What is the correct formula for
determining the voltage of an electrochemical cell?
A \( \cdot E_{\text {cell }}^{0}=E_{\text {cathode }}^{0}-E_{\text {anode }}^{0} \) added
C \( \cdot E_{\text {constant }}^{0}=E_{\text {cathode }}^{0}-E_{\text {ande }}^{0} \)
D. \( E_{\text {constant}}^{0}=E_{\text {cathode}}^{0}+E_{\text {anode}}^{0} \)
E . \( E_{c e l l}^{0}=-E_{\text {cathode }}^{0}+E_{\text {ande }}^{0} \)


A member of Lanthanide is:
This question has multiple correct options
A. Cesium
B. Lanthanum
C. Neoybium
D. Luticium


Which group element has greater tendency to form positive ions than elements of group IIA?
A . IA
B. IVA
\( c \cdot v B \)
D. None of these


When light enters a dispersive medium, light wave of different wavelength travels with different velocities.
A. Yes
B. No
c. Sometimes
D. When medium is a fibre


Show that the points (2,-1,3),(4,3,1) and (3,1,2) are collinear.


An isotope decays to \( 1 / 16^{\text {th }} \) of its mass in \( 1 h . \) What is the half-life period of the isotopes?
A . 15 min
B. 30 min
\( c .12 \) min
D. 10 min


\( \boldsymbol{A}=(\mathbf{0}, \mathbf{1}, \mathbf{2}), \boldsymbol{B}=(\mathbf{3}, \mathbf{0}, \mathbf{1}), \boldsymbol{C}= \)
\( (4,3,6), D=(2,3,2) \) are the
rectangular cartesian co-ordinates. Find the area of the triangle \( A B C \).
A. \( \sqrt{90} \)
B. \( \sqrt{\frac{45}{2}} \)
c. 45
D. 18


When dil. \( H_{2} S O_{4} \) is added to aqueous
solution of potassium chromate, yellow colour of solution turns to orange
colour. It indicates:
A. chromate ions are reduced
B. chromate ions are oxidized
c. mono-centric complex is converted into dicentricc complex
D. oxygen gets removed from chromate ions


As shown in the figure, light is incident normally on one face of the prism. A liquid of refractive index \( \$ \$ 1 \mathrm{my} \$ \$ \) is
placed on the horizontal face \( A C \). The
refractive index of prism is \( 3 / 2 \). If total
internal reflection taken place on face
\( A C, m \) should be less than \( \$ \$ \) ldfrac
Illsrat \( \{3\}\}\{4\} \$ \$, \) where \( I \) is an integer
Find the value of \( \boldsymbol{I} \)


Artificial kidney contains a number of tubes with a \( \ldots . . . . . . . . \) lining, suspended in the tank filled with dialysing fluid.
A. Permeable
B. Semi permeable
c. Impermeable
D. None of the above


The product formed in the reaction of
\( \boldsymbol{S O C l}_{2} \) with white phosphorus is?
A \( \cdot P C l_{3} \)
в. \( S o_{2} C l_{2} \)
c. \( S C l_{2} \)
D. \( P O C l_{3} \)


A constant torque acting on a uniform circular wheel changes its angular
momentum from \( A_{0} \) to \( 4 A_{0} \) in 4 sec. The
magnitude of this torque is:
\( \mathbf{A} \cdot 4 A_{0} \)
в. \( A_{0} \)
c. \( \frac{3}{4} A_{0} \)
D. \( 12 A_{0} \)


Pure water consists entirely of (ions /
molecules)


\( S_{1}, S_{2}, S_{3} \) are three concentric spherical
shells as shown in figure. \( S_{1} \) and \( S_{2} \) have
charge \( 4 Q \) and \( 8 Q \) respactively
Whereas \( S_{3} \) is unchanged. Find the
ratio of the flux passing through \( S_{1} \) to
that through \( S_{3} \)
A .1: 3
B . 1: 2
\( c \cdot 2: 1 \)
\( D \cdot 1: 6 \)


The price of an article was increased by \( P \% \). Later the new price was decreased
by \( P \% \). If the latest price was \( R S 1 \) then the original price was?
A. Rs.
B. \( R s \frac{1-p^{2}}{1000} \)
C . \( R s \frac{10.000}{10,000-p^{2}} \)
D. \( R s \sqrt{\frac{1-p^{2}}{100}} \)


Tow consecutive sides of a
parallelogram are \( 4 x+5 y=0 \) and
\( 7 x+2 y=0 . \) If the equation to one
diagonal is \( 11 x+7 y=9 \), then the
equation of the other diagonal is
A. \( x+y=0 \)
в. \( 2 x+y=0 \)
c. \( x-y=0 \)
D. None of these


\( \int_{0}^{1 / 2} e^{x}\left[\sin ^{-1} x+\frac{1}{\sqrt{1-x^{2}}}\right] d x= \)
\( ^{A} \cdot \frac{e^{4}}{4} \)
B. \( \frac{\pi \sqrt{6}}{6} \)
\( c \cdot \frac{\sqrt{\pi}}{_{1}} \)
D. \( \frac{\pi \sqrt{6}}{2} \)


If the function \( \boldsymbol{E}: \boldsymbol{R} \rightarrow \) defines by
\( f(x) \frac{3^{x}+3^{-x}}{2} \) than show that \( f(x+y)+ \)
\( \boldsymbol{f}(\boldsymbol{x}-\boldsymbol{y})=2 \boldsymbol{f}(\boldsymbol{x}) \boldsymbol{f}(\boldsymbol{y}) \)


Bond energies in \( N O, N O^{+} \) and \( N O^{-} \)
are such that:
A. \( N O>N O^{+}>N O^{-} \)
В. \( N O^{-}>N O>N O^{+} \)
c. \( N O^{+}>N O^{-}>N O \)
D. \( N O^{+}>N O>N O \)


Obtain an expression for the number of radioactive nuclei present at any
instant in terms of the decay constant
and initial number of nuclei


Which of the following is true about
rusting of iron?
A. The monetary loss due to rusting is huge.
B. For rusting, the presence of both oxygen and water (or water vapor) is essential
C. If the content of moisture in air is high, which means if it is more humid, rusting becomes faster
D. All of the above.


The potential difference between the terminals of an electric heater is \( 220 \mathrm{V} \)
and the current is 5A. What is the
resistance of the heater?
A . 22
B. 11
\( c \cdot 44 \)
D. 1100


On stretching a slinky, the regions
where the coils become closer are called
and the regions where coils are
further apart are called
A. rarefaction, compression
B. compression, rarefaction
c. compression, trough
D. rarefaction, trough


An equiconvex glass lens \( (i) \) has a focal
length \( f \) and power \( P . \) it is cut into symmetrical halves
\( (i i) \) by a plane containing the principle axis. The two pieces are recombined as shown in figure
\( (i i i) \) The power of new combination is:
(ii)
\( A \)
в. \( P / 2 \)
\( c .2 P \)
D. zero


Which of the following glucose transporters is insulin-dependent?
A . GLUTI
в. GLUTII
c. GLUT III
D. GLUTIV


A block of mass \( 1 \mathrm{kg} \) and a pan of equal mass are connected by a string going over a smooth light pulley. Initially the system is at rest when a particle of mass \( 1 \mathrm{kg} \) falls on the pan and stick to it. If the particle strike the pan with speed \( 6 m / s \) then the speed with which the system moves just after the collision is?
A. \( 3 m / s \)
в. \( 4 m / s \)
c. \( 2.5 m / s \)
D. \( 2 m / s \)


The position vector of a point \( \boldsymbol{P} \) such
that \( \overline{O P} \) is inclined to \( O X \) at \( 45^{\circ} \) and to
\( O Y \) at \( 60^{\circ} \) and \( O P=12 \) units, is
\( \mathbf{A} \cdot 6(\sqrt{2} \hat{i}+\hat{j} \pm \hat{k}) \)
B . \( 3(\sqrt{2} \hat{\imath}+\hat{j} \pm \hat{k}) \)
c. \( 2(\sqrt{2} \hat{i}+\hat{j} \pm \hat{k}) \)
D . \( 12(\sqrt{2} \hat{i}+\hat{j} \pm \hat{k}) \)


Synthetic polymer that resembles natural rubber is:
A. chloroprene
B. isoprene
c. neoprene
D. glyptal


Coal gas is mixture of:
\( \mathbf{A} \cdot C H_{4}+H_{2}+C O_{2}+H_{2} S \)
\( \mathbf{B} \cdot C H_{4}+H_{2}+C O+H_{2} S \)
\( \mathbf{c} \cdot C H_{4}+H_{2}+C O \)
D. ethane, propane, butane


The list gives four experiments carried out with calcium carbonate.
1 acid added
2 alkali added
3 heated strongly
4 water added
Which experiments produce carbon dioxide?
A. 1 and 2
B. 1 and 3
\( c \cdot 2 \) and 3
D. 2 and 4


Which of the following molecules has two sigma \( (\sigma) \) and two pi \( (\pi) \) bonds?
A. \( C_{2} H_{4} \)
в. \( N_{2} F_{2} \)
c. \( C_{2} H_{2} C l_{2} \)
D. \( H C N \)


In a monthly test. Sumit scored 97 out out of 100 in mathematics, 69 out
of 75 in science, out of 150 in hindi
and 42 out of 50 in English.
1) In which subject was his performance the best?
2) In which subject did he perform the
worst?
3) What was his aggregate percentage?


Assertion: \( N a C l(a q) \) is an electrolyte. Reason: It forms ions in solution.
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 Assertion and Reason are false


For a body of \( 50 \mathrm{kg} \) mass, the velocity
time graph is shown in figure. Then
force acting on the body is :-
\( A \cdot 25 N \)
B. 50N
c. \( 12.5 \mathrm{N} \)
D. 100N


In the figure, the chord BD is
perpendicular to the diameter AC. Find
the measures of the following angles.
a. \( \angle B A C \)
b. \( \angle B C D \)
c. \( \angle \boldsymbol{A} \boldsymbol{D} \boldsymbol{C} \)
\( \mathrm{d} . \angle C D M \)
e. \( \angle B A P \)


Select the correct statement.
A. Heterotrophs do not synthesize their own food.
B. Heterotrophs utilize solar energy for photosynthesis.
C. Heterotrophs synthesize their own food.
D. Heterotrophs are capable of converting carbon dioxide and water into carbohydrates.


The diameter of a sphere is decreased
by \( 25 \% . \) By what percent does its curved
surface area decrease?
A . \( 53.85 \% \)
B. \( 34.85 \% \)
c. \( 45.65 \% \)
D. \( 43.75 \% \)


The tallest inflorescence is shown by
which of the following angiosperm?
A. Wolffia microscopica
B. Amorphophallus
c. Puya raimondii
D. Rafflesia


Evaluate \( : \int_{0}^{1} \frac{2 x+3}{5 x^{2}+1} d x \)


\( 33.6 \mathrm{L} \) of water vapour at STP are condensed to liquid state. The volume occupied by it is approximately:
A . \( 1 \mathrm{mL} \)
B. 18 mL
c. 27 \( \mathrm{mL} \)
D. 127 mL


Soil rich in Fe and Al due to excessice
leaching is
A. Alluvial
B. Laterite
c. Loam
D. Both A and B


The maximum value of \( \left|\begin{array}{ccc}1+\sin ^{2} x & \cos ^{2} x & 4 \cos 2 x \\ \sin ^{2} x & 1+\cos ^{2} x & 4 \sin 2 x \\ \sin ^{2} x & \cos ^{2} x & 1+4 \sin 2 x\end{array}\right| \)
\( A \)
B.
\( c .5 \)
\( D \)


A ball of mass \( 400 \mathrm{gm} \) is dropped from a height of \( 5 \mathrm{m} \). A boy on the ground hits the ball vertically upwards with a bat with an average force of \( 100 \mathrm{N} \) so that it attains a vertical height of \( 20 \mathrm{m} . \) The time for which the ball remains in
contact with the bat is:
\( \left[\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right] \)
A. \( 0.12 s \)
B. \( 0.08 s \)
c. \( 0.04 s \)
D. 12


Phloem always flows from a
A. Sugar source to sugar sink
B. Sugar sink to sugar source
C. Leaf to the xylem to the phloem
D. Leaf to a root


The point \( P(a, b) \) is such that \( b- \) \( 25 a=4 \) and the arithmetic mean of \( a \)
an \( b \) is \( 28 . Q(x, y) \) is the point such that
\( x \) and \( y \) are two geometric means between \( a \) and \( b \) if \( O \) is the origin then
\( O P^{2}+O Q^{2} \) is equal to


Mature virus particle is
A. Virion
B. Virucide
c. capsid
D. Peptomere


There are \( 8.4 \times 10^{22} \) free electrons per
\( c m^{3} \) in copper, the current in the wire is
\( \mathbf{0 . 2 1} \boldsymbol{A}\left(\boldsymbol{e}=\mathbf{1 . 6} \times \mathbf{1 0}^{-\mathbf{1 9}} \boldsymbol{C}\right) . \) Then the
drifts velocity of electrons in a copper
wire of \( 1 \mathrm{mm}^{2} \) cross section will be:
A \( .2 .12 \times 10^{-5} \mathrm{m} / \mathrm{s} \)
B . \( 0.78 \times 10^{-5} \mathrm{m} / \mathrm{s} \)
c. \( 1.56 \times 10^{-5} \mathrm{m} / \mathrm{s} \)
D. none of these


Which of the following graph represent
the motion of a particle starting from
rest:
\( A \)
B.
\( c \)
D. All of the above


Starter is used in
A. high power electric motors
B. low power electric motors
C. transformers
D. galvanometer


Why the innermost zone of candle flame
is the least hot?
A. Unburnt wax vapour
B. No supply of oxygen
c. Presence of wick
D. All the above


Which of the following equations does not represent a simple harmonic motion
A. \( y-\alpha \omega t \)
B. \( y=\alpha \omega t \)
c. \( y=\alpha \omega t+b c o s \omega t \)
D. \( y=\alpha \) tanct


What is meant by lanthanoid contraction? The actinoid contraction is
grater than that of lanthanoid
contraction. Why?


Find the domain of:
\( \sec ^{-1} x-\tan ^{-1} x \)


For a 1 st order reaction of the form,
\( A \stackrel{k}{\longrightarrow} B, \) the correct representations
are:
\( \mathbf{I} \)
III
\( \mathbf{A} \cdot I \) and \( I I \)
B. III and \( I V \)
c. \( I \) and \( I V \)
D. II and III


Bulk of the tooth in mammals is made
up of
A. Dentine
B. Enamel
c. Pulp cavity
D. Root


Find the values of \( x \) and \( y \) in the figures
given below


If an electron is moving with velocity
\( 500 m s^{-1}, \) which is accurate up to
\( 0.005 \% \) then calculate uncertainty in its
position. \( \left[\boldsymbol{h}=\mathbf{6 . 6 3} \times \mathbf{1 0}^{-\mathbf{3 4}} \boldsymbol{J}-\right. \)
\( s, \) mass of electron \( =9.1 \times \)
\( \left.\mathbf{1 0}^{-\mathbf{3 1}} \quad \boldsymbol{K} \boldsymbol{g}\right] \)


When a woman with long hair puts her hands on a Van de Graaff Generator
large conducting sphere with a conveyor belt delivering charge to it) her hair stands on end. Which of the
following best explains this phenomenon?
A. Like charges attract
B. Like charges repel
c. Her hair will not stand on end
D. Her body is conducting a current to the ground
E. The Van de Graff generator makes a magnetic field that draws her hair up on end


Find the value of the principal argument of the complex number \( z=\frac{(1+i \sqrt{3})^{2}}{(1-i)^{3}} \)


A source of electrons or neutrons can be
located at \( S \). The beam is defined by
slits \( S_{1} \) and \( S_{2} . \) The particles pass
through two plates \( P_{1} \) and \( P_{2} \) such that
the first plate is at zero potential and
the second plate can be given any high potential. For using matter waves in a microscope of high resolution which of
the following combination must be chosen?
A. Electron beam with high accelerating potential
B. Electron beam with low accelerating potential
c. Neutron beam with high accelerating potential
D. Neutron beam with low accelerating potential


\( \sin ^{-1} \frac{3}{5}+\sin ^{-1} \frac{4}{5} \) is equal to
A \( \cdot \frac{\pi}{2} \)
в.
\( c \cdot \frac{\pi}{4} \)
D.


Which one of the following has a larger wave number?
A . Red
B. Blue
c. Green
D. Violet


In the magnetic meridian of a certain
place the horizontal component of earth's magnetic field is \( 0.25 \mathrm{G} \) and dip
angle is \( 60^{\circ} . \) The magnetic field of the earth at this location is?
A. 0.50 G
B. 0.52 G
c. 0.54 G
D. 0.56 G


Which of the following statements
is/are wrong?
A. The gas displaced in Victor Meyer's method is air
B. The simplest formula that shows the ratio of the atoms of various elements present in the molecule is called the empirical formula
C. Estimation of oxygen in an organic compound is also made by Aluise's method
D. An organic monoacidic base B on reaction with \( H_{2} P t C l_{6} \) forms an insoluble compound \( B_{2} H_{2} P t C l_{6} \)


Explain the following terms:
Electrophoresis


Two tailors, \( A \) and \( B \), earn Rs. 300 and
Rs. 400 per day, respectively. \( A \) can
stitch 6 shirts and 4 pairs of trousers while \( B \) can stitch 10 shirts and 4 pairs
of trousers per day. To find how many days should each of them work and if it
is desired to produce at least 60 shirts
and 32 pairs of trousers at a minimum
labour cost, formulate this as an LPP
and find the number of days \( A \) and \( B \) worked.


Find \( a_{n} \) in an \( A P \) if \( a=1, d=1, n=3 \)


Using differentials, find the
approximate value of the following:
\( \sqrt{37} \)


There are three sources of sound of
equal intensities and frequencies 400,401 and 402 vibrations per
second.The number of beats/sec is
A.
B.
\( c \cdot 3 \)
\( D \cdot 2 \)


The distance of point \( X(1,1) \) from
origin 0 is
A \( \cdot \sqrt{2} \)
B. \( 2 \sqrt{1} \)
c. \( 1 \sqrt{1} \)
D. None


Which of the following shows maximum number of isomers?
\( \mathbf{A} \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{4} C l_{2}\right] \)
B . \( \left[N i(e n)\left(N H_{3}\right)_{4}\right]^{2+} \)
c. \( \left[N i\left(C_{2} O_{4}\right)(e n)_{2}\right]^{2} \)
D. \( \left[C r(S C N)_{2}\left(N H_{3}\right)_{4}\right]^{+} \)


During unfavourable conditions
Chlamydomonas forms a colonial aggregate called
A. Palmitate stage
B. Palmella stage
c. Endospore stage
D. cyst stage


Solve the following equation:
\( \cos x=\frac{1}{2} \)


The stability of dihalides of \( \boldsymbol{S} \boldsymbol{i}, \boldsymbol{G} \boldsymbol{e}, \boldsymbol{S} \boldsymbol{n} \)
and \( P b \) increases steadily in the
sequence?
A \( \cdot P b X_{2}<<\operatorname{Sn} X_{2}<<\operatorname{Ge} X_{2}<<\operatorname{Si} X_{2} \)
в. \( G e X_{2}<<\operatorname{Si} X_{2}<<\operatorname{SnX}_{2}<<P b X_{2} \)
c. \( S i X_{2}<<G e X_{2}<<P b X_{2}<<S n X_{2} \)
D. \( S i X_{2}<<G e X_{2}<<S n X_{2}<<P b X_{2} \)


Smallest ionic radius is:
A \( \cdot L a^{3} \)
B. \( U^{3+} \)
\( \mathrm{c} \cdot Y b^{3} \)
D. \( C f^{3+} \)


The voltage required to balance an oil drop carrying 10 electrons between the plates of a capacitor which are \( 10 \mathrm{mm} \) apart, is (Given mass of the oil drop= \( \left.\mathbf{3} \cdot \mathbf{2} \times \mathbf{1 0}^{-\mathbf{1 5}} \mathbf{k g}, \boldsymbol{e}=\mathbf{1 . 6} \times \mathbf{1 0}^{-\mathbf{1 9}} \mathbf{C}\right) \)
A . \( 16 v \)
B. 160 V
c. \( 196 v \)
D. \( 19.6 v \)


Solve: \( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}} \mathbf{7} \boldsymbol{x} \)


Superphosphate of lime is a mixture
of :
A. primary calcium phosphate and epsom salt
B. primary magnesium phosphate and epsom salt
C . primary calcium phosphate
D. primary calcium phosphate and gypsum


represents the position-time graph for a
spring-mass system oscillating with simple harmonic motion. The colored, dashed graphs represent shapes of possible velocity time graphs
for the same motion.

The vertical axis stands for position or
velocity, but the scaling does not matter. The time axis is the same for all
graphs.
Which colored graph best represents
the possible velocity for the mass in
this spring-mass system?
A. Red
B. Blue
c. Green
D. The velocity graph is the same as the position graph
E. All three colored graphs are equally possible


A block of mass \( 15 \mathrm{kg} \) is placed on a long trolley The coefficient of friction between the block and trolley is 0.18
The trolley accelerates rest with \( 0.5 \mathrm{m} / \)
\( s^{2} \) for 20 s then what is the friction force
A. 3.5 N
B. 133.3 N
\( c \cdot 7.5 \mathrm{N} \)
D. N.O.T


\( \boldsymbol{V}-\boldsymbol{I} \) graph for two wires \( \boldsymbol{A} \) and \( \boldsymbol{B} \) are
shown in the figure. If the both wires are of same length and same thickness,
which of the two is made of a material
of high resistivity? Given justification
for your answer.


\( N H_{3} \) can be liquefied but \( P H_{3} \) is in
gaseous state.


Which person had convinced people on the fact that matter could be divided
forever?
A. Dalton
B. Democritus
c. Thomson
D. Aristotle
E. Rutherford


One way of preventing pollution of the air is by passing exhaust gases through a filter. Glass fibre or silicone-treated
bags of textile material are used for
filtering.
A. Hot gases
B. High pressure gases
c. cold gases
D. Reactive gases


ff \( z_{1}=1+i=\sqrt{3}+i, \) then the principle \( \arg \left(\frac{z_{1}}{z_{2}}\right) \)


A body is thrown up in a lift with a velocity u relative to the lift and the time of flight is t. Show that the lift is moving up with an acceleration \( \frac{2 u-t g}{t} \)


Two plane mirrors, each of length \( 10 c m \) are placed perpendicular to each other. How many images of an object, placed between the mirrors, are formed?
\( A \cdot 3 \)
B. 2
c. Infinite
\( D \)


If \( a+b+c=12 \) and \( a^{2}+b^{2}+c^{2}= \)
\( \mathbf{5 0} ; \) find
\( \boldsymbol{a} \boldsymbol{b}+\boldsymbol{b} \boldsymbol{c}+\boldsymbol{c} \boldsymbol{a} \)
\( \mathbf{A} \cdot 47 \)
B. 55
\( c \cdot 72 \)
D. 32


\( K M n O_{4} \) spot can be bleached by:
A. \( H_{2} O_{2} / H^{+} \)
в. \( S O_{2} / H^{+} \)
\( \mathrm{c} \cdot \mathrm{C}_{2} \mathrm{O}_{4}^{2-} / \mathrm{H}^{+} \)
D. all of these


When there is an electric current
through a conducting wire along its length then an electric field must exist
A. inside the wire but normal to it
B. inside the wire but parallel to it it
c. outside the wire but normal to it
D. outside the wire but parallel to it


Mark the correct options:
A. The total charge of the universe is constant.
B. The total positive charge of the universe is constant.
C. The total negative charge of the universe is constant.
D. The total number of charged particles in the universe is constant.


Factorise \( \boldsymbol{x}^{2}+\boldsymbol{x}-\mathbf{2} \)


Which of the following minerals does not contain Al?
A. Mica
B. cryolite
c. Felspar
D. Flourospar


The value of \( \cos ^{4}\left(\frac{\pi}{4}\right)-\cos ^{4}\left(\frac{\pi}{6}\right)+ \)
\( \sin ^{4}\left(\frac{\pi}{6}\right)+\sin ^{4}\left(\frac{\pi}{3}\right) \) is
A \( \cdot \frac{1}{16} \)
в. \( \frac{1}{8} \)
c. \( \frac{5}{16} \)
D. \( \frac{3}{16} \)


Hydrogen resembles alkali metals
because:
A. hydrogen has the same mass as alkali metals
B. hydrogen has the same size as that of alkali metals
C. hydrogen has only one electron in its outermost shell
D. none of the above


An open vessel at \( 27^{\circ} C \) is heated until
the three-fourths mass of the air in it
has been expelled. Neglecting the expansion of the vessel, find the temperature to which the vessel has been heated.
A \( \cdot T_{2}=723^{\circ} \mathrm{C} \)
В . \( T_{2}=958^{\circ} \mathrm{C} \)
c. \( T_{2}=927^{\circ} \mathrm{C} \)
D. None of these


What does taxonomic hierarchy refer
to?
A. Step-wise arrangement and naming of the organisms
B. Classification of a species based on fossil record
C. Naming the organisms based on their morphology
D. Sequential arrangement of all categories for classification of organisms


State True or False.
The set represented by the
shaded portion of the following Venn-
diagram is: \( (B-A)^{\prime} \)
A. True
B. False


The IUPAC name of the given structure
is :
\( \mathbf{A} \cdot \) bicyclo [5,2,0] nonane
B. biphenyl
C. cyclopropylcylohexane
D. spiro[2,5]octane


A thin wire of length \( L \) and uniform
linear mass density \( \rho \) is bent into a
circular loop with centre at \( \boldsymbol{O} \) as shown
in figure. Calculate the moment of in
inertia of the loop about the axis \( X X \)


Which hormone causes dilation of blood
vessels, increased oxygen consumption and gluconeogenesis?
A. Adrenaline
B. Glucagon
c. АСТН
D. Insulin


Assertion
The primitive atmosphere was reducing
one i.e., without oxygen.
Reason
In the primitive atmosphere, oxygen
was involved in forming ozone layer.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Both Assertion and Reason are incorrect.


A cylindrical bar magnet is kept along the axis of a circular coil. If the magnet is rotated about its axis, then -
A. a current will be induced in the coil
B. no current will be induced in the coil
c. only emf will be induced in the coil
D. an emf and current both will be induced in the coil


Distinguish between:
Convex mirror and concave mirror


Duramen'is
A. Sapwood
B. Heartwood
C. Bark
D. Periderm


Show that: \( \left|\begin{array}{ccc}\mathbf{1} & -\mathbf{2} \boldsymbol{i} & \mathbf{- 1} \\ \mathbf{3} \boldsymbol{i} & \boldsymbol{i}^{\mathbf{3}} & -\mathbf{2} \\ \mathbf{1} & \mathbf{- 3} & -\boldsymbol{i}\end{array}\right|=-\mathbf{7}+ \)
\( \mathbf{1 8 i}, \) where \( \boldsymbol{i}=\sqrt{-\mathbf{1}} \)


Write the equation of reaction of chlrobenzene:
Nitration


When the object is at focus of a concave mirror, the image is formed at
A. focus
B. centre of curvature
c. within focus
D. infinity


Which of the following is incorrectly
matched?
A. Explant - Excised plant part used for callus formation
B. Cytokins - Root initiation in callus
c. somatic embryo - Embryo produced from a vegetative cell
D. Anther culture - haploid plants
E. Callus - Undifferentiated mass of cells


Which of the following forms cationic micelles above certain concentration?
A. Sodium acetate
B. Urea
c. cetyl trimethylammonium chloride
D. Sodium dodecyl sulphonate


An open topped freight car of mass \( \mathbf{1 0}, \mathbf{0 0 0} \boldsymbol{k g} \) is coasting without friction along a level track in heavy rains, falling vertically downwards. Initially the car is empty and is moving with a velocity of \( 0.88 m / s . \) What is the velocity of the car after it has collected 1000 kg of water?


1-Butene and 2-Butene exhibits
isomerism.
A. position
B. metamerism
c. constitutional
D. functional group


The transition metal present in the alloy gun metal is \( \mathrm{Cu} \)


Evaluate:
\( \lim _{x \rightarrow 0} \tan ^{-1} \frac{a}{x^{2}}, \) where \( a \in \mathbb{R} \)


Assertion
Claviceps produces lysergic acid.
Reason
It is carcinogenic.
A. If both the assertion and the reason are true and the
reason
is a correct explanation of the assertion
B. If both the assertion and reason are true but the
reason is
not a correct explanation of the assertion
C. If the assertion is true but the reason is false
D. If both the assertion and reason are false


A ball is dropped on the ground from the height of \( 1 m . \) The coefficient of restitution is \( 0.6 . \) The height to which the ball will rebound is (in \( m) \)
A . 0.6
B. 0.4
\( c .0 .36 \)
D. 0.16


Which of the following metal is not manufactured by electrolysis?
A . Na a
в. Мв
\( c \cdot A \)
D. Fe


Assertion
From the relation \( Y=\frac{F l}{A \Delta l}, \) we can say
that, if length of a wire is doubled, its
Young's modulus of elasticity will also
becomes two times.
Reason
Modulus of elasticity is a material
property.
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


Explain energy changes in a chemical change.


If \( \boldsymbol{A}=\{\boldsymbol{x}: \boldsymbol{x} \in \boldsymbol{N}, \boldsymbol{x}<\mathbf{6}\} \) and \( \boldsymbol{B}= \)
\( \{x: x \in N, 3<x<8\}, \) then show that
\( A-B \neq B-A \) with the help of Venn
diagram.


NaCN is sometimes added in the froth
flotation process as a depressant when ZnS and Pbs minerals are expected because
A. \( P b(C N)_{2} \) is precipitated while no effect on ZnS.
B. znS forms soluble complex \( N a_{2}\left[Z n(C N)_{4}\right] \) while PbS forms froth
C . PbS forms soluble complex \( N a_{2}\left[P b(C N)_{4}\right] \) while zns forms froth
D. NaCN is never added in froth flotation process


A compound microscope consists of an objective of focal length \( 2 \mathrm{cm} \) and an eye piece of focal length \( 5 \mathrm{cm} \). When an object is kept \( 2.4 \mathrm{cm} \) from the objective, final image formed is virtual and \( 25 \mathrm{cm} \) from the eye piece. Determine magnifying power of this compound microscope in this set up i.e., in normal
use.


A step down transformer changes the
high input voltage used in our houses \( (120 V) \) into the low voltage used to charge an electric razor \( (24 V) . \) What must be the ratio of the turns of wire
from the primary side of the transformer to the secondary side?
A . 1: 5
в. 2: 7
\( c \cdot 1: 8 \)
D. 2: 9
E .1: 10


A solid cylinder \( C \) and a hollow pipe \( P \) of same diameter are in contact when they
are released from rest as shown in the
figure on a long incline plane. Cylinder \( C \) and pipe \( P \) roll without slipping. Determine the clear gap (in \( \mathrm{m} \) ) between them after \( 2 \sqrt{3} \) seconds.


Which one of the following pairs of
solution is not an acidic buffer?
A. \( H_{2} C O_{3} \) and \( N a_{2} C O_{3} \)
B. \( H_{3} P O_{4} \) and \( N a_{3} P O_{4} \)
c. \( H C l O_{4} \) and \( N a C l O_{4} \)
D. \( C H_{2} \) COOH and \( C H_{3} \) COONa


Ethylenediamine is an example of ligand.


A physical adsorption at low
temperature may pass into chemisorption as:
A. Temprarure decrease
B. Temperature increase
c. After some time at same temperature
D. physical adsorption never change into chemisorption


A uniform string of length \( l \) is fixed at both ends such that tension \( T \) is
produced in it. The string is excited to vibrate with maximum displacement
amplitude \( a_{o} . \) The maximum kinetic
energy of the string for its fundamental tone is given as \( \frac{a_{o}^{2} \pi^{2} T}{x l} . \) Find \( x \)


If \( \boldsymbol{T}_{\boldsymbol{n}}=\boldsymbol{6} \boldsymbol{n}+\mathbf{5}, \) find \( \boldsymbol{S}_{\boldsymbol{n}} \)


Find out whether the sequence
\( 1^{2}, 3^{2}, 5^{2}, 7^{2}, \dots \) is an AP. If it is, find out
the common difference.
\( A \cdot \) No
B. Yes, \( d=8 \)
\( \mathbf{c} . \) Yes, \( d=-8 \)
D. Yes, \( d=9 \)


What is the Primary and Secondary
Valence of \( \boldsymbol{P t} \boldsymbol{C l}_{2} \cdot \boldsymbol{2} \boldsymbol{N} \boldsymbol{H}_{3} ? \)


s-character in hybrid orbitals of \( \boldsymbol{C} \boldsymbol{H}_{4} \)
and \( B e C l_{2} \) are respectively:
A. 0.75,0.5
B. 0.25, 0.5
c. 0.75,0.334
D. 0.25, 0.33


In the tetrahedron \( \boldsymbol{A B C D}, \boldsymbol{A}= \)
(1,2,-3) and \( G(-3,4,5) \) is the
centroid of the tetrahedron. If \( P \) is the
centroid of the \( \Delta B C D, \) then \( A P= \)
A \( \cdot \frac{8 \sqrt{21}}{3} \)
B. \( \frac{4 \sqrt{21}}{3} \)
c. \( 4 \sqrt{21} \)
D. \( \frac{\sqrt{21}}{3} \)


Bohr's model explains:
A. the spectrum of hydrogen atom only
B. the spectrum of any atom or ion having one electron only
C. the spectrum of hydrogen molecule
D. the solar spectrum


Solve \( \frac{x}{5}=12 \) for the value of \( x \)


The potential difference across a \( 150 m H \) inductor as a function of time
is shown in figure. Assume that the initial value of the current in the
inductor is zero. What is the current
when \( t=4.0 m s ? \)
A \( \cdot 2.67 \times 10^{-4} \mathrm{A} \)
B \( \cdot 3.67 \times 10^{-2} \mathrm{A} \)
\( c \cdot 6.67 \times 10^{-2} \mathrm{A} \)
D. \( 9.67 \times 10^{-4} \mathrm{A} \)


\( F e C l_{3} \) on reaction with \( K_{4}\left[F e(C N)_{6}\right] \) in aqueous solution gives blue colour
These are separated by a
semipermeable membrane AB as
shown. Due to osmosis, there is:
A. Blue color formation in side \( x \)
B. Blue color formation in side Y.
c. Blue colour formation in both of the sides \( x \) and
D. No blue colour formation


A bottle of perfume is opened in the
room opposite to you and within minutes you begin to smell the perfume. This phenomenon is a classic example of
A. Dialysis
B. Osmosis
c. Active transport
D. Diffusion


Based on the structure shown, what is the empirical formula for this
compound?
A. \( C H O \)
в. \( C_{2} H_{3} O_{3} \)
\( \mathbf{c} \cdot C_{2} H_{3} O_{4} \)
D \( \cdot C_{3} H_{6} O_{6} \)
E \( . C_{4} H_{6} O_{6} \)


In the complex \( C o C l_{3} \cdot 5 N H_{3}, \) one \( C l^{-} \)
ion satisfies primary and secondary valencies of cobalt(III).
A . True
B. False


In which of the following arrangements, the sequence is not strictly according to the property written against it?
A \( \cdot \mathrm{CO}_{2}>\mathrm{SiO}_{2}<\mathrm{SnO}_{2}<\mathrm{PbO}_{2}: \) increasing oxidizing
power
B. HF < HCl < HBr < HI: increasing acid strength
C. \( \mathrm{NH}_{3}<\mathrm{PH}_{3}<\mathrm{A} s \mathrm{H}_{3}<\mathrm{SbH}_{3} \) : increasing basic
strength
D. \( \mathrm{B}<\mathrm{C}<\mathrm{O}<\mathrm{N}: \) increasing first ionization enthalpy


Which of the following set of quantum number represents highest energy of an atom?
\( A \cdot_{n=3, \mid=2, m=1, s=+\frac{1}{2}} \)
B. \( n=3,1=2, m=1, s=-\frac{1}{2} \)
\( c \cdot_{n=4,1=0, m=0, s=+\frac{1}{2}} \)
D. \( n=3, s=+\frac{1}{2} \)


Which of the following have peroxy
linkages?
This question has multiple correct options
A \( . K O_{2} \)
в. \( R u O_{4} \)
c. \( B a O_{2} \)
D. \( H_{3} P O_{5} \)


Give the equations of reactions for the
preparation of phenol from cumene.


Hydrogen reacts with a metal(A) to give an ionic hydride(B). The metal (A) gives a brick red color with bunsen flame. The
hydride formed is commonly known by its trade name. The compound (B) on
treating with water gives back \( \mathrm{H}_{2} \) and
(C). Identify the metal \( A \)
\( A \cdot K \)
B. Na a
c. мg
D. ca


If two soap bubbles of different radii
are connected by a tube,
A. air flows from the bigger bubble to the smaller bubble till the sizes are interchanged.
B. air flows from bigger bubble to the smaller bubble till the sizes are interchanged
c. air flows from the smaller bubble to the bigger
D. There is no flow of air


Write the name of the fraction that
constitutes \( 80 \% \) of starch and is water
insoluble.


\( f-1+\cos 56^{\circ}+\cos 58^{\circ}+\cos 66^{\circ}= \)
\( k \sin 28^{\circ} \sin 29^{\circ} \sin 33^{\circ}, \) then the value
of k is
A . 1
B. 3
\( c \cdot 4 \)
D. 5


Solid which undergoes sublimation is :
\( A \cdot \) argon
B. iodine
c. sodium chloride
D. water


n fig \( 6.41, \) if \( A B \| D E, \angle B A C=35^{\circ} \) and
\( \angle C D E=53^{\circ}, \) find \( \angle D C E \)


A/C to ohm's law
A \( \cdot V \propto \frac{1}{I} \)
в. \( I \propto V \)
c. \( I \propto R \)
D. \( I \propto \frac{1}{R} \)


Largest atomic size is:
A.
в.
\( c . F \)
D.


If \( \boldsymbol{y}=\sqrt{\boldsymbol{x}}+\sqrt{\boldsymbol{y}+\sqrt{\boldsymbol{x}+\sqrt{\boldsymbol{y}+\ldots \infty}}} \)
then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)
A \( \cdot \frac{y^{2}-x}{2 y^{3}-2 x y-1} \)
В. \( \frac{x^{2}-x}{2 x^{3}-2 x y-1} \)
C. \( \frac{x^{2}-x}{2 x^{3}-2 x y^{2}-1} \)
D. None of these


A vertical cylinder closed at both ends is fitted with a smooth piston dividing the volume into two parts each containing one mole of air. At the equilibrium
temperature of \( 320 \mathrm{K} \), the upper and
lower parts are in the ratio \( 4: 1 . \) The
ratio will become 3: 1 at a temperature
of?
A . \( 450 \mathrm{k} \)
в. 228 к
c. \( 420 \mathrm{K} \)
D. \( 570 k \)


A domain in ferromagnetic iron is in the
form of a cube of side length \( 2 \mu m \) then
the number of iron atoms in the domain
are (Molecular mass of iron \( =\mathbf{5 5 g} \)
\( m o l^{-1} \) and density \( =7.92 g c m^{-3} \) )
A \( \cdot 6.92 \times 10^{12} \) atoms
B. \( 6.92 \times 10^{11} \) atoms
c. \( 6.92 \times 10^{10} \) atoms
D. \( 6.92 \times 10^{13} \) atoms


Dacron is polymer of:
A. glycol and formaldehyde
B. glycol and phenol
C . glycol and phthalic acid
D. glycol and terephthalic acid


Let \( F, F_{N} \) and \( f \) denote the magnitudes
of the contact force, normal force and
the frictional force exerted by one surface on the other kept in contact. If none of these is zero,
This question has multiple correct options
A \( \cdot F>F_{N} \)
в. \( F>f \)
c. \( F_{N}>f \)
D. \( F_{N}-f<F<F_{N}+f \)


The main product obtained in the
reaction of acetamide and \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{2} \) is:
A. \( C H_{3} C N \)
в. \( C H_{3} N C \)
\( \mathbf{c} \cdot C H_{3} N H_{2} \)
D. \( C H_{3} \) СООН


A bulb of \( 100 \mathrm{W}-200 \mathrm{V} \) is connected to a
\( 160 \mathrm{V} \) supply. Find the power consumed.
A. \( 25 \mathrm{w} \)
B. 64 W
\( c \cdot 45 w \)
D. 20 W


A galvanometer of resistance \( 30 \Omega \) is connected to battery of emf \( 2 V \) with 1970 \Omega resistance in series. A full scale
deflection of 20 divisions is obtained in
the galvanometer. To reduce the deflection to 10 divisions, the resistance
in series required is
A. \( 4030 \Omega \)
в. 4000 \( \Omega \)
c. \( 3970 \Omega \)
D. 2000 \( \Omega \)


Evaluate the following by using the
identities:
\( 48^{2} \)


Assertion
At absolute zero, the molecular energy
is minimum
Reason
At absolute zero, the temperature is
minimum
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If the gravitational force of earth suddenly disappears, then which of the following is correct?
A. weight of the body is zero
B. mass of the body is zero
c. both mass and weight become zero
D. neither the weight nor the mass is zero


"Politics is the art of the possible." Similarly, "Science is the art of the
soluble." Explain this beautiful aphorism on the nature and practice of science.


f \( a \neq b \neq c \) Then one value of \( x \) which
satisfies the equation \( \left|\begin{array}{ccc}\mathbf{0} & \boldsymbol{x}-\boldsymbol{a} & \boldsymbol{x}-\boldsymbol{b} \\ \boldsymbol{x}+\boldsymbol{a} & \boldsymbol{0} & \boldsymbol{x}-\boldsymbol{c} \\ \boldsymbol{x}+\boldsymbol{b} & \boldsymbol{x}+\boldsymbol{c} & \boldsymbol{0}\end{array}\right|=0 \) is given by
A \( \cdot x=a \)
B. \( x=b \)
\( c \cdot x=c \)
D. x =


Which of the following monomers gives the polymer neoprene on polymerisation
?
A \( \cdot C C l_{2}=C C I_{2} \)
B . \( C H_{2}=C H C l \)
c. \( C H_{2}=C(C l)-C H=C H_{2} \)
\( \mathbf{D} \cdot C F_{2}=C F_{2} \)


\( X \) is defined by the number of protons. What is \( X ? \)
A. Cation
B. Inert Gas
c. crystal
D. Anion
E . Element


Iron and rust are the same substances.
A. True
B. False


The gas not having oxidizing as well as bleaching properties is :
A. Chlorine
B. Ozone
\( c \cdot s O_{2} \)
D. \( N_{2} \) O


\( \frac{x-1}{2 x+1}+\frac{2 x+1}{x-1}=\frac{5}{2} \)


Explain the process of secondary growth in stems of wood angiosperms with the help of schematic diagrams. What is its significance?


Water pollution can be classified into chemical and thermal pollution. Is the above statement correct?
A. True
B. False


\( \lim _{x \rightarrow 0}\left[\left(1-e^{x}\right) \frac{\sin x}{|x|}\right] \) is (where []
represents the greatest integer function)
A . -1
B. 1
\( c \cdot 0 \)
D. Does not exist


The flux passing through the surface \( S_{5} \)
will be
\( \mathbf{A} \cdot-0.135 N m^{2} C^{-} \)
B. \( -0.054 N m^{2} C^{-1} \)
\( c \cdot 0.081 N m^{2} C^{-1} \)
) \( 0.054 N m^{2} C^{-1} \)


Sound follow same laws of reflection as
light does?
A. True
B. False


The current and voltage functions in an AC circuit are \( i=100 \sin 100 t m A \)
\( \boldsymbol{V}=\mathbf{1 0 0} \sin \left(\mathbf{1 0 0 t}+\frac{\boldsymbol{\pi}}{\mathbf{3}}\right) \boldsymbol{V} \) The power
dissipated in the circuit is
\( A \cdot 10 w \)
B. 2.5 \( w \)
\( c \cdot 5 w \)
\( D \cdot 5 \mathrm{kW} \)


1 mole of an ideal gas is taken through
a cyclic process. The minimum
temperature during the cycle is \( 300 K \)
Then net exchange of heat for complete
cycle is:
Note \( :\left(\boldsymbol{T}_{\boldsymbol{A}}=\boldsymbol{6 0 0} \boldsymbol{K} ; \quad \boldsymbol{T}_{\boldsymbol{B}}=\right. \)
\( \left.\mathbf{1 2 0 0} \boldsymbol{K} ; \quad \boldsymbol{T}_{c}=\mathbf{6 0 0} \boldsymbol{K}\right) \)
\( \mathbf{A} \cdot 600 R \ln 2 \)
в. \( 300 R \ln 2 \)
c. \( -300 R \ln 2 \)
D. \( 900 R \ln 2 \)


Function of torus is to
A. Regulate water conduction
B. Stop water conduction
C. Inhibit water conduction
D. Help in water absorption


The Lassaigne's extract is boiled with
dil. \( H N O_{3} \) before testing for halogens
because
A. \( A g C N \) is soluble in \( H N O_{3} \)
B. Sliver halides are soluble in \( H N O_{3} \)
c. \( N a C N \) and \( N a_{2} S \) are decomposed by \( H N O_{3} \)
D. \( A g_{2} S \) is soluble in \( H N O_{3} \)


The displacement of a particle in SHM
is indicted by equation \( \boldsymbol{y}= \) \( 10 \sin \left(20 t+\frac{\pi}{3}\right) \) where \( y \) is in metres.
The value of the maximum velocity of the particle will be?
A. \( 100 \mathrm{m} / \mathrm{s} \)
в. \( 150 \mathrm{m} / \mathrm{s} \)
c. \( 200 m / s \)
D. \( 400 \mathrm{m} / \mathrm{s} \)


Find: the ninth term of the G.P.
\( \mathbf{1}, \mathbf{4}, \mathbf{1 6}, \mathbf{6 4}, \dots \)


Two lenses have power \( +2 D,-4 D \)
respectively. State their nature and focal length of the lens.


In the above diagram the shaded
regions \( A \) and \( B \) are the areas covered by
planet around the sun. \( \boldsymbol{d}_{A} \) and \( \boldsymbol{d}_{B}, \boldsymbol{t}_{\boldsymbol{A}} \)
and \( t_{B} \) are the distances traveled by the
planet and the time taken by it to cover
the paths PQ and RS respectively.
Choose the correct statement.
\( \mathbf{A} \cdot d_{A}=d_{B} \) if \( t_{4}=t_{B} \)
B \( \cdot d_{4}<d_{B} \) if \( t_{4}>t_{B} \)
\( \mathbf{c} \cdot d_{A}=d_{B} \) if \( t_{A}<t_{B} \)
D. \( d_{A}>d_{B} \) if \( t_{A}=t_{B} \)


Assertion
Silver bromide is used in photography.
Reason

Silver bromide is used in photography
because silver bromide is
photosensitive. It decomposes and is converted into metallic silver grains
when light is incident on it.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Give one word or phrase for the following
statement.

The property by which certain hydrated salts, when left exposed to atmosphere, lose their water of crystallization and crumble into powder.


Explain in brief:
(i) Any two names of enzymes and their functions.
(ii) Name of two water soluble vitamins
and deficiency diseases.


Q Type your question-
\( \mathbf{2} \boldsymbol{C H}_{3}-\boldsymbol{C} \equiv \boldsymbol{C}-\boldsymbol{H}+\boldsymbol{H} \boldsymbol{C} \equiv \)
\( \boldsymbol{C H} \frac{\text {Red hot}}{\text {tube}} ? \)
\( A \)
B.
\( c \)
\( D \)


The number of electron pair shared between two atoms of same or different
elements during its formation of molecules is known as:
A. covalency
B. tetravalecy
c. bivalency
D. trivalency


According to Stoke's law, the viscous drag force, on an oil drop is proportional
to:
A. \( \sqrt{V} \)
B. \( V^{2} \)
c. \( V^{-1} \)
D. \( V \)


A block of mass \( 2 k g \) is placed on the floor. The coefficient of static friction is
0.4. Force of \( 2.8 N \) is applied on the
block. The force of friction between the
block and the floor is (Taken \( g= \)
\( \left.10 m / s^{2}\right) \)
\( A \cdot 2.8 \mathrm{N} \)
B. 8 N
c. 2.0 N
D. zero


A transistor has \( \alpha=0.95 . \) If the emitter
current is \( 10 \mathrm{m} A \), the base current will
be
A. \( 0.1 \mathrm{mA} \)
в. \( 0.2 \mathrm{mA} \)
\( c .0 .3 m A \)
D. \( 0.5 \mathrm{mA} \)


shape of \( \mathbf{X e O F}_{4} \) is:
A . octahedral
B. square pyramidal
c. pyramidal
D. T-Shaped


Pyrosulphuricacid may be synthesiged by dissolving \( S O_{3} \) in :
A \( . H_{2} O \)
в. \( H_{2} S O_{3} \)
c. \( H_{2} S O_{4} \)
D. \( H_{2} S_{2} O_{8} \)


Two particles of mass \( m_{1} \) and \( M_{2} \)
approach each other due to their mutual gravitational attraction only.
Then
A. Accelerations of both the particles are equal
B. Accelerations of the particles of mass \( m_{1} \) is proportional to \( m_{1} \)
c. Accelerations of the particles of mass \( m_{1} \) is proportional to \( m_{2} \)
D. Accelerations of the particles of mass \( m_{1} \) is inversely
proportional to \( m_{1} \)


Which of the following is the function of
lymph?
A. Lymph keeps the body cells moist.
B. Lymph takes lymphocytes and antibodies from the lymph nodes to the blood
c. Lymph maintains the volume of the blood.
D. All of the above


Two point charges placed at a certain distance \( r \) in air exert a force \( F \) on each
other. The distance \( r \) at which these
charges will exert the same force in
medium if dielectric constant k is given by
\( A \)
в. \( \frac{r}{k} \)
c. \( \frac{r}{\sqrt{k}} \)
D. none of these


Which of the following ions is coloured in aqueous solution?
¡) \( C u^{2+} \)
ii) \( \boldsymbol{C} \boldsymbol{u}^{\mathbf{1}+} \)


Show that \( \int a^{x} e^{x} d x=\frac{a^{x} e^{x}}{\log a+1} \)


An aeroplane is flying horizontally with a velocity of \( 600 k m / h \) and at a height
of \( 1960 m . \) When it is vertically at a
point \( A \) on the ground a bomb is
released from it. The bomb strikes the
ground at point \( B \). The distance \( A B \) is:
A \( .1200 m \)
в. \( 0.33 k m \)
\( c .3 .33 k m \)
D. \( 33 k m \)


Fusion reaction takes place at high
temperature because
A. \( \mathrm{KE} \) is high enough to overcome repulsion between nuclei
B. Nuclei are most stable at this temperature
C. Nuclei are unstable at this temperature
D. None of the above


Evaluate the given integral:
\( \int_{0}^{4}\left(4 x-x^{2}\right) d x \)


A rectangular loop carrying a current is situated near a long straight wire such that the wire is parallel to the one
of the sides of the loop and is in the
plane of the loop. If a steady current lis established in wire as shown in figure,
the loop will:
A. rotate about an axis parallel to the wire
B. move away from the wire or towards right
c. move towards the wire
D. remain stationary


The correct IUPAC name of the
compound \( \left(\boldsymbol{C H}_{3} \boldsymbol{C H}_{2}\right)_{2} \boldsymbol{N C H}_{3} \) is:
A. N - Ethyl-N-methyl ethanamine
B. N, N-Diethylethanamine
c. N-methylethanamine
D. N-ethylethanamine


In a motor, a rotor is fitted with the
armature that has current of 10 A. The
rotor rotates with angular speed of 3 rad/s.Magnetic field of magnitude 2 T varies in direction is such a way that it
is always perpendicular to the loop area If the rotor coil has \( N \) number of turns
and area of each loop is \( 0.45 m^{2} \) then
find the value \( N . \) Given that motor
consumes 2106 W power and there are
no losses.


The order and degree of the differential guation \( \left(\frac{d^{3} y}{d x^{3}}\right)^{1 / 3}=2 \frac{d^{2} y}{d x^{2}}+\sqrt[3]{\cos ^{2} x} \)
are, respectively:
A. 3 and 1
B. 3 and 3
c. 1 and 3
D. 3 and 2
E. 2 and 2


The magnitude of two vectors \( a \) and \( b \)
having the same magnitude and such
that the angle between them is \( 60^{\circ} \) and their scalar product is \( \frac{1}{2}, \) are
A \( \cdot|a|=\frac{1}{2},|b|=1 \)
в. \( |a|=|b|=1 \)
c. \( |a|=1,|b|=\frac{1}{2} \)
D. None of these


Find out in the past if these were some
biotic and abiotic factors in the
ecosystems you have selected. But now
they are not found. If this is the situation, find out the reasons for their diminution.


The tangent to the curve \( x= \) \( a \sqrt{\cos 2 \theta} \cos \theta, y=a \sqrt{\cos 2 \theta} \sin \theta \) at
the point corresponding to \( \boldsymbol{\theta}=\boldsymbol{\pi} / \boldsymbol{6} \) is
A. parallel to the \( x \) -axis
B. parallel to the \( y \) -axis
c. parallel to line \( y=x \)
D. none of these


What is/are the use(s) of thin layer chromatography?
A. To monitor the progress of a reaction
B. To Identify compounds present in a given mixture
c. To Determine the purity of a substance
D. All of the above


A parallelogram is cut by two set of \( \boldsymbol{m} \)
lines parallel to its sides. The number of
parallelogram thus force is
A \( \cdot\left(^{m} C_{2}\right)^{2} \)
B. \( \left(^{m+1} C_{2}\right)^{2} \)
\( \mathbf{c} \cdot\left(^{m+2} C_{2}\right)^{2} \)
D. \( m+1 C_{2} \)


Among the four successive members of the first series of the transition metals
listed below in the options, which one has a positive standard potential \( \left(\boldsymbol{E}_{M^{2+} / M}^{0}\right) \) value?
A. \( N i(Z=28) \)
в. \( C u(Z=29) \)
c. \( F e(Z=26) \)
D. \( \operatorname{Co}(Z=27) \)


Occurrence of water blooms in a lake
indicates
A. Excessive nutrient availability
B. Nutrient defciency
c. Oxygen defciency
D. Absence of herbivores


A plank fitted with a gun is moving on a horizontal surface with speed of \( 4 \mathrm{m} / \mathrm{s} \) along the positive x-axis. The z-axis is in vertically upward direction. The mass of the plank including the mass of the mass of the gun is 50 kg. When the plank reaches the origin, a shell of
mass \( 10 \mathrm{kg} \) is fired at an angle of \( 60^{\circ} \) with the positive x-axis with a speed of \( \mathbf{v}=20 \mathrm{m} / \mathrm{s} \) with respect to the gun \( \mathrm{n} \mathbf{x}-\mathrm{z} \)
plane. Find the position vector of the shell at \( t=2 \) s after firing it. Take \( g= \) \( 9.8 m / s^{2} \)
A. \( [15 \hat{i}-24 \hat{k}] m \)
в. \( [28 \hat{i}+15 \hat{k}] m \)
c. \( [15 \hat{i}-18 \hat{k}] m \)
D. \( [14 \hat{i}-15 \hat{k}] m \)


Complete the following reaction
\( \boldsymbol{B} \boldsymbol{F}_{3}+\boldsymbol{M} \boldsymbol{e}_{3} \boldsymbol{N} \rightarrow \ldots \ldots \)


State the following statement true or false:

Each cardiac cycle lasts for 0.15 second
A. True
B. False


Evaluate
\( \left[\begin{array}{lll}\mathbf{3} & \mathbf{4} & \mathbf{1}\end{array}\right]\left[\begin{array}{c}\mathbf{3} \\ -\mathbf{1} \\ \mathbf{3}\end{array}\right] \)


The charge on an electron was calculated by:
A. Faraday
B. J.J Thompson
c. Millikan
D. Einstein


The solubility product of \( B a S O_{4} \) is
\( 1.5 \times 10^{-9} . \) The precipitation in a
\( 0.01 M B a^{2+} \) solution will start on
adding \( H_{2} S O_{4} \) of concentration:
A \( \cdot 1 \times 10^{-9} M \)
в. \( 1.5 \times 10^{-7} M \)
c. \( 2 \times 10^{-7} M \)
D. \( 1 \times 10^{-6} M \)


Ammonia can be dried by :
A . conc. \( H_{2} S O_{4} \)
B. \( P_{4} O_{10} \)
\( c \cdot C a O \)
D. \( \operatorname{CaCl}_{2} \)


If \( \vec{a}, \vec{b}, \vec{c} \) are unit vectors such that \( \vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}, \) then the value of
\( \vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a} \) is equal to
\( A \)
B. \( \frac{3}{2} \)
\( c \cdot 3 \)
D. \( -\frac{3}{2} \)


Which of the following forms a virtual and erect image for all positions of the object ?
A. Concave lens
B. Concave mirror
c. Convex mirror
D. Both (a) and (c)


If \( \boldsymbol{v}_{s}, \boldsymbol{v}_{\boldsymbol{x}} \) and \( \boldsymbol{v}_{m} \) are the velocities of soft
gamma rays, X-rays and Microwaves respectively in vacuum, then
A. \( v_{s}<v_{x}<v_{m} \)
В . \( v_{s}=v_{x}=v_{m} \)
c. \( v_{s}>v_{x}>v_{m} \)
D. \( v_{x}<v_{s}<v_{m} \)


The differential equation of the family of curves \( \boldsymbol{y}=\boldsymbol{A} \boldsymbol{e}^{\boldsymbol{3} \boldsymbol{x}}+\boldsymbol{B} \boldsymbol{e}^{\boldsymbol{5} \boldsymbol{x}}, \) where \( \boldsymbol{A} \) and
\( B \) are arbitrary constants, is
A \( \cdot \frac{d^{2} y}{d x^{2}}+8 \frac{d y}{d x}+15 y=0 \)
B. \( \frac{d^{2} y}{d x^{2}}-\frac{d y}{d x}+y=0 \)
c. \( \frac{d^{2} y}{d x^{2}}-8 \frac{d y}{d x}+15 y=0 \)
D. None of the above


In 'Aufbau principle', the term Aufbau
represents :
A. the name of scientist
B. german term meaning for building up
c. the energy of electron
D. the angular momentum of electron


The number of moles of \( K M n O_{4} \) that will be needed to react with one mole of ferrous oxalate in acidic solution is?
A . 0.4
B. 0.6
\( c .0 .8 \)
D. \( 0 . \)


Gauss's law is valid for
A. any closed surface
B. only regular close surface
C . any open surface
D. only irregular open surfaces


Virtual image can be caught on a
screen
A . True
B. False


A body thrown vertically up reaches a maximum height of 50 m. Another body with double the mass is thrown up with
double the initial velocity will reach a maximum height of :
A . \( 100 \mathrm{m} \)
B. 200 \( \mathrm{m} \)
c. \( 400 \mathrm{m} \)
D. 50 \( m \)


The slope of the tangent to the curve
\( \boldsymbol{x}=\boldsymbol{t}^{2}+\boldsymbol{3} \boldsymbol{t}-\mathbf{8}, \boldsymbol{y}=\boldsymbol{2} \boldsymbol{t}^{2}-\boldsymbol{2} \boldsymbol{t}-\mathbf{5} \) at the
point (2,-1) is
A \( \cdot \frac{22}{7} \)
B. \( \frac{6}{7} \)
\( c \cdot \frac{7}{6} \)
D. \( -\frac{6}{7} \)


If \( c_{0}, c_{1}, c_{2}, \ldots \ldots c_{n} \) are the coefficients in
the expansion of \( (1+x)^{n}, \) when \( n \) is a
positive integer, prove that
(1) \( c_{0}-c_{1}+c_{2}-c_{3}+\dots \dots+ \)
\( (-1)^{r} c_{r}=(-1)^{r} \frac{\mid n-1}{|\underline{r}| n-r-1} \)
(2) \( c_{0}-2 c_{1}+3 c_{2}-4 c_{3}+\dots \dots+ \)
\( (-1)^{n}(n+1) c_{n}=0 \)
(3) \( c_{0}^{2}-c_{1}^{2}+c_{2}^{2}-c_{3}^{2}+\dots \dots+ \)
\( (-1)^{n} c_{n}^{2}=0, \) or \( (-1)^{\frac{n}{2}} c_{\frac{n}{2}} \)
according as \( n \) is odd or even.


Determine whether the operation \( ^{\prime} *^{\prime} \) on
\( N \) defined by \( a * b=a+b-2 \) for al
\( a, b \in N \) is a binary operation or not:


A travelling acoustic wave frequency
\( 500 H z \) is moving along the positive \( x \)
direction with a velocity of \( 300 m s^{-1} \)
The phase difference between two
points \( x_{1} \) and \( x_{2} \) is \( 60^{\circ} . \) Then the minimum separation between the two
points is:
\( \mathbf{A} \cdot 1 m m \)
в. \( 1 \mathrm{cm} \)
\( c \cdot 10 \mathrm{cm} \)
D. \( 10 \mathrm{mm} \)


The number of photons emitted in 10 hours by a \( 60 \mathrm{W} \) sodium lamp are:
(take \( \lambda \) of photon \( =6000 \mathrm{A}, h c=12400 \)
eVA, \( h= \) Planck's constant, \( c= \) speed of
light)
A \( \cdot 6.50 \times 10^{24} \)
B. \( 6.40 \times 10^{23} \)
c. \( 8.40 \times 10^{23} \)
3
D. 3.40 \( \times 10^{23} \)


Mean of 40 terms is 25 and \( S . D \) is 4
then sum of the squares of all terms is
\( \mathbf{A} \cdot 25640 \)
B. 25000
c. 25645
D. 35645


The air density at Mount Everest is less than that at the sea level. It is found by mountaineers that for one trip lasting a few hours, the extra oxygen needed by them corresponds to \( 30,000 c c \) at sea level (pressure 1 atmosphere,
temperature \( 27^{\circ} \mathrm{C} \) ). Assume that the
temperature around Mount Everest is -
\( 73^{\circ} \mathrm{C} \) and that the oxygen cylinder has a capacity of 5.2 litters. The pressure at which oxygen be filled (at site) in the cylinder is
A. 3.86 atm
B. 5.00 atm
c. 5.77 atm
D. 1 atm


The word aromatic has been derived
from Greek word Aroma which means
unpleasant smell.
A. True
B. False


Let the magnetic field on earth be modelled by that of a point magnetic dipole at the centre of earth. The angle of dip at a point on the geographical equator is
A. always zero
B. positive, negative or zero
c. unbounded
D. always negative


A charge \( +q \) is placed at the origin 0 of
\( X-Y \) axes as shown in the figure. The
work done in taking a charge \( Q \) from \( A \)
to B along the straight line AB is:
A \( \cdot \frac{q Q}{4 \pi \epsilon_{0}}\left(\frac{a-b}{a b}\right) \)
В \( \cdot \frac{q Q}{4 \pi \epsilon_{0}}\left(\frac{b-a}{a b}\right) \)
c. \( \frac{q Q}{4 \pi \epsilon_{0}}\left(\frac{b}{a^{2}}-\frac{1}{b}\right) \)
D. \( \frac{q Q}{4 \pi \epsilon_{0}}\left(\frac{a}{b^{2}}-\frac{1}{b}\right) \)


Polarisation of electron in acrolein
\( \left(\boldsymbol{C H}_{2}=\boldsymbol{C H}-\boldsymbol{C H}=\boldsymbol{O}\right) \) or resonance
hybrid of acrolein can be written as:
\( A \)
\[
\stackrel{\partial^{+}}{\mathrm{CH}_{2}} \ldots \ldots \ldots \ldots \ldots
\]
B. \( \stackrel{\partial^{-}}{\mathrm{CH}}_{2} \cdots \ldots \ldots \ldots \ldots+\ldots 0^{+} \)
\( c \)
\( \partial^{-} \ldots \ldots \mathrm{CH}-\mathrm{CH} \cdots \cdot \mathrm{O}^{-} \)
\( \mathrm{CH}_{2} \cdots-\mathrm{O}^{-} \)
D. \( \stackrel{\partial^{+}}{\mathrm{CH}}_{2} \cdots \ldots+\cdots \cdot \mathrm{CH}=\ldots 0^{+} \)


If 'S' is stress and 'Y' is Young's modulus of a wire material, then energy stored in the wire per unit volume, is?
A \( \cdot \frac{s^{2}}{2 Y} \)
в. \( \frac{2 Y}{S^{2}} \)
c. \( \frac{s}{2 Y} \)
\( \mathbf{D} \cdot 2 S^{2} Y \)


Solve for \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}: \boldsymbol{x}^{2}+\boldsymbol{y}^{2}=\boldsymbol{r}^{2} \)


Simplify the algebraic expression: \( 2 x- \)
\( [3 y+\{5 x-(3 y-2 x)\}-2] \)


Assertion
Both \( S O_{2} \) and \( S O_{3} \) are reducing agents
Reason

Both \( S O_{2} \) and \( S O_{3} \) bleach the articles
by reduction
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Molecules must collide before they
react.
If true enter \( 1, \) if false enter 0


\( H_{2} O \) boils at higher temperature than
\( H_{2} S, \) because it is capable of forming:
A. ionic bonds
B. covalent bonds
c. hydrogen bonds
D. metallic bonds


Which of the following compounds is a soap?
A \( \cdot C H_{3}\left(C H_{2}\right)_{16} C O N a \)
в. \( C H_{3}\left(C H_{2}\right)_{16} \)СООМа
c. \( C H_{3}\left(C H_{2}\right)_{16} C O O H \)
D. \( C H_{3}\left(C H_{2}\right)_{16} C O O C H_{3} \)


S.D.of the first \( (\boldsymbol{n}+\mathbf{1}) \) natural number
is
A. \( \sqrt{\frac{n^{2}-1}{12}} \)
в. \( \sqrt{\frac{n^{2}+1}{12}} \)
c. \( \sqrt{\frac{n(n+2)}{12}} \)
D. None of these


Which of the following isotopes is used
for treatment of cancer?
A \( \cdot C_{o}^{6} \)
B. \( K^{4} \)
\( c \cdot S r^{90} \)
D. \( I^{13} \)


If \( \mathbf{0} \leq \boldsymbol{x} \leq \mathbf{3} \boldsymbol{\pi}, \mathbf{0} \leq \boldsymbol{y} \leq \)
\( 3 \pi \) and \( \cos x . \sin y=1 \) then the
possible number of values of the
ordered pair \( (x, y) \) is
\( A \cdot 6 \)
B. 12
c. 8
D. 15


A uniform thin ring of radius \( \boldsymbol{R} \) and
mass \( m \) suspended in a vertical plane from a point in its circumference its time period of oscillation is
A \( \cdot 2 \pi \sqrt{\frac{2 R}{g}} \)
В \( \cdot 2 \pi \sqrt{\frac{3 R}{2 g}} \)
c. \( \frac{\pi}{2} \sqrt{\frac{R}{g}} \)
D. \( \pi \sqrt{\frac{R}{2 g}} \)


A wire of uniform cross-section has a
resistance of \( R \). If it is drawn to three
times the length, but the volume remains constant, what will be its
resistance?
\( \mathbf{A} \cdot 3 R \Omega \)
B. \( 5 R \Omega \)
\( \mathbf{c} .7 R \Omega \)
D. \( 9 R \Omega \)


Find the value of \( \lambda, \) a non - zero scalar, if
\[
\left.\begin{array}{l}
\boldsymbol{\lambda}\left[\begin{array}{lll}
\mathbf{1} & \mathbf{0} & \mathbf{2} \\
\mathbf{3} & \mathbf{4} & \mathbf{5}
\end{array}\right]+\mathbf{2}\left[\begin{array}{ccc}
\mathbf{1} & \mathbf{2} & \mathbf{3} \\
-\mathbf{1} & \mathbf{- 3} & \mathbf{2}
\end{array}\right]= \\
\mathbf{4} & \mathbf{4} & \mathbf{1 0} \\
\mathbf{4} & \mathbf{2} & \mathbf{1 4}
\end{array}\right]
\]


Arrange \( F, C, O, N \) in the decreasing order electronegativity:
A. \( O>F>N>C \)
в. \( F>N>C>0 \)
c. \( C>F>N>O \)
D. \( F>O>N>C \)


Describe in detail the composition of human blood.


A moving sidewalk in an airport terminal building moves at a speed of
\( 1.0 m s^{-1} \) and is \( 35.0 \mathrm{m} \) long. If a woman
steps on at one end and walks at 1.5
\( m s^{-1} \) relative to the moving sidewalk,
then find the time that she requires to
reach the opposite end
(a) when she
walks in the same direction the
sidewalk is moving and
(b) when she
walks in the opposite direction.


Let \( A=\{x, y, z\} \) and \( B=\{p, q, r, s\} \)
What is the number of distinct relations
from \( \boldsymbol{B} \) to \( \boldsymbol{A} \) ?
A . 4096
в. 4094
c. 128
D. 126


State True or False.
The effect of a change in the concentration of a reactant or product on the cell voltage can be predicted by applying Le-chateliers principle.
A. True
B. False


A compass needle whose magnetic moment is \( 60 A m^{2} \) pointing geographical north at a certain place
where the horizontal component of earth's magnetic field is \( 40 \times 10^{-6} \mathrm{Wb} \)
\( m^{-2} \) experiences a torque of \( 1.2 \times 10^{-3} \)
N m. The declination of the place is?
A \( \cdot 20^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 30^{\circ} \)


The area of two similar triangles are in
ratio \( 16: 81 . \) Find the ratio of its sides.
A \( \cdot \frac{1}{9} \)
в. \( \frac{2}{9} \)
\( c \cdot \frac{3}{9} \)
D. \( \frac{4}{9} \)


The real part of
\( \left[\mathbf{1}+\cos \left(\frac{\pi}{5}\right)+i \sin \left(\frac{\pi}{5}\right)\right]^{-1} \) is
A .
в. \( \frac{1}{2} \)
c. \( \frac{1}{2} \cos \left(\frac{\pi}{10}\right) \)
D. \( \frac{1}{2} \cos \left(\frac{\pi}{5}\right) \)


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


Let the matrix \( A \) and \( B \) be defined as
\( A=\left|\begin{array}{ll}\mathbf{3} & \mathbf{2} \\ \mathbf{2} & \mathbf{1}\end{array}\right| \) and \( \boldsymbol{B}=\left|\begin{array}{ll}\mathbf{3} & \mathbf{1} \\ \mathbf{7} & \mathbf{3}\end{array}\right| \) then the
value of \( \operatorname{Det.}\left(2 A^{9} B^{-1}\right), \) is
\( A \cdot 2 \)
в.
\( c \cdot-1 \)
\( D .-2 \)


Which of the following compounds will not give ammonia on heating?
\( \mathbf{A} \cdot\left(N H_{4}\right)_{2} S O_{4} \)
B. \( \left(N H_{4}\right)_{2} C O_{3} \)
c. \( N H_{4} N O_{2} \)
D. \( N H_{4} C l \)


What parameter does an indicator changes, with change in the nature of
the solution?
A. colour
B. Odour
c. Both
D. None of these


If the length of the filament of a heater is reduced by \( 10 \%, \) the power of the heater will
A. increase by about \( 9 \% \)
B. increase by about 11\%
c. increase by about \( 19 \% \)
D. decrease by about 10\%


The diagram above shows the pattern of
the oil dripping on the road, at a
constant rate from a moving car. What information(s) do you get from it about
the motion of car?
A. Initially it is moving with a constant speed and then it speeds up.
B. Initially it is moving with a constant speed and then it slows down
C. It is moving with a constant speed.
D. None of the above.


The amplitude of two waves are in ratio
\( 5: 2 . \) If all other conditions for the two
waves are same, then what is the ratio
of their energy densities?
A . 5: 2
B. 5: 4
\( c \cdot 4: 5 \)
D. 25 : 4


\( -\left(\mathrm{CH}_{2}-\mathrm{CH}\right)_{\mathrm{n}} \)
\( \mathrm{CN} \)
\( \left(\mathrm{CH}_{2}-\mathrm{CH}-\right)_{\mathrm{n}} \)
\( \mathrm{Cl} \)
\( \mathrm{CH}_{2}-\mathrm{c}=\mathrm{cH}-\mathrm{cH}_{2}-\left.\right|_{\mathrm{n}} \)
\( \mathrm{cl} \)
\( \mathrm{C}_{6} \mathrm{H}_{5} \)


The number of unpaired electrons in \( M n^{4+}(z=25) \) is :
A. four
B. two
c. five
D. three


A body is accelerated by applying a force of 30 N. The change in the momentum of the body after 2 sec is?
A. \( 7.5 \mathrm{kg}-\mathrm{m} / \mathrm{s} \)
B. \( 30 \mathrm{kg}-\mathrm{m} / \mathrm{s} \)
c. \( 120 \mathrm{kg}-\mathrm{m} / \mathrm{s} \)
D. \( 60 \mathrm{kg}-\mathrm{m} / \mathrm{s} \)


From a complete ring of mass \( M \) and
radius \( R, \) a \( 30^{\circ} \) sector is removed. The
moment of inertia of the incomplete
ring about an axis passing through the
centre of the ring and perpendicular to the plane of the ring is
\( ^{A} \cdot \frac{9}{12} M R^{2} \)
\( ^{\text {В }} \frac{11}{12}^{M R^{2}} \)
\( ^{\mathrm{c}} \cdot \frac{11.3}{12} M R^{2} \)
D. \( M R^{2} \)


\( C l_{2} \) gas is passed into aqueous
solution of KBr and KI and \( C H C l_{3} \)
added . It is observed that there is:
A. violet colour in \( C H C l_{3} \) layer
B. yellow colour in \( C H C l_{3} \) layer
c. yellow colour in aqueous layer
D. violet colour in aqueous layer


Multiple Correct Answers Type
Let \( \left[\epsilon_{0}\right] \) denote the dimensional formula
of the permittivity of vacuum and \( \left[\mu_{0}\right] \) that of the permeability of vacuum. If \( \mathrm{M} \) \( = \) mass, \( L= \) length, \( T= \) time, and \( l= \) electric current, then
This question has multiple correct options
A \( \cdot\left[\epsilon_{0}\right]=M^{-1} L^{-3} T^{2} I^{2} \)
B . \( \left[\epsilon_{0}\right]=M^{-1} L^{-3} T^{4} I^{2} \)
c. \( \left[\mu_{0}\right]=M L T^{-2} I^{-2} \)
D. \( \left[\mu_{0}\right]=M L^{2} T^{-1} I \)


The square of its period of revolution around the sun is the cube of the mean distance of a
planet from the sun
A. Inversely proportional
B. Directly proportional
c. Not proportional
D. depend


An \( L-C \) circuit consists of a \( 20.0 m H \)
inductor and a \( 0.5 \mu F \) capacitor. If the
maximum instantaneous current is
\( 0.1 A, \) what is the greatest potential difference (in volts) across the
capacitor?


\( A B C D \) is a parallelogram with side \( A B=10 \mathrm{cm} . \) Its diagonals \( A C \) and \( B D \)
are of length \( 12 \mathrm{cm} \) and \( 16 \mathrm{cm} \) respectively. Find the area of a
parallelogram \( \boldsymbol{A B C D} \)


Match the columns
\( \mathbf{A} \)
\( B \)
(1) Speed of
(a) 4.3 light years away from light earth
(2) Light year
(b) \( 300,000 \mathrm{km} / \mathrm{s} \)
(3) Sun
(c) Nearest star
(4) Alpha
(d) distance travelled by light in Centauri \( \quad \) one year
(e) 18 light minutes away from the Earth
A. \( 1-d \) 2-d, \( 3-a, 4-e \)
B. \( 1-a, 2-b, 3-c, 4-e \)
\( \mathbf{C} \cdot 1-\mathrm{d}, 2-\mathrm{b}, 3-\mathrm{e}, 4-\mathrm{c} \)
D. \( 1-b, 2-d, 3-c, 4-a \)


Constant magnetic field in the coil induces
A . high
B. low
\( c \cdot n o \)
D. alternating


Which one of the following statements
does hold good when two balls of
masses \( m_{1} \) and \( m_{2} \) undergo elastic
collision?
A. When \( m_{1}<m_{2} \) and \( m_{2} \) at rest, there will be maximum
B. When \( m_{1}>m_{2} \) and \( m_{2} \) at rest, after collision the ball of mass \( m_{2} \) moves with four times the velocity of \( m_{1} \)
c. When \( m_{1}=m_{2} \) and \( m_{2} \) at rest, there will be maximum
transfer of K.E
D. When collision is oblique and \( m_{2} \) at rest with \( m_{1}=m_{2} \) after collision the ball moves in opposite direction


Which of the three components of
acceleration have non-zero values?
A . \( x \) and \( y \)
B. \( y \) and \( z \)
c. \( z \) and \( x \)
D. \( x, y \) and \( z \)


\( \int_{0}^{2 a} \frac{f(x) d x}{f(x)+f(2 a-x)} \)
\( A \)
B. \( \frac{a}{2} \)
\( c \cdot 0 \)
D. \( 2 a \)


The density of air at N.T.P. is \( 1.293 \mathrm{gm} / \mathrm{lit} \). If
the pressure is tripled keeping its temperature constant its density becomes
A. \( 3.87 g m / l t r \)
B. \( 1.293 g m / l t r r \)
c. \( 2.586 g m / l t r \)
D. \( 0.431 g m / l t r r \)


The major parts of the digestive system of grass hopper are
A. Gizzard, crop and hepatic caecae
B. Foregut, midgut and hind gut
c. Gizzard, ileum and midgut
D. Pharynx, oesophagus and stomach


Fill in the blank:
In a constellation, form a
recognizable shape.
A. stars
B. planets
c. meteroids
D. comets


The substance which is not used as an
antiseptic is:
A. bithionol
B. \( 0.2 \% \) phenol
\( c \cdot 2-3 \% \) iodine
D. norethindrone


Two billiard balls of the same size and
mass are in contact on a billiard table.
third ball of the same size and mass
strikes them symmetrically and remains at rest after the impact. The coefficient of restitution between the
ball is:
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{3} \)
\( c \cdot 2 \)
\( \overline{3} \)
\( D \cdot 3 \)
\( \bar{A} \)


If \( \bar{a} \) is unit vector, then \( |\overline{\boldsymbol{a}} \times \hat{\mathbf{i}}|^{2}+\mid \overline{\boldsymbol{a}} \times \)
\( \left.\hat{\boldsymbol{j}}\right|^{2}+|\overline{\boldsymbol{a}} \times \hat{\boldsymbol{k}}|^{2}= \)
\( A \cdot 2 \)
B.
\( c \cdot 0 \)
D. 3


When electric current is passed
through water, the dissociation is indicated
A. in the form of bubbles
B. by color change
\( c . \) both a and \( b \)
D. none of above


On a given condition, the equilibrium
concentration of \( \mathrm{HI}, \boldsymbol{H}_{2} \) and \( \boldsymbol{I}_{2} \) are 0.80 0.10 and 0.10 mole/litre. The equilibrium
constant for the reaction \( \boldsymbol{H}_{2}+\boldsymbol{I}_{2} \rightleftharpoons \)
\( 2 H I \) will be-
A . 64
B. 12
\( c \cdot 8 \)
D. 0.8


Select the correct orders for gases
represented with their characteristics:
This question has multiple correct options
A. Critical temperature < Boyle's temperature
B. van der Waal's constant 'a' : \( H_{2} O>N H_{3}>N_{2}>N e \)
C. Heat capacity: \( N H_{3}>C O_{2}>O_{2}=N_{2}>A r \)
D. Mean free path: \( H e>H_{2}>O_{2}>N_{2}>C O_{2} \)


Copy and complete the following
sentences?
With platinum electrodes hydrogen is
liberated at the \( \ldots \ldots \ldots . \) and oxygen at the
during the electrolysis of acidified
water


Find the distinct permutations of the letters of the word MISSISSIPPI?


How will you use two identical prisms so that a narrow beam of white light incident on one prism emerges out of the second prism as white light?
A. Just put them side by side.
B. one placed on top of the other
c. one placed inverted with respect to the other.
D. none of these.


Apoplastic movement of water occurs exclusively through the
(i) Intercellular spaces
(ii) Walls of the cells
(iii) Plasmodesmata
(iv) Cytoplasm
A . i, ii and iv
B. iii and iv
D. ii and ì
E. iv


Material used in fuse wire must have
A. high melting point
B. low melting point
c. high resistance
D. none


In hydrogen fuel cell the catalyst used ¡s/are:
This question has multiple correct options
A . \( A g \)
в. \( F e \)
\( c \cdot P t \)
D. \( Z n \)


Prove if \( \cot \theta+\frac{1}{\cot \theta}=2 \) then \( \cot ^{2} \theta+ \)
\( \frac{1}{\cot ^{2} \theta}=2 \)


If \( f(x)=x^{3} \) sgn \( x \) then
A. \( f \) is differentiable at \( x=0 \)
B. \( f \) is continous but not differentiable at \( x=0 \)
\( \mathbf{C} \cdot f^{\prime}\left(0^{-}\right)=1 \)
D. none of these


How many EDTA (ethylenediaminetetraccetic acid) molecules are required to make an
octahedral complex with a \( C a^{2+} \) ion?
A. Two
B. Six
c. Three
D. one


Give any two real-life examples for
congruent shapes.


Which of the following is an example of photochemical smog?
A. Ketones
B. Aldehydes
c. Ester
D. None of the above


A thin insulating ring of radius \( R \) has a
uniform linear charge density \( \lambda \). Now a
charge \( Q_{0} \) is placed at centre of this ring. The increment in the stretching
force of the wire due to the charge \( Q_{0} \)
is:
A. \( \frac{Q_{0} \lambda}{2 \pi \varepsilon_{\Omega}} \)
в. \( \frac{Q_{0} \lambda}{4 \pi \varepsilon_{0} R} \)
c. \( \frac{3 Q_{0} \lambda}{8 \pi \varepsilon_{0} R} \)
D. \( \frac{3 Q_{0} \lambda}{4 \pi \varepsilon_{0} R} \)


\( \frac{\sin ^{2} A-\sin ^{2} B}{\sin A \cos A-\sin B \cos B} \) is equal to
A \( \cdot \tan (A-B) \)
B \cdot \( \tan (A+B) \)
c. \( \cot (A-B) \)
D \cdot \( \cot (A+B) \)


Assertion
Species is a group of individuals with fundamental similarities
Reason
Indica, leo, tuberosum represent such group of individuals.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The property of metals by virtue of which they can be drawn into wires is called ductility.
A. True
B. False


Taxonomically, what is species?
A. A group of evolutionary related populations
B. A group of organism which can interbreed
C. Category to which most taxonomic information is attached
D. Fundamental unit of phylogenetic history oforganisms


Carbon and \( C O \) gas are used to reduce
which of the following pairs of metal oxides for extraction of metals?
A. \( F e O, S n O \)
в. \( \operatorname{Sn} O, Z n O \)
с. Ва а,\( _{N a_{2}} \)О\( _{2} \)
D. \( F e O, Z n O \)


Check if the following numbers are in
AP. If they form an AP, find the common
difference d and write three more terms.
\( 2,4,8,16 \dots \)


The magnitude of force (in \( N \) ) acting on a body varies with time \( t(\text { in } \mu s) \) as
shown. \( A B, B C \) and \( C D \) are straight
line segments. The magnitude of total
impulse of force on the body from \( t= \)
\( 4 \mu s \) to \( t=16 \mu s \) is :
\( \mathbf{A} \cdot 10^{-3} N s \)
B \( \cdot 10^{-2} N s \)
\( \mathbf{c} \cdot 10^{-4} N s \)
D. \( 5 \times 10^{-4} N s \)


Hydrogen is :
A. electropositive
B. electronegative
C. both electronpositive as well as electronegative
D. neither electropositive nor electronegative


Which one of the following polymers is
not properly matched to its monomer?
A. orion - acrylonirtile
B. synthetic rubber- - -chlorobuta - -1, 3 - diene
c. nylon - adipic acid \& hexamethylene diamine
D. teflon-vinyl chloride


One-fourth of a sphere of radius R is removed as shown in Fig. An electric field E exists parallel to the xy plane. Find the flux through the remaining curved part :
\( \mathbf{A} \cdot \pi R^{2} E \)
В. \( \sqrt{2} \pi R^{2} E \)
c. \( \pi R^{2} E / \sqrt{2} \)
D. none of these


What is the product formed when
benzene is heated with acetic
anhydride and anhydrous \( A l C l_{3} ? \)
A. Acetophenone
B. Toluene
c. Benzoic acid
D. Phenyl acetic acid


The ionization energy of the hydrogen atom is \( 13.6 \mathrm{eV} \). The potential energy of the electron in \( n=2 \) state of hydrogen atom is
A. \( +3.4 e V \)
B. - 3.4eV
\( \mathrm{c} .+6.8 \mathrm{eV} \)
D. \( -6.8 e V \)


IUPAC name of the given compound is:
A. 2,2,4 -trimethylpentyne
B. 2, 2,4-trimethylpentne
c. 2,2,4 -trimethylpentane
D. 2,4 -trimethylpentan


In the given figure points \( A, D, P, C \) and \( B \) lie on a circle with centre
\( \boldsymbol{O}, \angle \boldsymbol{B O D}=\mathbf{1 5 0}^{\circ} \) Find the measures
of \( \angle B P D, \angle B C D \) and \( \angle B A D \)


Which of the following is not correctly
matched with its IUPAC name?
\( \mathbf{A} \cdot C H F_{2} C B r C l F: 1- \) Bromo- 1 -chloro- \( 1,2,2- \) trifluoroethane
B. \( \left(C C l_{3}\right)_{3} C C l \) : 2-(Trichloromethyl)-1,1,1,2,3,3, 3 heptachioropropane
\( \mathbf{c} \cdot C H_{3} C\left(p-C l C_{6} H_{4}\right)_{2} C H(B r) C H_{3}: 2-\mathrm{Bromo}-3,3- \)
bis(4-chlorophenyl) butane
D \( \cdot o-B r C_{6} H_{4} C H\left(C H_{3}\right) C H_{2} C H_{3}: \) 2-Bromo-1-
methylpropylbenzene


Think about the objects which act as a
concave or convex mirrors in your surroundings. Make a table and display
it in your class room.


In carbon and hydrogen estimation, the saphnolite (a resin) absorbs:
A \( . N_{2} \)
B. Water vapours
\( c \cdot \operatorname{both} C O_{2} \) and \( H_{2} O \)
D. only \( C O_{2} \)


Which of the following statements
is/are not true?
A. Nitrogen differs markedly from the other members of its family
B. Nitrogen has five valency electrons
C. Nitrogen shows covalency greater than four
D. Nitrogen shows great stability as a free element


What kind of lens would form an
inverted diminished image?


Two particle \( A \) and \( B \) are located in \( x-y \) plane at points (0,0) and \( (0,4 \mathrm{m}) \). They simultaneously start moving with velocities. \( \vec{V}_{A}=2 \hat{j} m / s \) and \( \vec{V}_{B}= \)
2 ì \( m / s . \) Select the correct alternative(s).
This question has multiple correct options
A. The distance between them is constant
B. The distance between them first decreases and then increases
c. The shortest distance between them is \( 2 \sqrt{2} m \)
D. Time after which they are at minimum distance is 1 s


Fossils formed when a plant or animal
dies in a wet environment. The soft
tissue decomposes very fast and leaving bones aside. The significance of fossils is, they provide evidence of how
evolution is taking place. Type 1 for true and 0 for flase


\( B C l_{3} \) does not exist as dimer but \( B H_{3} \)
exists as dimer \( \left(B_{2} H_{6}\right) \) because:
A. Chlorine is more electronegative than hydrogen
B. There is \( p_{\pi}-p_{\pi} \) back bonding in \( B C l_{3} \), but \( B H_{3} \) does not contain such multiple bonding
c. Large-sized chlorine atoms do not fit in between the small boron atoms whereas small-sized hydrogen atoms fit between boron atoms
D. None of these


A triene is treated with ozone followed
by zinc in acetic acid to give the following three products. What is the structure of the triene
\( A \)
в.
\( c \)
D.


The following table shows the interest paid by a company (in lakhs):
1996- \( \quad 1997 \) Year
Interest
in lakhs
25
of
rupee
Draw the bar graph to represent the above information.


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


The value of \( \cos ^{-1}\left(\cos \frac{7 \pi}{6}\right)= \)
\( A \cdot \frac{7 \pi}{6} \)
в. \( \frac{5 \pi}{6} \)
\( c \cdot \frac{\pi}{3} \)
D.


Write down an isomer of \( C_{2} H_{5} O H \)


Among the following elements, which one has the highest ionisation potential?
A. Hydrogen
B. Lithium
c. Potassium
D. sodium


The variance of the random variable \( x \)
whose probability distribution is given by
\( \boldsymbol{X}=\boldsymbol{x}_{i}: \quad-1 \quad, \boldsymbol{0}, \quad+1 \)
\( \boldsymbol{p}\left(\boldsymbol{X}=\boldsymbol{x}_{i}\right): \mathbf{0 . 4}, \mathbf{0 . 2}, \quad \mathbf{0 . 4} \) is
A . 0.4
B. 0.6
\( c .0 .8 \)
D. 1.0


Statement-1: When two conducting wires of different resistivity having same cross section area are joined in
series, the electric field in them would
be equal when they carry current

Statement-2: When wires are in series
they carry equal current
A. Statement-1 is true and Statement-2 is correct explanation for Statement- -
B. Statement-1 is true and Statement-2 is NOT the correct explanation for Statement-
c. Statement-1 is true, Statement-2 is false
D. Statement-1 is false, Statement-2 is true


Why baking powder is used to prepare
cake?


Solve the following pairs of equations by
reducing them to a pair of linear
equations:
\( \frac{2}{\sqrt{x}}+\frac{2}{\sqrt{y}}=2, \frac{4}{\sqrt{x}}-\frac{9}{\sqrt{y}}=-1 \)


The triglycerides of which of the following unsaturated fatty acids are not present in oils and fats?
A. Oleic acid
B. Linoleic acid
C. Linolenic acid
D. Maleic acid


The transition metals (with the
exception of \( \mathrm{Zn}, \mathrm{Cd} \) and \( \mathrm{Hg} \) ) are hard and have high melting and boiling
points. If true enter 1 else 0


S and \( \mathrm{S}^{\prime} \) foci of an ellipse. \( \mathrm{B} \) is one end of
the minor axis. If \( \angle S B S^{\prime} \) is a right
angled isosceles triangle, then \( \mathrm{e}=? \)
\( ^{A} \cdot \frac{1}{\sqrt{2}} \)
B. \( \frac{1}{2} \)
c. \( \frac{\sqrt{3}}{2} \)
D. \( \frac{3}{4} \)


A plane electromagnetic wave of frequency 50 MHz travels in free space along the x-direction. At a particular point in space and time, \( \vec{E}=6.3 \hat{j} \vee m^{-1} \) At this point \( \vec{B} \) is equal to
A. \( 8.33 \times 10^{-8} \hat{k} T \)
B . \( 18.9 \times 10^{-8} \hat{k} T \)
c. \( 4.1 \times 10^{-8} \hat{k} T \)
D. \( 2.1 \times 10^{-8} \hat{k} T \)


How many triangles can be drawn
having its angles as \( 45^{0}, 64^{0} \) and \( 72^{0} ? \)
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
c. More than 2
D. None


Write the degree of each polynomial
given below:
\( \boldsymbol{x} \boldsymbol{y}+\boldsymbol{y} \boldsymbol{z}-\boldsymbol{z} \boldsymbol{x}^{3} \)


An electric charge is held at rest in a region of space filled with non-uniform magnetic field. As soon as it is left free.
A. it will move in the direction of the field
B. it will move opposite to the direction of the field
c. it will move perpendicular to the direction of the field
D. it will remain at rest


Which information can be obtained
from Le Chatelier's principle?
A. Shift in equilibrium position on changing \( P, T \) and concentration
B. Dissociation constant of a weak acid
c. Energy change in a reaction
D. Equilibrium constant of a chemical reaction


Which of the following is not a conjugate acid-base pair?
\( \mathbf{A} \cdot H P O_{3}^{2-}, P O_{3}^{3-} \)
B . \( H_{2} P O_{4}^{-}, H P O_{4}^{2-} \)
c. \( H_{2} P O_{4}^{-}, H_{3} P O_{4} \)
D. \( H_{2} P O_{4}^{-}, P O_{3}^{3-} \)


Find the total surface area of a
hemisphere of radius \( 10 \mathrm{cm} \)


If \( P(n) \) be the statement \( n(n+1)+1 \) is odd, then which of the following is
false?
A \( . P(2) \)
в. \( P(3) \)
c. \( P(4) \)
D. none of these


A square of side L meters lies in the \( x-y \) plane in a region, where the magnetic field given by \( \vec{B}=B_{o}(2 \hat{i}+3 \hat{j}+4 \hat{k}) T \)
where \( B_{o} \) is constant. The magnitude of flux passing through the square is :
B. \( 3 B_{o} L^{2} W b \)
\( \mathbf{c} \cdot 4 B_{o} L^{2} W b \)
D. \( \sqrt{29} B_{o} L^{2} W b \)


Why basic character in lanthanoid
hydroxides decreases across the
period?


If vector \( \overrightarrow{A B}=3 \hat{i}-3 \hat{k}, \overrightarrow{A C}=\hat{i}- \)
\( 2 \hat{j}+\hat{k} \) represents the sides of any triangle \( A B C \) then the length of median AM is-
A \( \cdot \sqrt{6} \)
B. \( \sqrt{3} \)
\( c \cdot 2 \sqrt{3} \)
D. \( 3 \sqrt{2} \)


Enthalpy of the reaction \( : \boldsymbol{C H}_{4}+ \)
\( \frac{1}{2} O_{2} \longrightarrow C H_{3} O H \) is negative. If
enthalpy of combustion of \( C H_{4} \) and
\( C H_{3} O H \) are \( x \) and \( y \) respectively which relation is correct?
A \( . x>y \)
В. \( x<y \)
\( \mathbf{c} \cdot x=y \)
D. \( x \geq y \)


Evaluate
\[
\left|\begin{array}{ccc}
2 & 7 & 3 \\
-4 & 3 & -1 \\
0 & -3 & 7
\end{array}\right|
\]


Which of the following statements is
correct?
This question has multiple correct options
A. \( S O_{2} \) is anhydride of sulphurous acid
B. \( S O_{2} \) acts as only oxidising agent
c. The coloured matter lost colour on exposure to \( S O_{2} \) can regain colour on exposure to atmosphere
D. \( S O_{2} \) can get oxidised to sulphur


Find the \( 5^{t h} \) term of the \( A . P . \)
\( 17,14,11, \dots \dots,-40 \)


Read the following statements and answer whether the given statement is true or false.
An electric generator works on the principle of electromagnetic induction
A. True
B. False


An object is placed at \( 15 \mathrm{cm} \) in front of convex lens of focal length 10 cm. Where shall we place a convex mirror of focal length \( 13 \mathrm{cm} \) so that real image and object coincide?
\( A \cdot 6 \mathrm{cm} \) from lens
B. 3 cm from lens
c. \( 4 \mathrm{cm} \) from lens
D. \( 2 \mathrm{cm} \) from lens


How many electrons constitute current
of one micro ampere in one second?
\( \mathbf{A} \cdot 6.25 \times 10^{8} \)
B. \( 6.25 \times 10^{12} \)
\( \mathbf{C} \cdot 6.25 \times 10^{9} \)
D. \( 6.25 \times 10^{15} \)


toppr
Q Type your question
uniform area of cross-section is
attached with the particle. The other end of the band is suspended from a
rigid support. A force \( \boldsymbol{K}\left(\boldsymbol{l}^{\prime 2}-\boldsymbol{l}^{2}\right)^{1 / 2} \) is
required to stretch the band to a length
\( l^{\prime} . \) The particle is moved to a distance \( S \)
(where \( S<<l \) ) and then released.
taking \( K=\frac{M g}{S} \) and \( \mu \) as the
coefficient of friction between the
particle and the groove, the velocity of
particle when passing through the
initial position is:
\( ^{A} \cdot\left(\frac{g S}{3 l}(2 S-3 \mu l)\right)^{1 / 2} \)
B. \( \left[\frac{g S}{3 l}(3 S-3 \mu l)^{1 / 2}\right] \)
c. \( \frac{g S}{l}(3 S-2 \mu l)^{1 / 2} \)
\( ^{\mathrm{D}}\left[\frac{g S}{2 l}(3 S-2 \mu l)\right]^{1 / 2} \)


In monocotyledons, the leaves
A. Arise at the tip of the stem only
B. Do not sheath the stem
C. Sheath the stem
D. Sheath the stem only in the lower portion


The number 0 (zero) is required for
A. transistor
B. abacus
c. computer
D. calculator


In \( N O_{3}^{-} \) ion, the number of bond pairs
and lone pairs of electrons on nitrogen
atom are:
A .2,2
B. 3,
\( c \cdot 1,3 \)
D. 3, o


Which one is not the property of Lithium by which it differs from the rest of the alkali metals?
A. Extremely small size of Lithium atom
B. Greater polarizing power of Lithium ion
c. Highest electropositive character and highest ionization energy
D. Non availability of vacant d-orbitals in the valence shell


Oxidation number of \( \mathrm{P} \) in \( \boldsymbol{P}_{2} \boldsymbol{O}_{7}^{4-} \) is :
\( A \cdot+3 \)
\( B \cdot+4 \)
\( c \cdot+5 \)
\( D \cdot+6 \)


Example of an element is:
A. water
B. Sodium hydroxide
c. Hydrogen
D. sugar


The boiling point of Propanone is:
\( A \cdot 321 K \)
в. з29 к
\( c . \) ззо \( k \)
D. 340 K


A coil has an inductance of \( 0.7 \mathrm{H} \) and is
joined in series with a resistance of 220
\Omega. When an alternating e.m.f. of \( 220 \mathrm{V} \) at 50 c.p.s. is applied to it, then the wattless component of the current in the circuit is
A. 5 ampere
B. 0.5 ampere
c. 0.7 ampere
D. 7 ampere


toppr
Q Type your question
3
\( c \)
\( D \)


If \( \triangle A B C \sim \triangle D E F B C=4 \mathrm{cm}, \mathrm{EF}=5 \mathrm{cm} \)
and ar \( (\triangle A B C)=80 c m 2 \),the ar
\( (\triangle D E F) \) is
A \( \cdot 120 \mathrm{cm}^{2} \)
B. \( 125 \mathrm{cm}^{2} \)
\( \mathrm{c} \cdot 150 \mathrm{cm}^{2} \)
D. \( 200 \mathrm{cm}^{2} \)


Which of the following are chemical changes?
(a) Growth of a plant
(b) Rusting of Iron
(c) Mixing of iron fillings and sand
\( (d) \) Cooking of food
(e) Digestion of food
\( (f) \) Freezing of water
\( (g) \) Burning of a candle.


Coefficient of \( \boldsymbol{x}^{\mathbf{5 0}} \)
\( (x>0), \) in \( (1+x)^{1000}+2 x(1+ \)
\( \boldsymbol{x})^{999}+\mathbf{3} \boldsymbol{x}^{2}(\mathbf{1}+\boldsymbol{x})^{998}+\ldots \) is
A. \( 1000 C_{50} \)
B. \( ^{1000} C_{50} \)
c. \( ^{1002} 250 \)
D. \( ^{1000} C_{49} \)


Which is the first group of vascular
plants?
A. Thallophyta
B. Bryophyta
c. Pteridophyta
D. spermatopohyta


Suggest a reason for each observation
given below.
i) In fireworks, powdered magnesium is used rather than magnesium ribbon
ii) Zinc and dilute \( H_{2} S O_{4} \) react much
more quickly when a few drops of copper sulphate solution are added
iii) The reaction between magnesium carbonate and dilute hydrochloric acid speeds up when some concentrated
\( H C l \) is added.


When light rays undergoes two internal reflection inside a raindrop, which of the rainbow is formed.?
A. Primary rainbow
B. Secondary rainbow
c. Both (a) and (b)
D. cant say


Which of the following is/are secondary prefix? This question has multiple correct options
A. Sulpho
B. Carbamoy
c. cyano
D. Isocyanide


Match the column:


The diagonals of a rhombus bisect each
other at \( _{\text {一一一一一一一 }} \) angles.
A . Acute
B. obtuse
c. Right
D. None


Partial roasting of sulfide ore is done in
the metallurgy of copper called
A. smelting
B. self/auto reduction
c. froth floatation
D. none of these


Chalcogens is the common name for some elements present in:
A. IV A group
B. V A group
c. vı A group
D. VI group


In the circle with centre \( \boldsymbol{O}, \boldsymbol{P Q} \) and \( \boldsymbol{R S} \)
are diameters. \( M \) and \( N \) are points on
the arcs \( Q R \) and \( Q S \) respectively and
\( \boldsymbol{R} \boldsymbol{X}=\boldsymbol{S} \boldsymbol{Y} \) then \( \boldsymbol{P} \boldsymbol{X} \boldsymbol{Q} \boldsymbol{Y} \) is a
parallelogram.
A. True
B. False


Construct triangle \( \boldsymbol{A B C} \) in which
\( B C=6 c m, A B-A C=3.1 c m \) and
\( \angle B=30^{\circ} \)


During charging by friction,
A. charge is created.
B. charged is destroyed.
c. charge is conserved.
D. None of these


The \( O N O \) angle is maximum in which
of the following compounds?
\( \mathbf{A} \cdot N O_{3}^{-} \)
в. \( N O_{2}^{-} \)
\( c \cdot N O_{2} \)
D. \( N O_{2}^{+} \)


Darwinism explains all except:
A. Within each species there are variations.
B. Variations are inherited from parents to offspring through genes.
C. Organisms tend to produce more offspring than can survive.
D. Organisms with better traits that overcome competition are best suited under the environment.


Which of the following is an primary alkyl halide?
A. \( C H I_{3} \)
в. \( C H_{3}-C l \)
\( \mathbf{c} \cdot C H_{2}-B r_{2} \)
D. None of these


Hydrolysis constants of two salts \( \boldsymbol{K} \boldsymbol{A} \)
and \( K B \) of weak acids \( H A \) and \( H B \) are
\( 10^{-8} \) and \( 10^{-6} \) respectively. If the
dissociation constant of third acid \( H C \)
is \( 10^{-2} \), then the order of
acidic strengths of three acids is:
A. \( H A>H B>H C \)
в. \( H B>H A>H C \)
c. \( H C>H A>H B \)
D. \( H A=H B=H C \)


The conductivity at infinite dilution of
\( N H_{4} C l, N a O H \) and \( N a C l \) are
\( 130,218,120 o h m^{-1} c m^{2} e q^{-1} . \) If
equivalent conductance of \( \frac{N}{100} \) solution
of \( N H_{4} O H \) IS \( 10, \) then degree of
dissociation of \( N H_{4} O H \) at this
dilution is:
A. 0.005
B. 0.043
c. 0.015
D. 0.025


Keeping the source frequency equal to
the resonating frequency of the series
LCR circuit, if the three elements, \( L, C \)
and \( R \) are arranged in parallel, show that the total current in the parallel LCR
circuit is minimum at this frequency.
Obtain the current RMS value in
each branch of the circuit for the
elements and source specified as below
for this frequency.
The figure shows a series LCR circuit
connected to a variable frequency \( 230 V \)
source. \( \boldsymbol{L}=\mathbf{5 . 0 H}, \boldsymbol{C}=\mathbf{8 0} \boldsymbol{\mu} \boldsymbol{F}, \boldsymbol{R}= \)
\( 40 \Omega \)


Find the value of \( \boldsymbol{\theta}, \) if
\( \cot \theta=0.2334 \)


An electron at rest has a charge of
\( 1.6 \times 10^{-19} C . \) It starts moving with a
velocity \( \boldsymbol{v}=\boldsymbol{c} / 2, \) where \( \boldsymbol{c} \) is the speed of
light, then the value the new charge on
it is
\( \mathbf{A} \cdot 1.6 \times 10^{-19} \) Coulomb
B. \( _{1.6} \times 10^{-19} \sqrt{1-\left(\frac{1}{2}\right)^{2}} \) Coulomb
c. \( _{1.6} \times 10^{-19} \sqrt{\left(\frac{1}{2}\right)^{2}-1 \text { Coulomb }} \)
\( \frac{1.6 \times 10^{-19}}{\sqrt{1-\left(\frac{1}{2}\right)^{2}}} \) Coulom


Rectangle ABCD is the image of
rectangle ABCD after which of the
following rotations?
A \( \cdot \) A \( 90^{\circ} \) clockwise rotation about the origin
B. A \( 180^{\circ} \) rotation about the origin
C. \( A 90^{\circ} \) counterclockwise rotation about the origin
D. A \( 90^{\circ} \) counterclockwise rotation about the point (1,1)


Select the coloured and paramagnetic ions.
A \( \cdot C u^{+}, Z n^{2+}, C a^{2+} \)
B \( \cdot S c^{3+}, T i^{4+}, V^{5+} \)
c. \( C u^{2+}, C r^{+}, M n^{2+} \)
D. \( N i^{2+}, C u^{+}, H g^{2+} \)


Choose the correct answer from the
alternatives given.
In most plants carbohydrate is transported from leaves, where it is synthesized, to other parts, where it is
used, in the form of
A. sucrose
B. fructose
c. maltose
D. starch


An arithmetic progression consists of
12 terms whose sum is 354 .The ratio of
the sum of the even terms to the sum of
the odd terms is \( 32: 27 . \) Find the
common difference of the progression.


How the following conversions can be carried out?
Propene to propan-1-ol


Read the following statements and select the correct option.
Statement 1: Ozone layer present in the stratosphere protects the living organisms from harmful UV rays coming from the sun by absorbing nearly all of them.

Statement 2: Ozone formed in the
troposphere by photochemical
reactions as a result of human
activities which is harmful to all living organisms.
A. Both statements 1 and 2 are correct
B. Statement 1 is correct but statement 2 is incorrect
c. statement 1 is incorrect but statement 2 is correct
D. Both statements1 and 2 are incorrect


What is the field in the cavity if a
conductor having a cavity is charged? Does the result depend on the shape and size of cavity or conductor?


Find the sum of the following arithmetic series: \( 2+9+16+23+30+ \)
\( \ldots . . \) to 20 terms.
A. 1310
в. 1340
c. 1370
D. 1350


The enzyme which has polymerising
activity in \( 5^{\prime} \rightarrow 3^{\prime} \) direction but
exonuclease activity in \( 3^{\prime} \rightarrow 5^{\prime} \)
direction only is :
A. RNA polymerase III
B. DNA polymerase II
c. DNA polymerase
D. All of these


All elements of the same group will
have:
A. same electronic configuration
B. similar outer electron configuration
C. same ionization potential value
D. different chemical properties


Predict which compound in each of the following pair is more reactive with \( H C l \) styrene or \( p- \) nitro styrene:
A. styrene
B. \( p \) -nitro styrene
c. Both doesn't react
D. None of these


Which of the following is incorrect regarding natural rubber?
A. It is cis-polyisoprene
B. It is amorphous in nature
c. It has syndiotactic stereochemistry
D. Molecules of rubber have coiled conformation


If a heavy nucleus has N/Z ratio higher than that required for stability, then:
A . it emits \( \beta^{-} \)
B. It emits \( \beta^{+} \)
c. It emits \( \alpha \) particle
D. None of these


Experiments demonstrating the importance of the nucleus in controlling the growth of the cell was performed in
A. Acetabularia
B. Neurospora
c. Fertilised egg of frog
D. star fish egg
E. Leucocytes


\( \frac{1}{a^{2}-x^{2}}= \)
A \( \cdot \frac{1}{a(a-x)}+\frac{1}{2 a(a+x)} \)
s. \( \frac{1}{3 a(a-x)}+\frac{1}{2 a(a+x)} \)
c. \( \frac{1}{2 a(a-x)}+\frac{1}{2 a(a+x)} \)
D. \( \frac{1}{2 a(a-x)}+\frac{1}{a(a+x)} \)


Volume percentage decreases with increase in temperature.
A. True
B. False


Which of the following is not the property of cathode rays: -
A. It produces heating effect
B. It does not deflect in electric field
c. It casts shadow
D. It produces flurosence


A planet has a core and on outer shell of
radii \( \boldsymbol{R} \) and \( 2 \boldsymbol{R} \) respectively. The density
of the core is \( x \) and that of outer shell is
\( y . \) The acceleration due to gravity at
the surface of planet is same as that at
depth \( R \) The ratio of \( x \) and \( y \) is \( \frac{-}{3} . \) Find
\( n \)


Observe the diagram and answer the question. What is the advantage of having this kind of circulation?


Formation of which tissue is example of dedifferentiation?
A. Interfascicular cambium
B. Apical meristem
c. Intrafascicular cambium
D. Intercalary meristem


A bi-convex lens is formed with two
plano-convex lenses as shown in the figure. Refractive index n of the first
lens is 1.5 and that of the second lens is
1.2. Both curved surfaces are of the
same radius of curvature \( \mathrm{R}=14 \mathrm{cm} . \) For
this bi-convex lens, for an object
distance of \( 40 \mathrm{cm}, \) the image distance will be
A. \( -280.0 \mathrm{cm} \)
B. \( 440.0 \mathrm{cm} \)
\( c .21 .5 \mathrm{cm} \)
D. \( 13.3 \mathrm{cm} \)


\( \int 4^{x}\left[\boldsymbol{g}^{\prime}(\boldsymbol{x})+\boldsymbol{g}(\boldsymbol{x}) \log \mathbf{4}\right] \boldsymbol{d} \boldsymbol{x}= \)
A \( \cdot \frac{4^{x}}{\log 4} g(x) \)
в. \( 4^{x} \)
c. \( 4^{x} \log 4 . g(x) \)
D \cdot \( 4^{x} g(x) \)


Let \( a=\hat{i}+2 \hat{j}+3 \hat{k} \) and \( b=3 \hat{i}+\hat{j} . \) Find
the unit vector in the direction of the
\( a+b \)
A \( \cdot \frac{4 \hat{i}+3 \hat{j}+3 \hat{k}}{\sqrt{34}} \)
B. \( \frac{4 \hat{i}+3 \hat{j}+3 \hat{k}}{\sqrt{44}} \)
D. None of these


Which alkene on ozonolysis gives above
mention product? \( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H O} \) and \( \boldsymbol{C H}_{3} \underset{\|}{C} \boldsymbol{C H}_{3} \)
A \( \cdot C H_{3} C H_{2} C H=C\left(C H_{3}\right) \)
B. \( C H_{3} C H_{2} C H=C H C H_{2} C H_{3} \)
c. \( C H_{3} C H_{2} C H=C H C H_{3} \)
D. \( C H_{3}-C_{\text {। }}=C H C H_{3} \)


A stone is moved in a horizontal circle of
radius \( 4 \mathrm{m} \) by means of a string at a height of \( 20 \mathrm{m} \) above the ground. The string breaks and the particle' flies off horizontally, striking the ground 10m away. The centripetal acceleration during circular motion is
A \( \cdot 6.25 m s^{-2} \)
B. \( 12.5 m s^{-2} \)
c. \( 18.75 \mathrm{ms}^{-2} \)
D. \( 25 m s^{-2} \)


The modern idea about ageing is that our body slowly loses the power of defence against the invasion of germs and pathogens. This gradual loss/decrease in the immunity can be attributed to which organ?
A. Spleen
B. Thymus gland
c. Pituitary gland
D. Parathyroid gland


Identify the compound 'X' :
A. Magnesium Nitride
B. Calcium nitride
C . Nitrolim
D. Sodium nitride


A collection of sporangia attached to placenta and covered over by indusium is known as
A. Sporophyll
B. Sorus
c. cone
D. Ramenta


The mercury barometer was invented
by:
A. Celsius
B. fahrenheit
c. Torricelli
D. Bernoulli


Integrate the function \( x \sin 3 x \)


\( \frac{\sin 30^{0}+\tan 45^{0}+\operatorname{cosec} 60^{0}}{\sec 30^{0}+\cos 60^{0}+\cot 45^{0}}= \)


The resistance of a wire at \( 20 C \) is 20
ohms and at \( 500 C \) is 60 ohms. At which
temperature its resistance will be 25 ohm?
A \( \cdot 80^{\circ} \mathrm{C} \)
B . \( 70^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 60^{\circ} C \)
D. \( 50^{\circ} \mathrm{C} \)


Find the first term and common
difference of the A.P.
(i) \( 5,2,-1,-4, \dots \)
(ii) \( \frac{1}{2}, \frac{5}{6}, \frac{7}{6}, \frac{3}{6}, \dots, \frac{17}{6} \)


Removal of fleece of sheep with skin is
A. Shaving
B. Refining
c. shearing
D. None of the above


The main reaction(s) which occur(s) in
blast furnace during extraction of iron from haematite is(are):
This question has multiple correct options
A. \( 2 F e_{2} O_{3}+3 C \rightarrow 4 F e+3 C O_{2} \)
в. \( F e O+S i O_{2} \rightarrow F e S i O_{3} \)
c. \( F e_{2} O_{3}+3 C O \rightarrow 2 F e+3 C O_{2} \)
D. \( C a O+S i O_{2} \rightarrow C a S i O_{3} \)


Find the value of wave number \( (\bar{V}) \) in
term of Rydberg's constant \( \left(R_{H}\right), \) when transition of electron takes place
between two levels of \( H e^{+} \) ion, whose
sum is 4 and difference is 2
A \( \cdot \frac{8}{9} R_{H} \)
В . \( \frac{32}{9} R_{H} \)
c. \( \frac{1}{9} R_{H} \)
D. none of these


\( \operatorname{Let} f(x)=\frac{\ln (1+x \tan x)}{4 x}, x \neq 0 \) is
continuous at \( \boldsymbol{x}=\mathbf{0}, \) then \( \boldsymbol{f}(\mathbf{0}) \) must be
equal to
A . 1
B. 0
\( c .3 \)
D.


State whether true or false:
During dispersion the violet colour suffers the maximum refraction.
A. True
B. False


Which is a polydentate ligand?
A. EDTA
B. Ethylene diamine
c. Oxalate ion
D. co


The solubility of solid in a liquid solution \( _{-1-} \) with a decrease in
pressure.
A . increases
B. decreases
c. remains same
D. none of these


Two artificial satellites of unequal
masses are revolving in a circular orbit around the earth with a constant speed.
Their time periods.
A. will be different.
B. will be same
c. will depend on their masses
D. will depend upon the place of their projection


Which of the following has formaldehyde as one of the starting material?
\( \mathbf{A} \cdot \) Melmac
B. Alkyd resin
c. PAN
D. Acrilan


is used as a Refrigerant.


The area of the coil must be.
A . \( 1.8 m^{2} \)
B. \( 18 m^{2} \)
\( c \cdot 8 m^{2} \)
D. none of these


A decinormal solution of \( A g N O_{3} \) was electrolysed between Pt electrodes. After passing a small current for two hours, a fall of concentration of
0.0005124 equivalent occurred in anodic solution. The mass of copper deposited in copper coulometer placed in series was found to be 0.03879 g.
Find the transport number of \( N O_{3}^{-} \) in
\( A g N O_{3} . \) Write answer to the nearest integer after multiplying transport number calculated with 10.


The motion of planets in the solar
system is an example of the conservation of
A . mass
B. linear momentum
c. angular momentum
D. energy


Assertion
If an object is submerged in fluid at rest, the fluid exerts a force on its
surface.
Reason
The force exerted by the fluid at rest has to be parallel to the surface in contact
with it.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Differentiate the following functions
with respect to \( \boldsymbol{x} \) \( \log \sqrt{\frac{\boldsymbol{x}-\mathbf{1}}{\boldsymbol{x}+\mathbf{1}}} \)


Myosin filaments are localized in
A. z-Band
B. H-Band
c. A-Band
D. None of the above