The maximum number of possible interference maxima for slit separation equal to $1.8\lambda$, where $\lambda$ is the wavelength of light used, in a Young's double slit experiment is
(1) zero
(2) 3
(3) infinite
(4) 5

Hydrogen atom is excited from ground state to another state with principal quantum number equal to 4. Then the number of spectral lines in the emission spectra will be
(1) 2
(2) 3
(3) 5
(4) 6

A diatomic molecule is made of two masses $m_{1}$ and $m_{2}$ which are separated by a distance $r$. If we calculate its rotational energy by applying Bohr's rule of angular momentum quantization, its energy will be given by ($n$ is an integer)
(1) $\dfrac{(m_{1}+m_{2})^{2}n^{2}h^{2}}{2m_{1}^{2}m_{2}^{2}r^{2}}$
(2) $\dfrac{n^{2}h^{2}}{2(m_{1}+m_{2})r^{2}}$
(3) $\dfrac{2n^{2}h^{2}}{(m_{1}+m_{2})r^{2}}$
(4) $\dfrac{(m_{1}+m_{2})n^{2}h^{2}}{2m_{1}m_{2}r^{2}}$

A doubly ionised Li atom is excited from its ground state $(n=1)$ to $n=3$ state. The wavelengths of the spectral lines are given by $\lambda_{32}$, $\lambda_{31}$ and $\lambda_{21}$. The ratio $\lambda_{32}/\lambda_{31}$ and $\lambda_{21}/\lambda_{31}$ are, respectively
(1) $8.1,\;0.67$
(2) $8.1,\;1.2$
(3) $6.4,\;1.2$
(4) $6.4,\;0.67$

$N$ divisions on the main scale of a vernier calliper coincide with $( N + 1 )$ divisions of the vernier scale. If each division of main scale is ' $a$ ' units, then the least count of the instrument is
(1) $a$
(2) $\frac { a } { N }$
(3) $\frac { N } { N + 1 } \times a$
(4) $\frac { a } { N + 1 }$

A 10 kW transmitter emits radio waves of wavelength 500 m. The number of photons emitted per second by the transmitter is of the order of
(1) $10^{37}$
(2) $10^{31}$
(3) $10^{25}$
(4) $10^{43}$

A spectrometer gives the following reading when used to measure the angle of a prism. Main scale reading: 58.5 degree. Vernier scale reading: 09 divisions. Given that 1 division on main scale corresponds to 0.5 degree. Total divisions on the vernier scale is 30 and match with 29 divisions of the main scale. The angle of the prism from the above data is
(1) $58.59^{\circ}$
(2) $58.77^{\circ}$
(3) $58.65^{\circ}$
(4) $59^{\circ}$

The logically equivalent preposition of $p \Leftrightarrow q$ is
(1) $(p \Rightarrow q) \wedge (q \Rightarrow p)$
(2) $p \wedge q$
(3) $(p \wedge q) \vee (q \neq p)$
(4) $(p \wedge q) \Rightarrow (q \vee p)$

The negation of the statement ``If I become a teacher, then I will open a school'' is
(1) I will become a teacher and I will not open a school
(2) Either I will not become a teacher or I will not open a school
(3) Neither I will become a teacher nor I will open a school
(4) I will not become a teacher or I will open a school

If $A = \{x \in z^{+} : x < 10$ and $x$ is a multiple of 3 or 4$\}$, where $z^{+}$ is the set of positive integers, then the total number of symmetric relations on $A$ is
(1) $2^{5}$
(2) $2^{15}$
(3) $2^{10}$
(4) $2^{20}$

Let $p$ and $q$ denote the following statements $p$: The sun is shining $q$: I shall play tennis in the afternoon The negation of the statement ``If the sun is shining then I shall play tennis in the afternoon'', is
(1) $q \Rightarrow \sim p$
(2) $q \wedge \sim p$
(3) $p \wedge \sim q$
(4) $\sim q \Rightarrow \sim p$

Two springs of force constants $300 \mathrm {~N} / \mathrm { m }$ (Spring A) and $400 \mathrm {~N} / \mathrm { m }$ (Spring B) are joined together in series. The combination is compressed by 8.75 cm . The ratio of energy stored in A and B is $\frac { E _ { A } } { E _ { B } }$. Then $\frac { E _ { A } } { E _ { B } }$ is equal to:
(1) $\frac { 4 } { 3 }$
(2) $\frac { 16 } { 9 }$
(3) $\frac { 3 } { 4 }$
(4) $\frac { 9 } { 16 }$

A bullet of mass 10 g and speed $500 \mathrm {~m} / \mathrm { s }$ is fired into a door and gets embedded exactly at the centre of the door. The door is 1.0 m wide and weighs 12 kg . It is hinged at one end and rotates about a vertical axis practically without friction. The angular speed of the door just after the bullet embeds into it will be :
(1) $6.25 \mathrm { rad } / \mathrm { sec }$
(2) $0.625 \mathrm { rad } / \mathrm { sec }$
(3) $3.35 \mathrm { rad } / \mathrm { sec }$
(4) $0.335 \mathrm { rad } / \mathrm { sec }$

A ring of mass $M$ and radius $R$ is rotating about its axis with angular velocity $\omega$. Two identical bodies each of mass $m$ are now gently attached at the two ends of a diameter of the ring. Because of this, the kinetic energy loss will be:
(1) $\frac { m ( M + 2 m ) } { M } \omega ^ { 2 } R ^ { 2 }$
(2) $\frac { M m } { ( M + m ) } \omega ^ { 2 } R ^ { 2 }$
(3) $\frac { M m } { ( M + 2 m ) } \omega ^ { 2 } R ^ { 2 }$
(4) $\frac { ( M + m ) M } { ( M + 2 m ) } \omega ^ { 2 } R ^ { 2 }$

The gravitational field, due to the 'left over part' of a uniform sphere (from which a part as shown, has been 'removed out'), at a very far off point, P , located as shown, would be (nearly) :
(1) $\frac { 5 } { 6 } \frac { G M } { x ^ { 2 } }$
(2) $\frac { 8 } { 9 } \frac { G M } { x ^ { 2 } }$
(3) $\frac { 7 } { 8 } \frac { G M } { x ^ { 2 } }$
(4) $\frac { 6 } { 7 } \frac { G M } { x ^ { 2 } }$

If the ratio of lengths, radii and Young's moduli of steel and brass wires in the figure are $a , b$ and $c$ respectively, then the corresponding ratio of increase in their lengths is :
(1) $\frac { 3 c } { 2 a b ^ { 2 } }$
(2) $\frac { 2 a ^ { 2 } c } { b }$
(3) $\frac { 3 a } { 2 b ^ { 2 } c }$
(4) $\frac { 2 a c } { b ^ { 2 } }$

On a linear temperature scale Y , water freezes at $- 160 ^ { \circ } \mathrm { Y }$ and boils at $- 50 ^ { \circ } \mathrm { Y }$. On this Y scale, a temperature of 340 K would be read as : (water freezes at 273 K and boils at 373 K )
(1) $- 73.7 ^ { \circ } \mathrm { Y }$
(2) $- 233.7 ^ { \circ } \mathrm { Y }$
(3) $- 86.3 ^ { \circ } \mathrm { Y }$
(4) $- 106.3 ^ { \circ } \mathrm { Y }$

In the isothermal expansion of 10 g of gas from volume V to 2V the work done by the gas is 575 J. What is the root mean square speed of the molecules of the gas at that temperature?
(1) $398 \mathrm {~m} / \mathrm { s }$
(2) $520 \mathrm {~m} / \mathrm { s }$
(3) $499 \mathrm {~m} / \mathrm { s }$
(4) $532 \mathrm {~m} / \mathrm { s }$

In a transverse wave the distance between a crest and neighbouring trough at the same instant is 4.0 cm and the distance between a crest and trough at the same place is 1.0 cm. The next crest appears at the same place after a time interval of 0.4 s. The maximum speed of the vibrating particles in the medium is:
(1) $\frac { 3\pi } { 2 } \mathrm {~cm} / \mathrm { s }$
(2) $\frac { 5\pi } { 2 } \mathrm {~cm} / \mathrm { s }$
(3) $\frac { \pi } { 2 } \mathrm {~cm} / \mathrm { s }$
(4) $2\pi \mathrm {~cm} / \mathrm { s }$

When two sound waves travel in the same direction in a medium, the displacements of a particle located at ' $x$ ' at time ' $t$ ' is given by : $\begin{aligned} & y _ { 1 } = 0.05 \cos ( 0.50 \pi x - 100 \pi t ) \\ & y _ { 2 } = 0.05 \cos ( 0.46 \pi x - 92 \pi t ) \end{aligned}$ where $y _ { 1 } , y _ { 2 }$ and $x$ are in meters and $t$ in seconds. The speed of sound in the medium is :
(1) $92 \mathrm {~m} / \mathrm { s }$
(2) $200 \mathrm {~m} / \mathrm { s }$
(3) $100 \mathrm {~m} / \mathrm { s }$
(4) $332 \mathrm {~m} / \mathrm { s }$

An engine approaches a hill with a constant speed. When it is at a distance of 0.9 km , it blows a whistle whose echo is heard by the driver after 5 seconds. If the speed of sound in air is $330 \mathrm {~m} / \mathrm { s }$, then the speed of the engine is :
(1) $32 \mathrm {~m} / \mathrm { s }$
(2) $27.5 \mathrm {~m} / \mathrm { s }$
(3) $60 \mathrm {~m} / \mathrm { s }$
(4) $30 \mathrm {~m} / \mathrm { s }$

The surface charge density of a thin charged disc of radius R is $\sigma$. The value of the electric field at the centre of the disc is $\frac { \sigma } { 2\epsilon _ { 0 } }$. With respect to the field at the centre, the electric field along the axis at a distance R from the centre of the disc:
(1) reduces by $70.7\%$
(2) reduces by $29.3\%$
(3) reduces by $9.7\%$
(4) reduces by $14.6\%$

A and B are two sources generating sound waves. A listener is situated at C. The frequency of the source at A is 500 Hz. A, now, moves towards C with a speed $4\mathrm{~m/s}$. The number of beats heard at C is 6. When A moves away from C with speed $4\mathrm{~m/s}$, the number of beats heard at C is 18. The speed of sound is $340\mathrm{~m/s}$. The frequency of the source at B is:
(1) 500 Hz
(2) 506 Hz
(3) 512 Hz
(4) 494 Hz

The gravitational field in a region is given by: $\vec { E } = ( 5 \mathrm{N/kg} ) \hat { i } + ( 12 \mathrm{N/kg} ) \hat { j }$. If the potential at the origin is taken to be zero, then the ratio of the potential at the points $( 12 \mathrm {~m} , 0 )$ and $( 0,5 \mathrm {~m} )$ is:
(1) Zero
(2) 1
(3) $\frac { 144 } { 25 }$
(4) $\frac { 25 } { 144 }$

Two balls of same mass and carrying equal charge are hung from a fixed support of length $l$. At electrostatic equilibrium, assuming that angles made by each thread is small, the separation, $x$ between the balls is proportional to :
(1) $l$
(2) $l ^ { 2 }$
(3) $l ^ { 2 / 3 }$
(4) $l ^ { 1 / 3 }$