Rate of change of displacement is
called -
A. speed
B. acceleration
c. velocity
D. retardation


State whether the given statement is True or False :

When silk is rubbed with glass, the silk gets positively charged.
A. True
B. False


Artery supplying blood to pericardium
is
A. Brachial artery
B. Vertebel artery
c. Coronary artery
D. Internal mammary artery


Another unit for the quantity having the unit \( \frac{C^{2}}{N m^{2}} \) is:
A. farad
в. \( \frac{\text { farad }}{m^{2}} \)
c. \( \frac{\text { farad }}{m} \)
D. \( \frac{m}{\text {farad}} \)


Characteristics \& Relation


What is the action of mixture of
\( N a N O_{2} \) and dil. \( H C l \) on
(a) Ethyl amine,
(b) Aniline, Diethyl amine How is nylon 6,6 prepared? What are 'antacids'?

Write any 'two' side effects of tranquilizers


The following reactions are carried out:
\( \boldsymbol{A}: \) Nitrogen \( + \) metal \( \rightarrow \) compound \( \boldsymbol{X} \)
\( B: X+ \) water \( \rightarrow \) ammonia \( + \) another
compound \( C: \) Ammonia \( + \) metal oxide \( \rightarrow \) metal \( + \)
water \( +N_{2} \)

One metal that can be used for reaction
\( A \) is magnesium. Write the correctly
balanced equation for reaction \( B \), where \( X \) is the compound formed
A \( . N a N_{2}+H_{2} O \rightarrow N H_{3}+N a_{2} O \)
B. \( M g_{3} N_{2}+3 H_{2} O \rightarrow 2 N H_{3}+3 M g O \)
c. \( C a_{3} N_{2}+H_{2} O \rightarrow N H_{3}+C a O \)
D. None of these


Three resistors are connected as shown
in the diagram.

Through the resistor 5 ohm, a current of
1 ampere is flowing.
(i) What is the current through the other
two resistors?
(ii) What is the p.d. across \( A B \) and \( A C ? \)
(iii) What is the total resistance?


A tank is filled with water up to a height
H. Water is let out of a hole \( P \) from one
of the walls, at a depth \( D \) below the
surface of the water. Express the range
of the efflux \( x \) in terms of \( H \) and \( D \)


If \( f(x)=\left(\frac{x-1}{x+1}\right), \) then which of the following statements is/are correct? This question has multiple correct options
\( ^{\mathrm{A}} \cdot f\left(\frac{1}{x}\right)=f(x) \)
B \( \cdot f\left(\frac{1}{x}\right)=-f(x) \)
c. \( f\left(-\frac{1}{x}\right)=\frac{1}{f(x)} \)
D \( f\left(-\frac{1}{x}\right)=-\frac{1}{f(x)} \)


If the attacking reagent is a nucleophile, the electrons are transferred away from the attacking
reagent and into the system. This is known as:
A. E Effect
B. +E Effect.
c. R Effect.
D. +R Effect.


Choose the correct statement from the
following:
This question has multiple correct options
A. Molecular collisions are unaffected by gravity
B. Real gases obey gas laws under any conditions
C. Gas laws have no significance at absolute zero
D. At \( 0^{\circ} \mathrm{C} \), the molecular motion ceases.


Which of the following statement is
wrong?
This question has multiple correct options
A. The stability of hydride increases from \( \mathrm{NH}_{3} \) to \( \mathrm{BiH}_{3} \) in group 15 of the periodic table.
B. Nitrogen cannot form \( \mathrm{d} \pi-\mathrm{p} \pi \) bond.
C. single \( \mathrm{N}-\mathrm{N} \) bond is weaker than the single P-P bond.
D. \( \mathrm{N}_{2} \mathrm{O}_{4} \) has two resonance structures.


What is to be used to convert an AC
generator into DC generator?
A. split-ring type commutator must be used
B. slip rings and brushes must be used
C. a stronger magnetic field has to be used
D. a rectangular wire loop has to be used


mass \( m \) carrying charge \( q . \) The bead
can freely move on the smooth fixed ring placed on a smooth horizontal plan.
In the same plane a charge \( +Q \) has also
been fixed as shown. The potential at
the point \( \boldsymbol{P} \) due to \( +\boldsymbol{Q} \) is \( \boldsymbol{V} \). The velocity
with which the bead should projected
from the point \( P \) so that it can complete
a circle should be greater than
A \( \cdot \sqrt{\frac{6 q V}{m}} \)
B. \( \sqrt{\frac{q V}{m}} \)
c. \( \sqrt{\frac{3 q V}{m}} \)
D. nont


The value of \( \lim _{x \rightarrow 2 a} \frac{\sqrt{x-2 a}+\sqrt{x}-\sqrt{2 a}}{\sqrt{x^{2}-4 a^{2}}} \)
is
A \( \cdot \frac{1}{\sqrt{a}} \)
B. \( \frac{1}{2 \sqrt{a}} \)
c. \( \frac{\sqrt{a}}{2} \)
D. \( 2 \sqrt{a} \)


Consider the function for \( \boldsymbol{x}=[-\mathbf{2}, \mathbf{3}] \)
\( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{cc}\boldsymbol{x}^{\mathbf{3}}-\mathbf{2} \boldsymbol{x}^{\mathbf{2}}-\mathbf{5} \boldsymbol{x}+\mathbf{6} & \boldsymbol{i} \boldsymbol{f} \boldsymbol{x} \neq \mathbf{1} \\ \boldsymbol{x}-\mathbf{1} & \boldsymbol{i} \boldsymbol{f} \boldsymbol{x}=\mathbf{1}\end{array}\right. \)
then
A. \( f \) is discontinuous at \( x=1 \Rightarrow \) Rolles theorem is not
applicable in [-2,3]
B. \( f(-2) \neq f(3) \Rightarrow \) Rolles theorem is not applicable in [-2,3]
C. \( f \) is not derivable in (-2,3)\( \Rightarrow \) Rolles theorem is not applicable
D. Rolles theorem is applicable as \( f \) satisfies all the
conditions and \( c \) of Rolles theorem is


table shows the number of students
studying one or more of the following
subjects in this class:
Number of Subject
Mathematics
Physics
Chemistry
Mathematics and Physics 30
Mathematics and Chemistry 28
Physics and Chemistry 23
Mathematics, Physics and 18 Chemistry
How many students are enrolled in
Mathematics alone, Physics alone and
Chemistry alone \( ? \) Are there students who have not offered any of these three
subjects ?


Current in a coil of self-inductance
\( 2.0 H \) is increasing as \( i=2 \sin t^{2} . \) The
amount of energy spent during the period when the current changes from 0
to \( 2 A \) is:
A . 15
в. 2 J
\( c .3 J \)
D. \( 4 J \)


If two sets \( A \) and \( B \) have 99 elements in
common, then the number of elements
common to each of the sets \( A \times B \) and
\( \boldsymbol{B} \times \boldsymbol{A} \) are
A . \( 2^{99} \)
B. \( 99^{2} \)
\( c \cdot 100 \)
D. 18


Which chloroderivative of benzene
among the following would undergo-
hydrolysis most readily with aq. NaOH
to furnish the correspoinding hydroxy derivative?
\( A \)
B.
\( c \)
\( D \)


The temperature coefficient of
resistance of conductor varies as
\( \boldsymbol{\alpha}(\boldsymbol{T})=\boldsymbol{3} \boldsymbol{T}^{2}+\boldsymbol{2} \boldsymbol{T} . \) If \( \boldsymbol{R}_{0} \) is resistance at
\( T=0 \) and \( R \) is resistance at \( T, \) then
A \( . R=R_{0}(6 T+2) \)
B . \( R=2 R_{0}(3+2 T) \)
C \( . R=R_{0}\left(1+T^{2}+T^{3}\right) \)
D. \( R=R_{0}\left(1-T+T^{2}+T^{3}\right) \)


If \( \omega \neq 1 \) is a cube root of unity and
\( (\omega+x)^{n}=1+12 \omega+69 \omega+\ldots . \) then
values of \( 4 n \) and \( \omega \) respectively are
A . 36,1
в. 12,2
c. \( 24,1 / 2 \)
D. \( 18,1 / 3 \)


\( \mathbf{2} \boldsymbol{x}-\boldsymbol{y}+\mathbf{3} \boldsymbol{z}-\mathbf{1}=\mathbf{0} \) and \( \mathbf{2} \boldsymbol{x}-\boldsymbol{y}+ \)
\( \mathbf{3} \boldsymbol{z}+\mathbf{3}=\mathbf{0} \)


In electrochemical passivity:
A. thin visible oxide film is formed
B. thin invisible oxide film is formed
C. thick visible oxide film is formed
D. thick invisible oxide films formed


What are the products formed when xenon hexafluoride react with silicon
dioxide?
A. \( \operatorname{XeSiO}_{4}+H F \)
B. \( X e F_{2}+S i F_{4} \)
\( \mathrm{c} \cdot \operatorname{Xe} \mathrm{OF}_{4}+\mathrm{SiF}_{4} \)
D. \( X e O_{3}+S i F_{2} \)


By the process of convection the
transfer of heat is always-
A. upwards
B. downwards
c. sideways
D. in all possible directions


Simplify: \( 9 \frac{5}{10} \)


Preeti reached the metro station and
found that the escalator was not
working. She walked up the stationary
escalator in time \( t_{1} . \) On other days, if
she remains stationary on the moving
escalator, then the escalator takes her
up in time \( t_{2} . \) The time taken by her to
walk up on the moving escalator will be
A \( \cdot \frac{t_{1}+t_{2}}{2} \)
B. \( \frac{t_{1} t_{2}}{t_{2}-t_{1}} \)
\( \mathbf{C} \cdot \frac{t_{1} t_{2}}{t_{2}+t_{1}} \)
D. \( t_{1}-t_{2} \)


\( \int_{-1 / \sqrt{3}}^{1 / \sqrt{3}} \frac{x^{4}}{1-x^{4}} \cos ^{-1} \frac{2 x}{1+x^{2}} d x= \)
\( \frac{\pi}{2}\left[\frac{1}{2} \log (2+\sqrt{3})+\frac{\pi}{6}-\frac{2}{\sqrt{3}}\right] \)
\( \frac{\pi}{2}\left[\frac{1}{2} \log (2+\sqrt{3})+\frac{\pi}{4}-\frac{2}{\sqrt{2}}\right] \)
D. \( \frac{\pi}{2}\left[\frac{1}{2} \log (2-\sqrt{3})-\frac{\pi}{6}+\frac{2}{\sqrt{3}}\right] \)
\( \frac{\pi}{2}\left[\frac{1}{3} \log (3+\sqrt{3})+\frac{\pi}{5}-\frac{1}{\sqrt{3}}\right] \)


Chemically Zinc group elements closely
resemble
A. I A group
B. II A group
c. III A group
D. IV A group


The sensitivity of a moving coil galvanometer increases with the decrease in
A. number of turns
B. area of coil
c. magnetic field
D. couple per unit twist


Identify the primary alkyl halide from following:
A. \( C H_{3} C H_{2} C l \)
в. \( C H_{3} C l \)
c. \( C H_{3} C H_{2} C H_{2} C l \)
D. all of these


Wind is blowing from west to east along two parallel tracks. A train is moving on each track in opposite directions. They have same speed when no wind is blowing. Now, one train has
speed double that of the other. The speed of each train is
A. Equal to that of wind
B. Double that of wind
c. Three times that of wind
D. Half of that of wind


Which of the following is a matter?
A. Chair
B. Smell
c. Love
D. cold


ff \( P(x, y) \) is equidistant from \( A(a+ \) \( \boldsymbol{b}, \boldsymbol{b}-\boldsymbol{a}) \) and \( \boldsymbol{B}(\boldsymbol{a}-\boldsymbol{b}, \boldsymbol{a}+\boldsymbol{b}), \) show that
\( \boldsymbol{b} \boldsymbol{x}=\boldsymbol{a} \boldsymbol{y} \)


Solution \( A, B \) and \( C \) of the same strong electrolyte offered resistances of
\( 50 \Omega, 100 \Omega, \) and \( 150 \Omega \) in a given conductivity cell. The resistance observed if they are mixed in a volume proportion which is reciprocal of their resistances and tested in the same
conductivity cell would be:
A . \( 67.3 \Omega \)
B. \( 81.8 \Omega \)
c. \( 100 \Omega \)
D. \( 300 \Omega \)


Compound (B) is:
A. 2,3 -Dimethylbutane
B. 2-Methylpentane
c. \( 2, \) 2-Dimethylbutane
D. 3-Methylpentane


Find the second term and \( n \) th term of
an AP whose 6 th term is 12 and 8 th
term is 22
A \( \cdot a_{2}=-9, a_{n}=3 n-43 \)
в. \( a_{2}=7, a_{n}=3 n-52 \)
c. \( a_{2}=-8, a_{n}=5 n-18 \)
D \( \cdot a_{2}=-9, a_{n}=5 n-38 \)


A small sphere of mass \( m \) and having charge \( q \) is suspended by a silk thread of length \( l \) in a uniform horizontal
electric filed. If it stands at a distance \( x \)
from the vertical line from point of suspension, then magnitude of electric field is :
A. \( \frac{m g}{q} \)
в. \( \frac{m g}{q} \)
c. \( \frac{m g x}{q \sqrt{l^{2}-x^{2}}} \)
D. \( \frac{m g l}{q \sqrt{x^{2}-l^{2}}} \)


Dependency rate is above in
India
A . 30
B. 33
c. 36
D. 37


Assume that impure copper contains only \( F e, A u \) and \( A g \) as impurities. After
passage of 140 ampere for 482.5 sec
the mass of anode decreased by 22.260 \( g \) and the cathode increased in mass by 22.011 g. Calculate the percentage of iron and percentage of copper originally present
A. \( F e=3 \% C u=93 \% \)
в. \( F e=2.5 \% C u=89 \% \)
c. \( F e=3.5 \% C u=93 \% \)
D. None of these


The probability mass function (p.m.f) of
\( X \) is given below:
\[
\begin{array}{lllll}
X=x & 1 & 2 & 3 \\
P(X=x) & \frac{1}{5} & \frac{2}{5} & \frac{2}{5}
\end{array}
\]


The figure shows two immiscible
liquids(Kerosene and water). Kerosene
has density \( \rho_{2} \) and water has density \( \rho_{1} \)
Find the velocity of water flow.


A long wire is bent into the shape
PQRST as shown in the following
Figure with \( Q R S \) being a semicircle
with centre \( O \) and radius \( r \) metre. \( A \)
current of \( I \) ampere flows through it in
the direction \( \boldsymbol{P} \rightarrow \boldsymbol{Q} \rightarrow \boldsymbol{R} \rightarrow \boldsymbol{S} \rightarrow \boldsymbol{T} \)
Then, the magnetic induction at the
point \( O \) of the figure in vacuum is
\( ^{\mathbf{A}} \cdot_{\mu_{0} i}\left[\frac{1}{2 \pi r}+\frac{1}{4 r}\right] \)
В \( \cdot \mu_{0} i\left[\frac{1}{2 \pi r}-\frac{1}{4 r}\right] \)
c. \( \frac{\mu_{0} i}{4 r} \)
D. \( \frac{\mu_{0} i}{\pi r} \)


\( \boldsymbol{P Q}=\boldsymbol{Q} \boldsymbol{R}=\boldsymbol{P S} . \) Calculate the size of
the labelled angles.
B . (b) \( a=42^{\circ}, b=48^{\circ}, c=69^{\circ}, d=111^{\circ} \)
C . (c) \( a=45^{\circ}, b=45^{\circ}, c=67.5^{\circ}, d=112.5^{\circ} \)
D \cdot (d) \( a=50^{\circ}, b=40^{\circ}, c=65^{\circ}, d=115^{\circ} \)


The value of integral \( \int_{0}^{\pi} \frac{x^{2} \sin x}{(2 x-\pi)\left(1+\cos ^{2} x\right)} d x \) is equal to
\( ^{A} \cdot \frac{\pi^{2}}{4} \)
в. \( \frac{\pi^{2}}{2} \)
c. \( \frac{\pi^{2}}{6} \)
D. none of these


A buffer solution is formed by mixing \( 100 \mathrm{mL} 0.01 \mathrm{M} C \mathrm{H}_{3} \mathrm{COOH} \) with \( 200 \mathrm{mL} \)
\( 0.02 \mathrm{M} C H_{3} C O O N a . \) If this buffer
solution is made to 1 lit by adding 700
mL of water, \( \boldsymbol{p} \boldsymbol{H} \) will change by a factor
of:


Block A mass 2 kg is placed over a block
B mass 8 kg. The combination is placed on a rough horizontal surface. If \( \mathrm{g}=10 \mathrm{ms}^{-2} \)
coefficient offiction between \( \mathbf{B} \) and
floor \( =0.5, \) coefficient offfiction
betweenA and \( \mathrm{B}=0.4 \) and a horizontal
force on \( 10 \mathrm{N} \) is placed of8 \( \mathrm{kg} \) block, then the force friction between \( A \)
and B is:
A. \( 100 N \)
B. 50N
c. \( 40 \mathrm{N} \)
D. None of these


Give the IUPAC name of the following compound.


Assertion
Among all elements of the Group-16 sulphur has the largest tendency to catenation.
Reason
Sulphur-Sulphur bond energy is very high.
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


Assertion
The points (2,1,5) and (3,4,3) lie on
opposite sides of the plane \( 2 x+2 y- \)
\( \mathbf{2} z-\mathbf{1}=\mathbf{0} \)
Reason
The algebraic perpendicular distance from the given points to line have opposite signs.
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 given graph shows the vapor pressure curves for some liquids.
Liquids \( A, B, C \) and \( D \) respectively
are:
A. diethyl ether, acetone, ethyl alcohol, water
B. acetone, ethyl alcohol, diethyl ether, water
c. water, ethyl alcohol, acetone, diethyl ether
D. ethyl alcohol, acetone, diethyl ether, water


A particle starts from rest. Its
acceleration (a) versus time (t) is as
shown in the figure. The maximum
speed of the particle will be:
A \( .110 m / s \)
B. \( 55 m / s \)
\( c .550 m / s \)
D. \( 660 m / s \)


The magnetic flux through a coil perpendicular to its plane and directed into paper is varying according to the relation \( \phi=\left(2 t^{2}+4 t+6\right) m W b \). The
emf induced in the loop at \( t=4 s \) is
\( \mathbf{A} \cdot 0.12 V \)
в. 2.4V
c. \( 0.02 V \)
D. \( 1.2 V \)


A bus shuttles between two places
connected by a straight road with uniform speed of \( 36 k m p h \). If it stops at
each place for 15 minutes and the
distance between the two places is
\( 60 k m, \) then what is average value of
velocity?
A. \( 28.5 k m p h \)
в. 28 втрь
c. \( 27.5 k m p h \)
D. \( 29.5 k m p h \)


Which of the above is aromatic?
(i)
(ii)
(iii)
\( (i v) \)
\( (\mathbf{v}) \)
\( A \)
c. iii
\( D \cdot \) iv
\( E \)


A force \( F \) is acting on an object of mass
\( m \) to give it an acceleration of \( a \). If \( m \) is
doubled and \( F \) becomes 16 th times,
what happens to \( a \) ?
A. It is divided by eight
B. It is divided by two
c. It remains unchanged
D. It is multiplied by two
E. It is multiplied by eight


A body of mass \( 3 \mathrm{kg} \) is under a constant force which causes a displacement s in
metres in it,given by the relation \( s= \) \( \frac{1}{2} t^{2}, \) where \( t \) is in seconds. Work done
by the force in 2 seconds is:-
A \( \cdot \frac{5}{19} \)
в. \( \frac{3}{8} \) 」
\( c \cdot \frac{8}{3} \)
D. \( \frac{19}{5} \)


Given \( \boldsymbol{A}=\{\mathbf{5}, \mathbf{6}, \mathbf{7}\} \) and \( \boldsymbol{B}=\{\mathbf{3}, \mathbf{4}\} \)
Form all possible ordered pairs and write the total number of ordered pairs formed so that the first component is from set \( A \) and second component is
from set B.
What is the total number of such pairs?


Per-oxodisulphuric acid has in its
structure :
A. s-s linkage
B. O-Olinkage
c. o-o-olinkage
D. s-o-s linkage


An experiment is performed to
determine the \( I-V \) characteristics of
a Zener diode, which has a protective
resistance of \( R=100 \Omega \), and a
maximum power of dissipation rating
of \( 1 W . \) The minimum voltage range of
the DC source in the circuit is
A. \( 0-24 V \)
В. \( 0-5 V \)
\( \begin{array}{ll}c-12 V & V \\ V V & -0.12\end{array}-12 \)
D. \( 0-8 V \)


Which of the following is redox
reaction?
\( \mathbf{A} \cdot N a O H+H C I \rightarrow N a C l+H_{2} O \)
B. \( A g N O_{3}+K l \rightarrow A g l+K N O_{3} \)
\( \mathbf{c} \cdot B a O_{2}+H_{2} S O_{4} \rightarrow B a S O_{4}+H_{2} O_{2} \)
\( \mathbf{D} \cdot \operatorname{Sn} C l_{2}+H g C l_{2} \rightarrow S n C l_{4}+H g \)


Why are vehicle tyres treaded?
A. To increase friction
B. To decrease friction
c. To multiply friction
D. To decrease grip


Explain corrosion on the basis of following points :
(i) Definition
(ii) Factors affecting any two
(iii) Prevention of corrosion any two


A single slit Fraunhoffer diffraction pattern is formed with white light. For what wavelength of light the third secondary maximum in the diffraction pattern coincides with the second secondary maximum in the pattern for red light of wavelength \( 6500 \stackrel{o}{A} \)
A \( \cdot 4400 \stackrel{\circ}{A} \)
B. 4100 ,
c. \( 4642.8 \stackrel{\circ}{A} \)
D. \( 9100 \stackrel{\circ}{A} \)


In photosynthesis, 6 molecules of
carbon dioxide combine with an
equal number of water molecules through a complex series of reactions to give a molecule of glucose having a
molecular formula \( C_{6} H_{12} O_{6} . \) How many
grams of water would be required to
produce \( 18 ~ g \) of glucose? Compute the volume of water so consumed
assuming the density of water to be
\( 1 g c m^{-3} \)


Which of the following hydrocarbon exists mostly in solid or liquid form under the earth surface?
A. Ethane
B. Methane
c. Pentane
D. Butane


The option(s) with only amphoteric oxides is (are):
This question has multiple correct options
A. \( C r_{2} O_{3}, B e O, S n O, S n O_{2} \)
в. \( C r_{2} O_{3}, C r O, S n O, P b O \)
c. \( Z n O, A l_{2} O_{3}, P b O, P b O_{2} \)
D. \( N O, B_{2} O_{3}, P b O, S n O_{2} \)


The phase difference between two
points is \( \pi / 3 \) and they are 5 mm apart. The frequency of the wave is 300 Hz. The velocity of the wave is
\( A \cdot 5 \mathrm{m} / \mathrm{s} \)
B. 20 \( \mathrm{m} / \mathrm{s} \)
\( c \cdot 9 m / s \)
D. \( 90 \mathrm{m} / \mathrm{s} \)


Among the following, the strongest base
is:
A \( \cdot C_{6} H_{5} N H_{2} \)
в. \( p-N O_{2} C_{6} H_{4} N H_{2} \)
\( \mathbf{c} \cdot m-N O_{2} C_{6} H_{4} N H_{2} \)
D. \( C_{6} H_{5} C H_{2} N H_{2} \)


Balance the reaction of copper sulphide
with dilute hydrochloric acid.
\( \mathbf{A} \cdot C u_{2} S+2 H C l \rightarrow 2 C u C l+H_{2} S \)
B \( \cdot C u_{2} S+H C l \rightarrow C u C l+H_{2} S \)
\( \mathbf{c} \cdot C u_{2} S+H C l \rightarrow C u C l_{2}+H_{2}+S \)
D. \( 2 C u_{2} S+2 H C l \rightarrow 2 C u C l_{2}+S_{2}+H_{2} S \)


Electromagnetic induction is not used
in
A. Transformer
B. Room heater
c. Ac generator
D. Choke coil


Only those elements of s-block can produce superoxides which have :
A. High ionisation energy
B. High electronegativity
c. High charge density
D. Low ionisation potential


\( \frac{1}{2}+\frac{1}{4}+\frac{1}{6}+\frac{1}{8}+\ldots . \) is a
A. sequence
B. series
c. term
D. constant


What is the range of pH of acid rain?
A. More than 5.6
B. Less than 5.6
c. In between 5.6 to 6.6
D. In between 6.0 to 6.6


A uniform solid ball of density \( d \) and of
radius \( r \) is moving vertically downward inside a viscous liquid (density \( =\frac{d}{6} \& \)
coefficient of viscosity \( =\eta \) ) with an
acceleration of \( g / 2 \) at an instant. Speed
of the ball at this instant is
A \( \cdot \frac{1}{6} \frac{r^{2} g d}{\eta} \)
В. \( \frac{5}{27} \frac{r^{2} g d}{\eta} \)
C \( \frac{2}{27} \frac{r^{2} g d}{\eta} \)
D. \( \frac{2}{9} \frac{r^{2} g d}{\eta} \)


Show that \( y=\frac{1}{x} \) is a solution of the differential equation \( \frac{d y}{d x}=\log x \)


Deuteromethane can be prepared if
\( D_{2} O \) reacts with:
\( \mathbf{A} \cdot A l_{4} C_{3} \)
в. \( C a C_{2} \)
c. both A and B
D. none of the above


Solve the following pair of equations by reducing them to a pair of linear equations:
\( \frac{1}{2 x}+\frac{1}{3 y}=2, \frac{1}{3 x}+\frac{1}{2 y}=\frac{13}{6} \)
A \( \cdot x=\frac{1}{4} \) and \( y=\frac{1}{7} \)
B. \( x=\frac{2}{5} \) and \( y=\frac{1}{3} \)
c. \( _{x}=\frac{3}{7} \) and \( y=\frac{1}{7} \)
D. \( x=\frac{1}{2} \) and \( y=\frac{1}{3} \)


Show that the relation \( R \) defined by
\( \boldsymbol{R}= \)
\( \{(a, b): 3 \text { divides } a-b \text { for } a, b \in Z\} \) is
an equivalence relation


State whether true or false.
The land and sea breezes are based on
the fact that the specific heat of
vaporisation of steam is very high.
A . True
B. False


Virtual image cannot be caught on a
screen
A . True
B. False


Which of the following show anaerobic respiration?
A. Earthworm
B. Rabbitt
c. Echinoderms
D. tapeworms


The relationship between the values of osmotic pressure of \( 0.1 \mathrm{M} \) solutions of \( \boldsymbol{K} \boldsymbol{N} \boldsymbol{O}_{3}\left(\boldsymbol{P}_{1}\right) \) and \( \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C O O H}\left(\boldsymbol{P}_{2}\right) \) is:
A \( \cdot P_{1}>P_{2} \)
в. \( P_{2}>P_{1} \)
\( \mathrm{c} \cdot P_{1}=P_{2} \)
D. \( \frac{P_{1}}{P_{1}+P_{2}}=\frac{P_{2}}{P_{1}+2 P_{2}} \)


For the given curve \( y^{2}=8 x, \) which of
the following statements are correct?
I. Length of the latus rectum 8
II. Focal distance to the point (2,4) is 4
III. One of the points on the curve is
(2,-4)
A. Only I and III
B. Only II and III
c. only land II
D. All the three


A bicycle is resting on its stand in the east-west direction and the rear wheel
is rotated at an angular speed of 50 revolutions per minute. If the length of
each spoke is \( 30.0 \mathrm{cm} \) and the
horizontal component of the earth's
magnetic field is \( 4 \times 10^{-5} T \), find the
emf induced between the axis and the
outer end of a spoke. Neglect centripetal
force acting on the free electrons of the spoke.


Assertion
Angular momentum of \( 1 s, 2 s, 3 s, \) etc., all have spherical shape.
Reason
1s, \( 2 s, 3 s, \) etc. all have spherical shape.
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


What describe the Einsteins equation
for the relativity of mass and energy?
A. a small amount of mass contains a lot of energy.
B. a small amount of energy can be converted into a large amount of mass.
C. a small amount of mass contains a small amount of
energy.
D. mass can be converted into energy, but energy cannot be converted mass.
E. energy can be converted into mass, but mass cannot be converted into energy.


If
\( [x] \) denotes the integral part of \( x, \) then domain of the function
\( \boldsymbol{f}(\boldsymbol{x})=\frac{\sqrt{3-x}}{(x-1)(x-2)(x-3)}+\sin ^{-1}\left[\frac{3 x-2}{2}\right] \) is
A . [0,2]
в. \( [0,2)-\{1\} \)
C \( .(-\infty, 3)-\{1,2\} \)
D. None of these


\( \int x\left(f\left(x^{2}\right) g^{\prime \prime}\left(x^{2}\right)-f^{\prime \prime}\left(x^{2}\right) g\left(x^{2}\right)\right) d x= \)
A \( \cdot f\left(x^{2}\right) g^{\prime}\left(x^{2}\right)-g\left(x^{2}\right) f^{\prime}\left(x^{2}\right)+c \)
B \( \cdot \frac{1}{2}\left(f\left(x^{2}\right) g\left(x^{2}\right) f^{\prime}\left(x^{2}\right)\right)+c \)
c. \( \frac{1}{2}\left(f\left(x^{2}\right) g^{\prime}\left(x^{2}\right)-g\left(x^{2}\right) f^{\prime}\left(x^{2}\right)\right)+c \)
D. none of these


Solubility of thorium phosphate (molar
\( \operatorname{mass}=\boldsymbol{m}) \) is \( \boldsymbol{w} \boldsymbol{g} / \mathbf{1 0 0} \mathrm{mL} \) at \( \mathbf{2 5}^{\boldsymbol{o}} \boldsymbol{C} \). The
\( K_{s p} \) of thorium phosphate is:
A
в. \( _{6.912 \times 10^{3}} \times\left(\frac{w}{m}\right)^{7} \)
c. \( _{1.08 \times 10^{7}} \times\left(\frac{w}{m}\right)^{5} \)
D. \( 10^{2} \times\left(\frac{w}{m}\right)^{2} \)


A current in a 240 turn solenoid varies
at \( 0.8 A / s . \) Find emf induced if the
length of the solenoid is \( 12 \mathrm{cm} \) and
radius \( 2 c m \)
A \( \cdot 6.14 \times 10^{-4} V \)
в. \( 6.4 \times 10^{-3} V \)
\( \mathrm{c} .3 .07 \times 10^{-3} \mathrm{V} \)
D. \( 3.07 \times 10^{-4} V \)


A \( 12 \Omega \) resistor and a \( 0.21 H \) inductor
are connected in series to an a.c source
operating at \( 20 ~ V, 50 \) cycle/second.
The phase angle between current and source voltage is
A . \( 30^{\circ} \)
В . \( 40^{\circ} \)
\( c \cdot 80^{\circ} \)
D. \( 90^{\circ} \)


\( 1-6+36-216+\ldots . . \) is a geometric
sequence, find \( r \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. - 6
\( c .36 \)
D . -216


The e/m ratio for electron was
determined by :
A. J.J Thomson
B. Planck
c. Einstein
D. schrodinger


Using properties of determinants, prove
the following:
\( \left|\begin{array}{ccc}a^{2} & b c & a c+c^{2} \\ a^{2}+a b & b^{2} & a c \\ a b & b^{2}+b c & c^{2}\end{array}\right|=4 a^{2} b^{2} c^{2} \)


Which of the following may have
tetragonal?
A \( \cdot K_{4}\left[\operatorname{Fe}(C N)_{6}\right] \)
B. ice
\( \mathrm{c} \cdot K_{2} \mathrm{Cr}_{2} \mathrm{O}_{2} \)
D. Diamond


\( \int_{0}^{\pi / 4} \log (1+\tan x) d x \) is equal to
A \( \cdot \frac{\pi}{8} \log _{e} 2 \)
в. \( \frac{\pi}{4} \log _{e} e \)
c. \( \frac{\pi}{4} \log _{e} 2 \)
D \( \cdot \frac{\pi}{8} \log _{e}\left(\frac{1}{2}\right) \)


In the adjacent figure, a line \( n \) falls on
lines \( l \) and \( m \) such that the sum of the
interior angle 1 and 2 is less than \( 180^{\circ} \)
then what can you say about lines \( l \) and


When the temperature of a body is equal to that of the surroundings then the body appears
A. in the thermal equilibrium
B. red
c. cold
D. hot


Which choice or choices demonstrate
amphoterism?
\( . H C l+H_{2} O \rightarrow H_{3} O^{+}+C l^{-} \) and
\( \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{N}_{3} \rightarrow \boldsymbol{O} \boldsymbol{H}^{-}+\boldsymbol{N} \boldsymbol{H}_{4}^{-} \)
ii. \( \boldsymbol{H} \boldsymbol{S}^{-}+\boldsymbol{H} \boldsymbol{C l} \rightarrow \boldsymbol{C l}^{-}+\boldsymbol{H}_{2} \boldsymbol{S} \) and
\( \boldsymbol{H} \boldsymbol{S}^{-}+\boldsymbol{N} \boldsymbol{H}_{3} \rightarrow \boldsymbol{N} \boldsymbol{H}_{4}^{+}+\boldsymbol{S}^{2-} \)
iii. \( \boldsymbol{H C l}+\boldsymbol{N a O H} \rightarrow \boldsymbol{N a C l}+\boldsymbol{H}_{2} \boldsymbol{O} \)
and \( N a C l+H_{2} O \rightarrow H C l+N a O H \)
A . i only
B. ii only
c. iii only
D. i and ii only
E. i and iii only


A proton of mass ' \( m^{\prime} \) moving with a
speed ' \( v_{0}^{\prime} \) approaches a stationary proton that is free to move. Assume impact parameter to be zero, i.e. headon collision. How close will the incident
proton go to other proton?
A \( \cdot \frac{\epsilon^{3}}{\pi \epsilon_{0} m^{2} v_{0}} \)
В. \( \frac{\epsilon^{3}}{\pi \epsilon_{0} m v_{0}} \)
\( ^{\mathrm{C}} \frac{\epsilon^{2}}{\pi \epsilon_{0} m v_{0}^{2}} \)
D. None of the above


A body of mass 15 kg moving with a
velocity of \( 10 \mathrm{ms}^{-1} \) is bought to rest. The work done by the brake is
A. \( -250 J \)
в. \( -500 J \)
c. \( -750 J \)
D. \( -1000 J \)


Write the negation of the following statement and check whether the
resulting statement is true.
The sum of 2 and 5 is 9


\( \frac{C_{0}}{1}+\frac{C_{1}}{2}+\frac{C_{2}}{3}+\ldots \ldots+\frac{C_{10}}{11}= \)
A \( \cdot \frac{2^{11}}{11} \)
B. \( \frac{2^{11}-1}{11} \)
c. \( \frac{3^{11}}{11} \)
D. \( \frac{3^{11}-1}{11} \)


The rate of change in concentration of \( C \) in the reaction \( 2 A+B \rightarrow 2 C+3 D \)
was reported as 1.0 mol litre \( ^{-1} \) sec \( ^{-1} \)
Calculate the reaction rate.
A. 0.05 mol litre \( ^{-1} \) sec \( ^{-1} \)
B. 0.01 mol litre \( ^{-1} \) sec \( ^{-1} \)
c. 0.5 mol litre \( ^{-1} \) sec \( ^{-1} \)
D. 5 mol litre \( ^{-1} \) sec \( ^{-1} \)


Which of the following is a subaeria
stem modification with long internode?
A. Rhizome
B. Offset
c. Runner
D. sucker


Assertion
Tin exhibits +2 and +4 oxidation
states only and not +3 oxidation state.
Reason
Inert pair effect of electrons in the sorbital is responsible.
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


State the given statement is true or false.
Statement: In calcination and roasting, volatile impurities are removed.
A. True
B. False


Energy required to break a bond of DNA is approximately
\( A \cdot-1 e V \)
B. 0.1 ev
c. \( \sim 0.01 \mathrm{ev} \)
D. 2.1 ev


The scores on standardized admissions
test are normally distributed with a mean of 500 and a standard deviation
of \( 100 . \) What is the probability that a randomly selected student will score between 400 and 600 on the test?
A. About \( 63 \% \)
B. About \( 65 \% \)
c. About \( 68 \% \)
D. About \( 70 \% \)


\( \boldsymbol{R} \) that carries a charge uniformly
distributed throughout its volume. The
volume charge density is \( \rho . \) A Gaussian
sphere of radius \( a \) is imagined that is
concentric to the charged sphere.

If \( a>R, \) what is the charge enclosed in
the Gaussian surface?
\( \mathbf{A} \cdot Q_{e n c}=4 \pi \rho R^{2} \)
\( ^{\mathbf{B}} Q_{e n c}=\frac{4}{3} \pi \rho a^{3} \)
\( \mathbf{c} \cdot Q_{e n c}=4 \pi \rho a^{2} \)
\( \mathrm{D} \)
\( E \cdot Q_{e n c}=\pi \rho a^{2} \)


Find the equation of the tangent to the curve \( \boldsymbol{y}=\sqrt{\mathbf{3} \boldsymbol{x}-\mathbf{2}} \) which is parallel to
the line \( 4 x-2 y+5=0 \)


Evaluate \( \int \frac{x}{\sqrt{x^{2}+2}} d x \)
A \( . I=\sqrt{x^{2}-2}+C \)
B. \( I=\sqrt{x^{2}+2}+C \)
c. \( I=\sqrt{x^{3}+2}+C \)
D. \( I=\sqrt{x^{3}-2}+C \)


The major site of absorption in alimentary canal is
A. Duodenum
B. Stomach
c. Ileum
D. Large intestine


If \( \left|\begin{array}{lll}a & a^{3} & a^{4}-1 \\ b & b^{3} & b^{4}-1 \\ c & c^{3} & c^{4}-1\end{array}\right|=0 \) and \( a, b, c \) are all
distinct, then \( a b c(a b+b c+c a) \) is
equal to
A. \( a+b+c \)
B. abc
\( c \cdot 0 \)
D. none of these


State whether the given statement is true or false if A triangle OAB where \( \overrightarrow{O A}=a, \overrightarrow{O B}=b \) Find the value of \( a \times \)
\( b+b \times c+c \times a \) will be perpendicular
to plane ABC.


Evaluate: \( \tan ^{-1} \sqrt{3}-\cot ^{-1}(-\sqrt{3}) \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( 2 \sqrt{3} \)
\( c \cdot-\frac{\pi}{2} \)
D.


Differentiate \( \log \sqrt{\frac{1+\cos x}{1-\cos x}} w . r . t . x \)


Complete the reaction.


What does an electric generator
generate?
A. current
B. Magnetism
c. Gravity
D. Light


A point source of light is moving at a rate of \( 2 \mathrm{cm}-s^{-1} \) towards a thin
convex lens of focal length \( 10 \mathrm{cm} \) along
its optical axis. When the source is
\( 15 c m \) away from the lens the image is
moving at
A \( \cdot 4 \mathrm{cm}-s^{-1} \) towards the lens
B. \( 8 \mathrm{cm}-s^{-1} \) towards the lens
C. \( 4 \mathrm{cm}-s^{-1} \) away from the lens
D. \( 8 \mathrm{cm}-s^{-1} \) away from the lens


An oxide of nitrogen contains \( 36.8 \% \) by weight of nitrogen. The formula of the compound is:
A \( . N_{2} \)
B. \( N_{2} O_{3} \)
c. \( N O \)
D. \( N O_{2} \)


When a drop of oil is spread on a water
surface, it displays beautiful colors in daylight because of
A. dispersion of light
B. reflection of light
c. polarization of light
D. interference of light


Two identical cells, each of emf \( \mathrm{E} \),
having negligible internal resistance are connected in parallel with each other across an external resistance \( R \)
what is the current through this resistance?


A vertical wire kept in Z-X plane carries
a current from \( Q \) to \( P \) (see figure.). The
magnetic field due to current will have
the direction at the origin 0 along
\( A \cdot O x \)
B. ox
\( c \cdot \) or
D. or


If
on a smooth horizontal surface. \( A \)
particle of mass ' \( m \) ' and velocity \( v_{0} \)
strikes as shown in figure. As a result of
the collision, the centre of mass of rod
attains a speed of \( v_{0} / 8 \) and the particle
rebounds back with a speed of \( \boldsymbol{v}_{\mathbf{0}} / \mathbf{4} \). The
ratio \( \frac{M}{m} \) is :
\( ^{\mathbf{A}} \cdot \frac{M}{m}=10 \)
B. \( \frac{M}{m}=4 \)
\( ^{\mathrm{C}} \cdot \frac{M}{m}=8 \)
D. \( \frac{M}{m}=5 \)


Which metal sulphide has maximum solubility in water?
A \( \cdot \operatorname{CdS}\left(K_{s p}=36 \times 10^{-30}\right) \)
B . \( \operatorname{Fe} S\left(K_{s p}=11 \times 10^{-20}\right) \)
C. \( \operatorname{Hgs}\left(K_{s p}=32 \times 10^{-54}\right) \)
D. \( Z n S\left(K_{s p}=11 \times 10^{-22}\right) \)


The lengths of the tangents (in \( c m \) ) measured by a ruler are:
\( \mathbf{A} \cdot \mathbf{6} \)
B. 7
c. 8
D. 9


A value of c which the conclusion of
Mean Value Theorem holds for the
function \( \boldsymbol{f}(\boldsymbol{x})=\log _{e} \boldsymbol{x} \) on the interval
[1,3] is
\( \mathbf{A} \cdot 2 \log _{3} e \)
B - \( \frac{1}{2} \log _{e} 3 \)
\( c \cdot \log _{3} \)
\( \mathrm{D} \cdot \log _{e} 3 \)


Derivation for weight pf an object on the surface of the moon.


If tangents are drawn from the endpoints of two radii that are inclined
at an angle \( 105^{\circ}, \) what is the angle
between the tangents?
A \( \cdot 5^{\circ} \)
B. 35
\( c \cdot 75 \)
D. None of these


The atoms of sample \( A \) after passing of
light through it
A. May be in the first excited state
B. May be in the second excited state
c. May be in both first and second excited states
D. None of the above


If \( \left(1+x^{2}\right)^{2}(1+x)^{n}=C_{0}+C_{1} x+ \)
\( C_{2} x^{2}+\cdots, \) and if \( C_{0}, C_{1}, C_{2} \) are in A.P.
find \( n \)
This question has multiple correct options
A .2
B. 3
\( c \cdot 4 \)
D. 5


The density of newly discovered planet is twice that of the earth. The
acceleration due to gravity at the surface of the planet is equal to that at the surface of the earth. If the radius of
the earth is It the radius of the plane would be
A \( .2 . R \)
в. \( 4 R \)
c. \( \frac{1}{4} R \)
D・\( \frac{1}{2} R \)


If \( \boldsymbol{x}=\mathbf{2}^{\mathbf{3}} \times \mathbf{4}^{\mathbf{2}} \times \mathbf{1} \mathbf{7}^{\mathbf{3}}, \) then which
number should be divided by \( x \) to get a
perfect cube.
\( A \cdot 2 \)
B. 4
c. 8
D. 17


\( \mathrm{CoCl}_{3} \cdot 3 \mathrm{NH}_{3} \) does not form any
precipitate with excess \( A g N O_{3} \) solution, whereas 1 mole of
\( \mathrm{CoCl}_{3} \cdot 5 \mathrm{NH}_{3} \) gives two moles of \( \mathrm{AgCl} \)
with excess \( A g N O_{3} . \) The van't Hoff factor for both the compounds
respectively are:
A. 0 and 2
B. O and 3
\( c \cdot 1 \) and 3
D. 1 and 2


Vessels are found in: -
A. All angiosperms and some gymnosperm
B. Most of the angiosperm and few gymnosperms
C. All angiosperms, all gymnosperms and some pteridophyta
D. All pteridophyta


The potential energy between two atoms in a molecule is given by, \( U_{(x)}=\frac{a}{x^{12}}- \) \( \frac{B}{X^{6}}, \) where a and b are positive
constants and \( x \) is the distance
between the atoms. The system is in stable equilibrium when -
\( \mathbf{A} \cdot x=0 \)
B \( \cdot x=\frac{a}{2 b} \)
c. \( x=\left(\frac{2 a}{b}\right)^{1 / 6} \)
D. \( x=\left(\frac{11 a}{5 b}\right) \)


Which is the important constituent \( (95 \%) \) of natural gas?
A. Methane
B. Propane
c. Ethane
D. Chlorine


A surface is hit elastically and normally by n balls per unit time. All the balls
have same mass \( \mathrm{m} \) and moves with the
same velocity u. The force on the
surface is :
A \( \cdot 1 / 2 \) mnu \( ^{2} \)
B. mnu \( ^{2} \)
\( c \cdot 2 m n u^{2} \)
D. 2 mnu


In the laboratory chlorine gas can be prepared from:
A. manganese dioxide and sodium chlorine
B. red lead
c. hypo
D. bleaching powder


Fermentation was discovered by:
A. Vant Hoff and Le Bell
B. Louis Pasteur
c. Berzelius
D. Kolbe


A person who is not taking food or beverages will have in urine
A. Little glucose
B. Less urea
c. Excess urea
D. Little fat


Compare and justify the dipole moment
of \( N H_{3} \) and \( N F_{3} \)


Why does starch form a thick paste
when it is boiled with water?
\( A \cdot O \)


Complete the following sentence : A rod is brought near the disc of a positively charged gold leaf electroscope. Ifthe divergence of leaves \( \ldots, \) the rod is positively charged; if the divergence of leaves ......... the rod is negatively charged; if the divergence of leaves \( \ldots \ldots . \) the rod is uncharged.
A. decreases, decreases, decreases
B. increases, decreases, increases.
c. increases, increases, decreases
D. increases, decreases, decreases.


What are the risk factors for
adolescents?


State True or False.
In the electrolysis of fused calcium hydride, hydrogen is liberated at cathode.
A. True
B. False


If two balls each of mass \( 0.06 \mathrm{Kg} \)
moving in opposite directions with speed \( 4 \mathrm{m} / \mathrm{sec} \) collides and rebound
with the same speed,then coefficient of restitution for the collision will be:-
\( A \cdot \frac{1}{4} \)
B.
\( c \)
D.


Both ATP and \( M g^{2+} \) are involved in the
activity of
A. Pyruvic Kinase
B. Glucokinase
c. Phosphogluco isomerase
D. PGA dehydrogenase


\( \alpha, \beta \) and \( \gamma \) radiations come out of a rodiactive substance
A. when it is heated
B. when put in atomic reactor
c. spontaneously
D. under pressure


An electric bulb generally uses a filament coated with
A. Platinum
B. Thorium
c. silver
D. Radium


Write the two steps involved in the
mechanism of the enzyme-catalyzed
reaction.


Prove that
\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left(\cot \boldsymbol{h}^{-1} \boldsymbol{x}\right)=\frac{-\mathbf{1}}{\left(\boldsymbol{x}^{2}-\mathbf{1}\right)} \)


What are the applications of
\( 45^{\circ}, 90^{\circ}, 45^{\circ} \) prism?
A. deviate a light through \( 90^{\circ} \)
B. deviate a light through \( 180^{\circ} \)
c. erect the inverted image without deviation
D. all of the above


Due to the loss of the following electrons, transition metal shows variable valency:
\( A \cdot n s \)
B. ns and np
\( c \cdot(n-1) d \)
D. (n-1)d and ns


If a diamagetic solution is poured into a U-tube and one arm of this U-tube is
placed between the poles of a strong magnet, with the meniscus in line with the field, then the level of solution will :
A . rise
B. fall
c. oscillate slowly
D. remain as such


A series R-C circuit is connected to an
alternating voltage source. Consider two situation:
(a) When capacitor is filled
(b) When capacitor is mica filled Current through resister is i and voltage across capacitor is \( V \) then :
A \( . V_{a}=V_{b} \)
в. \( V_{a}<V_{b} \)
c. \( V_{a}>V_{b} \)
\( \mathbf{D} \cdot i_{a}=i_{b} \)


Pollen extract stimulates the formation
of fruit in the unpollinated carpe because extract has which of the
following hormone?
A. Auxin
B. Cytokinin
c. Gibberellin
D. Auxin and cytokinin


Which element does not show allotropy?
\( A \cdot P b \)
B. si
\( c \cdot c \)
D. sn


Hydrolysis of d-sucrose result in change
of optical rotation because
A. number of moles of d-Glucose are less than number of
moles of I-Fructose produced during hydrolysis.
B. Angle of rotation of I-Fructose is greater than AOR of dGlucose
C. Both glucose and fructose are levorotatory.
D. Glucose is I and fructose is d and number of moles of glucose formed during reaction are greater than number of moles of fructose.


Write the differential equation
representing family of curves \( \boldsymbol{y}=\boldsymbol{m} \boldsymbol{x} \)
where \( m \) is arbitrary constant.


Bromine is
A . Liquid metal
B. Liquid non metal
C. Gaseous non metal
D. Solid non metal


If we wrote \( n^{3} \) as the sum of
consecutive odd numbers then what
will be the first term.
\( \mathbf{A} \cdot 2 n+1 \)
B. \( (2 n+1)(2 n-1) \)
c. \( 2 n-1 \)
D. \( n(n-1)+1 \)


Two conductors each of length \( 12 m \) lie
parallel to each other in air. The centre
to centre distance between the two
conductors is \( 15 \times 10^{-2} m \) and the
current in each conductor is \( 300 A \). The
force in newton tending to pull the conductors together is:
A . \( 14.4 N \)
B. \( 1.44 N \)
c. \( 144 N \)
D. \( 0.144 N \)


Prove that:
\( \tan x+\tan \left(\frac{\pi}{3}+x\right)-\tan \left(\frac{\pi}{3}-x\right)= \)
\( 3 \tan 3 x \)


The diameter of the circle is \( 2 \mathrm{cm} \). What
is the circumference?
\( \mathbf{A} \cdot 12.28 \mathrm{cm} \)
B. \( 6.2 \mathrm{cm} \)
c. \( 18.28 \mathrm{cm} \)
D. \( 10.28 \mathrm{cm} \)


The given graph shows an oxygen dissociation curve for haemoglobin.
Where in the body will haemoglobin be saturated at the percentages shown at
points 1,2 and 3 on the graph?
A. Left ventricle1Pulmonary vein2 Vena cava3
B. Left ventricle2Pulmonary vein1Vena cava3
c. Left ventricle2Pulmonary vein3Vena caval
D. Left ventricle3Pulmonary vein2Vena cava


The distance, from the origin, of the
normal to the curve, \( \boldsymbol{x}=\mathbf{2} \cos \boldsymbol{t}+ \)
\( \mathbf{2} t \sin t, y=2 \sin t-2 t \cos t \) at \( t=\frac{\pi}{4}, \) is
\( A \cdot 2 \)
B. 4
\( c \cdot \sqrt{2} \)
D. \( 2 \sqrt{2} \)


Leaf pores/ stomata help in
A. Intake of \( C O_{2} \) during photosynthesis
B. Release of \( O_{2} \) during photosynthesis
C. Release of water vapour during transpiration
D. All of these


When a divergent beam of light is incident on a plane mirror, the image formed is
A. Upright and real
B. Upright and virtual
c. Inverted and virtual
D. Inverted and real


For a real number r let \( [r] \) denote the
largest integer less than or equal to \( r \)
Let \( a>1 \) be a real number which is not
an integer, and let k be the smallest positive integer such that \( \left[\boldsymbol{a}^{k}\right]>[\boldsymbol{a}]^{k} \)
Then which of the following statements is always true?
A \( \cdot k \leq(2[a]+1)^{2} \)
B . \( k \leq([a]+1)^{4} \)
c. \( k<2^{[a]+1} \)
D. \( _{k \leq \frac{1}{a-[a]}}+1 \)


There are two lead spheres at the same temperature, the ratio of radii being 1
2. The ratio of heat capacities are:
A \( \cdot 1: 2 \)
B. 1: 4
\( c \cdot 1: 6 \)
D. 1: 8


\( 2 N O B r(g) \rightleftharpoons 2 N O(g)+B r_{2}(g) . \) If
nitrosyl bromide \( (N O B r) \) is \( 33.33 \% \)
dissociated at \( 25^{\circ} \mathrm{C} \) and a total
pressure of 0.28 atm. Calculate \( K_{p} \) for the dissociation at this temperature


When steam is passed through zinc,
then:
This question has multiple correct options
A. hydrogen gas is liberated
B. znc hydroxide is formed
\( \mathrm{C} \). znc oxide is formed
D. \( H C I \) is formed


The diagram shows the melting and
boiling points of four different substances. Which substance has a
melting point at \( -20^{\circ} \mathrm{C} \) and a boiling
point at \( 160^{\circ} \mathrm{C} \) ? Also identify the two
substances having same boiling points


the anode is kept at positive potential
with respect to the cathode.
A. themions are get attracted towards the anode and accelerate towards the anode
B. themions are get deviated towards the anode and accelerate towards the anode
C. themions get attracted towards the cathode and accelerate towards the cathode
D. none of these


\( U^{235}, U^{238}, U^{239} \) are the atoms of the uranium. Which are called as
A. Isomers
B. Isobars
c. Isotopes
D. None of these


The common ingredient required for making cement and glass is:
A. washing soda
B. baking soda
c. limestone
D. potash


Prove that the function \( f(x)=\log _{e} x \) is
increasing on \( (\mathbf{0}, \infty) \)


A mass m rotates in a vertical circle of
radius, \( R \) and has a circular speed \( v_{c} \) at the top.- If the radius of the circle is increased by a factor of \( 4, \) circular speed at the top will be
A. decreased by a factor of 2
B. decreased by a factor of 4.
c. increased by a factor of 2
D. increased by a factor of 4


Their contraction is involuntary, vigorous and rhythmic holds true for
A. Striated muscles
B. Cardiac muscles
c. Unstriated muscles
D. None of the above


A particle moves along a straight line such that its displacement at any time is given by \( s=\left(t^{3}-6 t^{2}+3 t+4\right) m \)
Find the velocity when the acceleration
is zero.


Potassium permanganate is used for purifying drinking water, because:
A. it is a sterilising agent
B. it dissolves the impurities of water
c. it is a reducing agent
D. it is an oxidising agent


Photoelectric effect supports quantum
nature of light because
This question has multiple correct options
A. there is a maximum frequency of light below which no photoelectrons are emitted
B. the maximum kinetic energy of photoelectrons depends only on the frequency of light and not on its intensity
C. even when the metal surface is faintly illuminated, the photoelectrons leave the surface immediately
D. electric charge of the photoelectrons is quantized


The equation of ellipse with the length
of major and minor axis as \( 12,16 \mathrm{cm} \) respectively is


Assertion
\( s p^{3} \) hybrid carbon atom is more electronegative than sp hybrid carbon
atom.
Reason
\( s p^{3} \) hybrid orbitals are more closer to
the nucleus
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


In the situation shown in figure, a
wedge of mass \( m \) is placed on a rough surface, on which a block of equal mass is placed on the inclined plane of wedge The friction coefficient between the
wedge and the block and also between
the ground and the wedge is \( \mu . A n \) external force \( F \) is applied horizontally
on the wedge towards the right, assuming block does not slide on the
wedge. Find the minimum value of Force
\( F \) at which the block will start slipping.


For a dilute solution containing 2.5 g of a non-volatile non-electrolyte solute in \( 100 \mathrm{g} \) of water, the elevation in boiling
point at 1 atm pressure is \( 2^{\circ} C \) Assuming concentration of solute is much lower than the concentration of
solvent, the vapour pressure (mm of Hg) of the solution is:
\( \left[\boldsymbol{K}_{\boldsymbol{b}}=\mathbf{0 . 7 6} \boldsymbol{K} \boldsymbol{K} \boldsymbol{g} \boldsymbol{m o l}^{-1}\right] \)
A . 724
в. 740
\( c \cdot 736 \)
D. 718


The pull or push acting on a body is commonly called force. State true or false.


A circular disc is rotating about its own natural axis. A constant opposing torque \( 2.75 N m \) is applied on the disc due to which it comes to rest in 28
rotations. If moment of inertia of disc is
\( 0.5 k g m^{2}, \) the initial angular velocity of
disc is:
A . 210 rpm
в. 280 rpm
c. \( 360 r p m \)
D. 420 rpm


\( H_{2} \) is best alternative to fossil fuels but
use of hydrogen as a fuel is dangerous
because:
A. it is chemically unstable.
B. the storage of \( H_{2} \) is very risky and can causes explosion.
c. it is very expensive.
D. it causes the corrosion of containers in which it is present


A point object is placed at the centre of
a glass sphere of radius \( 6 \mathrm{cm} \) and
refractive index \( 1.5 . \) The distance of
virtual image from the surface is:
A. \( 6 \mathrm{cm} \)
в. 4 ст
c. \( 12 \mathrm{cm} \)
D. 9 ст


What does Newton's colour disc
possess?
A. 7 segments in rainbow colours
B. 5 segments in rainbow colours
C. 4 segments in rainbow colours
D. 9 segments in rainbow colours


Radiation depends on:
A. the temperature of the substance
B. the colour of the substance
c. both the above
D. none of these


Which of the following is not related to the autonomic nervous system?
A . Peristalsis
B. Digestion
c. Excretion
D. Memory and learning


A balloon, which always remains
spherical, has a variable diameter \( \frac{3}{2}(2 x+1) . \) Find the rate of change of its volume with respect to \( x \)


\( \boldsymbol{C l}-\boldsymbol{C H}=\boldsymbol{C H}-\dot{C}_{\boldsymbol{H}}-\boldsymbol{C H}=\boldsymbol{C H} \)
\( C l \)
Find the total number of stereoisomers
of the following compound.


Safranin stains which element of the
tissues?
A. Starch elements
B. Lignified elements
\( c . \) Bast
D. Protein elements


\( N a O H+H_{2} S O_{4} \rightarrow N a_{2} S O_{4}+H_{2} O \)
Balance the given chemical equation


The remainder when the determinant
\( \left|\begin{array}{lll}2014^{2014} & 2015^{2015} & 2016^{2016} \\ 2017^{2017} & 2018^{2018} & 2019^{2019} \\ 2020^{2020} & 2021^{2021} & 2022^{2022}\end{array}\right| \)
is divided by 5 is.
A . 1
B . 2
\( c \cdot 4 \)
\( D \)


Assertion
If the length of the conductor is doubled, the drift velocity will become half of the original value (keeping potential difference unchanged).
Reason
At constant potential difference, drift
velocity is inversely proportional to the length of the conductor.
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


How are the following conversions carried out?
Propene to Propan-2-ol


Which of the following statement is
false?
A. Elements of \( n s^{2} n p^{6} \) electronic configuration lies in \( 1^{s t} \) to \( 6^{t h} \) period
B. Typical elements lies in \( 3^{r d} \) period
C. The seventh period will accommodate thirty two elements
D. Boron and silicon are diagonally related


If \( A \) and \( B \) are skew symmetric
matrices of order \( n \) then \( A+B \) is
A. skew symmetric
B. a diagonal matrix
c. a null matrix
D. symmetric matrix


\( \boldsymbol{C}+\boldsymbol{2} \boldsymbol{C u} \boldsymbol{O} \rightarrow \boldsymbol{X}+\boldsymbol{Y} \)
The compound \( X \) and \( Y \) are :
A. \( C O_{2}, 2 C u \)
в. \( C O, C u_{2} O \)
\( c . \) both \( A \) and \( B \)
D. none of the above


The vertices \( A \) and \( B \) of a triangle \( A B C \)
\( \operatorname{are}(2,1) \) and (3,-2) respectively. If the third vertex \( C \) lies on the locus \( y=x+ \)
9 and the centroid of \( \triangle A B C \) lies on \( Y \)
axis, then find the area.


In a hydraulic lift, used at a service station, the radius of the large and small piston is in the ratio of 20:
1. What weight placed on the small piston will be sufficient to lift a car of mass 1500 kg?
A. \( 3.75 \mathrm{kg} \)
B. 37.5 kg
c. \( 7.5 \mathrm{kg} \)
D. 75 kg


Which of the following is not a disproportionation reaction?
A. Cannizzaro reaction
B. Decomposition of \( H_{2} O_{2} \) to \( H_{2} O \) and \( O_{2} \)
c. Decomposition of ozone to \( O_{2} \)
D. Decomposition of \( K C l O_{3} \) to \( K C l O_{4} \) and \( K C l \)


Intramolecular H-bonding is present in:
A. \( O- \) nitrophenol
в. \( H C l \)
\( c . H B r \)
D. \( H F \)


The standard EMF of quantity electrode is \( 0.699 V . \) The EMF of the
quinhydrone electrode dipped in a solution with \( \mathrm{pH}=10 \) is:
A \( .0 .109 V \)
\( V \)
B. \( -0.109 V \)
c. \( 1.289 V \)
D . \( -1.289 V \)


The titanium (atomic number \( =22 \) )
compound that does not exist is :
A . \( T i O \)
в. \( T i O_{2} \)
\( \mathrm{c} . K_{2} T i O_{4} \)
D. \( K_{2} T i F_{6} \)


A conductor \( A B \) of length \( l \) moves in \( x-y \) plane with velocity \( \overrightarrow{\boldsymbol{v}}=\boldsymbol{v}_{0}(\hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}) \cdot \boldsymbol{A} \)
magnetic field \( \vec{B}=B_{0}(\hat{i}+\hat{j}) \) exists in the region. The induced emf is
A . zero
в. \( 2 B_{0} \) lv \( _{0} \),
c. \( B_{0} l v_{0} \)
D. \( \sqrt{2} B_{0} l v_{0} \)


What is the correct IUPAC name of the
following compound?
A. Bicyclo-octane
B. Tricyclo-octane
c. Bicyclo[3.2.1]octane
D. Bicyclo[1.2.3]octane


Dacron is an example of a/an:
A. elastomer
B. fibre
c. thermoplastic
D. thermosetting polymer


Assertion
NAND or NOR gates are called digital building blocks.
Reason
The repeated use of NAND (or NOR) gates can produce all the basis or complicated gates.
A. Assertion is true, Reason is true; Reason is a correct explanation for Assertion
B. Assertion is true, Reason is true; Reason is not a correct explanation for Assertion
C. Assertion is true, Reason is false
D. Assertion is false, Reason is true


A body of mass \( 10 \mathrm{kg} \) dropped from a height \( 20 \mathrm{m}, \) acquires a velocity of 10 \( \mathrm{m} / \mathrm{s} \) after falling through a distance of 20 \( \mathrm{m} \). What is the work done by the air resistance on the body?
A. 750 J
B. 1000
c. 1500
D. 2000 J


The temperature of boiling water in the Kelvin scale of temperature is:
\( \mathbf{A} \cdot 100 \mathrm{K} \)
B. 373.15 К
c. 212 к
D. 273.15 К


Apparent loss of weight of a body when immersed in a liquid can be explained on the basis of
A. molecular theory
B. electron theory
c. Archimedes' principle.
D. Bernoulli's principle.


Find the common difference and write
the next four terms of the \( A P: \)
\( -1, \frac{1}{4}, \frac{3}{2}, \)
A \( \cdot d=\frac{5}{2} ; a_{4}=\frac{11}{4}, a_{5}=\frac{16}{4}, a_{6}=\frac{21}{4}, a_{7}=\frac{26}{4} \)
B. \( d=\frac{5}{4} ; a_{4}=\frac{11}{4}, a_{5}=\frac{16}{4}, a_{6}=\frac{21}{4}, a_{7}=\frac{26}{4} \)
C. \( d=\frac{5}{4} ; a_{4}=\frac{11}{4}, a_{5}=\frac{16}{4}, a_{6}=\frac{21}{4}, a_{7}=\frac{25}{4} \)
D. \( d=\frac{5}{2} ; a_{4}=\frac{11}{4}, a_{5}=\frac{16}{4}, a_{6}=\frac{21}{4}, a_{7}=\frac{25}{4} \)


A conductor carries a constant current
along the closed path abcdefgha
nvolving 8 of the 12 edges each of
ength I.Find the magnetic dipole moment of the closed path. The answer
is \( M=x I l^{2} \hat{j} \) then \( x \) is


In the sequence of changes/processes in the following,identify XYZ. replication \( (X)-> \) transciption \( (Y) \rightarrow \)
(Z)translation
A. DNA, DNA and RNA
B. RNA, RNA and DNA
D. DNA, RNA and DNA


a) Using the phenomenon of polarization, show how transverse nature of light can be demonstrated.
b) Two polaroids \( P_{1} \) and \( P_{2} \) are placed
with their pass axes perpendicular to
each other. Unpolarised light of
intensity \( I_{0} \) is incident on \( P_{1} . \) A third
Polaroid \( P_{3} \) is kept in between \( P_{1} \) and \( P_{2} \)
such that its pass axis makes an angle
of \( 30^{\circ} \) with that of \( P_{1} \). Determine the intensity of light transmitted through
\( P_{1}, P_{2} \) and \( P_{3} \)


Maximum number of electrons held in
the d orbitals is :
\( A \cdot 2 \)
B. 6
c. 8
D. 10
E. 14


Pick up the correct statement:
(a) Synapsis of homologous chromosomes occurs during prophase I
(b) Division of centromeres takes place during anaphase I
(c) Spindle fibres disappear completely in telophase of mitosis.
(d) Nucleoli may reappear in telophase
A . a only
B. conly
c. a and bonly
D. a, c and d only


Solve the inequality with absolute value
\( -3|-2 x+4|<=4 \)
\( ^{A} \cdot\left(-\infty, \frac{7}{3}\right) \)
B \( \cdot\left(\frac{7}{3},+\infty\right) \)
\( ^{c} \cdot\left(\frac{7}{3},+\frac{7}{3}\right) \)
D \( \cdot\left(0, \frac{7}{3}\right) \)
E \( .(-\infty,+\infty) \)


Find the values of the unknown \( x \) and
n the following diagram.


Easily liquefied gases undergo chemisorption more efficiently
If true then enter 1 else enter 0 .


Which of the following is acidic?
A \( \cdot N H_{3} \)
в. \( N_{2} H_{4} \)
c. \( N_{2} H_{2} \)
D. \( N_{3} H \)


Two small square on a chess board are
chosen at random. Probability that they have a common side is
A \( \cdot \frac{1}{3} \)
в. \( \frac{1}{9} \)
c. \( \frac{1}{18} \)
D. None of these


A battery of \( V \) voltage is connected
across the potentiometer wire \( \boldsymbol{A} \boldsymbol{C} \) of
total resistance \( R_{0} \) as shown. Calculate
the potential across the resistance \( \boldsymbol{R} \) if
the sliding contact point \( B \) is exactly at
the middle of the potentiometer wire.
\( A \)
в. \( \frac{4 V R_{0}}{2 R_{0}+R} \)
c. \( \frac{2 V R}{R_{0}+4 R} \)
D. \( \frac{4 V R_{0}}{R_{0}+2 R} \)


Perform division
\( \left(y^{2}+7 y+10\right) \div 6(y+5) \)


The azeotropic mixture of water (boiling
point \( =100^{\circ} \mathrm{C} \) ) and \( H C l \) (boiling point
\( \left.=85^{\circ} \mathrm{C}\right) \) boils at about \( 110^{\circ} \mathrm{C} . \) During
distillation of this mixture, it is
possible to obtain:
A. pure \( H C l \)
B. pure \( H_{2} O \)
c. pure \( H C l \) as well as \( H_{2} O \)
D. neither pure \( H_{2} O \) nor pure \( H C l \)


Three bodies, a ring, a solid cylinder and
a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of the bodies
are identical. Which of the bodies
reaches the ground with maximum velocity?


A gas mixture \( 3.67 L \) in volume contain
\( C_{2} H_{4} \) and \( C H_{4} \) is proportion of 2: 1 by
moles and is at \( 25^{\circ} \mathrm{C} \) and 1 atm. If the
\( \triangle \boldsymbol{H}_{C}\left(\boldsymbol{C}_{2} \boldsymbol{H}_{4}\right) \) and \( \triangle \boldsymbol{H}_{C}\left(\boldsymbol{C H}_{4}\right) \) are
-1400 and \( -900 k J / \) mol. Find the heat evolved on burning this mixture.
A. \( 20.91 k J \)
В. \( 50.88 k J \)
c. \( 185 k J \)
D. 160 k


Aniline when diazotized in cold and then
treated with dimethylaniline gives a coloured product. Its structure would
be:
\( A \)
B.
\( c \)
\( D \)


Oxidation state of +1 for phosphorous is found in :
A. \( H_{3} P O_{3} \)
в. \( H_{3} P O_{4} \)
\( \mathrm{c} \cdot \mathrm{H}_{3} \mathrm{PO}_{2} \)
D. \( H_{2} P_{2} O_{7} \)


\( N O \) is free radical. What is the number
of unpaired electrons?


Factorise: \( 4 \sqrt{3} x^{2}+5 x-2 \sqrt{3} \)


possible reversible processes performed on a monatomic ideal gas
Process \( A \) is isobaris (constant
pressure). Pressure \( B \) is isothermal
(constant temperature). Process \( C \) is
adiabatic. Process \( D \) is isochoric
(constant volume). For which
process(es) does the temperature of the gas decreases
A. Process A only
B. Process C only
c. only process \( C \) and \( D \)
D. Only process \( B, C \) and


Staring at computer screen for a very long time may cause
A. dry eyes
B. blurry vision
c. eye strain
D. all of these


A thermistor:
A. Is a thermally sensitive resistor
B. Is made of a semiconductor
C. Has negative temperature coefficient of resistance
D. All the above


The temperature at the bottom of a high water fall is higher than that at the top
because
A. by itself heat flows from higher to lower temperature
B. the difference in height causes a difference in pressure
c. thermal energy is transformed into mechanical energy
D. mechanical energy is transformed into thermal energy


The time for half-life period of a certain reacting \( \boldsymbol{A} \rightarrow \) product is an hour. How
much time does it take for its
concentration to come from 0.50 to 0.25
\( \operatorname{mol} L^{-1} \) if it is a zero order reaction?
A . \( 0.25 h \)
B. 1h
\( c \cdot 4 h \)
D. 0.5h


An enzyme that converts disaccharides to monosaccharides is
A. Lactase
B. Kinase
c. zymogen
D. Lipase
E. Phosphatase


Match list - I with List - II
List -

List - II
a) Thermistor
e) High positive \( \boldsymbol{\alpha} \)
b) Carbon
f) \( \alpha \) almost zero
c) Nichrome
g) either positive or negative \( \boldsymbol{\alpha} \)
d) Constantan
h) Negative \( \alpha \) manganin
A. a-g, b-h, c-e, d-f
B. a-h, b-g, c-e, d-f
c. a-e, b-f, c-g, d-h
D. a-e, b-g, c-h, d-f


Which of the following increases blood
pressure and heart beat?
This question has multiple correct options
A. Noradrenaline
B. Dopamine
c. Serotonin
D. Adrenaline


The linear protein that has catalytic
function is
A. actin
B. collaagen
c. mysoin
D. trypsin


f \( P(A)=0.40, P(B)=0.35 \) and
\( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B})=\mathbf{0 . 5 5}, \) then \( \boldsymbol{P}(\boldsymbol{A} / \boldsymbol{B})= \)
\( A \)
5
B. \( \frac{8}{11} \)
\( c \cdot \frac{4}{7} \)
D.


Energy of the electron in Bohr's orbit is equal to?
A. potential energy only
B. Kinetic energy only
c. Sum of potential and kinetic energy
D. difference of kinetic and potential energy


The lens of a simple magnifier has a focal length of \( 2.5 \mathrm{cm} . \) Calculate the angular magnification produced when the image is at the least distance of distinct vision.
A . 10
B. 5
\( c \cdot 8 \)
D. 15


In how much times will a sum of money
becomes three times itself as \( 25 \% \) per
annum \( S I ? \)


In Kjeldahl's method,unreacted sulphuric acid left after absorption of ammonia is estimated by:
A. titrating with standard acid solution
B. titrating with standard alkali solution
c. any of the above
D. none


A body is projected vertically up with velocity \( 10 m / s . \) On reaching the ground, the magnitude of change in its velocity is
A. zero
в. \( 20 \mathrm{m} / \mathrm{s} \)
c. \( -20 m / s \)
D. None


¡) \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}+(\boldsymbol{o}) \)
ii) \( \boldsymbol{H}_{2} \boldsymbol{O}_{2}+\boldsymbol{2} \boldsymbol{I}^{-} \rightarrow \boldsymbol{I}_{2}+\boldsymbol{2} \boldsymbol{O} \boldsymbol{H}^{-}, \boldsymbol{H}_{2} \boldsymbol{O}_{2} \)
acts as:
A. oxidising agent in both (i) and (ii)
B. reducing agent in both (i) and (ii)
c. oxidising agent in (i) and reducing agent in (ii)
D. reducing agent in (i) and oxidising agent in (ii)


The direction cosines of the vectors \( 2 \vec{i}+\vec{j}-2 \vec{k} \) is equal to
A \( \cdot \frac{2}{3}, \frac{1}{3},-\frac{2}{3} \)
B. \( \frac{2}{3}, \frac{1}{3}, \frac{2}{3} \)
c. \( \frac{1}{3}, \frac{2}{3},-\frac{2}{3} \)
D. \( \frac{2}{3}, \frac{2}{3}, \frac{1}{3} \)


The set of isoelectronic ions amongst
the following is:
A. \( N a^{+}, C l^{-}, O^{2-} \)
B . \( K^{+}, C a^{2+}, F^{-} \)
c. \( C l^{-}, K^{+}, S^{2} \)
D. \( H^{+}, B e^{2+}, N a^{+} \)


In the diagram MN, is a straight line.
The distance between \( \mathrm{M} \) and \( \mathrm{N} \) is:
A. 6 units
B. 8 units
c. 9 units
D. 10 units


Match the column


For a process to be in equilibrium:
A. \( \Delta S_{\text {system}}+\Delta S_{S u r r}=0 \)
B. \( \Delta S_{\text {system}}=0 \)
c. \( \Delta S_{\text {system}}=\Delta S_{\text {Surr}} \)
D. \( \Delta S_{S u r r}=0 \)


Which of the following number lines, represents rational numbers?
\( A \)
B.
\( c \)
D. All of the above


Find the smallest number by which the number 108 must be multiplied to obtain a perfect cube
A .2
B. 3
\( c \cdot 4 \)
D. 5


Angle between an equipotential surface and electric lines of force is :
A . \( 0^{\circ} \)
B. \( 90^{\circ} \)
\( c \cdot 180^{\circ} \)
D. \( 270^{\circ} \)


Assertion
The \( 4 f- \) and \( 5 f \) - inner transition series of
elements are placed separately at the bottom of the periodic table.
Reason
(i) This prevents the undue expansion of the periodic table i.e., maintains its
structure.
(ii) This preserves the principle of classification by keeping elements with similar properties in a single column.
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


Explain \( -H_{2} O \) is Liquid but \( H_{2} S \) is a
gas.


Find \( \mathbf{v} \)
\( \lim _{x \rightarrow 0} \frac{x \cos x-\sin x}{x^{2} \sin x} \cdot \) is \( =-\frac{1}{v} \)


In the \( 3 d \) series from \( \operatorname{Sc}(z=21) \) to Zn
\( (z=30), \) enthalpy of atomisation of Zn
is the lowest.


A ray incident at a point at an angle of
incidence \( \theta \) enters into a glass sphere
placed in air which is reflected and
refracted at the farther surface of the
sphere as shown in the figure. The angle between reflected and refracted rays at
this surface is \( 90^{0} . \) If refractive index of
the sphere is \( \sqrt{3}, \) the angle \( \theta \) is :
A \( \cdot \frac{\pi}{3} \)
B. \( \frac{\pi}{4} \)
c. \( \frac{\pi}{6} \)
D. \( \frac{2 \pi}{3} \)


The order and degree of the differential equation, \( \left(\frac{d^{2} y}{d x^{2}}\right)^{3}=\sin y+3 x \quad \) are
A . 3,2
B . 2,3
\( c .3, \) not defined
D. Not defined, 2


Which of the following statement(s)
is/are true?
This question has multiple correct options
A. The ratio of the mean velocity to the rms velocity of a gas molecule is independent of temperature.
B. The square of the most probable speed of the gas molecules is equal to four times its average speed.
C. Mean kinetic energy of a gas depends on its mass and temperature but does not depend on volume or
pressure.
D. The difference between rms velocity and mean velocity at any temperature for different gases decreases for gases with large molar mass.


The number of \( S-S \) bonds in sulphur
trioxide trimer \( \left(\boldsymbol{S}_{3} \boldsymbol{O}_{9}\right) \) is :
\( A \cdot 3 \)
B. 2
\( c \)
D.


Name the two modes by which animals reproduce.


Using ruler and compasses only, construct a \( \triangle A B C \) having given
\( \angle A B C=60^{0}, \angle A C B=45^{0} \) and the
perpendicular from \( \boldsymbol{A} \) to \( \boldsymbol{B} \boldsymbol{C} \) equal to
\( 2.5 \mathrm{cm} . \) The length of \( A B \) is
A \( .2 .1 \mathrm{cm} \)
B. \( 2.9 \mathrm{cm} \)
\( c .3 .5 \mathrm{cm} \)
D. \( 4.2 \mathrm{cm} \)


Braille system is commonly used for:
A. mathematics
B. scientific notations
c. languages
D. all of the above


Vinegar is a solution of :
A. \( 50 \%-60 \% \) acetic acid in alcohol
B. 5 \% - 8 \% acetic acid in alcohol
C. \( 5 \%-8 \% \) acetic acid in water
D. 50 \% - 60 \% acetic acid in water


Among the methods for extracting metals from their ores, i.e., \( 1 . \) roasting a metal sulphide, 2. chemical reduction of a metal oxide, and 3. electrolysis, the preferred method depends on \( E^{\circ} \) value
for the reducing half-reaction:
\( M^{n+}(a q)+n e^{-} \rightarrow M(s) \)
Which method is preferred for the metals
with the most negative \( E^{\circ} \) values?


\( \int \frac{3 x+1}{(x-1)^{2}(x+3)} d x= \)
A. \( \log \left|\frac{x-1}{x+3}\right|-\frac{1}{x-1}+c \)
в. \( \frac{1}{2} \log \left|\frac{x-1}{x+3}\right|-\frac{1}{x-1}+c \)
c. \( \frac{1}{2} \log \left|\frac{x-1}{x+3}\right|+\frac{1}{x+1}+c \)
D. \( \frac{1}{2} \log \left|\frac{x+1}{x-3}\right|+\frac{1}{x+1}+c \)


If the one of the roots of the equation is zero find 'a'
\( \boldsymbol{x}^{2}-2 \boldsymbol{a} \boldsymbol{x}+\boldsymbol{a}^{2}+\boldsymbol{a}-\boldsymbol{2}=\mathbf{0} \)
Selective the positive answer.


Solve :
\( \frac{\mathbf{5}}{\boldsymbol{x}+\boldsymbol{y}}-\frac{\mathbf{2}}{\boldsymbol{x}-\boldsymbol{y}}+\mathbf{1}=\mathbf{0} \)
\( \frac{15}{x+y}+\frac{7}{x-y}-10=0 \)


The function of vitamin \( D \) is:
A. calcium absorption in the intestine
B. normal development of bones and teeth
c. deposition of calcium and phosphate in bones
D. all of the above


Combination of haemoglobin with \( O_{2} \) in lungs can be promoted by
\( A \cdot \) Increasing \( C O_{2} \) concentration in blood
B. Increasing \( O_{2} \) concentration in blood
C. Decreasing \( O_{2} \) concentration in blood
D. Introducing \( C O \) in blood


The sum of an infinitely decreasing
geometric progression is 1.5 and the sum of the squares of its terms is \( \frac{1}{8} \) Find the progression.


The side of a square is equal to the diameter of a circle. If the side and
radius change at the same rate, then the ratio of the change of their areas is
A . \( 2: \pi \)
в. \( \pi: 1 \)
\( c \cdot 4: \pi \)
D. 1: 2


Q Type your question
\( A \)
B.
\( c \)
\( D \)


Assertion: The value of \( \frac{\tan ^{-1} \frac{4}{3}}{\tan ^{-1} \frac{1}{2}} \) is equal
to
2
Reason: \( \forall \boldsymbol{x} \in[\mathbf{0}, \mathbf{1}], \tan ^{-1}\left(\frac{\mathbf{2} \boldsymbol{x}}{\mathbf{1 - x}^{2}}\right)= \)
\( 2 \tan ^{-1} x \)
A. Both A and R are true and R is the correct explanation of
B. Both A and R are true but R is not the correct explanation of A
c. \( R \) is true but \( A \) is false
D. A is true but R is false


Air is a natural resource and cannot be
exhausted by human activities. It is known as inexhaustible natural
resource. Which of the following is another inexhaustible natural
resource?
A . coal
B. Petroleum
c. sunlight
D. Minerals


If two coin are tossed, then find the
probability of the event that no head
turns up.


In a typical hydraulic press, a force of \( 20 \mathrm{N} \) is exerted on small piston of area \( 0.050 \mathrm{m} 2 . \) What is force exerted by large piston on load if it has an area of 0.50 m2?
A. 200N
B. 100N
c. 50N
D. 10N


What is the contribution of S. Chandra
sekhar to physics?


Assertion
\( H_{2} S O_{4} \) in more viscous than water.
Reason
\( \ln H_{2} S O_{4}, S \) has highest oxidation
state.
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


Select the correct statement
for electrolysis of \( A l_{2} O_{3} \) by Hall-Heroult
process.
A . Cryolite \( N a_{3}\left[A l F_{6}\right] \) lowers the melting point of \( A l_{2} O_{3} \) and increases its electrical conductivity.
B. Al is obtained at cathode and probably \( C O_{2} \) at anode.
C. Both of the above statements are correct.
D. None of the above statements are correct.


The solution of the equations \( \frac{\boldsymbol{m}}{\boldsymbol{x}}+ \) \( \frac{n}{y}=a \) and \( \frac{n}{x}+\frac{m}{y}=b \) is given by
A \( x=\frac{n^{2}+m^{2}}{a m-b n}, y=\frac{m^{2}-n^{2}}{b m-a n} \)
B. \( _{x}=\frac{m^{2}-n^{2}}{a m-b n}, y=\frac{n^{2}-m^{2}}{b m-a n} \)
c. \( _{x}=\frac{m^{2}-n^{2}}{a m-b n}, y=\frac{m^{2}-n^{2}}{b m-a n} \)
D. \( x=\frac{n^{2}-m^{2}}{a m-b n}, y=\frac{n^{2}-m^{2}}{b m-a n} \)


The major pollutants to deplete ozone
are
A. Chlorofluorocarbons
B. Nitrogen oxides
c. Hydrocarbons
D. All of the above


Factorise: \( \boldsymbol{x}^{2}+\boldsymbol{6} \boldsymbol{x}+\mathbf{5}=\mathbf{0} \)


Consider two arithmetic series:
\[
\begin{array}{l}
\boldsymbol{A}_{1}: \mathbf{2}+\mathbf{9}+\mathbf{1 6}+\mathbf{2 3}+\ldots \ldots \ldots+\mathbf{2 0} \\
\boldsymbol{A}_{\mathbf{2}}: \mathbf{5}+\mathbf{9}+\mathbf{1 3}+\mathbf{1 7}+\ldots \ldots \ldots+\mathbf{1 6}
\end{array}
\]
then the number of terms common to
the two series is
\( A \cdot 6 \)
B. 8
c. 10
D. 12


The relation between potential difference (V) and current (I) was
discovered by :
A. Newton
B. Ampere
\( c . \) onm
D. volt


At \( 672^{\circ} \mathrm{C} \) and one atmosphere, \( S O_{3} \) is
partially dissociated into \( S O_{2} \) and \( O_{2} \)
\( \boldsymbol{S} \boldsymbol{O}_{3(g)} \leftrightharpoons \boldsymbol{S} \boldsymbol{O}_{2(g)}+\frac{1}{2} \boldsymbol{O}_{2(g)} . \) If the
density of the equilibrium mixture is 0.925 g/litre, then what is the degree of dissociation?
A . 0.74
B. 0.34
c. 0.68
D. 0.64


\( n \) identical charged drops having charge
\( q_{0}, \) potential \( V_{0}, \) capacity \( C_{0} \) and energy
\( E_{0}, \) coalesce to form a big drop. The new
potential, charge, capacity, energy stored
will be:
B \( \cdot \frac{2}{n^{3}} V_{0} ; \frac{q_{0}}{n_{0}} ; \quad n^{\frac{1}{3}} C_{0} ; \quad n^{\frac{3}{5}} U_{0} \)
D. \( \frac{2}{n^{3}} V_{0} ; \frac{q_{0}}{n} ; n^{\frac{2}{3}} C_{0} ; n^{\frac{5}{3}} U_{0} \)


Raffinose on hydrolysis gives:
A. Two monosaccharides
B. Three monosaccharides
c. one disaccharide and one monosacharide
D. Two monosaccharides and one disaccharide


Why tin cans are used for storing food?


A food packet is released from a helicopter rising steadily at the speed of \( 2 m / s . \) After 2 seconds the velocity of the packet is (Take \( \boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2} \) ):
A \( .22 \mathrm{m} / \mathrm{s} \)
B. 20 \( m / s \)
c. \( 18 \mathrm{m} / \mathrm{s} \)
D. None of these


In a full wave rectifier circuit operating from \( 50 H z \) mains frequency, the
fundamental frequency in the ripple would be
\( \mathbf{A} \cdot 25 H z \)
B. \( 50 \mathrm{Hz} \)
c. \( 70.7 H z \)
D. \( 100 H z \)


Use Kirchhoff's rules to obtain condition
for the balance condition in a
Wheatstone bridge


On heating a mixture of \( N H_{4} C l \) and
\( \boldsymbol{K} \boldsymbol{N} \boldsymbol{O}_{2}, \) we get:
A \( . N H_{4} N O_{3} \)
в. \( K N H_{4}\left(N O_{3}\right)_{2} \)
c. \( N_{2} \)
D. \( N O \)


A spherical glass vessel has a
cylindrical neck which is \( 4 \mathrm{cm} \) long and
\( 2 \mathrm{cm} \) in diameter. The diameter of the
spherical part is \( 6 \mathrm{cm} \). Find the amount of water it can hold?


Transpiration increases with increase
in
A. Humidity
B. Temperature
c. Minerals
D. Soil moisture


Which of the following does not
illustrate the anomalous properties of
Li?
A. The m.p. and b.p. of \( L i \) are comparatively high
B. \( L i \) is much softer than the other I group metals
C . \( L i \) forms a nitride \( L i_{3} N \) unlike group I metals
D. The ion of \( L i \) and its compounds are more heavily hydrated than those of the rest of the group


Assertion Even Though \( \oint_{\mathbf{c}} \overrightarrow{\mathbf{B}} \mathbf{d} \bar{l} \) is zero along a
closed Amperian loop \( \mathrm{C} \), the magnetic
field \( \overline{\mathbf{B}} \) may not be zero over \( \mathbf{C} \)
Reason \( \oint_{\mathbf{s}} \overline{\mathbf{B}} \mathrm{d} \overline{\mathbf{S}} \) is always zero for any closed
surface S.
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 contrapositive of the following statement, "If the side of a square doubles, then its area increases four
times" is:
A. If the area of a square increases four times, then its side is not doubled
B. If the area of a square increases four times, then its side is doubled
C. If the area of a square does not increase four times then its side is not doubled
D. If the side of a square is not doubled, then its area does not increase four times


In the given figure, apply \( \operatorname{sss} \) congruence condition and state the
result in the symbolic form.


A hydrogen-like atom(atomic number
Z) is in a higher excited state of quantum number n. This excited atom can make a transition to the first state
by successively emitting two photons of energies 10.20 eV and 17.00 eV.
Alternatively, the atom from the same excited state can make a transition to
the second excited state by emitting two photons of energies 4.24 eV and 5.95
eV. The hydrogen-like atom is :
\( \mathbf{A} \cdot \mathrm{Li}^{2} \)
B \( \cdot \mathrm{He}^{+} \)
c. \( H \)
D. none


Instead of monitoring carbon dioxide, another gas that scientists could study
to substantiate the fact that \( C O_{2} \) concentration is steadily increasing in
the atmosphere is \( O_{2} \). Justify the
statement.


A \( 20 \mathrm{kg} \) object is lifted through a height of \( _{-1}-\ldots- \) m when 784 J of work is
done on it.
[Assume \( \left.\boldsymbol{g}=\mathbf{9 . 8 m} / \boldsymbol{s}^{2}\right] \)
\( A \cdot 2 \)
B. 4
c. 7.84
D. 3.92


\( t_{1} \) for first order reaction is:
\( \overline{\mathbf{2}} \)
A. \( \frac{0.7}{k} \)
в. \( \frac{0.693}{k} \)
c. \( \frac{0.683}{k} \)
D. \( \frac{0.10}{k} \)


Monomer of polythene is :
A. propene
B. isoprene
c. chloroprene
D. ethene


Find compound interest on Rs. 6250 at \( 16 \% \) per annum for 2 years, compounded annually.
\( \mathbf{A} \cdot \) Rs. 2160
B. Rs. 2340
c. Rs. 1520
D. Rs. 3120


ff \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{2} & \mathbf{- 1} \\ \mathbf{- 1} & \mathbf{2}\end{array}\right] \) Find \( \boldsymbol{A}^{2} \)


If the value of \( \tan ^{-1}\left(\tan \frac{3 \pi}{4}\right) \) is \( -\frac{\pi}{k} \)
then \( k \) is


Which of the following aldehyde is a gas at room temperature?
A. Methanal
B. Ethanal
c. Propanal
D. Butanal


f \( \sin \left\{\sin ^{-1} \frac{1}{5}+\cos ^{-1} x\right\}=1, \) then \( x \)
is equal to
\( A \cdot 1 \)
B.
\( c \cdot \frac{4}{5} \)
D.


At temperature \( T_{1} \) and composition
Q,which of the following is true?
This question has multiple correct options
A. Vapour phase is richer in B while liquid phase is richer in \( A \)
B. Distillation of composition Q gives only pure A
C. Distillation of composition \( Q \) gives pure \( A \) and pure \( B \)
D. Distillation of composition Q gives higher percentage of B than A.


Name two scales of temperature?
A. Kelvin and Celsius
B. Celsius and Ratio
C. Ordinal and Interval
D. None of the above


Two waves of same amplitude and frequency and travelling in same direction are superimposed each other to give rise to a resultant wave of amplitude \( 2 A \)
A. True
B. False


Which of the following is a
decomposition reaction?
\( \mathbf{A} \cdot 3 N a(s)+F e B r_{3}(a q) \rightarrow 3 N a B r(a q)+F e(s) \)
B. \( N a O H(a q)+H N O_{3}(a q) \rightarrow N a N O_{3}(a q)+H_{2} O(l) \)
\( \mathbf{c} \cdot 2 N a H C O_{3}(s) \rightarrow N a_{2} C O_{3}(s)+C O_{2}(g)+H_{2} O(l) \)
D. \( 3 H_{2}(g)+N_{2}(g) \rightarrow 2 N H_{3}(g) \)


An electron moving in a circular orbit of radius r makes n rotations per second. The magnetic field produced at the centre has magnitude
\( ^{\mathrm{A}} \cdot \frac{\mu_{o} n^{2} e}{r} \)
в. \( \frac{\mu_{o} n e}{2 r} \)
c. \( \frac{\mu_{o} n e}{2 \pi r} \)
D. zero


Give the absolute and gauge pressure of the gas in the enclosure for cases (a)
and (b)in units of cm of mercury


Ocean thermal energy is due to:
A. energy stored by waves in the ocean
B. temperature difference at different levels in the ocean
C. pressure difference at different levels in the ocean
D. tides arising out in the ocean


A bag contains 25 tickets, numbered from 1 to \( 25 . \) A ticket is drawn at
random. Find the probability that the ticket will show even number.


Write the features or characteristics of
types of reproduction


Protein found in eye lens is
A. Crystallin
B. Collagen
c. opsin
D. Rhodopsin


Which of the following is true about
refrigeration?
A. Heat is removed from the inside of the refrigerator
B. Cold air is produced inside the refrigerator
C. Hot air is removed from the inside of the refrigerator
D. Hot air is changed to a cold condensate inside the refrigerator
E. Hot air inside the refrigerator is expanded to remove its heat


A point charge \( +Q \) is placed just
outside an imaginary hemispherical
surface of radius \( R \) as shown in the
figure. Which of the following statements is/are correct?
This question has multiple correct options
A. The electric flux passing through the curved surface of the hemisphere is \( -\frac{Q}{2 \epsilon_{0}}\left(1-\frac{1}{\sqrt{2}}\right) \)
B. The component of the electric field normal to the flat surface is constant over the surface
Cotal flux through the curved and the flat surface is \( \frac{Q}{\epsilon_{0}} \)
D. The circumference of the flat surface is an
equipotential


Assertion
An astronaut inside a massive
spaceship orbiting around the earth will experience a finite but smal
gravitational force.
Reason
The centripetal force necessary to keep the spaceship in orbit around the earth is provided to keep the spaceship in orbit.
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 statements are
correct?
This question has multiple correct options
A. Whole of heat can be converted into work
B. Whole of work can be converted into heat
c. Temperature of a body can be raised without heating it
D. Temperature of a body may not rise on heating


Which of the following represents NAND
gate?
\( A \)
B.
\( c \)
\( D \)


In which one of the following, the set of
items are wrongly paired?
A. Lysine, glycine, thiamine - Amino acids
B. Myosin, oxytocin and gastrin - Hormones
c. Rennin, nuclease and hyaluronidase - Proteolytic enzymes
D. The nerves that carry signals away from the central nervous system - Afferent neurons


For the reaction \( A \rightarrow B \), it was found
that the concentration of \( B \) increased
by 0.3 mol \( L^{-1} \) in 2 hours. What is the
average rate of reaction?


During carbohydrate metabolism, NADH is produced in which of the following locations?
I. Cytosol
Il. Mitochondrial matrix
III. Nucleus.
A. I only
B. II only
c. I and II only
D. I, II and III


toppr
Q Type your question-
question.
The auxin was dissolved in a gelatin
block; gelatin does not affect the biological activity of the auxin. Several plant seedlings were prepared in a gelatin block; gelatin does not affect the biological, activity of the auxin. Several plant seedlings were prepared as described above and growth was
measured every 5 days.
Based on the results of the experiment,
one can conclude that the tip of the
plant contains
Plant Plant 2 Not cut, Tip removed Tip removed thing applied nothing applied gelatin alone applied
Plant premoved
Tip removed + auxin as past leaf
A. Gelatin
B. Paste
c. Auxin
D. None of these


Two particles \( A \) and \( B \) are in motion. If the wavelength associated with particle \( A \) is \( 5 \times 10^{-8} \) m. Calculated the
wavelength (in \( \dot{A} \) ) associated with
particle \( B \) if its momentum is half of \( A \)


Assertion
For \( I=2, m_{1} \) can be -2,-1,0,+1 and +2
Reason
For a given value of \( \mathrm{I},(2 \mathrm{l}+1) \) values of \( \boldsymbol{m}_{1} \)
are possible.
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


Rhombic sulphur remains stable below
\( 95.6^{\circ} \mathrm{C} \)
A. True
B. False


Why are particles least penetrating compared to \( \gamma \) rays?


The magnetic field at the origin due to a current element \( i . \vec{d} l \) placed at a
position \( \vec{r} \) is This question has multiple correct options
A \( \frac{\mu_{0} i}{4 \pi} \frac{\overrightarrow{d l} \times \vec{r}}{r^{3}} \)
В. \( \frac{\mu_{0} i}{4 \pi} \frac{\vec{r} \times \vec{d} l}{r^{3}} \)
\( ^{\mathrm{C}}-\frac{\mu_{0} i}{4 \pi} \frac{\vec{r} \times \vec{d} l}{r^{3}} \)
D. \( -\frac{\mu_{0} i}{4 \pi} \frac{\vec{d} l \times \vec{r}}{r^{3}} \)


Two bodies of masses ' \( m \) ' and '2m' are
thrown upwards with a velocity of ' \( u^{\prime} \)
and '3 \( u \) ' from the surface respectively.
What is the ratio of their potential energies at the highest point?
A . 1: 9
в. 3: 1
\( \mathbf{c} \cdot 1: 18 \)
D. 4: 1


A diverging lens of focal length \( 10 \mathrm{cm} \) is placed \( 10 \mathrm{cm} \) in front of a plane mirror
as shown in the figure. Light from a very far away source falls on the lens. The final image is at a distance?
A. \( 20 \mathrm{cm} \) behind the mirror
B. \( 7.5 \mathrm{cm} \) in front of the mirror
c. \( 7.5 \mathrm{cm} \) behind the mirror
D. \( 2.5 \mathrm{cm} \) in front of the mirro


A water tanker filled up to \( \frac{2}{3} \) of its height
is moving with a uniform speed. On sudden application of the brake, the water in the tank would:
A. move backward
B. move forward.
c. be unaffected.
D. rise upwards


A grain silo is built from two right circular cones and a right circular cylinder with internal measurements
represented by the figure above. Of the following, which is closest to the volume of the grain silo, in cubic feet?
A .261 .8
B. 785.4
\( c .916 .3 \)
D. 1,047.2


Which of the following disease is caused in human by ascaris?
A. Tuberculosis
B. Tineasis
c. Both A and B
D. Ascariasis


If \( f(x)=x^{n} \ln x \) and \( f(0)=0 \) then
value of \( \alpha \) for which Rolle's Theorem can
be applied in \( [\mathbf{0}, \mathbf{1}] \)
A . -2
B. -
c. 0
D.


Which of the following is the true
statement for carbon atoms:
A. A carbon atom loses 4 electrons
B. A carbon atom forms 4 covalent bonds.
C. A carbon atom share the 2 electrons in the first
principal energy level.
D. A carbon atom gains 4 electrons.


If octane number of gasoline sample is
70, then this sample will be similar to:
A. 70\% n-heptane + 30\% n-octane
B. 70\% n-octane + 30\% n-heptane
c. 70\% isooctane + 30\% n-heptane
D. 70\% n-heptane + 30\% isooctane


\( A \) is of order \( m \times n \) and \( B \) is of order \( p \times \)
\( q, \) addition of \( A \) and \( B \) is possible only if
A \( . m=p \)
B . \( n=q \)
c. \( n=p \)
D. \( m=p, n=q \)


The general solution of the differential equation \( \frac{d y}{d x}=\frac{1-x}{y} \) is a family of curves
which looks most like which of the
following?
\( (\mathbf{A}) \)
(B)
\( (\mathrm{C}) \)
\( (\mathbf{D}) \)


Non-metallic character
down the group.
A. increases
B. decreases
c. constant
D. none of these


What is formed by the reaction between metal oxide and water?
A. Acid
B. Base
c. salt
D. Metal


Among the naturally occurring carbohydrates, furanose ring is found in
the:
A. glucose unit of cane sugar
B. glucose unit of cellulose
c. fructose unit of cane sugar
D. galactose unit of lactose


\( \operatorname{Let} \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{3} & \mathbf{7} \\ \mathbf{2} & \mathbf{5}\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{ll}\mathbf{6} & \mathbf{8} \\ \mathbf{7} & \mathbf{9}\end{array}\right] . \) Verify
\( \operatorname{that}(A B)^{-1}=B^{-1} A^{-1} \)


Differentiate between:
Euchromatin and heterochromatin


Water is flowing out at the rate of
\( 6 m^{3} / \) min from a reservoir shaped like
a hemispherical bowl of radius \( R=13 \)
\( \mathrm{m} \) The volume of water in the
hemispherical bowl is given by \( v= \) \( \frac{\pi}{3} \cdot y^{2}(3 R-y) \) when the water is \( y \)
meter deep Find at what rate is the water level changing when the water is
\( 8 \mathrm{m} \) deep.
\( ^{\mathbf{A}} \cdot-\frac{1}{12 \pi} m / m i n \)
B. \( -\frac{1}{18 \pi} m / \) min
c. \( -\frac{1}{24 \pi} m / \) min
D. \( -\frac{1}{30 \pi} m / \) min


State whether the following statement is true or false.
Reactivity and reducing power decreases on going from group 1 to group 2.
A. True
B. False


What accounts for (1) the genetic similarity between daughter cells and the parent cell following mitosis, and
(2) the genetic dissimilarity between daughter cells and the parent cell following meiosis?


A series LCR circuit is tuned to resonance
If the angular frequency of the applied AC voltage at resonance is \( \omega \), the impedance
of the circuit then is:
A \( \cdot R+\omega L+\left(\frac{1}{\omega C}\right) \)
B.
c. \( \sqrt{R^{2}+\omega L+\left(\frac{1}{\omega C}\right)^{2}} \)
D. \( \sqrt{R^{2}+\left(\omega L-\frac{1}{\omega C}\right)^{2}} \)


Sodium on heating with moist air produces:
A. \( N a O \)
в. маОН
c. \( N a_{2} O \)
D. \( N a_{2} C O_{3} \)


Identify \( \mathbf{A}, \mathbf{B}: \)
\( \mathbf{A} \cdot A=N H_{3} ; B=N_{2} \)
B \( \cdot A=N O ; B=H N O_{3} \)
\( \mathbf{C} \cdot A=N_{2} ; B=N H_{3} \)
\( \mathbf{D} \cdot B=H N O_{3} ; A=N O \)


Let \( \boldsymbol{A}=\boldsymbol{x} \in \boldsymbol{R}: \boldsymbol{x} \leq \mathbf{1} \) and \( \boldsymbol{f}: \boldsymbol{A} \rightarrow \boldsymbol{A} \)
be defined as \( f(x)=x(2-x), \) then
\( f^{-1}(x) \) is
A. \( 1+\sqrt{1-x} \)
B. \( 1-\sqrt{1-x} \)
c. \( \sqrt{1-x} \)
D. \( 1 \pm \sqrt{1-x} \)


Evaluate \( \int_{1}^{2} \frac{-1}{x^{2}} d x \)


Liquids exerts force on wall of container because they don't have any preffered direction.
Mark 1 if true else mark 0


Assertion: We have lost all the direct evid
ences of origin of life.

Reason : The person responsible to protec
t the evidences were not skilled.
\( A . \) If both the assertion and the reason are true and the reason is a correct explanation of the assertion
B. If both the assertion and reason are true but the reason is not a correct explanation of the assertion
C. If the assertion is true but the reason is false
D. If both the assertion and reason are false
E. If the assertion is false but reason is true


Assume that,in a chemical reaction a
certain subtance decompses at rate
proportional to the amount present in 5 hours intial quantity of 10,000 gram reduced to 1000 gram. how much will left of an initial quantity of 20,000 gram after 15 hours rm?


Coefficient of \( \boldsymbol{x}^{\boldsymbol{9}} \) in \( \rightarrow(\mathbf{1}+\boldsymbol{x})(\mathbf{( 1}+\boldsymbol{t}) \)
\( \left.\left.\boldsymbol{x}^{2}\right)\left(\mathbf{1}+\boldsymbol{x}^{3}\right) \ldots \ldots\left(\boldsymbol{1}+\boldsymbol{x}^{\mathbf{1 0 0}}\right)\right) ? \)


Phycoerythrin, chlorophyll a and chlorophyll d are characteristics, of
A. Phaeophyceae
B. Xanthophyceae
c. chlorophyceae
D. Rhodophyceae


During mitosis, metaphase differs from anaphase in having
A. Same number of chromosomes and half number of chromatids
B. Half number of chromosomes and half number of chromatids
c. Half number of chromosomes and same number of chromatids
D. Same number of chromosomes and same number of chromatids


Woolen clothes are mostly used in:
A. summer days
B. rainy days
c. cold days
D. cloudy days


A deuteron of kinetic energy 50 keV is describing a circular orbit of radius 0.5 metre in a plane perpendicular to the
magnetic field \( B \). The kinetic energy of the proton that describes a circular
orbit of radius 0.5 metre in the same
plane with the same \( B \) is
A . \( 25 ~ k e V \)
В. \( 50 \mathrm{keV} \)
c. \( 200 \mathrm{keV} \)
D. \( 100 \mathrm{keV} \)


The numbers of d-electrons retained in
\( F e^{2+}(\text { atomic number } F e=26) \) ion is:
\( A \cdot 3 \)
B. 4
\( c .5 \)
D. 6


is called a space age
metal and used in militaryjets and spacecrafts.
A. zinc
B. Platinum
c. copper
D. Titanium


The vapour pressure of pure water is
\( 23.8 m m H g \) at \( 25^{0} C . \) What is the
vapour pressure of
2.50 molal \( C_{6} H_{12} O_{6} ? \)


Beauty of Taj may be destroyed by
A. Flood in Yamuna
B. Temperature mediated spoilage of marble
C. Air pollutants from Mathura refinery
D. All of the above


According to postulates of Bohr's atomic model, the electrons in atom
move round the nucleus:
A. in definite circular orbits known as stationary orbits
B. in energy levels or shell
c. both \( A \) and \( B \)
D. none of the above


How should a man using spectacles
work with a microscope?
A. He should keep on wearing the spectacles
B. He should take off the spectacles
C. Wearing or taking off spectacles make a little difference only
D. He cannot use microscope at all


Water is a good fire extinguisher. But it
is not used extinguish electrical fires
and oil for?


Which of the following is not a characteristic of meiosis?
A. It involves two stages of DNA replication one before meiosis-I and another before meiosis-II.
B. It involves recombination and crossing over.
c. sister chromatids separate during anaphase-II
D. Nuclear membrane disappears during prophase


Find the distance of the line \( 4 x+7 y+ \)
\( 5=0 \) from the point (1,2) along the
line \( 2 x-y=0 \)


Microscopic pores in plants through which they expire air are called
A. stigma
B. Thalamus
c. Gills
D. Stomata


Assertion
Ethers are regarded as a hydride of alcohols.
Reason
Ethers may be obtained by elimination of water molecule from two alcohol
molecules.
A. If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
B. If both Assertion and Reason are correct. but Reason is not the correct explanation of Assertion
C. If Assertion is correct but Reason is incorrect
D. If Assertion is incorrect but Reason is correct.


Heparin is a homopolysaccharide. Say
True or False:
A. True
B. False


Krebs cycle begins with
A . Citric acid
B. Pyruvic acid
c. Malic acid.
D. Hydrochloric acid.


Which point does not pertain to Bohr's model of atom?
A . Angular momentum is an integral multiple of \( h /(2 \pi) \)
B. The path of the electron is circular
C. Force of attraction towards nucleus = centrifugal force
D. The energy changes are taking place continuously


Name The Sl unit of mass.


Which of the following reaction \( (s) \)
involves oxidation reduction reaction?
\( A \)
B.
\( \mathrm{c} \cdot_{\mathrm{CH}_{3}-\mathrm{C} \equiv \mathrm{CH}+\mathrm{Hg} \mathrm{SO}_{4}} \stackrel{\mathrm{H}_{2} \mathrm{SO}_{4}}{\longrightarrow} \mathrm{CH}_{3}-\mathrm{C}-\mathrm{CH}_{3} \)
D.


Write the chemical reactions related to
Mond process for refining nickel metal.


Which of the following statement is
incorrect for nuclear forces?
A. These are strongest in magnitude
B. They are charge dependent
C. They are effective only for short ranges
D. They result for interaction of every nucleon with the nearest limited number of nucleons


\( 0.1 \mathrm{M} \) solution of which of the following has almost unity degree of dissociation?
A. Ammonium chloride
B. Potassium chlorid
c. sodium acetate
D. All of the above


Which one of the following relations on
\( R \) is equivalence redlation
A \( \cdot x R_{1} y \Leftrightarrow|x|=|y| \)
B . \( x R_{2} y \Leftrightarrow|x|>|y| \)
c. \( x R_{3} y \Leftrightarrow x \mid y \)
D. \( x R_{4} y \Leftrightarrow x<y \)


Because of its highly tilted axis, appears to roll along the orbital plane.
A. Uranus
B. Mercury
c. saturn
D. Venus


Assertion
Chlorination of water helps in its sterilization.
Reason
On passing chlorine into water it kills germs due to its storing oxidizing action.
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


If \( 3 \sin \theta+4 \cos \theta=5, \) then the value of
\( 4 \sin \theta-3 \cos \theta \) is
\( A \cdot 0 \)
B.
\( c .5 \)
D. none of these


\( \operatorname{Let} C_{k}=^{n} C_{k} \) for \( 0 \leq k \leq n \) and
\( \boldsymbol{A}_{\boldsymbol{k}}=\left[\begin{array}{cc}\boldsymbol{C}_{\boldsymbol{k}-1}^{2} & \boldsymbol{0} \\ \boldsymbol{0} & \boldsymbol{C}_{\boldsymbol{k}}^{2}\end{array}\right] \) for \( \boldsymbol{k} \geq 1, \) and \( \boldsymbol{A}_{1}+ \)
\( \boldsymbol{A}_{2}+\ldots+\boldsymbol{A}_{n}=\left[\begin{array}{cc}\boldsymbol{k}_{1} & \mathbf{0} \\ \mathbf{0} & \boldsymbol{k}_{2}\end{array}\right], \) then
This question has multiple correct options
A \( . k_{1}=k_{2} \)
B . \( k_{1}+k_{2}=^{2 n} C_{2 n}+1 \)
c. \( k_{1}=^{2 n} C_{n}-1 \)
D. \( k_{2}=^{2 n} C_{n+1} \)


A massless meter stick is in equilibrium about its center point.
If a mass, \( m_{1}=50 g \), is placed at the
\( 30 c m \) mark and a mass, \( m_{2}=75 g, \) is
placed at the \( 70 \mathrm{cm} \) mark, where must a
mass, \( m_{3}=50 g, \) be placed to keep the
system in equilibrium?
A. \( 10 \mathrm{cm} \)
в. \( 40 \mathrm{cm} \)
\( \mathbf{c} .50 \mathrm{cm} \)
D. \( 60 \mathrm{cm} \)
E. \( 90 \mathrm{cm} \)


Assertion (A) : Two systems which are in thermal equilibrium with a third system, are in thermal equilibrium with each other.

Reason (R) : The heat flows always from a system at higher temperature to a system at a lower temperature.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
c. Assertion is true but Reason is false
D. Both Assertion and Reason are false


An ideal gas undergoes a quasi static, reversible process in which its molar
heat capacity \( C \) remains constant. If
during this process the relation of
pressure \( \boldsymbol{P} \) and volume \( \boldsymbol{V} \) is given by
\( P V^{n}= \) constant, then \( n \) is given by
(Here \( C_{P} \) ad \( C_{V} \) are molar specific heat
at constant pressure and constant volume, respectively):
\( ^{\mathrm{A}} \cdot_{n}=\frac{C-C_{P}}{C-C_{V}} \)
B. \( n=\frac{C_{P}-C}{C-C_{V}} \)
c. \( _{n}=\frac{C-C_{V}}{C-C_{P}} \)
D. \( _{n}=\frac{C_{P}}{C_{V}} \)


Which is the last element in the series
of the actinoids? Write the electronic
configuration of this element. Comment on the possible oxidation state of this element


Write \( \frac{3}{5} \) as percentage.


During inelastic collision of two
particles.
\( \mathbf{A} \cdot(K E)_{\text {final }}=(K E)_{\text {initial }} \)
B. \( (K E)_{\text {final }} \) must be greater than \( (K E)_{\text {initial}} \)
\( \mathbf{C} \cdot(K E)_{\text {final}} \) must be less than \( (K E)_{\text {initial}} \)
D. \( (K E)_{\text {final }} \) must be greater or less than \( (K E)_{\text {initial }} \)


What is the molar heat capacity of the
gas?
A \( \cdot-\frac{R}{\gamma-1} \)
в. \( R(\gamma-1) \)
c. \( \frac{\gamma-1}{R} \)
D. \( \frac{\gamma}{R} \)


Choose the correct answers from the
alternatives given Heterothallism in fungi was first discovered by:
A . A. E Blakeslee
B. c. B. Huggins
c. Alexander Fleming
D. Robert Whittaker


A particle of mass \( \mathrm{m} \) is moving in a
circular path of constant radius r such
that its centripetal acceleration \( a_{c} \) is
varying with time \( t \) as \( a_{c}=k^{2} r t^{2} \) where
\( k \) is a constant. The power delivered to the particle by the forces acting on it, is?
A. zero
B. \( m k^{2} r^{2} t^{2} \)
\( \mathbf{c} \cdot m k^{2} r^{2} t \)
\( \mathbf{D} \cdot m k^{2} r t \)


The expression \( \frac{1}{\sqrt{2}}(\hat{i}+\hat{j}) \) is a :
A. unit vector
B. null vector
C. vector of magnitude \( \sqrt{2} \)
D. vector of magnitude \( \frac{1}{\sqrt{2}} \)


A body starts from rest and with a
uniform acceleration of \( 10 m s^{-2} \) for 5
seconds. During the next 10 seconds it moves with uniform velocity. The total distance travelled by the body is :-
\( \mathbf{A} \cdot 100 m \)
B. \( 125 \mathrm{m} \)
c. \( 500 m \)
D. \( 625 \mathrm{m} \)


Mention the harmful effect caused due
to depletion of ozone layer that is Bioamplification?


A tree increases annually by \( \frac{1}{8} \) th of its
height, By how much will it increase after 2 years, if it stands today \( 64 \mathrm{cm} \) high?
\( A \cdot 72 \mathrm{cm} \)
B. \( 74 \mathrm{cm} \)
c. \( 75 \mathrm{cm} \)
D. \( 81 \mathrm{cm} \)


For a reaction involving condensed phases, \( \Delta \boldsymbol{H}=\boldsymbol{\Delta} \boldsymbol{U} \)
A. true
B. false
c. insufficient data
D. none


A solenoid is a coil of insulated or
enameled wire wound on a rod-shaped
form made of solid iron, solid steel, or
powdered iron.

State whether this statement is true or
false.
Write 1 for True and 2 for False