The potential energy function for the
force between two atoms in a diatomic
molecule can be expressed approximately as \( U(r)=\frac{a}{r^{12}}-\frac{b}{r^{6}} \)
where \( a \) and \( b \) are constants and \( r \) is the
separation between the atoms.
(a) Determine the force function \( \boldsymbol{F}(\boldsymbol{r}) \)
(b) Find the value of for which the
molecule will be in the stable
equilibrium.


According to Bentham and Hooker's classification which family/order was considered most primitive?
A. Ranunculaceae / Ranales
B. orchidaceae / orchidales
c. Malvaceae / Malvales
D. Brassicaceae / Parietales


The number of significant figures in 500.06 is
A .2
B. 3
\( c \cdot 5 \)
D. o


Mass of one twelth of carbon atom is
called atomic mass unit.
A. True
B. False


Explain the various ways in which we
can conserve water at home and school


Two thin lenses of powers \( 2 D \) and \( 3 D \) are placed in contact. An object is placed at a distance of \( 30 \mathrm{cm} \) from the combination. The distance (in cm) of
the image from the combination is :
A . 30
B. 40
\( c .50 \)
D. 60


Botanical name of radish is
B. Brassica oleracea
c. Raphanus sativus
D. None of the above


100 surnames were randomly picked up from a local telephone directory and a frequency distribution of the number of letters in the English alphabet in the surnames was found as follows:
(i) Draw a histogram to depict the given information.
(ii) Write the class interval in which the
maximum number of surnames lie.
\begin{tabular}{|c|c|}
\hline Number of letters & Number of surnames \\
\hline \( 1-4 \) & 6 \\
\( 4-6 \) & 30 \\
\( 6-8 \) & 44 \\
\( 8-12 \) & 16 \\
\( 12-20 \) & 4 \\
\hline
\end{tabular}


Two cubes each with \( 12 \mathrm{cm} \) are joined
end to end. Find the surface area of the
resulting cuboid.


The frequency order for \( X \) -rays \( (A), \gamma \) rays(B), UV rays(C) is
\( \mathbf{A} \cdot B>A>C \)
в. \( A>B>C \)
c. \( C>B>A \)
D. \( A>C>B \)


A particle is projected horizontally with a speed u from the top of a plane inclined at an angle \( \theta \) with the horizontal. How far from the point of projection will the particle strike the
plane?
\( ^{\mathrm{A}} \cdot \frac{2 u^{2}}{g} \tan \theta \sec \theta \)
B. \( \frac{2 u}{8} \tan ^{2} \theta \sec \theta \)
c. \( \frac{2 u^{2}}{g} \tan \theta \cos \theta \)
D. \( \frac{2 u}{g} \tan \theta \cos ^{2} \theta \)


If \( \lim _{x \rightarrow 3} \frac{x^{n}-3^{n}}{x-3}=108, \) find the value of
\( \mathbf{n} \)


ABCD is a parallelogram with sides \( A B= \) \( 12 \mathrm{cm} \mathrm{BC}=10 \mathrm{cm} \) and diagonal \( \mathrm{AC}=16 \)
\( \mathrm{cm} \) The area of the parallelogram and
the distance between the shorter sides
are respectively
A \( \cdot 120.5 \mathrm{cm}^{2} ; 12.05 \mathrm{cm} \)
B . \( 119.8 \mathrm{cm}^{2} ; 11.98 \mathrm{cm} \)
c. \( 118.71 \mathrm{cm}^{2} ; 11.87 \mathrm{cm} \)
D. \( 117.9 \mathrm{cm}^{2} ; 11.79 \mathrm{cm} \)


Solution of alkali metals in liquid ammonia conducts electricity due to the presence of solvated electrons. If true enter 1 , if false enter 0 .
A
B.
c. explanation is wrong
D. Liquid ammonia not conduct electricity


The process which is catalysed by one of the product is called :-
A. Positive catalysis
B. Negative catalysis
c. Autocatalysis
D. None of these


A form of partition, adsorption, ion exchange, or affinity chromatography in which one phase is liquid (aqueous) flowing down a column packed with the second phase, a solid is called
A. partition chromatography
B. column chromatography
c. thin layer chromatography
D. adsorption chromatography


Construct a \( 2 \times 2 \) matrix \( A=\left[a_{i j}\right] \)
whose element \( a_{i j} \) is \( a_{i j}=\frac{|-3 i+j|}{2} \)


Based on equations reducible to linear equations Solve for \( x \) and \( y: \frac{16}{x+3}+\frac{3}{y-2}= \) \( \mathbf{5} ; \frac{\mathbf{8}}{\boldsymbol{x}+\mathbf{3}}-\frac{\mathbf{1}}{\boldsymbol{y}-\mathbf{2}}=\mathbf{0} \)
A. \( x=5, y=3 \)
В. \( x=7, y=2 \)
c. \( x=1, y=5 \)
D. None of these


Suggest two step through which soil erosion can be avoided.


The kinetic energy of the body after the
collision is
A \( \cdot \frac{11 m v^{2}}{54} \)
B. \( \frac{m v^{2}}{108} \)
c. \( \frac{17 m v^{2}}{54} \)
D. \( \frac{17 m v^{2}}{108} \)


Find Limit for following Question \( l \)


State whether true or false:
The substance with more specific heat
has greater ability to store heat.
A. True
B. False


A generator has an e.m.f. of 440 volt and internal resistance of 400 ohm. Its
terminals are connected to a load of
4000 ohm. The voltage across the load
is:
A . 220volt
B. 440volt
c. \( 200 v o l t \)
D. 400volt


(a) Account for the following:
(i) \( H_{2} O \) is a liquid while \( H_{2} S \) is a
gas.
(ii) Noble gases have very low boiling points.
(iii) \( N O_{2} \) dimerises to \( N_{2} O_{4} \)
(b) (i) What are interhalogen compounds?
(ii) Suggest any two examples on interhalogen compounds.


An alcohol of formula \( C_{9} \boldsymbol{H}_{12} \boldsymbol{O} \) reacts
with \( N a_{2} C r_{2} O_{7} \) to from a compound
having formula \( C_{9} \boldsymbol{H}_{10} \boldsymbol{O} \). The original alcohol might be
\( \langle\square\rangle-\mathrm{cH}_{2}-\mathrm{cH}_{2}-\mathrm{cH}_{2}-\mathrm{o} \)
B.
\( c \)
D


In the given figure, two connectric circles with centre \( \boldsymbol{O} \) have radii \( 21 \mathrm{cm} \)
and \( 42 \mathrm{cm}, \) If \( \angle A O B=60^{\circ}, \) find the
area of the shaded region \( \left[\mathbf{U} \mathbf{s e} \boldsymbol{\pi}=\frac{\mathbf{2 2}}{\mathbf{7}}\right] \)


Number of possible product:


If \( \bar{a}=\bar{i}+\bar{j}+t \bar{k} \) and \( \bar{b}=\bar{i}+2 \bar{j}+3 \bar{k} \)
then the value of \( t \) for which \( \bar{a}+\bar{b} \) and
\( \bar{a}-\bar{b} \) are perpendicular is
\( A \ldots \pm 2 \)
В. \( \pm 2 \sqrt{2} \)
\( \mathbf{c} \cdot \pm 2 \sqrt{3} \)
\( \mathrm{D} \cdot \pm 3 \)


Newton's third law is applicable to?


A block of mass \( 5 \mathrm{kg} \) rests on a rough horizontal surface. It is found that a
force of \( 10 \mathrm{N} \) is required to make the block just move. However, once the motion begins, a force of only \( 8 \mathrm{N} \) is enough to maintain the motion. Find the
coefficients of kinetic and static
friction between the block and the
horizontal surface.
\( \sqrt{38}-7 \)


Verify Rolle's theorem for \( \boldsymbol{f}(\boldsymbol{x})=|\cos \boldsymbol{x}| \)
in \( [\mathbf{0}, \boldsymbol{\pi}] \)


Write any three functions of epidermal
tissue system.


The distance between the vertex and the
center of mass of a uniform solid planar
circular segment of angular size \( \theta \) and
radius \( \boldsymbol{R} \) is given by
\( A \)
\( B \frac{\sin (\theta / 2)}{\theta} \)
\( ^{\mathrm{c}} \cdot \frac{4}{3} R \cos \left(\frac{\theta}{2}\right) \)
D \( \cdot \frac{2}{3} R \cos (\theta) \)


The strongest base among the following is:
A \( \cdot C l \)
в. \( C H_{3} C O O^{-} \)
\( \mathrm{c} \cdot \mathrm{H} \mathrm{SO}_{4}^{-} \)
D. \( N O_{3}^{-} \)


If \( A \) and \( B \) are events such that
\( \boldsymbol{P}(\boldsymbol{A} \mid \boldsymbol{B})=\boldsymbol{P}(\boldsymbol{B} \mid \boldsymbol{A}), \) then
A \( . A \subset B \) but \( A \neq B \)
в. \( A=B \)
c. \( A \cap B=\Phi \)
D \( \cdot P(A)=P(B) \)


The compound responsible for the flickering light in marshes is :
A. \( C_{2} H_{4} \)
в. \( P_{2} H_{4} \)
c. \( N_{2} H_{4} \)
D. none of these


Among
\( (a) N a_{2} O \)
\( (b) M g O,(c) A l_{2} O_{3} \)
\( (d) P_{2} O_{5} \)
the most basic, most acidic and amphoteric oxide can be respectively:
\( A \cdot a, b, c \)
B. b, e, c
\( c \cdot a, e, c \)
\( D \cdot e, c, a \)


For any two sets of \( A \) and \( B \), prove that \( \boldsymbol{B}^{\prime} \subset \boldsymbol{A}^{\prime} \Rightarrow \boldsymbol{A} \subset \boldsymbol{B} \)


Which among the following is a stage of meiosis during which pairs of homologous chromosomes align at the center of the cell?
A. Anaphase II
B. Metaphase!
c. Prophase II
D. Metaphase II I I Instaphse . meses
E. Prophase I


A body oscillates with SHM according to
the equation \( \boldsymbol{x}=\mathbf{5 . 0} \cos (2 \pi t+\boldsymbol{\pi}) . \) At
time \( t=1.5 s, \) its displacement, speed
and acceleration respectively is:
B . \( 5,0,-20 \pi^{2} \)
c. \( 2.5,+20 \pi, 0 \)
D. \( -5.0,+5 \pi,-10 \pi^{2} \)


If \( y=\frac{1}{2 x^{2}+3 x+1} \) then \( \frac{d^{2} y}{d x^{2}} \) at \( x= \)
-2 is :
\( A \cdot \frac{38}{27} \)
в. \( -\frac{38}{27} \)
c. \( \frac{27}{38} \)
D. None


toppr
Q Type your question_
\( \mathbf{A} \)
\( B \)
\( c \)
\( (c) \)
\( D \)


\( \boldsymbol{S} \boldsymbol{O}_{2} \) reduces \( \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4}^{-} \) to \( \boldsymbol{M} \boldsymbol{n}^{2+} . \) Number
of electrons involved in the reduction of
\( M n O_{4}^{-} \) to \( M n^{2+} \) is :


Which of the following is the best nuclear fuel?
A \( \cdot U^{23} \)
B. \( P u^{23} \)
C. \( N p^{239} \)
D. \( T h^{236} \)


Write the number of significant digits
in 100.10


ff \( x_{i}=a_{i} b_{i} c_{i}, i=1,2,3 \) are three-digit
positive integers such that each \( x_{i} \) is a
multiple of \( 19, \) then for some integer \( n \) prove that \( \left|\begin{array}{lll}\boldsymbol{a}_{1} & \boldsymbol{a}_{2} & \boldsymbol{a}_{3} \\ \boldsymbol{b}_{1} & \boldsymbol{b}_{2} & \boldsymbol{b}_{3} \\ \boldsymbol{c}_{1} & \boldsymbol{c}_{2} & \boldsymbol{c}_{3}\end{array}\right| \) is divisible
by 19


A game has 2 spinners. Spinner \( \# 1 \) has a
probability of landing red of \( 2 / 3 . \) And, spinner#2 has a probability of landing red of \( 1 / 5 \) What is the probability spinner#1 lands red AND spinner#2 does NOT land red?
A . \( 2 / 15 \)
B. \( 8 / 15 \)
c. \( 13 / 15 \)
D. 1
E. \( 3 / 5 \)


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


Identify the correct statement for freshwater ecosystems.
I. There is a seasonal mixing
of materials.
II. During the year, oxygen concentrations are
vertically uniform.
III. Materials are recycled more quickly
than in ocean ecosystems.
A. I only
B. II only
C. III only
D. I and III
E. II and III


The magnetic flux linked with a coil is changing with time \( t(\text { second }) \) according to \( \phi=6 t^{2}-5 t+1 . \) Where \( \phi \) is in \( \mathrm{Wb} \)
At \( t=0.5 \mathrm{S}, \) the induced current in the
coil is

The resistance
of the circuit is \( 10 \Omega \)
A . 1 A
B. 0.1A
c. \( 0.1 \mathrm{mA} \)
D. 10A


Which of the following statements is/are wrong?
I) \( B i^{3+} \) is more stable than \( B i^{5+} \)
II) \( M n \) shows +8 oxidation state.
III) The oxidation state of an element is
always less than or equal to its group number.
IV) \( s- \) Block elements show variable
oxidation states.
A. Il and IV
c. ।, ॥ and III
D. II, III and IV


In the extraction of copper, the copper
matte is a mixture of:
A. copper (II) sulphide and iron (II) sulphide
B. copper (II) sulphide and iron
(III) sulphide
C . copper
(I) sulphide and iron (II) sulphide
D. copper (I) sulphide and iron (III) sulphide


What is the S.I. unit of electric
potential?
A. ampere
B. volt
c. volt.m
D. coulomb


State whether the following statement is True or False.

It is not possible to recombine the lights of seven colours to obtain the white
light
A. True
B. False


Solve the following:
\( \lim _{x \rightarrow 0} \frac{2 \sin ^{2} 3 x}{3 x^{2}} \)
\( \mathbf{A} \cdot \mathbf{6} \)
B. 9
c. 18
D. 3


Some plants having pleasant odour and
attractive colours for
A. Hydrophily
B. Anemophily
c. Entomophily
D. None of the above


A wave of frequency \( 500 H z \) has a wave velocity of \( 350 m / s \). Find the phase difference in degrees between two displacements at a certain point at
times \( 10^{-3} \) s apart.


Elements of same group in the periodic table are characterised by the same:
A. ionization potential
B. electronegativity
c. electron affinity
D. number of valency electrons


The operation of a solar cell requires:
A. the absorption of light to generate electronhole pairs.
B. the separation of charge carriers of opposite types.
C. the separate extraction of charge carriers to an external circuit.
D. all of the above.


Archegoniatae include
A. Algae, Fungi, and Viruses
B. Algae, Lichens, and Bryophytes
C. Bryophytes, Pteridophytes, and Gymnosperms
D. Pteridophytes, Gymnosperms, and Angiosperms


The formula of Sodium Nitroprusside is
A \( \cdot \max _{4}\left[\operatorname{Fe}(C N)_{5} N O S\right] \)
в. \( \operatorname{Na}_{2}\left[\mathrm{Fe}(\mathrm{CN})_{5} \mathrm{NO}\right] \)
\( c \)
\( \operatorname{NaFe}\left[\operatorname{Fe}(C N)_{6}\right] \)
D \( \cdot \operatorname{Na}_{2}\left[\operatorname{Fe}(C N)_{6} N O_{2}\right] \)


Find out the major product of the
reaction.


An electron has a speed of \( 40 \mathrm{m} / \mathrm{s} \) accurate up to \( 99.99 \% \). what is the uncertainty in locating its position(in
\( \mathrm{m}) ? \)
A. \( 0.0144 \mathrm{m} \)
B. 0..0258m
c. \( 0.0568 \mathrm{m} \)
D. 0.0395m


In a circuit shown in the value of \( \beta \) is
100. \( I_{c}=1.5 m A . \) The transistor is in
A. Active state
B. Cut off state
c. Saturation state
D. Breakdown state


ff \( y=e^{x}(\sin x+\cos x), \) then prove that
\( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}-\boldsymbol{2} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+\boldsymbol{2} \boldsymbol{y}=\mathbf{0} \)


A cylinder of gas is assumed to contains 14 kg of butane. If a normal family needs \( 20,000 \mathrm{kJ} \) of energy per day for cooking, The cylinder will last:
(Given : The enthalpy of combustion, \( -\Delta H=-2658 \mathrm{kJ} / \) mole for butane
A. 24.33 days
B. 28.44 days.
c. 29.33 days
D. 32 days.


Determine the contrapositive of the following statement:
If Ravish skis, then it snowed.


Which of the following is a narcotic analgesic?
A. Ibuprofen
B. Aspirin
c. Paracetamol
D. Morphine


The area of the coil in a moving coil
galvanometer is \( 80 \mathrm{cm}^{2} \) and it has 200 turns. The magnetic induction of the radial field is \( 0.2 \mathrm{T} \) and the couple per unit twist of the suspension wire is \( 2 x \)
\( 10^{-6} N m \) per degree. If the deflection is
4, the current passing through it is
\( A \cdot 0.25 \mathrm{m} \mathrm{A} \)
в. 2.5 \( \mathrm{m} \) А
c. \( 0.025 \mathrm{mA} \)
D. 250 mA


DNA is directly involved in the synthesis except that of
A. DNA
B. Protein
c. tRNA
D. mRNA


A body of volume \( V \) and density \( \rho \) is raised through height \( h, \) in a liquid of density \( \sigma(\sigma<\rho) . \) The increment in
potential energy of the body is (Given acceleration due to gravity \( =g \) ):
A. \( V \rho g h \)
в. V\( \sigma g h \)
c. \( V(\rho+\sigma) g h \)
D. \( V(\rho-\sigma) g h \)


The shortest distance between the line \( y \)
\( -x=1 \) and the curve \( x=y^{2} \) is :
A \( \cdot \frac{2 \sqrt{3}}{8} \)
B. \( \frac{3 \sqrt{5}}{8} \)
c. \( \frac{\sqrt{3}}{4} \)
D. \( \frac{3 \sqrt{2}}{8} \)


The compound which does not contain
ionic bond is:
A . NaOH
в. нс
\( \mathrm{c} \cdot K_{2} \)
D. Lif


Which one of them is a radioisotope?
A. Cobalt-60
B. Carbon-12
c. carbon-14
D. None of the above


What is the correct sequence of
taxonomic categories?
A. Division, class, family, tribe, order, genus, species
B. Division, class, order, family, tribe, genus, species
C. Phylum, order, class, tribe, family, genus, species
D. Class, phylum, tribe, order, family, genus, species


Alkaptonuria is a disease where the
urine is
A. Yellow
B. White
c. orange
D. Black


If \( x^{y}=e^{x-y}, \) show that \( \frac{d y}{d x}= \) \( \frac{\boldsymbol{y} \log \boldsymbol{x}}{\boldsymbol{x}(\log \boldsymbol{x}+\mathbf{1})} \)


As we know, a code of three nitrogen bases is responsible for specifying one amino acid. In an ideal case, how many
nitrogen bases would be present on a messenger RNA that transcribes
a polypeptide containing 57 amino acids?
A \( \cdot 174 \)
B. 168
c. 17
D. 19


Backward reaction is favoured by
increase in the pressure of which of the following equilibrium?
A \( \cdot 2 S O_{2}+O_{2} \leftrightharpoons 2 S O_{3} \)
в. \( N_{2}+O_{2} \leftrightharpoons 2 N O \)
c. \( N_{2}+3 H_{2} \leftrightharpoons 2 N H_{3} \)
D. \( P C l_{5} \leftrightharpoons P C l_{3}+C l \)


Frying pan handles are made up of
A. thermoplastic
B. thermosetting Plastic
c. rayon
D. PVC


Number of real value of \( x \) satisfying the equation, arctan \( \sqrt{x(x+1)}+ \) \( \arcsin \sqrt{x(x+1)+1}=\frac{\pi}{2} \) is
A .
B.
\( c \cdot 2 \)
D. more than 2


If the angle of incidence is equal to
critical angle,then the angle of refractive is \( (\mathrm{C}) \)
A \( \cdot 0^{\circ} \)
B . \( 20^{\circ} \)
\( c .90^{\circ} \)
D. \( 180^{\circ} \)


The value of acceleration due to gravity at a height \( R \) from surface of the earth is then(R=radius of the earth and
geacceleration due to gravity on earth surface
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( \sqrt{g} \)
c. \( \frac{g}{4} \)
D. \( \frac{g}{2} \)


Construct \( \triangle \boldsymbol{A B C} \) given \( \boldsymbol{m} \angle \boldsymbol{A}=\boldsymbol{6 0}^{\boldsymbol{o}} \)
\( \boldsymbol{m} \angle \boldsymbol{B}=\mathbf{3 0}^{\boldsymbol{o}} \) and \( \boldsymbol{A B}=\mathbf{5 . 8 c m} \)


\( \int \frac{d x}{x(1+\sqrt[3]{x})^{2}} \) is equal to
A \( \cdot\left(\log \frac{x^{1 / 3}}{1+x^{1 / 3}}+\frac{1}{1+\sqrt[3]{x}}\right)+c \)
B. \( 3\left(\log \frac{1+\sqrt[3]{x}}{\sqrt[3]{x}}+\frac{1}{1+\sqrt[3]{x}}\right)+c \)
\( ^{\mathrm{C}} \cdot\left(\log \frac{x^{1 / 3}}{1+x^{1 / 3}}-\frac{1}{1+\sqrt[3]{x}}\right)+c \)
D. \( 3\left(\log \frac{1+\sqrt[3]{x}}{\sqrt[3]{x}}-\frac{1}{1+\sqrt[3]{x}}\right)+c \)


In the given circuit resistors \( A \) and \( B \)
made of same metal are of the same
length but A is thicker than B which of
the two ammeters will show a higher
reading? Justify your answer


Chronic intake of steroid can cause
A. osteoporosis
B. cushing syndrome
c. Reye's syndrome
D. Both A and B


The total kinetic energy of 8 litres of helium molecules at 5 atmosphere pressure will be
A. 6078 erg
B. 6078 Joule
\( c .607 \) erg
D. 607 Joule


A sphere \( A \) is released from rest i the
position shown and strikes the block \( B \)
which is at rest. If \( e=0.75 \) between \( A \)
and \( B \) and \( \mu_{k}=0.5 \) between \( B \) and the
support.The maximum displacement of \( B \) after impact is \( S_{A \max }=\frac{49}{x} m . \) Find \( x \)


\( \boldsymbol{C H I}_{3} \) is the structure of:
A. chloroform
B. lodoform
c. Both a and \( b \)
D. None of these


Assuming frictionless contacts, determine the magnitude of external
horizontal force \( P \) applied at the lower end for equilibrium of the rod as shown in figure. The rod is uniform and its
mass is ' \( m^{\prime} \)


Identify the correct statement(s)
This question has multiple correct options
A. Ozone is a powerful oxidizing agent as compared to \( O_{2} \)
B. Ozone reacts with KOH and gives an orange coloured solid \( K O_{3} \)
C. There is a decrease in volume when ozone
decomposed to form \( O_{2} \)
D. The decomposition of \( O_{3} \) to \( O_{2} \) is exothermic.


The probability of finding an electron in an orbital is approximately:
A . 95\%
B. 50\%
c. 60\%
D. 25\%


Match the following.
1) Morphine
a) Antipyretic
2) Ibuprofen
b) Narcotic analgesic
3) Paracetamol
c) Tranquilizer
4) Luminal
d) Non-narcotic analgesics
e) Antiseptic
A. \( 1-b, 2-d, 3-a, 4-c \)
B. \( 1-b, 2-c, 3-e, 4-d \)
c. \( 1-d, 2-b, 3-a, 4-e \)
D. \( 1-a, 2-e, 3-b, 4-d \)


Find the common ratio and \( 10^{t h} \) term of
G.P \( \frac{-2}{3},-6,-54, \dots \)


The value of \( \cos \left[\frac{1}{2} \cos ^{-1} \cos \left(-\frac{14 \pi}{5}\right)\right] \)
is
This question has multiple correct options
\( ^{A} \cdot \cos \left(-\frac{7 \pi}{5}\right) \)
B \cdot \( \sin \left(\frac{\pi}{10}\right) \)
c. \( \cos \left(\frac{2 \pi}{5}\right) \)
D. \( -\cos \left(\frac{3 \pi}{5}\right) \)


Which gas is released on the addition of dilute acid to calcium carbonate?
A \( . N_{2} \)
в. \( C a O O \)
\( c \cdot C l_{2} \)
D. \( N O_{2} \)
E \( . C O_{2} \)


An ideal gas is compressed isothermally until its pressure is doubled and then allowed to expand adiabatically to regain its original volume \( \left(\gamma=1.4 \text { and } 2^{-1.4}=0.38\right) . \) The ratio of the final to initial pressure is
A . 0.76: 1
B. 1: 1
\( c .0 .66: 1 \)
D. 0.86: 1


If \( a-b-2=0 \) and \( a^{3}-b^{3}-6 a b=k \)
then find the value of \( k \)


Strain energy per unit volume in a stretched string is
A. \( 1 / 2 \times \) Stress \( \times \) Strain
B. Stress x Strain
c. (Stress x Strain) \( ^{2} \)
D. Stress / Strain


Stress and pressure are both forces per
unit area. Then in what respect does
stress differ from pressure?


The standard deviation \( \sigma \) of \( (q+p)^{16} \) is
2. The mean of the distribution is
\( A \cdot 2 \)
B. 8
c. 16
D. 20


A copper weight and iron weight of the same mass were dropped from the same height on the ground Which of the weights had the higher temperature
after the impact ? (specific heat of \( \mathrm{Cu}= \)
\( 0.1 \mathrm{Kcal} / \mathrm{kg}^{o} \mathrm{C} \);specific heat of iron \( = \)
\( \left.0.11 \mathrm{Kcal} / \mathrm{kg}^{\circ} \mathrm{C}\right) \)
A. Iron weight
B. Copper weight
c. Both iron and copper
D. Cannot be answered


Whenever the magnetic flux linked with a coil changes, an induced e.m.f. is produced in the circuit. The e.m.f. lasts
A. for a short time
B. for a long time
c. for ever
D. so long as the change in flux takes place


Which of the following characters are not acquired?
A. Body weight
B. Body colour
c. Height
D. Eye colour


A shop has 600 shirts, out of which one-
fourth are defective.What percentage of shirts are defective.


If \( \overline{\boldsymbol{A}}=\mathbf{2} \hat{\mathbf{i}}+\mathbf{3} \hat{\boldsymbol{j}}-\hat{\boldsymbol{k}} \) and \( \overline{\boldsymbol{B}}=-\hat{\boldsymbol{i}}+\mathbf{3} \hat{\boldsymbol{j}}+ \)
\( 4 \hat{k}, \) then projection of \( \bar{A} \) on \( \bar{B} \) will be:
A \( \cdot \frac{3}{\sqrt{13}} \)
в. \( \frac{3}{\sqrt{26}} \)
c. \( \sqrt{\frac{3}{26}} \)
D. \( \sqrt{\frac{3}{13}} \)


Write the structure of \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{4} \)


How many metals are commercially
purified by Van Arkel method from the given metals? \( \boldsymbol{T} \boldsymbol{i}, \boldsymbol{B}, \boldsymbol{Z} \boldsymbol{r}, \boldsymbol{P} \boldsymbol{b}, \boldsymbol{H} \boldsymbol{g} \)


Which of the following statements is
not true about enzyme inhibitors?
A. Inhibit the catalytic activity of the enzyme.
B. Prevent the binding of substrate.
C. Generally, a strong covalent bond is formed between an inhibitor and an enzyme.
D. Inhibitors can be competitive or non-competitive.


What is the state of an ideal diode in
the region of nonconduction?
A. Open circuit
B. Short circuit
c. undefined
D. None of the above


Peroxonitrous acid is an unstable
intermediate formed in the oxidation of
\( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{2} \) by \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \)
"Peroxonitrous acid has the same
formula as nitric acid, \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \)
Answer whether the above statement is
true or false.lf true enter 1 , else 0


If \( \boldsymbol{R}=\left\{(\boldsymbol{x}, \boldsymbol{y}): \boldsymbol{x}, \boldsymbol{y} \in \boldsymbol{Z}, \boldsymbol{x}^{2}+\boldsymbol{y}^{2} \leq \mathbf{4}\right\} \)
is a relation in \( Z \) then domain \( D \) is
\( \mathbf{A} \cdot\{-2,-1,0,1,2\} \)
B \( \cdot\{-2,-1,0\} \)
c. \{0,1,2\}
D. None of these


Which of the following oxide is brown coloured gas:
A \( \cdot N O_{2} \)
B. \( N O \)
\( \mathrm{c} \cdot \mathrm{N}_{2} \mathrm{O} \)
D. \( N_{2} O_{5} \)


Explain denaturation of proteins.


Which of the following statements is
correct about the polymer?
This question has multiple correct options
A. It is thermoplastic polymer.
B. It is thermosetting polymer.
c. It is used in the manufacture of adhesive
D. It is not used in the manufacture of switches and
plugs


Show that the points \( A(1,2), B(1,6), C(1+ \) \( 2 \sqrt{3}, 4) \) are vertices of an equilateral triangle.


Vexillary aestivation is found in
A . Rosaceae
B. Cruciferae
c. Cucurbitaceae
D. Papilionaceae


A photon of energy 2.5 eV and
wavelength \( ^{\prime} \lambda^{\prime} \) falls on a metal surface
and the ejected electrons have
maximum velocity ' \( v^{\prime} . \) If the \( ^{\prime} \lambda^{\prime} \) of the
incident light is decreased by \( 20 \% \), the maximum velocity of the emitted electrons is doubled. The work function
of the metal is :
A . 2.6 ev
B. 2.23 ev
c. 2.5 ev
D. 2.29 ev


Kilowatt-hour is the unit of
A. potential difference
B. electric power
c. electric energy
D. charge


An oil drop has a charge \( -9.6 \times 10^{-19} C \)
and mass \( 1.6 \times 10^{-15} \) gm. When
allowed to fall, due to air resistance
force it attains a constant velocity. Then if a uniform electric field is to be
applied vertically to make the oil drop ascend up with the same constant speed, which of the following are correct. \( \left(\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} \boldsymbol{s}^{2}\right) \) (Assume that the
magnitude of resistance force is same in both the cases)
This question has multiple correct options
A. The electric field is directed upward
B. The electric field is directed downward
c. The intensity of electric field is \( \frac{1}{3} \times 10^{2} N C^{-} \)
D. The intensity of electric field is \( \frac{1}{6} \times 10^{5} \mathrm{NC}^{-1} \)


A highly rigid cubical block A of smal mass M and side L is fixed rigidly onto another cubical block B of same
dimensions and of low modulus of
rigidly \( \eta \) such that lower face of \( A \) completely covers the upper face of B. The lower face of B is rigidly held on a horizontal surface. A small force is
applied perpendicular to one the side face of A. After the force is withdrawn, block A executes small oscillations, the
time period of which is given by
в. \( 2 \pi \sqrt{\frac{M}{\eta L}} \)
c. \( 2 \pi \sqrt{\frac{M L}{\eta}} \)
D. \( \sqrt{\frac{M \eta}{L}} \)


I ne properties IIKe Ionızatıon potentıal, electronegativity, electron affinity and power of the catenation of the member
in a group depend on many factors. For example, the smaller the size of the
atom greater will be the ionization
potential. At the same time symmetry in the electronic configuration of the
elements also play a part in their ionization energy. Smaller the atomic
size, greater will be the mutual electronic repulsion and lesser will be
electron affinity. Similarly,
the catenation which is a direct result
of \( \mathbf{M}-\mathbf{M} \) bond strength is also affected by similar considerations.
The correct decreasing order of catenation among group 16 elements is
A. \( O>S>S e>T e \)
в. \( S>O>S e>T e \)
\( \mathbf{c} \cdot S>S e>T e>O \)
D. \( S>S e>O>T e \)


A thick plane mirror shows a number of images of the filament of an electric bulb. Of these, the brightest image is the -
A. First
B. Second
c. Last
D. Fourth


What is the formula of acrolein?
A. \( C H_{2}=C H-C N \)
В. \( C H_{2}=C H-C H O \)
c. \( C H_{2}=C H-C O O H \)
D. \( C H_{2}=C H-C O N H_{2} \)


Assertion
Actual atomic mass is greater than
mass number.
Reason
Mass of protons and neutrons is measured in daltons or atomic mass
unit (u) but the mass of each neutron
and proton is slightly greater than 1
dalton
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


Fill in the blanks:
(a) Burning of wood and coal causes of air.
(b) A liquid fuel, used in homes is
(c) Fuel must be heated to its
before it starts burning.
(d) Fire produced by oil cannot be controlled by


Identify an example of a successful way to dispose of hazardous waste.
A. Deep injection
B. Well burn it in an incinerator plant
c. Put it in a metal cask and throw it in the ocean
D. Bury in a metal drum in a regular landfill


A galvanometer, together with an unknown resistance in series, is connected across two identical
batteries of each \( 1.5 \mathrm{V} \). When the
batteries are connected in series, the
galvanometer records a current of \( 1 A \)
and when the batteries are connected in
parallel, the current is \( 0.6 A \), then the
internal resistance is \( 1 / x^{\prime} \) \Omega. What is
the value of \( x \) '?


Which of the following is more stable
complex and why? \( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right]^{3+} \) and
\( \left[\boldsymbol{C o}(\boldsymbol{e n})_{3}\right]^{3+} \)


In postulating the theory of evolution by natural selection, Darwin was greatly influenced by
A. Mutation theory of Hugo de Vires
B. Lamarck's theory of acquired characters
c. Malthus idea of population control
D. Environmental factors


Non-metals generally form:
A. cations
B. anions
c. anions and cations
D. do not form ions


From the following statements
regarding \( H_{2} O_{2}, \) choose the incorrect
statement?
A. It can act only as an oxidizing agentt
B. It decomposes on exposure to light.
c. It has to be stored in plastic or wax, lined glass bottles in dark.
D. It has to be kept away from dust


The actual product of 4.327 and 2.8 is 12.1156. The correctly reported answer will be :
A \( \cdot 12 \)
в. 12.1
c. 12.12
D. 12.116


On passing \( C \) ampere of current for
time \( t \) sec through \( 1 L \) of \( 2 M C u S O_{4} \)
solution (atomic weight of \( \boldsymbol{C u}=\mathbf{6 3 . 5} \) ), the amount \( m \) of \( C u \) (in gram) deposited on cathode will be:
A \( \cdot m=\frac{C t}{(63.5 \times 96500)} \)
в. \( _{m}=\frac{C t}{(31.75 \times 96500)} \)
c. \( _{m}=\frac{(C \times 96500)}{(31.75 \times t)} \)
D. \( m=\frac{(31.75 \times C \times t)}{96500} \mathrm{g} \)


Liquid water is present in
A. oceans
B. lakes
C. rivers
D. oceans, lakes, rivers, and even underground.


If \( \boldsymbol{x}+\boldsymbol{a}+\boldsymbol{b}+\boldsymbol{c}=\boldsymbol{0}, \) then what is the
value of \( \left|\begin{array}{ccc}\boldsymbol{x}+\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{a} & \boldsymbol{x}+\boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{a} & \boldsymbol{b} & \boldsymbol{x}+\boldsymbol{c}\end{array}\right| ? \)
\( \mathbf{A} \cdot \mathbf{0} \)
B \( \cdot(A+B+C)^{2} \)
c. \( A^{2}+B^{2}+C^{2} \)
D. \( A+B+C-2 \)


In the fig., \( O A B C \) is a square inscribed
in a quadrant \( O P B Q . \) If \( O A=20 \mathrm{cm} \)
Find the area of shaded region.
\( [\boldsymbol{\pi}=\mathbf{3 . 1 4}] \)


An air cored solenoid with length 20
\( \mathrm{cm}, \) area of cross section is \( 20 \mathrm{cm}^{2} \) and
the number of turns 400 carries a
current 2 A. The current is suddenly
switched off within \( 10^{-3} \) sec. The
average back emf induced across the
end of the open switch in the circuit is ignore variation in magnetic field near the end of the solenoid)
A. \( 2 v \)
B. 4
\( c \cdot 3 v \)
D. 5 v


A balloon is filled with gas. The gas occupies the whole space because
A. the gas is highly compressible
B. the particles of gases are free to move
c. the particles of gases are held by weak intermolecular forces
D. Both B and C


The value of \( \lim _{x \rightarrow 0}\left[\frac{a}{x}-\cot \frac{x}{a}\right] \) is
A . 0
B.
\( c \)
D. \( \frac{a}{3} \)


Violet light is incident on a thin convex
lens. If this light is replaced by red light, explain with reason, how the power of
the lens would change?


Which of the followings are redox titration?
A. Complexometric titration
B. Iodometric titration
c. Acid-base titration
D. Back titration
E. All of these


The horizontal component of earth's magnetic field at a place is \( \frac{1}{\sqrt{3}} \) times
the vertical component. Determine the angle of dip at that place.


How are the points (0,1),(3,1) and (1,3) situated with respect to the circle \( x^{2}+y^{2}-2 x-4 y+3=0 \)


Differentiate with respect to \( x \) :
\( e^{\tan ^{-1} \sqrt{x}} \)


The formula of the compound which gives violet colour in Lassiagnes test for sulphur with sodium nitroprusside is :
A \( \cdot N a_{4}\left[F e(C N)_{5} N O S\right] \)
B . \( N A_{3}\left[F e(C N)_{5} N O S\right] \)
c. \( \operatorname{Na}_{2}\left[\operatorname{Fe}(C N)_{5} S\right] \)
D. \( N a_{4}\left[F e(C N)_{4} S\right] \)


Given \( : a x+b y=d \) and \( y=m x+c \)
Find \( x \) in terms of \( b, c, d \) and \( m \)
A \( \cdot x=\frac{d-b c}{a-b m} \)
B. \( x=\frac{d+b c}{a+b m} \)
c. \( _{x}=\frac{d-b c}{a+c m} \)
D. \( x=\frac{d-b c}{a+b m} \)


Find the principle value of \( \sin ^{-1} \sin \frac{2 \pi}{3} \)


A satellite of mass m goes around the earth along a circular path of radius \( r \) (from the center of Earth), let me is the
mass of the earth and \( R \), its radius. Then
the linear speed of the satellite depends
on:
\( \mathbf{A} \cdot m_{e} \) and \( r \)
B . \( m_{e} \) only
\( \mathbf{c} \cdot \mu, m_{e}, V \)
D. \( m_{e}, R_{e} \) and \( r \)


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) of \( \boldsymbol{x}^{2}+\boldsymbol{x} \boldsymbol{y}+\boldsymbol{y}^{2}=\mathbf{1 0 0} \)


if \( y=e^{x} \cos x, \) prove that \( \frac{d y}{d x}= \)
\( \sqrt{2} e^{x} \cos \left(x+\frac{\pi}{4}\right) \)


The rate of emission of radiation of a
black body at \( 273^{\circ} \mathrm{C} \) is \( E \), then the rate of
emission of radiation of this body at \( 0^{\circ} \mathrm{C} \)
will be
A \( \cdot \frac{E}{16} \)
в. \( \frac{E}{4} \)
c. \( \frac{E}{8} \)
D. 0


A train of length \( 50 m \) is moving with a
constant speed of \( 10 m / s . \) Calculate the
time taken by the train to cross an electric pole and a bridge of length
\( \mathbf{2 5 0 m} \)


A chemical which turns red litmus to
blue is:
A . acidic in nature
B. basic in nature
c. neutral in nature
D. can be acidic or basic in nature


A circular wire of radius \( 42 \mathrm{cm} \) is cut
and bent it into the form of rectangle whose sides are in the ratio of \( 6: 5 . \) The
smaller side of the rectangle is
\( A .30 \mathrm{cm} \)
B. \( 60 \mathrm{cm} \)
\( c .72 \mathrm{cm} \)
D. \( 132 \mathrm{cm} \)


Assertion
In transition elements, radii of \( 5 d \) series are virtually the same as those of the
corresponding members of \( 4 d \) series.
Reason
The filling of \( 4 f \) orbitals before \( 5 d \) orbitals results in a regular decrease in atomic radii.
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


Reproduction in man
is
A. Asexual
B. Sexual
c. vegetative
D. Parthenogenetic


The charge \( Q \) flowing through a resistance \( \boldsymbol{R} \) varies with time \( t \) as \( \boldsymbol{Q}= \)
\( a t-b t^{2} . \) The total heat produced in \( R \) is
(up to the instant when instantaneous
current is zero)
\( ^{A} \cdot \frac{a^{3} R}{6 b} \)
B. \( \frac{a^{3} R}{3 b} \)
c. \( \frac{a^{3} R}{2 b} \)
D. \( \frac{a^{3} R}{b} \)


Which combinations of quantum number \( n, 1, m, s \) for the electron in an
atom does not provide a permissible solution of the wave equation?
A. \( 3,2,-2,1 / 2 \)
B. 3, 3, 1,-1/2
c. \( 3,2,1,1 / 2 \)
D. 3, 1, 1, -1/2


Which of the following is not a unit of time?
A. Calendar year
B. Solar year
c. Light year
D. Tropical year


A steady current is flowing in a cylindrical conductor.Then which one of the following statements is true?
A. Electric filed within the conductor is zero
B. Electric field exists only on the outer surface of the conductor
c. Electric field exists within the conductor
D. None of the above


A ball is thrown from the top of a tower
with an initial velocityof \( 10 \mathrm{m} / \mathrm{s} \) at an
angle of \( 30^{\circ} \) above the horizontal. It hits
theground at a distance of \( 17.3 \mathrm{m} \) from the base of the tower.The height of the
tower \( \left(\mathrm{g}=10 \mathrm{m} / \mathrm{s}^{2}\right) \) will be
A. \( 10 \mathrm{m} \)
B. \( 110 \mathrm{m} \)
\( c .12 \mathrm{m} \)
D. \( 100 \mathrm{m} \)


All harmonics in a stringed instrument
are
A. Standing waves
B. Progressive wave
c. Electromagnetic waves
D. Transverse waves


Find the angle between \( \overrightarrow{\boldsymbol{A}}=\mathbf{4} \hat{\mathbf{i}}+\hat{\mathbf{j}}+ \)
\( \mathbf{3} \hat{\boldsymbol{k}} \) and \( \overrightarrow{\boldsymbol{B}}=\hat{\boldsymbol{i}}+\mathbf{3} \hat{\boldsymbol{j}}+\boldsymbol{4} \hat{\boldsymbol{k}} \)


"Division of Labour" in multicellular
animals means
A. All functions by a single cell-type
B. A function performed jointly by many cells
C. Different functions by different cell-types
D. None of the above


Minor \( m_{33} \) of the determinant
\( \left|\begin{array}{ccc}2 & 3 & 5 \\ 2 & -1 & 8 \\ 1 & 2 & 4\end{array}\right| \) is


From means value theorem \( \boldsymbol{f}(\boldsymbol{b})- \)
\( \boldsymbol{f}(\boldsymbol{a})=(\boldsymbol{b}-\boldsymbol{a}) \boldsymbol{f}^{\prime}\left(\boldsymbol{x}_{1}\right) ; \mathbf{0}<\boldsymbol{a}<\boldsymbol{x}_{1}<\boldsymbol{b} \) if
\( f(x)=\frac{1}{x}, \) then \( x_{1}= \)
A \( \cdot \sqrt{a b} \)
в. \( \frac{a+b}{2} \)
c. \( \frac{2 a b}{a+b} \)
D. \( \frac{b-a}{b+a} \)


Which of the following factors does riot affect sustainable population size?
A. Predation
B. Resources
c. competition
D. All of these can affect population size


Find the value of \( \boldsymbol{\theta}, \) if
\( \cos \theta=0.9664 \)


The value of \( a \) for which the area
between the curves \( y^{2}=4 a x \) and \( x^{2}= \)
\( 4 a y \) is \( 1 s q . \) unit, is-
A. \( \sqrt{3} \)
B. 4
c. \( 4 \sqrt{3} \)
D. \( \frac{\sqrt{3}}{4} \)


A particle moves according to the equation \( x=a \sin \omega t \) and \( y=a(1- \)
\( \cos \omega t) . \) The path of the particle is
A . circle
B. parabola
c. hyperbola
D. cycloid
E . ellipse


The focal length of a convex lens of
glass \( (\mu=1.5) \) is \( 2 c m . \) The focal length of the lens when immersed in a liquid of
refractive index 1.25 will be :
A \( .5 \mathrm{cm} \)
B. \( 2.4 \mathrm{cm} \)
\( c .1 c m \)
D. \( 4 c m \)


When a body rests on a surface, then which force is applied on the surface by the body? (Gravitational, Upthrust)


In what time after its motion begins, will a particle oscillating according to
the equation \( x=5 c o s 0.2 \pi t \) move from
the mean position to maximum displacement position?


The oxidation number of \( \sin H_{2} S_{2} O_{8} \)
is:
\( A \cdot+2 \)
\( B \cdot+4 \)
\( c \cdot+6 \)
\( D \cdot+7 \)


\( \mathrm{IF} \boldsymbol{B}=\left[\begin{array}{cc}\mathbf{1} & \mathbf{3} \\ -\mathbf{2} & \mathbf{5}\end{array}\right] \) and \( \boldsymbol{C}=\left[\begin{array}{cc}-\mathbf{2} & \mathbf{5} \\ \mathbf{3} & \mathbf{4}\end{array}\right] \)
then find the value of \( B-4 C \)


Which of the following is not correct?
A. \( A l \) reacts with \( N a O H \) and liberate \( H_{2} \)
B. \( A l C l_{3} \) is a lewis acid
C. \( A l \) is used in the manufacture of electrical cables
D. \( N a O H \) is used during Hall's process of purification of bauxite


Find the value:
1. \( 7 x-5=2 x \)
2. \( 5 x-12=2 x-6 \)
3. \( 7 p-3=3 p+8 \)


Write down the chemical equation for the preparation of Bakelite from
formaldehyde?


\( A C r O_{4}^{2-} \) solution turns from yellow to another color upon addition of acid.
What is the another color?
A. Pink
B. Green
c. white
D. orange


Prove that:
\( \cos ^{-1}(x)+\cos ^{-1}\left\{\frac{x}{2}+\frac{\sqrt{3-3 x^{2}}}{2}\right\}=\frac{\pi}{3} \)


\( (p, q) \) is a point such that \( p \) and \( q \) are integers \( p \geq 50 \) and the equation \( p x^{2}+q x+1=0 \) has real roots. The
square of the least distance of the point from the origin is \( S \)
Find \( \frac{\boldsymbol{S}-\mathbf{2 2 5}}{\mathbf{5 0 0}} \)


Balance the following below equation.
\( \boldsymbol{A u}+\boldsymbol{N O}_{3}^{-}+\boldsymbol{C l}^{-}+\boldsymbol{H}^{+} \rightarrow \boldsymbol{A u} \boldsymbol{C l}_{4}^{-}+ \)
\( N O_{2}+H_{2} O \)
A \( \cdot A u+3 N O_{3}^{-}+4 C l^{-}+6 H^{+} \rightarrow A u C l_{4}^{-}+3 N O_{2}+ \)
\( 3 H_{2} O \)
B . \( A u+2 N O_{3}^{-}+5 C l^{-}+8 H^{+} \rightarrow A u C l_{4}^{-}+6 N O_{2}+ \)
\( 3 H_{2} O \)
c. \( A u+4 N O_{3}^{-}+2 C l^{-}+6 H^{+} \rightarrow A u C l_{4}^{-}+5 N O_{2}+ \)
\( 3 H_{2} O \)
D. None of these


Which of the following is an intensive
property?
A. Specific heat capacity
B. Heat capacity
c. Gibb's energy
D. Entropy


The orbit of Pluto is much more
eccentric than the orbits of the other
planets. That is, instead of being nearly
circular, the orbit is noticeably elliptical. The point in the orbit nearest
to the Sun is called the perihelion and
the point farthest from the Sun is called
the aphelion. At perihelion, the gravitational potential energy of Pluto
in its orbit has:
A. Its maximum value
B. Its minimum value
C. The same value as at every other point in the orbit
D. The value which depends on the sense of rotation


Assertion
Mendeleev's periodic table have some demerits.
Reason
There was no place for all isotopes of the elements and some heavy elements
were placed before lighter elements.
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 sum of n terms of GP:
\( \sqrt{7}, \sqrt{21}, 3 \sqrt{7}, \dots n \) terms.


Two bodies collide at the same
temperature. Which of the following must remain conserved?
(i) Velocity
(ii) Momentum
(iii) Kinetic energy
A. Only (i) and (ii)
B. Only (ii)
c. only (i) and (iii)
D. (i), (ii) and (iii)


The Van't Hoff's factor \( ^{\prime} \boldsymbol{i}^{\prime} \) accounts for:
A. extent of dissolution of solute
B. extent of mobility of solute
c. extent of solubility of solute
D. extent of dissociation of solute


If \( I \sin ^{-1} x-\cos ^{-1} x=\frac{\pi}{6}, \) then solve for
\( \boldsymbol{x} \) ?


Assertion
\( (A): \) Microwaves are better carries of signals than optical waves Reason \( (\boldsymbol{R}): \) Microwaves move faster than optical waves
A. Both \( A \) and \( R \) are true and \( R \) is correct explanation of \( A \)
B. Both \( A \) and \( R \) are true and \( R \) is not the correct explanation of
c. \( A \) is true but \( R \) is false
D. \( A \) is false but \( R \) is true


An excerpt from a book by Einstein and Infeld gives the following remarks concerning wave phenomena:
"A bit of gossip starting in Washington reaches New York [by word of mouth] very quickly, even though not a single individual who takes part in spreading it travels between these two cities.
There are two quite different motions involved, that of the rumor, Washington
to New York, and that of the persons who
spread the rumor."
Identify a correct inference from the above text.
A. The particles of the medium perform motion from one place to another
B. The particles of the medium perform random motion to constitute wave motion
c. The particles constituting the medium perform only small vibrations, but the whole motion is that of a progressive wave.
D. None of these


Which of the following is used as an anaesthetic agent?
A \( . C H_{4} \)
в. \( C O_{2} \)
\( c \cdot N_{2} O \)
D. \( N O_{2} \)


Spherical balls of radius \( \mathbf{R} \) are falling in a viscous fluid of viscosity \( \eta \) with a velocity v. The retarding viscous force acting on the spherical ball is:
A. directly proportional to R but inversely proportional to
B. directly proportional to both radius R and velocity v
C. inversely proportional to both radius R and velocity
D. inversely proportional to R but directly proportional to velocity v


Four identical charges each of charge
are placed at the corners of a square.
Then at the centre of the square the
resultant electric intensity E and the net electric potential V are
A. \( E \neq 0, V=0 \)
B. \( E=0, V=0 \)
c. \( E=0, V \neq 0 \)
D. \( E \neq 0, V \neq 0 \)


which ol the lomowing ilgures correculy
represents primary and secondary
rainbows?
\( A \)
B.
\( c \)
\( D \)


Compute the missing frequencies \( \boldsymbol{f}_{1} \) and \( f_{2} \) in the following data if the mean
is \( 166 \frac{9}{26} \) and the sum of the frequencies is 52
c.ı \( \begin{array}{lll}140- & 150- & 160- \\ 150 & 160 & 170\end{array} \) 170180
Freq. 5
\( f_{1} \)
20


The number of four digit numbers that can be formed from the digit 0,1,2,3,4,5 with at least one digit repeated is ?
A . 420
в. 560
\( c .750 \)
D. None


Atomic radii of fluorine is 42 pm. Atomic radii of oxygen is :
A. \( 42 \mathrm{pm} \)
B. 39 pm
c. \( 41 \mathrm{pm} \)
D. \( 48 \mathrm{pm} \)


Meeta's father was driving her to the school. At the traffic signal she noticed
that each traffic light was made of many tiny lights instead of a single bulb. When meeta asked this question
to her father. he explained the reason for
this.
Answer the following based on above information:
(i) What were the values displayed by meeta and her father?
(ii) What answer did meeta's father
give?
(iii) What are the tiny lights in traffic signals called and how do these
operate?


Simplify the following expression:
\( \frac{1+\sin +2 x}{(\sin x+\cos x)^{2}} \)


Assertion
Diffraction takes place for all types of
waves mechanical or non-mechanical,
transverse or longitudinal.
Reason
Diffraction's effect are perceptible only if wavelength of wave is comparable to dimensions of diffracting device.
A. Both Assertion are not correct and Reason is the correct
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect;Reason is not correct explanation for Assertion
D. Both Assertion is correct and Reason are incorrect


\( \frac{\sqrt{2}}{4} \)


Calculate the internal resistance of the
cell
\( A \cdot 4 \Omega \)
в. 2 \( \Omega \)
\( c \cdot 5 \Omega \)
D. \( 1 \Omega \)


Divide \( R s .1000 \) between Shubh and
Swastik such that one-third share of
Shubh and half the share of Swastik are
equal.


Find the value of :
\( \sec ^{2}\left(\tan ^{-1} 2\right)+\csc ^{2}\left(\cot ^{-1} 3\right) \)
A . 11
B. 15
c. 17
D. 21


Explain the activity which you performed to know that the stomach is protected from the damage being caused by secretion of its own acid?


If \( x \sin ^{3} \theta+y \cos ^{3} \theta=\cos \theta \sin \theta \) and
\( \boldsymbol{x} \sin \boldsymbol{\theta}=\boldsymbol{y} \cos \boldsymbol{\theta} \operatorname{then} \boldsymbol{x}^{2}+\boldsymbol{y}^{2}=\mathbf{1} \)
If the statement is True, enter 1 , else
enter 0
A.


A Malpighian body is constituted by
A. Glomerulus only
B. Glomerulus and Bowman's capsule
c. Glomerulus and Efferent vesse
D. Glomerulus, Bowman's capsule and Efferent vessel


Solve the following differential equation \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\boldsymbol{x}^{2}+\boldsymbol{3} \boldsymbol{x}+\boldsymbol{7} \)


If the distance between nuclei is \( 2 \times \)
\( 10^{-13} \mathrm{cm}, \) the density of nuclear
material is
A \( .3 .21 \times 10^{-12} k g / m^{3} \)
B . \( 1.6 \times 10^{-3} \mathrm{kg} / \mathrm{m}^{3} \)
c. \( 2 \times 10^{9} k g / m^{3} \)
D. \( 1 \times 10^{17} k g / m^{3} \)


Determine the contrapositive of the following statement:

Only if he does not tire will he win.


In the electrolysis of aqueous \( N a C l \) solution, side reactions taking place
are :
(I) \( 2 O H^{-}+C l_{2} \longrightarrow 2 O C l^{-}+H_{2} \)
(II) \( 2 N a+2 H_{2} O \longrightarrow 2 N a O H+H_{2} \)
(III) \( 4 O H^{-} \longrightarrow O_{2}+2 H_{2}+4 e^{-} \)
Select the correct alternate.
A . ।, ॥
B. ॥, ॥ I
c. ।, ॥ा
D. I, II and III


The minimum energy required to overcome the attractive forces between
an electron and the surface of Ag metal
is \( 5.52 \times 10^{-19} \mathrm{J} \). What will be the
maximum kinetic energy of electron ejected out from Ag which is being exposed to UV-light of \( =360 \mathrm{A} ? \)


Evaluate the following integrals:
\( \int \frac{1}{x^{2 / 3} \sqrt{x^{2 / 3}-4}} d x \)


A wire of length \( 50 \mathrm{cm} \) has a mass of 20
gm. It its radius is halved by stretching, its new mass per unit length will be
A. \( 0.4 \mathrm{g} \mathrm{cm}^{-1} \)
B. 0.2 \( \mathrm{kg} \mathrm{m}^{-1} \)
c. \( 0.1 \mathrm{g} \mathrm{cm}^{-1} \)
D. \( 0.2 \mathrm{g} \mathrm{cm}^{-1} \)


When hydrogen sulphide gas is passed through a blue solution of copper sulphate, a black precipitate of copper sulphide is obtained and the sulphuric acid so formed remains in the solution.
The reaction is an example of a:
A. Combination reaction
B. Displacement reaction
c. Decomposition reaction
D. Double displacement reaction


State the underlying principle of a cyclotron. Write briefly how this machine is used to accelerate charged particles to high energies.


A pair of angles with a common vertex and common arm are called
A. adjacent angles
B. complementary
c. supplementary
D. none


The heat capacity of a body depends on This question has multiple correct options
A. the heat given
B. the temperature raised
c. the mass of the body
D. the material of the body


Select the pairs of isotopes, isobars and isotones from the following nuclei \( _{11} N a_{12}^{22}, M g_{111}^{24} N a_{10}^{24} N e^{23} \)


What is the mass of \( 6.022 \times 10^{23} \)
molecules of \( \boldsymbol{N} \boldsymbol{H}_{3} \) ?
A. \( 45.06 g \)
в. \( 19.06 g \)
c. \( 17.04 g \)
D. \( 31.02 g \)


Lysigenous cavity in monocot stem vascular bundles develops by the dissolution of
A. protoxylem
B. metaxylem
c. phloem
D. ground tissue


In a hot water heating system, there is a
cylindrical pipe of length 28 m and diameter \( 5 \mathrm{cm} . \) Find the total radiating surface in the system.
A \( \cdot 4.4 m^{2} \)
B . \( 2.4 m^{2} \)
c. \( 4.1 \mathrm{m}^{2} \)
D. \( 3.4 m^{2} \)


The IUPAC name of the compound is:
\[
\begin{array}{l}
C H_{2}-C H-C H_{2}-C H_{2} \\
N_{2} \quad C H_{3} \quad \quad_{N H_{2}}
\end{array}
\]
A. 2 - Methyl - butane - 1,4 - diamine
B. 3 - Methyl - butane - 1, 4 - diamine
C . 2 - Methyl - butane - 1, 3 - diamine
D. 2 - Methyl pentane - 1, 5 - diamine


A sphere of solid material of specific
gravity 8 has a concentric spherical cavity and just sinks in water. The ratio
of radius of cavity to that of outer
radius of the sphere must be
\( \mathbf{A} \cdot 4^{1 / 3} \)
\( ^{\text {В } \cdot \frac{5^{1 / 3}}{2}} \)
c. \( \frac{9^{1 / 3}}{2} \)
D. \( \frac{3^{1 / 3}}{2} \)


Which of the following is an equation?
A. \( f(x)=2 x+3 \)
В. \( 2 x+3=4 y+5 \)
c. \( x=y \)
D. Both \( B \) and \( C \)


Prove that:
\( \int \frac{x^{2} d x}{(x \sin x+\cos x)^{2}} \)


Both the crown and root of a tooth is
covered by a layer of bony hard
substance called as
A. Enamel
B. Dentine
c. Bony socket
D. Cementum


A person carries a hammer on his
shoulder and holds the other end of its
light handle in his hand. Let \( y \) be the
distance between his hand and
the point of support. If the person
changes \( y \), the pressure on his hand will be proportional to:
\( \mathbf{A} \cdot y \)
В . \( y^{2} \)
\( c \cdot \frac{1}{y} \)
D. \( \frac{1}{y^{2}} \)


Melvin Calvin recieved nobel prize for
A. Botany
B. Plant Physiology
c. Biochemistry
D. Chemistry


By the fusion of male and female
gametes ............. is formed.
A . Zygote
B. Embryo
c. seed
D. Ovum


The properties of \( Z r \) and \( H f \) are same because
A. they have similar radii
B. they belong to d-b;ock
C. they have same valence electrons
D. None of the above


Which of the following doesnt represent
Maxwells equation?
\( \mathbf{A} \cdot \oint \vec{E} \cdot d \vec{A}=\frac{q}{\varepsilon_{0}} \)
B \( \cdot \oint \vec{B} \cdot d \vec{A}=0 \)
c. \( \oint \vec{E} \cdot \bar{d} l=\frac{-d B}{d t} \)
D \( \cdot \oint \vec{B} \cdot \bar{d} l=\mu_{0} I_{C}+\mu_{0} \varepsilon_{0} \frac{d \phi_{E}}{d t} \)


Electric lines of force about a negative
point charge are:
A. Circular anti-clockwise
B. Circular clockwise
c. Radially inwards
D. Radially outwards


Find the mean velocity of the particle averaged over the time that the particle takes to cover the first \( s m \) of the path.
A \( \cdot \frac{3 \alpha}{2 \sqrt{s}} \)
B. \( \frac{2 \alpha \sqrt{s}}{2} \)
c. \( \frac{\alpha \sqrt{s}}{2} \)
D. \( \frac{\alpha \sqrt{s}}{3} \)


1 femtometre is equivalent to
\( \mathbf{A} \cdot 10^{15} m \)
B. \( 10^{-12} m \)
\( \mathbf{c} \cdot 10^{-15} m \)
D. \( 10^{-9} m \)


What is the empirical formula of a compound that contains 0.05 mole of magnesium, 0.05 mole of sulfur, and 0.20 mole of oxygen?
A. \( M g S O \)
в. \( M g S O_{2} \)
\( \mathrm{c} \cdot \mathrm{MgSO}_{3} \)
D. \( M g S O_{4} \)


Which of the following statement is
incorrect statement about
interhalogen compound?
A. These compound can be used as non aqueous solvent
B. Interhalogen compound are very useful fluorinating agents
C. These all are covalent and diamagnetic in nature
D. Generally interhalogen compound are less reactive then halogens


Consider the following reversible chemical reactions:
\[
\begin{array}{l}
\boldsymbol{A}_{2}(\boldsymbol{g})+\boldsymbol{B} \boldsymbol{r}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{2} \boldsymbol{A} \boldsymbol{B}(\boldsymbol{g}) \ldots(1) \boldsymbol{K}_{1} \\
\boldsymbol{6} \boldsymbol{A} \boldsymbol{B}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{3} \boldsymbol{A}_{2}(\boldsymbol{g})+\boldsymbol{3} \boldsymbol{B}_{2} \ldots(\boldsymbol{2}) \boldsymbol{K}_{2}
\end{array}
\]
The relation between \( K_{1} \) and \( K_{2} \) is:
A \( \cdot K_{2}=K_{1}^{3} \)
В. \( K_{2}=K_{1}^{-3} \)
c. \( K_{1} K_{2}=3 \)
\( D \)
\[
K_{1} K_{2}=\frac{1}{3}
\]


Two closed vessel \( A \) and \( B \) of equal
volume containing air at pressure \( \boldsymbol{P}_{1} \)
and temperature \( T_{1} \) are connected to
each other through a narrow open tube. If the temperature of one is now
maintained at \( T_{1} \) and other at \( T_{2} \) (where
\( \left.T_{1}>T_{2}\right) \) then that what will be the final
pressure?
A \( \cdot \frac{T_{1}}{2 P_{1} T_{2}} \)
В. \( \frac{2 P_{1} T_{2}}{T_{1}+T_{2}} \)
\( \mathbf{c} \cdot \frac{2 P_{1} T_{1}}{T_{1}-T_{2}} \)
D. \( \frac{2 P_{1}}{T_{1}+T_{2}} \)


A cell of e.m.f \( 3 V \) and internal
resistance \( 4 \Omega \) is connected to two
resistance \( 10 \Omega \) and \( 24 \Omega \) joined in
parallel. Find the current through each resistance using kirchhoff's laws.


Statement 1: Crystals of sodium
chloride go into aqueous solution as ions.
Statement 2: The sodium ion has a \( 1+ \)
change and the chloride ion has a \( 1- \)
charge and they are hydrated by the
water molecules.
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 and 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.
E. Both the Statement 1 and Statement 2 are not correct.


Write the names of any two organic
compound semiconductors.


What is meant by pair production and annihilation?


For any integer \( n \geq 1 \), the sum \( \sum_{k=1}^{n} k(k+2) \) is equal to
A \( \cdot \frac{n(n+1)(n+2)}{6} \)
B. \( \frac{n(n+1)(2 n+1)}{6} \)
c. \( \frac{n(n+1)(2 n+7)}{6} \)
D. \( \frac{n(n+1)(2 n+9)}{6} \)


For the reaction \( \boldsymbol{H}^{+}+\boldsymbol{B} \boldsymbol{r} \boldsymbol{O}_{3}^{-}+ \)
\( 3 B r^{-} \rightarrow 5 B r_{2}+H_{2} O \) which of the
following relation correctly represents the consumption \( \& \) formation of reactants and product:
A \( \cdot \frac{d\left[B r^{-}\right]}{d t}=-\frac{3}{5} \frac{d\left[B r_{2}\right]}{d t} \)
B. \( \frac{d\left[B r^{-}\right]}{d t}=\frac{3}{5} \frac{d\left[B r_{2}\right]}{d t} \)
c. \( \frac{d\left[B r^{-}\right]}{d t}=-\frac{5}{3} \frac{d\left[B r_{2}\right]}{d t} \)
D. \( \frac{d\left[B r^{-}\right]}{d t}=\frac{5}{3} \frac{d\left[B r_{2}\right]}{d t} \)


A semiconductor has equal number of
electron and hole concentration of \( 2 \times \)
\( 10^{8} m^{-3} . \) On doping with a certain
impurity, the electron concentration increases to \( 4 \times 10^{10} m^{-3} \), then the new
hole concentration of the
semiconductor is
A \( \cdot 10^{6} m^{-3} \)
B. \( 10^{8} m^{-3} \)
c. \( 10^{10} m^{-3} \)
D. \( 10^{12} m^{-3} \)


In a fourier series, the fundamental frequency is the
A. Highest frequency sinusoid in the term
B. Lowest frequency sinusoid in the term
c. constant term
D. None of the above


In the diffraction pattern due to a single slit of width ' \( d \) with incident light of
wavelength ' \( \lambda^{\prime}, \) at an angle of
diffraction ' \( \boldsymbol{\theta}^{\prime} \), the condition for first
minimum is
\( \mathbf{A} \cdot \lambda \sin \theta=d \)
B. \( d \cos \theta=\lambda \)
\( \mathbf{c} \cdot d \sin \theta=\lambda \)
\( \mathbf{D} \cdot \lambda \cos \theta=d \)


The degree of dissociation of \( \boldsymbol{P C l}_{5} \)
A. increases with increasing pressure
B. decreases with increasing pressure
C. no effect on change in pressure
D. decreases with decreasing pressure


In triangle \( A B C, \) angle \( B \) is obtuse. \( D \)
and \( E \) are mid-points of sides \( A B \) and
\( B C \) respectively and \( F \) is a point on
side \( A C \) such that \( E F \) is parallel to \( A B \)
Then, \( B E F D \) is a parallelogram. State
True or False.
A. True
B. False


Frustule is refered to as
A. Silicated cell wall
B. Cellulosic cell wall
C . Stony cell wall
D. Lignified cell wall


The above transformation proceeds
through:
A. electrophilic-addition
B. benzyne intermediate
C . activated nucleophilic substitution
D. elimination, addition mechanism


About \( 88.6 \% \) of the universe is made up
of :
A. Helium
B. Oxygen
c. Nitrogen
D. Hydrogen


The junction diode shown in figure is
ideal. The current in the circuit is
A . \( 50 A \)
в. \( 30 A \)
\( c .20 m A \)
D. 30 \( m A \)


In a parallelogram ABCD if \( A B=2 x+5 \) \( \mathrm{CD}=\mathrm{y}+1, \mathrm{AD}=\mathrm{y}+5 \) and \( \mathrm{BC}=3 \mathrm{x}-4 \) then ratio
of \( A B: B C \) is
\( A \cdot 71: 21 \)
B. 12:11
c. 31: 35
D. 4 : 7


Assertion
Ice cube floats on water.
Reason
Density of ice is less than that of water.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Chlorine water oxidises thiosulphates
to:
A. sulphate
B. persulphate
c. sulphide
D. none of these


Which of the following statements are
correct about Friedel-crafts reaction?
This question has multiple correct options
A. It is an aromatic electrophilic substitution reaction.
B. The reaction intermediate is an \( \bar{e} \) deficient species.
C. The reaction involves alkylation and acylation.
D. A Lewis acid is used as a catalyst


If all the angles of a 14 -sided figure are equal, then the measure of each angle is equal to?
\( ^{A} \cdot\left(184 \frac{2}{7}\right)^{\circ} \)
B. \( \left(164 \frac{2}{7}\right) \)
\( ^{c} \cdot\left(134 \frac{2}{7}\right)^{\circ} \)
\( ^{\mathrm{D}} \cdot\left(154 \frac{2}{7}\right) \)


The number of free electrons in the
outermost shell of carbon in graphite is
A . four
B. one
c. two
D. three


The number of whorls present in a bisexual flower is
A. one
B. Three
c. Two
D. Four


State whether the following statement is True or False
If \( \boldsymbol{U}=\{\mathbf{1}, \mathbf{2}, \mathbf{3}, \mathbf{4}, \mathbf{5}, \mathbf{6}, \mathbf{7}\} \) and \( \boldsymbol{A}= \)
\( \{5,6,7\}, \) then \( U \) is the subset of \( A \)
A. True
B. False


A prism has a refracting angle of \( 60^{\circ} \) When placed in the position of minimum deviation, it produces a
deviation of \( 30^{\circ} . \) The angle of incidence
is:
\( A \cdot 30 \)
B. 45
\( c \cdot 15 \)
\( D \cdot 60 \)


C-14 has a half life of
A. 11520 yrs
B. 2880 yrs
c. 5760 yrs
D. 17280 yrs


The first ionisation energy of Be is
smaller than that of B while the second
ionisation energy of Be is higher than
that of B.

Answer whether the above statement is
true or false.
If true enter 1 , else enter 0


According to Thomson, an atom consists of :
A. embedded electrons
B. positively charged uniform sphere
c. positively charged nucleus
D. both a and


For the reaction \( 2 \mathrm{A}+\mathrm{B} \rightarrow \mathrm{C}+3 \mathrm{D} \) which of
the following is / are correct? This question has multiple correct options
\( ^{\mathbf{A}} \cdot+\frac{\Delta[D]}{\Delta t}=-\frac{1}{3} \frac{\Delta[C]}{\Delta t} \)
B. \( +\frac{\Delta[C]}{\Delta t}=-\frac{1}{2} \frac{\Delta[A]}{\Delta t} \)
c. \( -\frac{1}{2} \frac{\Delta[B]}{\Delta t}=-\frac{1}{3} \frac{\Delta[D]}{\Delta t} \)
D. \( \frac{\Delta[C]}{\Delta t}=+\frac{1}{3} \frac{\Delta[D]}{\Delta t} \)


When the temperature is raised,
viscosity of the liquid decreases. This is
because:
A. volume of the solution decreases
B. increase in temperature increases the average kinetic energy of the molecules which overcomes the attractive forces between them
C. covalent and hydrogen bond forces decreases
D. attraction between the molecule increases.


The length of tangent drawn from an
external point \( P \) to a circle with centre
0, is \( 8 \mathrm{cm} \). If the radius of the circle is 6
\( \mathrm{cm}, \) then the length of OP (in cm) is :
A \( 2 \sqrt{7} \)
7
B. \( 4 \sqrt{7} \)
\( c \cdot 10 \)
D. 10.5


If \( \boldsymbol{f}(\boldsymbol{x})=\frac{\boldsymbol{x}}{\sqrt{\boldsymbol{x}+1}-\sqrt{\boldsymbol{x}}} \) be a real
values function
then
\( A \cdot f(x) \) is continuous, but \( f^{\prime}(0) \) does not exist
B. \( f(x) \) is differentiable at \( x=0 \)
\( \mathrm{c} \cdot \mathrm{f}(\mathrm{x}) \) is not continuous at \( x=0 \)
D. \( f(x) \) is not differentiable at \( x=0 \)


A transformer is used to light a \( 120 W \) \( 24 V \) lamp from \( 240 V \) a.c. mains. The
current in the main cable is \( 0.6 A . \) The efficiency of the transformer is
A . \( 48 \% \)
B. \( 63.8 \% \)
c. \( 83.3 \% \)
D. \( 90 \% \)


Discuss the given process.
8


A small piece of wire bent into L shape such that the upright and horizontal portions are of equal length. It is placed with the horizontal portion along the
axis of concave mirror of radius of
curvature \( 20 \mathrm{cm} \). If the bend is \( 40 \mathrm{cm} \) from the pole of the mirror, then the ratio of the length of the images of the upright and horizontal portions of the wire is
A \( \cdot 1: 9 \)
в. 1: 3
\( c \cdot 3: \)
\( D \cdot 2: \)


Night blindness is due to:
A. Excess of vitamin A
B. Deficiency of vitamin A
c. Deficiency of vitamin B
D. None


Find the distance between parallel lines
\( (i) 15 x+8 y-34=0 \) and \( 15 x+8 y+ \)
\( \mathbf{3 1}=\mathbf{0} \)
\( (\text { ii })(x+y)+p=0 \) and \( (x+y)-r=0 \)


Solve the following differential \( \left(e^{x}+1\right) d y=(y+1) e^{x} d x \)


In the reaction of \( H_{2} O_{2} \) with acidified
\( \boldsymbol{K}_{4}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}\right], \) the oxidation state of
iron changes to:
\( \mathbf{A} \cdot+2 \) from +1
B. +3 from 0
\( \mathbf{c} \cdot+3 \) from +2
\( \mathbf{D} \cdot+2 \) from 0


If the point \( P(a, b, c), \) with reference to Eq. \( (i) \) lies on the plane \( 2 x+y+z=1 \)
then the value of \( 7 a+b+c \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B. 12
\( c \cdot 7 \)
D. 6


What is the commercial name of
PMMA? What is its use?


If the mass of the moving object is decreased \( 1 / 4 \) of its mass and its
velocity is increased to twice its previous velocity, what will be the kinetic energy of the object from the following?
A. \( 1 / 2 \) of the previous kinetic energy
B. 4 times of previous kinetic energy
c. Kinetic energy will remain constant
D. 2 times of the previous kinetic energy


Five identical plates are connected
across a battery as in figure. If the
charge on plate 1 be \( +q \), then the
charges on the plates 2,3,4 and 5 are:
\( \mathbf{A} .-q,+q,-q,+q \)
в. \( -2 q,+2 q,-2 q,+q \)
c. \( -q,+2 q,-2 q,+q \)
D. none of the above.


At \( 25^{\circ} \mathrm{C} \), the molar conductances at
infinite dilution for the strong
electrolytes \( N a O H, N a C l \) and \( B a C l_{2} \)
\( \operatorname{are} 248 \times 10^{-4}, 126 \times 10^{-4} \) and \( 280 \times \)
\( 10^{-4} S m^{2} m o l^{-1} \) respectively
\( \lambda_{m}^{\circ} B a(O H)_{2} \) in \( S m^{2} m o l^{-1} \) is
\( \mathbf{A} \cdot 52.4 \times 10^{4} \)
B \( .524 \times 10^{4} \)
c. \( 4.2 \times 10^{4} \)
D \( .262 \times 10^{4} \)


Name two non- metals whose oxides are
acidic in nature


Assem went to a stationary shop and
purchased 3 pens and 5 pencils for Rs.40. His cousin Manik bought 4
pencils and 5 pens for \( R s .58 . \) If cost of 1 pen is \( R s . x, \) then which of the following represents the situation algebraically?
A. \( 3 x+5 y=40,4 x+5 y=58 \)
B. \( 3 x+4 y=40,5 x+5 y=58 \)
c. \( 3 x+5 y=40,5 x+4 y=58 \)
D. \( 3 x+5 y=40,4 x+3 y=58 \)


Fig. \( 6.36, \frac{Q R}{Q S}=\frac{Q T}{P R} \) and \( \angle 1=\angle 2 \)
Show that \( \Delta P Q S \sim \Delta T Q R \)


A point at which all the three perpendicular coordinate axes meets is known as
A. Meeting point
B. Origin
c. Triple point
D. None of these


Solve \( 2 x+3=5 x+6 \& \) represent it as
¡) One variable
ii) Two variable


In the compound \( \boldsymbol{C H}_{2}=\boldsymbol{C H}- \)
\( \boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{C} \equiv \boldsymbol{C H}, \) the \( \boldsymbol{C}_{2}-\boldsymbol{C}_{3} \)
bond is of the type.
A \( \cdot s p-s p^{2} \)
B \( \cdot s p^{3}-s p^{3} \)
\( \mathbf{c} \cdot s p-s p^{3} \)
D. \( s p^{2}-s p^{3} \)


A certain dye absorbs light of \( \lambda=4500 \)
\( A^{\circ} \) and then fluoresces light of \( \lambda= \)
\( 5000 A^{\circ} . \) Assuming that under given conditions, \( 45 \% \) of the absorbed energy is re-emitted out as fluorescence,
calculate the ratio of qunts emitted out to the number of quanta absorbed.


Give the difference between open and
closed system of circulation.


A galvanometer of resistance, \( G \) is
shunted by a resistance \( S \) ohm. To keep
the main current in the circuit unchanged, the resistance to be put in series with the galvanometer is
A \( \cdot \frac{S^{2}}{(S+G)} \)
B. \( \frac{S G}{(S+G)} \)
c. \( \frac{G^{2}}{(S+G)} \)
D. \( \frac{G}{(S+G)} \)


f \( x, y, z \) are different and \( \left|\begin{array}{lll}\boldsymbol{x} & \boldsymbol{x}^{2} & \boldsymbol{1}+\boldsymbol{x}^{2} \\ \boldsymbol{y} & \boldsymbol{y}^{2} & \boldsymbol{1}+\boldsymbol{y}^{2} \\ \boldsymbol{z} & \boldsymbol{z}^{2} & \boldsymbol{1}+\boldsymbol{z}^{2}\end{array}\right|=\mathbf{0} \) then prove that
\( \mathbf{1}+\boldsymbol{x} \boldsymbol{y} \boldsymbol{z}=\mathbf{0} \)


Match the statements in Column A, with
those in Column B.


A ball collides with a smooth fixed wall
with a velocity \( 10 \mathrm{m} / \mathrm{s} \) and returns with
a velocity 6 m/s. Considering oblique
collision, the coefficient of restitution \( e \)
can not be:
A . 0.8
B. 0.6
c. 0.5
D. 0.4


n \( \triangle \boldsymbol{R} \boldsymbol{S T} \), line \( \boldsymbol{P Q} \| \) segST \( , \boldsymbol{R}-\boldsymbol{P}-\boldsymbol{S} \)
and \( \boldsymbol{R}-\boldsymbol{Q}-\boldsymbol{T} . \) If \( \boldsymbol{R} \boldsymbol{P}=\boldsymbol{4}, \boldsymbol{P} \boldsymbol{S}= \)
\( 8, R Q=3, \) then find \( Q T \)


Find the nature of the roots of \( 3 x^{2}- \)
\( 4 \sqrt{3} x+4=0 \)


In a cyclotron, If a deuteron can gain an energy of \( 40 \mathrm{MeV} \), then a proton can an
energy of:
A. 40 Mev
B. 80 Mev
c. 20 Mev
D. 160 Mev


The molar enthalpy of vaporization of benzene at its boiling point \( (353 K) \) is
\( 30.84 \mathrm{kJ} \) mol\( ^{-1} . \) What is the molar
internal energy change? For how long
would a 12 volt source need to supply a \( 0.5 A \) current in order to vaporise \( 7.8 g \) of
the sample at its boiling point?


Solve the given inequalities graphically:
\( x+y \geq 4 \) and \( 2 x-y>0 \)


State whether the statement is true or
false:

Lewis dot symbols indicate the number of electrons of the inner shell.


If the fourth term in the expansion of
\( \left(\sqrt{\frac{1}{x \log x+1}}+x \frac{1}{12}\right)^{6} \) is equal to
200 and \( x>1, \) then \( x \) is
A . 10
B. \( 10^{-4} \)
\( c \cdot 1 \)
D. -4


If \( \boldsymbol{\alpha}=\cos \left(\frac{\boldsymbol{8} \boldsymbol{\pi}}{\mathbf{1 1}}\right)+\boldsymbol{i} \sin \left(\frac{\boldsymbol{8} \boldsymbol{\pi}}{11}\right), \) then
\( \boldsymbol{R} e\left(\boldsymbol{\alpha}+\boldsymbol{\alpha}^{2}+\boldsymbol{\alpha}^{3}+\boldsymbol{\alpha}^{4}+\boldsymbol{\alpha}^{5}\right) \) is
A \( \cdot \frac{1}{2} \)
B. \( -\frac{1}{2} \)
\( c \cdot 0 \)
D. None of the above


A proton is projected horizontally eastward in a uniform magnetic field, which is horizontal and southward in
direction. The proton will be deflected
A. upwarddardpwardd
B. downward
c. northward
D. southward


An emulsion is a colloidal solution
consisting of:
A. two solids
B. two liquids
c. two gases
D. one solid and one liquid


Number of bivalent are 8 in prophase I. What is the number of chromosomes
during anaphase II ?
\( A \cdot 8 \)
B. 4
\( c \cdot 16 \)
D. 32


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


If \( \tan \theta \cdot \tan \phi=\sqrt{\frac{(a-b)}{(a+b)}}, \) then
\( (a-b \cos 2 \theta)(a-b \cos 2 \phi)= \)
A \( \cdot a^{2} \)
в. \( b^{2} \)
\( \mathbf{c} \cdot a^{2}+b^{2} \)
D. \( a^{2}-b^{2} \)


Which of the following are correct?
(i) \( \quad \) Diploblastic :
Poriferans, Coelenter " Diploni :
and What is and
Platyhelminthes to
(ii) \( \quad \) Triploblastic: \( \quad \) Chordates Triploblastic:
(iii) Acoelomata:
(iv) Pseudocoelomata
:
Aschelminthes/Roundv
Eucoelomata:
\( (v) \)
Annelids to Chordates
\( \mathbf{A} \cdot(\mathrm{i}),(\mathrm{iii}),(\mathrm{iv}) \) and \( (\mathrm{v}) \)
B. (iii) and (v)
C \( . \) (i), (ii), and (v)
D. (i), (ii), (iii), (iv) and (v)


Between the bark and the wood in a
woody stem, there is a layer of meristem called:
A. Zone of cell division
B. Vascular cambium
c. Cork cambium
D. Both B and C


Which of the following respiratory material requires the highest numbers
of \( O_{2} \) molecules for its complete
oxidation?
A . Malic acid
B. Triolein
c. Tartaric acid
D. Oleic acid


Ag is precipitated when \( Z n \) is added to
\( \left[\boldsymbol{A} \boldsymbol{g}(\boldsymbol{C} \boldsymbol{N})_{2}\right]^{-} \)
If \( 2\left[A g(C N)_{2}\right]^{-}+Z n \rightarrow \)
\( \left[Z n(C N)_{4}\right]^{2-}+2 A g \) is the reaction
enter 1 else 0.


An iron bar (Young's modulus \( = \) \( \left.10^{11} N / m^{2}, \alpha=10^{-6} /^{\circ} C\right) 1 m \) long and
\( 10^{-3} m^{2} \) in area is heated from \( 0^{\circ} C \) to
\( 100^{\circ} \mathrm{C} \) without being allowed to bend
or expand. Find the compressive force in newtons developed inside the bar


State whether true or false.
Motion of the needle of a sewing
machine is rotatory motion.
A. True
B. False


Evaluate:
\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left\{\tan ^{-1} \frac{\boldsymbol{x}}{\mathbf{1}+\boldsymbol{x}^{2}}+\tan ^{-1} \frac{\mathbf{1}+\boldsymbol{x}^{2}}{\boldsymbol{x}}\right\} \)
\( A \)
в.
\( c \cdot \frac{1}{2} \)
\( D \)


A rain in \( 50 \% \) completed om shown and \( 75 \% \) in \( \mathrm{d} 4 \) hours. Find the order of
reaction:


If \( \boldsymbol{y}=\cot ^{-1}\left(\frac{1-x}{1+x}\right) \) then \( \frac{d y}{d x}=? \)
A \( \cdot \frac{-1}{\left(1+x^{2}\right)} \)
B. \( \frac{1}{\left(1+x^{2}\right)} \)
c. \( \frac{1}{\left(1+x^{2}\right)^{3 / 2}} \)
D. none of these


A plank with a uniform sphere placed on it rests on a smooth horizontal plane.
The plank is pulled to the right by a constant force \( F \). If the sphere does not
slip over the plank, then This question has multiple correct options
A. both have the same acceleration
B. acceleration of the centre of sphere is less than that of the plank
c. work done by friction acting on the sphere is equal to its total kinetic energy
D. total kinetic energy of the system is equal to work done by the force \( F \)


In a room where the temperature is
\( 30^{\circ} \mathrm{C} \) a body cools from \( 61^{\circ} \mathrm{C} \) to \( 59^{\circ} \mathrm{C} \) in
4 minutes. The time taken by the body
to cool from \( 51^{\circ} \mathrm{C} \) to \( 49^{\circ} \mathrm{C} \) will be about
A. 5 minutes
B. 8 minutes
c. 4 minutes
D. 6 minutes


If \( \phi(x)=\frac{1}{1+e^{-x}} \) then the value of
\( \boldsymbol{\phi}(\mathbf{5})+\boldsymbol{\phi}(\mathbf{4})+\ldots+\boldsymbol{\phi}(-\mathbf{3})+\boldsymbol{\phi}(-\mathbf{4})+ \)
\( \phi(-5) \)
\( \mathbf{A} \cdot \mathbf{5} \)
B. \( \frac{9}{2} \)
c. \( \frac{11}{2} \)
D. none of these


Water sprinkler used for grass lawns begins to rotate as soon as the water is supplied. It is based on which law?
A. Newton's first law of motion
B. Newton's second law of motion
c. Newton's third law of motion
D. First law of thermodynamics


Ethylidene chloride is a/an
A. vicinal dihalide
B. gem-dihalide
c. allylic halide
D. vinylic halide


A convex mirror used for rear view on an
automobile has a radius of curvature of
\( 3.00 \mathrm{m} . \) If a bus is located at \( 5.00 \mathrm{m} \) from
this mirror, find magnification?
\( A \cdot+0.23 \)
B. - -0.23
\( c \cdot+0.45 \)
D. -0.45


Assertion
\( \operatorname{gmof} S O_{2} \) and \( 1 \mathrm{gm} \) of \( C O_{2} \) contains the same number of molecules under
similar conditions.
Reason
\( 64 \mathrm{gm} \) of \( S O_{2} \) and \( 44 \mathrm{gm} \) of \( C O_{2} \) contains the same number of atoms
under similar conditions.
Choose the correct option.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


A device that increases the voltage of
an alternating current is called a(n)
A. Electric motor
B. Galvanometer
c. step-up transformer
D. step-down transformer


The correct match for functions of
nematocysts is
A. Stenotele
(i) Paralysing
B. Volvent
(ii) Capturing
C. Large glutinant
(iii) Attachment
D. Small glutinant
(iv) Locomotion
A. A- (ii), B- (i), C- (iii), D- (iv)
B. A- (i), B- (ii), C- (iii), D- (iv)
C. \( A- \) (iv), \( B- \) (iii), \( C- \) (ii), D- (i)
D. A- (iv), B- (i), C- (ii), D- (iii)


The value of \( (-i)^{-i} \) equals?
A \( \cdot e^{4 n-1 \frac{\pi}{2}}, n \epsilon I \)
B . \( e^{i 4 n-1 \frac{\pi}{2}}, n \epsilon I \)
C . \( e^{4 n+1 \pi / 2}, n \epsilon I \)
D \cdot \( e^{-i 4 n+1 \frac{\pi}{2}}, n \epsilon I \)


Flower is a modified shoot as
A. Thalamus may elongate to show internodes.
B. There is aggregation into inflorescence.
C . It bears essential organs.
D. It may have epicalyx.


Which of the following is/are correct
regarding the working principle of LED?
This question has multiple correct options
A. When an electron makes a transition to the valance
band to fill up a hole in a p-njunction, it emits energy in the form of photon
B. The energy of this photon is equal to the energy gap between conducction band and valance band energy levels
C. Energy of a photon is the product of frequency of electromagnetic radiation (f) and Planck constant (h)
D. Both A and B


State the number of significant figures
in each of the following:
\( \mathbf{2 0 8 . 9 1} \)


The given figure shows a siphon in
action. The liquid flowing through the
siphon has a density of \( 1.5 g / c c \)
Calculate the pressure difference between
(i) points \( \boldsymbol{A} \) and \( \boldsymbol{D} \)
(ii) points \( C \) and \( B \)


Mechanism of Cannizzaros reaction of
benzaldehyde is Which of the following reactants can undergo Cannizaro's reaction?
A. \( _{\|}^{o} \)
\( H-C-H \)
в. \( R_{3} C C H O \)
\( c \)
D. All of these


How are isotopes of the same element
similar?
A. They have the same particles in the nucleus
B. They have the same number of neutrons
C. They are equally abundant in nature
D. They have the same number of protons
E. They have the same mass


\( (p \wedge \sim p) \wedge(p \vee q) \) is a
A. contradiction
B. tautology
c. negation
D. none


Which of the following oxides is most acidic?
A. \( A g_{2} O \)
в. \( V_{2} \), \( O_{5} \)
c. \( C O \)
D. \( N_{2} O_{5} \)


In the Boolean algebra : \( \overline{\boldsymbol{A}} . \overline{\boldsymbol{B}}=\ldots \)
\( \mathbf{A} \cdot \overline{A+B} \)
в. \( A . B \)
c. \( \overline{\bar{A}+\bar{B}} \)
D. \( A+B \)


A transistor having \( \alpha=0.99 \) is used in
common base amplifier. If the load resistance is \( 0.45 M \Omega \) and the dynamic resistance of the emitter junction is
\( \mathbf{5 0} \mathbf{\Omega}, \) the voltage gain of the amplifier will be
A .7910
0
в. 8910
\( c .9910 \)
D. 6910


Which of the following molecules is planar?
A. \( N F_{3} \)
в. \( N C l_{3} \)
c. \( P H_{3} \)
D. \( B F_{3} \)


A square loop \( A B C D, \) carrying a
current \( \boldsymbol{I}_{1}, \) is placed near and coplanar
with a long straight conductor \( \boldsymbol{X} \boldsymbol{Y} \)
carrying a current \( I_{1} \), as shown in
figure. The net force on the loop will be
A \( \cdot \frac{\mu_{0} I_{1} I_{2}}{2 \pi} \)
B. \( \frac{\mu_{0} I_{1} I_{2} L}{2 \pi} \)
c. \( \frac{2 \mu_{0} I_{1} I_{2} L}{2 \pi} \)
D. \( \frac{2 \mu_{0} I_{1} I_{2}}{3 \pi} \)


Which of the following are physical changes?
(i) Melting of iron metal
(ii) Rusting of iron
(iii) Bending of an iron rod
(iv) Drawing a wire of iron metal
A. (i), (ii) and (iii)
B. (i), (ii) and (iv)
c. (i), (iii) and (iv)
D. (ii), (iii) and (iv)


Do following addition with the help of
numberline:
\( (-4)+5 \)


If the displacement, velocity and acceleration of a particle at time \( t \) be \( x \) \( \mathbf{v} \) and \( f \) respectively, then which one is true?
A \( \cdot f=v^{3} \frac{d^{2} t}{d x^{2}} \)
B. \( f=-v^{3} \frac{d^{2} t}{d x^{2}} \)
c. \( f=v^{2} \frac{d^{2} t}{d x^{2}} \)
D. \( f=-v^{2} \frac{d^{2} t}{d x^{2}} \)


Give an example of a jawless fish.


Which is correct according to the
increasing elliptical nature of sub-
shell?
\( A \cdot 2 s<5 p<3 p<4 d \)
B. \( 4 d<2 s<5 p<3 p \)
\( \mathrm{C} \cdot 4 \mathrm{d}<2 \mathrm{s}<3 \mathrm{p}<5 \mathrm{p} \)
D. \( 3 p<4 d<2 s<5 p \)


If a photon of energy 14 eV is incident on an H-atom, what is true?
A. Atom will be ionised and electron will have a kinetic energy of 14 ev
B. Atom will be ionised and electron will have a kinetic energy of 0.4 ev
C. Photon passes through a tom without interacting with it
D. None of these


To protect iron from corrosion and rusting , it is electroplated with
A. zinc
B. Chromium
c. Nickel
D. Aluminum


Nuclides having the same atomic and mass numbers are known as:
A. isotones
B. isomers
c. isobars
D. isotopes


A capacitor of capacitance \( 0.5 \mu F \) is connected to a source of alternating electromagnetic force of frequency 100 \( H z . \) What is the capacitive
reactance? \( (\pi=3.142) \)


Electric lines of force about a negative
point charge are:
A . circular, anti-clockwise
B. circular, clockwise
c. radial, inwards
D. radial, outwards


Choose the correct statements from the
following:
This question has multiple correct options
A. Steel is more elastic than rubber.
B. The stretching of a coil spring is determined by the young's modulus of the wire of the spring.
C. The frequency of a tuning fork is determined by the shear modulus of the material of the fork.
D. When a material is subjected to a tensile (stretching) stress the restoring forces are caused by interatomic attraction.


Choose the minor carp from the following.
A. cyprinus
B. Labeo bata
c. Labeo calbasu
D. ctenopharyngodan idella


Select the correct option:
The best material for the study of structure of cell membrane is
\( A \cdot R B C \) of human
B. Liver cell
c. Kidney cell
D. Muscle cell


possess both sensory and motor functions.
A. Hypothalamus
B. Thalamus
c. Medulla
D. Cerebrum


A \( 0.5 m \) long solenoid of \( 10 t u r n s / c m \)
has area of cross-section \( 1 \mathrm{cm}^{2} \)
Calculate the voltage induced across its
ends if the current in the solenoid is
charged from \( 1 A \) to \( 2 A \) in \( 0.1 s \)


Find the total acceleration of the sphere as a function of \( \boldsymbol{\theta}, \) the angle of deflection of the thread from the
vertical.
A. \( w=g \sqrt{1+2 \cos ^{2} \theta} \)
В. \( w=g \sqrt{2+3 \cos ^{2} \theta} \)
c. \( w=g \sqrt{1+3 \cos ^{2} \theta} \)
D. \( w=g \sqrt{3+2 \cos ^{2} \theta} \)


A particle of unit mass undesgro one
dimension motion. Such that its
verocity varies accordingly to \( v(x)= \)
\( \beta \vec{x}^{2} \pi, \) where \( \beta \) and \( n \) are constant and \( x \)
is the position of the particle. The accelerationx is the position of the particle. The accelerationof the particle
a function of \( x, \) is given by
A. \( -2 n \beta^{2} x^{-} 2 n-1 \)
B . \( -2 n \beta^{2} x^{-4 n-1} \)
C \( .-2 \beta^{2} x^{-2 n+1} \)
D. \( -2 n \beta^{2} e^{-} 4 n+1 \)


A disaccharide which gives only glucose on hydrolysis is :
A. lactose
B. fructose
c. sucrose
D. maltose


The monohalogen derivatives of alkanes are called:
A. alkene halide
B. haloalkanes
c. halogen alky
D. none of the above


L-Dopa is used for treatment of which disease?
A. AlDS
B. Parkinson's
c. cancer
D. Heart attack


An open rectangular cistern when
measured from outside is 1.35 m long
\( 1.08 m \) broad and \( 90 \mathrm{cm} \) deep. It is
made up of iron, which is \( 2.5 \mathrm{cm} \) thick.
Find the capacity of the cistern and the volume of the iron used.


The rate at which the population of a city increases at any time is proportional to the population at that time. If there are 1,30,000 people in the city in 1960 and 1,60,000 in \( 1990, \) what approximate population may be anticipated in \( 2020 ? \) \( \left[\log _{e} \frac{16}{13}=0.2070, e^{0.42}=1.52\right] \)


In the figure shown, the lower pulley is free to move in a vertical direction only.
Block \( \boldsymbol{A} \) is given a uniform velocity \( \boldsymbol{u} \) as
shown, what is the velocity of block \( \boldsymbol{B} \)
as a function of angle \( \boldsymbol{\theta} \) ?
\( \mathbf{A} \cdot u \cos \theta \)
B. \( \frac{u}{\cos \theta} \)
c. \( \frac{u[1+\sin \theta]}{\cos \theta} \)
D. \( \frac{u[1+\cos \theta]}{\sin \theta} \)


The speed of the electron in the 1 st orbit of the hydrogen atom in the ground state is: \( (c \) is the velocity of light)
A \( \cdot \frac{c}{1.37} \)
в. \( \frac{c}{1370} \)
c. \( \frac{c}{13.7} \)
D. \( \frac{c}{137} \)


Pathway of water inside plant body after its absorption is by
A. Apoplast
B. Symplast
c. Both A and B
D. None of the above


Atomic mass of most of the elements is
fractional. This is because of :
A. mass is due to the sum of masses of p,n,e in it which are fractional
B. average atomic mass of different isotopes of elements
c. mass of \( ^{12} \mathrm{C} \) is in fraction
D. none of these


The temperature has dropped by 15 degree Celsius in the last 30 days. If the rate of temperature drop remains the same, how much more will the
temperature drop in the next 10 days?


Which is helpful in the formation of ionic bond?
A. Only small cation
B. Only small anion
c. Small cation and small anion both
D. Low positive charge cation and small anion


For a dilute solution containing 2.5 grams of non volatile non electrolyte solute in hundred grams of water, the
elevation in the boiling point at 1 atmosphere pressure is to degree Celsius asuming concentration of solute is much lower than
concentration of solvent, the vapour
pressure of the solution is?


Litmus paper is turned red by the action
of:
\( \mathbf{A} \cdot C H_{3} C H_{2} C H_{2} O H \)
B \( \cdot C H_{3} C H(B r) C H(B r) C H_{3} \)
\( \mathbf{c} \cdot C H_{3} C H_{2} C H(B r) C H_{3} \)
D. \( C H_{3} C H_{2} C H_{2} C O O H \)
\( \mathbf{E} \cdot C H_{3} C H_{2} C H_{2} C H_{3} \)


Two block masses \( m_{1} \) and \( m_{2} \) are
connected with the help of a spring of spring constant \( k \) initially the spring in its natural length as shown. A sharp
impulse is given to mass \( m_{2} \) so that it
acquires a velocity \( v_{0} \) towards right. If the system is kept on smooth floor then find:
(a) the velocity of the centre of mass
(b) the maximum elongation that the spring will suffer?


In the reaction \( C_{7} H_{8} \frac{3 C l_{2} / \Delta}{\longrightarrow} X \frac{B r_{2} / F e}{ } \)
\( \boldsymbol{Y} \stackrel{Z n / \boldsymbol{H} C l}{\longrightarrow} \boldsymbol{Z} \)
The compound \( Z \) is :
A. o-bromotoluene
B. m-bromotoluene
c. p-bromotoluene
D. 3-bromo-2, 2, 6-trichlorotoluene


The anode rays were discovered by:
A. Goldstein
B. Crookes
c. chadwick
D. Thomson


Assertion
\( \mathbf{C}-\mathbf{C} \) bond length in zeise's salt is same
as ethylene.
Reason
Double bond is Ionger as compare to
single bond.
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


Match the names of the structures
listed with the functions given. Choose the answer which gives the correct
combination of the alphabets of the
two columns.
\( \mathbf{A} \)
\( A-4, B-1, C-3, D-5 \)
B. A-3, B-2, C-5, D-4
C \( . A-2, B-5, C-1, D-3 \)
D. A-1, B-4, C-5, D-2


The reaction \( A \rightarrow B \) follows first-order
kinetics. The time taken for 0.8 mol of \( A \)
to produce 0.6 mol of \( \mathrm{B} \) is 1 hr. What is the time taken for the conversion of 0.9
mol of \( A \) to produce 0.675 mol of B?
\( A \cdot 1 h r \)
B. 0.5 hr
c. \( 0.25 \mathrm{hr} \)
\( D \cdot 2 h r \)


Choose the correct answers from the
following given. Which of the following does not constitute a part of a uriniferous
tubule?
A. Loop of Henlele
B. Distal convoluted tubule
c. Bowmans capsule
D. collecting duct


Find the term which has the exponent of \( x \) as 8 in the expansion of
\( \left(x^{\frac{5}{2}}-\frac{3}{x^{3} \sqrt{x}}\right)^{10} \)
\( \mathbf{A} \cdot T_{2} \)
В. \( T_{3} \)
c. \( T_{4} \)
D. Does not exist


Show that the number \( 3-\sqrt{5} \)
is irrational.


Which halogen sublimates?
A. Chlorine
B. Bromine
c. lodine
D. Fluorine


The Poisson's ratio \( \sigma \) should satisfy the relation:
A \( .-1<\sigma<0.5 \)
B. - \( 0.5<\sigma<1.0 \)
c. \( 0.5<\sigma<1.0 \)
D. -1.0 < \( \sigma<-0.5 \)


Define the following:
(a) Cationic detergents
(b) Broad spectrum antibiotics
(c) Tranquilizers


The capacity of a parallel plate condenser is inversely proportional to
A. Area of each plate
B. Dielectric constant
c. Permittivity of medium
D. Distance between two plates


The van't Hoff factor for a very dilute
aqueous solution of \( \boldsymbol{K}\left[\boldsymbol{A} \boldsymbol{g}(\boldsymbol{C} \boldsymbol{N})_{2}\right] \) is:
A . 4
B. 3
c. 2
D. 5


State True or False.
SONAR is an instrument used for
finding the heights of a mountain.


A parallel beam of diameter \( d \) is
incident on air-glass interface as shown in figure. The diameter of refracted light
beam is:
\( \left(\boldsymbol{d}=\mathbf{3} \boldsymbol{m} \boldsymbol{m}, \boldsymbol{\theta}=\mathbf{4} \mathbf{5}^{\mathbf{0}} \text { and } \frac{\boldsymbol{n}_{\boldsymbol{g} \operatorname{lass}}}{\boldsymbol{n}_{\boldsymbol{a} i \boldsymbol{r}}}=\frac{\boldsymbol{3}}{\boldsymbol{2}}\right) \)
\( A \cdot \sqrt{12} m m \)
В. \( \sqrt{14} \) тт
\( c \cdot \sqrt{6} m m \)
D. \( 4.5 \mathrm{mm} \)


The black thick liquid with unpleasant smell is known as:
A. naphtha
B. gasoline
c. coal tar
D. diesel oil


A piece of wire \( 28 \mathrm{m} \) long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How much wire should be used for the square in order to maximize the
total area?


Choose the correct answers from the
alternatives given Which of the following groups of components is found in all viruses?
A. Envelope, nucleic acid, capsid
B. DNA, RNA and proteins
c. Proteins and a nucleic acid
D. Proteins, nucleic acids, carbohydrates, and lipids


Effect to pressure on \( \Delta \boldsymbol{H} \) is negligible
if \( \Delta n= \)


In the equation,
\( 4 M+8 C N^{-}+2 H_{2} O+O_{2} \longrightarrow \)
\( \mathbf{4}\left[\boldsymbol{M}(\boldsymbol{C} \boldsymbol{N})_{2}\right]^{-}+\mathbf{4} \boldsymbol{O} \boldsymbol{H}^{-} \)
the metal M is:
This question has multiple correct options
A. copper
B. Silver
c. Gold
D. zinc


When 2 hydrogen atoms combine to
form \( \boldsymbol{H}_{2} \) molecule, the system
A. becomes stable and bond is covalent in nature
B. becomes unstable
c. becomes stable and bond is ionic in nature
D. becomes unstable and bond is metallic in nature


Find the principal value of the following:
\( \sec ^{-1}(-2) \)


If \( \sin \theta-\sqrt{6} \cos \theta=\sqrt{7} \cos \theta . \) Prove that
\( \cos \theta-\sqrt{6} \sin \theta-\sqrt{7} \sin \theta=1 \)


The electrolytes usually used in the electroplating of gold and silver, respectively are:
A \( \cdot\left[A u(O H)_{4}\right]^{-} \)and\( \left[A g(O H)_{2}\right] \)
B . \( \left[A u(C N)_{2}\right]^{-} a n d\left[A g\left(c l_{2}\right]^{-}\right. \)
C \( \left.\cdot\left[A u(N H)_{3}\right)_{2}\right]^{+} a n d\left[A g(C N)_{2}\right] \)
D. \( \left[A u(C N)_{2}\right]^{-} a n d\left[A g(C N)_{2}\right]^{-} \)


Match the reaction in list 1 with their
type in list 2


Write difference between ingestion and digestion


If \( f(x)=x^{3}+x^{2}-a x+b \) is divisible
by \( x^{2}-x \) write the value of a and \( b \)


The factors of \( \boldsymbol{x}^{\mathbf{4}}+\boldsymbol{y}^{\mathbf{4}}+\boldsymbol{x}^{\mathbf{2}} \boldsymbol{y}^{\mathbf{2}} \) are
\( \mathbf{A} \cdot\left(x^{2}+y^{2}\right)\left(x^{2}+y^{2}-x y\right) \)
\( \mathbf{B} \cdot\left(x^{2}+y^{2}\right)\left(x^{2}-y^{2}\right) \)
C \( \cdot\left(x^{2}+y^{2}+x y\right)\left(x^{2}+y^{2}-x y\right) \)
D. Factorization is not possible


Q Type your question-
Davisson and Germer demonstrated
this by diffracting electrons
from crystals. The law governing the
diffraction from a crystal is obtained by requiring that electron waves reflected
from the planes of atoms in a crystal
interfere constructively (see figure). Electrons accelerated by potential Vare
diffracted from a crystal. If \( \boldsymbol{d}=\mathbf{1} \boldsymbol{A}^{\boldsymbol{o}} \) and
\( i=30^{\circ}, V \) should be about :
\( \left(h=6.6 \times 10^{-34} j s, m=9.1 \times\right. \)
\( \mathbf{1 0}^{-\mathbf{3 1}} \mathbf{k g}, e=\mathbf{1 . 6} \times \mathbf{1 0}^{-\mathbf{1 9}} \mathbf{c} \)
A . 2000 v
B. \( 50 v \)
c. 500 v
D. \( 1000 \mathrm{v} \)


The ammonia \( \left(N H_{3}\right) \) released on
quantitative reaction of \( 0.6 g \) urea
\( \left(N H_{2} C O N H_{2}\right) \) with sodium hydroxide
\( (N a O H) \) can be neutralized by:
A . \( 200 \mathrm{ml} \) of \( 0.2 \mathrm{N} \) HCl
в. 200ml of 0.4N HCl
c. \( 100 m l \) of \( 0.1 N \) HCl
D. \( 100 m l \) of \( 0.2 N H C l \)


Which of the following reactions is not
feasible?
\( A \)
B.
\( c \)
\( D \)


The equation of a wave travelling on a string is \( y=0.1 \sin [1.4 x+314 t] . \) Then
In which direction does the wave travel?
Find the wave speed, the wavelength and the frequency of the wave. What is the maximum displacement
and the maximum speed of a portion of the string?


A particle moves in the \( x-y \) plane. Its
motion is given by equations \( x=\sin 2 t \)
and \( y=(1-\cos 2 t) . \) The distance
travelled by the particle during time \( \boldsymbol{t}=\boldsymbol{2} \boldsymbol{s} \) is
\( \mathbf{A} \cdot 1 m \)
в. \( 6 m \)
c. \( 4 m \)
D. \( 8 m \)


Suggest reasons why the \( B F \) bond
lengths in \( B F_{3}(130 \mathrm{pm}) \) and \( B F_{4}^{-}(143 \)
\( p m \) ) differ.


How is the working of a telescope different from that of a microscope?
The focal lengths of the objective and eyepiece of a microscope are \( 1.25 \mathrm{cm} \)
and \( 5 c m \) respectively. Find the position of the object relative to the objective in order to obtain an angular
magnification of 30 in normal adjustment.


Symbolic representation of photodiode
is-
\( A \)
B.
\( c \)
\( D \)


Arrange following compounds according to their reactivity with alc silver nitrate.
A. \( C C l_{4} \) > tert-Butyl chloride \( > \) sec- butyl chloride > nbutyl chloride
B. n- butyl chloride > sec- butyl chloride > tert-Butyl chloride \( >C C l \)
c. tert-Butyl chloride < sec -butyl chloride <n -buty chloride \( <C C l \)
D. tert-Butyl chloride > sec -butyl chloride >n- buty chloride \( >C C l_{4} \)


Cardiac muscle requires for
contraction to occur.
A. Sodium ions
B. Calcium ions
c. Phosphorous ions
D. Sulphur ions


The isothermal bulk modulus of
elasticity of a gas is \( 1.5 \times 10^{5} N m^{-2} \)
Its adiabatic bulk modulus of elasticity will be (if \( \gamma=1.4) \)
В. \( 2.1 \times 10^{5} \mathrm{Nm}^{-2} \)
c. \( 1.5 \times 10^{5} \mathrm{Nm}^{-2} \)
\( D \cdot \infty \)


Let \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ll}\int_{0}^{x}\{1+|1-t|\} d t & \text { if } x>2 \\ \mathbf{5 x - 7} & \text { if } x \leq 2\end{array} \) then \right.
A. \( f \) is not continuous at \( x=2 \)
B. \( f \) is continuous but not differentiable at \( x=2 \)
c. \( f \) is differentiable everywhere
D \( \cdot f^{\prime}(2+) \) doesn't exist


The temperature increases is not notices in which of the following
processed on providing heat to system?
(I) Fusion at melting point
(II) Phase transition at transition temperature
(III) Boiling at boiling point
(IV) A reaction in chemical equilibrium
A . ।, ॥।, ॥।
в. ।, ॥॥
c. ॥ा, । ॥
D. ॥, IV


Find the area bounded by the curve \( y= \)
\( 2 x-x^{2}, \) and the line \( y=x \)


The plot of \( \log _{10} K_{p} \) against \( 1 / T \) for the reaction:
\[
\boldsymbol{S O}_{2}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{S} \boldsymbol{O}_{3}(\boldsymbol{g})
\]
is a straight line with slope \( =4.95 \times \)
\( 10^{3} . \) If the \( K_{p} \) at 25 if standard
entropies for \( \boldsymbol{S O}_{2}(\boldsymbol{g}), \boldsymbol{O}_{2}(\boldsymbol{g}) \) and
\[
\boldsymbol{S O}_{3}(\boldsymbol{g}) \text { are } \mathbf{2 4 8 . 2}, \mathbf{2 0 5 . 1} \text { and }
\]
\( 256.8 J K^{-1} m o l^{-1} \) at 25 respectively is
\[
\boldsymbol{K}_{\boldsymbol{p}}=\boldsymbol{X} \times \mathbf{1 0}^{11} \text { then } \mathbf{1 0} \boldsymbol{X}
\]
is


Which of the following statements is/are correct in the case of
heterogeneous catalyst? This question has multiple correct options
A. The catalyst lowers the energy of activation
B. The catalyst actually forms a compound with the reactant.
c. The surface of the catalyst plays a very important role
D. There is no change in the energy of activation


Is this a negative rational number? \( \frac{-2}{3} \)


An electron enters a magnetic field directed to the right, with a velocity toward the bottom of the screen.
What is the direction of force on the
electron?
A. To the left
B. Into the screen
c. To the right
D. Out of the screen


14
field intensity at the center of a square having fixed point charges at their
vertices as shown in figure are zero.
Reason

If electric potential at a point is zero
then the magnitude of electric field at that point must be zero.
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


The molarity of a glucose solution containing 36 g of glucose per \( 400 \mathrm{mL} \) of the solution is:
A . 1.0
B. 0.5
c. \( 2 . \)
D. 0.05


The modern atomic mass unit is based
on the mass of :
A. C-12 isotope
B. hydrogen
c. oxygen
D. nitrogen


In scapigerous umbel the flowers are arranged in manner of
A. Corymb
B. Umbel
c. Panicle
D. Monochasial scorpioid cyme


A solution of hydrochloric acid is required for an experiment. The experimenter must first prepare the
solution for use by diluting \( 10.0 m L \) of
the hydrochloric acid to create \( 200 m L \)
of the solution.
Which of the following would be the poorest choice of glassware for measuring the solute for the dilution?
A. A graduated cylinder
B. A volumetric flask
c. A burrette
D. A volumetric pipette


Solve the following inequalities graphically in two-dimensional plane:
\( 3 x+4 y \leq 12 \)


\( \left|\begin{array}{ccc}\boldsymbol{b}+\boldsymbol{c} & \boldsymbol{a}-\boldsymbol{c} & \boldsymbol{a}-\boldsymbol{b} \\ \boldsymbol{b}-\boldsymbol{c} & \boldsymbol{c}+\boldsymbol{a} & \boldsymbol{b}-\boldsymbol{a} \\ \boldsymbol{c}-\boldsymbol{b} & \boldsymbol{c}-\boldsymbol{a} & \boldsymbol{a}+\boldsymbol{b}\end{array}\right|= \)
A. \( 4 a b c \)
B. \( 6 a b c \)
\( c .8 a b c \)
D. \( 2 a b c \)


Which of the following is the parallax angle in the shown diagram?
4
B.
\( c \)
2


Which of the following is not a physical change?
A. Tearing a paper
B. Bending an iron rod
c. Freezing water into ice
D. curdling of milk


Washing soaps are potassium and sodium salts of:
A. acetones, ketones and quinones
B. formic, acetic and maleic acids
c. oleic, palmitic and stearic acids
D. sulphur, chlorine and fluorine


The number of oxidation states is
exhibited by the actinoids more than by the lanthanide. The main reason for this
is:
A. more energy difference between 5 f and 6 d orbital than that between 4 f and 5 d orbitals.
B. the lesser energy difference between 5 and \( 6 d \) orbital than between \( 4 f \) and \( 5 d \) orbitals
C. the greater metallic character of the lanthanoids than that of the corresponding actinoids
D. more active nature of the actinoids


A mechanical wave travels in a
medium. Which of the following quantities is transferred from one place to another with the wave?
A . Mass
B. Speedd
c. Density
D. Energy


Consider a uniform electric field \( \boldsymbol{E}= \)
\( 3 \times 10^{3} \hat{i} N / C . \) What is the flux of this
field through a square of \( 10 \mathrm{cm} \) on a side whose plane is parallel to the yz plane?
A \( \cdot 30 \mathrm{Nm}^{2} / \mathrm{C} \)
В. \( 40 \mathrm{Nm}^{2} / \mathrm{C} \)
c. \( 50 N m^{2} / C \)
D. \( 60 \mathrm{Nm}^{2} / \mathrm{C} \)


Find the cost of white washing the four
walls of a cubical room of side \( 4 m \) at
the rate of \( \boldsymbol{R} \boldsymbol{s} . \boldsymbol{2} \boldsymbol{0} / \boldsymbol{m}^{2} \)


\( 0.3 \mathrm{g} \) of chloroplatinic acid of an organic diacidic base left 0.09 g of platinum on ignition. The molecular weight of the organic base is :
A . 120
B. 240
c. 180
D. 60


The relation between time \( t \) and
distance \( x \) is \( t=a x^{2}+b x \) where a and \( b \)
are constant. The acceleration is:
A . \( -2 a b v^{2} \)
B. \( 2 b v^{2} \)
c. \( -2 a v^{2} \)
D. \( 2 a v^{2} \)


What is the value of \( a \) for the following
equation: \( 3 a+4 b=13 \) and \( a+3 b=1 \)
\( ? \)
(Use cross multiplication method)
\( \mathbf{A} \cdot a=5 \)
B. \( a=6 \)
\( \mathbf{c} \cdot a=\mathbf{7} \)
\( \mathbf{D} \cdot a=8 \)