In the given figure a monkey of mass \( m \) is climbing a rope hanging from the roof with acceleration a. the coefficient of
static friction between the body of the
monkey and the rope is \( \mu \) find the
direction and value of friction on the
monkey.


Equilibrium can be achieved only in
open vessel.
A. True
B. False


Replace the blank with an integer to
make it a true statement.
\( (-3) \times----=27 \)


Nature of \( C-X \) bond in haloarene is Non-
Polar.
A . True
B. False


Who is given credit for coming up with the "plum pudding" model of the atom?
A. Niels Bohr
B. Earnest Rutherford
c. J.J. Thompson
D. James chadwick
E. Max Planck


Find the acceleration of block \( A \) in
terms of B. All surface are frictionless.


apacitor ( (1) so as to fill the gap eeping the battery remainc charge on each capacit
\( \frac{2 m}{1+(1 / 1 / k)} \)
\( \frac{\omega(10)}{1} \)
\( \frac{2 \omega}{(1+k)} \)
\( \frac{2 w}{10-k} \)


Find the area of a parallelogram having base \( 4 \mathrm{cm} \) and height \( 2 \mathrm{cm} \)
A. 6 sq. \( \mathrm{cm} \)
B. 8 sq. \( \mathrm{cm} \)
c. 10 sq. \( \mathrm{cm} \)
D. 12 sq. \( \mathrm{cm} \)


The contrapositive of \( (\sim p \wedge q) \rightarrow \sim r \) is
equivalent to
A. \( (p \wedge q) \rightarrow r \)
в. \( (p \wedge q) \vee r \)
c. \( r \rightarrow(p \vee \sim q) \)
D. none of these


The radius of sphere is measured as
then the percentage error in volume of the balls is


Power of \( 10 ~ W \) is emitted by a
loudspeaker. The sound intensity
radiated by it at a distance of \( 3 m \) is
\( 2 W / m^{2} . \) If the intensity of loudspeaker
is doubled the intensity at 6 m will be
\( \mathbf{A} \cdot 1 W / m^{2} \)
в. \( 4 \mathrm{W} / \mathrm{m}^{2} \)
c. \( 0.5 W / m^{2} \)
D. \( 2 \mathrm{W} / \mathrm{m}^{2} \)


Coordination compounds are mainly known for transition metals.
A. True
B. False


uniformly charged in such a way that the potential difference between
them is \( V_{2}-V_{1}=120 V . \) (i.e. plate 2 is
at a higher potential). The plates are
separated by \( \boldsymbol{d}=\mathbf{0 . 1 m} \) and can be
treated as infinitely large. An electron is
released from rest on the inner surface
of plate \( 1 . \) What is its speed when it hits
plate \( 2 ?\left(e=1.6 \times 10^{-19} C, m_{e}=\right. \)
\( \left.9.11 \times 10^{-31} k g\right) \)
\( \mathbf{A} \cdot 32 \times 10^{-19} \mathrm{m} / \mathrm{s} \)
B . \( 6.49 \times 10^{6} \mathrm{m} / \mathrm{s} \)
C \( .7 .02 \times 10^{12} \mathrm{m} / \mathrm{s} \)
D. \( 1.87 \times 10^{6} \mathrm{m} / \mathrm{s} \)


The acidic nature of halogen acids in methanoic acid is:
\( \boldsymbol{H} \boldsymbol{F}>\boldsymbol{H} \boldsymbol{C l}>\boldsymbol{H} \boldsymbol{B r}>\boldsymbol{H} \boldsymbol{I} . \) If true
write 1 , else write 0 .


Which of the following ions have zero value of magnetic moment?
A \( \cdot S c^{3} \)
в. \( T i^{4} \)
\( c \cdot Z n^{2} \)
D. None of these


If each element in a row of a
determinant is multiplied by the same
factor \( r, \) then the value of the
determinant:
A . Is multiplied by \( r^{3} \)
B. Is increased by \( 3 r \)
c. Remains unchanged
D. Is multiplied by \( r \)


What is the amount of charge on an
electron?
A \( \cdot 1.6 \times 10^{19} \) coulomb
B . 1.6 \( \times 10^{-10} \) coulomb
D. 1.6 \( \times 10^{-19} \) coulomb


0.585 is equal to
A \( \cdot \frac{589}{1000} \)
B. \( \frac{585}{10000} \)
c. \( \frac{1000}{585} \)
D. None of these


A cuprous ore among the following is
A . cuprite
B. malachite
c. chalcopyrites
D. azurite


\( y=\sin x \cos x \) find \( \frac{d y}{d x} \)


Assign the IUPAC names for the given
compounds:


Indicate the minimum number of
tosses by each skater required to avoid
collision.
Number of tosses by \( A= \) Number of tosses by B =


Which of the following bind the soil together?
A. Trees
B. Pond
c. River
D. Layers of the soil


Which protist causes Leucorrhoea?


Ip
experiment on scattering ot \( \boldsymbol{\alpha} \) -particles by a thin foil of gold, draw the trajectory
of \( \alpha \) -particles in the coulomb field of
target nucleus. Explain briefly how one gets the information on the size of the nucleus from this study. From the relation \( \boldsymbol{R}=\boldsymbol{R}_{0} \boldsymbol{A}^{1 / 3}, \) where \( \boldsymbol{R}_{0} \)
is constant and \( A \) is the mass number
of the nucleus, show that nuclear
matter density is independent of \( \mathbf{A} \)
OR

Distinguish between nuclear fission and fusion. Show how in both these
processes energy is released.
Calculate the energy release in MeV in the deuterium-tritium fusion reaction:
\( \mathbf{2} \boldsymbol{H}+_{\mathbf{1}}^{\mathbf{3}} \boldsymbol{H} \longrightarrow_{\mathbf{2}}^{\mathbf{4}} \boldsymbol{H} \boldsymbol{e}+\boldsymbol{n} \)
Using the data:
\( \boldsymbol{m}\left(_{1}^{2} \boldsymbol{H}\right)=\mathbf{2 . 0 1 4 1 0 2} \boldsymbol{u} \)
\( \boldsymbol{m}\left(_{1}^{3} \boldsymbol{H}\right)=\mathbf{3} . \mathbf{0} \mathbf{1 6 0} \mathbf{4 9} \boldsymbol{u} \)
\( \boldsymbol{m}\left(\begin{array}{l}4 \\ 2\end{array} \boldsymbol{H} e\right)=4.002603 \boldsymbol{u} \)
\( \boldsymbol{m}_{\boldsymbol{n}}=\mathbf{1 . 0 0 8 6 6 5 u} \)
\( \mathbf{1} \boldsymbol{u}=\mathbf{9 3 1 . 5} \boldsymbol{M} \boldsymbol{e} \boldsymbol{V} / \boldsymbol{c}^{2} \)


By selling a motor cycle for Rs. 23,000 a dealer gains \( 15 \% \). Find its cost price (in Rs.)


Find the common difference \( d \) and write
three more terms.2, \( \frac{5}{2}, 3, \frac{7}{2} \)


Show that the ratio of the sum of first \( n \)
terms of a G.P. to the sum of terms form \( (n+1)^{t h} \) to \( (2 n)^{t h} \) term is \( \frac{1}{r^{n}} \)


In milk, at \( 37^{\circ} \mathrm{C} \), lactobacillus
acidophilus is a generation time of
about 75 minutes. Calculate the
population relative to the initial value at 30,60,75,90 and 150 minutes.


Lowest oxidation state of phosphorous is in:
A. \( H_{3} P O_{2} \)
в. \( H_{3} P O_{4} \)
c. \( H_{4} P_{2} O_{7} \)
D. \( H_{3} P O_{3} \)


A condenser of capacity \( C \) is charged to
a potential difference of \( V_{1} . \) The plates
of the condenser are the connected to
an ideal inductor of inductance \( L \). The
current through the inductor when the
potential difference across the
condenser reduces to \( V_{2} \) is
\( ^{\mathbf{A}} \cdot\left(\frac{C\left(V_{1}^{2}-V_{2}^{2}\right)}{L}\right)^{1 / 2} \)
\( ^{\mathbf{B}} \cdot\left(\frac{C\left(V_{1}-V_{2}\right)}{L}\right)^{1 / 2} \)
\( ^{\mathbf{C}} \cdot \frac{C\left(V_{1}^{2}-V_{2}^{2}\right)}{L} \)
D. \( \frac{C\left(V_{1}-V_{2}\right)}{L} \)


The Sales Tax a Customer has to pay
A . Rs. 2,166.60
B. Rs. 2,097.60
c. Rs. 2,030.60
D. Rs. 2,966.60


With increase in the molecular weight, what happens to the density of ethers?
A. Increases
B. Decreases
c. remains same
D. cannot be predicted


Match the shell given in List-I with the value of \( l \) given in List-II.


In given Figure, a charge \( Q \) is fixed.
Another charge \( q \) is moved along a circular arc MN of radius r around it,
from the point \( \mathrm{M} \) to the point \( \mathrm{N} \) such
that the length of the arc \( M N=l . \) The
work done in this process is :
A. Zero
В. \( \frac{1}{4 \pi \epsilon_{0}} \cdot \frac{Q q}{r^{2}} l \)
c. \( \frac{Q q}{2 \epsilon_{0} r^{2}} l \)
D. \( \frac{Q q}{2 \pi \epsilon_{0} r^{2}} \)


Identify the region described by the shaded part in the graph above.
This question has multiple correct options
A. \( y=4 x-6 \)
B. \( y \neq 4 x-6 \)
c. \( y<4 x-6 \)
D. \( y>4 x-6 \)


Q Type your question
\( \mathbf{A} \)
\( (a) \)
\( B \)
\( \mathbf{C} \)
the
\( (c) \)
\( D \)


'The order of magnitude of a physical quantity must be expressed in proper unit'. Comment on this statement


Two identical metal balls \( A \) and \( B \)
moving in opposite directions with different speeds hit each other at point \( X \) as shown in the figure. Changes will most likely appear in their
1. Shapes
2. Speeds
3. Directions
4. Volumes
A . 1 and 3
B. 2 and 3
\( c \cdot 2 \) and 4
D. 1,2 and 3


Suppose for a differentiable function
\( \boldsymbol{f}, \boldsymbol{f}(\mathbf{0})=\mathbf{0}, \boldsymbol{f}(\mathbf{1})=\mathbf{1}, \boldsymbol{f}^{\prime}(\mathbf{0})=\mathbf{4}= \)
\( \boldsymbol{f}^{\prime}(\mathbf{1}) \)
If \( g(x)=f\left(e^{x}\right) e^{f(x)}, \) then \( g^{\prime}(0) \) is equal
to
A .4
B. 8
\( c \cdot 2 \)
D.


If \( \boldsymbol{y}=\sqrt{\boldsymbol{x}+\boldsymbol{y}}, \) prove that \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)
\( \frac{1}{(2 y-1)} \)


Calculate the quantity of heat required
to convet \( 1.5 \mathrm{kg} \) of ice at \( 0^{\circ} \mathrm{C} \) to water at
\( \mathbf{1 5}^{o} \boldsymbol{C} \cdot\left(\boldsymbol{L}_{\boldsymbol{i c e}}=\mathbf{3 . 3 4} \times\right. \)
\( \left.\mathbf{1 0}^{\mathbf{5}} \boldsymbol{J k g}^{-\mathbf{1}}, \boldsymbol{C}_{\boldsymbol{w a t e r}}=\mathbf{4 1 8 0} \boldsymbol{J} \boldsymbol{k g}^{-\mathbf{1} o} \boldsymbol{C}^{-\mathbf{1}}\right) \)
A \( .5 .85 \times 10^{5} J \)
В. \( 5.95 \times 10^{5} J \)
c. \( 3.95 \times 10^{5} J \)
D. \( 4.95 \times 10^{5} J \)


Which one is more elastic steel or
rubber.Explain.


Solve \( \int_{b}^{a} \frac{x}{\sqrt{a^{2}+x^{2}}} d x \)


Pebrine is a disease of
A. Honey bee
B. Fish
c. Silkworm
D. Lac insect


\( \int \frac{1}{(x+2)(x+3)} d x \)


The unit of coefficient of linear
expansion is
A . \( m \)
B \( \cdot m C^{-1} \)
\( c . c \)
D. \( C^{-1} \)


What is the pressure exerted by a man weighing 80 kg standing on his feet?
Area of his feet \( = \)
\( \left.160 \text { sq.cm. (Take } g=10 m s^{-2}\right) \)


Assertion
\( C s \) and \( F_{2} \) reacts violently.
Reason
Cs is most electropositive and \( \boldsymbol{F}_{2} \) is
most electronegative.

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. Assertion is incorrect but Reason is correct


State true or false:
The diagonal \( B D \) of a parallelogram
\( A B C D \) bisects angles \( B \) and \( D \). then
\( A B C D \) is a rhombus.
A. True
B. False


Allotrope of this element is the primary absorber of UV solar radiation in Earth's
atmosphere:
A. Carbon
B. Nitrogen
c. oxygen
D. Neon
E. Argon


The sum of \( n \) terms of the series \( 1+ \)
\( (\mathbf{1}+\boldsymbol{a})+\left(\mathbf{1}+\boldsymbol{a}+\boldsymbol{a}^{2}\right)+(\mathbf{1}+\boldsymbol{a}+ \)
\( \left.\boldsymbol{a}^{2}+\boldsymbol{a}^{3}\right)+\ldots . \) is
A \( \cdot \frac{n}{1+a}-\frac{1-a^{n}}{(1-a)^{2}} \)
в. \( \frac{n}{1-a}+\frac{a\left(1-a^{n}\right)}{(1-a)^{2}} \)
c. \( \frac{n}{1-a}+\frac{a\left(1+a^{n}\right)}{(1-a)^{2}} \)
D. none of the above


In the quantitative analysis of sulphur in the organic compound,compound is heated in carius tube with:
This question has multiple correct options
A. sodium oxide
B. sodium peroxide
c. fuming \( H N O_{3} \)
D. dil \( H N O_{3} \)


Benzene on ozonolysis followed by
reaction with \( Z n+H_{2} O \) gives:
A. 3 moles of glycerol
B. 3 moles of glyoxal
c. 3 moles of glyoxalic acid
D. 3 moles of acetylene


In a Wheatstone bridge shown in figure \( (x=y) \) and \( A>B . \) The direction of the
current between a and b will be:
A. From a to
B. From b to a
c. from a to b through c
D. from b to a through


A business man is expecting two telephone calls. Mr Walia may call any time between 2 p.m and 4 p.m. while \( \mathrm{Mr} \) Sharma is equally likely to call any time between 2.30 p.m. and 3.15 p.m. The probability that Mr Walia calls before Mr Sharma is:
A \( \cdot \frac{1}{18} \)
в. \( \frac{1}{9} \)
\( c \cdot \frac{1}{6} \)
D. None of these


\( \sqrt{0.01}+\sqrt{0.0064}=? \)
A . 0.3
B. 0.03
c. \( \sqrt{0.18} \)
D. None of these


Alternating current in circuit is given by
\( \boldsymbol{I}=\boldsymbol{I}_{0} \sin 2 \pi n t . \) Then the time taken by
the current to rise from zero to r.m.s.
value is equal to
A \( \cdot 1 / 2 n \)
B. \( 1 / n \)
\( c \cdot 1 / 4 n \)
D. \( 1 / 8 n \)


The p.d.f. of a continuous r.v. x is \( f(x)=\frac{7}{9} x^{2}-2, \quad 0<x<3 \)
\( =\mathbf{0} \)
otherwise
\( \boldsymbol{P}(\boldsymbol{X} \leq-1) \) is?
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( 1 / 2 \)
\( c \cdot 1 / 3 \)
D. \( 1 / 4 \)


A \( 10 \mathrm{kg} \) mass moves along \( \mathrm{X} \) -axis. Its
acceleration as a functions of its
position is shown in the figure. What is
the total work done on the mass by the
force as the mass moves from \( x=0 \) to
\( x=8 \mathrm{cm} ? \)
\( \mathbf{A} \cdot 8 \times 10^{-2} J \)
В. \( 16 \times 10^{-2} J \)
C. \( 4 \times 10^{-4} J \)
D. \( 1.6 \times 10^{-3} J \)


00
00
00
00


Two particle are oscillating along two close parallel straight lines side by side with the same frequency and amplitudes. They pass each other, moving in opposite directions when their displacement is half of the amplitude. The mean positions of the two particles lie on a straight line perpendicular to the paths of the two particles. The phase difference is:
A . 0
в. \( 2 \pi / 3 \)
\( c \)
D. \( \pi / 6 \)


\( H_{2} O \) is liquid but \( H_{2} S \) is gas. This is because of:
A. larger size of \( S \)
B. acidic nature of \( H_{2} S \)
c. hydrogen bonding
D. small size of \( O \)


If \( I=\int_{0}^{\pi}\left(\pi x-x^{2}\right)^{100} \sin 2 x d x, \) then
value of \( I \) is?
A . \( \pi^{100} \)
B. \( \frac{1}{2}\left(\pi^{100}-\pi^{97}\right) \)
c. \( \frac{1}{2}\left(\pi^{100}+\pi^{97}\right) \)
D.


Integrate the function \( x \sin x \)


Why do moss plants produce very large number of male gametes? Provide one reason. What are these gametes called?


Human organism is an internal
combustion machine because of
A. Assimilation of energy from food
B. Liberate \( C O_{2} \) during respiration
C. Expel waste food at the end state digestion
D. Secrete powerful digestive juices


The value of \( \mathrm{m} \) for which the lines \( 3 x= \)
\( \boldsymbol{y}-\mathbf{8} \) and \( \mathbf{6} \boldsymbol{x}+\boldsymbol{m} \boldsymbol{y}+\mathbf{1 6}=\mathbf{0} \) coincide
is
A . 2
B. -
\( c \cdot \frac{1}{2} \)
D. \( -\frac{1}{2} \)


Consider the motion of a particle
described by \( x=a \cos t, y=a \sin t \) and
\( z=t . \) The trajectory traced by the
particle as a function of time is
A. Helix
B. Circular
c. Elliptical
D. Straight line


An experiment is carried on a fixed
amount of gas at different temperature and at high pressure such that it
deviates from the ideal gas behaviour.
The variation of \( \frac{\boldsymbol{p} \boldsymbol{V}}{\boldsymbol{R T}} \) with \( \boldsymbol{p} \) is shown in
the diagram. The correct variation will
correspond to :
A. curve \( A \)
B. curve \( B \)
c. curve \( C \)
D. curve \( D \)


Action spectrum of photosynthesis was first studied by
A. Blackman
B. Van Mayer
c. Engelmann
D. Boussingault


A nuclide of an alkaline earth metal
undergoes radioactive decay by emission of three \( \alpha \) -particle in
succession. The group of the periodic table to which the resulting daughter element would belong is
A. Group 14
B. Group 16
c. Group 4
D. Group 6


Consider the following statements and arrange in the order of true/false as
given in the codes:
\( S_{1}: \) Oxides of boron \( \left(B_{2} O_{3}\right) \) and silicon
\( \left(S i O_{2}\right) \) are acidic in nature.
\( S_{2}: \) Oxides of aluminium \( \left(A l_{2} O_{3}\right) \) and
gallium \( \left(G a_{2} O_{3}\right) \) are amphoteric in
nature
\( S_{3}: \) Oxides of indium \( \left(l n_{2} O_{3}\right) \) and
thallium \( \left(T l_{2} O_{3}\right) \) are basic in nature.
\( \boldsymbol{S}_{4}: \) Oxides of germanium \( \left(\boldsymbol{G} \boldsymbol{e} \boldsymbol{O}_{2}\right) \) and
\( \operatorname{tin}\left(S n O_{2}\right) \) are acidic in nature.
\( \mathbf{A} \cdot \) Т \( F T T \)
B. F FTT
c. тт न
D. TF TF


The absorption of \( U V \) radiation by \( O_{3} \)
A. protects the inhabitants of our planet from injurious radiation
B. maintains an equilibrium between the concentrations of \( O_{2} \) and \( O_{3} \)
c. makes both the function A and B above effective
D. makes no function effective


Two conducting coils are placed coaxially now a cell is connected in one coil then they will :-
A. Attract to each other
B. Repel to each other
\( c . \) Both (1)\( \&(2) \)
D. They will not experience any force


At \( 90^{\circ} C \), pure water has \( \left[H_{3} O^{+}\right]= \)
\( 10^{-6} \mathrm{m} \) on the value of \( k_{w} \) at this
temperature is :
A \( \cdot 10^{-6} \)
- \( ^{-6}-10 \)
B. \( 10^{-12} \)
\( \mathbf{c} \cdot 10^{-13} \)
D. \( 10^{-14} \)


Find the value of current lin given
circuit.


The compound in which the number of
\( d \pi-p \pi \) bonds are equal to those
present in \( C l O_{4}^{-} \) is:
A. \( X e F_{4} \)
в. \( X e O_{3} \)
\( \mathrm{c} \cdot \mathrm{XeO}_{4} \)
D. \( X e F_{6} \)


A player tosses 2 fair coins. He wins Rs5
if 2 heads appear, Rs2 if head appears
and Rs1 if no head appears. Find his
expected winning amount and variance of winning amount.


If the equation \( 16 x^{2}+6 k x+4=0 \) has
equal roots, then the value of \( k \) is
\( \mathbf{A} \cdot \pm 8 \)
в. \( \pm \frac{8}{3} \)
\( c \cdot_{\pm \frac{3}{8}} \)
D. 0


The range of the function \( f(x)= \)
\( 7-x \boldsymbol{P}_{x-3} \) is:
A \( \cdot\{1,2,3\} \)
в. \{1,2,3,4,5\}
D. \{1,2,3,4,5,6\}


\( C l_{2} O_{7} \) can be regarded as an anhydride
of
A. Hypochlorous acid
B. chlorous acid
c. chloric acid
D. Perchloric acid


\( \int \frac{x^{3}-1}{x^{3}+x} d x \) is equal to
\( \mathbf{A} \cdot x-\log x+\log \left(x^{2}+1\right)-\tan ^{-1} x+c \)
B. \( x-\log x+\frac{1}{2} \log \left(x^{2}+1\right)-\tan ^{-1} x+c \)
c. \( x+\log x+\frac{1}{2} \log \left(x^{2}+1\right)+\tan ^{-1} x+c \)
D \( x+\log x-\frac{1}{2} \log \left(x^{2}+1\right)-\tan ^{-1} x+c \)


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


Chloro compound of vanadium has only
spin magnetic moment of \( 1.73 B M \) This vanadium chloride has the
formula:
[Atomic number of \( \boldsymbol{V}=\mathbf{2 3}] \)
A \( \cdot V C l_{2} \)
в. \( V C l_{4} \)
c. \( V C l_{3} \)
D. \( V C l_{5} \)


In a resistance thermometer, the
resistances at \( 0^{\circ} \mathrm{C} \) and \( 100^{\circ} \mathrm{C} \) are 6.74
and 7.74 ohm respectively. The temperature corresponding to 6.53 ohm resistance is.
\( \mathbf{A} \cdot+53^{\circ} C \)
B. \( +21^{\circ} \mathrm{C} \)
\( \mathbf{c} .-53^{\circ} \mathrm{C} \)
D. \( -21^{\circ} \mathrm{C} \)


Explain with proper examples - 'Motion is relative.


A planet is moving around the Sun in a
circular orbit of circumference \( C . \) The
work done on the planet by the gravitational force \( F \) of the Sun is \( k F C \)
then the value of \( k \) is


Longitudinal waves cannot travel
through
A . liquids
B. gases
c. vacuum
D. solid


Prove the following:
(iv) \( \frac{\cos \left(90^{\circ}-A\right) \sin \left(90^{\circ}-A\right)}{\tan \left(90^{\circ}-A\right)}= \)
\( \sin ^{2} A \)


Number of elements present in Period 1
are
\( A \cdot 2 \)
B. 4
\( c .6 \)
\( D \)


Which of the following is not a transition element?
A. Mn
B. Fe
\( c \cdot c u \)
D.


In the given circuit, the voltage across
the voltage across the load is
maintained at \( 12 \mathrm{V} \). The current in the
zener diode varies from 0-50 mA. What
is the maximum watage of the diode?
\( A \cdot 12 W \)
B. 6 w
c. \( 0.6 w \)
D. \( 1.2 \mathrm{w} \)


Ine magnetıc tıeld \( \boldsymbol{B} \) at the centre of a
circular coil of radius \( r \) is \( \pi \) times that
due to a long straight wire at a distance
\( r \) from it, for equal currents. The
following diagram shows three cases. In
all cases the circular part has radius \( r \)
and straight ones are infinitely long. For
the same current the field \( B \) at centre \( P \)
in cases 1,2,3 has the ratio:
\( ^{\mathbf{A}} \cdot\left(-\frac{\pi}{2}\right):\left(\frac{\pi}{2}\right):\left(\frac{3 \pi}{4}-\frac{1}{2}\right) \)
B \( \cdot\left(-\frac{\pi}{2}+1\right):\left(\frac{\pi}{2}+1\right):\left(\frac{3 \pi}{4}+\frac{1}{2}\right) \)
\( \left(-\frac{\pi}{2}\right):\left(\frac{\pi}{2}\right):\left(\frac{3 \pi}{4}\right) \)
D \( \cdot\left(-\frac{\pi}{2}-1\right):\left(\frac{\pi}{2}-\frac{1}{4}\right):\left(\frac{3 \pi}{4}+\frac{1}{2}\right) \)


When alpha particles are used to bombard gold foil, most of the alpha
particles pass through undeflected. This result indicates that
most of the volume of a gold atom
consists of:
A. deuterons
B. neutrons
c. protons
D. unoccupied space


A system of three charges are placed as shown in the figure:
If \( D>>d \) the potential energy of the
system is best given by
\( ^{\mathbf{A}} \cdot \frac{1}{4 \pi \varepsilon_{0}}\left[-\frac{q^{2}}{d}-\frac{q Q d}{2 D^{2}}\right] \)
в. \( \frac{1}{4 \pi \varepsilon_{0}}\left[+\frac{q^{2}}{d}+\frac{2 q Q d}{D^{2}}\right] \)
c. \( \frac{1}{4 \pi \varepsilon_{0}}\left[-\frac{q^{2}}{d}+\frac{q Q d}{D^{2}}\right] \)
D. \( \frac{1}{4 \pi \varepsilon_{0}}\left[-\frac{q^{2}}{d}-\frac{q Q d}{D^{2}}\right] \)


ATPase enzyme needed for muscle
contraction is located in
A. Actinin
B. Troponin
c. Myosin
D. Actin


The \( p H \) of \( 0.1 \mathrm{M} \) acetic acid is \( 3, \) the
dissociation constant of acid will be:
A \( \cdot 1.0 \times 10^{-4} \)
В. \( 1.0 \times 10^{-5} \)
c. \( 1.0 \times 10^{-3} \)
D. \( 1.0 \times 10^{-8} \)


Identify the reaction taking place at
cathode in fuel cell.
A. \( O_{2}+2 H_{2} O+4 e^{-} \rightarrow 4 O H^{-} \)
B \( \cdot 2 H_{2}+4 O H^{-} \rightarrow 4 H_{2} O+4 e^{-} \)
c. \( O_{2}+2 H_{2} O+4 e^{-} \rightarrow 4 O H^{-}+H^{+} \)
D. \( 4 H_{2} O+4 e^{-} \rightarrow 2 H^{2}+4 O H^{-} \)


Quantum theory of radiation was
proposed by
A. Pauli
B. Planck
c. Hund
D. Aufbau


Refer to the given diagrammatic representation of the mechanism of
action of a protein hormone. In which of the following options correct labelling of \( A, B, \) and \( C \) is given?
A. A-Generation of second messenger, B-Physiological responses, C-Biochemical responses
B. A-Activation of genes, B-Biochemical responses, CGeneration of second messenger
C. A-Generation of second messenger, B-Biochemical responses, C-Physiological responses
D. A-Biochemical responses, B-Activation of genes, C- Physiological responses


Thomson's atomic theory suggested that the atom is:
A . not divisible
B. divisible
c. electrons revolve around nucleus
D. both A and C


Find the equation of the quadratic function \( \boldsymbol{f} \) whose graph increases over the interval \( (-\infty,-2) \) and decreases over the interval \( (-2,+\infty), f(0)=23 \)
and \( \boldsymbol{f}(\mathbf{1})=\mathbf{8} \)
A \( \cdot f(x)=3(x+2)^{2}+35 \)
B. \( f(x)=-3(x+2)^{2}-35 \)
C. \( f(x)=-3(x-2)^{2}+35 \)
D. \( f(x)=-3(x+2)^{2}+35 \)


Isotope per Natural abundance
\[
\begin{array}{ll}
^{1} \boldsymbol{H} & \mathbf{9 9 . 9 8 5} \\
^{2} \boldsymbol{H} & \mathbf{0 . 0 1 5}
\end{array}
\]
The average atomic mass of hydrogen using the following data is


If \( n \geq 1 \) is any integer, \( d(n) \) denotes
the number of positive factors of \( n, \) then
for any prime number \( \mathbf{p}, \mathbf{d}\left(\mathbf{d}\left(\mathbf{d}\left(\mathbf{p}^{7}\right)\right)\right)= \)
A .
B . 2
\( c \cdot 3 \)
D. 4


When light is incident on a polished surface \( \ldots \ldots . . \) reflection takes place.
A. diffused
B. regular
c. i rregular
D. all


An ideal gas is filled in a closed rigid and thermally insulated container. A
coil of \( 100 \Omega \) resistor carrying current
1 A for 5 min supplies heat to the gas.
The change in internal energy of the gas is
A. \( 10 k J \)
B. \( 30 k J \)
c. \( 20 k J \)
D. \( 0 k J \)


The concentrated \( H C l \) acid strongly fumes in
A . air
B. water
\( c \cdot \) both
D. none of these


What is picric acid? How is it prepared from phenol?


State True or False.
If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are in the same ratio (proportional), then the triangles are similar.
A. True
B. False


Although both \( C O_{2} \) and \( H_{2} O \) are
triatomic molecules, the shape of \( \boldsymbol{H}_{2} \boldsymbol{O} \)
molecule is bent while that of \( C O_{2} \) is
linear. Explain this on the basis of dipole moment.


The coefficient of \( x^{30} \) in the expansion of
\( \left(1+2 x+3 x^{2}+\dots .21 x^{20}\right)^{2} \) is
A . 2706
в. 2450
\( c .1481 \)
D. 256


In a thermodynamic processes during each cycle, a heat engine absorbs \( 400 \mathrm{J} \) of heat from a higher- temperature source and release 300 J of heat to the
low-temperature sink. Calculate the efficiency of heat engine?
\( A \cdot 1 \)
7
B. \( \frac{1}{4} \)
\( c \cdot \frac{3}{7} \)
D. \( \frac{4}{7} \)
\( E \)
1


Give the electron configuration of the given metal (atom/ions)
\( \boldsymbol{C r}^{\mathbf{3}+} \)
\( \mathbf{A} \cdot[A r] 3 d^{1} 4 s^{2} \)
B \( \cdot[A r] 3 d^{2} 4 s^{1} \)
c. \( [A r] 3 d^{3} \)
D. none of these


Steroid hormones, estrogen and testosterone bind to
A. Membrane ion channels
B. Enzyme-linked membrane receptors
c. G-Protein linked membrane receptors
D. Cytoplasmic receptors


Fireman crawl when entering a burning building because:
A. It is easier to crawl
B. Smoke rises high in the air
c. It helps to move faster
D. To resist more heat


Select the correct option:
Which of the following statements about cell junctions are correct?
(i) All the cells of the epithelium are held together with little intercellular
materials
(ii) In almost all animal tissues
specialised junctions provide both structural and functional link between
its individual cells
(iii) Tight junctions prevent substances from leaking across a tissue
(iv) Adhering junctions provide cementing to keep neighbouring cells together.
(v) Gap junctions provide cytoplasmic channels between cells for passage of
ions, small molecules and sometimes
big molecules.
A. (ii) and (iii)
B. (i), (ii) and (iii)
c. (iv) and (v)
D. (i), (ii), (iii), (iv) and (v)


Why iron is not used in the lab
preparation of hydrogen?


Find emf of the cell \( E_{2} \)
A. \( 2 v \)
B. 1.5
\( c \cdot 1 v \)
D. 1.75 V


Find the vector and Cartesian equation of the line that passes through the points (3,-2,-5) and (3,-2,6)


In a car lift, compressed air exerts a force \( F \) on a small piston having a radius of \( 5 \mathrm{cm} . \) This pressure is transmitted to a second piston of
radius \( 15 \mathrm{cm} . \) If the mass of the car to
be lifted is \( 1350 k g \), what is \( F ? \)
A . \( 1.5 \times 10^{3} N \)
В. \( 2.5 \times 10^{3} N \)
c. \( 3.5 \times 10^{3} N \)
D. \( 4.5 \times 10^{3} N \)


Give two examples of Complex
compound.


Which of the following general electronic configuration for transition
elements is NOT correct?
This question has multiple correct options
A \( \cdot(n+1) s^{1-2} n d^{1-30} \)
B . \( \left.n s^{1-2}(n-1) d^{1-10} \text { (Where } n=2,3,4, \ldots \ldots\right) \)
C. \( n s^{1-2}(n-1) s^{2} p^{6} d^{1-10} \)
D \( \cdot(n-1) d^{1-10} n s^{0-2} \)


What is the role of light in plants?
A. It is necessary for photosynthesis.
B. It controls growth and movement.
C. It controls the distribution of hormones.
D. All of the above.


Let \( \mathbf{g}(\mathbf{x})=\log (\mathbf{f}(\mathbf{x})) \) where \( \mathbf{f}(\mathbf{x}) \) is a
twice differentiable positive function on \( (0, \infty) \) such that \( f(x+1)=x f(x) \)
Then, for \( \mathbf{N}=\mathbf{1}, \mathbf{2}, \mathbf{3}, \dots \mathbf{g}^{\prime \prime}\left(\mathbf{N}+\frac{\mathbf{1}}{\mathbf{2}}\right)- \)
\( \mathrm{g}^{\prime \prime}\left(\frac{1}{2}\right)= \)
A \( \cdot-4\left(1+\frac{1}{9}+\frac{1}{25}+\ldots+\frac{1}{(2 \mathrm{N}-1)^{2}}\right) \)
B. \( 4\left(1+\frac{1}{9}+\frac{1}{25}+\ldots+\frac{1}{(2 \mathrm{N}-1)^{2}}\right) \)
c. \( -4\left(1+\frac{1}{9}+\frac{1}{25}+\ldots+\frac{1}{(2 \mathrm{N}+1)^{2}}\right) \)
D \( 4\left(1+\frac{1}{9}+\frac{1}{25}+\ldots+\frac{1}{(2 \mathrm{N}+1)^{2}}\right) \)


Prove that \( \left|\begin{array}{ccc}\boldsymbol{y} \boldsymbol{z}-\boldsymbol{x}^{2} & \boldsymbol{z} \boldsymbol{x}-\boldsymbol{y}^{2} & \boldsymbol{x} \boldsymbol{y}-\boldsymbol{z}^{2} \\ \boldsymbol{z} \boldsymbol{x}-\boldsymbol{y}^{2} & \boldsymbol{x} \boldsymbol{y}-\boldsymbol{z}^{2} & \boldsymbol{y} \boldsymbol{z}-\boldsymbol{x}^{2} \\ \boldsymbol{x} \boldsymbol{y}-\boldsymbol{z}^{2} & \boldsymbol{y} \boldsymbol{z}-\boldsymbol{x}^{2} & \boldsymbol{z} \boldsymbol{x}-\boldsymbol{y}^{2}\end{array}\right| \)
divisible by \( (x+y+z) \) and hence find
the quotient


Extraction of chlorine from brine is
based on:
A. reduction
B. displacement
c. oxidation
D. evaporation


Find the area of a trapezium whose parallel sides are of length \( 10 \mathrm{cm} \) and 6 cm respectively and the perpendicular distance between the two parallel sides
is \( 4.5 \mathrm{cm} .\left(\text { in } c m^{2}\right) \)


The area of the region bounded by the curve \( \sqrt{\boldsymbol{x}}+\sqrt{\boldsymbol{y}}=\sqrt{\boldsymbol{a}}(\boldsymbol{x}, \boldsymbol{y} \geq 0) \) and the
coordinate axes is
A \( \cdot a^{2} / 6 \)
в. \( a^{2} / 2 \)
c. \( a^{2} / 3 \)
D. \( a^{2} \)


Select incorrect statement
A. Micelles are macromolecular colloids
B. The electrical charge on a colliod particle is indicated by electrophoresis
C. Formation of micelles takes place above kraft temperature
D. Formation of micelles takes place below CMC


If the matrix \( \left|\begin{array}{ccc}\mathbf{1} & \mathbf{3} & \boldsymbol{\lambda}+\mathbf{2} \\ \mathbf{2} & \mathbf{4} & \mathbf{8} \\ \mathbf{3} & \mathbf{5} & \mathbf{1 0}\end{array}\right| \) is singular
\( \operatorname{then} \lambda= \)
\( A \cdot-2 \)
B. 4
\( c \cdot 2 \)
D. - -


Coke is obtained from
A. petroleum
B. Diesel
c. coal
D. None of these


Distinguish between metaphase of mitosis and metaphase I of meiosis.


Fluorine always shows-1 oxidation state
Why?


Cyclohexane on chlorination gives:
A. chloro cyclohexane
B. 1,2 - dichloro cyclohexane
C. 1,4 - dichloro cyclohexane
D. a mixture of all the above


What is meant by torque due to gravity?


Match the columns:
\( \mathbf{A} \)
\( 1-b, 2-e, 3-a, 4-c, 5-d \)
B. \( 1-b, 2-c, 3-d, 4-e, 5-a \)
\( C \cdot 1-a, 2-e, 3-b, 4-d, 5-c \)
D. \( 1-e, 2-d, 3-c, 4-b, 5-a \)
\( \mathrm{E} \cdot 1-\mathrm{c}, 2-\mathrm{b}, 3-\mathrm{a}, 4-\mathrm{e}, \mathrm{S}-\mathrm{d} \)


If a mirror has a focal length of \( -20 \mathrm{cm} \)
it is a :
A. convex mirror
B. concave mirror
c. plane mirror
D. lens


Examine the table. (Each figure is
divided into triangles and the sum of the angles deduced from that)

What can you say about the angle sum
of a convex polygon with the number of
\( \operatorname{sides}(n)=8 ? \)
\begin{tabular}{|l|c|c|c|c|}
\hline Figure & & & & & \\
\hline side & 3 & & & & \\
\hline Ange sum & \( 180^{\circ} \) & \( 2 \times 180^{\circ} \) & 5 & 6 \\
\hline
\end{tabular}
A \( .720^{\circ} \)
B. \( 960^{\circ} \)
\( c \cdot 1020^{\circ} \)
D. \( 1080^{\circ} \)


The maximum value of static friction is
called limiting friction.
A. True
B. False
c. Ambiguous
D. Data insufficient


Which one of the following cocci appear as bunch of grapes under microscope
A. Streptococci
B. Diplococci
c. staphylococci
D. Pneumococci


In the diagram, \( P \) is the centre of the
circle with radius \( 4 \mathrm{cm} \) and \( Q \) is the
centre of the circle with radius \( 3 \mathrm{cm} \)
Of the points marked \( W, X, Y \) and \( Z \)
which point is \( 4 \mathrm{cm} \) from \( P \) and more
than \( 3 \mathrm{cm} \) from \( Q ? \)
\( A \cdot W \)
в. \( x \)
\( c . Y \)
D.


The solution to the differential equation
\( \boldsymbol{y} \ln \boldsymbol{y}+\boldsymbol{x} \boldsymbol{y}^{\prime}=\mathbf{0} \) where \( \boldsymbol{y}(\mathbf{1})=\boldsymbol{e}, \) is:
A. \( x(\ln y)=1 \)
в. \( x y(\ln y)=1 \)
c. \( (\ln y)^{2}=2 \)
D. \( \ln y+\left(\frac{x^{2}}{2}\right) y=1 \)


The product formed in the reaction of
\( \mathrm{SOCl}_{2} \) with white phosphorus is:
A \( \cdot P C l_{3} \)
в. \( S O_{2} C l_{2} \)
\( c \cdot S C l_{2} \)
D. \( P O C l_{3} \)


What quantity of heat would be given out by 200 gm of copper in cooling from
\( 80^{\circ} \mathrm{C} \) to \( 20^{\circ} \mathrm{C} \) (Specific heat of copper
\( \left.=\mathbf{0 . 0 9 c a l g}^{-1 o} \mathbf{C}^{-1}\right) ? \)
A. 1080 cal
B. 1000 cal
c. 1500 cal
D. 1100 cal


Assertion
In a meter bridge experiment null point for an unknown resistance is put inside
an enclosure maintained at a higher temperature. The null point can be obtained at the same point as before by decreasing the value of the standard resistance.
Reason
Resistance of metal increases with
increase in temperature.
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


(P) and (Q) respectively are:
\( \mathrm{Ph}-\mathrm{C}_{\mathrm{CH}_{3}}^{\mathrm{H}}-\mathrm{O}-\mathrm{CH}_{3} \quad \stackrel{\mathrm{HBr}}{\longrightarrow} \quad \begin{array}{l}(\mathrm{P}) \\ \text { Aiconol }\end{array}+\quad \begin{array}{l}(\mathrm{Q}) \\ \text { Alkynalide }\end{array} \)
\( A \)
\( \mathrm{Ph}-\mathrm{C}-\mathrm{OH}, \mathrm{CH}_{3}-\mathrm{Br} \)
B.
\( c \)
\( \mathrm{CH}_{3}-\mathrm{OH}, \mathrm{Ph}-\underset{\mathrm{Br}}{\mathrm{CH}}-\mathrm{CH}_{3} \)
\( D \)
\( \mathrm{Ph}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{Br}, \mathrm{CH}_{3}-\mathrm{OH} \)


What is the source of oxygen for
respiration in plants during daytime?


The effective capacitance in \( \mu F \) for the
following circuit will be:
A \( .28 / 9 \)
\( B \)
\( c \)
0.18


Classify the following into homoleptic \& heteroleptic complexes?
¡) \( \boldsymbol{K}_{4}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}\right] \)
ii) \( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5}\left(\boldsymbol{C O}_{3}\right)\right] \boldsymbol{C l} \)
iii) \( \boldsymbol{K}_{2}\left[\boldsymbol{Z} \boldsymbol{n}(\boldsymbol{O} \boldsymbol{H})_{4}\right] \)
iv) \( \left[\boldsymbol{P t}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2} \boldsymbol{C l}\left(\boldsymbol{N} \boldsymbol{O}_{2}\right)\right] \)


n Fig \( 31 A B C D \) is a rectangle with
diameter \( 32 m \) by \( 18 m . A D E \) is a
triangle such that \( E F \perp A D \) and \( E F= \)
14 \( c m . \) Calculate the area of the shaded
region.


The graph drawn between pressure and
temperature at constant volume for a
given mass of different molecular
weights \( M_{1} \) and \( M_{2} \) are the straight lines
as shown in the figure then
\( \mathbf{A} \cdot M_{2}>M_{1} \)
\( \mathbf{B} \cdot M_{1}>M_{2} \)
\( \mathbf{c} \cdot M_{1}=M_{2} \)
\( \mathbf{D} \cdot M_{1}^{3}=M_{2} \)


ff \( a \) and \( b \) unit vectors inclined at an
angle \( \theta \), then prove that :
\( \tan \frac{\boldsymbol{\theta}}{\mathbf{2}}=\frac{|\hat{\boldsymbol{a}}-\hat{\boldsymbol{b}}|}{|\hat{\boldsymbol{a}}+\hat{\boldsymbol{b}}|} \)


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


How many terms of the AP: \( 15,13,11, \)
are needed to make the sum 55?
Explain the reason for double answer.


Mating of an organism to double recessive for determining homozygosity or heterozygosity is called as
A. Reciprocal cross
B. Back cross
c. Dihybrid cross
D. Test cross


On heating one mole of \( N a_{2} C O_{3}, \) no. of
moles of \( C O_{2} \) obtained is 0
If true enter 1 , else enter 0 .
\( A \)


Find the mean of 43,54,64,53,36
A . 50
B. 40
\( c .60 \)
D. 30


Find the sum to indicated number of
terms in each of the geometric
progression. Exercise 7 to 10 \( \mathbf{0 . 1 5}, \mathbf{0 . 0 1 5}, \mathbf{0 . 0 0 1 5}, \mathbf{2 0} \) terms


A \( 300,000 k g \) commercial airlines is flying through the air with \( 150,000 N \) of
thrust.

For airplanes traveling at high speeds,
the drag force is related to the velocity by the following equation
\[
\boldsymbol{F}_{\text {drag}}=-\boldsymbol{b v}^{2}
\]
where drag force is opposite to the direction of the velocity. If the drag constant \( b \) is \( 3 k g / m \) and the
airplane is moving at \( 200 m / s, \) how would you describe its motion?
A. In equilibrium (cruising at constant speed)
B. Nearequilibrium, positive acceleration
c. Near equilibrium, negative acceleration
D. Greatly accelerating during takeoff
E. Greatly slowing down during landing


Deuterostomial coelomates are
A. Chordates
B. Mollusk
C. Arthropods
D. Annelids


Same quantity of electricity being used to liberate iodine (at anode) and a metal (at
cathode). The mass of metal liberated at
cathode is 0.617 g and the liberated iodine completely reduced by \( 46.3 \mathrm{ml} \) of \( 0.124 \mathrm{M} \) sodium thiosulphate solution. What is
equivalent weight of metal?
A . 23 \( g \)
в. \( 127 \mathrm{g} \)
c. \( 108 \mathrm{g} \)
D. 46


What are the basic layers of the wall of
alimentary canal?


The equation of the latus rectum of the parabola \( \boldsymbol{x}^{2}+\mathbf{4} \boldsymbol{x}+\mathbf{2} \boldsymbol{y}=\mathbf{0} \) is -
\( A \cdot 3 y=2 \)
B. \( 2 y+3=0 \)
c. \( 2 y=3 \)
D. \( 3 y+2=0 \)


Find the sum of the first 16 terms of the
A.P.10,6,2,..


Show that points
\( \boldsymbol{A}(\boldsymbol{a}, \boldsymbol{b}+\boldsymbol{c}), \boldsymbol{B}(\boldsymbol{b}, \boldsymbol{c}+\boldsymbol{a}), \boldsymbol{C}(\boldsymbol{c}, \boldsymbol{a}+\boldsymbol{b}) \)
are collinear.


\( \boldsymbol{C H}_{3}-\boldsymbol{C H}(\boldsymbol{C l})-\boldsymbol{C}_{2} \boldsymbol{H}_{5} \frac{\text {Alc.}}{\boldsymbol{K O H}} \)
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}=\boldsymbol{C H}-\boldsymbol{C H}_{3} \)
The above reaction proceeds via \( E_{1} c b \) mechanism?
A. It is second order and bumolecular
B. It is first order and unimolecular
c. It is first order an bimolecular
D. It is second order and unimolecular


If \( 15 \tan ^{2} \theta+4 \sec ^{2} \theta=23 \) then
\( \tan ^{2} \theta=\dots \)
A \( \cdot \frac{27}{15} \)
B. 45
\( c \cdot \frac{19}{11} \)
D.


Two point charges \( +q \) and \( -q \) are placed at a distance \( x \) apart. A third charge is placed in such a way so that all the three charges are in equilibrium.
Then :
A. unknown charge is \( -4 q / 9 \)
B. unknown charge is \( -9 q / 4 \)
c. it should be at \( (x / 3) \) from smaller charge between them
D. none of the above


Read the table and answer the question
below:
\( \begin{array}{llllll}\text { Elements } & \boldsymbol{A} & \boldsymbol{B} & \boldsymbol{C} & \boldsymbol{D} & \boldsymbol{E} \\ \begin{array}{l}\text { MASS } \\ \text { NO. }\end{array} & 1 & 7 & 14 & 40 & 40 \\ \begin{array}{l}\text { Atomic } \\ \text { No. }\end{array} & 1 & 3 & 7 & 18 & 20\end{array} \)


Three identical sphere each of mass \( M \)
are placed at the centre of a right angled triangle with mutually perpendicular sides equal to \( 2 m \) Taking their point of intersection on the origin, the position vector of the centre
of mass is:
\( \left.^{\mathrm{A}} \cdot \frac{2}{3}^{(\hat{\imath}}+\hat{j}\right) \)
B \( \cdot \frac{2}{3}(\hat{i}-\hat{j}) \)
c. Both A and B
D. None of the above


The direction cosines of the line
passing through \( \mathbf{P}(\mathbf{2}, \mathbf{3},-\mathbf{1}) \) and the origin are
A \( \cdot \frac{2}{\sqrt{14}}, \frac{3}{\sqrt{14}}, \frac{1}{\sqrt{14}} \)
B. \( \frac{2}{\sqrt{14}}, \frac{-3}{\sqrt{14}}, \frac{1}{\sqrt{14}} \)
c. \( \frac{-2}{\sqrt{14}}, \frac{-3}{\sqrt{14}}, \frac{1}{\sqrt{14}} \)
D. \( \frac{2}{\sqrt{14}}, \frac{-3}{\sqrt{14}}, \frac{-1}{\sqrt{14}} \)


Describe the estimation of nitrogen by
Dumas method.


If the distance between the sun and the
earth is increased by three times, then the gravitational force between the two will
A. remain constant
B. decrease by \( 63 \% \)
c. increase by \( 63 \% \)
D. decrease by \( 89 \% \)


Show that the family of curves for which \( \frac{d y}{d x}=\frac{x^{2}+y^{2}}{2 x y}, \) is given by \( x^{2}-y^{2}= \)
\( C X . \) differential equation is :


Assertion
A fair coin is being tossed four times. Consider the following events:
A is the event all four results are the
same.

B is the event exactly one Head occurs. \( \mathrm{C} \) is the event at least two Heads occur
\( \boldsymbol{P}(\boldsymbol{A})+\boldsymbol{P}(\boldsymbol{B})+\boldsymbol{P}(\boldsymbol{C})>1 \)
Reason
\( A, B \) and \( C \) are not Mutually Exclusive since events \( A \) and \( C \) have outcomes in
common.
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


Rhombic sulphur is the most stable allotropic form of sulphur.
A. True
B. False


Find the slope of a line passing through the following points:
\( (3-5) \) and (1,2)


The phase difference between two
waves represented by
\( \boldsymbol{y}_{1}=\mathbf{1 0}^{-6} \sin \left[\mathbf{1 0 0 t}+\frac{x}{50}+\mathbf{0 . 5}\right] \boldsymbol{m} \)
\( \boldsymbol{y}_{2}=\mathbf{1 0}^{-6} \cos \left[\mathbf{1 0 0} \boldsymbol{t}+\frac{\boldsymbol{x}}{50}\right] \boldsymbol{m} \)
where \( x \) is expressed in metres and t is expressed in seconds is approximately
A . 1.07 rad
B. 2.07 rad
c. 0.5 rad
D. 1.5 rad


When 2 moles of \( C_{2} H_{6}(g) \) are
completely burnt \( 3120 \mathrm{kJ} \) of heat is liberated. The enthalpy of
formation, of \( C_{2} H_{6}(g) \) in \( \mathrm{kJ} / \mathrm{mol} \) is \( \mathrm{X} \)
Then \( -X \) is

Given \( \Delta H \) for \( C O_{2}(g) \& H_{2} O(l) \) are
-395
\( \&-285 k J \) respectively


Three Mark Questions:
Women are often blamed for producing female children. Consequently they are ill treated and ostracized. How will you address this issue scientifically it you
were to conduct an awareness
programme to highlight the values
involved?


Of the following, the field of organic chemistry is LEAST concerned with the
study of
A. petroleum products
B. alloys
c. polymers
D. carbohydrates
E . alcohols


A number when divided by 114 leaves the remainder \( 21 . \) If the same number
is divided by 19 the remainder will be
A . 1
B . 2
\( c \cdot 7 \)
D. 21


Match List-I with List- II and select the
answer using the codes given below the
lists:
\begin{tabular}{lll|l}
List-I & \multicolumn{3}{l} { List-II } \\
A. & Microscope & 1. & To see objects on the surface by an observer in a trench \\
B. & Telescope & 2. & To see small objects \\
C. & Periscope & 3. & To see distant objects \\
D. & Camera & 4. & To take photographs of objects
\end{tabular}
\( A \)
\( \begin{array}{llll}2 & 1 & 4 & 3\end{array} \)
B. \( 1 \quad 2 \quad 3 \quad 4 \)
\( \begin{array}{llll}\mathbf{c} \cdot 2 & 3 & 4 & 1\end{array} \)
\( \begin{array}{ll}\text { D. } 2 & \text { (年) } 3\end{array} \)


Fill in the blank.
Keeping the surface area constant, if the force is doubled, pressure
A. remains same
B. become half
c. becomes double
D. becomes zero


Which of the following is a correct
statement?
A. Biogas contains \( 55 \% \) of nitrogen.
B. Producer gas contains \( 33 \% \) of carbon monoxide.
\( \mathrm{C} \cdot \mathrm{CO}_{2} \) is the major constituent in biogas and producer
gas.
D. None of the above


A convex lens of focal length \( 0.15 \mathrm{m} \) is
made of a material of refractive index 2
When it is placed in a liquid, its focal length increases by \( 0.225 m . \) The refractive index of the liquid is
A \( \cdot \frac{7}{4} \)
B. \( \frac{5}{4} \)
\( c \cdot \frac{9}{4} \)
D. \( \frac{3}{2} \)


the slowest to react the nitrosonium ion
\( \left(N O^{+}\right) ? \)
\( A \)
B.
\( c \)
D.


Discuss the relation between free
energy and EMF.


Powerful oxidizing agent is :
A. \( P_{2} O_{3} \)
в. \( \mathrm{HPO}_{3} \)
\( \mathrm{c} \cdot \mathrm{H}_{3} \mathrm{PO}_{4} \)
D. \( \mathrm{H}_{3} \mathrm{PO}_{2} \)


The reaction is given below, the rate constant for disappearance of A is
\( 7.48 \times 10^{-3} \)sec\( ^{-1} \). The time required for
the total pressure in a system containing \( A \) at an initial pressure of 0.1
atm to rise to 0.145 atm is:
\( \mathbf{2} \boldsymbol{A}(\boldsymbol{g}) \rightarrow \mathbf{4} \boldsymbol{B}(\boldsymbol{g})+\boldsymbol{C}(\boldsymbol{g}) \)
A. 0.80 min
B. 0.567 min
c. 0.433 min
D. 0.344 min


Two circular plates of radius \( 0.1 \mathrm{m} \) are used to form a parallel plate capacitor
if displacement current between the
plates is \( 2 \pi \) ampere, then find
magnetic field produced by
displacement current \( 4 \mathrm{cm} \) from the
axis of the plates.


Olecranon process is found in
A. Proximal end of ulna
B. Distal end of ulna
c. Proximal end of tibia
D. Proximal end of humerus


Evaluate \( \int_{0}^{2} 2 x d x \)


A plane mirror in \( y \) -z plane is moving
with -2i \( \mathrm{m} / \mathrm{s} \) as shown. The object shown
has velocity \( (3 i+j-4 k) m / s . \) What is
the velocity of the image?


In uniform circular motion the particle moves with a
A. Constant speed
B. Variable speed
c. constant acceleration
D. Variable acceleration


Write the IUPAC names of the given
compounds:


The graph shown in the figure represents a plot of current versus voltage for given semi-conductor Identify the region. if any, over which the semi-conductor has a negative
resistance


Moment of inertia of a thin rod of mass
\( M \) and length \( L \) about an axis passing through its center is \( \frac{M L^{2}}{12} . \) Its moment of inertia about a parallel axis at a distance of \( \frac{L}{4} \) from this axis is given by
A. \( \frac{M L^{2}}{48} \)
в. \( \frac{M L^{3}}{48} \)
c. \( \frac{M L^{2}}{12} \)
D. \( \frac{7 M L^{2}}{48} \)


Solve
\( \int \frac{x \cos ^{-1} x}{\sqrt{1-x^{2}}} d x \)


Source of solar energy is due to natural fusion in which hydrogen gets converted into helium with carbon
serving as a natural catalyst. This carbon cycle was proposed by
A. Bothe
B. Yukawa
c. Ferm
D. soddy


Find the area of the sheet required to make a cylindrical container which is open at one side and whose diameter is \( 28 \mathrm{cm} \) and height is \( 20 \mathrm{cm} \). find the approximate area of the sheet required to make a lid of height \( 2 \mathrm{cm} \) for this
container.


Find the length of the altitude of the
hypotenuse.
\( A \cdot 5.12 \)
3. 5.25
.5 .34
4
5.6


The sum of the oxidation number of the
carbon atoms in \( C H_{3} C H O \) is:
A . -2
B. +2
\( c .-4 \)
D. -


Cassiterite is concentrated by
Froth flotation process
2. Magnetic separation
3. Distillation method
4. Calcination method


A person can not see the distant objects clearly (though he can see the nearby object clearly). He is suffering from the
defect of vision called:
A. cataract
B. hypermetropia
c. myopia
D. presbyopia


A ball contains \( x \) white, \( y \) red, \( z \) blue
balls. A ball is drawn at the random
then, what is the probability of drawing
blue ball.


The reaction of the acid and the
produces carbon dioxide,
which causes dough and batters to rise.
A. baking soda
B. washing soda
c. sodium hydroxide
D. ammonium hydroxide


What is denoted by \( X \) and \( Y \) in the given
graph?
A. \( x \) -Activation energy without enzyme; Y-Activation energy with enzyme
B. X-Activation energy with enzyme; Y-Activation energy without enzyme.
c. \( x \) -substrate concentration with enzyme; \( Y \) - Substrate concentration without enzyme.
D. X-Substrate concentration without enzyme; YSubstrate concentration with enzyme.


\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}+\frac{1}{x}, \boldsymbol{x} \neq 0, \) then
A. \( f(x) \) has no point of local maxima
B. \( f(x) \) has no point local minima
C \( . f(x) \) has exactly has one point of local minima
D. \( f(x) \) has exactly has two point of local minima


Write \( (1+2 i) \cdot(1+3 i) \cdot(2+i)^{-1} \) in
the form \( (a+i b) \) and Find the square
roots of the given complex number \( (7+24 i) \)


What is the area of the circle whose
equation is \( (x-3)^{2}+(y+5)^{2}=18 ? \)
\( \mathbf{A} \cdot 9 \pi \)
B. \( 18 \pi \)
c. \( 72 \pi \)
D. \( 81 \pi \)
E . \( 324 \pi \)


Graphite is a good conductor of
electricity. Give reason


Which of the following is acidic?
\( A \cdot S O_{3} \)
в. \( N_{2} \),
\( c . B e O \)
D. \( H g O \)


Assertion: By roughening the surface of
a glass sheet its transparency can be
reduced.

Reason: Glass sheet with rough surface absorbs more light.
A. Both assertion and reason are true and reason is the correct explanation of assertion
B. Both assertion and reason are true but the reason is not the correct explanation of assertion
c. Assertion is true but reason is false
D. Both the assertion and reason are false
E. Reason is true but assertion is false


The capacitive reactance at \( 1600 \mathrm{Hz} \) is
\( 81 \Omega \).When the frequency is doubled then the capacitive reactance will be:
A . \( 40.5 \Omega \)
в. \( 81 \Omega \)
\( \mathbf{c} \cdot 162 \Omega \)
D. zero


Which of the following is/are correct
about blue per chromate?
This question has multiple correct options
A. It has two peroxide bonds.
B. It has four oxygen atoms having oxidation number -1.
C \( . \) It reacts with \( H_{2} S O_{4} \) to give oxygen
D. It acts as oxidant as well as reductant.


Underline the correct alternative:
(a) When a conservative force does
positive work on a body, the potential energy of the body increases decreases / remains unaltered.
(b) Work done by a body against friction always results in a loss of its kinetic / potential energy.
(c) The rate of change of total momentum of a many-particle system is proportional to the external force / sum of the internal forces on the system.
(d) In an inelastic collision of two
bodies, the quantities which do not change after the collision are the total kinetic energy / total linear momentum
/ total energy of the system of two bodies.


\( \lim _{x \rightarrow \frac{\pi}{2}} \frac{\left(\frac{\pi}{2}-x\right) \sec x}{\operatorname{cosec} x}= \)
\( A \)
B.
\( c \)
\( D \cdot \underline{1} \)


The equivalent capacitance between AB of the combination shown in figure is
\( A \)
B. 2C
\( c \cdot c / 2 \)
D. none of thes


Image formed by a plane mirror is:
This question has multiple correct options
A. of same size as that of object
B. at the same distance behind the mirror as the object in front
\( \mathbf{C} \). erect
D. real in nature


Express 120 as a product of prime factors


A uniform vertical electric field \( \boldsymbol{E} \) is
established in the space between two large parallel plates. A small conducting sphere of mass \( \boldsymbol{m} \) is suspended in the field from a string of
length \( L \). If the sphere is given \( a+q \) charge and the lower plate is charged positively, the period of oscillation of this pendulum is :
\( ^{\mathrm{A}} \cdot 2 \pi \sqrt{\frac{L}{g}} \)
в. \( 2 \pi \sqrt{\frac{L}{g+\frac{q E}{m}}} \)
c. \( _{2 \pi} \sqrt{\frac{L}{g-\frac{q E}{m}}} \)
D. \( 2 \pi \sqrt{\frac{L}{\left(g^{2}+\left(\frac{q E}{m}\right)^{2}\right)^{1 / 2}}} \)


Find the value of \( x \) in this equation:
\( \frac{392}{x}=-196 \)
\( A \cdot 2 \)
B. 4
\( c .-2 \)
D. -


How the eye of a person suffering from myopia can be corrected? Explain with the help of ray diagram.


Write condition under which a
bimolecular reaction is kinetically first order. Given an example of such a reaction.
(Given: \( \log 2=0.3010, \log 3= \)
\( \mathbf{0 . 4 7 7 1}, \log \mathbf{5}=\mathbf{0 . 6 9 9 0}) \)


A common emitter amplifier circuit,
built using an npn transistor, is shown
in the figure. Its dc current gain is
\( 250, R_{C}=1 k \Omega \) and \( V_{C E} \) to reach
saturation?
A. \( 100 \mu A \)
B. \( 7 \mu A \)
\( c .40 \mu A \)
D. \( 10 \mu A \)


The wavelength of radiation required to excite the electron from the first orbit to
the third orbit in a doubly ionized lithium atom will be
A \( .134 .25 \AA \)
В. \( 125.5 \AA \)
c. \( 113.7 \AA \)


A copper wire is held at the two ends
between two rigid supports. At \( 30^{\circ} \mathrm{C} \) the wire is just taut,with negligible tension. If \( \boldsymbol{Y}=\mathbf{1 3} \times \mathbf{1 0}^{\mathbf{1 1}} \mathbf{N m}^{-\mathbf{2}}, \boldsymbol{\alpha}= \)
\( 1.7 \times 10^{-5}\left(^{\circ} C\right)^{-1} \) and density \( \rho=9 \times \)
\( 10^{3} k g m^{-3}, \) then the speed of
transverse wave in this wire at \( 10^{\circ} \mathrm{C} \) is:
A \( \cdot 90 m s^{-1} \)
B. \( 70 m s^{-1} \)
\( \mathrm{c} \cdot 60 \mathrm{ms}^{-1} \)
D. \( 100 \mathrm{ms}^{-1} \)


Which of the following would be different in a ground state and in excited state of neon atom?
A. The number of neutrons
B. The number of electrons
c. The atomic weight
D. The electronic configuration
E. Everything would remain the same


Which of the following is not a combustible substance?
A. Camphor
B. Glass
c. Straw
D. Alcohol


The value of the term independent of
\( x \) in the expansion of \( \left(x^{2}-\frac{1}{x}\right)^{27} \) is :
\( \mathbf{A} \cdot \mathbf{9} \)
B. 18
c. 48
D. 84


Charge \( 2 Q \) and \( -Q \) are placed as shown in figure. The point at which electric field
intensity is zero will be somewhere:
A. Between-Q and 20
B. On the left of - \( Q \)
c. on the right of 2 Q
D. on the perpendicular bisector of line joining the charges


Calculate the freezing point of a solution containing \( 60 g \) of glucose
(Molar mass \( =180 g \) mol \( ^{-1} \) ) in \( 250 g \) of
water
\( \left(K f \text { of water }=1.86 K k g m o l^{-1}\right) \)


A bag contains 4 white balls and some red balls if the probability of of drawing a white ball from the bag is \( \frac{2}{5} \) Find the number of red balls in the bag
\( A \cdot 2 \)
B. 4
\( c \cdot 8 \)
D. 6


Which one of the following types of medicines is used for treating indigestion?
A. Antibiotic
B. Analgesic
c. Antacid
D. Antispetic


Why are carbon compounds so large in numbers?
A. Because of the study in the field.
B. Because of the property of catenation (self linking) of the carbon.
C. Both of \( A \) and \( B \).
D. Because of its affinity to hydrogen.


Two cars start off to race with velocities
\( 4 m / s \) and \( 2 m / s \) and travel in straight line with uniform accelerations \( 1 m / s^{2} \) and \( 2 m / s^{2} \) respectively. If they reach the final point at the same instant, then
the length of the path is
A . \( 30 m \)
B. \( 32 m \)
c. \( 20 m \)
D. \( 24 m \)


\( \int(\sin x \cdot \sin 3 x \cdot \cos 2 x) d x \)


What is the name of disaccharides
sugar present in milk?


Equations of motion in the same
direction is given by \( \boldsymbol{y}_{1}=\boldsymbol{A} \sin (\boldsymbol{\omega} \boldsymbol{t}-\boldsymbol{k} \boldsymbol{x}), \boldsymbol{y}_{2}=\boldsymbol{A} \sin (\boldsymbol{\omega} \boldsymbol{t}- \)
\( k x-\theta) . \) The amplitude of the medium
particle will be
A. \( \sqrt{2} A \cos \theta \)
B. \( 2 A \cos \theta \)
c. \( \sqrt{2} A \cos \frac{\theta}{2} \)
D. \( 2 A \cos \frac{\theta}{2} \)


Which of the following is the subaerial stem modification with long internodes?
A. Rhizome
B. Offset
c. Runner
D. sucker


Check the injectivity and surjectivity of the function \( \boldsymbol{f}: \boldsymbol{N} \rightarrow \boldsymbol{N} \) given by
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2} \)


Draw a triangle \( A B C \) with side \( B C= \)
\( \mathbf{6} c \boldsymbol{m}, \boldsymbol{A} \boldsymbol{B}=\mathbf{5} \boldsymbol{c m} \) and \( \angle \boldsymbol{A} \boldsymbol{B} \boldsymbol{C}=\mathbf{6 0}^{\boldsymbol{o}} \)
Then construct a triangle whose sides
\( \operatorname{are} \frac{3}{4} \) of the corresponding sides of the triangle \( \boldsymbol{A B C} \)


A rectangular coil \( 3 \times 3 \mathrm{cm} \) consisting of
100 turns caries 0.1 A. If it produces a
deflection \( 10^{0}, \) in a field of induction
\( 0.1 T, \) the couple per unit twist is
A \( \cdot 9 \times 10^{-2} \mathrm{Nm} / \) Degree
B. \( 9 \times 10^{-5} \mathrm{Nm} / \) Degree
C. \( 9 \times 10^{-2} \mathrm{Nm} / \mathrm{rad} \)
D. \( 0.9 \mathrm{Nm} / \) Degree


If \( f^{\prime}(x)=x+\frac{1}{x}, \) then value of \( f(x) \) is
A \( \cdot x^{2}+\log x+c \)
в. \( \frac{x^{2}}{2}+\log x+c \)
c. \( \frac{x}{2}+\log x+c \)
D. None of these


The van't Hoff factor of the benzoic acid
solution in benzene is \( 0.5 . \) In this
solution, benzoic acid:
A. dissociates
B. forms dimer
c. remains unchanged
D. forms tetramer


A spherical soap bubble of radius \( 1 \mathrm{cm} \)
is formed inside another soap bubble of
radius \( 3 c m . \) The radius of a single soap
bubble which maintains the same
pressure difference as inside the
smaller and outside the larger soap
bubble as
A . \( 0.75 \mathrm{cm} \)
B. \( 0.75 m \)
c. \( 7.5 \mathrm{cm} \)
D. \( 7.5 \mathrm{m} \)


State True or False.
Salt bridge is used to eliminate liquid
junction potential.
A. True
B. False


Find a unit vector in direction of \( \overrightarrow{\boldsymbol{A}}= \) \( \mathbf{5} \hat{\mathbf{i}}+\hat{\boldsymbol{j}}-\mathbf{2} \boldsymbol{k} \)


\( G_{0} \) state of cell denotes
A. Death of cell
B. Permanent pause
c. Exit of cell from cell cycle
D. Check point before entering the next phase


The best vital force theory was proposed
by
A . Godlewski
B. Strasburger
c. Dixon
D. Esau


A silver wire dipped in \( 0.1 \mathrm{M} \mathrm{HCl} \) solution saturated with AgCl develops a potential -0.25V. If \( E^{0}_{A g / A g^{+}}= \)
\( -0.799 V, K_{S P} \) of AgCl in pure water will
be
A \( .2 .95 \times 10^{-11} \)
B . \( 5.30 \times 10^{-11} \)
c. \( 3.95 \times 10^{-11} \)
D. \( 1.95 \times 10^{-11} \)


Cryolite is :
A. Sodium aluminium fluoride
B. Magnesium silicate
C. Calcium Magnesium Carbonate
D. Sodium borofluoride


The structure and hybridization of
\( \boldsymbol{S} \boldsymbol{i}\left(\boldsymbol{C} \boldsymbol{H}_{3}\right)_{4} \) respectively, is:
A. bent and \( s p \)
B. trigonal and \( s p^{2} \)
c. octahedral and \( s p^{3} d \)
D. tetrahedral and \( s p^{3} \)


The ratio of distance traversed in
successive intervals of time when a
body falls freely under gravity from certain height is
A. 1: 2: 3
B. 1: 5: 9
\( \mathrm{c} \cdot 1: 3: 5 \)
D. \( \sqrt{1}: \sqrt{2}: \sqrt{3} \)
E. 1: 4: 9


There are two candidates Bhiku and
Mhatre for an election. Bhiku gets \( 65 \% \) of the total valid votes. If the total votes
were \( 6000, \) what is the number of valid votes that the other candidate Mhatre
gets if \( 25 \% \) of the total votes were
declared invalid?
A. 1575
в. 1625
\( c .1675 \)
D. 1525


The points of intersection of the curves
\( |z-3|=2 \) and \( |z|=2 \) in an argand
plane are
\( \mathbf{A} \cdot \frac{1}{2}(3 \pm i \sqrt{7}) \)
B \( \cdot \frac{1}{2}(3 \pm i \sqrt{3}) \)
c. \( \frac{3}{2} \pm i \sqrt{\frac{7}{2}} \)
D \( \cdot \frac{7}{2} \pm i \sqrt{\frac{3}{2}} \) )


Who reported the presence of
associative nitrogen fixing bacteria with the roots of maize plants?
A. P. K. De
B. G. C. Fogg
c. J. Doberiner
D. N.J. Borlaug


In a transverse wave, the particles of the
medium
A. vibrate in a direction perpendicular to the direction of the propagation.
B. vibrate in a direction parallel to the direction of the propagation.
C. move in circle.
D. move in ellipse.


Find the last digit of \( 1^{5}+2^{5}+\ldots+99^{5} \)


Hybridization on carbon atoms in
diamond is :
\( A \cdot s p \)
B \( \cdot s p^{2} \)
\( c \cdot s p^{3} \)
D. \( s p^{3} d \)


Evaluate: \( \int_{-2}^{3} \frac{1}{x+5} d x \)


In solving an equation of the form \( a x+ \)
\( b=0 \) (a,b having only 1 as the common factor \( ), A \) made a mistake in copying \( b \) and \( \operatorname{got} \frac{7}{3} \) as the root whereas \( B \) made a mistake in copying \( a \) and \( \operatorname{got} \frac{8}{5} \) as the
root. The correct root is
\( A \cdot \frac{7}{5} \)
B. \( \frac{3}{8} \)
\( c \cdot \frac{8}{3} \)
D. \( \frac{8}{5} \)


Chord \( A B \) of the circle \( x^{2}+y^{2}=100 \)
passes through the point (7,1) and
subtends an angle of \( 60^{\circ} \) at the
circumference of the circle. If \( m_{1} \) and
\( m_{2} \) are the slopes of two such chords
then the value of \( m_{1} m_{2}, \) is
A . -1
B. 1
c. \( \frac{7}{12} \)
D. - 3


Which term is the best match for the
color of a chemical substance students
make note of:
A . qualitative data
B. inference
c. observation
D. quantitative data
E. hypothesis


The biggest drawback of tidal energy is:
A. it causes excessive pollution in oceans
B. locations where it can be harnessed are limited
c. the height difference of tides is low and much energy is not produced
D. it needs a lot of manpower


Find the quotient and remainder when \( x^{5}-5 x^{4}+9 x^{3}-6 x^{2}-16 x+13 \) is
divided by \( x^{2}-3 x+2 \)


Find the derivative of tan \( x \) using first principle of derivatives


If \( f(x)=12 x^{5} \) and \( g(x)=-3 x^{2} \)
determine \( (\boldsymbol{f} \cdot \boldsymbol{g})(-1) \)
\( [\text {Given }:(\boldsymbol{f} \cdot \boldsymbol{g})(\boldsymbol{x})=\boldsymbol{f}(\boldsymbol{x}) \cdot \boldsymbol{g}(\boldsymbol{x})] \)
A . 36
B . 42
\( c \cdot 32 \)
D. -36


Which of the following is not a connecting tissue?
A. Blood
B. Bone
c. Lymph
D. Nerve


Which of the following contains both covalent and ionic bonds:
A \( \cdot C C I_{4} \)
в. \( C a C I_{2} \)
c. \( N H_{4} C I \)
D. \( H_{2} O \)


Read the following five statements to \( \mathrm{E} \) ) and select the option with all
correct statements.
(A) Mosses and Lichens are the first
organisms to colonize bare rock.
(B) Selaginella is a homosporous
pteridophyte.
(C) Coralloid roots in Cycas have VAM.
(D) The main plant body in bryophytes is gametophytic whereas in pteridophytes it is sporophytic.
(E) In gymnosperms, male and female gametophytes are present within
sporangia located on sporophyte.
\( A \cdot(A),(D) \) and \( (E) \)
B. \( (B),(C) \) and \( (D) \)
c. \( (A),(C) \) and \( (D) \)
D. None of these


Which of the following is a point source
of water pollution?
A. Industries
B. Power plants
c. coal mines
D. All of the above


"BOD is commonly calculated as an index of water pollution."
(a) Do you agree with this statement? Why?
(b) Expand BOD.


Find the area of region lying between parabolas \( y^{2}=4 a x \& x^{2}=4 a y \) where \( a> \)
0


A man borrows Rs. 12500 from a bank at
\( 20 \% \) compound interest. At the end of every year, he pays Rs. 2000 as part repayment. How much does he still owe to the bank after three such instalments?
A. Rs. 15600
B. Rs. 12864
c. Rs. 12000
D. Rs. 14320


Integrate \( \frac{\tan ^{4} \sqrt{x}+\sec ^{2} \sqrt{x}}{\sqrt{x}} \)
The solution is \( \frac{2 \tan ^{3}(\sqrt{x})}{m}- \)
\( 2 \tan \sqrt{x}+2 \sqrt{x}+2 \tan \sqrt{x}+C . \) Find \( m \)


The Cartesian product \( \boldsymbol{P} \times \boldsymbol{P} \) has 16
elements among which two elements \( \operatorname{are}(a, b) \) and \( (c, d) . \) Find the set \( P \) and
the remaining elements of \( \boldsymbol{P} \times \boldsymbol{P} \)


Compare the potential energy and
kinetic energy of electrons in the 1 st
orbits of hydrogen and \( \boldsymbol{H} e^{+} \) ion.


A line passes through \( \left(x_{1}, y_{1}\right) \) and \( (h, k) \)
If slope of the line is \( m \), show that \( k- \)
\( \boldsymbol{y}_{1}=\boldsymbol{m}\left(\boldsymbol{h}-\boldsymbol{x}_{1}\right) \)


Mean deviation of the observations 70
42,63,34,44,54,55,46,38,48 from
median is
A . 7.8
B. 8.6
\( c .7 .6 \)
D. 8.8


What is the tension in string B?
A. \( \frac{3 m g}{5} \)
в. \( \frac{m g}{5} \)
c. \( \frac{6 m g}{5} \)
D. \( \frac{4 m g}{5} \)


On Friedel-Crafts acetylation, anisole
yields:
A. 2-methoxyacetophenone
B. 4-methoxyacetophenone
c. both (a) and (b)
D. none of the above


Two plane mirrors are inclined at an
angle \( \theta \) as shown. If at an angle \( 45^{\circ} \) the
final ray horizontal, then find angle \( \theta \)


The primary valency of a central metal ion in a complex is satisfied with


Total sales of branches \( B_{1}, B_{3}, \) and \( B_{5} \)
together for both the years (in
thousand numbers) is:
\( A \cdot 250 \)
3. 310
\( c .435 \)
0.560


For a given reaction, energy of
activation for forward reaction
\( \left(\boldsymbol{E}_{\boldsymbol{a} f}\right) \boldsymbol{i s} \boldsymbol{8 0 k} \boldsymbol{J} \cdot \boldsymbol{m o l}^{-1} \cdot \boldsymbol{\Delta} \boldsymbol{H}= \)
\( -40 k J . \) mol \( ^{-1} \) for the reaction. \( A \)
catalyst lowers \( E_{a f} \) to \( 20 k J . m o l^{-1} \) Find out the ratio of energy of activation for reverse reaction before and after
addition of catalyst.


A particle performs S.H.M of amplitude A along a straight line. When it is at a
distance \( \frac{\sqrt{3}}{2} A \) from mean position, its kinetic energy gets increased by an amount \( \frac{1}{2} m \omega^{2} A^{2} \) due to an impulsive force. Then its new amplitude becomes.
A. \( \frac{\sqrt{5}}{2} \)
B. \( \frac{\sqrt{3}}{2} \) A
c. \( \sqrt{2} \mathrm{A} \)
D. \( \sqrt{5} \mathrm{A} \)


Kohlrausch's Law states that at:
A. infinite dilution, each ion makes the definite contribution to the conductance of an electrolyte whatever be the nature of the other ion of the electrolyte.
B. infinite dilution, each ion makes a definite contribution to an equivalent conductance of an electrolyte whatever be the nature of the other ion of the electrolyte.
C. finite dilution, each ion makes the definite contribution to an equivalent conductance of an electrolyte whatever be the nature of the other ion of the electrolyte.
D. infinite dilution each ion makes the definite
contribution to an equivalent conductance of an electrolyte depending on the nature of the other ion of the electrolyte.


Choose the correct answer from the
alternatives givens. Which type of the following tissues forms the inner lining of a blood vessel?
A. Epithelial
B. Connective
c. Nervous
D. Muscular


\( H_{2}-O_{2} \) fuel cell is:
A. primary cell
B. secondary cell
\( c \cdot \) both
D. cant be predicted


Which of the respective orders are
correct?
This question has multiple correct options
\( \mathbf{A} \cdot N H_{3}>S b H_{3}>A s H_{3}>P H_{3}: \) Thermal stability
order
B. Liquid hydrogen <liquid helium: boiling point order
\( \mathbf{c} \cdot B e C O_{3}>S r C O_{3}>B a C O_{3}: k_{p} \) value order during
their thermal dissociation in closed container
\( \mathrm{D} \cdot \mathrm{O}_{2}>\mathrm{K} \mathrm{O}_{2}>\mathrm{K}_{2} \mathrm{O}_{2}: \) Magnetic moment order


When did the Indian National
Committee for Space Research form?
A. October 1960
B. November 1962
c. october 1962
D. November 1960


If \( \vec{P} \) is directly vertically upwards and \( \vec{Q} \) is directed towards north then direction of \( \vec{P} \times \vec{Q} \) vector is directed towards:
A. west
B. South
c. East
D. south west


An atom of an element has one electron
in the valence shell and the two inner
shells have 8 electrons each. Find the
atomic number of that element.


The osmotic pressure of a \( 5 \% \) solution of cane sugar (molecular mass 342 ) at
\( 15^{\circ} C \) is:
\( A \cdot 3.46 \) atm
B. 3.64 atm
c. 4.0 atm
D. 2.45 atm


Why is Hydrogen placed in group \( I \) of the modern periodic table ?


Which of the following is a
proper fraction?
\( A \)
B.
\( c \)
D. All the above


A particle of mass \( \mathrm{m} \) and charge \( \boldsymbol{q} \) is thrown in a region where uniform gravitational field and electric field are present. The path of particle :
This question has multiple correct options
A. may be straight line
B. may be a circle
c. may be a parabola
D. may be a hyperbola


The atomic number of an element is
more important to the chemist than its relative atomic mass. Why?


Which of the following reactions is called Rosenmund reaction?
A. Aldehydes are reduced to alcohols
B. Acids are converted to acid chlorides
c. Alcohols are reduced to hydrocarbons
D. Acid chloride are reduced to aldehydes


Which of the following behaves as both oxidizing and reducing agents?
A. \( H_{2} S O_{4} \)
в. \( S O_{2} \)
c. \( H_{2} \)
D. \( H N O_{3} \)


Which of the following hydrolysis product is not common in hydrolysis of
\( X e F_{2} \) and \( X e F_{4} \) respectively?
This question has multiple correct options
A. \( X e O_{3} \)
в. \( H F \)
\( c \cdot X e \)
D. \( O_{2} \)


Matter can be defined as something
that:
A. Occupies space
B. Has mass
c. Exists in three states
D. All of the above


A wave of frequency 500 Hz has a wave velocity of \( 350 \mathrm{m} / \mathrm{s} \). The distance
between two points which point are \( 60^{\circ} \)
out of phase is \( 116 \times 10^{-x} m . \) Find \( x \)


If \( A^{\prime} \) s income is \( 30 \% \) less than \( B^{\prime} s \)
then how much per cent is \( B^{\prime} \) s income
more than \( A^{\prime} \) s?
A \( 42 \frac{6}{7} \% \)
в. \( 32 \frac{1}{10} \% \)
c. \( 30 \% \)
D. \( 40 \% \)


Mass of the earth is:
A \( \cdot \frac{4}{3} \pi R^{3}(A-B R) \)
B \( \cdot 4 \pi R^{3}(A-B R) \)
\( ^{\mathbf{C}} \cdot \frac{4}{3} \pi R^{3}\left(A-\frac{3}{4} B R\right) \)
D \( \cdot 4 \pi R^{3}\left(A-\frac{3}{4} B R\right) \)


An element 'X' is yellow coloured solid, insoluble in water but soluble in carbon disulphide. It has a low melting point
\( 114.5^{\circ} \mathrm{C} . \) It boils at \( 445^{\circ} \mathrm{C} \) and it burns
with pale blue flame forming pungent smelling gas 'Y' which turns moist blue litmus red and finally colourless.'X' and
'Y' are:
A \( \cdot C, C O_{2} \)
в. \( N, N O_{2} \)
\( c \cdot S, S O_{2} \)
D. \( I_{2}, I_{2} O_{5} \)


In an acute angled triangle \( A B C, A P \) is
the altitude. Circle drawn with AP as its
diameter cuts the sides \( A B \) and \( A C \) at \( D \)
and \( \mathrm{E} \), respectively, then length DE is equal to
A \( \cdot \frac{\Delta}{2 R} \)
в. \( \frac{\Delta}{3 R} \)
c. \( \frac{\Delta}{4 R} \)
D. \( \frac{\Delta}{R} \)


An electric bulb is marked \( 100 \mathrm{W}, 230 \mathrm{V} \)
If the supply voltage drops to \( 115 V \), what will be the total heat and light energy,
total liberated by the bulb in 20 minutes?


Considering the elements \( F, C I, O \) and \( N \) the correct order of their chemical
reactivity in terms of oxidizing property is:
\( (a) F>C \mid>0>N \)
\( (b) F>0>C l>N \)
\( (c) C \mid>F>0>N \)
\( (d) O>F>N>C l \)


The motion of a particle is described by the equation \( \boldsymbol{x}=\boldsymbol{a}+\boldsymbol{b} \boldsymbol{t}^{2} \) where \( \boldsymbol{a}= \)
\( 15 \mathrm{cm} \) and \( b=3 \mathrm{cm} / \mathrm{sec}^{2} . \) Its
instantaneous velocity at time 3 sec
will be:
A. \( 36 \mathrm{cm} / \mathrm{sec} \)
B. \( 1 \mathrm{cm} / \mathrm{sec} \)
c. \( 18 \mathrm{cm} / \mathrm{sec} \)
D. \( 32 \mathrm{cm} / \mathrm{sec} \)


In earthworm, neurons are
A. Sensory
B. Motor
c. Mixed
D. None of these


An electric meter reads 8950 KWh at
the end of the month,while at the
beginning of the month the reading was
\( 8833 \mathrm{KWh} \). How many units of electricity are consumed? If one unit
\( \operatorname{costs} \) Rs. \( 4.30, \) find the cost of the
electrical energy consumed


Solve graphically the pair of equations \( x+3 y=6, \) and \( 3 x-5 y=18 . \) Hence
find the value of \( \boldsymbol{K} \) if \( \mathbf{7} \boldsymbol{x}+\mathbf{3} \boldsymbol{y}=\boldsymbol{K} \)
A. \( x=-3, y=1, K=13 \)
В. \( x=-8, y=5, K=8 \)
c. \( x=1, y=2, K=29 \)
D. \( x=6, y=0, K=42 \)


\( \lim _{x \rightarrow o}\left(\frac{1}{x^{2}}-\cot x\right) \)


Which pair of polymers have similar properties?
A. Nylon, \( P V C \)
в. \( P A N, P T F E \)
c. \( P C T F E, P T F E \)
D. Bakelite, alkyle resin


How fossil fuels are formed:
A. Formed from remains of dead plants and animals under the earth
B. Formed from remains of living plants and animals under the earth
C. Formed from charcoal
D. None


Under what conditions of temperature and pressure, the formation of molecular hydrogen from atomic hydrogen will be favoured most?
A. High temperature and high pressure
B. Low temperature and low pressure
c. High temperature and low pressure
D. Low temperature and high pressure


Two bodies of equal weight are kept at heights of \( h \) and \( 1.5 h \) respectively. The
ratio of their P.E. is:
\( A \cdot 3: 2 \)
B. 2: 3
c. 1: 1
D. None of these


Find the angle of inclination of straight line whose slope is \( \frac{1}{\sqrt{3}} \)


Between \( T i^{2+} \) and \( V^{2+} \) which ion
contains more number of unpaired electrons?


At the corners of an equilateral triangle
of side a \( (1 \text { metre }), \) three point charges
are placed (each of \( 0.1 C \) ). If this
system is supplied energy at the rate of
1 kw, then calculate the time required
to move one of the mid-point of the line
joining the other two.
A . \( 50 h \)
B. \( 60 h \)
\( \mathbf{c} \cdot 48 h \)
\( \mathbf{D} \cdot 54 h \)


Extent of a reaction can always be increased by increasing the temperature.
A. True
B. False


Fluid within the loop of Henle is
concentrated in the
A. Descending limb
B. Thick ascending duct
c. Hairpin bend between descending and ascending \( \operatorname{limbs} \)
D. Bend between the ascending limb and the distal tubule


Which of the following is the best method to measure microscopic distances?
A. optical microscope
B. Meter scale
c. screw gauge
D. Diffraction pattern


Find the number of zeroes of the
quadratic \( x^{2}+7 x+10 \) and verify the
relationship between the zeroes and the the co-efficients.


The inductance is measured in
A. ohm
B. farad
c. henery
D. none of these


In the ethylene molecule the two carbon atoms have the oxidation numbers.
A . -1,-1
в. -2,-2
c. -1,-2
D. +2,-2


When a coil is moved or rotated relative
a fixed magnet then
A. voltage increased
B. current is induced
\( c . \) both
D. voltage is induced


An electric dipole is along a uniform
electric field. If it is deflected by \( 60^{\circ} \)
work done by the agent is \( 2 \times 10^{-19} J \)
Then the work done by an agent if it is
deflected by \( 30^{\circ} \) further is:
A \( \cdot 2.5 \times 10^{-19} \mathrm{J} \)
В. \( 2 \times 10^{-19} J \)
c. \( 4 \times 10^{-19} \mathrm{J} \)
D. \( 2 \times 10^{-16} J \)


A mark placed on the surface of a sphere is viewed through glass from a position directly opposite. If the diameter of the sphere is \( 10 \mathrm{cm} \) and refractive index of glass is \( 1.5 . \) The position of the image will be :
\( A .-20 \mathrm{cm} \)
B. 30 cm
c. \( 40 \mathrm{cm} \)
D. -10 cm


Choose the correct statements among
the following given options.
A. Brewster's angle is independent of wavelength of light.
B. Brewster's angle is independent of the nature of reflecting surface.
C. Brewster's angle is different for different wavelengths.
D. Brewsters angle depends on wavelength but not on the nature of reflecting surface.


The North pole of a magnet is brought near a negatively charged conductor.
A. Force acting on the pole will be zero
B. Force acting on the pole will be maximum.
c. Force acting on the pole will be minimum.
D. none


The order of the differential equation \( 2 x^{2} \frac{d^{2} y}{d x^{2}}-3 \frac{d y}{d x}+y=0 \)
A . 2
B.
\( c \cdot 0 \)
D. Not defined


State to which quadrant does the following points belong:
\( D(-3,2) \)


Some salts although containing two different metallic elements give test for only one of them in solution. Such salts
are:
A. complexes
B. double salts
c. normal salts
D. both \( A \) and \( B \)


An ideal gas is that which
A. Cannot be liquified
B. Can be easily liquified
C. Has strong inter molecular forces
D. Has a large size of molecules


Write the value of \( \cot ^{-1}(-x) \) for all \( x \epsilon R \)
in terms of \( \cot ^{-1} x \)


Find the angle between the vectors \( \vec{a} \) and \( \vec{b} \) with magnitude \( \sqrt{3} \) and 2 respectively and \( \overrightarrow{\boldsymbol{a}} \cdot \overrightarrow{\boldsymbol{b}}=\sqrt{\mathbf{6}} \)


Two blocks, one of iron(i) and the other
of wood(w) are dropped from a height at the same time. If the time taken by the
blocks to reach the ground is \( T_{i} \) and \( T_{w} \) respectively, then find the relation
between them?
A \( . T_{i}<T_{w} \)
в. \( T_{i}=T_{w} \)
c. \( T_{i}>T_{w} \)
D. \( T_{i}=\frac{1}{2 T_{w}} \)


The efficiency of a full wave rectifier is?
A. Half of half wave rectifier
B. 3 times of half wave rectifier
C. Double of half wave rectifier
D. Same as half wave rectifier


During electrolysis, cations move towards the positive terminal.
A. True
B. False


Metals found in a combined state in the
earth's crust are known as:
A. native metal
B. minerals
c. metalloids
D. semi pure


\( 1 W h(\text { Watt hour }) \) is equal to
A. \( 36 \times 10^{5} J \)
B. \( 36 \times 10^{4} J \)
c. \( 3600 J \)
D. \( 3600 J s^{-1} \)


Metal \( A \) has electronic configuration of
2,8,1 and metal \( B \) has electronic
configuration of 2,8,2 Identify these metals:


Fidn the \( 7^{t h} \) term from the end in the
expansion of \( \left(9 x-\frac{1}{3 \sqrt{x}}\right)^{18}, x \neq 0 \)


What is the 25 th digit to the right of the decimal point in the decimal form of \( \frac{\mathbf{6}}{\mathbf{1 1}} \)
\( ? \)
A . 3
B. 4
c. 5
D. 6
E. 7


The block of mass \( m_{2}=10 \mathrm{kg} \) is given
a sharp impulse so that it acquires a velocity \( v_{0}=30 m / s \) towards right. Find the velocity of the centre of mass.
\[
\left.\boldsymbol{m}_{2}=\mathbf{5} \boldsymbol{k} \boldsymbol{g} \text { and } \boldsymbol{k}=\boldsymbol{3 0} \boldsymbol{N} / \boldsymbol{m}\right)
\]
A. \( 5 \mathrm{m} / \mathrm{s} \)
в. \( 10 \mathrm{m} / \mathrm{s} \)
c. \( 15 \mathrm{m} / \mathrm{s} \)
D. 20 \( m / s \)


Which group elements are called
carbon family?


Calculate the ratio of degree of
dissociation \( (a) \) when \( 1 ~ M \) acetic acid solution is diluted to times.
\( \left[\text { Given: } \boldsymbol{K}_{\boldsymbol{p}}=\mathbf{1 . 8} \times \mathbf{1 0}^{-\mathbf{3}}\right] \)


The helical structures of nucleic acids
can be studied by using:
A. Interference phenomenon
B. Diffraction pattern
C. Polarised light
D. Photoelectric effect


A body of mass \( 1 / 4 \mathrm{kg} \) is in S.H.M and its displacement is given by the relation \( \boldsymbol{y}=\mathbf{0 . 0 5 \operatorname { s i n }}\left(\mathbf{2 0 t}+\frac{\boldsymbol{\pi}}{\mathbf{2}}\right) \mathrm{m} . \) If \( \boldsymbol{t} \) is in
seconds, the maximum force acting on the particle is:
A . 5 N
B. 2.5 N
c. 10 N
D. 0.25 N


\( \sec ^{2}\left(\tan ^{-1} 2\right)+\operatorname{cosec}^{2}\left(\cot ^{-1} 3\right)= \)
A. 5
B. 10
c. 15
D. 20


The temperature of a furnace is \( 2327^{\circ} \mathrm{C} \)
and the intensity of maximum in its spectrum is nearly at 12000 A. If the intensity in the spectrum of a star is maximum nearly at 4800 A, then the surface temperature of the star is
\( \mathbf{A} \cdot 767^{\circ} C \)
в. \( 1040^{\circ} \mathrm{C} \)
c. \( 6500^{\circ} \mathrm{C} \)
D. \( 6227^{\circ} \mathrm{C} \)


Which of the following reactions have
\( \boldsymbol{K}_{\boldsymbol{p}}<\boldsymbol{K}_{\boldsymbol{c}} \)
This question has multiple correct options
A \( \cdot H_{2}(g)+I_{2}(g) \rightleftharpoons 2 H I(g) \)
в. \( C O(g)+C l_{2}(g) \rightleftharpoons C O C l_{2}(g) \)
c. \( 2 B r C l(g) \rightleftharpoons B r_{2}(g)+C l_{2}(g) \)
D. \( N_{2}(g)+3 H_{2}(g) \rightleftharpoons 2 N H_{3}(g) \)


The height above the surface of earth at which acceleration due to gravity is half the acceleration due to gravity at
surface of earth is \( \left(R=6.4 \times 10^{6} m\right) \)
A \( \cdot 6.4 \times 10^{6} m \)
В. \( 2.6 \times 10^{6} \mathrm{m} \)
c. \( 12.8 \times 10^{6} m \)
D. \( 19.2 \times 10^{6} \mathrm{m} \)


If the velocity of a particle is given by \( \boldsymbol{v}=(\mathbf{1 8 0 1 6 x})^{\frac{1}{2}} \boldsymbol{m} / \boldsymbol{s}, \) then the
acceleration is
A. \( -4 m / s^{2} \)
B. \( 8 m / s^{2} \)
\( \mathbf{c} \cdot-8 m / s^{2} \)
D. \( 4 m / s^{2} \)


Let \( A \) and \( B \) be square matrices of the
other \( 3 \times 3 . \) Is \( (A B)^{2}=A^{2} B^{2} ? \) Give
reasons.


\( \boldsymbol{a}=\mathbf{2} \overline{\mathbf{i}}+\overline{\boldsymbol{k}}, \overline{\boldsymbol{b}}=\mathbf{3} \overline{\boldsymbol{j}}+\mathbf{4} \overline{\boldsymbol{k}}, \overline{\boldsymbol{c}}=\mathbf{8} \overline{\mathbf{i}}-\mathbf{3} \overline{\boldsymbol{j}} \)
and \( \bar{a} \) is expressed as a linear combination of \( \bar{b} \) and \( \bar{c} \) then \( \bar{a}= \)
A \( \cdot \frac{1}{2}(\bar{b}+\bar{c}) \)
B \( \cdot \frac{1}{3}(\bar{b}+\bar{c}) \)
c. \( \frac{1}{4}(\bar{b}+\bar{c}) \)
D. \( \frac{1}{4}(\bar{b}-\bar{c}) \)


If \( \boldsymbol{A}=\left[\boldsymbol{a}_{i j}\right] \) and \( \boldsymbol{a}_{i j}=\boldsymbol{i}(\boldsymbol{i}+\boldsymbol{j}) \) then
trace of \( \boldsymbol{A}= \)
A \( \cdot \frac{n(n+1)(2 n+1)}{6} \)
B. \( \frac{n(n+1)(2 n+1)}{3} \)
c. \( \frac{n(n+1)}{2} \)
D. \( \frac{n^{2}(n+1)^{2}}{4} \)


A cylinder of length \( L \) and radius b has
its axis coincident with the x-axis. The
electric field in this region is \( \overrightarrow{\boldsymbol{E}}=\mathbf{2 0 0 \hat { \boldsymbol { i } }} \)
Find the flux through the left end of cylinder.
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( 200 \pi b^{2} \)
c. \( 100 \pi b^{2} \)
D. \( -200 \pi b^{2} \)


A \( 44 \mathrm{mH} \) inductor is connected to \( 220 \mathrm{V} \)
\( 50 \mathrm{Hz} \) ac supply. Determine the rms value of the current in the circuit.


The equation of a plane progressive wave is \( \boldsymbol{y}=\mathbf{0 . 9} \sin \mathbf{4} \boldsymbol{\pi}\left[\boldsymbol{t}-\frac{\boldsymbol{x}}{\mathbf{2}}\right], \) when it is
reflected at a rigid support, its amplitude becomes \( 2 / 3 \) of its previous value. The equation of the reflected wave is :
A \( \cdot y=0.9 \sin 4 \pi\left[t+\frac{x}{2}\right. \)
B・ \( y=-0.6 \sin 4 \pi\left[t+\frac{x}{2}\right] \)
c. \( y=0.9 \sin 8 \pi\left[t-\frac{x}{2}\right. \)
D. \( y=0.6 \sin 4 \pi\left[t+\frac{x}{2}\right] \)


Which of the following is not a cause for loss of biodiversity?
A. Destruction of habitat
B. Invasion by alien species
c. Keeping animals in zoological parks
D. Over-exploitation of natural resources


A chemist wants to produce \( C l_{2}(g) \)
from molten \( N a C l . \) How many grams could be produced if he uses a steady current of 2 ampere for 2.5 minutes :-
A. \( 3.55 g \)
в. \( 1.775 g \)
c. \( 0.110 g \)
D. \( 0.1775 g \)


Which of the following is a dispropprtonation reaction?
A \( \cdot C a C O_{3}+2 H^{+} \rightarrow C a^{2+}+C O_{2} \)
B \( \cdot 2 C r O_{4}^{2-}+\rightarrow C r_{2} O_{7}^{2+} H_{2} O \)
c. \( C r_{2} O_{4}^{2-}+\rightarrow 2 C r O_{4}^{2-}+H_{2} O \)
D. \( C u_{2} O+2 H^{+} \rightarrow C u^{2+}+H_{2} O \)


n mole of \( P C l_{3} \) and n mole \( C l_{2} \) are
allowed to react at constant
temperature \( T \) to have a total
equilibrium pressure \( \boldsymbol{P}, \) as \( : \boldsymbol{P} \boldsymbol{C l}_{3}(\boldsymbol{g})+ \)
\( \boldsymbol{C l}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{P} \boldsymbol{C l}_{5}(\boldsymbol{g}) . \) If \( \mathbf{y} \) mole of \( \boldsymbol{P} \boldsymbol{C l}_{3} \) are
formed at equilibrium, find \( k_{p} \) for the
given reaction.
A \( \cdot \frac{(2 n-y) y}{(n-y)^{2} . P} \)
B. \( \frac{y}{(n-y)^{2}(2 n-y) P} \)
c. \( \frac{(n-y)^{2} \cdot P}{(2 n-y) y} \)
D. \( \frac{(n-y)^{2}(2 n-y) P}{y} \)


How molar mass of a solute is
determined from osmotic pressure
measurements?


Find a unit vector perpendicular to \( \vec{A}= \) \( \mathbf{2} \hat{\mathbf{i}}+\mathbf{3} \hat{\mathbf{j}}+\hat{\boldsymbol{k}} \) and \( \overrightarrow{\boldsymbol{B}}=\hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) both
A \( .4 \hat{i}-\hat{j}-5 \hat{k} \)
B. \( \frac{1}{\sqrt{42}}(4 \hat{i}-\hat{j}-5 \hat{k}) \)
c. \( \frac{1}{\sqrt{21}}(4 \hat{i}-\hat{j}-5 \hat{k}) \)
D. \( \frac{1}{\sqrt{14}}(2 \hat{i}-\hat{j}-3 \hat{k}) \)


Write the name of fields produced by a moving charged particles.


Ammonia is released by plants during
\( A \cdot C \) A \( M \)
B. Dark respiration
c. Photorespiration
D. All of the above


Short / Long Answer Types:
How many atoms of oxygen are used
when a molecule of pyruvic acid is oxidised in Krebs cycle ? Give the. mechanism of oxygen utilisation and ATP formation.


Which of the following statement is not
true
A. Co-enzymes are organic compound
B. Association between apoenzyme and co-enzyme is permanent
C. NADP contain the vitamin niacin
D. Prosthetic group binds tightly to the apoenyme


If \( S \) is stress and \( Y \) is the Young's modulus of the material of a wire, the
energy stored in the wire per unit volume is :
\( \mathbf{A} \cdot 2 S^{2} Y \)
B. \( \frac{s^{2}}{2 Y} \)
c. \( \frac{2 Y}{S^{2}} \)
D. \( \frac{s}{2 Y} \)


Coordinates of point \( \boldsymbol{R} \) are
\( \mathbf{A} \cdot(1,1) \)
B. (-1,-1)
\( \mathbf{C} \cdot(-1,1) \)
D. (1,-1)


Which of the following terms describe human dentition?
A. Pleurodont, monophyodont, homodont
B. Thecodont, diphydont, homodont
c. Pleurodont, diphyodont, heterodont
D. Thecodont, diphyodont, heterodont


Two equally charged identical metal spheres \( A \) and \( B \) repel each other with a force F. Another identical uncharged sphere \( C \) is touched to \( A \) and then placed midway between \( A \) and \( B \). The net force on
\( \mathrm{C} \) is in the direction:
A. \( F \) towards \( A \)
B. \( F \) towards
\( \mathrm{c} .2 F \) towards \( \mathrm{A} \)
D. \( 2 F \) towards \( B \)


In a factory machine \( \boldsymbol{A} \) produce \( \mathbf{3 0 \%} \) of the total output, machine \( B \) produced
\( 25 \% \) and the machine \( C \) produced the remaining output. If defective items produced by machine \( A, B \) and \( C \) are \( 1 \%, 1.2 \%, 2 \% \) respectively. Three machine working together produced
10000 item in a day. An item is drawn at random from a day's output and found to be defective.
Find the probability that it was produced by machine \( \boldsymbol{B} \) ?


f \( a, b, c \epsilon R, \) find the number of real
roots of the equation given by \( \Delta=0 \)
where \( \boldsymbol{\Delta}=\left|\begin{array}{ccc}\boldsymbol{x} & \boldsymbol{c} & \boldsymbol{- b} \\ -\boldsymbol{c} & \boldsymbol{x} & \boldsymbol{a} \\ \boldsymbol{b} & \boldsymbol{-} \boldsymbol{a} & \boldsymbol{x}\end{array}\right| \)
A . 0
B.
\( c \cdot 2 \)
D. 3


What is the name for red azo dye?
A. p-hydroxy azo benzene
B. \( \beta \) - nathyl azo benzene
C . p-amino azo benzene
D. p- \( \mathrm{N}, \mathrm{N} \) dimethyl amino azo benzene


A quantity of 9.8 g of \( F e S O_{4} \cdot\left(N H_{4}\right)_{2} S O_{4} \cdot x H_{2} O \) was
dissolved in \( 250 \mathrm{ml} \) of its solution.
Twenty millilitres of this solution
requires \( 20 \mathrm{ml} \) of \( K M n O_{4} \) solution
containing 3.53 g of \( 90 \% \) pure \( K M n O_{4} \) dissolved per litre. The value of 'x' is
\( A \cdot 3 \)
B. 4
\( c \cdot 6 \)
D. 7


Kreb's cycle starts with the formation of
a six carbon compound by the reaction between
A. Malic acid and acetyl Co-A.
B. Succinic acid and pyruvic acid
c. Fumaric acid and succinyl Co-A.
D. Oxaloacetic acid and acetyl Co-A


Assertion (A): Decrease in free energy
causes spontaneous reaction.

Reason (R): Spontaneous reactions are invariable exothermic reactions.
A. Both Assertion and Reason are true and Reason is the
correct explanation of Assertion.
B. Both Assertion and Reason are true but Reason is not
the correct explanation of Assertion.
C. Assertion is true but Reason is false.
D. Both Assertion and Reason are false.


Use synthetic division to find the quotient \( Q \) and remainder \( R \) when dividing \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{5}+\boldsymbol{x}^{4}+\boldsymbol{x}^{3}+\boldsymbol{2} \boldsymbol{x}-\boldsymbol{5} \) by \( \boldsymbol{x}+\boldsymbol{i} \)
\( (i=\sqrt{(}-1) \text { imaginary unit }) \)


Industrial preparations of \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) by Ostwald's process involves:
A . reduction of \( N H_{3} \)
B. oxidation of \( N H_{3} \)
C. hydrogenation of \( N H_{3} \)
D. hydrolysis of \( N H_{3} \)


Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x} \) then in interval \( (\boldsymbol{0}, \boldsymbol{1}) \)
A. local minima of \( f(x) \) exists
B. local maxima of \( f(x) \) exists
c. Global maxima of \( f(x) \) exists
D. Maxima or minima of \( f(x) \) does not exist


The centre of gravity of a uniform ball is
A. at its geometrical centre.
B. at its bottom
c. at its topmost point.
D. at any point on its surface.


Angular momentum of a planet of mass \( m \) orbiting around sun is \( J \). Areal velocity of its radius vector will be:
A \( \cdot \frac{J}{2 M} \)
в. \( \frac{J}{M} \)
c. \( \frac{m}{2 J} \)
D. \( \frac{1}{2 m J} \)


The correct sequence of cell organelles
participating in photorespiration is
A. Chloroplast - Peroxisome - Mitochondria
B. Chloroplast - Vacuole - Peroxisome
C. Chloroplast - Golgi bodies - Mitochondria
D. Chloroplast - Rough endoplasmic reticulum Dictyosomes


Mesothelium or peritoneum originates from
A. Ectoderm
B. Endoderm
c. Ectomesoderm
D. Mesoderm


If \( x>0 \) and \( \cos ^{-1}\left(\frac{12}{x}\right)+ \)
\( \cos ^{-1}\left(\frac{35}{x}\right)=\frac{\pi}{2}, \) then \( x \) is
\( A \cdot 7 \)
B. 39
c. 37
D. -37


What do you understand by
(i) electron-
deficient,
(ii) electron-precise, and (iii) electron-rich compounds of hydrogen?


Total lung capacity is
A. 1 llit
B. 3 litt
c. 6 lit
D. 8 litt


The IUPAC name of the above shown
compound is :
A. 2 -bromo-3-methyl pentane
B. 2-bromo-3,3-dimethyl butane
C. 4 -bromo-3,3-dimethyl butane
D. 2-Bromo-3,3-dimethyl pentane


The density of a body is represented by the expression:
Where \( V \) is the volume and \( M \) is the
mass of a body
A \( \cdot D=\frac{V}{M} \)
B. D=M X V
c. \( _{D}=\frac{1}{M \times V} \)
D. \( D=\frac{M}{V} \)


The central atom of methane and water
is in the same state of hybridization, but the shapes of the two molecules are different. Discuss.


Mark the correct statement:
a) Damp air alone supplies both things needed for corrosion.
b) Ordinary water supplies both air and water for corrosion.
c) Moist air can't provide both things.
\( A \cdot a, b \)
в. а,
\( c \cdot b, c \)
D. All of the above


Emulsifier is an agent which:
A. accelerates the dispersion
B. homogenizes an emulsion
c. stabilizes an emulsion
D. aids the flocculation of an emulsion


A man has constructed a toy as shown
in figure. If the density of the material of the sphere is 12 times than of the cone
then determine the position of the
centre of mass. [Centre of mass of a
\( \boldsymbol{h} \)
cone of height \( h h \) is at height of \( \frac{-f r o m}{4} \) from
its base.


Expand \( (k+4)^{3} \)


Chloramphenicol prevents protein synthesis over
A. Prokaryotic ribosomes
B. Organelle ribosomes
c. Both A and B
D. 80 S ribosomes


Calculate \( \boldsymbol{K}_{c} \) for \( \boldsymbol{H} \boldsymbol{g}^{2+}+\boldsymbol{H} \boldsymbol{g} \rightleftharpoons \boldsymbol{H} \boldsymbol{g}_{2}^{2+} \)
Give that \( E_{2 H g / H g^{2+}}^{o}=-0.788 V \) and
\( \boldsymbol{E}_{\boldsymbol{H} \boldsymbol{g}_{2}^{2+} / \mathbf{2 H g}^{2+}}^{\boldsymbol{o}}=-\mathbf{0 . 9 2 0} \boldsymbol{V} \)
Write answer as nearest integer after dividing by 100


Which one of the following will make its way most easily through the tiny space between the fiber of the clothing:
A. glycerene at \( 10^{\circ} \mathrm{C} \)
B. water at \( 20^{\circ} \mathrm{C} \)
c. soap water at \( 20^{\circ} \mathrm{C} \)
D. water at \( 100^{\circ} \mathrm{C} \)


Show that the following poionts are
collinear
(i) \( \boldsymbol{A}(\mathbf{3}, \mathbf{2},-\mathbf{4}), \boldsymbol{B}(\mathbf{9}, \mathbf{8},-\mathbf{1 0}), \boldsymbol{C}(-\mathbf{2},-\mathbf{3}, \mathbf{1}) \)
(ii) \( P(4,5,2), Q(3,2,4), R(5,8,0) \)


Given \( \boldsymbol{P}(\boldsymbol{x})=\boldsymbol{x}^{4}+\boldsymbol{a} \boldsymbol{x}^{3}+\boldsymbol{b} \boldsymbol{x}^{2}+\boldsymbol{c} \boldsymbol{x}+\boldsymbol{d} \)
such that \( x=0 \) is the only real root of
\( \boldsymbol{P}^{\prime}(\boldsymbol{x})=\mathbf{0} . \) If \( \boldsymbol{P}(-1)<\boldsymbol{P}(1), \) then in the
interval [-1,1]
A. \( P(-1) \) is not minimum but \( P(1) \) is the maximum of \( P \)
B. \( P(-1) \) is the minimum but \( P(1) \) is not the maximum of \( P \)
c. neither \( P(-1) \) is the minimum nor \( P(1) \) is the maximum of \( P \)
\( D(-1) \) is the minimum and \( P(1) \) is the maximum of \( P \)


If \( \boldsymbol{x}=\sin (\boldsymbol{\alpha}-\boldsymbol{\beta}) \cdot \sin (\gamma-\boldsymbol{\delta}) ; \boldsymbol{y}= \)
\( \sin (\beta-\gamma) \cdot \sin (\alpha-\delta) \) and \( z= \)
\( \sin (\gamma-\alpha) \cdot \sin (\beta-\delta,) \) then
A. \( x+y+z=0 \)
в. \( x+y-z=0 \)
c. \( y+z-x=0 \)
D. None of these


If \( y=\frac{x}{|n| c x \mid} \) (where \( c \) is an arbitrary
constant) is the general solution of the differential equation \( \frac{d y}{d x}=\frac{y}{x}+\phi\left(\frac{x}{y}\right) \)
then the function \( \phi\left(\frac{x}{y}\right) \)
A \( \cdot \frac{x^{2}}{y^{2}} \)
в. \( -\frac{x^{2}}{y^{2}} \)
c. \( \frac{y^{2}}{x^{2}} \)
D. \( -\frac{y^{2}}{x^{2}} \)


If every element of third order determinant of \( \Delta \) is multiplied by 5 then value of new determinant equals
to,
A \( . \Delta \)
B. \( 5 \Delta \)
c. \( 25 \Delta \)
D. \( 125 \Delta \)


Match the soaps given in column I with items given in column II.


Which of the following is not an example of potential energy?
A. A vibrating pendulum at its maximum displacement from the mean position
B. A body at rest at some height from the ground
C. A wound clock-spring
D. A vibrating pendulum when it is just passing through the mean position


Does the center of mass of a system of
two particles lie on the lines joining the particles?


\( \operatorname{If}\left(1+2 x+x^{2}\right)^{n}=\sum_{r=0}^{2 n} a_{r} x^{r}, \) then \( a_{r}= \)
A \( \cdot\left(^{n} C_{r}\right)^{2} \)
В. \( ^{n} C_{r} \cdot^{n} C_{r+1} \)
\( c \cdot^{2 n} C_{r} \)
D. \( ^{2 n} C_{r+1} \)


The translation distances \( (d x, d y) \) is called as
A. Translation vector
B. Shift vector
c. Both A and B
D. Neither A nor B


If 18 pumps can raise 2170 tonnes of
water in 10 days, working 7 hours a day then in how many days will 16 pumps raise 1736 tonnes of water, working 9 hours a day?
\( A \cdot 6 \)
B. 7
\( c \cdot 8 \)
D.


\( N a H C O_{3} \) can be used on its own to make cakes or bread. Baking powder is more commonly used, and contains
\( N a H C O_{3}, C a\left(H_{2} P O_{4}\right)_{2} \) and starch. An
improved combination baking powder contains about \( 40 \% \) starch, \( 30 \% \)
\( N a H C O_{3} 20 \% N a A l\left(S O_{4}\right)_{2} \) and \( 10 \% \)
\( \boldsymbol{C a}\left(\boldsymbol{H}_{2} \boldsymbol{P} \boldsymbol{O}_{4}\right)_{2} \)
Answer the following questions based on above study.
Rise in bread and cakes is due
to when it decomposes
between \( 50^{\circ} C \) and \( 100^{\circ} C \)
A. \( C O_{2} \)
в. \( H_{2} O \)
\( c . \) both (a) and (b)
D. none of these


The main cause of acidity in the
stomach is :
A. release of extra gastric acids which decrease the pH level
B. indigestion and pain in large intestine
C. increase the pH level in stomach
D. release of extra bile juice which increases alkaline medium in stomach


(a) Using Bohr's second postulate of
quantization of orbital angular
momentum show that the
circumference of the electron in the \( n^{t h} \)
orbital state in hydrogen atom is \( n \) times the de Broglie wavelength
associated with it.
(b) The electron in hydrogen atom in initially in the third excited state.What is the maximum number of spectral lines which can be emitted.When it
finally moves to the ground state?


For the coagulation of \( 500 \mathrm{mL} \) of arsenious sulphide sol, 2 mL of \( 1 M \)
Na Cl is required. What is the
flocculation value of \( N a C l ? \)
This question has multiple correct options
A . 3
B. 2
c. 5
D. 4


If the length of a simple pendulum is recorded as \( (90.00 \pm 0.02) \mathrm{cm} \) and period as \( (1.90 \pm 0.02) \mathrm{s}, \) the
percentage of error in the measurement of acceleration due to
gravity is :
A . 4.2
B . 2.
c. 1.5
D. 2.8


Define Karyokinesis.


One card is drawn from a well-shuffled
deck of 52 cards. Find the probability of
drawing '2' of spades.
A \( \cdot \frac{5}{52} \)
в. \( \frac{1}{52} \)
c. \( \frac{4}{52} \)
D. \( \frac{2}{52} \)


Four cubic blocks with edge \( 4 \mathrm{cm} \) were
kept two on top of two and fused
together into a block as shown. Find the total surface area of the block and the
\( \operatorname{cost} \) of painting it at \( R s .32 \) per \( c m^{2} \)
\begin{tabular}{|c|c|}
\hline 1 & 2 \\
\hline 3 & 4 \\
\hline
\end{tabular}
A. \( R s .8992 \)
B . \( R s .8092 \)
c. \( R s .8192 \)
D. \( R s .8190 \)


A transverse wave is given by \( A \sin (t x) \)
where \( A \) and \( t \) are constants. The ratio
of wave velocity to maximum particle velocity is
A. \( A \)
B. \( \frac{1}{A} \)
c.
D. none of the above


A substance can be identified because
its chemical environment often shows
up like a finger print in a spectrum. This fine region of finger prints of the chemical environment of a chemical
compound is created by:
A . infrared radiation
B. ultraviolet light
c. nuclear magnetic resonance
D. \( X \) -rays


The two parallel sides of a trapezium
are \( 1.5 m \) and \( 2.5 m \) respectively. If the perpendicular distance between them is 6.5 metres, the area of the trapezium is:
\( \mathbf{A} \cdot 10 m^{2} \)
В. \( 13 m^{2} \)
c. \( 20 m^{2} \)
\( \mathbf{D} \cdot 26 m^{2} \)


A man moves on a straight horizontal road with a block of mass \( 2 k g \) in his
hand. If he covers a distance of \( 40 m \)
with an acceleration of \( 0.5 m / s^{2}, \) find
the work done by the man on the block during the motion.


Which of the following has an aldehyde functional group?
A. \( R-C O O H \)
в. \( R-C H O \)
c. \( R-C O-R \)
D. \( R-C O O-R \)
E \( . R-C O-N H_{2} \)


Choose the correct answer from the
alternatives given

The sodium potassium pump moves sodium and potassium ions across the plasma membrane by
A. Facilitated transport
B. Active transportt
c. cotransport
D. Endocytosis


Which of the following contains maximum number of atoms?
A. \( 4 \mathrm{gm} \) of oxygen
B. \( 4 \mathrm{gm} \) of carbon dioxide
c. \( 4 \mathrm{gm} \) of helium
D. 4 gm of methane


What are the main postulates of Bohr's theory of an atom?


If
\( \mathbf{1 0 0} \quad \mathbf{N} / \mathbf{5} \quad \mathbf{N H}_{4} \mathbf{O H} \) and HCl are
mixed. Find out the pH of the resultant
solution if \( p K_{b} \) for \( N H_{4} O H \) is \( 10^{-5} \)


Which of the following was used during discovery of Calvin cycle?
A. Spirogyra
B. Volvox
c. chlamydomonas
D. chlorella


Give any four differences between
Physisorption and Chemisorption.


Select the organic compounds, which will give red colour in Lassaigne's test?
A. NacNS
B.
\( c \)
\( D \)


Yogesh lent out Rs.7, 000 at \( 6 \% \) and Rs.
9,500 at \( 5 \% . \) Find his total income from
the interest in 3 years.
A. Rs.1, 966
B. Rs.2, 133
c. Rs. 2,685
D. Rs.3, 148


In a Young's double slit experiment, let
\( \beta \) is the fringe width, and let \( I_{o} \) be the intensity at the central bright fringe. At a distance \( x \) from the central bright
fringe, the intensity will be:
A \( \cdot I_{o} \cos \left(\frac{x}{\beta}\right) \)
B \( \cdot I_{o} \cos ^{2}\left(\frac{x}{\beta}\right) \)
\( \mathbf{c} \cdot_{I_{o} \cos ^{2}\left(\frac{\pi x}{\beta}\right)} \)
D. \( \left(\frac{I_{o}}{4}\right) \cos ^{2}\left(\frac{\pi x}{\beta}\right) \)


Dashrath and Naresh are friends
,Naresh is 2 years younger than Dashrath.If the sum of their age is 56
years, find their present age.
A. Naresh=27 years, Dashrath =29 years
B. Naresh=37 years, Dashrath =29 years
c. Naresh=27 years, Dashrath =39 years
D. Naresh=47 years, Dashrath =29 years