A beam of light consisting of red, green
and blue colours is incident on a rightangled prism as shown. The refractive index of the material of the prism for
the above red, green and blue wavelengths are 1.39,1.44 and 1.47
respectively. The prism will
A. seperate part of the red colour from the green and blue colours
B. seperate part of the blue colour from the red and green colours
C. seperate all the three colours from one another.
D. not seperate even partially any colour from the other two colours


When an a.c. source of e.m.f. \( \boldsymbol{E}= \)
\( E_{0} \sin 100 t \) is connected across a
circuit, it is observed that voltage leads the current by a phase angle \( \frac{\pi}{4} . \) If the circuit consists possible only R-L, R-C or L-C in series the two elements could be.
B. \( R=10 \Omega, C=1000 \mu F \)
c. \( R=100 \Omega, C=1000 \mu F \)
D. \( R=10 \Omega, L=100 m H \)


Arrange the following steps in the conversion of hydel energy to electricity
in a proper sequence.
(a) Released water is made to fall on the
blades of the turbines.
(b) Water in the dam is released
(c) Water is collected in the dam.
(d) Potential energy is converted to kinetic energy.
(e) The armature of the electric
generator rotates to produce electricity.
A. b c de a
B. a d b ce
\( c \cdot e c d b a \)
D. \( c b d \) a e


The equilibrium constant for the following reaction is:
\( 2 F e^{3+} 3 I^{\ominus} \rightleftharpoons 2 F e^{2+}+I_{3}^{\ominus} \)
The standard reduction potential in
acidic conditions is \( 0.78 V \) and \( 0.54 V \)
respectively, for \( \boldsymbol{F e}^{\mathbf{3}}+ \)
\( \left|\boldsymbol{F} \boldsymbol{e}^{2+} \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \boldsymbol{I}_{3}^{\ominus}\right| \boldsymbol{I}^{\ominus} \) couples
\( \mathbf{A} \cdot K_{e q}=10^{8} \)
В. \( K_{e q}=10^{7} \)
\( \mathbf{c} \cdot K_{e q}=10^{5} \)
D. None of these


A particle executes simple harmonic motion between \( \boldsymbol{x}=-\boldsymbol{A} \) and \( \boldsymbol{x}=+\boldsymbol{A} \)
The time taken for it to go from 0 to \( A / 2 \)
is \( T_{1} \) and to \( \operatorname{gofrom} A / 2 \) to \( A \) is \( T_{2} \). Then
A \( \cdot T_{1}<T_{2} \)
в. \( T_{1}>T_{2} \)
c. \( T_{1}=T_{2} \)
D. \( T_{1}=2 T_{2} \)


Draw MO energy level diagrams for
\( C_{2}, O_{2} \) and \( C O . \) Show which orbitals are
occupied, and work out the bond orders and magnetic properties of these molecules.


Which of the following statements is
incorrect?
A. Alum is a double salt.
B. EDTA salt of calcium is used in the treatment of leadd poisioning.
C. Effective atomic number of the metals in complexes \( \left[N i(C O)_{4}\right] \) and \( \left[F e(C N)_{6}\right]^{4-} \) is same
D. Chloridotris (triphenyl phosphine) rhodium(l) is effective heterogeneous catalyst for hydrogenation of alkenes.


What is the action of \( C o_{2} \) on quick lime.


Solve:\( \tan ^{-1}\left(\frac{6 x}{1-8 x^{2}}\right) \)


Karyoplasmic index (KI) is
A \( \cdot \frac{V_{V}}{V_{n}-V_{c}} \)
B. \( \frac{V_{V}}{V_{c}-V_{n}} \)
\( c \cdot \frac{V_{c}}{V_{n}} \)
D. \( \frac{V_{n}}{V_{n}+V_{c}} \)


"Li metal is used in photoelectric cells, while Cs is not used."

Answer whether the above statement is
true or false.
If true enter 1 , else enter 0


If \( \cos ^{2} x=\cos ^{4} x \) then find the
minimum and maximum value of
\( \sin ^{2} x+\cos ^{4} x, \) for all real values of \( \theta \)


The correct order for the wavelength of absorption in the visible region is:
\( \mathbf{A} \cdot\left[N i\left(N O_{2}\right)_{6}\right]^{4-}<\left[N i\left(N H_{3}\right)_{6}\right]^{2+}<\left[N i\left(H_{2} O\right)_{6}\right]^{2+} \)
B. \( \left[N i\left(N O_{2}\right)_{6}\right]^{4-}<\left[N i\left(H_{2} O\right)_{6}\right]^{2+}<\left[N i\left(N H_{3}\right)_{6}\right]^{2+} \)
\( ^{\mathbf{C}}\left[N i\left(H_{2} O\right)_{6}\right]^{2+}<\left[N i\left(N H_{3}\right)_{6}\right]^{2+}<\left[N i\left(N O_{2}\right)_{6}\right]^{4-} \)
D. \( \left[N i\left(N H_{3}\right)_{6}\right]^{2+}<\left[N i\left(H_{2} O\right)_{6}\right]^{2+}<\left[N i\left(N O_{2}\right)_{6}\right]^{4-} \)


Two spheres have their surface areas in
the ratio 9: 16 Their volumes are in the
ratio of
A .64: 27
B . 27: 64
c. 16: 27
D. 11: 27


Evaluate: \( \int \frac{\cos 2 x}{\sin x} d x \)


The energy of a photon of green light of wavelength \( 5000 A^{\circ} \) is
A . \( 3.459 \times 10^{-19} \) joule
в. \( 3.973 \times 10^{-19} \) joule
c. \( 4.132 \times 10^{-19} \) joule
D. \( 8453 \times 10^{-19} \) joule


Left lung is poorly developed in
A. Lizard
B. Snakes
c. crocodile
D. Man


The geometric mean of the numbers \( \mathbf{7}, \mathbf{7}^{2}, \mathbf{7}^{\mathbf{3}}, \dots, \mathbf{7}^{n} \mathbf{i} \mathbf{s} \)
\( A \cdot 7^{7 / 4} \)
B \( \cdot 7^{4 / 7} \)
\( c \cdot 7^{\frac{n-1}{2}-\frac{1}{2}-\frac{2}{2}-\frac{2}{2}} \)
\( D \cdot 7^{\frac{n-1}{2}} \)


Which is correct relationship?
\( \mathbf{A} \cdot E_{1} \) of \( H=\frac{1}{2} E_{2} \) of \( \mathrm{H} e^{+}=\frac{1}{3} E_{3} \) of \( L i^{+2}= \)
\( \frac{1}{4} E_{4} \) of \( B e^{+3} \)
B \( \cdot E_{1}(H)=E_{2}\left(H e^{+}\right)=E_{3}\left(L i^{+2}\right)=E_{4}\left(B e^{+3}\right) \)
C \( \cdot E_{1}(H)=2 E_{2}\left(H e^{+}\right)=3 E_{3}\left(L i^{+2}\right)=4 E_{4}\left(B e^{+3}\right) \)
D. No relation


Which of the following is a mild tranquilizer?
A. Valium
B. Meprobamate
c. Bithional
D. Norethindrone


Which equation represents the line that
passes through the point (-1,4) and is parallel to the \( y \) -axis?
A. \( y=-1 \)
B . \( x=-1 \)
c. \( x=4 \)
D. \( y=4 \)


The volume of \( \mathrm{H}_{2} \) in litre formed per
hour at STP is
(Give answer as greatest integer)


The value of \( n \) in the equation, \( \boldsymbol{C r}_{2} \boldsymbol{O}_{\mathbf{7}}^{2-}+\mathbf{1 4} \boldsymbol{H}^{+}+\boldsymbol{n} \boldsymbol{e}^{-} \rightarrow \boldsymbol{2} \boldsymbol{C r}^{\boldsymbol{3}+}+ \)
\( \mathbf{7} H_{2} O \) is:
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 6


When electric current passes through a bucket full of water, lot of bubbling is observed. This suggests that the type of supply is
A . AC
B. DC
c. any of the above two
D. None of the above


Are \( \frac{-1}{2} \) and \( \frac{-3}{6} \) represented by the same point on the number line?


A light ray is incident normally on a plane mirror.
(a) What is the angle of incidence?
(b) What is the path of reflected ray?
A \( \cdot(a) 180^{\circ},(b) \) same as incident ray
в. \( (a) 180^{\circ} \)
\( (b) \) opposite to incident ray
(b) opposite to incident ray
\( \mathbf{c} \cdot(a) 0^{\circ} \)
D. \( (a) 0^{\circ},(b) \) same as incident ray


Biot-Savart law indicates that the
moving electrons (velocity \( \overline{\boldsymbol{v}} \) ) produce a magnetic field \( \bar{B} \) such that:
\( \mathbf{A} \cdot \bar{B} \perp \bar{v} \)
B . \( \bar{B} \| \bar{v} \)
C . it obeys inverse cube law.
D. it is along the line joining the electron and point of observation.


The principal quantum number increases, the difference of energy between consecutive energy levels:
A . decreases
B. increases
c. remain same
D. sometimes increases and sometimes decreases


A smooth track of incline of length \( l \) is
joined smoothly with circular track of
radius \( R . \) A mass of \( m \) kg is projected up from the bottom of the inclined
plane. The minimum speed of the mass
to reach the top of the track is given by,
\( \boldsymbol{v}= \)
\( \mathbf{A} \cdot[2 g(l \cos \theta+R)(1+\cos \theta)]^{1 / 2} \)
B - \( (2 g l \sin \theta+R)^{1 / 2} \)
\( \mathbf{c} \cdot[2 g\{l \sin \theta+R(1-\cos \theta)\}]^{1 / 2} \)
D. \( (2 g l \cos \theta+R)^{1 / 2} \)


Which of the following is an example of
weak electrolyte?
A. \( H_{3} B O_{3} \)
в. \( H_{2} S O_{4} \)
c. \( H N O_{3} \)
D. \( H C l O_{3} \)


Which of the following reacts fastest
with conc. \( \boldsymbol{H} \boldsymbol{C l} \) ?
A. \( \left(C H_{3}\right)_{3} C O H \)
в. \( C H_{2}=C H-C H_{2} O H \)
\( c \)
D.


Chlorine is not collected over water
since chlorine is readily soluble in
water
A. True
B. False


Derive an equation for position-velocity relation \( \left(2 a s=v^{2}-u^{2}\right) \) by graphical
method


A transverse wave propagating along \( \boldsymbol{x}-\operatorname{axis} \) is represented by \( \boldsymbol{y}(\boldsymbol{x}, \boldsymbol{t})= \)
\( 8.0 \sin (0.5 \pi x-4 \pi t-\pi / 4), \) wherex is
in metres and \( t \) is in seconds. The speed
of the wave is
A. \( 8 m / s \)
в. \( 4 \pi m / s \)
\( \mathbf{c} \cdot 0.5 \pi m / s \)
D. \( \pi / 4 \mathrm{m} / \mathrm{s} \)


Nuclear fusion is possible:
A. only between light nuclei
B. only between heavy nuclei
C. between both light and heavy nuclei
D. only between nuclei which are stable against \( \beta- \) decay


If \( y^{2}+b^{2}=2 x y, \) then \( \frac{d y}{d x} \) equals
This question has multiple correct options
A \( \cdot \frac{1}{x y-b^{2}} \)
в. \( \frac{y}{y-x} \)
c. \( \frac{x y-b^{2}}{(y-x)^{2}} \)
\( \frac{x y-b^{2}}{y} \)


In a village of 120 families, 93 families
use firewood for cooking, 63 families use kerosene, 45 families use cooking
gas, 45 families use firewood and kerosene, 24 families use kerosene and
cooking gas, 27 families use cooking gas and firewood. Find how many use firewood, kerosene and cooking gas.
A . 10
B . 15
c. 20
D. 25


A sample of an ideal gas occupies a volume of 'V' at a pressure 'P' and absolute temperature 'T'. The mass of each molecule is 'm'. The equation for density is
A . mkT
B. P/kT
\( c \cdot P /(k T V) \)
D. Pm/kT


The order of coloured rings in a carbon resistor is red, yellow, blue and silver The resistance of the carbon resistor is :
A \( \cdot 24 \times 10^{6} \Omega \pm 5 \% \)
B . \( 24 \times 10^{6} \Omega \pm 10 \% \)
c. \( 34 \times 10^{4} \Omega \pm 10 \% \)
D . \( 26 \times 10^{4} \Omega \pm 5 \% \)


The disease of astigmatism in human eye is because of:
A. unequal and uneven curvature of eye lens
B. eye lens being of organic matter
c. eye membranes being thick
D. opacity development in eye lens


Stars produce heat energy and light due to the fusion of
A. oxygen
B. Hydrogen
c. helium
D. ozone


A block of mass \( 20 k g \) is pushed with a
horizontal force of \( 90 N . \) If the coefficent
of static \( \& \) kinetic friction are \( 0.4 \& 0.3 \)
the frictional force acting on the block
is
A. \( 90 N \)
N
в. \( 80 N \)
\( c \cdot 60 N \)
D. \( 30 N \)


A runner moves along the road at
\( 2 m s^{-1} \) in still air that is at a
temperature of \( 29^{\circ} \mathrm{C} . \) His surface area
is \( 1.4 m^{2}, \) of which approximately \( 85 \% \)
is exposed to the air. Coefficient of convection for dry air and bare skin at
wind speed \( 2 m s^{-1} \) is \( 22 W m^{-2 \circ} C^{-1} \)
The rate of convective heat loss from his
skin at a temperature \( 35^{0} C \) to the
outside air is :
\( A \cdot 10 W \)
B. 20 \( w \)
c. 30 \( w \)
D. 160 \( w \)


In a transformer, the number of turns in
the primary coil is 140 and that in the secondary coil is \( 280 . \) If the current in the primary coil is \( 4 A \), then that in the secondary coil is
\( A \cdot 4 A \)
B. 2 A
\( c \cdot 6 A \)
D. 10 A


The Richardson equation is given by \( \boldsymbol{I}=\boldsymbol{A} \boldsymbol{T}^{2} \boldsymbol{e}^{\frac{-B}{k T}} . \) The dimensional formula
for \( A B^{2} \) is same as that for:
A \( \cdot I T^{-2} \)
в. \( k \) Т
\( c \cdot I k^{2} \)
D. \( \frac{I k^{2}}{T} \)


The rate constant for a reaction can be
increased by \( \underline{a} \) the stability of the reactant or by \( \underline{b} \) the stability of the transition state. Select the correct
choice for a and \( b \)
A. decreasing, decreasing
B. increasing,decreasing
c. decreasing,increasing
D. increasing,increasing


70 cal of heat is required to raise the temperature of a diatomic gas at
constant pressure from 30 to \( 35^{\circ} \) C. The amount of heat required (in cal) to raise
the temperature of the same gas
through the same range \( \left(30 \text { to } 35^{\circ} C\right) \) at constant volume is:
A . 30
B. 60
c. 50
D. 70


The process of converting alternating current into direct current is known as
A. modulation
B. amplification
c. detection
D. rectification


\( 25 m l \) of a solution of barium hydroxide on titration with a 0.1 molar solution of
hydrochloric acid gave a titre value of 35 ml. The molarity of barium hydroxide solution was:
A . 0.14
B. 0.28
c. 0.35
D. 0.07


A block of mass \( 60 \mathrm{kg} \) just slides over a horizontal distance of \( 0.9 \mathrm{m} \). If the
coefficient of friction between their
surface is 0.15 then work done against
friction will be
B. 97.54 J
c. 105.25
D. None of these


Solve:
\( \left|\begin{array}{ccc}\mathbf{0} & \boldsymbol{a} & -\boldsymbol{b} \\ -\boldsymbol{a} & \boldsymbol{0} & -\boldsymbol{c} \\ \boldsymbol{b} & \boldsymbol{c} & \boldsymbol{0}\end{array}\right|=0 \)


Choose the correct answers from the
alternatives given. Some species of Anopheles mosquito live in brackish water, some in running fresh water, and others in
stagnant water. What type of reproductive barrier is most obviously separating these different species?
A. Ecological isolation
B. Temporal isolation
c. Behavioural isolation
D. Postzygotic barriers


State the number of significant figures
in each of the following:
\( \mathbf{0 . 0 0 4 5 6} \)


The partial charge separation between
the bonded atoms gives rise to
in that compound.
A. covalent character
B. coordinate character
c. ionic character
D. none of these


Displacement of a particle is given by the expression \( x=3 t^{2}+7 t-9, \) where
\( x \) is in meter and \( t \) is in second. What is
acceleration?
\( \mathbf{A} \cdot 1 m / s^{2} \)
B . \( 3 m / s^{2} \)
\( \mathbf{c} \cdot 6 m / s^{2} \)
D. \( 9 m / s^{2} \)


Two particles of masses \( m_{1} \) and \( m_{2} \) are
released from rest on a smooth wedge
of mass \( M, \) then
This question has multiple correct options
A. Reaction force on the wedge due to ground is equal to \( \left(m_{1}+m_{2}+M\right) g \)
B. The wedge remains at rest if \( m_{1}=m_{2} \)
C ' the wedge remains stationary if \( \frac{\left(m_{1}\right.}{m_{2}}=\tan \theta \)
D. if \( \left(m_{1}>m_{2}, \) the wedge will accelerate towards right \right.


Calculate the scalar product of the following vectors.

Resolve the vector \( d=\{1,1,1\} \) into
components with respect to three
noncoplanar vectors \( \boldsymbol{a}= \)
\( \{1,1,-2\}, b=\{1,-1,0\}, \) and \( c= \)
\{0,2,3\}


Calculate the molecular mass (u) of
Sulphuric acid \( \left(\boldsymbol{H}_{2} \boldsymbol{S O}_{4}\right) \)
A . 96
B. 97
\( c \cdot 98 \)
D. 49


Tropical plant like sugarcane show high
efficiency of \( C O_{2} \) fixation because of
A. TCA cycle
B. Calvin cycle
c. Hatch and slack cycle
D. EMP pathway


How many 6 -digit telephone numbers can be constructed using the digits 0 to
9 if each number starts with 67 and no
digit appears more than once?


Explain why:
Transition elements form coloured
compounds.


The current that passes through 20 ohm resistance when it is connected in
parallel with a 30 ohm resistance and this set is connected to a battery of \( 2 \mathrm{V} \)
is
A . \( 0.2 A \)
B. \( 0.3 \mathrm{A} \)
c. \( 0.1 \mathrm{A} \)
D. 0.016A


The electric energy density between the plates of charged condenser is
A \( \cdot q / 2 \varepsilon_{0} A^{2} \)
В \( \cdot q / 2 \varepsilon_{0} A \)
\( \mathbf{c} \cdot q^{2} /\left(2 \varepsilon_{0} A^{2}\right) \)
D. none of these


The number of solutions of the equation
\( z^{2}+\bar{z}=0 \) is: (where z is a complex
number)


Which of the following condition occurs
in the person with genotype \( X 0 ? \)
A. Cannot survive.
B. Will have immature, ambiguous (both male and female) reproductive systems.
C. Will be phenotypically female but sterile
D. Does not produce steroid hormones.
E. None of the above


How many unpaired electrons are present in \( N_{2}^{+} \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
D. 4


Given \( \vec{F}=(4 \hat{i}-10 \hat{j}) \) and \( \vec{r}=(5 \hat{i}-3 \hat{j}) . \) Then
torque \( \boldsymbol{\tau} \) is
A. - \( 62 \hat{j} \)
в. \( 62 \hat{k} \)
\( c .38 \hat{i} \)
D. \( 38 \hat{k} \)


A population grows at the rate of \( 5 \% \) per year. Then the population will be doubled at
A. \( 10 \log 2 \) years
B. 20 log 2 years
c. \( 30 \log 2 \) years
D. \( 40 \log 2 \) years


Write three difference between
diamagnetic and paramagnetic
substances.


In a squared sheet, draw two triangles of equal area such that the triangles are
not congruent. What can you say about their perimeters?


A salt 'X' is dissolved in water of \( \mathrm{pH}=7 . \) The resulting solution becomes alkaline
in nature. The salt is made up of:
A. A strong acid and strong base
B. A strong acid and weak base
c. A weak acid and weak base
D. A weak acid and strong base


On the interval [0,1] the function
\( f(x)=x^{1005}(1-x)^{1002} \) assumes
maximum value equal to.
A \( \cdot \frac{(1005)^{1002}}{(2007)^{2007}} \)
в. \( \frac{(2007)^{2007}}{(1005)^{12055}(1002)^{1002}} \)
c. \( \frac{(2007)^{2007}}{(1005)^{1202}(1002)^{1005}} \)
D. \( \frac{(1005)^{1005}(1002)^{1002}}{(2007)^{2007}} \)


State whether the given statement is True or False. The deviation produced by a prism is independent of the angle of incidence and is the same for all the colors of
light.
A. True
B. False


Two identical circular loops, \( P \) and \( Q \)
each of radius \( r \) and carrying equal
currents are kept in the parallel planes having a common axis passing through
O. The direction of current in \( \boldsymbol{P} \) is
clockwise and in \( Q \) is anti-clockwise as
seen from \( O \) which is equidistant from
the loops \( P \) and \( Q . \) Find the magnitude
of the net magnetic field at \( O \)


Tyndall effect is producted by


\( C_{v} \) for helium gas \( (H e) \) is
\( \left(i n J m o l^{-1} K^{-1}\right) \)
A . 2.5
B. 10.5
\( c \cdot 1.5 \)
D. 12.5


How many grams of \( N a O H \) are needed
to make \( 100 g \) of a \( 5 \% \) solution?
\( A \cdot 2 \)
B. 5
c. 20
D. 40
E . 95


On adding few drops of dilute \( H C l \) or
\( \boldsymbol{F} \boldsymbol{e} \boldsymbol{C l}_{3} \) to freshly precipitated ferric hydroxide, a red coloured colloidal solution is obtained. This phenomenon is known as:
A. peptization
B. dialysiss
c. protection
D. dissolution


Can we consider work energy theorem as a generalization in Physics for any system?
A. Yes
B. No, in some cases it fails particularly in thermodynamics
c. only for open systems
D. can not be said as such


In hydrogen spectrum, the spectral line of Balmer series having lowest wavelength is:
A. \( H_{\alpha}- \) line
B. \( H_{\beta}- \)line
\( \mathbf{c} \cdot H_{\gamma}-\operatorname{line} \)
D. \( H_{\delta}- \) line


In Young's double slit experiment. the fringe width with light of wavelength \( \mathbf{0} \)
\( 6000 A \) is \( 3 \mathrm{mm} \). The fringe width, when the wavelength of light is changed to
\( 4000 A \) is
\( A \cdot 3 m m \)
B. \( 1 \mathrm{mm} \)
\( c \cdot 2 m m \)
D. \( 4 \mathrm{mm} \)


Fill in the blank:
A shooting star is a
A . comet
B. meteor
c. meteorite
D. none of the above


The percentage of \( S e \) in peroxidase
anhydrous enzyme is \( 0.5 \% \) by weight (atomic weight \( =\mathbf{7 8 . 4} \) ). Then minimum
molecular weight of peroxidase anhydrous enzyme is:
A \( \cdot 1.568 \times 10^{4} \)
B . \( 1.568 \times 10^{3} \)
c. 15.68
D. \( 3.136 \times 10^{4} \)


In vacuum, to travel distance \( d \), light
takes time \( t \) and in medium to travel \( 5 d \)
it takes time \( T \). The critical angle of the
medium is :
A \( \cdot \sin ^{-1}\left(\frac{5 T}{t}\right) \)
в. \( \sin ^{-1}\left(\frac{5 t}{3 T}\right) \)
\( ^{\mathbf{c}} \cdot \sin ^{-1}\left(\frac{5 t}{T}\right) \)
D. \( \sin ^{-1}\left(\frac{3 t}{5 T}\right) \)


The number of lines of symmetry in a picture of Taj Mahal is - -
A.
B. 2
\( c \cdot 0 \)
\( D \)


The water vapour which enters into air to form clouds in the sky are obtained by which of the following process?
A. Condensation
B. Evaporation
c. Precipitation
D. None of the above


The reaction of \( P_{4} \) with \( X \) leads
selectively to \( \boldsymbol{P}_{4} \boldsymbol{O}_{6} . \) The \( \boldsymbol{X} \) is:
\( A \cdot \operatorname{dry} O_{2} \)
B. a mixture of \( O_{2} \) and \( N_{2} \)
\( \mathrm{c} \cdot \) moist \( O_{2} \)
D. \( O_{2} \) in presence of aq. \( N a O H \)


\( \boldsymbol{C} \boldsymbol{a}_{2} \boldsymbol{B}_{6} \boldsymbol{O}_{11}+\boldsymbol{2} \boldsymbol{N} \boldsymbol{a}_{2} \boldsymbol{C O}_{3} \rightarrow \boldsymbol{X}+ \)
\( 2 C a C O_{3}+2 N a_{2} B O_{2} . \) The compound \( x \)
in the above reaction is :
A. \( N a_{2} B_{4} O_{7} \)
в. \( H B O_{2} \)
c. \( H_{3} B O_{3} \)
D. \( H_{2} B_{4} O_{7} \)


The cost of an air cooler has increased
from Rs 2,250 to Rs 2,500 . What is the
percentage change?


10 moles of \( S O_{2} \) and 15 moles of \( O_{2} \) were
passed over a catalyst to produce 8 moles of \( S O_{3} \). The ratio of moles of \( S O_{2} \)
and \( S O_{3} \) in mixture is:
A \( \cdot \frac{5}{4} \)
B. \( \frac{1}{4} \)
\( c \cdot \frac{1}{2} \)
D. \( \frac{3}{4} \)


Name the axis on which following point
lie
(-5,-8)


Find the equation of line joining (1,2) and (3,6) using determinants.


Match the following
a) p-type
1) Pure semiconductor semiconductor
b) Intrinsic
2) Doped with impurity semiconductor
c) Extrinsic
3) majority carriers are semiconductor \( \quad \) electrons
d) \( n \) -type
4) majority carriers are semiconductor holes
\( A \cdot a-3, b-2, c-4, d-1 \)
B. \( a-1, b-2, c-4, d-3 \)
C. \( a-4, b-1, c-2, d-3 \)
D. \( a-2, b-1, c-4, d-3 \)


When an arrow is released from a bow,
potential energy changes into kinetic energy.
A. True
B. False
c. Ambiguous
D. Data insufficient


When \( \mathbf{U}^{238} \) nucleus originally at rest.
decays by emitting an alpha particle
having a speed 'u', the recoil speed of the residual nucleus is
A \( \cdot \frac{4 \mathrm{u}}{238} \)
в. \( -\frac{4 \mathrm{u}}{234} \)
c. \( \frac{4 \mathrm{u}}{234} \)
D. \( -\frac{4 \mathrm{u}}{238} \)


Q Type your question.
orbiting some star. The planet is closer to the star as it moves from point 1 to
point 2 than it is when it moves from
point 3 to point 4 in its orbit. The dotted
ine shows the orbital path.
If the time it takes the planet to get from point 1 to point 2 is equal to the time it takes the planet to get from point 3 to point 4 then which of the following statements is true, according to Kepler's laws of planetary motion?
A. The average speed as the planet travels from 1 to 2 is the same as when it travels from 3 to 4
B. Area 1 in the diagram is equal to Area 2
C. Area 1 in the diagram is smaller than Area 2
D. The planet moves further from 3 to 4 from 1 to 2
E. The average speed as the planet moves from 3 to 4 is greater than when the planet moves from 1 to


The bryophyte which can absorb water upto 18 times of its weight?
A. Anthoceros
B. Sphagnum
c. Davsonia
D. Marchantia


In isomeric alkyl halides:
A. the branch chain isomer have relatively high boiling point as compared to its straight chain isomer
B. the branch chain isomer have relatively low boiling point as compared to its straight chain isomer
C. the branch chain isomer boiling point equal to its straight chain isomer
D. none of these


topp
Q туре your question
ranges, of \( 0-2 V, 0-10 V \) and 0
\( 20 V \). The appropriate circuit to do so is
A \( \cdot R_{1}=1900 \Omega \)
\( R_{2}=9900 \Omega \)
\( R_{3}=19900 \Omega \)
B . \( R_{1}=2000 \Omega \)
\( R_{2}=8000 \Omega \)
\( R_{3}=10000 \Omega \)
c. \( R_{1}=19900 \Omega \)
\( R_{2}=9900 \Omega \)
\( R_{3}=1900 \Omega \)
D. \( R_{1}=1900 \Omega \)
\( R_{2}=8000 \Omega \)
\( R_{3}=10000 \Omega \)


For the given pair of \( S_{N} 2 \) reaction, the
first product occurs with larger rate
constant.
вि OH кон.


At inductance \( 1 H \) is connected in
series with an \( A C \) source of \( 220 \mathrm{V} \) and
\( \mathbf{5 0} \boldsymbol{H} z . \) The inductive resistance (in
ohm) is :
A \( .2 \pi \)
в. \( 50 \pi \)
\( c .100 \pi \)
D. \( 1000 \pi \)


If \( \boldsymbol{y}=\boldsymbol{s} \boldsymbol{e} \boldsymbol{c}^{-1}\left[\frac{\boldsymbol{x}+\mathbf{1}}{\boldsymbol{x}-\mathbf{1}}\right]+\boldsymbol{s i n}^{-1}\left[\frac{\boldsymbol{x}-\mathbf{1}}{\boldsymbol{x}+\mathbf{1}}\right] \)
\( z=\operatorname{cosec}^{-1}\left[\frac{2 x+3}{3 x+2}\right]+ \)
\( \cos ^{-1}\left[\frac{3 x+2}{2 x+3}\right] \) then
This question has multiple correct options
A. \( y=\pi / 2 \)
2
B. \( z=\pi / 2 \)
\( \mathbf{c} \cdot y+z=\pi \)
D. \( y+z=\pi / 2 \)


Assertion
On passing \( \boldsymbol{H} \boldsymbol{C l}(\boldsymbol{g}) \) through a
saturated solution of \( B a C l_{2}, \) a white
turbidity appears
Reason
The common ion effect is responsible for white turbidity
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


An AP consists of 37 terms. The sum of
the three middle most terms is 225 and
the sum of the last three is \( 429 . \) Find
the AP.


Beryllium forms hydrate peroxide,
\( B e O_{2} \cdot H_{2} O \)
A. True
B. False


\( \boldsymbol{S} \boldsymbol{R}=? \)
\( 4 . \overline{P Q} \)
3. \( \overline{P Q} \)
: Q
\( . \overline{S R} \)


A mercury thermometer reads \( 80^{\circ} \mathrm{C} \)
when the mercury is at \( 5.2 c m \) mark and
\( 60^{\circ} \mathrm{C} \) when the mercury is at \( 3.9 \mathrm{cm} \)
mark. The temperature (in \( ^{o} C \) ) when the
mercury level is at \( 2.6 \mathrm{cm} \) mark is \( 4 \times \)
\( \mathbf{1 0}^{x} \). Find the value of \( \boldsymbol{x} \)


A ray of light incident on a \( 60^{\circ} \) angled prism of refractive index \( \sqrt{2} \) suffers
minimum deviation. The angle of incidence is :
A \( \cdot 70^{\circ} \)
B . \( 0^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 60^{\circ} \)


Let \( \boldsymbol{f}(\boldsymbol{x})=[\boldsymbol{x}] \) and \( \boldsymbol{g}(\boldsymbol{x})= \)
\( \left\{\begin{array}{cc}\mathbf{0}, & \boldsymbol{x} \in \boldsymbol{Z} \\ \boldsymbol{x}^{2}, & \boldsymbol{x} \in \boldsymbol{R}-\boldsymbol{Z}\end{array} . \) Then which of the \right.
following is not true ([.] represents the greatest integer function)? This question has multiple correct options
A \( \cdot \lim _{x \rightarrow 1} g(x) \) exists but \( g(x) \) is not continuous at \( x=1 \)
B. \( \lim _{x \rightarrow 1} f(x) \) does not exist and \( f(x) \) is not continuous at
\[
x=1
\]
c. \( g o f \) is a continuous function.
D. gof is a discontinuous function.


Tensile strength is maximum in
A . Nylon
B. Bakelite
c. None of these
D. All of the above


Which two angles are supplementary?
A. \( \angle C O F \) and \( \angle A O C \)
B. \( \angle C O F \) and \( \angle C O E \)
\( \mathrm{c} . \angle \mathrm{COF} \) and \( \angle E O D \)
D. \( \angle C O F \) and \( \angle A O E \)


Find \( ^{\prime} x^{\prime} \) if
\( \left|\begin{array}{ccc}\mathbf{4} & \boldsymbol{x} & \mathbf{6} \\ \mathbf{2} & \mathbf{3} & \mathbf{4} \\ \mathbf{1} & \mathbf{1} & \mathbf{1}\end{array}\right|=\mathbf{1 0} \)


Using the data given below, establish that the vaporization of \( C C l_{4}(l) \) at 298K to produce \( C C l_{4}(g) \) at 1 atm
pressure does not occur spontaneously. Given
\( \boldsymbol{C C l}_{4}(\boldsymbol{l}, \mathbf{1 a t m}) \rightarrow \boldsymbol{C C l}_{4}(\boldsymbol{g}, \mathbf{1 a t m}) \)
\( \boldsymbol{\Delta} \boldsymbol{S}^{o}=\boldsymbol{9} \boldsymbol{4} . \boldsymbol{9} \boldsymbol{8} \boldsymbol{J} \boldsymbol{K}^{-1} \boldsymbol{m} \boldsymbol{o l}^{-1} \)
\( \boldsymbol{\Delta} \boldsymbol{H}_{f}^{o}\left(\boldsymbol{C} \boldsymbol{C l}_{4}, \boldsymbol{g}\right)=\mathbf{1 0 6 . 7} \boldsymbol{k} \boldsymbol{J} \boldsymbol{m o l}^{-1} \boldsymbol{z} \)
\( \Delta H_{f}^{o}\left(C C l_{4}, l\right)=139.3 k J m o l^{-1} \)
A \( \cdot \Delta G^{o}=4.3 k J / m o l \)
в. \( \Delta G^{o}=-4.3 k J / \) mol
c. \( \Delta G^{o}=2.15 k J / \) mol
D. None of these


An object is vibrating at 50 hertz. What is its time period?
A . \( 0.02 \mathrm{s} \)
B. 0.2
\( c \cdot 2 s \)
D. 20.0


A merry-go-round is moving with a constant speed of \( 12 m s^{-1}, \) The girl
sitting on it is
A. At rest
B. Moving with uniform velocity
c. In accelerated motion
D. Moving with no acceleration


Which of the following energy source is most costly?
A. Thermal Energy
B. Hydel Energy
c. Solar Energy
D. Fossil Energy


A flowering plant is planted in an earthen pot and irrigated. Urea is added
in high amounts to make the plant grow faster, but after some time the plant died. This may be due to
A. Exosmosis
B. Endosmosis
c. water logging
D. Suffocation


The first term of a geometric sequence
is 10 and the fourth term is \( 160 . \) What is
the common ratio?
A . 1
B . 2
\( c .3 \)
D. 4


Homologous chromosomes segregate during
A. Fertilization
B. Meiosis I
c. Meiosis II
D. Mitosis


are useful in providing
information for identification of names
of species found in an area.
A. Flora
B. Manuals
c. Monographs
D. catalogues


The diagram shows a resistor connected to a cell of e.m.f. \( 2 V \) How
much heat energy is produced in the resistor in six seconds?
A \( .2 .5 . \)
в. 4.8 .
\( c \cdot 10 J \)
D. \( 60 . \)


If \( \boldsymbol{z}_{1}=\boldsymbol{x}_{1}+\boldsymbol{i} \boldsymbol{y}_{1}, \quad \boldsymbol{z}_{2}=\boldsymbol{x}_{2}+\boldsymbol{i} \boldsymbol{y}_{2}, \) then
\( \mathbf{2} i\left|\begin{array}{ll}\boldsymbol{x}_{2} & \boldsymbol{y}_{2} \\ \boldsymbol{x}_{1} & \boldsymbol{y}_{1}\end{array}\right| \) equals
A \( \cdot \overline{z_{1}} z_{2}-z_{1} \overline{z_{2}} \)
B . \( z_{1} \overline{z_{2}}-z_{2} \overline{z_{1}} \)
C . \( \left|z_{1}\right|^{2}-\left|z_{2}\right|^{2} \)
D . \( \left|z_{1}\right|^{2}-\left|z_{1}-z_{2}\right|^{2} \)


Two electrical bulbs have tungsten
filament of same length. If one of them
gives 60 watts and other 100 watts, then
A. 100 watts bulb has thicker filament
B. 60 watt bulb has thicker filament
c. Both filaments are of same thickness
D. It is impossible to get different wattage unless lengths are different


A rocket is launched to travel vertically
upward with a constant velocity of 20 \( \mathrm{m} / \mathrm{s} . \) After travelling for 35 seconds, the rocket develops a snag and its fuel supply is cut off. The rocket then travels like a free body. The height achieved by
it is:


Which of the carbon atoms present in
the molecule given below are asymmetric?
\( A \cdot(i),(\text { ii) }, \) (iii), (iv)
B. (ii), (iii)
\( c \cdot(i),(i v) \)
D. (i), (ii), (iii)


If \( a-b=0.9 \) and \( a b=0.36 ; \) find \( a+b \)
\( A \ldots \pm 2 \)
в. ±1.5
\( c .\pm 3.5 \)
D. ±14


Illustrate water cycle with diagram.


Conversion of given reaction to the
given product will take place in how
many step?


What will be the molar conductance ' \( \boldsymbol{\Lambda} \);
if resistivity is \( x \) for \( 0.1 \mathrm{N} \mathrm{H}_{2} \mathrm{SO}_{4} ? \)
A \( . \quad \Lambda=\frac{x \times 1000}{0.1} \)
в. \( \Lambda=\frac{2 \times 1000}{x \times 0.1} \)
c. \( _{\Lambda}=\frac{x \times 1000}{0.5} \)
D. \( _{\Lambda}=\frac{0.5}{1000 x} \)


The velocity-time graph of a body is
shown in the given figure. It implies
that, over the section B the body
experiences
A. zero force
B. force towards motion
c. force opposing motion
D. only force of gravity


Consider the following reaction:
\( \boldsymbol{C l}_{2}+\boldsymbol{S}^{2-} \longrightarrow \boldsymbol{S}+\boldsymbol{C l}^{-} \)
The above reaction is a
disproportionation reaction. Is it True or False? Explain why?


The smallest eubacterium Dialister
pneumosintes \( (0.15-0.3 \mu) \) occurs in
A. Colon of man
B. Fat body of cockroach
c. Nasal chamber of man
D. Soil


Assertion
Points
\( \boldsymbol{A}(\boldsymbol{4}, \boldsymbol{0}, \boldsymbol{4}), \boldsymbol{B}(\boldsymbol{1}, \boldsymbol{2}, \boldsymbol{3}), \boldsymbol{C}(-\boldsymbol{2}, \boldsymbol{4}, \boldsymbol{2}) \) are
collinear
Reason
Three points \( A, B, C \) are collinear if
\( \boldsymbol{A B}+\boldsymbol{B C}=\boldsymbol{A C} \) and \( \boldsymbol{A B}, \boldsymbol{B C}<\boldsymbol{A C} \)
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


Let \( A, B \) and \( C \) are unit vectors
suppose \( A . B=A . C=0 \) and angle between \( B \) and \( C \) is \( \frac{\pi}{6} \) then
A \( . A=\pm 2(B \times C) \)
B. \( A=\pm \sqrt{2}(B \times C) \)
c. \( A=\pm 3(B \times C) \)
D. \( A=\pm \sqrt{3}(B \times C) \)


There are a large number of cells available, each marked \( (6 V, 0.5 \Omega) \) to be used to supply current to a device of resistance \( 0.75 \Omega, \) requiring \( 24 A \) current. How should the cells be
arranged, so that power is transmitted to the load using minimum number of
cells?
A. Six rows, each containing four cells
B. Four rows, each containing six cells
c. Four rows, each containing four cells
D. Six rows, each containing Six cells


For the reaction; \( \mathbf{4} \boldsymbol{N} \boldsymbol{H}_{\boldsymbol{3}(\boldsymbol{g})}+\mathbf{5} \boldsymbol{O}_{\boldsymbol{2}(\boldsymbol{g})} \rightarrow \)
\( 4 N O_{(g)}+6 H_{2} O_{(g)}, \) the rate of reaction
in terms of disappearance of \( N H_{3} \) is \( -\frac{\boldsymbol{d}\left[\boldsymbol{N} \boldsymbol{H}_{3}\right]}{\boldsymbol{d} t}, \) then write the rate
expression in terms of concentration of
\( O_{2}, N O \) and \( H_{2} O \)


Two cards are drawn successively with replacement from a well-shuffled pack
of 52 cards. The probability of drawing
two aces is.
A \( \cdot \frac{1}{13} \)
В \( \cdot \frac{1}{13} \times \frac{1}{17} \)
c. \( \frac{1}{52} \times \frac{1}{51} \)
D. \( \frac{1}{13} \times \frac{1}{13} \)


The graphs below show that position versus time for three different cars: 1,2 and \( 3 . \) Rank these cars according to the
magnitudes of their velocities, greatest
first
A. 1,2,3
B. 3,2,1
c. 2,1,3
D. 2,3,1
E. All tie


Why are wheels of cars, buses etc. are made circular?
A. to minimize friction
B. too add more electrostatic force
c. no particular reason
D. circle looks better


Two tailors \( X \) and \( Y \) are paid a total of Rs 550 per week by their employer. If \( X \) is paid 120 percent of the sum paid to \( Y \) how much is Y paid per week?
A. Rs. 200
B. Rs. 250
c. Rs. 300
D. None of these


An acid has a pH below:
A. 7
B. 8
\( c \cdot 9 \)
D. 10


For a paramagnetic material, the dependence of the magnetic susceptibility \( \chi \) on the absolute
temperature T is given by
A \( \cdot x \alpha T \)
B. \( \chi \alpha \) constant \( \times T \)
c. \( \chi \alpha \frac{1}{T} \)
D. \( x= \) constant


In cellulose, \( \beta \) -D-Glucose units are
joined by:
A \( \cdot \alpha-(1,4) \) glycosidic linkage
B. peptide linkage
c. \( \beta \) -(1,4) glycosidic linkage
D. \( \beta \) -(1,6) glycosidic linkage


The hardest constituent of the tooth is
A. Enamel
B. Dentine
c. Bone
D. Pulp


The hybridization associated with the central atom of a molecule in which all
the bond angles are \( 120^{\circ} \) is
\( \mathbf{A} \cdot s p \)
в. \( S p^{2} \)
\( c \cdot s p^{3} \)
D. \( s p^{3} d \)
E \( \cdot s p^{3} d^{2} \)


The gas not absorbed by coconut charcoal is :
A . не
B. Ne
c. Ar
D. kr


Determine whether following statements is true (T) or false (F) and
write the code in sequence.
1. Dialysis is a method of separation of
copper sulphate crystals from copper sulphate solution.
2. Synergic bonding means self strengthening bond
3. Chromate ion forms a octahedral
structure with all the four \( C r-O \) bond
lengths being equal.
4. Ligand field theory represents an application of molecular orbital theory to transition metal complexes.
A . FTFT
в. \( T F T F \)
c. \( F F T T \)
D. \( T T F F \)


For all positive value of \( x \) and \( y, \) the value of \( \frac{\left(1+x+x^{2}\right)\left(1+y+y^{2}\right)}{x y} \) is
\( A . \leq 9 \)
в. \( <9 \)
\( c \cdot \geq 9 \)
\( D \cdot>9 \)


The K.E of the photoelectons is E when the incident wave length is \( \frac{\lambda}{2} . \) The K.E becomes 2E when the incident wave length is \( \frac{\lambda}{3} . \) The work function of the metal is
A \( \cdot \frac{h c}{\lambda} \)
B. \( \frac{2 h c}{\lambda} \)
\( c \cdot \frac{3 h c}{\lambda} \)
D. \( \frac{h c}{3 \lambda} \)


Which of the following shows the Tyndal effect?
(I) Common salt
(ii) milk
(iii) Copper sulphate solution
(iv) Starch solution
A. (i) and (ii)
B. (ii) and (iv)
c. (iii) and (iv)
D. (ii) and (iii)


Which of the following could be used in purification of sewage?
A. Fungi
B. Mycoplasma
c. Unicellular green algae
D. All plants


Bleaching powder slowly decomposes to
form:
A \( \cdot C a C l_{2}+C a\left(C l O_{3}\right)_{2} \)
в. \( C a O+C l_{2} \)
c. \( C a C l_{2}+C a(O C l)_{2} \)
D. \( C a C O_{3}+C l_{2} \)


Ductless glands are also known as
A. Salivary glands
B. Endocrine glands
c. Exocrine glands
D. Both A and B


The hydride ion \( H^{-} \) is stronger base
than its hydroxide ion \( O H^{-} . \) Which of the following reaction will occur if sodium hydride is dissolved in water?
A \( \cdot H_{(a q)}^{-}+H_{2} O \rightarrow H_{3} O^{+} \)
B. \( H_{(a q)}^{-}+H_{2} O \rightarrow O H^{-}+H_{2} \)
c. \( H^{-}+H_{2} O \rightarrow H_{2}+O_{2} \)
D. \( H^{-}+H_{2} O \rightarrow \) No reaction


Arrange in the descending order of the values:
A: If (9,12) is one end of a focal chord of
the parabola \( y^{2}=16 x \) then the slope of
it is
B: The parabola \( x^{2}=p y \) passes
through \( (12,16), \) the focal distance of the point is
C: If the parabola \( y^{2}=k x \) passes
through (9,6) then the value of \( k \) is
D: The Ordinate of the point on the
parabola \( \boldsymbol{y}^{2}=\mathbf{3 6 x} \) whose ordinate is
three times its abscissa is
Write the value of the above statements
in the descending order
A. \( \mathrm{B}, \mathrm{D}, \mathrm{C}, \mathrm{A} \)
B. \( \mathrm{B}, \mathrm{D}, \mathrm{A}, \mathrm{C} \)
c. \( D, B, C, A \)
D. A,B,C,D


Find the charge in steady state of the capacitor.
\( A \cdot 10 \) nC
B. 20 nC
\( c .30 \mathrm{nc} \)
D. 40 nc
E. None of the above


In a reaction between \( A \) and \( B \), the
initial rate of reaction \( \left(r_{0}\right) \) was measured for different initial
concentrations of \( A \) and \( B \) as given
below:
\( \begin{array}{lll}A / m o l L^{-1} & 0.20 & 0.20 \\ B / m o l L^{-1} & 0.30 & 0.10\end{array} \) \( r_{0} / m o l L^{-1} s^{-1} \quad \begin{array}{ll}5.07 \times & 5.07 \times \\ 10^{-5} & 10^{-5}\end{array} \quad \begin{array}{l}1.43 \times \\ 10^{-4}\end{array} \)
What is the order of the reaction with
respect to \( A \) and \( B ? \)


Angular width of central maxima of a diffraction pattern of a single slit does not depend upon
A. Distance between slit and source
B. Wavelength of the light used
c. width of slitt
D. Frequency of light used


Evaluate the determinants \( \left|\begin{array}{cc}2 & 4 \\ -5 & -1\end{array}\right| \)


Let \( \bar{a}, \bar{b}, \bar{c} \) be non coplanar vectors. The vectors \( 3 \bar{a}-2 \bar{b}-4 \bar{c},-\bar{a}+2 \bar{c},-2 \bar{a}+ \)
\( \bar{b}+3 \bar{c} \) are
A. Linearly dependent
B. Linearly independent
c. Collinear
D. Non collinear


The potential value of standard hydrogen electrode is


If a continuous function \( f \) satisfies \( \int_{0}^{f(x)} t^{2} d t=x^{2}(1+x) \) for all \( x \geq 0 \)
then \( f(2) \) is equal to
A . 12
B. \( \sqrt[3]{36} \)
\( c .3 \)
D. \( \sqrt[3]{42} \)


Which of the following cycloalkane gives open chain compound when it reacts with bromine?
A. Cyclopropane
B. cyclopentane
c. cyclohexane
D. cyclo-octane


Mark the following statement is true or
false.

A ball thrown vertically up takes more
time to go up than to come down.


For a material \( \boldsymbol{Y}=\mathbf{6 . 6} \times \mathbf{1 0}^{\mathbf{1 0}} \boldsymbol{N} / \boldsymbol{m}^{2} \)
and bulk modulus \( K 11 \times 10^{10} N / m^{2} \) then its Poisson's ratio is:
A . 0.8
B. 0.35
\( c .0 .7 \)
D. 0.4


State True or False:
On subtracting \( -3 x^{3}+4 x^{2}-5 x+6 \)
from \( 3 x^{3}-4 x^{2}+5 x-6, \) the answer is
\( 6 x^{3}-8 x^{2}+10 x-12 \)
A. True
B. False


At constant temperature, if the pressure of a gas of volume \( \mathrm{V} \) in a container is doubled then the change in its volume is
\( A \cdot v \)
в. \( \frac{V}{2} \)
c. \( \frac{V}{4} \)
D. 2v


A solution has \( 0.05 M M g^{2+} \) and
\( 0.05 M N H_{3} . \) The concentration of
\( N H_{4} C l \) required to prevent the
formation of \( M g(O H)_{2} \) in solution is:
\( \boldsymbol{K}_{s p} \) of \( M \boldsymbol{g}(\boldsymbol{O} \boldsymbol{H})_{2}=\boldsymbol{9} \cdot \boldsymbol{0} \times 10^{-12} \) and
\( \boldsymbol{K}_{\boldsymbol{b}} \) of \( \boldsymbol{N} \boldsymbol{H}_{3}=\mathbf{1} . \boldsymbol{8} \times \mathbf{1 0}^{-\mathbf{5}} \)
\( \mathbf{A} \cdot 0.062 M \)
в. 0.067 М
\( \mathrm{c} .0 .075 \mathrm{M} \)
D. \( 0.070 M \)


Suppose an integer from 1 through 100 is chosen at random, find the probability that the integer is a multiple of 2 or a multiple of 9


State whether true or false:
When a body is at a depth 'd' from the earth surface its distance from the
center of the earth is \( \mathrm{R} \) -d \( (\mathrm{R}= \) Radius of
the earth)
A. True
B. False


If \( A \) and \( B \) are two mutually exclusive
events, then?
\( \mathbf{A} \cdot P(A) \leq P\left(B^{\prime}\right) \)
в. \( P(A) \leq P(B) \)
\( \mathbf{c} \cdot P(A) \geq P\left(B^{\prime}\right) \)
D. None of these


Which factor when increased will cause
an uncatalyzed reaction to proceed more quickly?
A. Exothermic
B. Particle Size
c. Endothermic
D. catalyst


The stress along the length of a rod(with rectangular cross section) is \( 1 \% \) of the Young's modulus of its material. What is the approximate percentage of change of its volume? (Poisson's ratio of
the material of the rod is 0.3 ).
A . \( 3 \% \)
B. 1\%
\( c .0 .7 \% \)
D. \( 0.4 \% \)


Explain the following giving example Saturated solution, Pure
substance, colliod.


Electromagnetic waves that include light belong to
A. light spectrum.
B. electronic spectrum.
c. electromagnet group.
D. electromagnetic spectrum.


Which one of the following statements
is not correct in case of a
semiconductor?
A. Temperature coefficient of resistance is negative
B. Doping increases conductivity
c. At absolute zero temperature, it behaves like an conductor
D. Resistivity is in between that of a conductor and insulator


Two blocks \( A \) and \( B \) of masses \( m \) and
\( 2 \mathrm{m} \) respectively placed on a smooth floor are connected by a spring. A third body \( C \) of mass \( m \) moves with velocity
\( \boldsymbol{v}_{0} \) along the line joining \( \mathbf{A} \) and \( \mathbf{B} \) and collides elastically with A. At a certain instant of time after collision it is found
that the instantaneous velocities of \( A \)
and \( \mathrm{B} \) are same then :
A. the common velocity of A and B at time to is \( v / 3 \).
в.
\[
\text { the spring constant is } \mathrm{k}=\frac{3 m v_{0}^{2}}{2 x_{0}^{2}}
\]
\( c \)
\[
\text { the spring constant is } \mathrm{k}=\frac{2 m v_{0}^{2}}{3 x_{0}^{2}}
\]
D. none of these


When a galvanometer is shunted with a
\( 4 \Omega \) resistance, the deflection is reduced
to one - fifth. If the galvanometer is
further shunted with a \( 2 \Omega \) wire,
determine current in galvanometer now
if initially current in galvanometer is \( I_{0} \) (given main current remain same).
A \( \cdot I_{0} / 13 \)
the
в. \( I_{0} / 5 \)
c. \( I_{0} / 8 \)
D. \( 5 I_{0} / 13 \)


Find the term of expansion of \( \left(x+\frac{1}{x}\right)^{n} \) which does not contain \( x \)


Which of the following groups is formed only of the hermaphrodite organisms?
A. Earthworm, tapeworm, housefly, frogg
B. Earthworm, tapeworm, sea horse, housefly
c. Earthworm, leech, sponge, roundworm
D. Earthworm, tapeworm, leech, sponge


A person has a tuning fork that sounds with a frequency of \( 250 H z . \) The person strikes the fork and plays a white key that sounds with a frequency of \( 220 H z \) Calculate the beat frequency that the piano person hears?
A. \( 0 H z \)
\( z \)
B. \( 0.8 \mathrm{Hz} \)
c. \( 1.25 H z \)
D. \( 30 H z \)
E . \( 450 \mathrm{Hz} \)


Suppose you hear music being played from a trumpet that is across the room from you. Compressions and rarefaction
from the sound wave reach your car, and you interpret these vibrations as
sound. Were the air particles that are vibrating near your ear carried across the room by the sound wave? How do you know?


If the mean deviation about mean
\( \mathbf{1}, \mathbf{1}+\boldsymbol{d}, \mathbf{1}+\mathbf{2} \boldsymbol{d}, \dots \mathbf{1}+\mathbf{1 0 0} \boldsymbol{d} \) from their
mean is \( 255, \) then the \( d \) is equal to
A . 10
B. 20
c. \( 10 . \)
D. 20.2


Bombykol is a pheromone secreted by the body of
A. wasp
B. House fly
c. spider
D. silk moth


In a compound, \( C, H \) and \( N \) atoms are
present in ratio of 9: 1: 3.5 by weight.
Molecular weight of compound is 108 Molecular formula of compound is:
A \( \cdot C_{2} H_{6} N_{2} \)
в. \( C_{2} H_{6} N \)
c. \( C_{6} H_{8} N_{2} \)
D. \( C_{9} H_{12} N_{3} \)


Expand the binomial \( \left(\frac{2 x}{3}+\frac{3 y}{2}\right)^{20} u p \) to four terms.


How many isomeric amines with the
molecular formula \( C_{7} H_{9} N \) contain a
benzene ring?
A. Two
B. Three
c. Four
D. Five


\( \mathbf{1} . \mathbf{3}+\mathbf{3 . 5}+\mathbf{5 . 7}+\ldots+(\mathbf{2 n}-\mathbf{1})(\mathbf{2 n}+ \)
1) \( = \)
A \( \frac{n\left(4 n^{2}+6 n-1\right)}{3} \)
в. \( \frac{n\left(3 n^{2}+5 n+1\right)}{3} \)
\( \frac{n\left(5 n^{2}+7 n-1\right)}{3} \)
D. \( \frac{n\left(7 n^{2}-5 n+1\right)}{3} \)


If \( x=a(\cos \theta+\sin \theta) \) and \( y= \)
\( a(\sin \theta-\cos \theta), \) then find \( \frac{d^{2} y}{d x^{2}} \)


A solid body of constant heat capacity \( 1 J /^{\circ} C \) is being heated by keeping it in contact with reservoirs in two ways:
(i) Sequentially keeping in contact with 2 reservoirs such that each reservoir
supplies same amount of heat
(ii) Sequentially keeping in contact with 8 reservoirs such that each
reservoir supplies same amount of heat
In both the cases body is brought from
initial temperature of \( 100^{\circ} \mathrm{C} \) to a final
temperature of \( 200^{\circ} \mathrm{C} \). Entropy change
of the body in two cases respectively is :
A. \( \ln 2,4 \ln 2 \)
B. \( \ln 2, \ln 2 \)
c. \( \ln 2,2 \ln 2 \)
D. \( 2 \ln 2,8 \ln 2 \)


Maximum bond angle is present in:
\( \mathbf{A} \cdot B B r_{3} \)
в. \( B C l_{3} \)
\( c . B F_{3} \)
D. none of these


If the plate is rotating alone and the
coin is gently placed on the rotating
plate, the frictional force on the coin is :
\( \mathbf{A} \cdot \mathbf{m g} \)
B.
\( c \cdot \frac{m g}{2} \)
\( D \)


Which of the following molecules has a trigonal pyramidal geometry?
A \( . B H_{3} \)
в. \( H_{2} \) 0
c. \( C H_{4} \)
D. \( N H_{3} \)
E . \( A l C l_{3} \)


\( P C l_{5} \) dissociates according to the
reaction \( \boldsymbol{P} \boldsymbol{C l}_{5} \rightleftharpoons \boldsymbol{P} \boldsymbol{C l}_{3}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \cdot \mathbf{A t} \)
\( \mathbf{5} \mathbf{2 3} \boldsymbol{K}, \boldsymbol{K}_{\boldsymbol{p}}=\mathbf{1 . 7 8} \boldsymbol{a t m} . \) Find the
density of the equilibrium mixture at a total pressure of 1 atm.
A. 2.96 g/ml
B. 4.51 \( g / m \) ।
c. 6.73 g/ml
D. 3.44 g/ml


Simplify: \( \sin . \cot ^{-1} \cot x \)


The graph (2) tells us that:
A. The reaction is irreversible
B. The reaction is reversible
C. The reaction is exothermic
D. The reaction is endothermic


Solve :
\( \int \tan ^{2}(2 x-3) d x \)


What happens to the speed of light
when it undergoes refraction in a
medium ? Hence define absolute
refractive index of a medium.


Using differentials, find the sum of digits approximate value of the following up to 3 places of decimal. \( \sqrt{49.5} \)


In an equilateral triangle of side \( 24 \mathrm{cm} \)
a circle is inscribed touching its sides. Find the area of the remaining portion
of the triangle.


What is the angle between vector \( \vec{A}= \) \( \hat{\mathbf{i}}+\hat{\mathbf{j}}+\sqrt{\mathbf{2}} \hat{\boldsymbol{k}} \) and the z-axis :
A \( \cdot 0^{\circ} \)
B . 45
\( c \cdot 60 \)
D. \( 90^{\circ} \)


Approximate diameter of Victoria regia leaf is
\( A \cdot 1 m \)
в. 1.3
\( c \cdot 4 m \)
D. 3m


Which elements are used in Atomic
Reactors to control the speed of
neturons?
A. Boron and Cadmium
B. Cadmium and Aluminiuminm
c. Boron and Iron
D. Sodium and Potassium


The third term of a geometric progression is \( 4 . \) The product of the first five terms is
\( A \cdot 4^{3} \)
B . \( 4^{4} \)
\( c \cdot 4^{5} \)
D. \( 4^{\circ} \)


The correct representation of 4
hydroxy- 2 -methylpent-2-en-1-al is:
\( \mathbf{A} \cdot C H_{3}-C H-C H=C-C H O \)
\( O_{H} \)
\( \begin{array}{rl}\mathbf{B} \cdot C H_{3}-C H-C H= & C-C H O \\ C H_{3} & O_{H}\end{array} \)
\( c \)
\( C H \) :
3.
\( C H_{3}-C_{C H_{3}}-C H=C_{C H_{3}}-C H O \)
\( \mathbf{D} \cdot C H_{3}-C H-C H_{2}-C H-C H O \)
\( O_{H}^{\mid} C H_{3} \)


Define main focus of a convex lens.


What amount of work is done in
increasing the length of a wire through unity?
A \( \cdot \frac{Y L}{2 A} \)
в. \( \frac{Y L^{2}}{2 A} \)
c. \( \frac{Y A}{2 L} \)
D. \( \frac{Y L}{A} \)


Assertion
Hydrostatic pressure is not a vector
quantity.
Reason
Pressure is force divided by area, and
force is a vector quantity.
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 acid which contains both \( -O H \) and
\( - \) COOH groups is:
A. phthalic acid
B. adipic acid
c. glutaric acid
D. salicylic acid


Which antibiotic inhibits interaction
between tRNA and mRNA during bacterial protein synthesis?
A. Neomycin
B. Streptomycin
c. Tetracycline
D. Erythromycin


Assertion
When an automobile while going too
fast around a curve overturns, its inner
wheels leave the ground first.
Reason

For a safe turn the velocity of automobile should be less than the
value of safe limit velocity.
A. If both Assertion and Reason are correct and Reason the correct explanation of the Assertion
B. If both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion
c. If Assertion is true but Reason is false
D. If Assertion is false but Reason is true


Atomic mass of which of the following element is \( 24 ? \)
A. Magnesium
B. Sodium
c. chlorine
D. Sulphur


If \( \boldsymbol{x}=\sin ^{-1}(\sin 10) \) and \( \boldsymbol{y}= \)
\( \cos ^{-1}(\cos 10), \) then \( y-x \) is equal to:
\( A \cdot \pi \)
в. \( 7 \pi \)
\( c \cdot 0 \)
D. 10


Suppose your writing desk is tilted a little, a book kept on it starts sliding down. The direction of frictional force
acting on it is
A. upwards
B. downwards
c. no direction
D. cant say


The statement - 'Heat cannot flow from
colder body to hotter body' is known as
A. 1 st law of Thermodynamics
B. Zeroth law
C. 2 nd law of Thermodynamics
D. Law of conservation of energy


If we sit near a fire,we feel warm.Give
reason


An artificial satellite is moving in a circular orbit around the earth with a
speed equal to half the magnitude of escape velocity from the earth's surface Total energy is always constant at any orbit. (Radius of the earth is \( 6400 k m \) )
The height of the satellite above the
Earth surface
A. \( 6400 k m \)
в. \( 3200 k m \)
\( c .9600 k m \)
D. \( 4800 k m \)


Study of interaction between living organisms and environment is called
A. Ecosystem
B. Phytogeography
c. Psychology
D. Mycology


an organic liquid (A), containing C,H
and 0 with boiling point \( 78^{\circ} \mathrm{C} \) and possessing a rather pleasant odour or heating with concenterated \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
gives a gaseous product (B) with the
empirical formula \( C H_{2} . \) B decolourises
bromine water as well as alkaline
\( K M n O_{4} \) solution and takes up one
mole of \( \boldsymbol{H}_{2}(\text { per mole of } \mathrm{B} \) ) in the presence of finely divided nickle at high
temperature. A and B are:
\( \mathbf{A} \cdot C_{2} H_{5} O H, C_{2} H_{2} \)
в. \( C H_{3} O H, C_{2} H_{2} \)
c. \( C_{2} H_{5} \) OH \( , C_{2} H_{4} \)
D \( \cdot\left(C H_{3}\right)_{2} C H O H, C_{3} H_{6} \)


State whether true or false.
The position of the centre of gravity of the pot before filling it with water will be at its base.
A. True
B. False


The following are the data for the reaction
\[
A+B \rightarrow \text { products }
\]
\( [A] \)
\( [\mathrm{B}] \)
Initial rate
\[
\begin{array}{l}
\left(\operatorname{mol} L^{-1} s^{-1}\right) \\
\begin{array}{llll}
\text { (i) } 0.1 \mathrm{M} & \text { 0.1 } \mathrm{M} & \text { 4. } 0 \times 10^{-4}
\end{array}
\end{array}
\]
(ii) \( 0.2 \mathrm{M} \quad 0.2 \mathrm{M} \)
\[
1.6 \times 10^{-3}
\]
(iii) \( 0.5 \mathrm{M} \)
\( 0.1 \mathrm{M} \)
\[
1.0 \times 10^{-2}
\]
(iv) \( 0.5 \mathrm{M} \quad 0.5 \mathrm{M} \)
\[
1.0 \times 10^{-2}
\]
The reaction rate when the
concentration of \( A \) and \( B \) are 0.4 M and
\( 0.7 \mathrm{M} \) respectively:
A \( \cdot 6.4 \times 10^{-2} \)
B. \( 6.4 \times 10^{-3} \)
c. \( 6.4 \times 10^{-4} \)
D. \( 6.4 \times 10^{-5} \)


Let \( f(x) \) and \( g(x) \) are two functions
which are defined and differentiable for
all \( \boldsymbol{x} \geq \boldsymbol{x}_{0} . \) If \( \boldsymbol{f}\left(\boldsymbol{x}_{0}\right)=\boldsymbol{g}\left(\boldsymbol{x}_{0}\right) \) and \( \boldsymbol{f}^{\prime}(\boldsymbol{x})> \)
\( g^{\prime}(x) \) for all \( x>x_{0} \) then
A \( \cdot f(x)<g(x) \) for some \( x>x_{0} \)
B. \( f(x)=g(x) \) for some \( x>x_{0} \)
C. \( f(x)>g(x) \) only for some \( x>x_{0} \)
D. \( f(x)>g(x) \) for all \( x>x_{0} \)


If \( \frac{4}{x}<\frac{1}{3}, \) what is the possible range of
value for \( x ? \)


Choose the correct options
This question has multiple correct options
A. Sl unit of magnetic flux is henry-ampere
B. SI unit of coefficient of self-inductance is \( J / A \)
C. Sl unit of coefficient of self inductance is
\( \frac{v o l t-s e c o n d}{a m p e r e} \)
D. Sl unit of magnetic induction is weber


The energy generated by hydel projects constitutes only \( --- \) of the total energy in the country.
A . \( 50 \% \)
B. \( 23 \% \)
c. \( 60 \% \)
D. \( 90 \% \)


Find the range of: \( |\sin x|+|\cos x| \)


A car weighing 2000 kg moving with a velocity \( 36 \mathrm{km} / \mathrm{h} \) retards uniformly to rest in 10 s. Find the change in momentum in 1s.
A. 2.629
B. 500 N
c. 2000
D. o(zero)


The value of Boltzmann constant is:
(in erg \( \boldsymbol{K}^{-1} \) molecule \( ^{-1} \) )
A \( \cdot 1.38 \times 10^{-16} \)
B . \( 1.38 \times 10^{-23} \)
c. \( 8.314 \times 10^{7} \)
D. \( 6.023 \times 10^{-16} \)


Find the direction cosines of the unit
vector perpendicular to the plane \( \vec{r} \cdot(6 \hat{i}-3 \hat{j}-2 \hat{k})+1=0 \)


Assertion
On a rainy day, it is difficult to drive a
car or bus at high speed.
Reason
The value of coefficient of friction is
lowered due to wetting of the surface.
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.


Bombaxleaf is
A. Tripinnate
B. Unipinnate
C. Multifoliate
D. Quadrifoliate
E. Trifoliate


State the following statement is True or
False

The reciprocal of 0 lie on the real line.
A. True
B. False


Assertion
Any physical system when disturbed will execute simple harmonic motion.
Reason

For executing SHM, the system must have elasticity and inertia.
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


\( \sqrt{x^{2}+2 x+5} d x \) is equal to
\( \mathbf{A} \cdot(x+1) \sqrt{x^{2}+2 x+5}+\frac{1}{2} \log |x+1+\sqrt{x^{2}+2 x+5}|+C \)
В . \( (x+1) \sqrt{x^{2}+2 x+5}+2 \log |x+1+\sqrt{x^{2}+2 x+5}|+C \)
c. \( (x+1) \sqrt{x^{2}+2 x+5-2} \log |x+1+\sqrt{x^{2}+2 x+5}|+C \)
D \( \cdot \frac{1}{2}(x+1) \sqrt{x^{2}+2 x+5}+2 \log |x+1+\sqrt{x^{2}+2 x+5}|+ \)


A graph showing two sets of data simultaneously is known as
A. pictograph
B. histogram
c. pie chart
D. double bar graph


\( \boldsymbol{A}+\boldsymbol{H}_{2} \boldsymbol{O}_{2} \rightarrow \boldsymbol{B}+\boldsymbol{O}_{2} . \) In this reaction
the role of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) is:
A. oxidant
B. reductant
\( c . \) both
D. catalyst


The fractional distillation of petroleum
is shown. Which fraction is the least
volatile?
A. Bitumen
B. Diesel oi
c. Gasoline fraction
D. Refinery gas


Which of the following species have the same number of electrons in its
outermost as well as penultimate shell?
A \( \cdot C l \)
B. \( O^{2} \)
c. \( N a^{+} \)
D. \( M g^{2+} \)


Which of the following is not a disproportionation reaction?
A \( \cdot 2 P h C H O \quad A l(O E t)_{3}, P h C O O C H_{2} P h \)
c. \( N a H+H_{2} O \longrightarrow N a O H+H_{2} \)
D. All


Calculate the enthalpy changes \( (\delta H) \) of
the following reaction. \( \mathbf{2} C_{2} \boldsymbol{H}_{2(g)}+\mathbf{5} \boldsymbol{O}_{2(g)} \rightarrow \mathbf{4} \boldsymbol{C} \boldsymbol{O}_{2(g)}+ \)
\( 2 H_{2} O_{(g)} \) given average bond enthalpies of various bonds, i.e \( \boldsymbol{C}-\boldsymbol{H}, \boldsymbol{C} \equiv \)
\( \boldsymbol{C}, \boldsymbol{O}=\boldsymbol{O}, \boldsymbol{C}=\boldsymbol{O}, \boldsymbol{O}-\boldsymbol{H} \) as
414,814,499,724 and \( 640 k J m o l^{-1} \)
respectively.


Which of the following is not a function of water in cell?
A. It provides energy for chemical reaction.
B. It act as a solvent
c. It provides medium for chemical reaction.
D. It releases hydrogen ions on ionisation.


Assertion
Two balls of different masses are
thrown vertically upward with same speed. They will pass through their point of projection in the downward direction with the same speed.
Reason
The maximum height and downward velocity attained at the point of projection are independent of the mass of the ball.
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 incorrect


Show that the diagonals of a rhombus divide it into four congruent triangles.


Fill in the blanks.
A field normal to the plane of a circular
wire \( n \) turns and radius r which carries
a current I is measured on the axis of
the coil at small h distance h from the
centre of the coil. This is smaller than
the field at the centre by a friction
A \( \cdot_{3} \frac{3 h^{2}}{2 r^{2}} \)
B. \( \frac{h^{2}}{2 r^{2}} \)
c. \( \frac{4 h^{2}}{2 r^{2}} \)
D. \( \frac{3 h^{2}}{2 r^{2}} \)


Genetic dwarfness can be overcome by treating with
A. Cytokinin
B. Auxins
c. Gibberellins
D. Ethylene


\( A 20 V, 750 \mathrm{Hz} \) source is connected to a
series combination of \( \mathrm{R}=100 \Omega, \mathrm{C}=10 \)
\( \mu F \) and \( L=0.1803 H . \) Calculate the time
in which resistance will get heated by
\( 10^{\circ} \mathrm{C} . \) (If thermal capacity of the
material \( =2 \mathrm{J} /^{\circ} \mathrm{C} \)
A. 328 sec
B. 348 sec
c. \( 3.48 \mathrm{sec} \)
D. \( 4.32 \mathrm{sec} \)


Lightning wants to get to ground. It will follow the path(s) of to do so.
A. most impedance
B. least impedance
c. least distance
D. least inductance


An electrochemical cell is constructed
with an open swtich as shown below:
When the switch is closed, mass of tin-
electrode increases. If \( \boldsymbol{E}^{\circ}\left(\boldsymbol{S} \boldsymbol{n}^{2+} / \boldsymbol{S} \boldsymbol{n}\right)= \)
\( -0.14 V \) and for \( E^{\circ}\left(X^{n+} / X\right)= \)
\( -0.78 V \) and initial emf of the cell is
\( 0.65 \mathrm{V}, \) determine \( n \)
\( A \cdot 3 \)
в.
\( c .5 \)
\( D \)


Two concentric spheres kept in air have radii 'R' and 'r'. They have similar charge
and equal surface charge density ' \( \sigma \) '.
The electric potential at their common
centre is \( _{-}-\ldots_{0}= \) permittivity of free space)
A \( \cdot \frac{\sigma(R+r)}{\epsilon_{0}} \)
В. \( \frac{\sigma(R-r)}{\epsilon_{0}} \)
c. \( \frac{\sigma(R+r)}{2 \epsilon_{0}} \)
D. \( \frac{\sigma(R+r)}{4 \epsilon_{0}} \)


State whether true or false.
In a completely dark room, if you hold up a mirror in front of you, you will
still see a reflection of yourself in the mirror.
A. True
B. False


The vapour pressure of a dilute solution
of a solute is not influenced by:
A. temperature of solution
B. melting point of solute
c. mole fraction of solute
D. degree of dissociation of solute


\( 10.6 \mathrm{g} \) of a substance of molecular weight 106 was dissolved in 100 ml. 10
\( \mathrm{ml} \) of this solution was pipetted out into
a \( 1000 \mathrm{ml} \) flask and made up to the mark with distilled water. The molarity
of the resulting solution is:
\( \mathbf{A} \cdot 1 M \)
в. \( 10^{-2} M \)
\( \mathrm{c} \cdot 10^{-3} M \)
D. \( 10^{-4} M \)


(a) Is it possible to have a regular polygon with measure of each exterior
angle as \( 22^{\circ} ? \)
(b) Can it be an interior angle of a regular polygon? Why?


White light is incident normally on a soap film of thickness \( 15 \times 10^{-5} \mathrm{cm} \)
and refractive index \( 1.33 . \) Which
wavelength is reflected maximum in the visible region?
A \( .26000 A^{\circ} \)
B. \( 8866 A^{\circ} \)
c. \( 5320 A^{\circ} \)
D. \( 3800 A^{\circ} \)


The sum of four consecutive numbers in
AP is 32 and the ratio of the product of the first and the last to the product of
two middle terms is \( 7: 15 . \) Find the
numbers.


A paricle executes SHM with time period of 4 s. find the minimum time interval in which the velocity of the particle changes by an amount equal to its maximum velocity:
A \( \cdot \frac{1}{2} s \)
B. \( \frac{2}{3} \) s
c. \( \frac{9}{3} \) s
D. \( \frac{5}{3} \) s


Assertion
An AC generator is which converts mechanical energy into electrical energy (alternating emf). It works on the principle of electromagnetic induction the magnet generates an emf (current)
in the coil.
Reason
The property of coil by which an emf is induced in it when the current flowing through it changes is mutual inductance
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 weight of the body is
A. \( V \rho g \)
в. \( \frac{V}{\rho g} \)
c. \( \frac{V g}{\rho} \)
D. None of the above


Which of the following is true about
notochord?
A. It is present in all adult chordates.
B. It is present in all echinoderms.
C. It is present in chordates during embryonic development
D. It is always a vestigial organ in chordates.
E. It forms a part of the nervous system of all vertebrates.


A solid uniform ball having volume \( \boldsymbol{V} \)
and density \( \rho \) floats at the interface of two immiscible liquids as shown in figure. The densities of the upper and
the lower liquids are \( \rho_{1} \) and \( \rho_{2} \)
respectively, such that \( \rho_{1}<\rho<\rho_{2} \)
What fraction of the volume of the ball
will be in the lower liquid :-
\( A \)
B.
c. \( \frac{\rho_{1}-\rho}{\rho_{1}-\rho_{2}} \)
D. \( \frac{\rho_{1}-\rho_{2}}{\rho_{2}} \)


The distance of the point (1,-2,3) from the plane \( \boldsymbol{x}-\boldsymbol{y}+\boldsymbol{z}=\mathbf{5} \) measured
parallel to the line \( \frac{x}{2}=\frac{y}{3}=\frac{z-1}{-6} \) is
A .
B . 2
\( c \cdot 4 \)
D. none of these


Q Type your question
A DNA template plus primer with the structure
\( 3 \mathrm{P}-\mathrm{TG} \mathrm{C} \) GAATTAG \( \mathrm{C} \) GACAT - PS
\( 5 \mathrm{P}-\mathrm{ATCGGTACGACGCTTAAC} \mathrm{OH} 3 \)
(where \( P=a \) phosphate group) is placed in an in vitro DNA synthesis system containing \( M g^{2+}, \) an excess of the four
deoxyribonucleoside triphosphates, etc.
and a mutant form of E. Coli DNA
polymerase I that lacks \( 5 \rightarrow 3 \)
exonuclease activity. The \( 5 \rightarrow 3 \)
polymerase and. \( 3 \rightarrow 5 \) exonuclease activities of this aberrant enzyme are
identical to those of normal E. Coli

DNA polymerase I. It simply has no \( 5 \rightarrow \) 3 exonuclease activity. What will be the structure of the final product?
A. 3P-TGCGAATTAGCGACAT- P
5 P-ATCG GTAC GACG СТТААТСG СТGТА-ОН 3
в. 3 Р-т6СGААТтGGСGАСАТ- Р 5
5 Р-АтсG GтАСGАС ясттААС с с стятА-Он 3
c. 3нотяСЯААТтАGСGАСАТ Р 5
5-ATCG GTAC GACG CTTAATCG CTGTA - P 3
D. 3 Р тяСЯААТТАGСGАСАТ Р 5
5 Р -АСGСТТААТСЯСТЯТА-Онз


In \( \triangle A B C, \angle C=90^{\circ} . \) If \( B C=a, A C= \)
\( b \) and \( A B=c, \) find \( c \) when \( a=8 c m \)
and \( b=6 \mathrm{cm} \)
\( \mathbf{A} \cdot 10 \mathrm{cm} \)
в. \( 14 \mathrm{cm} \)
c. \( 15 \mathrm{cm} \)
D. \( 20 \mathrm{cm} \)


Which are the correct statements for
\( N O_{2} ? \)
This question has multiple correct options
A. It is paramagnetic and dimerizes to \( N_{2} O_{4} \)
B. \( N_{2} O_{4} \) is planar and diamagnetic.
\( \mathrm{C} \cdot \mathrm{N} \mathrm{O}_{2} \) is linear containing an odd number of electrons.
D. N-O bonds in \( N O_{2} \) are different lengths.


Given unit vectors \( \overline{\boldsymbol{m}}, \overline{\boldsymbol{n}} \) and \( \overline{\boldsymbol{p}} \) such that
angle between \( \bar{m} \) and \( \bar{n}= \) angle between \( \bar{p} \) and \( (\bar{m} \times \bar{n})=\pi / 6 \) then
\( [\overline{\boldsymbol{n}} \overline{\boldsymbol{p}} \overline{\boldsymbol{n}}]= \)
A. \( \sqrt{3} / 4 \)
B. 3/4
\( c \cdot 1 / 4 \)
D. none


The value of \( \int \frac{10^{x / 2}}{\sqrt{10^{-x}-10^{x}}} d x \) is
A. \( \frac{1}{\log _{2} 10} \sin ^{-1}\left(10^{x}\right)+c \)
В. \( 2 \sqrt{10^{-x}+10^{x}}+c \)
c. \( \frac{1}{\log _{e} 10} \sin h^{-1}\left(10^{x}\right)+c \)
D. \( \frac{-1}{\log _{e} 10} \sin h^{-1}\left(10^{x}\right)+c \)


Find additive inverse of (-7)
A . -7
B. 0
\( c \cdot 7 \)
D. 6


Evaluate: \( \int_{0}^{\frac{\pi}{4}}[\sqrt{\tan x}+\sqrt{\cot x}] d x \)
A \( \cdot \frac{\pi}{\sqrt{2}} \)
в.
c. \( \frac{3 \pi}{\sqrt{2}} \)
D.


The diameter of a right circular cylinder is decreased by 10\%. The volume of cylinder remains the same then the
percentage increase in height is:
A . 20\%
B. 23.45\%
c. 5\%
D. 20.5\%


Who said that cathode rays consist of negatively charged particles?
A. Dalton
B. Rutherford
c. James chadwick
D. J.J. Thomson


Light of wavelength 500 nm goes through a pinhole of \( 0.2 m m \) and falls on
a wall at a distance of \( 2 m \). What is the
radius of the central bright spot formed
on the wall?
A \( .2 .37 \mathrm{cm} \)
в. 1.37 ст
\( c .3 .37 \mathrm{cm} \)
D. \( 7.37 \mathrm{cm} \)


An object of mass \( m \) and velocity \( v_{0} \)
strikes a rigid uniform rod of length \( l \)
and mass \( m_{r} . \) The rod is hanging by a frictionless pivot from the ceiling. Immediately after striking the rod, the object continues forward but its speed
reduces to \( \frac{v_{0}}{2} . \) The moment of inertia of
the rod about its centre of mass is
\( I_{C M}=\frac{1}{2} m_{r} l^{2} . \) For the collision to be
inelastic:
A. the rod and object are of equal mass
B. the rod is either heavier or lighter than the object
c. the rod is of negligible mass
D. none of these


Which of the following is a contact force
\( ? \)
A. Gravitational force
B. Friction
c. Electrostatic force
D. Magnetic force


\( \int\left[\frac{1+\sin (\log x)}{1+\cos (\log x)}\right] d x= \)
A. \( \frac{x}{1+\cos (\log x)}+c \)
в. \( \quad x \tan \frac{\log x}{2}+c \)
c. \( \quad-x \cot \frac{\log x}{2}+c \)
D. \( \frac{x}{1+\sin (\log x)}+c \)


How many numbers of three digits can be formed using the digits 1,2,3,4,5 without repetition of digits is x. How many of these are even is y.Find \( \mathbf{x}+\mathbf{y} \)


In the given figure, if \( E \) and \( F \) are the
midpoints of \( A B \) and \( C D \) of
parallelogram \( A B C D, \) which one is
true?
A \( . C E \) trisects \( B D \)
B. \( A F \) trisects \( B D \)
c. \( \Delta A D F \cong \Delta C B E \)
D. All of these


Which of the following are not correct?
This question has multiple correct options
A. The escape velocity for the Moon is \( 6 k m s^{-1} \)
B. The escape velocity from the surface of Moon is \( v \). The orbital velocity for a satellite to orbit very close to the surface of Moon is \( v / 2 \)
C. When an earth satellite is moved from one stable orbit to a further stable orbit, the gravitational potential energy increases
D. The orbital velocity of a satellite revolving in a circular path close to the planet is independent of the density of the planet.


Which of the following conditions is not correct for ideal solution
A. no change in volume on mixing
B. no change in enthalpy on mixing
c. it obeys Raoults law
D. lonisation of solute should occurs to a small extent


f \( x, y z \) are all different and if \( \left|\begin{array}{lll}\boldsymbol{x} & \boldsymbol{x}^{\boldsymbol{2}} & \boldsymbol{1}+\boldsymbol{x}^{\boldsymbol{3}} \\ \boldsymbol{y} & \boldsymbol{y}^{\boldsymbol{2}} & \boldsymbol{1}+\boldsymbol{y}^{\boldsymbol{3}} \\ \boldsymbol{z} & \boldsymbol{z}^{\boldsymbol{2}} & \boldsymbol{1}+\boldsymbol{z}^{\boldsymbol{3}}\end{array}\right|=0 \) then \( \mathbf{x y z}= \)
A . -1
B.
\( c . \)
D. ±1


In the given figure, 0 is the centre of the
circle and XOY is a diameter. If \( X Z \) is
any other chord of the circle, then which
of the following is correct?
\( A \cdot X Z<O Z \)
8. \( x y>x z \)
\( c \cdot 0 x+0 z \)
D. zX + ZY


The electronic configurations of three elements \( X, Y \) and \( Z \) are 2,\( 8 ; 2,8,7 ; \) and
2,8,2 respectively. Which of the following is correct?
A. \( X \) is a metal
B. \( Y \) is a metal
\( c \cdot Z \) is a non-metal
D. \( Y \) is a non-metal and \( Z \) is a metal


Who discovered the coenzymes?
A. James Sumner
B. Fritz Lipmann
c. Mayerhoff
D. Eduard Buchner


Noble gases have electron affinity.
A . high
B. low
c. zero
D. very low


Two capacitors of capacities \( 3 \mu \mathrm{F} \) and \( 6 \mu F \) are connected in series and connected to
120V. The potential differences across \( 3 \mu \)
\( \mathrm{F} \) is \( V_{0} \) and the charge here is \( q_{0} . \) We have :
A) \( q_{0}=40 \mu C \)
B) \( V_{0}=60 V \)
\( \left.\mathrm{C}) V_{0}=80 \mathrm{V} \quad \mathrm{D}\right) q_{0}=240 \mu C \)
\( A \cdot A, C \) are correct
B. A, B are correct
c. \( B, \) D are correct
D. \( c, \) D are correct


A ray of light travelling inside a rectangular glass block of refractive index \( \sqrt{2} \) is incident on the glass-air
surface at an angle o incidence of \( 45^{\circ} \)
The refractive index of air is one. Under
these conditions the ray will
A. emerge into the air without any deviation
B. be reflectived back into the glass
c. be absorbed
D. emerge into the air with an angle of refraction equal to \( 90_{o} \)


Acceleration due to gravity at surface of a planet is equal to that at surface of
the earth and density is 1.5 times that of earth. if radius of earth is \( R \), radius of
planet is
A \( \cdot \frac{R}{1.5} \)
в. \( \frac{2}{3} R \)
c. \( \frac{9}{4} R \)
D. \( \frac{4}{9} R \)


An inductor, a resistor and a capacitor are joined in series with an \( A C \) source. As the frequency of the source is
slightly increased from a very low value,
the reactance
A. of the inductor increases
B. of the resistor increases
c. of the capacitor increases
D. of the circuit increases


Consider two thin identical conducting wires covered with very thin insulating material. One of the wires is bent into a
loop and produces magnetic field \( B_{1} \) at
its centre when a current \( I \) passes
through it. The second wire is bent into
a coil with free identical loops adjacent to each other and produces magnetic
field \( B_{2} \) at the centre of loops with
current \( I / 3 \) passing through it. The
ratio \( \boldsymbol{B}_{1}: \boldsymbol{B}_{2} \)
A. 1: 1
B. 1: 3
c. 1: 9
D. 9: 1


If four number in A.P are such that their
sum is 50 and the greatest number is 4 times the least then the number are
\( A \cdot 5,10,15,20 \)
B. 4, 10, 16, 22
c. 3,7,11,15
D. None of these


A laser used to weld detached retinas
emits light with a wavelength of \( 652 n m \) in pulses that are of 20 ms duration. The average power during each pulse is \( 0.6 W . \) Find the energy in each pulse in
\( e V \) and in a single photon
A \( .7 .5 \times 10^{15} e V, 1.9 e V \)
В. \( 7.5 \times 10^{15} e V, 1.19 e V \)
c. \( 7.5 \times 10^{16} e V, 0.19 e V \)
D. \( 7.5 \times 10^{16} e V, 1.9 e V \)


A lake which is rich in organic waste
may result in
A. Increased population of fish due to lots of nutrients
B. Mortality of fish due to lack of oxygen
C. Increased population of aquatic organisms due to minerals
D. Drying of the lake due to algal bloom


Which of the following metal ion is present in Ziegler-Natta catalyst?
A \( \cdot F e^{2} \)
B. \( Z r^{4} \)
c. \( R h^{+} \)
D. \( T i^{4} \)


The area bounded by \( x^{2}=4 a y \) and \( y= \)
\( 2 a \) is?
A \( \cdot \frac{16 \sqrt{2} a^{2}}{3} \)
в. \( \frac{16 a^{2}}{3} \)
c. \( \frac{8 a^{2}}{3} \)
D. \( \frac{8 \sqrt{2} a^{2}}{3} \)


Unit of electric flux is:
A. \( V m \)
в. \( N m / C \)
c. \( V / m \)
D. \( C / N m \)


A trolley of mass \( 20 \mathrm{kg} \) is attached to a
block of mass \( 4 \mathrm{kg} \) by a massless string passing over a frictionless pulley as
shown in the figure. If the coefficient of
kinetic friction between trolley and the surface is \( 0.02, \) then the acceleration of
the trolley and block system is:
(Take \( \left.g=10 m s^{-2}\right) \)
\( A \cdot 1 m s^{-2} \)
B. \( 2 m s^{-2} \)
\( \mathbf{C} \cdot 1.5 \mathrm{ms}^{-2} \)
D. \( 2.5 \mathrm{ms}^{-2} \)


The speed of a car increases uniformly
from zero to \( 10 \mathrm{ms}^{-1} \) in \( 2 s \) and then
remain constant.
a. Find the distance travelled by the car
in the first two seconds.
b. Find the distance travelled by the car
in next two seconds.
c. Find the total distance travelled in 4 s.


Find the principal value of the following
\( \sin \left(\sec ^{-1} x+\csc ^{-1} x\right) \)


The resultant magnetic field at the center of a bar magnet is zero.
A. True
B. False


Draw parallelogram ABCD with the following measurements and calculate
its area.
\( A C=8 c m, B D=6 c m \) and \( \angle C O D= \)
\( 90^{\circ} \) where \( \overline{A C} \) and \( \overline{B D} \) intersect at 0


A box contains 20 identical balls of
which 5 are white and 15 black. The
balls are drawn at random from the box one at a time with replacement. The probability that a white ball is drawn fro
the \( 3^{r d} \) time on \( 6^{t h} \) drawn is


Identify the conjugate acids and bases in the following equation:
\( N H_{3}+H_{2} O \rightleftharpoons N H_{4}^{+}+O H^{-} \)
A \( \cdot\left(H_{2} O, O H^{-}\right) \) and \( \left(N H_{2}^{+}, N H_{3}\right) \)
B . \( \left(H_{2} O, O H^{-}\right) \) and \( \left(N H_{4}^{+}, N H_{2}^{2-}\right) \)
c. \( \left(H_{2} O, O H\right) \) and \( \left(N H_{3}, N H_{4}\right) \)
D. \( \left(H_{2} O, O H^{-}\right) \) and \( \left(N H_{4}^{+}, N H_{3}\right) \)


Electric field at \( r=1.25 \mathrm{cm} \)


For a particle moving along X-axis if acceleration(constant) is acting along -
ve X-axis, then match the entries of
Column-I with entries of Column II
Column I Column II
A. Initial
P. Particle may move in +ve \( x \) velocity>
B. Initial Q.Particle may move in +ve x velocityく \( \quad \) direction with decreasing speed
R. Particle may move in-ve
C. \( x>0 \quad \) direction with increasing speed
S. Particle may move in -ve X
D.X \( <0 \)
\( A \cdot A->Q, R ; B \rightarrow Q, R ; C->Q, R ; D \rightarrow R \)
B. A -> Q; B -> Q, R; C-> R; D -> Q, R
C. \( A \) -> \( Q, R ; B \) -> \( R ; C \) -> \( Q, R ; D \rightarrow Q, R \)
D. A -> Q, R; B -> R; C->R; D -> R


Two mirrors are inclined at an angle 60
an object is placed asymmetrically between them. Then number of images formed will be :
\( A \cdot 6 \)
B. 5
\( c \cdot 7 \)
\( D \)


During seed germination its stored food
is mobilized by
A. Ethylene.
B. Cytokinin.
\( c . \) АВА
D. Gibberellin


\( 2.8 \times 10^{-2} \mathrm{kg} \) of nitrogen is expanded
isothermally and reversibly at \( 300 K \) from \( 15.15 \times 10^{5} N m^{-2} \) when the work
done is found to be \( -17.33 \mathrm{kJ} \). Find the
final pressure.


The rate constant is given by the equation \( \boldsymbol{K}=\boldsymbol{P} \boldsymbol{Z} \boldsymbol{e}^{-\boldsymbol{E} / \boldsymbol{R} \boldsymbol{T}} . \) Which factor
should register a decrease for the
reaction to proceed more rapidly?
A . T
B. z
\( c \cdot E \)
D.


Which of the following is correct
relation between \( \lambda_{m} \) (wavelength corresponding to maximum energy of emission) and T (absolute
temperature)?
A \( \cdot \lambda_{m} / T= \) constant
B. \( \lambda_{m} T= \) constant
c. \( \lambda_{m}^{2} / T= \) constant
D. \( \lambda_{m} / T^{4}= \) constant


A single battery is connected to three
resistances as shown in Figure.
This question has multiple correct options
A. The current through 7 \( \Omega \) resistance is 4 A
B. The current through \( 3 \Omega \) resistance is 4 A
c. The current through \( 6 \Omega \) resistance is 2 A
D. The current through \( 7 \Omega \) resistance is 0


The angles of a pentagon in degrees are \( \boldsymbol{y}^{o},\left(\boldsymbol{y}+\mathbf{2 0}^{o}\right),\left(\boldsymbol{y}+\mathbf{4 0}^{o}\right),\left(\boldsymbol{y}+\mathbf{6 0}^{o}\right) \) and
\( \left(y+80^{\circ}\right) . \) The smallest angle of the
pentagon is
\( A \cdot 88^{\circ} \)
B. \( 78^{\circ} \)
\( c \cdot 68^{\circ} \)
\( D \cdot 58^{\circ} \)


A vehicle of \( 100 k g \) is moving with a velocity of \( 5 m / s . \) To stop it in \( 1 / 10 s e c \) required force in opposite direction is
\( N \)
A . 50
в. 500
c. 5000
D. 1000


After the first term in a sequence of
positive integers, the ratio of each term to the term immediately preceding it is
2 to \( 1 . \) What is the ratio of the \( 8^{t h} \) term
in this sequence to the \( 5^{t h} \) term?
\( A \cdot 6 \) to 1
B. 8 to 5
\( c \cdot 8 \) to 1
D. 64 to 1
E. 256 to 1


Potassium acetate on Koble's
electrolysis produces:
A. \( C_{2} H_{4} \)
в. \( C H_{4} \)
\( \mathbf{c} \cdot C_{2} H_{6} \)
D. \( C_{3} H_{8} \)


(a) What are characteristics of image
formed by a plane mirror?
(b) By giving sign conventions made, derive the mirror formula for a concave
mirror.


If the set natural numbers, is
partitioned into subsets \( \boldsymbol{S}_{1}= \)
\( \{1\}, S_{2}=\{4,5,6\}, S_{4}=\{7,8,9,10\} \)
The last terms of these groups is \( 1,1+ \) \( \mathbf{2}, \mathbf{1}+\mathbf{2}+\mathbf{3}, \mathbf{1}+\mathbf{2}+\mathbf{3}+\mathbf{4} \ldots \ldots . \) Find the
sum of the elements in the subset \( S_{50} \)


Assertion
When the distance between two bodies
is doubled and also the mass of each
body is doubled, the gravitational force between them remains the same
Reason
According to Newton's law of gravitation, force is directly
proportional to mass of the bodies and
inversely proportional to square of the distance between them
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


A lead storage battery has initially \( 200 g \) of lead and \( 200 g \) of \( P b O_{2}, \) plus
excess \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} . \) How long could this cell deliver a current of 10 amp, without
recharging, if it was possible to operate it so that the reaction goes to completion?
A. 2.48 hour
B. 3.48 hour
c. 4.48 hour
D. 6.48 hour


Find the direction cosines of the vector
\( \overrightarrow{\boldsymbol{r}}=(\boldsymbol{6} \hat{\boldsymbol{i}}+\boldsymbol{2} \hat{\boldsymbol{j}}-\boldsymbol{3} \hat{\boldsymbol{k}}) \)


Water can be tested by :
A. smell
B. test
c. Hydrated \( C u S O_{4} \)
D. Anhydrous \( C o C l_{3} \) which change the colour to pink


A catalyzed reaction mechanism has a
activation energy and thus,
causes a reaction rate.
A . higher, lower
B. higher, higher
c. lower, higher
D. lower, steady
E. higher, steady


The Molarity of \( 200 m l \) of \( H C l \) solution
which can neutralise \( 1.6 g \) of anhydrous
\( N a_{2} C O_{3} \) is:
\( \mathbf{A} \cdot 1 M \)
B. \( 0.1 M \)
c. \( 0.6 M \)
D. \( 0.75 M \)


The order of the stability of dihalides of Si, Ge, Sn and Pb changes in sequence:
A. \( S i X_{2}<S n X_{2}<G e X_{2}<P b X_{2} \)
в. \( \operatorname{SiX}_{2}<\operatorname{Ge} X_{2}<\operatorname{SnX}_{2}<\operatorname{PbX}_{2} \)
c. \( P b X_{2}<\operatorname{SnX}_{2}<\operatorname{GeX}_{2}<\operatorname{SiX}_{2} \)
D. \( G e X_{2}<\operatorname{Si} X_{2}<\operatorname{Sn} X_{2}<P b X_{2} \)


A road is \( 8 \mathrm{m} \) wide. Its average radius of curvature is \( 40 \mathrm{m} . \) The outer edge is above the lower edge by a distance of \( 1.28 \mathrm{m} . \) Find the velocity of vehicle for
which the road is most suited? \( (\boldsymbol{g}= \)
\( 10 m / s^{2} \)


1, \( 4- \) addition in butadiene gives kinetically favored product. If this is true enter 1 , else enter 0 .


Which of the following substance will have highest boiling point?
A. \( H e \)
в. \( C s F \)
c. \( N H_{3} \)
D. \( C H C l_{3} \)


Which is the most thermodynamically stable allotropic form of phosphorus?
A . Red
B. White
c. Black
D. Yellow


Which of the following may no be conserved for an isolated system
This question has multiple correct options
A. Energy
B. Potential energy
c. Mechanical energy
D. Kinetic energy


Nylon is obtained from :
A . coal
B. air
c. water
D. all of the above


Reaction of a carbonyl compound with one of the following reagents involves nucleophilic addition followed by elimination of water. The reagent is:
A. hydrocyanic acid
B. sodium hydrogen sulphite
c. a Grignard reagent
D. hydrazine in presence of feebly acidic solution


Human ancestors who left cave
paintings were
A. Neanderthal Man
B. Cro-Magnon Man
c. Java Man
D. Peking Man


What happens when ethanol is dissolved in water?
A. Absorption of heat and decrease in volume
B. Emission of heat and decrease in volume
c. Absorption of heat and increase in volume
D. Emission of heat and increase in volume


Two ideal batteries of emf \( V_{1} \) and \( V_{2} \)
and three resistances \( R_{1}, R_{2} \) and \( R_{3} \)
are connected as shown in the figure.
The current in resistance \( \boldsymbol{R}_{2} \) would be
zero if
This question has multiple correct options
A. \( V_{1}=V_{2} \) and \( R_{1}=R_{2}=R_{3} \)
B . \( V_{1}=V_{2} \) and \( R_{1}=2 R_{2}=R_{3} \)
c. \( V_{1}=2 V_{2} \) and \( 2 R_{1}=2 R_{2}=R_{3} \)
D. \( 2 V_{1}=V_{2} \) and \( 2 R_{1}=R_{2}=R_{3} \)


Name the organic acid present in
tomato is :
A. Tartaric acid
B. Malic acid
c. Lactic acid
D. Oxalic acid


In Alum: \( K_{2} S O_{4} . A l_{2}\left(S o_{4}\right)_{3} .24 H_{2} O \)
Which metal can replace \( \boldsymbol{A l} \)
A \( . C r \)
в. \( M n \)
c. \( I n \)
D. \( S c \)


Food articles like milk, vegetables, and
bread are kept in a refrigerator. Medicines are labeled 'Store in a cool,
dry place'. By keeping at low temperatures, they are prevented from decay or destruction, because:
A. bacteria are frozen
B. chemical reactions slow down
c. vitamins protect protein
D. micro organisms can not survive


metals occur free in
nature
A . Alkal
B. Noble
c. Iron
D. Aluminum


The value of
\( \sec \left[\sin ^{-1}\left(\sin \frac{50 \pi}{9}\right)+\cos ^{-1} \cos \left(\frac{31 \tau}{9}\right.\right. \)
is equal to
A \( \cdot \sec \frac{10 \pi}{9} \)
в. \( \sec 9 \pi \)
c. -1
D.


Consider the following classification. Lotus, Rose, Tiger, Cactus Which of the following is not suitable in given classification
A . Lotus
B. Rose
c. Tiger
D. cactus


A candle placed \( 25 \mathrm{cm} \) from a lens forms
an image on a screen placed \( 75 \mathrm{cm} \) on the other side of the lens. The focal
length and type of the lens should be?
A. \( +18.75 \mathrm{cm} \) and convex lens
B. \( -18.75 \mathrm{cm} \) and concave lens
c. \( +20.25 \mathrm{cm} \) and convex lens
D. \( -20.25 \mathrm{cm} \) and concave lens


A circular disc of radius 0.2 meter is
placed in a uniform magnetic field of induction \( \frac{1}{\pi}\left(W b / m^{2}\right) \) in such way that
its axis makes an angle of \( 60^{\circ} \) with \( \vec{B} \). The magnetic flux linked with the disc is
A. \( 0.08 \mathrm{wb} \)
B. 0.01 Wb
c. \( 0.02 \mathrm{wb} \)
D. \( 0.06 \mathrm{wb} \)


toppr
Q Type your question-
as the only product. The unbalanced equation for the reaction is
\( N_{2} O(g)+O_{2}(g) \rightarrow N_{2} O_{4}(g) \)
The \( N_{2} O / O_{2} \) mixture is shown in the
figure. Which of the following represents the composition of the system after reaction has gone to completion?
Legend
\( \bigcirc=\mathrm{o} \)
\( \mathrm{O}=\mathrm{N} \)
\( A \)
\begin{tabular}{|ccc|}
\hline 00 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 \\
0 & 0 & 0 \\
0 & 0 & 0 \\
& 0 & 0 \\
\hline
\end{tabular}
в. \( \begin{array}{lll}00 & 8 & 8 & 80 \\ 00 & 0 & 00 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{array} \)
\( c \)
D.


Speed of nerve impulse in mammals is
A. 1 meter / sec
B. 100 meter/sec
c. 1000 meter / sec
D. None of the above


Integrate \( \int_{a}^{b} \cos x d x \)


If \( \mathbf{a} \in[-\mathbf{1 0}, \mathbf{0}] \) then the probability that
the graph of the function \( \mathbf{y}=\mathbf{x}^{2}+ \)
\( 2(a+3) x-(2 a+3) \) is strictly above \( x \)
axis is
A \( \cdot \frac{3}{5} \)
B. \( \frac{2}{5} \)
\( c \cdot \frac{1}{5} \)
D. \( \frac{4}{5} \)


The van't Hoff factor of \( 0.005 M \)
aqueous solution of \( K C l \) is \( 1.95 . \) The
degree of ionisation of \( K C l \) is:
A . 0.95
В. 0.97
\( c .0 .94 \)
D. 0.96


By Rolles theorem for \( f(x)=(x- \)
\( a)^{m}(x-b)^{n} \) on \( [a, b] ; m, n \) being
positive integer. Find the value of \( c \) which lies between \( a \)
\& b.
A \( \cdot c=\frac{m b+n a}{m+n} \)
в. \( c=\frac{m b-n a}{m+n} \)
c. \( _{c}=\frac{n b+m a}{m+n} \)
D. \( c=\frac{n b-m a}{m+n} \)


Give the reaction of dichlorine gas with
cold and dilute and hot and
concentrated \( N a O H_{(a q)} \)


Q Type your question
village. After the check-up, he was shocked to see that most of the farmers
suffered from cancer due to regular
exposure to pesticides and many wore diabetic. They distributed free
medicines to them. Dr.
Satpal immediately reported the matter to the National Human Rights Commission (NHRC). On the
suggestions of NHRC, the government decided to provide medical care, financial assistance, setting up of super-specialty hospitals for
treatment and
prevention of the deadly disease in the a ffected villages all over India.
(i) Write the values shown by:
(a) Dr. Satpal
(b) NHRC.
(ii) What type of analgesics are chiefly used for the relief of pains of terminal cancer?
(iii) Give an example of artificial sweetener that could have
been recommended to diabetic
\( p_{\text {ts }} \)


If \( f(x)=\left\{\begin{array}{cl}\frac{\sin 5 x}{x^{2}+2 x}, & x \neq 0 \\ k+\frac{1}{2}, & x=0\end{array} \) is \right.
continuous at \( x=0, \) then the value of \( k \)
is
\( \mathbf{A} \cdot \mathbf{1} \)
B. - 2
\( c \cdot 2 \)
D.


Formation of \( N i(C O)_{4} \) and subsequently its decomposition into Ni and \( \mathrm{CO} \) (recycled) make the basis of Mond's process:
\( \mathbf{N i}+ \)
\( \mathbf{4} \boldsymbol{C O} \quad \boldsymbol{T}_{1} \quad \boldsymbol{N i}(\boldsymbol{C O})_{4} \quad \underline{\boldsymbol{T}}_{2} \quad \boldsymbol{N} \boldsymbol{i}+ \)
\( 4 C O \)
\( T_{1} \) and \( T_{2} \) are :
A \( \cdot 100^{\circ} \mathrm{C}, 50^{\circ} \mathrm{C} \)
B . \( 50^{\circ} \mathrm{C}, 100^{\circ} \mathrm{C} \)
c. \( 50^{\circ} \mathrm{C}, 230^{\circ} \mathrm{C} \)
D \( \cdot 230^{\circ} \mathrm{C}, 50^{\circ} \mathrm{C} \)


In the spectrum of visible light produced by a prism, dispersion is
A. Uniform throughout the spectrum
B. Maximum in the middle, decreases on either sides
c. Maximum towards yellow
D. Maximum towards violet


The number of significant figures in
0.06900 is the
A. 5
B. 4
\( c \cdot 2 \)
\( D \)


The maximum number of
stereoisomers that can exist for the
above shown compound is:
\( A \)
B.
\( c \cdot 10 \)
D.


Due to a small magnet, intensity at a distance \( x \) in the end on position is 9 gauss. What will be the intensity at a distance \( \frac{x}{2} \) on broad side on position.
A. 9 gauss
B. 4 gauss
c. 36 gauss
D. 4.5 gauss


Which of the following pairs will show common ion effect?
\( \mathbf{A} \cdot N a C N+K C N \)
в. \( N a C l+H C l \)
c. \( N H_{4} O H+N H_{4} C l \)
D. \( _{B a} G l_{2}+B a\left(N O_{3}\right)_{2} \)


Name the metal that is purified by placing the impure metal on sloping hearth of a reverberatory furnace and heating that above its melting point in the absence of air.
A. Mercury
B. Gallium
c. zirconium
D. copper


The following reaction is an example of what familiar synthesis?


An obtuse triangle will have one and only one angle.
A . acute
B. obtuse
c. scalene
D. right angled


Complete the following table


Conductivity (Unit Siemen's 'S') is
directly proportional to area of the
vessel and the concentration of the
solution in it and is inversely proportional to the length of the vessel,
then the unit of constant of
proportionality is
\( \mathbf{A} \cdot S m m o l^{-1} \)
B. \( S m^{2} m o l^{-1} \)
c. \( S^{-2} m^{2} \) mol
D. \( S^{2} m^{2} \) mol \( ^{-2} \)


The flux used in the extraction of iron
from haematite in blast furnace, is:
A. limestone
B. silica
\( c \cdot \) coke
D. quartz


The sweeteners value of aspartame in comparison to cane sugar is:
A. 550
B. 100
\( c \cdot 600 \)
D. 2000


Which of the following options is the
only correct representation of a process
in which \( \Delta U=\Delta Q-P \Delta V ? \)
A. \( (I I I)(i i i)(P) \)
B. \( (I I)(i i i)(P) \)
c. \( (I I)(i i i)(S) \)
D. \( (I I)((i v)(R) \)


Molar ratio of a mixture of water and
absolute alcohol is \( 0.2 . \) The mole
fraction ratio of alcohol and water is :


A sector of a circle of radius \( 8 \mathrm{cm} \)
contains an angle of \( 135^{\circ} . \) Find the area
of the sector.


Acetylene gives precipitate with ammonical silver nitrate is due to:
A. Acetylene possess \( s p^{2} \) carbon
B. Acetylene posses acidic hydrogen
C. Acetylene possess low electronegative
carbon
D. Acetylene posess - \( C \equiv C \) -triple bond


State whether true or false.
Magnetic lines of force emanate from south pole and enter into north pole.
A. True
B. False


Q Type your question
\( A \cdot A \cdot \) Cross arm
B. Actin binding site
C. Head
D. ATP binding site
B. A. Head
B. Cross arm
C. Actin binding site
D. ATP binding site
C . A. Actin binding site
B. Head
C. ATP binding site
D. Cross arm
D. A. ATP binding site
B. Actin binding site
C. Head
D. Cross arm


Identify the gate and match \( A, B, Y \) in
bracket to check.
\( \mathbf{A} \cdot \operatorname{AND}(A=1, B=1, Y=1) \)
B. OR \( (A=1, B=1, Y=0) \)
C . NOT \( (A=1, B=1, Y=1) \)
D. XOR \( (A=0, B=0, Y=0) \)


In a non harmonic motion;
A. Displacement and amplitude are independent of each other
B. Displacement and amplitude are dependent on each other
C . restoring force is proportional to displacement
D. restoring force is zero


Henry's Law constant for \( C O_{2} \) in water
is \( 1.67 \times 10^{8} \) Pa at \( 298 \mathrm{K} \). Calculate the
quantity in 1 L of soda water when packed under 2.5 atm pressure at 298 \( \mathrm{K} \)


A uniform wire (Young's modulus \( 2 \times \) \( \left.10^{11} N m^{-2}\right) \) is subjected to
longitudinal tensile stress of \( 5 \times \)
\( 10^{7} N m^{-2} . \) If the overall volume change
in the wire is \( 0.02 \%, \) the frictional
decrease in the radius of the wire is
close to
A \( .1 .0 \times 10^{-4} \)
B. \( 1.5 \times 10^{-4} \)
c. \( 0.25 \times 10^{-4} \)
D. \( 5 \times 10^{-4} \)


If the direction of position vector \( \vec{r} \) is towards south and the direction of force vector \( \vec{F} \) is towards east, then the
direction of torque vector \( \overrightarrow{\boldsymbol{T}} \) is
A. towards North
B. towards west
c. vertically upward
D. vertically downward


A spy plane is being tracked by a radar. At \( t=0, \) its position is reported as
\( (100 m, 200 m, 1000 m) .130 s \) later, its
position is reported to be
\( (2500 m, 1200 m, 1000 m) . \) Find a unit
vector in the direction of plane velocity
and the magnitude of its average
velocity.
A \( \cdot_{20 m s^{-1}} ; \frac{22 \hat{i}+5 \hat{j}}{13} \)
B. \( 20 m s^{-1} ; \frac{12 \hat{i}+5 \hat{j}}{13} \)
c. \( _{30 m s^{-1}} ; \frac{12 \hat{i}+5 \hat{j}}{13} \)
D. \( 20 m s^{-1} ; \frac{12 \hat{i}+6 \hat{j}}{13} \)


Highly electropositive metals cannot be extracted by carbon reduction because these:
A. metals form carbides
B. metals do not react with carbon
c. metal oxides are not reduced by carbon
D. metals are not oxidized by carbon


Define phase of \( \boldsymbol{S} . \boldsymbol{H} . \boldsymbol{M} \) ?


The first stage of demographic transition was experienced in India,
during the period of
A. \( 1891-1921 \)
B. 1821-1881
c. \( 1951-1981 \)
D. 1921-1951


An uncontrolled nuclear chain reaction
forms the basis of:
A. hydrogen bomb
B. atom bomb
c. hydro electric power plant
D. nuclear power plant


toppr
Q Type your que
microscope is the product of the lateral
magnification \( m_{1} \) of the objective and
the angular magnification \( M_{2} \) of the eyepiece. The former is given by \( \boldsymbol{m}_{1}=\frac{\boldsymbol{S}_{1}^{\prime}}{\boldsymbol{S}_{1}} \)
Where \( S_{1} \) and \( S_{1}^{\prime} \) are the object and image distance for the objective lens. Ordinarily the object is very close to the focus, resulting in an image whose distance from the objective is much
larger than the focal length \( f_{1} \). Thus \( S_{1} \)
is approximately equal to \( f_{1} \) and \( m_{1}= \) \( -\frac{S_{1}^{\prime}}{\boldsymbol{f}_{1}}, \) approximately. The angular magnification of the eyepiece from \( M=-\frac{u^{\prime}}{u}=\frac{y / f}{y / 25}=\frac{25}{f} \)
centimeters) is \( M_{2}=25 \mathrm{cm} / \mathrm{f}_{2}, \) Where
\( f_{2} \) is the focal length of the eyepiece, considered as a simple lens. Hence the overall magnification M of the compound microscope is, apart from a negative sign, which is customarily ignored, \( M=m_{1} M_{2}=\frac{(25 c m) S_{1}^{\prime}}{f} \)
1. What is the resolving power of the instrument whose magnifying power is given in the passage?
A \( \cdot \frac{\mu \sin \theta}{0.61 \lambda} \)
в. \( \frac{\mu \sin \theta}{1.22 \lambda} \)
c. \( \frac{\mu \sin \theta}{\lambda} \)
D. \( \frac{\sin \theta}{1.22 \lambda} \)


An oll company nas two depots \( A \) and \( B \)
with capacities of \( 7000 L \) and \( 4000 L \)
respectively. The company is to supply
oil to three petrol pumps \( D, E \) and \( F \)
whose requirements are \( 4500 L, 3000 L \)
and \( 3500 L \) respectively. The distance
(in \( \mathrm{km} \) ) between the depots and the
petrol pumps is given in the following
table:
Distance (in km)
From/To 1 \( \boldsymbol{A} \) \( B \)
7
\( D \)
3
6 4
A
Assuming that the transportation cost
of 10 litres of oil is Re.1 per \( \mathrm{km} \), how
should the delivery be scheduled in
order that the transportation cost is
minimum? What is the minimum cost?


Which of the following compounds will
\( \operatorname{give} S_{N} 1 \) and \( S_{N} 2 \) reactions with
considerable rate?
।. \( \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{5}}-\boldsymbol{C} \boldsymbol{H}_{\boldsymbol{2}}-\boldsymbol{B} \boldsymbol{r} \)
II. \( \boldsymbol{C H}_{2}=\boldsymbol{C H}-\boldsymbol{C H}_{2}-\boldsymbol{B r} \)
III. \( \boldsymbol{C H}_{3}-\boldsymbol{C H}(\boldsymbol{B r}) \boldsymbol{C H}_{3} \)
Select the correct answer from the
codes below below.
A. \( I, \) II and II
в. \( I, \) II and \( I V \)
c. \( I I, \) III and \( I V \)
D. I, III and IV


Prove that: \( 2 \tan ^{-1} x=\tan ^{-1} \frac{2 x}{1-x^{2}} \)


Which of the following relations are false?
This question has multiple correct options
A \( \cdot \tan \left|\tan ^{-1} x\right|=x \)
B . \( \cot \left|\cot ^{-1} x\right|=|x| \)
c. \( \tan ^{-1}|\tan x|=|x| \)
D \( \cdot \sin \left|\sin ^{-1} x\right|=|x| \)


With what minimum acceleration can a
fireman slide down a rope whose breaking strength is \( 3 / 4 \) th of his weight ?
A \( \cdot 1 / 4 \mathrm{g} \)
B. \( 1 / 2 g \)
c. \( 3 / 4 g \)
D. zero


A temperature difference of \( 15^{\circ} \mathrm{C} \) on the
Fahrenheit scale is
A \( \cdot 27^{\circ} \)
В. \( 59^{\circ} \)
c. \( -27^{\circ} \)
\( D \cdot-59^{o} \)


An electric iron draws a current of \( 15 A \)
from a \( 220 V \) supply. What is the cost of using iron for 30 min everybody for 15 days if the cost of unit is 2 rupees?
\( (1 u n i t=1 k W h) \)
A . Rs 49.50
B. Rs 60
c. Rs 40
D. Rs 10


Haemoglobin is a complex of \( \boldsymbol{F e}(\boldsymbol{I} \boldsymbol{I}) \)
bound to porphyrin rings. If true enter 1 , else enter 0 .


How many electronic charges from 1 coulomb?
A. \( 9.1 \times 10^{-31} \)
B . \( 1.6 \times 10^{18} \)
c. \( 62.5 \times 10^{17} \)
D. \( 1.76 \times 10^{11} \)


How do the characteristics of mother
and father get transmitted in a human
body?


The relation between \( \theta, b \) and \( D \) is:
(where \( \theta \) is the parallax angle, \( b \) is the distance between two points of separation, \( D \) is the distance of source from any point of observation)
A \( \cdot \theta=\frac{b}{D} \)
B. \( \theta=\frac{D}{b} \)
c. \( \theta=b \times D \)
D \( \cdot \theta=b^{2} \times D \)


In the following figure, the radius of the
circle is \( 7 \mathrm{cm} \) and \( m(a r c R Y S)=30^{\circ} \)
find find:
Area of the circle


Solve the following system of equations
for \( \boldsymbol{x} \) \& \( \boldsymbol{y} \)
\( \frac{5}{x-1}+\frac{1}{y-2}=2, \frac{3}{x-1}=1 \)


For high frequency a capacitor offer
A. more reactance
B. less reactance
c. zero reactance
D. inifinite reactance


Motion of the earth around the sun is
A. periodic
B. non- periodic
c. oscillatory
D. linear


If the mole fraction of a solute is
changed from \( \frac{1}{4} \) to \( \frac{1}{2} \) by adding some
solute in 800 g of \( H_{2} O \) solvent, then the ratio of molarity of two solutions will be:
A . 1: 3
B. 1: 4
\( c \cdot 2: 3 \)
D. 1: 2


Which part of the soap \( \left(R C O O^{-}\right) \) dissolves grease and forms micelle?
A. \( R \) part (called tail of the anion)
B. \( C O O^{-} \) part (called head of the anion)
c. both A and B
D. none of these


A wheel has diameters \( 84 \mathrm{km} \). Find how
many complete revolution must it take
to cover 792 meters


The monomers of a polyribonucleotide
are
A. Deoxyribonucleotides
B. Ribonucleosides
c. Polypeptides
D. Ribonucleotides


Which of the following transitions
involves maximum amount of energy?
\( \mathbf{A} \cdot M_{(s)} \rightarrow M_{(g)} \)
\( \mathbf{B} \cdot M_{(g)} \rightarrow M^{+}(g) \)
\( \mathbf{c} \cdot M^{+}(g) \rightarrow M^{2+}(g) \)
D. \( M^{2+}(g) \rightarrow M^{3+}(g) \)