The second I.P. for alkali metals shows a
jump while the third I.P. for alkaline earth metal shows a jump. Explain.


In Williamson's synthesis, ethoxy
ethane is prepared by:
A. heating sodium ethoxide with ethyl bromide
B. passing ethanol over heated alumina
C . treating ethyl alcohol with excess of conc. \( H_{2} S O_{4} \) at \( 430-440 K \)
D. heating ethanol with dry \( A g_{2} O \)


The approach to derive the properties of a bigger, more complex, system from the properties and interactions of its constituent simpler parts is called
A. Reduction
B. Simplification
c. Unification
D. Modification


toppr ०६
Q Type your question
spring is unsurtecritu. Next with the blue mass hanging, the
spring stretches.

Finally, with the red mass hanging, the
spring stretches twice as much as it
did with blue mass.
How much energy does the hanging red
mass store in the spring-mass system,
compared to the amount of energy the
hanging blue mass stores in the spring-
mass system?
A. The red mass stores twice as much energy as the blue mass
B. The red mass stores fours times as much energy as the blue mass
C. The red mass stores half as much energy as the blue mass
D. The red mass stores about 1.4 times as much energy as the blue mass
E. We cannot determined how much energy the red mass stores compared to the blue mass, because we do not know the unstretched length of the spring


The major binding force in graphite is
A. ionic bond
B. covalent bond
c. hydrogen bond
D. London force


Indicate the types of isomerism exhibited by the following complex and
draw the structure of this isomer.
\( \boldsymbol{K}\left[\boldsymbol{C r}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{2}\left(\boldsymbol{C}_{2} \boldsymbol{O}_{4}\right)_{2}\right. \)


\( 0.25 g \) of an organic compound gave
31.1ml of \( N_{2} \) at STP. The \% of N in the
organic compound is:
A . 15.5 5
B. 16.23
\( c \cdot 10.4 \)
D. 18.23


Assertion
\( \tan x\left(2+\sin ^{2} x\right)>6 x \forall x \in\left[0, \frac{\pi}{4}\right] \)
Reason
If \( f(x) \) and \( g(x) \) are continuous in \( [a, b] \) differentiable in \( (\boldsymbol{a}, \boldsymbol{b}), \boldsymbol{f}(\boldsymbol{a})= \)
\( \boldsymbol{g}(\boldsymbol{a}) \) and \( \boldsymbol{f}^{\prime}(\boldsymbol{x})<\boldsymbol{g}^{\prime}(\boldsymbol{x}) \forall \boldsymbol{x} \in(\boldsymbol{a}, \boldsymbol{b}) \)
\( \operatorname{then} f(x)<g(x) \forall x \in(a, b) \)
A. Assertion and Reason are correct and the Reason is the correct explanation for the Assertion
B. Assertion and Reason are correct and the Reason is Not the correct explanation for the Assertion
c. Assertion is correct while the Reason is incorrect
D. Assertion is incorrect while the Reason is correct


Prove that \( ^{n} c_{r} . r !=^{n} p_{r} \)


Two source of sound placed closed to each other, are emitting progressive
wave given by \( y_{1}=4 \sin 600 \pi t \) and
\( \boldsymbol{y}_{2}=\mathbf{5} \sin \mathbf{6 0} \mathbf{8} \boldsymbol{\pi} \boldsymbol{t} . \) An observed located
near these two sources will hear:
A. 8 beats per second with intensity ratio 81: 1 between waxing and waning
B. 4 beats per second with intensity ratio 81: 1 between waxing and waning
c. 4 beats per second with intensity ratio 25: 16 between waxing and waning
D. 8 beats per second with intensity ratio 25 : 16 between waxing and waning


An electron in hydrogen atom after absorbing an energy photon jumps from
energy state \( n_{1} \) to \( n_{2} \). Then it returns to
ground state after emitting six different wavelengths in emission spectrum. The energy of emitted photons is either
equal to less than the absorbed
photons. The \( n_{1} \) and \( n_{2} \) are
A \( . n_{2}=4, n_{1}=3 \)
в. \( n_{2}=5, n_{1}=3 \)
c. \( n_{2}=4, n_{1}=1 \)
D. \( n_{2}=5, n_{1}=1 \)


In Leclanche cell, Zinc rod is placed in:
A \( \cdot 10 \% \) NH \( _{4} \) С।
B. 20\% NH_CI
c. \( 30 \% \mathrm{NH}_{4} \) С।
D . 40\% NH \( _{4} \) C


Calculate the momentum of particle
whose de Broglie wavelength is \( 2^{\circ} A \)
A \( \cdot 3.313 \times 10^{-24} g m s^{-1} \)
В. \( 3.313 \times 10^{-24} k g m s^{-1} \)
c. \( 33.13 \times 10^{-20} k g m s^{-1} \)
D. none of these


A rod \( A B \) moves with a uniform velocity
\( \boldsymbol{v} \) in a uniform magnetic field as shown in figure :
\[
\begin{array}{llllll}
x & x & x & x & x & x \\
x & x & x & A & x & x \\
x & x & x & x & x & x \\
x & x & x & B x & x & x
\end{array}
\]
A. The rod becomes electrically charged
B. The end A becomes positively chargedd
C. The end B becomes positively charged
D. The rod becomes hot because of Joule heating


A cell is bound to divide, if it has
entered
A \( \cdot \mathrm{G}_{2} \) phase
B. G_phase
c. Prophase
D. S phase


n Fig., light is incident at an angle \( \theta \) is
incident at an angle \( \theta \) which is slightly greater than the critical angle. Now, keeping the incident angle fixed a
parallel slab of refractive index \( n_{3} \) is
placed on surface \( \boldsymbol{A B} \). Which of the
following statements are correct?
(a)
This question has multiple correct options
A. Total internal reflection occurs at \( A B \) for \( n_{3}<n \)
B. Total internal reflection occurs at \( A B \) for \( n_{3}>n_{1} \)
c. The ray will return back to the same medium for all
values of \( n_{3} \)
D. Total internal reflection occurs at \( C D \) for \( n_{3}<n_{1} \)


Differentiate the following function with
respect to \( x \) \( \boldsymbol{x}^{-4}\left(\boldsymbol{3}-\boldsymbol{4} \boldsymbol{x}^{-\boldsymbol{5}}\right) \)


Which of the following is not a characteristic of the standard unit?
A. It should be of convenient size
B. It should change with respect to space and time
c. It should not be perishable
D. It should be eerily reproducible


Positronium is converted into
A. 2 Photons each of energy \( 0.51 \mathrm{MeV} \)
B. 1 Photon of energy 1.02 MeV
C. 2 Photons each of energy 1.02MeV
D. 1 Photon of energy \( 0.51 \mathrm{MeV} \)


The field normal to the plane of a wire of \( n \) turns and radius r which carries a current
is measure on the axis of the coil at a
small distance h from the centre of the
coil. By what fraction this is smaller than
the field at the centre?


A steady current flows in a metallic
conductor of non-uniform cross-section.
The quantity/quantities constant along the length of the conductor is /are
A. current, electric current and drift velocity
B. drift speed only
c. current and drift speed only
D. current only


The negation of \( \sim s \vee(\sim r \wedge s) \) is
equivalent to
\( \mathbf{A} \cdot S \wedge r \)
В. \( S \wedge \sim(r \wedge \sim s) \)
c. \( S \vee \sim(r \wedge \sim s) \)
D. None of These


Fill in the blanks:
The organic compounds containing carbon and \( _{--}-_{-}- \) only are called hydrocarbons. These are and
unsaturated.


Speed of decomposition of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) is
reduced by :
A. \( N a_{2} C O_{3} \)
в. \( N a O H \)
c. alcohol
D. platinum


Evaluate \( \int_{0}^{\pi / 2} \frac{\cos x}{1+\sin ^{2} x} d x \)


Prove that \( \mid \begin{array}{ccc}b c-a^{2} & c a-b^{2} & a b \\ -b c+c a+a b & b c-c a+a b & b c+c \\ (a+b)(a+c) & (b+c)(b+a) & (c+a\end{array} \)
\( \mathbf{3} \cdot(\boldsymbol{b}-\boldsymbol{c})(\boldsymbol{c}-\boldsymbol{a})(\boldsymbol{a}-\boldsymbol{b})(\boldsymbol{a}+\boldsymbol{b}+ \)
\( c(a b+b c+c a) \)


Bleaching powder contains:
A. \( C a O \) and \( C l_{2} \) are molecules
B. \( C a^{2+} \) and 2 OCl \( ^{-\text {ions }} \)
c. \( C a^{2+}, C l^{-} \) and \( O C l^{-} \) ions
D. \( C a^{2+}, O^{2-} \) ions and \( C l_{2} \) molecule


If \( I=\int_{0}^{2 \pi} e^{x / 2} \sin \left(\frac{x}{2}+\frac{\pi}{4}\right) d x, \) then \( I \)
equals
\( A \)
B.
\( \mathbf{c} \cdot-\pi / 2 \)
D. \( 2 \pi \)


A bar magnet falls from a height 'h
through a metal ring. Will its
acceleration be equal to g? Give reasons
for your answer.


If the earth shrinks half in radius with
its mass remaining the same, the weight of an object on earth will :
A. decrease by \( 50 \% \)
B. increase by \( 50 \% \)
c. decrease by \( 25 \% \)
D. increase by \( 300 \% \)


How do I find
\( \boldsymbol{A}=\left[\begin{array}{ccc}1 & 2 & -2 \\ -1 & 3 & 0 \\ 0 & -2 & 1\end{array}\right]=|A|=? \)


Time period of simple pendulum in a satellite is
A . Infinite
B. Zero
c. 2 sec
D. Cannot be calculated


A car accelerates on a horizontal road
due to the force exerted by:
A. the engine of the ear
B. the driver of the car
c. the earth
D. the road


A uniform chain of length \( 2 m \) is kept on
a table such that a length of \( 60 \mathrm{cm} \) hanging freely from the edge of the table. The total mass of the chain is
\( 4 k g . \) The work done is pulling the entire
chain on the table (Take \( \left.g=m s^{-2}\right) \)
A . \( 12.9 J \)
B. \( 6.3 J \)
c. \( 3.6 J \)
D . \( 2.0 J \)


\( \int\left(\frac{1}{\log x}-\frac{1}{(\log x)^{2}}\right) d x_{-----}+c \)
A . \( x \log . x \)
B. \( \frac{x}{2}(\log x)^{2} \)
c. \( \frac{x}{\log x} \)
D. \( \frac{x}{(\log x)^{2}} \)


Sum of the natural number between
\( \mathbf{1 0 0} \) and \( \mathbf{2 0 0} \) whose HCF with \( \mathbf{9 1} \) should
be more than 1
A. 1121
в. 3210
\( c .3121 \)
D. 1520


Rutherford's alpha scattering experiment showed for the first time
that the atom has:
A . electrons
B. protons
c. nucleus
D. neutrons


If two events \( A \) and \( B \) such that
\( \boldsymbol{P}\left(\boldsymbol{A}^{c}\right)=\mathbf{0 . 3}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 4} \) and \( \boldsymbol{P}(\boldsymbol{A} \cap \)
\( \left.\left.\boldsymbol{B}^{c}\right)=\mathbf{0 . 5}, \boldsymbol{P}\left[\boldsymbol{B} / \boldsymbol{A} \cup \boldsymbol{B}^{c}\right)\right]=\frac{1}{k}, \) then
value of k is


The blocks of the periodic table are named for the \( \ldots \). orbital to be
occupied according to the building-up principle.
1. first
2. last
3. highest
4. lowest


Assertion
The flow of heat energy from one body to the other depends upon the amount of heat energy in them
Reason
Heat flows from lower temperature of the body to higher temperature of the body
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Find the directions cosines of \( x, y \) and \( z \)
axis.


Kepler's second law is a consequence of
A. conservation of energy
B. conservation of linear momentum
C. conservation of angular momentum
D. conservation of mass


\( S \) and \( T \) are the foci of an ellipse and \( B \)
is an end of the minor axis. If \( S T B \) is an
equilateral triangle, then what is the value of \( e \) ?
A \( \cdot \frac{1}{4} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{1}{2} \)
D. \( \frac{2}{3} \)


In electrochemical corrosion. the metal
undergoing corrosion:
A. acts as anode
B. acts as cathode
c. undergoes reduction
D. liquifies


If \( 4 x+4 y-k z=0 \) is the equation of
the plane through the origin that contains the line \( \frac{\boldsymbol{x}-\mathbf{1}}{\mathbf{2}}=\frac{\boldsymbol{y}+\mathbf{1}}{\mathbf{3}}=\frac{\boldsymbol{z}}{\mathbf{4}} \)
then \( \boldsymbol{k}= \)
A . 1
B. 3
\( c .5 \)
D.


The smoke from a fire looks white.
Which of the following statements is
true?
1. Molecules of the smoke are bigger than the wavelength of light.
2. Molecules of the smoke are smaller
than the wavelength of light.


Name a gas whose solution in water is
alkaline.
A. Ammonia
B. Chlorine
\( c \cdot s O_{2} \)
D. HCl


Select the correct I.U.P.A.C name for
\( \left[\boldsymbol{C r}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{3} \boldsymbol{C l}_{3}\right] \) complex:
A. Triamminetrichloridochromate \( (I I I) \)
B . Triamminetrichloridochromium(III)
C . Trichloridotriamminechromium(III)
D. Trichloridotriamminechromate(III)


The impurity atoms with which pure silicon may be doped to make it a \( \mathrm{p} \) type semiconductor are those of Imore than one option may he correct] This question has multiple correct options
A. phosphorus
B. boron
C. antimony
D. aluminium


Which one of the following electrolytes is most effective for the coagulation of
\( \boldsymbol{F e}(\boldsymbol{O} \boldsymbol{H})_{3} \) sol?
A . \( N a C l \)
в. \( N a_{2} S O_{4} \)
\( \mathbf{c} \cdot N a_{3} P O_{4} \)
D. \( A s_{2} S_{3} \)


Assertion: Muscle contraction force
increases with rise in strength of
stimulus

Reason: This is due to increased
contraction of individual muscle fibres
with an increase in stimulus strength.
A. Assertion and the reason are true and the reason is a correct explanation of the assertion
B. Both the assertion and reason are true but the reason is
not a correct explanation of the assertion
c. Assertion is true but the reason is false
D. If both the assertion and reason are false
E. Assertion is false but reason is true


4.16 \( g \) of \( B a C I_{2} \) contains \( 2.74 g \) of Ba.
The atomic weight of Ba is nearly:
A .137
B. 208
c. 67.3
D. 97.27


Find the perimeter of a parallelogram
with sides \( 9 \mathrm{cm} \) and \( 5 \mathrm{cm} \)


The complex ion in the compound
\( \boldsymbol{C s}\left[\boldsymbol{M n F}_{4}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{2}\right] \) is octahedral and
high spin. The name of the compound is
A \cdot cesiumdiaquatetrafluoridomanganese \( (I I I) \)
B . cesiumdiaquatetrafluoridomanganate \( (I I I) \)
C . cesiumdiaquatetrafluoridomanganese (IV)
D. cesiumdiaquatetrafluoridomanganate (IV)


Refer the following diagram and identify
the parts of a kidney indicated.
A. A- Cortex, B- Nephron, C- Pelvis, D- Medulla, E- Ureter
B. A- Cortex, B- Medulla, C- Nephron, D- Pelvis, E- Ureter
C. A- Nephron, B- Cortex, C- Medulla, D- Ureter, E- Pelvis
D. A- Nephron, B- Cortex, C- Medulla, D- Pelvis, E- Ureter
E. A- Nephron, B- Ureter, C- Pelvis, D- Medulla, E- Cortex


Ethylene is formed by dehydration of:
A \( \cdot C H_{3} C H O \)
в. \( C_{2} H_{5} O H \)
c. Propyl alcohol
D. Ethyl acetate


When temperature of a gas is \( 20^{\circ} \mathrm{C} \) and
pressure is changed from \( \boldsymbol{P}_{1}=\mathbf{1} . \mathbf{0} \times \)
\( 10^{5} P a \) to \( P_{2}=1.65 \times 10^{5} P a \) and the
volume is changed by \( 10 \% \). The bulk modulus is:
A \( .1 .55 \times 10^{5} P a \)
В. \( 1.15 \times 10^{5} P a \)
c. \( 1.4 \times 10^{5} P a \)
D. \( 1.01 \times 10^{5} \mathrm{Pa} \)


Length of rectangular tank is twice its
breadth. If the depth of the tank is \( 3 m \)
and area of its four walls is \( 108 m^{2} \), find
the length of the tank.


a) State any three findings of modem atomic theory
b) Write down any two applications of Avogadro's law.


Find the next term of the sequence:
\( \frac{1}{2}, \frac{1}{6}, \frac{1}{18}, \frac{1}{54}, \dots \)
A \( \cdot \frac{1}{168} \)
в. \( \frac{1}{164} \)
c. \( \frac{1}{162} \)
D. \( \frac{1}{17} \)


A body projected from the bottom of a smooth inclined plane with a velocity \( 9.8 m / \)sec. The angle of inclination of
the plane is \( 30^{\circ} . \) If it comes to rest after
reaching the top of the plane, then the time of ascent is
A. 2 sec
B. 1 sec
\( c .0 .5 \mathrm{sec} \)
D. 1.5 sec


Find the value of \( \sin \left(\cot ^{-1} x\right) \)


Non-metals are non-malleable due to
absence of:
A. covalent bonding
B. ionic bonding
c. metallic bonding
D. co-ordinate bonding


Differentiate with respect to \( \times \frac{(1+x)}{e^{x}} \)
A \( .-x e^{-x} \)
B . \( x e^{-x} \)
\( \mathrm{c} \cdot-x e^{-2 x} \)
D. \( x^{2} e^{-x} \)


The potential energy of a system
increases if work is done:
A. Upon the system by a non conservative force
B. By the system against a conservative force
C. By the system against a non conservative force
D. Upon the system by a conservative force


Fill in the blanks:
\( \sqrt[3]{8 \times \ldots \ldots}=8 \)


A transformer converts \( 200 V \) a.c. to
\( \mathbf{5 0} \boldsymbol{V} \) a.c.The secondary has \( \mathbf{5 0} \) turns
and load across it draws \( 300 m A \)
current.Calculate the current in the
primary:


Acid rain can be prevented by:
A. use of cleaner fuels
B. attaching devices known as scrubbers in the chimneys
C. both A and B
D. none of above


The length and breadth of a rectangle
are in the ratio \( 3: 2 . \) Total cost of
fencing it at \( R s 12.5 . \) Per meter is
\( R s 25000, \) find its length and breadth.


Why are metals like chromium and
molybdenum very hard?


Give a short description for
homogametes and heterogametes with example.


Which one of the following has magnesium?
A. Vitamin \( B_{12} \)
B. Chlorophyll
c. Haemocyanin
D. Carbonic anhydrase


In a gaseous mixture, if an alkane
\( \left(C_{x} H_{2 x+2}\right) \) and an alkene \( \left(C_{y} H_{2 y}\right) \) are taken in 2: 1 mole ratio, the average
molecular weight of the mixture is
observed to be \( 20 . \) If the same alkane
and alkene are taken in 1: 2 mole ratio,
the average molecular weight of the mixture is observed to be \( 24 . \) Then, the
value of \( x \) and \( y \) are respectively:
A . 2,1
в. 1,2
\( c \cdot 2,3 \)
D. 3.2


Mercury orbits the sun in about one-
fifth of the earth year. If \( 1 A U \) is defined
as the distance from the earth to the
sum, what is the approximate distance between mercury and the sun?
A \( \cdot 1 / 25^{1 / 3} A U \)
B . \( 1 / 9^{1 / 3} A U \)
\( \mathbf{c} \cdot 1 / 5^{1 / 3} A U \)
D. \( 1 / 3^{1 / 3} \) AU


Which of the following is/ are not paramagnetic? This question has multiple correct options
A . \( N O \)
в. \( B r_{2} \)
\( c \cdot c o \)
D. \( O_{2} \)


On a linear escalator running between
two points \( A \) and \( B, \) a boy takes time \( t_{1} \)
to move from \( A \) to \( B \), if the boy runs with a constant speed on the escalator. If the
boy runs from \( \mathrm{B} \) to \( \mathrm{A} \), he takes time \( t_{2} \) to
reach B from A. What is the time taken
by the boy to move from \( A \) to \( B \) if he stands still on the escalator?
[The escalator moves from A to B]


The de-Broglie wavelength of electron in second Bohr's orbit is equal to
A. circumference of the orbit
B. half the circumference of the orbitt
c. twice the circumference of the orbit
D. four times circumference of the orbit


Sound waves are passing through two routes-one in straight path and the other along a semicircular path of
radius \( r \) and are again combined into one pipe and superposed as shown in
the figure. If the velocity of sound waves in the pipe is \( v, \) then frequencies of
resultant waves of maximum
amplitude will be integral multiples of
\( A \)
в. \( \frac{v}{r(\pi-1)} \)
c. \( \frac{2 v}{r(\pi-1)} \)
D. \( \frac{v}{r(\pi+1)} \)


For the reaction: \( 2 H_{2(g)}+2 C l_{2(g)} \rightarrow \)
\( 4 H C l(g) ; \Delta H^{0}=-92.3 K J, \) choose
the correct statement(s) out of the
following:
(i) If the reaction equation is reversed,
the \( \Delta H^{0} \) value will become \( 92.3 K J \)
(ii) The \( 4(H-C l) \) bond in \( 4 H C l \) is
stronger than the \( 2(H-H) \) and
\( \mathbf{2}(\boldsymbol{C l}-\boldsymbol{C l}) \) bonds in \( \mathbf{2} \boldsymbol{H}_{2} \) and \( \mathbf{2} \boldsymbol{C l} \mathbf{l}_{\mathbf{2}} \)
respectively.
(iii) The \( \Delta H^{0} \) value will be \( -92.3 K J \), if
the \( H C l \) is produced as a liquid.
A. (i) only
B. (i) and (ii) only
C. (ii) and (iii) only
D. All of these


If speed(V), acceleration(A) and force(F) are considered as fundamental units,
the dimension of Young's modulus will
be?
A. \( V^{-2} A^{2} F^{2} \)
a \( \cdot F^{-2} F^{-} \)
В. \( V^{-4} A^{2} F \)
c. \( V^{-4} A^{-2} F \)
D. \( V^{-2} A^{2} F^{-2} \)


A toy car of mass \( 5 \mathrm{kg} \) moves up a ramp
under the influence of force \( F \) plotted
against displacement. The maximum height attained is given by
A \( \cdot y_{\max }=20 \mathrm{m} \)
B \( \cdot y_{\max }=15 \mathrm{m} \)
\( \mathbf{c} \cdot y_{\max }=11 m \)
\( y_{\max }=5 m \)


If true then enter 1 and if false then
enter 0
Can two obtuse angles be complement
to each other?


In alcohol fermentation
A. Triose phosphate is the electron donor while acetaldehyde is the electron acceptor
B. Triose phosphate is the electron donor while pyruvic acid is the electron acceptor
C. There is no electron donor
D. Oxygen is the electron acceptor


The difference between the length \( 2 a \) of the transverse axis of a hyperbola of
eccentricity \( e \) and the length of its latus
rectum is :
A \( \cdot 2 a\left|3-e^{2}\right| \)
В \( \cdot 2 a\left|2-e^{2}\right| \)
c. \( 2 a\left(e^{2}-1\right) \)
D. \( a\left(2 e^{2}-1\right) \)


Define quality factor.


Write the associative law for addition of
vectors


Assertion
Heat added to a system at lower temperature causes greater randomness than when the same
quantity of heat is added to it at higher
temperature
Reason
Entropy is a measure of the degree of randomness or disorder in the system.
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


toppr
Q Type your question-
\( A \)
\begin{tabular}{cc|c}
\( \boldsymbol{x} \) & \( \boldsymbol{y} \) & \( \boldsymbol{z} \) \\
\hline \( \mathbf{0} \) & \( \mathbf{0} \) & \( \mathbf{1} \) \\
\( \boldsymbol{0} \) & \( \mathbf{1} \) & \( \mathbf{1} \) \\
\( \mathbf{1} \) & \( \boldsymbol{0} \) & \( \mathbf{1} \) \\
\( \mathbf{1} \) & \( \mathbf{1} \) & \( \mathbf{0} \)
\end{tabular}
B. \begin{tabular}{cc|c}
\( \boldsymbol{x} \) & \( \boldsymbol{y} \) & \( \boldsymbol{z} \) \\
\hline \( \mathbf{0} \) & \( \mathbf{0} \) & \( \mathbf{0} \) \\
\( \mathbf{0} \) & \( \mathbf{1} \) & \( \mathbf{0} \) \\
\( \mathbf{1} \) & \( \mathbf{0} \) & \( \mathbf{0} \) \\
\( \mathbf{1} \) & \( \mathbf{1} \) & \( \mathbf{1} \)
\end{tabular}
\( c \)
\begin{tabular}{cc|c}
\( \boldsymbol{x} \) & \( \boldsymbol{y} \) & \( \boldsymbol{z} \) \\
\hline \( \mathbf{0} \) & \( \mathbf{0} \) & \( \mathbf{1} \) \\
\( \mathbf{0} \) & \( \mathbf{1} \) & \( \mathbf{1} \) \\
\( \mathbf{1} \) & \( \mathbf{0} \) & \( \mathbf{1} \) \\
\( \mathbf{1} \) & \( \mathbf{1} \) & \( \mathbf{1} \)
\end{tabular}
\( D \)
\begin{tabular}{cc|c}
\( \boldsymbol{x} \) & \( \boldsymbol{y} \) & \( \boldsymbol{z} \) \\
\hline \( \mathbf{0} \) & \( \mathbf{0} \) & \( \mathbf{0} \) \\
\( \mathbf{0} \) & \( \mathbf{1} \) & \( \mathbf{1} \) \\
\( \mathbf{1} \) & \( \mathbf{0} \) & \( \mathbf{1} \) \\
\( \mathbf{1} \) & \( \mathbf{1} \) & \( \mathbf{1} \)
\end{tabular}


Induction of cell division and delay in senescence is caused by
A. Cytokinin
B. IAA
c. Gibberellins
D. NAA


\( \int \frac{\cos x-\sin x}{7-9 \sin 2 x} d x \)
A. \( \frac{1}{24} \ln \frac{(4+3 \sin x+3 \cos x)}{(4-3 \sin x-3 \cos x)}+c \)
B. \( \frac{1}{24} \ln \frac{(4-3 \cos x-3 \sin x)}{(4-3 \cos x+3 \sin x)}+c \)
c. \( \frac{1}{12} \ln \frac{(4+3 \sin x-3 \cos x)}{(4-3 \sin x+3 \cos x)}+c \)
D. \( \frac{1}{12} \ln \frac{(4+3 \cos x+3 \sin x)}{(4-3 \sin x-3 \cos x)}+c \)


The motion described by a simple pendulum is motion
A. oscillatory
B. rotatory
c. rectilinear
D. curvilinear


A diploid cell which consist 46 chromosomes, than how many bivalant or tetrad found in Zygotene
A . 46
B. 23
\( c \cdot 92 \)
D. None


For what values of \( m \in R, \) both roots of
the equation \( x^{2}-6 m x+9 m^{2}- \)
\( 2 m+2=0 \) exceed \( 3 ? \)
B. \( \left(\frac{11}{9}, \infty\right) \)
c. \( [1, \infty] \)
D. \( [0, \infty] \)


If \( x^{3} y^{5}=(x+y)^{8}, \) then show that
\( \frac{d y}{d x}=\frac{y}{x} \)


Which of the following molecular interactions include not only London dispersion forces but also dipole-dipole
interaction?
A \( \cdot P F_{3}(l) \)
в. \( B F_{3}(l) \)
c. \( \operatorname{LaF}_{3}(l) \)
D. \( \operatorname{sif}_{4}(l) \)


The diameters of a bubble at the
surface of a lake is \( 4 m m \) and at the
bottom of the lake is 1 mm. If
atmospheric pressure is 1 atm and the temperature of the lake-water and the atmosphere are equal. What is the depth of the lake? [The density of lake-water and \( H g \) are
1 \( g m / m l \text { and } 13.6 g m / m l \text { respectively }] \)
A. \( 120.5 \mathrm{m} \)
B. 200.4 m
\( c \cdot 184.5 \mathrm{m} \)
D. 153.03 \( \mathrm{m} \)


The presence of which of the following in drinking water is responsible for
mottling of teeth?
A. Mercury
B. lodine
c. Chlorine
D. Fluorine


State whether the following statements
are true or false.

In atherosclerosis, deposition of lipids such as cholesterol, followed by precipitation of alcium salts, hastens hardening of a vessel
A. True
B. False


Tidal volume of air in a normal healthy man during inspiration is about
A . 300-400ml
B. 500-700ml
c. \( 900-1000 \mathrm{ml} \)
D. 100-250ml


Fill in the blank.
At least \( _{-}-_{-}-_{-}-_{-}-_{-} \) objects must
interact for a force to come into play.
\( A \)
B. 2
\( c \cdot 3 \)
D. 4


According to the Newlands' law of octaves, the properties of fluorine are similar to those of
A. hydrogen
B. lithium
c. sodium
D. potassium


Which of the following pairs have same dimensions.
a) Torque and work
b) Angular momentum and work
c) Energy and Youngs modulus
d) Light year and wavelength
\( A \cdot \) a and \( b \) are correct
B. b and c are correct
c. c and d are correct
D. d and a are correct


Which of the following is a property of
plastic?
A. Flame resistant
B. Non-corrosive
c. Mouldable
D. All of the above


If for \( 1 \leq m \leq n, f(m, n)=C_{0}-C_{1}+ \)
\( C_{2}-\ldots .(-1)^{m-1} C_{m-1}, \) find \( f(9,5) \)


If \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{0} & \mathbf{0} \\ \mathbf{4} & \mathbf{0}\end{array}\right], \) then find \( \boldsymbol{A}^{16} \)


Ascending imbricate corolla is found in
A. Pisum
B. Tamarindus
c. Mimosa
D. Datura


A \( 5 \% \) solution of cane sugar \( (\text { mol. } \boldsymbol{w} \boldsymbol{t}= \)
342) is isotonic with \( 1 \% \) solution of
substance \( X . \) The molecular weight of
\( \boldsymbol{X} \) is:
A . 34.2
B. 171.2
\( c .68 .4 \)
D. 136.8


Simplify: \( \boldsymbol{x}^{2}\left(\boldsymbol{3}-\boldsymbol{5} \boldsymbol{y}^{2}\right)+ \)
\( \boldsymbol{x}\left(\boldsymbol{x} \boldsymbol{y}^{2}-\boldsymbol{3} \boldsymbol{x}\right)-\boldsymbol{2} \boldsymbol{y}\left(\boldsymbol{y}-\boldsymbol{2} \boldsymbol{x}^{2} \boldsymbol{y}\right) \)
A \( \cdot 6 x^{2}-2 y^{2}-3 x^{2} y \)
В. \( 6 x^{2} \)
\( \mathrm{c} \cdot 3 x^{2} y \)
D. \( -2 y^{2} \)


A function \( f(x) \) is defined by \( f(x)= \)
\( \left\{\begin{array}{cl}\frac{\left[x^{2}-1\right]}{x^{2}-1} & \text { for } x^{2} \neq 1 \\ 0 & \text { for } x^{2}=1\end{array} \) Discuss the \right.
contiuuity of \( f(x) \) at \( x=1 \)


When an \( \alpha \) -particle is ejected, the
atomic number of the atom decreases
by


Among the following compounds, which
on heating do not produce \( N_{2} ? \)
A \( \cdot\left(N H_{4}\right)_{2} C r_{2} O_{7} \)
B. \( N H_{4} C l+N a N O_{2} \)
c. \( N H_{4} C l+C a O \)
D. \( B a\left(N_{3}\right)_{2} \)


The monomer of natural rubber is:
A. butadiene
B. chloroprene
C. isoprene
D. styrene


Mention four uses of chlorine.


Four electric charges are arranged as shown in the figure at the four corners of a square of side a. The potential energy of the system is:
A. Zero
B. Negative
c. Positive
D. Greater than \( \frac{1}{4 \pi \varepsilon} \frac{2 q^{2}}{a} \)


Let \( f(x) \) be a real value function not identically zero satisifes the equation, \( f\left(x+y^{n}\right)=f(x)+f(y)^{n} \) for all real
\( x, y \) and \( f^{\prime}(0) \geq 0 \) where \( n(>1) \) is an odd natural number. \( \boldsymbol{f}(\mathbf{1 0})=\mathbf{1 0 k . F i n d} \)
\( \boldsymbol{k} \) value


What is the wavelength of light emitted when the electron in a hydrogen atom undergoes transition from an energy
level with \( n=4 \) to \( n=2 ? \)


Using Huygen's wave theory, derive Snell's law of refraction.


If a wire of resistance \( R \) is stretched to
double of its length, then new resistance will be:
A . R/2
в. 2 R
\( c \cdot 4 R \)
D. 16 R


In nucleoside, the nitrogen base is attached to the first carbon of sugar by bond.
A. Glycosidic
B. Hydrogen
c. Phosphodiester
D. Phosphate


Multiply: \( \left(4 x^{4}-3 x^{2}-7 x+8\right) \) by
\( \left(5 x^{2}-2 x-3\right) \)
Answer: \( 20 x^{6}-8 x^{5}-27 x^{4}-29 x^{3}+ \)
\( 63 x^{2}+5 x-24 \)
A. True
B. False


If \( 4 a+2 b+c=0 \) then the equation
\( 3 a x^{2}+2 b x+c=0 \) has at least one
real root lying between
A. 0 and 1
B. 1 and 2
c. 0 and 2
D. none of these


A positively charged particle of \( 2.0 C \) moves upward into an area where both a magnetic field of the magnitude
\( 4.0 \times 10^{-4} T \) and an electric field of
the magnitude \( 0.1 N / C \) are acting. Find out the velocity at which particle must move if it is not deflected when it enters
this area?
A \( \cdot 4.0 \times 10^{-3} \mathrm{m} / \mathrm{s} \)
B. \( 125 \mathrm{m} / \mathrm{s} \)
c. \( 250 m / s \)
D. \( 500 m / s \)
E. The particle will be deflected to the left regardless of ts velocity


Assertion
Copper dissolves in dilute nitric acid but not in dilute \( \boldsymbol{H} \boldsymbol{C l} \)
Reason

Copper has positive \( \boldsymbol{E}^{\circ} \)
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


RQ of which diet is less than unit?
A. carbohydrate
B. Fats
c. organic acid
D. Sugar


Prove that \( \frac{\pi}{2}-\sin ^{-1} x= \)
\( \operatorname{cosec}^{-1} \frac{1}{\sqrt{1-x^{2}}} \)


Find the value of
\( \arg \left((1+i)^{i}\right) \)
A \( \cdot \frac{1}{4} \ln (2) \)
в. \( \frac{1}{2} \ln (2) \)
\( ^{\text {c. }} \frac{1}{2} \ln \left(\frac{1}{2}\right) \)
D \( \cdot \ln (2) \)


Work done on stretching a rubber will be stored in it as:
A. chemical energy
B. heat energy
c. muscular energy
D. potential energy


Select the wrong statement with respect to the structure of a plant cell
A. Cellulosic cell wall is present inside the cell membrane
B. Centrioles are usually absent
C. A large central vacuole is present
D. Golgi apparatus is formed of a number of unconnected units called dictyosomes


Assertion
consider the determinant \( \Delta= \) \( \left|\begin{array}{lll}a_{1}+b_{1} x^{2} & a_{1} x^{2}+b_{1} & c_{1} \\ a_{2}+b_{2} x^{2} & a_{2} x^{2}+b_{2} & c_{2} \\ a_{3}+b_{3} x^{2} & a_{3} x^{2}+b_{3} & c_{3}\end{array}\right|=0, \) where
\( \boldsymbol{x}_{i}, \boldsymbol{y}_{i}, \boldsymbol{z}_{i} \in \boldsymbol{R} \quad(\boldsymbol{i}=\mathbf{1}, \boldsymbol{2}, \boldsymbol{3}), \quad \boldsymbol{x} \in \boldsymbol{R} \)
The values of \( x \) satisfying \( \Delta=0 \) are
\( \boldsymbol{x}=\mathbf{1},-\mathbf{1} \)
Reason
\( \left|\begin{array}{lll}\boldsymbol{a}_{1} & \boldsymbol{b}_{1} & \boldsymbol{c}_{1} \\ \boldsymbol{a}_{2} & \boldsymbol{b}_{2} & \boldsymbol{c}_{2} \\ \boldsymbol{a}_{3} & \boldsymbol{b}_{3} & \boldsymbol{c}_{3}\end{array}\right|=\mathbf{0}, \) then \( \boldsymbol{\Delta}=\mathbf{0} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Assertion
Silica is added as a flux in a
reverberatory furnace, in the extraction
of copper for copper pyrites.
Reason
Silica acts as basic flux.
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


Based on equations reducible to linear
equations, solve for \( x \) and \( y \) \( \frac{\boldsymbol{x}-\boldsymbol{y}}{\boldsymbol{x} \boldsymbol{y}}=\mathbf{9} ; \frac{\boldsymbol{x}+\boldsymbol{y}}{\boldsymbol{x} \boldsymbol{y}}=\mathbf{5} \)
A \( \cdot x=-\frac{1}{2}, y=\frac{1}{7} \)
B. \( _{x}=-\frac{1}{5}, y=\frac{1}{2} \)
c. \( _{x=-\frac{1}{5}, y}=\frac{1}{7} \)
D. None of these


What is the abundance of oxygen in the universe?
A. 2nd most common element, by mass
B. 3rd most common element, by mass
c. 5th most abundant element, by mass
D. oxygen is relatively rare in the universe


Name the molecules of histone which
are organizeded to form histone
octamer?


Taxon Eucalyptus denotes
A. species
B. Genus
c. class
D. Divisions


What does 'like dissolves like' mean?
A. That compounds that are from the same period on the periodic table will dissolve each other.
B. Polar solutes dissolve in polar solvents.
C. Nonpolar solutes dissolve in polar solvents.
D. Polar solutes dissolve in nonpolar solvents.
E. That compounds from the same family on the periodic table will dissolve each other.


The equation of a line through (2,-3) parallel to y-axis is
A. \( y=-3 \)
B. \( y=2 \)
c. \( x=2 \)
D. \( x=-3 \)


A moving carrom board coin describes a motion
A. rectilinear
B. rotatory
c. periodic
D. oscillatory


Q Type your question-
speed of \( 2 \mathrm{cms}^{-1} \) on a \( \mathrm{V} \) -shaped
conductor each prong of which is \( 50 \mathrm{cm} \) in length immersed in a uniform
magnetic field \( \mathbf{B}=\mathbf{0 . 4 T}, \) perpendicular
and into the \( V \) -plane shown in the

Figure. To start with, at time \( \mathbf{t}=\mathbf{0} s, \) the
mid-point \( C \) of the rod is at \( 0 . \) Then [both conductor and rod have resistance of 10
\( ^2 \) per meter
A. the current in the circuit increases from zero to \( 300 \mathrm{mA} \) during \( 20 s \)
B. the current in the circuit is \( 300 \mathrm{mA} \) fort \( \leq 20 \) s and zero fort \( >20 \) s.
c. the current in the circuit is \( 150 \mathrm{mA} \), till the rod is in contact with \( V \) -conductor
D. the current in the circuit is \( 150 \mathrm{mA} \) for \( \mathrm{t} \leq 10 \mathrm{s} \) and is \( 300 m A \) for \( 10 s<t \leq 20 s \)


The domain of \( \mathbf{f}(\mathbf{x})= \) \( \cot ^{-1}\left(\frac{\mathbf{x}}{\sqrt{\mathbf{x}^{2}-\left[\mathbf{x}^{2}\right]}}\right) \) is
\( ([.] \) denotes the greatest integer function)
A. \( (0, \infty) \)
)
в. \( \mathrm{R}-\{0 \)
c. \( R-\{x: x \in Z\} \)
D. \( (-\infty, 0) \)


Thoracic cavity is enlarged by contraction of
A. Internal Intercostal muscles
B. Diaphragm
c. Lungs
D. All of above


Give biological reasons for the following
(i) The wall of the ventricle is thicker
than the auricles.
(ii) The renal cortex has a dotted
appearance.
(iii) Wooden frames of doors get
jammed during the monsoon season
(iv) Throat infections can lead to ear
infections.
(v) The hand automatically shows the direction to turn a cycle without
thinking.


Angle of incidence is the angle between
incident ray and the normal.
A. True
B. False


If the sum of maximum and minimum
values of \( \boldsymbol{E}=\left(\sin ^{-1} x\right)^{2}+ \)
\( 2 \pi \cos ^{-1} x+\pi^{2} \) is \( \frac{a \pi^{2}}{b}, \) where \( a \) and \( b \)
are coprime, then the value of \( (a-b) \) is


Which of the following colours of white light deviated most when passes through a prism.?
A. Red light
B. Violet light
c. Yellow light
D. Both (a) and (b)


Solve \( :\left(x^{2} D^{2}+3 x D+1\right) y=\frac{1}{(1-x)^{2}} \)


If the work done by stretching a wire by
1 \( m m \) is \( 2 J, \) the work necessary for stretching another wire of the same
material but with half the radius of
cross section and half the length by
1 mm is
\( ^{A} \cdot \frac{1}{4} J \)
в. 4.5
c. \( 8 J \)
D. 16.5


In the reaction: \( \boldsymbol{I}_{2}+2 \boldsymbol{S}_{2} \boldsymbol{O}_{3}^{2-} \rightarrow \boldsymbol{2} \boldsymbol{I}^{-}+ \)
\( \boldsymbol{S}_{4} \boldsymbol{O}_{6}^{2-} \)
A \( \cdot I_{2} \) is a reducing agent
B . \( I_{2} \) is an oxidising agent
c. \( S_{2} O_{3}^{2-} \) is a reducing agent
D. \( S_{2} O_{3}^{2-} \) is an oxidising agent


From the graph \( (3), \) it can be interpreted
that:
A. Equilibrium is achieved at \( X \)
B. Reaction is nearer to the completion
\( \mathbf{c} \cdot \Delta G=0 \)
D. All of the above


The relative velocity of \( B \) as seen from
\( A \) is
\( \mathbf{A} \cdot-8 \sqrt{2} \hat{i}+6 \sqrt{2} \hat{j} \)
B. \( 4 \sqrt{2} \hat{\imath}+3 \sqrt{3} \hat{j} \)
c. \( 3 \sqrt{5 \hat{\imath}}+2 \sqrt{3} \hat{\jmath} \)
D. \( 3 \sqrt{2 \hat{i}}+4 \sqrt{3} \hat{j} \)


If the magnitude of sum of two vectors
is equal to the magnitude of difference of the two vectors, the angle between
these vectors is:
\( \mathbf{A} \cdot 0^{\circ} \)
B. \( 90^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 180^{\circ} \)


\( -123-(-23)= \)
A . 146
B . -146
\( c .100 \)
D. - 100


If the activation energy of a reaction is \( 480.9 k J \) mol \( ^{-1} \), calculate the fraction
of molecules at \( 400^{\circ} C \) which have
enough energy to react to form the products.


Sulphur trioxide is dissolved in heavy water to form a compound \( X \). The state
of hybridisation of sulphur in \( \boldsymbol{X} \) is:
\( A \cdot s p^{2} \)
B \( \cdot s p^{3} \)
\( c \cdot s p \)
D. \( d s p^{2} \)


Mark the correct alternative of the
following.
For any \( \operatorname{set} A,\left(A^{\prime}\right)^{\prime} \) is equal to?
A \( \cdot A^{\prime} \)
B. A
\( c \cdot \phi \)
D. None of these


If \( e \) and \( e^{\prime} \) be the eccentricities of a
hyperbola and its conjugate, them \( \frac{1}{e^{2}}+\frac{1}{e^{2}} \) is equal to
A. 0
B.
\( c \cdot 2 \)
D. None of these


A beam of \( 13.0 e V \) electrons is used to
bombard gaseous hydrogen. The series obtained in emission spectra is/are
A. Lyman series
B. Balmer series
c. Brackett series
D. All of these


A sphere is melted and half of the
molten liquid is used to form 11 identical cubes, whereas the remaining
half is used to form 7 identical smaller
spheres. The ratio of the side of the cube to the radius of the new small sphere is
\( A \)
\[
\left(\frac{4}{3}\right)^{\frac{1}{3}}
\]
в.
\[
\left(\frac{8}{3}\right)^{\frac{1}{3}}
\]
c. \( (3)^{\frac{1}{5}} \)
D.


Pick out the plant with unipinnate type of compound leaves from the plant names given: Trifolium, Neem, Moringa.


Solve \( \tan \theta=2, \) then \( \theta=n \pi+ \)
\( a, \) where \( a=\tan ^{-1}(2), n \in I \)
If true then enter 1 and if false then
enter 0


The acidic, basic and amphoteric oxides, respectively, are:
A. \( N_{2} O_{3}, L i_{2} O, A l_{2} O_{3} \)
в. \( M g O, C l_{2} O, A l_{2} O_{3} \)
c. \( N a_{2} O, S O_{3}, A l_{2} O_{3} \)
D. \( C l_{2} O, C a O, P_{4} O_{10} \)


In Figure \( 5, \) rectangle \( A B C D \) is
inscribed in a circle. If the radius of the
circle is 1 and \( A B=1 \), find the area of
the shaded region.
\( \mathbf{A} \cdot 0.091 \)
B. 0.285
c. 0.614
D. 0.705
E . 0.732


A change q exists at a distance of \( \mathrm{R} \)
from a spherical concave mirror of
curvature R. Let mirror subtends a half
angle \( \theta=30^{\circ} \) at the change.Flux
passing through the mirror is
A \( \cdot 2 q \sin ^{2} 15^{\circ} \)
B. \( q \sin ^{2} 30 \)
c. \( 2 q \sin ^{2} 30^{\circ} \)
D. \( q \sin ^{2} 15^{\circ} \)


The vol of a cube \( =1000 \mathrm{cm}^{3} \), Find its
TSA in \( c m^{2} \)


How many secondary carbon atoms does methyl cyclopropane have?
A. None
B. One
c. Two
D. Three


If \( \boldsymbol{\alpha}=\boldsymbol{2} \boldsymbol{t a n}^{-1}(\boldsymbol{2} \sqrt{\boldsymbol{2}}-\boldsymbol{1}) \) and \( \boldsymbol{\beta}= \)
\( 3 \sin ^{-1}(1 / 3)+\sin ^{-1}(3 / 5) \) then
\( \mathbf{A} \cdot \alpha<\beta \)
B . \( \alpha=\beta \)
c. \( \alpha>\beta \)
D. none of these


The correct order of spin-only magnetic moments among the following is?
(Atomic number: \( M n=25, C o= \)
\( \mathbf{2 7}, \boldsymbol{N} \boldsymbol{i}=\mathbf{2 8}, \boldsymbol{Z} \boldsymbol{n}=\mathbf{3 0}) \)
A \( \cdot\left[Z n C l_{4}\right]^{2-}>\left[N i C l_{4}\right]^{2-}>\left[C o C l_{4}\right]^{2-}>\left[M n C l_{4}\right]^{2} \)
B . \( \left[C o C l_{4}\right]^{2-}>\left[M n C l_{4}\right]^{2-}>\left[N i C l_{4}\right]^{2-}>\left[Z n C l_{4}\right]^{2} \)
C \( \cdot\left[N i C l_{4}\right]^{2-}>\left[C o C l_{4}\right]^{2-}>\left[M n C l_{4}\right]^{2-}>\left[Z n C l_{4}\right]^{2} \)
D. \( \left[M n C l_{4}\right]^{2-}>\left[C o C l_{4}\right]^{2-}>\left[N i C l_{4}\right]^{2-}>\left[Z n C l_{4}\right]^{2} \)


Find the locus of coordinates of \( A \) and \( B \)
which are two points in place so that
\( \boldsymbol{P A}-\boldsymbol{P B}= \) constant.


Find the domain and range of the real
function \( \frac{x+2}{x^{2}-8 x-4} \)


The number of glucose molecules required to produce 38 ATP molecules under anaerobic conditions by a yeast
cell are
\( A \cdot 2 \)
B. 4
c. 19
D. 25
E. 38


The external ears of mammals
A. Are also called pinnae
B. Are absent in monotremes
C. Can be moved in various direction by many mammals
D. All of the above


If \( \theta \) is the angle between the lines
\( A B, A C \) where \( A, B, C \) are the three points with coordinates (1,2,-1)\( ;(2,0,3) ;(3,-1,2) \)
respectively, then \( \sqrt{462} \cos \theta \) is equal to
A . 20
B . 40
c. 60
D. 120


The largest value of Henry's law
constant for the liquid solvent \( \mathrm{H}_{2} \mathrm{O} \) will
be obtained with ............... gas as the solute
and a temperature of \( \ldots \)
A. \( C_{2} H_{4}, 45 \)
B. \( A r, 11 \)
с. \( H C l, 49 \)
D. \( C O_{2}, 32 \)


If the equation \( y_{1}=A \sin \omega t \) and \( y_{2}= \) \( \frac{\boldsymbol{A}}{\mathbf{2}} \sin \omega \boldsymbol{t}+\frac{\boldsymbol{A}}{\mathbf{2}} \cos \omega \boldsymbol{t} \) represent SHM
then the ratio of the amplitudes of the two motions is
A . 0.5
B. \( \sqrt{2} \)
c. 1
D. 2


\( \int_{0}^{\pi / 2} \frac{x d x}{\sin x+\cos x}= \)
A \( \cdot \frac{\pi}{2 \sqrt{2}} \log (\sqrt{2}+1) \)
\( \frac{\pi^{2}}{2 \sqrt{2}} \log (\sqrt{2}+1) \)
\( \mathbf{c} \cdot \pi \log (\sqrt{2}+1) \)
\( \mathbf{D} \cdot \log (\sqrt{2}+1) \)


In the adjoining diagram \( \boldsymbol{R}_{1}= \) \( \mathbf{1 0 \Omega}, \boldsymbol{R}_{2}=\mathbf{2 0 \Omega}, \boldsymbol{R}_{3}=\mathbf{4 0 \Omega}, \boldsymbol{R}_{4}=\mathbf{8 0 \Omega} \)
and \( V_{A}=5 V, V_{B}=10 V, V_{C}= \)
\( 20 V, V_{D}=15 V . \) The current in the
resistance \( \boldsymbol{R}_{1} \) will be
A. 0.4 A towards 0
B. 0.4 A away from 0
\( c . \) 0.6 A towards 0
D. 0.6 A away from 0


\( N H_{3} \) gas is liquefied more easily than
\( N_{2} . \) Hence:
A. vander Waals' constants a and b of \( N H_{3} \) > that of \( N_{2} \)
B. vander Waals' constants a and b of \( N H_{3} \) < that of \( N_{2} \)
C \( \cdot a\left(N H_{3}\right)>a\left(N_{2}\right) \) but \( b\left(N H_{3}\right)<b\left(N_{2}\right) \)
D・ \( a\left(N H_{3}\right)<a\left(N_{2}\right) \) but \( b\left(N H_{3}\right)>b\left(N_{2}\right) \)


Prove \( \mathbf{v}=\mathbf{u}+\mathbf{a} \mathbf{t} \)
where \( u= \) initial velocity, \( v= \) final velocity, a = acceleration and \( t= \) time period


The probability of an impossible event
is
\( \mathbf{A} \cdot \mathbf{3} \)
B.
c. 1
\( D \)


Write the equation of line passing through \( \boldsymbol{A}(-\mathbf{3}, \mathbf{4}) \) and \( \boldsymbol{B}(\mathbf{4}, \mathbf{5}) \) in the
form of \( a x+b y+c=0 \)


Let \( \vec{a} \) and \( \vec{b} \) two unit vectors such that \( |\vec{a}+\vec{b}|=\sqrt{3} \cdot \operatorname{lf} \vec{c}=\vec{a}+2 \vec{b}+ \)
\( 3(\vec{a} \times \vec{b}), \) then \( 2 \vec{c} \) is equal to
A . \( \sqrt{55} \)
B. \( \sqrt{37} \)
c. \( \sqrt{51} \)
D. \( \sqrt{43} \)


Wastewater released by houses is
called


Assertion
Radio waves are diffracted by buildings.
Reason
Radio waves are high energy waves.
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


Draw a \( \triangle A B C \) with side \( B C=7 \mathrm{cm} \)
\( \angle B=45^{\circ}, \angle A=105^{\circ} . \) Then, construct
a triangle whose sides are \( \frac{4}{3} \) times the
corresponding sides of \( \triangle \boldsymbol{A B C} \)


n figure, find the values of \( x, y \) and \( z \)


The areal velocity of an object of mass \( \mathrm{m}=2 \mathrm{kg} \) revolving around another object
is given by \( 2 m^{2} / s, \) what is the angular momentum of the particle
A \( \cdot 6 k g-m^{2} / s \)
в. \( 8 k g-m^{2} / s \)
c. \( 4 k g-m^{2} / s \)
D. \( 2 k g-m^{2} / s \)


A letter lock consists of three rings each
are marked with 10 different letters.
Find the number of ways in which it is possible to make an unsuccessful attempts to open the lock.


\( \mathbf{2} \cdot \mathbf{1}^{2}+\mathbf{3} \cdot \mathbf{2}^{2}+\mathbf{4} \cdot \mathbf{3}^{2}+\ldots \) up to \( \boldsymbol{n} \)
terms \( = \)
A \( \cdot \frac{n(n+1)(n+2)(3 n+1)}{12} \)
B \( \cdot \frac{n(n+2)(n+3)(n+11)}{12} \)
c. \( \frac{n(n+1)(n+2)(3 n-2)}{6} \)
D. \( \frac{n(n+2)(n+5)(n+8)}{6} \)


Explain:
1) Stability of +3 state in nitrogen family increases from top to bottom.
2)Amongst \( L i F \) and \( L i I \) which has more covalent character.


Electromagnetic waves do not transport
A . energy
B. charge
c. momentum
D. information


The above graph shows velocity as a function of time for an object moving along as straight line. During which time(s) is the object at rest??
I. 0.5 seconds
Il. From 1 to 2 seconds
III. 2.5 seconds
A. I only
B. Il only
c. ॥ only
D. I and III only


f \( y(n)=e^{x} e^{x^{2}} \ldots e^{x^{n}}, 0<x<1 \) then
\( \lim _{n \rightarrow \infty} \frac{\boldsymbol{d} \boldsymbol{y}(\boldsymbol{n})}{\boldsymbol{d} \boldsymbol{x}} \) at \( \frac{1}{2} \) is
\( A \)
B. \( 4 e \)
\( c \cdot 2 e \)
D. \( 3 e \)


In the given reaction, products are
\( A \)
and \( \mathrm{H}_{2} \)
B.
and \( \mathrm{CH}_{3} \mathrm{Br} \)
\( c \)
and \( \mathrm{CH}_{3} \mathrm{OH} \)
\( D \)
and \( \mathrm{CH}_{3} \mathrm{Br} \)


A lead storage cell is discharged which
causes the \( H_{2} S O_{4} \) electrolyte to
change from a concentration of \( 40 \% \) by weight (density \( =1.260 \) g/ml) to \( 28 \%, \) by weight. The original volume of
electrolyte was 1 L. Identify the correct
statement \( (s) \)
This question has multiple correct options
A. The overall cell reaction is : \( P b(s)+P b O_{2}(s)+ \) \( 2 H_{2} S O_{4}(a q) \rightarrow 2 P b S O_{4}(s)+2 H_{2} O(l) \)
B. A total of 2.0 moles of \( H_{2} S O_{4} \) is reacted
C. The total charge released from anode of the cell is \( 1.93 \times 10^{5} \) coulomb.
D. The mass of electrolytic solution has decreased.


Which of the following is octahedral?
A \( . S F_{6} \)
в. \( B F_{4}^{-} \)
c. \( P C l_{5} \)
D. \( B O_{3}^{3} \)


Impure copper containing \( \boldsymbol{F e}, \boldsymbol{A} \boldsymbol{u}, \boldsymbol{A} \boldsymbol{g} \)
as impurities is electrolytically refined. A current of \( 140 A \) for \( 482.5 s \) decreased
the mass of the anode by \( 22.26 g \) and increased the mass of cathode by \( 22.011 g . \) Percentage of iron in impure copper is :
(Given molar mass \( F e=55.5 g m o l^{-1} \)
molar mass \( C u=63.54 g m o l^{-1} \)
A .0 .85
в. 0.90
c. 0.95
D. 0.97


The density of a substance is \( 8 g c c^{-1} \). Its specific heat is 1 calg\( ^{-1} C^{-1} \). Find its
thermal capacity per unit volume.


A balloon which always remains spherical, is being inflated by pumping in 900 cubic centimetres of gas per second. The rate at which the radius of
the balloon is increasing when the radius is \( 15 \mathrm{cm} \) is.
A \( \cdot \frac{1}{\pi} c m / s e c \)
B \( \cdot \frac{2}{\pi} c m / \) sec
c. \( \pi c m / s e c \)
D. \( \frac{\pi}{2} \mathrm{cm} / \mathrm{sec} \)


How do elephants living in the tropical rainforests adapt themselves?


Which one of the following is not a
periodic motion?
A. Rotation of the earth about its axis.
B. A freely suspended bar magnet displaced from its N-S direction and released.
C. Motion of hands of a clock.
D. An arrow released from a bow.


What is the common point of similarity between DNA and RNA?
A. Both are double stranded
B. Both have identical sugar molecules
c. Both have identical pyrimidine bases
D. Both are polymers of nucleotides


Length of a chord of a circle is \( 24 \mathrm{cm} \)
and its distance from the centre is 5
\( \mathrm{cm} . \) Find the diameter of the circle.


Calculate the molarity and molality of a \( 13 \% \) solution (by weight of sulphuric acid). Its density is \( 1.090 \mathrm{g} / \mathrm{ml} \)


Time period of small oscillation (in a
vertical plane normal to the plane of
strings of the bob in the arrangement
shown will be
A.
B.
\( c \)
D.


The correct order of decreasing basic
strength is:
A \( . I>I I>I I I>I V \)
\( V \)
В. \( I I>I I I>I>I V \)
с. \( I I>I>I V>I I I \)
I I \( I I>I I I>I V>I \)
\( I \)


Find the adjoint of matrix \( A= \) \( \left[\begin{array}{lll}1 & 1 & 2 \\ 2 & 3 & 5 \\ 2 & 0 & 1\end{array}\right] \)


Solve \( \int_{0}^{\pi / 2} \frac{x \sin x \cos x}{\cos ^{4} x+\sin ^{4} x} d x \)


Which substance is used to extinguish fire in substances like oil, fat and
petrol?
A. \( C H_{3} C l \)
в. \( C H C l_{3} \)
\( \mathbf{c} \cdot C H_{2} C l_{2} \)
D. \( C C l_{4} \)


Which of the following statement is NOT
true
This question has multiple correct options
A. A freely falling body is acted upon by gravitational force
B. pressure on top of mount everest is much more than 1 \( \operatorname{atm} \)
C. S.I. unit of pressure is pascal
D. the blood vessels in our body maintains the internal pressure equal to the atmospheric pressure


Which of the following compounds cannot exhibit chain isomerism?
A. Propane
B. Butane
c. Pentane
D. Hexane


A disc of mass \( M \) and radius \( R \) rolls on
a horizontal surface and then rolls up
an inclined plane as shown in figure. If the velocity of the disc is \( v, \) height to
which the disc will rise will be
\( \mathbf{A} \cdot \frac{3 v^{2}}{2 g} \)
B. \( \frac{3 v^{2}}{4 g} \)
c. \( \frac{v^{2}}{4 g} \)
\( \frac{v^{2}}{2 g} \)


f \( A=\{a, b\}, B=\{x, y\} \) and \( C= \)
\( \{a, c, y\}, \) then verify that \( A \times \)
\( (\boldsymbol{B} \cap \boldsymbol{C})=(\boldsymbol{A} \times \boldsymbol{B}) \cap(\boldsymbol{A} \times \boldsymbol{C}) \)


Sporogenous tissue of a moss capsule
A. Develops from outermost cells of the amphithecium
B. Over arches the columella
C. Is an extensively developed tissue
D. Develops from entire amphithecium


A particle is projected up with a velocity of \( 20 \mathrm{m} \mathrm{s}^{-1} \) from the tower of height 25
m. Its velocity on reaching the ground is \( m s^{-1} \)
A . 30
B. 60
c. 120
D. 20


The value of \( \tan ^{-1}\left(\frac{x}{y}\right)- \)
\( \tan ^{-1}\left(\frac{x-y}{x+y}\right), x, y>0 \) is
\( A \cdot \frac{\pi}{4} \)
B. \( -\frac{\pi}{4} \)
\( c \cdot \frac{\pi}{2} \)
D. \( -\frac{\pi}{2} \)


For a junction diode the ratio of forward
current \( \left(I_{f}\right) \) and reserve current \( \left(I_{r}\right) \) is \( [e= \) electronic charges, \( \boldsymbol{V}= \) voltage applied across junction, \( K= \) Boltzmann constant
\( \boldsymbol{T}=\text { temperature in Kelvin }] \)
A \( \cdot e^{-V / K T} \)
\( \mathbf{B} \cdot e^{V / K T} \)
c. \( \left(e^{-e V / K T}+1\right) \)
D. \( e^{e V / K T}-1 \)


In which of the following acid peroxy linkage is present? This question has multiple correct options
A. \( H_{2} S O_{3} \)
в. \( H_{2} S O_{4} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{CO}_{4} \)
D. \( H_{2} S_{2} O_{8} \)


If \( \tan A=\frac{1}{2}, \tan B=\frac{1}{3} \) then
\( \tan (A+B)= \)
A .
в.
c. -1
D.


Two beams of red and violet colours are
made to pass separately through prism
(angle of the prism is \( 60^{\circ} \) ). In the position of minimum deviation, the angle of refraction will be:
\( A \cdot 30^{\circ} \) for both the colours
B. greater for the violet colour
c. greater for the red colour
D. equal but not \( 30^{\circ} \) for both the colours


A system which can neither exchange
matter nor energy with surrounding is called isolated system .If true enter 1 else 0
\( A \)


Match the column I with column II and
choose the correct option.
Column Column
a) Synaptonemal complex
1) Zygotene
2
b) Recombination nodules \( \quad \) Pachytene
c) Activation of recombinase
3 ) Diplotene enzyme
4)
d) Termination of chiasmata
\( A \cdot a-1, b-2, c-3, d-4 \)
B. a-1, b-2, c-4, d-3
\( c \cdot a-1, b-4, c-2, d-3 \)
D. \( a-1, b-3, c-2, d-4 \)


Which of the following would weight the least?
A. 2 gram atoms of nitrogen
B. 1 mole of silver
C. 22.4 liters of oxygen gas at 1 atmospheric pressure and \( 273 \mathrm{K} \)
D. \( 6.02 \times 10^{23} \) atoms of carbon


(a) Find the angle of incidence.
(b) Find the angle between the incident
and reflected rays.

Figure shows an incident ray \( A O \) and
the normal \( O N \) on a plane mirror. The
angle which the incident ray \( A O \) makes
with a mirror is \( 30^{\circ} \)
\( \mathbf{A} \cdot(a) 60^{\circ},(b) 60^{\circ} \)
B . \( (a) 120^{\circ},(b) 120^{\circ} \)
\( \mathbf{c} \cdot(a) 60^{\circ},(b) 120^{\circ} \)
D. \( (a) 120^{\circ},(b) 60^{\circ} \)


If \( \boldsymbol{y}=(\mathbf{1}+\boldsymbol{x})\left(\mathbf{1}+\boldsymbol{x}^{2}\right)\left(\mathbf{1}+\boldsymbol{x}^{4}\right) \dots . .(\mathbf{1}+ \)
\( \left.x^{2^{n}}\right), \) find \( \frac{d y}{d x} \) at \( x=0 \)
\( \mathbf{A} \cdot 2^{n} \)
B.
\( c .1 \)
D. \( 2 n \)


The oxidation state of iodine in \( \boldsymbol{H}_{4} \boldsymbol{I} \boldsymbol{O}_{\mathbf{6}}^{-} \)
is?
\( A \cdot+7 \)
B. -
\( c .+5 \)
D. +1


Industrial waste include:
A. chemical solvents, paints
B. sandpaper, paper products
C. industrial by-products, radioactive waste
D. all the above


A screen is placed \( 90 \mathrm{cm} \) from an object The image of the object on the screen is formed by convex lens at two different locations separated by \( 20 \mathrm{cm} \) Determine the focal length of the lens
(b) suppose the object has a size of 10 \( \mathrm{cm}, \) and in one case the image is half of its size. Determine image size when lens is displaced to second position


Enzymes in the human body function as a catalyst.
A. True
B. False


When spheres are given the same
amount of heat.
A. 1: 2: 3
B. 1: 1: 1
\( \mathrm{c} \cdot 3: 2: 1 \)
D. none of these


Statement-1: The point \( \boldsymbol{A}(\mathbf{3}, \mathbf{1}, \boldsymbol{6}) \) is the mirror image of the point \( B(1,3,4) \) in
the plane \( \boldsymbol{x}-\boldsymbol{y}+\boldsymbol{z}=\mathbf{5} \)
Statement-2: The plane \( \boldsymbol{x}-\boldsymbol{y}+\boldsymbol{z}=\mathbf{5} \)
bisects the line segment joining
\( \boldsymbol{A}(\boldsymbol{3}, \mathbf{1}, \boldsymbol{6}) \) and \( \boldsymbol{B}(\mathbf{1}, \boldsymbol{3}, \boldsymbol{4}) \)
A. Statement-1 is true and Statement-2 is true:
Statement-2 is not the correct explanation for Statement-1
B. Statement-1 is true, Statement-2 is false
c. Statement-1 is false, Statement-2 is true
D. Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-


State and prove Bayes' theorem


A positive integer which is just greater \( \operatorname{than}(1+0.0001)^{10000} \) is
\( A \cdot 3 \)
B. 4
\( c .5 \)
D. 6


\( N a^{+}, M g^{2+}, A l^{3+} \) and \( S i^{4+} \) are
isoelectronic ions. Their ionic size
follows the order:
A \( \cdot N a^{+}<M g^{2+}<A l^{3+}<S i^{4+} \)
B. \( N a^{+}>M g^{2+}<A l^{3+}>s i^{4+} \)
C. \( N a^{+}<M g^{2+}>A l^{3+}>S i^{4+} \)
D. \( N a^{+}>M g^{2+}>A l^{3+}>S i^{4+} \)


At the maximum height of a projectile, the velocity and acceleration are
A. parallel to each other
B. antiparallel to each other
c. perpendicular to each other
D. inclined to each other at \( 45^{\circ} \)


The components of a reflex arc are
A. Sensory neuron, receptor, motor neuron
B. Receptor, sensory neuron, center, motor neuron
C. Receptor, sensory neuron, center, motor neuron, effector organ
D. Motor neuron, sensory neuron, center, effector organ


Lyon hypothesis deals with
A. Centromere position
B. Genetic compatibility
c. Genetic incompatibility
D. Number of Barr bodies


Compute the electric flux through a square surface of edges \( 2 l \) due to a
charge \( +Q \) whose geometric centre is located on the \( x \) -axis at a
perpendicular distance \( l \) from the
centre of the square.
A \( \cdot \frac{Q}{\epsilon_{0}} \)
в. \( \frac{Q}{2 \epsilon_{0}} \)
c. \( \frac{Q}{4 \epsilon_{0}} \)
D. \( \frac{Q}{6 \epsilon_{0}} \)


When two bodies move uniformly towards each other,the distance
between them diminishes by \( 16 m \) every
10s.If bodies move with velocities of the
same magnitude and in the same direction as before the distance
between then will decease \( 3 m \) every \( 5 s \)
The velocity of each body is
\( \mathbf{A} \cdot 1.5 m / s, 0.8 m / s \)
B. \( 1.1 \mathrm{m} / \mathrm{s}, 0.5 \mathrm{m} / \mathrm{s} \)
c. \( 2.4 m / s, 1.5 m / s \)
D. \( 3.0 m / s, 1.5 m / s \)


What is passive and active uptake of ions? Give an account of the carrier
mediated uptake


If \( t_{3}=15, S_{10}=120 \) then the tenth
term of the series i:
A \( \cdot 6 \frac{3}{5} \)
B. \( s_{5}^{3} \)
\( c \cdot_{6} \frac{4}{5} \)
D. \( _{6} \frac{3}{4} \)


A flat plate moves normally towards a discharging jet of water at the rate of 3 \( \mathrm{m} / \mathrm{s} . \) The jet discharges the water at the rate of \( 0.1 m^{3} / s \) and at the speed of 18 \( \mathrm{m} / \mathrm{s} . \) The force exerted on the plate due to the jet is
A . \( 1800 \mathrm{N} \)
B. 2100 N
c. 2450
D. 1560 N


Use Euclids division lemma to show
that the square of any positive integer is either of the form \( 3 m \) or \( 3 m+1 \) for
some integer \( \boldsymbol{m} \)


Find the odd one.
A. Polychloroprene
B. Polyisoprene
C. Nitrile rubber
D. Thiokol rubber


Which of the following series in the spectrum of hydrogen atom lies in the visible region of the electromagnetic
spectrum?
A. Paschen series
B. Balmer series
c. Lyman series
D. Brackett series


Let \( y=x e^{-x} \) then prove that \( x \frac{d y}{d x}= \) \( (1-x) y \)


If \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{1} & -\mathbf{2} \\ \mathbf{4} & \mathbf{5}\end{array}\right] \) and \( \boldsymbol{f}(\boldsymbol{t})=\boldsymbol{t}^{2}-\boldsymbol{3} \boldsymbol{t}+\mathbf{7} \)
then \( \boldsymbol{f}(\boldsymbol{A})+\left[\begin{array}{cc}\mathbf{3} & \mathbf{6} \\ -\mathbf{1 2} & -\mathbf{9}\end{array}\right]= \)
\( \mathbf{A} \cdot\left[\begin{array}{cc}1 & 0 \\ 0 & 1\end{array}\right] \)
\( \mathbf{B} \cdot\left[\begin{array}{cc}0 & 0 \\ 0 & 0\end{array}\right] \)
\( \mathbf{c} \cdot\left[\begin{array}{cc}0 & 1 \\ 1 & 0\end{array}\right] \)
\( \mathbf{D} \cdot\left[\begin{array}{cc}1 & 1 \\ 0 & 0\end{array}\right] \)


lonisation energy of \( O_{2} \) to \( O^{+} \) O2is very
similar to the ionization energy of \( X e \) to
\( \boldsymbol{X} \boldsymbol{e}^{+} \)
A. True
B. False


The acceleration time graph of a
particle moving along a straight line is as shown in figure. At what time the particle acquires its initial velocity? (in seconds)
\( A \cdot 12 \)
B.
\( c \)
0.16


Name the polygon. Make two more
examples of same type.


A protons is about 1840 times heavier
than an electron. When it is accelerated
by a potential difference of \( 1 k V \), its
kinetic will be:-
A. \( 1840 \mathrm{keV} \)
B . \( 1 / 1840 \mathrm{keV} \)
c. \( 1 \mathrm{keV} \)
D. \( 920 \mathrm{keV} \)


A mass \( M \) attached to a spring oscillates with a period of 2 seconds. If
the mass is increased by \( 2 k g \), the
period increases by 1 second. Find the initial mass, assuming that Hooke's law is obeyed.


A wheel of radius r rolling on a straight line, the velocity of its centre being v. At a certain instant the point of contact of the wheel with the grounds is \( \mathrm{M} \) and \( \mathrm{N} \) is the highest point on the wheel(diametrically opposite to M). The incorrect statements is?
A. The velocity of any point P of the wheel is proportional to MP
B. Points of the wheel moving with velocity greater than form a larger area of the wheel than points moving with velocity less than v
C. The point of contact M is instantaneously at rest
D. The velocities of any two parts of the wheel which are equidistant from centre are equal


A beam of unpolarized light is passed
first through a tourmaline crystal \( \boldsymbol{A} \) and
then through another tourmaline
crystal \( B \) oriented so that its principal
plane is parallel to that of \( A \). The
intensity of final emergent light is \( I \). If
\( A \) is rotated by \( 45^{0} \) on a plane,
perpendicular to the direction of incident ray, then intensity of emergent light will be
A \( \cdot \frac{I}{8} \)
в. \( \frac{I}{4} \)
c. \( \frac{I}{2} \)
D. none of these


Sea breeze blows
A. During day
B. During night
C. Throughout day and night
D. None of these


Which of the following are polyamide polymers? This question has multiple correct options
A. Nylon - 6,10
B. Nylon - 6, 6
c. Nylon- 5
D. Perlon-U


Find the surface area of a \( 10 \mathrm{cm} \times \)
\( 4 c m \times 3 c m \) brick:
A. 84 sq. \( \mathrm{cm} \)
B. 124 sq.cm
c. 164 sq.cm
D. 180 sq.cm


Assertion:Chromium plating is done on many objects like car parts, wheel rims and bath taps. Reason:The chromed layer can be decorative, provide corrosion resistance, ease cleaning procedures, or increase surface hardness.
A. Assertion is correct and Reason is incorrect
B. Assertion is incorrect and Reason is correct
c. Both Assertion and Reason is correct and Reason is the correct explanation of Assertion
D. Both Assertion and Reason is correct but Reason is not the correct explanation of Assertion


If \( 3 x=\sec \theta \) and \( \frac{3}{x}=t a n \theta, \) then find the value of \( 9\left(x^{2}-\frac{1}{x^{2}}\right) \)


Which of the following lanthanide is commonly used?
A. Lanthanium
B. Nobelium
c. Thorium
D. Cerium


An ideal solution has two components
\( A \) and \( B . A \) is more volatile than \( B \), i.e.
\( \boldsymbol{P}_{A}^{\circ}>\boldsymbol{P}_{B}^{\circ} \) and also \( \boldsymbol{P}_{A}^{\circ}>\boldsymbol{P}_{\text {total}} . \) If \( \boldsymbol{X}_{\boldsymbol{A}} \)
and \( Y_{A} \) are mole fractions of
components \( A \) in liquid and vapour
phases, then :
A. \( X_{A}=Y_{A} \)
в. \( X_{A}>Y_{A} \)
c. \( X_{A}<Y_{A} \)
D. Data insufficient


Name two metals which form
Amphoteric oxide


The D.E whose solution is \( y=a e^{2 x}+ \)
\( \boldsymbol{b} \boldsymbol{e}^{\boldsymbol{3} \boldsymbol{x}} \boldsymbol{\text { is: }} \)
A \( \cdot y_{2}+5 y_{1}+6 y=0 \)
в. \( y_{2}-5 y_{1}-6 y=0 \)
c. \( y_{2}+5 y_{1}-6 y=0 \)
D. \( y_{2}-5 y_{1}+6 y=0 \)


If new moon day is day \( 1, \) then what is
the day of the gibbous moon?
A . 14
B. 3
\( c \cdot 7 \)
D. 10


Assertion
Colloidal solutions are purified by
dialysis.
Reason
In the process of dialysis, colloidal
particles pass through parchment
paper.
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


his profit percent.
\( \mathbf{A} \cdot 12 \% \)
B. \( 15 \% \)
\( c \cdot 10 \% \)
D. \( 25 \% \)


The polynomial \( f(x)=x^{4}+a x^{3}+ \)
\( b x^{2}+c x+d \) has real coefficients and
\( (2 i)=f(2+i)=0 . \) The value of \( (a+ \)
\( b+c+d \) ) equals to
A .
B. 4
\( c .9 \)
D. 10


Assertion
Emphysema disease is very common in
Kanpur and Kolkata.
Reason
It is a disease of respiratory tract
occuring due to pollution.
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.


State whether the given statement is true or false:

Lead poisoning can be removed by use of \( \boldsymbol{E} \boldsymbol{D} \boldsymbol{T} \boldsymbol{A} \)
A. True
B. False


Maximum current that can pass
through galvanometer is \( 0.002 A \) and
resistance of galvonameter is \( \boldsymbol{R}_{\boldsymbol{g}}= \) \( 50 \Omega \) find out shunt resistance to
convert in into ammeter of range \( 0.5 A \)
A . \( 0.5 \Omega \)
B. \( 0.2 \Omega \)
\( c .0 .7 \Omega \)
D. \( 0.9 \Omega \)


How many moles of \( H_{2} O_{2} \) are present in
2 litres of \( 6.8 \% \) w/v \( H_{2} O_{2} \) solution?


The longest wavelength of \( \boldsymbol{H} \boldsymbol{e}^{+} \) in Paschen series is ' \( m \) ' then shortest
wavelength of \( B e^{3+} \) in Paschen series
in terms of ' \( m \) ' is:
A \( \cdot \frac{7}{64} m \)
в. \( \frac{5}{36} m \)
c. \( \frac{64}{7} \) m
D. \( \frac{53}{8} m \)


Water flows at the rate of \( 15 k m \) per hr
through a pipe of a diameter \( 14 \mathrm{cm} \) into
a rectangle tank which is \( 50 m \) long and
\( 44 m \) wide, Find the time in which th
level of water in the tank will rise by
\( 21 c m \)


The act of throwing a die is called an
A . outcomes
B. event
c. experiment
D. sample


The inequality \( |z-4|<|z-2| \)
represents the following region
A. \( \operatorname{Re}(z)>0 \)
в. \( \operatorname{Re}(z)<0 \)
c. \( \operatorname{Re}(z)>2 \)
D. none of these


Find the value of \( (2-\sqrt{1-x})^{6}+(2+ \)
\( \sqrt{1-x})^{6} \)


\( 3,5,7,9,11,13,15 \dots \) is an
A. Geometric progression
B. Arithmetic series
C. Arithmetic progression
D. Harmonic progression


In stationary wave the distance between two successive nodes or two successive
antinodes is equal to:
\( A \cdot \lambda \)
B. \( \lambda / 2 \)
c. \( \lambda / 3 \)
D. \( \lambda / 4 \)


What happens when you join the free
ends of the tester for more than a few
minutes?
A. Cells of the battery will drain quickly.
B. The current will not be able to pass.
c. There would be no conduction of electricity
D. All of the above


If two waves of same frequency and amplitude respectively on superposition produce a resultant disturbance of the same amplitude, the wave differ in phase by :
\( A \)
B. zero
c. \( \pi / 3 \)
D. 2 \( \pi / 3 \)


The colloidal solution of a solid as the
dispersed phase and a gas as the dispersion medium is called:
A . sol
B. solid foam
c. aerosol
D. gel


A certain reaction is of first order. After
540 seconds, \( 32.5 \% \) of the reactant
remains.
(a) Calculate the rate constant.
(b) How long would it require for \( 25 \% \) of the reactant to be decomposed?


Construct a quadratic equation with real co-efficients one of whose root is
\( (2+3 i) \)


Assertion
All homogeneous substances are pure.
Reason
Alloys are homogeneous mixtures of
Solids.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Explain the difference between a double-salt and a complex, giving an example in each case.


Which of the following is not a covalent compound?
A. \( C O_{2} \)
B. \( C l_{2} \)
\( \mathbf{c} \cdot N a_{2} O \)
D. \( C H_{4} \)


Find the roots of the following equation \( 2 y^{2}+\frac{15}{y^{2}}=12, \) then
A \( \cdot \quad y=\pm \sqrt{\frac{6+\sqrt{6}}{4}}, y=\pm \sqrt{\frac{6-\sqrt{6}}{2}} \)
в. \( \quad y=\pm \sqrt{\frac{6+\sqrt{6}}{2}}, y=\pm \sqrt{\frac{6-\sqrt{5}}{2}} \)
c. \( y=\pm \sqrt{\frac{6+\sqrt{6}}{2}}, y=\pm \sqrt{\frac{6-\sqrt{6}}{2}} \)
D. \( y=\pm \sqrt{\frac{6+\sqrt{5}}{2}}, y=\pm \sqrt{\frac{6-\sqrt{6}}{2}} \)


The most lightest alkaline earth metal
is:
\( A . B e \)
в. \( M g \)
\( c . C a \)
D. Ba


Differentiate the following function w.r.t
\( x \)
\( \sqrt{x+\frac{1}{x}} \)


The force of attraction between two unit
point masses separated by a unit distance is called:
A . gravitational potential
B. acceleration due to gravity
c. gravitational field
D. universal gravitational constant


The differential equation whose solution is \( \boldsymbol{y}=\boldsymbol{a} \cos (\boldsymbol{3} \boldsymbol{x}+\boldsymbol{b}) \) is?
A \( \cdot y_{2}+3 y=0 \)
в. \( y_{2}+y=0 \)
c. \( y_{2}+9 y=0 \)
D. \( y_{2}+6 y=0 \)


An emulsifier is a substance which:
A. helps in the dispersion of liquid in liquid
B. stabilises the emulsion
c. coagulates the emulsion
D. purifies the emulsion


ntegrate the function \( \frac{1}{\sqrt{9 x^{2}+6 x+5}} \)


Amount in 4 years.


In the manufacture of nitric acid by
Ostwald's process, write
The chemical equation for the
dissolution of \( N O_{2} \) in water.


When sand is poured on a rotating disc, its angular velocity will be:-
A . Decrease
B. Increase
c. Remain constant
D. None of these


You are to examine these two
statements carefully and select the answers to these items using the code
given below:

Statement I: The acceleration due to
gravity decreases with increase in height from the surface of the Earth. Statement II : The acceleration due to gravity is inversely proportional to the square of the distance from the centre
of the Earth.
A. Both the statements are individually true and Statement II is the correct explanation of Statement
B. Both the statements are individually true but Statement II is not the correct explanation of Statement
c. statement lis true but Statement II is false
D. Statement lis false but Statement II is true


The second ionization enthalpy is \( ? \)
A. smaller than the first ionization enthalpy.
B. almost equal to the first ionization enthalpy.
C. smaller than the third ionization enthalpy.
D. equal to the second electron gain enthalpy.


DNA produce which is the
source of information for protein biosynthesis.
A . t-RNA
B. m-RNA
c. r-RNA
D. none of these


A bag contains 4 blue, 5 red and 7 green balls. If 4 balls are drawn one by one
with replacement, what is the probability that all are blue?
A \( \cdot \frac{1}{16} \)
в.
c. \( \frac{1}{256} \)
D. \( \frac{1}{64} \)


State whether true or false:
Gauss law is applicable only when there is a symmetric distribution of charge.
A. True
B. False


A parallel-plate capacitor is connected
to a cell. Its positive plate \( A \) and its
negative plate \( \boldsymbol{B} \) have charges \( +\boldsymbol{Q} \) and
\( -Q \) respectively. A third plate \( C \)
identical to \( A \) and \( B, \) with charge \( +Q \)
is now introduced midway between \( \boldsymbol{A} \)
and \( B, \) parallel to them. Which of the
following are correct?
This question has multiple correct options
A \( \cdot \) The charge on the inner face of \( B \) is now \( -\frac{3 Q}{2} \)
B. There is no change in the potential difference between
\( A \) and \( B \)
C. The potential difference between \( A \) and \( C \) is one-third of the potential difference between \( B \) and \( C \)
D. The charge on the inner face of \( A \) is now \( Q / 2 \)


Why iron is used widely in construction of buildings, bridges, railway lines etc?
A. Iron is a good conductor of electricity
B. Iron is ductile
c. Iron have high tensile strength
D. Iron is malleable


Which of the following physical quantities has same unit in all the
three system of units?
A . Mass
B. Length
c. Time
D. None of these


The polarising power of \( M g^{2+} \) is nearly
same as that of:
A \( \cdot L i \)
в. \( B a^{2} \)
\( \mathrm{c} \cdot A l^{3} \)
D. all of the above


\( (n-1) \) equal point masses each of
mass \( \mathrm{m} \) are placed at the vertices of a regular n-polygon. The vacant vertex has a position vector a with respect to the centre of the polygon. Find the positive
vector of centre of mass:
A \( \cdot \frac{1}{n-1} a \)
в. \( -\frac{1}{(n-1)} a \)
c. \( (n-1) a \)
D. \( -\left(\frac{n-1}{a}\right) \)


Find the breadth of a rectangular plot of land, if its area is \( \$ \$ 440 \backslash \mathrm{m}^{\wedge} 2 \$ \$ 2 \) and
the length is \( 22 m . \) Also find its perimeter (in metre)


The rms speed of hydrogen is \( \sqrt{7} \) times the rms speed of nitrogen. If T is the temperature of the gas, then :
\( \mathbf{A} \cdot T_{H_{2}}=T_{N_{2}} \)
\( \mathbf{B} \cdot T_{H_{2}}>T_{N_{2}} \)
\( \mathbf{c} \cdot T_{H_{2}}<T_{N_{2}} \)
D. \( T_{H_{2}}=\sqrt{7} T_{N_{N}} \)


Which vitamin is not obtained from
plants?
A. Cyanocobalamine
B. Thiamine
c. Pyridoxine
D. \( \alpha \) - tocopherol


A block of mass \( 2.9 \mathrm{kg} \) slides over a frictional floor. If it slides \( 10 \mathrm{m} \) in \( 5 \mathrm{s} \)
before coming to rest. Calculate the force of friction on the ball.
A . - 4N
B . - 1.6
c. - 0.8N
D. - 5N
E . - 2.32N


Four metals and their methods of
refinement are given :
(i) \( N i, C u, Z r, G a \)
(ii) Electrolysis, van Arkel process, Zone
refining, Monds process

Choose the right method for each metal.
A. \( N i: \) Electrolysis, \( C u: \) van Arkel process, \( Z r: \) zone refining \( G a: \) Monds process
B. \( N i: \) Monds process, \( C u \) : Electrolysis, \( Z r: \) van Arkel process, \( G a: \) Zone refining
C. \( N i: \) Monds process, \( C u \) : van Arkel process, \( Z r: \) Zone refining, \( G a \) : Electrolysis
D. \( N i \) : Electrolysis, \( C u \) : Zone refining, \( Z r \) : van Arkel process, \( G a: \) Monds process


In the given figure find \( O C \)


Number of electrons present in \( ^{26} \) Fe is
A . 26
B. 27
c. 28
D. 29


In the solvation of \( N a C l \) in water, which
of the following occur?
A. Hydrogen atom interacts with \( C l^{-} \) atom
B. Oxygen atom interacts with \( N a^{+} \) atom
c. Both \( A \) and \( B \)
D. None of these


(a) Give a schematic outline of
photorespiration.
(b)Differentiate between
photophosphorylation and photorespiration.


When a sound wave goes from one medium to another, the quantity that remains unchanged is
A. Frequency
B. amplitude
c. wavelength
D. speedd


Which one has same Van't Hoff factor \( ' i^{\prime} \)
as that of \( \boldsymbol{H} \boldsymbol{g}_{2} \boldsymbol{C l}_{2} \) ?
A . \( N a C l \)
в. \( N a_{2} S O_{4} \)
c. \( A l\left(N O_{3}\right)_{3} \)
D. \( A l_{2}\left(S O_{4}\right)_{3} \)


Show that
\( \sin ^{2}(\theta+A)+\sin ^{2}(\theta+B) \)
\( 2 \cos (A-B) \sin (\theta+A) \sin (\theta+B) \)
is independent of \( \boldsymbol{\theta} \boldsymbol{o r}=\sin ^{2}(\boldsymbol{A}- \)
\( \boldsymbol{B}) \)


One man takes 1 min to raise a box to a
height of 1 metre and another man takes \( 1 / 2 \) min. to do so. The potential energy in the two cases is
A. different
B. same
c. energy of the first is more
D. energy of the second is more


the car is moving towards east with a speed of \( 25 \mathrm{km} / \mathrm{h} \). To the driver of the
car, a bus appears to move towards north with a speed of \( 25 \sqrt{3} k m / h . \) What
is the actual velocity of the bus?
A \( \cdot 50 k m / h, 30^{\circ} \) east of north
B. \( 50 k m / h, 30^{\circ} \) north of east
\( \mathrm{c} \cdot 25 k m / h, 30^{\circ} \) east of north
D. \( 25 k m / h, 30^{\circ} \) north of east


\( \mathbf{f} \mathbf{A}=\left[\begin{array}{lll}\mathbf{1} & \mathbf{- 3} & \mathbf{- 4} \\ \mathbf{- 1} & \mathbf{3} & \mathbf{4} \\ \mathbf{1} & \mathbf{- 3} & \mathbf{- 4}\end{array}\right], \) then \( \mathbf{A}^{2}= \)
\( A \cdot A \)
в. -4
c. Null matrix
D. \( 2 A \)


The centre of curvature of a
mirror is behind it.
A. convex
B. concave
c. convex or concave
D. plane


The volume of the global hemisphere is \( 19404 i n^{3} . \) Find its diameter.
A . 21 in
B. 42 in
c. 10.5 in
D. 9 in


Classify Amino acids on basis of
function and on basis of Nature of
amino acids.


Select the correct alternative.
In the reaction of \( Z n+F e S O_{4} \rightarrow \)
\( Z n S O_{4}+F e \)
A. zn gets oxidized
B. Fe gets oxidized
c. zn is oxidized in agent
D. zn and Fe both get oxidized


Balance the following chemical equation and identify the type of chemical reaction? \( \boldsymbol{H} \boldsymbol{g} \boldsymbol{O}(\boldsymbol{s}) \stackrel{\boldsymbol{H} e a t}{\longrightarrow} \boldsymbol{H} \boldsymbol{g}(\boldsymbol{l})+\boldsymbol{O}_{2}(\boldsymbol{g}) \)


What is the physical state of water at
\( -20^{\circ} \mathrm{C} ? \)
A. Solid
B. Liquid
\( c . \) Gas
D. None of the above


The percentage change in the acceleration of the earth towards the
sun from a total eclipse of the sun to the
point where the moon is on a side of earth directly opposite to the sun is:
\( r_{1} \) is the distance of earth from sun, \( r_{2} \)
is the distance of earth from moon
A \( \cdot \frac{M_{s}}{M_{m}} \frac{r_{2}}{r_{1}} \times 100 \)
B. \( \frac{M_{s}}{M_{m}}\left(\frac{r_{2}}{r_{1}}\right)^{2} \times 100 \)
\( ^{\mathbf{C}} 2\left(\frac{r_{1}}{r_{2}}\right)^{2} \frac{M_{m}}{M_{s}} \times 100 \)
\( ^{\mathrm{D}}\left(\frac{r_{1}}{r_{2}}\right)^{2} \frac{M_{s}}{M_{m}} \times 100 \)


For which of the following change
\( \triangle \boldsymbol{H}=\triangle \boldsymbol{E} ? \)
A \( \cdot H_{2}(g)+I_{2(g)} \rightarrow 2 H I_{(g)} \)
B. \( H C l_{(a q)}+N a O H_{(a q)} \rightarrow N a C l_{(a q)}+H_{2} O \)
c. \( C_{(s)}+O_{2(g)} \rightarrow 2 C O_{(g)} \)
D. \( N_{2(g)}+3 H_{2(g)} \rightarrow 2 N H_{3(g)} \)


Among the following molecules, which of the following has non-polar covalent bonds?
A \( . H_{2} \)
в. \( O_{2} \)
\( c \cdot C l_{2} \)
D. All of the above


Find the critical constant
\( \left(P_{c}, V_{c} \text { and } T_{c}\right) \) in terms of \( A \) and \( B \)
also find compressibility factor \( (Z) \) for
the following equation of state.
\[
\boldsymbol{P} \boldsymbol{V}=\boldsymbol{R T}-\frac{\boldsymbol{A}}{\boldsymbol{V}}+\frac{\boldsymbol{2} \boldsymbol{B}}{\boldsymbol{V}^{2}}
\]
where \( A \) and \( B \) are constant, \( P= \)
pressure and \( V= \) molar volume.
\( \mathbf{A} \)
\[
\begin{array}{l}
V_{c}=\frac{6 B}{A}, T_{c}=\frac{A^{2}}{6 R B}, P_{c}=\frac{A^{3}}{108 R B}, \text { compressibility } \\
\text { factor }=\frac{P_{c} V_{c}}{R T_{c}} \frac{1}{3}
\end{array}
\]
B.
\[
V_{c}=\frac{3 B}{A}, T_{c}=\frac{A^{2}}{3 R B}, P_{c}=\frac{A^{3}}{108 R B}, \text { compressibility }
\]
\[
\text { factor }=\frac{P_{c} V_{c}}{R T_{c}} \frac{1}{3}
\]
\( c \)
\[
\begin{array}{l}
V_{c}=\frac{6 B}{A}, T_{c}=\frac{A^{2}}{6 R B}, P_{c}=\frac{A^{3}}{54 R B}, \text { compressibility } \\
\text { factor }=\frac{P_{c} V_{c}}{R T_{c}} \frac{1}{2}
\end{array}
\]
D. None of these


A plank with a box on it at one end is
gradually raised about the other end. As
the angle of inclination with the
horizontal reaches \( 30^{\circ}, \) the box starts to
slip and slides 4.0 m down the plank in
4.0 \( s \). The coefficients of static and
kinetic friction between the box and the
plank will be, respectively
A. 0.4 and 0.3
B. 0.6 and 0.6
c. 0.6 and 0.5
D. 0.5 and 0.6


Two bullets \( P \) and \( Q \), masses 10 and 20
g, are moving in the same direction towards a target with velocities of 20
and \( 10 \mathrm{m} / \mathrm{s} \) respectively. Which one of the bullets will pierce a greater distance through the target?
\( A \cdot P \)
B.
c. Both will cover the same distance
D. Nothing can be decided


A body cools from \( 80^{\circ} \mathrm{C} \) to \( 50^{\circ} \mathrm{C} \) in 5
minutes. Calculate the time it takes to
cool from \( 60^{\circ} \mathrm{C} \) to \( 30^{\circ} \mathrm{C} \). The
temperature of the surroundings is
\( \mathbf{2 0}^{\circ} \boldsymbol{C} \)


If \( 72 K \) is a perfect cube, then the value
of \( \boldsymbol{K} \) is:
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D.


Which of the following statements
regarding Lanthanides is false?
A. All lanethanides are solid at room temperature
B. Their usual oxidation state is +3
C. They can be separated from one another by ionexchange method
D. lonic radii of trivalent lanthanides steadily increases with increase in atomic number


What is he agriculture done in fresh water is known as?


\( \lim _{x \rightarrow \frac{\pi}{2}} \frac{\left(1-\tan \frac{x}{2}\right)(1-\sin x)}{\left(1+\tan \frac{x}{2}\right)(\pi-2 x)^{3}} \) is
A . 0
B. \( \frac{1}{32} \)
\( c \cdot \alpha \)
\( D \)


Why does acetylation of \( -N H_{2} \) group of
aniline reduce its activity?


Two isotopes \( P \) and \( Q \) of atomic weight 10 and \( 20, \) respectively are mixed in equal amount by weight. After 20 days their weight ratio is found to be 1: 4 Isotope \( P \) has a half-life of 10 days. The half-life of isotope \( Q \) is
A . zero
B. 5 days
c. 20 days
D. infinite


Arrange the following step in correct sequence found during the mechanism of lipid insoluble hormone (epinephrine) function or action.
A. Second messenger formation
B. Binding to the surface receptor
C. Glycogenolysis
D. Adenylate cyclase activation
\( A \cdot C, A, D \) and \( B \)
B. B, D, A and C
\( c . D, B, c \) and \( A \)
D. None of the above


\( \boldsymbol{A}=\{1,2,3,4\} \) and \( \boldsymbol{B}=\{\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}\} . \) The
relations from \( \boldsymbol{A} \) to \( \boldsymbol{B} \) is
A \( \cdot\{(1,2),(1,3),(2,3),(2,4),(3,4),(3,1)\} \)
B \( \cdot\{(a, b),(a, c),(b, a),(b, c),(c, a)\} \)
c. \( \{(1, a),(1, b)(1, c),(2, a),(2, b),(2, c),(3, a),(3, b),(3, c),(4 \)
D \cdot \( \{(a, 1),(1,3),(b, 2),(c, 3),(b, 3),(b, 4)\} \)


s nucuct
length \( L=2 m, \) and a resistance \( r= \)
\( 10 \Omega \) is moving with velocity \( v= \)
\( (2 m / s) \hat{i} . \) Three mutually perpendicular
sides are parallel to \( x, y \) and \( z \) axis as
shown in figure. The corner A lies
at origin at \( t=0 . \) There is a magnetic
field in the region \( (\mathbf{0} \leq \boldsymbol{x} \leq \boldsymbol{L}) \) is \( \overrightarrow{\boldsymbol{B}}= \)
\( (-5 \hat{k}) T \) and \( B=0, \) otherwise. Which
of the following is correct?
A. current through \( b c \) is \( 2 A \) at \( t=0.25 s \)
B. current through \( f g \) is \( 1 A \) at \( t=0.25 s \)
C. potential difference across \( g h \) is \( 20 V \) at \( t=0.25 s \)
D. potential difference across \( d h \) is \( 5 V \) at \( t=0.25 s \)
E. potential difference across \( d h \) is \( 10 V \) at \( t=0.25 \)


A uniform circular loop of radius \( a \) and resistance \( R \) is placed perpendicular to
a uniform magnetic field \( B \). One half of
the loop is rotated about the diameter
with angular velocity \( \omega \) as shown in
figure. Then, the current in the loop is:
This question has multiple correct options
A. zero, when \( \theta \) is zer
B. \( \frac{\pi a^{2} B \omega}{2 R}, \) when \( \theta \) is zero
c. zero, when \( \theta=\pi / 2 \)
\( \stackrel{\pi a^{2} B \omega}{2 R}, \) when \( \theta=\frac{\pi}{2} \)


A chord of a circle divides the circular
region in two parts the region which contains the centre is known as
A. minor Arc
B. major Arc
c. minor Segment
D. major Segment


Which one of the following is a general form of geometric progression?
A. 1,1,1,1,1
в. 1,2,3,4,5
c. 2,4,6,8,10
D. -1,2,-3,4,-5


Acetic acid is:
A. Methanoic acid
B. Ethanoic acid
C. Propanoic acid
D. None of these


Which of these is true for most of the
organic compounds?
A. Low melting and boiling points
B. High melting and boiling points
c. Low melting point but high boiling point
D. High melting point but low boiling point


The equilibrium constant for the
reaction is 9.40 at \( 900^{\circ} C \)
\( \boldsymbol{S}_{2}(\boldsymbol{g})+\boldsymbol{C}(s) \rightleftharpoons \boldsymbol{C} \boldsymbol{S}_{2}(\boldsymbol{g}) \)
Calculate the pressure of two gases at
equilibrium, when 1.42 at \( m \) of \( S_{2} \) and
excess of \( C(s) \) come to equilibrium.


The IUPAC name of the compound is:
\[
\begin{array}{c}
\mathbf{B r}-\mathbf{C H}_{2}-\mathbf{C H}-\mathbf{C O}-\mathbf{C H}_{2}-\mathbf{C H}_{2}-\mathbf{C H}_{\mathbf{3}} \\
\mathbf{C O N H}_{2}
\end{array}
\]
A. 2 - Bromo methyl- 3 - oxo hexanamide
B. 1- Bromo - 2 - amido-3 - oxo - hexane
c. 1 - Bromo - 2 - amido - n- propyl ketone
D. 3 - Bromo - 2 -proponyl - propanamide


Which component from the inhaled air is used by the body?
A. Carbon dioxide
B. Nitrogen
c. oxygen
D. Hydrogen


In triangle \( A B C, 3 \angle A=4 \angle B=6 \angle C . \) The
smallest angle of the triangle is \( 50^{\circ} \)
A. True
B. False


Which of the following complexes are
chelates?
This question has multiple correct options
A. bis-(dimethyl glyoximato) nickel (II)
B. Potassium ethylenediaminetetracyanato chromate (111)
C. Tetraamminedicyanocobalt (II)
D. trans-diglycinatopalladium (II)


The exchange of gases between which of the following is called external respiration?
A. Lung alveoli and blood capillaries
B. Lung alveoli and bronchi
c. The buccal cavity and the external atmosphere
D. Lung alveoli and pulmonary artery


Dimensional formula of \( \Delta Q, \) heat
supplied to the system is
\( \mathbf{A} \cdot\left[M L^{2} T^{-2}\right] \)
B. \( \left[M L T^{-2}\right] \)
\( \mathbf{c} \cdot\left[M L^{2} T^{-1}\right] \)
D . \( \left[M L T^{1}\right. \)


On a new scale of temperature (which is linear) and called the \( \mathrm{W} \) scale, the
freezing and boiling points of water are \( 39^{\circ} \mathrm{W} \) and \( 239^{\circ} \mathrm{W} \) respectively. What will be the temperature on the new scale, corresponding to a temperature of \( 39^{\circ} \mathrm{C} \) on the Celsius scale?
В . \( 139^{\circ} \mathrm{W} \)
\( \mathbf{c} \cdot 78^{\circ} W \)
D. \( 117^{\circ} W \)


solve
\( 4 x^{2}+8 x \)


Consider three waves represented by
\( \boldsymbol{y}_{1}=\boldsymbol{3} \sin (\boldsymbol{k} \boldsymbol{x}-\boldsymbol{\omega} \boldsymbol{t}) \)
\( \boldsymbol{y}_{2}=\boldsymbol{3} \sin \left(\boldsymbol{k} \boldsymbol{x}-\boldsymbol{\omega} \boldsymbol{t}+\frac{2 \pi}{3}\right) \)
\( \boldsymbol{y}_{3}=\boldsymbol{3} \sin \left(\boldsymbol{k} \boldsymbol{x}-\boldsymbol{\omega} \boldsymbol{t}+\frac{4 \pi}{3}\right) \)
What is the amplitude or resultant of
waves at \( x=0 ? \)
\( A \cdot O \)
B. 9
\( c \cdot 6 \)
\( D \)


According to Huygens principle, during refraction of light from air to a denser medium
A. Wavelength and speed increase
B. Wavelength decreases but speed increases
c. wavelength and speed decrease
D. Wavelength increases but speed decreases


Find the area bounded by the parabola
\( x^{2}=4 y \) and the straight line \( x=4 y- \)
2


Density of a sphere of mass \( M, \) radius \( R \) varies with distance \( r \) from its centre \( \operatorname{as} \boldsymbol{P}=\boldsymbol{P} \cdot\left(1+\frac{\boldsymbol{r}}{\boldsymbol{R}}\right) \boldsymbol{P}_{0} \) is \( \mathbf{a}+\boldsymbol{v} \boldsymbol{e} \)
constant find its MOI about its
diameter.


Total number of moles for the reaction
\( 2 H I \rightleftharpoons H_{2}+I_{2}, \) if \( \alpha \) is degree
of dissociation is :
A . 2
B. \( 2-\alpha \)
c. 1
D. \( 1-\alpha \)


A stationary particle of mass \( \boldsymbol{m}= \)
\( 1.5 k g \) is acted upon by a variable force.
The variation of force with respect to
displacement is plotted in fig. Calculate the velocity acquired by the particle after getting displaced through
\( 6 m \)


ff \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) defined by \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{2} \boldsymbol{x}+\mathbf{5} \)
if \( \boldsymbol{x}>\mathbf{0} ; \boldsymbol{f}(\boldsymbol{x})=\mathbf{3} \boldsymbol{x}-\mathbf{2}, \) if \( \boldsymbol{x} \leq \mathbf{0}: \) then \( \boldsymbol{f} \)
is
A . a function
B. one one
c. onto
D. one-one and onto


What will be the current flowing through the \( 6 K \Omega \) resistor in the circuit shown
where the breakdown voltage of the
zener is \( 6 \mathrm{V} \) ?
A \( \cdot \frac{2}{3} \mathrm{mA} \)
B. 1mA
c. \( 10 \mathrm{mA} \)
D. \( \frac{3}{2} \mathrm{mA} \)


A triangular prism of glass is shown in
the figure. A ray incident normally to
one face is totally reflected. If \( \boldsymbol{\theta}=\mathbf{4 5}^{\mathbf{0}} \)
the refractive index of glass is :
\( A \cdot<1.4 \)
\( B \). \( =1.4 \)
\( \mathbf{c} .>1.41 \)
D. 1.732


Which statement is wrong about the
function of brain?
A. Hypothalamus mainly controls autonomic nervous system.
B. Voluntary muscle activity is started by cerebellum.
C. Medulla oblongata regulates involuntary activity of our body.
D. Thalamus is responsible for crude sensation.


In an R-C circuit, select the correct
options among the following:
This question has multiple correct options
A. Instantaneous A.C is given by \( I=I_{0} \sin (w t+\phi) \)
B. The alternating current in the circuit leads the emf by a phase angle
C. Its impedance is \( \sqrt{R^{2}+(w C)^{2}} \)
D. Its capacitive reactance is \( \omega C \)


Among the following four compounds
(i) Phenol
(ii) Methyl phenol
(iii) Meta-nitrophenol
(iv) Para-nitrophenol The acidity order is:
A \( \cdot(i v)>(i i i)>(i)>(i i) \)
в. \( (i i i)>(i v)>(i)>(i i) \)
c. \( (i)>(i v)>(i i i)>(i i) \)
D. \( (i i)>(i)>(i i i)>(i v) \)


Four metallic plates are arranged as
shown in the figure. If \( d \) is the distance
between each plate then capacitance of
the given system between points \( A \) and
\( B \) is :
\( (\operatorname{given} \boldsymbol{d}<<\boldsymbol{A}) \)
\( \mathbf{A} \cdot \frac{\epsilon_{0} A}{d} \)
B. \( \frac{2 \epsilon_{0} A}{d} \)
c. \( \frac{3 \epsilon_{0} A}{d} \)
D. \( \frac{4 \epsilon_{0} A}{d} \)


Two events \( A \) and \( B \) will be independent
if
\( \mathbf{A} \cdot P\left(A^{\prime} \cap B^{\prime}\right)=(1-P(A))(1-P(B)) \)
B \( \cdot P(A)+P(B)=1 \)
\( \mathbf{c} \cdot P(A)=P(B) \)
D. \( A \) and \( B \) are mutually exclusive


Fill in the blanks
During refraction of light, the character of light which does not change is


Which of the following is a non-reducing sugar?
A. Glucose
B. Sucrose
c. Maltose
D. Lactose


The number of the integers from 1 to 120 which are divisible by 3 or 5
A . 56
B. 40
\( c \cdot 24 \)
\( D \cdot 8 \)


From the given data of the following reactions;
\[
\begin{aligned}
\boldsymbol{C a O}(\boldsymbol{s})+\boldsymbol{H}_{2}(\boldsymbol{g}) & \rightleftharpoons \boldsymbol{C a}(\boldsymbol{s})+\\
\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) ; & \boldsymbol{K}=\mathbf{6 7 0} \\
\boldsymbol{C a O}(\boldsymbol{s})+\boldsymbol{C O}(\boldsymbol{g}) & \rightleftharpoons \boldsymbol{C a}(\boldsymbol{s})+\\
\boldsymbol{C O}_{2}(\boldsymbol{g}) ; & \boldsymbol{K}=\mathbf{4 9 0}
\end{aligned}
\]
The value of \( K_{c} \) (nearest integer) for the given reaction is
\[
\begin{array}{c}
\boldsymbol{C O}_{2}(\boldsymbol{g})+\boldsymbol{H}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{C} \boldsymbol{O}(\boldsymbol{g})+ \\
\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g})
\end{array}
\]


\( \mathrm{Q}(\mathrm{charge})=? \)
\( \mathbf{A} \cdot n / e \)
B. \( n e \)
\( c \cdot e / n \)
D. All


Given Reaction.
Y in reaction is:
\( \left\langle\mathrm{Br} \frac{\text { ether }}{\mathrm{Mg}}>\mathrm{x} \frac{(\mathrm{i}) \mathrm{H}_{2} \mathrm{O}}{(\mathrm{ii}) \mathrm{HCl}}>\mathrm{Y}(\text { main product })\right. \)
\( A . \) Hexane
B. Cyclohexane
C . Cyclohexylcyclohexane
D. Cyclohexylether


The properties of \( Z r \) and \( H f \) are similar because:
A. both belong to d-block
B. both belong to same group of the periodic table
c. both have similar radii
D. both have same number of electrons


Match the following:
Left column lists the level of integration and right column lists the number of circuit components.


A solution of sulphuric acid in water exhibits:
A. negative deviations from Raoult's law
B. positive deviations from Raoult's law
c. ideal properties
D. the applicability of Henry's law


The maximum of \( \mathbf{f}(\mathbf{x})=\frac{\log \mathbf{x}}{\mathbf{x}^{2}}(\mathbf{x}>\mathbf{0}) \)
occurs at \( \mathbf{x}= \)
\( A \)
B. \( \sqrt{e} \)
\( c \cdot \frac{1}{e} \)
D. \( \frac{1}{\sqrt{\mathrm{e}}} \)


When a conducting ring is moved in a magnetic field then the total charge induced in it depends on
A. initial magnetic flux
B. final magnetic flux
c. the rate of change of magnetic flux
D. the total change in magnetic flux


Find \( \int \frac{d x}{x^{2}-a^{2}} \) and hence evaluate \( \int \frac{d x}{3 x^{2}+13 x-10} \)


resultant of the three forces
hown in the figure is
\( (\sqrt{2}+1) \)


Equipotential surfaces are shown in the
figure. Find the magnitude and the
direction of the resultant electric field.
A. \( 200 \mathrm{V} / \mathrm{m} \) making an angle \( 60^{\circ} \) with the positive x-axis.
B. 200 V/m making an angle \( 120^{\circ} \) with the positive \( x \) axis
c. \( 200 \mathrm{V} / \mathrm{m} \) making an angle \( 120^{\circ} \) with the negative \( \mathrm{x} \) axis.
D. \( 100 \mathrm{V} / \mathrm{m} \) making an angle \( 60^{\circ} \) with the \( \mathrm{x} \) -axis


Water rises to a height of \( 10 \mathrm{cm} \) in a
capillary tube and mercury falls to a depth of the same capillary tube. If the density of water is \( 1 \mathrm{gm} / \mathrm{c} . \mathrm{c} \) and its
angle of contact is \( 0^{\circ}, \) then the ratio of
such of two liquids is \( \left(\cos 135^{\circ}=0.7\right) \)


When an element of very low
ionization potential reacts with an element of very high electron affinity, then :
A. a weak ionic bond is formed
B. a strong ionic bond is formed
c. a polar covalent bond is formed
D. no bond is formed


A circular grassy plot of land, \( 42 m \) in diameter, has a path \( 3.5 m \) wide running around it on the outside. Find
the cost of gravelling the path at \( R s .4 \)
per square metre
A. \( R s .2002 \)
B. Rs.2003
c. \( R s .2004 \)
D. \( R s .2000 \)


For an equilibrium reaction involving gases, the forward reaction is first order
while the reverse reaction is second
order. The units of \( \boldsymbol{K}_{\boldsymbol{p}} \) for forward equilibrium is:
A . atm
B \( . a t m^{2} \)
c. \( a t m^{-1} \)
D. \( a t m^{-2} \)


When a student looks into a plane mirror, she sees a virtual image of herself. However, when she looks into a sheet of paper, no such image forms. Which light phenomenon occurs at the
surface of the paper?
A. Regular reflection
B. Diffuse reflection
c. Polarization
D. Resonance


In which of the following process, human excreta is completely converted to vermi cakes?
A. Vermicomposting
B. Vermi-processing toilets
c. Biogas production
D. None of the above


The phase difference between light waves from two slits in Young's double
slit experiment is \( \pi . \) Will the central fringe be bright or dark?


The IUPAC name of the given compound
is:
A. 4 - pentanone
B. pentanone -
c. Pentan-2-one
D. none of the above


A dielectric slab of thickness dis
inserted in a parallel plate capacitor
where negative plate is at \( x=0 \) and
positive plate is at \( x=3 d . \) The slab is
equidistant from the plates. The capacitor is given some charge. As \( x \)
goes from 0 to \( 3 d \)
This question has multiple correct options
A. The magnitude of electric field remains the same
B. The direction of electric field remain the same
c. The electric potential increases continuously.
D. The electric potential increase at first then decrease and again increase.


Combination of haemoglobin with \( C O_{2} \)
in lungs can be promoted by
A . Increasing \( C O_{2} \) concentration in blood
B. Increasing \( O_{2} \) concentration in blood
C. Decreasing \( O_{2} \) concentration in blood
D. None of the above


List-I
A) Polystyrene
\( \mathbf{p}) \boldsymbol{C}_{6} \boldsymbol{H}_{\mathbf{5}}- \)
\( \boldsymbol{C H}=\boldsymbol{C H}_{2} \)
B) Buna-S
q) \( C H_{2}=C H- \)
\( \boldsymbol{C H}=\boldsymbol{C H}_{2} \)
C) Buna - N
r) \( C H_{2} O H- \)
\( C H_{2} O H \)
D) Terylene
s) Condensation polymer This question has multiple correct options
A \( \cdot a-p \)
B. b-p.q
\( c \cdot c- \)
D. d-r.s


An electron is projected with velocity \( \mathbf{v}_{\mathbf{0}} \) in a uniform electric field \( \mathbf{E} \)
perpendicular to the field. Again it is projected with velocity vo perpendicular
to a uniform magnetic field B. If \( r_{1} \) is initial radius of curvature just after
entering in the electric field and \( \mathbf{r}_{2} \) is
initial radius of curvature just after entering in magnetic field then the ratio
\( \mathbf{r}_{1} / \mathbf{r}_{2} \) is equal to :
A \( \cdot \frac{\mathrm{Bv}_{0}^{2}}{\mathrm{E}} \)
в. \( \frac{\mathrm{B}}{\mathrm{E}} \)
c. \( \frac{\mathrm{Ev}_{0}}{\mathrm{B}} \)
D. \( \frac{\mathrm{Bv}_{0}}{\mathrm{E}} \)


In the definition of electric potential, the electric potential at infinity is assumed to be
A . infinity
B. zero
c. 1
D. None of these


In LCR series circuit, an alternating
e.m.f. 'e' and current 'i' are given by the equations \( e=100 \sin (100 t) \) volt, \( i= \)
\( \mathbf{1 0 0} \sin \left(\mathbf{1 0 0}+\frac{\boldsymbol{\pi}}{\mathbf{3}}\right) \mathrm{m} \mathrm{A} . \) The average
power dissipated in the circuit will be
\( \mathbf{A} \cdot 100 \mathrm{w} \)
B. 10w
\( c .5 w \)
D. 2.5w


On a scale of map, \( 0.6 \mathrm{cm} \) represents 6.6km. If the distance between the
points on the map is \( 80.5 \mathrm{cm}, \) the actualdistance between these points is
\( \mathbf{A} \cdot 9 \mathrm{km} \)
в. \( 72.5 \mathrm{km} \)
c. \( 190.75 \mathrm{km} \)
D. \( 885.5 \mathrm{km} \)


The ratio of volumes of \( C H_{3} C O O H \)
\( (0.1 N) \) to \( C H_{3} C O O N a(0.1 N) \)
required to prepare a buffer solution of \( p H 5.74 \) is:
(Given \( \left.p K_{a} \text { of } C H_{3} C O O H \text { is } 4.74\right) \)
A . 10: 1
B. 5: 1
\( c \cdot 1: 5 \)
D. 1: 10


The value of \( g \) at a height \( h \) above the surface of the earth is the same as at a
depth \( d \) below the surface of the earth.
When both \( d \) and \( h \) are much smaller
than the radius of earth, then which one
of the following is correct
A \( \cdot d=\frac{h}{2} \)
B. \( d=\frac{3 h}{2} \)
\( c \ldots d=2 h \)
\( \mathbf{D} \cdot d=h \)


Factorise: \( 27 a^{3}+\frac{1}{64 b^{3}}+\frac{27 a^{2}}{4 b}+\frac{9 a}{16 b^{2}} \)


Resistance of a metal wire of length 1 m is \( 104 \Omega \) at \( 20 C . \) If the diameter of the
wire is 0.15 mm, find the resistivity of
the metal at that temperature.


\( A 2 \mathrm{kg} \) disc of radius \( 0.5 \mathrm{m} \) accelerates from rest to 25 rad/s in 5 seconds. The
average power exerted on the disc is
A. 78.1 watts
B. 15.6 Watts
c. 28.1 watts
D. 40.6 watts


With increasing quantum number, the energy difference between adjacent energy levels in atoms
A . decreases
B. increases
c. remains constant
D. decreases for low \( Z \) and increases for high \( Z \)


A solution is defined as a:
A. homogeneous mixture of two or more substances
B. hetrogeneous mixture of two or more substances
C. homogeneous mixture of liquid and solid components only
D. homogeneous mixture consisting of water as one of the components


A hemispherical bowl is made of steel, \( 0.25 \mathrm{cm} \) thick. The inner radius of the
bowl is \( 5 \mathrm{cm} \). Find the outer curved
surface area of the bowl


If ' \( N^{\prime} \) is the number of turns in a
circular coil then the value of self
inductance varies as.
A . \( N^{0} \)
в. \( N \)
\( c \cdot N^{2} \)
D. \( N^{-2} \)


Assertion
If the current of a lamp increases by \( 20 \% \), the percentage increase in the illumination of the lamp is \( 40 \% \)
Reason
Illumination of the lamp is directly proportional to the square of the current through the lamp.
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


An LCR series circuit is
under resonance. If \( I_{m} \), is current
amplitude, \( V_{m} \) is voltage amplitude, \( R \) is the resistance, \( Z \) is the impedance,
\( X_{L} \) is the inductive reactance and \( X_{C} \)
is the capacitive reactance, then
\( ^{\mathrm{A}} \cdot_{I_{m}}=\frac{Z}{V_{m}} \)
в. \( _{I_{m}}=\frac{V_{m}}{X_{L}} \)
\( \mathbf{c} \cdot_{I_{m}}=\frac{V_{m}}{X_{C}} \)
D. \( _{I_{m}}=\frac{V_{m}}{R} \)


The isotopes of hydrogen are :
A. Tritium and protium only
B. Deuterium and tritium only
C. Protium and deuterum only
D. Protium, deuterium and trititum