If equation of line is \( (\boldsymbol{y}-\mathbf{2} \sqrt{\mathbf{3}})= \)
\( \frac{\sqrt{3}+1}{\sqrt{3}-1}(x-2), \) then find the slope


A block of mass \( M \) is hanging over a
smooth and light pulley through a light string. The other end of the string is pulled by a constant force \( \boldsymbol{F} \). The kinetic energy of the block increases by \( 40 J \) in
1 \( s . \) The tension in the string is:
A. \( F \)
в. \( M g \)
c. \( F+M g \)
D. \( F-M g \)


List the hormones secreted by the Kidney.


Find \( : A^{2} \) if
\( \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{3} & \mathbf{2} \\ -\mathbf{5} & \mathbf{1} & \mathbf{0} \\ \mathbf{1} & \mathbf{2} & \mathbf{5}\end{array}\right] \)


\( \ln a \triangle A B C, \) the sides \( A B \) and \( A C \) have
been produced to \( \mathrm{D} \) and \( \mathrm{E} \). Bisectors of \( \angle C B D \) and \( \angle B C E \) meet at \( 0 . \) If \( \angle A= \)
\( 64^{0}, \) then \( \angle B O C \) is
\( A \cdot 52^{0} \)
B. \( 58^{\circ} \)
\( c \cdot 26^{0} \)
D. \( 112^{\circ} \)


A student measures the time period of
100 oscillations of a simple pendulum four times. The data set is
\( 90 s, 91 s, 95 s \) and \( 92 s . \) If the minimum
division in the measuring clock is \( 1 s \) then the reported mean time should be:
A \( .92 \pm 2 s \)
В. \( 92 \pm 5.0 s \)
c. \( 92 \pm 1.8 s \)
D. \( 92 \pm 3 \) s


When a silver foil (Z=47) was used in an
\( \alpha \) -ray scattering experiment, the
number of \( \alpha \) partied scattered at \( 30^{\circ} \)
aws found to be 200 per minute. If the silver foil is replaced by aluminium \( (z=13) \) foil of same thickness, the
number of \( \alpha \) -particles scattered per
minute at \( 30^{\circ} \) is nearly equal to
A . 15
B. 30
c. 10
D. 26


The correct order of ionic radii of
\( \boldsymbol{Y} \boldsymbol{b}^{3+}, \boldsymbol{L} \boldsymbol{a}^{3+}, \boldsymbol{E} \boldsymbol{u}^{3+} \) and \( \boldsymbol{L} \boldsymbol{u}^{3+} \) is:
\( \mathbf{A} \cdot Y b^{3+}>L u^{3+}>E u^{3+}>L a^{3+} \)
B. \( L u^{3+}<Y b^{3+}<E u^{3+}<L a^{3+} \)
c. \( L u^{3+}<E u^{3+}<L a^{3+}<Y b^{3+} \)
D. \( L a^{3+}<E u^{3+}<L u^{3+}<Y b^{3+} \)


Which of the following is not a colloid?
A. Smoke
B. Haemoglobin
c. Latex
D. Air


A ball moving with a speed of \( 30 \mathrm{m} / \mathrm{s} \)
hits the wall and bounces back with
same speed. The contact time between the ball and the wall is 0.1 s. Calculate
the force exerted by the wall on the ball if mass of the ball is 0.25kg.
A. on
B. - 100N
c. - 300N
D. - 150N
E. \( 100 N \)


A body weighs \( 60 \mathrm{kg} \) on the earth's surface. What would be its weight at the centre of the earth?
A. 60 kg-wt
B. 6 kg-wt
c. \( 60 \times 9.8 \mathrm{kg} \) -wt
D. zero


Which is the lightest gas?
A . \( N_{2} \)
в. \( H e \)
\( c \cdot O_{2} \)
D. \( H_{2} \)


A convex lens forms a real image three
times larger than the object on a screen Object and screen are moved until the
image becomes twice the size of the
object. If the shift of the object is \( 6 \mathrm{cm} \)
The shift of screen is
\( \mathbf{A} \cdot 36 c m \)
B. \( 72 \mathrm{cm} \)
\( \mathbf{c} \cdot 18 c m \)
D. 9 cm


Two particles each of the same mass move due north and due east
respectively with the same velocity \( ^{\prime} V^{\prime} \) The magnitude and direction of the velocity of the center of mass is:
A \( \cdot \frac{V}{\sqrt{2}} N E \)
в. \( \sqrt{2} V N E \)
c. \( 2 V S W \)
D. \( \frac{V}{2} S W \)


Which of the following is the correct word to indicate the molar mass of an
ionic substance?
A. Molecular weight
B. Formula weight
c. Equivalent weight
D. All


The number of electrons that must be
removed from an electrically neutral silver dollar to give it a charge of \( +2.4 C \)
is
A \( .2 .5 \times 10^{19} \)
B. \( 1.5 \times 10^{19} \)
c. \( 1.5 \times 10^{-19} \)
D. \( 2.5 \times 10^{-19} \)


How is chemosynthesis and
photosynthesis similar?
A. Both are found in hydrophytes
B. Both are associated with heterotrophy
C. Both are dependent on solar energy
D. Both are autotrophic mode of nutrition


\( 0.10 g \) of an organic compound containing phosphorus gave \( 0.222 g \) of
\( M g_{2} P_{2} O_{7} . \) Then, the percentage of
phosphorus in it is:
A . 62\%
в. 6.२\%
c. 31\%
D. 13\%


What should be added to \( 4 \frac{8}{15} \) to get \( 9 \frac{2}{5} \) \( ? \)


Reactions in which energy is absorbed are known as............. reactions.
A. endothermic
B. exothermic
c. synthesis
D. combination


and mass \( 1 k g \) are placed (fixed) symmetrically about a movable central charges of magnitude \( 5 \times 10^{-5} C \) and
mass \( 0.5 k g \) as shown. The charge at \( P_{1} \) is removed. The acceleration of the
central charge is
\( \left[\text { Given } \boldsymbol{O} \boldsymbol{P}_{1}=\boldsymbol{O} \boldsymbol{P}_{2}=\boldsymbol{O} \boldsymbol{P}_{3}=\boldsymbol{O} \boldsymbol{P}_{4}=\right. \)
\( O P_{5}=1 m ; \frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9} \) in \( S I \) units
\( A \cdot 9 m s^{-2} \) upwards
B. \( 9 m s^{-2} \) downwards
c. \( 4.5 m s^{-2} \) upwards
D. \( 4.5 m s^{-2} \) downwards


How many isomeric dienes with a six-
membered ring are possible for the
compound with molecular formula \( \mathrm{C}_{7} \mathrm{H} \)
\( 10 ? \)
A. 5
B. 6
c. 7
D. 8


Which one of the following is a correct
set?
A \( \cdot C l_{2} O, s p^{3}, \) Angular
B. \( B F_{3}, s p^{2}, \) T-shape
C. \( S O_{3}, s p^{3}, \) Trigonal pyramidal
D. \( N O_{2}, s p, \) Linear
E. \( S F_{4}, s p^{3} d^{2}, \) Square pyramidal


The name of the water reservoirs in the
figure is
A. Pond
B. Dam
C. Ocean
D. None of the above


Coal, natural gas and petroleum are examples of This question has multiple correct options
A . fossils
B. natural resources
c. artificial resources
D. fuels


Two small bar magnets are placed in a line at certain distance \( d \) part. If the
length of each magnet is negligible compared to \( d \), the force between them will be inversely proportional to:
\( \mathbf{A} \cdot d^{2} \)
B. \( d \)
\( c \cdot d^{3} \)
D. \( d^{4} \)


Evaluate the integrals:
\( \int(2 x+9)^{5} d x \)


Which statements concerning Bohr's
model are true?
This question has multiple correct options
A. Predicts that probability of electron near nucleus is
more
B. Angular momentum of electron in H-atom \( =\frac{n h}{2 \pi} \)
C. Introduces the idea of stationary states
D. Explain line spectrum of hydrogen


At what rate, in mega gram per minute, must hydrogen be consumed in fusion reaction to provide the sun with the energy it radiates? (Take mass defect
per reaction to be 0.028706 a.m.u)
A . \( 3.66 \times 10^{14} \) mega gram \( \min ^{-1} \)
B. \( 3.66 \times 10^{16} \) mega gram \( \min ^{-1} \)
C. \( 3.66 \times 10^{15} \) mega gram \( \min ^{-1} \)
D. 3.66 \( \times 10^{10} \) mega gram \( \min ^{-1} \)


Number of electrons present in the antibonding axially overlapping orbital
in \( N O^{+}, \) are:
A .4
B . 2
\( c .6 \)
D.


\( \lim _{x \rightarrow \sqrt{10}} \frac{\sqrt{7+2 x}-(\sqrt{5}+\sqrt{2})}{x^{2}-10} \) is equal to
A \( \cdot \frac{1}{\sqrt{40}(\sqrt{5}+\sqrt{2})} \)
B. \( \frac{-1}{\sqrt{10}[\sqrt{7+2 \sqrt{10}}+\sqrt{5}+2]} \)
c. 1
D. \( \frac{1}{\sqrt{10}(\sqrt{5}+\sqrt{2})} \)


If \( \mathrm{A}=\left[a_{i j}\right]_{2 \times 2} \) such that \( a_{i j}=i-j+3 \)
then find \( \boldsymbol{A} \)
\( \mathbf{A} \cdot\left[\begin{array}{ll}2 & 3 \\ 4 & 2\end{array}\right] \)
в. \( \left[\begin{array}{ll}3 & 4 \\ 2 & 3\end{array}\right] \)
c. \( \left[\begin{array}{ll}4 & 2 \\ 2 & 3\end{array}\right] \)
D. \( \left[\begin{array}{ll}3 & 2 \\ 4 & 3\end{array}\right] \)


Obtain the product of \( 2,4 y, 8 y^{2}, 16 y^{3} \)
A \( \cdot 1045 y^{5} \)
В. \( 1024 y^{6} \)
c. \( 1634 y^{3} \)
D. \( 102 y^{5} \)


In which case will the particle move in a
straight line with constant velocity?
A \( .(I I)(i i i)(S) \)
B. \( (I I I)(i i)(R) \)
D. \( (I I I)(i i i)(P) \)


In the figure given below, the value of
\( (\angle x+\angle y) \) is :
4. \( 110^{\circ} \)
B . \( 100^{\circ} \)
\( c \cdot 120 \)
D. \( 60^{\circ} \)


For a given surface the Gauss's law is stated as \( \int E \cdot d s=0 . \) From this we can conclude that:
A. \( E \) is necessarily zero on the surface
B. \( E \) is perpendicular to the surface at every point
c. the total flux through the surface is zero
D. the flux is only going out of the surface


In a common base transistor circuit, the
current gain is \( 0.98 . \) On changing the emitter current by \( 5.00 \mathrm{mS} \), the change
in collector current is?
A. \( 0.196 \mathrm{mA} \)
B. \( 2.45 \mathrm{mA} \)
c. \( 4.9 \mathrm{mA} \)
D. \( 5.1 \mathrm{m} \) A


Solid \( C O_{2} \) is known as dry ice because:
\( \mathbf{A} \cdot \) it melts at \( 0^{\circ} C \)
B. its b.p. is more than \( 199^{\circ} \mathrm{C} \)
C . it evaporates at \( -78^{\circ} \mathrm{C} \) without melting
D. none of the above


Which of the following can be zero, when a particle is in motion for some time?
A. Distance
B. Displacement
c. speed
D. None of these


Evaluate the following integral:
\( \int_{-1}^{1}|2 x+1| d x \)


The 8 th term of the sequence 1,1,2,3,5
8
is
A . 25
B. 24
\( c \cdot 23 \)
D. 21


A sonar device on a submarine sends
out a signal and receives an echo \( 5 s \)
later. Calculate the speed of sound in water if the distance of the object from
the submarine is \( 3625 m \)


ff \( f(x)=2 x-5, \) then what is the value
of \( \boldsymbol{f}(\mathbf{2})+\boldsymbol{f}(\mathbf{5}) ? \)


Which metal plays an important role in neuromuscular functions,
interneuronal transmissions, cell
membrane integrity and blood coagulation?
\( A \cdot B e \)
в. Мв
\( c \cdot c a \)
D. Ba


Which term of the A.P. 5,12,19,26
is 145
A . 12
B. 18
\( c \cdot 25 \)
D. 21


Aftab tells his daughter, "Seven years ago, I was seven times as old as you were then. Also, three years from now, shall be three times as old as you will be." Is not this interesting? Represent this situation algebraically.


Hydrogen at the moment of its generation (newly born hydrogen) is generally called:
A. protium
B. nascent hydrogen
c. atomic hydrogen
D. heavy hydrogen


A body of mass ' \( m \) ' is raised to a height
\( 10 R^{\prime} \) from the surface of the Earth,
where ' \( R^{\prime} \) is the radius of the Earth. The
increase in potential energy is \( G= \) universal constant of gravitation,
\( M= \) mass of earth and \( g= \) acceleration due to gravity)
\( ^{A} \cdot \frac{G M m}{11 R} \)
в. \( \frac{G M m}{10 R} \)
c. \( \frac{m g R}{11 G} \)
D. \( \frac{10 G M m}{11 R} \)


Gravity separation process is used for the concentration of
A. calamine
B. haematite
c. chalcopyrites
D. bauxite


Who was the first person to set foot on the moon?
A. Neil Armstrong
B. Yuri Gagarin
c. valentina Tereshkova
D. Steven Sptelberg


Choose the correct statements:
This question has multiple correct options
A. It is easier to fabricate 10000 AND gates using circuit components than on an integrated chip.
B. It is easier to fabricate 10000 AND gates on an integrated chip than fabricating them using circuit components.
C. It is easier to fabricate a single AND gate using circuit components as compared to on an IC.
D. It is easier to fabricate a single AND gate on an IC as compared to using circuit components.


Evaluate: \( \lim _{x \rightarrow 0} \frac{e^{\alpha x}-e^{\beta x}}{\sin \alpha x-\sin \beta x} \)


State the function of \( \boldsymbol{N a O H} \)


Q Type your question
light string of length 2a. The whole
system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance a from centre P(as shown in the figure)
Now, the mid-point of the string is pulled vertically upwards with a small but constant force \( F \). As a result, the
particles move towards each other on the surface. The magnitude of acceleration, when the separation
between them becomes \( 2 x \) is:
\( ^{A} \cdot \frac{F}{2 m} \frac{a}{\sqrt{a^{2}-x^{2}}} \)
в. \( \frac{F}{2 m} \frac{x}{\sqrt{a^{2}-x^{2}}} \)
c. \( \frac{F}{2 m} \frac{x}{a} \)
D. \( \frac{F}{2 m} \frac{\sqrt{a^{2}-x^{2}}}{x} \)


The synthetic polymer which resembles natural rubber is:
A. Neoprene
B. Buna-s
c. Nylon
D. Rayon


The coil \( X \) and \( Y \) have the same number
of turns and length. Each has a flux
density \( B \) in the middle and a flux
density \( 0.5 B \) at the ends when carrying the same current. When the coils are
joined to form a long coil of twice the
length of \( X \) or \( Y \) and the current \( I \) is sent through the coil, the flux density in the middle is given by:
A. 0
в. \( 0.5 B \)
c. \( 2 B \)
D. \( B \)


\( C_{v} \) for ammonia gas is
\( \left(i n J m o l^{-1} K^{-1}\right) \)
A . 29.0
в. 12.5
c. 20.7
D. 31.2


Which of the following are uses of ductility of metals?
A. Thin electrical wires
B. Electrical pipes
c. Plates
D. All of the above


Rusting of iron is:
A. an oxidation reaction
B. a reduction reaction
c. a redox reaction
D. a displacement reaction


A sphere of mass m moving with a constant velocity hits another stationary sphere of the same mass. If e is the coefficient of restitution, then a
ratio of the speed of the first sphere to the speed of the second sphere after head-on collision will be:
\( ^{A} \cdot\left(\frac{1-e}{1+e}\right) \)
в. \( \left(\frac{1+e}{1-e}\right) \)
c. \( \left(\frac{e+1}{e-1}\right) \)
D. \( \left(\frac{e-1}{e+1}\right) \)


If 1 degree \( =0.017 \) radians, then the
approximate value of \( \sin 46 \) degrees is
A .0 .7194
B. \( \frac{0.017}{\sqrt{2}} \)
c. \( \frac{1.017}{\sqrt{2}} \)
D. none of these


Which one of the following statements
is not correct with reference to a
histogram?
A. Frequency curve is obtained by joining the midpoints of the top of the adjacent rectangles with smooth curves
B. Histogram is drawn for continuous data
C. The height of the bar is proportional to the frequency of that class
D. Mode of the distribution can be obtained from the
histogram


What can you say about the nature of motion of a body if its displacementtime graph is a straight line parallel to
time axis ?
A. body is stationary (or no motion)
B. body has non zero acceleration
c. body has non zero velocity
D. None of the above


\( M g^{2+}+2 e^{-} \rightarrow M g ; E_{c e l l}^{\circ}(V)=-2.37 \)
\( \boldsymbol{C u}^{2+}+\mathbf{2} e^{-} \rightarrow \boldsymbol{C u} ; \boldsymbol{E}_{c e l l}^{\circ}=\mathbf{0 . 3 4} \)
Analyze the data above.
Which substance should be used for
electrode B in this galvanic cell?
A \( \cdot M g^{2} \)
в. \( M g \)
\( c \cdot C u^{2} \)
D. \( C_{7} \)


Aluminate ion in aqueous solution actually exists as:
\( \mathbf{A} \cdot\left[A l(O H)_{6}\right]^{3} \)
в. \( \left[A l(O H)_{4}\left(H_{2} O\right)_{2}\right]^{-} \)
\( \mathbf{c} \cdot\left[A l(O H)_{3}\left(H_{2} O\right)_{3}\right. \)
D・ \( \left[A l(O H)_{5} H_{2} O\right]^{-2} \)


During an isothermal expansion, a confined ideal gas does 150 J of work against its surroundings. This implies
that:
A. 150 J of heat has been removed from the gas
B. 300 J of heat has been added to the gas
c. no heat is transferred because the process is isothermal
D. 150 J of heat has been added to the gas


Which of the following \( \alpha \) -amino acids does not contain a chiral carbon?
A . Glycine
B. Alanine
c. Phenylalanine
D. valine


The force \( F \) acting on a particle of mass
1 kg is indicated by the force-time graph
as shown. If the partial starts from rest,
then the speed of the particle at the end
of 6 s will be
\( \mathbf{A} \cdot 3 \mathrm{m} \cdot^{-1} \)
B. \( 12 \mathrm{m} \mathrm{s}^{-1} \)
\( \mathbf{C} \cdot 9 m s^{-1} \)
D. \( 18 \mathrm{m} \mathrm{s}^{-1} \)


What is \( i^{1000}+i^{1001}+i^{1002}+i^{1003} \) equal
to (where \( \boldsymbol{i}=\sqrt{-1} \) )?
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot-i \)
\( D \)


Which oxyacid of sulphur contains \( \boldsymbol{S}- \)
\( \boldsymbol{S} \) single bond?
A. Oleum
B. Marshall's acid
c. Dithionic acid
D. Thiosulphuric acid


Fill in the blanks:
\( N a C l \) an electrovalent compounds is formed as a result of tranfer of
[one,two, three] valence electrons from metallic sodium to non-metallic
chlorine atom. \( C a O \) is similarly formed
as a result of transfer of [one,
two, three] valence electrons from
metallic calcium to non-metallic
oxygen and magnesium chloride by transfer of \( _{----} \) [one, two, three] valence electrons from \( _{---} \) [one, two] magnesium atom/s to [one, two]
chlorine atom/s.


Sieve tubes differ from sieve cells in
A. Being shorter
B. Being dead
c. Lacking nuclei
D. Having sieve pores at end walls


The wind flows from
A. High pressure to low pressure
B. Low pressure to high pressure
C. Low temperature to high-temperature
D. All of the above


The work function of a substance is
4.0 \( e V \). The longest wavelength of light that can cause photo-electric emission from this substance is approximately
A . \( 220 \mathrm{nm} \)
в. 310 пт
\( c .540 n m \)
D. 400 nm


\( \therefore \)


\( = \)
\( \sigma \)
\( \sigma \)


Platelets helps in
A. Transport of gases
B. clotting
C. Fight against disease
D. None of the above


What gives a perception of depth or three dimensional vision to human eye?


Solve \( (-10)^{3}+(7)^{3}+(3)^{3} \)


Fill in the blanks with approriate words. After deep inspiration, capacity of
maximum expiration of lungs is called


Elements of the group- 15 form
compounds in +5 oxidation state. However, bismuth forms only one wellcharacterized compound in +5 oxidation state. The compound is:
A. \( B i_{2} O_{5} \)
в. \( B i F_{5} \)
c. \( B i C l_{5} \)
D. \( B i_{2} S_{5} \)


Hydrogen gas adsorbed on surface of platinum is an example of solid in gas solution.
A. True
B. False


Two coins are tossed simultabeously.
Find the probability of getting:
(i) at least one Tail
(ii) atmost two Head
(iii) one Head


Mark the following rational numbers on
the number line.
\( \frac{1}{2} \)


If the path difference between the slits
\( S_{1} \) and \( S_{2} \) is \( \lambda, \) the central fringe will
have an intensity of
A. 0
B . \( a^{2} \)
\( c \cdot 2 a^{2} \)
D. \( 4 a^{2} \)


A point charge -q placed at the point \( \mathbf{A} \)
is
This question has multiple correct options
A. In stable equilibrium along x-axis.
B. In unstable equilibrium along y-axis
c. In stable equilibrium along y-axis.
D. In unstable equilibrium along x-axis.


Two current carrying wires are a
distance \( a \) apart and experience a Force
\( F \) between them. The wires are moved a
distance \( 2 a \) apart. Which of the following is a possible value for the new force between the
wires?
A \( \cdot \frac{1}{4} F \)
в. \( \frac{1}{2} \)
\( c . F \)
D. \( 2 F \)
E . \( 4 F \)


As longer the interaction between two
objects exist
A. The force remains
B. The force stops after the initial interaction
c. Both a and
D. The force remains for a specific time interval


Name the following compound according to the IUPAC system or
nomenclature.
\( \boldsymbol{p}-\boldsymbol{O} \boldsymbol{H} \boldsymbol{C} \boldsymbol{C}_{6} \boldsymbol{H}_{4} \boldsymbol{C} \boldsymbol{H} \boldsymbol{O} \)


If \( a \neq b \neq c, \) the value of \( x \) which
satisfies the question \( \left|\begin{array}{ccc}\mathbf{0} & \boldsymbol{x}-\boldsymbol{a} & \boldsymbol{x}-\boldsymbol{b} \\ \boldsymbol{x}+\boldsymbol{a} & \mathbf{0} & \boldsymbol{x}-\boldsymbol{c} \\ \boldsymbol{x}+\boldsymbol{b} & \boldsymbol{x}+\boldsymbol{c} & \mathbf{0}\end{array}\right|=\mathbf{0} \) is
\( \mathbf{A} \cdot x=0 \)
B. \( x=a \)
\( \mathbf{c} \cdot x=b \)
D. \( x=c \)


In which reactants are not contained
within the cell but are continuously supplied from external source?
A. Fuel cell
B. Dry cell
c. Lithium battery
D. Lead storage battery


The phases of the light wave at \( \mathbf{c}, \mathbf{d}, \mathbf{e} \)
and \( \mathbf{f} \) are \( \phi_{\mathrm{c}}, \phi_{\mathrm{d}}, \phi_{\mathrm{e}} \) and \( \phi_{\mathrm{f}} \) respectively.
It is given that \( \phi_{\mathrm{c}} \neq \phi_{\mathrm{f}} \)
A \( \cdot \phi_{\mathrm{c}} \) cannot be equal to \( \phi_{\mathrm{d}} \)
B. \( \phi_{\mathrm{d}} \) can be equal to \( \phi_{\mathrm{e}} \)
C \( \cdot\left(\phi_{\mathrm{d}}-\phi_{\mathrm{f}}\right) \) is equal to \( \left(\phi_{\mathrm{c}}-\phi_{\mathrm{e}}\right) \)
\( \mathbf{D} \cdot\left(\phi_{\mathrm{d}}-\phi_{\mathrm{c}}\right) \) is not equal to \( \left(\phi_{\mathrm{f}}-\phi_{\mathrm{e}}\right) \)


Select the correct schematic
representation of blood circulation in
human from the following.
\( A \)
B.
\( c \)
D.


If, is continuous at \( x=2, \) find the value
of \( k \)
\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{ll}\frac{\boldsymbol{x}^{3}+\boldsymbol{x}^{2}-\mathbf{1 6} \boldsymbol{x}+\mathbf{2 0}}{(\boldsymbol{x}-\mathbf{2})^{2}}, & \boldsymbol{x} \neq \mathbf{2} \\ \boldsymbol{k}, & \boldsymbol{x}=\mathbf{2}\end{array}\right. \)


Parthenocarpy can be induces by increasing the concentration of
A . Gibberelic acid
B. Auxin
c. cytokinin
D. Ethylene


4 molecules of gas have speeds of \( 1,2,3,4 \mathrm{cm} / \mathrm{s} \) respectively. The root mean square velocity is:
A. \( \sqrt{7.5} \mathrm{cm} / \mathrm{s} \)
B. 30 cm/s
c. \( 45 \mathrm{cm} / \mathrm{s} \)
D. \( 15 \mathrm{cm} / \mathrm{s} \)


Fill in the blank:
The size of the visible part of the Moon gradually after the full moon
day till the new moon day.
A. remains the same
B. increases
c. decreases
D. either increases or decreases


Express 1.2 rad in nereast integer
degree measure.


\( y=\frac{x^{2}}{1+x} \) Find \( \frac{d y}{d x} \)


Quantity of matter contained in a body
is
A. Mass
B. density
c. relative density
D. volume


\( \boldsymbol{K}_{p} \) values for, \( \boldsymbol{C}_{2} \boldsymbol{H}_{4}+\boldsymbol{H}_{2} \rightleftharpoons \boldsymbol{C}_{2} \boldsymbol{H}_{6}, \) is
\( \mathbf{5} \times \mathbf{1 0}^{18} \mathbf{a t m}^{-1} \) and \( \boldsymbol{K}_{p} \) for, \( \boldsymbol{C}_{2} \boldsymbol{H}_{2}+ \)
\[
\boldsymbol{H}_{2} \rightleftharpoons \boldsymbol{C}_{2} \boldsymbol{H}_{4}, \text { is } \mathbf{5} \times \mathbf{1 0}^{26} \boldsymbol{a} \boldsymbol{t} \boldsymbol{m}^{-1} \text {at } \mathbf{5 0 . ~ I f}
\]
\( \boldsymbol{K}_{\boldsymbol{p}} \) for :
\[
\mathbf{2} \boldsymbol{H}_{2}+\boldsymbol{C}_{2} \boldsymbol{H}_{2} \rightleftharpoons \boldsymbol{C}_{2} \boldsymbol{H}_{6} \text { is } \boldsymbol{x} \times
\]
\( 10^{45}, \) then \( 10 x \) is


Curie temperature is the temperature
above which
A. a paramagnetic material becomes ferromagnetic
B. a ferromagnetic material becomes paramagnetic
C . a paramagnetic material becomes diamagnetic
D. a ferromagnetic material becomes diamagnetic


f \( n(U)=50, n(A)=20, n\left((A \cup B)^{\prime}\right)=18 \)
then \( n(B-A) \) is
A . 14
B. 12
c. 16
D. 20


The correct IUPAC name of the following
compounds is :
A. \( 1, \) 2-dimethylpropyleyelopropane
B. 2-cyclopropyl-3-methylbutane
C. 2 -methyl-3-cyclopropylbutane
D. isopentylcyclopropane


The acid used in the detection of
phosphorus in an organic compound is:
A \( \cdot H_{2} S O_{4} \)
в. \( H N O_{3} \)
c. \( H C l \)
D. any of the above


Name the pioneer and the climax species in a water body. Mention the changes observed in the biomass and the biodiversity of the successive seral communities developing in the
water body


A parallel plate capacitor is to be designed with a voltage rating \( 1 \mathrm{kV} \) using a material of dielectric constant
3 and dielectric strength about \( \mathbf{1 0}^{\mathbf{7}} \boldsymbol{V} \boldsymbol{m}^{-1} . \) (Dielectric strength is the
maximum electric field a material can
tolerate without breakdown, i.e., without
starting to conduct electricity through partial ionisation.) For safety, we should like the field never to exceed, say \( 10 \% \) of the dielectric strength.What minimum area of the plates is required to have a capacitance of 50 pF ?


An oligosaccharide (A) on hydrolysis gives 5 molecules of aldohexoses. The number of 'H' atoms in 1 molecule of (A)
are equal to \( 10 x+y \) where \( x \) and \( y \) are single digit natural numbers. Calculate(x-y).


Self-reduction of the sulphide ore takes place during:
A. roasting
B. smelting
c. calcination
D. cupellation


Designs of wallpapers and fabrics are obtained with the help of:
A. periscopes
B. kaleidoscopes
c. telescopes
D. microscopes


If \( S_{n}=\sum_{n}^{r=0} \frac{1}{n C_{r}} \) and \( t_{n}=\sum_{n}^{r=0} \frac{r}{n C_{r}} \)
then \( \frac{t_{n}}{S_{n}} \) is equal to
A \( \cdot \frac{1}{2} n \)
в. \( \frac{1}{2} n-1 \)
\( c \cdot n-1 \)
D. \( \frac{2 n-1}{2} \)


Name an anthrogenic ecosystem.


Solve the following quadratic equations by factorization method:
\( \mathbf{3}\left(x^{2}-6\right)=x(x+7)-3 \)
A \( \cdot\left\{-\frac{3}{2}, 5\right\} \)
в. \( \left\{\frac{3}{2}, 5\right\} \)
\( ^{c} \cdot\left\{-\frac{3}{2},-5\right\} \)
D. None of these


A mixture of two immiscible liquids at
a constant pressure of 1.0 atm boils at
temperature
A. Equal to the normal boiling point of more volatile liquid
B. Equal to the mean of the normal boiling points of two liquids.
C. Greater than normal boiling point of either of liquids.
D. Smaller than the normal boiling point of either of liquids.


An inverted cone has a depth of \( 40 \mathrm{cm} \)
and a base of radius \( 5 \mathrm{cm} \). Water is
poured into it at a rate of 1.5 cubic centimetres per minute. Find the rate at
which the level of water in the cone is
rising when the depth is 4 cm.


Meter bridge works on the principle of


The energy of the first orbit of \( \boldsymbol{H} \boldsymbol{e}^{+} \) is \( -871.6 \times 10^{-20} J . \) The energy of the
electron in the first orbit of hydrogen would be:
\( \begin{array}{lll}\text { A. }-871.6 \times & 10^{-20} J\end{array} \)
B . \( -435.8 \times \quad 10^{-20} J \)
\( \begin{array}{lll}\text { C. }-217.9 \times & 10^{-20} J\end{array} \)
\begin{tabular}{ll}
D. \( -108.9 \times \) & \( 10^{-20} \mathrm{J} \) \\
\hline
\end{tabular}


If \( a_{r}>0, r \epsilon N \) and \( a_{1}, a_{2}, a_{3}, \dots, a_{2 n} \) are in
AP then
\( \frac{\boldsymbol{a}_{1}+\boldsymbol{a}_{2 n}}{\sqrt{\boldsymbol{a}_{1}}+\sqrt{\boldsymbol{a}_{2}}}+\frac{\boldsymbol{a}_{2}+\boldsymbol{a}_{2 n-1}}{\sqrt{\boldsymbol{a}_{2}}+\sqrt{\boldsymbol{a}_{3}}}+ \)
\( \frac{\boldsymbol{a}_{\boldsymbol{3}}+\boldsymbol{a}_{\boldsymbol{2} \boldsymbol{n}-\boldsymbol{2}}}{\sqrt{\boldsymbol{a}_{\boldsymbol{3}}}+\sqrt{\boldsymbol{a}_{\boldsymbol{4}}}}+\ldots+\frac{\boldsymbol{a}_{\boldsymbol{n}}+\boldsymbol{a}_{\boldsymbol{n}+1}}{\sqrt{\boldsymbol{a}_{\boldsymbol{n}}}+\sqrt{\boldsymbol{a}_{\boldsymbol{n}+\mathbf{1}}}} \)
is equal to
A . n-
B. \( \frac{n\left(a_{1}+a_{2 n}\right)}{\sqrt{a_{1}}+\sqrt{a_{n+1}}} \)
c. \( \frac{n-1}{\sqrt{a_{1}}+\sqrt{a_{n+1}}} \)
D. none of these


Incomplete combustion of petrol or diesel oil in automobile engines can be best detected by testing the fuel gases
for the presence of
A. carbon Monoxide and water vapour
B. carbon monoxide
c. nitrogen dioxide
D. sulphur dioxide


For a process to be spontaneous, \( \Delta G \)
must be:
A . negative.
B. positive
c. zero
D. None of these


Prove that:
\[
\frac{3^{-3} \times 6^{2} \times \sqrt{98}}{5^{2} \times \sqrt[3]{1 / 25} \times(15)^{-4 / 3} \times 3^{1 / 3}}=
\]
\( 28 \sqrt{2} \)


A beam of light converges at a point \( \mathrm{P} \) Now a lens is placed in the path of the convergent beam \( 12 \mathrm{cm} \) from P. At what
point does the beam converge if the lens
is
(a) a convex lens of focal length 20 \( \mathrm{cm}, \) and (b) a concave lens of focal
length \( 16 \mathrm{cm} ? \)


Which of the following fuel is a mixture of butane and propane?
A . LPG
в. смG
c. Petroleum
D. Kerosene


Iron reacts with conc. \( H C l \) and conc.
\( H_{2} S O_{4} . \) But it does not react with conc
\( H N O_{3} . \) Suggest your answer with
proper reason.


Find the charge appearing on capacitor
of capacitance \( 4 \mu F \)
A \( .32 \mu C C \)
B. \( 96 \mu C \)
c. \( 12 \mu C \)


The displacement of a particle starting from rest \( (a t t=0) \) is given by \( s= \)
\( 6 t^{2}-t^{3} . \) The time at which the particle
will attain zero velocity again is
A . \( 4 s \)
B. 8 s
\( c \cdot 12 s \)
D. 16 \( s \)


Charge distribution in iodine
monochloride is best represented as:
\( \mathbf{A} \cdot I^{+} C l \)
B . \( I^{\delta+}-C l^{\delta-} \)
c. \( I^{-} C l^{+} \)
D. \( I^{\delta-}-C l^{\delta+} \)


The force between two charge bodies is
called
A. muscular force
B. gravitational force
c. magnetic force
D. electrostatic force


The metal whose oxide, which is
amphoteric, is reduced to metal by
carbon reduction
\( (\boldsymbol{F} \boldsymbol{e} / \boldsymbol{M} \boldsymbol{g} / \boldsymbol{P b} / \boldsymbol{A l}) \)


Which of the following points are collinear?
A . (2a,0), (3a,0), (a, 2a)
в. \( (3 a, 0),(0,3 b),(a, 2 b) \)
c. \( (3 a, b),(a, 2 b),(-a, b) \)
D. (a,-6),(-a,3b),(-2a,-2b)


The reaction at hinge 1 , before hinge 2 breaks, is:
A \( .24 N \)
в. 12 N
\( c \cdot 11 N \)
D. \( 10 N \)


Why don't two magnetic lines of force intersect with each other?


The equation of the straight line passing through the point of intersection of the straight lines \( \frac{x}{a}= \) \( \frac{\boldsymbol{y}}{\boldsymbol{b}}=1 \) and \( \frac{\boldsymbol{x}}{\boldsymbol{b}}+\frac{\boldsymbol{y}}{\boldsymbol{a}}=\mathbf{1} \) and having
infinite slopes is


Mendel's experiments stand for


Let
\( \boldsymbol{p}: \mathbf{5 7} \) is an odd prime number \( q: 4 \) is a divisor of 12 \( \boldsymbol{r}: \mathbf{1 5} \) is the LCM of \( \boldsymbol{3} \) and \( \mathbf{5} \)
be three simple logical statements. Which one of the following is true?
A \( . p \vee(\sim q \wedge r) \)
В \( . \sim p \vee(q \wedge r) \)
c. \( (p \wedge q) \vee \sim r \)
D. \( (p \vee(q \wedge r) \)
E . \( (p \vee q) \wedge r \)


Which of the following oxoacids of phosphorous is a reducing agent and a monobasic acid as well
A \( \cdot H_{4} P_{2} O_{5} \)
в. \( H P O_{3} \)
\( \mathrm{c} \cdot H_{3} P O_{3} \)
D. \( H_{3} P O_{2} \)


A line \( A B \) in three-dimensional space
males angles \( 45^{\circ} \) and \( 120^{\circ} \) with the
positive \( x \) -axis and the positive \( y \) -axis respectively. If \( A B \) makes an acute
angle \( \theta \) with the positive z-axis, then \( \theta \)
equal
A \( \cdot 45^{\circ} \)
В. \( 60^{\circ} \)
\( \mathrm{c} \cdot 75^{\circ} \)
D. \( 30^{\circ} \)


As temperature of medium increases
the critical angle :
A. Increases
B. Decreases
c. Remains same
D. First increases then decreases


How an atom becomes a negative ion, if:
A. a proton leaves the atom
B. an electron joins the atom
c. an electron leaves the atom
D. a protonjoins the atom
E. a proton and an electron leave the atom


Which of the following statements
is/are wrong?
This question has multiple correct options
A. Sulphur is estimated by Carius method as \( B a S O_{4} \)
B. Victor Meyer's method is used for the determination of molecular mass of a non-volatile compound
C. Kjeldahl's method is used for all nitrogen-containing organic compounds
D. Phosphorous is estimated by Carius method as \( M g\left(N H_{4}\right) \cdot P O_{4} \)


Zeroth law of thermodynamics was enunciated by
A. Clausius
B. Carnot
c. R.H. Fowler
D. Gibb


Which of the following has the maximum value of dipole moment?
\( A \)
в.
c.
D.


Assertion
Statement -1: The melting point of
noble gases increases as its atomic mass increases.
Reason
Statement -2: Instantancous dipole induced dipole attraction increases with increase in atomic mass.
A. Statement -1 is true, Statement -2 is true and Statement -2 is correct explanation for Statement -
1
B. Statement
-1 is true, Statement -2 is true and Statement - 2 is NOT the correct explanation for Statement - 1.
c. Statement -1 is true, Statement -2 is false
D. Statement -1 is false, Statement -2 is true.


Solve the following quadratic equation by factorization, the roots are: \( 0, a+b \) \( \frac{x-a}{x-b}+\frac{x-b}{x-a}=\frac{a}{b}+\frac{b}{a} \)
A. True
B. False


Assertion
In meter bridge experiment, a high resistance is always connected in
series with a galvanometer.
Reason
As resistance increases, current
through the circuit increases.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Find \( \boldsymbol{x}+\boldsymbol{y} \) if \( \left[\begin{array}{cc}-2 & 0 \\ 3 & 1\end{array}\right]\left[\begin{array}{l}-1 \\ 2 x\end{array}\right]+ \)
\( \left[\begin{array}{c}-2 \\ 1\end{array}\right]=2\left[\begin{array}{l}y \\ 3\end{array}\right] \)


The quantity of \( C O_{2} \) in \( 500 \mathrm{ml} \) of soda
water when packed under 2.5 atm \( C O_{2} \)
pressure at \( 298 \mathrm{K} \) is gm ( Henry's law constant \( 1.67 \times 10^{8} \) pa at \( 298 \mathrm{K} \) )
A . 0.64
B. 1.86
\( c \cdot 6.4 \)
D. 18.6


Which of the following are natura polymers? This question has multiple correct options
A. Proteins
B. Cellulose
c. Teflon
D. Natural rubber


Erythroblastosis foetalis is related with
A. Blood group
B. Rh factor
c. Infectious disease
D. All of these


The conclusion of Rutherford from his \( \alpha \)
-ray scattering experiment is:
A. many particles were deflected from their path, indicating that the positive charge of the atom occupies very small space.
B. many particles were deflected from their path, indicating that the positive charge of the atom occupies very large space.
C. most of the space inside the atom is empty because most of the \( \alpha \) -particles passed through the gold foil without getting deflected.
D. a very large fraction of alpha-particles were deflected by \( 180^{\circ} \), indicating that all the positive charges and mass of the gold atom were concentrated in a very small volume within the atom


The refractive index of water with
respect to air is \( _{a} \mu_{w} \) and of glass with respect to air is \( _{a} \mu_{\mathrm{g} \cdot} \) So, \( \frac{a \mu_{g}}{a \mu_{w}} \) should
express:
A. refractive index of glass with respect to water
B. refractive index of water with respect to glass
C. refractive index of air
D. none of these


Two blocks of masses \( \mathrm{m} \) and \( \mathrm{M} \) are
connected by means of a metal wire passing over a frictionless fixed pulley. The area of a cross-section of the wire is
\( 6.5 \times 10^{-9} m^{2} \) and its breaking stress is
\( 2 \times 10^{9} N m^{-2} . \) If \( m=1 \mathrm{kg}, \) then calculate
the maximum value of \( \mathrm{M}\left(\mathrm{g}=10 \mathrm{m} / \mathrm{s}^{2}\right) \)
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5


Show that
\( \tan 3 x \tan 2 x \tan x=\tan 3 x- \)
\( \tan 2 x-\tan x \)


Which metal forms hydrogen gas when reacts with cold water?
A . Na a
в. Мв
c. \( \mathrm{Fe} \)
D. zn


Steric number of sulphur is DMS is:
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5


Which is the family of 'Arhar'
A . Malvaceae
B. Liliaceae
c. Papilionaceae
D. Solanaceae


Evaluate \( (-9) \times 7 \times(-11) \)


To construct a triangle similar to given \( \triangle A B C \) with its sides \( \frac{2}{3} \) of that of
\( \Delta A B C, \) locate points on ray \( B X \) at
equal distances as \( B_{1}, B_{2}, B_{3}, \ldots \) such
that \( \angle C B X \) is acute. The points to be
joined in the next step are:
A. \( B_{4}, C \)
в. \( B_{3}, C \)
c. \( B_{1}, C \)
D. \( B_{2}, C \)


Which of the following materials has a negative temperature coefficient of resistance?
A. copper
B. Aluminium
c. carbon
D. brass


The commonest living organism, which
can respire in the absence of \( O_{2} \) is
A . Fish
B. Yeast
c. Potato
D. Chlorella


Which of the following is/are diamagnetic?
This question has multiple correct options
A. Super oxide ion
B. Oxygen molecule
c. Carbon molecule
D. Nitrogen molecule


\( \int_{1}^{2} \frac{d x}{\left(x^{2}-2 x+4\right)^{\frac{3}{2}}}=\frac{k}{k+5}, \) then \( k \) is
equal to
A . 1
B. 2
\( c .3 \)
D. 4


What is the product of the reaction of
\( P_{4} O_{10} \) with carbon?
A. Carbon monoxide
B. Red phosphorus
c. Carbon dioxide
D. Both \( A \) and \( B \)


The Span materials are less water
soluble than the
materials. The same
material could be a detergent and a wetting agent.
A. Carboxylate
B. Ampholytic elements
c. Surfactants
D. Tween


Fill in the blanks.
The type of electric current that
changes its direction twice during one cycle of the dynamo is called


A body moving along the positive \( x- \) axis
with uniform acceleration of \( -4 m s^{-2} \). Its
velocity at \( x=0 \) is \( 10 m s^{-1} \). The time
taken by the body to reach a point at \( x= \)
\( 12 \mathrm{cm} \) is:
A. \( (2 s) \)
B . \( (0.25 s) \)
c. \( (3 s) \)
D. \( (0.0125 s) \)


How many of the following are soluble in
water?
(i) Ethylamine
(ii) Aniline


Interference event is observed
A. only in transverse waves
B. only in longitudinal waves
c. in both types of waves
D. none


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


Oxidation number of \( ^{\prime} \boldsymbol{N}^{\prime} \) in \( \boldsymbol{N}_{3} \boldsymbol{H} \)
(hydrazoic acid) is:
\( ^{A} \cdot-\frac{1}{3} \)
B. +3
c. 0
D. -


During dry weather, while combing hair, sometimes we experience hair flying apart. The force responsible for this is
A. force of gravity.
B. electrostatic force
c. force of friction.
D. magnetic force.


Instantaneous displacement of a particle is \( y=4 \cos ^{2}\left(\frac{t}{2}\right) \sin 1000 t \)
The particle is displaced due to:
A. only one wave
B. two waves
c. three waves
D. four waves


If the current through a resistor in a circuit increases by \( 3 \%, \) the power dissipated by the resistor
A. Increases approximately by 3\%.
B. Increases approximately by 6\%.
c. Increases approximately by \( 9 \% \)
D. Decreases approximately by 3\%


State whether the following statement is true or false.

If two rectangles have equal area, they
are congruent.
A. True
B. False


What is the vapour pressure of the solution containing \( 34.2 \mathrm{g} \) of sucrose per 100 g of water at \( 25^{\circ} \mathrm{C} \) ? The vapour
pressure of water at \( 25^{\circ} \mathrm{C} \) is \( 23.75 \mathrm{mm} \)
\( A \cdot 20.3 \mathrm{mm} \)
B. 23.10 mm
c. Unpredictable
D. 23.33 mm


In an experiment, the amplitude of intensity variation of two sources is
focused to be \( 3 \% \) of the avg. intensity. Find the ratio of intensity of two interfering sources.


The standard e.m.f. of the cell involving
the reaction, \( 2 A g^{+}(a q)+H_{2}(g) \rightarrow \)
\( 2 A g(s)+2 H^{+}(a q), \) is \( 0.80 \mathrm{V} . \) The
standard oxidation potential of \( \mathrm{Ag} \) electrode is:
A . \( 0.80 V \)
в. \( -0.80 V \)
c. \( 0.40 V \)
D. \( 0.20 V \)


Which of the following characteristics is/are common in animals belonging to platyhelminthes, coelenterate, echinodermata, mammals, amphibians?
A. Coelom
B. Symmetry
c. Appendages
D. None of the above


Prove \( 6+3 \sqrt{5} \) is irrational


The population \( p(t) \) at time \( t \) of a certain mouse species satisfies the differential equation \( \frac{\boldsymbol{d} \boldsymbol{p}(\boldsymbol{t})}{\boldsymbol{d} \boldsymbol{t}}= \)
\( 0.5 p(t)-450 . \) If \( p(0)=850, \) then the time at which the population becomes
zero is
A \( \cdot \frac{1}{2} \ln 18 \)
B. \( \ln 18 \)
c. \( 2 \ln 18 \)
D. \( \ln 9 \)


A rocket is in the shape of a cone mounted on a right circular cylinder their common base diameter is \( 8 \mathrm{cm} \)
the height of cylindrical and concial shapes are \( 6 \mathrm{cm} \) and \( 3 \mathrm{cm} \) respectively. Find the volume of the rocket.


A ring of radius \( \mathrm{R} \) rolls without slipping on a rough horizontal surface with a constant velocity. The radius of curvature of the path followed by any
particle of the ring at the highest point
of its path will be :
\( A \cdot 5 R \)
в. 2 В
\( c .4 R \)
D. Noneofthese


\( 0.25 \mathrm{M} \) solution of pyridine chloride
\( C_{5} H_{6} N^{+} C l^{-} \) was found to have a pH of
2.699. What is \( \boldsymbol{K}_{\boldsymbol{b}} \) for pyridine, \( \boldsymbol{C}_{\boldsymbol{5}} \boldsymbol{H}_{\boldsymbol{5}} \boldsymbol{N} \) ?
\( (\log 2=0.3010) \)


toppr
Q Type your question
magnet, carrying magnetic effect, electricity, the magnitude of current deflection increases, eastwards,
southwards.
Oersted was the first to put forth the direct relation between \( _{\text {thend }} \) and
magnetism. He conducted several experiments to determine the of a current wire
The following describes the Oersted experiment conducted to establish that
a current carrying wire acts as a

A long straight wire is connected to an external battery and an electric current is passed through it. When a magnetic needle is placed below the wire such
that the wire is parallel to the axis of the
magnetic needle and the current flows in the south to north direction, a
deflection in the needle is observed. It is
observed that the north pole of the needle is deflected westwards and as
the \( _{\text {一一一一一一一 }} \) is increased, the
deflection, \( _{\text {一一一一一一一 }} \) till the north pole
of the needle turns towards exact west.
t is also observed that if instead of
placing the magnetic needle below the wire, if it was placed above the wire, the
north pole of the magnetic needle is deflected


Biogas plant is generally made of what?
A. Bricks
B. wood
c. Tiles
D. Plaster of Paris


What is the free energy change \( \triangle G \)
when 1.0 mole of water \( \operatorname{at} 100^{\circ} C \) and 1
atm pressure is converted steam at
\( 100^{\circ} \mathrm{C} \) and 1 atm pressure:
A. +540 cal
B . -9800 cal
c. +9800 cal
D. o cal


If the specific heat capacity of iron is 0.108 cal/g'C. Then how much heat is sufficient to raise the temperature of 1 g of iron through \( 1^{\prime} \mathrm{C} ? \)
A. 0.108 calories
B. 108 calories
c. 0.0108 calories
D. 10.8 calories


Electric charges \( \boldsymbol{q}, \boldsymbol{q} \) and \( -\boldsymbol{2} \boldsymbol{q} \) are placed at the corners of an equilateral triangle \( A B C \) of side \( L . \) The magnitude of electric dipole moment of the system is
\( \mathbf{A} \cdot q L \)
в. \( 2 q L \)
c. \( (\sqrt{3}) q L \)
D. \( 4 q L \)


One half of a convex lens of focal length \( 10 \mathrm{cm} \) is covered with a black paper. Can such a lens produce an image of a complete object placed at a distance of \( 30 \mathrm{cm} \) from the lens? Draw a ray
diagram to justify your answer. A \( 4 \mathrm{cm} \) tall object is placed perpendicular to its principal axis of a convex lens of focal length \( 20 \mathrm{cm} . \) The distance of the object from the lens is 15 cm. Find the nature, position and the size of the image.


From the base of hemisphere, a right \( \boldsymbol{R} \)
cone of height \( \frac{1}{2} \) and same base has
been scooped out. Find the C.M of the
remaining part


\( I=\int \sec x \tan x d x \) is
equal to
A. \( \sec x+c \)
B. \( \cos x+c \)
c. \( \tan x+c \)
D. None of these


f \( x \sin (a+y)=\sin y, \) then \( y^{\prime}=? \)


It is difficult to cut cloth using a pair of scissors with blunt blades. Explain.


With the help of a neat and labelled diagram, describe reflex arc.


Find the derivative of
\( \left(5 x^{3}+3 x-1\right)(x-1) \)


Among solids, liquids and gases, which posses the greatest bulk modulus?
A. Solids
B. Liquids
c. Gases
D. Both solids and liquids


Let \( E_{1} \) and \( E_{2} \) be the binding energies of two nuclei \( A \) and \( B . \) It is observed that
two nuclei of A combine together to
form a B nucleus. This observation is
correct only if
A \( \cdot E_{1}>E_{2} \)
в. \( E_{2}>E_{1} \)
c. \( E_{2}<2 E_{1} \)
D. nothing can be said


The device used to detect and measure
electric charges is


Measurement of rate of oxygen
utilisation by the unit volume of polluted water over a period of time is referred to as:
A. fermentation
B. chemical oxygen demand
c. oxidation potential
D. biological oxygen demand


The area (in sq.units) of the region
\( \left\{(x, y): y^{2} \geq 2 x \text { and } x^{2}+y^{2} \leq\right. \)
\( 4 x, x \geq 0, y \geq 0 \) is
A \( \cdot \pi-\frac{8}{3} \)
B. \( _{\pi-\frac{4 \sqrt{2}}{3}} \)
\( ^{\mathrm{C}} \cdot \frac{\pi}{2}-\frac{2 \sqrt{2}}{3} \)
D. \( \pi-\frac{4}{3} \)


Change each of the given temperature
to the Celsius and Kelvin scales:
\( 68^{\circ} F, 5^{\circ} F \) and \( 176^{\circ} F \)


Which of the following will produce only
one product on reduction with \( L i A l H_{4} ? \)
A \( \cdot C H_{3} O C O C H_{2} C H_{3} \)
в. \( C H_{3} C H_{2} \) ОСОСН\( _{2} \)СН\( _{3} \)
\( \mathrm{c} \cdot \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{O} \mathrm{COCH}_{3} \)
D. \( C H_{3} C H_{2} O C O C H_{2} C H_{2} C H_{3} \)


Find the square root of following:
(i) \( 3+4 i \)
(ii) \( -5+12 i \)


When Neils Bohr shook hands with
Werner Heisenberg, what kind of force they exerted?
A . Gravitational
B. Electromagnetic
c. Nuclear
D. weak


The natural frequency \( \left(\omega_{0}\right) \) of
oscillations in LC Circuit is given by:
A \( \cdot \frac{1}{2 \pi} \frac{1}{\sqrt{L C}} \)
B. \( \frac{1}{\pi} \frac{1}{\sqrt{2 L C}} \)
c. \( \frac{1}{\sqrt{L C}} \)
D. \( \sqrt{L C} \)


Find domain and range \( . \) If \( \boldsymbol{y}=\sqrt{\boldsymbol{x}-\mathbf{1}} \)


In a polygon, there are 5 right angles and the remaining angles are equal to
\( \mathbf{1 9 5}^{\circ} \) each. Find the number of sides in
the polygon.
A . 5
B. 11
c. 8
D. 7


Glacial acetic acid is:
A \( .100 \% \) acetic acid free of water
B. solidified acetic acid
C . gaseous acetic acid
D. frozen acetic acid


The mass of 5 moles of \( H_{2} S O_{4} \) is
\( A .98 g \)
B. 196 g
c. \( 356 g \)
D. 490 g


The sparks caused due to friction between two machine parts are:
A. similar to lighting
B. not similar to lightning
c. lightning on a very small scale
D. none of the above


Which of the following transition will emit maximum energy in hydrogen atom?
A. \( 4 f \rightarrow 2 s \)
В. \( 4 d \rightarrow 2 p \)
\( \mathrm{c} .4 p \rightarrow 2 s \)
D. All have same energy


Four elements \( A, B, C, D \) have 1,2,6,7
valence electrons in their atoms.
Assuming that they belong to the same period identify the strongest oxidizing agent among them.
\( A \cdot A \)
B. B
\( c \cdot c \)
D.


locate the point representing the
complex numbers \( z \) on the Argand diagram for which
\( |z+i|=|z-2| \)


The median of the first 100 natural
numbers is
A . 49.5
B. 22.75
c. 23.75
D. 50.5


A black sulphide when treated with ozone becomes white. The white
compound is :
A. \( Z n S O_{4} \)
в. \( \mathrm{CaSO}_{4} \)
\( c \cdot B a S O_{4} \)
\( \mathrm{D} \cdot \mathrm{PbSO}_{4} \)


In the diagram, \( \ell \) and \( m \) are parallel line.
The sum of the angles \( A \), Band \( C \) marked
in the diagram is-
A \( \cdot 180^{\circ} \)
B \( .270^{\circ} \)
\( c \cdot 360^{\circ} \)
D. \( 300^{\circ} \)


Why is distilled water considered to be
the purest form of water?


Find to five places of decimals the value
of :
\( \sqrt[3]{1003} \)


In diabetes melitus the patient drinks more water as there is urinary loss of
A. Salt
B. Insulin
c. Protein
D. Glucose


All rational numbers are real numbers.
A . True
B. False


According to principle of moments:
A. product of anticlockwise force = product of clockwise force
B. Sum of anticlockwise moments = sum of clockwise moments
c. both
D. none


Assuming that the earth's orbit round
the sun be circular, find the linear
velocity of its motion and the period of revolution about the sun. Given \( G= \)
\( 6.67 \times 10^{-11} \) S.I. units, mass of the
\( \operatorname{sun}=1.99 \times 10^{30} k g, \) mean distance
between the sun and the earth \( = \)
\( 1.497 \times 10^{-11} m \)


The wave number of first line of Balmer
series of hydrogen is \( 15200 \mathrm{cm}^{-1} . \) The
wave number of the first Balmer line of
\( L i^{2+} \) ion is:
A \( \cdot 15,200 \mathrm{cm}^{-1} \)
В. \( 60,800 \mathrm{cm}^{-1} \)
c. \( 76,000 \mathrm{cm}^{-1} \)
D. \( 1,36,800 \mathrm{cm}^{-1} \)


Pick out the only vector quantity in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction, charge.


If \( \sin \Theta+\cos \Theta=\sqrt{2}, \) and \( \Theta \) is actual
then \( \tan \Theta \) is equal to
A \( \cdot \frac{1}{\sqrt{3}} \)
B.
\( c \cdot \sqrt{3} \)
D. \( \infty \)


Co-ordination compounds have great importance in biological systems. In this context which of the
following statements is incorrect?
A. Chlorophylls are green pigments in plants and contain calcium
B. Haemoglobin is the red pigments of blood and contains iron
c. Cyanocobalamin is vitamin B12 and contains cobalt
D. Carboxypeptidase-A is an enzyme and contains zinc


Which of the following compound affects mercury?
\( A \cdot D_{2} O \)
в. \( H_{2} \) о
c. \( O_{3} \)
D. \( d i l . H C l \)


Which teeth are different in shape, size
and function then these are called as
A. Acrodont
B. Pleurodont
c. Homodont
D. Heterodont


\( A \) and \( B \) are two points and \( C \) is any
point collinear with \( A \) and \( B . \) IF \( A B= \)
\( \mathbf{1 0}, \boldsymbol{B C}=\mathbf{5}, \) then \( \boldsymbol{A} \boldsymbol{C} \) is equal to:
A. either 15 or 5
B. necessarily 5
c. necessarily 16
D. none of these


A shopkeeper sells an article at its list price (Rs. 3,000) and charges sales-tax at the rate of \( 12 \% \). If the VAT paid by the
shopkeeper is Rs. \( 72, \) at what price did the shopkeeper buy the article inclusive of sales-tax?
A. Rs. 2688
B. Rs. 2966
c. Rs. 3422
D. Rs. 3966


A strong argument for particle nature of
cathode rays is that they
A. Produce fluorescence
B. Travel through vacuum
C. Get deflected by electric and magnetic fields
D. cast shadows


Which of the following are correctly matched?
(a) \( D_{2} O- \) Hard water
(b) \( H_{2} O- \) Heavy water
\( (c) D- \) Heavy hydrogen
\( (d) B a O_{2} \cdot 8 H_{2} O- \) True peroxide
\( \mathbf{A} \cdot a, b, c, d \) are correct
B. \( c, d \) are correct
c. \( a, b, c \) are correct
D. \( a, c, d \) are correct


Which of the following is/are correct?
This question has multiple correct options
A. Parabola is symmetric with respect to the axis of the parabola.
B. Length of latus rectum of a parabola, \( y^{2}=4 a x \) is \( 4 a \)
C. A line through the focus and perpendicular to the directrix is called the axis of the parabola.
D. The point of intersection of a parabola with the axis is called the vertex of the parabola.


State whether true or false:
\( \underline{e} \) ratio of proton is greater than that of \( \bar{m} \)
electron.
A . True
B. False


Read the following statements carefully
and select the incorrect statement
A. Carbon monoxide binds to Hb with higher affinity than oxygen and forms carboxyhemoglobin
B. Nearly \( 23 \% \) of oxygen is transported as oxyhemoglobin in RBC's of blood.
C. \( 100 \mathrm{ml} \) of deoxygenated blood delivers approximately \( 4 \mathrm{ml} \) of \( \mathrm{CO}_{2} \) to the alveoli under normal physiological conditions.
D. About 72\% of \( C O_{2} \) gets transported via blood plasma.


A substance reacts according to \( I \) order
kinetics and rate constant for the
reaction is \( 1 \times 10^{-2} \mathrm{sec}^{-1} . \) If its initia
concentration is \( 1 M \)
(a) What is initial rate?
(b) What is rate after 1 minute?


Find the degree of the given polynomials.
\( x^{0} \)


The terminal velocity of a sphere moving through a viscous medium is
A. directly proportional to the radius of the sphere
B. inversely proportional to the radius of the sphere
C. directly proportional to the square of the radius of sphere
D. inversely proportional to the square of the radius of sphere


If \( \Delta_{r}=\left|\begin{array}{ccc}r-1 & n & 6 \\ (r-1)^{2} & 2 n^{2} & 4 n-2 \\ (r-1)^{3} & 3 n^{3} & 3 n^{2}-3 n\end{array}\right| \)


For a zero order chemical reaction,
\( \mathbf{2} \boldsymbol{N} \boldsymbol{H}_{3}(\boldsymbol{g}) \rightarrow \boldsymbol{N}_{2}(\boldsymbol{g})+\boldsymbol{3} \boldsymbol{H}_{2}(\boldsymbol{g}) \)
rate of reaction \( =0.1 \) atm/sec. Initially
only \( N H_{3} \) is present and its pressure
\( =3 \) atm. Calculate total pressure at
\( t=10 \mathrm{sec} \)


Factorise the following \( 9 x^{2}+6 x y+y^{2} \)


Which of the following is not true about helium?
A. It has the lowest boiling point
B. It has the highest first ionization energy
c. It can diffuse through rubber and plastic materia
D. It can form clathrate compounds


The
determines how electrons respond to forces (via the concept of effective mass).
A. electrostatic forces
B. dispersion relation
c. magnetic force
D. lorentz force


A ball is dropped from the top of a tower of height \( h . \) It covers a distance of \( \frac{h}{2} \) in
the last second of its motion. How long does the ball remain in air?


Greenhouse effect corresponds to
A. Water pollution
B. Global warming
\( \mathbf{C} \cdot S O_{2} \) poisoning
D. Production of green manure


A radiation \( X \) is focused by a particular device on the bulb of a thermometer
and mercury in the thermometer shows a rapid increase. Name the radiation \( X \)


Positive point charges are placed at the
vertices of a star shape as shown in the
figure. Direction of the electrostatic
force on a negative point charge at the
centre \( \boldsymbol{O} \) of the star is:
A. Neither along horizontal or vertical direction,
B. Vertically up
C. Towards left
D. Vertically down


Neha and Priya borrowed \( R s 5400 \) and
Rs 6000 respectively at the same rate of interest for \( 1 \frac{3}{5} \) years. If Priya paid Rs 240 more then, Neha, then find the
rate of interest.


The effect of parallax is used to
measure:
A. distances to nearby objects
B. distances to nearby stars
C. nearness of atoms in substances
D. the object and image distance in optical experiments


Write short note on 'Pressure Cooker'.


Rhizopus reproduces by the method of
A. Regeneration
B. Spore formation
c. Budding
D. Fragmentation


The products formed when heavy water
is reacted with magnesium nitride, is/are
A \( \cdot N H_{3} M g(O H)_{2} \)
В \( \cdot \operatorname{NH}_{3} M g(O D)_{2} \)
\( \mathbf{c} \cdot_{N D_{3}} M g(O H)_{2} \)
D. \( _{N D_{3} M g}(O D)_{2} \)


\( \boldsymbol{H}_{3} \boldsymbol{B} \boldsymbol{O}_{3} \stackrel{\boldsymbol{T}_{1}}{\longrightarrow} \boldsymbol{X} \stackrel{\boldsymbol{T}_{2}}{\longrightarrow} \boldsymbol{Y} \stackrel{r e d h o t}{\longrightarrow} \boldsymbol{B}_{2} \boldsymbol{O}_{3} \)
\( T_{1}<T_{2} \) then \( X \) and \( Y \) respectively are :
A. \( x= \) Metaboric acid and \( Y= \) Tetraboric acid
B. X=Tetraboric acid and Y= Metaboric acid
c. \( x= \) Borax and \( Y= \) Metaboric acid
D. x=Tetraboric acid and Y= Borax


The amplitude of
\( \sin \frac{\pi}{5}+i\left(1-\cos \frac{\pi}{5}\right) \)
A.
в. \( \frac{2 \pi}{5} \)
c. \( \frac{\pi}{10} \)
D. \( \frac{\pi}{15} \)


Two trains, each of length \( 100 \mathrm{m} \) moving in opposite directions along parallel lines, meet each other with speeds of \( 50 \mathrm{kmh}^{-1} \) and \( 40 \mathrm{kmh}^{-1} \). If
their accelerations are \( 30 \mathrm{cms}^{-2} \) and
\( 20 \mathrm{cms}^{-2}, \) respectively, find the time they will take to pass each other


If \( z=4+i \sqrt{7}, \) then value of \( z^{3}-4 z^{2}- \)
\( 9 z+91 \) equals
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot-1 \)
D. 2


State whether true or false:
The air pressure can support \( 13.10 m \) vertical column of mercury.
A. True
B. False


The energy of the em waves is of the order of 15 keV. To which part of the spectrum does it belong?
A. \( \gamma \) rays
B. x rays
c. Infra - red rays
D. Ultraviolet rays


toppr
Q Type your question
Minimum value of \( y= \)
\( A \)
\( 4 \sec ^{2} x+\cos ^{2} x \) for
permissible real values of \( x \) is equal to
If \( m, n \) are positive
integers and \( m+n \sqrt{2}= \)
B. \( \quad \sqrt{41+24 \sqrt{2}} \), then \( (m+ \)
to
\( n) \) is equal
Number of solutions of then equation
\( \mathrm{C} \)
\( \log _{\left(\frac{3 x-x^{2}-14}{7}\right)}(\sin 3 x-\sin x) \) 3. \( =\log _{\left(\frac{9 x-x^{2}-14}{7}\right)} \cos 2 x \) is
equal to
Consider arithmetic sequence of positive the integers. If the sum of first ten terms is al to
D. equal 4. the \( 58^{n} \) term, then the e of the least possible value first term is equal to
5.
\( \mathbf{A} \cdot A-4, B-5, C-1, D-3 \)
\( \mathbf{B} \cdot A-4, B-5, C-3, D-1 \)
\( \mathbf{c} \cdot A-5, B-4, C-1, D-3 \)
D . \( A-1, B-5, C-4, D-3 \)


Illustrate with examples the limitations
of Williamson's synthesis for the preparation of certain types of ethers.


Dynamo is
A. a device
B. a typr of magnet
C . a current carrying wire
D. none of these


If \( \boldsymbol{x}+\boldsymbol{y} \leq \mathbf{2}, \boldsymbol{x} \leq \mathbf{0}, \boldsymbol{y} \leq \mathbf{0} \) the point at
which maximum value of \( 3 x+2 y \)
attained will be.
\( \mathbf{A} \cdot(0,0) \)
в. \( \left(\frac{1}{2}, \frac{1}{2}\right) \)
D. (2,0)


\( \boldsymbol{C} \boldsymbol{a}_{3}\left(\boldsymbol{P} \boldsymbol{O}_{4}\right)_{2}(\boldsymbol{s}) \leftrightharpoons \boldsymbol{3} \boldsymbol{C} \boldsymbol{a}^{2+}(\boldsymbol{a} \boldsymbol{q})+ \)
\( \mathbf{2} \boldsymbol{P} \boldsymbol{O}_{4}^{3-}(\boldsymbol{a} \boldsymbol{q}) \)
What is the equilibrium expression for
the dissolution of \( C a_{3}\left(P O_{4}\right)_{2} \) where the above is true?
\( \mathbf{A} \cdot K_{s p}=\left[C a^{2+}\right]^{3}\left[P O_{4}^{3-}\right]^{2} \)
B. \( K_{s p}=\left[C a^{2+}\right]^{3}\left[P O_{4}^{3-}\right]^{3} \)
C \( \cdot K_{s p}=\left[C a^{2+}\right]\left[P O_{4}^{3-}\right] /\left[C a_{3}\left(P O_{4}\right)_{2}\right. \)
D. \( K_{s p}=\left[C a^{2+}\right]^{3}\left[P O_{4}^{3-}\right]^{2} /\left[C a_{3}\left(P O_{4}\right)_{2}\right] \)
E \( \cdot K_{s p}=\left[C a^{2+}\right]^{2}\left[P O_{4}^{3-}\right]^{3} /\left[C a_{3}\left(P O_{4}\right)_{2}\right. \)


The wave theory of light, in its original form, was first postulated by.
A. Isaac Newton
B. Christian Huygens
c. Thomas Young
D. Augustin Jean Fresnel


Find a rational number between -1 and
1
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \frac{1}{\sqrt{-2}} \)
\( c \cdot \frac{-8}{5} \)
D. \( \frac{3}{2} \)


A strong bar magnet placed vertically above a horizontal wooden board. The
magnetic lines of force will be
A. only in horizontal plane around the magnet
B. only in vertical plane around it magnet.
c. in horizontal as well as vertical plane around the magnet
D. in all the planes around the magnet


In the reaction between \( C l_{2} \) and hot
conc. NaOH, which is correct?
A. The oxidation number of \( C l_{2} \) changes from 0 to +5 and o to -
B. \( C l_{2} \) undergoes disproportionation
C. \( C l_{2} \) undergoes self or auto redox change
D. All of these


Where does cyclic
photophosphorylation take place in the leaves?Why is this process called cyclic? Describe cyclic photophosphorylation.


A proton enters a magnetic field of flux density \( 1.5 W b / m^{2} \) with a speed of \( 2 \times \)
\( 10^{7} \mathrm{m} / \mathrm{s} \) at angle of \( 30^{\circ} \) with the field.
The force on a proton will be
A. \( 0.44 \times 10^{-12} N \)
B . \( 2.4 \times 10^{-12} N \)
c. \( 24 \times 10^{-12} N \)
D. \( 0.024 \times 10^{-12} N \)


Which catalyst is used in the preparation of dacron?


Match column I with column II.
Column I
P. Non-stick coating
(i). Melamine
Q. Flame resistant
(ii). Polystyrene
R. First fully synthetic fibre
(iii). Teflon
S. Thermoplastic
(iv). Nylon
Choose the correctly matched option.
\( A \cdot(P)-(i i),(Q)-(i),(R)-(i i i),(S)-(i v) \)
B. (P) - (iii), (Q) - (i), (R) - (iv), (S) - (ii)
c. (P) - (ii), (Q) - (iii), (R) - (iv), (S) - (i)
D. (P) - (iii), (Q) - (iv), (R) - (ii), (S) - (i)


If \( 10 g \) of the ice at \( 0^{0} C \) is mixed with
\( 10 g \) of water at \( 10^{0} C, \) then the final
temperature of the mixture will be :
\( \mathbf{A} \cdot 5^{0} C \)
B. \( 0^{\circ} \mathrm{C} \)
c. \( 100 K \)
D. \( 40^{\circ} \mathrm{C} \)


The pair of compounds that can exist
together is:
\( \mathbf{A} \cdot F e C l_{3}, S n C l_{2} \)
\( \mathbf{B} \cdot H g C l_{2}, S n C l_{2} \)
\( \mathbf{c} \cdot F e C l_{2}, S n C l_{2} \)
\( \mathbf{D} \cdot F e C l_{3}, K I \)


Ribosome in eukaryotes involves in
A. Transformation
B. Translation
c. Transcription
D. Translocation
E. Replication


The dissociation of \( N_{2} O_{4} \) takes place
as per the equation \( N_{2} O_{4}(g) \Leftrightarrow \)
\( 2 N O_{2}(g) . N_{2} O_{4} \) is \( 20 \% \) dissociated
while, the equilibrium pressure of mixture is \( 600 \mathrm{mm} \) of Hg. Calculate
\( K_{p} \) assuming the volume to be
constant.
A . 50
B. 100
\( c \cdot 166.8 \)
D. 600


Assertion
The electric potential due to an electric dipole at a point on the perpendicular bisector of the dipole axis is 0 .
Reason
Any point on the perpendicular bisector of the dipole axis is equidistant from the the two equal and opposite charges.
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


What is the equivalent capacitance of
the combination?


How do you explain the role of oxygen in combustion process?


Find the \( 10^{t h} \) term \( \& \) nth term of the G.P.
5,25,125


The probability that exactly one of the
independent events \( A \) and \( B \) occurs is
equal to
This question has multiple correct options
\( \mathbf{A} \cdot P(A)+P(B)-2 P(A \cap B) \)
B \( \cdot P(A)+P(B)-P(A \cap B) \)
C \( . P(\bar{A})+P(\bar{B})-2 P(\bar{A} \cap \bar{B}) \)
D. None of the above


Evaluate \( \int e^{x} \sin e^{x} d x \) on \( R \)


According to adsorption theory of catalysis, the rate of reaction increases with the use of a catalyst because:
A. the heat liberated during adsorption increases the rate of reaction
B. the kinetic energy of reactants increases which increases the rate of reaction
C. the activation energy of reaction increases which increases the rate of reaction
D. the concentration of reactants at the active centres
becomes high due to adsorption resulting in increase in the rate of reaction.


Two particles of different masses \( m_{1} \)
and \( m_{2}, \) different charges \( Q_{1} \) and \( Q_{2} \)
are accelerated through the same potential difference and then enter a
uniform magnetic field in a direction perpendicular to the field. If they trace circular paths of same radius, then the
ratio of their masses \( \left(m_{1} / m_{2}\right) \) must be
A \( \cdot Q_{2} / Q_{1} \)
в. \( Q_{1} / Q_{2} \)
c. \( \left(Q_{1} / Q_{2}\right)^{1 / 2} \)
the
D. \( \left(Q_{2} / Q_{1}\right)^{1 / 2} \)


Assertion
Paraffin wax is a white or colourless
soft solid derivable from petroleum.
Reason
Paraffins are unsaturated hydrocarbons with straight or branched chains which contain only carbon and hydrogen.
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 uniform cylinder of radius \( r \) and
length L and mass \( m \) is lying on the ground with the curved surface touching the ground. If it is to be oriented on the ground with the flat circular end in contact with the ground the work to be done is:
\( ^{\mathbf{A}} \cdot_{m g}\left[\left(\frac{L}{2}\right)-r\right] \)
\( ^{\mathrm{B}}_{m g}\left[\left(\frac{g}{2}\right)-r\right] \)
c. \( m(g L-1) \)
D. \( M g L r \)


Define the darg?


Give structure and IUPAC name of the
tert- pentyl.


density \( +\sigma \) and \( -\sigma \) are parallel to each other as show in figure. Electric field at
the
This question has multiple correct options
A. points to the left or to the right of the sheets is zero.
B. midpoint between the sheets is zero.
C. midpoint of the sheets is \( \sigma / \varepsilon_{0} \) and is directed towards right
D. midpoint of the sheets is \( 2 \sigma / \varepsilon_{0} \) and is directed towards right


How will you identify the given sequence is a geometric sequence?
A. common difference
B. common ratio
c. number of terms
D. number of constant


Which is correct about leucocytes?
A. They are red coloured
B. They can cross capillaries.
c. They are enucleate
D. Decrease in their number causes leukemia


Assertion
Diabetes insipidus is marked by excessive urination and too much thirst
of water
Reason
Anti-diuretic hormone (ADH) is
secreted by the posterior lobe of pituitary gland.
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


How an increase in concentration is
related to number of collisions?
A. Directly
B. Inversely
c. Has no effect
D. None


The van't Hoff factor for \( 0.1 M \) barium
nitrate is \( 2.74 . \) The percentage of dissociation of barium nitrate is:
A . \( 91.3 \% \)
B. \( 87 \% \)
c. \( 100 \% \)
D. \( 74 \% \)


A researcher wanted to know if there is
an association between exercise and
sleep for the population of 16 -year-olds in the United States. She obtained
survey responses from a random sample of 2,000 United States 16 -year-
olds and found convincing evidence of a positive association between exercise
and sleep. Which of the following
conclusions is well supported by the
data?
A. There is a positive association between exercise and sleep for 16 -year-olds in the United States
B. There is a positive association between exercise and sleep for 16 -year-olds in the world
c. Using exercise and sleep as defined by the study, an increase in sleep is caused by an increase of exercise for 16 -year-olds in the United States
D. Using exercise and sleep as defined by the study, an increase in sleep is caused by an increase of exercise for 16 -year-olds in the world.


If the size of the sample increases, the
curve becomes
A. continuous
B. severely skewed to one side
c. more symmetrical
D. intermittent


toppr \( t \)
Q Type your question
shown in figure. The graph of magnitude of induced emf in the coil is
represented by
\( A \)
B.
\( c \)
D.


Sludge is:
A. created from combination of gases released from industries and water
B. a semi-solid slurry and can be produced as sewage sludge from wastewater treatment processes
C. a type of household waste
D. a type of industrial waste


If \( A \) is to the south of \( B \) and \( C \) is to the
east of \( \mathrm{B} \), in what direction is \( \mathrm{A} \) with
respect to C?
A. North-east
B. North-west
c. South-west
D. None of the above


"If natural numbers are whole numbers, then rational numbers are integers" or "If rational numbers are integers, then natural numbers are whole numbers" is
A. a tautology
B. a contradiction
c. a contingency
D. not a statement


Find the value of \( x \) in the following
figure.


\( \frac{2 x}{3}-\frac{x-1}{6}+\frac{7 x-1}{4}=2 \frac{1}{6} \)
Hence, find the value of \( x \) and \( a \), if \( \frac{1}{a}+ \)
\( \mathbf{5} \boldsymbol{x}=\mathbf{8} \)
A \( x=2 \) and \( a=\frac{1}{2} \)
B. \( x=3 \) and \( a=\frac{1}{4} \)
c. \( _{x}=4 \) and \( a=\frac{1}{5} \)
D. \( x=1 \) and \( a=\frac{1}{3} \)


From the circuit shown below, the
maximum and minimum value of zener
diode current are :
\( \mathbf{A} \cdot 6 m A, 5 m A \)
B. \( 14 \mathrm{mA}, 5 \mathrm{mA} \)
\( \mathbf{c} .9 m A, 1 m A \)
D. \( 3 m A, 2 m A \)


If the polynomial \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left(6 x^{4}+8 x^{2}+17 x^{2}+21 x+7\right) \) is
divided by another polynomial \( g(x)= \)
\( 3 x^{2}+4 x+1 \) the remainder is \( (a x+b) \)
Find \( a \) and \( b \)


In a test an examinee either guesses or copies or knows the answer to a
multiple choice question with 4 choices. The probability that he makes a guess is \( \frac{1}{3} \) and the probability that he copies the answer is \( \frac{1}{6} . \) The probability
that his answer is correct given that he copied it, is \( \frac{1}{8} . \) Find the probability that he knew the answer to the question
given that he correctly answered it.
A \( \cdot \frac{11}{29} \)
B. \( \frac{18}{29} \)
c. \( \frac{15}{29} \)
D. \( \frac{24}{29} \)


Unicellular organisms evolved earlier than multicellular organisms around 3.5 thousand million years ago. Justify


Avogadro number is equal to:
\( \mathbf{A} \cdot 6.023 \times 10^{21} \)
B . \( 6.023 \times 10^{22} \)
C \( \cdot 6.023 \times 10^{23} \)
D. \( 6.023 \times 10^{24} \)


Draw the structure(s) of the following
compound:
3-Methylbutanal


Let \( \mathbf{A} \) be a square matrix. Consider
\( \left.\left.\text { 1) }\left.\mathbf{A}+\mathbf{A}^{\mathbf{T}} \text { 2 }\right) \mathbf{A} \mathbf{A}^{\mathbf{T}} \mathbf{3}\right) \mathbf{A}^{\mathbf{T}} \mathbf{A} \mathbf{4}\right) \mathbf{A}^{\mathbf{T}}+\mathbf{A} \)
5) \( \left.\mathbf{A}-\mathbf{A}^{\mathbf{T}} \mathbf{6}\right) \mathbf{A}^{\mathbf{T}}-\mathbf{A}, \) Then
A. all are symmetric matrices
B. (2),(4), (6) are symmetric matrices
c. (1),(2),(3),(4) are symmetric matrices \&
(5),(6) are skew symmetric matrices
D. 5,6 are symmetric


Find the equation of the line having an
inclination \( 45^{\circ} \) with the positive direction of \( X \) axis and cut off an
intercept of 4 on the positive side of \( Y \)
axis.


A short electric dipole (which consists
of two point charges \( +\boldsymbol{q} \) and \( -\boldsymbol{q} \) ) is
placed at the centre 0 and inside a
large cube (ABCDEFGH) of length L, as shown in figure. The electric flux,
emanating through the cube is:
\( A \cdot q / 4 \pi \varepsilon_{0} L \)
B. zero
c. \( q / 2 \pi \varepsilon_{0} L \)
D \( \cdot q / 3 \pi \varepsilon_{0} L \)


Express the following statements as a linear equation in two variable.

The cost of a ball pen is Rs. 5 less than half the cost of a fountain pen.


Assertion
Helium shows only positive deviations
from ideal behaviour.
Reason

Helium is an inert gas.
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


In the reaction, \( \boldsymbol{C u}(\boldsymbol{s})+\boldsymbol{2} \boldsymbol{A} \boldsymbol{g}^{+}(\boldsymbol{a} \boldsymbol{q}) \rightarrow \)
\( \boldsymbol{C u}^{2+}+\mathbf{2} \boldsymbol{A} \boldsymbol{g}(\boldsymbol{s}) \)
A \( \cdot \) cu(s) is oxidised to \( C u^{2} \)
B. \( \operatorname{Cu}(\mathrm{s}) \) reduced to \( C u^{2+}(a q) \)
c. \( \operatorname{Ag} \) (aq) is oxidised to \( \mathrm{Ag} \) (s)
D. Both Cu(s) and \( A g^{+} \) (aq) are oxidised


Which of the following two morphologically similar population are intersterile?
A. One species
B. Two biospecies
c. Two sibling species
D. None of these


\( \Delta H_{f}^{o} \) of \( N_{2} O \) is \( 82 k J / m o l \) and bond
energy for \( N_{2}, N=N, O=O \) and
\( N=O \) bonds are 946,418,498 and
\( 607 k J / \) mol respectively. Resonance
energy of \( N_{2} O \) is:
A. \( -170 k J / m o l \)
в. \( -252 k J / m o l \)
c. \( -88 k J / m o l \)
D. \( -1195 k J / \) mol


Evaluate each of the following:
\( \frac{2}{3}-\frac{3}{5} \)


Explain the following properties of group 16 elements:
(i) Electro negativity
(ii) Melting and boiling points
(iii) Metallic character
(iv) Allotropy


In a group of 15,7 have studied German, 8 have studied French, and 3 have not studied either. How many of these have
studied both German and French?
A . 0
B. 3
\( c \cdot 4 \)
D. 5


A jet plane having a wing-span of \( 25 \mathrm{m} \) is travelling horizontally towards east with a speed of \( 3600 \mathrm{km} / \) hour. If the Earth's magnetic field at the location is
\( 4 \times 10^{-4} \mathrm{T} \) and the angle of dip is \( 30^{\circ} \)
then, the potential difference between
the ends of the wing is?
A. \( 4 \mathrm{v} \)
B. 5 v
\( c \cdot 2 v \)
D. 2.5


What are interstitial compounds? Why are such compounds well known for transition metals?


is a water-carried waste, in
solution or suspension, that is intended
to be removed from a community.
A. Pollutant
B. Sewage
c. Aerosol
D. None of the above


Which bond in B-DNA will have to be
rotated to convert it from syn to anti
conformation?
A. Hydrogen bond
B. Glycosidic bond
c. Phosphodiester
D. Hydropbobic


A child breathes nearly
A. 13 times a minute
B. 26 times a minute
c. 52 times a minute
D. 72 times a minute


Match the List-II ans List-II and List III:
\( \begin{array}{lll}\text { List-I } & \text { List-II } & \text { List-III } \\ \text { A. } \Delta G>0 & \begin{array}{l}\text { X. } \Delta S> \\ 0\end{array} & \begin{array}{l}\text { 1. Non- } \\ \text { spontaneous }\end{array} \\ \begin{array}{l}\text { B. } \Delta G< \\ 0\end{array} & \text { Y. } \Delta S<0 & \text { 2. Spontaneous } \\ \begin{array}{l}\text { C. } \Delta G= \\ 0\end{array} & \text { Z. } \Delta S=0 & \text { 3. Equilibrium }\end{array} \) select the correct answering from the
following codes:
\( A \cdot A-(Y, 1) B-(X, Y) C-(Z, 3) \)
B. \( A-(X, 2) B-(Y, 3) C-(Z, 1) \)
C. \( A-(X, 3) B-(Y, 1) C-(Z, 2) \)
D. \( A-(Y, 1) B-(X, 3) C-(Z, 2) \)


Find the integral of
\( \int\left(\sqrt{\boldsymbol{x}}-\frac{\mathbf{1}}{\sqrt{\boldsymbol{x}}}\right)^{2} \boldsymbol{d} \boldsymbol{x} \)


In the figure, \( m \) ? \( P O Q=30 \) ? and radius \( O P \)
\( =12 \mathrm{cm}, \) then find the given area of segment PRQ (Given \( \pi=3.14) \)
A \( \cdot 1.68 c m^{2} \)
B \( \cdot 2 \cdot 46 c m^{2} \)
\( c \cdot 0.68 c m^{2} \)
D. none of these


(major) is :
\( A \)
в.
c.
D.


The free electron gas theory explains conduction in
A. metals only
B. semiconductors only
c. insulators only
D. all of these


Apatite is an ore of:
\( \mathbf{A} \). fluorine
B. chlorine.
c. bromine.
D. iodine


The position vector of a particle is given
by \( \vec{r}=\vec{r}_{0}(1-a t) t, \) where \( t \) is the time
and \( a \) as well as \( \vec{r}_{0} \) are constant. After
what time the particle returns to the
starting point?
\( A \cdot a \)
B. \( \frac{1}{a} \)
\( c \cdot A^{2} \)
D. \( \frac{a}{a^{2}} \)


The value of \( \boldsymbol{P}(\boldsymbol{S} \text { or } \boldsymbol{T}) \) is:
A . 0.6900
в. 1.19
c. 0.8450
D. 0


Among \( N H_{3}, H_{2} \) and \( H F \) which would
you expect to have the highest magnitude of hydrogen bonding and why?


Draw a rough sketch of a regular hexagon. Connecting any three of the draw a triangle. Identify the type of the triangle you have drawn.


Explain the important features of Rutherford's Planetary model and write
its defects


In Allene \( \left(C_{3} H_{4}\right), \) the type(s) of
hybridization of the carbon atoms is \( (\operatorname{are}) ? \)
A. \( s p \) and \( s p^{3} \)
B. \( s p \) and \( s p^{2} \)
C . only \( s p^{2} \)
D. \( s p^{2} \) and \( s p^{3} \)


Assertion
Lichens and mosses are said to form
the pioneer community in xerarch
succession
Reason
It is because these species get
established later, during the course of
succession.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of the following statements
is/are wrong?
This question has multiple correct options
A. Beilstein test is a reliable test for halogens in organic compounds.
B. In Lassaigne's test for N, Prussian blue colour is due to the formation of ferro-ferri cyanide.
C. When \( F e C l_{3} \) solution is added to the Lassaigne's extract, a blue solution is obtained, which indicates the presence of both \( \mathrm{N} \) and \( \mathrm{S} \)
D. Molecular mass of an acid = Equivalent mass \( x \) acidity.


The G.M of the numbers \( 3^{1}, 3^{2}, 3^{3}, \ldots, 3^{3 n} \) is
A \( \cdot \frac{n}{2} \)
в. \( \frac{3 n}{2} \)
c. \( \frac{3 n+1}{2} \)
D. \( \frac{n+1}{2} \)


Air pollution effects are usually found
on
A . Leaves
B. Flowers
c. stems
D. Roots


A circular loop of wire has current going
through it in the clockwise direction.
What is the direction of the magnetic
field that is caused by this current
through the wire?
A. Inside the loop: out of the screen
Outside the loop: into the screen
B. Inside the loop: out of the screen
Outside the loop: out of the screen
C. Inside the loop: into the screen
Outside the loop: out of the screen
D. Inside the loop: into the screen
Outside the loop: into the screen


When sulphur in the form of \( S_{8} \) is
heated at \( 900 K \) and constant volume,
the initial pressure of 1 atm increases
by \( 27 \% \) at equilibrium. This is because
of conversion of some \( S_{8} \) to \( S_{2} \). Find the
value of the equilibrium constant for this reaction.


the specific heat capacity of liquid.
\( \mathbf{A} \cdot 0.3 \times 10^{3} J k g^{-1} K^{-1} \)
B \( \cdot 12 \times 10^{3} J k g^{-1} K^{-1} \)
C \( .3 \times 10^{3} \mathrm{Jkg}^{-1} \mathrm{K}^{-1} \)
\( \mathbf{D} \cdot 6 \times 10^{3} J k g^{-1} K^{-1} \)


The oxidation number of oxygen in
\( \mathrm{K}_{2} \mathrm{O}, \mathrm{K}_{2} \mathrm{O}_{2} \) and \( \mathrm{KO}_{2} \) are respecitvely:
A \( \cdot-2,-1,-\frac{1}{2} \)
в. \( -\frac{1}{2},-1,-2 \)
\( c \cdot_{-1,-2,-\frac{1}{2}} \)
D. \( _{-2,-\frac{1}{2},-1} \)


Two identical calorimeter \( \boldsymbol{A} \) and \( \boldsymbol{B} \)
contain equal quantity of water at \( 20^{\circ} C \)
A \( 5 g m \) piece of metal \( X \) of specific
heat 0.2 cal \( g^{-1}\left(C^{\circ}\right)^{-1} \) is dropped into
\( A \) and a \( 5 g m \) piece of metal \( Y \) into \( B \) The equilibrium temperature in \( A \) is
\( 22^{\circ} \mathrm{C} \) and in \( B 23^{\circ} \mathrm{C} . \) The initial
temperature of both the metals is \( 40^{\circ} \mathrm{C} \)
Find the specific heat of metal \( Y \) in cal
\( \boldsymbol{g}^{-1}\left(\boldsymbol{C}^{\circ}\right)^{-1} \)


Consider \( \boldsymbol{a} \boldsymbol{z}^{2}+\boldsymbol{b} \boldsymbol{z}+\boldsymbol{c}=\mathbf{0}, \) where
\( a, b, c \in R \) and \( 4 a c>b^{2} \)
In the argand's plane. if \( A \) is the point
represnting \( z_{1} . \) B is the point representing \( z_{2} \) and \( z=\frac{\overrightarrow{O A}}{\partial B} \) then z is:
A. z is purely real
B. z is purely imaginary
c \( \cdot|z|=1 \)
D. \( \Delta A O B \) is a scalene triangle


In the figure given, \( A \) and \( B \) are the
centres of the two congruent circles
with radius 17 units. If \( A B=30 \) units,
the length of the common chord \( D C \) is
A . 25 units
B. 18 units
c. 10 units
D. 16 units


The weight of \( 1 \times 10^{22} \) molecules of
\( \boldsymbol{C u} \boldsymbol{S O}_{4} \cdot \mathbf{5} \boldsymbol{H}_{2} \boldsymbol{O} \) is:
(nearest integer)


Calculate the amount of work done in
turning an electric dipole of dipole
moment \( 3 \times 10^{-8} C \) -m from its position
of unstable equilibrium to the position of stable equilibrium in a uniform
electric field of intensity \( 10^{3} N C^{-1} \)


The ratio of the volume and surface area
of a sphere of unit radius:
A .4: 3
B. 3: 4
c. 1: 3
D. 3: 1


The circle drawn on the minor axis as
diameter passes through the foci of the ellipse \( \mathbf{S}=\mathbf{0}, \) then its eccentricity \( \mathbf{e}= \)
\( \mathbf{A} \cdot \sin 18^{0} \)
B. \( \sin 30^{\circ} \)
c. \( \cos 45^{\circ} \)
D. \( \cos 30^{\circ} \)


What is nutrition? What is the mode of
nutrition in amoeba known as? Draw
diagram and explain.


The value of the integral \( \int_{-\pi / 4}^{\pi / 4} \log (\sec \theta-\tan \theta) d \theta \) is
\( A \cdot \frac{\pi}{4} \)
B.
\( c \cdot 0 \)
\( D \)


Which term of an AP 3,15,27,39
will be 120 more than its
\( 21^{s t} \) term


A committee of 12 is to be formed from
nine women and eight men. In how
many ways this be done if at least five
women have to be included in a
committee? In how many of these
committees
a. the women hold majority?
b. the men hold majority?


These ions have the same number of
electrons.
A. \( M g^{+} \) and \( F^{+} \)
B. \( L i \) and \( N e \)
\( c \cdot O^{2-} \) and \( O^{-} \)
D. \( N \) and \( P^{3-} \)
E \( \cdot C a^{2+} \) and \( C l^{-} \)


The parallel plate capacitor on the left \( C L \) has a separation distance of \( 1 \mathrm{cm} \)
and the sides of the square plate are each \( 0.5 m . \) While the smaller paralle
plate capacitor on the right \( C R \) has a
separation distance of \( 0.2 \mathrm{cm} \) and each
side of the square plate is \( 0.1 m \) in length. Determine the ratio of capacitance
\( \boldsymbol{C} \boldsymbol{L}: \boldsymbol{C} \boldsymbol{R} \)
A . 1:
B. 5:
\( c .1: 5 \)
\( D .3 \)


There are 30 tickets numbered from 1 to
30 in a box. A ticket is drawn at random
from the box and if \( A \) is the event that
the number on the ticket is a multiple
of five, write the sample space \( \boldsymbol{S}, \boldsymbol{n}(\boldsymbol{S}) \) the event \( \boldsymbol{A} \) and \( \boldsymbol{n}(\boldsymbol{A}) \)


Angiosperm flowers may be monoecious, cleistogamous or may show self-incompatibility. Describe the characteristic features of each one
of them and state which one of these
flowers promotes inbreeding and outbreeding respectively.


A charged particle \( \left(Q=10^{-4} C\right) \) is
released from rest at \( z=0 \) in magnetic field given as \( \overrightarrow{\boldsymbol{B}}=\boldsymbol{B}_{0} \cos (\boldsymbol{\omega} \boldsymbol{t}-\boldsymbol{k} \boldsymbol{z}) \hat{\boldsymbol{i}}+ \)
\( B_{1} \cos (\omega t+k z) \hat{j} \) where \( B_{0}=3 x \)
\( 10^{-5} T \) and \( B_{1}=2 \times 10^{-6} T . \) Then the
rms value of force acting on particle is?
A. \( 3 \times 10^{-2} \)
B. 0.6
c. 0.9
D. \( 0 . \)


Which is not true for a standard
hydrogen electrode?
A. It can act both as cathode and anode
B. Temperature is \( 273 \mathrm{K} \)
C. Pressure is 0 atm.
D. It contains a metallic conductor which does not
absorb hydrogen


For image magnification one needs at least
A. two convex lenses
B. one concave and one convex lens
c. one concave lens
D. one convex lens


Due to low concentration of oxygen in blood, climber become weak and unable to think clear -
(i) Write specific name of above condition?
(ii) Explain the reason of such
condition?


Which of the following give the correct increasing order of the atomic radii of
\( \boldsymbol{O}, \boldsymbol{F}, \boldsymbol{a} \boldsymbol{n} \boldsymbol{N} ? \)
A. \( O, F, N \)
в. \( N, F, O \)
c. \( O, N, F \)
D. \( F, O, N \)


The earth's magnetic field at some place on magnetic equator of the earth is \( 0.5 \times 10^{-4} \) T. Consider the radius of
the earth at that place as \( 6400 k m \)
Then, magnetic dipole moment of the
earth is \( \boldsymbol{A} \boldsymbol{m}^{2} \)
\( \left(\mu_{0}=4 \pi \times 10^{-7} T m A^{-1}\right) \)
A \( \cdot 1.31 \times 10^{23} \)
B. \( 1.05 \times 10^{23} \)
C. \( 1.15 \times 10^{23} \)
D. \( 1.62 \times 10^{23} \)


Two particles having masses \( 1 k g \) and
7 kg respectively attract each other. Initially they are at rest and infinite separation.The velocity of approach of the particles are at a separation of \( 1 \boldsymbol{m} \) is (G=universal gravitational constant)
\( \begin{array}{lll}\text { A } \cdot \sqrt{2} G & \text { m/s }\end{array} \)
B . \( 4 \sqrt{G} \) m/s
c. \( \sqrt{\frac{G}{2} m / s} \)
D. \( \frac{G}{4} m / s \)


Complete and balance the following
compound \( \boldsymbol{C a}_{\mathbf{5}}\left(\boldsymbol{P O}_{4}\right)_{3} \boldsymbol{F}+\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O} \stackrel{\boldsymbol{H} e a t}{\rightarrow}-\ldots-\ldots-+\boldsymbol{C} \boldsymbol{a} \boldsymbol{S} \boldsymbol{O}_{4} \)
\( 2 H_{2} O+_{-}-_{-}-- \)


If \( \boldsymbol{A} \cap \boldsymbol{B} \subseteq \boldsymbol{C} \) and \( \boldsymbol{A} \cap \boldsymbol{B} \neq \boldsymbol{\phi} \). Then
which of the following is incorrect
\( \mathbf{A} \cdot(A \cup B) \cap C \neq \phi \)
в. \( B \cap C=\phi \)
c. \( A \cap C \neq \phi \)
D. If \( (A-C) \subseteq C \) then \( A \subseteq C \)


Sulphurous anhydride is:
\( A \cdot \operatorname{so}_{3} \)
B. \( S O_{4}^{2-} \)
\( \mathrm{c} \cdot \mathrm{SO}_{3}^{2-} \)
D. \( S O_{2} \)


Which of the following statement is
incorrect:
This question has multiple correct options
\( \mathbf{A} \cdot O_{2} \) is paramagnetic, \( O_{3} \) is also paramagnetic
B. \( O_{2} \) is paramagnetic, \( O_{3} \) is diamagnetic
\( \mathrm{C} \cdot B_{2} \) is paramagnetic, \( C_{2} \) is also paramagnetic
D. Different observation is found in their bond length when \( N O \rightarrow N O^{+} \) and \( C O \rightarrow C O^{+} \)


How does the temperature of the gas change?
A. Increases
B. Decreases
c. Remains Same
D. cannot be predicted


The products of the hydrolysis of \( \mathbf{P C l}_{3} \)
are :
A \( . \) HCl, \( \mathrm{H}_{3} \mathrm{PO}_{4} \)
в. \( \mathrm{HCl}, \mathrm{H}_{3} \mathrm{PO}_{3} \)
c. \( \mathrm{Cl}_{2}, \mathrm{H}_{3} \mathrm{PO}_{3} \)
D. HCl, POCls, H \( _{3} \mathrm{PO}_{4} \)


The cable of an electric fan becomes so
worn that the live wire makes electrical
contact with the metal case The case is
earthed The plug to the fan contains a 5 A fuse There is a current of 4 A when the
fan works normally What will happen in
this case?
A. The current will run to earth and the fuse will not be affected
B. The metal case will become very hot
c. The metal case will become live and dangerous
D. The fuse will melt and switch off the circuit


Find the slope of the line that passes through the points (7,4) and (-9,4)
\( A \cdot O \)
B.
\( c \cdot-1 \)
\( D \cdot 2 \)


Is it possible to have a regular polygon
whose each interior angle is \( 138^{\circ} \)
State true or false:
A. True
B. False


Find the total number of cations for
which I.P of cation is lower than
corresponding atom: \( \boldsymbol{K}^{+}, \boldsymbol{O}^{+}, \boldsymbol{N} \boldsymbol{e}^{+}, \boldsymbol{P}^{+} \)
\( \boldsymbol{B} \boldsymbol{e}^{+}, \boldsymbol{N} \boldsymbol{a}^{2+} \)


The average power transmitted through a given point on a string with a sine wave is 0.40 watt, when the amplitude of the wave is \( 2 \mathrm{mm} \). What average
power will be transmitted through this point its amplitude is increased to 4
\( \mathrm{mm} \)
A. 0.40 watt
B. 0.80 watt
c. 1.2 watt
D. 1.6 watt


\( f(x)=\frac{a \sin x-b x+c x^{2}+x^{3}}{2 x^{2} \ell n(1+x)-2 x^{3}+x^{4}} \)
when \( x \neq 0 \) and \( f(x) \) is continuous at
\( \boldsymbol{x}=\mathbf{0}, \) find value of \( \mathbf{2 0 0} \times \boldsymbol{f}(\mathbf{0}) \)


\( \int 3 V-V^{3} d V \)


Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{\alpha} \log \boldsymbol{x} \) for \( \boldsymbol{x}>\mathbf{0} \) and \( \boldsymbol{f}(\boldsymbol{x}) \)
follows Rolle's theorem for [0,1] then \( \alpha \)
is :
A . -2
B. -
c. 0
D. \( 1 / 2 \)


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


Compared to other acids like
\( \boldsymbol{H} \boldsymbol{C l}, \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3}, \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) is highly syrupy
and viscous in nature. Identify the
correct reason.
A \( \cdot H_{2} S O_{4} \) is highly concentrated
B. \( H_{2} S O_{4} \) is a stronger acid than \( H C l, H N O_{3} \)
C. \( H_{2} S O_{4} \) is associated by more number of hydrogen bonds
D. Both (A) and (B)


A machine part consist of two
homogeneous solid cylinders coaxially.
Then find the distance of center of mass
from 0
\( \mathbf{A} \cdot \frac{17}{2} m m \)
\( \mathbf{B} \cdot \frac{52}{7} m m \)
\( \mathbf{c} \cdot \frac{15}{17} m m \)
\( \mathbf{D} \cdot \frac{12}{7} m m \)


1 L sample of impure water containing sulphide ion is made ammonial and is
titrated with \( 300 \mathrm{mL} \) of \( 0.1 M A g N O_{3} \) solution. Which of the following statements is/are correct about the
above reaction?
This question has multiple correct options
A. The strength of \( H_{2} S \) in water is \( 0.51 \mathrm{g} / \mathrm{L} \)
B. The strength of \( H_{2} S \) in water is \( 5.1 \mathrm{g} / \mathrm{L} \)
C. The concentration of \( H_{2} \) S in water in ppm is 510
D. The concentration of \( H_{2} S \) in water in ppm is 51


A sample of neon gas is contained by a closed 5-liter vessel. The temperature of
container is \( 25^{\circ} \mathrm{C} \) and pressure is 1.5 atmospheres (R is equal to \( 0.08 \mathrm{L} \) \( \operatorname{atm} / \operatorname{mol} \mathrm{K} \)
Find the expressions which is equal to the molar quantity of gas in the sample?
A \( \frac{(1.5)(5.0)}{(0.08)(25)} \)
B. \( \frac{(0.08)(25)}{(1.5)(5.0)} \)
c. \( \frac{(1.5)(25)}{(0.08)(5.0)} \)
D. \( \frac{(0.08)(298)}{(1.5)(5.0)} \)
E \( \frac{(1.5)(5.0)}{(0.08)(298)} \)


The cost of 97 metre of cloth is Rs
242.50. What length of this can be purchased for Rs \( 302.50 ? \)


A polar bond is formed between two
atoms of different electronegativity. A polar molecule results when there is
only one polar bond, or more than one polar bond within it is not sufficiently symmetrically oriented to cancel the effects of the others.
Select the correct order of boiling point.
\( \mathbf{A} \cdot H_{2} O<H F \)
в. \( H_{2} O>H F \)
\( \mathbf{c} \cdot H F=H_{2} O \)
D. None of these


In the figure, ABCD is a parallelogram.
\( \boldsymbol{A} \boldsymbol{E} \perp \boldsymbol{D} \boldsymbol{C}, \boldsymbol{C} \boldsymbol{F} \perp \boldsymbol{A} \boldsymbol{D} . \) If \( \boldsymbol{A} \boldsymbol{B}=\mathbf{1 6} \mathrm{cm} \)
\( A E=8 \mathrm{cm} \)
and \( C F=10 \mathrm{cm} \) then \( A D \) is equal to
\( A \cdot 12 c m \)
B. \( 15 \mathrm{cm} \)
c. \( 12.8 \mathrm{cm} \)
D. \( 15.5 \mathrm{cm} \)


A man of mass \( m \) starts falling towards
a planet of mass \( M \) and radius R. As he
reaches near to the surface, he realizes that he will pass through a small hole in the planet. As he enters the hole, he sees that the planet is really made of two pieces a spherical shell of negligible thickness of mass \( 2 M / 2 \) and a point
mass \( M / 3 \) at the centre. Change in the force of gravity experienced by the man is
A \( \cdot \frac{2 G M m}{3} \frac{G M m}{R^{2}} \)
B. 0
c. \( \frac{1}{3} \frac{G M m}{R^{2}} \)
D. \( \frac{4 G M m}{3} \frac{G M m}{R^{2}} \)


Glutamic acid has two carboxyl groups.
A. True
B. False


The standard heat of combustion of
solid boron is equal to:
\( A \cdot \Delta H_{f}^{\circ}\left(B_{2} O_{3}\right) \)
B \( \cdot 1 / 2 \Delta H_{f}^{\circ}\left(B_{2} O_{3}\right) \)
\( \mathrm{c} \cdot 2 \Delta H_{f}^{\circ}\left(B_{2} O_{3}\right) \)
D. \( 6 / 2 \Delta H_{f}^{\circ}\left(B_{2} O_{3}\right) \)


In the adjoining diagram, a currentcarrying loop pqrs placed with its sides parallel to a long current-carrying wire.
The currents \( i_{1} \) and \( i_{2} \) in the wire and
loop are \( 20 \mathrm{A} \) and 16 A respectively. If \( a= \) \( 15 \mathrm{cm}, \mathrm{b}=6 \mathrm{cm}, \) and \( \mathrm{d}=4 \mathrm{cm}, \) what will
be the force on current \( i_{2} \) in the loop is
clockwise instead of anticlockwise?


Which of the following is highly compressible?
A. Solids
B. Liquids
c. Gases
D. None of these


ff \( \boldsymbol{A}=\left[\begin{array}{cc}\boldsymbol{i} & \mathbf{0} \\ \boldsymbol{0} & \boldsymbol{i}\end{array}\right], \) find \( \boldsymbol{A}^{2} \)


Prepare four questions you will ask a nephrologist about kidney failure.


A particle executes SHM with a period
of \( T \) seconds. \( t \) seconds after it has
crossed the equilibrium position it is at
a point \( P . \) After how much time it will be
again at \( P ? \)
A \( \cdot \frac{T}{2}-t \)
в. \( \frac{T}{4}-t \)
c. \( \frac{T}{2}-2 t \)
D. \( \frac{T}{4}-2 t \)


In his classic experiment on pea plants, Mendel did not use
A. Seed colour
B. Pod length
c. seed shape
D. Flower position


f \( a=2 i+5 j+k \) and \( b=4 i+m j+ \)
\( n k \) are collinear vectors, then find \( m+n \)


\( 1: \Delta U \) is state function
2: Heat and work are not state
functions.
A. only 1 is true
B. only 2 is true
c. both are true
D. none of the above


If \( a+\frac{1}{a}=2, \) then find \( a^{4}+\frac{1}{a^{4}} \)


A small coil is introduced between the
poles of an electromagnet so that its axis coincides with the magnetic field
direction. The cross-sectional area of
the coil is equal to \( S=3.0 m m^{2}, \) the
number of turns is \( N=60 . \) When the
coil turns through \( 180^{\circ} \) about its diameter, a galvanometer connected to the coil indicates a charge \( \boldsymbol{q}=\mathbf{4 . 5} \boldsymbol{\mu} \boldsymbol{C} \)
flowing through it. Find the magnetic induction magnitude between the poles, provided the total resistance of the electric circuit equals \( R=40 \Omega \)


When a plane mirror is placed horizontally on level ground at a distance of \( 60 \mathrm{m} \) from the foot of
a tower, the ray coming from the top of the tower and its reflected ray from
the mirror subtends an angle of \( 90^{\circ} \)
What is the height of the tower?
A. 30
B. 60 \( m \)
\( c \cdot 90 m \)
D. 120


One green house gas contributes \( 14 \% \) to total global warming and another contributes \( 6 \% . \) These are respectively
identified as
A. \( N O_{2} \) and \( C O_{2} \)
B. CFC and \( N_{2} \) O
c. Methane and \( C O_{2} \)
D. Methane and CFCs
E. cres and \( C O_{2} \)


Azide ion \( \left(N_{3}^{-}\right) \) exhibits on \( N-N \)
bond order of 2 and may be represented by resonance structures I, II and III given below. \( \overline{\boldsymbol{N}}=\dot{\boldsymbol{N}}=\overline{\boldsymbol{N}}: \longleftrightarrow^{2-}: \ddot{\boldsymbol{N}}-\dot{\boldsymbol{N}} \equiv \boldsymbol{N} \)
\( \longleftrightarrow: N \equiv \vec{N}-\ddot{N}:^{2-} \)
\( \| \)
Select correct statements
A. structures land II make greater contributions than "
B. Structures II and III make smaller contributions than
c. structures land II make greater contributions than II
D. All the three structures make equal contributions


BOD refers to
A. The amount of oxygen consumed if all the organic matter in \( 1000 \mathrm{ml} \) of water were oxidized by bacteria
B. The amount of oxygen released when all the organic matter was consumed by bacteria in 1 litre of water
C. The oxygen required for bacteria to grow in 1 litre of effluent
D. The amount of oxygen released if all the organic matter in \( 1000 \mathrm{ml} \) of water were oxidized by bacteria


If \( \boldsymbol{f}(\boldsymbol{x})=\int_{0}^{x}(\cos (\sin t)+\cos (\cos t) d t \)
then \( f(x+\pi) \) is?
\( \mathbf{A} \cdot=f(\pi)+2 f\left(\frac{\pi}{2}\right) \)
B. \( =f(\pi)+6 f\left(\frac{\pi}{6}\right) \)
\( \mathbf{c} \cdot=f(\pi)+9 f\left(\frac{\pi}{11}\right) \)
\( \mathbf{D} \cdot=f(\pi)+10 f\left(\frac{\pi}{3}\right) \)


Given four capacitors each of capacity \( 12 \mu \)
F. To get a capacity of \( 9 \mu \mathrm{F} \), what
combination can be used:
A. All in series
B. All in parallel
c. 3 in parallel and 1 series with them
D. 2 in parallel and 2 in series


The number of monochloro derivaties of
2-methoxy propane are possible are:
A .2
B.
\( c \cdot 3 \)
\( D \)


If a point moves along the curve \( y^{2}=x \)
At what point on the curve does the \( y \)
coordinate change at the same rate as the \( x \) coordinate.


The critical density of the \( \operatorname{gas} C O_{2} \) is \( 0.44 g c m^{-3} \) at a certain temperature. If
\( r \) is the radius of the molecule, \( r^{3} \) in
\( c m^{3} \) is approximate:
[N is Avogadro number]
A \( \frac{25}{\pi N} \)
в. \( \frac{100}{\pi N} \)
c. \( \frac{6}{\pi N} \)
D. \( \frac{25}{4 N \pi} \)


Global warming leads to:
A. increase in actual temperature of earth
B. decrease in actual temperature of earth
C. no change in temperature
D. change in pressure


If \( \operatorname{cosec} \theta-\sin \theta=a^{3} \) and \( \sec \theta- \)
\( \cos \theta=b^{3}, \) prove that \( a^{2} b^{2}\left(a^{2}+b^{2}\right)=1 \)


A large solid sphere of diameter \( 18 \mathrm{cm} \) is melted and recast into several small
spheres of diameter \( 3 \mathrm{cm} \) The percentage increase in the surface area of the smaller spheres over that of
the larger sphere is
A . 500\%
B . 350\%
c. \( 450 \% \)
D. 545\%


If \( y \sin x=x+y \) then \( \left(\frac{d y}{d x}\right)_{x=0} \) equals
\( \mathbf{A} \cdot \mathbf{1} \)
B. -
\( c \cdot 0 \)
D. 2


A house has four tubelights, three fans and a television. Each tubelight draws
\( 40 W . \) The fan draws \( 80 W \) and the
television draws \( 100 \mathrm{W} \). On an average,
all the tubelights are kept on for 5 hours, all fans for 12 hours and the
television for 6 hours everyday. Find the
\( \operatorname{cost} \) of electric energy used in 30 days at the rate of \( R s .3 .00 \) per KWH


If \( \vec{a}, \vec{b}, \vec{c} \) are three unit vector such that \( \overrightarrow{\boldsymbol{a}} \times \overrightarrow{\boldsymbol{b}}=\overrightarrow{\boldsymbol{c}}, \overrightarrow{\boldsymbol{b}} \times \overrightarrow{\boldsymbol{c}}=\overrightarrow{\boldsymbol{a}}, \overrightarrow{\boldsymbol{c}} \times \overrightarrow{\boldsymbol{a}}=\overrightarrow{\boldsymbol{b}} . \) Show
that \( \vec{a}, \vec{b}, \vec{c} \) from an orthogonal right handed tried of unit vectors.


Value(s) of m for which the system
remains at rest (pulleys and strings are
ideal) is/are: \( \left(\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right) \)
This question has multiple correct options
\( A \cdot 1 \mathrm{kg} \)
B. 2 kg
c. \( 18 \mathrm{kg} \)
D. 20 kg


In which of the following pathways, movement of water occurs from one cell
to another cell through plasmodesmata?
A. Apoplast pathway
B. Symplast pathway
c. vacuolar pathway
D. Transmembrane pathway


\( \frac{3}{2} O_{2}(g) \longrightarrow O_{3}(g) K_{p} \) for this reaction
is \( 2.47 \times 10^{-29} . \) At \( 298 \mathrm{K}, \Delta_{r} G^{o} \) for
conversion of oxygen to ozone will be:
A \( \cdot \) 100 \( k \) J mol \( ^{-1} \) -
B . 150 kJ mol-
c. \( 163 \mathrm{kJ} \mathrm{mol}^{-1} \)
D. 2303 kJ mol-1


An electron in the hydrogen atom is excited from the first orbit to the fifth
orbit. The frequency of radiation is:
A \( \cdot 0.44 \times 10^{9} \mathrm{Hz} \)
В. \( 0.317 \times 10^{15} \mathrm{Hz} \)
c. \( 6.2 \times 10^{8} H z \)
D. \( 1.13 \times 10^{12} \mathrm{Hz} \)


List the different scales of
electronegativity and briefly describe the theoretical basis behind each.


If \( \boldsymbol{A}=\operatorname{diag}(\mathbf{2}-\mathbf{5} \mathbf{9}), \boldsymbol{B}=\operatorname{diag}(\mathbf{1} \mathbf{1}- \)
4) and \( C=\operatorname{diag}(-634), \) then find \( \mathbf{2} \boldsymbol{A}+\mathbf{3} \boldsymbol{B}-\mathbf{5} \boldsymbol{C} \)


If points \( (a, 0),(0, b) \) and \( (x, y) \) are
collinear, prove that \( \frac{x}{a}+\frac{y}{b}=1 \)


The seeds respirate at the time of germination. While showing this experiment a test tube with \( K O H \) is kept in the conical flask to
A. Supply oxygen necessary for respiration.
B. Create space in the conical flask by absorbing co2.
c. Absorb water from the seeds and dry them
D. Make the air in the conical flask, acidic


The principal value of \( \sin ^{-1}\left(\frac{-1}{2}\right) \) is
A \( \cdot \frac{-\pi}{6} \)
В. \( \frac{5 \pi}{6} \)
c. \( \frac{7 \pi}{6} \)
D. none of these