Answer the following very briefly:
Why should the blood that goes away from the stomach and intestines pass
through the liver and not directly to the heart?


Which of the following burns to form an
oxide, which is gaseous at room temperature?
A. Hydrogen
B. Phosphorus
c. Calcium
D. Sulphur


Major source of protein is
A . Oryza sativa
B. Cicer arietinum
c. Beta vulgaris
D. Rhizobium leguminosarum


The second's hand of a watch is \( 2 \mathrm{cm} \)
long. The speed of the tip of this hand is:
A. \( 0.21 \mathrm{cm} / \mathrm{s} \)
B. \( 2.1 \mathrm{cm} / \mathrm{s} \)
c. \( 21.0 \mathrm{cm} / \mathrm{s} \)
D. None of these


Factorise \( 2 \sqrt{2} a^{3}+8 b^{3}-27 c^{3}+ \)
\( 18 \sqrt{2} a b c \)


For combustion of 1 mole of benzene at
\( 25^{0} C, \) the heat of reaction at constant
pressure is - 780.9 kcal. What will be the
heat of reaction at constant volume?
\( \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{6}(\boldsymbol{I})}+\boldsymbol{7} \frac{1}{2} \boldsymbol{O}_{2(\boldsymbol{g})} \rightarrow \boldsymbol{6} \boldsymbol{C} \boldsymbol{O}_{2(\boldsymbol{g})}+ \)
\( \mathbf{3} \boldsymbol{H}_{2} \boldsymbol{O}_{(l)} \)
A . -781.8 kcal
в. -780.0 kcal
c. +781.8 kcal
D. +780.0 kcal


What is the empirical formula for a compound containing \( 63.8 \% N \) and
\( 36.2 \% \) O?
A. \( N_{2} O_{5} \)
в. \( N_{2} O_{3} \)
c. \( N O_{2} \)
D. \( N O \)
E \( . N_{2} \)


If \( X \) and \( Y \) are two sets then \( X \cap(Y \cup \)
\( X)^{\prime} \) equals:
\( \mathbf{A} \cdot X \)
в. \( Y \)
\( c \cdot \phi \)
D. \{0\}


Angle of minimum deviation for a prism of refractive index \( 1.5, \) is equal to the
angle of the prism. Then the angle of the
prism is : (Given \( \left.\cos 41^{\circ}=0.75\right) \)
\( \mathbf{A} \cdot 62^{\circ} \)
B . 41
\( c \cdot 82 \)
D. 31


Glucose is carbohydrate.
A. True
B. False


In a G.P. of positive terms, if any term is
equal to the sum of next two terms, find
the common ratio of the G.P.


Two streams of protons move parallel to each other in the same direction. They
will
A. attract each other
B. repel each other
c. neither attract nor repe
D. rotate


A Gaussian surface
A. may pass though a continuous charge distribution
B. must pass through a continuous charge distribution
C. must never pass through a continuous charge distribution
D. None of these


The beating of heart of man is heard on the left side because
A. The left ventricle is towards the left side
B. Both the ventricles are towards the left side
c. Entire heart is on the left side
D. The aorta is on the left side


\( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}| \) has
A. minimum at \( x=0 \)
B. maximum at \( x=0 \)
c. neither a maximum nor a minimum at \( x=0 \)
D. none of these


It is known that \( \sum_{r=1}^{\infty} \frac{1}{(2 r-1)^{2}}=\frac{\pi^{2}}{8}, \) then
\( \sum_{r=1}^{\infty} \frac{1}{r^{2}} \) is equal to
A \( \cdot \frac{\pi^{2}}{24} \)
B. \( \frac{\pi^{2}}{3} \)
c. \( \frac{x^{2}}{6} \)
D. none of these


Multiply the binomials.
\( (y-8) \) and \( (3 y-4) \)


Assertion
Solids in finely divided state act as
good adsorbents
Reason
Adsorption is a surface phenomenon.
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


\( D_{2} O \) or graphite is a moderator in
nuclear reactor
A. True
B. False


If the fourth term in the expansion of \( \left(\sqrt{\frac{1}{x^{\log x+1}}}+x^{1 / 12}\right)^{6} \) is equal to 200
and \( x>1, \) then \( x \) is equal to
A \( \cdot 10^{\sqrt{2}} \)
2 \( \sqrt{2} \)
B. 10
\( c \cdot 10^{4} \)
D. None of these


Moment of momentum is called:
A. Torque
B. Impulse
c. couple
D. Angular momentum


If the \( (p+q)^{t h} \) term of a geometric
series is \( \mathrm{m} \) and the \( (p-q)^{t h} \) term is \( n \)
then the \( p^{t h} \) term is
\( \mathbf{A} \cdot(m n)^{1 / 2} \)
в. \( m \) n
\( c \cdot m+n \)
D. m-n


A Bryophyte suddenly started reproducing parthenogenetically. Then the number of chromosomes of the
second generation compared to parent
plant will be
A. Same
B. One-half
c. Double
D. Triple


Assertion
Androgens stimulate muscular growth.
Reason

Androgens produce anabolic effects on protein and carbohydrate metabolism.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The value of \( (\sqrt{5}+1)^{5}-(\sqrt{5}-1)^{5} \) is:
A . 252
в. 352
c. 452
D. 552


\( C O \) is not true acid anhydride but is
formal anhydride of \( H C O O H . \) If true
write 1 , else write 0 .


If the derivatives of \( \tan ^{-1}(a+b x) \) takes
the value 1 at \( x=0, \) prove that \( 1+ \)
\( a^{2}=b \)


\( \frac{a}{a} \)


Position of an object in plane can be easily find out by the help of:
B. Trignometry
c. coordinate geometry
D. Proportions


Air has refractive index \( 1.0003 . \) Find the
thickness of air column which will
contain one more wavelength of yellow
light of \( 6000 A^{0} \) than in same thickness
of vacuum.
\( \mathbf{A} \cdot 1 \mathrm{mm} \)
B. \( 2 \mathrm{mm} \)
c. \( 3 \mathrm{mm} \)
D. \( 5 \mathrm{mm} \)


If agas absorbs \( 200 J \) of heat and expands by \( 500 \mathrm{cm}^{3} \) against a constant
pressure of \( 2 \times 10^{5} N m^{-2}, \) then the
change in internal energy is
A. -300
B. -100
c. +100
\( \mathbf{D} \cdot+300 \)


During heavy exercise the breathing rate of a person slows down.
A. True
B. False


Solve:
\( \int \frac{\sin ^{3} x+\cos ^{3} x}{\sin ^{2} x \cos ^{2} x} d x \)


A transverse wave moves along a rope.
The diagram shows the position of the
rope at one particular time.
Which two labelled points are one
wavelength apart?
\( \mathbf{A} \cdot W \) and \( X \)
B. \( W \) and \( Z \)
c. \( X \) and \( Z \)
D. \( Y \) and \( Z \)


\( \lim _{x \rightarrow 0} \frac{1-\cos \left(x^{2}\right)}{x^{3}\left(4^{x}-1\right)} \) is equal to
This question has multiple correct options
A \( \frac{1}{4 \log 2} \)
B. \( \frac{1}{2 \log 4} \)
\( \mathbf{c} \cdot \log 4 \)
D \( \quad 1-\frac{1}{2} \log \left(\frac{e^{2}}{4}\right) \)


The vapours of organic compound was burnt in oxygen. Equal volume of both gaseous substance were taken at same
pressure and temperature. After the reaction, the system was returned to the original condition and it turn out that its volume has not changed. The product of combustion contain \( 50 \% \)
\( C O_{2}(g) \) and \( 50 \% H_{2} O(g) \) by volume and
no other gas. Find the molecular weight of organic compound (in gram/mol) in
question.
A . 30
B. 35 5
\( c \cdot 40 \)
D. 46


Assertion
\( 1 m m^{2}=10^{-6} m^{2} \)
Reason
The numerical value of physical quantity is less for a smaller unit.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The line \( \boldsymbol{x}-\mathbf{2} \boldsymbol{y}+\mathbf{4} \boldsymbol{z}+\mathbf{4}=\mathbf{0}, \boldsymbol{x}+\boldsymbol{y}+ \)
\( z-8=0 \) intersects the plane \( x-y+ \)
\( \mathbf{2} z+\mathbf{1}=\mathbf{0} \) at the point
A \( \cdot(3,2,3) \)
B . (5,2,1)
c. (2,5,1)
D . (3,4,1)


The value(s) of \( \lambda \), for which the triangle with vertices \( (\mathbf{6}, \mathbf{1 0}, \mathbf{1 0}),(\mathbf{1}, \mathbf{0},-\mathbf{5}) \) and
\( (6,-10, \lambda) \) will be a right angled
triangle is/ are
A . 1
в. \( \frac{70}{3}, 0 \)
c. 35
D. \( 0,-\frac{70}{3} \)


In Pteridophytes, prothallus shows
A. Lack of gametophyte
B. Spore production
c. The presence of tracheids
D. Root, stem and leaf


The set for which \( 2 \cos ^{-1} x= \)
\( \cos ^{-1}\left(2 x^{2}-1\right) \) is valid is
\( \mathbf{A} \cdot x \in[0,1] \)
B \( \cdot x \in(0,1) \)
\( \mathbf{c} \cdot x \in[0,1) \)
D. \( x \in(0,1] \)


Displacement of a particle of mass \( 2 k g \) moving in a straight line varies with
time at \( s=\left(2 t^{3}+2\right) m . \) Impulse of the
force acting on the particle over a time interval between \( t=0 \) and \( t=1 s \) in
A. \( 10 N-s \)
В. \( 12 \mathrm{N}-\mathrm{s} \)
c. \( 8 N-s \)
D. \( 6 N-s \)


Let \( A B C \) be an equilateral triangle and
suppose KLMN be a rectangle with \( \boldsymbol{K}, \boldsymbol{L} \) on \( \mathrm{BC}, \mathrm{M} \) on \( \mathrm{AC} \) and \( \mathrm{N} \) on AB. If \( \frac{A N}{N B}=2 \) and area of triangle BKN is \( 6, \) then area of triangle \( A B C \) is equal to
A . 48
B. 54
c. 96
D. 108


Mendel's conclusion was first published
in
A. Journal of plant breeding
B. Journal of genetics and plant breeding
c. Nature forschender verein
D. None of the above


The number of valence electrons of
caesium is :
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 6 \)
\( D \)


(a) State Ohm's law.
(b) Describe an experiment to verify this law.


The element in between lithium and
potassium in Dobereiner's classification is:
A . Mg
B. Na
\( c \cdot c a \)
D. Rb


Trans-1,2-dideuterocyclopropane
\( (\boldsymbol{A}) \)
undergoes a first-order decomposition. The observed rate constant at a certain
temperature measured in terms of
disappearance of ' \( \boldsymbol{A} \) ' has \( 1.52 \times \) \( 10^{-4} s e c^{-1} . \) Analysis of products showed
that the reaction followed two parallel paths, one leading to dideuteropropane
\( (B) \) and the other to cis- 1,2
dideuterocyclopropane \( (C) .(B) \) was
found to constitute \( 11.2 \% \) of the
reaction product, independently of the extent of reaction. What is the order of
reaction for each path and what is the
value of the rate constant for the
formation of each of the products?


Which is Prussian blue?
A \( \cdot K F e^{I I I}\left[F e^{I I}(C N)_{6}\right] \)
B. \( K F e^{I I I}\left[F e^{I I I}(C N)_{6}\right] \)
C. \( K_{2}\left[F e^{I I}(C N)_{6}\right] \)
D. \( K_{3}\left[F e(C N)_{6}\right] \)


A deactivating group:
A. deactivates only ortho and para positions
B. deactivates only meta position
C. deactivates ortho and para more than meta positions
D. deactivates meta more than ortho and para positions


Addition of which of the following material to water does not make it
hard?
\( \mathbf{A} \cdot M g_{3}\left(P O_{4}\right)_{2} \)
B. \( \operatorname{Fe}\left(\mathrm{NO}_{3}\right)_{3} \)
c. \( V\left(N O_{3}\right)_{3} \)
D. \( T i\left(C l O_{4}\right)_{4} \)


Heat flows between two bodies due to
difference in their


If \( A, B, C \) are the angles of a triangle, show that \( \frac{\cos A \cos C+\cos (A+B) \cos (B+C)}{\cos A \sin C-\sin (A+B) \cos (B+C)} \)
\( \cot C \)


Dry air was passed successively through a solution of 5 g of a solute in \( 180 \mathrm{g} \) of water and then through pure water. The loss in weight of solution was \( 2.50 \mathrm{g} \) and that of pure solvent 0.04 g. The molecular weight of the solute is:
\( \mathbf{A} \cdot 31.25 \)
B. 3.125
c. 312.5
D. None of the above


\( \vec{A}=3 \hat{i}+4 \hat{j}+2 \hat{k} \)
\( \vec{B}=6 \hat{i}-\hat{j}+3 \hat{k} \)
Find a vector parallel to \( \vec{A} \) whose magnitude is equal to that of \( \vec{B} \).
A \( \cdot \sqrt{\frac{46}{29}}(3 \hat{i}+4 \hat{j}+2 \hat{k}) \)
В. \( \sqrt{\frac{46}{29}}(6 \hat{i}-\hat{j}+3 \hat{k}) \)
c. \( \sqrt{\frac{29}{46}}(3 \hat{i}+4 \hat{j}+2 \hat{k}) \)
D. None


A particle of mass \( m_{1} \) moving at
certain velocity collides elastically
head on with a particle of mass \( m_{2} \) at rest. After collision their velocities will
be in the ratio of
A \( \cdot \frac{m_{1}-m_{2}}{m_{1}+m_{2}} \)
в. \( \frac{m_{1}-m_{2}}{2\left(m_{1}+m_{2}\right)} \)
c. \( \frac{2 m_{1}}{m_{1}-m_{2}} \)
D. \( \frac{m_{1}-m_{2}}{2 m_{1}} \)


The metal used in solar cells is:
A. Na
B. Li
\( c \cdot c s \)
D. Mg


Enlist the characteristic features of
cnidarians which show advancement
over poriferans?


If \( \sin A=\frac{1}{2} \) and \( \cos B=\frac{\sqrt{3}}{2} \) where \( A \)
lies in second quadrant and B lies in first quadrant, find the values of (a) \( \sin (A-B)(b) \cos (A-B)(c) \tan (A+ \)
\( \boldsymbol{B}) \)


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


The complex formed by a pair of synapsed homologous chromosomes is called :Homologous chromosome are
paired and synapsed during zygotene stage of meiosis-I and known as
bivalent
Arrows numbered \( 4,8, \) and 12 can all be
A. NADH
B. ATP
\( c \cdot H_{2} \circ \)
D. \( F A D^{+} \) or \( F A D H_{2} \)


IUPAC naming of the compound is:
A. 3-octanoic acid
B. octane-3-oic acid
c. 2-ethylhexanoic acid
D. 3-ethylhexanoic acid


Prokaryotes reproduce by
A. Sexual
B. Asexual
C. Both A and B
D. They do not produce


The ppm strength of \( C O_{2}(g) \) volume by
volume \( \left(\mathrm{mL} \text { of } C \mathrm{O}_{2} \text { per } 10^{6} \mathrm{mL} \) of air) is: \right.
A .224
в. 2240
c. 100
D. 1000


Construct a triangle \( A B C \) in which
\( B C=8 c m, \angle B=45^{\circ} \) and \( A B \)
\( \boldsymbol{A C}=\mathbf{3 . 5} \boldsymbol{c m} \)


The total momentum of electrons in a
straight wire of length \( l=1000 m \)
carrying a current \( \mathrm{I}=\mathbf{7} \mathbf{0} \boldsymbol{A}, \) will be (in
\( N-s) \)
A . \( 0.40 \times 10^{-6} \)
B. \( 0.20 \times 10^{-6} \)
c. \( 0.80 \times 10^{-6} \)
D. \( 0.16 \times 10^{-6} \)


Draw a ray diagram to illustrate how a ray of light incident obliquely on one
face of a rectangular glass slab of uniform thickness emerges.


If \( y=\log _{10}(\sin x), \) then \( \frac{d y}{d x} \) equals to:
A \( \cdot \sin x \log _{10} e \)
B. \( \cos x \log _{10} e \)
C. \( \cot x \log _{10} e \)
D. \( \cot x \)


Let \( A \) and \( B \) be two independent event then show that \( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})=\mathbf{1}- \)
\( \boldsymbol{P}\left(\boldsymbol{A}^{\prime}\right) \boldsymbol{P}\left(\boldsymbol{B}^{\prime}\right) \)


The volume of a cinema theatre is \( 100 \mathrm{m} \)
\( x 60 m \times 20 m \) and total acoustic
absorption in it is 6800 metric
sabine. The reverberation time in
that theatre is
A . 1.5 s
B. 2
\( c \cdot 3 s \)
D. 4 s


What is IUPAC name of the following
compound?
\( \mathbf{C H}_{3}-\mathbf{C H}_{2}-\mathbf{C H}_{2}-\mathbf{O H} \)
A. Propane-1-ol
B. Propane-2-ol
c. Ethane-1-ol
D. Ethane-2-ol


Light of wavelength \( 5880 A^{\circ} \) is incidents
on a thin glass plate \( (\mu=1.5) \) such
that the angle of refraction in the plate is \( 60^{0} \). The minimum thickness of the
plate, so that it appears dark in the reflected light will be
A \( .3920 A^{\circ} \)
\( ^{\circ} \)
B. \( 4372 A^{\circ} \)
\( c .5840 A^{\circ} \)
D. \( 6312 A^{\circ} \)


If \( \boldsymbol{A}=\{\mathbf{1}, \mathbf{2}, \mathbf{3}\} \) and \( \boldsymbol{B}=\{\mathbf{3}, \mathbf{8}\}, \) then
\( (\boldsymbol{A} \cup \boldsymbol{B}) \times(\boldsymbol{A} \cap \boldsymbol{B}) \) is
A \( \cdot\{(3,1),(3,2),(3,3),(3,8)\} \)
B・ \{(1,3),(2,3),(3,3),(8,3)\}
c. \{(1,2),(2,2),(3,3),(8,8)\}
D \( \cdot\{(8,3),(8,2),(8,1),(8,8)\} \)


(B), (C), and (D), respectively, are:
\( A \)
\( (\mathrm{I}) \)
\( (\mathrm{III}) \)
B. (I), (III), (II)
c. \( (\| 1),(\text { II ) },(1) \)
D. (III), (I), (II)


According to Wien's law:
A \( \cdot \lambda_{m} T= \) constant
B. \( \frac{\lambda_{m}}{T}= \) constant
c. \( \lambda_{m} \sqrt{T}= \) constant
D. \( \frac{\lambda_{m}}{\sqrt{T}}= \) constant


In a histogram, the area of each rectangle is proportional to the class size of the corresponding class interval?
If not, correct the statement.
If true then enter 1 and if false then
enter 0
A . 1
B.
c. can't determine
D. None of these


In case of a right circular cylinder the radius of base and height are in the ratio \( 2: 3 . \) Therefore, the ratio of lateral
surface area to the total surface area is
A .5: 3
B. 3: 5
c. 2: 5
D. 2: 3


LEDs are better than conventional
incandescent power lamps because:
A. LEDs have higher efficiency.
B. LEDs look beautiful.
c. LEDs are cheap.
D. all of the above


Hydrolysis of \( N C l_{3} \) results in the
formation of


In the figure shown which one is correct
diagram for LED?
(b)
(c)
da
\( A \cdot b \)
B.
\( c \)
D.


A path \( 5 \mathrm{cm} \) wide runs along inside a
square park of side \( 100 \mathrm{cm} \). Find the area of the path. Also find the cost of
cementing at the the rate of Rs 250 per
10 sq.cm.


If new moon day is day \( 1, \) then what is
the day of the crescent moon?
A. 7
B. 10
\( c .3 \)
D. 14


n the \( \triangle A B C \),we have \( \angle A>\angle B>\angle C \)
then determine the shortest and the
longest side of the triangle.
A. Shortest side is \( A B \) and the longest side is \( B C \)
B. Shortest side is \( B C \) and the longest side is \( A B \)
C. Shortest side is \( A B \) and the longest side is \( A C \)
D. Shortest side is \( A C \) and the longest side is \( B C \)


n the given figure, \( \angle B=60^{\circ}, A B=8 \)
\( \mathrm{cm} \) and \( \mathrm{BC}=25 \mathrm{cm} . \) Calculate :
(i) \( B E \)
(ii) \( \boldsymbol{A C} \)


Homo sapiens have evolved in :
A. Pliocene
B. Pleistocene
c. oligocene
D. Miocene


Depending on Lewis structure,
\( O F_{2}, O_{2} F_{2} \) and \( S_{2} F_{2} \) which of the
following statement is incorrect?
\( \mathbf{A} \cdot S_{2} F_{2} \) has two possible isomeric structures, whereas
\( O_{2} F_{2} \) has only one
B. The bond angle in \( O F_{2} \) is greater than in \( O C l_{2} \)
C. The O-O bond length in \( O_{2} F_{2} \) is smaller than in \( H_{2} O_{2} \)
D. The O-F bond length in \( O_{2} F_{2} \) is larger than in \( O F_{2} \)


Hydrolysis of one mole of
peroxydisulphuric acid produces:
A. two moles of sulphuric acid
B. two moles of peroxymonosulphuric acid
C. one mole of sulphuric acid and one mole of peroxymonosulphuric acid
D. one mole of sulphuric acid, one mole of peroxymonosulphuric acid, and one mole of hydrogen peroxide


If \( \operatorname{Tr}(\mathbf{A})=\mathbf{2}+\mathbf{i}, \) Then \( \operatorname{Tr}[(\mathbf{2}-\mathbf{i}) \mathbf{A}]= \)
A \( .2+i \)
в. \( 2-i \)
\( c .3 \)
D. 5


The oxidation of \( S O_{2} \) by \( O_{2} \) to \( S O_{3} \) is an
exothermic reaction. The yield of \( \boldsymbol{S O}_{3} \)
will be maximum if:
A. temperature is increased and pressure is kept constant
B. temperature is reduced and pressure is increased
c. both temperature and pressure are increased
D. both temperature and pressure are reduced


The mass of a compound is 2.4 g and
the mass of \( C O_{2} \) formed is 7.3 g. Estimate the percentage of oxygen.
A . \( 23.5 \% \)
B . \( 82.7 \% \)
c. \( 42.5 \% \)
D. None of these


Find the acceleration of the bar.
A. \( w_{0}=\frac{2 g m r^{2}}{I} \)
B. \( w_{0}=\frac{g m r^{2}}{I} \)
c. \( _{w_{0}}=\frac{g m r^{2}}{2 I} \)
D. \( w_{0}=2 \frac{g m r^{2}}{I} \)


Male cockroach can be distinguished from female cockroach through
A. Longer antennae
B. Longer abdomen
c. wingless body
D. All the above


The probability distribution of a random
variable \( \boldsymbol{X} \) is given below:
\[
\boldsymbol{X}=\boldsymbol{x} \quad 0 \quad 1 \quad 2 \quad 3
\]
\( P(X=x) \quad \frac{1}{10} \quad \frac{2}{10} \quad \frac{3}{10} \)
\[
\begin{array}{r}
\frac{4}{10} \\
\hline 0
\end{array}
\]
Then the variance of \( \boldsymbol{X} \) is
\( A \)
B. 2
\( c \cdot 3 \)
D. 4


The equivalent capacitance between
points \( \mathrm{M} \) and \( \mathrm{N} \) is :
A . Infinity
в. \( c_{1}+\frac{C_{2}}{C_{1}} \)
\( c_{C_{2}+\frac{C_{2}}{C_{1}}} \)
D. \( \frac{C_{1} C_{2}}{C_{1}+C_{2}} \)


Construct a quadrilateral \( P Q R S \) with
\( Q R=8 \mathrm{cm}, R S=4 \mathrm{cm}, S P=9 \mathrm{cm} \)
\( \boldsymbol{P Q}=\mathbf{5 . 5} \mathrm{cm} \) and \( \boldsymbol{Q} \boldsymbol{S}=\boldsymbol{6} \mathrm{cm} \)


A metal rod of length \( 1 \mathrm{m} \) is clamped at
two points as shown in the figure. Distance of the lamp from the two ends
are \( 5 c m \) and \( 15 c m \) respectively. Find the minimum and next higher
frequency of natural longitudinal oscillation of the rod. Given that Young's modulus of elasticity and density of aluminium are \( \boldsymbol{Y}=\mathbf{1 . 6} \times \mathbf{1 0}^{\mathbf{1 1}} \mathbf{N m}^{-\mathbf{2}} \)
and \( p=2500 k g m^{-3} \) respectively.
\( A \cdot 40 \mathrm{kHz}, 120 \mathrm{kHz} \)
B. 120 kHz, 40 kHz
c. \( 40 \mathrm{kHz}, 40 \mathrm{kHz} \)
D. 1200 kHz, 120 kHz


It is observed that for a ratio \( \frac{\boldsymbol{m}_{1}}{\boldsymbol{m}_{2}}= \)
\( \left(3-x^{2}+x\right), \) maximum transfer of
momentum takes places from body 1 to body \( 2 . \) Then This question has multiple correct options
A \( . x=1 \)
B. \( x=2 \)
\( c \cdot x=3 \)
D. x = -


How many lines of symmetry are in this
isosceles triangle?
\( A \)
B. 2
\( c \cdot 3 \)
\( D \)


When \( 1.375 g \) of cupric oxide is reduced on heating in a current of hydrogen, the weight of copper remaining \( 1.098 g . \) In another experiment, \( 1.179 g \) of copper is dissolved in nitric acid and resulting
copper nitrate converted into cupric oxide by ignition. The weight of cupric oxide formed is \( 1.476 g \). This is in agreement with:
A. Law of definite proportion
B. Law of mass conservation
c. Law of momentum conservation
D. None of the above


A bag containing 4 red and 4 blue balls
/ four balls are drawn one by one from
the bag, the find the probability that the drawn balls are in alternate colour.


Write the probability of getting each number top face when a die was rolled in the following table and find the sum of the probabilities of all outcomes.


Write the value of \( 2 \sin ^{-1} \frac{1}{2}+ \)
\( \cos ^{-1}\left(-\frac{1}{2}\right) \)


Consecutive elements \( X, Y \) and \( Z \) are in
Period 3 of the Periodic Table. Element \( Y \)
has the highest first ionisation energy and the lowest melting point of these three elements.

What are the identities of \( X, Y \) and \( Z ? \)
A. Sodium, magnesium, aluminium
B. Magnesium, aluminium, silicon
c. Aluminium, silicon, phosphorus
D. silicon, phosphorous, sulfur


The figure shown a ball striking the floor
at an angle \( \alpha \) with speed \( u \) and
rebounds at an angle \( \beta \) from the floor
with speed \( v . \) The value of co-efficient of restitution (e) is
A \( \cdot \frac{v}{u} \)
в. \( \frac{u}{v} \)
c. \( \frac{v \sin \beta}{u \sin \alpha} \)
D. \( \frac{v \sin \beta}{u \cos \alpha} \)


Two particles \( A \) and \( B \) move on a circle. Initially particles \( A \) and \( B \) are diagonally opposite to each other.
Particle \( A \) moves with angular velocity
\( \pi \) rad \( s^{-1} \) and angular acceleration
\( \pi / 2 r a d s^{-2} \) and particle \( B \) move with
constant angular velocity \( 2 \pi \) rad \( s^{-2} \)
Find the time after which both the
particles \( A \) and \( B \) will collide.


For a common emitter amplifier,
current gain is \( 60 . \) If the emitter current
is \( 6.6 ~ m A \) the collector current is :
A. \( 0.108 \mathrm{mA} \)
B. 6.492 m \( A \)
c. \( 1.1 \mathrm{m} \) А
D. 3.3 \( m A \)


STATEMENT - 1: Dependent events are those in which the outcome of one does not affect and is not affected by the
other.
STATEMENT - 2 : Dependent events are
those in which the outcome of one
affects and is affected by the other.
A. Statement - 1 is True, Statement - 2 is True, Statement 2 is a correct explanation for Statement- -
B. Statement-1 is True, Statement- 2 is True: Statement 2 is NOT a correct explanation for Statement-
c. statement- 1 is True, Statement - 2 is False
D. Statement - 1 is False, Statement- 2 is True


Magnetic moment of the spinning electron is in the direction of its spin
angular momentum.
B. Spin Velocity
c. spin angular velocity
D. angular acceleration


A block of wood floats in water with \( \frac{4}{5} \) th of its volume submerged, but it just floats in another liquid. The density of
liquid is? \( \left(\operatorname{in} \mathrm{kg} / m^{3}\right) \)
\( \mathbf{A} \cdot 750 \)
в. 800
c. 1000
D. 1250


A straight line \( x=y+2 \) touches the
\( \operatorname{circle} 4\left(x^{2}+y^{2}\right)=r^{2} . \) The value of \( r \) is
A \( \cdot \sqrt{2} \)
B. \( 2 \sqrt{2} \)
\( c \cdot 2 \)
\( D \)


Moment of inertia of a bar magnet of mass \( m \) length \( l \) breath \( n \) is \( I \). then moment of inertia of another bar
magnet of mass \( 2 m \) length \( 2 l \) breath \( 2 b \) would be
\( A \cdot 81 \)
B. 4 1
c. 21
D.


Mineral which helps in formation of
RBCs is
A. Fe (iron)
B. Mn (manganese)
c. \( \mathrm{Mg} \) (magnesium)
D. K (potassium)


The equation \( \frac{x^{2}}{10-a}+\frac{y^{2}}{4-a}=1 \)
represents an ellipse if
\( \mathbf{A} \cdot a<4 \)
B \( . a>4 \)
c. \( 4<a<10 \)
D. None of these


Body cavity between the body and
internal organs is called


Find the first term of an A.P. in which
sum of any number of terms is always three times the squared number of these terms.


If \( f(x)=\left\{\begin{array}{l}\frac{1-\sqrt{2} \sin x}{\pi-4 x} x \neq \frac{\pi}{4} \frac{\pi}{4} \\ a, x=\frac{\pi}{4}\end{array}\right. \)
is continuous at \( x=\frac{\pi}{4} \) then \( a= \)
\( \mathbf{A} \cdot \mathbf{4} \)
B. 2
c. 1
D.


Total number of cis \( N-M n-C l \) bond
angles (that is, \( M n-N \) and \( M n-C l \)
bonds in cis position) present in a
molecule of cis \( \left[M n(e n)_{2} C l_{2}\right] \) complex
is
\( \left(e n=N H_{2} C H_{2} C H_{2} N H_{2}\right) \)


Human body temperature is well measured by
A. A clinical thermometer
B. A laboratory thermometer
c. Thermostat
D. Both A \& B can be used


Propene on hydration gives
A. propan-1-ol
B. propan-2-ol
c. propanal
D. methoxy ethane


If two variates \( X \) and \( Y \) are connected
by the relation \( \boldsymbol{Y}=\frac{\boldsymbol{a} \boldsymbol{X}+\boldsymbol{b}}{\boldsymbol{c}}, \) where
\( a, b, c \) are constants such that \( a c<0 \)
then
\( ^{\mathbf{A}} \cdot_{\sigma_{Y}}=_{c}^{a} \sigma_{X} \)
в. \( _{\sigma_{Y}}=-\frac{a}{c} \sigma_{X} \)
c. \( _{\sigma_{Y}}=\frac{a}{c} \sigma_{X}+b \)
D. none of these


Coenocytic mycelium is found in
A. Rhizopus
B. Mucor
c. Penicillium
D. Both A and B


As a matter of convention, an
anticlockwise moment is taken as
and a clockwise moment is
taken as


Explain the bonding in coordination compounds in terms of Werners postulates.


I: Gas-phase elements absorb or emit only specific wavelengths of visible light when excited by an electric
current.
Il: The energy levels that electrons can
occupy in gas-phase atoms and molecules are continuous.


Perform the division: \( x^{4}-16 \) by \( x-2 \)


In dynamic equilibrium condition, the reaction on both the sides occurs at the
same rate and the mass on both sides
of the equilibrium does not undergo any change. This condition can be achieved
only when the value of \( \Delta G \) is :
\( A \cdot-1 \)
B. +1
\( c \cdot+2 \)
\( D \)


Which one is largest and smallest
(a) Eosinophi
(b)Basophil
(c)Neutrophil
(d)Monocyte
(e) T-lymphocyte


If \( \boldsymbol{A}=\left[\begin{array}{ccc}1 & 1 & -1 \\ 2 & -3 & 4 \\ 3 & -2 & 3\end{array}\right] \) and \( B= \)
\( \left[\begin{array}{ccc}-1 & -2 & -1 \\ 6 & 12 & 6 \\ 5 & 10 & 5\end{array}\right], \) then which of the
following is/are correct?
1. \( A \) and \( B \) commute.
2. AB is null matrix.
Select the correct answer using the
code given below:
A. 1 only
B. 2 only
c. Both 1 and 2
D. Neither 1 nor 2


Which one of the following has largest number of isomers? \( (\mathbf{R}= \) alkyl group,
en \( = \) ethylenediamine
\( \mathbf{A} \cdot\left[\operatorname{Ru}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{C} 1_{2}\right]^{+} \)
B \( \cdot\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{C} 1\right]^{2+} \)
\( \mathbf{c} \cdot\left[\operatorname{Ir}\left(\mathrm{PR}_{3}\right)_{2} \mathrm{H}(\mathrm{CO})\right]^{2+} \)
D. \( \left[\mathrm{Co}(\mathrm{en})_{2} \mathrm{C} 1_{2}\right] \)


If \( \cos x=\sqrt{1-\sin 2 x}, 0 \leq x \leq \pi, \) then
possible value of \( x \) is
This question has multiple correct options
A . \( \pi \)
B.
\( c \cdot \tan ^{-1} 2 \)
D. \( 3 \pi \)


Write the formulas for the following
coordination compounds.
a)Tetraammineaquachloro cobalt (III) chloride
b)Potassium tetrahydroxozincate
c) Potassium trioxalatoaluminate (III)
d) Tetracarbonylnickel (0)


Lungs become empty after forceful expiration.
A. True
B. False


The displacement at a point due to two waves are \( y_{1}=\sin (500 \pi t) \) and \( y_{2}= \)
\( 2 \sin (506 \pi t) . \) The result due to their
superposition will be


Two coherent sources of equal
intensities produce a maximum of 100 units. If the amplitude of one of the
sources is reduced by \( 20 \% \), then the maximum intensity produced will be:
A . 100
B. 81
c. 89
D. 60


The nuclear reaction that takes place in a nuclear reactor is a/an
A. controlled fission reaction
B. uncontrolled fission reaction
c. nuclear fusion reaction
D. none of the above


Modified stem present in Gladiolus is
A. Bulb
B. Rhizome
c. corm
D. Bulbils


Evaluate \( \int_{0}^{3} \frac{x}{\sqrt{x^{2}+16}} d x \)


\( \ln \) an \( A C \) generator, the rate of change of
magnetic flux through the coil is maximum when the angle between the
plane of the coil and the lines of force is
A . \( 0^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 30^{\circ} \)
D. \( 90^{\circ} \)


The value of \( \mathbf{f}(\mathbf{0}) \) such \( \mathbf{f}(\mathbf{x})= \)
\( \frac{1-\cos ^{2} x+\sin ^{2} x}{\sqrt{x^{2}+1}-1}(x \neq 0) \) is
continuous at \( \mathbf{x}=\mathbf{0} \) is


In the following reactions:
\( (i) P C l_{5}+S O_{2} \rightarrow A+B \)
\( (i i) A+M e C O O H \rightarrow C+S O_{2}+ \)
\( \boldsymbol{H} \boldsymbol{C l} \)
\( (i i i) 2 C+M e_{2} C d \rightarrow 2 D+C D C l_{2} \) The
compound (C) is:
A. \( M e-C H-C l_{2} \)
в. \( M e-C H_{2}-C l \)
c. \( M e-\underset{\| O}{C}-C l \)
D. \( M e-C-C l_{3} \)


Find the value of \( a, \) if \( x-a \) is factor of
\( \boldsymbol{x}^{3}-\boldsymbol{a}^{2} \boldsymbol{x}+\boldsymbol{x}+\boldsymbol{2} \)


The focal length of a mirror is given by \( \frac{2}{f}=\frac{1}{v}-\frac{1}{u} . \) In finding the values of
and \( v, \) the errors are equal and equal to
'p'. The the relative error in \( f \) is
A \( \cdot \frac{p}{2}\left(\frac{1}{u}+\frac{1}{v}\right) \)
в. \( p\left(\frac{1}{u}+\frac{1}{v}\right) \)
c. \( \frac{p}{2}\left(\frac{1}{u}-\frac{1}{v}\right) \)
D. \( _{p}\left(\frac{1}{u}-\frac{1}{v}\right) \)


Tempering of steel:
A. is the heating the steel to appropriate temperature and then cooling it rapidly
B. increases mechanical strength
C. changes ratio of carbon in cementite
D. all of the above


What are the most favourable
conditions for the reaction;
\( \boldsymbol{S} \boldsymbol{O}_{2}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \leftrightharpoons \boldsymbol{S} \boldsymbol{O}_{3}(\boldsymbol{g}) ; \boldsymbol{\Delta} \boldsymbol{H}^{o}= \)
\( - \) ve to occur?
A. Low temp and high press
B. Low temp and low press
c. High temp and low press
D. High temp and high press


The 'Descent of Man' was published by
A. Charles Darwin in 1871
B. Charles Darwin in 1859
c. Hugo de Vries in 1901
D. Lamarck in 1809


The dimensional formula of a physical quantity is \( M^{1} L^{2} T^{3} I^{-1} \).What is its \( S \)
unit?
A \( \cdot k g \quad m^{2} s^{3} A^{-1} \)
B. \( k g \quad m^{2} s^{2} A \)
c. \( k g \quad m s^{-3} A^{2} \)
D. \( k g^{2} m^{2} s^{3} A^{-1} \)


Which of the following is not a general characteristic of equilibria involving physical processes?
A. Equilibrium is possible only in a closed system at a given temperature.
B. All measurable properties of the system remain constant
C. All the physical processes stop at equilibrium.
D. The opposing processes occur at the same rate and there is dynamic but stable condition


Direction of induced EMF can be found
from
A. Lenz law
B. Laplace law
c. Fleming law
D. None of the above


The manometer shown below is used to
measure the difference between water
level of the two tanks. Calculate this
difference for the conditions indicated
\( A \cdot 4 \mathrm{cm} \)
B. \( 40 \mathrm{cm} \)
\( c .100 \mathrm{cm} \)
D. \( 12 \mathrm{cm} \)


The dimension of permittivity of
vacuum
B \( \cdot\left[M^{-1} L^{-3} T^{4} A^{3}\right] \)
\( \mathbf{c} \cdot\left[M^{-1} L^{-3} T^{4} A^{2}\right] \)
\( \mathbf{D} \cdot\left[M^{-1} L^{-5} T^{4} A^{2}\right] \)


\( \arg (\mathrm{bi}),(b>0) \) is
A . \( \pi \)
в. \( \frac{\pi}{2} \)
\( c \cdot-\frac{\pi}{2} \)
D.


Myosin head separates from actin when?
A. ATP hydrolysis
B. When ATP attached to myosin headd
c. When ATP releases from myosin head
D. When ATP releases from Actin


An infinite number of charges 'q' each are placed along the \( x \) - axis at \( x=1, x=4 \)
\( x=8 \) and \( s o \) on. If the distance are in meters calculate the electric potential
at \( x=0 \)
\( A \cdot \frac{3 q}{8 F C_{0}} \)
B. \( \frac{q}{2 \pi_{0}} \)
\( c \cdot \frac{2 q}{\pi_{0} q} \)
D. \( \frac{49}{\pi_{0} q} \)


Name the process where cytoplasmic
material is divided into daughter cells.
A. Cell division
B. Cytokinesis
c. Karyokinesis
D. All of the above


Which of the following exerts profound effect on the reproductive growth of a flowering plant?
A. Quality of light
B. Quantity of light
c. Direction of light
D. Duration of light cycles


How does the cork act as a protective
tissue?


A radioactive atom \( _{Y}^{X} M \) emits two \( \alpha^{-} \) particles and one \( \beta \) -particle
respectively. The number of neutrons in
the product nucleus will be :
\( \mathbf{A} \cdot X-Y-4 \)
B. \( X-5-Y \)
c. \( X-3-Y \)
D. \( X-Y-6 \)


AU the particles of a system are situated at a distance \( r \) from the origin. The distance of the centre of mass of
the system from the origin is :
\( A \cdot=r \)
B. \( \leq r \)
\( c \cdot>r \)
\( D . \leq 0 \)


The distance \( x \) covered by a body
moving in a straight line in \( t \) is given by
the relation \( 2 x^{2}+3 x=t . \) If \( v \) is the
velocity of the body at a certain of time, its acceleration will be :
A \( .-v^{3} \)
B. \( -2 v^{3} \)
c. \( -3 v^{3} \)
D. \( -4 v^{3} \)


Both the parents contribute equal
amount of material to the
offspring.
A. Genetic
B. RNAA
c. Phenotypic
D. None of the above


Find the area of the region enclosed
between the two circles \( x^{2}+y^{2}=4 \)
and \( (x-2)^{2}+y^{2}=4 \)


A Carnot refrigerator extracts heat from
water at \( 0^{\circ} \mathrm{C} \) and rejects it to a room at
\( 24.4^{\circ} \mathrm{C} . \) The work required by the
refrigerator for every \( 1 \mathrm{kg} \) of water converted into ice is
(Latent heat of ice \( =336 \mathrm{kj} \mathrm{kg}^{-1} \) )
A . \( 24.4 k j \)
в. \( 30 k j \)
c. \( 336 k j \)
D. \( 11.2 k j \)


If a conductance of a conductor (G) is \( \frac{I^{2} t}{W}, \) where I is current, t is time and \( w \) is work done then write the unit of
conductance expressed in terms of fundamental units.
A. \( \frac{A^{2} s^{3}}{k g} m^{2} \)
в. \( \frac{A^{3} s^{2}}{k g} m^{2} \)
c. \( \frac{A^{2} s^{3}}{k g} m^{1} \)
D. \( \frac{A^{3} s^{2}}{k g \quad m^{1}} \)


The position of a particle varies
according to expression \( \boldsymbol{x}= \)
\( \boldsymbol{t}(\boldsymbol{t}-\mathbf{1})(\boldsymbol{t}-\mathbf{2}), \) velocity of the particle
is zero at times.
A \( \cdot\left(1-\frac{1}{\sqrt{3}}\right), 0 \)
в. \( \left(1+\frac{1}{\sqrt{3}}\right) \)
\( c \cdot 0,1 \)
D \( \cdot\left(1-\frac{1}{\sqrt{3}}\right),\left(1+\frac{1}{\sqrt{3}}\right) \)


Find the values of \( x \) which satisfy \( \left|\frac{x^{2}}{x-1}\right| \leq 1 \)
\( ^{\mathbf{A}} \cdot_{x} \in\left[\frac{-1-\sqrt{3}}{2}, \frac{-1+\sqrt{3}}{2}\right] \)
в. \( _{x} \in\left[\frac{-1-\sqrt{5}}{2}, \frac{-1+\sqrt{5}}{2}\right] \)
\( ^{\mathbf{c}} \cdot_{x} \in\left[\frac{-1-\sqrt{7}}{3}, \frac{-1+\sqrt{7}}{3}\right] \)
D. None of these


\( \sec ^{2} x \tan y d y+\sec ^{2} y \tan x d x=0 \)


Compound \( X \) react with sodium
phosphate in presence of conc. \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{\boldsymbol{3}} \)
from a yellow ppt, than \( \boldsymbol{X} \) is:
A \( \cdot M n O_{4}^{2} \)
в. \( M o C l_{4} \)
c. \( M o O_{4}^{2} \)
D. \( A I O_{2}^{-} \)


If \( \frac{a-b}{b-c}=\frac{a}{a}, \) then \( a, b, c \) are in
\( A \cdot G P \)
в. нР
\( c \cdot A P \)
D. sp


\( \ln \) a \( \Delta P R S, \angle P R S=120^{\circ} . A \) point \( Q \) is
taken of \( P R \) such that \( P Q=Q S \) and
\( Q R=R S \) then \( \angle Q P S=\dots \)
A \( \cdot 15^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 12^{\circ} \)


Which of the following is the most important part of chordate?
A. Hermichordate
B. Vertebrata
c. Mollusca
D. All of the above


A body is submerged in water. It is taken out and then submerged in mercury. What happens to its relative density with respect to the liquid in which it is submerged?
A . increases
B. decreases
c. remains constant
D. can't say


A p-type semiconductor is made from a silicon specimen by doping on a
average one indium atom per \( 5 \times 10^{7} \)
silicon atoms. If the number density of
atoms in the silicon specimen is \( 5 \times \) \( 10^{26} \) atoms \( / m^{3}, \) then the number of
acceptor atoms in silicon per cubic centimeter will be:
A \( .2 .5 \times 10^{30} \)
В. \( 1.0 \times 10^{13} \)
c. \( 1.0 \times 10^{15} \)
D. \( 2.5 \times 10^{36} \)


The primary coil of an idea step up transformer has 100 turns and
transformation ratio is also \( 100 . \) The
input voltage and power are respectively \( 220 V \) and \( 1100 W \)
calculate \( (2 M) \)
1. Number of turns in secondary
2. Current in primary
3. Voltage across secondary
4. Current in secondary
5. Power in secondary


Choose the correct answers from the
alternatives given.

Directions for question 71 to 73: Study the following bar chart and answer the questions based on it. The histogram below shows the marks of 50 students in an examination.
Examine the diagram and answer the
questions.

How many students obtained less than
40 marks?
\( A \)
\( B .2 \)
\( c \)
\( D \)


At \( 10^{\circ} \mathrm{C}, \) the osmotic pressure of urea
solution is 500 mm. The solution is
diluted and the temperature is raised to
\( 25^{\circ} C, \) when the osmotic pressure is
found to be 105.3 mm. Determine
extent of dilution?
A. Sol. \( \left(V_{\text {final}}=5 V_{\text {original}}\right) \)
B. Sol. ( \( \left.V_{\text {final}}=7 V_{\text {original}}\right) \)
c. sol. \( \left(V_{\text {final}}=3 V_{\text {original}}\right) \)
D. None of the above


\( l, m, n \) are parallel lines. If \( p \) intersects
them at \( A, B, C \) and \( q \) at \( D, E, F, \) then
A. \( A B=D E \) and \( B C=E F \) always
B. At least one of the pairs \( A B, D E \) and \( B C, E F \) are necessarily equal
c. At least one of the pairs \( A B, B C \) and \( D E, E F \) are necessarily equal
D. \( \frac{A B}{B C}=\frac{D E}{E F} \)


The first atomic reactor was made by
A. Fermi
B. Bohr
c. Taylor
D. Rutherford


How many \( \alpha \) and \( \beta \) -particles should be
eliminated so that an isodiaphere is
formed?
\( \mathbf{A} \cdot n \alpha, n \beta \)
B . \( n \alpha,(n+1) \beta \)
\( c \cdot n a \)
D. \( n \beta \)


If \( \tan \alpha \) and \( \tan \beta \) are the roots of the
equation \( \boldsymbol{x}^{2}+\boldsymbol{p} \boldsymbol{x}+\boldsymbol{q}=\boldsymbol{0}(\boldsymbol{p} \neq \boldsymbol{0}), \) then
This question has multiple correct options
A \( \cdot \sin ^{2}(\alpha+\beta)+p \sin (\alpha+\beta) \cos (\alpha+\beta)+q \cos ^{2}(\alpha+\beta)= \)
\( q \)
B. \( \tan (\alpha+\beta)=\frac{p}{q-1} \)
\( \mathbf{c} \cdot \cos (\alpha+\beta)=1-q \)
\( \mathbf{D} \cdot \sin (\alpha+\beta)=-p \)


In ATG ACC AGG ACC CCA ACA sequence,
the first base gets mutated. It will affect
A. Change in types and sequence of amino acids
B. Change in first amino acid only
c. No change
D. One amino acid less


Number of Partial Fractions of
\( \frac{x^{3}+x^{2}+1}{x^{4}+x^{2}+1} \) is
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D.


The ray diagram could be correct
A \( \cdot \) If \( n_{1}=n_{2}=n_{g} \)
B. If \( n_{1}=n_{2} \) and \( n_{1}<n_{g} \)
\( \mathrm{c} \cdot \) If \( n_{1}=n_{2} \) and \( n_{1}>n_{g} \)
D. under no circumstances


If the perimeter and the area of a circle are numerically equal, then the radius of the circle is:
A . 2 units
B. \( \pi \) units
c. 4 units
D. 7 units


A coil mean area \( 500 \mathrm{cm}^{2} \) and having
1000 turns is held perpendicular to a uniform field of 0.4 gauss. The coil is turned through \( 180^{0} \) in \( \frac{1}{10} \) second. The average induced emf is
\( \mathbf{A} \cdot 0.02 V \)
B. \( 0.04 V \)
c. \( 1.4 V \)
D. \( 0.08 V \)


In the given circuit \( R \) in pure resistance
and \( X \) is unknown circuit element. An
AC voltage source is applied across \( \boldsymbol{A} \)
and \( C . \) If \( V_{A B}=V_{A C}, \) then \( X \) is
A. Pure resistance
B. Pure inductance
C. Combination of inductance and capacitance at
resonance
D. None of the above


Electrical field is used to deflect :
A. \( \alpha \) and \( \beta \) particles
B. \( \alpha \) and \( \gamma \) particles
c. \( \alpha, \beta \) and \( \gamma \) particles
D. \( \beta \) and \( \gamma \) particles


Which of the following is not an isomer of 1-butyne?
A. But-2-yne
B. Buta -1,3- dine
c. But-z-ene
D. Methyl cyclopropene


Identify the correct sequence of
taxonomic hierarchical arrangement in
ascending order.
A. Spermatophyta, Sapindales, Dicotyledons, Anacardiaceae, Mangifera
B. Mangifera, Dicotyledons, Anacardiaceae, Spermatophyta, Sapindales
C. Mangifera, Anacardiaceae, Sapindales, Dicotyledons, Spermatophyta
D. Dicotyledons, Anacardiaceae, Sapindales, Spermatophyta, Mangifera


Obtain an expression for the self-
inductance of a long solenoid.


If the radius of a nucleus with mass
number 125 is 1.5 Fermi, then radius
of a nucleus with mass number 64 is
A . 0.48 Fermi
B. 0.96 Fermi
c. 1.92 Fermi
D. 1.2 Fermi


In a uniform circular motion
(horizontal) of a ball tied with a string,
velocity at any time is at an angle, \( \boldsymbol{\theta} \)
with acceleration. Then \( \boldsymbol{\theta} \) is:
A \( \cdot 60^{\circ} \)
B. \( 30^{\circ} \)
\( c .90^{\circ} \)
D. none of the above


Which of the following pairs of homologous series is represented by the general molecular formula
\( \boldsymbol{C}_{\boldsymbol{n}} \boldsymbol{H}_{2 \boldsymbol{n}-2} ? \)
A. Alkene and alkyne
B. Alkyne and alkadiyne
c. Alkane and alkadiene
D. Alkyne and alkadiene


The atomic mass of deuterium isotope
of hydrogen is \( 2 . \) The atomic mass of oxygen is 16. Then what is the
molecular mass of heavy water?
A . 16
B . 18
c. 20
D. 24


(i) Write the truth tables of the logic
gates market \( \boldsymbol{P} \) and \( \boldsymbol{Q} \) in the given
circuit.
(ii) Write the truth table for the circuit


Normal force is a type of
A. Contact force
B. Non contact force
C. Both A and B
D. None


In the extraction of copper from its sulphide ore, the metal is finally obtained by the reduction of cuprous
oxide with:
A. copper(I) sulphide
B. sulphur dioxide
c. iron(II) sulphide
D. carbon monoxide


According to 1921 census the population of India was approximately
A. 20 crores
B. 25 crores
c. 30 crores
D. 35 crores


The radius of two cylinders are in the ratio 2: 3 and their heights are in the
ratio \( 3: 5 . \) Find the ratio of their
volumes.
A \( \cdot \frac{2}{3} \)
B. \( \frac{3}{5} \)
c. \( \frac{4}{15} \)
D. \( \frac{3}{2} \)


Cultivation of plants by placing the roots in the nutrient solution is called
as
A. Geoponics
B. Hydroponics
c. Aeroponics
D. None of the above


Complete the reaction:
\[
\langle\mathrm{Br}+\mathrm{Mg} \stackrel{\mathrm{dry} \text { ether }}{\rightarrow} \mathrm{A} \stackrel{\mathrm{H}_{2} \mathrm{O}}{\longrightarrow} \mathrm{B}
\]


What is the wavelength of light emitted
when the electron in hydrogen atom undergoes transition from an energy level with \( n=4 \) to an energy level with \( n=2 \)
? What is the colour of the radiation?


Five balls numbered 1,2,3,4,5 are
suspended using reparate threads. The balls (1,2),(2,4) and (4,1) show electrostatic attraction, while (2,3) and (4,5) show repulsion. Therefore, ball 1
must be
A. negatively charged
B. positively chargedd
c. neutral
D. made of metal


The lowest value of paramagnetism is shown by?
\( \mathbf{A} \cdot\left[\operatorname{Co(CN)}_{6}\right]^{3} \)
B . \( \left[F e(C N)_{6}\right]^{3-} \)
c. \( \left[C r(C N)_{6}\right]^{3-} \)
D. \( \left[M n(C N)_{6}\right]^{3} \)


A sample of air is saturated with benzene (vapour pressure =100 mm Hg at \( 298 \mathrm{K} \) ) at \( 298 \mathrm{K}, 750 \mathrm{mm} \) Hg pressure. If it is isothermally compressed to one third of its initial volume, the final
pressure of the system is:
A. 2250 torr
B . 2150 torr
c. 2050 torr
D. 1950 torr


Which one of the following is aromatic amine?
\( A \)
B.
\( c \)
D. Both \( A \) and \( B \)


If 3.65 got \( \mathrm{HCl} \) is dissolved in \( 16.2 \mathrm{g} \) of water then the mole fraction of HCl in
the resulting solution is:


Among the three isomers of the nitrophenol, the one that is least soluble in water is:
A. m-nitrophenol
B. o-nitrophenol
c. p-nitrophenol
D. none of these


Pressure of an ideal gas is increased by keeping temperature constant. What is effect on kinetic energy of molecules?
A. Increase
B. Decrease
c. No change
D. Cannot be determined


The source of retinol (vitamin A) is:
A . liver
B. kidney
C. fish oils
D. all the above


One gram molecule of any gas at \( N T P \) occupies 22.4 L. This fact was derived from:
A. Dalton's theory
B. Avogardro's hypothesis
c. Berzelius hypothesis
D. Law of gaseous volume


Which of the following is not
isostructural with \( S i C l_{4} ? \)
\( \mathbf{A} \cdot P O_{4}^{3-} \)
B. \( N H_{4}^{+} \)
\( c \cdot s C l \)
\( \mathbf{D} \cdot S O_{4}^{2-} \)


Match the scientist and their
discoveries given in Column I and I
correctly and choose the correct
combination from the following.
\( \mathbf{A} \)
\( A-p, B-q, C-r, D-t \)
B. \( A-q, B-p, C-s, D-t \)
C. \( A-q B-p, C-r, D-t \)
D. \( A-q, B-p, C-t \)
\( D \)


\( \mathrm{f}\left|\begin{array}{ccc}\boldsymbol{x} & \boldsymbol{x}+\boldsymbol{y} & \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z} \\ \mathbf{2} \boldsymbol{x} & \mathbf{3} \boldsymbol{x}+\mathbf{2} \boldsymbol{y} & \boldsymbol{4} \boldsymbol{x}+\boldsymbol{3} \boldsymbol{y}+\boldsymbol{2} \boldsymbol{z} \\ \boldsymbol{3} \boldsymbol{x} & \boldsymbol{6} \boldsymbol{x}+\boldsymbol{3} \boldsymbol{y} & \boldsymbol{1} \mathbf{0} \boldsymbol{x}+\boldsymbol{6} \boldsymbol{y}+\boldsymbol{3} \boldsymbol{z}\end{array}\right|=\mathbf{6} \boldsymbol{4} \)
then find \( x \)


A conducting rod of length \( l \) falls
vertically under gravity in a region of uniform magnetic field \( \vec{B} \). The field vectors are inclined at an angle \( \boldsymbol{\theta} \) with
the horizontal as shown in figure. If the
instantaneous velocity of the rod is \( \boldsymbol{v} \)
the induced emf in the rod \( a b \) is:
\( \mathbf{A} \cdot B l v \)
B. \( B l v \cos \theta \)
c. \( B l v \sin \theta \)
D. zero


Which one of the amine have highest boiling point?
A. Primary amine
B. Secondary amine
c. Tertiary amine
D. all of these


The value of \( ^{19} C_{18}+^{19} C_{17} \)
\( \mathbf{A} \cdot 1200 \)
B. 2000
\( \mathbf{C} \cdot 190 \)
D. None of these


The Sl unit of electric potential is
A. \( V m^{-1} \)
в. \( C \)
c. \( N C^{-1} \)
D. \( V \)


Name the first organic compound which obtained from an inorganic compound with formulae.


By splitting a total mass \( M \) in two
masses \( M_{1} \) and \( M_{2} \), the maximum
value of tension that can be produced in
the string 1 as shown in the figure is:
A. \( \frac{M g}{2} \)
в. \( M g \)
\( c \cdot \frac{M g}{4} \)
D. \( 4 M g \)


\( f(x)=\left\{\begin{array}{ll}\frac{1-\sin ^{3} x}{3 \cos ^{2} x}, & \text { if } \quad x<\frac{\pi}{2} \\ a, \quad \text { if } x= & \frac{\pi}{2} \\ \frac{b(1-\sin x)}{(\pi-2 x)^{2}}, & \text { if } \quad x>\frac{\pi}{2}\end{array}\right. \)
so that \( f(x) \) is continuous at \( x=\frac{\pi}{2} \)
then
This question has multiple correct options
A \( a=\frac{1}{2} \)
в. \( b=4 \)
\( c \cdot a=1 \)
D. \( b=-4 \)


In Jeeps we use
A. Mechanical brakes
B. Hydraulic brakes
C. Air brakes
D. water brakes


The solubility of \( A g C l \) is \( 1 \times \)
\( 10^{-5} \) mol \( / L . \) Its solubility in 0.1 molar
sodium chloride solution is:
A \( \cdot 1 \times 10^{-10} \)
В. \( 1 \times 10^{-5} \)
c. \( 1 \times 10^{-9} \)
D. \( 1 \times 10^{-4} \)


Genus is a group of similar and related
A. Classes
B. Phyla
c. species
D. Orders


Fermentation refers to
A. Anaerobic respiration
B. Incomplete oxidation of carbohydrate
C. Complete oxidation of carbohydrate
D. Both A and B


Assertion
\( B F_{3} \) is a weaker Lewis acid than \( B C l_{3} \)
Reason

The planar \( B F_{3} \) molecule is stabilised
to a greater extent than \( B C l_{3} \) by \( B-X \)
\( \pi \) -bonding.
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


Find the distance of a perpendicular from the centre of a circle to the chord if
the diameter of the circle is \( 30 \mathrm{cm} \) and
its chord is \( 24 \mathrm{cm} \)
\( \mathbf{A} \cdot 6 \mathrm{cm} \)
в. \( 7 \mathrm{cm} \)
\( \mathrm{c} .9 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)


If \( |\boldsymbol{x}|<1 \) then \( \mathbf{7}^{\text {th}} \) term in the expansion
of \( (1-x)^{-2} \) is
A \( \cdot 7 x^{8} \)
В . \( 7 x^{6} \)
\( c \cdot 6 x^{7} \)
D. \( 6 x^{6} \)


The energy band diagrams for three
semiconductor sample of silicon are
shown. It follows that.
A. Sample X is undoped while samples Y and Z have been doped with a third group and a fifth group impurity respectively
B. Sample X is undoped while both samples Y and Z have been doped with a fifth group impurity
c. Sample X has been doped with equal amounts of third and fifth group impurities while samples \( Y \) and \( z \) are undoped
D. Sample X is undoped while samples Y and Z have been doped with a fifth group and a third group impurity respectively


is rich in source of
vitamin C.


The covalent alkaline earth metal halide
\( (\boldsymbol{X}=\boldsymbol{C l}, \boldsymbol{B r}, \boldsymbol{I}) \) is:
A. \( \operatorname{CaX}_{2} \)
в. \( \operatorname{Sr} X_{2} \)
\( \mathbf{c} \cdot B e X_{2} \)
D. \( M g X_{2} \)


A substance that prevents electric
current from passing through it is called
A. a conductor
B. an insulator
c. a semiconductor
D. a superconductor


Which of the following statements is
true for collisions-
A. Momentum is conserved in elastic collisions but not in inelastic collisions
B. Total kinetic energy is conserved in elastic collisions but momentum is not conserved
C. Total kinetic energy is not conserved in inelastic collisions but momentum is conserved
D. Total kinetic energy and momentum both are conserved in all types of collisions


A body dropped from the top of a tower
covers a distance \( 7 x \) in the last second
of its journey, where \( x \) is the distance
covered in the first second. How much
time does it take to reach the ground?
A . \( 3 s \)
B. \( 4 s \)
\( c .5 s \)
D. \( 6 s \)


Prove that the mid-point of the hypotenuse of right angled triangle is equidistant from its vertices.


What is the molarity of \( 0.2 \mathrm{N} \mathrm{Na}_{2} \mathrm{CO}_{3} \)
solution?
A. \( 0.1 \mathrm{m} \)
B. O M
c. \( 0.4 \mathrm{M} \)
D. 0.2 M


In which one of the following enzymes, is copper necessarily associated as an activator?
A. Lactic dehydrogenase
B. Tyrosinase
c. carbonic anhydrase
D. Trytophanase


Explain Huygen's principle of secondary
wavelets.


A fruit-seller sells 4 oranges for Rs. 3 gaining \( 50 \% \) If S.P. of one orange is 0.75 Rs, then type
1 or else type 0


Assertion
e/m ratio of anode rays is independent
of nature of gas.
Reason
All anode rays are protons
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


Find the value of \( x \) such that
\( \frac{(x+\alpha)^{2}-(x+\beta)^{2}}{\alpha+\beta}=\frac{\sin 2 \theta}{\sin ^{2} \theta} . \) when \( \alpha \)
and \( \beta \) are the roots of \( t^{2}-2 t+2=0 \)
A. \( x=i \)cot \( \theta-1 \)
B. \( x=-(i \text { cot } \theta+1) \)
\( \mathbf{c} \cdot x=i \cot \theta \)
D. \( x= \) itan \( \theta-1 \)


The first and last elements of actinides
are:
A. Actinium and Thorium
B. Actinium and Nobelium
c. Actinium and Mendelevium
D. Actinium and Lawrencium


If \( A \) is \( 3 x 3 \) matrix and \( \operatorname{det} \operatorname{adj}(A)=k \)
then
\( \operatorname{det}(\operatorname{adj} 2 A)= \)
\( A \cdot 2 k \)
в. 8k
\( c \cdot 16 k \)
D. \( 64 k^{2} \)


Solve :
\( \left(14 x^{3} \times 2 x^{4} \times 8 x^{8}\right) \div 7 x^{3} \)


Determined the molecular mass of
water


The growth of fish gets inhibited if the concentration of dissolved oxygen in water is:
A. less than 2ppm
B. less than 6ppm
c. less than 15 ppm
D. less than 17ppm


Two cards are drawn with replacement
from a well shuffled deck of 52 cards.
Find the mean and variance for the
number of aces


In the electric network shown in the
figure, use Kirchhoff's rules to calculate
the power consumed by the resistance
\( R=4 \Omega \)


Which one is responsible for radial conduction of water and food in woody
stems?
A. vessels
B. Vascular rays
c. Endodermis
D. Xylem fibers


What is meant by
In honey bee, males don't have fathers
\& thus can't have sons...but have a
grand father \( \& \) can have grand sons...??


The very toxic gas which causes a headache, visual difficulty, paralysis, and even death in the human beings is:
A) \( C O_{2} \)
B) \( \boldsymbol{O}_{3} \)
C) \( C O \)
\( A \cdot A \& B \)
B. A
\( c \cdot c \)
D. B


Two charges \( q_{1} \) and \( q_{2} \) are placed \( 30 c m \)
a part as shown. A third charge \( q_{3} \) is
moved along the circle of radius \( 40 \mathrm{cm} \)
from \( C \) to \( D \). The change in the potential energy of the system is \( \frac{q_{3} K}{4 \pi \epsilon_{0}} \)
Find K?
\( \mathbf{A} \cdot 8 q_{2} \)
B. \( 8 q \)
\( c \cdot 6 q_{2} \)
D. \( 6 q \)


A substance of mass \( M \) requires a
power input of \( \boldsymbol{P} \) watts to ramain in the
molten state at its melting point. When the power source is turned off, the
sample completely solidifies in time \( t \)
sec. The specific latent heat of fusion of the substance is:
A \( . P t \)
в. \( \frac{P t}{M} \)
c. \( P t M \)
D. \( \frac{P M}{t} \)


Which of the following is more covalent among the following and why?
1) Cuo and Cus
2)AgCI and Agl
3) \( P b c l_{2} \) and \( p b C l_{4} \)
4)NaCl and CuCl


On placing an inverted tumbler over a burning candle, the flame extinguishes after some time. This is because of the
non-availability of:
A. oxygen
B. water vapour
c. carbon dioxide
D. wax


Human population is directly affected by which of the following?
A. Availability of medical facilities
B. Standard of living
c. Availability of food and shelter
D. All of the above


A particle executing simple harmonic motion has an angular frequency of \( 6.28 s^{-1} \) and an amplitude of \( 10 \mathrm{cm}, \) the speed when the displacement is \( 6 \mathrm{cm} \) from the mean position is:
A. \( 50.2 \mathrm{cm} / \mathrm{s} \)
в. \( 60.2 \mathrm{cm} / \mathrm{s} \)
c. \( 70.2 \mathrm{cm} / \mathrm{s} \)
D. \( 80.2 \mathrm{cm} / \mathrm{s} \)


\( \boldsymbol{F} \boldsymbol{e} \boldsymbol{C l}_{3} \cdot \boldsymbol{6} \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{C}\left(\boldsymbol{C} \boldsymbol{H}_{3}\right)_{2}\left(\boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{O}\right)_{2} \rightarrow \)
Products.
Reaction products are:
A. \( F e C l_{3}, C H_{3} O H \) and \( C H_{3} C O C H_{3} \)
B. \( \left.C H_{3} O\right)_{3} \) Fe, HCl and \( H_{2} \) O
c. \( F e C l_{2}, H C l \) and \( C H_{3} C O C H_{3} \)
D. \( F e(O H)_{3}, F e C l_{3} \) and \( C H_{3} C O C H_{3} \)


What change will you observe if you test soap with litmus paper (red and blue)?
A. It will turn red litmus blue
B. It will turn blue to red
c. Red litmus paper won't change colour
D. None of these


Determine the potential drop between
the points \( A \) and \( C \) in the following
circuit. Resistances \( 1 \Omega \) and \( 2 \Omega \) (internal
resistance of cell) :
A. \( \frac{4}{5} v \)
B . \( 1.75 V \)
c. \( 2.25 V \)
\( D \cdot \frac{5}{1} V \)


When chlorine water is exposed to
sunlight \( O_{2} \) is liberated. Hence :
A. hydrogen has little affinity to \( O_{2} \)
B. hydrogen has more affinity to \( O_{2} \)
c. hydrogen has more affinity to chlorine
D. it is a reducing agent


Which of the following is correct order of
stability?
\( \mathbf{A} \cdot T i^{3+}>B i^{3+} \)
в. \( P b O_{2}>P b O \)
c. \( B i I_{5}<B i F_{5} \)
D. \( S n^{2+}<G e^{2} \)


A body is dropped from a height \( 39.2 m \)
After it crosses the half distance, the
acceleration due to gravity ceases to
act. Then the body will hit the ground
with a velocity of (Take \( \boldsymbol{g}=\mathbf{9 . 8} \mathbf{m s}^{-\mathbf{2}} \mathbf{)} \)
\( \mathbf{A} \cdot 19.6 \mathrm{ms}^{-1} \)
В. \( 20 m s^{-1} \)
c. \( 1.96 \mathrm{ms}^{-1} \)
D. \( 196 \mathrm{ms}^{-1} \)


Two elements \( A \) and \( B \) form ideal
compounds of formula \( A B_{2} \) and \( A B_{4} \) When dissolved in \( 20.0 g \) of benzene 1.0 \( g \) of \( A B_{2} \) lowers freezing point by \( 2.3^{0} C \) whereas \( 1.0 g \) of \( A B_{4} \) lowers
freezing point by \( 1.3^{0} \mathrm{C} \). The \( K_{f} \) for
benzene is \( 5.4 . \) The atomic masses of \( A \)
and \( B \) are:
A .27,45
в. 42,25
c. 52,48
D. 48,52


The magnetic moment of an electron
with orbital angular momentum \( \boldsymbol{J} \) will
be:
\( ^{\mathbf{A}} \cdot \frac{e \vec{J}}{m} \)
B. \( \frac{e \vec{J}}{2 m} \)
c. \( \frac{2 m}{e \bar{J}} \)
D. zero


State the location and functions of
different types of meristems.


Write the S.I. unit of capacitance.


Growth promoting hormone is
A. \( 2,4- \) D
B. ABA
c. Gibberellin
D. IAA


A small body of super dense material, with mass equal to half of that of earth
but whose size is very small compared
to that of earth, starts from rest at the
height h<
\( A \cdot \sqrt{\frac{2 h}{q}} \)
в. \( \sqrt{\frac{4 h}{3 g}} \)
c. \( \sqrt{\frac{2 h}{3 g}} \)
D. \( \sqrt{\frac{h}{g}} \)


\( F e^{3+} \) oxidises \( N H_{2} O H \) to give:
A \( . N O_{2} \)
в. \( N_{2} \) 0
c. \( N_{2} \)
D. \( N O \)


Find the electric field for \( \mathbf{0}<\boldsymbol{r}<\boldsymbol{R} \)
\( ^{\mathbf{A}} \cdot_{E}=\frac{\rho_{0} r^{2}}{3 R \epsilon_{0}} \)
В. \( \quad E=\frac{\rho_{0} r^{2}}{4 R \epsilon_{0}} \)
\( ^{\mathrm{C}} E=\frac{\rho_{0} r^{2}}{2 R \epsilon_{0}} \)
D. \( \quad E=\frac{\rho_{0} r^{2}}{R \epsilon_{0}} \)


\( \lim _{x \rightarrow 0} \frac{3^{2 x}-2^{3 x}}{x} \) is equal to
A \( \cdot \log \frac{3}{2} \)
B.
c. \( \log \frac{9}{8} \)
D.


A ring rolls without slipping on a horizontal surface. At any instant, its
position is as shown in the figure.
This question has multiple correct options
A. Section ABC has greater kinetic energy than section ADC
B. Section BC has greater kinetic energy than section CD
c. Section BC has the same kinetic energy as section DA.
D. The section AB, BC, CD, and DA have the same kinetic
energy


A boat is moving with velocity \( 3 \hat{i}+4 \hat{j} \)
with respect to ground. The water in the river is moving with velocity \( -3 \hat{i}-4 \hat{j} \) with respect to ground. The relative velocity of the boat with respect to water is
A. 83
B . \( -6 \hat{i}-8 \hat{j} \)
c. \( 6 \hat{i}+8 \hat{j} \)
D. \( 6 \hat{i} \)


A gas cylinder has a diameter of \( 14 \mathrm{m} \)
and height is \( 0.2 \mathrm{m} \). Find its surface area. \( (\pi=22 / 7) \)
A. \( 316.512 m m^{2} \)
B. \( 316.512 m \)
\( \mathbf{c} \cdot 316.512 m^{3} \)
D. \( 316.512 m^{2} \)


Let \( z \neq-i \) be any complex number such that \( \frac{z-i}{z+i} \) is a purely imaginary
number. Then \( z+\frac{1}{z} \) is :
A. 0
B. Any non-zero real number other than 1.
C. Any non-zero real number
D. A purely imaginary number


Using a ruler and compass only.
(i) Construct a \( \triangle A B C \) with the
following data. \( A B=3.5 \mathrm{cm}, B C=6 \mathrm{cm} \) and
\( \angle A B C=120^{\circ} \)
(ii) In the same diagram, draw a circle
with \( B C \) as diameter. Find a point \( P \) on the circumference of the circle which is
equidistant from \( A B \) and \( B C \)
(iii) Measure \( \angle B C P \)


which type of the hybridisation of each of the carbon is there in the compound?
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}=\boldsymbol{C H}-\boldsymbol{C N} \)
B \( \cdot s p^{3}, s p^{2}, s p^{2}, s p^{3} \)
C \( \cdot s p^{3}, s p^{2}, s p^{3}, s p^{3} \)
D. \( s p^{3}, s p^{2}, s p, s p^{3} \)


Albert buys 4 horses and 9 cows for Rs.
\( 13400 . \) If he sells the horses at \( 10 \% \)
profit and the cows at \( 20 \% \) profit, then
he earns a total profit of Rs. 1880. The \( \operatorname{cost} \) of a horse is
A. Rs. 1000
B. Rs. 2000
c. Rs. 2500
D. Rs. 3000


Solve the following Linear Programming problems graphically:
1. Maximize \( Z=3 x+4 y \quad \) Subject to
the constraints \( : x+y \leq 4, x \geq 0, y \geq \)
\( \mathbf{0} \)
2. Minimize \( Z=-3 x+4 y \quad \) subject
to \( x+2 y \leq 8,3 x+2 y \leq 12, x \geq \)
\( \mathbf{0}, \boldsymbol{y} \geq \mathbf{0} \)


\( \mathbf{f} \mathbf{\Delta}=\left|\begin{array}{cc}\mathbf{f}(\boldsymbol{x}) & \boldsymbol{f}\left(\frac{\mathbf{1}}{\boldsymbol{x}}\right)+\boldsymbol{f}(\boldsymbol{x}) \\ \mathbf{1} & \boldsymbol{f}\left(\frac{\mathbf{1}}{\boldsymbol{x}}\right)\end{array}\right|=\mathbf{0} \)
where;
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{a}+\boldsymbol{b} \boldsymbol{x}^{n} \) and \( \boldsymbol{f}(\boldsymbol{2})=\mathbf{1 7}, \) then
\( \boldsymbol{f}(\mathbf{5}) \) is:
A . 126
в. 326
\( c .428 \)
D. 626


Who introduced the term species?


If \( \boldsymbol{S}=^{404} \boldsymbol{C}_{4}-^{4} \boldsymbol{C}_{1} \cdot^{303} \boldsymbol{C}_{4}+^{4} \)
\( C_{2} \cdot^{202} C_{5}-^{4} C_{3} \cdot^{101} C_{4}=(101)^{k} \) then \( k \)
equal to
A . 1
B . 2
\( c \cdot 4 \)
D. 6


Why are potassium and caesium used,
rather than lithium used in
photoelectric cells?


Fill in the blanks:
Light is a form of that we
detect with our
A. energy, ears
B. corpuscles, eyes
c. energy, eyes
D. sensation, skin


A quantity \( X \) is given by \( \epsilon_{0} L \frac{\Delta V}{\Delta T} \) where so is the permittivity of the free space, is a length. \( \Delta V \) is a potential difference
and \( \Delta t \) is a time interval. The
dimensional formula for \( X \) is the same
as that of
A . resistance
B. charge
c. voltage
D. current


The probability that \( \boldsymbol{P} \cap \boldsymbol{Q}=\boldsymbol{A} \)
contains just one element, is
\( ^{\mathrm{A}} \cdot_{n}\left(\frac{3}{4}\right)^{n} \)
B. \( \left(\frac{1}{4}\right)^{n} \)
c. \( \frac{n}{3}\left(\frac{1}{2}\right)^{n} \)
D. \( \left(\frac{3}{4}\right)^{n} \)


Which site of the RNA pairs through hydrogen boding with the triplet codes on mRNA?
A. codon
B. \( 5^{\prime} \) end of tRNA
c. \( 3^{\text {' end of tRNA }} \)
D. Anticodon
E. Amino acid acceptor end


When hydrogen is passed over a black solid compound \( A, \) the products are 'a colourless liquid' and 'a reddish brown
metal B'.

Substance B is divided into two parts,
each placed in separate test tubes. Dilute HCl is added to one part of
substance B and dilute \( H N O_{3} \) to the
other. What happens to substance \( A \) when it reacts with hydrogen ? Give
reasons for your answer


A body \( B \) is capable of remaining
stationary inside a liquid at the position shown in Fig.4.205 (a). If the whole system in gently placed on smooth inclined plane (Fig.4205 (b)) and is allowed to side down, then
\( \left(\boldsymbol{O}<\boldsymbol{\theta}<\boldsymbol{9 0}^{o}\right) \)
(a)
(b)
A. The body will move up (relative to liquid)
B. The body will move down (relative to liquid)
C. The body will remain stationary (relative to liquid)
D. The body will move up for some inclination \( \theta \) and will move down for another inclination \( \theta \)


Find the value of
\( 13+21+29+. .173 \)


Reorganisation of genetic material or genetic recombination occurs during
A. Metamorphosis
B. Organogenesis
c. Mitosiss
D. Meiosis


Find the equation of the line in vector and in Cartesian form that passes through the point with position vector \( 2 \hat{i}-\hat{j}+4 \hat{k} \) and is in the direction \( \hat{i}+ \) \( \mathbf{2} \hat{\boldsymbol{j}}-\hat{\boldsymbol{k}} \)


The structural component of ribosome
is
A . t-RNA
B. m-RNA
c. r-RNA
D. DNA


At \( 300 K, \) the initial pressure of a
reactant \( R \) is 100 mm. After 60 secs, the
pressure becomes 75 mm. Find the
average rate of the reaction.
A \( \cdot 10 \times 10^{-5} \) molL \( ^{-1} \) se \( c^{-1} \)
B. \( 5 \times 10^{-5} \) molL \( ^{-1} \) sec \( ^{-1} \)
C. \( 4.22 \times 10^{-5} \) molL \( ^{-1} \) sec \( ^{-1} \)
D. \( 2.22 \times 10^{-5} \) molL \( ^{-1} \) sec \( ^{-1} \)


Name the organ which performs the following function in humans
(a) Absorption of digested food
(b) Absorption of water


Evaluate the following integral:
\( \int \sec ^{4} x \tan x d x \)


Which of the following is a quadratic polynomial?
A. \( p(x)=5 x+1 \)
в. \( p(x)=1-5 x \)
C \( \cdot p(x)=5 x^{2}-25 \)
D・ \( p(x)=5^{2}-4^{2} \)


Water gas is prepared by passing:
[EAMCET - 95 -M]
A. steam over HCl
B. air over red hot coke
c. steam and air over red hot coke
D. steam over red hot coke


What mass of \( H_{2} S O_{4} \) could be
produced in the process given below if \( 1.00 k g \) of \( F e S_{2} \) is used? The
unbalanced equations for the process
are:
\[
\begin{array}{l}
\boldsymbol{F e} \boldsymbol{S}_{2}+\boldsymbol{O}_{2} \longrightarrow \boldsymbol{F} \boldsymbol{e}_{2} \boldsymbol{O}_{3}+\boldsymbol{S} \boldsymbol{O}_{2} \\
\boldsymbol{S} \boldsymbol{O}_{2}+\boldsymbol{O}_{2} \longrightarrow \boldsymbol{S} \boldsymbol{O}_{3} \\
\boldsymbol{S} \boldsymbol{O}_{3}+\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \longrightarrow \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{7} \\
\boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{7}+\boldsymbol{H}_{2} \boldsymbol{O} \longrightarrow \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}
\end{array}
\]
A . \( 1.55 \mathrm{kg} \)
в. \( 1.63 \mathrm{kg} \)
c. \( 3.26 \mathrm{kg} \)
D. \( 1.65 \mathrm{kg} \)


The circuit diagram shows that resistors \( 2 \Omega, 4 \Omega \) and \( R \Omega \) connected to
a battery of e.m.f. 2 V and
internal resistance \( 3 \Omega \). A main
current of 0.25 A flows through the
circuit. The p.d. across the internal
resistance of the cell is :
A . \( 0.75 \mathrm{v} \)
B. 2
\( c \cdot 0.5 v \)
0.11


When reflection takes place from a
spherical mirror, positions of the object and its image are known as:
A . poles
B. conjugate foci
c. focal length
D. center of focus


A resistor \( R, \) an inductor \( L \) and
capacitor \( C \) are connected in series to
an oscillator of frequency \( n \). If the
resonant frequency is \( n_{r}, \) then the current lags behind voltage, when
\( \mathbf{A} \cdot n=0 \)
в. \( n<n_{r} \)
c \( \cdot n=n_{r} \)
\( \mathbf{D} \cdot n>n_{r} \)


\( \boldsymbol{S} \boldsymbol{O}_{2} \) behaves as a reducing agent
when :
A. Passed over hot \( C u O \)
B. Mixed with moist \( H_{2} S \)
c. Passes through acidified \( K M n O_{4} \) solution
D. Passed through \( F e S O_{4} \) solution.


Colemanite is
\( \mathbf{A} \cdot N a_{2} B_{4} O_{7} \cdot 10 H_{2} O \)
B \( \cdot C a_{2} B_{6} O_{11} \cdot 5 H_{2} O \)
\( \mathbf{c} \cdot N a B O_{2} \)
\( \mathbf{D} \cdot H_{3} B O_{3} \)


Allyl chloride is more reactive than vinyl chloride.
A . True
B. False


Which of the following is not a characteristic of equilibrium?
A. Rate is equal in both directions
B. Measurable quantities are constant at equilibrium
C . Equilibrium occurs in reversible condition
D. Equilibrium occurs only in open vessel at constant temperature


A parallel beam of diameter \( d \) is
incident on air-glass interface as shown
in figure. The diameter of refracted light beam is :
\( \left(d=3 m m, \theta=45^{\circ} \text { and } \frac{n_{g l a s s}}{n_{a i r}}=\frac{3}{2}\right) \)
A . \( \sqrt{12} \) mm
B. \( \sqrt{14} \) mm
\( c \cdot \sqrt{6} m m \)
D. \( 4.5 \mathrm{mm} \)


Which of the following gas molecules have a maximum value of enthalpy of physisorption?
A. \( C_{2} H_{6} \)
в. \( N e \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \)
D. \( H_{2} O \)


Short / long answer type questions. Gaseous exchanges continue in lungs without interruption even during expiration. Explain.


Which of the following statements is
not true?
A. The coefficient of friction between two surfaces increases as the surface in contact are made rough
B. The force of static friction acts in a direction opposite to the applied force
C. Rolling friction is greater than sliding friction
D. The coefficient of friction between wood and wood is less than 1


\( A B, A_{2} \) and \( B_{2} \) are diatomic molecules
If the bond enthalpies of \( A_{2}, A B \& B_{2} \) are in the ratio 1: 1: 0.5 and enthalpy of
formation of \( A B \) from \( A_{2} \) and \( B_{2} \) is -100
kJ/mol \( ^{-1} \). What is the bond enthalpy of
\( \boldsymbol{A}_{2} \)
A. \( 400 \mathrm{kJ} / \mathrm{mol} \)
B. 300 kJ/mole
c. \( 500 \mathrm{kJ} / \mathrm{mole} \)
D. 900 kJ/mole


A magnetizing field of \( 1600 \mathrm{A} / \mathrm{m} \) producers a magnetic flux of \( 2 \times 10^{-5} \) Wh in a bar of iron of cross section \( 0.2 x \)
\( 10^{-4} m^{2} . \) Calculate the susceptibility of
the bar.
A . 596.8
B . 288.9
\( c \cdot 2 \)
D. 1328


A copper wire 4 m long has diameter of
1 \( m m \), if a load of \( 10 k g \) wt is attached
at other end. What extension is
produced, if Poisson's ratio is \( 0.26 ? \) How much lateral compression is produced in it? \( \left(\boldsymbol{Y}_{\boldsymbol{c u}}=\mathbf{1 2 . 5} \times \mathbf{1 0}^{\mathbf{1 0}} \boldsymbol{N} / \boldsymbol{m}^{2}\right) \)


\( f\left(\begin{array}{cc}a & b \\ c & -a\end{array}\right) \) such that \( A^{2}-I \) then


An infinitely long rod lies along the axis
of a concave mirror of focal length \( f \). The near end of the rod is at a distance \( u> \)
\( f \) from the mirror. Its image will have a
length :
\( \mathbf{A} \cdot f^{2} /(u-f) \)
B. \( u f /(u-f) \)
c. \( f^{2} /(u+f) \)
D. \( u f /(u+f) \)


If \( f(x)+f\left(\frac{1}{1-x}\right)=x \) for all \( x \neq 0,1 \)
then
A \( \quad f(x)=\frac{1}{2}\left(x-1+\frac{1}{x}-\frac{1}{1-x}\right) \)
B. \( f(x)=\frac{1}{2}\left(1+x-\frac{1}{x}+\frac{1}{1-x}\right) \)
c. \( f(x)=\frac{1}{2}\left(1+x-\frac{1}{x}-\frac{1}{1-x}\right) \)
D \( f(x)=\frac{1}{2}\left(1-x+\frac{1}{x}-\frac{1}{1-x}\right) \)


Evaluate the following determinants
without expansion as far as possible. \( \left|\begin{array}{ccc}1 & b c & b c(b+c) \\ 1 & c a & c a(c+a) \\ 1 & a b & a b(a+b)\end{array}\right| \)


The probability a radioactive nucleus
will survive 10 times longer than its half life is


Gradient of line of velocity time graph is tells us the
A. velocity
B. acceleration
c. distance
D. time


If the incidence is at polarising angle,
the angle between Reflected ray and the
Refracted ray from a surface is


The straight lines \( 4 x-3 y-5=0, x- \)
\( 2 y-10=0,7 x+y-40=0 \) and \( x+ \)
\( 3 y+10=0 \) form the sides of a
A. plain quadrilateral
B. cyclic quadrilateral
c. rectangle
D. parallelogram


While plotting decrease in mass against time, a flat curve shows:
A. fastest reaction
B. reaction is slower
c. reaction is over.
D. None of these.


n given figure \( D \) and \( E \) are respectively
the points on the sides \( A B \) and \( A C \) of a
\( \triangle A B C \) such that \( A B=5.6 \mathrm{cm}, A D= \)
1.4 \( c m, A C=7.2 \mathrm{cm} \) and \( A E=1.8 \mathrm{cm} \)
show that \( D E \| B C \)


In an insulator, band gap of the order of?
A \( .0 .1 e V \)
B. \( 1 e V \)
c. \( 5 e V \)
D. \( 100 e V \)
E . \( 1 \mathrm{MeV} \)


A thin hollow sphere of mass \( m \) is
completely filled with an ideal liquid of
mass \( m . \) When sphere rolls with a
velocity \( v, \) kinetic energy of the system is equal to:
A \( \cdot m v^{2} / 2 \)
B. \( m v^{2} \)
C. \( 4 m v^{2} / 3 \)
D. \( 4 \mathrm{mv}^{2} / 5 \)


The diagram below represents five
different same-length identical wires(red) carrying the same amount of
current in the same magnetic field (blue) with current directions and
magnetic field directions indicated by
arrows.

Which wire(s) experience(s) the most force due to the magnetic field?
\( A \cdot 3 \) only
B. 2 only
\( c \cdot 2 \) and 5
D. 1 only
E. 1 and 4


In a bakery, baking powder was not added while preparing cake. The cake obtained was hard and small in size.
What is the reason for this?


Electronic configuration of a transition
element \( X \) in +3 oxidation State is
\( [A r] 3 d^{5} . \) What is its atomic number?
A . 25
B. 26
c. 27
D. 24


In the equilibrium \( N H_{4} H S(s) \Leftrightarrow \) \( N H_{3}(g)+H_{2} S(g) \) If the equilibrium
pressure is 2 atm at \( 80^{\circ} \mathrm{C} \mathrm{K}_{p} \) for the reaction is;
A. 0.5
B. 2
\( c \)
D. 1.5


Newton is written in fundamental units
\( \operatorname{as} k g m / s^{x} . \) Value of \( x \) is:
\( A \cdot 2 \)
B. 3
\( c \cdot 1 \)
\( D \cdot-2 \)


State the laws of reflection.


Show that \( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}-\mathbf{2}|+|\boldsymbol{x}-\mathbf{3}| \) is
not differentiable at \( x=2 \)


Speed of sound in air is \( 350 m s^{-1} \)
fundamental frequency of an open
organ pipe of \( 50 \mathrm{cm} \) length will be
\( \mathbf{A} \cdot 175 H z \)
в. \( 350 H z \)
c. \( 700 H z \)
D. \( 500 H z \)


A body of mass \( m \) is accelerated to
velocity \( v \) in time \( t^{\prime} . \) The work done by the force as a function of time \( t \) will be
A \( \cdot \frac{m}{2} \frac{v^{2} t^{2}}{t^{2}} \)
B \( \cdot \frac{1}{2}\left(\frac{m v}{t^{\prime}}\right)^{2} t^{2} \)
c. \( \frac{m v}{2 t^{\prime}} t^{2} \)
D. \( \frac{m v t^{2}}{2 t^{\prime}} \)


Which of the following is the method of controlled aerobic combustion of
wastes inside chambers at
temperatures as high as \( 900^{0}-1300^{0} \mathrm{C} ? \)
A. Sludge burning
B. Pyrolysis
c. Incineration
D. Source reduction


Find derivative of \( \tan ^{-1} \frac{\cos x}{1+\sin x} \)
A \( \cdot \frac{1}{2} \)
B. \( -\frac{1}{2} \)
\( c \cdot \frac{3}{2} \)
D. \( -\frac{3}{2} \)


A parallel plate capacitor is charged and the charging battery is then
disconnected. If the plates of the
capacitor are moved farther apart by
means of insulating handle:
This question has multiple correct options
A. the charge on the capacitor increases
B. the voltage across the plates increases
C. the capacitance increases
D. the electrostatic energy stored in the capacitor increases


Write one difference between \( \alpha \) -helix
and \( \beta \) -pleated structures of proteins.


A particle executes simple harmonic oscillation with an amplitude \( a \). The period of oscillation is T. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is
A \( \cdot \frac{T}{4} \)
в. \( \frac{T}{8} \)
c. \( \frac{T}{12} \)
D. \( \frac{T}{2} \)


A rod of weight \( \boldsymbol{w} \) is supported by two parallel knife edges \( A \& B \) and is in
equilibrium in a horizontal position. The
knives are at a distance \( d \) from each
other. The center of mass of the rod is at
a distance \( x \) from \( A \). The normal
reactions at \( A \) and \( B \) will be
A \( . N_{A}=2 w(1-x / d), N_{B}=w x / d \)
B . \( N_{A}=w(1-x / d), N_{B}=w x / d \)
c. \( N_{A}=2 w(1-x / d), N_{B}=2 w x / d \)
D. \( N_{A}=w(2-x / d), N_{B}=w x / d \)


IUPAC name for the complex
\( \left[C u\left(N H_{3}\right)_{4}\right] S O_{4} \) is:
A. cupramonium sulphate
B. copper sulphate tetraamonia
c. tetrammine copper
(II) sulphate
D. copper amonium
(IV) sulphate


\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\underset{\boldsymbol{C H}_{3}}{\boldsymbol{C}}^{\boldsymbol{C H}_{3}}- \)
\( C H_{2}-C H_{2}-O H \frac{H^{+}}{\Delta}(A) \)
Product (A) is:
A. \( C H_{3}-C H_{2}-C H_{2}-C H_{2}-C_{C H_{3}}=C H-C H_{3} \)
в. \( C H_{3}-\left(C H_{2}\right)_{3}-C\left(C H_{3}\right)=C\left(C H_{3}\right)_{2} \)
c. \( C H_{3}-C H_{2}-C H_{2}-C H_{2}-C_{I H_{3}}=C H_{2} \)


The solution of \( \frac{d y}{d x}+\frac{x^{2}}{y^{2}}=0 \) is:
A \( \cdot x^{2}+y^{2}=c \)
B . \( x^{2}-y^{2}=c \)
c. \( x^{3}-y^{3}=c \)
D. \( x^{3}+y^{3}=c \)


Fill up the blanks. The lightest isotope is


List- -
List-II
A) Haber's process
1) Nitric acid
B) Ostwald's process
2) \( N_{2}+ \)
\( \mathbf{3} \boldsymbol{H}_{2} \leftrightharpoons \mathbf{2} \boldsymbol{N} \boldsymbol{H}_{3} \)
C) Contact process
3) Ammonia
\( +C a C O_{3} \)
D) Cynamide process
4) Sulphuric
acid
Perdisulphuric acid
The correct match is :
A \( \cdot \) A- \( -1, \) B- \( -4, \) C-5, D-2
B. A-2, B-1, C-4, D-3
c. \( A-1, B-4, C-3, D-2 \)
D. A-5, B-3, C-1, D-4


Thin filaments in myofibrils consists of
A. Actin and accessory proteins
B. Sarcomeres
c. cross-bridges
D. z lines


Classify the following organism based on the absence/presence of
true coelom.
Horse
A . Coelomate
B. Acoelomate
c. Pseudocoelomate
D. All of the above


Citric acid is present in lemon. Apple contains:
A . lactic acid
B. malic acid
c. tartaric acid
D. oxalic acid


when does the current flow from A to B?
A. p is open, q is open, ris closed
B. p is closed, q is open, ris closed
c. p is closed, q is closed, ris open
D. p is open, q is closed, ris closed


The hollow sphere, in which the circus motor cylist performs his stunts, has a diameter of \( 7 \mathrm{m} \). Find the area available
to the motor cylist for riding.


After filling the \( 4 d \) -orbitals, an electron
will enter in:
\( \mathbf{A} \cdot 4 p \)
B . \( 4 s \)
c. \( 5 p \)
D. \( 4 f \)


Which has pyramidal shape
A. \( X e O_{4} \)
в. \( X e O F_{2} \)
c. \( X e F_{4} \)
D. \( X e O_{3} \)


Are the following name correct according to IUPAC system of nomenclature? If not, give the correct
names.
4,4,3-Trimethylhex-1-yne


The conversion factor to change
kilograms to pounds is:
A \( \cdot \frac{1 \mathrm{kg}}{2.20 \mathrm{lb}} \)
B. \( \frac{2.20 l b}{1 k g} \)
C. \( \frac{1 l b}{454 k g} \)
D. \( \frac{454 \mathrm{kg}}{1 \mathrm{lb}} \)


During strenuous exercise, which of the following changes occur?
A. Glucose is converted into glycogen
B. Glucose is converted into pyruvic acid
c. starch is converted into glucose
D. Pyruvic acid is converted into lactic acid


Concentration terms like mass
percentage, ppm, mole fraction and
molality do not depend on temperature.
However, molarity is a function of
temperature because:
A. volume depends on temperature and molarity involves volume
B. molarity involves non-volatile solute while all other terms involve volatile solute
C. number of moles of solute change with change in temperature
D. molarity is used for polar solvents only


Two towns \( A \) and \( B \) are \( 60 \mathrm{km} \) apart. \( A \)
school is to be built to serve 150
students in town \( A \) and 50 students in
town B. If the total distance to be
travelled by all 200 students is to be as small as possible, then the school be built is
A. town B
B. \( 45 \mathrm{km} \) from town
c. town A
D. \( 45 \mathrm{km} \) from town \( \mathrm{B} \)


The absolute abundance ratio of
\( N^{14} / N^{15} \) in atomspheric nitrogen was
found to be \( 272 . \) Calculate at. wt. of
atmospheric nitrogen.


The YDSE apparatus is as shown in the
figure. The condition for point \( \boldsymbol{P} \) to be a
dark fringe is \( (l= \) wavelength of light
waves)
A \( \cdot\left(l_{1}-l_{3}\right)+\left(l_{2}-l_{4}\right)=n \lambda \)
\( \left(l_{1}-l_{2}\right)+\left(l_{3}-l_{4}\right)=\frac{(2 n+1) \lambda}{2} \)
c. \( \left(l_{1}+l_{3}\right)+\left(l_{2}+l_{4}\right)=\frac{(2 n-1) \lambda}{2} \)
\( \left(l_{1}-l_{2}\right)+\left(l_{4}-l_{3}\right)=\frac{(2 n-1) \lambda}{2} \)


Which of the following molecules has no dipole moment?
A \( . C H_{3} C l \)
в. \( C H C l_{3} \)
c. \( C H_{2} C l_{2} \)
D. \( C C l_{4} \)


The envelope of a family of curves is a
curve \( f(x, y, c)=0 \) whose equation is
obtained by eliminating the parameter \( c \) from \( f(x, y, c)=0 \) and \( \frac{\partial f}{\partial c}=0 \)
where \( \frac{\partial f}{\partial c} \) is the differential coefficient of f with respect to c, treating x and y as constants. Moreover, the envelope of the family of normals to a curve is known as the evolute of the curve. The envelope of the family of straight lines whose sum of intercepts on the axes is 4 is:
A \( \cdot \sqrt{x}+\sqrt{y}=2 \)
в. \( (x-y)^{2}-8(x+y)+16=0 \)
c. \( (x-y)^{2}=4(x+y) \)
D. \( (x+y)^{2}=4(x-y) \)


The cost of a vehicle is Rs. \( 1,75,000 . \) If its value depreciates at the rate of \( 20 \% \) per annum, then the total depreciation
after 3 years will be:
A. Rs. 86,400
B. Rs. 82,500
c. Rs. 84,500
D. Rs. 85,400


Which of the following is/are non-polar dielectrics?
\( \mathbf{A} \cdot H C L \)
B. water
c. Benzene
D. \( N H_{3} \)


You did 150 joules of work lifting a
120Newton backpack.
a) How high did you lift the backpack?
b) How much did the backpack weigh in pounds? [Hint: 1 pound = 4.448 newtons]


If \( 0, \alpha, \beta<\frac{\pi}{4} \) such that \( \cos (\alpha+\beta)=\frac{4}{5} \)
andsin \( (\alpha-\beta)=\frac{5}{13}, \) then the value of
\( \tan 2 \alpha= \)
A. \( \frac{56}{65} \)
в. \( \frac{56}{23} \)
c. \( \frac{56}{33} \)
D. \( \frac{56}{36} \)


Integrate:
\( \frac{e^{2 x}-1}{e^{2 x}+1} \)


In above circuit, what is the potential
drop across \( Z Y ? \)
A \( \cdot 160 \)
B. \( 80 \sqrt{80} \)
\( c \cdot 80 v \)
\( D \)


Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}+\boldsymbol{\phi}(\boldsymbol{x}) \) where \( \phi(\boldsymbol{x}) \) is an
even function then find the value of
\( \int_{-1}^{1} x f(x) d x \)


A short dipole is placed along the \( x \) -mds at \( x=x \text { (Fig. } 3.120) \)
a. Find the force acting on the dipole due to a point charge q placed at the origin.
b. Find the force on the dipole if the dipole
is rotated by \( 180^{\circ} \) about the z-axis.
c. Find the force on dipole if the dipole is
rotated by \( 90^{\circ} \) anticlockwise about z-axis,
i.e., it becomes parallel to the \( y \) -axis.


Molarity of the situation is depend on:
A. temperature
B. nature of solute dissolved
c. mass of solvent
D. pressure


What is the value of \( \sqrt{79.62} ? \)
A . 8.923
B. 8.9230
c. 8.92300
D. 8.9326


Solve \( \int_{1}^{-1} \frac{d}{d x} \tan ^{-1}\left(\frac{1}{x}\right) d x \)


A boy begins to walk eastward along a
street in front of his house and the
graph of his position from home is
shown in the following figure. His
average speed for the whole time interval is equal to?
\( A .8 \mathrm{m} / \mathrm{min} \)
B. \( 6 \mathrm{m} / \mathrm{min} \)
c. \( \frac{8}{3} \mathrm{m} / \mathrm{min} \)
\( \mathrm{D} \cdot 2 \mathrm{m} / \mathrm{min} \)


In the contact process for the
manufacture of sulphuric acid give equations for the conversion of sulphur trioxide to sulphuric acid.


Two simple harmonic motions are
denoted as \( \mathbf{S}_{1} \) and \( \mathbf{S}_{2} \) as below
\( \mathbf{S}_{1}: \mathbf{x}=\mathbf{6} \sin ^{2} \boldsymbol{\pi} \boldsymbol{t} \)
\( \mathbf{S}_{2}: \mathbf{x}(\boldsymbol{x}-\mathbf{2})=\cos \mathbf{3} \boldsymbol{\pi} \boldsymbol{t} \)
where \( x \) is displacement (In \( c m \) ) and \( t \) is time (In second)


The \( x \) -t graph of a particle undergoing simple harmonic motion is as shown in
the figure.

The acceleration of the particle at \( t= \)
is the
2
A \( \cdot \frac{\sqrt{3}}{32} \pi^{2} c m s^{-2} \)
B. \( -\frac{\pi^{2}}{32} c m s^{-2} \)
\( c \)
D.


Assertion
\( \boldsymbol{S} \boldsymbol{O}_{3} \) has a planar structure
Reason
Sulphur atom in \( S O_{3} \) is \( S p^{2} \) hybridized
and \( O-S-O \) bond angle in \( 120^{\circ} \)
A. If both assertion and reason are CORRECT and reason is the CORRECT explanation of the assertion
B. If both assertion and reason are CORRECT, but reason is NOT THE CORRECT explanation of the assertion.
C. If assertion is CORRECT, but reason is INCORRECT
D. If assertion is INCORRECT, but reason is CORRECT


Which of the following is a correct
match?
A. Centrolecithal egg - insect
B. Megalecithal egg - eutherian mammals
C. Microlecithal egg - reptiles
D. Alecithal egg - birds


Consider a cuboid all of whose edges
are integers and whose base is a square. Suppose the stun of all its
edges is numerically equal to the sum of the areas of all its six faces. Then the
sum of all its edges is
A \( \cdot 12 \)
B. 18
\( c \cdot 24 \)
D. 36


Prove the following:
\( \cos ^{-1}\left(\frac{12}{13}\right)+\sin ^{-1}\left(\frac{3}{5}\right)= \)
\( \sin ^{-1}\left(\frac{56}{65}\right) \)


Which of the following bulbs offers more resistance?
(A) \( 60 \mathrm{W}-220 \mathrm{V}(\mathrm{B}) 100 \mathrm{W}-250 \mathrm{V} \)


If \( A \times\left(\begin{array}{l}1 \\ 0\end{array}\right)=(12), \) then the order of \( A \) is
A \( .2 \times 1 \)
B. \( 2 \times 2 \)
c. \( 1 \times 2 \)
D. 3 \( \times 2 \)


Which of the following is not an example of phytohormone?
A. cytokinins
B. ethylene
c. auxins
D. insulin


If \( 4 i+7 j+8 k, 2 i+7 j+7 k \) and \( 3 i+ \)
\( 5 j+7 k \) are the position vectors of the
vertices \( A, B \) and \( C \) respectively of triangle \( A B C . \) The position vector of the point where the bisector of angle \( \boldsymbol{A} \)
meets \( B C \).
A \( \cdot \frac{1}{3}(5 j+12 k) \)
B. \( \frac{1}{3}(6 i+13 j+18 k) \)
c. \( \frac{2}{3}(6 i+8 j+6 k) \)
D \( \cdot \frac{2}{3}(-6 i-8 j-6 k) \)


For the measures of central tendency,
of the following is not true.
A. \( Z=3 M-2 \bar{x} \)
в. \( 2 \bar{x}+Z=3 M \)
c. \( 2 \bar{x}-3 M=-Z \)
D. \( 2 \bar{x}=Z-3 M \)


Prove that point (1,1),(-2,7) and
(3,-3) are collinear.


Assertion: Two equipotential surfaces
cannot cut each other.

Reason: Two equipotential surfaces are
parallel to each other.
A. Both Assertion and Reason are true and the Reason is
the correct explanation of the Assertion
B. Both Assertion and Reason are true but the Reason is
not the correct explanation of the Assertion
C. Assertion is true statement but Reason is false
D. Both Assertion and Reason ale false statements


The electronic configuration of an element is \( 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{2} . \) The
oxidation number of the element in its
compounds can be:
\( A \cdot+2 \)
B. +8
\( c \cdot+1 \)
\( D \)


What is the source of coelomic fluid?


You are provided with a mixture containing sand, iron filings, ammonium chloride and sodium
chloride. Describe the procedures you would use to separate these constituents from the mixture?


\( \int \frac{1}{x^{4}-1} d x \)


Which of the following is not an antihistamine?
A. Brompheniramine
B. Terfenadine
c. Iproniazid
D. Ranitidine


If \( C C l_{3} F \) is present in the stratosphere, it will react with which of the following:
A) Ozone
\( \begin{array}{ll}\text { B) } N_{2} & \text { C) } C O_{2}\end{array} \)
\( A \cdot A \)
B. B
c. \( A \& B \)
\( D \cdot c \& A \)


Which of the following is diamagnetic ion?
A \( . Z n^{2} \)
the \( ^{2} n^{n^{n}} \)
B. \( N i^{2} \)
\( c \cdot C o^{2} \)
D. \( C u^{2} \)


Solve
\( 3 x^{2}+20 x+8 \)


Let \( f \) be a twice differentiable such that
\( \boldsymbol{f}^{\prime \prime}(\boldsymbol{x})=-\boldsymbol{f}(\boldsymbol{x}) \) and \( \boldsymbol{f}^{\prime}(\boldsymbol{x})=\boldsymbol{g}(\boldsymbol{x}) . \) If
\( \boldsymbol{h}(\boldsymbol{x})=\{\boldsymbol{f}(\boldsymbol{x})\}^{2}+\{\boldsymbol{g}(\boldsymbol{x})\}^{2}, \) where
\( h(5)=11 . \) Find \( h(10) \)
\( \mathbf{A} \cdot \mathbf{1} \)
B . 10
c. 11
D. 100


Which of the above given metal oxides
can be reduced by \( \boldsymbol{F} \boldsymbol{e} \) (reducing
agent) to its respective metal at
temperature \( \boldsymbol{T}_{\mathbf{1}} \) ?
\( A \cdot Z r O_{2} \)
B. \( C a O \)
\( c . M g O \)
D. None of the above


Unique feature of mammalian body is the presence of
A. Four chambered heart
B. Presence of diaphragm
c. Homeothermy
D. Rib cage


Assertion
Genes are stretches of DNA that make
up the different codes for the different
proteins.
Reason
DNA is the complex bio molecule made up of sugars,phosphorus and nitrogen
bases
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


Consider the epoxidation with peroxy benzoic acid. Which statement best
describes the activation entropy of this
reaction?
A. large and negative since, the reaction is bimolecular and the transition state is highly ordered
B. slightly negative and typical for bimolecular reactions
c. activation entropy is negligible
D. large and positive since, the reaction is bimolecular and the transition state is highly ordered


Two \( C u^{64} \) nuclei touch each other. The
electrostatics repulsive energy of the system will be
A. 0.788 MeV
в. 7.88 Ме \( V \)
c. 126.15 MeV
D. 788 MeV


Let \( A, G \) and \( H \) are the A.M., G.M. and H.M. respectively of two unequal positive
integers. Then the equation \( A x^{2}- \) \( |G| x+\frac{H}{4}=0 \) has
This question has multiple correct options
A. Both roots as fractions
B. At least one root which is a negative fraction.
c. Exactly one positive root
D. At least one root which is an integer
E. None of these.


A mercury barometer is known to be defective. It contains a small quantity of air in the space above the mercury. When an accurate barometer reads 770
\( \mathrm{mm}, \) the defective one reads \( 760 \mathrm{mm} \)
and when the accurate one reads 750
\( \mathrm{mm}, \) the defective one reads \( 742 \mathrm{mm} \)
The true atmospheric pressure when the defective barometer reads \( 750 \mathrm{mm} \)
is
A. \( 68 \mathrm{cm} \) of \( \mathrm{Hg} \)
в. \( 79.88 \mathrm{cm} \) of \( \mathrm{Hg} \)
\( c .75 .88 \mathrm{cm} \) of \( \mathrm{Hg} \)
D. 72.15 cm of Hg


Determine the volume contraction of a
solid copper cube, \( 10 \mathrm{cm} \) on an edge,
when subject to a hydraulic pressure of \( \mathbf{7} \times \mathbf{1 0}^{\mathbf{6}} \) Pa. \( \boldsymbol{K} \) for copper \( =\mathbf{1 4 0} \times \mathbf{1 0}^{\mathbf{9}} \)
\( P a \)


A certain mass of hydrogen gas is introduced into a vessel at room
temperature, the final pressure of the gas
in the vessel is
\( A \cdot 85 \mathrm{cm} \) of \( \mathrm{Hg} \)
B. 78 cm of Hg
\( c \cdot 63 \mathrm{cm} \) of \( \mathrm{Hg} \)
D. \( 58 \mathrm{cm} \) of \( \mathrm{Hg} \)


\( \boldsymbol{N} \boldsymbol{a}^{+}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{N} \boldsymbol{a} \)
The reaction occurs at:
A. cathode
B. anode
c. both A and B
D. none of the above


Choose the correct statement about
inflammable substances from the
following statements. They have:
A. low ignition temperature and cannot catch fire easily
B. high ignition temperature and can catch fire easily
c. low ignition temperature and can catch fire easily
D. high ignition temperature and cannot catch fire easily


The two half-cell reactions of an
electrochemical cell is given as
\( \boldsymbol{A} \boldsymbol{g}^{+}+\boldsymbol{e}^{-} \longrightarrow \boldsymbol{A} \boldsymbol{g} ; \boldsymbol{E}_{\boldsymbol{A} \boldsymbol{g}^{+} \mid \boldsymbol{A} \boldsymbol{g}}= \)
\( -0.3995 V \)
\( \boldsymbol{F} \boldsymbol{e}^{2+} \longrightarrow \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+}+\boldsymbol{e}^{-} ; \boldsymbol{E}_{\boldsymbol{F} e^{3+} \mid \boldsymbol{F} e^{2+}}= \)
\( -0.7120 V \)
The value of cell EMF will be:
A. \( -0.3125 V \)
B. \( 0.3125 V \)
c. \( 1.114 V \)
D. \( -1.114 V \)


A billiard ball is struck by a cue. The line of action of applied impulse is horizontal and passes through the
center of the ball. The initial velocity \( V_{0} \) of the ball, radius \( R \), mass \( m \) and
coefficient of friction \( \mu \) between ball
and table are known. The ball moves distance \( \frac{12 V_{0}^{2}}{X \mu g} \) before it ceases to slip on the table. What is the value of \( X ? \)
A .49
в. зб
\( c \cdot 25 \)
\( D \cdot 64 \)


State the following set is finite or
infinite :
\( \mathrm{B}=(x: x \in W \text { and } 5 x-3 \leq 20\} \)
If it is finite then write 1 else write 0


An aeroplane can carry a maximum of
200 passengers. A profit of Rs.1000 is made on each executive class ticket
and a profit of Rs.600 is made on each economy class ticket. The airline
reserves at least 20 seats for executive
class. However, at least 4 times as many passengers prefer to travel by economy class than by the executive class. Determine how many tickets of
each type must be sold in order to maximize the profit for the airline. What is the maximum profit?
A . 136000
в. 1360000
c. 13600
D. 1360


Q Type your question
z. Here z is the vertical distance inside
the slab, measured from the top. The slab is placed between two media with
uniform refractive indices \( n_{1} \) and \( n_{2} \)
\( \left(>n_{1}\right), \) as shown in the figure. A ray of
light incident with angle \( \boldsymbol{\theta}_{\boldsymbol{i}} \) from
medium 1 and emerges in medium 2
with refraction angle \( \theta_{f} \) with lateral
displacement \( l \) Which of the following statement(s) is (are) true?
This question has multiple correct options
A. \( l \) is dependent on \( n(z) \)
B \( \cdot n_{1} \sin \theta_{1}=\left(n_{2}-n_{1}\right) \sin \theta_{f} \)
\( \mathbf{c} \cdot n_{1} \sin \theta_{i}=n_{2} \sin \theta_{f} \)
dependent of \( n \)


The kinetic energy of 1 gram mole of a gas at normal temperature and pressure is \( (\mathrm{R}=8.31 \mathrm{J} / \mathrm{mole}-\mathrm{K}) \)
A \( \cdot 0.56 \times 10^{4} J \)
В. \( 1.3 \times 10^{2} J \)
c. \( 2.7 \times 10^{2} J \)
D. 3.4 \( \times 10^{3} \mathrm{J} \)


Calculate \( \Delta G \) for the following cell
reaction.
\( \boldsymbol{Z} \boldsymbol{n}_{(s)}+\boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{O}_{(s)}+\boldsymbol{H}_{2} \boldsymbol{O}_{(l)} \rightarrow \boldsymbol{Z} \boldsymbol{n}_{(a q)}^{2+}+ \)
\( \mathbf{2} \boldsymbol{A} \boldsymbol{g}_{(s)}+\mathbf{2} \boldsymbol{O} \boldsymbol{H}^{-}(\boldsymbol{a} \boldsymbol{q}) \)
\( \boldsymbol{E}_{A \boldsymbol{g}^{+} / \boldsymbol{A} \boldsymbol{g}}^{0}=+\mathbf{0 . 8 0} \boldsymbol{V} \) and \( \boldsymbol{E}_{\boldsymbol{Z n}^{+2} / Z \boldsymbol{n}}^{0}= \)
\( -0.76 V \)
A . -305 k \( J / \operatorname{mol} \)
в. \( -301 k J / \) mol
c. \( 305 k J / \) mol
D. 301 kJ/mol


Water sprinkler used for grass lawns
begins to rotate as soon as the water is supplied. It is based on which law?


A particle is executing simple harmonic motion with an amplitude \( A \) and time
period \( T . \) The displacement of the
particles after \( 2 T \) period from its initial position is
A . \( A \)
в. \( 4 A \)
c. \( 8 A \)
D. zero


A parallel plate capacitor with air between the plates is charged to a potential difference of \( 500 V \) and then
insulated. A plastic plate is inserted between the plates filling the whole gap. The potential difference between the plates now becomes \( 75 V . \) The dielectric
constant of plastic is :
A \( .10 / 3 \)
B. 5
\( c \cdot 20 / 3 \)
D. 10


Assertion
In the absence of atmosphere the sky
would appear black.
Reason
Atmosphere scatters the light and
hence we get blue colour.
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


What do you observes when:
Hydrogen chloride gas is passed through Silver nitrate solution and the product thus form treated with excess of Ammonium hydroxide?


If the radius of the earth is reduced to
half of its present value, with no change in the mass, how will the acceleration
due to gravity, be affected?


A ladder \( A B, 2.5 m \) long and of weight \( 150 N \) has its centre of gravity \( 1 m \) from \( A \) is lying flat on ground. \( A \) weight
of \( 40 N \) is attached to the end \( B \). The
work required (in joule) to raise the ladder from the horizontal position to vertical position so that the bottom end \( A \) is resting in a ditch 1 m below the ground level will be :
A . 60
B. 30
c. 20
D. 120


The formula that gives the symbolic representation of the actual number of
atoms of various elements present in one molecule of the compound, is called:
A. molecular formula
B. empirical formula
c. molecular mass
D. formula mass


Ligand with two or more points of attachment to single metal atoms are called:
A. Monodentate ligand
B. Chelating ligand
c. Ambidentate ligand
D. None of these


The amount of power delivered by the
AC source in the capacitor \( \& \) resistance
\( R_{1} \) of the circuit given above is \( \frac{X}{8} \times 10^{3} \)
watt. Then x is:


The resistance \( R=10 \Omega \), inductance \( L= \)
\( 2 \mathrm{mH} \) and capacitance \( \operatorname{cof} 5 \mu F \) are
connected in same to an AC source of
frequency \( 50 \mathrm{Hz} \), then at resonance the impedance of circuit is
A. zero
B. \( 10 \Omega \)
c. \( 1000 \Omega \)
D. \( 10 k \Omega \)


Find whether \( x-1 \) is a factor of \( 2 x^{2}- \)
\( \mathbf{5} \boldsymbol{x}+\mathbf{3} \)


Assertion
Phellogen is cork cambium formed in dicot roots and shoots to protect underlying tissues.
Reason
It secretes phellem which substitutes
epidermis after secondary growth.
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


If a binary operation is defined \( a \star b= \)
\( a^{b} \) then \( 2 \star 2 \) is equal to:
A . 4
B. 2
c. 9
D.


Identify the correct statement:
A. The electric potential on bigger sphere is higher
B. The electric potential on bigger sphere is lower
C. The electric potential on the two spheres is equal
D. None of these


Which of the following is a polysaccharide?
A. Maltose
B. Raffinose
c. Glycogen
D. Galactose


Which of the following orders are
Correct?
A. \( A g C l>A g F: \) Covalent character order
B \( \cdot B a O>B a F_{2}: \) Melting point order
\( \mathbf{C} \cdot B e F_{2}>B a F_{2}: \) Solubility order
D. \( L i N O_{3}<R b N O_{3}: \) Thermal stability order


In the figure shown a circular current carrying conductor lies in yz plane and
its centre is at point O.If \( B_{A} \) and \( B_{B} \) are
the
A \( . B_{A}=B_{B} \)
В. \( B_{A}>B_{B} \)
c. \( B_{A}<B_{B} \)
D. None of these


A star initially has \( 10^{40} \) deuterons. It
produces energy through the processes \( 1 H^{2}+_{1} 1 H^{2} \rightarrow_{2} H^{3}+P \) and \( _{1} H^{2}+_{1} \rightarrow_{2} \)
\( \boldsymbol{H} \boldsymbol{e}^{\boldsymbol{4}} \boldsymbol{+} \boldsymbol{n} \)
If the average power radiated by the star
is \( 10^{16} W \), the deutron supply of the
star is exhausted in a time of the order
of
\( A \cdot 10^{6} \)
B. \( 10^{8} \)
\( c \cdot 10^{12} \)
D. \( 10^{16} \)