A gram mole of a gas at \( 127^{\circ} \mathrm{C} \) expands isothermally until its volume is doubled. find the amount of work done
and heat absorbed.
A . 238 call \( l \)
в. 548 са। \( l \)
\( c .548 J \)
D. \( 238 J \)


At \( 90^{\circ} C, \) the following equilibrium is established
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{S}(s) \rightleftharpoons \boldsymbol{H}_{2} \boldsymbol{S}(\boldsymbol{g}) \boldsymbol{K}_{\boldsymbol{p}}=\mathbf{6 . 8} \times \)
\( \mathbf{1 0}^{\mathbf{2}} \)
If 0.2 mol of hydrogen and 1.0 mol of
sulphur are heated to \( 90^{\circ} \mathrm{C} \) in a 1.0 litre vessel, what will be the partial pressure
of \( \boldsymbol{H}_{2} \boldsymbol{S} \) at equilibrium?
A . 0.19 atm
B. 0.379 atm
c. 0.75 atm
D. None of these


Which of the following is a secondary amine?
A. Dimethylamine
B. Aniline
c. Isobutylamine
D. Secondary butyl amine


If \( y \) -coordinate of a point is zero then
the point will always lie
A . in \( I \) quadrant
B. in \( I I \) quadrant
c. on \( X \) -axis
D. on \( Y \) -axis


The figure shows a potentiometer
arrangement. D is the driving cell. C is
the cell whose emf is to be determined.
AB is the potentiometer wire and \( G \) is a
galvanometer.J is a sliding contact
which can touch any point on AB. Which
of the following are essential conditions
for obtaining balance?
This question has multiple correct options
A. The emf of D must be greater than the emf of \( C \).
B. Either the positive terminals of both D and C or the negative terminals of both \( D \) and \( C \) must be joined to
\( A \)
C. The positive terminals of D and C must be joined to A.
D. The resistance of G must be less than the resistance of
\( A B \)


Find the distance between the points (1,5) and (5,8)


You can make an organic acid from
ethanol and that is:
\( \mathbf{A} \cdot C_{3} H_{7} O H \)
B. found in bees and ants
c. acetic acid
D. formic acid
E. butanoic acid


Ordinary rubber is an insulator. But the
special rubber tyres of aircrafts are made slightly conducting. Why is this
necessary?


Assertion
The melting point of ice decreases with
increase of pressure.
Reason
Ice contracts on melting.
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


Cane sugar is made up of:
A. 5 membered glucose ring and 5 membered fructose ring
B. 6 membered glucose ring and 5 membered fructose ring
C. 6 membered glucose ring and 6 membered fructose ring
D. 6 membered glucose ring and 5 membered galactose ring


Even today there is a need of movement like 'Chipko' movement. Explain this
with the help of an example that you have experienced.


Proteins are condensation polymers of:
A. \( \alpha \) -amino acids.
B. \( \beta \) -amino acids
c. \( \alpha \) -hydroxy acids.
D. \( \beta \) -hydroxy acids


A radio isotope \( X \) has a half life of \( 10 s \) Find the number of active nuclei in the
sample (if initally there are 1000 isotopes which are falling from rest from a height of \( 3000 m \) ) when it is at a height of \( 1000 m \) from the reference
plane:
\( \mathbf{A} .50 \)
в. 250
c. 29
D. 100


Equal masses of \( \boldsymbol{H}_{2}, \boldsymbol{O}_{2} \) and methane have been taken in a container of
volume \( \boldsymbol{V} \) at temperature \( \mathbf{2 7}^{\circ} \boldsymbol{C} \) in identical conditions. The ratio of the
volumes of gases \( H_{2}: O_{2}: \) methane
would be:
A. 8: 16: 1
B . 16: 8: 1
c. 16: 1: 2
D. 8: 1: 2


What is the moment of intertia for a
solid sphere w.r.t. a tangent touching to its surface?
\( ^{\mathbf{A}} \cdot \frac{2}{5} M R^{2} \)
B. \( \frac{7}{5} M R^{2} \)
c. \( \frac{2}{3} M R^{2} \)
D. \( \frac{5}{3} M R^{2} \)


During cell cycle, RNA and proteins are synthesised in
A. \( S \) - phase
B. \( G_{1}- \) phase
c. \( G_{2}- \) phase
D. Both B and C


1,2,3,6,8 is a set of five positive integers whose mean is 4 and median
is
3. Write down two other sets of five
positive integers, each having the same mean and median as this set.


Write the structural formula of
following derivatives of benzene. \( \mathbf{2}, \mathbf{4}, \mathbf{6}- \) Trinitortoluene


From a lot of 10 bulbs, which includes 3
detectives, a sample of 2 bulbs is drawn at random. Find the probability
distribution of the number of defective
bulbs.


The angle subtended at the centre of a
circle by an arc whose length is equal to the diameter of the circle is:
A . radian
B. 2 radian
c. \( \pi \) radian
D. \( \pi / 2 \) radian


The quadrilateral \( A B C D \) formed by the point \( \boldsymbol{A}(\mathbf{0}, \mathbf{0}) ; \boldsymbol{B}(\mathbf{3}, \mathbf{4}) ; \boldsymbol{C}(\mathbf{7}, \mathbf{7}) \) and
\( D(4,3) \) is a
A. rectangle
B. rhombus
c. square
D. parallelogram


The function \( f \) is continuous and has
the property \( f(f(x))=1-x, \) then the
value of \( \boldsymbol{f}\left(\frac{1}{4}\right)+\boldsymbol{f}\left(\frac{3}{4}\right) \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot \frac{-1}{2} \)
D. -1


\( \left|\begin{array}{ccc}\frac{1}{a} & a^{2} & b c \\ \frac{1}{b} & b^{2} & c a \\ \frac{1}{c} & c^{2} & a b\end{array}\right|= \)
A \( \cdot \) abc
B. \( a+b+c \)
\( c \cdot 0 \)
D. \( 4 a b c \)


Assertion
In an electrochemical cell, the electrode
that is the site of reduction is called the
anode.
Reason
Oxidation always occurs at the cathode.
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 first ionization potential of \( N a \) is 5.1 \( e V \). The value of electron gain
enthalpy of \( N a^{+} \) will be :
A. \( -5.1 \mathrm{eV} \)
B. \( -10.2 \mathrm{eV} \)
\( \mathbf{c} .+2.55 \mathrm{eV} \)
D. -2.55 eV


\( n P_{r} \) and \( n C_{r} \) are equal when:
\( \mathbf{A} \cdot n=r \)
B . \( n=r+1 \)
\( \mathbf{c} \cdot r=1 \)
D. \( n=r-1 \)


There are 700 students in a school out
of which 420 are girls. Find the
percentage of boys in the school


In which of the following, scientific
name, family and common name are correctly mentioned?
A. Scientific name-Batrachospermum, FamilyRhodophyceae, Common name-Frog's spawn algae
B. Scientific name-Spirogyra, Family-Chlorophyceae, Common name-Water net
c. Scientific name-Lycopodium, Family-Lycopodiaceae, Common name-sanjeevani
D. scientific name-Selaginella, Family-Lycopodiaceae, Common name-Little club moss


The plant used as an alternative of
cotton is
A. Sphagnum
B. Funaria
c. Riccia
D. Andria


The chance that a person with two dices, the faces of each being numbered 1 to \( 6, \) will throw aces exactly
4 times in 6 trials is
\( ^{\mathrm{A}} \cdot\left(\frac{1}{36}\right)^{4} \)
\( ^{\mathrm{B}}\left(\frac{1}{36}\right)^{4}\left(\frac{35}{36}\right)^{2} \)
\( ^{\mathbf{c}} \cdot_{4} C\left(\frac{1}{36}\right)^{4}\left(\frac{35}{36}\right)^{2} \)
\( ^{\mathrm{D}} \cdot_{4}^{6} C\left(\frac{1}{36}\right)^{2}\left(\frac{35}{36}\right)^{4} \)


A ball falling in a lake of depth \( 200 \mathrm{m} \) show \( 0.1 \% \) decrease in its volume at the
bottom. What is the bulk modulus of the
material of the ball:-
A \( \cdot 19.6 \times 10^{8} N / m^{2} \)
B . \( 19.6 \times 10^{-10} \mathrm{N} / \mathrm{m}^{2} \)
C. \( 19.6 \times 10^{10} N / m^{2} \)
D. \( 19.6 \times 10^{-8} N / m^{2} \)


If in the resultant wave the frequency and amplitude remains equals to
amplitude of superimposing waves. Then phase diff. between them is: -
Two waves having equation
\[
\begin{array}{l}
\mathbf{x}_{1}=\mathbf{a} \sin \left(\omega \mathbf{t}+\mathbf{\phi}_{1}\right) \\
\mathbf{x}_{2}=\mathbf{a} \sin \left(\omega \mathbf{t}+\phi_{2}\right)
\end{array}
\]
A \( \cdot \frac{\pi}{6} \)
в. \( \frac{2 \pi}{3} \)
c. \( \frac{\pi}{4} \)
D. \( \frac{\pi}{3} \)


Equilibrium constant \( \boldsymbol{K}_{c} \) for the
reaction will be:
\( \mathbf{A} \cdot 0.66 M \)
в. \( 0.56 M \)
c. \( 0.46 M \)
D. \( 0.36 M \)


\[
\operatorname{ftg}\left[\begin{array}{ccc}
3 & 2 & -1 \\
2 & -2 & 0 \\
1 & 3 & 1
\end{array}\right], B\left[\begin{array}{ccc}
-3 & -1 & 0 \\
2 & 1 & 3 \\
4 & -1 & 2
\end{array}\right]
\]
and \( X=A+B \) then find \( X \)


The equation of progressive wave is \( \boldsymbol{Y}=\mathbf{4} \sin \left\{\boldsymbol{\pi}\left(\frac{\boldsymbol{t}}{\mathbf{5}}-\frac{\boldsymbol{x}}{\mathbf{9}}\right)+\frac{\boldsymbol{\pi}}{\mathbf{6}}\right\} \) where \( \boldsymbol{x} \)
and \( y \) are in \( \mathrm{cm}, \) which of the following
statement is true?
\( \mathbf{A} \cdot \lambda=18 \mathrm{cm} \)
B. Amplitude = 0.04cm
c. velocity \( v=50 \mathrm{cm} / \mathrm{s} \)
D. frequency \( f=20 \mathrm{Hz} \)


When the angle between two
plane mirrors is \( 30^{\circ}, \) how many multiple images will be formed by the mirrors?
A . 1
B. 12
\( c \cdot 5 \)
\( D \cdot 13 \)


\( \left|\begin{array}{ccc}\boldsymbol{a}+\boldsymbol{x} & \boldsymbol{a}-\boldsymbol{x} & \boldsymbol{a}-\boldsymbol{x} \\ \boldsymbol{a}-\boldsymbol{x} & \boldsymbol{a}+\boldsymbol{x} & \boldsymbol{a}-\boldsymbol{x} \\ \boldsymbol{a}-\boldsymbol{x} & \boldsymbol{a}-\boldsymbol{x} & \boldsymbol{a}+\boldsymbol{x}\end{array}\right|=\mathbf{0} \) then
the non-zero value of \( x=\dots \)
\( A \)
B. \( 3 a \)
\( c .2 a \)
D. \( 4 a \)


The number of orbitals in \( n=3 \) are:
\( \mathbf{A} \cdot \mathbf{1} \)
B. 4
\( c \cdot 9 \)
D. 16


No. of wave in third Bohr's orbit of
hydrogen is


\( \mathbf{f} \boldsymbol{y}=\int \frac{\boldsymbol{d} \boldsymbol{x}}{\left(\mathbf{1}+\boldsymbol{x}^{2}\right)^{3 / 2}} \) and \( \boldsymbol{y}=\mathbf{0} \) when
\( \boldsymbol{x}=\mathbf{0}, \) then value of \( \mathbf{y} \) when \( \boldsymbol{x}=\mathbf{1}, \) is


Which of the following has S-S bond?
A \( \cdot H_{2} S_{2} O_{6} \)
в. \( H_{2} S_{2} O_{7} \)
c. \( H_{2} S_{2} O_{8} \)
D. mustard gas


State true or false.
The sum of interior angles of a triangle
is \( 180^{\circ} \)
A. True
B. False


The temperature of first object is \( 36^{\circ} \mathrm{C} \)
and that of second object is \( 36^{\circ} \mathrm{F} \). Which
is hotter than the other?
A. First object
B. Second object
c. Both have same hotness
D. cannot be determined


consists of isosceles triangular frame
of base length \( l_{1} \) and expansivity \( \alpha_{1} \) and side length \( \frac{l_{1}}{l_{2}} \) and expansivity \( \alpha_{2} . \) The pendulum is supported as shown in the
figure. What is the correct ratio of
lengths, so that the length of the
pendulum remains unchanged at all
temperatures?
A \( \cdot l_{1} \alpha_{1}=l_{2} \alpha_{2} \)
B. \( \frac{l_{1}}{l_{2}}=2 \sqrt{\frac{a_{2}}{a_{1}}} \)
\( \mathbf{c} \cdot l_{1}^{2} \alpha_{1}=l_{2}^{2} \alpha_{2} \)
D. \( l_{1} l_{2}=\alpha_{1} \alpha_{2} \)


Two particles are shown in the figure. at \( \boldsymbol{t}=\mathbf{0} \) a constant force \( \boldsymbol{F}=\mathbf{6} \boldsymbol{N} \) starts
acting on the \( 3 k g \) man. Find the velocity of the center of mass of these particles
at \( t=5 s \)
\( A \cdot 5 m / s \)
B. \( 4 m / s \)
\( c \cdot 6 m / s \)
D. \( 3 m / s \)


\( 25 g \) of an unknown hydrocarbon upon
burning produces \( 88 g \) of \( C O_{2} \) and \( 9 g \) of
\( H_{2} O . \) This unknown hydrocarbon
contains.
A. \( 20 g \) of carbon and \( 5 g \) of hydrogen
B. \( 24 g \) of carbon and \( 1 g \) of hydrogen
c. \( 18 g \) of carbon and \( 7 g \) of hydrogen
D. \( 22 g \) of carbon and \( 3 g \) of hydrogen


The angle made by the vector \( \vec{A}=\hat{i}+\hat{j} \)
with \( x- \) axis is
A \( \cdot 90^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 22.5^{\circ} \)
D. \( 30^{\circ} \)


Reflex arc located in the brain is called
as
A. Somatic reflex
B. Cerebral reflex
c. Autonomic reflex
D. Both A and B


Aqueous solution of hydrogen sulphide and sulphur dioxide when mixed
together,yield
A. Sulphur and water
B. Sulphur reioxide and water
c. Hydrogen peroxide and sulphur
D. Hydrogen and sulphurous acid


Indicate the point of the complex plane
\( z \) which satisfy the following equation. \( z^{2}+|\bar{z}|=0 \)


When the object is placed \( 4 \mathrm{cm} \) from the objective of microscope, the final image formed coincides with the object. The final image is at the least distance of distinct vision \( (24 \mathrm{cm}) . \) If the focal
length of eye piece is \( 8 \mathrm{cm} \) then the focal length of objective is
A . \( 3.25 \mathrm{cm} \)
B. \( 2 c m \)
\( \mathrm{c} .3 .9 \mathrm{cm} \)
D. \( 4.2 \mathrm{cm} \)


For which of the following, number of
neutrons and protons is same?
A. Chlorine
B. Deuterium
c. Protium
D. Fluorine


Which animal do not possess larval stage in its life cycle?
A. Ascaris
B. Frog
c. Taenia
D. Pheretema


Heart of humans is ............ chambered.
A. One
B. Two
c. Three
D. Four


Q Type your question
as on
the same direction, while in 3 is in the
opposite direction. Match the following
table
Table 1 Table - 2
(a) When the current in 1 is
(p) current in 1 will increased increased i
(b) When the current in 2 is
(q) current in 2 will increase increased
(r)Current in 3 will
(c) When the current in 3 is increase
increased
\( A \cdot a-r ; b-r ; c-p, q \)
B. \( a-p ; b-p ; c-q \)
\( \mathrm{C} \cdot \mathrm{a}-\mathrm{q} ; \mathrm{b}-\mathrm{q} ; \mathrm{c}-\mathrm{r} \)
D. \( a-r ; b-q ; c-p \)


The bonds present in \( \left(N_{2} O_{5}\right) \) are:
A. only ionic
B. covalent
c. dative
D. both ionic and covalent


Give equations for the reactions of
ethylene with \( \boldsymbol{O}_{3} \)


Arrange the following aqueous solutions in the order of their increasing boiling points
\( (\mathrm{i}) 10^{-4} M N a C l \)
(ii) \( 10^{-4} M \) Urea
\( (\text { iii }) 10^{-3} M M g C l_{2} \)
(iv) \( 10^{-2} M N a C l \)
A \( \cdot(i)<(i i)<(i v)<(i i i) \)
B. \( (i i)<(i)<(i i i)<(i v) \)
c. \( (i i i)<(i)<(i i)<(i v) \)
D. \( (i v)<(i i i)<(i)=(i i) \)


Some pieces of chalk were taken and mixed with water. In this change, how many new substances are formed?
\( A \)
B. 2
\( c \cdot 3 \)
D. No new substance is formed


Match List I with List II and select the
correct answer using the codes given:
List-I List-II
A. I langerhans
1. Calcitonin
в. Pituitary
2. Epinephrine rygland
c. Growth
hormone Thyroidgland 3. medere dgland s.
D. Adrenal gland 4. Insulin
\( A \cdot A-3, B-4, C-1, D-2 \)
B. \( A-4, B-3, C-1, D-2 \)
C. \( A-4, B-3, C-2, D-1 \)
D. A - 3, B - 2, C - 4, D-


\( \lim _{x \rightarrow 0} \frac{x \tan 2 x-2 x \tan x}{(1-\cos 2 x)^{2}}= \)
\( A \cdot 2 \)
B. - 2
\( c \cdot \frac{1}{2} \)
D. \( -\frac{1}{2} \)


Assertion
For good conductors, the \( \boldsymbol{I}-\boldsymbol{V} \) graph is
a perfect straight line inclined to current axis.
Reason
By Ohm's law, voltage across the ends of a conductor is directly proportional to the resistance of the conductor.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Gemmae are asexual reproductive
bodies of
A. Algae
B. Liverworts
c. Mosses
D. Both B and C


Two trains \( A \) and \( B \) of length \( 400 m \)
each are moving on two parallel tracks with a uniform speed of \( 72 \mathrm{km} / \mathrm{h} \)
the same direction, with \( A \) ahead of \( B \)
The driver of \( B \) decides to overtake \( A \)
and accelerates by \( 1 \boldsymbol{m} / \boldsymbol{s}^{1} . \) If after \( \mathbf{5 0} \boldsymbol{s} \)
the guard of \( B \) just brushes past the
driver of \( A, \) what was the original
distance between the guard of \( B \& \)
driver of \( A \) ?


The diameter of a spherical ball is 21 \( \mathrm{cm} . \) How much leather is required to prepare 5 such balls.


Draw separate energy band diagrams for conductors, semi-conductors and insulators and label each of them.


A boy standing between two cliffs claps
and hears 2 echoes after 2 s and 2.5 s
respectively. If the velocity of sound is \( 330 m s^{-1}, \) find the distance between he
two cliffs:
A. \( 742.50 \mathrm{m} \)
B. 274.50 \( \mathrm{m} \)
c. 472.50 \( \mathrm{m} \)
D. 442.50 \( \mathrm{m} \)


Select correct statement(s).
A. Hydrophilic colloid is a colloid in which there is a strong attraction between the dispersed phase and water.
B. Hydrophobic colloid is a colloid in which there is a lack of attraction between the dispersed phase and water.
C. Hydrophobic sols are often formed when a solid crystallises rapidly from a chemical reaction or a supersaturated solution.
D. All of the above.


In aq. \( s o l^{n} \) oxalic acid exist as dihydrate \( \left(\begin{array}{c}\operatorname{COOH} \cdot 2 H_{2} O \\ _{C O O H}\end{array}\right) . \) If \( 6.3 g m \) oxalic
acid dissolve in \( 3 L \) water. Calculate \( P H \)
of \( s o l^{n} \)


A bar magnet of magnetic moment \( M \) is
divided into ' \( n \) ' equal parts by cutting
parallel to length. Then one part is suspended in a uniform magnetic field of
strength \( 2 T \) and held making an angle \( 60^{0} \)
with the direction of the field. When
the magnet is released, the kinetic energy of the magnet in the equilibrium position
is:
A. \( \frac{M}{n} \)
B. \( M n \) J
c. \( \frac{M}{n^{2}} \)
D. \( M n^{2} \)


Write the IUPAC name of the compound
in the picture.


Which of the following is the branchy part of a tree?
A. Stem tip
B. Apical stem
c. crown
D. Axillary stem


In what pressure range will the
compound sublime?
A. pressures less than \( P_{b} \)
B. pressures between \( P_{b} \) and \( P_{c} \)
C. pressures between \( P_{d} \) and \( P_{c} \)
D. pressures between \( P_{b} \) and \( P_{d} \)
E. The compound will not sublime under any Pressure


Which one of the following statement is
INCORRECT?
A. A cyclic parallelogram is a rectangle
B. Set of points joining the middle points of all parallel chords of a circle constitute the longest chord of the circle
C. Total surface area of a hemisphere is \( 2 \pi r^{2} \)
D. A fair coin is tossed The chance that it shows up head is 50\%


Phosphorus has the oxidation state of +3
in:
A. ortho phosphoric acid
B. phosphorus acid
C. meta phosphoric acid
D. pyrophosphoric acid


During discharging of a lead storage
battery, which of the following is/are
true?
This question has multiple correct options
\( \mathbf{A} \cdot H_{2} S O_{4} \) is produced
B. \( H_{2} O \) is consumed
\( \mathrm{C} \cdot P b S O_{4} \) is formed at both electrodes
D. Density of electrolytic solution decreases


Which element with lowest atomic
number
\( \mathbf{A} \cdot_{19} K \)
В \( \cdot_{24} C r \)
\( \mathbf{c} \cdot_{11} N a \)
D・ \( _{29} C u \)


Let \( \boldsymbol{A}=\{\boldsymbol{x}: \boldsymbol{x} \in \boldsymbol{N}, \mathbf{1}<\boldsymbol{x} \leq \mathbf{3}\} \) and
\( \boldsymbol{B}=\left\{\boldsymbol{y}: \boldsymbol{y}^{2}-\mathbf{5} \boldsymbol{y}+\boldsymbol{6}=\mathbf{0}\right\}, \) then
A \( . A \subset B \)
в. \( B \subset A \)
\( \mathbf{c} \cdot A=B \)
D. \( A \neq B \)


Prove the following identities:
\( \boldsymbol{a b c}\left(\sum \boldsymbol{a}\right)^{3}-\left(\sum \boldsymbol{b c}\right)^{3}=\boldsymbol{a b c} \sum \boldsymbol{a}^{3}- \)
\( \sum b^{3} c^{2}=\left(a^{2}-b c\right)\left(b^{2}-c a\right)\left(c^{2}-a b\right) \)


\( \frac{1-\frac{9}{y^{2}}}{1-\frac{3}{y}}-\frac{3}{y}, \) where \( (y \neq 0)= \)
A. \( \frac{y-3}{y} \)
в. \( \frac{y+3}{y} \)
\( c \cdot 3 \)
D.
E \( .3 y-1 \)


Sum of the series
\( \boldsymbol{S}=\mathbf{1}+\frac{\mathbf{1}}{\mathbf{2}}(\mathbf{1}+\mathbf{2})+\frac{\mathbf{1}}{\mathbf{3}}(\mathbf{1}+\mathbf{2}+\mathbf{3})+ \)
\( \frac{1}{4}(1+2+3+4)+\ldots \) upto 20 terms is
A. 110.5
B. 111.5
c. 115.5
D. 116.5


The capacity between two adjacent plates of parallel plate condenser is \( 5 \mu F \). The number of plates used if we want to get a capacity of \( 40 \mu F \) are (alternate plates are connected together):
\( A \cdot 8 \)
B. 9
\( c \cdot 7 \)
D. 10


Express 6762 as a product of prime factors


A transistor has \( \beta=40 . \) A change in
base current of \( 100 \mu \) A, produces
change in collector current
A. \( 40 \times 100 m A \)
в. \( (100-40) m A \)
c. \( (100+40) m A \)
D. \( 100 / 40 m A \)


\( \vec{r}=\vec{x} \hat{i}+\vec{y} \hat{j} \) is the equation of:
A \( . \) yoz plane
B. a straight line joining the points \( \vec{i} \) and \( \vec{j} \)
c. zox plane
D. \( x \) oy plane


Phenolphthalein indicator is colourless in an acid and turns pink in an alkaline solution. When an aqueous
solution of potassium iodide is electrolysed with phenolphthale in indicator, what colours appear at the
electrodes?
Cathode: \( 2 H_{2} O_{(l)}+2 e^{-} \rightarrow H_{(g)}+ \)
\( 2 O H^{-}(a q) \)
Anode: \( 2 I_{(a q)}^{-} \rightarrow I_{2(s)}+2 e^{-} \)
A. Brown at the cathode and pink at the anode
B. Red at the cathode and pink at the anode
c. Brown at the anode and colourless at the cathode
D. Pink at the cathode and brown at the anode


Which of the following statements is/are true for fullerene?
A. It is a non-crystalline form of carbon
B. It was discovered by Buckminster fuller
c. All the fullerenes have even number of atoms
D. All of these


The quadratic polynomial
A. has the highest power equal to 2
B. has the highest power equal to 1
C. has the highest power equal to 3
D. None of the above.


Dumas and Kjeldahl's methods are used for thequantitative estimation of
A. \( c \) and
B. Halogens, S, and P
c.
D. All


How is this process of \( m R N A \)
synthesis different from that in prokaryotes?


An organic compound (Mol. wt. \( =60 \) ) is found to contain \( \boldsymbol{C}=\mathbf{2 0 \%}, \boldsymbol{H}= \)
\( \mathbf{6 . 6 7} \%, N=\mathbf{4 6 . 6 7} \% \) and remaining
is oxygen. On heating, it gives \( \boldsymbol{N} \boldsymbol{H}_{3} \)
along with a solid residue. The solid residue gives violet colour with alkaline
\( C u S O_{4} . \) The compound is:
A. \( C H_{3} N C O \)
в. \( C H_{3} C O N H_{2} \)
c. \( N H_{2} C O N H_{2} \)
D. \( C H_{3} C H_{2} C O N H_{2} \)


Condition for maximum yield of
\( \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{C l} \) is:
A \( \cdot C_{2} H_{6}(\text { Excess })+C l_{2} \stackrel{\text { UVIight }}{\longrightarrow} \)
в. \( C_{2} H_{6}+C l_{2} \underset{R . T}{\longrightarrow} \)
c. \( C_{2} H_{6}+C l_{2}(\text { Excess }) \stackrel{\text { UVI lant }}{\longrightarrow} \)
D. \( C_{2} H_{6}+C l_{2} \underset{D a r k}{D a r k} \)


The sum of first \( n \) terms of an AP is
given by \( S_{n}=\left(1+T_{n}\right)(n+2) \) Then \( T_{2} \)
is
A \( \cdot-\frac{11}{6} \)
B. \( -\frac{-5}{3} \)
\( c \cdot-\frac{5}{3} \)
D. 2


The internal resistance of cell of e.m.f.
\( 2 V \) is \( 0.1 . \) It is connected to a resistance
of \( 3.9 . \) The voltage across the cell is
\( \mathbf{A} \cdot 2.71 V \)
B . \( 1.95 V \)
c. \( 1.68 V \)
D. \( 0.52 V \)


Acetic acid is titrated with \( N a O H \)
solution. Which of the following statement is correct for this titration?
A. Conductane increases upto equivalence point, then it it decreases
B. Conductance decreases upto equivalence point, then it increases
c. First conductance increases slowly upto equivalence point and then increases rapidly
D. First conductance increases slowly upto equivalence point and then drops rapidly


\( 2 Z n S(s)+3 O_{2}(g) \stackrel{\text {heat}}{\rightarrow} 2 Z n O(s)+ \)
\( 2 S O_{2}(g) \) is an example of which type of
reaction?
A. Calcination
B. Roasting
c. Both A and B
D. None of the above


In the reaction:
\( \boldsymbol{C H}_{3} \boldsymbol{C N} \frac{\boldsymbol{H}_{3} \boldsymbol{O}^{+}}{\text {heat}} \boldsymbol{C H}_{3} \boldsymbol{C O O H} \)
The hybridization state of the functional carbon changes from:
A \( \cdot s p^{3} \) to \( s p^{2} \)
B. \( s p^{2} \) to \( s p^{3} \)
c. \( s p \) to \( s p^{2} \)
D. \( s p^{2} \) to sp


A thin equiconvex lens of refractive index \( 3 / 2 \) is placed on a horizontal plane mirror as shown in figure. The
space between the lens and the mirror
is filled with a liquid of refractive index 4/3. It is found what when a point object is placed \( 15 \mathrm{cm} \) above the lens on its
principal axis, the object coincides with its own image.
If another liquid is filled instead of
water, the object and the image coincide at a distance \( 25 \mathrm{cm} \) from the
lens. Calculate the refractive index of
the liquid.
\( \mathbf{A} \cdot 1.6 \)
в. 2.6
\( c .2 .8 \)
D. 3.2


Glomerulus and its surrounding Bowman's capsule together form the specialised structure called as
A. Malpighian tubule
B. Rete Mirabilia
c. Malpighian corpuscle
D. Green gland


A machine gun fires bullets of \( 50 \mathrm{gm} \) at the speed of \( 1000 \mathrm{m} / \mathrm{sec} . \) If an average force of \( 200 \mathrm{N} \) is exerted on the gun, the maximum number of bullets fired per
minutes is:
A . 240
B. 180
\( c \cdot 60 \)
D. 30


Enzyme facilitates a reaction through
A. Reduction in activation energy
B. Increase in activation energy
C. Altering ph
D. Altering temperature


Insects are able to run on the surface of
water because:
A. insects have less weight
B. insects swim on water
c. of the Archimede's upthrust
D. surface tension makes the surface behave as elastic membrane


State True or False.
A binary solution which has same composition in liquid, as well as vapour phase, is called azeotropic mixture.
A. True
B. False


Locating position vector of a point object


State True or False.
A barometric liquid having high density produces a shorter column of liquid.
A. True
B. False


Three charges each \( 20 \mu C \) are placed at
the corners of an equilateral triangle of side of \( 0.4 m . \) The potential energy of the
system is :
\( \mathbf{A} \cdot 18 \times 10^{-6} J \)
B. \( 9 J \)
c. \( 9 \times 10^{-6} J \)
D. 27J


According to The United States Geological Survey, water having less than \( 1000 \mathrm{mg} / \) litre of total dissolved
solids is:
A. fresh water
B. slightly saline
c. moderately saline
D. brine water


A coil of area \( 2 m^{2} \) and resistance \( 4 \Omega \) is
placed perpendicular to a uniform
magnetic field of 4 T. The loop is rotated
by \( 90^{\circ} \) in 0.1 second. Choose the correct
options This question has multiple correct options
A. Average induced emf in the coil is \( 8 V \)
B. Average induced current in the circuit is \( 20 A \)
c. \( 2 C \) charge will flow in the coil in above period
D. Heat produced in the coil in the above period can be determined from the given data


The metal oxide reacts with a
The oxide is
metal and reducing agent is Net Gibb's energy changes is
A. reducing agent, oxidised, reduced, negative
B. reducing agent, reduced, oxidised, negative
c. oxidising agent, reduced, oxidised, positive
D. reducing agent, reduced, oxidised, positive


For square matrix \( \boldsymbol{A}, \boldsymbol{A} \boldsymbol{A}^{\boldsymbol{T}} \) is -
A. unit matrix
B. symmetric matrix
c. skew symmetric matrix
D. diagonal matrix


If an angel visits an asteroid called
\( B 612 \) which has a radius of \( 20 m \) and
mass of \( 104 k g \), what will be the
acceleration due to gravity in \( B \) 612?


If \( \vec{a}=2 \hat{i}+2 \hat{j} \) and \( \vec{b}=3 \hat{i}+4 \hat{j} \) then \( \vec{a}+ \)
\( \vec{b} \) is
\( \mathbf{A} \cdot \hat{i}+2 \hat{j} \)
B. \( 5 \hat{i}+6 \hat{j} \)
c. \( 5 \hat{i}+2 \hat{j} \)
D. \( \hat{i}+6 \hat{j} \)


Types of drugs that mimic the natural
messenger by switching on the receptor are called?
A. Antagonists
B. Chemical messengers
c. Receptors
D. Agonists


Most liquids that conduct electricity are solutions of :
A . acids
B. bases
c. salts
D. all of the above


If mole fraction of urea in 11.11 mola
aqueous solution?
A . 0.1
B. 0.17
\( c .0 .2 \)
D. 0.37


State whether given statement is True or False
Heat is an invisible form of energy,
which causes the sensation of hotness
or coldness.
A. True
B. False


Which choice is a gas which has a low
solubility in water?
A \( \cdot N H_{3} \)
в. \( C s H \)
c. \( C H_{4} \)
D. \( G a H_{3} \)


In a two-slit experiment, with
monochromatic light, fringes are obtained on a screen placed at some distance from the slits. If the screen is
moved by \( 5 \times 10^{-2} \mathrm{m} \) towards the slits,
the change in fringe width is \( 10^{-3} \mathrm{m} \) The the wavelength of light used is
(given that distance between the slits is
\( 0.03 \mathrm{mm} \)
\( A \cdot 4500 \stackrel{\circ}{A} \)
B . 5000 ,
c. 5500 ,
D. 6000 ,


Statement: During electrolysis of
acidified water, at the cathode, \( \boldsymbol{H}_{2} \) is
evolved and at the anode, \( O_{2} \) is evolved.
Enter 1 if true else 0


Assertion
Sound waves cannot pass through
vacuum.
Reason
Sound waves are mechanical waves,
which require a medium for their
propagation.
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


Which of the following compounds can form \( \boldsymbol{H} \) -bonding with each other?
A. \( C H_{3} C O O H \) and \( H_{2} O \)
B. Phenol and \( C H_{4} \)
\( \mathrm{c} \cdot C H F_{3} \) and acetone
D. \( P H_{3} \) and \( H F \)


Figure shows two blocks in contact
sliding down an inclined surface of
inclination \( 30^{\circ} . \) The friction coefficient
between the block of mass \( 2.0 \mathrm{kg} \) and
the incline is \( \mu_{1}=0.20 \) and that
between the block of mass \( 4.0 \mathrm{kg} \) and
the incline \( \mu_{2}=0.30 . \) is Find the
acceleration of \( 2.0 \mathrm{kg} \) block. \( (\mathrm{g}= \) \( \left.10 m / s^{-2}\right) \)
A \( \cdot 2.7 m / s^{2} \)
B \( .2 .2 m / s^{2} \)
\( \mathrm{c} \cdot 3.7 \mathrm{m} / \mathrm{s}^{2} \)
D. \( 3.2 m / s^{2} \)


Mother, father and son line up at
random for a family photo. If \( A \) and \( B \) are two events given by \( A= \) Son on one
end, \( B= \) Father in the middle, find
\( \boldsymbol{P}(\boldsymbol{A} / \boldsymbol{B}) \) and \( \boldsymbol{P}(\boldsymbol{B} / \boldsymbol{A}) \)


Which of the following catalysis is an example of negative catalysis?
A \( \cdot 2 S O_{2}+O_{2} \stackrel{V_{2} O_{5}}{\longrightarrow} 2 S O_{3} \)
в. \( C H C l_{3}+O_{2} \stackrel{\text { агсодо } l}{\longrightarrow} 2 C O C l_{2}+2 H C l \)
\( ^{\mathrm{c}} \cdot 2 K C l O_{3} \frac{M n O_{2}}{\Delta} 2 K C l+3 O_{2} \)
D. \( C O+3 H_{2} \stackrel{N i}{\longrightarrow} C H_{4}+H_{2} O \)


Radha takes some flowers in a basket
and visit three temples one by one. At
each temple, she offers one half of the flowers from the basket. If she is left
with 3 flowers at the end, find the number of flowers she had in the
beginning.


Choose the correct option
A. A: Virtual Image
B: Real Image
B. A: Real Image
B: Virtual Image
C . A: Real Image
B: Real Image
D. A: Virtual Image
B: Virtual Image


Assertion
On moon barometer height will be six times compared to the height or earth.
Reason

Value of \( g \) on moon's surface is \( 1 / 10 \) the
value of \( g \) on earth's surface.
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


ff \( z=\sqrt{20 i-21}+\sqrt{21+20 i} \) then
principal value of arg z can not be


What do you observe when you are visiting a nearby tailoring shop?


Choose the source of energy which is different from others.
A. woodd
B. Falling water
c. wind
D. Petroleum


Heisenberg Uncertainity principle is not valid for:
A. moving electron
B. motor car
c. stationary particles
D. both B and C


A mixture of two moles of \( N_{2} \) and 8
moles of \( H_{2} \) are heated in a 2 lit vessel
At equilibrium, 0.4 moles of \( N_{2} \) was
observed, the equilibrium
concentration of \( \boldsymbol{H}_{2} \) was:


A study of chemical kinetics of the
reaction \( \mathbf{A}+\mathbf{B} \rightarrow \) products, gave the
following data at \( 25^{\circ} \mathrm{C} \)
Experiment
\( [\mathrm{A}] \)
\( [\mathrm{B}] \)
\[
\frac{\boldsymbol{d}[\boldsymbol{P r o d u c t s}]}{\boldsymbol{d t}}
\]
1.0
0.15
\( 4.20 \times 10^{-6} \)
2 \( \begin{array}{lll}\text { 2.0 } & \text { 0.15 } & 8.40 \times 10^{-6}\end{array} \)
3 1.0 0.20 \( \quad 5.60 \times 10^{-6} \)
Find:
(1) The order of reaction with respect to
\( \mathbf{A} \)
(2) The order of reaction with respect to
B.
(3) The rate law.


The magnetic nature of elements depends on the presence of unpaired electrons. Identify the configuration of transition elements which shows
highest magnetic momentum:
\( \mathbf{A} \cdot 3 d^{7} 4 s^{2} \)
B. \( 3 d^{5} 4 s^{1} \)
c. \( 3 d^{8} 4 s^{2} \)
D. \( 3 d^{2} 4 s^{2} \)


The oxidation states of \( P \) atom in
\( \boldsymbol{P O C l}_{3}, \boldsymbol{H}_{2} \boldsymbol{P O}_{3} \) and \( \boldsymbol{H}_{4} \boldsymbol{P}_{2} \boldsymbol{O}_{6} \)
respectively are:
\( \mathbf{A} \cdot+5,+4,+4 \)
B. +5,+5,+4
\( \mathbf{c} \cdot+4,+4,+5 \)
\( \mathbf{D} \cdot+3,+4,+5 \)


State true or false.
1 ppm is equal to 1 mg per \( \mathrm{kg} \)
A. True
B. False


Simplify \( -3 x y z \div z^{2} \)


Power emitted by a black body at
temperature \( 50^{\circ} C \) is \( P . \) Now,
temperature is doubled i.e. temperature
of black body becomes \( 100^{\circ} \mathrm{C} \). Now,
power emitted is:
A. greater than \( P \) but less than \( 16 P \)
B. greater than \( 16 P \)
\( c . P \)
D. 16 \( P \)


Which of the following is (are) true?
A. PAHs generally have a high degree of acute toxicity in humans.
B. PAHs have been associated with increased incidences of lung, skin, and bladder cancers from occupational exposures.
C. Specific PAHs can easily be linked to observed health effects in epidemiologic studies.
D. All of these


If both the mean and the standard
deviation of 50 observations
\( x_{1}, x_{2}, \dots \dots, x_{50} \) are equal to \( 16, \) then the
mean of
\( \left(x_{1}-4\right)^{2},\left(x_{2}-4\right)^{2}, \dots . .\left(x_{50}-4\right)^{2} \) is
A . 525
в. 380
\( c .480 \)
D. 400


Identify the protein with more than one
polypeptide chain.
A. Myoglobin
B. Trypsin
c. Immunoglobulin
D. Lysozyme


Vicinal dihalides undergo double dehydrohalogenation to give terminal
alkyne. How many moles of \( N a N H_{2} \) are used in the overall reaction?
A. one
B. Two
c. Three
D. Four


If \( \mathrm{E} \& \mathrm{F} \) are events with \( \boldsymbol{P}(\boldsymbol{E}) \leq \boldsymbol{P}(\boldsymbol{F}) \& \)
\( \boldsymbol{P}(\boldsymbol{E} \cap \boldsymbol{F})>0, \) then?
A. Occurrence of \( E \Rightarrow \) occurrence of \( F \)
B. Occurrence of F \( \Rightarrow \) occurrence of E
c. Non-occurrence of \( E \Rightarrow \) non-occurrence of \( F \)
D. None of the above implications holds


Which of the following compound is not a strong oxidizing agent?
A. \( P b O_{2} \)
в. \( P b C l_{4} \)
\( \mathbf{c} \cdot P b_{2} O_{3} \)
D. \( C C l_{4} \)


The solubility of silver bromide in hypo
solution is due to the formation of:
A. \( A g_{2} S O_{3} \)
B. \( A g_{2} S_{2} O_{3} \)
\( \mathbf{c} \cdot\left[A g\left(S_{2} O_{3}\right)\right] \)
D. \( \left[A g\left(S_{2} O_{3}\right)_{2}\right]^{3} \)


Find the volume of a sphere whose
radius is
(i) \( 7 \mathrm{cm} \)
(ii) \( 0.63 \mathrm{m} \)


Assertion
Transition metals are weak reducing
agents.
Reason
Due to high heat of sublimation, high ionization energy and low \( \boldsymbol{E}_{\boldsymbol{R} . \boldsymbol{P}}^{\boldsymbol{0}} \)
Read the above assertion and reason
and choose the correct option regarding
¡t.
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


Why is cambium considered to be a
lateral meristem?


Calculate the median from the following distribution
\( \begin{array}{lllll}\text { Class } & \begin{array}{l}5- \\ 10\end{array} & \begin{array}{l}10 \\ 15\end{array} & \begin{array}{l}15- \\ 20\end{array} & 2\end{array} \) \( 20- \)
25
Frequency \( \quad 4 \quad \) 7
10


Hydrocarbons are mainly composed of which of these?
A. hydrogen
B. hydrogen, oxygen and carbon
c. hydrogen and carbon
D. hydrogen, carbon and nitrogen


Assertion
The order of the differential equation whose primitive is \( y=A+\ln B x \) is 2
Reason
f there are 'n' independent arbitrary constant in a family of curve then the order of the corresponding differential equation is 'n'
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


Methanol is now prepared from:
A. water gas
B. sugar through fermentation
c. wood
D. both \( A \) and \( B \)


Apart from water what is secreted by the large intestine?
\( A \cdot K+ \)
B. Nat
c. с।
D. Both A and C


A circular loop of radius \( r, \) having \( N \)
turns of a wire, is placed in a uniform
and constant magnetic field \( \boldsymbol{B} \). The
normal loop makes an angle \( \theta \) with the
magnetic field. Its normal rotates with an angular velocity \( \omega \) such that the angle \( \theta \) is constant. Choose the correct
statement from the following. This question has multiple correct options
A . emf in the loop is \( N B \omega r^{2} / 2 \cos \theta \)
B. emf induced in the loop is zero
c. emf must be induced as the loop crosses magnetic lines
D. emf must not be induced as flux does not change with time
E. answer required


Assertion
The molecules of the dissolved gas
present in a liquid gain kinetic energy as temperature is raised.
Reason
Gases tends to be more soluble in
liquids as the temperature is raised.
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


Identify tertiary alkyl halide:
A. Tert-butylbromide
B. 2-Methyl-2- bromopropane
C. Both A and B
D. None of these


Write the sum of first five terms of the
following Arithmetic Progressions where, the common difference \( d \) and the
first term \( a \) are given,
\( \boldsymbol{a}=\mathbf{2}, \boldsymbol{d}=\mathbf{2 . 5} \)
A .32
B. 33
\( c .34 \)
D. 35


For hypothetical reaction \( \boldsymbol{A} \rightarrow \boldsymbol{B} \) takes
place according to:
\( \boldsymbol{A} \stackrel{\boldsymbol{k}_{1}}{\rightleftharpoons} \boldsymbol{C}(\text { fast }), \boldsymbol{A}+\boldsymbol{C} \stackrel{\boldsymbol{k}_{2}}{\longrightarrow} \boldsymbol{B}(\text { slow }) \)
Rate law will be:
\( \mathbf{A} \cdot k_{2}[A][C] \)
В . \( k_{1} k_{2}[A] \)
\( \mathbf{c} \cdot k_{1} k_{2}[A]^{2} \)
\( \mathbf{D} \cdot k_{1} k_{2}[A][C] \)


Determine the nature of roots of the
equation \( x^{2}+2 x \sqrt{3}+3=0 \)
A. Real and distinct
B. Non-real and distinct
c. Real and equal
D. Non-real and equal


After culturing the anther of a plant, a few diploid plants were got along with haploid plants. Which of the following parts might have given rise to diploid plants?
A. Vegetative cell of pollen
B. Cells of anther wall
c. Generative cell of pollen
D. Intine of pollen wall


Evaluate \( \int \frac{d x}{1+\sqrt{x^{2}+2 x+2}} \)
\( \mathbf{A} \cdot I=\ln (x+1-\sqrt{x^{2}+2 x+2})+ \)
\( \frac{2}{(x+2)+\sqrt{x^{2}+2 x+2}}+C \)
B \( \cdot I=\ln (x-2-\sqrt{x^{2}-2 x-4})+ \)
\( \frac{2}{(x+2)+\sqrt{x^{2}+2 x+2}}+C \)
C \( . I=\ln (x+1+\sqrt{x^{2}+2 x+2})+ \)
\( \frac{2}{(x+2)+\sqrt{x^{2}+2 x+2}}+C \)
D. None of these


\( \left|\begin{array}{lll}\mathbf{a}+\mathbf{b} & \mathbf{a} & \mathbf{b} \\ \mathbf{a} & \mathbf{a}+\mathbf{c} & \mathbf{c} \\ \mathbf{b} & \mathbf{c} & \mathbf{b}+\mathbf{c}\end{array}\right|= \)
\( A \cdot 4 \) abc
B. abç
\( c \cdot 2 a^{2} b^{2} c^{2} \)
D. \( 4 a^{2} b^{2} c^{2} \)


How much does the monkey's velocity
change from \( t=2 s \) to \( t=7 s ? \)
A. \( +3 m / s \)
B. \( +1 m / s \)
\( \mathrm{c} \cdot 0 \mathrm{m} / \mathrm{s} \)
\( \mathbf{D} \cdot-1 m / s \)
\( \mathrm{E} \cdot-3 \mathrm{m} / \mathrm{s} \)


The resultant of \( \vec{A} \) and \( \vec{B} \) makes an angle \( \alpha \) with \( \vec{A} \) and an angle \( \beta \) with \( \vec{B} \)
then :-
\( \mathbf{A} \cdot \alpha<\beta \)
B. \( \alpha<\beta \) if \( A<B \)
c. \( \alpha<\beta \) if \( A>B \)
D. \( \alpha<\beta \) if \( A=B \)


Three copper wires of lengths and cross sectional areas are \( (\ell, \boldsymbol{A}),(2 \ell, \boldsymbol{A} / 2) \)
and \( (\ell / 2,2 A) . \) Resistance is minimum in:
A. wire of cross-sectional area \( A / 2 \)
B. wire of cross-sectional area A
c. wire of cross-sectional area \( 2 A \)
D. same in all the three cases


The driver of a train moving with a
speed \( v_{1} \) sights another train at a
distance \( s, \) ahead of him moving in the
same direction with a slower speed \( v_{2} \) He applies the brakes and gives a
constant deceleration \( a \) to his train. For
no collision, \( s \) is
\( \stackrel{\mathbf{A}}{=}=\frac{\left(v_{2}-v_{1}\right)^{2}}{2 a} \)
\( ^{\mathrm{B}} \cdot \quad \frac{\left(v_{1}-v_{2}\right)^{2}}{2 a} \)
\( ^{\mathrm{C}}<\frac{\left(v_{1}-v_{2}\right)^{2}}{2 a} \)
D. \( <\frac{v_{1}-v_{2}}{2 a} \)


Write any three salient features of oxidation states of transition elements.


A moist leaf on exposure to \( \boldsymbol{S} \boldsymbol{O}_{2} \) became rather colourless. But, it
regained colour on exposure to atmospheric air. Explain.


Assertion
Ohm's law is applicable for all conducting elements
Reason
Ohm's law is a fundamental law.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If for a continuous function \( \boldsymbol{f}, \boldsymbol{f}(\mathbf{0})= \)
\( \boldsymbol{f}(1)=\mathbf{0}, \boldsymbol{f}^{\prime}(1)=\mathbf{2} \) and \( \boldsymbol{g}(\boldsymbol{x})= \)
\( f\left(e^{x}\right) e^{f(x)}, \) then \( g^{\prime}(0) \) is equal to
A . 1
B. 2
\( c \cdot 0 \)
D. None of these


In the Bohr's model of \( \boldsymbol{H} \) -atom, the ratio
of kinetic energy to the total energy of
the electron in the quantum state \( n \) is :


You are given a lump of an unknown metal. You perform an experiment and figure out the specific heat is close to
\( 0.89 J / g^{o} C . \) What could be the identity of the metal?
A. Gold
B. Silver
c. Iron
D. Aluminum
E. None of the above


Carbohydrate are stored in human body
as the :
A . starch
B. glucose
c. glycogen
D. galactose
E. Fructose


What is \( I_{1} \) equal to?
A \( \cdot \frac{\pi}{24} \)
B. \( \frac{\pi}{18} \)
c. \( \frac{\pi}{12} \)
D. \( \frac{\pi}{6} \)


Find the equation to the parabola whose focus is (1,-1) and vertex is (2,1)


\( \int \frac{\log x}{x} d x \) is equal to


State true or false:
In \( \triangle A B C, A B=B C=C A=2 a \) and
\( A D \) is perpendicular to side \( B C, \) then \( A D=2 a \sqrt{3} \)
A. True
B. False


In the following equilibrium \( N_{2} O_{4(g)} \rightleftharpoons \) \( \mathbf{2} N \boldsymbol{O}_{2(\boldsymbol{g})} \boldsymbol{N} \boldsymbol{O}_{2(g)} \) is \( \mathbf{5 0 1 \%} \) of the total
volume. hence degree of dissociation and vant hoff factor (i) respectively are:
A. 0.5,1.5
B. 0.25,1.25
c. 0.33,1.33
D. 0.66,1.66


If \( A \) is the areal velocity of planet of
mass \( M . \) its angular momentum is
\( \mathbf{A} \cdot M \)
B. \( 2 M A \)
c. \( A^{2} M \)
D. \( A M^{2} \)


Select the correct statement \( (s) \)
A. The velocity at which distribution of molecules is maximum is called most probable velocity
B. Most probable velocity of a gas is larger than root mean square velocity
C. Both (a) and (b)
D. None of above is correct


Find the magnitude and direction of the force vector applied to the loop if the
vector \( \vec{p}_{m} \) coincides in direction with
the magnetic field produced by the current \( I \) at the point where the loop is located
A \( \cdot \vec{F}=-\frac{\mu_{0} I p_{m}}{\pi r^{2}} \vec{e}_{r} ; \vec{F} \uparrow \downarrow \vec{r} \)
B・ \( \vec{F}=-\frac{\mu_{0} I p_{m}}{2 \pi r^{2}} \overrightarrow{e_{r}} ; \vec{F} \uparrow \downarrow \vec{r} \)
C・ \( \vec{F}=-\frac{\mu_{0} I p_{m}}{3 \pi r^{2}} \overrightarrow{e_{r}} ; \vec{F} \uparrow \downarrow \vec{r} \)
D・ \( \vec{F}=-\frac{\mu_{0} I p_{m}}{4 \pi r^{2}} \overrightarrow{e_{r}} ; \vec{F} \uparrow \downarrow \vec{r} \)


The order of stability of the alkenes is:
\( \mathrm{R}_{2} \mathrm{C}=\mathrm{CR}_{2}, \mathrm{R}_{2} \mathrm{C}=\mathrm{CHR}, \mathrm{R}_{2} \mathrm{C}=\mathrm{CH}_{2}, \mathrm{RCH}=\mathrm{CHR} \)
and \( \mathrm{RCH}=\mathrm{CH}_{2} \)
1
\( \| \)
\( \mathbf{V} \)
\( A \cdot|>||>|||>\mid V>V \)
B. \( |=||>|||>\mid V>v \)
c. \( \|>|>| V>\|>v \)
D. \( v>|V>|||>|>| \mid \)


Lindlar's catlyst is used for conversion
of:
A. alkynes to alkenes
B. alkane to alkyne
c. alkyne to alkane
D. alkene to alkyne


What is the effect of the shape of Earth
on value of ' \( g \) '?


If the salts, \( M_{2} X, Q Y_{2} \) and \( P Z_{3} \) have
same solubilities \( \left(\left\langle\langle<1), \text { their } \boldsymbol{K}_{s p}\right.\right. \) values are related as:
\( \mathbf{A} \cdot M_{2} X>Q Y_{2}>P Z_{3} \)
в. \( M_{2} X<Q Y_{2}>P Z_{3} \)
c. \( M_{2} X=Q Y_{2}>P Z_{3} \)
D. \( M_{2} X=Q Y_{2}=P Z_{3} \)


If one root of \( x^{2}-x-k=0 \) is square of
the other, then \( k= \)
A \( .2 \pm \sqrt{5} \)
B . \( 2 \pm \sqrt{3} \)
\( c \cdot 3 \pm \sqrt{2} \)
D. \( 5 \pm \sqrt{2} \)


f \( ^{n} C_{4},^{n} C_{5},^{n} C_{6} \) of \( (1+x)^{n} \) are in A.P.
then \( n= \)
A . 12
B. 1
\( c \cdot 7 \)
\( D .8 \)


Find mode for the following data:
\( \begin{array}{llll}\text { Size } & \boldsymbol{2}- & \boldsymbol{5}- & \boldsymbol{8}- & \boldsymbol{1} \mathbf{1}- \\ & \boldsymbol{5} & \boldsymbol{8} & \boldsymbol{1} \mathbf{1} & \boldsymbol{1} \mathbf{4}\end{array} \) \( \mathbf{1 4} \) Number
of
shoes \( \quad 1 \quad 4 \quad 8 \quad 7 \)
\( \mathbf{A} \cdot 10.4 \)
B. 11.4
c. 12.4
D. 13.4


Which one of the following reaction conditions are used for preparing diethyl ether from ethyl alcohol?
A \( \cdot H I / 200^{\circ} C \)
в. Сопс.Н\( _{2} \) S \( O_{4} / 140^{\circ} \mathrm{C} \)
c. \( N a O H / 70^{\circ} \mathrm{C} \)
D. \( \operatorname{NaOC}_{2} \mathrm{H}_{5} / 27^{\circ} \mathrm{C} \)


The total number of bonding and
antibonding electrons in \( \boldsymbol{O}_{2}^{+} \) are respectively. (If the answer is 14 and
7, then represent as 0147 )
A. 0105
B. 0205
\( c .0104 \)
D. 0202


Long-sightedness is to hypermetropia as short-sightedness is to :
A. myopia
B. focusing
c. astigmatism
D. accomodation


Find the length of the perpendicular
from the point (5,4) on the straight line.


An ideal spring with a pointer attached to its end, hangs next to a scale. With a \( 100 \mathrm{N} \) weight attaches and in
equilibrium, the pointer indicates '40 on the scale as shown. Using a \( 200 \mathrm{N} \) weight instead in'60' on the scale. Using
an unknown weight 'X' instead results in '30' on the scale. The value of X is
\( A \cdot 80 N \)
B. 60 N
\( c \cdot 50 N \)
D. \( 40 \mathrm{N} \)


Evaluate:
\( \left(\begin{array}{c}1+\cos \frac{\pi}{6}-i \sin \frac{\pi}{6} \\ 1+\cos \frac{\pi}{6}+i \sin \frac{\pi}{6}\end{array}\right) \)
\( A \)
B. -1
\( c \cdot 2 \)
\( D \cdot \underline{1} \)


The value of \( k \) if the equation \( k x+ \) \( \sin ^{-1}\left(x^{2}-8 x+17\right)+\cos ^{-1}\left(x^{2}-\right. \)
\( 8 x+17)=\frac{9 \pi}{2} \) has atleast one solution
is
\( \mathbf{A} \cdot 2 \pi \)
в. \( \pi \)
\( c \cdot 1 \)
D.


When an aqueous solution of \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{N} \boldsymbol{O}_{3} \) is
electrolysed between platinum electrodes, the substances liberated at anode and cathode are:
A. silver is deposited at cathode and \( O_{2} \) is liberated at
anode
B. Silver is deposited at cathode and \( H_{2} \) is liberated at anode
C. Hydrogen is liberated at cathode and \( O_{2} \) is liberated at anode
D. Silver is deposited at cathode and Pt is dissolved in electrolyte


Name the functional groups present in the following compounds.
(i) \( \boldsymbol{C H}_{2}-\boldsymbol{C O}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}- \)
\( \boldsymbol{C H}_{2}-\boldsymbol{C H}_{3} \)
(ii) \( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{C O O H} \)
(iii) \( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}- \)
\( C H O \)
(iv) \( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{O H} \)


This month, Kami sold 70 figurines in 2 sizes. The large figurines sold for \( \$ 12 \) each, and the small figurines sold for \( \$ \) 8 each. The amount of money he
received from the sales of the large
figurines was equal to the amount of money he received from the sales of the
small figurines. How many large figurines did Kami sell this month?
A .20
B . 28
\( c .35 \)
D. 42


In a parallelogram \( \mathrm{ABCD}, \angle B=(2 x+ \)
25)\( ^{0} \) and \( \angle D=(3 x-5)^{0} . \) Find:
(i) The value of \( x \)
(ii) Measure of angle.
B. \( x=32, b=91 \) degrees, de \( =89 \) degrees
c. \( x=30, b=89 \) degrees, d=91 degrees
D. \( x=32, b=89 \) degrees, d=91 degrees


Statement: In the above reaction, first
compound in the product side is the major product.

State whether the given statement is
true or false
A . True
B. False


There is \( 900 \mathrm{mA} \) of current through a wire with 40 turns. What is the
reluctance of the circuit if the flux is
\( 400 \mu \mathrm{Wb} ? \)
A \( .14,400 A t / W b \)
в. \( 1,440 A t / W b \)
c. \( 9,000 A t / W b \)
D. \( 90,000 A t / W b \)


After a mutation at a genetic locus, the
character of an organism changes due to the change in which one of the following?
A. Protein synthesis pattern
B. RNA transcription pattern
c. Protein structure
D. DNA replication


Assertion
Free electrons always keep on moving in a conductor even when no magnetic
force act on them in a magnetic field
unless a current is passed through it.
Reason

The average velocity of free electron 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 spherical conducting shell of inner
radius \( r_{1} \) and outer radius \( r_{2} \) has a
charge \( Q . A \) charge \( -q \) is placed at the
center of the shell. The surface of the
shell will be
A \( \cdot \frac{q}{4 \pi r_{1}^{2}} \) and \( \frac{Q}{4 \pi r_{2}^{2}} \)
В. \( \frac{-q}{4 \pi r_{1}^{2}} \) and \( \frac{Q+q}{4 \pi r_{2}^{2}} \)
c. \( \frac{q}{4 \pi r_{1}^{2}} \) and \( \frac{Q-q}{4 \pi r_{2}^{2}} \)
D. 0 and


Average kinetic energy of a gas (Molar mass \( =4) \) at "T/2" Kelvin is \( 8 \times 10^{8} \)
ergs. RMS velocity of the gas at "T/2" Kelvin will be cm/sec.
A \( \cdot 2 \times 10^{4} \)
B . \( 4 \times 10^{4} \)
c. \( 2 \times 10^{3} \)
D. \( 4 \times 10^{2} \)


\( 9_{2} U^{235} \) nucleus absorbs a neutron and disintegrates into \( _{54}^{92} X e^{139},_{38} S r^{94} \) and
\( \boldsymbol{X} \)
A. 3 neutrons
B. 2 neutrons
c. - \( \alpha \) particle
D. - \( \beta \) particle


At the time of expiration, diaphragm
becomes
A. oblique
B. Normal
c. Flattened
D. Dome-shaped


Vapour Pressure of a mixture of
benzene and toluene is given by \( \boldsymbol{P}= \)
\( \mathbf{1 7 9 X}_{B}+\mathbf{9 2}, \) Where \( \boldsymbol{X}_{B} \) is mole
fraction of benzene.
If Vapours are removed and condensed
in to liquid then what will be the ratio of mole fraction of benzene and toluene in
first condensate:
A . 2.8
B. 1.5
c. 3.
D. 4.5


A wheel makes 360 revolutions in one
minute. Through how many radians does it turn in one second?


The coding strand of DNA is
\( \mathbf{5}^{\prime} \boldsymbol{A} \boldsymbol{A} \boldsymbol{T} \boldsymbol{T} \boldsymbol{C} \boldsymbol{A} \boldsymbol{A} \boldsymbol{T} \boldsymbol{T} \boldsymbol{A} \boldsymbol{G} \boldsymbol{G} \mathbf{3}^{\prime} \)
What is the sequence of mRNA?
A . \( 3^{\prime} \)TTAAGTTTAATCC
c. \( 3^{\prime} \) ААUUСААUU АGG5
D. \( 5^{\prime} \)TTAAGTTTAATCC


The ureter transports urine to the urinary bladder
A. True
B. False


After absorbing a slowly moving
neutron of Mass \( m_{N} \) (momentum \( \approx 0 \) )
a nucleus of mass M breaks into two
nuclei of masses \( \boldsymbol{m}_{1} \) and \( \mathbf{5 m}_{\mathbf{1}}\left(\boldsymbol{6} \boldsymbol{m}_{\mathbf{1}}=\right. \)
\( \left.M+\boldsymbol{m}_{N}\right) \) respectively. If the de Broglie
wavelength of he nucleus with mass \( m_{1} \)
is \( \lambda, \) the de Broglie wavelength of the
nucleus will be.
A \( .5 \lambda \)
B. \( \lambda / 5 \)
\( c \cdot \lambda \)
D. \( 25 \lambda \)


Find the sum of all the odd positive integers less than 100
A . 2400
B. 2500
\( c .2525 \)
D. 2600
E . 2650


\( \boldsymbol{f}:\left(-\frac{\boldsymbol{\pi}}{2}, \frac{\boldsymbol{\pi}}{2}\right) \rightarrow(-\infty, \infty) \) defined by
\( \boldsymbol{f}(\boldsymbol{x})=\mathbf{1}+\mathbf{3} \boldsymbol{x} \) is
A. one-one but not onto
B. onto but not one-one
c. neither one - one nor onto
D. bijective


The formation of \( \boldsymbol{P} \boldsymbol{H}_{\mathbf{4}}^{+} \) is difficult
compared to \( N H_{4}^{+} \) because :
A. lone pair of phosphorus is optically inertt
B. lone pair of phosphorus resides in almost pure \( p \) orbital
C. lone pair of phosphorous resides at \( s p^{3} \) orbital
D. lone pair of phosphorus resides in almost pure s orbital


Two insulated charged spheres of radii
\( R_{1} \) and \( R_{2} \) having charges \( Q_{1} \) and \( Q_{2} \)
respectively are connected to each other, then there is:
B. an increase in the energy of the system
C. always a decrease in the energy of the system
D. a decrease in energy of the system unless \( q_{1} R_{2}=q_{2} R_{1} \)


Noble gases are group of elements which exhibit very:
A. High chemical activity
B. Much paramagnetic proeprties
C. Minimum electronegativity
D. Low chemical activity


In a triangle \( \triangle A B C, 3 \sin A+ \)
\( 4 \cos B=6 \) and \( 4 \sin B+3 \cos A=1 \)
then the angle \( C \) is
A \( .150^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 30^{\circ} \)


What \( \% \) the fraction represents:
\( \frac{47}{50} \times \frac{100}{1000} \)


Define infinite set
Is \( \{x: x \in R: 1 \leq x \leq 3\} \) a infinite
set?
A. True
B. False


Write the definition of wavefront.


When two objects vibrate at the resonance frequency, the first object increases the of the
vibrations of the second object.
A. amplitude
B. wavelength
c. frequency
D. speedd
E. period


A dip needle shows an angle of dip \( \theta \) in a place which is in the magnetic meridian. Now, the dip circle is rotated through an angle \( x \) in the horizontal plane and then it
shows an angle of dip \( \theta_{1} . \) Value of
\( \tan \theta_{1} / \tan \theta \) is :
A \( \cdot \frac{1}{\cos x} \)
B. \( \frac{1}{\sin x} \)
c. \( \frac{1}{\tan x} \)
D. \( \cos x \)


A plastic box 1.5 m long, 1.25 m wide
and \( 65 \mathrm{cm} \) deep is to be made. It is
opened at the top. Ignoring the thickness of the plastic sheet, determine the area of the sheet
required for making the box?


Meson was discovered by:
A. Powel
B. Seaborg
c. Anderson
D. Yukawa


\( H_{2} O_{2} \) has greater reactivity in acidic medium. It is because acids catalyse
the decomposition of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \)
A. True
B. False


Calculate the percentage of deuterium
in heavy water.


The incorrect statement is
\( \mathbf{A} \cdot \sin \theta=-\frac{1}{5} \)
\( \mathbf{B} \cdot \cos \theta=1 \)
\( \mathbf{c} \cdot \sec \theta=\frac{1}{2} \)
\( \mathbf{D} \cdot \tan \theta=20 \)


State whether true or false.
Equal masses of iron and common salt have different volume.
A. True
B. False


The protistans in which cell size decreases with each division are
A. Dinoflagellates
B. Diatoms
c. slime Moulds
D. Radiolarians


In Lassaigne's test, if both \( N \) and \( S \) are
present in the organic compound, they
are converted to:
A. \( N a_{2} S \) and \( N a C N \)
B. \( N a S C N \)
c. \( N a_{2} S O_{3} \) and \( N a C N \)
D. \( N a_{2} S \) and \( N a C N O \)


Express \( \tan ^{-1} x+\tan ^{-1} \frac{2 x}{1-x^{2}} \) in the
terms of \( \tan ^{-1} \frac{3 x-x^{3}}{1-3 x^{2}} \)


What role is performed by pancreas in
order to deal with an increased blood
glucose level above normal range?
A. Releases insulin, signaling muscle cells to release glucose
B. Releases glucagon, signaling muscle cells to take up glucose
C. Releases glucagon, signaling adipose cells to take up glucose
D. Releases insulin, signaling the liver to convert glucose to glycogen
E. Releases glucagon, signaling the liver to convert glucose to glycogen


For a longitudinal wave,
A. the disturbance direction is perpendicular to the propagation direction.
B. the disturbance direction is parallel to the propagation direction.
C. the disturbance direction is independent of the propagation direction.
D. None of these


By investing \( R s .45000 \) in \( 10 \% \) for \( 2 y r s \) find the Simple interest gained.


Express each of the following without using decimals:
\( \boldsymbol{R} \boldsymbol{s} . \mathbf{5} . \mathbf{2 5} \)


Suppose the acceleration due to gravity
at the earth's surface is \( 10 \mathrm{m} / \mathrm{s}^{2} \) and at
the surface of mars it is \( 4.0 \mathrm{m} / \mathrm{s}^{2} . \) A
\( 60 \mathrm{kg} \) passenger goes from the earth to the mars in a spaceship moving with a constant velocity. Neglect all other
object in the sky. Which part of the
figure best represent the weight (net gravitational force) of the passenger as a function of time?
\( A \cdot A \)
В. \( B \)
\( D \)


Which of the following is a super oxide?
A \( . \) К \( O_{2} \)
в. \( N a_{2} O_{2} \)
c. \( L i_{2} O \)
D. \( \mathrm{CeO} \)


The back and forth motion of an object is called
A . vibration
B. rotation
c. translation
D. linear motion


State whether the given statement is
true or false:
The above reaction proceeds better with NaF than with KF.
\[
>c-c l+M F \longrightarrow->c-F+M C l
\]


Starch is a mixture of two components, a water soluble component amylose(15\( 20 \% \) and a water insoluble component
amylopectin (80-85\%). The aqueous solution of amylose gives a blue colour with iodine solution due to the
formation of:
A. amylose iodide
B. amylose iodate
c. inclusion complex
D. amylose tetraiodide complex


The following table shows the percentage of the students of a school who participated in Election and Drawing competitions.

Competition Election Drawing
Percentage of Students
Draw a Venn diagram to represent this information and use it to find the
percentage of the students who
(i) Participated in Election only
(ii) Participated in Drawing only
(iii) Did not participate in any one of the competitions.


The position of \( \ldots \ldots . . . . \) could not be explained in the plum pudding model.
A. nucleus
B. electrons
c. protons
D. all of the above


Solve \( : \int_{0}^{1} e^{e^{x}}\left(1+x \cdot e^{x}\right) d x \)


Which of the following is not showing the essential difference between
electrostatic shielding by a conducting shell and magnetostatic shielding?
A. Electrostatic field lines can end on charges and conductors have free charges
B. Magnetic field lines can end but conductors cannot end them.
c. Lines of magnetic field cannot end on any material and perfect shielding is not possible.
D. shells of high permeability materials can be used to divert lines of magnetic field from the interior region


Subtract the second expression from
the first expression \( 5 x^{2}+3 x y+7 y^{2}, 3 x^{2}+x y+2 y^{2} \)


Two points \( A \) and \( B \) are located at distance of \( 100 \mathrm{cm} \) from on electric
dipole. A is sn axial point while B is in perpendicular bisector. The electric field intensity at \( A \) is \( \vec{E} \). Then the intensity at B will be
\( A \cdot \vec{E} \)
в. \( 2 \vec{E} \)
\( c \cdot-\vec{E} \)
D. \( -\frac{\vec{E}}{2} \)


When a coil is connected to a \( 100 \mathrm{V} \) d
supply. The current is 2 A. When the same coil is connected to a.c. source \( E=100 \sqrt{2} \sin \omega t, \) the current is \( 1 A \)
Find the inductive reactance used :


The correct statement (s) about the
compound given below is /are:
A. The compound is optically active.
B. The compound possesses centre of symmetry.
C. The compound possesses plane of symmetry
D. The compound possesses axis of symmetry.


(a) Find out the position of the image of an object situated at \( A \) in the plane mirror.
(b) Can Paheli at B see this image?
(c) Can Boojho at C see this image?
(d) When Paheli moves from B to C,
where does the image of A move?
1


A freely falling body has a velocity after falling through a distance h. The distance it has to fall down further for
its velocity to become 2 V is :
\( A \cdot 3 h \)
B. 2h
\( c \cdot h \)
D. \( 4 h \)


Work done in carrying an electric
charge \( Q_{1} \) once round a circle of radius
\( R \) with a charge \( Q_{2} \) at the centre of the circle:
A. \( \frac{Q_{1} Q_{2}}{4 \pi \varepsilon_{\Omega} R} \)
B. \( \infty \)
c. \( \frac{Q_{1} Q_{2}}{4 \pi \varepsilon_{0} R^{2}} \)
D.


Q Type your question-
body of mass \( \mathrm{m} \) and charge \( \mathrm{q} \) is placed
perpendicular to the centre of sqaure at
a distance \( h \) from the centre. Take the
distance between centre and vertices of
the sqaure to be ' \( a \) '. What should be the
value of \( Q \) in order that this body may be
in equilibrium?
A \( \cdot \pi \varepsilon_{0} \frac{m g}{2 h q}\left(h^{2}+2 a^{2}\right)^{3 / 2} \)
B. \( \pi \varepsilon_{0} \frac{m g}{h q}\left(h^{2}+a^{2}\right)^{3 / 2} \)
c. \( \pi \varepsilon_{0} \frac{2 m g}{h q}\left(h^{2}+2 a^{2}\right)^{3 / 2} \)
P. \( \quad \frac{m g}{h q}\left(h^{2}-a^{2}\right)^{3 / 2} \)


Let \( f(x) \) be defined on \( [0, \pi] \) by \( f(x)= \) \( \left\{\begin{array}{ll}x+a \sqrt{2} \sin x & , 0 \leq x \leq \pi / 4 \\ 2 x \cot x+b & , \frac{\pi}{4}<x \leq \frac{\pi}{2} . \text { If } f \\ a \cos 2 x-b \sin x & , \frac{\pi}{2}<x<\pi\end{array}\right. \)
is continuous on \( [0, \pi] \) then
This question has multiple correct options
A \( a=\frac{\pi}{6} \)
в. \( b=-\frac{\pi}{12} \)
c. \( a=\frac{\pi}{6} \) and \( b=-\frac{\pi}{12} \)
D・ \( a=\frac{\pi}{3} \) and \( b=-\frac{\pi}{12} \)


Mile is used as a unit to measure
A. distance
B. speedd
c. acceleration
D. weight


If the lateral surface area of a cube is
\( 1600 \mathrm{cm}^{2} \) then its edge is
\( \mathbf{A} \cdot 15 \mathrm{cm} \)
B. \( 18 \mathrm{cm} \)
\( c .20 \mathrm{cm} \)
D. \( 24 \mathrm{cm} \)


If two medians of a triangle are equal in length, then the new triangle formed as a result of the medians is:
A. right angled but not isosceles
B. isosceles but not right angle
c. right angled isosceles
D. equilateral


The work done in shifting a particle of mass \( m \) from the centre of earth to the
surface of the earth is
A. \( -m g R \)
B. \( \frac{1}{2} m g R \)
c. zero
D. \( m g R \)


The ratio of coefficient of
\( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3}, \boldsymbol{F} \boldsymbol{e}\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{2} \) and \( \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{N} \boldsymbol{O}_{3} \) in
the following redox equation, \( \boldsymbol{F e}+ \)
\( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \rightarrow \boldsymbol{F} \boldsymbol{e}\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{2}+\boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{N} \boldsymbol{O}_{3}+ \)
\( H_{2} O \) in the balanced form will be?
A .10: 1: 4
B . 10: 4: 1
c. 4: 10: 1
D. 4: 1: 10


The volume strength of \( 15 \% \) (w/v)
solution of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) is :
A . 50
в. 4.94
c. 494
D. 0.494


In a uniform circular motion, the
magnitude and direction of velocity at different points remain the same.
A. True
B. False


Find \( f: \)
\( \mathbf{0 . 2 5}[\mathbf{4 f}-\mathbf{3}]=\mathbf{0 . 0 5}[\mathbf{1 0} \boldsymbol{f}-\mathbf{9}] \)


Copper is purified by:
A. distillation
B. liquation
c. carbon-reduction
D. electrolytic refming


The rate of a reaction expressed in terms of change in concentration of products at two different times, that is the average rate in terms of product, can be written as ?
This question has multiple correct options
A \( \cdot \frac{x_{2}-x_{1}}{t_{2}-t_{1}} \)
B. \( +\Delta x / \Delta t \)
c. \( -\frac{x_{2}-x_{1}}{t_{2}-t_{1}} \)
D. \( -\Delta x / \Delta t \)


\( \frac{1}{2} \)


Which of the following compound is the final product of Solvay process?
A. Ammonium carbonate
B. Ammonium bicarbonate
c. sodium carbonate
D. Sodium bicarbonate


The Henry's law constant for the
solubility of \( N_{2} \) gas in water at \( 298 \mathrm{K} \) is
\( 1 \times 10^{5} \) atm. The mole fraction of \( N_{2} \) in
air is \( 0.8 . \) The number of moles of \( N_{2} \)
from a dissolved in 100 moles of water
at \( 298 \mathrm{K} \) and 5 atm pressure is?
A. \( 4 \times 10^{-4} \)
В. \( 4 \times 10^{-5} \)
c. \( 4 \times 10^{-3} \)
D. \( 5 \times 10^{-4} \)


Total number of equivalence relation defined in the set \( s=\{a, b, c\} \) is
A . 5
B. 31
\( c \cdot 2^{3} \)
D. \( 3^{3} \)


Using integration find the area of the following region \( (x, y):|x+2| \leq y \leq \)
\( \sqrt{20-x^{2}} \)


which of the following fluorides does not exists?
A. \( N F_{5} \)
в. \( P F_{5} \)
c. \( A s F_{5} \)
D. \( S b F_{5} \)


What is the angle between \( (\hat{\mathbf{i}}+\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}) \)
and \( \hat{i} ? \)
A \( \cdot \frac{\pi}{6} \)
в. \( \frac{\pi}{4} \)
\( c \cdot \frac{\pi}{3} \)
D. \( \cos ^{-1}\left(\frac{1}{\sqrt{3}}\right) \)


Arrange these haloalkanes in correct
order of density:
A \( \cdot C H_{3} I<C_{2} H_{5} I<C_{3} H_{7} \)
в. \( C H_{3} I>C_{2} H_{5} I>C_{3} H_{7} I \)
c. \( C H_{3} I<C_{2} H_{5} I>C_{3} H_{7} \)
D. \( C H_{3} I>C_{2} H_{5} I<C_{3} H_{7} I \)


A cuboid is such that its length is 2 times the width and the width is 2
times its height. The side of a square, whose area is equal to the total surface area of the cuboid, in terms of the height of the cuboid is
\( \mathbf{A} \cdot 4 h \)
в. \( 6 h \)
c. \( 2 \sqrt{7} h \)
D. \( 4 \sqrt{7} h \)


The acid present in tea is:
A . citric
B. tannic
c. formic
D. lactic


AD is the bisector of \( \angle A \) of
\( \Delta A B C, A C=4.2 c m, D C= \)
\( 6 c m, B C=10 c m, \) then \( A B \) is:
\( \mathbf{A} \cdot 2.8 \mathrm{cm} \)
B. 3 cm
\( \mathrm{c} .3 .5 \mathrm{cm} \)
D. none of these


According to Le-chatelier's principle,
adding heat to a solid \rightleftharpoons् liquid equilibrium will cause the:
A. temperature to increase
B. temperature to decrease
c. amount of liquid to decrease
D. amount of solid to decrease


An element ' \( X^{\prime} \) has valency of \( H . \) Write its formula for carbonate?


Which among the following elements is metalloid?
A. Berellium
B. Barium
c. Boron
D. Bismuth


Arrange the following in the ilncreasing hydrated ion size: \( \boldsymbol{C} \boldsymbol{s}_{\boldsymbol{a q}}^{+}<\boldsymbol{R} \boldsymbol{b}_{\boldsymbol{a q}}^{+}< \)
\( \boldsymbol{K}_{a q}^{+}<\boldsymbol{N} \boldsymbol{a}_{a q}^{+} \)
If true enter 1 , else enter 0 .
\( A \)


A vessel full of hot water is kept in a
room and it cools from \( 80^{\circ} \mathrm{C} \) to \( 75^{\circ} \mathrm{C} \) in
\( T_{1} \) minutes, from \( 75^{\circ} \mathrm{C} \) to \( 70^{\circ} \mathrm{C} \) in \( T_{2} \)
minutes and from \( 70^{\circ} \mathrm{C} \) to \( 65^{\circ} \mathrm{C} \) in \( T_{3} \)
minutes. Then:
A. \( T_{1}=T_{2}=T_{3} \)
в. \( T_{1}>T_{2}>T_{3} \)
c. \( T_{1}<T_{2}=T_{3} \)
D. \( T_{1}<T_{2}<T_{3} \)


If \( a^{2}+b^{2}+c^{2}=1, \) find the range of
\( \boldsymbol{a} \boldsymbol{b}+\boldsymbol{b} \boldsymbol{c}+\boldsymbol{c} \boldsymbol{a} \)


The length of each side of a square field is \( 63 \mathrm{m} \). What is the area of the field?


Sodium hydride \( (N a H) \) when dissolved
in water produces:
A . acidic solution
B. basic solution
c. neutral solution
D. cannot be predicted


In an astronomical telescope the focal lengths of objective and eyepiece should respectively be :
A. large and small
B. small and large
c. equal
D. too small are too large


A LCR circuit behaves like a damped harmonic oscillator. Comparing it with a physical spring-mass damped oscillator having damping constant 'b', the correct equivalence would be :
A. \( L \leftrightarrow m, C \leftrightarrow k, R \leftrightarrow b \)
в. \( L \leftrightarrow \frac{1}{b}, C \leftrightarrow \frac{1}{m}, R \leftrightarrow \frac{1}{k} \)
c. \( L \leftrightarrow k, C \leftrightarrow b, R \leftrightarrow m \)
D \( \cdot L \leftrightarrow m, C \leftrightarrow \frac{1}{k}, R \leftrightarrow b \)


A particle is going with constant speed
along a uniform helical and spiral path
separately as shown in figure then

Essume that the vertical acceleration
of the particle is negligible in case (a)]
A. The velocity of the particle is constant in both cases
B. The magnitude of acceleration of the particle is constant in both cases
C. The magnitude of acceleration is constant in (a) and decreasing in (b)
D. The magnitude of acceleration is decreasing continuously in both the cases


A force \( \overrightarrow{\boldsymbol{F}}=(\mathbf{5} \hat{\boldsymbol{i}}+\boldsymbol{4} \hat{\boldsymbol{j}}) \boldsymbol{N} \) acts on a body
and produced a displacement \( \overrightarrow{\boldsymbol{S}}= \) \( (6 \hat{i}-5 \hat{j}+3 \hat{k}) m . \) The work done will be
A . \( 10 J \)
в. 20 \( J \)
\( c .30 J \)
D. \( 40 J \)


Consider the reaction \( 2 S(g) \rightarrow \) \( 3 B(g)+C(g) . \) Starting with pure \( A \)
initially, the total pressure doubled in 3 hrs. The order of the reaction might possibly be?
A . zero
B. first
c. second
D. unpredictable from this data


What is mineralisation?


Two bodies \( A \) and \( B \) are said to be in
thermal equilibrium with each other, if
A. heat flows from A to B
B. heat flows from B to A
c. both the bodies lose equal amount of heat to the atmosphere
D. heat does not flow from either A or B


Oxygen is collected by downward displacement of water since it weighs as/than air.
A. heavier
B. lighter
c. same
D. none of the above


Find the value of \( 87^{2}-13^{2} \)
A . 7300
B. 7350
\( c .7400 \)
D. 7450


Which of the following is NOT a noncontact force?
A. Magnetic force
B. Electrostatic force
c. Gravitational force
D. Muscular force


Let \( \boldsymbol{f} \cdot \boldsymbol{R} \rightarrow \boldsymbol{R} \) be defined as \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{cl}0, & x \text { is rational } \\ \sin |x|, & x \text { is rational }\end{array}\right. \)
Then which of the following is true?
A. \( f \) is discontinuous for all \( x \)
B. \( f \) is continuous for all \( x \)
c. \( f \) is discontinuous at \( x=k \pi \), where \( k \) is an integer
D. \( f \) is continuous at \( x=k \pi, \) where \( k \) is an integer


If \( A \) and \( B \) are independent events such
that \( \mathbf{0}<\boldsymbol{P}(\boldsymbol{A})<\mathbf{1}, \mathbf{0}<\boldsymbol{P}(\boldsymbol{B})<\mathbf{1} \) then
This question has multiple correct options
A . \( A, B \) are mutually exclusive
B. \( A \) and \( \bar{B} \) are independent
c. \( \bar{A}, \bar{B} \) are independent
D. \( P(A / B)+P(\bar{A} / B)=1 \)


Find the sum of:
256 from -312


Write the multiplicate inverse of:
\( -\mathbf{5} \frac{\mathbf{6}}{7} \)


If \( f(x)=4 x^{2}-1 \) and \( g(x)=8 x+ \)
\( 7, g^{o} f(2)= \)
A . 15
B. 23
\( c \cdot 127 \)
D. 345
E . 2115


Give reason:
(a) Cerium(Ce) exhibits +4 oxidation
state.
(b) Actinoid contraction is greater from element to element than lanthanoid
contraction.


Assertion
When variable frequency AC source is connected to a capacitor, displacement
current increases with increase in
frequency
Reason
As frequency increases conduction
current also increases
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A reaction attains equilibrium state under standard conditions. Identify the incorrect option regarding this
statement.
A. Equilibrium constant \( K=0 \)
B. Equilibrium constant \( K=1 \)
c. \( \Delta G^{0}= \) O and \( \Delta H^{0}=\neg \Delta S^{0} \)
D. All options are correct


If \( P C l_{5} \) exsits, why \( N C l_{5} \) does not?
A. because N has high electronegativity
B. because N has high ionisation energy
c. because \( \mathrm{N} \) has lowest atomic size
D. because N has no vacant d-orbital


If a ray of light is incident normally on a surface, then
A. Angle of incidence = infinity
B. Angle of reflection = infinity
C. Angle of incidence \( =90^{\circ} \)
D. Angle of incidence \( =0^{\circ} \)


For the following reactions:
\( Z n \rightarrow Z n^{2+}+2 e^{-} ; E=+0.76 V \)
\( \boldsymbol{A u} \rightarrow \boldsymbol{A u}^{3+}+\mathbf{3} e^{-} ; \boldsymbol{E}=-\mathbf{1 . 4 2} \boldsymbol{V} \)
If gold foil is placed in a solution
containing \( Z n^{2+}, \) the reaction potential
would be:
A . \( -1.34 V \)
в. \( -2.18 V \)
c. \( -0.66 V \)
D. \( +2.18 V \)
E . \( +1.34 V \)


Water is brought to boil under the pressure of 1.0 atm. When an electric
current of \( 0.50 A \) from a \( 12 ~ V \) supply is
passed for \( 300 s \) through resistance in
thermal contact with it is found that
\( 0.798 g \) of water is vapourised. Calculate the molar internal energy
change at boiling point \( (373.15 K) \)
B. \( 3.75 k J \) mol \( ^{-1} \)
c. \( 42.6 k J \) mol \( ^{-1} \)
D. \( 4.26 k J \) mol \( ^{-1} \)


Choose the correct oxidation states of
Chlorine in species:
This question has multiple correct options
\( \mathbf{A} \cdot(\mathrm{a}) \mathrm{HOCl}-+1 \)
B. (b) \( H O C l O-+3 \)
\( \mathbf{c} \cdot(\mathrm{c}) H O B r-+3 \)
D. (d) \( H O B r O_{2}-+5 \)
E \( \cdot(\text { e }) H O I O_{3}-+7 \)
\( F \cdot(f) H O C l O_{3}-+5 \)
G. None of the above


The wavelength of the first line of Lyman series for hydrogen is identical to that of the second line of Balmer series for
some hydrogen-like ion \( X \). Calculate
energies of the first four levels of \( \boldsymbol{X} \) Also, find its ionization potential. (Given: Ground state binding energy of
the hydrogen atom is \( 13.6 e V \) )


If the mean deviation of number \( 1,1+ \) \( \boldsymbol{d}, \mathbf{1}+\mathbf{2} \boldsymbol{d}, \dots, \mathbf{1}+\mathbf{1 0 0} \boldsymbol{d} \) from their mean
is 255 then \( d \) is equal to
A . 10.0
B. 20.0
c. \( 10 . \)
D. 20.2


If \( A \) is skew-symmetric, then \( A^{n} \) for
\( \boldsymbol{n} \in \boldsymbol{N} \) is
This question has multiple correct options
A. Symmetric
B. Skew-symmetric
c. Diagonal
D. None of these


This iron is used in making water taps
\( G I \text { pipes }), \) since they have :
A. low resistance to corrosion
B. high resistance to corrosion
c. low resistance to flow of water
D. high resistance to flow of water


A ball is thrown upwards with a velocity of \( 25 m / s . \) What is the time taken by the
ball to return to the thrower \( (g= \)
\( \left.10 m / s^{2}\right) \)
A . 5 sec
B. 2.5 sec
\( c .3 s e c \)
D. 4.2 sec


Two stretched wires of same length,
diameter and same material are in
unison. The tension in one is increased
by \( 2 \% \) and 2 beats per second are heard What was the frequency of the note produced when they were in unison
A . \( 100 \mathrm{Hz} \)
в. \( 200 H z \)
c. \( 500 H z \)
D. \( 400 H z \)


Read the following four statements
carefully.
(i) Ventral respiratory group of neurons of medulla oblongata can cause both inspiration and expiration.
(ii) The part of the respiratory system starting with the external nostrils up to the terminal bronchioles constitutes
the respiratory or exchange part of the respiratory system.
(iii) During swallowing epiglottis can be covered by a thin elastic cartilaginous flap called glottis to prevent the entry of food into the larynx.
(iv) Binding of oxygen with haemoglobin is primarily related to
partial pressure of \( \boldsymbol{O}_{2} \) Which of the above two statements are
correct?
A. (ii) and (iii)
B. (iii) and (iv)
c. (i)and(ii)
D. (i) and (iv)


The flux of magnetic field through closed conducting loop of resistance 0.4 Whanges with time according to the
equation \( \phi=0.20 t^{2}+0.40 t+0.60 \) where
is time in seconds. Find
(i) the induced
emf at \( t=2 s . \) (ii) the average induced emf in \( t=0 \) to \( t=5 \) s. (iii) change passed through the loop in \( t=0 \) to \( t=5 s . \) (iv) average current in time interval \( t=0 \) to
\( t=5 s \)
(v) heat produced in \( t=0 \) to \( t=5 s \)


Show that the curve such that the
distance between the origin and the tangent at an arbitrary point is equalto the distance between the origin and the normal at the same point, \( \sqrt{x^{2}+y^{2}}= \) \( \boldsymbol{c} e^{\pm \tan ^{-1} \frac{y}{x}} \)


What happens when a p-njunction is
(a) forward biased
(b) reverse biased?


A commutator changes the direction of current in the coil of
A. a DC motor
B. a DC motor and an AC generator
c. a DC motor and a DC generator
D. an Ac generator


A particle executes linear simple harmonic motion with an amplitude of \( 3 \mathrm{cm} . \) When the particle is at \( 2 \mathrm{cm} \) from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period in seconds is
\( ^{\mathrm{A}} \cdot \frac{\sqrt{5}}{\pi} \)
в. \( \frac{\sqrt{5}}{2 \pi} \)
c. \( \frac{4 \pi}{\sqrt{5} \pi} \)
D. \( \frac{2 \pi}{\sqrt{3}} \)


The common point of the tangent and circle is called
A. Intersecting points
B. Secant
c. Point of contact
D. None


Choose the correct answer from the
alternatives given
Blood enters the heart because muscles
of:
A . atria relax
B. ventricles relax
c. atria contract
D. ventricles contract


A satellite of mass \( 1000 k g \) is supposed
to orbit the earth at a height of \( 2000 k m \) above the earth's surface. Find its speed
in the orbit.


If the third and \( 11^{t h} \) term of an A.P are 8
and 20 respectively, find the sum of first
ten terms.
A \( \cdot 105 \frac{1}{2} \)
в. 108
c. \( _{117} \frac{1}{2} \)
D. \( 203 \frac{1}{2} \)


Which of the following metals are pyrophoric in nature? This question has multiple correct options
A. Barium
B. Rubidium
C. Francium
D. Caesium


Write the dimension of coefficient of
viscosity.


State whether given statement is True or False
A germanium crystal is doped with boron impurity
A. True
B. False


In Annelids, excretory organs are
A. Nephridia
B. Malpighian tubules
c. Green glands
D. Kidneys


In a reaction, 4 mol of electrons are
transferred to one mol of \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) when it acts as an oxidant. The possible reduction product is :
A. 0.5 mol \( N_{2} \)
B. 0.5 mol \( N_{2} \),
c. 1 mol \( N O_{2} \)
D. 1 mol \( N H_{3} \)


In how many ways can the letters of the word COMBINE be arranged so as to
begin and end with a vowel? Also find the number of words that can be formed
without changing the relative order of
the vowels and consonants.


Evaluate the integral \( \int_{0}^{1}\left(1-x^{2}\right) d x \)


The Discriminant value of equation \( \mathbf{5} \boldsymbol{x}^{2}-\mathbf{6} \boldsymbol{x}+\mathbf{1}=\mathbf{0} \) is
A . 16
B. \( \sqrt{56} \)
\( c \cdot 4 \)
D. 56


A current \( I=5.0 A \) flows along a thin
wire shaped as shown in figure above. The radius of a curved part of the wire is equal to \( R=120 m m \), the angle
\( 2 \varphi=90^{\circ} . \) Find the magnetic induction
of the field at the point \( O \) in \( \mu T . \) If the
answer is \( X \) then enter \( \frac{X}{7} \)


Four light waves are represented by
(i) \( y=a_{1} \sin \omega t \)
(ii) \( y=a_{2} \sin (\omega t+\varepsilon) \)
(iii) \( y=a_{1} \sin 2 \omega t(\text { iv }) y=a_{2} \sin 2(\omega t+ \)
\( \varepsilon \)
We obtain sustained interference due to
super-position of This question has multiple correct options
\( A \cdot \) (i) and (ii)
B. (i) and (iii)
c. (ii) and (iv)
D. (iii) and (iv)


Describe the bonding in \( \boldsymbol{H} \boldsymbol{F} \) ?
A. s-s bonds
B. s-p bonds
c. p-p bonds
D. \( s p^{3}-p \) bonds
E \( \cdot s p^{2}-s p^{2} \) bonds


The function \( \boldsymbol{f}:\left[-\frac{\mathbf{1}}{\mathbf{2}}, \frac{\mathbf{1}}{\mathbf{2}}\right] \rightarrow\left[-\frac{\boldsymbol{\pi}}{\mathbf{2}}, \frac{\boldsymbol{\pi}}{\mathbf{2}}\right] \)
defined by \( \sin ^{-1}\left(3 x-4 x^{3}\right) \) is
A. both one-one onto
B. onto but not one-one
c. one-one but not onto
D. niether one-one nor onto


Development of animal by asexual
reproduction is called as
A. Ontogenesis
B. Embryogenesis
c. Blastogenesis
D. Morphallaxis


As a balloon is filled with water,it expands and increases in weight,This shows that water:
A. Has mass
B. Occupies space
c. Is a kind of matter
D. All of these


Figure shows tracks of three charged particles in a uniform electrostatic field. Given the signs of the three charges.Which particle has the highest charge to mass ratio.


If the frequency of the particle
performing circular motion increases from 60 rmp to 180 rpm is 20 seconds,
its angular acceleration is
A \( \cdot 0.1 \mathrm{rad} / \mathrm{s}^{2} \)
B. 3.142 \( r a d / s^{2} \)
c. 0.6284 rad \( / s^{2} \)
D. 0.3142 rad/s \( ^{2} \)


Which of the following types of tissue forms the framework of the external
ear?
A. Epithelial
B. Connective
c. Nervous
D. Muscular


\( 92^{38} U \) atom disintegrates to \( _{84}^{214} \) Po with a half life of \( 4.5 \times 10^{9} y r s \) by emitting six
alpha particles and \( n \) -electrons. Here \( n \)
is:
\( A \cdot 6 \)
B. 4
c. 10
D. 7


Write the appropriate structural
formulae for the molecule with the
formula \( \mathrm{C}_{6} \mathrm{H}_{12} \) that contains one ring
and are enantiomers of each other.


\( A t-50^{0} C, \) liquid \( N H_{3} \) has ionic
product is \( 10^{-30} \). How many amide
\( \left(N H_{2}^{-}\right) \) ions are present per \( m m^{3} \) in
pure liquid \( \left.\boldsymbol{N} \boldsymbol{H}_{3} \text { ? (take } \boldsymbol{N}_{\boldsymbol{A}}=\boldsymbol{6} \times \mathbf{1 0}^{\mathbf{2 3}}\right) \)


Some of the reactions taking place
during bessemerisation possibly are -
\( \boldsymbol{A}: \boldsymbol{F} \boldsymbol{e} \boldsymbol{O}+\boldsymbol{S} \boldsymbol{i} \boldsymbol{O}_{2} \rightarrow \boldsymbol{F} \boldsymbol{e} \boldsymbol{S} \boldsymbol{i} \boldsymbol{O}_{3} \)
\( B: 2 F e S+3 O_{2} \rightarrow 2 F e O+2 S O_{2} \)
\( \boldsymbol{C}: \mathbf{2} \boldsymbol{C u}_{2} \boldsymbol{S}+\mathbf{3} \boldsymbol{O}_{2} \rightarrow \boldsymbol{2} \boldsymbol{C} \boldsymbol{u}_{2} \boldsymbol{O}+ \)
\( 2 S O_{2} \)
\( \boldsymbol{D}: \boldsymbol{2} \boldsymbol{C} \boldsymbol{u}_{2} \boldsymbol{O}+\boldsymbol{C} \boldsymbol{u}_{2} \boldsymbol{S} \rightarrow \boldsymbol{6} \boldsymbol{C} \boldsymbol{u}+\boldsymbol{S} \boldsymbol{O}_{2} \)
Select reactions actually taking place :
\( A \cdot A, B \)
B. B,
\( c \cdot A, C \)
D. \( c, D \)


A copper wire of diameter \( 1.6 m m \)
carries a current of \( 20 A \). Find the
maximum magnitude of the magnetic field \( \vec{B} \) due to this current.


Find the value(s) of \( a \) for which \( f(x)= \)
\( x^{3}-a x \) is an increasing function on \( R \)


\( \text { Four points }\boldsymbol{A}(\mathbf{6}, \mathbf{3}), \boldsymbol{B})-\mathbf{3}, \mathbf{5}) \)
\( C(4,-2) \) and \( D(x, 3 x) \) are given such that \( \frac{\Delta D B C}{\Delta A B C}=\frac{1}{2}, \) find \( x \)


If \( \alpha \) -current gain of a transistor is 0.98
What is the value of \( \beta \) -current gain of
the transistor?
A . 0.49
B. 49
c. 4.9
D. 5


A Father is four times as old as his son.
The age of the father at the time of the
birth of his son was \( 30 . \) Find the age of
his son


A radioactive element \( X \) converts into
another stable element \( Y \). Half-life of \( \boldsymbol{X} \)
is 2 \( h \). Initially, only \( X \) is present. After
time \( t, \) the ratio of atoms of \( X \) and \( Y \) is
found to be \( 1: 4 . \) Then \( t \) in hours is
A . 2
B. 4
c. between 4 and 6
D. 6


We need blocks to build a building. In
the same way are basic
blocks to form all natural numbers.
A. prime numbers
B. real numbers
c. unique numbers
D. negative numbers


The rate constant for a first order
reaction is \( 60 s^{-1} \). How much time will
it take to reduce the initial
concentration of the reactant to its
\( 1 / 16^{t h} \) value?


Calcium cyanamide on treatment with steam under pressure gives ammonia and :
A . calcium carbonate
B. calcium hydroxide
c. calcium oxide
D. calcium bicarbonate


In gymnosperms, how many male gametes are produced by each pollen grain?
\( A \cdot 4 \)
B. 3
\( c \cdot 2 \)
D.


In which of the following pairs do the two species resemble each other closely in chemical properties?
A \( \cdot \frac{1}{1} H \) and \( _{1}^{2} H \)
B. \( _{8}^{16} O \) and \( _{8}^{16} O^{2-} \)
C \( \cdot \frac{24}{12} M g \) and \( _{12}^{24} M g^{2+} \)
D. \( \frac{14}{7} N \) and \( \frac{14}{7} N^{3}- \)


Construct the graphs of the following
functions.
\( \boldsymbol{y}=(\boldsymbol{x}+\mathbf{3}) /(\boldsymbol{x}-\mathbf{1}) \)


CE and DF are two walls of equal height
(20 meter) from which two particles \( A \) and \( \mathrm{B} \) of same mass are projected as
shown in the figure.A is projected
horizontally towards left while B is
projected at an angle \( 37^{0} \) (with horizontal towards left) with
velocity \( 15 ~ m / s e c \). If \( A \) always sees \( B \) to
be moving perpendicular to EF, then the range of A on ground is
A \( .24 m \)
в. \( 30 m \)
\( c .26 m \)
D. \( 28 m \)


If the diameter of a circle is increased
by \( 200 \% \) then its area is increased by
A. \( 100 \% \)
B . 200\%
c. 300\%
D. 800\%


\( \operatorname{Let} f(x)=\sin ^{2} \frac{x}{2}+\cos ^{2} \frac{x}{2} \) and \( g(x)= \)
\( \sec ^{2} x-\tan ^{2} x . \) The two functions are
equal over the set
A. \( \Phi \)
в. \( R \)
c. \( R-\left\{x \mid x=(2 n+1) \frac{\pi}{2}, n \in Z\right\} \)
D. None of these


A parallel beam of white light is
incident normally on a water film \( 1.0 \times \)
\( 10^{-4} \mathrm{cm} \) thick. Find the wavelength in
the visible range \( (400 n m-700 n m) \)
which are strongly transmitted by the film. Refractive index of water \( =1.33 \)
\( A .538 n m \)
В. 534 пт
\( \mathrm{c} .532 \mathrm{nm} \)
D. 548 пт


If \( \boldsymbol{y}=\boldsymbol{x}+\boldsymbol{e}^{\boldsymbol{x}}, \) then what will be the
value of \( \frac{d^{2} x}{d y^{2}} ? \)


\( \int_{0}^{1} \sqrt{\boldsymbol{x}(1-\boldsymbol{x})} \boldsymbol{d} \boldsymbol{x}= \)
\( \mathbf{A} \cdot \pi / 2 \)
в. \( \pi / 4 \)
c. \( \pi / 6 \)
D . \( \pi \)


At what temperature is the kinetic energy of a gas molecule half of its
value at \( 327^{\circ} \mathrm{C} \) ?
A . \( 13.5^{\circ} \mathrm{C} \)
B . \( 150^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 27^{\circ} C \)
D. \( -123^{\circ} \mathrm{C} \)


A concave mirror always forms a real
image
A . True
B. False


Which of the following catalyt is used during the hydrogenation of oil?
\( A \cdot F e \)
B. Ni
\( c \cdot P t \)
D. Mo


Bottles containing \( P h I \) and \( P h C H_{2} I \)
lost their original labels. They were
labelled as \( (A) \) and \( (B) \) for testing. \( (A) \)
and \( (B) \) were separately taken in test
tubes and boiled with \( N a O H \) solutions
The end solution in each tube was made
acidic with dilutie \( H N O_{3} \) and some
\( A g N O_{3} \) solution was added. Substance
\( (B) \) gave a yellow precipitate. Which of the following statements is true for this experiment?
A. Addition of \( H N O_{3} \) was unnecessary
в. (A) was PhI
c. \( (A) \) was \( P h C H_{2} I \)
D. \( (B) \) was \( P h I \)


The degree of a polynomial \( x^{3}-27 \) is
\( \mathbf{A} \cdot \mathbf{3} \)
B.
c. 26
D. 27


If the equations of alternating voltage and alternating current in an A.C. circuit
\( \operatorname{are} \boldsymbol{E}=\boldsymbol{E}_{0} \sin \omega \boldsymbol{t} \) volt and \( \boldsymbol{I}= \)
\( I_{0} \sin (\omega t-\pi / 2) \) ampere
respectively. The power loss in the circuit will be
A . zero
в. \( \frac{E_{0} I_{0}}{\sqrt{2}} \)
c. \( \frac{E_{0} I_{0}}{2} \)
D. \( \frac{E I}{\sqrt{2}} \)


Molar conductivity \( \left(\lambda_{M}\right) \) and equivalent
conductivity \( \left(\lambda_{e q}\right) \) for an electrolyte
\( A_{x} B_{y} \) at any dilution are related as:
A \( . \lambda_{M}=\lambda_{e q} . \times(x+y) \)
B . \( \lambda_{M}=\lambda_{e q} \). \( \times x \times y \)
c. \( \lambda_{M}=\frac{\lambda_{e q}}{x+y} \)
D. \( \lambda_{M}=\frac{\lambda_{e q}}{x \times y} \)


While charging the lead storage battery,
This question has multiple correct options
\( \mathbf{A} \cdot P b S O_{4} \) on anode is reduced to \( P b \)
B. \( P b S O_{4} \) on cathode is reduced to \( P b \)
\( \mathrm{C} \cdot P b S O_{4} \) on cathode is oxidised to \( P b \)
D. \( P b S O_{4} \) on anode is oxidised to \( P b O_{2} \)


Solid \( P C l_{5} \) exist as:
A \( \cdot P C l_{4}+\& P C l_{6}^{-} \)
в. \( P C l_{3}+\& P C l_{2} \)
c. \( P C l_{4}+\& P C l_{8} \)
D. none of the above


A heavy chain with a mass per unit
length \( p \) is pulled by the constant force \( F \) along a horizontal surface consisting
of a smooth section and rough section.
The chain is initially at rest on the
rough surface with \( \boldsymbol{x}=\mathbf{0} . \) If the coefficient of kinetic friction between
the chain and the rough surface is \( \mu_{k} \)
determine the velocity \( v \) of the chain when \( x=L . \) The force \( F \) is greater than
\( \mu_{k}, p g L \) in order to initiate the motion.
\( ^{\text {A }} \cdot \sqrt{\frac{2 F}{P}-\mu_{k} g L} \)
в. \( \sqrt{\frac{F}{P}-\mu_{k} g L} \)
\( c \)


The function \( f(x)=\tan ^{-1}(\sin x+ \)
\( \cos x) \) is strictly increasing function in
A \( \cdot\left(\frac{\pi}{4}, \frac{\pi}{2}\right) \)
B \( \cdot\left(-\frac{\pi}{2}, \frac{\pi}{4}\right) \)
c. \( \left(0, \frac{\pi}{4}\right) \)
D. \( \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \)


A catalyst is a substance which:
A. increases the average kinetic energy of reacting molecules
B. alters the reaction mechanism
c. increases the frequency of collisions of reaction species.
D. None of these


In a series LCR circuit \( \mathbf{R}=200 \) Omega
and the voltage and the frequency of the main supply is \( 220 \mathrm{V} \) and \( 50 \mathrm{Hz} \)
respectively. On taking out the capacitance from the circuit the
current lags behind the voltage by \( 30^{0} \) On taking out the inductor from the
circuit the current leads the voltage by
\( 30^{0} . \) The power dissipated in the LCR
circuit is
A . \( 305 \mathrm{W} \)
B. \( 210 \mathrm{W} \)
c. ZeroW
D. \( 242 \mathrm{W} \)


has a 250 mm diameter propeller that
discharges the water at a velocity of
\( 12 m / s . \) Given that the density of
seawater is \( 1030 \mathrm{kg} / \mathrm{m}^{3} . \) The effect of
propeller hub is negligible. The
magnitude of thrust produced \( \boldsymbol{F} \) is (in
\( N) \)
A. 1030
B. 2730
\( c \cdot 4660 \)
D. 98


The fire terms of an arithmetic
sequence are given:- -7, -4, -1, 2, 5 .........
Find their common difference and next
term of the sequence.
A. common difference \( =3 ; a_{6}=8 \)
B. Common difference \( =2 ; a_{4}=7 \)
C. common difference \( =1 ; a_{6}=5 \)
D. common difference \( =0 ; a_{6}=0 \)


Calculate variance for following data:
\( \begin{array}{llll}\text { Length } & \mathbf{1 7 0 0}- & \mathbf{1 9 0 0}- & \mathbf{2 1 0 0}- \\ \text { of wire } & \mathbf{1 9 0 0} & \mathbf{2 1 0 0} & \mathbf{2 3 0 0}\end{array} \)
Number 10 16 20
\( \mathbf{A} \cdot 55,822.22 \)
B . 55,238.51
c. 55832.55
D. 56,823.50


Selaginella and fern shares which of the following character?
A. Leptosporangiate sporangium
B. Heterospory
c. Absence of ovule
D. Protostele cell


Define the following terms:
(i) Mole fraction
(ii) Molality
(iii) Molarity
(iv) Mass percentage.


Earth's greenhouse effect causes:
A. warmer surface temperatures
B. cooler surface temperature
C. there is no change in surface temperature
D. None of these


\( 110^{\circ} 30^{\prime} \) in radians is :
A \( \cdot \frac{221 \pi^{c}}{360} \)
в. \( \frac{225 \pi^{c}}{360} \)
c. \( \frac{231 \pi^{c}}{360} \)
D. \( \frac{229 \pi^{c}}{360} \)


A particle is released on a vertical
smooth semicircular track from point
\( X \) so that \( O X \) makes an angle \( \theta \) from
the vertical (see figure). The normal reaction of the track on the particle
vanishes at point \( Y \) where \( O Y \) makes
and angle \( \phi \) with the horizontal. then:
\( A \cdot \sin \phi=\cos \theta \)
B. \( \sin \phi=\frac{1}{2} \cos \theta \)
c. \( \sin \phi=\frac{2}{3} \cos \theta \)
D. \( \sin \phi=\frac{3}{4} \cos \theta \)


n figure, if lines \( \mathrm{PQ} \) and \( \mathrm{RS} \) intersect at
point \( \mathrm{T} \), such that \( \angle \boldsymbol{P} \boldsymbol{R} \boldsymbol{T}= \)
\( 40^{\circ}, \angle R P T=95^{\circ} \) and \( \angle T S Q=75^{\circ} \)
find \( \angle S Q T \).
\( 4 \cdot 20 \)
3.60
\( c \cdot 30 \)
\( D \)


In Fraunhoffer diffraction experiment, is the distance between screen and the obstacle, b is the size of obstacle and \( \lambda \)
is wavelength of incident light. The general condition for the applicability of Fraunhoffer diffraction is:
\( ^{\mathbf{A} \cdot} \cdot \frac{b^{2}}{l \lambda}>>1 \)
B. \( \frac{b^{2}}{l \lambda}=1 \)
c. \( \frac{b^{2}}{l \lambda}<<1 \)
D. \( \frac{b^{2}}{l \lambda} \neq 1 \)


Match the following from Table \( A, \) in the
case of gases, with those in Table B.
Table - A Table - B
(a) Work done in isobaric
\[
n R T \log _{e}\left(\frac{V_{2}}{V_{1}}\right)
\]
process
(b) Wok done in isothermal
(e) \( P\left(V_{2}-V_{1}\right) \) process
\( T \)
(c) Work done in adiabatic process \( \frac{n R T\left(T_{1}-T_{2}\right)}{\gamma-1} \)
(g) Zero
\( \mathbf{A} \cdot a \rightarrow h, b \rightarrow g, c \rightarrow e \)
В . \( a \rightarrow e, b \rightarrow d, c \rightarrow g \)
\( \mathbf{c} \cdot a \rightarrow g, b \rightarrow h, c \rightarrow e \)
D \( . a \rightarrow e, b \rightarrow d, c \rightarrow f \)


A certain mass of gas is taken from an
initial thermodynamic state \( A \) to
another state B by process I and II. In
process I the gas does 5 joules of work
and absorbs 4 joules of heat energy. In process II, the gas absorbs 5 joules of
heat. The work done by the gas in
process II (see figure) is
A. +6 joules
B. - -6 joules
c. +4 joules
D. - 4 joules


A force of \( 10 N \) acts on a body of mass
\( 20 k g \) for \( 10 s . \) Change in its momentum
is:
\( \mathbf{A} .5 k g m / s \)
в. \( 100 k g m / s \)
c. \( 200 k g m / s \)
D. \( 1000 k g m / s \)


The Inner Transition elements are
classified as
A. Lanthanides and Actinides
B. Metals and Non-metals
c. Both A and B
D. None of these


Evaluate \( \int_{0}^{\pi / 4} \frac{\cos x-\sin x}{10+\sin 2 x} d x \)
A \( \cdot \frac{1}{3}\left(\tan ^{-1} \frac{\sqrt{2}}{3}+\tan ^{-1} \frac{1}{3}\right) \)
B. \( \frac{1}{3}\left(\tan ^{-1} \frac{\sqrt{1}}{3}-\cot ^{-1} \frac{2}{3}\right) \)
c. \( \frac{1}{3}\left(\tan ^{-1} \frac{\sqrt{2}}{3}-\tan ^{-1} \frac{1}{3}\right) \)
D. \( \frac{1}{3}\left(\tan ^{-1} \frac{\sqrt{1}}{3}-\cot ^{-1} \frac{1}{3}\right) \)


The portal system seen in all vertebrates is
A. Hepatic
B. Renal
c. Pulmonary
D. Both A and B


The position vector of a particle is \( r= \)
\( a \sin \omega t \hat{i}+a \cos \omega t \hat{j} \)
The velocity of the particle is
A. Parallel to position vector
B. Perpendicular to position vector
c. Directed towards origin
D. Directed away from the origin


The standard enthalpy of combustion at
\( 25^{\circ} \mathrm{C} \) of hydrogen, cyclohexene \( \left(C_{6} H_{10}\right) \)
and cyclohexane \( \left(C_{6} H_{12}\right) \) are -241,-3800 and \( -3920 k J / \) mole
respectively. Calculate the heat of hydrogenation of cyclohexene
A. \( -111 k J / \) mole
B . \( -121 k J / \) mole
c. \( -118 k J / \) mole
D. \( -128 k J / \) mole


Short / Long answer type questions. How do neutral solutes move across the
plasm membrane ? Can the polar molecules also move across it in the
same way? If not, then how are these transported across the membrane?


Which of the following has least tendency in +3 oxidation state to show disproportionation reaction.
A . \( N \)
в. \( P \)
\( c . B i \)
D. \( S b \)


A sample of \( C a C O_{3} \) has \( C a=40 \% \)
\( C=12 \% \) and \( O=48 \% \). If the law of
constant proportion is true then the weight of calcium in \( 5 g \) of a sample of
\( \mathrm{CaCO}_{3} \) from another source will be:
A. \( 0.20 g \)
в. \( 2.0 g \)
c. \( 2.5 g \)
D. \( 4.0 g \)


Common enteritis infection in India
occurs by
A. Mosquito bite
B. Viruses
c. Ingesting cysts with food and drinks
D. Eating spice rich food


During the working of the cell:
\( \boldsymbol{P b}- \)
\( \boldsymbol{H} \boldsymbol{g}(\mathbf{1} . \boldsymbol{0} \boldsymbol{M})\left|\boldsymbol{P} \boldsymbol{b}^{2+}(\boldsymbol{a} \boldsymbol{q})(\boldsymbol{1} \boldsymbol{M})\right| \boldsymbol{P} \boldsymbol{b}^{2+}(\boldsymbol{a} \boldsymbol{q})(\mathbf{1} \)
\( \boldsymbol{H} \boldsymbol{g}(\mathbf{0 . 5} \boldsymbol{M}) \)
This question has multiple correct options
\( \mathbf{A} \cdot\left[P b^{2+}\right] \) in right half cell decreases
B \( \cdot\left[P b^{2+}\right] \) in left half cell decreases
c. \( \left[P b^{2+}\right] \) does not change in either of the half cells
D. molarity of lead amalgam in right half cell increases while that of left half cell decreases


What is sewage? Explain why it is
harmful to discharge untreated sewage into rivers or seas.


What are the assumptions made during the calculation of net gain of ATP?


Which is the most common source of
eutrophication?
A. Industrial effluent
B. Textile effluent
c. Sewage water
D. Both B and C


Starch is converted to maltose by the
enzyme
A. lipase
B. protease
c. amylase
D. none of the above


Assertion
The most widely used compound as
source of ethylene is ethephon.
Reason
Ethephon hastens fruit ripening in tomatoes and apples and accelerates abscission in stems and leaves.
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 current liberates \( 0.50 g \) of hydrogen in
2 hours. The weight of copper(At.wt. \( = \)
63.5 ) deposited at the same time by the
same current through copper sulphate solution is:
\( \mathbf{A} \cdot 63.5 g \)
в. \( 31.8 g \)
c. \( 15.9 g \)
D. \( 15.5 g \)