An infinite sheet carrying a uniform surface charge density \( \sigma \) lies on the \( x y- \) plane. The work done to carry a charge \( q \) from the point \( \vec{A}=a(\hat{i}+2 j+3 \hat{k}) \) to point \( \vec{B}=a(\hat{i}-2 \hat{j}+6 \hat{k}) \) (where a is
constant with the dimension of length
and \( \varepsilon_{0} \) is the permittivity of free space)
is :
A. \( \frac{3 \sigma a q}{2 \varepsilon_{0}} \)
В \( \cdot \frac{2 \sigma a q}{\varepsilon_{0}} \)
c. \( \frac{5 \sigma a q}{2 \varepsilon_{0}} \)
D. \( \frac{3 \sigma a q}{\varepsilon_{0}} \)


A ray of light falls on a transparent glass plate \( (\mu=\sqrt{3}) \) part of it is
reflected and part is refracted. If the reflected and refracted
rays are perpendicular to each other
then the angle of incidence is
\( A \cdot 30 \)
B. 45
\( c \cdot 60 \)
D. 90


Colloidal particles are filtered through filter paper.
A . True
B. False


Cinnabar is
A. Нg S
в. \( H g O \)
c. \( H g C l \)
D. НgО.Н \( g \)С\( l \)


Let \( \boldsymbol{f}(\boldsymbol{x}) \) be defined \( \forall \boldsymbol{x} \in \boldsymbol{R} \) and
continuous.
\( \operatorname{Let} \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{y})-\boldsymbol{f}(\boldsymbol{x}-\boldsymbol{y})=\boldsymbol{4} \boldsymbol{x} \boldsymbol{y} \forall \boldsymbol{x}, \boldsymbol{y} \in \)
\( \boldsymbol{R} \) and \( \boldsymbol{f}(\mathbf{0})=\mathbf{0}, \) then \( \boldsymbol{f}(\boldsymbol{x})<\mathbf{2} \boldsymbol{x}+\mathbf{3} \) will
have solution:
A. (-1,3)
B . \( (1-\sqrt{5}, 1+\sqrt{5}) \)
c. \( (1-\sqrt{5},-1) \cup(3,1+\sqrt{5}) \)
D. \( (3,1+\sqrt{5}) \)


A body is projected from the ground with a velocity \( v=(3 \hat{i}+10 \hat{j}) m s^{-1} \) The
maximum height attained and the range of the body respectively are (given \( \boldsymbol{g}=\mathbf{1 0 m} \boldsymbol{s}^{-2} \mathbf{)} \)
A. \( 5 \mathrm{m} \) and \( 6 \mathrm{m} \)
B. 3 m and 10 \( \mathrm{m} \)
\( c .6 \mathrm{m} \) and \( 5 \mathrm{m} \)
D. 3 m and 5 m


When two capacitors are joined in series the resultant capacity is \( 2.4 \mu F \) and when the same two are joined in parallel the resultant capacity is \( 10 \mu F \). Their individual capacities are :
\( \mathbf{A} \cdot 7 \mu F, 3 \mu F \)
в. \( 1 \mu F, 9 \mu F \)
\( \mathbf{c} \cdot 6 \mu F, 4 \mu F \)
D. \( 8 \mu F, 2 \mu F \)


For any real number a, prove that \( a \times \) \( \mathbf{0}=\mathbf{0} \)


The commonest thing which can respire in the absence of oxygen is
A. Yeast.
B. Clostridium.
c. Muscles.
D. All of the above.


If each angle of a regular polygon is
\( 135^{\circ}, \) how many sides does it have?
\( A \cdot 6 \)
B. 7
\( c \cdot 8 \)
D. 9


If \( |\overrightarrow{\boldsymbol{a}} \cdot \overrightarrow{\boldsymbol{b}}|=\sqrt{\mathbf{3}}|\overrightarrow{\boldsymbol{a}} \times \overrightarrow{\boldsymbol{b}}|, \) then the angle
between \( \vec{a} \) and \( \vec{b} \) is :-
A \( \cdot \frac{\pi}{6} \)
B.
\( c \cdot \frac{\pi}{3} \)
D.


A uniformly charged solid sphere or
radius \( \boldsymbol{R} \) has potential \( \boldsymbol{V}_{\mathbf{0}} \) (measured
with respect to \( \infty \) ) on its surface. For
this sphere the equipotential surfaces with potentials \( \frac{3 V_{0}}{2}, \frac{5 V_{0}}{4}, \frac{3 V_{0}}{4}, \frac{V_{0}}{4} \)
have radius \( \boldsymbol{R}_{1}, \boldsymbol{R}_{2}, \boldsymbol{R}_{3} \) and \( \boldsymbol{R}_{4} \)
respectively. Then
A \( \cdot R_{1}=0 \) and \( R_{2}\left(R_{4}-R_{3}\right) \)
B . \( R_{1} \neq 0 \) and \( \left(R_{1}-R_{1}\right)>\left(R_{4}-R_{3}\right) \)
c. \( R_{1}=0 \) and \( R_{2}>\left(R_{4}-R_{3}\right) \)
D. none of these


Butylated hydroxy toluene is antioxidant why?


When excess of \( C_{2} H_{5} O H \) at \( 140^{0} C \)
reacts with concentrated \( H_{2} S O_{4}, \) the
product obtained is:
A. diethyl ether
B. diethyl sulphate
c. ethylene
D. ethylene hydrogen sulphate


Find the circumference of a circle
whose radius is \( 35 \mathrm{cm} \)


Rusting of iron is prevented by
A. applying paint
B. keeping in contact with water
c. keeping in contact with oxygen
D. reacting with acid


Assertion
\( N C l_{3} \) undergoes hydrolysis
Reason
Chlorine possesses vacant ' \( d \) orbitals
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of the following pair have almost
similar size
A \( \cdot T i_{22} \) and \( Z r_{4} \)
B. \( N b_{41} \) and \( T a_{73} \)
C \( \cdot Y_{39} \) and \( L a_{57} \)
D. \( C a_{20} \) and \( I r_{r} \)


Assertion
A brass tumbler feels much colder than
a wooden tray on a chilly day.
Reason
The thermal conductivity of brass is more than the thermal conductivity of
wood.
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


\( 200 g \) of a cold ball at \( 20^{\circ} \mathrm{C} \) is dropped in
an equal amount of water at \( 80^{\circ} \mathrm{C} \). The
resulting temperature is \( 60^{\circ} \mathrm{C} \). This means that specific heat of solid is.
A. One fourth of water
B. One half of water
C. Twice of water
D. Four times of water


If \( \boldsymbol{x} \in \boldsymbol{R}, \) find the minimum value of the
expression \( 3^{x}+3^{1-x} \)
\begin{tabular}{l}
A \( 3 \sqrt{2} \) \\
\hline
\end{tabular}
B. \( 2 \sqrt{3} \)
\( c \cdot 3 \sqrt{3} \)
D. none of these


Which of the following factor does not affect an enzyme's activity?
A. pH levels
B. Inhibitors
c. Temperature
D. Enzyme cofactors
E. Enzyme concentration


Units of parts per million (ppm) or parts per billion (ppb) are often used to describe the concentrations of solutes
in very dilute solutions. The units are defined as the number of grams of solute per million or per billion grams of solvent. Bay of Bengal has 1.89 ppm of
lithium ions. The molality of \( L i^{+} \) in this
water is (atomic number of \( L i=7 \) ) :
A \( \cdot 1.5 \times 10^{-4} \mathrm{m} \)
в. \( 1.7 \times 10^{-4} \mathrm{m} \)
\( \mathbf{c} \cdot 2.5 \times 10^{-4} m \)
D. \( 2.7 \times 10^{-4} \mathrm{m} \)


Define quality factor of resonance in
series LCR circuit. What is its Sl unit?


Which of the following is not tetrahedral in shape?
\( \mathbf{A} \cdot N H_{4}^{+} \)
в. \( \operatorname{Si} C l_{4} \)
c. \( S F_{4} \)
D. \( S O_{4}^{2-} \)


Of the following radiation emissions,
which has no mass??
A. Alpha particle
B. Beta particle
c. Proton
D. Neutron
E. Gamma ray


Coal found in deeper strata of earth is:
A . goodd
B. badd
c. can't say
D. both A and B


ABCDEF is a regular hexagon with
centre \( 0 . \) If area of triangle 0 AB is
\( 9 c m^{2}, \) find the area of the hexagon.


An aqueous solution containing a nonvolatile solute is heated in an open
vessel till the boiling point is reached. Thereafter, the boiling is continued and the temperature and the vapour
pressure of the solution are recorded at
\( 5 \min , 10 \) min, and 15 min. The
corresponding temperatures and
pressures are \( \boldsymbol{T}_{5}, \boldsymbol{T}_{10}, \boldsymbol{T}_{15} \) and
\( P_{5}, P_{10}, P_{15}, \) respectively.
The correct relationship among them is:
A \( \cdot T_{5}<T_{10}<T_{15} \) and \( P_{5}=P_{10}=P_{15} \)
B . \( T_{5}=T_{10}=T_{15} \) and \( P_{5}=P_{10}=P_{15} \)
C \( \cdot T_{5}=T_{10}=T_{15} \) and \( P_{5}<P_{10}<P_{15} \)
D. \( T_{5}<T_{10}<T_{15} \) and \( P_{5}<P_{10}<P_{15} \)


Find the quotient and remainder when
\( p(x)=x^{3}-3 x^{2}+5 x-3 \) is divided by
\( g(x)=x^{2}-2 \)


A spherical rigid ball is released from rest and starts rolling down an inclined
plane from height \( h=7 m \), as shown in
the figure, It hits a block at rest on the horizontal plane (assume elastic collision). If the mass of the both the
ball and the block is \( m \) and the ball is
rolling without sliding, then the speed of the after collision is close to :
\( A \cdot 6 m / s \)
в. \( 8 m / s \)
c. \( 10 m / s \)
D. \( 12 m / s \)


The separation between the two nearest
points on the string that do not move at all is
A. 0.163 m n \( m \).
в. 0.325 т
c. 0.202 m
D. 0.244 m
E. none


Matrices \( A \) and \( B \) satisfy \( A B=B^{-1} \) where \( \boldsymbol{B}=\left[\begin{array}{cc}2 & -1 \\ 2 & 0\end{array}\right], \) then
find without finding \( B^{-1}, \) the value of \( K \)
for which \( \boldsymbol{K} \boldsymbol{A}-\mathbf{2} \boldsymbol{B}^{-\mathbf{1}}+\boldsymbol{I}=\boldsymbol{O} \)


If \( \frac{\left(a^{2}+1\right)^{2}}{2 a-i}=x+i y, \) then \( x^{2}+y^{2} \) is equal to
\( ^{\mathrm{A}} \cdot \frac{\left(a^{2}+1\right)^{4}}{4 a^{2}+1} \)
B. \( \frac{(a+1)^{2}}{4 a^{2}+1} \)
c. \( \frac{\left(a^{2}-1^{2}\right)}{\left(4 a^{2}-1\right)^{2}} \)
D. None of these


Arithmetic mean of 2 and 8 is
\( \mathbf{A} \cdot \mathbf{5} \)
B. 10
c. 16
D. 3.2


the sum of the first 25 terms of natural
numbers
A. 325
в. 675
\( c .625 \)
D. 552


The half-life of the source is 30 min.
What correct readings would you expect to obtain, with no absorber present, one hour after original readings were taken?


Ducts of Bellini open in
A. Minor calyx
B. Major calyx
c. Renal pyramid
D. Renal sinus


Identify the heteropolymer from the list given below.
A. Polythene
B. Nylon-6
c. Teflon
D. Nylon-6,6


Fill in the blank.
Thermodynamics is the branch of science concerned with
and their relation to
energy and work.
A. heat, temperature
B. temperature, pressure
c. heat, volume
D. volume, pressure


The term blastogenesis is used for
A. Formation of blastula
B. Formation of blastocoel
c. Formation of blastomeres
D. Asexual reproduction


The number of terms in a sequence
\( 6,12,24, \dots .1536 \) represents a
A . arithmetic progression
B. harmonic progression
c. geometric progression
D. geometric series


Which of the following cannot be considered an example of precession?
A. A spinning top
B. A spinning wheel
c. Rolling ball
D. Spinning of the earth


Find the locus of complex number \( \boldsymbol{z}=\boldsymbol{x}+\boldsymbol{i} \boldsymbol{y} \) if \( |\boldsymbol{z}+\boldsymbol{4} \boldsymbol{i}|+|\boldsymbol{z}-\boldsymbol{4} \boldsymbol{i}|=\mathbf{1 0} \)


Which of the following is \( s p^{3} \) -hybridized
\( ? \)
A \( \cdot N H_{3} \)
в. \( B e H_{2} \)
c. \( P C l_{5} \)
D. \( A l C l_{3} \)


Identify the dimension of electric potential,
A \( \cdot L^{2} M T^{-3} I^{-1} \)
B . \( L^{1} M T^{-2} I^{-1} \)
\( \mathbf{c} \cdot L^{-2} M T^{-2} I^{-1} \)
D. none of the above


In a circular current-carrying conductor if the current is flowing in anticlockwise direction, then for an observer facing the coil, the coil behaves like a
A. North pole
B. South pole
c. can be north or south pole
D. Neither north nor south pole


At a time \( t=t_{0}, \) the string is suddenly
broken and the balls are released to
move. Mark the incorrect statement.
Consider the momentum and angular momentum after and before string
breaks.
A. Total angular momentum of system is conserved in table reference frame as well as center of mass reference frame
B. In the centre of mass frame, angular momentum of each of the mass is separately conserved
c. Total linear momentum of system is conserved in table reference frame
D. In the table frame momentum of individual balls is ss conserved
E. Answer required


The extension produced in a wire by the application of a load is \( 3.0 \mathrm{mm} \). The
extension produced in a wire of the same material and length but half the radius by the same load is:
\( \mathbf{A} \cdot 5 \mathrm{mm} \)
B. \( 9 \mathrm{mm} \)
\( c .12 \mathrm{mm} \)
D. \( 13 \mathrm{mm} \)


Assertion
Zone refining method is used to produce pure metals which are used as
semiconductors.
Reason
Semiconductors are used in highly pure
form.
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


Salts of calcium and magnesium like
cause harness of
water
This question has multiple correct options
A. bicarbonates
B. chlorides
c. sulphates
D. phosphates


The percentage of water in a human body is:
A . 80\%
B. 70\%
c. \( 60 \% \)
D. 50\%


If the area of rectangle is given by \( x^{2}+ \) \( 5 x+6 \) then write the possible length
and breadth.


Is the sperm or the egg responsible for the sex of the chicks?


What is anodising? Give its
applications.


Maturation of genetically engineered
proinsulin into insulin
A. Joining of C-peptide
B. Removal of C-peptide
c. Removal of Disulphide bridge
D. All of the above


Which of these organisms reproduce in the same way as yeast?
A. Hydra
B. Amoeba
c. starfish
D. Flatworm


Give band gap Eg value for conductor,
insulator and semiconductor?
A. Conductor \( <1 M e V \), insulation \( \geq 6 e V \), semiconductor
\( \approx 8 e V \)
B. Conductor \( <1 M e V \), insulation \( \geq 6 e V \), semiconductor
\( \approx 1 e V \)
C. Conductor \( <2 M e V \), insulation \( \geq 6 e V \), semiconductor
\( \approx 1 e V \)
D. Conductor< \( 1 \mathrm{MeV} \), insulation \( \geq 7 \mathrm{eV} \), semiconductor
\( \approx 1 e V \)


A solid compound "A" consists of simple ions. Nature of the bond present in A will be:
A . ionic
B. covalent
c. molecular
D. hydrogen bond


Which stages of cell division do the
following figures \( A \) and \( B \) represent
respectively?
A. Prophase and anaphase
B. Metaphase and telophase
C. Telophase and metaphase
D. Late Anaphase and prophase


A boy has two spare light bulbs in his drawer. One is marked \( 240 \mathrm{V} \) and \( 100 \mathrm{W} \)
and the other is marked \( 240 \mathrm{V} \) and \( 60 \mathrm{W} \)
He tries to decide which bulb should be
used and why??
A. The 60 W light bulb has more resistance and therefore burns more brightly
B. The 60W light bulb has less resistance and therefore burns less brightly
c. The 100 w bulb has more resistance and therefore burns more brightly
D. The 100 W bulb has less resistance and therefore burns less brightly


Two different liquids are flowing in two tubes of equal radius. The ratio of
coefficient of viscosity of liquids is 52:
49 and the ratio of their densities is
\( 15.6: 1, \) then the ratio of their critical
velocities will be:
A . 0.068
B. 0.68
\( c \cdot 6.8 \)
\( D \cdot 68 \)


A capacitor is charged by a cell of emf \( \boldsymbol{E} \)
and the charging battery is then removed. If an identical capacitor is now inserted in the circuit in parallel with the previous capacitor, the potential difference across the new capacitor is :
\( A \cdot 2 E \)
в. \( E \)
c. \( E / 2 \)
D. zero


The e.m.f of the cell obtained by combining Zn and Cu electrode of a Daniel cell with \( \mathrm{N} \) calomel electrode in
two different arrangements are \( 1.083 \mathrm{V} \)
and \( 0.018 \mathrm{V} \) respectively at \( 25^{\circ} \mathrm{C} \). If the standard reduction potential of \( \mathrm{N} \)
calomel electrode is \( 0.28 \mathrm{V} \) the emf
(V) of Daniel cell is (write the
value to the nearest integer)


A block of mass \( 10 ~ k g \) is held at rest
against a rough vertical wall \( [\boldsymbol{\mu}=\mathbf{0 . 5}] \)
under the action a force \( F \) as shown in
figure. The minimum value of \( \boldsymbol{F} \)
required for it is \( \left(\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} / \boldsymbol{s}^{2}\right) \)
A .162 .6
B. \( 89.7 N \)
c. \( 42.7 N \)
D. 95.2


Water is filled upto same height in two
identical closed containers \( A \) and \( B \).
Container \( A \) has vacuum over the water
while container \( B \) has air over the
water. At the same depth of both the
containers there is an opening on which identical balloons \( A \) and \( B \) are attached
as shown in the figure given below. Then
A. Balloon - \( A \) will bulge more than balloon - \( B \)
B. Balloon - \( B \) will bulge more than balloon - \( A \)
c. Both the balloons will bulge equally
D. None of the balloons will bulge


Which of the following kinds of venation is present in banana?
A . Reticulate unicostate
B. Reticulate multicostate
c. parallel unicostate
D. parallel multicostate


Describe the construction and working theory of cyclotron.


Cessation of menstrual cycle in a
woman is called
A. Lactation
B. Ovulation
c. Menopause
D. Parturition


Solve the following equations by graphical method \( 2 x+3 y=0 \)


The velocity and acceleration vectors of a particle undergoing circular motion \( \operatorname{are} \overrightarrow{\boldsymbol{v}}=2 \hat{\boldsymbol{i}} \boldsymbol{m} / \boldsymbol{s} \) and \( \overrightarrow{\boldsymbol{a}}=\boldsymbol{2} \hat{\boldsymbol{i}}+ \)
\( 4 \hat{j} m / s^{2} \) respectively at an instant of
time. The radius of the circle is
A . \( 1 m \)
B. \( 2 m \)
\( c .3 m \)
D. \( 4 m \)


Which combination is used in fruit
ripening?
A. \( 80 \% C H_{4}+20 \% O_{2} \)
в. \( 80 \% C_{2} H_{4}+20 \% \mathrm{CO}_{2} \)
c. \( 80 \% \mathrm{CO}_{2}+20 \% \mathrm{C}_{2} \mathrm{H}_{4} \)
D. \( 80 \% C H_{4}+20 \% C O_{2} \)


Assertion
The kinetic energy of electrons in a metallic wire will increase, if the
temperature of the wire is increased
Reason
On increasing temperature, conductivity of metallic wire decreases
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


Arrange the following in the increasing order of their ability as a leaving group:
\( \boldsymbol{C F}_{3} \boldsymbol{S O}_{3}^{-}, \boldsymbol{C H}_{3} \boldsymbol{S O}_{3}^{-} \boldsymbol{a n d} \boldsymbol{C H}_{3} \boldsymbol{C O O} \)
A \( \cdot C H_{3} S O_{3}^{-}>C F_{3} S O_{3}^{-}>C H_{3} C O O^{-} \)
в. \( C F_{3} S O_{3}^{-}>C H_{3} S O_{3}^{-}>C H_{3} C O O \)
c. \( C F_{3} S O_{3}^{-}>C H_{3} C O O^{-}>C H_{3} S O_{3}^{-} \)
D. \( C F_{3} S O_{3}^{-}<C H_{3} S O_{3}^{-}<C H_{3} C O O^{-} \)


A body is thrown vertically upwards
from ground with a speed of \( 10 m / s . \) If
coefficient of restitution of ground, \( e= \)
1/2. If the total distance travelled by the
time it almost stops is \( \frac{33+x}{3} m, \) find the value of \( x \)


A cannon of mass \( 10 \times 10^{3} k g \) is
rigidly bolted to the earth so it can recoil only by a negligible amount. The cannon fires a \( 2.1 \times 10^{3} k g \) shell
horizontally with an initial velocity of \( 550 m / s . \) Suppose the cannon is then
unbolted from the earth and no external force hinder its recoil. What would be the velocity (in \( \boldsymbol{m} / \boldsymbol{s} \) ) of a shell fired horizontally by the loose cannon? (Hint:
In both cases assume that the burning gunpowder imparts the same kinetic energy to the system.)


lonisation constant of \( C H_{3} C O O H \) is
\( 1.7 \times 10^{-5} \) and concentration of \( H^{+} \)
ions is \( 3.4 \times 10^{-4} . \) Then find out initia
concentration of \( \boldsymbol{C H}_{3} \) COOH
molecules:
A \( .3 .4 \times 10^{-4} \)
B . \( 3.4 \times 10^{-3} \)
c. \( 6.8 \times 10^{-4} \)
D. \( 6.8 \times 10^{-3} \)


The perpendicular from the centre of a circle to a chord bisects the chord.


Simplify:
\( \left(\left(3 x^{2}-2 a x\right)+3 a^{2}\right)^{3} \)


Which of the following are biopolymers? This question has multiple correct options
A. Nucleic acids
B. Leather
c. Baklite
D. Orlon


Define unit vector.


The displacements is given by \( \boldsymbol{x}=\mathbf{2}+ \)
\( 4 t+5 t^{2} . \) Find the value of
instantaneous acceleration?


Evaluate \( \int \sin x \sin (\cos x) d x \)


n given figure, \( \angle B A C=90^{\circ} \) and
segment \( A D \perp B C . \) Prove that \( A D^{2}= \)
\( \boldsymbol{B} \boldsymbol{D} \times \boldsymbol{D} \boldsymbol{C} \)


Which of the following statements are wrong w.r.t the specific resistance of
wire?
This question has multiple correct options
A. It varies with its length
B. It varies with its cross-section
c. It varies with its mass
D. It varies with nature of material


Fill in the blanks with appropriate
words.
The function of a ureter is........... of urine.


The truth table given below is for (A and B are the inputs, \( Y \) is the output)
\( A B Y \)
001
011
101
110
A. NOR
B. AND
c. хок
D. NAND


Octane burns in air is
A. Decomposition
B. Synthesis
c. combustion
D. single replacement
E . Double replacement


Keeping the pressure constant, the volume of a given mass of any gas increases or decreases by \( \frac{1}{273} \) of its
volume at \( \boldsymbol{O}^{\circ} \boldsymbol{C} \) for each \( \mathbf{1}^{\circ} \) rise in
temperature. This law is known as:
A. Boyle's law
B. Charles's law
c. Gay-lussac's law
D. None of the above


A \( 10 \% \) solution (by mass) of sucrose in water has a freezing point of \( 269.15 K \)
Calculate the freezing point of \( 10 \% \) glucose in water if the freezing point of
pure water is \( 273.15 K \)
(Given : molar mass of sucrose \( = \)
\( 342 g \) mol \( ^{-} ?, \) Molar mass of glucose \( = \)
\( \left.180 g m o l^{-1}\right) \)
A. 275. 53 K
B. 265. 53 K
c. २७१. 32 \( \mathrm{K} \)
D. 282.43 K


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


The given graph shows the number of
toy cars some children have. Who has
thrice as many toy cars as the total
number of toy cars Samay and Kiara have?
A. Trishu
B. Kiara
c. Pratik
D. samay


Chlorophyll a, chlorophyll d and phycoerythrin pigments are found in
A. Cyanophyceae
B. Bacillariophyceae
c. Rhodophyceae
D. Chlorophyceae


In the expression for Boyle's law, the product 'PV' has dimensions of
A. Force
B. Impulse
c. Energy
D. Momentum


Write the differences between:
Blood and Lymph


Find the surface area of a sphere of diameter: \( 21 \mathrm{cm} \)


If \( \tan B=\frac{2 \sin A \sin C}{\sin (A+C)} \) then
\( \tan A, \tan B, \tan C \) are in
A . A.
в. G.
c. н.
D. AGP


For which of the following substances, the magnetic susceptibility is independent of temperature?
A. diamagnetics only
B. paramagnetics only
c. ferromagnetics only
D. diamagnetics and paramagnetics both


A ball is dropped downwards. After 2 second another ball is dropped downwards from the same point. What
is the distance between them after 3
second?
\( A \cdot 25 \mathrm{m} \)
B. 20 \( m \)
\( c \cdot 50 m \)
D. 9.8 \( m \)


Plane of both loops circle and ellipse are held perpendicularly to the uniform magnetic field of strength B, Compare the magnetic flux passing through both
loops if \( \phi_{c}, \) the magnetic flux through
the circular loop and \( \phi_{E}, \) the magnetic
flux through the elliptical loop given
that area of both loops are same.
\( \mathbf{A} \cdot \phi_{c}=2.5 \phi_{E} \)
B \( \cdot \phi_{c}=\sqrt{2.5} \)
\( \mathbf{c} \cdot \phi_{c}=\phi_{E} \)
\( \mathbf{D} \cdot \phi_{E}=\sqrt{2.5} \phi_{c} \)
E \( \cdot \phi_{E}=2.5 \phi_{c} \)


Assertion
The stress-strain relationship in elastic region need not be linear and can be
non-linear.
Reason
Steel has non linear,profile in elastic
zone
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The most widely used semiconductors
are
(i) silicon
(ii) germanium
(iii) phosphorus (iv) arsenic
A \( \cdot \) (i) and (ii)
B. (ii) and (iii)
c. (iii) and (iv)
D. (i), (ii), (iv) (iii)


\( 80 \% \) of a first order reaction was
completed in 70 min. How much it will take for \( 90 \% \) completion of a reaction?
A. 100 min
B. 110 min
c. \( 120 \mathrm{min} \)
D. None of these


If \( 5 \% \) of the energy supplied to a bulb is radiated as visible light, the number of visible quanta emitted per second by a
100W bullb, assuming the wavelength
of visible light to be \( 5.6 \times 10^{-5} \mathrm{cm}, \) is
A. \( 1.4 \times 10^{19} \)
B . \( 1.4 \times 10^{20} \)
\( \mathrm{c} \cdot 2 \times 10^{19} \)
D. \( 2 \times 10^{20} \)


Sound cannot travel through
A. vacuum
B. solids
c. liquids
D. gases


In hydrosere succession, which stage
comes just before sedge meadow stage?
A. Rooted submerged stage
B. Phytoplankton stage
c. Reed swamp stage
D. climax stage


The element which could be extracted
by electrolytic reduction of its oxide dissolved in a high-temperature melt is:
A. sodium
B. magnesium
c. fluorine
D. aluminium


The minimum value of \( p x+q y \) when
\( \boldsymbol{x} \boldsymbol{y}=\boldsymbol{r}^{2} \) is
A \( .2 r \sqrt{p q} \)
B. \( r \sqrt{p q} \)
c. \( r \sqrt{q / p} \)
D. None of the above


Find \( \angle C \) in the figure if \( \overline{A B} \| \overline{D C} \)


Assertion
Dipole moment of \( C-F \) bond is less
than that of \( C-C l \) bond
Reason
\( \boldsymbol{F} \) is more electronegative than \( \boldsymbol{C l} \)
Read the above assertion and reason and
choose the correct option regarding it.
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 circuit shown in the figure, the
ammeter reading is:
\( A \cdot 0.8 A \)
B. 1.2 A
\( c \cdot 2 A \)
D. \( 0.4 \mathrm{A} \)


Adj \( \left[\begin{array}{ccc}1 & 0 & 2 \\ -1 & 5 & -2 \\ 0 & 2 & 1\end{array}\right]= \)
\( \left[\begin{array}{ccc}\mathbf{9} & \boldsymbol{a} & \mathbf{- 2} \\ \mathbf{- 1} & \mathbf{1} & \mathbf{0} \\ \mathbf{- 2} & \mathbf{2} & \boldsymbol{b}\end{array}\right] \Rightarrow\left[\begin{array}{ll}\boldsymbol{a} & \boldsymbol{b}\end{array}\right]= \)
\( \left.\begin{array}{ll}\text { A. }[-4 & 5\end{array}\right] \)
B \( \cdot\left[\begin{array}{ll}-4 & -1\end{array}\right] \)
\( \mathbf{c} \cdot\left[\begin{array}{ll}4 & 1\end{array}\right] \)
D・[4 -1


Gases can easily change volume
because
A. little attraction between particles
B. little spacing between particles
C . huge attraction between particles
D. none of above


Anhydride of nitrous acid is:
в. \( N O \)
c. \( N_{2} O_{3} \)
D. \( N_{2} O_{4} \)


Which of the following is most reactive towards electrophilic nitration?
A. Toluene
B. Benzene
c. Benzoic acid
D. Nitrobenzene


0.614 can be represented as
A \( \cdot \frac{61.4}{10} \)
в. \( \frac{614}{1000} \)
c. \( \frac{614}{10} \)
D. None of the above


toppr
Q Type your question
velocity of the chain suddenly and without frictional resistance or
interference from the support or from
adjacent links Choose the incorrect
statement (when \( x=0, \text { then } v=0) \)
(length of the chain is L and p is the
mass per unit length of the chain)
A \( \cdot \) the velocity v of the chain as a function of \( x \) is \( \sqrt{\frac{2 g x}{3}} \)
B. the acceferation of a of the falling chain as a function
fris \( \frac{g}{3} \)
C. the energy Q lost from the system as the last link leaves the plafform is \( \frac{p g L^{2}}{6} \)
D. tension at the middle point of falling chain is \( \frac{p g x}{3} \)


A ball \( A \) is moving with velocity \( 5 m / s \) collides elastically with another identical ball \( B \) which is initially at rest
such that the velocity of \( B \) after the
collision makes an angle of \( 37^{\circ} \) with the
initial velocity of \( A \). Then the
INCORRECT statement is :
A. speed of \( A \) after collision is \( 3 m / s \)
B. Speed of \( B \) after collision is \( 4 m / s \)
c. Balls \( A \) and \( B \) move at right angle after collision
D. Kinetic energy is not conserved as the collision is not head on


\( \mathbf{A} \)
\( 2.0 \mathrm{cm} \) long object is placed perpendicular to the principal axis of a concave mirror. The distance of the
object from the mirror is \( 30 \mathrm{cm}, \) and its image is formed \( 60 \mathrm{cm} \) from the mirror
on the same side of the mirror as the
object. Find the height of the image formed:
A. 3 cm
в. 4 ст
\( c .5 \mathrm{cm} \)
D. \( 8 \mathrm{cm} \)


The specific heat capacity of a
substance depends on its This question has multiple correct options
A. nature
B. mass
c. rise in temperature
D. Both (2) and (3)


Find the equations to the straight lines which pass through the origin and are
inclined at \( 75^{\circ} \) to the straight line \( (x+y) \sqrt{3}+y-x=a \)


Two thin long wires carry currents \( \boldsymbol{I}_{\mathbf{1}} \)
and \( I_{2} \) along \( x \) -and \( y \) -axes respectively
as shown in figure. Consider the points
only in \( x \) -y plane.
This question has multiple correct options
A. Magnetic field is zero at least at one point in each quadrant
B. Magnetic field can be zero somewhere in the first quadrant
c. Magnetic field can be zero somewhere in the second quadrant
D. Magnetic field is non-zero in second quadrant


The area enclosed by the curves \( x^{2}= \)
\( y, y=x+2 \) and \( x \) -axis is:
A \( \cdot \frac{5}{6} \)
B. \( \frac{5}{4} \)
\( c \cdot \frac{5}{2} \)
D.


A man has 9 friends, 4 boys and 5 girls.
In how many ways can be invite them, if there have to be exactly three girls in
the invites?
A . 320
в. 160
c. 80
D. 200


Two stones \( A \) and \( B \) are projected simultaneously from the top of a \( 100- \)
\( m \) high tower. Stone B is projected
horizontally with speed \( 10 m s^{-1} \). and stone \( A \) is dropped from the tower. Find out the following:
(a) Time of flight of the two stone
(b) Distance between two stones after 3
\( \mathbf{S} \)
(c) Angle of strike with ground


Range of the function \( \boldsymbol{f}(\boldsymbol{x}) \) \( \sqrt{\left|\sin ^{-1}\right| \sin x||-\cos ^{-1}|\cos x|} \)
\( A \cdot\{0\} \)
B. \( [0, \sqrt{\frac{\pi}{2}}] \)
c. \( [0, \sqrt{\pi}] \)
D. none of these


Which of the following compounds has weakest \( C-X \) bond?
A. \( C H_{3} F \)
в. \( C H_{3} C l \)
\( \mathrm{c} . C H_{3} B r \)
D. \( C H_{3} I \)


Name on animal having single circulation of blood and another having double circulation.


Write the option which have more than
three number of hydrogen for hyper conjugation.
This question has multiple correct options
\( A \)
B.
\( c \)
D.


Assertion
\( \ln C_{4} \) plants, photo respiration does not
occur
Reason
\( C_{4} \) plants have a mechanism that
increases the concentration of \( C O_{2} \) at
the enzyme site.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Write the structures of aldehydes that
are obtained on ozonolysis of
(i) but-1-ene and
(ii) but-2-ene


The power dissipated in the circuit
shown in the figure is 30 watts. The
value of R is
A . \( 20 \Omega \)
В. \( 5 \Omega \)
\( c .10 \Omega \)
D. \( 30 \Omega \)


\( 2 K(s)+2 H_{2} O(l) \rightarrow 2 K O H(a q)+ \)
\( \boldsymbol{H}_{2}(\boldsymbol{g}) \)
If 3.0 moles of potassium react with excess water, what volume of hydrogen gas will be produced?
A . \( 1.5 L \)
B. 22.4L
c. \( 67.2 L \)
D. 33.6L


The table below classifies 60 students
in a class according to their heights.
\begin{tabular}{ll}
Height \( (\mathrm{cm}) \) & Number of students \\
\( 140-145 \) & 5 \\
\( 145-150 \) & 8 \\
\( 150-155 \) & 12 \\
\( 155-160 \) & 16 \\
\( 160-165 \) & 11 \\
\( 165-170 \) & 5 \\
\( 170-175 \) & 3 \\
\hline
\end{tabular} Find the median of the amount paid.


Two sources of equal emf are connected to an external resistance R. The internal
resistances of two sources are \( \boldsymbol{R}_{1} \) and
\( \boldsymbol{R}_{2}\left(\boldsymbol{R}_{2}>\boldsymbol{R}_{1}\right) . \) If the potential difference
across the source having internal
resistance \( R_{2} \) is zero, then;
в. \( R=R_{1} R_{2} /\left(R-R_{1}\right) \)
C. \( R=R_{2} \times\left(R_{1}+R_{2}\right) /\left(R_{2}-R_{1}\right) \)
D. \( R=R_{2}-R_{1} \)


Define cell constant. Draw a neat and
well labelled diagram of primary reference electrode.


Grain alcohol is the common name of:
A. propyl alcohol
B. methyl alcohol
c. ethyl alcohol
D. isopropyl alcohol


Three containers are used in a
chemistry lab. All containers have the same bottom area and the same height. A chemistry student fills each of the containers with the same liquid to the maximum volume. Which of the
following is true about the pressure on the bottom in each container?
A \( . P_{1}=P_{2}=P_{3} \)
в. \( P_{1}>P_{2}>P_{3} \)
c. \( P_{1}<P_{2}=P_{3} \)
D. \( P_{1}<P_{2}>P_{3} \)


fungal cell with different parts labelled as \( A, B, C \) and \( D . \) Which of the following statements are true with regard to the
fungal cell structure?
(i) A contains mucopolysaccharides
which are also present in exoskeleton of insects and crustaceans.
(ii) D are usually more than one in number in case of aseptate hyphae.
(iii) Carotenes and xanthophylls are
present in \( C, \) which harvest light energy
for photosynthesis.
(iv) \( \mathrm{B} \) is the reserve food material,
usually stored in the form of starch and
oil.
A. (i) and (ii)
B. (iii) and (iv)
C. (i), (ii) and (iv)
D. (ii), (iii) and (iv)


A wire of resistance 18 ohm is drawn until its radius reduce \( \frac{1}{2} t h \) of its original radius then resistance of the wire is:
\( \mathbf{A} \cdot 188 \Omega \)
B. \( 72 \Omega \)
c. \( 288 \Omega \)
D. \( 388 \Omega \)


Which of the following statements
regarding equilibrium is /are true?
A. Equilibrium constant varies with temperature.
B. Equilibrium constant varies with catalyst.
C. The reaction stops when the equilibrium is reached.
D. The equilibrium constant depends on the concentration of reactants.


Human ears can sense sound wave
travelling in air having wavelength of
A \( \cdot 10^{-3} \mathrm{m} \)
B. \( 10^{-2} \mathrm{m} \)
\( c \cdot 1 m \)
D. \( 10^{2} \mathrm{m} \)


A \( 10 m \) long horizontal wire extends
from North East to South West. It is
falling with a speed of \( 5.0 m s^{-1}, \) at right angles to the horizontal component of the earth's magnetic field, of \( 0.3 x \) \( 10^{-4} W b / m^{2} . \) The value of the induced
emf in wire is:
A \( \cdot 2.5 \times 10^{-3} V \)
В. \( 1.1 \times 10^{-3} V \)
c. \( 0.3 \times 10^{-3} V \)
D. \( 1.5 \times 10^{-3} V \)


Which one of the following statements
is incorrect
A. The principle of countercurrent flow facilitates efficient respiration in gills of fishes.
B. The residual air in lungs slightly decreases the efficiency of respiration in mammals.
C. The presence of non-respiratory air sacs,increases the efficiency of respiration in birds.
D. In humans, circulating body fluids serve to distribute oxygen to tissues.


An electric dipole is placed in an electric
field generated by a point charge. Choose the correct option:
A. the net electric force on the dipole must be zero
B. the net electric force on the dipole may be zero
C. the torque on the dipole due to the field must be zero
D. the torque on the dipole due to the field is not equal to zero


Fraction for 0.004 is:
A \( \cdot \frac{4}{10000} \)
В. \( \frac{4}{1000} \)
c. \( \frac{4}{100} \)
D. \( \frac{4}{10} \)


Compare the properties of metals and
non-metals with respect to electronic
configuration.
A. Metals have 1,2 valence electrons while non metals have 3,5,6 or 7 valence electrons
B. Metals have 1 or 3 valence electrons while non metals have 2,5 valence electrons
C. Metals have 2 or 3 valence electrons while non metals have 1,5,6 or 7 valence electrons
D. Metals have 1,2 or 3 valence electrons while non
metals have 4,5,6 or 7 valence electrons


Calculate the pressure inside a small air bubble of radius \( r \) situated at a
depth \( h \) below the free surface of liquids
of densities \( \rho_{1} \) and \( \rho_{2} \) and surface
tension \( T_{1} \) and \( T_{2} . \) The thickness of the
first and second liquids are \( h_{1} \) and \( h_{2} \)
respectively. Take atmosphere pressure
\( =\boldsymbol{P}_{0} \)
\( ^{\mathrm{A}} \cdot P_{0}+\rho_{1} g h_{1}+\rho_{2} g\left(h-h_{1}\right)-\frac{2 T_{2}}{r} \)
в. \( P_{0}+\rho_{1} g h_{1}+\rho_{2} g\left(h-h_{1}\right)+\frac{2 T_{2}}{r} \)
c. \( \quad P_{0}-\rho_{1} g h_{1}+\rho_{2} g\left(h-h_{1}\right)+\frac{2 T_{2}}{r} \)
D. None of these


30 children were asked about the
number of hours they watched TV programmes last week. The results are
recorded as under:
\( \begin{array}{lllll}\begin{array}{l}\text { Number } \\ \text { of }\end{array} & \mathbf{0}- & \mathbf{5}- & \mathbf{1 0}- & \mathbf{1 5}- \\ \text { hours } & \mathbf{5} & \mathbf{1 0} & \mathbf{1 5} & \mathbf{2 0}\end{array} \)
frequncy
16
What is the number of children who
watched TV for 10 or more hours a week?
A . 8
B. 6
c. 10
D. 4


Evaluate: \( \int \sec ^{4} x \cdot \operatorname{cosec}^{2} x d x \)
A. \( \frac{1}{3} t^{3}+t \)
B \( \cdot \frac{1}{3} t^{3}+2 t-\frac{1}{t} \)
c. \( \frac{1}{2} t^{3}+2 t-\frac{1}{t} \)
D. \( \frac{1}{3} t^{3}-t-\frac{1}{t} \)


In the circuit shown in figure, the \( 5 \Omega \)
resistance develops 20.00 cal/s due to the current flowing through it. The heat
developed in \( 2 \Omega \) resistance (in cal/s) is
A. 23.8
B. 14.2
\( c \cdot 11.9 \)
D. 7.


Write principal argument of \( \frac{-\sqrt{11} i}{17} \)


Heating chloroform with aqueous sodium hydroxide solution forms:
A. sodium acetate
B. sodium oxalate
c. sodium formate
D. chloral


f a proton and anti-proton come close to each other and annihilate, how much energy will be released?
A . \( 1.5 \times 10^{-10} \mathrm{J} \)
B . \( 3 \times 10^{-10} J \)
c. \( 4.5 \times 10^{-10} J \)
D. \( 2 \times 10^{-10} \mathrm{J} \)


\( 200 g \) of a certain metal at \( 83^{\circ} \mathrm{C} \) is
immersed in \( 300 g \) of water at \( 30^{\circ} \mathrm{C} \). The
final temperature is \( 33^{\circ} \mathrm{C} \). Calculate the specific heat capacity of the metal. Assume that the specific heat capacity of water is \( 4.2 J g^{-1} K^{-1} \)
A \( \cdot 0.378 \mathrm{Jg}^{-1} \mathrm{K}^{-1} \)
B. \( 0.578 \mathrm{Jg}^{-1} \mathrm{K}^{-1} \)
C. \( 0.778 \mathrm{Jg}^{-1} \mathrm{K}^{-1} \)
D. None of the above


An aircraft pilot flies it at a distance of
\( 800 k m \) with some average speed. He
could have saved 40 minutes by increasing the average speed of the aircraft by \( 40 k m / h . \) Find actual speed of the aircraft.


If the difference between the mean and
variance of binomial distribution for 5
trials is \( 5 / 9, \) the distribution is of the
form
A \( \cdot\left(5, \frac{1}{2}, \frac{1}{2}\right) \)
B. \( \left(5, \frac{1}{3}, \frac{2}{3}\right) \)
\( ^{c} \cdot\left(5, \frac{3}{4}, \frac{1}{4}\right) \)
D. \( \left(5, \frac{3}{5}, \frac{2}{5}\right) \)


A stone of mass \( 8 \mathrm{kg} \) has been lifted to a height of \( 2 \mathrm{m} \) from the ground. Calculate the rise in its potential
energy.
A . 156.8
B . 165.8 J
c. 16
D. 160 J


The other name for Syngas is:
A. Producer gas
B. Water gas
c. Tear gas
D. Fuel gas


\( \int \frac{\sec ^{8} x}{\cos e c x} d x= \)
A \( \cdot \frac{\cos ^{7} x}{7}+c \)
в. \( \frac{7}{\cos ^{7} x}+c \)
c. \( \frac{1}{7 \cos ^{7} x}+c \)
D. \( \frac{1}{\cos ^{7} x}+c \)


Find the multiplicative inverse of the complex numbers given the following:
\( -i \)


Just as hydrochloric acid : pepsinogen
so is
A. Enterokinase : trypsinogen
B. Haemoglobin: oxygen
c. Bile juice : fat
D. Glucagon: glycogen


Which one of the following has the
greatest mass?
A. Alpha particle
B. Beta particle
c. Neutron
D. Gamma ray
E . Positron


The position of centre of mass of a system consisting of two particles of
masses \( m_{1} \) and \( m_{2} \) separated by a
distance \( L \) apart, from \( m_{1} \) will be
A \( \cdot \frac{m_{1} L}{m_{1}+m_{2}} \)
В. \( \frac{m_{2} L}{m_{1}+m_{2}} \)
c. \( \frac{m_{2}}{m_{1}} L \)
D. \( \frac{L}{2} \)


In the adjoining circuit, calculate the inductive reactance and the capacitive
reactance. What should be the source
frequency so that the two reactance become equal in magnitude? What would then be the impedance(in ohms) of the circuit?


What are the following substances? Give one example of each one of them.
(i) Tranquilizers
(ii) Food preservatives
(iii) Synthetic detergents


Elemental Boron cannot be obtained
from Van Arkel method.
A. True
B. False


\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left[\sin ^{-1}\left(\frac{\sqrt{\mathbf{1}+\boldsymbol{x}}+\sqrt{\mathbf{1}-\boldsymbol{x}}}{\mathbf{2}}\right)\right] \mathbf{w} \cdot \mathbf{r} \)
to \( x \) equals
A \( \cdot \frac{1}{2 \sqrt{1-x^{2}}} \)
в. \( \frac{-2}{\sqrt{1-x^{2}}} \)
c. \( \frac{-1}{2 \sqrt{1-x^{2}}} \)
D. None of these


The centre of mass of the shaded
portion of the disc is (The mass is
uniformly distributed in the shaded
portion):
\( A \cdot \frac{R}{20} \) to the left of \( A \)
B. \( \frac{R}{12} \) to the left of \( A \)
C. \( \frac{R}{40} \) to the right of \( A \)
D. \( \frac{R}{12} \) to the right of \( A \)


Ethylene burns in air to form?
A \( \cdot C O_{2} \) and water
B. \( C O \) and hydrogen and oxygen
c. \( C O_{2} \) and hydrogen and oxygen
D. \( C O \) and water


Cardiac ouput is blood
A. Received by heart per minute
B. Pumped by ventricles per sec
c. Pumped by left ventricle per minute
D. Pumped by left ventricle per hour


What volume of \( 0.10 \mathrm{M} \) sodium formate
solution should be added to \( 50 \mathrm{ml} \) of
\( 0.05 \mathrm{M} \) formic acid to produce a buffer
solution of \( p H 4.0 ? \)
\( \left[p K_{a} \text { for formic acid is } 3.80\right] \)
A . \( 3.96 \mathrm{ml} \)
B. 25m
c. \( 39.6 \mathrm{ml} \)
D. \( 100 \mathrm{ml} \)


Which of the following is not a normal oxide?
A. \( \mathrm{Na}_{2} \mathrm{O} \)
B. \( \mathrm{Al}_{2} \mathrm{O}_{3} \)
c. \( \mathrm{KO}_{2} \)
D. \( \mathrm{MgO} \)


Which of the following pair of quantities do not have the same dimensions?
A. Potential gradient, electric field
B. Torque, kinetic energy
c. Light year, time period
D. Impedance, reactance


wo lutitical vedus, tach ndve d mass
\( m \) and charge \( q . \) When placed in
a hemispherical bowl of radius \( \boldsymbol{R} \) with
frictionless, non-conducting walls,
the beads move and at equilibrium they
are at a distance \( R \) apart (as shown in
figure). Determine the charge on each
bead:
\( ^{\mathbf{A}} \cdot\left(\frac{4 \pi \varepsilon_{0} m g R^{2}}{\sqrt{3}}\right)^{1 / 2} \)
\( ^{\mathbf{B}}\left(\frac{2 \pi \varepsilon_{0} m g R^{2}}{\sqrt{3}}\right)^{1 / 2} \)
\( \left(\frac{4 \pi \varepsilon_{0} m g R^{2}}{\sqrt{6}}\right)^{1 / 2} \)
\( \left(\frac{\pi \varepsilon_{0} m g R^{2}}{\sqrt{3}}\right)^{1 / 2} \)


Which of the following element belongs to the halogen group? This question has multiple correct options
A \( \cdot 1 s^{2}, 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{5} \)
B . \( 1 s^{2}, 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6}, 4 s^{2} \)
C \( \cdot[A r] 3 d^{10}, 4 s^{2} 4 p^{5} \)
D . \( [K r] 4 d^{10}, 5 s^{2} 5 p^{5} \)


The graph is drawn between \( \sqrt{\boldsymbol{K} \boldsymbol{E}} \)
\& momentum of a body taking on \( \times 8 \) y-axis respectively, having inclination
\( 60^{\circ} . \) Then the mass of the body is?
\( ^{\mathbf{A}} \cdot \frac{3}{2} k g \)
в. \( 6 k g \)
\( \mathrm{c} \cdot 3 \mathrm{kg} \)
D. \( 18 k g \)


Write the IUPAC names of the given
compounds:


The fire algae responsible for red tides
are


Which of the following is not correctly matched?
A. Laterite- Contains aluminium
B. Terra Rosa- Most suitable for roses
c. chernozem- Richest soil
D. Black cotton soil- Rich in calcium carbonate


At what altitude will the acceleration
due to gravity be \( 25 \% \) of that at the earth's surface (given radius of earth is
\( R) ? \)
A. \( R / 4 \)
в. \( R \)
c. \( 3 R / 8 \)
D. \( R / 2 \)


How many primary volts must be applied to a transformer with a
secondary to primary turns ratio of 0.1
to obtain a secondary voltage of \( 9 V ? \)
A . \( 9 V \)
B. \( 90 V \)
\( \mathbf{c} .900 V \)
D. \( 0.9 V \)


A particle of mass m is under the
influence of a force \( \mathrm{F} \) which varies with
the displacement \( x \) according to the
relation \( F=-k x+F_{0} \) in which \( k \) and \( F_{0} \)
are constants.The particle when
disturbed will oscillate
A. about \( x=0, \) with \( \omega \neq \sqrt{k / m} \)
B. about \( x=0, \) with \( \omega=\sqrt{k / m} \)
C . about \( x=F_{0} / k, \) with \( \omega=\sqrt{k / m} \)
D. about \( x=F_{0} / k, \) with \( \omega \neq \sqrt{k / m} \)


First country in the world which adopted family planning programme is
A. Japan
B. USA
c. India
D. Bangladesh


Marks in an aptitude test given to 800 students of a school was found to be
normally distributed. 10\% of the
students scored below 40 Marks and
\( 10 \% \) of the students scored above 90
marks. Find the number of students
who scored between 40 and 90


Find the AM between 20 and 26
A . 23
B. 22
\( c \cdot 21 \)
D . 24


Number of value \( x \) satisfying the equation \( \sin ^{-1}\left(\frac{5}{x}\right)+\sin ^{-1}\left(\frac{12}{x}\right)= \)
\( \frac{\pi}{2} \) is
A .
B.
\( c \cdot 2 \)
D. more than 2


How does an age pyramid for human population at given point of time helps the policy makers in planning for future?


Two small spheres have mass \( m_{1} \) and
\( m_{2} \) and hanging from massless
insulating threads of lengths \( l_{1} \) and \( l_{2} \)
Two spheres carry charges \( \boldsymbol{q}_{1} \) and \( \boldsymbol{q}_{2} \)
respectively. The spheres hang such that they are on the same horizontal
level and the threads are inclined to the
vertical at angle \( \theta_{1} \) and \( \theta_{2} \) respectively
If \( F_{1}=F_{2}, \) then:
A \( \cdot \theta_{1}=\theta_{2} \)
в. \( M_{1}=M_{2} \)
c. \( \frac{l_{1}}{\tan \theta_{1}}=\frac{l_{2}}{\tan \theta_{2}} \)
\( \frac{q_{1}}{\tan \theta_{1}}=\frac{q_{2}}{\tan \theta_{2}} \)


The rate of reaction:
This question has multiple correct options
A. decreases with time
B. decreases with decrease in conc. of reactant
c. decreases with increase in time and decrease in conc.
of reactant
D. none of the above


Neanderthal man was followed by
A. Cro-Magnon man
B. Homo sapiens
c. Homo erectus
D. Homo neanderthal


In a simultaneous throw of a pair of dice, if the probability of getting odd number on the first and 6 on the second is \( \frac{1}{a} . \) Find \( a \)


When the particle reaches its maximum height, which of the following MUST be true about the particle?
A. It has the same horizontal speed it had initially
B. It has the same vertical speed it had initially
C. Its net acceleration is momentarily zero
D. It is momentarily at rest
E. All of the above


Which one of the following methods is used in the concentration of sulphide ore ?
A. Froth floation
B. Smelting
c. Roasting
D. Leaching


\( \lim _{x \rightarrow \frac{1}{2}} \frac{8 x-3}{2 x-1}-\frac{4 x^{2}+1}{4 x^{2}-1} \)


The correct sequences of reagents for
the following conversation will be:
A \( \cdot C H_{3} M g B r, H^{+} / C H_{3} O H,\left[A g\left(N H_{3}\right)_{2}\right]^{+} O H \)
B. \( C H_{3} M g B r,\left[A g\left(N H_{3}\right)_{2}\right]^{+} O H^{-}, H^{+} / C H_{3} O H \)
c. \( \left[A g\left(N H_{3}\right)_{2}\right]^{+} O H^{-}, C H_{3} M g B r, H^{+} / C H_{3} O H \)
\( \mathrm{D} \cdot\left[A g\left(N H_{3}\right)_{2}\right]^{+} O H^{-}, H^{+} / C H_{3} O H, C H_{3} M g B r \)


Find the efficiency of the cycle.


A conducting rod \( P Q \) of length \( L= \)
1.0 \( m \) is moving with a uniform speed
\( \boldsymbol{v}=20 \boldsymbol{m} / \boldsymbol{s} \) in a uniform magnetic field
\( B=4.0 T \) directed into the paper \( A \)
capacitor of capacity \( \boldsymbol{C}=\mathbf{1 0} \boldsymbol{\mu} \boldsymbol{F} \) is
connected as shown in figure. Then
\( \mathbf{A} \cdot q_{A}=+800 \mu C \) and \( q_{B}=-800 \mu C \)
B \( \cdot q_{A}=-800 \mu C \) and \( q_{B}=+800 \mu C \)
\( \mathbf{c} \cdot q_{A}=0=q_{B} \)
D. charged stored in the capacitor increases exponentially with time


If true enter 1 , else enter 0 .
\( H C H O \) disproportionates in presence
of \( \boldsymbol{O} \boldsymbol{H}^{-} \)
\( A \)


ff \( x+2 y+3 z=0 \) and \( x^{3}+4 y^{3}+ \)
\( \mathbf{9} z^{3}=18 x y z ; \) evaluate:
\( \frac{(x+2 y)^{2}}{x y}+\frac{(2 y+3 z)^{2}}{y z}+ \)
\( \frac{(3 z+x)^{2}}{z x} \)
A . 18
B. 23
c. 16
D. 11


A particle moves along the \( x \) -axis from \( x=0 \) to \( x=5 m \) under the influence of
a force given by \( \boldsymbol{F}=\mathbf{7}-\mathbf{2} \boldsymbol{x}+\mathbf{3} \boldsymbol{x}^{2} \boldsymbol{N} \)
The work done in the process is
\( \mathbf{A} \cdot 107 J \)
B. \( 270 J \)
c. \( 100 J \)
D. \( 135 J \)


The self inductance of a coil is \( 1 / 2 \) henry.
At what frequency will its inductive
reactance be \( 3140 \Omega \)
A \( .100 H z \)
B. \( 10 H z \)
c. \( 1000 H z \)
D. \( 10000 H z \)


Spot the statement which is true for
temperature of gas and every kinetic
model of gas:
A. Temperature \( \propto \) Average kinetic energy of the gas molecule
B. temperature \( \propto \frac{1}{K . E_{\text {of gas molecule}}} \)
C. Temperature has no effect on kinetic energy of gas not
D. All true according to condition


Synergic bonding involves
A. The transference of electrons form ligands to metal
B. The transference of electrons from filled metal orbitals
to anti-bonding orbitals of ligands
C. Both (A) and (B)
D. None of these


Sclerenchymatous bundle sheath is found in
A. Sunflower
B. Mango
c. Grass
D. Banyan


The circuit breaker device which can be
used in place of a fuse is called
A. свD
в. мсв
c. мсо
D. свF


When soap is added to hard water \( N a^{+} \)
of soap is replaced by \( C a^{2+} \) or \( M g^{2+} \)
ions and precipitates as \( C a \) or \( M g \)
soap.
A. True
B. False


If the switch at point \( P \) is opened
(shown in the figure) choose the correct
option
A. the current in \( R_{1} \) would not change
B. the potential difference between point \( X \) and the ground would increas
c. the current provided by the battery would increase
D. the emf produced by the battery (assumed to have internal resistance) would change


Oxygen consists of isotopes \( \mathbf{O}^{16}, \mathbf{O}^{\mathbf{1 7}} \) and \( \mathrm{O}^{18} \) carbon consists of isotopes of \( \mathbf{C}^{12} \) and \( \mathbf{C}^{13} \) Total number of \( \mathbf{C O}_{\mathbf{2}} \)
molecules possible are
\( A \cdot 6 \)
B. 12
\( c \cdot 18 \)
D.


Which of the following molecules
exhibit resonance?
I. \( \boldsymbol{A} \boldsymbol{s} \boldsymbol{F}_{\mathbf{5}} \)
।. \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{\mathbf{3}} \)
III. \( \boldsymbol{S O}_{2} \)
A. I only
B. II only
c. II and III
D. III and IV
E . ।, II, and III


Solve:
\( \cos ^{-1}\left(\sin \frac{4 \pi}{3}\right) \)
A. \( -\frac{5 \pi}{6} \)
в.
\( c \cdot \frac{7 \pi}{6} \)
D. \( \frac{5 \pi}{6} \)


Which of the following exist in monoatomic state?
A. Phosphorus
B. Nitrogen
c. Antimony
D. Bismuth


Water is formed by the hydrogen and oxygen combined in the ratio 1: 9 by
weight
A. True
B. False


Find the number of sides of a regular polygon if each exterior angle is equal
to one third of its adjacent interior
angle


A planet in a distant solar system is 10 times more massive than the earth and
its radius is 10 times smaller. Given
that the escape velocity from the earth
is \( 11 k m s^{-1}, \) the escape velocity from
the surface ofthe planet would be
A. \( 110 k m s^{-1} \)
B. \( 0.11 k m s^{-1} \)
c. \( 1.1 k m \mathrm{s}^{-1} \)
D. \( 11 k m s^{-1} \)


Use Euclid's Division Lemma, prove that
for any positive integer \( n, n^{3}-n \) is
divisible by 6


energy is converted into
energy by an electric generator.
A. mechanical, mechanical
B. electrical, electrical
c. electrical, mechanical
D. mechanical, electrical


A glass test tube containing some water is immersed in boiling water so
that the upper end of the test is outside.
It is found that water in the test tube
does not boil even if it is kept there for a
long time. Why?


State whether true or false:
An electromagnet can produce very strong magnetic force as compared to permanent magnet
A. True
B. False


Dielectric constant, property of an electrical insulating material (a dielectric) equal to
A. the ratio of the capacitance of a capacitor filled with the given material to the capacitance of an identical capacitor in a vacuum without the dielectric material.
B. the ratio of the capacitance of a capacitor filled with the given material to the capacitance of an identical capacitor in a vacuum with the dielectric material
c. the capacitance of a capacitor filled with the given material
D. none of the above


Pick out the incorrect statement
amongst the following.
A. Nylon clothing can stand high temperature and are therefore good to wear in summers
B. Thermosetting plastics do not become soft on heating
c. Addition polymers are formed without the elimination of by-product molecules
D. Natural rubber is obtained as latex from rubber trees


How many molecules are present in 18 of hydrogen?
A \( \cdot 6.02 \times 10^{23} \)
B. \( 3.01 \times 10^{23} \)
c. \( 1.50 \times 10^{23} \)
D. \( 6.02 \times 10^{22} \)


Which pair of oxides of nitrogen is paramagnetic ?
A. \( N O, N_{2} \)
в. \( N_{2} O_{5}, N O_{2} \)
c. \( N_{2} O-5, N_{2} O \)
D. \( N O, N O_{2} \)


To send \( 10 \% \) of the main current through a moving coil galvanometer of resistance 99 the shunt required is-
A . 1
B. 9
\( c \cdot 100 \)
\( D \cdot 19 \)


\( \int \frac{1}{\sqrt{x}} \tan ^{4} \sqrt{x} \sec ^{2} \sqrt{x} d x= \)
A \( \cdot 2 \tan ^{5} \sqrt{x}+c \)
B. \( \frac{1}{5} \tan ^{5} \sqrt{x}+c \)
c. \( \frac{2}{5} \tan ^{5} \sqrt{x}+c \)
D. None of these


A small magnet is suspended by a silk thread from a rigid support such that the magnet can freely swing. Describe its behaviour.


The electric field of a plane polarized electromagnetic Wave in free space at time \( t=0 \) i given by an expression \( \overrightarrow{\boldsymbol{E}}(\boldsymbol{x}, \boldsymbol{y})=10 \hat{j} \cos [(\boldsymbol{6} \boldsymbol{x}+\boldsymbol{8} \boldsymbol{z})] \)
The magenetic field \( \vec{B}(x, z, t) \) is given by ; (c is the velocity of light will be:
A \( \cdot \frac{1}{c}(4 \hat{k}+8 \hat{i}) \cos [(2 x-8 z+20 c t)] \)
B \( \cdot \frac{1}{c}(6 \hat{k}-8 \hat{i}) \cos [(6 x+8 z-10 c t)] \)
c. \( \frac{1}{c}(5 \hat{k}+8 \hat{i}) \cos [(6 x+8 z-80 c t) \)
D \( \cdot \frac{1}{c}(4 \hat{k}-8 \hat{i}) \cos [(6 x+8 z+70 c t)] \)


Integrate \( \int \frac{\log x}{x^{2}} d x \)


\( \left(\frac{1}{1-2 i}+\frac{3}{1+i}\right)\left(\frac{3+4 i}{2-4 i}\right)= \)
A. \( \frac{1}{2}+\frac{9}{2} i \)
B \( \cdot \frac{1}{2}-\frac{9}{2} i \)
c. \( \frac{1}{4}-\frac{9}{4} i \)
D. \( \frac{1}{4}+\frac{9}{4} i \)


Two balls of same density falls in a
viscous medium.The radius of first ball
being double than the radius of second ball, then how many times is the sedimentation velocity of second ball to that of first ball will be:
A . 1
B. 2
\( c \cdot 4 \)
\( D \)


Estuaries are considered as nutrient
trap due to the mixing of
A. River and sea water
B. Pond and lake
c. Lake and river
D. Ocean and pond


The \( K_{s p} \) for a sparingly soluble \( A g_{2} C r O_{4} \) is \( 4 \times 10^{-12} . \) The molar
solubility of the salt is:
\( \begin{array}{lll}\text { A } \cdot 2.0 \times 10^{-6} & \text {mol } & L^{-1}\end{array} \)
\( \begin{array}{lll}\text { В. } 1.0 \times 10^{-4} & \text {тод } L^{-1}\end{array} \)
\( \begin{array}{lll}\text { C. } 2.0 \times 10^{-12} & \text {mol } & L^{-1}\end{array} \)
D. \( 1.0 \times 10^{-15} \) mol \( L^{-1} \)


The radii of two circle are \( 4 \mathrm{cm} \) and 3
\( \mathrm{cm} \) respectively, The diameter of the circle having area equal to the sum of the areas of the two circles(in cm) is
A . 5
B. 7
c. 10
D. 14


The ground state energy of hydrogen atom is \( -13.6 e V . \) If an electron make a
transition from an energy level \( -0.85 e V \) to \( -1.51 e V \), calculate the
wavelength of the spectral line emitted. To which series of hydrogen spectrum does this wavelength belong?


The kinetic energy of a particle is equal to the energy of a photon. The particle moves at \( 5 \% \) of the speed of light. The ratio of the photon wavelength to the de Broglie wavelength of the particle is [No need to used relativistic formula for the particle.]
A . 40
B. 4
\( c \cdot 2 \)
D. 80


Common salt containing small amount of sodium iodide, is called iodised salt.
A. True
B. False


Consider the following reactions-
The correct set of reagents for these
reactions is :
A \( \cdot R_{1}: H_{2} / \) Lindlarcatalyst, \( R_{2}: N a / l i q . N H_{3}, R_{3} \)
\( (i) O_{3},(i i) H_{2} O, R_{4}: H_{2} O H_{2} S O_{4}, H g S O_{4} \)
B. \( R_{1}: H_{2} / \) Lindlarcatalyst, \( R_{2}: \) Na/liq..NH \( _{3}, R_{3} \)
\( H_{2} O, H_{2} S O_{4}, H g S O_{4}, R_{4}:(i) O_{3},(i i) H_{2} O \)
C. \( R_{1}:(i) O_{3},(i i) H_{2} O, R_{2}: H_{2} O H_{2} S O_{4}, H g S O_{4}, R_{3} \)
Na /liq.NH \( _{3}, R_{4}: H_{2} / \) Lindlarcatalyst
D. \( R_{1}: H_{2} O H_{2} S O_{4}, H g S O_{4}, R_{2} \)
\( H_{2} / \)Lindlarcatalyst\( , R_{3}:(i) O_{3} \)
\( (i i) H_{2} O, R_{4}: \)
Na/liq.NH


Two copper rods of the same length, but
of different diameters of cross section
are given the same amount of heat.
Assuming no heat losses:
A. Thick rod expands more linearly
B. Thin rod expands more linearly
C. Both rods expand equally linearly
D. For large quantities of heat thick rod expands more and thin rod expands more for small quantities of heat.


There are 3 books on mathematics 4 on
physics and 5 on english.How many different collections can be made such
that each collections consists of :
Atleast one book of english


\( A C \) and \( B D \) are the diagonals of a quadrilateral \( A B C D, \) prove that: \( \overrightarrow{A B}+ \) \( \overrightarrow{D C}=\overrightarrow{A C}+\overrightarrow{D B} \)


A fraction becomes \( \frac{1}{3} \) when 1 is
subtracted from the numerators and it
becomes \( \frac{1}{4} \) when 8 is added to its denominator. Find the fraction.


In a solvent \( 50 \% \) of benzoic acid
dimerises while rest ionises,
determines molar mass of acid which is
observed and also its van't Hoff factor.


Evaluate \( \int \frac{\boldsymbol{d x}}{\sqrt{\mathbf{2 a x}-\boldsymbol{x}^{2}}} \)


General solution of equation \( \cot \theta+ \) \( \operatorname{cosec} \theta=\sqrt{3} \) is
A \( \cdot 2 n \pi+\frac{\pi}{4} \)
B . \( (2 n-1) \pi \)
c. \( 2 n \pi+\frac{\pi}{3} \)
D. \( 2 n \pi+\frac{\pi}{6} \)


In which stage of cell cycle, DNA replication occurs?
A. Gi phase
B. s phase
c. \( \mathrm{G}_{2} \) phase
D. M phase


A unıtorm magnetıc tıeld, tılls
cylindrical volume of radius \( 10 \mathrm{cm} \) as
shown is figure. If the magnitude of
magnetic field increases in the
direction of field at a constant rate of
10T/s then the emf induced in the rod
AB is:
A \( .24 \mathrm{mV} \)
3. \( 96 \mathrm{mV} \)
\( c .48 m v \)
\( D \)


If a mixture containing 3 moles of
hydrogen and 1 mole of nitrogen is converted completely into ammonia, the ratio of initial and final volumes under
the same temperature and pressure would be:
A. 3:
B. 1: 3
c. 2: 1
D. 1: 2


Brain Nurtures
If \( A, B, C, D, E, F, G, H, I, J \) and \( K \) represent metals in the decreasing order of their reactivity, which one of them is most likely to occur in a free state in nature?


Given Function \( f(x)== \) \( \left\{\begin{array}{cc}x^{2}, & \text { for } 0 \leq x<1 \\ \sqrt{x}, & \text { for } 1 \leq x \leq 2\end{array}\right\} \) Evaluate
\( \int_{0}^{2} f(x) d x \)
A \( \cdot \frac{1}{3}(4 \sqrt{2}-1) \)
B. \( \frac{1}{3}(2 \sqrt{2}-1) \)
c. \( \frac{2}{3}(4 \sqrt{2}-1) \)
D \( \cdot \frac{2}{3}(2 \sqrt{2}-1) \)


Read the following statements:
(A) Nasal chamber opens into
nasopharynx which is a portion of
pharynx
(B) Larynx produces sound during inspiration as well as expiration
(C) During swallowing gullet can be covered by a thin elastic cartilagenous flap called epiglottis
(D) Trachea is get divided at the level of the 6th thoracic vertebra into right and
left primary bronchi.
(E) The braching network of bronchi, bronchioles and alveoli comprise the lungs.

How many statements are not correct-
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D.


The unit vector orthogonal to \( -\hat{\mathbf{i}}+ \) \( \hat{k}, 2 \hat{j}-\hat{k} \) and forming a right handed
system with them is
\( \mathbf{A} \cdot 2 \hat{i}+\hat{j}+2 \hat{k} \)
B. \( \frac{2 \hat{i}+\hat{j}+2 \hat{k}}{3} \)
c. \( -\frac{2 \hat{i}+\hat{j}+2 \hat{k}}{3} \)
D. \( -\frac{2 \hat{i}+\hat{j}+2 \hat{k}}{9} \)


The economically important plant of Malvaceae is
A. Gossypium hirsutum
B. Hibiscus cannabinus
c. Abelmoschus esculentus
D. All of the above


In which layer of atmosphere ozone is maximum concentrated?
A. Troposphere
B. Stratosphere
c. Mesosphere
D. Ionosphere


Glucose and cane sugar can be distinguished by tollen's reagent or fehling's solution.
If true enter 1 else 0
\( A \)


What was the initial speed of the alpha
particle?
A \( \cdot 132 . \times 10^{2} m s^{-1} \)
В. \( 1.32 . \times 10^{7} \mathrm{ms}^{-1} \)
c. \( 13.2 . \times 10^{2} m s^{-1} \)
D. \( 0.13 . \times 10^{7} \mathrm{ms}^{-1} \)


Calcium absorption is always enhanced by the action of the following vitamin
\( A \cdot \) Vitamin A
B. Vitamin B
c. Vitamin D
D. Vitamin K


Water in boiling water reactor is used
as
A. Coolant
B. Moderator
c. Both coolant and moderator
D. None of these


Let \( \quad A=\left(\begin{array}{ccc}x^{2} & 6 & 8 \\ 3 & y^{2} & 9 \\ 4 & 5 & z^{2}\end{array}\right) \) and \( B= \)
\( \left(\begin{array}{ccc}2 x & 3 & 5 \\ 2 & 2 y & 6 \\ 1 & 4 & 2 z-3\end{array}\right) \) be two matrices
and if \( \operatorname{Tr}(\boldsymbol{A})=\boldsymbol{T} \boldsymbol{r}(\boldsymbol{B}), \) then the value of
\( (x+y+z) \) is equal to
(Note: \( \operatorname{Tr}(P) \) denotes trace of matrix \( P \) )
\( A \)
B.
\( c \)
\( D \)


Find the GP whose \( 5^{t h} \) term is 48 and \( 9^{t h} \)
term is768.
\( \mathbf{A} \cdot 3,6,12,24 \)
В. 2,4,8,16
c. 6,12,24,48
D. 12,24,36,48


Assertion
The circle of smallest radius passing through two given points \( A \& B \) must be of radius \( \frac{1}{2} A B \)
Reason
A straight line is a shortest distance between two points.
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


Williamson synthesis is a method of preparation of
A. symmetrical ethers
B. unsymmetrical ethers
c. diaryl ethers
D. both A and B


Capacitance of a capacitor made by a
thin metal foil is \( 2 \mu F \). If the foil is folded with paper of thickness \( 0.15 \mathrm{mm} \) dielectric constant of paper is 2.5 and width of paper is \( 400 \mathrm{mm} \), the length of foil will be
A. \( 0.34 \mathrm{m} \)
B. 1.33 \( m \)
c. \( 13.4 \mathrm{m} \)
D. 33.9 m


Osmosis is
A. Passage of solvent only through a semipermeable membrane.
B. Passage of solutes only through a membrane.
C. Passage of both solvent and solute through a membrane.
D. Passage of solution through a protoplasm.


State Faraday's first law of electrolysis.


A loop of area \( 1 \mathrm{m}^{2} \) is placed in a magnetic
field \( B=2 T, \) such that plane of the loop
is parallel to the magnetic field. If the loop is rotated by 180 , the amount of net charger passing through any point of loop, if its resistance is \( 10 \Omega \) is then
A. \( 0.4 \mathrm{c} \)
B. \( 0.2 \mathrm{c} \)
c. \( 0.8 \mathrm{c} \)
D. o c


An electron is allowed to move freely in
a closed cubic box of length of side 10 cm. The uncertainty in its velocity will be:
A . \( 3.35 \times 10^{-4} \mathrm{msec}^{-1} \)
B. \( 5.8 \times 10^{-4} \mathrm{m} \mathrm{sec}^{-1} \)
c. \( 4 \times 10^{-5} \mathrm{msec}^{-1} \)
D. \( 4 \times 10^{-6} \mathrm{msec}^{-1} \)


A ball falls vertically onto a floor with
momentum \( p \) and then bounces repeatedly, the coefficient of restitution is \( e . \) The total momentum imparted by
the ball to the floor is
A \( \cdot \rho(1+e) \)
B. \( \frac{1}{1-e} \)
\( ^{c} \rho\left(\frac{1+e}{1-e}\right) \)
\( ^{\mathrm{D}} \rho\left(1-\frac{1}{e}\right) \)


Select the best combination of regents
which will bring the following
conversion
\( \mathbf{A} \cdot B r_{2} / F e B r_{3} ; H N O_{3} / H_{2} S O_{4} ; N a O H ; H_{2} / P t \)
B. \( C H_{3} C O C l / A l C l_{3} ; B r_{2} / F e B r_{3} ; N a B H_{4} / C H_{3} O H \)
C. \( C H_{3} C l / A l C l_{3} ; K M n O_{4} ; C H_{3} C l / A l C l_{3} ; N B S / h v ; L \)
D. \( C H_{3} C l / A l C l_{3} ; H N O_{3} / H_{2} S O_{4} ; N B S / h v / N a O H \)


Element 'X' has twelve protons in its nucleus. To which group of the periodic table it will belong?
\( A \)
B. 2
\( c \cdot 6 \)
D. 8


\( \boldsymbol{A} \stackrel{\boldsymbol{H C N}}{\longrightarrow} \boldsymbol{B} \stackrel{\boldsymbol{H}_{3} \boldsymbol{O}^{+}}{\longrightarrow} \boldsymbol{L} \boldsymbol{a} \boldsymbol{c t i c} \boldsymbol{a c i d} \)
Identify \( \boldsymbol{A} \)
A. \( H C H O \)
в. \( C H_{3} C H O \)
с. \( C_{6} H_{5} \) СНО
D. \( C H_{3} \) СОСН \( _{3} \)


In cloning of cattle, a fertilized egg is
taken out of the mother's womb and
A. The egg is divided into 4 pairs of cells which are implanted into the womb of other cows.
B. In the eight cell stage, cells are separated and cultured until small embryos are formed which are implanted into the womb of other cows
C. In the eight cell stage, the individual cells are separated under electrical field for further development in culture media.
D. From this, upto eight identical twins can be produced.


Which of the following is/are true regarding the following linear equation:
\( \boldsymbol{x}-\mathbf{3}=\frac{\mathbf{2}}{\mathbf{5}}(\boldsymbol{y}+\mathbf{1}) \)
A. It passes through (0,-2.5) and \( m=-8.5 \)
B. It passes through (0,-2.5) and \( m=8.5 \)
c. It passes through (0,8.5) and \( m=-2.5 \)
D. It passes through (0,-8.5) and \( m=2.5 \)


\( S \) and \( T \) are the foci of an ellipse and \( B \)
is an end of the minor axis. If \( \triangle \boldsymbol{S T B} \) is
an equilateral triangle, the eccentricity of the ellipse is equals to:
A \( \cdot \frac{1}{4} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{1}{2} \)
D. \( \frac{2}{3} \)
E. None of these


In the circuit shown, the current in the
1 \( \Omega \) resistor is
\( \mathbf{A} \cdot 1.3 A, \) from \( P \) to \( Q \)
B. \( 0 A \)
c. \( 0.13 A \), from \( Q \) to \( P \)
\( 0.13 A, \) from \( P \) to \( Q \)


One mole of \( S O_{3} \) was placed in a two
litre vessel at a certain temperature. The following equilibrium was established in the vessel :
\[
\mathbf{2} \boldsymbol{S} \boldsymbol{O}_{3}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{S} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{O}_{2}(\boldsymbol{g})
\]
The equilibrium mixture reacted with
0.2 mole \( K M n O_{4} \) in acidic medium.
Hence, \( \boldsymbol{K}_{c} \) is :
A. 0.50
в. 0.25
\( c \cdot 0.125 \)
D. None of these


Methanogens belong to
A. Slime moulds
B. Eubacteria
C. Archaebacteria
D. Dinoflagellates.


A power transmission line feeds input power at \( 2300 V \) to a step-down transformer, with its primary winding having 4000 turns. What should be the
number of turns in the secondary winding in order to get output power at
\( \mathbf{2 3 0} \boldsymbol{V} ? \)
A . 300
в. 250
\( c .400 \)
D. 450


Transcription is the transfer of genetic
code from a DNA molecule to
A. RNA molecule
B. Second DNA molecule
C. Ribosomal sub unit
D. Sequence of amino acids in a protein molecule


What is the hybridisation of the metal in following complex?
\( \left[\boldsymbol{F e}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right]^{3+} \)
A \( \cdot d^{3} s p^{2} \)
в. \( d s p^{4} \)
\( \mathbf{c} \cdot d^{2} s p^{3} \)
D. None of these


Two plants belong to same species if
they
A. Have more then \( 90 \% \) similar genes.
B. Look similar and posses identical secondary metabolites
C. Have similar number of chromosomes.
D. Can reproduce freely with each other and form seeds.


Which of the following pairs of metals is purified by van Arkel method?
A. Ga and In
B. Zr and Ti
c. \( A g \) and \( A u \)
D. Ni and Fe


The value of the limit \( \lim _{x \rightarrow 1} \frac{\sin \left(e^{x-1}-1\right)}{\log x} \)
is
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( e \)
\( c \cdot \frac{1}{e} \)
D.


Carbamates are used as a
A. Insecticide
B. Herbicides
C . Fungicides
D. All of the above


The function has \( \boldsymbol{f}(\boldsymbol{x})= \)
\( (\log (x-1))^{2}(x-1)^{2} \) has
A. local extremum at \( x=1 \)
B. point of inflection at \( x=1 \)
c. local extremum at \( x=2 \)
D. point of inflection at \( x=2 \)


The value of \( \sqrt{\boldsymbol{i}} \) is
A. \( 1-i \)
в. \( 1+i \)
\( \mathbf{c} \cdot \pm(1+i) \)
D. \( i-1 \)
E . \( \frac{\pm 1}{\sqrt{2}}(1+i) \)


A pole \( 15 \mathrm{m} \) long rests against a vertical
wall at an angle of \( 30^{\circ} \) with the ground
How high up the wall does the pole reach?
\( A \cdot 5 m \)
в. 7
c. \( 7.5 \mathrm{m} \)
\( D \cdot 8 m \)


A closed vessel contains some gas at a
given temperature and pressure. If the vessel is given a very high velocity, the temperature of the gas
A. increases
B. decreases
C. may increase or decrease depending upon the nature of the gas
D. does not change


Heat energy required to raise the
temperature of a body of mass \( m \) in \( \mathrm{kg} \)
by \( \Delta t k \) is
A \( \cdot \frac{m c}{\Delta t} \) Joule
B. \( \frac{m \Delta t}{c} \) Joule
c. \( \frac{c}{m \Delta t} J \)
\( \mathbf{D} \cdot m c \Delta t \)


A person has to make electric switches
and plugs. Which material is recommended ?
A. Teflon
B. Bakelite
c. Rayon
D. PVC


A single letter is selected at random from the word'PROBABILITY'. The
probability that it is a vowel is:
A . \( 3 / 11 \)
B. \( 4 / 11 \)
c. \( 2 / 11 \)
D.


State True or False.
A cell works if its e.m.f. is negative.
A. True
B. False


What is the difference between a soap
and a synthetic detergent?


The atomic numbers of Lanthanides are
from:
A 57 to 71 1
B. 90 to 103
\( c .21 \) to 30
D. 39 to 48


During an electrochemical process,
A. Gibbs free energy increases
B. Gibbs free energy remain constant
C. No prediction can be made about Gibbs free energy
D. Gibbs free energy of decreases


The density of a nucleus varies with the mass number \( \boldsymbol{A} \) as:
\( A \cdot(A)^{2} \)
B. \( (A)^{1 / 3} \)
c. \( (A)^{0} \)
D. \( (A) \)


\( \begin{array}{ccccc}\boldsymbol{x} & \mathbf{2} & \boldsymbol{4} & \mathbf{2 0} & \mathbf{1 5} \\ y & 3 & 7 & 10 & 12 \\ z & 10 & 5 & 1 & 4 / 3\end{array} \) Observe the table and find the
quantities which are in inverse
proportion
A. \( x \) and \( y \)
B. \( x \) and \( z \)
\( \mathbf{c} \cdot y \) and \( z \)
D. None of the above


\( \int \frac{\cos ^{2} x}{1+\tan x} d x \)
A \( \cdot \frac{1}{4} \ln (\cos -\sin x)+\frac{x}{2}+\frac{1}{8}(\sin 2 x-\cos 2 x) \)
B. \( \frac{1}{4} \ln (\cos +\sin x)+\frac{x}{2}+\frac{1}{8}(\sin 2 x+\cos 2 x) \)
C \( \frac{1}{4} \ln (\cos +\sin x)+\frac{x}{2}+\frac{1}{8}(\sin 2 x-\cos 2 x) \)
\( \frac{1}{4} \ln (\cos -\sin x)+\frac{x}{2}+\frac{1}{8}(\sin 2 x+\cos 2 x) \)


Gas mask contains:
A. charcoal granules.
B. calcium carbonate.
C. fuller's earth.
D. powdered charcoal


When an unpolarized light of intensity
\( I_{0} \) is incident on a polarizing sheet, the intensity of the light which does not get transmitted is:
A \( \cdot \frac{1}{2} I_{0} \)
в. \( \frac{1}{4} I_{0} \)
c. zero
D. \( I_{0} \)


If \( \boldsymbol{P}=\{\boldsymbol{x} \mid \mathbf{2 4}<\boldsymbol{x}<\mathbf{3 0}\} \) and \( \boldsymbol{Q}= \)
\( \{\boldsymbol{x} \mid \mathbf{2 5}<\boldsymbol{x}<\mathbf{3 2}\}, \) prove that \( \boldsymbol{P}-\boldsymbol{Q} \neq \)
\( \boldsymbol{Q}-\boldsymbol{P} \)


An element with electrons in an
outermost shell is said to possess an
octet.
A \( \cdot 12 \)
B. 8
c. 10
D. 6


Who first proposed that light was wavelike in character?
A. Huygens
B. Newton
c. Young
D. Maxwell


If the refractive indices of crown glass
for red, yellow and violet colours are
respectively \( \mu_{r}, \mu_{y} \) and \( \mu_{v}, \) then the dispersive power of this glass would be:
A \( \cdot \frac{\mu_{v}-\mu_{r}}{\mu_{y}-1} \)
в. \( \frac{\mu_{v}-\mu_{y}}{\mu_{r}-1} \)
c. \( \frac{\mu_{v}-\mu_{y}}{\mu_{y}-\mu_{r}} \)
D. \( \frac{\mu_{v}-\mu_{r}}{\mu_{y}}-1 \)


Find the length of the longest side of the triangle formed by the line \( 3 x+4 y= \)
12 with the coordinate axes.


If \( f^{\prime}(x) \) exists for all \( x \in R \) and \( g(x)= \)
\( \boldsymbol{f}(\boldsymbol{x})-(\boldsymbol{f}(\boldsymbol{x}))^{2}+(\boldsymbol{f}(\boldsymbol{x}))^{3} \) for all \( \boldsymbol{x} \in \boldsymbol{R} \)
then
A. \( g(x) \) is increasing whenever \( f \) is increasing
B. \( g(x) \) is increasing whenever \( f \) is decreasing
\( \mathrm{c} . g(x) \) is decreasing whenever \( f \) is increasing
D. none of these


The fastest mode of transfer of heat is
A. conduction
B. convection
c. radiation
D. all the above three


\( \boldsymbol{C u}\left|\boldsymbol{C u}^{+2}(\mathbf{1} \boldsymbol{M})\right|\left|\boldsymbol{Z} \boldsymbol{n}^{+2}(\mathbf{1} \boldsymbol{M})\right| \boldsymbol{Z} \boldsymbol{n} \)
A cell represented above should have
emf:
A. positive
B. negative
c. zero
D. cannot be predicted


Friction does not depend on the nature of the surface in contact.
A. True
B. False
c. Ambiguous
D. Data insufficient


A factory production line is manufacturing bolts using three machines, \( A, B \) and \( C . \) Of the total
output, machine A is responsible for 25 \( \%, \) machine \( \mathrm{B} \) for \( 35 \% \) and machine \( \mathrm{C} \) for the rest. It is known from previous
experience with the machines that \( 5 \% \)
of the output from machine \( A \) is defective, \( 4 \% \) from machine \( B \) and \( 2 \% \)
from machine C. A bolt is chosen at
random from the production line and found to be defective. What is the
probability that it came from machine c?
A. 0.232
в. 0.862
\( c \cdot 0.123 \)
D. 0.286


The maximum number of possible interference maxima for slit separation equal to twice the wavelength in Young's double slit experiment is :
A . infinite
B. five
c. three
D. zero


The following graph shows the variation of velocity of a rocket with time. Then
the maximum height attained by the
rocket is
\( A \cdot 1.1 \mathrm{km} \)
\( B .5 \mathrm{km} \)
\( c .55 \mathrm{km} \)
D. None of these


The ratio of modulus of rigidity to modulus of elasticity for a Poisson's ratio of 0.25 would be
A. 0.5
B. 0.4
\( c \cdot 0.3 \)
D. 1.0


A ray of light travelling in a transparent medium of refractive index \( \mu, \) falls on a
surface separating the medium from
air at an angle of incidence of \( 45^{\circ} . \) For
which of the following value of \( \mu \) the ray can undergo total internal reflection?
A. \( \mu=1.33 \)
в. \( \mu=1.40 \)
c. \( \mu=1.50 \)
D. \( \mu=1.25 \)


Which one of the following is not a
correct statement?
A. Herbarium houses dried, pressed and preserved plant specimens.
B. Botanical gardens have collection of living plants for reference.
C. A museum has collection of photographs of plants and animals.
D. Key is a taxonomic aid for identification of specimens.


Boiling point of water on the Fahrenheit scale is
\( \mathbf{A} \cdot 100^{\circ} \mathrm{F} \)
В. \( 112^{\circ} \mathrm{F} \)
c. \( 212^{\circ} \) F
D. 32 \( ^{\circ} \)


Geometry as sulphur is bent in
\( \mathrm{I} \cdot \boldsymbol{S}_{8}\left\|\cdot \boldsymbol{S} \boldsymbol{F}_{2}\right\| \boldsymbol{S} \boldsymbol{O}_{2} \)
A . ।, ॥।, ॥।
B. ।, ॥
c. ॥, ॥ ॥
D. I, III


The property required for propagation of
transverse wave is :
A. longitudinal strain
B. lateral strain
c. shearing strain
D. poisson's ratio


Which type of tissue forms spinal cord and brain?
A. Muscular tissue
B. Nervous tissue
c. Epithelial tissue
D. connective tissue


A player throws 2 ordinary die with faces numbered 1 to 6. What is the
probability of obtaining a total score of atmost \( 6 ? \)
A \( \cdot 12 / 36 \)
B. \( 16 / 36 \)
c. \( 15 / 36 \)
D. \( 10 / 36 \)


Prove that \( \triangle= \)
\( \left|\begin{array}{ccc}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{a} \boldsymbol{\alpha}+\boldsymbol{b} \\ \boldsymbol{b} & \boldsymbol{c} & \boldsymbol{b} \boldsymbol{\alpha}+\boldsymbol{c} \\ \boldsymbol{a} \boldsymbol{\alpha}+\boldsymbol{b} & \boldsymbol{b} \boldsymbol{\alpha}+\boldsymbol{c} & \boldsymbol{0}\end{array}\right|=\boldsymbol{0} \) if \( \mathbf{a}, \mathbf{b}, \mathbf{c} \)
\( \operatorname{arcin} \mathrm{G} . \mathrm{P} \)


Chemical effect of electric current may
cause:
A. formation of gas bubbles at the electrodes
B. deposit of metal on the electrodes
C. change in colour of the solution
D. all of above


Solo man belongs to
A. Java only
B. Africa
c. china
D. China and Africa


Fill in the blanks with appropriate
words.
Watery fluid present inside the internal
ear is known as


Solve \( \left(\boldsymbol{x}^{2}-\boldsymbol{x}+\mathbf{1}\right)\left(\boldsymbol{x}^{4}+\boldsymbol{x}^{3}+\boldsymbol{x}+\mathbf{1}\right) \)


The difference between the outer and
the inner curved surface areas of an
open cylinder is \( 88 \mathrm{cm}^{2} \). If its length is \( 14 \mathrm{cm} \) and volume of the material in it
is \( 176 \mathrm{cm}^{3}, \) find the inner diameter of
the cylinder.
A. \( 3 \mathrm{cm} \)
в. \( 4 \mathrm{cm} \)
\( c \cdot 2 \mathrm{cm} \)
D. \( 1 \mathrm{cm} \)


What is an agent orange?
A. A biodegradable insecticide
B. A weedicide containing dioxin
C. Colour used in fluorescent lamp
D. A hazardous chemical used in luminous plants


The minimum and maximum values of
\( F \) to keep the cylinder in static
equilibrium just after the water starts
to spill through the hole, if the coefficient of static friction between
contact surfaces is 0.01 , are
A \( 0,40 N \)
N
B. \( 5.4 N, 52.2 N \)
\( c .0,70 N \)
D. \( 0,52.2 N \)


\( 4^{3.5}: 2^{5} \) is the same as


Why does moist blue litmus turn red
and finally becomes colourless in the presence of chlorine?


State whether the following statement
is True or False.
\( f(x, y)=(3,5) ; \) then \( x=3 \) and \( y=5 \)
A. True
B. False


A physicist took a hollow metallic sphere of radius \( 4 \mathrm{cm} \) at a temperature
of \( 27^{\circ} \mathrm{C} . \) He heated metallic sphere up
to \( 127^{\circ} \mathrm{C} \) and found that diameter of the
sphere increased to \( 8.2 \mathrm{cm}, \) then what is the coefficient of real expansion.


C-C-C bond angle in benzene is about:
\( \mathbf{A} \cdot 109^{0} 28^{\prime} \)
B . \( 180^{\circ} \)
\( c \cdot 120^{\circ} \)
D. \( 100^{\circ} \)


The current produced in a generator
armature is AC because
A. the magnetic field reverses at intervals
B. The current in the field coils is AC
C. the rotation of the armature causes the field through it to reverse
D. the commutator feeds current into it in opposite directions every half cycle


The discovery of Balmer and Lyman series was made before
proposing model for structure of atom.
This question has multiple correct options
A. Thomson
B. Rutherford
c. Bohr
D. Planck


Which type of phenomenon is used when coloured dye is removed from solution of sugar by charcoal?
A. Absorption
B. Adsorption
c. Both absorption and adsorption
D. None of the above


A particle of mass \( m \) is moving a
uniform velocity \( v_{1} . \) It is given an impulse such that its velocity becomes
\( \boldsymbol{v}_{2} . \) The impulse is equal to
A \( \cdot m\left[\left|v_{2}\right|-\left|v_{1}\right|\right] \)
B . \( 1 / 2 m\left[v_{1}^{2}-v_{1}^{2}\right] \)
\( \mathbf{c} \cdot m\left[v_{1}+v_{2}\right] \)
D. \( m\left[v_{2}-v_{1}\right] \)


A particle makes a to and from motion
between two points \( A \) and \( B . \) On its onward path (from A to B), it moves with
a constant velocity \( \boldsymbol{v}=\mathbf{5} \mathrm{m} / \mathrm{s}, \) while in
its return path, it moves with a constant
acceleration of \( a=v t . \) The particle
comes to rest at the extremes. Can this
motion be termed as SHM
A. SHM from A to B
B. SHM from B to A
C. SHM is not performed in any direction by the particle
D. SHM is performed in both the directions


If two triangles are \( _{--}- \) they are similar.
A. Not equal
B. Equiangular
c. Different
D. Not proportionate


Assertion
The positive charge particle is placed in
front of a spherical uncharged conductor. The number of lines of forces
terminating on the sphere will be more than those emerging from it.
Reason
The surface charge density at a point on the sphere nearest to the point charge will be negative and maximum in magnitude compared to other points on the sphere
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


A carbon film resistor has colour code
Green Black Violet Gold. The value of the
resistor is:
A \( .50 M \Omega \)
в. 500 М \( \Omega \)
\( \mathrm{c} .500 \pm 5 \% \) М\( \Omega \)
D. \( 500 \pm 10 \% \) M \( \Omega \)


ff \( f(x), g(x), h(x) \) are polynomials in \( x \) of \( \operatorname{degree} 2 \) and \( F(x)=\left|\begin{array}{ccc}\boldsymbol{f} & \boldsymbol{g} & \boldsymbol{h} \\ \boldsymbol{f}^{\prime} & \boldsymbol{g}^{\prime} & \boldsymbol{h}^{\prime} \\ \boldsymbol{f}^{\prime \prime} & \boldsymbol{g}^{\prime \prime} & \boldsymbol{h}^{\prime \prime}\end{array}\right|, \) then
\( F(x) \) is equal to
\( A \cdot 1 \)
B.
\( c \cdot-1 \)
D. \( f(x) . g(x) . h(x) \)


Which of the following reaction is used
to make a fuel cell?
\( \mathbf{A} \cdot C d(s)+2 N i(O H)_{3}(s)+H_{2} O(l) \longrightarrow C d O(s)+ \)
\[
2 N i(O H)_{3}(s)+H_{2}(g)
\]
B \( .2 \mathrm{Fe}(s)+\mathrm{O}_{2}(g)+4 H^{+}(a q) \longrightarrow 2 \mathrm{Fe}^{2+}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l) \)
\( \mathbf{c} \cdot P b(s)+P b O_{2}(g)+2 H_{2} S O_{4}(a q) \longrightarrow 2 P b S O_{4}(s)+ \)
\( 2 H_{2} O(l) \)
D. \( 2 H_{2}(g)+O_{2}(g) \longrightarrow 2 H_{2} O(l) \)


In a parallelogram \( A B C D, \angle D A B= \)
\( 40^{\circ} \) find the other angles of the
parallelogram


\( \boldsymbol{C l O}^{-} \rightleftarrows \boldsymbol{C l O}_{3}^{-}+\boldsymbol{C l}^{-} \)
When the equation for the reaction represented above is balanced with
coefficients reduced to the lowest
whole-umber terms, correct statements
include which of the following?
I. The coefficient for \( C l^{-} \) is 4
II. The coefficient for \( C l O_{3}^{-} \) is 2
III. The coefficient for \( C l O^{-} \) is 3
A. I only
B. II only
C. III only
D. I and II only
E . I, II and III only


A certain color of light towards the purple end of the visible spectrum has a wave length of \( 420 n m \) in vacuum.

What is the frequency of this light? (The speed of light in a vacuum is \( 3.00 \times \) \( \left.10^{8} m / s\right) \)
A \( .126 \mathrm{Hz} \)
B. \( 1.26 \times 10^{11} \mathrm{Hz} \)
c. \( 7.1 \times 10^{14} \mathrm{Hz} \)
D. \( 1.4 \times 10^{15} \mathrm{Hz} \)
E . \( 1.4 \times 10^{6} \mathrm{Hz} \)


What is meant by photophosphorylation ? Discuss the cyclic
photophosphorylation.


Which of the following patterns of reproduction is the major cause of variation?
A. Sexual reproduction
B. Asexual reproduction
c. Both of these
D. None of these


Solve \( \int_{\boldsymbol{\pi} / \mathbf{6}}^{\boldsymbol{\pi} / \mathbf{3}} \frac{\mathbf{1}}{\sin \mathbf{2} \boldsymbol{x}} \boldsymbol{d} \boldsymbol{x} \)


A body of weight 1 newton has a potential energy of 1 joule relative to the ground when it is at a height of:
A . \( 1 \mathrm{m} \)
B. 9.8 m
\( \mathrm{c} \cdot 1 / 9.8 \mathrm{m} \)
D. o m


Identify the correct aestivations.
A. a-valvate, b-Twisted, c-Vexillary, d-Imbricate
B. a-Valvate, b-Twisted, c-lmbricate, d-Vexillary
C. a-Valvate, b-Vexillary, c-Twisted, d-Imbricate
D. a-Vexillary, b-Imbricate, c-Twisted, d-Valvate
\( \mathrm{E} \). a-Valvate, b-lmbricate, c-Twisted, d-Vexillary


Coconut charcoal, having adsorbed \( A r \) \( \mathrm{Kr} \) and \( \mathrm{Xe} \) is brought into contact with
charcoal maintained at \( 77 \mathrm{K} \). The
following gas diffuses into the latter:
\( A \cdot A r \)
B. Kr
\( c \cdot x e \)
D. al


\( \int_{0}^{1} \tan ^{-1} x d x \)
A. \( \frac{\pi}{2}-\frac{1}{2} \log 2 \)
B. \( \frac{\pi}{4}+\frac{1}{2} \log 2 \)
c. \( \frac{\pi}{2}-\frac{1}{4} \log 2 . \)
D. \( \frac{\pi}{4}-\frac{1}{2} \log 2 \)


\( \left[\begin{array}{cc}\mathbf{1} & \mathbf{1} \\ \mathbf{0} & \mathbf{1}\end{array}\right]\left[\begin{array}{ll}\mathbf{1} & \mathbf{2} \\ \mathbf{0} & \mathbf{1}\end{array}\right]\left[\begin{array}{ll}\mathbf{1} & \mathbf{3} \\ \mathbf{0} & \mathbf{1}\end{array}\right] \cdot\left[\begin{array}{cc}\mathbf{1} & \boldsymbol{n}-\mathbf{1} \\ \mathbf{0} & \mathbf{1}\end{array}\right]= \)
\( \left[\begin{array}{cc}\mathbf{1} & \mathbf{7 8} \\ \mathbf{0} & \mathbf{1}\end{array}\right] \)
If \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{1} & \boldsymbol{n} \\ \mathbf{0} & \mathbf{1}\end{array}\right] \operatorname{then} \boldsymbol{A}^{-\mathbf{1}}=? \)
A \( \cdot\left[\begin{array}{cc}1 & 12 \\ 0 & 1\end{array}\right] \)
B \( \cdot\left[\begin{array}{cc}1 & -13 \\ 0 & 1\end{array}\right] \)
c. \( \left[\begin{array}{cc}1 & -12 \\ 0 & 1\end{array}\right] \)
D. \( \left[\begin{array}{cc}1 & 0 \\ -13 & 1\end{array}\right] \)


A man take a step forward with
probability 0.4 and backward with probability \( 0.6 . \) The probability that at the end of eleven steps he is one step away from the starting point, is
A . 0.37
в. 0.57
c. 0.3
D. None of these


First man to stand erect was
A. Cro-Magnon man
B. Java man
C. Neanderthal man
D. Peking man


Complete the following equation.
a) \( 2 N a O H+C l_{2} \rightarrow \)
coldanddil
b) \( C l_{2}+\underset{(e x c e s s)}{3 F_{2}} \stackrel{573 K}{\rightarrow} \)


State whether the following statement is True or False.
2 is the only even prime number
A. True
B. False


Bananas can be prevented from overripening by
A. Maintaining them at room temperature
B. Refrigeration
c. Dipping in ascorbic acid solution
D. storing in a freezer


Explain the significance of 'palindromic nucleotide sequence' in the formation of recombinant DNA.


and \( m \) are two parallel lines
intersected by another pair of paralle
lines \( p \) and \( q . \) Then
A. \( \triangle A B C \cong \triangle C D A \)
B. \( \triangle A B C \cong \triangle A D C \)
c. \( \triangle A B C \cong \triangle D C A \)
\( \triangle A B C \cong \triangle C A D \)


What is that condition when
androecium consists of 4 long and 2
short stamens?
A. Didynamous
B. Tetradynamous
c. Diplostemonous
D. None of the above


Area laying between the curves \( y= \)
\( \tan x, y=\cot x \) and \( x- \)
\( \boldsymbol{a x i s}, \boldsymbol{x}\left[\boldsymbol{o}, \frac{\pi}{2}\right] \boldsymbol{i s} \)


An impeachment motion against the President, in order to be passed by a House, should be supported by
A. Not less than one-third members present and voting ir the House
B. Not less than two-third members of total membership of the House
c. The simple majority of the House
D. The special majority of the House


Which of the following have wires with lowest resistivity?
A. Hair dryers
B. Electric ovens
c. Toasters
D. None of the above


When the frequency of the source voltage decreases, the impedance of a parallel RC circuit
A . increases
B. decreases
c. does not change
D. decreases to zero


Calculate all solutions of \( |z-1| \times \mid z- \)
\( \mathbf{1} \mid=\mathbf{1} \)
A. intersecting straight line passing through (1,0)
B. solutions are exactly the points of the circle with center (1,0) and radius 1
c. solutions are exactly the points of the circle with center (1,0) and radius \( \sqrt{2} \)
D. none of these


Who among the following are cannibal?
A. Peking man
B. Java ape man
c. Homo habilis
D. Both A and B


A block of mass 2 kg. is free to move
along the \( x \) -axis. It is at rest and from
\( t=0 \) onwards it is subjected to a time-
dependent force \( F(t) \) in the \( x \) direction. The force \( F(t) \) varies with \( t \) as shown in the figure. The kinetic energy of the block after 4.5 second is :


In its covalent compounds, the
hydrogen atom has the electronic configuration analogous to that of
A. neon
B. helium
c. argon
D. lithium


A sphere of radius \( \mathrm{R} \) has a uniform
volume charge density \( \rho . \) The
magnitude of electric field at a distance
from the centre of the sphere, where
\( \boldsymbol{r}>\boldsymbol{R}, \) is?
A \( \cdot \frac{\rho}{4 \pi \varepsilon_{0} r^{2}} \)
B. \( \frac{\rho R^{2}}{\varepsilon_{0} r^{2}} \)
C \( \cdot \frac{\rho R^{3}}{\varepsilon_{0} r^{2}} \)
D \( \cdot \frac{\rho R^{3}}{3 \varepsilon_{0} r^{2}} \)
E \( \cdot \frac{\rho R^{2}}{4 \varepsilon_{0} r^{2}} \)


A plant that has well differentiated body, special tissues for transport of water and other substances, but does
not have seed or fruits is a
A. Bryophyte
B. Angiosperm
c. Gymnosperm
D. Pteridophyte


Find \( \frac{d y}{d x} \) for \( 2 x^{2}+5 x y+3 y^{2}=1 \)


The earth \( \left(\operatorname{mas} s=6 \times 10^{24} k g\right) \) revolves
around the sun with an angular velocity
of \( 2 \times 10^{-7} \) radian/sec in a circular
orbit of radius \( 1.5 \times 10^{8} k m . \) The force
exerted by the sun, on the earth is :-
A \( \cdot 6 \times 10^{19} N \)
B . \( 18 \times 10^{25} N \)
c. \( 36 \times 10^{21} N \)
D. \( 27 \times 10^{39} N \)


Who discovered fluid mosaic model of
plasma membrane?


The area bounded by the curves \( y= \)
\( \sqrt{5-x^{2}} \) and \( y=|x-1| \) is
\( ^{\mathbf{A}} \cdot\left(\frac{5 \pi}{4}-2\right) \) square unit
B. \( \frac{(5 \pi-2)}{4} \) square units
c. \( \frac{(5 \pi-2)}{2} \) square units
D \( \cdot\left(\frac{5 \pi}{2}-2\right) \) square unit


What precautions should be taken to
avoid heart attack?


Halides of alkaline earth metals from
hydrates such as, \( M g C l_{2} \cdot 6 H_{2} O, C a C l_{2} \)
\( 6 H_{2} O, B a C l_{2} \cdot 2 H_{2} O, \) and \( S r C l_{2} \)
\( 2 H_{2} O \)
This shows that halides of group II elements:
A. are hygroscopic in nature
B. act as dehydrating agents.
c. can absorbs moisture from air
D. cannot absorbs moisture from air


In which of the following acid, the maximum number of hydrogen atoms are joined directly with phosphorous?
A. Phosphoric acid
B. Phosphorous acid
c. Pyrophosphoric acid
D. None of these


The mass of a lead ball is \( M \). It falls
down in a viscous liquid with terminal velocity \( V \). The terminal velocity of
another lead ball of mass \( 8 M \) in the
same liquid will be:
A . \( 64 . V \)
B. \( 4 V \)
\( c \cdot 8 V \)
D. \( V \)


In the figure, a circle is inscribed in a
quadrilateral ABCD in which \( \angle B=90^{\circ} \)
If \( A D=23 c m, A B=29 c m \) and \( D S= \)
\( 5 c m \) find the radius of the circle


The cost at 5 paise / KWH of operating an
electri
motor for 8 hours which takes 15 ampere
at \( 110 \mathrm{V} \) is:
A. Rs.66
B. 66 paise
c. 37 paise
D. Rs.6.60


Three oxides of nitrogen, \( N O, N O_{2} \) and
\( N_{2} O, \) can be formed under different
conditions.
\( N O_{2} \) can be formed by different
chemical reactions.
Write equation for the formation of \( N O_{2} \)
by:
the reaction of \( N_{2} \) with \( O_{2} \)
the thermal decomposition of magnesium nitrate.


If \( \boldsymbol{x y}=\boldsymbol{e}^{\boldsymbol{x}-\boldsymbol{y}} \) then
This question has multiple correct options
A \( \cdot \frac{d y}{d x} \) doesn't exist at \( x=0 \)
B. \( \frac{d y}{d x}=0 \) when \( x=1 \)
C. \( \frac{d y}{d x}=\frac{1}{2} \) when \( x=0 \)
D. none of these


Separation of lanthanides from their mixture is not easy because of:
A. Shielding effect
B. Pentetrating effect
c. consequences of lanthanide contraction
D. inert pair effect


If a charged particle kept at rest experiences an electromagnetic force This question has multiple correct options
A. the electric field must not be zero
B. the magnetic field must not be zero
c. the electric field may or may not be zero
D. the magnetic field may or may not be zero


Let \( \boldsymbol{f}(\boldsymbol{x})= \)
\( (x-4)(x-5)(x-6)(x-7) \) then
A \( \cdot f^{\prime}(x)=0 \) has four roots
B. three roots of \( f^{\prime}(x)=0 \) lie in (4,5)\( \cup(5,6) \cup(6,7) \)
C. the equation \( f^{\prime}(x)=0 \) has only one root
D. three roots of \( f^{\prime}(x)=0 \) lie in (3,4)\( \cup(4,5) \cup(5,6) \)


The tidal power plants are constructed near the mouth of \( \ldots . . . . . . . . . . \) bays.
A . renewable
в. huge
c. narrow
D. broad


Genus is a group of similar and related
A. Order
B. Genera
c. Families
D. species


The number which is not a perfect cube, from the following is:
A. 1,331
B . 216
c. 243
D. 512


Consider the following processes.
\( \begin{array}{ll} & \boldsymbol{\Delta} \boldsymbol{H}(\boldsymbol{k} \boldsymbol{J} / \boldsymbol{m o l}) \\ 1 / 2 A \rightarrow B & +150 \\ 3 B \rightarrow 2 C+D & -125 \\ E+A \rightarrow 2 D & +350\end{array} \)
For \( \boldsymbol{B}+\boldsymbol{D} \rightarrow \boldsymbol{E}+\mathbf{2} \boldsymbol{C}, \boldsymbol{\Delta} \boldsymbol{H} \) will be:
A . 325 kJ/mol
B. 525 kJ/mol
c. -175 kJ.mol
D. -325 kJ/mol


Two stars each of one solar mass \( (= \)
\( \left.2 \times 10^{30} k g\right) \) are approaching each other
for a head on collision. When they are a
distance \( 10^{9} k m, \) their speeds are
negligible. What is the speed with which they collide? The radius of each star is \( 10^{4} k m . \) Assume the stars to remain
undistorted until they collide. (Use the
known value of \( G \) )


Cloud is a colloidal suspension of water
droplets in air.
If true then enter 1 , else enter 0


Name two safety devices which are
connected to the live wire of a
household electric circuit.


During photorespiration the oxygen consuming reaction occur in
A. Grana of chloroplast and peroxisomes
B. Stroma of chloroplasts
c. Stroma of chloroplasts and mitochondria
D. Stroma of chloroplasts and peroxisomes


A car and a lorry are travelling with
same velocity on a straight horizontal road. Which of the two has got greater
momentum?


\( A: \) The angle between \( 2 \hat{i}-m \hat{j}+3 m \hat{k} \)
and \( (1+m) \hat{i}-2 m \hat{j}+\hat{k} \) is acute angle
for \( \boldsymbol{m} \notin\left[-\mathbf{2},-\frac{\mathbf{1}}{\mathbf{2}}\right] \)
\( \boldsymbol{R}: \) If \( (\boldsymbol{a}, \boldsymbol{b}) \) is acute, then \( \boldsymbol{a} \cdot \boldsymbol{b}>0 \)
A. Both \( A \) and \( R \) are true and \( R \) is the correct explanation of \( A \)
B. Both \( A \) and \( R \) are true and \( R \) is not correct explanation of \( A \)
c. \( A \) is true but \( R \) is false
D. \( A \) is false but \( R \) is true


The population of a city increases at a rate proportional to the number of inhabitants present at any time t. If the population of the city was 200000 in 1990 and 250000 in \( 2000, \) what will be
the population in \( 2010 ? \)


Particle 1 collides a stationary particle 2 head on elastically. Find their mass ratio if after collision they move in opposite direction with equals velocities.
\( A \)
B. \( 1 / 2 \)
\( c \cdot 1 / 3 \)
D. \( 1 / 4 \)


A 0.4 molal aqueous solution of \( \boldsymbol{M}_{\boldsymbol{x}} \boldsymbol{A} \)
has freezing point \( 3.72^{\circ} \mathrm{C} \). The \( K_{f} \) of
\( H_{2} O \) is \( 1.86 K m o l a l i t y^{-1} . \) The value of \( x \) is :


Construct \( \Delta T E N \) such that \( \mathrm{TE}=3 \mathrm{cm} \)
\( \angle E=90^{\circ} \) and \( \mathrm{NE}=4 \mathrm{cm} \)


If \( y=a \sin x+b \cos x, \) then \( y^{2}+ \)
\( \left(\frac{d y}{d x}\right)^{2} \) is a
A. Function of \( x \)
B. Function of \( y \)
c. Function of \( x \) and \( y \)
D. constant


Which IS BASIC OXIDE
\( \mathbf{A} \cdot T l_{2} O_{3} \)
B. \( B_{2} O_{3} \)
\( \mathbf{c} \cdot G a_{2} O \)
D. \( \operatorname{In} 0 \)


After forceful inspiration, the amount of air that can be breathed out by maximum forced expiration is equal to
A \( \cdot \operatorname{lRV}+\operatorname{ERV}+\operatorname{TV}+\operatorname{RV} \)
B. IRV + RV + ERV
C. \( \operatorname{IRV}+\mathrm{TV}+\mathrm{ERV} \)
D. \( T V+R V+E R V \)


Ductility is the physical property of metals by the virtue of which it can be stretched into thin wires without
breaking.
A. True
B. False


The angular velocity of rotation of a star (mass \( \mathrm{M} \) and radius \( \mathrm{R} \) ), such that the
matter will start escaping from its equator is:
A \( \cdot \sqrt{\frac{2 G R}{M}} \)
в. \( \sqrt{\frac{2 G M}{R^{3}}} \)
c. \( \sqrt{\frac{2 G M}{R}} \)
D. \( \sqrt{\frac{2 G M^{2}}{R}} \)


toppr
Q Type your question
each piston moves within a particular section. One mole of a gas enclosed
between the pistons which are tied with non-stretchable threads. The difference
in cross-sectional area of pistons
\( 10 \mathrm{cm}^{2} \) The mass of gas confined between pistons is \( 5 \mathrm{kg} \). The outside pressure is 1 atmosphere \( =10^{5} N / m^{2} \)
By how many degrees must the gas
between pistons be heated to shift the piston by \( 5 \mathrm{cm} ? \) Given \( \boldsymbol{R}=\mathbf{8 . 3} \)
A \( \cdot 0.9^{\circ} \mathrm{C} \)
В. \( 1.2^{\circ} \mathrm{C} \)
\( c \cdot 1.5^{\circ} \mathrm{C} \)
D. \( 0.5^{\circ} \mathrm{C} \)


After dividing each term of the arithmetic progression with a fixed number, the common difference is
A. Added by the same fixed number.
B. Divided by the same fixed number.
c. Multiplied by another fixed number.
D. Multiplied by the same fixed number


Which one is the first compound which is common for both glucose and fructose in glycolysis?
A. Fructose \( 6- \) -
B. Glucose 6-P
c. Fructose 1, 6-biphosphate
D. Fructose 1-P


If the angle of elevation of a cloud from a point h meters above a lake is \( \alpha \) and
the angle of depression of its reflection in the lake is \( \beta \) then height of the cloud is \( h\left(\frac{1+r}{1-r}\right) \) where \( r=\frac{\text { tan } \alpha}{\tan \beta} \)
A. True
B. False


Find the length of altitude through \( A \) of
the triangle \( A B C, \) where \( A \equiv \)
\( (-\mathbf{3}, \mathbf{0}), \boldsymbol{B} \equiv(\mathbf{4},-\mathbf{1}), \boldsymbol{C} \equiv(\mathbf{5}, \mathbf{2}) \)


The degree of dissociation of \( N_{2} O_{4} \) into
\( N O_{2} \) at 1.5 atmosphere and \( 40^{\circ} C \) is
0.25. Calculate its \( K_{p} \) at \( 40^{\circ} \mathrm{C} \). Also report degree of dissociation at 10 atmospheric pressure at same
temperature:
A. \( K_{P}=0.2, \alpha \simeq 0.2 \)
B . \( K_{P}=0.4, \alpha \simeq 0.1 \)
c. \( K_{P}=0.8, \alpha \simeq 0.4 \)
D. None of these


A light particle moving horizontally with a speed of \( 12 m / s \) strikes a very heavy
block moving in the same direction at
\( \mathbf{1 0} \boldsymbol{m} / \boldsymbol{s} . \) The collision is one-
dimensional and elastic. If the speed of
the block does not change after the collision, the particle will
A. Move at \( 2 \mathrm{m} / \mathrm{s} \) in its original direction
B. Move at \( 8 \mathrm{m} / \mathrm{s} \) in its original direction
c. Move at \( 8 \mathrm{m} / \mathrm{s} \) opposite to its original direction
D. Move at \( 12 \mathrm{m} / \mathrm{s} \) opposite to its original direction


Solubility of \( A s_{2} S_{3} \) in aqueous solution
is \( \operatorname{Smol} L^{-1} \). Its solubility product is
\( 108 S^{n} . \) What will be the value of \( n ? \)


The transverse nature of
electromagnetic radiation is
demonstrated by.
A. Interference experiment
B. Diffraction experiment
c. Polarisation experiment
D. optical activity experiment