Amongst the following elements present in an organic compound, the
one which has no direct test for
detection is :
A . \( C l \)
в. \( N \)
\( c . s \)
D.


On a rainy day, out of 150 students in a school 25 were absent. Find the
percentage of students absent from the
school? What percentage of students
are present?


Two rods \( A \) and \( B \) of the same material
and length have radii \( r_{1} \) and \( r_{2} \)
respectively. When they are rigidly fixed at one end twisted by the same torque applied at the other end, the ratio \( \left[\begin{array}{lllllll}\text {the} & \text {angle} & \text {of} & \text {twist} & \text {at} & \text {the} & \text {er} \\ \hline \text {the} & \text {angle} & \text {of} & \text {twist} & \text {at} & \text {the} & \text {er}\end{array}\right. \)
equals to:
A \( \cdot \frac{r_{1}^{2}}{r_{2}^{2}} \)
B \( \cdot \frac{r_{1}^{3}}{r_{2}^{3}} \)
\( c \cdot \frac{r_{2}^{4}}{r_{1}^{4}} \)
D \( \cdot \frac{r_{1}^{4}}{r_{2}^{4}} \)


Which of the following is a partial root parasite?
A. Sandal wood
B. Mistetone
c. orobanche
D. Ganodema


What is the concept of diffusion and
Brownian motion?


The lines \( 2 x-3 y=5 \) and \( 3 x-4 y=7 \)
are the diameters of a circle of area 154
square units. An equation of this circle is \( (\boldsymbol{\pi}=\mathbf{2 2} / \mathbf{7}) \)
A \( \cdot x^{2}+y^{2}+2 x-2 y=62 \)
B. \( x^{2}+y^{2}+2 x-2 y=47 \)
c. \( x^{2}+y^{2}-2 x+2 y=47 \)
D. \( x^{2}+y^{2}-2 x+2 y=62 \)


The area of a square park is the same
as a rectangular park. If the side of the square park is \( 60 \mathrm{m} 60 \mathrm{m} \), find the breadth (in meter) of the rectangular park. Given: Length of the rectangular park is \( 90 \mathrm{m} \)


The ions which plays major role in generating hormone action
A. Calcium ions
B. Magnesium ions
c. Sodium ions
D. None of these


State the electronic configuration for Boron \( [p=5, n=6] \)
A . 2,3
B. 5, 10
c. 5,12
D. 5,1


After electrolysis of NaCl solution with
inert electrodes for a certain period of
time, \( 600 \mathrm{mL} \) of the solution was left. Which was found to be \( 1 \mathrm{N} \) in \( \mathrm{NaOH} \) During the same time, 31.75 g \( \mathrm{Cu} \) deposited in the copper voltameter in series with the electrolytic cell. Calculate the percentage yield of NaOH obtained.
A. \( n=60 \% \)
a
B . \( n=50 \% \)
c. \( n=70 \% \)
D. None of these


\( P \) is a point on the line through the point \( A \) whose position vector is \( \vec{a} \) and the line is parallel to the vector \( \vec{b} \). If
\( \boldsymbol{P A}=\mathbf{6}, \) the position vector of \( \boldsymbol{P} \) is
A \( \cdot \vec{a}+6 \vec{b} \)
B \( \cdot \vec{a}+\frac{6}{|\vec{b}|} \vec{b} \)
c. \( \vec{a}-6 \vec{b} \)
D \( \cdot \vec{b}+\frac{6}{|\vec{a}|} \vec{a} \)


depends on mass and kind of material of the body.
A. specific heat
B. Heat capacity
c. Temperature
D. kinetic energy


\( \mathrm{f}\left|\begin{array}{lll}\boldsymbol{a}+\boldsymbol{b} & \boldsymbol{b}+\boldsymbol{c} & \boldsymbol{c}+\boldsymbol{a} \\ \boldsymbol{c}+\boldsymbol{a} & \boldsymbol{a}+\boldsymbol{b} & \boldsymbol{b}+\boldsymbol{c} \\ \boldsymbol{b}+\boldsymbol{c} & \boldsymbol{c}+\boldsymbol{a} & \boldsymbol{a}+\boldsymbol{b}\end{array}\right|=\boldsymbol{t} \times \operatorname{det} \) of
circulant matrix whose elements of first
column are \( a, b, c \) then \( t \) equals
A. 5
B. 6
\( c \cdot-2 \)
\( D \)


How many nucleons are present in phosphorous?
A . 15
B. 16
c. 30
D. 31


Fine the odd one.
A. Adiantum
B. Equisetum
c. Selaginella
D. Riccia


Which of the following occurs due to the stomatal opening?
I. Increased photosynthesis
II. Increased transpiration
III.Decreased chlorophyl
A. I only
B. II only
c. ॥ only
D. I and II only
E . I, II and III only


Select the correct option on the basis of given features, to which they belong:
A. Cambium - Develops later
B. Pith - Absent
C. Epidermis -Possess unicelluiar hairs
A . Dicot stem
B. Monocot stem
c. Dicot root
D. Monocot root


Methanol can be distinguished from ethanol by:
A . heating with \( I_{2} \) and alkal
B. treating with schiff's reagent
C . treating \( C r O_{3} \) solution in dil. \( H_{2} S O_{4} \)
D. treating with Lucas reagent


Henry's law holds for a slightly soluble
gas as long as the gas:
A. Has a high molecular weight
B. Has a low molecular weight
c. Is diatomic
D. Does not react chemically with the solvent


Einstein's photo-electric equation
states that \( \boldsymbol{E}_{\boldsymbol{k}}=\boldsymbol{h v}-\boldsymbol{W} . \) In this
equation, \( \boldsymbol{E}_{\boldsymbol{k}} \) refers to:
A. kinetic energy of all ejected electrons
B. mean kinetic energy of emitted electrons
c. minimum kinetic energy of emitted electrons
D. maximum kinetic energy of emitted electrons


A rectangle DEFG is plotted in \( X Y \) plane. The co-ordinates of D , E , F and G \( \operatorname{are}(2,2),(9,2),(9,10) \) and (2,10)
Find the new co-ordinates of D when
DEFG is rotated \( 270^{\circ} \) around origin.
A \( \cdot(-2,-2) \)
в. (2,-2)
c. (2,4)
(年. \( (2,4)) \)
D. (-2,4)


Explain zone - refining (figure not necessary.


A long straight wire carries a current 10 amp. An electron travels with a velocity \( \mathbf{5 . 0} \times \mathbf{1 0}^{\mathbf{6}} \mathrm{m} / \mathrm{sec} \) parallel to the wire 0.1
\( \mathrm{m} \) away from it and in a direction
opposite to the current. What force does the magnetic field of current exert on the electron?
В. \( 0.8 \times 10^{-16} N \)
c. \( 1.6 \times 10^{-17} N \)
D. \( 1.6 \times 10^{-16} N \)


If \( Z_{r}=\left(\cos \frac{r \pi}{10}+i \sin \frac{r \pi}{10}\right) . \) Then
find the value of \( Z_{1} \cdot Z_{2} \cdot Z_{3} \cdot Z_{4} \)


Rms value of current \( \boldsymbol{i}=\mathbf{3}+ \)
\( 4 \sin \left(\omega t+\frac{\pi}{3}\right) \) is:
A . \( 5 A \)
в. \( \sqrt{17} A \)
\( c \cdot \frac{5}{\sqrt{2}} A \)
D. \( \frac{7}{\sqrt{2}} A \)


The name of the compound is
Cyclopent-1-en-3-ol
If true enter 1 , else enter 0 .


(a) What is selectivity of catalyst? Write example.
(b) What happens when hydrated ferric oxide sol is mixed with arsenius
sulphide sol?
(c) Explain Tyndall effect with labelled diagram.


An empty freight car of mass \( \boldsymbol{m}_{1}= \)
\( \mathbf{1 0}, \mathbf{0 0 0 k g} \) rolls at speed \( u_{1}=2 m / s \) on
a level road and collide with a loaded
car of mass \( \boldsymbol{m}_{2}=\mathbf{2 0}, \mathbf{0 0 0 k g} \) standing
at rest. If the cars couple together, find
their speed \( V \) after the collision and
also the loss in kinetic energy. What should be speed of the loaded car towards the empty car, in order that both be brought to rest by the collision?


Birds take nectar by
A. Chewing
B. Swallowing
c. sucking
D. Biting


Which of the following statement is
correct?
This question has multiple correct options
A. when the magnetic flux linked with conducting loop is zero then emf induced is always zero
B. when the emf induced in conducting loop is zero, then the magnetic flux linked with the loop must be zero
C. transformer works on mutual induction
D. all of these


\( 0.5 g \) of an organic compound containing nitrogen on kjeldahlising
required \( 29 m l \) of \( N / 5 H_{2} S O_{4} \) for
complete neutralisation of ammonia. The percentage of nitrogen in the compound is :
A. 34.3
B. 16.2
c. 13.6
D. 24.5


The following reaction is known by the
name:
A. Acetylation reaction
B. Schotten-Baumen reaction
c. Friedel-craft's reaction
D. Perkin's reaction


The resonant frequency of an L-C circuit
is
\( ^{\mathrm{A}} \cdot \frac{1}{2 \pi \sqrt{L C}} \)
в. \( \frac{1}{2 \pi} \sqrt{\frac{L}{C}} \)
c. \( \frac{1}{4 \pi} \sqrt{\frac{L}{C}} \)
D. \( \frac{1}{2 \pi} \sqrt{\frac{C}{L}} \)


A tungsten wire of length \( 20 \mathrm{cm} \) is stretched by \( 0.1 \mathrm{cm} . \) Find the strain on the wire.
A .0 .002
B. 0.005
\( c \cdot 0.001 \)
D. 0.004


The boiling point of an azeotropic mixture of water and ethyl alcohol is
less than that of theoritical value of
water and alcohol mixture. Hence the
mixture shows:
A. that solution is saturated
B. positive deviation from Raolt's law
c. negative deviation from Raoult's law
D. that solution is super saturated


Each side of a cube is measured to be
7.203 \( \mathrm{m} \). What is the volume of the cube
to appropriate significant figure?
A \( \cdot 373.7 m^{3} \)
в. \( 311.3 m^{3} \)
\( \mathrm{c} \cdot 211.3 m^{3} \)
D. \( 3737 m^{3} \)


In Young's double slit experiment with monochromatic source of light of
wavelength \( 6000 A^{\circ}, \) if the path difference at a point on the screen is 6
\( \times 10^{-6} m \) the number of the bright band
formed at that point is:
\( A \cdot 2 \)
B. 4
\( c \cdot 6 \)
D. 10


Write equations for the following
statements:
If you take away 6 from 6 times \( y, \) you
\( \operatorname{get} 60 \)


If the amount of heat given to a system is \( 35 J \) and the amount of work done on
the system is \( 15 J \), then the change in
internal energy of the system is
A. \( -50 J \)
в. \( 20 J \)
\( c .30 J \)
D. \( 50 J \)


An electric iron is rated \( 220 \vee, 2 k W . \) If
the iron is used for 2 h daily find the cost
of running it for one week if it costs Rs.
4.25 per kWh.


Amount of \( C O_{2} \) mixed annually is
about
A. \( 70 \times 10^{10} \mathrm{Kg} \)
в. \( 70 \times 10^{11} \mathrm{Kg} \)
c. \( 70 \times 10^{13} \mathrm{Kg} \)
D. \( 70 \times 10^{13} g \)


According to IUPAC convention, name of
the following compound is:
A. 3 -chloro-5-ethyl ethylbenzoate
B. ethyl-3-chloro-5-ethylbenzoate
C. metachloro-metaethyl ethylbenzoate
D. both 'b' and 'c' are correct


Lymph carries digested and absorbed
fat from
A. Stomach
B. Small intestine
c. colon
D. Oesophagus


Which of the following contraceptive methods do involve a role of hormone?
A. Lactational amenorrhea, Pills Emergency contraceptives
B. Barrier method, Lactational amenorrhea, Pills
c. CuT, Pills, Emergency contraceptives
D. Pills, Emergency contraceptives, Barrier methods


Active transport is characterized by
A. Requires special membrane proteins
B. Highly selective
C . Requires energy
D. All of the above


Out of the given oxides, how many of these are the anhydrides of dibasic oxyacid?
(i) \( \boldsymbol{S O}_{2} \)
(ii) \( P_{4} O_{10} \)
(iii) \( N O_{2}(\text { iv }) C O_{2}(v) \)
\( \boldsymbol{L} \boldsymbol{i}_{2} \boldsymbol{O}\left(v_{i}\right) \boldsymbol{C O}\left(v_{i i}\right) \boldsymbol{C l O}_{2}\left(v_{i i i}\right) \boldsymbol{C l}_{2} \boldsymbol{O}(i \mathbf{x}) \)
\( \boldsymbol{I}_{2} \boldsymbol{O}_{5} \)


Match the reactions in Column I with
nature of the reactions/type of the products in Column II.


Which of the following helps eye to adjust the focal length of the lens?
A. Cornea
B. Iriss
c. ciliary body
D. Retina


What reagent and/or reaction sequence below would convert trans-3-hexene to
meso-3,4-hexanediol?
A \( \cdot O s O_{4},\left(C H_{3}\right)_{3} C C O O H,\left(C H_{3}\right)_{3} C O H, N a O H \)
B. \( O_{3} \) followed by \( Z n / H_{2} O \)
C. \( B_{2} H_{6} / \) diglyme followed by \( H_{2} O_{2} / N a O H \)
D. \( C H_{3} C O_{3} H \) followed by \( N a O H / H_{2} O \)


Compound (A) will be:
condensation
\( \mathbf{A} \cdot P h-C \equiv C-C \equiv C-C H O \)
B \( . P h-C \equiv C-C H=C H-C H O \)
\( \mathbf{c} \cdot P h-C H=C H-C \equiv C-C H O \)
\( \mathbf{D} \cdot P h-C H=C H-C=C H-C O_{2} H \)


There are \( _{\text {一一一一一一 }} \) isotopes of oxygen
A. 0
B.
\( c \cdot 2 \)
D.


The reaction of the benzyl chloride with sodium cyanide followed by reduction with hydrogen in the presence of nickel gives:
A. \( \beta \) -phenyl ethylamine
B. N-isobutylaniline
c. benzyl amine
D. aniline


One of the methods of producing He is to bombard \( L i \) with the following
projectile
A . \( \alpha \) -particles
B. electrons
c. protons
D. neutrons


The correct statement(s) pertaining to
the adsorption of a gas on a solid surface is/are:

This question has multiple correct options
A. Adsorption is always exothermic
B. Physisorption may transform into chemisorption at high temperature
C. Physisorption increases with increasing temperature but chemisorption decreases with increasing temperature
D. Chemisorption is more exothermic than physisorption, however it is very slow due to higher energy of activation


Assertion
If \( A, B, C \) are three events such that \( P(A)=\frac{1}{4}, P(B)=\frac{1}{6} \& P(C)=\frac{2}{3} \)
then events \( A, B, C \) are mutually exclusive.
Reason
If \( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B} \cup \boldsymbol{C})=\boldsymbol{P}(\boldsymbol{A})+\boldsymbol{P}(\boldsymbol{B})+ \)
\( \boldsymbol{P}(\boldsymbol{C}) \) then \( A, B, C \) are mutually
exclusive events.
A. Both Assertion \& Reason are individually true \& Reason is correct explanation of Assertion
B. Both Assertion \& Reason are individually true but Reason is not the , correct (proper) explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true


\( \left\{\begin{array}{ccc}\text { Find } \lim _{x \rightarrow 0} f(x) & \text { where } f(x)= \\ x-1 & \text { if } & x<0 \\ 0 & \text { if } & x=0 \\ x+1 & \text { if } & x>0\end{array}\right. \)


"Every great physical theory starts as a heresy and ends as a dogma."Give some examples from the history of science of the validity of this incisive
remark.


When 100 volt dc is applied across a
coil, a current of \( 1 a m p \) flows through it,
when \( 100 v o l t \) ac of \( 50 H z \) is applied to
the same coild only \( 0.5 a m p \) flows.
Calculate the resistance and
inductance of the coil.


The surface area of the drop is:
Spherical drop
\( \mathbf{A} \cdot 4 \pi R^{2} \)
\( \mathbf{B} \cdot 4 \pi\left(9 t^{2} R^{4}\right)^{1 / 3} \)
\( \mathbf{C} \cdot 4 \pi\left(9 t^{4} R^{2}\right)^{1 / 3} \)
D. \( 4 \pi R(t+R) \)


Assertion
A body having the uniform density has
same point, as centre of gravity and
centre of buoyancy
Reason
While formulating the equation for positioning centre of mass and centre of buoyancy,has difference of the term
of uniform density only.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


In the set of triangles in a plane the relation 'is similar to' is an equivalence relation. Prove


Gravitational force acts on all objects in proportion to their masses. Why then, a heavy object does not fall faster than a light object?


What is asthma?


A planet in solar system has a mass double that of earth and density equal to that of earth. An object weigh Won the earth, will weigh on the other
planet as \( W^{1} . \) Then:
\( \mathbf{A} \cdot W^{1}=W \)
В. \( W^{1}=2 W \)
c. \( w^{1}=\frac{W}{2} \)
D.
\[
W^{1}=2^{\frac{1}{3}} W
\]


\( p H \) of water is 7 when any substance \( Y \)
is dissolved in water then \( p H \) becomes
13. Substance \( Y \) is a salt of:
A. strong acid and strong base
B. strong acid and weak base
c. weak acid and weak base
D. weak acid and strong base


Portion of gene which is transcribed but not translated is
\( A \). Exon
B. Intron
c. cistron
D. codon


The displacement of a particle along the
\( x \) -axis is given by \( x=a \sin ^{2} \omega t . \) The
motion of the particle corresponds to.
A. simple harmonic motion of frequency \( \omega / \pi \)
B. Simple harmonic motion of frequency \( 3 \omega / 2 \pi \)
c. Non simple harmonic motion
D. Simple harmonic motion of frequency \( \omega / 2 \pi \)


Which Lewis structure below has
been drawn incorrectly?
A . H: H
B. \( \mathrm{H}: \mathrm{C}::: \mathrm{N} \)
\( c \)
\( \mathbf{H}: \dot{\mathbf{O}} \)
D. : N ::: N:
\( \mathbf{F} \cdot \underset{\mathbf{F}}{\mathbf{B}}: \mathbf{F} \)


At poles, how is the direction of Polar
winds?
A. Air from Polar region moves in towards the \( 60^{\circ} \) latitude belt
B. Air from the \( 60^{\circ} \) latitude belt moves in towards Polar
region
C. Air from Polar region moves in towards the equatorial region
D. Air from equatorial region moves in towards the Polar region


Ribose sugar differs from deoxyribose in having
A. two extra oxygen molecules
B. one extra oxygen molecules
c. no oxygen
D. Hydroxyl group


Which do you think is a more basic characteristic for classifying
organisms?
a) the place where they leave
b) the kind of cells they are made of
Why?


An electric bulb P rated \( 220 V, 60 W \) is
working at full efficiency. Another identical bulb \( Q \) is connected across the
mains as shown in the figure. The total
power consumed is :
A . \( 20 W \)
в. \( 40 W \)
\( c .30 W \)
D. \( 70 W \)


Classify the following equilibrium
reactions into homogeneous and
heterogeneous
\( \mathbf{A} \cdot 2 N O_{2}(g) \rightleftharpoons 2 N_{2}(g)+O_{2}(g) \)
B \( .2 N H_{3}(g) \rightleftharpoons N_{2}(g)+3 H_{2}(g) \)
\( \mathbf{c} \cdot 2 C u\left(N O_{3}\right)(s) \rightleftharpoons 2 C u O(s)+4 N O_{2}(g) \)
D \( \cdot P C I_{5}(g) \rightleftharpoons P C I_{3}(g)+C I_{2}(g) \)


The binding energy per nucleon of \( _{17}^{35} C l \) nucleus is
\( \left(_{17}^{35} C l=34.98000 \mathrm{amu}, m_{P}=1.007825\right. \)
\( \operatorname{amu,m}_{n}=1.008665 \) amu and 1 amu is
equivalent to \( 931 \mathrm{MeV} \) )
A \( .4 .6 \mathrm{MeV} \)
B. \( 5.8 \mathrm{MeV} \)
c. \( 6.5 \mathrm{MeV} \)
D. \( 8.2 \mathrm{MeV} \)


The contents of 100 match boxes were
checked to determine the number of
matches they contained.
No. of \( \quad 35 \quad 36 \)
37
matches
No. of match
\( \begin{array}{ll}\text { 12 } & \text { 15 }\end{array} \)
boxes
Calculate the mean number of matches
per box
A . 38
B. 42
c. 67
D. 51


Luke Autbeloe drops a pile of roof shingles from the top of a roof located
8.52 meters above the ground. Determine the time required for the shingles to reach the ground.
\( \mathbf{A} \cdot 1 s \)
в. 1.32
c. \( 1.3 s \)
D. \( 1.2 s \)


\( \operatorname{Let} \mathbf{h}(\mathbf{x})=\mathbf{f}(\mathbf{x})-[\mathbf{f}(\mathbf{x})]^{2}+[\mathbf{f}(\mathbf{x})]^{3} \) for
every real number x then
A. h is increasing whenever fis increasing
B. h is increasing whenever f is decreasing
c. \( h \) is decreasing whenever \( f \) is increasing
D. Nothing can be said in general


An unbiased die is thrown twice. Let the
even \( A \) be \( ^{\prime} \) odd \( ^{\prime} \) number on the first
throw and \( B \) the event \( ^{\prime} \) odd number on
the second throw'. Check the
independence of the events \( A \) and \( B \).


If true enter 1 , else enter 0
When ethene reacts with \( H_{2} \), ethane is
formed. The \( \pi \) bond of \( C=C \) is affected.
Thus, \( \pi \) bond is more reactive than \( \sigma \)
bond.


When the direction of nerve impulse is reversed, the condition is
A. Axo - Axonic synapse
B. Axo - Dendritic synapse
c. Both of the above
D. None of the above


A wire of length L can support a load W. If the wire is broken in to two equal parts then how much load can be suspended by one of those cut wires?
A . Half
B. Same
c. Double
D. One fourth


The comparatively high b.pt of \( \boldsymbol{H} \boldsymbol{F} \) is
due to:
A. high reactivity of fluoring
B. small size of hydrogen atom
C. formation of hydrogen bonds and consequent association
D. high IE of flourine


Ketoenol tautomerism is not observed
in:
This question has multiple correct options
A. phenol
B. glycerol
\( \mathbf{c} \cdot H C N \)
D. benzophenone


Snow blindness is cause due to
A. Ozone hole
B. Nuclear winter
c. Acid rain
D. Green house effect


A respiratory cycle where \( N A D H_{2} \) is
produced is the
A. Calvin cycle.
B. Krebs cycle.
c. EMP pathway
D. HMP shunt


Which of the following does not react with xenon to form compunds?
A \( . O S e F_{5} \)
в. \( O T e F_{5} \)
\( c \cdot F_{2} \)
D. \( N_{2} \)


Consider the following two statements:
1) Kirchoff's junction law follows from
the conservation of charge
2) Kirchoff's loop law follows from the conservation of energy. Which of the following is correct?
A. both 1 and 2 are wrong
B. 1 is correct and 2 is wrong
C. 1 is wrong and 2 is correct
D. both 1 and 2 are correct


Match the columns
i. amount of light entering into eye
a. rodes controlled by
ii. colour sensing cells
b. cones
iii.cells helping in vision in dim light
c. iris
d.
iv.junction of optic nerve and retina \( \quad \) blindspot
\( A \cdot i-a, i i-b, i i i-c, i v-d \)
B. \( i-d, i i-c, i i i-b-i v-a \)
\( \mathbf{C} \cdot \mathbf{i}-\mathrm{c}, \mathrm{i} \mathbf{i}-\mathrm{b}, \mathrm{i} \) ii-a, \( \mathrm{iv}-\mathrm{d} \)
D. i-b,ii-a,iii-c,iv-b


As per Census 2011 , India has \( 2.4 \% \) of
world's land area and is home to
of the total world population.
\( A \). \( 23.1 \% \)
B . 10.5\%
c. \( 17.5 \% \)
D. 12.8\%


The Fermi level in intrinsic semi-
conductors at \( 0 K \) temperature lies:
A. Near the conduction band
B. Near the valence band
C. In the middle of valence and conduction band
D. Inside the conduction band


Find the surface area of the hemisphere
whose radius is \( 7 \mathrm{cm} \)


Earthly particles in an ore are removed from heavier metal ore using
water in:
This question has multiple correct options
A. levigation
B. hydraulic washing
c. leaching
D. gravity separation


In rectangle \( A B C D, \) diagonal \( B D=26 \mathrm{cm} \) and cotangent of angle \( A B D=1.5 . \) Flnd the area and the perimeter of the rectangle ABCD
A. Area = 436 sq. cm and perimeter = \( 11 \sqrt{13} \mathrm{cm} \)
B. Area = 842 sq. cm and perimeter = \( 15 \sqrt{13} \mathrm{cm} \)
c. Area \( =312 \) sq. \( \mathrm{cm} \) and perimeter \( =20 \sqrt{13} \mathrm{cm} \)
D. Area = 231 sq. cm and perimeter = \( 12 \sqrt{13} \mathrm{cm} \)


How many times is the weight of the air filling a room in winter \( \left(7^{0} C\right) \) greater than
weight in summer \( \left(37^{0} C\right) \) ? Assume that
pressure is constant.
A . 1.1
B. 0.90
c. 11.1
D. 9.0


Points are to be recognised on X-Y plane
to draw graph of equation \( 2 x+3 y=12 \)
So fill the boxes given below and
identify points.
\begin{tabular}{|c|c|c|c|c|}
\hline\( x \) & \( -2 . \) & 3 & 6 & \( \square \) \\
\hline\( y \) & 4 & \( \square \) & \( \square \) & 6 \\
\hline\( (x, y) \) & \( \square \) & \( \square \) & \( \square \) & \\
\hline
\end{tabular}


The equilibrium of the reaction
\( N_{2}(g)+3 H_{2}(g) \Leftrightarrow 2 N H_{3}(g) \) will shift
to the product side when
A. Concentration of \( N_{2} \) is increased
B. Concentration of \( N_{2} \) is decreased
c. concentration of \( N H_{3} \) is increased
D. concentration of \( H_{2} \) is decreased


An artificial satellite is revolving round the earth. The radius of its circular orbit is half the orbital radius of moon. The
time taken by this satellite in completing one revolution will be
A. 2 lunar months
B \( \cdot 2^{-2 / 3} \) lunar months
\( \mathrm{c} \cdot 2^{-3 / 2} \) lunar months
D. \( 1 / 2 \) lunar months


Nucleic acids are called acids
mainly because of the presence of
A. \( -C O O H \) group
B. - OH group of sugar unitt
c. \( -O H \) group of the heterocyclic base
D. - OH group of phosphate unitt


Why plastic sulphur is elastic in
nature?


Find the sum of bond order and number
of \( \pi \) bonds in \( B_{2} \) molecule.


Metal oxide can be reduced by
A . \( F e \)
в. \( S n \)
\( c . c \)
D. All of these


Open circulatory system occurs in
A. Octopus
B. Pheretima
c. Periplaneta
D. Rana


What is the time required for the same
amount of water to flow out if the water
level in tank is maintained always at a height of \( 1 m \) from orifice?


Number of moles of \( 1 m^{3} \) gas, at \( \mathrm{STP} \)
are:
A . 44.6
B. 40.6
c. 42.6
D. 48.6


Evaluate the following limits. \( \lim _{x \rightarrow 0}(\cos x+\sin x)^{1 / x} \)


An emulsion is a colloidal solution of:
A . two solids
B. two liquids
c. two gases
D. one solid and liquid


Find the slope of the line passing
through the points \( G(-4,5) \) and \( \boldsymbol{H}(-\mathbf{2}, \mathbf{1}) \)


Which of the following devices is used to detect the presences of a charge on a body?
A. Multimeter
B. Electroscope
c. Angiogram
D. Microscope


\( n s^{1} \) electronic configuration is not
present in:
\( A \cdot A g \)
в. мп
\( c \cdot c r \)
D. cu


Find the values of \( x \) and \( y \) in the following figures
A \( . x=80^{0} ; y=120 \)
В . \( x=50^{0} ; y=30^{0} \)
C . \( x=50^{\circ} ; y=130^{\circ} \)
D . \( x=20^{0} ; y=10^{0} \)


A toroid has a core (non -ferromagnetic) of inner radius \( 25 \mathrm{cm} \) and outer radius
\( 26 \mathrm{cm}, \) around which 3500 turns of a
wire are wound. If the current in the wire
is \( 11 A, \) what is the magnetic field (a) outside the toroid,
(b) inside the core of
the toroid, and
(c) in the empty space surrounded by the toroid.


From the given figure calculate:
¡) \( \angle A D C \)
ii) \( \angle A B C \)
iii) \( \angle B A C \)


The smallest number by which 3600 can be divided to make it a perfect cube is:
\( A \cdot 9 \)
B. 50
\( c .300 \)
D. 450


The term water-pollution can be defined in several ways. Which of the following
statements does not give the correct definition?
A. The addition of undersirable substances to water bodies
B. The removal of dersirable substances from water bodies
c. A change in pressure of the water bodies.
D. A change in temperature of the water bodies


Aluminum hydroxide is used for:
A. fire extinguishers
B. antacid
C . water purification
D. all of the above


Green house effect means
A. Increase in the temperature of earth due to high
concentration of \( \mathrm{NO}_{2} \)
B. Increase in the temperature of earth due to high concentration of \( \mathrm{SO}_{2} \)
C. Increase in the temperature of earth due to high concentration of CO
D. Increase in the temperature of earth due to high concentration of \( \mathrm{CO}_{2} \)


The process of removing dissolved
impurities from a colloidal system by means of diffusion through suitable
membrane under the influence of an
electric field is called:
A . electro-osmosis
B. electrodialysis
c. electrophoresis
D. peptization


The liquid or solid on the surface of which the molecule of the substance
are adsorbed is called adsorbate.
If this is true enter 1 , if false enter 0 .


The electric current in a circular coil of
two turns produced a magnetic
induction of \( 0.2 \mathrm{T} \) at its centre. The coil
is unwound and then rewound into a
circular coil of four turns. If same
current flows in the coil, the magnetic induction at the centre of the coil now
is:
A. \( 0.2 T \)
в. \( 0.4 \mathrm{T} \)
\( c .0 .65 \)
D. 0.8 T


Aspirin is known as:
A. Acetyl salicylic acid
B. Phenyl salicylate
C . Acetyl salicylate
D. Methyl salicylic acid


Which one of the following compounds has the electron-pair geometry as di trigonal bipyramidal with three equatorial positions occupied by lone pairs of electrons?
\( \mathbf{A} \cdot\left[A l C l_{3}\right] \)
в. \( X e F_{2} \)
\( \mathbf{c} \cdot\left[P t\left(N H_{3}\right)_{2} C l_{2}\right] \)
D. \( C H_{3}-M g-B r \)


Find the sum of the following APs:
\( 0.6,1.7,2.8, \dots \dots \) to 100 terms
A. 5475
B. 5505
\( c \cdot 6589 \)
D. 3844


A survey conducted on 20 household in a locality by a group of statement resulted in the following frequency table for the number of family Members in a house hold.
Family size \( \begin{array}{ccc}1- & 3- & 5 \\ 3 & 5 & 7\end{array} \)
Number of families
Find the mode of the data.


Find the amount and the compound
interest on Rs.120000 at 8\% per annum
for 1 year, compounded half-yearly.


Which of the following will give \( S_{N} \)
reaction?
A. \( R-B r \)
в. \( R-N_{3} \)
c \( \cdot R-O_{H_{2}}^{\oplus} \)
D. All


The twinkling of stars is due to atmospheric
A. Refraction of light
B. Reflection of light
c. scattering of light
D. Dispersion of light


1.0 g of magnesium is burnt with 0.56 g \( O_{2} \) in a closed vessel. Which reactant is
left in excess and how much ? (At.wt. \( \mathrm{Mg}=24 ; 0=16) \)
A. \( \mathrm{Mg}, 0.16 \mathrm{g} \)
в. \( O_{2}, 0.16 \mathrm{g} \)
c. \( \mathrm{Mg}, 0.44 \mathrm{g} \)
D. \( O_{2}, 0.28 \mathrm{g} \)


Match column I with column II and
select the correct answer using the codes given below:
Column I \( \quad \) Column
(A) \( \frac{14}{6} C \) and \( _{6}^{13} C \)
(p) Different
number of neutrons
(B) 40
20 \( \mathrm{Ca} \) and \( _{18}^{40} \boldsymbol{A r} \)
(q) Different
number of protons and neutrons
(C) \( \boldsymbol{K}(\mathbf{1} \mathbf{9}) \)
(r) Non-metal
(D) Chlorine (17)
(s) Metal
\( A \cdot A-(p) ; B-(q) ; C-(r) ; D-(s) \)
B. \( A-(q) ; B-(p) ; C-(s) ; D-(r) \)
c. \( A-(p) ; B-(q) ; C-(s) ; D-(r) \)
\( D \cdot A-(p) ; B-(s) ; C-(q) ; D-(r) \)


Silver is removed electrolytically from
\( 200 m L \) of a \( 0.1 N \) solution of \( A g N O_{3} \)
by a current of 0.1 A. How long will it take to remove half of the silver from the solution?
A . \( 0.1 s \)
B. \( 100 s \)
\( \mathbf{c} .965 s \)
D. \( 9650 s \)


Which of the following is least volatile?
\( \mathbf{A} \cdot H F \)
в. \( H C l \)
\( \mathbf{c} \cdot H B r \)
D. \( H I \)


A neuron transmits information
through
A. Electrical signals
B. Chemical signals
c. Both A and B
D. None of the above


Concentrated \( H_{2} S O_{4} \) cannot be used to
prepare \( H B r \) from \( N a B r \) because it
A. reacts slowly with NaBr
B. oxidises HBr
c. reduces HBr
D. disproportionates HBr


Which of the following is the most basic?
\( \mathbf{A} \cdot C e(O H)_{3} \)
в. \( L u(O H)_{3} \)
\( \mathbf{c} \cdot Y b(O H)_{3} \)
D. \( A l(O H)_{3} \)


\( A \) and \( B \) are two events on a sample
space \( S \) such that \( P(A)=0.8, P(B)= \)
\( \mathbf{0 . 6} \) and \( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B})=\mathbf{0 . 9} \) find \( (\boldsymbol{A} \cap \boldsymbol{B}) \)
A . 0.3
B. 0.4
\( c \cdot 0.5 \)
D. 0.6


The least vlue of the function \( f(x)= \) \( \boldsymbol{a x}+\frac{\boldsymbol{b}}{\boldsymbol{x}}(\boldsymbol{a}>\mathbf{0}, \boldsymbol{b}>\mathbf{0}, \boldsymbol{x}>\mathbf{0}) \) is


The commonly used pain reliever, aspirin, has the molecular formula
\( C_{9} H_{8} O_{4} . \) If a sample of aspirin contains
\( 0.968 g \) of carbon, what is the mass of hydrogen in the sample?
A \( .0 .717 g \)
в. \( 0.0717 g \)
c. \( 8.000 g \)
D. \( 0.645 g \)


An object moving with a speed of 6.25 \( \mathrm{m} / \mathrm{s}, \) is decelerated at a rate given by \( \frac{d v}{d t}=-2.5 \sqrt{v} \) where \( v \) is the instantaneous speed. The time taken by the object, to come to rest, would be then
\( \mathbf{A} \cdot 2 s \)
B . \( 4 s \)
c. \( 8 s \)
D. \( 1 s \)


The moles of oxygen and carbondioxide involved in glycolysis are respectively:
A .4,6
в. 4,4
c. 6,6
D. 8,6


Write the differences between convex
and concave lens.


Solve:
\( \tan \left(\cos ^{-1} \frac{1}{x}\right)=\sin \left(\cot ^{-1} \frac{1}{x}\right) \)


Answer the following questions for Zn
atom:

How many electrons have \( l-m=1 ? \)


A wheel has moment of inertia \( 5 x \)
\( 10^{-3} k g m^{2} \) and is making 20 rev/sec.
The torque needed to stop it in 10 sec is
\[
\mathbf{x} \mathbf{1 0}^{-\mathbf{2}} \mathbf{N}-\boldsymbol{m}:
\]
A . \( 2 \pi \)
в. \( 2.5 \pi \)
c. \( 4 \pi \)
D. \( 4.5 \pi \)


Light of two different frequencies whose photos have energies leV and 2.5eV respectively illuminate a metallic surface whose work function is \( 0.5 e v \)
successively. Ratio of maximum speeds of emissions will be
\( A \cdot 1: 4 \)
B. 1:
\( c \cdot 1: \)
D. 1:


Match the Following:


If the frequency of a transverse wave is \( 10 H z . \) And the distance between the
two consecutive wave crests is \( 2 m \)
Calculate the wave speed.


It is chemisorption if chemical forces exist between adsorbate and adsorbent.
A. True
B. False


Which quantity of a two particles system depend only on the separation between the two particles?
A. Kinetic energy
B. Total mechanical energy
c. Potential energy
D. Both (A) and (B)


A wheel is rotating at 1800 rpm about its own axis. When the power is switched oft it comes to rest in 2 min.
Then, the angular retardation in rad \( s^{-1} \)
is
\( \mathbf{A} \cdot 2 \pi \)
в. \( \pi \)
c. \( \pi / 2 \)
D . \( \pi / 4 \)
E . \( \pi / 6 \)


The compounds whose structures are
shown below would have:
A. different melting points
B. the same melting point
C . equal but opposite optical rotations
D. none of these


The non-protein component in enzymes, which is necessary for its biological activity, is called:
A . nucleic acid
B. lipid
c. phosphoric acid
D. coenzyme


Name the following compounds.
(i)
(ii)
(iii) \( \mathrm{H}_{3} \mathrm{C}-\mathrm{C}=\mathrm{CH} \)
(iv)
(v) \( \mathrm{H}_{6} \mathrm{C}-\mathrm{C} \equiv \mathrm{C}-\mathrm{CH} \)


State whether the given statement is true or false:

Copper metal reduces \( F e^{2+} \) in an acid
medium.


Consider the following statements and arrange in the order of true/false as
given in the codes.
\( S_{1}: \) Change in state function between
two states is a definite quantity and
does not depend on path.
\( S_{2}: \) Intensive properties cannot be
algebraically added or subtracted.
\( S_{3}: \) Ratio of two extensive properties
result in a parameter that depends on the amount of substance.
\( S_{4}: \) Molar heat capacity is a state
function.
The correct order to true/false of the
above statements is:
\( A \). FT FT
B. FF FT
c. TT FT
D. TTTF


Compared to the first ionization potential, the value of second ionization potential of an element is:
A. Negligible
B. Smaller
c. Greater
D. Double


A solution containing \( 25.6 g m \) of
sulphur dissolved in \( 1000 g \) of
naphthalene gave a freezing point lowering of 0.680 , then molecular formula of sulphur is:
\( A \cdot S_{2} \)
в. \( S_{4} \)
c. \( S_{6} \)
D. \( S_{8} \)


A dip needle in a plane perpendicular to magnetic meridian will be :
A. Vertical
B. Horizontal
C. At an angle of \( 4^{\circ} \) to the horizontal
D. At an angle of dip to the horizontal


\( \underbrace{\frac{2}{k}}{\frac{k}{k}} \)


Which one of the following is not a
correct match?
A. Teflon- Tetrafluoroethylene
B. Plexi glass - Methyl methacrylate
c. orlon - Glycerol, phthalic anhydride
D. Buna-S- - Styrene, 1-3 butadiene


In the following reaction, the correct
statements are:
\( M g+2 H^{+} \rightarrow M g^{2+}+H_{2} \)
1. \( M g \) is a reducing agent, \( H^{+} \) is an oxidising agent
2. \( M g \) is oxidising agent, \( H^{+} \) is a reducing agent.
A. only 1
B. only 2
c. both
D. none


The tenth term of the series 9,8,7,6
\( \ldots . \) is


Find the values of the following determinants where \( i=\sqrt{-1} \)
\( (i)\left|\begin{array}{cc}2 i & -3 i \\ i^{3} & -2 i^{5}\end{array}\right| \)
\( (i i)\left|\begin{array}{cc}\mathbf{1}+\mathbf{3} i & \boldsymbol{i}-\mathbf{2} \\ \boldsymbol{i}+\mathbf{2} & \mathbf{1}-\mathbf{3} i\end{array}\right| \)


The high reactivity and low volatility of white phosphorus is due to :
A. Tetrahedrally arranged \( P_{4} \) units
B. bonds angle of \( 60^{\circ} \)
c. weak van der Waal's force of attraction
D. increased steric (strain) factor


A mass \( m_{1} \) moves with a grate velocity.
It strikes another mass \( m_{2} \) at rest in
head-on collision. It comes back along
its path with low speed after collision. Then :
\( \mathbf{A} \cdot m_{1}>m_{2} \)
В. \( m_{1}<m_{2} \)
\( \mathbf{c} \cdot m_{1}=m_{2} \)
D. there is no relation between \( m_{1} \) and \( m_{2} \)


A mass of \( 5 \mathrm{kg} \) is suspended on a spring of stiffness \( 4000 \mathrm{N} / \mathrm{m} \). The system is fitted with a damper with a damping ratio of 0.2. The mass is pulled down 50 \( \mathrm{mm} \) and released. Calculate the
displacement after 0.3 sec:
\( \mathbf{A} \cdot 4.07 \mathrm{mm} \)
в. \( 4.7 \mathrm{mm} \)
\( c .7 .4 \mathrm{mm} \)
D. 7.04 mm


Match the List I with the List II.


Which of the following is not an oligosaccharide?
A. Xylose
B. Maltose
c. Raffinose
D. stachyrose


Give scientific name of Cabagge. Name the family to which it belongs.


The statement form \( (\boldsymbol{p} \Leftrightarrow \boldsymbol{r}) \Rightarrow(\boldsymbol{q} \Leftrightarrow \boldsymbol{r}) \)
is equivalent to
\( \mathbf{A} \cdot[(\sim p \vee r) \wedge(p \vee \sim r)] \vee \sim[(\sim q \vee r) \wedge(q \vee \sim r)] \)
\( \mathbf{B} \cdot \sim[(\sim p \vee r) \wedge(p \vee \sim r)] \wedge[(\sim q \vee r) \vee(q \vee \sim r)] \)
\( \mathbf{c} \cdot[(\sim p \vee r) \wedge(\sim p \vee \sim r)] \wedge[(\sim q \vee r) \wedge(q \vee \sim r)] \)
\( \mathbf{D} \cdot \sim[(\sim p \vee r) \wedge(p \vee \sim r)] \wedge[(\sim q \vee r) \wedge(q \vee \sim r)] \)


Borax is used as cleansing agent because on dissolving in water it gives
A. alkaline solution
B. acidic solution
c. bleaching solution
D. colloidal solution


The following is the frequency
distribution of time (in minutes) a
worker takes to complete the work. Find mean time taken by a worker to
complete the work by using 'Assumed Mean Method'.
\begin{tabular}{ll}
Time (in minutes) & No. of Workers \\
\( 20-24 \) & 2 \\
\( 25-29 \) & 10 \\
\( 30-34 \) & 20 \\
\( 35-39 \) & 28 \\
\( 40-44 \) & 25 \\
\( 45-49 \) & 15 \\
\hline
\end{tabular}


n the figure, \( \angle P Q S=\angle P R T \) and
\( \mathrm{QS}=\mathrm{TR} . \) then \( \Delta P Q S \cong \Delta P R T \mathrm{by} \)
congruence postulate
\( A \cdot \operatorname{sas} \)
B. sss
\( c . \) RHS
D. AAS


Find the sum of the following infinite
G.P.:
\( \frac{1}{3}, \frac{-2}{9}, \frac{4}{27}, \frac{-8}{81}, \dots \)
A \( \cdot \frac{1}{2} \)
B.
\( c \cdot \frac{1}{3} \)
D.


Why welders generally wear mask during welding?


Atomic weight of weight of an element is 30 its equivalent wt. is 10 The valency of element will be-
\( A \)
B. 2
\( c \cdot 3 \)
D. 4


Let \( R \) be a reflexive relation on a finite
set \( A \) having \( n \) elements, and let there
be \( m \) ordered pairs in \( R, \) then:
A \( . m \geq n \)
в. \( m \leq n \)
c. \( m=n \)
D. \( m<n \)


Which of the following does has no \( S- \)
\( \boldsymbol{S} \) bond?
A \( \cdot H_{2} S_{2} O_{4} \)
в. \( H_{2} S_{2} O_{5} \)
\( \mathbf{c} \cdot H_{2} S_{2} O_{6} \)
D. \( H_{2} S_{2} O_{7} \)


Match the following


Which statement is correct for alkaline
earth
metals?
A. They are diatomic and form ions of the type \( M^{2} \)
B. They are highly electronegative elements
c. They are monoatomic in vapour state and form
ions of the type \( M^{2+} \)
D. They are diatomic and form ions of the type \( M^{2+} \)


Formation of periderm is the function of
A. vascular cambium
B. Cork cambium
c. Both vascular and cork cambium
D. None


The rank of the word \( N U M B E R \)
obtained, if the letters of the word
\( N U M B E R \) are written in all possible
orders and these words are written out
as in a dictionary is
A .468
в. 469
c. 470
D. 471


In the reaction, \( A g_{2} O+H_{2} O_{2} \rightarrow \)
\( 2 A g+H_{2} O+O_{2}, \) the \( H_{2} O_{2} \) acts as:
A. oxidising agent
B. bleaching agent
c. acid
D. reducing agent


In Aulosira, Tolypothrix and Nostoc, are the sites for nitrogen fixation
A. Vesicles
B. Arbuscles
c. Akinetes
D. Heterocysts


Which of the following combinations of combining atoms of elements gives rise to the strongest ionic bond?
A. Sodium and iodine
B. Sodium and chlorine
c. Sodium and bromine
D. Sodium and fluorine


In an electromagnetic wave, the direction of the magnetic induction \( \vec{B} \)
is
A. parallel to the electric field \( \vec{E} \)
B. perpendicular to the electric field \( \vec{E} \)
C . antiparallel to the pointing vector \( \vec{S} \vec{S} \)
D. random


In an ideal parallel LC circuit, the capacitor is charged by connecting it to a D.C. source which is then
disconnected. The current in the circuit
A. Becomes zero instantaneously
B. Grows monotonically
c. Decays monotonically
D. oscillates instantaneously


The solution of \( \int_{\sqrt{2}}^{x} \frac{d t}{\sqrt{t^{2}-1}}=\frac{\pi}{12} \) is
A .
B. 2
\( c \cdot 3 \)
D. 4
E . 5


To stop a heavy vehicle moving with high velocity, a device working on Pascal's law is used, That device is
A. hydraulic lift
B. hydraulic brake
c. hydraulic jack
D. none


What is the percent \( \boldsymbol{X} \) by mass for
compound \( X Y_{2} \) if compound \( X Y \) is 74
\( \% X \) by mass?
A . \( 25 \% \) \%
B . \( 40 \% \)
c. \( 60 \% \)
D. 75\%


Solve \( : \tan ^{-1}\left(\frac{x-1}{x-2}\right)+ \)
\( \tan ^{-1}\left(\frac{x+1}{x+2}\right)=\frac{\pi}{4} \)


\( \boldsymbol{y}=\boldsymbol{x}^{3}-\boldsymbol{3} \boldsymbol{x}+\boldsymbol{2} \)
Find \( \frac{d y}{d x} \) if the given function is
continuous.


The direction ratios of a vector are
\( 2,-3,4 . \) Find its direction cosines


If \( \boldsymbol{y}= \)
\( \tan ^{-1}\left(\cot \left(\frac{\pi}{2}-x\right)\right) \) then \( \frac{d y}{d x}= \)
\( A \)
B. - -
\( c \cdot 0 \)
D.


Assertion
Emphysema is a chronic disorder in which alveolar walls are damaged.
Reason

Emphysema is closely related to cigarette smoking.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The highest magnetic moment is shown by the transition metal ion with which of
the following outermost electronic configuration?
\( A \cdot 3 d^{2} \)
в. \( 3 d^{5} \)
\( c \cdot 3 d^{7} \)
D. \( 3 d^{9} \)


A wire carrying current of \( 10 A \) supports
a wire of \( 10 \mathrm{cm} \) long and weighing \( 1 \mathrm{g} \)
vertically above it at a distance of \( 1 \mathrm{cm} \)
The current that is passing through the wire is :
\( \mathbf{A} \cdot 490 A \)
B . \( 205 A \)
\( c \cdot 408 A \)
D. \( 316 A \)


A physical quantity \( Q \) is found to depend on observables \( x, y \) and \( z \) obeying relation \( Q=\frac{x^{2 / 5} z^{3}}{y} . \) The
percentage error in the measurements of \( x, y \) and \( z \) are \( 1 \%, 2 \% \) and \( 4 \% \)
respectively. What is percentage error in the quantity \( Q \) will be :
\( A \cdot 5 \% \)
в. \( 4.5 \% \)
c. \( 11 \% \)
D. \( 7.75 \% \)


The term independent of \( x \) in the
binomial expansion of \( \left(1-\frac{1}{x}+3 x^{5}\right)\left(2 x^{2}-\frac{1}{x}\right)^{8} \)
\( \mathbf{A} \cdot-496 \)
B . -400
c. 496
D. 400


Among \( N H_{3}, P H_{3}, A s H_{3} \) and \( S b H_{3} \)
which one is a strongest reducing agent?
A \( \cdot N H_{3} \)
в. \( P H_{3} \)
c. \( A s H_{3} \)
D. \( S b H_{3} \)


Given, \( f(x)= \) sum of all natural
numbers which can divide \( x \) completely Find \( : \$ \$ f(6) \$ \$ \)


An ideal gaseous mixture of ethane and ethene occupy \( 28 L \) as STP. The mixture
required \( 128 g O_{2} \) combustion, mole fraction of ethene in the mixture is:
A . 0.4
B. 0.5
c. 0.6
D. 0.8


A current carrying small loop behaves like a small magnet. If \( A \) be its area and
\( M \) its magnetic moment, the current in the loop will be
A. \( M / A \)
в. \( A / M \)
\( c . M A \)
D. \( A m^{2} \)


What is rotatory motion?


Explain the term EMF


If \( 4 x^{4}-12 x^{3}+x^{2}+3 a x-b \) is divided
by \( x^{2}-1 \) then \( a=-1 \)
\( b= \)
\( \mathbf{A} \cdot 5,4 \)
в. 4,9
\( c \cdot 4,5 \)
D. 1,-1


Lateral inversion is generally seen in
case of:
A. convex mirror
B. concave mirror
c. plane mirror
D. all of the above


Assertion
In trigonal bipyramidal structure two axial bonds are longer than the
equitorial bonds.
Reason
Axial bonds suffer more repulsion as
compared to equitorial bonds.
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


Liquids can flow. Why? We can keep a gas in an open container.
Do you agree? Given reason.


The ratio of the concentration of electrons to that of holes in a semiconductor is \( \frac{7}{4}, \) then what is the ratio of their drift velocities:
A \( \cdot \frac{5}{8} \)
B. \( \frac{4}{5} \)
\( c \cdot \frac{5}{4} \)
\( D \cdot \frac{4}{7} \)


If the first term in a geometric sequence is \( 3, \) and if the third term is
\( 48, \) find the \( 11^{t h} \) term.
A . 228
в. 528
c. 110592
D. 3145728
E . 12582912


A straight line drawn through (1,2)
intersects \( x+y=4 \) at a distance \( \frac{\sqrt{6}}{3} \)
from \( (1,2) . \) The angle made by the line with the positive direction of \( x \) -axis
is \( \alpha . \) Find the greater of the two values
of \( \boldsymbol{\alpha} \)
A . \( 105^{\circ} \)
B \( \cdot 75^{\circ} \)
\( c \cdot 60^{0} \)
D. \( 15^{\circ} \)


Which of the following pollutants cannot be degraded by natural process?
A . DDT
B. Nuclear Waste
c. Heavy Metalss
D. All of the above


In an experiment, it is found that \( 2.0769 g \) of pure \( X \) produces \( 3.6769 g \) of
pure \( X_{2} O_{5} . \) The number of moles of \( X \)
is:
A . 0.04
B. 0.06
c. 0.40
D. 0.02


A particle of mass m strikes a horizontal smooth floor with a velocity u
making an angle \( \theta \) with the floor and rebounds with velocity v making an angle \( \phi \) with the floor. The coefficient of
restitution between the particle and the floor is e. Then
A. the impluse delivered by the floor to the body is \( m u(1-e) \sin \theta \)
B. \( \tan \phi=\operatorname{etan} \theta \)
c. \( v=u \sqrt{1-\left(1+e^{2}\right) \sin ^{2} \theta} \)
D. the ratio of the final kinetic energy to the initial kinetic energy is \( \cos ^{2} \theta+\operatorname{esin}^{2} \theta \)


In Solar cooker:
A. Electricity is used to cook food
B. Chemical energy is converted to electrical energy
C. Radiation from the sun is used to cook food
D. Heat energy is converted light energy


Let \( X \) be the solution set of the equation \( \boldsymbol{A}^{x}=\boldsymbol{I}, \) where \( \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{0} & \mathbf{1} & \mathbf{- 1} \\ \mathbf{4} & \mathbf{- 3} & \mathbf{4} \\ \mathbf{3} & \mathbf{- 3} & \mathbf{4}\end{array}\right] \) and
is the corresponding unit matrix and
\( \boldsymbol{x} \subseteq \boldsymbol{N}, \) then the minimum value of
\( \sum\left(\cos ^{x} \theta+\sin ^{x} \theta\right), \theta \in R \)


How many of the structures (A to D) in
the following diagram are diploid?
\( \mathbf{A} \)
\( B \)
\( c \)
\( D \)


If \( a=2 \overline{3}+2 \overline{3}, \) then
A. \( a^{3}-6 a-6=0 \)
В . \( a^{3}-6 a+6=0 \)
c. \( a^{3}+6 a-6=0 \)
D. \( a^{3}+6 a+6=0 \)


\( G_{2} \) phase occurs between
\( A \cdot G_{1} \) and \( S \)
B. \( M \) and \( s \)
c. s and M
D. \( G_{1} \) and \( M \)


Arrange following oxides in increasing
acidic nature.
\( \boldsymbol{L} \boldsymbol{i}_{2} \boldsymbol{O}, \boldsymbol{B} \boldsymbol{e} \boldsymbol{O}, \boldsymbol{B}_{2} \boldsymbol{O}_{3} \)
A. \( L i_{2} O<B e O<B_{2} O_{3} \)
в. \( B e O<L i_{2} O<B_{2} O_{3} \)
c. \( L i_{2} O<B_{2} O_{3}<B e O \)
D. None of these


At \( 298 K, \) the equilibrium constant of reaction.
\( Z n^{+2}+4 N H_{3} \rightleftharpoons\left[Z n\left(N H_{3}\right)_{4}\right]^{+2} \) is
\( \mathbf{1 0}^{\mathbf{9}} \)
If \( \boldsymbol{E}_{\left[Z n\left(N H_{3}\right)_{4}\right]^{+2} / Z n+4 N H_{3}}^{o}=-1.03 V . \) The
value \( \boldsymbol{E}_{\boldsymbol{Z n} / \boldsymbol{Z} \boldsymbol{n}^{+2}} \) will be:
A. \( 0.7645 v \)
B . -1.1
\( c .+1.1 v \)
D. none of these


Show that \( \left(\frac{1}{a+} \frac{1}{b+} \frac{1}{c+} \dots\right)\left(c+\frac{1}{b+} \frac{1}{a+} \frac{1}{c_{1}} \dots .\right)= \)
\( \frac{1+b c}{1+a b} \)


Using integration find the area of the triangular region whose sides have the
equations \( \boldsymbol{y}=\mathbf{2} \boldsymbol{x}+\mathbf{1}, \boldsymbol{y}=\mathbf{3} \boldsymbol{x}+\mathbf{1} \) and
\( \boldsymbol{x}=\mathbf{4} \)


\( \operatorname{Given} \frac{x-x \tan ^{2} 30^{\circ}}{1+\tan ^{2} 30^{\circ}}=\sin ^{2} 30^{\circ}+ \)
\( 4 \cot ^{2} 45^{\circ}-\sec ^{2} 45^{\circ} . \) Then the value of
\( \boldsymbol{x} \)
\( A \cdot \frac{3}{2} \)
в. \( \frac{5}{2} \)
\( c \cdot \frac{9}{2} \)
D. none of these


Write the pair of vertically opposite
angles.


The blood circulation in human heart
is called as
A. Triple circulation
B. Double circulation
c. Quadruple circulation
D. single circulation


Arrange the following hydrocarbons in the increasing order of volume of oxygen required for complete
combustion per mole under the same
conditions.
(a) Ethane
(b) Propyne
(c) Ethyne
(d) Propene
(e) Propane
(f) Ethene
A. \( c<f<a<b<d<e \)
в. \( e<d<b<a<f<c \)
c. \( c<b<f<d<a<e \)
D. \( e<b<d<f<a<c \)


In the given figure, \( A B C D \) is a
rhombus in which \( \angle B C D=110^{\circ}, \) find
\( (x+y) \)


What are the possible products?
\[
\widehat{\mathrm{NH}_{2}} \stackrel{\mathrm{HNO}_{2}}{\longrightarrow}
\]


State the whether given statement is
true or false

If the \( 9^{t h} \) term of an \( A . P . \) is zero, then
show that the \( 29^{t h} \) term is twice the
\( 19^{t h} \) term
A . True
B. False


A fiat circular coil, carrying a current,
has a magnetic moment \( \mu \)
This question has multiple correct options
A. \( \mu \) has only magnitude; it does not have direction
B. the direction of \( \mu \) is along the normal to the plane of the coil
C. the direction of \( \mu \) depends on the direction of the current flow
D. the direction of \( \mu \) does not change if the current in the coil is reversed


Say true or false. The distance of the point (5,3) from the \( X \) -axis is 5 units.
A . True
B. False


Increase in nuclear charge of an atom decreases the tendency of the atom to loose electrons.
A. True
B. False


A resistance of \( 50 \Omega \) is registered when
two electrodes are suspended into a beaker containing a dilute solution of a
strong electrolyte such that exactly half of the them are submerged into solution. If the solution is diluted by
adding pure water (negligible conductivity) so as to just completely submerge the electrodes, the new resistance offered by the solution would
be:
A . \( 50 \Omega \)
B. \( 100 \Omega \)
\( c .25 \Omega \)
D. 200 \( \Omega \)


Out of the following, whose velocity is equal to that of light?
A. of \( \beta \) rays
B. of sound waves
c. of ultrasonic waves
D. none of these


Milk is colloid in which:
A. liquid is dispersed in liquid
B. gas is dispersed in water
C. sugar is dispersed in water
D. solid is dispersed in liquid


Coal is a fossil fuel and it cannot be
prepared in a laboratory or industry because the formation of coal:
a. is very slow process.
b. needs very low pressure and low
temperature.
c. needs very high pressure and high
temperature.
d. causes air pollution.
Select the correct alternative.
\( A \cdot a, c \) and \( d \)
B. b and d
\( c \cdot c \) and \( a \)
D. dand c


Gas cap over crude oil is formed by:
A. methane
B. natural gas
c. butane
D. producergas


The domain of function \( y=\log _{3}(5+ \)
\( \left.4 x-x^{2}\right) \) is
A \( .(0,2] \)
B . \( (-\infty,-1) \cup(5, \infty) \)
c. (0,9]
D. (-1,5)


If the function \( f(x) \) satisfies \( \lim _{x \rightarrow 1} \frac{f(x)-2}{x^{2}-1}=\pi, \) then \( \lim _{x \rightarrow 1} f(x)= \)
A . 2
B. 3
c. 1
D.


\( \lim _{x \rightarrow 0} \frac{\sin x-\frac{x}{6}}{6 x}=? \)
A \( \cdot \frac{5}{36} \)
B. \( \frac{2}{360} \)
c. \( \frac{7}{360} \)
D. \( \frac{11}{360} \)


In a first order reaction with time the
concentration of the reactant
decreases:
A. Linearly
B. Exponentially
c. No change
D. None of these


Prove that \( \frac{C_{1}}{C_{0}}+\frac{2 C_{2}}{C_{1}}+\frac{3 C_{3}}{C_{2}}+\ldots+\frac{n \cdot C_{n}}{C_{n-1}}= \)
\( \frac{n(n+1)}{2} \)


If \( \operatorname{Arg}(z+i)-\operatorname{Arg}(z-i)=\frac{\pi}{2}, \) then \( z \)
lies on a circle.
If statement is True, enter 1 , else enter 0


Construct a frequency distribution
table for the data on weights \( (\text { in } k g \) ) of
20 students of a class using intervals \( 30-35,35-40 \) and so on
\( \mathbf{3 9}, \mathbf{3 8}, \mathbf{4 7}, \mathbf{4 4}, \mathbf{4 2}, \mathbf{6 5}, \mathbf{4 9}, \mathbf{5 5}, \mathbf{4 9}, \mathbf{3 6}, \mathbf{3 4}, \mathbf{4} \)
Also, draw histrogram for the above data


Statements:
(i) All rats are cats.
(ii) All cats are dogs.
Conclusions:
(i) All rats are dogs.
(ii) Some cats are rats.
A. Only conclusion I is true
B. Only conclusion Il is true
c. Both conclusion I and II are true
D. Neither conclusionl nor conclusion II is true


geometric interpretation. namely, a function \( f \) defined on an interval lis
continuous on I if its graph has no 'holes' or 'jumps'.f is said to have a removable discontinuity at \( c \) if \( f(x) \) has
a limit at \( c \) but \( \lim \lim _{x \rightarrow c} f(x) \neq f(c) \)
If \( \lim _{x \rightarrow c+} f(x) \) and \( \lim _{x \rightarrow c-} f(x) \) exist
but are not equal then \( c \) is called jump discontinuity.
If \( \lim _{x \rightarrow c+} f(x) \) and \( \lim _{x \rightarrow c-} f(x) \) fail to
exist then c is called infinite
discontinuity.
\( \operatorname{Let} g(x)=\left\{\begin{array}{ll}x^{2}+5 & x<2 \\ 10 & x=2 \text { then } x=2 \\ 1+x^{3} & x>2\end{array}\right. \)
A. a point of continuity
B. is a removable discontinuity
C. is a jump discontinuity
D. is.an infinite discontinuity


Which of the following enzymes are not proteinaceous in nature?
A. Kinetase
B. Ribozyme
c. carboxylase
D. Catalase


A freshly formed precipitate of \( S n O_{2} \) is
peptized by a small amount of NaOH. These colloidal particles may be represented as :
\( \mathbf{A} \cdot\left[S n O_{2}\right] S n O_{3}^{2-} ; 2 N a^{\oplus} \)
B . \( \left[S n O_{2}\right] S n^{4+} ; O^{2-} \)
c. \( \left[S n O_{2}\right] N a^{\oplus} ; O H^{\ominus} \)
D \( \cdot\left[\operatorname{Sn} O_{2}\right] S n^{4+} ; O H^{\oplus} \)


The magnetic moment of \( M^{x+} \) (atomic number \( =25 \) ) is \( \sqrt{15} . \) Then, the
oxidation number \( x \) of \( M \) is:
A . 4
B. 3
\( c \cdot 2 \)
D. none of these


A ball of mass \( 50 \mathrm{g} \) is thrown upwards. Its rises to a maximum height of \( 100 \mathrm{m} \) At what height its kinetic energy will be
reduced to \( 70 \% \) :
A. 30 m
B. \( 40 \mathrm{m} \)
\( c . \) 60m
D. 70m


An ideal gas \( (\gamma=1.5) \) is expanded
adiabatically. How many times has the gas to be expanded to reduce the root mean square velocity of the molecules
2.0 times?
A. 4 times
B. 16 times
\( c .8 \) times
D. 2 times


If \( ^{49} \boldsymbol{C}_{3 r-2}=^{49} \boldsymbol{C}_{2 r+1} \) find \( ^{\prime} \boldsymbol{r}^{\prime} \)


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


The color of \( C o C l_{3} .5 N H_{3} . H_{2} O \) is:
A . red
B. orange
c. orange-yellow
D. pink


The buckling of a beam is found to be
more if
A. The breadth of the beam is large
B. The beam material has large value of Young's modulus
c. The length of the beam is small
D. The depth of the beam is small


The pressure on a swimmer \( 20 \mathrm{m} \) below the surface of water at sea level is
A. 1.0 atm
B. 2.0 atm
\( c .2 .5 \mathrm{atm} \)
D. 3.0 atm


A magnifying glass has \( f=12 \) cm Where shall an object be placed to produce maximum angular magnification? Least distance of clear vision \( =25 \mathrm{cm} \)
A. \( 7.1 \mathrm{cm} \)
B. \( 6.8 \mathrm{cm} \)
\( c \cdot 8.4 \mathrm{cm} \)
D. 8.1 \( \mathrm{cm} \)


The maximum possible number of hydrogen bonds, a water molecule can form is?
A .4
B. 3
\( c \cdot 2 \)
D.


Solve \( \frac{\sin \theta+\cos \theta}{\sin \theta-\cos \theta}+\frac{\sin \theta-\cos \theta}{\sin \theta+\cos \theta}= \)
\( \frac{2 \sec ^{2} \theta}{\tan ^{2} \theta-1} \)


Two homogeneous spheres \( A \) and \( B \) masses \( \mathrm{m} \) and \( 2 \mathrm{m} \) having radii \( 2 \mathrm{a} \) and a respectively are placed in touch. The distance of centre of mass from first
sphere is:
\( A \)
B. 2a
c. 3a
D. None of these


Obtain expressions for the center of mass of a system consisting of
(A) two particles
(B) a large number of particles.


Which of the following has lowest oxidising power?
A. Halous acid
B. Halic acid
c. Hypohalous acid
D. All are same


Among the following liquids, specific
heat is minimum for
A. acetone
B. water
c. bromine (liquid)
D. ammonia (liquid)


The following real numbers have decimal expansions as given below. In each case, decide whether they are
rational or not. If they are rational and of the from \( \frac{p}{q}, \) what can you say about the prime factors of \( q ? \)
¡) 43.123456789


Arrangement of sepals and petals with respect to each other in flower bud is
A. Aestivation
B. Phyllotaxy
c. Vernation
D. Venation


In the reaction of benzene with an
electrophile \( E^{+}, \) the structure of the
intermediate \( \sigma \) -complex can be
represented as:
\( A \)
в.
\( c \)
D.


In an election between two candidates,
the candidate who gets \( 30 \% \) of the votes polled is defeated by 15000 votes.What is the number of votes polled for the winning candidate?
A . 37500
B. 30000
c. 26250
D. 11250


If an electron is moving with velocity \( \bar{v} \) produces a magnetic field \( \bar{B} \), then
A. the direction of field \( \bar{B} \) will be same as the direction of
velocity \( \bar{v} \)
B. the direction of field \( \bar{B} \) will be opposite as the direction of velocity \( \bar{v} \)
C. the direction of field \( \bar{B} \) will be perpendicular as the direction of velocity \( \bar{v} \)
D. the direction of field \( \bar{B} \) does not depend upon the direction of velocity \( \bar{v} \)


Sedum is a long day plant. Its critical duration of light is 13 hours Under which of the following conditions would it flower?
[Key: \( \square \) = Period of light \( \quad \) Period of darkness
\( A \cdot C \)
в. \( \cap \)
\( c \cdot C \)


Ramu got injured while playing Kabaddi. His blood clotted within
6 minuteS. Write the procedure involved in it.


In \( B r F_{3} \) molecule, the lone pairs
occupy equatorial positions to
minimize:
A. bond pair bond pair repulsion only
B. Ione pair lone pair repulsion and lone pair bond pair repulsion
C. lone pairlone pair repulsion only
D. lone pairbond pair repulsion only


In the basic \( C s C l \) crystal structure,
\( C s^{+} \) and \( C l^{-} \) ions are arranged in a bcc
configuration as shown in the figure. The net electrostatic force exerted by
the eight \( C s^{+} \) ions on the \( C l^{-} \) ion is :
\( ^{A} \cdot \frac{1}{4 \pi \varepsilon_{0}} \frac{4 e^{2}}{3 a^{2}} \)
B. \( \frac{1}{4 \pi \varepsilon_{0}} \frac{16 e^{2}}{3 a^{2}} \)
c. \( 1 \frac{32 e^{2}}{3 a^{2}} \)
\( D \)


Find general solution of \( y-x \frac{d y}{d x}= \)
\( b\left(1+x^{2} \frac{d y}{d x}\right) \) is:
\( \begin{array}{ll}\text { A. } & b+k x=y(1+b x)\end{array} \)
В. \( \quad b+k y=x(1+b x) \)
\( \begin{array}{ll}\text { c. } & b+k y=x(1+b y)\end{array} \)
D. \( \quad b+k x=x(1+b y) \)


Four point charges, each equal to \( q=4 \mu C \)
are held at the corners of a square ABCD of side \( a=10 \mathrm{cm} . \) Find the magnitude and sign of a charge \( Q \) placed at the centers of the square so that the system of charges is in equilibrium.


Which of the following is incorrect
statement?
A. The heats of hydration of the dipositive alkaline earth metal ions decrease with an increase in their ionic size
B. \( N a N O_{3} \) forms \( N a_{2} O \) on heating
C. Hydration energy of alkali metal ion is less than that of II \( A \)
D. Alkaline earth metal ions, because of their much large charge to size ratio, exert a much stronger electrostatic attraction on the oxygen of water molecule surrounding them


For the reaction, \( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{B} \boldsymbol{r}_{2}(\boldsymbol{g}) \rightarrow \)
\( 2 H B r(g), \) then reaction rate\( = \)
\( \boldsymbol{K}\left[\boldsymbol{H}_{2}\right]\left[\boldsymbol{B} \boldsymbol{r}_{2}\right]^{1 / 2} . \) Which statement is
true about this reaction:
A. The reaction is of second order
B. Molecularity of the reaction is \( 3 / 2 \)
c. The unit of \( k \) is sec \( ^{-1} \)
D. Molecularity of the reaction is 2


Why we do not observe de Broglie wave in daily life?


The electropositive character is the maximum for which of the following elements in group 13?
\( A . A l \)
B. B
c. Ga
D. In


The conductivity of an electrolytic
solution decreases on dilution due to:
A. decrease in number of ions per unit volume
B. increase in ionic mobility of ions
C. increase in percentage ionisation
D. increase in number of ions per unit volume


Few values are given in the table in the
direction from left to right and top to
bottom. Predict the property which
could be depicted in the table.
A. Atomic number
B. Ionisation enthalpy
c. Atomic radius
D. Electron gain enthalpy


Give an account of different type of symmetry in animals along with body cavity \( \& \) its various types
Or
Briefly describe the various animal body plans with example


If the \( \% \) composition of \( \mathrm{Cl} \) in \( \mathrm{HCl} \) is \( 46 \% \) what is the mass of Cl in HCl?
A. \( 13.3 \mathrm{g} \)
в. 66 g
\( c \cdot 25 g \)
D. 16.76 g


The laws of reflection hold true for:
A. plane mirrors only
B. concave mirrors only
c. convex mirrors only
D. all reflecting surfaces


A transverse harmonic wave on a string is described by
\( \boldsymbol{y}(\boldsymbol{x}, \boldsymbol{t})=\mathbf{3} \cdot \mathbf{0} \sin (\mathbf{3 6} \boldsymbol{t}+\mathbf{0 . 0 1 8} \boldsymbol{x}+\boldsymbol{\pi} / \mathbf{4}) \)
where \( x \) and \( y \) are in \( c m \) and \( t \) in s. The
positive direction of \( x \) is from left to
right.
(a) Is this a travelling wave or a stationary wave? If it is travelling what are the speed and direction of its propagation?
(b) What are its amplitude and
frequency?
(c) What is the initial phase at the
origin?
(d) What is the least distance between
two successive crests in the wave?


Evaluate: \( \int \frac{(x-1)(x-2)(x-3)}{(x-4)(x-5)(x-6)} d x \)


Discuss the continuity and differentiability of \( \boldsymbol{f}(\boldsymbol{x})=|\log | \boldsymbol{x} \| \)


A farmer has to go \( 500 m \) due north,
\( 400 m \) due east and \( 200 m \) due south to
reach his field. If he takes 20 minutes to
reach the field. What is the average
velocity of farmer during the walk?
A. \( 25 m / \min \)
в. \( 50 m / \min \)
c. \( 55 m / \min \)
D. \( 110 \mathrm{m} / \mathrm{min} \)


In major product, Chlorine is at which
position?
\( \mathbf{A} \)
B. 2
\( c \cdot 3 \)
\( D \cdot 4 \)


Assertion
Fe is protected from corrosion by
connecting Mg metal with it.
Reason
Fe acts as cathode and Mg as anode
which gradually disappears.
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


Teeth that are different in shape, size and function are called as
A. Acrodont
B. Pleurodont
c. Homodont
D. Heterodont


Differentiate the following w.r.t.x:
\( 5^{x} \cdot \sec ^{-1} 2 x \)


The quantity which tells the distance an object travels in a certain time is called
A. acceleration
B. speedd
c. velocity
D. none of these


Coordination number of Ni in
\( \left[N i\left(C_{2} O_{4}\right)_{3}\right]^{4-} \) is:
\( A \cdot 3 \)
B. 6
\( c \cdot 4 \)
D.


Which one does not occur in Cockroach
leg?
A. Tibia
B. Femur
c. Fibula
D. coxa


Which of the following statements is
incorrect?
A. Cassiterite is an oxide ore of tin.
B. Tin metal is obtained by the carbon reduction of black tin (purified ore of tin)
C. In the extraction of lead from galena, the roasting and self-reduction are carried out in the same furnace at
different temperatures.
D. Reducing agent of hematite in blase-furnace is coke in the upper part and \( \mathrm{CO} \) in the lower part of the furnace.


Which is correct?
\( \mathbf{A} \cdot t_{1}=t_{2} \)
B \( \cdot t_{1}>t_{2} \)
\( \mathbf{C} \cdot t_{1}<t_{2} \)
D. Depends upon the mass


Common name of chloroethene is:
A. Benzyl chloride
B. Vinyl chloride
c. Allyl bromide
D. none of these


Three simple harmonic motions in the
same direction having the same amplitude \( A \) and same period are superposed. If each differs in phase
from the next by \( 45^{0}, \) then
A . the resulting amplitude is \( (1+\sqrt{3}) A \)
B. the resulting motion is not simple harmonic
C. The energy associated with the resulting motion \( (3+ \) \( 2 \sqrt{2} \) ) times the energy associated with any single motion
D. The phase of the resultant motion relative to the first is \( 90^{\circ} \)


Pressure is a scalar quantity because
A. it is the ratio of force to area and both force and area
are vectors
B. it is the ratio of the magnitude of the force to area.
C. it is the ratio of the component of the force normal to the area.
D. it depends on the size of the area chosen.


The balancing structures in medusae of
cnidarians are
A. Otoliths
B. Statoliths
c. statocysts
D. None of the above


The "geocenter" of two positive numbers is defined as the positive square root of their product. If the geocenter of 5 and \( x \)
is \( 9, \) calculate the value of \( x \)
A . 6.7
в. 7.0
c. 11.3
D. 13.0
E . 16.2


The nuclei of which one of the following
pairs of nuclei are isotones:
\( A \cdot_{34} \mathrm{Se}^{74},_{31} \mathrm{Ga}^{71} \)
B \( \cdot_{38} \mathrm{Sr}^{84},_{38} \mathrm{Sr}^{86} \)
C \( \cdot_{42} \mathrm{Mo}^{92},_{40} \mathrm{Zr}^{9} \)
D. \( _{20} \mathrm{Ca}_{2}^{40},_{16} \mathrm{S}^{32} \)


All of these will directly or indirectly
reduce the contribution to greenhouse
gases except
A. Encouraging the use of public transportation
B. Walking
C. Biking
D. Increasing the cost of car ownership and fuel costs
E. Creating car-free zones


Ethanol is heated with excess
concentrated \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) at \( 443 \mathrm{K} \)
i) Name the reaction that occurs and
explain it.
ii) Write the equation for the above reaction.
iii) What is the product formed? What happens when this gas is passed through bromine water?
iv) When ethanol vapour is passed through bromine water, why does no change occur?


Given the sequence of numbers
\( \boldsymbol{x}_{1}, \boldsymbol{x}_{2}, \boldsymbol{x}_{3}, \ldots \ldots . . \boldsymbol{x}_{2013} \) which satisfies
\( \frac{\boldsymbol{x}_{\mathbf{1}}}{\boldsymbol{x}_{\mathbf{1}}+\mathbf{1}}=\frac{\boldsymbol{x}_{\mathbf{2}}}{\boldsymbol{x}_{\mathbf{2}}+\mathbf{3}}=\frac{\boldsymbol{x}_{\mathbf{3}}}{\boldsymbol{x}_{\mathbf{3}}+\mathbf{5}}=\dots \dots \)
\( \frac{x_{2013}}{x_{2013}+4025}, \) nature of the sequence is
A . A.P
в. \( G . P \)
c. \( H . P \)
D. A.G.P


The wavelength of light of a particular colour is 5800 A. What is its order of
magnitude in meter?


Why is it important for plants to scatter seeds?
A. To avoid overcrowding which results in unhealthy plants
B. To prevent the seeds from becoming parasites to the parent plants
c. To ensure that plants of a particular type will be spread to new places
D. Both A and C


If \( \boldsymbol{A}=\{\boldsymbol{p}, \boldsymbol{q}, \boldsymbol{r}, \boldsymbol{s}\}, \boldsymbol{B}=\{\boldsymbol{r}, \boldsymbol{s}, \boldsymbol{t}, \boldsymbol{u}\}, \) then
\( \boldsymbol{A} / \boldsymbol{B} \) is:
\( A \cdot(p, q) \)
\( B \cdot\{r, s\} \)
c. \( \{t, u\} \)
D. \( \{p, q, t, u\} \)


Two liquids \( A \) and \( B \) form an ideal
solution. What is the vapour pressure of solution containing 2 moles of \( A \) and 3
moles of \( B \) at \( 300 K ? \)
[Given: At \( 300 K \), vapour pressure of
pure liquid \( \boldsymbol{A}\left(\boldsymbol{P}_{A}^{\circ}\right)=\mathbf{1 0 0} \) torr, Vapour
pressure of pure liquid \( B\left(P_{B}^{\circ}\right)= \) \( 300 \text { tor } r] \)
A. 200 torr
B. 220 torr
c. 180 tor
D. None of these


How many of following are electrophile? \( \boldsymbol{C H}_{3}, \stackrel{\oplus}{\boldsymbol{N}} \boldsymbol{H}_{4}, \boldsymbol{H}_{3} \boldsymbol{O}^{\oplus}, \boldsymbol{C} \boldsymbol{O}_{2}, \boldsymbol{S} \boldsymbol{O}_{3}, \boldsymbol{C} \stackrel{\ominus}{\boldsymbol{H}}_{3} \)


State True or False.
\( C O_{2} \) is a polar molecule but not have
polar bond
A. True
B. False


The two compounds \( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C} \|_{2}-\boldsymbol{C H}_{2}- \)
\( \boldsymbol{C H}_{3} \) and \( \boldsymbol{C H}_{3}-\stackrel{\boldsymbol{O} \|}{\boldsymbol{C}}-\underbrace{\boldsymbol{C H}_{3}}_{\mid \boldsymbol{C H}_{3}}-\boldsymbol{C H}_{3} \)
may be considered as:
A. position isomers
B. metamers
c. stereoisomers
D. tautomers


Red phosphorus is less reactive than
yellow phosphorus because
A. It is red in colour
B. It is highly polymerised
C. It is insoluble in \( C_{2} H_{5} O H \)
D. It is hard


For the properties mentioned, the correct trend for the different species
is :
A. inert pair effect - \( A l>G a>I n \)
B. first ionization enthalpy \( -B>A l>T l \)
C . strength as Lewis acid - \( B C l_{3}>A l C l_{3}>G a C l_{3} \)
D. oxidising property \( -A l^{+3}>I n^{+3}>T l^{+3} \)


In male grasshoppers and moths, there are two pairs of autosomes and
A. \( x \) only
B. x and
c. Y only
D. None of the above


\( \ln \Delta A B C, \) D is a point on BC such that
\( A B=A D=B D=D C \). then
\( \angle A D C: \angle C=4: 1 \)
State whether the above statement is
true or false.
A. True
B. False


Eliminate the arbitrary constants and obtain the differential equation satisfied by it: \( \boldsymbol{y}=\left(\frac{\boldsymbol{a}}{\boldsymbol{x}^{2}}\right)+\boldsymbol{b} \boldsymbol{x} \)
A \( \cdot x^{2} y^{\prime \prime}+2 x y^{\prime}-2 y=0 \)
B . \( x^{2} y^{\prime \prime}+2 x^{2} y^{\prime}-2 y=0 \)
C \( \cdot x^{2} y^{\prime \prime}+2 x y^{\prime}+2 x y=0 \)
D. \( x^{2} y^{\prime \prime}-2 x y^{\prime}+2 x y=0 \)


A circular current carrying coil has a radius \( R \). The distance from the centre
of the coil on the axis where the
magnetic induction will be \( \left(\frac{1}{8}\right)^{t h} \) of its value at the centre of the coil is
A \( \cdot \frac{R}{\sqrt{3}} \)
в. \( R \sqrt{3} \)
с. \( 2 R \sqrt{3} \)
।
D. \( \left(\frac{2}{\sqrt{3}}\right)^{R} \)


In the Molisch reagent the substance
used is:
A. \( \beta \) naphthol in alchol
B. \( \alpha \) naphthol in alchol
c. Reasrcinol in alchol
D. Rosaniline in water


Find the ratio of magnetic dipole moment to angular momentum in a hydrogen like atom:
A \( \cdot \frac{e}{m} \)
B. \( \frac{e}{2 m} \)
c. \( \frac{e}{3 m} \)
D. \( \frac{2 e}{m} \)
E \( \cdot \frac{3 e}{m} \)


The number of straight lines which are equally inclined to both the axes is ;
A . 4
B.
\( c \cdot 3 \)
\( D \)


Evaluate the integral \( \int_{0}^{1}\left(3 x^{2}+2 x\right) d x \)


In a n-type semiconductor, which of the following statement is true?
A. Electrons are majority carriers and trivalent atoms are dopants
B. Electron are minority carriers and pentavalent atoms are dopants.
C. Holes are minority carriers and pentavalent atoms are dopants.
D. Holes are majority carriers and trivalent atoms are dopants


A point charge \( -q \) is carried from a
point \( A \) to another point \( B \) on the axis of a charged ring of radius 'r' carrying a charge \( +q / \) If the point \( A \) is at \( a \) distance \( \frac{4}{3} r \) from the centre of the ring and the point \( \mathrm{B} \) is \( \frac{3}{4} r \) from the centre but on the opposite side, what is the net work that need to be done for this?
\( ^{\mathrm{A}} \cdot-\frac{7}{5} \frac{q^{2}}{4 \pi \varepsilon_{0} r} \)
В. \( -\frac{1}{5} \frac{q^{2}}{4 \pi \varepsilon_{0} r} \)
c. \( \frac{q^{2}}{54 \pi \varepsilon_{0} r} \)
D. \( \frac{q^{2}}{54 \pi \varepsilon_{e} r} \)


\( \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \sin ^{2} x \cdot \cos ^{3} x d x \) is equal to
A. \( \frac{4 \pi}{30} \)
B. \( \frac{4}{15} \)
c. \( \frac{\pi}{30} \)
D. \( \frac{1}{15} \)


Acidified solution of \( K_{2} C r_{2} O_{7} \) on
treatment with \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) yields:
A. \( C r O_{3}+H_{2} O+O_{2} \)
в. \( C r_{2} O_{2}+H_{2} O+O_{2} \)
\( \mathrm{c} \cdot \mathrm{Cr} \mathrm{O}_{5}+\mathrm{H}_{2} \mathrm{O}+\mathrm{K}_{2} \mathrm{SO}_{4} \)
D. \( H_{2} C r_{2} O_{7}+H_{2} O+O_{2} \)


For a given distance from a current
element, the magnetic induction is
maximum at an angle measured with
respect to axis of the current. The angle
is :
A \( \cdot \frac{3 \pi}{4} \)
B. \( \frac{\pi}{4} \)
c. \( \frac{\pi}{2} \)
D. \( 2 \pi \)


Derive van't Hoff general solution
equation.


There are following extraction process
of silver but not:
A. as a side product in electrolytic refining of copper
B. Parke's process in which Zn is used to extract silver by solvent extraction from molten lead
C. by reaction of silver sulphide with \( K C N \) and then reaction of soluble complex with \( \mathrm{Zn} \).
D. by heating \( N a\left[A g(C N)_{2}\right] \)


The IUPAC name of the following compound is:
\( \begin{aligned} \boldsymbol{C}_{2} \boldsymbol{H}_{5}-& \underset{\|}{\boldsymbol{C}}-\boldsymbol{C} \boldsymbol{H}-\boldsymbol{C} \boldsymbol{H}_{3} \\ & \boldsymbol{C H}_{2} \quad \boldsymbol{C} \boldsymbol{H}_{3} \end{aligned} \)
A. 3-methyl-2-ethylbut-1-yne
B. 2-ethyl-3-methylbut-1-ene
c. 3-ethyl-3-methylbutene
D. ethylisopropylethane


Aradhya buys \( 9,000 K g \) potatoes for
Rs.15 per Kg. She dries it for chips. The
chips becomes one-third of the total weight. She sells the chips for Rs.50 per Kg. How much money will
she get as profit?


Select the basic strength order of following molecules.
A. \( I I I>I I>I \)
B. \( I I>I I I>I \)
\( c . I>I I I>I I \)
D. \( I I I>I>I I \)


The moon revolves round the earth 13
times in one year. If the ratio of sunearth distance to earth-moon distance
is \( 392, \) then the ratio of masses of sun
and earth will be
A . 365
B. 356
c. \( 3.56 \times 10^{5} \)
D.


One hundred identical coins, each with probability, \( p, \) of showing up heads are
tossed once. If \( 0<p<1 \) and the
probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, then the value of \( p \) is:
\( A \cdot \frac{1}{2} \)
в. \( \frac{49}{101} \)
c. \( \frac{50}{101} \)
D. \( \frac{51}{101} \)


Cod liver oil is:
A. fat dispersed in water
B. water dispersed in fat
C . water dispersed in oil
D. fat dispersed in fat


Assertion
\( f \) is a function defined on the interval
[-1,1] such that \( f(\sin 2 x)=\sin x+ \)
\( \cos x \)
Statement I: If \( \boldsymbol{x} \in\left[-\frac{\boldsymbol{\pi}}{\boldsymbol{4}}, \frac{\boldsymbol{\pi}}{\boldsymbol{4}}\right], \) then
\( f\left(\tan ^{2} x\right)=\sec x \)
Reason
Statement II: \( \boldsymbol{f}(\boldsymbol{x})=\sqrt{\mathbf{1}+\boldsymbol{x}}, \forall \boldsymbol{x} \in \)
[-1,1]
A. Statement I is true, Statement II is also true:
Statement II is the correct explanation of Statement
B. Statement I is true, Statement II is also true Statement II is not the correct explanation of Statement
c. statement lis true, statement II is false
D. statement lis false, statement II is true


Dry hydrogen can oxidise copper oxide to form copper metal.
A . True
B. False


Which among the following is a rational
number?
A. \( \sqrt{2} \)
в. \( \sqrt{\pi} \)
\( c \cdot \sqrt{7} \)
D. \( \sqrt{\frac{5}{25}} \)
E \( \cdot \sqrt{\frac{64}{49}} \)


The least stable hydride is:
A . \( N H_{3} \)
в. \( P H_{3} \)
c. \( A s H_{3} \)
D. \( S b H_{3} \)


An adaptation in the structure and
function of loop of Henle to xerophytic
environment is
A. A short loop of Henle, which allows more filtrate to be removed from the blood
B. A short loop of Henle, which allows less water to be removed from the filtrate
C. A long loop of Henle, which allows more filtrate to be removed from the blood
D. A long loop of Henle, which allows more water to be removed from the filtrate
E. A long loop of Henle, which allows less filtrate to be removed from the blood


The oil layer on the surface of water appears coloured, due to interference. For this effect to be visible the
thickness of oil layers will be
A . \( 1 m m \)
B. \( 1 c m \)
c. \( 100 A^{\circ} \)
D. \( 1000 A^{\circ} \)


A square is a
A. kite
B. trapezium
C . triangle
D. rhombus


For a triangle \( A B C, \) the true statement is:
A \( \cdot A C^{2}=A B^{2}+B C^{2} \)
B. \( A C=A B+B C \)
c. \( A C>A B+B C \)
D. \( A C<A B+B C \)


Which of the following is true?
A. The electron density in the xy-plane in 3d \( _{x y} \) orbital si
zero
B. The electron densities in the xy and xz-plane in 3d \( _{y z} \) orbital are zero
C. The electron density in the xy-plane in \( 3 d_{x}^{2} \) orbital is
zero
D. Pauli exclusion principle is followed by bosons which have integral spin


Hormone involved in breaking dormancy of winter buds is
A. Ethylene
B. Gibberellin
c. Auxin
D. Cytokinin


Sodium bicarbonate solution has \( \boldsymbol{p} \boldsymbol{H} \)
less than 7 .
State True or False:
A. True
B. False
c. cannot be determined
D. None of the above


A line that intersects a circle at two
distinct points is called
A . a diameter
B. a secant
c. a tangent
D. a radius


Mr. Verma (50 \( K g \) ) and Mr. Mathur \( (60 K g) \) are sitting at the two extremes
of a \( 4 m \) long boat \( (40 K g) \) standing still in water. To discuss a mechanics
problem, they come to the middle of the boat. Neglecting friction with water, how far does the boat move in the water
during the process:
A \( .40 / 3 c m \)
в. \( 20 / 3 \) ст
c. \( 10 / 3 c m \)
D. \( 10 \mathrm{cm} \)


A man is unable to see closer than \( 1 \mathrm{m} \)
clearly.The power of lenses of his spectacles should be to see nearby object.
\( A \cdot 3 D \)
B. 6 D
\( c \cdot 10 \)
D. 2


The number of seats for admission is
increased by \( 10 \% \) every year. If the number of seats in 2001 was \( 400, \) what
were the number of seats in 2003?
A. 824
B. 484
\( c .500 \)
D. 480


During laboratory preparation of oxygen by hydrogen peroxide and potassium chlorate, the gas is collected by displacement of water
A. downward, upward
c. downward


What is \( \sin ^{2} 20^{\circ}+\sin ^{2} 70^{\circ} \) equal to?
\( \mathbf{A} \cdot \mathbf{1} \)
B. 0
\( c \cdot-1 \)
D.


The bond energy of \( C-C \) bond in
kcal/mol is?
A . 58
B. 83
\( c .145 \)
D. 192


Which of the following reactions does
not occur?
A \( \cdot F_{2}+2 C l^{-} \rightarrow 2 F^{-}+C l_{2} \)
B. \( C l_{2}+2 F^{-} \rightarrow 2 C l^{-}+F_{2} \)
c. \( B r_{2}+2 I^{-} \rightarrow 2 B r^{-}+I_{2} \)
D. \( C l_{2}+2 B r^{-} \rightarrow 2 C l^{-}+B r_{2} \)


Give reasons of the following:
\( N_{2} O_{5} \) is more acidic than \( N_{2} O_{3} \)


Primary circuit of potentio meter is as
shown in the diagram find potentia
gradient.


\( \boldsymbol{n} \stackrel{L t}{\rightarrow} \infty\left[\frac{\boldsymbol{n}+\mathbf{1}}{\boldsymbol{n}^{2}+\mathbf{1}^{2}}+\frac{\boldsymbol{n}+\boldsymbol{2}}{\boldsymbol{n}^{2}+\mathbf{2}^{2}}+\ldots+\right. \)
\( \left.\frac{\boldsymbol{n}+\boldsymbol{n}}{\boldsymbol{n}^{2}+\boldsymbol{n}^{2}}\right]= \)
A. \( \frac{\pi}{4}+\frac{1}{2} \log 2 \)
B. \( \frac{\pi}{4}-\frac{1}{2} \log 2 \)
c. \( \frac{\pi}{2}+\frac{1}{2} \log 2 \)
D. \( \frac{\pi}{4}+\frac{1}{4} \log 2 \)


The solution of the equation \( \frac{d y}{d x}+ \)
\( \boldsymbol{x}(\mathbf{2} \boldsymbol{x}+\boldsymbol{y})=\boldsymbol{x}^{3}(\boldsymbol{2} \boldsymbol{x}+\boldsymbol{y})^{3}-\boldsymbol{2} \) is \( (C \)
being arbitrary constant):
A \( \cdot \frac{1}{2 x+x y}=x^{2}+1+C e^{x} \)
B. \( \frac{1}{(2 x+y)^{2}}=x^{2}+1+C e^{x^{2}} \)
c. \( \frac{1}{2 x+y}=x+1+C e^{-x^{2}} \)
D. \( \frac{1}{(2 x+y)^{2}}=x^{2}+1+C \)


Who coined the term ecosystem?
A. Tansley
B. Odum
c. Warming
D. Darwin


Two ideal junction diodes \( D_{1}, D_{2} \) are
connected as shown in the figure. A \( 3 V \)
battery is connected between \( A \) and \( B \) The current supplied by the battery, if its positive terminal is connected to B
is
A \( .0 .15 ~ A \)
в. 0.3 А
\( c .3 A \)
D. 1.4


Assertion
Divalent compounds of alkaline earth metals are diamagnetic.
Reason
\( M^{2+} \) ions of group 2 have noble gas conguration.
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


Mention the types of solutions based on
the \( p H \) value.


Where must an object be placed in front of a convex lens so that the image formed is at infinity?


Find the derivative of the following functions:
(i) \( \tan x \cos x \)
(ii) \( \sec x \)


Assertion
Excess nitrate in drinking water causes
blue baby' syndrome.
Reason
The maximum limit of nitrate in
drinking water is 50 ppb.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The tendency of a body to resist acceleration is called:
A. Force
B. Retardation
c. Inertia
D. mass


Explain the following reactions:
(i) Reimer-Tiemann reaction
(ii) Williamson synthesis


The strongest - \( \mathrm{CO} \) bond is present in:
A \( \cdot\left[C r(C O)_{6}\right]^{+} \)
в \( \cdot\left[F e(C O)_{5}\right] \)
\( \mathbf{c} \cdot\left[V(C O)_{6}\right]^{-} \)
D. all have equal strength


When each term of a sequence is
connected using \( a+ \) or \( a-\operatorname{sign}, \) then it
is referred to as the of numbers
A. Series
B. Progression
c. Arithmetic Progression
D. Geometric Prpgression


ff \( y=2 \tan ^{-1} x+\sin ^{-1} \frac{2 x}{1+x^{2}} \) then
A. \( -\pi / 2<y<\pi / 2 \)
в. \( -3 \pi / 2<y<3 \pi / 2 \)
c. \( -\pi<y<\pi \)
D. \( -\pi / 4<y<\pi / 4 \)


A ball thrown upwards at an angle describes \( -\ldots- \) motion
A . curvilinear
B. rectilinear
c. periodic
D. oscillatory


the pressure exerted by atmosphere is
\( ? \)
A. large
B. small
c. zero
D. none of the above


The net charge on a condenser is :
A . infinity
B. \( 9 / 2 \)
\( c \cdot 29 \)
D. zero


The point lying on angle bisector of the
planes \( \boldsymbol{x}+\mathbf{2} \boldsymbol{y}+\mathbf{2} \boldsymbol{z}-\mathbf{6}=\mathbf{0} \) and \( \mathbf{2} \boldsymbol{x}- \)
\( \boldsymbol{y}+\boldsymbol{4}=\mathbf{0} \) is
A. (2,4,0)
B. (-1,3,2)
D. (-2,4,0)


Write the domain of the relation \( \boldsymbol{R} \)
defined on the set \( \mathbb{Z} \) of integers as
follows:
\( (a, b) \in R \Leftrightarrow a^{2}+b^{2}=25 \)


If \( \boldsymbol{A}=\left[\begin{array}{ll}2 & 3 \\ 5 & 7\end{array}\right], \) then find \( A+A^{T} \)


What do you understand by the term
Echo?


State whether true or false.
Pure water is a good conductor of electricity.
A. True
B. False


One gram atom of an element contains \( 6.02 \times 10^{23} \) atoms.
(a) Find the number of oxygen atoms in
\( 4 g \) of \( O_{2} \)
(b) Which is heavier, one oxygen atom
or 10 hydrogen atoms?


What is the value of unknown
resistance \( R \), of galvanometer shows
null deflection in the given meter bridge
set up shown in the fig?
A \( .97 .50 \Omega \)
3. \( 105 \Omega \)
\( c .220 \Omega \)
\( 0.110 \Omega \)


Find the weight of a box on earth having a mass of \( 20 \mathrm{kg} \)
\( A \cdot 196 N \)
B. 19.6 N
c. \( 1.96 \mathrm{N} \)
D. 0.19 N


An aqueous solutions of diabasic acid (molecular mass \( =118 \) ) containing
\( 35.4 \mathrm{g} \) of acid per litre of the solution has density \( 1.0077 g m L^{-1} \). Find the mole fraction of the solvent.


The heart of man beats 75 times a
minute. What is its frequency?


A person looks into the mirror by placing it close to his face. if the image of the face was found erect and
magnified, then the mirror must be
A. plane
B. concave
c. convex
D. none of these


The total number of possible isomer for the complex compound:
\( \left[\boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right]\left[\boldsymbol{P t} \boldsymbol{C l}_{4}\right] \)
\( A \cdot 3 \)
B. 6
\( c \cdot 5 \)
\( D \)


A system goes from \( A \) to \( B \) in two
processes I and II as shown in the fig. If
\( \Delta U_{1} \) and \( \Delta U_{2} \) are the changes in
internal energies in the processes I and
II respectively then.
A \( . \Delta U_{2}<\Delta U_{1} \)
B \( . \Delta U_{2}>\Delta U_{1} \)
C. Relation between \( \Delta U_{2} \) and \( \Delta U_{1} \) can not bedetermined
D. \( \Delta U_{2}=\Delta U_{1} \)


The surface tension of soap solution is \( 0.03 N / m . \) The work done in blowing to form a soap bubble of surface area
\( 40 c m^{2}, \) in Joules, is:
A \( \cdot 1.2 \times 10^{-4} \)
B. \( 2.4 \times 10^{-4} \)
c. \( 12 \times 10^{-4} \)
D. \( 24 \times 10^{-4} \)


The value of \( \sin \left(\frac{1}{4} \sin ^{-1} \frac{\sqrt{63}}{8}\right) \) is
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{1}{2 \sqrt{2}} \)
D.


Statement 1: The addition of \( \boldsymbol{H}_{2} \) to
ethene will form an unsaturated
compound called ethane Statement 2: Ethane, has as many
hydrogen atoms bonded to the carbon atoms as possible
A. Both Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement
B. Both Statement 1 and Statement 2 are correct and Statement 2 is not the correct explanation of Statement'
c. statement 1 is correct but Statement 2 is not correct
D. Statement 1 is not correct but Statement 2 is correct
E. Both the Statement 1 and Statement 2 are not correct


The single \( X-X \) bond made by \( N \) is
weaker than that of \( P \) because:
A. of repulsion between nitrogen nucleus due to smaller size of nitrogen atom
B. of repulsion between non-bonded electrons due to smaller size of nitrogen atom
c. of higher bond enthalpy of nitrogen
D. all of the above


Observe the following statements.
1. Lanthanides actively participate in chemical reactions.
2. The basic nature of hydroxides of
lanthanides increases from \( L a(O H)_{3} \)
to \( L u(O H)_{3} \)
3. Lanthanides do not form coordinate
compounds as readily as d-block metals.
The correct statements are:
A. \( 1,2 \& 3 \)
В. 183
\( c \cdot 1 \& 2 \)
D. 2 \& 3


The criterion of spontaneity in terms of
Gibbs energy is the same as that laid down by second law of thermodynamics. How?


Which of the following rational numbers lies between \( \frac{3}{4} \) and \( \frac{13}{8} ? \)
A \( \cdot \frac{11}{16} \)
в. \( \frac{12}{16} \)
c. \( \frac{19}{16} \)
D. \( \frac{26}{16} \)


If \( m \) th term of an A.P. is \( n \) and \( n \) th term
is \( m, \) then the \( (m+n) \) th term is
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( m+n-1 \)
\( \mathrm{c} \cdot m+n \)
D. \( \frac{m n}{m+n} \)


In the figure, \( Q X \) and \( R X \) are the
bisectors of angles \( Q \) and \( R \)
respectively of \( \triangle \boldsymbol{P Q R} \). If \( \boldsymbol{X} \boldsymbol{S} \perp \boldsymbol{Q} \boldsymbol{R} \)
and \( X T \perp Q R, \) then \( \triangle X T Q \cong \triangle X S Q \)
by \( _{\text {一一一一一一一一一一 }} \) congruency
A. \( S A S \)
B. \( R H S \)
c. \( A A S \)
D. \( A S A \)


What do you understand by the terms nomenclature and classification?


A material B' has twice the specific
resistance of \( \mathbf{A}^{\prime} . \) A circular wire made of
B' has twice the diameter of a wire
made of \( \mathbf{A}^{\prime} . \) Then for the two wires to
have the same resistance, the ratio
\( \boldsymbol{P}_{\mathrm{A}} / \boldsymbol{P}_{\mathrm{B}} \) of their respective lengths must
be
\( A \cdot 2 \)
B. 1
\( c \cdot \frac{1}{2} \)
D.


How did Mendeleev predict the existence of some yet to be discovered elements in his periodic table?
A. Gaps
B. Atomic number
c. Mass number
D. None of the above


A die is thrown. Find the probability of
getting:
2 or 4


Assertion
Amount of biodegradable present in water is measured by BOD organic
matter
Reason
During biodegradation of organic compounds, oxygen is released.
A. Both A and R are true and R is the correct explanation of
B. Both A and R are true and R is not the correct explanation of
c. A is true but R is false
D. Both A and R are false


A very high magnetic field is applied to a stationary charge. Then, the charge experiences
A. A force in a direction of magnetic field
B. A force perpendicular to the magnetic field
c. A force in an arbitrary direction
D. No force


The relative magnetic permeability of a magnetic material is 800 . Identify the nature of magnetic material and state its own properties.


How can we be safe when there is
occurrence of lightning?
A. Taking shelter under building or house
B. When travelling through car or bus, making sure windows and doors are shutt
C. If in forest, taking shelter under short trees
D. All of the above


Water potential in the leaf tissue is positive (+ve) during
A. Excessive transpiration
B. Low absorption
c. Low transpiration
D. Guttation


Statement 1: A charge is outside the
Gaussian sphere of radius \( R \). Then
electric field on the surface of sphere is
zero

Statement 2: As \( \oint \vec{E} . \overrightarrow{d s}=\frac{q_{i n}}{\varepsilon_{0}}, \) for the
sphere \( \boldsymbol{q}_{\boldsymbol{i n}} \) is zero, so \( \oint \overrightarrow{\boldsymbol{E}} \cdot \overrightarrow{\boldsymbol{d} s}=\mathbf{0} \)
A. Statement 1 is true, statement 2 is true and statement 2 is correct explanation for statement
B. Statement 1 is true, statement 2 is true and statement 2 is NOT the correct explanation for statement
c. Statement 1 is true, statement 2 is false
D. Statement 1 is false, statement 2 is true


A potentiometer wire has length \( 4 \mathrm{m} \) and resistance \( 8 \Omega \).What should be the
resistance that must be connected in
series with the wire and an accumulator
of emf \( 2 \mathrm{V}, \) so as to get a potential gradient \( 1 \mathrm{m} \mathrm{V} \) per \( \mathrm{cm} \) on the wire?
A . \( 32 \Omega \)
B. \( 36 \Omega \)
c. \( 40 \Omega \)
D. \( 30 \Omega \)


\( 13.8 g \) of \( N_{2} O_{4} \) was placed in a \( 1 L \)
reaction vessel at \( 400 K \) and allowed
attain equibrium \( N_{2} O_{4}(g) \rightleftharpoons 2 N O_{2}(g) \)
The total pressure at equilibrium was
found to be 9.15 bar. Calculate \( K_{c}, K_{p} \) and partial pressure at equilibrium.


The degree and order of
the differential equation
\( \left[1+2\left(\frac{d y}{d x}\right)^{2}\right]^{1 / 2}=5 \frac{d^{2} y}{d x^{2}} \) are
\( A \cdot 1,2 \)
B. 2,
c. 3,1
D. 4,3


A steamer crosses a river having a width of \( 240 m \) which is flowing with a
speed of \( 8 m / s . \) In order to cross the
river along the shortest path, find the time of crossing the river. [velocity of steamer in still water is \( 10 \mathrm{ms}^{-1} \) ].


A gas consisting of rigid diatomic molecules is expanded adiabatically. How many times has the gas to be expanded to reduce the r.m.s. velocity of the molecules to \( \left(\frac{2}{3}\right) \) rd of initial value.
A . 0.13
B. 7.6
\( c .5 \)
D. 3.8


Identify the functional group in the
following detergent molecule. \( \boldsymbol{C H}_{\mathbf{3}}- \)
\( \left(\boldsymbol{C} \boldsymbol{H}_{2}\right)_{10}-\boldsymbol{C H}_{2} \boldsymbol{O S O}_{3}^{-} \boldsymbol{N a}^{+} \)


"Sporeine" is used to control
A. Bacterial pathogen
B. Fungal pathogen
c. Nematodes
D. Insects pest


The frequency of a light wave in a material is \( 2 \times 10^{14} \mathrm{Hz} \) and wavelength is 5000 A. The refractive index of
material will be
A . 1.40
в. 1.50
\( c .3 .00 \)
D. 1.33


Nitrogen has unique ability to form \( \boldsymbol{P} \boldsymbol{\pi}-\boldsymbol{P} \boldsymbol{\pi} \) multiple bonds with itself and
with other elements due to:
A. small size and low electronegativity
B. large size and high electronegativity
c. large size and low electronegativity
D. small size and high electronegativity


Two resistances \( r_{1}=(5.0 \pm 0.2) \Omega \) and
\( r_{2}=(10.0 \pm 0.1) \Omega \) are connected in
parallel. Find the value of equivalent resistance with limits of percentage
error.
A \( \cdot r_{p}=4 \Omega \pm 7 \% \)
B . \( r_{p}=3.3 \Omega \pm 14 \% \)
\( \mathbf{c} \cdot r_{p}=3.3 \Omega \pm 3.5 \% \)
D . \( r_{p}=3.3 \Omega \pm 7 \% \)


In bridge rectifier circuit, (see fig.), the input signal should be connected
between
A. A and D
\( B . B \) and \( C \)
c. \( A \) and \( C \)
D. \( B \) and \( D \)


Which of the following shows the correct order of decreasing basicity in aqueous medium:
\( \mathbf{A} \cdot\left(C H_{3}\right)_{3} N>\left(C H_{3}\right)_{2} N H>C H_{3} N H_{2}>N H_{3} \)
в. \( \left(C H_{3}\right)_{2} N H>\left(C H_{3}\right)_{3} N>C H_{3} N H_{2}>N H_{3} \)
C \( \cdot\left(C H_{3}\right)_{2} N H>C H_{3} N H_{2}>\left(C H_{3}\right)_{3} N>N H_{3} \)
D. \( \left(C H_{3}\right)_{2} N H>C H_{3} N H_{2}>N H_{3}>\left(C H_{3}\right)_{3} N \)


In the diagrams (i) to (iv) of variation of
volume with changing pressure is
shown. A gas is taken along the path
\( A B C D A \). The change in internal energy
of the gas will be
\( (\mathbf{i}) \)
\( (\text { iii }) \)
A. Positive in all cases (i) to (iv)
B. Positive in cases
(i), (ii) and
(iii) but zero in case (iv)
c. Negative in cases
(i), (ii) and
(iii) but zero in case (iv)
D. zero in all the four cases


What is the difference between lymph
and blood?


Permanent magnets are made from
A. diamagnetic substances
B. paramagnetic substance
C. ferromagnetic substances
D. wood


Substances like glucose, amino acids, Nat etc in filtrate are reabsorbed by
A. Passive transportt
B. Active transport
C. Both active and passive transport
D. Facilitated diffusion


Which of the following plots represents an ideal binary mixture?
\( \mathbf{A} \cdot \) Plot of \( P_{\text {total}} v / s 1 / X \) is linear \( \left(X_{B}= \) mole fraction of \right. 'B' in liquid phase).
B. Plot of \( P_{\text {total}} v / s Y_{A} \) is linear \( \left(Y_{B}= \) mole fraction of 'A' \right. in vapour phase)
C ef of \( \frac{1}{P_{\text {total}}} v / s Y_{A} \) is linear
D. plot of \( \frac{1}{P_{\text {total}}} v / s Y_{B} \) is non linear


Expalin the following:
The \( E^{o} c u^{21} / c u \) for copper metal is
positive \( (+0.34), \) unlike the remaining members of the first transition series


Besides water and light, which is more essential as a raw material for food
formation in plants?
\( A \cdot O_{2} \)
B. \( \mathrm{cO}_{2} \)
c. Minerals salts
D. NAD


The rate of the elementary reaction
\( \mathbf{2} N \boldsymbol{O}(\boldsymbol{g})+\boldsymbol{O}_{2}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{N} \boldsymbol{O}_{2}(\boldsymbol{g}) \) at \( \boldsymbol{3} \boldsymbol{8} \boldsymbol{0}^{\circ} \boldsymbol{C} \)
is given by Rate \( =2.6 \times \)
\( \mathbf{1 0}^{-\mathbf{3}}[\mathbf{N O}]^{\mathbf{2}}\left[\mathbf{O}_{\mathbf{2}}\right] . \) The rate of the reverse
reaction is given by under identical conditions is given by Rate \( = \)
\( 4.1\left[N O_{2}\right]^{2} . \) Calculate equilibrium
constant.


A list of reactions are given below.
(a) \( \boldsymbol{F e}+\mathbf{2 H C l} \rightarrow \boldsymbol{F e C l}_{2}+\boldsymbol{H}_{2} \)
(b) \( \boldsymbol{F e} \boldsymbol{S}+\boldsymbol{2} \boldsymbol{H} \boldsymbol{C l} \rightarrow \boldsymbol{F} \boldsymbol{e} \boldsymbol{C l}_{2}+\boldsymbol{H}_{2} \boldsymbol{S} \)
(c) \( \boldsymbol{F} \boldsymbol{e}+\boldsymbol{S} \stackrel{\boldsymbol{\Delta}}{\longrightarrow} \boldsymbol{F} \boldsymbol{e} \boldsymbol{S} \)
(d) \( \boldsymbol{N a C l}+\boldsymbol{H}_{2} \boldsymbol{S O}_{4} \stackrel{<200^{\circ} \boldsymbol{C}}{\longrightarrow} \)
\( N a H S O_{4}+H C l \)
\( (e) C u S O_{4}+H_{2} S \rightarrow C u S+H_{2} S O_{4} \)
\( (f) S+H_{2} S O_{4} \rightarrow 3 S O_{2}+H_{2} O \)
Identify redox reactions.
\( A \cdot a, c \) and \( f \)
B. d and f
\( c \cdot c \) and \( d \)
D. c, d and f


The oxide of nitrogen formed in atmosphere during lightning
is
\( A \cdot N_{2} O \)
в. NO
\( \mathrm{c} \cdot \mathrm{N}_{2} \mathrm{O}_{3} \)
D. \( \mathrm{N}_{2} \mathrm{O}_{5} \)


One mole of radium has an activity of \( 1 / 3.7 \) killo curie. Its decay constant will be
A \( \cdot \frac{1}{6} \times-10 s^{-1} \)
В. \( 10^{-10} s^{-1} \)
\( \mathbf{c} \cdot 10^{-11} s^{-1} \)
D. \( 10^{-8} s^{-1} \)


The length and breadth of a rectangular
piece of land are \( 500 \mathrm{m} \) and \( 300 \mathrm{m} \) respectively.
Find the cost of the land, if \( 1 m^{2} \) of the
land costs Rs. 10,000


Find the average age of the people given below in the tabular column. Use step
deviation method.
A. 12 years
B. 11 years
c. 13 years
D. 14 years


Polarisation is the distortion of the
shape of an anion by an adjacently
placed cation. Which of the following statements is correct?
This question has multiple correct options
A. Maximum polarisation is brought about by a cation of high charge
B. Maximum polarisation is brought about by a cation of low radius
c. A large cation is likely to bring about a large degree of polarisation
D. Polarising power of a cation is less than that of anion


Find the magnitude \( \& \) direction of
frictional force between block \( A \) and
table, if block \( A \) is pulled towards left
with a force of \( 50 N \)
\( \mathbf{A} \cdot 10 \hat{i} \)
B . \( 10 \hat{j} \)
\( c \cdot 20 \hat{i} \)
D. \( 20 \hat{j} \)


the time when relative motion between
them will stop.
A \( .1 / 4 s \)
B. 2/4s
\( c \cdot 3 / 4 s \)
D. \( 5 / 4 s \)


A person with a normal near point (25 \( \mathrm{cm} \) ) using a compound microscope with objective of focal length \( 8.0 \mathrm{mm} \) and an eyepiece of focal length \( 2.5 \mathrm{cm} \)
can bring an object placed at \( 9.0 \mathrm{mm} \)
from the objective in sharp focus. What is the separation between the two lenses? Calculate the magnifying power of the microscope.


You are required to make an electromagnet from a soft iron bar by using a cell, an insulated coil of copper wire and a switch. Draw a circuit
diagram to represent the process.


Assume that configurations consisting of a completely filled or half filled set of
\( \boldsymbol{d} \) -orbitals is spherically symmetrical The species having spherical symmetry
are:
This question has multiple correct options
A. \( Z n \)
в. \( C u^{+} \)
c. \( P d \)
D. \( C r \)


(i) It is observed that the temperature of the surroundings starts falling when the ice in a frozen lake starts melting.
Give a reason for the observation.
(ii) How is the heat capacity of the body related to its specific heat capacity?


State the property illustrated by the statement. \( \frac{4}{5} \times 1=1 \times \frac{4}{5} \) is multiplicative inverse
A. multiplicative
B. multiplicative inverse
c. data inadequate
D. none of these


3 spheres \( A, B \) and \( C \) having radii
\( R, 2 R \) and \( 3 R \) respectively are coated
with carbon black on their surfaces.
The wavelengths corresponding to
maximum intensity are 3000,4000 and
\( \mathbf{5 0 0 0} \) respectively. The power radiated
by them are \( Q_{A}, Q_{B} \) and \( Q_{C} . \) Then
A \( \cdot Q_{A} \) is maximum among all
B. \( Q_{B} \) is maximum among all
c. \( Q_{C} \) is maximum among all
D. \( Q_{A}=Q_{B}=Q_{C} \)


Mass number is also called as
A. weight
B. molecular weight
c. Both A and B
D. atomic mass number


toppr
Q Type your question
aimed towards \( Q \) and velocity \( \vec{u} \) of \( Q \) is
perpendicular to \( \vec{v} \). The two projectiles
meet at time \( \boldsymbol{T}= \)
\( A \)
B.
\[
\frac{(v+u) d}{v^{2}}
\]
\( c \)
\[
\frac{v(v-u)}{d}
\]
D.
\[
\frac{v d}{\left(v^{2}-u^{2}\right)}
\]


If \( \int \frac{x \cos ^{-1} x}{\sqrt{1-x^{2}}} d x= \)
\( -k\left[\sqrt{1-x^{2}} \cos ^{-1} x+x\right]+C . \) what will
be the value of \( k ? \)