Heat transfer through radiation cannot take place in vacuum. True or false
A. True
B. False


By how much does \( 3 x-4 x y+2 z \) exceed \( 8 x+5 z-7 x y ? \)


The word species was coined by
A. Aristotle
B. Linnaeus
c. John Ray
D. Engler


Non-metal which is used to
sterilize water is :
A. iodine
B. bromine
c. chlorine
D. sulphur


In potentiometer experiment, null point
is obtained at a particular point for a cell on potentiometer wire \( x \) cm long. If the length of the potentiometer wire is increased without changing the cell, the balancing length will (Driving source is not changed)
A. increase
B. decrease
c. not change
D. becomes zero


Which of the following consists of one electron, one proton and zero neutron?
\( \mathbf{A} \cdot_{1} H^{2} \)
в. \( _{1} H^{1} \)
\( \mathbf{c} \cdot_{1} H^{3} \)
\( \mathrm{D} \cdot_{2} \mathrm{He}^{4} \)


Which one of the following inflorescences is found in a sunflower?
A. Capitulum
B. Cyathium
c. Panicle
D. spadix


A proton, a neutron, an electron and an
\( \alpha \) -particle have same energy. Then their de Broglie wavelengths compare as:
\( \mathbf{A} \cdot \lambda_{p}=\lambda_{n}>\lambda_{e}>\lambda_{\alpha} \)
B . \( \lambda_{\alpha}<\lambda_{p}=\lambda_{n}<\lambda_{e} \)
\( \mathbf{c} \cdot \lambda_{e}<\lambda_{p}=\lambda_{n}>\lambda_{\alpha} \)
\( \mathbf{D} \cdot \lambda_{e}=\lambda_{p}=\lambda_{n}=\lambda_{\alpha} \)


A gun of mass M fires a bullet of mass \( \mathrm{m} \) with a velocity v relative to the gun. The average force required to bring the gun to rest in 0.5 sec. is
A \( \cdot \frac{2 \mathrm{Mmv}}{\mathrm{M}+\mathrm{m}} \)
в. \( \frac{M m v}{2(M+m)} \)
c. \( \frac{3 \mathrm{Mmv}}{2(\mathrm{M}+\mathrm{m})} \)
D. \( \frac{\mathrm{Mmv}}{(\mathrm{M}+\mathrm{m})} \)


Assertion
In the present form of periodic table, the period number corresponds to the
highest principal quantum number of the elements in the period.
Reason
Elements having similar outer electronic configurations in their atoms
belong to same period.
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


Assertion
Hydroquinone is used as a developer for developing black and white photographic film.
Reason
Hydroquinone reduces silver bromide to
black silver particles and an inverted
image of the object is produced on a celluloid film.
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


Derive the expression for gravitational potential energy?


A solution of \( 9.65 A \) flowing for 10 min
deposits \( 3.0 g \) of the metal which
is monovalent. The atomic mass of the
metal is :
A . 10
B. 50
c. 30
D. 96.5


\( \cos \left[2 \sin ^{-1} \sqrt{\frac{1-x}{2}}\right]= \)
\( A \cdot x \)
B. \( \frac{1}{x} \)
\( c \cdot 2 x \)
D. 3x


A buffer solution is used in:
A. preparation of potash alum
B. the removal of \( P O_{4}^{3-} \) ions
C. increasing the pH value of a solution
D. precipitation of \( C r(O H)_{3} \) from \( \$ \$ \) Cr \( \{C \mid\}_{-}\{3\} \$ p \)


Solve the following systems of equations. \( \boldsymbol{x}+\mathbf{2} \boldsymbol{y}-\boldsymbol{6}=\mathbf{0},|\boldsymbol{x}-\mathbf{3}|-\boldsymbol{y}=\mathbf{0} \)


The only haploid stage in an animal life cycle is the
A. zoospores
B. Spores
c. Gametes
D. None of the above


Which of the following are excretory products in animals?
A. Urea
B. Uric acid
c. Ammonia
D. All of the above


The magnetic field existing in a region is given by \( \overrightarrow{\boldsymbol{B}}=\boldsymbol{B}_{0}\left(1+\frac{\boldsymbol{x}}{\boldsymbol{l}}\right) \hat{\boldsymbol{k}} \)
A square loop of edge I and carrying a
current i, is placed with its edges parallel to the \( X \) -Y axes, Find the magnitude of the net magnetic force experienced by the loop.


Which of the following is/are correct statement(s)?
This question has multiple correct options
A. p-nitrophenol and o-nitrophenol can be separated by steam distillation
B. p-nitrophenol is less acidic than o-nitrophenol
c. p-hydroxybenzonic acid is less acidic than ohydroxybenzonic acid
D. \( C C l_{4} \) does not give reaction with aq. \( A g N O_{3} \) solution


Two fuse wires of the same length are rated 5 A and 20 A.Which of the fuse
wires is thicker and why?
A. 5 A
B. 20 A
c. Both have same thickness
D. Cannot be same


Evaluate
\( \int \sqrt{1+t^{3}} d t \)


The angle of a pentagon are in the ratio \( 4: 8: 6: 4: 5 . \) Find the greatest angle of
the pentagon.
\( \mathbf{A} \cdot 120^{\circ} \)
B. \( 140^{\circ} \)
\( c \cdot 160^{\circ} \)
D. 150


The observation of discrete energy lines suggests that an electron in an atom can have only certain or definite energies.
A . True
B. False


Select the instrument that works on the
principle of multiple reflection of sound.
A. Watthour meter
B. Sonar
c. stethoscope
D. Decibel meter


Which of the follwoing statements is
correct?
A. \( \mathrm{HCl} \) is covalent both in aqueous solution and in the gaseous state
B. HCl is covalent in the gaseous state but ionic in aqueous solution
C. \( \mathrm{HCl} \) is ionic both in the gaseous state and in aqueous solution
D. None of the above


Which one has maximum electron
affinity?
A. \( N \)
в. \( B e \)
\( c . B \)
D. \( C l \)


Choose the correct answers from the
alternatives given :
The primary energy carrier between the
Krebs cycle and the electron
transport system is
\( A \). NADH
B. ADP
c. FADH \( _{2} \)
\( D \cdot c O_{2} \)


One calorie is defined as the heat
required to raise the temperature of
1 gm of water by \( 1^{\circ} \mathrm{C} \) in a certain pressure. The pressure is
A. \( 76 m m \) of \( H g \)
в. \( 760 \mathrm{cm} \) of \( \mathrm{Hg} \)
c. \( 760 \mathrm{mm} \) of \( \mathrm{Hg} \)
D. \( 7.6 \mathrm{m} \) of \( \mathrm{Hg} \)


Lens \( A \) produces a magnification of -0.8 whereas lens B produces a magnification of \( +0.8 . \) Which one of the following applies to lenses \( A \) and \( B ? \)
A. Both A and B are convex lenses
B. Both A and Bare concave lenses
c. A is a concave lens and B is a convex lens
D. A is a convex lens and B is a concave lens


State any two postulates of Bohr's theory of hydrogen atom


Which process is responsible in Hydrogen bomb? If \( 20 \mathrm{N} \) force is applied on a wall which doesn't move the wall than work done by wall is.


Pyrolysis is a
A. Biochemical process
B. Biological process
C. Thermochemical process
D. Petrochemical process


In Cycas, fertilisation occurs through.
A. Isogamy
B. Siphonogamy
c. zoidiogamy
D. Both B and C


All hydrocarbons contain
A. carbon
B. germanium
c. antimony
D. water


The fraction of a radioactive sample
that will decay during half of its half life period is
A \( \cdot \frac{1}{\sqrt{2}} \)
в. \( \frac{1}{\sqrt{2}-1} \)
c. \( \frac{\sqrt{2}-1}{\sqrt{2}} \)
D. \( \frac{1}{2} \)


Which of the following explains the
reason for nitrogen's three unpaired
electrons?
A. Hund's rule
B. Aufbau principle
c. Pauli's principle
D. Heisenberg's principle


A mixture of ethanol and water contains
\( 54 \% \) water by mass. Calculate the mole fraction of ethanol in this solution.
A. 0.25
B. 0.15
\( c \cdot 0.20 \)
D. 0.30


The value of the definite integral, \( \boldsymbol{I}= \) \( \int_{0}^{\sqrt{10}} \frac{x}{e^{x^{2}}} d x \) is equal to


\( (5 x+2 y+3 z)^{2} \)
\( \mathbf{A} \cdot 25 x^{2}+4 y^{2}+9 z^{2}+20 x y+12 y z+30 z x \)
B \( \cdot 25 x^{2}-4 y^{2}+9 z^{2}+20 x y+12 y z+30 z x \)
\( \mathbf{c} \cdot 25 x^{2}+4 y^{2}-9 z^{2}+20 x y+12 y z+30 z x \)
D. None of these


Which of the metal does not show
malleability?
A. zinc
B. Aluminium
c. Iron
D. Silver


Which of the following statement is
false?
A. Work is a state function.
B. Temperature is a state function.
C. Change of state is completely defined when initial and final states are specified.
D. Work appears at the boundary of the system.


Which of the following is an example of non-biodegradable detergent?
\( A \)
\[
\mathrm{CH}_{3}-\left(\mathrm{CH}_{2}\right)_{\mathrm{n}}-\sqrt{1}-\mathrm{s} \mathrm{O}_{3} \mathrm{Na}
\]
в.
\[
\left.\mathrm{CH}_{3}-\left(\mathrm{CH}_{2}\right)_{9}-\underset{\mathrm{CH}_{3}}{\mathrm{CH}}-\sqrt{\prime}_{-}\right\rangle-\mathrm{SO}_{3} \mathrm{Na}
\]
\( c \)
D. \( C H_{3}-\left(C H_{2}\right)_{10}-C H_{2}-O S O_{3} N a \)


ff \( y=\sec ^{-1}\left(\frac{\sqrt{x}+1}{\sqrt{x}-1}\right)+\sin ^{-1}\left(\frac{\sqrt{x}-1}{\sqrt{x}+1}\right) \)
then find \( \frac{d y}{d x} \)


Calculate x. (Similar arrow markings
show parallel lines).
\( A \cdot 102 \)
3.56
\( c_{1}+a_{4} \)
\( D \)


Name the method used for refining of
nickel.


The valves of the heart are attached to
papillary muscles by
A. Columnae carneae
B. Chordae tendineae
c. Tendon
D. Pectinate muscles


Primary, secondary and tertiary amines
are:
A. chain isomers
B. position isomers
c. functional isomers
D. tautomers


Match the animals of Column I with
their respective classes in
Column II and choose the correct
answer.
0. Sr.No Column I Sr.No. Column II \( \begin{array}{llll}1 . & \text { Aptenodytes } & \text { I. } & \text { Aves } \\ \text { 2. } & \text { Hemidactylus } & \text { II. } & \text { Chondrich } \\ \text { 3. } & \text { Carcharodon } & \text { III. } & \text { Mammaliz } \\ \text { 4. } & \text { Pteropus } & \text { IV. } & \text { Reptilia } \\ & \text { V. } & \text { Osteichth }\end{array} \)
\( \mathbf{A} \cdot 1-V ; 2-I I ; 3-I V ; 4-I \)
B . \( 1-I ; 2-I V ; 3-I I I ; 4-I I \)
\( \mathbf{c} \cdot 1-V ; 2-I ; 3-I I ; 4-I I I \)
D. \( 1-I ; 2-I V ; 3-I I ; 4-I I I \)


The value of \( \sqrt{1^{3}+2^{3}+3^{3}} \) is
A. 5
B. 6
\( c \cdot 7 \)
D. 8


The first term of an arithmetic
sequence is equal to 200 and the
common difference is equal to -10
Find the value of the 20 th term.


The theory of electrolytic dissociation
suggests that:
This question has multiple correct options
A. the electrolytes on dissolution in water split up in two types of charged particles, i.e., cation and anions
B. the dissociation being a reversible process in nature
C. the properties of electrolytes in solutions are the properties of ions furnished by them
D. none of above


\( \lim _{x \rightarrow 2}\left[\frac{1}{x-2}-\frac{2(2 x-3)}{x^{3}-3 x^{2}+2 x}\right] \)


Oxidation means
(gain/loss) of \( O_{2} \) and reduction means
gain of hydrogen.


Only few stars of a constellation are
clearly visible through naked eyes because:
A. those are the prominent ones
B. those are close to the Earth while others are far away
c. others are covered by clouds
D. others are a myth


Top view of the triangluar prism will
be
A. Square
B. Rectangle
c. circle
D. Triangle


Classify the following salts as acid
salt or normal salt:
\( N a H_{2} P O_{4} \)


A flask containing 0.5 atm pressure of
\( A_{2}(g), \) some solid \( A B \) added into flask which undergoes dissociation according to :
\[
\boldsymbol{2} \boldsymbol{A} \boldsymbol{B}(\boldsymbol{s}) \rightleftharpoons \boldsymbol{A}_{2}(\boldsymbol{g})+\boldsymbol{B}_{2}(\boldsymbol{g})
\]
\( \boldsymbol{K}_{\boldsymbol{p}}=\mathbf{0 . 0 6} \boldsymbol{a t m}^{2} . \) The total pressure (in
atm) at equilibrium is :
A . 0.70
B. 0.6
c. 0.10
D. none of these


Match the following items in column I
with the corresponding items in column
\( \| \)
Column I
Portland
(i) \( N a_{2} C O_{3} \cdot 10 H_{2} O \)
(A) \( \quad \) cement ingredient
castner
(ii)
\[
M g\left(H C O_{3}\right)_{2}
\]
(B) \( \quad \) Keller process
(iii) \( \quad N a O H \) Solvay
(C) process
Temporary
\( \begin{array}{llll}\text { (iv) } & \mathrm{Ca}_{3} \mathrm{Al}_{2} \mathrm{O}_{6} & \text { (D) } & \text { hardness }\end{array} \)
A \( \cdot(i) \rightarrow(C) ;(i i) \rightarrow(B) ;(i i i) \rightarrow(D) ;(i v) \rightarrow(A) \)
B . \( (i) \rightarrow(C) ;(i i) \rightarrow(D) ;(i i i) \rightarrow(B) ;(i v) \rightarrow(A) \)
c. \( (i) \rightarrow(D) ;(i i) \rightarrow(A) ;(i i i) \rightarrow(B) ;(i v) \rightarrow(C) \)
D. \( (i) \rightarrow(B) ;(i i) \rightarrow(C) ;(i i i) \rightarrow(A) ;(i v) \rightarrow(D) \)


If \( a_{1}=1, a_{n+1}=\frac{1}{n+1} a_{n}, \forall n \geq 1, \) then
\( \boldsymbol{a}_{\boldsymbol{n}}= \)
A \( \cdot \frac{1}{n !} \)
в. \( \frac{1}{(n+2) !} \)
c. \( \frac{1}{(n+1) !} \)
D. none of these


Chlorine has two isotopes of atomic
mass units 34.97 and \( 36.97 . \) The relative
abundance of isotope is 0.755 and 0.245 respectively. Find the average atomic mass of chlorine.


If the cathode is cesium \( (\phi=1.9 e V) \)
what will be the cut off voltage?
A. zero
B . 0.36 V
c. \( 0.46 \mathrm{v} \)
D. \( 0.56 \mathrm{v} \)


A copper disc of radius 0.1 m rotated
about its centre with 10 revolutions per
second in a uniform magnetic field of
0.1 tesla with it's plane perpendicular to the field. The e.m.f. induced across the
radius of disc is:
A \( \cdot \frac{\pi}{10} \) volt
в. \( \frac{2 \pi}{10} \) volt
c. \( \pi \times 10^{-2} \) volt
D. 2 \( \pi \times 10^{-2} \) volt


Sum of the series,
\( \mathbf{1},-\boldsymbol{a}, \boldsymbol{a}^{2},-\boldsymbol{a}^{3}, \ldots \quad \boldsymbol{n} \quad \) terms \( \quad(\boldsymbol{i} \boldsymbol{f} \quad \boldsymbol{a} \)
土1)。


Calculate the molality of 1 litre solution
containing \( 93 \% H_{2} S O_{4}(W / V) \) if the
density of the solution is \( 1.84 g m L^{-1} \)


If yellow light emitted by sodium lamp in Young's double slit experiment is replaced by monochromatic blue light of same intensity keeping other parameters constant the new fringe width will :
A. Remain unchanged
B. Increase
c. Decrease
D. Can't be predicted


Which is the first law university in
India?
A. Al-Ameen College of law
B. Alliance School of law
c. R.K Law college
D. National Law School of India


To prepare \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{\mathbf{6}} \) at \( 573 \mathrm{K}, \mathbf{5 0}-60 \)
atm pressure, the ratio of xenon and
fluorine used is :
A \( \cdot 1: 2 \)
B. 1: 5
\( c \cdot 1: 20 \)
D. 10:1


In a longitudinal section of a root, starting from the tip and going upwards, the four zones occur in the following order
A. Root cap, cell division, cell maturation, cell enlargement
B. Cell division, cell enlargement, cell maturation, root cap
c. cell division, cell maturation, cell enlargement, root cap
D. Root cap, cell division, cell enlargement, cell maturation


Atmosphere is classified into different
zones, which of the following is not among this classification?
A. lonosphere
B. Ozonosphere
c. Lithosphere
D. None of these


is the functional and structural
unit of the nervous system.
A. Neuron
B. Nephron
c. Cerebrum
D. Cerebellum


\( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{\boldsymbol{y}+\boldsymbol{x} \tan \left(\frac{\boldsymbol{y}}{\boldsymbol{x}}\right)}{\boldsymbol{x}} \Rightarrow \sin \frac{\boldsymbol{y}}{\boldsymbol{x}}= \)
\( \mathbf{A} \cdot c x^{2} \)
в. \( c x \)
\( c \cdot c x^{3} \)
\( D \cdot c x^{4} \)


The tangent at any point of a circle is perpendicular to the radius through the point of contact.
A. True
B. False
c. Either
D. Neither


The greatest value of \( f(x)=(x+1)^{\frac{1}{3}}- \)
\( (x-1)^{\frac{1}{3}} \) on [0,1] is
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
D.


If there is \( 20 \% \) adenine in DNA, the
percentage of guanine will be
A . 20\%
B. 40\%
c. \( 10 \% \)
D. None of the above


All ethers are lighter than
A. benzene
B. phenol
c. acetone
D. water


A body slides down a rough inclined
plane of inclination \( \theta \) with constant
velocity \( v \). If it is projected up the plane with velocity \( 2 v, \) then it moves up the
plane with
A. constant velocity
B. retardation g \( \sin \theta \)
c. retardation \( 2 \mathrm{g} \sin \theta \)
D. acceleration g sin \( \theta \)


Discuss briefly giving an example in each case the role of coordination
compound in biological system.


A tank is filled with water and two holes
\( A \) and \( B \) are made in it. For getting same
\( \boldsymbol{h} \)
ranges, ratio of \( \frac{\pi}{h^{\prime}} \) is
\( A \)
B. 1 \( \overline{2} \)
\( c \cdot 1 \)
3
\( D \)


Assertion
Thinner lenses have smaller power.
Reason

Power is directly proportional to the
focal length
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of the following is a universal solvent?
A. water
B. alcohol
c. acetic acid
D. both A and


Explain alternation of generations in bryophytes.


Phosphine is obtained by This question has multiple correct options
A. \( C a_{3} P_{2}+H_{2} O \rightarrow \)
B . \( P_{4}+N a O H \rightarrow \)
c. \( C H C l_{3}+O_{2} \rightarrow \)
D. \( C C l_{4}+O_{2} \rightarrow \)


If Aufbau rule is not followed in filling of sub orbitals, then block of the element
will change in:
A. K(19) (i) (19) (19) 19
B. \( \operatorname{Sc}(21) \)
\( c \cdot v(23) \)
\( D \cdot N i(28) \)


The substrate for photorespiration is
A. Glycolate.
B. Glucose.
c. Lipid.
D. sucrose.


Solve the differential equation:
\( (x-\sin y) d y+\tan y d x=0 \)


A person is in between two vertical
mountains. The person fires a gun then hears the first echo from the nearby mountain in a time 3 s and
hears second echo from far mountain in
a time 4s. The person hears the third echo after
A . 5 s
B. 6 s
\( c \cdot 7 s \)
\( D \cdot 8 s \)


When nitric acid is exposed to light,nitrogen changes its oxidation state from:
\( \mathbf{A} \cdot+5 \) to +3
B. +4 to +3
\( c \cdot+5 t o+4 \)
D. +4 to +2


Product of this reaction is:
\( A \)
B.
c.
D.


A solution of \( K M n O_{4} \) is reduced to
various products depending upon its pH. At pH \( <7 \) it is reduced to a colourless solution \( (A), \) at \( p H=7 \) it forms a brown precipitate (B) and at pH > 7 it gives a green solution (C)
\( (A),(B) \) and \( (C) \) are :
A \( \cdot(A)-M n^{2+},(B)-M n O_{2}(C)-M n O_{4}^{2-} \)
B . \( (A)-M n O_{2},(B)-M n^{2+},(C)-M n O_{4}^{2} \)
c. \( (A)-M n^{2+},(B)-M n O_{4}^{2-},(C)-M n O_{2} \)
D. \( (A)-M n O_{4}^{2-},(B)-M n^{2+},(C)-M n O_{2} \)


The dissociation constant on n-butyric
acid is \( 1.6 \times 10^{-5} \) and the molar
conductivity at infinite dilution is
\( 380 \times 10^{-4} S m^{2} m o l^{-1} . \) The specific
conductance of the \( 0.01 \mathrm{M} \) acid solution
is:
A \( \cdot 1.52 \times 10^{-5} \mathrm{Sm}^{-1} \)
В. \( 1.52 \times 10^{-2} \mathrm{Sm}^{-1} \)
C. \( 1.52 \times 10^{-3} \mathrm{Sm}^{-1} \)
D. None


If \( * \) is defined by \( a * b=a-b^{2} \) and \( \oplus \) is
defined by \( a \oplus b=a^{2}+b, \) where \( a \) and
\( b \) are integers, then \( (3 \oplus 4) * 5 \) is equal
to
A . 164
B. 38
c. -12
D. -28
E .144


The area in the first quadrant bounded by the curves \( x^{2}=2 y, y^{2}=2 x \) and
\( x^{2}+y^{2}=3 \) is


A body weighs \( 250 \mathrm{N} \) on the surface of the earth. How much will it weigh half way down to the centre of the earth.?
\( A \cdot 125 N \)
B. 150 N
c. \( 175 \mathrm{N} \)
D. 250 N.


Divergent evolution of a single group of organism in a new environment is called
A. Adaptive radiation
B. Catastrophism
c. convergent evolution
D. None of the above


Let there be as first-order reaction of the
type, \( \boldsymbol{A} \rightarrow \boldsymbol{B}+\boldsymbol{C} \). Let us assume that
only \( A \) is gaseous. We are required to calculate the value of rate constant
based on the following date.
\[
\begin{array}{lcc}
\text { Time } & \text { o } & \text { T } \\
\text { Partial pressure of A } & P_{0} & P_{t}
\end{array}
\]
Calculate the expression of rate
constant.
A \( \cdot k=\frac{1}{t} \ln \left(\frac{P_{0}}{T_{l}}\right) \)
B . \( k=\frac{1}{t} \ln \left(\frac{P_{t}}{T_{D}}\right) \)
C . \( k=\frac{1}{t} \ln \left(\frac{2 P_{0}}{P_{t}}\right) \)
D・ \( k=\frac{1}{t} \ln \left(\frac{P_{F}}{2 P_{0}}\right) \)


\( \ln \) a \( G . P \) if \( T_{p-1}+T_{p+1}=3 T_{p} \) then
prove that the common ratio of \( G . P \) is
an irrational number.


Two moles of a monoatomic ideal gas
undergo a cyclic process ABCDA as
shown in figure. BCD is a semicircle.
Find the efficiency of the cycle in \( \% \)


If the differential equation of all straight
lines which are at a fixed distance of 10
units from origin is
\( \left(y-x y_{1}\right)^{2}=A\left(1+y_{1}^{2}\right) \) then \( \frac{A}{100} \) is
equal to \( \ldots \) units.


Element that is backbone of organic molecules:
A. carbon
B. hydrogen
c. oxygen
D. all of the above


\( C H_{3} C H_{2} O H \stackrel{O}{\longrightarrow} C H_{3} C H O \stackrel{O}{\longrightarrow} \)
\( C H_{3} C O O H \)
Give the oxidizing agent in the given reactions


If \( A \) and \( B \) are square matrices of order
n' such that \( A^{2}-B^{2}=(A-B)(A+ \)
\( B \) ), then which of the following will be
true?
A. Either of A or B is zero matrix
в. \( A=B \)
c. \( A B=B A \)
D. Either of A or B is an identity matrix


Which of the following can be used as a
solvent for cellulose acetate, cellulose
nitrate, and celluloide?
A. Formaldehyde
B. Acetaldehyde
c. Acetic acid
D. Acetone


The final step for the extraction of
copper from copper pyrites in Bessemer converter the reaction involves is as:
A \( \cdot C u_{2} S+2 F e O \rightarrow 2 C u+2 F e+S O_{2} \)
в. \( C u_{2} S+2 C u O \rightarrow 6 C u+S O_{2} \)
c. \( 4 C u_{2} S+F e S \rightarrow 8 C u+2 F e S O_{4} \)
D. \( 2 C u_{2} O+F e S \rightarrow 4 C u+2 F e+S O_{2} \)


The petroleum product used as fuel for stoves, lamps and jet aircraft is :
A. kerosene
B. petrol
c. diesel
D. None of these


Evaluate using limit of sum:
\( \int_{1}^{3}(x+1)^{2} d x \)


Compound \( (X) \) is:
\( A \)
B.
\( c \)
D.


Which molecule has both shape and geometry identical?
(।) \( \boldsymbol{S} \boldsymbol{n} \boldsymbol{C l}_{2} \)
(II) \( \boldsymbol{N} \boldsymbol{H}_{3} \)
\( (\| I) P C l_{5} \)
\( (1 \vee) S F_{4} \)
A . I, III and IV
B. II, III and IV
c. ॥
D. All


Which of the following structures is not related to body balance?
A. Maculae
B. Crista
c. organ of Corti
D. Ampulla


Which of the following is not a colloidal solution?
A . Solid-Solid
B. Liquid-Liquid
c. Gas-Gas
D. Solid-Liquid


Given a relation \( \boldsymbol{R}=\{(\mathbf{1}, \mathbf{2}),(\mathbf{2}, \mathbf{3})\} \) on
the set of natural numbers,Find the
minimum number of ordered pairs should be added so that the enlarged
relation is symmetric,transitive and
reflexive.


Q Type your question
radius of the semicircle is \( r . \) The speed
of sound in air is \( v \). The source of sound
is capable of generating frequencies in
the range \( f_{1} \) to \( f_{2}\left(f_{2}>f_{1}\right) . \) If \( n \) is an
integer, frequency for maximum intensity is given by :
A \( \cdot \frac{n v}{r} \)
B. \( \frac{n v}{r(\pi-2)} \)
c. \( \frac{n v}{\pi r} \)
D. \( \frac{n v}{(r-2) \pi} \)


Conifers differ from grasses in the
A. Absence of pollen tubes
B. Formation of endosperm before fertilization
c. Production of seeds from ovules
D. Lack of xylem tracheids


Tyres are made circular because:
A. they can be inflated
B. they require less materaial
C. they look beautiful
D. they face less friction


When a rectangular coil is rotated in a uniform magnetic field about an axis passing through its centre and perpendicular to the field, the induced
emf in the coil is maximum when the
plane of the coil is
A. Perpendicular to the field
B. Parallel to the field
c. Inclined at 60 with the field direction
D. Inclined at 45 with the field direction


A train travels a distance of \( 480 k m \) at a
uniform speed. If the speed had been \( 8 k m / h r \) less, then it would have taken
3 hours more to cover the same
distance. Formulate the quadratic equation in terms of the speed of the train.


Bond energy is highest in the following?
A \( . C O \)
в. \( O_{2} \)
c. \( N O \)
D. \( N_{2} \)


If \( S=i+2 i^{2}+3 i^{3}+\ldots \) up to 200 term
then S equals
A . \( 200 i \)
B . \( 100(1+i) \)
c. \( 100(1-i) \)
D. \( 200(1-i) \)


Which of the following is a physical
property of sugar?
A. It is a white crystalline solid.
B. Carbon, hydrogen, and oxygen are its constituents.
C . It turns black when concentrated \( H_{2} S O_{4} \) reacts with it.
D. When heated it decomposes.
E. It decomposes readily.


The energy levels of an atom are as
shown here. Which of them will result in
the transition of a photon of wavelength
\( 275 n m ? \) which of this transitions
corresponds to emissions of radiations of (1)maximum (11)Minimum


Verify Lagrange's Mean Value Theorem for the function \( f(x)=x^{2}+x-1 \) in
the interval \( [\mathbf{0}, \mathbf{4}] \)


Speed can be positive, zero or negative. True or false
A . True
B. False


Out of 2 men and 3 women a team of
two persons is to be formed such that there is exactly one man and one woman. Write the sample space of this
experiment, then the total no. of combinations of team possible are
A . 9
B. 6
\( c \cdot 4 \)
D. 12


Mala - D was developed by
A. CDRI Dehradun
B. Central marcotic Institute National
C . Central drug research Institute Lucknow
D. Central narcotic research institute Hyderabad


The basic source of wind energy, hydro energy, and fossil fuel energy is


Let \( A \) and \( B \) be points with position vectors \( \bar{a} \) and \( \bar{b} \) with respect to origin \( O \)
If the point \( C \) on \( O A \) is such that \( \mathbf{2} \overline{\boldsymbol{A} \boldsymbol{C}}=\overline{\boldsymbol{C} \boldsymbol{O}}, \overline{\boldsymbol{C} \boldsymbol{D}} \) is parallel to \( \overline{\boldsymbol{O} \boldsymbol{B}} \) and
\( |\overline{C D}|=3|\overline{O B}| \) then \( A D \) is
A \( \cdot \bar{b}-\frac{a}{9} \)
в. \( 3 \bar{b}-\frac{a}{3} \)
C \( \cdot \bar{b}-\frac{a}{3} \)
D. \( \bar{b}+\frac{a}{3} \)


A thin lens of focal length \( f \) and
aperture diameter \( d \) forms an image of intensity \( I . \) If the central part of the aperture upto diameter \( \boldsymbol{d} / 2 \) is blocked by an opaque paper, then the new focal length and intensity of image will be
A \( \cdot \frac{f}{2}, \frac{l}{2} \)
B. \( \frac{f}{2}, \frac{3}{4} l \)
\( c \cdot_{f, \frac{1}{2}} \)
D. \( f, \frac{3}{4} l \)


A particle initially moving towards south in a vertically downward magnetic field is deflected toward the
east. What is the sign of the charge on
the particle?


A biconvex lens has radii of curvature of
two faces \( 0.1 \mathrm{m} \) and 0.12 respectively. If the focal length of the lens is \( 0.1 \mathrm{m} \). Find
(i) the refractive index of the material of
lens
(ii) power of lens (iii) nature and position of the image of an object placed at a distance of \( 6 \mathrm{cm} \) from the lens.


Heart of Cyclostomata is chambered.
A . 2
B. 3
\( c \cdot 4 \)
D. None of these


Darwin's finches provide evidence of evolution from
A. Anatomy
B. Morphology
c. Biogeography
D. All the above


A large steel wheel is to befitted on to a
shaft of the same material. At \( 27^{\circ} \mathrm{C} \), the
outer diameter of the shaft is \( 8.70 \mathrm{cm} \)
and the diameter of the central hole in
the wheel is, \( 8.69 \mathrm{cm} . \) The shaft is cooled using 'dry ice'. At what temperature of the shaft does the whee slip on the shaft? Assume coefficient of linear expansion of the steel to be
constant over the required temperature range \( \boldsymbol{a}_{\text {steel}}=\mathbf{1 . 2 0} \times \mathbf{1 0}^{-\mathbf{5}} \mathbf{K}^{-\mathbf{1}} \)


Which has maximum pH in aqueous
solution?
A. \( N a C l O \)
в. \( N a C l O_{2} \)
c. \( N a C l O_{3} \)
D. \( N a C l O_{4} \)


The change in the gravitational
potential energy when a body of mass \( m \)
is raised to a height \( n R \) above the
surface of the earth is (here \( R \) is the
radius of the earth)
A \( \cdot\left(\frac{n}{n+1}\right) m g R \)
B \( \cdot\left(\frac{n}{n-1}\right) m g R \)
c. \( n m g R \)
D. \( \frac{m g R}{n} \)


Which of the following is not related to photorespiration?
A. Peroxisomes
B. Lysosomes
c. Mitochondria
D. chloroplasts


f \( x y+y z+z x=1 \) then find the value
of \( \tan ^{-1} x+\tan ^{-1} y+\tan ^{-1} z \)


The solubility of iodine in carbon tetrachloride is due to
A. lonic solvent-solute interaction
B. Charge-transfer phenomenon
c. van der Waals interaction
D. Dissociation of iodine


Sum to \( n \) terms the series:
\( \mathbf{1} \times \mathbf{3}+\mathbf{3} \times \mathbf{5}+\mathbf{5} \times \mathbf{7}+\mathbf{7} \times \mathbf{9}+\dots \)


A science student takes 100
observations in an experiment. Second
time he takes 500 observations in the
same experiment. By doing so the possible error becomes:
A. 5 times
B. \( 1 / 5 \) times
c. unchanged
D. none of these


There is a small hole in a hollow
container. At what temperature should it be maintained in order that it emits
one calorie of energy per second per
meter \( ^{2} \) ?
\( A \cdot \) 10K
в. \( 100 k \)
c. २००к
D. 500k


Yellow oils of sulphur is/are:
A \( . H_{2} S \)
в. \( H_{2} S_{2} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{SO}_{4} \)
D. \( C S_{2}, N H_{2} C S N H_{2} \)


Eutrophication is caused by
A. Acid rain
B. Nitrates and phosphates
c. Sulphates and carbonates
D. \( C O_{2} \) and \( c 0 \)


\( \int_{0}^{\pi / 2} \frac{\cos x}{1+\sin x} d x= \)
\( A \cdot \log 2 \)
B. \( \log \) e
\( c \cdot \frac{1}{2} \log 3 \)
D.


Solve the following:
f \( \boldsymbol{L}=\mathbf{1 0}, \boldsymbol{f}_{1}=\mathbf{7} \mathbf{0}, \boldsymbol{f}_{0}=\mathbf{5 8}, \boldsymbol{f}_{2}= \)
\( 42, h=2, \) then find the mode by using
formula.


When the angle between incident ray
and mirror is \( 20^{\circ}, \) calculate the angle of
incidence and angle of reflection.
A. Angle of incidence \( =20^{\circ} \)
Angle of reflection \( =50^{\circ} \)
B. Angle of incidence \( =20^{\circ} \)
Angle of reflection \( =20^{\circ} \)
C. Angle of incidence \( =70^{\circ} \)
Angle of reflection \( =70^{\circ} \)
D. Angle of incidence \( =160^{\circ} \)
Angle of reflection \( =50^{\circ} \)


\( \boldsymbol{F} e^{2+} \rightarrow \boldsymbol{F} e^{3+}+\boldsymbol{e}^{-} ; \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4}^{-}+\boldsymbol{5} \boldsymbol{e}^{-} \rightarrow \)
\( M n^{2+}, \) the ratio of stoichiometric
coefficient of \( F e^{2+} \) and \( M n O_{4}^{-} \) in the balanced redox reaction is:
A .1: 5
B. 5: 1
c. 2: 3
\( D \cdot 6: 1 \)


The first term of an AP is unity and common difference is \( 5 . \) Which of the
following will be a term of this AP. This question has multiple correct options
A. 4880
B. 7881
\( c .5890 \)
D. 789


When required the following logarithms may be used. \( \log 2=.3010300, \log 3=.4771213 \)
\( \log 7=.8450980, \log 11=1.0413927 \)
In how many years will a sum of money double itself at 5 per cent. compound interest?


Vectors \( \boldsymbol{a} \times(\boldsymbol{b} \times \boldsymbol{c}), \boldsymbol{b} \times(\boldsymbol{c} \times \boldsymbol{a}) \) and
\( \boldsymbol{c} \times(\boldsymbol{a} \times \boldsymbol{b}) \) are
A. linearly dependent vectors
B. equal vectors
c. parallel vectors
D. none of these


Malleability is the ability of a metal to
be beaten into the sheet


Sl unit for the average velocity is
\( A \cdot m / s \)
B. km/s
\( \mathrm{c} \cdot \mathrm{cm} / \mathrm{s} \)
D. none of these


Two stereo isomers are obtained on
treating Bromine molecule with trans2-pentene. What are these isomers?
A. d and I
B. E and z
c. cis and trans
D. None of these


A loaded truck travels \( 18 \mathrm{km} \) in 25
minutes. If the speed remains the same,
how far car travel in 5 hours?


Differentiate each of the functions with
respect to \( ^{\prime} \boldsymbol{x}^{\prime} \)
\( \frac{a x+b}{c x+d} \)


Let \( \Delta= \)
\( \left|\begin{array}{ccc}\sin \theta \cos \phi & \sin \theta \sin \phi & \cos \theta \\ \cos \theta \cos \phi & \cos \theta \sin \phi & -\sin \theta \\ -\sin \theta \sin \phi & \sin \theta \cos \phi & 0\end{array}\right|, \) ther
\( A \cdot \Delta \) is independent of \( \theta \)
B. \( \Delta \) is independent of \( \phi \)
\( c \cdot \Delta \) is a constant
D. \( \Delta \) is dependent of \( \phi \)


The state of hybridization of \( C_{2}, C_{3}, C_{5} \)
and \( C_{6} \) of the hydrocarbon is in the
following sequence:
A \( \cdot s p, s p^{2}, s p^{3} \) and \( s p^{2} \)
B . \( s p, s p^{3}, s p^{2} \) and \( s p^{3} \)
\( \mathbf{c} \cdot s p^{3}, s p^{2}, s p^{2} \) and \( s p \)
D. \( s p, s p^{2}, s p^{2} \) and \( s p^{3} \)


Find the solution of lines:
\[
\begin{array}{l}
\boldsymbol{x}+\boldsymbol{y}=\boldsymbol{4} \\
\boldsymbol{2} \boldsymbol{x}-\boldsymbol{3} \boldsymbol{y}=\boldsymbol{3}
\end{array}
\]


Write the compound statement, "If \( \mathrm{p} \) then \( q \) and if \( q, \) then \( p^{\prime \prime} \) in symbolic form.
A \( (p \wedge q) \wedge(q \wedge p) \)
a \( (p \wedge q) \wedge(q \wedge p) \)
в. \( (p \Longrightarrow q) \vee(q \Longrightarrow p) \)
c. \( (q \Longrightarrow p) \wedge(p \Longrightarrow q) \)
D. \( (p \wedge q) \vee(q \wedge p) \)


One of the following can flourish at high
temperature of \( 87^{\circ} \mathrm{C} \)
A. Volvox
B. Spirogyra
c. Ulothrix
D. None of the above


If a particle is slowly brought from
reference point to another point \( \boldsymbol{P} \) in a gravitational field, then work done per
unit mass by the external agent is (at that point)
A. gravitational force
B. gravitational field intensity
c. gravitation potential
D. none of the above


The doubly ionized lithium atom is
hydrogen-like with the atomic number \( z=3 . \) Find the wavelength of the
radiation required to excite the electron
in \( L i^{2+} \) from the first to the third Bohr
orbit is:
\( \left[\text { Given: } \frac{1}{\boldsymbol{R}_{\boldsymbol{H}}}=\mathbf{9 1 2} \boldsymbol{A}\right] \)
\( \mathbf{A} \cdot 114 \stackrel{\circ}{A} \)
B \( \cdot 156^{\circ} \)
\( \mathbf{c} \cdot_{180 \stackrel{\circ}}{\mathbf{h}} \)
D \( \cdot 201 \stackrel{\circ}{A} \)


In the uniform electric field shown in
figure, \( \boldsymbol{V}_{\boldsymbol{A}}-\boldsymbol{V}_{\boldsymbol{D}} \) is :
\( A \cdot 5 V \)
B. \( 10 V \)
\( c .20 V \)
D. \( 0 V \)


The velocity-time graph being a straight line parallel to the velocity axis implies
A. zero acceleration
B. positive acceleration
c. negative acceleration
D. infinite acceleration


A small body \( A \) starts sliding off the top
of a smooth sphere of radius \( R \). Find the
angle \( \theta \) (shown in figure
above) corresponding to the point at which the body breaks off the sphere as
well as the break-off velocity of the body
A \( \quad \theta=\arccos \left(\frac{1}{3}\right) \approx 52^{\circ}, v=\sqrt{\frac{2 g R}{3}} \)
B. \( \theta=\arccos \left(\frac{2}{3}\right) \approx 48^{\circ}, v=\sqrt{\frac{2 g R}{3}} \)
\( ^{\mathrm{c}} \cdot_{\theta}=\arccos \left(\frac{2}{3}\right) \approx 48^{\circ}, v=\sqrt{\frac{g R}{3}} \)
D. \( _{\theta}=\arccos \left(\frac{1}{3}\right) \approx 52^{\circ}, v=\sqrt{\frac{g R}{3}} \)


Assertion
Fluorine molecule has bond order one.
Reason

The number of electrons in antibonding
molecular orbitals is two less than in
bonding molecule orbitals.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Solve:
\( (x+y) \frac{d y}{d x}=1 \)


ff \( \left[\begin{array}{ll}\boldsymbol{x} & \mathbf{0} \\ \mathbf{1} & \boldsymbol{y}\end{array}\right]+\left[\begin{array}{cc}-\mathbf{2} & \mathbf{1} \\ \mathbf{3} & \mathbf{4}\end{array}\right]=\left[\begin{array}{ll}\mathbf{3} & \mathbf{5} \\ \mathbf{6} & \mathbf{3}\end{array}\right]- \)
\( \left[\begin{array}{ll}2 & 4 \\ 2 & 1\end{array}\right], \) then
A. \( x=-3, y=-2 \)
в. \( x=3, y=-2 \)
c. \( x=3, y=2 \)
D. \( x=-3, y=2 \)


The internal resistance of a cell of emf
\( 1.5 V, \) if it can deliver a maximum
current of \( 3 A \) is
A . \( 0.5 \Omega \)
B. 4.5\Omega
\( c .2 \Omega \)
D. 1\Omega


Which of the companies shows the
maximum percentage difference in
sales turnover between the two years?
Sales Turnover of 5 Companies (in Rs
A. Honda
B. GM
c. Hyundai
D. Maruti


What is soap? Explain the preparation of soap giving chemical equation.


For the reaction in equilibrium,
\[
N_{2} O_{4}(g) \rightleftharpoons 2 N O_{2}(g)
\]
The concentrations of \( N_{2} O_{4} \) and \( N O_{2} \)
at equilibrium are \( 4.8 \times 10^{-2} \) and
\[
1.2 \times 10^{-2} \text {mol } L^{-1} \text {respectively. The }
\]
value of \( K_{c} \) for this reaction is:
A \( \cdot 3 \times 10^{-3} \) molL \( ^{-1} \)
-
B. \( 3 \times 10^{3} \) molL \( ^{-1} \)
c. \( 3.3 \times 10^{2} \) molL \( ^{-1} \)
D. \( 3 \times 10^{-1} \mathrm{molL}^{-1} \)


The chloride of a solid metallic element
contains \( 57.89 \% \) by mass of the element. The specific heat of the element is 0.0324 cal \( d e g^{-1} g^{-1} \)
Calculate the exact atomic mass of the
element.


A solid cylindrical unchanged conductor of radius \( r \) and length \( l \) is placed in a region of space where a uniform electric field \( \vec{E} \) exits. The
electric field inside the conductor due
to the charge induced on its surface is :
A . \( \vec{E} \)
B . \( 2 \vec{E} \)
\( c \cdot-\vec{E} \)
D. \( -2 \vec{E} \)


The method of dimensional analysis
can be used to derive which of the
following relations?
A. \( N_{0} e^{-\lambda} \)
B. \( \operatorname{Asin}(\omega+k x) \)
c. \( \frac{1}{2} m v^{2}+\frac{1}{2} \omega^{2} \)
D. None of these


Which of the following can form adducts with lewis base?

This question has multiple correct options
\( A \cdot S O_{2} \)
в. \( \operatorname{Se} O_{3} \)
\( c \cdot S O_{3} \)
D. \( \operatorname{Se} O_{2} \)


If \( z_{1}, z_{2}, \dots, z_{n} \) lie on \( |z|=r \) and \( \operatorname{Re}\left(\sum_{j=1}^{n} \sum_{k=1}^{n} \frac{z_{j}}{z_{k}}\right)=0, \) then
This question has multiple correct options
\( ^{\mathbf{A}} \cdot \sum_{j=1}^{n} z_{j}=0 \)
\( ^{\mathbf{B}} \cdot\left|\sum_{j=1}^{n} z_{j}\right|=0 \)
\( ^{\mathrm{c}} \cdot \sum_{j=1}^{n} \frac{1}{z_{j}}=0 \)
D. None of these


Animals belonging to phylum Cnidarian
are symmetrical.
A . Not
B. Spherically
c. Radially
D. Bilaterally


When 2 -ethylanthraquinol dissolved in a mixture of benzene and cyclohexanol is oxidized, the product is:
A. Ethanol
B. Hydrogen peroxide
c. Anthracene
D. None of these


The basic amino acids are:
A. Iysine, arginine
B. alanine, glutamic acid
c. proline, valine
D. alanine, cystein


Show that \( 2 \tan ^{-1} \frac{3}{5}=\tan ^{-1} \frac{15}{8} \)


Show that the cube of any positive integer is of the form \( 9 m, 9 m+1 \) or
\( 9 m+8 . \) Using Euclid's division lemma.


What is the molecular formula of
pyrogallol?
\( \mathbf{A} \cdot C_{6} H_{4}(O H) \)
в. \( C_{6} H_{5}(O H)_{3} \)
c. \( C_{6} H_{3}(O H)_{3} \)
D. \( C_{6} H_{5} O H \)


A circular coil of magnetic moment
\( 0.355 J T^{-1} \) rests with its plane normal
to an external field of magnitude \( 5.0 \times \)
\( 10^{-2} \mathrm{T} . \) The coil is free to turn about an
axis in its plane perpendicular to the field direction. When the coil is turned
slightly and released, it oscillates about its stable equilibrium with a frequency
of \( 2 \mathrm{Hz} \). The moment of inertia of the coil
about its axis of rotation is?
A \( \cdot 1.13 \times 10^{-1} \mathrm{kg} \mathrm{m}^{2} \)
B . \( 1.13 \times 10^{-2} \) kg \( m^{2} \)
C \( \cdot 1.13 \times 10^{-3} \mathrm{kg} \mathrm{m}^{2} \)
D. \( 1.13 \times 10^{-4} \mathrm{kg} \mathrm{m}^{2} \)


A particle of mass \( m_{1} \) is projected to
the right with a speed \( v_{1} \) onto a smooth
wedge of mass \( m_{2} \) which is
simultaneously projected due to the left
with a speed \( v_{2} \). Highest point on the wedge attained by the particle is \( \frac{\boldsymbol{m}_{2}\left(\boldsymbol{v}_{1}+\boldsymbol{v}_{2}\right)^{2}}{\boldsymbol{x} \boldsymbol{g}\left(\boldsymbol{m}_{1}+\boldsymbol{m}_{2}\right)} \cdot \) Find \( \boldsymbol{x} \)


Whether a reaction is endothermic or
exothermic can be indicated by:
A. enthalpy change.
B. entropy change.
c. gibbs free energy change
D. activation energy
E. specific heat capacity


In the figure find the values of \( x \) and \( y \)


Does the following pairs represent the same rational number:
\( \frac{-16}{20} \) and \( \frac{20}{-25} \)


are chemicals of low molecular
masses \( (\approx 100-500 u) . \) These interact
with macromolecular targets and
produce a biological response.
A. Drugs
B. Medicines
c. Enzymes
D. None of these


Write the truth values of following
statements
(i) 9 is a perfect square but 11 is a prime number.
(ii) Moscow is in Russia.
(iii) London is in France.


A uniform rod of length \( ^{\prime} L^{\prime} \) and density
\( \rho^{\prime} \) is being pulled along a smooth floor
with horizontal acceleration \( \alpha \) as shown
in the figure. The magnitude of the stress at the transverse cross-section
through the mid-point of the rod is
A \( \frac{\rho l \alpha}{4} \)
в. \( 4 \rho l \) d
\( c \cdot 2 \rho l \)
D. \( \frac{\rho l \alpha}{2} \)


Which of the following 0.1 M aqueous solutions will have the lowest freezing point?
A. Potassium sulphate
B. Sodium chloride
c. urea
D. Glucose


\( \boldsymbol{C H}_{3}-\boldsymbol{C H}(\boldsymbol{B r})-\boldsymbol{C H}_{3} \stackrel{\text {alc. } \boldsymbol{K O H}}{\longrightarrow} \)
\( \boldsymbol{A} \frac{\boldsymbol{H} \boldsymbol{B} \boldsymbol{r}}{\text {peroxide}} \boldsymbol{B} \frac{\boldsymbol{N a I}}{\text {acetone}} \boldsymbol{C} \)
The compound \( C \) is :
\( \mathbf{A} \cdot C H_{3}-C H_{2}-C H_{2}-I \)
B. \( C H_{3}-C H(I)-C H_{3} \)
c. \( C H_{3}-C H I-C H_{2}-I \)
D. \( C H_{3}-C H=C H-I \)


Given the best condition for this
transformation:
\( \mathbf{A} \cdot C H_{3} O H, H^{+}(\mathrm{cat.}), \) heat
B. \( H_{2} O, H_{+} \) (cat.), heat
\( \mathbf{c} \cdot M g, \) ether \( , C H_{3} O H \)
\( \mathbf{D} \cdot S O C l_{2}, C H_{3} O H \)


The point \( (-a,-b),(0,0),(a, b) \) and
\( \left(a^{2}, a b\right) \) are
A. collinear
B. concyclic
c. vertices of a rectangle
D. vertices of a parallelogram


Find a vector \( \overrightarrow{\boldsymbol{v}} \) which is co-planar with the vectors \( \vec{a}=\hat{i}-2 \hat{j}+\hat{k} \) and \( \vec{b}=\hat{i}- \)
\( \hat{\boldsymbol{j}}+2 \hat{\boldsymbol{k}} \) and is orthogonal to the vector \( \vec{c}=-2 \hat{i}+\hat{j}+\hat{k} . \) It is given that the projection of \( \overrightarrow{\boldsymbol{v}} \) along the vector \( \hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}+ \)
\( \hat{k} \) is equal to \( 16 \sqrt{3} \)
\( \mathbf{A} \cdot 6 \hat{j}-12 \hat{k} \)
B . \( 12 \hat{i}-6 \hat{j}+30 \hat{k} \)
c. \( 9(\hat{i}-\hat{j}+\hat{k}) \)
D. None of these


Factorize
\( 2 x^{2}+4 x+2=0 \)


n fig, there is a uniform conducting
structure in which each small square
has side \( a \). The structure is kept in a
uniform magnetic field \( B \). Then the
magnetic force on the structure will be:
\( A \cdot 2 \sqrt{2} i B a \)
B. \( \sqrt{2} i \) Ва \( a \)
\( c .2 i B a \)
D. \( i B a \)


If the dividend and divisor have unlike
signs then the quotient will be
A. Positive
B. Negative
c. zero
D. none of these


Oxides of sulphur present in the atmosphere are washed down by rain and would result in:
A. lowering of \( p H \) of the soil
B. increase in \( p H \) of the soil
c. increase in \( O_{3} \) quantities
D. none of these


How many grams of \( N a_{2} S O_{4} \) can be
produced by reacting \( 98 ~ g H_{2} S O_{4} \) with 40 g \( N a O H ? \)
A . 18 g
B . \( 36 g \)
c. \( 71 \mathrm{g} \)
D. \( 142 \mathrm{g} \)
E . \( 150 \mathrm{g} \)


The weight of a man is \( 750 \mathrm{N} \) The total
area of the soles of his shoes is \( 250 \mathrm{cm}^{2} \)
Find the pressure he applies on the floor
\( \mathbf{A} \cdot 30,000 P a \)
B. \( 15,000 P a \)
c. \( 60,000 P a \)
D. \( 90,000 P a \)


The heat added to the heat engine is
A . 150
B. 100
c. 50
D. 2.
E. zero


The \( 17^{t h} \) term of an \( A . P \) succeed \( 10^{t h} \) term by \( 7 . \) Find common difference \( d \) ?


Which one of the following statements
is not correct?
A. The two main organs of the human body where the magnetic field produced is quite significant are the heart and the brain.
B. In a house circuit, lamps are used in parallel
C. Switches,fuses and circuit breakers should be placed in the neutral wire
D. A generator with commutator produces direct current


If the shortest wavelength of the
spectral line of \( H e^{+} \) in Lyman series is
\( x, \) then longest wavelength of the line in Balmer series of \( L i^{2+} \) is:
A. \( \frac{5 x}{4} \)
в. \( \frac{4 x}{5} \)
c. \( \frac{16 x}{5} \)
D. \( 9 x \)


Sclerenchyma is a simple permanent tissue with thick secondary lignified cell walls. In which of the following cells the secondary cell walls are present?
A. The cells containing cytoplasm only
B. The cells with protoplast
c. The cells which are living at maturity
D. The cells which are non living at maturity


Price of shirt decreased from Rs. 80 to
Rs. \( 60 . \) Find the percentage of decreased price?


The position of a body moving along \( x- \)
axis as a function of time \( t \) is given as
\( x=4-2 t \) metre. The distance travelled
by the body in first two seconds is :
A. Zero
в. \( 1 m \)
c. \( 2 m \)
D. \( 4 m \)


A cylindrical vessel of height \( 24 \mathrm{cm} \) and
diamater \( 40 \mathrm{cm} \) is full of water. Find the
exact number of small cylindrical bottles, each of height \( 10 \mathrm{cm} \) and diameter \( 8 \mathrm{cm}, \) which can be filled with this water.


A thermally insulated vessel is divided
into two parts by a heat-insulating piston which can move in the vessel without friction. The left part of the
vessel contain one mole of an ideal
monoatomic gas, \( \& \) the right part is
vacuum. The piston is connected to the right wall of the vessel through a spring whose length in free state is equal to the length of the vessel as shown in the
figure. Determine the heat capacity \( C \) of the system, neglecting the heat capacities of the vessel, piston and
spring.


Transponder is a device in satellites to:
A. correct the orbit of satellite
B. photograph features of the Earth
C. receive and broadcast audio and video signals
D. spy on criminals


Which of the following is a pollutant?
A. Sooty particle
B. Sulpur-dioxide
c. carbon-monoxide
D. All of above


Explain the saying "ontogeny repeats phylogeny"


The force which tries to bring the body back to its mean position is called
A. deforming force
B. restoring force
c. gravitational force
D. buoyant force


The correct increasing order of trans-
effect of the following species is:
A \( \cdot B r^{-}>C N^{-}>N H_{3}>C_{6} H_{5} \)
B . \( C N^{-}>B r^{-}>C_{6} H_{5}^{-}>N H_{3} \)
c. \( N H_{3}>C N^{-}>B r^{-}>C_{6} H_{5} \)
D. \( C N^{-}>C_{6} H_{5}^{-}>B r^{-}>N H_{3} \)


An instrument used in electrostatics to
detect the presence of electric charge on a body is called
A . leaf electroscope
B. compound microscope
c. telescope
D. magnetoscope


In the following reaction which element is oxidized?
\( \boldsymbol{M} \boldsymbol{g}(\boldsymbol{s})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{M} \boldsymbol{g} \boldsymbol{C l}_{2}(\boldsymbol{s}) \)
\( \mathbf{A} \cdot M g \)
в. \( C l_{2} \)
\( \mathrm{c} \cdot M g^{+} \)
D. \( C l^{-} \)


In which phase, proteins for spindle fibre formation are synthesized?
A. Gi phase
B. Ga phase
c. s phase
D. Anaphase


Which of the following pairs is not
correctly matched?
A. Allotropic form of sulphur which is more stable at room temperature - Rhombic
B. The hydride of group 16 which is liquid at room temperature - Water
C. The gas formed in the upper layers of atmosphere by action of U V radiations - Nitrogen
D. The catalyst used in the manufacture of \( H_{2} S O_{4} \) by contact process - Vanadium pentoxide


\( C l^{-} \) ion is the conjugate base of:
A. \( H C l \)
в. НОС\( l \)
c. \( H C l O \)
D. \( H C l O_{4} \)


\( l x+m y+n=0 \) is a tangent line to
the circle \( x^{2}+y^{2}=r^{2}, \) if
A \( \cdot l^{2}+m^{2}=n^{2} r^{2} \)
B . \( l^{2}+m^{2}=n^{2}+r^{2} \)
C \( \cdot n^{2}=r^{2}\left(l^{2}+m^{2}\right) \)
D. none of these


The efficiency of an hypothetical cell is about \( 84 \% \) which involves the following
reaction:
\( \boldsymbol{A}(s)+\boldsymbol{B}^{2+}(\boldsymbol{a} \boldsymbol{q}) \rightarrow \boldsymbol{A}^{2+}(\boldsymbol{a} \boldsymbol{q})+ \)
\( B(s): \Delta H=-285 k J \)
Then, the standard electrode potential of the cell will be: (Assume as \( \Delta S=0 \) )
A . 1.20
B. 2.40
c. \( 1.10 v \)
D. 1.24


Evaluate each of the following:
\( \frac{13}{15}-\frac{12}{25} \) is \( \frac{x}{75} \) find 'x'


If \( P(E)=0 \) Then \( P(\text { not } E) \) is
A . 1
B. - -
\( c \cdot 0 \)
D. \( 1 / 2 \)


A bird flies 1 kilometer in one minute.
Can you express the distance covered by the bird in terms of its flying time in
minutes? [use \( t \) for flying time in minutes


There is a current of 40 amperes in a
wire of \( 10^{-16} m^{2} \) area of cross-section. If
the number of free electrons per \( m^{3} \) is
\( 10^{29}, \) then the drift velocity will be:
A \( \cdot 1.25 \times 10^{3} \mathrm{m} / \mathrm{s} \)
в. \( 2.50 \times 10^{3} \) т/ \( s \)
c. \( 2.0 \times 10^{6} \mathrm{m} / \mathrm{s} \)
D. \( 25 \times 10^{6} \mathrm{m} / \mathrm{s} \)


\( \sqrt{3}+2 \sqrt{2}-\sqrt{3}-2 \sqrt{2} \) is equal to
A . 2
B.
\( c \cdot 2 \sqrt{2} \)
D. \( \sqrt{6} \)


The lengths of the shorter and longer
parallel sides of a trapezium are \( \boldsymbol{x} \) cm
and \( y \) cm respectively. If the area of the
trapezium is \( \left(x^{2}-y^{2}\right), \) then the height
of the trapezium is:
A . \( x \)
в. \( (x+y) \)
c. \( y \)
D. \( 2(x-y) \)


Acetone and methanol can be separated by:
A. steam distillation
B. fractional distillation
c. vacuum distillation
D. none of the above


n figure, sides QP and RQ of \( \Delta P Q R \) are
produced to points \( \mathrm{S} \) and \( \mathrm{T} \) respectively
If \( \angle S P R=135^{\circ} \) and \( \angle P Q T=110^{\circ} \)
find \( \angle P R Q \)
4.85
3.65
\( c \cdot 45 \)
0.35


Match the following
List I List 1
a. frictional force \( \quad \) e. reduction of friction
b. rolling friction
f. causes wear and tear
c. ball bearing less than kinetic friction g.
d. trading of surface \( \quad \) h. increase of friction
The correct match is
\( \mathbf{A} \cdot a \rightarrow i ; b \rightarrow e ; c \rightarrow h ; d \rightarrow f \)
B \( \cdot a \rightarrow f ; b \rightarrow f ; c \rightarrow e ; d \rightarrow g \)
\( \mathbf{c} \cdot a \rightarrow f ; b \rightarrow g ; c \rightarrow e ; d \rightarrow h \)
D \( . a \rightarrow i ; b \rightarrow f ; c \rightarrow h ; d \rightarrow e \)


You know that myopia is a common refractive defects of vision. A person with this defect can clearly see only objects that are near. Using concave lens of suitable power this defect is corrected.
i) Mention the other two types of
defects.
ii) Explain how they can be corrected.


For any vector \( \vec{r}, \) prove that \( \vec{r}= \) \( (\vec{r} . \hat{i}) \hat{i}+(\vec{r} \cdot \hat{j}) \hat{j}+(\vec{r} \cdot \hat{k}) \hat{k} \)


If \( \tan A-\tan B=x \) and \( \cot B- \)
\( \cot A=y \) then \( \cot (A-B)= \)
A \( \cdot \frac{1}{y}-\frac{1}{x} \)
в. \( \frac{1}{x}-\frac{1}{y} \)
c. \( \frac{1}{x}+\frac{1}{y} \)
D. None of these


The half life period of \( N^{13} \) is 10.1 minute. Its mean life time is :
A. 5.05 minutes
B. 20.2 minutes
c. \( \frac{10.1}{0.6931} \) minutes
D. Infinity


There are 10 points in a plane of which 4 are collinear. How many different straight lines can be drawn byjoining these points.


What causes difference in velocity of colours while passing from one medium to another through glass prism?
A. Different wavelengths
B. Different amplitudes
c. Different colours
D. None of the above


How many nucleotides in messenger RNA's sequence makes a codon for an amino acid?
A. Three
B. Four
c. one
D. Two


A compound added to lower the fusion temperature of the electrolytic bath in the extraction of Al is
A. cryolite and fluorspar
B. Bauxite
c. Iron and fluorspar
D. none of these


Solve the given quadratic equation by using the formula method, \( (2 x+ \)
\( \mathbf{3})(\mathbf{2} \boldsymbol{x}-\mathbf{2})+\mathbf{2}=\mathbf{0} \)


With excess of \( C l_{2}, \) ammonia forms:
A. ammonium chloride
B. nitrogen trichloride
c. nitrosyl chloride
D. nitrogen


If the velocity of centre of mass of a
rolling body is \( V \) then velocity of highest point of that body is :
A. \( \sqrt{2} V \)
в. \( V \)
c. \( 2 V \)
D. \( \frac{V}{\sqrt{2}} \)


Cryolite, \( N a_{3} A l F_{6} \) is added to \( A l_{2} O_{3} \) in
Hall-Heroult process to \( _{---}- \) m.p. and
to electrical
conductivity.
A. higher, increase
B. higher, decrease
c. lower, increase
D. lower, decrease


If \( \overline{D A}=\bar{a} ; \overline{A B}=\bar{b} \) and \( \overline{C B}=k \bar{a} \)
where \( k>0 \) and \( x, y \) are the midpoints
of \( D B \) and \( A C \) respectively such that \( |\overline{\boldsymbol{a}}|=\mathbf{1 7} \) and \( |\overline{\boldsymbol{X}} \boldsymbol{Y}|=\mathbf{4}, \) then \( \mathbf{k}= \)
A. \( \frac{8}{17} \)
в. \( \frac{9}{17} \)
c. \( \frac{11}{17} \)
D. \( \frac{4}{17} \)


The reaction, \( Z n^{2+}(a q)+2 e^{-} \rightarrow Z n(s) \)
is:
A. oxidation
B. reduction
c. redox reduction
D. none of the above


Which of the following motion is/are periodic as well as oscillatory motion?
(i)
(ii)
(iii)
(iv)
A. (i), (ii) and (iii)
B . (ii) only
c. (i), (iii) and (iv)
D. (iii) only


The surface area of a cube of side is
\( 27 \mathrm{cm} \) is:
\( \mathbf{A} \cdot 2916 \mathrm{cm}^{2} \)
В. \( 729 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 4374 c m^{2} \)
D. \( 19683 c m^{2} \)


Van't Hoff factor for an electrolyte is
greater than


Do you know that the corneal-
impairment can be cured by replacing
the defective cornea with the cornea of
the donated eye? How and why should we organize groups to motivate the community members to donate
their eyes after death?


The momentum of a system with
respect to centre of mass-
A. Is zero only if the system is moving uniformly.
B. Is zero only if no external force acts on the system.
C. Is always zero.
D. Can be zero in certain conditions.


Prevention of corrosion of iron by \( Z n \)
coating is called:
A . galvanization
B. cathodic protection
c. electrolysis
D. photoelectolysis


During bond formation, potential energy
of the system:
A. increases
B. decreases
c. remains the same
D. cannot be predicted


If the velocity of a particle is \( \boldsymbol{v}=\boldsymbol{A} \boldsymbol{t}+ \)
\( B t^{2}, \) where \( A \) and \( B \) are constants, then
the distance travelled by it between 1 s
and \( 2 s \) is
A \( \cdot \frac{3}{2} A+4 B \)
B. \( 3 A+7 B \)
c. \( \frac{3}{2} A+\frac{7}{3} B \)
D. \( \frac{A}{2}+\frac{B}{3} \)


In the diagram shown, the leaves of the electroscope diverge when a positively charged rod is brought near the knob of an uncharged electroscope. The leaves diverge because:
A. They are both negatively charged
B. They are both positively charged
c. One is positive and one is negative
D. One leaf is neutral and one is positive
E. Both leaves are neutral


Consider \( \boldsymbol{f}:\{1,2,3\} \rightarrow\{\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}\} \) and
\( \boldsymbol{g}:\{\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}\} \rightarrow\{\text { apple,ball,cat }\} \) defined
as \( \boldsymbol{f}(\mathbf{1})=\boldsymbol{a}, \boldsymbol{f}(\mathbf{2})=\boldsymbol{b}, \boldsymbol{f}(\mathbf{3})=\boldsymbol{c}, \boldsymbol{g}(\boldsymbol{a})= \)
apple, \( g(b)= \) ball and \( g(c)= \) cat. Show
that \( f, g \) and \( g \circ f \) are invertible. Find
\( f^{-1}, g^{-1} \) and \( (g \circ f)^{-1} \) and show that \( (g \circ f)^{-1}=f^{-1} \circ g^{-1} \)


A particle in one-dimensional motion:
A. with zero speed at an instant may have non-zero acceleration at that instant
B. with zero speed may have non-zero velocity
c. with constant speed must have zero acceleration
D. with positive value of acceleration must be speeding up


A ball of mass \( =100 g m \) is released
from a height \( h_{1}=2.5 m \) above the
ground level and then rebounds to a
height \( h_{2}=0.625 m . \) The time of
contact of the ball with the ground is \( \Delta t=0.01 \) sec. Find the impulsive
(impact) force offered by the ball on the ground.


If the vectors \( \hat{i}+\hat{j}+\hat{k} \) and \( 3 \hat{i} \) form two
sides of a triangle, the area of the triangle is..........
A. \( \frac{3}{\sqrt{2}} \)
B. 3
\( c \cdot 2 \)
D. \( 2 / 3 \)


In an experiment during the analysis of
a carbon compound, 145 cc of \( H_{2} \) was collected at 760 mm of Hg pressure and
\( 27^{\circ} \mathrm{C} \) temperature. The mass of \( \boldsymbol{H}_{2} \) is
nearly:
A . \( 10 \mathrm{mg} \)
B. \( 12 \mathrm{mg} \)
c. \( 24 m g \)
D. \( 6 \mathrm{mg} \)


What is Force?


When \( 1.04 g \) of \( B a C l_{2} \) is present in \( 10^{5} g \)
of solution, the concentration of
solution is:
A. 0.104 ppm
в. 10.4 ррт
c. 0.0104 ppm
D. 104 ppm


Evaluate \( \int \frac{d x}{x+4-x^{2}} \)


The displacement of the point of a whee initially in contact with the ground when the wheel rolls forward half a
revolution where radius of the wheel is
1 \( m \), is (Assume the forward direction
as \( x \) -axis


Find \( A_{2}^{n}, \) if the fifth term of the
expansion of \( \left(\sqrt[3]{x}+\frac{1}{x}\right)^{n} \) does not
depend on \( \boldsymbol{x} \)


In which group of organism, the male has one less chromosome than female?
A. Roundworms
B. All insects
c. Birds
D. Reptiles
E. Round worms and few insects


The nuclear fusion reaction between
deuterium and tritium takes place
A. at ordinary temperature and pressure
B. at low temperature and low pressure
C . at very high temperature and very high pressure
D. when the temperature is near absolute zero


Select the correct order of
polymerization tendency from the following:
A. \( S i-O>P-O>S-O>C l-O \)
в. \( P-O>S-O>C l-O>S i-O \)
c. \( C l-O>S-O>P-O>s i-O \)
D. \( s i-O<P-O<S-O<C l-O \)


Energy in a current carrying coil is stored in the form of
A . electric field
B. magnetic field
c. dielectric strength
D. heat


Why will a sheet of paper fall slower
than one that is crumpled into a ball?


The displacement equation of a particle is \( x=3 \sin 2 t+4 \cos 2 t . \) The amplitude
and maximum velocity will be respectively
A .5,10
в. 3,2
c. 4,2
D. 3,4


A ball is thrown up,what is its velocity and acceleration at the top?


The time in which the ball strikes the
floor of elevator is given by
A . 2.13 s
в. 2.0
\( c \cdot 1.0 s \)
D. 3.12


A coin is tossed and a die is thrown
simultaneously :
\( P \) is the event of getting head and a odd
number.
\( Q \) is the event of getting either \( H \) or \( T \)
and an even number.
\( R \) is the event of getting a number on
die greater than 7 and a tail.
\( S \) is the sample space.
Which of the following options is
correct?
A \( . n(S)=12, n(P)=3, n(Q)=2, n(R)=0 \)
В. \( n(S)=12, n(P)=3, n(Q)=3, n(R)=0 \)
c. \( n(S)=12, n(P)=3, n(Q)=6, n(R)=0 \)
D. \( n(S)=12, n(P)=3, n(Q)=5, n(R)=0 \)


Write down all possible subsets of the following set. \{0,1\}


State whether given statement is True or False.
An object experiences a net zero external unbalanced force. Is it possible for the object to be travelling with a nonzero velocity?
A. True
B. False


A gas \( (X) \) is obtained when copper reacts with dilute HNO3. The gas thus formed reacts with oxygen to give brown fumes of (Y). (Y) when dissolved in
water gives an important acid (Z) and the \( \operatorname{gas}(X) . X, Y, \) and \( Z \) respectively are:
A \( \cdot \) NO; \( N O_{2} ; H N O_{3} \)
в. \( N O_{2} ; \) NO; \( H N O_{3} \)
\( \mathrm{c} \cdot N_{2} \mathrm{O} ; \mathrm{NO} ; \mathrm{H} N O_{2} \)
D. NO; \( N_{2} O ; H N O_{3} \)


Which radical is most likely to form by the homolytic fission of one covalent bond in bromochloromethane,
\( \boldsymbol{C H}_{2} \boldsymbol{B r C l} \) ?
\( A \cdot \cdot C H_{2} C l \)
В \( \ldots C H_{2} B r \)
\( \mathbf{c} \cdot \boldsymbol{c} C H B r C l \)
\( \mathrm{D} \cdot \cdot \mathrm{CH}_{2} \mathrm{BrCl} \)


If \( \alpha \) and \( \beta \) are different complex number with \( |\beta|=1 \) then find \( \left|\frac{\beta-\alpha}{1-\bar{\alpha} \beta}\right| \)


Which of the following statement(s) is/are correct?
i) Na reacts with liq. \( N H_{3} \) to form
paramagnetic species.
ii) \( O_{2} \) reacts with 2 -
ethylanthraquinol form to paramagnetic species.
iii) Hydrolysis of 1 mol of peroxodisulphric acid produces 1 mol of sulphuric acid and 2 mole of
peroxomono sulphuric acid
A.
B. i
c. i and i
D. i and iii


At \( 25^{\circ} \mathrm{C} \), the molar conductances at
infinite dilution for the strong
electrolytes \( N a O H, N a C l \) and \( B a C l_{2} \)
\( \operatorname{are} 248 \times 10^{-4}, 126 \times 10^{-4} \) and \( 280 \times \)
\( 10^{-4} S m^{2} m o l^{-1} \) respectively.
\( \wedge_{m}^{\circ} B a(O H)_{2} \) in \( S m^{2} m o l^{-1} \) is :
A. \( 52.4 \times 10^{-4} \)
В. \( 524 \times 10^{-4} \)
c. \( 402 \times 10^{-4} \)
\( \mathbf{D} \cdot 262 \times 10^{-4} \)


A fair coin is tossed 99 times. If \( X \) is the
number of times heads occur then \( P(X= \)
r) is maximum when \( r \) is
\( \mathbf{A} \cdot 49 \)
B. 50
c. 51
D. none of these


For a given material, the Young's modulus is 2.4 times its modulus of
rigidity. Its Poisson's ratio is
A . 0.2
B. 0.4
c. 1.2
D. 2.4


State whether true or false:
Blind spot is found in the eyes of a blind person only.
A. True
B. False


A car is moving with speed \( 30 m s^{-1} \) on a
circular path of radius \( 500 \mathrm{m} \). Its speed
is increasing at a rate of \( 2 m s^{-2}, \) what is the acceleration of the car?
A \( \cdot 2 m s^{-2} \)
B. \( 2.7 m s^{-2} \)
c. \( 1.82 m s^{-2} \)
D. \( 9.82 m s^{-2} \)


A light ray makes an angle of incidence
\( 60^{\circ}, \) when it falls on a plane reflecting
sheet
The angle of reflection will be.
A \( \cdot 60^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 90^{\circ} \)


What is the difference between
anaerobic \& aerobic respiration? Name some organism that uses the aerobic mode of respiration?


write the quotient and the remainder
\( \left(2 x^{4}+3 x^{3}+4 x-2\right) \div(x+2) \)


Assertion
With the help of redox titration, we can determine the the concentration of
unknown solution using a standard
solution of known concentration
Reason

We can determine the unknown
concentration using the formula:
\( \boldsymbol{N}_{\mathbf{1}} \boldsymbol{V}_{\mathbf{1}}=\boldsymbol{N}_{\mathbf{2}} \boldsymbol{V}_{\mathbf{2}} \)
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 following table gives the
distribution of IQ of 60 pupils of class X
in a school.
\( \begin{array}{ll}\text { IQ } & \text { No. of pupils } \\ \text { 60-70 } & \text { 2 } \\ \text { 70-80 } & \text { 3 } \\ \text { 80-90 } & \text { 5 } \\ \text { 90-100 } & \text { 16 } \\ \text { 100-110 } & \text { 14 } \\ \text { 110-120 } & \text { 13 } \\ \text { 120-130 } & \text { 7 }\end{array} \) Convert the above distribution to a more
than type cumulative frequency distribution and draw its ogive


Calculate the number of chromatids if a
cell has 20 bivalents in prophase I.
A . 40
B. 80
c. 20
D. 60


The \( \alpha \) -particles with initial kinetic
energy 4.8 mev are shot at gold atoms \( (z=79) . \) The potential of \( \alpha \) -particle at the closest distance to the gold nucleus
is
A \( .4 .8 M V \)
в. zero
\( \mathrm{c} .9 .6 \mathrm{MV} \)
D. 2.4MV


The nuclei \( _{13} A l^{27} \) and \( _{14} S i^{28} \) are examples of:
A. isotopes
B. isobars
c. isotones
D. isomers


Find the value of \( \cos 210^{\circ} \sin 300^{\circ} \)


In a trapezium \( \mathrm{ABCD}, \mathrm{AB}|| \mathrm{CD} . \) If \( \angle \boldsymbol{A}= \)
\( 60^{\circ} \) then \( \angle D=? \)
A \( .100^{\circ} \)
B. \( 120^{\circ} \)
\( c \cdot 70 \)
D. 300


A steel wire has a mass of \( 5 g / m \) and is under tension \( 450 N . \) The maximum
average power that can be carried by
the transverse wave in the wire if the
amplitude is not to exceed \( 20 \% \) of the wavelength is \( x \times 10^{4} W \). Find \( x \)


Identify the wrong statement in the
following.
A. Ozone layer does not permit infrared radiation from the sun to reach the earth
B. Acid rain is mostly because of oxides of nitrogen and sulphur
C. Chlorofluorocarbons are responsible for ozone layer depletion
D. Greenhouse effect is responsible for global warming


Solar cell or panels are black in color due to
A. They absorb more heat
B. They reflect all the heat
C. Neither A nor B
D. None


All the stars appear to move from
A. west to east
B. east to west
c. north to south
D. south to north


The synthetic fibre orlon is prepared by the polymerization of:
A. chloroethene
B. propene
c. propenenitrile
D. 2-chloro-1,3-butadiene


In optical instruments, the lenses are used to form image by the phenomenon of
A . Reflection
B. Refraction
c. scattering
D. Diffusion


An aerosol is a colloidal system of :
This question has multiple correct options
A. solid dispersed in gas
B. liquid dispersed in gas
C . gas dispersed in solid
D. gas dispersed in liquid


A Cassegrain telescope uses two mirrors as shown in above figure.
Such a telescope is built with the
mirrors 20 mm apart. If the radius
of curvature of the large mirror is
\( 220 m m \) and the small mirror is
\( 140 m m, \) where will the final image of
an object at infinity be?


Define azeotropes.What type of azeotrope is formed by a positive deviation from Raoult's law? Give an
example


What is meant by long-sightedness?
How can this defect be corrected?


Assertion
The columnar epithelium lining the intestinal mucosa appears to have a
brush like an appearance.
Reason
A large number of microvilli are present
on brush bordered columnar
epithelium.
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


Identify \( (\boldsymbol{E}) \) and \( (\boldsymbol{F}) \) in the following:
\( \boldsymbol{C a} \boldsymbol{C O}_{3} \rightarrow(\boldsymbol{A})+(\boldsymbol{B}) \)
\( (B)+H_{2} O \rightarrow(C) \stackrel{(A)}{\rightarrow}(D) \stackrel{(A) e x c e s s}{\rightarrow}(E) \)
\( (\boldsymbol{A})+\boldsymbol{N} \boldsymbol{H}_{3} \stackrel{\boldsymbol{\Delta}}{\rightarrow}(\boldsymbol{F}) \)
A \( \cdot(E) C a\left(H C O_{3}\right)_{2} ;(F) N H C O N H_{3} \)
B . \( (E) C a\left(H C O_{3}\right) ;(F) N H_{3} C O N H \)
C \( \cdot(E) C a\left(H C O_{3}\right)_{2} ;(F) N H_{2} C O N H_{2} \)
D. None of these


\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{6} \boldsymbol{x}+\mathbf{5} \) find \( \boldsymbol{f}(-\mathbf{1}) \)
\( A \cdot-1 \)
B.
\( c \cdot c \)
D. None of these


Thomson"s atomic model concluded
that is the constituent particle of all kinds of atom.
A . electron
B. protron
c. neutron
D. None of these


In Amoeba, \( N H_{3} \) is excreted through
A. Food vacuole
B. Plasma membrane
c. contractile vacuole
D. All of the above


Mesophyll is usually differentiated in
A. Monocot leaf
B. Isobilateral leaf
c. Dorsiventral leaf
D. Both A and B


A square frame of side \( 10 \mathrm{cm} \) and a long straight wire carrying current \( 1 A \) are in
the plane of the paper. Starting from close to the wire, the frame moves
towards right with a constant speed of \( 10 m / s \) (see figure). The e.m.f.
induced at the time the left arm of the
frame is at \( x=10 \mathrm{cm} \) from the wire is:
A. \( 2 \mu V \)
B. \( 1 \mu V \)
c. \( 0.75 \mu V \)
D. \( 0.5 \mu V \)


For a curve at which the tangent lines at
two distinct points coincide, then the curve cannot be
A. a cubic curve
B. a quadratic curve
c. a curve of 4th power
D. none of these


How does lightning help the atmosphere?
A. Increases the temperature
B. Brings rain
c. Increases the ozone layer
D. Unsure


The angular frequency of a spring block system is \( \omega_{0} \) This system is suspended from the ceiling of anelevator moving
downwards with a constant speed \( v_{0} \)
The block is at rest relative to the
elevator. Lift issuddenly stopped. Assuming the downwards as a positive direction, choose the wrong statement:
A \( \cdot \) The amplitude of the block is \( \frac{v_{0}}{\omega_{0}} \)
B. The initial phase of the block is \( \pi \)
C . The equation of motion for the block is \( \frac{v_{0}}{\omega_{0}} \sin \omega_{0} \mathrm{t} \)
D. The maximum speed of the block is \( v_{0} \)


If \( \boldsymbol{f}(\boldsymbol{x})= \)
\[
\left\{\begin{array}{cc}
\frac{x^{2}}{2}, & \text { if } 0 \leq x \leq 1 \\
2 x^{2}-3 x+\frac{3}{2}, & \text { if } 1<x \leq 2
\end{array},\text { Show }\right.
\]
that \( f \) is continuous at \( x=1 \)


Which of the following portion of intestine is blind sac?
A. Caecum
B. Anus
c. colon
D. None of the above


If \( y=\sqrt{x \log _{e} x, \text { then } \frac{d y}{d x} \text { at } x=e \text { is }} \)
\( A \cdot \frac{1}{e} \)
B. \( \frac{1}{\sqrt{e}} \)
\( c \cdot \sqrt{e} \)
D. None of these


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


\( \left|\begin{array}{cc}\mathbf{2 x} & \mathbf{5} \\ \mathbf{8} & \boldsymbol{x}\end{array}\right|=\left|\begin{array}{cc}\mathbf{6} & \mathbf{- 2} \\ \mathbf{7} & \mathbf{3}\end{array}\right|, \) write the value of
\( \boldsymbol{x} \)


\( 2 \tan ^{-1}(\cos x)=\tan ^{-1}(2 \operatorname{cosec} x) \) then
\( \boldsymbol{x}=? \)
\( \mathbf{A} \cdot \pi / 4 \)
в. \( \pi / 6 \)
c. \( \pi / 2 \)
D. no solution


Chemical volcano is an example of which type of reaction? Explain.


Which of the following is the most basic oxide?
A. \( S O_{3} \)
в. \( \operatorname{Se} O_{3} \)
\( \mathrm{c} \cdot \operatorname{Po} O_{2} \)
D. \( T e O_{2} \)


A large rectangular box falls vertically with an acceleration a. A toy gun fixed
at \( A \) and aimed towards 0 fires a
particle P. Which of the following is
false
A. P will hit \( \mathrm{C} \) if \( \mathrm{a}=\mathrm{g} \)
B. P will hit the roof BC if a \( >g \)
c. P will hit the wall cD if \( a<g \)
D. may be either
\( (a),(b) \) or
(c), depending on the projection speed of


To remove a single electron from its outer most shell, which of the following
will require a shortest wave length
photon?
\( \mathbf{A} \cdot M g \)
B. \( S \) i
\( c . P \)
D.
ह. \( C l \)


Let \( \boldsymbol{A}=\{1,2,3,4,5\} \) and \( B=\{1,4,5\} \)
Let \( R \) be a relation 'is less than' from \( A \)
to \( B \). Find the domain, co domain and
range of \( \boldsymbol{R} \)


toppr
Q туре your question
produced in liver cells. The production of AAT is dependent upon various hormonal stimuli. Human liver cells were cultured;
nalf the cultured cells were used to
measure the amount of AAT mRNA
present, and half were used to measure
the amount of AAT present.

Measurements were taken at five-minute
ntervals following hormonal stimulation of the cells. Figure 1 shows the results of
this experiment. This experiment was
repeated by the addition of an inhibitor of protein synthesis along with the hormone and its result is shown in figure
2. The figure 2 shows that the AAT is a/an
Figure
Minutes after hormone added
Figure 2
A. Protein
B. Hormon
c. Lipid
D. Inhibito
E. Amino acid


Explorer \( 38, \) a radio-astronomy satellite of mass \( 200 k g \) circles the earth in an orbit of average radius \( \frac{3 R}{2}, \) where \( R \) is the radius of the earth. Assuming the gravitational pull on the mass of \( 1 k g \) at
the earth's surface to be \( 10 N \), calculate
the pull on the satellite.
\( \mathbf{A} \cdot 889 N \)
B. \( 8.89 N \)
\( c .8889 N \)
D. \( 88.9 N \)


First few leaves on a stem which are
different from other leaves are called as
A. Prophylls
B. Sporophylls
c. cataphylls
D. Hypsophylls


Maximum boiling point would be shown by:
A. \( C H_{3}-O-C H_{3} \)
в. \( C_{2} H_{5}-O-C_{2} H_{5} \)
c. \( C H_{3}-C H_{2}-C H_{2}-O H \)
D. \( \left(C H_{3}\right)_{2} C H-O H \)


A student drops an object of mass \( 10 \mathrm{kg} \) from a height of 5 m. What is the
velocity of the object when it hits the ground? Assume, for the purpose of this
question, that \( g=10 m / s^{2} \)


Reaction of acetamide with bromine
water and \( K O H \) gives:
A. \( C H_{3} \) СООН
в. \( C H_{3} C H_{2} N H_{2} \)
c. \( C H_{3} C O O N H_{4} \)
D. \( C H_{3} N H_{2} \)


Oxidation of glyceraldehyde phosphate is accompanied by
A. oxidation of \( N A D^{\text {th }} \)
B. Substrate level phosphorylation
c. Reduction of \( N A D^{+} \)
D. Oxidative phosphorylation


At the same temperature and pressure which of the following gas will have highest \( \boldsymbol{K} \boldsymbol{E} \) per mole:
A. Hydrogen
B. Oxygen
c. Methane
D. All of the above


The least value of the product xyz for which the determinant \( \left|\begin{array}{lll}\boldsymbol{x} & \mathbf{1} & \mathbf{1} \\ \mathbf{1} & \boldsymbol{y} & \mathbf{1} \\ \mathbf{1} & \mathbf{1} & \boldsymbol{z}\end{array}\right| \) is
non-negative, is :
\begin{tabular}{l}
A \( -16 \sqrt{2} \) \\
\hline
\end{tabular}
В. \( -2 \sqrt{2} \)
\( c \cdot-1 \)
D. - -


If \( \omega, \omega^{2} \) be the complex cube roots of
unity, and \( \boldsymbol{f}(\boldsymbol{x})= \)
\[
\left|\begin{array}{ccc}
\boldsymbol{x}+\mathbf{1} & \boldsymbol{\omega} & \boldsymbol{\omega}^{2} \\
\boldsymbol{\omega} & \boldsymbol{x}+\boldsymbol{\omega}^{2} & \mathbf{1} \\
\boldsymbol{\omega}^{2} & \boldsymbol{1} & \boldsymbol{x}+\boldsymbol{\omega}
\end{array}\right|
\]
then \( \int_{\frac{-\pi}{2}}^{\frac{\pi}{2}} f(x) d x \) is equal to?
A \( \cdot \frac{x^{4}}{4} \)
в. \( \frac{3}{4} x \)
c. 0
D. None of the above


In a LCR series resonating circle circuit Give the value of average power loss.


The transformer turns ratio is 1: 5 and
\( 0.4 \mathrm{A} \) current flows through the second
when power developed across it is 200
W. Calculate secondary voltage
A . 2000 v
B. 1500 v
c. \( 1000 \mathrm{v} \)
D. 500 v


If three points (0,0),(3,45) and \( (3, \lambda) \) form en equilateral triangle, then the value of \( \lambda, \) is
A . 96
B. 18
c. 50
D. No possible value of \( \lambda \) to make an equilateral triangle


Sulphide ore of copper can be concentrated by froth floatation
process.
A. True
B. False


An urn contains 25 balls of which 10
bear a mark ' \( X \) ' and the remaining 15
bear a mark 'Y'. A ball is drawn at
random from the urn, its mark noted
down and it is replaced. If 6 balls are drawn in this way, find the probability that
(i) All will bear mark ' \( \boldsymbol{X} \)
(ii) Not more than two will bear ' \( Y \) ' mark


Let \( A \) and \( B \) be events such that
\( P(A)-\frac{1}{6}, P(B)=\frac{1}{4} \) and \( P(A \cap B)= \)
\( \frac{1}{12} \cdot \operatorname{Find} P(B / A) \cdot P(A / B) \)


The recent ancestors of modern man we
re
A. Java ape man and Peking man
B. Peking man and Rhodesian Man
C. Rhodesian man and Cro-Magnon man
D. Cro-Magnon man and Neanderthal man


Prove that \( 3+\sqrt{5} \) is an rational
number.


An object is placed \( 15 \mathrm{cm} \) from a diverging mirror, of radius of curvature 20 em. What is the image
magnification produced?
\( A \cdot+0.4 \)
B. -0.4
\( c \cdot+2 \)
\( D \ldots-2 \)


Evaluate: \( \left\{\left(5^{2}+12^{2}\right)^{\frac{1}{2}}\right\} 3 \)
A . 54
B. 34
c. 39
D. 59


There are 6 articles in a box. Write the
total numbers of article in 10 such
boxes.


Which of the following pairs of compounds are chain isomers?
A. Isobutyl alcohol and s-pentyl alcohol
B. Isobutyl alcohol and t-butyl alcohol
c. Secpentyl alcohol and neopentyl alcohol
D. Ethyl alcohol and ethylene glycol


What is Modacrylic?
A. Modified acrylic
B. Natural fibre acrylic
C . Acrylic and polyester
D. None of above


If initial concentration is doubled, the
time for half reaction is also doubled.
The order of reaction is:
A. zero
B. one
c. two
D. three


The release of \( C O_{2} \) into air can cause:
A. Global warming
B. Eutrophication
c. Acid rain
D. Respiratory problems


I am located above the kidneys and
hence are called as supra renal glands. have two regions adrenal cortex and adrenal medulla. Adrenal cortex
secretes the hormones like cortisol,
aldosterone and androgens. Adrenal medulla secretes the hormones like
adrenaline and nor-adrenaline. I also
secrete hormone of fight or flight or the emergency hormone. Who am I?
A. Adrenal gland
B. Thyroid gland
c. Pancreas
D. Pineal gland


A diet of a sick person must contains at
least 48 units of vitamin \( A \) and 64 units
of vitamin \( B \). Two foods \( F_{1} \) and \( F_{2} \) are
available. Food \( F_{1} \) costs Rs. 6 per unit
and Food \( F_{2} \) costs Rs. 10 per unit. One
unit of food \( F_{1} \) contains 6 units of vitamin \( A \) and 7 units of vitamin \( B \). One
unit of food \( F_{2} \) contains 8 units of
vitamin \( A \) and 12 units of vitamin \( B \).
Find the minimum cost for the diet that
consists of mixture of these two foods
and also meeting the minimum nutritional requirements.


In the figure it is shown that the velocity
of lift is \( 2 \mathrm{ms}^{-1} \) while string ins winding
on the motor shaft with velocity \( 2 \mathrm{ms}^{-1} \)
and shaft \( A \) is moving downward with
velocity \( 2 \mathrm{ms}^{-1} \) with respect lift, then find
out the velocity of block \( \mathrm{B} \)
\( \mathbf{A} \cdot 2 \mathbf{m s}^{-1} \uparrow \)
B. \( 2 \mathrm{ms}^{-1} \downarrow \)
\( \mathbf{C} \cdot 4 \mathrm{ms}^{-1} \uparrow \)
D. None of these


Describe various types of epithelial
tissues with the help of labelled
diagrams


A Centigrade and Fahrenheit thermometers are dipped in boiling water. The water temperature is lowered until the Fahrenhit thermometer
registers \( 140 . \) The fall in temperature as registered by centigrade thermometer
is
\( A \cdot 30 \)
B . 40
\( c \cdot 60 \)
D. \( 80^{\circ} \)


Define the power of a lens


From Rutherford's \( \boldsymbol{\alpha}- \) particle
scattering experiment give the experimental evidence for deriving the conclusion that:
the nucleus of an atom is positively charged.


loaw


Convert given percents to decimal fractions and also to fractions in
simplest forms:
\( \mathbf{1 5 0 \%} \)


Which of these are correct
regarding Freundlich adsorption isotherm, if \( \frac{x}{m} \) is the amount adsorbed per unit mass of adsorbent?
This question has multiple correct options
A \( \cdot \frac{X}{m} \alpha(P)^{1 / n} \)
в. \( \log \frac{X}{m}=\log K+\frac{1}{n} \log P \)
c. \( _{\text {At low } P,} \frac{X}{m} \alpha P_{(V)} \)
D. at high \( P, \frac{X}{m}=K_{(V)} \)


In one plant, adventitious roots are
modified for storage and in the other plant a lateral branch with short
internodes and each node bearing a rosette of leaves and a tuft of roots. They
are
A. Sweet Potato and Pistia
B. Eichhornia and Jasmine
c. carrot and Mint
D. Turni and Chrysanthemum
E. Sweet potato and mint


Determine whether the points are
collinear.
\( \boldsymbol{P}(-\mathbf{2}, \mathbf{3}), \boldsymbol{B}(\mathbf{1}, \mathbf{2}), \boldsymbol{C}(\mathbf{4}, \mathbf{1}) \)


Assertion
Aryl halides undergo nucleophilic substitution with ease.
Reason
The carbon-halogen bond in aryl halides has partial double bond character.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


A solid conducting sphere of radius \( ^{\prime} a^{\prime} \)
having charge \( q \) is surrounded by a
concentric conducting spherical shell of
inner radius \( 2 a \) and outer radius \( 3 a \) as
shown in figure. If the amount of heat
produced when switch is closed is \( \alpha\left(\frac{K q^{2}}{24 a}\right) . \) Fill the value of \( \alpha \)


What is an electric dipole?


The stalk of leaf is called
A. Sessile
B. Plumule
c. stipule
D. Petiole


Nectaries are found in
A . Cruciferae
B. Compositae
c. Papilionatae
D. Ceasalpinoidae


The value of e is
A . \( 1.36 \mathrm{v} \)
B. 2.63
c. \( 1.83 \mathrm{v} \)
D. none


The product of 2 rational numbers is \( \frac{-28}{81} . \) If one of them is \( \frac{14}{27} \) then the other one?


What are the value of \( a \) and \( b \)
respectively in the reaction \( _{9}^{4} B e+ \)
\( _{2}^{4} H e \rightarrow_{b}^{a} X+_{0}^{1} n \)
A .17,7
B. 7,11
\( c \cdot 12,6 \)
D. 6,12


Processes occur in leaves, which may lower their temperature is
A. Respiration
B. Photosynthesis
c. Hydrolysis
D. Transpiration


Find the smallest number by which 26244 is divided to get the quotient as a perfect cube
A . 4
B. 9
c. 18
D. 36 6


f a function \( f \) is continuous at \( x=0 \)
where
\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{l}\frac{\sin 3 x}{\mathbf{5} \boldsymbol{x}}+\boldsymbol{a} \text { for } \boldsymbol{x}<\mathbf{0} \\ \boldsymbol{x}+\mathbf{4}-\boldsymbol{b} \text { for } \boldsymbol{x} \geq \mathbf{0}\end{array}\right. \)
find the value of \( a+b \)


What is the volume occupied by \( x \)
molecules of \( N_{2} ? \)
A \( .2 v \)
B. 4V
c. v/2
D.


Surface expansion is seen most commonly in:
A. Plate
B. Sphere
c. Thin rod
D. All


Is the magnetic dipole moment a vector or a scalar quantity? Write its unit


Laminaria (kelp) and Fucus (rock weed) are the examples of
A. Green algae
B. Brown algae (Phaeophyceae)
c. Red algae (Rhodophyceae)
D. Golden brown algae


The metal \( X \) is prepared by the electrolysis of fused chloride. It reacts with hydrogen to form colourless solid from which hydrogen is released on treatment with water. The metal is :
A \( \cdot \) Al
B. ca
\( c \cdot c u \)
D. zn


\( \frac{\sin 30^{\circ}}{\sin 45^{\circ}}+\frac{\tan 45^{\circ}}{\sec 60^{\circ}}-\frac{\sin 60^{\circ}}{\cot 45^{\circ}}-\frac{\cos 30^{\circ}}{\sin 90^{\circ}} \)


The problem of erythroblastosis foetalis
OCCUrS when
A. Both father and mother are Rh positive
B. Both father and mother are Rh negative
C. Mother is Rh positive and father is Rh negative
D. Father is Rh positive and mother is Rh negative


A particle of mass \( 4 m \) initially at rest
explodes into three fragments. If two fragments each of mass \( m \) move mutually perpendicular to each other
with speed \( v, \) then the total energy released in the process of explosion will
be
\( ^{\mathrm{A}} \cdot \frac{3}{2}^{m v^{2}} \)
B. \( \frac{2}{3} m v^{2} \)
\( \mathrm{c} \cdot 4 m v^{2} \)
D. \( v^{2} \)


Adding acids to cellulose gives gun-
cotton from which we can make cordite.
Cordite is:
A. an insect repellant
B. a bullet propellant
c. a rocket propellant
D. an insulator


The moving striker of the carom board
will possess- - - energy
A. Kinetic
B. Potential
c. solar
D. Electric


Two concentric circular coils \( X \) and \( Y \) of
radii \( 16 \mathrm{cm} \) and \( 10 \mathrm{cm}, \) respectively, lie in the same vertical plane containing the north to south direction. Coil X has
20 turns and carries a current of \( 16 \mathrm{A} \)
coil \( Y \) has 25 turns and carries a current
of 18 A. The sense of the current in \( X \) is
anticlockwise, and clockwise in \( Y \), for an observer looking at the coils facing west. Give the magnitude and direction of the net magnetic field due to the coils at their centre


When bleaching powder is treated with
mineral acids,the gas evolved is:
A \( \cdot C l_{2} \)
в. \( O_{2} \)
c. \( H_{2} \)
D. none of these


Write the IUPAC name of the compound.


How is Orlon prepared?


If \( a, b, c \) are in A.P., then value of the
expression \( a^{3}+c^{3}-8 b^{3} \) is equal to
A . \( 2 a b c \)
B. \( 6 a b c \)
c. \( 4 a b c \)
D. \( -6 a b c \)


Calculate the amount of work done in
moving a charged particle of charge \( q \)
through a potential difference of \( V \)
A \( \cdot \frac{q}{V} \)
в. \( \frac{V}{q} \)
c. \( \frac{1}{q V} \)
D. \( q V \)


Following are the thermochemical reactions:
\( C(\text { graphite })+\frac{1}{2} O_{2} \rightarrow C O ; \Delta H= \)
\( -110.5 \mathrm{kJ} / \mathrm{mol} \)
\( C O+\frac{1}{2} O_{2} \rightarrow C O_{2} ; \Delta H=-283.2 \)
kJ/mol
The heat of reaction (in kJ/mol) for the
following reaction is:
\( C(\text { graphite })+O_{2} \rightarrow C O_{2} \)
\( \mathbf{A} \cdot+393.7 \)
В. -393.7
c. -172.7
D. +172.7


NA heat engine has an efficiency
n.Temperatures of source and sink are each decreased by \( 100 \mathrm{K} \). The efficiency of the engine:
A. increases
B. decreases
c. remains constant
D. becomes


Halley's comet was first seen by
A. Galileo
B. Copernicus
c. Halley
D. Newton


Which halogen reacts only partially with hydrogen even at high temperature and in the presence of a catalyst?
\( A \cdot F_{2} \)
в. \( \mathrm{Cl}_{2} \)
\( c \cdot \operatorname{Br}_{2} \)
D. I \( _{2} \)


Calculate the volume of carbondioxide
produced by the combustion of \( 40 \mathrm{ml} \) of acetone vapours in presence of excess of oxygen?
\( A \cdot 12 \mathrm{m} \)
B. 1.20 \( m \)
c. \( 120 \mathrm{ml} \)
D. 11.2 m1


Let \( y=x^{2}-2 x+1 \) then find the value
of \( y \) for which \( \frac{d y}{d x}=-2 \)


Identify the ascending order of the work done in the following cases.
a) Work done in increasing the radius of soap bubble from \( 2 \mathrm{cm} \) to \( 4 \mathrm{cm}(\mathrm{T}= \)
\( 0.04 \mathrm{Nm}^{-1} \) ).
b) Work done in increasing the radius of a soap bubble from \( 2 \mathrm{cm} \) to \( 4 \mathrm{cm}(\mathrm{T}= \)
\( \left.0.08 N m^{-1}\right) \)
c) Work done in breaking a liquid drop
of radius \( 1 \mathrm{cm} \) into \( 10^{6} \) droplets of same
\( \operatorname{size}\left(T=0.08 N m^{-1}\right) \)
\( A \cdot b, \) a \& \( c \)
B. \( c, a \& b \)
\( c \cdot a, b \& c \)
D. \( c, b \& \) a


Which of the following is least reactive in a nucleophilic subtitution reaction?
\( \mathbf{A} \cdot\left(C H_{3}\right)_{3} C-C l \)
в. \( C H_{2}=C H C l \)
c. \( C H_{3} C H_{2} C l \)
D. \( C H_{2}=C H C H_{2} C l \)


When aniline reacts with excess of alkyl
halide, it gives:
A. amino compound
B. tertiary compound
c. azomethane
D. quaternary ammonium compound


If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) is defined by \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{2} \boldsymbol{x}- \)
2, then \( (f \circ f)(x)+2= \)
A. \( f(x) \)
B. \( 2 f(x) \)
c. \( 3 f(x) \)
D. \( -f(x) \)


Assertion
Insulin is an anabolic hormone.
Reason
A fall in blood amino acids also
increases insulin secretion.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of these possesses good regenerating power
A. Brain
B. Kidney
c. Lung
D. Liver


A helicopter is flying south with a speed of \( 50 k m h^{-1} . A \) train is moving at the
same speed towards east. The relative velocity of the helicopter as seen by the passengers in the train will be towards
A. North east
B. South east
c. North west
D. south west


Write the formula for integration by
parts.


When two coins are tossed one after
another list the outcomes of getting at least one head.
\( \mathbf{A} \cdot\{H H\} \)
в. \( \{H T, T H\} \)
c. \( \{T T\} \)
D. \( \{T H, H T, H H\} \)


A sinusoidal wave is travelling along a rope. The oscillator that generates the wave completes 60 vibrations in 30 s. Also a given maximum travels \( 425 \mathrm{cm} \) along the rope in 10.0 s. What is the
wavelength of the wave?
A. \( 21.25 \mathrm{cm} \)
B. 36.32 \( \mathrm{cm} \)
c. \( 48.26 \mathrm{cm} \)
D. 42.50 \( \mathrm{cm} \)


On diluting solution, its normality and molarity changes but molality remains
constant.
A. True
B. False


An electron in the hydrogen atom is excited from \( 1^{s t} \) orbit to \( 5^{t h} \) orbit. The
frequency of radiation is:
A \( \cdot 0.44 \times 10^{-9} \mathrm{Hz} \)
В. \( 3.15 \times 10^{15} \mathrm{Hz} \)
c. \( 6.2 \times 10^{8} \mathrm{Hz} \)
D. \( 1.13 \times 10^{-12} \mathrm{Hz} \)


Share of \( A, B \) and \( C \) respectively, are
if Rs. \( \mathbf{5 4 6 0} \) is divided in \( \frac{1}{2}: \frac{1}{3}: \frac{1}{4} \)
A . Rs. 1680 , Rs. 2520 , Rs. 1260
B. Rs. 2520, Rs. 1680, Rs. 1260
c. Rs. \( 1260, \) Rs. \( 2100, \) Rs. 2520
D. Rs. \( 2520, \) Rs. \( 1260, \) Rs. 1680


Draw the geometrical representation of the atom of the element \( _{8}^{16} \boldsymbol{O} \)


A uniform bar AB of mass m and a ball
of the same mass are released from
rest from the same horizontal position.
The bar hinged at end A. There is gravity downwards. What is the distance of the
point from point \( \mathrm{B} \) that has the same acceleration as that of ball, immediately after release.?


In which process volume increases?
\( A \cdot A B, C D \)
B. АВ, ВС
c. \( \operatorname{co}, \) DA
D. BC, CD


Draw the structure of the following
compound:
p,p'-Dihydroxybenzophenone


A charged particle moves through a magnetic field in a direction perpendicular to it. Then the
A. Speed of the particle remains unchanged
B. Direction of the particle remains unchanged
c. Acceleration remains unchanged
D. Velocity remains unchanged


How many moles of methane are
required to produced 22 g \( C O_{2}(g) \) after
combustion?


The total number of diprotic acids among the following is:
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4}, \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}, \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3}, \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{O}_{3}, \boldsymbol{H}_{2} \)
\( \mathbf{A} \cdot \mathbf{6} \)
B. 5
\( c \cdot 4 \)
\( D \)


Find the derivative of \( f(x)= \) \( \frac{x+\cos x}{\tan x} w . r . t . x \)


A step-down transformer converts
transmission line voltage from \( 11000 V \)
to \( 220 V \) The primary of the transformer has 6000 turns and the efficiency of the transformer is \( 60 \% \). If the output power
is \( 9 k W, \) then the input power will be
\( \mathbf{A} \cdot 11 k W \)
в. \( 12 k W \)
c. \( 14 k W \)
D. \( 15 k W \)


Solve :
\( \int \frac{1+x \cos x}{x\left(1-x^{2} e^{2 \sin x}\right)} d x= \)
\( k \ell n \sqrt{\frac{x^{2} e^{2 \sin x}}{1-x^{2} e^{2 \sin x}}}+C \) then \( k \) is equal
to


Which has maximum \% of (P) out of :
A. superphosphate.
B. triple superphosphate.
c. fluoroapatite rock.
D. None of the above.


State the following statements are true
or false.
In mitosis, all chromosomes become
aligned at the spindle equator at the end of anaphase
A. True
B. False


Which of the following groups cannot participate in response with other suitable group:
A) \( - \) COOH
B) \( -C O O^{-} \)
C) \( -C O C l \)
D) \( -N H_{3}^{+} \)
E) \( -\boldsymbol{C H}_{2}^{+} \)


What information about the motion of a
body can be obtained from its
displacement-time graph?
A. Velocity of the body
B. Acceleration of the body
c. Force on the body
D. Retardation of the body


Which of the following turns lead acetate paper black?
\( A \cdot S O_{2} \)
B. \( \mathrm{SO}_{3} \)
c. \( \mathrm{H}_{2} \).
\( \mathrm{D} \cdot \mathrm{H}_{2} \mathrm{SO}_{4} \)


In humans, cellulose is digested in
A. The caecum
B. The colon
c. The appendix
D. Not digested at all


In Young's double slit experiment if the
slit widths are in the ratio \( 1: 9 . \) The
ratio of the intensity at minima to that at maxima will be :
A .
в. \( \frac{1}{9} \)
\( c \cdot \frac{1}{4} \)
D. \( \frac{1}{3} \)


Two balls \( A \) and \( B \) having masses \( 1 k g \)
and \( 2 k g, \) moving with speeds \( 21 m / s \) and \( 4 m / s \) respectively in opposite direction, collide head on. After collision \( A \) moves with a speed of \( 1 m / s \) in the same direction, the correct statements
is :
This question has multiple correct options
A. The velocity of \( B \) after collision is \( 6 m / s \) opposite to the direction of motion before collision
B. The coefficient of restitution is 0.2
c. The loss of kinetic energy due to collision is 200 J
D. The impulse of the force between the two balls is \( 40 \mathrm{Ns} \)


Choose the correct statements from the
following:
This question has multiple correct options
A. Steel is more elestic than rubber
B. Fluids have Youngs modulus as well as shear modulus
C. Solids have Youngs modulus, bulk modulus as well as shear modulus
D. Bulk modulus of water is greater than that of copper.


Three rods of the same mass are placed as shown in the figure. What will be the coordinate of centre of mass of the
system?
A \( \cdot\left(\frac{2 a}{3}, \frac{2 a}{3}\right) \)
B・ \( \left(\frac{4 a}{3}, \frac{4 a}{3}\right) \)
\( \mathbf{c} \cdot\left(\frac{a}{3}, \frac{a}{3}\right) \)
D. \( \left(\frac{5 a}{6}, \frac{4 a}{9}\right) \)


Find the incorrect match (with respect
to ATP gain) -
A. Bacterial cell - 38 ATP or 2 ATp
B. Citric Acid Cycle - 12 ATP
c. Nerve cell - 38 ATP
D. Liver cell - 38 ATP


The perimeter of a rectangle having area equal to \( 144 \mathrm{cm}^{2} \) and sides in the
ratio 4: 9


Aluminium metal is:
A. magnetic substance
B. bad conductor of heat
C . good conductor of electricity
D. bad conductor of electricity


Which of the following is not correct about translation?
A. It starts with AUG.
B. Stopped at termination codon
c. Based on operon model.
D. Occurs in nucleus


The coefficient of \( x^{49} \) in the product
\( (x-1)(x-3) \ldots(x-99) \) is
A . \( -99^{2} \)
B.
c. -2500
D. none of these


Only one particular optical isomer of amino acids are used in our body to
make:
A. protein
B. lipids
c. oxygen
D. carbohydrates.


Choose the correct options (s) that gives (s) aromatic compound as the
major product:
This question has multiple correct options
\( A \)
B.
\( c \)
D.


How many grams are there in:
i) 5 moles of water
ii) 2 moles of
ammonia iii) 2 moles of glucose


Nitrogenous waste in the Malpighian
tubule flows into
A. Haemocoel
B. Vacuole
c. Intestine
D. Duodenum


Determine the value of \( k \) for which \( k^{2}+ \)
\( 4 k+8,2 k^{2}+3 k+6 a n d 3 k^{2}+4 k+4 \)
are in A.P.


In a regular polygon, the exterior and interior angles are in the ration 1: 4
The number of sides of the polygon is
A . 10
B. 12
c. 15
D. 16


The side of an equilateral triangle is 'a'
units and is increasing at the rate of \( \lambda \) units /sec. The rate of increase of its
area is
A \( \cdot \frac{2}{\sqrt{3}} \lambda a \)
в. \( \sqrt{3} \lambda a \)
c. \( \frac{\sqrt{3}}{2} \lambda a \)
D. none of these


Consider the following reactions:
\( \boldsymbol{C a C O}_{3} \rightarrow \boldsymbol{C a O}+\boldsymbol{C O}_{2} \)
\( \boldsymbol{E}+\boldsymbol{C O}_{2} \rightarrow \boldsymbol{F} \)
\( N a C l+F \rightarrow A+N a H C O_{3} \)
where \( \boldsymbol{E} \) and \( \boldsymbol{F} \) are respectively:
A. \( N H_{4} H C O_{3} \) and \( N H_{4} C l \)
B. \( N a O H \) and \( N a H C O_{3} \)
c. \( c a(O H)_{2} \) and \( C a\left(H C O_{3}\right)_{2} \)
D. none of the above


In which stage, the centromere lie at equator and arms are directed towards
poles?
A. Metaphase of mitosis
B. Metaphase
c. Metaphase II
D. Both A and C


The constituent present in baking powder is:
A. sodium benzoate
B. acetic acid
c. sodium lactate
D. tartaric acid


The number of terms which are free
from radical signs in the expansion of \( \left(y^{\frac{1}{5}}+x^{\frac{1}{10}}\right)^{55} \) are
A. 5
B. 6
\( c \cdot 7 \)
D. none of these


A person inhales 640 gm of \( O_{2} \) per day.
If all the \( O_{2} \) is used for converting sugar
into \( C O_{2} \) and \( H_{2} O, \) the sucrose
\( \left(C_{12} H_{22} O_{11}\right) \) consumed in gram in the
body in one day and the heat evolved are
Given: \( \left(\Delta \boldsymbol{H}_{\text {combustion of sucrose}}=\right. \)
\( \left.-5645 k J m o l^{-1}\right) \)
A. \( 250,8608.94 k J \)
B. \( 630,6552.52 k J \)
\begin{tabular}{l}
с. \( 850,9522.21 k J \) \\
\hline
\end{tabular}
D. \( 570,9408.34 k J \)


In the given \( A P \), find 3 missing term :
\( 2, \dots, 26 \)


What is a projectile? Derive an equation of the path of a projectile


\( \frac{3}{5} \) as a percent is
\( A \cdot 30 \% \)
B. \( 40 \% \)
\( \mathbf{c} .45 \% \)
D. \( 60 \% \)


The order and the degrees of the differential equation of all ellipses with centre at the origin, major axis along \( x- \)
axis and eccentricity \( \frac{\sqrt{\mathbf{3}}}{2} \) are
respectively:
A . 1,1
в. 2,1
c. 1,2
D. 2,


A point on XOZ-plane divides the join of (5,-3,-2) and (1,2,-2) at
\( ^{\mathrm{A}} \cdot\left(\frac{13}{5}, 0,-2\right) \)
в. \( \left(\frac{13}{5}, 0,2\right) \)
c. (5,0,2)
D. (5,0,-2)


A train is approaching towards a platform with a speed of \( 10 m s^{-1} \) while blowing a whistle of frequency \( 340 \mathrm{Hz} \)
What is the frequency of whistle heard by a stationary observer on the platform? Given speed of sound \( =340 m s^{-1} \)
A. зЗО н 2
в. 350 нz
c. 340 н \( z \)
D. 360 нz


Two concentric and coplanar circular
coils have radii \( a \) and \( b(>>a) \) as
shown in figure. Resistance of the inner coil is \( R \) Current in the outer coil is
increased from 0 to \( i \), then find the total
charge circulating the inner coil :
\( ^{\text {A }} \cdot \frac{\mu_{0} \pi a^{2} i}{2 R b} \)
в. \( \frac{2 \mu_{0} \pi a^{2}}{2 R b} \)
c. \( \frac{\mu_{0} \pi a^{2} i}{4 R b} \)
D. \( \frac{\mu_{0} \pi a^{3} i}{4 R b} \)


Excessive exposure of humans to UVrays results in
This question has multiple correct options
A. damage to immune system
B. damage to lungs
c. skin cancer
D. peptic ulcers


State true or false:
\( \left(\frac{2}{3}\right)^{4} \div\left(\frac{2}{3}\right)^{6}=\left(\frac{2}{3}\right)^{2} \)
A. True
B. False
c. Ambiuous
D. Data insufficient


The hybridisation of carbon in carbon
dioxide molecule is:
\( A \cdot s p^{2} \)
B. \( s p \)
\( c \cdot s p^{3} \)
D. none


Which of the following molecules do not have regular geometry?
A \( \cdot I F_{5} \)
в. \( C H_{4} \)
\( \mathrm{c} \cdot B F_{3} \)
D. \( C C l_{4} \)


Which of the following should be most stable?
A. \( H e_{2} \)
в. \( H_{2} \)
c. \( H e_{2}^{+} \)
D. \( H_{2}^{+} \)


Which of the following can be the
solution for water scarcity caused by
agriculture?
A. Knowledge and resources for producing more and better crops with less water.
B. Drip water irrigation.
C. More efficient water management systems adapted to climate variability.
D. All of the above.


Assertion
Human regulated environment is also
called noosphere.
Reason
Man is the main cause for pollution in
our ecosystem due to exploitation of
natural resources.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Both Assertion and Reason are incorrect.


If \( x>0, \) then find greatest value of the
expression \( \frac{\boldsymbol{x}^{100}}{1+\boldsymbol{x}+\boldsymbol{x}^{2}+\boldsymbol{x}^{3}+\ldots .+\boldsymbol{x}^{200}} \)