Which of the following property of an element never changes?
A. Valency
B. Atomic weight
c. Equivalent Mass
D. All the above


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


A black body at \( 200 \mathrm{K} \) is found to emit
maximum energy at a wavelength of 14
\( \mu \mathrm{m} . \) When its temperature is raised to
1000 \( \mathrm{K}, \) the wavelength at which maximum energy is emitted is :
\( A \cdot 14 \mu m \)
B. 70 \( \mu \) m
c. \( 1.8 \mu \mathrm{m} \)
D. 2.8 \( \mu \) m


The Hydrogen bond is always formed
between the molecules of the same
substance.
A. True
B. False


In a large metropolitan area, the probabilities are 0.87,0.36,0.36,0.30
that a family (randomly chosen for a sample survey) owns a color television set, a black and white television set, or
both kinds of sets. What is the
probability that a family owns either any one or both kinds of sets


Osmosis and diffusion differs, that
osmosis is one way traffic and diffusion
is a two -way traffic
A. True
B. False


If \( (8,1),(k,-4),(2,-5) \) are collinaer,
then \( k= \)
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D. 4


Find the number of terms in the
expansion of \( \left(1-2 x+x^{2}\right)^{7} \)


Identify the correct statement(s) for the
given reaction.
\( \boldsymbol{H} \boldsymbol{C l}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{H}_{3} \boldsymbol{O}^{+}+\boldsymbol{C l}^{-} \)
a) Conjugate base of \( \boldsymbol{H} \boldsymbol{C l} \) is \( \boldsymbol{C l}^{-} \)
b) Conjugate acid-base pair is \( \boldsymbol{H}_{3} \boldsymbol{O}^{+} \)
and \( \boldsymbol{H}_{2} \boldsymbol{O} \)
c) Conjugate base of \( \boldsymbol{H}_{2} \boldsymbol{O} \) is \( \boldsymbol{H}_{3} \boldsymbol{O}^{+} \)
d) Conjugate acid-base pair is \( \boldsymbol{H} \boldsymbol{C l} \) and
\( \boldsymbol{H}_{3} \boldsymbol{O}^{+} \)
\( A \cdot a \) and \( b \) are correct
B. a and c are correct
c. \( c \) and \( d \) are correct
D. a and d are correct


When mole of \( C o C l_{3} .6 N H_{3} \) is treated
with excess of \( \mathrm{AgNO}_{3} \) solution. The number of moles of AgCl precipitated is:
A. 3
B.
\( c \)
D.


For ordinary terrestial experiments, which of the following observers below are inertial?
A. a child revolving in a "giant wheel"
B. a driver in a sports car moving with a constant high speed of \( 200 \mathrm{km} / \mathrm{h} \) on a straight road
c. the pilot of an aeroplane which is taking off
D. a cyclist negotiating a sharp turn


When we burn nylon, why we do not get
the smell of burning paper or burning
hair?


Which one of the following statements
about \( C_{2} \) molecule is wrong?
A. The bond order of \( C_{2} \) is 2 .
B. In vapour phase, \( C_{2} \) molecule is diamagnetic.
C. Double bond in \( C_{2} \) molecule consists of both \( \pi \) - bonds
because of the presence of 4 electrons in two \( \pi^{-} \) molecular orbitals.
D. Double bond in \( C_{2} \) molecule consists of one \( \sigma \) bond
and one \( \pi \) bond.


The plane \( x+2 y-z=4 \) cuts the
sphere \( \boldsymbol{x}^{2}+\boldsymbol{y}^{2}+\boldsymbol{z}^{2}-\boldsymbol{x}+\boldsymbol{z}-\boldsymbol{2}=\mathbf{0} \) in
a circle of radius
A . 1
B. 3
\( c \cdot \sqrt{2} \)
D.


The radius of the curved part of the wire
is \( R, \) the linear parts are assumed to be
very long. Find the magnetic induction
of the field at the point \( O \) if a current-
carrying wire has the shape shown in figure above.
\( ^{\mathbf{A}} \cdot B=\frac{\mu_{0}}{4 \pi} \frac{I}{R}\left[1+\frac{3 \pi}{2}\right] \)
в. \( B=\frac{\mu_{0}}{\pi} \frac{I}{R}\left[1+\frac{3 \pi}{2}\right] \)
c. \( _{B}=\frac{\mu_{0}}{2 \pi} \frac{I}{R}\left[1+\frac{3 \pi}{2}\right] \)
D. \( B=0 \)


A body falls freely towards the earth
with:
A. uniform speed
B. uniform velocity
c. uniform acceleration
D. none of these


Expression for potential energy


The electric field \( \mathrm{E} \), current density and conductivity \( \sigma \) of a conductor are
related as
A \( . \sigma=E / J \)
В . \( \sigma=J / E \)
\( \mathrm{c} \cdot \sigma=J E \)
D. \( \sigma=1 / E \)


A body is projected at an angle of \( 60^{\circ} \) with the horizontal. If its kinetic energy at maximum height is \( 10 \mathrm{J} \), then the height at which potential energy and kinetic energy have equal values (consider P.E. at the point of projection to be zero) is :
A. half of the maximum height
B. two third of the maximum height
c. one sixth of the maximum height
D. insufficient data to solve the problem.


The differential equation representing the SHM of a particule is \( \frac{\mathbf{9} d^{2} \boldsymbol{y}}{d t^{2}}+\mathbf{4} \boldsymbol{y}= \)
0. The time period of the particle is
given by :
A \( \cdot \frac{\pi}{3} \) sec
B . \( \pi \) sec
c. \( \frac{2 \pi}{3} \) sec
D. \( 3 \pi \) sec


There are two identical small holes of
area of cross section a on the opposite
sides of a tank containing a liquid of
density \( \rho . \) The difference in height
between the holes is \( h \). The tank is
resting on a smooth horizontal surface.
The horizontal force which will have to
be applied on the tank to keep it in equilibrium is:
A \( \cdot g h \rho a \)
в. \( \frac{2 g h}{\rho a} \)
c. 2 pagh
D. \( \frac{\rho g}{\text { an }} \)


The line passing through the points \( 10 \hat{i}+3 \hat{j}, 12 \hat{i}+5 \hat{j} \) also passes through
the point \( a \hat{i}+11 \hat{j}, \) then \( a= \)
A . -8
B. 4
c. 18
D. 12


Express as kilogram (kg) using decimals:
\( 150 g \)


Consider a spherical Gaussian surface
of radius \( r, \) where \( c>r>b, \) the net
charge enclosed by this surface is \( \boldsymbol{Y} \times \)
Q. Find \( Y ? \)


A uniform chain of length \( 2 m \) is kept on a table such that a length of \( 60 \mathrm{cm} \) hangs freely from the edge of the table. The total mass of the chain is \( 4 k g \)
What is the work done in pulling the
entire chain on the table?
A .125
\( J \)
B. 3.6 J
\( c .7 .25 \)
D. \( 1200 J \)


Find one rational number between the
following pairs of rational numbers
(i) \( \frac{4}{3} \) and \( \frac{2}{5} \)
(ii) \( \frac{-2}{7} \) and \( \frac{5}{6} \)
(iii) \( \frac{5}{11} \) and \( \frac{7}{8} \)
(iv) \( \frac{7}{4} \) and \( \frac{8}{3} \)


On based temperature plants are classified by
A. Worming
B. Climent
c. Haeckel
D. Raunkiaer


In the pressence of a catalyst, the activation energy of a reaction is
lowered by \( 2 k c a l \) at \( 27^{\circ} C . \) The rate of reaction will increase by:
\( (\text {Antilog} 1.43=28) \)
A. 2 times
B. 14 times
c. 28 times
D. 20 times


The colour that appears in concentrated nitric acid when it is left standing in an ordinary glass bottle is :
A. yellow
B. black
c. blue
D. brown


Oxidation state of carbon in \( \boldsymbol{C} \boldsymbol{H} \boldsymbol{C l}_{3} \) is :
\( A \cdot+1 \)
\( B .+2 \)
\( c \cdot+4 \)
D. - -


Complete and balance the following
compound. Acidic solution of \( F e^{2+} \) ion gives a brown ring when it comes in
contact with \( N O^{-} 3 \) ion. Complete the
following reaction of this process.
\[
\begin{array}{l}
{\left[\boldsymbol{F e}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right]^{2+}+\boldsymbol{N} \boldsymbol{O}_{3}^{-}+\boldsymbol{H}^{+} \rightarrow} \\
------+\left[\boldsymbol{F} e\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right]^{3+}+\boldsymbol{H}_{2} \boldsymbol{O}
\end{array}
\]


A convex lens of diameter \( 8 \mathrm{cm} \) is used
to focus a parallel beam of light of wavelength \( 620 n m . \) Light is focused at a distance \( 20 c m, \) from the lens. What would be the radius of central bright fringe?


Consider the following reaction:
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{I}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{2} \boldsymbol{H} \boldsymbol{I}(\boldsymbol{g})= \)
\( \boldsymbol{k}\left[\boldsymbol{H}_{2}\right]\left[\boldsymbol{I}_{2}\right] \)
Which one of the following statements is correct?
A. The reaction must occur in a single step
B. This is a second order reaction overal
c. Raising the temperature will cause the value of \( k \) to decrease
D. Raising the temperature lowers the activation energy for the reaction


\( \lim _{x \rightarrow a} \frac{\sqrt{a+2 x}-\sqrt{3 x}}{\sqrt{3 a+x}-2 \sqrt{x}} \) is equal to
A \( \cdot \frac{2}{\sqrt{3}} \)
B. \( -\frac{1}{\sqrt{3}} \)
\( c \cdot \frac{2}{3 \sqrt{3}} \)
D. \( \frac{1}{\sqrt{3}} \)


Assertion
In a simple electric circuit, positive terminal of the battery is a point of lowest potential
Reason
The electronic current flow in a circuit
is from a point of highest potential to a point of lowest potential
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


In the following figure, \( A E \perp B C, D \) is the
mid point of BC, then \( x \) is equal to
A \( \cdot \frac{1}{a}\left[b^{2}-d^{2}-\frac{a^{2}}{4}\right] \)
B. \( \frac{h+d}{3} \)
c. \( \frac{c+d-h}{2} \)
\( \frac{a^{2}+b^{2}+d^{2}-c^{2}}{4} \)


A particle can move only along \( x- \) axis.
Three pairs of initial and final positions
of particle at two successive times are
given
Initial poistion Final positioin Pair \( 1 \quad-3 m \) The \( +5 m \)
\( 2 \quad-3 m \) \( -7 m \)
3 \( +7 m \) \( -3 m \)
Find the sum of magnitudes of
displacement in the pairs which give
negative displacement in \( \boldsymbol{m} \)


In which of following system, scientific data can be exchanged between different parts of the world?
A. M.K.S.
B. C.G.S
c. F.P.S.
D. s..


The angular frequency of the damped
oscillator is given by \( \omega= \) \( \sqrt{\left(\frac{k}{m}-\frac{r^{2}}{4 m^{2}}\right)} \) where \( k \) is the spring
constant, \( m \) is the mass of the oscillator
and \( r \) is the damping constant. If the ratio \( \frac{r^{2}}{m k} \) is \( 8 \% \), the changed in time
period compared to the undamped oscillator is approximately as follows:
A. Increases by \( 1 \% \)
B. Decreases by 1\%
c. Decreases by \( 8 \% \)
D. increases by 8\%


Which one of the following is not a derived unit?
A . joule
B. watt
c. kilogram
D. newton


In the arrangement shown in figure pulleys are small, light and frictionless,
threads are inextensible and mass of
blocks \( A, B \) and \( C \) is \( m_{1}=5 k g, m_{2}=4 \)
kg and \( m_{3}=2.5 \) kg respectively.
Coefficient of friction for both the
planes is \( =\mathbf{0 . 5 0} \)
Acceleration of block \( \mathrm{C}\left(\text { in } \boldsymbol{m} / \boldsymbol{s}^{2}\right) \) is :
\( A \)
\( B .2 \)
\( c \)
D. None of these


Generators used in power stations to
generate electricity are
A. DC generators
B. AC generators
\( c \cdot \) Both
D. None


Figure here shows the vertical cross-
section of a vessel filled with a liquid of
density \( \rho \)

The normal thrust per unit area on the
walls of the vessel at point \( P \) as shown
will be :
A \( . \) hog
в. Нр р
\( \mathbf{c} \cdot(H-h) \rho g \)
D \( \cdot(H-h) \) pgcos


The charge on a parallel plate capacitor
is varying as \( \boldsymbol{q}=\boldsymbol{q}_{0} \sin (2 \pi n t) . \) The
plates are very large and close together. neglecting the edge effects, the displacement current through the capacitor is:
\( ^{\text {A. }} \frac{q}{\varepsilon_{0}} \)
в. \( \frac{q_{0}}{\varepsilon_{0}} \sin 2 \pi n t \)
\( \mathbf{c} \cdot 2 \pi n q_{0} \cos 2 \pi n t \)
\( \stackrel{\mathrm{D}}{\cdot} \frac{2 \pi n q_{0}}{\varepsilon_{0}} \cos 2 \pi n t \)


If \( \bar{a}-\bar{b} \) is perpendicular to \( \bar{a},|b|= \) \( \sqrt{2}|\bar{a}|, \) then
A \( .2 \bar{a}+b \) parallel to \( \bar{a} \)
B . \( (2 \bar{a}+\bar{b}) \) is perpendicular to \( \bar{b} \)
C . \( (2 \bar{a}-\bar{b}) \) is perpendicular to \( \bar{b} \)
D. \( (2 \bar{a}-\bar{b}) \) is parallel to \( \bar{a} \)


How would you convert ethyne into
benzene?


Which series of compounds can be prepared by oxidation of primary alcohols?


Mark the WRONG statement:
When two plane mirrors are placed parallel to each other:
A. no image will be formed
B. infinite number of images will be formed
c. brightness of the images will decrease
D. images are erect


\( \mathbf{n} \)
fig., \( A B \) and \( C D \) are two diameters of \( a \)
circle (with centre 0) perpendicular to
each other and 0 D is the diameter of the
smaller circle. If \( \boldsymbol{O} \boldsymbol{A}=\mathbf{1 4} \boldsymbol{c m}, \) find the
area of the shaded region


Assertion
Distance covered by a moving body is always greater than zero.
Reason
Displacement of a particle can be
greater than or less than or equal to
zero.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


The number density of molecules of a
gas depends on their distance \( r \) from the origin as, \( n(r)=n_{0} e^{-\alpha r^{4}} . \) Then the
total number of molecules is
proportional to:
A \( \cdot n_{0} \alpha^{1 / 4} \)
B . \( n_{0} \alpha^{-3} \)
\( \mathbf{c} \cdot n_{0} \alpha^{-3 / 4} \)
D. \( \sqrt{n_{0}} \alpha^{1 / 2} \)


In the case of linearly polarized light, the magnitude of the electric field
vector
A. is parallel to the direction of propagation
B. does not change with time
c. increases linearly with time
D. varies periodically with time


Elements which generally exhibit variable oxidation states and form
colored ions are
A. metalloids
B. transition elements
c. non-metals
D. gases


Which is a correct representation the
propagation of sound waves in gases?
\( A \)
B.
C. Either A or B
D. None of these


What is Glycolysis? Write main steps of ¡t.


A woman has only daughters. Which of the following is the suitable explanation
for it?
A. The man produces sperms with \( x \) and \( Y \) chromosome but only that with \( Y \) chromosomes are viable
B. The man produces sperms with \( x \) and \( Y \) chromosome but only that with \( x \) chromosomes are viable
c. The man produces sperms with \( x \) and \( Y \) chromosome and all are viable
D. None of the above


\{9,12,15,18,21\}
Which of the following pairs of numbers, when added to the set above, will
increase the standard deviation of the
set?
I. 14,16
Il. 9,21
III. 15,100
A. Il only
B. III only
c. I and ॥
E . ।, ॥।, and III


On nerve fibres, to prevent leakage of an impulse, a layer of \( \ldots \ldots \) is found.
A. Rod cells
B. Neurilemma
c. Axons
D. Myelin sheath


From a well shuffled pack of 52 playing cards two cards drawn at random. The
probability that either both are red or both are kings is:
\( ^{\mathrm{A}} \cdot \frac{\left(^{26} C_{2}+^{4} C_{2}\right)}{^{52} C_{2}} \)
B. \( \frac{\left(^{26} C_{2}+^{4} C_{2}-^{2} C_{2}\right)}{^{52} C_{2}} \)
\( ^{\mathrm{c}} \cdot \frac{30}{^{52} C_{2}} \)
D. \( \frac{39}{52} C_{2} \)


A body is in equilibrium under the influence of a number of forces. Each
force has a different line of action. The
minimum number of forces required is :
This question has multiple correct options
A. 2 , if their lines of action pass through the centre of mass of the body
B. 3, if their lines of action are not parallel.
\( \mathrm{c} .3 \), if their lines of action are parallel
D. \( 4, \) if their lines of action are parallel and all the forces have the same magnitude


The ether which on hydrolysis gives single product is:
A. phenetol
B. tetrahydrofuran
c. anisole
D. all of the above


Definition of thermodynamic?


Which of the following parameter can
be used in the measurement of the
speed of a reaction?
A. Pressure
B. Concentration
c. Volume of gas given off
D. Particle size


The minimum potential difference between the base and emitter required
to switch a silicon transistor \( O N \) is
approximately
\( \mathbf{A} \cdot 1 V \)
B. \( 3 V \)
c. \( 5 V \)
D. \( 4.2 V \)


The probability that a student \( x \)
participates in a competition is 0.4
while that for student \( y \) is \( 0.5 . \) The
probability that \( x \) participates in
competition, given that \( y \) also
participates is \( 0.7 . \) Then This question has multiple correct options
A. The probability that both \( x \) and \( y \) participates in that competition simultaneously is 0.35
B. The probability that \( y \) participates in that competition given that \( x \) also participates is \( \frac{7}{8} \)
C. The probability that atleast one of them participates in that competition is 0.55
D. The probability that exactly one of them participates in that competition is 0.20


In an isosceles trapezium, the length of one of the parallel sides, and the lengths of the non-parallel sides are all equal to
\( 30 . \) In order to maximize the area of the
trapezium, the smallest angle should be
A \( \cdot \frac{\pi}{6} \)
B.
\( c \cdot \frac{\pi}{3} \)
D.


How many of the following statements
are correct?
This question has multiple correct options
A. In crystalline compounds of group- 2 , number of molecules of water of crystallization generally decreases as the ions become larger.
B. As the electropositive character of alkali metals increase down the group, the stabilities of their carbonates and hydrogen carbonates increases.
C. The oxide and hydroxide of beryllium are amphoteric in nature
D. \( B e C l_{2} \) has a chain structure in vapour phase and in solid state tends to form a chloro-bridged dimer
E. Alkaline earth metal nitrates on heating decompose \( \operatorname{giving~both} N O_{2} \) and \( O_{2} \)
F. The crystal structures of \( N a H C O_{3} \) and \( K H C O_{3} \), both show hydrogen bonding.


A parallel plate capacitor of plate
separation 2 mm is connected in an electric circuit having source voltage \( 400 V . \) What is the value of the
displacement current for \( 10^{-6} \) second if
the plate area is \( 60 \mathrm{cm}^{2} . ? \)


The factor or process which best explain the rise of water from roots \( (100 \mathrm{mts}) \) to
the top of tree is
A. Break down of ATP
B. Root pressure
c. capillary rise of water in xylem
D. cohesion of water and transpiration pull


Bricks measuring \( 40 \mathrm{cm} \times 5 \mathrm{cm} \times \)
\( 7 \mathrm{cm} \) are to be painted. If there are 60
bricks, find the total area to b painted.


Which of the following hormones is used in root formation on stem cutting?
A. Kinetin
B. GAA
c. ABA
\( D \cdot \) IBA


The number of intersection points of diagonals of 2009 sides polygon, which lie inside the polygon.
A \( .^{2009} \mathrm{C}_{4} \)
В. \( 2009 \mathrm{C}_{2} \)
c. \( 2008 C_{4} \)
D. \( 2008 \mathrm{C}_{2} \)


Simplify: \( y(x-2 y)^{2}-13+4(x-1) \)


Rutherford experiment of scattering of \( \alpha \) -particles shows for the first time that
the atom has:
A. proton
B. nucleus
c. electron
D. neutron


Given \( \boldsymbol{x}-\boldsymbol{y}+\mathbf{3} \boldsymbol{z}=\mathbf{5} ; \mathbf{4} \boldsymbol{x}+\mathbf{2} \boldsymbol{y}-\boldsymbol{z}=\mathbf{0} \)
\( ;-\boldsymbol{x}+\mathbf{3} \boldsymbol{y}+\boldsymbol{z}=\mathbf{5} \)
If
\( \mathbf{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{- 1} & \mathbf{3} \\ \mathbf{4} & \mathbf{2} & -\mathbf{1} \\ -\mathbf{1} & \mathbf{3} & \mathbf{1}\end{array}\right], \boldsymbol{X}=\left[\begin{array}{l}\boldsymbol{x} \\ \boldsymbol{y} \\ \boldsymbol{z}\end{array}\right], \boldsymbol{D}= \)
\( \left.\begin{array}{l}\mathbf{5} \\ \mathbf{0} \\ \mathbf{5}\end{array}\right\} \) such that \( \mathbf{A X}=\mathbf{D} \)
Show that \( A \) is non singular and the
cofactor elements of a matrix \( \boldsymbol{A} \) is
\( \left[\begin{array}{ccc}+(2+3) & -(4-1) & +(12+2) \\ -(-1-9) & +(1+3) & -(3-1) \\ +(1-6) & -(-1-12) & +(2+4)\end{array}\right) \)


Which of the following rules is not correct regarding IUPAC nomenclature of complex ions?
A. Cation is named first and then anion
B. In coordination sphere, the ligands are named alphabetically.
c. Positively charged ligands have suffix 'ate'
D. More than one ligand of a particular type are indicated by using di, trii, tetra, etc.


Electronic configuration of \( G a \) is
A \( \cdot[H e] 2 s^{2} 2 p^{1} \)
В \( \cdot[N e] 3 s^{2} 2 p^{1} \)
\( \mathbf{c} \cdot[K r] 4 d^{10} 5 s^{2} 5 p^{1} \)
\( \mathbf{D} \cdot[A r] 3 d^{10} 4 s^{2} 4 p^{1} \)


Cataract is a condition of eye when:
A. eye sight becomes foggy
B. eye lens becomes cloudy
C. there is a loss of vision
D. all of the above


A student performs an experiment for determination of \( \left(g=\frac{4 \pi^{2} l}{T^{2}}\right), \mid=1 \mathrm{m} \)
and he commits an error of \( \Delta l \) For T he
takes the time of \( n \) oscillations with the
stop watch of least count \( \Delta \boldsymbol{T} \) and he
commits a human error of 0.1 s. For
which of the following data, the
measurement of \( g \) will be most
accurate?
A. \( \Delta L=0.5, \Delta T=0.1, n=20 \)
B . \( \Delta L=0.5, \Delta T=0.1, n=50 \)
c. \( \Delta L=0.5, \Delta T=0.01, n=20 \)
D. \( \Delta L=0.5, \Delta T=0.05, n=50 \)


Which of the following orbitals is not
cylindrically symmetrical about \( z \) -axis?
\( \mathbf{A} \cdot 3 d_{22} \)
в. \( 4 p_{z} \)
\( c \cdot 6 s \)
D. \( 3 d_{y_{z}} \)


The ages of \( A \) and \( B \) are in the ratio 8: 3
Six years hence, their ages will be in the ratio 9: 4 Find the sum of their present
ages.


Which of the following are related with photorespiration?
A. spherosome
B. Lysosomes
c. Glyoxysomes
D. Peroximomes


Which of the following organic compounds has same hybridization as
its combustion product, \( C O_{2} ? \)
A. Ethane
B. Ethyne
c. Ethene
D. Ethanol


A, \( B, C \) are three elements with atomic
numbers, Z-1, Z and Z+1 respectively. B is an inert gas. Identify the elements having same valence shell.
\( A \cdot A, B \)
B. В, с
c. \( A, C \)
D. A, B, C


Which of the following concentration terms are independent of temperature? This question has multiple correct options
A. Mass \%
B. Molality
c. Mole fraction
D. Molarity


A galvanometer of number of turns 175
having \( 1 \mathrm{cm}^{2} \) area, turns through \( 1^{\circ} \)
when a current of \( 1 m A \) is passed. Find
magnetic field if torsional constant of spring is \( 10^{-6} N-m \)
A \( \cdot 10^{-4} T \)
B. \( 10^{-3} T \)
c. \( 10^{-5} T \)
D. \( 10^{-2} T \)


If \( a^{2}-5 a-1=0 \) and \( a \neq 0 ; \) find:
\( (i) a-\frac{1}{a} \)
\( (\mathrm{ii}) \boldsymbol{a}+\frac{\mathbf{1}}{\boldsymbol{a}} \)


Most solid materials are classified as
insulators why?
A. They offer large resistance to the flow of electric current
B. They doesnt do anything
c. They offer large force to other particles
D. None


Organisms undergo processes that require energy and produce energy. Processes such as photosynthesis,
cellular respiration, reproduction, and movement are just a few of these
processes. Which of these best
describes the energy available to do cellular work?
A. Heat
B. Free energy
c. Potential energy
D. Kinetic energy


The curved surface area of a
hemisphere is \( 77 \mathrm{cm}^{2} \). The radius of the
hemisphere is :
\( \mathbf{A} \cdot 3.5 \mathrm{cm} \)
в. \( 7 \mathrm{cm} \)
c. \( 10.5 \mathrm{cm} \)
D. \( 11 \mathrm{cm} \)


Antimony and Arsenic belong to the
category of
A. metals
B. metalloids
c. non-metals
D. minerals


For an ellipse with axes are coordinate axes, \( A \) and \( L \) are the ends of major axis and latusrectum respectively. Area of \( \triangle O A L=8 s q . \) units and, \( e=\frac{1}{\sqrt{2}}, \) then
equation of the ellipse is:
\( ^{\text {A }} \cdot \frac{x^{2}}{16}+\frac{y^{2}}{8}=1 \)
B. \( \frac{x^{2}}{32}+\frac{y^{2}}{16}=1 \)
c. \( \frac{x^{2}}{64}+\frac{y^{2}}{32}=1 \)
D. \( \frac{x^{2}}{8}+\frac{y^{2}}{4}=1 \)


In pachytene stage of meiosis, the chromosomes appear
A. single stranded
B. Double stranded
c. Three stranded
D. Four stranded


The vector \( \vec{P} \) makes \( 120^{\circ} \) with the \( x- \)
axis and the vector \( \vec{Q} \) makes \( 30^{\circ} \) with \( \boldsymbol{y}- \) axis. What is the resultant vector?
A. \( P+Q \)
в. \( P-Q \)
c. \( \sqrt{P^{2}+Q^{2}} \)
D. \( \sqrt{P^{2}-Q^{2}} \)


Assertion
In the measurement of physical quantities direct and indirect methods
are used.
Reason
The accuracy and precision of
measuring instruments along with
errors in measurements should be
taken into account, while expressing
the result.
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


11 men can dig \( 6 \frac{3}{4} \) metre long trench in one day. How many men should be employed for digging 27 metre long trench of the same type in one day?


The compound \( ^{\prime} C^{\prime} \) in the following
reaction is :
\( \boldsymbol{C}_{7} \boldsymbol{H}_{8} \frac{3 C l_{2} / \text {Delta}}{\longrightarrow} \boldsymbol{A} \frac{\boldsymbol{B r}_{2} / \boldsymbol{F e}}{\boldsymbol{\beta}} \boldsymbol{B} \frac{\boldsymbol{Z n} / \boldsymbol{H C l}}{\boldsymbol{1}} \)
\( C \)
A. o-bromotoluene
B. m-bromotoluene
c. p-bromotoluene
D. 3-bromo-2, 4, 6-trichlorotoluene


If \( y=\sqrt{\frac{1-x}{1+x}} \) then \( \frac{d y}{d x} \) equals-
A \( \cdot \frac{y}{1-x^{2}} \)
в. \( \frac{y}{x^{2}-1} \)
c. \( \frac{y}{1+x^{2}} \)
D. \( \frac{y}{y^{2}-1} \)


A ball is vertically downwards with a speed of \( 6 \mathrm{m} / \mathrm{s} \) from a hight of \( 3.2 \mathrm{m} . \) It strikes a horizontal floor and rebounds
back to the same height. The value of corfficient of restitutions
\( (e) \) is :
A. 0.5
B. 0.6
\( c .0 . \)
D. 0.8


Using the method of integraton find the area of the region bounded by lines:
\( 2 x+y=4,3 x-2 y=6 \) and \( x-3 y+ \)
\( 5=0 \)


In joly's differential steam calorimeter,
3 g of an ideal gas is contained in a rigid closed sphere at 20 The sphere is
heated by steam at 100 and it is found that an extra


The IUPAC name of the compound
glycerine is:
A .1,2,3 -trihydroxy propane
B. 3-hydroxy pentane-1,5-diol
c. 1,2,3 -hydroxy propane
D. propane-1,2,3-triol


Subtract \( 5 x y \) from \( 8 x y \)


If the roots of the equation \( 4 x^{3}-12 x^{2}+ \)
\( 11 x+k=0 \) are in A.P. Then \( k= \)
A . -3
B.
\( c \cdot 2 \)
D. 3


The Blackman's law of limiting factor is an elaboration of
A. Liebig's law of minimum.
B. Hatch and Slack mechanism.
c. sach's cardinal points.
D. None of the above


A cubical box has each edge \( 10 \mathrm{cm} \) and
another cuboidal box is \( 12.5 \mathrm{cm} \) long, 10
cm wide and \( 8 \mathrm{cm} \) high.
i) Which box has the greater lateral
surface area and by how much?
ii) Which box has the smaller total
surface area and by how much?


How much ice must be added to 100 g water at 30 Celsius in order to reduce its
temperature to 20 Celsius?
\( A \cdot 108 \)
B. 80g
c. \( 400 \mathrm{g} \)
D. None of these


Two point charges \( 4 \mu C \) and \( -6 \mu C \) are
seperated by a distance of \( 10 \mathrm{cm} \) in air.
At what point between the charges on the line joining the charges is the potential zero.


With respect to oxygen maximum oxidation state is shown
by
A. Halogen family
B. Oxygen family
c. Nitrogen family
D. Boron family


\( H C l \) is prepared by heating \( N a C l \) with
conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) but \( \boldsymbol{H} \boldsymbol{I} \) cannot be
prepared by treating \( N a I \) with conc.
\( H_{2} S O_{4} \). Identify the reason.
A \( \cdot H_{2} S O_{4} \) is oxidised by \( H I \) and not oxidised by \( H C l \)
B. \( H I \) is oxidised by \( H_{2} S O_{4} \) and \( H C l \) is not oxidised by \( H_{2} S O_{4} \)
C. \( H I \) dissociates on treatment with \( H_{2} S O_{4} \) and \( H C l \) does not dissociate.
D. The reaction of \( H_{2} S O_{4} \) with \( H I \) Is reversible whereas with \( H C l \) is irreversible


A ball of mass \( 50 \mathrm{g} \) is dropped from a height \( h=10 \mathrm{m} . \) It rebounds losing 75 percent of its total mechanical energy. If it remains in contact with the ground
for \( \triangle \boldsymbol{t}=\mathbf{0 . 0 1} \) sec, find the impulse of
the impact force.


Froth floatation process is used for the concentration of sulphide ores. This is an illustration of the practical application of:
A. Adsorption
B. Absorption
c. Sedimentation
D. coagulation


\( 2 \mathrm{Mg}(s)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{MgO}(s) \)
If 48.6 grams of magnesium are placed in a container with 64 grams of oxygen gas and the reaction above proceeds to completion, what is the mass of MgO(s) produced?
A. 15.4 grams
B. 32.0 grams
c. 80.6 grams
D. 96.3 grams
E . 112 grams


The mirror used in automobiles to see
the rear field of view is
A. concave
B. convex
c. plane
D. none of these


is polymorphic cell organelles.
A. Ribosome
B. Lysosome
c. chloroplast
D. Nucleus


Arsenic drugs are mainly used in the
treatment of:
A. Jaundice
B. Typhoid
c. syphilis
D. Cholera


"Ag dissolves in dilute \( H N O_{3} \) yielding
a colorless gas." Answer whether the above statement is
true or false.
If true enter 1 , else enter 0 .


Which one of the following is a matching pair?
A. Lub - sharp closure of AV valves at the beginning of ventricular systole
B. Dup- - Sudden opening of semilunar valves at the beginning of ventricular diastole
C. Pulsation of the radial artery - Valves in the blood vessels
D. Initiation of the heart beat - Purkinje fibres


Cycas stem has mucilagenous canals which are
A. Schizogenous
B. Schizolysigenous
c. Lysigenous
D. Both A and B


Add: \( 3 a-2 b, 10 a-4 b,-2 a+5 b \)


What are the main feature of
Mendeleev's periodic table?


Does the principle of conservation of energy hold for interference and
diffraction phenomena? Explain briefly.


A bomb travelling in a parabolic path under the effect of gravity, explodes in mid-air. The centre of mass of
fragments will:
A. Move vertically upwards and then downwards
B. Move vertically downwards
c. Move in irregular path
D. Move in the parabolic path the unexploded bomb would have travelledd


Assertion: Zinc is coated on the iron to
prevent corrosion in a process called galvanization. Reason: Zinc is a stronger reducing agent than iron and is more easily oxidized than iron.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false


The type of asexual reproduction found in Hydra is
A. multiple fission
B. budding
c. sporulation
D. binary fission
E. gemmule formation


The perpendicular distance from the origin to the plane containing the two lines, \( \frac{\boldsymbol{x}+\mathbf{2}}{\mathbf{3}}=\frac{\boldsymbol{y}-\mathbf{2}}{\mathbf{5}}=\frac{\boldsymbol{z}+\mathbf{5}}{\mathbf{7}} \) and \( \frac{\boldsymbol{x}-\mathbf{1}}{\mathbf{1}}= \)
\( \frac{\boldsymbol{y}-\boldsymbol{4}}{\boldsymbol{4}}=\frac{\boldsymbol{z}+\boldsymbol{4}}{\boldsymbol{7}} \) is :
A \( \cdot \frac{11}{\sqrt{6}} \)
B. \( 6 \sqrt{11} \)
c. 11
D. \( 11 \sqrt{6} \)


In the reaction \( q_{(p)=} \Delta E+P \Delta V ; \Delta E \)
refers to
A. internal energy of the system
B. heat content of the system
c. change in internal energy
D. change in the heat content


In which species does the specifed atom have an incomplete outer shell?
A. \( B F_{3} \) (B)
B. \( C H_{3}^{-}(\mathrm{C}) \)
\( \mathrm{c} \cdot F_{2} \mathrm{O}(\mathrm{F}) \)
D. \( H_{2} O^{+}(0) \)


Which among the following sets of compounds is used as raw material for the preparation of sodium carbonate by
solvay process?
A. \( N a O H, H C l, C O_{2} \)
в. \( N H_{4} C l, H_{2} O, N a C l \)
c. \( N a C l, N H_{3}, C a(O H)_{2} \)
D. \( N a C l, C a C O_{3}, H_{2} S O_{4} \)


One mole of \( H N O_{3} \) absorbs 5 moles of
electrons in a redox reaction. The
reduced product of this reaction is :
A. 1 mole \( N_{2} \)
B. 1 mole \( N_{2} \) O
c. 1 mole \( N O_{2} \)
D. 1 mole \( N H_{3} \)


For which of the following substances, the magnetic susceptibility is independent of temperature:
A. diamagnetic
B. ferromagnetic
c. paramagnetic
D. diamagnetic and ferromagnetic


Each side of a cube is measured to be
\( 5.402 \mathrm{cm} . \) Find the total surface area
and volume of the cube in appropriate significant figures.


The term reverberation time is generally understood to be the reverberation time
at which of the following frequencies?
A . \( 1024 \mathrm{Hz} \)
B . 2048 Hz
c. 512 \( \mathrm{H} \)
D. 256Hz


Create a poster/flowchart to depict all that you have learnt in this chapter
about plant tissues.


If the compound interest on a certain sum for three years at \( 10 \% \) is Rs. 993 What would be the simple interest on the same sum at the same rate for the
same time?
A . Rs. 930
B. Rs. 920
c. Rs. 900
D. Rs. 890


Write the answer in one sentence each:
Where did the grinding of food in Grasshopper?


Boron trifluoride \( \left(B F_{3}\right) \) has no dipole
moment \( (\mu=0 D) . \) Explain how this
observation confirms the geometry of
\( B F_{3} \) predicted by VSEPR theory.


Which of the following characteristics
must remain constant for undamped oscillations of the particle?
A. acceleration
B. phase
c. amplitude
D. velocity


The efficiency of a transformer is \( 98 \% \) The primary voltage and current are \( 200 V \) and \( 6 A . \) If the secondary voltage is \( 100 V \), the secondary current is :
A . \( 11.76 A \)
B. \( 12.25 A \)
c. \( 3.06 A \)
D. \( 2.94 A \)


How many times does an AC electric
current of frequency \( 50 \mathrm{Hz} \) change its direction?
A . 25
B. 50
\( c \cdot 100 \)
D. 200


The lightest element in the world is?
A. Oxygen
B. Helium
c. Hydrogen
D. Chlorine


Which of the following represents the
oxidation half-reaction for the
unbalanced redox equation?
\( \boldsymbol{C u}+\boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \rightarrow \boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{2}+\boldsymbol{N} \boldsymbol{O}_{2} \)
A \( \cdot C u^{2+}+2 e^{-} \rightarrow C u \)
в. \( C u \rightarrow C u^{2+}+2 e^{-} \)
c. \( N O_{3}^{-} \rightarrow N O_{2}+1 e \)
D. \( 2 H^{+}+N O_{2}^{-}+1 e^{-} \rightarrow N O_{2}+H_{2} O \)


f \( p, q \) and \( r \) in \( A P \), then prove that \( (p+ \) \( \mathbf{2} \boldsymbol{q}-\boldsymbol{r})(\boldsymbol{2} \boldsymbol{q}+\boldsymbol{r}-\boldsymbol{p})(\boldsymbol{r}+\boldsymbol{p}-\boldsymbol{q})=\boldsymbol{4} \boldsymbol{p} \boldsymbol{q} \boldsymbol{r} \)


Factorize the following expressions:
\( 2 x+6 \)


Many grain products, including cereals and others that identify themselves as a 'source of iron' list something called reduced iron' among the ingredients. To which of the following would the term reduced iron' most likely be referring?
A. Compounds containing iron (III) ions
B. Compounds containing iron (II) ions
c. Iron metal
D. oxides of iron


Is demineralised or distilled water
useful for drinking purposes? If not, how can it be made useful?


A ray of light makes an incident angle half as that of the angle that it makes with the surface of reflection. Find the
angle of reflection for this ray.
A \( .90^{\circ} \)
B . \( 0^{\circ} \)
\( c \cdot 30^{\circ} \)
D. \( 60^{\circ} \)


The length, I metres, of a garden is 78.5
metres, correct to the nearest half
metre. Complete this statement about
the value of I.
\( \leq 1< \)


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


A body is acted on by a force given by \( \boldsymbol{F}=(\mathbf{1 0}+\mathbf{2 t}) \mathrm{N} . \) The impulse received
by the body during the first four seconds is :
A . \( 40 \mathrm{N} \) s
B. 56 N s
c. 72 N s
D. 32 N s


Explain parallax method for measuring distance of a nearly star


Assertion
Let \( \boldsymbol{f} \) and \( \boldsymbol{g} \) be increasing and
decreasing function respectively from
\( [\mathbf{0}, \infty] \) to \( [\mathbf{0}, \infty] . \) Let \( h(\boldsymbol{x})=\boldsymbol{f}(\boldsymbol{g}(\boldsymbol{x})) . \) If
\( h(0)=0, \) then \( h(x) \) is always zero
Reason
\( h(x) \) is an increasing function of \( x \)
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


In the pulley-block arrangement shown
in figure. Find relation between \( \boldsymbol{a}_{\boldsymbol{A}}, \boldsymbol{a}_{\boldsymbol{B}} \)
and \( \boldsymbol{a}_{C} \)
\( \mathbf{A} \cdot a_{A}+2 a_{B}+a_{C}=0 \)
в. \( 2 a_{A}+a_{B}+a_{C}=0 \)
c. \( a_{A}+a_{B}+2 a_{C}=0 \)
D. \( a_{A}+a_{B}+a_{C}=0 \)


A man of mass \( m \) moves on a plank of
mass \( M \) with a constant velocity \( u \) with
respect to the plank. as shown in Fig.
a) If the plank rests on a smooth
horizontal surface, determine the
velocity of the plank.
b) If the man travels a distance \( L \) with
respect to the plank, find the distance
travelled by the plank with respect to the ground.


Match the column I with column II and
mark the appropriate choice.
Column I
(i) Saturated
(A) Liquid \( \leftrightarrow \) Vapour
(B) Solid \( \leftrightarrow \) Liquid
(ii) Boiling point
(C) Solid \( \leftrightarrow \)
(iii) Sublimation vapour \( \quad \) point
(D) Solute
\( (s) \leftrightarrow \)
(iv) Melting point Solute(solution)
\( A \cdot(A)-(i),(B)-(i i i),(C)-(i i),(D)-(i v) \)
B. (A) - (ii), (B) - (iv), (C) - (iii), (D) - (i)
C. \( (A)-(i v),(B)-(i i),(C)-(i),(D)-(i i i) \)
D. (A) - (iii), (B) - (iv), (C) - (ii), (D) - (i)


Earth radius is \( \boldsymbol{R} \) and spin angular
velocity of Earth is \( \omega . \) At what height
above the North pole the acceleration
due to gravity will be same as that at
the equation? \( (g \) is acceleration due to
gravity at North pole).


Which of the following electronic configuration is impossible?
A \( \cdot 1 s^{2}, 2 s^{2}, 2 p^{6} \)
B . \( 1 s^{2}, 2 s^{2}, 2 p^{7} \)
\( \mathrm{c} \cdot 1 s^{2}, 2 s^{2} \)
D. \( 1 s^{2}, 2 s^{2}, 2 p^{5} \)


If 0.5 mole of silver salt is taken and the
weight of residue obtained is 216 g. \( (\mathrm{Ag} \) \( =108 \mathrm{g} / \mathrm{mol} \) ).Than which the following
is correct?
\[
\begin{array}{c}
C_{2} H_{3} \\
(C \quad H-C O O H)_{3}+ \\
C_{2} H_{3} \\
A g N O_{3}(E x c e s s) \longrightarrow S i l v e r s a l t \longrightarrow \\
A g(m e t a l)
\end{array}
\]
\( \mathbf{A} \cdot n=4 \)
B \( . n=2 \)
C. M.wt. of silver salt is 718 g/mol
D. M.wt. of silver salt is \( 388 \mathrm{g} / \mathrm{mol} \)


Lenticels are found in
A. The stem in which secondary growth has taken place
B. The root where secondary growth has occurred
C. The roots as well as the stem where secondary growth has occurred
D. None of these


Identify the correct statement.
A. Static friction depends on the area of contact.
B. Kinetic friction depends on the area of contact.
C. Coefficient of static friction does not depend on the surface in contact.
D. Coefficient of kinetic friction is less than the
coefficient of the static friction.


A metal oxide is reduced by heating it in a stream of hydrogen. It is found that after complete reduction, 3.15 g of the oxide have yielded 1.05 g of the metal. We may conclude that:
A. atomic mass of the metal is 4
B. atomic mass of the metal is 8
c. equivalent mass of the metal is 4
D. equivalent mass of the metal is 8


Find the mode of the following data
1) 74,81,62,58,77,74
2) 43,36,27,25,36,66,20,25
3) 55,51,62,71,50,32
4) 24,20,27,32,20,28,20


Match column A with column B and
select the correct option:
Column A
(Ore) Column B
(Nature of
ore)
(a)
\( (b) \)
(a) Copper
glance
\( (c) \)
\( b(i i), c(i i i), d(i v) \)
\( \mathbf{A} \cdot \mathbf{a}(\mathbf{i}) \)
,
B. \( a(\text { iv }), b(\text { ii) }, c(\text { iii), } d(i) \)
\( \mathbf{c} \cdot \mathbf{a}(\text { iii }), b(\text { iv }), c(\text { ii }), d(i) \)
D. \( a(\text { iv }), b(i), c(i i), d(\text { iii }) \)


The equation of a transverse wave is \( \boldsymbol{y}=\boldsymbol{a} \sin 2 \boldsymbol{\pi}[\boldsymbol{t}-(\boldsymbol{x} / \mathbf{5})], \) then the ratio of
maximum particle velocity and wave velocity is :
A \( \cdot \frac{2 \pi a}{\sqrt{5}} \)
в. \( \frac{2 \pi a}{5} \)
\( c \cdot \frac{a}{5} \)
D. \( 2 \pi a \sqrt{5} \)


The electron with The electron with de
Broglie wavelength \( \lambda \) is bombarded on a metal target. Found that photons are emitted through de Broglie wavelength.


A neutron of energy 1 Me \( V \) and mass
\( 1.6 \times 10^{-27} \) kg passes a proton at such
a distance that the angular momentum of the neutron relative to the proton approximately equals \( 10^{-33} \mathrm{J} \) s. The distance of closest approach neglecting the interaction between particles is
A. \( 0.44 n m \)
B. \( 0.44 m m \)
c. \( 0.44^{\circ} \)
D. \( 0.44 f m \)


Define acceleration due to gravity


The coordinate that the chord \( x \cos \alpha+ \)
\( \boldsymbol{y} \sin \boldsymbol{\alpha}-\boldsymbol{p}=\mathbf{0} \) of \( \boldsymbol{x}^{2}+\boldsymbol{y}^{2}-\boldsymbol{a}^{2}=\mathbf{0} \) may
subtend a right angle at the centre of the circle is?
A \( \cdot a^{2}=2 p^{2} \)
B \( \cdot p^{2}=2 a^{2} \)
c. \( a=2 p \)
D. \( p=2 a \)


Assertion
A charge moving in a circular orbit can
produce electromagnetic wave.
Reason
The source of electromagnetic wave
should be in accelerated motion.
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 armature of a generator of resistance \( 1 \Omega \) is rotated at its rated
speed and produces \( 125 V \) without load
and \( 115 V \) with full load. The current in
the armature coil is
\( \mathbf{A} \cdot 240 A \)
в. \( 10 A \)
\( c .1 A \)
D. \( 2 A \)


If a body is acted upon by a constant
force then it will have a uniform
A. velocity
B. acceleration
c. inertia
D. momentum


Thorns with leaves and flowers are
found in
A. Bougainvillea
B. Carissa
c. Duranta
D. Artabotrys


What is a pressure on the smaller piston if both the pistons are at same
horizontal level? (Take \( \left.\boldsymbol{g}=\mathbf{1 0 m} \boldsymbol{s}^{-2}\right) \)
\( A \cdot 3 P a \)
В. \( 4 \times 10^{3} P a \)
\( \mathbf{c} \cdot 6 \times 10^{5} P a \)
D. 1000 Pa


The vertices of a convex polygon point
are
A. outwards
B. inwards
c. middle
D. extreme corner


The focal lengths of the eyepiece and an objective lens of a compound microscope are \( 10 \mathrm{cm} \) and \( 20 \mathrm{cm} \) respectively. if the length of the tube is \( 100 \mathrm{cm}, \) what is the magnification obtained at the least distance of
distinct vision?
A . 25
в. 17.5
c. 50
D. 60


A ball thrown in the air reaches a height of \( 10 \mathrm{m} \) and drops down to the ground. Find the time taken by the ball to complete this entire journey.
A . \( 2.78 \mathrm{sec} \)
B. 3.40 sec
c. 1.43 sec
D. 2.86 sec


Assertion
STATEMENT-1
The total translational kinetic energy of all the molecules of a given mass of an ideal gas is 1.5 times the product of its pressure and its volume
Reason
STATEMENT-2
The molecules of a gas collide with each
other and the velocities of the
molecules change due to the collision.
A. Statement-1 is True, Statement-2 is True; Statement- is a correct explanation for Statement- -
B. Statement- - is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-
c. Statement- - 1 is True, Statement- 2 is False
D. Statement- - is False, Statement-2 is True


Compute the work which must be performed (in \( K g f-m \) ) to slowly
pump water out of a hemispherical reservoir of radius \( \boldsymbol{R}=\mathbf{0 . 6 m} \)


In girls, the muscles of the body grow more prominently than in the boys.
A. True
B. False


Nitrogen can be obtained by thermal decomposition of ammonium dichromate.
A. True
B. False


Statement I: Cl and Na form an ionic
bond.

Statement II: Cl donates an electron to
Na.
A. Statement I is True, Statement II is True and statement II is correct explanation of statements
B. Statement I is True, Statement II is True and statement II is NOT correct explanation of statements
C. Statement I is True, Statement II is False
D. Statement I is False, Statement II is True
E. Statement I is False, Statement II is False


One angle of a triangle is \( 78^{\circ} \) and the
other two angles are in the ratio 7: 10 Calculate the bigger angle of the triangle.


Hydrogen gas will not reduce:
A. heated cupric oxide
B. heated ferric oxide
C. heated stannic oxide
D. heated aluminium oxide


A cylinder of radius \( 12 \mathrm{cm} \) contains
water upto the height of \( 20 \mathrm{cm} . A \)
spherical iron ball is dropped into the cylinder and thus water level is raised by \( 6.75 \mathrm{cm} \) what is the radius of the ball?


\( \ln \mathrm{F}_{2} \) generation, quantitative
inheritance ratio \( 1: 4: 6: 4: 1, \) is
obtained instead of
\( A \cdot 9: 3: 3: 1 \)
B. 8: 6: 4: 1
c. 7: 4: 1: 4
D. 6: 6: 4: 7


When a light ray falls on a perfectly reflective mirror at an angle. Identify which of the following statement is true about the ray?
A. The frequency of the light ray changes
B. The wavelength of the light ray changes
C. The velocity of the light ray changes
D. The period of the light ray changes
E. The direction of motion of the light ray changes


Write the formula terminal velocity


An equiconvex lens is cut into two
halves a long (i) \( \mathrm{XOX} \) and (ii) YOY as
shown in the figure let \( f . f^{\prime}, f^{\prime \prime} \) be the
focal lengths of the complete lens of each half in case (i) and of each half in
case (ii) respectively Choose the correct statement from the
following:
\( \mathbf{A} \cdot f^{\prime}=f, f^{\prime \prime}=f \)
B. \( f^{\prime}=2 f, f^{\prime \prime}=2 f \)
C . \( f^{\prime}=f, f^{\prime \prime}=2 f \)
D. \( f^{\prime}=2 f, f^{\prime \prime}=f \)


The rate of reaction between \( A \) and \( B \)
increases by a factor of \( 100, \) when the concentration of \( A \) is increased 10
folds. The order of reaction with respect
to \( \boldsymbol{A} \) is:
A . 10
B. 2
\( c \cdot 1 \)
D. 20


Beaked, syngenesious anthers and epipetalous stamens are found in
A . Liliaceae
B. Solanaceae
c. compositae
D. Malvaceae


Two masses \( A \) and \( B \) of \( 10 \mathrm{Kg} \) and \( 5 \mathrm{Kg} \) respectively are connected with a string passing over a frictionless pulley at a
corner of a table a shown in the
adjoining diagram. The coefficient of friction of \( A \) with the table is \( 0.2 . \) The
minimum mass of \( C \) that may be placed on \( A \) to prevent it from moving is equal
to?


A hot body placed in the air is cooled according to Newton's law of cooling. The rate of decrease of the temperature
being k times the temperature difference from the surroundings, starting from \( t=0, \ln \frac{\ln (x)}{k} \) time, the body will lose half the maximum
temperature it can lose. Find the value
of \( \boldsymbol{x} \)


The least positive integral value of \( x \) which satisfies the in equality \( ^{10} C_{x-1}>2 .^{10} C_{x} \) is
A. 7
B. 8
c. 9
D. 10


If the molar heat capacity of a gas in the process \( P T=c o n s t a n t \) is \( 5 R \), the
number of degrees of freedom of molecules in the gas is
A . 4
B. 5
\( c .6 \)
D.


Who defined element as basic form of
matter that cannot be broken down into
simpler substances by chemical reactions?
A. Wilhelm weins
B. William J. Crooke
c. Antonie L. Lavoisier
D. Carl Bosch


If \( \cos B=\frac{1}{3}, \) find the other five
trigonometric ratios


Three isotopes of oxygen, each containing 8,9,10 neutrons respectively has the \( \% \) of one isotope (containing 8 neutrons) \( 90 \% . \) The abundance of other
isotopes is :
(The atomic weight of oxygen is 16.12 )
A . 7\%, 3\%
B. 5\%, 5\%
c. 8\%, २\%
D. none of these


Find the area of the region included
between
the parabola \( y=x^{2}+3 \) and the line
\( \boldsymbol{y}=\boldsymbol{x}+\boldsymbol{3} \)


The \( \mathrm{S} \) in buna-S refers to:
A. sulphur
B. styrene
\( c . \) sodium
D. salicylate


During ventricular diastole
A. The auricles relax
B. The heart contracts
C. The heart pumps blood
D. The ventricles relax


Which type of chemical mechanism is followed by an antacid?
A. rearrangement
B. neutralization
c. condensation
D. none of these


In a potentiometer experiment the balancing with a cell is at length 240 \( \mathrm{cm} . \) On shunting the cell with a resistance of \( 2 \Omega \) the balancing length
becomes \( 120 \mathrm{cm} . \) The internal
resistance of the cell is?
A . \( 1 \Omega \)
в. \( 0.5 \Omega \)
\( c .4 \Omega \)
D. \( 2 \Omega \)


The mitral valve is supported by
A. Bundle of Hiss
B. Ductus Arteriosus
c. Foramen ovale
D. chordae tendineae


The pH of a carbonated drink is
A. less than 7
B. more than 7
c. equal to 7
D. approximately 7.8


Conversion of pyruvic acid into ethyl alcohol is mediated by
A. Phosphatase
B. Dehydrogenase.
c. Decarboxylase and dehydrogenase.
D. catalase.


Given below is a diagram of electrostatic precipitator. Identify \( \mathbf{A}, \mathbf{B} \)
\( \mathrm{C} \) and \( \mathrm{D} \) and select the correct option.
A. A- Negatively charged wire, B- Negatively charged dust particles, C- - Discharge corona, D- collection
B. A- Negatively charged wire, B- Discharge corona, CCollection plate, D- Negatively charged dust particles
c. A- Positively charged wire, B- Positively charged dust particles, C- Discharge corona, D- -collection plate
D. A-Positively charged wire, B- Discharge corona, CCollection plate, D- Positively charged dust particles


Two forces, each of magnitude \( F, \) act at
points \( V \) and \( W \) on an object.

The two forces form a couple. The shape
of the object is a right-angled triangle with sides of
lengths \( x \) and \( y, \) as shown.
Which expression gives the torque
exerted by the couple?
\( \mathbf{A} \cdot F x \)
B. \( F y \)
\( \mathbf{c} \cdot 2 F x \)
D. \( 2 F y \)


The bisectors of angles of a
parallelogram makes a figure which is
A. rectangle
B. circle
c. pentagon
D. octagon


What the movement of solid particles caused by collisions with the constantly moving molecules of a gas is called?


A man \( 1.5 \mathrm{m} \) tall walks away from a
lamp post \( 4.5 \mathrm{m} \) high at the rate of 4 km/hr. How fast is the farther end of
shadow moving on the pavement
A. \( 4 \mathrm{km} / \mathrm{hr} \)
B. \( 2 \mathrm{km} / \mathrm{hr} \)
c. \( 6 \mathrm{km} / \mathrm{hr} \)
D. None of these


Which of the following is correct regarding the Langmuir's model of
adsorption of a gas on a solid surface?
A. The rate of desorption of adsorbed molecules from the surface does not depend on the surface covered
B. The adsorption at a single site on the surface may involve multiple molecules at the same time
C. The mass of gas striking a given area of surface is proportional to the pressure of the gas
D. The mass of gas striking a given area of surface is independent of the pressure of the gas


A thin conducting ring is ruptured when it is given a charge q. Consider another thin conducting ring, radius of which is n times and tensile strength is k times of the former ring. How much maximum charge can this second ring be given
without rupturing?
\( \mathbf{A} .<q n k \)
B. \( <q n \sqrt{k} \)
\( \mathbf{c} \cdot<q n^{2} \sqrt{k} \)
D. Insufficient information


Alga rich in protein is
A. Chlorella
B. Spirogyra
c. oscillatoria
D. Ulothrix


Write \( I U P A C \) Name of the following:


In an aquatic ecosystem, zooplankton
are represented as
A. Producer
B. Primary consumer
c. Secondary consumer
D. Tertiary consumer
E. Decomposer


The e/m ratio of anode rays is constant irrespective of the gas filled inside the discharge tube
A. True
B. False


Expand using suitable identities
\( (2 a-3 b)^{3} \)


Assertion
Equivalent mass of \( N_{2} H_{4} \) is 8 in acidic
medium or basic medium
Reason
It is oxidised to \( N_{2} \) with loss of four
electron per \( N_{2} H_{4} \) unit
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 and Reason both are incorrect


Find the general solution of \( \frac{d y}{d x}=\frac{2 y}{x} \)
A \( \cdot y=e^{5 \log x+c} \)
B . \( y=e^{3 \log x+c} \)
C \( \cdot y=e^{2 \log x+c} \)
D. None of these


Which one of the following is an example of viviparous animal?
A. Amphibians
B. Bony fish
c. Fish
D. Shark


What is heterotrophic nutrition?
Describe its types.


Ankit secured \( 75 \% \) marks in a
examination if he secured 450 marks
find the maximum marks.


If \( \boldsymbol{f}(\sin 2 \boldsymbol{x})= \)
\( \frac{\left(2 \tan x+\sec ^{2} x\right)(1+\cos 2 c)}{2}, \) then
determine the range of \( \boldsymbol{f}(\boldsymbol{t}) \) if range is \( [a, b], \) then \( b=? \)


Metaboly is characteristics of
A. Amoebids
B. Heliozoans
c. Euglenoids
D. Dinoflagellates


A block of mass 2 kg slides down an
incline plane of inclination \( 30^{0} . \) The coefficient of friction between block and
plane is \( 0.5 . \) The contact force between block and plank is:
A. 20 N
B. \( 10 \sqrt{3} \) N
c. \( 5 \sqrt{7} \) N
D. \( 5 \sqrt{15} \) N


Which one of the organelles is responsible for the formation of aster in cell division?
A. Chromosome
B. Lysosome
c. Ribosome
D. centrosome


Hydrogen and Deuterium can be
separated by gas diffusion principle. If this is true enter 1 , if false enter 0 .


Soil is a natural medium for growth of land plants. Organic soil contains organic number upto a depth of
A. Two and a half feet
B. One foot
c. six inches
D. Ten feet


Explain the reason for exceptional electroic congiguration of copper and chromium.


Which of the following elements shows more number of oxidation state in its
compound?
\( A \cdot A m \)
B. Gd
c. \( \mathrm{La} \)
D. Eu


If the electric field at points In between,
and is \( K \sigma / \varepsilon_{0} . \) Find \( \mathrm{K} ? \)


Find the middle term in the expansion
of \( \left(1-2 x+x^{2}\right)^{n} \)
A \( \cdot \frac{(2 n) !}{(n !)^{2}}(-1)^{n} x^{n} \)
B. \( \frac{(2 n) !}{(n !)}(-1)^{n} x^{2} n \)
c. \( \frac{(2 n) !}{(n !)^{2}} x^{n} \)
D. None of these


What will be the solubility of the \( \boldsymbol{C a}(\boldsymbol{O H})_{2} \) solution when \( \boldsymbol{N a O H} \) is
dissolved in it, compared with that in
pure water?
A. Unaffected
B. Increased
c. Decreased
D. None


In an SHM, the total energy of a particle
is
A . a constant
B. increases with time
c. decreases with time
D. oscillates with time


2 December 1942 is known for.
A. The formation of the Big Bang theory
B. The activation of the first operational nuclear reactor
C. The creation of the first controlled chain reaction
D. The development of the first thermonuclear device


The composition of water gas is:
A. \( C O+N_{2} \)
в. \( C O+H_{2} \)
\( \mathrm{c} \cdot \mathrm{CO}+\mathrm{CO}_{2} \)
D. \( C O+C O_{2}+C H_{4} \)


The horizontal and the vertical
components of earth's magnetic field at any place are equal. The angle of dip at that place will be:
\( \mathbf{A} \cdot 0^{\circ} \)
В . \( 45^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 90^{\circ} \)


Muscles can survive anoxic episodes because they receive ATP in the absence of oxygen due to one of the following cycles.
A. Glycolysis
B. ETS
c. Krebs cycle
D. HMP pathway


Atomicity of white phosphorus is:
A .4
B. 3
\( c \cdot 2 \)
D. 8


A stretched rope having linear mass density \( 5 \times 10^{-2} k g m^{-1} \) is under a
tension of 80 N. The power that has to be supplied to the rope to generate harmonic waves at a frequency of \( 60 \mathrm{Hz} \) and an amplitude of \( 6 \mathrm{cm} \) is (nearly)
A . 215 \( \mathrm{w} \)
B. 251 W
c. \( 10368 \mathrm{w} \)
D. 521


Find the sum to \( n \) terms of the \( A . P . \)
whose \( k^{t h} \) term is \( 5 k+1 \)


Flagellum of Astasia / Euglena is
A. Pantonematic
B. Pentachronematic
c. Both A and B
D. Stichonematic


Positive integer \( y \) is 50 percent of 50
percent of positive integer \( \boldsymbol{x}, \) and \( \boldsymbol{y} \)
percent of \( x \) equals 100 . What is the
value of \( x ? \)
A . 50
в. 100
\( c \cdot 200 \)
D. 1000
E . 2000


The sum of first \( n \) terms of a sequence
is \( \frac{6^{n}-5^{n}}{5^{n}} \)
Find its \( n^{t h} \) term and examine whether
the sequence is an A.P of G.P.


Solve:
\( \boldsymbol{f}(\boldsymbol{x})=\mathbf{9}-\mathbf{2} \boldsymbol{x}^{2},-\mathbf{5} \leq \boldsymbol{x} \leq-\mathbf{3} \)


If water is polluted, its BOD (biochemical oxygen demand) value is:
\( A .<1 \mathrm{ppm} \)
B. <2 ppm
\( c .<3 p p m \)
\( D \ldots 6 \) ppm


For the Bohr's first orbit of
circumference \( 2 \pi r, \) the de-Broglie wavelength of revolcing electron will be.
A \( .2 \pi r \)
B . \( \pi r \)
c. \( \frac{1}{2 \pi r} \)
D. \( \frac{1}{4 \pi r} \)


A car falls of a ledge and drops to the
ground in \( 0.5 s\left(g=10 m / s^{2}\right) \)
(a)Find the speed on striking the ground.
(b)How high is the ledge from the
ground.
(c) If car is of mass \( 100 \mathrm{kg} \),what will be the force by which car will hit the ground.


Chlorofluorocarbons are not being used in refrigerators because they
A. Increase temperature
B. Cause allergic reactions
c. Deplete ozone
D. Both A and B


When iodoform is heated with silver
powder, it forms:
A. methane
B. ethane
c. acetylene
D. ethylene


The position vectors of point \( A \) and \( B \) \( \operatorname{are} \hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}+\boldsymbol{3} \hat{\boldsymbol{k}} \) and \( \boldsymbol{3} \hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}+\boldsymbol{3} \hat{\boldsymbol{k}} \)
respectively. The equation of a plane is
\( r \cdot(5 \hat{i}+2 \hat{j}-7 \hat{k})+9=0 . \) The point \( A \)
and \( B \)
A. lie on the plane
B. are on the same side of the plane
c. are on the opposite side of the plane
D. None of these


Find union of \( A \) and \( B, \) and represent it
using Venn diagram:
\( \boldsymbol{A}=\{1,2,3,4,5\}, B=\{4,5,7,9\} \)


The value of refractive index of diamond
is :
A . 1.45
B. 2.45
\( c .3 .40 \)
D. 1.54


For mercury at \( 0^{\circ} \mathrm{C} \) specific
conductance,
\( \boldsymbol{K}=\mathbf{1 . 0 6 2 9 6 3} \times \mathbf{1 0}^{\mathbf{6}} \boldsymbol{S} / \boldsymbol{m} \)
(a) If the resistance of a cell containing mercury is 0.243166 ohm, What is the
cell constant of the cell?
(b) If the same cell is fixed with \( K C l \)
solution at \( 0^{\circ}, \) the resistance of the cell
is \( 3.966 \times 10^{4} \) ohm. What is the
conductivity of \( K C l \) solution?
(c) If the average cross-sectional area of
the cell is \( 0.9643 m m^{2}, \) what is the
effective distance between the
electrodes?


Shearing stress causes change in
A . Length
B. Breadth
c. shape
D. Volume


How many tetrads are visible in a cell during pachytene stage of reduction division of there are 20 chromosomes in
a meiocyte?
A . 5
B. 10
c. 20
D. 40


Stomata on the surface of the leaf open
by
A. Decreasing the solute concentration in the guard cells.
B. Increasing the solute concentration in the guard cells.
C. Increasing the water potential in the guard cells.
D. Both B and C.


Which of the terms is not used in a
linear programming problem?
A. Optimal solution
B. Feasible solution
c. concave region
D. objective function


What are plants hormones? Name the
plant hormones responsible for the
following:
(i)Growth of stem
(ii)Promotion cell division
(iii)Inhibition of growth (iv)Elongation of cells


On oxymercuration-demercuration, the given compound produces the major product:
\[
\widehat{O} \int^{C H_{2}-C H}=C H_{2}
\]
\( A \)
\( \widehat{\mathrm{O}} \mathrm{CH}_{2}-\mathrm{CH}-\mathrm{CH}_{3} \)
\( \mathrm{OH} \)
в.
\( \widehat{O} \int^{C H}_{2}-C H_{2}-C H_{2}-O H \)
\( c \)
\( \begin{array}{c}\widehat{\mathrm{O}} \mathrm{CH}_{2}-\mathrm{CH}-\mathrm{CH}_{2} \\ \mathrm{OH}\end{array}_{\mathrm{OH}}^{\mathrm{T}} \)
D.
\( \widehat{O} \int^{C H_{2}-C O O H} \)


Volume of \( N_{2}, \) in litres, liberated on
heating 6.4 g of \( N H_{4} N O_{2} \) is:
A . 44.8
в. 22.4
c. 11.2
D. 2.24


Two points \( P \) and \( Q \), diametrically opposite on a disc of radius \( R \) have
linear velocities \( v \) and \( 2 v \) as shown in
figure. The angular speed of the disc is
\( \overrightarrow{r R} \)
Find the value of \( x \)


Methods used for the preparation of colloidal solutions are:
This question has multiple correct options
A. peptization
B. hydrolysis
c. ultrasonic dispersion
D. coagulation


Which of the following does not play a role in blood coagulation?
\( \mathbf{A} \cdot \) Vitamin \( \mathbf{K} \)
B. Vitamin D
c. calcium ions
D. Fibrinogen


What is the value of \( \vec{A}+A \) in the
boolean algebra?
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot A \)
D. \( \vec{A} \)


The ratio of wavelengths of electron
waves in two orbits is \( 3: 5 . \) The ratio of
kinetic energy of electrons will be:
\( \mathbf{A} \cdot 25: 9 \)
B. 5: 3
\( \mathbf{c} \cdot 9: 25 \)
D. 3: 5


The diagram below shows the melting and boiling points of four different substances.Which substance has a
melting point at \( -20^{\circ} \mathrm{C} \) ? Arrange the four substances in ascending order of their melting and boiling points.
Melting


A student Identify the organism under microscope and investigate that the organism have streamlined body. Identify the organism.


The fructose molecule in sucrose exists
as:
A. furanose
B. pyranose
c. open chain
D. all of these


Brush border of small intestine cells is
formed of
A. Microvilli
B. cilia
c. vill
D. circular folds


The formation of violet colour by the addition of sodium nitroprusside to the Lassaigne's solution is the indication of, \( _{\text {十一一一一一一一一 }} \) element in the organic compound.


Ampere's circuital law holds good for:
A. conduction current only
B. displacement current only
C. both conduction current and displacement current
D. none of these


A balloon is negatively charged by rubbing and then clings to a wall. Does this mean that the wall is positively
charged ? why does the balloon eventually fall?


For an \( A . P . \) if \( T_{n}=6 n+5 \) then find \( S_{n} \)


Which of the following bonds has the
higher energy?
A. \( S e-S e \)
в. \( T e-T e \)
c. \( s-s \)
D. \( O-O \)


A wheel with 10 metallic spokes each \( 0.5 \mathrm{m} \) long is rotated with a speed of 120 rev/min in a plane normal to the earth's magnetic field at the place.lf the magnetic of the field is \( 0.4 \mathrm{G} \), what is the induced emf between the axle and the
rim of the wheel?


A spherical ball of density \( \rho \) and radius
\( 0.003 m \) is dropped into a tube
containing a viscous fluid up to the
\( 0 \mathrm{cm} \) mark as shown in the figure.
Viscosity of the fluid \( =1.26 N-s / m^{2} \)
and its density \( \rho_{L}=\frac{\rho}{2}=1260 k g / m^{3} \)
Assume the ball reaches a terminal
speed at \( 10 c m \) mark. The time taken by
the ball to travel the distance between
the \( 10 c m \) and \( 20 c m \) mark is \( (g= \)
\( \left.\mathbf{1} \mathbf{0} \boldsymbol{m} / \boldsymbol{s}^{\mathbf{2}}\right) \)
A \( .2 s \)
B. \( 1 s \)
c. \( 0.5 s \)
D. \( 5 s \)


Examine the figures of diploblastic (i) and triploblastic (ii) organisation in animals given below and identify the
labelled parts A to D.
A. A - Mesoglea, B - Ectoderm, C - Endoderm,
D- Mesoderm
B. A- Endoderm, B - Mesoderm,
C - Mesoglea, Ectoderm
c. A - Mesoderm, B - Mesoglea, C - Ectoderm, Endoderm
D. A - Ectoderm, B - Endoderm
C - Mesoglea, Mesoderm


Which of the following factors were responsible for the period of stagnant
growth of India's population from 1901
\( 1921 ? \)
Poor health and medical services.
2. Illiteracy of people at large.
2. Inefficient distribution system of food and other basic necessities.
A. Only 1 and 2
B. Only 1 and 3
c. only 2 and 3
D. 1,2 and 3


If \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{3} & -\mathbf{4} \\ \mathbf{1} & -\mathbf{1}\end{array}\right], \) then prove that \( \boldsymbol{A}- \)
\( A^{T} \) is a skew-symmetric matrix.


\( M Y \) and \( N Y_{3}, \) two nearly insoluble
salts, have the same \( \boldsymbol{K}_{s p} \) values of
\( 6.2 \times 10^{-13} \) at room temperature
Which statement would be true in
regards to \( M Y \) and \( N Y_{3} ? \)
A. The molar solubilities of \( M Y \) and \( N Y_{3} \) in water are identical.
B. The molar solubility of \( M Y \) in water is less than that of \( N Y_{3} \)
C. The salts \( M Y \) and \( N Y_{3} \) are more soluble in \( 0.5 M K Y \) than in pure water.
D. The addition of the salt of KY to solution of \( M Y \) and
\( N Y_{3} \) will have no effect on their solubilities


If energy required to remove one of the two electron from He atom is \( 29.5 e V \)
then what is the value of energy
required to convert a helium atom into
\( \boldsymbol{\alpha}- \) particle?
A . \( 54.4 e V \)
B. \( 83.9 e V \)
c. \( 29.5 e V \)
D. 24.9eV


Which of the following is not a waste product produced by plants?
A. Water vapour
B. Oxygen
c. Gum Arabic
D. carbon dioxide


Assertion
Among the second group peroxides, barium peroxide is thermally most stable.
Reason
Positive charge density is maximum for
\( B a^{2+} \) among group II cations
A. The Assertion is True, Reason is True; Reason is a correct explanation for Assertion
B. The Assertion is True, Reason is True; Reason is not a correct explanation for Assertion
C. Assertion is True, Reason is False
D. Assertion is False, Reason is True.


The point (3,0,-4) lies on the
A. Y-axis
B. z-axis
c. XY-plane
D. xz-plane
E. YZ-plane


Indicate the position where the electrophile can attack in the following
compounds:
\( (\mathbf{i} \)


Whenever a hydrogen atom emits a
photon in the Balmer series
A. It need not emit any more photon
B. It may emit another photon in the Paschen series
C. It must emit another photon in the Lyman series
D. It may emit another photon on the Balmer series


What does the negative electronic energy (negative sign for all values of energy) for hydrogen atom means?
A. The energy of an electron in the atom is lower than the energy of a free electron at rest which is taken as zero
B. When the electron is free from the influence of nucleus it has a negative value which becomes more negative
c. When the electron is attracted by the nucleus the energy is absorbed which means a negative value
D. Energy is released by hydrogen atom in ground state


Integrate:
\( \int \frac{\boldsymbol{d} \boldsymbol{x}}{\boldsymbol{x}^{5}\left(1+\boldsymbol{x}^{-4}\right)} \)


Find the values of \( x \) and \( y \) such that the vectors \( 2 \hat{i}+3 \hat{j} \) and \( x \hat{i}+y \hat{j} \) are equal.


Which of the following statement(s)
is/are correct?
This question has multiple correct options
A. If n identical cells are connected in series and then the
battery thus formed is short circuited by a conduction wire, current through the wire will be independent of \( n \)
B. If n identical cells are connected in parallel and then the battery thus formed is short circuited by a conducting wire, current through the wire will be directly proportional to \( n \)
C. If \( n \) identical cells are connected in parallel and then the battery thus formed is short circuited by a wire having a constant resistance, current through the wire will be directly increase as n increases.
D. None of the above.


An analysis of monthly wages paid to workers in two firms \( A \) and \( B \) belonging to the same industry gives the following results :
Firm
A
No.of wage earners 586
Mean of monthl wages Rs
5253
Variance of the distribution
(i) Which firm \( A \) or \( B \) pays larger
amount as monthly wages?
(ii) Which firm \( A \) or \( B \) shows greater variability in individual wages?


When three parts of conc. HCl and one
part of conc. \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) is mixed, a compound 'X' is formed. The correct option related to 'X' is:
A . 'X' 'is known as aqua-regia
B. 'X' is used for dissolving gold
C. 'X'is used for decomposition of salts of weaker acids
\( D . \) both (a) and (b)


Find the sum of even numbers between
and 25
A. 155
в. 156
c. 157
D. 158


Select correct IUPAC naming of given
compound:
A. 2,3,4,5,6 -pentahydroxyhexanoicacid
B. 2,3,4,5,6 -pentahydroxyhexanol
C. 2,3,4,5,6 -pentahydroxyhexanal
D. 2,3,4,5,7 -pentahydroxyhexanal


A proton strikes another proton at rest
with speed \( V_{0} . \) Assume impact
parameter to be zero. Their closest distance of approach is (mass of proton
is \( \boldsymbol{m} \) )
\( ^{\mathbf{A}} \cdot \frac{e^{2}}{4 \pi \varepsilon m v_{0}} \)
в. \( \frac{e^{2}}{\pi \varepsilon_{0} m v_{0}^{2}} \)
c. \( \frac{e^{2}}{m v_{0}^{2}} \)
D. zero


This section contains questions each
with two columns-I and II. Match
the columns-I with columns-I.


Amongst 38 ATP, 34 ATP are derived
from
A. HMP
B. Krebs cycle
c. Glycolosis
D. Electron chain transport


Food is absorbed in the state when it
may be
A. Monosaccharides
B. Amino acids
c. Glycerol and fatty acids
D. All of the above


The conductivity of a semi conductor can be increased by:
A. Heating the semi conductor
B. Doping the semi conductor
c. Both (a) and (b)
D. None


Which of the following is used for making parachutes and stockings?
A. cotton
B. Nylon
c. wool
D. Bakelite


n \( O F_{2} \) molecule, the total number of
bond pairs and lone pairs of electrons present is/are:
[f ans is \( 3 \text { and } 6, \text { represent as } 36] \)


What is meant by resonance in an LCR circuit?


In the refining of iron, phosphorous
separates as:
\( \mathbf{A} \cdot \operatorname{slag} C a_{3}\left(P O_{4}\right) \)
B. volatile, \( P_{2} O_{5} \)
c. slag, \( F e P O_{4} \)
D. \( C a_{3} P_{2} \)


You are given the two circuits as shown In Fig. Show that circuit (a) acts as OR gate while the circuit (b) acts as AND
gate.


Write \( \frac{36}{50} \) as percentage.


Is lightning static electricity?
A. Yes
B. No
c. sometimes
D. None of the above


Which of the following is minimum at the poles?
A. Angle of dip
B. Horizontal component of the earth's magnetic field
c. Angle of declination
D. Vertical component of the earth's magnetic field


Sex chromosomes of a female bird are
A. xo
B. zz
c. zw
D. xx
E. \( x y \)


Calculate the maximum speed with which a car can be driven safely along a curved road of radius \( 30 m \) and banked
at \( 30^{\circ} \) with the horizontal. Given, \( g= \)
\( 9.8 m s^{-2} \)
A \( \cdot 13.03 \mathrm{ms}^{-1} \)
B . \( 12.08 \mathrm{ms}^{-1} \)
\( \mathbf{c} \cdot 15.08 m s^{-1} \)
D. \( 14.02 \mathrm{ms}^{-1} \)


Find the angular momentum \( \vec{M} \) of the
system of particles relative to a point \( \boldsymbol{O} \) of the reference frame \( \boldsymbol{K}, \) if \( \tilde{\boldsymbol{m}} \) is its proper angular momentum (in the reference frame moving translationally
and fixed to the centre of inertia), \( r_{c} \) is
the radius vector of the centre of inertia
relative to the point \( \boldsymbol{O}, \overrightarrow{\boldsymbol{p}} \) is the total momentum of the system of particles in the reference frame \( \boldsymbol{K} \)


The concentration of which of the
following solution has the highest
value?
A. Dilute solution
B. Concentration solution
c. saturated solution
D. Supersaturated solution


Which of the following particle would follow the path as shown in the above
figure?
A. Proton
B. Electron
C . Neutron
D. x-ray
E. Photon of red ligth


A \( 5 m \) long cylindrical steel wire with
radius \( 2 \times 10^{-3} \mathrm{m} \) is suspended
vertically from a rigid support and carrics a bob of mass \( 100 \mathrm{kg} \) at the
other end. If the bob gets snapped,
calculate the change in temperature of the wire ignoring radiation losses. \( \left(\text { Take } g=10 m / s^{2}\right) \) (For the steel wire:
Young's modulus \( =2.1 \times 10^{11} N / m^{2} \)
Density \( =7860 k g / m^{3} \) Specific heat \( = \)
\( 420 J / k g C) \)


Six particles situated at the corners of a regular hexagon of side \( a \) move at a
constant speed \( v \). Each particle maintains a direction towards the
particle at the next corner. Calculate the time the particles will take to meet each other.
A \( \cdot \frac{2 a}{3 v} \)
в. \( \frac{v}{a} \)
c. \( \frac{2 a}{v} \)
D. \( \frac{a}{3 v} \)


Which of the following is correct
regarding reflection.
A. Reflection is a phenomenon by which light incident on a surface is sent back into the same medium
B. Reflection is a phenomenon by which light incident on a surface passes into another medium
C. Reflection is a phenomenon by which light incident on a surface is scattered
D. Reflection is a phenomenon by which light incident on a surface is absorbed by the surface


Toluene is nitrated and the resulting product is reduced with tin and hydrochloric acid. The product so obtained is diazotised and then heated
with cuprous bromide. The reaction mixture so formed contains:
A. mixture of o- and p-bromotoluenes
B. mixture of o- and p-dibromobenzenes
c. mixture of o- and p-bromoanilines
D. mixture of o- and m-bromotoluenes


Name the gas Which is liberated when an acid reacts with a metal? Illustrate
with an example. How will you test the presence of this act?


With what velocity should a ball be
thrown vertically upward with so that it reaches a height of \( 40 m \)
\( \mathbf{A} \cdot 7 m s^{-1} \)
B. \( 14 \mathrm{ms}^{-1} \)
\( \mathrm{c} \cdot 21 \mathrm{ms}^{-1} \)
D. \( 28 m s^{-1} \)


The refrigerator cools your food and drink. The cooling is due to:
A. expansion of ice
B. the expansion of the refrigerant gas
c. the work of the electric motor
D. reaction of the refrigerant gas


One of the constituents of baking powder is sodium hydrogen carbonate, the other constituent is:
A . acetic acid
B. oxalic acid
c. carbonic acid
D. tartaric acid


An ultrasonic source emits sound of frequency \( 220 \mathrm{kHz} \) in air. If this sound meets a water surface, what is the
wavelength of the transmitted sound? (At the atmospheric temperature, speed of sound in air \( = \)
\( 352 m s^{-1} \)andinwater\( =1.496 m s^{-1} \)
A \( .5 .8 \times 10^{-3} \mathrm{m} \)
В. \( 6.8 \times 10^{-3} \mathrm{m} \)
c. \( 7.8 \times 10^{-3} m \)
D. \( 8.8 \times 10^{-3} \mathrm{m} \)


The value of \( \Delta_{\circ} \) for complexes given below follow the order
(i) \( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right]^{+3} \)
(ii) \( \left[\boldsymbol{R h}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right]^{+3} \)
(iii) \( \left[\operatorname{Ir}\left(N H_{3}\right)_{6}\right]^{+3} \)
A. \( I<I I I<I I \)
В. \( I>I I>I I I \)
c. \( I<I I<I I I \)


The weight of an object
A. is the quantity of the matter it contains
B. refers to its inertia
C. is same as its mass but is expressed in different units
D. is the force with which it is attracted towards the earth


\( \boldsymbol{P H}_{3} \) forms bubbles when passed slowly
in water but \( N H_{3} \) dissolves. Explain
why?


Auto reduction process is used for the extraction of:
This question has multiple correct options
A. cu
в. \( \mathrm{Hg} \)
\( c \cdot P b \)
D. Al


Structure of \( A \) and the type of
isomerism in the above reaction are respectively:
\( \boldsymbol{C H}_{3}-\boldsymbol{C} \equiv \boldsymbol{C H} \frac{40 \% \boldsymbol{H}_{2} \boldsymbol{S O}_{4}}{1 \% \boldsymbol{H g S O}_{4}} \)
\( \boldsymbol{A} \stackrel{\text {Isomerisation}}{\longrightarrow} \boldsymbol{C H}_{3} \boldsymbol{C O C H}_{3} \)
A. prop-1-en-2-ol, metamerism
B. prop-1-en-2-ol, tautomerism
c. prop-z-en-2-ol, cis and trans isomerism
D. prop-2-en-1-ol, tautomerism


If the mean of \( x \) and \( 1 / x \) is \( M \) then the
mean of \( x^{2} \) and \( 1 / x^{2} \) is
A \( \cdot M^{2} \)
B . \( M^{2} / 4 \)
c. \( 2 M^{2}-1 \)
D. \( 2 M^{2}+1 \)


A body is taken to a height of \( n R \) from the surface of the earth. The ratio of the acceleration due to gravity on the
surface to that at the altitude is
A \( \cdot(n+1)^{2} \)
B \( \cdot(n+1)^{-2} \)
c. \( (n+1)^{-1} \)
D. \( (n+1) \)


Which of the one is correct about
Hydrogen?
A. resembles in IA since it forms monovalent cation \( H^{+} \)
B. resembles in VIIA (halogen family) since it forms monovalent anion \( H^{-} \)
C. resembles in IVA(carbon family) since both have a half filled shell of electron
D. all of the above


Find the principal value of:
\( \cos ^{-1}\left(\sin \frac{4 \pi}{3}\right) \)


Evaluate \( :(98)^{3} \)


is usually picked by hands and fibres are then separated from the seeds by combing.
A. Jute
B. Moonj
c. cotton
D. None of the above


What is the equation for the
equilibrium constant \( \left(K_{c}\right) \) for the
following equilibrium reaction?
\( \frac{1}{2} A(g)+\frac{1}{3} B(g) \rightleftharpoons \frac{3}{2} C(g) \)
\( ^{\mathbf{A}} \cdot_{K_{C}}=\frac{[A]^{\frac{1}{2}}[B]^{\frac{1}{3}}}{[C]^{\frac{3}{2}}} \)
\( ^{\mathrm{B}} K_{C}=\frac{[C]^{\frac{3}{2}}}{[A]^{2}[B]^{2}} \)
\( ^{\mathbf{c}}_{K_{C}}=\frac{[C]^{\frac{3}{2}}}{[A]^{\frac{1}{2}}[B]^{\frac{1}{5}}} \)
\( ^{\mathrm{D}} K_{C}=\frac{[C]^{\frac{3}{2}}}{[A]^{\frac{1}{2}}+[B]^{\frac{1}{3}}} \)


The ratio of heats liberated at \( 298 K \)
from the combustion of one kg of coke and by burning water gas obtained from kg of coke is:
Given: Enthalpies of combustion of
\( C, C O \) and \( H_{2} \) as
\( 393.5 k J, 285 k J, 285 k J \) respectively
all at \( 298 K . \) (Assume coke to be \( 100 \% \)
carbon).
A .0 .69: 1 \)
B. 0.96: 1
c. 0.79: 1
D. 0.86: 1


\( \lim _{x \rightarrow 0^{+}} \frac{\sin ^{-1} 2 x}{\tan ^{-1} 3 x}=? \)


The diagram below in Fig. shows the core of a transformer and its input and
output connections.
The name of the transformer is
(step-up, stepdown) transformer.


In which case does the normal force act
between the object and table?
\( \mathbf{A} \cdot \) Both \( A \) and \( B \)
B. Only \( A \)
C. Only \( B \)
D. None of these


t is desired to measure the magnitude of field between the poles of a powerful loud speaker magnet. A small flat search coil of area \( 2 \mathrm{cm}^{2} \) with 25 closely
wound turns, is positioned normal to the field direction, and then quickly snatched out of the field region.
Equivalently, one can give it a quick \( 90^{\circ} \)
turn to bring its plane parallel to the field direction). The total charge flown in the coil (measured by a ballistic galvanometer connected to coil) is 7.5
mC. The combined resistance of the coil
and the galvanometer is \( 0.50 \Omega \) Estimate the field strength of magnet.


A boy moving with a velocity of \( 20 k m / h \)
along a straight line joining two stationary objects. According to him both objects
A. move in the same direction with the same speed of
\( 20 \mathrm{km} / \mathrm{h} \)
B. move in different direction with the same speed of \( 20 \mathrm{km} / \mathrm{h} \)
c. move towards him
D. remains stationary


A particle is travelling along a straight line \( O X . \) The distance \( x \) (in metre) of
the particle from \( \boldsymbol{O} \) at a time \( ^{\prime} \boldsymbol{t}^{\prime} \) is given
by \( \boldsymbol{x}=\mathbf{3 7}+\mathbf{2 7 t}-\boldsymbol{t}^{3}, \) where 't' is time in
second. The distance of the particle
from \( O \),when it comes to rest is:
A. \( 81 m \)
в. \( 91 m \)
c. \( 101 m \)
D. \( 111 m \)


The position vectors of four points \( \boldsymbol{P}, \boldsymbol{Q}, \boldsymbol{R}, \boldsymbol{S} \) are \( \boldsymbol{2} \overline{\boldsymbol{a}}+\boldsymbol{4} \overline{\boldsymbol{c}}, \boldsymbol{5} \overline{\boldsymbol{a}}+\boldsymbol{3} \sqrt{\boldsymbol{3} \boldsymbol{b}}+ \)
\( 4 \bar{c}),-2 \sqrt{3 b}+\bar{c} \) and \( 2 \bar{a}+\bar{c} \)
respectively, then
A. \( \overline{P Q} \) is parallel to \( \overline{R S} \)
B. \( \overline{P Q} \) is not parallel to \( \overline{R S} \)
c. \( \overline{P Q} \) is equal to \( \overline{R S} \)
D. \( \overline{P Q} \) is parallel and equal to \( \overline{R S} \)


The role of fluorspar \( \left(C a F_{2}\right) \) which is added during the electrolytic reduction of alumina dissolved in fused cryolite
is:
A. to act as a catalyst
B. to make the fused mixture very conducting
c. to increase the temperature of the melt
D. to decrease the rate of oxidation of carbon at the anode


ff \( x \) follows binomial distribution with
mean 4 variance \( 2 . \) Find \( P(|x-4|) \leq 2 \)


If \( A, B \) be two events such that \( P(A \cup \)
\( B)=\frac{5}{6}, P(A \cap B)=\frac{1}{3} \) and \( P\left(B^{\prime}\right)=\frac{1}{2} \)
then events \( A, B \) are
A. dependent
B. independent
c. mutually exclusive
D. none of these


Ramesh number of ways in which the
letters of the word RAMESH can be
placed in the squares of the given figure
so that no row remains empty, is
A . 17280
B. 18720
c. 15840
D. 14400


Find the equation of the line joining the points (-1,3) and (4,-2)


Assuming that shear stress at the base of a mountain is equal to the force per
unit area due to its weight. Calculate the maximum possible height of a mountain on the earth if breaking stress of a typical rock is \( 3 \times 10^{8} N m^{-2} \)
and its density is then \( 3 \times 10^{3} k g \quad m^{-3} \)
(Take \( \left.g=10 m s^{-2}\right) \)
\( A .4 k m \)
в. \( 8 k m \)
c. \( 10 k m \)
D. \( 16 k m \)


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


A ray of light travels from air to glass at
an angle of incidence of \( 37^{\circ}, \) the angle
of refraction is \( 24^{\circ} . \) What is the
refractive index of glass? (Given: \( \left.\sin 37^{\circ}=0.60, \sin 24^{\circ}=0.40\right) \)
A . 0.66
B. 0.133
\( c .1 .5 \)
D. None


Mark the correct alternative of the
following. In figure, AOB is a straight line such that \( \angle A O C=(3 x+10)^{o}, \angle C O D= \)
\( \mathbf{5 0}^{\circ} \) and \( \angle B O D=(x-8)^{\circ} . \) The value of
\( x \) is?
\( A \cdot 32 \)
B. 36
\( c \cdot 42 \)
D. 52


The area between the curve \( y^{2}=9 x \) and
the line \( y=3 x \) is
A \( \cdot \frac{1}{3} \) sq units
B. \( \frac{8}{3} \) sq. units
c. \( \frac{1}{2} \) sq. units
D. \( \frac{1}{5} \) sq. units


A car is initially traveling due north at \( 23 m / s . \) Find the velocity of the car after
\( 4 s \) if its acceleration is \( 2 m / s^{2} \) due south. \( (\text { in } \mathrm{m} / \mathrm{s}): \)
A. 10 due south
B. 15 due north
c. 14 due north
D. 12 due south


The oxidation number of sulphur in
\( \mathrm{Na}_{2} \mathrm{S}_{4} \mathrm{O}_{6} \) is :
A . -2.5
в. +2.5
c. -10
D. +10


Looking at the Venn diagram list the elements of the following sets:
\( \boldsymbol{B} \backslash \boldsymbol{A} \)


Which of the following does not occur when the sewage is discharged into
water?
A . Increase in \( O_{2} \)
B. Cyanophycean blooms occur
c. Depletion of \( O_{2} \) layers
D. Eutrophication


The metallic oxide of a divalent metal
which on thermal decomposition liberates oxygen is:
A. \( C O_{2} \)
в. \( P_{2} O_{5} \)
c. \( H g O \)
D. \( N_{2} \),


A condenser of \( 250 \mu F \) is connected in parallel to a coil of inductance \( 0.16 \mathrm{mH} \) while its effective resistance is \( 20 \Omega \)
Determine the resonant frequency.
A \( \cdot 9 \times 10^{4} H z \)
B . \( 16 \times 10^{7} \mathrm{Hz} \)
c. \( 8 \times 10^{5} H z \)
\( \mathbf{D} \cdot 9 \times 10^{3} H z \)


A metal \( M \) which is not affected by
strong acids like conc.
\( H N O_{3}, \) conc. \( H_{2} S O_{4} \) and conc. solution
of alkalies like \( N a O H, K O H \) forms
\( M C l_{3} \) which finds use for toning in
photography. The metal \( M \) is :
A . \( A g \)
в. \( H g \)
c. \( A u \)
D. \( C u \)


The magnetic field of the earth can be modelled by that of a point dipole placed at the centre of the earth. The
dipole axis makes an angle of \( 11.3^{\circ} \)
with the axis of the earth. At Mumbai,
declination is nearly zero. Then
A. the declination varies between \( 11.3^{\circ} \mathrm{W} \) to \( 11.3^{\circ} \mathrm{E} \)
B. the least declination is \( 0^{\circ} \)
C. the plane defined by dipole axis and Earth axis passes through Greenwich
D. declination averaged over Earth must be always negative


Assertion
An electric field is preferred in comparison to magnetic field for detecting the electron beam in a television picture tube
Reason
Electric field requires low voltage.
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 meant by the term bond order?
Calculate the bond order of: \( N_{2}, O_{2}, O_{2}^{+} \)
and \( \boldsymbol{O}_{2}^{-} ? \)


Answer the Following:
Explain the techniques of drawing a Histogram.


The waves relevant to
telecommunications are
A. visible light
B. infrared
c. ultraviolet
D. microwave


A block of mass \( m \) is moving with a
constant acceleration \( a \) on a rough
horizontal plane. If the coefficient of friction between the block and ground is
\( \mu, \) the power delivered by the external
agent in a time interval \( t \) from the
beginning is equal to:
A \( \cdot m a^{2} t \)
в. \( \mu \) mgat
\( \mathbf{c} \cdot \mu m(a+\mu g) g t \)
D. \( m(a+\mu g) a t \)


In X-ray spectrum, transition of an electron from an outer shell to an inner
shell gives a characteristics X-ray spectral line. If we consider the spectral
\( \operatorname{lines} K_{\beta}, L_{\beta}, M_{\alpha} \) then
A. \( K_{\beta} \) and \( L_{\beta} \) have a common inner shell
B. \( K_{\beta} \) and \( L_{\beta} \) have a common outer shell
c. \( L_{\beta} \) and \( M_{\alpha} \) have a common outer shel 1
D. \( L_{\beta} \) and \( M_{\alpha} \) have a common inner shell


Sita is driving along a straight highway
in her car. At time \( t=0, \) when Sita is
moving at \( 10 m s^{-1} \) in the positive \( x \)
direction, she passes a signpost at \( \boldsymbol{x}= \)
\( \mathbf{5 0} \) m. Here acceleration is a function of
time:
\( \boldsymbol{a}=\mathbf{2} . \mathbf{0} \boldsymbol{m} \boldsymbol{s}^{-2}-\left(\frac{\mathbf{1}}{\mathbf{1 0}} \boldsymbol{m} \boldsymbol{s}^{-\mathbf{3}}\right) \boldsymbol{t} \)
Derive expressions for her velocity and position as functions of time.


Assertion
If a dielectric is placed in external field then field inside dielectric will be less
than applied field.
Reason
Electric field will induce dipole moment
opposite to field direction.
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 conductivity of a saturated solution of \( B a S O_{4} \) is \( 3.06 \times 10^{-6} \) ohm \( ^{-1} c m^{-1} \)
and its molar conductance is \( 1.53 o h m^{-1} c m^{2} m o l^{-1} . \) The \( K_{s p} \) of
\( B a S O_{4} \) will be:
A \( \cdot 4 \times 10^{-12} \)
В. \( 2.5 \times 10^{-9} \)
c. \( 2.5 \times 10^{-13} \)
D. \( 4 \times 10^{-6} \)


The escape velocity of a projectile from the earth is approximately
A. \( 7 \mathrm{km} / \mathrm{sec} \)
в. \( 112 \mathrm{km} / \mathrm{sec} \)
c. \( 11.2 \mathrm{km} / \mathrm{sec} \)
D. \( 1.1 \mathrm{km} / \mathrm{sec} \)


A transverse wave is passing through a light string shown in the figure.The
equation of wave is \( y=A \sin (\cos t- \)
\( k x) \). The area of cross-section of string
is \( A \) and density is \( p \).The hanging
mass is:
A. \( A \omega \)
B. \( \frac{\omega}{k g} \)
c. \( \frac{\rho A \omega^{2}}{k^{2} g} \)
D. \( \underline{k^{2}} \)


A particle is moving with a constant acceleration. Its velocity is reduced to zero in 5 s and it covered a distance of
\( 100 \mathrm{m} \) in this direction. The distance covered by the particle in the next 5 s is
A. Zero
B. 250 m
c. \( 100 \mathrm{m} \)
D. 500 \( \mathrm{m} \)


\( k g m s^{-1} \) is the Sl unit of
A. Impulse
B. Force
c. Angular velocity
D. None of these


An electron enters a chamber in which a
uniform magnetic field is present as
shown.
An electric feild of appropriate magnitude is also applied so that the electron travels undeviated without any
change in its speed through the
chamber. We are ignoring gravity. Then,
the direction of the electric field is
A. Opposite to the direction of the magnetic field.
B. Opposite to the direction of the electron's motion.
C. Normal to the plane of the paper and coming out of the plane of the paper.
D. Normal to the plane of the paper and into the plane of the paper.


Which of the following is not an intermediate of Krebs cycle?
A. Acetyl CoA
B. Citric acid
c. succinic acid
D. Lactic acid


Two particle move in a uniform gravitational field with an acceleration
\( g . \) At the initial moment the particles
were located over a tower at one point
and moved with velocities \( \boldsymbol{v}_{1}=\mathbf{3} \boldsymbol{m} / s \)
and \( v_{2}=4 m / s \) horizontally opposite
directions. Find the distance between
the particles at the moment when their velocity vectors become mutually perpendicular.


What weight of sodium nitrate will
separate when a saturated solution
containing 50 gram of water is cooled
from \( 50^{\circ} \mathrm{C} \) to \( 30^{\circ} \mathrm{C} \) ? The solubility of
\( N a N O_{3} \) at \( 50^{\circ} C \) and \( 30^{\circ} C \) is 114 g and 86 g respectively.


Differentiate the following w.r.t. \( x \) \( e^{x^{3}} \)


The unit in which we pay the cost of electricity is
A. kilowatt hour
B. watt hour
c. joules
D. ergs


Find the surface area of a sphere of
radius \( 21 \mathrm{cm} \)


Hyperol is an addition product of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \)
with :
A. ethanol
B. urea
c. ethylene.
D. ammonia


Total number of orbitals present in the given stationary state for the principal quantum number having value of \( n=3 \)
?
A . 9
B. 7
\( c \cdot 4 \)
D. 6


By how much does \( x^{2}-2 a x+5 \) exceed
\( 3 x^{2}-5 x+6 ? \)


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


The extent of actinoid contraction is
greater than lanthanoid contraction
explain


If \( a<b<c<d, \) then for any real non-
zero \( \lambda \), the quadratic equation \( (x- \)
\( a)(x-c)+\lambda(x-b)(x-d)=0 \) has
This question has multiple correct options
A. Non-real roots
B. One real root between \( a \) and \( c \).
c. one real root between \( b \) and \( d \)
D. Irrational roots.


End-product of the complete hydrolysis
of \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{6} \) is :
A. \( X e F_{4} O \)
в. \( X e F_{2} O_{2} \)
\( \mathbf{c} \cdot X e O_{3} \)
D. \( X e O_{3}^{ } \)


Cube of all even natural numbers are
even
A . True
B. False
c. Ambiguous
D. Data insufficient


A Carnot engine absorbed \( 227^{\circ} C \)
Calculate works done for the cycle by an engine of its single is maintained at
\( 127^{\circ} \mathrm{C} \)


The mutual inductance of the system of
two coils is \( 5 m H . \) The current in the
first coil varies according to the
equation \( \boldsymbol{I}=\boldsymbol{I}_{o} \sin \boldsymbol{w} \boldsymbol{t} \) where \( \boldsymbol{I}_{\boldsymbol{o}}=\mathbf{1 0} \boldsymbol{A} \)
and \( W=100 \pi r a d / s . \) The value of
maximum induced emf in the second
coil is
A \( .2 \pi V \)
в. \( \pi V \)
\( c .5 \pi V \)
D. \( 4 \pi V \)


\( \boldsymbol{I} \boldsymbol{f}\left(\boldsymbol{x}_{1}-\boldsymbol{x}_{2}\right)^{2}+\left(\boldsymbol{y}_{1}-\boldsymbol{y}_{2}\right)^{2}=\boldsymbol{a}^{2}\left(\boldsymbol{x}_{2}-\right. \)
\( \left.x_{3}\right)^{2}+\left(y_{2}-y_{3}\right)^{2}=b^{2} \) and \( \left(x_{3}-x_{1}\right)^{2}+ \)
\( \left(y_{3}-y_{1}\right)^{2}=c^{2} \operatorname{then} 4\left|\begin{array}{ccc}x_{1} & y_{1} & 1 \\ x_{2} & y_{2} & 1 \\ x_{3} & y_{3} & 1\end{array}\right| \) is
equal to
\( \mathbf{A} \cdot \sqrt{a b c(\mathrm{a}+\mathrm{b}+\mathrm{c})} \)
B. \( \sqrt{(a+b+c)^{4}} \)
c. \( 2 \sqrt{(a+b+c)(a+b-c)(b+c-a)(c+a-b)} \)
D. \( (a+b+c)\left(a^{2}+b^{2}+c^{2}\right) \)


If \( z+\sqrt{2}|z+1|+i=0 \) and \( z=x+i y \)
then
A. \( x=-2 \)
B. \( x=2 \)
c. \( y=-2 \)
D. \( y=1 \)


Which of the following is an excellent
substrate for \( S_{N} 1 \) reaction?
A \( \cdot R-C H_{2}-X \)
B. \( A r-C H_{2}-X \)
c. \( C H_{2}=C H-C H_{2}-X \)
D. \( C H_{2}=C H-X \)


A charged particle of mass \( 5 \times 10^{-6} k g \)
is held stationary in space by placing it
in an electric field of strength \( 10^{6} N C^{-1} \) directed vertically downwards. The charge on the particle is \( \left(\boldsymbol{g}=\mathbf{1 0 m} \boldsymbol{s}^{-2}\right) \)
A. \( -20 \times 10^{-5} \mu C \)
B. \( -5 \times 10^{-5} \mu C \)
c. \( 5 \times 10^{-5} \mu C \)
D. \( 20 \times 10^{-5} \mu C \)


A steel plate of thickness \( h \) has the
shape of a square whose side equals \( l \)
with \( h \ll l . \) The plate is rigidly fixed to a
vertical axle \( O O \) which is rotated with a
constant angular acceleration \( \boldsymbol{\beta} \) (figure
shown above). Find the deflection \( \lambda \)
assuming the sagging to be small.
A \( \cdot \lambda=\frac{9 \rho \beta l^{5}}{5 E h^{2}} \)
B. \( \lambda=\frac{7 \rho \beta l^{5}}{3 E h^{2}} \)
c. \( \lambda=\frac{7 \rho \beta l^{5}}{5 E h^{2}} \)
D. None of these


If \( \boldsymbol{A}=\left(\begin{array}{l}832 \\ 591\end{array}\right) \) and \( B=\left(\begin{array}{c}1-1 \\ 0\end{array}\right) . \) Find \( A+B \)
if it exists.


Answer the following question in one
word or one sentence or as per exact requirement of the question. Write the value of \( \lim _{x \rightarrow 0^{-}} \frac{\sin x}{\sqrt{x}} \)


Two opposite forces \( \boldsymbol{F}_{1}= \)
\( 120 N \) and \( F_{2}=80 N \) act on an heavy
elastic plank of modulus of elasticity \( \boldsymbol{y}=\boldsymbol{2} \times \mathbf{1 0}^{11} \boldsymbol{N} / \boldsymbol{m}^{2} \) and length \( \boldsymbol{L}=\mathbf{1} \boldsymbol{m} \)
placed over a smooth horizontal surface. The cross-sectional area of
plank is \( A=0.5 m^{2} . \) If the change in the
length of plank is (in \( \mathrm{nm} \) )
\( A \)
B. 0.5
\( c \cdot 5 \)
\( D \)


Write any two significance of meosis?
How does anaphase of mitosis different
from anaphase of meiosis


A mixture of three proteins \( (\boldsymbol{A}) \) \( (\text { pepsin }),(B) \) (haemoglobin) and \( (C) \)
(lysozyme) was separated by
eletrophoresis method at \( \boldsymbol{p} \boldsymbol{H}=\mathbf{7} \). The
\( \boldsymbol{p} \boldsymbol{H} \) at isoelectric point \( (\boldsymbol{p} \boldsymbol{I}) \) of the
proteins are \( \boldsymbol{p} \boldsymbol{I} \) of \( (\boldsymbol{A}),(\boldsymbol{B}) \) and \( (\boldsymbol{C}) \)
which are 1.1,6.7 and 11.0 respectively.
Which of the statement are correct?
This question has multiple correct options
A. Pepsin \( (A) \) will migrate to the cathode
B. Lysozyme \( (C) \) will migrate to the anode
C. Haemoglobin will not migrate
D. At \( p H=7,(A) \) and \( (C) \) would precipitate out while \( (B) \) would remain in the solution.


If \( a, b, c, d \) are positive real numbers such that \( a+b+c+d=2 \) then \( M= \)
\( (a+b)(c+d) \) satisfies the relation
A. \( 0<M \leq 1 \)
в. \( 1 \leq M \leq 2 \)
c. \( 2 \leq M \leq 3 \)
D. \( 3 \leq M \leq 4 \)


Which one is used in balancing?
A. Organ of cortit
B. Vestibular region
c. Middle ear
D. cochlea


Find the value of \( \boldsymbol{\theta}, \) if
\( \tan \theta=\sqrt{3} \)


An incident ray strikes a plane mirror at
an angle of incidence of \( 40^{\circ} . \) What is the
percentage decrease in the angle of reflection if the incident ray moves to an
angle of incidence of \( 30^{\circ} ? \)
A . \( 10 \% \)
B . 20\%
c. \( 25 \% \)
D. 30\%


Construct a \( 3 \times 2 \) matrix \( A=\left[a_{i j}\right] \)
whose elements are given by \( \boldsymbol{a}_{\boldsymbol{i} j}= \) \( \frac{(i-2 j)^{2}}{2} \)


State three differences between a real
image and virtual image.


Assertion
\( A \beta \) keto acid is decarboxylated to a ketone on simple heating, even in absence of sodalime catalyst.
Reason
A resonance stabilized carbonion is
formed
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


Name the defect of vision which makes
the eye-lens cloudy resulting in blurred.


Let \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{5} & \mathbf{8} \\ \mathbf{8} & \mathbf{1 3}\end{array}\right] \) then show that \( \boldsymbol{A} \)
satisfies the equation \( x^{2}-18 x+1= \)
\( \mathbf{0} \)


Which of the following set contains only amphoteric oxides?
A \( \cdot Z n O, P b O, S n O, A l_{2} O_{3} \)
в. \( Z n O, B a O, S O_{2}, C O \)
c. \( C O, P b O, B a O_{2}, S O_{2} \)
D. \( P_{2} O_{5}, N_{2} O_{5}, C I_{I} O_{7}, B a O \)


\( \ln S O_{3}^{2-} \)
A. \( d \pi-p \pi \) bond between \( S \) and \( O \) is delocalised
B. bonds between \( S \) and \( O \) are equivalents
C. there is \( s p^{3} \) hybridised sulphur atom
D. all of the facts given above are true


lonisation constant of \( \boldsymbol{C H}_{3} \) COOH is
\( 1.7 \times 10^{-5} \) and concentration of \( H^{+} \)
ions is \( 3.4 \times 10^{-4} . \) Then find out initial
concentration of \( \boldsymbol{C H}_{3} \boldsymbol{C O O H} \)
molecules:


The cranial capacity was largest among
the
A. Peking man
B. African man
c. Java ape man
D. Neanderthal man


Under minimum deviation condition in
a prism, if a ray is incident at an angle
\( 30^{\circ}, \) the angle between the emergent ray and the second refracting surface of the prism is:
\( A \cdot 0^{\circ} \)
B. 30 \( ^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 60^{\circ} \)


1.0 mole of ethyl alcohol and 1.0 mole
of acetic acid are mixed. At equilibrium, 0.666 mole of ester is formed. The value
of equilibrium constant is:
A . \( 1 / 4 \)
в. \( 1 / 2 \)
\( c \cdot 4 \)
\( D \)


Let \( \boldsymbol{R} \) be a relation in \( \boldsymbol{N} \) defined by \( \boldsymbol{R}= \)
\( \{(x, y): x+2 y=8, x, y \epsilon N\} . \) The
range of \( \boldsymbol{R} \) is
A \( \cdot\{2,4,6\} \)
в. \{1,2,3\}
\( \mathbf{c} \cdot\{1,2,3,4,5,6\} \)
D. None of these


The measures of two complements are
\( x \) and \( (x+50)^{\circ} . \) Find the measure of
each of them


Find the square of \( a+2 b+c \)
\( \mathbf{A} \cdot a^{2}+b^{2}+c^{2}+a b+b c+a c \)
B \( \cdot a^{2}+4 b^{2}+c^{2}+4 a b+4 b c+2 a c \)
C \( \cdot a^{3}+4 b^{3}+c^{3}+8 a b+8 b c+8 a c \)
D. \( a^{3}+b^{3}+c^{3}+4 a b+4 b c+2 a c \)