Complete the above reactions:
A. Cyclohexanone
B. Cyclohexanoic acid
\( \mathrm{C} \). Cyclopentanone
D. Cypentanoic acid


A metal cube of length \( 10.0 \mathrm{mm} \) at \( 0^{\circ} \mathrm{C} \)
\( (273 \mathrm{K}) \) is heated to \( 200^{\circ} \mathrm{C}(473 \mathrm{K}) . \) Given
its coefficient of linear expansion is
\( 2 \times 10^{-5} K^{-1} . \) The percent change of its
volume is
A . \( 0 . \)
B. 0.2
\( c \cdot 0.4 \)
D. 1.2


The standard emf for the cell reaction,
\( Z n+C u^{2+} \rightarrow Z n^{2+}+C u \)
is 1.10 volt at \( 25^{\circ} \mathrm{C} \). The emf for the cell
reaction when \( 0.1 M C u^{2+} \) and
\( 0.1 M Z n^{2+} \) solutions are used at \( 25^{\circ} \mathrm{C} \)
is:
A. 1.10 volt
B. 0.110 volt
c. -1.10 volt
D. -0.110 volt


Why does tea cool rapidly in a saucer
than in a cup?


The magnetic moment of an ion in its +3
oxidation state is 3.85 BM. The number of
unpaired electrons present in the ion is
A
B. 4
\( c \cdot 3 \)
D. 5


The sum to infinity of \( \frac{1}{7}+\frac{2}{7^{2}}+\frac{1}{7^{3}}+ \)
\( \frac{2}{7^{4}}+\dots \) is
A \( \cdot \frac{1}{5} \)
в. \( \frac{7}{24} \)
c. \( \frac{5}{48} \)
D. \( \frac{3}{16} \)


Internal energy does not include:
A. vibrational energy
B. rotational energy
c. nuclear energy
D. energy arising by gravitational pull


f \( (p, q, r) \) is equidistant from
(1,2,-3),(2,-3,1) and \( (-3,1,2), \) then
\( \boldsymbol{p}+\boldsymbol{q}+\boldsymbol{r}= \)
A . -1
B.
c. 0
D.


An inductor is connected to a direct
voltage source through a switch. Now
A. Very large emf is induced in inductor when switch is closed
B. Larger emf is induced when switch is opened
C. Large emf is induced whether switch is closed or opened
D. No emf is induced whether switch is closed or opened


A ball is let fall from a height \( h_{0} \). There are \( n \) collisions with the earth. If the
velocity of rebound after n collision is
\( u_{n} \) and the ball rises to a height \( h_{n}, \) then coefficient of restitution e is given by-
\( ^{\mathbf{A}} \cdot e^{n}=\sqrt{\frac{h_{n}}{h_{0}}} \)
B. \( e^{n}=\sqrt{\frac{h_{0}}{h_{n}}} \)
\( ^{\mathrm{c}} \cdot_{n e}=\sqrt{\frac{h_{n}}{h_{0}}} \)
D. \( \sqrt{n e}=\sqrt{\frac{h_{n}}{h_{0}}} \)


The genetic information to the site of
translation is carried by nucleic acid
A. DNA
B. mRNA
c. rRNA
D. snRNA
E. tRNA


Which of the following has the maximum \( C-H \) bond length?
A. \( C_{2} H_{4} \)
в. \( C_{2} H_{2} \)
\( \mathbf{c} \cdot C_{2} H_{6} \)
D. \( C_{6} H_{6} \)


The figure shows three circuits I, II and
III which are connected to a \( 3 V \) battery.
If the powers dissipated by the
configurations \( \boldsymbol{I}, \boldsymbol{I} \boldsymbol{I} \) and \( \boldsymbol{I} \boldsymbol{I} \boldsymbol{I} \) are \( \boldsymbol{P}_{1}, \boldsymbol{P}_{2} \)
and \( P_{3} \) respectively, then :
\( \mathbf{A} \cdot P_{1}>P_{3}>P_{2} \)
В \( \cdot P_{2}>P_{1}>P_{3} \)
\( \mathbf{c} \cdot P_{1}>P_{2}>P_{3} \)
\( \mathbf{D} \cdot P_{3}>P_{2}>P_{1} \)


A resistance 'R' draws power'P' when connected to an AC source. If an
inductance is now placed in series with the resistance, such that the
impedance of the circuit becomes 'Z',
the power drawn will be
\( \mathbf{A} \cdot P\left(\frac{R}{Z}\right) \)
в. \( P \)
c. \( P\left(\frac{R}{Z}\right)^{2} \)
D. \( P \sqrt{\frac{R}{Z}} \)


Find \( k \) if \( P Q \| \) RS and
\( \boldsymbol{P}(\mathbf{2}, \boldsymbol{4}) \boldsymbol{Q}(\boldsymbol{3}, \boldsymbol{6}), \boldsymbol{R}(\boldsymbol{3}, \boldsymbol{1}), \boldsymbol{S}(\boldsymbol{5}, \boldsymbol{k}) \)


What is the use of kink in clinical
thermometer?


When 2 -butyne is treated with \( H_{2} \)
/Lindlar's catalyst, compound \( \boldsymbol{X} \) is
produced as the major product and
when treated with \( N a / \)lliq. \( N H_{3} \) it produced \( Y \) as the major product. Which of the following statements is correct?
(1) \( X \) will have higher dipole moment
and higher boiling point than \( Y \)
(2) \( Y \) will have higher dipole
moment and higher boiling point than
\( \boldsymbol{X} \)


Determine \( \boldsymbol{V}(\boldsymbol{x}) \)
A . \( 20 x \)
B . \( -20 x \)
c. \( 10 x \)
D. \( -10 x \)


Two solid discs of radii \( r \) and \( 2 r \) roll
from the top of an inclined plane without slipping. Then
A. The bigger disc will reach the horizontal level first
B. The smaller disc will reach the horizontal level first
c. The time difference of reaching of the discs at the horizontal level will depend on the inclination of the plane
D. Both the discs will reach at the same time


The grid voltage of any triode valve is changed from -1 volt to -3 volt and the mutual conductance is \( 3 \times 10^{-4} \) mho.
The change in plate circuit current will be
A. \( 0.8 \mathrm{mA} \)
B. \( 0.6 \mathrm{mA} \)
c. \( 0.4 \mathrm{mA} \)
D. \( 1 \mathrm{m} \)


The probability of picking a number which ends with 3 from first 100 natural
numbers is
A . \( 0 . \)
B. 0.3
c. 0.13
D. none


Solve:
\( \frac{3 x-2}{2 x-1}=\frac{4}{3} \)


\( i+\frac{1}{i}= \)
A.
B. -
c.
D. 2


A guitar string is \( 90 \mathrm{cm} \) long and has a fundamental frequency of \( 124 H z . \) To produce a fundamental frequency of
\( 186 H z, \) the guitar should be pressed at
\( ? \)
\( \mathbf{A} \cdot 60 \mathrm{cm} \)
в. \( 30 \mathrm{cm} \)
\( c \cdot 20 c m \)
D. \( 10 \mathrm{cm} \)


The work done in blowing a soap bubble
of radius \( R \) is \( W_{1} \) and that to a radius
\( 3 R \) is \( W_{2} . \) the ratio of work done is
A .1: 3
B. 3: 1
c. 1: 9
D. 9: 1


A man is 24 years older than his son. 12 years ago, he was five times as old as
his son. Find the present ages of both.
A. Present age of father is 44 years and Present age of son is 20 years
B. Present age of father is 42 years and Present age of son is 18 years
c. Present age of father is 60 years and Present age of son is 36 years
D. Present age of father is 48 years and Present age of son is 24 years


In pteridophytes, phloem is without
A. Bast fibers
B. Sieve tubes
c. companion cells
D. Both B and C


Draw parallelogram ABCD with the
following measurements and calculate
its area.
\( A B=8 \mathrm{cm}, A C=10 \mathrm{cm} \) and \( \angle A B C=100^{\circ} \)


Write balanced redox reactions of the
following:
4 moles of \( S n^{2+}(a q) \) reduces \( I O_{4}^{-} \) to
\( \boldsymbol{I}^{-}(\boldsymbol{a} \boldsymbol{q}) \)
A \( \cdot 4 S n^{2+}+I O_{4}^{-}+8 H^{+} \rightarrow 6 S n^{4+}+I^{-}+4 H_{2} O \)
B . \( 4 S n^{2+}+I O_{8}^{-}+8 H^{+} \rightarrow 4 S n^{4+}+I^{-}+4 H_{2} O \)
c. \( 4 S n^{2+}+I O_{4}^{-}+8 H^{+} \longrightarrow 4 S n^{4+}+I^{-}+4 H_{2} O \)
D. none of these


Calculate the arithmetic mean, range,
median and mode of the given data:
\( \mathbf{2}, \mathbf{4}, \mathbf{7}, \mathbf{4}, \mathbf{9}, \mathbf{5}, \mathbf{7}, \mathbf{3}, \mathbf{6}, \mathbf{7} \)


Which cells do not form layer and
remain structurally separate?
A. Epithelial cells
B. Muscle cells
c. Nerve cells
D. Gland cells


Assertion
Hydrides of \( N, O \) and \( F \) have lower boiling points than the hydrides of their subsequent group members.
Reason

Boiling point depends upon the molecular mass only.
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


Name the types of teeth and salivary glands found in humans.


If the S.D. of \( \boldsymbol{y}_{1}, \boldsymbol{y}_{2}, \boldsymbol{y}_{3}, \dots . . \boldsymbol{y}_{n} \) is \( \boldsymbol{6}, \) then
the variance of \( \boldsymbol{y}_{1}-\boldsymbol{3}, \boldsymbol{y}_{2}-\boldsymbol{3}, \boldsymbol{y}_{3}- \)
\( \mathbf{3}, \dots . . y_{n}-3, \) is
\( A \cdot 6 \)
B. 36
\( c .3 \)
D. 27


A force of \( 20 \mathrm{N} \) acts on the ball for short
duration. If ball of mass \( 0.5 \mathrm{kg} \) acquire a speed of \( 4 \mathrm{m} / \mathrm{s} \) from the rest. For how
long did this force act on the ball?
A . \( 0.01 \mathrm{s} \)
B. 0.02
\( c \cdot 0.1 \mathrm{s} \)
D. 0.2
E. \( 1 \mathrm{s} \)


The diagram represents the cell cycle.
Compared to a cell in the \( \mathrm{G}_{2} \) phase, \( \mathrm{a} \)
cell in the \( G_{1} \) phase has
A. Twice as much DNA
B. Half as much DNAA
C. Twice as many centromeres
D. Half as many centromeres
E. Twice as many chromosomes


What is a transistor? Why is it so
called? What are the advantages of transistors over vacuum tubes?


Number of d-electrons in chromium of
\( \left[C r\left(H_{2} O\right)_{6}\right]^{+3} \) ion are:
\( A \)
B. 2
\( c \cdot 3 \)
D. 4


Two similar circular loops carry equal
currents in the same direction. On
moving the coils further apart, the
electric current will
A. increase in both
B. decrease in both
C. remain unaltered
D. increases in one and decreases in the second


Light from a point source in air falls on a spherical glass surface whose radius of curvature and refractive index are 20
\( \mathrm{cm} \) and 1.5 respectively. If the distance of light source from the glass surface is \( 100 \mathrm{cm}, \) then at which position image will be formed?
\( A \cdot 25 \mathrm{cm} \)
B. 50 \( \mathrm{cm} \)
\( c .100 \mathrm{cm} \)
D. 200 cm


The binding energies per nucleon for
deuterium and helium are \( 1.1 \mathrm{MeV} \) and
\( 7.0 \mathrm{MeV} \) respectively. How much amount energy, in joules, will be
liberated when \( 10^{6} \) deuterons take part
in the reaction.


The construction of a triangle \( A B C \)
given that \( B C=6 \mathrm{cm}, B=45^{\circ} \) is not
possible when difference of \( A B \) and \( A C \) is equal to:
\( A .6 .9 \mathrm{cm} \)
B. \( 5.2 \mathrm{cm} \)
c. \( 5.0 \mathrm{cm} \)
D. \( 4.0 \mathrm{cm} \)


Induced current is produced in a coil,
only when its ends are
A. not closed
B. closed
\( c \cdot \operatorname{both} A \& B \)
D. None of the above


\( \frac{e^{1 / x}-e^{-1 / x}}{e^{1 / x}+e^{-1 / x}} \) check continuity at \( x= \)
\( \mathbf{0}^{-} \)


Insulin contains \( 3.4 \% \) sulphur. The
minimum molecular weight of insulin is :
A . 941.176
B. 944
c. 945.27
D. none


Under what condition will the direction
of sum and difference of two vectors be
same?


What is the SI prefix for \( 10^{-2} ? \)
A . Centi
B. Deci
c. мill
D. Kilo


What are the limitations of Rutherford's
nuclear model?
A. Electrons should undergoes spiral path and fall into nucleus
B. Could not explain hydrogen spectrumm
c. Electron lose energy while in motion
D. All of these


Tossing a coin is an example of
A. space
в. sample
c. experiment
D. event


A wire of length \( L \) and cross-sectional \( A \)
is made of a material of Young's
modulus. If the wire is stretched by an amount \( x, \) the work done is


Which is the human organ which
behaves like an optical instrument
having lens and a screen?
A. Ear
B. Eye
c. Nose
D. skin


Two coils, \( A \) and \( B \), are lined such that
emf \( \epsilon \) is induced in \( B \) when the current
in \( A \) is changing at the rate \( I \). If \( i \) current
is now made to flow in \( \mathrm{B} \), the flux linked
with \( A \) will be :
A. \( (\epsilon / I) i \)
i
B. \( \epsilon i I \)
c. \( (\epsilon I) \)
D. \( i I / \epsilon \)


Assertion
Positive catalysts increase the rate of
reaction.
Reason
Catalysts decrease the value of \( \Delta G^{o} \)
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


Force of attraction between two point charges \( Q \) and \( -Q \) separated by \( d \)
meter is \( F_{e} . \) When these charges are
placed two identical sphere of radius \( R=0.3 d \) whose centries are \( d \) meter
apart the force of attraction between
them is
A. Greater than \( F_{e} \)
B. Equal to \( F_{e} \)
c. Less than \( F_{e} \)
D. None of these


An electron in a Bohr orbit of a hydrogen
atom with the quantum number \( n_{2} \) has
an angular momentum \( 4.2176 \times \) \( 10^{-34} k g m^{2} s^{-1} . \) If electron drops from
this level to the next lower level, then the
wavelength of this line is:
A \( \cdot 18.75 \times 10^{-7} m \)
B. \( 1.87 \times 10^{-7} \mathrm{m} \)
c. \( 187.5 \times 10^{-7} \mathrm{m} \)
D. \( 0.187 \times 10^{-7} m \)


If \( A \) and \( B \) are two disjoint sets and \( N \) is
universal set, then \( \boldsymbol{A}^{\circ} \cup\left[(\boldsymbol{A} \cup \boldsymbol{B}) \cap \boldsymbol{B}^{\circ}\right] \)
is
\( A \cdot \phi \)
в. \( A \)
\( c . B \)
D. \( N \)


A flexible chain of length I and mass \( \mathrm{m} \) is slowly pulled at constant speed up over the edge of a table by a force \( F \) parallel to the surface of the table. Assuming that there is no friction between the table and chain, calculate
the work done by force \( F \) till the chain
reaches to the horizontal surface of the
table.


A solid material is supplied with heat at
a constant rate. The temperature of the
material is changing with heat input as shown in the figure. What does slope
DE represent?
A. latent heat of liquid
B. latent heat of vapour
c. heat capacity of vapour
D. inverse of heat capacity of vapour


The angular velocity of a body changes
fro \( \omega_{1} \) to \( \omega_{2} \) without applying a torque
but by changing the moment of inertia. The ratio of corresponding radii of
gyration \( \boldsymbol{K}_{\mathbf{1}}: \boldsymbol{K}_{\mathbf{2}} \) is
\( A \cdot \omega_{1}: \omega_{2} \)
B . \( \sqrt{\omega_{1}}: \sqrt{\omega_{2}} \)
D. \( \omega_{2}: \omega_{1} \)


The number of ordered triplets of positive integral solutions of \( \left|\begin{array}{ccc}\boldsymbol{y}^{3}+\mathbf{1} & \boldsymbol{y}^{2} \boldsymbol{z} & \boldsymbol{y}^{2} \boldsymbol{x} \\ \boldsymbol{y} \boldsymbol{z}^{2} & \boldsymbol{z}^{3}+\mathbf{1} & \boldsymbol{z}^{2} \boldsymbol{x} \\ \boldsymbol{y} \boldsymbol{x}^{2} & \boldsymbol{x}^{2} \boldsymbol{z} & \boldsymbol{x}^{3}+\mathbf{1}\end{array}\right|=\mathbf{1 1} \)


If \( \tan \theta=\frac{1}{\sqrt{2}}, \) find the value of \( \frac{\operatorname{cosec}^{2} \theta-\sec ^{2} \theta}{\operatorname{cosec}^{2} \theta+\cot ^{2} \theta} \)
A \( \cdot \frac{1}{10} \)
в. \( \frac{2}{10} \)
\( c \cdot \frac{3}{10} \)
D. \( \frac{4}{10} \)


In a study of diabetic patients in a village, the following observations were noted:
\( \begin{array}{llll}\text { Age in } & \mathbf{1 0}- & \mathbf{2 0}- & \mathbf{3 0}- \\ \text { years } & \mathbf{2 0} & \mathbf{3 0} & \mathbf{4 0}\end{array} \)
No. of \( ^{f}_{n t s}^{2} \) patien
Calculate the mean and standard
deviation. Also interpret the results


A solid copper sphere (density \( \rho \) and specific capacity \( C \) ) of radius \( r \) at an initial temperature of \( 200 \mathrm{K} \) is supended inside a chamber whose walls are at almost 0 K. The time
required for the temperature of the sphere to drop to \( 100 \mathrm{K} \) is
A \( \cdot \frac{7 r \rho C}{72 \times 10^{6} \sigma} \)
в. \( \frac{r \rho C}{6 \sigma} \)
c. \( \frac{r \rho C}{\sigma} \)
D. none of the above


If \( \boldsymbol{y}=\boldsymbol{a}^{\boldsymbol{x}}+\log \boldsymbol{x}+\boldsymbol{3} \boldsymbol{x}^{2}, \) find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \)


Match the following
\( \begin{array}{llll} & \text { List I } & & \text { List II } \\ & & & \\ \begin{array}{l}\text { Streamlined body } \\ \text { structure }\end{array} & \text { a } & \begin{array}{l}\text { Less no. of } \\ \text { irregularities }\end{array} \\ \text { 2 } & \begin{array}{l}\text { objects harder } \\ \text { againsteach } \\ \text { other }\end{array} & \text { b } & \text { Lubricant } \\ \text { 3 } & \text { Grease } & \text { c } & \begin{array}{l}\text { Increase } \\ \text { friction }\end{array} \\ \text { 4 } & \text { Smooth surface } & \text { d } & \begin{array}{l}\text { Decrease } \\ \text { friction }\end{array}\end{array} \)
A . \( 1-d, 2-c, 3-b, 4-a \)
\( , 4-b \)
B. \( 1-d, 2-c, 3-a \)
c. \( 1- \) a, \( 2-d, 3-b, 4-c \)
D. 1-a, 2-b, 3-c, 4-d


Anbarasan purchased a house for 17,75,000 and spent 1,25,000 on its interior decoration. He sold the house to
make a profit of \( 20 \% \). Find the S.P. of the
house.


The molar concentrations of \( A, B \) and \( C \) at equilibrium for the reaction \( \boldsymbol{A}+ \) \( 2 B \Leftrightarrow 3 C \) are 2,3 and 4 moles/lit
respectively. Its \( \boldsymbol{K}_{c} \) is:
\( A \cdot 2 \)
в. 3.56
\( c \cdot 0.2 \)
D. 0.026


Column I shows different positions in
which one pole of a magnet is placed near that of the other.
Column II indicates the resulting action between them for each situation. Fill in
the blanks.
Column I ||
\( N-N \)
Attraction
\( s-1 \)
Repulsion


Which element has a mass number of
20 and contains 11 neutrons??
A. copper
B. Gallium
c. calcium
D. Sodium
E. Fluorine


Simple pendulum of length I has a
maximum angular displacement \( \theta \). The maximum kinetic energy of the bob is?
A . \( m g \mid(1-\cos \theta) \)
B. \( 0.5 \mathrm{mgl} \)
c. \( \mathrm{mg} \)
D. 2mgl


6-furfuryl amino purine, \( 2-4 \)
dichlorophenoxy acetic acid and indole-
3 acetic acid are examples respectively
for
A. Synthetic auxin, kinetin and natural auxin
B. Gibberellin, natural auxin and kinetin
C. Natural auxin, kinetin and synthetic auxin
D. Kinetin, synthetic auxin and natural
E. Natural auxin, gibberellin and kinetin


The relative density of substance is numerically equal to its density in the system of units.


n the figure, two identical regular
hexagons are placed side by side as shown, then find the value of z.
A \( \cdot 60^{\circ} \)
В. \( 90^{\circ} \)
\( c \cdot 120^{\circ} \)
D. \( 160^{\circ} \)


Solve: \( \cos ^{2} x \frac{d y}{d x}+y=\tan x \)


Tracheids differ from other tracheary elements in
A. Having Casparian strips
B. Being imperforate
c. Lacking nucleus
D. Being lignified


When the left arm of a mercury manometer is connected to a cylinder filled with a gas, the level of the mercury in the right arm rises by \( 2 \mathrm{cm} \). If the pressure of the gas in the container \( 110160 \mathrm{Pa}, \) the atmospheric pressure is
cm of Hg. ( take \( g= \)
\( \left.10 m s^{-2}\right) \)
A . 79
B. 85 5
c. 76
D. 81


\( \boldsymbol{p} \boldsymbol{K}_{\boldsymbol{b}} \) for \( \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{O} \boldsymbol{H} \) at certain
temperature is 4.74 The pH of basic buffer containing equimolar
concentration of \( N H_{4} O H \) and \( N H_{C} I \)
will be:


Find out the most efficient engine in the following
A. An engine converts \( 80 \mathrm{K} \). of heat energy into \( 20 \mathrm{KJ} \) of work
B. An engine converts 50 KJ of heat energy into 15 KJ of work
C. An engine converts 30 KJ of heat energy into 6 KJ of work
D. An engine converts 60 KJ of heat energy into 24 KJ of work


Among fluorine and chlorine, the electron affinity of the latter is high. This is due to:
A. high electronegativity of fluorine
B. low dissociation energy of fluorine
c. fluorine repels with the added electron due to its small size
D. small size of chlorine atom


The height at which liquid will stand in
the open end of the pipe is
A. \( 4 m \)
B. \( 3.5 m \)
c. \( 4.5 m \)
D. \( 5.6 m \)


Photosynthesis in plants is a change
A. chemical
B. physical
c. both \( A \) and \( B \)
D. none of the above


\( F e(O H)_{3} \) sol can be more easily
coagulated by \( N a_{3} P O_{4} \) in comparison
to \( K C l \) because:
A. mass of \( N a_{3} P O_{4} \) is more than \( K C l \) hence it is more effective than \( K C l \)
B. phosphate ion \( \left(P O^{3-}\right) \) has higher negative charge than \( C l^{-} \) ion hence are more effective for coagulation
c. \( K C l \) is more soluble than \( N a_{3} P O_{4} \) hence less effective
for coagulation
D. \( N a^{+} \) ions are more effective than \( K^{+} \) ions for coagulation


Solve the given equation for \( y: \) \( \frac{1-9 y}{19-3 y}=\frac{5}{8} \)
A \( -\frac{66}{103} \)
в. \( \frac{38}{73} \)
\( c \cdot-\frac{87}{57} \)
D. None of these


The father of modern chemistry is:
A. Priestley
B. Lavoisier
c. Dalton
D. Mendeleev


Earthquake can cause
A. Tsunami
B. Floods
c. Landslide
D. All of the above


"Heat cannot by itself flow from a body at lower temperature to a body at higher temperature" is a statement of the
consequence of
A. second law of thermodynamics
B. conservation of momentum
c. conservation of mass
D. first law of thermodynamics


The population in India is characterised
by birth rate and
death rate.
A. high, high
B. high, low
c. low, high
D. low, low


The resistance of germanium with rise in temperature.
A. increases
B. decreases
c. remains the same
D. first increases then decreases


A tent is in the form of a cylinder of diameter \( 8 \mathrm{m} \) and height \( 2 \mathrm{m}, \) and mounted by a cone of equal base and height 3 m. The canvas used for making the tent is equal to
\( \mathbf{A} \cdot 36 \pi m^{2} \)
В. \( 28 \pi m^{2} \)
\( \mathbf{c} \cdot 24 \pi m^{2} \)
D. \( 38 \pi m^{2} \)


\( \operatorname{Let} \overrightarrow{\boldsymbol{a}}=\hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{b}}=\hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) and
\( \vec{c}=\hat{i}-\hat{j}-\hat{k} \) be three vectors. A vector \( \vec{v} \) in the plane of \( \vec{a} \) and \( \vec{b}, \) whose projection on \( \vec{c} \) is \( \frac{1}{\sqrt{3}}, \) is given by
A \( \cdot \hat{i}-3 \hat{j}+3 \hat{k} \)
B . \( -3 \hat{i}-3 \hat{j}-3 \hat{k} \)
\( \mathbf{c} \cdot_{3 \hat{i}-\hat{j}+3 \hat{k}} \)
D \( \cdot \hat{i}+3 \hat{j}-3 \hat{k} \)


The coordinates of a point which divides the line joining the points \( P(2,3,1) \) and \( Q(5,0,4) \) in the ratio 1: 2 are
\( ^{\mathbf{A}} \cdot\left(\frac{7}{3}, 1, \frac{5}{3}\right) \)
в. (4,1,3)
c. (3,2,2)
D. (1,-1,1)


An unknown metal of mass 192 g heated
to a temperature of \( 100^{\circ} \mathrm{cwas} \) immersed into a brass calorimeter of mass \( 128 g \) containing 240 g of water a temperature of \( 8.4^{\circ} \mathrm{C} \) calculate the specific heat of the unknown metal if
water temperature stabilizes at \( 21.5^{\circ} c \)
(specific heat of brass is \( 394 j K g^{-1} k^{-1} \)
A . 1232 J \( k g^{-1} K^{-1} \)
B . 458 J \( k g^{-1} K^{-1} \)
c. 654 J \( k g^{-1} K^{-1} \)
D. 916 J \( k g^{-1} K^{-1} \)


You measure two quantities as \( A= \)
\( \mathbf{1 . 0 m} \pm \mathbf{0 . 2 m}, \boldsymbol{B}=\mathbf{2 . 0 m} \pm \mathbf{0 . 2 m .} \mathrm{We} \)
should report correct value for \( \sqrt{A B} \) as
A. \( 1.4 m \pm 0.4 m \)
в. \( 1.41 m \pm 0.15 m \)
c. \( 1.4 m \pm 0.3 m \)
D. \( 1.4 m \pm 0.2 m \)


Radish is an example of
A. Fusiform root
B. Napiform root
c. conical root
D. Tuberous root


What is rectifier? Explain with neat circuit diagram the action of semiconductor diode as a full wave
rectifier.


Which of the following statements is wrong? Magnetic lines of force
A. Form closed circuits
B. Never intersect
c. Are densest near the poles
D. None of the above


The quantity of heat required to raise the temperature of unit mass of a substance through one degree Celsius
is known as
A. Heat Capacity of body
B. Specific heat capacity of a body
c. Latent heat of body
D. Specific latent heat of a body


If \( \triangle \mathrm{ABC} \) and \( \triangle \mathrm{AMP} \) are right triangles, right-angled at \( \mathrm{B} \) and \( \mathrm{M} \) respectively and \( \angle M A P=\angle B A C \)
Prove that
(i) \( \triangle A B C \sim \triangle A M P \)
(ii) \( \frac{\boldsymbol{C A}}{\boldsymbol{P A}}=\frac{\boldsymbol{B C}}{\boldsymbol{M P}} \)


Find the mobility of the conduction electrons in a copper conductor if in Hall effect measurements performed in the magnetic field of induction \( \boldsymbol{B}= \)
100 \( m T \) the transverse electric field
strength of the given conductor turned out to be \( \eta=3.1 \times 10^{3} \) less than that of
the longitudinal electric field.


(i) Metals can be recovered from their ores by chemical methods.
(ii) High purity metals can be obtained by zone refining method.
Which one is true /false.
A . (i) is true and (ii) is false
B. (ii) is true and (i) is false
c. (i) and (ii) are true
D. (i) and (ii) are false


Solubility curves of two ionic salts \( X \& \)
W are given below:
In which case the value of \( \Delta \boldsymbol{H}_{\text {sol.}}<\mathbf{0}: \)
\( A \cdot x \)
B. W
\( c \cdot \operatorname{Both}(x) \&(w) \)
D. None of these


The mole percentage of oxygen in a
mixture of \( 7 g N_{2} \) and \( 8 g O_{2} \) is :
A . 25
B. 75
c. 50
D. 40


Paulings values of electronegativities are dependent upon:
A. ionisation potentials
B. bond energies
c. electron affinities
D. atomic radii


The pair whose both species are used in antacid medicinal preparation is:
A. \( \operatorname{NaH} \mathrm{CO}_{3} \) nad \( \mathrm{Mg}(\mathrm{OH})_{2} \)
в. \( N a_{2} C O_{3} \) and \( C a\left(H C O_{3}\right) \)
c. \( C a\left(H C O_{3}\right)_{2} \) and \( M g(O H)_{2} \)
D. \( C a(O H)_{2} \) and \( N a H C O_{3} \)


Thermal stability of \( B a C O_{3}, C a C O_{3} \)
and \( M g C O_{3} \) is:
А. \( B a C O_{3}>C a C O_{3}>M g C O_{3} \)
в. \( B a C O_{3}>M g C O_{3}>C a C O_{3} \)
с. \( C a C O_{3}>M g C O_{3}>B a C O_{3} \)
D. \( M g C O_{3}>C a C O_{3}>B a C O_{3} \)


Why is it difficult to hold a school bag having a strap made of a thin and strong string?
A. The pressure exerted on the shoulder is very large
B. The pressure exerted on the shoulder is less than usual
c. The pressure exerted on the shoulder is almost zero
D. The thin string always slips down


If \( \cos A=\frac{4}{5} \) find \( \tan A \)


Which one of the following precedes reformation of the nuclear envelope, during M phase of the cell cycle?
A. Decondensation from chromosomes and reassembly of the nuclear lamina
B. Transcription from chromosomes and reassembly of the nuclear lamina
c. Formation of the contractile ring and formation of the phragmoplast
D. Formation of the contractile ring and transcription from chromosomes


\( \int\left[\log (1+\cos x)-x \tan \left(\frac{x}{2}\right)\right] d x \)
A \( \cdot x \log (1+\tan x) \)
B \( \cdot x \log (1+\sin x) \)
\( \mathbf{C} \cdot \log (1+\sin x) \)
D. \( x \log (1+\cos x) \)


Choose the correct sequence of events
occur in human reproduction.
A. Gametogenesis \( \rightarrow \) gestation \( \rightarrow \) insemination \( \rightarrow \) fertilization \( \rightarrow \) implantation \( \rightarrow \) parturition
B. Gametogenesis \( \rightarrow \) insemination \( \rightarrow \) gestation \( \rightarrow \) implantation \( \rightarrow \) fertilization \( \rightarrow \) parturition
C. Gametogenesis \( \rightarrow \) insemination \( \rightarrow \) fertilization \( \rightarrow \rightarrow \) implantation \( \rightarrow \) gestation \( \rightarrow \) parturition
D. Gestation \( \rightarrow \) gametogenesis \( \rightarrow \) insemination \( \rightarrow \) implantation \( \rightarrow \) fertilization \( \rightarrow \) parturition


If \( \boldsymbol{A}=\left[\begin{array}{cc}\cos \boldsymbol{\alpha} & \sin \boldsymbol{\alpha} \\ -\sin \boldsymbol{\alpha} & \cos \boldsymbol{\alpha}\end{array}\right], \) then verify that
\( \boldsymbol{A}^{\boldsymbol{T}} \boldsymbol{A}=\boldsymbol{I}_{2} \)


If
\( f(x) \) be an increasing function defined
on
\( [a, b] \) then \( \max \{f(t) \text { such that } a \leq t \leq x, a \leq x \leq \)
\( b\}=f(x) \)
\( \& \min \{\mathrm{f}(\mathrm{t}), a \leq t \leq x, a \leq x \leq \)
\( b\}=f(a) \) and if \( f(x) \) be decreasing
function defined on \( [a, b] \) then \( \max \{f(t), a \leq t \leq x, a \leq x \leq b\}=f(a) \)
\( \min \{f(t), a \leq t \leq x, a \leq x \leq b\}=f(x) \)
On the basis of above information
answer the following questions. \( \int_{0}^{\pi / 2} \min \{\sin x, \cos x\} d x \) equals
\( \mathbf{A} \cdot 2(\sqrt{3}-1) \)
B . \( \sqrt{2}(\sqrt{2}-1) \)
\( \mathbf{c} \cdot(\sqrt{3}-1) \)
D \cdot \( \sqrt{2}(\sqrt{2}+1) \)


Write the IUPAC name of the above
compound.


A water tap leaks such that water drops
fall at regular intervals. Tap is fixed \( 5 m \)
above the ground. First drop reaches the
ground and at that very instant third drop leaves the tap. At this instant the second drop is at a height of
\( A, 3 m \)
в. 4.5 т
\( \mathbf{c} .3 .75 \mathrm{m} \)
D. 2.5 .


Which of the following human activities is used to meet the ever-increasing demand in factories and for shelter?
A. Soil erosin
B. Pollution
c. Deforestation
D. Data insufficient


If the radius of a sphere is measured as
\( 7 \mathrm{m} \) with an error of \( 0.02 \mathrm{m}, \) find the
approximate error in calculating its volume


Q Type your question
conducting rod of length I. Another point
particle of the same mass is attached to the other end of the rod. The two
particles carry charges \( +q \) and \( -q \) respectively. This arrangement is held
in a region of a uniform electric field \( \mathrm{E} \)
such that the rod makes a small angle \( \theta \)
(say of about 5 degrees) with the field direction. Find an expression for the minimum time needed for the rod to
become parallel to the field after it is set free.
A \( \cdot \frac{\pi}{2}, \sqrt{\frac{M L}{2 q E}} \)
В \( \cdot \frac{\pi}{2}, \sqrt{\frac{M L}{q E}} \)
c. \( \pi, \sqrt{\frac{M L}{q E}} \)
D. None of these


In a reaction, 4 moles of electrons are
transferred to 1 mole of \( H N O_{3} \) when acted as an oxidant. The possible reduction product is:
A \( \cdot 1 / 2 \) mole of \( N_{2} \)
B. \( 1 / 2 \) mole of \( N_{2} O \)
c. 1 mole of \( N O_{2} \)
D. 1 mole of \( N H_{3} \)


Find \( \mathbf{5 0}-[\mathbf{4 0}]-[-\mathbf{2}] \)


Explain brown ring test with the help of chemical equation.


Meiosis is significant in terms of
evolution because it results
in
A. Genetically similar daughters
B. Four daughter cells
c. Eggs and sperms
D. Recombinations


The products obtained at cathode and anode on electrolysis of aqueous sodium succinate are :
A. anode: ethene \( +C O_{2} \), cathode : \( H_{2} \)
B. anode: ethyne \( +C O_{2} \), cathode : \( H_{2} \)
c. anode : ethyne + \( H_{2} \), cathode : Na
D. anode: ethyne \( +C O_{2} \), cathode : Na


Solve \( \int_{0}^{2}\left(x^{2}+1\right) d x \)
A \( \cdot \frac{2}{3} \)
в. \( \frac{14}{3} \)
\( c \cdot \frac{8}{3} \)
D. \( \frac{11}{3} \)


Derive an expression for integrated rate law for a zero order reaction.


Compare the motion of a body dropped to that of a horizontal projectile, both
falling from the same height.


In the expression \( \left(\frac{x}{m}\right)=K P^{1 / n}, x \)
represents the mass of adsorbent
If true enter 1 , else enter 0
A.


If in two triangles \( P Q R \) and \( D E F \)
\( \boldsymbol{P R}=\boldsymbol{E F}, \boldsymbol{Q} \boldsymbol{R}=\boldsymbol{D} \boldsymbol{E} \) and \( \boldsymbol{P Q}=\boldsymbol{F D} \)
then \( \triangle \boldsymbol{P Q R} \cong \triangle_{---} \)
\( \mathbf{A} \cdot F D E \)
в. \( D E F \)
c. \( F E D \)
D. \( D F E \)


Assertion
f more and more solute is added to a
solvent, the freezing point of the solution keeps on becoming higher and
higher.
Reason
Presence of large amount of the solid
solute does not allow the solution to
freeze.
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 mean deviation from the mean 10 of
the data \( 6,7,10,12,13, \alpha, 12,16 \) is
A . 3.5
B. 3.25 5
\( c .3 \)
D. 3.75 5


The value of \( \frac{1}{1 \cdot 2 \cdot 3}+\frac{1}{2 \cdot 3 \cdot 4}+ \)
\( \frac{1}{3 \cdot 4 \cdot 5}+\frac{1}{4 \cdot 5 \cdot 6} \) is equal to
\( A \cdot \frac{7}{30} \)
в. \( \frac{11}{30} \)
c. \( \frac{13}{30} \)
D. \( \frac{17}{30} \)


Plot the given points on a graph paper and join them with straight lines. Give a special name to the figure obtained:
(3,2),(3,-4),(-2,2) and (-2,-4)


Which of the following pairs are
correctly matched?
a. spirogyra Fragmentatio an -
Planaria
ponges
b. \( \quad \) Regeneration Hydra, Planari
and sponges
\( \mathrm{c} \)
Scion an \( - \) The part of the
plant that is
grafted to other
plant
Development of
d. Parthenogenesis organisms
from an
unfertilized degg
The correctly paired ones are given
\( A \cdot a, c \) and \( d \)
B. \( a, b, c \) and \( d \)
\( c . b, c \) and \( d \)
D. a, b and d


Four \( 1-1 \) litre flasks are separately filled
with the gases \( H_{2}, H e, O_{2} \) and ozone.
The ratio of total number of atoms of
these gases present in different flask would be:
A .1: 1: 1: 1
B. 1: 2: 2: 3
c. 2: 1: 2: 3
D. 3:2:2:1


If linear function \( f(x) \) and \( g(x) \) satisfy \( \int[(3 x-1) \cos x+(1-2 x) \sin x] d x= \)
\( \boldsymbol{f}(\boldsymbol{x}) \cos \boldsymbol{x}+\boldsymbol{g}(\boldsymbol{x}) \sin \boldsymbol{x}+\boldsymbol{C}, \) then
A. \( f(x)=3 x-3 \)
B. \( g(x)=3+x \)
C. \( f(x)=3(x-1) \)
D. \( g(x)=3(x-1) \)


The arrow in following diagram shows
the direction a sailing ship moves. What happens if a strong wind blows from the same direction?
A. The sailing ship moves faster
B. The sailing ship moves slower
C. The sailing ship come to rest
D. Nothing happens


obtained by carbon reduction is In
liquid state?
\( A \)
B
\( c \)
fthes


Solve \( : \int \frac{2 x^{3}-3 x^{2}-8 x-26}{2 x^{2}-5 x+2} d x \)


How is nuclear power derived?
A. It is derived from energy i.e. released when relatively large atoms of uranium, thorium are split by shooting neutrons on them.
B. It is derived from energy i.e. released when relatively small atoms of uranium, thorium are split by shooting neutrons on them.
C. It is derived from energy i.e. released when relatively large atoms of uranium, thorium are split by shooting electrons on them.
D. None


The triple points of neon and carbon
dioxide are \( 24.57 \mathrm{K} \) and \( 216.55 \mathrm{K} \)
respectively. Express these
temperatures on the Celsius and
Fahrenheit scales


The correct order of increasing acidic
strength of the following acids is:
\( A \cdot|<1|<\| \)
c. ॥ा < ॥ ।
D. II<IIIS


The displacement \( x \) of a particle along
the \( x \) -axis at time \( t \) is given by \( x= \) \( \frac{a_{1}}{2} t+\frac{a_{2}}{3} t^{2} . \) Find the acceleration of the
particle.


According to Bharat IV, the emission of carbon monoxide should be
\( A \cdot 0.18 \mathrm{gm} / \mathrm{km} \)
B. \( 0.1 \mathrm{gm} / \mathrm{km} \)
c. \( 0.5 \mathrm{gm} / \mathrm{km} \)
D. \( 1 \mathrm{gm} / \mathrm{km} \)


If \( a, b, c \) and \( d \) are in \( G P, \) then \( (a+b+ \)
\( \boldsymbol{c}+\boldsymbol{d})^{2} \) is equal to:
\( \mathbf{A} \cdot(a+b)^{2}+(c+d)^{2}+2(b+c)^{2} \)
B. \( (a+b)^{2}+(c+d)^{2}+2(a+c)^{2} \)
\( \mathbf{C} \cdot(a+b)^{2}+(c+d)^{2}+2(b+d)^{2} \)
D. \( (a+b)^{2}+(c+d)^{2}+(b+c)^{2} \)
E \( \cdot(a+b)^{2}+(c+d)^{2}+(b-c)^{2} \)


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


Which of the following is an outcome?
A. Rolling a pair of dice
B. Landing on red
c. choosing 2 marbles from a jar
D. None of the above


Which particle among the following will have the smallest de Broglie wavelength, assuming that they have the same velocity?
A. Positron
B. Photon
c. \( \alpha \) - particle
D. Neutron


\( \ln \operatorname{acircle} \) of radius \( 21 \mathrm{cm}, \) an arc
subtends an angle of \( 60^{\circ} \) at the
centre.Find
(i) the length of the arc
\( (i i) \) the area of the sector
(iiii) the area of the minor segment and
\( (i v) \) the area of the major segment.


The ratio of the drifty velocity \( v_{d} \) and
r.m.s. velocity of electrons is
\( \mathbf{A} \cdot 10^{-10} \)
B . \( 10^{-5} \)
\( \mathbf{c} \cdot 10^{-3} \)
D. \( 10^{-6} \)


An object placed at a distance of \( 16 \mathrm{cm} \) from first principal focus of convex lens, produces a real image at a distance of \( 36 \mathrm{cm} \) from its second principal focus
Then the focal length of the lens is :
\( \mathbf{A} \cdot 9 c m \)
B. \( 25 \mathrm{cm} \)
\( \mathbf{c} \cdot 24 c m \)
D. \( 17 \mathrm{cm} \)


\( \ln \) an A.P if sum of its first \( n \) terms is
\( 3 n^{2}+5 n \) and its \( k^{t h} \) term is \( 164, \) find
the value of \( k \)


A hole of radius \( R / 2 \) is cut from a solid
sphere of radius \( R \). If the mass of the
remaining part of sphere is \( M, \) then
find moment of inertia of the body about
an axis through \( \boldsymbol{O} \)


Write each of the following polynomials in the standard form. Also, write their
degree:
\( a^{2}+4+5 a^{6} \)


A ball thrown with a velocity of \( 49 m s^{-1} \) got the maximum range recorded in the atmosphere as \( 225 m \). The decrease in
range due to the atmosphere is
A. \( 0 m \)
B. \( 245 m \)
\( \mathbf{c} .225 m \)
D. 20m


Fill in the blanks by choosing the appropriate word/words from those given in the brackets:
(square pyramidal, electrical, 74, 26 \( s p^{3} d^{2}, s p^{3} d, \) chemical, 68,32
tetrahedral, yellow, white, iodoform, Lucas)
Propan-2-ol on reaction with iodine and sodium hydroxide gives precipitate and the reaction is called
test.


The ordinary pressure of air surrounding us is
A. 15 pounds
B. 16 pounds
c. 14.2 pounds
D. 14.7 pounds


Centrosome includes a pair of
centrioles that help in cell division by spindle formation. The non-dividing cells in human are
A. Chondrocytes
B. Epithelial cells
c. Neurons
D. Neuroglial cells


Average velocities for time intervals \( t= \)
0 to \( 2 s, t=2 \) to 4 s and \( t=0 \) to 4 s are
respectively equal to
A \( .2 .5 \mathrm{m} / \mathrm{s},-2.5 \mathrm{m} / \mathrm{s}, 2.5 \mathrm{m} / \mathrm{s} \)
B. \( 1.25 \mathrm{m} / \mathrm{s},-1.25 \mathrm{m} / \mathrm{s}, 0 \mathrm{m} / \mathrm{s} \)
\( c \cdot 5 m / s,-5 m / s, 0 m / s \)
D. \( 2.5 \mathrm{m} / \mathrm{s},-2.5 \mathrm{m} / \mathrm{s}, 0 \mathrm{m} / \mathrm{s} \)


The sex of every animal depends on the fusion.
A. Chromosomal
B. Bloodd
c. RNA
D. None of these


Which non-metal has a shining
surface?
A. Graphite
B. Phosphorous
c. sulphur
D. None of the above


Tow monochromatic coherent source of
wavelength \( 5000 A \) are placed along the
line normal to the screen as shown in
the figure.
(a) Determine the condition for maxima
at the point \( \boldsymbol{P} \)
(b) Find the order of the centre bright
fringe if \( \boldsymbol{d}=\mathbf{0 . 5} \boldsymbol{m m}, \boldsymbol{D}=\mathbf{1} \boldsymbol{m} \)


You are given \( 5 m \) length of heating wire,
it has resistance of \( 24 \Omega . \) It is cut into
two and connected to 110 volt line
individually. The total power for the two half lengths is:
A. 500 watts
B. 1000 watts
c. 2000 watts
D. 2500 watts


The constraints
\( -\boldsymbol{x}_{1}+\boldsymbol{x}_{2} \leq 1 \)
\( -\boldsymbol{x}_{1}+\mathbf{3} \boldsymbol{x}_{2} \leq \mathbf{9} \)
\( \boldsymbol{x}_{1}, \boldsymbol{x}_{2} \geq \mathbf{0} \) defines on
A. Bounded feasible space
B. Unbounded feasible space
C. Both bounded and unbounded feasible
D. None of the above


Find intervals in which \( f(x)=\frac{4 x^{2}+1}{x} \)
is increasing and decreasing.


Assertion
Increasing the current sensitivity of a galvanometer necessarily increases the voltage sensitivity.
Reason
Voltage sensitivity is inversely proportional to current sensitivity.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


In which of the following cases of rolling body, translatory and rotational kinetic energies are equal
A. Circular ring
B. Circular plate
c. Solid sphere
D. solid cylinder


Given two compounds, one more polar than the other, which one will move up the silica stationery phase higher than the other in TLC?
A. Polar compound
B. Non polar compound
c. Both will move equally
D. None will move


The vapour pressure of \( 2.1 \% \) of an aqueous solution of a non-electrolyte at
\( 373 K \) is \( 755 \mathrm{mm} \). Calculate the molar
mass of solution \( \left(M_{2}\right) \)
A . \( 46.1 \mathrm{gm} / \mathrm{mol} \) le
B. \( 57.456 \mathrm{gm} / \mathrm{mole} \)
c. \( 10 \mathrm{gm} / \mathrm{mole} \)
D. \( 87.12 \mathrm{gm} / \mathrm{mole} \)


Which of the following statements
about Grignard reagent is false?
A. Grignard reagents (RMgBr) add to the carbonyl group of aldehydes and ketones
B. An organosodium compound is not very reactive compared to a Grignard reagent
C . Grignard reagents are prepared in ether or tetrahydrofuran (THF)
D. Grignard reagents are decomposed by water and alcohol


Evaluate \( \lim _{x \rightarrow 4} \frac{3-\sqrt{5+x}}{1-\sqrt{5-x}} \)
A \( \cdot \frac{1}{3} \)
B. \( -\frac{1}{3} \)
\( c \cdot \frac{2}{3} \)
D. \( -\frac{2}{3} \)


A proton takes \( 10^{-12} \) seconds to
complete one revolution in uniform
magnetic field. The time taken in another orbit of double the radius in
the same field is
B . \( 2 \times 10^{-12} \) seconds
c. \( 4 \times 10^{-12} \) seconds
D. \( 10^{-12} \) seconds


How many numbers amongst the numbers 9 to 54 are there which are
exactly divisible by 9 but not by \( 3 ? \)
\( A \cdot 8 \)
B. 6
\( c \cdot 5 \)
D. Nil


Which of the following would not be attracted or deflected while traveling through an electric field?
I. Gamma ray
II. Beta particle
III. neutron.
A . i only
B. ii only
c. i and ii only
D. i and iii only


The relation connecting acceleration due to gravity and gravitational constant is:
A \( \cdot g=\frac{G M}{R^{2}} \)
В . \( g=\frac{G M}{R} \)
c. \( g=G M R^{2} \)
D. \( g=G M R \)


Benzene \( \stackrel{X}{\longrightarrow} \) Benzene sulphonicacid
Identify \( X ? \)
A. Sulphuric acid
B. Hydrochloric acid
c. Sulphur
D. Both A and C


Present day view regarding
photosynthesis is
A. It converts light energy into chemical energy
B. It creates useful energy
\( \mathrm{C} \cdot \) It fixes \( \mathrm{CO}_{2} \) into carbohydrates
D. It reverses the action of respiration


The most penetrating atom smashing particle is
A. neutron
B. proton
c. alpha particle
D. deuteron


\( \mathbf{f}_{\mathbf{1}}=\left|\begin{array}{ccc}\mathbf{7} & \boldsymbol{x} & \mathbf{2} \\ -\mathbf{5} & \boldsymbol{x}+\mathbf{1} & \mathbf{3} \\ \mathbf{4} & \boldsymbol{x} & \mathbf{7}\end{array}\right|, \boldsymbol{\Delta}_{2}= \)
\( \left|\begin{array}{ccc}\boldsymbol{x} & \boldsymbol{2} & \boldsymbol{7} \\ \boldsymbol{x}+\boldsymbol{1} & \boldsymbol{3} & -\boldsymbol{5} \\ \boldsymbol{x} & \boldsymbol{7} & \boldsymbol{4}\end{array}\right| \) then \( \boldsymbol{\Delta}_{1}-\boldsymbol{\Delta}_{2}=\boldsymbol{0} \) for
\( \mathbf{A} \cdot x=2 \)
B. all real \( x \)
c. \( x=0 \)
D. none of these


An \( \alpha- \) particle of energy 5 MeV is
scattered through \( 180^{\circ} \) by a fixed
uranium nucleus. The distance of
closest approach is of the order of
A \( \cdot 10^{-12} \mathrm{cm} \)
B . \( 10^{-10} \mathrm{cm} \)
\( c \cdot 1 A \)
D. \( 10^{-15} \mathrm{cm} \)


Interference fringes are obtained due to the interference of waves from two
coherent sources of light with
amplitudes \( a_{1} \) and \( a_{2}\left(a_{1}=2 a_{2}\right) . \) What
is the ratio of the maximum and
minimum intensities of light in the
interference pattern?
A .2
B. 4
\( c .9 \)
D. \( \infty \)


A magnetic field directed along \( Z \) axis
varies as \( \boldsymbol{B}=\boldsymbol{B}_{0} \boldsymbol{x} / \boldsymbol{a}, \) where \( \boldsymbol{B}_{0}= \)
2 tesla and \( a=1 m . \) A conducting
square loop of side \( \ell=\frac{1}{2} m \) is placed
with its edges parallel to \( X \) and \( Y \) axes. If
the loop is made to move with a
constant velocity \( v_{0}=6 m / s \) directed
along \( X \) axis, the induced emf (in volts) in the loop is :


A Student planned an experiment that
would use \( 0.10 M \) propionic acid,
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C O O H} . \) Calculate the value
of \( \left[\boldsymbol{H}^{+}\right] \) and the \( \boldsymbol{p} \boldsymbol{H} \) for this solution. For
propionic acid, \( \boldsymbol{K}_{\boldsymbol{a}}=\mathbf{1 . 3 4} \times \mathbf{1 0}^{-\mathbf{5}} \)


Match the Column-I with Column-II.


For alkali metals, only electrolytic reduction is employed.
A. True
B. False


What are the DR's of vector parallel to
(2,-1,1) and (3,4,-1)\( ? \)
A \( \cdot(1,5,-2) \)
B \( \cdot(-2,-5,2) \)
\( \mathbf{c} \cdot(-1,5,2) \)
D \( \cdot(-1,-5,-2) \)


The converse of "if in a triangle
\( A B C, A B>A C, \) then \( \angle C=\angle B^{\prime \prime}, \) is
\( \mathbf{A} \cdot \) If in a triangle \( A B C, \angle C=\angle B, \) then \( A B>A C \)
B. If in a triangle \( A B C, A B \not=A C, \) then \( \angle C \not=\angle B \).
C. If in a triangle \( A B C, \angle C \not=\angle B, \) then \( A B \not=A C \)
D. If in a triangle \( A B C, \angle C \not=\angle B, \) then \( A B>A C \).


The current gain in common base
amplifier is
A . high
B. very low
c. about 1
D. very high


Few algae show
A. External fertilisation
B. Heterogametes
C . Internal fertilisation
D. Zygotic mitosis to develop embryo


A \( 3 m \) long ladder weighing 20 kg leans
on a frictionless wall. Its feet rest on the
floor \( 1 \mathrm{m} \) from the wall as shown in Fig.
Find the reaction forces of the wall and
the floor


Calculate the work done injoules when
3 moles of an ideal gas at \( 27^{\circ} C \) expands isothermally and reversibly from 10 atm to 1 atm \( (1 a t m=1.013 x \)
\( 10^{5} N m^{-2} \) ). What will be the work done
if the expansion is against the constant
pressure of 1 atm?


Which one of the following statement is
false
A. Work is a state finction
B. temperature is a state function
c. change in the state is completely defined when the initial and final states are specified
D. Work appears at the boundary of the system


What are phytoplankton?


Assertion
A beam of white light shows no dispersion on emerging from a glass slab.
Reason
Dispersion in a glass slab is zero.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A standing wave \( \zeta= \) \( (5 m m) \sin \pi x . \cos (200 t) \) is maintained
in a homogeneous rod with cross-
sectional area \( 0.04 m^{2} \) and density
\( 1000 k g / m^{3} . \) The total mechanicalenergy confined between the sections corresponding to the adjacent displacement nodes is
A. \( 10 J \)
\( J \)
B. \( 20 J \)
c. \( 40 J \)
D. None of these


Match column I with column II and
select the correct option from the codes
given below.

Column II Column I (Phytohormone) where it is synthesised
Tissues
\( \begin{array}{llll}\text { A. } & \text { IAA } & \text { (i) } & \text { undergoing }\end{array} \) senescence
B. Cytokinins \( \quad \) (ii) \( \quad \) Shoot apices
C. Ethylene \( \quad \) (iii) \( \quad \) Root apices
\( A \cdot A-(i i), B-(i i i), C-(i) \)
B. A-(iii), B-(ii), C-(i)
C \( . A \) -(i), B-(ii), C-(iii)
D. A-(ii), B-(i), C-(iii)


Lye is used in soap-making. It is a
concentrated solution of which ionic
compound?
A . \( N a C l \)
в. \( N a O H \)
c. \( C u S O_{4} \)
D. \( K_{2} C O_{3} \)


An observer moves towards a stationary
plane mirror at a speed of \( 4 \mathrm{ms}^{-1} \). What
is the relative speed of the image with respect to the observer?
A \( \cdot 2 \mathrm{ms}^{-1} \)
B. \( 4 \mathrm{ms}^{-1} \)
\( c \cdot 8 m s^{-1} \)
D. the image will stay at rest


The process in which embryo develops from unfertilized oosphere is called as
A. Parthenogenesis
B. Apospory
c. Apogamy
D. None of the above


The de-Broglie wavelength associated with an electron accelearated to
potential difference of V volt is:
A. \( V \times 10^{-10} m \)
в. \( \sqrt{\frac{150}{V}} A^{0} \)
c. \( \frac{150}{V} A^{0} \)
D. \( 150 V \times 10^{-8} \mathrm{m} \)


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


Rutherford's scattering experiment led to the discovery of :
A. nucleus
B. presence of neutrons in the nucleus
\( c \cdot \) both (1) and (2)
D. revolving nature of electrons around the nucleus


\( \mid \begin{array}{ccc}\mathbf{2} \boldsymbol{a}_{1} \boldsymbol{b}_{1} & \boldsymbol{a}_{1} \boldsymbol{b}_{1}+\boldsymbol{a}_{2} \boldsymbol{b}_{1} & \boldsymbol{a}_{1} \boldsymbol{b}_{3}+\boldsymbol{a}_{3} \boldsymbol{b}_{1} \\ \boldsymbol{a}_{1} \boldsymbol{b}_{2}+\boldsymbol{a}_{2} \boldsymbol{b}_{1} & \boldsymbol{2} \boldsymbol{a}_{2} \boldsymbol{b}_{2} & \boldsymbol{a}_{2} \boldsymbol{b}_{3}+\boldsymbol{a}_{3} \boldsymbol{b}_{2} \\ \boldsymbol{a}_{1} \boldsymbol{b}_{3}+\boldsymbol{a}_{3} \boldsymbol{b}_{1} & \boldsymbol{a}_{3} \boldsymbol{b}_{2}+\boldsymbol{b}_{3} \boldsymbol{a}_{2} & \boldsymbol{2} \boldsymbol{a}_{3} \boldsymbol{b}_{3}\end{array} \)
\( A \)
B.
\( \mathbf{c} \cdot a_{1} b_{1} a_{2} b \)
D. \( a_{1} b_{1}+a_{2} b_{2} \)


\( \left(1+x^{2}\right)\left(1+y^{2}\right)\left(1+z^{2}\right) \) can be
expressed as \( \left(1-\sum x y\right)^{2}+ \)
\( \left(\sum x-x y z\right)^{2} . \) If this is true enter 1
else enter 0


A student prepares a \( 0.10 M \) CoCl \( _{2} \)
solution and determines the
absorbance of the solution at various
wavelengths using a
spectrophotometer. A graph of the results is shown below.

Identify the optional wavelength for
absorbance.
\( \mathbf{A} \cdot 300 n m \)
B. \( 375 n m \)
\( \mathbf{c} \cdot 410 n m \)
D. \( 550 n m \)


What is the common ratio of the
geometric sequence \( 81,27,9,3, \dots ? \)
A \( \cdot \frac{1}{2} \)
B.
\( c \cdot \frac{1}{4} \)
D.


\( 18.0 g \) of \( \operatorname{glucose}\left(C_{6} H_{12} O_{6}\right) \) is added to
\( 178.2 g \) of water. The vapour pressure of water for this aqueous solution at \( 100^{\circ} \mathrm{C} \)
is :
A . \( 759 . .00 \) Torr
B. 7.60 Torr
c. 76.00 torr
D. 752.40 Torr


Which of the following statements is incorrect for \( \sigma \) and \( \pi \) -bonds formed
between two carbon atoms?
A. \( \sigma \) -bond is stronger than a \( \pi \) -bond
B. Bond energies of \( \sigma \) and \( \pi \) -bonds are of the order of \( 264 k J / m o l \) and \( 347 k J / m o l \)
C. Free rotation of surrounding atoms about a \( \sigma \) -bond is allowed but not in case of a \( \pi \) -bond
D. \( \sigma \) -bond determines the direction between carbon atoms but a \( \pi \) -bond has no primary effect in this regardd


Which of the following set contains oxide in the sequence, basic, amphoteric and acidic respectively?
A. \( S O_{2}, P_{2} O_{5}, C O \)
в. \( B a O, A l_{2} O_{3}, \) SiO \( _{2} \)
c. \( C a O, \operatorname{si} O_{2}, A l_{2} O_{3} \)
D. \( A l_{2} O_{3} . C O_{2}, C O \)


What will be the polarities at \( A \& B \) if the direction of current is reversed in
the circuit??


Rewrite the equation \( |\boldsymbol{y}|=|\boldsymbol{x}| \) as two
equations of two lines.


\( 4 \sqrt{2} m \) and breadth \( 4 m \) carrying a
current of \( 5 A \) in the anti-clockwise
direction is placed in the xy-plane. The
magnitude of the magnetic induction
field vector \( B \) at the intersection of the
diagonal is \( \left(U s e u_{0}=4 \pi x\right. \)
\( \left.10^{-7} N A^{-2}\right) \)
A \( .1 .2 \times 10^{-6} T \)
B . \( 1.2 \times 10^{-5} T \)
c. \( 2.4 \times 10^{-6} T \)
D. \( 2.4 \times 10^{-5} T \)
E \( .1 .2 \times 10^{-7} T \)


Where is the basement membrane
derived from?
A. Ectoderm
B. Endoderm
c. Epidermis
D. Epidermis and connective tissue


How many distinct monochlorinated
products, (including stereoisomers)
may be obtained when the alkane
shown below is heated in the
presence of \( \boldsymbol{C l}_{2} \) ?
\( A \cdot 2 \)
B. 4
\( c \cdot 5 \)
D. 6
E. 8


If 12 g of alkaline earth metal gives 14.8 g of its nitride, then what is the atomic
weight of metal?
A \( \cdot 12 \)
B. 20
\( c \cdot 40 \)
D. 14.8


Diatoms float in water due to
A. Stored fats
B. Gas vacuoles
c. Flagella
D. Air chambers


Among the following compounds, which one is not responsible for the depletion of ozone layer?
A \( \cdot C H_{4} \)
в. \( C F C l_{3} \)
c. \( N O \)
D. \( C l_{2} \)


What is the oxidation number of
carbonyl carbon in acetophenone?
\( A \cdot+3 \)
B. +1
\( c \cdot+2 \)
D. zero


Two short dipoles are situated parallel
to each other separated by a distance \( x \)
The force of interaction is
A \( \cdot \) A force of attraction of \( \frac{2 K p_{1} p_{2}}{x^{4}} \)
B. A force of repulsion of \( \frac{2 K p_{\eta} p_{2}}{x^{4}} \)
C . A force of attraction of \( \frac{3 K p_{1} p_{2}}{x^{4}} \)
D. A force of repulsion of \( \frac{3 K p_{\eta} p_{2}}{x^{4}} \)


On increasing the temperature, the solubility of the solute in the
solvent


If \( g(f(x))=|\sin x| \) and \( f(g(x))= \)
\( (\sin \sqrt{x})^{2}, \) then
A \( \cdot f(x)=\sin ^{2} x \cdot g(x)=\sqrt{x} \)
B. \( f(x)=\sin x, g(x)=|x| \)
C. \( f(x)=x^{2}, g(x)=\sin \sqrt{x} \)
D. f and g can not be determined


The ratio of the difference in energy
between the first and second Bohr orbit
to that between second and third Bohr
in H-atom is:
\( A \cdot 4 / 9 \)
B. \( 1 / 3 \)
c. \( 27 / 5 \)
D. \( 1 / 2 \)


Two stars of masses \( m_{1} \) and \( m_{2} \) are
parts of a binary star system. The radii
of their orbits are \( r_{1} \) and \( r_{2} \) respectively,
measured from the centre of mass of
the system. The magnitude of
gravitational force \( \boldsymbol{m}_{1} \) exerts on \( \boldsymbol{m}_{2} \) is
then
A. \( \frac{m_{1} m_{2} G}{\left(r_{1}+r_{2}\right)^{2}} \)
в. \( \frac{m_{1} G}{\left(r_{1}+r_{2}\right)^{2}} \)
c. \( \frac{m_{2} G}{\left(r_{1}+r_{2}\right)^{2}} \)
D. \( \frac{G\left(m_{1}+m_{2}\right)}{\left(r_{1}+r_{2}\right)^{2}} \)


The stage when the reproductive organs reach sexual maturity is called as
A. Puberty
B. Menstruation
c. Gestation
D. Fertilization


What is the direction cosine of angle which the vector \( \sqrt{2 \hat{i}}+\hat{j}+ \)
\( \hat{k} \) makes with \( y- \) axis \( ? \)


Which of the following is true?
A. Lyman series is a continuous spectrum
B. Paschen series is a line spectrum in the infrared
C. Balmer series is a line spectrum in the ultraviolet
D. The spectral series formula can be derived from the Rutherford model of the hydrogen atom


An acid produces free \( \boldsymbol{H}+ \) ions in
aqueous solution.
A. True
B. False


\( \mathrm{CH}_{3}-\mathrm{C}_{\mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{C}}^{\mathrm{O}} \mathrm{CH}_{3} \)


A bob is suspended from the ceiling of a car which is accelerating uniformly on a horizontal road
choose the wrong statement
A. the bob stays a constant angle \( \theta \) with vertical with respect to car in equilibirum
B. the magnitude linear momentum of a bob as seen from the rod is increasing with time
c. linear momentum is conserved only in car reference of frame
D. linear momentum is conserved in car as well as ground reference of frame


A mass at the end of a spring executes harmonic motion about an equilibrium position with an amplitude A.lts speed as it passes through the equilibrium position is V.If extended 2A and released, the speed of the mass passing through the equilibrium position will be
A \( .2 v \)
B. 4V
c. v/2
D. V/4


Menstrual cycle occurs in
A. Female primates
B. Human females
C. Mammalian females
D. Rabbit


Find the matrices \( A \) and \( B \) such that \( \boldsymbol{A}+\boldsymbol{B}=\left[\begin{array}{ll}\mathbf{5} & \mathbf{4} \\ \mathbf{7} & \mathbf{3}\end{array}\right] \) and \( \boldsymbol{A}-\boldsymbol{B}= \)
\( \left[\begin{array}{cc}11 & 2 \\ -1 & 7\end{array}\right] \)


Identify the following shows the application of pressure in our everyday life?
This question has multiple correct options
A. The blade of Ice-skating shoe is very sharp
B. It is easier to drive a sharp tipped nail into wood
c. Sharp knife cuts better
D. Foundation of high-rise building are kept narrow


A monatomic gas is compressed adiabatically to \( \frac{1}{4} \) of its original volume, the final pressure of gas in terms of initial pressure P is:
A . 7.08 \( \mathrm{P} \)
B. 8.08 P
c. 9.08 p
D. 10.08


Which of the following has metallic as well as non-metallic character?
(i) Arsenic
(ii) Antimony (iii) Lead
\( A \cdot( \) i) only
B . (ii) only
c. (i) and (ii) only
D. (i), (ii) and (iii)


The equilibrium state can be attained from both sides of the chemical
reaction.
A. True
B. False


The binary number of decimal number
\( (9.25)_{10} \) is
A . 1101.01
в. 1001.01
c. 1001.10
D. 1110.010


A chemical equation is balanced according to the law of:
A. multiple proportions
B. constant proportions
c. reciprocal proportions
D. conservation of mass


Define anti-histamines. Give one
example


In which of the following cell \( (s): E_{c e l l}= \)
\( \boldsymbol{E}_{c e l l}^{o} ? \)
This question has multiple correct options
\( \mathbf{A} \cdot C u(s)\left|C u^{2+}(0.01 M) \| A g^{+}(0.1 M)\right| A g(s) \)
B. \( P t, H_{2}(g)|p H=1|\left|Z n^{2+}(0.01 M)\right| Z n(s) \)
\( \mathbf{c} \cdot P t, H_{a t m}(g)\left|p H=1 \| Z n^{2+}(1 M)\right| Z n(s) \)
D. \( P t, H_{2}(g)\left|H^{+}=0.1 M\right|\left|Z n^{2+}(0.01 M)\right| Z n(s) \)


Which of the following is not a scientific name of banana
A. Musa paradisiaca
B. Musa superba
c. Musa textilis
D. Hibiscus mutabilis


n the following figure, \( \boldsymbol{O A}=\boldsymbol{O C} \) and
\( A B=B C . \) Prove that
\( \angle A O B=90^{\circ} \)
ii) \( \Delta A O D \cong \Delta C O D \)
iii) \( \boldsymbol{A} \boldsymbol{D}=\boldsymbol{C} \boldsymbol{D} \)


Primary alcohols can be prepared from alkenes by:
A. mercuration and demercuration of alkenes
B. direct hydration of alkenes
c. hydroboration of alkenes
D. all of the above


Magnesium hydroxide is the white milky substance in milk of magnesia.
What mass of \( M g(O H)_{2} \) is formed when \( 15 m l \) of \( 0.2 M-N a O H \) is
combined with \( 12 \mathrm{ml} \) of \( 0.15 M- \)
\( M g C l_{2} ? \)
A. \( 0.087 g \)
в. \( 0.079 g \)
c. \( 0.1044 g \)
D. \( 0.522 g \)


A diver under water, looks obliquely at a
fisherman standing on the bank of a
lake. Would the fisherman look taller or
shorter to the diver than what he
actually is?


For which change \( \Delta \boldsymbol{H} \neq \Delta \boldsymbol{U} \) ?
\( \mathbf{A} \cdot H_{2}(g)+I_{2}(g) \rightleftharpoons 2 H I(g) \)
B. \( H C l(l)+N a O H(l) \longrightarrow N a C l(l)+H_{2} 0(l) \)
\( \mathbf{c} \cdot C(s)+O_{2}(g) \rightleftharpoons C O_{2}(g) \)
D. \( N_{2}(g)+3 H_{2}(g) \longrightarrow 2 N H_{3}(g) \)


During adolescence, the body of a girl does not show which of the following changes?
A. Acne and pimple on face
B. Deep voice
c. Development of mammary gland
D. Growth of pubic hair


Based on the Maxwell-Boltzmann graph
below, which of the following
statements is TRUE?
\( A \cdot T_{1} \) is at a higher temperature than \( T_{2}, \) so more molecules will react to form products
B. The reaction is exothermic, so increasing kinetic energy decreases the rate of the reaction
\( \mathrm{c} \cdot T_{2} \) is at a higher temperature than \( T_{1}, \) so more molecules will react to form products
D. The reaction is endothermic, so increasing kinetic energy increases the rate of the reaction


The INCORRECT statement is:
A. The spin - only magnetic moments of \( \left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+} \) and \( \left[C r\left(H_{2} O\right)_{6}\right]^{2+} \) are nearly similar
B. The spin-only magnetic moment of \( \left[N i\left(N H_{3}\right)_{4}\left(H_{2} O\right)_{2}\right]^{2+} \) is \( 2.83 B M \)
C. The gemstone, ruby, has \( C r^{3+} \) ions occupying the octahedral sites of beryl
D. The color of \( \left[\mathrm{CoCl}\left(\mathrm{NH}_{3}\right)_{5}\right]^{2+} \) is violet as it absorbs the yellow light


Write the special characteristics/features of the human
digestive system


Calculate the HCF of \( 3^{3} \times 5 \) an \( 3^{2} \times 5^{2} \)


\( 6.022 \times 10^{20} \) atoms of silver (at mass
\( =108 u) \) weigh
A \( \cdot 108 \times 10^{3} g \)
B. \( 108 \mathrm{g} \)
c. 0.108 g
D. 10.8 g


A piece granulated zinc was dropped into copper sulphate solution. After sometime the colour of the solution
changed from blue to colourless. Why?


Reverse process of sublimation is:
A. fusion
B. condensation
c. deposition
D. freezing


The sum of integers from 1 to 100 which are divisible by 2 or 5 is-
A. 300
B. 3050
c. 3200
D. 3250


A basket contains 20 apples and 10 oranges out of which 5 apples and 3 oranges are defective. If a person takes out 2 at random, then the probability that either both are apples or both are \( \operatorname{good} \) is \( \frac{316}{435} \)
A. True
B. False


What causes the existence of very large
number of carbon compounds?


Define random experiment


The velocity of a ball of mass m density
d1d1 becomes constant after some
time.The viscous force acting on the
ball will be:
A. non of these
в. \( _{m g}\left(1-\frac{d_{2}}{d_{1}}\right) \)
c. \( m g\left(\frac{d_{1}+d_{2}}{d_{1}}\right) \)
D. \( _{m g}\left(\frac{d_{1}+d_{2}}{d_{2}}\right) \)


The diffraction effect can be observed in
A. only sound waves
B. only light waves
C. only ultrasonic waves
D. sound as well as light waves


What precautions should be taken
against nuclear radiations?
A. The radioactive elements should be kept in containers made up of thick lead walls.
B. The people working in the plants should wear special jackets and gloves made of lead linings.
C. The handling of the plants should be carried out from a distance.
D. All of the above.


In the redox reaction given below:
\( \boldsymbol{x} \boldsymbol{N} \boldsymbol{O}_{3}^{-}+\boldsymbol{y} \boldsymbol{A} \boldsymbol{s}_{2} \boldsymbol{S}_{3}+\boldsymbol{z} \boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \)
\( \boldsymbol{A} \boldsymbol{s} \boldsymbol{O}_{4}^{3-}+\boldsymbol{N} \boldsymbol{O}+\boldsymbol{S} \boldsymbol{O}_{4}^{2-}+\boldsymbol{H}^{+} \)
What is the value of \( \frac{x}{z} ? \)


Prove that the line joining a mid point of
a chord to the centre of circle is
perpendicular to it


An electron of charge 'e' and mass 'm' is
accelerated from rest by a potential difference 'V'. The de Broglie wavelength
is
A. Directly proportional to the square root of potential difference
B. Inversely proportional to the square root of potential difference
c. Directly proportional to the square root of electron mass
D. Inversely proportional to the cube root of electron mass


In the hystersis cycle, the value of \( \mathrm{H} \)
needed to make the intensity of magnetisation zero is called
A. retentivity
B. coercivity
c. Lorentz force
D. Pseudo force


The order decreasing reactivity towards an electrophilic reagent for the
following compound is:
(a) Benzene
(b) Toluene
(c) Chlorobenzene and
(d) Phenol
A. \( d>b>a>c \)
в. \( a>b>c>d \)
c. \( b>d>a>c \)
D. \( d>c>b>a \)


(i) If \( \sin (\theta+\alpha)=\cos (\theta+\alpha) \) then
express tan \( \theta \) in terms of \( \alpha \)
(ii) Find the value of \( \tan (\pi / 4+ \)
\( \theta) \cdot \tan (\pi / 4-\theta) \)


Find the value of \( \lim _{n \rightarrow \infty} \frac{1}{n} \sum_{r=1}^{n} \sin ^{2} \frac{r \pi}{n} \)


Corrosion of metals can be
prevented when contact between metal and \( \ldots \ldots \ldots . \) is cut off.
A. nitrogen
B. hydrogen
c. oxygen
D. carbon


Addition of phosphate and nitrate/fertilizers into water leads to:
A. increased growth of decomposers
B. reduced of algae growth
c. increased growth of algae
D. nutrient enrichment


Which of the following is not a noble
gas?
A. Helium
B. Neon
c. Argon
D. Hydrogen


If very small amount of phenolphthalein is added to 0.15 mol litre \( ^{-1} \) solution
of sodium benzoate, what fraction of the
indicator will exist in the coloured
form? State any assumption that you make.
\( K_{a}(\text { Benzoic acid })=6.2 \times \)
\( \mathbf{1 0}^{-\mathbf{5}}, \boldsymbol{K}_{\boldsymbol{w}}\left(\boldsymbol{H}_{\mathbf{2}} \boldsymbol{O}\right)=\mathbf{1} \times \mathbf{1 0}^{-\mathbf{1 4}} \)
\( \boldsymbol{K}_{l n} \) (Phenolphthalein) \( \mathbf{3} . \mathbf{1 6} \times \mathbf{1 0}^{-\mathbf{1 0}} \)


The unit vector which is orthogonal to the vector \( \vec{a}=3 \vec{i}+2 \vec{j}+6 \vec{k} \) and is coplanar with the vectors \( \overrightarrow{\boldsymbol{b}}=\mathbf{2} \overrightarrow{\mathbf{i}}+\overrightarrow{\boldsymbol{j}}+ \)
\( \vec{k} \) and \( \vec{c}=\vec{i}-\vec{j}+\vec{k} \) is
A \( \cdot \frac{1}{\sqrt{41}}(2 \vec{i}-6 \vec{j}+\vec{k}) \)
B. \( \frac{2 \vec{i}-3 \vec{j}}{\sqrt{13}} \)
c. \( \frac{3 \vec{j}-\vec{k}}{\sqrt{10}} \)
D. \( \frac{4 \vec{i}+3 \vec{j}-3 \vec{k}}{\sqrt{14}} \)


Find \( \int\left(1-\frac{1}{x^{2}}\right) e^{\left(x+\frac{1}{x}\right)} d x \) on I where \( I= \)
\( (0, \infty) \)


If air is blown through the space between a calendar suspended from a nail on wall and the wall, then:
A. The calendar moves close to the wall.
B. The calendar moves farther from the wall.
c. The position of the calendar does not change.
D. The position of the calendar may or maynot change


\( 1 \mathrm{mA}=_{-}-_{-}---^{\mathrm{A}} \)
\( \mathbf{A} \cdot 10^{3} A \)
B. \( 10^{-3} A \)
\( c \cdot 10^{6} A \)
D. \( 10^{-6} A \)


What is the nature of carbon atom
marked with asterisk \( (*) \) sign in the given compounds?


Under low glomerular blood flow, juxta glomerular cells release
A. Angiotensin I
B. Angiotensin I
c. Aldosterone
D. Renin


Give Nernst equation:
Calculate the electrode potential of the
following single electrode. \( \boldsymbol{C u}_{(a q)}^{++}(\boldsymbol{C}=\mathbf{0 . 0 1 M}) / \boldsymbol{C u} ;\left(\boldsymbol{E}^{\circ}=\right. \)
\( +0.337 V) \)


Chlorine displaces the following from their salts:
This question has multiple correct options
A. fluorine
B. nitrogen
c. bromide
D. iodine


The glass bulb of electric bulbs becomes black due to the deposition of vapour from the:
A. glass of the bulb
B. metal filament
c. gas in the bulb
D. joint in the glass


The current flowing in the circuit is
\( \mathbf{A} \cdot 2.5 A \)
B. \( 5 A \)
\( c \cdot 1 A \)
\( \mathbf{D} \cdot 2 A \)


Compute \( \boldsymbol{P}(\boldsymbol{A} \mid \boldsymbol{B}), \) if \( \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 2 5} \) and
\( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})=\mathbf{0 . 1 8} \)


\( \operatorname{Let} z_{k}(k=0,1,2, \dots \dots \dots .6) \) be the roots
of the equation \( (z+1)^{7}+z^{7}=0, \) then
\( \sum_{k=0}^{6} R e\left(z_{k}\right) \) is equal to
\( A \cdot 0 \)
B. \( \frac{3}{2} \)
c. \( -\frac{7}{2} \)
D. \( \frac{7}{2} \)


The S.I. unit of universal gas constant is
A. \( W a t t K^{-1} m o l^{-1} \)
B. \( N K^{-1} \) mol \( ^{-1} \)
c. \( J K^{-1} m o l^{-1} \)
D. \( \operatorname{erg} K^{-1} \)mol\( ^{-1} \)


Distance between two parrallel lines, \( \overline{\boldsymbol{r}}=\overline{\boldsymbol{a}}_{1}+\boldsymbol{\lambda} \overline{\boldsymbol{b}} \) and \( \overline{\boldsymbol{r}}=\overline{\boldsymbol{a}}_{2}+\boldsymbol{\mu} \overline{\boldsymbol{b}}, \) is given
by
A \( \cdot d=\mid \frac{\left(\bar{a}_{2}-\bar{a}_{1}\right)}{\hat{b}} \)
B . \( d=\mid\left(\bar{a}_{2}-\bar{a}_{1}\right) \times \hat{b} \)
c. \( d=\mid\left(\bar{a}_{2}+\bar{a}_{1}\right) \times \hat{b} \)
D . \( d=\mid\left(\bar{a}_{2}-\bar{a}_{1}\right) \)


A truck weighing 1000 kgf changes its
speed from \( 36 k m h^{-1} \) to \( 72 k m h^{-1} \) in 2
minutes. \( \left(\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} \boldsymbol{s}^{-2}\right) . \) Calculate the
work done by the engine
A \( \cdot 1.5 \times 10^{4} J \)
В. \( 1 \times 10^{5} J \)
c. \( 7.2 \times 10^{5} J \)
D. \( 0 . J \)


Explain tropospheric pollution in 100
words.


What occurs most often in nature:
oxidation or reduction?
A. Oxidation.
B. Reduction.
c. Both occur equally
D. Depends on the scenario


Which of the following are not nonluminous objects?
A. Moon
B. Planets
c. sun
D. Earth


Write the formula of the following compounds:
(i) Potassium trioxalatoaluminate (III)
(ii) Hexaaquairon(II) sulphate.


ff \( x y(y-x)=2 a^{3}, \) at what point does \( y \)
have a minimum value
A . a, 2a
B. a,-a
c. २а,२а
D. None of these


An object is placed at a distance of 30 \( \mathrm{cm} \) from a concave tens of focal length \( 30 \mathrm{cm} \)
(i) Use lens formula to determine the
distance of the image from the lens.
(ii) List four characteristics of the
image (nature position, size, erect/inverted) in this case.
(iii) Draw a labelled diagram to justify
your answer apart (ii)


The physical quantity can be expressed
as


\( 0.394 \mathrm{g} \) of an organic compound containing iodine on treatment by Carius method gave 0.705 g of silver iodide. Find the percentage of halogen in the compound.
A . \( 99 \% \)
B . \( 96.7 \% \)
c. \( 95 \% \)
D. \( 92 \% \),


Which of the following ions is encouraging for the formation of algae in water?
\( \mathbf{A} \cdot S O_{4}^{2-} \)
в. \( P O_{4}^{3} \)
c. \( A s O_{4}^{3} \)
D. \( C O_{3}^{2-} \)


Clean water would have Biochemical
oxygen demand (BOD) value of less
than:
A \( .17 \mathrm{ppm} \)
B. 5 ppm
c. 200,000 ppm
D. 10 ppm


If \( V_{A} \) and \( V_{B} \) denote the potentials of \( A \)
and \( \mathrm{B} \), then the equivalent resistance
between \( A \) and \( B \) in the adjoint electric
circuit is
\( A \cdot 10 \Omega \) if \( V_{A}>V_{B} \)
B. \( 5 \Omega \) if \( V_{A}<V_{B} \)
\( \mathrm{c} \cdot 5 \Omega \) if \( V_{A}>V_{B} \)
D. \( 20 \Omega \) if \( V_{A}>V_{B} \)


The p-V diagram of a gas system undergoing cyclic process is shown
here. The work done during isobaric
compression is
A . 100 J
в. 200
c. 600 J
D. 500
E. 400


Is \( x^{8}+a^{8} \) divisible by \( x+a ? \)


The value of \( \sin 75^{\circ}= \)
\( ^{A} \cdot \frac{2-\sqrt{3}}{\sqrt{2}} \)
в. \( \frac{\sqrt{3}+1}{2 \sqrt{2}} \)
c. \( \frac{\sqrt{3}-1}{2 \sqrt{2}} \)
D. \( \frac{\sqrt{3}+1}{\sqrt{2}} \)


Assertion: In a galvanic cell, the half-cel with higher reduction potential provides a reducing agent Reason: Easily reducible substances are good oxidants.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false


Virat and Samrat together invested
5000 and 12000
rupees to start a business they
suffered a loss of \( 20 \% \)
How much lost did each of them incur.


If 'M' is the molecular weight of a gas, what volume in \( l \) at STP would be
occupied by M/4 g of that gas?
A . 11.2
B. 2.24
\( c .5 .6 \)
D. 22.4


We increase the charge on the plate of a capacitor, it means
A. increasing the capacitance
B. increasing P.D. between plates
c. decreasing P.D. between plates
D. no change in field between plates


Write down each pair of adjacent angles
shown in figure.


A wheel as the angular acceleration of
\( 3.0 \mathrm{rad} / \mathrm{sec}^{2} \) and initial angular speed of
2.00 rad/sec. In a time of 2 sec, it has
rotated through an angle (in radians) of
\( A \cdot 4 \)
B. 6
c. 10
D. 12


If the equation \( x^{2}+b x+c=0 \) and
\( \boldsymbol{x}^{2}+\boldsymbol{c} \boldsymbol{x}+\boldsymbol{b}=\mathbf{0},(\boldsymbol{b} \neq \boldsymbol{c}) \) have a
common root then
A. \( b+c=0 \)
B. \( b+c=1 \)
c. \( b+c+1=0 \)
D. None of these


Calculate the molar solubility of zinc tetrathiocyanato-N-mercurate (II) if its \( \boldsymbol{K}_{\boldsymbol{S P}}=\boldsymbol{2} \cdot \boldsymbol{2} \times 10^{-7} \)
A. 0.00380
B. 0.000469
c. 0.0095
D. 0.0183


An ideal gas as compared to a real gas at very high pressure occupies:
A. more volume
B. less volume
c. same volume
D. unpredictable behaviour


Amides are transported to the other parts of the plants via
A. phloem parenchyma
B. phloem companion cells
c. xylem vessels
D. phloem fibre


represents the variation of particle momentum with associated de Broglie
wavelength?
\( \mathbf{A} \)
B.
\( c \)
\( D \)


A steel wire of length \( 7 m \) and cross
section 1 mm\( ^{2} \) is hung from a rigid
support with a steel weight of volume 1000 \( c c \) hanging from the other end. Find the decreases in the length of wire, when steel weight is completely immersed in water
\( \left(\boldsymbol{Y}_{\text {steel}}=\mathbf{2} \times \mathbf{1 0}^{\mathbf{1 1}} \mathbf{N} / \boldsymbol{m}^{2}\right) \)
Density of water \( =\mathbf{1} \boldsymbol{g} / \boldsymbol{c} . \boldsymbol{c} \)


The difference between two positive numbers is 4 and difference of their
cubes is \( 316 . \) Find their product.
A .22
B . 20
\( c \cdot 21 \)
D. 19


\( C O \) can be used as a fuel but not \( C O_{2} \)
because
A. \( C O_{2} \) is not a good fuel.
B. \( C O \) is a good fuel
c. \( C O \) can be oxidized but \( C O_{2} \) can not can be oxidized
D. \( C O_{2} \) can be oxidized but not \( C O \)


The function of a fuse in independent of


A circuit has a section \( \mathrm{ABC} \) as shown in
figure. If the potentials at points \( A, B \)
and \( \mathrm{C} \) are \( V_{1}, V_{2} \) and \( V_{3} \) respectively.
The potential at point 0 is?
A \( \cdot V_{1}+V_{2}+V_{3} \)
\( ^{\mathbf{B}} \cdot\left[\frac{V_{1}}{R_{1}}+\frac{V_{2}}{R_{2}}+\frac{V_{3}}{R_{3}}\right]\left[\frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}}\right]^{-1} \)
c. zero
\( ^{\mathrm{D}} \cdot\left[\frac{V_{1}}{R_{1}}+\frac{V_{2}}{R_{2}}+\frac{V_{3}}{R_{3}}\right]\left(R_{1}+R_{2}+R_{3}\right) \)


What are complementary and supplementary angles?


If \( y=\frac{\sin ^{-1} x}{\sqrt{1-x^{2}}}, \) prove that
\( \left(1-x^{2}\right) \frac{d y}{d x}-x y=1 \)


The quantity of heat taken or given out by a unit mass of a substance when it
changes from solid to liquid state or liquid to solid state at constant temperature is known as


How would you rewrite Euclid's fifth postulate so that it would be easier to understand?


Solve \( \sin x+\sqrt{3} \cos x \geq 1 \)


Fill in the blank.
When we drink liquid with a straw,the
air pressure acting on the surface of liquid then becomes than
the pressure inside the straw
A. Greater
B. Smaller
c. Equal
D. None


The set of points where the function
\( \boldsymbol{f}(\boldsymbol{x})=[\boldsymbol{x}]+|\mathbf{1}-\boldsymbol{x}|,-\mathbf{1} \leq \boldsymbol{x} \leq \mathbf{3} \)
where [.] denotes the greatest integer
function, is not differentiable, is
A \( \cdot\{-1,0,1,2,3\} \)
B \( \cdot\{-1,0,2\} \)
c. \{0,1,2,3\}
D \( \cdot\{-1,0,1,2\} \)


The volume of a cube is \( 1000 \mathrm{cm}^{3} \). Find
its total surface area in \( \mathrm{cm}^{2} \)


\( K M n O_{4} \) is acidified for redox
titrations by:
A. \( H C l \)
в. \( H N O_{3} \)
c. \( H_{2} S O_{4} \)
D. any of these


Two point masses each equal to \( 1 k g \) attract one another with a force of
\( 10^{-9} k g w t . \) Find the distance between
the two point masses. Take: \( g= \)
\( 9.8 m / s^{2} \)
\( A \cdot 8 c m \)
B. \( 0.8 \mathrm{cm} \)
c. \( 80 \mathrm{cm} \)
D. \( 0.08 \mathrm{cm} \)


According to Faraday's law, the total charge induced in a conductor that is moved in a magnetic field depends up
on:
A. Initial magnetic flux
B. Final magnetic flux
c. Rate of change of magnetic flux
D. change in magnetic flux


A hydraulic press has a ram of \( 15 \mathrm{cm} \) diameter and plunger is \( 1.5 \mathrm{cm} . \) It is required to lift a weight of 1 tonne. The force required on plunger is
A. \( 10 \mathrm{kg} \)
B. \( 100 \mathrm{kg} \)
c. \( 1000 \mathrm{kg} \)
\( D \cdot 1 \mathrm{kg} \)


The statement "The change of enthalpy
of a chemical reaction is same whether
the reaction takes place in one or several steps" is:
A . Le Chatelier's law
B. van't Hoff's law
c. first law of thermodynamics
D. Hess's law.


An \( \alpha \) - particle of \( \mathrm{KE} \mathbf{5 . 4} M e V \) is projected towards \( C r \) - nucleus \( (Z= \)
24). What is its distance of closest
approach? \( \left(e=1.6 \times 10^{-19} C\right) \)


Suppose \( \boldsymbol{E}_{1}, \boldsymbol{E}_{2}, \boldsymbol{E}_{3} \) be three mutually
exclusive events such that \( \boldsymbol{P}\left(\boldsymbol{E}_{i}\right)=\boldsymbol{p}_{i} \)
for \( \boldsymbol{i}=\mathbf{1}, \mathbf{2}, \mathbf{3} \)
\( \operatorname{then} P\left(E_{1} \cap E_{2}^{\prime}\right)+P\left(E_{2} \cap E_{3}^{\prime}\right)+ \)
\( \boldsymbol{P}\left(\boldsymbol{E}_{3} \cap \boldsymbol{E}_{1}^{\prime}\right) \) equals
A \( \cdot p_{1}\left(1-p_{2}\right)+p_{2}\left(1-p_{3}\right)+p_{3}\left(1-p_{1}\right) \)
В. \( p_{1} p_{2}+p_{2} p_{3}+p_{3} p_{1} \)
c. \( p_{1}+p_{2}+p_{3} \)
D. None of these


Let \( \boldsymbol{f}: \mathbb{R} \rightarrow \mathbb{R} \) be a differentiable function such that \( \boldsymbol{f}(\mathbf{0})=\mathbf{0}, \boldsymbol{f}\left(\frac{\boldsymbol{\pi}}{\mathbf{2}}\right)=\mathbf{3} \)
and \( \boldsymbol{f}^{\prime}(\mathbf{0})=\mathbf{1 .} \) If \( \boldsymbol{g}(\boldsymbol{x})= \)
\( \int_{x}^{\frac{\pi}{2}}\left[f^{\prime}(t) \operatorname{cosec} t-\cot t \operatorname{cosec} t f(t)\right] d t \) for
\( \boldsymbol{x} \in\left(\mathbf{0}, \frac{\boldsymbol{\pi}}{\mathbf{2}}\right], \) then \( \lim _{\boldsymbol{x} \rightarrow 0} \boldsymbol{g}(\boldsymbol{x})= \)


Identify the correct statement from the
following in a chemical reaction.
A. The entropy always increases
B. The change in entropy along with suitable change in enthalpy decides the rate of reaction
C. The enthalpy always decreases
D. Both the enthalpy and the entropy remains constant


If the percentage error in measuring the
surface area of a sphere is \( \alpha \% \), then the error in its volume is
A \( \cdot \frac{3}{2} \alpha \% \)
в. \( \frac{2}{3} \alpha \% \)
\( c .3 \alpha \% \)
D. none of these


Oxidation number of iodine varies from:
A. -1 to +1
B. -1 to +7
\( \mathbf{c} .+3 \) to +5
D. -1 to +5


Two blocks of the same metal having
the same mass and at temperature \( T_{1} \)
and \( T_{2}, \) respectively. are brought in
contact with each other and allowed to
attain thermal equilibrium at constant
pressure. The change in entropy, \( \Delta S \), for this process is :
\( ^{\mathbf{A}} \cdot 2 C_{p} \ln \left(\frac{T_{1}+T_{2}}{4 T_{1} T_{2}}\right) \)
\( ^{\mathrm{B}} 2 C_{p} \ln \left[\frac{\left(T_{1}+T_{2}\right)^{\frac{1}{2}}}{T_{1} T_{2}}\right] \)
\( ^{\mathbf{c}} \cdot_{C_{p} l n}\left[\frac{\left(T_{1}+T_{2}\right)^{2}}{4 T_{1} T_{2}}\right] \)
D \( \cdot 2 C_{p} \ln \left[\frac{T_{1}+T_{2}}{2 T_{1} T_{2}}\right] \)


Assertion
Tetravalency of carbon leading to formation of single, double and triple bonds.
Reason
The electronic configuration of carbon is \( 1 s^{2} 2 s^{2} 2 p^{2} . \) Carbon has 4 valence electrons and by sharing 4 electrons. It will have a stable configuration. It has all the valence electrons unpaired in the excited state.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The solubility curve of \( \boldsymbol{K} \boldsymbol{N} \boldsymbol{O}_{3} \) in water is shown below.

The amount of \( K N O_{3} \) that dissolves in
\( 50 g \) of water at 40 is closest to:
A . 100 g
B. 150 g
c. \( 200 g \)
D. \( 50 g \)


Sphere (1) moving with velocity \( 4 \mathrm{m} / \mathrm{s} \)
collides another sphere (2) at rest. Find
final velocity of sphere (1) after collision collision perfectly elastic
\( A \cdot 2 \hat{\imath}+\sqrt{3} \hat{\jmath} \)
B . \( 2 \hat{i}-\sqrt{3} \hat{j} \)
\( c \cdot \hat{i}+\sqrt{3} \hat{j} \)
D. \( \hat{i}-\sqrt{3} \hat{j} \)


Write the converse, inverse and
contrapositive of the following statements: "If a function is
differentiable then it is continuous".


Determination of age of a tree by counting annual rings is known as
A. Dendrochronology
B. Dendrology
c. Gyrochronology
D. Chronology


The work done by external agent to shift a point mass from infinity to the centre of earth is :
\( \mathbf{A} \cdot=0 \)
\( \mathbf{B} \cdot>0 \)
\( c \cdot<0 \)
\( \mathrm{D} \cdot<0 \)


The sum \( \frac{1}{1+1^{2}+1^{4}}+\frac{2}{1+2^{2}+2^{4}}+ \)
\( \frac{\mathbf{3}}{\mathbf{1}+\mathbf{3}^{2}+\mathbf{3}^{4}}+\ldots+\frac{\mathbf{9 9}}{\mathbf{1}+\mathbf{9 9}^{2}+\mathbf{9 9}^{4}} \) lies
between
A. 0.46 and 0.47
7
B. 0.52 and 1.0
c. 0.48 and 0.49
D. 0.49 and 0.50


As per given figure to complete the
circular loop what should be the radius
if initial is \( 5 m \)
A . \( 4 m \)
B. 3 m
c. \( 2.5 m \)
D. \( 2 m \)


Prove that:
\( \left[1+\cot \theta-\sec \left(\theta+\frac{\pi}{2}\right)\right][1+\cot \theta+\sec \)
\( 2 \cot \theta \)


Find the \( n t h \) term and the sum of \( n \)
terms of the series \( 1.2 .4+2.3 .5+ \)
\( 3.4 .6+\ldots \)


\( 1+\frac{3}{2}+\frac{5}{4}+\frac{7}{8}+\ldots . . \) n terms


f there was no photosynthesis what would happen?


The weakest interparticle forces are
present in:
A. Thermosetting polymers
B. Thermoplastic polymers
c. Fibers
D. Elastomers


Find the value of \( \lambda \) if the following equations are consistent \( \boldsymbol{x}+\boldsymbol{y}-\mathbf{3}=\mathbf{0} \)
\( (1+\lambda) x+(2+\lambda) y-8=0 \)
\( \boldsymbol{x}-(\mathbf{1}+\boldsymbol{\lambda}) \boldsymbol{y}+(\boldsymbol{2}+\boldsymbol{\lambda})=\mathbf{0} \)


From a building two balls \( A \) and \( B \) are thrown such that \( A \) is thrown upwards
and B downwards (both vertically). If \( v_{A} \)
and \( v_{B} \) are their respective velocities on
reaching the ground, then
A \( \cdot v_{A}>v_{B} \)
В. \( v_{A}=v_{B} \)
c. \( v_{A}<v_{B} \)
D. Their velocities depend on their masses


If \( f \) and \( g \) are two decreasing function such that \( f o g \) is defined, then fog will
be
A. increasing function
B. decreasing function
c. neither increasing nor decreasing
D. None of these


Compensation point is the value of the factor where there is
A. Neither photosynthesis nor respiration
B. Little photosynthesis
c. Photosynthesis is equal to the rate of respiration
D. Beginning of photosynthesis


A man standing unsymmetrically between two parallel cliffs, claps his hand and starts hearing a series of echoes at intervals of 1 s. If the speed of
sound in air is \( 340 \mathrm{ms}^{-1} \), then the distance between the two prallel cliffs,
is
A . \( 170 \mathrm{m} \)
B. 340 \( \mathrm{m} \)
\( c .510 \mathrm{m} \)
D. \( 680 \mathrm{m} \)


Fill in the blanks with suitable words
The rays used to show bone structure is


An alcohol with \( D . U=1 \) exists having
a \( 2^{\circ} \) hydroxy group with the
molecular formula of \( C_{3} H_{6} O \) is:
A. isopropanol
B. propenol
c. cyclopropenol
D. cyclopropanol


Four charges, all of the same magnitude placed at the four corners of a square. At centre of the square, the
potential is \( V \) and the field is \( E . B y \) suitable choices of the signs of four charges, which of the following can be obtained?
This question has multiple correct options
A. \( V=0, E=0 \)
B. \( V=0, E \neq 0 \)
c. \( V \neq 0, E=0 \)
D. \( V \neq 0, E \neq 0 \)


An atom has the symbol \( p \) \( q \) Which value determines the position of the element in the periodic table?
A .
B. 9
\( c \cdot p-q \)
D. p+q


Which of the following is an analgesic?
A. Chloramphenicol
B. Penicillin
c. Paracetamol
D. streptomycin


The correct IUPAC name of the
coordination compound
\( \boldsymbol{K}_{\mathbf{3}}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{\mathbf{5}} \boldsymbol{N} \boldsymbol{O}\right] \) is \( \boldsymbol{?} \)
A. potassium pentacyanonitrosylferrate (II)
B. potassium pentacyanonitro-N-ferrate(III)
C . potassium nitritopentacyanoferrate(IV)
D. potassium nitritepentacyanoiron(II)


If \( \vec{a} \) and \( \vec{b} \) two collinear vectors then
which of the following are incorrect
A \( \cdot \vec{b}=\lambda \vec{a} \) for some scalar
B \( \cdot \vec{a}=\pm \vec{b} \)
C. The respective components of \( \vec{a} \) and \( \vec{b} \) are proportional
D. Both the vectors \( \vec{a} \) and \( \vec{b} \) have same direction, but different magnitude.


\( \lim _{n \rightarrow \infty} \frac{1}{n^{3}}\left[\left(1^{2}+2^{2}+\ldots+n^{2}\right)\right]=? \)
A . \( 1 / 3 \)
B. 1/16
c. \( 1 / 12 \)
D.


An atom has 7 electrons in its \( \mathrm{M} \) - shell
and contains 18 neutrons in its nucleus.
What is its mass number
A . 22
B. 30
\( c . \) 35
D. 45


Octet rule was given by
A. Rutherford
B. Soddy
c. Lewis \& Kossel
D. none of the above


A radio station transmits waves of
wavelength \( 400 \mathrm{m} \). If the speed of the waves is \( 4 \times 10^{8} m s^{-1} \), Find the
frequency of the radio station
\( \mathbf{A} \cdot 1 \mathrm{MHz} \)
в. 2 МНz
c. 4 Мнz
D. 5 Мнд


Short / Long Answer Types:
Explain the major steps of glycolysis. Where does this process occur in a cell?


If \( A B C D \) is a parallelogram, \( A B= \) \( \mathbf{2} \hat{\mathbf{i}}+\mathbf{4} \hat{\mathbf{j}}-\mathbf{5} \hat{\boldsymbol{k}} \) and \( \boldsymbol{A} \boldsymbol{D}=\hat{\boldsymbol{i}}+\mathbf{2} \hat{\boldsymbol{j}}+\mathbf{3} \hat{\boldsymbol{k}} \)
then the unit vectors in the direction of
\( B D \) is
A \( \cdot \frac{1}{\sqrt{69}}(\hat{i}+2 \hat{j}-8 \hat{k}) \)
B \( \cdot \frac{1}{69}(\hat{i}+2 \hat{j}-8 \hat{k}) \)
c. \( \frac{1}{\sqrt{69}}(-\hat{i}-2 \hat{j}+8 \hat{k}) \)
D \( \cdot \frac{1}{69}(-\hat{i}-2 \hat{j}+8 \hat{k}) \)


Discuss the applicability of Rolle's
theorem for the following function on the indicated interval:
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2 / 3} \) on [-1,1]


A beam of width \( t \) is incident at 45 o on
air-water boundary. The width of the
beam in water is


Value of \( c \) of Rolles theorem for \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \sin x-\sin 2 x \) on \( [0, \pi] \)
\( ^{\mathbf{A}} \cdot \cos ^{-1}\left(\frac{1+\sqrt{33}}{8}\right) \)
B. \( \cos ^{-1}\left(\frac{1+\sqrt{35}}{8}\right) \)
\( ^{\mathbf{c}} \cdot \cos ^{-1}\left(\frac{1-\sqrt{38}}{5}\right) \)
D. does not exist


In a given process on an ideal gas \( d W=0 \) and \( d Q<0, \) then for the gas :
A. The temperature will decrease
B. The volume will increase
C. The pressure will remain constant
D. The temperature will increase


A man can swim with a speed of 4.0 \( k m / h r \) in still water. How long does
he take to cross a river \( 1.0 \mathrm{km} \) wide, if
the river flows steadily at \( 3.0 \mathrm{km} / \mathrm{hr} \) and he makes his strokes normal to the
river current? How far down the river
does he go, when he reaches the other bank?


Find how the tangential acceleration \( \omega_{\tau} \)
of the balloon depends on the height of
ascent.
A \( \cdot_{\omega_{\tau}}=\frac{2 a^{2} y}{\sqrt{1+\left(\frac{a y}{v_{0}}\right)^{2}}} \)
B. \( _{\omega_{\tau}}=\frac{a^{2} y}{\sqrt{1+\left(\frac{a y}{v_{0}}\right)^{2}}} \)
\( ^{\mathbf{c}} \cdot_{\omega_{\tau}}=\frac{a^{2} y}{\sqrt{1+\left(\frac{2 a y}{v_{0}}\right)^{2}}} \)
D. \( \omega_{\tau}=\frac{a^{2} y}{2 \sqrt{1+\left(\frac{a y}{v_{0}}\right)^{2}}} \)


Evaluate the following determinant:
\( \left|\begin{array}{lll}a & h & g \\ h & b & f \\ g & f & c\end{array}\right| \)


Which of the following is least reactive?
A. White phosphorus
B. Yellow phosphorus
c. Red phosphorus
D. Black phosphorus


IUPAC name of hydroxybutyraldehyde is
A. 1-hydroxybutanal
B. 2-hydroxybutanol
c. 2-Hydroxybutanal
D. 2-hydroxybutyraldehyde


The angle between two vectors \( \vec{A}= \) \( 4 \hat{i}+3 \hat{j}-2 \hat{k} \) and \( \vec{B}=-8 \hat{i}-6 \hat{j}+4 \hat{k} \) is
\( \mathbf{A} \cdot \pi / 4 \)
в. \( \pi / 3 \)
\( c \)
D. \( \pi / 2 \)


Write about Gabriel phthalimide synthesis?


The axial endoskeleton of
Elasmobranchs is made up of
A. Cartilage
B. Ossified cartilage
c. Bone
D. Hyaline cartilage


A planet of mass \( 3 \times 10^{29} \mathrm{gm} \) moves
around a star with a constant speed of
\( 2 \times 10^{8} m s^{-1} \) in a circle of radii \( 1.5 \times \)
\( 10^{12} \mathrm{m} . \) The gravitational force exerted
on the planet by the star is
A \( .6 .67 \times 10^{22} \) dyne
B . \( 6.67 \times 10^{26} \) N
c. \( 8 \times 10^{26} \mathrm{N} \)
D. \( 8 \times 10^{27} \) dyne


What is glycolysis? Sketch the pathway showing different stages in glycolysis.


A South pole and North pole of each strength 'm' are placed at the two corners of an equilateral triangle of side 'a'. The resultant magnetic induction field
strength at the third vertex is :
A. o (zero)
в. \( \frac{2 \mu_{0}}{4 \pi} \frac{m}{d^{2}} \)
c. \( \frac{\mu_{0}}{4 \pi} \frac{m}{d^{2}} \)
D. \( \frac{3 \mu_{0}}{4 \pi} \frac{m}{d^{2}} \)


Let \( f \) be a function defined for all \( \boldsymbol{x} \boldsymbol{\epsilon} \boldsymbol{R} \)
If \( f \) is differentiable and \( f\left(x^{3}\right)=x^{5} \) for
all \( \boldsymbol{x} \boldsymbol{\epsilon} \boldsymbol{R}(\boldsymbol{x} \neq \boldsymbol{0}) \) then the value of
\( \boldsymbol{f}^{\prime}(\mathbf{2 7}) \) is
A . 15
B. 45
c. 0
D. None


Two oxidation states for chlorine are
found in the compound?


Chlorine has a slight sour taste due to acidic nature.
A . True
B. False


Which of the following material can not undergo rapid combustion?
A. woodd
B. Petrol
c. Paper
D. Match stick


Cod liver oil is:
A. fat dispersed in water
B. water dispersed in fat
C . water dispersed in oil
D. fat dispersed in fat


Due to an electric dipole shown in fig., the
electric field intensity is parallel to dipole
axis
\( A \cdot \) at \( P \) only
B. at Qonly
c. both at \( P \) and at \( Q \)
D. neither at \( P \) nor at \( Q \)


For any two events \( A \) and \( B \)
\( \mathbf{A} \cdot P(A)+P(B)>P(A \cap B) \)
B \( \cdot P(A)+P(B)<P(A \cap B) \)
\( \mathbf{c} \cdot P(A)+P(B) \geq P(A \cap B) \)
D \( . P(A)+P(B) \leq P(A \cap B) \)


If \( a=\frac{(3 i+1)}{10} \) and \( b=(2 i+3) \times 10 \), then
the value of \( (2 a b) \) is


The correct hierarchical order with
respect to the level of organization in animals is
A. Organ system, organ, tissue, cell
B. Cell, tissue, organ, organ system
C. Tissue, cell, organ, organ system
D. Cell, organ, organ system, tissue


If Avogadro's number have been \( 1 \times \)
\( 10^{10} \) instead of \( 6.02 \times 10^{23}, \) then
the mass of one atom of \( H \) in a.m.u.
would have been


The precipitating agent used in the estimation of sulphur is:
A. barium sulphate
B. calcium sulphate
c. barium chloride
D. calcium chloride


The specific resistance of the material
of a wire is \( \rho, \) its volume is \( 3 m^{3} \) and its
resistance is \( 3 \Omega \). The length of the wire will be
A \( \cdot \frac{\sqrt{1}}{\rho} \)
B. \( \frac{3}{\sqrt{\rho}} \)
c. \( \frac{1}{\rho} \sqrt{3} \)
D. \( \rho \sqrt{\frac{1}{3}} \)


Which of the following processes carries food through the digestive
tract?
A. Peristalsis
B. Resorption
c. Pinocytosis
D. Neurotransmitters


The term hydroponic was coined by
A. Sachs
B. Gericke
c. Pristely
D. None of the above


The important function of lymph is to?


Available chlorine can be liberated from
bleaching powder by the reaction with:
This question has multiple correct options
A \( \cdot \) conc. \( H_{2} S O_{4} \)
в. \( d i l . H_{2} S O_{4} \)
\( c \cdot C O_{2} \)
D. \( d i l . H N O_{3} \)


If \( \boldsymbol{A}=\{1,2,3,4\}, \) what is the number of
subsets of A with at least three
elements?
\( \mathbf{A} \cdot \mathbf{3} \)
B. 4
\( c .5 \)
D. 10


Evaluate: \( \tan ^{-1}\left[2 \cos \left(2 \sin ^{-1}\left(\frac{1}{2}\right)\right)\right]= \)
- Find a
\( A \cdot 4 \)
B. 5
\( c \cdot 6 \)
\( D \)


For any two complex numbers \( z_{1} \) and \( z_{2} \) with \( \left|z_{1}\right| \neq\left|z_{2}\right|,\left|\sqrt{2} z_{1}+i \sqrt{3} \overline{z_{2}}\right|^{2}+ \)
\( \left|\sqrt{3} \overline{z_{1}}+i \sqrt{2} z_{2}\right|^{2} \) is
A \( \cdot \) Less than \( 5\left(\left|z_{1}\right|^{2}+\left|z_{2}\right|^{2}\right) \)
B \cdot Greater than \( 10 \mid z_{1} z_{2} \)
c. Equal to \( \left(2\left|z_{1}\right|^{2}+3\left|z_{2}\right|^{2}\right) \)
D. zero


Write the constant term of each of the
following algebraic expressions: \( a^{3}- \) \( 3 a^{2}+7 a+5 \)


State whether given statement is True/False?

Lightning conductor is made up of
copper.
A. True
B. False


Draw the number line and represent the following rational numbers on it:
\( \frac{-3}{16} \)


Body of lichen consists of two dissimilar organisms. Choose the correct option w.r.t. component which
form bulk of the thallus
A. Autotrophic component
B. Prepare food for fungi
c. Form sexual reproductive structure
D. Provide belongs to ascomycetes or sometimes


\( \begin{array}{lll}\text { Weight (Kg) } & \text { Frequency } \\ \text { 60 up to 70 } & 13 \\ \text { 70up to 75 } & 2 \\ \text { 75 up to 95 } & 45 \\ \text { 95 up to 100 } & \text { 7 }\end{array} \)
Given the table above, find the modal
class.
\( A \cdot 70 \) up to 75
\( B .75 \) up to 95
\( \mathbf{C} \cdot 60 \) up to 70
D. 95 up to 100


The arithmatic mean of 4,6,8 is
\( A \cdot 4 \)
B. 6
\( c .8 \)
D. 4.5


\( \int x^{2}\left(1-\frac{1}{x^{2}}\right) d x \)


Write short note on retina.


Electrolysis of dilute aqueous \( \mathrm{NaCl} \) solution was carried out by passing 10 milli ampere current. The time required
to liberate 0.01 mol of \( \mathbf{H}_{2} \) gas at the
cathode is (1 Faraday \( =\mathbf{9 6 5 0 0 C} \) mol \( ^{-1} \) )
A \( \cdot 9.65 \times 10^{4} \mathrm{sec} \)
B . \( 19.3 \times 10^{4} \mathrm{sec} \)
c. \( 28.95 \times 10^{4} \) sec
D. \( 38.6 \times 10^{4} \mathrm{sec} \)


Fill in the blank.
When a force is applied on a soft object,it changes the of
the object.
A. Shape
B. Size
c. Direction of force
D. Both a and


A. Its main component is methane and
is used as a fuel in motor cars.
B. It is used as the raw material for
manufacturing of fertilizers.
C. It is an inexhaustible natural source.
\( A \cdot A, B \)
B. \( B, C \) and \( D \)
\( c \cdot c, D \) and \( A \)
\( D \cdot D, A \) and \( B \)


If number of electrons in an atom is 8
and number of protons is also \( 8, \) then
\( (i) \)
what is the atomic number of the atom
? and
(II) what is the charge on the
atom?


In an organism, if the normal diploid number of chromosomes is \( 8, \) how
many chromatids are present in each
daughter cell at the end of meiosis I?
\( A \cdot 2 \)
B. 4
\( c \cdot 8 \)
\( D \cdot 16 \)


In which of the following molecules, central atom used orbitals of different quantum number in the hybridisation :-
\( \mathbf{A} \cdot\left[F e(C O)_{5}\right] \)
в. \( I F_{7} \)
c. \( N i(C O)_{4} \)
D. \( X e O_{4} \)


A student sitting in the last row of the class-room is not able to read clearly
the writing on the blackboard.
(I) Name the type of defect he suffering from.
(II) How can these defect by corrected?


Find the value of \( \frac{\boldsymbol{a}+\boldsymbol{b}-\boldsymbol{c}}{\mathbf{2} \boldsymbol{a}} \) when \( \boldsymbol{a}= \)
\( \mathbf{5}, \boldsymbol{b}=\mathbf{7} \) and \( \boldsymbol{c}=\mathbf{2} \)


Draw the Lewis structure for \( C O_{3}^{2-} \)


A light moves from denser to rarer medium, which of the following is
correct?
A. Energy increases
B. Frequency increases
C. Phase changes by \( 90^{\circ} \)
D. Velocity increases


The \( I-V \) characteristics of a metal
wire at two different temperatures \( \left(T_{1}\right. \)
and \( T_{2} \) ) are given in the adjoining
figure. Here, we can conclude that:
\( A \cdot T_{1}>T_{2} \)
в. \( T_{1}<T_{2} \)
\( c \cdot T_{1}=T_{2} \)
D \( \cdot T_{1}=2 T_{2} \)


A concave spherical surface of radius of
curvature \( 10 \mathrm{cm} \) separates two
medium \( \boldsymbol{x} \) \& \( \boldsymbol{y} \) of refractive index \( 4 / 3 \& \)
\( 3 / 2 \) respectively. If the object is placed
along principal axis in medium \( X \) then:
A. image is always real
B. image is real if the object distance is greater than 90 \( \mathrm{cm} \)
C. image is always virtual
D. image is virtual if the object distance is less than 90 \( \mathrm{cm} \)


Which of the following reacts with water
and aqueous solution become acidic \( \boldsymbol{S} \boldsymbol{i} \boldsymbol{C l}_{4} \) or \( \boldsymbol{C C l}_{4} ? \)


Write a relation for polarisation \( \vec{P} \) of \( a \) dielectric material in the presence of an external electric field \( \vec{E} \).


Which one of the following compounds is heated with slaked lime to produce ammonia?
A \( . N H_{4} C l \)
в. \( N a N O_{3} \)
c. \( K N O_{3} \)
\( \mathbf{D} \cdot C a\left(N O_{3}\right)_{2} \)


Find the values of \( a \) for which the
function \( f(x)=\sin x-a x+4 \) is
increasing function on \( \boldsymbol{R} \)


A small metallic sphere carrying charge \( +Q \) is located at the center of a
spherical cavity in a large uncharged metallic spherical shell. Write the charges on the inner and outer surfaces of the shell. Write the expression for the electric field at some point outside and inside the metallic sphere.


The term \( B W R \) stands for
A. Bureau of Workers Rights
B. Boiling Water Reactor
c. Bilateral Water Reactor
D. Bureau of Waste Research


Determine the difference \( L_{1}-L_{2}(= \)
\( \Delta L) \) in terms of \( \lambda_{0} \)
A \( \frac{4 \lambda_{0}}{\mu} \)
в. \( \frac{7 \lambda_{0}}{2 \mu} \)
\( c \cdot \frac{3 \lambda_{0}}{\mu} \)
D. none of the above


The G.M. of the numbers \( a+\sqrt{a^{2}-b^{2}} \)
and \( a-\sqrt{a^{2}-b^{2}}, \) is
\( A \)
B. \( b \)
\( c \cdot a b \)
D. \( \sqrt{a^{2}+b^{2}} \)


If \( A \) is an invertible matrix of order \( n \)
then the determinant of adj \( A \) is equal
to:
\( \mathbf{A} \cdot|A|^{n} \)
В \( \cdot|A|^{n+1} \)
c. \( |A|^{n-1} \)
D. \( |A|^{n+2} \)


Figure shows a square loop of side \( 5 \mathrm{cm} \)
being moved towards right at a
constant speed of \( 1 \mathrm{cm} / \mathrm{sec} \). The front
edge just enters the \( 20 \mathrm{cm} \) wide
magnetic field at \( t=0 . \) Find the
induced emf in the loop at \( t=2 s \) and
\( t=10 s \)


If the hypotenuse and one of the other two sides of a right angles triangle are equal to the hypotenuse and one of the sides of the other right-angled triangle respectively, then the two right-angled triangles are
A. congruent
B. unequal
c. equilateral
D. None of the these


Hydrocarbon derivatives is:
A. compounds formed by replacing one or more hydrogen atoms of the corresponding hydrocarbon with another atom or a group of atoms.
B. compounds formed by replacing one or more carbon atoms of the corresponding hydrocarbon with another atom or a group of atoms.
C. compounds formed by replacing one or more functional group of the corresponding hydrocarbon with another atom or a group of atoms.
D. Both A and B


A light of wavelength \( \lambda \) is incident on
a metal sheet of work function \( \phi=2 e V \)
The wavelength \( \lambda \) varies with time as
\( \lambda=3000+40 t, \) where \( \lambda \) is in and \( t \) is in
second. The power incident on metal sheet is constant at 100 W. This signal is switched on and off for time intervals
of 2 minutes and 1 minute respectively.
Each time the signal is switched on, the
\( \lambda \) start from an initial value of \( 3000 . \) The
metal plate is grounded and electron clouding is negligible. The efficiency of photoemission is \( 1 \%(h c=12400 e V) \)
The time after which photo-emission will stop is
A. 79 s
B. 80 s
c. \( 81 \mathrm{s} \)
D. 78 s


What do you mean by reflection?


List the criteria a molecule that can act
as genetic material must fulfill. Which one of the criteria are best fulfilled by
DNA or by RNA thus making one of them a better genetic material than the other?


The reactivities of these ions in azo-
coupling reactions will be in the order:
\( \mathbf{A} \cdot 3<1<4<2 \)
В. \( 1<4<2<3 \)
c. \( 1<2<3<4 \)
D. \( 3<1<2<4 \)