Find dimensions of $\frac{\mathrm{A}}{\mathrm{B}}$ if $\left(\mathrm{P} + \frac{\mathrm{At}^{2}}{\mathrm{B}}\right) + \frac{1}{2}\rho\mathrm{V}^{2} =$ constant, where $\mathrm{P} \rightarrow$ pressure, $\rho \rightarrow$ density, $V \rightarrow$ speed.
(A) $\mathrm{ML}^{1}\mathrm{T}^{-4}$ (B) $\mathrm{ML}^{-1}\mathrm{T}^{-4}$ (C) $\mathrm{ML}^{2}\mathrm{T}^{-4}$ (D) $\mathrm{ML}^{-1}\mathrm{T}^{-2}$

1 g of an organic compound produces 1.49 g of $\mathrm{Mg_2P_2O_7}$. Determine \% of P.
Given: mass of $\mathrm{Mg_2P_2O_7} = 222$, atomic mass of $P = 31$

In series R-L circuit, voltage of battery is $\mathbf { 1 0 ~ V }$. Resistance and inductance are $\mathbf { 1 0 } \boldsymbol { \Omega }$ and $\mathbf { 1 0 } \mathbf { ~ m H }$ respectively. Find energy stored in the inductor when current reache $\frac { 1 } { e }$ times of maximum value.
(A) 0.33 mJ
(B) 1.33 mJ
(C) 0.67 mJ
(D) 2.33 mJ

using a simple pendulum experiment g is determined by measuring its time period T, Which of the following plots represent correct relation between the pendulum length $\underline { \ell }$ time period T.

Find A for dispersion without deviation.\ (A) 3\ (B) 4\ (C) 5\ (D) 4.5

Three uniformly concentric charged shells are kept as shown. Find potential of each shell.
(A) $V _ { A } = \frac { k Q _ { 1 } } { a } + \frac { k Q _ { 2 } } { b } + \frac { k Q _ { 3 } } { c } , V _ { B } = \frac { k \left( Q _ { 1 } + Q _ { 2 } + Q _ { 3 } \right) } { b } , V _ { C } = \frac { k \left( Q _ { 1 } + Q _ { 2 } + Q _ { 3 } \right) } { c }$
(B) $V _ { A } = \frac { k Q _ { 1 } } { a } + \frac { k Q _ { 2 } } { b } + \frac { k Q _ { 3 } } { c } , V _ { B } = \frac { k \left( Q _ { 1 } + Q _ { 2 } \right) } { b } + \frac { k Q _ { 3 } } { c } , V _ { C } = \frac { k \left( Q _ { 1 } + Q _ { 2 } + Q _ { 3 } \right) } { c }$
(C) $V _ { A } = \frac { k Q _ { 1 } } { a } + \frac { k \left( Q _ { 2 } + Q _ { 3 } \right) } { c } , V _ { B } = \frac { k \left( Q _ { 1 } + Q _ { 2 } \right) } { b } + \frac { k Q _ { 3 } } { c } , V _ { C } = \frac { k \left( Q _ { 1 } + Q _ { 2 } + Q _ { 3 } \right) } { c }$
(D) $V _ { A } = \frac { k Q _ { 1 } } { a } + \frac { k Q _ { 2 } } { b } + \frac { k Q _ { 3 } } { c } , V _ { B } = \frac { k \left( Q _ { 1 } + Q _ { 2 } \right) } { a } + \frac { k Q _ { 2 } } { b } , V _ { C } = \frac { k \left( Q _ { 1 } + Q _ { 2 } + Q _ { 3 } \right) } { c }$

When monochromatic light of wavelength $\lambda$ is incident on a photoelectric emitter, the stopping potential is $\underline { 3.2 \mathrm {~V} }$. When light of wavelength $2 \lambda$ is incident on the same emitter, the stopping potential becomes 0.7 V . Determine the value of $\lambda$.

Two point charges of magnitudes $\mathbf { 1 } \boldsymbol { \mu C }$ and $\mathbf { 2 } \boldsymbol { \mu C }$ are placed at two vertices of an equilateral triangle of side $\mathbf { 3 ~ c m }$. Another charge of $\mathbf { 3 ~ } \boldsymbol { \mu } \mathbf { C }$ is brought from infinity to the third vertex of the triangle. Find the work done in bringing the charge to the third vertex. (A) 0.9 J (B) 1.8 J (C) 4.5 J (D) 2.7 J

Which of the following physical quantities is not directly measurable? (A) Displacement. (B) Electric potential (C) Potential difference (D) Acceleration

Match the list I with list II.
List-I (Reagent): (1) $\mathrm{H_2/Pd/BaSO_4}$ (2) (i) $\mathrm{CrO_2Cl_3/CCl_4}$ (ii) $\mathrm{H_3O^+}$ (3) $\mathrm{CO + HCl + AlCl_3}$ (4) $\mathrm{SnCl_2 +}$ dil. HCl
List-II (Name Reaction): (P) Rosamund Reaction (Q) Etard Reaction (R) Gattermann Koch Reaction (S) Stephen's Reaction

In a potentiometer null point for two resistance $R _ { 1 }$ and $R _ { 2 }$ is at 40 cm . If $16 \Omega$ is connected in parallel to $R _ { 2 }$ then null point is at 50 cm then $\mathrm { R } _ { 1 }$ and $\mathrm { R } _ { 2 }$ are respectively.
(A) $16 \Omega , 48 \Omega$
(B) $16 / 3 \Omega , 8 \Omega$
(C) $32 / 3 \Omega , 8 \Omega$
(D) $12 / 3 \Omega , 12 \Omega$

Two balls of mass 2 m and m collides with rod of mass m and length L as shown balls stick to the rod after collision. Find $\frac { V } { \omega }$ if rod is hinged at centre. ( $\mathrm { L } = 8 \mathrm {~m}$ ) (A) $11 / 2$ (B) $11 / 3$ (C) $11 / 4$ (D) $9 / 4$

Which of the following material has bigger Young's modulus?\ (5) D\ (B) C\ (B) A\ (D) A

DNA \& RNA both arc (optically active) due to (A) Presence of D sugar (B) presence of L-sugar (C) presence of same unit (D) presence of diphosphate ester

Find the work done. (Given: $\mathrm { G } = 6.67 \times 10 ^ { - 11 } \mathrm {~N} - \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } $)
(A) $1.7342 \times 10 ^ { - 7 } \mathrm {~J}$
(B) $1.6253 \times 10 ^ { - 7 } \mathrm {~J}$
(C) $2.5232 \times 10 ^ { - 7 } \mathrm {~J}$
(D) $6.6325 \times \mathbf { 1 0 } ^ { \boldsymbol { - } \mathbf { 7 } } \mathbf { ~ J }$

A particle attached to an ideal string is projected from position B (lowest position). At position A, tension in string becomes zero. Find speed in string at B.
(A) $\sqrt { 5 \mathrm { gl } }$
(B) $\sqrt { \frac { 7 \mathrm { gl } } { 2 } }$
(C) $\sqrt { \frac { 3 \mathrm { gl } } { 2 } }$
(D) $\sqrt { 2 \mathrm { gl } }$

A block of mass 5 kg is placed on a rough inclined plane making an angle of $30 ^ { \circ }$ with the horizontal. The coefficient of friction between the block and the plane is $\sqrt { 3 }$. Find the minimum force applied down the incline required to just start moving the block. (Take $\mathrm { g } = 10 \mathrm {~m} \mathrm {~s} ^ { - 2 } $) (A) 0 N (B) 25 N (C) 50 N (D) 75 N

Two light sources of 450 nm and 550 nm are used for YDSE with slit distanc 2.25 mm and distance between the slits and screen is 1.5 m . Then the distance from central maxima for which minima of both waveléngth coincide? (A) 1.65 mm (B) 1.20 mm (C) 1.30 mm (D) 1.40 mm

\% of C in given optically active compound
(I) n-propyl chloride (II) Isopropyl chloride (III) Sec-butyl chloride (IV) Neopentyl chloride

The escape velocity of a planet A is $\mathbf { 1 0 ~ k m } / \mathbf { s }$. Another planet B has density equal to $10 \%$ of planet A and radius equal to $10 \%$ of planet A . What is the escape velocity of planet B?
(A) $3.16 \mathrm {~km} / \mathrm { s }$
(B) $1.0 \mathrm {~km} / \mathrm { s }$
(C) $0.316 \mathrm {~km} / \mathrm { s }$
(D) $0.10 \mathrm {~km} / \mathrm { s }$

A gas undergoes a process in which state variable changes from $\left( 1 \mathrm {~atm} , 60 \mathrm { ml } , 27 ^ { \circ } \mathrm { C } \right)$ to $\left( \mathrm { P } \mathrm { atm } , 30 \mathrm { ml } , 77 ^ { \circ } \mathrm { C } \right)$ then P is (A) $\frac { 7 } { 3 } \mathrm {~atm}$ (B) 2 atm (C) 5 atm (D) 7 atm

For the given circuit the breakdown voltage of Zener diode is $\mathbf { V } _ { \mathbf { 7 } } = \mathbf { 5 }$ volts. And it can with stand maximum circuit of $\mathbf { I } _ { \mathbf { Z } } = \mathbf { 5 ~ m A }$. Find the value of R .\ (A) $5 / 3 \mathrm { k } \Omega$\ (B) $14 / 3 \mathrm { k } \Omega$\ (C) $8 \mathrm { k } \Omega$\ (D) $10 / 3 \mathrm { k } \Omega$

In Carius method for estimation of halogens, $\mathbf { 1 8 0 ~ m g }$ of an organic compound produced $\mathbf { 1 4 3 . 5 } \mathbf { ~ m g }$ of $\mathbf { A g C l }$. The percentage composition of chlorine in the compound is $\_\_\_\_$ \%. [Given : molar mass in $\mathbf { g ~ m o l } ^ { - \mathbf { 1 } }$ of Ag: 108, $\mathbf { C l } = \mathbf { 3 5 . 5 }$ ]

Find current through ammeter (in A).
(A) 0.75
(B) 1
(C) 2
(D) 0.5

An object is being dropped from height $h$ above the ground. Apart from force of gravity additional drag force, $\mathrm { F } = - \mathrm { kv }$ acts on the object. Find the graph of $\mathbf { v }$ versus $\mathbf { t }$.