1.2 mol of \( \boldsymbol{C H}_{3} \boldsymbol{N} \boldsymbol{H}_{2}\left(\boldsymbol{p} \boldsymbol{K}_{\boldsymbol{b}}=\boldsymbol{3} . \boldsymbol{3}\right) \) is
added to 0.8 moles of \( H C l \) and the
solution is diluted to one litre, resulting \( \boldsymbol{p} \boldsymbol{H} \) of solution is:
A . 10.7
в. 3.6
c. 10.4
D. 11.3


Let \( f \) be differentiable for all \( x \). If \( f(1)= \)
-2 and \( f^{\prime}(x) \geq 2 \) for \( x \in[1,6], \) then
\( \mathbf{A} \cdot \mathbf{f}(6) \geq 8 \)
B. \( f(6)<8 \)
\( \mathrm{c} \cdot \mathrm{f}(6)<5 \)
D. \( f(6)=5 \)


Probability of impossible event is
\( A \cdot 1 \)
B. 0
\( c \cdot \frac{1}{2} \)
D. -


A particle of mass \( 1 k g \) starts from rest
under a time dependent force \( \boldsymbol{F}=\mathbf{1}+ \)
2 \( t . \) The work done by the force in time
interval \( t=0 \) to \( t=2 s \) is
A . \( 18 J \)
в. \( 20 J \)
c. \( 30 J \)
D. \( \frac{70}{3} \)


Answer the questions based on the
following flow-sheet.
Following are some statements about
species \( C \)
Select correct statement(s).
This question has multiple correct options
\( \mathbf{A} \cdot \mathrm{C} \) is \( N H_{4} C l \)
B. \( \mathrm{C} \) is \( \mathrm{NaHCO}_{3} \)
C \( \cdot \mathrm{C} \) is recycled into \( \mathrm{Ca}(\mathrm{OH})_{2} \) chamber to from \( \mathrm{NH}_{3} \)
\( D \cdot \mathrm{C} \) is \( N a_{2} C O_{3} \)


Explain the difference in reactivity of the group I metals with water.


Direction ratios of the line which is perpendicular to the lines with direction ratios -1,2,2 and 0,2,1 are
\( \mathbf{A} \cdot 1,1,2 \)
B. 2,-1,2
c. -2,1,2
D. 2,1,-2


A point source of light \( \mathrm{S} \) is placed in
front of two large mirrors as shown
Which of the following observers will
see only one image of \( s ? \)


The points (5,1),(1,-1) and (11,4) are
A. Collinear
B. Vertices of right angled triangle
c. vertices of equilateral triangle
D. Vertices of isosceles triangle


Which of the following pair of species is not isostructural?
A. \( K r F_{2}, I C l_{2} \)
в. \( S O_{3}, S O_{3}^{2} \)
c. \( C O_{3}^{2-}, B O_{3}^{3} \)
D. \( \operatorname{si} O_{4}^{4-}, I O_{4} \)


In a Wheatstone's bridge, there resistances \( \mathbf{P}, \boldsymbol{O} \) and \( \mathbf{R} \) connected in
the three arms and the fourth arm is
formed by two resistances \( \mathbf{S}_{1} \) and \( \mathbf{S}_{\mathbf{2}} \)
connected in parallel. The condition for
bridge to be balanced will be
A \( \cdot \frac{P}{O}=\frac{R}{S_{1}+S_{2}} \)
B. \( \frac{P}{O}=\frac{2 R}{S_{1}+S_{2}} \)
c. \( \frac{P}{O}=\frac{R\left(S_{1}+S_{2}\right)}{S_{1} S_{2}} \)
D. \( \frac{P}{O}=\frac{R\left(S_{1}+S_{2}\right)}{2 S_{1} S_{2}} \)


Represent graphically the relation between interest and time, when a sum
of Rs. 500 is deposited in a bank at a rate of \( 9 \% \) per annum simple interest.


If \( \alpha \) is the reaction of HI dissociated at
equilibrium in the reaction \( 2 H I \rightarrow \)
\( \boldsymbol{H}_{2}+\boldsymbol{I}_{2} \) then starting with 2 moles of
HI, the total number of moles of
reactants and products at equilibrium
are:
\( A \)
B. 2
\( c \cdot 1+a \)
D. \( 2+2 \alpha \)


What is compound \( z: \)
\[
\begin{array}{l}
\boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{B} \boldsymbol{r} \stackrel{\boldsymbol{N a C} \boldsymbol{N}}{\longrightarrow} \boldsymbol{X} \stackrel{\boldsymbol{H}_{3} \boldsymbol{O}^{+}}{\rightarrow} \\
\boldsymbol{Y} \stackrel{\boldsymbol{C H}_{3} C \boldsymbol{H}_{2}}{\longrightarrow} \boldsymbol{O} \boldsymbol{H}_{\boldsymbol{H}^{+}}
\end{array}
\]
\( \mathbf{A} \)
\[
\begin{array}{c}
\mathbb{N} \\
\| \\
\mathrm{CH}_{3} \mathrm{CH}=\mathrm{CH} \mathrm{COH}
\end{array}
\]
B. \( C H_{3} C H_{2} C H_{2} C H=N O C H_{2} C H_{3} \)
\( \mathbf{c} \cdot C H_{3} C H_{2} C H_{2} C H\left(O C H_{2} C H_{3}\right)_{2} \)
D.
\[
\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{COCH}_{2} \mathrm{CH}_{3}
\]


If \( A \) and \( B \) are two event such that
\( P(A)=\frac{6}{11}, P(B)=\frac{5}{11} \) and \( P(A \cup \)
\( B)=\frac{7}{11}, \) find \( P(A r \)
\( \boldsymbol{B}), \boldsymbol{P}(\boldsymbol{A} / \boldsymbol{B}), \boldsymbol{P}(\boldsymbol{B} / \boldsymbol{A}) \)


A male child will be born if
A. Father is healthy.
B. Mother is well fed during pregnancy.
C . Genetic composition of child has XY set of chromosomes.
D. Genetic composition of child has \( X X \) set of chromosomes.


Lithium on heating in air forms mainly
\( L i_{2} O \) (oxide) and not peroxide \( \left(L i_{2} O_{2}\right) \)
If true enter 1 else 0


ATP synthesis during light reaction is
A. Oxidative phosphorylation
B. Photolysis
c. Photophosphorylation
D. Phosphorylation


Which of the following is responsible for 21 trisomy in humans?
A. Pleiotropy
B. Polygenic inheritance
c. Epistasis
D. X-inactivation
E. Nondisjunction


Respiration initiated in chloroplast and occurs in light is called as
A. Aerobic respiration
B. Anaerobic respiration
c. Photorespiration
D. Fermentation


The correct order for decreasing atomic radius of the five atoms \( \mathrm{H}, \mathrm{Br}, \mathrm{I}, \mathrm{He} \) and
Sis?
\( A \cdot \mid>B r>S>H e>H \)
\( \mathbf{B} \cdot \mid>S>B r>H>H e \)
\( \mathrm{c} \cdot \mid>\mathrm{S}>\mathrm{Br}>\mathrm{He}>\mathrm{H} \)
\( \mathbf{D} \cdot \mathbf{B r}>\mid>\mathbf{S}>\mathrm{He}>\mathbf{H} \)


Write down Gauss's theorem of
electrostatics. Find out intensity of the electric field at a point outside a uniformly charged thin spherical shell with its help.


An aldehyde as well as a ketone can be represented by the same molecular
formula, say \( C_{3} H_{6} O . \) Write their
structures and name them, State the
relation between the two in the
language of science.


57 Co will emit
27
radiation
\( \mathbf{A} \cdot \beta^{-} \)
в. \( \beta^{+} \)
\( c \cdot \alpha \)
D. electron capture


On rubbing a glass rod with silk cloth,
\( 6.84 \times 10^{16} \) electrons are transferred
from glass rod to silk cloth. Find the total charge transferred.
\( \mathbf{A} \cdot-1.09 \times 10^{-4} C \)
в. \( -1.09 \times 10^{-3} C \)
c. \( -1.09 \times 10^{-5} C \)
D. \( -1.09 \times 10^{-2} C \)


One molecule of a substance absorbs
one quantum of energy. The energy involved when 1.5 moles of the
substance absorb red light of frequency
\( 7.5 \times 10^{14} s e c^{-1} \) will be?
A \( \cdot 4.49 \times 10^{5} J \)
B . \( 2.24 \times 10^{5} J \)
c. \( 9.23 \times 10^{7} J \)
D. \( 2.24 \times 10^{7} J \)


Assertion
Copper-T is an effective contraceptive
device in human females.
Reason
Copper-T prevents passage of sperms from vagina upwards into fallopian
tubes.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The determinant \( \left|\begin{array}{ccc}\sin \alpha & \cos \alpha & 1 \\ \sin \beta & \cos \beta & 1 \\ \sin \gamma & \cos \gamma & 1\end{array}\right| \) is
equal to
This question has multiple correct options
\( ^{\mathrm{A}} \cdot_{-4 \sin } \frac{\alpha-\beta}{2} \sin \frac{\alpha-\gamma}{2} \sin \frac{\gamma-\alpha}{2} \)
\( \mathbf{B} \cdot \sin \alpha+\sin \beta+\sin \gamma \)
c. \( \sin (\alpha-\beta)+\sin (\beta-\gamma)+\sin (\gamma-\alpha) \)
D. none of these


A plano convex lens \( (\mu=1.5) \) has a
maximum thickness of 1 mm
If diameter of its aperture is \( 4 \mathrm{cm} \). Find
(i) Radius of curvature of curved
surface,
(ii) its focal length in air


A light rod of length \( 1 \mathrm{m} \) is pivoted at its
centre and two masses of \( 5 \mathrm{kg} \) and \( 2 \mathrm{kg} \) are hung from the ends as shown in figure. Find the initial angular acceleration of the rod assuming that it was horizontal in the beginning.


2 g of \( A l \) is treated separately with excess of dil. \( H_{2} S O_{4} \) and excess of
NaOH. The ratio of the volumes of
hydrogen evolved is :
A .2: 3
B. 1: 1
c. 2: 1
D. 1: 2


Let \( \overrightarrow{\boldsymbol{a}}=\hat{\boldsymbol{i}}+2 \hat{\boldsymbol{j}} \) and \( \overrightarrow{\boldsymbol{b}}=\boldsymbol{2} \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}} \)
\( |\vec{a}|=|\vec{b}| \) ? Are the vectors \( \vec{a} \) and \( \vec{b} \)
equal?


Is the work done in an open vessel at
\( 300 K, \) when 56 g iron reacts with dilute
\( H C I \) is?
A . 600 cal
в. 300cal
c. 150 cal
D. 100 cal


Ray \( P Q \) and ray \( P R \) are perpendicular to each other. Points \( B \) and \( A \) are in the
interior and exterior of \( \angle Q P R \)
respectively. Ray \( P B \) and ray \( P A \) are
perpendicular to each other. Draw a figure all this rays and write-A pair of complementary angles A pair of supplementary anglesA pair of congruent angles.


Assertion
The quantity \( L / R \) possesses dimension of time
Reason
To reduce the rate of increase of current
through a solenoid, we should increase the time constant \( (\boldsymbol{L} / \boldsymbol{R}) \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A compound absorb light in the wavelength region \( 490-500 \mathrm{nm} . \) Its complementary colour is :
A . red
B. blue
c. orange
D. blue-green


A bundle of ............. number of chains of
cellulose molecule is called micelle.
number of micelles are
aggregated parallel to each other to form a microfibril.
A. 200, 10
B. 20, 100
\( c \cdot 10,200 \)
D. 100, 20


\( \int \cos x \cdot \cos 2 x \cdot \cos 3 x d x \)


The amines are basic in nature, hence
they form salts with a hydrochloric acid. Which of the following will be insoluble
in dil. \( \boldsymbol{H} \boldsymbol{C l} \) ?
A. \( C_{6} H_{5} N H_{2} \)
в. \( \left(C_{6} H_{5}\right)_{3} N \)
c. \( C_{2} H_{5} N H_{2} \)
D. \( C H_{3} N H C H_{3} \)


The electric field intensity \( E, \) current
density \( J \) and specific resistance \( k \) are related to each other through the relation
\( A \cdot E=\frac{J}{k} \)
в. \( E=J k \)
c. \( _{E}=\frac{k}{J} \)
D. \( k=J E \)


\( \boldsymbol{R}-\underset{\boldsymbol{O}}{\|}-\boldsymbol{C l} \frac{\boldsymbol{H}_{2}}{\boldsymbol{P} \boldsymbol{d}-\boldsymbol{B a S O}_{4}} \boldsymbol{P} \)
In the following reaction, product ' \( P \) ' is
A \( \cdot R C H_{2} O H \)
в. \( R C O O H \)
c. \( R C H O \)
D. \( R C H_{3} \)


A' block 'B' is pushed momentarily along a horizontal surface with an
initial velocity ' \( v \) '. If ' \( \mu \) ' is the coefficient of friction between 'B' and the surface,
block 'B' will come to rest after a time
A \( \cdot \frac{v}{g \mu} \)
в. \( \frac{g \mu}{v} \)
\( c \cdot \frac{g}{v} \)
D. \( \frac{v}{g} \)


The correct Biot-Savart law in vector
form is?
\( ^{\mathbf{A}} \cdot d \vec{B}=\frac{\mu_{0}}{4 \pi} \frac{I(d \vec{l} \times \vec{r})}{r^{2}} \)
в. \( d \vec{B}=\frac{\mu_{0}}{4 \pi} \frac{I(d \vec{l} \times \vec{r})}{r^{3}} \)
\( ^{\mathrm{c}} \cdot d \vec{B}=\frac{\mu_{0}}{4 \pi} \frac{I d \bar{l}}{r^{2}} \)
D \( \cdot d \vec{B}=\frac{\mu_{0}}{4 \pi} \cdot \frac{I d \vec{l}}{r^{3}} \)


The correct order of atomic radii is :
\( \mathbf{A} \cdot C e>S m>Y b>L u \)
в. \( S m>C e>L u>Y b \)
c. \( L u>Y b>S m>C e \)
\( \mathrm{D} \cdot S m>Y b>C e>L u \)


Automobile tyres have generally irregular projections over their surfaces.Why?


Three \( 10 \Omega, 2 W \) resistors are as in
figure. The maximum possible voltage
between points \( A \) and \( B \) without exceeding the power limits of any of the
resistors is
\( \mathbf{A} \cdot 5 \sqrt{3} V \)
B. \( 3 \sqrt{5} V \)
\( \mathbf{c} .15 V \)
\( D \cdot \frac{5}{2} V \)


What is slow and fast reaction? Give
example.


How many times does a ray of light undergo refraction when it passes through a water droplet?


Which of the following is a proper
sequence?
A. proportional limit, elastic limit, yielding, failure
B. elastic limit, proportional limit, yielding, failure
C . yielding, proportional limit, elastic limit, failure
D. proportional limit, yielding, elastic limit, failure


One atomic mass unit (amu) is
approximately equal to
A . \( 931.4 \mathrm{MeV} \)
B . \( 251.2 \mathrm{MeV} \)
c. \( 120.4 \mathrm{MeV} \)
D. \( 170.5 \mathrm{MeV} \)


Which of the following is/are correct for
group 14 elements?
This question has multiple correct options
A. The stability of dihalide is in the order of \( P b X_{2}> \)
\( \operatorname{Sn} X_{2}>\operatorname{Ge} X_{2}>\operatorname{Si} X_{2}>C X_{2} \)
B. the ability to form \( p \Pi-p \Pi \) multiple bonds among
themselves increases down the group
C. the tendency for catenation decreases down the group
D. they all from oxides with the formula MO


A monkey is descending from the branch of a tree with constant
acceleration if the breaking strength is \( 75 \% \) of the weight of the monkey, The minimum acceleration with which
monkey can slide down without breaking branch is
\( A \cdot g \)
в. \( \frac{3 g}{4} \)
c. \( \frac{g}{4} \)
D. \( \frac{g}{2} \)


Which of the following statements is/are correct for \( 0<\theta<\frac{\pi}{2} ? \)
This question has multiple correct options
A \( \cdot(\cos \theta)^{1 / 2} \leq \cos \frac{\theta}{2} \)
B. \( (\cos \theta)^{3 / 4} \geq \cos \frac{3 \theta}{4} \)
c. \( \cos \frac{5 \theta}{6} \geq(\cos \theta)^{5 / 6} \)
D. \( \cos \frac{7 \theta}{8} \geq(\cos \theta)^{7 / 8} \)


Assertion
Oxy hydrogen blow torch is used for
welding.
Reason
The temperature produced here is
above \( 2000^{0} C \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Evaluate :
\( \int e^{x}\left[\frac{1+x \log x}{x}\right] d x \)


A \( 4 \mu F \) capacitor is charged to \( 400 V . \) If its plates are joined through a resistance \( 2 k \Omega, \) then heat produced in the resistance is
\( \mathbf{A} \cdot 0.16 J \)
в. \( 0.32 J \)
c. \( 0.64 J \)
D. \( 1.28 J \)


The most important forces for the
ascent of sap in plants are?
A. Imbibition and capillary
B. Suction pressure and cohesion
c. Capillary and root pressure
D. Root pressure and pulsation


\( (\vec{a} \cdot \vec{i})^{2}+(\vec{a} \cdot \vec{\jmath})^{2}+(\vec{a} \cdot \vec{k})^{2} \) is equal to
A \( \left.\left.\cdot|\vec{a}|^{2}\right|^{2}\right|^{\vec{l}} \)
B. 3
c \( \cdot|\vec{a} \cdot(\vec{i}+\vec{j}+\vec{k})|^{2} \)
D. None of these


If the ratio of the \( 11^{t h} \) term of an A.P. to
its \( 18^{t h} \) term is \( 2: 3, \) find the ratio of the
sum of first five terms to the sum of its
first 10 terms


A circular disc is rotating about its own
axis, the direction of its angular momentum is:
A . radial
B. along the axis of rotation
c. along the tangent
D. perpendicular to the direction of angular velocity


How many structure isomers can you
draw for pentane?
A .2
B. 3
\( c \cdot 4 \)
D. 5


The IUPAC name of
\( \left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{N} \boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right)_{2} \) is:
A. N,N-dimethyl-2-propanamine
B. N,N-dimethyl amino isopropane
c. N,N-dimethyl amino ethane
D. Methyl-N-isopropyl methyl amine


N characters of information are held on
magnetic tape, in batches of \( x \) characters each,the batch processing
time is \( \alpha+\beta x^{2} \) seconds, \( \alpha \) and \( \beta \) are
constants. The optical value of \( x \) for fast
processing is,
\( \mathbf{A} \cdot \alpha / \beta \)
в. \( \beta / \alpha \)
c. \( \sqrt{\alpha / \beta} \)
D. \( \sqrt{\beta / \alpha} \)


The velocity \( n m / s \) of a particle is
proportional to the cube of the time. If the velocity after \( 2 s \) is \( 4 m / s, \) then \( n \) is
equal to.
A \( \cdot t^{3} \)
в. \( \frac{t^{3}}{2} \)
c. \( \frac{t^{3}}{3} \)
D. \( \frac{t^{3}}{4} \)


\( \boldsymbol{n}[\boldsymbol{P}(\boldsymbol{A})]=\boldsymbol{n}[\boldsymbol{P}(\boldsymbol{B})], \) then \( A \) and \( \mathrm{B} \) are
sets
A . Equal
B. Overlapping
c. Equivalent
D. Dissoint


Five resistances are connected as
shown in the figure. The equivalent
resistance between A and C is
\( A \cdot \frac{10}{3} \Omega \)
B. \( 22 \Omega \)
c. \( 15 \Omega \)
D. \( 10.6 \Omega \)


Which of the following is not ultimately derived from the Sun's energy?
A. geothermal energy
B. wind energy
c. nuclear energy
D. bio-mass


The decreasing order of hydration
enthalpies earth metal ions is:
\( \mathbf{A} \cdot B e^{2+}>B a^{2+}>C a^{2+}>S r^{2+} \)
B \( \cdot B a^{2+}>S r^{2+}>C a^{2+}>M g^{2+}>B e^{2+} \)
\( \mathbf{C} \cdot B e^{2+}>C a^{2+}>M g^{2+}>B e^{2+} \)
D \( \cdot B e^{2+}>M g^{2+}>C a^{2+}>S r^{2+}>B a^{2+} \)


Write short notes on Antiseptics and Disinfectants.


In a plane progressive harmonic wave
This question has multiple correct options
A. phase difference between displacement and acceleration of particle is zero
B. phase difference between displacement and acceleration of particle is \( \pi \)
C. phase difference between displacement and velocity of particle is \( \frac{\pi}{2} \)
D. phase difference between velocity and acceleration of particle is \( \frac{\pi}{2} \)


Diesel vehicles pollute the environment largely through:
A) \( C O \)
B) \( N O_{x} \)
C) ParticulatesNOx
\( A \cdot A \& B \)
B. B \& C
\( c \cdot c \& A \)
D. \( A, B \& C \)


Fill in the blanks with appropriate
words.

Synapsis, chiasma formation and crossing over occur between homologous chromosomes in of meiosis.


The molar conductivity of acetic acid at
infinite dilution is 390.7 and for \( 0.1 \mathrm{M} \)
acetic acid solution is \( 5.2 \mathrm{mhocm}^{2} \) mol
\( -1 . \) The degree of dissociation of \( 0.1 \mathrm{M} \)
\( \mathrm{CH}_{3} \mathrm{COOH} \) solution is:
A . \( 13.3 \% \)
B. 0.0133\%
c. 1.33\%
D. 133\%


The common name of
\( \boldsymbol{K}\left[\boldsymbol{P t C l}_{3}\left(\boldsymbol{\eta}^{2} \cdot \boldsymbol{C}_{2} \boldsymbol{H}_{4}\right)\right] \) is
A. Potassium salt
B. Zeise's salt
c. complex salt
D. None of these


On passing \( 1.5 F \) charge, the number of moles of aluminum deposited at the
cathode is:
[Molar mass of \( \boldsymbol{A l}=\mathbf{2 7} \) gram mol \( ^{-1} \) ]
A . 1.0
в. 13.5
c. 0.50
D. 0.75


Let \( \mathbf{f}(\mathbf{x})=(\mathbf{x}+\mathbf{1})^{2}-\mathbf{1}, \mathbf{x} \geq-\mathbf{1} \)
Statement-1: The set \( \left\{\mathbf{x}: \mathbf{f}(\mathbf{x})=\mathbf{f}^{-1}(\mathbf{x})\right\} \)
\( =\{\mathbf{0},-\mathbf{1}\} \)
Statement-2: \( f \) is a bijection
A. Statement 1 is true, Statement 2 is true,Statement 2 is correct explanation for statement
B. Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation for statement 1
c. statement 1 is true, statement 2 is false.
D. Statement 1 is false, Statement 2 is true


\( \operatorname{Let} \int_{0}^{x}\left(\frac{b t \cos 4 t-a \sin 4 t}{t^{2}}\right) d t= \)
\( \frac{a \sin 4 x}{x} \) then \( a \) and \( b \) are given by
A \( \cdot a=\frac{1}{4}, b=1 \)
В. \( a=2, b=2 \)
c. \( a=-1, b=4 \)
D. \( a=2, b=4 \)


In circular motion if \( \bar{v} \) is velocity vector,
\( \bar{a} \) is acceleration vector, \( \bar{r} \) is
instantaneous position vector, \( \bar{p} \) is momentum vector and \( \bar{\omega} \) is angular velocity of particle, then:
This question has multiple correct options
A \( . \bar{v}, \bar{\omega}, \bar{r} \) are mutually perpendicular
B . \( \bar{p}, \bar{v}, \bar{\omega} \) are mutually perpendicular
c. \( \bar{r} \times \bar{v}=0 \) and \( \bar{r} \times \bar{\omega}=0 \)
D. \( \bar{r} . \bar{v}=0 \) and \( \bar{r} . \bar{\omega}=0 \)


Ammonia is an inorganic water pollutant.
A. True
B. False


If the observed and theoretical
molecular mass of NaCl is found to be
31.80 and \( 58.50, \) then the degree of dissociation of NaCl is:
A . 83.96\%
B . 8.39\%
c. \( 90 \% \)
D. 100\%


Assertion
Due to catenation a large number of carbon compounds are formed.
Reason
Carbon compounds show the property of allotropy.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A block of mass \( 1 \mathrm{Kg} \) is connected with a fixed wall through a light spring of constant \( \mathrm{K}=100 \mathrm{n} / \mathrm{m} . \) The surface are
frictionless. Initially spring is in relaxed position. A horizontal force \( F \) of 50 N is applied on the block. Find the maximum
elongation of the spring.


Statement 1: Metameric animals are
triploblastic Statement 2: Triploblastic animals are
bilaterally symmetrical
A. Both are correct
B. Both are incorrect
\( c .1 \) is correct, 2 is incorrect
D. 1 is incorrect, 2 is correct


Choose the correct option for the flow of
energy in an ecosystem
A. Sun- - - >> Producer- - - - -> Herbivore- - - -> Carnivore
B. Producer - - - -> Herbivore- - - -> Carnivore- - - -> Sun
c. Herbivore- - - -> Carnivore- - - -> Sun- - - -> Producer
D. Carnivore- - - -> Sun- - - -> Producer- - - -> Herbivore


In periodic motion, the displacement is
A. directly proportional to the restoring force
B. inversely proportional to the restoring force
c. independent of restoring force
D. independent of any force acting on the particle


Which of the following is a polysaccharide?
A. Glucose
B. Fructose
c. sucrose
D. Cellulose


\( \cos 60^{0} \times \cos 30^{0}-\sin 60^{0} \times \sin 30^{0}=0 \)


The first order rate constant for the
decomposition of ethyl iodide by the
reaction \( C_{2} H_{5} I_{(g)} \rightarrow C_{2} H_{5(g)}+H I_{(g)} \)
at \( 600 K \) is \( 1.60 \times 10^{-5} S^{-1} \) Its energy of
activation is \( 209 \mathrm{kJ} / \mathrm{mol} \). Calculate the
rate constant of the reaction at \( 700 \mathrm{K} \)


The maximum height attained by a projectile is found to be equal to 0.433 of horizontal range. The angle of projection of this projectile is
A \( .30^{\circ} \)
В \( \cdot 45^{\circ} \)
\( c \cdot 60^{0} \)
D. \( 75^{\circ} \)


Find the median of the following set of values.
1) 83,66,86,30,82
2) 45,49,46,44,38,37,55,51
3) 70,71,70,68,67,69,70
4) 51,55,46,47,53,55,51,46


Assertion
Two identical blocks are placed over a
rough inclined plane. One block is given
an upward velocity and the other in downward direction. If \( \mu=\frac{1}{3} \) and \( \theta= \)
\( 30^{\circ} \) the ratio of magnitudes of
accelerations of two blocks is 2: 1
Reason
The desired ratio is \( \frac{1+\mu}{1-\mu} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Select correct statement.
A. Across a transition series (from Cr to CO), there is only a small decrease in atomic radius from one element to another due to very small increase in effective nuclear charge
B. The rate of decrease in the size across the lanthanide
series is less than the across the first transition series
C. Both A and B are correct statements
D. Both \( A \) and \( B \) are incorrect statements


In an experiment of verification of Ohm's law, following observations are obtained:
Potential difference \( 0.5 \quad 1.0 \quad 1.5 \) \( v \) (in volt')
Current in 0.2
\( 0.4 \quad 0.6 \)
ampere
What will be the current I when the
potential difference V is 0.75 V ?
A . \( 0.5 A \)
в. \( 0.3 A \)
c. \( 0.75 A \)
D. \( 0.6 A \)


\( H_{2} O_{2} \) is obtained by the action of dilute
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) on:
\( \mathbf{A} \cdot M n O_{2} \)
в. \( P b O_{2} \)
\( \mathrm{c} \cdot B a O_{2} \)
D. \( S n O_{2} \)


The sum of angles of a triangle is equal
to
A \( .90^{\circ} \)
B . \( 120^{\circ} \)
\( c \cdot 150^{\circ} \)
D. \( 180^{\circ} \)


Assertion
In Young's interference experiment fringes become brighter if one of the slits is covered by cellophone paper.
Reason
The intensity of light emerging from the slit increases and the two interfering
beams have unequal intensities.
A. Statement I is True and Statement 2 is True and is correct explanation of Statement 1
B. Statementl is True and Statement 2 is True but not the correct explanation of Statement t.
c. statement lis False and statement 2 is False
D. Statement lis True and Statement 2 is False


What odorant is added to LPG to detect
the leakage with smell?
A. alcohol
B. organo sulphur compounds
c. coal tar
D. chlorine gas


A point \( \boldsymbol{P}(\mathbf{2},-\mathbf{1}) \) is equidistant from
points \( (a, 7) \) and \( (-3, a) \). Find \( a \)


Which of the statements about the
reaction below are incorrect?
\( 2 P b O(s)+C(s) \rightarrow 2 P b(s)+C O_{2}(g) \)
(a) Lead is getting reduced.
(b) Carbon dioxide is getting oxidised.
(c) Carbon is getting oxidised.
(d) Lead oxide is getting reduced.
A \( \cdot(a) \) and \( (b) \)
B. (a) and (c)
\( c \cdot(a),(b) \) and \( (c) \)
D. All


Solve:
\( (b+c) \sin \frac{A}{2}=a \cos \frac{B-C}{2} \)


Simplify: \( (2) \frac{1}{4} .(4)^{\frac{1}{8}} .(8) \frac{1}{16} .(16)^{\frac{1}{32}} \)


Read the following statements and answer whether the given statement is true or false.
Lenz's law is used to find out the
magnitude of the induced e.m.f.
A. True
B. False


Which of the following electron transitions in hydrogen atom will require largest amount of energy?
A. From \( n=1 \) to \( n=2 \)
B. From \( n=2 \) to \( n=3 \)
c. From \( n=\infty \) to \( n=1 \)
D. From \( n=3 \) to \( n=5 \)


A solid metallic sphere of diameter
\( 28 c m \) is melted and recast into a
number of smaller cones, each of
diameter \( 4 \frac{2}{3} c m \) and height \( 3 c m . \) Find the number of cones so formed.


Two moving coil meters, \( M_{1} \) and \( M_{2} \)
have the following particulars:
\( \boldsymbol{R}_{1}=\mathbf{1 0} \boldsymbol{\Omega}, \boldsymbol{N}_{\mathbf{1}}=\mathbf{3 0} \)
\( \boldsymbol{A}_{\mathbf{1}}=\mathbf{3 . 6} \times \mathbf{1 0}^{-\mathbf{3}} \boldsymbol{m}^{\mathbf{2}}, \boldsymbol{B}_{\mathbf{1}}=\mathbf{0 . 2 5} \boldsymbol{T} \)
\( \boldsymbol{R}_{2}=\mathbf{1 4} \boldsymbol{\Omega}, \boldsymbol{N}_{2}=\boldsymbol{4} \boldsymbol{2} \)
\( \boldsymbol{A}_{2}=\mathbf{1 . 8} \times \mathbf{1 0}^{-\mathbf{3}}, \boldsymbol{B}_{\mathbf{2}}=\mathbf{0 . 5 0} \boldsymbol{T} \)
(The spring constants are identical for the two meters).Determine the ratio
of (a) current sensitivity and
(b) voltage
sensitivity of \( M_{2} \) and \( M_{1} \)


If \( 2\left[\begin{array}{ll}1 & 3 \\ 0 & x\end{array}\right]+\left[\begin{array}{ll}y & 0 \\ 1 & 2\end{array}\right]=\left[\begin{array}{ll}5 & 6 \\ 1 & 8\end{array}\right], \) then
the value of \( x \) and \( y \) are
A \( . x=3, y=3 \)
в. \( x=-3, y=3 \)
c. \( x=3, y=-3 \)
D. \( x=-3, y=-3 \)


The graph represented by equations \( x=\sin ^{2} t, y=2 \cos t \) is
A. hyperbola
B. sine graph
c. parabola
D. straight line


Two charges \( 5 \times 10^{-8} C \) and \( -3 x \)
\( 10^{-8} C \) are located \( 16 \mathrm{cm} \) apart. At what
point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
A. \( 20 \mathrm{cm} \) away from the positive charge on the side of negative charge
B. \( 40 \mathrm{cm} \) away from the negative charge on the side of positive charge
c. \( 40 \mathrm{cm} \) away from the positive charge on the side of negative charge
D. \( 20 \mathrm{cm} \) away from the negative charge on the side of positive charge


\( H_{2} O_{2} \) can be obtained when following
reacts with \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) except
with
A \( \cdot P b O_{2} \)
в. \( B a O_{2} \)
c. \( N a_{2} O_{2} \)
D. \( \operatorname{sr} O_{2} \)


For the given combination of gates, if
the logic states of inputs \( A, B, C \) are as
follows \( \boldsymbol{A}=\boldsymbol{B}=\boldsymbol{C}=\mathbf{0} \) and \( \boldsymbol{A}=\boldsymbol{B}= \)
\( 1, C=0 \) then the logic states of
output D are
A. 0,0
B. 0,1
\( c \cdot 1,0 \)
D. 1


Symbolic representation of NOR gate is?
\( A \)
в.
\( c \)
D.


The velocity distribution curve of the stream line flow of a liquid advancing through a capillary tube is:
A. Circular
B. eliptical
c. parabolic
D. a straight line


\( \int \frac{d x}{16 x^{2}-25} \)


MTP involves
A. Opening and dilating of the cervix to evacuate the uterus by suction.
B. Opening and dilating of the fallopian tube to evacuate the uterus by suction.
C. Opening and dilating of the vagina to evacuate the uterus by suction.
D. None of the above


For the reaction; \( \boldsymbol{A}+\boldsymbol{B} \rightleftharpoons \mathbf{3} \boldsymbol{C}, \) at \( \mathbf{2 5}^{\boldsymbol{o}} \boldsymbol{C} \)
a 3 litres vessel contains 1,2 and 4
moles of \( A, B \) and \( C \) respectively. If \( K_{c} \)
for the reaction is \( 10, \) the reaction will
proceed in :
A. forward reaction
B. backward direction
C. either direction
D. equilibrium


Give the formulae of the following complexes:
(i) ammineaquadibromidocopper (II)
(ii) potassium tetracyanocuperate (II)
(iii) diamminedichloridoplatinum (II)
(iv)potassiumpentacyanonitrosylferrat
\( e(11) \)
(v) amminechloridobis (ethane-1,2-
diamine)cobalt (III) ion
(vi) tetraamminedichloridocobalt (III)
ion


A metal sphere of \( 4 \mathrm{cm} \) radius is suspended within a hollow sphere of 6 cm radius. The inner sphere is charged
to potential 3 esu and the outer sphere is earthed. The charge on the inner sphere is
A . 54 esu
B. 1/4 esu
\( c . \) 30 esu
D. 36 esu


The solubility product of silver bromide
is \( 5.0 \times 10^{-13} . \) The quantity of
potassium bromide (molar mass is
\( \operatorname{taken} \operatorname{as} 120 \) g \( m o l^{-1} \) ) to be added to 1
liter of \( 0.05 \mathrm{M} \) solution of silver nitrate to
start the precipitate of AgBr is:
A \( .5 .0 \times 10^{-8} \mathrm{g} \)
B . \( 1.2 \times 10^{-10} \mathrm{g} \)
c. \( 1.2 \times 10^{-9} \mathrm{g} \)
D. \( 6.2 \times 10^{-5} \mathrm{g} \)


Bony plates along with scales is characteristic of
A. Seahorse
B. Eel
c. Hag fish
D. Flying fish


Evaluate \( \int_{0}^{x}[\cos t] d t, \) where \( n \in \)
\( \left(2 n \pi,(4 n+1) \frac{\pi}{2}\right), n \in N, \) and
denotes the greatest integer function.


How many valence electrons does the structure of \( \boldsymbol{S C l}_{\mathbf{6}} \) possess?
A . 118
B. 34
c. 48
D. 56


With the increase in temperature, the density of substance, in general,
A. increases
B. decreases
c. first increases then decreases
D. first decreases then increases


Which of the following does not exist in solid state at room temperature? This question has multiple correct options
A. \( 1,4- \) dichlorobenzene
B. 1,3 -dichlorobenzene
c. 1,2 -dichlorobenzene
D. All of the above


\( \left(\frac{1+i}{1-i}\right)^{4}+\left(\frac{1-i}{1+i}\right)^{4}= \)
A.
B.
\( c \cdot 2 \)
\( D \)


Find the unit vector perpendicular to the plane \( \vec{r} .(2 \hat{i}+\hat{j}+2 \hat{k})=5 \)


The coefficient of mutual induction
between two coils is 1.25 H. If the rate
of fall of current in the primary is 80 As
\( -1, \) then the induced emf in the
secondary coil will be
A. \( 100 V \)
в. \( 64 V \)
c. \( 12.5 V \)
D. \( 0.016 V \)


A mixture of iodine and sand can be
separated by:
A. separating funnel
B. magnetic separation
c. sublimation
D. centrifugation


Find \( x, \) if \( \triangle A B C \) is right-angled at \( A \)
where \( \boldsymbol{A} \equiv(\mathbf{4}, \mathbf{2}, \mathbf{3}), \boldsymbol{B} \equiv(\mathbf{3}, \mathbf{1}, \mathbf{8}), \boldsymbol{C} \equiv \)
\( (x,-1,2) \)


A factory has 500 workers, 15 percent of whom are women. If 50 additional
workers are to be hired and all of the
present workers remain, how many of the additional workers must be women
in order to raise the percent of women employees to 20 percent?
\( \mathbf{A} \cdot \mathbf{3} \)
B. 10
c. 25
D. 30
E. 35


Which is not a disproportionation
reaction?
\( A \)
B.
\[
\begin{array}{l}
\mathrm{CHO} \\
\mathrm{COOH}
\end{array}+\mathrm{OH}^{-} \longrightarrow \begin{array}{l}
\mathrm{CH}_{2} \mathrm{OH} \quad \mathrm{COO}^{-} \\
\mathrm{COO}^{-}+\mid \\
\mathrm{COO}^{-}
\end{array}
\]
c. \( N a H+H_{2} O \longrightarrow N a O H+H_{2} \)
D. All of the above


The maximum amount of sulphur is
given by:
\( \mathbf{A} \cdot A g S\left(K_{s p}=6 \times 10^{-29}\right) \)
B. \( C u S\left(K_{s p}=4 \times 10^{-27}\right) \)
C. \( P b S\left(K_{s p}=8 \times 10^{-28}\right) \)
D. \( Z n S\left(K_{s p}=8 \times 10^{-30}\right) \)


Two discs of moments of inertia \( I_{1} \) and
\( I_{2} \) about their respective axes (normal to the disc and passing through the centre), and rotating with angular
\( \operatorname{speeds} \omega_{1} \) and \( \omega_{2} \) are brought into contact face to face with their axes of
rotation coincident.
(a) What is the
angular speed of the two-disc system?
(b) Show that the kinetic energy of the combined system is less than the sum of the initial kinetic energies of the
two discs. How do you account for this
loss in energy? Take \( \omega_{1} \neq \omega_{2} \)


Distance between sun and earth is \( 2 \times \)
\( 10^{8} \mathrm{km}, \) temperature of sun \( 6000 \mathrm{K} \)
radius of \( \operatorname{sun} 7 \times 10^{5} \mathrm{km}, \) if emissivity
of earth is \( 0.6, \) then find out
temperature of earth in thermal
equilibrium.
A . 400 к
в. 300 к
\( c .500 k \)
D. 600 к


A river with an inflow of domestic
sewage rich in organic waste may
result in
A. Drying of the river very soon due to algal bloom
B. Increased population of aquatic food web organisms
c. An increased production of fish due to biodegradable nutrients
D. Death of fish due to lack of oxygen


0.2008 is equal to
A \( \cdot \frac{252}{1250} \)
в. \( \frac{251}{1250} \)
c. \( \frac{250}{1250} \)
D. None of these


The medians AD and BE of a triangle with vertices \( \boldsymbol{A}(\mathbf{0}, \boldsymbol{b}), \boldsymbol{B}(\mathbf{0}, \boldsymbol{0}) \) and
\( C(a, 0) \) are perpendicular to each other
if


An observer moves towards a stationary
source of sound with a speed1 \( / 5^{t h} \) of speed of sound. the wavelength and
frequency of the source emitted are \( \lambda \)
and f respectively. The apparent frequency recorded by the observer


A uniform wire is cut into two pieces
such that 1 piece is twice as long as the other. The 2 pieces are connected in
parallel in the left gap of meter bridge. When a resistance of \( 20 \Omega \) is connected
in the right gap, the neutral point is obtained at a distance of \( 60 \mathrm{cm} \) from
the right end of the wire. Find out the original resistance of wire before it was
cut into 2 pieces.


The rate of forward reaction is two
times that of the reverse reaction at a
given temperature and identical concentration, \( \mathrm{K} \) at equilibrium is:
A. 0.5
B. 1.5
\( c \cdot 2.5 \)
D. 2.0


In the case of renal failure and uraemia
which one of the following is employed?
A. Kindey replacement
B. Lithotripsy
c. Haemodialysis
D. Kidney removal


The relation between voltage sensitivity
\( \sigma_{v} \) and the current sensitivity \( \sigma_{i} \) of \( a \)
moving coil galvanometer is (Given that
\( G \) is the resistance of the
galvanometer)
A \( \cdot \sigma_{v}=G \sigma_{i} \)
в. \( \sigma_{v}=\frac{\sigma_{i}}{G} \)
\( \mathbf{c} \cdot \sigma_{v} \sigma_{i}=G \)
D. \( \sigma_{v} \sigma_{i}=\frac{1}{G} \)


Ascent of sap is due to which of the following force?
A. Imbibition
B. Cellular force
c. cohesive force
D. Atmospheric pressure


The time period of an earth's satellite in
circular orbit is independent of:
A. the mass of the satellite
B. radius of it's orbit
c. both the mass and radius of the orbit
D. neither the mass of the satellite nor the radius of its orbit


The presence of polar bonds in a
polyatomic molecule suggests that the molecule has non-zero dipole moment.
If true enter 1 , else enter 0 .


Which of the following inert gas participate in chemical reaction?
A. \( X e \)
в. \( H e \)
c. \( N e \)
D. None


Axis of Inflorescence is
A. Pedicle
B. Peduncle
c. Petiole
D. All of the above


Define the term "tissue""


Amoeba reacts
A. Negatively to strong light and positively to weak light
B. Positively to strong light and negatively to weak light
C. Unaffected by light intensity
D. Positive to both strong and weak light


Specific heat capacity of a substance \( A \) is \( 3.8 J g^{-1} K^{-1} \) and of substance \( B \) is
\( 0.4 J g^{-1} K^{-1} \) is a good conductor of heat?
\( A \cdot A \)
B. B
c. both A \& B are equally good
D. cant say


If electron charge e, electron mass \( \mathrm{m} \) speed of light in vacuum c and Planck's constant \( h \) are taken as fundamental
constant \( h \) are taken as fundamental
quantities, the permeability of vacuum
\( \mu_{0} \) can be expressed in units of
\( ^{\mathrm{A}} \cdot\left(\frac{m c^{2}}{h e^{2}}\right) \)
в. \( \left(\frac{h}{m e^{2}}\right) \)
c. \( \left(\frac{h c}{m e^{2}}\right) \)
D \( \cdot\left(\frac{h}{c e^{2}}\right) \)


Which substance is a polar, molecular
compound?
A. \( B e C l_{2} \)
в. \( C H_{2} \) О
c. \( M g F_{2} \)
D. \( C_{2} H_{2} \)


Assertion
Conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) as a drying agent.
Reason
HCl prepared from NaCl is dried by passing through conc.sulphuric acid.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The number of structural isomers for
\( C_{4} H_{10} O \) are:
\( A \cdot 6 \)
B. 7
\( c \cdot 4 \)
D. 5


8
\( \infty \)
\( \infty \)
\( \infty \)
0


Identify the low-cost onsite sewage disposal system.
A. Septic tank
B. Composting pits
c. chemical toilets
D. All of the above


A wire loop \( P Q R S \) formed by joining
two semi-circular wires of radii \( \boldsymbol{R}_{1} \) and
\( R_{2} \) carries a current \( I \) as shown in the
following diagram. The magnetic
induction at the centre \( O \) is
A \( \cdot \frac{\mu_{0} I}{4 R_{1}} \)
в. \( \frac{\mu_{0} I}{4 R_{2}} \)
c. \( \frac{\mu_{0}}{4 \pi} I\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right) \)
D \( \cdot \frac{\mu_{0}}{4} I\left(\frac{1}{R_{1}}+\frac{1}{R_{2}}\right) \)


Choose the correct answer from the
alternatives given. In order establish an instantaneous
displacement current of 1 mA in the space between the plates of \( 2 \mu F \) parallel plate capacitor. the rate of change of potential difference is:
A \( \cdot 100 \mathrm{V} 5^{-1} \)
B . \( 200 \mathrm{V} 5^{-1} \)
c. \( 300 V 5^{-1} \)
D. \( 500 \mathrm{V} 5^{-1} \)


The fluid itself exerts pressure whose
force component is equal to its Complete the
sentence.
A . Height
B. Weight
c. Depth
D. None


A thin circular ring of area \( A \) is held
perpendicular to a uniform magnetic
field of induction \( B \). A small cut is
made in the ring and a galvanometer is connected across the ends such that
the total resistance of the circuit is \( \boldsymbol{R} \)
When the ring suddenly squeezed to
zero area, the charge flowing through the galvanometer is :
A \( \cdot \frac{B R}{A} \)
\( \mathbf{B} \cdot(A B) / R \)
c. \( A B R \)
D \cdot \( \left(E^{2} A\right) / R^{2} \)
E . none


Explain why pure liquids and solids can
be ignored while writing the equilibrium constant expression.


The vertices of the triangle \( A B C \) are
\( (2,1,1),(3,1,2),(-4,0,1) . \) The area of
triangle is
A \( \cdot \frac{3 \sqrt{38}}{2} \)
B. \( \sqrt{38} \)
c. \( \frac{\sqrt{38}}{2} \)
D. 4


8
\( x \)
\( \frac{\pi}{\sigma} \)


Rate constant for a reaction \( \boldsymbol{H}_{2}+\boldsymbol{I}_{2} \rightleftharpoons \)
\( 2 H I \) is \( 49, \) then rate constant for
reaction \( 2 H I \rightleftharpoons H_{2}+I_{2} \) is :
\( A \cdot 7 \)
B. 1/49
\( c \cdot 49 \)
D. 21


What is the colour of the mass obtained
when potassium permanganate is decomposed?
A. Pink
B. Purple
c. Green
D. Black


Explain the term 'Organic Chemistry'


Consider a classroom of dimensions
\( (5 \times 10 \times 3) m^{3} \) at temperature \( 20^{\circ} C \)
and pressure 1 atm. There are 50 people in the room, each losing energy at the average of 150 watts. Assuming that the walls, ceiling, floor, and furniture are perfectly insulated and none of them is absorbing heat. How much time will be needed for raising the temperature of air in the room to the
body temperature \( \left(37^{\circ} C\right) ?\left[\text { For air } C_{p}=\right. \) \( \frac{7}{2} R \) and neglect the loss of air to the outside as the temperature rises
A .422 sec
в. \( 411.3 \mathrm{sec} \)
c. \( 421.1 \mathrm{sec} \)
D. \( 413.1 \mathrm{sec} \)


You are given a hammer, a battery, a bulb, wires and a switch.
(a) How could you use them to distinguish between samples of metals
and non-metals?
(b) Assess the usefulness of these tests
in distinguishing between metals and
non-metals.


The prime contaminants in the lakes undergone eutrophication by sewage and agricultural wastes are
A. Sulphates and phosphates
B. Nitrates and sulphates
c. Nitrates and phosphates
D. Nitrates and carbonates


If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) is a differentiable function
such that \( f^{\prime}(x)>2 f(x) \) for all \( x \in R \)
and \( f(0)=1, \) then
This question has multiple correct options
A \( \cdot f(x) \) is decreasing in \( (0, \infty) \)
B \( \cdot f^{\prime}(x)<e^{2 x} \) in \( (0, \infty) \)
C \( \cdot f(x) \) is increasing in \( (0, \infty) \)
D. \( f(x)>e^{2 x} \) in \( (0, \infty) \)


Simplify: \( \sqrt{\boldsymbol{x}^{2}}+\sqrt{\boldsymbol{y}^{2}}-\boldsymbol{x}-\boldsymbol{y}+ \)
\( \sqrt{(\boldsymbol{a}+\boldsymbol{b})^{2}} \)


Choose the correct answers from the
alternatives given

Name the process by which the suns energy is trapped as the source of energy used by virtually all living organisms
A. Metabolism
B. Glycolysis
c. Homeostasis
D. Photosynthesis


Photosynthesis is a/an
A. Reduction reaction
B. Oxidation reaction
c. oxidation-reduction reaction
D. None of the above.


If the angle of a prism is \( 60^{\circ} \) and angle
of minimum deviation is \( 40^{\circ}, \) then the
angle of refractive in the prism will be
A \( .30^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 50^{\circ} \)
D. 20


Which of the following reactions is not
correct?
\( \mathbf{A} \cdot M n O_{4}^{-}+8 H^{+}+5 F e^{2+} \rightarrow 5 F e^{3+}+M n^{2+}+4 H_{2} O \)
B \( \cdot 2 M n O_{2}+4 K O H+O_{2} \rightarrow 4 K M n O_{4}+2 H_{2} O \)
\( \mathbf{c} \cdot 2 N a_{2} C r O_{4}+2 H^{+} \rightarrow N a_{2} C r_{2} O_{7}+2 N a^{+}+H_{2} O \)
D. \( K_{2} C r_{2} O_{7}+7 H_{2} S O_{4}+6 K I \rightarrow 4 K_{2} S O_{4}+ \)
\( C r_{2}\left(S O_{4}\right)_{3}+3 I_{2}+7 H_{2} O \)


Two sound sources are moving in
opposite direction with velocity \( v_{1} \) and
\( v_{2}\left(v_{1}>v_{2}\right) . \) Both are moving away from
a stationary observer.the frequency of
both the source is 900 Hz.What is the
value of \( v_{1}-v_{2} \) so that the beat
frequency observed will be \( 6 H z ? \)
Speed of sound \( =300 m s^{-1} \)
A \( \cdot 1 \mathrm{ms}^{-1} \)
B. \( 4 m s^{-1} \)
c. \( 3 m s^{-1} \)
D. \( 2 m s^{-1} \)


What is conservation?


The piston in the cylinder head of a locomotive has a stroke of 6 m. If the
piston executing simple harmonic motion with an angular frequency of
200 rad \( m i n^{-1}, \) its maximum speed is
A \( .5 \mathrm{ms}^{-1} \)
B . \( 10 \mathrm{ms}^{-1} \)
c. \( 15 \mathrm{ms}^{-1} \)
D. \( 20 m s^{-1} \)


A ball dropped from one metre above the top of a window, crosses the window in
\( t_{1} s . \) If the same ball is dropped from \( 2 m \) above the top of the same window,
time taken by it to cross the window is
\( t_{2} s . \) Then
\( \mathbf{A} \cdot t_{2}=t_{1} \)
в. \( t_{2}=2 t \)
c. \( t_{2}>t_{1} \)
D \( \cdot t_{2}<t_{1} \)


If the energy difference between two electronic states is 46.12 kcal/mol;
What will be the frequency of light emitted when the electrons dropped from higher to lower states \( (N h= \)
\( 9.52 \times 10^{-14} \) kcal sec mol \( ^{-1} \) ) where \( N \)
is the Avogadro number


The radioactivity of a sample is \( \boldsymbol{R}_{1} \) at a
time \( T_{1} \) and \( R_{2} \) at a time \( T_{2} . \) If the half-
life of the specimen is \( T, \) the number of atoms that have disintegrated in the \( \operatorname{time}\left(T_{2}-T_{1}\right) \) is proportional to:
A \( . R_{1} T_{1}-R_{2} T_{2} \)
B \( . R_{1}-R_{2} \)
c. \( \frac{\left(R_{1}-R_{2}\right)}{T} \)
D. \( \left(R_{1}-R_{2}\right) T \)


The number of antibonding electrons
present in \( O_{2} \) molecular ion is:
A . 8
B. 6
\( c .5 \)
D. 4


If by selling 110 mangoes, the \( \mathrm{CP} \) of 120 mangoes is realised, the gain per cent is
A \( \cdot_{9} \frac{1}{11} \% \)
в. \( 9 \frac{1}{9} \% \)
\( \mathrm{c} \cdot_{10} \frac{10}{11} \% \)
D. \( 11 \frac{1}{9} \% \)


Find magnification for lens.
\( A \)
B.
\( c \cdot 7 \)
D. 12


Galilee's law of inertia is another name
for newton's (...) law of motion.
A. First
B. second
c. Third
D. Anyone of the above


Draw a \( \triangle A B C \) in which \( B C= \)
\( \mathbf{6} c \boldsymbol{m}, \boldsymbol{A} \boldsymbol{B}=\mathbf{4} \boldsymbol{c m} \) and \( \boldsymbol{A} \boldsymbol{C}=\mathbf{5} \boldsymbol{c m} \)
Draw a triangle similar to \( \triangle A B C \) with its sides equal to \( \left(\frac{3}{4}\right)^{t h} \) of the corresponding sides of \( \triangle \boldsymbol{A B C} \)


If the vectors \( 2 i+\lambda j-k \) and \( 2 i-2 j+ \)
\( 2 k \) are perpendicular to each other then
find \( \lambda \)


Catalytic decomposition of nitrous
oxide by gold at \( 900^{\circ} \mathrm{C} \) at an initial pressure of \( 200 \mathrm{mm}, \) was \( 50 \% \) in 53 minutes and \( 73 \% \) in 100 minutes.
Velocity constant of the reaction is:
[Note: assume decomposition as the first order.
A \( .1 .308 \times 10^{-2} \)
В. \( 2.317 \times 10^{-2} \)
c. \( 3.208 \times 10^{-3} \)
D. none of these


A NOR gate and a NAND gate are connected as shown in the figure. Two different sets of inputs are given to this setup. In the first case, the inputs to the gates are \( \boldsymbol{A}=\mathbf{0}, \boldsymbol{B}=\mathbf{0}, \boldsymbol{C}=\mathbf{0} . \) In the
second case, the inputs are \( \boldsymbol{A}=\mathbf{1}, \boldsymbol{B}= \)
\( 0, C=1 . \) The output \( D \) in the first case
and second case respectively are:
A. 0 and 0
B. 0 and 1
c. 1 and 0
D. 1 and 1


Find a point on \( \boldsymbol{y}-\boldsymbol{a} \boldsymbol{x} \boldsymbol{i} \boldsymbol{s} \) which is
equidistant from (-5,-2) and (3,2)


The vapour pressure of mercury is 0.002
\( \mathrm{mm} \) at \( 27^{\circ} \mathrm{C} \cdot \boldsymbol{H} \boldsymbol{g}(\boldsymbol{I}) \rightleftharpoons \boldsymbol{H} \boldsymbol{g}(\boldsymbol{g}) . \) The
value of equilibrium constant \( \boldsymbol{K}_{C} \) is:
A \( \cdot 1.07 \times 10^{-7} \)
B. \( 3.95 \times 10^{-5} \)
c. \( 8.12 \times 10^{-5} \)
D. \( 2.63 \times 10^{-6} \)


Detergents are:
A. ammonium or sulphonate salts of long chain carboxylic acids
B. ammonium or sodium salts of long chain carboxylic acids
C. ammonium or calcium salts of long chain carboxylic acids
D. ammonium or magnesium salts of long chain carboxylic acids


Four phases of cell cycle in sequence
are
A \( \cdot G_{1} \rightarrow S \rightarrow G_{2} \rightarrow M \)
B . \( S \rightarrow G_{1} \rightarrow G_{2} \rightarrow M \)
\( \mathbf{c} \cdot G_{1} \rightarrow G_{2} \rightarrow S \rightarrow M \)
D. \( M \rightarrow G_{1} \rightarrow G_{2} \rightarrow S \).


What is \( \left[\boldsymbol{H}^{+}\right] \) in mol/L of a solution that
is \( 0.20 \mathrm{M} \) in \( C H_{3} C O O N a \) and \( 0.10 \mathrm{M} \) in
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H} ? \)
\( \boldsymbol{K}_{a} \) for \( \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C O O H}=\mathbf{1 . 8} \times \mathbf{1 0}^{-\mathbf{5}} \)
A \( .3 .5 \times 10^{-4} \)
В. \( 1.1 \times 10^{-5} \)
c. \( 1.8 \times 10^{-5} \)
D. \( 9.0 \times 10^{-6} \)


Which of the following is a quadratic polynomial in one variable?
A. \( \sqrt{2 x^{3}}+5 \)
.
B. \( 2 x^{2}+2 x^{-2} \)
c. \( x^{2} \)
D. \( 2 x^{2}+y^{2} \)


The probability that a student will pass
the final examination in both English and Hindi is 0.5 and the probability of passing neither is \( 0.1 . \) If the probability of passing the English examination is 0.75 What is the probability of passing the Hindi examination


The value of \( \log _{10} \mathrm{K} \) for a reaction \( \boldsymbol{A} \longrightarrow \boldsymbol{B} \) is :
\( \left(\text { Given }: \Delta_{\mathrm{r}} \mathbf{H}_{298 \mathrm{K}}^{\circ}=\right. \)
\( -\mathbf{5 4 . 0 7 k J m o 1}^{-1}, \quad \Delta_{\mathbf{r}} \mathbf{S}_{298 K}^{0}= \)
\( 10 \mathrm{JK}^{-1} \mathrm{mol}^{-1} \) and
\( \mathbf{R}=\mathbf{8 . 3 1 4} \mathbf{J K}^{-1} \mathbf{m o 1}^{-1} ; \quad \mathbf{2 . 3 0 3} \times \)
\( 8.314 \times 298=5705) \)
A. 5
B. 10
c. 95
D. 100


Bleaching powder is used:
This question has multiple correct options
A. for bleaching cotton, wood pulp
B. as a disinfectant and germicide
C. for the manufacture of chloroform
D. as a reducing agent in industries


A die is thrown. Find the probability of getting a prime number.


toppr
Q Type your question
does this affect the size and intensity of
the central diffraction band?
(b) In what way is diffraction from each
slit related to the interference pattern in a double-slit experiment?
(c) When a tiny circular obstacle is placed in the path of light from a distant source, a bright spot is seen at the centre of the shadow of the obstacle.
Explain why?
(d) Two students are separated by a \( 7 \mathrm{m} \) partition wall in a room \( 10 \mathrm{m} \) high. If both light and sound waves can bend
around obstacles, how is it that the
students are unable to see each other
even though they can converse easily.
(e) Ray optics is based on the assumption that light travels in a straight line. Diffraction effects (observed when light propagates through small apertures/slits or around small obstacles) disprove this assumption. Yet the ray optics assumption is so commonly used in understanding location and several other properties of images in optical instruments. What is the justification?


Why is water not used as solvent
synthesis of Grignard reagent?


What are the solution(s) to the system
of equations \( \boldsymbol{y}=\boldsymbol{x}^{2}-\mathbf{9} \) and \( \boldsymbol{y}-\boldsymbol{3}= \)
\( x ? \)
A. -3,0 and 4,7
в. -3,0
c. 4,7
D. 4,-3


Four point charges \( -Q,-q, 2 q \) and \( 2 Q \) are placed, one at each corner of the square. The relation between \( Q \) and \( q \) for
which the potential at the centre of the square is zero is
A. \( Q=-q \)
в. \( Q=-\frac{1}{q} \)
c. \( Q=q \)
\( \mathrm{D} \cdot Q=\frac{1}{q} \)


For driving current of \( 2 A \) for 6 minute in a circuit. \( 1000 J \) of work is to be done.
The e.m.f. of the source in the circuit is
A . \( 1.38 V \)
в. \( 1.68 V \)
c. \( 2.03 V \)
D. 3.10V


Define:
(a) Saturated hydrocarbon.
(b) Unsaturated hydrocarbon.
(c) Catenation.


\( \int \frac{e^{x}(1+x)}{\cos ^{2}\left(x e^{x}\right)} d x \)


The ratio of the base and height of a parallelogram is \( 5: 2 . \) If area of the
parallelogram is \( 1000 m^{2} \), find the base
and height?


The relationship between osmotic pressure at \( 273 \mathrm{K} \) when 10 g glucose
\( \left(P_{1}\right), 10 \) g urea \( \left(P_{2}\right) \) and 10 g sucrose
\( \left(P_{3}\right) \) are dissolved in \( 250 \mathrm{mL} \) of water is
A \( . P_{1}>P_{2}>P_{3} \)
в. \( P_{3}>P_{1}>P_{2} \)
c. \( P_{2}>P_{1}>P_{3} \)
D. \( P_{2}>P_{3}>P_{1} \)


Name the principle on which metre bridge is based.


If the de Broglie wavelength of the
electron in \( n^{t h} \) Bohr orbit in a
hydrogenic atom is equal to \( 1.5 \pi a_{0}\left(a_{0}\right. \)
is Bohr radius), then the value of \( n / z \) is:
A . 1.0
в. 0.75
c. 0.40
D. 1.50


A small body of mass 10 gram is making harmonic oscillations along a straight line with a time period of \( \frac{\pi}{4} \) and the maximum displacement is 10 cm. The energy of oscillation is
в. \( 0.16 \times 10^{-2} \mathrm{J} \)
c. \( 0.6 \times 10^{-2} J \)
D. \( 0.56 \times 10^{-2} J \)


A transverse sinusoidal wave moves
along a string in the positive x-direction at a speed of \( 10 \mathrm{cm} / \mathrm{s} \). The wavelength
of the wave is \( 0.5 m \) and its amplitude is
10cm. At a particular time \( t \), the snap shot of the wave is shown in figure.
The velocity of point P when its
displacement is \( 5 c m \) is
A \( \cdot \frac{\sqrt{3} \pi}{50} \hat{j} m / s \)
B. \( -\frac{\sqrt{3} \pi}{50} \hat{j} m / s \)
c. \( \frac{\sqrt{3} \pi}{50} \hat{i} m / s \)
D. \( -\frac{\sqrt{3} \pi}{50} \hat{i} m / s \)


When 5 V potential difference is applied
across a wire of length \( 0.1 \mathrm{m} \), the drift speed of electrons is \( 2.5 \times 10^{-4} m s^{-1} . \) If
the electron density in the wire is \( 8 x \)
\( 10^{28} m^{-3}, \) the resistivity of the material
is close to:
A \( \cdot 1.6 \times 10^{-7} \Omega \) m
В \( \cdot 1.6 \times 10^{-6} \Omega \) m
c. \( 1.6 \times 10^{-5} \Omega \) m
D. \( 1.6 \times 10^{-8} \Omega \) m


Assertion
Graphite cannot be converted into
diamond.
Reason
Graphite is conducting in nature.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Both Assertion and Reason are incorrect.


Which of the following are correct?
This question has multiple correct options
A. An astronaut going from the earth to the Moon will experience weightlessness once.
B. When a thin uniform spherical shell gradually shrinks maintaining its shape, the gravitational potential at its centre decreases
C. In the case of a spherical shell, the plot of \( V \) versus \( r \) is continuous.
D. In the case of a spherical shell, the plot gravitational field intensity \( I \) versus \( r \) is continuous


In an equilibrium reaction for which
\( \Delta G^{\circ}=0 . \) Determine the value of
equilibrium constant \( \mathrm{K} . \delta G=0 \)
A . 1.0
B. 2.7
\( c .7 .6 \)
D. 8.5


\( \mathbf{1}+\mathbf{4}+\mathbf{1 0}+\mathbf{1 9}+\ldots \frac{\mathbf{3} \boldsymbol{n}^{2}-\mathbf{3} \boldsymbol{n}+\mathbf{2}}{\mathbf{2}}= \)
A \( \cdot \frac{n^{2}\left(n^{2}+1\right)}{2} \)
B \( \cdot \frac{n\left(n^{2}+1\right)}{2} \)
c. \( \frac{n^{2}(n+1)}{2} \)
D. \( \left\{\frac{n(n+1)}{2}\right\}^{2} \)


Mention one application of the property of adsorption of gas by charcoal


Breathing by ribs is more pronounced in
A. Male
B. Female
c. Pregnant female
D. None of the above


At a place the angle of dip is \( 30^{\circ} \). If the horizontal component of the earth's magnetic field is \( H, \) then the total field
intensity will be given by
A \( \cdot \frac{H}{2} \)
в. \( \frac{2 H}{\sqrt{3}} \)
c. \( \frac{H}{\sqrt{2}} \)
D. \( H \sqrt{2} \)


Assertion
Ferro-magnetic substances become paramegnetic above Curie temp
Reason

Domains are destroyed at high
temperature.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A disc, sliding on an inclined plane, is found to have its position (measured from the top of the plane) at any instant
given by \( \boldsymbol{x}=\mathbf{3} \boldsymbol{t}^{2}+\mathbf{1} \) where \( \boldsymbol{x} \) is in meter
and \( t \) in second. Its average velocity in
the time interval between 2 s to 2 is
\( \mathbf{A} \cdot 10.2 \mathrm{ms}^{-1} \)
B . \( 15.5 \mathrm{ms}^{-1} \)
\( \mathbf{c} \cdot 12.3 \mathrm{ms}^{-1} \)
D. \( 9.7 m s^{-1} \)


Which of the two, sperm or egg cell (ovum), decides the sex of the child?


A gas at temperature \( 27^{\circ} \mathrm{C} \) and pressure
30 atmospheres is allowed to expand to one atmospheric pressure. If the volume becomes 10 times its initial volumes, the
final temperature becomes:
\( A \cdot 100^{\circ} \mathrm{C} \)
в. з7з к
c. \( 373^{\circ} \mathrm{C} \)
D. \( -173^{\circ} \mathrm{C} \)


The shape of \( X e O_{2} F_{2} \) molecule is:
A. trigonal bipyramidal
B. square planar
c. tetrahedral
D. see-saw


Molecular mass of dry air is
A. less than moist air
B. greater than moist air
C . equal to moist air
D. may be greater or less than moist air


Choose the correct increasing order of density of the following compound.
A \( \cdot C_{3} H_{7} C l<C_{3} H_{7} I<C H_{2} C l_{2}<C C l_{4} \)
в. \( C_{3} H_{7} I<C_{3} H_{7} C l<C H_{2} C l_{2}<C C l_{4} \)
c. \( C_{3} H_{7} I<C_{3} H_{7} C l<C C l_{4}<C H_{2} C l_{2} \)
D. \( C C l_{4}<C H_{2} C l_{2}<C_{3} H_{7} I<C_{3} H_{7} C l \)


Which one of the following reactions is an example for calcination process?
A \( \cdot 2 A g+2 H C l+(O) \rightarrow 2 A g C l+H_{2} O \)
в. \( 2 Z n+O_{2} \longrightarrow 2 Z \) пО
\( \mathrm{c} \cdot 2 Z n S+3 O_{2} \rightarrow 2 Z n O+2 S O_{2} \)
D. \( M g C O_{3} \rightarrow M g O+C O_{2} \)


Chlorophyll, the green component of plants contains:
A \( \cdot C a^{2} \)
B. \( B e^{2} \)
c. \( M g^{2+} \)
D. \( B a^{2} \)


The first element of a group in many ways differs from the other heavier
members of the group. This is due to:
This question has multiple correct options
A. the smaller size
B. the high electronegativity and high ionisation potential
c. the unavailability of d-orbitals
D. the higher shielding effect


The properties of the elements, as well as the formulae and properties of their compounds depend in a periodic manner on the atomic weights of the elements. This periodic law was given by :
A. J. Lothar Meyer
B. John A. R. Newlands
c. Dobernier
D. D.I. Mendleev


The common oxidation states exhibited
by VA group elements are:
\( A \cdot+3 \) and +5
\( B \cdot+3 \) and +4
\( c \cdot+1 \) and +3
\( D \cdot+3 \) and -5


Find the two third life \( \left(t_{2 / 3}\right) \) of a first order reaction in which \( \boldsymbol{K}=\mathbf{5 . 4 8} \times \)
\( 10^{-14} s e c^{-1} \)
A \( \cdot t_{2 / 3}=5 \times 10^{13} \) sec
B . \( t_{2 / 3}=2 \times 10^{13} \) sec
C \( \cdot t_{2 / 3}=1.25 \times 10^{13} \mathrm{sec} \)
D. none of these


The seventh term of a G.P. is 8 times the
fourth term and 5th term is \( 48 . \) Find the
G.P.


A positively charged particle (proton) is projected towards east.The magnetic field is towards south.The particle will
be deflected towards
A. North
B. Down
c. up
D. west


Tell whether the following is certain to happen, possible can happen but not certain.

A die when tossed shall land up with 8 on top.


The S.I. unit of weight is:
A. kilogram
B. gram
c. newton
D. milligram


A person is throwing two balls in the air one after the other. He throws the
second ball when the first ball is at the
highest point. If he is throwing the balls every second, how high do they rise?
\( A \cdot 5 m \)
B. 3.75 m
c. \( 2.50 \mathrm{m} \)
D. 1.25 \( m \)


When a conductance cell was filled with
\( 0.0025 \mathrm{M} \) solution of \( \mathrm{K}_{2} \mathrm{SO}_{4} \), its
resistance was 326 ohm. Length of cell
\( =100 \mathrm{cm} \) and cross-sectional area \( 2.14 \times \)
\( 10^{-4} \mathrm{cm}^{2} . \) The specific resistance of \( \mathrm{K}_{2} \mathrm{SO}_{4} \)
is:
\( \mathbf{A} \cdot 4.994 \times 10^{-4} \)
B . \( 5.997 \times 10^{-4} \)
\( \mathbf{c} \cdot 6.997 \times 10^{-4} \)
D. \( 7.997 \times 10^{-4} \)


A body starts from rest and moves with a uniform acceleration. The ratio of the
distance covered in the \( n \) th second to
distance covered in \( n \) seconds is
A \( \cdot \frac{2}{n}-\frac{1}{n^{2}} \)
в. \( \frac{1}{n^{2}}-\frac{1}{n} \)
c. \( \frac{2}{n^{2}}-\frac{1}{n} \)
D. \( \frac{2}{n}+\frac{1}{n^{2}} \)


The coefficient of \( \boldsymbol{x}^{r}[\mathbf{0} \leq \boldsymbol{r} \leq \boldsymbol{n}-\mathbf{1}] \) in
the expression of \( (x+2)^{n-1}+(x+ \)
2) \( ^{n-2} \cdot(x+1)+(x+2)^{n-3} \cdot(x+1)^{2}+ \)
\( \ldots+(x+1)^{n-1} \) is
A \( \cdot^{n} C_{r}\left(2^{r}-1\right) \)
B. \( ^{n} C_{r}\left(2^{n-r}-1\right) \)
c. \( ^{n} C_{r}\left(2^{r}+1\right) \)
D. \( ^{n} C_{r}\left(2^{n-r}+1\right) \)


Which of the following choices correctly
ranks these objects by increasing moments of Inertia?
\( A \cdot B, D, A, C, E \)
B. D, B, E, A, C
\( c \cdot B, D, E, A, C \)
D. B, D, A, E, C
E. D, B, A, E, C


(i) In a cathode ray tube what is the function of anode?
(ii) State the energy conversion taking place in a cathode ray tube.
(iii) Write one use of cathode ray tube.


Why do some metals conduct heat
better than others?
A. Because of free electrons
B. Because they do not have any free electrons
C. Because of the difference in the strength of metals
D. All of above


Which one of the following statements
about NO is wrong?
A. NO is an odd electron molecule
B. It is a free radical and highly reactive
C. It readily forms complexes with transition metal ions
D. It can be prepared by heating \( N H_{4} N O_{3} \) at \( 250^{\circ} C \)


Aluminium can be used as a reducing agent for extraction of metals that are:
A. above aluminium
B. below aluminium
c. both \( A \) and \( B \)
D. none of above


Which functional group is present in a
molecule of \( \boldsymbol{C H}_{3} \boldsymbol{O C H}_{2} \boldsymbol{C H}_{3} \) ?
\( A \). Ether
B. Carboxy!
c. Ketone
D. Aldehyde
E. Ester


Heart of the prawn carries
A. Oxygenated bloodd
B. Deoxygenated blood
c. Mixed blood
D. No blood


Observe the reflex arc pathway shown in
the flow the chart given below. Which of
the following is represented by \( X \) and \( Y ? \)
\begin{tabular}{|l|l|}
\hline \multicolumn{2}{|l|} {\multirow{2}{*} { Hot plate \( \rightarrow \) Receptors }\text { Hot plate } \rightarrow \text { Receptors }} \\
\cline { 2 - 3 } & \\
\hline Response & Effectors \\
\hline
\end{tabular}
A. \( x \) - Brain, Y - Sensory neuron
B. X - Spinal cord, Y - Motor neuron
c. \( x \) - Brain, \( Y \) - Motor neuron
D. \( x \) - sensory neuron, Y - spinal cord


is used in making electromagnets.


Active mass of \( 5 g \) CaO is:
A . 56
B.
\( c .3 .5 \)
D. 2


crystallised the TMV and found it to be largely composed of
A. Ivanowsky, RNA
B. Beijerinck, DNA
c. Twort, protein
D. Stanley, protein


State whether true or false:
The magnification produced by a spherical mirror is the ratio of the height of the image to the height of the object.
A. True
B. False


If \( \mathbf{A}-\mathbf{2 B}=\left[\begin{array}{cc}\mathbf{1} & -\mathbf{2} \\ \mathbf{3} & \mathbf{0}\end{array}\right] \) and \( \mathbf{2} \mathbf{A}-\mathbf{3} \mathbf{B}= \)
\( \left[\begin{array}{cc}-\mathbf{3} & \mathbf{3} \\ \mathbf{1} & \mathbf{- 1}\end{array}\right], \) then \( \mathbf{B}= \)
A \( \cdot\left[\begin{array}{cc}-5 & 7 \\ 5 & 1\end{array}\right] \)
B. \( \left[\begin{array}{cc}-5 & 7 \\ -5 & -1\end{array}\right] \)
c. \( \left[\begin{array}{cc}-5 & 7 \\ 5 & -1\end{array}\right] \)
D. \( \left[\begin{array}{cc}-5 & -7 \\ -5 & -1\end{array}\right] \)


Statement I : The reactivity of powdered zinc will be greater than the larger piece of zinc of the same mass with \( H C l \)
Statement II : The larger piece of zinc of the same mass has more surface area
than the powdered zinc.
A. True, False
B. False, True
c. True, True
D. False, False


In comparative study of grassland, arid
pond ecosystems
A. Biotic components are almost similar
B. Abiotic components are almost similar
C. Primary and secondary consumers are similar
D. Biotic and abiotic components are different


Identify an extensive property amongst the following.
A. Viscosity
B. Heat capacity
c. Density
D. Surface tension


Solve: \( \int \frac{\log x}{(1+\log x)^{2}} d x \)


Metals exhibit ..... oxidation states in
their compounds.
A. Positive
B. Negative
c. Neutral
D. none of these


A bomb of mass \( \mathrm{m} \) at rest at the
coordinate
origin explodes into three equal pieces. At a certain instant one piece is on the
\( \mathbf{x} \) -axis at \( \boldsymbol{x}=\mathbf{4 0} \boldsymbol{c m} \) and another is at
\( \boldsymbol{x}=\mathbf{2 0} \boldsymbol{c m}, \boldsymbol{y}=-\mathbf{6 0} \boldsymbol{c m} . \) The position
of the third piece is:
A. \( x=60 \mathrm{cm}, y=60 \mathrm{cm} \)
в. \( x=-60 \mathrm{cm}, y=-60 \mathrm{cm} \)
c. \( x=60 \mathrm{cm}, y=-60 \mathrm{cm} \)
D. \( x=-60 c m, y=60 c m \)


Which of the following will not be
oxidised by \( \mathrm{O}_{3} ? \)
A . KI
в. \( \mathrm{FeSO}_{4} \)
\( c \cdot \) кмпО
D. \( \mathrm{K}_{2} \mathrm{Mn} \mathrm{O}_{4} \)


pH of \( 0.1 \mathrm{M} \) solution of \( N a A \) (sodium
salt of a weak acid \( H A \) ) is 8.92

Calculate \( p K_{a} \) of \( H A \). If a drop of HPh
\( \left(p K_{i n}=9.52\right) \) be added to the above
solution, predict whether the pink colour will visible or not under the
medical fact that our eyes can see the pink colour if the mole \( \% \) of ionized form
of indicator is \( 25 \% \) or more.
A. Pink colour will be visible
B. Pink colour will not be visible
c. cannot be predicted
D. None of the above


Which one of the following statement(s)
is/are true?
This question has multiple correct options
\( \mathbf{A} \cdot \Delta E=0 \) for combustion of \( C_{2} H_{6}(g) \) in a sealed rigid
adiabatic container
\( \mathbf{B} \cdot \Delta_{f} H^{o}(S, \text { monolithic}) \neq 0 \)
C . If dissociation energy of \( C H_{4}(g) \) is \( 1656 k J / \) mol and
\( C_{2} H_{6}(g) \) is \( 2812 k J / m o l, \) then value of \( C-C \) bond energy will be \( 328 k J / m o l \)
D. If \( \Delta H_{f}\left(H_{2} O, g\right)=-242 k J / m o l ; \Delta H_{v a p}\left(H_{2} O, l\right)= \)
\( 44 k J / m o l \) then \( \Delta_{f} H^{o}\left(O H^{-}, a q\right) \) will be \( -142 k J / m o l \)


At \( 100^{0} C, \) the gaseous reaction \( A \rightarrow \)
\( 2 B+C \) is found to be of first order
Starting with pure \( A, \) if at the end of 10 min, the total pressure of the system is \( 140 \mathrm{mm} \) and after a long time it is 300
\( \mathrm{nm}, \) the partial pressure of \( \boldsymbol{A} \) at the end of \( 10 \mathrm{min} \) is:
A. 70 mm
B. 160 mm
\( c \cdot 60 \mathrm{mm} \)
D. 80 mm


Identify the least reactive element from the following.
B . \( _{10}^{20} \mathrm{X} \)
\( \mathbf{c} \cdot \frac{23_{3} X}{1 X} \)
D. \( _{9}^{9} X \)


Assertion
A hollow shaft is found to be stronger
than a solid shaft made of same
material.
Reason
The torque required to produce a given twist in hollow cylinder is greater than
that required to twist a solid cylinder of same size and material.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Convert \( 25^{\circ} \) into radian.


Which of the following statements are true (T) and which are false (F) :

Sum of the three angles of a triangle is
\( \mathbf{1 8 0}^{\circ} \)
A. True
B. False


Explain total internal reflection. state the conditions.


The students in a class are seated
according to their marks in the previous examination. Once, it so happens that four of the students got equal marks and therefore the same rank. To decide
their seating arrangement, the teacher wants to write down all possible arrangements one in each of separate
bits of paper in order to choose one of these by lots. How many bits of paper are required?


Fill in the blanks.
sulphur is prepared by passing hydrogen sulphide gas into an aqueous solution of sulphur dioxide.


Construct a \( \triangle A B C \) in which \( B C= \)
\( \mathbf{5 . 6} c \boldsymbol{m}, \angle \boldsymbol{B}=\mathbf{3 0}^{\circ} \) and the difference
between the other sides is \( 3 \mathrm{cm} \).


Arrange
\( \boldsymbol{N} \boldsymbol{a}^{+}, \boldsymbol{M} \boldsymbol{G}^{2+}, \boldsymbol{O}^{2-}, \boldsymbol{F}^{-} \boldsymbol{A} \boldsymbol{l}^{3+}, \boldsymbol{N}^{3-} \)
(each having 10 electrons) in increasing
ionic radii.
\( \mathbf{A} \cdot A l^{3+}<M g^{2+}<N a^{+}<F^{-}<O^{2-}<N^{3-} \)
B. \( N^{3-}<O^{2}<F^{-}<N a^{+}<M g^{2+}<A l^{3+} \)
C \( \cdot A l^{3+}<M g^{2+}<F^{-}<N a^{+}<O^{2-}<N^{3-} \)
D. None of these


Using the definition, show that the
function.
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x} \sin (1 / \boldsymbol{x}) \) if \( \boldsymbol{x} \neq \mathbf{0}, \boldsymbol{0} \) if \( \boldsymbol{x}=\mathbf{0} \)
is continuous at the point \( \boldsymbol{x}=\mathbf{0} \)


\( A=\left[\begin{array}{lll}3 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 3\end{array}\right], \) then \( \operatorname{Adj}(A) \)
\( A \cdot 3 A \)
B. \( 6 A \)
\( \mathrm{c} \cdot 9 A^{T} \)
D. \( 2 A^{\text {? }} \)


An angled vector is shown in the
diagram above. What is the correct way to calculate the magnitude the
component of this vector in the \( x \)
direction?
\( \mathbf{A} \cdot 50 \times \sin (20) \)
B. \( 50 \times \cos (20) \)
\( \mathbf{c} \cdot 50 \div \sin (20) \)
D. \( 50 \div \cos (20) \)


In the following monobromination
reaction, the number of possible chiral
products is:
(enantiomerically pure)


The correct order of strength of acidity
of the following compounds is:
A \( . \) (ii) \( >(\mathrm{i})>(\text { iii })>(\text { iv }) \)
B. (i) > (ii) > (iii) > (iv)
\( c \cdot(\text { iv })>(\text { iii })>(\text { ii })>(i \)
\( D \cdot(\text { iv })>(\text { iii })>(i)>(\text { ii }) \)


A solution is prepared by dissolving \( \left.0.6 g \text { of urea (molar mass }=60 g m o l^{-1}\right) \)
and \( 1.8 g \) of glucose (molar mass \( = \)
\( \left.180 g m o l^{-1}\right) \) in \( 100 m L \) of water at
\( 27^{0} C . \) The osmotic pressure of the solution is :
\( \left(R=0.08206 L a t m K^{-1} m o l^{-1}\right) \)
A. 4.92 atm
B. 1.64 atm
c. 2.46 atm
D. 8.2 atm


The correct relationship between the boiling points of very dilute solutions of \( A l C l_{3}\left(t_{1}\right) \) and \( C a C l_{2}\left(t_{2}\right), \) having the same molar concentration, is :
A \( \cdot t_{1}=t_{2} \)
В. \( t_{1}>t_{2} \)
c. \( t_{2}>t_{1} \)
D. \( t_{2} \geq t_{1} \)


The property which regularly increases down the group in the periodic table is:
A. ionisation energy
B. electronegativity
c. reducing nature
D. electron affinity


The energy of a charged conductor is
given by the expression:
\( \mathbf{A} \cdot q^{2} / 2 c \)
B. \( q^{2} / c \)
\( \mathbf{c} \cdot 2 q c \)
D. \( q / 2 c^{2} \),where q is charges on the conductor,c is its capacity


A metal bullet moving at \( 400 \mathrm{ms}^{-1} \) strikes on a tree trunk and get
embedded inside it. Assuming total kinetic energy is converted to heat and \( 50 \% \) of heat is absorbed by the bullet,
find the increase in its temperature. (specific heat capacity of metal \( = \) \( 200 J k g^{-1} K^{-1} \) and bullet not melts


The area bounded by the curve \( y=\sqrt{x} \)
the line \( 2 y+3=x \) and the \( x \) -axis in
the first quadrant is
\( \mathbf{A} \cdot \mathbf{9} \)
в. \( \frac{27}{4} \)
\( c .36 \)
D. 18


Optical activity can be measured using:
A. calorimeter
B. polarimeter
c. thermometer
D. lactometer


For the following circuits, the equivalent
resistance between \( X \) and \( Y \) is
\( A \cdot 15 \Omega \)
В. 30 ?
\( c .45 \Omega \)
\( 0.20 \Omega \)


Which one of the following statements
is correct?
\( \mathbf{A} \cdot \mathbf{G}_{1}>\mathbf{G}_{2}>\mathbf{G}_{3}> \)
B \( \cdot \mathrm{G}_{1}<\mathrm{G}_{2}<\mathrm{G}_{3}<\ldots \)
c. \( \mathrm{G}_{1}=\mathrm{G}_{2}=\mathrm{G}_{3}= \)
D. \( G_{1}<G_{3}<G_{5}<\ldots \) and \( G_{2}>G_{4}>G_{6}>\ldots \)


Moon's phase cycle repeats on an average of \( _{-}--_{-}- \) days
A . 365
в. 120
c. 15
D. 30


The activity of sieve tube is controlled by nucleus of
A. Companion cells
B. Bast fibres
c. Phloem parenchyma
D. Xylem vessels.


Solve the following differential equation:
\( \boldsymbol{x} \cos \boldsymbol{y} \boldsymbol{d} \boldsymbol{y}=\left(\boldsymbol{x} e^{x} \log \boldsymbol{x}+\boldsymbol{e}^{\boldsymbol{x}}\right) \boldsymbol{d} \boldsymbol{x} \)


A gaseous mixture enclosed in a vessel
consists of one \( g \) mole of a gas \( A \) with \( \gamma=\left(\frac{5}{3}\right) \) and some amount of gas \( \mathrm{B} \) with \( \gamma=\frac{7}{5} \) at a temperature The
gasses \( A \) and \( B \) do not react with each
other and are assumed to be ideal Find
the number of \( g \) moles of the gas \( B \) if \( \gamma \) for the gaseous mixture is \( \left(\frac{19}{13}\right) \)
\( A \cdot 2 \)
\( B .5 \)
\( c \cdot 4 \)
D. 3


\( \frac{4}{9^{\frac{1}{3}}-3^{\frac{1}{3}}+1} \) is equal to
\( A \cdot 3^{\frac{1}{5}}+1 \)
B. \( 3^{\frac{1}{5}}-1 \)
c. \( 3^{\frac{1}{5}}+2 \)
D. \( 3^{\frac{1}{5}}-2 \)


What are the necessary conditions for total internal reflection to take place?


For the same mass, which one of the
following has the maximum thermal capacity?
A. wood
B. copper
c. water
D. Ice


Show that the points are collinear
(1)
\( \boldsymbol{A}(\mathbf{3}, \mathbf{2},-\mathbf{4}), \boldsymbol{B}(\mathbf{9}, \mathbf{8},-\mathbf{1 0}), \boldsymbol{C}(-\mathbf{2},-\mathbf{3}, \mathbf{1}) \)


The value of \( \frac{1}{\cos 290^{\circ}}+\frac{1}{\sqrt{3} \sin 250^{\circ}} \) is?
\( A \cdot \frac{2 \sqrt{3}}{3} \)
B. \( \frac{4 \sqrt{3}}{3} \)
\( c \cdot \sqrt{3} \)
D. None


A computer solved several problems in succession. The time it took the
computer to solve each successive
problem was the same number of times smaller than the time it took it to solve
the preceding problem. How many problems were suggested to the
computer if it spent \( 63.5 \mathrm{mm} \) to solve al the problems except for the first, 127 \( \mathrm{mm} \) to solve all the problems except for the last one, and \( 31.5 \mathrm{mm} \) to solve all the
problems except for the first two?


For a body starting from rest, what will be the ratio of the distance travelled by
the body the 4 th and 3 rd second during its journey?
A \( \cdot \frac{7}{5} \)
в. \( \frac{7}{3} \)
\( c \cdot \frac{5}{7} \)
D. \( \frac{3}{7} \)


If \( \boldsymbol{x}=\sin t, \boldsymbol{y}=\cos \boldsymbol{p} \boldsymbol{t}, \) then
B . \( \left(1-x^{2}\right) y_{2}+x y_{1}-p^{2} y=0 \)
C \( \cdot\left(1+x^{2}\right) y_{2}-x y_{1}+p^{2} y=0 \)
D. \( \left(1-x^{2}\right) y_{2}-x y_{1}+p^{2} y=0 \)


When the angle of incidence of a ray is
greater than the critical angle, the refracted ray is in the same medium,
i.e., the light is totally reflected in the same medium. This is known as
A. Total internal reflection
B. Critical reflection
c. Mirage
D. Optical illusion


White light is used to illuminate the two slits b distance apart and the
screen is placed at a distance directly
in front of one of the slits on the screen.
It is found that certain wavelength are missing then find the wavelength if \( (b<<d) \)


Differentiate the following functions
with respect to \( \boldsymbol{x} \) \( \tan ^{-1}\left\{\frac{5 x}{1-6 x^{2}}\right\},-\frac{1}{\sqrt{6}}<x<\frac{1}{\sqrt{6}} \)


\( \boldsymbol{E}_{\boldsymbol{n}}=-\frac{\mathbf{3 1 3 . 6}}{\boldsymbol{n}^{2}}, \) if the value of \( \boldsymbol{E}_{\boldsymbol{n}}= \)
-34.84 to which value 'n' corresponds:
\( A \cdot 4 \)
B. 3
\( c \cdot 2 \)
\( D \)


Draw a schematic diagram to show the components of a reflex arc. Use arrows to indicate the flow of impulse.


If diagonals of the parallelogram are equal,then show that it is a rectangle.


In photoelectric effect, the photocurrent
A. depends both on intensity and frequency of the incident light.
B. does not depend on the frequency of incident light but depends on the intensity of the incident light.
C. decreases with increase in frequency of incident light.
D. increases with increase in frequency of incident light.


Heat is
A. kinetic energy of molecules
B. potential and kinetic energy of molecules
C. Energy in transit
D. work done on the system


Minerals from which metals can be
preferably extracted are called:
A. ores
B. Source
c. Alloy
D. None of these


Find \( \boldsymbol{f} \circ \boldsymbol{g} \) and \( \boldsymbol{g} \circ \boldsymbol{f}, \) if \( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}| \)
\( g(x)=\sin x \)


When two vessels containing different quantity of water in it are heated to the same temperature difference, then
which vessel will heat up fast?
A. The vessel with less quantity of water
B. The vessel with more quantity of water
c. Both vessels will be equally heated
D. Cannot be said


The heat of combustion of \( \boldsymbol{H}_{2}(\boldsymbol{g}) \) at
constant pressure and \( 300 K \) is \( -280 \mathrm{kJ} \)
\( \operatorname{mol}^{-1} \)
What will be the heat of combustion at
constant volume and \( 300 K ? \)
A. \( \Delta U=- \) -276.2587 k
B. \( \Delta U=+276.2587 \mathrm{kJ} \)
c. \( \Delta U=-27.63 \mathrm{kJ} \)
D. None of these


\( 50 \mathrm{mL} \) aqueous solution of \( \mathrm{Fe} \boldsymbol{S O}_{4} \)
required 12 mL of 0.2 M \( K M n O_{4} \) in
acidic medium for complete oxidation. Calculate the molarity of ferrous sulphate solution. The reaction is:
\( M n O_{4}^{-}+5 F e^{2+}+8 H^{+} \rightarrow M n^{2+}+ \)
\( \mathbf{5} \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+}+\mathbf{4} \boldsymbol{H}_{2} \boldsymbol{O} \)
A. 0.024
B. 0.24
c. 2.4
D. \( 2.4 \times 10^{-3} \)


Emulsions can be destroyed by:
A. the addition of emulsifier which tends to form another
emulsion
B. electrophoresis with high potential
C. filltaration
D. all of the above


A rectangular loop PQRS made from a
uniform wire has length a, width b and mass m. It is free to rotate about the
\( \operatorname{arm} \mathrm{PQ}, \) which remains hinged along a horizontal line taken as the y-axis. Take the vertically upward direction as the zaxis. A uniform magnetic field \( \vec{B}= \) \( (3 \hat{i}+4 \hat{k}) B_{0} \) exists in the region. The
loop is held in the \( x \) -y plane and a current I is passed through it. The loop is now released and is found to stay in
the horizontal position in equilibrium. Find the magnetic force on the arm RS.


8 have studied French and 3 have not
studied either. The Venn diagram
showing the number of students who
have studied both is :
\( \mathbf{A} \)
B.
\( c \)
\( D \)


The four quantum numbers of the
valence electron of potassium are:
\( \mathbf{A} \cdot 4,0,1,+\frac{1}{2} \)
B. \( 4,1,0,+\frac{1}{2} \)
\( \mathbf{c} \cdot 4,0,0,+\frac{1}{2} \)
D. \( 4,1,1,+\frac{1}{2} \)


Which of the following is used for any person who is suffering from minor eye defect or for a partly blind person?
A . Electronic aids
B. Auditory aids
c. Non-optical aids
D. optical aids


The species that do not contain peroxide ions is :
A. \( P b O_{2} \)
в. \( H_{2} O_{2} \)
\( \mathrm{c} \cdot \operatorname{sr} \mathrm{O}_{2} \)
D. \( B a O_{2} \)


\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{B r} \frac{\boldsymbol{N H}_{3}}{\text {excess}} \)
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{N H}_{2} \)
f given product is right then, enter 1 else 0.


A boat covers a certain distance
between two spots in a river taking \( t_{1} \)
hrs going downstream and \( t_{2} \) hrs going upstream. What time will be taken by boat to cover same distance in still
water?
A \( \cdot \frac{t_{1}+t_{2}}{2} \)
B \( .2\left(t_{2}=t_{1}\right) \)
c. \( \frac{2 t_{1} t_{2}}{t_{1}+t_{2}} \)
D. \( \sqrt{t_{1} t_{2}} \)


Factors affecting the strength of electromagnet
A. the number of turns in the coil
B. the current flowing in the coil
c. the length if air gap between the poles.
D. all


For the following geometric progression
find the \( n^{t h} \) term \( 2,6,18,54, \dots \dots \)


Urea and uric acid are


Explain why friction is necessary to make the disc in Fig. roll in the direction indicated.
(a) Give the direction of frictional force
at \( \mathrm{B} \), and the sense of frictional torque,
before perfect rolling begins.
(b) What is the force of friction after
perfect rolling begins?


\( 7+3 x \) is a factor of \( 3 x^{3}+7 x \)
A. True
B. False


When sunlight passes through the
window of your house, the dust particles scatter the light making the path of the light visible. This phenomenon is called
as


Heavy water is called so because:
A. it has dissolved salts in it
B. it is an oxide of heavy hydrogen
C. it is a hydride of heavy oxygen
D. all of the above


Which part of a bone reduces friction at
joints and which produces blood cells?


The distance between two planets of
masses \( \mathrm{M} \) and \( 4 \mathrm{M} \) is 'a' what is the
gravitational potential at a point on a line joining them of which the gravitational intensity is zero?
\( \mathbf{A} \cdot-\frac{9 G M}{r} \)
B. \( -\frac{5 G M}{a} \)
\( \mathbf{c} \cdot-\frac{3 G M}{a} \)
D. \( -\frac{7 G M}{a} \)


Comment on the nature of above
compound(aromatic/anti-
aromatic/non-aromatic)


The acceleration of a particle varies with time \( t \) seconds according to the
relation \( a=6 t+6 m s^{-2} . \) Find velocity
and position as functions of time. It is given that the particle starts from
origin at \( t=0 \) with velocity \( 2 m s^{-1} \)


In how many ways can the letter of the
word SUCCESS be arranged so that
(i) The two \( C^{\prime} s \) are together bot no two
\( S^{\prime} s \) are together
(ii) No two \( C^{\prime} s \) and no two \( S^{\prime} s \) are
together.


Ammonia on reaction with hypochlorite
anion forms:
A. NO
в. \( \mathrm{NH}_{4} \mathrm{Cl} \)
c. \( \mathrm{N}_{2} \mathrm{H}_{4} \)
D. \( \mathrm{HNO}_{2} \)


Solve
\[
\boldsymbol{x}^{2}+\mathbf{5}=-\mathbf{6} \boldsymbol{x}
\]


Bouquet stage is observed in stage of the cell division.
A. Leptotene
B. Zygotene
c. Diplotene
D. Pachytene


The slope and y-intercept of the following line are respectively
\( 2 y+2 x-5=0 \)
A \( \cdot \) slope \( =m=1 \quad \) and \( \quad y- \) intercept \( =c=\frac{5}{2} \)
B. slope \( =m=1 / 5 \) and \( y- \) intercept \( =c=\frac{2}{5} \)
C \( \cdot \) slope \( =m=-1 \) and \( y- \) intercept \( =c=\frac{5}{2} \)
D. slope \( =m=-1 / 5 \) and \( y- \) intercept \( =c=\frac{2}{5} \)


In gymnosperms, the pollen chamber
represents
A. A cell in the pollen grain in which the sperms are formed
B. A cavity in the ovule in which pollen grains are stored after pollination
C. An opening in the megagametophyte through which the pollen tube approaches the egg
D. The microsporangium in which pollen grains develop


Which of the following conditions is incorrect for a well behaved wave
function \( (\mathbf{\Psi}) ? \)
A. \( \Psi \) must be finite
B. \Psi must be single valued
c. \( \Psi \) must be infinite
D. \( \Psi \) must be continuous


The salary of an officer is increased by \( 25 \% . \) By what per cent should the new salary be decreased to restore the
original salary?
\( A \cdot 5 \% \)
B. \( 10 \% \)
c. \( 15 \% \)
D. \( 20 \% \)


For any distribution of speeds \( V_{r m s} \geq \)
\( V_{a v} . \) Is this statement true or false?


Mendel choose pea plant due to
A. Its economic importance
B. Presence of contrasting characters
C . Its availability
D. Its cheapness


There are four concentric shells \( A, B, C \)
and D of radii a, \( 2 a, 3 a \) and \( 4 a \) respectively. Shells B and D are given charges \( +q \) and \( -q \) respectively. Shell \( C \) is now earthed. The potential difference \( V_{A}-V_{c} \) is \( k=\frac{1}{4 \pi \varepsilon_{0}} \)
A \( \cdot \frac{k q}{2 a} \)
в. \( \frac{k q}{3 a} \)
\( c \cdot \frac{k q}{4 a} \)
D. \( \frac{k q}{6 a} \)


Total number of structural isomers of
\( C_{4} H_{7} C l \)


The angle of elevation of a jet plane from a point \( A \) on the ground is \( 60^{0} \). After a
flight of 15 seconds, the angle of elevation changes to \( 30^{0} . \) If the plane at a constant height of \( 1500 \sqrt{3} m \), then the
speed of jet plane is :
A. \( 200 \mathrm{m} / \mathrm{s} \)
B. 1980 m/s
c. \( 240 \mathrm{m} / \mathrm{s} \)
D. 220 \( \mathrm{m} / \mathrm{s} \)


Represent the number 19 as the
difference between the cubes of natural
numbers.


The distance between two DNA strands
is
A . \( 20 \AA \)
в. \( 34 \dot{h} \)
c. \( 3.4 \dot{A} \)
D. 2 a


Let \( R_{0} \) denote the set of all non-zero real
numbers and let \( \boldsymbol{A}=\boldsymbol{R}_{0} \times \boldsymbol{R}_{0} . \) If \( ^{\prime} *^{\prime} \) is a
binary operation on A defined by \( (a, b) * \) \( (c, d)=(a c, b d) \) for all \( (a, b)(c, d) \in A \)
Show that \( ^{\prime} *^{\prime} \) is both commutative and
associative on \( \mathbf{A} \)


Assertion
Algal blooms occur in nutrient poor
water.
Reason
Algal blooms make water unfit for
human consumption but cause enormous growth of fish.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Write the types of allotropes of carbon Give any three examples of each.


The enthalpy of neutralisation of a strong acid by a strong base is \( -57.32 k J \) mol \( ^{-1} . \) The enthalpy of
formation of water is
\( -285.84 k J \) mol\( ^{-1} . \) The enthalpy of
formation of hydroxy ion is:
A \( .+228.52 k J \) mol \( ^{-1} \)
B. \( -114.26 k J \) mol\( ^{-} \)
c. \( -228.52 k J \) mol \( ^{-1} \)
D. \( +114.2 \mathrm{kJ} \mathrm{mol}^{-1} \)


A domestic electrical appliance requires alternating current of \( 15 \mathrm{V} \). If
\( 220 \mathrm{V} \) of alternating current is supplied to the house, then the device that helps in the functioning of that electrical appliance is
A. Induction coil
B. Step-up transformer
c. AC dynamo
D. Step-down transformer


Can you find at least one vector perpendicular to \( 3 \hat{i}-4 \hat{j}+7 \hat{k} ? \)
A \( \cdot \hat{i}+2 \hat{j}+\frac{6}{7} \hat{k} \)
B・ \( _{\hat{i}+2 \hat{j}}+\frac{5}{7} \hat{k} \)
\( \mathbf{c} \cdot \hat{i}+3 \hat{j}+\frac{5}{7} \hat{k} \)
D・ \( \hat{i}+2 \hat{j}+\frac{5}{6} \hat{k} \)


Assertion
Plants lack excretory organs.
Reason
Plant usually absorb essential nutrients
and lead a passive life.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Assertion is incorrect but the reason is correct.


A cell placed in a strong salt solution will shrink because
A. Mineral salts will break the cell wall
B. Salt water will enter the cell
c. water comes out by exosmosis
D. cytoplasm will decompose


The intrinsic conductivity of
germanium at \( 27^{\circ} \mathrm{C} \) is \( 2.13 \mathrm{mho} / \mathrm{m} \)
and mobilities of electrons and holes
are 0.38 and \( 0.18 m^{2} / V s \) respectively. The density of charge carriers is
\( \mathbf{A} \cdot 2.37 \times 10^{19} / m^{3} \)
B. \( 3.28 \times 10^{19} / m^{3} \)
C. \( 7.83 \times 10^{19} / m^{3} \)
D. \( 8.47 \times 10^{19} / m^{3} \)


The circuit shown in Fig. acts as a
A. tuned filter
B. low pass filter
c. high pass filter
D. rectifier


Given that \( \overrightarrow{\boldsymbol{A}}+\overrightarrow{\boldsymbol{B}}=\overrightarrow{\boldsymbol{C}} \). If \( |\overrightarrow{\boldsymbol{A}}|=4,|\overrightarrow{\boldsymbol{B}}|= \)
\( \mathbf{5} \) and \( |\overrightarrow{\boldsymbol{C}}|=\sqrt{\mathbf{6 1}}, \) the angle between \( \boldsymbol{A} \)
and \( B \) is
A \( .30^{\circ} \)
B. \( 60^{\circ} \)
\( c .90^{\circ} \)
D. \( 120^{\circ} \)


The horizontal component of earth's magnetic field at a certain place is \( 3.0 \times 10^{-5} \mathrm{T} \) and having a direction
from the geographic south to geographic north. The force per unit length on a very long straight conductor carrying a steady current of \( 1.2 \mathrm{A} \) in east to west direction is then
A. \( 3.0 \times 10^{-5} \mathrm{N} \mathrm{m}^{-1} \)
В. \( 3.2 \times 10^{-5} \mathrm{N} \mathrm{m}^{-1} \)
c. \( 3.6 \times 10^{-5} \mathrm{N} \mathrm{m}^{-1} \)
D. \( 3.8 \times 10^{-5} \mathrm{N} \mathrm{m}^{-1} \)


Water filled in two glasses \( A \) and \( B \) have \( B O D \) values of 10 and 20
respectively. The correct statement regarding them, is:
\( \mathbf{A} \cdot A \) is more polluted than \( B \)
B. A is suitable for drinking, whereas \( B \) is not
\( \mathrm{c} . B \) is more polluted than \( A \)
D. Both \( A \) and \( B \) are suitable for drinking


At what distance on the axis, from the
centre of a circular current carrying coil of radius \( r, \) the magnetic field becomes 1/8th of the magnetic field at centre?
A \( \cdot \sqrt{2} r \)
B \( \cdot 2^{3 / 2} \)
\( c \cdot r \sqrt{3} \)
D. \( 3 \sqrt{2} r \)


For the reaction, \( 2 N O+C l_{2} \longrightarrow \)
\( 2 N O C l \) at \( 300 K \) following data are
obtained
\( \begin{array}{ll}\underset{\mathrm{No}}{\operatorname{Exp}} & \frac{\text {InitialConcentration}}{[\mathrm{NO}]\left[\mathrm{CI}_{2}\right]}\end{array} \)
1 \( \begin{array}{ll}\text { 0. } 0.010 & \text { 0.010 }\end{array} \)
2 \( \begin{array}{cc}0.010 & 0.020\end{array} \)
3 \( \begin{array}{cc}0.020 & 0.020\end{array} \)
Write rate law for the reaction. What is
the order of the reaction? Also calculate
the specific rate constant.


Energy flow and energy transformations in living system strictly conform to the
A. Law of limiting factors
B. Liebig's law of minimum
c. Laws of thermodynamics
D. Biogenetic law


Write the special characteristics/features of symmetry
with an example.


Universe is:
A. a dialect between two people
B. the study of light propagation between Sun and the Earth
C. the vast surrounding space which includes everything that exists from the Earth to the most distant parts of space that one can possibly see
D. the solar system


State whether the statement is true or
false :
IUPAC name of the complex
\( \boldsymbol{K}_{3}\left[\boldsymbol{F} e(\boldsymbol{C} \boldsymbol{N})_{6}\right] \) is Potassium
hexacyanoferrate(II).


What are the geometric shape and the oxidation number of the copper atom, respectively, for the complex ion,
\( \left[\boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\left(\boldsymbol{O} \boldsymbol{H}_{2}\right)_{2}\right]^{2+} \)
A. Tetrahedral; +2
B. Square planar; - -
c. Linear; +3
D. Octahedral; +2


The nuclear radius of a nucleus with
nucleon number 16 is \( 3 \times 10^{-15} m \)
Then, the nuclear radius of a nucleus
with nucleon number 128 is :
A \( \cdot 3 \times 10^{-15} \mathrm{m} \)
B . \( 1.5 \times 10^{-15} m \)
\( \mathbf{c} \cdot 6 \times 10^{-15} m \)
D. \( 4.5 \times 10^{-15} \mathrm{m} \)


Consider the following equilibrium system: \( S O_{2}(g)+\frac{1}{2} O_{2}(g) \rightleftharpoons S O_{3}(g) \)
set up in a cylinder fitted with a piston. Some inert gas is added and the piston is moved outwards to keep the total
gaseous pressure constant. Predict which of the following is true?
A. Addition of inert gas does not affect the equilibrium
B . Less \( S O_{2}(g) \) is produced
c. More \( S O_{2}(g) \) is produced
D. The system moves to new equilibrium position which cannot be predicted theoritically


If a central atom of a molecule only has two electron domains, what is the only possible shape the molecule can have?
A. Linear.
B. Bent.
c. Pyramidal.
D. opposite.


Write Newton's formula for refraction of
Light through a lens. Explain the meaning of symbols used.


Consider two spherical planets of same average density, Planet 2 is 8 limes as massive as planet 1. The ratio ot the
acceleration due to gravity on the second planet to that on the first is.
\( A \)
B. 2
\( c \cdot 4 \)
D. 8


If \( \boldsymbol{I}=\int \sqrt{\frac{\mathbf{5}-\boldsymbol{x}}{\mathbf{5}+\boldsymbol{x}}} \boldsymbol{d} \boldsymbol{x}, \) then \( \boldsymbol{I} \) equals
A \( \cdot 5 \sin ^{-1}\left(\frac{x}{5}\right)+\sqrt{25-x^{2}}+C \)
B. \( 10 \sin ^{-1}\left(\frac{x}{5}\right)+\sqrt{25-x^{2}}+C \)
c. \( 5 \sin ^{-1}\left(\frac{x}{5}\right)-\sqrt{25-x^{2}}+C \)
D. none of these


Two metallic rings of radius \( R \) are
rolling on a metallic rod. A magnetic
field of magnitude \( B \) is applied in the
region. The magnitude of potential
difference between points \( A \) and \( C \) on
the two rings (as shown), will be:
\( A \)
в. \( 4 B \omega R^{2} \)
\( \mathbf{c} \cdot 8 B \omega R^{2} \)
\( D \cdot 2 B \omega R^{2} \)


Which symbol is used for element thorium?
\( \mathbf{A} \cdot W \)
в. \( T h \)
c. \( T m \)
D. \( Y \)
E . \( T i \)


Find the average of first twelve natural
numbers.


When a force \( F_{1} \) acts on a particle,
frequency \( 6 \mathrm{Hz} \) and when a force \( F_{2} \) acts frequency is 8 Hz. What is the frequency when both the force act simultaneously in same direction?
A . 12 нᅩ
в. 25нд
с. 10 н
D. \( 5 \mathrm{Hz} \)


An aeroplane is flying from city \( A \) to \( B \) along path 1. The path 1 is a circular arc whose centre coincides with the centre
of the earth. Another aeroplane is flying along path 2 from \( A \) to \( B \). The path 2 is
circular arc whose centre is at \( \mathrm{C} \). O is
the centre of the earth. Then
A. The distance travelled by \( 1^{s t} \) aeroplane is greater than that of \( 2^{n d} \) aeroplane
B. The distance travelled by \( 1^{\text {st}} \) aeroplane is less than that of \( 2^{n d} \) aeroplane
c. The displacement of both aeroplane is different
D. None of these


What is the far point of a normal human
eyes?


An electron in a circular orbit of radius
\( 0.5 A^{o} \) makes \( 7 \times 10^{15} \) revolutions in
each second. This electron orbit is
equivalent to a magnetic shell of moment \( (\text { in } A m) \)
A. \( 88 \times 10^{-25} \)
B . \( 8.89 \times 10^{-25} \)
c. \( 44 \times 10^{-25} \)
D. 4.4 \( \times 10^{-25} \)


A triangle \( A B C \) is placed so that the
mid-points of the sides are on the \( x, y, z \)
axes. Lengths of the intercepts made by the plane containing the triangle on
these axes are respectively \( \boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\gamma} \)
Coordinates of the centroid of the
triangle \( \boldsymbol{A B C} \) are
A \( \cdot(-\alpha / 3, \beta / 3, \gamma / 3) \)
B. \( (\alpha / 3,-\beta / 3, \gamma / 3) \)
c. \( (\alpha / 3, \beta / 3,-\gamma / 3) \)
D. \( (\alpha / 3, \beta / 3, \gamma / 3) \)


If \( x \lambda y=2 x-y \) and \( x \nu y=3 x \times y \)
then \( (5 \nu 2) \lambda 9 \)


The number of sigma and pi bonds in
the structure:
\( \boldsymbol{C H}_{2}=\boldsymbol{C H}-\boldsymbol{C} \equiv \boldsymbol{C H} \)
A. 7 and 3
B. 6 and 2
\( c \cdot 4 \) and 3
D. All are sigma bonds


Edge of a cube whose volume is \( \frac{1}{125} \) cu \( \mathrm{m} \) is
A \( \cdot \frac{1}{15} \mathrm{m} \)
в. \( \frac{1}{5} \mathrm{m} \)
c. \( \frac{1}{25} \mathrm{m} \)
D. 125 \( \mathrm{m} \)


An oscillator is nothing but an amplifier
with
A. Positive feedback
B. Large gain
c. No feedback
D. Negative feedback


If \( 9^{t h} \) term of an \( A . P . \) is zero, Prove that
its \( 29^{t h} \) term is double the \( 19^{t h} \) term.


n the circuit shown in the figure, find
the current in \( 45 \Omega \)
ugure, una tne current in
A. \( 4 A \)
В. 2.5
\( c .2 A \)
D. None of these


The \( p K_{a} \) of oxoacids of chlorine in water
follows the order:
A. \( H C l O<H C l O_{3}<H C l O_{2}<H C l O_{4} \)
в. \( H C l O_{4}<H C l O_{3}<H C l O_{2}<H C l O \)
c. \( H C l O_{4}<H C l O_{2}<H C l O_{3}<H C l O \)
D. \( H C l O_{2}<H C l O<H C l O_{3}<H C l O_{4} \)


Fill in the blanks:
Very fine particles mainly scatter light.


The number of coulombs required to deposit \( 5.4 g \) of Aluminium when the
given electrode reaction is represented
as \( A l^{3+}+3 e^{-} \rightarrow A l \)
A \( \cdot 1.83 \times 10^{5} C \)
в. \( 57900 C \)
\( \mathbf{c} \cdot 5.86 \times 10^{5} C \)
D. \( 3 F \)


Multiple Choice Questions Biochemical oxygen demand may not be good index for water bodies receiving
effluents from.
A. Sugar industry
B. Domestic sewage
c. Dairy industry
D. Petroleum industry


The time constant of an inductance coil
is \( 2 \times 10^{-3} \) s. When a \( 90 \Omega \) resistance is
joined in series, the same constant becomes \( 0.5 \times 10^{-3} \) s. The inductance
and resistance of the coil are
A. \( 30 m H ; 30 \Omega \)
в. \( 60 m H ; 30 \Omega \)
c. \( 30 m H ; 60 \Omega \)
D. \( 60 m H ; 60 \Omega \)


\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left(\tan ^{2} \boldsymbol{a} \boldsymbol{x}\right) \)
A \( \cdot 2 a \tan a x \sec ^{2} a x \)
B. \( -2 a \tan a x \sec ^{2} a x \)
\( \mathbf{c} \cdot a \tan a x \sec ^{2} a x \)
D. \( 2 a \cot a x \sec ^{2} a x \)


Fruits and vegetables advisable for
good vision are:
A. apple, banana, carrots
B. mango, papaya, carrots
c. cabbage, sunflower oil, groundnut
D. all fruits and vegetables


A car is to be hoisted by elevator to the fourth floor of a parking garage, which is 14 m above the ground. If the elevator
can have maximum acceleration of \( \mathbf{0 . 2} \)
\( m / s^{2} \) and maximum deceleration of 0.1 \( m / s^{2} \) and can reach a maximum speed of \( 2.5 m / s, \) the shortest time to make
the lift, starting form rest and ending at
rest is \( K \). The value of \( 2 K \) will be


The part of a meteor which reaches the earth's surface is called a
A . comet
B. meteorite
c. shooting car
D. nebulae


Nitrogen shows different oxidation states ranging from:
A. -3 to +5
B. -5 to +5
c. 0 to -5
D. -3 to +3


Critical temperature of a gas is its Boyle temperature.
A. higher than
B. equal to
c. lower than
D. no relation


Find force constant for small oscillation
around equilibrium:
A. \( 580 N m^{-1} \)
B. \( 58 N m^{-1} \)
c. \( 400 N m^{-1} \)
D. none of these


The wire having a green plastic covering is a
A. live wire.
B. neutral wire
c. earth wire.
D. none of these


Which of the following is thermally stable?
A. Silicone polymers
B. Rayon
c. Bakelite
D. Perlon - L


The ionic enthalpy of hydrogen atom is \( 1.312 \times 10^{6} J \) mol \( ^{-1} . \) The energy
required to excite the electron in the
atom from \( n_{1}=1 \) to \( n_{2}=2 \) is:
A . \( 8.51 \times 10^{5} \mathrm{Jmol}^{-1} \)
B. \( 6.56 \times 10^{5} \mathrm{Jmol}^{-1} \)
c. \( 7.56 \times 10^{5} \mathrm{Jmol}^{-1} \)
D. \( 9.84 \times 10^{5} \mathrm{Jmol}^{-1} \)


Find the ratio of atomic masses of
Magnesium and Carbon.
A.
B. 2
\( c \cdot 3 \)
\( D \)


The three physical quantities \( x, y \) and \( z \)
have units \( g \quad c m^{2} s^{-5}, g s^{-1} \) and \( c m s^{-2} \) respectively.
The relation between \( x, y \) and \( z \) is
A \( \cdot x=y z^{2} \)
B . \( x=y^{2} x \)
c. \( y^{2}=x z \)
D. \( z=x^{2} y \)


Assertion
Oxidation number of \( S \) in \( F e S_{2} \) is -1
Reason
\( F e S_{2} \) is made of \( F e^{+2} \) and \( (S-S)^{2-} \)
ions.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Two nichrome wires \( A \) and \( B \), each of
length \( 5 \mathrm{cm} \) and of radius \( 1 \mathrm{cm} \) and
\( 3 \mathrm{cm} \) respectively are connected to each
other in series. If a current of \( 5 A \) flows
through the combination of wires, the ratio of potential difference across wire \( A \) to that across wire \( B \) will be
A .1: 3
B. 3: 1
c. 9: 1
D. 1: 9


Excess salt inhibits growth in pickles by
A. Endosmosis
B. Exomosis
c. oxidation
D. Denaturation