For the given set of measurement find relative error. 20.00, 19.75, 18.25, 17.01\ (A) 0.12\ (B) 0.06\ (C) 0.17\ (D) 0.09

From a uniform disc of radius R and mass M two small discs of radius R/4 is being cut as shown in figure. Find the moment of inertia of the system about axis $\mathrm { AA } ^ { \prime }$. (A) $\frac { \mathbf { 7 9 } } { \mathbf { 1 2 8 } } \mathbf { M R } ^ { \mathbf { 2 } }$ (B) $\frac { 79 } { 256 } \mathrm { MR } ^ { 2 }$ (C) $\frac { 109 } { ( 56 ) } \mathrm { MR } ^ { 2 }$ (D) $\frac { 109 } { 128 } \mathrm { MR } ^ { 2 }$

Find force on charge $\mathrm { q } = 1 \mu \mathrm { C }$ as due to uniformly charged rod as shown in the figure.
(A) 15 N
(B) 6 N
(C) 12 N

Find radius of gyration of solid sphere about give axis of rotation

Find kinetic energy of disc when block has fallen by $\mathbf { 3 ~ m }$.

Statement A: but-2-e show 0.1.
Statement B: Propanal \& Propanone are F.G.I
Statement C: Pentane \& 2,2-Dimethyll propane are C.I
Correctly statement
(A) Only A \& B (B) Only A \& C (C) Only B \& C (D) All

Width of river is 200 m flowing with velocity $10 \text{ m/sec}$. A boat can move with speed $20 \text{ m/sec}$ perpendicular to river flow. Find minimum time to cross the river and displacement along the river bank.

In adiabatic compression temperature of gas becomes 4 times while volume decreased $\mathbf { 1 } \boldsymbol { / } \mathbf { 2 }$ times find $\boldsymbol { \gamma }$.
(A) 1
(B) 2
(C) 3
(D) 4

In a photoelectric effect experiment, the maximum possible kinetic energy of the emitted photoelectrons is zero. The work function of the metal is $\phi = 20 \times 10 ^ { - 19 } \mathrm {~J}$. Find the frequency of the incident photon. (A) $3.0 \times \mathbf { 1 0 } ^ { \mathbf { 1 4 } } \mathbf { ~ H z }$ (B) $3.02 \times 10 ^ { 15 } \mathrm {~Hz}$ (C) $\mathbf { 1 . 5 } \boldsymbol { \times } \mathbf { 1 0 } ^ { \mathbf { 1 5 } } \mathbf { ~ H z }$ (D) $6.6 \times \mathbf { 1 0 } ^ { \mathbf { 1 4 } } \mathbf { ~ H z }$

A simple pendulum of length 30 cm complete 40 revolutions in 10 sec then how much length of this pendulum should be increased so that it complete 20 revolutions in 10 sec .

In equilateral triangular frame, the is current of 2 A . The side of frame is $\mathbf { 4 } \sqrt { \mathbf { 3 } } \mathbf { ~ c m }$. Magnetic field at center $\mathbf { C }$ is (A) $\mathbf { 1 0 } \sqrt { \mathbf { 1 0 } } \boldsymbol { \mu } \mathbf { T }$ (B) $3 \sqrt { 10 } \mu \mathrm {~T}$ (C) $20 \sqrt { 3 } \mu \mathrm {~T}$ (D) $30 \sqrt { 3 } \mu \mathrm {~T}$

For the given ac circuit find the power factor.
(A) $4 / 5$
(C) $4 / 3$
(D) $3 / 4$
(E) $3 / 5$

Velocity of particle varies with position as shown in the below graph. Find the correct variation of acceleration with position.

Equation of an EMW in a medium is given by $\mathrm { E } = 2 \sin \left( 2 \times 10 ^ { 15 } \mathrm { t } - 10 ^ { 7 } \mathrm { x } \right)$. Find refractive index of the medium. (A) $3 / 2$ (B) 2 (C) $5 / 3$ (D) $4 / 3$

If position vector is given as $\overrightarrow { \mathbf { r } } = ( \mathbf { x } \hat { \mathbf { i } } + \mathbf { y } \hat { \mathbf { j } } + \mathbf { z } \hat { \mathbf { k } } )$ and if its signs are reversed then which of the following physical quantity remains unaffected? (A) Acceleration (B) Velocity (C) Displacement (D) Torque

In 'S' estimation $\mathbf{0.7~g}$ of an organic compound gives $\mathbf{1g~}\mathrm{BaSO}_{4}$ in Carius method. What is the \% of 'S' in compound?
(A) 19.61 (B) 61.20 (C) 80.20 (D) 17.54

In isobaric expansion work done is 100 J. Find heat given to the gas ($\gamma = 1.4$)

A ray of light is incident at an angle $i$ on an equilateral prism. If the ray emerges grazing the second face, find angle of refraction at first surface. Refractive index of prism $\sqrt { 2 }$.
(A) $10 ^ { \circ }$
(B) $15 ^ { \circ }$
(C) $30 ^ { \circ }$
(D) $45 ^ { \circ }$

Find speed of blocks when $\mathbf { 2 m }$ has move by $\mathbf { 3 . 6 }$ m,initially system is at rest.

Find out the correct energy for the ground state or energy transition. (symbols have usual meaning \& $\mathrm { n } \rightarrow \mathrm { m }$ gives the transition)\ (A) $\mathrm { Be } _ { 2 \rightarrow 1 } ^ { 3 + } ( + 13.6 \mathrm { eV } ) \times$\ (b) $\mathrm { H } ( - 6.8 \mathrm { eV } )$\ (C) $\mathrm { He } _ { 2 \rightarrow 1 } ^ { + } ( 40.8 \mathrm { eV } )$\ (P) $\mathrm { Li } ^ { 2 + } ( - 13.6 \mathrm { eV } )$

A parallel plate capacitor with plate separation 5 mm is Charged by a battery. On introducing a mica sheet of 2 mm and maintaining the connections of the plates with the terminals of the battery, it is found that it draws 25\% more charge from the battery. The dielectric constant of mica is $\_\_\_\_$ . (A) 1.0 (B) 2.0

A voltmeter of 400 W resistance is in parallel with 100 W resistor. And the combination is connected with $\mathbf { 1 0 0 } \mathbf { W }$ resistor and a battery of $\mathbf { 9 }$ volt in series as shown. Find the reading of voltmeter ${ } _ { \Delta V }$
(A) 3 volts
(B) 4 volts
(C) 5 volts
(D) 6 volts

The frequency of the 5 th harmonic of a closed organ pipe is equal to the fundamental frequency of an open organ pipe. Find the ratio of the lengths of the closed organ pipe to the open organ pipe.

Find equivalent resistance between $\mathbf { A B }$

If the mass number of nucleus is $\alpha$, its radius is $R _ { \alpha }$. And another mass number is $\beta$ then its radius is $\mathrm { R } _ { \beta }$; then $\mathrm { R } _ { \alpha } / \mathrm { R } _ { \beta } =$ ? [Given $\beta = \mathbf { 8 } \boldsymbol { \alpha }$ ] (A) 1 (B) $1 / 2$ (C) $1 / 3$ (D) 2