State whether the given statement is
true or false:

A solution of a substance \( X \) is used for
white washing. The reaction of the
substance \( X \) is with water is:
\( \boldsymbol{C a O}(\boldsymbol{s})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \rightarrow \)
Calcium oxide
\( \boldsymbol{C} \boldsymbol{a}(\boldsymbol{O} \boldsymbol{H})_{2}(\boldsymbol{a} \boldsymbol{q}) \)
Calcium hydroxide
A. True
B. False


f \( P=(1,2,3) \) and \( Q=(4) \) find sets
\( \boldsymbol{P} \times \boldsymbol{Q} \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \boldsymbol{Q} \times \boldsymbol{P} \)


If the road is banked, then there should
be a range of velocities which is
permissible. Write the permissible velocities.


The source of energy for carbon assimilation is
A. sunlight
B. water
c. chlorophyll
D. \( C O_{2} \)


A planet revolves around the sun in an
orbit with an eccentricty \( =0.99, \) the orbit is:
A. almost circular
B. almost elliptical
c. almost straight
D. parabolic


The parking charges of a vehicle in a
shopping centre is \( R s 40 \) for first 2
hours and \( R s 5 \) for each subsequent
hour. Write an equation for 8 hours.


If \( \boldsymbol{x}+\frac{\mathbf{1}}{\boldsymbol{x}}=\mathbf{2}, \) then what is the value of
\( \boldsymbol{x}^{64}+\boldsymbol{x}^{121} ? \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. - -


Name the two types of cytokinesis.


Why is electrostatic potential constant throughout the volume of the conductor and has the same value (as inside) on
its surface?


Which of the following expressions is
true?
\( \mathbf{A} \cdot H_{f}^{o}(C O, g)=\frac{1}{2} \Delta H_{f}^{o}\left(C O_{2}, g\right) \)
B \( \cdot \Delta H_{f}^{o}(C O, g)=\Delta H_{f}^{o}(C, \text { graphite })+\frac{1}{2} \Delta H_{f}^{o}\left(O_{2}, g\right) \)
C \( \cdot \Delta H_{f}^{o}(C O, g)=\Delta H_{f}^{o}\left(C O_{2}, g\right)-\frac{1}{2} \Delta H_{f}^{o}\left(O_{2}, g\right) \)
D. \( \Delta H_{f}^{o}(C O, g)=\Delta H_{\text {comb}}^{o}(C, \text { graphite})-\Delta H_{\text {comb}}^{o}(C O, g) \)


A fighter plane flying horizontally at an altitude of \( 1.5 k m \) with speed \( 720 k m / h \) passes directly overhead an anti-aircraft gun. At what angle from the vertical should the gun be fired for
the shell with muzzle speed 600 ms\( ^{-1} \) to hit the plane ? At what minimum altitude should the pilot fly the plane to avoid being hit ? Take \( g=10 m s^{-2} \)


The area of the region(s) enclosed by the curves \( y=x^{2} \) and \( y=\sqrt{|x|} \) is:
\( A \cdot 1 / 3 \)
B. 2/3
\( c \cdot 1 / 6 \)
D.


f \( 2 x-1=14-x \), then \( x= \)
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
c. 9
D.


Give a clear idea about how
\( M n O_{4}^{-}, C r O_{4}^{2-}, C r_{2} O_{7}^{2-} \) changes its
oxidation state when it is in the acidic,
basic and neutral medium.


What is the product obtained when
carbon tetrachloride reacts with water?
A. \( C H_{3} O H \)
в. \( C H_{3} C l \) and \( H C l \)
c. \( C O_{2} \) and \( H C l \)
D. No reaction takes place


The strength of an acid refers to its ability or tendency to lose a:
A . electron
B. proton
c. neutron
D. none of above


Evaluate the following definite integrals
\( \int_{0}^{1} \frac{1}{1+x^{2}} d x \)


Assertion
The order of the differential equation
whose solution is \( \boldsymbol{y}=\boldsymbol{c}_{1} \boldsymbol{e}^{2 \boldsymbol{x}+\boldsymbol{c}_{2}}+ \)
\( c_{3} e^{2 x+c_{4}} \) is 4
Reason
Order of the differential equation is the order of the highest order derivative occurring in the differential equation.
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


Natural gas is composed primarily of:
A. Methane
B. n-butane
c. n-octane
D. a mixture of octanes


\( \sum_{n=0}^{\infty}(-1)^{n} \frac{x^{2 n+1}}{2 n+1} \) is equal to
\( (-1<x<1) \)
A \( \cdot \tan ^{-1} x-x+c \)
B \( \cdot \log (1+x) \)
c. \( \frac{1}{1-x}+\frac{1}{1+x} \)
\( \mathbf{D} \cdot \sin ^{-1} x \)


Verify that: \( ^{10} C_{4}+^{10} C_{3}=^{11} C_{4} \)


The value of \( 1+2+4+8 \ldots . \) of G.P.
where \( n=6 \) is
A . 61
B. 62
\( c \cdot 63 \)
D. 64


Write the formula to calculate the
molality.


Which of the following is not a physical change?
A. Boiling of water to give water vapour
B. Melting of ice to give water
c. Dissolution of salt in water
D. combustion of Liquefied Petroleum Gas (LPG)


Vertical displacement of a plank with a body of mass 'm' on it is varying according to law \( y=\sin \omega t+\sqrt{3} \cos \omega t \)
The minimum value of \( \omega \) for which the
mass just breaks off the plank and the
moment it occurs first after \( t=0 \) are
given by: ( y is positive vertically upwards)
A \( \cdot \sqrt{\frac{g}{2}}, \frac{\sqrt{2}}{6} \frac{\pi}{\sqrt{g}} \)
В \( \cdot \frac{g}{\sqrt{2}}, \frac{2}{3} \sqrt{\frac{\pi}{g}} \)
c. \( \sqrt{\frac{g}{2}}, \frac{\pi}{3} \sqrt{\frac{2}{g}} \)
D \( \cdot \sqrt{2 g}, \sqrt{\frac{2 \pi}{3 g}} \)


Write down the formula of the
compound formed between \( C \) and \( D \)
A \( . C D \)
в. \( C D_{2} \)
\( c \cdot C_{2} D \)
D. \( C D_{3} \)


The molar conductivities of \( K C l, N a C l \)
and \( K N O_{3} \) are 152,128 and 111
Scm \( ^{2} \) mol \( ^{-1} \) respectively. What is the
molar conductivity of \( N a N O_{3} ? \)


The velocity of progressive wave which produces the stationary wave, \( y=2 \)
\( \sin \left(\frac{\pi x}{100}\right) \cos (\pi t) \mathrm{m}: \)
A. \( 100 m / s \)
в. \( 1 \mathrm{m} / \mathrm{s} \)
c. \( 50 m / s \)
D. \( 1000 \mathrm{m} / \mathrm{s} \)


A projectile has velocity \( V=(6 \hat{i}+ \) \( 4 \hat{j}) m / s \) at height of \( 1 m \) from horizontal Then angle of projection is
A \( .30^{\circ} \)
B. \( 37^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 60^{\circ} \)


Which of the following structure is most
expected for molecule \( X e O F_{4} ? \)
A. Tetrahedral
B. Square pyramidal
c. Square planar
D. Octahedral


Method by which information reaches
from DNA to RNA is
A. Transcription
B. Translation
c. Transformation
D. Transduction


Epithelial cells with cilia are found in
of our body
A. Digestive tract
B. Urinary tract
c. Respiratory tract
D. None of the above


Nicotiana and potato belongs to
A. Malvaceae
B. Liliaceae
c. Solanaceae
D. Cruciferae


With respect to the figure, write all
pairs of adjacent angles and all the linear pairs.
This question has multiple correct options
A. Adjacent angles: \( \angle A O D \& \angle C O D \)
B. Adjacent angles: \( \angle B O C \& \angle C O D \)
C. Linear pairs: \( \angle A O D \& \angle B O D \)
D. Linear pairs: \( \angle A O C \& \angle B O C \)


A manufacturer produces nuts and bolts. It takes 1 hour of work on
machine \( A \) and 3 hours on machine \( B \)
to produce a package of nuts. It takes 3 hours on machine \( A \) and 1 hour on
machine \( B \) to produce a package of bolts. He earns a profit of \( R s .17 .50 \) per
package on nuts and \( R s .7 .00 \) per
package on bolts. How many packages of each should be produced each day so as to maximise his profit, if he operates
his machines for at the most 12 hours a
day?


If the unit of rate constant of a reaction
is \( m o l^{-1} L S^{-1} \) then mention its order.


\( \frac{h}{2 \pi} \) is angular momentum in orbit of \( \boldsymbol{H} \boldsymbol{e}^{+} \)
A . first
B. second
c. third
D. infinite


The framework system of classification in which various taxonomic categories are arranged in order of logical sequence is called
A. Systematics
B. Classification
c. Hierarchy
D. taxon


What is the oxidation number of
underlined element?
\[
\boldsymbol{B} \boldsymbol{a}\left(\boldsymbol{H}_{2} \underline{\boldsymbol{P}} \boldsymbol{O}_{2}\right)_{2}
\]


Study the given statements and select
the correct answer.
(I) Lipids are macromolecules but obtained under-macromolecular
fraction due to their insoluble nature in
the aqueous medium of a cell.
(II) Water is the most abundant
chemical in a living organism.
(III) The first respiratory substrate is lipid.
(IV) Dihydroxyacetone occurs in d and I form.
A. I, II and IV are correct
B. I, II \& III are correct
c. I, I lare correct
D. III and IV are correct


The possible structure(s) of
monothiocarbonate ion is:
\( A \)
B.
\( c \)
D.


Which statement best explains why a
rubber rod becomes negatively charged
when rubbed with fur?
A. The rubber that the rod is made of is a better insulator than fur.
B. The fur is a better insulator than the rubber.
C. Molecules in the rubber rod have a stronger attraction for electrons than the molecules in the fur.
D. Molecules in the fur have a stronger attraction for electrons than the molecules in the rubber rod.


In 3 mins a total charge of \( 108 c \) flows through a bulb when it is connected to a cell. Find the electric current flowing through the bulb.
\( \mathbf{A} \cdot 36 A \)
в. \( 0.6 A \)
\( c .1 .8 A \)
D. None


Arrange the following in increasing order of lattice energy:
\( \mathrm{NaF}, \mathrm{NaCl}, \mathrm{NaBr}, \mathrm{Nal} \)
A. \( N a I<N a B r<N a C l< \) NaF
в. \( N a F<N a C l<N a B r<N a I \)
c. \( N a I<N a C l<B a B r<N a F \)
D. None of these


An electrical device operate at 12 A current and \( 120 \mathrm{V} \) D.C. If it is connected
with \( 250 \mathrm{V} \) and \( 30 \mathrm{Hz} \) AC. then power consumption:
A. 625 w
B. 1250 W
\( c . \) 6250 \( w \)
D. zero


Quiescent centre is present in
A. Shoot apex
B. Root apex
c. Both A and B
D. Meristematic tissue


For the system shown in the figure, the
cylinder on the left at \( L \) has a mass of
\( 600 k g \) and a cross sectional area of
\( 800 \mathrm{cm}^{2} . \) The piston on the right, at \( S \)
has a cross sectional area \( 25 \mathrm{cm}^{2} \) and
negligible weight. If the apparatus is
filled with oil. \( \left(\rho=\mathbf{7} \mathbf{5} g \boldsymbol{m} / \mathbf{c m}^{3}\right) \) Find
the force \( \boldsymbol{F} \) required to hold the system
in equilibrium.


Solve \( \lim _{x \rightarrow 0} \frac{\sin 4 x}{\sin 2 x} \)


Assertion
Steel is more elastic than rubber.
Reason
For same strain, steel requires more stress to be produced in it
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


List- List-II
A) \( H_{3} P O_{2} \)
1) Tribasic
B) \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3} \)
2) Mono
basic
C) \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \)
3
Tetrabasic
D) \( \boldsymbol{H}_{4} \boldsymbol{P}_{2} \boldsymbol{O}_{6} \)
4) Di-
basic
The correct match is :
A \( . \) A-3, \( B \) -2, \( c-1, D-5 \)
B. A-2, B-4, C-1, D-3
c. \( A-2, B-5, C-3, D-4 \)
D. A-1, B-2, C-3, D-4


Match the following list of animals with their level of organization.
Division of Labour Animal What is and
organ level A. Organ level Pheritima
B. Cellular aggregate level
ii. Fasciola
c. Tissue level
D. organ system level
¡v. Obelia
Choose the correct match showing division of labour with animal example.
A. i-B, ii-C, iii-D, iv-A
B. i-B, ii-D, iii-C, iv-A
c. i-D, ii-A, iii-B, iv-C
D. i-A, ii-D, iii-C, iv-B


\( \boldsymbol{A}=\left[\begin{array}{cc}\boldsymbol{a} & \boldsymbol{b} \\ \mathbf{0} & \boldsymbol{c}\end{array}\right] \) then \( \boldsymbol{A}^{-1}+(\boldsymbol{A}-\boldsymbol{a} \boldsymbol{I})(\boldsymbol{A}-1) \)
\( \boldsymbol{c} \boldsymbol{I})= \)
A \( \cdot \frac{1}{a c}\left[\begin{array}{cc}a & b \\ 0 & -c\end{array}\right] \)
в. \( \frac{1}{a c}\left[\begin{array}{cc}-a & b \\ 0 & c\end{array}\right] \)
c. \( \frac{1}{a c}\left[\begin{array}{cc}c & -b \\ 0 & a\end{array}\right] \)
D \( \cdot \frac{1}{a c}\left[\begin{array}{cc}c & b \\ 0 & a\end{array}\right] \)


The product of \( r \) consecutive integers is
divisible by \( r ! \)
A. True
B. False


The sequence of reagent which can efficiently bring about the above conversion is (are) ?
Consider the following synthesis
This question has multiple correct options
A. \( B r_{2} \) -hv/heat
B . \( B r_{2} \) -hv/heat, \( C_{2} H_{5} O N a / C_{2} H_{5} O H ; N B S- \) \( h v ; B_{2} H_{6}-T H F \) then \( C H_{3} C O O H \)
C. \( B r_{2} \) -hv/heat \( ;\left(C H_{3}\right)_{3} C O N a-\left(C H_{3}\right)_{3} C O H H B r- \)
ROOR
D. NBS-hv/CCl_


is the additive used in
transparent soaps.
A. Potassium bicarbonate
B. Stearic acid
c. Salicyclic acid
D. Glycerine


Compund \( (C) \) is :
\( A \)
\[
\begin{array}{c}
\mathrm{OH} \\
\mathrm{CH}_{3}-\mathrm{CH}-\mathrm{CH}_{2}-\mathrm{CH}-\mathrm{CH}_{3} \\
\mathrm{Cl}
\end{array}
\]
в. \( H O C H_{2}-C H_{2}-C H_{2}-C H_{2}-C H_{2}-C H_{2}-C l \)
\( c \)
\[
\mathrm{HO}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{CH}-\mathrm{CH}_{3}
\]
\( D \)
\[
\mathrm{HO}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\underset{\mathrm{Cl}}{\mathrm{CH}}-\mathrm{CH}_{2}-\mathrm{CH}_{3}
\]


Which of the following vitamin is insoluble in water and fat both?
A.
B.
\( c \cdot H \)
D.


The reason for not storing \( X e F_{6} \) in a glass or a quartz vessel is that:
A . It forms an explosive having the formula \( X e O_{2} F_{2} \)
B. It forms an explosive having the formula \( X e O F_{4} \)
c. It forms \( X e O_{2} \) which is explosive substance
D. It forms \( X e O_{6}^{4-} \) which is explosive in nature


Which is the major constituent of gun
powder?
A. Nitre
B. Sulphur
c. charocal
D. Chile salt petre


The slope of current (I) versus voltage
(V) is called:
A . resistance
B. resistivity
c. conductivity
D. conductance


The most important function of villi in
the small intestine is
A. To provide strength to the intestine
B. To provide space for capillaries and lacteals
C . To provide increased surface area for absorption of digested food
D. To provide habitat for bacteria


If \( \vec{A}=\vec{B}+\vec{C} \) and the magnitude of
\( A, B \) and \( C \) are 5,4 and 3 minutes
respectively,then the angle between \( \boldsymbol{A} \) and \( C \) is:
A \( \cdot \cos ^{-1}(4 / 5) \)
B \( \cdot \cos ^{-1}(3 / 5) \)
c. \( \tan ^{-1}(3 / 4) \)
D \( \cdot \sin ^{-1}(3 / 5) \)


Three infinitely long charge sheets are
placed as shown in the figure. The
electric field at point \( P \) is going to be
\( A \)
B. \( -\frac{2 \sigma}{\varepsilon_{0}} \)
\( c \)
D.


The properties which repeats repeatedly
at a regular interval is called
A. Diagonal properties
B. Anomalous properties
c. Periodic properties
D. None


A uniform rod \( A B \) of mass \( m \) and length is at rest on a smooth horizontal
surface. An impulse J is applied to the end B perpendicular to the rod in horizontal direction. Speed of particle \( P \)
at a distance I/6 from the centre
towards \( A \) of the rod after time \( t=\frac{\pi m l}{12 J} \)
is
A \( \cdot_{2} \frac{J}{m} \)
B. \( \frac{J}{\sqrt{2} m} \)
c. \( \frac{J}{m} \)
D. \( \sqrt{2} \frac{J}{m} \)


In cell cycle, during interphase,
A. Two daughter cells are produced.
B. The nucleus is divided into two daughter nuclei
c. The chromosome condenses
D. The DNA is replicated.


An iron tyre \( 100 \mathrm{cm} \) in diameter is to be fitted on to a wooden wheel of \( 100.4 \mathrm{cm} \)
in diameter if \( \alpha \) of Iron is \( 1 \times 10^{-5} /^{\circ} C \)
the temperature increase required for this purpose is :
A \( \cdot 40^{\circ} \mathrm{C} \)
B . \( 100^{\circ} \mathrm{C} \)
c. \( 400^{\circ} \mathrm{C} \)
D. \( 1000^{\circ} \mathrm{C} \)


Which of the following gives nitrogen on thermal decomposition?
This question has multiple correct options
A. Ammonium nitrite
B. Ammonia
c. Ammonium dichromate
D. Air


Assertion
Alkali metals cannot be prepared by electrolysis of their chlorides in
aqueous solution.
Reason
Reduction potentials of alkali metal
cations is much lower than that of \( \boldsymbol{H}^{+} \)
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 cell,
\( Z n\left|Z n^{2+}(1 M) \| C u^{2+}(1 M)\right| C u, \) was
allowed to be completely discharged at 298 K. The relative concentration of \( Z n^{2+} \) to \( C u^{2+}\left(\frac{\left[Z n^{2+}\right]}{\left[C u^{2+}\right]}\right) \) is :
\( \left[\boldsymbol{E}_{c e l l}^{0}=\mathbf{1 . 1 0} \boldsymbol{V}\right] \)
\( \mathbf{A} \cdot 9.65 \times 10^{4} \)
B . antilog (24.08)
c. 37.3
D. \( 10^{37.3} \)


\( \cos \theta+\frac{1}{3} \cos ^{3} \theta+\frac{1}{5} \cos ^{5} \theta+\ldots= \)
\( \mathbf{A} \cdot \log (\tan \theta) \)
B. \( \log (\cot \theta) \)
\( ^{\mathbf{c}} \cdot \log \left(\tan \frac{\theta}{2}\right) \)
D. \( \log \left(\cot \frac{\theta}{2}\right) \)


Diethylene triamine is :
A. chelating agent.
B. polydentate ligand
c. tridentate ligand
D. All of these.


Which of the following changes
represents a disproportional
reaction(s)?
\( \mathbf{A} \cdot C l_{2}+2 O H^{-} \rightarrow C l O^{-}+C l^{-}+H_{2} O \)
B. \( C u_{2} O+2 H^{+} \rightarrow C u+C u^{2+}+H_{2} O \)
\( \mathbf{C} \cdot 2 H C u C l_{2} \frac{\text {dilution with}}{\text {water}} C u+C u^{2+}+4 C l^{-}+2 H^{+} \)
D. All of the above


Increasing order of magnetic moment among the following species is:
\( N a^{+}, F e^{+3}, C o^{+2}, C r^{+2} \)
A. \( N a^{+}<C o^{2+}<C r^{2+}<F e^{3+} \)
B. \( N a^{+}<F e^{3+}<C r^{2+}<C o^{2+} \)
c. \( C r^{2+}<C o^{2+}<N a^{+}<F e^{3+} \)
D. \( C o^{2+}<N a^{+}<C r^{2+}<F e^{3+} \)


What is the national tree of India?
A. Ficus religiosa
B. Mangifera indica
c. Ficus benghalensis
D. Azadirachta indica


A sum of money at compound interest amounts to Rs. 10580 in 2 years and to
Rs. 12167 in 3 years. The rate of interest
per annum is
A . \( 12 \% \)
B . \( 14 \% \)
\( c .15 \% \)
D. \( 16 \frac{2}{3} \% \)


Write the following in the expanded
form:
\( (x+2 y+4 z)^{2} \)


A tank of large base area is filled with
water up to a height of 5 m. A hole of
\( 2 \mathrm{cm}^{2} \) cross section section in the
bottom allows the water to drain out in
continuous streams. For this situation,
mark out the correct statement(s) (take
\[
\left.\boldsymbol{\rho}_{\boldsymbol{w} \boldsymbol{a} \boldsymbol{t} e r}=\mathbf{1 0 0 0} \boldsymbol{k} \boldsymbol{g} /^{2}, \boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} / \boldsymbol{s}^{2}\right)
\]
This question has multiple correct options
A. The cross sectional area of the emerging stream of water decreases as it falls down
B. The cross sectional area of the emerging stream of water increases as it falls down
C. At a distance of \( 5 \mathrm{m} \) below the bottom of the tank, the
cross-sectional area of the stream is \( 1.414 \mathrm{cm}^{2} \)
D. At a distance of \( 5 m \) below the bottom of the tank, the cross-sectional area of the stream is \( 2.86 \mathrm{cm}^{2} \)


Find the principal value of the following
\( \tan ^{-1}\left(\tan \frac{3 \pi}{4}\right) \)


An ideal solution was obtained by mixing methanol and ethanol. If the partial vapour pressure of methanol
and ethanol are \( 2.619 \mathrm{kPa} \) and \( 4.556 \mathrm{kPa} \)
respectively, the composition of vapour (in terms of mole fraction) will be:
A. 0.635 Меон, 0.365 Еtон
B. 0.365 МеОН, 0.635 Еtон
c. 0.574 МеОН, 0.326 Еtон
D. 0.173 МеОН, 0.827 Еtон


A simple pendulum completes 40 oscillation in a minute.Find its (a)
frequency
(b) time period.


The potential difference between \( A \) and
\( B \) in the circuit shown in figure will be
A . \( 1 V \)
в. \( 2 V \)
\( c .3 V \)
D. \( 4 V \)


Assertion
pH of blood does not change inspite of taking acidic foods.
Reason
Blood behaves as buffer solution.
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


Find the equation of the tangent line to
the curve \( y=x^{2}-2 x+7 \) which
is perpendicular to the line \( 5 y-15 x= \)
\( \mathbf{1 3} \)


Identify the constituents of soil
A. Gravel
B. Salt
c. мineral
D. All of the above


Find the 12 th term from the last term of
the A.P. \( 2,6,10 \ldots . .58 \)
A . 110
B. 102
\( c \cdot 160 \)
D. 120


The rest energy involved in a mass of
one atomic mass unit is
\( \mathrm{eV} \)
A. \( 931 \mathrm{MeV} \)
B. 1.6 ev
\( \mathrm{c} .9 .3 \mathrm{MeV} \)
D. 9.


A functional isomer of 1-butyne is:
A. 2-butyne
B. 1-butene
c. 2-butene
D. 1,3-butadiene


In half-wave rectification, what is the
output frequency if the input frequency
is \( 50 H z \)

What is the output frequency of a fullwave rectifier for the same input
frequency.


how many people (in millions) have
preferred to play Tennis in all the years
altogether?
(Preferences of people in playing different games over the years.)
A . 3200
В. 2100
c. 1200
D. 1700


If \( \boldsymbol{A}=\left[\begin{array}{cc}2 & \boldsymbol{4} \\ -\mathbf{1} & \boldsymbol{k}\end{array}\right] \) and \( \boldsymbol{A}^{2}=\mathbf{0}, \) find \( \boldsymbol{k} \)


Let \( \boldsymbol{E} \) and \( \boldsymbol{F} \) be events with \( \boldsymbol{P}(\boldsymbol{E})= \)
\( \frac{3}{5}, P(F)=\frac{3}{10} \) and \( P(E \cap F)=\frac{1}{5} . \) Are
\( E \) and \( F \) independent?
A. True
B. False


Find the area of the given parallelogram


Arrange the following bonds according
to their average bond energies in
descending order:
\( \boldsymbol{C}-\boldsymbol{C l}, \boldsymbol{C}-\boldsymbol{B r}, \boldsymbol{C}-\boldsymbol{F}, \boldsymbol{C}-\boldsymbol{I} \)
A. \( C-B r>C-I>C-C l>C-F \)
B. \( C-F>C-C l>C-B r>C-I \)
c. \( C-I>C-B r>C-C l>C-F \)
D. \( C-C l>C-B r>C-I>C-F \)
\( F \)


Solve:
\( \int_{0}^{1} \frac{\boldsymbol{d} \boldsymbol{x}}{\sqrt{\boldsymbol{x}+\mathbf{1}}+\sqrt{\boldsymbol{x}}} \boldsymbol{d} \boldsymbol{x}= \)
A \( \cdot \frac{4}{3}(\sqrt{2}+1) \)
B. \( \frac{4}{3}(\sqrt{2}-1) \)
c. \( \frac{3}{4}(\sqrt{2}-1) \)
D. \( \frac{3}{4}(\sqrt{2}-2) \)


Bleaching powder loses its power on
keeping for a long time because:
A. it changes into calcium hypochlorate
B. it changes into calcium chloride and calcium hydroxide
C. it absorbs moisture
D. it changes into calcium chloride and calcium chlorate


When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy supplied which increases the internal energy of the gas is:
\( A \cdot\left(\frac{2}{5}\right) \)
B. \( \left(\frac{3}{5}\right) \)
\( c \cdot\left(\frac{3}{7}\right) \)
D. \( \left(\frac{5}{7}\right) \)


The number of vibrations made by a
vibrating body in one second is called
its :
A. wavelength
B. time period
c. amplitude
D. frequency


Let \( A \) and \( B \) be sets containing 2 and 4 elements respecetively. The number of subsets \( \boldsymbol{A} \times \boldsymbol{B} \) having 3 or more
elements is
A . 219
в. 211
c. 256
D. 220


One diagonal of a parallelogram is
\( 40 \mathrm{cm} \) and the perpendicular distance of
this diagonal from either of the outlying
vertices is \( 19 \mathrm{cm} . \) The area of the
parallelogram (in sq. cm) is
4. \( 700 \mathrm{cm}^{2} \)
\( 3 \cdot 380 c m^{2} \)
\( c \cdot 760 c m^{2} \)
) \( 1140 \mathrm{cm}^{2} \)


\( \lim _{x \rightarrow 0} \frac{\sqrt{2+x}-\sqrt{2}}{x} \)


The element which, forms oxides in all
oxidation states varying from +1 to +5 is:
A. \( N \)
в. \( P \)
c. \( A s \)
D. \( S b \)


Two adjacent sides of a parallelogram
are \( 10 \mathrm{cm} \) and \( 12 \mathrm{cm} . \) If one diagonal of
it is \( 16 \mathrm{cm} \) long; find area of the parallelogram. Also, find distance between its shorter sides.
A \( \cdot 119.8 \mathrm{cm}^{2} ; 11.42 \mathrm{cm} \)
В. \( 136.74 \mathrm{cm}^{2} ; 19.58 \mathrm{cm} \)
c. \( 127 \mathrm{cm} ; 5.85 \mathrm{cm} \)
D. None of these


Difference between a rupee and \( 1 \% \) of a
rupee is
A. 99 paise
B. 1.01 paise
c. 11 paise
D. None


Sodium metal can be stored under:
A. benzene
B. kerosene
\( c . \) alcoho
D. water


When the light of frequency \( 2 v_{0} \) (where
\( v_{0} \) is threshold frequency), is incident
on a metal plate, the maximum velocity
of electrons emitted is \( v_{1} \). When the
frequency of the incident radiation is
increased to \( 5 v_{0}, \) the maximum velocity
of electrons emitted from the same
plate is \( v_{2} \). The ratio of \( v_{1} \) to \( v_{2} \) is?
A . 4: 1
B. 1: 2
c. 2: 1
D. 1: 4


Thermistor material is pressed
A. under zero pressure
B. under low pressure
c. under high pressure
D. under low volume


The elongation of a steel wire stretched
by a force is 'e'. If a wire of the same material of double the length and half the diameter is subjected to double the force, its elongation will be
A. \( 16 e \)
B . \( 4 e \)
c. \( \left(\frac{1}{4}\right) e \)
D. \( \left(\frac{1}{16}\right) \)


Find the sum of the series whose nth
term is :
\( \boldsymbol{n}^{3}-\boldsymbol{3}^{n} \)


The diagram below shows two sources,
\( A \) and \( B, \) vibrating in phase in the same
uniform medium and producing
circular wave fronts.
Which phenomenon occurs at point \( P ? \)
A. Destructive interference
B. Constructive interference
C . Refletion
D. Refraction


Which 3 has greater place value 64.363
\( ? \)
A. 3 at one tenth place.
B. 3 at one hundredth plcae
c. both have equal
D. can not say


Four point charges \( \boldsymbol{q}_{\boldsymbol{A}}=\boldsymbol{2 \mu} \boldsymbol{C}, \boldsymbol{q}_{B}= \)
\( \mathbf{5} \mu C, \boldsymbol{q}_{C}=2 \mu C, \boldsymbol{q}_{D}=5 \mu C \) are located
at the four corners of a square ABCD of side \( 10 \mathrm{cm} . \) The force on a charge of
\( 1 \mu C \) placed at the centre of the square
is
A. zero
B. Towards AB
c. Towards BC
D. Towards AD


Lothar Meyer obtained the curve for the
known elements by plotting their atomic volumes against:
A. atomic numbers
B. atomic masses
c. densities
D. ionization energies


In the DNA molecule
A. The proportion of adenine in relation of thymine varies with the organism.
B. There are two strands which run antiparallel one in \( 5^{\prime} \) \( \rightarrow 3^{\prime} \) direction and other in \( 3^{\prime} \rightarrow 5 \)
C. The total amount of purine nucleotides and pyrimidine nucleotides is not always equal.
D. There are two strands which run parallel in the \( 5^{\prime} \rightarrow 3^{\prime} \) direction.


Which of the following is an allotropic form of carbon?
A. Diamond
B. Graphite
c. Fullerence
D. All of these


A gas mixture consists of 2 moles of
oxygen and 4 moles of Argon at temperature T. Neglecting all
vibrational moles, the total internal
energy of the system is
A . \( 4 \mathrm{RT} \)
в. 15RT
c. 9 RT
D. 11RT


If the scalar projection of the vector \( x \hat{i}-\hat{j}+\hat{k} \) on the vector \( 2 \hat{i}-\hat{j}+5 \hat{k} \) is
\( \frac{1}{\sqrt{30}}, \) then value of \( x \) is equal to
A \( \cdot \frac{-5}{2} \) units
B. 6 units
c. -6 units
D. 3 units


The reaction between \( H_{2} O_{2} \) and
\( \boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4} \) is \( \boldsymbol{2} \boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4}+\boldsymbol{3} \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}+ \)
\( \mathbf{5} \boldsymbol{H}_{2} \boldsymbol{O}_{2} \rightarrow \boldsymbol{K}_{2} \boldsymbol{S} \boldsymbol{O}_{4}+\boldsymbol{2} \boldsymbol{M} \boldsymbol{n} \boldsymbol{S} \boldsymbol{O}_{4}+ \)
\( 8 H_{2} O+5 O_{2} \)
In a reaction excess of \( H_{2} O_{2} \) is added to
0.1 mole of acidified \( K M n O_{4} \) solution.
Then the STP volume of \( O_{2} \) liberated is:
A . 5.6
B. 6.6
c. \( 11.2 L \)
D. 22.4 L


Solve:
¡) \( \boldsymbol{y}=\boldsymbol{e}^{2 x}(\boldsymbol{a}+\boldsymbol{b} \boldsymbol{x}) \quad \boldsymbol{y}= \)
\( e^{x}(a \cos x+b \sin x) \)
ii) Form the differential equation of the family of circle touching the y-axis at origin.


Who first discovered nucleus in cell in
1831?
A. Robert Hooke
B. Robert Brown
c. Altmann
D. Swanson


Select the odd one out w.r.t. conduction
of heat (gold, silver, copper, asbestos)
A . asbestos
B. gold
c. silver
D. copper


Speed of sound is greater in solids than in liquids because.
A. The solids have high elasticity
B. The liquids have high elasticity
c. The atoms in solids are regularly arranged
D. The atom in liquids are closely packed


Two large, parallel conducting plates \( x \) and \( Y, \) kept close to each other, are given charges \( Q_{1} \) and \( Q_{2}\left(Q_{1}>Q_{2}\right) \). The
four surfaces of the plates are \( A, B, C \) and \( D, \) as shown in figure. Then :
This question has multiple correct options
A ' the charge on A is \( \frac{1}{2}\left(Q_{1}+Q_{2}\right) \)
B ' the charge on B is \( \frac{1}{2}\left(Q_{1}-Q_{2}\right) \)
c. The charge on \( c \) is \( -\frac{1}{2}\left(Q_{1}-Q_{2}\right) \)
D ' the charge on D is \( \frac{1}{2}\left(Q_{1}+Q_{2}\right) \)


A body of mass \( 3 k g \) hits a wall at an
angle of \( 60^{\circ} \) and returns at the same
angle. The impact time was 0.2 sec. The
fores exerted on the wall
B. \( 50 \sqrt{3} N \)
c. \( 100 N \)
D. \( 75 \sqrt{3} N \)


Two identical short magnets having magnetic moment M are placed perpendicular to each other centres
coinciding as shown in adjacent figure. The magnitude of the magnetic field at
a point \( P \) at angle distance 'd' on the bisector of right angle will be :
A. \( \frac{\sqrt{2} \mu_{0} M}{4 \pi d^{3}} \)
B. \( \frac{2 \sqrt{2} \mu_{0} M}{4 \pi d^{3}} \)
c. \( \frac{2 \mu_{0} M}{4 \pi d^{3}} \)
D. \( \frac{\sqrt{3} \mu_{0} M}{4 \pi d^{3}} \)


Write a chemical equation for photodecomposition reaction.


Balance the following equation.
\( \boldsymbol{F} \boldsymbol{e} \boldsymbol{S}_{2}+\boldsymbol{O}_{2} \rightarrow \boldsymbol{F} \boldsymbol{e}_{2} \boldsymbol{O}_{3}+\boldsymbol{S} \boldsymbol{O}_{2} \)


Two cars are travelling towards each other on a straight road at velocities \( 15 m / s \) and \( 16 m / s \) respectively. When
they are \( 150 \mathrm{m} \) apart, both the drivers
apply the brakes and the cars
decelerate at \( 3 m / s^{2} \) and \( 4 m / s^{2} \) until they stop. Separation between the cars
when they come to rest is :
\( \mathbf{A} \cdot 86.5 m \)
в. \( 89.5 m \)
c. \( 85.5 m \)
D. \( 80.5 m \)


Which of the following alkyl bromides will eliminate \( H B r \) fastest?
A. Ethyl bromide
B. Propyl bromide
c. Isopropyl bromide
D. t-Butyl bromide


\( \int_{0}^{1} \frac{\sqrt{x}}{1+x} d x= \)
A . \( 2-\pi / 2 \)
B. \( 1-\pi / 2 \)
c. \( \pi / 2 \)
D. \( 2+\pi / 2 \)


Assertion
\( 35 C l \) and \( _{17}^{37} C l \) have the same chemical
\( 17^{7} \)
properties.
Reason
Isotopes have the same number of
protons and electrons and the same
chemical reactions.
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


After electrolysis of a sodium chloride
solution with inert electrodes for a
certain period of time, \( 600 m L \) of the
solution was left which was found to be
\( 1 N \) in \( N a O H . \) During the same period
\( 31.75 g \) of copper was deposited in the copper voltameter in series with the
electrolytic cell. Calculate the percentage theoretical yield of \( N a O H \) obtained.


The voltage gain of an amplifier with 9 negative feedback is \( 10 . \) The voltage gain without feedback will be
A . 90
B. 100
c. 10
D. 1.25


When 3 L of \( 0.5 ~ M \) NaCl is mixed with
\( 9 \mathrm{L} \) of \( 0.2777 M N a C l, \) determine the
concentration of the final solution, assuming that volumes are additive?
A. 0.33 M .
В. 0.39 М
c. \( 0.5777 M \)
D. \( 0.7777 M \)
E. None of the above


is among the by-products when coal is carbonized to make coke.
A. Coal tar
B. coal
c. Carbon dioxide
D. All of above


Glycolysis takes place in the
A . Cytoplasm
B. Chloroplast
c. Ribosome
D. Mitochondria


When two bodies stick together after collision, the collision is said to be:
A. partially elastic
B. elastic
c. inelastic
D. perfectly inelastic


For every natural number \( n, n(n+3) \) is
always :
A. multiple of 4
B. multiple of 5
c. even
D. odd


The least number by which 216 must be divided to make the result a
perfect square, is
\( A \cdot 3 \)
B. 4
\( c \cdot 6 \)
D.


A particle starts from rest and moves with uniform acceleration. If covers a
displacement of \( y^{2}-x^{2} \) in the first
\( 10 \sec \) and \( y^{2}+x^{2} \) in the next first
\( 10 s e c, \) then
A \( . x=\sqrt{2} y \)
в. \( x=3 y \)
c. \( y=3 x \)
D. \( y=\sqrt{2} x \)


The length, breadth and thickness of a rectangular sheet of metal are \( 4.234 \mathrm{m} \) \( 1.005 \mathrm{m}, \) and \( 2.01 \mathrm{cm} \) respectively. Give
the area and volume of the sheet to
correct significant figures.


Which of the following types of forces bind together the carbon atoms in diamond?
A. Van der Waal's forces
B. lonic
c. covalent
D. Dipolar


Assertion: In a Daniell cell, electrons
flow from zinc electrode to copper
electrode outside the cell.
Reason: In Daniell cell, Zn electrode is
anode and Cu is cathode.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false


\( \left|\begin{array}{cc}\mathbf{2} & -\mathbf{4} \\ \mathbf{9} & \boldsymbol{d}-\mathbf{3}\end{array}\right|=\mathbf{4} \) then \( \boldsymbol{d}= \)
A . 1
B. -11
c. 12
D. -13


The gaseous reaction \( A_{2} \rightarrow 2 A \) is first
order in \( A_{2} . \) After 12.3 minutes \( 65 \% \) of
\( A_{2} \) remains undecompensed. \( 90 \% \) of \( A_{2} \)
? What is the half life of the reaction?


(a) How is Ozonised oxygen prepared in the laboratory? Give reason.
(b) Give the composition of "Oleum".


Where on the surface of the earth is the
vertical component of earth's Magnetic field zero.


energy in plants is used by man in the form of food.
A. Chemical
B. Electrical
\( c \cdot \) Bio
D. Physical


Perimeter of rectangle is- -
A \( .2(l \times b) \)
в. \( 2(l+b) \)
c. \( (l \times b \times h) \)
D. None of these


The shaded part in the given figure is
covered with cement. If its costs Rs. 84
to cement an area of \( 3 \mathrm{cm}^{2} \), find the
total cost of cementing.
A. Rs. 8820
B. Rs. 8125
c. Rs. 8610
D. Rs. 8804


Study the given graph and choose the
correct option.
A. \( \Delta H \) is the net heat absorbed from the surroundings
B. \( \Delta H \) is the net heat given to the surroundings
\( \mathrm{c} \cdot \Delta H \) is positive for the reaction
D. \( \Delta H \) is the total energy possessed by the reactants


In the case of a moving body, pick the
correct statement
A. if speed changes with change in direction, velocity does not change
B. if velocity changes, speed may or may not change but acceleration does change
C. if velocity changes, speed also changes with same acceleration
D. if speed changes without change in direction, the velocity may remain constant


The space between a proton and electron in hydrogen atom is :
A. full of air
B. full of ether
c. full of electromagnetic radiations
D. empty


Obtain an expression for magnetic flux density B at the centre of a circular coil of radius \( \mathrm{R} \), having \( \mathrm{N} \) turns and carrying
a current \( \boldsymbol{I} \)


\( 298 K \) is what temperature in
Fahrenheit?
A \( .76 .73 F \)
в. \( 80 F \)
\( c .75 F \)
D. \( 27 F \)


Which of the following statement is not
true for stomatal apparatus?
A. Guard cells are always surrounded by subsidiary cells
B. Stomata are involved in gaseous exchange
C. Inner walls of guard cells are thick
D. Guard cells invariably possess chloroplasts and mitochondria


The velocity \( v \) of a particle at time \( t \) is
given by \( v=a t+\frac{b}{t+c}, \) where \( a, b \) and \( c \)
are constants.The dimensions of
\( a, b \) and \( c \) are respectively:
\( \mathbf{A} \cdot \mathrm{LT}^{-2}, \mathrm{L} \) and \( \mathrm{T} \)
B. \( L^{2}, \) T and \( L T^{2} \)
c. \( L^{2} \), LT and \( L \)
D. L, LT and \( T^{2} \)


A plane flies 50 degrees east of south for \( 100 k m \) then \( 400 k m \) north and then
20 degrees north of west for \( 250 k m \)
What is the magnitude of the net displacement? (in km)
A . 335
в. 365
c. 395
D. 345


Hooke's law essentially defines
A. stress
B. strain
c. yeild point
D. elastic limit


Force \( 3 \mathrm{N}, 4 \mathrm{N} \) and \( 12 \mathrm{N} \) act at a point in mutually perpendicular directions. The magnitutde of the resultant force is :-
\( A \cdot 19 N \)
B. 13 N
c. \( 11 \mathrm{N} \)
D. 5 N


Expand \( (\sqrt{10} x-\sqrt{5} y)^{2} \) using
appropriate identity


Two straight parallel wires carrying current in the opposite directions repe each other, because of
A. Electrical force between them
B. Magnetic force between them
c. Gravitational force between them
D. Nuclear force between them


According to Robert Constanza, \( 50 \% \) of
the total cost of ecosystem services
goes to
A. Climate regulation
B. Soil formation
c. Recreation
D. Nutrient cycling


State the following statement is True or False \( \frac{15}{1600} \) has a terminating decimal expansion
A. True
B. False


Solve:
\( \frac{d y}{d x}=2 x^{2}+x ; \) find \( y \) when \( x=0 \)


A light ray falls on a mirror and deviates
by \( 30^{\circ}, \) then the angle of incidence will
be:
A .75
B. \( 60^{\circ} \)
\( c \cdot 90 \)
D. 180


Organic solids can be purified by:
A. steam distillation
B. crystallisation
c. fractional distillation
D. simple distillation


The diagonal BD of parallelogram ABCD
intersects \( A E \) at 'F'.' E' is any point on BC.
Prove that DE.EF = FB. FA


Get the algebraic expressions in the following case using variable, constants and arithmetic operations. One-half of the sum of numbers x and y


Which one of the following leads to redox reaction?
A. \( A g N O_{3}+H C l \)
в. \( K O H+H C l \)
c. \( K I+C l_{2} \)
D. \( N H_{3}+H C l \)


As shown in fig., an object \( O \) is at the
position (-10,2) with respect to the
origin \( P . \) The concave mirror \( M_{1} \) has
radius of curvature \( 30 \mathrm{cm} . \) A plane
mirror \( M_{2} \) is kept at a distance of
\( 40 \mathrm{cm} \) in front of the concave mirror


Three particles of masses \( 1 \mathrm{kg}, 2 \mathrm{kg} \) and \( 3 \mathrm{kg} \) are situated at the corners of the equilateral triangle move at speed \( 6 \mathrm{ms} \) \( -1,3 \mathrm{ms}^{-1} \) and \( 2 \mathrm{ms}^{-1} \) respectively
Each particle maintains a direction
towards the particle at the next corner symmetrically. Find velocity of COM of the system at this instant:
\( \mathbf{A} \cdot 3 m s^{-1} \)
B. \( 5 m s^{-1} \)
\( \mathrm{c} \cdot 6 \mathrm{ms}^{-1} \)
D. zero


When \( H_{2} S \) gas is passed through nitric acid, the product is:
A. rhombic sulphur
B. prismatic sulphur
c. amorphous sulphur
D. monoclinic sulphur
E. plastic sulphur


If monochromatic red light is replaced by green light, then the fringe width:
A . increases
B. remains same
c. can't say
D. decreases


Carbylamine test is performed in alcoholic \( K O H \) by heating a mixture of
A. chloroform and silver powder
B. trinalogenated methane and a primary amine
c. an alkyl halide and a primary amine
D. an alkyl cyanide and a primary amine


The least distance of distinct vision is
25cm. The focal length of a convex lens of a simple microscope is \( 5 \mathrm{cm} \). Its magnifying power if the image is at near point
\( A \cdot 4 \)
B. 5
\( c \cdot 6 \)
D.


Which of the following statements related to the modern periodic table is incorrect?
(a) The p-block has 6 columns because a maximum of 6 electrons can occupy
all
the orbitals in a p-shell
(b) The d-block has 8 columns because
a maximum of 8 electrons can occupy
all the orbitals in a d-subshell
(c) Each block contains a number of
columns equal to the number of electrons that can occupy that subshell
(d) The block indicates value of
azimuthal quantum number (I) for the last subshell that received electrons
in building up the electronic configuration


Resonance energy per benzene ring
decreases in the order
A. Naphthalene \( > \) benzene \( > \) Anthracene \( > \) Phenanthrene
B. Benzene \( > \) Nephthalene \( > \) Anthracene \( > \) Phenanthrene
C. Benzene \( > \) Naphthalene \( > \) Phenanthrene \( > \) Anthracene
D. All have equal resonance energy


Which of the following is the most common solvent used for
crystallization?
A. organic solvent benzene
B. Plain water
c. A salt solution of water
D. Dilute solution of sulphuric acid


The Jupiter's period of revolution around
the Sun is 12 times that of the

Earth. Assuming the planetary orbits to be circular, find how many times the distance between the Jupiter and the Sun exceeds that between the Earth and
the Sun.
A . 5.2 times
B. 10.2 times
c. 6.4 times
D. 3 times


The diagram below show a coil
connected to a centre zero
galvanometer \( G . \) The galvanometer
shows a deflection to the right when the
\( N \) -pole of a powerful magnet is moved
to the right as shown. Does the direction of the current in the coil appear
clockwise or anticlockwise viewed from
this end \( A ? \)
A. The direction of induced current at end \( A \) is anti clockwise
B. The direction of induced current at end \( A \) is clockwise
c. The direction of induced current at end \( A \) is firsts clockwise and then anticlockwise
D. The direction of induced current at end \( A \) cannot be determined


A wave of frequency \( 100 \mathrm{Hz} \) is sent
along a string towards a fixed end.
When this wave travels back after
reflection, a node is formed at a distance of \( 10 \mathrm{cm} \) from the fixed end of
the string. The speeds of incident(and reflected) waves are?
A \( .5 \mathrm{cms}^{-1} \)
B. \( 10 \mathrm{cms}^{-1} \)
c. \( 20 \mathrm{cms}^{-1} \)
D. \( 40 \mathrm{cms}^{-1} \)


'More the mass, the more difficult it is
to move the body from rest'. Type 1 for true and 0 for false


A conducting circular loop of radius carries a constant current i. It is placed in a uniform mangetic field \( \vec{B}_{0} \) such
that \( \vec{B}_{0} \) is perpendicular to the plane of the loop. The magnetic force acting on the loop is
A . ir \( B_{0} \)
В . \( 2 \pi \) ir \( B_{0} \)
c. zero
\( \mathbf{D} \cdot \pi \) ir \( B_{0} \)


VSEPR notation of \( \boldsymbol{P C l}_{5}, \boldsymbol{H}_{2} \boldsymbol{O} \) and \( \boldsymbol{I} \boldsymbol{C l}_{\mathbf{4}}^{-} \)
are:
A \( \cdot P C l_{5}-A X_{5}, H_{2} O-A X_{2} E_{2}, I C l_{4}^{-}-A X_{4} E_{2} \)
B. \( P C l_{5}-A X_{5}, H_{2} O-A X_{2} E, I C l_{4}^{-}-A X_{4} E \)
\( \mathrm{c} \cdot P C l_{5}-A X_{5}, H_{2} O-A X_{2}, I C l_{4}^{-}-A X_{4} E \)
D. \( P C l_{5}-A X_{5}, H_{2} O-A X_{2} E_{2}, I C l_{4}^{-}-A X_{4} E \)


If \( \cos ^{-1}\left(\frac{1}{x}\right)=\theta \) then the value of \( \tan \theta \)
is
A \( \cdot \frac{1}{\sqrt{x^{2}-1}} \)
B. \( \sqrt{x^{2}-1} \)
c. \( \sqrt{1-x^{2}} \)
D. \( \sqrt{1+x^{2}} \)


The radius of a spherical balloon increases from \( 7 \mathrm{cm} \) to \( 14 \mathrm{cm} \) as air is
being pumped into it. Find the ratio of
surface areas of the balloon in the two
cases.
A .1: 4
B . 4: 1
c. 1: 2
D. 2: 1


Cards marked with the numbers 2 to
101 are put in a box and mixed thoroughly. One card is drawn from this box. Find the probability that the number on the card is a perfect square.
A \( \cdot \frac{9}{100} \)
в. \( \frac{5}{100} \)
c. \( \frac{4}{100} \)
D. \( \frac{7}{100} \)


Unevenness in the surfaces of the
moving body and the surface on which
it moves causes:
A . Gravitational force
B. Frictional force
c. centripetal force
D. Centrifugal force


When two capillary tubes of different diameters are dipped vertically, the rise of the liquid is :
A. same in both the tubes
B. more in tube of larger diameter
c. less in the tube of smaller diameter
D. more in the tube of smaller diameter


Write electron density order in the
following


A particle of mass \( M \) is executing oscillations about the origin on the \( x \)
axis. Its potential energy is \( |\boldsymbol{U}|=\boldsymbol{K}\left|\boldsymbol{x}^{2}\right| \)
where \( K \) is a positive constant. If the
amplitude of oscillations is \( a \), then its
period \( \boldsymbol{T} \) is
A. proportional to \( 1 / \sqrt{a} \)
B. independent of \( a \)
c. proportional to \( \sqrt{a} \)
D. proportional to \( a^{1 / 2} / 2 \) poorional


ff \( \left[\begin{array}{cc}1 & 2 \\ 3 & -5\end{array}\right], \) then \( A^{-1} \) is equal to
\( ^{\mathbf{A}} \cdot\left[\begin{array}{cc}\frac{5}{11} & \frac{2}{11} \\ \frac{3}{11} & -\frac{1}{11}\end{array}\right] \)
в. \( \left[\begin{array}{rr}-\frac{5}{11} & -\frac{2}{11} \\ -\frac{3}{11} & -\frac{1}{11}\end{array}\right] \)
\( ^{\mathbf{C}} \cdot\left[\begin{array}{cc}\frac{5}{11} & \frac{2}{11} \\ \frac{3}{11} & \frac{1}{11}\end{array}\right] \)
D. \( \left[\begin{array}{ll}5 & 2 \\ 3 & -1\end{array}\right] \)


The correct electronic configurationfor
the ground state of silicon (atomic
number 11 ) is
\( \mathbf{A} \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{2} \)
B \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 p^{4} \)
C \( \cdot 1 s^{2} 2 s^{2} 2 p^{4} 3 s^{2} 3 p^{4} \)
D. \( 1 s^{2} s^{2} 2 p^{5} 3 s^{1} 3 p^{3} \)


To get an output \( Y=1 \) from the circuit
above, the input must be
A. A-O B-1 C-O
B. A-1 B-O C-O
c. A-1 B-O C-
D. A-1 B-1 C-O


Teleost fishes are characterized by the
presence of
A . Air bladder
B. Claspers
c. Placoid scales
D. None of the above


When bauxite is treated with sodium
hydroxide solution what happens to the iron \( (I I I) \) oxide (main impurity).


The electrolyte in lead storage battery is dilute sulphuric acid. The concentration of sulphuric acid in a lead-storage battery must be between \( 4.8 \mathrm{M} \) and 5.3 M for most efficient functioning: A 5 mL sulphuric acid sample of a particular battery requires \( 50 \mathrm{mL} \) of \( 1.0 \mathrm{M} \) NaOH for complete neutralization. Which of the following statements about the functioning of battery is the, most appropriate?
A. The acid concentration in the battery is not in the mos effective range
B. The acid concentration in the battery is in the most effective range
c. The add concentration in the battery is hardly in the most effective range
D. only a good mechanic can tell whether or not the acid concentration in the battery is in the most effective range


The force between two current carrying wires is due to the force.
A. magnetic
B. electric
c. centripetal
D. centrifugal


What will be the velocity at \( t=5.00 \) s?


In general, as the temperature increases, the solubility of gases in water \( _{\text {十一一一一一一一一一 }} \) and the solubility of most solids in water
A. decreases, decreases
B. decreases, increases
c. increases, decreases
D. increases, increases


The vapour pressure of pure benzene at
a certain temperature is 640 mm \( H g \). A
non-volatile solid weighing \( 2.715 g \) is
added to \( 39.0 g \) of benzene.

The vapour pressure of the solution is
\( 600 m m H g . \) What is the molar mass of
the solid substance?


Oxygen is more electronegative than
sulphur yet \( \boldsymbol{H}_{2} \boldsymbol{S} \) is acidic While \( \boldsymbol{H}_{2} \boldsymbol{O} \) is
neutral. This is because:
A. water is a highly associated
B. \( H-S \) bond is weaker than \( H-O \) bond
c. \( H_{2} S \) is a gas while \( H_{2} O \) is a liquid
D. The molecular weight of \( H_{2} S \) is more than that of \( H_{2} O \)


\( 1 \times 0= \)
\( \mathbf{A} \cdot \mathbf{1} \)
B.
\( c \cdot 2 \)
D. 10


At what temperature would the rms speed of a gas molecule have twice its
value at \( 100^{\circ} \mathrm{C} ? \)
A \( .4192 K \)
в. \( 1492 K \)
c. \( 9142 K \)
D. 2491 K


A monkey standing on the ground wants to climb to the top of a vertical pole 13 \( \mathrm{m} \) tall. He climbs \( 5 \mathrm{m} \) in \( 1 \mathrm{s} \) and then
slips downwards \( 3 \mathrm{m} \) in the next second
He again climbs \( 5 \mathrm{m} \) in \( 1 \mathrm{s} \) and slips by \( 3 \mathrm{m} \) in the next second as so on. How much time will the monkey take to reach the top of the pole?
\( \mathbf{A} \cdot 7 \sec \)
B. 9 sec
c. 11 sec
D. 13 sec


Lassaigne's test is used for the detection of:
A. carbon only
B. hydrogen only
c. oxygen only
D. nitrogen, sulphur and halogens


Biologists believe that the current DNA
\( \rightarrow \mathrm{RNA} \rightarrow \) Protein system is the result of a long period of evolution because
A. The transcription of DNA to mRNA and translation of mRNA into proteins consists of many steps.
B. DNA replication is complicated but relatively error-free and the current system is very complex and precise
c. Evidence indicates that RNA preceded DNA as the genetic material
D. All of the above


Match List I with List II.


The radiation of an electric room heater
is most effective when it is :
A. uncleaned
B. polished to shine
c. painted green
D. painted black


Assertion
The ratio of inertial mass to
gravitational mass is equal to one.
Reason

The inertial mass and gravitational mass of a body are equivalent.
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. If Assertion is incorrect but Reason is correct


Calculate the molarity of each of the following solutions:
(a) \( 30 g \) of \( C o\left(N O_{3}\right)_{2} \cdot 6 H_{2} O \) in \( 4.3 \mathrm{L} \) of
solution
(b) \( 30 \mathrm{mL} \) of \( 0.5 \mathrm{M} H_{2} S O_{4} \) diluted to 500
mL.


The nuclear reaction \( n+_{5}^{10} B \rightarrow_{3}^{7} L i+_{2}^{4} \)
He is observed to occur even when very
slow-moving neutrons \( \left(M_{n}=\right. \) 1.0087amu \( ) \) strike a boron atom at
rest. For a particular reaction in which \( \boldsymbol{K}_{n}=\mathbf{0}, \) the helium \( \left(\boldsymbol{M}_{\boldsymbol{H} e}=\right. \)
\( 4.0026 a m u) \) is observed to have a
speed of \( 9.30 \times 10^{6} m s^{-1} . \) Determine
(a) the kinetic energy of the lithium
\( \left(M_{L i}=7.0160 a m u\right) \) and
(b) the \( Q \)
value of the reaction.


The value of \( \lim _{x \rightarrow \infty}(x-\sqrt{\left(x^{2}-x\right)}) \)
is
A \( \cdot \frac{1}{2} \)
в. \( -\frac{1}{2} \)
\( c \cdot 1 \)
D.


toppr OGII
Q Type your question_
opened, the piston moves slightly to the right, towards the tap.
What can be deducted about the
pressure of gas \( X ? \)
before opening after opening tap \( \operatorname{tap} \)
ess than pre than atmospheric \( \quad \) atmospheric pressure
\( \operatorname{mec} \)
more than atmospheric \( \quad \) atmospheric pressure \( \quad \) pressure
ore than less than atmospheric \( \quad \) atmospheric pressure
more than \( \quad \) same as atmospheric \( \quad \) atmospheric pressure ressurr
atmosphere
\( A \cdot A \)
B.
\( c . \)
\( D \)


In a DC generator, the ends of the coil are connected to
A. two slip rings
B. the split ring commutator
c. either (1) or (2)
D. None of these


The number of turns in the coil of an \( A C \)
generator ar e100 and its cross-
sectional area is \( 2.5 m^{2} . \) The coil is
revolving in a uniform magnetic field of strength \( 0.3 T \) with the uniform angular velocity of 60 rad/s. The value of maximum value produced is \( \mathbf{k V} \)
A . 1.25
в. 4.50
c. 6.75
D. 2.25


A solution with \( \mathrm{pH}=2 \) is more acidic then one with a \( \mathrm{pH}=6 \) by a factor of
A . 4
B. 12
\( c \cdot 400 \)
D. \( 10^{4} \)


Get the algebraic expressions in the
following case using variables, constants and arithmetic operations. Number 5 added to three times the
product of \( \mathrm{m} \) and \( \mathrm{n} \)


From the data given below state which
group is more variable \( \boldsymbol{A} \) or \( \boldsymbol{B} \)
\( \begin{array}{llllll}\text { Marks } & \begin{array}{l}10- \\ 20\end{array} & \begin{array}{l}20- \\ 30\end{array} & \begin{array}{l}30- \\ 40\end{array} & \begin{array}{l}\text { 40- } \\ \text { 50 }\end{array} & \begin{array}{l}\text { 50 } \\ 60\end{array}\end{array} \)
Group
A 32 33 17
25 \begin{tabular}{l|l|l|l}
Group & 10 & 20 & 30 \\
B & (年) & (年)
\end{tabular}


A man generates a symmetrical plus in a string by moving his hand up and down. At \( t=0 \) the point in his hand
moves downward. The pulse travels with speed \( 3 m / s \) on the string \( \& \) his hands
passes 6 times in eacgh seconds from the mean position. Then the point on the string at a distance \( 3 m \) will reach its upper extreme first time at time \( t= \)
A. 1.25 sec
в. 1 sec
\( \mathbf{c} \cdot \frac{13}{12} \sec \)
D. None


Calculate the percentage ionization of
\( 0.01 M \) acetic acid in \( 0.1 M H C l . K_{a} \) of
acetic acid is \( 1.8 \times 10^{-5} \)
A. \( 0.18 \% \)
B. \( 0.018 \% \)
\( \mathrm{c} .1 .8 \% \)
D. \( 18 \% \)


Copper can be extracted by hydrometallurgy but not zinc, Explain.


Find the sum of an infinite \( \mathrm{G.P}: 1+ \) \( \frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\dots \dots \)
A \( \cdot \frac{3}{5} \)
B. \( \frac{3}{2} \)
c. \( \frac{49}{27} \)
D. 8 \( \overline{5} \)


Who amongst the following used corpuscular theory to explain the nature of light?
A. Max Planck
B. Newton
c. Young
D. Einstein


In a class there are 14 boys and 10 girls If
one child
is absent the probability that it is a boy is
A \( \cdot \frac{5}{12} \)
в. \( \frac{7}{12} \)
c. \( \frac{10}{14} \)
D.


The locus of a projectile relative to another projectile is a
A. straight line
B. circle
c. ellipse
D. parabola


If the distance of \( P(x, y) \) from \( A(5,1) \) and \( \mathrm{B}(-1,5) \) are equal, then prove that \( 3 x=2 y \)


The ionising power of \( \alpha, \beta \) and \( \gamma \) -rays is in the decreasing order:
A \( . \alpha>\beta>\gamma \)
в. \( \beta>\alpha>\gamma \)
c. \( \gamma>\alpha>\beta \)
D. \( \beta>\gamma>\alpha \)


Magnitude of specific rotation of a compound is independent of:
A. solvent
B. concentration
c. length of tube
D. temperature


In the figure \( : \angle P S Q=90^{\circ}, P Q= \)
\( \mathbf{1 0} c \boldsymbol{m}, \boldsymbol{Q} \boldsymbol{S}=\boldsymbol{6} \boldsymbol{c m} \) and \( \boldsymbol{R} \boldsymbol{Q}=\boldsymbol{9} \boldsymbol{c m} \)
Calculate the length of \( \boldsymbol{P} \boldsymbol{R} \)


If the number of diagonals in a polygon
is 44 then find its number of sides.


If \( f(x)=\left(a-x^{n}\right)^{1 / n} \) where \( a>0 \) and \( n \)
is a positive integer then \( (\text { fof })(x) \) is
A \( . f(x) \)
B.
\( c \cdot 0 \)
D.


Which of the following sets contain only thermoplastics?
A. Glytal, Melmac, PAN
B. Polythene, Bakelite, Nylon - 6
c. PVC, PMMA, Polystyrene
D. Polypropylene, Urea-formaldhyde, Teflon


Trees are known as lungs of forest.
A. True
B. False


Using the method of slope, show that the following points are collinear:
\( (i) A(4,8), B(5,12), C(9,28) \)
\( (i i) A(16,-18), B(3,-6), C(-10,6) \)


Statement 1: Water boils below \( 100^{\circ} \mathrm{C} \)
at high altitudes. Statement 2: Atmospheric pressure varies inversely with altitude.
A. Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement
B. Both the Statement 1 and Statement 2 are correct and Statement 2 is NOT the correct explanation of Statement 1.
c. statement 1 is correct but Statement 2 is not correct.
D. Statement 1 is not correct but Statement 2 is correct
E. Both the Statement 1 and Statement 2 are not correct


The incorrect statement for d-block
element is:
A. it shows magnetic property
B. it has variable valency
c. it has tendency to form coloured ions
D. it has complete d-orbitals


The current in the primary circuit of a potentiometer wire is \( 0.5 \mathrm{A}, \rho \) for the
wire is \( 4 \times 10^{-7} \Omega-m \) and area of
cross-section of wire is \( 8 \times 10^{-6} m^{2} \)
The potential gradient in the wire would be
A. 25 mV/meter
B. 2.5 mV/meter
c. 25 v/meter
D. 10 V/meter


\( \int \frac{x^{4}+1}{x^{6}+1} d x= \)
A \( \cdot \tan ^{-1} x-\tan ^{-1} x^{3}+c \)
B. \( \tan ^{-1} x-\frac{1}{3} \tan ^{-1}\left(x^{3}\right)+c \)
c. \( \tan ^{-1} x+\tan ^{-1}\left(x^{3}\right)+c \)
D. \( \tan ^{-1} x+\frac{1}{3} \tan ^{-1}\left(x^{3}\right)+c \)


Assertion
Covalent bonds are broken when sugars
are dissolved in water.
Reason
In molecules with covalent bonds,
electrons are shared by two or more
atoms
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 incorrect but Reason is correct
D. Both Assertion and Reason are incorrect


Which one of the following order is correct with respect to the bond angle?
A. \( N O F>N O_{2} \)
в. \( O F_{2}>N O_{2} \)
c. \( N F_{2}>N O_{2} \)
D. \( N O F>N F_{2} \)


State true or false:
\( \frac{3+2 i \sin \theta}{1-2 i \sin \theta}=\frac{\left(3-4 \sin ^{2} \theta\right)+8 i \sin \theta}{1+4 \sin ^{2} \theta} \)


What is reflection of light? Explain
reflection of light with the help of an
activity?


The IUPAC name of the Wilkinsons
catalyst \( \left[R h C l\left(P P h_{3}\right)_{3}\right] \) is
A. Chlorotris (triphenylphopshine) rhodium (I)
B. Chlorotris (triphenylphosphine) rhodium (IV)
C. Chlorotris (triphenylphosphine) rhodium (0)
D. Chlotrotris (triphenylphosphine) rhodium (VI)


Q Type your question_
\( A \)
B.
\( c \)
D.


Show the region of feasible solution
under the following constraints \( 2 x+ \) \( \boldsymbol{y} \leq \mathbf{8}, \boldsymbol{x} \geq \mathbf{0}, \boldsymbol{y} \geq \mathbf{0} \) in answer book


Micronutrients are needed in amounts
equivalent to
A. \( 8 \mathrm{m} \) mole/kg of dry matter
B. 18m mole/kg of dry matter
c. 25m mole/kg of dry matter
D. 30m mole/kg of dry matter


State whether True or False:
A semiconductor at absolute zero
become a insulator.
A. True
B. False


Consider \( f(x)=[1 x], 1 \leq x \leq 2 \) and \( g(x) \)
\( =f(x)+b \sin \frac{\pi}{2} x, 1 \leq x \leq 2 \) then
which of the following is correct?
A \( \cdot \) Rolles theorem is applicable to both \( f, g \) and \( b=\frac{3}{2} \)
B. LMVT is not applicable to f and Rolles theorem is applicable to g with \( b=\frac{1}{2} \)
c. LMVT is not applicable to fand Rolles theorem is applicable to g with \( b=1 \)
D. Rolles theorem is not applicable to both f, g for any real


If \( \boldsymbol{x}=\mathbf{1}+\boldsymbol{i} \tan \boldsymbol{\alpha}, \) where \( \boldsymbol{\pi}<\boldsymbol{\alpha}<\frac{\mathbf{3} \boldsymbol{\pi}}{\mathbf{2}} \)
then \( |z| \) is equal to?


The value of the fraction \( \frac{1}{3}+\frac{3}{4} \) is equal
to
A \( \cdot \frac{1}{12} \)
в. \( \frac{13}{12} \)
\( c \cdot \frac{16}{12} \)
D. none of the above


The electronic configurations of the first
four members of the actinoid series
cannot be written accurately in a
regular manner because of :
A. small difference in energy between \( 5 f \) and \( 6 d \) orbitals
B. large difference in energy between \( 5 f \) and \( 6 d \) orbitals
C. small difference in energy between \( 5 f \) and 6 s orbitals
D. violation of the Pauli exclusion principle


For Bohr's model of the hydrogen atom,
the energy of the electron in its ground state is found to be \( -13.6 e V \). (i) Draw
an energy level diagram for the hydrogen atom and mark the values of energy (in eV) at \( n=2 \) to \( n=\infty \) to.
Obtain the maximum energy of a
photon emitted by the hydrogen atom in \( \mathrm{eV} \)


The approximate value of \( \sqrt[5]{33} \) correct
to 4 decimal places is
A . 2.0000
B. 2.1001
c. 2.0125
D. 2.0500


Factorise \( : \boldsymbol{m}^{2}-\mathbf{1 0 m}-\mathbf{1 4 4} \)


Ores in the form of sulphide and carbonate are converted into:
A. water
B. oxides
c. aldehyde
D. alcohol


n fig, then \( \angle A+\angle B+\angle C+\angle D+ \)
\( \angle \boldsymbol{E}+\angle \boldsymbol{F}= \)
A \( \cdot 180^{\circ} \)
B. \( 270^{\circ} \)
\( c .360^{\circ} \)
D. \( 540^{\circ} \)


A pollutant that affects the lungs and the respiratory track is:
\( A \cdot S O_{2} \)
B. Hydrocarbons
\( c \cdot O_{3} \)
D. \( C O_{2} \)


Hydrated cobalt(II) chloride
decomposes on heating. The equation for the reaction is
\( \boldsymbol{C o C l}_{2} \cdot \boldsymbol{6} \boldsymbol{H}_{2} \boldsymbol{O C o C l}_{2}+\boldsymbol{6} \boldsymbol{H}_{2} \boldsymbol{O} \)
The reaction is reversed by adding
water.
Which row describes the colour change
and the type of reaction for the reverse
reaction?
A. Colour change - blue to pink, type of reaction endothermic
B. Colour change - blue to pink, type of reaction exothermic
c. Colour change - pink to blue, type of reaction endothermic
D. Colour change - pink to blue, type of reaction exothermic


The eccentricity of the ellipse \( 25 x^{2}+ \)
\( 16^{2}=400 \) is
A \( \cdot \frac{3}{5} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{2}{5} \)
D.


If \( A^{\prime} \) is the transpose of a square matrix
A, then
A \( \cdot|A| \neq \mid A^{\prime} \)
B \( \cdot|A|=\left|A^{\prime}\right| \)
c \( \cdot|A|+\left|A^{\prime}\right|=0 \)
D \cdot \( |A|=\left|A^{\prime}\right| \) only when A is symmetric


A mixture of volatile components \( A \) and B has total vapour pressure (in torr) as \( \boldsymbol{P}=\mathbf{2 5 4}-\mathbf{1 1 9} \chi_{A}, \) where \( \chi_{A} \) is the
mole fraction of \( A \) in the mixture. Hence,
\( P_{A}^{o} \) and \( P_{B}^{o} \) respectively are (in torr):
A. 254,119
в. 119,254
C. 135,254
D. 154, 119


Difference in the physical properties of cis and trans isomer is due to :
A. the difference in the shape of the molecul
B. the difference in the overall dipole moment of the molecule
c. both a and \( b \)
D. none of these


A 5 watt source emits monochromatic
light of wavelength 5000 A when placed \( 0.5 \mathrm{m} \) away, it liberates photoelectric
from a photosensitive metallic surface. When the source is moved to a distance
of \( 1.0 \mathrm{m}, \) The numbers of photo electrons liberated will:
A. be reduced by a factor of 2
B. be reduced by a factor of 4
c. be reduced by a factor of 8
D. be reduced by a factor of 16


\( y \)
\( y \)
\( x \)


Which of the following is a proteolytic
enzyme?
A. Pepsin
B. Trypsin
c. Renin
D. All of the above


State and explain Ampere's circuital
law.


Alkali metals are characterised by:
This question has multiple correct options
A. good conductor of heat and electricity
B. high oxidation potential
C. high melting point
D. solubility in liquid ammonia


\( P, Q \) and \( R \) are three sets and \( \xi P \cup Q \cup \)
\( R . \) Given that \( n(\xi)=60, n(P \cap Q)=5 \)
\( n(Q \cap R)=10, n(p)=20 \) and \( n(Q)=23 \)
find \( n\left(P^{\prime} \cup Q\right) \)
A. 37
3. 38
\( c \cdot 45 \)
D. 52


f \( \boldsymbol{\pi} \boldsymbol{x}+\mathbf{3} \boldsymbol{y}=\mathbf{2 5}, \) write \( \boldsymbol{y} \) in terms of \( \boldsymbol{x} \)


The activity of a radioactive sample is measured as 9750 count \( / \) min at \( t=0 \)
and 975 count/min at \( t=5 \) min.The
decay constant is nearly
A. 0.922 min \( ^{-1} \)
B. \( 0.691 \mathrm{min}^{-1} \)
c. \( 0.461 \min ^{-1} \)
D. 0.230 \( \min ^{-1} \)


Q Type your question
dropper and placed it in the bottle shown in the adjoining diagram. The bottle has some aluminium foil. After
the addition of acid, a colourless gas is evolved which is collected by placing a balloon around the mouth of the bottle.
Answer the following now:
¡) Aluminium is a
ii) The formula of Sulphuric acid is
iii) The formula of Aluminium Sulphate
is
iv) The chemical reaction is given
below in word equation: Now write the same using symbols. Aluminium + Sulphuric acid \( \rightarrow \) Aluminium Sulphate + Hydrogen gas


A closed switch has a resistance of :
A. zero ohm
B. about 50 ohms
c. about 500 ohms
D. infinity


The velocity of particle P due east is \( 4 m / s \) and that of \( Q \) is \( 3 m / s \) due north. What is the velocity of P w.r.t Q


Which of the following functions of time represent (a) periodic and (b) nonperiodic motion? Give the period for each case of periodic motion. \( [\omega \) is any positive constant].
A \( \cdot \frac{2 \pi}{\omega} \)
B. \( \sin \omega t+\cos 2 \omega t+\sin 4 \omega t \)
\( c \cdot e^{-\omega t} \)
\( \mathbf{D} \cdot \log (\omega t) \)


The graph of \( \ln \left(R / R_{O}\right) \) versus \( \ln A \) of nucleus is :
\( \left(R_{0} \text { is a constant } 1.2 \times 10^{-12}, \mathrm{R} \) is \right.
radius and \( A \text { is the atomic number }) \)
A. a straight line
B. a parabola
c. an ellipse
D. a circle


The diagram shows a molecule
of hydrogen fluoride
In the molecule:
A. the hydrogen and fluorine share a pair of electrons
B. the hydrogen and fluorine share a pair of protons
C. the hydrogen gives the fluorine an electron
D. the hydrogen gives fluorine a proton


Among the following, the surfactant that will form micelles in aqueous solution at the lowest
molar concentration at ambient
conditions is:
A \( \cdot_{C H_{3}}\left(C H_{2}\right)_{15} N^{+}\left(C H_{3}\right)_{3} B r^{-} \)
B. \( C H_{3}\left(C H_{2}\right)_{11} O S O_{3}-N a^{+} \)
c. \( _{C H_{3}}\left(C H_{2}\right)_{6} \) COO\( ^{-} N a^{+} \)
D. \( C H_{3}\left(C H_{2}\right)_{11} N a^{+}\left(C H_{3}\right)_{3} B r \)


The volume of the water needed to
dissolve 1 g of \( B a S O_{4}\left(K_{s p}=1.1 \times\right. \)
\( \left.10^{-10}\right) \) at \( 25^{\circ} C \) is:
A . 820 litre
B. 450litre
c. 205 litre
D. none of these


Two balls are dropped from different heights at different instants. Second
ball is dropped 2 sec after the first ball. If both balls reach the ground simultaneously after 5 sec. of dropping the first ball, the difference of initial
heights of the two balls will be: \( (g= \)
\( \left.9.8 m / s^{2}\right) \)
\( \mathbf{A} \cdot 58.8 \mathrm{m} \)
B. \( 78.4 \mathrm{m} \)
c. \( 98.0 \mathrm{m} \)
D. \( 117.6 \mathrm{m} \)


Which of the following is not changed for the observations
\( \mathbf{3 1}, \mathbf{4 8}, \mathbf{5 0}, \mathbf{6 0}, \mathbf{2 5}, \mathbf{8}, \mathbf{3 x}, \mathbf{2 6}, \mathbf{3 2} ? \) (where \( \boldsymbol{x} \)
lies between \( 10 \text { and } 15) \)
A . A.M
B. Range
c. Median
D. Q.D


Why is it proper to say that almost all
living things are dependent on solar
energy?


Three forms of water are solid,
and


The solubility of \( F e(O H)_{2} \) is greater
\( \operatorname{than} F e(O H)_{3} \) in water
If true write 1 , else write 0


The enthalpy of combustion of methane,
graphite and dihydrogen at \( 298 K \) are \( -890.3 k J m o l^{-1},-393.5 \)
\( k J m o l^{-1},-285.8 k J m o l^{-1} \)
respectively. Enthalpy of formation of \( \boldsymbol{C H}_{4(g)} \) will be:
A \( .-74.8 k J m o l^{-1} \)
В. \( -52.27 k J \) mol \( ^{-1} \)
c. \( +74.8 k J m o l^{-1} \)
D. \( +52.26 k J m o l^{-1} \)


Assertion
The resolving power of both microscope and telescope depends on the wavelength of light used.
Reason
The resolving power of a lens is the ability to resolve the two images so they are distinctly identified.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


The shape of the orbital with the value of \( l=2, m=0 \) is :
A. spherical
B. double dumb-bell
c. trigonal planar
D. square planar


Water is formed if a heated metallic
oxide reacts with hydrogen.
A. True
B. False


Which one of the following reactions
represents the oxidising property of
\( \boldsymbol{H}_{2} \boldsymbol{O}_{2} ? \)
\( \mathbf{A} \cdot 2 K M n O_{4}+3 H_{2} O_{4}+5 H_{2} O_{2} \rightarrow K_{2} S O_{4}+ \)
\[
2 M n S O_{4}+8 H_{2} O+5 O_{2}
\]
B.
\[
2 K_{3}\left[F e(C N)_{6}\right]+2 K O H+H_{2} O_{2} \rightarrow 2 K_{4}\left[F e(C N)_{6}\right]+
\]
\( 2 H_{2} O+O_{2} \)
\( \mathbf{c} \cdot P b O_{2}+H_{2} O_{2} \rightarrow P b O+H_{2} O+O_{2} \)
D. \( 2 K I+H_{2} S O_{4}+H_{2} O_{2} \rightarrow K_{2} S O_{4}+I_{2}+2 H_{2} O \)


Two coherent sources of wavelength \( 6.2 \times 10^{-7} \mathrm{m} \) produce interference. The
path difference corresponding to \( 10^{t h} \) order maximum will be?
A \( .6 .2 \times 10^{-6} \mathrm{m} \)
В. \( 3.1 \times 10^{-6} \mathrm{m} \)
c. \( 1.5 \times 10^{-6} \mathrm{m} \)
D. \( 12.4 \times 10^{-6} \mathrm{m} \)


A particle is projected vertically
upwards with velocity \( 80 \mathrm{m} / \mathrm{s} \). Then the
(Take \( \left.\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} / \boldsymbol{s}^{2}\right) \)
A. Displacement and distance travelled by the particle in \( 2 \sec \) in \( 160 \mathrm{m} \)
B. Displacement and distance travelled by the particle in \( 4 \sec \) in \( 240 \mathrm{m} \)
C. Displacement and distance travelled by the particle in \( 6 \sec \) in \( 300 \mathrm{m} \) and \( 100 \mathrm{m} \)
D. Displacement and distance travelled by the particle in \( 8 \sec \) is \( 320 \mathrm{m} \) and \( 10 \mathrm{m} \)


Which of these does not represent a
wave equation
A \( . y=\operatorname{Asin}(\omega t-k x) \)
B. \( y=\operatorname{Asin}(\omega t+k x) \)
c. \( y=A \cos (\omega t-k x) \)
D. \( y=A(\omega t-k x) \)


Write the principles of the following
methods.
(i) Froth floatation method
(ii) Electrolytic refining


Why is solubility of halo alkanes in water is very how although they polar in
nature


Indigestion is painful so to relieve indigestion, we take an antacid such as milk of magnesia, which contains:
A. magnesium hydroxide
B. hydrochloric acid
c. tartaric acid
D. calcium hydroxide


Paris green is an insecticide made from basic copper acetate, arsenious and acetic acid.
A. True
B. False


Which metal is considered best for
protecting the other metal? \( E^{0}_{F e^{2+} / F e}=-0.44 V, E^{0}_{Z n^{2+} / Z n}=-0.76 V \)
\( E^{0}_{M g^{2+} / M g}=-2.37 V, E^{0}_{C u^{2+} / C u}=-0.34 V \)
A . \( F e \)
в. \( A g \)
\( c . M g \)
D. \( Z n \)


\( \frac{8}{8} \)


Certain sun glasses having small crystals of \( A g C l \) incorporated in the
lenses, on exposure to light of
appropriate wavelength turns to grey colour to reduce the glare following the reaction:
\( \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l} \stackrel{\boldsymbol{h} \boldsymbol{v}}{\rightarrow} \underset{(\boldsymbol{G} \boldsymbol{r} \boldsymbol{e} \boldsymbol{y})}{\boldsymbol{A} \boldsymbol{g}}+\boldsymbol{C l} \)
If the heat of reaction for the
decomposition of \( A g C l \) is \( 248 k J m o l^{-1} \) what maximum wavelength is needed to induce the desired process?
A \( \cdot 4.83 \times 10^{-4} \mathrm{m} \)
в. \( 9.6 \times 10^{-7} m \)
c. \( 6 \times 10^{-7} m \)
D. \( 4.83 \times 10^{-7} \mathrm{m} \)


Which is incorrect?
\( \mathbf{A} \cdot K \cdot E \cdot \propto(\operatorname{moment} u m)^{2} \)
B. \( K . E . \propto(\text {velocity})^{2} \)
C. \( K . E . \propto(\operatorname{mas} s)^{2} \)
D. \( K . E . \propto \) mass


If \( l_{1}, m_{1}, n_{1} \) and \( l_{2}, m_{2}, n_{2} \) are DCs of the two lines inclined to each other at an
angle \( \theta \), then the DCs of the internal bisector of the angle between these lines are
A \( \cdot \frac{l_{1}+l_{2}}{2 \sin \frac{\theta}{2}}, \frac{m_{1}+m_{2}}{2 \sin \frac{\theta}{2}}, \frac{n_{1}+n_{2}}{2 \sin \frac{\theta}{2}} \)
в. \( \frac{l_{1}+l_{2}}{2 \cos \frac{\theta}{2}}, \frac{m_{1}+m_{2}}{2 \cos \frac{\theta}{2}}, \frac{n_{1}+n_{2}}{2 \cos \frac{\theta}{2}} \)
c. \( \frac{l_{1}-l_{2}}{2 \sin \frac{\theta}{2}}, \frac{m_{1}-m_{2}}{2 \sin \frac{\theta}{2}}, \frac{n_{1}-n_{2}}{2 \sin \frac{\theta}{2}} \)
D. \( \frac{l_{1}-l_{2}}{2 \cos \frac{\theta}{2}}, \frac{m_{1}-m_{2}}{2 \cos \frac{\theta}{2}}, \frac{n_{1}-n_{2}}{2 \cos \frac{\theta}{2}} \)


The life and appearance of the historic monuments like Taj are likely to be
damaged by the presence of :
A. hydrocarbons
B. excess of \( S O_{2} \)
c. \( C F C \)
D. \( C l_{2} \)


\( \mathbf{2} N_{2} O_{5}(g) \rightarrow 4 N O_{2}(g)+O_{2}(g) \)
What is the ratio of the rate of
decomposition of \( N_{2} O_{5} \) to rate of
formation of \( N O_{2} ? \)
\( A \cdot 1: 2 \)
B. 2:
\( c \cdot 1: 4 \)
\( D \cdot 4: \)


When synapsis is complete all along the chromosome, the cell is said to have
entered a stage called as
A. Zygotene
B. Pachytene
c. Diplotene
D. Diakinesis


The energy of ATP in Glycolysis is used
for
A. Oxidative phosphorylation.
B. Substrate level phosphorylation.
c. The dephosphorylation of ADP.
D. Pyruvate.


The solutions set of inequality \( \cos ^{-1} x<\sin ^{-1} x \) is
A \( \cdot[-1,1] \)
B. \( \left[\frac{1}{\sqrt{2}}, 1\right] \)
c. [0,1]
D. \( \left(\frac{1}{\sqrt{2}}, 1\right] \)


The nature of inter-molecular forces
among benzene molecule is:
A. hydrogen bonding
B. dispersion forces
c. dipole-dipole attraction
D. ion-dipole attraction


Can cyclotron accelerate uncharged
particles?Why?


Consider the following sequence on mRNA, AUGGCAGUGCCA. Assuming that genetic code is overlap then how many number of codon may be present on this genetic code?
\( A \cdot 9 \)
B. 10
\( c \cdot 8 \)
D. 1


A plane wave of wavelength \( 6250 A \) is incident normally on a slit of width \( 2 \times \)
\( 10^{-2} \mathrm{cm} . \) The width of the principle
maximum of diffraction pattern on a
screen at a distance of \( 50 \mathrm{cm} \) will be:
A \( \cdot 312 \times 10^{-3} \mathrm{cm} \)
B . \( 312.5 \times 10^{-4} \mathrm{cm} \)
c. 312 ст
D. \( 312.5 \times 10^{-5} \mathrm{cm} \)


For any two events \( A \) and \( B \)
This question has multiple correct options
\( \mathbf{A} \cdot P(A \cap B) \geq P(A)+P(B)-1 \)
B \( \cdot P(A \cap B) \geq P(A)+P(B) \)
\( \mathbf{c} \cdot P(A \cap B)=P(A)+P(B)-P(A \cup B) \)
D \( \cdot P(A \cap B)=P(A)+P(B)+P(A \cup B) \)


In the following reaction \( P b \) undergoes:
\( \boldsymbol{P b}(s)+\boldsymbol{P b O}_{2}(\boldsymbol{s})+\mathbf{2} \boldsymbol{H}_{2} \boldsymbol{S O}_{4}(\boldsymbol{a q}) \rightarrow \)
\( 2 P b S O_{4}(s)+2 H_{2} O(l) \)
A. disproportionation
B. comproportionation
c. reduction
D. oxidation


Construct a triangle \( A B C \) in which
\( A B=5 c m, B C=4.3 c m \) and \( A C= \)
\( 4 c m \)


Which of the following is a Hydride of Nitrogen:
\( A \cdot N H_{3} \)
в. \( \mathrm{N}_{2} \mathrm{H}_{4} \)
c. \( \mathrm{HN}_{3} \)
D. All


A survey of 850 students in a University yields that 680 students like music and
215 like dance. What is the least
number of students who like both
music and dance?
A . 40
B . 45
c. 50
D. 55


Why are shields made of iron usually provided around precision instruments?
A. For protection against the effect of moisture in the air
B. For guiding the instruments against unauthorised handling
c. For protection against the effect of external magnetic fields
D. For absorbing heat generated during the functioning of the instruments


Say true or false.
If \( y=2 \sec x, \) then \( \frac{d y}{d x} \) is \( 2 \sec x \tan x \)
A. True
B. False


what is the potential difference between two points, if 2 J of work must be done to move a \( 4 \mathrm{mC} \) charge from one point to
another is:
A. \( 50 v \)
B. 500
\( c \cdot 5 v \)
D. 5000


There are three coins. One is a two-
headed coin (having head on both faces), another is a biased coin that
comes up heads \( 75 \% \) of the times and
third is also a biased coin that comes
up tails \( 40 \% \) of the times. One of the three coins is chosen at random and
tossed, and it shows heads. What is the probability that it was the two-headed
\( \operatorname{coin} ? \)


When a mixture of conc. \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) and
\( H C l \) is warmed, we get?
A \( \cdot C l_{2}, N O_{2} \) and \( H_{2} O \)
B. \( N O, C l_{2} \) and \( H_{2} O \)
c. \( N O C l, C l_{2} \) and \( N O_{2} \)
D. \( N O C l, C l_{2} \) and \( H_{2} O \)


Plant 'P' is different from Plant 'Q' in
having
A. Fruits and seeds
B. Conducting tissues
c. A well-defined nucleus
D. A rigid cell wall


If two tangents are drawn to a circle
circle from an external point, the
(i) they subtend equal angles at the centre
(ii) they are equally inclined to the segment,joining the centre to that
point.


The length of a metal wire is \( l_{1} \) when the tension in it is \( F_{1} \) and \( l_{2} \) when the
tension in it is \( F_{2} \). The natural length of
the wire is
A. \( \frac{l_{1} F_{1}+l_{2} F_{2}}{F_{1}+F_{2}} \)
в. \( \frac{l_{2}-l_{1}}{F_{2}-F_{1}} \)
c. \( \frac{l_{1} F_{2}-l_{2} F_{1}}{F_{2}-F_{1}} \)
D. \( \frac{l_{1} F_{1}-l_{2} F_{2}}{F_{2}-F_{1}} \)


Two concentric conducting thin spherical shells have radii a and b \( (a< \)
b). If they are charged to \( +Q \) and \( -2 Q \) the graph of electric field as a function of
the distance r from center is:
A.
B.
\( c \)
D.


What is the maximum flow speed of
water for laminar flow in a pipe having a diameter \( 5 c m \) given that coeficient of
visocity of water is \( 10^{-3} \) Pa sec.


Two identical blocks of weight W are placed one on top of the other as shown in figure. The upper block is tied to the
wall. The lower block is pulled to the right with a force F. The coefficient of static friction between all surfaces in
contact is \( \mu . \) What is the largest force
that can be exerted before the lower
block starts to slip?
A \( \cdot \mu W \)
в. \( 2 \mu W \)
\( c \cdot 3 \mu W \)
D. \( 4 \mu W \)


Find the mean for the following data using step deviation method.
\( A \cdot 4 \)
B. 5
\( c .6 \)
D.


Deforestation means
A. Planting more trees
B. Designing a forest
C . Demanding a forest
D. Clearing of forests and using that land for other
purposes


A magnetic field of flux density \( 1.0 \mathrm{Wb} \)
\( m^{-2} \) acts normal to a 80 tum coil of 0.01
\( m^{2} \) area. The e.m.f. induced in it, if this coil is removed from the field in 0.1
second is :
\( A \cdot 8 v \)
B. \( 4 v \)
c. \( 10 v \)
D. \( 6 v \)


\( \int e^{2 x}\left(\frac{1+\sin 2 x}{1+\cos 2 x}\right) d x \) is equal to
A \( \cdot e^{2 x} \tan x+C \)
B . \( e^{2 x} \cot x+C \)
\( ^{\mathrm{c}} \cdot \frac{e^{2 x} \tan x}{2}+C \)
\( ^{\mathrm{D} \cdot \frac{e^{2 x} \cot x}{2}}+C \)


If \( \boldsymbol{P}=\{1,2\}, \) Find the \( \operatorname{set} \boldsymbol{P} \times \boldsymbol{P} \times \boldsymbol{P} \)


Difference of 99.999 and 100 is
A. 1.11
B. 1.000
\( c .0 .00 \)
D. 0.01


Check the continuity of the following
function at \( ^{\prime} \mathbf{2}^{\prime} \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{cc}\frac{x^{2}-4}{2} i f & 0<x<2 \\ 0 \quad \text { if } x=2 & \\ 2-8 x^{-3} \text {if } x>2\end{array}\right. \)


Find the distance between the points (-4,-5) and (-1,1)
\( A \cdot O \)
B. \( 3 \sqrt{2} \)
\( c \cdot 3 \sqrt{5} \)
\( D \cdot 3 \sqrt{3} \)


The velocity of an object fired directly upward is given by \( V=80-32 t \), where \( t \)
is in seconds. When will the velocity be
between 32 and 64 feet per second?
A. The velocity will be between 32 and 64 feet per second between 0.8 seconds after launch and 1.5 seconds
after launch.
B. The velocity will be between 32 and 64 feet per second between 0.5 seconds after launch and 1.5 seconds after launch.
C. The velocity will be between 32 and 64 feet per second between 0.4 seconds after launch and 1.2 seconds
after launch.
D. None of the above


A transition of electron from an higher
orbit to \( 2^{n d} \) orbit produces 10 spectral lines. The higher orbit no. is :
A. seven
B. eight
c. six
D. five


A solid cube and a solid sphere of
identical material and equal masses
are heated to the same temperature and left to cool in the same
surroundings. Then
A. The cube will cool faster because of its sharp edges
B. The cube will cool faster because it has a larger surface area
C. The sphere will cool faster because it is smooth
D. The sphere will cool faster because it has a larger surface area


If \( a+b+c=6 \) and \( a b+b c+c a=11 \)
Find \( \left(a^{2}+b^{2}+c^{2}\right) ? \)
A . 14
B . 25
\( c \cdot 36 \)
D. 47


Verify Lagrange's mean value theorem for the following function on the indicated interval. In each case find a
point \( ^{\prime} c^{\prime} \) in the indicated interval as stated by the Lagrange's mean value theorem:
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}-\boldsymbol{2} \boldsymbol{x}+\boldsymbol{4} \) on \( [\mathbf{1}, \boldsymbol{5}] \)


In a double-slit experiment the angular
width of a fringe is found to be \( 0.2^{\circ} \) on a
screen placed 1 m away. The
wavelength of light used is \( 600 n m \) What will be the angular width of the fringe is the entire experimental apparatus is immersed in water? Take refractive index of water to be \( \frac{4}{3} \)


The electrical charge on a colloidal particle is observed by:
A. ultramicroscope
B. scattering
c. brownian movement
D. electrophoresis


Difference between \( n^{t h} \) and \( (n+1)^{t h} \)
Bohr's radius of H atom is equal to it's
\( (n-1)^{t h} \) Bohr's radius. The value of \( n \)
is:
\( A \cdot 1 \)
B. 2
\( c \cdot 3 \)
D. 4


Write Henderson - Hasselbalch
equation?


A man bought a plot of land for
Rs. 8,47,500 to build a house. He spent Rs. 3,94,252 on building materials and
he paid \( R s .95,846 \) to laboures build
the house. How much money did he spend in all?


Identify the decimal and whole number
from the following.
\( \mathbf{0 . 5 7} \)


Two circular coils 'X' and 'Y' are placed
closed to each other. If the current in the
coil 'X' is changed, will some current be induced in the coil 'Y'? Give reason.


The sum of two numbers is \( 184 . \) If one-
third of the one exceeds one-seventh of
the other by \( 8, \) find the smaller number.


\( \mathbf{1}+\mathbf{2}+\mathbf{3}+\mathbf{4}+\mathbf{5}+\ldots . . \) is a
A. sequence
B. term
c. constant
D. series


The equation of the latusrecta of the ellipse \( 9 x^{2}+4^{2}-18 x-8 y-23=0 \)
are
A \( . y=\pm \sqrt{5} \)
В. \( x=\pm \sqrt{5} \)
c. \( y=1 \pm \sqrt{5} \)
D. \( x=1 \pm \sqrt{5} \)


Cisplatin compound is used in the treatment of which disease?


Amylase enzymes act on
A. Starch
B. Protein
\( c . \) Fat
D. sugar


The vectors \( \vec{A} \) and \( \vec{B} \) are such that \( \vec{A}+ \) \( \vec{B}=\vec{C} \) and \( A^{2}+B^{2}=C^{2} \). Angle \( \theta \)
between positive directions of \( \vec{A} \) and \( \vec{B} \) is
A \( \cdot \frac{\pi}{2} \)
B.
c. \( \pi \)
D. \( \frac{2 \pi}{3} \)


Which sol can be prepared directly by mixing the dispersed phase with dispersion medium?
A. Lyophobic sol
B. Lyophilic sol
c. Both
D. None


Determine whether the following polynomial has \( (x+1) \) as a factor.
\( \boldsymbol{x}^{4}-\boldsymbol{x}^{3}+\boldsymbol{x}^{2}-\boldsymbol{x}+\mathbf{1} \)


State whether the given statement is True or False:

Whenever there is a lightning, there is an earthquake.
A. True
B. False


When conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) is electrolysed with high current using Pt electrodes, the product obtained at anode is:
\( A \cdot S O_{2} \)
в. \( S O_{3} \)
\( c \cdot O_{2} \)
D. \( H_{2} S O_{4} \)


f matrix \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{2} \\ \mathbf{4} & \mathbf{3}\end{array}\right] \) such that \( \boldsymbol{A} \boldsymbol{x}=\boldsymbol{I} \)
then \( \boldsymbol{x}= \)
\begin{tabular}{r}
\( \mathbf{A} \cdot \frac{1}{5}\left[\begin{array}{rr}1 & 3 \\
2 & -1\end{array}\right] \) \\
\hline
\end{tabular}
в. 1
\[
\begin{array}{ll}\overline{\overline{5}} & {\left[\begin{array}{ll}4 & -1\end{array}\right]}\end{array}
\]
c. \( 1\left[\begin{array}{ll}-3 & 2 \\ 5 & -1\end{array}\right] \)
D. \( \frac{1}{5}\left[\begin{array}{ll}-1 & 2 \\ -1 & 4\end{array}\right] \)


The end products of fermentation when sugar is used as raw materials is/are
A. Alcohol and \( C O_{2} \).
B. Alcohol and pyruvate.
c. \( C O_{2} \)
D. Alcohol.


Differentiate the following w.r.t. \( \boldsymbol{x} \)
\( \tan x^{2} \)
A \( \cdot \sec ^{2}\left(x^{2}\right) \)
B. \( \sec ^{2}\left(x^{2}\right) 2 x \)
c. \( \sec ^{2}\left(x^{3}\right) 2 x \)
D. \( \tan ^{2}\left(x^{2}\right) 2 x \)


Assertion
Sulphuric acid reacts with sodium chloride in the following way:
\( 2 \mathrm{NaCl}+\boldsymbol{H}_{2} \boldsymbol{S O}_{4} \rightarrow 2 \mathrm{HCl}+\boldsymbol{N} \boldsymbol{a}_{2} \boldsymbol{S O}_{4} \)
Reason
Sulphuric acid because of its low
volatility can be used to manufacture
more volatile acids from their
corresponding salts.
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


Among \( L i C l, B e C l_{2}, B C l_{3} \) and \( C C l_{4} \)
the covalent charecter varies as:
A \( \cdot \operatorname{Li} C l<B e C l_{2}>B C l_{3}>C C l \)
в. \( L i C l>B e C l_{2}<B C l_{3}<C C l_{4} \)
c. \( L i C l<B e C l_{2}<B C l_{3}<C C l \)
D. \( L i C l>B e C l_{2}>B C l_{3}>C C l_{4} \)


Which gives only glucose by hydrolysis?
A. Sucrose
B. Raffinose
c. Maltose
D. Galactose


If \( \frac{2}{3}, k, \frac{5 k}{8} \) are in A.P. then \( \mathbf{k}= \)


A relation \( \rho \) on the set of real number \( \boldsymbol{R} \)
is defined as follows:
\( x \rho y \) if any only if \( x y>0 . \) Then which of
the following is/are true? This question has multiple correct options
A \( . \rho \) is reflexive and symmetric
B. \( \rho \) is symmetric but not reflexive
c. \( \rho \) is symmetric and transitive
D. \( \rho \) is an equivalence relation


In Drosophila, a set of homeotic genes which control body plan at the time of organ differentiation is known as
A. TATA box
B. Homeobox
c. Pribnow box
D. All of the above


Which of the following non-metal can be used as plant fertilizer and for plant fixation?
A. Nitrogen
B. Carbon
c. sulphur
D. lodine


Heat of combustion of benzoic acid
\( \left(C_{6} H_{5} C O O H\right) \) at constant volume at
\( 25^{0} \) is \( 3233 \mathrm{KJ} / \) mole. When \( 0.5 \mathrm{g} \) of
benzoic acid is burnt in bomb
calorimeter, the temperature of
calorimeter increased by \( 0.53^{0} C . \) Now in the same bomb calorimeter 1g of
\( C_{2} H_{6} \) burnt then temperature
increased by \( 2.04^{0} C . \triangle H \) for
combustion of \( \boldsymbol{C}_{2} \boldsymbol{H}_{6} \) is?


Graphite and diamond are:
A. polymorphs
B. allotropes
c. different crystal structure
D. all of these


What is the electric current required to deposit 0.972 g of chromium in three hours?
(E.C.E. of chromium is 0.00018 g/c)
A . \( 0.50 A \)
B. 1A
c. zero
D. 2.5A


\( \int_{\alpha}^{\beta} \sqrt{(x-\alpha)(\beta-x)} d x \) equals
A \( \cdot \frac{\pi}{2}(\beta-\alpha) \)
В \( \cdot \frac{\pi}{8}(\beta-\alpha) \)
c. \( \frac{\pi}{8}(\beta-\alpha)^{2} \)
D. None of these


A circle passes through (0,0) and (1,0) and touches the circle \( x^{2}+y^{2}=9 \)
then the centre of circle is
\( ^{\mathbf{A}} \cdot\left[\frac{3}{2}, \frac{1}{2}\right] \)
В. \( \left[\frac{1}{2}, \frac{3}{2}\right] \)
c. \( \left[\frac{1}{2}, \frac{1}{2}\right] \)
D. \( \left[\frac{1}{2}, \pm \sqrt{2}\right] \)


M is the midpoint of \( \overline{A B} \). The coordinates of \( A \) are (-2,3) and the coordinates of \( \mathrm{M} \) are \( (1,0) . \) Find the coordinates of B.
A \( \cdot(-1 / 2,3 / 2) \)
в. (4,-3)
c. (-4,3)
D. (-5,6)
E. none of these


If \( A B=D E, B C=E F \) and \( A C=D F \)
then \( \Delta A B C_{-}-_{-} \Delta D E F \)
\( A \cdot \cong \)
B. \( \approx \)
\( c \cdot t \)
D. >


The pressure exerted by the weight of a
cubical block of a side \( 3 \mathrm{cm} \) on the
surface is \( 5 P a . \) The force acting on the
surface \( \boldsymbol{p} \times \mathbf{1 0}^{-4} \boldsymbol{N} \) then \( \mathrm{p}= \)


A sonometer wire, \( 100 \mathrm{cm} \) in length has a fundamental frequency of 330 Hz. The velocity of propagation of transverse waves along this wire is :
A \( .330 \mathrm{ms}^{-1} \)
B. \( 660 \mathrm{ms}^{-1} \)
C. \( 115 \mathrm{ms}^{-1} \)
D. \( 990 \mathrm{ms}^{-1} \)


The elements in the middle of the
periodic table are called:
A. metalloids
B. transition elements
c. rare earth element
D. noble gases


If \( \vec{r}=2 \hat{i}+\hat{j} \mathrm{m} \) and \( \vec{F}=\hat{i}+2 \hat{j} N . \) Then
the magnitude and direction of torque \( \tau \)
is :
A \( \cdot 4 N m \) along \( 45^{\circ} \) with \( x \) -axis or \( y \) -axis
B. 3Nm along 45 \( ^{\circ} \) with \( x \) -axis or \( y \) -axis.
c. \( 4 N m \) along \( z \) -axis
D. \( 3 N m \) along \( z \) -axis


\( \int\left(a-a^{n x}\right) d x= \)
A. \( a x-\frac{a^{n x}}{n \log a}+c \)
в. \( a x+\frac{a^{n x}}{n \log a}+c \)
c. \( a x+\frac{a^{n x}}{\log a}+c \)
D. \( a x+\frac{a^{n x+1}}{\log a}+c \)


When pure ammonium chloride is dissolved in pure water, the \( p H \) of the resulting solution is not \( 7 . \) This is
because:
A. ammonium ions accept protons from water molecules leaving free \( O H^{-} \) ions in the solution
B. ammonium ions donate protons to water molecules forming \( H_{3} O^{+} \) ions in the solution
c. ammonium ions combine with water molecules to give the weak base, ammonium hydroxide
D. chloride ion make the solution acidic


The phenomenon of rotation of plane polarized light is called:
A. Kerr effect
B. Double refraction
c. optical activity
D. Dichroism


Which one of the following is an example of a hydrophilic colloidal sol?
A. Sulphur
в. \( A s_{2} S_{3} \)
c. Gold sol
D. Starch


Light travels in two media \( A \) and \( B \) with
speeds \( 1.8 \times 10^{8} m s^{-1} \) and \( 2.4 \times \)
\( 10^{8} m s^{-1} \) respectively. Then the critical
angle between them is
A \( \cdot \sin ^{-1}\left(\frac{2}{3}\right) \)
в. \( \tan ^{-1}\left(\frac{3}{4}\right) \)
\( ^{\mathbf{c}} \cdot \tan ^{-1}\left(\frac{2}{3}\right) \)
D. \( \sin ^{-1}\left(\frac{3}{4}\right) \)


Zener diode is used as


f \( y=\sin \left(2 \sin ^{-1} x\right), \) then prove that
\( \frac{d y}{d x}=2 \sqrt{\frac{1-y^{2}}{1-x^{2}}} \)


The ratio of \( e / m \) for a cathode ray:
A. varies with a gas in a discharge tube
B. is fixed
C. varies with different electrodes
D. is maximum if hydrogen is taken


A gramophone disc is rotating at 78 rotations per minute. Due to power cut,
it comes to rest after \( 30 s \). The angular retardation of the disc will be :
A. 0.27 radians \( / \sec ^{2} \)
B. 0.127 radians \( / \) sec \( ^{2} \)
c. 12.7 radians \( / \mathrm{secc}^{2} \)
D. zero.


In the given figure distance of the point from A where the electric field is zero is
\( \mathbf{A} \cdot 10 \mathrm{cm} \)
B. 33 cm
c. \( 20 \mathrm{cm} \)
D. None of these


A reaction of first - order completed \( 90 \% \) in 90 minutes, hence, it is
completed \( 50 \% \) in approximately:
A. 50 min
в. 54 min
c. 27 min
D. 62 min


In trees, death of protoplasts is
essential for vital function such as
A. Stomatal movements
B. Food transport
c. water transport
D. Both water and food transport


When a vehicle travels very fast, a region of is created
temporarilyjust behind it.
A. High pressure
B. Low pressure
c. High density
D. Cyclone


Sodium sulphate is soluble in water,
whereas barium sulphate is sparingly
soluble because:
This question has multiple correct options
A. the hydration energy of sodium sulphate is more than its lattice energy
B. the lattice energy of barium sulphate is more than its hydration energy
C. the lattice energy has no role to play in solubility
D. the hydration energy of sodium sulphate is
less than its lattice energy


White of an egg whipped with water
acts as:
A. macromolecular colloid
B. associated colloid
c. molecular colloid
D. normal electrolytic solution


IUPAC name of, \( \boldsymbol{H}_{\mathbf{2}} \boldsymbol{N}-\boldsymbol{C} \boldsymbol{H}_{\mathbf{2}}-\boldsymbol{C} \boldsymbol{H}_{2}- \)
\( \boldsymbol{C H}_{3} \) is:
A. propan-1-amine
B. propanamine-1,2
c. dipropane-1,2-amine
D. diamino-1, 2-propane


The \( X-X \) bond length is \( 1.00 \dot{A} \) and \( C-C \) bond length is 1.54 A. If
electronegativities of ' \( X^{\prime} \) and ' \( C^{\prime} \) are 3.0
and 2.0 respectively, the \( C-X \) bond
length is likely to be:
A. 1.27 an a
в. 1.18 \( \dot{A} \)
c. \( 1.08 \AA \)
D. \( 1.28 \dot{A} \)


If the sum and sum of squares of 10
observations are 12 and 18 resp., then, The \( S . D \) of observations is :
A \( \cdot \frac{1}{5} \)
B. \( \frac{2}{5} \)
\( c \cdot \frac{3}{5} \)
D. \( \frac{4}{5} \)


\( \boldsymbol{A}=\left|\begin{array}{ccc}\mathbf{1} & \mathbf{1} & \mathbf{1} \\ \mathbf{1} & \mathbf{1}+\boldsymbol{x} & \mathbf{1} \\ \mathbf{1} & \mathbf{1} & \mathbf{1}+\boldsymbol{y}\end{array}\right|= \)
A . \( x y \)
в. \( x+y \)
c \( . x-y \)
D. \( x^{2} y^{2} \)


\( C \)
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}-\boldsymbol{C H}_{3} \)
IUPAC name of the compound is:
A. Isopropylchloride
B. 2-Chloropropane
c. 1 -chloro-1-methylethane
D. None of the above


In the given figure, \( B O \) and \( C O \) are the
bisectors of the exterior angles meeting
each other at \( 0 . \) If \( \angle A=70^{\circ} \) find \( \angle B O C \)
in degrees.


The bond order of \( H e_{2}^{+} \) molecule ion is:
A .
B. 2
\( c \cdot \frac{1}{2} \)
D.


Select and write the most appropriate answer from the given alternatives for the following:A particle rotates in U.C.M. with tangential velocity \( v \) along a horizontal circle of diameter \( D \). Total
angular displacement of the particle in
time 't' is
A. \( v t \)
B. \( \left(\frac{v}{D}\right)-t \)
c. \( \frac{v t}{2 D} \)
D. \( \frac{2 v t}{D} \)


In a certain loaded transformer, the
secondary voltage is one-fourth the primary voltage. The secondary current is
A. one-fourth the primary current
B. four times the primary current
c. equal to the primary current
D. one-fourth the primary current and equal to the primary current


toppr
Q туре your question
reactions that are physically separated. So that the electrons must travel
through a wire from the reducing agent to the oxidizing agent.

The reducing agent loses electrons and is oxidized in a reaction that takes
place at an electrode is called the anode. The oxidizing agent gains electrons and is reduced in a reaction
that takes at an electrode is called the
cathode.

To maintain a net zero charge in each compartment, there is a limited flow of ions through a salt bridge. For example, in a car battery the reducing agent is oxidized by the following reaction, which involves a lead
\( (P b) \) anode and sulfuric acid \( \left(H_{2} S O_{4}\right) \)
Lead sulfate \( \left(P b S O_{4}\right), \) protons \( (H) \)
and electrons \( \left(e^{-}\right) \) are produced
At the cathode, the below reaction
occurs :
\( \boldsymbol{P b O}_{2}+\boldsymbol{H}_{2} \boldsymbol{S O}_{4}+\mathbf{2 H}^{+}+\boldsymbol{2} \boldsymbol{e}^{-} \rightarrow \)
PbSO \( _{-} 4+2 H_{-} 20 \$ \$ \)
At the anode, the below reaction occurs
\( \boldsymbol{P b}+\boldsymbol{H}_{2} \boldsymbol{S O}_{4} \rightarrow \boldsymbol{P b S O}_{4}+\boldsymbol{2} \boldsymbol{H}^{+}+\boldsymbol{2} \boldsymbol{e}^{-} \)
Electrons are produced by a chemical reaction that takes place at the:
A. anode
B. cathode
c. lead oxide electrode
D. oxidizer
E. salt bridge,


The process of expelling waste from the organism is called
A. Digestion
B. Ingestion
c. Excretion
D. Reflex action


What is a lone pair of electrons,explain with suitable example?


Scientific name of plant family ends in
A . -ales
B . -ata
c. - sida
D. -eae / aceae


Antineutrino can be detected during the emission of :
A . \( \alpha \) -rays
B. \( \beta \) -particles
c. protons
D. X-rays


Cellulose is the major component of cell
walls of
A. Pseudomonas
B. Saccharomyces
c. Pythium
D. xanthomonas


If a water falls from a dam into a turbine
wheel \( 19.6 m \) below, then the velocity of
water at the turbines is ( take \( g= \)
\( \left.9.8 m / s^{2}\right) \)
A \( .9 .8 m / s \)
в. \( 19.6 \mathrm{m} / \mathrm{s} \)
c. \( 39.2 \mathrm{m} / \mathrm{s} \)
D. \( 98.0 m / s \)


Fill in the blank:
In the carbon cycle, from which stars, hotter than the Sun, obtain their energy,
the \( _{6} C^{12} \) isotope
A. splits up into three alpha particles
B. fuses with another \( _{6} C^{12} \) nucleus to form \( _{12} M g^{2} \)
c. is completely converted into energy
D. is regenerated at the end of the cycle


The number of molecules of pyruvic
acid formed from one molecule of
glucose at the end of glycolysis is
\( A \)
B. 2
\( c \cdot 3 \)
\( D \cdot 4 \)


Determine the mode of the following
data.
\begin{tabular}{llllll}
Marks & 10 & 16 & 12 & 19 & 13 \\
Number of Students & 3 & 3 & 4 & 2 & 6 \\
\hline
\end{tabular}
A . 12
B . 13
c. 14
D. 20


Let \( *: \boldsymbol{R} \times \boldsymbol{R} \rightarrow \boldsymbol{R} \) given by \( (\boldsymbol{a}, \boldsymbol{b}) \rightarrow \)
\( a+4 b^{2} \) is a binary operation, compute
(-5)\( *(2 * 0) \)


If the cube root of \( n \) is \( 4, \) then find the
square root of \( n \)
A .4
B. 6
\( c \cdot 8 \)
D. 16


\( * \boldsymbol{f}(\boldsymbol{x})= \)
\( \frac{1-\sin x}{(\pi-2 x)^{2}} \cdot \frac{\log \sin x}{\log \left(1+\pi^{2}-4 \pi x+4 x^{2}\right)}, x \)
\( \pi / 2 \) The assigned to function at \( x= \)
\( \pi / 2 \) in order that it may be continuous
at \( x=\pi / 2 \) is \( -\frac{1}{m} . \) Find \( m \)


In the circuit shown in figure, when the
circuit is completed, the hammer strikes the gong. Which of the following
force is responsible for the movement of
hammer?
A. Gravitational force alone
B. Electrostatic force alone
c. Magnetic force alone
D. Frictional force alone


If \( a^{2}+b^{2}=34 \) and \( a b=12 ; \) find :
\( 7(a-b)^{2}-2(a+b)^{2} \)
A. 186
B . 46
c. -46
D. -186


State whether the given statement is True or False:
The equation \( F=\frac{G M_{1} M_{2}}{r^{2}} \) is valid for all bodies.
A. True
B. False


Which of these molecules have non-
bonding electron pairs on the central
atom?
\( \mathbf{I}: \boldsymbol{S} \boldsymbol{F}_{\mathbf{4}} \quad \|: \boldsymbol{I} \boldsymbol{C} \boldsymbol{l}_{3} \)
\( \| \mathrm{II}: \boldsymbol{S} \boldsymbol{O}_{2} \)
A. II only
B. I and II only
c. I and III only
D. I, II and III


1 kg ice at \( -20^{\circ} \mathrm{C} \) is mixed with 1 kg
steam at \( 200^{\circ} \mathrm{C} \). Then find equilibrium
temperature and mixture content.
A \( \cdot T=100^{\circ} \mathrm{C}, \frac{20}{27} \mathrm{kg} \) steam and \( \frac{34}{27} \mathrm{kg} \) water
B \( \cdot T=0^{\circ} C, \frac{20}{27} \) kg steam and \( \frac{34}{27} \) kg water
c. \( T=100^{\circ} \mathrm{C}, \frac{34}{27} \mathrm{kg} \) steam and \( \frac{20}{27} \) kg water
D. \( T=0^{\circ} C, \frac{10}{27} \) kg steam and \( \frac{38}{27} \) kg water


A uniform field of induction \( B \) is
changing in magnitude at a constant rate \( d B / d t . \) You are given a mass \( m \) of copper which is to be drawn into a wire
of radius \( r \) and formed into a circular
loop of radius \( R \). Show that the induced current in the loop does not depend on the size of the wire of the loop.

Assuming \( B \) perpendicular the loop
prove that the induced current \( i= \) \( \frac{m}{4 \pi \rho \delta} \frac{d B}{d t} \) where \( \rho, \) is the resistivity and
\( d \) is the density of copper


State whether the set is finite or
infinite:

The set of all schools in this world


Find the value of :
\( \frac{i^{6}+i^{7}+i^{9}}{i^{2}+i^{3}} ? \)


If the roots of the equation \( x^{3}-12 x^{2}+ \)
\( 39 x-28=0 \) are in A.P., then their
common difference will be,


Show that \( : \cot \left(A+15^{\circ}\right)- \)
\( \tan \left(A-15^{\circ}\right)=\frac{4 \cos 2 A}{1+2 \sin 2 A} \)


Write five important aspects of chemical equilibrium.