When no current is passed through a
conductor
This question has multiple correct options
A. the free electrons do not move
B. the average speed of a free electron over a large period of time is zero
C. the average velocity of a free electron over a large period of time is zero
D. the average of the velocities of all the free electrons at an instant is zero


Assertion
Magnetic force between two short
magnets, when they are co-axial follows
inverse square law of distance.
Reason
The magnetic forces between two poles
do not follow inverse square law of
distance.
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.


Evaluate: \( \left(7 a^{2}-5 a\right) \div 5 a \)
A \( .7 a-1 \)
B. \( 7 a-5 \)
c. \( \frac{1}{5}(7 a-5) \)
D. \( \frac{1}{5}(7 a-1) \)


Evaluate
\( \int \frac{x+1}{x^{2}+3 x+12} d x \)


\( (-24)+(-28)= \)
A . -52
B. +52
c. 0
D. None


Aluminothermy used for the spot
welding of large iron structures is
based upon the fact that:
This question has multiple correct options
A. As compared to iron, aluminium has greater affinity for oxygen.
B. As compared to aluminium, iron has greater affinity for oxygen.
C. Reaction between aluminium and oxygen is endothermic.
D. Reaction between iron oxide and aluminium is
exothermic.


When \( H_{2} O \) is shaken with an acidified
solution of \( K_{2} C r_{2} O_{7} \) in the presence of ether, the ethereal layer turns blue due to the formation of :
A. \( C r_{2} O_{3} \)
B. \( C r O_{5} \)
\( \mathrm{c} \cdot \mathrm{Cr} \mathrm{O}_{4}^{-} \)
D. none of these


Two light rays \( P \) and \( Q \) are incident an
optical device \( ^{\prime} X^{\prime} \) which finally goes
along \( ^{\prime} \boldsymbol{R}^{\prime} \) and \( ^{\prime} \boldsymbol{S}^{\prime} . \) Identify optical device
\( \boldsymbol{X}^{\prime} \)
A. Concave lens
B. Concave mirror
c. Convex lens
D. Convex mirror


Find the tenth term of G.P :
\( \mathbf{5}, \mathbf{2 5}, \mathbf{1 2 5}, \dots \dots \)


The element with the electronic
configuration \( [\boldsymbol{X} \boldsymbol{e}] \boldsymbol{4} \boldsymbol{f}^{14} \boldsymbol{5} \boldsymbol{d}^{1} \boldsymbol{6} \boldsymbol{s}^{2} \) is a
A. representative element
B. transition element
c. actinide element
D. Lanthanides element


If \( \boldsymbol{A}=\left\{\boldsymbol{x} \epsilon \boldsymbol{R} / \frac{\pi}{4} \leq \boldsymbol{x} \leq \frac{\pi}{3}\right\} \quad \) and
\( \boldsymbol{f}(\boldsymbol{x})=\sin \boldsymbol{x}-\boldsymbol{x} \quad, \) then \( \boldsymbol{f}(\boldsymbol{A})= \)
A \( \cdot\left[\frac{\sqrt{3}}{2}-\frac{\pi}{3}, \frac{1}{\sqrt{2}}-\frac{\pi}{4}\right] \)
B. \( \left[-\frac{1}{\sqrt{2}}-\frac{\pi}{4}, \frac{\sqrt{3}}{2}-\frac{\pi}{3}\right] \)
\( \mathbf{c} \cdot\left[-\frac{\pi}{3}, \frac{-\pi}{4}\right] \)
D. \( \left[\begin{array}{c}\pi \\ \hline 4\end{array}, \frac{\pi}{3}\right. \)


A vector equation of the line of
intersection of the planes \( \boldsymbol{r}=\boldsymbol{b}+ \)
\( \boldsymbol{\lambda}_{1}(\boldsymbol{b}-\boldsymbol{a})+\boldsymbol{\mu}_{1}(\boldsymbol{a}+\boldsymbol{c}) \)
\( \boldsymbol{r}=\boldsymbol{c}+\boldsymbol{\lambda}_{2}(\boldsymbol{b}-\boldsymbol{c})+\boldsymbol{\mu}_{1}(\boldsymbol{a}+\boldsymbol{b}) \boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c} \)
being non-coplanar vectors is.
A \( \cdot r=a+\mu_{1}(b+c) \)
B . \( r=b+\mu_{1}(a+2 c) \)
C . \( r=a+\mu_{1}(b+2 c) \)
D. \( r=b+\mu_{1}(a+c) \)


Reduce the equation \( 2 x-3 y+5=0 \)
to intercept form.Hence find the length of the segment intercepted between the
axes.


When a diode is heavily doped the
A. Zener voltage will be low
B. Avalanche voltage will be high
C. Depletion region will be thin
D. Leakage current will be low


Write the structure and IUPAC names of
the following compounds.
(i) Isobutyl amine.
(ii) Ethyl methyl amine.


In the half wave rectifier circuit
operating from 50 \( \boldsymbol{H} \boldsymbol{z} \) mains frequency, the fundamental frequency in the ripple would be
\( \mathbf{A} \cdot 2.5 H z \)
B. \( 50 \mathrm{Hz} \)
c. \( 70.7 H z \)
D. \( 100 H z \)


There is an infinite straight chain
of alternating charges \( q \) and \( -q \)
The distance between the two
neighbouring charges is equal to a. Find the interaction energy of any charge with all the other charges.
A \( \cdot \frac{2 q^{2}}{4 \pi \varepsilon_{0} a} \)
B \( \cdot \frac{2 q^{2} \log _{e} 2}{4 \pi \varepsilon_{0} a} \)
\( ^{\mathbf{C}}-\frac{2 q^{2} \log _{e} 2}{4 \pi \varepsilon_{0} a} \)
D. none of these


What is the role of cholesterol in the cell
membrane?
A. It functions in joining adjacent cells together.
B. It functions in recognizing foreign cells.
c. It increases the rate of transport of ions across the membrane
D. It stabilizes the cell membrane.


are the green stems of limited growth which have taken over the function of photosynthesis fro leaves.
A. phylloclades
B. cladodes
c. phyllodes
D. Stem thorns


Sucrose on hydrolysis gives:
A. glucose and maltose
B. glucose and lactose
c. glucose and fructose
D. only glucose


Why should adolescent pregnancy be avoided?


If the ionization energy for the hydrogen atom is \( 13 e V \), the energy required to excite it from the ground state to the next higher state is nearly
A . \( 3.4 e V \)
B. \( 10.2 e V \)
c. \( 12.1 e V \)
D. \( 1.5 e V \)


Select the correct statement(s).
This question has multiple correct options
\( \mathbf{A} \cdot \) When \( T \longrightarrow \infty \) or \( E_{a} \longrightarrow 0, \) then \( k=A \)
B. A positive catalyst can change \( \Delta H \) of the reaction.
C. A mixture of reactants may be thermodynamically unstable but kinetically stable
D. A negative catalyst increases the activation energy of the reaction.


The velocity of the wind over the surface
of the wing of an aeroplane is 80 and
under the wing 60 if the area of the wing is 4 the dynamic lift experienced by the wing is density of air.


Write the IUPAC names of following ketone or aldehyde. If possible, give common name(s) also.
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}(\boldsymbol{B r}) \boldsymbol{C H}_{2} \boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right) \boldsymbol{C H} \)


Which of the following is an example of a closed system?
A . a cup of tea
B. an air-tight container
c. a jug of water
D. all of the above


What is the Brewster angle for air to glass transition? (Refractive index of
glass is 1.5 ).


\( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}| \) in [-1,1] verify Rolle's
theorem.


A square paper is kept on cartesian plane coinciding the points \( (2,0),(4,0),(0,2) . \) Find the perimeter of the paper.
A. 8 Units
B. 12 Units
c. 16 Units
D. None of these


Pyrenoid consists of
A. Starch around protein
B. Protein around starch
c. Protein only
D. Starch only


In the figure, if \( \boldsymbol{O A}=\mathbf{1 7 c m}, \boldsymbol{A B}= \)
\( 30 \mathrm{cm} \) and \( 0 \mathrm{D} \) is perpendicular to \( \mathrm{AB} \)
then \( \mathrm{CD} \) is equal to:
\( A \cdot 8 c m \)
в. \( 9 \mathrm{cm} \)
\( c \cdot 10 c m \)
D. \( 11 \mathrm{cm} \)


Foetal sex is determined by examining
cells from amniotic fluid looking for
A. Chiasmata
B. Barr bodies and sex chromosomes
c. only Barr bodies
D. Drumsticks


How will you prepare chlorobenzene from benzene diazonium chloride?


18 g of glucose, \( C_{6} H_{12} O_{6}, \) is dissolved in \( 1 \mathrm{kg} \) of water in a saucepan. At what temperature will the water boil (1.013
bar pressure)? \( K_{b} \) for water is \( 0.52 \mathrm{K} \mathrm{kg} \)
\( m o l^{-1} \)


The atomic masses of He and Ne are 4
and 20 a.m.u. respectively. The value of the de Broglie wavelength of He gas at
\( -73^{\circ} \mathrm{C} \) is \( \mathrm{M} \) times that of the de Broglie
wavelength of Ne at \( 727^{\circ} \mathrm{C} . \) M is:


The number of nodal planes in \( p_{x} \) orbital is ?
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
D.


A spherical balloon is filled with \( 4500 \pi \)
cubic meters of helium gas. If a leak in
the balloon causes the gas to escape at the rate of \( 72 \pi \) cubic meters per
minute, then the rate (in meters per minute) at which the radius of the
balloon decreases 49 minutes after the
leakage began is:
A \( \cdot 6 / 7 \)
B. \( 4 / 9 \)
c. \( 2 / 9 \)
D. None of these


The tracheae of cockroach are .......... type
A. Holopneustic
B. Hemipneusticç
c. Apneustic
D. Perineustic


If \( P \) is a two-rowed matrix satisfying
\( P^{T}=P^{-1}, \) then \( P \) can be
\( \mathbf{A} \cdot\left[\begin{array}{cc}\cos \theta & -\sin \theta \\ -\sin \theta & \cos \theta\end{array}\right] \)
B. \( \left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right] \)
\( \mathbf{c} \cdot\left[\begin{array}{cc}-\cos \theta & \sin \theta \\ \sin \theta & -\cos \theta\end{array}\right] \)
D. none of these


"Action at a distance" is revealed most
prominently in:
A. Magnetic force
B. Electric force
c. Gravitational force
D. All of them


Two solid discs of radii \( r \) and \( 2 r \) roll
from the top of an inclined plane without slipping. Then
A. The bigger disc will reach the horizontal level first
B. The smaller disc will reach the horizontal level first
c. The time difference of reaching of the discs at the horizontal level will depend on the inclination of the plane
D. Both the discs will reach at the same time


Find the value of \( (-12) \times(+21) \)
A \( .-2412 \)
B . -242
\( \mathbf{c} .-252 \)
D. +252


In \( 1932, \) which medicine was prepared
by Paul Ehrlich?
A. Sulpha drug
B. Prontosil
c. azodye
D. none of these


\( 500 g \) of hot water at \( 60^{\circ} C \) is kept in the
open till its temperature falls to \( 40^{\circ} \mathrm{C} \) Calculate the heat energy lost to the surroundings by the water. ( specific heat of water \( =4200 \mathrm{J} \mathrm{kg}^{-1^{\circ}} \mathrm{C}^{-1} \)
A . \( 2400 J \)
B. \( 5000 J \)
c. \( 40000 J \)
D. \( 42000 J \)


Let \( f(x) \) be a continous and differentiable function on \( [0,1], \) such
that \( f(0) \neq 0 \) and \( f(1)=0 . \) We can
conclude that there exists \( c \in(0,1) \)
such that
A \( \cdot c . f^{\prime}(c)-f(c)=0 \)
B. \( f^{\prime}(c)+c . f(c)=0 \)
c. \( f^{\prime}(c)-c . f(c)=0 \)
D. \( c . f^{\prime}(c)+f(c)=0 \)


Choose the correct statement(s).
A. Fermentation is the process of conversion of pyruvate into ethanol and \( C O_{2} \) under aerobic conditions.
B. Pyruvate breakdown into \( C O_{2} \), water and energy occurs in the mitochondria during anaerobic respiration.
C. Glycolysis is the breakdown of glucose into pyruvate by means of ten step reactions in the cytoplasm.
D. The common respiratory substrate is glycogen.


the two balls will collide at time \( t= \)
\( A \cdot 2 s \)
В. 5 s
\( c .10 s \)
\( 0.3 s \)


Identify the IUPAC name of the above compound. \( \boldsymbol{H}_{3} \boldsymbol{C}-\underset{\mathbf{2} \mid}{\boldsymbol{C}} \boldsymbol{H}-\boldsymbol{C l} \)


The focus of the parabola \( \boldsymbol{y}^{2}-\boldsymbol{x}- \)
\( 2 y+2=0 \) is
\( ^{\mathrm{A}} \cdot\left(\frac{1}{4}, 0\right) \)
в. (1,2)
c. \( \left(\frac{5}{4}, 1\right) \)
D. \( \left(\frac{3}{4}, \frac{5}{2}\right) \)


Prove that
\( \boldsymbol{L}=\lim _{\boldsymbol{n} \rightarrow \infty}\left(1+\frac{4}{n}\right)^{3 n}=\mathbf{1 2} \)


When 5 V potential difference is applied across a wire of length \( 0.1 \mathrm{m} \), the drift speed of electrons is \( 2.5 \times 10^{-4} \)
\( \mathrm{m} / \mathrm{s} . \) If the electron density in the wire is \( 8 \times 10^{28} m^{-3}, \) calculate the resistivity of
the material of the wire.


polycyclic aromatic hydrocarbon enters
water through:
A. discharges from industries
B. discharges from waste water treatment plant
C. municipal solid waste treatment plant
D. all of these


A trader purchases \( 70 \mathrm{kg} \) of tea at Rs 15 per kg and 30 kg of tea at Rs. 18.50 per kg. If the packing charges are 2 percent, then at what price he must sell the mixture of two to gain \( 15 \% ? \)
A. Rs. 18.80 per kg
B. Rs. 18 per kg
c. Rs. 18.50 per \( \mathrm{kg} \)
D. Rs. 17.80 per kg


Solid \( N a C l \) is a bad conductor of
electricity because:
A. Solid \( N a C l \) is covalent
B. In solid state there are no ions
C. In solid \( N a C l \), there is no migration of ions
D. In solid \( N a C l \), there are no electrons.


Which of the following is the most basic
\( A l_{2} O, T l_{2} O_{3}, T l_{2} O \)


In mammals, the digestion of starch
starts from
A. Mouth
B. Stomach
c. oesophagus
D. Duodenum


Which one of following statements is not correct in respect of lyophilic sols?
A. There is a considerable interaction between the dispersed phase and dispersion medium.
B. These are quite stable and are not easily coagulated.
c. They carry charge
D. The particles are hydrated.


\( \mathbf{A} \)
unit does not change
with respect to space and time.
A. derived
B. standard
c. regular
D. Iarge


State which has a higher resistance. A
\( 50 \mathrm{W} \) or \( 25 \mathrm{W} \) lamp. Also find the ratio of
their resistances.


A small mass attached to a string rotates on a frictionless table top as
shown. If the tension in the string is increased by pulling the string causing the radius of the circular motion
to decrease by a factor of \( 2, \) the kinetic energy of the mass will
A. decrease by a factor of 2
B. remain constant
c. increase by a factor of 2
D. increase by a factor of 4


The resultant capacity between the terminals \( P \) and \( Q \) of the given figure is :
A \( .37 \mu F \)
в. \( \frac{15}{7} \mu F \)
\( c .3 \mu F \)
D. \( \frac{30}{9} \mu F \)


Bile secreted by liver is normally stored in the
A . Gallbladder
B. Stomach
c. Small intestine
D. Large intestine


Consider the four statements below
concerning limiting reactants in chemical systems. Identify the one that correctly describes the role of the limiting reactant.
A. The limiting reactant is the one with the greatest coefficient in the balanced equation
B. The limiting reactant determines the overall order of reaction in the rate law
c. The limiting reactant is the one with the smallest coefficient in the balanced equation
D. The limiting reagent is the reactant that is completely used up in a reaction,


Which of the following is gem-dihalide:
\( A \)
в.
\( c \)
D.


\( \boldsymbol{Y} \stackrel{\boldsymbol{\Delta}, 205^{\circ} \boldsymbol{C}}{\boldsymbol{C}} \boldsymbol{C a S} \boldsymbol{O}_{4} \cdot \boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O} \stackrel{\boldsymbol{\Delta}, \mathbf{1 2 0}^{\circ} \boldsymbol{C}}{\longrightarrow} \boldsymbol{X} \)
\( X \) and \( Y \) are respectively
A. plaster of paris, dead burnt plaster
B. dead burnt plaster, plaster of paris
c. \( C a O \), plaster of paris
D. plaster of paris, mixture of gases


If mass of neutron is assumed to half of
its original value, whereas that of proton is assumed to be twice of its original value, then the atomic mass of \( _{6}^{14} C \) will be:
A. same
B. 14.28\% more
c. 14.28\%
D. 28.56\% less


How much heat is needed to melt the
block of ice?
A \( \cdot 1.26 \times 10^{4} \) 」
B . 4.2 \( \times 10^{5} \) j
c. \( 3.3 \times 10^{5} \) j
D. \( 6.6 \times 10^{5} \mathrm{J} \)
E . \( 9.9 \times 10^{5} \mathrm{J} \)


Give reason -
a) Muscular floor of chest cavity
b) Tiny pores on the surface of leaf.


When isobutane is chlorinated in the
presence of diffused sunlight, then the product formed is:
A. tertiary butyl chloride in major amount
B. isobutyl chloride in major amount
c. both \( 50 \% \) each
D. n-butyl chloride, isobutyl chloride and sec-buty chloride are formed


How many types of leaf venation are there?


A mixture of \( 2 \times 10^{21} \) molecular of \( P \)
and \( 3 \times 10^{21} \) molecular of \( Q \) weight
\( 0.60 g . \) If the molecular mass of \( P \) is 45
the molecular mass of \( Q \) will be \( \left(N_{A}=\right. \)
\( \left.6 \times 10^{23}\right) \)
A . 45
в. 180
c. 90
D. 270


In \( \Delta A B C, \angle B=30^{\circ}, \angle C=80^{\circ} \) and
\( \angle A=70^{\circ} \) then
A \( . A B>B C<A C \)
В. \( A B<B C>A C \)
c. \( A B>B C>A C \)
D. \( A B<B C<A C \)


Column \( \mathbf{A} \) \( - \) Column B
(A) Third trophic level
(p) Ozone
(B) Accumulation of pesticides at higher trophic
(q) CFCs level
(C) Green plants
(r) Herbivore
(D) Flow of energy in an ecosystem
of
(E) Consists of 3 atoms
(t) Decomposers oxygen
nof
(F) Main cause of depletion
(u) Producers ozone layer
(G) Second trophic level
(v) Unidirectional
(H) Break-down of dead
(w) Carnivores organic compounds If


An equimolar solution of \( N a N O_{2} \) and
\( H N O_{2} \) can act as a:
A. strong reductant
B. strong oxidant
c. buffer solution
D. none of these


Two points \( \mathbf{P} \) and \( \mathbf{Q} \) are maintained at
the potentials of \( 10 \mathrm{V} \) and \( -4 \mathrm{V} \) respectively. The work done in moving
100 electrons from \( \mathbf{P} \) to \( \mathbf{Q} \) is :
В \( \cdot 9.60 \times 10^{-17} \mathrm{J} \)
c. \( -2.24 \times 10^{-16} \mathrm{J} \)
D \( .2 .24 \times 10^{-16} \mathrm{J} \)


A conic surface is placed in a uniform electric field \( E \) as shown in Fig. such
that the field is perpendicular to the
surface on the side \( A B \). The base of the
cone is of radius \( R, \) and the height of the
cone is h. The angle of the cone is \( \theta \). Find
the magnitude of the flux that enters
the cone's curved surface from the left
side. Do not count the outgoing flux
\( \left(\theta<45^{\circ}\right) \)
A \( . E R[h \cos \theta+\pi(R / 2) \sin \theta \)
B. \( E R[h \sin \theta+\pi R / 2 \cos \theta] \)
c. \( E R[h \cos \theta+\pi R \sin \theta \)
D. none of these


Find intervals in which the function given by \( f(x)=\frac{3}{10} x^{4}-\frac{4}{5} x^{3}-3 x^{2}+ \)
\( \frac{36}{5} x+11 \) is
(a) strictly increasing
strictly decreasing.


Rolle's theorem cannot be applicable
for:
A \( \cdot f(x)=\cos x-1 \) in \( (0,2 \pi) \)
B - \( f(x)=x(x-2)^{2} \) in (0,2)
c. \( f(x)=3+(x-1)^{\frac{3}{5}} \) in (0,3)
D. \( f(x)=\sin ^{2} x \) in \( (0, \pi) \)


(a) Define prism angle and angle of deviation for a prism.
(b) Write the sequence of colours in the spectrum formed by the passage of white light through a prism.
(c) Explain the process of formation of rainbow.


A rod \( 0.5 \mathrm{m} \) long has two masses each
of 20 gram stuck at its ends. If the
masses are treated as point masses and if the mass of the rod is neglected, then the moment of inertia of the
system about a transverse axis passing
through the centre is
A \( \cdot 1.25 \times 10^{-3} \mathrm{kg}-\mathrm{m}^{2} \)
B . \( 2.5 \times 10^{-3} \mathrm{kg}-\mathrm{m}^{2} \)
C \( \cdot 4 \times 10^{-3} \mathrm{kg}-\mathrm{m}^{2} \)
D. \( 5 \times 10^{-3} \mathrm{kg}-\mathrm{m}^{2} \)


If
(i) \( A=\left[\begin{array}{cc}\cos \alpha & \sin \alpha \\ -\sin \alpha & \cos \alpha\end{array}\right], \) then verify
that \( \boldsymbol{A}^{\prime} \boldsymbol{A}=\boldsymbol{I} \)
(ii) \( A=\left[\begin{array}{cc}\sin \alpha & \cos \alpha \\ -\cos \alpha & \sin \alpha\end{array}\right], \) then verify
that \( \boldsymbol{A}^{\prime} \boldsymbol{A}=\boldsymbol{I} \)


A parallelogram whose all sides are
equal is called
A. Square
B. Rhombus
c. Rectangle
D. Trapezium


Assertion
In series \( L C R \) circuit if a ferromagnetic
rod is inserted inside an inductor,
current in the circuit may be increase
or decrease
Reason
By doing so \( X_{L} \) will increase.
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


\( I P_{1} \) and \( I P_{2} \) of Mg are 178 and \( 348 \mathrm{K} \)
cal \( m o l^{-1} . \) The enthalpy required for the reaction \( M g \rightarrow M g^{2+}+2 e^{-} \) is:
A \( . .+170 \) K.cal
B. +526 K.cal
c. -170 K.cal
D . -526 K.cal


8
directions and collide with each other
and with the wall of the container. It is
difficult to determine the speed of an
individual molecule but it has become
possible to work out the distribution of molecules among different molecular
speeds. This is known as Maxwell
Boltzmann distribution.

Consider the following graph about
Maxwell's distribution of speeds at two
different temperatures \( T_{1} \) and \( T_{2} \)
Relation between \( T_{1} \) and \( T_{2} \) is
A \( \cdot T_{1}=T_{2} \)
\( \mathbf{B} \cdot T_{1}>T_{2} \)
\( \mathbf{c} \cdot T_{1}<T_{2} \)
D. Cannot be predicted


The IUPAC name of \( \boldsymbol{X} \boldsymbol{e}\left[\boldsymbol{P} \boldsymbol{t} \boldsymbol{F}_{6}\right] \) is
A. hexafluoridoplatinate (VI) xenon
B. xenon hexafluoridoplationate (V)
c. xenon hexafluoridoplatinate (VI)
D. xenonium hexfluoridoplatinum (V)


If statement \( \boldsymbol{P}(\boldsymbol{n}) \) is \( " \boldsymbol{3} \boldsymbol{n}+1 \) is even"
Then verify that statement \( \boldsymbol{P}(\mathbf{1}) \) is true
but \( \boldsymbol{P}(2) \) is not true


The flagellate structures in acellular slime moulds are
A. Myxamoebae
B. Swarm cells
c. spores
D. Both B and C


Find the sum to n terms of the sequence
\( 8,88,888,8888 \dots \)


State True or False.
The ratio of gases liberated at cathode
and anode during electrolysis of \( \mathrm{CH}_{3} \) COONa(aq) is 1: 3
A. True
B. False


The 24 hour (diurnal) rhythm of our body such as the sleep-wake cycle is regulated by the hormone
A. Calcitonin
B. Prolactin
c. Adrenaline
D. Melatonin


Of the total incident solar radiation the
proportion of PAR is
A. More than \( 80 \% \)
B. About 70\%
c. About 60 \%
D. Less than 50 \%


Sketch the graph for \( y=\cos ^{-1}(\cos x) \)


In general, the relation between limiting
friction
rolling friction.


Evaluate \( \int \frac{\left(1+2 x^{2}\right) d x}{x^{2}\left(1+x^{2}\right)} \)


\( \left|\begin{array}{ccc}\mathbf{1} & \boldsymbol{w} & \boldsymbol{w}^{2} \\ \boldsymbol{w} & \boldsymbol{w}^{2} & \mathbf{1} \\ \boldsymbol{w}^{2} & \boldsymbol{w} & \mathbf{1}\end{array}\right| \) Where \( \mathbf{w} \) is a complex
cube root of unity


The instability of a nucleus is due is
due to:
A. high proton electron ratio
B. high electron neutron ratio
c. low proton electron ratio
D. low protons neutron ratio


Which of the following gases cannot be kept in a glass bottle because it chemically reacts with glass?
A. Sulphur
B. Chlorine
C. Fluorine
D. Methane


When a charge of amount \( Q \) is given to an isolated metal plate \( X \) of surface area \( A, \) its surface charge density
becomes \( \sigma_{1} . \) When an isolated identical
plate \( Y \) is brought close to \( X, \) the surface charge density on X becomes
\( \sigma_{2} . \) When \( y \) is earthed, the surface
charge density becomes \( \sigma_{3} \)
This question has multiple correct options
A \( \cdot \sigma_{1}=\frac{Q}{A} \)
В. \( \sigma_{1}=\frac{Q}{2 A} \)
\( \mathbf{C} \cdot \sigma_{1}=\sigma_{2} \)
D. \( _{\sigma_{3}}=\frac{Q}{A} \)


For complete combustion of ethanol
\( \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O} \boldsymbol{H}(\boldsymbol{l})+\boldsymbol{3} \boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \)
\( \mathbf{2} \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{3} \boldsymbol{H}_{2} \boldsymbol{O}(l) \)
the amount of heat produced as measured in bomb calorimeter, is
\( 1364.47 k J \quad m o l^{-1} \) at \( 25^{\circ} C \)
Assuming ideality the enthalpy of
combustion, \( \Delta_{c} H \) for the reaction will
be:
\( \left(\boldsymbol{R}=\mathbf{8 . 3 1 4 k J} \quad \boldsymbol{m o l}^{-1}\right) \)
\( \begin{array}{ll}\text { A. }-1366.95 k J & \text { mol }^{-1}\end{array} \)
B. \( -1361.95 k J \) mol\( ^{-1} \)
\( \begin{array}{ll}\text { c. }-1460.95 k J & \text { mol }^{-1}\end{array} \)
D. \( -1350.50 k J \) mol \( ^{-1} \)


The angular momentum of electron in
\( n^{t h} \) orbit is given by
\( A \cdot n h \)
в. \( \frac{h}{2 \pi n} \)
c. \( n \frac{h}{2 \pi} \)
D. \( n^{2} \frac{h}{2 \pi} \)


A ship is steaming towards east with speed of \( 8 m / s . A \) women runs across
the deck at a speed of \( 6 m s^{-1} \) towards
north. What is the velocity of the women relative to the sea?


Rafiq exercised for \( \frac{3}{6} \) of an hour, while Rohit exercised for \( \frac{3}{4} \) of an hour.Who exercised for a longer time?


An element undergoes reaction as shown:
\( X+2 e-, \) energy released \( = \)
\( 30.87 e V / \) atom. If the energy released,
is used to dissociate 4 g of \( \boldsymbol{H}_{2} \)
molecules, equally into \( \boldsymbol{H}^{+} \) and \( \boldsymbol{H}^{*} \)
where \( \boldsymbol{H}^{*} \) is excited state of \( \mathrm{H} \) atoms,
where the electrons travels in in orbit
whose circumference equal to four times it's de Broglie's wavelength.
Determine the least moles of \( X \) that
would be required:

Given: I.E. of \( \mathrm{H}=13.6 \mathrm{eV} / \) atom, bond
energy of \( \boldsymbol{H}_{2}=\mathbf{4 . 5 2 6 e V} / \) molecule
A . 1
B. 2
\( c .3 \)
D. 4


The two triangles below are similar
\( \Delta A B C \sim \Delta E F D \)
What is the value of \( \angle B ? \)
A . \( 80^{\circ} \)
B. 30
\( c \cdot 70^{\circ} \)
D. 60


The force of attraction between two
masses each of \( 1 k g \) kept at a
separation of \( 1 m \) is:
\( \mathbf{A} \cdot 9.8 N \)
B. \( 6.7 N \)
c. \( 980 N \)
D. \( 6.7 \times 10^{-11} N \)


For a \( 1^{s t} \) order reaction (gaseous)
(costant \( \vee, T) \)
\( \boldsymbol{a} \boldsymbol{A} \rightarrow(\boldsymbol{b}-\mathbf{1}) \boldsymbol{B}+\mathbf{1} \boldsymbol{C}(\text { with } \mathbf{b}>\mathbf{a}) \) the
pressure of the system rose by
\( 50\left(\frac{b}{a}-1\right) \% \) in a time of 10 min. The half
life of the reaction is therefore:
\( A \cdot 10 \) min
B. 20 min
\( c . \) 30 min
D. 40 min


In the extraction of iron from haematite,
the charge used is haematite, coke and lime stone in the following weight ratio.
A. 1: 1: 1
B. 8: 4: 1
\( c \cdot 8: 1: 4 \)
D. 1: 4: 8


Which one of the following reactions is not a redox reaction?
A \( \cdot I_{2}+2 F e^{2+} \rightarrow 2 I^{-}+2 F e^{3+} \)
в. \( H C l+N a O H \rightarrow N a C l+H_{2} O \)
c. \( 2 M g+O_{2} \rightarrow 2 M g O \)
D. \( Z n+C u^{2+} \rightarrow Z n^{2+}+C u \)


A uniform pressure p is exerted on all
sides of a solid cube at temperature
\( t^{0} C . \) By what amount should the
temperature of the cube be raised in
order to bring its volume back to the value it had before the pressure was applied? The coefficient of volume expansion of the cube y and the bulk modulus is B.
\( \mathbf{A} \cdot \frac{p}{\sqrt{2 y} B} \)
B. \( \frac{p}{2 y B} \)
c. \( \frac{2 p}{y B} \)
D. \( \frac{p}{y B} \)


What are conjugate foci? Deduce the following relationship between the focal length \( f, \) of a spherical mirror, distance
of object of \( u \) and distance of image \( v \) \( \frac{1}{u}+\frac{1}{v}=\frac{1}{f} \)


Short / Long Answer Types:
What is the significance of Krebs cycle in the economy of the cell?


If the parabola \( y^{2}=4 a x \) passes
through (3,2) then the length of latus
rectum is
A \( \cdot \frac{1}{3} \)
B. \( \frac{2}{3} \)
c. 1
D.


The value of \( 3 \tan ^{-1} \frac{1}{2}+2 \tan ^{-1} \frac{1}{5}+ \)
\( \sin ^{-1} \frac{142}{65 \sqrt{5}} \) is
A \( \cdot \frac{\pi}{4} \)
B. \( \frac{\pi}{2} \)
c. \( \pi \)
D. none of these


Speed of a chemical reaction increases with \( _{-}--_{-}-_{-}-_{-}-_{-} \) in temperature
A. decreases
B. increases
c. no change
D. can't say


Integrate the function \( \frac{x+2}{\sqrt{4 x-x^{2}}} \)


Which of the following is a polyamide?
A. Nylon-6, 6
B. Terylene
c. Polythene
D. Buna-s


On heating, sodium and sulphur can be melted. Molten sodium and molten
sulphur are used?
A. For refining lead
B. As a medium for extracting metals
c. As catalysts
D. As electrodes in a modern kind of battery


Oxygen molecule is paramagnetic
because:
A. no. of bonding electrons \( > \) no. of antibonding electrons
B. no. of bonding electrons \( < \) no. of antibonding electrons
C. no. of bonding electrons = no. of antibonding electrons
D. presence of unpaired electrons in molecular orbitals.


For \( \boldsymbol{f}(\boldsymbol{x})=\sin ^{2} \boldsymbol{x}, \boldsymbol{x} \in(\mathbf{0}, \boldsymbol{\pi}) \) point of
inflection is
A \( \cdot \frac{\pi}{6} \)
в. \( \frac{2 \pi}{4} \)
\( c \cdot \frac{3 \pi}{4} \)
D. \( \frac{4 \pi}{3} \)


If \( t_{1}, t_{2} \) and \( t_{3} \) distinct. and the points
\( \left(t_{1} \cdot 2 a t_{1}+a t_{1}^{3}\right) \cdot\left(t_{2} \cdot 2 a t_{2}+a t_{2}^{3}\right),\left(t_{3} \cdot 2 a\right. \)
are collinear, then \( t_{1}+t_{2}+t_{3}= \)
A \( \cdot t_{1} t_{2} t_{3}=-1 \)
B \( \cdot t_{1}+t_{2}+t_{3}=t_{1} t_{2} t \)
\( \mathbf{c} \cdot t_{1}+t_{2}+t_{3}=0 \)
D. \( t_{1}+t_{2}+t_{3}=-1 \)


The number of covalent bonds in
ethylene is :
A. 2 double bonds, 2 single bonds
B. 2 double and 4 single bonds
c. 2 single and 2 double bonds
D. 1 double and 4 single bonds


What correctly defines mycorrhiza?
A. Plants that have no vascular tissue.
B. Nitrogen fixing bacteria that live in nodules on the roots of legumes.
C. Primitive plants like mosses, which show a dominant gametophyte stage.
D. Vascular bundles in the stems of tracheophytes.
E. Symbiotic structures living in the roots of plants that increase uptake of nutrients from the soil.


Use Euclid's 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 \( m \), but not of the form
\( 3 m+2 \)


The domestic sewage in large cities
A. Has a high BOD as it contains both aerobic and bacteria
B. Is processed by aerobic and then anaerobic bacteria in the secondary treatment in Sewage Treatment Plants (STPs)
C. When treated in STPs does not really require the aeration step as the sewage contains adequate oxygen
D. Has very high amounts of suspended solids and dissolved salts


During charging of lead accumulator?
A. concentration of \( H_{2} S O_{4} \) decreases
B. specific gravity of \( H_{2} S O_{4} \) increases
\( \mathrm{C} \cdot P b \mathrm{O}_{2} \) dissolves in electrolyte
D. lead is deposited at positive terminal


Van't Hoff factor, (i), of a \( 0.5 \% \) (w/W)
aqueous solution of \( K C l \) which freezes
at \( -0.24^{\circ} \mathrm{C} \) is:
\( \left(K_{f} \text { of water }=1.86 \mathrm{K} \mathrm{kg} \text { mol}^{-1}\right. \)
molecular weight of \( K C l=74.5 \) )
A . 1.52
B. 2.32
c. 1.92
D. 1.32


Is permanganate, a suitable oxidizing agent for quantitative estimation of
\( F e^{2+} \) in presence of \( H C l ? \)


Emission of \( \beta \) -particles by an atom of an element results in the formation of
A. isobar
B. isomer
\( c . \) isotope
D. isotone


Very short answer type.
Enumerate the main functions of the
large intestine


In the truncus arteriosus of frog, synangium is separated from pylangium by which valve?
A. Spiral valve
B. Distal row of semilunar valves
c. Proximal row of semilunar valves
D. secondary septum


\( \ln 2- \) Chloro \( -3- \) methyl hexanoic
acid, the primary suffix is
A. \( 2- \) Chloro-
в. \( -3- \) Methyl
\( c . \) ane
D. oic acid


The graph is drawn between the applied force \( F \) and the strain \( (x) \) for a thin
uniform wire. The wire behaves as
a liquid in the part:
\( A \cdot a b \)
B. bc
\( c \cdot c d \)
D. oa


Which taxonomic aid gives comprehensive account of complete compiled information of a genus or family at a particular time?
A. Taxonomic key
B. Herbarium
c. мonograph
D. Flora


The rate constant for a given reaction is \( \boldsymbol{K}=\mathbf{3} \times \mathbf{1 0}^{-5} \boldsymbol{S}^{-1} \boldsymbol{a} \boldsymbol{t} \boldsymbol{m}^{-1} . \) Express it in
units of \( L m o l^{-1} s e c^{-1}(T=273.15 K) \)


What are the disadvantages of global warming?


Kamal and Monika appeared for an
interview for two vacancies. The
probability of Kamal's selection is \( \frac{1}{3} \) and that of Monika's selection is \( \frac{1}{5} . \) Find the probability that none of them will be
selected.


Which of the following is wrongly matched?
A. Barometer-Pressure
B. Lactometer-Milk
c. coulomb's law-charges
D. Humidity -Calorimeter


Bottles containing \( C_{6} H_{5} I \) and
\( C_{6} H_{5} C H_{2} I \) lost their original labels.
They are labelled \( A \) and \( B \) for testing. \( A \)
and B were separately taken in a test
tube and boiled with \( N a O H \) solution.
The end solution in each tube was made
acidic with dilute \( H N O_{3} \) and then
some \( A g N O_{3} \) solution was added.
Substance B gave a yellow precipitate. Which one of the following statements is true for this experiment?
A \( \cdot \) A was \( C_{6} H_{5} \)
B. A was \( C_{6} H_{5} C H_{2} I \)
c. в was \( C_{6} H_{5} I \)
D. Addition of \( H N O_{3} \) was unnecessary


\( 1 \frac{3}{-} \) is \( a_{-}-_{-}- \) fraction 4
A. proper
B. improper
c. mixed
D. none


unplece the given labıe about absorption of nutrients through small intestine by selecting the correct option.
Process Nutrients
Active transport and II Fructose and
II
Simple Diffusion

IV and \( v \)
A. \( I \) -Amino Acids
\[
I I-C a^{2+}
\]
\( I I I- \) Passive transport, \( I V- \) Glycerol \( V \) -Fatty Acids
B. I-Galactose,
\( I I- \) Amino Acids \( I I I- \) Passive transport \( I V-V \) itamin \( -C \)
\( V \) - water
c. \( I \) - Glucose, \( I I- \) Galactose
III-Facilitated diffusion,
\( I V- \) Glycerol \( V \) - water
D. \( I \) -Glucose,
\( I I- \) Short chain fatty acids,
III - Facilitated diffusion, \( I V- \) Water
\( V \) - Vitamin-B complex


The value of the expression \( \left(1+\cos \frac{\pi}{10}\right)\left(1+\cos \frac{3 \pi}{10}\right)\left(1+\cos \frac{7 \pi}{10}\right)(1 \)
is


Identify which of the following is the smallest discrete value of
electromagnetic energy?
A. photon
B. proton
c. electron
D. neutron
E. quark


\( \mathrm{BE}=\mathrm{DF} \)
f the above statement is true then
mention answer as 1 , else mention 0 if
false


Assertion
The equation \( \sin x=1, \) has infinite
number of solutions
Reason
The domain of \( f(x)=\sin x \) is \( (-\infty, \infty) \)
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


Water cannot be used as fire
extinguisher to put out
A. burning wood
B. burning oil
c. burning cloth
D. burning charcoal


Stored food in fungi is
A. Starch
B. Proteins
c. Glycogen
D. chitin


In neutral or faintly alkaline medium, thiosulphate is quantitatively oxidized
by \( K M n O_{4} \) to:
\( \mathbf{A} \cdot S O_{3}^{2-} \)
B. \( S O_{4}^{2-} \)
\( c \cdot s O_{2} \)
D. \( S O_{5}^{2-} \)


If the points \( (0,0),(3, \sqrt{3}),(p, q) \) form
an equilateral triangle and \( \boldsymbol{q}_{1}, \boldsymbol{q}_{2} \) are
the two values of \( \boldsymbol{q} \) then \( \boldsymbol{q}_{1}+\boldsymbol{q}_{2}=? \)
A \( \cdot 2 \sqrt{3} \)
B. \( \sqrt{3} \)
\( c \cdot-\sqrt{3} \)
D.


By his famous experiment, Otto von Guericke demonstrated the presence of
A. atmospheric pressure
B. force
c. magnetic force
D. friction


\( \sum_{0 \leq i \leq j \leq 10}^{10} C_{j}^{j} C_{i} \) is equal to
\( A \cdot 3^{10} \)
B. \( 3^{10}-1 \)
\( c \cdot 2^{10} \)
D. \( 2^{10}-1 \)


According to Ohms law
A. The current increases with the increase in voltage
B. The resistance increase with the increase in current
C. The resistance increase with the increase in Voltage
D. The resistance and current both increases with the increases in voltage


Which metal is refined by Van-Arkel method?
A . \( N i \)
в. \( A l \)
\( c \cdot s i \)
D. \( T i \)


The Gram negative bacteria detect and respond to chemical in their surrounding by
A. Lipopolysaccharide
B. Muramic acid
c. Porins
D. volutin granules
E. Mesosomes


Which of the following reactions is not
balanced?
\( \mathbf{A} \cdot 2 N a H C O_{3} \longrightarrow N a_{2} C O_{3}+H_{2} O+C O_{2} \)
B \( \cdot 2 C_{4} H_{10}+12 O_{2} \longrightarrow 8 C O_{2}+10 H_{2} O \)
\( \mathbf{c} \cdot 2 A l+6 H_{2} O \longrightarrow 2 A l(O H)_{3}+3 H_{2} \)
D. \( 4 N H_{3}+5 O_{2} \longrightarrow 4 N O+6 H_{2} O \)


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


Ball A strikes with velocity u elastically
with identical ball \( B \) at rest, inclined at an angle of with line joining the centers of two balls. What will be the speed of
ball B after the collision:
A . u
B. \( \frac{u \sqrt{3}}{2} \)
c. \( \frac{u}{2} \)
D. \( \frac{u}{\sqrt{2}} \)


From \( N a\left[A g(C N)_{2}\right] \) solution, silver can
be displaced by:
A. \( Z n \)
в. \( A l \)
\( c . C a \)
D. All of the above


Which of the following pair of atomic numbers represents s-block elements?
A .7,15
B. 6,12
\( \mathrm{c} .9,17 \)
D. 3,12


\( \operatorname{Let} a_{1}, a_{2}, \dots a_{3 n} \) be an arithmetic
progression with \( a_{1}=3 \) and \( a_{2}=7 . \) If
\( a_{1}+a_{2}+\ldots+a_{3 n}=1830 \) then what is
the smallest positive integer \( m \) such
that \( \boldsymbol{m}\left(\boldsymbol{a}_{1}+\boldsymbol{a}_{2}+\ldots+\boldsymbol{a}_{n}\right)>\mathbf{1 8 3 0} ? \)


The particles present in the nucleus of an atom are :
A. the proton and the electron
B. the electron and the neutron
c. the proton and the neutron
D. none of these


Assertion
Statement 1 If \( n \) is positive integer then \( \int_{0}^{n \pi}\left|\frac{\sin x}{x}\right| d x \geq \)
\( \frac{2}{\pi}\left(1+\frac{1}{2}+\frac{1}{3}+\ldots+\frac{1}{n}\right) \)
Reason
Statement \( 2 \frac{\sin x}{x} \geq \frac{2}{\pi} \) on \( (0, \pi / 2) \)
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


Let \( k \) be a positive real number and let
\[
\begin{array}{l}
\boldsymbol{A}=\left[\begin{array}{ccc}
2 \boldsymbol{k}-\mathbf{1} & \mathbf{2} \sqrt{\boldsymbol{k}} & \mathbf{2} \sqrt{\boldsymbol{k}} \\
\mathbf{2} \sqrt{\boldsymbol{k}} & \mathbf{1} & -\mathbf{2} \boldsymbol{k} \\
-\mathbf{2} \sqrt{\boldsymbol{k}} & \mathbf{2} \boldsymbol{k} & \mathbf{1}
\end{array}\right] \\
\boldsymbol{B}=\left[\begin{array}{ccc}
\mathbf{0} & \mathbf{2} \boldsymbol{k}-\mathbf{1} & \sqrt{\boldsymbol{k}} \\
\mathbf{1}-\mathbf{2} \boldsymbol{k} & \mathbf{0} & \mathbf{2} \sqrt{\boldsymbol{k}} \\
-\sqrt{\boldsymbol{k}} & -\mathbf{2} \sqrt{\boldsymbol{k}} & \mathbf{0}
\end{array}\right] \\
\text { If det }(\boldsymbol{A} \boldsymbol{d} \boldsymbol{j}(\boldsymbol{A}))+\operatorname{det}(\boldsymbol{A} \boldsymbol{d} \boldsymbol{j}(\boldsymbol{B}))=\mathbf{1 0}^{\boldsymbol{o}}
\end{array}
\]
then \( [k] \) is equal to
4
3.6
\( c \)
\( D \)


Choose the correct answer from the
alternatives given

A parallel plate capacitor with plate
area \( A \) and separation between the
plates \( d \) is charged by a constant current \( I . \) Consider a plane surface of area \( \frac{\boldsymbol{A}}{\mathbf{2}} \) parallel to the plate and drawn between the plates. The displacement current through the area is :
\( A \)
в. \( \frac{I}{2} \)
c. \( \frac{I}{4} \)
D. \( \frac{I}{8} \)


In the fusion process there are
A. isotopes of hydrogen
B. isotopes of helium
c. isotopes of carbon
D. isotopes


A vertical column of liquid \( h_{0} \) long at \( 0^{\circ} C \)
balances another column of same liquid
at \( t^{o} C . \) If \( r \) is the absolute expansion of
that liquid, height of second liquid column is :
\( \mathbf{A} \cdot h_{0}(1-r t) \)
в. \( \frac{h_{0}}{(1-r t)} \)
c. \( h_{0}(1+r t) \)
D. \( \frac{h_{0}}{1+r t} \)


Find the value of \( ^{\prime} a^{\prime} \) for which the
function \( f \) defined by
\( f(x)=\left\{\begin{array}{l}a \sin \frac{\pi}{2}(x+1), x \leq 0 \\ \frac{\tan x-\sin x}{x^{3}}, x>0\end{array}\right. \)
continuous at \( \boldsymbol{x}=\mathbf{0} \)


Mirror made by silvering the inner surface of the piece of a hollow sphere is:
A. convex mirror
B. concave mirror
\( c \cdot \) both
D. none


Assertion
A special line will be seen for \( 2 p_{x}-2 p_{y} \)
transition.
Reason
Energy is released in the form of wave of
light when the electron drops from \( 2 p_{x} \)
to \( -2 p_{y} \) orbital.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


What is the minimum coefficient of
friction for a solid sphere to roll without slipping on an incined plane of
inclination \( \boldsymbol{\theta} \) ?
A \( \cdot \frac{2}{7} \tan \theta \)
B \( \cdot \frac{1}{3} g \tan \theta \)
c. \( \frac{1}{2} \tan \theta \)
D. \( \frac{2}{5} \tan \theta \)


Two circular rings of identical radii
and resistance of \( 36 \Omega \) each are placed
in such a way that they cross
each others center \( C_{1} \) and \( C_{2} \) as shown
n Fig. Conducting joints are made at intersection points \( A \) and \( B \) of the rings.
An ideal cell of emf \( 20 V \) is connected
across \( A \) and \( B \). If the power delivered by
the cell is \( X \times 10^{2} W . \) Find out the
value of \( X ? \)


The sum of the present ages of the father and his son is 45 years. 5 years ago, the age of the father was 6 times
that of son. What is the present age of
the son?


The maximum tendency to form unipositive ion is for the element which has the following electronic configuration:
A \( \cdot 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{2} \)
B . \( 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{2}, 3 p^{1} \)
c. \( 1 s^{2}, 2 s^{2}, 2 p^{6} \)
D. \( 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{2}, 3 p^{3} \)


A rigid massless rod of length 3 l has two masses attached art each end as
shown in the figure. The rod is pivoted at point \( P \) on the horizontal position, its instantaneous angular acceleration will
be:
A \( \cdot \frac{g}{2 l} \)
в. \( \frac{7 g}{3 l} \)
c. \( \frac{g}{13 l} \)
D. \( \frac{g}{3 l} \)


Name an artificial sweetener which is
derivative of sucrose.
A. Saccharine
B. Sucrolose
c. Sucrobenzamide
D. Aspartame


what is the product on the IOIIOwIng
reaction?
\( A \)
\( B \)
\( c \)
\( D \)


State True or False.
Teflon, it is non-reactive, because of the strength of carbon-fluorine bonds.


A particle moving along \( x- \) axis whose position is given by \( \boldsymbol{x}=\mathbf{4}-\mathbf{9} \boldsymbol{t}+\frac{\boldsymbol{t}^{\mathbf{3}}}{\mathbf{3}} \)
then choose the correct statement(s)
for this motion-
This question has multiple correct options
A. Direction of motion is not changing at any of the instants
B. For \( 0<t<3 s \), the particle is slowing down
c. Direction of motion is changing at \( t=3 \)sec
D. For \( 0<t<3 s \) the particle is speeding up


Find the length of the straight line joining the pairs of points whose polar coordinates are \( \left(a, \frac{\pi}{2}\right) \) and \( \left(3 a, \frac{\pi}{6}\right) \)


For the given A.P. \( 10,15,20,25, \ldots . . ., \) find
the common difference ' \( d \)


The hydrogen, ion concentration of a
solution is 0.001 M. What is the \( p H \) of
the solution?


Two radioactive materials \( X_{1} \) and \( X_{2} \)
have decay constants \( 10 \lambda \) and \( \lambda \) respectively. If finally they have the same number of nuclei, then the ratio of
the number of nuclei of \( X_{1} \) to that of \( X_{2} \)
will be \( 1 / \) e after a time
A. \( \frac{1}{10 \lambda} \)
в. \( \frac{1}{11 \lambda} \)
c. \( \frac{11}{10 \lambda} \)
D. \( \frac{1}{9 \lambda} \)


Lead is extracted from its chief ore
galena by both carbon reduction as well
as self-reduction.
A. True
B. False


Two bodies of mass \( 4 \mathrm{kg} \) and \( 5 \mathrm{kg} \) are moving along east and north directions with velocities \( 5 m / s \) and \( 3 m / s \) respectively. Magnitude of the velocity of centre of mass of the system is:
\( ^{\mathrm{A}} \cdot \frac{25}{9} m / s \)
в. \( \frac{9}{25} m / s \)
c. \( \frac{41}{9} m / s \)
D. \( \frac{16}{9} m / s \)


topp
ge eva


When conc. \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) is heated, it
decomposes to give-
A. \( O_{2} \) and \( N_{2} \)
B. NO
c. \( N_{2} O_{5} \)
D. \( N O_{2} \) and \( O_{2} \)


The differential coefficient of
\( a^{\log _{10}\left(\operatorname{cosec}^{-1} x\right)} \) is
A \( \cdot \frac{a^{\log _{10}\left(\operatorname{cosec}^{-1} x\right)}}{[\operatorname{cosec}]^{-1} \mathrm{x}} \frac{1}{\mathrm{x} \sqrt{\mathrm{x}^{2}-1}} \log _{10} \mathrm{a} \)
\( ^{\mathrm{B}}-\frac{a^{\log _{10}\left(\operatorname{cosec}^{-1} x\right)}}{[\operatorname{cosec}]^{-1} \mathrm{x}} \frac{1}{|x| \sqrt{\mathrm{x}^{2}-1}} \log _{10} \mathrm{a} \)
\( ^{\mathbf{C}} \cdot \frac{a^{\log _{10}\left(\operatorname{cosec}^{-1} x\right)}}{[\operatorname{cosec}]^{-1} \mathbf{x}} \frac{1}{|x| \sqrt{\mathrm{x}^{2}-1}} \log _{\mathrm{a}} 10 \)
D. \( \frac{a^{\log _{10}\left(\operatorname{cosec}^{-1} x\right)}}{[\operatorname{cosec}]^{-1} \mathrm{x}} \frac{1}{\mathrm{x} \sqrt{\mathrm{x}^{2}-1}} \log _{\mathrm{a}} 10 \)


It is desired to produce a real image on a screen using a convex lens of focal length \( 10 \mathrm{cm} . \) The minimum distance between the object and the screen should be then
A. 20 cm
B. 40 cm
\( c .100 \mathrm{cm} \)
D. The real image is obtained at all distances


If a sine wave of amplitude \( 5 \mathrm{cm} \) wavelength \( 3 \mathrm{cm} \) and frequency \( 10 \mathrm{Hz} \) moves in space, what is its speed
\( A \cdot 3 m / s \)
B. \( 0.3 \mathrm{m} / \mathrm{s} \)
\( c \cdot 0.6 m / s \)
D. \( 0.03 \mathrm{m} / \mathrm{s} \)


Draw the structural formula of \( 2- \)
methylpropan-2-ol molecule.


In flowering plants, the fruit is derived
from
\( A \)
\( \mathrm{B} \)
\( c \)
\( D \)
\( E \)


Select dimensionless quantity(ies). This question has multiple correct options
A. vapour density
B. molality
c. specific gravity
D. mass fraction


The order of reactivity of carbonyl compounds for nucleophilic addition is:
\( \mathbf{A} \cdot H_{2} C=O>R C H O>A r C H O>R_{2} C=O> \)
\( A r_{2} C=O \)
B \( \cdot A r C H O>A r_{2} C=O>R C H O> \)
\( R_{2} C=O>C H_{2} C=O \)
\( \mathbf{c} \cdot A r_{2} C=O>R_{2} C=O>A r C H O>R C H O> \)
\( H_{2} C=O \)
D. \( H_{2} C=O>R_{2} C=O>A r_{2} C=O>R C H O> \)
\( A r C H O \)


Write the balanced chemical reaction
for the dehydration of concentrated
sulphuric acid with sugar crystals.


Calculate the mean of the following data with the help of shortcut method.
\begin{tabular}{|l|l|l|l|l|l|l|}
\hline Classinterval & \( 0-5 \) & \( 5-10 \) & \( 10-15 \) & \( 15-20 \) & \( 20-25 \) & \( 25-30 \) \\
\hline Frequency & 4 & 6 & 5 & 8 & 3 & 7 \\
\hline
\end{tabular}
A . 7.58
в. 5.78
c. 6.87
D. 8.67


increases effective
collisions without increasing average
energy.
A. An increase in the reactant concentration
B. An increase in the temperature
c. A decrease in pressure
D. Catalysts
E \( . p H \)


The intensity of sound reduces by \( 20 \% \) on passing through a glass slab. If sound of intensity 1 is made to cross through two such slabs, then the
intensity of emergent sound will be
A. 36 \%
B. 64\%
c. \( 40 \% \)
D. 80\%


Bag A contains 2 red and 3 black balls
while another bag \( \mathrm{B} \) contains 3 red and
4 black balls. One ball is drawn at
random from one of the bag and it is
found to be red. Find the probability that it was drawn from bag B.


If the salts \( M_{2} X, Q Y_{2} \) and \( P Z_{3} \) have
the same solubilities,their \( \boldsymbol{K}_{s p} \) values are related as \( -(S<1) \)
A \( \cdot K_{s p}\left(M_{2} X\right)=K_{s p}\left(Q Y_{2}\right)<K_{s p}\left(P Z_{3}\right) \)
в. \( K_{s p}\left(M_{2} X\right)>K_{s p}\left(Q Y_{2}\right)=K_{s p}\left(P Z_{3}\right) \)
C. \( K_{s p}\left(M_{2} X\right)=K_{s p}\left(Q Y_{2}\right)>K_{s p}\left(P Z_{3}\right) \)
D. \( K_{s p}\left(M_{2} X\right)>K_{s p}\left(Q Y_{2}\right)>K_{s p}\left(P Z_{3}\right. \)


In an equilateral triangle if 3 times the square of one side is equal to \( \mathrm{K} \) times the square of its altitude then Kequals
A \( \cdot \frac{4}{3} \)
B. 2
\( c \cdot 4 \)
D. \( \frac{9}{4} \)


The equations of two displacement sound waves propagating in a medium are given by \( s_{1}=2 \sin (200 \pi t) \) and
\( s_{2}=5 \sin (150 \pi t) \) The ratio of
intensities of sound produced is :
A . 4: 25
B. 9: 100
c. 8: 15
D. 64:225


Why does a guitarist need to tighten the strings of the guitar to get the correct music and sound?
A. Tight strings force the entire guitar to vibrate.
B. It is easy to play a guitar with tight strings.
c. Tight strings look good and enhance the look of the guitar.
D. It is not important to tighten the string


The radius of a hypothetical nucleus (atomic number= 79 ) is about \( 7 \times \)
\( 10^{-15} \mathrm{m} . \) Assuming that charge
distribution is uniform, the electric
field at the surface of the nucleus is :
A. \( 2.9 \times 10^{-21} \)
B. \( 2.32 \times 10^{21} \)
C. \( 4.64 \times 10^{21} \)
D.


In a Zener regulated power supply a
Zener diode with \( V_{z}=6.0 V \) is used for
regulation. The load current is to be \( 4.0 m A \) and the unregulated input is
\( 10.0 V . \) What should be the value of
series resistor \( \boldsymbol{R}_{s} \)


Which of the following is an example of symmetrical ether?
A. Diisopropyl ether
B. Methoxy ethane
c. 1-Methoxy-2-methyl propane
D. None of these


Assertion
Baking powder contains \( N a H C O_{3} \)
\( C a\left(H_{2} P O_{4}\right)_{2}, \) starch and \( N a A l\left(S O_{4}\right)_{2} \)
Reason
\( N a H C O_{3} C a\left(H_{2} P O_{4}\right)_{2} \) is acidic in
aqueous solution. Acidic solution of
\( C a\left(H_{2} P O_{4}\right)_{2} \) liberates \( C O_{2} \) on reaction
with \( \left.N a H C O_{3} \text { Starch }\right] \) as a filter
\( N a A l\left(S O_{4}\right)^{2} \) retarder so that \( C O_{2} \) is given off more slowly while preparing cake or bread.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The ratio of Sl unit of G to its CGS unit is
A . 100: 1
в. 1000: 1
c. 10: 1
D. 10000: 1


The voltages across the two resistors are given by ohm's law as:
\( \mathbf{A} \cdot V=I R \)
в. \( V=I+R \)
\( c \cdot V=\frac{I}{R} \)
D. \( V=I+\frac{1}{R} \)


The compound (B) is:
\( A \)
B. \( \mathbf{M e}-\mathbf{C H}=\mathbf{O} \)
\( c \)
D.


If equal concentrations of products and reactants are mixed, then which of the following reactions will proceed to the right and which will proceed to the left?
\( (A) H_{2} S O_{4}(a q)+N H_{3}(a q) \rightleftharpoons \)
\( N H_{4}^{+}(a q)+H S O_{4}^{-}(a q) \)
(B) \( \boldsymbol{H} \boldsymbol{C O}_{3}^{-}(\boldsymbol{a q})+\boldsymbol{S O}_{4}^{2-}(\boldsymbol{a q}) \rightleftharpoons \)
\( \boldsymbol{H} \boldsymbol{S} \boldsymbol{O}_{4}^{-}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{C} \boldsymbol{O}_{3}^{2-}(\boldsymbol{a} \boldsymbol{q}) \)


Let \( X \) be a set of 5 elements. The number
d of ordered pairs \( (A, B) \) of subsets of \( X \) such that \( \boldsymbol{A} \neq \mathbf{\Phi}, \boldsymbol{B} \neq \mathbf{\Phi}, \boldsymbol{A} \cap \boldsymbol{B}=\mathbf{\Phi} \)
satisfies.
A \( .50 \leq d \leq 100 \)
в. \( 101 \leq d \leq 150 \)
c. \( 151 \leq d \leq 20 \)
D. \( 201 \leq d \)


Anadromous fishes move
A. From sea to fresh water
B. From sea to estuary
c. From river to sea
D. From estuary to sea


Which of the following is correct for
Lactose
A. It is nonreducing sugar
B. Glycosidic bond [1,4] between glucose and galactose
c. Glycosidic bond [1, 4 ] between glucose and fructose
D. Glycosidic bond [1,2] between glucose and galactos


The period of a particle in linear SHM is
8 s. \( A t t=0 \) it is at the mean position. Find the ratio of distance traveled by it
in 1 st second and 2 nd second
A . 3.2:
B. 2.4:
c. 1.6:
D. 4.2:


The Sl unit of stress is same as the SI
unit of
A. Strain
B. Modulus of elasticity
c. Pressure
D. Both (2) and (3)


Given, \( \boldsymbol{f}(\boldsymbol{x})=-\frac{\boldsymbol{x}^{3}}{\mathbf{3}}+\boldsymbol{x}^{2} \sin \mathbf{1 . 5} \boldsymbol{a}- \)
\( x \sin a \cdot \sin 2 a-5 a r c \sin \left(a^{2}-8 a+17\right) \)
then
A. \( f(x) \) is not defined at \( x=\sin 8 \)
B. \( f^{\prime}(\sin 8)>0 \)
c. \( f^{\prime}(x) \) is not defined at \( x=\sin 8 \)
D. \( f^{\prime}(\sin 8)<0 \)


During delocalization of electron, which
statement is incorrect?
A. Net charge remains same
B. Number of paired electrons remain same
c. Number of unpaired electrons remain same
D. Energy of resonating structures always remains same


If the angle between the vectors \( \vec{A} \) and
\( \vec{B} \) is \( \theta, \) then the value of the product \( (\vec{B} \times \vec{A}) \cdot \vec{A} \) equals
A. \( B A^{2} \sin \theta \)
B. \( B A^{2} \cos \theta \sin \theta \)
c. \( B A^{2} \cos \theta \)
D. zero


Determine the nature of roots of the
given quadratic equation \( 3 x^{2}+ \) \( \mathbf{2} \sqrt{\mathbf{5}} \boldsymbol{x}-\mathbf{5}=\mathbf{0} \)


Which of the following molecules has highest dipole moment?
A \( . C H_{3} C l \)
в. \( C H_{2} C l_{2} \)
c. \( C H C l_{3} \)
D. \( C C l_{4} \)


\( \operatorname{Let} y=\sqrt{x}+2 x^{\frac{3}{4}}+3 x^{\frac{5}{6}}(x>0) . \) Find
the derivative of \( y \) with respect to \( x \)


The area of a side of a box is 120 sq. \( \mathrm{cm} \) The area of the other side of the box is
72 sq. \( \mathrm{cm} . \) If the area of the upper surface of the box is 60 sq. \( \mathrm{cm} \), then find the volume of the box.
\( \mathbf{A} \cdot 259200 \mathrm{cm}^{3} \)
B. \( 84000 \mathrm{cm}^{3} \)
c. \( 86400 c m^{3} \)
D. \( 720 \mathrm{cm}^{3} \)


The oxidation number and covalency of sulphur in sulphur molecule \( \left(\mathrm{S}_{8}\right) \) are :
A. 0 and 2
B. +6 and 8
\( c .0 \) and 8
D. none of these


An observer is moving with half the speed of light toward a stationary microwave source emitting waves frequency \( 10 \mathrm{GHz} \). What is the frequency of the microwave measured by the observer? (speed of the light=3 \( x \) \( 10^{8} m s^{-1} \)
A. \( 17.3 \mathrm{GHz} \)
B . 15.3 GHz
c. 10.1 Gн
D. 12.1 GHz


A particle moves according to the equation \( \boldsymbol{x}=\boldsymbol{\alpha} \boldsymbol{t}^{3}+\boldsymbol{\beta} \boldsymbol{t}^{2} \). Find
instantaneous acceleration at any time
\( \mathbf{A} \cdot 6 \alpha+2 \beta \)
B. \( 3 \alpha t+2 \beta \)
\( \mathbf{c} \cdot 3 \alpha t+\beta \)
D. \( 6 \alpha t+2 \beta \)


Which of the following is not a vector quantity?
A. Distance
B. Displacement
c. Acceleration
D. Velocity


How many arrangements of four \( 0^{\prime} s \) (zeroes), two \( 1^{\prime} s \) and two \( 2^{\prime} s \) are there in
which the first 1 occur before the first
2?
A . 420
в. 360
\( c \cdot 310 \)
D. 210


Assertion
Free energy of both reactants and products are minimum at equilibrium.
Reason

The free energy of both reactants and products decreases with passage of time and become equal at equilibrium.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


A parallel plate capacitor with air as dielectric is charged to a potential 'V using a battery. Removing the battery, the charged capacitor is then connected across an identical
uncharged parallel plate capacitor filled with wax of dielectric constant 'K' the
common potential of both the
capacitor is
A. V volts
B. kV volts
\( c \cdot(k+1) v v o l t s \)
D. \( \frac{V}{k+1} \) volts


Fuels that provide most of the energy needs of the world is:
A. petroleum and coal
B. petroleum and wood
c. coal and wood
D. wood and petroleum


Give the electronic configuration of the following on the basis of crystal field splitting theory
\( \left[\boldsymbol{C o F}_{6}\right]^{3-} \) and \( \left[\boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right]^{2+} \)


Write the following in the expanded
form:
\( (m+2 n-5 p)^{2} \)


Among the following four compounds the acidity order is:
(a) Phenol
(b) methyl phenol
(c) meta nitrophenol
(d) para-nitrophenol
A \( . c>d>a>b \)
в. \( a>d>c>b \)
c. \( b>a>c>d \)
D. \( d>c>a>b \)


Three particles \( A, B \) and \( C \) are situated at the vertices of an equilateral triangle ABC of side d at time \( t=0 . \) Each of the
particles moves with constant speed v. A always has its velocity along \( \mathrm{AB}, \mathrm{B} \) along BC and \( C \) along CA. At what time will the particles meet each other?
A \( \cdot \frac{2 d}{3 v} \)
в. \( \frac{3 d}{2 v} \)
c. \( \frac{4 d}{3 v} \)
D. \( \frac{3 d}{4 v} \)


The marks obtained by 20 students of Class \( X \) of a certain school in a English
paper consisting of 100 marks are
presented in table below. Find the mean of the marks obtained by the students using step deviation method.
A . 61
B. 62
\( c \cdot 63 \)
D. 64


In bradycardia, the heart beat
A . Decreases
B. Increases
c. Becomes irregular
D. Remains same


\( N O_{2} \) is not obtained when following is
heated :
A \( \cdot P b\left(N O_{3}\right)_{2} \)
в. \( A g N O_{3} \)
c. \( L i N O_{3} \)
D. \( K N O_{3} \)


Assertion
Basic difference between an electric
line and magnetic line of force is that former is discontinuous and the later is
continuous or endless.
Reason
No electric lines of force exist inside a
charged body but magnetic lines do
exist inside a magnet.
A. Both Assertion and Reason are correct and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion
C. Assertion is correct but Reason is incorrect.
D. Assertion is incorrect but Reason is correct.


If the points \( \boldsymbol{A}(\overline{\boldsymbol{a}}), \boldsymbol{B}(\overline{\boldsymbol{b}}), \boldsymbol{C}(\overline{\boldsymbol{c}}) \) satisfy
the relation \( 3 \bar{a}-8 \bar{b}+5 \bar{c}=0 \) then the
points are
A. vertices of an equilateral triangle
B. collinear
c. vertices of a right angled triangle
D. vertices of an isosceles triangle


Consider the following statements and
predict the wrong statement(s)
a. Half filled and fully filled orbitals have greater stability due to greater exchange energy and symmetrical
distribution
b. The energy of \( 3 s \) orbital is less than
\( 3 p \) orbital for hydrogen atom.
c. The uncertainty principle is \( \Delta \boldsymbol{E} \times \) \( \Delta t \leq \frac{h}{4 \pi} \)
\( \boldsymbol{d} \boldsymbol{E}=-\boldsymbol{2} . \boldsymbol{1} \boldsymbol{7} \boldsymbol{8} \times \boldsymbol{1} \boldsymbol{0}^{-18}\left(\frac{\boldsymbol{Z}^{2}}{\boldsymbol{n}^{2}}\right) \boldsymbol{J} \boldsymbol{a t o m}^{-1} \)
can be used to calculate the change in
energy when the electron changes orbit in H-atom
A. b and conly
B. b, c and donly
c. a and b only
D. a and donly


The diagram below shows a cathode ray
tube in which the arrow indicates a
beam of charged particles approaching an electric field between the plates \( A \) and B. Name the charged particles.
A. Electron
B. Proton
c. Neutron
D. Alpha


The helical structure of DNA was
discovered by
A. sanger
B. Bloor
c. L.Pauling
D. watson and Crick


Write the IUPAC name of
\( \left[\boldsymbol{P t}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{3}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)\right] \boldsymbol{C l}_{2} \)


The oxidation reaction always takes place with a reduction reaction. Why is isolated oxidation reaction not
possible?


A cube has sides of length \( L=0.2 \mathrm{m} \). It is placed with one corner at the origin as shown in figure.The electric field is uniform and given by \( \overrightarrow{\boldsymbol{E}}= \) \( (2.5 N / C) \dot{I}-(4.2 N / C) j . \) Find the
electric flux through the entire cube.


The diagram is drawn on a square grid
Of the triangles marked \( P, Q, R \) and \( S \)
which is the image of triangle \( X \) under
a reflection in the line \( M N ? \)
\( A \)
3. \( Q \)
\( c . R \)
\( D \)


Complexes formed in the following
methods are:
(1) Mond's process for purification of nicke
(II) Removal of unreacted AgBr from photographic plate
(III) Removal of lead poisoning from the
body
A \( \cdot \) ।. \( N i(C O)_{4}, \) II. \( \left[A g(C N)_{2}\right]^{-}, \) ॥I. \( [P b(E D T A)]^{2} \)
B . I. \( N i(C O)_{4}, \) II. \( \left[A g\left(S_{2} O_{3}\right)_{2}\right]^{3-}, \) ॥I. \( [P b(E D T A)]^{2} \)
c. ।. \( N i(C O)_{6}, \) ॥. \( \left[A g\left(S_{2} O_{3}\right)_{2}\right]^{3-}, \) ॥I. \( [P b(E D T A)]^{4} \)
D. I. \( N i(C O)_{6}, \) II. \( \left[A g\left(S_{2} O_{3}\right)\right]^{-}, \) III. \( [P b(E D T A)]^{2} \)


What is the maximum amount of
nitrogen dioxide that can be produced by mixing \( 4.2 \mathrm{gm} \) of \( \mathrm{NO}(\mathrm{g}) \) and \( 3.2 \mathrm{gm} \) of
\( o_{2}(g) ? \)
A. (a) \( 4.60 \mathrm{gm} \)
B. (b) 2.30 gm
c. (c) 3.22 gm
D. (d) \( 6.44 \mathrm{gm} \)


Uncertainty in the position of an electron \( \left(\text {mass}=\mathbf{9 . 1} \times \mathbf{1 0}^{-\mathbf{3 1}} \mathbf{k g}\right) \)
moving with a velocity \( 300 m s^{-1} \)
accurate upon \( 0.001 \% \) will be:
\( \left[\boldsymbol{h}=\mathbf{6 . 6 3} \times \mathbf{1 0}^{-\mathbf{3 4}} \boldsymbol{J}-\boldsymbol{s}\right] \)
A \( \cdot 19.2 \times 10^{-2} \mathrm{m} \)
в. \( 5.76 \times 10^{-2} \) т
c. \( 1.92 \times 10^{-2} \mathrm{m} \)
D. \( 3.84 \times 10^{-2} \mathrm{m} \)


In the given five sided closed figure,
find \( \angle \boldsymbol{E} \boldsymbol{A} \boldsymbol{B}+\angle \boldsymbol{A} \boldsymbol{B} \boldsymbol{C}+\angle \boldsymbol{B} \boldsymbol{C} \boldsymbol{D}+ \)
\( \angle C D E+\angle D E A \)
\( 4 \cdot 520 \)
B. \( 540^{\circ} \)
\( c .530 \)
D. 140


Balance the following redox reaction \( M n O_{4}^{\ominus}(a q)+I^{\ominus}(a q) \rightarrow M n O_{2}(s)+ \)
\( \boldsymbol{I}_{2}(\boldsymbol{s}) \)
What is the coefficient of \( \boldsymbol{I}^{-} \) ?


Two parallel-plate vacuum capacitors
have areas \( A_{1} \) and \( A_{2} \) and equal plate spacing d. Show that when the capacitors are connected in parallel, the equivalent capacitance is the same as for a single capacitor with plate area
\( A_{1}+A_{2} \) and spacing d.


The half-life period of a first-order
reaction is 30 min. The percentage of the reactant remaining after 70 min will be:
A . 80
B . 40
c. 20
D. 10


What causes R. Q. to vary?
A. Respiratory substrates
B. Light and \( O_{2} \)
C . Respiratory products
D. Temperature


Sensitivity of a moving coil galvanometer can be increased by:
A. decreasing the number of turn of coil
B. increasing the number of turn of coil
c. decreasing the area of a coil
D. by using a week magnet


When 97.52 is divided by 2.54 , the correct result is :
A. 38.3937
в. 38.394
c. 38.39
D. 38.4


Using remainder theorem, find the reminder when \( x^{3}-a x^{2}+2 x-a \) is
divided by \( \boldsymbol{x}-\boldsymbol{a} \)
\( A \cdot a \)
B. \( a+2 \)
\( \mathbf{c} \cdot a+1 \)
D. \( a-2 \)


\( \mathrm{IF} \tan \Theta=\frac{8}{15} \) then the value of
\( \frac{17 \sin \Theta+\frac{5}{\cos \theta}}{5 \tan \Theta+\frac{8}{\sin \theta}} \)
A \( \cdot \frac{59}{41} \)
в. \( \frac{35}{41} \)
c. \( \frac{41}{59} \)
D. \( \frac{41}{35} \)


Assertion
Most probable velocity is the velocity possessed maximum fraction of
molecules at the same temperature.
Reason

On collision, more and more molecules
acquire has speed at the same temperature
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of the following does not help in excretion?
A. Liver
B. Sweat glands
c. Pancreas
D. Both A and B


When PNjunction os forward biased the current in junction
A. Increase
B. decrease
c. remains same
D. None of these


\( \boldsymbol{n} \) small drops of small size are charged
to \( V \) volt each. If they collapse to form a
single large drop, then its potential will be
\( \mathbf{A} \cdot(V / n) \)
в. \( V n \)
\( \mathbf{c} \cdot V n^{2 / 3} \)
D. None of these


Study the following about endocrine
disorder
\begin{tabular}{lll}
Hormones & Hyposecretion & Hypersecreti \\
(I) Insulin & Diabetes mellitus & Unconsciousr and shock \\
(II) Thyroxine & Simple Goitre & Myxoedema \\
(III) Parathormone & Tetany & Osteoporosis \\
\hline (IV) Cortisol & Cushing's syndrome & Addison's diseases
\end{tabular}
A. Only I,III and IV
B. Only I,II and II
C. Only I and III
D. All are true


If a charged particle goes unaccelerated in a region containing electric and magnetic fields, then This question has multiple correct options
A. \( \vec{E} \) must be perpendicular to \( \vec{B} \)
B . \( \vec{v} \) must be perpendicular to \( \vec{E} \)
C. \( \vec{v} \) must be perpendicular to \( \vec{B} \)
D. E must be equal to vB


The sum and product of matrices A and B exist. Which of the
following implications are necessarily true?
1. A and B are square matrices of
same order.
2. A and B are non-singular matrices.
Select the correct answer using the
code given below:
A . 1 only
B. 2 only
c. Both 1 and 2
D. Neither 1 nor 2


Evaluate
\( \int \frac{\sin x+\cos x}{(\sin x-\cos x)^{2}} d x \)
A \( \cdot \frac{1}{\sin x-\cos x}+C \)
в. \( \frac{-1}{\sin x-\cos x}+C \)
c. \( \frac{-1}{\sin x+\cos x}+C \)
D. None of these


Which of the following statements
is/are true about the P-Cl bonds in
\( \boldsymbol{P C l}_{5} ? \)
This question has multiple correct options
A. Three bonds are of one type and two of another type
B. Two bonds are of one type and three of another type
C. All the bonds are of the same type
D. Each P-Cl bonds is unique


If \( a \) and \( b \) are real numbers, find the
value of \( b, \) if \( (a+b)+5 i=9+a i \) and
given that \( i^{2}=-1 \)
A . 4
B. 5
\( c .9 \)
D. \( 4+5 i \)
E. \( 5+4 i \)


In Sl unit 1 eu is:
A. 41.84 EU
B. 4.184 EU
c. 418.4 EU
D. 4184 EU


What type of waves are generated by SONAR device fixed to a fishing ship
A)water waves
A. Water waves
B. Radio waves
c. sound waves
D. Infrared waves


Which of the following is a consequence of the fact that the rotation and
revolution periods of the moon are the same?
A. The moon keeps the same face turned toward the earth
B. The moon can never be seen from one hemisphere of the earth
c. All lunar phases can be seen from the earth
D. There are about 12 months per year


Which of the following is involved in the transport of water in the tall plants?
A. Root pressure theory
B. Transpirational pull
c. cohesion and adhesion
D. Both A and C


A metal bar \( 70 \mathrm{cm} \) long and \( 4.00 \mathrm{kg} \) in mass supported on two knife-edges placed \( 10 \mathrm{cm} \) from each end. \( \mathrm{A} 6.00 \mathrm{kg} \)
load is suspended at \( 30 \mathrm{cm} \) from one
end. Find the reactions at the knife-
edges. (Assume the bar to be of uniform
cross section and homogeneous.)
\( \mathbf{A} \cdot 45 N \) and \( 43 N \)
B. \( 50 N \) and \( 35 N \)
\( \mathbf{c} .55 N \) and \( 43 N \)
D. \( 54 N \) and \( 30 N \)


Cumene on reaction with oxygen
followed by hydrolysis gives?
\( \mathbf{A} \cdot C H_{3} O H \) and \( C_{6} H_{5} C O C H_{3} \)
B. \( C_{6} H_{5} O H \) and \( \left(C H_{3}\right)_{2} O \)
\( \mathbf{c} \cdot C_{6} H_{5} O C H_{3} \) and \( C H_{3} O H \)
D. \( C_{6} H_{5} O H \) and \( C H_{3} C O C H_{3} \)


What is the temperature of the triplepoint of water on an absolute scale
whose unit interval size is equal to that
of the Fahrenheit scale?


Calculate the energy associated with
the first orbit of \( H e^{+} . \) Compare the energy of electron in first Bohr orbit of
hydrogen.


The light emitting diode (LED) is
A. a heavily doped p-n junction with no external bias
B. a heavily doped p-n junction with reverse bias
C. a heavily doped p-njunction with forward bias
D. a lightly doped p-n junction with no external bias
E . a lightly doped p-n junction with reverse bias


A car accelerates steadily so that it goes from a velocity of \( 20 \mathrm{m} / \mathrm{s} \) to a velocity of \( 40 \mathrm{m} / \mathrm{s} \) in 4 seconds. What is its acceleration?
A. \( 0.2 \mathrm{m} / \mathrm{s}^{2} \)
В. \( 4 m / s^{2} \)
c. \( 5 \mathrm{m} / \mathrm{s}^{2} \)
D. \( 10 \mathrm{m} / \mathrm{s}^{2} \)
E . \( 80 \mathrm{m} / \mathrm{s}^{2} \)


The radius of Jupiter is \( 7.1 \times 10^{3} m \) and
that of the Earth is \( 6.3 \times 10^{6} m \)
Compare the volume of the two.


Which logic gate is represented by the following combination of logic gates:
A. OR
B. NAND
\( c . \) AND
D. NOR


a germanium crystal with arsenic \( (Z= \)
33). A second semi-conductor Y is made
by doping germanium with indium \( Z=49 \). The two are joined end to end
and connected to a battery as shown.
Which of the following statements is
correct-
A. \( x \) is \( p \) -type, \( Y \) is \( n \) -type and the junction is forward biased
B. \( x \) is \( n \) -type, \( Y \) is \( p \) -type and the junction is forward biased
c. \( x \) is \( p \) -type, \( Y \) is \( n \) -type and the junction is reverse biased
D. \( x \) is \( n \) -type, \( Y \) is \( p \) -type and the junction is reverse biased


Primary alcohols are obtained by the reaction of Grignard reagent with:
A. \( C H_{3} C O C H_{3} \)
в. \( H C O O H \)
с. НСН О
D. \( C H_{3} C H O \)


Mullets, bhetki, pearl spots, prawns, mussels are the examples of
A. marine fish
B. fresh water fish
c. finned fish
D. shell fish.


If \( \tan A=\frac{5}{12}, \) find the value of \( (\sin A+ \)
\( \cos A) \times \sec A: \)
A \( \cdot \frac{6}{13} \)
в. \( \frac{7}{12} \)
c. \( \frac{17}{12} \)
D. \( \frac{12}{17} \)


The IUPAC name of the compound is:
\[
\begin{array}{cc}
0 & 0 \\
C H_{3}-C H_{2}-C-C H_{2}-C-C H_{3}
\end{array}
\]
A. Hexane-2,4-dione
B. hexane-2,4-diol
c. pentane- 2,4 -dione
D. heptane-2,4-dione


\( 50 g \) of ice at \( 0 \mathrm{C} \) mixed with \( 50 g \) of
water at 20 C. The final temperature of the mixture would be:
A. -30 C
B. -10 C
\( c \cdot 0 \)
D. 10 C


In the circuit, the potential difference
between \( A \) and \( B \) is?
A. \( 6 v \)
B. 1 v
\( c \cdot 3 v \)
D. 2 v


Two sinusoidal waves of the same
frequency travel in the same direction
along a string. If \( \boldsymbol{A}_{\mathbf{1}}=\mathbf{3 . 0} \boldsymbol{c m}, \boldsymbol{A}_{\mathbf{2}}= \)
\( 4.0 \mathrm{cm}, \phi_{1}=0, \) and \( \phi_{2}=\pi / 2 \mathrm{rad}, \) what
is the amplitude of the resultant wave?
A. \( 5 \mathrm{cm} \)
B. \( 6 \mathrm{cm} \)
\( c \cdot 7 \mathrm{cm} \)
D. \( 8 \mathrm{cm} \)


A girl is pushing on a crate with a force
as great as the force of friction between
the crate and the floor (see figure)
Which one of the following is correct?
A. The net force on the crate is zero
B. The crate may be at rest or just start sliding
c. The crate must not be accelerating
D. All of the above


Which of the following salts when dissolved in water undergoes hydrolysis
?
A. Nacı
в. \( N H_{4} C l \)
c. кс।
D. \( N a_{2} S O_{4} \)


Show that the binary operation \( * \) on \( Z \) defined by \( a * b=3 a+7 b \) is not
commutative.


In the given circuit, value of \( Y \) is:
A . toggles between 0 and 1
B.
c. will not execute
\( D \)


A box has to be moved from point \( A \) to point B. Which is the easiest way to
move it?
A. To push it across the distance
B. To slide it using an inclined plane
c. To use a wheeled trolley
D. To lift it and place it in the desired place


Duplicate of holotype from same collection of same locality, date and same branch of plant is called
A. Syntype
B. Paratype
c. Neotype
D. Isotype


Select pair of compounds in which both have different hybridization but have the same molecular geometry.
A. \( B F_{3}, B r F_{3} \)
B . \( I C l_{2}^{-}, B e C l_{2} \)
c. \( B C l_{3}, P C l_{3} \)
D. \( P C l_{3}, N C l_{3} \)


A step down transformer is used on a
1000V line to deliver \( 20 A \) at \( 120 V \) at the
secondary coil If the the efficiency of the transformer is \( 80 \% \) the current drawn
from the lines is
\( A \cdot 3 A \)
B. 30A
\( c .0 .3 \mathrm{A} \)
D. 2.4A


The number of triangles are less than the number of sides formed
by the diagonals from one vertex.
\( A \cdot 3 \)
B. 5
\( c \cdot 8 \)
D.


\( \frac{7}{8} \times\left(\frac{17}{13}+\frac{14}{13}\right)=\left(\frac{7}{8} \times \frac{14}{13}\right)+ \)
\( \left(\frac{7}{8} \times \frac{17}{13}\right) \)
If true then enter 1 and if false then
enter 0


Variation in the Acceleration Due to
Gravity:
Inside the earth: \( g=g_{0} \frac{x}{R_{0}}(x \) is
distance from the centre of the earth).


Assertion
In the refrigerator, the evaporator is located in the freezer section.
Reason
In the heat pump, the evaporator is located outside the room which is to be
heated.
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


Assertion: The \( O-O \) bond length in
\( H_{2} O_{2} \) is shorter than that of \( O_{2} F_{2} \)
Reason: \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) is an ionic compound
A. If both assertion and reason are true and the reason is a correct explanation of the assertion
B. If both assertion and reason are true but reason is not a correct explanation of the assertion
c. If the assertion is true but reason is false
D. If both the assertion and reason are false
E. If the assertion is false but the reason is true


Which is most reactive towards soda -
lime decarboxylation?
\( A \)
B.
\( c \)
D.


The length of a potentiometer wire is \( l . \) A cell of emf \( \boldsymbol{E} \) is balanced at length \( \boldsymbol{l} / \mathbf{3} \)
from the positive end of the wire. If the length of the wire is increased by \( l / 2 \)
Then, at what distance will the same
cell give a balance point?
A \( \frac{2 l}{3} \)
B. \( \frac{l}{2} \)
\( c \cdot \frac{l}{6} \)
D. \( \frac{4 l}{3} \)


While you are traveling in a car on a straight road at \( 90 k m / h, \) another car passes you in the same direction; its
speedometer reads \( 120 k m / h \). What is your velocity relative to the other driver? (in \( \mathrm{km} / \mathrm{h}) \)
A . 30
B. -30
\( c \cdot 210 \)
D. -210


Assertion
\( P b_{3} O_{4} \) react with \( H N O_{3} \) and form
\( P b O_{2} \)
Reason
Lead is stable in +4 oxidation state.
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


Medicine, which is an antibiotic is :
A. ampicillin
B. aspirin
c. compose
D. chloroquin


For the system \( 3 A+2 B \rightarrow 2 C \), the
expression for equilibrium constant \( \boldsymbol{K} \)
is:
A \( \cdot \frac{[3 A] \times[2 B]}{[C]} \)
B. \( \frac{[A]^{3} \times[B]}{[C]} \)
c. \( \frac{[C]^{2}}{[A]^{3} \times[B]^{2}} \)
D. \( \frac{[C]}{[3 A] \times[2 B]} \)


Which of the following compound is obtained by fermentation reaction of
Molasses?
A. Chlormethane
B. acetone
c. Ethanol
D. All of the given


The condition for a reaction to occur
spontaneously is:
A. \( \triangle H \) must be negative
B. \( \triangle S \) must be negative
c. \( (\triangle H-T \triangle S) \) must be negative
D. \( (\triangle H+T \triangle S) \) must be negative


Catalyst makes the reaction more exothermic.
A . True
B. False
c. Ambiguous
D. Data insufficient


Two interfering waves have amplitudes in the ratio \( 5: 1 . \) The ratio of the
maximum to the minimum intensity is
A . 25:
B. 4:
c. 6: 4
D. 9:


Prepare carbolic acid from benzene
sulphonic acid. Write a chemical
equation for the action of neutral ferric chloride on phenol.


Assertion
\( O_{3} \) acts as a powerful oxidising agent.
Reason
\( O_{3} \) oxidises lead sulphide to lead
sulphate and iodide ions to iodine.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The electric potential between a proton and an electron is given by \( \boldsymbol{V}= \) \( \mathbf{V}_{0} \ln \frac{\mathbf{r}}{\mathbf{r}_{0}}, \) where \( \mathbf{r}_{0} \) is a constant
Assuming Bohr's model to be
applicable, write variation of \( \mathbf{r}_{\mathbf{n}} \) with
\( \mathbf{n}, \mathbf{n} \) being the principal quantum number?
\( A \cdot r_{n} \propto n \)
в . \( \mathrm{r}_{\mathrm{n}} \propto 1 / \mathrm{n} \)
\( c \cdot r_{n} \propto n^{2} \)
D. \( \mathrm{r}_{\mathrm{n}} \propto 1 / \mathrm{n}^{2} \)


The \( \left[A g^{+}\right] \) in a saturated solution of
\( A g_{2} C r O_{4} \) is \( 1.5 \times 10^{-4} M . \) What is the
solubility product of \( A g_{2} C r O_{4} ? \)
A \( \cdot 3.375 \times 10^{-12} \)
B. \( 1.6875 \times 10^{-10} \)
C \( .1 .6875 \times 10^{-11} \)
D. \( 1.6875 \times 10^{-12} \)


The pH value of blood does not appreciably change by a small addition of an acid or a base, because the blood
A. is a body fluid
B. can be easily coagulated
c. contains iron as a part of the molecule
D. contains serum protein which acts as buffer


What is true for an ideal transistor
switch when turned OFF?
This question has multiple correct options
A. It has an infinite resistance
B. It has low resistance
c. It has maximum current flow
D. It has zero current flow


The centre of gravity of regular shaped objects is at their


Like \( U \) and \( H, S \) is also a state function
A. True
B. False


Find the differential equation of the
family of curves \( \boldsymbol{y}=\boldsymbol{A} \boldsymbol{e}^{2 \boldsymbol{x}}+\boldsymbol{B} \boldsymbol{e}^{-\boldsymbol{2 x}} \)
where \( A \) and \( B \) are arbitrary constants.


Which of the following reaction is not correct during the formation of acid rain?
A. \( S+O_{2} \rightarrow S O_{2} \)
в. \( H_{2} O+S O_{2} \rightarrow H_{2} S O_{3} \)
c. \( H_{2} O+S O_{2} \rightarrow H_{2} S O_{4} \)
\( \mathrm{D} \cdot 2 \mathrm{SO}_{2}+\mathrm{O}_{2} \rightarrow 2 \mathrm{SO}_{3} \)


The blood with no oxygen is received in
the
A . Left atrium
B. Left ventricle
c. Right atrium
D. Right ventricle


The absorption transition between the
first and the fourth energy states of hydrogen atom are 3. The emission transition between these states will be:
A . 3
B. 4
\( c .5 \)
D. 6


In the formation of \( N_{2} O_{5} \) by the
dehydration of nitric acid with phosphorous pentoxide. The phosphorous pentoxide converts into:
A. Phosphorous trioxide
B. Meta phosphoric acid
c. ortho phosphoric acid
D. Both B and C


An incident ray passing through the focus will be reflected:
A. straight away
B. through the pole of the mirror
c. back and passes through the centre of curvature
D. parallel to the principal axis


In which of the following S-S link is
present?
A. Caro's acid
B. Dithionic acid
c. Pyrosulphuric acid
D. Sulphuric acid


A particle executing SHM has amplitude of \( 4 \mathrm{cm} ., \) and its acceleration at a distance of \( 1 \mathrm{cm} \) from the mean
position is \( 3 \mathrm{cm} s^{-2} . \) Its velocity be when it is at a distance of \( 2 \mathrm{cm} \) from its mean
position is
A. \( 2 c m / s \)
в. \( 3 \mathrm{cm} / \mathrm{s} \)
c. \( 4 c m / s \)
D. \( 6 \mathrm{cm} / \mathrm{s} \)


The complex ion which has no \( ^{\prime} d^{\prime} \)
electrons in the central metal atom is:
\( \mathbf{A} \cdot\left[M n O_{4}\right]^{-} \)
B \( \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{6}\right]^{3+} \)
c. \( \left[F e(C N)_{6}\right]^{3-} \)
D・ \( \left[C r\left(H_{2} O\right)_{6}\right]_{6}^{3+} \)


Axis vertebrae is identified by
A. olecranon process
B. odontoblast
c. odontoid process
D. None of the above


Find \( a \) and \( b \) for the ellipse \( b^{2} x^{2}+ \) \( a^{2} y^{2}=a^{2} b^{2} \) if the distance between the
directrices is \( 5 \sqrt{5} \) and the distance
between the foci is \( 4 \sqrt{5} \). Give answer to
the nearest integer


Diffraction of sound is very easy, to observe in day-to-day life. This is not so with light. This is so because
\( A \cdot \lambda_{S}>\lambda_{L} \)
в. \( \lambda_{s}<\lambda_{L} \)
c. light waves are transverse and sound waves are longitudinal
D. \( \lambda_{S}=\lambda_{L} \)


\( \mathbf{f} \mathbf{A}=\left[\begin{array}{lll}\mathbf{1} & \mathbf{5} & \mathbf{- 6} \\ \mathbf{- 8} & \mathbf{0} & \mathbf{4} \\ \mathbf{3} & \mathbf{- 7} & \mathbf{2}\end{array}\right], \) then the
cofactor of \( -7= \)
A . 44
B. 43
\( c \cdot 40 \)
D. 39


Isotopes could find a position in Mendeleev's periodic table.
A. True
B. False


Two pith balls carrying equal charges are suspended from a common point by strings of equal length, the equilibrium separation between them is r. Now the
strings are rigidly clamped at half the height. The equilibrium separation between the balls now become:
\( A \)
B. \( \left(\frac{r}{3 \sqrt{2}}\right) \)
c. \( \left(\frac{2 r}{\sqrt{3}}\right) \)
D. \( \frac{2 r}{3} \)


When one faraday of electric current is passed, the mass deposited is equal to:
A. one gram equivalent
B. one gram mole
c. electrochemical equivalent
D. half gram equivalent


\( \operatorname{In} \) a reaction \( \Delta H \) and \( \Delta S \) both are
positive. In which of the following cases, the reaction would not be spontaneous?
A \( . \Delta H>T \Delta S \)
в. \( T \Delta S>\Delta H \)
c. \( \Delta H=T \Delta S \)
D. All of these


In a typical DNA molecule, the proportion of thymine is \( 30 \% \) of the \( \mathrm{N} \) bases. Find out the percentages of other N bases.


Which of the following are the Green house gases?
A. \( C O_{2}, C H_{4}, N_{2} O \) and \( O_{3} \)
B. \( C O_{2} \), Octane, chlorine, Nitrogen
c. Methane, Oxygen, Helium, Neon
D. None of these


The standard reduction potentials of \( \boldsymbol{C u}^{2+} / \boldsymbol{C u} \) and \( \boldsymbol{C u}^{2+} / \boldsymbol{C u}^{+} \) are \( \boldsymbol{0 . 3 3 7} \)
and \( 0.153 \mathrm{V} \) respectively. The standard electrode potential of \( C u^{+} / C u \) half cell
is:
A . \( 0.184 \mathrm{v} \)
B. \( 0.827 \mathrm{V} \)
c. \( 0.521 \mathrm{v} \)
D. \( 0.490 v \)


Find \( \boldsymbol{A}^{c} \)


State whether the following statement
is true or false.

Some organisms store wastes in body
parts
A. True
B. False


The transverse nature of light is shown by
A. interference of light
B. refraction of light
c. polarization of light
D. dispersion of light


Plants which disregard the requirement of a definite day length for flowering are called
A. Short day plants
B. Long day plants
c. Day neutral plants
D. Long-short day plants


Four identical parallel conductors,
carrying charges \( Q,-2 Q, 3 Q \) and \( 4 Q \)
are placed as shown in the figure. The
plates carrying charges \( Q \) and \( 4 Q \), are
connected through a switch, as shown.
The amount of charge flowing through the switch, after closing it is found to be
\( n Q . \) Find \( n \)


The ion that has different number of
electrons in the ultimate and
penultimate shells is :
A . \( N a^{\text {t }} \)
в. \( K^{+} \)
c. \( C l^{-} \)
D. \( C a^{2} \)


The movement of a molecule across a
typical plant cell about 50mm takes aproximately
A. 2.5m
B. 2.5
\( c .2 .5 s \)
D. none of these


Find \( \frac{d y}{d x}, \) if \( y=\sqrt{1+\sin 2 x} \)


If \( \bar{a}=a_{1} \hat{i}+a_{2} \hat{j}+a_{3} \hat{k}, \bar{b}=b_{1} \hat{i}+b_{2} \hat{j}+ \)
\( b_{3} \hat{k}, \bar{c}=c_{1} \hat{i}+c_{2} \hat{j}+c_{3} \hat{k} \) are non zero
vectors such that \( \bar{c} \) is a unit vector \( \perp \) to
both the vectors \( \bar{a} \) and \( \bar{b} \), if angle between \( \bar{a} \) and \( \bar{b} \) is \( \frac{\pi}{6} \) then \( \left|\begin{array}{lll}\boldsymbol{a}_{1} & \boldsymbol{a}_{2} & \boldsymbol{a}_{3} \\ \boldsymbol{b}_{1} & \boldsymbol{b}_{2} & \boldsymbol{b}_{3} \\ \boldsymbol{c}_{1} & \boldsymbol{c}_{2} & \boldsymbol{c}_{3}\end{array}\right|^{2} \) equals
A \( \cdot \frac{1}{4}\left(a_{1}^{2}+a_{2}^{2}+a_{3}^{2}\right)\left(b_{1}^{2}+b_{2}^{2}+b_{3}^{2}\right) \)
B \( \cdot \frac{3}{4}\left(a_{1}^{2}+a_{2}^{2}+a_{3}^{2}\right)\left(b_{1}^{2}+b_{2}^{2}+b_{3}^{2}\right)\left(c_{1}^{2}+c_{2}^{2}+c_{3}^{2}\right) \)
c. 1
D. 0


Find the value of \( x \)
If \( , \sin ^{-1} x+\sin ^{-1} 2 x=\frac{\pi}{3} \)


The rational number equivalent to the rational number \( \frac{\mathbf{7}}{\mathbf{1 9}} \) is:
A \( \cdot \frac{17}{119} \)
в. \( \frac{14}{57} \)
c. \( \frac{21}{38} \)
D. \( \frac{21}{57} \)


Solve the following pair of linear (simultaneous) equations by the method of elimination:
\( 8 x+5 y=9 \)
\( \mathbf{3} \boldsymbol{x}+\mathbf{2} \boldsymbol{y}=\mathbf{4} \)
A. \( x=1 \) and \( y=-2 \)
B. \( x=1 \) and \( y=-5 \)
c. \( x=3 \) and \( y=6 \)
D. \( x=-2 \) and \( y=5 \)


If a variable \( x \) takes values \( 0,1,2, \dots n \)
with frequencies proportional to the binomial coefficients
\( n_{0},^{n} C_{1},^{n} C_{2}, \dots \dots^{n} C_{n}, \) then mean of
distribution is
A \( \cdot \frac{n(n+1)}{2} \)
в. \( \frac{n}{2} \)
\( c \cdot \frac{2}{n} \)
D. \( \frac{n(n-1)}{2} \)


Match the column.


triangle has three different sides.
A. Equilateral
B. Isosceles
c. Right angled
D. Scalene


If \( \bar{E} \) and \( \overline{\boldsymbol{F}} \) are the complementary
events of events \( \boldsymbol{E} \) and \( \boldsymbol{F} \) respectively
and if \( \mathbf{0}<\boldsymbol{P}(\boldsymbol{F})<\mathbf{1}, \) then:
This question has multiple correct options
\( \mathbf{A} \cdot P(E / F)+P(\bar{E} / F)=1 \)
B \cdot \( P(E / F)+P(E / \bar{F})=1 \)
C \( \cdot P(\bar{E} / F)+P(E / \bar{F})=1 \)
D \( \cdot P(E / \bar{F})+P(\bar{E} / \bar{F})=1 \)


A rectangle has two opposite vertices at the points (1,2) and \( (5,5) . \) If the other
vertices lie on the line \( x=3 \), then the
coordinates of the other vertices are
\( \mathbf{A} \cdot(3,-1),(3,-6) \)
в. (3,1),(3,5)
C . (3,2),(3,6)
D. (3,1),(3,6)


Let \( \boldsymbol{O}= \) Set of odd natural numbers \( = \)
\( \{1,3,5,7,9, \dots\} \) and \( E=\operatorname{set} \) of even
natural numbers \( =\{2,4,6,8,10, \dots \dots .\} \)
Then show that \( 3 \in E \)


Solve the given inequalities graphically:
\( \boldsymbol{x}+\mathbf{2} \boldsymbol{y} \leq \mathbf{1 0}, \boldsymbol{x}+\boldsymbol{y} \geq \mathbf{1}, \boldsymbol{x}-\boldsymbol{y} \leq \mathbf{0}, \boldsymbol{x} \geq \)


Two pulses in a stretched string whose centers are initially \( 8 \mathrm{cm} \) apart are moving towards each other as shown in figure. The speed of each pulse is 2 \( \mathrm{cm} / \mathrm{s} . \) After 2 seconds, the total energy
of the pulses will be :
A . zero
B. purely kinetic
c. purely potential
D. partly kinetic and partly potential


What is shape selective catalysis?


The principle of fractional crystallisation is involved in which one of the following processes?
A. Van Arkel's method
B. Distillation
c. cupellation
D. zone refining


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


Benzene was first synthesized by passing acetylene through red hot tube (Berthelot). This is an example of condensation polymerisation.
A. True
B. False


What type of a quadrilateral do the
points \( \boldsymbol{A}(\mathbf{2}, \mathbf{2}), \boldsymbol{B}(\mathbf{7}, \mathbf{3}), \boldsymbol{C}(\mathbf{1 1}, \mathbf{1}) \) and
\( D(6,6) \) taken in that order, form?
A. Scalene quadrilateral
B. Square
c. Rectangle
D. Rhombus


Write the derivative of \( f(x)=|x|^{3} \) at
\( \boldsymbol{x}=\mathbf{0} \)


Which one of the following pairs of structure is correctly matched with their correct description?
A. Tibia and radius - Both form parts of knee joint
B. Cartilage and cornea - No blood supply but do require oxygen for respiratory need
c. shoulder joint - Gliding type of joint
D. Premolars and molars - 20 in all 3-rooted


The relation \( \boldsymbol{R}=\{(1,1),(2,2),(3,3)\} \)
on the set \{1,2,3\} is
A. Symmetric only
B. Reflexive only
c. An equivalence relation
D. transitive only


Which of the following constellation is seen in June in the northern part of the
sky at night?
A. Ursa Major
B. Ursa Minor
c. scorpio
D. Orion


Warming ammonium chloride with sodium hydroxide in a test tube is an example of:
A. closed system
B. isolated system
D. none of these


A mixture of ethane and neon having a volume of \( 20 \mathrm{ml} \), requires \( 49 \mathrm{ml} \) of
oxygen for complete combustion. The percentage of ethane in the mixture is:
A . \( 70 \% \)
B. 30\%
c. \( 35 \% \)
D. \( 64 \% \)


Which of the following statement is
correct for diborane?
A. Small amines like \( N H_{3}, C H_{3} N H_{2} \) give
unsymmetrical cleavage of diborane
B. Large amines such as \( \left(C H_{3}\right)_{3} N \) and pyridine gives symmetrical cleavage of diborane
C. Small as well as large amines both gives symmetrical cleavage of diborane
D. \( (A) \) and
(B) both


How many anti bonding electrons are
there in \( O_{2} \) molecule?
A . 10
B. 8
\( c \cdot 6 \)
D.


Match the following:
List

List 2
a)Reversible \( \quad \) 1)Temperature remains constant Process
b)Isothermal
2) Combustion reaction of Process \( \quad \) mixture of petrol and air
c) Irreversible
3)No heat flow between the Process \( \quad \) system and surrounding
d)Adiabatic
4) Temperature change in Process \( \quad \) atmosphere
\( A \cdot a-4, b-1, c-2, d-3 \)
B. a-3,b-2,c-4,d-1
c. a-3,b-1,c-2,d-4
D. a-2,b-3,c-1,d-4


In a unit fraction, the numerator is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
\( D \)


Assertion
In free expansion of a gas inside an adiabatic chamber \( Q, W \) and \( \Delta U \) all
are zero.
Reason In such an expansion \( \boldsymbol{P} \boldsymbol{\alpha} \frac{\mathbf{1}}{\boldsymbol{V}} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


(a) List three common refractive defects
of vision. Suggest the way of correcting these defects.
(b) About 45 lac people in the developing countries are suffering from corneal blindness. About 30 lac children
below the age of 12 years suffering from this defect can be cured by replacing the defective cornea with the cornea of
a donated eye. How and why can students of your age involve themselves to create awareness about this fact
among people ?


The area of a rhombus is \( 240 \mathrm{cm}^{2} \) and
one of the diagonal is \( 16 \mathrm{cm} . \) Find
another diagonal.


The difference in maximum kinetic
energy of photoelectrons from the \( A \) and
from B
A. increases with increases in \( E \)
B. decreases with decreases in \( E \)
c. first increases than decrease with increase in \( E \)
D. remain constant


If we apply oil on door hinges, the friction will:
A. increase
B. decrease
c. disappear altogether
D. will remain unchanged


A uniform solid sphere of mass \( \mathrm{M} \) and
radius \( R \) is kept on the horizontal
surface.

Find potential energy of the solid
sphere
A \( \cdot \frac{m g R}{2} \)
в. тg R
\( c \cdot \frac{m g R}{4} \)
D. \( \frac{2 m g}{B} \)


A bag contains \( 6 \mathrm{R}, 4 \mathrm{W} \) and \( 8 \mathrm{B} \) balls. If 3 balls are drawn simultaneously at random determine the probability of the
event
(1) all 3 are red.
(2) all 3 are black
(3) at least 1 is red
(4) 1 of each colour are drawn
(5) the balls are drawn in the order of
red, white, black
(6) 2 are white and 1 is red.


In the given figure, \( \angle \boldsymbol{X}= \)
\( \mathbf{6 2}^{\circ}, \angle \boldsymbol{X} \boldsymbol{Y} \boldsymbol{Z}=\mathbf{5 4}^{\boldsymbol{o}} . \ln \triangle \boldsymbol{X} \boldsymbol{Y} \boldsymbol{Z} \) If YO and
ZO are the bisectors of \( \angle X Y Z \) and
\( \angle X Z Y \) respectively find \( \angle O Z Y \) and
\( \angle Y O Z \)


Which of the following functions are not injective map
(A) \( f(x)=x+\frac{1}{x} ; x \in(0, \infty) \)
(B) \( g(x)=x^{2}+4 x-5 ; x \in(0, \infty) \)


The unit of torque is :
A \( . N m^{-1} \)
в. \( N m \)
c. \( N m^{-2} \)
D. \( N m^{2} \)


A man starts his job with a certain monthly salary and earns a fixed increment every year. If his salary was
Rs 1500 after 4 year of service and Rs
1800 after 10 years of service, what was
his starting salary and what is the annual increment?


What is commercial unit a energy? Give its relationship with S.I. unit of energy.


A certain reaction is non-spontaneous at \( 300 \mathrm{K} \). The entropy change during the reaction is \( 120 J K^{-1} \). Then the
minimum value of \( \Delta H \) for the reaction
and the nature of the reaction will be:
A. 36.0 kj; endothermic
B. 36.0 kJ; exothermic
c. \( 2.8 \mathrm{kJ} \); endothermic
D. \( -2.8 \mathrm{kJ} \); exothermic


Which is the sequence of four whorls of
flower from outside to inside?
A. Calyx \( \rightarrow \) Corolla \( \rightarrow \) Androceium \( \rightarrow \) Gynoceium
B. Gynoceium \( \rightarrow \) Androceium \( \rightarrow \) Corolla \( \rightarrow \) Calyx
C . Calyx \( \rightarrow \) Androceium \( \rightarrow \) Corolla \( \rightarrow \) Gynoceium
D. Gynoceium \( \rightarrow \) Corolla \( \rightarrow \) Androceium \( \rightarrow \) Calyx


Which of the following molecule deviates from octet rule with respect to
central atom?
A \( . P C l_{3} \)
в. \( H_{2} \).
c. \( N H_{3} \)
D. \( X e F_{4} \)


Silicosis occurs due to
A. Acid rain
B. Ozone depletion
C. Inhalation of aerosols
D. Inhalation of silica dust


The highest oxidation state of a transition metal is usually exhibited in its oxide and fluoride.


The highest magnetic moment is shown by
A . \( N i \)
в. \( C o \)
c. \( F e \)
D. \( S c \)


The potential of hydrogen electrode at
\( 25^{\circ} C \) will be:
\( \left(P_{H_{2}}=1 \text { atm, concentration of } \boldsymbol{H}^{+}=\right. \)
\( \mathbf{0 . 1} \boldsymbol{M} \)
\( \mathbf{A} \cdot 0.00 V \)
В. \( -0.059 V \)
c. \( 0.118 V \)
D. \( 0.059 V \)


A person cannot see fundamental colours (red, blue, green). This defect is called:
A. myopia
B. presbyopia
c. colour blindness
D. astigmatism


On hydrolysis of starch, we finally get:
A. Glucose
B. Fructose
c. Both (a) and (b)
D. sucrose


Solve:
\( \frac{x}{x+1}=\frac{2}{3} \)


The major reason for treating severe emotional disorders with tranquilizers
is to:
A. reduce the neurotic syndrome
B. prevent secondary complication
c. prevent destructiveness by the client
D. make the client more amenable to psychotherapy


Magnetic field can be defined as the:
A. space surrounding the magnet in which magnetic force acts
B. space surrounding the magnet in which electric force acts
C. space surrounding the magnet in which no force acts
D. none


A pendulum bob of mass \( \mathrm{m} \) is held in
the horizontal position and then released show that the velocity of bob at
lowest position is \( \sqrt{2 g l} \)


Find \( \int \frac{x^{4}+1}{x\left(x^{2}+1\right)^{2}} \)


The major portion of the dry weight of plant comprises of
A. Nitrogen, phosphorus and potassium
B. Calcium, magnesium and sulphur
c. carbon, nitrogen and hydrogen
D. Carbon, hydrogen and oxygen


Explain how xerarch succession progresses from xeric to mesic
condition and forms a stable climax
community.


In snells law \( \mu_{1} \sin \theta_{1}=\mu_{2} \sin \theta_{2} \)
Type 1 for true and 0 for flase


In the circuit shown, the resistances are
given in ohms and the battery is
assumed ideals with emf equal to 3.0 volts. The resistor that dissipated the
most power is
\( A \cdot R_{1} \)
B. \( R_{2} \)
\( c \cdot R_{3} \)
D. \( R_{4} \)


In the following, the coordinates of the three vertices of a rectangle \( A B C D \) are given. By plotting the given points; find, the coordinates of the fourth vertex:
\( B(10,4), C(0,4) \) and \( D(0,-2) \)
Claim: The co-ordinates of the fourth vertex are (10,-2)

If true then enter 1 and if false then
enter 0


The total number of different
combinations of one
or more letters which can be made from
the letter of the word MISSISSIPPI is,
A. 150
в. 148
\( c \cdot 149 \)
D. 146


A spherical convex surface separates object and image spaces of refractive indices 1.0 and \( 4 / 3 . \) If radius of curvature of the surface is \( 10 \mathrm{cm}, \) find its power.
A . \( 3.5 D \)
в. \( 2.5 D \)
\( c .25 D \)
D. \( 1.5 D \)


\( f A=\left[\begin{array}{ccc}1 & -5 & 7 \\ 0 & 7 & 9 \\ 11 & 8 & 9\end{array}\right], \) then trace of
matrix \( \boldsymbol{A} \) is
A . 17
B . 25
\( c .3 \)
D. 12


Tautomers are?
A. readily interconvertible but a catalyst is required
B. readily interconvertible without any catalyst
C. not interconvertible at all
D. in some cases interconvertible and in some other
cases not interconvertible


Which of the following plants reproduce without forming seeds?
A. Mango
B. Sugarcane
c. Rose
D. Both B and C


\( \lambda^{\infty} \) of \( N H_{4} O H \) at infinite dilution is
\( \boldsymbol{S} \boldsymbol{c m}^{2} \boldsymbol{m o l}^{-1} \operatorname{given} \boldsymbol{\lambda}^{\infty} \boldsymbol{o f} \)
\( O H^{-}=174, \lambda^{\infty} \) if \( C l^{-}=66 \) and \( \lambda^{\infty} \) of
\( N H_{4} C l=130 S c m^{2} m o l^{-1} \)
A . 140
в. 218
c. 238
D. 198


In fission, the products have less mass than the starting materials do.
A. True
B. False
c. Ambiguous
D. Data Insufficient


Calculate the magnetic field generated
by n segment of an right triangle.


Nitrogen and phosphorus are both in Group 15 of the Periodic Table.

Phosphorus forms a chloride with the
formula \( P C l_{5} \) but nitrogen does not
form \( \boldsymbol{N} \boldsymbol{C l}_{5} \)
Which statements help to explain this?
1. Nitrogen's outer shell cannot contain more than eight electrons.
2. Nitrogen cannot have an oxidation
state of +5
3. Nitrogen is less electronegative than phosphorus.
A .1,2 and 3 are correct
B. 1 and 2 only are correct
c. 2 and 3 only are correct
D. 1 only is correct


Which of the following is not a fossil fuel?
A. coal
B. Alcohol
c. Natural gas
D. Petroleum gas


If \( \int \frac{(x+1)}{x\left(1+x e^{x}\right)^{2}} d x=\log |1-f(x)|+ \)
\( f(x)+C, \) then \( f(x)= \)
A. \( \frac{1}{x+e^{x}} \)
B. \( \frac{1}{1+x e^{x}} \)
c. \( \frac{1}{\left(1+x e^{x}\right)^{2}} \)
D. \( \frac{1}{\left(x+e^{x}\right)^{2}} \)


Find the latus rectum, the eccentricity, and the coordinates of the foci, of the
ellipses
(1) \( x^{2}+3 y^{2}=a^{2}, \) (2) \( 5 x^{2}+4 y^{2}=1 \)
and
(3) \( 9 x^{2}+5 y^{2}-30 y=0 \)


Curie-Weiss law is obeyed by iron.
A. At curie temperature only
B. At all temperatures
C . Below curie temperature
D. Above curie temperature


Which of the following is covered by pericardium membrane?
A. Heart
B. Kidneys
c. Small intestine
D. Stomach


A polynomial of 4 is called a
A. quadratic polynomial
B. biquadratic polynomial
c. cubic polynomial
D. none of these


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