What is the oxidation state of \( C r \) in
\( \left[\boldsymbol{C r}\left(\boldsymbol{O}_{2}\right)_{4}\right]^{3-} ? \)
\( A \cdot+3 \)
\( B \cdot+4 \)
\( c \cdot+5 \)
\( D \cdot+6 \)


Which scale is best for measuring the length of a ladybug?
A. Millimeters
B. Centimeters
c. Meters
D. Kilometers


If 12 persons are seated at a round
table, what is the probability that two particular persons sit together?
A \( .2 / 11 \)
B. 1/11
c. \( 1 / 12 \)
D. \( 5 / 12 \)


After five half lives, percentage of original radioactive atoms left is:
A . 1\%
B. 0.3\%
c. \( 3.125 \% \)
D. 0.2\%


A wedge of mass \( M \) is kept at rest on
smooth surface, a particle of mass \( \boldsymbol{m} \)
hits the wedge normally. Find the velocity of wedge and particle just after collision. Take coefficient of restitution
as \( e \)


What are natural and synthetic
polymers? Give two examples of each type.


Water at \( 0^{\circ} C \), contained in a closed
vessel, is abruptly opened in an evacuated chamber specific latent heats of fusion and vapourization at
\( 0^{\circ} C \) are in the ratio \( \lambda: 1, \) the water
evaporated will be :


The value of \( \int_{-\pi}^{\pi} \frac{\sin ^{2} x}{1+7^{x}} d x \) is
A \( \cdot 7^{x} \)
B. \( \pi \)
\( c \cdot \frac{\pi}{2} \)
\( D \cdot 2^{\pi} \)
E . \( 7 \pi \)


Which of the following set of elements cannot be a triad?
A. \( L i, N a, K \)
B. \( B, A l, G a \)
c. \( B e, M g, C a \)
D. \( C l, B r, I \)


Which of the following is associated with the vermi-processing toilets?
A. Low water use toilet
B. Electronic toilet
c. Kid's toilet
D. None of the above


For the reduction of FeO at the
temperature corresponding to point \( \mathrm{D} \)
which of the following statement is
correct?
\( \mathbf{A} \cdot \triangle G^{0} \) value for the overall reduction with carbon
monoxide is zero
B. \( \triangle G^{0} \) value for the overall reaction with a mixture of
mol carbon and 1 mol oxygen is positive.
C \( . \triangle G^{0} \) value for the overall reduction with a mixture of 2 mol carbon and 1 mol oxygen will be positive.
D. \( \triangle G^{0} \) value for the reduction reaction with carbon
monoxide is negative


For a process given by \( \boldsymbol{P}=\frac{\boldsymbol{C}}{\boldsymbol{V}}, \) where \( \mathbf{C} \)
is a constant, the work done by the ideal
gas when the volume changes form \( V_{1} \)
to \( V_{2} \) is
\( ^{\mathrm{A}} \cdot_{R T \ln }\left(\frac{V_{2}}{V_{1}}\right) \)
B . \( P\left(V_{2}-V_{1}\right) \)
\( ^{\mathbf{c}} \cdot_{R T \ln }\left(\frac{V_{1}}{V_{2}}\right) \)
D. \( P\left(V_{1}-V_{2}\right) \)


A plank with a small block on top of it is undergoing vertical SHM. Its period is 2 sec.The minimum amplitude at which the block will separate from plank is :
A \( \cdot \frac{10}{\pi^{2}} \)
в. \( \frac{\pi^{2}}{10} \)
c. \( \frac{20}{\pi^{2}} \)
D. \( \frac{\pi}{10} \)


The dissociation of \( C a C O_{3} \) is
suppressed at high pressure.
If true enter 1 , if false enter 0 .


Very short answer type.
Which hormone keeps leaves green for a
longer time?


Define the term 'Heat capacity' and
state its S.I. unit.


Hydra is the small simple freshwater animals. They do not have a recognisable brain or true muscles. Nerve fibres are in the forms of
network. The type of neurons possessed by Hydra is
A. Apolar
B. Bipolar
c. Unipolar
D. Multipolar


Statement-
If the earth did not have an atmosphere,
it would become extremely cold. Statement-2
Heat energy is transferred through air mainly by convection.
A. Statement-1 is true, Statement-2 is true and Statement-2 is the correct explanation for Statement-
B. Statement-1 is true, Statement-2 is true but Statement-2 is not the correct explanation for Staement-
c. Statement- 1 is true, Statement- 2 is false.
D. Statement- 1 is false, Statement-2 is true


\( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{6}+\boldsymbol{H}_{2} \boldsymbol{O} \longrightarrow \boldsymbol{I}+\boldsymbol{A} \)
A. \( I: X e O_{3} \)
в. \( I: X e_{2} O_{5} F_{2} \)
c. \( I: X e_{2} O_{3} F_{6} \)
D. None of these


Which of the following is true regarding the symmetry of the function: \( f(x)= \) \( \boldsymbol{x}^{\boldsymbol{5}}+\boldsymbol{x}^{\boldsymbol{3}}+\boldsymbol{3} \)
A. \( f(x)=c \)
B. Symmetric about x-axis
c. Its an odd function
D. None of these


The second stage of hydrosere is occupied by plants like
A . Azolla
B. Typha
c. salix
D. Vallisneria


Ortho-xylene on ozonolysis followed by reductive hydrolysis gives:
A. \( C H O-C H O \) and \( C H_{3}-C O O H \)
в. \( C H_{3}-C O-C O-C H_{3}, C H O-C H O \) and \( C H_{3}- \)
\( C O-C H O \)
c. \( C H_{3}-C O-C O-C H_{3} \) and \( C H O-C H O \)
D. \( C H_{3}-C O-C O-C H_{3}, C H_{3}-C O-C H O \) and
\( C H O-C H O \)


Poor conductors of electricity consist of
A . silver
B. aluminum
c. distilled water
D. copper


Solve the following equation:
\( \tan x=-1 \)


Ammonium ion is detected by the addition of an alkali.
A. True
B. False


The elements whose atomic weight was corrected by Mendeleev are
A. Uranium.
B. Indium
c. Beryllium
D. All of these


Heat of hydrogenation of ethene is \( x_{1} \)
and that of Benzene is \( x_{2} \) Hence
resonance energy is ?
A \( \cdot x_{1}-x_{2} \)
В. \( x_{1}+x_{2} \)
\( \mathbf{c} \cdot 3 x_{1}-x_{2} \)
D. \( x_{1}-3 x_{2} \)


Select the correct alternative(s).
A. Elastic forces are always conservative
B. Elastic forces are not always conservative
C. Elastic forces are conservative only when Hooke's law is obeyed
D. Elastic forces may be conservative even when Hooke's law is not obeyed


The formula of the complex hydridotrimethoxidoborate ( III ) ion is:
\( A \)
\( \left[B H\left(O C H_{3}\right)_{3}\right]^{2} \)
в. \( \left[B H_{2}\left(O C H_{3}\right)_{3}\right]^{2} \)
c. \( \left[B H\left(O C H_{3}\right)_{3}\right] \)
D. \( \left[B H\left(O C H_{3}\right)_{3}\right] \)


Edible part of cauliflower is
A . cotyledons
B. Mesocarp
c. Endocarp
D. Inflorescence


What is the minimum size of a plane
mirror in which a person can see his complete images?


The fraction of atoms of radioactive
element that decays in 6 days is \( 7 / 8 \) The fraction that decays in 10 days will
be
A. \( \frac{77}{88} \)
в. \( \frac{71}{80} \)
c. \( \frac{31}{32} \)
D. \( \frac{15}{16} \)


An ideal gas having molar specific heat capacity at constant volume is \( \frac{3}{2} R, \) the molar specific heat capacities at constant pressure is :
A \( \cdot \frac{1}{2} R \)
в. \( \frac{5}{2} \) R
c. \( \frac{7}{2} \) R
D. \( \frac{9}{2} \) R


Which of the following is the nodal
plane of \( d_{x y} \) orbital? This question has multiple correct options
A. \( x y \)
B. YZ
\( c \cdot z x \)
D. All


In double refraction:
A. the velocity of the E-ray varies with direction
B. e-ray does not obey Snell's law
C \( . \mu \) of E-ray is constant
D. both \( A \) and \( B \)


The structural formula of iso-butene is:
A. \( C H_{3} C H_{2} C H=C H_{2} \)
B. \( C H_{3} C H=C H-C H_{3} \)
c. \( C H_{3}-C H-C H_{3} \)
\[
\begin{array}{l}_{c H_{3}}\end{array}
\]
D. \( C H_{2}=\underset{c H_{3}}{C}-C H_{3} \)


Melting of ice involves increase in randomness and increase in enthalpy.If true enter 1 else o
\( A \)


What is the function of vegetative organs of a plant?


Thermal decomposition of a compound
is of first order. If 50 percent of a sample of compound is decomposed in 120 mins, how long will it take for 90 percent of compound to decompose?
\( \mathbf{A} \cdot 299 \mathrm{mins} \)
B. 399 mins.
c. 99 mins.
D. 9.9 mins.


Three vectors satisfy the relation \( \vec{A} \). \( \vec{B}=0 \) and \( \vec{A} \bullet \vec{C}=0, \) then \( \vec{A} \) is
parallel to
A . \( \vec{c} \)
в. \( \vec{B} \)
c. \( \vec{B} \times \vec{C} \)
D. \( \vec{B} \cdot \vec{C} \)


Remote sensing satellites are placed in which of the following orbits?
A. Geo-synchronous
B. Semi-synchronous
c. Sun-synchronous
D. Sub-synchronous


A body executes simple harmonic motion. The potential energy (P.E.), the kinetic energy(K.E.) and total energy (T.E.) are measured as function of
displacement x. Which of the following
statement is true?
A. K.E. is maximum when \( x=0 \)
B. T.E. is zero when \( x=0 \)
c. K.E. is maximum when x is maximum
D. P.E. is maximum when \( x=0 \)


If \( \lambda_{1}, \lambda_{2}, \lambda_{3} \) are the wavelength of the
waves giving resonance to the fundamental, first and second overtone
modes respectively in a string fixed at both ends. The ratio of the wavelengths \( \boldsymbol{\lambda}_{1}: \boldsymbol{\lambda}_{2}: \boldsymbol{\lambda}_{3} \) is
A. 1: 2: 3
B. 1: 3: 5
c. \( 1: \frac{1}{2}: \frac{1}{3} \)
D. \( 1: \frac{1}{3}: \frac{1}{5} \)


The activation energy for a hypothetical
reaction, \( \boldsymbol{A} \longrightarrow \) Product, is
\( 12.49 k c a l / \) mol. If the temperature is
raised from \( 295 ~ K \) to \( 305 K \), the rate of reaction increases by:
A . \( 60 \% \)
B. \( 100 \% \)
c. \( 50 \% \)
D. 20\%


In a test a student got a mark of \( 49 . \) His report card showed that he had scored
70 per cent. What was the maximum
mark on the test?
A. 60
B. 70
c. 80
D. none of these


Consider the following diagram where
\( A B \) and \( C D \) are congruent arcs and
chords. The measure of \( \angle A O B=50^{\circ} \)
Then the value of \( \angle C O D=? \)
A \( .45^{\circ} \)
В. \( 50^{\circ} \)
\( c \cdot 56^{\circ} \)
D. \( 90^{\circ} \)


A copper ball of mass 100 gm is at a
temperature \( T . \) It is dropped in a copper
calorimeter of mass \( 100 g m \), filled with
\( 170 g m \) of water at room temperature. Subsequently, the temperature of the
system is found to be \( 75^{\circ} \mathrm{C} . \boldsymbol{T} \) is given
by :
(Given : room temperature \( =\mathbf{3 0}^{\circ} \boldsymbol{C} \)
specific heat of copper \( =0.1 \mathrm{cal} / \mathrm{gm}^{\circ} \mathrm{C} \)
\( \mathbf{A} \cdot 825^{\circ} C \)
B. \( 800^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 885^{\circ} C \)
D. \( 1250^{\circ} \mathrm{C} \)


Lead shows oxidation states of:
\( \mathbf{A} \cdot+2 \) only
B. +4 only
\( \mathbf{c} .+2 \) and +4
D. -2,+2 and +4


Identify the solute \( \& \) the solvent in the following solutions:
(a) Sugar solution
(b) Air
(c) Grains (d)
Aerated drinks.


Assertion
Triangles on the same base and between the same parallel lines are
equal in area.
Reason
The distance between two parallel lines
is same everywhere.
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


toppr
Q Type your question
an electric field that decreases with
altitude. Near the surface of the earth,
the field is about \( 100 V m^{-1} . \) Why then
do we not get an electric shock as we
step out of our house into the open?
(Assume the house to be a steel cage so
there is no field inside!)
(b) A man fixes outside his house one evening a two metre high insulating slab
carrying on its top a large aluminium sheet
of area \( 1 m^{2} \). Will he get an electric shock if
he touches the metal sheet next morning?
(c) The discharging current in the atmosphere due to the small conductivity of
air is known to be 1800 A on an average
Over the globe. Why then does the atmosphere not discharge itself completely
in due course and become electrically
neutral? In other words, what keeps the atmosphere charged?
(d) What are the forms of energy into which the electrical energy of the atmosphere is dissipated during a lightning?
(Hint: The earth has an electric field of
about \( 100 \mathrm{Vm}^{-1} \) at its surface in the
downward direction, corresponding to a Surface charge density \( =-10^{-9} \mathrm{Cm}^{-2} \). Due
to the slight conductivity of the atmosphere
up to about \( 50 \mathrm{km} \) (beyond which it is
good conductor), about \( +1800 \mathrm{C} \) is pumped every second into the earth as a whole. The earth, however, does not get discharged since thunderstorms and lightning occurring continually allover the globe pump an equal amount of negative charge on the earth.)


In Carius method for the quantitative
estimation of phosphorous, by using magnesia mixture, phosphorous is
estimated by
A. \( M g N H_{4} \cdot P O_{4} \)
В. \( M g_{2} P_{2} O_{7} \)
c. \( \left(N H_{4}\right)_{3} P O_{4} \cdot 12 M o O_{3} \)
D. All


A. Carnallite
1. Zinc
B. Calamine
2. Titanium
C. Limonite
3. Magnesium
D. Chalcopyrite
4. Copper
Match List I with List II and select the
correct answer using the codes given below the lists.
A. A-1,B-3,C-2,D-4
B. A-1,B-3,C-4,D-2
C . A-3,B-1,C-4,D-2
D. A-3,B-1,C-2,D-4


Find the length of the latus rectum, the eccentricity and the coordinates of the foci of the ellipse
\( \mathbf{5} \boldsymbol{x}^{2}+\mathbf{4} \boldsymbol{y}^{2}=\mathbf{1} \)


\( \mathrm{f} \sum_{r=1}^{10} r(r-1)^{10} C_{r}=k .2^{9}, \) then \( k \) is
equal to
A . 10
B. 45
\( c .90 \)
D. 100


If \( K_{a} \) is more (or) \( p k_{a} \) is less then more
stronger is the acid.
lonic order: \( \boldsymbol{H} \boldsymbol{C O O H}>\boldsymbol{C}_{\mathbf{6}} \boldsymbol{H}_{\mathbf{5}} \boldsymbol{C O O H} \)


The compound in which all carbon
atoms use only \( s p^{3} \) - hybrid orbitals for
bond formation is?
A. \( C H_{3} C H O \)
в. \( C H_{3} C O C H_{3} \)
\( \mathrm{c} \cdot\left(\mathrm{CH}_{3}\right)_{3} \mathrm{COH} \)
D. \( H C O O H \)


The enthalpy of combustion of propane
\( C_{3} H_{8} \) ) gas in terms of given data is :
Bond energy (kJ/mol)
\[
\begin{array}{llll}
\varepsilon_{C-H} & \varepsilon_{O=O} & \varepsilon_{C-=0} & \varepsilon_{O-H} \\
+x_{1} & +x_{2} & +x_{3} & +x_{4}
\end{array}
\]
Resonance energy of \( C O_{2} \) is \( -z k J / m o l \) and \( \Delta \boldsymbol{H}_{\text {vaporization}}\left[\boldsymbol{H}_{\mathbf{2}} \boldsymbol{O}(\boldsymbol{l})\right] \) is
\[
\boldsymbol{y}(\boldsymbol{k} \boldsymbol{J} / \boldsymbol{m o l})
\]
A \( \cdot 8 x_{1}+2 x_{5}+5 x_{2}-6 x_{3}-8 x_{4}-4 y-3 z \)
B . \( 6 x_{1}+x_{5}+5 x_{2}-3 x_{3}-4 x_{4}-4 y-3 z \)
c. \( 8 x_{1}+2 x_{5}+5 x_{2}-6 x_{3}-8 x_{4}-y-z \)
D. \( 8 x_{1}+x_{5}+5 x_{2}-6 x_{3}-8 x_{4}-4 y+3 z \)


Name the two groups into which phenomenon of catalysis can be divided. Give an example of each group with the chemical equation involved.


Simplify \( \frac{1}{1+a^{m-n}}+\frac{1}{1+a^{n-m}} \)


What displacement at an angle \( 60^{\circ} \) the \( x \) -axis has an \( x \) -component of \( 5 m ? \hat{i} \) and \( \hat{j} \) are unit vectors in \( x \) and \( y \) directions, respectively.
A . \( 5 i \)
B. \( 5 \hat{i}+5 \hat{j} \)
c. \( 5 \hat{i}+5 \sqrt{3} \hat{j} \)
D. All of the above


Write the additive inverse of \( \frac{8}{5} \)


Find the area of the region bounded by
the curve \( y^{2}=4 x, y-a x i s \& \) the line
\( \boldsymbol{y}=\mathbf{3} \)


Oxygen gas is poisonous.
A. True
B. False


According to Euclid's division algorithm, using Euclid's division lemma for any two positive integers \( a \)
and \( b \) with \( a>b \) enables us to find the
A. нс
в. Lсм
c. Decimal expansion
D. Probability


Explain the preparation of phenol from
cumene.


Match the following:
\( A \cdot A-r, B-s, C-p \)
D-q, \( E-L \)
1, E-U \( D-q \)
\( B \cdot A-S, B-r, C-p, \)
\( C \cdot A-r, B-S, C-u, D-q, E-p \)
D. A-q, B-s, C-p, D-r \( E-L \)


Find the range of \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \tan ^{-1}(\sqrt{x^{2}-2 x+2}) \)


If \( r, s, t \) are prime numbers and \( p, q \) are the positive integers such that LCM of \( \boldsymbol{p} \) \( q \) is \( r^{2} t^{4} s^{2}, \) then the number of ordered
pair \( (\boldsymbol{p}, \boldsymbol{q}) \) is
A . 252
в. 254
c. 225
D . 224


To what extent do the electronic
configurations decide the stability of oxidation states in the first series of the
transition elements? IIlustrate your
answer with examples.


Thermosetting polymer, bakelite is formed by the reaction of phenol with:
A. \( C H_{3} C H_{2} C H O \)
в. \( C H_{3} C H O \)
с. НСН О
D. \( H C O O H \)


A circular ring of diameter \( 40 \mathrm{cm} \) and mass I kg is rotating about an axis normal to its plane and passing through the (time with a frequency of 10 rotations per second. Calculate the
angular momentum about its axis of
rotation.


Heterophylly is shown in the following plants
A. cotton
B. Larkspur
c. Butter cup
D. All of the above


Sun tanning is a/an:
A . physical change
B. chemical change
\( c . \) both a and \( b \)
D. intermediate


a. Why 3 d-series of elements acts as
good catalyst?
b. Given reason: \( \boldsymbol{T} \boldsymbol{i}^{4+} \) salts are
colourless where as \( C r^{3+} \) salts are
coloured.


The isothermal elasticity of a medium
is \( \mathrm{E}_{i} \) and the adiabatic elasticity in \( \mathrm{E}_{a} \)
The velocity of sound in the medium is proportional to
\( \mathbf{A} \cdot E_{j} \)
в. \( E_{a} \)
c. \( \sqrt{E_{i}} \)
D. \( \sqrt{E_{a}} \)


Solve \( (\boldsymbol{x}+\boldsymbol{y})^{2} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\boldsymbol{a}^{2} \)


Find the value of \( (-144) \div(+16) \)
\( A \cdot+9 \)
B. +11
\( c .-9 \)
D. -11


H.G. Wells wrote a famous novel about a
man who made himself invisible by changing his index of refraction. What
would his index of refraction have to be
to accomplish this?


\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C l} \stackrel{N a C N}{\longrightarrow} \boldsymbol{X} \stackrel{\boldsymbol{P t} / \boldsymbol{H}_{2}}{\longrightarrow} \)
\( \boldsymbol{Y} \frac{\text {Acetic}}{\text {anhydride}} \boldsymbol{Z} \)
In the above sequence, \( Z \) is:
A. \( C H_{3} C H_{2} C H_{2} N H C O C H_{3} \)
в. \( C H_{3} C H_{2} C H_{2} N H_{2} \)
c. \( C H_{3} C H_{2} C H_{2} C O N H C H_{3} \)
D. \( C H_{3} C H_{2} C H_{2} C O N H C O C H_{3} \)


Can you draw a triangle which has no lines of symmetry? Sketch a rough figure.


what is the rinal proauct or the
following reaction?
\( A \)
\( B \)
\( c \)
\( D \)


Define adolescence.


Relative decrease in vapor pressure is 0.4 for a solution containing 1 mole AB in 3 mol \( H_{2} O \), therefore \( A B \) is ionised at the
extent(percentage) of:
\( \mathbf{A} \cdot 60 \% \)
B. \( 50 \% \)
\( c \cdot 100 \% \)
D. \( 40 \% \)


Among the choices of an alkyl bromide,
the least reactive bromide in \( S_{N} 2 \)
reaction is:
A. 1-bromopentane
B. 2-bromo-2-methylbutane
c. 1-bromo-3-methylbutane
D. 1-bromo-2-methylbutane


Madhu worked \( 2 \frac{1}{2} \) hours on Monday, \( 3 \frac{1}{4} \) hrs. on Tuesday, and \( 2 \frac{3}{4} \) hrs. on Wednesday. What is the mean number of hours she worked on these three
days?


The solution set of the equation \( \tan ^{-1} x-\cot ^{-1} x=\cos ^{-1}(2-x) \) is
A \( .(0,1) \)
в. (-1,1)
\( c \cdot[1,3) \)
D. (1,3)


If for a real number \( x,[x] \) denotes the
greatest integer less than or equal to \( x \) then for any \( \boldsymbol{n} \in \boldsymbol{N},\left[\frac{\boldsymbol{n}+\mathbf{1}}{\mathbf{2}}\right]+ \)
\( \left[\frac{n+2}{4}\right]+\left[\frac{n+4}{8}\right]+\left[\frac{n+8}{16}\right]+\ldots= \)
\( A \)
B. \( n-1 \)
\( \mathbf{c} \cdot n+1 \)
D. \( n+2 \)


Which of the diene has highest heat of
hydrogenation?
\( A \)
в.
c.
\( D \)


The equilibrium constant \( \boldsymbol{K}_{c} \) for \( \boldsymbol{A}_{(g)} \rightleftharpoons \) \( B_{(g)} \) is \( 1.1 . \) Which gas has a molar
concentration greater than \( 1 ? \)


Every source of sound has to be a
body
A. vibrating
B. resting
c. climbing
D. elastic


A particle undergoing simple harmonic motion has time dependent displacement given by \( \boldsymbol{x}(\boldsymbol{t})=\boldsymbol{A} \sin \frac{\boldsymbol{\pi} \boldsymbol{t}}{\mathbf{9 0}} \)
The ratio of kinetic to potential energy of this particle at \( t=210 \) s will be :
\( \mathbf{A} \cdot \mathbf{3} \)
B. \( \frac{1}{9} \)
\( c \cdot \frac{1}{3} \)
D.


A line passes through a point (2,5) and has a slope of \( -3 . \) What is the equation of a line perpendicular to this line through (2,5)\( ? \)
A \( \cdot y=\frac{1}{3} x+\frac{13}{3} \)
B. \( y=-3 x+17 \)
c. \( y=-3 x+11 \)
D. \( _{y}=\frac{1}{3} x-\frac{2}{3} \)


A beam of cathode rays moves from left
to right in a plane of the paper and it enters into a uniform magnetic field acting perpendicular to the plane of the paper and inwards. Now, the cathode rays are deflected:
A. Downwards
B. Upwards
c. In a direction perpendicular to the plane of the paper and inwards
D. In a direction perpendicular to the plane of the paper and outwards


All are true about Shigella sonnei except
A. It causes the mildest form of dysentery.
B. It causes enteric fever.
\( \mathbf{c} \). It is a late lactose fermenter
D. It is motile.


The value of machine depreciates \( 10 \% \) every year. If its present value is Rs.38700, what was its value 1 year
ago?


The path of a projectile is a parabola
A. True
B. False


Among the following, the compound that can be most readily sulphonated is
A. benzene
B. nitrobenzene
c. toluene
D. chlorobenzene


Assertion (A): Anhydrous Calcium chloride is used as catalyst in cyanamide process Reason (R): Catalyst increases the rate
of reaction.
A. Both (A) and (R) are true and (R) is the correct explanation of (A)
B. Both (A) and (R) are true and (R) is not the correct explanation of (A)
\( c . \) (A) is true and
(R) is false
D. (A) is false but (R) is true


In an ecosystem, the biotic components herbivores are
A. Photosynthetic
B. Chemosynthetic
c. Macroconsumers
D. Microconsumers


Glycogenolysis is a
A. Anabolic reaction
B. Catabolic reaction
C. Both A and B
D. None of the above


\( \boldsymbol{C H}_{2}=\boldsymbol{C H}_{2}+\boldsymbol{H}_{2} \frac{N i / 300^{0} \boldsymbol{C}}{\longrightarrow} \boldsymbol{C H}_{3}- \)
\( \boldsymbol{C H}_{3} \)
The above reaction is known as:
A. Kolbe's
B. Wurtz
c. Sabatier - Senderens
D. Berthelot


The dimensions of universal gas
constant are
\( \mathbf{A} \cdot\left[L^{2} M^{1} T^{-2} K^{-1}\right] \)
B \( \cdot\left[L^{1} M^{2} T^{-2} K^{-1}\right] \)
c. \( \left[L^{1} M^{1} T^{-2} K^{-1}\right] \)
D \( \cdot\left[L^{2} M^{2} T^{-2} K^{-1}\right] \)


Suppose the object in figure shown is the brass plate of an outdoor sculpture.
If experiences shear forces as a result of
an earthquake. The frame is \( 0.80 m \) and
\( 0.50 c m \) thick. Calculate the shear
strain produced in this object if the
displacement x is 0.16mm (Shear
modulus=\( \left.3.5 \times 10^{10} P a\right) \)


Ethyl alcohol is manufactured by the fermentation of :
A. molasses
B. starch
c. both A and B
D. none of the above


A hydrocarbon of molecular formula
\( C_{5} H_{10} \) on monochlorination gives one
product and on dichlorination gives three products (excluding stereoisomers). Identify the
hydrocarbon.


Force \( \boldsymbol{F} \) is given in terms of time \( t \) and
distance \( \boldsymbol{x} \) by \( \boldsymbol{F}=\boldsymbol{A} \boldsymbol{\operatorname { s i n }} \boldsymbol{C t}+\boldsymbol{B} \cos \boldsymbol{D} \boldsymbol{x} \)
Then the dimensions of \( \frac{A}{B} \) and \( \frac{C}{D} \) are given by :
A \( \cdot M L T^{-2}, M^{\circ} L^{\circ} T^{-} \)
B. \( M L T^{-2}, M^{\circ} L^{-1} T^{c} \)
c. \( M^{\circ} L^{\circ} T^{\circ}, M^{\circ} L^{1} T^{-1} \)
D. \( M^{\circ} L^{1} T^{-1}, M^{\circ} L^{\circ} T^{\circ} \)


\( \int \frac{2 x+3}{(2 x+1)(1-3 x)} d x= \)
A. \( \frac{2}{5} \log |2 x+1|-\frac{11}{15} \log |1-3 x|+c \)
B \( \cdot \frac{2}{5} \log |2 x+1|-\frac{11}{15} \log |1+3 x|+c \)
c. \( \frac{2}{3} \log |2 x-1|+\frac{11}{15} \log |1-3 x|+c \)
D. \( \frac{2}{5} \log |2 x+1|-\frac{21}{5} \log |1+3 x|+c \)


What is most commonly used as the refrigerant in heat pumps?
A. Chlorofluorohydrocarbons
B. Fluorine gas
c. Hydrogen gas
D. Carbon gas


Which of the following is not a
correct statement about an ionic
compound?
A. Higher the temperature, more is the solubility
B. Higher the dielectric constant of the solvent, more is the solubility
C. Higher the dipole moment of the solvent,more is the solubility
D. Higher the lattice energy, more is the solubility


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


The period of the function \( f(x)= \) \( \sin 3 x \cos [3 x]-\cos 3 x \sin [3 x], \) where \( \square \)
denotes the greatest integer function is
\( \mathbf{A} \cdot \mathbf{6} \)
B. 3
c. \( 1 / 3 \)
D. 1/6


A potential difference of \( 20 K V \) is applied across an \( X-r a y \) tube. Find
the minimum wavelength of \( \boldsymbol{X}-\boldsymbol{r} \boldsymbol{a} \boldsymbol{y} \)
generated


The dimensions of a cuboid are in the
ratio of 1: 2: 3 and its total surface area
is \( 88 m^{2} \). Find the dimensions of the
cuboid.


A uniform solid right circular cone of
base radius \( \mathrm{R} \) is joined to a uniform
solid hemisphere of radius \( R \) and of the
same density, as shown. The centre of
mass of the composite solid lies at the
centre of base the cone. The height of
the cone is
\( \mathbf{A} \cdot 1.5 \mathrm{R} \)
B. \( \sqrt{3} \) R
\( c \cdot 3 R \)
D. \( 2 \sqrt{3} \) R


A particle of mass \( \mathrm{m} \) is released from a certain height h with zero initia velocity. It strikes the ground elastically (direction of its velocity is reversed but magnitude remains the same). Plot the graph between its kinetic energy and time till it returns to its initial position.


Endothermic reactions, having \( \Delta S= \)
+ \( \boldsymbol{v} e \) may be spontaneous if:
This question has multiple correct options
A \( . \Delta H>T \Delta S \)
в. \( \Delta H<T \Delta S \)
c. \( \Delta H=T \Delta S \)
D. \( T \) is very high


How many molecules would be there in
0.01 moles of sodium hydroxide?
В. \( 6.023 \times 10^{21} \)
c. \( 6.023 \times 10^{22} \)
D. \( 6.023 \times 10^{20} \)


Mobit bought an article for Rs 2,500 and sold it at \( 25 \% \) above its cost. If \( 4 \% \) of the
selling price is paid by Mohit as the tax; find Mobit's net profit on the whole transaction.


\( \int_{a / 4}^{3 a / 4} \frac{\sqrt{x}}{\sqrt{a-x}+\sqrt{x}} d x \) is equal to?
A \( \cdot \frac{a}{4} \)
в.
\( c .-a \)
D. none of these


Duck-billed Platypus is connecting link between
A. Reptiles and mammals
B. Reptiles and birds
c. Echinoderms and chordates
D. Living and non-livinggg


For a transistor amplifier in common emitter configuration for load
impedance of \( 1 \mathrm{k} \Omega\left(\mathrm{h}_{f e}=50 \text { and } \mathrm{h}_{\mathrm{o} e}=\right. \)
\( 25 \mu A / V \), the current gain is:
A. -5.2
B . -15.7
c. -24.8
D. -48.78


The price of 357 mangoes is Rs.1517.25. What will be the
approximate price of 49 dozens of such mangoes?
A. \( R s .3000 \)
в. \( R s .3500 \)
c. \( R s .4000 \)
D. \( R s .2500 \)


Find the value of \( n \) for carbon
A . 0.15
в. 0.3
\( c .0 .9 \)
D. 0.6


A conductor wire, having \( 10^{29} \) free
electrons per \( m^{3} \) carries a current of
\( 20 A . \) If the cross-section of the wire is
\( 1 m m^{2}, \) then the drift velocity of
electrons will be of the order of:
A \( \cdot 10^{-5} m s^{-1} \)
B. \( 10^{-3} \mathrm{ms}^{-1} \)
c. \( 10^{-4} m s^{-1} \)
D. \( 10 m s^{-1} \)


Name the prosthetic group in following
1) Lipoprotein
2) Glycoprotein


A train runs along an unbanked circular
track of radius \( 30 m \) at a speed of
\( \mathbf{5 4} k m / h . \) The mass of the train is \( 10^{6} k g \) What provides the centripetal force required for this purpose?


Which one of the following is not a series?
A. adding first \( n \) natural numbers
B. multiplying first 10 odd numbers
c. adding first 20 even numbers
D. adding last 20 natural numbers


Find the A.P whose \( 3^{r d} \) term is 16 and
the \( 7^{t h} \) term exceeds its \( 5^{t h} \) term by 12


Commercial nitrogen is passed through copper chips kept in ammonia solution for removing oxygen.Why?


Match the name of the scientists with
their important contributions given under. Choose the answer which gives
correct combination.
\( A \cdot A-4, B-1, C-3, D-2 \)
B. \( A-1, B-4, C-2, D-3 \)
c. \( A-2, B-1, C-3, D-4 \)
D. \( A-4, B-3, C-2, D-1 \)
E . \( A-3, B-2, C-1, D \)


A man of mass \( \mathrm{m} \) speeds up while running from rest to a speed v in a straight track along an inclined plane, after rising through a height h.
\( W_{\text {gravity}}= \) work done by gravity on the
man.
\( W_{\text {friction}}= \) work done by gravity on the
man.
\( W_{\text {man}}= \) work done by man
If in the previous problem, we replace the man by a block of mass \( \mathrm{m} \) and release it from top of the inclined plane, and let it gain a speed \( v, \) then This question has multiple correct options
A \( \cdot W_{f r i c t i o n}=-m g h+\frac{1}{2} m v^{2} \)
B. \( W_{\text {gravity}}=-m g h \)
C. \( W_{\text {friction}}=0 \)
D. \( W_{\text {friction}}=-\mu g x, \) where \( x \) is the horizontal distance covered and \( \mu \) is the coefficient of friction between the block and the ground


A water hose \( 2 \mathrm{cm} \) in diameter is used
to fill a 20 litre bucket. If it takes 1
minute to fill the bucket, then the speed vat which the water the water leaves
the hose is,


Element A burns in nitrogen to give an ionic compound B. Compound B reacts with water to give \( C \) and \( D \). A solution of C becomes milky on bubbling carbon dioxide. Identify \( A, B, C \) and \( D: \)
A \( \cdot A=N a ; B=N a_{3} N_{2} ; C=N a(O H)_{2} ; D=N H_{3} \)
B. \( A=K ; B=K_{3} N_{2} ; C=K O H ; D=N H_{3} \)
C. \( A=C a ; B=C a_{3} N_{2} ; C=C a(O H)_{2} ; D=N H_{3} \)
D. \( A=B a ; B=B a_{3} N_{2} ; C=B a(O H)_{2} ; D=N H_{3} \)


Let \( f(x)=\frac{2025^{x}}{45+2025^{x}}, \) then the value of \( f\left(\frac{1}{2025}\right)+f\left(\frac{2}{2025}\right)+ \)
\( f\left(\frac{3}{2025}\right)+\ldots+f\left(\frac{2024}{2025}\right) \) is equal to
A. 1011
в. 1012
\( c .1013 \)
D. 2024


To produce interference in sound waves This question has multiple correct options
A. sources shall emit monochromatic wavelength.
B. sources shall emit monochromatic wavelength in same phase (i.e., source be Coherent).
C. sources shall emit sound intensity irrespective of frequency.
D. sources shall be very far away


Which one of the following traits studied by Mendel in garden pea was a recessive character?
A. Axial flower positon
B. Green cotyledon colour
c. Green pod colour
D. Yellow seed colour


The temperature coefficient of a wire is \( 0.00125^{0} C^{-1} . \) At \( 300 \mathrm{K} \) its resistance is
one ohm.The resistance of the wire will
be \( 2 \Omega \) at
\( \mathbf{A} \cdot \) 1154 \( \mathbf{K} \)
B. \( 1100 \mathrm{k} \)
\( c \cdot 1400 k \)
D. 1127 K


By inserting an iron core in a coil carrying current, the strength of its magnetic field will:
A. Increase
B. Decrease
C. Remain Same
D. Become Zero


Four charges are rigidly along the Y axis as shown. A positive charge approaches the system along the X axis with initial
speed just enough to cross the origin. Then its total energy at the origin is
A. zero
B. positive
C . negative
D. data insufficient


Which of the following hydrides has the lowest melting point:
A \( . N H_{3} \)
в. \( P H_{3} \)
c. \( A s H_{3} \)
D. \( S b H_{3} \)


Examples of elements belonging to \( s, p, d \) or \( f- \) block are given below.
Identify the wrong example.
A. \( s \) -block element - Caesium
B. \( p \) -block element - Barium
c. \( d \) - block element - Chromium
D. \( f \) -block element - Thorium


Find the sine of the angle between the vectors \( \hat{i}+2 \hat{j}+2 \hat{k} \) and \( 3 \hat{i}+2 \hat{j}+6 \hat{k} \)


Write the number of significant digits in 0.6464:
A . 4
B. 3
\( c \cdot 5 \)
D. None of the above


The wall of urinary bladder has a thick layer of smooth muscle called
A. Dartos
B. Detrusor
c. Deltoid
D. Depressor


The left auricle opens into left ventricle
through an aperture guarded by
A. Tricuspid valve
B. Bisuspid valve
c. Mitral valve
D. Both B and C


Resolving power of a telescope
increases with:
A. increase in focal length of eyepiece
B. increase in focal length of objective
C. increase in aperture of eyepiece
D. increase in aperture of objective


The rate of the chemical reaction
doubles for and an increase of \( 10 K \) in
absolute temperature from \( 298 K \)
Calculate \( \boldsymbol{E}_{\boldsymbol{a}} \)


The domain of \( \mathbf{f}(\mathbf{x})=\log \{(\boldsymbol{x}-\mathbf{3})(\mathbf{6}- \)
\( x)\} \) is
\( A \cdot(3, \infty) \)
в. (3,6)
\( c \cdot(0, \infty) \)
D. \( (-\infty, \infty) \)


A pan filled with hot food cools from
\( 50.1^{\circ} \mathrm{C} \) to \( 49.9^{\circ} \mathrm{C} \) in 5 sec. How long in
seconds will it take to cool from \( 40.1^{\circ} \mathrm{C} \) to
\( 39.9^{\circ} \mathrm{C} \) if room temperature is \( 30^{\circ} \mathrm{C} \) ?


Factors of \( 27-6 x-x^{2} \) are:
A . \( (3-x)(9+x) \)
в. \( (x-3)(x+9) \)
c. \( (x-2)(x+7) \)
D. None of these


Hydrogen bonding is maximum in
A. diethyl ether
B. triethyl amine
c. ethanol
D. None of these


A magnifying glass is made of a combination of convergent lens of power +20 diopters and a divergent lens of power -4 diopters. If the least distance of distinct vision is \( 25 \mathrm{cm}, \) the
magnifying power is:
\( A \cdot 3 \)
B. 4
\( c .5 \)
\( D \)


Define probability of an event?


In a dynamic equilibrium, the concentrations of reactants and
products remains
A. differs with substance
B. changes
c. constant
D. equilibrium


A radioactive element decays by \( \alpha- \)
emission. A detector records n beta
particles in 2 s and in next 2 s, it records 0.75 n beta particles. Find mean life correct to nearest whole number.
Given \( l n 2=0.6031, l n 3=1.0986 \)


Find the additive inverse of \( \frac{9}{2+i \sqrt{5}} \)


\( y=\sin \left(2 \sin ^{-1} x\right), \frac{d y}{d x}= \)
A \( \cdot \sqrt{\left(\frac{1-y^{2}}{1-x^{2}}\right)} \)
в. \( \sqrt[2]{\left(\frac{1+y^{2}}{1-x^{2}}\right)} \)
\( ^{\mathrm{c}} \cdot \sqrt{\left(\frac{1-y^{2}}{1+x^{2}}\right)} \)
D. \( \sqrt{\left(\frac{1+y^{2}}{1+x^{2}}\right)} \)


Which of the following is considered as superior quality of coal?
A. Bituminous coal
B. Peat
c. Lignite
D. coke


Melting of butter is a physical change.
A. True
B. False


For a particle executing simple harmone motion, the kinetic energy k is
given by \( k=k_{0} \cos ^{2} \omega t . \) The maximum
value of potential energy is?
\( A \cdot k_{0} \)
B. zero
\( c \cdot k_{0} / 2 \)
D. not obtainable


The stored food material in plants
A. Starch
B. Glycogen
c. Glucose
D. sucrose


The chemical formula of feldspar is :
A. \( K A l S i_{2} O_{8} \)
в. \( N a_{3} A l F_{6} \)
c. \( N a A l O_{8} \)
D. \( K_{2} O_{4} A l_{2}\left(S O_{4}\right)_{4} A l(O H)_{4} \)


What is \( \frac{x^{2}-3 x+2}{x^{2}-5 x+6} \div \frac{x^{2}-5 x+4}{x^{2}-7 x+12} \)
equal to
A. \( \frac{x+3}{x-3} \)
B.
c. \( \frac{x+1}{x-1} \)
D.


A die is thrown three times,
\( \boldsymbol{E}: \mathbf{4} \) appears on the third toss, \( \boldsymbol{F}: \boldsymbol{6} \)
and 5 appears respectively on first two
tosses.
Determine \( 36 P \) where \( P(E \mid F) \)


Sucrose decomposes in acid solution into glucose and fructose according to
first order rate law with \( t_{1 / 2}=3 \) Hrs. What fraction of the sample of sucrose
remains after 8 hours?


Which of the following correctly shows the difference in the products of glycolysis and Krebs cycle per glucose molecule?
A. Glycolysis - 4 ATP, 1 reduced NAD, Krebs Cycle - 4 reduced NAD, 1 reduced FAD, 1 ATP
B. Glycolysis - 4 ATP, 2 reduced NAD, Krebs Cycle - 8 reduced NAD, 2 reduced FAD, 2 ATP
c. Glycolysis - 2 ATP, 1 reduced NAD, Krebs Cycle - 3 reduced NAD, 1 reduced FAD, 1 ATP
D. Glycolysis - 2 ATP, 2 reduced NAD, Krebs Cycle - 6 reduced NAD, 2 reduced FAD, 2 ATP


Name the acid formed when sulphur dioxide dissolves in water.


Tollen's reagent is used for the detection
of aldehyde when a solution of \( A g N O_{3} \)
is added to glucose with \( N H_{4} O H \) then
fluconic acid is formced
\( A g^{+}+e^{-} \rightarrow A g \)
\( \boldsymbol{E}_{r e d}^{o}=\mathbf{0 . 8} \boldsymbol{V} \)
\( \boldsymbol{C}_{6} \boldsymbol{H}_{12} \boldsymbol{O}_{6}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{C}_{6} \boldsymbol{H}_{12} \boldsymbol{O}_{7} \)
(Gluconic acid) \( +2 \boldsymbol{H}^{+}+\mathbf{2} e^{-} ; \boldsymbol{E}_{r e d}^{o}= \)
\( -0.05 V \)
\( A g\left(N H_{3}\right)_{2}+e^{-} \rightarrow A g(s)+2 N H_{3} \)
(Use \( 2.202 \times \frac{R T}{F}=0.0592 \) and \( \frac{F}{R T}= \)
\( 38.92 a t 298 K) \)
\( \mathbf{2} \boldsymbol{A} \boldsymbol{g}^{+}+\boldsymbol{C}_{6} \boldsymbol{H}_{22} \boldsymbol{O}_{6}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \)
\( \mathbf{2} \boldsymbol{A} \boldsymbol{g}(\boldsymbol{s})+\boldsymbol{C}_{6} \boldsymbol{H}_{212} \boldsymbol{O}_{7}+\mathbf{2} \boldsymbol{H}^{+} \)
Find \( \ln K \) of this reaction?
A .66 .13
в. 58.38
c. 28.30
D. 46.29


Most basic hydroxide among the following is:
\( \mathbf{A} \cdot L u(O H)_{3} \)
B \( \cdot E u(O H)_{3} \)
\( \mathbf{c} \cdot Y b(O H)_{3} \)
D. \( \operatorname{Ce}(O H)_{3} \)


In the given Haber's Process, find out \( E \)
A. \( N a C l \)
3. \( \mathrm{NaCO}_{3} \)
\( c \cdot C a C l \)
\( \mathrm{D} \cdot \mathrm{Ca}(\mathrm{OH})_{2} \)


The nephrons discharge their urine at
the:
A. Urinary bladder
B. Urethra
c. Renal pelvis
D. Renal pyramid (calyses)


Water drops fall at regular intervals from a tap \( 5 \mathrm{m} \) above the ground. How far above the ground is the second drop at that instant when the 3 rd drop left
the tap and \( 1_{s t} \) drop reaches the
ground. \( \left(g=10 m / s^{2}\right) \)
A . \( 1.25 \mathrm{m} \)
B. 2.50 \( \mathrm{m} \)
c. \( 3.75 \mathrm{m} \)
D. 4.00 \( m \)


Show that the following set of points are
collinear.
(2,5),(4,6) and (8,8)


Let a sequence \( \left\{a_{n}\right\} \) be defined by
\( \boldsymbol{a}_{\boldsymbol{n}}=\frac{\mathbf{1}}{\boldsymbol{n}+\mathbf{1}}+\frac{\mathbf{1}}{\boldsymbol{n}+\mathbf{2}}+\frac{\mathbf{1}}{\boldsymbol{n}+\mathbf{3}}+\dots \dots+ \)
\( \frac{1}{3 n}, \) then
This question has multiple correct options
A \( a_{2}=\frac{7}{12} \)
B. \( a_{2}=\frac{19}{20} \)
\( ^{\mathbf{C}} \cdot a_{n+1}-a_{n}=\frac{9 n+5}{(3 n+1)(3 n+2)(3 n+3)} \)
D. \( a_{n+1}-a_{n}=\frac{-2}{3(n+1)} \)


Extraction of silver is achieved by initia complexation of the ore (Argentite) with \( X \) followed by reduction with \( Y . X \) and
\( \boldsymbol{Y}, \) respectively, are:
A . \( C N^{-} \) and \( Z n \)
B. \( C N^{-} \) and \( C u \)
c. \( C l^{-} \) and \( Z n \)
D. \( B r^{-} \) and \( Z n \)


Thermodynamics is concerned in part
with transformations between
A. different forms of heat energy
B. internal energy at various tempratures
C. one form of mechanical energy into other forms
D. heat, internal energy and mechanical work


Potential difference across capacitor of
capacitance \( C \) when the current in the
circuit is maximum is:
a. \( \frac{V_{0}}{4} \)
в. \( \frac{3 V_{0}}{4} \)
\( c \cdot \frac{5 V_{0}}{4} \)
D. none of these


Assertion
The mass number of hydrogen is equal
to its atomic number
Reason
H-atom has no neutrons
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


The alkali metal that reacts with
nitrogen directly to form nitride is:
A \( . L i \)
в. \( N a \)
c. \( K \)
D. \( R b \)


Nick surveyed a random sample of the freshman class of his high school to determine whether the Fall Festival
should be held in October or November.
Of the 90 students surveyed, \( 25.6 \% \) preferred October. Based on this information, about how many students in the entire 225 -person class would be expected to prefer having the Fall Festival in October?
A. 50
в. 60
\( c \cdot 75 \)
D. 80


Which among the following is used in
the treatment of cancer?
\( \mathbf{A} \cdot \operatorname{cis}-\left[P t(e n)_{2} C l_{2}\right] \)
B \cdot \( \operatorname{cis}-\left[P t C l_{2}\left(N H_{3}\right)_{2}\right] \)
c. trans- \( \left[P t(e n)_{2} C l_{2}\right. \)
D. trans- \( \left[P t\left(N H_{3}\right)_{2} C l_{2}\right] \)


Two identical metal plates, separated by a distance d form a parallel plate
capacitor. A metal sheet of thickness \( \frac{a}{2} \) of the same area as that of either plate, is
inserted between the plates. The ratio of the capacitance's after the insertion of the sheet to that before insertion is:
2
\( \mathbf{A} \cdot \sqrt{2}: 1 \)
B. 2:
c. 1:
D. \( 1: \sqrt{2} \)


The compound (s) used as an antifreeze in radiators of automobiles is/are?
This question has multiple correct options
A. methyl alcohol
B. ethyl alcohol
c. ethyl alcohol + water
D. methyl alcohol + water


In the adjoining figure, it is given that
\( A B \| C D, \angle B A O=108^{\circ} \) and
\( \angle O C D=120^{\circ}, \) then \( \angle A O C= \)
\( \mathbf{A} \cdot 120 \)
B. 72
\( c \cdot 132^{\circ} \)
D. 150


When a force is applied on a rigid object
A. It changes the inter spacing between its constituent particles.
B. It changes the dimension of the object
c. It only causes motion in it
D. All


Which of the following options are
correct regarding the complex
\( \left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right]^{\boldsymbol{3}-} \operatorname{and}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right]^{\boldsymbol{4}-} \)
This question has multiple correct options
A. number of unpaired electrons are 1 and 0 respectively.
B. number of unpaired electrons are 0 and 1 respectively.
C. magnetic moment are \( \sqrt{3} B M \) and 0 respectively.
D. magnetic moment are 0 and \( \sqrt{3} B M \) respectively.


Kjeldahl's method cannot be used to estimate nitrogen for which of the following compounds?
A. \( C_{6} H_{5} N H_{2} \)
в. \( N H_{2}-C-N H_{2} \)
c. \( C_{6} H_{5} N O_{2} \)
D. \( C H_{3} C H_{2}-C \equiv N \)


A long solenoid has magnetic field strength of \( 3.14 \times 10^{-2} \mathrm{T} \) inside it
when a current of \( 5 A \) passes through it The number of turns in 1 m of the
solenoid is
A. 1000
B. 3000
c. 5000
D. 10000


If \( \lim _{x \rightarrow 1} \frac{x^{4}-1}{x-1}=\lim _{x \rightarrow k} \frac{x^{3}-k^{3}}{x^{2}-k^{2}} \) then \( k=? \)
A \( \cdot \frac{2}{3} \)
B. \( \frac{4}{3} \)
\( c \cdot \frac{8}{3} \)
D. none


For each of the following, find the least number that must be added so that the
resulting number is a perfect square. 55078
A . 157
B. 147
\( c \cdot \) 156
D. 164


Study the figure given below and
answer the questions that follow:
Name another gas which has the same
property and can be demonstrated
through this experiment.


Which one of the following elements shows maximum number of different
oxidation states in its compounds?
A . Eu
B . La
\( c \cdot \) Gd
\( D \cdot A m \)


If \( \boldsymbol{A B}=\mathbf{3} \boldsymbol{i}+\boldsymbol{j}-\boldsymbol{k} \) and \( \boldsymbol{A} \boldsymbol{C}=\boldsymbol{i}-\boldsymbol{j}+ \)
3k. If the point \( P \) on the line segment
\( B C \) is equidistant from \( A B \) and \( A C \)
then \( \boldsymbol{A P} \) is
A. \( 2 i-k \)
B. \( i-2 k \)
c. \( 2 i+k \)
D. none of these


Define dielectric constant of a medium.
What is its \( S . I . \) unit?


\( \begin{array}{llll}\text { class } & 10- & 25- & 40- \\ \text { Interval } & 25 & 40 & 55\end{array} \) 70
Frequency 3 2 2
How do you find the deviation from the
assumed mean for the above data?


An ice block having two similar metallic pieces is floating in water in a vessel as
shown in figure. After sometime the ice melts completely then
A. the water level rises in the vessel
B. the water level falls in the vessel
c. the water level does not change in vessel
D. the water level may rise or fall depending upon the ratio of masses of ice and metallic pieces


The current gain in the common emitter amplifier mode of a transistor is \( 10 . \) The input impedance is \( 20 k \Omega \) and load of resistance is \( 100 k \Omega \). The power gain is :
A. 300
в. 500
\( c \cdot 200 \)
D. 100


Solve \( \boldsymbol{x}^{2}-\mathbf{4} \boldsymbol{x}-\mathbf{5}=\mathbf{0} \)
\( A \cdot\{-1,5\} \)
B . \{1,5\}
\( \mathbf{c} \cdot\{-1,-5\} \)
D. None of these


Which transition in \( L i^{2+} \) would have the
same wavelength as the \( 2 \rightarrow 4 \)
transition in \( \boldsymbol{H} \boldsymbol{e}^{+} \) ion?
\( A \cdot 4 \) to 6
B. 4 to 3
\( c \cdot 5 \) to 6
D. 5 to 4


Solve:
\( \lim _{x \rightarrow 0}\left(\left[x^{2}\right]-[x]^{2}\right) \)


The common difference of the AP \( \frac{1}{P}, \frac{1-P}{P}, \frac{1-2 P}{P}, \ldots \)
\( A \cdot P \)
\( B .-1 \)
\( c .- \)
\( D \)


\( \left|\begin{array}{ccc}\boldsymbol{x}^{2}+\boldsymbol{x} & \boldsymbol{3} \boldsymbol{x}-\boldsymbol{1} & -\boldsymbol{x}+\boldsymbol{3} \\ \boldsymbol{2} \boldsymbol{x}+\mathbf{1} & \boldsymbol{2}+\boldsymbol{x}^{2} & \boldsymbol{x}^{3}-\boldsymbol{3} \\ \boldsymbol{x}-\boldsymbol{3} & \boldsymbol{x}^{2}+\boldsymbol{4} & \boldsymbol{3} \boldsymbol{x}\end{array}\right|=\boldsymbol{a}_{0}+ \)
\( a_{1} x+a_{2} x^{2}+\ldots+a_{7} x^{7}, \) then the value
of \( a_{0} \) is
A . 25
B . 24
\( c \cdot 23 \)
D. None of the above


What is the apparent oxidation state of
\( M g \) element in the compound \( M g S O_{4} ? \)
A \( .+1 \)
B. -
\( c \cdot+2 \)
D. -
\( \mathrm{E} \cdot+3 \)


Which of the following remains
constant:
A. None of these
B. Kinetic energy
c. Potential energy
D. Sum of kinetic energy and potential


The I.U.P.A.C name of the coordination
compound \( \boldsymbol{K}_{3}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}\right] \) is :
A. Potassium hexacyanidoferrate(II)
B. Potassium hexacyanidoferrate(III)
c. Potassium hexacyanidoiron(II)
D. Tripotassium hexacyanidoiron(II)


In triangle \( A B C, \angle A=30^{\circ}, H \) is the
orthocentre and \( D \) is the midpoint of
BC. Segment \( H D \) is produced to \( T \)
such that \( \boldsymbol{H} \boldsymbol{D}=\boldsymbol{D} \boldsymbol{T} . \) The length \( \boldsymbol{A} \boldsymbol{T} \) is
equal to
A. \( 2 B C \)
в. \( 3 B C \)
c. \( \frac{4}{3} B C \)
D. None of these


The highest oxidation state shown by
transition element is :
This question has multiple correct options
\( A \cdot+7 \) by \( \mathrm{Mn} \)
B. +8 by Os
\( \mathbf{c} \cdot+8 \) by Ru
D. +7 by \( \mathrm{Fe} \)


In the light of Watson and Cricks model, describe the detailed structure of DNA.


What is Biomass?
A. Organic fuel that is used for treatment of wastes.
B. Organic fuel that is used as a source of energy.
C . Organic matter that has a large mass.
D. Waste products from industries


If the number of function from the set
\( A=\{0,1,2\} \) and \( B= \)
\{0,1,2,3,4,5,6,7\} such that \( f(i), \leq \)
\( \boldsymbol{f}(\boldsymbol{j}), \boldsymbol{i}<\boldsymbol{j} ; \boldsymbol{i}, \boldsymbol{j} \epsilon \boldsymbol{A} \mathbf{2 0} \boldsymbol{k}, \) then the value of
\( k \) is


The type of inflorescence in Ocimum
sanctum is
A. Hypanthodium
B. Cyathium
c. verticillaster
D. Thyrse


If \( \frac{l z_{2}}{m z_{1}} \) is purely imaginary number then \( \left|\frac{\boldsymbol{\lambda} \boldsymbol{z}_{1}+\boldsymbol{\mu} \boldsymbol{z}_{2}}{\boldsymbol{\lambda} \boldsymbol{z}_{1}-\boldsymbol{\mu} \boldsymbol{z}_{2}}\right| \) is equal to
A \( \cdot \frac{l}{m} \)
B. \( \frac{\lambda}{\mu} \)
\( c \cdot \frac{-\lambda}{\mu} \)
\( D \)


The equation of the circle having centre (1,-2) and passing through the point of intersection of the lines \( 3 x+y=14 \)
and \( 2 x+5 y=18 \) is
A \( \cdot x^{2}+y^{2}-2 x+4 y-20=0 \)
B . \( x^{2}+y^{2}-2 x-4 y-20=0 \)
C. \( x^{2}+y^{2}+2 x-4 y-20=0 \)
D. \( x^{2}+y^{2}+2 x+4 y-20=0 \)


A ray of light falls on the surface of spherical glass paperweight making an angle \( \alpha \) with the normal and is
refracted in the medium at an angle \( \beta \) The angle of deviation of the emergent
ray from the incident ray is
A \( \cdot(\alpha-\beta) \)
B \( \cdot 2(\alpha-\beta) \)
c. \( \frac{(\alpha-\beta)}{2} \)
D \cdot \( (\alpha+\beta) \)


\( B C l_{3}+H g \stackrel{\Delta}{\longrightarrow} \) white ppt \( +X \) in gas
phase what is the maximum number of
coplanar atoms in \( X \)
\( A \cdot 4 \)
B. 5
\( c \cdot 6 \)
D. 7


The compound that smells like chlorine
is:
A. \( C H C l_{3} \)
в. \( C a O C l_{2} \)
c. chloretone
D. none of these


Mark the correct alternative of the
following. The sum of two non-zero numbers is 8
the minimum value of the sum of their
reciprocals is?
A \( \cdot \frac{1}{4} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{1}{8} \)
D. None of these


Write the electron dot structure of
ethene molecule \( \left(C_{2} H_{4}\right) \)


The equilibrium constant for a reaction,
\( A+B \rightleftharpoons C+D \) is \( 1.0 \times 10^{-2} \) at 298
and is 2.0 at 373 K. The chemical
process resulting in the formation of \( C \)
and D is :
A. Exothemic
B. Endothermic
c. unpredictable
D. none


Green house effect of global warming
causes:
A. rise in temperature of earth
B. rise in pressure on earth
c. decrease in oxygen content earths atmosphere
D. decrease in \( C O_{2} \) content


Sodium oxalate on heating with conc
\( H_{2} S O_{4} \) gives:
A. \( C O \) only
B. \( C O_{2} \) only
c. \( C O \) and \( C O_{2} \)
D. \( S O_{2} \) and \( S O_{3} \)


Construct \( \triangle A B C \) with \( A B= \)
\( 5 c m, B C=5 c m \) and \( A C=5 c m \)


\( 2 P b O+C \rightarrow 2 P b+C O_{2} \) is an
example of
A. oxiation reaction
B. reduction reaction
c. redox reaction
D. none


A wire has a non-uniform cross-section
as shown in figure. A steady current
flows through it. The drift speed of
electrons at points \( \mathrm{P} \) and \( \mathrm{Q} \) is \( v_{P} \) and \( v_{Q} \)
then?
\( \mathbf{A} \cdot v_{P}=v_{Q} \)
в. \( v_{P}<v_{Q} \)
\( \mathbf{c} \cdot v_{P}>v_{Q} \)
D. Data is insufficient


Hormones which regulate the secretion of other endocrine glands are


18 carat gold is ........... \% pure.


For the given pair of \( S_{N} 2 \) reaction, the
first product occurs with larger rate
constant.
\[
\bigwedge_{\mathrm{Br}}+\mathrm{HO}^{-} \longrightarrow \sim_{\mathrm{Y}} \mathrm{Br}+\mathrm{HO}^{-} \rightarrow
\]


Starch can be used as an indicator for
the detection of traces of?
A. Glucose in aqueous solution
B. Protein in blood
c. lodine in aqueous solution
D. Urea in blood


If \( \boldsymbol{A}=\left[\begin{array}{lll}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{b} & \boldsymbol{c} & \boldsymbol{a} \\ \boldsymbol{c} & \boldsymbol{a} & \boldsymbol{b}\end{array}\right], \) where \( \boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c} \) are real
positive numbers \( a b c=1 \) and \( A^{T} A=1 \)
then:
This question has multiple correct options
\( \mathbf{A} \cdot a b+b c+c a=0 \)
B. \( a^{2}+b^{2}+c^{2}=1 \)
c. \( a^{3}+b^{3}+c^{3}=4 \)
D. \( a+b+c=2 \)


Super phosphate is a mixture of:
A. Calcium phosphate and sulphuric acid
B. Sodium phosphate and sulphuric acid
c. potassium phosphate and sulphuric acid
D. None of the above


Read the following statements about
forest biome and select the correct
answer
I. Temperature is generally lower in summer and higher in winter.
Il. The days are cooler and nights are warmer than in the surroundings.
III. The floor of the forest is carpeted
with lichens and mosses.
IV. Moisture content of the soil remains
stable for longer periods because of absence of evaporation.
A. I and II are correct
B. II and III are correct
c. ।, III and IV are correct
D. All are correct


\( \underbrace{\left[x_{i}^{-}\right]} \)


What kind of lens is there in our eyes?
A. concave
B. convex
c. Plano-concave
D. Plano-convex


Match the following:


Consider following features
(a) Organ system level of organisation
(b) Bilateral symmetry
(c) True coelomates with segmentation
of body
Select the correct option of animal groups which possess all the above characteristic's.
A. Annelida, Arthropoda and Chordata
B. Annelida, Arthropoda and Mollusca
c. Arthropoda, Mollusca and chordata
D. Annelida, Mollusca and Chordata


A bag contains 100 tickets bearing
numbers \( 1-100 . \) A ticked is taken out
randomly, find the probability of getting a ticket bearing a number which is the
multiple of 25
A . 0.5
B. 0.04
c. 1.0
D. 0.05


Which of the following has an optical isomer?
\( \mathbf{A} \cdot\left[\mathrm{CO}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}\right]^{+} \)
B . \( \left[\mathrm{CO}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2}\right]^{2-} \)
\( \mathbf{c} \cdot\left[\mathrm{CO}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}(\mathrm{en})\right]^{3+} \)
D \( \cdot\left[\mathrm{CO}(\mathrm{en})_{2}\left(\mathrm{NH}_{3}\right)_{2}\right]^{3+} \)


Which one of the following is a nonsteroidal hormone?
A . Estradiol
B. Prostaglandin
c. Estrone
D. Progesterone


Select the principal functional group when the following groups are present
in the molecule:
\( \boldsymbol{B} \boldsymbol{r}, \boldsymbol{C} \boldsymbol{H}_{3},-\boldsymbol{C} \boldsymbol{H} \boldsymbol{O} \)


In a transistor, forward bias is always
smaller than the reverse bias. This is
done to :
A. Maintain constant current supply
B. get good output
c. Avoid excessive heating of transistor
D. Maintain flow of majority charge carriers


Assertion
When people have muscle cramps
during exercise, they are asked to use the hot bag to relieve the muscle cramp.
Reason
Anaerobic respiration happens in muscle cells during intense workout.
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 polynomial
\( \left(a x^{2}+b x+c\right)\left(a x^{2}-d x-c\right), a c \neq 0 \)
has?


The equation of the normal to the curve
\( x^{4}=4 y \) through the point (2,4) is
A. \( x+8 y=34 \)
B. \( x-8 y+30=0 \)
c. \( 8 x-2 y=0 \)
D. \( 8 x+y=20 \)


Which of the following is not lyophilic?
This question has multiple correct options
A . Gelatin sol
B. Silver sol
c. Sulphur sol
D. \( A s_{2} S_{3} \) sol


The potential gradient along the length of a uniform wire is 10 volt/m \( B \) and \( C \)
are two points at \( 30 \mathrm{cm} \) and \( 60 \mathrm{cm} \) in a scale fitted along the wire. The pd between B and C is
A . \( 3 V \)
B. \( 0.4 V \)
\( c .7 V \)
D. \( 4 V \)


When the angle of reflection is \( 60^{\circ} . \) then the angle between the incident ray and
the mirror will be
\( A \cdot 30 \)
B. \( 60^{\circ} \)
\( c \cdot 90^{\circ} \)
D. \( 45^{\circ} \)


When compared to other kinds of energy
providing fuels like petrol and wood, electricity is better because it :
A. causes minimum pollution
B. is renewable
c. is cheaper
D. all of these


\( \boldsymbol{A}+\boldsymbol{B}=\frac{\boldsymbol{\pi}}{\mathbf{3}} ; \cos \boldsymbol{A}+\cos \boldsymbol{B}=\mathbf{1}, \) value of
\( |\cos A-\cos B| \) is
A \( \cdot \frac{1}{3} \)
B. \( \sqrt{\frac{2}{3}} \)
\( c \cdot \sqrt{\frac{3}{2}} \)
D.


Two point dipoles of dipole moment \( P_{1} a n d \overline{P_{2}} \) are at a distance \( x \) from each other and \( \overline{\boldsymbol{P}_{1}} \| \overline{\boldsymbol{P}_{2}} \)
The force between the dipoles is


\( 0.16 \mathrm{g} \) of methane was subjected to combustion at \( 27^{\circ} \mathrm{C} \) in a bomb
Calorimeter. The temperature of
calorimeter system (including water)
was found to rise by \( 0.5^{\circ} \) C. The heat of combustion of methane at :
(i) constant volume and ( ii ) constant
pressure.
[Given: The thermal capacity of
calorimeter system is \( 17.7 \mathrm{kJ} K^{-1} \)
\( \left.\left(\boldsymbol{R}=\mathbf{8 . 3 1 4} \boldsymbol{J} \boldsymbol{m o l}^{-\mathbf{1}} \boldsymbol{K}^{-1}\right)\right] \)
B. (i) -785 kJ / mol ( ii) - 859.95 kJ / mol
c. (i) -587kJ / mol ( ii) -789.95 kJ / mol
D. (i) -985 kJ/ mol ( ii ) - 999.95 kJ / mol


Evaluate \( : \int \frac{\sec x}{1+\operatorname{cosec} x} d x \)


A steel cylindrical rod of length \( l \) and
radius \( r \) is suspended by its end from
the ceiling. Define \( U \) in terms of tensile
\( \operatorname{strain} \frac{\Delta l}{l} \) of the rod
A \( \quad U=\frac{2}{3} \pi r^{2} l E\left(\frac{\Delta l}{l}\right)^{2} \)
в. \( U=\frac{4}{3} \pi r^{3} l E\left(\frac{\Delta l}{l}\right)^{3} \)
\( ^{\mathrm{c}} \cdot u=\frac{2}{4} \pi r^{3} l E\left(\frac{\Delta l}{l}\right)^{2} \)
D. None of these


Nitrogen in the inspired air is
A. Required by the cells
B. Mixed with the blood
c. Remain almost unused
D. All of the above


The shape of \( N H_{3} \) molecule is:
A . tetrahedral
B. triagonal planar
c. trigonal pyramidal
D. linear


All the statements about temperature
effects is true, with an exception of
A. Raising the temperature may reduce the activity of an enzyme.
B. Raising the temperature may increase the activity of an enzyme to some extent
C. Raising the temperature may denature an enzyme.
D. The isozymes of an enzyme have the same optimal temperature.


What is a rainbow? Draw a labelled
diagram to show the formation of a rainbow.


State True or False.
In an electrochemical cell, in the inner
circuit current is carried by ions and in the external circuit, current of electrons
flows through the metal conductors.
A. True
B. False


Write any two uses of Plaster of Paris?


In a Wheatstone's bridge all the four arms have equal resistance R. If the resistance of the galvanometer is also
R, the equivalent resistance of the combination across the battery is
A . R/2
B.
\( c \cdot 2 R \)
D. R/4


The force exerted by a compression device is given by \( F(x)=k x(x-l) \) for
\( 0 \leq x \leq l, \) where \( l \) is the maximum
possible compression, \( x \) is the compression and \( k \) is the constant
Work done to compress the device by a distance \( d \) will be maximum when
A \( \cdot d=\frac{l}{4} \)
в. \( d=\frac{l}{\sqrt{2}} \)
\( c \cdot d=\frac{l}{2} \)
D. \( d=l \)


In figure the voltmeter and ammeter
shown are ideal. Then voltmeter and
ammeter readings, respectively, are:
A . \( 32.978 \vee, 3 \mathrm{A} \)
B. 3 V, 0.236 A
c. \( 120 \vee, 4.198 \) A
D. \( 120 \vee, 3 \mathrm{A} \)


Ketones reacts with Mg - Hg over water
and give:
A. Alcohols
B. pinacolones
c. pinacols
D. none of these


During fermentation what does not
occurs
A. Oxidation of glucose into pyruvate
B. Substrate level phosphorylation
c. oxidation of \( N A D H_{2} \)
D. Oxidative phosphorylation.


A kettle with \( 2 L \) water at \( 27^{\circ} C \) is
heated by operating coil heater power
\( 1 k W \$ . \) The heat is lost to the
atmosphere at constant rate \( 160 \mathrm{J} / \mathrm{s} \) when its lid is open. In how much time
will water heated to \( 77^{\circ} C \) with the lid
open \( ? \) (specific heat of water \( = \)
\( \left.4.2 k J /^{\circ} C-k g\right) \)
A. 8 min 20 s
B. 6 min 2 sec
\( c .14 \) min
D. 7 min


If \( \mathrm{N}_{2} \) gas is hubbled through water at
\( 293 \mathrm{K}, \) how many millimoles of \( \mathrm{N}_{2} \) gas would dissolve in 1 litre of water?
Assume that \( \mathrm{N}_{2} \) exerts a partial
pressure of 0.987 bar. Given that Henry's
law constant for \( \mathrm{N}_{2} \) at \( 293 \mathrm{K} \) is 76.48
kbar
A . \( 0.561 \mathrm{mmol} \)
B. 0.222 mmol
c. \( 0.716 \mathrm{mmol} \)
D. \( 0.828 \mathrm{mmol} \)


Two persons having mass \( 50 \mathrm{kg} \) each, are standing such that their centre of
gravities are 1 m apart. Calculate the force of gravitation between them. (Take \( G=6.67 \times 10^{-11} N m^{2} k g^{-2} \)
mass of earth \( M=6 \times 10^{24} k g, \) Radius
of earth \( \left.R=6.4 \times 10^{6} m\right) \)
В. \( 1.67 \times 10^{-7} N \)
c. \( 1.32 \times 10^{-7} N \)
D. \( 1.67 \times 10^{-9} N \)


If \( \boldsymbol{A}=\{\mathbf{5}, \mathbf{7}\}, \boldsymbol{B}=\{\mathbf{7}, \mathbf{9}\} \) and \( \boldsymbol{C}= \)
\( \{7,9,11\}, \) find
Whether \( \boldsymbol{A} \times(\boldsymbol{B} \cup \boldsymbol{C})=(\boldsymbol{A} \times \boldsymbol{B}) \cup \)
\( (A \times C) \) holds true or not?


The proportional limit of steel is \( 8 x \) \( 10^{8} N / m^{2} \) and its Young's modulus is
\( \mathbf{2} \times \mathbf{1 0}^{11} \mathbf{N} / \mathbf{m}^{2} . \) The maximum
elongation, a one metre long steel wire can be given without exceeding the proportional limit is
\( A \cdot 2 m m \)
B. \( 4 \mathrm{mm} \)
\( \mathrm{c} \cdot 1 \mathrm{mm} \)
D. 8 mm


During change of \( O_{2} \) to \( O_{2}^{-} \) ion, the electron adds on which one of the
following orbitals?
\( A \cdot \pi \) orbital
B \( \cdot \sigma^{*} \) orbital
c. \( \sigma \) orbital
D・ \( \pi^{*} \) orbital


\( \operatorname{Let} f(x)=\left\{\begin{array}{cc}-1, & -2 \leq x<0 \\ x^{2}-1, & 0<x \leq 2\end{array} \) and \right.
\( \boldsymbol{g}(\boldsymbol{x})=|\boldsymbol{f}(\boldsymbol{x})|+\boldsymbol{f}|\boldsymbol{x}| \) then the number
of points which \( g(x) \) is non
differentiable, is
A. at most one point
B. 2
c. exactly one point
D. infinite


A simple wave motion represented by \( \boldsymbol{y}=\mathbf{5}(\sin 4 \boldsymbol{\pi} \boldsymbol{t}+\sqrt{\boldsymbol{3}} \cos \boldsymbol{4} \boldsymbol{\pi} \boldsymbol{t}) . \) Its
amplitude is:
\( A \cdot 5 \)
B. \( 5 \sqrt{3} \)
c. \( 10 \sqrt{3} \)
the
D. 10


The salary of a men which was \( R s .500 / \) earlier increases to \( R s .600 /- \) What is
the \% change in salary?


A pair of stationary and infinitely long bent wires is placed in the \( x \) -y plane as shown in figure. Each wire carries
current of \( 10 A . \) Segments \( L \) and \( M \) are
along the x-axis.Segments \( P \) and \( Q \) are
parallel to the y-axis such that \( O S= \)
\( O R=0.02 m . \) Find the magnitude and
direction of the magnetic induction at
origin \( O \) in the form of \( x \times 10^{-4} \). What
is \( x \)


State whether the following statement
is True or False.

The inverse of an identity function is the identity function itself.
A. True
B. False


The equivalent resistance between the points \( x \) and \( y \) of the circuit. If each resistance is 25 ohm is
\( A \cdot 25 \Omega \)
B. 1000
\( c .50 \Omega \)
D. 12.5\Omega


\( f\left(\begin{array}{lll}1 & 0 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 4\end{array}\right], \) then show that
\[
|\mathbf{3} \boldsymbol{A}|=\mathbf{2 7}|\boldsymbol{A}|
\]


\( \mathrm{A} 50 \mathrm{Hz}, 20 \mathrm{V} \mathrm{AC} \) source is connected
\( \operatorname{across} R \) series circuit as shown in Figure
If the voltage across \( R \) is \( 12 \mathrm{V} \) then
voltage across capacitor is
\( A \cdot 8 V \)
B. \( 16 \mathrm{V} \)
c. \( 10 \mathrm{V} \)
D. cannot be predicted as values of \( \mathrm{R} \) and \( \mathrm{C} \) are not given.


A physical quantity P is related to four observables \( a, b, c \) and \( d \) as follows:
\( \mathrm{P} \boldsymbol{a}^{3} \boldsymbol{b}^{2} / \sqrt{\boldsymbol{c}} \mathrm{d} \)
The percentage errors of measurement in \( a, b, c \) and \( d \) are \( 1 \%, 3 \%, 4 \% \) and \( 2 \%, \) respectively. What is the percentage error in the quantity P ? If the value of P calculated using the above relation turns out to be \( 3.763, \) to what value
should you round off the result?


Which of the following compounds do not have all \( C-C \) bonds of same
length?
\( A \)
B.
D.


Saline hydrides are known to react with
water violently producing fire. \( \operatorname{Can} C O_{2} \) a well known fire extinguisher, be used in this case? Explain.


During the bond formation, energy is absorbed.
A . True
B. False


Two particles having mass ratio \( n: 1 \)
are interconnected by a light in extensible string that passes over a smooth pulley. If the system is released, then the acceleration of the centre of
mass of the system is :
A \( \cdot(n-1)^{2} g \)
\( ^{\text {B }}\left(\frac{n+1}{n-2}\right)^{2} \)
\( ^{\mathbf{c}} \cdot\left(\frac{n-1}{n+2}\right)^{2} \)
D. \( \left(\frac{n-1}{n+2}\right) g \)


Figures show a sinusoidal wave at a
given instant
Which points are in phase?
4.4 .8
B. В,
\( c \cdot B, D \)
D. c.


Highly electropositive metals are best produced by
A. electrolytic methods
B. reduction with carbon of their oxides
c. straight thermal decomposition of salts
D. reduction of their halides by hydrogen


Light moves from air into water. The
light makes an angle of \( 47^{\circ} \) with the normal in the air. What angle will it
make with the normal in the water?
The index of refraction for air is 1.00
The index of refraction for water is 1.33
A \( \cdot 47^{\circ} \)
B. 77
\( c \cdot 43 \)
D. 25
\( E \cdot 33 \)


Assertion
A person standing on the land appears taller than his actual height to a fish inside a pond.
Reason
Light bends away from the normal as it
enters air from water.
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


Explain the method of preparation of hydrogen gas in laboratory with chemical equation and diagram.


Find out the points on the line joining two charges \( +\boldsymbol{q} \) and \( \boldsymbol{3} \boldsymbol{q} \) (kept at a
distance of \( 1.0 m \) in that order), where
electric potential is zero. This question has multiple correct options
A. \( 0.5 m \) to the left of \( q \)
B. \( 0.5 m \) to the right of \( q \)
c. \( 0.25 m \) to the right of \( q \)
D. \( 0.75 m \) to the right of \( q \)


The property of a conductor which enables to induce an EMF due to change
of current in the same coil is


The following circuit is equivalent to
A. AND gate
B. NOR gate
c. or gate
D. NAND gate


State the characteristics of the
magnetic lines of force.


If the ratio of sum of \( n \) terms in two A.P's
is \( 2 n: n+1, \) then the ratio of \( 8^{t h} \) terms
is
\( \mathbf{A} \cdot 15: 8 \)
B. 8: 133
\( \mathbf{c} .5: 17 \)
D. none


This question contains STATEMENT-I (Assertion) and STATEMENT-2 (Reason) and has 4 choices \( (a),(b),(c) \) and \( (d) \)
out of which ONLY ONE is correct.
STATEMENT-I: p-Hydroxybenzoic acid has a lower boiling point than o-
hydroxybenzoic acid. STATEMENT-2: 0-Hydroxybenzoic acid has a intramolecular hydrogen bond.
A. Statment-1 is True, Statement-2 is True; Statement-2 is correct explanation for Statement-
B. Statment-l is True, Statement-2 is True; Statement-2 is NOT correct explanation for Statement-
c. Statement-1 is True, Statement-2 is False.
D. Statement-1 is Flase, Statement-2 is True


The equilibrium constant for the reaction \( \boldsymbol{w}+\boldsymbol{x} \rightleftharpoons \boldsymbol{y}+\boldsymbol{z} \) is \( 9 . \) If one mole
of each of wand \( x \) are mixed and there is
no change in volume, the number of moles of y for formed is :
A . 0.10
B. 0.50
c. 0.75
D. 0.54


\( n^{\prime} \) identical bulbs, each designed to draw a power \( P \) from a certain voltage supply are joined in series across the supply. The total power which they will draw is :-
A. \( P \)
в. \( n P \)
c. \( \frac{P}{n^{2}} \)
D. \( \frac{P}{n} \)


What is the physical state of water at
\( \mathbf{1 2 5}^{\circ} \boldsymbol{C} ? \)
A. Solid
B. Liquid
\( c . \) Gas
D. None of the above


A potentiometer consists of a wire of length \( 4 \mathrm{m} \) and resistance \( 10 \Omega \). It is connected to a cell of e.m.f. 3V. The
potential gradient of wire is
A. \( 0.75 \mathrm{V} / \mathrm{m} \)
B. 2 V /m
\( c \cdot 6 v / m \)
D. \( 10 \mathrm{V} / \mathrm{m} \)


\( 5 g \) of \( N a C l \) can be dissolved in \( 50 g \) water
Then the solubility of \( N a C l \) is:
\( \mathbf{A} \cdot 10 g \)
B. \( 5 g \)
c. \( 20 g \)
D. none of the above


In sea-walnuts and comb-jellies the fertilization is
A. External
B. Internal
c. Both
D. None


Digestive system has muscles.
A. Voluntary
B. Involuntary
\( c . \) cardiac
D. All of the above


Which of the following compounds is
used in the formation of nylon-6,6?
A. Sulphur hexafluride
B. Adipic acid
c. Sulphurous acid
D. Phthalic acid


Let \( f(x)=x^{2}-3 x+2 \) then area
bounded by the curve \( f(|x|) \) (in square
units) and \( x \) -axis is
A \( \cdot \frac{1}{3} \)
в. \( \frac{5}{6} \)
c. \( \frac{5}{3} \)
D. None of thes


Match List-I with List-II and select the
correct answer using the code given
below the Lists:
List-II İ List-I
(Region) (Characteristic vegetation)
A. Selvas Tropophytes
B.
2. Mosses and lichens :
Savanna
C. Tundra 3. Epiphytes \( \pi_{n} n_{r_{a}} \) 3.
\( D \)
Monsoon
land Grasses and trees
A. A-3, B-2, C-4, D-1
B. A-1, B-4, C-2, D-3
C. A-1, B-2, C-4, D-3
D. \( A-3, B-4, C-2, D-1 \)


1 \( |\Delta| \) \begin{tabular}{|l|}
\hline\( \Delta \) \\
\hline\( \square \) \\
\hline\( \square \) \\
\hline\( + \) \\
\hline
\end{tabular} \begin{tabular}{|c|}
\hline\( A \) \\
\hline\( \square \) \\
\hline
\end{tabular}


If \( \int \frac{2 x^{2}+3}{\left(x^{2}-1\right)\left(x^{2}+4\right)} d x= \)
\( \operatorname{Alog}\left(\frac{\boldsymbol{x}+\mathbf{1}}{\boldsymbol{x}-\mathbf{1}}\right)+\boldsymbol{B} \tan ^{-1}\left(\frac{\boldsymbol{x}}{\mathbf{2}}\right)+\boldsymbol{C} \) then
\( (A, B) \) is
A \( \cdot\left(-\frac{1}{2}, \frac{1}{2}\right) \)
B \( \cdot\left(\frac{1}{2},-\frac{1}{2}\right) \)
\( \left(\frac{1}{2}, \frac{1}{2}\right) \)
D. (1,-1)


Which of the following will give \( \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+} \) ions in the solution?
A \( \cdot\left[F e(C N)_{6}\right]^{3-} \)
B . \( \left[F e(C N)_{6}\right]^{4-} \)
c. \( N H_{4}\left(S O_{4}\right)_{2} \cdot F e S O_{4} \cdot 6 H_{2} O \)
D. \( F e_{2}\left(S O_{4}\right)_{3} \)


Two long straight parallel conductors
carry steady current \( \boldsymbol{I}_{1} \) and \( \boldsymbol{I}_{2} \) separated by a distance d. If the currents are flowing in the same direction, show how the magnetic field set up in one produces an attractive force on the other. Obtain the
expression for this force. Hence define
one ampere


Calculate the mole fraction of \( N_{2} \) gas in
a mixture of \( N_{2} \) and \( O_{2} \). If the partial
pressure of \( \boldsymbol{O}_{2} \) is \( 63 \mathrm{cm} \) of \( \mathrm{Hg} \) and the
total pressure of the mixture is \( 90 \mathrm{cm} \) of Hg.


Volume and total surface area of a solid
hemisphere are equal in magnitude.
The volume is expressed in \( \mathrm{cm}^{3} \) and the
area is expressed in \( \mathrm{cm}^{2} \). Find the
radius of hemisphere.
A. \( 3 \mathrm{cm} \)
B. \( 4 \mathrm{cm} \)
c. \( 4.5 \mathrm{cm} \)
D. \( 5.5 \mathrm{cm} \)


A wire of resistance \( 4 \Omega \) is stretched to
double its original length. The resistance of the stretched wire would
be
A . \( 2 \Omega \)
в. \( 4 \Omega \)
c. \( 8 \Omega \)
D. \( 16 \Omega \)


A small block oscillates back and forth
on a smooth concave surface of radius
R. Find the time period of small oscillations.
A \( \cdot \pi \sqrt{\frac{2 R}{g}} \)
в. \( 2 \pi \sqrt{\frac{R}{3 g}} \)
c. \( 2 \pi \sqrt{\frac{2 R}{3 g}} \)
D. \( 2 \pi \sqrt{\frac{R}{g}} \)


Assertion
The presence of \( C O_{2} \) in the air
accelerates corrosion.
Reason
\( C O_{2} \) is a poisonous gas.
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


A proton moving with a constant speed passes through a region of space without any change in its speed. If \( \boldsymbol{E} \)
and \( B \) represent the electric and magnetic fields respectively, this region of space may have
a) \( \boldsymbol{B} \neq \mathbf{0}, \boldsymbol{E}=\mathbf{0} \)
b) \( \boldsymbol{B}=\mathbf{0}, \boldsymbol{E} \neq \mathbf{0} \)
c) \( B=0, E=0 \)
d) \( \boldsymbol{B} \neq \mathbf{0}, \boldsymbol{E} \neq \mathbf{0} \)
\( A \cdot a, b, c \) are true
B. b, c, dare true
\( c \cdot a, b, d \) are true
D. a, c, d are true


High concentration of greenhouse gases has resulted in maximum rise of
atmospheric temperature in
A. Tropic region
B. Middle latitude
c. Polar region
D. Temperate region


Equal net forces act on two different
blocks \( A \) and \( B \) of masses \( m \) and \( 4 m \)
respectively. For same displacement, identify the correct statement.
A ' their kinetic energies are in the ratio \( \frac{K_{A}}{K_{B}}=\frac{1}{4} \)
B. Their speeds are in the ratio \( \frac{v_{A}}{v_{B}}=\frac{1}{1} \)
c. work done on the blocks are in the ratio \( \frac{W_{A}}{W_{B}}=\frac{1}{1} \)
D. All of the above


Using mass \( (M), \) length \( (L), \) time \( (T) \)
and current \( (A) \) as fundamental
quantities, the dimensional formula of
permittivity is
\( \mathbf{A} \cdot\left[M L^{-2} T^{2} A\right] \)
B \( \cdot\left[M^{-1} L^{-3} T^{4} A^{2}\right] \)
\( \mathbf{c} \cdot\left[M L T^{-2} A\right] \)
D・ \( \left[M L^{2} T^{-1} A^{2}\right] \)


Find the Odd one among : 123,14,246 56,369,125
A . 123
B. 14
c. 246
D. 125


connected to a resistance \( R \) and two
ideal inductors \( L_{1} \) and \( L_{2} \) through a
switch \( S \) as shown. There is no mutual
inductance between the two inductors.
The switch \( S \) is initially open. At \( t=0 \)
the switch is closed and current beings
to flow. Which of the following options is/are correct?
A. After a long time, the current through \( L_{1} \) will be \( \frac{V L_{2}}{R L_{1}+L_{2}} \)
B. After a long time, the current through \( L_{2} \) will be \( \frac{V L_{2}}{R L_{1}+L_{2}} \)
c. The ratio of the currents through \( L_{1} \) and \( L_{2} \) is fixed at all times \( (t>0) \)
Det the current through the resistance \( R \) is \( \frac{V}{R} \)


Two points sources separated by \( 2.0 m \)
are radiating in phase with \( \lambda=0.50 m \)
A detector moves in a circular path
around the two sources in a plane
containing them. How many maxima
are detected?
\( A \cdot 16 \)
B . 20
\( c \cdot 24 \)
D. 32


A regular octagon is formed by cutting congruent isosceles right-angled triangles from the corners of a square. If the square has side-length 1 , the sidelength of the octagon is
A \( \cdot \frac{\sqrt{2}-1}{2} \)
B. \( \sqrt{2}-1 \)
c. \( \frac{\sqrt{5}-1}{4} \)
D. \( \frac{\sqrt{5}-1}{3} \)


Kritika needs to receive completed
surveys from at least 3800 potential
voters in her city. She notices that for
every 5 surveys she sends out, only 1 survey is completed. Last week she
received 1350 completed surveys, and
this week she received 900 completed
surveys. Kritika plans to send out \( s \) additional surveys. Find the inequality which shows all possible for 's' that
would ensure that she received 3800
completed surveys?
A \( . s \geq 1550 \)
B . \( s \geq 2250 \)
\( \mathbf{c} \cdot s \geq 7750 \)
D. \( s \geq 12250 \)


Assertion
Carbon dioxide produced as a result of cellular respiration combines with water to form carbonic acid that
decreases the blood pH.
Reason
\( \mathrm{CO}_{2} \) must be eliminated from the body
to maintain homeostasis.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect.
D. Both Assertion and Reason are incorrect.


A ship of mass \( 3 \times 10^{7} \) kg, initially at
rest, is pulled by a force of \( 5 \times 10^{4} N \)
through a distance of 3 m. Assuming
that the resistance due to water is
negligible, the speed of the ship is
A \( .1 .5 m / s \)
в. \( 60 \mathrm{m} / \mathrm{s} \)
c. \( 0.1 m / s \)
D. \( 5 m / s \)


Which of the following converts acetone to acetone oxime?
A. \( H_{2} N-N H_{2} \)
в. \( 2,4- \) DNP
c. \( C_{6} H_{5} N H N H_{2} \)
D. \( N H_{2} O H \)


The graph shows the variation of
magnification \( m \) produced by convex
lens with image distance \( \vartheta \). The focal
length of the lens used is:
\( A \cdot b \)
в. \( \frac{b}{c a} \)
\( c \cdot \frac{b c}{a} \)
\( D \cdot \frac{c}{b} \)


Unit of the rate of reaction is:
A. concentration
B. concentration \( \times \) time
c. concentration
D. concentration \( ^{2} \)


The angular shape of ozone molecule
\( \left(O_{3}\right) \) consists of:
A. 1 sigma and 1 pi bonds
B. 2 sigma and 1 pi bonds
c. 1 sigma and 2 pi bonds
D. 2 sigma and 2 pi bonds


Codeine is used as an analgesic. Which of the following statements is false?
A. The structure is a weaker analgesic than morphine.
B. The structure acts as a prodrugs
c. The structure is converted to morphine in the brain
D. The coloured methyl group masks an important binding group


If the pressure of \( N_{2} / H_{2} \) mixture in a
closed apparatus is 100 atm and \( 20 \% \) of the mixture reacts,then the pressure at same temperature would be:
A. 100
B. 90
\( c \cdot 85 \)
\( D \cdot 80 \)


Silver atom has completely filled d
orbitals \( \left(4 d^{10}\right) \) in its ground state. How
can you say that it is a transition element?


A particle of rest mass \( m_{0} \) is moving
with speed \( c / 2 . \) What is its momentum?
A \( \cdot \frac{m_{0}}{2} \)
в. \( \frac{1}{\sqrt{3}} m_{0} c \)
c. \( \frac{2}{\sqrt{3}} m_{0} c \)
D. none of the above


Mass flow hypothesis was put forward
by
A. Swanson
B. Munch
c. curtis
D. De Vries.


For a nuclear reactor to run in crtitcal
condition the reproduction factor should be
\( A \cdot=1 \)
B \( .>1 \)
\( c \cdot<1 \)
D. >>>1


The temperature of a room heated by a
heater is \( 20^{\circ} \mathrm{C} \) when outside
temperature is \( -20^{\circ} \mathrm{C} \) and it is \( 10^{\circ} \mathrm{C} \) when the outside temperature is
\( -40^{\circ} \mathrm{C} . \) The temperature of the heater is
A \( \cdot 80^{\circ} \mathrm{C} \)
B. \( 100^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 40^{\circ} \mathrm{C} \)
D. \( 60^{\circ} \mathrm{C} \)


Which of the following is the correct relation between solubility and
solubility product of \( M X_{4} ? \)
\( ^{\mathrm{A}} S=\left[\frac{K_{s p}}{256}\right]^{1 / 5} \)
B. \( S=\left[128 K_{s p}\right]^{1 / 4} \)
\( \mathbf{c} \cdot S=\left[256 K_{s p}\right]^{1 / 5} \)
\( ^{\mathrm{D}} S=\left[\frac{K_{s p}}{128}\right]^{1 / 4} \)


PVC is prepared by the polymerisation of:
A. ethylene
B. 1-chloropropene
c. propene
D. 1-chloroethene


The vapour pressure of an aqueous solution is found to be 750 torrs at
certain temperature 'T'. If 'T' is the temperature at which pure water boils under atmospheric pressure and same solution show elevation in the boiling
point \( \Delta T_{b}=1.04 K, \) find the
atmospheric pressure?
\( \left[\boldsymbol{K}_{\boldsymbol{b}}=\mathbf{0 . 5 2} \boldsymbol{K} \boldsymbol{k g m o l}-\mathbf{1}\right] \)
A . 77
в. 779
\( c .782 \)
D. 746


f PQRS is a square, \( A B \| S Q \) and
\( A C=C B, \) which one is true?
A \( . S A=B Q \)
B. PC is the bisector of \( \angle S P Q \)
c. PC if produced will pass through
D. All of these


A man bought a second hand car for Rs.
76000 and a \( T V \), for Rs. \( 27500 . \) He sold
the car at a gain of \( 15 \% \) and the T.V. at a
loss of \( 12 \% \). Find the total amount
gained or lost from the two transactions.
A . lost Rs. 1800
B. gained Rs. 1800
c. gained Rs. 8100
D. lost Rs. 8100


Number of different permutation, each containing all letters of the word "STATESMAN" is
A . 90720
B. 45360
c. 22680
D. None of these


In a saturated of the sparingly soluble
strong electrolyte \( A g l O_{3} \) (Molecular mass \( =283 \) ), the equilibrium which
sets in is
\( \boldsymbol{A} \boldsymbol{g} \boldsymbol{I} \boldsymbol{O}_{3}(\boldsymbol{s}) \rightleftharpoons \boldsymbol{A} \boldsymbol{g}^{+}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{I} \boldsymbol{O}^{-}(\boldsymbol{a} \boldsymbol{q}) \)
If the solubility product constant \( \boldsymbol{K}_{s p} \) of
\( A g l O_{3} \) at a given temperature is \( 1.0 \times \)
\( 10^{-8}, \) what is the mass of \( A g l O_{3} \)
contained in \( 100 m L \) of its saturated
solution?
A \( \cdot 1.0 \times 10^{-7} \)
В. \( 1.0 \times 10^{-4} \)
c. \( 28.3 \times 10^{-2} \)
D. \( 2.83 \times 10^{-3} \)


Amorphous boron of \( 95 \% \) to \( 98 \% \) purity
is obtained by:
\( \mathbf{A} \cdot \) heating \( B_{2} O_{3} \) with \( H_{2} \)
B. heating \( B_{2} O_{3} \) with \( M g \) or \( N a \) at high temperature
C. heating \( K B F_{4} \) with \( N a \) or \( K \)
D. heating \( B B r_{3} \) with \( H_{2} \) in presence of a catalyst


How much energy is required to ionise \( \mathrm{H} \) atom if the electron occupies \( n=5 \) orbits? Compare your answer with the ionization enthalpy of H atom [ energy required to remove the electron from \( n=1 \text { orbit }] \)


If \( A \) is a square matrix of order \( 3, \) then \( \left|A d j\left(A d j A^{2}\right)\right|= \)
A \( \cdot\left|A^{2}\right| \)
B \cdot \( \left|A^{4}\right| \)
c. \( \left|A^{8}\right| \)
\( \mathbf{D} \cdot\left|A^{16}\right| \)


Consider the word \( W= \)
MISSISSIPPI Number of ways in
which the letters of the word \( W \) can be
arranged if at least one vowel is separated from rest of the vowels
A \( \frac{8 ! .16 !}{4 ! 4 ! ! 2 !} \)
в. \( \frac{8 ! .16 !}{4.4 ! .2 !} \)
c. \( \frac{8 ! .16 !}{4 ! .2 !} \)
D. \( \frac{8 !}{4 ! .2 !} \cdot \frac{165}{4 !} \)


Example for fossil fuel is
A. copper
B. Iron
c. Magnesium
D. coal


By reference to two waves, state:
(i) the principle of superposition.
(ii) what is meant by coherence.


Calculate \( : \lim _{x \rightarrow 0}\left(\frac{1}{x^{2}}-\frac{1}{\sin ^{2} x}\right) \)
A. \( \infty \)
B. \( \frac{1}{3} \)
\( c \cdot-\frac{1}{3} \)
D. does not exist


Mention two scales of temperature used
in everyday life. Give at least two examples


Given the reactions of ozone with the
following and give equations.
(i) \( P b S \)
(ii) \( \operatorname{Sn} C l_{2} / H C l \)
(iii) Moist \( \boldsymbol{K} \boldsymbol{I} \)
(iv) \( B a O_{2} \)


What is the largest distance (in a straight line) that can be measured
with a meter scale of length \( 1 \mathrm{m} \) and smallest division of \( 1 \mathrm{mm} \) ?
\( \mathbf{A} \cdot 1 \mathrm{mm} \)
в. \( 1 \mathrm{m} \)
c. \( 100 \mathrm{m} \)
D. No upper limit exists for measurement of length with meter scale.


A circular conductor is made of a
uniform wire of resistance \( 2 \times \)
\( 10^{-3} \) ohm / meter and the diameter of
this circular conductor is 2 meter. Then
the resistance measured between the
ends of the diameter is (in ohms):
A \( \cdot \pi \times 10^{-3} \)
В. \( 2 \pi \times 10^{-3} \)
c. \( 4 \pi \times 10^{-3} \)
D. \( 4 \times 10^{-3} \)


When two magnetic poles having same
pole strength are separated by a distance of \( 20 \mathrm{cm}, \) a force of \( 5 \mathrm{N} \) acts
between them. If the distance is halved, the force becomes
A . 20 N
B. 10 N
\( c .15 \mathrm{N} \)
D. 25 N


Petroleum was formed from organisms:
A. living on the land
B. living on the plants
c. living in the sea
D. living on the rocks


Ferrous ion can be oxidised by which of the following ions?
\( \mathbf{A} \cdot L i^{+} \)
B. \( M n^{+2} \)
c. \( A g^{+} \)
D. \( A l^{+} \)


A solid is in the form of a right circular
cone mounted on a hemisphere. The
radius of the hemisphere is \( 3.5 \mathrm{cm} \) and
the height of the cone is \( 4 \mathrm{cm} . \) The solid
is placed in a cylindrical tub, full of
water, in such a way that the whole
solid is submerged in water. If the
radius of the cylinder is \( 5 \mathrm{cm} \) and its
height is \( 10.5 \mathrm{cm}, \) find the volume of
water left in the cylindrical tub \( \left(\boldsymbol{U} \boldsymbol{s e} \boldsymbol{\pi}=\frac{\boldsymbol{2} \boldsymbol{2}}{\boldsymbol{7}}\right) \)


An aqueous solution of a non-volatile
solute boils as \( 100.17^{\circ} \mathrm{C} \). What is the
depression in the freezing point for the
solution in \( ^{\circ} \mathrm{C} \) ?
\( \left[K_{b} \text { and } K_{f} \text { for water is } 0.512 \) and \right.
\( \mathbf{1 . 8 6}^{\circ} \boldsymbol{C} / \boldsymbol{m} \) respectively
A . 0.93
B. 0.11
\( c \cdot 0.62 \)
D. 0.31


If \( |a|=5 .|\vec{b}|=4, \) and \( |c|=3 . \) then what will be the value of \( \vec{a} . \vec{b}+\vec{b} . \vec{c}+\vec{c} . \vec{a} \) given that \( \vec{a}+\vec{b}+\vec{c}=0 \)
A . 25
B. 50
c. -25
D. -50


Identify the options in which increase in rate of reaction will be maximum:
(1) \( E_{a}=40 \) Id/mole Temperature change
300 to \( 310 \mathrm{K} \)
(II) \( E_{a}=80 \mathrm{kJ} / \mathrm{mole} \) Temperature change
200 to \( 210 \mathrm{K} \)
(III) \( E_{a}=60 \) Id/mole Temperature
change 400 to \( 410 \mathrm{K} \)
A . I
B.
\( c . \) ॥
D. All four will experience same change


Pancreas secrete which of the following hormone?
A. Growth hormone
B. Thyroxine
c. Adrenalin
D. Insulin


A 10 V battery connected to \( 5 \Omega \)
resistance coil having inductance \( 10 \mathrm{H} \) through a switch drives a constant
current in the circuit. The switch is
suddenly opened and the time taken to open it is 2 ms. The average emf
induced across the coil is
A \( \cdot 4 \times 10^{4} \)
B \( .2 \times 10^{4} \)
\( c \cdot 2 \times 10^{2} \)
D. \( 1 \times 10^{4} \)


Using the table given below, determine
the heat of combustion of one mole of
\( C_{2} H_{4} \) at \( 298 \mathrm{K} \) and 1 atm?
\begin{tabular}{ll}
Compound & \( \Delta \) of formation (kcal/mol) \\
\( H_{2} O(g) \) & -57.8 \\
\( C_{2} H_{6}(g) \) & \( -20 / 2 \) \\
\( C_{2} H_{4}(g) \) & 12.5 \\
\( C_{2} H_{2}(g) \) & 54.2 \\
\( C O(g) \) & -26.4 \\
\( C O_{2}(g) \) & -94.1 \\
\hline
\end{tabular}
A . 316.3 kcal
B. 12.5 kcal
c. -291.3 kcal
D. -316.3 kcal
kca
E . 57.8


Protein is a polymer of :
A. Glucose
B. Terephthalic acid
C. Amino acid
D. Glycol


The rectangular surface of area \( 8 \mathrm{cm} \times \)
\( 4 c m \) of a block body at a temperature of
\( 127^{\circ} C \) emits energy at the rate of \( E \) per
second. If the length and breath of the surface are each reduced to half of the
initial value and the temperature is
raised to \( 327^{\circ} \mathrm{C} \), the rate of emission of
energy will become
\( ^{\mathbf{A}} \cdot \frac{3}{8}^{E} \)
B \( \cdot \frac{81}{16} E \)
c. \( \frac{9}{16} E \)
D. \( \frac{81}{64} \)


A source of wave produces 3 crest and 2 troughs in \( 2 \mathrm{ms} \), the frequency of the wave is:
A . 1250 \( \mathrm{Hz} \)
в. 500 нz
\( c .800 \mathrm{Hz} \)
D. 750 нz


Total number of nodes present in \( 4 d^{-} \) orbitals will be
\( \mathbf{A} \cdot \mathbf{3} \)
B . 2
c. 1
D. 0


Two point charges of magnitude \( +10^{8} \) coulomb each are placed 0.5 metre in air. At the mid point of line joining then
A. The field is zero, the potential is zero
B. The field is zero, the potential is not zero
c. The field is zero the potential is -720
D. The field is zero the potential is + 720


Which of the following metal sulphides
has maximum solubility in water?
\( \mathbf{A} \cdot C d S\left(K_{s p}=36 \times 10^{-30}\right) \)
B \( \cdot \operatorname{Fe} S\left(K_{s p}=11 \times 10^{-20}\right) \)
\( \mathbf{c} \cdot H g S\left(K_{s p}=32 \times 10^{-54}\right) \)
D. \( Z n S\left(K_{s p}=11 \times 10^{-22}\right) \)


Which of these groups of words means
the same thing?
A. Autotrophs and consumers
B. Autotrophs and producers
c. Heterotrophs and producers
D. Autotrophs and carnivore


Using differentials, find the approximate value of \( (3.968)^{\frac{3}{2}} \)


What is the ratio of powers delivered by \( 20 \mathrm{V} \mathrm{dc} \) and \( 20 \mathrm{V} \) peak ac to the same load?


On differentiating an identity function,
we get?
A. Signum function
B. sinc function
c. constant function
D. None


In a quark model of elemetary particles, a neutron is made of one up quark of charge \( \frac{2}{3} e \) and two down quark of charges \( \left(-\frac{1}{3} e\right) . \) If they have a triangle configuration with side length of the order of \( 10^{-15} \) m. The electrostatic
potential energy of neutron in \( M e V \) is
A. 7.68
B . -5.21
c. -.048
D. 9.34


If population of city is 15000 and it
increase with \( 9 \% \) rate, find population of city after 2 years


Determine the voltage across the
inductor as a function of time(in \( \mathrm{mV} \) )


Number of professionally managed zoos/ zoological parks world wide is
A . 297
B. 400
\( c \cdot 650 \)
D. 800


Let \( S \) be the set of all rational numbers
except 1 and \( * \) be defined on \( S \) by \( a * \)
\( b=a+b-a b, \) for all \( a, b \in S . \) Prove
that \( * \) is a binary operation on \( S \)


Find the area of a circle whose
circumference is \( 484 \mathrm{cm} \)


Without actual deviation, prove that
\( 2 x^{4}+2 x^{2}-x+2 \) is divisible by \( x^{2}- \)
\( 3 x+2 \)


A vector perpendicular to \( \hat{i}+\hat{j}+\hat{k} \) is
\( \mathbf{A} \cdot \hat{i}-\hat{j}+\hat{k} \)
B. \( \hat{i}-\hat{j}-\hat{k} \)
c. \( -\hat{i}-\hat{j}-\hat{k} \)
D. \( 3 \hat{i}+2 \hat{j}-5 \hat{k} \)


In a Compound microscope, the intermediate image is :
A. virtual, erect and magnified
B. real, erect and magnifiedd
c. real, inverted and magnified
D. virtual, erect and diminished


\( n \) arithmetic means are inserted
between 3 and \( 17 . \) If the ratio of last and
the first arithmetic mean is \( 3: 1, \) then
the value of \( n \) is
\( \mathbf{A} \cdot \mathbf{9} \)
B. 6
\( c \cdot 7 \)
D.


Which of the following electronic
configuration shows transition metal?
A \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} \dots . . n s^{2} n p^{2} \)
B \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} \ldots . . n s^{2} n p^{2} n d^{3}(n+1) s^{2} \)
C \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} \ldots . . n s^{2} n p^{6} \)
D. \( 1 s^{2} 2 s^{2} 2 p^{6} \ldots . . n s^{2} n p^{1} \)


Indentify the correct statement from the
following
This question has multiple correct options
A. Wave nature of light was proposed by Huygen.
B. The direction of light ray and its wave front are opposite.
C. Huygen's wave theory could not explain phenomenon of reflection.
D. A monochromatic ray of light after passing through the prism should be made of one colour only.


Which of the following is important features of fossils which help in the study of evolution?
A. Fossils help in establishing evolutionary traits among organisms and their ancestors
B. Fossils help in establishing the time period in which organisms lived
c. Fossils represent modes of preservation of ancient species
D. All of the above


A beam of light consisting of red green and blue colours is incident on a right
angled prism. The refractive index of the
material of the prism for the above red,
green and blue wavelengths are 1.39 1.44 and \( 1.47, \) respectively. The prism
will:
XII
Gree
Red
A. separate the red colour part from the green and blue colours
B. separate the blue colour part front the red and green colours
C. separateall all three colours from one another
D. not separate the three colours at all


The decay constant of the parent nuclide in uranium series is / lambda.
Then the decay constant for the stable
end product of the series will be?
A. \( \lambda / 238 \)
B. \( \lambda / 206 \)
\( c \cdot \lambda / 208 \)
D. zero


The north pole of a magnet is moved
into a coil through the end \( \boldsymbol{A} \) Simultaneously the north pole of another magnet is moved into the coil through the end \( B \) as shown in the
figure. The direction of induced emf will:
A. Be in the anticlockwise direction as seen through the end \( A \)
B. Be in the clockwise direction as seen through the end \( B \)
c. Depend on the speed with which the two magnets are moved
D. Depend on the speed with which the magnets are moved and the strengths of the magnets


Identify the matrix given below:
\( \left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 2\end{array}\right] \)
A. unit matrix
B. scalar matrix
c. zero matrix
D. diagonal matrix


Three identical batteries each emf 4 V
and zero of negligible internal
resistance are connected as shown
in figure below. The potential difference
between the poilints \( A \) and \( G\left(V_{A}-V_{G}\right) \)
A . 4 v
B . \( -4 V \)
\( c \cdot 8 v \)
\( \mathbf{D} \cdot-8 V \)


Two simple harmonic motions are
represented by the equations \( \boldsymbol{Y}_{1}=\mathbf{1 0} \sin \left(\boldsymbol{3} \boldsymbol{\pi} \boldsymbol{t}+\frac{\boldsymbol{\pi}}{\boldsymbol{4}}\right) \) and \( \boldsymbol{Y}_{2}= \)
\( 5(\sin 3 \pi t+\sqrt{3} \cos 3 \pi t) \)
Their amplitudes are in the ratio of
A . 2:
B. 3:
c. 1: 3
D. 1:


\( \ln C H_{4} \) molecule, there are four \( C-H \)
bonds. If two adjacent bonds are in \( \hat{\mathbf{i}}+ \) \( \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) and \( \hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}-\hat{\boldsymbol{k}} \) direction, then find
the angle between these bonds.
A \( \cdot \sin ^{-1}\left(\frac{-1}{3}\right) \)
B. \( \cos ^{-1}\left(\frac{1}{3}\right) \)
\( ^{c} \cdot \sin ^{-1}\left(\frac{1}{3}\right) \)
D. \( \cos ^{-1}\left(\frac{-1}{3}\right) \)


Among the following, which is the strongest acid?
A. \( C H F_{2}-C H_{2}-C H_{2}-C O O H \)
в. \( C H_{3}-C H_{2}-C F_{2}- \) СООН
c. \( C H_{2} F-C H F-C H_{2}-C O O H \)
D. \( C H_{3}-C F_{2}-C H_{2}-C O O H \)


The reaction,
\( \mathbf{2} N \boldsymbol{O}(\boldsymbol{g})+\boldsymbol{O}_{2}(\boldsymbol{g}) \leftrightharpoons \mathbf{2} \boldsymbol{N} \boldsymbol{O}_{2}(\boldsymbol{g}) \) is first
order. If volume of reaction vessel is reduced to \( \frac{1}{3}, \) the rate of reaction would
be:
A \( \cdot \frac{1}{3} \) times
B. \( \frac{2}{3} \) times
c. 3 times
D. 6 times


Draw a labelled diagram of dialysis method, for purification of colloidal solutions.


Find the correct match between given
set of organisms, their characteristics
and exception among them.
Organism Characteristic Exception
A. Rana, Alytes Without post Alytes
Bufo anal tail
B. Chelone Oviparous Testudo
Testudo
Calotes
C. Neophron Comb-like Apteryx
Corvus pecten
Apteryx
D. Fasciola Exhibit Dasypus
Dasypus Polyembryony
Echidna


(a) Number of compounds which are aromatic \( =\boldsymbol{w} \)
(b) Number of compounds which are
non-aromatic \( =x \)
(c) Number of compounds which are
anti-aromatic \( =\boldsymbol{y} \)
(d) Number of compounds which are readily undergo Dimerization at room
temperature \( =z \)
Sum of \( \boldsymbol{w} \) \( v+x+y+z= \)


A wire carrying a current of 5 A is placed perpendicular to a magnetic induction of \( 2 \mathrm{T} \). The force on each centimeter of
the wire is :
A . \( 0.1 \mathrm{N} \)
B. 10 N
\( c \cdot 100 N \)
D. 1N


The fundamental purpose of is
to describe feeding relationship among species in a community.


The force primarily responsible for the existence of the solar system is the
A. force of friction
B. gravitational force
c. electrostatic force
D. magnetic force


Example of adaptive radiation is
A. Darwin's finches
B. Human evolution
c. Black winged moth
D. (1) \& (2) both


Assertion
STATEMENT-1: m-Chlorobenzoicacid is a
stronger acid than p-chlorobenzoic acid
Reason

STATEMENT-1: In m-chlorobenzoicacid,
both - I effect and +M effect of \( C l \)
operate, but in p-isomer only +M effect
of \( C l \) operates.
A. STATEMENT-1 is True, STATEMENT-2 is True:
STATEMENT-2 is a correct explanation for STATEMENT
B. STATEMENT-1 is True, STATEMENT-2 is True:
STATEMENT-2 is NOT a correct explanation for STATEMENT-1
c. stateMENT-1 is True, stateMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True


Which of the above is incosistent for the
given meter bridge:
\( \begin{array}{lll}\text { 1. } & 1000 \Omega & \text { 60 cm } \\ \text { 2. } & 100 \Omega & \text { 13 cm } \\ \text { 3. } & 10 \Omega & 1.5 \mathrm{cm} \\ \text { 4. } & 1 \Omega & 1 \mathrm{cm}\end{array} \)
\( A \)
B.
\( c \)
\( D \)


The conductivity of 0.001 mol \( L^{-1} \) acetic
acid is \( 5 \times 10^{-5} s c m^{-1} \). Calculate it's
dissociation constant if \( \lambda_{m}^{o} \) m for acetic
\( \operatorname{acid} \) is \( 250 \operatorname{scm}^{2} m o l^{-1} ? \)


In \( \mathrm{CaF}_{2} \), the number of electron(s)
transferred from calcium to fluorine
atoms are
\( A \cdot 1 \)
B. 2
\( c \cdot 3 \)
D. 4


Blackman's law was conceived in
connection with
A. Photosynthesis
B. Respiration
c. Transpiration
D. Root pressure.


A solenoid of length \( 0.4 \mathrm{m}, \) having 500 turns and 3 A current flows through it. A coil of radius \( 0.01 \mathrm{m} \) and have 10 turns
and carries current of 0.4 A has to
placed such that its axis is perpendicular to the axis of solenoid then torque on coil will be
A \( \cdot 5.92 \times 10^{-7} N \cdot m \)
В. \( 5.92 \times 10^{-5} \mathrm{N} . \mathrm{m} \)
c. \( 5.92 \times 10^{-4} N . m \)
D. \( 5.92 \times 10^{-3} N . m \)


In how many ways can 3 prizes be distributed among 4 boys, when
(i) no boy gets more than one prize?
(ii) a boy may get member of prizes?
(iii) no boy gets all the prizes?


Molarity of \( 0.2 \mathrm{N} H_{2} S O_{4} \) is:
A. 0.2
B. 0.4
\( c .0 .6 \)
D. 0.1


Methanol and ethanol are miscible with
water due to their:
A. covalent character
B. hydrogen bonding character
c. oxygen bonding character
D. non-polar nature


Factors of \( \boldsymbol{x}^{\boldsymbol{4}}-(\boldsymbol{y}+\boldsymbol{z})^{\boldsymbol{4}} \) are
This question has multiple correct options
\( \mathbf{A} \cdot(x-y-z) \)
B.
\( \mathbf{c} \cdot(x+y+z) \)
D. \( \left(x^{2}+y^{2}+z^{2}+2 y z\right) \)


For \( 2 A+B+C \rightarrow 2 D \), determine the
rate law for the reaction based on the
following data.
\( \begin{array}{lllll}\operatorname{Exp} & {[\boldsymbol{A}]} & {[\boldsymbol{B}]} & {[\boldsymbol{C}]} & \begin{array}{l}\text { Rate of } \\ \text { disappearance } \\ (\mathrm{M} / \mathrm{s})\end{array} \\ & & & & \\ 1 & 0.1 & 0.1 & 0.1 & X \\ 2 & 0.2 & 0.2 & 0.1 & 8 X \\ & & & & \\ 3 & 0.2 & 0.1 & 0.1 & 4 X \\ & & & & \\ 4 & 0.2 & 0.1 & 0.2 & 32 X\end{array} \)
A \( . \) Rate \( =k[A]^{2}[B][C] \)
B . Rate\( =k[A]^{2}[B][C]^{3} \)
c. Rate\( =k[A]^{2}[B]^{3}[C] \)
D. \( \operatorname{Rate}=k[A]^{2}[B]^{2}[C]^{3} \)


Assertion
An atom is smallest particle in an element that has the properties of the element.
Reason
Molecules are formed by the
combination of two or more atoms
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 products in a hydrogen atom are independent of the
principal quantum number ' \( n \) '? The symbols have their usual meanings. This question has multiple correct options
A . \( v n \)
в. \( E r \)
\( c . E n \)
D. \( v r \)


Can a satellite move in a stable orbit in
a plane not passing through the earth's centre? Explain.


The monomers used in preparation of dextron are:
A. lactic acid and glycolic acid
B. 3-hydroxy butanoic acid and 3-hydroxy pentanoic acid
c. styrene and 1, 3-butadiene
D. hexamethylenediamine and adipic acid


Find out the modal class for the
following table:
\( \begin{array}{llllll}x & 1- & 3- & 5- & 7- & 9- \\ 3 & 5 & 7 & 9 & 11\end{array} \)
frequency 2
A . \( 1-3 \)
B. \( 3-5 \)
c. \( 5-7 \)
D. \( 7-9 \)


An organic compound \( A \) with molecular
formula \( C_{3} H_{6} O \) is resistant to
oxidation but forms compound \( \boldsymbol{B} \)
\( C_{3} H_{8} O \) on reduction, compound \( B \)
reacts with \( H B r \) from \( C \) and \( C \) reacts
with \( M g \) from Grignard reagent. \( D \)
reacts with \( A \) to form a product which
on hydrolysis gives \( E \). Identify
\( \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C}, \boldsymbol{D}, \boldsymbol{E} \)


The Integrating factor of the differential equation \( \left(1-y^{2}\right) \frac{d x}{d y}+y x=a y \) is
A \( \cdot \frac{1}{y^{2}-1} \)
B. \( \frac{1}{\sqrt{y^{2}-1}} \)
c. \( \frac{1}{1-y^{2}} \)
D. \( \frac{1}{\sqrt{1-y^{2}}} \)


An inductor may store energy in:
A. its electric field
B. its coil
C . its magnetic field
D. both electric and magnetic fields