Extraction of zinc from zinc blende is
achieved by :
A. electrolytic reduction
B. roasting followed by reduction with carbon
c. roasting followed by reduction with another metal
D. roasting followed by self-reduction


Fungus used in genetic experiment is
A. Rhizopus
B. Mucor
c. Neurospora
D. Claviceps


A particle is dropped under gravity from
rest from a height \( h\left(g=9.8 m / s^{2}\right) \) and it travels a distance \( \frac{\mathbf{9 h}}{\mathbf{2 5}} \) in the last second the height 'h' is:
\( \mathbf{A} \cdot 100 m \)
B. \( 125 \mathrm{m} \)
\( \mathbf{c} \cdot 145 m \)
D. \( 167.5 \mathrm{m} \)


Which of the following statements is
true about the process shown in the given box?
[Food \( + \) Oxygen \( \rightarrow \) Carbon dioxide \( + \) Water \( +\text { Energy }] \)
A. It is caused by the decay of organic substances.
B. It is an important process in the nitrogen cycle.
C. It is an essential process of aerobic respiration in living organisms.
D. It Is carried out only by green plants and certain type of bacteria.


A light non-stretchable thread is wound
on a massive fixed pulley of radius \( \boldsymbol{R} \). A
small body of mass \( m \) is tied to the free
endof the thread. At a moment \( t=0 \) the
system is released and starts moving. Find its angular momentum relative to
the pulley axle as a function of time \( t \)


From Brewster's law, it follows that the
angle of polarization depends upon
A. the wavelength of light
B. orientation of the plane of polarization
c. orientation of the plane of vibration
D. none of these


A block is moving down a smooth inclined plane staring from rest at time
\( t=0 \) let \( S_{n} \) be the distance travel by the
block in the interval \( t=n-1 \) to \( t=n \). The ratio \( \frac{\boldsymbol{S}_{\boldsymbol{n}}}{\boldsymbol{S}_{\boldsymbol{n}+1}} \boldsymbol{i} \boldsymbol{s} \)


Let \( x \) and \( a \) stand for distance. Show that \( \int \frac{d x}{\sqrt{a^{2}-x^{2}}}=\frac{1}{a} \sin ^{-1} \frac{a}{x} \)
dimensionally correct.


In the given figure, find
\( \angle \boldsymbol{P} \boldsymbol{N} \boldsymbol{M} \)


When the plane of the rectangular coil is parallel to the direction of the magnetic field in a dynamo, then
A. Induced current will be zero
B. Induced current is maximum
c. AC is produced.
D. DC is produced.


Solve the following simultaneous equations using graphical method \( \boldsymbol{x}+\boldsymbol{y}=\boldsymbol{6} \)
\( \boldsymbol{x}-\boldsymbol{y}=\boldsymbol{4} \)


Divide the polynomial by monomial:
\( y^{3}-64 ; y-4 \)
\( \mathbf{A} \cdot(y-4)\left(y^{2}+4 y+16\right)+0 \)
B \( \cdot(y+2)\left(y^{2}+y+16\right)+0 \)
\( \mathbf{c} \cdot(y+74)\left(y^{2}-4 y+16\right)+0 \)
D. \( (y-3)\left(y^{2}+3 y+2\right)+0 \)


\( \int \frac{\cot \sqrt{x}}{2 \sqrt{x}} d x \) is equal to \( =-\ldots+C \)
B . \( \log |\sin \sqrt{x}| \)
c. \( \frac{1}{2} \log |\sin \sqrt{x}| \)
D. None of these


An ideal gas follows a process described by \( \boldsymbol{P} \boldsymbol{V}^{2}=\boldsymbol{C} \) from \( \left(\boldsymbol{P}_{1}, \boldsymbol{V}_{1}, \boldsymbol{T}_{1}\right) \)
to \( \left(P_{2}, V_{2}, T_{2}\right)(\mathrm{C} \text { is a constant }) . \) Then
A. If \( P_{1}>P_{2} \) then \( T_{2}>T_{1} \)
B. If \( V_{2}>V_{1} \) then \( T_{2}<T_{1} \)
c. If \( V_{2}>V_{1} \) then \( T_{2}>T_{1} \)
D. If \( P_{1}>P_{2} \) then \( V_{2}>V_{2} \)


The population of a city decreased from
25,000 to \( 24,500 . \) Find the percentage
decrease.


Construct a triangle \( P Q R \), whose
perimeter is \( 14 \mathrm{cm} \) and whose sides are
in the ratio 2: 4: 5


State True or False.
Heat travels much faster in insulators
than in conductors.


Select correct statement
A. Tomato, dicots and plants represent same taxa at different levels
B. Species is genetically open system
C. A breed of tiger and lion is a fertile true species
D. Biological concept of species is based on reproductive isolation


A force \( F \) is applied on a lawn mower at
an angle of \( 60^{\circ} \) with the horizontal. If it
moves through a distance \( x \) in horizontal direction, the work done by
the force is:
A \( \cdot \frac{F x}{2} \)
в. \( \frac{\sqrt{3} F x}{2} \)
c. \( 2 F x \)
D. None of the above


A waxing crescent moon
A. is a phase where in the crescent increases from one day to another
B. is a phase where in the crescent decreases from one day to another
C. is a phase where in the next day to the crescent is a new moon day
D. is a phase where in the next day to the crescent is a full moon day


A beam of white light is incident on glass air interface from glass to air such that green light just suffers total internal reflection. The colors of the light which will come out to air are
A. Violet, Indigo, Blue
B. All colours except Green
c. Yellow, orange, Redd
D. White light


If \( A=\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right], B=\left[\begin{array}{ll}2 & 3 \\ 4 & 5\end{array}\right], \) and \( 4 A-3 B+C \)
\( =0, \) then \( C= \)
A. \( \left[\begin{array}{cc}2 & -1 \\ 0 & 1\end{array}\right] \)
В. \( \left[\begin{array}{cc}2 & 1 \\ 0 & -1\end{array}\right] \)
\( \mathbf{c} \cdot\left[\begin{array}{cc}-2 & 1 \\ 0 & -1\end{array}\right] \)
D. None


The group of cells having similar origin,
structure and function are called
as
A. organs
B. Tissues
c. Cell membrane
D. None of these


The human excreta can be used for the
production of
A. Vermi cakes for fertilizer
B. Vermi cakes as manure
c. vermi cakes as animal food
D. Both A and B


Light is a form of
A. Energy
B. wave
\( c . \) Both
D. none


Which of the following is important for transcription?
A. CAAT box
B. Promoter
c. RNA polymerase
D. All of the above


Solve for \( x: \sin x+\sin 2 x+\sin 3 x=3 \)
where \( x \in(0, \pi) \)


The time at which they collide after the projection of the first ball is
A . \( 3.5 s \)
B. \( 6.5 s \)
c. \( 4.5 s \)
D. \( 4.0 s \)


The equilibrium constant , Kp for
thegaseous reaction \( A \Leftrightarrow 2 B \) is related
to degree of dissociation \( \alpha \) of \( A \) and
total pressure \( P \) as
A \( \frac{4 \alpha^{2} P}{1-\alpha^{2}} \)
B. \( \frac{4 \alpha^{2} P^{2}}{1-\alpha^{2}} \)
c. \( \frac{4 \alpha^{2} P^{2}}{1-\alpha} \)
D. \( \frac{4 \alpha^{2} P}{1-\alpha} \)


Which of the following are done to reduce friction?
a) Making grooves in the shoes
b) Polishing rough surfaces
c) Using wheels, ball bearings
d) Creating an air cushion
\( A \cdot a, b \) and \( c \)
B. c and d
\( c . b, c \) and \( d \)
D. All of the above


A current of \( 9.65 A \) flowing for 10 minutes 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


Milk of magnesia is used as:
A. antichlor
B. antacid
c. antiseptic
D. food preservative


Work done by the gas in the process \( A \)
\( \rightarrow \mathrm{B} \) is
\( 4.5312 .5 . \)
3. 1875 J
\( c \)
D. \( 8854 J \)


Among the Fresnel zones the operative zones contributing intensity are :
A. last zones
B. first few zones
c. middle zones
D. all the zones


A particle having a mass of 1.0 mg has
a velocity of \( 3600 k m / h \). Calculate the wavelength of the particle:
\( \left(h=6.626 \times 10^{-27} e r g-s e c\right) \)
A \( \cdot 6.626 \times 10^{-28} \mathrm{cm} \)
B. \( 6.626 \times 10^{-29} \mathrm{cm} \)
C. \( 6.626 \times 10^{-30} \mathrm{cm} \)
D. \( 6.626 \times 10^{-31} \mathrm{cm} \)


Find the derivative of \( \frac{2^{x} \cot x}{\sqrt{x}} \)
A \( \cdot \frac{2^{x}}{\sqrt{x}}\left\{\log 2 \cot x-\csc ^{2} x-\frac{\cot x}{2 x}\right\} \)
B. \( \frac{2(x+1)}{\sqrt{x}}\left\{\log 2 \cot x-\csc ^{2} x-\frac{\cot x}{2 x}\right\} \)
C \( \frac{2^{x}}{\sqrt{x}}\left\{\log 2 \cot x-\csc ^{2} x-\frac{\cot x}{x^{2}}\right\} \)
D. None of these


What element has a H-like spectrum, whose lines have wavelengths four times shorter than those of atomic
hydrogen?
A . не
B . \( \mathrm{He}^{+} \)
\( c \cdot H \)
\( D \cdot L i^{2} \)


A metal rod of Young's modulus \( 2 \times \) \( 10^{10} N m^{-2} \) undergoes an elastic strain
of \( 0.06 \% \). The energy per unit volume stored in \( J m^{-3} \) is
A. 3600
в. 7200
c. 10800
D. 14400


With increase in frequency of an AC supply, the impedence of an L-C-R series circuit
A. remains constant
B. increases
c. decreases
D. decreases at first, becomes minimum and then increases


During electrolysis of fused calcium hydride, the hydrogen is produced at:
A. cathode
B. anode
c. hydrogen is not liberated at all
D. \( H_{2} \) produced reacts with oxygen to form water


The distance of the point (1,-2,3) from
the plane \( \boldsymbol{x}-\boldsymbol{y}+\boldsymbol{z}=\mathbf{5} \) measured
parallel to the line \( \frac{x}{2}=\frac{y}{3}=\frac{z-1}{-6} \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c \cdot 4 \)
D. None of these


Give the properties of water responsible
for controlling the temperature of our
body


Hydride of nitrogen is called:
A. dinitrogen hydride
B. urea
c. ammonia
D. nitrous hydride


What is concentration of ore?
A. Increasing the concentration of metal
B. Reducing the concentration of metal
C. Reducing hydrogen ions
D. Both \( A \) and \( C \)


\( \operatorname{Let} P(x)=x^{3}-6 x^{2}+B x+C \) has \( 1+5 \)
as a zero and \( \mathrm{B}, \mathrm{C} \) real number, then
value of \( (\mathrm{B}+\mathrm{C}) \) is
A . -70
B. 70
\( c \cdot 24 \)
D. 138


Some statements about heavy water
are given below:
(i) Heavy water is used as a moderator
in nuclear reactors.
(ii) Heavy water is more associated than ordinary water.
(iii) Heavy water is a more effective
solvent than ordinary water.

Which of the above statements are
correct?
A \( \cdot \) (i) and (ii)
B. (i), (ii) and (iii)
c. (ii) and (iii)
D. (i) and (iii)


The probability of finding the electron in
\( \boldsymbol{p}_{\boldsymbol{x}} \) -orbital is:
This question has multiple correct options
A. maximum on two opposite sides of the nucleus along \( x \) -axis
B. zero at the nucleus
c. same on all the sides around the nucleus
D. zero on the \( z \) -axis


Which of the following gas is formed at the electrode, connected to the positive terminal of the battery?
A. Nitrogen gas
B. Hydrogengas
c. oxygen gas
D. carbon dioxide gas


The predominant yellow line in the spectrum of a sodium vapour lamp has a wavelength of 590nm. What minimum accelerated potential is needed to excite this line in an electron
tube having sodium vapours?
A. 8.44 volt.
B . 2.11 volt.
c. 6.11 volt.
D. 4.22 volt.


Which of the following has lowest \( C-0 \) bond order?
\( \mathbf{A} \cdot\left[N i(C O)_{4}\right] \)
В \( \cdot\left[\mathrm{CoCO}_{4}\right]^{-} \)
c. \( \left[F e(C O)_{4}\right]^{2} \)
D. \( \left[M n(C O)_{6}\right]^{+} \)


Predict respectively' \( X^{\prime} \) and \( ^{\prime} Y^{\prime} \) in the
following reactions \( \boldsymbol{A r}-\boldsymbol{N} \boldsymbol{H}_{2} \stackrel{\boldsymbol{X}}{\longrightarrow} \boldsymbol{A} \boldsymbol{r}-\dot{\boldsymbol{N}} \equiv \)
\( N . C l^{-} \quad^{Y} \quad A r-C l \)
A. \( N a N O_{3} \& C l_{2} \)
в. \( N a N O_{3}-H C l \& H C l \)
c. \( N a N O_{2}-H C l \& C u / H C l \)
D. \( N a N O_{2}-H C l \& N a N H_{2} \)


Every action has its equal and opposite reaction is Newton's:
A. First law of motion
B. Second law of motion
c. Third law of motion
D. Fourth law of motion


Determine the values of ' \( a^{\prime} \) for which
both roots of the quadratic equation \( \left(a^{2}+a-2\right) x^{2}-(a+5) x-2=0 \)
exceed the number minus one.


Kepler's second law states that the straight line joining the planet to the sun sweeps out equal areas in equal times. This statement is equivalent to saying that
A. Total acceleration is zero
B. Tangential acceleration is zero
c. Longitudinal acceleration is zero
D. Radial acceleration is zero


The IUPAC name for the compound is:
A. trans-3-iodo-4-chloro-3-pentene
B. cis-3-chloro-3-iode-2-pentene
C. trans-2-chloro-3-iodo-2-pentene
D. cis-3-iodo-4-chlore-3-pentene


When sodium is dissolved in pure
liquid ammonia, then along with \( \boldsymbol{H}_{2} \)
the other product formed is:
A. sodium
B. sodium amide
c. sodium ammoniate
D. sodium tetra ammoniate


Solve \( \sin ^{-1}\left\{\frac{\sin x+\cos x}{\sqrt{2}}\right\},-\frac{3 \pi}{4}< \)
\( x<\frac{\pi}{4} \)


ATP was discovered by
A. Blackman
B. Bowman
C. Lipmann
D. Karl Lohmann


Which of letter shows the enthalpy
change \( (\triangle \boldsymbol{H}) \) of the reaction?
\( A \)
B.
\( c . c \)
\( D \)
E.


Coordination compounds have great
importance in biological systems. In
this context which of the following
statements is incorrect?
A. Carboxypeptidase-A is an enzyme and contains zinc.
B. Haemoglobin is the red pigment of blood and contains iron
C. Cyanocobalamin is \( B^{12} \) and contains cobalt.
D. Chlorophylls are green pigments in plants and contain calcium.


In a polymer sample \( 30 \% \) of molecules have a molecular mass of \( 20,000,40 \% \) have 30,000 and the rest \( 60,000 . \) What is the weight average molecular mass of the polymer?
A .40,300
в. 30,600
c. 43,333
D. 50,400


In a LR circuit of 3 m \( H \) inductane and
\( 4 \Omega \) resistance, emf \( E=4 \cos (1000 t) \)
volt is applied. The amplitude of current is:
\( \mathbf{A} \cdot 0.8 A \)
B. \( \frac{4}{7} \)
c. \( 1.0 A \)
D. \( \frac{4}{\sqrt{7}} A \)


When heat is reflected from the earth's
surface and trapped in the atmosphere, this phenomenon is referred to as:
A. Global warming
B. Ozone depletion
c. The Greenhouse effect
D. Thermal pollution


\( N H_{2} \)
\( \boldsymbol{C H}_{3}-\stackrel{1}{\boldsymbol{C} \boldsymbol{H}}-\boldsymbol{C O O H} \)
IUPAC name of the given compound is:
A. propanamine-oic acid
B. 2-Aminopropanoic acid
c. amino propanoic acid
D. none of these


"When mixture of \( N H_{4} C l \) and \( N a N O_{2} \)
is heated, gaseous product formed is
\( N_{2} \)
Answer whether the above statement is
true or false.
If true enter 1 , else enter 0 .


Calculate the wave number of the
highest energy transition in the Balmer series of the hydrogen atom:
\( \left[\boldsymbol{R}_{\boldsymbol{H}}=\mathbf{1 0 9 6 7 8 c m}^{-1}\right] \)
A \( .27419 .5 \mathrm{cm}^{-1} \)
В. 2741.95 \( c m^{-1} \)
c. \( 274.195 \mathrm{cm}^{-1} \)
D. 274195.1 \( c m^{-} \)


Which of the following mixture is given the name aquaregia?
A. \( H_{3} P O_{3}, H_{2} S O_{4} \)
в. \( 3 H C l, H N O_{3} \)
\( \mathrm{c} \cdot 3 \mathrm{HNO}_{3}, \mathrm{HCl} \)
D. \( H C l, C H_{3} C O O H \)


If the domain of the function \( f(x)= \) \( \sqrt{3 \cos ^{-1}(4 x)-\pi} \) is [a,b] then the
value of \( (4 a+64 b) \) is


The probability that a student entering a university will graduate is \( 0.4 . \) If the probability that out of 3 students of the university, only one will graduate is \( \frac{432}{10^{x}} \)
then the value of \( x \) is


\( N a H C O_{3} \) can be used on its own to
make cakes or bread. Baking powder is more commonly used, and contains
\( N a H C O_{3}, C a\left(H_{2} P O_{4}\right)_{2} \) and starch. An
improved combination baking powder contains about \( 40 \% \) starch, \( 30 \% \)
\( N a H C O_{3} 20 \% N a A l\left(S O_{4}\right)_{2} \) and \( 10 \% \)
\( \boldsymbol{C a}\left(\boldsymbol{H}_{2} \boldsymbol{P} \boldsymbol{O}_{4}\right)_{2} \)
Answer the following questions based
on above study.
n improved baking powder,
\( N a A l\left(S O_{4}\right)_{2} \) is used for :
A. makes the decomposition of \( \operatorname{NaH} \mathrm{CO}_{3} \) faster
B. slows the decomposition of \( N a H C O_{3} \)
c. acts as filler
D. makes the bread rise


The synthesis of proteins requires 20 standard amino acids in the living
systems. However, some organisms use selenocysteine as an additional amino acid for synthesizing proteins. Selenocysteine is biosynthesized from
A. Cysteine
B. Serine
c. Threonine
D. Proline


Find the emf and internal resistance of
the equivalent cell between \( A \) and \( B \). put
\[
\begin{array}{l}
\varepsilon_{1}=3 \mathrm{V}, r_{1}=2 \Omega \varepsilon_{2}=2 V, r_{2}=1 \Omega \\
\varepsilon_{3}=6 V, r_{3}=1 \Omega
\end{array}
\]


Which one of the following mineral is obtained form ocean water?
A. Aluminium
B. Sulphur
c. Magnesium
D. Iron


In \( \triangle \boldsymbol{L} M \boldsymbol{N}, \triangle \boldsymbol{L}=\boldsymbol{6} \boldsymbol{0}^{\circ}, \angle \boldsymbol{M}=\mathbf{5 0}^{\circ} \) If
\( \angle L M N \sim \triangle P Q R \) then the value of \( \angle R \)
is
A \( .40^{\circ} \)
B . \( 60^{\circ} \)
\( c \cdot 70^{\circ} \)
D. \( 110^{\circ} \)


The type of muscles present in our
A. Thigh are striated and voluntary
B. Upper arm are smooth muscle fibres fusiform in shape
C. Heart are involuntary and unstriated smooth muscles
D. Intestine are striated and involuntary


In what the study of \( X X-X O \) type method was done initially?
A. Drosophila
B. Butterfly
c. Grass hopper
D. squash - bug


Choose the incorrect statement for
Autonomic nervous system.
A. Acts on skeletal muscles
B. Acts on smooth muscles
C. Consists of ganglia formed by pre and post ganglionic neurons
D. Consists of sympathetic and parasympathetic nervous system


The earth and the moon are attracted to
each other by gravitational force.Does
the earth attract the moon with a force
the moon attracts the earth? Why?


Guttation is due to
A. Negative root pressure
B. Positive root pressure
C. Transpiration
D. None of the above


A converging beam of the light forms a sharp image on a screen. A lens is placed in the path of the beam, the lens being \( 10 \mathrm{cm} \) from the screen. It is found
that the screen has to be moved \( 8 \mathrm{cm} \)
further away from the lens to obtain a sharp image. Find the focal length and nature of lens.
A. \( 12.5 \mathrm{cm} \)
B. \( 20 \mathrm{cm} \)
\( c .13 \mathrm{cm} \)
D. 22.5 \( c m \)


The tissue respiration refers to
A . Inspiration
B. External respiration
c. Internal respiration
D. Expiration


Java Ape Man was discovered by
A. Dubois
B. Leakey
c. cuter
D. Black


Figure shows a irreversible
thermodynamic process mole one mole
of gas. How does the work done in process changes with time?
A. decreases continuously
B. increases continuously
c. remains constant
D. first increases then decreases


The element with atomic number 36
belongs to block in the
periodic table.


with each other with the help of a
massless spring of spring-constant \( k \)
Mass \( M_{1} \) is in contact with a wall and
the system is at rest on the frictionless
floor. \( M_{2} \) is displaced by distance \( x \)
to compress the spring and released.
The velocity of COM (centre of mass) of
the system when \( M_{1} \) is detached from
wall is :
\( \mathbf{A} \cdot \frac{x \sqrt{k M_{1}}}{M_{1}+M_{2}} \)
B. \( \frac{x \sqrt{k M_{2}}}{M_{1}+M_{2}} \)
c. \( \frac{k x \sqrt{M_{2}}}{M_{1}+M_{2}} \)
D. \( \frac{x}{\sqrt{k M_{1}}\left(M_{1}-M_{2}\right)} \)


The time taken by the particle in SHM for maximum displacement is ?
A. \( T / 8 \)
B. T/6
\( c \cdot \pi / 2 \)
D. T/4


A tree is broken at a height of \( 5 \mathrm{m} \) from the ground and its top touches the
ground at a distance of \( 12 \mathrm{m} \) from the
base of the tree. Find the original height
of the tree.


Two identical blocks \( A \) and \( B \) of mass
\( m \) joined together with a massless
spring as shown in the figure are placed on a smooth surface. If the block \( \mathbf{A} \)
moves with an acceleration \( a_{0} \), then the
acceleration of the block \( B \) is
A \( \cdot a_{0} \)
в. \( -a_{0} \)
\( c \)
\[
\frac{f}{m}-a_{0}
\]
D. \( \frac{f}{m} \)


Which of the following represent
saponification reaction?
\( \mathbf{A} \cdot C H_{3} C O O H+N a O H \stackrel{C a O}{\longrightarrow} C H_{4}+N a_{2} C O_{3} \)
B \( \cdot C H_{3} C O O H+C_{2} H_{5} O H \frac{H_{2} S O_{4}}{\longrightarrow} C H_{3} C O O C_{2} H_{5}+ \)
\( H_{2} O \)
\( \mathbf{c} \cdot 2 C H_{3} C O O H+2 N a \rightarrow C H_{3} C O O N a+H_{2} \)
D. \( C H_{3} C O O C_{2} H_{5}+N a O H \rightarrow C H_{3} C O O N a+C_{2} H_{5} O H \)


What is the function of holdfast in a
algae?


Poise is the unit of :
A. surface tension
B. capillarity
c. viscosity
D. buoyancy


Thermal stability of hydrates of group 18 elements:
A. increases down the group
B. decreases down the group
c. remains unchanged
D. first increases up to Ar and then decreases


Seema invested an amount of Rs.
\( 16,000 /- \) for two years at C.I. and received an amount of Rs. 17640 on
maturity. What is the rate of interest?
A . \( 8 \% \)
B. \( 5 \% \)
c. \( 7 \% \)
D. \( 6 \% \)


Find out the letters of English alphabet or any other language known to you in which the image formed in a plane
mirror appears exactly like the letter itself. Discuss your findings.


A point moves along a circle with a velocity \( v=a t, \) wherea \( =0.50 m / s^{2} \) Find the total acceleration of the point at the moment when it has covered the \( \boldsymbol{n}^{t h}(\boldsymbol{n}=\mathbf{0 . 1 0}) \) fraction of the circle after
beginning of the motion.
A \( \cdot 0.8 \mathrm{m} / \mathrm{s}^{2} \)
B. \( 0.3 \mathrm{m} / \mathrm{s}^{2} \)
c. \( 0.2 \mathrm{m} / \mathrm{s}^{2} \)
D. \( 0.50 \mathrm{m} / \mathrm{s}^{2} \)


The moment of a force of \( 10 N \) about a
fixed point \( \boldsymbol{O} \) is \( \mathbf{5} \boldsymbol{N} \boldsymbol{m} . \) Calculate the
distance of the point \( O \) from the line of action of the force.
A. \( 5 m \)
в. \( 1 m \)
\( c .50 m \)
D. \( 0.5 m \)


A double convex lens made of glass has
both radii of curvature of magnitude 20
cm. Incident light rays parallel to the axis of the lens will converge at a distance at [Given refractive index of glass \( =1.5] \)
A . 20
B. 10
\( c \cdot 40 \)
D. \( \frac{40}{3} \)


Two persons having mass \( 50 \mathrm{kg} \) each,
are standing 1 m apart from each other
Calculate the force of gravitation and also calculate the force of gravity on each. (Take \( G=6.67 \times 10^{-11} N m^{2} k g^{-2} \)
mass of earth \( M=6 \times 19^{24} k g \)
Radius of earth \( \boldsymbol{R}=\mathbf{6 . 4} \times \mathbf{1 0}^{\mathbf{6}} \boldsymbol{m} \) )?


Which of the following leads to formation of \( 1^{0} \) alcohol?
A \( \cdot C H_{3}-C H=C H_{2} \frac{H_{2} O}{H^{+}} \)
B. \( C H_{3}-C H=C H_{2} \frac{N a B H_{4} / O H^{\circ}}{H g\left(O A c_{2} / T H F\right.} \)
c. \( C H_{3}-C H=C H_{2} \frac{H_{2} Q_{2} / O H^{6}}{B_{2} H_{6} / T H F} \)
D. \( C H_{3}-C \equiv C-C H_{3} \) dil.Haso \( _{\text {di.HgS }} \),


\( \lim _{x \rightarrow-\infty} \sqrt{x^{2}+1}-x \)


Find area between:
\( \boldsymbol{x}=\mathbf{2} \boldsymbol{y}-\boldsymbol{y}^{2} \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \boldsymbol{y}=\boldsymbol{2}+\boldsymbol{x} \)


If a heater draws \( 5 A \) current from a
\( 240 V \) supply, what is the potential on
the neutral wire?
A . \( 0 V \)
в. \( 5 V \)
c. \( 120 V \)
D. \( 240 V \)


In the given figure \( \overrightarrow{A B} \| \overrightarrow{D E} \) and area
of the parallelogram ABFD is \( 24 c m^{2} \)
Find the area of \( \Delta A F B \)


Who proposed valence bond theory?


Cells of connective tissue is produced
by
A. Fibroblast
B. Mast cell
c. Plasma cell
D. Mesenchymal cells


Group of bacteria used in biogas production is
A. Eubacteria
B. Organotrophs
c. Methanotrophs
D. Methanogens


Which of the following is not the name
of \( \boldsymbol{C H}_{\mathbf{3}} \boldsymbol{N C} \) ?
A. Methyl isocyanide
B. Aceto isonitrile
c. Methyl carbylamine
D. Acetonitrile


Saline water is useful for:
A. washing clothes
B. drinking
c. for agriculture
D. None of these


A hydrogen atom in a state having a binding energy of \( 0.85 e V \) makes transition to a state with excitation
energy \( 10.2 e V \)
Identify the quantum numbers \( n \) of the
upper and the lower energy states involved in the transition.


On the application of a constant torque, a wheel is turned from rest through 400
radian in \( 10 s . \) Calculate its angular
acceleration. \( \left(\operatorname{in} r a d / s^{2}\right) \)
A . 8
B. 9
\( c \cdot 4 \)
D.


Factorize \( : \frac{36 m^{2}}{289}-81 \)


The sodium salt of a certain weak
monobasic organic acid is hydrolysed
to an extent of \( 3 \% \) in its \( 0.1 ~ M \) solution
at \( 25^{0} C . \) Given that the ionic product of
water is \( 10^{-14} \) at this temperature,
what is the dissociation constant of the
acid?
A. \( \approx 1 \times 10^{-10} \)
0
В \( \cdot \approx 1 \times 10^{-9} \)
c. \( 3.33 \times 10^{-9} \)
D. \( 3.33 \times 10^{-10} \)


Find the following limit:
\( \lim _{x \rightarrow 4} \frac{\sqrt{1+2 x}-3}{\sqrt{x}-2} \)


Evaluate \( \int x e^{x} d x \)
A \( .-x e^{x}-e^{x}+c \)
B. \( -x e^{x}+e^{x}+c \)
c. \( x e^{x}+e^{x}+c \)
D. \( x e^{x}-e^{x}+c \)


Choose the correct options -
A. Reaction between lead nitrate and potassium iodide is double decomposition reaction.
B. Reaction between copper oxide and hydrogen is redox reaction.
C. Reactions in which heat is absorbed are called exothermic reactions
D. Both (A) and (B).


Assertion
Only one out of every 12000 alpha particles rebound in Rutherford's experiment.
Reason
Most of the space in the atom is empty.
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 \( A \) is a scalar matrix \( k I \) with scalar
\( k \neq 0 \) of order \( 3, \) the \( A^{-1} \) is:
A \( \cdot \frac{1}{k^{2}} I \)
B. \( \frac{1}{k^{3}} \)
c. \( \frac{1}{k} I \)
D. \( k I \)


Function \( f(x)=\left\{\begin{array}{ll}5 x-4 & \text { for } 0<x \leq 1 \\ 4 x^{2}-3 x & \text { for } 1<x<2 \\ 3 x+4 & \text { for } x \geq 2\end{array}\right. \)
A. continuous at \( x=1 \) and \( x=2 \)
B. continuous at \( x=1 \) but not derivable at \( x=z \)
c. continuous at \( x=2 \) but not derivable at \( x=1 \)
D. none of these


What are the values (at least two)
displayed by Rupali?


Explain the terms: Vital capacity of lungs in terms of IRV (Inspiratory Reserve Volume), ERV (Expiratory Reserve Volume), TV (Tidal Volume) and
RV (Residual Volume)


Construct a \( \triangle A B C \) such that \( A B=7 \mathrm{cm} \)
\( A C=6 \mathrm{cm}, B C=9 \mathrm{cm} \) measure
\( \angle A, \angle B a n d \angle C \)


Q Type your question.
and 142 as
shown. If an object O(a thin small rod) is placed upright on principal axis at a distance \( R \) from pole (i.e., placed at centre of curvature), then the size of image is different from size of object. STATEMENT-2: If a point object is
placed at centre of curvature of spherical surface separating two media of different refractive index, then the
image is also formed at centre of
curvature, i.e image distance is equal
to object distance.
A. Both Statement-1 and Statement-2 are True:
Statement-2 is a correct explanation for Statement-
B. Both Statement-1 and Statement-2 are True but Statement-2 is NOT a correct explanation for Statement-1
c. statement-1 is True but Statement-2 is False


For the circuit shown in the adjoining figure, match the entries of column
with the entries of column II


The radius of a flywheel is \( 10 \mathrm{cm} \). It is
rotated at the rate of 25 rads \( ^{-2} \). When a
constant force \( 40 N \) is applied on the rim of wheel along its tangent. The moment of inertia of wheel is:
\( \mathbf{A} \cdot 0.01 \mathrm{kgm}^{2} \)
B. \( 0.1 \mathrm{kgm}^{2} \)
\( \mathbf{c} \cdot 0.16 k g m^{2} \)
D. \( 1.6 k g m^{2} \)


A neutral particle is at rest in a uniform magnetic field \( \bar{B} \). At \( t=0 \), particle decays into two particles each of mass
\( m^{\prime} \) and one of them having charge \( ^{\prime} q^{\prime} \)
Both of these move off in separate paths lying in plane perpendicular to \( \bar{B} \). At later time, the particles collide. If this time of collision is \( x \pi m / q B \) then \( x \) is (neglecting the interaction force).


In allene structure, three carbon atoms are joined by :
A. three \( \sigma \) - and three \( \pi \) -bond
B. two \( \sigma \) - and one \( \pi \) -bond
c. two \( \sigma \) - and two \( \pi \) - bonds
D. three \( \pi \) - bonds only


Divide:
5.8 by 100


Which of the following halogen can be purified by sublimation?
\( \mathbf{A} \cdot F_{2} \)
в. \( C l_{2} \)
c. \( B r_{2} \)
D. \( I_{2} \)


In coaltar fraction of heavy oil, the aromatic compound present is
A . cresol
B. pyridine
c. benzene
D. anthracen


A plano-concave lens is made of glass of refractive index 1.5 and the radius of
curvature of its curved face is \( 100 \mathrm{cm} \)
What is the power of the lens?
A \( .+0.5 D \)
в. \( -0.5 D \)
\( c .2 D \)
D. \( +2 D \)


Krebs cycle starts with the formation of six carbon compound by reaction between
A. Malic acid and acetyl CoA
B. Succinic acid and pyruvic acid
c. Fumaric acid and pyruvic acid
D. Acetyl CoA and oxaloacetic acid


For what value of \( \boldsymbol{K} \) will the following
pair of linear equations have infinitely many solutions?
\( \boldsymbol{K} \boldsymbol{x}+\boldsymbol{3} \boldsymbol{y}-(\boldsymbol{K}-\boldsymbol{3})=\mathbf{0} \)
\( \mathbf{1 2} \boldsymbol{x}+\boldsymbol{K} \boldsymbol{y}-\boldsymbol{K}=\mathbf{0} \)


Assertion - On reflection from a rigid boundary there takes place a complete reversal of phase.
Reason - On reflection from a denser
medium, both the particle velocity and wave velocity are reversed in sign.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A: Tetracyanomethane
B: Carbondioxide
C: Benzene
\( \mathbf{C}: \mathbf{1}, \mathbf{3}-\boldsymbol{b} \boldsymbol{u} \boldsymbol{t} \boldsymbol{a}-\boldsymbol{d} \boldsymbol{i}-\boldsymbol{e} \boldsymbol{n} \boldsymbol{e} \)
Ratio of \( \sigma \) and \( \pi: \)
A . in A and B are equal
B. in C and D are equal
\( c . \) is same in \( A, B, C, \) and \( D \)
D. in B and D are equal


Alpha particles are positively charged and contains the nucleus of
atom.
A. \( H e \)
в. \( H \)
c. \( L i \)
D. \( H^{+} \)


One kg of tea and one kg of sugar
together cost \( 95 . \) If the price of tea falls by \( 10 \% \) and that of sugar rises by \( 20 \% \) then the price of one kg of each
combined comes to Rs.90. Find the
original price of tea.


Draw a square of \( 4 \mathrm{cm} . \) Constuct angle bisectors of 4 angles.Let all meet at 0 measure \( A O \) and \( 0 C . \) Then \( A O^{2}+O C^{2}= \)
\( \mathbf{A} \cdot \mathbf{8} \)
B. 4
c. 16
D. 32


Vacuum Distillation is a separation
technique that is used to separate a solid that has dissolved in a liquid and
made a solution.
If true enter \( 1, \) else 0


A laboratory thermometer is dipped in a beaker containing hot water. As the thermometer is removed the mercury
level will
A . rise
B. fall
C. it may rise or fall depending upon how much water is kept inside the beaker
D. neither rise nor fall


Express the following as mixed fraction \( \frac{17}{7} \)


The conjugates of
a) \( -2+3 i \)
b) \( 1-i \)
c) 4
d) \( 4 i \)
in order are:
A . \( 2-3 i, 1+i, 4,-4 i \)
B. \( +2-3 i, 1+i, 4,-4 i \)
c. \( 2-3 i, 1+i, 4,4 i \)
D. \( -2-3 i, 1+i, 4,-4 i \)


What is the value of \( p \) for which the
polynomial \( \boldsymbol{x}^{\mathbf{3}}+\mathbf{4} \boldsymbol{x}^{\mathbf{2}}-\boldsymbol{p} \boldsymbol{x}-\boldsymbol{6} \) is
completely divisible by \( (x-1) \)


An astronaut on the surface of an
unexplored planet gently throws a rock
upwards. It takes 4.00 sec for the rock
to reach a maximum height of \( 24.00 m \)
relative to where it was released before
coming back down.

If we take gravitational acceleration to
be constant, what is the planet's
gravity?
A \( .-3.00 m / s^{2} \)
B . \( -2.00 \mathrm{m} / \mathrm{s}^{2} \)
c. \( -1.00 m / s^{2} \)
D. \( -0.50 m / s^{2} \)
E. Cannot be determined


If the determinant
\( \left|\begin{array}{ccc}\boldsymbol{b}-\boldsymbol{c} & \boldsymbol{c}-\boldsymbol{a} & \boldsymbol{a}-\boldsymbol{b} \\ \boldsymbol{b}^{\prime}-\boldsymbol{c}^{\prime} & \boldsymbol{c}^{\prime}-\boldsymbol{a}^{\prime} & \boldsymbol{a}^{\prime}-\boldsymbol{b}^{\prime} \\ \boldsymbol{b}^{\prime \prime}-\boldsymbol{c}^{\prime \prime} & \boldsymbol{c}^{\prime \prime}-\boldsymbol{a}^{\prime \prime} & \boldsymbol{a}^{\prime \prime}-\boldsymbol{b}^{\prime \prime}\end{array}\right| \)
is expressible as \( m\left|\begin{array}{lll}a & b & c \\ a^{\prime} & b^{\prime} & c^{\prime} \\ a^{\prime \prime} & b^{\prime \prime} & c^{\prime \prime}\end{array}\right|, \) then
the value of \( \mathrm{m} \) is
A . -
B.
\( c \)
\( D \)


If \( \triangle A B C \cong \triangle P Q R, \angle B=40^{0} \) and
\( \angle C=95^{0}, \) find \( \angle P \)
A . \( 45^{\circ} \)
B . 40
\( c .95 \)
D. None of these


Which of the following cause alkalinity in natural water?
A. Sodium carbonate
B. Potassium carbonate
c. Potassium bicarbonate
D. All of the above


If charge on left plate of the \( 5 \mu F \)
capacitor in the circuit segment shown
in the figure is \( -20 \mu C \), the charge on
the right plate of \( 3 \mu F \) capacitor is :
\( \mathbf{A} \cdot+8.57 \mu C \)
B. \( -8.57 \mu C \)
c. \( +11.42 \mu C \)
D. \( -11.42 \mu C \)


The degree of \( \frac{d^{2} y}{d x^{2}}+ \)
\( \left[1+\left(\frac{d y}{d x}\right)^{2}\right]^{3 / 2}=0 \)
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D.


A ray of light in a liquid of refractive index \( 1.4, \) approaches the boundary surface between the liquid and air at an angle of incidence whose sine is 0.8
Which of the following statements is correct about the behaviour of the light
A. It is impossible to predict the behaviour of the light ras on the basis of the information supplied.
B. The sine of the angle of refraction of the emergent ray will less than 0.8
c. They ray will be internally reflected.
D. The sine of the angle of refraction of the emergent ray will be greater than 0.8


For a pulse moving in a heavy string the junctions of the string behaves as a
A. perfectly rigid end
B. free end
c. partially rigid end
D. rigid end


Find the surface area of a cone
\( \mathbf{A} \cdot 8635 m^{2} \)
\( \mathbf{B} \cdot 86.35 m^{2} \)
c. \( 0.8635 m \)
\( \mathbf{D} \cdot 8.635 m^{2} \)


Nucleus of a donor embryonal cell/somatic cell is transferred to an
enucleated egg cell. Then after the formation of organism, what shall be
true?
A. organism will have extranuclear genes of the donor cell
B. Organism will have extranuclear genes of recipient cell
c. organism will have extranuclear genes of both, donor and recipient cell
D. organism will have nuclear genes of recipient cell


What is the role of slaked lime and
animal charcoal in the manufacture of
sugar from sugarcane?


A company packages its milk powder in cylindrical container whose base has a
diameter of \( 14 \mathrm{cm} \) and height \( 20 \mathrm{cm} \)
Company places a label around the surface of the container (as shown in
the figure). If the label is placed \( 2 \mathrm{cm} \)
from top and bottom, what is the area of
the label?


Find the equations of the lines for which \( \tan \theta=\frac{2}{3}, \) where \( \theta \) is the angle of
inclination of the line and \( x- \) intercept
is 5


\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{e}^{\boldsymbol{x}} \sin \boldsymbol{x} \) in the interval \( [\mathbf{0}, \boldsymbol{\pi}] \)
Is Rolle's theorem applicable?


If \( ^{n} C_{8}=^{n} C_{27}, \) then what is the value of
\( \boldsymbol{n} ? \)
A . 35
B. 22
c. 28
D. 41


Two particles \( P \) and \( Q \) describe SHM of same amplitude a and frequency along the same straight line. The
maximum distance between the two
particles is \( a \sqrt{2} . \) The initial phase difference between the particle is
\( \mathbf{A} \cdot \pi / 3 \)
в. \( \pi / 2 \)
c. \( \pi / 6 \)
D. zero


Magnetic moments of \( \boldsymbol{C r}(\boldsymbol{Z}=\mathbf{2 4}) \)
\( \operatorname{Mn}(Z=25) \) and \( F e(Z=26), \) are
\( \boldsymbol{x}, \boldsymbol{y}, \boldsymbol{z} \)
They are in order:
A. \( x<y<z \)
В. \( x=y<z \)
c. \( x>y>z \)
D. \( x=y=z \)


Which of the following measurements is most precise?
A. \( 4.00 \mathrm{mm} \)
B. 4.00 cm
c. \( 4.00 \mathrm{m} \)
D. \( 40.00 \mathrm{m} \)


In Rutherford experiment, most of the alpha particles go straight through the foil because
A. alpha particles are much heavier than electron
B. alpha particles are positively charged
c. alpha particles move with high velocity
D. most part of the atom is empty


(1) Define atmosphere and atmospheric
pressure.
(2) What do you mean by the state of
motion?
(3) On what factors does the effect of
force depend?


Match the name of the animal with one
characteristics and the phylum or class to which it belongs.
A. Petromyzon - Ectoparasite - Cyclostomata
B. Ichthyophis - Terrestrial - Reptilia
c. Limulus - Body covered by chitinuous exoskeleton Pisces
D. Adamsia - Radially symmetrical- Porifera


Choose the correct statement from the
following:
This question has multiple correct options
A. Kinetic energy of a body is quadrupled, when its velocity is doubled.
B. Kinetic energy is proportional to square of velocity.
C. Kinetic energy does not depend on mass of the body.
D. The change in kinetic energy of a particle is equal to the work done on it by the net force.


In which of the following cases, the former change would require lesser energy than the latter?
This question has multiple correct options
A \( \cdot B e^{+}(g) \rightarrow B e^{2+}(g)+e^{-} ; \operatorname{Be}(g) \rightarrow B e^{+}(g)+e^{-} \)
B . \( N a(g) \rightarrow N a^{+}(g)+e^{-} ; C l^{-}(g) \rightarrow C l(g)+e^{-} \)
C. \( A g(g) \rightarrow A g^{+}(g)+e^{-} ; A u(g) \rightarrow A u^{+}(g)+e^{-} \)
D. \( O^{-}(g) \rightarrow O(g)+e^{-} ; S^{-}(g) \rightarrow S(g)+e^{-} \)


The density of an ideal gas
\( \mathbf{A} . \) is directly proportional to its pressure and absolute temperature
B. is directly proportional to its pressure and inversely proportional to its absolute temperature
C. is inversely proportional to its pressure and directly proportional to its absolute temperature
D. is inversely proportional to both its pressure and absolute temperature of the gas


A schematic plot of \( \ln \boldsymbol{K}_{e q} \). versus
inverse of temperature for a reaction is
shown below:
The reaction must be:
A. Exothermic
B. Endothermic
c. one with negligible enthalpy change
D. Highly spontaneous at ordinary temperature


Find the middle terms in the expansion
of \( \left(2 x^{2}-\frac{1}{x}\right)^{7} \)
В. \( -280 x^{5}, 560 x^{2} \)
C \( .560 x^{5},-280 x^{2} \)
D . \( 280 x^{5},-560 x^{2} \)


What is sexual reproduction in human?


If the concentration of water vapour in
the air is \( 1 \% \) and the total atmospheric pressure equals 1 atm, then the partial
pressure of water vapour is?
A. \( 0.1 \mathrm{atm} \)
В. \( 1 \mathrm{mm} \) нв
\( \mathbf{c} .7 .6 \mathrm{mm} \mathrm{Hg} \)
D. 100 atm


Two particles \( A \) and \( B \), initially at rest, moves towards each other under a
mutual force of attraction. At the instant
when the speed of \( A \) is \( u \) and the speed of
\( \mathrm{B} \) is \( 2 u, \) the speed of centre of mass is
A. zero
в. \( u \)
\( c .1 .5 u \)
D. \( 3 u \)


The image of a star (effectively a point source) is made by a convergent lens of focal length \( 1 \mathrm{m} \) and diameter of aperture \( 5.0 \mathrm{cm} . \) If the lens is ideal and the effective wavelength in image
formation is taken as \( 5 \times 10^{-3} \mathrm{cm} \), the
diameter of the image formed will be
nearest to
A. zero
B. \( 10^{-6} \mathrm{cm} \)
\( \mathbf{c} \cdot 10^{-5} \mathrm{cm} \)
D. \( 10^{-3} \mathrm{cm} \)


State whether true or false.
Two balls are dropped from heights \( h_{1} \)
and \( h_{2} \) respectively. The ratio of their velocities on reaching the ground is equal to \( \sqrt{\boldsymbol{h}_{1}}: \sqrt{\boldsymbol{h}_{2}} \)
A. True
B. False


How many \( \sigma \) bonds are present in
\( \boldsymbol{H}_{2} \boldsymbol{N}-\boldsymbol{N} \boldsymbol{O}_{2} ? \)


The condition occurring due to gradual decrease in power of accommodation because of ageing is called
A. Near-sightedness
B. Hypermetropia
c. Presbyopia
D. cataract


Which of the following pair of compounds illustrate the law of multiple proportions? This question has multiple correct options
A. \( S O_{2} \) and \( S O_{3} \)
B. \( N O_{2} \) and \( N_{2} O \)
c. \( M g O \) and \( M g(O H)_{2} \)
D. \( N O \) and \( N_{2} O_{5} \)


Given solid sphere is in pure rolling on a
rough surface. Pick correct statement(s): (Take \( \left.\pi=\frac{22}{7}\right) \)
This question has multiple correct options
A. There are two points in sphere having velocity in vertical direction
B. There is no point in sphere having velocity in vertical direction
C . Ratio of distance travelled by A and O is \( \frac{14}{11} \) in one
complete round
D. Ratio of distance travelled by A and O is 1 in one complete round


Figure shows the circuit of an electronic
device
(i) Which electronic device: a rectifier,
an amplifier or an oscillator does the
circuit represent?
(ii) State where the input voltage is
applied and where the output voltage is
available.
(iii) Compare the output voltage of this circuit with its input voltage.


Statement I: Atomic radius generally increases as you move across the periodic table from left to right. Statement II: The atomic number is
increasing from left to right as you move across the periodic table
A. Both Statement I and Statement II are correct and Statement II is the correct explanation of Statement
B. Both Statement I and Statement II are correct, but Statement II is not the correct explanation of Statement I.
c. Statement lis correct, but Statement II is incorrect
D. Statement I is incorrect, but Statement II is correct


In a sample of ethyl ethanoate
\( \left(C H_{3} C O O C_{2} H_{5}\right), \) the two oxygen
atoms have the same number of
electrons but different number of
neutrons. Which of the following is the correct reason for it?
A. One of the oxygen atoms has gained electrons
B. One of the oxygen atoms has gained two neutrons
c. The two oxygen atoms are isotopes
D. The two oxygen atoms are isobars


The D.E whose solution is \( y=A \sin 2 x+B \) \( \cos 2 x \) given as:
A \( \cdot y_{2}=4 y \)
B . \( y_{2}+3 y=0 \)
\( \mathbf{c} \cdot y_{2}+y=0 \)
D . \( y_{2}+4 y=0 \)


select correct statement(s):
This question has multiple correct options
A. Alkali metals ozonides are coloured and
paramagnetic.
B. Alkali metal-ozonides are colourless and diamagnetic
C. Sesquioxides of alkali metal are peroxides disuperoxides \( \left(M^{+}\right)_{4}\left(O_{2}^{2-}\right)\left(O_{2}^{-}\right)_{2} \)
D. Sesquioxides are paramagnetic due to presence of superoxide ion \( O_{2}^{-} \)


Large intestine has
A. Large lumen
B. Large length
c. Large Diameter
D. A and C


A circular coil of \( n \) turns is kept in a uniform magnetic field such that the plane of the coil is perpendicular to the field. The magnetic flux associated with
the coil is now \( \phi . \) Now the coil is opened
and made into another circular coil
of twice the radius of the previous coil and kept in the same field such that the plane of the coil is perpendicular to the field. The magnetic flux associated with this coil now is:
\( A \cdot \phi \)
B. 2
\( c \cdot \frac{\phi}{4} \)
D. \( \frac{\phi}{2} \)


Which of the following hydrocarbons has the lowest dipole moment?
A. \( O F_{2} \)
в. \( C H_{3} C \equiv C C H_{3} \)
c. \( C H_{3} C H_{2} C O O H \)
D. \( C H_{2}=C H-C O O H \)


In a circuit \( \mathrm{L}, \mathrm{C} \) and \( \mathrm{R} \) are connected in series with an alternating voltage source of frequency f. The current leads
the voltage by \( 45^{\circ} . \) The value of \( \mathrm{C} \) is
A. \( \frac{1}{2 \pi f(2 \pi f L-R)} \)
в. \( \frac{1}{2 \pi f(2 \pi f L+R)} \)
c. \( \frac{1}{\pi f(2 \pi f L-R)} \)
D. \( \frac{1}{\pi f(2 \pi f L+R)} \)


If \( z \) is a complex number such that \( z+ \) \( |z|=8+12 i, \) then the value of \( \left|z^{2}\right| \) is
A . 228
в. 144
\( c \cdot 121 \)
D. 169
E. 189


In above shown graph of position versus
time, two trains, \( X \) and \( Y \) are moving on
parallel track from the same starting
position from the rest. At time \( T \)
A. Train \( X \) is moving faster than train \( Y \)
B. Train Y is moving faster than train \( x \)
C. Trains \( \mathrm{X} \) and \( \mathrm{Y} \) are moving at the same speed
D. Train \( X \) is ahead of train \( Y \)
E. Train Y is ahead of train \( x \)


Polynuclear hydrocarbons are non carcinogenic.
A. True
B. False


\( a-(0)-_{i_{f, a}}^{i}(\Omega)-a \)
\( a-[0]_{i}^{i}(0)-a \)
\( a-(0)-_{i}^{i}(0)-a \)
\( a-(0)-\underset{c c_{3}}{c_{0}}<0-c \)


The normals to the curve \( y=x^{2}-x+ \)
1, drawn at the points with the abscissa
\( \boldsymbol{x}_{1}=\mathbf{0}, \boldsymbol{x}_{2}=-\mathbf{1} \) and \( \boldsymbol{x}_{3}=\frac{\mathbf{5}}{\mathbf{2}} \)
A. are parallel to each other
B. are pair wise perpendicular
c. are concurrent
D. are not concurrent


Gauss's law follows
This question has multiple correct options
A. Coulomb's law
B. Superposition principle
C. Faraday's law
D. Quantisation principle


is the best evidence for the lock
and key theory of enzyme reaction.
A. All isolated enzymes have been identified as proteins.
B. Compounds similar in structure to substrate inhibit reactions
C. Enzymes are found in living organisms speed up certain reactions
D. Enzymes determine the direction of reaction


Find the value of \( 52^{2} \) using standard
identity.
A . 2604
в. 2704
c. 2804
D. 2904


Of all land plants, bryophytes alone have independent and attached, dependent
A. Sporophytes, gametophytes
B. Rhizoids, zygotes
c. Gametophytes, sporophytes
D. Rhizoids, stalked sporangia


If the length of a wire is doubled, then
its resistance becomes.
A. four times
B. two times
c. one-fourth
D. half


State whether the given statement is
true or false:
When \( N a C l(a q) \) is electrolysed, sodium metal is formed at the cathode
and chlorine gas is formed at anode.
A. True
B. False


With the length of vocal chord, voice
quality
A. changes
B. remains same
c. may or may not change
D. remains same but loudness changes


Define reproduction.


Then,
This question has multiple correct options
\( f(x) \) is continuous at \( x=0 \) if \( a=-1, b=\frac{1}{2} \)
B. \( f(x) \) is discontinuous at \( x=0 \) if \( b \neq \frac{1}{2} \)
C \( . f(x) \) has irremovable discontinuity at \( x=0 \) if \( a \neq-1 \)
D. \( f(x) \) has removable discontinuity at \( x=0 \) if \( a= \)
\( -1, b \neq \frac{1}{2} \)


calculate the torque developed by an airplane engine whose output is 2000
\( \mathrm{HP} \) at an angular velocity of 2400 rev/min.


When light travels from air to water
there is
A. Reflection of light
B. Refraction of light
c. Diffraction of light
D. scattering of light


The hydrated salt \( N a_{2} S O_{4}, 10 H_{2} O \)
undergoes \( X \% \) loss in weight on
heating and becomes anhydrous. The value of \( \boldsymbol{X} \) will be:
A . 10
B . 45
c. 56
D. 70


Write down and simplify \( 6^{t h} \) term in the
expansion of \( \left(\frac{2 x}{3}+\frac{3 y}{2}\right)^{9} \)


The chemical added to LPG to help detect its leakage is:
\( A \). isobutene
B. ethylamine
c. methyl mercaptan
D. ethyl mercaptan


Which of the following is called "biological middle man"?
A. Hormone
B. Vitamin
c. Enzyme
D. All of the above


Calculate how many ATP are
synthesised and deduct the number of ATP utilised during glycolysis.


100 tickets are numbered as 00,01,02
\( \ldots .09,10,11,12, \ldots .99 . \) Out of them, one
ticket is drawn at random. The
probability that the sum of the digits of the number on the ticket is 9 is
A. \( \frac{7}{100} \)
в. \( \frac{9}{100} \)
c. \( \frac{1}{10} \)
D. \( \frac{1}{100} \)


5 moles of \( N H_{4} O H \) and 1 mole of \( \mathrm{HCl} \)
are mixed and diluted to 1 litre. \( p K b \) of
\( N H_{4} O H \) is 4.8. The \( p H \) of the solution
is:
A . 4.8
в. 4.1979
c. 9.8021
D. 9.2


The smallest planet in the solar system is
A. Mars
B. Jupiter
C. Mercury
D. Earth


Which of the following is a property of ethanol?
A. lonic compound
B. Noble gas
c. Polar covalent compound
D. Nonpolar covalent compound
E. Metallic substance


One mole of ideal gas expands freely at \( 310 \mathrm{K} \) from five litre volume to 10 litre
volume. Then \( \Delta E \) and \( \Delta H \) of the process
are respectively:
A . 0 and 5 cal
B. 0 and \( (5 \times 300) \) cal
c. 0 and 0
D. 5 and 0 cal


What is the cause of Presbyopia?


A block of mass \( 5.0 \mathrm{kg} \) slides down an incline of inclination \( 30^{0} \) and length 10
m. Find the work done by the force of gravity in joules?
A . 245
B. 300
\( c .350 \)
D. 400


Which statements are correct?
1. Addition of \( A g N O_{3} \) drop by drop in excess of \( K I \) leads to the formation of
+vely charged sol of \( A g I \)
2. Adsorption characteristic of an adsorbent may be increased by making it in finely divided form.
3. Catalyst help in attaining the equilibrium earlier but does not influence equilibrium constant in reversible reactions.
4. Decolorisation of raw sugar is based on absorption.
5. Gas masks containing animal charcoal acts on the basis of selective
adsorption.
6. The micelle formation of soaps
depends upon hydrophobic and hydrophilic entities present in soap.
A .2,3,5,6
В. 2,3,4,5
c. 1,2,5,6
D. 1,2,3,4


If \( \int \frac{2 x^{2}+3}{\left(x^{2}-1\right)\left(x^{2}+4\right)} d x= \)
\( a \log \left(\frac{x-1}{x+1}\right)+b \tan ^{-1}\left(\frac{x}{2}\right)+c, \) then
values of a and \( b \) are
A. (1,-1)
в. (-1,1)
c. \( \left(\frac{1}{2},-\frac{1}{2}\right. \)
D. \( \left(\frac{1}{2}, \frac{1}{2}\right) \)


Which is most directly responsible for the sequence of amino acids in a protein?
A. Sequence of the anticodons
B. Number of codons in mRNA
c. Proteins associated with rRNA
D. The sequence of codons in mRNA


The molecules of metals and non-
metals in vapour state
are
A. Monoatomic and polyatomic respectively
B. Polyatomic and diatomic respectively
C. Diatomic
D. Polyatomic


If there is an error of \( a \% \) in measuring
the edge of a cube, then the percentage error in its surface area is
\( \mathbf{A} \cdot 2 a \)
B. \( \frac{a}{2} \)
\( c .3 a \)
D. None of the above


Which of the following statement is
CORRECT?
A. Word done by static friction is always zero
B. Work done by kinetic friction is always negative
C. The negative of the work done by the conservative internal forces on a system equals the change in kinetic energy
D. The work done by all the forces on a system equal to change in kinetic energy


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


Gynobasic style can be traced in
A. Mangifera
B. Tagets
c. Ocimum
D. All of the above


Write opposite of the following:
a)30 \( k m \) north
b)Increase in weight
c) Loss of \( R s .700 \)
d) \( 100 m \) above sea level


Statement 1:If \( \vec{A} \cdot \vec{B}=\vec{B} \cdot \vec{C} \) then \( \vec{A} \) may
not always be equal to \( \overrightarrow{\boldsymbol{C}} \) Statement 2: The dot product of two vector involves cosine of the angle
between the two vectors.
A. a) Statement- - is false, Statement- 2 is true
B. b) Statement-1 is true, Statement-2 is true, Statement
2 is a correct explanation for statement-
c. c) Statement- - is true, Statement-2 is true; Statement
2 is not a correct explanation for statement-
D. d) Statement-1 is true, Statement-2 is false


The charge on solid sphere is
A \( \cdot-9 / 2 \)
B. - -व/4
\( c \cdot-q / 8 \)
D. - q/16


During electrolytic refining of Alumina, the molten electrolyte used contains
A. cryolite
B. Fluorspar
c. Pure alumina
D. All of the above


An element has atomic number 19
Where would you expect this element in
the periodic table and why?


Find:
\( \int \frac{x e^{x}}{(1+x)^{2}} d x \)


Photolithotrophs (photoautotrophs)
obtain energy from
A. Radiations and carbon from inorganic compounds
B. Radiations and carbon from organic compounds
C . Organic compounds
D. Inorganic compounds


Arrange the following in the decreasing order of their melting points.
I. Decane
II. Nonane
III. Octane
IV. Heptane
\( A \cdot(1)>(11)>(111)>(1 v) \)
B. (IV) > (III) > (II) > (I)
\( c \cdot(1)>((11)>(11)>(11)) \)
\( D \cdot(\mid V)>(||)>(\| \mid)>(\mid) \)


If the line, \( \frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4} \) and
\( \frac{\boldsymbol{x}-\mathbf{3}}{\mathbf{1}}=\frac{\boldsymbol{y}-\boldsymbol{k}}{\mathbf{2}}=\frac{\boldsymbol{z}}{\mathbf{1}} \) intersect, then find
the value of \( k \)


Which of the following statement is
wrong about Abscisic acid:
A. It helps in general plant metabolism
B. It is antagonistic to \( G A_{3} \)
C. It helps in seed maturation \& dormancy
D. Morphogenesis


A current of \( 10 A \) is maintained in a
conductor of cross-section \( 1 \mathrm{cm}^{2} \). If the
number density of free electrons be \( 9 \times 10^{28} m^{-3}, \) the drift velocity of free
electrons is
A. \( 6.94 \times 10^{-6} \mathrm{m} / \mathrm{s} \)
B. \( 5.94 \times 10^{-2} \mathrm{m} / \mathrm{s} \)
c. \( 1.94 \times 10^{-3} \mathrm{m} / \mathrm{s} \)
D. \( 2.94 \times 10^{-4} \mathrm{m} / \mathrm{s} \)


The function \( y=f(x) \) is ?
A . odd
B. even
c. increasing
D. decreasing


\( \int \frac{\left(t^{2}+1\right)^{2}}{t^{6}+1} d t \)


Assertion
In pigeons, females are heterogametic and males are homogametic.
Reason
In pigeons, females have \( z \) W sex chromosomes and males have \( \mathrm{ZZ} \) sex
chromosomes.
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


Write the chemical reactions involved in
the process of extraction of Gold. Explain the role of dilute NaCN and Zn
in this process.


In the sequence of reaction \( C_{2} H_{2} \frac{H_{2} S O_{4}}{H g S O_{4}} A \stackrel{[O]}{\longrightarrow} B \) The compound
B is:
A. ethanoic acid
B. propanone
c. ethanol
D. methanal


Acetic acid was added to a solid \( X \)
taken in a test tube. A colourless and
odourless gas was evolved. The gas was passed through lime water which did not turn milky. However, the gas burnt
with a pop sound. It was concluded
that
A. Solid \( x \) is sodium and the gas evolved is \( C O_{2} \)
B. Solid X is sodium and the gas evolved is \( H_{2} \)
c. solid \( x \) is sodium acetate and the gas evolved is \( C O_{2} \)
D. Solid \( x \) is sodium chloride and the gas evolved is \( H_{2} \)


What is the arithmetic mean of the
squares of first five natural numbers?
\( \mathbf{A} \cdot \mathbf{9} \)
B. 11
c. 13
D. 15


Evaluate
\( \frac{\sin ^{2} 63^{\circ}+\sin ^{2} 27^{\circ}}{\cos ^{2} 17^{\circ}+\cos ^{2} 73^{\circ}} \)
2) \( \sin 25^{\circ} \cos 65^{\circ}+\cos 25^{\circ} \sin 65^{\circ} \)


Two liquids \( X \) and \( Y \) form an ideal solution.
The mixture has a vapour pressure of \( 400 \mathrm{mm} \) at \( 300 \mathrm{K}, \) when mixed in the
molar ratio of 1: 1 and a vapour pressure of \( 350 \mathrm{mm} \) when mixed in the molar
ratio of 1: 2 at the same temperature. The vapour pressures of the two pure liquids \( X \) and \( Y \) respectively are?
A. 250mm, 550mm
B. 350mm, 450mm
c. \( 350 \mathrm{mm}, 700 \mathrm{mm} \)
D. 550mm, 250mm


A force when applied on a non rigid object
A. Does not change the inter spacing between its constituent particles
B. Do not cause any change in its dimension
c. Do not produce motion in it
D. None


Prove that the general equation \( a x^{2}+ \)
\( 2 h x y+b y^{2}+2 g x+2 f y+c=0 \) will
represent two parallel straight lines if
\( h^{2}=a b \) and \( b g^{2}=a f^{2} . \) Also prove that
the distance between them is \( 2 \sqrt{\left\{\frac{g^{2}-a c}{a(a+b)}\right\}} \)
Also prove that \( \frac{a}{h}=\frac{h}{b}=\frac{g}{f} \)


A wave is propagating in positive \( x- \)
direction. A time \( t=0 \) its snapshot is
taken as shown.lf the wave equation is
\( \boldsymbol{y}=\boldsymbol{A} \sin (\boldsymbol{\omega} \boldsymbol{t}-\boldsymbol{k} \boldsymbol{x}+\boldsymbol{\phi}), \) then \( \boldsymbol{\phi} \) is
A. \( \phi=0 \)
В. \( \phi=\pi \)
\( c \cdot \phi=\frac{\pi}{2} \)
D. \( \phi=3 \pi / 2 \)


An electric heater of resistance \( 8 \Omega \)
draws \( 15 A \) from the service mains 2
hours. Calculate the rate at which heat
is developed in the heater.


Find the circumference of a wheel
whose diameter is \( 126 \mathrm{cm} \). Find the
distance covered by it in taking 50 rounds in meters.


Image of an object is seen in a plane
mirror, the distance from the mirror to
the image depends on:
A. the distance of the observer from the mirror
B. the distance of the object from the mirror
c. the distance of both the observer and the object to the mirror
D. the thickness of the mirror


Which of the following pairs are isotopes?
A. Oxygen and Ozone
B. Ice and Steam
c. Nitric oxide and Nitrogen dioxide
D. Hydrogen and Deuterium


Milk can be preserved by adding a few drops of:
A. formic acid solution
B. formaldehyde solution
c. acetic acid solution
D. acetaldehyde solution


The energy of hydrogen atom in its ground state is \( -13.5 e V . \) The energy of the level corresponding to the quantum number \( n=5 \) is:
A. \( -5.4 e V \)
в. -0.54 eV
c. -2.72 eV
D. \( -0.85 e V \)


What are isoelectronic spices? give example?


The geometric mean of three numbers 3,5,7 is
A. 4.717
B. 3.717
c. 2.717
D. 1.717


Let \( A=\{1,2\} \) and \( B=\{3,4\} \). Find the number of relations from A to B.


Diatoms/Diatomaceous earth belong to
class
A. xanthophyceae
B. Bacillariophyceae
c. Phaeophyceae
D. Chlorophyceae


The species which are isoelectronic
with CO is:
A \( \cdot C l \)
в. \( O H^{-} \)
\( \mathrm{c} \cdot \mathrm{CH}_{3}^{+} \)
D. \( N_{2} \)


f a proton is released from rest at point p in the diagram, what will it do?
A. Move to the right
B. Move to the left
c. Move toward the top of the screen
D. Move toward the bottom of the screer


The standard reduction potential of metals \( X, Y \) and \( Z \) are \( -0.403 \vee, 0.337 V \) and \( 0.79 \mathrm{V} \) respectively. Which of the following reaction is not possible?
A \( \cdot X+H_{2} S O_{4} \rightarrow X S O_{4}+H_{2} \)
в. \( 2 Z+2 H N O_{3} \rightarrow 2 Z N O_{3}+H_{2} \)
c. \( Y+Z_{S} O_{4} \rightarrow Y S O_{4}+2 Z \)
D. \( X+2 Z N O_{3} \rightarrow X\left(N O_{3}\right)_{2}+2 Z \)


At a place, the horizontal and vertical components of earth's magnetic field are equal. What is the angle of dip at that place?
A . 45
B. 55
\( c \cdot 65 \)
D. 76


Which of the following energy level diagram for \( \left[F e F_{6}\right]^{3-} \) is correct on the basis of crystal field theory?


Which is most acidic oxide?
A \( \cdot C l_{2} O \)
в. \( C l_{2} O_{3} \)
c \( \cdot C l_{2} O_{6} \)
D. \( C l_{2} O_{7} \)


The magnifying power of a compound microscope is 20 and the distance between its two lenses is \( 30 \mathrm{cm} \) when
the final image is at the near point of the eye. If the focal length of eyepiece is \( 6.25 \mathrm{cm}, \) the focal length of objective is :
A. \( 2.5 \mathrm{cm} \)
B. 3.5 \( \mathrm{cm} \)
\( c .4 .5 \mathrm{cm} \)
D. 5.0 \( \mathrm{cm} \)


Law of conservation of mass is also
known as:
A. Law of indestructibility
B. Law of mass action
C. the mass law
D. None of the above


The reaction of toluene with \( C l_{2} \) in
presence of \( F e, \) the product(s) formed
is/are:
A . o- and p-chlorotoluene
B. benzyl chloride
c. m-chlorotoluene
D. only p-chlorotoluene


The co-ordinates of head and tail of a
vector are \( (\mathbf{2}, \mathbf{1}, \mathbf{0}) \) and \( (-\mathbf{4}, \mathbf{2},-\mathbf{3}) \)
respectively. The magnitude of the vector is:
A. \( \sqrt{23} \) units
B. \( \sqrt{46} \) units
c. \( \sqrt{84} \) units
D. \( \sqrt{12} \) units


Assertion
Chloroplast is a cell organelle.
Reason
An organelle is a distinct part of a cell
which has a particular structure and
function.
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.


Copy the picture.
(a) Label the parts \( A, B \) and \( C \)
(b) Note down the functions of \( \mathrm{B} \), \( \mathrm{C} \) and
D.


Eutrophication is
A. Excessive oxygen in ponds
B. Abundant fertilizers in the lake
C. The lack of algae in the lake
D. Abundant nektons in the lake


Angles opposite to equal sides of an isosceles triangle are equal. Prove this
result


A galvanometer of resistance \( 50 \Omega \) is
connected to a battery of \( 8 V \) along with a resistance of \( 3950 \Omega \) in series. A full
scale deflection of 30 div is obtained in
the galvanometer. In division, the resistance in series should be
A. 1950
в. 7900
c. 2000
D. 7950


Quartz is the form?
A. \( C O_{2} \)
в. \( \operatorname{si} 0_{2} \)
\( c \cdot S O_{2} \)
D. \( N O_{2} \)


Let \( S \) be a set containing \( n \) elements. Then the total number of binary
operations on \( \boldsymbol{S} \) is
\( \mathbf{A} \cdot n^{n} \)
B \( .2^{n} \)
c. \( n^{n^{2}} \)
D. \( n^{2} \)


Assertion
Van-Arkel method is used to prepare samples of some metals.
Reason
It involves the reaction of \( \mathrm{CO} \) with
metals to form volatile carbonyls that decompose on heating to give pure metal

Read the above assertion and reason
and choose the correct option regarding
¡t.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which colour of light is most refracted during dispersion by a prism?
A . Red
B. yellow
c. Green
D. Violet


Calculate the potential of hydrogen electrode in contact with a solution of
\( 5 \times 10^{-3} M \) of \( B a(O H)_{2} \) at 1 atm
pressure and \( 298 \mathrm{K} \) temperature:
A . - \( 0.059 v \)
B. 0.059v
c. \( 0.59 v \)
D - -0.59V


\( \tan \left(3 \tan ^{-1} 3\right)+\cos \left(3 \cos ^{-1}(1 / 3)\right)+1 \)
is equal to
\( A \cdot 1 \)
B. 9/13
c. \( 4 / 27 \)
D. 295/351


The term independent of \( x \) in \( (2 x- \) \( \left.\frac{1}{2 x^{2}}\right)^{12} \) is
\( \mathbf{A} \cdot-^{12} C_{3} \cdot 2^{6} \)
B. \( -^{12} C_{5} .2^{2} \)
c. \( 12 C_{6} \)
D. \( ^{12} C_{4} .2^{4} \)


For the reaction, \( \boldsymbol{P C l}_{5}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{P} \boldsymbol{C l}_{3}(\boldsymbol{g})+ \)
\( C l_{2}(g), \) the position of equilibrium can
be shifted to the right by:
A. doubling the volume
B. increasing the temperature
c. addition of equimolar quantities of \( P C l_{3} \) and \( P C l_{5} \)
D. addition of \( C l_{2} \) at constant volume


Following polynomars write the degree
of each.
1). \( 6 x^{2}+x+1 \)
2). \( y^{9}-3 y^{7}+\frac{3}{2} y^{2}+4 \)
3). \( 2 x+1 \)
4). \( 5 t-\sqrt{11} \)


Which one of the following correctly describes the location of some body parts in the earthworm (Pheretima)?
A. Four pairs of spermathecae in 4 - 7 segments
B. One pair of ovaries attached at inter-segmental septum of 14th and 15th segments
c. Two pairs of testes in 10 th and 11 th segments
D. Two pairs of accessory glands in 16-18th segments


A class teacher has the following absentee record of 40 students of a
class for the whole term. Find the mean
number of days a student was absent.
\( \begin{array}{lllll}\text { Number } & 0- & 6- & 10- & 14- \\ \text { of days } & 6 & 10 & 14 & 20\end{array} \)
Numbe of student


The weakest \( C-C l \) bond is present in:
\( A \)
B.
\( c \)
D.


Draw a clover leat structure of tRNA
showing the following.
(i) Tyrosine attached to its amino acid site.
(ii) Anticodon for this amino acid in its correct site (codon for tyrosine is UCA)


The amount of heat energy required to raise the temperature off 1 kg of water
through \( 1^{\circ} C \) is
A. Calorie
B. Thermal capacity
c. specific Heat
D. Kilo calorie


Because of the which of the following reason/s, growth stops completely during the stationary phase?
A. Lack of nutrients
B. Saturation of nutrients
c. over availability of nutrients
D. None of the above


Differentiate between normal elements
and transition elements.


Write the name and structure of any five
oxyacids of sulphur?


Which of the following compounds is most widely used as an oxidizing agent in the volumetric analysis?
A. \( C e O_{2} \)
B. \( \left(N H_{4}\right)_{2}\left[C e\left(N O_{3}\right)_{6}\right] \)
\( \mathrm{c} \cdot \mathrm{Ce}\left(\mathrm{SO}_{4}\right)_{2} \)
D. \( C e F_{3} \)


Which of the following brings about dry bleaching?
A. ozone
B. chlorine
c. sulphurdioxide
D. hydrogen peroxide


Two wires \( X \) and \( Y \) are made of different
metals. The Young modulus of wire \( X \) is
twice that of wire Y. The diameter of
wire \( X \) is half that of wire \( Y \).

The wires are extended with the same
strain and obey Hooke's law.
What is the ratio
A \( \cdot \frac{1}{8} \)
B. \( \frac{1}{2} \)
\( c \cdot 1 \)
D.


\( \vec{A} \) and \( \vec{B} \) are two vectors, find the angle
between them, if \( |\overrightarrow{\boldsymbol{A}} \times \overrightarrow{\boldsymbol{B}}|=\sqrt{\mathbf{3}}(\overrightarrow{\boldsymbol{A}} \cdot \overrightarrow{\boldsymbol{B}}) \) the value of is :-
A \( .90^{\circ} \)
В. \( 60^{\circ} \)
\( c \cdot 45 \)
D. 30


Which of the following phenols has the
largest \( p K_{a} \) value (i.e. is least acidic)?
\( A \)
B.
\( c \)
\( D \)


If different words are formed with all the
letters of the word 'AGAIN' and are
arranged alphabetically among themselves as in a dictionary, the word at the 50th place will be
A . NAAGI
c. IAAGN


The number of significant figure In the
numbers \( 4.8000 \times 10^{4} \) and 48000.50
are respectively then
A. 5 and 6
B. 5 and 7
\( c .2 \) and 7
D. 2 and 6


Solve:
\( \frac{\tan \theta}{\sec \theta+1}+\frac{\tan \theta}{\sec \theta-1}=2 \csc \theta \)


Which of the following is NOT true for
comets?
A. Some comets are believed to have originated in a region near the edge of the orbit of the outer planets in our solar system called the "scattered disk" that overlaps a region called the Kuiper belt
B. Some comets are believed to have originated in the outer-most region associated with our solar system, called the Oort cloud
C. The tail of a comet gives the comet its propulsion, like rocket fuel out the back end of a rocket
D. The tails of comets generally point away from the sun and are made of two major parts-a dusty part (that curves a bit) and an ionic part
E. Comets often contain significant amounts of water


Meiosis takes place in Chlamydomonas in
A. zygospore
B. Zoospore
c. Hypnospores
D. Aplanospores


A piece of copper and another of germanium are cooled from room temperature to \( 80 \mathrm{K} \). The resistance of:
A. each of them increases
B. each of them decreases
c. copper increases and germanium decreases
D. copper decreases and germanium increases.


Find the equation of the ellipse referred to its centre whose foci are the points
(4,0) and (4,0) and whose eccentricity is \( \frac{1}{3} \)


Active transport of ions by the cell
requires
A. High temperature
B. ATP
c. Alkaline pH
D. Salts


The \( p K_{a} \) values for the three ionizable
groups \( X, Y \) and \( Z \) of glutamic acid \( 4.3,9.7 a n d 2.2 \) respectively.
The isoelectric point for the amino acid
is:
\[
\begin{aligned}
\mathrm{H} \mathrm{O}_{2} \mathrm{C}-\mathrm{CH}_{2} &-\mathrm{CH}-\mathrm{CO}_{2} \mathrm{H} \\
\mathrm{X} &+\mathrm{NH}_{3}
\end{aligned}
\]
A . 7.00
B. 3.25
c. 4.95
D. 5.95


Which has the least entropy?
A. Graphite
B. Diamond
\( c \cdot N_{2}(g) \)
\( D \cdot N_{2} O(g) \)


The product obtained at anode when \( \mathbf{5 0 \%} \boldsymbol{H}_{\mathbf{2}} \boldsymbol{S O}_{\mathbf{4}} \) aqueous solution is
electrolysed using platinum electrodes is :
A. \( H_{2} S O_{3} \)
B. \( H_{2} S_{2} O_{8} \)
\( c \cdot O_{2} \)
D. \( H_{2} \)


The theory of evolution proposed by Charles Darwin is known as
A. Theory of natural selection
B. Synthetic theory of evolution
c. Lamarckism inheritance
D. All of the above
E. None of the above


The rms value of a.c. voltage with peack
of \( 311 V \) is
\( \mathbf{A} \cdot 220 V \)
в. \( 311 V \)
\( \mathbf{c} \cdot 180 V \)
D. 320V


According to Boyle's Law PV=C the value of
C depends on:
a) Mass of the gas
b) Type of gas
c) Temperature
\( A \cdot a, b \)
B. \( b, c \)
\( c \cdot a, c \)
D. a,b,c.


f \( x+y=3 \) and \( 3 x-2 y-4=0 \) find
\( \boldsymbol{x}, \boldsymbol{y} \)


The number of metameric ethers
possible with the formula \( C_{4} H_{10} O \) is/are:
A .4
B. 3
\( c \cdot 2 \)
D. 5


What do you mean by retardation? What
is its SI unit?


\( \sum \)


Write the names of two important processes which occur on formation of
p-njunction. Define the 'depletion region' and 'potential barrier' in it.


Assertion
When small amount of acid or base is
added to pure water, its pH undergoes a change.
Reason
Addition of an acid or a base increases
the degree of ionisation of water.
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 correct?
A. \( S_{3} O_{9} \) contains no \( S-S \) linkage.
B. \( S_{3} O_{9} \) contains \( O-O \) linkage.
C. \( \left(H P O_{3}\right)_{3} \) contains \( P-P \) linkage
D. \( S_{2} O_{8}^{2-} \) contains \( S-S \) linkage


If earth revolves around the sun in an
orbit of double its present radius, then the year on earth will be of
A \( \cdot \frac{365}{4} \) day
B. \( 365 \times 2 \sqrt{2} \) day
c. \( \frac{365}{2 \sqrt{2}} \) day
D. \( 365 \times 4 \) day


Group 18 of the periodic table is known by the name as:
A . alkal
B. alkaline
c. halogen
D. noble


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


Anode rays are also called as:
A. Cathode Rays
B. Canal Rays
c. \( x \) -rays
D. None of these


If the momentum of a particle which
has a de Broglie wave length of 10 nm is \( A \times 10^{-26} \mathrm{ms}^{-1} \) then nearest integer
value of \( A \) is :


A survey was conducted by a group of students as a part of their environment
awareness programme, in which they collected the following data regarding the number of plants in 20 houses in a locality.
Find the mean number of plants per house.
Number
\[
\begin{array}{lll}
\mathbf{0}- & \mathbf{2}- & \mathbf{4}- \\
\mathbf{2} & \mathbf{4} & \mathbf{6}
\end{array}
\]
of plants
Number
of
houses
Which method did you use for finding
the mean, and why?


State the respective lowest and highest value of respiratory volumes.
A . TV, VC
B. ERV, IC
c. TV, TLC
D. RV, VC


Given \( \boldsymbol{A}=(\mathbf{1}, \mathbf{2}, \mathbf{5}), \boldsymbol{B}=(\mathbf{5}, \mathbf{7}, \mathbf{9}) \) and
\( C=(3,2,-1) . \) Find a until vector
normal to the plane of the triangle ABC.
A. \( \frac{-13 i+9 j-7 k}{\sqrt{(299)}} \)
в. \( \frac{13 i-9 j+7 k}{\sqrt{(299)}} \)
c. \( \frac{-15 i+16 j-5 k}{\sqrt{(506)}} \)
D. \( \frac{15 i-16 j+5 k}{\sqrt{(506)}} \)


The number of positive integral
solutions of the equation
\( \boldsymbol{x}_{1} \boldsymbol{x}_{2} \boldsymbol{x}_{3} \boldsymbol{x}_{4} \boldsymbol{x}_{5}=\mathbf{1 0 5 0} \) is
A. 1800
B. 1600
\( c \cdot 1400 \)
D. 1875


An object mass \( m_{1} \) moving with speed
collides with another object of mass \( \boldsymbol{m}_{2} \)
at rest and stick to it. Find the impulse imparted to the second object.


Find the area bounded by the curves \( \boldsymbol{y}=\sqrt{1-\boldsymbol{x}^{2}} \) and \( \boldsymbol{y}=\boldsymbol{x}^{3}-\boldsymbol{x} . \) Also find
the ratio in which the y-axis divide this
area
A \( \cdot \frac{\pi}{2} ; \frac{\pi-1}{\pi+1} \)
В. \( \frac{\pi}{4} ; \frac{\pi-1}{\pi+1} \)
c. \( \frac{\pi}{2} ; \frac{\pi+1}{\pi-1} \)
D. None of these


\( \boldsymbol{C o}^{2+}(\boldsymbol{a} \boldsymbol{q} \cdot)+\boldsymbol{S C N}^{-}(\boldsymbol{a q}) \rightarrow \) Complex
\( (\boldsymbol{X}) \)
\( N i^{2+}(a q)+ \) dimethylglyoxime Complex \( (\boldsymbol{Y}) \) The coordination number of cobalt and
nickel in both the complexes \( (X) \) and \( (Y) \)
is four. The IUPAC names of the
complexes \( (X) \) and \( (Y) \) are respectively:
A. tetrathiocyanato-S-cobalt(II) and bis(dimethylglyoximate)nickel(II)
B. tetrathiocyanato-S-cobaltate(II) and bis(dimethylglyoximato)nickel(II)
C. tetrathiocyanato-S-cobaltate(II) and bis(dimethylglyoximato)nickelate(II)
D. tetrathiocyanato-S-cobaltate(III) and bis(dimethylglyoximato)nickel(II)


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


In the plant part having two generations
is
A. embryo
B. unfertilized ovule
c. germinated pollen grain
D. seed


The reduction potential at \( \mathrm{pH}=14 \) for the \( \boldsymbol{C u}^{2+} / \boldsymbol{C u} \) couples is:
\( \left[\mathrm{Given}, \boldsymbol{E}_{\boldsymbol{C u}^{2+} / \boldsymbol{C u}}^{\boldsymbol{o}}=\right. \)
\( \left.\mathbf{0 . 3 4} \boldsymbol{V} ; \quad \boldsymbol{K}_{s p} \boldsymbol{C u}(\boldsymbol{O H})_{2}=\mathbf{1} \times \mathbf{1 0}^{-\mathbf{1 9}}\right] \)
A . \( 0.34 \mathrm{V} \)
в. \( -0.34 \mathrm{V} \)
c. \( 0.22 V \)
D. \( -0.22 V \)


What is the basicity of orthophosphorous acid?
A. one
B. Two
c. Three
D. Four


Which of the following pairs of metals is purified by van-Arkel method?
A . \( N e \) and \( F e \)
B. \( G a \) and \( I n \)
\( \mathbf{c} . Z r \) and \( T i \)
D. \( A g \) and \( A u \)


What may be expected to happen when phosphine gas is mixed with chlorine gas?
A. \( P C l_{3} \) and \( H C l \) are formed and the mixture warms up
B. \( P C l_{3} \) and \( H C l \) are formed and the mixture cools down
C. The mixture only cools down
D. None of the above


If area of a triangle is 35 sq units with
vertices (2,-6),(5,4) and \( (k, 4), \) then find the value of \( k \)


Heart of a crocodile is
A. single chambered
B. Two chambered
C. Three chambered
D. Four chambered
E . Multi chambered


Indicate in each reaction which one is
oxidised or reduced if any:
\( \mathbf{2} N \boldsymbol{a}_{2} \boldsymbol{S}+\mathbf{4} \boldsymbol{H} \boldsymbol{C l}+\boldsymbol{S} \boldsymbol{O}_{3} \rightarrow \mathbf{4} \boldsymbol{N} \boldsymbol{a} \boldsymbol{C l}+ \)
\( 3 S+2 H_{2} O \)
In the above reaction, which one of the following is oxidised?
A \( \cdot N a_{2} S \)
в. \( H C l \)
c. \( N a C l \)
D. None of these


1)Write down IUPAC name and symbol of the following atomic number:
\( 111,105,102,115 ? \)
2)Why do Zr and Hf have similar radius?


A system consisting of two masses connected by a mass less rod lie along the \( x- \) axis. \( A 0.4 k g \) mass is at a
distance \( x=2 m \) while a 0.6 kg mass is
at a distance \( \boldsymbol{x}=\mathbf{7} \) m. The \( \boldsymbol{x} \)
coordinate of the centre of mass is
\( \mathbf{A} \cdot 5 m \)
B. \( 3.5 m \)
c. \( 4.5 \mathrm{m} \)
D. \( 4 m \)


A man is standing on a platform of a balance and takes a quick step, then
his weight:
A . decreases
B. increases
c. remains unchanged
D. first increases and then decreases


If \( \boldsymbol{A}_{\boldsymbol{i}}=\frac{\boldsymbol{x}-\boldsymbol{a}_{\boldsymbol{i}}}{\left|\boldsymbol{x}-\boldsymbol{a}_{\boldsymbol{i}}\right|} \) where \( \boldsymbol{i}=\mathbf{1}, \boldsymbol{2}, \boldsymbol{3} \) and
\( \boldsymbol{a}_{1}<\boldsymbol{a}_{2}<\boldsymbol{a}_{3} \) then \( \lim _{\boldsymbol{x} \rightarrow \boldsymbol{a}_{2}} \boldsymbol{A}_{1} \boldsymbol{A}_{2} \boldsymbol{A}_{3}= \)
A . -1
B.
\( c \cdot 0 \)
D. does not exist


Match List I with List II and select the
correct answer using the codes given below the list
\begin{tabular}{ll}
List I & List II \\
P. Boltzmann constant & 1. \( \left[M L^{2} T^{-1}\right] \) \\
Q. Coefficient of viscosity & 2. \( \left[M L^{-1} T^{-1}\right] \) \\
R. Planck constant & 3. \( \left[M L T^{-3} K^{-1}\right] \) \\
S. Thermal conductivity & 4. \( \left[M L^{2} T^{-2} K^{-1}\right] \) \\
\hline
\end{tabular}
\( A \cdot 3124 \)
B. 3 214
\( c \cdot 4213 \)
D. 4 1 2 3


If \( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{ll}\boldsymbol{x} & \text { for }-\boldsymbol{3}<\boldsymbol{x} \leq-1 \\ |\boldsymbol{x}| & \text { for }-1<\boldsymbol{x}<1 \\ |\boldsymbol{x}| & \text { for } \boldsymbol{x} \geq \mathbf{1}\end{array}\right. \)
then find \( \{\boldsymbol{x}: \boldsymbol{f}(\boldsymbol{x}) \geq \mathbf{0}\} \)
A \( \cdot(-1, \infty) \)
B. [-1,3]
c. (-1,3
D. \( I-1 \)


A glass flask of volume \( 200 \mathrm{cm}^{3} \) is just
filled with mercury at \( 20 C \). The amount of
mercury that will overflow when the
temperature of the system is raised to \( 100 C \) is: \( \gamma_{\text {glass}}=1.2 \times 10^{-5} / C^{\circ}, \gamma_{\text {mercury}}= \)
\( 1.8 \times 10^{-4} / C^{\circ} \)
A \( .2 .15 \mathrm{cm}^{3} \)
В. \( 2.69 c m^{3} \)
\( c .2 .52 c m^{3} \)
D. \( 2.25 \mathrm{cm}^{3} \)


If \( |z-2+i| \leq 2 \),then find the least
value of \( |z| \)


Two capacitors \( C_{1} \) and \( C_{2} \) are
connected in parallel. Assume that
\( C_{1}<C_{2} . \) The equivalent capacitance of
this arrangement is \( C, \) where
A. \( C<C_{1} / 2 \)
в. \( C_{1}<C<C_{1} \)
c. \( C_{1}<C<C_{2} \)
D. \( C_{2}<C<2 C_{2} \)


\( \mathbf{f} \boldsymbol{y}=\tan ^{-1}\left[\frac{\sqrt{\mathbf{1}+\boldsymbol{x}^{2}}-\mathbf{1}}{\boldsymbol{x}}\right], \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} ? \)


The activation energy of a reaction is zero. The rate constant of reaction:
A. increases with increase of temperature
B. decreases with decrease of temperature
c. decreases with increase of temperature
D. independent of temperature


Froth flotation process which is used for
the concentration of sulphide ore:
\( A . \) is based on the difference in wettability of different minerals
B. uses sodium ethyl xanthate, \( C_{2} H_{5} O C S_{2} N a \) as
collector
C. uses NaCN as depresent in the mixture of ZnS and PbS when ZnS forms soluble complex and PbS forms froth
D. All of the above are correct


Calculate \( \Delta G^{o} \) for the following
reaction:
\( \boldsymbol{C O}(\boldsymbol{g})+\frac{\mathbf{1}}{\mathbf{2}} \boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g}) ; \boldsymbol{\Delta} \boldsymbol{H}^{o}= \)
\( -282.84 k J \)
Given, \( S_{C O_{2}}^{o}= \)
\( 213.8 J K^{-1} m o l^{-1}, S_{C O(g)}^{o}= \)
\( \mathbf{1 9 7 . 9 J K}^{-1} \mathbf{m o l}^{-\mathbf{1}}, \boldsymbol{S}_{\boldsymbol{O}_{2}}^{\boldsymbol{o}}= \)
\( \mathbf{2 0 5 . 0} \boldsymbol{J} \boldsymbol{K}^{-1} \boldsymbol{m o l}^{-\mathbf{1}} \)


If \( f(x)=\cos u x+\cot x, \) find \( f^{\prime}\left[\frac{\pi}{4}\right] \)


Evaluate \( \int_{0}^{1}\left(x+x^{2}\right) d x \)


if the total surface area of a solid
hemisphere is \( 462 \mathrm{cm}^{2} \) find its volume


How will you find out the maximum number of electrons in the main energy level?
A . \( n \)
B. \( n^{2} \)
\( c \cdot 2 n^{4} \)
D. \( 2 n^{2} \)


Under hydrolytic conditions, the
compounds used for preparation of linear polymer and for chain termination respectively are:
B. \( \left(C H_{3}\right)_{2} \) SiCl \( _{2} \) and \( \left(C H_{3} \text { ) }_{3} \) SiCl \right.
c. \( \left(C H_{3}\right)_{3} \) SiCl \( _{2} \) and \( C H_{3} \) SiCl \( _{2} \)
D. \( \operatorname{SiCl}_{4} \) and \( \left(C H_{3}\right)_{3} \)SiCl


How increasing population is
responsible for water crises?
A. Increasing population creates demand for construction of houses this, in turn, decreases the seepage of rainwater into the ground.
B. Increasing population creates demand for construction of houses this, in turn, increases the seepage of rainwater into the ground.
C. both \( A \) and \( B \)
D. none of these


When connected to the \( 220 \mathrm{V} \) mains
supply, the current in a toaster, a kettle, a lamp and a fan is \( 5.2 \mathrm{A}, 9.4 \mathrm{A}, 0.5 \mathrm{A} \) and 2.6A respectively. Which appliance has the greatest electrical resistance?
A. toaster
B. kettlein
c. lamp
D. fan


A stone is dropped into water from a bridge \( 44.1 \mathrm{m} \) above the water. Another
stone is thrown vertically downward one second later. Both strike the water
simultaneously, then the initial speed of the second stone is
A \( \cdot 12.25 \mathrm{ms}^{-1} \)
B . \( 14.75 \mathrm{ms}^{-1} \)
c. \( 16.23 m s^{-1} \)
D. \( 17.15 \mathrm{ms}^{-1} \)


Which of the following is a tetrabasic acid?
A. Hypophosphorous acid
B. Metaphosphoric acid
c. Pyrophosphoric acid
D. orthophosphoric acid


A pendulum beats seconds on the earth. Its time period on a stationary satellite of the earth will be
A. zero
B. \( 1 s \)
\( c \cdot 2 s \)
D. Infinity


\( \boldsymbol{C H}_{3} \boldsymbol{C H}=\boldsymbol{C H}_{2} \stackrel{C l-\boldsymbol{I}}{\longrightarrow} \boldsymbol{P}, \boldsymbol{P} \) is:
A. \( C H_{3}-C H I-C H_{2} C l \)
в. \( C H_{3} C H C l-C H_{2} I \)
c. \( C H_{3}-I C H C l-C H_{2} \)
D. \( C H_{3}-C H_{2}-I C H C l \)


The ionization constant of a weak acid
is \( 1.6 \times 10^{-5} \) and the molar
conductivity at infinite dilution is \( 380 \times 10^{-4} S m^{2} m o l^{-1} . \) If the cell
constant is \( 0.01 \mathrm{m}^{-1} \) then conductance
of \( 0.01 M \) acid solution is:
A \( \cdot 1.52 \times 10^{-5} \mathrm{S} \)
в. \( 1.52 \times 10^{-7} \) S
c. \( 1.52 \times 10^{-3} \) S
D. \( 1.52 \times 10^{-4} \) S


We consider the radiation emitted by
the human body. Which of the following
statements if true?
A. The radiation is emitted during the summers and absorbed during the winters
B. The radiation emitted lies in the ultraviolet region and hence is not visible
C. The radiation emitted is in the infra-red region
D. The radiation is emitted only during the day


The alternating emf applied and the current flowing in an \( A C \) circuit are
represented by \( \boldsymbol{E}=\boldsymbol{E}_{0} \sin \omega \boldsymbol{t} \) and
\( I_{0} \sin \left(\omega t+\frac{\pi}{2}\right) \) respectively. The power
loss in the circuit will be
A . zero
в. \( \frac{E_{0} I_{0}}{2} \)
c. \( \frac{E_{0} I_{0}}{\sqrt{2}} \)
D. \( \frac{E_{0} I_{0}}{4} \)


In a buffer solution containing an
equal concentration of \( \mathrm{B}^{-} \) and \( \mathrm{HB} \), the \( \mathrm{K} \)
\( b \) for \( \mathrm{B}^{-} \) is \( 10^{-10} . \) The \( \mathrm{pH} \) of the buffer
solution is:
A . 10
B. 7
\( c \cdot 6 \)
D. 4


Show that any positive odd integer is of
the form \( 4 q+1 \) or \( 4 q+3 \) where \( q \) is
some integer.


Find the square root of \( 1024 . \) Hence find the value of \( \sqrt{10.24}+\sqrt{0.1024}+ \)
\( \sqrt{10240000} \)


Draw the diagram of dispersion of light through prism and show the position of different colours of light obtained on
screen


Let \( a_{1}, a_{2}, a_{3} \) and \( a_{4} \) be in AP. If \( a_{1}+ \)
\( a_{4}=10 \) and \( a_{2} \cdot a_{3}=24, \) then the least
term of them is
A . 1
B. 2
\( c .3 \)
D. 4
E. 5


Read the passage and answer the
following question.

Shigella is a bacterium that is very closely related to E. coli but is incapable of fermenting lactose (lactose negative). A gene for resistance to the
antibiotic ampicillin (amR) was inserted in between two of the
structural genes of the lac operon and then inserted into Shigella.
The effect of this insertion would be
A. The cell would immediately be resistant to ampicillin.
B. The cell would be resistant to ampicillin only in the presence of tryptophan
c. The cell would produce the enzyme \( \beta \) -lactamase as soon as it started to grow exponentially.
D. The cell would spontaneously utilize DNA-editing enzymes to restore the original genotye.
E. The cell would be resistant to ampicillin only in the presence of lactose.


Current 1 in a long \( 4 y- \) axis is paced through a square metal frame of side
\( 2 a \) oriented in the \( y-z \) p[lane a shown.
The linear mass density of the frame is
\( \lambda . \) A uniform magnetic field \( B \) is now
switched on along \( x- \) axis. Then the
instantaneous angular acceleration of
the frame will be:
A \( \cdot \frac{4 I B}{\lambda_{n}} \)
В. \( \frac{12 I B}{\lambda a} \)
c. \( \frac{4 I B}{3 \lambda a} \)
\( D \)


If the planes \( \boldsymbol{x}-\boldsymbol{b} \boldsymbol{z}=\mathbf{0}, \boldsymbol{c} \boldsymbol{x}-\boldsymbol{y}+=\mathbf{0} \)
and \( b x+a y-z=0, \) pass through a
line, then find the value of \( a^{2}+b^{2}+ \)
\( c^{2}+2 a b c \)
A.
B.
c. -1
D. \( \frac{1}{2} \)


Hydrogen resembles halogens in many respects for which several factors are responsible. Of the following factors which one is the most important in this respect?
A. Its tendency to lose an electron to form a cation
B. It tendency to gain a single electron in its valence shell to attain stable electronic configuration
c. Its low negative electron gain enthalpy value
D. Its small size


What do you understand by work?


Find the greater number in \( 300 ! \) and \( \sqrt{300^{300}} \)


Two pigment system theory of photosynthesis was proposed by
A. Hill
B. Blackman
c. Emerson
D. Arnon


un
connected in the circuit as shown in fig.
Initially capacitor A has no charge and
capacitor \( \mathrm{B} \) has \( \mathrm{CV} \) charge. Assume that
the circuit has no resistance at all. At
\( t=0, \) switch \( S \) is closed, then \( [ \) given \( \boldsymbol{L} \boldsymbol{C}=\frac{\boldsymbol{2}}{\boldsymbol{\pi}^{2} \times \mathbf{1 0}^{4}} \boldsymbol{s}^{2} \) and \( \boldsymbol{C V}=\mathbf{1 0 0 m C} \)
This question has multiple correct options
A. when current in the circuit is maximum, charge on each capacitor is same
B. when current in the circuit is maximum, charge on capacitor A is twice the charge on capacitor
C \( . q=50(1+\cos 100 \pi t) m C, \) where \( q \) is the charge on
capacitor B at time t
D. \( q=50(1-\cos 100 \pi t) m C \), where q is the charge on
capacitor B at time t


Fill in the blank: \( \left(-\frac{1}{3}\right)+ \) \( \left[\left(\frac{-4}{3}\right)+\frac{3}{7}\right]=\left[\left(\frac{-1}{3}\right)+\dots . .\right]+\frac{3}{7} \)
\( A \cdot \frac{-1}{3} \)
B. \( \frac{-4}{3} \)
\( c \cdot \frac{3}{7} \)
D. \( \frac{-3}{7} \)


What happen to cell if nucleus is
removed? Give reasons to support your
answer? (AS 1)


The three point \( \boldsymbol{A}(\mathbf{0}, \mathbf{0}, \mathbf{0}), \boldsymbol{B}(\mathbf{2},-\mathbf{3}, \mathbf{3}), \boldsymbol{C}(-\mathbf{2}, \mathbf{3},-\mathbf{3}) \) are
collinear. Find in what ratio each point
divides the segment joining other two


\( H_{3} P O_{2} \) is a weak monobasic acid.
A. True
B. False


Evaluate :
\( \lim _{n \rightarrow \infty} \frac{n !}{(n+1) !-n !} \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. 3


Which one of the following is a secondary alcohol?
A. 2-methyl-2-propanol
B. 1-propanol
c. 1-butanol
D. 2-pentanol


Hydrogen has high ionization energy than alkali metals because it has:
A. ionic bond
B. covalent bond
c. large size
D. small size


The value of \( c \) in Lagrange mean
value theorem for \( f(x)=\log (\sin x) \) in \( \left[\frac{\pi}{6}, \frac{5 \pi}{6}\right] \) is
This question has multiple correct options
A \( \cdot \frac{\pi}{4} \)
в. \( \frac{\pi}{2} \)
c. \( \frac{2 \pi}{3} \)
D. \( \frac{3 \pi}{4} \)


Figure shows two rays \( A \) and \( B \) being
reflected by a mirror and going as 'A'
and 'B'. The mirror
A. is plane
B. is convex
\( c . \) is concave
D. may be any spherical mirror


Lycopersicon esculentum belongs to the family
A. Solanaceae
B. Malvaceae
c. cruciferae
D. Cucurbitaceae


The value of \( \lim _{x \rightarrow b} \frac{\sqrt{x-a}-\sqrt{b-a}}{x^{2}-b^{2}} \) for
\( b>a \) is
A \( \cdot \frac{1}{4 b \sqrt{a-b}} \)
В. \( \frac{1}{4 b \sqrt{b-a}} \)
c. \( \frac{1}{4 a \sqrt{a-b}} \)
D. \( \frac{1}{b \sqrt{b-a}} \)


The compound interest on a certain
sum of money for 2 years at \( 10 \% \) per
annum is \( R s 420 . \) Find the simple
interest on the same sum at the same
rate anf for the same time.
A . \( R s 350 \)
B. \( R s 375 \)
c. \( R s 380 \)
D. \( R s 400 \)


Without using trigonometric tables,find the value of the following:
\( \left(\frac{\tan 20^{\circ}}{\operatorname{cosec} 70^{\circ}}\right)^{2}+\left(\frac{\cot 20^{\circ}}{\sec 70^{\circ}}\right)^{2}+ \)
\( 2 \tan 15^{\circ} \tan 45^{\circ} \tan 75^{\circ} \)


Which of the following is a halide ore?
A. Cassiterite
B. Anglesite
c. siderite
D. carnallite


Which one is the test for gibberellin?
A. Bolting in Cabbage
B. Morphogenesis in tobacco callus
C . Rapid division in Carrot cells
D. Elongation of Oat coleoptile


What is the action of the following reagents on ammonia?
Na metal.


Which of the following is not the correct
difference between I yophobic and
Iyophilic sols?
A. (Lyophobic sols) Require special methods for preparation (Lyophilic sols) Can be prepared by shaking with the solvent
B. (Lyophobic sols)Are reversible (Lyophilic sols) Are irreversible
C. (Lyophobic sols) Easily coagulated by electrolytes (Lyophilic sols)Cannot be easily coagulated
D. (Lyophobic sols) Are less stable (Lyophilic sols) Are more stable


A body freely falling from rest has a velocity v after it falls through distance
h.The distance it has to fall down further
for its velocity to becomes double is?


For the galvanic cell :
\( \boldsymbol{A l}(\boldsymbol{s})\left|\boldsymbol{A} \boldsymbol{l}^{3+}(\boldsymbol{a} \boldsymbol{q})(\boldsymbol{0} \cdot \boldsymbol{1} \boldsymbol{M})\right| \boldsymbol{A} \boldsymbol{g}^{+}(\boldsymbol{a} \boldsymbol{q})(\boldsymbol{0} \cdot \boldsymbol{1} \boldsymbol{M}) \)
which of the following is/are correct? This question has multiple correct options
A. Reaction quotient \( Q=1.0 \times 10^{-2} \)
в. \( \log _{10} Q=2 \)
c. \( Q=1.0 \times 10^{3} \)
D. \( Q=1.0 \times 10^{2} \)


Prove the following identities. \( \frac{1+\sin \alpha}{1+\cos \alpha} \cdot \frac{1+\sec \alpha}{1+\operatorname{cosec} \alpha}=\tan \alpha \)


For an atom of a given element, the number of electrons is given by
A. the number of protons \( + \) number of neutrons
B. the atomic number of the element
c. the number of proton - number of neutrons
D. the mass number of the element


Which of the following shows positive deviation from Raoult's law?
A. \( C_{6} H_{6} \) and \( C_{6} H_{5} C H_{3} \)
B . \( C_{6} H_{6} \) and \( C C l_{4} \)
c. \( C H C l_{3} \) and \( C_{2} H_{5} O H \)
D. \( C H C_{3} \) and \( C H_{3} C O C H_{3} \)


A bullet leaves the rifle of mass one kg and the rifle recoils thereby with a velocity of \( 30 \mathrm{cm} / \mathrm{s} \). If the mass of bullet is \( 3 g, \) find the velocity of the bullet.
\( \mathbf{A} \cdot 10 m / s \)
в. \( 100 \mathrm{m} / \mathrm{s} \)
c. \( 200 m / s \)
D. \( 50 m / s \)


The main defect of Bohr's atom model is
A. mixing of classical and quantum theories
B. exclusion of nuclear motion
c. failed to explain the fine structure of spectral lines
D. failed to explain larger atoms


The average velocity of gas molecules is \( 400 \mathrm{m} / \mathrm{sec} . \) Calculate its (rms) velocity
at the same temperature:


If \( \mathbf{A} \) is \( 3 x 4 \) matrix \( B^{T} \) is a matrix such
that \( A^{T} B \) and \( B A^{T} \) are both defined
then \( B \) is of the type
\( A \cdot 3 \times 4 \)
B. \( 3 \times 3 \)
c. \( 4 \times 3 \)
D. \( 4 \times 4 \)


The correctly reported difference of 16.4215 and 6.01 will have significant
figures equal to:
A. three
B. four
c. five
D. six


\( \mathrm{O}_{2} \) is denser than air and \( \mathrm{so} \), it is
collected over:
\( A \cdot H_{2} O \)
B. spirit
c. \( H g \)
D. kerosene oi


stated that Sun was the
centre of our universe and not Earth.
A. Albert Einstein
B. Isaac Newton
c. Nicolaus coppernicus
D. Galileo Galilei


Dentine is secreted by
A. Odontoblast
B. Elaioblast
c. osteoblast
D. Ehondroblast


Find the equations to the straight lines which are conjugate to the coordinate
axes with respect to the conic \( A x^{2}+ \)
\( 2 H x y+B y^{2}=1 \)
Find the condition that they may
coincide, and interpret the result.


A single wave is called
A. a wave pulse
B. a crest
c. a trough
D. a crest and a trough


Complete and balance the following
compound \( \boldsymbol{S n}+\mathbf{2 K O H}+\mathbf{4 H}_{\mathbf{2}} \boldsymbol{O} \rightarrow \)
\( t \)


Assertion: Dark periods play a more important part in flowering than light
period.

Reason: Flowering occurs in short-day plant if the dark period is interrupted by light break.
A. If both the assertion and reason are true and the reason is a correct explanation of the assertion
B. If both the assertion and reason are true but the reason is not a correct explanation of the assertion
c. If the assertion is true but the reaon is false
D. If both the assertion and reason are false
E. If the assertion is false but reason is true


I: The area bounded by the line \( y=x \)
and the curve \( y=x^{3} \) is \( 1 / 2 \) sq. units.
II: The area bounded by the curves \( \boldsymbol{y}= \)
\( x^{3} \) and \( y=x^{2} \) and the ordinates \( x=1 \)
\( x=2 \) is \( \frac{7}{12} \) sq. units.
Which of the above statement is
correct?
A. onlyı
c. Both I and II
D. Neither I nor II.


What is the ratio of the number of
neutrons present in potassium and magnesium atoms with mass number
39 and 24 respectively?
A .19: 12
2
B. 5: 3
\( c .5: 6 \)
D. 4: 3


Vessels and companian cells are
characteristic feature of
A. Gymnosperm
B. Angiosperm
c. Pteridophyta
D. Bryophyta


If the number \( 3 k+4,7 k+1 \) and \( 12 k- \)
5 are in A.P., then the value of \( k \) is
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5


\( 1^{0}, 2^{0}, 3^{0} \) and \( 4^{0} \) carbon atoms are
present in :
A. 2, 2, 3-trimethyl pentane
B. 2, 3, 4-trimethyl pentane
\( c . \) both \( (A) \) and \( (B) \)
D. none of these


Find out the angular acceleration of a washing machine, starting from rest, accelerates within \( 3.14 s \) to a point
where it is revolving at a frequency of
\( \mathbf{2 . 0 0 H z} \)
A. \( 0.100 r a d / s^{2} \)
B. \( 0.637 r a d / s^{2} \)
c. 2.00 rad \( / s^{2} \)
D. 4.00 rad \( / s^{2} \)
E \( .6 .28 \mathrm{rad} / \mathrm{s}^{2} \)


Guanine is an example of:
A. Nucleotide
B. Nucleoside
c. Purine base
D. Pyrimidine base


\( \left(x^{2}-y^{2}\right) \frac{d y}{d x}=x y . \) Solve the above
equation
A \( \cdot e^{-x^{2} / 2 y^{2}}=k x \)
B . \( e^{-x^{2} / 2 y^{2}}=k y \)
C \( \cdot e^{x^{2} / 2 y^{2}}=k x \)
D \cdot \( e^{x^{2} / 2 y^{2}}=k y \)


A parallel plate capacitor has 91 plates all are identical and arranged with same spacing between them. If the capacitance between adjacent plates is \( 3 p F . \) What will be the resultant
capacitance?
A . 273 pF
B . \( 30 p F \)
c. \( 94 p F \)
D. 270 \( p F \)


Identify the gas filled in the container \( A \)
and B:
A \( . N_{2}, N e \)
в. \( \mathrm{He}, \mathrm{H}_{2} \)
\( \mathrm{c} \cdot O_{2}, A r \)
\( \mathrm{D} \cdot A r, O_{2} \)


A reversible adiabatic path on a P-V diagram for an ideal gas passes
through sate A where \( \boldsymbol{P}=\mathbf{0 . 7} \times \) \( \mathbf{1 0}^{5} \boldsymbol{N} / \boldsymbol{m}^{-2} \) and \( \boldsymbol{v}=\mathbf{0 . 0 0 4 9} \boldsymbol{m}^{3} . \) The
ratio of specific heat of the gas is 1.4 The slope of path at \( A \) is:
A . \( 2.0 \times 10^{7} N m^{-5} \)
B . \( 1.0 \times 10^{7} \mathrm{Nm}^{-5} \)
c. \( -2.0 \times 10^{7} \mathrm{Nm}^{-5} \)
D. \( -1.0 \times 10^{7} \mathrm{Nm}^{-5} \)


Which of the following statements are
true:
A: Charge cannot exist without mass but mass can exist without charge
B: Charge is invariant but mass varies
with velocity
C: Charge is conserved but mass alone
may not be conserved
\( A \cdot A, B, C \) are true
B. A, B, C are not true
c. \( A, B \) are only true
D. \( A, B \) are false, \( C \) is true


Hormone involved in inhibition of
growth is
\( A \cdot \) ABA
B. Ethylene
c. None of the above
D. Both A and B


The perianth is the term used when
A. Androecium and gynoecium are similar
B. Androecium and calyx are similar.
C. Corolla and gynoecium are similar.
D. Calyx and corolla are similar


Which of the following is the correct arrangement of ligands in terms of field
strength?
A \( \cdot C l^{-}<F^{-}<N C S^{-}<N H_{3}<C N^{-} \)
B. \( N H_{3}<F^{-}<C l^{-}<N C S^{-}<C N^{-} \)
c. \( C l^{-}<F^{-}<N C S^{-}<C N^{-}<N H_{3} \)
D. \( N H_{3}<C N^{-}<N C S^{-}<C l^{-}<F^{-} \)


Friction is \( \quad \) in some situations.
A. desirable
B. undesirable
c. both \( A \) and \( B \)
D. none of the above


Name the switch/switches to be closed
so as to light all the three lamps
\( A \cdot 2 \) and
B. 1 and 3
c. only 2
D. 1 and


A small sphere of mass \( \boldsymbol{m}=\mathbf{1} \boldsymbol{k} \boldsymbol{g} \) is
moving with a velocity \( (4 \hat{i}-\hat{j}) m / s . \) It
hits fixed smooth wall and rebounds with velocity \( (\hat{\mathbf{i}}+\mathbf{3} \hat{\mathbf{j}}) \boldsymbol{m} / \boldsymbol{s} . \) The
coefficient of restitution between the
sphere and the wall is \( n / 16 . \) Find the
value of \( n \)


In the case of a zero-order reaction, the
ratio of time required for \( 75 \% \) completion to \( 50 \% \) completion is:
A \( . \ln 2 \)
B . 2
c. 1.5
D. none


Assertion
Xylem and, , phloem are also called as leptons and syndrome respectively
Reason

Xylem and phloem form conducting tissue of the plant
A. If both the assertion and the reason are true and the reason is a correct explanation of the assertion
B. If both the assertion and reason are true but the reason is not a correct explanation of the assertion
c. If the assertion is true but the reason is false
D. If both the assertion and reason are false


Two triangular walls of a flyover have been used for advertisements from both
sides. The sides of each wall are \( 120 \mathrm{m} \)
\( 110 \mathrm{m} \) and \( 20 \mathrm{m} . \) The advertisements
yield an earning of R.s 100 per \( m^{2} \) per
year. Find the amount of revenue earned
in one year. (Take \( \sqrt{7}=2.65) \)
A. Rs. 3,97,500
B. Rs. 3,47,500
c. Rs. 5,73,300
D. Rs. 4,73,500


\( \int x \sin x \sec ^{3} x d x= \)
A. \( \frac{1}{2}\left[\sec ^{2} x-\tan x\right]+c \)
B. \( \frac{1}{2}\left[x \sec ^{2} x-\tan x\right]+c \)
c. \( \frac{1}{2}\left[x \sec ^{2} x+\tan x\right]+c \)
D. \( \frac{1}{2}\left[\sec ^{2} x+\tan x\right]+c \)


Find domain and range of the function
\( f(x) \) given by \( f(x)=\frac{x}{1+x^{2}} \)
A. Domain \( =R \) and Range \( =N \)
B. Domain \( =N \) and Range \( =R \)
c. Domain \( =R \) and \( \operatorname{Range}=R \)
D. Domain \( =R-\{0\} \) and Range \( =N \)


The ionisation energy of the hydrogen atom is given to be \( 13.6 \mathrm{eV} \). A photon falls on a hydrogen atom which is initially in the ground state and excites it to the \( (n=4) \) state.
The wavelength of the photon is:
A \( \cdot 973.5 \AA \)
B \( \cdot 210 \stackrel{\circ}{A} \)
\( \mathrm{c} \cdot 389.3 \stackrel{\circ}{\mathrm{A}} \)
D. \( 849.6 \AA^{\circ} \)


The product of \( \frac{2}{3} x y \) and \( \frac{3}{2} x z \) is equal to
A \( \cdot \frac{1}{6} x y z \)
в. \( x^{2} y z \)
c. \( 6 x^{2} y z \)
D. none of these


A closed surface in the shape of a cube
is placed in a uniform electric field \( \boldsymbol{E} \)
along one of the sides of the cube as
shown here. The length of the side is \( l \)
The total electric flux through two
faces 1 and 2 is:
A . zero
B. \( -E l^{2} \)
\( c \cdot 2 E l^{2} \)
D. \( \frac{E l^{2}}{2} \)