The hybrid states of phosphorous atoms
in \( P C l_{5} \) and \( P B r_{3} \) in gaseous phase
\( \operatorname{are} s p^{3} d . \) But in solid \( P C l_{5} \)
phosphorous shows \( s p^{3} d^{2} \) hybrid state. While \( P \) in \( P B r \) is in \( s p^{3} \) hybrid state. This is because:
This question has multiple correct options
A. \( P C l_{5} \) in solid form exists as \( \left[P C l_{4}\right]^{+}\left[P C l_{6}\right] \)
B. \( P B r_{5} \) in solid form exists as \( \left[P C l_{4}\right]^{+}\left[P B r_{6}\right]^{-} \)
c. \( P C l_{5} \) in solid form exists as \( \left[P C l_{4}\right]^{+} C l^{-} \)
D. \( P B r_{5} \) in solid form exists as \( \left[P B r_{4}\right]^{+} B r^{-} \)


Which one of the following is not a
base?
в. \( N H_{2} O H \)
\( ^{\mathbf{c}} \cdot\left(C H_{3}\right)_{3} N \)
D. \( H N_{3} \)


Solve
\( \left|\begin{array}{ccc}\boldsymbol{a}^{2}+\mathbf{1} & \boldsymbol{a} \boldsymbol{b} & \boldsymbol{a} \boldsymbol{c} \\ \boldsymbol{a} \boldsymbol{b} & \boldsymbol{b}^{2}+\mathbf{1} & \boldsymbol{b} \boldsymbol{c} \\ \boldsymbol{a} \boldsymbol{c} & \boldsymbol{b} \boldsymbol{c} & \boldsymbol{c}^{2}+1\end{array}\right|=\boldsymbol{a}^{2}+\boldsymbol{b}^{2}+ \)
\( c^{2}+1 \)


A satellite of mass 'm', moving around
the earth in a circular orbit of radius \( \boldsymbol{R} \)
has angular momentum \( L \). The areal velocity of satellite is:
\( \mathbf{A} \cdot L / 2 m \)
в. \( L / m \)
\( \mathbf{c} \cdot 2 L / m \)
D. \( 2 L / m_{e} \)


lon uptake is called active because
A. Ions are active
B. Energy is expended
c. lons move freely
D. Ions move passively


Fungi lacking cross walls in the mycelium belong to
A. Ascomycetes
B. Phycomycetes
c. Deuteroomycetes
D. Basidioomycetes


Impulse of force is
A. Product of average force and time
B. Division of average force and time
C. Integration of average force and time
D. All of the above


Calculate the molar mass of the
following substances
(a) Ethyne \( C_{2} H_{2} \)
(b) Sulphur molecule \( \boldsymbol{S}_{8} \)
(c) Phophorous
molecule \( P_{4}(d) \) Nitric acid \( H N O_{3}(e) \) Hydrochloride acid \( \$ \boldsymbol{H} \boldsymbol{C l} \)


A train moves in straight line with a uniform acceleration. If \( x \) and \( y \) be the velocities with which the front and rear end of the train respectively cross a fixed pole then the velocity with which the middle of the train crosses the pole is:
\( ^{\text {A } \cdot} \frac{x^{2}+y^{2}}{2} \)
в. \( \frac{2 x y}{x+y} \)
c. \( \sqrt{\frac{1}{2}\left(x^{2}+y^{2}\right)} \)
D. \( \sqrt{\frac{1}{2}\left(y^{2}-x^{2}\right)} \)


A vernier callipers has its main scale of \( 10 \mathrm{cm} \) equally divided into 200 equal parts. Its vernier scale of 25 divisions
coincides with \( 12 \mathrm{mm} \) on the main
scale. The least count of the instrument
is -
\( A \cdot 0.020 \mathrm{cm} \)
B. \( 0.002 \mathrm{cm} \)
c. \( 0.010 \mathrm{cm} \)
D. \( 0.001 \mathrm{cm} \)


Which of the following is used as life saving substance as blood plasma?
A. Cellulose
B. Teflon
c. Bakelite
D. Polyvinyl pyrrolidone


In anaerobic respiration, acetaldehyde is reduced to form alcohol by utilising
\( \mathrm{NADH}_{2} \) obtained from
A. Glycolysis.
B. Terminal oxidation
c. Krebs cycle.
D. Acetylation.


If 'n' represents total number of asymmetric carbon atoms in a compound, the possible number of optical isomers of the compound is :
A \( .2 n \)
B . \( n^{2} \)
\( c \cdot 2^{n} \)
D. \( 2 n+2 \)


What are the postulates of Rutherford? What are his drawbacks?


What type of a relation is "Less than" in the set of real numbers?
A. only symmertric
B. only transitive
c. only reflexive
D. equivalence relation


Find the oxidation number of elements
in each case.
\( S \) in \( N a_{2} S_{2} O_{3}, S_{4}, S_{8} \) and \( N a_{2} S_{2} O_{7} \)
\( \mathbf{A} \cdot+2,0,0,+6 \)
B. +1,1,0,+5
c. 0,0,1,+4
D. None of these


Which of the following is not a carp?
A. Labeo rohita
B. Catla catla
c. cyprinus caprio
D. Mystus


If true enter 1 , else enter 0 .
Major elimination product if the given
compounds is heated with strong base
is \( \boldsymbol{C H}_{3}-\boldsymbol{C H}=\boldsymbol{C H}- \)
COOH \( (\text { trans }) \)


A sinusoidal wave travelling in the positive direction of \( x \) on a stretched string has amplitude \( 2.0 \mathrm{cm} \) wavelength \( 1 \mathrm{m} \) and wave velocity 5.0 \( \mathrm{m} / \mathrm{s} \cdot \mathrm{At} \mathrm{x}=0 \) and \( \mathrm{t}=0, \) it is given that
displacement \( y=0 \) and \( \frac{\partial y}{\partial t}<0 . \) Express the wave function correctly in the from \( y \) \( =f(x, t):- \)
A \( \cdot y=(0.04 \mathrm{m})\left[\sin \left(\pi m^{-1} 1\right) \mathrm{x}-\left(10 \pi s^{-1} 1\right) t\right] \)
B. \( y=(0.02 \mathrm{m}) \cos 2 \pi(x-5 t) \)
c. \( y=(0.02 \mathrm{m})\left[\sin \left(2 \pi m^{-1} 1\right) x-\left(10 \pi s^{-1}\right)\right] t \)
D \( \cdot y=(0.02 \mathrm{m}) \cos \pi\left(x-5 t+\frac{1}{4}\right) \)


The function \( f(x)=x^{3}-27 x+8 \) is
increasing when
A . \( |x|<3 \)
в. \( |x|>3 \)
c. \( -3<x<3 \)
D. none of these


The average kinetic energy of thermal
neutron is of the order of :
(Boltzmann's constant \( k_{B}=8 \times \)
\( \left.10^{-5} e V / K\right) \)
A . \( 0.03 e V \)
в. \( 3 e V \)
c. \( 3 k e V \)
D. 3MeV


(a) Find the unit vector which is parallel to the vector \( \overrightarrow{\mathrm{A}}=2 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}-2 \widehat{\mathrm{k}} \)
(b) Find the unit vector which is
perpendicular to both of the vector \( \overrightarrow{\mathrm{A}}=2 \hat{\mathrm{i}} \) and \( \vec{B}=3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+12 \widehat{\mathrm{k}} \)


Which the following commercial application of phytohormones are correct?
A. Auxins are extensively used in agriculture to promote flowering in pineapples
B. Ethephon is used for promoting female flower in cucumbers, thereby increase the yield
C. Abscisic acid is of great use in the ripening the fruits like mango, orange, pineapple etc.
D. Cytokinins are used for keeping freshness in leafy and green vegetables.
\( A \cdot a, b \) and \( c \)
B. b, cand d
\( c \cdot a, \) cand d
D. a band d


A wire of length L and radius r fixed at
one end and a force \( F \) applied to the other end produces and extension \( l \). The
extension produced in another wire of the same material of length 2Land radius \( 2 r \) by a force \( 2 F \) is:
\( \mathbf{A} \cdot l \)
в. \( 2 l \)
\( c \cdot \frac{l}{2} \)
D. 4


\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\ddot{\boldsymbol{S}}-\boldsymbol{C H}_{2}-\boldsymbol{B r} \stackrel{\boldsymbol{H O H}}{\longrightarrow} \)
\( [\boldsymbol{X}] \)
In the given reaction, \( [\boldsymbol{X}] \) is:
A \( \cdot C H_{3}-C H_{2}-S-C H_{2}-O H \)
B. \( C H_{3}-C H_{2}-S-C H_{2}-C H_{2}-O H \)
c. 1: 1 mixture of \( (A) \) and \( (B) \)
D. 2: 1 mixture of (A) and (B)


The magnetic moment vectors \( \mu_{s} \) and
\( \mu_{l} \) associated with the intrinsic spin angular momentum \( S \) and orbital angular momentum \( l, \) respectively, of an electron are predicted by quantum theory (and verified experimentally to a high accuracy) to be given by:
\( \boldsymbol{\mu}_{s}=-(e / \boldsymbol{m}) \boldsymbol{S} \)
\( \boldsymbol{\mu}_{l}=-(e / 2 m) l \)
Which of these relations is in
accordance with the result
expected classically? Outline the derivation of the classical result.


The beautiful natural phenomenon of
the rainbow is a combination of which
of the following different phenomena?
A. Refraction, reflection
B. Dispersion, refraction
c. Refraction, dispersion, reflection
D. Reflection, dispersion


A lead bullet pertrates into a solid object and melts. Assuming that \( 50 \% \) of its kinetic energy was used to heat it, if the initial speed (in \( \mathrm{m} / \mathrm{s} \) ) of the bullet is \( 100 \times 100 \times J / K g \) and specific heat capacity of lead \( =125 \mathrm{J} / \mathrm{kg} \mathrm{K} \)


One mole of an ideal monoatomic gas is
heated at a constant pressure of one
atmosphere from \( 0^{\circ} \mathrm{C} \) to \( 100^{\circ} \mathrm{C} \). Then the change in the internal energy is :
A \( .20 .80 \times 10^{2} J \)
\( J \)
B . \( 12.48 \times 10^{2} J \)
c. \( 832 \times 10^{2} J \)
D. \( 6.25 \times 10^{2} J \)


Silk worm feeds on
A. Mango leaves
B. Apple leaves
C . Grape leaves
D. None of the above


The persistence of sound in a closed enclosure, due to continuous reflections
at the walls, even after the source has
stopped producing sound is known as
A. The persistence of hearing
B. An echo
c. Reverberation
D. The ultra sounds


A particle is falling freely under gravity.
In first \( t \) second it covers distance \( x_{1} \)
and in the next \( t \) second it covers
distance \( x_{2}, \) then \( t \) is given by
A. \( \sqrt{\frac{x_{2}-x_{1}}{g}} \)
B. \( \sqrt{\frac{x_{2}+x_{1}}{g}} \)
c. \( \sqrt{\frac{\left(x_{2}-x_{1}\right)}{2 g}} \)
D. \( \sqrt{\frac{\left(x_{2}+x_{1}\right)}{g}} \)


Hydrogen does not combine with
\( A \cdot S b \)
B. Na
c. не
D. zn


Find the equation of the circle of minimum radius which contains the
three circles
\( \boldsymbol{S}_{1} \equiv \boldsymbol{x}^{2}+\boldsymbol{y}^{2}-\boldsymbol{4} \boldsymbol{y}-\boldsymbol{5}=\boldsymbol{0} \)
\( \boldsymbol{S}_{2} \equiv \boldsymbol{x}^{2}+\boldsymbol{y}^{2}+\mathbf{1 2} \boldsymbol{x}+\boldsymbol{4} \boldsymbol{y}+\boldsymbol{3 1}=\mathbf{0} \)
and \( S_{2} \equiv x^{2}+y^{2}+6 x+12 y+ \)
\( \mathbf{3 6}=\mathbf{0} \)


An electron in \( 2^{n d} \) orbit gains energy
and goes to \( 4^{t h} \) orbit. What are the
differences in angular momentums experienced by the electron due to the transition?
A \( \cdot \frac{2 h}{\pi} \)
в. \( \frac{h}{2 \pi} \)
\( c \cdot \frac{h}{\pi} \)
D. \( \frac{3 h}{4 \pi} \)


A step-down transformer is connected to 2400 volts line and 80 amperes of current is found to flow in output load.
The ratio of the turns in primary and secondary coil is \( 20: 1 . \) If transformer efficiency is \( 100 \% \), then the current flowing in primary coil will be :
\( A \cdot 8 A \)
в. \( 4 A \)
\( c .5 A \)
D. \( 9 A \)


Sound waves travel fastest in.
A. solids
B. liquids
c. gases
D. vacuum


Identify the coral islands from the following.
A. Fij
B. Maldives
c. Laccadives
D. All of the above


A thermodynamic system is said to be in thermal contact with another system
if it can exchange:
A. energy through the process of heat transfer
B. energy through the process of work
c. matter
D. all of the above


A parallel plate condenser consists of two circular plates each of radius \( 2 \mathrm{cm} \) separated by a distance of 0.1 m
time varying potential difference of \( 5 \times \) \( 10^{13} v / s \) is applied across the plates of the condenser. The displacement
current is:
\( \mathbf{A} \cdot 5.50 A \)
B . \( 5.56 \times 10^{2} A \)
c. \( 5.56 \times 10^{3} A \)
D. \( 2.28 \times 10^{4} A \)


The number of solution of the equation \( |\cot x|=\cot x+\frac{1}{\sin x} \operatorname{in}[0,2 \pi] \) is
\( A \cdot 2 \)
B. 4
c. 0
\( D \)


Polymer used in making capsules is:
A. poly glycolic acid
B. poly lactic acid
c. Nylon - 2 - Nylon - 6
D. PHBV


A smaller block of mass 'm' is placed on another block of mass M. When a
horizontal force \( F \) is applied on the block of mass \( \mathrm{M} \) as shown in the figure, the smaller block does not slide. If the
magnitude of friction between the
bigger block and ground is 'f',
determine the magnitude and direction
of friction between the two blocks.
A \( \cdot \frac{F}{M+m} \)
в. \( \frac{F-f}{M+m} \)
c. \( \frac{F+f}{M+m} \)
D. \( \frac{F-f}{m} \)


At least a half of the total \( C O_{2} \) fixation
on- Earth is carried out through photosynthesis by
A. angiosperms
B. gymnosperms
c. algae
D. bryophytes


In an a.c., circuit with phase voltage \( \boldsymbol{V} \)
and current \( I \), the power dissipated is
\( ^{A} \cdot \frac{V I}{2} \)
B. \( \frac{V I}{\sqrt{2}} \)
c. \( V I \)
D. VIcos\theta


Which one of the following forms a colourless solution in an aqueous medium?
[Atomic number \( \boldsymbol{S c}=\mathbf{2 1}, \boldsymbol{T} \boldsymbol{i}= \)
\( \mathbf{2 2}, \boldsymbol{V}=\mathbf{2 3}, \boldsymbol{C r}=\mathbf{2 4}] \)
\( \mathbf{A} \cdot V^{3} \)
в. \( C r^{3} \)
\( c \cdot T i^{3} \)
D. \( S c^{3} \)


Using differentials, find the sum of digits approximate value of the following up to 3 places of decimal. \( (26)^{\frac{1}{3}} \)


A series LCR circuit with \( R=20 \Omega, L=1.5 \) \( \mathrm{H} \) and \( \mathrm{C}=35 \mu \mathrm{F} \) is connected to a
variable-frequency \( 200 \mathrm{V} \) ac supply. When the frequency of the supply equals the natural frequency of the circuit, what is the average power transferred to the circuit in one
complete cycle?


What is true of bacillariophyceae?
A. Epitheca is smaller
B. Hypotheca is smaller.
c. Both epitheca and hypotheca have same size
D. Any of the two can be larger.


A silver article generally turns black when kept in the open for a few days. The article when rubbed with
toothpaste again starts shining. Name the black substance formed and give its chemical formula:
A . silver oxide, \( \left(A g_{2} \text { , } \) ) \right.
B. Silver chloride, \( (A g C l) \)
C. Silver sulphide, \( \left(A g_{2} S\right) \)
D. silver iodide,( \( (A g I) \)


constant pressure. The thermal capacity of calorimeter system is \( 17.7 k J K^{-1} .(R= \)
\( \left.8.313 m o l^{-1} K^{-1}\right) \) (only magnitude in
nearest integer in \( \mathrm{kj} / \mathrm{mol} \) )


The hydrolysis of ethyl acetate is a reaction of:
\( \boldsymbol{C H}_{3} \boldsymbol{C O O C}_{2} \boldsymbol{H}_{5}+\boldsymbol{H}_{2} \boldsymbol{O} \stackrel{\boldsymbol{H}^{+}}{\longrightarrow} \)
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H}+\boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O H} \)
A. zero order
B. first order
c. second order
D. third order


Two identical travelling waves, moving in the same direction, are out of phase by \( \pi / 2 \) rad. What is the amplitude of
the resultant wave in terms of the
common amplitude \( y_{m} \) of the two
waves.


The substance \( A \), when dissolved in
solvent \( \mathrm{B} \), shows the molecular mass
corresponding to \( A_{3} . \) The Vant Hoff's factor will be:
A . 1
B. 2
\( c \cdot 3 \)
D. \( 1 / 3 \)


Dinoflagellates belongs to
A. Pyrrophyta
B. chrysophyta
c. Sporozoa
D. zooflagellata


What is true for \( \left[\boldsymbol{F} e(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right]^{3-} \) and
\( \left[\boldsymbol{F e} \boldsymbol{F}_{6}\right]^{3-}: \)
A. Both are paramagnetic.
B. Only [Fe \( \left.(C N)_{6}\right]^{3-} \) is paramagnetic
C. only \( \left[F e F_{6}\right]^{-3} \) is paramagnetic
D. Both are diamagnetic


The cation responsible for turning moist neutral litmus red on reaction with dil
\( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) is
A . \( H^{+} \)
B. \( N H_{4}^{+} \)
\( c \cdot O^{-} \)
D. \( O_{3}^{+} \)


The produce of a square field when sold at the rate of Rs. 1.50 per 100 sq. metres fetches Rs. \( 1350 . \) What will be the cost of
putting a fence all round the field at the rate of 50 paise per metre?
A. Rs. 549
B. Rs. 575
c. Rs. 675
D. Rs. 600


Which of the following conditions make the process non spontaneous at all temperatures.
A. \( \Delta \mathrm{H}=+\mathrm{ve} ; \Delta \mathrm{s}=-\mathrm{ve} \)
B. \( \Delta \) H \( =- \) -ve; \( \Delta S=+v e \)
c. \( \Delta \) H \( =+v e ; \Delta s=+v e \)
D. \( \Delta H=- \) -ve; \( \Delta S=-v e \)


A baised coin with probability \( \boldsymbol{p}(\mathbf{0}< \)
\( p<1) \) of heads is tossed until a head
appears for the first time. If the probability that the number of tosses required is even is \( \frac{2}{5}, \) find \( 3 p \)


Light is a form of energy.
A. True
B. False


Among the following, water is an example of a/an:
A. element
B. mixture
c. compound
D. none of these


If \( \tan \theta=\frac{b}{a}, \) then the value of
\( a \cos 2 \theta+b \sin 2 \theta \) is
\( \mathbf{A} \cdot b \)
в.
c. \( \frac{a}{b} \)
D. \( \frac{a}{a+b} \)


A simple harmonic motion has an
amplitude \( A \) and time period \( T \). Find the time required by it to travel directly from \( \boldsymbol{x}=\mathbf{0} \) to \( \boldsymbol{x}=\frac{\boldsymbol{A}}{\mathbf{2}} \)


When iron is rusted, it is :
A. reduced
B. oxidised
c. evaporated
D. decomposed


For the hydrolysis of methyl acetate in
aqueous solution the above
tabulated results were obtained:
(a) Show that it follow pseudo first order reaction, as the concentration of water
remains constant.
(b) Calculate the average rate of
reaction between the time interval 10 to
20 seconds.
(Given : log 2=0.3010, log 4 =0.6021)
\begin{tabular}{|c|c|c|c|}
\hline \( \mathrm{t} / \mathrm{s} \) & 0 & 10 & 20 \\
\hline \( \mathrm{r} \mathrm{CH}_{3} \mathrm{COOH}_{3} \mathrm{J} / \mathrm{moll}^{-1} \) & 0.10 & 0.05 & 0.025 \\
\hline
\end{tabular}


Two particles of masses \( m_{1} \) and
\( \boldsymbol{m}_{2}\left(\boldsymbol{m}_{1}>\boldsymbol{m}_{2}\right), \) initially at rest, move
towards each other under an inverse
square law force of attraction. Pick out
the correct statement about the centre
of mass (CM) ofthe system
A. The CM moves towards \( m_{1} \)
B. The CM moves towards \( m_{2} \)
c. The CM remains at rest
D. The motion of CM is accelerated


The freezing point of aqueous solution that contains \( 3 \% \) urea, \( 7.45 \% K C l \) and
\( 9 \% \) of glucose is: \( \left(\operatorname{given} K_{1} \text { of water }=\right. \)
1.86 and assume molarity \( = \) molality
).
A . \( 290 K \)
в. 285.5 К
c. \( 267.42 K \)
D. 250 K


If \( \tan A+\cot A=2 \) then find the value
of \( \tan ^{2} A+\cot ^{2} A \)


What are isotopes of an element?
A. Atoms of a different element with a different number
of neutrons
B. Atoms of a different element with a different number
of protons
C. Atoms of the same element with a different number of
neutrons
D. Atoms of the same element with a different number of
protons


If the equations \( (\boldsymbol{b}+\boldsymbol{c}) \boldsymbol{x}+(\boldsymbol{c}+\boldsymbol{a}) \boldsymbol{y}+(\boldsymbol{a}+\boldsymbol{b})= \)
\( \mathbf{0}, \boldsymbol{c} \boldsymbol{x}+\boldsymbol{a} \boldsymbol{y}+\boldsymbol{b}=\mathbf{0} \) and \( \boldsymbol{a} \boldsymbol{x}+\boldsymbol{b} \boldsymbol{y}+\boldsymbol{c}=\mathbf{0} \)
are consistent, then show that either
\( \boldsymbol{a}+\boldsymbol{b}+\boldsymbol{c}=\boldsymbol{0} \) or \( \boldsymbol{a}=\boldsymbol{b}=\boldsymbol{c} \)


A nucleic acid can be synthesized only in the direction of
A. \( 5-3 \)
B. 3-5
\( c \cdot 5-5 \)
\( D \cdot 3-3 \)


What is a toroid? Mention an expression
for magnetic field at a point inside a toroid?


Identify the name of sheep of Indian breed shown in the image.
A. Nellore sheep
B. Bannur sheep
c. Deccani sheep
D. Ram sheep


Find the \( \lim _{x \rightarrow 0} \frac{\tan x \sin x}{\sin ^{3} x} \)


The displacement \( x \) of a body of mass 1 kg on smooth horizontal surface as a function of time \( t \) is given by \( x=\frac{t^{3}}{3} \)
(where \( x \) is in metres and \( t \) is in
seconds). Find the work done by the external agent for the first one second.


In human beings sex is determined
A. At the time of fertilization of ovum
B. During 6th week of foetal life when androgens are produced
C . Before fertilization of ovum
D. During 7th and 8th weeks of foetal Life when gonads differentiate into testis and ovaries


Q Type your question.
\( \operatorname{arm} \mathrm{PQ}, \) which remains hinged along a
horizontal line taken as the y-axis. A uniform magnetic field \( \overrightarrow{\boldsymbol{B}}=(\mathbf{3} \hat{\mathbf{i}}+ \)
\( 4 \hat{k}) B_{0} \) exists in the region. The loop is
held in the \( x \) -y plane and a current lis passed through it. The loop is now released and is found to stay in the
horizontal position in equilibrium.
(a) What is the direction of the current
n PQ?
(b) Find the magnetic force on the arm
RS.
(c) Find the expression for I in terms of
\( B_{0}, \) a b and \( m \)


Which of the following types of reactions occur when a hydrocarbon has a double bond?
A. Substitution reaction
B. Addition reaction
c. Photolysis
D. None of the above


A woman started developing male characteristics. It may be due to
A. overproduction of adrenal androgens
B. overproduction of-estrogen
c. Damage to mammary estrogen
D. Damage to posterior pituitary


The role of zinc stearate in the process
of vulcanisation is:
A. to accelerate the process
B. to slow down the process
c. to stop the process
D. to initiate the process


The area of the shaded region in the given figure is
\( A \)
в.
c. \( \frac{\pi}{4} \) sq.units
D. \( \pi^{2} \) sq.unis


The coordinate of any point, which lies
in \( \boldsymbol{x} \boldsymbol{y} \) plane, is
\( \mathbf{A} \cdot(x, 0, y) \)
в. \( (x, x, 0) \)
c. \( (x, 0, x) \)
D. \( (y, 0, x) \)


Use of \( _{\text {十一一一一一一一 }} \) in agricultural activities has grown quite a lot hazardous ammonia gases in the atmosphere.
A . insecticides
B. pesticides
c. fertilizers
D. all of the above


A quantity of 15.8 g of \( K M n O_{4} \) can be decolourized in acidic medium by \( (\mathrm{K}= \)
\( 39, M n=55, F e=56 \)
This question has multiple correct options
A . \( 18.25 \mathrm{g} \) HCll
B . \( 22.5 g H_{2} C_{2} O_{4} \)
c. \( 32 g S O_{4} \)
\( \mathrm{D} \cdot 38 \mathrm{g} \mathrm{FeSO}_{4} \)


Arrange the following five steps of
nutrition in correct sequence:
(digestion, assimilation, ingestion, egestion, absorption)


In iodine charge transfer test the color of ether compound formed is:
A. blue
B. pale yello
c. brown
D. dark red


The over-stretching of tendons and ligaments is called as
A. Tonus
B. Tetany
c. sprain
D. Fatigue


A lake ecosystem is
A . Artificial
B. Abiotic
c. Natural
D. Hydrological


On increasing the resistance in a
circuit, the current in it :
A. decreases
B. increases
c. remains unchanged
D. nothing can be said


Which of the following is a true
statement?
A. Plastic is soluble in water
B. Plastic is not a polymer
c. Rayon is made from cellulose
D. All plastics are fire-resistant


n fig \( 1, \) AB and \( \mathrm{CD} \) are parallel to each
others. The value of \( x \) is :
\( 4 \cdot 90^{\circ} \)
B. \( 100^{\circ} \)
\( c \cdot 120 \)
D. 140


In hepatitis yellowing of urine is due to
A. Bilirubin
B. Bile salts
c. Pancreatic juices
D. sperms


Which of the following is known as fusion mixture?
A. mixture of \( N a_{2} C O_{3}+N a H C O_{3} \)
в. \( N a_{2} C O_{3}+10 H_{2} O \)
c. mixture of \( K_{2} C O_{3}+N a_{2} C O_{3} \)
D. \( N a H C O_{3} \)


Technically porous wood is .............. wood.
A. Hard
B. Soft
c. sap
D. Heart


While orbiting around the earth in a spaceship, an astronaut weight becomes
A. greater than their real weight
B. lesser than their real weight
c. zero
D. infinity


Is the following situation possible? If so, determine their present ages.

The sum of the ages of two friends is 20 years.Four years ago, the product of their ages in years was 48
A. Not Possible
B. Yes, 8 and 6
c. Yes \( , 12 \) and 4
D. none


The energy levels of the hydrogen spectrum is shown in figure. There are some transitions \( A, B, C, D \) and \( E \)
Transition \( A, B \) and \( C \) respectively represent
A. first member of Lyman series, third spectral line of Balmer series and the second spectral line of Paschen series
B. ionization potential of hydrogen, second spectral line of Balmer series, third spectral line of Paschen series
c. series limit of Lyman series, third spectral line of Balmer series and second spectral line of Paschen series
D. series limit of Lyman series, second spectral line of Balmer series and third spectral line of Paschen series


Prove that \( : \frac{\tan \Theta}{1-\cot \Theta}+\frac{\cot \Theta}{1-\tan \Theta}=1+ \)
\( \tan \Theta+\cot \Theta \)


Green house effect is mainly due to increase in the levels of
\( A \cdot O_{2} \)
в. \( C O \)
\( c \cdot C O_{2} \)
D. \( N_{2} \)


A flower characterised by
monoadelphous tubular stamens belongs to
A. Solanaceae
B. Liliaceae
c. Malvaceae
D. Brassicaceae


Let \( f \) be a linear function for which
\( \boldsymbol{f}(\boldsymbol{6})-\boldsymbol{f}(2)=12 . \) The value of \( \boldsymbol{f}(\mathbf{1 2})- \)
\( f(2) \) is equal the
A . 12
B . 18
\( c \cdot 24 \)
D. 30


Preparation of ethers by acid dehydration of alcohol a suitable method for:
A. primary alcohol
B. secondary alcohol
c. tertiary alcohol
D. all of these


On heating with bleaching powder, ethyl alcohol is converted into:
A. \( C H_{3} \) СООН
в. \( C H_{3} C H O \)
c. \( C H_{3} C O C H_{3} \)
D. \( C H C l_{3} \)


In the pancreas, there are groups of cells that make insulin. What describes
these cells?
A. An organ in an organism
B. An organ system in an organism
c. Cells within a cell wall
D. Tissue in an organ


The probabilities of \( x, y \) and \( z \) becoming manager are \( \frac{4}{9}, \frac{2}{9} \& \frac{1}{3} \) respectively. The probabilities that the bonus scheme will be introduced if \( x, y \) and \( z \) become managers are \( \frac{3}{10}, \frac{1}{2} \& \frac{2}{5} \) respectively. Find
(i) What is the probatility that the bonus scheme will be introduced? (ii) if
the bonus scheme has teen introduced,
What is the probability that the manager appointed wax \( x ? \)


Two charges are placed at a distance apart. If a glass slab is placed between them, force between them will
A. be zero
B. increase.
c. decrease.
D. remains the same


Arun owns 560 shares of a company
The face value of each shares is Rs. 25
The company declares a dividend of \( 9 \% \)
Calculate the dividend Arun would
received.


A person writes letters to six friends
and addresses the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that at least two of them are in wring envelope.


The four elements called "big-four" which make up \( 95 \% \) of all elements found in a living system are
A. \( \mathrm{C}, \mathrm{H}, \mathrm{O}, \mathrm{N} \)
B. \( \mathrm{C}, \mathrm{H}, \mathrm{O}, \mathrm{P} \)
c. \( \mathrm{c}, \) н, \( 0, \mathrm{s} \)
D. \( \mathrm{C}, \mathrm{N}, \mathrm{O}, \mathrm{P} \)


A cylinder of radius \( R \) and length \( L \) is
placed in a uniform electric field \( \boldsymbol{E} \)
parallel to the cylinder axis. The total flux for the surface of the cylinder is given by :
\( \mathbf{A} \cdot 2 \pi R^{2} E \)
в. \( \frac{\pi R^{2}}{E} \)
c. \( \frac{R}{E} \)
D. zero


A charge is placed at the edge of a cube
of each side ' \( a^{\prime} \). Calculate the electric
flux through each face of the cube.
\( A \cdot \frac{Q}{40} \)
B. \( \frac{Q}{240} \)
\( c \cdot \frac{Q}{20} \)
D. \( \frac{Q}{15 \varepsilon_{0}} \)


Hypo is used in photography because it is :
A. A strong reducing agent
B. A strong oxidizing agent
c. A strong Complexing agent
D. Photo sensitive Compound


If true enter 1 , else enter 0 .
Electronegativity is a derived quantity and can also be directly measured.
\( A \)


Which of the following is a weedicide?
A . IAA
B. 2,4-D
\( c \cdot \) ।ВА
D. NAA


You can increase the amount of force
applied on a body by repeatedly:
A. pushing it
B. pulling it
c. dragging it
D. any or all of the above


Calculate solubility of \( C a_{3}\left(P O_{4}\right)_{2}\left(K_{s p}=10^{-15}\right) \) in presence
of \( 0.1 \mathrm{M} \) Ca \( C l_{2} \) solution.


The marks obtained by 60 students in a
test are given as follows:
\( \begin{array}{lllll}\text { Marks } & 5- & 15- & 25- & 35 \\ 15 & 25 & 35 & 45\end{array} \)
No. of its 8 12 studen
Calculate the mean and standard
deviation of the distribution. Also
interpret the results.


For the cell reaction,
\( \boldsymbol{C u}_{(a q)}^{2+}\left(\boldsymbol{c}_{2}\right)+\boldsymbol{Z} \boldsymbol{n}_{(s)} \rightarrow \boldsymbol{Z} \boldsymbol{n}_{(a q)}^{2+}\left(\boldsymbol{c}_{1}\right)+ \)
\( \boldsymbol{C} \boldsymbol{u}_{(s)} \)
the change in free energy \( (\Delta G) \) at a
given temperature is a function of:
\( A \cdot \ln c_{1} \)
B . \( \ln \left(c_{2} / c_{1}\right) \)
\( c \cdot \ln \left(c_{1}+c_{2}\right) \)
D. \( \ln c \)


Which one of the following pairs of compounds illustrate the law of multiple proportions?
A. \( H_{2} O, N a_{2} O \)
в. \( M g O, N a_{2} O \)
c. \( N a_{2} O, \)Ва О
D. \( S n C l_{2}, S n C l_{4} \)


A change that alters the composition of a substances is known as a chemical
change.


An electron with energy 12.09 eV strikes hydrogen atom in ground state and gives its all energy to the hydrogen atom. Therefore hydrogen atom is excited to
A. Fourth
B. Third
c. second
D. First


In convection process rate of heat transfer is compared in the option between gas and liquid,choose
the correct statement
A. gas convects more as compared to other
B. liquid convects more as compared to other
C. liquid convects more as compared to other only if certain factors assists water
D. none of the above


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


A real image \( , 4 / 5 \) times size of the object is formed \( 18 \mathrm{cm} \) from a lens.
Calculate the focal length of the lens.


Ball bearings reduce friction because they - - - - rather than slide.
A . roll \( l \)
B. swing
c. bounce
D. None of the above


Example of noble gas is
A. Helium
B. Argon
c. xenon
D. all of these


Which of the following cannot act as an acid as well as a base according to the protonic concept?
A. \( H S O_{4} \)
в. \( H_{2} O \)
c. \( H S^{-} \)
D. \( C l O_{4}^{-} \)


The least stable oxide of carbon is :
A. \( c o \)
в. \( C O_{2} \)
\( \mathrm{c} \cdot \mathrm{C}_{3} \mathrm{O}_{2} \)
D. \( C_{2} O_{3} \)


\( \beta \) Sulphur is stable between:
A \( \cdot 114^{\circ} \mathrm{C} \) to \( 160^{\circ} \mathrm{C} \)
B. 95.6 ^ \( C \) to \( 119^{\circ} C \)
c. \( 160^{\circ} \mathrm{C} \) to \( 230^{\circ} \mathrm{C} \)
D. 112.8 ' \( C \) to \( 140^{\circ} \mathrm{C} \)


A chain of length \( L \) and mass \( m \) is
allowed to fall on a table such that the
part falling on the table comes to rest simultaneously. The force acting on the
table when \( l \) part of it has lied on the
table is:
\( ^{\text {A } \cdot \frac{3 m l g}{L}} \)
\( ^{\text {в. }} \frac{2 m l g}{L} \)
c. \( \frac{m l g}{L} \)
D. \( \frac{3 m l g}{2 L} \)


You work is a material testing lab and
your bess tells you to increase the
temperature of a sample by \( 40.0^{\circ} \mathrm{C} \) The only thermometer you can find at your
workbench reads in \( ^{\circ} \boldsymbol{F} \). If The initial
temperature of the sample is \( 68.2^{\circ} F \)
What is its temperature in \( ^{\circ} \boldsymbol{F} \), when the
desired temperature increase has been achieved?


Sulphurous acid turns
A. blue litmus into red
B. red litmus into blue
C. no change to any of the litmus paper
D. can't say


The nerves that carry the messages
towards the CNS from sense organs are
A. Afferent neurons
B. Efferent neurons
c. Interneurons
D. none of the above


The refractive indices of glass and water are \( 3 / 2 \) and \( 4 / 3 \) respectively. The refractive index of glass with respect to
water is :
\( A \cdot 2 \)
B. 8/9
\( c \cdot 9 / 8 \)
D. \( 5 / 3 \)


Differentiate:
\( \frac{d}{d x}\left(\tan ^{-1} x\right) \)


The photoelectric effect of Ba consists of emission of electrons from its
ionisation energy on irradiation with light from the ionization energy of \( \boldsymbol{H} e- \) atom is irradiation with light. A photon
with a minimum energy of \( 3.97 \times \)
\( 10^{-19} J \) is necessary to eject electron
from Ba.
(a)What is the frequency of radiation corresponding to this value?
(b) Will a blue light of wavelength
\( 450 n m \) be able to eject at electron from
Ba? (Given \( h=6.626 \times 10^{-27} \) erg \( - \)
\( \boldsymbol{s} \boldsymbol{e} \boldsymbol{c} \)
\( \mathbf{A} \cdot 6 \times 10^{13} H z, \) yes
B. \( 6 \times 10^{13} H z \), no
C \( .5 .99 \times 10^{14} \mathrm{Hz} \), yes
D. \( 3.6 \times 10^{13} \mathrm{Hz} \), no


Wavefront is the locus of all points, where the particles of the medium
vibrate with the same.
A . phase
B. amplitude
c. frequency
D. period


Define Thallophyta


Take two similar shapes. If you slide rotate or flip one of them, does the
similarity remain.


A rectangular tank of mass \( m_{o} \) and charge \( Q \) over it is placed over a smooth horizontal floor. A horizontal electric
field \( E \) exist in the region. Rain drops are falling vertically in the tank at the constant rate of \( n \) drops per second
Mass of each drop is m. Find velocity of \( \operatorname{tank} \) as function of time.


A man writes his biodata with carbon
pencil on the plane paper having mass 150 mg. After writing his biodata, he weighs the written paper and find its mass \( 152 \mathrm{mg} \). What is the number of carbon atoms present in the paper?
A \( .1 .0036 \times 10^{20} \)
B . \( 5.02 \times 10^{20} \)
\begin{tabular}{l}
\( c .1 .0036 \times 10^{23} \) \\
\hline
\end{tabular}
D. \( 0.502 \times 10^{20} \)


Which complex is most stable?
\( \mathbf{A} \cdot\left[C u(C N)_{2}\right]^{-} K_{d}=1 \times 10^{-16} \)
B \( \cdot\left[F e(C N)_{6}\right]^{4-} K_{d}=1 \times 10^{-37} \)
\( \mathbf{c} \cdot\left[F e(C N)_{6}\right]^{3-} K_{d}=1 \times 10^{-44} \)
\( \mathbf{D} \cdot\left[A g(C N)_{2}\right]^{-} K_{d}=1 \times 10^{-20} \)


Who have tried to put price tags on natures life support services?
A. Robert Constanga et al
B. Nile Perch et al
c. Herbert Boyer et a
D. Ram Deo Misra et al


A girl walks \( 4 k m \) towards West, then
she walks \( 3 k m \) in a direction \( 30^{\circ} \) East
of North and stops. Then, the girl's displacement from her initial point of departure is
A \( -\frac{5}{2} \hat{i}+\frac{3 \sqrt{3}}{2} \)
B. \( \frac{1}{2} \hat{i}+\frac{\sqrt{3}}{2} \hat{j} \)
c. \( -\frac{1}{2} \hat{i}+\frac{3 \sqrt{3}}{2} \)
D. None of these


When alpha particles are sent through a thin metal foil, most of them go straight through the foil because:
A. Alpha particles are much heavier than electrons
B. Alpha particles are positively charged.
c. Most part of the atom is empty
D. Alpha particles move with the high velocity


With the help of neat labelled circuit diagram explain the working of half wave rectifier using semiconductor
diode. Draw the input and output waveforms.


Which of the following figure represents the electric field lines due to the
combination of one positive and one negative charge?
\( A \)
в.
\( c \)
D.


Coordination compounds are mainly known for transition metals.
A. True
B. False


Calculate the oxidation number:
(i) \( M o \) in \( \left(N H_{4}\right)_{2} M o O_{4} \)
(ii) \( N i \) in \( N i(C N)_{4}^{2-} \)


\( \Delta_{r} H \) of which of the following reaction
is zero?
\( \mathbf{A} \cdot H_{2(g)} \rightarrow 2 H_{(g)}^{+}+2 e^{-} \)
B. \( 2 H_{(g)}+a q \rightarrow 2 H_{(a q)}^{+}+2 e^{-} \)
\( \mathbf{c} \cdot 2 H_{(g)} \rightarrow 2 H_{(g)}^{+}+2 e^{-} \)
D. \( H_{2(g)}+a q \rightarrow 2 H_{(a q)}^{+}+2 e^{-} \)


Assertion
When two charged metal spheres are connected by a long wire, then, the
surface charge density on each sphere is inversely proportional to the radius.
Reason

When two charged metal spheres are
connected, charge will flow from one to the other until their potentials are
equal.
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


Find Mode, if Mean \( =70.4 \) and Median is \( = \)
\( 71_{--} \)
A . 71.06
в. 72.9
\( c \cdot 69.6 \)
D. 72.2


In a certain electronic transition in the
hydrogen atom from an initial state (1) to a final state (2), the difference in the
orbital radius \( \left(r_{1}-r_{2}\right) \) is 24 times the
first Bohr radius. Identify the transition:
\( \mathbf{A} \cdot 5 \rightarrow 1 \)
B . \( 25 \rightarrow 1 \)
c. \( 8 \rightarrow 3 \)
D. \( 1 \rightarrow 5 \)


Which of the following is an \( (n . p) \) reaction?
A \( \cdot \frac{13}{5} C+\frac{1}{1} C \longrightarrow_{6}^{14} C \)
B \( \cdot \frac{4}{7} N+\frac{1}{1} H \rightarrow_{8}^{15} O \)
C・ \( 133 l+\frac{1}{0} n \rightarrow 27 M g+1 \)
\( 13 A l+0 \)
D \( \cdot \frac{235}{92} U+_{1}^{0} N \longrightarrow_{54}^{140} X e+_{38}^{94} S r+_{30}^{1} n \)


are included in squamata.
A. Snakes
B. Lizards
C. Both of the above
D. None of the above


Show that:
\[
\left|\begin{array}{ccc}
(\boldsymbol{b}+\boldsymbol{c})^{2} & \boldsymbol{b} \boldsymbol{a} & \boldsymbol{c} \boldsymbol{a} \\
\boldsymbol{a} \boldsymbol{b} & (\boldsymbol{c}+\boldsymbol{a})^{2} & \boldsymbol{c b} \\
\boldsymbol{a c} & \boldsymbol{b c} & (\boldsymbol{a}+\boldsymbol{b})^{2}
\end{array}\right|=
\]
\( 2 a b c(a+b+c)^{3} \)


The lens of a simple magnifier has a focal length of \( 2.5 \mathrm{cm} . \) Calculate the angular magnification produced when
(a) the image is at least distance of distinct vision, and
(b) infinity.
A \( \cdot 11,10 \)
B. 11,13
\( c \cdot 10,13 \)
D. 11,12


Draw the schematic/diagrammatic presentation of the lac operon.


Assuming covalent bonding between Ca and \( O \) (though not), What is the
expected bond order of \( C a O ? \)
A . 1
B . 2
c. 1.5
D. 0


Aeroplanes are streamlined to reduce:
A. fluid friction
B. sliding friction.
c. kinetic friction
D. limiting friction.


Find the frictional force on the \( 2-\mathrm{kg} \)
block in the arrangement shown in Fig.


A constant external torque \( \tau \) acts for a
very brief period \( \Delta t \) on a rotating
system having moment of inertia \( \boldsymbol{I} \)
then
This question has multiple correct options
A. the angular momentum of the system will change by \( \tau \Delta t \)
B. the angular velocity of the system will change by \( \tau \Delta t / I \)
c. if the system was initially at rest, it will acquire rotational kinetic energy \( (\tau \Delta t)^{2} / 2 I \)
D. the kinetic energy of the system will change by \( (\tau \Delta t)^{2} / 2 I \)


Identify the alga known for a biological activity called bioluminescenence.
A. Cyclotella
B. Noctiluca
c. Spirogyra
D. chlorella


When charge is given to a soap bubble, it shows:
A. an increase in size
B. sometimes an increase and sometimes a decrease in size
c. no change in size
D. none of the above


A thin layer chromatography is performed on a sheet of glass, plastic or aluminium foil, which is coated with a
thin layer of adsorbent material. Which of these can be used as an adsorbent
material?
A. Silica gel
B. Aluminium oxide
c. cellulose
D. All of these


At room temperature the solid compound is :
A. \( C O_{2} \)
в. \( \operatorname{si} 0_{2} \)
\( c \cdot N O_{2} \)
D. \( S O_{2} \)


Lucy invested \( \$ 10,000 \) in a new mutual fund account exactly three years ago. The value of the account increased by
10 percent during the first year,increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?
A. \( \$ 10,350 \)
в. \( \$ 10,395 \)
c. \( \$ 10,500 \)
D. \( \$ 11,500 \)
E. \( \$ 12,705 \)


Find the limits of the following expression \( \frac{(x-3)(2-5 x)(3 x+1)}{(2 x-1)^{3}} \)
(1) when \( x=\infty,(2) \) when \( x=0 \)


The force of repulsion between two parallel wires is \( f \) when each one of
them carries a certain current \( I \). If the
current in each is doubled, the force between them would be
A \( \cdot \frac{4}{f} \)
B. \( 4 f \)
c. \( 2 f \)
D. \( f \)


Justify that the following reactions are
redox reactions:
\( \boldsymbol{C u O}(\boldsymbol{s})+\boldsymbol{H}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{C u}(\boldsymbol{s})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \)


State whether True or False:
In a uniform electric field, the dipole experiences no net force; but experiences a torque having a relation with \( P \) and \( E \) which is given by \( \vec{P} \times \vec{E} \)
where the parameters \( P \) and \( E \) have their usual meaning.
A. True
B. False


The electric potential at a point
situated at a distance r on the axis of a
short electric dipole of moment p will be
\( \mathbf{1} / \mathbf{4}\left(\boldsymbol{\pi} \varepsilon_{\mathbf{0}}\right) \) times
\( A \cdot p / r^{3} \)
B. plre
\( c \cdot p / r \)
D. none of the above


What is the resistance of the wire at
\( 30^{\circ} \mathrm{C}, \) if at \( 5^{\circ} \mathrm{C}, \) the resistance of same
wire is \( 200 \Omega \) and \( a t 10^{\circ} C, \) the
resistance is \( 200.2 \Omega ? \)
A \( .200 \Omega \)
B. \( 201 \Omega \)
c. \( 204 \Omega \)
D. \( 195 \Omega \)


Solve:
\( \mathbf{3}(\mathbf{2 u}+\boldsymbol{v})=\mathbf{7} \boldsymbol{u} \boldsymbol{v} \) and
\( \mathbf{3}(\boldsymbol{u}+\mathbf{3} \boldsymbol{v})=\mathbf{1 1} \boldsymbol{u} \boldsymbol{v} \)


The standard emf for the cell reaction
\( Z n+C u^{2+} \longrightarrow Z n^{2+} C u 1.10 \) volt at
\( 25 C . \) The emf for the cell reaction when \( 0.1 M C u^{2+} \) and \( 0.1 M Z n^{2+} \) solutions
are used at \( 25 C \) is:
A . 1.10 volt
B. 0.110 volt
c. 1.70 volt
D. 0.225 volt


Length of 40 bits of wire, correct to the nearest centimetre are given below. Calculate the variance.
\( \begin{array}{lllll}\text { Length } & 1- & 11- & 21- & 31- \\ \mathrm{cm} & 10 & 20 & 30 & 40\end{array} \)
No. of
bits \( \quad 2 \quad 3 \)


Given is a diagram of a human blood
smear.

Study the diagram and answer the question that follow. Name the soluble protein found in part
\( ^{\prime} 4^{\prime} \) which forms insoluble threads
during clotting of blood.


How are xenon fluorides \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{2}, \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{4} \)
and \( X e F_{6} \) obtained?


If \( \frac{1}{1 ! 10 !}+\frac{1}{2 ! 9 !}+\frac{1}{3 ! 10 !}+\ldots+ \)
\( \frac{1}{1 ! 10 !}=\frac{2}{k !}\left(2^{k-1}-1\right) \) then find the
value of k.


The length of hour hand of a wrist watch
is \( 1.5 \mathrm{cm} . \) Find magnitude of angular acceleration?
A. \( 0 r a d / s e c^{2} \)
B. \( 2 \pi r a d / s e c^{2} \)
C \( .2 \mathrm{rad} / \mathrm{sec}^{2} \)
D. \( 1 r a d / s e c^{2} \)


Davisson and Germer experiment
represents nature of the
electron.
A. Wave
B. Particle
c. wave and particle
D. Doesn't represent any nature


Pyrenoids are commonly found in
A. Red algae
B. Green algae
c. Brown algae
D. Blue green algae


Assertion
Some cells enter \( G_{0} \) phase leading to
inactivation of cell cycle.
Reason
\( G_{0} \) phase occurs due to non-availability
of mitogen and energy rich compounds.
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


Select the correct diagram for anti-
bonding molecular orbitals which are formed by side-way overlapping
This question has multiple correct options
\( A \)
B.
\( c \)
\( D \)


Fins the area of the trapezium whose
bases are \( 6 \mathrm{cm}, 4 \mathrm{cm} \) and height is \( 3 \mathrm{cm} \)


Which number is larger (1.1) \( ^{100000} \) or
\( \mathbf{1 0}, \mathbf{0 0 0} ? \)


Find the ratio in which (the plane) \( 2 x+ \) \( 3 y+5 z=1 \) divides the line joining the
points (1,0,-3) and (1,-5,7)
A .1: 2
B . 2: 3
\( c .3: 1 \)
D. None of these


Which of the following numbers form pythagorean triplet?
¡) 2,3,4
ii) 6,8,10
iii) 9,10,11
iv) 8,15,17
A . (ii), (iv)
B. (i), (ii)
c. (i), (ii), (iii)
D. (ii), (iii)


When a force 6 N is exerted at \( 30^{\circ} \) to a
wrench at a distance of \( 8 \mathrm{cm} \) from a nut
as shown in Fig, it is just able to loosen
it. What force \( F \) is required to loosen the
nut if applied \( 16 \mathrm{cm} \) away to the wrench
and normal to the wrench ?
\( A \cdot 3 N \)
B. \( \sqrt{3} N \)
c. 1.5
D. None


Let \( X \) be any point on the side \( B C \) of \( a \) triangle ABC. If \( \mathrm{XM}, \mathrm{XN} \) are drawn parallel to BA and CA meeting CA, BA in M, N respectively; MN meets BC
produced in \( T, \) prove that \( \boldsymbol{T} \boldsymbol{X}^{2}=\boldsymbol{T} \boldsymbol{B} \times \)
\( \boldsymbol{T} \boldsymbol{C} \)


Nitration of which among the following compounds yields cyclonite?
A. Formaldehyde
B. Benzaldehyde
c. Urotropine
D. Acetaldehyde-ammonia


We can see the objects only when:
A. reflected light from the objects reaches our eyes
B. the objects absorb all the light
C. when the objects allow all the light to pass through them
D. none of the above


When the price of TV set was increased by \( 30 \% \), then number of TV sets sold
decreased by \( 20 \% . \) What was the effect
on the sales?
A. \( 5 \% \) decrease
B. \( 7 \% \) increase
c. \( 6 \% \) decrease
D. \( 4 \% \) increase


Which of the following is not characteristic of chemisorption?
A. Adsorption is specific
B. Heat of adsorption is of die order of \( 200 \mathrm{kJmol}^{-1} \)
c. Adsorption is irreversible
D. Adsorption may form multimolecular layers


There are four possible relative motions
between the source of a sound and the
listener
1) source moves towards stationary
listener
2) source moves away from stationary listener
3) listener moves towards stationary
source
4) listener moves away from stationary
source
In which of the cases, the change in frequency is the same. The magnitude of velocity of source or listener being
the same.
\( A \cdot 1 \) and 2
B. 2 and 3
\( c \cdot 3 \) and 4
D. 1 and 4


A spherical ball of iron of radius \( 2 \mathrm{mm} \) is falling through a column of glycerine. If densities of glycerine and iron are respectively \( 1.3 \times 10^{3} \mathrm{kg} / \mathrm{m}^{3} \) and \( 8 \times \)
\( 10^{3} \mathrm{kg} / \mathrm{m}^{3} . \) \eta for glycerine \( = \)
\( 0.83 \mathrm{Nm}^{-2} \) sec, then the terminal
velocity is:
A. \( 0.7 \mathrm{m} / \mathrm{s} \)
B. \( 0.07 \mathrm{m} / \mathrm{s} \)
c. \( 0.007 \mathrm{m} / \mathrm{s} \)
D. \( 0.0007 \mathrm{m} / \mathrm{s} \)


The vapour density of unsturated acyclic aliphatic compound \( \boldsymbol{X} \) is \( \mathbf{3 5} \) Mention the chain isomers of alcohol
with same number of carbon atoms as
\( \operatorname{in} \boldsymbol{X} \)


Minimize and maximize \( \boldsymbol{z}=\mathbf{5} \boldsymbol{x}+\mathbf{1 0} \boldsymbol{y} \)
subject to the constraints \( x+2 y \leq 120 \)
\( \boldsymbol{x}+\boldsymbol{y} \geq \mathbf{6 0} \)
\( x-2 y \geq 0 \) and \( x \geq 0, y \geq 0 \) by
graphical method.


Prove that the electric potential at a point in broad side on position due to an electric dipole is zero.


Length of chromosome/ chromatid to
increase in
A. Anaphase
B. Prophase
c. Metaphase
D. Telophase


There are ....... rational number which
when multiplied by \( 0, \) gives product as
1.
A . 0
B. 2
\( c \cdot 4 \)
D. infinite


Let \( \boldsymbol{f}(\boldsymbol{x})=\mathbf{2}^{100} \boldsymbol{x}+\mathbf{1} \)
\( \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{3}^{100} \boldsymbol{x}+\mathbf{1} \)
Then the set of real numbers x such that
\( \boldsymbol{f}(\boldsymbol{g}(\boldsymbol{x}))=\boldsymbol{x} \) is
A. Empty
B. A singleton
c. A finite se with more than one element
D. Infinite


If \( \cos ^{-1} x+\cos ^{-1} y=2 \pi \) then
\( \sin ^{-1} x+\sin ^{-1} y= \)
\( A \cdot \pi \)
в. \( -\pi \)
\( c \cdot \frac{\pi}{2} \)
D. None of these


\( \frac{\frac{1}{1.2 .3}+\frac{1}{2.3 .4}+\frac{1}{3.4 .5}+\ldots .+}{m(n+1)(n+2)}=\frac{n(n+3)}{4(n+1)(n+2)} \)


Parasexuality was first discovered in
A. Bacteria
B. Virus
c. Fungi
D. None of the above


Read the bar graph given in fig. and
answer the following questions:
In which year is the increase in
expenditure maximum over the
expenditure in previous year? What is
the maximum increase?
Bar graph of the expend health and family planning during the Sixth Five Year Plan in India


The change that does not increase
entropy:
A. evaporation of liquid
B. condensation
c. sublimation
D. melting of solid


\( \triangle A B C \) is an isosceles triangle with
\( A B=A C . \) Then the line of symmetry
for the \( \triangle A B C \) will be:
This question has multiple correct options
A. Perpendicular bisector of \( B C \)
B. Angle bisector of \( \angle B \)
C. Altitude from vertex \( A \) on line \( B C \)
D. Median from vertex \( C \) to side \( A B \)


Which alcohol is prepared from water gas?
A. \( C_{2} H_{5} O H \)
в. \( C H_{3} C H_{2} C H_{2} O H \)
\( \mathbf{c} \cdot C H_{3} O H \)
D. \( C_{6} H_{5} C H_{2} O H \)


The unit of second order reaction rate
constant is
\( \mathbf{A} \cdot L^{-1} m o l s^{-1} \)
B. \( L^{-1} \)mols\( ^{-2} \)
c. \( L m o l^{-1} s^{-1} \)
D. None


Amongst the following compounds, the optically active alkane having the
lowest molecular mass is:
A. \( C H_{3}-C H_{2}-C \equiv C H \)
в. \( C H_{3}-C H_{2}-C H\left(C H_{3}\right)-C H_{3} \)
\( c \)
D. \( C H_{3}-C H_{2}-C H_{2}-C H_{3} \)


was the most logical and abstract creator of Euclid's
geometry approach.
A. Hilbert
B. Bhasharacharya
c. Thelus
D. Pythagorous


If non zero numbers \( a, b, c \) are in A.P. then \( a+\frac{1}{b c}, b+\frac{1}{c a}, c+\frac{1}{a b} \) are in :
A. G.P
B. Н.Р.
\( c . \) A.P
D. None of these


If the mean of a observations
\( x_{1}, x_{2}, \dots \dots x_{n} \) is \( \bar{x}, \) then the sum of
deviations of observations from mean is
A. 0
в. \( n \bar{x} \bar{x} \)
c. \( \bar{x} \)
D. None of these


Give the electronic configuration of fifth element of the first transition series.


A black powder when heated with conc.
HCl gives a greenish yellow gas. The gas acts as an oxidizing and a bleaching agent. When it is passed over slaked lime, a white powder is formed which is a ready source of gas. The black powder
and white powder respectively are:
A \( . K C l O_{3} \) and \( N a C l O_{3} \)
B. \( M n O_{2} \) and \( C a(O C l)_{2} \)
\( \mathrm{c} \cdot \mathrm{M} n \mathrm{O}_{2} \) and \( \mathrm{KClO}_{3} \)
D. \( M n C l_{4} \) and \( C O C l_{2} \)


A bus starts from rest moving with acceleration \( 2 m / s^{2} . \) A cyclist \( 96 m \)
behind the bus starts simultaneously towards the bus at \( 20 m / s . \) At what
earliest time the cyclist will be able to overtake the bus:
\( \mathbf{A} \cdot 8 s \)
B. \( 10 s \)
\( c \cdot 12 s \)
D. \( 14 s \)


How many orbitals are present in the second energy level of a neon atom?
A . 1
B. 3
\( c \cdot 4 \)
\( D \)


A circular loop of radius R carries a current I. Obtain an expression for the magnetic field at a point on its axis at a distance \( x \) from its centre


The stability of a flexible body depends
on:
A. height of the center of gravity from the ground.
B. base area of the body.
c. shape of the body.
D. all the above


Which of the following statement(s) is/are correct?
S1: Dialysis is the method of purification of colloidal solution from electrolytic \& non-electrolytic impurities. S2: Banana bonding occurs in
\( \boldsymbol{A l}_{2}\left(\boldsymbol{C H}_{3}\right)_{6}, \boldsymbol{G a}_{2}\left(\boldsymbol{C H}_{3}\right)_{6}, \boldsymbol{B e} \boldsymbol{H}_{2}(\boldsymbol{S}) \)
S3: There are two types of \( C r-O \) bond
length in \( \boldsymbol{C r} \boldsymbol{O}_{4}^{2-} \)
S4: Total number of stereoisomers in
\( \boldsymbol{K}_{4}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}\right] \) is 0
A. \( F T F T \)
в. \( T F T F \)
c. \( F F T T \)
D. \( T T F F \)


In the given transformation, which of
the following is the most appropriate
reagent?
A. \( N H_{2} N H_{2}, O H \)
в. \( Z n-H g / H C l \)
c. \( N a, \) liq. \( N H_{3} \)
D. \( N a B H_{4} \)


Water is flowing steadily through a horizontal tube of non-uniform cross-
section.If the pressure of water is \( 4 \times \) \( 10^{4} N / m m^{2} \) at a point when cross
section is \( 0.02 m^{2} \) velocity of flow is
\( 2 \mathrm{m} / \mathrm{s} \) what is pressure at a point where \( \operatorname{cross} \) section reduces to \( 0.01 m^{2} \)
A \( \cdot 1.4 \times 10^{4} N m^{2} \)
B. \( 3.4 \times 10^{4} N m^{2} \)
c. \( 2.4 \times 10^{-4} N m^{2} \)
D. none of these


Calculate by how much will the sound
level decrease if the observer moves
from a distance of \( 2 \mathrm{m} \) to a distance of
\( 20 \mathrm{m} \) from the source.
\( A \cdot 1 d B \)
B. 2 dB
\( c \cdot 10 d B \)
D. 18 dB
E . \( 20 d B \)


\( f\left(a_{1}, a_{2}, a_{3}, \dots, a_{n}, \dots \) are in GP, then \right.
the value of the determinant \( \begin{array}{|ccc|}\log a_{n} & \log a_{n+1} & \log a_{n+2} \\ \log a_{n+3} & \log a_{n+4} & \log a_{n+5} \\ \log a_{n+6} & \log a_{n+7} & \log a_{n+8}\end{array} \mid \), is
A . 0
B. 1
\( c \cdot 2 \)
\( D .-2 \)


Taxol and cisplatin are:
A. life saving drugs used in cancer therapy
B. used for treating lung diseases
C . used for treating kidney diseases
D. used for treating joints


A microscope using suitable photons is employed to locate an electron in an atom within a distance of 0.1 A. The uncertainty of its velocity is
A. \( 5.79 \times 10^{5} \mathrm{ms}^{-1} \)
B. \( 8.79 \times 10^{5} \mathrm{ms}^{-1} \)
C. \( 5.79 \times 10^{4} \mathrm{ms}^{-1} \)
D. \( 3.79 \times 10^{5} \mathrm{ms}^{-1} \)


\( \int \frac{\ln (\cos x+\sqrt{\cos 2 x})}{\sin ^{2} x} d x= \)
\( \frac{\sqrt{\cos 2 x}}{\sin x}-x+\cot x \times \ln [e(\cos x+\sqrt{\cos 2 x})]+c \)
\( \frac{\sqrt{\cos 2 x}}{\sin x}+x-\cot x \times \ln [e(\cos x+\sqrt{\cos 2 x})]+c \)
\( \frac{\sqrt{\cos 2 x}}{\sin x}+x+\cot x \times \ln [e(\cos x+\sqrt{\cos 2 x})]+c \)


Given, \( |\vec{a}|=|\vec{b}|=1 \) and \( |\vec{a}+\vec{b}|=\sqrt{3} .1 \)
\( \vec{c} \) be a vector such that \( \vec{c}-\vec{a}-2 \vec{b}= \) \( \mathbf{3}(\overrightarrow{\boldsymbol{a}} \times \overrightarrow{\boldsymbol{b}}), \) then \( \overrightarrow{\boldsymbol{c}} . \overrightarrow{\boldsymbol{b}} \) is equal to
A \( \cdot-\frac{1}{2} \)
в. \( \frac{1}{2} \)
\( c \cdot \frac{3}{2} \)
D.


A neutral atom of an element has \( 2 \mathrm{K}, 8 \mathrm{L} \)
\( 9 \mathrm{M} \) and \( 2 \mathrm{N} \) electrons. The total number
of \( s \) electrons are:
\( A \cdot 8 \)
B. 6
\( c \cdot 4 \)
D. 10


A man stands in front of a plane mirror at a distance of 2 metres. The distance
of his image from him will be -
\( \mathbf{A} \cdot 2 \) metres
B. 1 metres
c. 3 metres
D. 4 metres


The sun is a typical star
which is classified as having a temperature in the range of 5000 to
\( \mathbf{6 0 0 0 K} \)
A. \( G 1 \)
в. \( G 2 \)
\( c . G 3 \)
D. \( G 4 \)


An iron spherical ball has been melted
and recast into smaller balls of equal size. If the radius of each of the smaller balls is \( \frac{1}{4} \) of the radius of the original ball, how many such balls are made? Compare the surface area, of all the
smaller balls combined together with
that of the original ball.


If the relation between acceleration and
time of an object is given by \( a=2 t+ \)
\( 4 t^{2} . \) Calculate the position of the object
from the origin at \( t=4 s \)


In \( \triangle A B C, \) right angled at \( B, A B=10 \)
and \( A C=26 . \) Find the six
trigonometric ratios of the angles \( A \) and \( C \)


A solid conducting sphere having charge \( 4 \mu C \) is placed on nonconducting stand. A point charge \( 2 \mu C \)
is placed at a distance from the centre
of the sphere, at a double distance of radius of the sphere as shown in the
figure. If conducting sphere is earthed
then charge flow into the ground is :
\( A \cdot 5 \mu C \)
B. \( 2 \mu C \)
\( c \cdot 10 \mu C \)
D. \( 1 \mu C \)


Name two metals which can be refined
by Van Arkel Method.


If \( \boldsymbol{A}=\left[\begin{array}{c}-2 \\ 4 \\ 6\end{array}\right] \) and \( B=[14-6] \) then
find \( \boldsymbol{A B} \)


decreases by \( 3 \% \)


Both geometrical and optical isomerisms are not shown by:
This question has multiple correct options
A. Dichlorobis (ethylenediamine) cobalt (III) ion
B. Triamminetrichloro cobalt (III) ion
C. Tetraamminedichloro cobalt (III) ion
D. Trioxalatochromate (III) ion


\( A s_{2} S_{3} \) solution has negative charge, capacity to precipitate is highest in:
A. \( A l C l_{3} \)
в. \( N a_{3} P O_{4} \)
c. \( C a C l_{2} \)
D. \( K_{2} S O_{4} \)


The balanced equation in basic
medium is :
\( \boldsymbol{S}_{2} \boldsymbol{O}_{4}^{2-}+\boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{O} \stackrel{O H^{-}}{\rightarrow} \boldsymbol{A} \boldsymbol{g}+\boldsymbol{S} \boldsymbol{O}_{3}^{2-} \)
A \( \cdot S_{2} O_{4}^{2-}+A g_{2} O+2 O H^{-} \rightarrow 2 A g+2 S O_{3}^{2-}+H_{2} O \)
B. \( S_{2} O_{4}^{2-}+2 A g_{2} O+2 O H^{-} \rightarrow 2 A g+S O_{3}^{2-}+H_{2} O \)
\( \mathbf{c} \cdot 2 S_{2} O_{4}^{2-}+3 A g_{2} O+2 O H^{-} \rightarrow 2 A g+2 S O_{3}^{2-}+H_{2} O \)
D. none of these


Solve: \( \int \sqrt{\tan x}+\sqrt{\cot x} \cdot d x \)


The general solution of differential
equation is \( y=a e^{b x+c} \) where \( a, b, c \) are
arbitrary constant. The order of differential equation is:
\( A \cdot 3 \)
B . 2
\( c \cdot 1 \)
D. none of these


The value of G does not depend on
A. nature of the interacting bodies
B. size of the interacting bodies
c. mass of the interacting bodies
D. all the above


A bucket full of hot water is kept in a
room and it cools from \( 75^{\circ} \mathrm{C} \) to \( 70^{\circ} \mathrm{C} \) in
\( T_{1} \) minutes, from \( 70^{\circ} C \) to \( 65^{\circ} C \) in \( T_{2} \)
minutes and from \( 65^{\circ} \mathrm{C} \) to \( 60^{\circ} \mathrm{C} \) in \( T_{3} \) minutes. Then
A. \( T_{1}=T_{2}=T_{3} \)
в. \( T_{1}<T_{2}<T_{3} \)
c. \( T_{1}>T_{2}>T_{3} \)
D. \( T_{1}<T_{2}>T_{3} \)


A body of mass \( M \) and radius \( R \) is
rolling on a horizontal plane with speed
v. It then rolls up an inclined plane upto a height \( h=\frac{v^{2}}{g} . \) What is the nature of
the body?
A. Ring
B. Solid sphere
c. spherical shell
D. Cylinder


In the figure shown \( \mathrm{S} \) is the source of
white light kept at a distance \( x_{0} \) from
the plane of the slits. The source moves with a constant speed u towards the slits on the line perpendicular to the plane of the slits and passing through the slit \( S_{1} \). Find the instantaneous velocity (magnitude and direction) of the central maxima at time t having range \( 0 \leq t<<\frac{x_{0}-d}{u} . \) Assume that
\( D>>d \)


What is the key principle of the EBB and flow system in hydroponics?
A. It floods and drains periodically
B. It makes a tide flowing over the roots
C. It sprays a mist of nutrients on the roots
D. None of the above


Coulomb's Law is true for
A \( . \) atomic distances \( \left(=10^{-11} \mathrm{m}\right) \)
B. nuclear distances \( \left(=10^{-15} \mathrm{m}\right) \)
C. charged as well as uncharged particles
D. all the distances


Minimum amount of \( A g_{2} C O_{3}(s) \) required to produce sufficient oxygen
for the compelete combusion of \( C_{2} H_{2} \)
which produces \( 11.2 l t r \) of \( C O_{2} \) at S.T.P after combusion is : \( [\mathrm{Ag}=108] \)
\( \boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{C} \boldsymbol{O}_{3}(\boldsymbol{s}) \rightarrow \boldsymbol{2} \boldsymbol{A} \boldsymbol{g}(\boldsymbol{s})+\boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})+ \)
\( \mathbf{1} / \mathbf{2} \mathbf{o}_{\mathbf{2}}(\boldsymbol{g}) \)
\( \boldsymbol{C}_{2} \boldsymbol{H}_{2}+\mathbf{5} / \mathbf{2} \boldsymbol{O}_{2} \rightarrow \boldsymbol{2} \boldsymbol{C} \boldsymbol{O}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \)
A \( .276 g \)
в. \( 345 g \)
\( c .690 g \)
D. \( 1380 g \)


Solve \( :\left(x^{2}-1\right) \frac{d y}{d x}+2 x y=\frac{1}{x^{2}-1} \)


Gametophytic plant body is nonvascular in
A. Algae and liverworts
B. Mosses and ferns
c. Gymnosperms and angiosperms
D. All of these


If \( \left[\mathbf{3} \boldsymbol{x}^{2}+\mathbf{1 0 x y}+\mathbf{5 y}^{2}\right]=\left[\begin{array}{ll}\boldsymbol{x} & \boldsymbol{y}\end{array}\right] \boldsymbol{A}\left[\begin{array}{l}\boldsymbol{x} \\ \boldsymbol{y}\end{array}\right] \)
and \( A \) is a symmetric matrix then \( \mathbf{A}= \)
\( \mathbf{A} \cdot\left[\begin{array}{ll}3 & 10 \\ 10 & 5\end{array}\right] \)
B. \( \left[\begin{array}{ll}10 & 3 \\ 5 & 10\end{array}\right] \)
\( \mathbf{c} \cdot\left[\begin{array}{cc}+3 & -5 \\ -5 & +5\end{array}\right] \)
D. \( \left[\begin{array}{ll}3 & 5 \\ 5 & 5\end{array}\right] \)


Buffer solution can be obtained by mixing aqueous solution of
A. Sodium acetate and excess of HCI
B. Sodium acetate and acetic acid
c. sodium chloride and нс
D. Acetic acid and excess of Naol


The number of sigma and pi-bonds in 1 butene-3-yne are:
A. 6 sigma and 4 pi
B. 7 sigma and 3 pi
c. 5 sigma and 5 pi
D. none of these


\[
\operatorname{Let}\left|\begin{array}{ccc}
\boldsymbol{x}^{2}+\boldsymbol{x} & \boldsymbol{2} \boldsymbol{x}-\mathbf{1} & \boldsymbol{x}+\boldsymbol{3} \\
\boldsymbol{3} \boldsymbol{x}+\mathbf{1} & \boldsymbol{2}+\boldsymbol{x}^{2} & \boldsymbol{x}^{\boldsymbol{3}} \\
\boldsymbol{x}-\boldsymbol{3} & \boldsymbol{x}^{\boldsymbol{2}}+\boldsymbol{4} & \boldsymbol{2} \boldsymbol{x}
\end{array}\right|=\boldsymbol{p} \boldsymbol{x}^{2}+
\]
\( \boldsymbol{q} \boldsymbol{x}^{\boldsymbol{6}}+\boldsymbol{r} \boldsymbol{x}^{\boldsymbol{5}}+\boldsymbol{s} \boldsymbol{x}^{4}+\boldsymbol{t} \boldsymbol{x}^{\boldsymbol{3}}+\boldsymbol{u} \boldsymbol{x}^{\boldsymbol{2}}+\boldsymbol{v} \boldsymbol{x}+\boldsymbol{w} \)
then which of the following is not true?
A. \( w=21, v=75 \)
B . \( q=0, s=-4 \)
c. \( p=0, t=-8 \)
D. \( p=q=-1 \)


Four masses (each of \( \mathrm{m} \) ) are placed at the vertices of a regular pyramid (triangular base) of side 'a'. Find the work done by the system while taking them apart so that they form the pyramid of side '2a'
\( ^{\text {A }} \cdot \frac{3 G m^{2}}{a} \)
в. \( -\frac{3 G m^{2}}{a} \)
c. \( -\frac{2 G m^{2}}{a} \)
D. \( \frac{2 G m^{2}}{a} \)


\( \frac{x^{4}+2}{(x-1)^{2}(x+1)}= \)
A \( \cdot x+1+\frac{3}{4(x-1)}+\frac{3}{2(x-1)^{2}}+\frac{5}{4(x+1)} \)
B. \( x+1+\frac{5}{4(x-1)}+\frac{3}{2(x-1)^{2}}+\frac{5}{4(x+1)} \)
\( ^{\mathbf{C}} \cdot x+1+\frac{5}{4(x-1)}+\frac{3}{2(x-1)^{2}}+\frac{3}{4(x+1)} \)
D \( x+1+\frac{5}{4(x-1)}+\frac{5}{2(x-1)^{2}}+\frac{3}{4(x+1)} \)


The protein alpha-1 antitrypsin is used to treat the disease
A. Cancer
B. Rheumatoid arthritis
c. Alzheimer's disease
D. Emphysema
E. ADA deficiency disease in children


Water flows through the tube as shown
in figure. The areas of cross-section
of the wide and the narrow portions of
the tube are \( 5 c m^{2} \) and \( 2 c m^{2} \)
respectively. The rate of flow of water
through the tube is \( 500 \mathrm{cm}^{3} / \mathrm{s} \). Find the
difference of mercury levels in the U-
tube.


Form the differential equation representing the family of curves \( y= \)
\( a e^{2 x}+b e^{-2 x} \) where a and \( b \) are arbitrary
constants.


Which of the following presents the correct order of the acidity in the given compounds?
A. \( F C H_{2} C O O H>C l C H_{2} C O O H>B r C H_{2} C O O H> \)
\( C H_{3} C O O H \)
в. \( C H_{3} C O O H>B r C H_{2} C O O H>C l C H_{2} C O O H> \)
\( F C H_{2} C O O H \)
c. \( F C H_{2} C O O H>C H_{3} C O O H>B r C H_{2} C O O H> \)
\( _{C l C H_{2} C O O H} \)
D. \( B r C H_{2} C O O H>C l C H_{2} C O O H>F C H_{2} C O O H> \)
\( C H_{3} C O O H \)


1 mole of \( N O \) and 1 mole of \( O_{3} \) are
taken in \( 10 L \) vessel and heated. At
equilibrium, \( 50 \% \) of \( N O \) (by mass)
reacts with \( O_{3} \) according to the equation:
\( N O(g)+O_{3(g)} \rightleftharpoons N O_{2(g)}+O_{2(g)} \)
What will be the equilibrium constant for this reaction?
\( A \)
B. 2
\( c .3 \)
D.


What kind of lens would form an erect
and diminished image?


Find the vector equation of a plane at a distance of 5 units from the origin and has \( \hat{i} \) as the unit vector normal to it.


What is coordination compound?


For each set of ordered pairs below, state whether it is a function or not give
reasons
\( (i)\{(3,2),(4,2),(5,2)\} \)
if a function enter 1 else 0


Plaster of paris should be stored in a moisture proof container because:
A. it absorbs moisture from the atmosphere and becomes hard
B. it cannot be stored in plastic
c. it will change its colour
D. it will become soft


The correct electron dot structure of a
water molecule is:
\( A \)
H ợ \( \cdot \) H
в. H :ö. H
c. H :ö: H
D. H : \( 0: H \)


In the double helix model of DNA, what
would be the distance between two
consecutive base pairs?
A. \( 3.4 \mathrm{nm} \)
B. 2 nm
\( c \cdot 20 \mathrm{nm} \)
D. \( 0.34 \mathrm{nm} \)


Arrange the following in the increasing order of bond energy: \( \boldsymbol{F}_{2}<\boldsymbol{C l}_{2}<\boldsymbol{O}_{2}< \)
\( N_{2} \)
If true enter 1 , else enter 0 .


A transformers has an efficiency of \( 80 \% \)
.It is connected to a power output of kw and 100 V.If the secondary voltage is \( 240 \mathrm{V} \),the secondary current is
A \( .4 .6 \mathrm{A} \)
B. 40 A
\( c \cdot 4.3 \mathrm{A} \)
D. 13.3 A


Strong odoriferous fungus is
A. Phallus
B. Rhizoclonium
c. Helminthosporium
D. Fusarium


A \( 70 \mathrm{kg} \) astronaut in a \( 110 \mathrm{kg} \) MMU experiences an acceleration of 0.029
\( \mathrm{ms}^{-2} \) when he fires one of the MMU's
thrusters, if the speed of escaping \( N_{2} \) gas is \( 490 \mathrm{ms}^{-1} \), how much amount of
gas is used in 5 s.
A. \( 5.53 g \)
в. \( 5.53 k g \)
c. \( 555.3 g \)
D. \( 55.3 g \)


A parallel beam of monochromatic light is incident on one face of an equilateral
prism the angle of incidence being \( 55^{\circ} \)
The angle of emergence of the beam
from the other face is \( 46^{\circ} . \) The angle of
minimum deviation is :
\( \mathbf{A} \cdot<41^{\circ} \)
B. equal to \( 41^{\circ} \)
\( \mathbf{c} \cdot>41^{\circ} \)
\( \mathrm{D} \cdot \geq 41^{\circ} \)


Discuss the characteristics of order of a
reaction.


Assertion
For rubber and water, \( V(I)<V(s) \)
Reason
The density of both rubber and water is
more in liquid state.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Given below are the half-cell reactions:
\( M n^{2+}+2 e^{-} \rightarrow M n ; E^{0}=-1.18 V \)
\( \mathbf{2}\left(\boldsymbol{M} \boldsymbol{n}^{3+}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{M} \boldsymbol{n}^{2+}\right) ; \boldsymbol{E}^{0}= \)
\( +1.51 V \)
The \( \boldsymbol{E}^{0} \) for \( \boldsymbol{3} \boldsymbol{M} \boldsymbol{n}^{2+} \rightarrow \boldsymbol{M} \boldsymbol{n}+\boldsymbol{2} \boldsymbol{M} \boldsymbol{n}^{3+} \)
will be:
A. \( -0.33 V \); the reaction will not occur
B. \( -0.33 V ; \) the reaction will occur
c. \( -2.69 V \); the reaction will not occur
D. \( -2.69 V \); the reaction will occur


Calculate the mutual conductance \( g_{m} \)
of the triode valve?
A \( .5 .33 \times 10^{-3} \mathrm{ohm}^{-1} \)
B. \( 53.3 \times 10^{-3} \) ohm \( ^{-1} \)
c. \( 4.32 \times 10^{-3} \mathrm{ohm}^{-1} \)
D. \( 5.00 \times 10^{-3} \mathrm{ohm}^{-1} \)


The area of cross section of the wider
tube shown in fig. is \( 900 \mathrm{cm}^{2} . \) If the body standing on the position weighs \( 45 \mathrm{kg}, \) find the difference in the levels of
water in the two tubes.


Draw the Resonance hybrid of \( S O_{3} \)


The lifetime of an electron in the state
\( \boldsymbol{n}=2 \) in the hydrogen atom is about
\( \mathbf{A} \cdot 10 n s \)
в. 1000 ns
\( c \cdot 1 m s \)
D. \( 10 m s \)


If \( \vec{a}+\vec{b}+\vec{c}=\overrightarrow{0} \) show that \( \vec{a} \times \vec{b}=\vec{b} \times \)
\( \overrightarrow{\boldsymbol{c}}=\overrightarrow{\boldsymbol{c}} \times \overrightarrow{\boldsymbol{a}} \)


The sum of numeretor and deniminator
of a faction 4 more than its numerator If
3 is added to numerator and
denominator, its ratio becomes 2: 3
Find the fraction


The Sl unit of hydro-static pressure is :
A. Pa
B. \( N m^{-1} \)
c. \( \mathrm{Nm} \)
D. \( k g \) wt \( m^{-2} \)


Write the formula of probability.


Two thin plano-convex lenses each of
focal length \( f \) are placed as shown in
the figure. The ratio of their effective
focal lengths in the three cases is
(i)
(ii)
A .1: 2: 3
B. 1: 2: 1
c. 1: 1: 1
D. 3: 2: 1


Ramesh is travelling from the Pacific Ocean towards Indian Ocean. In the
Pacific Ocean he has a balloon with 2
litre capacity at \( 18^{0} \) C. When he reaches
the Indian Ocean, the temperature will
be \( 25^{0} \) C. What will be the volume of the
balloon?


Length of the common chord of the
\( \operatorname{circles}(x-1)^{2}+(y+1)^{2}= \)
\( c^{2} \) and \( (x+1)^{2}+(y-1)^{2}=c^{2} \) is
A \( \cdot \frac{1}{2} \sqrt{c^{2}-2} \)
B. \( \sqrt{c^{2}-2} \)
c. \( 2 \sqrt{c^{2}-2} \)
D. \( (c+2) \)


\( f\left|\begin{array}{ccc}\mathbf{1} & \boldsymbol{a} & \boldsymbol{b} \boldsymbol{c} \\ \mathbf{1} & \boldsymbol{b} & \boldsymbol{c a} \\ \mathbf{1} & \boldsymbol{c} & \boldsymbol{a b}\end{array}\right|=\boldsymbol{\lambda}\left|\begin{array}{ccc}\boldsymbol{a}^{2} & \boldsymbol{b}^{2} & \boldsymbol{c}^{2} \\ \boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \mathbf{1} & \boldsymbol{1} & \boldsymbol{1}\end{array}\right|, \) then \( \lambda \) is
equal to
\( A \cdot 1 \)
B. -1
\( c \cdot 2 \)
\( D .-3 \)


Which of the following is produced by
the reaction of zinc metal, \( Z n \) and
hydrochloric acid, \( \boldsymbol{H} \boldsymbol{C l} \) ?
I. \( \boldsymbol{H}_{2}(\boldsymbol{g}) \)
II. \( C l_{2}(g) \)
III. \( Z n^{2+}(a q) \)
A. Il only
B. III only
c. I and II only
D. I and III only
E . I, II, and III


Shown in the figure below is a meter-
bridge set up with null deflection in the
galvanometer

The value of the unknown resistor \( \boldsymbol{R} \) is
A. \( 13.75 \Omega \)
B. \( 220 \Omega \)
\( c \cdot 110 \Omega \)
D. \( 55 \Omega \)


Drive an expression for equivalent focal length of two thin lenses kept in
contact


Solve \( : \int_{0}^{1} \sqrt{9-4 x^{2}} d x \)


Which of the following options is the only INCORRECT combination?
A \( \cdot(I I)(i i i)(P) \)
B. \( (I I)(i v)(Q) \)
c. \( (I)(i i i)(P) \)
D. \( (I I I)(i)(R) \)


N lamps each of resistance \( r, \) are fed by a machine of resistance R. If light
emitted by any lamp is proportional to
the square of the heat produced, prove that the most efficient way of arranging
them is to place them in parallel arcs,
each containing n lamps, where n is the
integer nearest to.
\( ^{\mathbf{A}} \cdot\left(\frac{r}{N R}\right)^{3 / 2} \)
\( ^{\mathbf{B}} \cdot\left(\frac{N R}{r}\right)^{1 / 2} \)
\( \mathbf{C} \cdot(N R r)^{3 / 2} \)
D. \( (N R r)^{1 / 2} \)


Refer to the given figure which represents a section of vascular bundle
as seen in \( \mathrm{T} \). S. of a monocot stem and
select the option that correctly labels
\( A, B, C \) and \( D \)
A. A-Protoxylem vessel, B-Metaxylem vessel, CProtoxylem cavity, D-Phloem
B. A-Protoxylem vessel, B-Metaxylem vessel, CMetaxylem cavity, D-Phloem
C. A-Metaxylem vessel, B-Protoxylem vessel, CProtoxylem cavity, D-Phloem
D. A-Metaxylem vessel, B-Protoxylem vessel, CProtoxylem cavity, D-Sclerenchyma


If metallic circular plate of radius \( 50 \mathrm{cm} \)
is heated so that its radius increases at
the rate of \( 1 \mathrm{mm} \) per hour, then the rate
at which the area of the plate increases \( \left(\operatorname{in} c m^{2} / h r\right) \) is
A . \( 5 \pi \)
в. \( 10 \pi \)
c. \( 100 \pi \)
D. \( 50 \pi \)


Charges \( -\boldsymbol{q}, \boldsymbol{Q} \) and \( -\boldsymbol{q} \) are placed at an equal distance on a straight line. If the
total potential energy of the system of three charges is zero, then find the ratio \( \boldsymbol{Q} / \boldsymbol{q}: \)
A. \( 1 / 2 \)
в. \( 1 / 4 \)
\( c \cdot 2 / 3 \)
D. \( 3 / 4 \)


n Figure, \( \boldsymbol{B A} \| \boldsymbol{E} \boldsymbol{D} \) and \( \boldsymbol{B C} \| \boldsymbol{E F} \). Show
that \( \angle A B C+\angle D E F=180^{\circ} \)


A bone left in dilute HCI for about three
days will
A. Crack into pieces
B. Become soft and elastic
c. Dissolve completely
D. Remain as it is


Which symptoms are commonly seen in case of diarrhea?
A. Blood in stool
B. Death
c. Blood clot
D. Nausea


Which of the following enhances lathering property of soap?
A. Sodium carbonate
B. Sodium rosinate
c. sodium stearate
D. Trisodium phosphate


When \( N_{2}^{+} \) is form \( N_{2} \) bond-order \( \ldots \)
and when \( O_{2}^{+} \) is formed from \( O_{2} \) bond-
order
A. increases
B. decreases
c. increases, decreases
D. decreases, increases


A physical quantity \( \rho \) is related to four variables \( \boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\gamma} \) and \( \boldsymbol{\eta} \) as \( \boldsymbol{\rho}=\frac{\boldsymbol{\alpha}^{3} \boldsymbol{\beta}^{2}}{\sqrt{\boldsymbol{\gamma} \boldsymbol{\eta}}} \) The
percentage errors of measurements in \( \boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\gamma} \) and \( \boldsymbol{\eta} \) are \( 1 \%, 3 \%, 4 \% \) and \( 2 \% \)
respectively. Find the percentage error
in \( \rho \)
A . 6.5\%
B. 12\%
c. 21\%
D. 26\%


Which of the following statements
is/are correct?
This question has multiple correct options
\( \mathbf{A} \cdot \) A plot of \( \log k_{p} \) versus \( 1 \backslash \mathrm{T} \) is linear
B. A plot of log [X] versus time is linear for a first order reaction, \( x \rightarrow p \)
C. A plot of log p versus 1/T is linear at constant volume.
D. A plot of p versus 1/V is linear at constant temperature


Evaluate the given integral. \( \int \frac{\log (\log x)}{x} d x \)


Select the wrong statement.
A. Rennin helps in digestion of fats.
B. Lacteals belong to Iymph vessels.
C. HCl makes the gastric pH 1 to 2.
D. If gastric lipase is present its function is very small.


Assertion: PV/T=constant for 1 gram of
gas. This constant varies from gas to gas.
Reason: 1 gram of different gases at \( \mathrm{NTP} \) Occupy different volumes.
A. Both assertion (A) and reason (R) are correct and R gives the correct explanation
B. Both assertion (A) and reason (R) are correct but R doesnt give the correct explanation
C. A is true but R is false
D. A is false but R is true


Which of the following is an intensive
property?
A. Temperature
B. Viscosity
c. Surface tension
D. All of these


If \( 2 x^{2}+x y-3 y^{2}+x+a y-10= \)
\( (2 x+3 y+b)(x-y-2), \) the value of a
and b are
A. 11 and 5
B. 1 and -5
c. -1 and -5
D. -11 and 5


Evaluate the following question.
\( \lim _{x \rightarrow 0} x^{2}-3 \)


If \( A B=-\bar{i}-2 \bar{j}-6 \bar{k}, B \bar{C} C=2 \bar{i}-\bar{j}+ \)
\( \bar{k}, \bar{A} C=\bar{i}-3 \bar{j}-5 \bar{k} . \) Then \( \angle B=? \)
A \( \cdot \)
\[
\begin{array}{l}\cos ^{-1}(\sqrt{\frac{40}{41}}) \\ \text { B } \cdot \\ \qquad \begin{array}{l}\text { cos }^{1}(\sqrt{\frac{6}{41}}) \\ \text { c. } \cos ^{-1}\left(\frac{6}{41}\right)\end{array} \\ \text { D. } \cos ^{-1}\left(\frac{62}{63}\right)\end{array}
\]


Unit of radioactivity is :
A. Fermi
B. Farad
c. Curie
D. Hertz


If vector \( \vec{A}=\hat{i}+c \hat{j}+5 \hat{k} \) and vector
\( \vec{B}=2 \hat{i}+\hat{j}-\hat{k} \) are perpendicular,then calculate the value of \( c \)


The solubility of a solid solute in a liquid solvent increases with increase
in temperature
A. True
B. False


Within a group of the periodic table as one goes from downward to upward, the metallic character:
A . decreases
B. increases
c. first increases then decreases
D. does not change


The value of \( x \) between 0 and \( 2 \pi \) which
satisfy the equation \( \sin x \sqrt{8 \cos ^{2} x}=1 \)
are in A.P. The common difference of the
A.P. is
A \( \cdot \frac{\pi}{8} \)
B. \( \frac{\pi}{4} \)
c. \( \frac{3 \pi}{8} \)
D. \( \frac{5 \pi}{8} \)


Match the columns (I), (II) and (III)


The figure below shows a pattern of two
fishes. Write the mapping rule for the
rotation of Image A to Image B.
A. Image B has to be rotated by 90 degrees anticlockwise to map with image \( A \)
B. Image B should first have a mirror reflection and then be rotated to map with image \( A \)
C. The width of image B should be reduced by 1 unit ( square in the graph shown) and then rotated by 90 degrees to map with image \( A \)
D. The width of image B should be increased by 1 unit square in the graph shown) and then rotated by 90 degrees to map with image \( A \)


The thin stretched membrane at the end
of the ear canal is
A. Pinna
B. Cochlea
c. Eardrum
D. stapes


The population of a town at percent is \( 80000 . \) If the annual rate of increase is
\( 4 \% \), find the population after 4 years (use the formula: \( \boldsymbol{A}=\boldsymbol{p}\left(1+\frac{\boldsymbol{r}}{\mathbf{1 0 0}}\right)^{\boldsymbol{n}} \)
where \( p \) is the original population)


Which parts of the black sheep have
wool?


A rubber string is tied to a nail on the wall. The rubber string is pulled gently to stretch slightly. Which of the following phenomena may occur after the release of the string?
A. Sound is produced
B. Rubber string moves up and down
c. The quality of sound changes with the tension of the string
D. All the above happen


Which \( M O \) is the HOMO of \( O_{2} \)
molecule?
A \( \cdot 2 \pi^{*} \)
В \( \cdot 2 \sigma^{*} \)
\( c \cdot 2 \pi \)
D. \( 2 \sigma \)


Electric field lines are shown in Fig.
State whether the electric potential
is greater at A or B.


A fully loaded Boeing aircraft has a mass of \( 3.3 \times 10^{5} \mathrm{kg}, \) its total wing area
is \( 500 m^{2} . \) It is in level flight with speed of \( 960 \mathrm{km} / \mathrm{h} \)
(a) Estimate the pressure difference between the lower and upper
surfaces of the wings.
(b) Estimate the
fractional increase in the speed of the
air on the upper surface of the wing relative to lower surface. (The density of
\( \left.\operatorname{air} \text { is } \rho=1.2 k g m^{-3}\right) \)


On heating with concentrated \( N a O H \)
solution in an inert atmosphere of \( \boldsymbol{C O}_{2} \)
white phosphorous gives a gas.Which of the following statement is incorrect
about the gas?
A . It is less basic than \( N H_{3} \)
B. It is more basic than \( N H_{3} \)
c. It is highly poisonous and has smell like rotten fish
D. It's solution in water decomposes in the presence of light


If the units of length and force are increased four times, then unit of energy will
A. becomes 8 times
B. becomes 16 times
c. decrease 16 times
D. increase 4 times


Which of the following is the use of gum arabic?
A. Food item
B. Fibre
c. Thickening agent
D. Dye


Isotherms are the graphs drawn at constant
A. pressure
B. temperature
c. volume
D. all of these


Determine whether \( (x+1) \) is a factor of
the polynomial:
\( 3 x^{3}+8 x^{2}-6 x-5 \)


The mass of photon at rest is
A \( \cdot h \nu / e^{2} \)
в. \( h \nu / c \)
c. \( h \nu \)
D. Zero


DNA differs from RNA in
A . Only Sugar
B. Nitrogen base only
c. Nitrogen base and sugar
D. None of the above


The dispersion of liquid or solid in air is called :
A . aerosol.
B. foam.
c. gelss
D. sol.


De Broglie theorized that all moving objects emit waves (matter waves) based on their momentum \( \left(\frac{\boldsymbol{h}}{\boldsymbol{m v}}\right) \) Accordingly, as your team's defensive end, it is your job to stop the other team's 250 pound fullback. If you could hear the fullback's matter waves and
you listened as the opposing fullback
received the ball and accelerated
toward you, what sound would you hear?
A. An increase in loudness and an increase in frequency
B. An increase in loudness and a decrease in frequency
c. A decreasing loudness and an increasing frequency
D. A decreasing loudness and a decreasing frequency
E. Just a loud thump! thump! thump!


Why don't we have interference when
two candles are placed close to each other and the intensity is seen at a distant screen? What happens if the
candles are replaced by laser sources?


Isotactic polypropylene polymer is one,
in which:
A. all methyl groups are on one side of the extended chain. It is a highly crystalline, has high melting point and forms strong fibres
B. the methyl groups present alternates regularly from one side to the other
C. the methyl groups are distributed at random. It is a soft, elastic, and rubbery material
D. None of these


What is photorespiration? How are
photorespiratory losses overcome by \( C_{4} \)
plants ?


\( C u S O_{4} \cdot 5 H_{2} O \) is blue in colour
whereas anhydrous \( C u S O_{4} \) is
colourless.Why?


An electric charge \( 10^{-3} \mu C \) is placed at the origin (0,0) of \( X \) -Y co-ordinate system. Two points A and B are situated \( \operatorname{at}(\sqrt{2}, \sqrt{2}) \) and (2,0) respectively. The potential difference between the points \( A \) and \( B \) will be :
A . 4.5 volt
B. 9 volt
c. zero
D. 2 volt


The mass of one mole \( ^{12} \mathrm{C} \) atom in
grams is :


An object of size \( 3.0 \mathrm{cm} \) is placed \( 14 \mathrm{cm} \) in front of a concave lens of focal length
21cm. Describe the image produced by the lens. What happens if the object is moved further away from the lens?


\( \int_{0}^{\pi / 8} \cos ^{3} 4 \theta d \theta \) is equal to:
\( A \cdot \frac{5}{3} \)
B. \( \frac{5}{4} \)
\( c \cdot \frac{1}{3} \)
D.


A sample of gas in a box is at pressure
\( P_{0} \) and temperature \( T_{0} . \) If number of
molecules is doubled and total kinetic
energy of the gas kept constant then final temperature and pressure will be
\( \mathbf{A} \cdot T_{0} \cdot P_{0} \)
в. \( T_{0} .2 P_{0} \)
c. \( \frac{T_{0}}{2} .2 P_{0} \)
D. \( \frac{T_{0}}{2} \cdot P_{0} \)


Two bodies at different temperatures
are mixed in a calorimeter. Which of the
following quantities remains conserved?
A. sum of the temperatures of the two bodies
B. total heat of the two bodies
c. total internal energy of the two bodies
D. internal energy of each body


Out of the following which does not
liberate \( N_{2} \) gas on heating?
A \( . N a N O_{2}+N H_{4} C l \)
в. \( B a\left(N_{3}\right)_{2} \)
\( c \cdot O_{3}+N O \)
D. \( \left(N H_{4}\right)_{2} C r_{2} O_{7} \)


If the diagonals of a quadrilateral are perpendicular to each other, the figure would always be included under the general classification:
A. rhombus
B. rectangle
c. square
D. isosceles trapezoid
E. none of these


When alpha particles are sent through a thin metal foil, most of them go straight through the foil because:
A. alpha particles are much heavier than electrons
B. alpha particles are positively charged
c. most part of the atom is empty space
D. alpha particles move with very high velocity


\( 1+0.5+0.25+0.125 \ldots . \) is an example
of
A. finite geometric progression
B. infinite geometric series
c. finite geometric sequence
D. infinite geometric progression


Construct a triangle similar to a given \( \triangle A B C \) such that each of its sides is
\( (5 / 7)^{t h} \) of the corresponding sides of \( \triangle A B C . \) It is given that \( A B= \)
\( \mathbf{5} c \boldsymbol{m}, \boldsymbol{B} \boldsymbol{C}=\mathbf{7} \boldsymbol{c m} \) and \( \angle \boldsymbol{A} \boldsymbol{B} \boldsymbol{C}=\mathbf{5 0}^{\circ} \)


A parallel beam of light is incident on
the system of two convex lenses of focal
lengths \( f_{1}=20 c m \) and \( f_{2}=10 c m \)
What should be the distance between
the two lenses so that rays after
refraction from both the lenses pass
undeviated?
\( \mathbf{A} \cdot 60 \mathrm{cm} \)
B. \( 30 \mathrm{cm} \)
\( \mathrm{c} \cdot 90 \mathrm{cm} \)
D. \( 40 \mathrm{cm} \)


The charge per unit length for a very long straight wire is \( \lambda \). The electric field
at points near the wire (but outside it)
and far from the ends varies with
distance r as:
A . r
B. \( 1 / \)
\( c \cdot 1 / r^{2} \)
\( D \cdot 1 / r^{3} \)


Show that \( f(x)=\tan ^{-1} x-x \) is a
decreasing function on \( \boldsymbol{R} \)


A body of mass 5 kg falls from a height of \( 10 m \) to 4 m. Calculate the loss in
potential energy of the body. (Take \( g= \) \( \left.10 m s^{-2}\right) \)
A . \( 0 . J \)
в. \( 300000 J \)
c. \( 3 J \)
D. \( 300 J \)


A body is just floating on the surface of liquid. The density of the body is same as that of the liquid. The body is slightly pushed down. Then it will
A. come back slowly to its earlier position
B. remain submerged where it is left.
c. sink in liquid
D. come out vigoursly


An ac generator produced an output voltage \( \boldsymbol{E}=\mathbf{1 7 0} \sin \mathbf{3 7 7 t} \) volts, where \( t \)
is in seconds. The frequency of ac voltage is
\( \mathbf{A} \cdot 50 H z \)
в. \( 110 H z \)
\( \mathbf{c} \cdot 60 H z \)
D. \( 230 H z \)


Solve: \( \boldsymbol{x}^{4}-\boldsymbol{x}^{\mathbf{3}}+\boldsymbol{x}^{2}-\boldsymbol{x}+\mathbf{1}=\mathbf{0} \)


The rod or stem of a gold leaf electroscope is made of
A. wood
B. Brass
c. Glass
D. Ebonite


A solenoid with 600 turns per metre and
a radius of \( 2 \mathrm{cm}, \) carries a time varying
current \( i(t)=\left(6+4 t^{2}\right) \) A. The electric
field at a distance \( 4 \mathrm{cm} \) from the axis of
the solenoid at \( t=2 s \) will be \( (\operatorname{in} \mu \vee \mathrm{m} \)
-1 to the nearest integer
4.48
3.60
\( c .68 \)
38


\( A, B \) and \( C \) are three mutually
exclusive and exhaustive events such
that \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{2} \boldsymbol{P}(\boldsymbol{B})=\mathbf{3} \boldsymbol{P}(\boldsymbol{C}) \)
What is \( \boldsymbol{P}(\boldsymbol{B}) \) ?
A \( .6 / 11 \)
B. \( 6 / 22 \)
c. \( 1 / 6 \)
D. \( 1 / 4 \)


Q Type your question.
pendulum of length \( R \) attached to its
other end as shown in the figure. The
disc is rotated with a constant angular
velocity \( \omega . \) The string is making an
angle \( 30^{0} \) with the rod. The angular
velocity \( \omega \) of the disc is :
\( ^{\mathrm{A}} \cdot\left(\frac{\sqrt{3} g}{R}\right)^{1 / 2} \)
\( ^{\mathrm{B}}\left(\frac{\sqrt{3} g}{2 R}\right)^{1 / 2} \)
\( \left(\frac{g}{\sqrt{3} R}\right)^{1 / 2} \)
\( \left(\frac{2 g}{3 \sqrt{3} R}\right)^{1 / 2} \)


The area of the region bounded by the
curve \( \boldsymbol{y}=\boldsymbol{x}^{3}, \) its tangent at \( (\mathbf{1}, \mathbf{1}) \) and \( \boldsymbol{x} \)
-axis, is
A \( \cdot \frac{1}{12} \) sq unit
B \( \cdot \frac{1}{6} \) sq unit
c. \( \frac{2}{17} \) sq unit
D. \( \frac{2}{15} \) sq unit


Order Primata contains
A. Shrew and hedge hog
B. Bats and vampire
C. Monkeys and man
D. Horses and zebra


What are the two possible reasons that cause this defect?


Noble gases are placed extremely left in the periodic table.
A . True
B. False


Which of the following factors is of no significance for roasting sulphide ores to the oxides and not subjecting the sulphide ores to carbon reduction directly?
A. Metal sulphides are thermodynamically more stable \( \operatorname{than} C S_{2} \)
B. \( C O_{2} \) is thermodynamically more stable than \( C S_{2} \)
c. Metal sulphides are less stable than the corresponding oxides
\( \mathrm{D} \cdot \mathrm{CO}_{2} \) is more volatile than \( \mathrm{CS}_{2} \)


Reason out in which case the frictional
force between the car and the road is
less.


Solve:
\( \cos ^{-1}\left(\frac{x-x^{-1}}{x+x^{-1}}\right) \)


Joseph jogs from one end \( A \) to the other
end B of the straight \( 300 \mathrm{m} \) road in 2
minutes 50 seconds and then turns
around and jogs \( 100 \mathrm{m} \) back to point \( \mathrm{C} \) in another 1 minutes. Joseph's average
speeds and velocities in jogging, between points \( A \) and \( B \)
respectively, will be
A. \( 1.76 \mathrm{ms}^{-1}, 1.76 \mathrm{ms}^{-1} \)
B . \( 0.869 \mathrm{ms}^{-1}, 0.869 \mathrm{ms}^{-1} \)
c. \( 1.76 m s^{-1}, 0.869 m s^{-1} \)
D. \( 0.869 \mathrm{ms}^{-1}, 1.76 \mathrm{ms}^{-1} \)


Heavier crude oils have too much of:
A. Carbon
B. Hydrogen
c. Both Carbon and Hydrogen
D. Sulfur


Pulp cavity of teeth is lined by
A. Odontoblast
B. chondroblast
c. osteoblast
D. Amyloblast


What is minimum frequency of the
photon required to carry out transition
A \( \cdot 1.21 \times 10^{15} H z \)
B . \( 1.61 \times 10^{15} \mathrm{Hz} \)
c. \( 1.21 \times 10^{14} H z \)
D. \( 1.61 \times 10^{14} \mathrm{Hz} \)


How do \( m-R N A, t-R N A \) and ribosomes
help in the process of translation?


The value of \( _{(0,0,0)}^{(1,1,1)} \int E . d l \) is
A. \( -1 V \)
в. \( 0 V \)
\( c .-2 V \)
D. \( 1 V \)


Solve \( \int x \sin ^{-1} x d x \)


Evaluate \( \int_{4}^{12} x d x \)


Find the second component of an ordered pair (2,-3)
A . 2
B. 3
c. 0
D. - 3


An alloy contains \( 15 \% \) zinc, \( 25 \% \) brass
and rest copper. How much copper is there in 75 kg of that alloy?
A. \( 20 \mathrm{kg} \)
в. \( 30 \mathrm{kg} \)
c. \( 45 \mathrm{kg} \)
D. \( 10 \mathrm{kg} \)


If saturated vapours are compressed slowly (temperature remaining constant) to half the initial volume, the
vapour pressure will :
A. Become four times
B. Become doubled
c. Remain unchanged
D. Become half


The capacity of a normal human eye to see the smallest objects is :
A. \( 5000 \mathrm{nm} \)
B. \( 10000 \mathrm{nm} \)
\( c \cdot 18000 \mathrm{nm} \)
D. 25000 nm


Select the incorrect statement among
the following:
\( \mathbf{A} \cdot \) the \( C-O-C \) bond angle in ether is \( 110^{0} \)
B. diethyl ether reacts with excess of HI to form ethyl iodide
C. ethers and alcohols are functional isomers
D. ethers are Lewis base hence do not react with bronsted
acid like \( H_{2} S O_{4} \)


1500 families with 2 children were
selected randomly, and the following
data were recorded:
No. of girls in family

No. of families
\[
\begin{array}{ll}
475 & 814
\end{array}
\]
Compute the probability of a family, chosen at random, having
(i) 2 girls
(ii) 1 girl
(iii) No girl
Also check whether the sum of these
probabilities is 1


Bakelite is obtained from phenol by
reaction with : 1
A. Acetaldehyde
B. Acetal
c. Formaldehyde
D. Chlorobenzene


Which of the following pairs represent the same rational number?
\( \frac{-2}{-3} \) and \( \frac{2}{3} \)


Find the inclination of the line passing through (-5,3) and (10,7)
A. 14.73
B . 14.93
\( c \cdot 14.83 \)
D. 14.63
E. none of these


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:
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}-\mathbf{5} \boldsymbol{x}-\boldsymbol{3} \) on \( [\mathbf{1}, \boldsymbol{3}] \)


Which of the following factors affect
friction?
A. Nature of the surface
B. Weight of the object placed over other
C. Motion or speed of the object
D. All of the above


Which of the following organism was the cytoplasmic donor of Dolly?
A. Scottish black face sheep
B. Finn Dorset sheep
c. Bonnie
D. Sally


A die is thrown 200 times and the
outcomes 1,2,3,4,5,6 have
frequencies as below:
Outcome
Frequency
\( \begin{array}{llll}10 & 38 & 43 & 29\end{array} \)
Find the probabilities of getting a number more than 1 and less than 6 in a toss
(trial)
A . 0.65
в. 0.55
c. 0.69
D. None of these


The angle made by \( \overrightarrow{\mathrm{j}}+\overrightarrow{\mathrm{k}} \) with \( \mathrm{y} \) -axis is:
A \( \cdot 60^{\circ} \)
B. \( 30^{\circ} \)
\( \mathbf{c} \cdot 45^{\circ} \)
D. \( 90^{\circ} \)


toppr
Q Type your question_
-
\( 2 I^{-}(a q)+S_{2} O_{8}^{2-}(a q) \rightarrow I_{2}(a q)+ \)
\( 2 S_{2} O_{4}^{-2}(a q)(s l o w) \)
\( \boldsymbol{I}_{2}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{2} \boldsymbol{S}_{2} \boldsymbol{O}_{3}^{2-}(\boldsymbol{a} \boldsymbol{q}) \rightarrow \boldsymbol{2} \boldsymbol{I}^{-}(\boldsymbol{a} \boldsymbol{q})+ \)
\( \boldsymbol{S}_{4} \boldsymbol{O}_{\boldsymbol{6}}^{\boldsymbol{2}-}(\boldsymbol{a} \boldsymbol{q})(\boldsymbol{f} \boldsymbol{a} \boldsymbol{s} \boldsymbol{t}) \)
A little of these sulphate ions along with starch are added in the first
reaction. The iodine formed in the first
reaction reacts with sulphate ions and
the blue colour of iodine starts
developing as soon as the whole \( S_{2} O_{3}^{2-} \)
are used up. The sulphur containing
atoms in the course of reactions are:
This question has multiple correct options
\( \mathbf{A} \)
\[
\left[\begin{array}{c}
o \\
o-S^{\prime}-O \\
_{o}
\end{array}\right]^{2}
\]
B.
\[
\left[\begin{array}{cc}
o & o \\
O-S^{\prime}-O-O-S^{\prime}-O \\
_{O} & _{O}^{\prime}
\end{array}\right]^{2-}
\]
\( c \)
\[
\left[\begin{array}{c}
o \\
O-\underset{S}{S}-S \\
o
\end{array}\right]^{2}
\]
D.
\[
\left[\begin{array}{cc}
o & o \\
O-S & -S-S-S^{\prime} \\
\rho & \vdots \\
o
\end{array}\right]^{2-}
\]


What is the action of the following
reagents on aniline?
Hot and conc. sulphuric acid.


An unknown alkyl halide [X] reacts with alcoholic KOH and produces a
hydrocarbon \( \left(C_{4} H_{8}\right) \) as the major product. Ozonolysis of this hydrocarbon affords one mole of propanaldehyde and one mole of formaldehyde. Suggest
which organic compound among the following has the correct structure of the above alkyl halide \( [\mathbf{X}] ? \)
A \( \cdot C H_{3} C H_{2} C H_{2} C H_{2} B r \)
в. \( C H_{3} C H(B r) C H_{2} C H_{3} \)
c. \( C H_{3} C H(B r) C H(B r) C H_{3} \)
D. \( B r\left(C H_{2}\right)_{4} B r \)


\( S O_{2} \) acts as
This question has multiple correct options
A. bleaching agent
B. oxidising agent
c. reducing agent
D. disinfectant


A copper rod and \( A l \) rod are placed in
conc. \( H N O_{3} \) in separate containers.
Which of the following observations are found after some time?
A. Copper rod and Aluminium rod continue to deteriorate at the same rate.
B. Copper rod continues to deteriorate while aluminium rod deteriorates initially then stops
c. There is no deterioration in either copper rod or aluminium rod
D. Aluminium rod continues to deteriorate while copper rod deteriorates initially and then stops


Franklin showed that
the spark from our clothes during winters are the same phenomena. Fill in the blanks.
A. thunder-storm
B. earthquake
c. lightning
D. rain


What is the structure of phosphorus
trichloride?
A. Trigonal Pyramidal
B. Trigonal Planar
c. Tetrahedral
D. Square Planar


Plants having vascular tissues but lacking seeds are
A. Bryophyta
B. Pteridophyta
c. Gymnosperms
D. Angiosperms


By what smallest number should we
multiply 8788 so that the product becomes a perfect cube. Find the cube
root of the product
A .2,26
B. 2,6
c. 22,26
D. 22, 21


A bird flying in the sky has
A. K.E. only
B. P.E. only
C. Neither K.E. nor P.E.
D. Both K.E. and P.E.


Which of the following properties must be known in order to calculate the
amount of heat needed to melt \( 1.0 \mathrm{kg} \) of
ice at \( 0^{\circ} C ? \)
I. The specific heat of water
I. The latent heat of fusion for water
III. The density of water.
A. I only
B. I and II only
c. ।, II, and III
D. II only
E. I and III only


Solution of the differential equation
\( \tan y \cdot \sec ^{2} x d x+\tan x \cdot \sec ^{2} y d y=0 \) is
A. \( \tan x+\tan y=k \)
B. \( \tan x-\tan y=k \)
c. \( \frac{\tan x}{\tan y}=k \)
D. \( \tan x \cdot \tan y=k \)


An organic compound on analysis gave \( C=54.2 \%, H=9.2 \% \) by mass. Its
empirical formula is :
A. \( C H O_{2} \)
в. \( C H_{2} \) О
\( \mathrm{c} \cdot C_{2} H_{8} \mathrm{O} \)
D. \( C_{2} H_{4} O \)


Which of the following reagent is used as fixer in photography?
\( \mathbf{A} \cdot A g B r \)
в. \( A g N O_{3} \)
c. \( N a_{2} S_{2} O_{3} \cdot 5 H_{2} O \)
D. Both A and C


In the following figure \( r_{1} \) and \( r_{2} \) are \( 5 \mathrm{cm} \) and \( 30 \mathrm{cm} \) respectively. If the moment of inertia of the wheel is
\( 5100 k g-m^{2} \) about the axis passing
through its centre and perpendicular to the plane of wheel, then what will be its angular acceleration?


A square of side \( 2.0 \mathrm{m} \) is placed in a
uniform magnetic field \( \mathbf{B}=\mathbf{2 . 0} \mathbf{T} \) in a
direction perpendicular to the plane of the square inwards. Equal current
\( \mathbf{i}=\mathbf{3 . 0 A} \) is flowing in the directions shown in figure. Find the magnitude of the magnetic force on the loop.


Find the equations to the circles in which the line joining the points \( (a, b) \) and \( (b,-a) \) is a chord subtending an
angle of \( 45^{\circ} \) at any point on its circumference.


Energy of all molecules of a monatomic gas having a volume \( V \) and pressure \( P \) is
\( \frac{3}{2} \boldsymbol{P} \boldsymbol{V} \). The total translational kinetic energy of all molecules of a diatomic
gas at the same volume and pressure is
A \( \cdot \frac{1}{2} P V \)
в. \( \frac{3}{2} P V \)
c. \( \frac{5}{2} P V \)
D. 3PV


IUPAC name of the compound is:
A. 3,4 -Dihydroxybenzoic acid
B. 4,5-dihydroxybenzoic acid
c. 2,3-dihydroxybenzoic acid
D. none of these


Among:
\( \boldsymbol{a}) \boldsymbol{N} \boldsymbol{a}_{2} \boldsymbol{O} \)
b) \( M g O \)
\( \boldsymbol{c}) \boldsymbol{A l}_{2} \boldsymbol{O}_{3} \)
\( \boldsymbol{d}) \boldsymbol{P}_{2} \boldsymbol{O}_{5} \)
the most basic, most acidic and amphoteric oxide can be
\( A \cdot a, b, c \)
в. b, е,
\( c . \) a, \( e, c \)
D. e,c,


Find the value of \( b \) for which the
polynomial \( 2 x^{3}-9 x^{2}-x-b \) is
divisible by \( 2 x+3 \)


Nitric acid is yellow in colour when:
A. freshly prepared
B. dissolved oxides of nitrogen are present
c. water is dissolved
D. None of the above


What do you mean by linear pair of angles?


A wire of length L and Density \( \phi \) and young's modulus Y is hanging from a support .Find the elongation in the length of the wire at which wire will break:
\( \mathbf{A} \cdot \frac{L^{2} \phi g}{Y} \)
B. \( \frac{L^{2} \phi g}{2 Y} \)
\( ^{\mathrm{c}} \cdot \frac{2 L^{2} \phi g}{Y} \)
D. \( \frac{L^{2} \phi g}{4 Y} \)


State whether given statement is True or False.

A quantity which can be represented completely by magnitude only, is called a vector quantity.
A. True
B. False


What is buffer solution? Give an
example.


If the difference between the mode and
the median is \( 36, \) then find the
difference between the median and the
mean.
A . 16
B. 33
c. 18
D. 32


For what value of \( k \) does \( (k-12) x^{2}+ \)
\( \mathbf{2}=\mathbf{0} \) have equal roots?


If the quotient on dividing \( 2 x^{4}+x^{3}- \)
\( 14 x^{2}-19 x+6 \) by \( 2 x+1 \) is \( x^{3}+ \)
\( a x^{2}-b x-6 \)
Find the values of a and \( b \), also the remainder


A solenoid \( 30 c m \) long is made by
winding 2000 loops of wire on an iron
rod whose cross-section is \( 1.5 \mathrm{cm}^{2} \). If
the relative permeability of the iron is
6000. What is the self-inductance of the
solenoid?
\( \mathbf{A} \cdot 15 H \)
в. 25H
\( c .35 H \)
D. \( 5 H \)


For a material \( Y=6.6 \times 10^{10} \mathrm{N} / \mathrm{m}^{2} \) and
bulk modulus \( \mathrm{K}=11 \times 10^{10} \mathrm{N} / \mathrm{m}^{2}, \) then its
Poissons's ratio is
A. 0.8
B. 0.35
\( c . \) о.
D. 0.4


In Earthworm, mouth is situated on
A. Prostomium
B. Peristomium
c. Stomium
D. Protostomium


Period of \( \boldsymbol{f}(\boldsymbol{x})=\{\boldsymbol{x}\}+\left\{\boldsymbol{x}+\frac{1}{3}\right\}+ \)
\( \left\{x+\frac{2}{3}\right\} \) is equal to (where \( \{.\} \) denotes fraction part function
\( \mathbf{A} \cdot \mathbf{1} \)
B. \( \frac{2}{3} \)
\( c \cdot \frac{1}{2} \)
D.


What chemicals are obtained
industrially from sodium chloride? Outline the process.


A clinical thermometer reads
temperature from
A \( \cdot 35^{\circ} \) Cto \( 42^{\circ} \) C
B . \( 0^{\circ} \) Cto \( 100^{\circ} \) C
\( \mathbf{c} \cdot 25^{\circ} \mathrm{Cto} 42^{\circ} \mathrm{C} \)
D. \( 35^{\circ} \) Cto \( 62^{\circ} \) C


Which molecule/ion among the
following cannot act as a ligand in complex compounds?
A. \( C O \)
в. \( C H_{4} \)
c. \( C N^{-} \)
D. \( B r^{-} \)


\( \boldsymbol{y}=\frac{1}{1+x+x^{2}+x^{3}}\left[\frac{d y^{2}}{d y^{2}}\right]_{x=0}=? \)


The oxidation number of phosphorus in \( \boldsymbol{B} \boldsymbol{a}\left(\boldsymbol{H}_{2} \boldsymbol{P} \boldsymbol{O}_{2}\right)_{2} \) is:
\( A \cdot+3 \)
B. +2
\( c \cdot+1 \)
D. -


A ray of light is incident on a hollow
glass prism as shown. Then the ray will
undergo:
A. deviation and dispersion both
B. deviation but not dispersion
c. dispersion but no deviation
D. neither deviation nor dispersion