10mL of gaseous hydrocarbon on
combustion gives \( 40 \mathrm{mL} \) of \( \mathrm{CO}_{2} \mathrm{g} \) and 50
\( \mathrm{mL} \boldsymbol{H}_{2} \boldsymbol{O}(\text { vapour }) . \) The hydrocarbon is:
A \( \cdot C_{4} H_{5} \)
в. \( C_{8} H_{10} \)
\( \mathbf{c} \cdot C_{4} H_{8} \)
D. \( C_{4} H_{10} \)


Alpha particles are projected towards fixed at a nucleus. Which of the paths
shown in figure, is not possible
\( A \)
B.
\( c \)
\( D \)


A buffer solution is prepared in which the concentration of \( N H_{3} \) is \( 0.30 M \) and
the concentration of \( N H_{4}^{+} \) is \( 0.20 M . \) If
the equilibrium constant, \( \boldsymbol{K}_{\boldsymbol{b}} \) for \( \boldsymbol{N} \boldsymbol{H}_{3} \)
equals \( 1.8 \times 10^{-5}, \) what is the pH of
this solution? \( (\log 2.7=0.433) \)
A . 9.08
B. 9.43
c. 11.72
D. 8.73


When the brakes are applied to bike the back seater moves forward why?
A. Due to height
B. Due to weight
c. Due to inertia
D. None


Which of the following animal has enucleated erythrocytes?
A. Earthworm
B. Cuttlefish
c. Frog
D. Rat


A neutral metal rod \( A B \) of length \( l \)
rotates with a constant angular velocity
\( \omega \) about an axis passing through 0 and normal to its length as shown in the figure.The potential difference between
\( A \& B \) will be:
(e is the charge of an electron)
A \( \cdot V_{A}-V_{B}=\frac{1}{3} \frac{m \omega^{2} l^{2}}{e} \)
в. \( \quad V_{A}-V_{B}=\frac{m l^{2} \omega^{2}}{e} \)
c. \( _{V_{B}-V_{A}}=\frac{1}{2} \frac{m \omega^{2} l^{2}}{e} \)
D. \( _{V_{B}-V_{A}}=\frac{1}{4} \frac{m \omega^{2} l^{2}}{e} \)


A rectangle and a parallelogram have equal areas. If the sides of the rectangle
are \( 10 m \) and \( 12 m \) and the base of the
parallelogram is \( 20 m, \) then the altitude of the parallelogram is:
A . \( 7 m \)
B. \( 6 m \)
\( c .5 m \)
D. \( 3 m \)


Which step(s) in glycolysis require the input of energy?
A. The glucose priming step
B. The phosphorylation of glucose
c. The phosphorylation of fructose 6-phosphate
D. All of these steps require the input of energy


A convex lens is immersed in a liquid,
whose refractive index is equal to the
refractive index of the material of the
lens. Then its focal length will
A. Decrease
B. Become zero
c. Become infinite
D. Increase


Represent the following mixed infinite decimal periodic fractions as common fractions:
\( \frac{2 \sqrt{b}}{\sqrt{a}+\sqrt{b}}+ \)
\[
\left(\frac{a^{3 / 2}+b^{3 / 2}}{\sqrt{a}+\sqrt{b}}-\frac{1}{(a b)^{-1 / 2}}\right)(a-b)^{-1}
\]


One mole of an ideal gas expands against a constant external pressure of
atm from a volume of \( 10 d m^{3} \) to a
volume of \( 30 d m^{3} . \) What would be the
work done in joules?
A \( .-2026 J \)
в. +20265
\( \mathrm{c} .-1947 \mathrm{J} \)
D. \( 1648 J \)


The most favourable conditons for
the formation of \( S O_{3} \) via the equation
\( \boldsymbol{S O}_{2}+\frac{1}{2} \boldsymbol{O}_{2} \rightarrow \boldsymbol{S} \boldsymbol{O}_{3}, \boldsymbol{\Delta} \boldsymbol{H}= \)
\( -95 k J m o l^{-1} \) are
A. Low concentration of reactants and high presure
B. High concentration of reactants and atmospheric pressure
C. High concentration of reactants and high pressure
D. Low concentration of reactants and atmospheric presure


\( \int \frac{3 x^{2}}{1+x^{6}} d x \)


Amongst the following, which is correct
about the metal sulphide sols?
A. The sol particles are positively charged due to preferential adsorption of metal ions
B. The sol particles are negatively charged due to preferential adsorption of sulphide ions
C. The anion of added electrolytes are effective in causing the coagulation of the sol
D. The sol is unstabilized due to both the electric charge and hydration of the particles


\( \operatorname{Let} \boldsymbol{f}(\boldsymbol{x})=\frac{\boldsymbol{9}^{\boldsymbol{x}}}{\mathbf{9}^{\boldsymbol{x}}+\mathbf{3}} \cdot \operatorname{Show} \boldsymbol{f}(\boldsymbol{x})+\boldsymbol{f}(\mathbf{1}- \)
\( x)=1, \) and hence evaluate \( f\left(\frac{1}{1996}\right)+f\left(\frac{2}{1996}\right)+ \)
\( \boldsymbol{f}\left(\frac{\mathbf{3}}{\mathbf{1 9 9 6}}\right)+\ldots+\boldsymbol{f}\left(\frac{\mathbf{1 9 9 5}}{\mathbf{1 9 9 6}}\right) \)


One of the factors required for the maturation of erythrocytes is
\( A \). Vitamin D
B. Vitamin A
c. vitamin B \( _{12} \)
D. vitamin C


The amplitude of simple harmonic motion represented by the displacement equation \( y(c m)=4(\sin 5 \) \( \pi t+\sqrt{2} \cos 5 \pi t) \) is :
\( A \cdot 4 \mathrm{cm} \)
B. \( 4 \sqrt{2} \mathrm{cm} \)
c. \( 4 \sqrt{3} \mathrm{cm} \)
D. \( 4(\sqrt{2}+1) \) cm


The reflected ray from a plane mirror is incident on another plane mirror which is placed perpendicular to the first. If the angle of incidence on the first mirror
is \( 30^{0}, \) determine the glancing angle of
reflection on the second mirror
A . \( 15^{\circ} \)
B . \( 120^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 30^{\circ} \)


For an ideal gas, the value of \( \left(\frac{d U}{d V}\right)_{T} \) is:
A. positive
B. zero
c. negative
D. interchangeable


For the combustion of benzene to
gaseous carbon dioxide and liquid water, \( \Delta H \) is more than \( \Delta U \)
A . True
B. False
c. Ambiguous
D. insufficient data


Find the value of \( x \) for which
\( (5 x+2),(4 x-1) \) and \( (x+2) \) are in
A.P


Explain what you understand by sexual reproduction.


Write the structure of chlorous acid
\( [\boldsymbol{H} \boldsymbol{O C l O}] \)


How many ascospores are found in an
ascus?
A. 6
B. 8
\( c \cdot 4 \)
\( D \)


The mean of 3 observations is 12 and
mean of 5 observations is 4 the
combined mean is
A. 7
B. 8
\( c \cdot 9 \)
D. 10


The units of molarity is \( m o l ~ l i t^{-1} \)
A. True
B. False


Tellurium forms which types of oxides?
A. Monoxide
B. Dioxide
c. Trioxide
D. All of the above


Determine the value of \( (x+y) \) if \( \left[\begin{array}{cc}2 x+y & 4 x \\ 5 x-7 & 4 x\end{array}\right]=\left[\begin{array}{cc}7 & 7 y-12 \\ y & x+6\end{array}\right] \)


Which of the following is/are true?
A. Acetylene is stored and transported in acetone solution.
B. Acetylene is soaked on porous solid like asbestos.
c. Acetylene is kept in steel cylinders under high pressure.
D. All of the above


At the college entrance examination each candidate is admitted or rejected according to whether he has passed or failed the tests. Of the candidate who
are really capable, \( 80 \% \) pass the test and of the incapable, \( 25 \% \) pass the test. Given that \( 40 \% \) of the candidates are
really capable, then the proportion of capable college students is about
A . \( 68 \% \)
B. 70\%
c. \( 73 \% \)
D. 75\%


Antibiotics are classfied into broad
spectrum antibiotics and narrow spectrum antibiotics. Write one example each for these antibiotics.


Dimensions of Gyromagnetic ratio are?
A \( \cdot\left[L^{1} M^{0} T^{1} I^{1}\right] \)
B . \( \left[L^{0} M^{-1} T^{1} I\right] \)
C \( \cdot\left[L^{1} M^{0} T^{0} I^{-1}\right] \)
D \cdot \( \left[L^{-1} M^{0} T^{1} I^{1}\right] \)


A ball is dropped from a height \( 8 \mathrm{m} \) on a smooth horizontal surface. If height attained by the ball after the second
collision is \( 2 \mathrm{m} \), then the coefficient of
restitution is :
A \( \cdot \frac{1}{4} \)
B. \( \frac{1}{2} \)
c. 1
D. \( \frac{1}{\sqrt{2}} \)


Chromosomes become visible during
A. Leptotene
B. Zygotene
c. Pachytene
D. Diplotene


Balance the following equation by
oxidation number method.
\( M n O_{4}^{2-}+H^{+} \rightarrow M n O_{2}+ \)
\( M n O_{4}^{-}+H_{2} O \)


Edible part in mushrooms is
A. Basidiospores
B. Mycelium
c. Pseudomycelium
D. Complete basidiocarp


What happens when white light passes through a glass prism?
A. Light dispersion and formation of a 7 colors spectrum.
B. Light dispersion and formation of a 6 colors spectrum.
c. Light reflection and a formation of a 6 colors spectrum.
D. Light reflection and a formation of a 7 colors spectrum.


Find the number of solutions of the
equations;
\( |\cot x|=\cot x+\frac{1}{\sin x}, \) where \( x \in \)
\( [0,2 \pi] \)


In a step-up transformer, the number of turns in the primary are than the
number turns in the secondary.
A. more
B. less
c. same as
D. None of the above


In the given figure, what is the
magnetic field at the point '0'?
A \( \cdot \frac{\mu_{0} I}{4 \pi r}+\frac{\mu_{0} I}{2 \pi r} \)
\( B \cdot \frac{\mu_{0}}{1 \pi} \)
C. \( \frac{\mu_{0} I}{4 r}+\frac{\mu_{0} I}{4 \pi r} \)
D. \( \frac{\mu_{0} I}{4 r}-\frac{\mu_{0} I}{4 \pi r} \)


The equation \( \frac{x^{2}}{2-r}+\frac{y^{2}}{r-5}+1=0 \)
represents an ellipse, if


Nitrogen is used to fill electric bulbs
because:
A. it is lighter than air
B. it makes the bulb to glow
c. it does not support combustion
D. it is non-toxic.


Evaluate:-
\( \lim _{x \rightarrow 36} \frac{x-36}{\sqrt{x}-6} \)


Two coherent point sound sources \( \boldsymbol{S}_{1} \)
and \( S_{2} \) are placed as shown in the
figure. Both are emitting sound of
frequency \( 165 \mathrm{Hz} . S_{1} \) is ahead of \( S_{2} \) in
phase by \( \pi- \) radian. (Speed of sound is
\( 330 \mathrm{m} / \mathrm{s} \) ) How many times maximum sound can be observed on line AB?
A. 7
B. 6
\( c \cdot 5 \)
\( D \)


Find the Particular solution of the
differential equations
\( x^{2} d y+\left(x y+y^{2}\right) d x=0 ; y=1 \) when
\( \boldsymbol{x}=\mathbf{1} \)


If \( P(n) \) is the statement \( n^{2}-n+41 \) is
prime, prove that \( \boldsymbol{P}(\mathbf{1}), \boldsymbol{P}(2) \) and \( \boldsymbol{P}(\boldsymbol{3}) \)
are true.
Prove also that \( P(41) \) is not true.


The high ionistion potential of magnesium compared with aluminium is due to:
A. filled orbitals in magnesium
B. high nuclear charge in magnesium
c. low radius of magnesium atom
D. low effective nuclear charge in magnesium


Which one of the following statements
İs incorrect?
A. In the aluminothermite process, aluminium acts as reducing agent
B. Lead is extracted from its chief ore by both carbon reduction and self-reduction.
C. Zinc is extracted from its chief ore by carbon reduction.
D. Extraction of gold involves the leaching of ore with cyanide solution followed by reduction with zinc.
E. In Hall-Heroult process, the electrolyte used is a molten mixture of alumina, sodium hydroxide and cryolite.


Safai karamcharis collect the garbage in trucks and take it to a low lying open area. This area is called as
A. Dust bin
B. Garbage
c. Landfill
D. waste


The decreasing basic order of the
following compounds is:
A \( \cdot(i)>(i i)>(i i i)>(i v) \)
B. \( (i v)>(i i i)>(i i)>(i) \)
c. \( (i i)>(i)>(i i i)>(i v) \)
D. \( (i i)>(i)>(i v)>(i i i) \)


LED stands for:
A. light emitting diode
B. loose emitting diode
C . light emission device
D. light emitting device


Three particles \( A, B \) and \( C \) of equal
mass move with equal speed \( V \) along the medians of an equilateral triangles as shown in the figure. They collide at
the centroid \( G \) of the triangle. After the
collision, \( A \) comes to rest, \( B \) retraces
its path with the speed \( V \). What is the velocity of \( C ? \)


\( \lim _{x \rightarrow 0}\left(\frac{x-\sin x}{x}\right) \sin \left(\frac{1}{x}\right) \)


4 mol of a solution containing \( \boldsymbol{A}^{\boldsymbol{n}} \) requires 1.6 mol of \( M n O_{4}^{\ominus} \) for the oxidation of \( A^{n+} \) to \( A O_{3}^{\ominus} \) in acidic
medium. The value of \( n \) is :
A . 1
B . 2
\( c .3 \)
D.


\( \sec ^{-1} x+\tan ^{-1} x \) is real if
\( \boldsymbol{x} \boldsymbol{\epsilon}(-\infty,-\boldsymbol{a}] \cup[\boldsymbol{b}, \infty) \)
Find the value of \( a+b \)
A . -1
B. 0
c.
D.


Two light waves are represented by
\( \boldsymbol{y}_{1}=\mathbf{4} \sin \omega \boldsymbol{t} \) and \( \boldsymbol{y}_{2}=\boldsymbol{3} \sin \left(\boldsymbol{\omega} \boldsymbol{t}+\frac{\pi}{2}\right) \)
The resultant amplitude due to interference will be
A \( .5 \mathrm{cm} \)
B. \( 7 \mathrm{cm} \)
c. \( 1 \mathrm{cm} \)
D.


The number of ways of arranging the letters \( A A A A A, B B B, D, E E \& F \) in a row
if the letter \( C \) are separated from one another is
\( \mathbf{A} \cdot_{13} s_{3} \cdot \frac{12 !}{5 ! 3 ! 2 !} \)
в. \( \frac{13 !}{5 ! 3 ! 2 !} \)
c. \( \frac{14 !}{3 ! 32 !} \)
D. none


In a series resonant L-C-R circuit, the
voltage across \( \mathrm{R} \) is \( 100 \mathrm{V} \) and \( \boldsymbol{R}=\mathbf{1} \boldsymbol{k} \boldsymbol{\Omega} \)
with \( C=2 \mu F . \) The resonant frequency
is 200 rads \( ^{-1} \). At resonance the voltage
across Lis:
A . \( 2.5 \times 10^{-2} V \)
В. \( 4 \times 10^{-8} V \)
c. \( 250 V \)
D. \( 4 \times 10^{-3} V \)


Arrange \( \frac{5}{8}, \frac{3}{16},-\frac{1}{4} \) and \( \frac{17}{32} \) in
descending order of their magnitudes, the sum of the lowest and the largest of these fractions is


The electric current flowing through a conductor is directly proportional to the across the two ends of the
conductor.
A. conductance
B. capacitance
c. inductance
D. potential difference


Select from below, how are temperature
and kinetic energy of molecules related
to each other?
A. Temperature is directly proportional to average kinetic
energy
B. Temperature is indirectly proportional to kinetic energy
C. Temperature and kinetic energy have no relation
D. Temperature is directly proportional to mechanical energy


In an examination, the probability of a candidate solving a question is \( \frac{1}{2} . \) Out of given 5 questions in the examination, what is the probability that the candidate was able to solve at least 2
questions?
A \( \cdot \frac{1}{64} \)
в. \( \frac{3}{16} \)
\( c \cdot \frac{1}{2} \)
D. \( \frac{13}{16} \)


In the given figure, QP II ML and other
angles are shown. Find the value of \( x \)
\( \mathbf{A} \cdot 60^{\circ} \)
B \( .35^{\circ} \)
\( c \cdot 20^{\circ} \)
\( D \cdot 30^{\circ} \)


Evaluate \( : \lim _{x \rightarrow 0} \frac{(1+x)^{1 / x}-e}{x}=? \)
A . 1
B . e/2
c. \( -\mathrm{e} / 2 \)
D. \( 2 / c \)


Calculate the electric potential
difference between the outside and the
inside cylinders in \( V \)


The saturated vapour pressure of water at \( 100^{0} \mathrm{C} \) is
A. \( 750 \mathrm{mm} \) o fHg
B. 760 mm of Hg
c. \( 76 \mathrm{mm} \) of \( \mathrm{Hg} \)
D. 7.6 mm of Hg


element has one
electron in its outermost shell and
attains duplet configuration after one more electron and attains stability.
A. Hydrogen
B. Fluorine
c. Helium
D. Berrylium


A wheel completes 2000 revolutions to cover the \( 9.5 \mathrm{km} \) distance, then the diameter of the wheel is
A . \( 1.5 \mathrm{m} \)
B. \( 1.5 \mathrm{cm} \)
c. \( 7.5 \mathrm{cm} \)
D. 7.5 \( m \)


Assuming that the degree of hydrolysis
is small, the \( p H \) of \( 0.1 \mathrm{M} \) solution of
sodium acetate \( \left(\boldsymbol{K}_{\boldsymbol{a}}=\mathbf{1 . 0} \times \mathbf{1 0}^{-\mathbf{5}}\right) \) will
be:
A. 6.0
B. 8.0.
\( c .9 .0 \)
D. 5.0


\( K C l \) is used in salt bridge because:
A. it forms a good jelly with agar-agar
B. it is a strong electrolyte
c. it is a good conductor of electricity
D. the transference number of \( K^{+} \) and \( C l^{-} \) ions are almost equal


Urethane is:
в.
\[
\mathrm{H}_{2} \mathrm{N}-\mathrm{C}-\mathrm{OH}
\]
c. \( H O-C \equiv N \)
D.
\[
\mathrm{H}_{2} \mathrm{N}-\underset{\mathrm{O}}{\|}-\mathrm{OC}_{2} \mathrm{H}_{5}
\]


The formation of violet colour when the
sodium nitroprusside is added to sodium extract indicates the presence
of :
A. Nitrogen
B. Sulphur
c. oxygen
D. Halogens


The end product of the decay of \( _{90}^{232} \) Th is \( 208 \mathrm{Pb} \). The number of alpha and beta
22
particles emitted are
A. 3,3
в. 6,4
c. 6,0
D. 4,6


Average per capita forest cover for the world is
A. 0.16 ha
B. 0.34 ha
\( c \cdot 0.64 \) ha
D. 1.06 ha


Solve
\( 4 x^{2}-7 x+5 \)


The structure which prevents the entry of food particles into the respiratory passage is
A. Epiglottis
B. Glottis
c. Larynx
D. Pharynx


Simplify and express the result in the form of a rational number :
\( \left(\frac{3}{11} \times \frac{2}{9}\right)+\left(\frac{-6}{21} \div \frac{1}{-42}\right)- \)
\( \left(-1 \frac{1}{3} \times \frac{9}{24}\right)-\left(\frac{-2}{7} \times-21\right) \)


A sphere of mass \( m \) and radius \( r \) is
placed on a rough plank of mass \( M . \) The
system is placed on a smooth
horizontal surface. A constant force \( \boldsymbol{F} \) is
applied on the plank such that the
sphere rolls purely on the plank. If the
acceleration of the sphere is \( \frac{2 F}{x M+2 m} \) find the value of \( x \)


Choose the correct answer among the alternatives given:
Study the following sequence of reaction and identify the compounds
\( (X) \) and \( (Y) \)
A. \( X= \) Benzaldehyde, \( Y= \) Benzoic acid
B. \( X=2 \) -Chlorotoluene, \( Y=2 \) -chlorobenzoic acid
c. \( X=2, \) 4 - Dichlorobenzene, \( Y= \) Benzoic acid


In a monoadelphous condition, stamens
have
A. Filaments of all united in one group but anthers are free
B. Filaments united in groups and anthers are absent.
C. Anthers are fused but filaments are free.
D. Both, anthers and filaments are fused.


Elements with low ionization potential
and high electron affinity form ionic
type of bonds. Which type of bonds are formed among the elements with high ionization potential and high electron
affinity?


Which of the following triangle is a type of triangle, classified on the basis of its sides?
A. Acute angle triangle
B. Right angle triangle
c. obtuse angle triangle
D. Equilateral triangle


Simplify:
(i) \( \left(a^{2}-b^{2}\right)^{2} \)
(ii) \( (2 x+5)^{2}-(2 x-5)^{2} \)
(iii) \( (7 m-8 n)^{2}+(7 m+8 n)^{2} \)
\( (i v)(4 m+5 n)^{2}+(4 n+5 m)^{2} \)
\( (v)(2.5 p-1.5 q)^{2}-(1.5 p-2.5 q)^{2} \)
\( (v i)(a b+b c)^{2}-2 a b^{2} c \)
\( (v i i)\left(m^{2}-n^{2} m\right)^{2}+2 m^{3} n^{2} \)


Select the odd one our w.r.t. porins.
A. Not associated with the inner membrane of plastids
B. Associated with the outer membrane of mitochondria
C. Found in outer membrane of gram positive bacteria
D. Allow movement of low molecular weight hydrophilic substances


Complete the following sentences:
Like charges \( \ldots \ldots, \) while unlike charges
each other.
A . attract, attract
B. repel, repel
c. attract, repel
D. repel, attract


Solve \( \sqrt{3} \sec 2 \theta=2 \)


A length of \( 150 \mathrm{cm} \) of a potentiometer wire is required to balance the emf of a cell. When a \( 5 \Omega \) resistor is connected
across the terminals of the cell, the
length required for balance is \( 125 \mathrm{cm} \)
The internal resistance of the cell is
A . 1 ohm
B. 1.1 ohm
c. 1.2 ohm
D. 1.3 ohm


f \( \mathbf{y}=\boldsymbol{a} \cos (\log \mathbf{x})+\mathbf{b} \sin (\log \mathbf{x}), \) then
\( \boldsymbol{x}^{2} \boldsymbol{y}^{\prime \prime}+\boldsymbol{x} \boldsymbol{y}^{\prime}= \)
A. \( -y \)
B.
\( c \cdot y \)
D. \( y^{2} \)


The middle term in the expansion of
\( (1+x)^{2 n} \) is
A. \( \frac{1.3 .5 \ldots(2 n-1)}{n} x^{n} \)
B. \( \frac{1.3 .5 \ldots(2 n-1)}{n !} 2^{n-1} x^{n} \)
c. \( \frac{1.3 .5 \ldots(2 n-1)}{n !} x^{n} \)
D. \( \frac{1.3 .5 \ldots(2 n-1)}{n !} 2^{n} x^{n} \)


Consider the statement, Given that
people who are in need of refuge and
consolation are apt to do odd things, it
is clear that people who are apt to do odd things are in need of refuge and consolation. This statement, of the form \( (P \Rightarrow Q) \Rightarrow(Q \Rightarrow P), \) is logically
equivalent to
A. People who are in need of refuge and consolation are not apt to do odd things.
B. People are apt to do odd things if and only if they are in need of refuge and consolation.
C. People who are apt to do odd things are in need of refuge and consolation.
D. People who are in need of refuge and consolation are apt to do odd things


Which among the following is not a disproportionation reaction i?
A \( \cdot 3 H_{3} P O_{3} \rightarrow 2 H_{3} P O_{2}+P H_{3} \)
c. \( 4 P+3 N a O H+3 H_{2} O \rightarrow P H_{3}+3 N a H_{2} P O_{2} \)
D. \( N H_{4} N O_{3} \rightarrow N_{2} O+2 H_{2} O \)


A solution containing 500 g of a protein per liter is isotonic with a solution
containing 3.42 g of sucrose per liter. The molecular mass of protein is:
\( A \cdot 58 \)
B. \( 146 \mathrm{g} \)
c. \( 34200 \mathrm{g} \)
D. 50000 \( g \)


The number of electrons in the valence
shell of group 1 elements.
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
\( D \)


Write down the number of significant figures in \( 0.00628 \mathrm{cm} \)
A. four
B. three
c. two
D. one


toppr
Q Type your question
\( A \)
\( B \)
\( c \)
\( D \)


An attribute found in plants but not
animals is
A. Metabolism
B. Sexual reproduction
c. Autotrophy
D. Asexual reproduction


Which of the following statement is/are
true?
This question has multiple correct options
\( \mathbf{A} \cdot C H_{2} C l-C H_{2} C l \) is a gem dihalide.
B. Alkyl iodides develops colour when exposed to light.
C. Halogenation of alkanes proceeds by addition mechanism.
D. Swarts reaction is used to prepare alkyl fluorides.


Carbon suboxide has the formula \( C_{3} O_{2} \)
\( \mathrm{C}-\mathrm{C} \) ditance are found to be \( 130 \mathrm{pm} \) and
\( \mathrm{C}-\mathrm{O} \) distances are \( 120 \mathrm{pm} . \) Lewis structures is \( \boldsymbol{O}=\boldsymbol{C}=\boldsymbol{C}=\boldsymbol{C}= \)
\( \boldsymbol{O}, \overline{\boldsymbol{O}}-\boldsymbol{C} \equiv \boldsymbol{C}-\boldsymbol{C} \equiv \boldsymbol{O}^{+} \)
If true enter 1 , else enter 0 .


What is the role of plants in controlling air pollution and soil erosion?


The properties of light can be best explained by assuming that light is composed of :
I particles
II : waves
III : atoms
A. I only
B. II only
c. I and ॥
D. II and III
E. I, II and III


Action of endocrine glands is mediated through
A. Hormones
B. Enzymes
c. Minerals
D. Vitamins


(a) For what kinetic energy of a neutron will the associated de

Broglie wavelength be \( 1.40 \times 10^{-10} \mathrm{m} ? \)
(b) Find the de Broglie wavelength of a neutron in thermal equilibrium with
matter having an average kinetic energy of \( (3 / 2) k T \) at \( 300 K \)


Which two moons are also called half
moons?
A. First Quarter \& Third Quarter
B. Waning Crescent \& Waxing Crescent
c. waxing crescent \& First Quarter
D. Full \& New Moon


At \( t=0, \) the position and velocities of
two particle are as shown in the figure. They are kept on a smooth surface and being mutually attracted by gravitational force. Find the position of
center of mass at \( t=2 s \)
A. \( X=5 \) m
в. \( X=7 m \)
c. \( x=3 \) т
D. \( X=2 m \)


Study the \( C_{1} \) bonding in the image
above. How does the strength of the \( C=O \) bond compare to the \( C-O H \)
bond?
A. The \( C=O \) bond is a stronger than the \( C-O H \) bond
B. The \( C=O \) bond is a weaker than the \( C-O H \) bond
C. The \( C=O \) bond and the \( C-O H \) bonds are of equal
strength.
D. The strength cannot be determined without knowing the average bond enthalpies.


The centroid of triangle \( \boldsymbol{A}(\mathbf{3}, \mathbf{4}, \mathbf{5}) ; \boldsymbol{B}(\mathbf{6}, \mathbf{7}, \mathbf{2}) ; \boldsymbol{C}(\mathbf{0},-\mathbf{5}, \mathbf{2}) \) is
A \( .(3,2,3) \)
в. (5,2,1)
c. (2,5,1)
D. (3,4,1)


Two identical plano-convex lenses
\( \boldsymbol{L}_{1}\left(\boldsymbol{\mu}_{1}=\mathbf{1} . \boldsymbol{4}\right) \) and \( \boldsymbol{L}_{2}\left(\boldsymbol{\mu}_{2}=\mathbf{1 . 5}\right) \) of radii
of curvature \( \boldsymbol{R}=\mathbf{2 0 c m} \) are placed as
shown in fig. Find the position of the image of the parallel beam of light
relative to the common principal axis.
A. \( 14.3 \mathrm{cm} \)
В. \( 22.2 \mathrm{cm} \)
\( c .31 .2 c m \)
D. \( 21.8 \mathrm{cm} \)


Statement \( 1: L i O H \) is considered a
strong base. Statement 2: It undergoes neutralization reactions with acids.
A. Both Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1
B. Both Statement 1 and Statement 2 are correct, but Statement 2 is NOT the correct explanation of Statement 1.
c. statement 1 is correct, but statement 2 is not correct
D. Statement 1 is not correct, but Statement 2 is correct


3 mole of \( A g \) is heated from \( 300 K \) to
1000 \( K \). Calculate \( \Delta H \) when \( P=1 \) at \( m \)
and \( C_{p}=23+0.01 T \)
A. \( 62 k J / m o l \)
B. \( 45 \mathrm{kJ} / \mathrm{mol} \)
c. \( 38 k J / m o l \)
D. \( 54 ~ k J / m o l \)


On the basis of quantum numbers, justify that the sixth period of the periodic table should have 32 elements.


Rate constant K varies with
temperature by equation
\[
\log K\left(m i n^{-1}\right)=\log 5-
\]
\( \frac{2000}{R T \quad X \quad 2.303} \) we can conclude that?
A. Pre-exponential factor A is \( 10^{5} \)
B . \( E_{a} \) IS \( 2000 \mathrm{K} \) cal
C. \( E_{a} \) is \( 9.12 \mathrm{K} \) cal
D. The pre-exponential factor A is 5


Select one donor impurity among the following:
Boron \( (B), \) Aluminium \( (A l), \) and Arsenic \( (A s) \)


An oxidation number can be:
A . positive
B. negative
c. zero
D. all of these


Of the following solutions, the one that
is acidic is:
A \( \cdot Z n S O_{4}(a q .) \)
в. \( \operatorname{NaAl}(O H)_{4}(\text {аq.}) \)
\( \mathbf{c} \cdot \operatorname{NaH} C O_{3}(a q) \)
D \( \cdot K N O_{3}(a q .) \)


Which of the following statement is
correct regarding induced electric field (symbols have their usual meanings)? This question has multiple correct options
A. Work done in moving a test charge in an induced electric field can be zero
B. Induced electric field is non-conservative is nature
C. Induced electric lines of force form closed loops
D. Induced e.m.f. in the loop in \( \varepsilon=\oint \vec{E} . \overline{d \iota}=-\frac{d \phi}{d t} \)


A carbohydrate \( X \) having molecular weight \( 180 g m o l^{-1} \) has one primary
alcohol group and four secondary alcoholic groups. It reacts with acetic anhydride to form pentaacetate. The molecular weight of pentaacetate formed is:
A. 180
в. 210
\( c .390 \)
D. 42


Let \( A=\{1,2\} \) and \( B=\{3,4\} . \) Write
\( A \times B . \) How many subsets will \( A \times B \)
have?


Which polysaccharide is a main constituent of cell wall in plants?


\( f(1,2,3,4,5\}, Y=\{1,3,5,7,9\} \)
determine which of the following relations from \( X \) to \( Y \) are functions?
Give reason for your answer. If it is a function, state its type.
(i) \( R_{1}=\{(x, y) \mid y=x+2, x \in X, y \in Y\} \)
(ii) \( R_{2}=\{(1,1),(2,1),(3,3),(4,3),(5,5)\} \)
(iii) \( R_{3}=\{(1,1),(1,3),(3,5),(3,7),(5,7)\} \)
(iv) \( R_{4}=\{(1,3),(2,5),(4,7),(5,9),(3,1)\} \)


Draw the diagram representing the schematic arrangement of the GeigerMarsdon experimental setup tor the alpha particle scattering.


An extinct bird of Mauritius is the
\( A \). Bubo
B. Dodo
c. Peacock
D. Pigeon


According to Henry's law 'the partial pressure of the gas in vapour phase \( (p) \) is proportional to the mole fraction of
the gas in solution. The correct statement about Henry's constant is:
A . higher the value of \( K_{H} \) at a given pressure, higher is the solubility of the gas
B. higher the value of \( K_{H} \) at a given pressure, lower is the solubility of the gas
\( \mathrm{c} \cdot K_{H} \) is not a function of nature of gas
D. \( K_{H} \) value for all gases is same at a given pressure


The correct statements about squaric
acid?
acid
A. It is stronger acid than phenol
B. It can form two conjugate base
C. It can liberate \( C O_{2} \) from \( N a H C O_{3} \)
D. The diconjugate base of squaric acid has all \( C-C \)
bond lengths are equal


The angle subtended at the centre of
circle of radius 3 metres by an arc of length 1 metre is equal to
A \( \cdot 20^{\circ} \)
B . \( 60^{\circ} \)
c. \( \frac{1}{3} \) radian
D. 3 radian


Which of the following molecules exists as a pair of enantiomers?
A. 2-Bromopropane
B. 1-Bromo-3-methylbutane
c. Cis-1,2-dichlorocyclobutane
D. 2-cyclohexen-1-ol


Digestion of protein is completed in
A. Stomach
B. Duodenum
c. lleum
D. Duodenum and ileum


Dyad is a pair of
A. sister chromatide
B. non-sister chromatids
C. homologous chromosomes
D. non-homologous chromosomes


If \( a \) and \( b \) are distinct integers, prove
that \( a-b \) is a factor of \( a^{n}-b^{n} \)
whenever \( n \) is a positive integer.


A boat is streamlined to reduce the
resistance to motion offered by water
A. True
B. False


Name two force in nature that have
longest and shortest range


The gas oxygen from thermal
decomposition of \( \left(N H_{4}\right)_{2} C r_{2} O_{7} \)
A. Oxygen
B. Nitric oxide
c. Ammonia
D. Nitrogen


We define p value of a term (say \( x \) ) as
\( p_{x}=-\log x . \) Sea water contains an
average of \( 1.08 \times 10^{3} \) ppm of \( N a^{+} \) and
270 ppm of \( S O_{4}^{2-} . \) Calculate \( 2 p_{S O_{4}^{2-}} \) for sea water.
[Write value to the nearest integer].


Find the values of \( c \) that satisfy the MVT for integrals on \( \left[\frac{3 \pi}{4}, \pi\right] \) \( \boldsymbol{f}(\boldsymbol{x})=\cos (\boldsymbol{2} \boldsymbol{x}-\boldsymbol{\pi}) \)
A \( \cdot c=\frac{5 \pi}{2}-\frac{1}{2} \cos ^{-1}\left(-\frac{2}{\pi}\right) \)
в. \( c=\pi-\frac{1}{2} \cos ^{-1}\left(-\frac{2}{\pi}\right) \)
\( c \cdot c=\frac{\pi}{2}+\frac{1}{2} \sin ^{-1}\left(-\frac{2}{\pi}\right) \)
D \( c=\frac{\pi}{2}+\frac{1}{2} \sin ^{-1}\left(\frac{2}{\pi}\right) \)


E. coli cells with a mutated Z gene of the
lac operon cannot grow in medium containing only lactose as the source of energy because
A. In the presence of glucose, E. coli cells do not utilize lactose
B. They cannot transport lactose from the medium into the cell.
c. The lac operon is constitutively active in these cells.
D. They cannot synthesize functional \( \beta \) -galactosidase.


The acceleration of block \( \mathrm{B} \) in the figure
will be:
\( \mathbf{A} \)
B.
c. \( \frac{2 M_{1} g}{\left(M_{1}+4 M_{2}\right)} \)
D. \( \frac{2 M_{1} g}{\left(M_{1}+M_{2}\right)} \)


Scouring soaps and soap powder contain soap along with:
A . lime
B. powdered pumice
c. \( A l_{2}\left(S O_{4}\right)_{3} \)
D. All of the above


Two plano-convex lenses each of focal
3
length \( 10 c m \) s refractive index \( \frac{-a r e}{2} \) are
placed as shown in the figure in the
space left, water \( \left(\boldsymbol{R} \boldsymbol{I}-\frac{\boldsymbol{4}}{\mathbf{3}}\right) \) is filled.The
whole arrangement is in air. The optical power of the system is (in dioptre):
A . 6.67
B . -6.67
\( c \cdot 33.3 \)
D. 20


Canal rays are:
A. alpha rays
B. light emitted when an electron falls into the nucleus
C. ionized gaseous atoms
D. light emitted when electron comes from a higher orbit to lower orbit


\( \boldsymbol{P b}+ \) Conc. \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) gives:
A \( \cdot P b\left(N O_{3}\right)_{2}+N O_{2} \)
в. \( P b\left(N O_{3}\right)_{2}+N O \)
c. \( P b\left(N O_{3}\right)_{2}+N O_{3} \)
D. \( P b\left(N O_{3}\right)_{2}+N_{2} O \)
E. None of these


The line \( \frac{x-2}{3}=\frac{y+1}{2}=\frac{z-1}{-1} \)
intersects the curve \( x y=c^{2}, z=0 \) if \( c \) is
equal to:
\( A \cdot \pm 1 \)
B. \( \pm \frac{1}{3} \)
\( \mathrm{c} \cdot \pm \sqrt{5} \)
D. None of these


Give the proper term for the following:
Finger-like projections of the smal intestine.


Study the following information carefully and answer the questions
given below.

The sub divided bar diagram given
below depicts the result of Class XII students of a school for three years.
The number of students passed with
second class in the year 2002 is
\( A \cdot 80 \)
в. 130
\( c .50 \)
D. 10


If two equal chords of a circle intersect
each other, then prove that the
segments of one chord are equal to
corresponding segment of the other
chord.


Find :
\( \cos \frac{\pi}{65} \cos \frac{2 \pi}{65} \cos \frac{4 \pi}{65} \cos \frac{8 \pi}{65} \cos \frac{16 \pi}{65} \)
A \( \cdot \frac{1}{64} \)
в. \( \frac{1}{32} \)
\( c \cdot \frac{1}{16} \)
D. None of these


The existence of the nucleus was
discovered by :
A. J. J. Thomson
B. Rutherford
\( c . \) Bohr
D. Goldstein


Name two features of procaryotes, one
of which should be about the genetic
material.


Itching causing \( _{-}-_{-}-_{-}- \) crystals are found in colocasia leaves.
A. calcium carbonate
B. calcium oxalate
c. calcium sulphate
D. calcium chloride


The number of moles of Grignard
reagent consumed per mole of the
compound is:
\( A \)
B.
\( c \)
\( D \)


The volume of an air bubble becomes
three times as it rises from the bottom
of a take to its surface.

Assuming atmospheric pressure to be \( 75 \mathrm{cm} \) of \( \mathrm{Hg} \) and the density of water to be \( \frac{1}{10} \) of the density of mercury, the
depth of the take is :
\( \mathbf{A} \cdot 5 m \)
в. 10 т
\( c .15 m \)
D. \( 20 m \)


Which of the following is incorrect
about the given graph?
A. The curve, is called oxygen dissociation curve
B. The part'A' represents percentage saturation of haemoglobin with oxygen
c. The part'B' represents partial pressure of carbon dioxide
D. This curve is highly useful in studying the effect of factors like \( P C O_{2} \), H+ concentration, etc. on binding
\( C O_{2} \) with haemoglobin


Point at which all rays converge is termed as
A. Converging point
B. Focal point
c. Focal center
D. Converging center


If \( x=(2+\sqrt{5})^{1 / 2}+(\sqrt{5}-2)^{1 / 2} \) and
\( y=(2+\sqrt{5})^{1 / 2}-(\sqrt{5}-2)^{1 / 2} \), then
evaluate \( x^{2}+y^{2} \).


\( \boldsymbol{x}+\boldsymbol{y}- \)
\( (z-x-[y+z-(x+y-\{z+x-(y \)
is equal to
A . \( 3 x \)
B. \( 2 y \)
c. \( x \)
D.


A half cell reaction: \( \boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{S}(\boldsymbol{s})+\boldsymbol{2} \boldsymbol{e}^{-} \rightarrow \)
\( \mathbf{3} A \boldsymbol{g}(s)+\boldsymbol{S}^{2-} \) is carried out in a half
\( \operatorname{cell} P t_{A g_{2}} s \mid A g, H_{2} S(0.1 M) \boldsymbol{a t}\left[\boldsymbol{H}^{\oplus}\right]= \)
\( 10^{-3}, \) The EMF of the half cell is:
\( \left[\boldsymbol{E}_{A \boldsymbol{g}^{\oplus} \mid \boldsymbol{A} \boldsymbol{g}}^{\ominus}=\mathbf{0 . 8 0} \boldsymbol{V}, \boldsymbol{K}_{a\left(\boldsymbol{H}_{2} \boldsymbol{S}\right)}=\right. \)
\( \left.\mathbf{1 0}^{-\mathbf{2 1}}, \boldsymbol{a n d} \boldsymbol{K}_{s p} \boldsymbol{o} \boldsymbol{f} \boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{S}=\mathbf{1 0}^{-49}\right] \)
\( \mathbf{A} \cdot-0.1735 V \)
в. \( -0.19 V \)
c. \( +0.1735 V \)
D. \( +0.19 V \)


The burning of fossil fuels causes air
pollution, acid rains and increases the temperature of the globe.
A. True
B. False


A small block of mass of \( 0.1 k g \) lies on a
fixed inclined plane PQ which makes an
angle \( \theta \) with the horizontal. A horizontal
force of \( 1 ~ N \) acts on the block through
its center of mass as shown in the
figure. The block remains stationary if
\( \left(\operatorname{take} g=10 m / s^{2}\right) \)
This question has multiple correct options
\( \mathbf{A} \cdot \theta=45^{\circ} \)
B. \( \theta>45^{\circ} \) and a frictional force acts on the block towards
\( P \)
C \( \cdot \theta>45^{\circ} \) and a frictional force acts on the block towards
Q.
D. \( 45^{\circ} \) and a frictional force acts on the block towards \( Q \).


Which of the following is not correctly
matched?
A. Hard soaps - sodium salts of fatty acids
B. Soft soaps - potassium salts of fatty acids
C. \( \mathrm{CMC} \) - used to keep the dirt suspended in water
D. Hydrophilic - water insoluble


The associated figure shows an electric
charge \( +q \) located at the centre of a hollow uncharged conducting metal sphere. Outside the sphere is a second
charge \( +Q . \) Both charges are positive.
Choose the description below that
describes the net electrical forces on
each charge in this situation.
A. Both charges experience the same net force directed
B. No net force experienced by either charge.
c. There is no net force on Q but a net force on q
D. There is no net force on q but a net force on \( Q \)
E. Both charges experience a net force but they are diff


The dominant factor in determining the IE of the elements on moving down the groups is its:
A. atomic radius
B. effective nuclear charge
c. Both (a) and (b)
D. None of the above


The earth behaves as a magnet with magnetic field pointing approximately from the geographic
A. North to South
B. South to North
c. East to west
D. west to East


A body cools from \( 70^{\circ} \mathrm{C} \) to \( 60^{\circ} \mathrm{C} \) in 8
minute. The same body cools from \( 60^{\circ} \mathrm{C} \)
to \( 50^{\circ} \mathrm{C} \) in
A. 8 minute
B. less than 8 minute
c. More than 8 minute
D. 1 or 2 or 3 , depending on the specific heat of the body


Which of the following is not an
accessory excretory organ of vertebrates?
A. skin
B. Lungs
c. Liver
D. Heart


Choose the incorrect relation among the following:
A . Ampere = \( \frac{\text { coulon }}{\text { secodd }} \)
B. Volt = cooulom
\( \mathrm{c} \cdot \mathrm{ohm}=\frac{\mathrm{Vort}}{\text {Ampere}} \)
D. 1 coulomb \( =6.25 \times 10^{18} \) electroncharg


Calcium carbonate reacts with aqueous
\( H C I \) to give \( C a C l_{2} \) and \( C O_{2} \) according
to the reactions:
\( \boldsymbol{C a C O}_{3(s)}+\mathbf{2 H C l}_{(a q)} \rightarrow \boldsymbol{C a C l}_{2(a q)}+ \)
\( \boldsymbol{C O}_{2(g)}+\boldsymbol{H}_{2} \) OWhat mass of \( \boldsymbol{C a C O}_{3} \) is
required to completely react with
\( 25 m L \) of \( 0.75 M H C l ? \)
A \( .0 .253 \mathrm{g} \)
B. \( 0.425 \mathrm{g} \)
c. \( 0.9375 \mathrm{g} \)
D. None of these


The \( [X e F]^{+} \) ions are attached to anion
\( \left[\boldsymbol{A} \boldsymbol{s} \boldsymbol{F}_{6}\right]^{-}: \)
A. with a linear F-bridge
B. with an angular F-bridge
c. with H-bond
D. with tetrahdral F-bridge


Change of the position of an object with respect to the observer is called.
A. speed
B. distance
c. displacement
D. motion


Attempt the following:
The table gives the ages of husbands and wives:
Find:
a. The marginal frequency
distribution of the age of husbands.
b. The conditional frequency distribution of the age of husbands
when the age of wives lies between 25
35
\begin{tabular}{|c|c|c|c|c|}
\hline Age of wires (in years) & \multicolumn{3}{|c|} { Age of husbands (in years) } \\
\hline \( 15-25 \) & \( 20-30 \) & \( 30-40 \) & \( 40-50 \) & \( 50-60 \) \\
\hline \( 25-35 \) & \( - \) & 9 & 3 & \( - \) \\
\hline \( 35-45 \) & \( - \) & 10 & 25 & 2 \\
\hline \( 45-55 \) & \( - \) & \( - \) & 4 & 2 \\
\hline \( 55-65 \) & \( - \) & \( - \) & \( - \) & 16 \\
\hline
\end{tabular}


Assertion: When a solution of
\( C H_{3} C O O H \) in water is shaken with
charcoal, the pH of the solution will get decreased.
Reason: The degree of ionisation of
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H} \) increases.
Read the above assertion and reason
and choose the correct option regarding
¡t.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
E. Both Assertion and Reason are incorrect


The value / values of \( x \) is/are
\( \mathbf{A} \cdot \pm 5 \sqrt{5} \)
B. \( \pm \sqrt{5} \)
\( ^{\mathrm{c}}+\frac{1}{\sqrt{5}} \)
D. none of these


Dog is an example of class
A. Amphibia
B. Aves
c. Mammalia
D. None of the above


Let \( S_{n} \) denotes the sum of first \( n \) terms
of an A.P. If \( S_{3 n}=5 S_{n}, \) then \( S_{2 n}: S_{n} \)
A .8: 3
B. 3: 8
c. 6: 1
D. 2: 3


Prove that \( \frac{\tan \theta}{1-\cot \theta}+\frac{\cot \theta}{1-\tan \theta}=1+ \)
\( \sec \theta \operatorname{cosec} \theta \)


Mark the correct alternative of the
following.
The angles of a triangle are in the ratio \( 2: 3: 7 . \) The measure of the largest angle is?
\( A \cdot 84^{\circ} \)
B. \( 91^{\circ} \)
\( c \cdot 105 \)
D. \( 98^{\circ} \)


The ratio of the corresponding sides of
the two similar triangles is 2: 3 and the
area of the smaller triangle is 64 sq.cm.
Find the area of larger triangle.


Which of the following halides has the least dipole moment?
A. 1,2 -Dichlorobenzene
B. Dichloromethane
c. Trichloromethane
D. Ethyl chloride


What is the next term to this series, 2 \( 3,7,16,32, \) and \( 57, \dots \)
A . 94
B. 93
c. 92
D. 95


The binding of the substrate induces
the enzyme to alter its shape fitting more tightly around the substrate.


Two projectiles, one fired from the surface of the earth with speed \( 5 m / s \) and the other fired from the surface of a
planet with initial speed \( 3 m / s, \) trace identical trajectories. Neglecting friction effect the value of acceleration
due to gravity on the planet is:
A. \( 5.9 \mathrm{m} / \mathrm{s}^{2} \)
в. \( 3.5 \mathrm{m} / \mathrm{s}^{2} \)
\( \mathbf{c} \cdot 16.3 \mathrm{m} / \mathrm{s}^{2} \)
D. \( 8.5 \mathrm{m} / \mathrm{s}^{2} \)


An ideal mono-atomic gas of given
mass is heated at constant pressure. In this process, the fraction of supplied energy used for the increase of the
internal energy of the gas is
A \( \cdot \frac{3}{8} \)
B. \( \frac{3}{5} \)
\( c \cdot \frac{3}{4} \)
D. \( \frac{2}{5} \)


It takes 10 minutes to cool a liquid
from \( 61^{\circ} \mathrm{C} \) to \( 59^{\circ} . \) If room temperature
is \( 30^{\circ} C \) then time taken in cooling from
\( 51^{\circ} C \) to \( 49^{\circ} C \) is
A . 10 min
B. 11 min
c. 13 min
D. 15 min


Hexa ammine nickel (II) hexa nitro
cobaltate (III) can be written as:
\( \mathbf{A} \cdot\left[N i\left(N H_{3}\right)_{6} C o\left(N O_{2}\right)_{6}\right] \)
B . \( \left[N i\left(N H_{3}\right)_{6}\right]_{3}\left[C o\left(N O_{2}\right)_{6}\right]_{2} \)
c. \( \left[N i\left(N H_{3}\right)_{6}\right]\left[C o\left(N O_{2}\right)_{6}\right]_{2} \)
D. \( \left[N i\left(N H_{3}\right)_{6}\left(N O_{2}\right)_{6}\right] C o \)


Find all possible integers whose
geometric mean is 16
A \( .(1,256),(2,128),(4,64),(8,32),(16,16) \)
B . (1,256),(2,128),(4,64),(16,1),(1,16)
C \( .(1,256),(4,4),(4,64),(8,32),(16,16) \)
D. (1,256),(2,128),(1,4),(8,32),(16,16)


Multiplication of a negative integer for
even times gives a result
A. negative
B. 0
c. positive
D. none


Conductivity of \( C a C l_{2} \) solution is:
A \( \cdot 4.87 \times 10^{-4} \mathrm{Scm}^{1} \)
B. \( 7.84 \times 10^{-4} \mathrm{Scm}^{1} \)
c. \( 8.47 \times 10^{-4} \mathrm{Scm}^{1} \)
D. None of these


Among the following, the isoelectronic species is/ are:
(i) \( \boldsymbol{O}^{2-}, \boldsymbol{F}^{-}, \boldsymbol{N} \boldsymbol{a}^{+}, \boldsymbol{M} \boldsymbol{g}^{2+} \)
\( (\text { ii }) N a^{+}, M g^{+}, A l^{3+}, F^{-} \)
(iii) \( N^{3-}, O^{2-}, F^{-}, N e \)
\( A \cdot \) (i) and (ii)
B. (i), (ii) and (iii)
c. (ii) and (iii)
D. (i) and (iii)


Two identical bullets are fired one by a light rifle and another by a heavy rifle with the same force. Which rifle will
hurt the shoulder more and why?
A. Light rifle
B. Heavy rifle
c. Both of them will hurt equally
D. None of these


The process employed for the purification of copper with cuprous oxide as the impurity is:
A . poling
B. liquation
c. electrolytic process
D. oxidation


Two absolute scales \( A \) and \( B \) have triple points of water defined to be 200 A and \( 300 \mathrm{B} \) (given triple point of water is \( = \)
276.16 K). The relation between \( T_{A} \) and
\( T_{B} \) is
A \( \cdot T_{A}=T_{B} \)
В \( \cdot T_{B}=\frac{3}{2} T_{A} \)
c. \( _{T_{B}}=\frac{2}{3} T_{A} \)
D. \( T_{B}=\frac{3}{4} T_{A} \)


I. Conductance of electrolyte solution increases with temperature.
II. Resistivity is reciprocal of molar conductivity of electrolyte.
III. Cell constant has unit \( c m^{-1} \)
Which of the above statements are
correct?
A. All the statements are correct
B. II and III are correct
c. I and III are correct
D. Only II is correct


The Lanthanoid have the genera
configuration
A \( \cdot 5 f^{1-14} 5 s^{2} p^{6} d^{0-1} 6 s^{2} \)
B . \( (n-2) f^{1-14}(n-1) d^{1-2} n s^{2} \)
\( \mathbf{c} \cdot 5 f^{1-14} 6 s^{2} p^{6} 6 s^{2} \)
D. \( n s^{2} n p^{1-6} \)


Use the following data for the gas phase decomposition of hydrogen iodide to find the average rate of the reaction in moles HI/litre over the first 2 hours.
t, hours \( \quad \) o \( \quad 2 \quad \) 4
\[
\begin{array}{llll}
\text { [HI], M } & 1 & 0.5 & 0.33
\end{array}
\]
A. 0.25
B. 0.35
\( c \cdot 0.5 \)
D. 2


The common feature among the species
\( C N^{-}, C O \) and \( N O^{+} \) are:
A. bond order three and isoelectronic
B. bond order three and weak field ligands
c. bond order two and \( \pi \) -acceptors
D. isoelectronic and weak field ligands


Resistance of \( 0.2 M \) solution of an
electrolyte is \( 50 \Omega \). The specific
conductance of the solution is \( 1.4 S \)
\( m^{-1} . \) The resistance of \( 0.5 M \) solution
of the same electrolyte is \( 280 \Omega \). The molar conductivity of \( 0.5 ~ M \) solution of
the electrolyte in \( S m^{2} m o l^{-1} \) is:
A \( .5 \times 10^{3} \)
В . \( 5 \times 10^{2} \)
c. \( 5 \times 10^{-4} \)
D. \( 5 \times 10^{-3} \)


When one molar concentrations of
reactants are taken, rate of reaction is
equal to:
A. molar concentration
B. reaction rate
c. rate constant
D. equilibrium rate


Benzene and toluene form ideal solution
occur the entire range of composition
The vapour pressure of pure benzene and toluene at \( 300 K \) are \( 50: 71 \mathrm{mm} \)
\( H g \) and \( 32.06 \mathrm{mm} H g \) respectively
calculate the mole fraction of benzene
is vapour phase if \( 80 g \) of benzene is mixed \( [100 \mathrm{g} \text { of toluene }] \)


Very Short Answer Types:
Name the connecting link between
glycolysis and the Krebs cycle.


A group 13 element \( X \) reacts with
chlorine gas to produce a compound
\( X C l_{3} . X C l_{3} \) is electron deficient and
easily reacts with \( N H_{3} \) to form
\( \boldsymbol{C l}_{3} \boldsymbol{X} \rightarrow \boldsymbol{N} \boldsymbol{H}_{3} \) adduct; however, \( \boldsymbol{X} \boldsymbol{C l}_{3} \)
does not dimerize \( \boldsymbol{X} \) is:
A. \( B \)
в. \( A l \)
\( c . G a \)
D. In


Variable valency of transition elements is
on account of :
A. incomplete s - orbitals
B. incomplete d - orbitals
C . completely filled d- orbitals
D. incomplete p-orbitals


If \( y=\cos ^{-1} \cos x, \) then \( \frac{d y}{d x} \) at \( x=\frac{5 \pi}{4} \)
A . 1
в. - 1
c. \( \frac{1}{\sqrt{2}} \)
D. \( \frac{5 \pi}{4} \)


Very short answer type. How many molecules of oxygen can one haemoglobin molecule transport?


The length of the rod is \( 150 \mathrm{cm} \) at \( 25^{\circ} \mathrm{C} \)
Find its length when it is heated \( 150^{\circ} \mathrm{C} \)
\( \left(\alpha \operatorname{steel}=2.2 \times 10^{-5} /^{o} C\right) \)


In a Wheatstone's bridge, there resistances \( P, Q \) and \( R \) connected in the three arms and the fourth arm is
formed by two resistances \( S_{1} \) and \( S_{2} \) connected in parallel. The condition for bridge to be balanced will be :
\( ^{\text {A } \cdot \frac{P}{Q}}=\frac{R}{S_{1}+S_{2}} \)
в. \( \frac{P}{Q}=\frac{2 R}{S_{1}+S_{2}} \)
c. \( \frac{P}{Q}=\frac{R\left(S_{1}+S_{2}\right)}{S_{1} S_{2}} \)
D. \( \frac{P}{Q}=\frac{R\left(S_{1}+S_{2}\right)}{2 S_{1} S_{2}} \)


single-celled eukaryotes are included in
A. Monera
B. Protista
c. Fungi
D. Archaea


State whether true or false:
Coins can be made up of pure metals.
A. True
B. False


Evaluate the given integral. \( \int e^{x}\left(\frac{\sin x \cos x-1}{\sin ^{2} x}\right) d x \)


Which one of the following is correct with reference to haemodialysis?
A. Absorbs and resends excess of ions
B. The dialysis unit has a coiled cellophane tube
C. Blood is pumped back through a suitable artery after haemodialysis
D. Anti-heparin is added prior to haemodialysis


\( i^{n} . i^{n+1} i^{n+3}= \)
\( \mathbf{A} \cdot(i)^{n} \)
B. \( -i \)
\( \mathbf{C} \cdot(-i)^{n} \)
D. 1


The digits 4,5,6,7 and 8 written in every possible order. The number of numbers greater than 56,000 is
\( \mathbf{A} \cdot 78 \)
B. 72
c. 90
D. 88


At the end of glycolysis, X is the net energy gain from one molecule of glucose via \( Y \), but there is also energy stored in the form of Z. identify \( X, Y, \) and
Z.
A. \( x \) -1 ATP ; Y-Oxidative phosphorylation ; Z- NADH+H
B. X- 2 ATP ; Y-Oxidative phosphorylation; Z- NADH+H
c. \( x \) - 1АTP ; Y-Substrate level phosphorylation ; z\( F A D H_{2} \)
D. x- 2ATP ; Y-substrate level phosphorylation; zNADH+H \( ^{+} \)


Neon gas is used in neon signs.
A. True
B. False


Mark correct option or options.
A. The body of greater mass needs more forces to move due to more inertia
B. Force versus time graph gives impulse
C. Microscopic area of contact is about \( 10^{-4} \) times actual area of the contact
D. All of the above


If the area and the circumference of
circle are numerically equal, then the radius the circle is
\( ^{A} \cdot \frac{5}{2} \)
B. 2
c. 1
D. 2 \( \overline{5} \)


Assertion
Ultraviolet radiations of higher
frequency waves are dangerous to human being
Reason
Ultraviolet radiation are absorbed by
the atmosphere
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Find the least number which must be
added to the following number so as to get a perfect square. 1750
A . 26
в. 209
c. 14
D. 50


Mankind has existed for about \( 10^{6} \)
years whereas the universe is about
\( 10^{10} \) years old. If the age of universe is taken to be one day, for how many seconds has the mankind existed?
A . \( 10 \mathrm{sec} \)
B. 8 sec
c. 8.64 sec
D. 64 sec


If pressure and temperature of an ideal gas are doubled and volume is halved, the number of molecules of the gas
A. becomes half
B. becomes two times
c. becomes 4 times
D. remains constant


The brownish yellow colour of nitric acid is removed by :
A. bubbling air through warm acid
B. bubbling acid
c. passing ammonia through acid
D. adding little \( M g \) powder


Why is phosphorus stored in water?
A. It is very reactive
B. It does not react with water
C. It reacts with air and catches fire
D. All of the above


Vestibule is constituted by
A. Semicircular canals and utriculus
B. Sacculus and utriculus
C. Sacculus and ampullae
D. Ampullae and lagena


Faraday can be defined as:
A. the magnitude of the charge of 1 mole of electrons
B. the magnitude of the electric dipole
C. a fundamental constant of nature equal to \( 6.63 \times \) \( 10^{-34} J s / \)photon
D. a constant that accounts for the existence of ions in
solution
E. the assignment of charges to individual atoms


In the figure shown, a spherical part of
\( \boldsymbol{R} \)
radius \( \frac{-k}{2} \) is removed from a bigger solid
sphere of radius \( R \). Assuming uniform mass distribution, shift in the centre of
mass will be:
\( A \cdot \frac{R}{7} \)
в. \( \frac{R}{14} \)
\( c \cdot \frac{R}{9} \)
D. \( \frac{R}{6} \)


The reading of a manometer fitted to a closed tap is \( 3.5 \times 10^{5} N m^{2} . \) If the valve
is opened the reading of the manometer falls to \( 3 \times 10^{5} N m^{2} . \) The velocity of
water is :
A \( \cdot 0.1 m s^{-} \)
B. \( 1 m s^{-1} \)
\( \mathrm{c} \cdot 10 \mathrm{ms}^{-1} \)
D. \( 100 \mathrm{ms}^{-1} \)


Dietician has to develop a special diet using two foods \( P \) and \( Q . \) Each packet (containing \( 30 g \) ) of food \( P \) contains 12
units of calcium, 4 units of iron, 6 units
of cholesterol and 6 units of vitamin \( A \)
while each packet of the same quality of food \( Q \) contains 3 units of calcium, 20 units of vitamin A. The diet requires atleast 240 units of calcium, atleast
460 units of iron and almost 300 units
of cholesterol. How many packets of each food should be used to maximize
the amount of vitamin \( A \) in the diet?
What is the maximum amount of
vitamin A?


What is power of accommodation?


Let \( \boldsymbol{f}(\boldsymbol{x})=\cos \boldsymbol{x} \) and \( \boldsymbol{g}(\boldsymbol{x})=[\boldsymbol{x}+\mathbf{2}] \)
where [.] denotes the greatest integer function. Then, \( (g o f)^{\prime}\left(\frac{\pi}{2}\right) \) is?
\( \mathbf{A} \cdot \mathbf{1} \)
B.
c. -1
D. Does not exist


All temperatures in the absolute (Kelvin) scale are in positive figures.
Give the reasons.


The length of latus rectum of the ellipse \( 4 x^{2}+9 y^{2}=36 \) is
A \( \cdot \frac{4}{3} \)
B. \( \frac{8}{3} \)
\( c .6 \)
D. 12


Complete the following sentence:
The current is induced in a closed
circuit only if there is
A. change in number of magnetic field lines linked with the circuit.
B. no change in number of magnetic field lines linked with the circuit
C. change in number of gravitational field lines linked with the circuit.
D. no change in number of gravitational field lines linked with the circuit.


The magnetic induction at 0 due to a current in conductor shaped as shown
in figure is:
A \( \cdot \frac{\mu_{0} i}{4 \pi}\left[\frac{3 \pi}{2 a}+\frac{\sqrt{2}}{b}\right] \)
В \( \cdot \frac{\mu_{0} i}{4 \pi}\left[\frac{3 \pi}{4 a}-\frac{\sqrt{2}}{b}\right] \)
\( ^{\text {c. }} \cdot \frac{\mu_{0} i}{2 \pi}\left[\frac{3 \pi}{4 a}-\frac{1}{\sqrt{2} b}\right] \)
D. \( \frac{\mu_{0}}{2 \pi}\left[\frac{1}{a}+\frac{1}{b}\right. \)


The equation of the standing wave in a string clamped at both ends, vibrating in its third harmonic is given by : \( y= \) \( 0.4 \sin (0.314 x) \cos (600 \pi t) \) where, \( x \)
and \( y \) are in \( \mathrm{cm} \) and \( t \) in sec.
a) the frequency of vibration is \( 300 H z \)
b) the length of the string is \( 30 \mathrm{cm} \)
c) the nodes are located at \( x= \)
\( 0,10 c m, 30 c m \)
A. a,
в. а,
\( c \cdot b, c \)
D. a,b,


Grills of doors and windows are
always painted before they are used :
A. To look beautiful
B. To avoid corroison
c. To protect from rain
D. None of these


Which of the following is the composition of red lead?
A. \( P b O \)
в. \( P b O_{2} \)
\( \mathbf{c} \cdot P b_{3} O_{4} \)
D. \( P b I_{2} \)


A. wavelength of microwave is greater than that of ultraviolet rays.
B. The wave length of infrared rays is lesser than that of ultraviolet rays.
C. wavelength of microwave is lesser than that of ultraviolet rays
D. Gamma rays has shortest wavelength in the electromagnetic spectrum. Choose the correct option from the
given options.
\( A \). A and \( B \) are true
B. B and C are true
c. \( c \) and \( D \) are true
D. A and D are true


Why shouldn't one stand under a tree or
a tall building during a thunderstorm?
A. Lightning can strike trees and buildings,
B. Trees and buildings may fall causing damage,
C. Trees and buildings do not offer enough escape ground,
D. None of the above,


Na is used in reduction of \( Z n \) salt
because:
A \( \cdot E Z n(o x i)>E N a(o x i) \)
B . \( E Z n(r e d)<E N a(r e d) \)
C. \( E Z n(o x i)<E N a(o x i) \)
D. Both (A) and (B)


Erythropoietin is produced by
A. Thymus
B. Pituitary
c. Heart
D. Kidney


The first order rate constant for the
decomposition of ethyl iodide by the
reaction:
\( \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{I}(\boldsymbol{g}) \rightarrow \boldsymbol{C}_{2} \boldsymbol{H}_{4}(\boldsymbol{g})+\boldsymbol{H} \boldsymbol{I}(\boldsymbol{g}) \)
at \( 600 \mathrm{K} \) is \( 1.60 \times 10^{-5} s^{-1} . \) Its energy
of activation is \( 209 \mathrm{kJ} \) mol\( ^{-1} \). The rate
constant of the reaction at \( 700 \mathrm{K} \) will be:
A \( .2 .88 \times 10^{-3} s^{-1} \)
В. \( 2.96 \times 10^{-3} s^{-1} \)
c. \( 2.76 \times 10^{-3} s^{-1} \)
D. None of these


If sale price is \( R s .200 \) and \( \mathrm{CST} \) is \( R s .4 \)
then find the actual selling price


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) for \( \boldsymbol{y}= \)
\( \sin ^{-1}\left(\frac{\boldsymbol{6} \boldsymbol{x}-\boldsymbol{4} \sqrt{\boldsymbol{1}-\boldsymbol{4} \boldsymbol{x}^{2}}}{\mathbf{5}}\right) \)


A movie projector forms real images. Why is it not inverted?
A. Real images are erect in nature
B. Final image is formed using virtual image
c. Multiple mirrors are used
D. Films are inverted


If \( \operatorname{Tr}(\mathbf{A})=\mathbf{8}, \operatorname{Tr}(\mathbf{B})=\mathbf{6}, \operatorname{Tr}(\mathbf{A}-\mathbf{2 B})= \)
A . -4
B. 4
\( c \cdot 2 \)
D. 11


Differentiate between Orbit and Orbital.


Assertion
\( \mathbf{9} \mathbf{2} \mathbf{3} \mathbf{U}(\boldsymbol{I} \boldsymbol{I} \boldsymbol{I} \boldsymbol{B})-\boldsymbol{\alpha} \quad \boldsymbol{A} \)
\( \boldsymbol{B} \stackrel{-\boldsymbol{\beta}}{\longrightarrow} \boldsymbol{C} \)
Reason
Element \( \boldsymbol{B} \) will be of \( \boldsymbol{I} \boldsymbol{I} \boldsymbol{A} \) group.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The snow on the mountain does not
melt all at once when it is heated by the sun because it
A. Becomes very hard
B. reflects most of the heat from the sun
c. has a low specific heat capacity
D. has a high latent heat of fusion


The equation of perpendicular bisector of the line segment joining the points (-1,-2) and (2,0) is
A \( .5 x+2 y=1 \)
в. \( 4 x+6 y=-1 \)
c. \( 6 x+4 y=-1 \)
D. none of these


A \( 5.80 \mu F \) parallel-plate air capacitor
has a plate separation of \( 5.00 \mathrm{mm} \) and is charged to a potential difference of \( 400 \mathrm{V} . \) Calculate the energy density in
the region between the plates, in \( J / m^{3} \)


Bond length is maximum in:
Refer above image.
\( A \)
B.
\( c \)
\( \mathbf{C H}_{3}-\ddot{\mathbf{C}} \mathbf{H}=\stackrel{*}{\mathbf{C}} \mathbf{H}-\mathbf{C H}_{3} \)
D.


\( X \) and \( Y \) are two radioactive isobars.
Then the daughter nuclei formed after the emission of a \( \beta \) particle from each
of them are
A. isosters
B. isotones
\( c . \) isobars
D. isotopes


The number of turns in the primary and secondary of a transformer are, respectively 100 and \( 50 . \) If the input power and input current are, respectively \( 60 \mathrm{W} \) and \( 1 \mathrm{A} \), and the efficiency of the transformer is
\( 0.95, \) then, the output power and the output current will be, respectively
\( A \cdot 60 \mathrm{W}, 2 \mathrm{A} \)
B. \( 60 \mathrm{W}, 1 \mathrm{A} \)
c. \( 57 \mathrm{w} \), 2 \( \mathrm{A} \)
D. 57 W, 1.9 A


Assertion : If the amplitude of a simple harmonic oscillator is doubled, its total
energy becomes double. Reason : The total energy is directly proportional to the amplitude of vibration of the harmonic oscillator.
A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true and reason is not the correct explanation of assertion.
c. If assertion is true but reason is false
D. If both assertion and reason are false


Fill in the blank.
Shrillness: \( _{\text {toudness : }} \)
Amplitude
\( A \). Pitch
B. Speedd
c. Frequency
D. None of the above


A pack of cards is counted with face downwards. It is found that one card is
missing, One card is drawn and is found
to be red. Find the probability that the missing card is red.


Let \( n \) be a natural number and \( X= \)
\( \{1,2, \dots \dots, n\} . \) For subsets \( A \) and \( B \) of
\( X, \) we denote \( A \Delta B \) to be the set of all
those elements of \( X \) which belong to
exactly one of \( A \) and \( B . \) Let \( F \) be a
collection of subsets of \( X \) such that for
any two distinct elements \( A \) and \( B \) in \( F \)
the \( \operatorname{set} A \Delta B \) has at least two elements.
Show that \( F \) has at most \( 2^{n-1} \) elements
Find all such collections \( \boldsymbol{F} \) with \( \mathbf{2}^{n-1} \)
elements.


\( [(\sqrt{\mathbf{3}}+i)(\sqrt{\mathbf{3}}-i)]^{-\mathbf{3} / 2} \)
\( A \cdot \frac{1}{8} \)
B. \( \left(\frac{1}{8}\right)^{1 / 2} \)
\( c \cdot \frac{1}{4} \)
D.


Biodegradable wastes are deposited in land fills and are converted into
A. compost
B. dust
c. pesticides
D. none of these


Which letter corresponds to the closest representation of \( \sqrt{7} \) on the number line
below?
A. \( A \)
в. \( B \)
\( c . c \)
D. \( D \)


If the magnification of a body of size \( 1 \mathrm{m} \) is \( 2, \) what is the size of the image?
\( A \cdot 1 m \)
в. 2m
\( c \cdot 3 m \)
\( D \cdot 4 m \)


The rate of the first order reaction,
\( A \longrightarrow \) Products, is \( 7.5 \times 10^{-4} \) mol
\( L^{-1} s^{-1}, \) when the concentration of \( A \) is
0.2 mol \( L^{-1} . \) The rate constant of the
reaction is:
A \( \cdot 2.5 \times 10^{-5} s^{-1} \)
в. \( 8.0 \times 10^{-4} s^{-1} \)
D. \( 3.75 \times 10^{-3} s^{-1} \)


Switch \( \mathrm{S} \) is closed at \( \mathrm{t}=0 . \) After
sufficiently long time an iron rod is inserted into the inductor L. Then, the
bulb :
A. glows more brightly
B. gets dimmer
c. glows with the same brightness
D. gets momentarily dimmer and then glows right


Two thin infinite parallel sheets have uniform surface densities of charge \( +\sigma \)
and \( -\sigma . \) The value of \( E \) in the
space outside the sheets is:
A \( \cdot \frac{\sigma}{\epsilon_{0}} \)
в. \( \frac{\sigma}{2 \epsilon_{0}} \)
c. zero
D. \( \frac{2 \sigma}{\epsilon_{0}} \)


The major product obtained in the
following reaction is:
A \( \cdot C_{6} H_{5} C H=C H C_{6} H_{5} \)
\( \mathbf{B} \cdot(+) C_{6} H_{5} C H\left(O^{t} B u\right) C H_{2} C_{6} H_{5} \)
\( \mathbf{c} \cdot(-) C_{6} H_{5} C H\left(O^{t} B u\right) C H_{2} C_{6} H_{5} \)
\( \mathbf{D} \cdot(\pm) C_{6} H_{5} C H\left(O^{t} B u\right) C H_{2} C_{6} H_{5} \)


Top view of a block on a table is shown
\( \left(g=10 m / s^{2}\right) \)
Find out the acceleration of the block.
A. 0.6
3. 0.8
\( c .1 . \)
D. 0.5


The ligand \( N\left(C H_{2} C H_{2} N H_{2}\right)_{3} \)
A. bidentate
B. tridentate
c. tetradentate
D. pentadentate.


Find the value of \( 1.05 \times 0.95 \) using
standard identity
A . 0.9985
B. 0.9975
c. 0.9875
D. 0.9995


Which of the following has highest boiling point?
A. \( C_{2} H_{5} O H \)
в. \( C H_{3} \) СООН
c. \( C H_{3} \) СОСН \( _{3} \)
D. \( C_{2} H_{6} \)


Read the given statements and select
the correct option.
Statement 1: Bryophytes are amphibians of plant kingdom. Statement 2 : They live in soil but
depend on water for sexual
reproduction.
A. Both statements 1 and 2 are correct
B. Statement 1 is correct but statement 2 is incorrect
c. statement 1 is incorrect but statement 2 is correct.
D. Both statements 1 and 2 are incorrect.


The height of mercury which exerts the
same pressure as \( 20 \mathrm{cm} \) of water column, is
A \( .1 .47 \mathrm{cm} \)
B. \( 14.8 \mathrm{cm} \)
\( c \cdot 148 \mathrm{cm} \)
D. none of these


A certain number of spherical drops of a liquid of radius 'r' coalesce to form a
single drop of radius 'R' and volume 'V'. If 'T' is the surface tension of the liquid
then:
A . Energy \( =4 V T\left(\frac{1}{r}-\frac{1}{R}\right) \) is released
B . Energy \( =3 V T\left(\frac{1}{r}+\frac{1}{R}\right) \) is released
C. Energy \( =3 V T\left(\frac{1}{r}-\frac{1}{R}\right) \) is released
D. Energy is neither released nor absorbed


is used in the preparation of chloroform, sulphonal, cordite etc.
A. formalin
B. ethyl alcoho
c. acetone
D. none of these


A bus decreases its speed from 60 \( \mathrm{km} / \mathrm{hr} \) to \( 30 \mathrm{km} / \mathrm{hr} \) in 5 sec. Find the
acceleration of the bus.


The path difference between the two waves \( y_{1}=a_{1} \sin \left(\omega t-\frac{2 \pi x}{\lambda}\right) \) and
\( \boldsymbol{y}_{2}=\boldsymbol{a}_{2} \cos \left(\boldsymbol{\omega} \boldsymbol{t}-\frac{\boldsymbol{2} \boldsymbol{\pi} \boldsymbol{x}}{\boldsymbol{\lambda}}+\boldsymbol{\phi}\right) \)
\( ^{A} \cdot \frac{\lambda}{2 \pi} \)
в. \( \frac{\lambda}{2 \pi}\left(\phi+\frac{\pi}{2}\right) \)
c. \( \frac{\lambda}{2 \pi}\left(\phi-\frac{\pi}{2}\right) \)
\( D \cdot \frac{2 \pi}{\lambda} d \)


Find the nearest integer to the cube root
of 331776:


A shell is fired from a cannon with a
speed of \( 100 \mathrm{m} / \mathrm{s} \) at an angle \( 30^{\circ} \) with the horizontal (positive \( y- \) direction). At the highest point of its trajectory, the
shell explodes into two equal fragments
of masses in the ratio \( 1: 2 . \) The lighter
fragment moves vertically upwards with an initial speed of \( 200 \mathrm{m} / \mathrm{s} \). What is the
speed of the other fragment at the time of explosion?


Hydrogen gas is prepared in the laboratory by reacting dilute \( H C l \) with granulated zinc. Following reaction takes place:
\( Z n+2 H C l \rightarrow Z n C l_{2}+H_{2} \)
What would be the volume of hydrogen gas is liberated at STP when 32.65 g of zinc reacts with \( \boldsymbol{H} \boldsymbol{C l} \) ?
A . \( 10.03 \mathrm{L} \)
B. 11.35 L
c. \( 11.57 \mathrm{L} \)
D. 9.53 L


The eggs of which parasite are bile stained
A. Ascaris lumbricoides
B. Ancylostoma duodenale
c. Enterobius vermicularis
D. Necator Americans


is the only rational number which is equal to its additive inverse.
A .
B. - 1
c. 0
D. \( \frac{1}{2} \)


If a body is projected with certain
velocity making an angle \( 30^{\circ} \) with the horizontal, then
A. its horizontal velocity remains constant
B. its vertical velocity changes
c. on falling to the ground its vertical displacement is zero
D. All of the above


Liquid chlorine boils at:
\( \mathbf{A} \cdot-24.6^{\circ} \mathrm{C} \)
B. \( -44.6^{\circ} \mathrm{C} \)
c. \( -14.6^{\circ} \mathrm{C} \)
D. \( -34.6^{\circ} \mathrm{C} \)


The radius of nucleus varies with mass
no. as \( A^{1 / n} . \) The value of \( n \) is :


Two sides of a triangle are \( 12 \mathrm{cm} \) and
14 cm. The perimeter of the triangle is
\( 36 \mathrm{cm} . \) What is the length of third side


Name the petroleum product used for surfacing of roads.


The sum of the coefficient of first 3
terms in the expansion \( \left(x-\frac{3}{x^{2}}\right)^{m} \) in
\( 559 . \) Find the term of the expansion containing \( \boldsymbol{x}^{\mathbf{3}} \)


In mesophytes, maximum transpiration
occurs through
A. Cuticle
B. Lenticel
c. Stomata
D. Hydathodes


A certain sum of money, lent out at compound interest, amounts to Rs.
14,520 in 2 years and to Rs. 17,56920 in 4
years. Find the rate of interest per annum and the sum.


toppr
Q Type your question
the following:
4
B.
\( c \)
\( D \)


Given that the events \( A \) and \( B \) are such
\( \operatorname{that} \boldsymbol{P}(\boldsymbol{A})=\frac{1}{2}, \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B})=\frac{\boldsymbol{3}}{\mathbf{5}} \) and
\( \boldsymbol{P}(\boldsymbol{B})=\boldsymbol{p} . \) Find \( \boldsymbol{p} \) if they are (i)
mutually exclusive (ii) independent.
A . 0.5,0.6
в. 0.1,0.2
c. 0,2,0.4
D. 0.1,0.6


When does a gas deviate the most from its ideal behavior?
A. At low pressure and high temperature
B. At high pressure and high temperature
c. At low pressure and low temperature
D. At high pressure and low temperature


A bead of mass \( 1 / 2 \) kg starts from rest
from A to move in a vertical plane along
a smooth fixed quarter ring of radius
\( 5 m, \) under the action of a constant
horizontal force \( F=5 \mathrm{N} \) as shown in Fig.
\( 8.263 . \) The speed of bead as it reaches
point B is
A . \( 14.14 m s^{-1} \)
B. \( 7.07 \mathrm{ms}^{-1} \)
\( \mathrm{c} \cdot 5 \mathrm{ms}^{-1} \)
D. \( 25 \mathrm{ms}^{-1} \)


The sum of \( n \) terms of an \( A P \) is \( 3 n^{2}+5 n \)
find the AP. Hence find its \( 16^{t h} \) term.


Differentiate between the following pairs on the basis of what is mentioned in brackets :
(i) Photolysis and Photophosphorylation (Definition)
(ii) Bicuspid valve and Tricuspid valve. (Function)
(iii) Vasectomy and Tubectomy. (Explain)
(iv) Cerebrum and Spinal cord. (Arrangement of nerve cells)
(v) Bowman's capsule and Malpighian
capsule. (Parts included)


Identify the solute \( \& \) the solvent in the following solution:
a) sugar solution
b) Air
c) Rain water
d) Aerated drinks


Oxidation number of \( C r \) in the following
compounds are \( \boldsymbol{x}, \boldsymbol{y}, \boldsymbol{z} \) and \( \boldsymbol{w} \)
respectively. \( \boldsymbol{K}[\underset{\boldsymbol{x}}{\boldsymbol{C r} \boldsymbol{O}\left(\boldsymbol{O}_{2}\right)(\boldsymbol{O} \boldsymbol{H})}], \quad \boldsymbol{K}_{\boldsymbol{3}}[\underset{\boldsymbol{y}}{\boldsymbol{C r}\left(\boldsymbol{O}_{2}\right)_{4}}] \)
These values are, respectively:
A. 6,13,5,6
в. 4,4,4,6
c. 4,5,4,6
D. 4,5,6,6


At which depth, we get the necessary temperature for OTEC in the ocean?
\( A \cdot O m \) to \( 20 m \)
B. 100 m to 300 m
c. \( 400 \mathrm{m} \) to \( 600 \mathrm{m} \)
D. 700 \( \mathrm{m} \) to \( 900 \mathrm{m} \)


If magnetic field produced by a straight current carrying wire at a distance 10cm from it is X. Then the magnetic field produced at a distance \( 29 \mathrm{cm} \) will be
\( A \cdot>x \)
B.
D. all
December 27, 2019
Anjan Chatterjee
\( B \)
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A cloud carries a charge of 1000 C at a potential of \( 5 \mathrm{kV} \). If the cloud discharge,
the amount of energy released:
A \( .5 \times 10^{6} J \)
В. \( 2.5 \times 10^{6} J \)
\( c \cdot 10^{7} J \)
D \( .5 \times 10^{3} J \)


Haemoglobin in the blood cells mainly contains:
A. Iron
B. copper
c. zinc
D. Silver


If \( a_{1}, a_{2}, a_{3}, \dots, a_{n} \) are in A.P. and \( a_{i}>0 \) for all i, then show that \( \frac{1}{a_{1} a_{2}}+\frac{1}{a_{2} a_{3}}+ \)
\( \ldots+\frac{1}{a_{n-1} a_{n}}=\frac{n-1}{a_{1} a_{n}} \)


Which of the following statement is
correct?
A. Acetophenone is an ether
B. Diastase is an enzyme
c. cycloheptane is aromatic
D. All of the above


The magnitude of charge present on one azide ion in coulombs is:
\( \mathbf{A} \cdot 96500 \)
B . \( 4.8 \times 10^{19} \)
c. \( 4.8 \times 10^{-19} \)
D. \( 1.6 \times 10^{-19} \)


ratio \( \boldsymbol{O P}: \boldsymbol{O} \boldsymbol{D}=\boldsymbol{m}: \boldsymbol{n} . \) Find \( \boldsymbol{m}+\boldsymbol{n} \)


The index of refraction of diamond is
2.0. The velocity of light in diamond in cm/s is -
A \( .6 \times 10^{10} \)
В. \( 2 \times 10^{10} \)
C \( .3 \times 10^{10} \)
D. \( 1.5 \times 10^{10} \)


Name and state the principle of a simple a.c. generator. What is its use?


In \( \triangle A B C, \angle A=45^{\circ} \) and \( \angle B=65^{\circ} \)
Name the side of the triangle which is
shortest


If \( \boldsymbol{A}=\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right] \) then show
that for all the positive integers \( n A^{n}= \) \( \left[\begin{array}{cc}\cos n \theta & \sin n \theta \\ -\sin n \theta & \cos n \theta\end{array}\right] \)


The position vectors of \( \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C}, \boldsymbol{D} \) are
\( \vec{a}, \vec{b}, 2 \vec{a}+3 \vec{b} \) and \( \vec{a}-2 \vec{b} \) respectively
Show that \( \overrightarrow{D B}=3 \vec{b}-\vec{a} \) and \( \overrightarrow{A C}= \) \( \vec{a}+3 \vec{b} \)


Write the IUPAC name of the following compound.
\( \boldsymbol{H}-\boldsymbol{C H}=\boldsymbol{C H}-\boldsymbol{C H}_{3} \)


From the following figure, choose the
statements that are correct.
i) Congruent chords have congruent
\( \operatorname{arcs} \)
ii) Congruent chords have equal centra
angles.
iii) Congruent arcs have congruent
central angles.
iv) Chords equidistant from the center
are congruent.
A. ii and iii only
B. iii and iv
D. All of the above


Which of the following is a consequence of atmospheric pressure?
A. Drinking a soft drink through a straw
B. Natural breathing process
c. working of a liquid dropper
D. All of these


In a 1 lit. container following equilibrium
is established with equal moles of \( N O_{2} \)
(g) \( \& N_{2} O_{4}(g) \)
\( N_{2} O_{4}(g) \rightleftharpoons 2 N O_{2}(g), \) at equilibrium
\( M_{\text {avg.}}=\frac{184}{3}, \) thenratioofK_\( \{\mathrm{C}\} \$ \$ 8 \)
total initial moles is.
A. 3
B. 3/2
c. 27/4
D. 6


In geometry, we take a point, a line and a plane as undefined terms.
A. True
B. False
c. Ambiguous
D. Data Insufficient


\( \mathbf{A B} \)


Figure shows two processes a and b for
a given sample of a gas> If \( \triangle Q_{1}, \triangle Q_{2} \) are the amounts of heat absorbed by
the system in the cases and \( \triangle \boldsymbol{U}_{1}, \triangle \boldsymbol{U}_{2} \)
are changes in internal energies
respectively, then
A. \( \triangle Q_{1}=\Delta Q_{2} ; \Delta U_{1}=\Delta U_{2} \)
B. \( \Delta Q_{1}>\Delta Q_{2} ; \Delta U_{1}>\Delta U_{2} \)
\( \mathbf{c} \cdot \Delta Q_{1}<\Delta Q_{2} ; \Delta U_{1}<\Delta U_{2} \)
D. \( \triangle Q_{1}>\triangle Q_{2} ; \triangle U_{1}=\triangle U_{2} \)


\( C H_{3} \)
The reaction, \( C H_{3}-C H-C H_{2}- \)
\( \boldsymbol{O}-\boldsymbol{C H}_{2} \boldsymbol{C H}_{3}+\boldsymbol{H} \boldsymbol{I} \stackrel{\boldsymbol{\Delta}}{\longrightarrow} ? \)
Which of the following compound will be formed?
\( \mathbf{A} \cdot C H_{3}-C H-C H_{2}-I+C H_{3} C H_{2} O H \)
\( \left._{C H_{3}}^{\prime}\right|_{C} \)
в. \( C H_{3}-C H-C H_{3}+C H_{3} C H_{2} O H \)
I \( _{C H_{3}} \)
c. \( C H_{3}-\underset{C H_{3}}{C H}-C H_{2} O H+C H_{3} C H_{3} \)
D. \( C H_{3}-C H-C H_{2} O H+C H_{3} C H_{2} I \)
\[
\begin{array}{l}_{C H_{3}}\end{array}
\]


If relative decrease in vapour pressure is 0.4 for a solution containing 1 mol
NaCl in 3 mol \( H_{2} \) O. NaCl is
\( \% \) ionised.
A . \( 60 \% \)
B. 50\%
c. \( 100 \% \)
D. 40\%


A plot of velocity versus time is shown
in figure. A single force acts on the body
The correct statement is
A. In moving from \( c \) to \( D \), work done by the force on the body is positive
B. In moving from B to C, work done by the force on the body is positive
c. In moving from A to B, the body does negative work
D. In moving from o to
A, work is done by the body and negative


Carbon has unique property due to which it forms covalent bonds with
other carbon atoms
A. True
B. False


Which one of the following is an acidic
salt?
This question has multiple correct options
A. \( N a H S O_{4} \)
в. NaH S
c. \( \operatorname{NaHSO}_{3} \)
D. \( N a_{2} S O_{4} \)


If \( [\boldsymbol{x} \quad \boldsymbol{y}]=\left[\begin{array}{ll}1 & 5\end{array}\right], \) then \( 2 \boldsymbol{x}+\mathbf{5} \boldsymbol{y}= \)
A . 26
B. 27
c. 29
D. None of these


Two unequal masses are tied together
with a cord with a compressed spring in
between
Which one is correct?
A. Both masses will have equal KE.
B. Lighter block will have greater KE.
C . Heavier block will have greater KE.
D. None of above answers is correct.


\( \int \frac{3 a x}{b^{2}+c^{2} x^{2}} d x \)


Novolac on heating with formaldehyde undergoes to form an
infusible solid mass called
A. polymerization, melamine
B. vulcanization, resin
c. cross-liking, bakelite
D. condensation, polystyrene


For two particles \( A \) and \( B \), given that \( \overline{\boldsymbol{r}}_{\boldsymbol{A}}=\mathbf{2} \overline{\boldsymbol{i}}+\boldsymbol{3} \overline{\boldsymbol{j}}, \overline{\boldsymbol{r}}_{\boldsymbol{B}}=\boldsymbol{6} \overline{\boldsymbol{i}}+\boldsymbol{7} \overline{\boldsymbol{j}}, \overline{\boldsymbol{V}}_{\boldsymbol{A}}= \)
\( \mathbf{3} \overline{\mathbf{i}}+\overline{\boldsymbol{j}} \) and \( \overline{\boldsymbol{V}}_{B}=\boldsymbol{x} \overline{\mathbf{i}}+\mathbf{5} \bar{j} . \) What is the
value of \( x \) if they collide.
\( A \cdot 1 \)
B. 7
\( c \cdot 2 \)
\( D \ldots-2 \)


\( \mathbf{2} \boldsymbol{S} \boldsymbol{n}^{2+} \rightarrow \boldsymbol{S} \boldsymbol{n}^{4+}+\boldsymbol{S} \boldsymbol{n} \)
This reaction is an example of:
A. Comproportionation reaction
B. Disproportionation reaction
c. Decomposition reaction
D. Neutralisation


A function \( y=f(x) \) satisfying the
differential equation \( \frac{d y}{d x} \cdot \sin x- \)
\( y \cos x+\frac{\sin ^{2} x}{x^{2}}=0 \) such that \( y \rightarrow 0 \) as
\( x \rightarrow \infty \) then the correct statement
which is correct is
\( \mathbf{A} \cdot \lim _{x \rightarrow 0} i t f(x)=1 \)
B. \( \int_{0}^{\pi / 2} f(x) d x \) is less than \( \frac{\pi}{2} \)
c. \( \int_{0}^{\pi / 2} f(x) d x \) is greater than unit
D \cdot \( f(x) \) is an odd function


Which statement represents the inverse of the statement "lf it is snowing, then
Skeeter wears a sweater."?
A. If Skeeter wears a sweater, then it is snowing
B. If Skeeter does not wear a sweater, then it is not snowing.
C. If it is not snowing, then Skeeter does not wear a sweater
D. If it is not snowing, then Skeeter wears a sweater


You provided hard water and soft water is two seperate test tube what do you observe on adding equal quantity of
soap soln to each sample of \( H_{2} O \) and
shaking them 10 times.


If the capacitance between two successive plates is \( C, \) then the capacitance of the equivalent system between \( A \) and \( B \) is
A \( \cdot \frac{C}{3} \)
в. \( 3 C \)
c. \( \frac{2 C}{3} \)
D. \( \frac{3 C}{2} \)


Tenth fringe of wavelength \( 4000 A^{\circ} \)
coincides with \( 8 t h \) fringes of
wavelength \( \lambda \). Then \( \lambda \) is
\( \mathbf{A} \cdot 50 n m \)
B. \( 555 n m \)
c. 450 n \( m \)
D. none


Eccentricity of ellipse \( \frac{x^{2}}{a^{2}+1}+\frac{y^{2}}{a^{2}+2}= \)
1 is \( \frac{1}{\sqrt{3}} \) then length of Latus rectum is
A \( \cdot \frac{2}{\sqrt{3}} \)
B. \( \frac{4}{\sqrt{3}} \)
\( c \cdot 2 \sqrt{3} \)
D. \( \frac{\sqrt{3}}{2} \)


Two cubes of edge \( 6 \mathrm{cm} \) are joined to
form a cuboid. Find the total surface
area of the cuboid.


If the moment of force is assigned a
negative sign then will the turning
tendency of the force be clockwise or anticlockwise?


Find the derivative of \( \cos ^{2} x, \) by using
first principle of derivatives.


IUPAC name of \( \boldsymbol{C H}_{3}-\boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right)- \)
\( \boldsymbol{C} \equiv \boldsymbol{C}-\boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right)-\boldsymbol{C H}_{3} \) is:
A. 2,5 dimethyl-3-hexyne
B. 2,5 dimethyl 2- hexyne
c. 3,5 dimethyl- 3 - hexyne
D. 2 - pentane


The line \( 2 y=3 x+12 \) cuts the
parabola \( 4 y=3 x^{2} . \) What is the area
enclosed by the parabola and the line?
A. 27 square unit
B. 36 square unit
c. 48 square unit
D. 54 square unit


Equilibrium constant for the following
equilibrium is given at \( 0^{\circ} \mathrm{C} \)
\( N a_{2} H P O_{4} \cdot 12 H_{2} O(s) \rightleftharpoons \)
\( N a_{2} H P O_{4} \cdot 7 H_{2} O(s)+5 H_{2} O(s) \)
\( \boldsymbol{K}_{\boldsymbol{p}}=\mathbf{3 1 . 2 5} \times \mathbf{1 0}^{-\mathbf{1 3}} \)
The partial pressure of water is:
A \( \cdot \frac{1}{5} \times 10^{-3} \) at
B . \( 0.5 \times 10^{-3} \) atm
c. \( 5 \times 10^{-2} a t m \)
D. \( 5 \times 10^{-3} a \) tm


The number of gram atoms present in
\( 10 \mathrm{g} \) of \( \mathrm{CaCO}_{3} \) is:
A . 5.0
B. 0.5
c. \( 0 . \)
D. 0.02


If \( R \) is the radius of a planet, \( g \) is the acceleration due to gravity then find the mean density of the planet
A \( \cdot \frac{3 g}{4 G \pi R} \)
в. \( \frac{3 g}{8 G \pi R} \)
c. \( \frac{2 g}{4 G \pi R} \)
D. \( \frac{6 g}{4 G \pi R} \)


Boron shows single oxidation state due to absence of :
A. inner pair effect
B. screening effect
c. isotope effect
D. none


In Pteridophytes, reduction division takes place in
A . Zygote
B. Prothallus
c. sporangia
D. None of the above


Cell plate is referred as
A . Germplast
B. Idioblast
c. Phragmoplast
D. Middle lamella


The value of \( \int \frac{\cos x+x \sin x}{x^{2}+x \cos x} d x \) is
\( \mathbf{A} \cdot \log \left|\frac{\sin x}{1+\cos x}\right|+C \)
\( \mathbf{B} \cdot \log \left|\frac{\sin x}{x+\cos x}\right|+C \)
\( \mathbf{C} \cdot \log \left|\frac{2 \sin x}{x+\cos x}\right|+C \)
\( ^{\mathbf{D}} \cdot \log \left|\frac{x}{x+\cos x}\right|+C \)


Sum to infinite terms the following
series:
\( \mathbf{1}+\mathbf{3} \boldsymbol{x}+\mathbf{5} \boldsymbol{x}^{2}+\mathbf{7} \boldsymbol{x}^{3}+\ldots .,|\boldsymbol{x}|<\mathbf{1} \)


Find the mean deviation from the
median for the following data:
\[
\begin{array}{ccccc}
x_{1} & 6 & 9 & 3 & 12 \\
f_{1} & 4 & 5 & 3 & 2
\end{array}
\]


A particle moves in a straight line and its speed depends on time as \( \boldsymbol{v}=\mid \mathbf{2 t}- \)
3). Find the displacement of the particle
in \( 5 s \)


A transmitter transmits at a wave
length of 300 meters. A capacitor of a
capacitance \( 9.6 \mu \mathrm{F} \) is being used. The value of the inductance for the resonant
circuit is approximately
A . 2.5 \( \mathrm{mH} \)
в. 2.5 \( \mu \) Н
c. 2.5 n
D. 2.5 ph


\( (0)(0)-a+x= \)
\( \{0\rangle \mathbb{D} \mid-\infty \)
\( -0 \times 0= \)
\( 0 \times 0 \)
\( 0 \times 0 \)


A rectangular room is \( 6 m \) long, \( 5 m \)
wide and \( 4 m \) high. Find the total surface area of the four walls.


Sound can be
\( \mathbf{A} \cdot \) seen
B. felt
c. heard
D. seen, felt and heard at the same time


A well stirred \( (1 L) \) solution of
\( 0.1 M C u S O_{4} \) is electrolysed at \( 25^{\circ} C \)
using copper electrodes with a current of 25 m \( A \) for 6 hours. If current
efficiency is \( 50 \% \). At the end of the duration what would be the
concentration of copper ions in the solution?
A \( .0 .0856 M \)
В. \( 0.092 \mathrm{M} \)
c. \( 0.0986 M \)
D. \( 0.1 M \)


Match the following and mark the
correct set.
Column I
\( \| \)
I. Arum Vegetative reproduction
II. Micropropagation
B. Flytrap mechanism
III. Heterothallie
Entomophilly
IV. Coloured petal and nectar Sexual reproduction
\( A \cdot|-A,| I-B,|I|-C, I V-D \)
B. I-B, II - A, III - D, IV - C
c. \( 1-\mathrm{c}, \) ।। \( -\mathrm{B}, \) ।I \( -\mathrm{D}, \mathrm{IV}-\mathrm{A} \)
D. I - A, II - C, III - D, IV - B


The taxi driver has to be more careful
when driving car in winter because of
morning dew. That means the friction on road during winter is friction during summer. Fill in the blank.
A. more than
B. less than
c. same as
D. having no relation with


Which of the following process occurs in glycolysis?
A. Oxidation
B. Reduction
c. Hydrogenation
D. Fixation


A Carnot engine has an efficiency of \( 1 / 6 \) When the temperature of the sink is
reduced by \( 62^{\circ} \mathrm{C} \), its efficiency is
doubled. The temperatures of the source and the sink are, respectively
A \( \cdot 124^{\circ} \mathrm{C}, 62^{\circ} \mathrm{C} \)
B . \( 37^{\circ} C, 99^{\circ} \mathrm{C} \)
c. \( 62^{\circ} \mathrm{C}, 124^{\circ} \mathrm{C} \)
D. \( 99^{\circ} \mathrm{C}, 37^{\circ} \mathrm{C} \)


The unit vector along \( 2 i-3 j+k \) is
A. \( \frac{2 i-3 j+k}{\sqrt{14}} \)
в. \( \frac{2 i-3 j+k}{\sqrt{5}} \)
c. \( \frac{2 i-3 j+k}{\sqrt{15}} \)
D. None of these


Which of the following order is correct about the rate of photosynthesis under the light?
A. Blue yellow > orange > red
B. Blue > red > yellow > orange
c. Red > Blue > yellow > orange
D. Yellow > orange > blue > red


State two safety measures to be taken while establishing a nuclear power plant.
A. Use uranium rod and inside environment is not shielded
B. Use uranium rod and inside environment should be shielded
c. Use copper rod and inside environment is not shielded
D. None of the above


Name the following coordination entities and draw the structures of their
steroisomers:
(i) \( \left[\boldsymbol{C o}(\boldsymbol{e n})_{2} \boldsymbol{C l}_{2}\right]^{+}(\boldsymbol{e n}=\boldsymbol{e t h a n e}- \)
1, 2 - diamine)
(ii) \( \left[\boldsymbol{C r}\left(\boldsymbol{C}_{2} \boldsymbol{O}_{4}\right)_{3}\right]^{3-} \)
(iii) \( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{3} \boldsymbol{C l}_{3}\right] \)
(Atomic number \( \boldsymbol{C r}=\mathbf{2 4}, \boldsymbol{C o}=\mathbf{2 7}) \)


If \( \triangle A B C \) is right angled at \( A \) and \( A D \perp B C, \) then \( \frac{B D}{D C}= \)
\( ^{\mathrm{A}} \cdot\left(\frac{A B}{A C}\right)^{2} \)
в. \( \frac{A B}{A C} \)
\( ^{\mathrm{c}}\left(\frac{A B}{A D}\right)^{2} \)
D. \( \frac{A B}{A D} \)


The breathing organ in the plant is
A. Lungs.
B. Stomata.
c. Gills
D. Seeds


As compound to other parts of root apical meristem, DNA content of quiescent centre is
A . Low
B. Highh
c. same
D. Very high


Minimize \( Z=7 x+y \) subject to
\( \mathbf{5} \boldsymbol{x}+\boldsymbol{y} \geq \mathbf{5}, \boldsymbol{x}+\boldsymbol{y} \geq \mathbf{3}, \boldsymbol{x} \geq \mathbf{0}, \boldsymbol{y} \geq \mathbf{0} \)


In a question on division the divisor is 7
times the quotient and 3 times the
remainder. If the remainder is 28 then
what is the dividend?
A . 1008
B. 1516
c. 1036
D. 2135


lonic interactions are directional.
A. True
B. False


The rusting of iron is a reaction.
A. very slow
B. slow
c. moderate
D. fast


Tetany is sustained contraction of muscle is due to
A. Parathyroid deficiency
B. \( C a^{++} \) deficiency
c. Both A and B
D. Autoimmune disease


Let \( S=\{1,2,3, \dots \dots n\} \) and \( A= \)
\( \{(a, b) \mid 1 \geq a, b \geq n\}=S \times S . A \)
subset \( B \) of \( A \) is said to be a good subset if \( (x, x) \in B \) for every \( x \in S \)
Then the number of good subsets of \( \boldsymbol{A} \)
is
\( A \cdot 1 \)
B. \( 2^{n} \)
\( c \cdot 2^{n(n-1)} \)
D. \( 2^{n^{2}} \)


Simplify :\( x^{2}+z^{2}-2 x z \)


Balance the following reaction
\( M n O_{4}^{-}+H_{2} O_{2} \rightarrow M n O_{2}+O_{2} \)


The potential energy of a body of mass \( \boldsymbol{m} \) is \( \boldsymbol{U}=\boldsymbol{a} \boldsymbol{x}+\boldsymbol{b} \boldsymbol{y} \)
where \( x \) and \( y \) are position co-ordinates of the particle. The acceleration of the particle is
A \( \cdot \frac{\left(a^{2}+b^{2}\right)^{1 / 2}}{m} \)
B. \( \frac{a^{2}+b^{2}}{m} \)
c. \( \frac{(a+b)^{1 / 2}}{m} \)
D. \( \frac{a+b}{m} \)


If \( \frac{\mathbf{x}^{4}+\mathbf{2 4 x}^{2}+\mathbf{2 8}}{\left(\mathbf{x}^{\mathbf{2}}+\mathbf{1}\right)^{\mathbf{3}}} \)
\( =\frac{\mathbf{A} \mathbf{x}+\mathbf{B}}{\mathbf{x}^{2}+\mathbf{1}}+\frac{\mathbf{C} \mathbf{x}+\mathbf{D}}{\left(\mathbf{x}^{2}+\mathbf{1}\right)^{2}}+\frac{\mathbf{E} \mathbf{x}+\mathbf{F}}{\left(\mathbf{x}^{2}+\mathbf{1}\right)^{3}} \)
then \( \boldsymbol{A}= \)
\( A \)
B. -
c.
\( D \)


When the right ventricle contracts the blood is pumped into
A. Superior vena cava
B. Dorsal aorta
c. Pulmonary artery
D. Pulmonary veins


A piece of copper wire has twice the radius of steel wire. One end of the
copper wire is joined to one end of steel wire so that both of them can be
subjected to the same longitudinal force. \( Y \) for steel is twice that of copper.
When the length of copper wire is increased by \( 1 \% \), the steel wire will be stretched by
A . 2\% of its original length
B. 1\% of its original length
c. \( 4 \% \) of its original length
D. 0.5\% of its original length


ends so that it lies horizontally and
without tension. A weight \( W \) is
suspended from the middle point of the wire. The vertical depression is
(Young's modulus is \( Y \).)
A \( \cdot \sqrt{\frac{2 T l^{2}}{4 A Y}+\frac{T^{2} l^{2}}{4 A^{2} Y^{2}}} \)
B. \( \sqrt{\frac{2 T l^{2}}{4 A Y}-\frac{T^{2} l^{2}}{4 A^{2} Y^{2}}} \)
c. \( \sqrt{\frac{2 T l^{2}}{4 A Y}} \)
D. \( \frac{T l}{2 A Y} \)


The velocity of the body at the end of 1 s from the start is:
A . 2N
в. \( \frac{M+2 N}{4} \)
c. \( 2(M+N) \)
D. \( \frac{2 M+N}{4} \)


A cube has a side of length \( 2.342 m \). The surface area and volume in correct
significant figures are respectively:
A . \( 32.90 m^{2}, 12.85 m^{3} \)
B . \( 5.49 m^{2}, 12.85 m^{3} \)
c. \( 5.485 \mathrm{m}^{2}, 12.9 \mathrm{m}^{3} \)
D. \( 5.49 m^{2}, 12.9 m^{3} \)


ff \( \boldsymbol{x}=\boldsymbol{a} \sin \boldsymbol{\theta}+\boldsymbol{b} \cos \boldsymbol{\theta}, \boldsymbol{y}=\boldsymbol{a} \cos \boldsymbol{\theta} \)
\( -b \sin \theta \)
then show that \( (a x+a y)^{2}+(b x-a y)^{2} \)
\( =\left(a^{2}+b^{2}\right)^{2} \)


Among the following, the molecule that will have the highest dipole moment is :
A. \( H_{2} \)
в. \( H I \)
c. \( H B r \)
D. HCl
E . \( H F \)


If the racing cars move on a circular road of radius \( 100 \mathrm{m}, \) with a speed of \( 30 \mathrm{m} / \mathrm{s}, \) with an angle of banking equal to 15 degrees, what will be the coefficient of friction for safe driving
A . \( 0 . \)
B. 0.3
\( c \cdot 0.5 \)
D. 0.8


A \( T \) shaped object with dimensions
shown in fig, is lying on smooth floor. \( \mathbf{A} \) force \( F \) is applied at point \( P \) parallel to
AB such that the object has only translation motion without rotation.
Find location of \( \boldsymbol{P} \) from \( \boldsymbol{C} \)
A \( \cdot \frac{2}{3} l \)
в. \( \frac{3}{2} l \)
\( c \cdot \frac{4}{3} l \)
D.


Q Type your question
capacitor is \( 6 m F \) and is decreasing at
the constant rate \( 0.5 m F s^{-1} . \) The
potential difference across the
capacitor at the shown moment is changing as follows \( \frac{\boldsymbol{d} \boldsymbol{V}}{\boldsymbol{d} \boldsymbol{t}}=\boldsymbol{2} \boldsymbol{V} \boldsymbol{s}^{-1} \)
\( \frac{\boldsymbol{d}^{2} \boldsymbol{V}}{\boldsymbol{d t}^{2}}=\frac{1}{2} \boldsymbol{V} \boldsymbol{s}^{-2} \) and the current in the
\( 4 \Omega \) resistor is decreasing at the rate of
\( 1 m A s^{-1} . \) What is the potential
difference (in \( m V) \) across the inductor
at this moment?
\( A \cdot 4 \)
B. 3
\( c \cdot 8 \)
\( D \)


On a foggy day, two drivers spot in front of each other when 80 metre apart. They
were traveling at \( 70 \mathrm{kmph} \) and \( 60 \mathrm{kmph} \) Both apply brakes simultaneously which retard the cars at the rate
\( 5\left[\boldsymbol{m} / \boldsymbol{s}^{2}\right] \) Which of the following statements is correct?
A. The collision will be averted
B. The collision will take place
c. They will across each other
D. They will just collide


If \( \lim _{x \rightarrow \infty}\left\{\frac{x^{3}+1}{x^{2}+1}-(a x+b)\right\}=2, \) then
A \( . a=1, b=1 \)
B. \( a=1, b=2 \)
c. \( a=1, b=-2 \)
D. None of these


Evaluate \( \int \frac{\cos x}{(2+\sin x)(3+4 \sin x)} d x \)


One drop of methyl orange solution when added to the solution obtained
after electrolysis of a concentrated
solution of \( N a C l \) with \( P^{+} \) electrodes, the colour of the solution will turn:
A . orange
B. pink
c. yellow
D. colourless


A particle of mass \( 1 \mathrm{kg} \) has a velocity of
\( 2 \mathrm{m} / \mathrm{s} . \) A constant force of \( 2 \mathrm{N} \) acts on
the particle for 1 s in a direction perpendicular to its initial velocity. Find the velocity and displacement of the particle at the end of 1 s.


What is the process in which heat energy of both hot and cold body equalizes?
A. Calorimetry
B. Fermentation
c. Latent heat
D. Hidden heat


Compare the concentrations of each of the species \( N a^{+}, H^{+} \) and \( C N \) in the
solution.
A \( \cdot N a^{+}>O H^{-}>C N^{-} \)
В. \( C N^{-}>O H^{-}>N a^{+} \)
c. \( N a^{+}>C N^{-}>O H^{-} \)
D. \( O H^{-}>C N^{-}>N a^{+} \)


What is the action of the sodium metal
on ammonia?
A. Ammonia gas is released
B. Hydrogen gas is releasedd
c. Oxygen gas is released
D. Nitrogen gas id released


With the help of labelled circuit diagram derive a formula to find combined resistance (R) when two or
more resistance \( \left(\boldsymbol{R}_{1}, \boldsymbol{R}_{2}, \boldsymbol{R}_{3} \ldots \ldots\right) \) are
connected in parallel taking symbols potential difference \( (V) \) and current \( (I) \)


The current 'i' in the circuit given is
\( A \cdot O \cdot 1 A \)
B. \( 0.2 \mathrm{A} \)
\( c \cdot 1.0 A \)
D. 2.0 A


In the equation, \( 4 M+8 C N^{-}+ \)
\( \mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{O}_{2} \rightarrow \boldsymbol{4}\left[\boldsymbol{M}(\boldsymbol{C} \boldsymbol{N})_{2}\right]^{-}+\mathbf{4} \boldsymbol{O} \boldsymbol{H}^{-} \)
Identify the metal \( \mathrm{M} \)
A. copper
B. Iron
c. Gold
D. zinc


Write the equations for the \( x \) -and \( y \)
axes.


Acceleration of a body projected upwards with a certain velocity is
A \( \cdot 9.8 m / s^{2} \)
B. \( -9.8 m / s^{2} \)
c. zero
D. Insufficient data


The organ that helps us to recall and analyse is
A. Muscles
B. Brain
c. spinal cord
D. Nerve


The prefix used for denoting an order of
magnitude of \( 10^{6} \) is:
B. mega
c. kilo
D. micro


A real valued function \( f(x) \) satisfies the functional equation \( \boldsymbol{f}(\boldsymbol{x}-\boldsymbol{y})= \)
\( \boldsymbol{f}(\boldsymbol{x}) \boldsymbol{f}(\boldsymbol{y})-\boldsymbol{f}(\boldsymbol{a}-\boldsymbol{x}) \boldsymbol{f}(\boldsymbol{a}+\boldsymbol{y}), \) where \( \boldsymbol{a} \)
is a given constant and \( \boldsymbol{f}(\mathbf{0})= \)
\( \mathbf{1}, \boldsymbol{f}(\mathbf{2} \boldsymbol{a}-\boldsymbol{x}) \) is equal to
A \( .-f(x) \)
в. \( f(x) \)
c. \( f(a)+f(a-x) \)
D. \( f(a)-f(a-x) \)


\( 112 \mathrm{cm}^{3} \) of hydrogen gas at STP
contains:
A . 0.01 mole
B. 0.5 mole
c. 0.005 mole
D. 0.02 mole


A dilute Ferrous sulphate solution was gradually added to the beaker containing acidified permanganate solution. The light purple colour of the solution fades and finally disappears. Which of the following is the correct explanation for the observation?
A. \( K M n O_{4} \) is an oxidizing agent, it oxidizes \( F e S O_{4} \)
B. \( F e S O_{4} \) acts as an oxidizing agent and oxidizes \( K M n O_{4} \)
c. The colour disappears due to dilution: no reaction is involved
D. \( K M n O_{4} \) is an unstable compound and decompose presence of \( F e S O_{4} \) to a colourless compound


In which of the following reactions,
\( H_{2} O_{2} \) acts as a reducing reagent?
A \( \cdot P b O_{2(s)}+H_{2} O_{2(a g)} \rightarrow P b O_{(s)}+H_{2} O_{(i)}+O_{2(g)} \)
B. \( N a_{2} S O_{3(a g)}+H_{2} O_{2(a g)} \rightarrow N a_{2} S O_{4(a g)}+H_{2} O_{(i)} \)
C \( \cdot 2 K I_{(a)}+H_{2} O_{2(a)} \rightarrow 2 K O H_{(a q)}+I_{2(s)} \)
D. All the above


The electromagnetic waves travel with
A. the same speed in all media
B. the speed of sound in free space
C . the speed of light \( c=3 \times 10^{8} \mathrm{ms}^{-1} \) in solid medium
D. the speed of light \( c=3 \times 10^{8} \mathrm{ms}^{-1} \) in fluid medium
E. the speed of light \( c=3 \times 10^{8} m s^{-1} \) in free medium


Find the complement of each of the
following angles:


State whether the following statements
are true or false.

Ethylene evolution is highest when the fruit is unripe but diminishes as the
fruit matures.
A. True
B. False


Beats are produced due to the superposition of two progressive notes of same amplitude. Maximum intensity is \( n \) times the intensity of either note.
The value of \( n \) is :
\( A \)
B. 2
\( c \cdot 3 \)
D. 4


\( 1300 J \) of heat energy is supplied to
raise the temperature of \( 0.5 k g \) of lead
from \( 20^{\circ} C \) to \( 40^{\circ} C . \) Calculate the
specific heat capacity of lead.
A \( \cdot 65 \mathrm{J} k g^{-1} K^{-1} \)
B \( \cdot 260 J k g^{-1} K^{-1} \)
c. \( 130 \mathrm{Jkg}^{-1} \mathrm{K}^{-1} \)
D. \( 1300 \mathrm{Jkg}^{-1} \mathrm{K}^{-1} \)


Find the distance between (4,5) and (5,6)
A \( \cdot \sqrt{2} \)
B. \( \sqrt{3} \)
\( c \cdot \sqrt{6} \)
D. \( \sqrt{7} \)


Atoms in hydrogen have abundance of:
A \( \cdot_{1} H^{1} \) atoms
B. \( _{1} D^{2} \) atoms
\( \mathbf{c} \cdot_{1} T^{3} \) atoms
D. all three are in equal proportions


An infinite number of charges, each
equal to q, are placed along the x-axis
at \( x=1, x=2, x=4, x=8 \) and so on
What is the potential at \( x=0 \) due to
this set of charges?


If \( x^{2}+\frac{1}{x^{2}}=83 . \) Find the value of \( x^{3}- \)
\( \frac{1}{m^{3}} \)


For what type of ions the ionic radius is less than the atomic radius?


A pair of linear equations in two
variables \( x \) and \( y \) is \( a_{1} x+b_{1} y+c_{1}=0 \)
and \( a_{2} x+b_{2} y+c_{2}=0, \) such that
\( \frac{a_{1}}{a_{2}} \neq \frac{c_{1}}{c_{2}}, \) then it has
A. Unique solution
B. No solution
c. Infinitely many solutions
D. Can't say


The most ideal gas among real gases is:
A. Hydrogen
B. Helium
c. Carbon dioxide
D. Nitrogen


A block is executing SHM on a rough horizontal surface under the action of an external variable force.The force is
plotted against the position \( x \) of the
particle from the mean position


A neutral atom of an element has \( 2 \mathrm{K}, 8 \mathrm{L} \) and \( 5 M \) electrons. What is the maximum number of electrons having
same spin?
A. 5
B. 8
\( c \cdot 9 \)
D.


State True or False:
Due to high specific heat index of water it helps in regulating the rate of temperature change between seasons.
A . True
B. False


Assertion
Tapeworm, roundworm and pinworm are
endoparasites of human intestine.
Reason
Improperly cooked food is the source of
intestinal infections.
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 system \( S \) consists of two coils \( A \) and
B. The coil \( A \) have a steady current \( I \)
while the coils \( B \) is suspended near by
as shown in figure. Now the system is
heated as to raise the temperature of
two coils steadily, then :
A. the two coils show attraction
B. the two coils show repulsion
C. there is no change in the position of the two coils
D. induced currents are not possible in coil \( B \)


The equilibrium constants for the
reactions are:
\[
\begin{array}{l}
\boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \stackrel{\boldsymbol{K}_{1}}{\rightleftharpoons} \boldsymbol{H}^{+}+\boldsymbol{H}_{2} \boldsymbol{P} \boldsymbol{O}_{4}^{-} ; \boldsymbol{K}_{\mathbf{1}} \\
\boldsymbol{H}_{2} \boldsymbol{P} \boldsymbol{O}_{4}^{-} \frac{\boldsymbol{K}_{2}}{\rightleftharpoons} \boldsymbol{H}^{+}+\boldsymbol{H} \boldsymbol{P} \boldsymbol{O}_{4}^{2-} ; \boldsymbol{K}_{2} \\
\boldsymbol{H} \boldsymbol{P} \boldsymbol{O}_{4}^{2-} \stackrel{\boldsymbol{K}_{3}}{\rightleftharpoons} \boldsymbol{H}^{+}+\boldsymbol{P} \boldsymbol{O}_{4}^{3-} ; \boldsymbol{K}_{3}
\end{array}
\]
The equilibrium constant for
\[
\boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \rightleftharpoons \mathbf{3} \boldsymbol{H}^{+}+\boldsymbol{P} \boldsymbol{O}_{4}^{3-} \text { will be: }
\]
\( A \)
\[
\frac{K_{1}}{K_{2} \times K_{3}}
\]
В. \( K_{1} \times K_{2} \times K_{3} \)
\( c \)
\[
\frac{K_{2}}{K_{1} \times K_{3}}
\]
D. \( K_{1}+K_{2}+K_{3} \)


The antiseptic present in Dettol is:
A. Codeine
B. Chloroxylenol
c. Bithional
D. None of these


Consider statement "If I do not work, I
will sleep. If I am worried, I will not sleep. Therefore if I am worried, I will work".
This statement is
A. valid
B. invalid
c. a fallacy
D. none of these


For the reaction: \( \boldsymbol{C O}_{2}(\boldsymbol{g})+\boldsymbol{H}_{2}(\boldsymbol{g}) \leftrightharpoons \)
\( \boldsymbol{C O}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}), \mathrm{K} \) is found to be 16 at
a given temperature. Originally equal
numbers of moles of \( \boldsymbol{H}_{2} \) and \( \boldsymbol{C} \boldsymbol{O}_{2} \) were
placed in the flask. At equilibrium, the
pressure of \( \boldsymbol{H}_{2} \) is 1.20 atm. What is the
partial pressure of \( \boldsymbol{C O} \) and \( \boldsymbol{H}_{2} \boldsymbol{O} \) ?
\( A \cdot 4.80 \) atm each
B. 9.60 atm each
c. 2.40 atm each
D. 1.20 atm each


The following table gives production yield per hectare wheat of 100 farms of a village.
\( \begin{array}{llll}\text { production } & \mathbf{5 0}- & \mathbf{5 5}- & \mathbf{6 0}- \\ \text { of fields } & \mathbf{5 5} & \mathbf{6 0} & \mathbf{6 5}\end{array} \)
Numbers of
farms 2
Change the distribution to a more than type distribution and its ogive.


f \( \boldsymbol{y}=\boldsymbol{x} \sin (\boldsymbol{a}+\boldsymbol{y}), \) then prove that
\( \frac{d y}{d x}=\frac{\sin ^{2}(a+y)}{\sin (a+y)-y \cos (a+y)} \)


Show that every positive even integer is
of the form \( 2 q \) and every positive odd integer is of the form \( 2 q+1 \), where q is a whole number.


What is the exact atomic weight of arsenic?
A. 74.94
B . 24.98
c. 80.00
D. 182.47