentage will be. ($𝑔=10 m/s^2$)

A force acts for 20 s on a body of mass 20 kg, starting from rest, after which the force ceases and then body describes 50 m in the next 10 s. The value of force will be:

The time taken by an object to slide down 45° rough inclined plane is n times as it takes to slide down a perfectly smooth 45° incline plane. The coefficient of kinetic friction between the object and the incline plane is:

Heat energy of 735J is given to a diatomic gas allowing the gas to expand at constant pressure Each gas molecule rotates around an internal axis but do not oscillate The increase in the intemal energy of the gas will be :

For the given logic gates combination, the correct truth table will be

Given below are two statements :
Statement I : For transmitting a signal, size of antenna ( $f$ ) should be comparable to wavelength of signal (at least $l=\frac{\lambda}{4}$ in dimension)
Statement II : In amplitude modulation, amplitude of carrier wave remains constant (unchanged)
In the light of the above statements, choose the most appropriate answer from the options given below,

The ratio of de-Broglie wavelength of an $\alpha$ particle and a proton accelerated from rest by the same potential is $\frac {1}{\sqrt 𝑚}$ , the value of $m$ is-

At $300 K$ the rms speed of oxygen molecules is $\sqrt {\frac {\alpha+5}{\alpha}}$ times to that of its average speed in the gas. Then, the value of $\alpha$ will be
(used $\pi=\frac {22}{7}$)

Substance A has atomic mass number 16 and half-life of 1 day. Another substance 𝐵 has atomic mass number 32 and half life of $\frac1{ 2}$ day. If both 𝐴 and 𝐵 simultaneously start undergo radio activity at the same time with initial mass 320 g each, how many total atoms of A and B combined would be left after 2 days.

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R)
Assertion (A): Gypsum is used for making fireproof wall boards
Reason (R): Gypsum is unstable at high temperatures
In the light of the above statements, choose the correct answer from the options given below :

Let $A =\left[ a _{i j}\right], a _{i j} \in Z \cap[0,4], 1 \leq i, j \leq 2$ The number of matrices $A$ such that the sum of all entries is a prime number $p \in(2,13)$ is _____

Let the area of the region $\left\{(x, y):|2 x-1| \leq y \leq\left|x^2-x\right|, 0 \leq x \leq 1\right\}$ be $A$ Then $(6 A +11)^2$ is equal to ____

The coefficient of $x^{-6}$, in the expansion of $\left(\frac{4 x}{5}+\frac{5}{2 x^2}\right)^9$, is______