Which one of the following reactions is catalyzed by the enzyme reverse transcriptase?
A. Transfer of information from RNA to RNA
B. Transfer of information from DNA to RNA
c. Transfer of information from Protein to DNA
D. Transfer of information from RNA to DNA


\( X Y_{2} \) dissociates \( X Y_{2}(g) \rightleftharpoons X Y(g)+ \)
\( Y(g) . \) When the initial pressure of \( X Y_{2} \)
is \( 600 \mathrm{mm} \) Hg, the total equilibrium pressure is \( 800 \mathrm{mm} \) Hg. Calculate \( K \) for the reaction. Assuming that the volume of the system remains unchanged:
A . 50.0
B. 100.0
c. 166.6
D. 400.0


There point charges of
\( +2 \mu C,-3 \mu C,-3 \mu C \quad \) are kept at
the vertices \( A, B \) and \( C \) respectively of an
equilateral triangle of side \( 20 \mathrm{cm} \) as shown in the figure.What should be the
sign and magnitude of the charge to be
placed at the mid - point (M) of side BC
so that the charge at A remains in
equilibrium?


The relation 'has the same father as'
over the set of children is:
A. Only reflective
B. Only symmetric
c. only transitive
D. An equivalence relation


What is the eccentricity of the conic \( 4 x^{2}+9 y^{2}=144 \)
A \( \frac{\sqrt{5}}{3} \)
в. \( \frac{\sqrt{5}}{6} \)
c. \( \frac{3}{\sqrt{5}} \)
D. \( \frac{2}{3} \)


Increase of temperature of an aqueous
solution will cause:
A. decrease in molality of the solution
B. decrease in molarity of the solution
c. decrease in mole fraction of the solution
D. decrease in percentage (w/w) of the solution


The curve of binding energy per nucleon
as a function of atomic mass number
has a sharp peak of helium nucleus. This implies that helium:
A. can easily be broken up
B. is very stable
c. can be used as fissionable material
D. is radioactive


Convert the following fraction into percents \( =\frac{1}{8} \)


A particular work can be completed by 6 men and 6 women in 24 days; whereas the same work can be completed by 8 men and 12 women in 15 days, according to the amount of work done one man is equivalent to how many women?
A \( \cdot_{\frac{1}{2}} \) women
в. \( 5 \frac{1}{3} \) women
\( ^{\mathrm{c}} \cdot_{5} \frac{2}{3} \) women
D. \( \frac{3}{2} \) women


According to Dalton's atomic theory, atoms of a given element are identical
in:
A. chemical properties and size
B. weight and colour
c. properties and colour
D. colour and size


Area of the region bounded by rays \( |x|+y=1 \) and \( X \) -axis is
A \( \cdot \frac{1}{2} \)
B. 2
c.
D.


\( f \tan (\pi \cos \theta)=\cot (\pi \sin \theta) \) then
\( 19208 \cos ^{2}(\theta-\pi / 4) \) is equal to


The area of parallelogram whose two
sides are \( \boldsymbol{y}=\boldsymbol{x}+\mathbf{3}, \mathbf{2} \boldsymbol{x}-\boldsymbol{y}+\mathbf{1}=\mathbf{0} \)
and remaining two sides are passing through (0,0) is?
A. 2 sq. unit
B. 3 sq. unit
c. \( \frac{5}{2} \) sq. unit
D. \( \frac{7}{2} \) sq. unit


The mass percentage of nitrogen in
histamine is


In typical structure of the plasma membrane
a) The lipids are amphipathic.
b) Proteins are arranged
asymmetrically and shows flip flop
movement.
c) Extrinsic proteins are abundant towards cytoplasmic face.
A. All are correct
B. a, b is correct
\( c . b, \) c is correct
D. a, cis correct


Study carefully the given flow chart and fill in the blanks \( (A),(B),(C),(D) \) and \( (E) \)
A. A- -Cellular level, B - Bilateral symmetry, C - Radial symmetry, D - Pseudo-coelomates, E - coelomates
B. A - Cellular level, B - Radial symmetry, c- - Bilatera symmetry, D - coelomates, E - Pseudo-coelomates
c. A - cellular level, B - Bilateral symmetry, C- Radial symmetry, D - coelomates, E - Pseudo-coelomates
D. A - cellular level, B - Radial symmetry, c- - Bilatera symmetry, D - Pseudo-coelomates, E - coelomates


Give the diazotisation reaction of
aniline. Also give the chemical reaction
involved in the preparation of red azo dye and light yellow azo dye.


The \( \chi-\left(\frac{1}{T}\right) \) graph for an alloy of
paramagnetic nature is shown in figure
The curie constant is, then
\( A \cdot 57 K \)
B . \( 2.8 \times 10^{-3} K \)
c. \( 570 K \)
D. \( 17.5 \times 10^{-3} K \)


The percentage composition of a gas is as follow:
Nitrogen \( 82.35 \% \), Hydrogen \( 17.64 \% \) Find the empirical formula for the gas.


A uniform disc of mass \( M \) and radius \( R \)
is suspended in vertical plane from a point on its periphery. Its time period of oscillation is
A \( \cdot 2 \pi \sqrt{\frac{3 R}{g}} \)
в. \( 2 \pi \sqrt{\frac{R}{3 g}} \)
\( ^{\mathrm{c}} \cdot_{2 \pi} \sqrt{\frac{2 R}{3 g}} \)
D. \( 2 \pi \sqrt{\frac{3 R}{2 g}} \)


Covalency of sulphur in \( S O_{4}^{2-} \) ion is:
\( A \cdot 4 \)
B. 6
\( c \cdot 2 \)
D. 5


A \( 150 m \) long train is moving north at a speed of \( 20 m / s . A \) bird flying south at a
speed of \( 5 m / s \) crosses the train. What
is the time taken by the bird to cross the train?
A . \( 30 s \)
в. \( 15 s \)
\( c \cdot 6 s \)
D. \( 3 s \)


A bottle is filled with water. A cap is put on the bottle and it is turned upside down. There is no air inside the bottle.
The area of the cap in contact with the
water is \( 4.0 \times 10^{-4} \mathrm{m}^{2} . \) The density of
water is \( 1000 \mathrm{kg} \mathrm{m}^{-3} \) and the
gravitational field strength is
\( 10 N k g^{-1} . \) The water produces a force
on the cap.What is the value of this force?
B. \( 0.12 N \)
c. \( 1.2 N \)
D. 13 \( N \)


Heat given (H) to a substance was
plotted against rise in temperature \( (\boldsymbol{\theta}) \)
Which of the following parts of the
graph, most correctly depicts the latent heat of the substance?
\( A \cdot A B \)
в. вс оп!
\( c \cdot c D \)
D. BC and DE


Solve:
\( \frac{2 x-1}{x+4}-2 x-5 x+3=0 \)


This compound forms a sodium salt
upon reacting with \( N a N H_{2} \). Identify the compound.
A. \( C_{2} H_{2} \)
в. \( C_{2} H_{4} \)
\( \mathbf{c} \cdot C_{6} H_{6} \)
D. \( C_{2} H_{6} \)


An electric motor operating on \( 50 V \) D.C.
supply draws a current of \( 10 A \). If the efficiency of the motor is \( 40 \% \), then the resistance of the winding of the motor is:
A. \( 1.5 \Omega \)
B. 3\Omega
c. \( 4.5 \Omega \)
D. \( 6 \Omega \)


All domestic electrical circuits are
connected
A. In series
B. In parallel
c. Both
D. None of these


Glycolysis occurs in the of the
cells.


A body cools from \( 70^{\circ} \mathrm{C} \) to \( 50^{\circ} \mathrm{C} \) in 5
minutes. Temperature of surroundings
is \( 20^{\circ} \mathrm{C} . \) Its temperature after next 10 minutes is
A \( \cdot 26^{\circ} \mathrm{C} \)
В. \( 30^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 35^{\circ} C \)
D. \( 45^{\circ} \mathrm{C} \)


The freezer in the refrigerator is generally mounted on the top for proper cooling. Which of the following property of air is demonstrated by this?
A. The cold air settles down
B. The hot air rises up
c. The low temperature causes uniform cooling.
D. None of the above


Terylene is
A. an addition polymer with a benzene ring in every repeating unit.
B. a condensation polymer with a benzene ring in every repeating unit
C . an addition polymer with two carbon atoms in every repeating unit.
D. a condensation polymer with two nitrogen atmos in every repeating unit


The component of a vector \( \vec{r} \) along \( x \) axis will have a maximum value if:
A. \( \vec{r} \) along +ve \( x \) -axis
B. \( \vec{r} \) along +ve \( y \) -axis
c. \( \vec{r} \) along -ve \( y \) -axis
D. \( \vec{r} \) makes an angle of \( 45^{\circ} \) with the \( x \) -axis


What are coinitial vectors.?
A. Two or more vectors having the same magnitude are called coinitial vectors.
B. Two or more vectors are said to be coinitial if they are parallel to the same line, irrespective of their magnitudes and directions.
C. Two or more vectors having the same initial point are called coinitial vectors.
D. None of the above


State Brewster's Law.
The polarising angle of a transparent medium is \( 60^{\circ} . \) Find the refractive index
and the angle of refraction \( \left(\tan 60^{\circ}=\right. \) \( \sqrt{3}) \)


Which of the following figure has six faces?
\( A \)
в.
\( c \)
\( D \)


Describe an activity to show that thermosetting plastic is a poor conductor of electricity.


Answer the following questions:
a) Calculate the EMF of the cell for the
reaction
\( \boldsymbol{M} \boldsymbol{g}_{(s)}+\mathbf{2} \boldsymbol{A} \boldsymbol{g}_{(a q)}^{+} \rightarrow \boldsymbol{M} \boldsymbol{g}_{(a q)}^{2+}+\boldsymbol{2} \boldsymbol{A} \boldsymbol{g}_{(s)} \)
Given :
\( \boldsymbol{E}_{M g^{2+} / M g}^{0}=-\mathbf{2 . 3 7} \boldsymbol{V} \)
\( \boldsymbol{E}_{A g^{+} / A g}^{0}=\mathbf{0 . 8 0} \boldsymbol{V} \)
\( \left[\boldsymbol{M} \boldsymbol{g}^{2+}\right]=\mathbf{0 . 0 0 1} \boldsymbol{M} ;\left[\boldsymbol{A} \boldsymbol{g}^{+}\right]=\mathbf{0 . 0 0 0 1} \boldsymbol{M} \)
b) What are fuel cells?


Two equal electric currents are flowing perpendicular to each other as shown in figure. AB and CD are perpendicular to each other and symmetrically placed with respect to the currents. Where do
we expect the resultant magnetic field to be zero?
\( A \cdot \) on \( A B \)
B. on CD
\( c \). on both \( A B \& \) CD
D. on both OD \& BO


\( \frac{0.25}{0.4} \) is equal to
This question has multiple correct options
\( \mathbf{A} \cdot \frac{5}{8} \)
B. \( \frac{25}{40} \)
c. \( \frac{16}{19} \)
D. None of the above


Three \( 60 \mathrm{W} \), 120 \( \mathrm{V} \) light bulbs are
connected across a \( 120 \mathrm{V} \) power line as
shown in Fig. Find the voltage across
each bulb.


DNA replication occurs during
A. Prophase
B. Metaphase
c. Cytokinesis
D. Interphase
E. Telophase


Express \( 0 C \) in kelvin.


Which of the following will show Tyndall effect?
A. Aqueous solution of soap below critical micelle concentration
B. Aqueous solution of soap above critical micelle concentration
c. Aqueous solution of sodium chloride
D. Aqueous solution of sugar


Name the Indian scientist who has
contributed in the discovery of inelastic scattering of light by molecules.
A. C.V. Raman
B. M.N. Saha
c. S.N. Bose
D. None of the above


Comment on the element lithium.


What do you mean by zero-waste procedure? What are its advantages?


Why distillation is a chemical reaction?
A. Formation of products occur
B. Change in state of reactants
c. Both \( A \) and \( B \)
D. Distillation is not a chemical reaction


The metal obtained in the Pidgeon
process is:
A. \( N a \)
в. \( M g \)
\( c . C a \)
D. \( A l \)


Two straight segments of wire \( a b \) and \( b c \)
each carrying current \( I \), are parallel as
shown in fig. The cube edge is \( 50 \mathrm{cm} \) and magnetic field is uniform along \( Y \)
axis having magnitude 0.4 T. If \( \boldsymbol{I}=\mathbf{3} \boldsymbol{A} \)
the force experienced by wire abc in the
presence of magnitude field is :
A . \( 0.6 \hat{i} \)
B . \( 1.2(\hat{i}+\hat{k}) \)
c. \( 0.6(\sqrt{2} \hat{\imath}+\hat{j}-\sqrt{2} \hat{k} \)
D. \( 0.6(\sqrt{2 i}-\hat{k}) \)


Holme's signal uses chemical compound?
A . calcium carbide
B. calcium phosphide
c. calcium carbide and calcium phosphide
D. calcium carbide and aluminium carbide


\( \boldsymbol{K}_{\boldsymbol{p}} \) for the following reaction at \( \mathbf{7 0 0} \boldsymbol{K} \) is
\( 1.3 \times 10^{-3} a t m^{-1} . \) The \( K_{C} \) at same
temperature of the reaction \( 2 S O_{2}+ \)
\( \boldsymbol{O}_{2} \rightleftharpoons \mathbf{2} \boldsymbol{S} \boldsymbol{O}_{3} \) will be :
В. \( 3.1 \times 10^{-2} \)
C \( .5 .2 \times 10^{-2} \)
D. \( 7.4 \times 10^{-2} \)


Solve:
\( (\mathbf{1}-\boldsymbol{y}) \boldsymbol{x} \frac{d \boldsymbol{y}}{d \boldsymbol{x}}+(\mathbf{1}+\boldsymbol{x}) \boldsymbol{y}=\mathbf{0} \)


An electron moves at right angle to a
magnetic field of \( 1.5 \times 10^{-2} T \) with a
speed of \( 6 \times 10^{7} m / s . \) If the specific
charge on the electron is \( 1.7 \times \) \( 10^{11} C / k g, \) the radius of the circular
path will be
A . \( 2.9 \mathrm{cm} \)
B. 3.9 \( \mathrm{cm} \)
c. \( 2.35 \mathrm{cm} \)
D. \( 2 \mathrm{cm} \)


According to Newton's law of cooling, the rate of cooling is proportional to
\( (\Delta \theta)^{n}, \) where \( \Delta \theta \) is the temperature
difference between the body and the
surroundings and \( n \) is equal to
A. Three
B. Two
c. one
D. Four


Mark the correct statement(s):
A. The magnitude of the velocity of particle is equal to its speed
B. The magnitude of average velocity in an interval is equal to its average speed in that interval.
C. It is possible to have a situation in which the speed of a particle is always zero but the average speed is not
zero.
D. It is possible to have a situation in which the speed of the particle is never zero but the average speed in an interval is zero.


A wire of length L and resistance R is
stretched so that the length is doubled
and area of cross section halved. How
will
(i) resistance change and (ii) resistivity change


Given a function 'g' whcih has a
derivative \( g^{\prime}(x) \) for every real ' \( x \) ' and
which satisfy \( g^{\prime}(0)=2 \) and \( g(x+y)= \)
\( e^{y} \cdot g(x)+e^{x} \cdot g(y) \) for all \( x, y . \) Find \( g(x) \)
\( A \cdot 2 x e^{x} \)
В. \( x e^{x} \)
c. \( x+e^{x} \)
D. \( x-e^{x} \)


An endoscope is employed by a physician to view the internal parts of a body organ. It is based on the principle
of:
A. refraction
B. reflection
c. total internalreflection
D. dispersion


An ideal binary solution is prepared by
two liquids \( A \) and \( B, \) with \( p_{A}^{o}>p_{B}^{o} . \) Then :
A. A-B interactions are stronger than A-A and B-B
B. A and B have same molecular masses
c. A-B interactions are similar to A-A and B-B interactions
D. Both A and B are non-polar substances


Based on equations reducible to linear
equations

Solve for \( x \) and \( y: 9+25 x y=53 x \) and
\( 27-4 x y=x \)
A. \( x=1, y=4 \)
в. \( x=2, y=7 \)
c. \( x=6, y=2 \)
D. \( x=3, y=2 \)


Prove that out of all the chords
which passing through any point circle, that chord will be smallest which is
perpendicular on diameter which passes through that point.


The \( O A \) and \( A B \) part of the graph
correspond to
A. uniform retardation, variable acceleration
B. uniform acceleration, uniform velocity
c. constant velocity, uniform acceleration
D. uniform acceleration, varying velocity


Brown ring complex known as:
\( \mathbf{A} \cdot K_{4}\left[F e(C N)_{6}\right] \)
\( \mathbf{B} \cdot\left[F e(N O)\left(H_{2} O\right)_{5}\right] S O_{4} \)
\( \left.\mathbf{c} \cdot\left[F e(N O)_{2}\right)\left(H_{2} O\right)_{4}\right] B r_{2} \)
\( \mathbf{D} \cdot\left[F e F_{6}\right]^{3-} \)


A long solenoid carrying a current
produces a magnetic field B along its axis. If the current is doubled and the
number of turns per cm is halved, the new value of the magnetic field is
\( A \cdot 4 B \)
B. B/2
\( c . \) в
D. 2 B


The median of the following items \( \mathbf{2 5}, \mathbf{1 5}, \mathbf{2 3}, \mathbf{4 0}, \mathbf{2 7}, \mathbf{2 5}, \mathbf{2 3}, \mathbf{2 5} \) and \( \mathbf{2 0} \) is
A .27
B . 40
c. 25
D. 23


If an endothermic reaction is non-
spontaneous at freezing point of water and becomes feasible at its boiling point, then
A. \( \Delta H \) is -ve, \( \Delta S \) is +ve
B. \( \Delta H \& \Delta S \) both are +ve
c. \( \Delta H \& \Delta S \) both are -ve
D. \( \Delta H \) is tve, \( \Delta S \) is-ve


Milk caesin- - - -Y- - -> Paracaesin- - - -M- - ->
Calcium paracaesinate (curding of milk). In the above equation 'Y' and 'M' indicates
A. Rennin and \( C a^{++} \) respectively
B. \( C a^{++} \) and Renin respectively
C. Renin and HCl, \( C a^{++} \) respectively
D. Renin and \( C a^{++} \) respectively


Matter is neither created nor destroyed. Which law is stated?
A. Law of multiple proportion
B. Law of conservation of energy
c. Law of constant composition
D. Law of conservation of mass


When the switch of an electric bell is
pushed
A. Flow of the current stops through the electromagnet in the bell
B. Current starts to flow through the electromagnet
c. voltage decreases in the current flowing through the electromagnet
D. Circuit is closed in the electric bell


Find the relation between \( a \) and \( b \). If the
points \( \boldsymbol{P}(1,2), Q(0,0) \) and \( P(a, b) \) are collinear


An object can have
A. more than one center of gravity.
B. only one center of gravity
C . always two center of gravity
D. none of the above


The freezing point of equimolal aqueous solution will be highest for:
A. \( C_{6} H_{5} N H_{3}^{+} C l^{-} \)
в. \( \quad C a\left(N O_{3}\right)_{2} \)
c. \( _{L a}\left(N O_{3}\right)_{2} \)
D. \( C_{6} H_{12} O_{6} \)


Evaluate the integral \( \int_{0}^{1} \frac{\sin ^{-1} x}{x} d x \)
\( A \cdot \pi \log 2 \)
в. \( -\pi \log 2 \)
C \( \cdot-\frac{\pi}{2} \log 2 \)
D. \( \frac{\pi}{2} \log 2 \)


The Total Surface Area of a cube in \( c m^{2} \)
is equal to the volume of the cube in
\( c m^{3} \) The edge of the cube is \( _{--}-- \) (in \( \mathrm{cm} \)
\( A \cdot 3 \)
B. 4
\( c \cdot 5 \)
D. 6


Derive expression for self inductance of a long air-cored solenoid of length \( L \)
cross- sectional area \( A \) and having number of turns N.


Which of the following products is formed when phosphine is absorbed in
copper sulphate solution?
A \( \cdot C u(O H)_{2} \)
в. \( \left[C u\left(P H_{3}\right)_{4}\right] S O_{4} \)
c. \( C u_{3} P_{2} \)
D \( \cdot C u_{3}\left(P O_{4}\right)_{2} \)


The correct explanation of the
organisms is
\( \begin{array}{llll} & \text { A } & \text { B } & \text { c } \\ \text { a) } & \text { Saprophyte } & \text { Heterotrophs } & \text { Autotrop } \\ \text { b) } & \text { Heterotrophs } & \text { Autotrophs } & \text { Saproph } \\ \text { c) } & \text { Autotrophs } & \text { Saprophyte } & \text { Autotrop } \\ \text { d) } & \text { Autotrophs } & \text { Heterotrophs } & \text { Heterotrc }\end{array} \)


Find the \( 9^{t h} \) term and the general term of the progression \( \frac{1}{4},-\frac{1}{2}, 1,-2, \dots \)


The slow process of conversion of dead vegetation into coal is called:
A. carbonization
B. hydrogenation
c. oxidation
D. reduction


In which one of the following compounds does sulphur have the least oxidation number?
\( A \cdot S O_{2} \)
в. \( \mathrm{H}_{2} \mathrm{SO}_{4} \)
\( \mathrm{c} \cdot \mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{3} \)
D. \( \mathrm{Na}_{2} \mathrm{S}_{4} \mathrm{O}_{6} \)


In a plane mirror, the image is as far behind the mirror as the object is in front of it.
A. True
B. False


Find the sum of exterior angles \( \boldsymbol{x}+\boldsymbol{y}+ \)
\( \boldsymbol{z}+\boldsymbol{p}+\boldsymbol{q} \)


The efficiency of a fuel cell is given by:
A \( \cdot \frac{\Delta s}{\Delta G G} \)
в. \( \frac{\Delta H}{\Delta G} \)
c. \( \frac{\Delta G}{\Delta S G} \)
D. \( \frac{\Delta G}{\Delta H} \)


\( \operatorname{Let} \boldsymbol{P}(\boldsymbol{n})=\mathbf{5}^{n}-\mathbf{2}^{n} . \boldsymbol{P}(\boldsymbol{n}) \) is divisible by
\( 3 \lambda \) where \( \lambda \) and \( n \) both are odd positive integers, then the least value of \( n \) and \( \lambda \)
will be
A . 13
B. 11
\( c \cdot 1 \)
D. 5


Two deuterium nuclei each of mass ' \( \boldsymbol{m}^{\prime} \)
fuse together to form a Helium nucleus,
releasing an energy \( \boldsymbol{E} \). If \( ^{\prime} \boldsymbol{c}^{\prime} \) is the
velocity of light, the mass of Helium nucleus formed will be:
A \( \cdot 2 m+\frac{E}{c^{2}} \)
в. \( \frac{E}{m c^{2}} \)
c. \( _{m+\frac{E}{c^{2}}} \)
D. \( 2 m-\frac{E}{c^{2}} \)


The value of
\( \cot 15^{\circ} \cot 20^{\circ} \cot 70^{\circ} \cot 75^{\circ} \) is equal
to
A . -1
B. 0
\( c .1 \)
D. 2


The substance that has the lowest
boiling point is:
A. \( H C l \)
в. \( H_{2} \).
\( \mathrm{c} . P H_{3} \)
D. \( \operatorname{si} H_{4} \)


Assertion
Path of a particle in SHM is always a
straight line.
Reason
All straight line motions are not simple
harmonic.
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 difference between a freely falling particle and a bouncing particle on the floor is
A. Freely falling particle has uniformly accelerated motion, while a bouncing particle is periodic
B. Freely falling particle has uniform velocity motion, while a bouncing particle is periodic
c. Both the particles move with uniform velocity
D. Both of them are periodic


Hydrogen peroxide when reacts with NaOH forms:
A. sodium hydroperoxide
B. sodium peroxide
c. sodium oxide
\( D \cdot \operatorname{both} A \& B \)


In the figure, 'O' is the centre of the
circle and \( 0 \mathrm{M}, \) On are the
perpendiculars from the centre to the
chords \( P Q \) and \( R S . \) If \( O M=O N \) and \( P Q=6 \)
\( \mathrm{cm} . \) Find RS


Given below is an example of a certain structure and its special functional
activity:
Kidney and excretion. Fill in the blanks on a similar pattern:
C-shaped cartilage rings and


The direction of the flow of current
through electric circuit is?
A. From low potential to high potential
B. From high potential to low potential
c. Does not depend upon potential value
D. Current cannot flow through circuit


If
0.1 mol of salt is added to \( 1 L \) water,
which of these salts is expected to produce the most acidic solution?
A. \( N a C_{2} H_{3} O_{2} \)
B. \( N H_{4} N O_{3} \)
\( \mathrm{c} \cdot \mathrm{CuSO}_{4} \)
D. \( A l C l_{3} \)


State True or False.
For hydrogen atom, the energies of the sub-shells \( 4 s, 4 p, 4 d \) and \( 4 f \) are in the
order: \( 4 \boldsymbol{f}>\mathbf{4} \boldsymbol{d}>\mathbf{4} \boldsymbol{p}>\mathbf{4} \boldsymbol{s} \)
A . True
B. False


Polycyclic aromatic hydrocarbon enter air as release from:
This question has multiple correct options
A. volcanoes
B. forest fires
c. burning coal
D. automobile exhaust


Write the following based on the graph. The ordinate of Lis
\( 4 .-7 \)
B
\( c_{1}-5 \)
None of these


Two moles of a gas is expanded to double its volume by two different processors. One is isobaric and the
other is isothermal. If \( w_{1} \) and \( w_{2} \) are the
works done respectively, then
A. \( w_{2}=\frac{w_{1}}{\ln 2} \)
В \( . w_{2}=w_{1} \)
c. \( w_{2}=w_{1} \ln 2 \)
D. \( w_{1}^{2}=w_{2} \ln 2 \)


Which observation is definite sign that a chemical change has occurred?
A. color change
B. Bubble formation
c. change in temperature
D. Precipitate formation
E. Salt dissolving


The protective power of the lyophilic colloids is expressed in terms of gold number a term introduced
by Zsigmondy. The gold number is the number of milligrams of the protective colloid which prevents the
coagulation of \( 10 \mathrm{mL} \) of red gold sol.
When \( 1 ~ m L \) of a 10 percent solution of
sodium chloride is added to it. Thus, the smaller the gold number of lyophilic colloids, the greater is the protective
power.

Which of the following statement(s) is/are correct
This question has multiple correct options
A. Higher the gold number, more protective power of colloid
B. Lower the gold number, more the protective power
c. Higher the coagulation value, more the coagulation power
D. Lower the coagulation value, higher the coagulation power


For what value of \( ^{\prime} \boldsymbol{k}^{\prime},\left(\boldsymbol{k}^{2}-\mathbf{4}\right) \boldsymbol{x}^{2}+ \)
\( 2 x-9=0 \) can not be quadratic
equation?


The molar conductivity of
\( 0.1 M C H_{3} C O O H \) solution is
\( 4 S c m^{2} m o l^{-1} . \) What is the specific
conductivity and resistivity of the solution.


Which letter represents appendix in the
figure given below?
\( A \)
B. \( Q \)
\( c \cdot R \)
\( D \)
E. None of these


The transpose of a row matrixis
A. zero matrix
B. diagonal matrix
C. column matrix
D. row matrix


Bernoulli's equation is conservation of:
A. Energy
B. Momentum
c. Angular momentum
D. Mass


The pH of \( D_{2} O \) and \( H_{2} O \) at \( 298 \mathrm{K} \) is:
A. 7.0, 7.0
B. 7.35, 7.0
c. 7.0,6.85
D. 6.85,7.35


Three charged particles are in equilibrium under their electrostatic forces only, then:
This question has multiple correct options
A. The particle are collinear
B. All the charges cannot have the same magnitude
c. All the charges cannot have the same sign
D. The equilibrium is unstable


In cycloalkanes the hybridisation of \( \boldsymbol{C} \) atoms is:
\( \mathbf{A} \cdot s p \)
B \( \cdot s p^{2} \)
\( c \cdot s p^{3} \)
\( D \cdot s p^{2} d \)


If \( l \) is an identity matrix and \( A \) is a
square matrix such that \( A^{2}=A \), then
find the value of \( (\boldsymbol{l}+\boldsymbol{A})^{2}-\mathbf{3} \boldsymbol{A} \)


Assertion
Fertilization of bryophytes require water for antherozoids.
Reason
They are amphibians of plant kingdom.
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


000
0
0
\( \infty \)
00


Solve \( \sin x+\cos x=\sqrt{2}, \) then \( x= \)
\( 2 n \pi+\frac{\pi}{4}, n \in I \)
If true then enter 1 and if false then
enter 0


The S.D. of the following freq. dist.
\( \begin{array}{lllll}\text { class } & \begin{array}{c}0 \\ 10\end{array} & \begin{array}{c}10 \\ 20\end{array} & \begin{array}{c}20 \\ 30\end{array} & \begin{array}{c}30- \\ 40\end{array}\end{array} \)
2 \( f_{i} \quad 1 \quad 3 \)
A . 7.8
B. 9
c. \( 8 . \)
D. 0.9


The diagram, given below shows two paths drawn inside a rectangular field \( 80 \mathrm{m} \) long and \( 45 \mathrm{m} \) wide. The widths of
the two paths are \( 8 \mathrm{m} \) and \( 15 \mathrm{m} \) as shown. Find the area of the shaded
portion


Length of the latus rectum of the parabola \( 25\left[(x-2)^{2}+(y-3)^{2}\right]= \)
\( (3 x-4 y+7)^{2} \) is :
\( A \cdot 4 \)
B. 2
\( c \cdot 1 / 5 \)
D. 2/5


\( \lim _{x \rightarrow 1}\left(\frac{1+x}{2+x}\right)^{\frac{(1-\sqrt{x})}{(1-x)}}= \)
\( \mathbf{A} \cdot \mathbf{1} \)
в. \( \ln 2 \)
\( c \cdot \sqrt{\frac{2}{3}} \)
D. Does not exist


A source \( S \) and a detector \( D \) of high
frequency waves are a distance d apart
on the ground. The direct wave from S is found to be in phase at D with the wave
from \( S \) that is reflected rays make the
same angle with the reflecting layer. When the layer rises a distance \( h, \) no
signal is detected at D. Neglect absorption in the atmosphere and find the relation between \( \mathrm{d}, \mathrm{h}, \mathrm{H} \) and the wavelength \( \lambda \) of the waves.


Which of the following colors has maximum refractive index?
A . Red
B. Violet
c. Green
D. Yellow


A 0.5 kg body performs simple harmonic motion with a frequency of 2
\( \mathrm{Hz} \) and an amplitude of \( 8 \mathrm{mm} \). Find the
maximum velocity of the body, its maximum acceleration and the
maximum restoring force to which the body is subjected.


In the circle shown \( \boldsymbol{L}=\mathbf{1} \boldsymbol{\mu} \boldsymbol{H}, \boldsymbol{C}=\mathbf{1} \boldsymbol{\mu} \boldsymbol{F} \)
and \( R=1 k \Omega . \) They are connected in
series with a.c. source \( V=V_{0} \sin \omega t \) as
shown.Which of the following option
is/are correct?
This question has multiple correct options
A. The frequency at which the current will be in the phase with the voltage is independent of \( R \)
B. At \( \omega \sim 0 \) the current flowing through the circuitt
becomes nearly zero
C. \( A t \omega>>10^{6} r a d . s^{-1}, \) the circuit behave like a capacitor
D. The current will be in phase with the voltage if \( \omega= \) \( 10^{4} r a d \cdot s^{-1} \)


If \( y=f(x)=\frac{x+2}{x-1}, \) than it is incorrect
to say:
A. \( x=\frac{y+2}{y-1} \)
B. \( f(0)=-2 \)
c. \( f(1)=0 \)
D. \( f(-2)=0 \)
E . \( f(y)=x \)


Electrons present in the outermost orbit are called:
A. valence Electrons
B. free Electrons
c. forced Electrons
D. none of these


Choose the correct answer from the
allternatives given

What type of circulatory system is
found in cockroach?
A. Lacunar
B. closed
c. Peritrophic
D. Penestrated


The difference between the atom \( U^{235} \)
and \( U^{238} \) is that
B. \( U^{238} \) contains 3neutrons and 3 electrons more
c. \( U^{238} \) contains 3 protons more
D. \( U^{238} \) contains 3 proton and 3 electron more


How many double bonds are there in a saturated hydrocarbon?
A. one
B. three
c. two
D. zero


Which of the following is a Lanthanoid?
A. Ta
B. Rh
\( c . \) Th
D. Lu


These clothes are used best in summer
A. wool
B. Silk
c. cotton
D. Nylon


People who have migrated from the planes to an area adjoining Rohtang
Pass about six month back.
A. Have more RBCs and their haemoglobin has a lower binding affinity to \( O_{2} \)
B. Are not physically fit to play games like football
c. suffer from altitude sickness with symptoms like nausea, fatigue, etc
D. Have the usual RBC count but their haemoglobin has very high binding affinity to \( O_{2} \)


A filament bulb \( 500 \mathrm{W}, 100 \mathrm{V} \) is to be used in a \( 230 \mathrm{V} \) main supply. When a resistance \( R \) is connected in series, it
works perfectly and the bulb consumes \( 500 \mathrm{W} \). The value of \( \mathrm{R} \) is :-
A . \( 26 \Omega \)
B. 13\Omega
c. \( 236 \Omega \)
D. \( 46 \Omega \)


Pico is used as prefix in SI system. True \( =1, \) false \( =0 \)


Solve:
\( \int_{0}^{1} \sqrt{\frac{1-x}{1+x} d x} \)


A metallic conductor of irregular cross-
section is as shown in the figure. A
constant potential difference is applied
across the ends (1) and \( (2) . \) Then
(1)
A. the current at the cross-section \( P \) equal the current at the cross-section \( Q \)
B. the electric field intensity at \( P \) is less than that of \( Q \)
C. the rate of heat generated per unit time at \( Q \) is greater than that at \( P \)
D. the number of electrons crossing per unit area of cross-section at \( P \) is less than that at \( Q \)


Identify the group \( 16(V I A) \) elements which is the most electronegative?
A. \( O \)
B. \( S \)
\( c . T e \)
D. \( P o \)


Three charges \( 29,-q .-q \) are located at the vertices of an equilateral triangle. At the triangle
A . field is zero but potential is non-zero
B. field is non- zero and potential are zero.
c. Both field potential are zero
D. Both field potential are non zero


A mass is attached to the end of a
string of which is tied to a fixed point 0 The mass is released from the initial
horizontal position of the string. Below the point 0 at what minimum distance a peg \( P \) be should fixed so that the mass
tums about \( P \) and can describe a
complete circle in the vertical plane?
A \( \cdot\left(\frac{3}{5}\right) l \)
B・(\frac{2 } { 5 } )
\( c \)
\( D \cdot \frac{2}{3} \)


The area ( in square unit) of the circle which touches the lines \( 4 x+3 y=15 \)
and \( 4 x+3 y=5 \) is \( m \pi . \) Find \( m \)


If \( A((2,1,3), B(5,3,9), C(1,-1,3) \text { and } D(2, \)
3, 11 ), find the angle between the lines \( A B \) and \( C D \)


Which of the following is characterized by the tightly coiled, condensed form of DNA that is not transcribed?
A. Promoter
B. Enhancer
c. operator
D. Euchromatin
E. Heterochromatin


Consider the following statements \( A \) and B. Identify the correct choice in the
given answer
\( A: \ln a \) one - dimensional perfectly
elastic collision between two moving
bodies of equal masses, the bodies
merely exchange their velocities after
collision
\( \mathrm{B}: \) If a lighter body at rest suffers perfectly elastic collision with a very
heavy body moving with a certain velocity, after collision both travel with
same velocity
\( A \cdot A \) and \( B \) are correct
B. Both A and B are wrong
C. A is correct B is wrong
D. A is wrong B is correct


If two subshells have equal value of
\( (n+1) \) and one of them has \( n=4, l=3, \) while
second subshell has dumbbellshape.
Then which of the bfollowing statement is/are correct?
This question has multiple correct options
A. Second subshell has value of \( n=6 \)
B. One of the orbitals of second subshell has one nodal plane
c. second subshell is d-subshell.
D. First subshell is f-subshell


Assertion
The expression \( ^{40} \boldsymbol{C}_{r} .^{60} \boldsymbol{C}_{0}+^{40} \)
\( C_{r-1} .^{60} C_{1}+\ldots \) attains maximum value
when \( r=50 \)
Reason \( ^{2 n} C_{r} \) is maximum when \( r=n \)
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


\( 10,12,16,24,40, \dots \)
A . 60
B. 56
c. 70
D. 72


Dinoflagellates are mostly
A. marine and saprophytic
B. freshwater and photosynthetic
C. marine and photosynthetic
D. terrestrial and photosynthetic


A \( 6.90 M \) KOH solution in water has
\( 30 \% \) by weight of \( K O H . \) The density of
KOH solution is:
A. \( 1.288 g / m L \)
в. \( 12.88 g / m L \)
c. \( 0.1288 g / m L \)
D. none of these


If the sum of \( n \) terms of a GP (with
common ratio \( r \) ) beginning with the \( p^{t h} \)
term is \( k \) times the sum of an equal
number of the same series beginning with the \( q^{t h} \) term, then the value of \( k \) is
A \( \cdot r^{p / q} \)
B \( \cdot r^{a / p} \)
c. \( r^{p-q} \)
D. \( r^{p+q} \)


A resistor \( R \) on inductance \( 0.2 H \) and a
capacitor of capacitance \( C \) are
connected in series. A sinusoidal
voltage of \( r m s \) value \( 200 V \) is applied across the combination using a fixed
frequency oscillator. If the rms value of current through the circuit is \( 2.828 A \) and the inductive and capacitive reactances are \( 3 R \) and \( 2 R \) respectively. Calculate (i) resistance of the resistance of the resistor
(ii) frequency of \( A C \) (iii) capacitance of the capacitor.
\( \begin{array}{ll}\text { A. } & (500 \Omega, 119.3 H z, 13.3 \mu F)\end{array} \)
B. \( \quad(50 \Omega, 119.3 H z, 13.3 \mu F) \)
C. \( \quad(50 \Omega, 1193 H z, 133 \mu F) \)
D. \( \quad(50 \Omega, 0.1193 H z, 133 \mu F) \)


The test charge used to measure
electric field at a point should
be
A. infinitely large
B. vanishingly small
c. negative
D. zero


The electronic configuration of an element is \( 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{2} 3 p^{3} . \) What is
the atomic number of the element
which is just below the given element in the periodic table?
\( \mathbf{A} \cdot 34 \)
B . 49
c. 33
D. 31


A card is drawn from a deck of cards.
What is the probability that it is either a spade or an ace or both
A \( \cdot \frac{7}{13} \)
в. \( \frac{10}{13} \)
c. \( \frac{4}{13} \)
D. \( \frac{5}{13} \)


The heart sounds normally heard by a physician while holding a stethoscope onto the left side of the chest of the
patient are due to
A. contraction of atrial chambers
B. Contraction of ventricular chambers
c. closure of the atrioventricular valves.
D. Relaxation of the semilunar valves


The artificial sweetener, which is a
derivative of sucrose, is:
A . stevia.
B. saccharin
c. aspartame.
D. sucrolose.


Organisms are able to capture free energy from small inorganic molecules through a process called
chemosynthesis. These inorganic elements may include
A. water
B. Sulfur
c. Carbon dioxide
D. Hydrogen.


Identify the rational numbers represented by \( \mathrm{B}, \mathrm{C} \) and \( \mathrm{D} \) if \( \mathrm{AB}=\mathrm{CD}=\mathrm{DE} \)
as drawn on the number line.
\[
\begin{array}{|c|c|c|}
\hline E D & C & A \\
\hline-2 & 0 & 2 \\
\hline
\end{array}
\]
A. 0,-1,-2
в.
\[
\frac{-1}{2},-1, \frac{-3}{2}
\]
c.
\[
\frac{1}{2}, 1, \frac{3}{2}
\]
D.
\[
\frac{-1}{4},-1, \frac{-5}{2}
\]


An inorganic salt (A) is decomposed at about \( 523 \mathrm{K} \) to give products \( (\mathrm{B}) \) and
(C). Compound (C) is a liquid at room temperature and is neutral to litmus
paper while oxide (B) on burning with phosphorous, given a dehydrating agent
(D). Compounds \( (A),(B),(C) \) and \( (D) \) will be identified as :
A. \( N H_{4} N O_{3}, N_{2} O, H_{2} O, P_{2} O_{5} \)
B. \( N H_{4} N O_{2}, k_{2} O, H_{2} O, P_{2} O_{5} \)
c. \( C a C O_{3}, C a O, H_{2} O, C a C l_{2} \)
D. \( C a C O_{3}, C a O, H_{2} O, C a(O H)_{2} \)


Two electrons are moving with the same velocity, one electron enters a region of uniform electric field while the other
enters a region of uniform magnetic field. Then, after sometime, if the de-
Broglie wavelength of two are \( \lambda_{1} \) and \( \lambda_{2} \) respectively, then
\( A \cdot \lambda_{1}=\lambda_{2} \)
в. \( \lambda_{1}>\lambda_{2} \)
c. \( \lambda_{1}<\lambda_{2} \)
D. \( \lambda_{1}>\lambda_{2} \) or \( \lambda_{1}<\lambda_{2} \)


\( N a H C O_{3} \) represent the formula of
which one of the following?
A. Sodium carbonate
B. Baking soda
c. Sodium acetate
D. washing soda


Fill in the blanks:
Electrolysis is the passage of \( _{\text {一一一一一一一 }} \) (electricity / electrons) through a liquid or a solution accompanied by a (physical/ chemical) change.


A trait may be inherited, but may not be
expressed. Justify this statement with the help of a suitable example.


Which one of the following equations does not correctly represent the first law of thermodynamics for the given processes involving an ideal gas? (Assume non-expansion work is zero)
A. Cylic process : \( q=-w \)
B. Isothermal process : \( q=-w \)
c. Adiabatic process: \( \Delta U=-w \)
D. Isochoric process: \( \Delta U=q \)


If \( A, B \) and \( C \) are three finite sets then
what is \( [(\boldsymbol{A} \cup \boldsymbol{B}) \cap \boldsymbol{C}]^{\prime} \) equal to?
A \( \cdot\left(A^{\prime} \cup B^{\prime}\right) \cap C^{\prime} \)
B \( \cdot A^{\prime} \cap\left(B^{\prime} \cap C^{\prime}\right) \)
c. \( \left(A^{\prime} \cap B^{\prime}\right) \cup C^{\prime} \)
D. \( (A \cap B) \cap C \)


One end of massless rope, which passes over a massless and frictionless pulley
\( P \) is tied to a hook \( C \) while the other end
is free. Maximum tension that the rope
can bear is \( 360 N . \) With what value of
maximum safe acceleration \( \left(\text { in } m s^{-2}\right) \)
can a man of \( 60 \mathrm{kg} \) climb on the rope?
\( A \cdot 16 \)
B. 6
\( c \cdot 4 \)
D. None of these


A transformer steps up an ac supply from 220 to 2200 V. If the secondary coil of the transformer has 2000 turns, Then
find the number of turns in its primary coil :
\( \mathbf{A} \cdot N_{p}=250 \) turns
B. \( N_{p}=300 \) turns
C \( . N_{p}=100 \) turns
D. \( N_{p}=200 \) turns


Following statements regarding the periodic trends of chemical reactivity of
alkali metals and the halogens are
given.Which of these statements give
the correct picture?
A. In alkali metals, the reactivity increases but for halogens it decreases with increase in atomic number down the group.
B. The reactivity decreases in the alkali metals but increases in the halogens with increase in atomic number down the group.
C. In both the alkali metals and the halogen the chemical reactivity decreases with increase in atomic number down the group.
D. Chemical reactivity increases with increase in atomic number down the group.


In \( C_{4} \) pathway carboxylation occurs
twice. Discuss.


The concentration of a solution is
\( \mathbf{1 0}^{-4} \boldsymbol{M} \) for \( \boldsymbol{C l}^{-}, \mathbf{1 0}^{-\mathbf{5}} \boldsymbol{M} \) for \( \boldsymbol{B r}^{-} \) and
\( 10^{-3} M \) for \( I^{-} . A g N O_{3}(s) \) is added slowly to the solution. The minimum
concentration of \( A g^{+} \) required to start precipitation of all three ions is:
\( \left[\text { Given, } \boldsymbol{K}_{s p(A g C l)}=\mathbf{1 0}^{-10}, \boldsymbol{K}_{s p(A g B r)}=\right. \)
\( \mathbf{1 0}^{-\mathbf{1 3}}, \mathbf{K}_{s p(A g I)}=\mathbf{1 0}^{-\mathbf{1 7}} \mathbf{]} \)
A \( \cdot 10^{-9} \)
B. \( 10^{-6} \)
\( \mathbf{c} \cdot 10^{-8} \)
D. \( 10^{-10} \)


Prove that: \( \frac{\cos 5 x+\cos 4 x}{2 \cos 3 x-1}=\cos x+ \)
\( \cos 2 x \)


Given that: \( \sqrt{\mathbf{2}}=\mathbf{1 . 4 1 4}, \sqrt{\mathbf{3}}= \)
\( 1.732, \sqrt{5}=2.236 \) and \( \sqrt{7}=2.646 \)
evaluate each of the following:
\( \sqrt{\frac{2500}{3}} \)


The enzyme peptidyl transferase of prokaryotes resides in
A. 50 s ribosome
B. 30s ribosome
c. 40 s ribosome
D. 60 ribosome


Solve the following equations by the substitution method
\( 11 x-8 y=27,3 x+5 y=-7 \)
A. \( x=0, y=1 \)
в. \( x=0, y=-5 \)
c. \( x=2, y=3 \)
D. \( x=1, y=-2 \)


What is the total translational and
rotational energy of 1 mole of oxygen at
\( 300 K: \)
\( \left[\boldsymbol{R}=\mathbf{8 . 3 1 4} \boldsymbol{J} \boldsymbol{m o l}^{1} \boldsymbol{K}^{1}\right] \)
A. \( 6235.5 J \)
B. 623.25 \( J \)
c. \( 62.325 J \)
D. 6.2325 \( J \)


Differentiate between rhizome and bulb


\( \mathbf{N H}_{3} \) on burning in oxygen gives:
A. \( \mathrm{NOandH}_{2} \mathrm{O} \)
B. \( N O_{2} \) and \( H_{2} O \)
c. \( \mathrm{N}_{2} \) and \( \mathrm{H}_{2} \mathrm{O} \)
D. \( \mathrm{N}_{2} \mathrm{OandH}_{2} \)


Some hyperthermophilic organisms, that grow in highly acidic \( (\mathrm{pH}=2) \) habitats, belong to the two groups
which are
A. Liverworts and yeasts
B. Eubacteria and archaea
c. cyanobacteria and diatoms
D. Protists and mosses


It is known that the decay rate of radium is directly proportional to its quantity at each given instant. Find the law of variation of a mass of radium as
a function of time if at \( t=0, \) the mass of
the radius was \( m_{0} \) and during time \( t_{0} \alpha \)
\( \% \) of the original mass of radium decay.
A \( \quad m=m_{0} e^{-k t} \) where \( k=\frac{1}{t_{0}} \ln \left(1-\frac{\alpha}{100}\right) \)
B. \( m=m_{0} e^{-k(t-1)} \) where \( k=\frac{1}{t_{0}} \ln \left(1+\frac{\alpha}{100}\right) \)
c. \( m=m_{0} e^{-k(t-1)} \) where \( k=\frac{1}{t_{0}} \ln \left(1-\frac{\alpha}{100}\right) \)
D. \( m=m_{0} e^{-k t} \) where \( k=\frac{1}{t_{0}} \ln \left(1+\frac{\alpha}{100}\right) \)


A ship moving in sea can't be stopped quickly by applying brakes due to:
A . low friction
B. excessive friction
c. high speed
D. none of the above


In an A.C. circuit the potential difference across an inductance and resistance
joined in series are respectively \( 16 \mathrm{V} \) and 20V. The total potential difference across the circuit is
A . \( 20.0 v \)
B. 25.6v
c. \( 31.9 v \)
D. 53.5v


The following table shows the heights
\( (c m) \) of 50 girls of class \( X \) of a school
\( \begin{array}{ll}\text { Height }(\mathrm{cm}) & \text { Number of girls } \\ 120-130 & 2 \\ 130-140 & 8 \\ 140-150 & 12 \\ 150-160 & 20 \\ 160-170 & 8 \\ & \\ \text {Total} & 50\end{array} \)
Find the mean of the above data by step
deviation method.


Which structure of Pheretima plays the
role of liver?
A . Calciferous cells
B. Chloragogen cells
c. clitellar cells
D. Gland cells


The angle that the vector \( \vec{A}=2 \hat{i}+3 \hat{j} \)
makes with \( x \) -axis is
\( A \cdot \tan ^{-1}(3 / 2) \)
B \cdot \( \tan ^{-1}(2 / 3) \)
\( c \cdot \sin ^{-1}(2 / 3) \)
D \( \cdot \cos ^{-1}(3 / 2) \)


\( 2 H_{2} S(g)+3 O_{2}(g) \rightarrow 2 S O_{2}(g)+ \)
\( 2 H_{2} O(g)+ \) heat
Which quantity is increased when the volume of the system is decreasing?
I. Rate of reaction
Il. Equilibrium concentration of
reactants
III. Value of \( \boldsymbol{K}_{e q} \)
A . I only
B. III only
c. I and II only
D. II and III only
E . I, II, and III


Average quantity of urea excreted daily humans per day is
A . \( 10-15 \) g
B. 25 - 30 g
c. \( 40-50 \mathrm{g} \)
D. 100 - 500 mg


If the probability of India winning a particular hockey match is \( 0.81 . \) What is the probability of India losing that match?
A . 0.19
B. 0.29
c. 0.59
D. 0.49


If each one of the above ionic species is
in turn kept in a magnetic field, which one will get attracted?
A \( \cdot C_{0}^{+2} \)
B. \( M n^{+7} \)
\( c \cdot S c^{+3} \)
D. \( T i^{+} \)


Match the following
List -

List - II
\( A \)
Sandwich । Three dimensional image ELISA
B. QRS
II. Substrate linked antibody complex
\( \mathrm{C} \)
III. Ventricular depolarisation Allograft
D. CT
IV. Transplantation between Scan \( \quad \) genetically non-identical individuals
A. \( A-\| I, B-11, C-1, D-1 V \)
B. \( A-I, B-11, C-111, D-1 V \)
C. \( A-I V, B-\| I, C-11, D-1 \)
D. \( A-11, B-111, C-1 V, D-1 \)


If \( c \) is the middle point of \( A B \) and \( P \) is any point outside \( A B \) then
\( \mathbf{A} \cdot \overrightarrow{P A}+\overrightarrow{P B}=\overrightarrow{P C} \)
в . \( \overrightarrow{P A}+\overrightarrow{P B}=2 \overrightarrow{P C} \)
c. \( \overrightarrow{P A}+\overrightarrow{P B}+\overrightarrow{P C}=0 \)
D \( \cdot \overrightarrow{P A}+\overrightarrow{P B}+2 \overrightarrow{P C}=0 \)


State true or false.
1. Position of isotopes was clearly defined in Mendleev's periodic table.
2. Position of lanthanides and actinides
was clearly defined in Mendleev's
periodic table.
\( \mathbf{A} \). True, True
B. True, False
c. False, True
D. False, False


Boron rods, in a nuclear reactor, are
used as.
A. moderator
B. Protective shield
c. coolants
D. control rods


Find the angle between the line whose
direction cosines are given by \( l+m+ \)
\( \boldsymbol{n}=\mathbf{0} \) and \( l^{2}+\boldsymbol{m}^{2}=\boldsymbol{n}^{2} \)


If the lines \( 3 x+2 y-5=0,2 x-5 y+ \)
\( \mathbf{3}=\mathbf{0}, \mathbf{5 x}+\mathbf{b y}+\mathbf{c}=\mathbf{0} \) are concurrent
then \( \mathbf{b}+\mathbf{c}= \)
A. 7
B. - -
\( c \cdot 6 \)
D.


What are the compounds in which two
same halogen atoms are attached to the same carbon called?


A slit of width \( a \) is illuminated by white
light. The first minimum for red light \( (\lambda \)
\( =6500 A) \) will fall at \( \theta=30^{\circ} \) when \( a \) will
be
A \( \cdot \) з250 \( \stackrel{\circ}{A} \)
B. \( 6.5 \times 10^{-4} \)
c. 1.3 micron
D. \( 2.6 \times 10^{-4} \)


A conducting disc of radius \( r \) spins about its axis with an angular velocity
\( \omega . \) There is a uniform magnetic field of
magnetude B perpendicular to the plane of the disc. \( C \) is the centre of the
ring. This question has multiple correct options
A. No emf is induced in the disc.
B. The potential difference between C and the rim is \( \frac{1}{3} B r^{2} \omega \)
c. \( c \) is at a higher potential than the rim
D. Current flows between c and the rim


Substances which dissolve in water to
give ions or substances that dissociate into
ions when dissolved in water is called-?
A. Electrolytes
B. Elements
c. Acids
D. None of these


The largest possible bond angle is observed in:
A. \( B F_{3} \)
в. \( B e F_{2} \)
c. \( N F_{3} \)
D. \( C F_{4} \)


\( n(\geq 5) \) persons are sitting in a row. Three of these are selected at random,
the probability that no two of the
selected persons are together is This question has multiple correct options
\( ^{\mathbf{A}} \cdot \frac{n-3}{^{n} P_{2}} P_{2} \)
в. \( \frac{n-3}{^{n} C_{2}} \)
c. \( \frac{(n-3)(n-4)}{n(n-1)} \)
D. \( \frac{n-3}{n P_{2}} \)


A transistor-oscillator using a resonant circuit with an inductor \( L \) (of negligible resistance) and a capacitor \( \mathrm{C} \) in series produce oscillations of frequency f. If is doubled and \( C \) is changed to \( 4 C \), the frequency will be:-
\( A \cdot \frac{f}{4} \)
B. 8f
\( c \cdot \frac{f}{2 \sqrt{2}} \)
\( D \cdot \frac{f}{2} \)


Which of the following statements
regarding hydrides iis not correct?
A. Ionic hydrides are crystalline, non-volatile and nonconducting in solid state
B. Electron-deficient hydrides act as Lewis acids or electron acceptors
C. Elements of group-13 form electron-deficient hydride
D. Elements of group \( 15-17 \) form electron-precise
hydrides


Analyse the following observation table showing variation of image - distance
(v) with object - distance
(u) in case of a
convex lens and answer the questions that follow without doing any calculations:
(a) what is the focal length
of the convex lease? Give reason to
justify your answer
(b) Write serial number of the
observation which is not correct. On
what basis have you arrived at this conclusion?
(c) Select an appropriate scale and draw a ray diagram for the observation
at S.No. 2. Also the approximate value of magnification.


The diagram shows the sketch of an
electrolytic cell used in the extraction of
aluminium. At which electrode (A or B)
is the aluminium formed?
A. A (Cathode)
B. B (Anode)
c. At both A and B
D. Cannot be determined


Explain the following reactions:
(i) Diazotization
(ii) Carbylamine reaction


The given distribution shows the number of wickets taken by bowlers in inter-school competitions:
Find the median.


Silver is used in making mirrors.
A. True
B. False


A fixed mass of a gas is first heated isobarically to double the volume and then cooled isochorically to decrease the temperature back to the initial
value. By what factor would the work done by the gas decrease, had the process been isothermal?
\( A \cdot 2 \)
B. 1/2
\( c \cdot \ln 2 \)
D. \( \ln 3 \)


The radius of a sphere is changing at the rate of \( 0.1 \mathrm{cm} / \) sec. The rate of its
surface area when the radius is \( 200 \mathrm{cm} \)
is
A \( \cdot 8 \pi c m^{2} / \) sec
В . \( 12 \pi c m^{2} / \) sec
c. \( 160 \pi c m^{2} / \) sec
D. \( 200 \pi c m^{2} / \) sec


At what temperature the reading on Celsius scale is half of that on
Fahrenheit scale?
A \( \cdot 160^{\circ} \mathrm{C} \)
B . \( 170^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 180^{\circ} C \)
D. \( 190^{\circ} \mathrm{C} \)


Prove that if chords of congruent circles
subtend equal angles their centres, then the chords are equal.


Elastic waves need material medium
for their propagation.
A. True
B. False


Which of the following process(es) occur(s) during the convective transfer
of heat within a large volume of air?
This question has multiple correct options
A. A continuous flow of warmer and cooler parts of air is established.
B. The flow of air molecules results in flow of heat.
C. The cooler portion of the air surrounding a warmer part exerts a buoyant force on it.
D. As the warmer part of the air moves, it is replaced by cooler air that is subsequently warmed up.


Raindrops are spherical in shape
because
A. Spheres have highest surface area and hence least surface tension
B. Spheres have least surface area and hence least surface tension
C. Spheres have highest surface area and hence highest surface tension
D. Spheres have least surface area and hence highest surface tension


Assertion
Assertion: When ice and water are kept in a perfectly insulated thermos flask at
\( 273 \mathrm{K} \) and the atmospheric pressure,
there is no change in mass of ice and
water.
Reason
Reason : The system is in static equilibrium.
A. If both the assertion and reason are true and reason is the correct explanation of assertion
B. If both the assertion and reason are true but reason is not the correct explanation of assertion.
C. If assertion is true but reason is false.
D. If both assertion and reason are false


In family Liliaceae flowers are
A. Trimerous and hypogynous
B. Pentamerous and epigynous
C. Trimerous and epigynous
D. Pentamerous and hypogynous


Escape velocity of a particle depends on
its mass
\( \mathbf{A} \cdot m^{2} \)
в. \( m \)
\( \mathrm{c} \cdot m^{0} \)
D. \( m^{-1} \)


A card sheet divided into squares each
of size \( 1 \mathrm{mm}^{2} \) is being viewed at a
distance of \( 9 \mathrm{cm} \) through a magnifying glass (a converging lens of focal length
\( 9 c m \) ) held close to the eye and the
magnifying glass if the virtual image of each square is to have an area of
\( 6.25 m m^{2} . \) Would you be able to see
the squares distinctly with your eyes very close to the magnifier?


what is the angular momentum of an electron of de-broglie wavelength \( \lambda ? \)
given \( r \) is the radius of orbit
\( A \cdot \frac{r h}{\lambda} \)
B. \( \frac{2 r h}{\lambda} \)
\( c \cdot \frac{3 r h}{\lambda} \)
D. \( \frac{4 r h}{\lambda} \)


\( 5 \mathrm{cm} \) high object is placed at a distance
of \( 25 \mathrm{cm} \) from a converging lens of focal
length \( 10 \mathrm{cm} \). Determine the position,
size and also type of the image.


Explain the role of citizen in pollution
control.


An angular conductor is moving with
velocity \( v \) along its angular bisector in a
perpendicular magnetic field \( (B) \) as
shown in the figure. The induced potential difference between its free
ends will be
\( A \)
\[
2 B v l \sin \frac{\theta}{2} \frac{\theta}{2}
\]
B. \( 2 B v l \)
c. \( 2 B v l \sin \theta \)
D. zero


\( \int_{0}^{2 \pi}(\sin x+|\sin x|) d x \) is equal to
A .
B. 4
\( c \cdot 8 \)
D.


A particular point moves on the parabola \( y^{2}=4 a x \) in such a way that
its projection on \( y \) -axis has a constant
velocity. Then its projection on \( x \) -axis
moves with
This question has multiple correct options
A. constant velocity
B. constant acceleration
c. variable velocity
D. variable acceleration


Heart of elephant is
A. Neurogenic
B. Myogenic
c. Loop of Henle
D. Bowman's capsule


bond is formed, between
atoms of elements possessing electronegativities of 3.5 and 0.8
A. Covalent
B. lonic
c. Dative
D. None of these


toppr OGII
Q Type your question_
What is an
centered on point \( P \)
The segments are connected by straight
wires as shown, and an unseen source
of EMF creates a constant
counterclockwise current in the wire.
What is the direction of the magnetic
field created at point \( P \) due to each wire
segment?
A. Both segments 1 and 2 create magnetic field that is into the page at point \( P \)
B. Both segments 1 and 2 create magnetic field that is out of the page at point \( P \)
c. Segment 1 creates magnetic field that is out of the page; Segment 2 creates magnetic field that is into the page at point P.
D. Segment 1 creates magnetic field that is into the page:
Segment 2 creates magnetic field that is out of the page at point P.


\( \mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq})+\mathrm{Ba}(\mathrm{OH})_{2}(\mathrm{aq}) \rightarrow \)
In the above reaction, the products are:
I. \( \mathrm{O}_{2}(g) \)
II. \( \mathrm{H}_{2} \mathrm{O}(1) \)
III. \( \operatorname{BaSO}_{4}(s) \)
\( A \)
в. III
c. I and ॥
D. I and III
E. Il and III


A transformer consisting of 300 turns in the primary and 150 turns in the
secondary gives output power of \( 2.2 k W \) .f the current in the secondary coil is
\( \mathbf{1 0} A, \) then the input voltage and current in the primary coil are :
A . \( 220 V \) and \( 10 A \)
B. \( 440 V \) and \( 5 A \)
c. \( 440 V \) and \( 20 A \)
D. 220V and 20A


What is eddy current? Mention two
applications of eddy current.


Druse is
A. Calcium-oxalate crystals
B. Bicarbonate crystals
\( \mathbf{c} \cdot \mathrm{CaCO}_{3} \) crystals
D. None of the above


Define hydroponics.


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


Monochromatic light of wavelength \( 4500 A \) falls on slit of width \( ^{\prime} a^{\prime} . \ln \)
diffraction pattern second maxima
deviates through \( 30 . \) The slit width is


A ladder \( 13 \mathrm{m} \) long leans against a wall. The foot of the ladder is pulled along the
ground away from the wall, at the rate
\( 1.5 \mathrm{m} / \mathrm{sec} . \) How fast is the angle \( \theta \) between the ladder and the ground is changing when the foot of the ladder is
\( 12 \mathrm{m} \) away from the wall.


Wood commonly used for making cricket bat is
A. Cedrus
B. Salix
c. Tectona
D. Morus


In froth flotation process, pine oil is usually added to the gangue particles in the ore.
A. True
B. False


In a mixture A and B components show
negative deviation as:
\( \mathbf{A} \cdot \Delta V_{m i x}=+v e \)
B. \( \Delta H_{\text {mix}}=- \)ve.
C. A-B interaction is weaker than A-A and B-B interaction.
D. None of the above reason is correct.


A wire ABCDEF (with each side of length
L) bent as shown in figure and carrying
a current I is placed in a magnetic field.
Force on the wire is :
A. BiL along z-axis
B. BiL along -z axis
C. BiL along +x-axis
D. BiL along -x-axis


Check whether \( x^{2}-\frac{29}{4} x+5=0 \) is
a quadratic equation


From (1,4) you travel \( 5 \sqrt{2} \) units by making \( 135^{0} \) angles with positive \( x \) axis (anticlockwise) and then 4 units by
making \( 120^{0} \) angle with positive \( x \) -axis (clockwise) to reach Q. Find co-
ordinates of point \( Q \)
A \( \cdot(+6,9-2 \sqrt{3}) \)
в. \( (-6,9-2 \sqrt{3}) \)
c. \( (-6,9+2 \sqrt{3}) \)
D. \( (+6,9+2 \sqrt{3}) \)


In adjoining fig two semicircles are
drawn on sides \( A D \) and \( B C \) of a square
\( A B C D . \) If \( A B=10 \mathrm{cm},(\pi=3.14) \)
then the total area of semicircles is :
A \( .78 .50 \mathrm{cm}^{2} \)
B. \( 68.50 \mathrm{cm}^{2} \)
\( c \cdot 70 \mathrm{cm}^{2} \)
D. \( 70.48 \mathrm{cm}^{2} \)


The following deuterium reactions and corresponding reaction energies are found to occur
\( ^{14} N(d, p)^{15} N, Q=8.53 M e V \)
\( ^{15} N(d, \alpha)^{13} C, Q=7.58 M e V \)
\( ^{13} C(d, \alpha)^{11} B, Q=5.16 M e V \)
The rotation \( ^{14} N(d, p)^{15} N \) represents the reaction \( ^{14} N+d \rightarrow^{15} N+p \)
\( _{2}^{4} \boldsymbol{H} \boldsymbol{e}=\boldsymbol{4} . \boldsymbol{0} \boldsymbol{0} 2 \boldsymbol{6} \boldsymbol{a} \boldsymbol{m} \boldsymbol{u}_{, 1}^{2} \boldsymbol{H} e= \)
\( 2.014 a m u_{, 1}^{1} H=1.0078 a m u, n= \)
\( \mathbf{1 . 0 0 8 7 a m u}(\mathbf{1 a m u}=\mathbf{9 3 1 M e V}) \)
The Q values of the reaction
\( ^{11} \boldsymbol{B}(\boldsymbol{\alpha}, \boldsymbol{n})^{14} \boldsymbol{N} \) is
A. \( 0.5 e V \)
в. 0.5 Ме \( V \)
c. \( 0.05 \mathrm{MeV} \)
D. \( 0.05 e V \)


\( \boldsymbol{y}=\sec ^{-1}\left(\frac{1}{2 x^{2}-1}\right) \)
Prove that: \( \boldsymbol{y}=2 \cos ^{-1} \boldsymbol{x} \)


\( \mathbf{f} \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{2} & \mathbf{- 1} \\ -\mathbf{1} & \mathbf{1} & \mathbf{2} \\ \mathbf{2} & \mathbf{- 1} & \mathbf{1}\end{array}\right], \) then
\( \operatorname{det}(\operatorname{adj}(\operatorname{adj} A)) \) is equal to
A \( \cdot 14^{4} \)
B. \( 14^{\text {? }} \)
\( c \cdot 14^{2} \)
D. 14


\( 0.15 g \) of an organic compound gives \( 0.12 g \) of silver bromide by the Carius method. The percentage of bromine in the compound is :
A . 42.06
B . 38.96
c. 24.08
D. 34.04


Verify \( \boldsymbol{A}=\{\mathbf{1}, \mathbf{2}\} \)
\( \boldsymbol{B}=\{1,2,3,4\} C=\{5,6\} D= \)
\( \{5,6,7,8\} . \) Prove \( A \times(B \cap C)=(A \times \)
\( \boldsymbol{B}) \cap(\boldsymbol{A} \times \boldsymbol{C}) \)


Solve:
\( \tan ^{-1}\left(\tan \frac{7 \pi}{6}\right) \)


The speed-time graph of a particle moving along a fixed direction is shown
in the figure. The distance traversed by
the particle between \( t=2 s t o t=6 s \) is
\( A \cdot 26 m \)
B. 36
\( c \cdot 46 m \)
\( 0.56 \mathrm{m} \)


A solution of 1.25 g of \( \mathrm{P} \) in 50 g of water lowers freezing point by 0.3. Molar mass of 'Pis 94. \( \boldsymbol{K}_{f(\text {water})}=\mathbf{1 . 8 6} \mathrm{K} \mathrm{kg} \mathrm{mol}^{-1} \)
The degree of association of P in water is:
A . \( 60 \% \)
B. 75\%
c. \( 80 \% \)
D. 65\%


What is the probability of selecting two spade cards from a pack of 52 cards?
A . \( 1 / 17 \)
B. 15/17
c. \( 32 / 64 \)
D. 5/17


What will come in place of the question mark (?) in the following question? \( (0.08 \% \text { of } 363+0.6 \% \text { of } 241) \times 500=? \)
A. 846.2
B. 868.2
c. 84.62
D. 86.82
E. None of these


Hydraulic machines work on the application of
A. Pascal's law
B. Newton's law
C. Law of Gravity
D. none of these


\( A B C \) is an equilateral triangle of side \( a \) The value of \( \overrightarrow{\boldsymbol{A B}} \cdot \overrightarrow{\boldsymbol{B C}}+\overrightarrow{\boldsymbol{B C}} \cdot \overrightarrow{\boldsymbol{C A}}+ \)
\( \overrightarrow{C A} \cdot \overrightarrow{A B} \) is equal to
A \( \cdot \frac{3 a^{2}}{2} \)
В. \( 3 a^{2} \)
c. \( -\frac{3 a^{2}}{2} \)
D. None of these


Cellophane is used as a plastic wrapper It is made from:
A. gummmmmmm
B. chitin
c. cellulose
D. petroleum


In the reaction of \( 2 N O+O_{2} \rightarrow 2 N O_{2} \)
if the rate of disappearance of \( \boldsymbol{O}_{2} \) is 16 \( g m \) min \( ^{-1}, \) then the rate of
apperance of \( N O_{2} \) is:
A \( .90 \mathrm{gm} \mathrm{min}^{-1} \)
B. \( 46 \mathrm{gm} \) min\( ^{-1} \)
\( \mathrm{c} \cdot 28 \mathrm{gm} \min ^{-1} \)
D. 32 gm min\( ^{-1} \)


Sekar bought a computer for 38,000 and a printer for \( 8,000 . \) If the rate of sales tax is \( 7 \% \) for these items, find the price he has to pay to buy these two items.


Parallax is the apparent displacement of an object because of:
A. change in observer's point of view
B. change in object's position
c. changes both in observers point of view and object's position
D. consistency in observer's point of view


Whales live in water. They belong to the group of vertebrates called
A . Fish
B. Amphibians
c. Reptiles
D. Mammals


What is the degree of the given
monomial \( \boldsymbol{x} \boldsymbol{y}^{2} \boldsymbol{z}^{2} ? \)
\( A \cdot 3 \)
B. 4
\( c .5 \)
D. 6


A box of mass \( 8 k g \) is placed on a rough inclined plane of inclination \( \theta \). Its downward motion can be prevented by applying an upward pull \( F \) and it can be made to slide upwards by applying a force \( 2 F \)

The coefficient of friction between the
box and the inclined plane is
A \( \cdot \frac{1}{3} \tan \theta \)
B. \( 3 \tan \theta \)
c. \( \frac{1}{2} \tan \theta \)
D. \( 2 \tan \theta \)


Derive the relation between object distance (u) and image distance (v) in terms of refractive index of the medium
(n) and the radius of curvature (R) of the spherical surface.
A \( \cdot \frac{\mu_{1}}{\mu_{2}} \)
в. \( \frac{\mu_{2}}{\mu_{1}} \)
c. \( \frac{\mu_{2}}{2} \)
D. \( \frac{\mu_{1}}{2} \)


A mass of \( 50 \mathrm{kg} \) is suspended from a spring of stiffness \( 10 \mathrm{kN} / \mathrm{m} \). It is set oscillating and it is observed that
two successive oscillations have
amplitudes of \( 10 \mathrm{mm} \) and \( 1 \mathrm{mm} \) Determine the damping ratio.
A. 0.315
B. 0.328
c. 0.344
D. 0.353


\( \operatorname{Let} y=\left(x+\frac{4}{x^{2}}\right) \) and \( x \in+R \)
The minimum value of \( y \) is
A . -4
B. 3
c. 8
D. 7


Find the area of the region enclosed by
the parabola \( x^{2}=y, \) the line \( y=x+2 \)
and \( x \) -axis.


A matrix consists of 30 elements. What
are the possible orders it can have?


Which of the following species has the highest electron affinity?
A. \( F \)
в. \( O \)
\( c \cdot O \)
D. \( N a^{+} \)


\( \int \frac{3+4 \sin x+2 \cos x}{3+2 \sin x+\cos x} d x \)
A \( \cdot 2 x+3 \tan ^{-1}\left(\tan \frac{x}{2}+1\right)+c \)
B . \( 2 x-3 \tan ^{-1}\left(\tan \frac{x}{2}+1\right)+c \)
c. \( 2 x-6 \tan ^{-1}\left(\tan \frac{x}{2}+1\right)+c \)
D・ \( x-3 \tan ^{-1}\left(\tan \frac{x}{2}+1\right)+c \)


The chemical formula of magnesium sulphate is:
A. \( M g_{2} S O_{4} \)
B . \( M g S O_{4} \)
c. \( M g_{2}\left(S O_{4}\right)_{2} \)
D. \( M g\left(S O_{4}\right)_{2} \)


A pea plant with blue colour flower BB is cross-breed with a pea plant with white flower denoted by ww. What will be the percentage of plants
bearing white flower in \( F_{2} \) generation,
when the flowers of \( F_{1} \) plants were selfed?


The missing reagent in the sequence
of synthesis shown is:
A. bromocyclopentane
B. 1,5 -dibromopentane
C. 1,4 -dibromobutane
D. 1,1 -dibromocyclopentane


The following cannot be explained by wave nature of light
A . Interference
B. Photo electric effect
c. Diffraction
D. Refraction


Q Type your question
When in equilibrium, there is a gap of
\( \Delta l \) between the sphere and the floor. The
sphere is gently pushed aside so that it
makes an angle \( \theta \) with the vertical. Find
\( \theta_{\max } \) so that sphere fails to rub the
Floor, Young's modulus of the wire is \( Y \)
A \( \cdot \sin ^{-1}\left(1-\frac{Y \pi d^{2} \Delta l}{8 M g L}\right) \)
B. \( \tan ^{-1}\left(1-\frac{Y \pi d^{2} \Delta l}{8 M g L}\right) \)
c. \( \cos ^{-1}\left(1-\frac{Y \pi d^{2} \Delta l}{8 M g L}\right) \)
\( D \)


In Rutherford's experiment, generally the thin foil of heavy atoms like gold, platinum etc. have been used to be
bombarded by the \( \alpha \) -particles. If the thin foil of light atoms like aluminium etc. is used, what difference would be
observed from the above results?


Removal of charge from colloids:
A. Peptizaiton
B. Coagulation
c. Dialysiss
D. Bredig arc method


A tangent is drawn to each of the
circles
\( \boldsymbol{x}^{2}+\boldsymbol{y}^{2}=\boldsymbol{a}^{2}, \boldsymbol{x}^{2}+\boldsymbol{y}^{2}=\boldsymbol{b}^{2} \)
Show that if the two tangents are
mutually perpendicular, the locus of their point of intersection is a circle concentric with the given circles.


The area of the trapezium is 34 sq \( \mathrm{cm} \) and the length of one of the parallel side
is \( 10 \mathrm{cm} \) and its height is \( 4 \mathrm{cm} \). Find the length of the parallel side.


Toss three fair coins
simultaneously and record the outcomes. Find the probability of
getting atmost one head in the three tosses.
A \( \cdot \frac{1}{6} \)
B. \( \frac{1}{4} \)
\( c \cdot \frac{1}{2} \)
D.


Which of the following contains macronutrients only?
A. Calcium, sulphur and zinc
B. Nitrogen, potassium and phosphorus
c. Calcium, magnesium and copper
D. Nitrogen, Iron and chlorine


In periscopes, the parallel rays entering the cylindrical tube from the upper end from an object, strike the plane mirror at an angle of and hence are
reflected through an angle of
A \( .30^{\circ}, 30^{\circ} \)
\( ^{0} \)
B . \( 45^{\circ}, 45^{\circ} \)
\( \mathbf{c} \cdot 45^{0}, 30^{0} \)
D. \( 90^{0}, 90^{0} \)


An aqueous solution freezes at \( 272.4 K \)
while pure water freezes at \( 273.0 K \)
while pure water freezes at \( 273.0 K \) Determine
(a) the molality of the solution
(ii) boiling point of the solution
(iii) lowering of vapour pressure of water at \( 298 K \)
(Given, \( \boldsymbol{K}_{\boldsymbol{f}}=\mathbf{1 . 8 6 K} \boldsymbol{k g} \boldsymbol{m o l}^{-1}, \boldsymbol{K}_{\boldsymbol{b}}= \)
\( 0.512 K k g \) mol\( ^{-1} \) and vapour pressure
of water at \( 298 K=22.756) \)


Which out of the following belongs to \( 3 d \)
-series?
This question has multiple correct options
A . copper
B. cobalt
c. gold
D. silver


Give Reason:
A square can be thought of as a special rectangle.


In a galvanic cell electron flow will be
from:
A. negative electrode to positive electrode
B. positive electrode to negative electrode
C. there will be no flow of electrons
D. cathode to anode in the extenal circuit


How many arithmetic progressions with 10 terms are there, whose first term is
in the set \{1,2,3,4\} and whose
common difference is in the set
\{3,4,5,6,7\}\( ? \)


A radio transmitting station operating
at a frequency of 120 MHz has two
identical antennas that radiate in
phase. Antenna \( B \) is \( 9 m \) to the right of
antenna \( A . \) Consider point \( P \) at \( a \)
horizontal distance \( x \) to the right of
antenna \( A \) as shown figure. The value of
\( x \) and order for which the constructive
interference will occur at point \( \boldsymbol{P} \) are
This question has multiple correct options
\( \mathbf{A} \cdot x=14.95 m, n=1 \)
B \( . x=5.6 m, n=2 \)
\( \mathbf{c} \cdot x=1.65 m, n=3 \)
D. \( x=0, n=3.6 \)


An artificial satellite of mass \( m \) is
moving in circular orbit at a height equal to the radius \( R \) of the earth.
Suddenly due to internal explosion the satellite breaks into two parts of equal pieces. One part of the satellite stops just after the explosion. The increase in the mechanical energy of the system due to explosion will be (Given:
acceleration due to gravity on the surface of earth is \( g \) )
A. \( m g R \)
в. \( \frac{m g R}{2} \)
c. \( \frac{m g R}{4} \)
D. \( \frac{3 m g R}{4} \)


Copper- \( T \) is a device that prevents
A. Fertilisation
B. Implantation of blastocyst
c. Egg maturation
D. Ovulation
E. Both A and B


In figure, a particle has mass \( \boldsymbol{m}=\mathbf{5} \boldsymbol{g} \)
and charge \( \boldsymbol{q}^{\prime}=\mathbf{2} \times \mathbf{1 0}^{-\mathbf{9}} \boldsymbol{C} \) starts from
rest at point \( a \) and moves in a straight line to point \( b \). What is its speed \( v \) at point \( b ? \)
A \( .2 .65 \mathrm{cms}^{-1} \)
B. \( 3.65 \mathrm{cms}^{-1} \)
c. \( 4.65 \mathrm{cms}^{-1} \)
D. \( 5.65 \mathrm{cms}^{-1} \)


Which of the following is a metal?
A. Potassium
B. Sulphur
c. Argon
D. Diamond


Chromosome theory of sex determination was propounded by
A. Bridges
B. Balbiani
c. Goldschmidt
D. None of the above


The voltage and the current of an a.c circuit are \( V=100 \sin (100 t) \) volt and
\( \boldsymbol{i}=\mathbf{1 0 0} \sin (\mathbf{1 0 0} \boldsymbol{t}+\boldsymbol{\pi} / \mathbf{3}) \boldsymbol{m} \boldsymbol{A} \)
receptively. The power dissipated in the circuit is:
A \( \cdot 10^{4} W \)
в. \( 10 W \)
c. \( 2.5 W \)
D. \( 5.0 W \)


In the case of forward biasing of a p-n junction diode,which one of the
following figure correctly depicts the
direction of conventional current?
\( A \)
\( B \)
\( c \)
\( D \)


In case of theory of light nature of light
match the following:
List - I List - II
a) Light is a collection of
e) Newton's theory photons
b) Light is a form of
f) Huygen's theory electromagnetic wave
g) Maxwell's
c) Light is a wave
d) Light is a stream of
h) Max planck's corpuscles theory
\( \mathbf{A} \cdot \mathrm{a}-\mathrm{h} ; \mathrm{b}-\mathrm{g} ; \mathrm{c}-\mathrm{f} ; \mathrm{d}-\mathrm{e} \)
B. \( a-e ; b-f ; c-g ; d-h \)
C. \( a-g ; b-h ; c-g ; d-f \)
D. \( a-h ; b-g ; c-e ; d-f \)


Kelvin scale has
A. one fixed point
B. two fixed point
C. three fixed point
D. one fixed point and two variable points


\( \frac{-}{\infty} \)


Find the dipole moment of a system
where the potential \( 2.0 \times 10^{-5} V \) at a
point \( P, 0.1 m \) from the dipole is \( 3.0 \times \)
\( 10^{4} .\left(\operatorname{Use} \theta=30^{\circ}\right) \)
A . \( 2.57 \times 10^{-17} \mathrm{Cm} \)
B . \( 1.285 \times 10^{-15} \mathrm{Cm} \)
c. \( 1.285 \times 10^{-17} \mathrm{Cm} \)
D. \( 2.57 \times 10^{-15} \mathrm{Cm} \)


State True or False.
According to Charles' law,
A. True
B. False


Secondary growth in thickness with
distinct annual rings occur in plants growing in
A. Arctic regions
B. Tropical regions
c. Regions with seasonal changes
D. Any region


Assertion: A 1 m NaCl(aq) solution will
freeze at a temperature below \( 273 K \)
Reason: As a solute is added to a
Solvent, the boiling point increases
while the freezing point decreases.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
C. Assertion is true but Reason is false.
D. Assertion is false but Reason is true.
E. Both Asssertion and Reason are false


4 protons, 5 neutrons, and 4 electrons
are there in an atom of beryllium. Its
mass number is:
A . 10
B. 5
c. 8
D. 9


Total number of pencils required are \( \operatorname{given} \operatorname{by} 4 x^{4}+2 x^{3}-2 x^{2}+62 x-66 . \) If
each box contains \( x^{2}+2 x-3 \) pencils,
then find the number of boxes to be
purchased.


An insurance company insured 2000
scooter drivers, 4000 car drivers and
6000 truck drivers. The probability of an
accidents are 0.01,0.03 and 0.15 respectively. One of the insured person meets with an accident. What is the
probability that he is a scooter driver?


If \( f(x)=\left\{\begin{array}{cc}x^{2} \sin \frac{1}{x} & x \neq 0 \\ 0 & x=0\end{array} \) then R.H.D \right.
is
\( \mathbf{A} \cdot \mathbf{1} \)
B . -
\( c \)
D. None


Which one of the following forces is a
contact force?
A. Force of gravity
B. Force of friction
c. Magnetic force
D. Electrostatic force


Equation of trajectory of a projectile is
given by \( y=-x^{2}+10 x \) where \( x \) and \( y \)
are in meters and \( x \) is along horizontal
and y is vertically upward and particle is projected from origin. Then which of the following options is/are correct.
\( \left(g=10 m / s^{2}\right) \)
A. Initial velocity of particle is \( \sqrt{505} \mathrm{m} / \mathrm{s} \)
B. Horizontal range is \( 10 \mathrm{m} \)
c. Maximum height is 25 m
D. Angle of projection with horizontal is \( \tan ^{-1}(5) \)


If \( A \) and \( B \) are skew symmetric
matrices of same order then
A. \( A B \) is skew symmetric
B. \( A B+B A \) is symmetic
C. \( A B-B A \) is symmetric
D. none of these


Verify Rolle's theorem for the function
\( \boldsymbol{y}=\boldsymbol{x}^{2}+\mathbf{2} . \boldsymbol{x} \boldsymbol{\epsilon}|-\mathbf{2}, \mathbf{2}| \)


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}, \) if \( \boldsymbol{a} \boldsymbol{x}+\boldsymbol{b} \boldsymbol{y}^{2}=\cos \boldsymbol{y} \)


The primary succession in a sere is a
A. Sub sere
B. Meso sere
c. Pioneer sere
D. None of the above


An integer is chosen at random from the
first 200 positive integers. The probability that the integer chosen is divisible by 6 or 8 is
A \( \cdot \frac{1}{4} \)
B. \( \frac{2}{3} \)
c. \( \frac{1}{5} \)
\( D \)


Antioxidants are added to foods
containing fats/oil. Why?


Which of the following species has more number of protons than the number of electrons?
\( A \cdot F^{-} \)
в. \( N a^{+} \)
\( c \cdot O^{2} \)
D. Ne


If \( n \in N, \) then \( n^{3}+2 n \) is divisible by
\( A \cdot 2 \)
B. 3
c. 5
D. 6


The displacement of charge \( q \) in the electric field \( \overrightarrow{\boldsymbol{E}}=\boldsymbol{e}_{1} \hat{\boldsymbol{i}}+\boldsymbol{e}_{2} \hat{\boldsymbol{j}}+\boldsymbol{e}_{3} \hat{\boldsymbol{j}} \) is \( \overrightarrow{\boldsymbol{r}}= \)
\( a \hat{i}+b \hat{j} . \) The work done is
A \( \cdot Q\left(e_{1}+e_{2}\right) \sqrt{a^{2}+b^{2}} \)
в. \( Q(a+b) \sqrt{e_{1}^{2}+e_{2}^{2}} \)
c. \( Q\left(a e_{1}+b e_{2}\right) \)
D. \( Q \sqrt{\left(a e_{1}\right)^{2}+\left(b e_{2}\right)^{2}} \)


If
\( [x] \) denotes the greatest integer \( \leq x \)
then the system of linear equations \( [\sin \theta] x+[-\cos \theta] y=0[\cot \theta] x+y=0 \)
A \( \cdot \) Have infinitely many solutions if \( \theta \epsilon\left(\frac{\pi}{2}, \frac{2 \pi}{3}\right) \cup \) \( \left(\pi, \frac{7 \pi}{6}\right) \)
B. Have infinitely many solutions if \( \theta \epsilon\left(\frac{\pi}{2}, \frac{2 \pi}{3}\right) \) and has unique solution if \( \theta \epsilon\left(\pi, \frac{7 \pi}{6}\right) \)
c. Has a unique solution if \( \theta \epsilon\left(\frac{\pi}{2}, \frac{2 \pi}{3}\right) \) and have nfinitely many solutions if \( \theta \epsilon\left(\pi, \frac{7 \pi}{6}\right) \)
D. Has a unique solution if \( \theta \epsilon\left(\frac{\pi}{2}, \frac{2 \pi}{3}\right) \cup\left(\pi, \frac{7 \pi}{6}\right) \)


Acetaldehyde on treatment with aluminium ethoxide gives:
A. ethyl methanoate
B. ethyl acetate
c. ethyl propionate
D. ethyl formate


Find the particular solution of the differential equation \( (x-y) \frac{d y}{d x}=x+ \)
\( 2 y, \) given that when \( x=1, y=0 \)


If \( \sin ^{-1}\left(x-\frac{x^{2}}{2}+\frac{x^{3}}{4}-\dots \dots \infty\right)+ \)
\( \cos ^{-1}\left(x^{2}-\frac{x^{4}}{2}+\frac{x^{6}}{4}-\dots \dots\right)= \)
\( \frac{\pi}{2} \) and \( 0<x<\sqrt{2} \) then \( x= \)
\( A \cdot \frac{1}{2} \)
B.
\( c \cdot-\frac{1}{2} \)
D. -


Solve:det \( \left|\begin{array}{lll}\boldsymbol{x} & \boldsymbol{x}^{2} & \boldsymbol{y} \boldsymbol{z} \\ \boldsymbol{y} & \boldsymbol{y}^{2} & \boldsymbol{z} \boldsymbol{x} \\ \boldsymbol{z} & \boldsymbol{z}^{2} & \boldsymbol{x} \boldsymbol{y}\end{array}\right| \)


Work done in lifting a body is
calculated by
A. Mass of the body \( \times \) vertical distance moved
B. Force acting on a body \( \times \) vertical distance moved
C. Weight acting on the body \( \times \) vertical distance moved
D. None of the above


Why can aromatic primary amines not be prepared by Gabriel phthalimide synthesis?


Find the first term \( a_{1} \) and the common
difference \( d \) of the arithmetic
progression in which \( \boldsymbol{a}_{\mathbf{2}}+\boldsymbol{a}_{\mathbf{5}}-\boldsymbol{a}_{\mathbf{3}}= \)
\( \mathbf{1 0}, \boldsymbol{a}_{\mathbf{2}}+\boldsymbol{a}_{\mathbf{9}}=\mathbf{1 7} \)


A particle of mass is executing oscillations about the origin on the \( x \) axis. Its potential energy is \( V(x)= \)
\( k|x|^{3}, \) where \( k \) is a positive constant. If
the amplitude of oscillation is \( a \), then
its time period \( T \) is proportional
A . proportional to \( \frac{1}{\sqrt{a}} \)
B. proportional to \( \sqrt{a} \)
C . Independent \( a^{\frac{3}{2}} \)
D. None of these


If \( z+\frac{1}{z}=2 \cos 6^{0}, \) then \( z^{1000}+\frac{1}{z^{1000}}+1 \)
is equal to
A .
в.
\( c \cdot-1 \)
D.


The geometry and hybridisation of \( \boldsymbol{X} \boldsymbol{e} \)
in \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{4} \) is:
A . see-saw, \( s p^{3} d \)
B. octahedral, \( s p^{3} d^{2} \)
C. planar, \( s p^{3} d^{2} \)
D. T-shaped, \( s p^{3} d^{3} \)


Two small bodies of masses \( 10 \mathrm{kg} \) and \( 20 \mathrm{kg} \) are kept a distance \( 1.0 \mathrm{m} \) apart and released. Assuming that only mutual gravitational forces are acting, find the speeds of the particles when the separation decreases to \( 0.5 \mathrm{m} \)


When the equation: \( C_{2} H_{6}+O_{2} \rightarrow \)
\( \boldsymbol{C O}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \) is completely
balanced using the lowest whole number coefficients, the sum of
the coefficients will be :
A . 4
B. 9.
c. 19
D. 15.5
E. 1


100ml of \( 0.01 \mathrm{M} C H_{3} \) COOH reacts
with \( 40 \mathrm{ml}, 0.01 \mathrm{M} N a O H\left(K_{a}=10^{-5}\right) \)
Find \( p H \) when \( 1 \mathrm{ml} \) of \( 0.01 \mathrm{M} \) HCl is
added.


The sum of the digits of a two digit number is \( 7 . \) If the digits are reversed, the new number decreased by 2 , equals twice the original number. Find the
number.
A . 25
B . 28
c. 43
D. 32


The measure of an angle is three times the measure of its complement. The angles are:
A \( \cdot 20^{\circ}, 60^{\circ} \)
B. \( 30^{\circ}, 60^{\circ} \)
c. \( 45^{\circ}, 135^{\circ} \)
D . 22.5^, 67.5 \( ^{\circ} \)


The basic difference between mitosis
and meiosis is that
A. Homologous chromosomes form tetrads in mitosis but not in meiosis
B. Homologous chromosomes form tetrads in meiosis but not in mitosis
C. The nuclear membrane disappears in mitosis but not in meiosis
D. A spindle forms in mitosis but not in meiosis
E. A spindle forms in meiosis but not in mitosis


In \( I C l_{4}^{\ominus} \) the shape is square planar. The number of bond pair-lone pair repulsion
at \( 90^{\circ} \) are:
A. 6
B. 8
c. 12
D. 4


Sleeping movements commonly occur
in plants of family
A. Leguminosae
B. Liliaceae
c. Malvaceae
D. compositae


Unit vector perpendicular to the plane of the triangle \( A B C \) with position vectors of the vertices \( A, B, C, \) is (where \( \Delta \)
is the area of the triangle \( A B C \) ).
\( \frac{(\vec{a} \times \vec{b}+\vec{b} \times \vec{c}+\vec{c} \times \vec{a})}{\Delta} \)
B. \( \frac{(\vec{a} \times \vec{b}+\bar{b} \times \vec{c}+\vec{c} \times \vec{a})}{2 \Delta} \)
\( \overbrace{\frac{(\vec{a} \times \vec{b}+\vec{b} \times \vec{c}+\vec{c} \times \vec{a})}{3 \Delta}}^{\text {c. }} \)
\( \frac{(\vec{a} \times \vec{b}+\vec{b} \times \vec{c}+\vec{c} \times \vec{a})}{4 \Delta} \)


A spherical surface of radius of curvature R separates air (refractive index 1.0 ) from glass (refractive index
1.5). The center of curvature is in the
glass.A point object P placed in air is found to have a real image \( Q \) in the glass. The line PQ cuts the surface at a
point \( 0, \) and \( P O=O Q . \) The distance PO
is equal to:
\( A .5 R \)
в. зв
c. 2 R
D. 1.5R


Which of the following solutions is an example of negative deviation from
Raoult's law?
A. Acetone + Ethanol
B. Carbon tetrachloride + Chloroform
c. Acetone + chloroform
D. water + Ethanol


The dimensions of self- induction are :
\( \mathbf{A} \cdot\left[M L T^{-2}\right] \)
B . \( \left[M L^{2} T^{-1} A^{-2}\right. \)
\( \mathbf{c} \cdot\left[M L^{2} T^{-2} A^{-2}\right. \)
D・ \( \left[M L^{2} T^{-2} A^{2}\right] \)


If \( \boldsymbol{x}-\frac{\mathbf{1}}{\boldsymbol{x}}=\frac{\mathbf{1}}{\mathbf{2}}, \) then write the value of
\( 4 x^{2}+\frac{4}{x^{2}} \)


Verify \( f(x)=2 x^{3}+11 x^{2}-7 x-6 \) is
the factor of \( (x-1) \) using factor
theorem.


Two point masses \( m \) and \( 3 m \) are placed
at distance. The moment of inertia of the
system about an axis passing through the center of mass of system and perpendicular to the line joining the point masses is
A \( \cdot \frac{3}{5} m r^{2} \)
в. \( \frac{3}{4} m r^{2} \)
c. \( \frac{3}{2} m r^{2} \)
D. \( \frac{6}{7} m r^{2} \)


A transformer consists of a coil of 1200
turns and another coil, with a total of
120 turns, which can be tapped at various places. Primary voltage is \( 240 V . \) At which pair of terminals would
you connect to a \( 12 V, 24 W \) lamp for it
to be lit normally?
A. \( N_{s}=60 \)
is \( N_{s}=60 \)
В. \( N_{s}=40 \)
\( \mathbf{C} \cdot N_{s}=80 \)
D. \( N_{s}=50 \)


In YDSE, having slits of equal width, let
\( \beta \) be the fringe width and \( I_{0} \) be the
maximum intensity. At a distance \( x \) from the central bright fringe, the intensity will be
\( ^{\mathbf{A}} \cdot_{I_{0}} \cos \left(\frac{x}{\beta}\right) \)
B. \( _{I_{0} \cos ^{2}} \frac{2 \pi x}{\beta} \)
c. \( _{I_{0} \cos ^{2}} \frac{\pi x}{\beta} \)
D. \( \frac{I_{0}}{4} \cos ^{2} \frac{\pi x}{\beta} \)


Evaluate the following integral:
\( \int_{0}^{2}\left(x^{2}+x\right) d x \)


What will be the order of reaction for a
chemical change having \( \log t_{1 / 2} \) vs log
a? (where a = initial concentration of
reactant; \( t_{1 / 2}= \) half-life?
A. zero order
B. First order
c. second order
D. None of these


\( 10^{-6} M N a O H \) is diluted by 100 times The pH of diluted base is?
A. Between \( 6 \& 7 \)
B. Between 10 \& 11
c. Between \( 7 \& 8 \)
D. Between \( 5 \& 6 \)


If the angle between the vectors \( \vec{A} \) and \( \vec{B} \) is \( \theta, \) the value of the product \( (\vec{B} \times \)
\( \vec{A}) \cdot \vec{A} \) is equal to:
A. \( B A^{2} \cos \theta \)
B. \( B A^{2} \sin \theta \)
c. \( B A^{2} s \) in \( \theta \cos \theta \)
D.


A majority of farmers in India depend
upon for irrigating their crops.
\( A \cdot \) rains
B. oceans
c. both of the above
D. none of the above


Briefly describe rain water harvesting.


Organisms such as ........... can regenerate if they are broken into pieces.
A. Man
B. Lizard
c. Hydra
D. cockroach


When lime is added to water
it reacts vigorously to form slaked lime.


Rutherfords alpha particle scattering experiment was responsible for the
discovery
(a) Atomic nucleus(b) Electron (c)
Protone
(d) Neutron


Find the enthalpy of \( S-S \) bond from
the following data (only magnitude in nearest integer in \( \mathrm{kJ} / \mathrm{mol} \) ):
\( (i) C_{2} H_{5}-S-C_{2} H_{5}(g) \Delta H_{f}^{o}= \)
\( -147.2 k J / m o l \)
\( (i i) C_{2} H_{5}-S-S-C_{2} H_{5}(g) \)
\( \Delta \boldsymbol{H}_{f}^{o}=-\mathbf{2 0 1 . 9 k J / m o l} \)
\( (i i i) S(g) \Delta H_{f}^{o}=222.8 k J / m o l \)


The teeth present in humans are
A . Milk teeth
B. Permanent teeth
c. Deciduous teeth
D. All of the above


Draw a labelled diagram to show
\( (i) \)
reddish appearance of the sun at the
sunrise or the sunset


Two circular coils can be arranged in any of the three situations shown in the
figure. Their mutual inductance will be
A. maximum in situation (A)
B. maximum in situation (B)
c. maximum in situation (C)
D. the same in all situations


lonisation enthalpy \( \left(\Delta_{i} H_{1} k J m o l^{-1}\right) \)
for the elements of Group 13 follows the order:
A. \( B>A l>G a>I n>T l \)
в. \( B<A l>G a<I n>T l \)
c. \( B<A l>G a>I n>T l \)
D. \( B>A l<G a>I n<T l \)


What is the wavelength range of visible
light?
\( \mathbf{A} \cdot 4 \times 10^{-7} m \) to \( 8 \times 10^{-7} m \)
B . \( 4 \times 10^{-9} \mathrm{m} \) to \( 8 \times 10^{-9} \mathrm{m} \)
c. \( 4 \times 10^{-5} m \) to \( 8 \times 10^{-5} m \)
D. \( 4 \times 10^{-6} \mathrm{m} \) to \( 8 \times 10^{-6} \mathrm{m} \)


A body travels \( 200 \mathrm{cm} \) in the first two
seconds and \( 220 \mathrm{cm} \) in the next 4
seconds. The velocity at the end Of the
eleventh second is
A. 0
B. \( 10 \mathrm{cms}^{-1} \)
\( \mathbf{c} \cdot 82 c m s^{-1} \)
D. \( 100 \mathrm{cms}^{-1} \)


Given the marks scored by Rita's out of \( 100, \) in five subjects in a particular
test.
\( \begin{array}{ll}\text { Subject } & \text { Marks } \\ \text { English } & \text { 78 } \\ \text { Hindi } & \text { 72 } \\ \text { Maths } & \text { 96 } \\ \text { Science } & \text { 88 } \\ \text { s.st } & \text { 80 }\end{array} \) Can we draw the bar graph for above
data?
If yes enter 1 else 0


For the function \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}-\boldsymbol{6} \boldsymbol{x}^{2}+ \)
\( \boldsymbol{a} \boldsymbol{x}+\boldsymbol{b} . \) If Rolle's theorem holds in \( [\mathbf{1}, \boldsymbol{3}] \)
with \( c=2+\frac{1}{\sqrt{3}} \) then \( (a, b) \)
A \( \cdot(11,12) \)
B . (11,11)
c. \( (11, \text { any real value }) \)
D. (any real value, 0 )


In algae, the bacteriological filter is
A. oscillatoria
B. Batrachospermum
c. Nostoc
D. cosmarium


Among the following, the wrong statement in the case of semiconductor
is:
A. Resistivity is in between that of a conductor and insulator
B. Temperature coefficient of resistance is negative
c. Doping increases conductivity.
D. At absolute zero temperature, it behaves like a conductor


Divide the following and write your answer in lowest terms: \( \frac{x}{x+1} \div \) \( \frac{x^{2}}{x^{2}-1} \)
A \( \cdot \frac{x-1}{x} \)
в. \( \frac{x+1}{x} \)
c. \( \frac{x-1}{x^{2}} \)
D. None of these


Two matrices are equal if and only if they have the and
corresponding elements are
A. rows, equal
B. order, equal
C . columns, equal
D. order, unequal


In photosrespiration, glycine passes
from
A. Chloroplast to peroxisome
B. Chloroplast to mitochondrion
c. Peroxisome to mitochondrion
D. Mitochondrion to peroxisome


What is \( \angle D A E \) from the figure, if
\( B C=D E=5 \) and \( \angle B A C=45^{\circ} ? \)
A . \( 30^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 50^{\circ} \)
D. \( 60^{\circ} \)


The early transition metals on the left
hand side of the d-block generally occur
as oxides because
Silicates
A. they are above hydrogen in electrochemical series
B. they are more electropositive and thus form ionic compounds (in the form of oxides) by more electronegative oxygen by exchange of electrons
c. these oxides are soluble in water
D. these oxides remain insoluble in water


The potential at a point due to a charge of \( 5 \times 10^{-7} C \) located \( 10 c m \) away is
\( 4.5 \times 10^{4} V . \) The work done in bringing a
charge of \( 4 \times 10^{-9} C \) from infinity to
that point is:
A \( .2 .4 \times 10^{-4} J \)
В. \( 1.8 \times 10^{-4} \mathrm{J} \)
c. \( 3.2 \times 10^{-5} J \)
D. \( 4.1 \times 10^{-5} J \)


Pressure (P) exented by liquid on walls of the container when \( h= \) height of the liquid column, \( f= \) density, \( g \) is acceleration due to gravity
A. \( p=h f g \)
в. \( p=\frac{d f}{g} \)
c. \( _{p}=\frac{h g}{f} \)
D. \( p=\frac{d f}{h} \)


At \( 373 K, \) gaseous reaction \( A \rightarrow \)
\( 2 B+C \) is found to be first order.
Starting with pure \( A \), the total pressure at the end of 10 min. was 176 mm and
after a long time when \( A \) was
completely dissociated, it was 270 mm.
The pressure of \( A \) at the end of 10 minutes was:
A . \( 94 \mathrm{mm} \)
B. \( 47 \mathrm{mm} \)
c. 43 mm
D. \( 90 \mathrm{mm} \)


is engineered to protect an
elevated structure in the event of
lightning strike.
A. A lightning conductor
B. Copper wire
c. A lightening shield
D. All of the above


Maximum value of \( f(x)=\frac{x^{2}-x+1}{x^{2}+x+1} \)
is
A.
B. 3
\( c \cdot \frac{3}{7} \)
D.


The equivalent capacity between the
points 'A' and 'B' in the following figure
will be:
\( A \cdot 9 \mu F \)
в. \( 1 \mu F \)
c. \( 4.5 \mu F \)
D. \( 6 \mu F \)


For this reaction relate \( \Delta \boldsymbol{H} \) and \( \boldsymbol{\Delta} \boldsymbol{U} \)
\( \mathbf{2} N \boldsymbol{O}_{2}(\boldsymbol{g}) \quad \longrightarrow \boldsymbol{N}_{2} \boldsymbol{O}_{4}(\boldsymbol{g}) \)
A. \( \Delta H=\Delta U \)
в. \( \Delta H>\Delta U \)
\( \mathbf{c} \cdot \Delta H<\Delta U \)
D. None of these


For a solution of chloroform and
acetone, if \( \boldsymbol{p}_{\boldsymbol{x}}(\boldsymbol{a} \boldsymbol{c t u a l}) \) is compared
with \( p_{s}(\text { Raoult }), \) then which of the following is/are true? This question has multiple correct options
A \( \cdot p_{s}(a c t u a l)<p_{s}(\text { Raoult }) \)
B. \( \quad \begin{array}{c}L t \\ X_{\text {chootsm}} \rightarrow 0\end{array}\left(p_{\text {actone}}^{o}-p_{s}(\text {actual})\right)=0 \)
C. \( \operatorname{Lt}_{X_{\text {attoce }} \rightarrow 0}\left(p_{\text {chloroform }}^{o}-p_{s}(\text { actual })\right)=0 \)
D. \( p_{\text {actone}}^{o}>p_{\text {chloroform}}^{o} \) near room temperature


Subtract the following with the help of
numberline:
\( (-3)-6 \)


The products obtained when chlorine gas reacts with cold and dilute aqueous
NaOH are:
A \( \cdot C l O^{-} \) and \( C l O_{3}^{-} \)
в. \( C l O_{2}^{-} \) and \( C l O_{3}^{-} \)
c. \( C l^{-} \) and \( C l O^{-} \)
D. \( C l^{-} \) and \( C l O_{2}^{-} \)


Consider the following statements:
\( A: p-p, p-n, n-n \) forces between
nucleons are not equal and charge
dependent
B: In nuclear reactor the fission reaction
will be in accelerating state if the value
of neutron reproduction factor \( k>1 \)
A. Both A and B are correct
B. Both A and B are wrongg
C. A is wrong and B is correct
D. A is correct and B is wrong


f \( a, b, c \) are three consecutive terms of
A.P,Then \( \boldsymbol{b}= \)


Write minors and cofactors of the
elements of the following determinants:
\( (i)\left|\begin{array}{cc}2 & -4 \\ 0 & 3\end{array}\right| \)
\( (i i)\left|\begin{array}{ll}a & c \\ b & d\end{array}\right| \)
\( (i i i)\left|\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right| \)
\( (i v)\left|\begin{array}{ccc}1 & 0 & 4 \\ 3 & 5 & -1 \\ 0 & 1 & 2\end{array}\right| \)


The colour imparted by \( \operatorname{Co}(\boldsymbol{I} \boldsymbol{I}) \)
compounds to glass is
A. green
B. deep blue
c. yellow
D. red


Two spheres of masses \( m \) and \( M \) are
situated in air and the gravitational force between them is \( F \). The space
around the masses is now filled with a
liquid of specific gravity \( 3 . \) The gravitational force will now be
A \( .2 F \)
в. \( F \)
c. \( \frac{F}{3} \)
D. \( \frac{F}{9} \)


If \( \int_{0}^{k} \frac{\cos x}{1+\sin ^{2} x} d x=\frac{\pi}{4} \) then \( k=? \)
A .
в. \( \pi / 4 \)
c. \( \pi / 2 \)
D. \( \pi / 6 \)


Solve graphically:
\( 2 x-3 y=7 \) and \( 5 x+y=9 \)
A. \( x=2, y=-6 \)
в. \( x=8, y=-9 \)
c. \( x=0, y=-3 \)
D. \( x=2, y=-1 \)


For equilibrium of the system, value of
mass \( m \) should be
\( A \cdot 9 K g \)
B. \( 15 \mathrm{Kg} \)
c. \( 21 K g \)
D. 1 Ка


For which of the following orbital wave function does not change from positive to negative at any distance from
nucleus?
A . \( 1 s \)
в. \( 2 p \)
c. \( 2 s \)
D. \( 3 d \)


When a small amount of garden soil is put into a glass jar containing water, stirred and allowed to stand for two
hours, the layers from top to bottom
would be
A. Debris, water, sand and clay
B. Humus, water, clay and sand
c. Debris, clay, gravel and sand
D. Humus, clay, gravel and sand


A particle executes SHM of period 12 s. After two seconds, it passes through the centre of oscillation, the velocity is
found to be \( 3.142 \mathrm{cm} s^{-1} . \) The amplitude of oscillation is:
A. \( 6 \mathrm{cm} \)
в. 3 ст
\( \mathrm{c} \cdot 24 \mathrm{cm} \)
D. \( 12 \mathrm{cm} \)


Two persons appear for an interview.Probability of their selection \( \operatorname{are} \frac{1}{4} \) and \( \frac{1}{6} \) respectively. Find the probability that none of them gets selected.


All the voltage drops and the source
voltage added together in a series circuit is equal to
A. the total of the voltage drops
B. the source voltage
c. zero
D. the total of the source voltage and the voltage drops


An element R belongs to III A group.
Which is true with respect to R?
A. It is a gas at room temperature
B. It has an oxidation state of +4
C. It forms an oxide of the type \( R_{2} O_{3} \)
D. It forms a halide of the type \( R x_{2} \)


At the centre of which of the following four circular rings is the magnetic field strongest, for equal magnitude of
current?
A . 3
B.
\( c \cdot 4 \)
\( D \)


If \( \int_{0}^{1} \frac{\tan ^{-1} x}{x} d x \) is equal to
A \( \cdot \int_{0}^{\frac{\pi}{2}} \frac{\sin x}{x} d x \)
B \( \cdot \int_{0}^{\frac{\pi}{2}} \frac{x}{\sin x} d x \)
\( ^{\mathbf{C}} \cdot \frac{1}{2} \int_{0}^{\frac{\pi}{2}} \frac{\sin x}{x} d x \)
\( ^{\mathrm{D}} \cdot \frac{1}{2} \int_{0}^{\frac{\pi}{2}} \frac{x}{\sin x} d x \)


A wave is moving towards positive \( x \)
axis as shown in figure. Then the point(s) at which acceleration and velocity of particle are parallel to each
other
\( A \cdot A, D \)
B. В, C
\( \mathbf{c} \)
D. A.


It is known that some varieties of wheat
are sown in autumn but are harvested
around next mid summer.
(a) what could be the probable reason
for this.
(b) What term is used for this
promotion of flowering under low temperature?


Find the equilibrium constant for the reaction \( I n^{2+}+C u^{2+} \rightarrow I n^{3+}+C u^{+} \) at
298 K. Given, \( E^{o} \mathrm{Cu}^{2+} / \mathrm{Cu}^{+}= \)
\( 0.15 V, E_{I n^{3+} / I n^{+}}^{o}=-0.42 V E^{o}_{I n^{2+} / I n^{+}}= \)
\( -0.40 V \) is approximately:
A \( \cdot 10^{10} \)
B. \( 10^{11} \)
c. \( 10^{12} \)
D. \( 10^{14} \)


When a solid ball of volume \( V \) is
dropped into a viscous liquid, then a viscous force \( F \) acts on it. If another ball
of volume \( 2 V \) of the same material is
dropped in the same liquid then the viscous force experienced by it will be
\( \mathbf{A} \cdot 2 n F \)
в. \( \frac{n F}{2} \)
\( c .2 F \)
D. \( \frac{F}{2} \)


Convert part of the ratio of percentage:
2: 3: 5


Which among the following statements
is not correct for Graphite?
A. It is a non metal
B. It can be used as a lubricant
C. Each carbon atom is linked into a three- dimensional
network with four other carbon atoms with strong covalent bonds.
D. It has low melting point


How are vitamins classified? Name the
vitamin responsible for the coagulation of blood.


From below which is the type of energy
from sea?
A. Tidal Energy
B. Wave Energy
c. ocean Thermal Energy
D. All of above


Find real values of \( x \) and \( y \) if
\( \frac{x-1}{3+i}+\frac{y-1}{3-i}=i \)


Complete the following statement with an appropriate word/term to be filled in the blank space.

Froth floatation process is used for the
concentration of
A. Sulphide
B. Oxide
c. Carbonate
D. All the above


Assertion
Oxidation number of sulphur in \( \boldsymbol{H}_{2} \boldsymbol{S O}_{5} \)
is +6
Reason
It has one peroxy linkage.
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


\( \operatorname{Let} \cos ^{-1}(x)+\cos ^{-1}(2 x)+\cos ^{-1}(3 x) \)
be \( \pi \) If \( x \) satisfies the equation \( a x^{3}+ \) \( b x^{2}+c x-1=0, \) then the value of
\( (b-a-c) \) is


If the earth were to suddenly contract to \( \frac{1}{m} \) th of its present radius without any \( \boldsymbol{n} \)
change in its mass then the duration of the new day will be close to
\( ^{\mathrm{A}} \cdot \frac{24}{n} \) hour
B. \( 24 n \) hour
c. \( \frac{24}{n^{2}} \) hour
D. \( 24 n^{2} \) hour


What is the magnitude of the gravitational force between the earth and a \( 1 k g \) object on its surface? (Mass
of the earth is \( 6 \times 10^{24} k g \) and radius of
the earth is \( 6.4 \times 10^{6} \) m.)


If \( n \) is an integer and \( (1+i \sqrt{3})^{n}+(1-i \sqrt{3})^{n}=2^{n+1} \cos \theta \)
\( \operatorname{then} \theta= \)
A \( \cdot \frac{n \pi}{3} \)
в. \( \frac{n \pi}{2} \)
c. \( \frac{n \pi}{4} \)
D. \( \frac{n \pi}{6} \)


Solve:
A sphere of mass \( 10 \mathrm{kg} \) is attracted by another sphere of mass \( 150 \mathrm{kg} \), with a force equal to \( 1.28 \times 10^{-6} N, \) when their
centers are separated by a distance of \( 0.28 \mathrm{m} . \) Calculate the gravitational
constant.


Guard cells are found in
A. Stomata
B. Root tips
c. Ovary
D. Lenticels


State whether true or false.
A cone resting on its side is an example of a body in neutral equilibrium.
A. True
B. False


\( \int \frac{-\sin x}{5+\cos x} d x \)


A cyclist leans with the horizontal at an
angle of \( 30^{\circ}, \) while negotiating round a circular road of radius \( 20 \sqrt{3} \) meters.
Speed of the cycle should be:
A. \( 7 \sqrt{3} \mathrm{m} / \mathrm{s} \)
в. \( 14 \mathrm{m} / \mathrm{s} \)
\( \mathbf{c} \cdot 7 \sqrt{6} m / s \)
D. \( 14 \sqrt{3} \mathrm{m} / \mathrm{s} \)


Solve \( \int \frac{x}{\sqrt{x+4}} d x \)


A conductance cell was filled with 0.01
molar KCl. Its resistance was found to
be 150 ohm at \( 25^{\circ} \mathrm{C} \). The conductivity
was observed to be \( 0.00177 S c m^{-1} . \) The
cell was when washed and filled with
0.05 molar solution of NaCl whose
resistance was found to be 325 ohm.
Conductivity of NaCl solution is:
B. \( 9.168 \times 10^{-4} \mathrm{Scm}^{-1} \)
c. \( 8.169 \times 10^{-4} \mathrm{Scm}^{-1} \)
D. None of these


Let \( A \) be a \( 2 \times 2 \) matrix and \( B=A+ \)
\( A^{T} . \) Then show that \( B \) is a symmetric
matrix.


The load versus elongation graph for
four wires of the same materials shown
in the figure. The thinnest wire is
represented by the line:
A. oc
B. OD
\( c \cdot O A \)
D. OB


How many valence electrons are present
in element Q?


Transmission of heat by the movement of heated particles is called
A. Conduction
B. convection
c. Radiation
D. Regelation
E. Expansion


A substance is placed in a non uniform magnetic field. It experiences weak force towards the strong field. The substance is \( _{-}-_{-}-_{-}-_{-}-_{-} \) type.
A. Ferromagnetic
c. Paramagnetic
D. None of these


If the potential at each point on a conductor is same to each other, then
A. Electric lines of force may begin or end on the same conductor
B. No electric lines of force may begin or end on the same conductor
c. The electric field inside the conductor may be non-zero
D. None of the above


Kirchoff's first law, i.e., \( \sum i=0 \) at a junction, deals with the conservation of
A. charge
B. energy
c. momentum
D. angular momentum


At \( 27^{\circ} \mathrm{C}, \) the combustion of ethane
takes place according to the reaction
\[
\begin{array}{c}
C_{2} H_{6}(g)+\frac{7}{2} O_{2}(g) \rightarrow 2 C O_{2}(g)+ \\
3 H_{2} O(l)
\end{array}
\]
\( \Delta E-\Delta H \) for this reaction at \( 27^{\circ} \mathrm{C} \) will
be:
A \( .+1247.1 \mathrm{J} \)
B. - 1247.1
c. - 6235.5 J
D . +6235.5 J