A charged particle is moving with velocity \( \vec{v} \) in a uniform magnetic field \( \vec{B} \) The magnetic force acting on it will be maximum when
A \( \cdot \vec{v} \& \vec{B} \) are in same direction
B . \( \vec{v} \& \vec{B} \) are in opposite direction
c. \( \vec{v} \& \vec{B} \) are mutually perpendicular
D. \( \vec{v} \& \vec{B} \) make an angle of \( 45^{\circ} \) with each other


What are the hydrolysis products of
sucrose?
A. Fructose + Fructose
B. Glucose + Glucose
c. Glucose + Galactose
D. Glucose + Fructose


Molecular mass of \( N a_{2} S O_{4} .10 H_{2} O \)
is:
A . 320
в. 321
\( c \cdot 322 \)
D. 324


Which of the following are properties of
the pole star?
This question has multiple correct options
A. It lies far from the axis of rotation of Earth
B. It does not appear to move
C. It appears to be overhead when seen from either North or South Pole
D. It can be located with the help of Ursa Major.


A short bar magnet of moment \( 3.2 A m^{2} \)
lies in magnetic meridian with its north pole pointing north. A neutral point is
obtained at a distance of \( 20 \mathrm{cm} \) from the
centre of the magnet. Find the horizontal.


For which of the following reactions will the equilibrium mixture contain an
appreciable concentration of both reactants and products?
A \( \cdot C l_{2}(g) \rightleftharpoons 2 C l(g) ; K_{c}=6.4 \times 10^{-39} \)
B. \( C l_{2}(g)+2 N O(g) \rightleftharpoons 2 N O C l(g) ; K_{c}=3.7 \times 10^{8} \)
c. \( C l_{2}(g)+2 N O(g) \rightleftharpoons 2 N O_{2} C l(g) ; K_{c}=1.8 \)
D. \( H_{2}(g)+I_{2}(g) \rightleftharpoons 2 H I(g) . K_{c}=49 \)


Man (Homo) originated in
A. Palaeocene
B. Miocene
c. oligocene
D. Pleistocene


Why the decrease in size between Li and Be is much greater than that between
Na and Mg or K and Ca?


The value of \( \int \frac{\log x}{(x+1)^{2}} d x \) is
A \( \cdot \frac{-\log x}{x+1}+\log x-\log (x+1)+C \)
B. \( \frac{\log x}{x+1}+\log x-\log (x+1)+C \)
c. \( \frac{\log x}{x+1}-\log x-\log (x+1)+C \)
D. \( \frac{-\log x}{x+1}-\log x-\log (x+1)+C \)


Draw an equilateral triangle. Draw angle
bisector of angle A .Let it meet the side
\( B C \) at \( D \)

Measure the Length BD and CD. Then:
\( \mathbf{A} \cdot B D>C D \)
в. \( B D<C D \)
c. \( B D=C D \)
D. None


For periodic motion of small amplitude
\( A, \) the time period \( T \) of this particle is
proportional to
\( \mathbf{A} \cdot A \sqrt{\frac{m}{\alpha}} \)
B. \( \frac{1}{A} \sqrt{\frac{m}{\alpha}} \)
c. \( A \sqrt{\frac{\alpha}{m}} \)
D. \( A \sqrt{\frac{2 \alpha}{m}} \)


Give reasons.
(a) After a hot sunny day, we sprinkle water on the roof or open ground.
(b) Perspiration keeps our body cold.
(c) Ice is rubbed on burnt part of the skin


Arrange the following compound in decreasing order of rate of electrophilic aromatic substitution reaction.
\( (\mathbf{I I}) \)
\( (\mathrm{III}) \)
\( A \cdot(\mid)>(|| \mid)>(||)>(\mid V) \)
B. \( (\| I)>(|D>(\mid I)>(\mid V) \)
\( c \cdot(1)>(11)>(111)>(1 v) \)


The space between the lens and the
cornea of the human eye is
A. Vitreous chamber
B. Anterior chamber
c. Retina
D. Iriss


Three identical cylinders of radius R are
in contact. Each cylinder is rotating
with angular velocity \( \omega . A \) thin belt is
moving without sliding on the cylinders
Calculate the magnitude of velocity of
point \( P \) with respect to \( Q . P \) and \( Q \) are two points of belt which are in contact
with the cylinder.


Primary and secondary valency of Pt in
\( \left[\boldsymbol{P t}(\boldsymbol{e n})_{2} \boldsymbol{C l}_{2}\right] \boldsymbol{C l}_{2} \) are:
\( A \cdot 4,4 \)
B. 2,6
\( c \cdot 6, \)
D. None of these


In a compound microscope, the intermediate image is :
A. virtual, erect and magnified
B. real, erect and magnifiedd
c. real, inverted and magnified
D. virtual, erect and reduced


In improper fraction the numerator is
always the denominator
A. less than
B. greater than
c. equal to
D. none


In a certain reaction. \( 10 \% \) of the
reactant decomposes in one hour, \( 20 \% \) in two hours, \( 30 \% \) in three hours, and so
on. The dimension of the velocity constant (rate constant) are:
A \( \cdot h r^{-1} \)
B. \( \operatorname{Mol} L^{-1} h r^{-1} \)
c. \( L m o l^{-1} s^{-1} \)
D. Mols"


What are metal hydroxide better alternatives than sodium hydrogen
carbonate in antacids?


Which of the following oxidation states are the most characteristic for lead and
tin respectively:
\( \mathbf{A} \cdot+2,+2 \)
B. +4,+2
\( c \cdot+2,+4 \)
\( \mathrm{D} \cdot+4,+4 \)


Integrate the following functions with respect to t: \( \int \frac{\boldsymbol{d t}}{(\boldsymbol{6 t}-\mathbf{1})} \)
A \( \cdot \frac{1}{6} \ln (6 t-1)+C \)
B \( \cdot \ln (6 t-1)+C \)
c. \( -\ln (6 t-1)+C \)
D. \( -\frac{1}{6} \ln (6 t-1)+C \)


Explain analytically how stationary waves are formed. What are nodes and
antinodes? Show that the distance
between two adjacent nodes or antinodes is \( \frac{\lambda}{2} \)


Divide
\( \left(2 a^{2}-13 a b+15 b^{2}\right) b y(a-5 b) \)


Which statement defines force?
A. When a force acts on a body that is free to move, the force is the product of the mass of the body and its acceleration
B. When a force acts on a body that is free to move, the force is the rate of change of momentum of the body
C. When a force acts on a body that is free to move, the force is the work done by the force divided by the distance moved by the body
D. When a force acts on a lever and causes a moment, the force is the moment divided by the perpendicular distance of the force from the pivot


Given \( N=10, \Sigma x=60 \) and \( \Sigma x_{i}= \)
1000. The standard deviation is


In Mendeleev's Periodic Table, why was
there no mention of Noble gases like
Helium, Neon and Argon?


Find the elastic deformation energy (in
J) of a steel rod whose one end is fixed
and the other is twisted through an
angle \( \varphi=6.0^{\circ} . \) The length of the rod is
equal to \( l=1.0 m, \) and the radius to
\( \boldsymbol{r}=\mathbf{1 0} \boldsymbol{m m} \cdot(\mathrm{G}=77.2 \mathrm{GPa}) \)


Number of faradays required to convert 1 mole of \( \boldsymbol{C r}_{2} \boldsymbol{O}_{\mathbf{7}}^{2-} \) into \( \boldsymbol{C r}^{\mathbf{3}+} \) ions is
\( A \cdot 6 \)
B. 4
\( c \cdot 3 \)
D. none of these


There is a pair of points, one on each of the lines, whose combined equation is
\( (4 x-3 y+5)(6 x+8 y+5)=0 . \) If they
are such that the distance of the point on one line is 2 units from the other line
then the points are
\( ^{\mathbf{A}} \cdot\left(\frac{1}{10}, \frac{9}{5}\right)\left(\frac{1}{2},-1\right) \)
в. \( \left(\frac{1}{2},-1\right)\left(-\frac{23}{10}, \frac{7}{3}\right) \)
\( ^{\mathbf{C}} \cdot\left(\frac{1}{10}, \frac{9}{5}\right)\left(-\frac{23}{10},-\frac{7}{5}\right) \)
D. none of these


A metal disc of radius \( a \) rotates with a
constant angular velocity \( \omega \) about its axis. The potential difference between the center and the rim of the disc is \( \boldsymbol{m}= \) mass of electron, \( \boldsymbol{e}= \) charge on
electron)
\( ^{\mathrm{A}} \cdot \frac{m \omega^{2} a^{2}}{e} \)
B. \( \frac{1 m \omega^{2} a^{2}}{2} \)
\( ^{\mathrm{c}} \cdot \frac{e \omega^{2} a^{2}}{2 m} \)
D. \( \frac{e \omega^{2} a^{2}}{m} \)


Which of the following element has the smallest atomic radius?
\( \mathbf{A} \cdot K \)
в. \( C a \)
\( c . B r \)
D. \( K r \)
E. \( Z n \)


Find the similarity statement
A. \( \Delta T S R \sim \Delta P Q R \)
B. \( \Delta T P S \sim \Delta Q R T \)
c. \( \Delta R P Q \sim \Delta T R P \)
D. \( \Delta S R Q \sim \Delta P Q S \)


The width of a plane incident wavefront
is found to be doubled in a denser
medium. If it makes an angle of \( 70^{\circ} \) with the surface, calculate the refractive index for the denser medium.


Assertion
The system of linear equations \( \boldsymbol{x}+(\sin \boldsymbol{\alpha}) \boldsymbol{y}+(\cos \boldsymbol{\alpha}) \boldsymbol{z}=\mathbf{0} \)
\( x+(\cos \alpha) y+(\sin \alpha) z=0 \quad \) has a non
\( -\boldsymbol{x}+(\sin \boldsymbol{\alpha}) \boldsymbol{y}-(\cos \boldsymbol{\alpha}) \boldsymbol{z}=\mathbf{0} \)
trivial solution for only one value of \( \boldsymbol{\alpha} \)
Iying between 0 and \( \pi \)
Reason \( \left|\begin{array}{ccc}\sin x & \cos x & \cos x \\ \cos x & \sin x & \cos x \\ \cos x & \cos x & \sin x\end{array}\right|=0 \) has no
solution in the interval \( -\frac{\pi}{4}<x<\frac{\pi}{4} \)
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


If \( f(x)=2^{x} \) then \( \frac{f(x+3)}{f(x-1)}= \)
A \( . f(x) \)
в. \( \frac{1}{f(x)} \)
c. \( f(4) \)
D. \( f(2) \)


Which of the following is not a function of visual aid?
A. It can magnify words
B. Can provide suitable intensity of light
c. can provide suitable material at proper distance
D. All


In case of an electrolyte which
dissociates in the solution, the van't
hoff factor \( i \) is :
\( A \cdot>1 \)
в. \( <1 \)
c. 1
\( \mathrm{D} \cdot>1 \) or \( <1 \)


At which part does the arm rotate?


Using properties of determinants, prove
that:
\[
\left|\begin{array}{ccc}
1+a & 1 & 1 \\
1 & 1+b & 1 \\
1 & 1 & 1+c
\end{array}\right|=a b c+b c+
\]
\( c a+a b \)


Fill in the blank.
exert pressure on the walls of the containers.
A. Only gases
B. Only liquids
c. Gases and liquids
D. Neither gases nor liquids


Distinguish between Thermoplastics and thermosetting plastics.


Convert \( 290^{\circ} \) into radian measure


Chasmogamy is pollination in.
A. Bud condition
B. Closed flowers
c. open flowers
D. Unrelated flowers


Find out the potential energy of the force \( \boldsymbol{F}=\boldsymbol{y} \hat{\boldsymbol{i}}+\boldsymbol{x} \hat{\boldsymbol{j}} \boldsymbol{N} \)
A. \( -x y+c \)
B. \( x y+c \)
c. \( -x y-c \)
D. \( x y-c \)


Write the formula for limit of resolution
of microscope and explain the symbols
used.


Calculate EMF of \( \left.Z n\right|_{(0.01 M)} ^{Z n^{2+}} \|_{(0.1 M)}^{A g^{+}} \mid A g \)
\( E_{Z n / Z n^{+2}}^{0}=0.762 V E_{A g^{+} / A g}^{0}=+0.80 V \)
A. \( 1.56 v \)
B. 2.36V
c. \( 0.236 v \)
D. 0.118v


The Southern blot technique is used for the detection of
A. DNA
B. RNAA
c. Protein
D. RNA and DNA


Why two streamlines never intersect?


A man sets his watch by the noon
whistle of a factory at a distance of
1.5 \( k m \). Then the number of seconds his
watch slower than the clock of the
factory (velocity of sound \( =\mathbf{3 3 2 m} / \mathrm{s} \)
is
A. 4.52 sec
B. 5.35 sec
c. 2.18 sec
D. 3.76 sec


Inter fascicular cambium:
A. Is same as fascicular cambium
B. Are cylindrical meristems
C . Cannot produce secondary tissues
D. Are actually cork-cambium


During the melting of a slab of ice at
\( 273 \mathrm{K} \) at atmospheric pressure.
This question has multiple correct options
A. Positive work is done by the ice-water system on the atmosphere
B. Positive work is done on the ice-water system by the atmosphere
C. The internal energy of ice-water system increases
D. The internal energy of the ice-water system decreases


The bright streaks of light seen occasionally in the sky are
A. planets
B. satellites
c. meteors
D. constellations


An intense stream of water of cross-
sectional area \( A \) strikes a wall at an
angle \( \theta \) with the normal to the wall and
returns back elastically. If the density of
water is \( \rho \) and its velocity is \( v, \) then the
force exerted in the wall will be
A .2 Avpcos \( \theta \)
B . \( 2 A v^{2} \rho \cos \theta \)
\( \mathbf{c} \cdot 2 A v^{2} \rho \)
D. 2 Av \( \rho \)


State whether true or false:
A dynamo converts electric energy into mechanical energy.
A. True
B. False


Petroleum oil is found:
A. deep underground (sea beds)
B. in mountains
C . in glacier
D. in river


Relative permittivity and permeability
of a material are \( \epsilon_{\mathrm{r}} \) and \( \mu_{\mathrm{r}}, \) respectively.
Which of the following values of these quantifies are allowed for a diamagnetic material?
A \( \cdot \epsilon_{\mathrm{r}}=0.5, \mu_{\mathrm{r}}=0.5 \)
B . \( \epsilon_{\mathrm{r}}=1.5, \mu_{\mathrm{r}}=1.5 \)
\( \mathbf{c} \cdot \epsilon_{\mathrm{r}}=0.5, \mu_{\mathrm{r}}=1.5 \)
D. \( \epsilon_{\mathrm{r}}=1.5, \mu_{\mathrm{r}}=0.5 \)


The lateral magnification of the lens with an object located at two different
positions \( u_{1} \) and \( u_{2} \) are \( m_{1} \) and \( m_{2} \) respectively. Then the focal length of the lens is :
\( \mathbf{A} \cdot f=\sqrt{m_{1} m_{2}}\left(u_{2}-u_{1}\right) \)
в. \( \frac{m_{2} u_{2}-m_{1} u_{1}}{m_{2}-m_{1}} \)
c. \( \frac{\left(u_{2}-u_{1}\right)}{\sqrt{m_{2} m_{1}}} \)
D. \( \frac{\left(u_{2}-u_{1}\right)}{\left(m_{2}\right)^{-1}-\left(m_{1}\right)^{-1}} \)


The outputs of two NOT gates are fed to
a NOR gate. Draw the logic circuit of the combination of gates. Give its truth
table. Identify the gate represented by this combination.


Passivity of iron is due to formation of:
A. \( F e_{2} O_{3} \)
в. \( F e_{3} O_{4} \)
\( \mathrm{c} \cdot \mathrm{FeSO}_{4} \)
D. none of these


Size of the agriculture holding in a survey of 200 families is given in the following table:
\( \begin{array}{lll}\text { Size of } & \text { o- } & \text { 5- } \\ \text { Agriculture } & \text { 5 } & \text { 10 }\end{array} \)
10
15 २०
Number of
family \( \quad 10 \)
15 \( \quad \) 30 \( \quad 80 \)
Complete median and mode size of the
holdings.


Observe the given figures of three
different plant tissues and select the correct option.
28
A. 'a' and 'b' consist of living cells while 'c' consits of dead cells
B. Cytoplasm is present in cells of 'a' while it is absent in cells of 'b' and 'c'.'
C. Cell walls of 'a' 'b' and 'c' bear uniform tickening of suberin
D. 'a' provides mechanical strength to the plant while 'b' and 'c' serve as storage tissues.


The number of ways in which one can
post 5 letters in 6 post boxes
\( \mathbf{A} \cdot 6^{5} \)
B . 30
\( \mathbf{c} \cdot 5^{6} \)
D. 11


What is metallurgy?


The binding energies per nucleon for deuteron and helium are \( 1.1 \mathrm{MeV} \) and 7
MeV respectively. Calculate the energy released when two deuterons fuse to
form a helium nucleus.
A. 23.6 MeV
B. 25.8 MeV
c. \( 19.2 \mathrm{MeV} \)
D. 28.8 MeV


Not considering the electronic spin, the degeneracy of the second excited state
\( (n=3) \) of \( H \) -atom is \( 9, \) while the
degeneracy of the second excited state
of \( \boldsymbol{H}^{-} \) is


When we inhale helium gas funny sound appear which is due to:
A. high density of helium than air
B. low density of air than helium
c. low density of helium than air
D. reaction between air and helium


A person needs a lens of power -4.5 D for correction of her vision. What is the
focal length of the corrective lens?
A. \( f=-0.25 \mathrm{m} \)
B. \( f=+0.22 \mathrm{m} \)
c. \( f=1.22 \mathrm{m} \)
D. \( f=-0.22 \mathrm{m} \)


Calculate the values of the
determinants:
\( \left|\begin{array}{cccc}\mathbf{1} & \mathbf{1} & \mathbf{1} & \mathbf{1} \\ \mathbf{1} & \mathbf{2} & \mathbf{3} & \mathbf{4} \\ \mathbf{1} & \mathbf{3} & \mathbf{6} & \mathbf{1 0} \\ \mathbf{1} & \mathbf{4} & \mathbf{1 0} & \mathbf{2 0}\end{array}\right| \)


The elements of groups, 1,2,13,14,15,16 and 17 are collectively called:
A. Noble gases
B. Representative or normal elements
c. Transition elements
D. Inner transition elements


During the formation of rain, when water vapour changes back to liquid in the form of rain drops:
A. Heat is absorbed
B. Heat is released
c. Heat is first absorbed and then released
D. Both (A) and (B)


A chord of a circle of radius \( 6 \mathrm{cm} \)
subtends a right angle at centre. The area of the minor segment \( (\pi=3.14) \)
is
A \( \cdot 9.82 \mathrm{cm}^{2} \)
B. \( 10.14 \mathrm{cm}^{2} \)
c. \( 10.26 \mathrm{cm}^{2} \)
D. \( 12.35 \mathrm{cm}^{2} \)


Refer to the given figure and select the
correct option.
A. (A) - Stipe, (B) - Holdfast, (C) - Frond
B. (A) - Frond, (B) - Stipe, (C) - Holdfast
C. (A) - Holdfast, (B) - Frond, (C) - Stipe
D. (A) - stipe, (B) - Frond, (C) - Holdfast


If the atomic number of an element is
\( 33, \) it will be placed in the periodic table in the
A. First group
B. Second group
C. Fifth group
D. Fourth group


At what value of \( \omega \) will the frequency
band width registered by stationary
receiver be equal to \( 200 H z ? \)
A . \( 24 r a d / \)
B. 34rad/s
c. \( 44 r a d / s \)
D. \( 54 r a d / \)


If \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{5} \boldsymbol{a} & -\boldsymbol{b} \\ \mathbf{3} & \mathbf{2}\end{array}\right] \) and \( \boldsymbol{A} \) adj \( \boldsymbol{A}=\boldsymbol{A} \boldsymbol{A}^{\boldsymbol{T}} \)
then \( 5 a+b \) is equal to:
A . 13
B. -
c. 5
D.


Peroxy linkage is present in oleum \( \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{7} \)
A. True
B. False


Two persons of masses \( 55 k g \) and \( 65 k g \)
respectively, are at the opposite ends of a boat. The length of the boat is \( 3.0 m \)
and weights 100kg. The 55kg man
walks up to the \( 65 k g \) man and sits with
him. If the boat is in still water the
centre of mass of the system shifts by:
A. zero
B. \( 0.75 m \)
\( c .3 .0 m \)
D. \( 2.3 m \)


\( \left|\begin{array}{ccc}\mathbf{0} & \boldsymbol{a} \boldsymbol{b}^{2} & \boldsymbol{a} \boldsymbol{c}^{2} \\ \boldsymbol{a}^{2} \boldsymbol{b} & \boldsymbol{0} & \boldsymbol{b} \boldsymbol{c}^{2} \\ \boldsymbol{a} \boldsymbol{c}^{2} & \boldsymbol{b}^{2} \boldsymbol{c} & \boldsymbol{0}\end{array}\right|= \)
\( \mathbf{A} \cdot a^{3} b^{3} c^{3}+a^{2} b^{3} c^{4} \)
B \( \cdot a^{3} b^{3} c^{3} \)
\( \mathbf{c} \cdot 2 a^{3} b^{3} c^{3} \)
D・ \( (2 a b c)^{3} \)


Which of the following statements is
not correct?
A. The shape of an atomic orbital depends on the azimuthal quantum number
B. The orientation of an atomic orbital depends on the magnetic quantum number
C. The energy of an electron in an atomic orbital of multielectron atom depends on the principal quantum number
D. The number of degenerate atomic orbitals of one type depends on the values of azimuthal and magnetic quantum numbers


Let \( 2 x+3 y+4 z=9, x, y, z>0, \) then
the maximum value of
\( (1+x)^{2}(2+y)^{3}(4+z)^{4} \) is
A \( \cdot 2^{9} \)
в. \( 4^{\text {? }} \)
\( ^{c} \cdot\left(\frac{11}{3}\right)^{9} \)
D. \( \left(\frac{11}{6}\right)^{9} \)


\( \operatorname{Let} \boldsymbol{f}\left(\frac{\boldsymbol{x}+\boldsymbol{y}}{\mathbf{2}}\right)=\frac{\mathbf{1}}{\mathbf{2}}[\boldsymbol{f}(\boldsymbol{x})+\boldsymbol{f}(\boldsymbol{y})] \) for
real \( x \) and \( y . \) If \( f^{\prime}(0) \) exists and equals
-1 and \( f(0)=1 \) then the value of \( f(2) \)
is
A . 1
B. -
c. \( 1 / 2 \)
D. 2


Convert 0.25 into fraction.
A \( \cdot \frac{3}{4} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{1}{4} \)
D. none of the above


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) if \( \boldsymbol{y}=\sin ^{-1}(\boldsymbol{2} \boldsymbol{x} \sqrt{\mathbf{1}-\boldsymbol{x}^{2}}) \)
\( \frac{\mathbf{- 1}}{\sqrt{\mathbf{2}}}<\boldsymbol{x}<\frac{\mathbf{1}}{\sqrt{\mathbf{2}}} \)


One gas bleaches the coloured matter by reduction temporary while the other one by oxidation permanently. The
gases are respectively:
A. \( S O_{2} \) and \( C l_{2} \)
в. \( O_{3} \) and \( C l_{2} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{S} \) and \( \mathrm{CO}_{2} \)
D. \( C l_{2} \) and \( C O_{2} \)


Assertion
There are two neutral points on a horizontal board when a magnet is held vertically on the board
Reason
At the neutral point the net magnetic field due to the magnetic and magnetic field of the earth is 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. Both Assertion and Reason are incorrect


Colchicum plant which gives colchicine alkaloid belongs to which family?
A. Leguminosae
B. Malvaceae
c. Liliaceae
D. cruciferae


The pressure \( \boldsymbol{P} \) and the volume \( \boldsymbol{v} \) of \( \mathbf{a} \)
gas are connected by the relation \( p v^{1.4}= \) const. Find the percentage error in \( p \) corresponding to a decrease of \( \frac{1}{2} \% \)
in \( \boldsymbol{v} \)


A thin lens of focal length \( 10 \mathrm{cm} \) is cut
into two equal halves and are kept as
shown in figure. It an object \( \boldsymbol{O} \) is placed
at distance \( 10 \mathrm{cm} \) from the optical
centre of combination. then the
distance of image from object will be
\( A \cdot 5 \mathrm{cm} \)
B. 7.5 \( \mathrm{cm} \)
\( c \cdot 10 \mathrm{cm} \)
D. 20 cm


Find the acceleration of \( 3 \mathrm{kg} \) mass when
acceleration of \( 2 \mathrm{kg} \) mass is \( 2 m s^{-1} \) as
shown in figure


Looking at the alkali metals, which one would have the strongest Coulombic forces leading to the highest melting point when paired with the corresponding Halogen in the same
row?
A . Lithium
B. Sodium
c. Potassium
D. Rubidium


Benny thinks of a number subtracts 18
from it and divides the difference by 3 The result is \( -4 . \) What is the number


Which of the following does not form peroxides?
\( A . B a \)
в. \( B e \)
\( c . C a \)
D. \( M g \)


The roots of the following quadratic equation are not real \( 2 x^{2}-3 x+5=0 \)
A . True
B. False


Assertion
Sulphuric acid is more viscous than
water.
Reason
Concentrated sulphuric acid has a great affinity for water
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 eggs of silk moth are
A. Homolecithal
B. Telolecithal
c. Mesolecithal
D. Centrolecithal


Choose the correct alternative, in
relation to properties of magnetic lines of force.
A. Magnetic lines of force start from south pole and end on north pole
B. Magnetic lines of force intersect each other at the poles
c. Magnetic lines of force are far from each other where the field is strong
D. Tangent at any point on the magnetic lines of force gives the direction of the magnetic field at that point.


Answer the following question very
shortly.
What is weather?


Match List 1 with List 2:


Write the formula for each of the
following complexes:
(a) hexamine cobalt (III) chloride
(b) potassium iron (III)
hexacyanoferrate (II)
(c) diamminedichloroplatinum (II)
(d) tetracarbonylnickel (0)
(e) triamminechlorocyanonitrocobalt
\( (\| I) \)
(f) lithium tetrahydridoaluminate (III)
(g) sodium bis (thisulphato)argentate
(1)
(h) nickel hexachloroplatinate (IV)
(i) tetraammineplayinum(II) amminetri chloroplatinate (II)


Assertion
\( C_{P} \) is always greater than \( C_{V} \) in gases.
Reason

Work done at constant pressure is more
than at constant volume.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Both Assertion and Reason are incorrect.


If \( a=\cos \frac{4 \pi}{3}+i \sin \frac{4 \pi}{3} \) then \( (1+a)^{3 n} \)
\( A \)
B.
c. 1
D・ \( (-1)^{n} \)


State true or false:
\( \boldsymbol{F}(\boldsymbol{x}, \boldsymbol{y})=\boldsymbol{e}^{\boldsymbol{y} / \boldsymbol{x}}+\ln \boldsymbol{x}-\ln \boldsymbol{y} \) is
homogeneous function of degree zero.
A . True
B. False


There is \( S-S \) linkage in:
This question has multiple correct options
\( \mathbf{A} \cdot S_{2} O_{3}^{2-} \)
B. \( S_{2} O_{4}^{2-} \)
\( \mathbf{c} \cdot S_{2} O_{5}^{2-} \)
\( \mathrm{D} \cdot S_{2} O_{7}^{2-} \)


What is the smallest positive integer for which \( (1+i)^{2 n}=(1-i)^{2 n} ? \)


Silver containing ore can be converted
into silver in cyanide process.
If true enter 1 , else enter 0


\( \lim _{x \rightarrow-1} \frac{\sqrt{\pi}-\sqrt{\cos ^{-1} x}}{\sqrt{x+1}} \) is equal to
\( \mathbf{A} \cdot \frac{1}{\sqrt{2 \pi}} \)
B. \( \frac{1}{\sqrt{\pi} \pi} \)
\( c \cdot \frac{1}{\sqrt{2}} \)
D. none of these


A satellite moves around the earth in a
circular orbit with speed \( V \). If \( m \) is
mass of the satellite then its total
energy is
A \( \cdot \frac{1}{2} m V^{2} \)
в. \( m V^{2} \)
c. \( -\frac{1}{2} m V^{2} \)
D. \( \frac{3}{2} m V^{2} \)


Assertion
Set of any four vectors is always linearly dependent
Reason
If a subset of \( n \) vectors is \( L . D, \) then set
of those \( n \) vectors is linearly dependent
\( \boldsymbol{L} \cdot \boldsymbol{D} \)
A. Both Assertion \& Reason are individually true \& Reason is correct explanation of Assertion
B. Both Assertion \& Reason are individually true but Reason is not the , correct (proper) explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true


The daughter cells produced by a sexual reproduction are genetically identical to the parent cell.
A. True
B. False


A random variable \( X \) has the following probability distribution:
\[
\begin{array}{lllll}
\boldsymbol{X} & 0 & 1 & 2 & 3 \\
P(X= & \frac{1}{4} & 2 a & 3 a & 4 a
\end{array}
\]
Then \( P(1 \leq X \leq 4) \) is:
A. \( \frac{10}{21} \)
в.
c. \( \frac{1}{14} \)
D.


The dimensional formula for magnetic flux is
A \( \cdot\left[M L^{2} T^{-2} A^{-1}\right] \)
B \( \cdot\left[M L^{3} T^{-2} A^{-2}\right] \)
c. \( \left[M^{0} L^{-2} T^{-2} A^{-2}\right] \)
D・ \( \left[M L^{2} T^{-1} A^{2}\right] \)


Three unequal resistance are connected in parallel. Two of these resistances are
in the ratio \( 1: 2 . \) The equivalent
resistance of these three connected in
parallel is \( 1 \Omega . \) What is the highest resistance value among these three resistances if no resistance is
fractional?
A . \( 10 \Omega \)
B. \( 8 \Omega \)
\( c .15 \Omega \)
D. \( 6 \Omega \)


Solve: \( 14 y-8=13 \)
A . 1.9
в. 1.5
c. \( 1 . \)
D. 1.6


Explain working of electroscopes?


The value of \( \sin \left(2 \sin ^{-1}(0.8)\right) \) is equal
to
\( A \cdot \sin 1.2^{\circ} \)
B. \( \sin 1.6^{\circ} \)
c. 0.48
D. 0.96


If the number of turns and length of the long solenoid are doubled without
changing the area, then its self-
inductance \( L \) will be:
A . same
B. 2 times
c. 3 times
D. 4 times


Divide 96 into four parts which are in
A.P. and the ratio between product of their means to product of their
extremes is 15: 7


Aluminium occurs as a compound
whereas gold is found in the free state.
Why?


Which of the following statements are true (T) and which are false (F)?
If three sides of a quadrilateral are equal, it is a parallelogram.
A . True
B. False


Q Type your question.
100010
equilateral triangular body of side \( l \) This body is placed on a horizontal frictionless table (x-y plane) and is
hinged at point \( A \) so that it can move
without friction about the vertical axis
through \( A \). The body is set into
rotational motion on the table about
this axis with a constant angular
velocity \( \omega(a) \) Find the magnitude of the
horizontal force exerted by the hinge on
the body (b) At time \( T \), when side \( B C \) is
parallel to x-axis, force \( \boldsymbol{F} \) is applied on
\( B \) along \( B C \) (as in the figure). Obtain
the \( x \) -component and the \( y \) -component of the force exerted by the hinge on the body, immediately after time \( T \)


The value of \( \frac{\left(1+\tan ^{2} \theta\right)}{\left(1+\cot ^{2} \theta\right)} \) is
\( \mathbf{A} \cdot \tan ^{2} \theta \)
B \( \cdot \cot ^{2} \theta \)
\( \mathbf{c} \cdot \sec ^{2} \theta \)
D. \( \operatorname{cosec}^{2} \theta \)


If \( A \) and \( B \) are two events in a sample
space \( S \) such that \( P(A) \neq 0, \) then
\( P\left(\frac{B}{A}\right)= \)
A \( \cdot P(A) \cdot P(B) \)
в. \( \frac{P(A \cap B)}{P(B)} \)
c. \( \frac{P(A \cap B)}{P(A)} \)
D \( \cdot P(B) \)


Mention the enthalpy of mixing
\( \left(\triangle_{m i x} H\right) \) value to form an ideal
solution.


General second degree equation in \( x \) and \( y \) is \( a x^{2}+2 h x y+b y^{2}+2 g x+ \)
\( 2 f y+c=0, \) Where \( a, h, b, g, f \) and \( c \) are
constats.

Prove that condition for it to be a circle
is: \( a=b \) and \( h=0 \)


The process of vulcanization was introduced by
A. Charles Goodyear
B. Kolbe
c. wohler
D. zeigher


For \( \frac{N}{100} H_{2} S O_{4}, \) pH value is:
\( A \cdot 2 \)
B. 0.586
c. 0.856
D. none


A string of length \( 20 \mathrm{cm} \) and linear
mass density \( 0.4 g / c m \) is fixed at both ends and is kept under a tension of
16 \( N . \) A wave pulse is produced at \( t=0 \)
near an end as shown in figure which travels towards the other end. The string have the shape shown in the figure \( \operatorname{again} \operatorname{in} 2 \times 10^{-x} \) sec. Find \( x \)
\( A \)
B.
\( c \)
D.


Take a glass and fill it up with water up to the brim. Make sure that there are no
air bubbles. Take a thick, stiff piece of
cardboard and put it over the glass.
Place your hand over the card and
quickly turn the glass upside down. Now slowly remove your hand.
What does this experiment show?
A. Air occupies space.
B. Air exerts pressure
C. Air has weight
D. All of these


f \( z_{1}, z_{2}, z_{3} \) are unlmodular complex
numbers then the greatest value of
\( \left|z_{1}-z_{2}\right|^{2}+\left|z_{2}-z_{3}\right|^{2}+\left|z_{3}-z_{1}\right|^{2} \) equal
to
\( A \cdot 3 \)
B. 6
\( c \cdot s \)
\( D \cdot \frac{27}{2} \)


Who was the first civilized man?
A. Cromagnon man
B. Neanderthal man
c. Heidelberg man
D. Ternifier man


Which of the following processes
creates high osmotic pressure in
uriniferous tubule?
A. Active secretion of \( N a^{+} \) into efferent arteriole followed
by Cl secretion
B. Active \( N a^{+} \) absorption followed by Cl absorption
C. Active secretion of \( C l^{-} \) and absorption of \( N a^{+} \) into efferent arteriole
D. Active Cl absorption followed by absorption of \( N a^{+} \)


How does the standard enthalpy of
formation help to predict the relative stabilities of compounds.


\( I^{\prime} \) is the incentre of triangle of \( A B C \)
whose corresponding sides are \( a, b, c \) respectively, \( a \overrightarrow{I B}+b \overrightarrow{I B}+c \overrightarrow{I C} \) is
always equal to
A. 0
в. \( (a+b+c) \overrightarrow{B C} \)
c. \( (\vec{a}+\vec{b}+\vec{c}) \overrightarrow{A C} \)
D. \( (a+b+c) \overrightarrow{A B} \)


Assertion
An aqueous solution of ammonium
acetate can act as a buffer.
Reason
Acetic acid is a weak acid and
\( N H_{4} O H \) is a weak base.
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 most common respiratory
substrate.


For the reaction, \( N_{2}+3 H_{2} \rightleftharpoons 2 N H_{3} \)
the rate of change of concentration for hydrogen is \( 0.3 \times 10^{-4} M s^{-1} \)
The rate of change of concentration of
ammonia is \( \left(\operatorname{in} M s^{-1}\right) \)
A . \( -0.2 \times 10^{-4} \)
В. \( 0.2 \times 10^{-4} \)
c. \( 0.1 \times 10^{-4} \)


Metacoel is the cavity in the
A. Cerebral hemispheres
B. Diencephalon
c. cerebellum
D. Medulla oblongata


Sulfur containing amino acid is :
A. Alanine
B. Proline
c. Tyrosine
D. Cysteine


Find the Odd one among : 7, 26, 65, 124, 215,342
A. 7
B. 26
\( c \cdot 65 \)
D. 124


The differential equation of all nonhorizontal lines in a plane is
A \( \cdot \frac{d^{2} y}{d x^{2}}=0 \)
B. \( \frac{d^{2} x}{d y^{2}}=0 \)
c. \( \frac{d y}{d x}=0 \)
D. \( \frac{d x}{d y}=0 \)


In the cyanide extraction process of
silver from argentite ore, the oxidising
and reducing agents used are:
A. \( O_{2} \) and \( C O \) respectively
B. \( O_{2} \) and \( Z n \) dust respectively
C. \( H N O_{3} \) and \( Z n \) dust respectively
D. \( H N O_{3} \) and \( C O \) respectively


At \( 1000 \mathrm{K}, \) the equilibrium constants for
the following equilibrium are \( K_{1} \) and
\( \boldsymbol{K}_{2} \)
\( \operatorname{COCl}_{2}(g) \rightleftharpoons C O(g)+C l_{2}(g) ; K_{1}= \)
\( \mathbf{0 . 3 2 9} \)
\( 2 C O(g)+O_{2}(g) \rightleftharpoons 2 C O_{2}(g) ; K_{2}= \)
\( 2.24 \times 10^{22} \)
For the equilibrium, \( 2 C O C l_{2}(g)+O_{2}(g) \rightleftharpoons 2 C O_{2}(g)+ \)
\( 2 C l_{2}(g), \) the equilibrium constant \( K_{3} \)
is
A \( .2 .424 \times 10^{22} \)
В. \( 2.424 \times 10^{21} \)
c. \( 4.84 \times 10^{20} \)
D. 2.424 \( \times 10^{20} \)


Find the distance of a perpendicular
from the centre of a circle to the chord if
the diameter of the circle is \( 30 \mathrm{cm} \) and
its chord is \( 24 \mathrm{cm} \)
A \( .6 \mathrm{cm} \)
B. \( 7 \mathrm{cm} \)
\( c .9 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)


In the extraction of copper from pyrites,
iron is removed as:
A. \( F e S O_{4} \)
в. Fesi Оз\( _{3} \)
\( \mathbf{c} \cdot F e_{3} O_{4} \)
D. \( F e_{2} O_{3} \)


Assertion
Carbon monoxide is a poisonous gas.
Reason
Carbon monoxide combines with
haemoglobin to form carboxyhaemoglobin whch prevents absorption
of oxygen by it.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Pruning of plants promotes branching due to sensitisation of axillary buds by
\( A \cdot \) IAA
B. Ethylene
c. Gibberellin
D. cytokinin


The rate of reaction increases with rise
in temperature because of :
A. increase in the number of activated molecules
B. increase in the activation energy
C. decrease in the activation energy
D. increase in the number of molecular collisions


For an electrochemical reaction
occuring in a galvanic cell. \( \mathbf{2} \boldsymbol{F} \boldsymbol{e}_{(\boldsymbol{a q})}^{+\mathbf{3}}+\boldsymbol{Z} \boldsymbol{n}_{(s)} \rightarrow \boldsymbol{Z} \boldsymbol{n}_{(a q)}^{+2}+\mathbf{2} \boldsymbol{F} \boldsymbol{e}_{(a q)}^{+\mathbf{2}} \)
if concentration of \( F e^{+2} \) is increased.
A. \( E_{\text {cll}} \) will remain unchanged
B. \( E_{\text {cll}} \) will decrease
c. \( p H \) of the solution will change
D. less non P-V work will be obtained


\( \boldsymbol{H} \boldsymbol{B r} \) reacts with \( \boldsymbol{C H}_{2}=\boldsymbol{C H}-\boldsymbol{O C H}_{3} \)
under anhydrous conditions at room temperature to give:
\( \mathbf{A} \cdot C H_{3} C H O \) and \( C H_{3} B r \)
в. \( B r C H_{2} C H O \) and \( C H_{3} O H \)
c. \( B r C H_{2} C H_{2} O C H_{3} \)
D. \( C H_{3}-C H(B r)-O C H_{3} \)


Correct IUPAC naming of the given
compound is:
A . pent-3-ene
B. 2, 2-diethylethene
c. hexene
D. 2-ethylbutene


Assertion
Super oxide ion is paramagnetic whereas peroxide ion is diamagnetic.
Reason
Super oxide ion has one unpaired electron whereas per oxide ion has no unpaired electron.
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


Write the arithmetic progression when
first term \( a \) and common difference \( d \)
are as follows:
\( \boldsymbol{a}=-\mathbf{1} ; \boldsymbol{d}=\frac{\mathbf{1}}{\mathbf{2}} \)


Isotopes are the atoms of the same element which contain equal number of
A . nucleons
B. neutrons
c. protons
D. neutrons and protons


In RNA, nucleotides are bonded by
\( A . \) H bonds
B. Phospodiester bonds
c. lonic bonds
D. None of the above


A vector \( a \) is collinear with vector \( b= \) \( \left(6,-8,-\frac{15}{2}\right) \) and make an acute
angle with the positive direction of \( z^{-} \) axis. If \( |a|=50, \) then \( a= \)
в. (24,-32,30)
c. (-24,32,30)
D. None of these


A bullet of mass 10 g moving with velocity of \( 100 \mathrm{m} / \mathrm{sec} \) hits a wooden log and penetrates it up to thickness of 5 \( \mathrm{cm} . \) The resistance force of log is:
A . 200
B. 500 N
c. \( 1000 N \)
D. 600 N


Assertion
The equation \( V=R i \). does not apply to
those conducting devices which do not obey Ohm's law.
Reason
\( V=R i \) is a statement of Ohm's law.
A. Both Assertion and Reason are correct and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


When \( S O_{2} \) is passed through acidified
\( K_{2} C r_{2} O_{7} \) solution:
A. the solution truns blue.
B. \( S O_{2} \) is reduced.
C. green \( C r_{2}\left(S O_{4}\right)_{3} \) is formed
D. the solution is decolourised


Which of the following sequences is correct to initiate inspiration?
(i) The contraction of external
intercostal muscles raises the ribs and
sternum
(ii) Volume of thorax increases in the dorso-ventral axis
(iii) Intrapulmonary pressure decreases
(iv) Diaphragm contraction
(v) Air rushes into lungs
(vi) Volume of thorax increases in the
anterior-posterior axis
\( A \cdot(i),(i i),(i v),(v),(i i i),(v i) \)
B. (i), (ii), (iii), (iv), (vi), (v)
c. (i), (ii),(iv),(vi),(iii),(v)
D. (vi), (v), (i), (ii), (iii), (iv)


Evaluate the integral:
\( \int_{0}^{2} \frac{x}{3} d x \)


Carbon has four electrons in its valence
shell. Which type of compounds can be formed by carbon atom and why? Give any one example of such compounds.


\( 2 y=-x+1 \)


The sum of two numbers is 80 and the
greater number exceed twice the
smaller by 11. Find the larger numbers.


Octahedral complex of \( N i(I I) \) must be:
A. inner orbital
B. outer orbital
c. inner or outer orbital depending upon the strong or weak field ligand
D. none of these


Classify the following curve as open or
closed


Let \( R \) be the set of real numbers and the
functions \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) and \( \boldsymbol{g}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be
defined by \( f(x)=x^{2}+2 x-3 \) and
\( g(x)=x+1 . \) Then the value of \( x \) for
which \( f(g(x))=g(f(x)) \) is
A . -1
B.
c. 1
\( D \)


Plots for \( 2 s \) orbital are:
\( X, Y \) and \( Z \) are respectively
\( \mathbf{A} \cdot R, R^{2} \) and \( 4 \pi r^{2} R^{2} \)
B \( \cdot R^{2}, R \) and \( 4 \pi r^{2} R^{2} \)
\( \mathbf{C} \cdot 4 \pi r^{2} R^{2}, R^{2} \) and \( R \)
D \( \cdot R^{2}, 4 \pi r^{2} R^{2} \) and \( R \)


Day Number of coffee sold
3
21
4
35
5
\[
53
\]
6
\[
75
\]
7
101
The above data shows the number of
coffee sold by the famous coffee shop at
a particular venue. If the number is
shown by \( v \) and days as \( t, \) then they are
related by
\( \mathbf{A} \cdot v(t)=2 t^{2}+3 \)
\( B \)
\[
v(t)=\frac{t^{2}}{2}+3
\]
C \( \cdot v(t)=2 t^{2}+21 \)
D.
\[
v(t)=\frac{t^{2}}{2}+21
\]


The thermos bottles have a highly polished interior made of stainless steel, which makes them almost
unbreakable. These thermos bottles
also covered with insulated material to
keep substances hot by reducing heat loss. Identify which of the following mode of heat transfer is restricted by the insulated material?
A. Absorption
B. Conduction
c. convection
D. Radiation
E. Evaporation


Study the figure given below and mark
the correct statement about \( K_{c} \) and
dependence of extent of reaction on it.
A. \( x \) - Reaction does not occur
Y - Reaction proceeds to completion; Z - Reaction does not occur
B. X- Reaction completes; Y - Reaction does not occur; Z Reactants and products are at equilibrium
c. \( x \) - Reaction hardly occurs;
Y - Reactants and products are at equilibrium; Z - Reaction proceeds completion
D. \( x \) - Reaction proceeds completion; \( Y \) - Reactants and products are at equilibrium; Z - Reaction hardly occurs


Based upon your understanding of the basic principles of molecular orbitals it
should be possible to answer the following question.Consider the six
molecular orbitals of benzene shown.
How many of these orbitals will contain
electrons?
(I)
\( (\mathrm{II}) \)
(III)
\( (\mathrm{IV}) \)
\( (\mathrm{V}) \)
A. Only one molecular orbitals
B. Only two molecular orbitals
C. Only three molecular orbitals
D. All six molecular orbitals


What is the length of arc AB making angle of \( 126^{0} \) at center of radius \( 8 ? \)
A . \( 2.6 \pi \)
в. \( 5.6 \pi \)
c. \( 7.6 \pi \)
D. \( \frac{1}{2} \pi \)


If the figure PQRS is a square M is the midpoint of PQ \& RM \( \perp \) AB. Prove that
\( \mathrm{RA}=\mathrm{RB} \)


The weight of a person on earth is \( 600 N . \) His weight on moon will appear
as:
A . zero
B. \( 100 N \)
c. \( 600 N \)
D. 3600 N


Dim light causes the pupil to
A. Open
B. close
c. contract
D. Expand


Which of the following conditions apply to resonating structures? This question has multiple correct options
A. The contributing structures should have nearly same energies.
B. The contributing structures should be represented such that like charges reside on atoms that are far
C. The more electropositive element should preferably have positive charge and more electronegative element should have negative charge
D. The contributing structures must have the same number of unpaired electrons


In a reaction between two gaseous reactants the number of binary collisions per second (Z) is given by:
A \( \cdot Z=\pi \sigma_{A-B}^{2} \sqrt{\frac{8 K T}{\pi \mu}} n_{A} \cdot n_{B} \)
В . \( Z=\pi \sigma_{A-B} \sqrt{\frac{8 K T}{\pi \mu}} \)
c. \( Z=\sigma_{A-B}^{2} \sqrt{\frac{8 K T}{\pi \mu}} n_{A} . n_{B} \)
D \( \cdot Z=\sigma_{A-B} \sqrt{\frac{8 K T}{\pi \mu}} n_{A} \cdot n_{B} \)


A plastic ball is dropped from a height of \( 1 m \) and rebounds several times from
the floor. If 0.13 sec elapse from the moment it is dropped to the second impact with the floor, what is the
coefficient of restitution?
A . 0.85
B. 0.25
c. 0.39
D. 0.65


A moving coil galvanometer, having a
resistance \( G \), produces full scale
deflection when a current \( I_{g} \) flows
through it. This galvanometer can be
converted into (i) an ammeter of range
\( \mathbf{0} \operatorname{to} \boldsymbol{I}_{\mathbf{0}}\left(\boldsymbol{I}_{\mathbf{0}}>\boldsymbol{I}_{\boldsymbol{g}}\right) \) by connecting a shunt
resistance \( \boldsymbol{R}_{\boldsymbol{A}} \) to it and (ii) into a
voltmeter of range 0 to \( V\left(V=G I_{0}\right) \) by
connecting a series resistance \( \boldsymbol{R}_{\boldsymbol{V}} \) to it.
Then
\( \mathbf{A} \cdot_{R_{A} R_{V}}=G^{2}\left(\frac{I_{g}}{I_{0}-I_{g}}\right) \) and \( \frac{R_{A}}{R_{V}}=\left(\frac{I_{0}-I_{g}}{I_{g}}\right) \)
\( ^{\mathrm{B}} R_{A} R_{V}=G^{2} \) and \( \frac{R_{A}}{R_{V}}=\left(\frac{I_{g}}{I_{0}-I_{g}}\right)^{2} \)
\( ^{\mathbf{c}} \cdot_{R_{A} R_{V}}=G^{2} \) and \( \frac{R_{A}}{R_{V}}=\frac{I_{g}}{I_{0}-I_{g}} \)
\( ^{\mathrm{D}} R_{A} R_{V}=G^{2}\left(\frac{I_{0}-I_{g}}{I_{g}}\right) \) and \( \frac{R_{A}}{R_{V}}=\left(\frac{I_{g}}{I_{0}-I_{g}}\right)^{2} \)


\( \sqrt[3]{-512}=? \)
\( \mathbf{A} \cdot-64 \)
B . -8
C. Not defined
D. None of these


The \( \overrightarrow{\boldsymbol{v}} \) for the first emission line of
hydrogen atomic spectrum in the Balmer series with respect to the
Rydberg constant \( \boldsymbol{R} \) is:


Find multiplicative inverse of :
\( \frac{3+4 i}{4-5 i} \)


Calculate the percentage ionization of
\( 0.01 \mathrm{M} \) acetic acid in \( 0.1 \mathrm{M} \) HCl. \( \boldsymbol{K}_{\boldsymbol{a}} \) of
acetic acid is \( 1.8 \times 10^{-5} \)
A . \( 0.18 \% \)
B. 0.018\%
c. \( 1.8 \% \)
D. 18\%


Indicate whether the following
conversions represent an oxidation, a reduction or none (neither oxidation nor
reduction)
(i) \( \boldsymbol{H} \boldsymbol{C l O}_{3} \) to \( \boldsymbol{H} \boldsymbol{C l} \boldsymbol{O}_{\mathbf{4}} \)
\( (\text { ii }) N H_{4}^{+} \) to
\( N H_{3} \)
(iii) \( N O_{2} \) to \( N_{2} O_{4} \)
\( (\text { iv }) \boldsymbol{H} \boldsymbol{S} \boldsymbol{O}_{3}^{-} \) to \( \boldsymbol{S} \boldsymbol{O}_{4}^{2-} \)
\( (v) H_{2} O_{2} \) to \( H_{2} O \)
A \( \cdot \) (i) Oxidation
(ii) Reduction
(iii) None (iv) None (v) Oxidation
B. (i) Oxidation (ii) None (iii) None (iv) Oxidation (v) Reduction
c. (i) Reduction
(ii) Oxidation
(iii) Reduction (iv) None (v) Reduction
D. (i) Oxidation (ii) Reduction (iii) None (iv) Reduction (v) Reduction


One of the following having square planar structure is:
\( \mathbf{A} \cdot N H_{4}^{+} \)
B. \( B F_{4}^{-} \)
c. \( x e F_{4} \)
D. \( S C l_{4} \)


IUPAC name of allyl chloride is:
A. 1 -chloroethane
B. 3-chloro-1-propyne
c. 3-chloro-1-propene
D. 1-chloropropene


The figure shows a circuit
When the circuit is switched on, the
ammeter reads \( 0.5 A \)
(i) Calculate the value of the unknown
resistor \( \boldsymbol{R} \)
(ii) Calculate the charge passing
through the \( 3 \Omega \) resistor in \( 120 s \)
(iii) Calculate the power dissipated in
the \( 3 \Omega \) resistor.


If \( \boldsymbol{f}: \boldsymbol{R}-\{-1,1\} \rightarrow \boldsymbol{R} \) is defined by
\( f(x)=\frac{x}{x^{2}-1}, \) verify whether \( f \) is one
to-one or not.


Write Freundlich isotherm equation at
low pressure.


Steam undergoes decomposition at high temperature as per the reaction
\( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{H}_{2}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}), \boldsymbol{\Delta} \boldsymbol{H}^{\circ}= \)
\( 200 k J m o l^{-1} \Delta S^{\circ}=40 J m o l^{-1} \)
The temperature at which equilibrium constant is unit is :
A. 3000 Kelvin
B. 5000 Kelvin
c. 5333 Kelvin
D. 5 Kelvin


Assertion
A load when lifted vertically up requires greater effort than to roll the same load
up the ramp.
Reason
The work done in lifting the load vertically up is less.
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 a saturated solution of \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l}\left(\boldsymbol{K}_{s p}=\right. \)
\( \left.1.6 \times 10^{-10} \text {at } 25^{\circ} C\right), \) the \( \left[A g^{+}\right]= \)
\( 1.3 \times 10^{-5} \) mol \( / L . \) Then enough
potassium chloride is added to this
solution so that \( \left[\boldsymbol{C l}^{-}\right]=\mathbf{0 . 0 2 0} \boldsymbol{M} . \) The
solubility of \( A g C l \) in this solution of potassium chloride is:
A. \( 3.2 \times 10^{-8} \) mol \( / L \)
B. \( 8 \times 10^{-11} m o l / L \)
C \( .8 \times 10^{-8} \mathrm{mol} / \mathrm{L} \)
D. \( 8 \times 10^{-9} \) mol \( / L \)


Area of a triangle whose vertices are
0), (2,3),(5,8) is
A \( .1 / 2 \)
B.
\( c \cdot 2 \)
D. 3/2


A man stands between two cliffs and
fires a gun. He hears two successive
echoes after 3 s and 5 s. Find the
distance between the two cliffs?


Two stereo speakers are separated by a
distance of \( 2.4 \mathrm{m} . \) A person stands at a
distance of \( 3.2 \mathrm{m} \) as shown directly in
front of one of the speakers. Find the
frequencies in audible range for which
the listener will hear a minimum sound
intensity:

Speed of the sound in air is \( 320 m s^{-1} \)
\( \mathbf{A} \cdot 160(2 n+1) \)
B. \( 320(2 n+1) \)
\( \mathbf{c} \cdot 200(2 n+1) \)
D. \( 100(2 n+1) \)


An electric iron rated \( 750 \mathrm{W} \) is operated
for 2 hours/day. How much energy is consumed by the electric iron for 30 days?


On electrolysis of \( \mathrm{CaH}_{2} \) solution in
water, \( 0_{2} \) gas is liberated at anode
and \( \mathrm{H}_{2} \) gas is liberated at cathode.
If true enter 1 , else enter 0 .


Find the ratio by mass of the combining
elements in the \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
A. 1: 16: 32
B . 15: 16: 32
\( \mathbf{c} \cdot 1: 16: 16 \)
D. none of these


For a moving body, distance and displacement will be equal if
A. the body moves along a circle
B. the body moves along a straight line
c. the body moves along a triangle
D. the body comes back to its initial position


A force \( \overrightarrow{\boldsymbol{F}}=(-\boldsymbol{y} \hat{\boldsymbol{i}}+\boldsymbol{x} \hat{\boldsymbol{j}}) \boldsymbol{N} \) acts on a
particle as it moves in an anticlockwise
circular motion in \( x \) -y plane. The centre of the circle is at the origin. If the work done by the force is \( 32 \pi J \) in one
complete revolution then assuming \( x, y \)
to be in meters, find the radius of the
path
A. 5
B. 4
\( c \cdot 6 \)
D.


The diagram represents a stage during cell division. Answer the following.
i. Name the parts labelled 1,2
i. Identify the above stage and give a
reason to support your answer.
iii. Mention where in the body this type
of cell division occurs.
iv. Name the stage prior to this stage
and draw a diagram to represent the
same
v. Give any two difference between
mitosis and meiosis.


Which diagram is correct for the
circulation of blood through human
heart?
\( (\mathbf{a}) \)
(b)
\( (c) \)
\( (\mathbf{d}) \)


Three horses \( A, B \) and \( C \) are in a race, \( A \)
is twice as likely to win as \( \mathrm{B} \) and \( \mathrm{B} \) is twice as likely to win as C. What are their probabilities of winning?


The percentage of population living in rural areas in India, as per Census 2011
stands at
A . 62.17\%
B. 68.84\%
c. 56.61\%
D. 31.16\%


From 7 gentlemen and 4 ladies, a
committee of 5 is to be formed. The
probability that this can be one so as to include at least one lady is
A \( \cdot \frac{^{7} C_{5}}{^{11} C_{5}} \)
в. \( \frac{4}{^{11} C_{5}} \)
\( ^{\mathbf{C}} \cdot_{1-\frac{^{7} C_{5}}{11} C_{5}} \)
D. \( _{1-\frac{4}{11} C_{5}} \)


Progesterone which is the most
important component of oral
contraceptive pills prevents pregnancy
by
A. Preventing the formation of egg
B. Preventing the cleavage of the fertilised egg
c. Creating unfavourable chemical environment for the sperms to survive in the female reproductive tract
D. Blocking ovulation


In the diagram, 0 is the centre of the
circle. The angles CBD is equal to
\( A \cdot 120 \)
B. \( 55^{\circ} \)
\( c \cdot 65 \)
D. 75


\( A \) pole is slightly inclined towards the
east. \( A t \) two points due west of it at
distances a and \( b \), the angles of
elevation of the top of the pole are \( \alpha \) and
\( \beta \) respectively. The inclination of the pole to the horizon is
A. \( \tan ^{-1} \frac{a+b}{b \operatorname{Cot} \alpha-a \operatorname{Cot} \beta} \)
в. \( \tan ^{-1} \frac{b-a}{b C o t \alpha-a C o t \beta} \)
c. \( \cos ^{-1} \frac{a-b}{b \cos \alpha-a \cos \beta} \)
D. \( \sin ^{-1} \frac{a-b}{b C o t \alpha-a \cot \beta} \)


Consider the three statements about
reaction energy diagrams and the relative magnitudes of the activation
energy, \( E_{a}, \) and the enthalpy of reaction,
\( \Delta \boldsymbol{H} \)
One or more of the statements is true.
Identify the correct statement or
combination of statements from the
four choices below.
Statement
For an endothermic reaction, the magnitude
of \( E_{a} \) is always greater than \( \triangle H \)

For an exothermic reaction, the magnitude of
| \( E_{a} \) is always greater than \( \triangle H \)
For an exothermic reaction, adding a catalyst
III \( \quad \) will decrease the magnitude of \( \triangle H \)
A. Statement I only is true.
B. Statement II only is true.
C. Both statements I and II are true.
D. Both statements I and III are true.


Strong magnetic field produced inside a solenoid can be used to magnetise a
A. piece of magnetic material
B. soft iron
\( c . \) both
D. none


Let \( \vec{p} \) is the position vector of the
orthocentre \( \& \vec{g} \) is the position vector of the centroid of the triangle \( A B C \) where circumcentre is the origin. If \( \overrightarrow{\boldsymbol{p}}=\boldsymbol{K} \overrightarrow{\boldsymbol{g}} \)
then \( \boldsymbol{K}= \)
A . 3
B. 2
c. \( \frac{1}{3} \)
D. \( \frac{2}{3} \)


In the adjoining figure, \( D \) and \( E \) are
respectively the midpoints of sides \( A B \) and \( A C \) of \( \triangle A B C . \) If \( P Q \| B C \) and
\( C D P \) and \( B E Q \) are straight lines then prove that \( \boldsymbol{a} \boldsymbol{r}(\triangle \boldsymbol{A} \boldsymbol{B} \boldsymbol{Q})=\boldsymbol{a} \boldsymbol{r}(\triangle \boldsymbol{A} \boldsymbol{C} \boldsymbol{P}) \)


Two systems are in thermal equilibrium. The quantity which is common for them is
A . heat
B. momentum
c. specific heat
D. temperature


The function \( f(x)=2 x^{3}-15 x^{2}+ \)
\( 36 x+6 \) is strictly decreasing in the
interval
A. (2,3)
(年) (2,3,3)
в. \( (-\infty, 2) \)
c. (3,4)
(年. \( (3,4)) \)
D. \( (-\infty, 3) \cup(4, \infty) \)
E \( .(-\infty, 2) \cup(3, \infty) \)


How many terms of G.P \( 3,3^{2}, 3^{3}, \ldots \) are
needed to give the sum \( 120 ? \)


Pick up the correct statement from the
following:
A. Glucose exists in two different crystalline forms, \( \alpha- \) \( D- \) glucose and \( \beta-D- \) glucose.
B. Cyclic structure of \( \alpha-D- \) glucose and \( \beta-D- \)
glucose is called pyranose structure.
C \( . \alpha-D- \) -glucose and \( \beta-D- \) glucose are
enantiomers.
D. Cellulose is a straight chain polysaccharide made up of only \( \beta \) - glucose units.


If \( \boldsymbol{A}=\{\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}\}, \boldsymbol{B}=\{\boldsymbol{c}, \boldsymbol{d}, \boldsymbol{e}\}, \boldsymbol{C}= \)
\( \{a, d, f\}, \) then \( A \times(B \cup C) \) is
A \( \cdot\{(a, d),(a, e),(a, c)\} \)
в. \( \{(a, d),(b, d),(c, d)\} \)
c. \( \{(d, a),(d, b),(d, c)\} \)
D. none of these


A long solenoid has 200 turns per \( \mathrm{cm} \)
and carries a current \( i . \) The magnetic field at its centre is \( 6.28 \times \) \( 10^{-2} W b / m^{2} \) Another long solenoid has
100 turns per cm and it carries a
current \( i / 3 . \) The value of the magnetic field at its centre
is :
A \( \cdot 1.05 \times 10^{-4} W b / m^{2} \)
B . \( 1.05 \times 10^{-2} \mathrm{Wb} / \mathrm{m}^{2} \)
c. \( 1.05 \times 10^{-5} \mathrm{Wb} / \mathrm{m}^{2} \)
D. \( 1.05 \times 10^{-3} \mathrm{Wb} / \mathrm{m}^{2} \)


Find the principal value of \( \sin ^{-1}\left(-\frac{1}{2}\right) \)


In thermal inversion.
A. Warm ground air gets overlapped by cool air
B. Cool ground air gets overlapped by warm air
C. Ground temperature becomes high in winter
D. Ground temperature becomes low in summer


A capacitor of \( 20 \mu F \) is connected in
series with a \( 25 \Omega \) resistance to a peak
e.m.f \( 240 v, 50 H z \) A.c. Calculate
(i)the capacitive reactance of the
circuit.
(ii)an impedance of the circuit


After adding a solute freezing point of
water solution decreases to \( -0.186^{\circ} \mathrm{C} \)
Calculate \( \Delta T_{b} .\left(K_{f}=1.86^{\circ} C k g m o l^{-1}\right. \)
and \( K_{b}=0.512^{\circ} C k g m o l^{-1} \)
A \( \cdot 0.521^{\circ} \mathrm{C} \)
B . \( 0.0521^{\circ} \mathrm{C} \)
c. \( 1.86^{\circ} \mathrm{C} \)
D. \( 0.0186^{\circ} \mathrm{C} \)


The sum of the fourth and twelfth term
of an arithmetic progression is 20 What is the sum of the first 15 terms of
the arithmetic progression?
A . 150
B. 200
\( c .250 \)
D. 500


Which among the following can show the maximum of four covalencies?
A . \( A l \)
в. \( G a \)
c. \( I n \)
D. \( B \)


The electromagnetic waves travel in free space with the velocity of
A. Sound
B. Light
c. Greater than that of light
D. Greater than that of sound


If a function \( f(x) \) has \( f^{\prime}(a)=0 \) and
\( f^{\prime \prime}(a)=0, \) then
A. \( x=a \) is a maximum for \( f(x) \)
B. \( x=a \) is minimum for \( f(x) \),
c. It is difficult to say \( (a) \) and \( (b) \)
D. \( f(x) \) is necessarily a constant function.


Simplify: \( \cos \theta\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right]+ \)
\( \sin \theta\left[\begin{array}{cc}\sin \theta & -\cos \theta \\ \cos \theta & \sin \theta\end{array}\right] \)


The speed of transverse wave \( v \) in a
stretched string depends on tension \( \boldsymbol{T} \) in the string and linear mass density (mass per unit length) \( \mu . \) Find the relation using method of dimensions.


An acidic buffer solution can be
prepared by mixing the solutions of:
A. sodium acetate and acetic acid
B. ammonium chloride and ammonium hydroxide
c. sulphuric acid and sodium sulphate
D. sodium chloride and sodium hydroxide


Which of the following cell surface differentiation is not likely to play a role in inter-cellular communication?
A. Desmosome
B. Gap junction
c. Tight junction
D. None of the above


How chlorine react with Cold and dilute
NaoH?


toppr
Q Type your question
Thumbtacks were fixed with wax on
each material and then the materials
were fixed to a trough containing hot water as shown in the diagram. Vijay tabulated his results as shown here.
Time taken for thumbtacks to Material drop(minutes)
5
0
6
2
What can be inferred from his
experiment?
A. Material R is a better conductor of heat than material
\( S \)
B. Material S is a better conductor of heat than material
\( \mathrm{R} \)
C. Material Q is a better conductor of heat than material
\( P \)
D. Materials \( \mathrm{P}, \mathrm{Q}, \mathrm{R} \) and \( \mathrm{S} \) are equally good conductors of heat.


The rate \( _{--}-_{--} \) as the temperature of water reduces due to cooling.


An electric dipole made up of a positive and negative charge, each of \( 1 \mu C \) separated by a distance of \( 2 \mathrm{cm} \), is placed in an electric field of \( 10^{5} N / C \).The work
done in rotating the dipole from the position of stable equilibrium through an angle of \( 180^{0} \) is :
A \( \cdot 2 \times 10^{-3} \) Joule
B . \( 2 \times 10^{-8} \) Joule
c. \( 4 \times 10^{-3} \) Joule
D. Zero


If \( N^{A} \) is number density of acceptor
atoms added and \( N^{D} \) is number
density of donor atoms added to a
semiconductor, \( n^{e} \) and \( n^{n} \) are the
number density of electrons and holes in it,then
A \( \cdot n^{e}=N^{D}, n^{n}=N^{A} \)
B . \( n^{e}=N^{A}, n^{h}=N^{D} \)
c. \( N^{A}+n^{n}=N^{D}+n^{\text {ศ }} \)
D. \( n^{e}+N^{A}=n^{n}+N^{D} \)


The melting point of most of the solid substances increases with an increase in pressure. However ice melts at a temperature lower than its usual melting points when pressure is increased. This is because:
A. the density of ice is lesser than \( H_{2} O \)
B. pressure generates heats
c. the chemical bonds break under pressure
D. ice is not a true solid


A number is selected from the set \( \{1,2, \) 3,4,5,6,7,8\}\( . \) What is the probability that it will be the root of the equation
\( x^{2}-6 x+8=0 ? \)


Permanent magnets should have
A. High retentivity and low coercivity.
B. Low retentivity and high coercivity.
C. High retentivity and high coercivity.
D. Low retentivity and low coercivity.


If \( \theta=\frac{11 \pi}{4}, \) find the value of \( \sin ^{2} \theta \)
\( \cos ^{2} \theta+2 \tan \theta-\sec ^{2} \theta \)


Give one word or phrase for the following
statement.
The tendency of an element to form chains of identical atoms.


Two balls are drawn at random with
replacement from a box containing 10
black and 8 red balls. Find the
probability that one of them is black and other is red.


Two particles are executing SHM of same amplitude and frequency along the same straight line path. They pass each other when going in opposite directions, each time their displacement is half of their magnitude.
What is the phase difference between them?
\( \mathbf{A} \cdot \pi / 6 \)
в. \( 4 \pi / 6 \)
c. \( \pi / 3 \)
D. 2\pi/6


The solution of differential equation
\( x \cos ^{2} y d x=y \cos ^{2} x d y \) is
A \( \cdot x \tan x-y \tan y-\log \left(\frac{\sec x}{\sec y}\right)=c \)
B. \( y \tan x-x \tan y-\log (\sec x \cdot \sec y)=c \)
c. \( x \tan x-y \tan y+\log (\sec x \cdot \sec y)=c \)
D. None of the above


Two wires each carrying a steady
current I are shown in four
configurations in Column I. Some of the resulting effects are described in Column II. Match the
statements in Column I with the
statements in Column II and indicate
your
answer by darkening appropriate bubbles in the \( 4 \mathrm{X} 4 \) matrix given in the
ORS.


Which wavelength of light has the LOWEST frequency?
\( \mathbf{A} \cdot 2 m m \)
B. \( 1 n m \)
c. \( 10 n m \)
D. \( 20 n m \)


Which of the following elements has the highest electronegativity?
A . \( S \)
в. \( C l \)
\( c \cdot s i \)
D. \( A l \)


Find the unknown angles marked in the
following figure.


Solve the following system of equation:
\( \frac{1}{2 x}-\frac{1}{y}=-1 \)
\( \frac{1}{x}+\frac{1}{2 y}=8, \) where \( x \neq 0, y \neq 0 \)


Assertion
The atmospheric concentration of \( \boldsymbol{C O}_{2} \)
at which photosynthesis just compensates for respiration is referred
to as \( C O_{2} \) compensation point.
Reason
The \( C O_{2} \) compensation point is reached
when the amount of \( C O_{2} \) uptake is less
than that generated through
respiration, because the level of \( C O_{2} \) in
the atmosphere is more than that
required for achieving \( C O_{2} \)
compensation point.
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.


Ram is 7 years younger than Ravi. In 4 years' time, Ram will be half of Ravi'sage. The sum of their ages now is
A . 13
B . 15
c. 17
D. 19


Which of the following statements does
not apply to eutrophication.
A. It is natural ageing of a lake by nutrient enrichment of its water
B. In a young lake the water is cold and clear and supports less life
C. The nutrients such as sulphur and phosphorus encourage the growth of aquatic organisms in the lake
D. Pollutants released by man radically accelerate the ageing process of a lake
E . Overgrowth of algae leads to scum that depletes the level of dissolved oxygen in water


If \( n \) geometric means be inserted
between \( a \) and \( b \), then prove that their products is \( (\boldsymbol{a} \boldsymbol{b})^{\boldsymbol{n} / 2} \)


Match the columns
\( \begin{array}{ll}\boldsymbol{A} & \boldsymbol{B} \\ \text { (1) Stars } & \text { (a) Pollution free } \\ \text { (2) Objects in the sky } & \text { (b) Do not twinkle } \\ \text { (3) Planets } & \text { (c) Twinkling bodies } \\ \text { (4) Clearsky } & \text { (d) Celestial bodies }\end{array} \)
A. \( 1-c, 2-d, 3-b, 4-a \)
B. \( 1-d, 2-a, 3-c, 4-b \)
C. \( 1-b, 2-c, 3-a, 4-d \)
D. \( 1-c, 2-a, 3-d, 4-b \)


State one important advantage and disadvantage each of using nuclear energy for producing electricity.


A variable air capacitor has 11 movable plates and 12 stationary plates, The
area of each plate is \( 0.0015 m^{2} \) and
separation between opposite plates is \( 0.001 m . \) The maximum capacitance of
the capacitor is
A . \( 292.2 F \)
В. \( 292.2 \mathrm{mF} \)
c. \( 292 \mu F \)
D. 292 p


Which of the following is the effect of a plant hormone, which is synthesised more in absence of light?
A. Inhibits the development of seedless fruits
B. Responsible for closing of stomata
c. Induces the dormancy of seeds
D. Length of intenodes increases


A body initially at rest travels a distance of \( 100 m \) in \( 5 s \) with a constant
acceleration. Find the final velocity at
the end of \( 5 s \)
\( \mathbf{A} \cdot 20 m s^{-1} \)
B. \( 30 m s^{-1} \)
\( \mathbf{c} \cdot 35 m s^{-1} \)
D. \( 40 \mathrm{ms}^{-1} \)


During photosynthesis, the gross primary productivity is the rate of production of
A. organic matter
B. Oxygen
c. Carbon dioxide
D. chlorophyll


A balanced chemical equation is in accordance with the law of conservation
of masses
A. True
B. False


In an acute angled triangle \( A B C \), the
minimum value of \( \tan ^{n} A+\tan ^{n} B+ \)
\( \tan ^{n} C . \) is
\( (\text { When } n \epsilon N, n>1) \)
A \( \cdot \frac{n}{3} \)
B. \( 3^{n} \)
c. \( \frac{n}{3}^{+1} \)
D. \( _{3} \frac{n}{2}-1 \)


The spectral lines corresponding to the
radiation emitted by an electron jumping from 6 th, 5 th and 4 th orbits to second orbit belong to:
A. Lyman series
B. Balmer series
c. Paschen series
D. Pfund series


The octahedral complex ions \( \left[\boldsymbol{F e C l}_{6}\right]^{3-} \)
and \( \left[\boldsymbol{F e}(\boldsymbol{C N})_{6}\right]^{3-} \) are both
paramagnetic but the former is high spin and the latter is low spin. In the low
spin complex, \( \left[\boldsymbol{F e}(\boldsymbol{C N})_{\boldsymbol{6}}\right]^{3-} \) has the d-
configuration as:
\( \mathbf{A} \cdot t_{2 g}^{3} e_{g}^{2} \)
B . \( t_{2}^{5} \)
\( \mathbf{c} \cdot t_{2}^{2} \)
D. \( e^{5} \)


Find inclination (in degrees) of a line perpendicular to x-axis.


For the function \( \boldsymbol{f}(\boldsymbol{x})= \)
\( (x-1)(x-2)(x-3) \) in [0,4] value of
c' in Lagrange's mean value theorem is
A \( \cdot 2 \pm \frac{2}{\sqrt{3}} \)
B. \( _{1-\frac{\sqrt{21}}{6}} \)
c. \( 1+\frac{\sqrt{21}}{6} \)
D. \( 4-2 \sqrt{3} \)


Write the name and formula of the
second member of the carbon
compounds having functional group-
ОН.


A network of four \( 10 \mu F \) capacitors is
connected to a \( 500 V \) supply, as shown
in fig. Determine
(a) the equivalent
capacitance of the network and
(b) the
charge on each capacitor.(Note, the
charge on a capacitor is the charge on
the place with higher potential, equal
and opposite to the charge on the plate
with lower potential)


At temperature \( 0 K, \) the germanium behaves as a/an
A. conductor
B. insulator
c. super-conductor
D. ferromagnetic


Raffinose is a:
A. trisaccharide
B. monosaccharide
c. disaccharide
D. none of the above


A current of \( 4.0 \mathrm{A} \) is passed for 5 hours
through 1L of 2M solution of nitrate using two nickel electrodes. The molarity of the solution at the end of the electrolysis will be:
A . 1.5 м
в. 1.2
c. \( 2.5 \mathrm{M} \)
D. 2.0 M


In going from one city to another, a car travels \( 75 k m \) north, \( 60 k m \) north-west and \( 20 k m \) east. The magnitude of
displacement between the two cities is (take \( \sqrt{\mathbf{2}}=\mathbf{0 . 7}) \)
A. \( 170 k m \)
в. \( 137 k m \)
c. \( 119 k m \)
D. \( 140 k m \)


If \( \operatorname{CoO}(s)+H_{2}(g) \rightleftharpoons C o(s)+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}), \boldsymbol{K}_{1}=\boldsymbol{6} \boldsymbol{0} ; \boldsymbol{C} \boldsymbol{o} \boldsymbol{O}(\boldsymbol{s})+ \)
\( \boldsymbol{C O}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{C o}(s)+\boldsymbol{C O}_{2}, \boldsymbol{K}_{2}=180 \) then
the equilibrium constant of the
reaction \( \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{H}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{C} \boldsymbol{O}(\boldsymbol{g})+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \) will be -
\( A \cdot 0.44 \)
в. 0.1
c. 0.22
D. 0.33


Which molecule is T-shaped?
A. \( B e F_{2} \)
в. \( B C l_{3} \)
c. \( N H_{3} \)
D. \( C l F_{3} \)


Soft soap are made with potassium,
rather than sodium salts.
If true enter 1 ,if false enter 0
\( A \)


A solenoid of self-inductance \( 1.2 H \) is in
series with a tangent galvanometer of reduction factor \( 0.9 A \). They are connected to a battery and the tangent
galvanometer shows a deflection of \( 53^{\circ} \)
The energy stored in the magnetic field of the solenoid is:
\( \left(\tan 53^{\circ}=4 / 3\right) \)
\begin{tabular}{l}
A. 0.8645 \\
\hline
\end{tabular}
в. \( 0.72 J \)
c. \( 0.173 J \)
D. \( 1.44 J \)


(a) Complete the following chemical equations:
(i) \( \underset{(\text {hot and conc.})}{N a O H}+C l_{2} \rightarrow \)
(ii) \( \boldsymbol{X}_{e} \boldsymbol{F}_{4}+\boldsymbol{O}_{2} \boldsymbol{F}_{2} \rightarrow \)
(b) Draw the structures of the following molecules:
(i) \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{2} \)
(ii) \( \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{7} \)
(iii) \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{O} \boldsymbol{F}_{4} \)


Which choice below is the rate law of
the following reaction?
\( \mathbf{2} \boldsymbol{H}_{\mathbf{2}}(\boldsymbol{g})+\boldsymbol{O}_{\mathbf{2}}(\boldsymbol{g}) \rightarrow \boldsymbol{H}_{\mathbf{2}} \boldsymbol{O}(\boldsymbol{g}) \)
A . Rate\( =k[H][O] \)
B. Rate \( =k\left[H_{2}\right]^{x}\left[O_{2}\right]^{y} \)
c. Rate\( =k\left[H_{2}\right]^{2}\left[O_{2}\right] \)
D. Rate \( =k\left[H_{2}\right]\left[O_{2}\right] \)


A bus appears to move northwards at a speed of \( 20 \sqrt{3} k m h^{-1}, \) to a man driving
his car eastwards with speed \( 20 k m h^{-1} \)
Find the velocity of the bus w.r.t. ground.


Photodiode is a device
A. Which is always operated in reverse bias
B. Which is always operated in forward bias
C. In which photo current is independent of intensity of incident radiation
D. Which may be operated in forward or reverse bias


The IUPAC name of the complex
\( \left[(\boldsymbol{C O})_{3} \boldsymbol{F e}(\boldsymbol{C O})_{3} \boldsymbol{F e}(\boldsymbol{C O})_{3}\right] \) is:
A. nonacarbonyldiiron (0)
B. tricarbonyliron (0)-m-tricarbonyl iron (0)
c. hexacarbonyliron (0)-m-tricarbonyl iron (0)
D. tri- \( \mu \) -carbonylbis(tricarbonyliron (0))


A salivary gland
is
A. Brunners gland
B. Sublingual gland
c. Lacrimal gland
D. Adrenal gland


A frame of mass \( 200 g \) when suspended from a massless spring extends it by 10 \( c m . \) A lump of clay of mass \( 200 g \) is dropped from rest on to the frame from
a height of \( 30 \mathrm{cm} \) as shown in figure.
What is the maximum distance
through which pan moves downwards?


The first husband-wife team to get the Nobel Prize for Physics was.
A. Frederick Joliot-Irene Joliot-Curie
B. Pierre Curie-Marie Curie
c. carl cori-Gerty corir
D. Gunnar Myrdal-Alva Myrdal


The approximate depth of an ocean is
\( 2700 m . \) The compressibility of water is
\( 45.4 \times 10^{-11} P a^{-1} \) and density of water
is \( 10^{3} k g / m^{3} . \) What fractional compression of water will be obtained at the bottom of the ocean?(Take \( g= \)
\( 10 m s^{-2} \)
A \( \cdot 1.2 \times 10^{-2} \)
В. \( 1.4 \times 10^{-2} \)
C \( .0 .8 \times 10^{-2} \)
D. \( 1.0 \times 10^{-2} \)


A body cools from \( 80^{\circ} \mathrm{C} \) to \( 50^{\circ} \mathrm{C} \) in 5
minutes. Calculate the time it takes to
cool from \( 60^{\circ} \mathrm{C} \) to \( 30^{\circ} \mathrm{C} \). The temperature
of the surroundings is \( 20^{\circ} \mathrm{C} \)


Atmospheric pressure is measured by a
A. Doctor's thermometer
B. Speedometer
c. Mercury barometer
D. all of these


(a) Draw ray diagram of refraction of light through a prism and explain the phenomenon of dispersion of light.
(b) Write the formula for lens power and define its unit.


Movement of molecule of gases, liquids and solids from a region of higher concentration to a region of lower concentration is termed as
A. Diffusion
B. Evaporation
c. Transpiration
D. Osmosis


What are the exceptions of the octet
rule?
A. The incomplete octet of central atom
B. An odd number of electrons on central atom
C. Expanded octet of the central atom
D. All of these


Soham is 6 years old. He was playing in the garden. One of his teeth fell as he
dashed a pillar. He started crying because he was hurt. He also felt that
his teeth will never come back and he
will not be able to eat chocolates. How
will you console him?
A. By telling him that his tooth was milk tooth
B. By telling him that his tooth was permanent tooth
c. By telling him that his tooth will be replaced
D. Both A and C


8 different shapes are given in the
following figure. How many shapes have
0 lines of symmetry?


Convert the given fractional numbers to
percent
\( \frac{2}{7} \)


A laser beam of pulse power \( 10^{12} W \) is
focussed on an object of area \( 10^{-4} \mathrm{cm}^{2} \)
The energy flux in \( W / c m^{2} \) at the point of focus is
A \( \cdot 10^{4} \)
B. \( 10^{8} \)
\( \mathbf{c} \cdot 10^{16} \)
D. \( 10^{20} \)


Match the extraction processes listed in
Column I with metals listed in Column
\( \|: \)


Using differentials, find the sum of digits approximate value of the
following up to 3 places of decimal. \( (401)^{\frac{1}{2}} \)


Prove that
\[
\left|\begin{array}{ccc}
\boldsymbol{x}+\boldsymbol{y}+\mathbf{2} \boldsymbol{z} & \boldsymbol{x} & \boldsymbol{y} \\
\boldsymbol{z} & \boldsymbol{y}+\boldsymbol{z}+\mathbf{2} \boldsymbol{x} & \boldsymbol{y} \\
\boldsymbol{z} & \boldsymbol{x} & \boldsymbol{z}+\boldsymbol{x}+\boldsymbol{2} \boldsymbol{y}
\end{array}\right|
\]
\( 2(x+y+z)^{3} \)


Which of the following is / are true?
A. the inner ear consists of a cochlea, the semicircular canals and the auditory nerve
B. the middle ear is an air filled cavity that consists of an ear drum and three tiny interconnected bones the hammer, anvil and stirrup
C. the human ear consists of three basic parts - outer ear. middle ear and inner ear
D. all of these


Which of the following statement is
correct?
a. The unit of force is Newton
b. The unit of force is newton


LED glows even when a electric
current passes through it. Fill in the
blank.
\( A \). weak
c. can't predicted
D. none of the above


\( c \)
Using the information ab bove, complete
the following

Metal atoms tend to have a maximum
of electrons in the
outermost energy level


The \( r^{t h}, s^{t h} \) and \( t^{t h} \) terms of a certain
\( G . P \) are
\( R, S \) and \( T \) respectively. Prove that
\( \boldsymbol{R}^{s-t} \boldsymbol{S}^{t-r} \boldsymbol{T}^{r-s}=\mathbf{1} \)


Hardening of leather in tanning industry
is based on:
A. Electrophoresis
B. Electro-osmosis
c. Mutual coagulation
D. Persistent dialysis


A (nonrotating) star collapses onto
itself from an initial radius \( \mathrm{R}_{i} \) with its
mass remaining unchanged. Which
curve in figure best gives the
gravitational acceleration \( a_{g} \) on the
surface of the star as a function of the
radius of the star during the collapse?
4
B.
\( c \)
D.


A student is viewing under a microscope a permanent slide showing various stages of asexual reproduction by budding in yeast. Draw diagrams of what he observes (in proper sequence).


If a rod has resistance \( 4 \Omega \) and if rod is
turned as half circle, then the
resistance along diameter is
\( \mathbf{A} \cdot 1.56 \Omega \)
B . \( 2.44 \Omega \)
c. \( 4 \Omega \)
D. 2\Omega


A wire is placed to the lines of force in a
magnetic field and a current flows in
the wire. Then
A. the wire will experience a force in the direction of magnetic field
B. the wire will not experience any force at all
C. the wire will experience a force in a direction opposite to the field
D. it experiences a force in a direction perpendicular to lines of force


Solve \( 6 x+1=3(x-1)+7 \) for the
value of \( x \)


Which of the following statements is the contrapositive of "If you understand logic, you will be a good consumer."?
A. If you are a good consumer, then you do not understand logic
B. If you are not a good consumer, then you do not understand logic
c. If you do not understand logic, then you will not be a good consumer
D. None of these


If the diameter of the earth becomes
half of the present value but its average
density remains unchanged then how would be the wieght of an object on earth been affected


Which is not a characteristic of
haloalkanes?
A. Alkyl halides are colourless in pure pure form
B. Alkyl bromides and iodides develop colour when exposed to light
C. Many volatile halogen compounds have sweet smell
D. Intermolecular forces are less as compared to hydrocarbons


State the laws of refraction of light.


A plant hormone used for inducing morphogenesis in plant tissue culture
is
A. Cytokinins
B. Ethylene
c. Abscisic acid
D. Gibberellins


Speed of a chemical reaction depends on which of the following parameters?
A. Temperature
B. Concentration
c. Pressure
D. All of the above


The largest value in the collection of data is \( 7.44 . \) If the range is \( 2.26, \) then find the smallest value in the collection
A . 5.18
B. 9.70
\( c .2 .26 \)
D. 1.13


The minimum energy required to dissociate \( A g B r \) bond in \( 0.6 e V . A \)
photographic flim is coated with a sliver bromide layer. Find the maximum
wavelength whose signature can be
recorded on the film
A. \( 207 n m \)
в. 702 \( n m \)
c. 207 \( A^{\circ} \)
D. 2070 \( n m \)


\( \frac{5}{7}+\frac{4}{7}-\frac{3}{7} \) is equal to
A \( \cdot \frac{3}{7} \)
B. \( \frac{5}{7} \)
\( c \cdot \frac{6}{7} \)
D. \( \frac{12}{7} \)


\( \boldsymbol{f}(\boldsymbol{x})=\mathbf{1}+\frac{\mathbf{1}}{\boldsymbol{x}} ; \boldsymbol{g}(\boldsymbol{x})=\frac{\mathbf{1}}{\mathbf{1}+\boldsymbol{f}(\boldsymbol{x})} \Rightarrow \)
\( \boldsymbol{g}^{\prime}(\mathbf{2})= \)
\( A \cdot \frac{1}{5} \)
в. \( \frac{1}{25} \)
c. 5
D. \( \frac{1}{16} \)


Complete the illustration by adding \( A, B \)
\( c \) and \( D \)
\begin{tabular}{|c|c|c|}
\hline \multirow{2}{*} {\multicolumn{2}{|c|} { Blood }\text { Blood }} \\
\cline { 2 - 3 } & \\
\hline Corpuscles & \\
\hline & \\
\cline { 2 } & ? \\
\hline\( ? \) & \\
\hline
\end{tabular}


What is the direction of magnetic field at the centre of a coil carrying current
in anticlockwise direction?
A. Perpendicular to the axis of coil inwards.
B. Perpendicular to the axis of coil outwards
c. Along the axis of coil inwards
D. Along the axis of coil outwards


A circuit shown in Fig. has resistances
\( R_{1}=20 \Omega \) and \( R_{2}=30 \Omega . \) At what
value of the resistance \( R_{x} \) will the
thermal power generated in it be practically independent of small variations of that resistance. The
voltage between the points \( A \) and \( B \)
is supposed to be constant in this case.


Prepare slogans on greenhouse effect to
announce in your school assembly.


The soil near the surface is usually darker, than the soil about one meter down. This is because the topsoil is
A. Young and wet
B. Richer in organic matter
c. Richer in Ca and Mg
D. Dry


A \( 2 \mathrm{m} \) long conductor, carries a current
of \( 50 \mathrm{A} \) at a magnetic field of \( 10^{-1} \) T. The force on the conductor is:
A . 10 N
B. 100 N
\( c \cdot 1000 N \)
D. \( 10,000 \mathrm{N} \)


A car moving with constant acceleration covered the distance
between two points \( 60.0 \mathrm{m} \) apart in 6.00
s. Its speed as it passes the second point was \( 15.0 \mathrm{m} / \mathrm{s} \). What was the speed at the first point?


Which bomb works on the principle of Nuclear fusion?
A. Atom bomb
B. Hydrogen bomb
c. Neutron bomb
D. Nuclear reactor


Arrange following compounds in decreasing order of reactivity of ring towards attack of electron deficient
species.
A \( . i>i i>i i i>i v \)
в. \( i i i>i v>i i>i \)
c. \( i>i v>i i> \) ii i
\( \mathbf{D} \cdot i>i i>i v>i i i \)


Two plane mirrors \( A \) and \( B \) are aligned parallel to each other, as shown in the figure A light ray is incident at an angle
\( 30^{\circ} \) at a point just inside one end of \( A \) The plane of incidence coincides with
the plane of the figure The maximum
number of times the ray undergoes reflections (including the first one ) before it emerges out is
\( A \cdot 30 \)
B. 3
\( c \cdot 32 \)
\( D \cdot 34 \)


Dinitrogen pentoxide \( \left(N_{2} O_{5}\right), \) a colourless solid, is prepared by:
A . heating \( N H_{4} N O_{2} \) with an excess of oxygen
B. dehydrating \( H N O_{3} \) with \( C a O \)
C. dehydrating \( H N O_{3} \) with \( P_{4} O_{10} \)
D. heating a mixture of \( H N O_{2} \) and \( C a\left(N O_{3}\right) \)


Which of the following is an endothermic
reaction
\( \mathbf{A} \cdot N_{2}(g)+3 H_{2}(g)-92 k J \rightarrow 2 N H_{3}(g) \)
B \( \cdot N_{2}(g)+O_{2}(g)+180.8 k J \rightarrow 2 N O(g) \)
\( \mathbf{c} \cdot H_{2}(g)+C l_{2}(g) \rightarrow 2 H C l(g)+184.6 k J \)
\( \mathbf{D} \cdot C(g r)+2 H_{2}(g) \rightarrow C H_{4}(g)+74.8 k J \)


Identify the cubic polynomial.
A \( \cdot x^{5}+y^{3}-x^{3}+x^{4} \)
В. \( x^{3}+y^{3}-x^{2} \)
c. \( 2 x^{3}+8 y^{3}-9 x^{5} \)
D. \( -7 x^{7}+x^{3} \)


Steroid hormones are produced by which of the following:
a) Adrenal cortex
b) Pancreas
c) Thyroid
d) Testis
e) Pitutiary
\( A \cdot \) a and \( d \)
B. \( a, b, \) and \( c \)
c. \( c, d \)
D. d,


A cylindrical disc of a gyroscope of \( \operatorname{mass} \boldsymbol{m}=15 k g \) and radius \( \boldsymbol{r}=\mathbf{5 . 0} \boldsymbol{c m} \)
spins with an angular velocity \( \omega= \) 330 rad/s.The distance between the
bearings in which the axle of the disc is mounted is equal to \( l=15 \mathrm{cm} \). The
axle is forced to oscillate about a
horizontal axis with a period \( \boldsymbol{T}=\mathbf{1 . 0} \boldsymbol{s} \)
and amplitude \( \varphi_{m}=20^{\circ} . \) Find the
maximum value of the gyroscopic forces exerted by the axle on the bearings in \( \boldsymbol{N} \)


The function of ATP in photosynthesis is the transfer of energy from the
A. Dark reaction to the light reaction
B. Light reaction to the dark reaction
c. chloroplasts to mitochondria
D. Mitochondria to chloroplasts


State Huygen's principle. Using Huygen's wave theory, prove the laws of reflection


Two resistors are connected a) in series
b) in parallel. The equivalent resistance in two cases are 9 ohm and 2 ohm respectively. Then the resistance of the component
resistors are.
A. 2 ohm and 7 ohm
B. 3 ohm and 6 ohm
c. 3 ohm and 9 ohm
D. 5 ohm and 4 ohm


A lot consists of 144 ball pens of which
20 are defective and others are good.
Nuri will buy if it is defective. The shopkeeper draws one pen at random and gives it to her. What is the
probability that
(i) She will buy it
(ii) She will not buy it


If \( |\vec{a}|=1, \) the projection of \( \vec{r} \) along \( \vec{a} \) is 2 and \( \vec{a} \times \vec{r}+\vec{b}=\vec{r}, \) then \( \vec{r}= \)
A \( \cdot \frac{1}{2}[\vec{a}-\vec{b}+\vec{a} \times \vec{b}] \)
B \( \cdot \frac{1}{2}[2 \vec{a}+\vec{b}+\vec{a} \times \vec{b}] \)
c. \( \vec{a}+\vec{a} \times \vec{b} \)
D . \( \vec{a}-\vec{a} \times \vec{b} \)


If \( \boldsymbol{a}: \boldsymbol{b}=\mathbf{5}: \mathbf{9} \) and \( \boldsymbol{b}: \boldsymbol{c}=\boldsymbol{4}: \mathbf{7} \) find \( \boldsymbol{a}: \)
\( \boldsymbol{b}: \boldsymbol{c} \)
This question has multiple correct options
A \( \cdot 5: 9: \frac{63}{4} \)
B. 20: 63: 36
\( \mathbf{c} \cdot 4: 36: 63 \)
D. 20: 36: 63


Two coins are tossed. What is the
conditional probability that two heads result, given that there is at least one head?
A \( \cdot \frac{1}{4} \)
в. \( \frac{2}{3} \)
\( c \cdot \frac{1}{3} \)
D. \( \frac{3}{4} \)


Which pair of following quantities has dimensions different from each other.
A. Impulse and linear momentummmmmmmmm
c. Moment of inertia and moment to force
D. Young's modulus and pressure


A monoatomic ideal gas undergoes a process in which the ratio of \( \boldsymbol{P} \) to \( \boldsymbol{V} \) at
any instant is constant and equal to unity. The molar heat capacity of gas is:
\( \mathbf{A} \cdot 1.5 R \)
B. \( 2.0 R \)
c. \( 2.5 R \)
D. 0


Write any two events occurring the
process of photosynthesis.


2 years back the age of Sushil's father was 7 times Sushil's age then. If the
sum of their present age is 36 years,
what is the age of Sushil's father at
present in years?
A .28
B . 30
c. 40
D. None of these


Two magnetic poles of pole strengths \( 324 m A-m \) and \( 400 m A-m \) are kept at
a distance of \( 10 \mathrm{cm} \) in air. The null point will be at a distance of
on the line joining the two poles, from the weak pole if they are like poles:
A. 4.73
B. 5
\( c .6 .2 \)
D. 5.27


A circular track of radius \( 100 \mathrm{m} \) is
designed for an average speed \( 54 \mathrm{km} / \mathrm{h} \) Find the angle of banking.
A \( \cdot \tan ^{-1}\left(\frac{3}{20}\right) \)
B. \( \tan ^{-1}\left(\frac{9}{40}\right) \)
c. \( \tan ^{-1}\left(\frac{3}{10}\right) \)
D. None of these


The energies of activation for forward
and reverse reactions for \( \left(\boldsymbol{A}_{2}+\boldsymbol{B}_{2} \rightleftharpoons\right. \)
\( 2 A B \) are \( 180 k J \) mol \( ^{-1} \) and \( 200 k J \) mol
-1 respectively. The presence of a
catalyst lowers the activation energy of both (forward and reverse) reactions by
\( 100 k J \) mol \( ^{-1} . \) The enthalpy change of
the reaction \( \left(A_{2}+B_{2} \rightarrow 2 A B\right) \) in the
presence of catalyst will be (in kJ mol-1
A. 300
B. 120
c. 280
D. 20


To purify a phosphorus compound from impurities, it is absorbed in \( H I \) to form its iodide, which on treatment with
which of the following compound gives off the initial phosphorus compound?
A . \( N a O H \)
в. \( H B r \)
c. \( H C l \)
D. \( K O H \)


Which one of the following quantity is dependent on path?
A. Molar internal energy
B. Volume
c. \( w \)
D. \( Q+w \)


India's Mangalyan was sent to the Mars
by launching it into a transfer orbit EOM around the sun. It leaves the earth at \( \mathrm{E} \)
and meets Mars at M. If the semi-major
axis of Earth's orbit is \( a_{e}=1.5 \times \)
\( 10^{11} m, \) that of Mars's orbit \( a_{m}= \)
\( 2.28 \times 10^{11} m, \) taken Kepler's laws, the
estimate of time of Mangalyan to reach
Mars from Earth to be close to
A. 500 days
B. 320 days
c. 260 days
D. 220 days


Nirenberg synthesized an mRNA containing 34 poly-Adenine (A-A-A-A-A\( \left.A^{-}-\cdots-\right) \) and found a polypeptide formed of 11 poly-lysine this proved that genetic code for lysine was
A. One-adenine
B. A-A doublet
c. A-A-A triplet
D. Many adenines


4 moles of \( H_{2} \) at \( 500 \mathrm{K} \) is kept in an
adiabatic rigid container.After some time it was found that 1 mole of the gas
dissociated intoHatoms. The
dissociation energy permole of \( \boldsymbol{H}_{2} \) gas is 2000 cal,Let the new temperature of
the gas be 100 T. The integral value of \( T \) is : (Use \( \mathrm{R}=2 \mathrm{cal} / \mathrm{mole}-\mathrm{K}) \)
A. 3
B. 4
\( c \cdot 5 \)
D. 6
E. 2


For \( 2 A g^{+}+C_{6} H_{12} O_{6}+H_{2} O \rightarrow \)
\( \mathbf{2} \boldsymbol{A} \boldsymbol{g}(\boldsymbol{s})+\boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\mathbf{1 2}} \boldsymbol{O}_{\boldsymbol{7}}+\boldsymbol{2} \boldsymbol{H}^{+}, \) In K of the
change is:
\( \mathbf{A} \cdot 66.13 \)
B. 58.38
c. 28.30
D. 46.29


Show that the effective capacitance, \( C \) of a series combination, of three
capacitors, \( C_{1}, C_{2} \) and \( C_{3} \) is given by
\( \boldsymbol{C}=\frac{C_{1} C_{2} C_{3}}{\left(C_{1} C_{2}+C_{2} C_{3}+C_{3} C_{1}\right)} \)


If \( 7 t h \) and \( 13 t h \) terms of an \( A . P . \) Be 34
and \( 64, \) respectively, then its 18 th
terms is:
\( A \cdot 87 \)
B. 88
c. 89
D. 90


Sets of travellling waves are given as shown in above figure. Identify which of
the following set of wave will soon show
constructive interference?
\( A \cdot A \)
B. B
\( c \cdot c \)
D.
E.


\( \operatorname{Let} \overrightarrow{A B}=3 \hat{i}+\hat{j}-\hat{k} \) and \( \overrightarrow{A C}=\hat{i}- \)
\( \hat{j}+3 \hat{k} . \) If the point \( P \) on the line
segment \( B C \) is equidistant from \( A B \) and \( A C \) then \( \overrightarrow{A P} \) is
A \( \cdot 2 \hat{i}-\hat{k} \)
в. \( \hat{i}-2 \hat{k} \)
\( c \cdot 2 \hat{i}+\hat{k} \)
D. None of these


Universal gas constant per molecule is called
A. Rydberg constant
B. Kelvin constant
c. Boltzman constant
D. Stefan's constant


Which of the following carbohydrates is most abundant in nature?
A. Glucose
B. Fructose
c. starch
D. Cellulose


Mass\( \times \)velocity\( = \)
A. Impulse
B. Momentum
c. Area
D. Force


Dipole-dipole forces act between the
molecules possessing permanent dipole. Ends of dipoles possess 'partial charges'. The partial charge is:
A. more than unit electronic charge
B. equal to unit electronic charge
c. less than unit electronic charge
D. double the unit electronic charge


The equation \( \frac{x^{2}}{2-r}+\frac{y^{2}}{r-5}+1=0 \)
represents an ellipse, if
\( \mathbf{A} \cdot r>2 \)
В. \( 2<r<5 \)
\( \mathbf{c} \cdot r>5 \)
D. \( r \in(2,5) \)


A string is hanging from a rigid support.
A transverse wave pulse is set up at the
bottom. The velocity \( v \) of the pulse related to the distance covered by it is given as
A \( \cdot v x \)
B. \( v-x \)
\( \mathbf{c} \cdot v / x \)
D. none of these


toppr
Q Type your question
OB are resistanceless and rotating with
constant angular velocity \( \omega \) in the same
plane as that ring, about hinge point '0
and the separation between 0 and
\( \mathrm{C} \) (centre of ring) is' \( 2 \ell \) as shown in the
figure. Find the current in the rod 'OA' when the both rod becomes tangent
to the ring.
A. Zero
B.
\[
\frac{B a V}{R} e \frac{-3 t}{2 C R}
\]
\( c \)
\[
\frac{B a V}{R} e \frac{3 t}{2 C R}
\]
D.
\[
\frac{B a V}{R} e \frac{-4 t}{2 C R}
\]
E. None of the above


The equation of perpendicular bisector of the line segment joining the points
(1,2) and (-2,0) is-
A \( .5 x+2 y=1 \)
B. \( 4 x+6 y=1 \)
c. \( 6 x+4 y=1 \)
D. None of these


The dispersed phase consists of micelles.What is the name of the
colloid?


Which oxide does not act as a reducing
agent? This question has multiple correct options
A . \( N O \)
в. \( N O_{2} \)
\( \mathrm{c} \cdot \mathrm{N}_{2} \mathrm{O} \)
D. \( N_{2} O_{5} \)


What is the resistance between \( P \) and
Q?
\( A \cdot \frac{3}{4} s \)
B. \( \frac{4}{3} \)
c. \( \frac{16}{3} \)
D. Infinity


If \( B=15^{\circ}, \) prove that \( 4 \sin 2 B \cdot \cos 4 B \)
\( \sin 6 B=1 \)


Distinguish between vital capacity and total lung capacity.


The mass number of nucleus is:
A. Sometimes equal to its atomic number
B. Sometimes less than and sometimes more than its
atomic number
C. Always less than its atomic number
D. Always more than its atomic number


In which pairs do both species have the same number of unpaired electrons in \( \mathrm{p} \)
orbitals?
10 and \( C l^{+} \)
2. \( F^{+} \) and \( G a^{-} \)
3. \( \mathrm{N} \) and \( \boldsymbol{K} \boldsymbol{r}^{\boldsymbol{3}+} \)
A. 1,2 and 3 are correct
B. 1 and 2 only are correct
c. 2 and 3 only are correct
D. 1 only is correct


Transition metals are good catalytic
agent. Why?


\( \operatorname{Given} f(x)\left\{\begin{array}{ll}|x-2|+\lambda & \text { if } x \leq 2 \\ x^{2}+1 & \text { if } x>2\end{array}\right. \)
If \( f(x) \) has a local minimum at \( x=2 \)
then which of the following is most appropriate
A. \( \lambda \leq 5 \)
в. \( \lambda \geq 5 \)
c. \( \lambda \leq 0 \)
D. \( \lambda \geq 0 \)


Select from the list the gas that matches the descriptions given in each
case:
[ammonia, ethane, hydrogen chloride, hydrogen sulphide, ethyne]
This gas is used for welding purpose.


Given that in the H-atom the transition
energy for \( n=1 \) to \( n=2, \) Rydberg
states in \( 10.2 \mathrm{eV} \). The energy for the
same transition in \( B e^{3+} \) is:
A. 20.4 ev
B. 163.2 eV
c. 30.6 ev
D. 40.8 ev


Find the value of \( x \) if
\( \left|\begin{array}{ccc}\mathbf{3} & \mathbf{4} & \mathbf{1} \\ \mathbf{0} & \boldsymbol{x} & \mathbf{8} \\ \mathbf{3} & \mathbf{- 1} & \mathbf{4}\end{array}\right|=\mathbf{0} \)


\( \lim _{x \rightarrow 0} \frac{3^{x}-2^{x}}{4^{x}-3^{x}} \) is equal to
\( \mathbf{A} \cdot \mathbf{1} \)
B . - -
\( c \cdot 0 \)
D. none of these


Churning of milk cream to get butter is
\( a \)
changes.


A body starts with an initial velocity of
\( 10 m s^{-1} \) and acceleration \( 5 m s^{-2} \). Find
the distance covered by it in 5 s.
\( \mathbf{A} \cdot 62.5 m \)
в. 32.5 т
c. \( 112.5 m \)
D. \( 50 m \)


A chord of a circle of radius \( 10 \mathrm{cm} \)
subtends a right angle at the centre. Find the area of corresponding minor
segment \( (\boldsymbol{\pi}=\mathbf{3 . 1 4}) \)


Explain two activities for the formation of artificial rainbow.


The shearing strain is equivalent to
A. Tensile strain + compression strain
B. Tensile strain - compression strain
C. Shear strain + tensile strain
D. Shear strain + compression strain


The rate constant of a first order
reaction at \( 25^{\circ} \mathrm{C} \) is \( 0.24 s^{-1} . \) If the
energy of activation of the reaction is
\( 88 k J \) mol \( ^{-1}, \) at what temperature
would this reaction have rate constant
of \( 4 \times 0^{-2} s^{-1} ? \)


The mode of exchange of energy due to temperature difference is known as:
A. heat energy
B. electric energy
c. potential energy
D. kinetic energy


The following frequency distribution gives the monthly consumption of 68 consumers of a locality. Find the median.
\( \begin{array}{llll}\text { Monthly } & 65- & 85- & 105- \\ \text { Consumption } & 85 & 105 & 125\end{array} \)
No. of 4


Most atmospheric pollutants do not rise above.
\( \mathbf{A} \cdot 600 \mathrm{m} \)
B. 1000m
c. \( 2000 \mathrm{m} \)
D. 200m


Which is the expression for resistivity of a wire of length \( l \) and cross-section area
A?
A \( \cdot \rho=\frac{R l}{A} \)
B. \( \rho=\frac{R A}{l} \)
\( c \cdot \rho=\frac{A}{R l} \)
D. \( \rho=\frac{R A}{l^{2}} \)


According to Langmuir adsorption isotherm, the amount of gas adsorbed at very high pressure :
A. reaches a constant limiting value
B. goes on increasing with pressure
c. goes on decreasing with pressure
D. increases first and decreases later with pressure


Differentiate w.r.t. \( \mathbf{x} \)
\( f(x)=\sqrt{\sin (\cos x)} \)


A small conducting sphere of radius \( r \) is Iying concentrically with a bigger
hollow conducting sphere of radius \( \boldsymbol{R} \)
The bigger and smaller spheres are
charged with \( Q \) and \( q \) respectively
\( (Q>q) . \) The two spheres are insulated
from one another. The potential difference between the spheres will be :
A \( \cdot \frac{1}{4 \pi \epsilon_{0}}\left(\frac{q}{r}-\frac{Q}{R}\right) \)
В. \( \frac{1}{4 \pi \epsilon_{0}}\left(\frac{q}{r}-\frac{q}{R}\right) \)
\( ^{\mathbf{C}} \cdot \frac{1}{4 \pi \epsilon_{0}}\left(\frac{q}{r}+\frac{Q}{R}\right) \)
D. \( \frac{1}{4 \pi \epsilon_{0}}\left(\frac{q}{R}-\frac{Q}{r}\right) \)


A chemistry student trying to detect the metallic ion in a salt makes a paste on
the clean \( P t \) wire-loop of the salt with
concentrated \( H C l . \) When he takes a
small amount of this paste and keeps it in a non-luminous Bunsen flame, the
color of the flame changes to grassy
green. He should, therefore, conclude
that the metal is:
A. \( M g \)
в. \( C a \)
c. \( B a \)
D. \( R a \)


Find the 5 th term from the end of the
\( A P 7,10,13, . .154 \)


Write the number of significant digits
in 100.1


Two mirrors at an angle \( \theta \) produce 5 images of a point. The number of images produced when \( \theta \) is decreased
to \( \theta-30 \) is
\( \mathbf{A} \cdot \mathbf{9} \)
B. 10
c. 11
D. 12


Consider the reaction.
\( \left[N i\left(H_{2} O\right)_{6}\right]^{2+}(a q)+3 e n(a q) \rightarrow \)
\( \left[N i(e n)_{3}\right]^{2+}+2 H_{2} O \)
Which of the following property of compound is changed in reaction?
A. Co-ordination number
B. Geometry of complex
c. Hybridization of central atom
D. wavelength of absorbed light


The value of \( \cos ^{2} A+\cos ^{2} B- \)
\( \mathbf{2} \cos \boldsymbol{A} \cos \boldsymbol{B} \cos (\boldsymbol{A}+\boldsymbol{B})- \)
\( \sin ^{2}(\boldsymbol{A}+\boldsymbol{B}) \)


A planet is revolving in an elliptical orbit around the sun. Its closest
distance from the sun is \( r \) and the
farthest distance is \( R \). If the velocity of
the planet nearest to the sun be \( v \) and
that farthest away from the sun be \( V \)
then \( \boldsymbol{v} / \boldsymbol{V} \) is :
A \( \cdot R^{2} / r^{2} \)
B . \( r^{2} / R^{2} \)
c. \( R / r \)
D. \( r / R \)


\( \ln \left[\boldsymbol{P t}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2} \boldsymbol{C l}_{2}\right], \boldsymbol{P} \boldsymbol{t}-\boldsymbol{C l} \) bond length
is \( 2 A \) and \( C I-C I \) distance is \( 2.88 A \) then
the compound is:
A. tetrahedral
B. square pyramidal
c. cis-square planar
D. trans-square planar


Integrated circuits are preferred over conventional circuits because:
A. They are very compact in size.
B. They are cheap.
c. They are fast and more efficient.
D. All of the above


The type of hybrid orbitals used by chlorine atom in \( C l O^{-}, C l O_{2}^{-}, C l O_{3}^{-} \)
and \( C l O_{4}^{-} \) is/are:
A \( \cdot s p, s p^{2}, s p^{3} \) and \( s p^{3} d \)
B. \( s p \) and \( s p \)
C . only \( s p^{3} \)
D. only sp


The name of the compound is
Cyclopropanecarboxylic acid.
A. True
B. False


A rigid body is rotating about a vertical
axis at \( n \) rotations per minute. If the
axis slowly becomes horizontal in \( t \)
seconds and the body keeps on rotating
at \( n \) rotations per minute then the
torque acting on the body will be, if the moment of inertia of the body about axis of rotation is \( \boldsymbol{I} \)
A. Zero
В. \( \frac{2 \pi n I}{60 t} \)
c. \( \frac{2 \sqrt{2} \pi n I}{60 t} \)
D. \( \frac{4 \pi n I}{60 t} \)


Each edge of a cube is increased by
\( 50 \% . \) What is the percent of increase in
the surface area of the cube?
\( A \cdot 50 \% \)
B. \( 125 \% \)
c. \( 150 \% \)
D. 300\%


The value of \( \lim _{\boldsymbol{\theta} \rightarrow \mathbf{0}} \frac{\mathbf{1}-\cos \mathbf{4} \boldsymbol{\theta}}{\mathbf{1}-\cos \mathbf{6} \boldsymbol{\theta}} \) is
A. \( 9 / 4 \)
B. 3/4
\( c \cdot 4 / 9 \)
D. \( 9 / 3 \)


The number of workers increased the
days to complete the work decreased."is
example of
A. Inverse ratio
B. Direct ratio
C. Both of A and B
D. none of above


Under what condition is the force acting
on a charge moving through a uniform magnetic field minimum?


In how many ways four members be
selected from a group of eleven
members?

This question has multiple correct options
A . \( ^{11} C_{5} \)
в. \( ^{11} C_{7} \)
\( c \cdot^{11} C_{4} \)
D. \( ^{11} C_{6} \)


Factorise \( : \boldsymbol{x}^{2}+\mathbf{4} \boldsymbol{x}+\mathbf{3} \)


Which of the following options are based on the principle of Electromagnetic induction?
A. A resistor
B. An electric generator
c. A capacitor
D. A battery
E. An electroscope


Thomson's model was rejected
because:
A. it was not clearly specified in detail
B. it could not explain how both positively and negatively charged particles protect their identity being together
C. it does not explain any repulsions which might result since all the positive charges are together in an cluster and same is the case with negative charges as well
D. all of these


The K.E of \( N \) molecule of \( O_{2} \) is xjoules
at \( _{--} 123^{\circ} \) C. Another sample of \( O_{2} \) at
\( 327^{\circ} \mathrm{C} \) has a \( \mathrm{K.E} \) of \( 2 x \) joules. The latter sample contains:
A. \( N \) molecules of \( O_{2} \)
B. 2 N molecules of \( O_{2} \)
C. \( N / 2 \) molecules of \( O_{2} \)
D. \( N / 4 \) molecules of \( O_{2} \)


A short bar magnet has a magnetic moment of \( 0.48 J T^{-1} . \) Give
the direction and magnitude of the magnetic field produced by the magnet at a distance of \( 10 \mathrm{cm} \) from the
centre of the magnet on
(a) the axis, (b) the equatorial lines (normal bisector) of
the magnet


State True or False.
\( B C l_{3} \) in aqueous solution exists as
\( B^{3+} \) and \( C l \)
A . True
B. False


Under what conditions gases generally deviate from ideal behaviour?
A. At high temperature and low pressure
B. At low temperature and high pressure
c. At high temperature and high pressure
D. At low temperature and low pressure


When \( 12.044 \times 10^{23} \) molecule of
\( H_{2} S O_{4} \) is dissolve in \( 195 \mathrm{cm}^{3} \) solution.
What is mass percent \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) in the solution. If the density of the solution is \( 1.25 g c m^{-3} \)


Solve the given differential equation
\( \left(x y^{2}+x\right) d x+\left(y x^{2}+y\right) d y=0 \)
\( \mathbf{A} \cdot\left(x^{2}+1\right)\left(y^{2}+1\right)=c \)
B \( \cdot \log \left(x^{2}+1\right) \log \left(y^{2}+1\right)=c \)
c. \( \left(x^{2}+1\right)+\left(y^{2}+1\right)=c \)
D. none of these