The orbital with zero orbital angular
momentum is :
A . s
B.
\( c \cdot d \)
\( D \)


Double-helical structure is found in


The longest wavelength doublet absorption transition is observed at 589
and \( 589.6 \mathrm{nm} \)
Calculate the frequency of each
transition and energy difference between two excited states.


Ahars, Kattas, Bhundhis and Khadins are the modes of
A. afforestation
B. deforestation
c. soil conservation
D. water harvesting


A free particle with initial kinetic energy \( \mathrm{E} \) and de-broglie wavelength \( \lambda \) enters a region in which it has potential energy U. What is the particle's new de-
Broglie wavelength?
A \( \cdot \lambda(1-U / E)^{-1 / 2} \)
в. \( \lambda(1-U / E) \)
c. \( \lambda(1-U / E)^{-1} \)
D. \( \lambda(1-U / E)^{1 / 2} \)


Assertion
Photodiode and solar cell work on same
mechanism.
Reason
Area is large for solar cell.
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


There are three copies each of four different books. The number of ways in
which they can be arranged in a shelf is
A \( \cdot \frac{12 !}{(3 !)^{4}} \)
в. \( \frac{12 !}{(4 !)^{3}} \)
c. \( \frac{12 !}{(3 !)^{4} 4 !} \)
D. \( \frac{12 !}{(4 !)^{3} 3 !} \)


The colour of Iymph is
\( \mathbf{A} \cdot \operatorname{Red} \)
B. Pale yellow
c. colourless
D. Milky


If \( r \) is non-real and \( r=\sqrt[5]{1}, \) then the
value of \( 2\left|1+r+r^{2}+r^{-2}-r^{-1}\right| \) is
equal to


Excess cholesterol is responsible for ulcers. If this is true enter 1 , if false enter 0 .


The diameter of the moon is
approximately one fourth of the diameter of the earth. Find the ratio of
their surface areas.


Let \( Z \) be the set of all integers and \( Z_{0} \) be
the set of all non-zero integers. Let a
relation \( \boldsymbol{R} \) on \( \boldsymbol{Z} \times \boldsymbol{Z}_{\mathbf{0}} \) be defined as
follows:
\( (a, b) R(c, d) \Leftrightarrow a d=b c \) for all
\( (a, b),(c, d) \in Z \times Z_{0} \)
Prove that \( R \) is an equivalence relation
on \( Z \times Z_{0} \)


Coal tar is used in manufacture of
A. synthetic dyes
B. drugs
c. explosives
D. all of these


Which of the following has the largest radius?
A \( . S r \)
в. \( P \)
c. \( M g \)
D. \( A l^{3} \)
E \( . M g^{2+} \)


Which of the following carbides produces propyne on reaction with water?
A. \( C a C_{2} \)
в. \( B e_{2} C \)
c. \( A l_{4} C_{3} \)
D. \( M g_{2} C_{3} \)


Which of the following is NOT soluble in
water?
A. Salt
B. Sugar
c. oxygen
D. None of these


In the circuit shown in figure, the diode
is ideal. The potential difference
between A and B is?
A. \( V / 4 \)
B.
c. zero
D. \( V / 2 \)


Study the bar graph and answer the questions. The graph shows the quantities of different crop production in different states of India.

What is the difference of the average
wheat produced by the two highest and the two lowest wheat producing states?
A. 50 tonnes
B. 85 tonnes
c. 75 tonnes
D. 100 tonne:


If the concentration of reactants is
reduced by n times then the value of rate constant of the first order will?
A. Increase by n times
B. Decrease by factor of \( n \)
c. Not change
D. None of these


Current \( I_{1} \) in the following circuit is
\( A, O, 4 A \)
B . -0.4A
\( c . \) о.вА
D . -0.8A


Calculate the equilibrium constant for
the reaction:
\( \mathbf{3} \boldsymbol{S} \boldsymbol{n}(\boldsymbol{s})+\boldsymbol{2} \boldsymbol{C r}_{2} \boldsymbol{O}_{7}^{2-}+\boldsymbol{2} \boldsymbol{8} \boldsymbol{H}^{+} \rightarrow \)
\( \mathbf{3} \boldsymbol{S} \boldsymbol{n}^{+\mathbf{4}}+\mathbf{4} \boldsymbol{C} \boldsymbol{r}^{\mathbf{3}+}+\mathbf{1 4} \boldsymbol{H}_{\mathbf{2}} \boldsymbol{O} \)
\( E^{\circ} \) for \( S n / S n^{2+}=0.136 V E^{\circ} \) for
\( \boldsymbol{S} \boldsymbol{n}^{2+} / \boldsymbol{S} \boldsymbol{n}^{4}=-\mathbf{0 . 1 5 4} \boldsymbol{V} \)
\( E^{\circ} \) for \( C r_{2} O_{7}^{2-} / C r^{3+}=1.33 V \), if the
ans is \( K=10^{c}, \) what is c?
A . 261
в. 273
\( c \cdot 128 \)
D. none of these


If \( z \neq 1 \) and \( \frac{z^{2}}{z-1} \) is real, then the
point represented by the complex
number z lies:
A. either on the real axis or on a circle passing through the origin.
B. on a circle with centre at the origin
c. either on the real axis or on a circle not passing through the origin.
D. on the imaginary axis


In a cylinder of cooling gas \( 11.2 \mathrm{kg} \) butane is filled. If \( 1500 \mathrm{KJ} \) energy is required for cooking food daily then
calculate that for how many days this cylinder is sufficient for fuel; whereas enthalpy of combustion of butane is \( 2658 k J m o l^{-1} \)


How many calories of heat are required by gram of water at \( 99^{\circ} \mathrm{C} \) to boil off:
A. 530
B. 640
\( c \cdot 540 \)
D. 500


An organic compound \( \boldsymbol{A}\left(\boldsymbol{C}_{\mathbf{9}} \boldsymbol{H}_{8} \boldsymbol{O}_{3}\right) \) does
not react with an aqueous solution of
\( N a H C O_{3} \) and does not change the
color of litmus paper. A on acid
hydrolysis gives \( B\left(C_{9} H_{8} O_{4}\right) \) whereas \( A \) on treatment with methanol in acid
medium gives \( C\left(C_{10} H_{14} O_{4}\right) \) as the major alcoholysis product. B on heating with excess of soda-lime produces toluene. Deduce structures of \( A \) to \( C \)


Which number should come in place of
\( \frac{\mathbf{0}}{\mathbf{7}}+\frac{\mathbf{2}}{\mathbf{7}}+\frac{\square}{\mathbf{7}}=\mathbf{1} \frac{\mathbf{3}}{\mathbf{7}} \)
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D. 7


A fixed volume of iron is drawn into a wire of length \( l \). The extension produced
in this wire by a constant force \( \boldsymbol{F} \) is
proportional to :
A \( \cdot \frac{1}{l^{2}} \)
B. \( \frac{1}{l} \)
\( c \cdot l^{2} \)
D. \( l \)


Choose the correct answers from the
alternatives given Pseudopodia in Amoeba are important
for:
A. locomotion only
B. feeding only
c. both locomotion and feeding
D. none of these


Infrared radiation are detected by
A. spectrometer
B. pyrometer
c. nanometer
D. photometre


The mass of the jupiter is \( 1.9 \times 10^{2} \mathrm{kg} \)
and that of sun is \( 1.99 \times 10^{30} \) kg. The
mean distance of jupiter from the sun is \( 7.8 \times 10^{11} \mathrm{m} . \) Speed of jupiter is
(assuming that jupiter moves in circular orbit around the sun)


Assertion : In damped oscillations, the energy of the system is dissipated continuously. Reason: For the small damping, the oscillations remain approximately periodic.
A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true and reason is not the correct explanation of assertion.
c. If assertion is true but reason is false
D. If both assertion and reason are false


What is complementary base pairing?


Eye teeth are
A. Upper incisors
B. Lower incisors
C. Lower canines
D. Upper canines


Show that the mid-point of the line segment joining the points (5,7) and (3,9) is also the mid-point of the line segment joining the points (8,6) and (0,10)


In which of the following species, each atom carries same number of lone pair
electrons on it?
A \( \cdot X e O_{4}^{2} \)
в. \( X e F_{2} \)
c. \( X e O_{6}^{4} \)
D. \( O_{3} \)


A hemispherical tank is made up of an iron sheet of thickness \( 1 \mathrm{cm} \). If the inner
radius is \( 1 m, \) then find the volume of
the iron used to make the tank.


The correct order of increasing atomic
size of element \( N, F, S i \& P \) is:
\( \mathbf{A} \cdot N<F<S i<P \)
B \( . F<N<P<S i \)
\( \mathbf{c} \cdot F<N<S i<P \)
D. \( N<S i<F<P \)


The oxidation number of \( F e \) in
Magnetite \( \left(\boldsymbol{F e}_{3} \boldsymbol{O}_{4}\right) \) is:


For a circuit, \( L, C \) and \( R \) represent the
inductance, capacitance and resistance. Then, the dimensional
formula for \( C^{2} L R \) is
\( \mathbf{A} \cdot[M L T] \)
B . \( \left[M^{0} L^{0} T I^{0}\right] \)
c. \( \left[M^{2} L^{2} T^{0} I^{0}\right. \)
D \cdot \( \left[M^{0} L^{0} T^{3} I^{0}\right] \)


Read the assertion and reason carefully
and answer the question on the basis of the following options. You have to select
the one that best describes the two
statements.
Assertion: Potassium and caesium are
used in photoelectric cells. Reason: Potassium and caesium emit
electrons on exposure to light.
A. If both assertion and reason are true and the reason is correct explanation of the assertion
B. If both assertion and reason are true but reason is not a correct explanation of the assertion
c. If the assertion is true but reason is false
D. If both the assertion and reason are false
E. If the assertion is false but the reason is true


Assertion
STATEMENT-1:
\( \int \frac{\left\{\boldsymbol{f}(\boldsymbol{x}) \boldsymbol{\phi}^{\prime}(\boldsymbol{x})-\boldsymbol{f}^{\prime}(\boldsymbol{x}) \phi(\boldsymbol{x})\right\}}{\boldsymbol{f}(\boldsymbol{x}) \phi(\boldsymbol{x})}\{\log \phi(\boldsymbol{x}) \)
\( \frac{1}{2}\left\{\log \frac{\phi(x)}{f(x)}\right\}^{2}+c \)
Reason STATEMENT-2 : \( \int(\boldsymbol{h}(\boldsymbol{x}))^{\boldsymbol{n}} \boldsymbol{h}^{\prime}(\boldsymbol{x}) \boldsymbol{d} \boldsymbol{x}= \)
\( \frac{(h(x))^{n+1}}{n+1}+c \)
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-
c. STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True


Exprience that a aquired traits during lifetime are not passed to the next generation justify?


i) A circle can have \( _{--} \) -parallel tangents.
ii) The point common to the tangent and the circle is called


A purse contains four coins each of
which is either a rupee or two rupees coin. Find the expected value of a coin in
that purse.


Choose the correct statement from the
following. A good fuel is one which:
This question has multiple correct options
A. is readily available
B. produces a large amount of heat
c. leaves behind many undesirable substances
D. burns easily in air at a moderate rate


Fill in the blanks with the correct choice.
The undesired impurities present in the
the volatile impurities from the ore, the
(ii) process is carried out. Flux combines with non-fusible impurities to form
(iii) \( C a O \) acts as a
(iv) flux.
A. (i) - gangue,
(iii) - slag, (iv) -acidic
(ii) -roasting,
(ii) - calcination, (iii) - slag, (iv) - basic
B. (i) - gangue,
c. (i) - anode mud,
(ii) - - leaching,
(iii) - matrix, (iv) -acidic
D. (i) - gangue,
(ii) -roasting, (iii) - solution, (iv) -acidic


A particle is projected with an angle of
projection \( \theta \) to the horizontal line
passing through the points \( (P, Q) \) and
\( Q, P) \) referred to horizontal and vertical
axes (can be treated as x-axis and y-
axis respectively).

The angle of projection can be given by
\( ^{\mathbf{A}} \cdot \tan ^{-1}\left[\frac{P^{2}+P Q+Q^{2}}{P Q}\right] \)
B. \( \tan ^{-1}\left[\frac{P^{2}+Q^{2}-P Q}{P Q}\right] \)
\( ^{\mathbf{c}} \tan ^{-1}\left[\frac{P^{2}+Q^{2}}{2 P Q}\right] \)
D. \( \tan ^{-1}\left[\frac{P^{2}+Q^{2}+P Q}{2 P Q}\right] \)


Kirchhoff's second law is based on the
law of conservation of
A. charge
B. energy
c. momentum
D. sum of mass and energy


One angle of linear pair is a right angle, then find the measure of another angle.


The roots of the equation \( a x^{2}+b x+ \)
\( c=0 \) will be in reciprocal if
\( \mathbf{A} \cdot a=b \)
B . \( a=b c \)
\( \mathbf{c} \cdot c=a \)
D. \( c=b \)


In which of the following parts of the alimentary canal does absorption of nutrients and drugs takes place?
A. Mouth
B. Stomach
c. Small intestine
D. All of the above


A stationary wheel starts rotating about its own axis with an angular acceleration of 5.5 rad \( / s^{2} . \) To acquire an angular velocity 420 revolutions per minute, the number of rotations made
by the wheel is:
A . 14
B . 21
\( c \cdot 28 \)
D. 35


A particle of mass \( m_{1} \) moving with a velocity of \( 5 m / s \) collides head on with a
stationary particle of mass \( m_{2} . \) After collision both the particle move with a
common velocity of \( 4 m / s, \) then the
value \( \boldsymbol{m}_{1} / \boldsymbol{m}_{2} \) is:
A .4:
B. 2:
\( c \cdot 1: 8 \)
D. 1:


Which of the following aromatic compound is least reactive towards
electrophilic substitutions?
\( A \)
в.
\( c \)
D.


When a comb rubbed with dry hair
attracts pieces of paper. This is
because the
A. comb polarizes the piece of paper
B. comb induces a net dipole moment opposite to the direction of field
c. electric field due to the comb is uniform
D. comb induces a net dipole moment perpendicular to the direction of field
E. paper acquires a net charge


When a lead storage battery is discharged:
A. lead sulphate is consumed
B. oxygen gas is evolved
c. lead sulphate is formed
D. lead sulphide is formed


What is sludge? Explain how it is
treated.


If the the hyperbola \( \frac{x^{2}}{4}-\frac{y^{2}}{b^{2}}=1 \)
passses though (4,3)
\( \mathbf{A} \cdot b^{2}=3 \)
B. \( b^{2}=9 \)
\( \mathbf{c} \cdot b^{2}=4 \)
D. \( b^{2}=100 \)


Absolute refractive index of a material
depends upon:
This question has multiple correct options
A. Frequency of incident light
B. Size of material
c. Density and temperature of material
D. wavelength of incident light


Which of the following is an electrica insulator?
A. Rubber
B. Silver
c. Iron
D. Gold


Calculate the numbers of times \( \boldsymbol{f}(|\boldsymbol{x}|) \) \( \operatorname{crosses} \boldsymbol{x}-\boldsymbol{a x i s} \) where \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}-1 \)
\( A \cdot 2 \)
B.
\( c .3 \)
D. None of these


Which of the following reagents is used for the separation of acetaldehyde from acetophenone?
A. \( N H_{2} O H \)
в. \( N a O H I_{2} \)
c. \( _{N a H S O_{3}} \)
D. \( C_{6} H_{5} N H N H_{2} \)


Sir C.V.Raman got Nobel Prize in physics
for the
A. refraction of light
B. reflection of light
c. scattering of light
D. dispersion of light


Integrate the rational function
\( \frac{\boldsymbol{x}}{\left(\boldsymbol{x}^{2}+\mathbf{1}\right)(\boldsymbol{x}-\mathbf{1})} \)


Mention the hybridised state of carbonyl
carbon atom.


The sum of first \( n \) terms of an AP is
given by \( S_{n}=5 n^{2}+3 n, \) then find its
nth term.


Among the following molecules/ions, \( C_{2}^{2-}, N_{2}^{2-}, O_{2}^{2-}, O_{2} \)
which one is diamagnetic and has the shortest bond length?
A \( \cdot C_{2}^{2} \)
B . \( N_{2}^{2} \)
\( c \cdot O_{2} \)
D. \( O_{2}^{2} \)


The polymerisation of propene to linear polypropene is represented by the reaction
where \( n \) ahs large integral value, the average enthalpies of bond dissociation for \( (C==C) \) and \( (C--C) \) at \( 298 k \)
are +590 and \( +331 k J m o l^{-1} \)
respectively. The enthalpy of polymerisation is \( -360 k J m o l^{-1} \). Find
the value of \( n \)
\[
n\left(\begin{array}{l}
\mathrm{CH}_{3} \\
\mathrm{CH}=\mathrm{CH}_{2}
\end{array}\right) \longrightarrow-\left(\begin{array}{l}
\mathrm{CH}_{3} \\
1 \\
\mathrm{CH}--\mathrm{CH}_{2}-
\end{array}\right)_{n}
\]
A \( . n=5 \)
в. \( n=2 \)
\( c \cdot n=7 \)
D. None of these


A vector of length \( l \) is turned through
the angle \( \theta \) about its tail. What is the
change in the position vector of its head-
A. \( l \cos (\theta / 2) \)
B. \( 2 l \sin (\theta / 2) \)
c. \( 2 l \cos (\theta / 2) \)
D. \( l \sin (\theta / 2) \)


If cost price of an article is Rs. 10 and its selling price is Rs. \( 15 /- \) then profit \( \% \) is
A. 5
B. 10
\( c \cdot 20 \)
D. 50


Naman purchased an old bike for Rs.
20000. If the cost of his bike is
depreciated at a rate of \( 5 \% \) per annum, then find the cost of the bike after 2
years?
A. Rs. 18050
B. Rs. 15000
c. Rs. 1900
D. Rs. 18000


Find the distance between (345) plane is a cubic batteries of length \( 7-7 A \)


Two wires of the same material but of
different diameters carry the same current I. If the ratio of their diameters
is \( 2: 1, \) then the corresponding ratio of their mean drift velocities will be
\( A \cdot 4: \)
B. 1: 1
\( c \cdot 1: 2 \)
\( D \cdot 1: 4 \)


Mark the incorrect statement.
A. The building blocks of lipids are amino acids.
B. Majority of enzymes contain a non-protein part called the prosthetic group.
C. The thylakoids are arranged one above the other like a stack of coins forming a granum.
D. Crossing-over occurs at pachytene stage of meiosis I.
E. Steroids are complex compounds commonly found in cell membranes and animal hormones.


If one mole electrons is passed through
the solutions of \( A l C l_{3}, A g N O_{3} \) and
\( M g S O_{4}, \) in what ratio \( A l, A g \) and \( M g \) will be deposited at the electrodes?
A .3: 6: 2
B . 2: 6: 3
\( \mathrm{c} \cdot 1: 2: 3 \)
D. 3: 2: 1


How long would it take a radio-wave of frequency, \( 6 \times 10^{3} \) sec \( ^{-1} \) to travel from
Mars to the Earth, a distance of \( 8 \times \) \( 10^{7} k m \)


A current I ampere flows along an infinitely long straight thin walled hollow metallic cylinder of radius \( r . \) The magnetic field at any point inside the cylinder at a distance \( x \) from the axis of the cylinders is:
A \( \cdot \frac{\mu_{0} I}{4 \pi r} \)
В. \( \frac{\mu_{0} I}{2 \pi r} \)
c. \( \frac{\mu_{0} I}{2 \pi x} \)
D. zero


Which of the following is the correct representation of organisation levels in living beings?
A. Subcellular \( \rightarrow \) Cellular \( \rightarrow \) Individual \( \rightarrow \) Community Population
B. Atomic \( \rightarrow \) Molecular \( \rightarrow \) Subcellular \( \rightarrow \) Cellular \( \rightarrow \) Tissue \( \rightarrow \) Organ system \( \rightarrow \) Individual
c. Individual \( \rightarrow \) Population \( \rightarrow \) organ system \( \rightarrow \) Tissue \( \rightarrow \) Cellular \( \rightarrow \) Molecular \( \rightarrow \) Atomic
D. Atomic \( \rightarrow \) Molecular \( \rightarrow \) Tissue \( \rightarrow \) Individual \( \rightarrow \) Ecosystem \( \rightarrow \) Community


Calculate the dissociation constant of
water at \( 25^{\circ} \mathrm{C} \) from the following data.
Specific conductance of \( \boldsymbol{H}_{2} \boldsymbol{O}=\mathbf{5} . \boldsymbol{8} \times \)
\( 10^{-8} m h o c m^{-1},: \lambda_{H^{+}}^{\infty}=350.0 \) and
\( \lambda_{O H^{-}}^{\infty}=198.0 m h o c m^{2} \)
The ans is \( k \times 10^{-16} \) mole/litre. find \( k \)
A . 1.8
в. 100
\( c . \)
D. 0.01


Cytosis is absent in
A. Diatoms
B. Eubacteria
c. Algae
D. Plantae.


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


Draw an angle and label it as \( \angle B A C \)
Construct another angle, equal to \( \angle B A C \)


\( " C C l_{4} \) is kinetically stable towards
hydrolysis." Answer whether the above statement is
true or false.
If true enter 1 , else 0


Find the surface area of a sphere of radius \( 1.4 \mathrm{cm} .\left(\pi=\frac{22}{7}\right) \)


\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g})=\boldsymbol{2} \boldsymbol{H} \boldsymbol{C l}(\boldsymbol{g}) \)
\( \Delta H(298 K)=-22.06 \mathrm{kcal} . \) For this
reaction, \( \Delta U \) is equal to:
A \( .-22.06+2 \times 10^{-3} \times 298 \times 2 \mathrm{kcal} \)
В. \( -22.06+2 \times 298 \) kcal
c. \( -22.06-2 \times 298 \times 4 \) kcal
D. -22.06 kcal


Select the renewable and non-renewable
sources of energy from the following:
(a) Coal
(b) Wood
(c) Water
(d) Diesel
(e) Wind
(f) Oil
A. Renewable-(a), (d) and (f) and Non-renewable-(b), (c) and (e)
B. Renewable-(b),(c) and
(e) and Non-renewable-(a), (d) and (f)
c. Renewable-(a),
(c) and (e) and Non-renewable-(b), (d) and (f)
D. Renewable-(b),(d) and (e) and Non-renewable-(a), (c) and (f)


A point charge \( q \) is at centre of an
unchanged spherical conducting shell
of inner radius \( a \) and outer radius \( b \)
Work needed to move the charge out to
infinity will be
\( ^{\mathbf{A}} \cdot \frac{q^{2}}{4 \pi \varepsilon_{0}}\left(\frac{1}{a}-\frac{1}{b}\right) \)
B. \( \frac{1}{8 \pi \epsilon_{0}} \frac{q^{2}}{a} \)
\( ^{\mathbf{c}} \cdot \frac{q^{2}}{8 \pi \epsilon_{0}}\left[\frac{1}{b}-\frac{1}{a}\right] \)
\( ^{\mathrm{D}} \cdot \frac{q^{2}}{8 \pi \epsilon_{0}}\left[\frac{1}{a}-\frac{1}{b}\right] \)


Botanical name of peat moss is
A. Sphagnum
B. Funaria
c. Anthoceros
D. Polytrichum


Find the number of ways in which 5 boys and 5 girls be seated in a row so that no two girls may sit together.


Two wires are made of the same
material and have the same volume.
However wire 1 has cross-sectional area
\( A \) and wire 2 has cross- sectional area
3 A. If the length of wire 1 increases by \( \Delta x \) on applying force \( F, \) how much force is needed to stretch wire 2 by the same
amount ?
A.
B. 4 F
\( c .6 \mathrm{F} \)
D. 9 F


Consider the following reactions:
\( C(s)+O_{2}(g) \rightarrow C O_{2}(g)+x k J \)
\( C O(g)+\frac{1}{2} O_{2}(g) \rightarrow C O_{2}(g)+y k J \)
The heat of formation of \( \mathrm{CO}(\mathrm{g}) \) is :
\( A \cdot-(x+y) k J / m o l \)
B. \( (x-y) \) kJ/mol
c. \( (y-x) \) k) \( \int m o \)
D. None of these


If a function satisfies \( (\boldsymbol{x}-\boldsymbol{y}) \boldsymbol{f}(\boldsymbol{x}+ \)
\( \boldsymbol{y})-(\boldsymbol{x}+\boldsymbol{y}) \boldsymbol{f}(\boldsymbol{x}-\boldsymbol{y})=\boldsymbol{2}\left(\boldsymbol{x}^{2} \boldsymbol{y}-\right. \)
\( \left.\boldsymbol{y}^{3}\right), \forall \boldsymbol{x}, \boldsymbol{y} \in \boldsymbol{R} \) and \( \boldsymbol{f}(1)=2, \) then
This question has multiple correct options
A. \( f(x) \) must be polynomial function
В. \( f(3)=12 \)
c. \( f(0)=0 \)
D. \( f(x) \) may not be differentiable


Q Type your question
blood. Study the same and answer the
following questions
(i) Name the blood vessels labelled 1
and 2
(ii) State the function of blood vessels
labelled 5 and 8
(iii) What is the importance of the blood
vessel labelled 6?
(iv) Which blood vessel will contain a
high amount of glucose after a meal?
(v) Draw a diagram of the different
blood cells as seen in an amino acids
smear of human blood.


Can not be broken down chemically.
A. Anions
B. Cations
c. Element
D. Isotope
E. Atom


Q Type your question
on point \( P \) as shown in the diagram
below. All point charges are of the same
magnitude.

Which table gives the best description
of the electric field at point \( P \) and the
electric potential at point P?
A . Electric Field at \( \mathrm{P} \) - Electric Potential at \( \mathrm{P} \), Zero - Zero
B. Electric Field at \( P \) - Electric Potential at \( P \), downward -
downward
C. Electric Field at \( P \) - Electric Potential at P, upward positive
D. Electric Field at \( P \) - Electric Potential at \( P \), downward
Zero
\( \mathrm{E} \), ic Field at \( \mathrm{P} \) - Electric Potential at \( \mathrm{P} \), upward -


Find \( : \lim _{x \rightarrow a} \sqrt{x} \)


Who is regarded chief of solar system?
A. Sun
B. Moon
c. Earth
D. sky


If a point \( P \) in the space such that \( \overline{O P} \)
is inclined to \( O X \) at 45 and \( O Z \) to 60
then \( \overline{O P} \) inclined to \( O Y \) is
A \( .75^{\circ} \)
B . \( 75^{\circ} \) or \( 105^{\circ} \)
C. \( 60^{\circ} \) or \( 120^{\circ} \)
D. None of these


Solar water-heater works on renewable
energy system. Is it true or false?


The standard molar heat of formation
of ethane, \( C O_{2} \) and water are
respectively -21.1,-94.1 and -68.3 kcal. The standard molar heat of
combustion of ethane will be :
\( \mathbf{A} \cdot-372 \) kcal
B . 162 kcal
c. -240 kcal
D. 183.5 kcal


A particle moves according to the equation \( t=\sqrt{x}+3 . \) When the particle
comes to rest for the first time?
A . \( 3 s \)
в. 2.5 \( s \)
\( \mathrm{c} .3 .5 \mathrm{s} \)
D. None of these


With the help of a diagram, show how you can use several NAND gates to
obtain an OR gate.


An object is placed at a distance of \( 12 \mathrm{cm} \) in front of a concave mirror, it forms a
real and inverted image. Where is the
image formed if image height is double the object?


The half-life of that radioactive
substance, which reduces to \( 1 / 64 \) of its initial value in 15 hours, will be
A. 5 hours
B. 2 hours
c. 2.5 hours
D. 4 hours


Which of these will produce the highest yield in Friedel Crafts reaction?
\( A \)
в.
c.
D.


Evaluate the following integral:
\( \int \frac{1}{2 x^{2}-x-1} d x \)


\( V^{3+} \) is coloured
If the given statement is true enter 1
else enter 0


\( \lim _{x \rightarrow 0} \frac{\sin \left(\pi \cos ^{2} \pi\right)}{x^{2}} \) is equal to
\( ^{A} \cdot \frac{\pi}{2} \)
B.
\( c .-\pi \)
\( D \)


This graph is for
A. Ohmic conductor
B. Non-ohmic conductor
C . Electrolytes
D. Diodes


Let \( l_{1} \) and \( l_{2} \) be the moment of inertia of
a uniform square plate about axes APC
and OPO' respectively as shown in the figure. \( P \) is centre of square. The ratio \( \frac{I_{1}}{I_{2}} \) of moment of inertia is :
A \( \cdot \frac{1}{\sqrt{2}} \)
B. 2
\( c \cdot \frac{1}{2} \)
D.


What is the mangitude of a point
charge chosen so that electric field 50 \( \mathrm{cm} \) away has magnitude \( 2.0 \mathrm{N} / \mathrm{C} \) ?


Quick lime is:
A. \( C a\left(H C O_{3}\right)_{2} \)
в. \( C a C O_{3} \)
\( \mathbf{c} \cdot \operatorname{Ca}(O H)_{2} \)
D. \( C a O \)


If the flux of the electric field through a closed surface is zero,
This question has multiple correct options
A. the electric field must be zero everywhere on the surface
B. the electric field may be zero everywhere on the surface
c. the charge inside the surface must be zero
D. the charge in the vicinity of the surface must be zerç


The number of angular and radial nodes
of \( 4 d \) orbital respectively are:
A .3,1
B. 1,2
\( c .3,0 \)
D. 2,


Which of the following bonds has the highest energy?
A. Se-Se
в. Te-Te
c. s-s
D. 0-0


A conic \( C \) satisfies the differential
equation \( \left(1+y^{2}\right) d x-x y d y=0 \) and
passes through the point (1,0) An ellipse \( \boldsymbol{E} \) which is confocal with \( \boldsymbol{C} \) having its eccentricity equal to \( \sqrt{2 / 3} \)
(a) Find the length of the latus rectum
of the conic \( C \)
(b) Find the equation of the ellipse \( \boldsymbol{E} \)
(c) Find the locus of the point of intersection of the perpendicular
tangents to the ellipse \( \boldsymbol{E} \)


The standard absolute entropy of a substance, \( \left(S^{\ominus}\right) \) is the entropy of the substance in its standard state at 1
atm, temperature being (in K)


The solution of \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{\boldsymbol{y}}{\boldsymbol{x}}+\sin \left(\frac{\boldsymbol{y}}{\boldsymbol{x}}\right) \) is


Various processes involved on the
extraction of metals from their ores and
refining are known as:
A. concentration of ore
B. enrichment of ore
c. refining of ore
D. metallurgy


In autogenic succession
A. Early and continued dominance of autotrophic organism takes place like green plants.
B. Replacement of existing communities cause largely by any other extremal condition.
C. Early dominance of heterotrophs takes place such as bacteria, fungi and other animals
D. Community itself modifies its own environment thus, causing its own replacement by new communities.
E. Starts with previously built up substrata with already existing matter.


Sodium salt \( (A) \) of a dibasic acid \( \stackrel{H C l}{ } \)
gas\( (B) \) and clear solution

Gas \( (B) \) turns lime water milky. Identify
\( (A) \)
A. Sodium carbonate
B. Sodium sulphate
c. Sodium oxalate
D. Sodium nitride


When 3 -hydropropanal is treated q with methylmagnesium iodide in equimolar amounts, the most probable product
will be:
\( A \)
B.
\( c \)
D. There will be no net reaction


The time, in which a force of \( 2 \mathrm{N} \)
produces a change as momentum of 0.4
kg \( m s^{-1} \) in the body is :
A. \( 0.2 s \)
B. 0.02s
c. \( 0.5 \mathrm{s} \)
D. 0.05s


Illustrate a condition in which :
Electric field is zero but potential is not
zero.


Find \( \boldsymbol{x} \)
\( \frac{5 x}{2}+\frac{3 x}{4} \geq \frac{39}{4} \)


The solution of \( (2 \cos x-1)(3+ \)
\( 2 \cos x)=0 \) in the interval \( 0 \leq \theta \leq 2 \pi \)
is
\( \mathbf{A} \cdot(\pi / 3) \)
В. \( (\pi / 3,5 \pi / 3) \)
c. \( [\pi / 3,5 \pi / 3] \)
D. none of these


Power of a lens can't be measured in
A. \( m \)
B. \( W \)
c. Horse power
D. None of these


A woman can give birth to how many
children in her lifetime?


How many statements are wrong about
asthma?
(i) The respiratory surface is decreased.
(ii) The only cause of it is cigarette
smoking.
(iii) Due to inflammation of bronchi and
bronchioles.
(iv) Alveolar walls are damaged altogether
(v) Difficulty in breathing causes wheezing.
A. one
B. Two
c. Three
D. Five


Which one of the following elements constitutes a major impurity in pig iron?
A. Silicon
B. Oxygen
c. sulphur
D. Graphite


The value of \( Z_{c} \) at \( T_{c}, P_{c} \) and \( V_{c} \) is \( \frac{3}{x} \)
Value of \( x \) is


The value of \( \sum_{r=1}^{n} r\left(^{n} C_{r}+^{r} P_{r}\right) \) is
A \( \cdot n \cdot 2^{n-1}-1 \)
B . \( n \cdot 2^{n-1}+(n+1) ! \)
C \( \cdot n \cdot 2^{n-1}+(n+1) !-1 \)
D. \( n^{2}+n+5 \)


In a series of \( 2 n \) observations, half of
them equal \( a \) and remaining half equal
\( -a . \) If the \( S . D . \) of the observations is 2
then \( |a| \) equals
A \( \cdot \frac{1}{n} \)
B. \( \sqrt{2} \)
\( c \cdot 2 \)
D. \( \frac{\sqrt{2}}{n} \)


Prenatal growth in higher vertebrate is
A. Auxetic
B. Accretionary
c. Multipilicative
D. None of the above


Evaluate the following question.
\( \lim _{x \rightarrow 2} 2 x+5 \)


A particle is moving in a straight line with maximum slope and at some moment it occupied the position
-1,-2)\( . \) Then the position of the particle when it is on \( x \) -axis is


Two identical plano-convex lenses can be combined in three ways, as shown The ratio of the focal lengths of these
combinations will be
(i)
(ii)
(iii)
A .2: 2: 1
B. 1: 1: 1
\( c \cdot 1: 2: 2 \)
D. 2: 1: 1


A secant intersects the circle at
points.
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
\( D \)


In the fig, \( \square P Q R S \) and \( \square A B C R \) are
two parallelograms.
f \( \angle P=110^{\circ} \) then find the measures of
all angles of \( \square A B C R \)


Assertion
The unshared pairs residing in pure
\( \sigma-o r-\pi \) -orbital do not contribute in
dipole moment.
Reason
The \( \sigma \) -orbital is spherically symetrical, hence it contributes nothing. Similarly,
the two lobes of a pure \( \pi \) -orbital are
projected in opposite directions to
cause no effect.
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 solid sphere of mass \( \mathrm{m} \) and radius \( \boldsymbol{R} \)
is rolling without slipping as shown in figure. Find angular momentum of the sphere about z-axis.


Which is not stable?
\( \mathbf{A} \cdot K H F_{2} \)
в. \( K l_{3} \)
c. \( C H_{3}-C H(O H)_{2} \)
D. \( C l_{3} C-C H(O H)_{2} \)


In which of the following aestivation of sepals \( \& \) petals one margin covers the other \( \& \) its margin is covered by previous one
A. valvate
B. Twisted
c. Imbricate
D. Quincuncial


experimentally proved the existence of protons in the
atom.
A. Goldstein
B. J.J.Thompson
c. chadwick
D. None of thea above


When a body of mass \( m_{1} \) moving with uniform velocity \( 40 m s^{-1} \) collides with
another body of mass \( m_{2} \) at rest, then the two together begin to move with
uniform velocity of \( 30 m s^{-1} . \) The ratio of the mass (i.e., \( \frac{m_{1}}{m_{2}} \) ) of the two bodies will be
A .1: 3
в. 3: 1
c. 1: 1.33
D. 1: 0.75


Solve \( :-5(x+4)>30 ; x \in Z \)


toppr
Q Type your question
configuration is :
\( A \)
B.
\( c \)
\( D \)


How many grams of copper will be
deposited from a solution of \( C u S O_{4} \)
bypassing 0.5 faradays of electricity? [Atomic weight of \( \boldsymbol{C u}=\mathbf{6 3 . 5} \text { g/mole }] \)
A. \( 31.75 \mathrm{g} \)
B. 63.6 g
c. \( 15.875 \mathrm{g} \)
D. 127 g


A posıtively chargea partıcle or cnarge
\( q^{\prime} \) enters in a uniform magnetic field 'B
directed inward and is deflected a
distance \( \boldsymbol{y}_{0} \) after traveling a distance
shown in the figure. Then
the pe
use coos FathER30DAY
\( A \)
UPGRADE NOWI
B.
\( c \)
D.
\( E \)


How many of the following oxides are basic oxides?
\( \boldsymbol{C O}_{2}, \boldsymbol{S n O}_{2}, \boldsymbol{P b O}, \boldsymbol{P b O}_{2}, \boldsymbol{P b}_{3} \boldsymbol{O}_{4}, \boldsymbol{A l}_{2} \boldsymbol{O}_{3} \)


Anti - markonikoff's addition of HBr is
not observed in:
A. Propene
B. But-1- ene
c. 2-butene
D. 2-pentene


Heat lost by the gas in the process \( B \rightarrow \)
\( C \) is
\begin{tabular}{l}
\( 4.5312 .5 . \) \\
\hline
\end{tabular}
3. 1875 J
\( c \)
D. \( 8854 J \)


If an excess of \( A g N O_{3} \) solution is added to \( 100 \mathrm{ml} \) of \( 0.024 \mathrm{M} \) solution of dichlorobis (ethylene diamine) cobalt
(III) chloride, how many moles of \( A g C l \) will be precipitated?
A . 0.0012
B. 0.0016
c. 0.0024
D. 0.0048


The change in reflected wave, when light wave suffers reflection at the interface
from air to glass is?
A . 0
в. \( \frac{\pi}{2} \)
\( c . \pi \)
D . \( 2 \pi \)


The coefficient of self induction of two
inductor coils are \( 20 m H \) and \( 40 m H \)
respectively. If the coils are connected
in series so as to support each other and the resultant inductance is \( 80 m H \)
then the value of mutual inductance
between the coils will be
\( \mathbf{A} \cdot 5 m H \)
в. \( 10 m H \)
c. \( 20 m H \)
D. \( 40 m H \)


Water waves are both longitudinal and
transverse. State whether true or false
A. True
B. False


If \( \int_{a}^{b} f(t) g o h(t)= \)
\( \int_{a}^{b} f o h(t) g(t) d(t), \) where \( f, g, h, \) are
non negative continuous functions on
\( [a, b] \) then possible choice of \( h(t) \) is
This question has multiple correct options
\( \mathbf{A} \cdot t \)
B. \( a-b-t \)
c. \( a+b-t \)
D. \( b-t \)


Assertion
(A) : In a metrebridge ; Copper wire is connected in the left gap and
silicon is connected in the right gap. When the temperature of both wires increase, balancing point shifts to right. Reason
(R) :Temperature coeficient of copper is (-)Ve and that of silicon is \( (+) \)
Ve.
A. Both A \& R are true and R is the correct explanation of \( A \)
B. Both A \& R are true and R is not a correct explanation of
c. A is true but R is false
D. A is false but R is true


An organic compound \( (B) \) is formed by the reaction of ethylmagnesium iodide
\( \left(\boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{M} \boldsymbol{g} \boldsymbol{I}\right) \) with a substance \( (\boldsymbol{A}) \)
follow by treatment with dilute aqueous
acid. Compound \( (B) \) dose not react with
\( P C C \) in dichloromethane. Identify \( (A) ? \)
A. 0
\( C H_{3}-C-H \)
B. \( \quad o \)
I
\[
C H_{3} C H_{2} C C H_{3}
\]
\( \mathbf{c} \cdot H_{2} C=O \)
D.


The basis on the mode of their
formation, the polymers can be classified:
A. As addition polymers only
B. As condensation polymers only
c. As copolymers
D. Both as addition and condensation polymers


Three man \( A, B, C \) of mass \( 40 \mathrm{kg}, 50 \mathrm{kg} \)
\( \& 60 \mathrm{kg} \) are standing on a plank of mass \( 90 \mathrm{kg}, \) which is kept on a smooth
horizontal plane. If \( A \& C \) exchange their
positions then mass B will shift
\( \mathbf{A} \cdot 1 / 3 \mathrm{m} \) towards left
B. 1/3 m towards right
c. will not move w.r.t. ground
D. \( 5 / 3 \) m toward left


Prove for \( \boldsymbol{n} \in \mathbb{N} \)
\( \mathbf{1} . \mathbf{3}+\mathbf{2} . \mathbf{3}^{2}+\mathbf{3} . \mathbf{3}^{3}+\ldots+\boldsymbol{n} . \mathbf{3}^{n}= \)
\( \frac{(2 n-1) 3^{n+1}+3}{4} \)


Catalysts lower the activation energy of a reaction:
A. Providing a surface and orientation
B. Providing an alternative mechanism with a lower activation energy
c. Increasing temperature
D. Both a and


The thermo-emf of a copper-constant
couple is \( 40 \mu V \) per degree. The smallest temperature difference that can be detected with this couple and
galvanometer of \( 100 \Omega \) resistance capable of measuring the minimum
current of \( 1 \mu A \) is
A \( \cdot 2.5^{\circ} \mathrm{C} \)
B. \( 2^{\circ} C \)
\( \mathbf{c} \cdot 1.5^{\circ} \mathrm{C} \)
D. \( 1^{\circ} \mathrm{C} \)


Two plane mirrors are set at right angles and a flower is placed in any position in between the mirrors. The number of images of the flower which will be seen is
A. one
B. Two
c. Three
D. Four


f the collision is elastic find verticle
component of velocity of block at B.just
after collision.
A \( \cdot \sqrt{45} \)
B. \( \sqrt{15} \)
\( c \cdot-\sqrt{15} \)
D. 20


Graph showing the variation of current
versus voltage for a material GaAs is
shown in the figure. Identify the region
of
(i) Negative resistance
(ii) Where Ohm's law is obeyed.


If \( \cos ^{2} x+\cos ^{2} 2 x+\cos ^{2} 3 x=1 \) then
A \( \cdot x=(2 n+1) \frac{\pi}{4}, n \epsilon I \)
B. \( x=(4 n+1) \frac{\pi}{4}, n \in I \)
c. \( x=n \pi \frac{\pi}{4}, n \epsilon I \)
D. none of these


If the valence shell electronic
configuration for an element is \( n s^{2} n p^{5} \) this element belongs to the group of
A. alkali metals
B. inert metals
c. noble gases
D. halogens


A boy is running around a rectangular
park, whose sides are in the ratio of 4
\( 3, \) at the rate of 10 metre per second
and completes a round in 42 seconds. Calculate the area of the park.


The correct sequence of decreasing acidity is:
\( \mathbf{A} \cdot\left(C H_{3}\right)_{3} C O H>\left(C H_{3}\right)_{2} C H O H>C_{2} H_{5} O H> \)
\( C H_{3} O H \)
B \( \cdot C H_{3} O H>C_{2} H_{5} O H>\left(C H_{3}\right)_{2} C H O H> \)
\( \left(C H_{3}\right)_{3} C O H \)
\( \mathbf{c} \cdot C_{2} H_{5} O H>C H_{3} O H>\left(C H_{3}\right)_{3} C O H> \)
\( \left(C H_{3}\right)_{2} C H O H \)
\( \mathbf{D} \cdot\left(C H_{3}\right)_{2} C H O H>\left(C H_{3}\right)_{3} C O H>C_{2} H_{5} O H> \)
\( C H_{3} O H \)


In the Lassaigne's test, the nitrogen
present in the organic compound is converted into


The nearest star to the earth
is
A. Moon
B. Proxima centauri
c. sirius
D. sun


A plane mirror is placed at the origin so that the direction ratios of its normal
\( \operatorname{are}(1,-1,1) . \) A ray of light, coming along the positive direction of the \( x \) axis, strikes the mirror. The direction \( \operatorname{cosines} \) of the reflected ray are
A \( \cdot \frac{1}{3}, \frac{2}{3}, \frac{2}{3} \)
B. \( -\frac{1}{3}, \frac{2}{3}, \frac{2}{3} \)
c. \( -\frac{1}{3},-\frac{2}{3},-\frac{2}{3} \)
D. \( -\frac{1}{3},-\frac{2}{3}, \frac{2}{3} \)


The given truth table is for
\( \begin{array}{lll}\text { Input } & \text { Input } & \text { Output } \\ \mathrm{A} & \mathrm{B} & \mathrm{Y} \\ 0 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0\end{array} \)
A. AND gate
B. OR gate
C. NAND gate
D. NOR gate


Nitrogen is a poisonous gas because animals die in their presence why?


The number of de Broglie waves of an
electron in the \( n^{t h} \) orbit of an atom is :
A . \( n \)
B. \( n-1 \)
\( c \cdot n+1 \)
D. \( 2 n \)


Write short notes.
Chipko movement of Bishnoi


A stone is thrown vertically upward with a speed of \( 28 m / s \) Find the maximum height reacted by
the stone.


Spectroscopy useful for gas analysis is
A. Absorption spectroscopy
B. Infra-red spectroscopy
c. Emission spectroscopy
D. Nuclear magnetic resonance spectroscopy


Which of the following statements is
not true about fertilization in a fern
plant?
A. An egg is produced in an archegonium
B. A sperm is produced in an antheridium
c. sperm is carried by the wind to the egg
D. Eggs and sperm are produced on the same plan


Common link between apes and man
was
A. Ramapithecus
B. Dryopithecus
c. Homo erectus
D. Homo neanderthalensis


Depo-provera refers to
A. Injectible contraceptive
B. Intra uterine device
C . Implant
D. Oral contraceptive


Select the correct option regarding \( \mathbf{A}^{\prime} \) or
'B' given in the flow charts
\begin{tabular}{|l|l|l|l|l|}
\hline \( \mathrm{A} \) & \( \mathrm{B} \) & \multirow{2}{*} { Organs } & \multirow{2}{*} { Organ Systems } & \multirow{2}{*} { Organism } \\
\cline { 3 - 4 } & & & & \\
\hline
\end{tabular}
A. 'A' is cell and 'B' is tissue
B. 'A' is unicellular organism
C . 'A' is tissue
D. 'B' is cell


Mark the correct order of decreasing
acid strength of the following
compounds.
\( (b) \)
\( (c) \)
\( (d) \)
\( \mathrm{e} \)
\( A \cdot e>d>b>a>c \)
\( B \cdot b>d>a>c>e \)
\( c \cdot d>e>c>b>a \)
\( D \cdot e>d>c>b>a \)


Find the distance between the lines
\( \mathbf{3} \boldsymbol{x}+\mathbf{4} \boldsymbol{y}=\mathbf{9} \) and \( \boldsymbol{6} \boldsymbol{x}+\mathbf{8} \boldsymbol{y}=\mathbf{1 5} \)


Which of the following causes indigestion?
A. Ulcer
B. Thyroidism
c. Pancreatitis
D. All of the above


The temperature (T) of one mole of an ideal gas varies with its volume (V) as \( \boldsymbol{T}=-\boldsymbol{\alpha} \boldsymbol{V}^{3}+\beta \boldsymbol{V}^{2}, \) where \( \boldsymbol{\alpha} \) and \( \boldsymbol{\beta} \) are
positive constants. The maximum pressure of gas during this process is
A \( \cdot \frac{\alpha \beta}{2 R} \)
B. \( \frac{\beta^{2} R}{4 \alpha} \)
c. \( \frac{(\alpha+\beta) R}{2 \beta^{2}} \)
D. \( \frac{\alpha^{2} R}{2 \beta} \)


The value of \( \cos ^{-1}\left(\cos \left(\frac{4 \pi}{3}\right)\right) \) is
A \( \cdot 2 \pi / 3 \)
в. \( -2 \pi / 3 \)
c. \( 4 \pi / 3 \)
D. \( -4 \pi / 3 \)


The solution of \( \frac{d y}{d x}+y \tan x=\cos ^{2} x \) is:
A \( \cdot y \sec ^{2} x=c+\sin x \)
B. \( y \sec x=c+\cos x \)
c. \( y \sec ^{2} x=c+\cos x \)
D. \( y \sec x=c+\sin x \)


Which structure is cut and tied off in a
vasectomy?
A. Penis
B. Epididymis
c. Urethra
D. Vas deferens


Examine the continuity of the following function at the point \( \boldsymbol{x}=-\frac{1}{2} \) \( f(x)=\left\{\begin{array}{ll}\frac{4 x^{2}-1}{2 x+1} & x \neq-\frac{1}{2} \\ -2, & x=-\frac{1}{2}\end{array}\right. \)


Find the A.P in which the sum of any
number of terms is always equal to
three times the square of number of
terms.


Solve :-
\[
\sin 45^{\circ}+\cos 45^{\circ}
\]


If the focal length of a spherical mirror is
\( 50 \mathrm{cm}, \) then its radius of curvature is
\( \mathrm{cm} \)
A . 100
B. 50
\( c \cdot 25 \)
D. 75


Write the dispersed phase and dispersion medium of the following collodial system?
(i) Smoke
(ii) Milk


Assertion
Ernst Haeckal developed binomial system of nomenclature
Reason
Vernacular names are chosen for
nomenclature.
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


Two spherical bodies of mass \( \mathrm{M} \) and \( 5 \mathrm{M} \) and radii R and \( 2 \mathrm{R} \) respectively are released in free space with initial
separation between their centres equal to 12R. If they attract each other due to gravitational force only. then the
distance covered by the smaller body just before collision is
A . 1.5 R
в. 2.5
c. 4.5 R
D. 7.5R


If the \( \% \) composition of a 'x' component is \( 35 \%, \) find the mass of the dried 'x'
component in 100 g? mixture \( + \) beaker \( = \) \( 50 \mathrm{g}, \) mass of beaker \( =23 \mathrm{g} \)
A. \( 15.5 \mathrm{g} \)
B. \( 9.45 \mathrm{g} \)
c. \( 35.5 \mathrm{g} \)
D. \( 13.4 \mathrm{g} \)


The sum of the series \( \frac{1}{2 !}-\frac{1}{3 !}+\frac{1}{4 !} \ldots \ldots . \)
upto infinity is-
A \( \cdot e^{-2} \)
B \( \cdot e^{-1} \)
\( c \cdot e^{-\frac{1}{2}} \)
D. \( e^{+\frac{1}{2}} \)


The weak zone around the boundaries of
plates underneath the Earth, which is prone to slide and cause an earthquake is commonly known as:
A. Fault zone
B. Eruption zone
c. Explosive zone
D. Sliding zone


In a parallelogram, \( \angle A: \angle B=1: 2 \)
then \( \angle A \) is
A . 45
B. 60
\( c \cdot 30^{\circ} \)
D. \( 90^{\circ} \)


When light falls on semiconductors, their resistance:
A. Decreases
B. Increases
c. Initially decreases and then increasess
D. Initially increases and then decreases


Gases are good conductors of electricity
This question has multiple correct options
A . low pressure
B. high pressure
c. low temperature
D. high temperature


The heat capacity of liquid water is \( \mathbf{7 5 . 6 J} / \boldsymbol{K}-\boldsymbol{m o l}, \) while the enthalpy of
fusion of ice is \( 6.0 k J / \) mol. What is the
smallest number of ice cubes at \( 0^{\circ} C \)
each containing \( 9.0 g \) of water, needed
to cool \( 500 g \) of liquid water from \( 20^{\circ} \mathrm{C} \)
to \( 0^{\circ} C ? \)
A . 1
B. 7
c. 14
D. 21


Trait that masks the other trait is called
as
A. Dominant
B. Recessive
c. Mutant
D. None of the above


Select the correct pair in which one photosynthesizes, whereas the other does not.
A. Cyanobacteria and algae
B. Algae and fungi
c. Mosses and ferns
D. Ferns and gymnosperms
E. Gymnosperms and angiosperms


Why are coils of electric toasters and
electric irons made of an alloy rather
that an pure metal?


Give the range of wavelength of the electromagnetic waves visible to us.
A . \( 1000 A^{\circ} \) to \( 4000 A^{\circ} \)
B . \( 4000 A^{\circ} \) to \( 8000 A^{\circ} \)
c. \( 8000 A^{\circ} \) to \( 9000 A^{\circ} \)
D. \( 400 A^{\circ} \) to \( 800 A^{\circ} \)


Which of the following is (are) unsaturated compounds?

This question has multiple correct options
A. Benzene
B. Hexane
c. cyclohexene
D. Propene


As speed decreases, if we change medium of electromagnetic waves from air to water, frequency
A . also decreases
B. also increases.
c. remains same.
D. may increase or decrease


Which of the following is the strongest
acid?
A. \( C H_{3} \) СООН
в. \( C H_{2} \) СlСООН
c. \( C H C l_{2} C O O H \)
D. \( C C l_{3} \) СООН


The change in internal energy of the
methanol is
A \( \cdot 9.6 \times 10^{5} J \)
B . \( 7.14 \times 10^{5} \mathrm{J} \)
c. \( 6.89 \times 10^{4} J \)
D. \( 6.86 \times 10^{5} J \)


Assertion
Net charge given to a conductor resides on its outer surface under electrostatic
conditions.
Reason
Electric field lines do not enter a
conductor under electrostatic
conditions.
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


n the given figure, which of the
following is a line of symmetry?
A. Line A
B. Line B
c. Line
D. Non


Out of the following whose specific heat is maximum?
A . lead
B. brass
c. glass
D. iron


In the diagram, section A represents:
\( C \)
\( D \)
A. N-type germanium
B. P-type germanium
C. Anode
D. Diode


The rate law for the reaction below is
given by the expression \( \boldsymbol{k}[\boldsymbol{A}][\boldsymbol{B}] \)
\( A+B \rightarrow \) Product
If the concentration of \( B \) is increased
from 0.1 to 0.3 mole, keeping the value
of \( A \) at 0.1 mole, the rate constant will
be:
\( \mathbf{A} \cdot 3 k \)
B. \( 9 k \)
c. \( k / 3 \)
D.


If the concentration of \( O H^{-} \) ions in the
reaction \( \boldsymbol{F e}(\boldsymbol{O H})_{3}(\boldsymbol{s}) \rightleftharpoons \boldsymbol{F} \boldsymbol{e}^{+3}(\boldsymbol{a q} \cdot)+ \)
\( 3 O H^{-}(a q .) \) is decreased upto \( \frac{1}{4} \) times
then equilibrium concentration of \( \boldsymbol{F} \boldsymbol{e}^{+} \) will increase upto:
A. 16 times
B. 64 times
c. 4 times
D. 8 times


The figure shows the \( P \) - \( V \) plot of an ideal gas taken through a cycle ABCDA. The part \( A B C \) is a semi-circle and CDA is
half of an ellipse. Then
This question has multiple correct options
A. the process during the path \( A \rightarrow B \) is isotherma
B. heat flows out of the gas during the path \( B \rightarrow C \rightarrow D \)
c. work done during the path \( A \rightarrow B \rightarrow C \) is zero
D. positive work is done by the gas in the cycle ABCDA


An object of height \( 10 \mathrm{cm} \) is placed at a distance of \( 100 \mathrm{cm} \) before the convex
mirror perpendicular below the
principal axis. If the focal length of the mirror is \( 10 \mathrm{cm}, \) on applying the Cartesian sign convention, find the object distance
A . -100cm
B. \( +100 \mathrm{cm} \)
c. \( 50 \mathrm{cm} \)
D. -50 cm


What is the smallest natural number
that should be multiplied with 840 to
make it a perfect square?


If \( \alpha \) and \( \beta \) are different complex
numbers with
\( |\beta|=1 \) then \( \left|\frac{\beta-\alpha}{1-\bar{\alpha} \beta}\right| \) is equal to
A .
B. \( \frac{1}{2} \)
\( c \cdot 1 \)
D.


For the reaction \( \boldsymbol{A}+\mathbf{2} \boldsymbol{B} \rightleftharpoons \mathbf{2} \boldsymbol{C} \) at
equilibrium \( [\boldsymbol{C}]=\mathbf{1 . 4} \boldsymbol{M} \cdot[\boldsymbol{A}]_{o}= \)
\( \mathbf{1} \boldsymbol{M},[\boldsymbol{B}]_{o}=\mathbf{2} \boldsymbol{M},[\boldsymbol{C}]_{o}=\mathbf{3} M . \) The value
of \( K_{c} \) is:
(Given: volume =1 litre, [ ] \( _{o} \) is initial concentration)
A .0 .084
B. 8.4
\( c \cdot 48 \)
D. None of these.


If \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{1} & \mathbf{0} \\ -\mathbf{1} & \mathbf{7}\end{array}\right] \) and \( \boldsymbol{A}^{2}=\mathbf{8} \boldsymbol{A}+\boldsymbol{K} \boldsymbol{I}_{2} \)
then \( K \) is equal to
A . -1
B.
\( c .-7 \)
D. 7


Distinguish between Primary, Secondary and Teritary amines.


A spherical uniform planet is rotating about its axis. The velocity of a point on its equator is \( V \). Due to the rotation of
planet about its axis the acceleration due to gravity \( g \) at equator is \( \frac{1}{2} \) of \( g \) at
poles. The escape velocity of a particle on the pole of planet in terms of \( V \)
A. \( V_{e}=2 V \)
B . \( V_{e}=V \)
\( \mathbf{c} \cdot V_{e}=V / 2 \)
D. \( V_{e}=\sqrt{2} V \)


How many non-negative integral values of \( x \) satisfy the equation \( \left[\frac{x}{5}\right]=\left[\frac{x}{7}\right] ? \)
(Here \( [x] \) denotes the greatest integer
less than or equal to \( x \). For example \( [3.4]=3 \) and \( [-2.3=-3) \)


\( f A=\left[\begin{array}{lll}1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1\end{array}\right], \) prove that
\( \boldsymbol{A}^{n}=\left[\begin{array}{ccc}\mathbf{3}^{n-1} & \mathbf{3}^{n-1} & \mathbf{3}^{n-1} \\ \mathbf{3}^{n-1} & \mathbf{3}^{n-1} & \mathbf{3}^{n-1} \\ \mathbf{3}^{n-\mathbf{1}} & \mathbf{3}^{n-\mathbf{1}} & \mathbf{3}^{n-1}\end{array}\right], \boldsymbol{n} \in N \)


Be, \( M g, C a, S r, B a \) are group 2 metals. Which of these will form ions
most readily?
A. \( B e \)
в. \( M g \)
\( c \cdot S r \)
D. \( B a \)


Explain the process of formation of complex protein?


Show that \( \left|\begin{array}{ccc}\boldsymbol{b}+\boldsymbol{c} & \boldsymbol{c}+\boldsymbol{a} & \boldsymbol{a}+\boldsymbol{b} \\ \boldsymbol{a}+\boldsymbol{b} & \boldsymbol{b}+\boldsymbol{c} & \boldsymbol{c}+\boldsymbol{a} \\ \boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c}\end{array}\right|= \)
\( \boldsymbol{a}^{3}+\boldsymbol{b}^{3}+\boldsymbol{c}^{3}-\boldsymbol{3} \boldsymbol{a} \boldsymbol{b} \boldsymbol{c} \)


Find the smallest number by which 128
must be divided, so that the quotient is a perfect cube
A .2
B. 3
\( c \cdot 7 \)
D. 12


One half mole each of nitrogen, oxygen and carbon dioxide are mixed in
enclosure of volume 5 litres and
temperature \( 27^{\circ} \mathrm{C} . \) The pressure exerted by mixture is \( \left(\boldsymbol{R}=\mathbf{8 . 3 1} \boldsymbol{J} \boldsymbol{m o l}^{-1} \boldsymbol{K}^{-1}\right) \)
A \( \cdot 7.48 \times 10^{5} \mathrm{N} \mathrm{m}^{-2} \)
B. \( 4 \times 10^{5} \mathrm{N} \mathrm{m}^{-2} \)
\( \mathbf{c} \cdot 6 \times 10^{5} \mathrm{N} m^{-2} \)
D. \( 3 \times 10^{5} \mathrm{N} m^{-2} \)


Write any three properties of magnetic
lines of force.


toppr
Q Type your question
at the eye by the virtual image produced by a magnifying glass. In what sense then does a magnifying glass provide angular magnification?
(b) In viewing through a magnifying glass, one usually positions ones eyes very close to the lens. Does angular
magnification change if the eye is
moved back?
(c) Magnifying power of a simple microscope is inversely proportional to the focal length of the lens. What then stops us from using a convex lens of
smaller and smaller focal length and achieving greater and greater magnifying power?
(d) Why must both the objective and the eyepiece of a compound microscope have short focal lengths?
(e) When viewing through a compound microscope, our eyes should be positioned not on the eyepiece but a short distance away from it for best viewing. Why? How much should be that short distance between the eye and eyepiece?


A point charge 'q' is placed outside solid copper sphere at a distance 'r'from its centre. Consider point 'p' inside the solid sphere at a distance 'x' from the point charge. Then
A. Charge density is uniform on the surface of the sphere
B. Electric field due to induced charge at point 'p' is \( \frac{k q}{x^{2}} \)
c. Electric potential due to induced charge at point 'p' is \( \frac{k q}{r} \frac{k q}{x} \)
D. There is a net force in the sphere towards the point charge 'q'


The term \( p H \) comes from:
A. hydrogen purity
B. pure Hydrogen
c. hydrogen power
D. purity of Hydrogen


Leathery egg are found in
A. Amphibia
B. Reptiles
c. Birds
D. Mammals


the given statements is true or false.
(P) \( C \) recycled more newspapers than \( D \)
(Q) \( \mathrm{B} \) recycled 80 bunches of newspaper
more than \( \mathbf{A} \)
(R) In all 5 hundred bunches of
newspaper were recycled.
(S) The ascending order of the
newspaper recycled by schools is \( \mathrm{D}, \mathrm{C} \)
\( A, B, E \)
\( \begin{array}{llll}\text { (P) } & \text { (Q) } & \text { (R) } & \text { (S) }\end{array} \)
A. True True False False
B. True True False True
c. False True False True
D. False False True True


The four figures \( (A, B, C \text { and } D) \) given
below represent four different types of animals tissues. Which one of these is
correctly identified in the given options along with its correct location and function?
A. Tissue-
B- Glandular epithelium; Location- Intestine; Function- Secretion
B. Tissue C- Collagen fibres; Location- Cartilage; Function- Attach bone to bone
c. Tissue D- Smooth muscle tissue; Location- Heart:
Function- Heart contraction
D. Tissue A- Columnar epithelium; Location- Nephron; Function- Secretion and absorption


If cost price of 8 pens \( = \) Selling price of 6 pens. Find percentage profit


If the coefficient of three consecutive
terms in the expansion of \( (1+x)^{n} \) be
\( 165,330, \) and \( 462 . \) Find \( n \)


In which of the following period a maximum number of 32 elements are
present? This question has multiple correct options
\( \mathbf{A} \cdot 4^{t h} \)
B. \( 6^{\text {th }} \)
\( c \cdot 3^{r d} \)
D. \( 7^{t h} \)


Which of the following is not a polyhalogen compound?
A. Chloroform
B. Freon
c. Carbon tetrachloride
D. Chloro benzene


If \( \boldsymbol{A}=\left[\begin{array}{cc}\boldsymbol{4} & \boldsymbol{3} \\ \boldsymbol{1} & \boldsymbol{2}\end{array}\right] \boldsymbol{B}=\left[\begin{array}{ll}\boldsymbol{2} & \boldsymbol{1} \\ \boldsymbol{1} & \boldsymbol{2}\end{array}\right] \)
Verify \( (\boldsymbol{A} \boldsymbol{B})^{\prime}=\boldsymbol{B}^{\prime} \boldsymbol{A}^{\prime} \)


Four particles of equal masses are
placed on the vertices of a square and
are rotated with a uniform angular
velocity about one of the edges \( (A) \) as
shown in the figure. Which particle will
have a larger angular momentum
\( A \cdot A \)
B. B
\( c . c \)


Find the radius of the circle passing the points (0,0),(1,0) and (0,1)


Fill in the blank.
The length of the vocal chords in men and women is approximately and \( _{--}-_{-} \) respectively
A. \( 15 \mathrm{mm}, 20 \mathrm{mm} \)
B. 20 \( \mathrm{mm}, 30 \mathrm{mm} \)
c. \( 20 \mathrm{mm}, 15 \mathrm{mm} \)
D. 25 mm, 15 mm


When the negative feedback is applied to an amplifier of gain \( 50, \) the gain after feedback falls to \( 25 . \) Calculate the
feedback ratio.


If uncertainity in position and momentum are equal, then uncertainity in velocity is:
A \( \cdot \sqrt{\frac{h}{\pi}} \)
в. \( \frac{1}{2} \sqrt{\frac{h}{\pi}} \)
\( ^{\mathrm{c}} \cdot \frac{1}{2 m} \sqrt{\frac{h}{\pi}} \)
D. \( 2 m \frac{1}{2} \sqrt{\frac{h}{\pi}} \)


\( 6 \mathrm{ml} \) of a standard soap solution \( (1 \mathrm{ml} \)
\( =0.001 \mathrm{g} \) ) of \( \mathrm{CaCO}_{3} \) were required in
titrating \( 50 \mathrm{ml} \) of water to produce a good lather. Its degree of hardness is:
A. 120 ppm
В. 100 ppm
c. 50 ppm
D. 60 ppm


A system consists of two parallel planes carrying currents producing a uniform magnetic field of induction \( \boldsymbol{B} \)
between the planes. Outside this space
there is no magnetic field. If the magnetic force acting per unit area of each plane is \( F_{1}=\frac{B^{2}}{x \mu_{0}} . \) Find \( x \)


\( \mathbf{f} \boldsymbol{y}=\left(\sin ^{-1} x\right)^{2}, \) then prove that
\( \left(1-x^{2}\right) \frac{d^{2} y}{d x^{2}}-x \frac{d y}{d x}-2=0 \)


A cistern 6 m long and 4 m wide
contains water up to the depth of 1 \( m 25 \) cm. The total area of the wet
surface is :
\( \mathbf{A} \cdot 49 m^{2} \)
B. \( 50 m^{2} \)
\( \mathrm{c} \cdot 53.5 \mathrm{m}^{2} \)
D. \( 55 m^{2} \)


The distance between the lines \( 3 x+ \)
\( \mathbf{4} \boldsymbol{y}=\mathbf{9} \) and \( \mathbf{6} \boldsymbol{x}+\mathbf{8} \boldsymbol{y}-\mathbf{1 5}=\mathbf{0} \) is
\( A \cdot \frac{3}{10} \)
в. \( \frac{33}{10} \)
\( c \cdot \frac{33}{5} \)
D. none of these


Which of the following drives
spontaneous reactions?
A. Low enthalpy values and high entropy values.
B. Low enthalpy values and low entropy values.
C. High enthalpy values and low entropy values.
D. High enthalpy values and high entropy values
E. High temperatures and low pressures.


Photons of an electromagneitc
radiation has an energy \( 11 k e V \) each. To which region of electromagnetic spectrum does it belong?
A. \( X- \)ray region
в. Ultra violet region
c. infrared region
D. visible region


Which of the following is an example for heterogeneous catalysis reaction?
\( \mathbf{A} \cdot 2 S O_{2}(g)+O_{2}(g) \quad N O(g) \quad 2 S O_{3}(g) \)
B. Hydrolysis of aqueous sucrose solution in the presence of a aqueous mineral acid
\( \mathbf{c} \cdot 2 H_{2} O_{2}(l) \quad P t(s) \quad 2 H_{2} O(l)+O_{2}(g) \)
D. Hydrolysis of liquid in the presence of aqueous mineral acid


Describe the different types of vascular bundles.


The typical floral formula of Gramineae
is
\( A \)
\( \mathrm{Br} \% \mathrm{GP}_{2} \mathrm{A}_{3} \mathrm{G}_{1} \)
в. \( \mathrm{Br} \oplus \widehat{\mathrm{G}} \mathrm{P}_{2} \mathrm{A}_{3} \mathrm{G}(2) \)
\( \mathrm{c} \cdot \mathrm{Br} \oplus \mathrm{GP}_{2} \mathrm{A}_{2} \mathrm{G}(3) \)
D. \( \mathrm{Br} \oplus \oint \mathrm{P}_{2} \mathrm{A}_{3} \mathrm{G}_{3} \)


For the process \( \boldsymbol{H}_{2} \boldsymbol{O}(l) \rightarrow \)
\( \boldsymbol{H}_{2} \boldsymbol{O}(\mathbf{1} \boldsymbol{b} \boldsymbol{a} \boldsymbol{r}, \boldsymbol{3} \boldsymbol{7} \boldsymbol{3} \boldsymbol{K}), \) the correct set of
thermodynamic parameters is:
A. \( \triangle G=0, \Delta S=+v e \)
B. \( \triangle G=0, \Delta S=-v e \)
c. \( \Delta G=+v e, \Delta S=0 \)
D. \( \triangle G=-v e, \Delta S=+v e \)


In the Rosenmund reduction, the
catalyst used is :
\( \mathbf{A} \cdot P d / B a S O_{4} \)
B. Raney \( N i \)
\( \mathbf{c} \cdot S n / H C l \)
D. \( Z n / H C l \)


Heat of combustion is always:
A. positive
B. negative
C. zero
D. may be positive or negative


The equilibrium constant of a reaction
at \( 298 K \) and \( 1000 K \) is \( 5 \times 10^{-3} \) and
\( 2 \times 10^{-3} \) respectively. The \( \Delta H \) for the
reaction is:
A. positive
B. negative
c. either positive or negative
D. zero


Two moles of oxygen is mixed with eight moles of helium. The effective specific heat of the mixture at constant volume
is:
A . 1.3 R
B. 1.4R
c. \( 1.7 \mathrm{R} \)
D. 1.9R


In Uniform circular motion direction of
velocity is along the drawn
to the position of particle on the circumference of the circle.
A. normal
B. tangent
c. can be both
D. none of these


Fill in the blank:
In a geostationary orbit, a satellite is at
a distance of from the
Earth
\( \mathbf{A} \cdot 53,880 \mathrm{km} \)
B . \( 25,880 \mathrm{km} \)
c. \( 36,000 k m \)
D. \( 1,12,000 \mathrm{km} \)


Long answer type questions. Why were micronutrients discovered
later than macronutrients? With one
example each, mention the physiological role and deficiency disease caused by
(i) nitrogen, (ii)
phosphorus, (iii) copper, and (iv) iron.


\( 2 C H_{3} C O C H_{3}+6 C a O C l_{2} \rightarrow \)
\( \boldsymbol{C a}\left(\boldsymbol{C H}_{3} \boldsymbol{C O O}_{2}\right)_{2}+\boldsymbol{2 C H} \boldsymbol{C l}_{3}+ \)
\( \mathbf{3} C a C l_{2}+2 C a(O H)_{2} \)
If the yield of chloroform obtainable from acetone and bleaching powder is
\( 58 \% \). The weight of acetone required for
producing \( 47.8 \mathrm{g} \) of chloroform is :
A . 40
в. 20
\( c \cdot 4 \)
D. 10


If the resistance in a parallel resonant circuit is reduced, the bandwidth:
A. increases
B. decreases
c. disappears
D. become sharper


The maximum shear stress induced in
a member which is subjected to an axial load is equal to
A. maximum normal stress
B. half of maximum normal stress
c. twice the maximum normal stress
D. thrice the maximum normal stress


\( \underbrace{\frac{-}{L}}_{L} \)


A block of mass \( 2 \mathrm{kg} \) is resting over another block of mass 6 kg. 2 kg is connected to one end of a string fixed to a vertical wall as shown. If the
coefficient of friction between the
blocks is \( 0.4, \) the force required to pull out the \( 6 \mathrm{kg} \) block with an acceleration
of \( 1.5 \mathrm{m} / \mathrm{s}^{2} \) will be \( \left(\mathrm{g}=10 \mathrm{ms}^{-2}\right) \)
A . 17
B. 9 N
\( c \cdot 8 n \)
D. 1 N


In the above reaction sequence, the
correct structures of \( \mathrm{E}, \mathrm{F} \) and \( \mathrm{G} \) are :
\( A \)
\( B \)
\( c \)
\( D \)


What is \( \lim _{h \rightarrow 0} \frac{\sqrt{2 x+3 h}-\sqrt{2 x}}{2 h} \) equal to?
\( ^{\mathbf{A}} \cdot \frac{1}{2 \sqrt{2 x}} \)
в. \( \frac{3}{\sqrt{2 x}} \)
c. \( \frac{3}{2 \sqrt{2 x}} \)
D. \( \frac{3}{4 \sqrt{2 x}} \)


The energy emitted by the electrons when 18 of hydrogen atom undergo transition, giving the spectral lines of
lowest energy in the visible region of
atomic spectra is \( n \times 10^{-19} J . \) The value
of \( n \) (nearest integer) is :


What needs to exist in order for a
dipole-dipole force to happen?
A. The molecules need to be very close to each other.
B. The molecules need to be very far apart from each other
C. The molecules need to include hydrogen.
D. The molecules need to include carbon.
E. Dipole-dipole forces can happen in any molecule in any situation.


If \( R=r \) adius of the earth and \( g= \) acceleration due to gravity on the
surface of the earth, the acceleration
due to gravity at a distance (r>R) from the centre of the earth is proportional to
\( A \)
в. \( r^{2} \)
\( c \cdot r^{-2} \)
D. \( r^{-1} \)


Diastema is
A. A part of pelvic girdle in rabbit.
B. A type of tooth in rabbit.
C. Space in teeth lines in some mammals.
D. Structure in eye of rabbit.


A pulse of a wave travelling on a string towards the fixed rigid end as shown in the figure above. The pulse is:
A. Reflected and transmitted
B. Reflected and refracted
c. Reflected and reduced
D. Reflected and magnified
E. Reflected and inverted


Solve: \( \int \frac{d x}{\left(2 x^{2}+3\right)\left(x^{2}-4\right)} \)


Write chemical equations for the following conversions:
(i) Nitrobenzene to benzoic acid.
(ii) Benzyl chloride to 2 phenylethanamine.
(iii) Aniline to benzyl alcohol.


A car starts from rest and has an
acceleration \( a=1 \mathrm{m} / \mathrm{s}^{2} . \) A truck is
moving with a uniform velocity of \( 6 \mathrm{m} / \mathrm{s} \) At what distance will the car overtake
the truck? direction \( (\text { at } t=0 \) both start
their motion in the same direction from the same position)
A. 36
B. 8 m
c. 32 \( \mathrm{m} \)
D. \( 4 \mathrm{m} \)


Compute \( \boldsymbol{P}(\boldsymbol{A} \mid \boldsymbol{B}), \) if \( \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 5} \) and
\( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})=\mathbf{0 . 3 2} \)


Match the species in in \( C \) olumn \( I \) with
their corresponding properties in Column II


Ethyl alcohol on oxidation with acidified
\( K_{2} C r_{2} O_{7} \) gives ethanal
A. True
B. False


A simple harmonic motion has an amplitude \( A \) and time period T. Find the time required by it to travel directly from \( \boldsymbol{x}=\frac{\boldsymbol{A}}{\sqrt{\mathbf{2}}} \) to \( \boldsymbol{x}=\boldsymbol{A} \)


Producer gas is formed by passing over hot biomass.
A. Steam
B. Air
c. Hydrogen
D. Both A and B


Coal tar has an smell.
A . unpleasant
B. pleasant
\( c . \) Both (a) \& (b)
D. None of these


A solution of \( K M n O_{4} \) containing 3 g/L
is titrated with a solution of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \)
containing 2 g/L. The volume (in ml) of \( \boldsymbol{K} \boldsymbol{M n O}_{4} \) required
to react with \( 20 \mathrm{mL} H_{2} O_{2} \) solution is:
(as nearest integer)
A . 28
B. 17
c. 20
D. 25


Find the values of \( x, y \) and \( z \) from the
matrix equation. \( \left(\begin{array}{cc}5 x+2 & y-4 \\ 0 & 4 z+6\end{array}\right)=\left(\begin{array}{cc}12 & -8 \\ 0 & 2\end{array}\right) \)


Peptization denotes:
A. digestion of food
B. hydrolysis of proteins
C. breaking and dispersion into colloidal state
D. precipitation of solid from colloidal dimension


The hormone that helps increase the reabsorption of water from the kidney tubules.


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


A monochromatic beam of light is used for the formation of fringes on the screen by illuminating the two slits in the Youngs double-slit interference
experiment. When a thin film of mica is interposed in the path of the interference beams, then
A. The fringe width increases
B. The fringe width decreases
c. The fringe width remains the same but the pattern shifts
D. The fringe pattern disappears


A steady current flow in a metallic conductor of non-uniform cross-section.
The quantity/quantities remaining constant along the whole length of the conductor is/are:
A. current, electric field and drift speedd
B. drift speed only
c. current and drift speed
D. current only


Forest is also called as
A. Lung of Earth
B. Heart of Earth
C. Brain of Earth
D. None of the above


Two bodies, initially separated by \( x \) m
and having an initial velocity \( 2 \mathrm{m} s^{-1} \) each, are moving towards each other along a straight line. If the rate of increase of their speeds is \( 3 \mathrm{m} s^{-2} \) and
\( 2 m s^{-2} \) respectively and the two meet after 4 seconds, find \( x \)
A \( \cdot 12 \)
B. 40
\( c .56 \)
D. 66


Which of the following processes
described below is irreversible?
A. The increase in temperature of an iron rod by hammering it.
B. A gas in a small container at a temperature \( T_{1} \) is brought in contact with a big reservoir at a higher temperature \( T_{2} \) which increases the temperature of the gas.
C. An ideal gas is enclosed in a piston cylinder arrangement with adiabatic walls.A weight \( \mathrm{W} \) is added to the piston resulting in compression of gas.
D. All of above


Two soap bubbles \( A \) and \( B \) are formed
at the two open ends of a tube. The
bubble \( A \) is smaller than bubble \( B \). If
valve \( V \) is opened and air can flow freely
between the bubbles, then
A. There is no change in the size of the bubbles
B. The two bubbles will become of equal size
C. \( A \) will become smaller and \( B \) will become larger
D. \( B \) will become smaller and \( A \) will become larger


All are non-metals except:
\( \mathbf{A} \cdot \) hydrogen \( \left(H_{2}\right) \) and carbon (C)
B. potassium (K)
C. inert gases (helium, neon and argon)
D. sulphur (S), phosphorus (P), and fluorine (F)


A person can hold his breath longer if he gradually exhales than if he keeps his lungs fully expanded. This phenomenon is due to the fact that
A. the concentration of \( \mathrm{CO}_{2} \), in the blood decreases lessening the excitatory input to the carotid bodies
B. he is then using less 0 , as his thoracic muscles are not working as hard
c. stretch receptors in his lungs are then not firing as much thus lessening the excitatory input to the expiratory centress
D. he is preventing the pressure in his lungs from increasing too much


Find the two missing numbers in the arithmetic mean between 14 and 50
A. 25 and 35
B. 26 and 38
c. 27 and 34
D. 21 and 32


Which one is not a dominant trait
amongst seven Pea traits chosen by
Mendel?
A. Flower Colour - Purple
B. Pod Colour - Yellow
c. Shape of Seed - Round
D. Flower - Axial.


In a series of 3 one-day cricket matches between teams \( A \) and \( B \) of a college, the probability of team A winning or drawing are \( 1 / 3 \) and \( 1 / 6 \) respectively. If a
win, loss or draw gives 2,0 and 1 point
respectively, then what is the
probability that team A will score 5
points in the series?
A \( \cdot \frac{17}{18} \)
B. \( \frac{11}{12} \)
\( c \cdot \frac{1}{12} \)
D. \( \frac{1}{18} \)


A solution of weak acid \( \boldsymbol{H} \boldsymbol{A} \) was
titrated with base \( N a O H . \) The
equivalent point was reached when \( 40 m L \) of \( 0.1 M \) NaOH has been
added. Now 20 m \( L \) of \( 0.1 M \) HCl were
added to titrated solution, the \( p H \) was
found to be \( 5.0 . \) What will be the \( p H \) of
the solution obtained by mixing \( 20 m L \)
of \( 0.2 M N a O H \) and \( 20 m L \) of
\( \mathbf{0 . 2} \boldsymbol{M} \boldsymbol{H} \boldsymbol{A} ? \)
A . 7
B. 9
c. 11
D. None of the above


Which of the following represents the electric field lines due to a combination
of two negative charges?
\( A \)
B.
\( c \)
\( D \)


Evaluate :
\( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{\boldsymbol{x}+\boldsymbol{y}+\mathbf{1}}{\boldsymbol{2} \boldsymbol{x}+\boldsymbol{2} \boldsymbol{y}+\boldsymbol{3}} \)


The shaded region is represented by the inequality:
A. \( y-2 x \leq-1 \)
B . \( x-2 y \leq-1 \)
c. \( y-2 x \geq-1 \)
D. \( x-2 y \geq-1 \)


Find the following squares by using the identity
\( \left(\frac{x^{2}}{y z}+\frac{y^{2}}{x z}\right)^{2} \)


The \( p H \) of pure water at \( 25^{\circ} C \) and \( 60^{\circ} C \)
are 7 and 6.5 respectively. HCl gas is
passed through water at \( 25^{\circ} \mathrm{C} \) till the resulting 1 litre solution aquires a \( p H \)
of
3. Now \( 4 \times 10^{-3} \) mole of \( N a C N \) are
added into this solution. Also a fresh
\( 0.1 M H C N \) solution has \( p H 5.1936 \)
Now in the one part of solution obtained after addition of \( N a C N \), one millimole
of \( N a O H \) are added and in the second
part of this solution 0.5 miili mole of
\( H C l \) are added.

The volume of \( H C l \) passed through the
solution at \( 25^{\circ} C \) and 1 atm is :
A. \( 24.46 \mathrm{mL} \)
в. \( 2.446 \mathrm{mL} \)
c. \( 244.6 \mathrm{mL} \)
D. \( 0.2446 \mathrm{mL} \)


Write the direction cosines of \( x \) -axis


Represent these number on number line: \( \frac{7}{8}, \frac{-5}{3} \)


Propose structure/structures for the
hydrocarbon that gives the following products on oxidative cleavage by
\( \boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4} / \boldsymbol{H}^{\oplus} \)


Assertion
Microwaves are better carrier of signals
than the optical waves.
Reason
Microwaves move faster than optical
waves.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Assertion
In a meter bridge experiment, a high resistance is always connected in
series with a galvanometer.
Reason
As resistance increases, current
through the circuit increases.
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


Trimethyl phosphine oxide is stable
because
A. It has two resonating structure
B. Phosphurus-oxygen double bond has highh dissociation energy
c. Both (A) and (B)
D. None of the above


If \( \sqrt{\frac{\boldsymbol{v}}{\boldsymbol{\mu}}}+\sqrt{\frac{\boldsymbol{\mu}}{\boldsymbol{v}}}=\mathbf{6}, \) then \( \frac{\boldsymbol{d} \boldsymbol{v}}{\boldsymbol{d} \boldsymbol{\mu}}= \)
A. \( \frac{17 \mu-v}{\mu-17 v} \)
в. \( \frac{\mu-17 v}{17 \mu-v} \)
c. \( \frac{17 \mu+v}{\mu-17 v} \)
D. \( \frac{\mu+17 v}{17 \mu-v} \)


\( H_{2} O_{2} \) turns starch iodide paper to
green colour.

If this is true enter 1 , if false enter 0 .


Number of permutations of 1,2,3,4,5,6,7,8 taken all at a time are
such that the digit appearing some where to the left of 2 3 appearing to the left of 4 5 some where to the left of 6
(e.g.815723946 would be one such permutation)
A .9 .7
B. 8!
c. \( 5 ! .4 \)
D. 8!.4


A uniform sphere of mass \( \boldsymbol{m}=\mathbf{5 . 0} \boldsymbol{k g} \)
and radius \( R=6.0 \mathrm{cm} \) rotates with an
angular velocity \( \omega=1250 \mathrm{rad} / \mathrm{s} \) about
a horizontal axle passing through its centre and fixed on the mounting base
by means of bearings. The distance between the bearings equals \( l=15 \mathrm{cm} \)
The base is set in rotation about a
vertical axis with an angular velocity
\( \omega^{\prime}=5.0 \) rad \( / s . \) Find the magnitude of
the gyroscopic forces in \( \mathrm{N} \)


Integument of humans
A. Conserves heat in winter
B. Loses heat during summer
c. Protects body
D. All of the above


The addition of soap changes the
surface tension of water to \( T_{1} \) and that
of salt solution changes to \( T_{2} \). Then:
A \( \cdot T_{1}=T_{2} \)
в. \( T_{1}>T_{2} \)
c. \( T_{1}<T_{2} \)
D. \( T_{1} \geq T_{2} \)


The standard reduction potential for the
half-cell reaction, \( C l_{2}+2 e^{-} \rightarrow 2 C l^{-} \)
will be:
\( \boldsymbol{P t}^{2+}+\boldsymbol{2} \boldsymbol{C l}^{-} \rightarrow \boldsymbol{P t}+\boldsymbol{C l}_{2}, \boldsymbol{E}_{c e l l}^{o}= \)
\( -0.15 V \)
\( \boldsymbol{P t}^{2+}+\boldsymbol{2} \boldsymbol{e}^{-} \rightarrow \boldsymbol{P t}, \boldsymbol{E}^{o}=\mathbf{1 . 2 0} \mathbf{v} \)
A . \( -1.35 v \)
B. \( +1.35 v \)
c. \( -1.05 v \)
D. \( +1.05 v \)


The number of distinct real roots of the
\[
\text { guation, }\left|\begin{array}{ccc}
\cos x & \sin x & \sin x \\
\sin x & \cos x & \sin x \\
\sin x & \sin x & \cos x
\end{array}\right|=0
\]
in the interval \( \left[-\frac{\pi}{4}, \frac{\pi}{4}\right] \) is/are
\( A \)
B . 2
\( c \cdot 1 \)
\( D \)


Carbon monoxide is not used in:
A. fire extinguisher
B. the manufacture of water gas
C. the manufacture of methanol and synthetic petrol
D. metal operations as a reducing agent.


Two mutually perpendicular long straight conductors carrying uniformly distributed charges of linear charge
densitites \( \lambda_{1} \) and \( \lambda_{2} \) are positioned at a
distance a from each other. How does
the interaction between the rods
depend on a?


Assertion
Metallic character increases from left to
right in a period.
Reason
The higher the value of ionization energy, electronegativity and electron affinity the more is the metallic
character of the element.
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


Resonance is not possible in
\( A \)
в.
c.
\( \mathrm{CH}_{2}=\mathrm{CH}-\mathrm{Cl} \)
D.


Family \( y=a x+a^{3} \) of curve
repersented by the differential equation of degree
\( A \). three
B. two
c. one
D. four


\( \int \frac{\cos 4 x}{\sin 2 x} d x \)


Find the mean of the following frequency distribution by the assumed
mean method:
\( \begin{array}{lllll}\text { No. of } & \mathbf{5 0}- & \mathbf{5 3 -} & \mathbf{5 6 -} & \mathbf{5 9 -} \\ \text { apples } & \mathbf{5 3} & \mathbf{5 6} & \mathbf{5 9} & \mathbf{6 2}\end{array} \)
No of
boxes 150 115


Two moles of an ideal monoatomic gas
occupies a volume \( V \) at \( 27^{\circ} \mathrm{C} \). The gas expands adiabatically to a volume \( 2 \mathrm{V} \) Calculate (a) the final temperature of the gas and (b) change on its internal
energy.
B. (a) \( 195 K \) (b) 2.7 k
\( c .(a) 189 K(b) 2.7 k J \)
D. (a) \( 195 \mathrm{k} \) (b) \( -2.7 \mathrm{kJ} \)


Why nitrogen exists as diatomic
molecule \( \left(N_{2}\right) \) and Phosphorus as \( P_{4} ? \)


\( S_{1} \) and \( S_{2} \) are two coherent sources of
sound having no initial phase
difference. The velocity of sound is 330 \( \mathrm{m} / \mathrm{s} . \) No maxima will be formed on the
line passing through \( S_{2} \) and
perpendicular to the line joining
\( \boldsymbol{S}_{1} \) and \( S_{2} . \) If the frequency of both the
sources is :
A. 330 \( \mathrm{Hz} \)
в. 120 Н \( z \)
\( c \cdot 100 \mathrm{Hz} \)
D. 220 нz


\( 50 \% \) of a radio active substance decays
in 5 hours. The time required for the
\( 87.5 \% \) decay is
A. 10 hours
B. 15hours
c. 12.5 hours
D. 17.5 hours


Two magnetic monopoles are kept apart by a distance 'd. The magnetic force acting on each pole is ' \( \boldsymbol{F} \) ". How much percentage must the distance between the magnetic poles be changed so that the magnetic force acting on each pole
be \( 4 F \)
A. Decreases by \( 50 \% \)
B. Decreases by 20\%
c. Increased by \( 50 \% \)
D. Increased by \( 20 \% \)


A body dropped from the top of a tower covers \( \frac{7}{16} \) of the height in the last second of its fall. The time of fall is :
\( A \cdot 2 \sec \)
B. 4 sec
c. \( 1 \mathrm{sec} \)
D. \( \left[\frac{50}{7}\right] \) sec


What is the surface area of a cube of
side \( 15 \mathrm{cm} ? \)


Let \( a_{1}, a \) and \( b_{1}, b_{2}, \dots . \) be the arithmetic
progressions such that \( a_{1}=25, b_{1}= \)
75 and \( a_{1} 00+b_{100} . \) The sum of the first
one hundred terms of the progressions
\( \left(a_{1}+b_{1}\right),\left(a_{2}+b_{2}\right), \dots \dots \) is
\( A \cdot O \)
B. 100
\( c \cdot 10,000 \)
D. 5,05,000


The cycle is shown in figure is made of
one mole of perfect gas in a cylinder
with a piston. The processes \( A \) to \( B \) and \( \mathrm{C} \) to \( \mathrm{D} \) are isochoric whereas process \( \mathrm{B} \)
to \( C \) and \( D \) to \( A \) are adiabatic, the work
done in one cycle is \( \left(V_{A}=V_{B}=V, V_{C}=\right. \)
\( \left.V_{D}=2 V \text { and } \Upsilon=5 / 3\right) \)
A \( \cdot\left[1-4^{3 / 2}\right]\left(P_{B}-P_{A}\right) V \)
B \( \cdot \frac{3}{2}\left[1-3^{2 / 3}\right]\left(P_{B}-P_{A}\right) V \)
c. \( \frac{3}{2}\left[1-2^{-2 / 3}\right]\left(P_{B}-P_{A}\right) V \)
D. \( \frac{5}{2}\left[1-2^{-2 / 3}\right]\left(P_{B}-P_{A}\right) V \)


Identify the correct statement in the
following:
A. Propan-1-ol and propan-2-ol are position isomers
B. Ethanoic acid and methyl methanoate are position isomers
C. N-butane and isobutene are functional isomers
D. Dimethyl ether and ethanol are chain isomers


The compound in which cation is
isoelectronic with anion is:
A . \( N a C l \)
в. \( C s F \)
c. \( N a I \)
D. \( K_{2} \)


Bond length depends upon
This question has multiple correct options
A. bond order
B. \( \pi \) -bonding
C. state of hybridization
D. none of these


Muscle growth during puberty occurs
A. only in males
B. Only in females
c. In both genders
D. Very slowly in females


Construct the graphs of the following
function.
\( \boldsymbol{y}=|\boldsymbol{x}-1|+|\boldsymbol{x}-2|+\boldsymbol{x} \)


The following configuration of gate is
equivalent to
A. NAND gate
B. XOR gate
c. or gate
D. NOR gate


A strip of copper and another of germanium are cooled from room
temperature to \( 80 K \). The resistance of
A. each of these decreases.
B. copper strip decreases and that of germanium decreases
C. copper strip decreases and that of germanium increases
D. each of these increases.


\( f(x)=\sin x \) -ax is decreasing in \( R \) if
\( \mathbf{A} \cdot \mathbf{a}>1 \)
B. \( a<13 \)
c. \( _{a>\frac{1}{2}} \)
D. \( a<\frac{1}{2} \)


Size of atom is measured in


Which of the following cannot act as a ligand :
\( A \cdot B F_{3} \)
B. NH
\( c \cdot \) No
D. cN


An electron collides with a Hydrogen atom in its ground state and excites it
to \( n=3 \) state. The energy given to the
Hydrogen atom in his inelastic collision (neglecting the recoil of Hydrogen atom) is
A . \( 10.2 e V \)
в. \( 12.1 e V \)
c. \( 12.5 e V \)
D. \( 13.6 e V \)


The fraction \( \frac{\sqrt{\mathbf{3 x - a}}-\sqrt{x+a}}{x-a} \)
becomes \( \frac{\mathbf{0}}{\mathbf{0}} \) when \( \boldsymbol{x}=\boldsymbol{a} \)


Two particles execute SHM of same amplitude and same time period, about
same mean position but with a phase difference between them. At an instant
they are found to cross each other at
\( x=+\frac{A}{3} . \) The phase difference between
them is:
\( \mathbf{A} \cdot 2 \cos ^{-1}\left[\frac{1}{5}\right] \)
B \( \cdot 2 \sin ^{-1}\left[\frac{1}{5}\right] \)
C \( \cdot 2 \cos ^{-1}\left[\frac{1}{3}\right] \)
D. \( 2 \sin ^{-1}\left[\frac{1}{3}\right] \)


In an adiabatic change, the pressure
and temperature of a monoatomic gas
are related with relation as \( \boldsymbol{P} \propto \boldsymbol{T}^{C} \)
where \( C \) is equal to
A \( \cdot \frac{5}{4} \)
B. \( \frac{5}{3} \)
\( c \cdot \frac{5}{2} \)
D. \( \frac{3}{5} \)


The area of the region bounded by the curve \( y=x^{2} \) and \( y=4 x-x^{2} \) is
A \( \cdot \frac{16}{3} \) sq.units
B. \( \frac{8}{3} \) sq.units
c. \( \frac{4}{3} \) sq.units
D. \( \frac{2}{3} \) sq.units


The maximum kinetic energy of electron emitted in the photoelectric effect linearly depends on the of
the incident radiations.
A. temperature
B. amplitude
c. number
D. frequency


The moment of inertia of a circular of
mass \( M \) and radius \( R \) about an axis
passing through the center of mass is
10. The moment of inertia of
another circular disc of same mass and
thickness but half the density about the
same axis is
A \( \cdot \frac{I_{0}}{8} \)
B. \( \frac{I_{0}}{4} \)
\( c \cdot 8 I_{0} \)
D. \( 2 I_{0} \)


Assertion
0.2 per cent solution of phenol is an
antiseptic while its one percent solution is disinfectant.
Reason
Antiseptics are also called disinfectant.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


In the number \( 0.257, \) which of the
following does the digit 7 represent??
A \( \cdot 7 \times \frac{1}{10} \)
в. \( 7 \times \frac{1}{100} \)
c. \( _{7 \times \frac{1}{1000}} \)
D. \( 7 \times \frac{1}{10000} \)
E \( \cdot 7 \times \frac{1}{100000} \)


For a particular reaction, \( \Delta \boldsymbol{H}^{o}= \)
\( -38.3 k J \) and \( \Delta S^{o}= \)
\( -113 J K^{-1} m o l^{-1} . \) This reaction is:
A. spontaneous at all temperatures
B. non-spontaneous at all temperatures
C. spontaneous at temperatures below \( 66^{\circ} \mathrm{C} \)
D. spontaneous at temperatures above \( 66^{\circ} \mathrm{C} \)


Number of faradays' required to generate one gram atom of magnesium
from molten \( M g C l_{2} \) is
A . 1
B . 2
\( c .3 \)
D.


The ages of two persons differ by 16 years. If 6 years ago, the elder one be 3 times as old as the younger one, find their present ages.
A. 15 years and 31 years
B. 14 years and 30 years
c. 12 years and 28 years
D. 10 years and 26 years


While orbiting around the earth in a apaceship, an astronaut experiences
A. more weight
B. lesser weight
c. weightlessness
D. nothing at all


The end of a wire of length \( 0.5 \mathrm{m} \) and
radius \( 10^{-3} m \) is twisted through 0.80
radian. The shearing strain at the surface of wire will be :
A \( .1 .6 \times 10^{-3} \)
B . \( 1.6 \times 10^{3} \)
C \( .16 \times 10^{3} \)
D. \( 16 \times 10^{6} \)


Integrate the following \( \int \frac{1}{x^{2}+8 x+20} d x \)
A \( \cdot \frac{1}{2} \sin ^{-1} \frac{x+4}{2}+C \)
B. \( \frac{1}{2} \cot ^{-1} \frac{x+4}{2}+C \)
c. \( \frac{1}{2} \tan ^{-1} \frac{x+4}{2}+C \)
D. None of these


What is the strength of the electric field in the velocity selector?
A \( \cdot 2 \times 10^{5} N C^{-1} \)
B . \( 2 \times 10^{3} N C^{-1} \)
c. \( 2 \times 10^{6} N C^{-1} \)
D. \( 2 \times 10^{4} N C^{-1} \)


solve: \( \left|\begin{array}{ccc}\boldsymbol{x} & \boldsymbol{2} & -\mathbf{1} \\ \boldsymbol{3} & -\boldsymbol{1} & \boldsymbol{4} \\ \boldsymbol{x} & \boldsymbol{2} & -\boldsymbol{5}\end{array}\right|=\mathbf{0} \)


One of the characteristics of nuclear
reactions is that in their decayed or fused parts
A. total mall number keeps on changing
B. total charge number keeps on changing
c. total charge number remains constant
D. all the above


The value of \( m \) for which the
expressions \( 2 m-5 \) and \( 5 m-11 \)
become equal is
A . -2
B. 0
\( c \cdot 2 \)
D. -


A student investigates the rate of
reaction between marble chips and
hydrochloric acid.
The mass of the reaction flask is
measured.

The graph shows the results of two
experiments, \( P \) and \( Q \)
Which change explains the difference
between \( \boldsymbol{P} \) and \( \boldsymbol{Q} \) ?
A. A catalyst is added in \( P \)
B. A higher temperature is used in \( P \)
c. Bigger marble chips are used in \( Q \)
D. Hydrochloric acid is more concentrated in \( Q \)


Work done during the combustion of
one mole of \( C H_{4} \) in bomb calorimeter
is:
A . zero
в. -101 Л
c. \( -24.2 J \)
D. \( -1 J \)


GnRH of hypothalamus stimulates secretion of
A. Aldosterone from adrenals
B. ADH from posterior pituitary
C. FSH and LH from anterior pituitary
D. Thyroxine from thyroid


What is Global Warming? Write their main five reasons.


Write the structures of the given compounds whose IUPAC names are
given as:
1,2,3-propoantriol


Choose the correct set of True/False for
the following statements:
(i) Silver chloride is more soluble in very
concentrated sodium chloride solution
than in pure water.
(ii)The pH od a buffer solution does not change on addition of small amountof
an acid or a base.


Suhail wants to paint the flour walls of a
room having dimensions \( 20 m \times 6 m \)
From each can of paint, 96 sq. \( \mathrm{m} \) of the area is painted. How many cans of paint will he need to paint the room?


Suppose the earth shrinks such that its
radius decreases to half the present
value. What will be the acceleration due
to gravity on the surface of the earth?


Match the following:
Section - A section - B
(P) Converts electric energy into
(1) Fuse \( \quad \) mechanical energy
(2) Electric
(Q) Heating effect of electric current
(3) Electric
(R) Converts mechanical energy Motor \( \quad \) into electrical energy
A \( \cdot(1-\mathrm{Q}),(2-\mathrm{R}),(3-\mathrm{P}) \)
B. (1 - Q), (2 - P), (3 - R)
c. \( (1-P),(2-Q),(3-R) \)
D. \( (1-P),(2-R),(3-Q) \)


Which of the following properties is not exhibited by planets?
A. Do not have their own light
B. Revolve around the sun and rotate around itself
c. Keep changing their position
D. Follow randomly changing orbits


During the purification of copper by electrolysis:
This question has multiple correct options
A. the anode used is made of copper ore
B. pure copper is deposited on the cathode
C. the impurities such as \( A g, A u \) present in solution as ions
D. concentration of \( C u S O_{4} \) solution remains constant
during dissolution of \( C u \)


The internal energy of 1 mol of an ideal gas depends on
A. only volume
B. only temperature
c. only pressure
D. temperature and pressure


Chambers in human heart
A . 1 auricle, 1 ventricle
B. 2 auricles, 1 ventricle
c. 1 auricle, 3 ventricles
D. 2 auricles, 2 ventricles


What is the value of universal gas
constant


An ideal battery of emf \( 2 V \) and a series
resistance \( R \) are connected in the
primary circuit of a potentiometer of length \( 1 \mathrm{m} \) and resistance \( \Omega \). The value of \( \boldsymbol{R} \) to give a potential difference of \( \mathbf{5} \) \( m V \) across the \( 10 \mathrm{cm} \) of potentiometer wire is:
\( \mathbf{A} \cdot 180 \Omega \)
в. \( 190 \Omega \)
c. \( 195 \Omega \)
D. 200\Omega


In the diagram 0 is the centre of a
circle. \( A E+E B=C E+E D O P \perp A B \) and \( 0 Q \)
\( \perp \) CD then true relation between OP and
OQ is
A. ор > \( 0 Q \)
B. op < \( 0 Q \)
\( c \cdot o p=\frac{1}{2} o Q \)
D. OP = OO


Q Type your question
speed \( v \) in such a way that \( K \) always
moves directly towards \( L, L \) directly
moves towards \( M, M \) directly towards
\( N \) and \( N \) directly towards \( K . \) The four
persons will meet at time \( t= \)
\( ^{A} \cdot \underline{4 d} \)
\( v \)
в. \( \frac{3 d}{v} \)
c. \( \frac{2 d}{v} \)
\( D \cdot d \)


Passive absorption of minerals depend
on:
A. Temperature
B. Temperature and metabolic inhibitor
c. Metabolic inhibitor
D. Humidity


Let \( G \) and \( G^{1} \) be the centroids of the
triangles \( A B C \) and \( A^{1} B^{1} C^{1} \)
respectively, then \( \boldsymbol{A} \boldsymbol{A}^{1}+\boldsymbol{B} \boldsymbol{B}^{1}+\boldsymbol{C} \boldsymbol{C}^{1} \)
is equal to
\( \mathbf{A} \cdot 2 G G^{1} \)
B. \( 3 G^{1} G \)
\( \mathbf{c} \cdot 3 G G^{1} \)
D. \( \frac{3}{2} G G^{1} \)


liquid is kept on a table in a vacuum. The force exerted by the liquid on the
base of the flask is \( W_{1} \). The force exerted
by the flask on the table is \( W_{2} \)
This question has multiple correct options
A \( . W_{1}=W_{2} \)
\( \mathbf{B} \cdot W_{1}>W_{2} \)
c. \( W_{1}<W_{2} \)
D. The force exerted by the liquid on the walls of the flask
is \( \left(W_{1}-W_{2}\right) \)


(i) Solve the equation \( \left|\begin{array}{ccc}\boldsymbol{x}-\mathbf{1} & \boldsymbol{2} & \boldsymbol{3} \\ \mathbf{0} & \boldsymbol{x}-\boldsymbol{2} & \boldsymbol{4} \\ \boldsymbol{0} & \boldsymbol{0} & \boldsymbol{x}-\boldsymbol{3}\end{array}\right| \)
(ii) Show that \( \left|\begin{array}{ccc}\mathbf{1} & \boldsymbol{a} & \boldsymbol{b} \boldsymbol{c} \\ \mathbf{1} & \boldsymbol{b} & \boldsymbol{c a} \\ \mathbf{1} & \boldsymbol{c} & \boldsymbol{a b}\end{array}\right|=\left|\begin{array}{ccc}\mathbf{1} & \boldsymbol{a} & \boldsymbol{a}^{2} \\ \mathbf{1} & \boldsymbol{b} & \boldsymbol{b}^{2} \\ \mathbf{1} & \boldsymbol{c} & \boldsymbol{c}^{2}\end{array}\right| \)


Factorize the expression: \( 9 x^{4}+\frac{1}{x^{4}}+2 \)


In an experiment with 15 observation on \( x, \) the following results were available \( \sum x^{2}=2830, \sum x=170, \) one
observation was that +20 was found to
be wrong and was replaced by the correct value \( 30, \) then the corrected
variance is
A . 188.66
B. 177.33
\( c \cdot 8.33 \)
D. 78.00


Find out what do the terms algal bloom and red-tides signify.


Which of the following statements
is/are correct?
This question has multiple correct options
A. Molecular formula or molecular mass of a gaseous hydrocarbon can be determined even without knowing their percentage composition by audiometry
B. In Lassaigne's test, N and S both present in the organic compounds are converted into \( C N S \) ion
\( \mathrm{C} \cdot K_{2} S O_{4} \) and \( C u S O_{4} \) are added in Kjeldahl's method. \( K_{2} S O_{4} \) acts as a catalyst while \( C u S O_{4} \) raises the
boiling point of \( H_{2} S O_{4} \)
D. Layer test is used to distinguish \( C l^{\ominus} \) and \( B r^{\ominus} \) ions


Choose the most appropriate answer.
(a) Internal fertilization occurs
(i) in female body.
(ii) outside female body.
(iii) in male body
(iv) outside male body.
(b) A tadpole develops into an adult frog
by the process of
(i) fertilization
(ii) metamorphosis (iii) embedding (iv) budding
(c) The number of nuclei present in a
zygote is
(i) none
(ii) one
(iii) two
(iv) four


The half-life period of a first order process is \( 1.6 \mathrm{min} \). It will be \( 90 \% \)
complete in:
A. 5.3 min
B . 10.6 min
c. 43.3 min
D. 99.7 min


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


The electron configuration for \( C u \) is \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{1} 3 d^{10} \)
How many inner core electrons does
copper contain?
\( \mathbf{A} \cdot \mathbf{1} \)
B . 10
c. 18
D. 28


Two cells of ends \( E_{1} \) and \( E_{2}\left(E_{1}>E_{2}\right) \)
are connected as shown In figure. When a potentiometer is connected between \( A \) and \( B \), the balancing length of the potentiometer wire is \( 300 \mathrm{cm} . \) On connecting the same potentiometer between \( A \) and \( C, \) the balancing length is \( 100 \mathrm{cm} . \) The ratio I is \( \frac{E_{1}}{E_{2}} \) is
A . 3: 1
B. 1: 3
\( c \cdot 2: 3 \)
D. 3: 2


In a class, the number of girls is \( 20 \% \)
more than that of boys. The strength of the class is \( 66 . \) If 4 more girls are
admitted to the class, what will be the
ratio of the number of boys to that of the girls?
A .3: 4
B. 5: 2
c. 1: 3
D. 2: 7


The hybrid orbital of the central atom in
\( A l F_{4}^{-} \) is:
\( \mathbf{A} \cdot s p \)
B . \( s p^{2} \)
\( \mathbf{c} \cdot s p^{3} \)
D. \( d s p^{2} \)


The phenomenon of interference is
shown by
A. longitudinal mechanical waves only
B. transverse mechanical waves only
C. non-mechanical transverse waves only
D. All of the above


\( \lim _{x \rightarrow 2} \frac{x^{7}-128}{x^{5}-32}= \)
A \( \cdot \frac{5}{28} \)
в. \( \frac{7}{5} \)
c. \( \frac{28}{5} \)
D. 5 \( \overline{7} \)


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


For \( \tan ^{-1}\left(\frac{1-x}{1+x}\right), 0 \leq x \leq 1 \)
What is the sum of the smallest and the
largest values of function.
A \( \cdot \frac{\pi}{4} \)
в. \( \frac{\pi}{2} \)
c. \( \frac{3 \pi}{4} \)
D. \( \frac{3 \pi}{2} \)


If \( \tan \theta, 2 \tan \theta+2,3 \tan \theta+3 \) are in
G.P, then the value of \( \frac{7-5 \cot \theta}{9+4 \sqrt{\sec ^{2} \theta-1}} \)
is
A \( \cdot \frac{12}{5} \)
в. \( \frac{-33}{28} \)
c. \( \frac{33}{100} \)
D. \( \frac{12}{13} \)


The equilibrium constant for the
reaction, \( \boldsymbol{C H}_{3} \boldsymbol{C O O H}(\boldsymbol{l})+ \)
\( \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O} \boldsymbol{H}(\boldsymbol{l}) \rightleftharpoons \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C O O} \boldsymbol{C}_{2} \boldsymbol{H}_{5}(\boldsymbol{l})+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O}(l) \) is \( 4 . \) What will be the
composition of the equilibrium mixture
when 1 mole of acetic acid is taken
along with 4 moles of ethyl alcohol?


During lightning, the oxygen present in the atmosphere is converted
into
A. ozone
B. nascent oxygen
c. oxygen atoms
D. None of the above


Ellingham diagram represents change
of:
A. \( \Delta G \) with temperature
B. \( \Delta H \) with temperature
c. \( \Delta G \) with pressure
D. \( (\Delta G-T \Delta S) \) with temperature


Assertion
Pulmonary circulation consists of flow of deoxygenated blood from right ventricle to the lungs and flow of oxygenated blood from lungs to the left atrium.
Reason
Systemic circulation consists of flow of
oxygenated blood from the left ventricle to all parts of the body and deoxygenated blood from different parts to right atrium.
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


When the following is added to \( 20 \mathrm{ml} \) of
\( 0.1 \mathrm{M} C H_{3} C O O H+20 \mathrm{ml} \) of
\( \boldsymbol{C H}_{3} \boldsymbol{C O O N a} . \) The pH of the solution
does not change:
A. \( 10 \mathrm{ml} \) of \( 0.1 \mathrm{M} C \mathrm{CH}_{3} \mathrm{COOH} \).
B . 10 \( \mathrm{ml} \) of \( 0.1 \mathrm{M} C \mathrm{CH}_{3} \mathrm{COONa} \)
c. \( 10 \mathrm{ml} \) of water
D. 20 mI of 0.2 M \( C H_{3} \) COOH


If \( f(x)=\frac{a^{x}}{x^{a}} \) then \( f^{\prime}(a)= \)
A. \( \log a-1 \)
B. \( \log a-a \)
\( \mathbf{c} \cdot a \log a-a \)
D. a log \( a+a \)


If \( A \) is a \( 3 x 3 \) non singular matrix and
\( |\boldsymbol{a} \boldsymbol{d} \boldsymbol{j} \boldsymbol{A}|=|\boldsymbol{A}|^{x},|\boldsymbol{a} \boldsymbol{d} \boldsymbol{j}(\boldsymbol{a} \boldsymbol{d} \boldsymbol{j} \boldsymbol{A})|= \)
\( |\boldsymbol{A}|^{y},\left|\boldsymbol{A}^{-1}\right|=|\boldsymbol{A}|^{z} \) then the values of
\( \mathbf{x}, \mathbf{y}, \mathbf{z}, \) in descending order
A. \( \mathrm{x}, \mathrm{Y}, \mathrm{z} \)
в. Z, Y, х
c. \( \mathrm{z}, \mathrm{x}, \mathrm{y} \)
D. Y, x, z


Find the sum of Arithmetic
progressions of 20 terms \( 1,5,9,13, \dots . \) Also find last term.


Represent follow complex no. in polar
form.
\( \boldsymbol{z}=-\mathbf{1}+\sqrt{\mathbf{3}} \boldsymbol{i} \)


Casparian strips are present in
of the root.
A. Epiblema
B. cortex
c. Pericycle
D. Endodermis


The correct order of increasing acid strength of the compounds:
\( (A) C H_{3} C O_{2} H \)
(B) \( M e O C H_{2} C O_{2} H \)
\( (\mathrm{C}) \mathrm{C} \boldsymbol{F}_{3} \boldsymbol{C O}_{2} \boldsymbol{H} \)
(D) \( \left(C H_{3}\right)_{2} C C O O H: \)
A. \( b<d<a<c \)
в. \( d<a<c<b \)
c. \( d<a<b<c \)
D. \( a<d<c<b \)


ZW method of sex determination is
applicable to
A. Birds
B. Fish
c. Butterfly
D. All of the above


The nitrogen atoms in \( N H_{3}, N H_{2}^{-} \) and
\( N H_{4}^{+} \) are all surrounded by eight electrons. When these species
are arranged according to \( H N H \) bond angle, the correct order is :
A \( . N H_{3}<N H_{2}^{-}<N H_{4}^{+} \)
B. \( N H_{4}^{+}<N H_{2}^{-}<N H_{3} \)
C \( . N H_{3}<N H_{4}^{+}<N H_{2}^{-} \)
D. \( N H_{2}^{-}<N H_{3}<N H_{4}^{+} \)


\( x^{3}-15 x^{2}+59 x-45=0 \) solve for \( x \)


Why R streamlines never intersect.


The energy of electron is maximum at:
A. nucleus
B. ground state
C. first excited state
D. infinite distance from the nucleus