A die is thrown. If \( A \) is the event that the
number on upper face is a prime, then
write sample space and event \( \boldsymbol{A} \) in set
notation.


Teflon polymer is formed by the polymerisation of
A \( \cdot C H_{2} C N-C N \)
в. \( F_{2} C=C F_{2} \)
c. \( C l_{2} C=C H_{2} \)
D. \( H_{2} C=C H C l \)


\( \ln \) an \( A C \) circuit, the potential difference
\( \boldsymbol{V} \) and current \( \boldsymbol{I} \) are given respectively by \( \boldsymbol{V}=\mathbf{1 0 0} \sin (\mathbf{1 0 0} \boldsymbol{t}) \boldsymbol{V} \)
and \( \boldsymbol{I}=\mathbf{1 0 0} \sin \left(\mathbf{1 0 0 t}+\frac{\boldsymbol{\pi}}{\mathbf{3}}\right) \boldsymbol{m} \boldsymbol{A} \)
The power dissipated in the circuit will be
A \( \cdot 10^{4} K W \)
в. \( 10 K W \)
c. \( 2.5 K W \)
D. \( 5 K W \)


If the difference between the C.I.
compounded half yearly and simple interest on a sum at \( 10 \% \) per annum for one year is Rs. 25 , the sum is:
A. Rs.9000
B. Rs.9500
c. \( R s, 10,000 \)
D. Rs.10,500


Solve the given inequalities graphically:
\( 2 x+y \geq 6 \) and \( 3 x+4 y \leq 12 \)


The value of \( \int_{0}^{\frac{\pi}{4}} \tan ^{2} \theta d \theta= \)
A \( \cdot \frac{\pi}{4}-1 \)
B. \( \frac{\pi}{4} \)
\( c \cdot 1-\frac{\pi}{4} \)
D. none of these


Differentiate between.
Lymphocytes and monocytes.


In a class of 75 students, 15 are above
average, 45 are average and the rest below average achievers. The probability that an above average achieving student fails is \( 0.005, \) that an average achieving student fails is 0.05
and the probability of a below average achieving student failing is \( 0.15 . \) If \( a \) student is know to have passed, what is
the probability that he is a below average achiever?


A metal carbonate \( X \) on reacting with an acid gives a gas which when passed through a solution Y gives the carbonate back. On the other hand, a
gas G that is obtained at anode during electrolysis of brine is passed on dry \( Y, \) it gives a compound Z,used for disinfecting drinking water. Identity \( \mathbf{X} \)
\( Y, G \) and \( Z . \) Also,write the chemical
reactions involved.


Three ketones with the formula \( C_{5} H_{10} O \)
are


Absolute scale of temperature is a
consequence of:
A. Boyles law
B. Charles law
c. Gay-Lussacs law
D. Grahams law


Methylene blue is adsorbed on
activated charcoal at \( 25^{0} C \) from its
aqueous solution. Which is the correct statement for this process?
A. The adsorption requires activation at \( 25^{\circ} \mathrm{C} \)
B. The adsorption is accompanied by a decrease in enthalpy.
c. The adsorption increases with increase of temperature.
D. The adsorption is irreversible.


If the first line of Lyman series has a wavelength \( 1215.4 A \), the first line of Balmer series is approximately
\( \mathbf{A} \cdot 4864 \hat{A} \)
в. \( 1025.5 \AA \)
c. \( 6563 \dot{h} \)
D. 6400 月


Choose the correct option.
\( \mathbf{A} \cdot \mathrm{CsH}>\mathrm{KH}>\mathrm{NaH}<\mathrm{LiH}(\text { Order of stability }) \)
B. \( H_{2} O<N H_{3}<C H_{4} \) (Order of dipole moment)
C \( \left.\cdot P H_{3}<A s H_{3}<N H_{3}<S b H_{3} \text { (Order of boiling point }\right) \)
D. \( x \ldots \ldots \ldots \ldots . . . H_{---} X, X=0>F>N>S>C \)
(Order of strength of H-bonding)


If a wire is stretched to make its length three times, its resistance will become
A. Three times
B. One-third
c. Nine times
D. One-ninth


Ashok went to a casino to play a card game. In each round, he happened to double the amount with himself and in
each round he gave Rs. \( x \) to his friend. At
the end of three rounds, he was left with
no money. If the amount he gave to his
friend in each round was Rs. 20 more
than the amount he started with, find
the amount (in Rs.) that he started with
A. 110
в. 120
\( c .130 \)
D. 140


Draw the structures of the following compounds:
1) Propionic acid
2) 2-chlorobutanoic acid
3) Trifluoro acetic acid
4) 4 -methoxypentanoic acid
5) 2-Bromobutanoic acid
6) Isobutyric acid
7) 2,2-dibromoheptanoic acid


\( (\cos (\log x) d x= \)
\( \mathbf{A} \cdot x[\cos (\log x)-\sin (\log x)]+c \)
B. \( \frac{x}{2}[\cos (\log x)-\sin (\log x)]+c \)
c. \( \frac{\log x}{2}[\cos x+\sin x]+c \)
D \( \cdot \frac{x}{2}[\cos (\log x)+\sin (\log x)]+c \)


The incorrect statement regarding the
lines of force of the magnetic field B is:
A. magnetic intensity is a measure of lines of force passing through unit area held normal to it.
B. magnetic lines of force form a closed curve.
C. inside a magnet, its magnetic lines of force move from north pole of a magnet towards its south pole.
D. magnetic lines of force never cut each other.


Complete the following ray diagram


The thermal capacity of \( 40 g \) of aluminium (specific heat =
\( 0.2 \mathrm{calg}^{-10} \mathrm{C}^{-1} \) ) is :
A \( \cdot 40 \) cal \( ^{\circ} C^{-1} \)
B . 160 cal \( ^{\circ} C^{-} \)
c. 200 cal' \( C^{-1} \)
D. 8 cal \( ^{\circ} \mathrm{C}^{-1} \)


Minimise \( Z=3 x+2 y \)
subject to the constraints:
\( \boldsymbol{x}+\boldsymbol{y} \geq \mathbf{8} \ldots(\mathbf{1}) \)
\( 3 x+5 y \leq 15 \dots(2) \)
\( \boldsymbol{x} \geq \mathbf{0}, \boldsymbol{y} \geq \mathbf{0} \ldots(\mathbf{3}) \)


The total surface area of a hollow
cylinder, which is open from both the
sides, is \( 3575 \mathrm{cm}^{2} \); area of its base ring
is \( 357.5 \mathrm{cm}^{2} \) and its height is \( 14 \mathrm{cm} \)
then the thickness of the cylinder is 3.5
\( \mathbf{c m} \)


A particle accelerates from rest at a constant rate for some time and attains
a velocity of \( 8 m / \) sec. Afterwards it
decelerates with the constant rate and
comes to rest. If the total time taken is
4 sec, the distance travelled is
A . \( 32 m \)
B. \( 16 m \)
\( c .4 m \)
D. None of the above


Find solution of following inequality also show it graphically.
\( \boldsymbol{x}<\mathbf{5}, \boldsymbol{x} \in \boldsymbol{W} \)
\( A \)
B.
\( c \)
\( D \)


What are isobars?
A. Atoms of different elements having same A but different Z
B. Atoms of same element having same A but different z
C. Atoms of different elements having different A but same \( z \)
D. Atoms of same element having different A but same \( z \)


If \( \left|z+\frac{2}{z}\right|=2, \) then the maximum value of \( |z| \) is \( \sqrt{m}+1 . \) Find \( m \)


Chloroform, on warming with \( \boldsymbol{A} \boldsymbol{g} \) powder, gives:
A. \( C_{2} H_{2} \)
в. \( C_{2} H_{4} \)
c. \( C_{2} H_{6} \)
D. \( C_{6} H_{6} \)


Let \( u, v \) and \( w \) be such that \( |u|= \)
\( \mathbf{1},|\boldsymbol{v}|=\mathbf{3} \) and \( |\boldsymbol{w}|=2 . \) If the projection
of \( v \) along \( u \) is equal to that of \( w \) along \( u \) and vectors \( v \) and \( w \) are perpendicular
to each other, then \( |\boldsymbol{u}-\boldsymbol{v}+\boldsymbol{w}| \) equals
A . 2
B. \( \sqrt{7} \)
c. \( \sqrt{14} \)
D. 14


Find the time taken by the boat to reach
the opposite bank.


If the sum of first 8 and 19 terms of an
A.P. are 64 and 361 respectively, find the common difference and sum of its n
terms.


Four different objects 1,2,3,4 are distributed at random in four places
marked \( 1,2,3,4 . \) What is the probability that none of the objects occupy the place corresponding to their number?
A \( \cdot \frac{17}{24} \)
в. \( \frac{3}{8} \)
c. \( \frac{1}{2} \)
D.


An organic compound A on reduction gives compound B, which on reaction with trichloro methane and caustic
potash forms C. The compound 'C' on catalytic reduction gives N-methyl benzenamine, the compound 'A' is :
A. nitrobenzene
B. nitromethane
c. methanamine
D. benzenaminç


There are 40 students in a class and
their results is presented as below:
Result (Pass/Fail) Pass Fail
Number of Students 30
If a student chosen at random out of the
class, find the probability that the student has passed the examination
A . 0.12
B. 0.36
c. 0.65
D. 0.75


In a city, three daily newspapers \( A, B, C \) are published, \( 42 \% \) read \( A ; 51 \% \) read \( B \); \( 68 \% \) read \( C ; 30 \% \) read \( A \) and \( B ; 28 \% \) read \( \mathrm{B} \) and \( \mathrm{C} ; 36 \% \) read \( \mathrm{A} \) and \( \mathrm{C} ; 8 \% \) do not read any of the three newspapers.
What is the percentage of persons who read only one paper?
\( A .38 \% \)
в. \( 48 \% \)
\( c .51 \% \)
D. None of the above


An artificial satellite is used for :
A. communication
B. weather monitoring
c. remote sensing
D. all the above


According to Darwin, adaptive ability is
:-
A. Acquired
B. Mutation
c. Inherited
D. Branching descent


In a class of 60 students, 45 students
like music, 50 students like dancing, 5 students like neither. Then the number
of students in the class who like both
music and dancing is
A . 35
B. 40
c. 50
D. 55


A dwarf pea plant was treated with gibberellic acid (GA), it grew as tall as the homozygous tall pea plant. If this GA-treated plant is now crossed with a pure tall pea plant then the phenotypic ratio in the next generation is likely to be
A. All dwarf.
B. 50\% dwarf, 50\% tall.
c. 75\% tall, 25\% dwarf
D. All tall


Two identical glass \( \left(\mu_{g}=\frac{3}{2}\right) \) equiconvex lenses of focal length fare
kept in contact. The space between the two lenses is filled with water \( \left(\mu_{w}=\frac{4}{3}\right) . \) The focal length of the combination is :
A. \( f \)
в. \( \frac{f}{2} \)
c. \( \frac{4 f}{3} \)
D. \( \frac{3 f}{4} \)


Calculate the perimeter and area of the
shapes.
Perimeter


A lamp of \( 6 \mathrm{V} \) and \( 30 \mathrm{W} \) is used in a laboratory but the supply is of \( 120 \mathrm{V} \) what will be done to make use of the
lamp?
(1) A resistance may be used
(2) A resistance may be used in series with lamp.
(3) The resistance should be of \( 18 \Omega \)
A. 1,2 and 3 are correct
B. 1 and 2 are correct
c. 1 and 3 are correct
D. 2 and 3 are correct


The value of \( \frac{1}{(2 n-1) ! 0 !}+ \)
\( \frac{1}{(2 n-3) ! 2 !}+\frac{1}{(2 n-5) ! 4 !}+\dots+ \)
\( \frac{1}{1 !(2 n-2) !} \) equal to
A \( \cdot 2^{2 n-1} \)
B. \( 2^{2 n-2} \)
\( \mathrm{c} \cdot 2^{2 n-3} \)
D. \( \frac{2^{2 n-2}}{(2 n-1) !} \)


There are two samples \( A \) and \( B . A \) is
Methanol and \( B \) is Ethanol. Both are
heated both at the same rate in closed
container separately. Which one is correct about the above test?
A \( \cdot \) At \( 60^{\circ} \mathrm{C} \), container \( A \) and \( B \) both have liquids in them
B. At \( 80^{\circ} \) C, container \( A \) and \( B \) both have vapours in them
C. At \( 70^{0} \mathrm{C} \), container \( B \) has liquid and \( A \) has vapours
D. All the above


Find the value of \( x \) when \( D E \| A B \)
A. 8
\( B \)
\( c \cdot 16 \)
D. none


Greenhouse gas \( C O_{2} \) can be converted
to \( C O(g) \) by the following reaction
\( \boldsymbol{C O}_{2}(\boldsymbol{g})+\boldsymbol{H}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{C O}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \)
termed as water gas reaction.
\( \Delta G \) for the reaction at \( 1000 \mathrm{K} \) is :
\( \left(\Delta H_{1000} K=\right. \)
\( \mathbf{3 5 0 4 0} \boldsymbol{J} \boldsymbol{m o l}^{-1} ; \boldsymbol{\Delta} \boldsymbol{S}_{1000} \boldsymbol{K}= \)
\( \left.32.11 J m o l^{-1} K^{-1}\right) \)
A. \( 2930 J \)
\( J \)
B. 2934 J
c. \( 2300 J \)
D. None of these


Which of the following lens is used to minimise hypermetropia?
A. Convex lens
B. Concave lens
c. Cylindrical lens
D. Planar lens


Assertion
If \( \lim _{\boldsymbol{x} \rightarrow \mathbf{0}} \boldsymbol{f}(\boldsymbol{x}) \) and \( \lim _{\boldsymbol{x} \rightarrow \mathbf{0}} \boldsymbol{g}(\boldsymbol{x}) \) exists finitely
\( \operatorname{then} \lim _{x \rightarrow 0} f(x) \cdot g(x) \) exists finitely
Reason
If \( \lim _{x \rightarrow 0} f(x) \cdot g(x) \) exists finitely then
\( \lim _{x \rightarrow 0} f(x) \cdot g(x)=\lim _{x \rightarrow 0} f(x) \cdot \lim _{x \rightarrow 0} g(x) \)
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 and Reason is correct


A body of mass \( 2 k g \) is lying on a floor
The coefficient of static friction is 0.54
What will be the value of frictional force
if the force is \( 2.8 N \) and \( g=10 m s^{-2} ? \)
A . zero
в. \( 2 N \)
\( c .2 .8 N \)
D. \( 8 N \)


Match the entries in column A with
appropriate ones from column B.


The inequality \( n !>2^{n-1} \) is true
\( A \). For all \( n>1 \)
B. For all \( n>2 \)
c. For all \( n \epsilon N \)
D. None of these


All nucleic acids are
A. Polymers of nucleotides
B. Polymers of amino acids
C. Double - stranded
D. Double - helical and contain deoxyribose


When \( H_{2} O_{2} \) reacts with ozone, and
forms \( H_{2} O \) and \( O_{2} . \) In this reaction \( O_{2} \)
is released by:
This question has multiple correct options
A \( . H_{2} O \)
в. \( O_{3} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{O}_{2} \)
D. \( O_{2} \)


Find the area enclosed between the
parabola \( 4 y=3 x^{2} \) and the straight line
\( 3 x-2 y+12=0 \)


What is the oxidation state of sulphur in the following.
a) \( \boldsymbol{S F}_{\mathbf{6}} \)
b) \( N a_{2} S_{2} O_{3} \)


Which part of the flower forms the fruit?
A. Whole flower
B. Only stamens and carpel
c. Only ovary
D. only carpel


Rakesh went to a stationary shop to
purchase a total of 38 pens, erasers and sharpeners. He purchased at least 11 items of each. He purchased more sharpeners than erasers and more
erasers than pens. How many pens did he purchase?
A . 11
B. 12
c. 13
D. 14


Q Type your question-
reaction:
\( 4 C O(g)+8 H_{2}(g) \longrightarrow 3 C H_{4}(g)+ \)
\( \boldsymbol{C O}_{2}(\boldsymbol{g})+\boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \)
Given that
\( \boldsymbol{C}(\text {graphite})+\mathbf{1} / \mathbf{2 O}_{2}(\boldsymbol{g}) \longrightarrow \)
\( \boldsymbol{C O}(\boldsymbol{g}) ; \boldsymbol{\Delta} \boldsymbol{H} / \boldsymbol{k} \boldsymbol{J}=-110.5 \boldsymbol{k} \boldsymbol{J} \)
\( \boldsymbol{C O}(\boldsymbol{g})+\mathbf{1} / \mathbf{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \)
\( \boldsymbol{C O}_{2}(\boldsymbol{g}) ; \boldsymbol{\Delta} \boldsymbol{H} / \boldsymbol{k} \boldsymbol{J}=-\boldsymbol{2} \boldsymbol{8} \boldsymbol{2} . \boldsymbol{9} \boldsymbol{k} \boldsymbol{J} \)
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\mathbf{1} / 2 \boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \)
\( \boldsymbol{H}_{2} \boldsymbol{O}(l) ; \boldsymbol{\Delta} \boldsymbol{H} / \boldsymbol{k} \boldsymbol{J}=-\boldsymbol{2} \boldsymbol{8} \boldsymbol{5} . \boldsymbol{8} \boldsymbol{k} \boldsymbol{J} \)
\( \boldsymbol{C}(\boldsymbol{g} \boldsymbol{r} \boldsymbol{a} \boldsymbol{p} \boldsymbol{h} \boldsymbol{i} \boldsymbol{e})+\boldsymbol{2} \boldsymbol{H}_{2}(\boldsymbol{g}) \longrightarrow \)
\( \boldsymbol{C H}_{4}(\boldsymbol{g}) ; \boldsymbol{\Delta} \boldsymbol{H} / \boldsymbol{k} \boldsymbol{J}=-\mathbf{7 4 . 8 k J} \)
A \( .584 .9 \mathrm{kJ} \mathrm{mol}^{-1} \)
в. \( 279.8 \mathrm{kJ} \mathrm{mol}^{-1} \)
c. \( 747.4 \mathrm{kJ} \mathrm{mol}^{-1} \)
D. 925 kJ mol \( ^{-1} \)


What will be the value of the magnetic field at the centre in the given figure? The coil is made of a uniform wire and
is connected with two long straight
wires. Assumes r is the radius of coil.
A \( \cdot \frac{\mu_{0}}{4 \pi}\left[\frac{i}{r}\right] \)
в. \( \frac{\mu_{0}}{4 \pi}\left[\frac{2 \pi i}{r}\right] \)
c. \( \frac{\mu_{0}}{4 \pi}\left[\frac{2 i}{r}+\frac{2 \pi i}{r}\right] \)
\( D \)


Betaine \( C_{5} H_{11} O_{2} N, \) occurs in beet sugar molasses. It is water soluble solid
that melts with decomposition at
\( 300^{\circ} \mathrm{C} . \) It is unaffected by a base but
reacts with hydrochloric acid to form a
crystalline product \( C_{5} H_{12} O_{2} N C l . \) It can be made from glycine with methyl iodide or treatment of chloroacetic acid
with trimethyl amine. Draw structure
for betaine which will account for all
properties given above.


What do you molar by electric change?


9.2 grams of \( N_{2} O_{4}(g) \) is taken in a
closed one litre vessel and heated till
the following equilibrium is reached,
\( N_{2} O_{4}(g) \rightleftharpoons 2 N O_{2}(g) . \) At equilibrium,
\( 50 \% N_{2} O_{4}(g) \) is dissociated. What is
the equilibrium constant? (in \( M) \)
(molecular weight of \( N_{2} O_{4}=92 \) )
A . \( 0 . \)
B. 0.4
c. 0.3
D. 0.2


Organisms that can prepare their own food.
A. Autotrophs
B. Heterotrophs
c. Phototrophs
D. None of the above


What is pH formula?
A. \( -\log _{e}\left[H^{+}\right] \)
B. \( -\log _{10}\left[H^{-}\right] \)
c. \( -\log _{10}\left[O H^{-}\right] \)
D. \( -\log _{10}\left[H^{+}\right] \)


The bottom of glass beaker is made of a
thin equiconvex lens having bottom
side silver polished as shown in fig. Now the water is filled in the beaker up to a
height of \( h=4 m . \) The image of point
object floating at middle point of beaker at the surface of water coincides with it.
Find out the value of radius (in \( \mathrm{m} \) ) of
curvature of lens. \( \left(a \boldsymbol{\mu}_{\boldsymbol{g}}=\mathbf{3} / \mathbf{2},_{\boldsymbol{a}} \boldsymbol{\mu}_{\boldsymbol{w}}=\right. \)
\( \mathbf{4} / \mathbf{3}) \)


The elements having more masses were placed before elements having lower masses in Mendleev's periodic table. Guess the pair of elements (higher mass, lower mass)
A. Cobalt, Nickel
B. Vanadium, Chromium
c. Tellurium, lodine
D. All of the above


If \( 3 x+\frac{1}{3 x}=3 \) find \( 9 x^{2}+\frac{1}{9 x^{2}} \)


A thermos bottle containing coffee is vigorously shaken. If the coffee is considered as a system, then the temperature of the coffee will
A. increase slightly
B. fall
c. remain the same
D. never be determined


The chord of a \( \odot(0,5) \) touches \( \odot(0,3) \)
The length of the chord is
\( \mathbf{A} \cdot \mathbf{8} \)
B. 6
\( c \cdot 7 \)
D.


Prove that \( \frac{1}{2} \cos ^{-1}\left(\frac{1-x}{1+x}\right)=\tan ^{-1} \sqrt{x} \)


In a covalent bond formation:
A. transfer of electrons takes place
B. equal sharing of electrons between two atoms takes place
C . electrons are shared by one atom only
D. electrons are donated by one atom and shared by both atoms.


Intake of more food than necessary
causes


Aluminium is extracted by:
A. Heating sodium aluminium silicate to a high temperature
B. Treating cryolite with sodium hydroxide solution under
pressure
C. Heating aluminium oxide with coke in a furnace
D. The electrolysis of molten aluminium oxide in fused cryolite


Main disadvantage of intrauterine
contraceptive devices is,
A. the devices are permanently placed in Uterus and cannot be removed even if couple want to have children
B. the device has to be inserted by physician in the uterus through vagina
c. the devices are expelled out without the knowledge of the wearers
D. both (a) and (c)


The environmental factor that
influences the elongation of polypeptide chain is
A. Light
B. Oxygen
c. Humidity
D. Temperature


The position vector of a particle changes with time according to the relation \( \vec{r}(t)=15 t^{2} \hat{i}+\left(4-20 t^{2}\right) \hat{j} \)
What is the magnitude of the acceleration at \( t=1 ? \)
A . 40
в. 100
c. 25
D. 50


Ethyl alcohol fermentation occurs in
A. Lactobacillus
B. Muscles of Humans
c. Rhizopus
D. All of these


The value of \( x \) if \( 4,6, x \) are in GP
A. 9
B. 5
\( c . \pi \)
D. \( \frac{22}{7} \)


Which of the following is a mixed gland?
A. Thyroid gland
B. Adrenal gland
c. Pituitary gland
D. Pancreas


\( 2^{x}-2^{x} \)
\( \frac{d}{x} \)


A metal on combustion in excess air
forms \( X, X \) upon hydrolysis with water
yields \( H_{2} O_{2} \) and \( O_{2} \) along with another
product. The metal is:
\( A \cdot R b \)
в. \( N a \)
c. \( M g \)
D. \( L i \)


What shows the sequence of organs through which urea passes as it travels from where it is produced to where it is removed from the blood?
A. Kidneys \( \rightarrow \) Heart \( \rightarrow \) Lungs \( \rightarrow \) Heart \( \rightarrow \) Liver
B. Kidneys \( \rightarrow \) Heart \( \rightarrow \) Liver \( \rightarrow \) Lungs \( \rightarrow \) Heart
c. Liver \( \rightarrow \) Heart \( \rightarrow \) Lungs \( \rightarrow \) Heart \( \rightarrow \) Kidneys
D. Liver \( \rightarrow \) Lungs \( \rightarrow \) Heart \( \rightarrow \) Kidneys \( \rightarrow \) Heart


Genetic information in a DNA molecule
is coded by the
A. Sequence of nucleotides
B. Base pairing
c. Turning pattern of the helix
D. Proportion of each base present


Assertion
ADH and RAAS work in response to low
blood volume and blood pressure.
Reason
ANF works in response to high blood
volume and blood pressure.
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 block is moved from A to C along
three different paths. Find the Work done by friction when the block is
displaced from \( A \) to \( B \) and then from \( B \) to
\( \mathrm{C} \)
A. \( W=-\mu m g(a+b) \)
в. \( W=-\mu m g \)
C. \( W=-\mu m g(a+b) / 2 \)
D. None of the above


A ball is dropped off a high building and strikes the ground with an impact velocity of \( 30 \mathrm{m} / \mathrm{s} \). Calculate the height of building:
\( A \cdot 15 \mathrm{m} \)
B. 20 \( \mathrm{m} \)
c. 30 \( m \)
D. 45 \( m \)
E. \( 60 \mathrm{m} \)


Using ASA congruence. What is the
ength of \( \boldsymbol{P Q} \) ?
\( A \cdot 9 \)
3. 10
\( c \cdot 12 \)
D. 14


A potential energy function for a twodimensional force is of the form \( U= \)
\( 3 x^{2} y-7 x . \) Find the force that acts at
the point \( (x, y) \)


Given \( \boldsymbol{A}=\{\mathbf{5}, \mathbf{6}, \mathbf{7}\} \) and \( \boldsymbol{B}=\{\mathbf{3}, \mathbf{4}\} \)
Form all possible ordered pairs and write the total number of ordered pairs formed. So that :
Both the components are from A
Find the total number of such pairs.


Figure below shows two infinitely long
and thin current carrying conductors \( \boldsymbol{X} \)
and \( Y \) kept in vacuum, parallel to each
other, at a distance \( ^{\prime} a \)

How much force per unit length acts on
the conductor \( Y \) due to the current
flowing through \( X ? \) Write your answer in terms of \( \left(\frac{\mu_{0}}{4 \pi}\right), I_{1}, I_{2} \) and \( a \)
(Derivation of formula is not required)


A ball of mass \( m=1 \mathrm{kg} \) strikes smooth
horizontal floor as shown in figure. The
impulse exerted on the floor is
A. 6.25 Ns
B. 1.76 Ns
c. \( 7.8 \mathrm{Ns} \)
D. 2.2 Ns


\( \boldsymbol{C H} \equiv \boldsymbol{C H} \) is more electronegative as
compared to \( C H_{2} \equiv C H_{2} \) Explain.


What are fossils? What do they tell us
about evolution? How do we determine
the age of fossils?


Among \( 0.1 ~ M \) solutions of
\( N a C l, C a C l_{2} \) and \( A l_{2}(S O)_{3}, \) the one with highest vapour pressure is:
A \( . N a C l \)
в. \( C a C l_{2} \)
c. \( A l_{2}(S O)_{3} \)
D. All have equal vapour pressure


Which of the following statements is
wrong about the following reaction?
PhO \( \boldsymbol{E} \boldsymbol{t} \frac{1 . \boldsymbol{B} \boldsymbol{B} \boldsymbol{r}_{3}}{\boldsymbol{2} \cdot \boldsymbol{H}_{2} \boldsymbol{O}} \) Products
\( \mathbf{A} \cdot B B r_{3} \) plays a role similar to the \( H \) in \( H I \) by forming a complex with the ether
B. The liberated \( B r \) attacks \( E t \), displacing \( P h O B B r_{2} \) which is ultimately hydrolysed to give the products
C . The products are \( P h O H+E t B r+H_{3} B O_{3} \)
D. The products are \( P h B r+E t O H+H_{3} B O_{3} \)


When a gold sheet is bombarded by a beam of \( \alpha \) -particles, only a few of them
get deflected whereas most go straight,
undeflected because:
This question has multiple correct options
A. the force of attraction exerted on the \( \alpha \) -particles by the oppositely charged electrons is not sufficient
B. a nucleus has a much smaller volume than that of an atom
c. the force of repulsion acting on the fast-moving \( \alpha \) particles is very small
D. the neutrons in the nucleus do not have any effect on the \( \alpha \) -particles


By passing electric current, \( N a C l O_{3} \) is
converted into \( N a C l O_{4} \) according to
the following equation \( N a C l O_{3}+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{N} \boldsymbol{a} \boldsymbol{C l} \boldsymbol{O}_{4}+\boldsymbol{H}_{2} \)
How many moles of \( N a C l O_{4} \) will be
formed when three Faradays of charge
is passed through \( N a C l O_{3} ? \)
A . 1.5
в. 1.0
\( c .3 .0 \)
D. 0.75


What is an earthquake? List the precautions that need, to be taken during an earthquake if one is staying indoors or outdoors.


For \( _{24} C r, \) which of the following statements is/are correct?

This question has multiple correct options
A. Number of electrons with principle quantum number is 13
B. Number of electrons with azimuthal quantum number is 12
c. Number of electrons with magnetic quantum number 0 is 12
D. Number of minimum or maximum electrons with spin quantum number \( +1 / 2 \) is 9 or 15


When a liquid is flowing through a tube or variable diameter, the pressure is?
A. Maximum where the velocity is maximum
B. Maximum where the velocity is minimum
c. Minimum where the velocity is minimum
D. None of the above is correct


Catalytic hydrogenation of ethene produces
A. Ethane
B. Acetylene
c. Methane
D. Ethyne


Can we measure a resistance of the
order of \( 0.160 \Omega \) using a Wheatstone's
bridge? Support your answer with reasoning?


Using ruler and compasses only, construct an isosceles \( \Delta A B C \)
in which \( B C=5 \mathrm{cm}, A B=A C \) and
\( \angle B A C=90^{0} \) Locate the point \( P \) such
that:
(i) \( P \) is equidistant from \( B C \) and \( A C \)
(ii) \( P \) is equidistant from \( B \) and \( C \)


The strength of the Earth's magnetic field is?
A. Constant everywhere
B. Zero everywhere
c. Having very high value
D. Varying from place to place on the Earth's surfact


The capacitive reactance of a condenser
of capacity \( 25 \mu \mathrm{F} \) for an \( \mathrm{AC} \) of frequency
\( 4000 \mathrm{Hz} \) will be
A \( \cdot \frac{5}{\pi} \Omega \)
в. \( \frac{10}{\pi} \Omega \)
c. \( 5 \pi \Omega \)
D. \( \frac{\pi}{5} \Omega \)


Find the first term and common
difference in the given sequence:
\( \frac{3}{2}, \frac{1}{2},-\frac{1}{2},-\frac{3}{2}, \dots \)


Any article of iron if left in open for some
time, acquires a film of brownish
substance (rust) having chemical formula:
\( \mathbf{A} \cdot F e_{3} O_{4} \)
в. \( F e_{2} O_{3} \)
c. Feo
D. \( \operatorname{Fe}(O H)_{2} \)


Why are ball bearings used in machinery?


Let \( \boldsymbol{f}(\boldsymbol{x})=[\boldsymbol{x}] \) and \( \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{x}-[\boldsymbol{x}], \) then
which of the following is false?
A \( \cdot(f+g)(x)=x \)
в. \( (f o g)(x)=0 \)
c. \( (g o f)(x)=0 \)
D. None of these


Which of the following is always true regarding the spontaneity of reaction occuring in a galvanic cell?
A \( \cdot E^{0}_{c e l l}>0, \Delta G^{0}<0 \) and \( Q>K_{c} \)
B . \( E^{0}_{c e l l}>0, \Delta G^{0}<0 \) and \( Q<K_{c} \)
C \( \cdot E_{\text {cell }}^{0}>0, \Delta G^{0}>0 \) and \( Q>K_{c} \)
D . \( E^{0}_{c e l l}>0, \Delta G^{0}>0 \) and \( Q<K_{c} \)


Coffee is coming out from a conical filter, with height and diameter both \( 25 \mathrm{cm} \) into a cylindrical coffee pot with
diameter \( 15 \mathrm{cm} . \) The constant rate at
which coffee comes out from the filter
into the pot is \( 100 \mathrm{cm}^{3} / \) min. The rate in
cm / min at which the level in the pot is rising at the instance when the coffee in the pot is \( 10 \mathrm{cm} \), is
A \( \cdot \frac{9}{16 \pi} \)
В \( \cdot \frac{25}{9 \pi} \)
c. \( \frac{5}{3 \pi} \)
D. \( \frac{16}{9 \pi} \)


A bag contains 4 balls. Two balls are
taken out without replacement and found to be white. Find the probability that all the balls of the bag are white.


A sphere \( A \) moving with speed \( u \) and
rotating with an angular velocity \( \omega \)
makes a head-on elastic collision with
an identical stationary sphere \( \boldsymbol{B} \). There
is no friction between the surfaces of \( \boldsymbol{A} \)
and \( B . \) Choose the correct
alternative(s). Discard gravity.
This question has multiple correct options
A. \( A \) will stop moving but continue to rotate with an angular velocity \( \omega \)
B. \( A \) will come to rest and stop rotating
C. \( B \) will move with speed \( u \) without rotating
D. \( B \) will move with speed \( u \) and rotate with an angular velocity \( \omega \)


What is Reverberation? and How it can
be reduced in an Auditorium?


Match the following:
Set- Set - II
A) Tear gas
1)
\( \left[\boldsymbol{C}_{2} \boldsymbol{H}_{4} \boldsymbol{C l}\right]_{2} \boldsymbol{S} \)
B) Musturd gas
2) \( C O C l_{2} \)
C) Phosgene
3) \( C C l_{3} N O_{2} \)
D) Teflon
4) \( \left(C_{2} F_{4}\right)_{n} \)
A. \( A-3, B-1, C-2, D-4 \)
в. \( A-1, B-2, C-4, D-3 \)
c. \( A-2, B-3, C-4, D-1 \)
D. \( A-4 . B-2, C-1, D-3 \)


Out of the following ores, how many ores
do not contain more than one metal in
their composition. Argentite, Barytes, Magnesite, Fluorspar, Carnalite, Dolomite, Chalcocite, Asbestos, Calamine.
\( A \cdot 6 \)
B. 4
\( c \cdot 5 \)
\( D \)


Q Type your question
ルIVA
A. Uraci
B. Cytosine
C. Guanine
D. Thymine


If \( \frac{(1+i)^{2}}{2-i}=x-i y, \) then find the value of \( \boldsymbol{x}+\boldsymbol{y} \)


The cathode used in the electrolytic cell during aluminium extraction is made
of
A. aluminium
B. carbon lining
\( c . \) iron
D. steel


The hydrophilic end of synthetic
detergent is:
A. \( C H_{3}\left(C H_{2}\right)_{10}-C H_{2}- \)
в. \( -C H_{3} \)
\( \mathrm{c} .-C H_{2}-C H_{3} \)
D. \( -C O O^{-} N a^{+} \)


Calculate the net flux emerging from
gives enclosed surface \( -N m^{2} \quad C-1 \)
A \( \cdot 4.5 \times 10^{11} \)
B . \( 45 \times 10^{12} \)
c. zero
D. \( 1.12 \times 10^{12} \)


Megakaryocytes, special cells in the
bone marrow that produce cell fragments are called:
A. Leucocytes
B. Erythrocytes
c. Thrombocytes
D. Fibrinogen


Yamini and Fatima, two students of
Class IX of a school, together contributed Rs 100 towards the
Prime Minister's Relief Fund to help the earthquake victims. Write a linear equation which the given data will satisfy and also plot its graph.
A. \( x+y=100 \)
в. \( x+y=112 \)
c. \( x+y=50 \)
D. \( x+2 y=100 \)


Calculate the values of the
determinants:
\( \left|\begin{array}{lll}\boldsymbol{a} & \boldsymbol{h} & \boldsymbol{g} \\ \boldsymbol{h} & \boldsymbol{b} & \boldsymbol{f} \\ \boldsymbol{g} & \boldsymbol{f} & \boldsymbol{c}\end{array}\right| \)


Subtract the first rational number from
the second in each of the following:
\( \frac{1}{4}, \frac{-3}{8} \)


For a coil having \( L=2 m H, \) current
flow through it is \( I=t^{2} e^{-t} \) then the
time at which emf becomes zero:
\( \mathbf{A} \cdot 2 \sec \)
B. 1 sec
\( \mathbf{c} \cdot 4 \sec \)
D. 3 sec


Which one of the following statements
is correct?
A. Hybrid orbitals do not form \( \sigma \) bonds
B. Lateral overlap of p-orbitals or p- and d- orbitals produces \( \pi \) bonds
c. The strength of bonds follows the order
\( \sigma_{p-p}<\sigma_{s-s}<\pi_{p-p} \)
D. s-orbitals do not form \( \sigma \) bonds


A gas mixture contains \( 24 \% \) nitrogen, \( 32 \% \) oxygen and remaining is hydrogen by volumes at a given temperature and pressure then what is the mole fraction
of hydrogen? (assume there is no reaction between
the gases)
A .0 .44
B. 0.24
c. 0.91
D. 0.56


If \( \cos ^{-1} x+\cos ^{-1} y+\cos ^{-1} z=\pi \) then,
prove that \( x^{2}+y^{2}+z^{2}+2 x y z=1 \)


With in each set, select the compound which is more reactive to nucleophilic addition at carbonyl carbon.
\( (I) C H_{3} C O C H_{2} C H_{2} B r \) or \( C H_{3} C O C \)
\( (\boldsymbol{I I}) \boldsymbol{C H}_{3} \boldsymbol{C H O} \) or \( \boldsymbol{C H}_{3} \boldsymbol{C O C H}_{3} \)
\( (I I I) C H_{3} C O C H_{3} \) or \( C H_{3} C O C F_{3} \)
\( (I V) P h C H O \) or \( C H_{3} C H O \)


Zeatin has been obtained from
A. Wheat
B. Rice
c. Maize
D. Oat


The line passes through the points \( (5,1, a) \&(3, b, 1) \) crosses the \( y z \) plane at the point \( \left(0, \frac{17}{2},-\frac{13}{2}\right), \) then
A \( . a=4, b=6 \)
B. \( a=6, b=4 \)
c. \( a=8, b=2 \)
D. \( a=2, b=8 \)
8


A steel wire of diameter \( 1 \times 10^{-3} \) m is
stretched by a force of \( 20 N . \) Calculate
the strain energy per unit volume. \( (Y \)
steel \( \left.=2 \times 10^{11} N / m^{2}\right) \)


Are the following statements true or false? Given reasons for your answer. Every rational number is a whole
number.
A. True
B. False


The value of \( \boldsymbol{S}=\sqrt{\mathbf{1}+\frac{\mathbf{1}}{\mathbf{1}^{2}}+\frac{\mathbf{1}}{\mathbf{2}^{2}}}+ \)
\( \sqrt{1++\frac{1}{2^{2}}+\frac{1}{3^{2}}}+\ldots+ \)
\( \sqrt{1++\frac{1}{(2014)^{2}}+\frac{1}{(2015)^{2}}} \)
A . 2015
в. \( _{2015}-\frac{1}{2015} \)
c. \( _{2016}-\frac{1}{2016} \)
D. \( _{2014}-\frac{1}{2014} \)


When potassium ferrocyanide crystal are heated with concentrated sulphuric acid,the gas evolved as?
A. carbon monoxide
B. sulphur dioxide
c. ammonia
D. carbon dioxide


The output of OR gate is 1:
A. If either one or both inputs are 1
B. Only if both inputs are 1
C. If either input is zero
D. If both inputs are zero


Out of 50 tickets numbered
\( 00,01,02, \ldots ., 49 \) one ticket is drawn randomly, the probability of the ticket
having the product of its digits 7 given that the sum of the digits is \( 8, \) is
A \( \cdot \frac{1}{14} \)
B. \( \frac{3}{14} \)
\( c \cdot \frac{1}{5} \)
D. None of these


Sanguivores are
A. Animals which mainly depend on fruits
B. Animals which feed on the blood of other animals
C. Animals which feed on organic matter present in soil
D. Insect eating animals


A line passes through the points (6,-7,-1) and \( (2,-3,1) . \) The direction cosines of the line so directed that the
angle made by it with the positive direction of x-axis is acute, is?
A \( \cdot \frac{2}{3},-\frac{2}{3},-\frac{1}{3} \)
B. \( -\frac{2}{3}, \frac{2}{3}, \frac{1}{3} \)
c. \( \frac{2}{3},-\frac{2}{3}, \frac{1}{3} \)
D. \( \frac{2}{3}, \frac{2}{3}, \frac{1}{3} \)


A proton is moving with velocity \( 10^{4} m / s \) parallel to the magnetic field of
intensity 5 tesla.The force on the proton
is
A. \( 8 \times 10^{15} N \)
B . \( 10^{4} N \)
c. \( 1.6 \times 10^{-19} N \)
D. zero


The correct order for homolytic blood dissociation energies \( (\Delta H \) in \( k c a l / m o l \) ) for
\( \boldsymbol{C H}_{4}(\boldsymbol{A}), \boldsymbol{C}_{2} \boldsymbol{H}_{6}(\boldsymbol{B}), \boldsymbol{C H}_{3} \boldsymbol{B r}(\boldsymbol{C}) \) is
\( \mathbf{A} \cdot C>B>A \)
В. \( B>C>A \)
c. \( C>A>B \)
D. \( A>B>C \)


If \( 5 x+6=10, \) what is the value of
\( 10 x+3 ? \)
\( A \cdot 4 \)
B. 9
\( c \cdot 11 \)
D. 20


Find the following squares by using the
identities.
\( (0.4 p+0.5 q)^{2} \)


In a thermo-nuclear reaction, \( 10^{-3} \mathrm{Kg} \) of
Hydrogen is converted into \( 0.99 \times 10^{-3} \)
kg of Helium. If the efficiency of the generator is \( 50 \% \), the electrical energy
generated in KWH is
A \( \cdot 10^{5} \)
B . \( 1.5 \times 10^{5} \)
c. \( 1.25 \times 10^{5} \)
D. \( 1.3 \times 10^{5} \)


Two positive point charges of \( 12 \mu C \) and
\( 8 \mu C \) are \( 10 c m \) apart. The work done in
bringing them \( 4 c m \) closer is
A . \( 5.8 . J \)
B. \( 5.8 e V \)
c. \( 13 . J \)
D. \( 13 e V \)


Assuming that the seventh period is 32 members long, what should be the atomic number of the noble gas following radon \( (R n) ? \)
A. 120
в. 118
c. 116
D. 122


The points (6,2),(2,5) and (9,6) form the vertices of a \( _{--} \) triangle.
A . right
B. equilateral
c. right isosceles
D. scalene


A bulb is placed between two plane
mirrors inclined at an angle of \( 60^{0} \). The number of images formed is :
\( \mathbf{A} \cdot \mathbf{5} \)
B. 6
\( c \cdot 4 \)
D. 3


IUPAC name of \( \boldsymbol{N} \boldsymbol{a}_{3}\left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{O}_{2}\right)_{6}\right] \) is:
A. Sodium cobaltinitrite
B. Sodium hexanitrocobaltate(III)
c. Sodium hexanitrocobalt(III)
D. Sodium hexanitrocobaltate


The distance of the point (1,1,1) from
the plane passing through the points (2,1,1),(1,2,1) and (1,1,2) is
A \( \cdot \frac{1}{\sqrt{3}} \)
B.
\( c \cdot \sqrt{3} \)
D. None of these


Find the equation of a circle.
(i) Which touches both the axes at a
distance of 6 units from the origin.
(ii) Which touches x-axis at a distance
5 from the origin and radius 6 units.
(iii) Which touches both the origin,
radius 17 and ordinate of the centre is
-15
(iv) Passing through the origin, radius
17 and ordinate of the centre is -15


Which one of the following has plantings life cycle?
A. Funaria
B. Polytrichum
c. ustilago
D. Triticum


The number of solutions of the equation \( |\cos x|=2[x] \) are (where [.] denotes the
greatest integer function) is/are
\( A \cdot 0 \)
B.
\( c \cdot 2 \)
D. 3


The moon is at a distance of \( 4 \times 10^{8} m \)
from the earth. What is the nature of
radar signal transmitted from earth?
A. Remain fixed
B. Vibrate to and fro about their mean position
c. Move along the wave
D. change their positions permanently


Which one of the following is the correct matching of three items and their grouping category?
A. Actin, myosin, rhodopsin : Muscle proteins
B. cytosine, uracil, thiamine : Pyrimidines
c. Malleus, incus, cochlea : Ear ossicles
D. None of these


The above structures are isomers.
A. True
B. False


Find the ratio \( m_{1}: m_{2} ? \)
\( A \)
B. \( \sqrt{2} \)
c. \( 1 / \sqrt{2} \)
D. 2


The best vital force theory was proposed
by?
A. Godlewski
B. Strasburger
c. Dixon
D. Esau


Why is nitric acid added to sodium
extract before adding silver nitrate for testing halogens?


Compensation point is
A. Where there is neither photosynthesis nor respiration
B. When rate of photosynthesis is equal to the rate of respiration
C. When entire food synthesized into photosynthesis remain utilized
D. When there is enough water just to meet the requirement of plant


The circumstance of first of hydrogen
atom is s.Then the Broglie wavelength of electron to that orbit is
A \( \cdot \frac{S}{2} \)
в. \( 2 S \)
\( c . s \)
D. \( 3 S \)


\( \operatorname{Let} \int_{0}^{a} f(x) d x=\lambda \) and
\( \int_{0}^{a} \boldsymbol{f}(\boldsymbol{2} \boldsymbol{a}-\boldsymbol{x}) \boldsymbol{d} \boldsymbol{x}=\boldsymbol{\mu} \)
Then \( \int_{0}^{2 a} f(x) d x \) is equal to?
\( A \cdot \lambda+\mu \)
B. \( \lambda-\mu \)
\( c \cdot 2 \lambda-\mu \)
D. \( \lambda-2 \mu \)


A car priced at \( R S 3600 \) is reduced by
\( 25 \% \). What is the reduced price?


Solve the following system of equations:
\( \mathbf{8} \boldsymbol{v}=\mathbf{3} \boldsymbol{u}+\mathbf{5} \boldsymbol{u} \boldsymbol{v} \)
\( \mathbf{6} \boldsymbol{v}-\mathbf{5} \boldsymbol{u}=-\mathbf{2} \boldsymbol{u} \boldsymbol{v} \)


An air tight container having a lid with
negligible mass and an area of \( 8 \mathrm{cm}^{2} \) is
partially evacuated. If a \( 48 \mathrm{N} \) force is required to pull the lid off the
container and the atmospheric
pressure is \( 1.0 \times 10^{5} \) Pa, the pressure in the container before it is opened must
be:
A . \( 0.6 a t m \)
B. \( 0.5 a t m \)
c. \( 0.4 a t m \)
D. \( 0.2 a t m \)


A tennis racket can be idealized as a
uniform ring of mass \( \mathrm{M} \) and radius \( \mathrm{R} \) attached to a uniform rod also of mass
M and length L. The rod and the ring are coplanar, and the line of the rod passes through the centre of the ring. The moment of inertia of the object (racket) about an axis through the centre of the ring and perpendicular to its plane is
A \( \cdot \frac{1}{12} M\left(6 R^{2}+L^{2}\right) \)
B \cdot\frac{12 } { 1 2 } M ( 1 8 R ^ { 2 } + L ^ { 2 } )
C \( \cdot \frac{1}{3} M\left(6 R^{2}+L^{2}+3 L R\right) \)
D. None of these


Convert 3.25 mile to kilometers.
A. 2.02 km
B. 4.95 km
c. \( 5.23 \mathrm{km} \)
D. 1.91 km


The weight of the silver (atomic number: 108 ) displaced by a quantity of electricity which displaces \( 5600 \mathrm{ml} \) of
\( O_{2} \) at \( S T P \) will be:
A. \( 10.8 g \)
в. \( 50.0 g \)
c. \( 108.0 g \)
D. \( 5.4 g \)


When \( C_{6} H_{5} N_{2} C l \) is reduced with
\( N a_{2} S n O_{2} \) the product is:
\( A \)
в.
c.
D.


A system or a group of systems, in which there is no net macroscopic flow of energy or matter either within the system or in between systems is known as?
A. Chemical equilibrium
B. Thermal equilibrium
c. Thermodynamic equilibrium
D. Radiative equilibrium


Assertion
The solubility of noble gases in water decreases with increasing size of the
noble gas.
Reason
Solubility of noble gases in water is due
to dipole-dlpole interaction
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


Assertion
Two thin blankets put together are warmer than a single blanket of double the thickness.
Reason
Thickness increases because of air
layer enclosed between the two blankets.
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


Integrate the rational function \( \frac{x^{3}+x+1}{x^{2}-1} \)


Three concentric spherical metallic shells \( A, B \) and \( C \) of radii \( a, b \) and \( c(c>b \)
a) have charge densities \( \sigma,-\sigma \) and \( \sigma \) respectively.The potential of shell B is :
A \( \cdot(a+b+c) \frac{\sigma}{\varepsilon_{0}} \)
B \( \cdot\left(\frac{a^{2}}{b}-b+c\right) \frac{\sigma}{\varepsilon_{0}} \)
\( ^{\mathbf{c}} \cdot\left(\frac{a^{2}}{c}-\frac{b^{2}}{c}+c\right) \frac{\sigma}{\varepsilon_{0}} \)
D. \( \frac{\sigma c}{\varepsilon_{0}} \)


A block of mass \( 10 \mathrm{kg} \) is kept on a fixed
rough \( (\mu=0.8) \) inclined plane of angle
of inclination \( 30 . \) The frictional
force acting on the block is
\( \mathbf{A} \cdot 50 \mathrm{N} \)
B. \( 50 \sqrt{3} \) N
\( \mathbf{c} \cdot 52 \mathrm{N} \)
\( \mathbf{D} \cdot 54 \mathrm{N} \)


The number of neutrons in the nucleus
of an atom which has 26 electrons and
has a mass number 56 are :
A . 26
B. 36
\( c . \) 30
D. 56


Assertion
A capacitor can be given only a limited
quantity of charge
Reason
A capacitor is an arrangement which can store sufficient quantity of charge
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


A diver at a depth of \( 12 m \) in water \( \left(\mu=\frac{4}{3}\right) \) sees the sky in a cone of semi-vertical angle of :
\( ^{\mathbf{A}} \cdot \sin ^{-1}\left(\frac{4}{3}\right) \)
B \( \cdot \tan ^{-1}\left(\frac{4}{3}\right) \)
\( ^{c} \cdot \sin ^{-1}\left(\frac{3}{4}\right) \)
D. \( 90^{\circ} \)


An analyser is inclined to a polarizer at
an angle of \( 30^{\circ} . \) the intensity of light emerging from the analyser is \( \frac{1}{n} \) of that is incident on the polarizer. Then \( n \) is equal to
A .4
B. \( \frac{4}{3} \)
\( c \cdot \frac{8}{3} \)
D. \( \frac{1}{4} \)


In a family there are 10 adults and 6 children. In how many ways can they be
seated around table so that all the
children do not sit together?
A . 16
B. \( 15 ! \)
c. \( 16 !-(11 ! \times 6 !) \)
D. \( 15 !-(10 ! \times 6 !) \)


When light is reflected from the a
spherical or curved surface:
A. the laws of reflections are followed
B. the laws of reflections are not followed
C. the laws of reflections may or may not be followed
D. one of the laws is followed, the other is not


What is \( X \) in the following sequence of
reactions? \( Y \frac{N a}{-H_{2}} Y \frac{N a O H}{C a O} C H_{4} \)
A. Methanoic acid
B. Ethanoic acid
c. Propane
D. Methane


A scooter going due east at \( 10 \mathrm{m} / \mathrm{s} \)
turns right through an angle of \( 90^{\circ} . \) If
the speed of the scooter remains unchanged in taking this turn, the change in the velocity of the scooter is
A. \( 20.0 \mathrm{m} / \mathrm{s} \) in south-east direction
B. \( 17.5 \mathrm{m} / \mathrm{s} \) in a south-west direction
c. \( 10.0 m / s \) in south-east direction
D. \( 14.14 \mathrm{m} / \mathrm{s} \) in south-west direction


On comparing the ratios \( \frac{\boldsymbol{a}_{1}}{\boldsymbol{a}_{2}}, \frac{\boldsymbol{b}_{1}}{\boldsymbol{b}_{2}} \) and \( \frac{\boldsymbol{c}_{1}}{\boldsymbol{c}_{2}} \)
find out whether the following pairs of linear equations are consistent, or inconsistent.
\( \mathbf{5} \boldsymbol{x}-\mathbf{3} \boldsymbol{y}=\mathbf{1 1} ;-\mathbf{1 0} \boldsymbol{x}+\mathbf{6} \boldsymbol{y}=\mathbf{2 2} \)
A. Consistent
B. Inconsistent
c. Ambiguous
D. Data insufficient


The intrinsic semi conductor becomes
an insulator at
\( \mathbf{A} \cdot 0^{\circ} C \)
в. \( 0 K \)
c. \( 300 K \)
D. \( -100^{\circ} \mathrm{C} \)


The reaction intermediate produced by homolytic cleavage of a bond is called:
A. carbene
B. carbocation
c. carboanion
D. free redical


Two concentric shells have radii R and
2R, charges \( \boldsymbol{q}_{A} \) and \( \boldsymbol{q}_{B} \) and potentials \( 2 \mathbf{V} \)
and (3/2)V respectively. Now shell B is earthed and let charges on them
become \( \boldsymbol{q}_{A}^{\prime} \) and \( \boldsymbol{q}_{B}^{\prime} . \) Then
This question has multiple correct options
B \( \cdot\left|q_{A}^{\prime}\right| / q_{B}^{\prime} \mid=1 \)
c. Potential of A after earthing becomes (3/2)V
D. Potential difference between A and B after earthing becomes V/2


Hydrogen peroxide molecules are:
A. monoatomic and form \( X_{2}^{2-} \) ions
B. diatomic and form \( X^{-} \) ions
C . diatomic and form \( H O_{2}^{-} \) ions
D. monoatomic and form \( X^{-} \) ions


A juggler performs in a room whose ceiling is \( 3 \mathrm{m} \) above the level of his hands. He throws a ball vertically upward so that it just reaches the ceiling.
(b) what times is required for the ball to reach the ceiling?


\( S_{N} 2 \) reaction can be best carried out
with:
A. primary alkyl halide
B. secondary alkyl halide
c. tertiary alkyl halide
D. all of the above


AgBr dissolved in \( N a_{2} S_{2} O_{3} .1 \) mol of
AgBr is dissolved in \( x \) mol of \( N a_{2} S_{2} O_{3} \) What is the value of \( x ? \)
\( A \)
B. 0.5
\( c \cdot 0.3 \)
D. 1.5


The catalytic efficiency of two different enzyme can be compared by the
A. The K \( _{m} \) value
B. The pH optimum value
C. Formation of the product
D. Molecular size of the enzyme


If \( \overrightarrow{\boldsymbol{A}}=\mathbf{3} \hat{\boldsymbol{i}}-\mathbf{2} \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{B}}=\hat{\boldsymbol{i}}-\boldsymbol{3} \hat{\boldsymbol{j}}+ \)
5 \( \hat{k} a n d \vec{C}=2 \hat{i}+\hat{j}-4 \hat{k} \) form a right
angled triangle then out of the following which one is satisfied?
A \( \cdot \vec{A}=\vec{B}+\vec{C} \)and \( A^{2}=B^{2}+C^{2} \)
B . \( \vec{A}=\vec{B}+\vec{C} \)and\( B^{2}=A^{2}+C^{2} \)
c. \( \vec{B}=\vec{A}+\vec{C} a n d B^{2}=A^{2}+C^{2} \)
D. \( \vec{B}=\vec{A}+\vec{C} a n d A^{2}=B^{2}+C^{2} \)


type of reproduction takes place in
Hydra.
A. Budding
B. Binary fission
c. Multiple fission
D. None of the above


The chemiosmotic theory of ATP synthesis in the chloroplasts and mitochondria is based on
A. Proton gradient
B. Accumulation of K ions
c. Accumulation of Na ions
D. Membrane potential


What is the maximum number of
emission lines obtained when the
excited electron of a H atom in \( n=5 \)
drops to the ground state?
A \( \cdot 12 \)
B. 15
\( c \cdot 2 \)
D. 10


Maximum and minimum scattering in visible range are respectively
A. Violet and red
B. Red and violet
c. Blue and green
D. None of the above


Acidic oxides react with water to give
A. base
B. acids
c. salt
D. none of these


The probability of getting number less than or equal to \( 6, \) when a die is thrown once, is
A. An impossible event
B. A sure event
c. An exhaustive event
D. A complementary event


A thick strip of copper is mounted as a compound pendulum about O.If it is made to swing through a uniform magnetic field B normal to the plane of the strip then (neglecting air resistance) it is found that
A. strip swings almost freely.
B. motion of the strip is heavily damped.
c. strip does not oscillate at all but immediately comes to rest in the vertical position
D. strip swings almost freely but its temperature decreases


If the different permutations of all the letter of the words \( \boldsymbol{E} \boldsymbol{X} \boldsymbol{A} \boldsymbol{M} \boldsymbol{I} \boldsymbol{N} \boldsymbol{A} \boldsymbol{T} \boldsymbol{I} \boldsymbol{O} \boldsymbol{N} \)
are listed as in a dictionary, how many words are there in this list before the
first word starting with \( \boldsymbol{E} \) ?


Very short answer type.
Under what conditions does Mendels
law of independent assortment apply?


Write the application of sodium
bicarbonate (baking soda)?


For a liquid, the coefficients of apparent
expansion ' \( \gamma_{a} \) 'and real expansion \( ^{\prime} \gamma_{r} \)
are related as:
\( A \cdot \gamma_{a}=\gamma_{r} \)
в. \( \gamma_{a}<\gamma_{r} \)
c. \( \gamma_{a}>\gamma_{r} \)
D. \( \frac{\gamma_{a}}{\gamma_{r}}= \) constant


The mass of uniform square plate is
\( 120 g \) and its side length is \( 20 c m \). About an axis perpendicular to the plane of plate and passing through its centre, the moment of inertia is :
A \( \cdot 8 \times 10^{-3} k g m^{2} \)
B . \( 8 \times 10^{-4} k g m^{2} \)
c. \( 4 \times 10^{-3} k g m^{2} \)
D. \( 4 \times 10^{-4} k g m^{2} \)


\( p H \) of a \( 0.001 \mathrm{M} \) NaOH solution will be:
\( A \cdot 9 \)
B. 3
\( c \)
D. 12


Werner Heisenberg is known for his
work on
A. Inelastic scattering of light by molecules
B. Quantum mechanics: Uncertainty principle
C. Theory of super conductivity
D. Expanding universe


If \( A=\{2,3\} \) and \( B=\{1,2\}, \) find \( A \times \)
\( \boldsymbol{B} \)
A \( \cdot\{(2,1),(2,2),(3,1),(3,2)\} \)
в. \{(2,1),(2,1),(3,1),(3,2)\}
\( \mathbf{c} \cdot\{(2,1),(2,2),(2,1),(3,2)\} \)
D. \( \{2,1),(2,2),(3,1),(2,2)\} \)


Photochemical smog is related to the pollution of
A. Soil
B. water
c. Noise
D. Air


Find approximately the volume of the
sphere of radius 1.001


How could two waves on a rope interfere
so that the rope did not move at all?


Consider the following facts about
energy.
I. The electrical energy can be stored in
a capacitor to be recovered on its
discharge.
Il. It is stored in the electromagnetic radiations in electric and magnetic
fields.
III. In a closed system, the total energy is variable.
IV. Potential energy is stored in a body when it changes its configuration.
\( A \cdot \) ।, III and \( 1 V \)
B. I, II and IV
C. I, II and III
D. II, III and IV


The magnitude of average atmospheric pressure on the surface of the earth is:
A. 1 bar
B. 10 bar
c. 100 bar
D. 0.1 bar


Assertion
Atria act as primer pumps that
increase the ventricular pumping.
Reason

About 80 percent of the blood flows directly through the atria into
ventricles.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If \( E_{1}, E_{2} \) and \( E_{3} \) are the kinetic energies
of a proton, \( \alpha \) -particle and deuteron
respectively, which all have the same
wavelength, then
A \( \cdot E_{1}>E_{2}>E_{3} \)
в. \( E_{1}>E_{3}>E_{2} \)
c. \( E_{3}>E_{2}>E_{1} \)
D. \( E_{3}>E_{1}>E_{2} \)


The cost price of 10 articles is equal to the selling price of 9 articles. Find the profit percent.


solve the equation using substitution method:
\( 2 x+3 y=13 \) and \( 4 x+5 y=23 \)
A \( \cdot(-2,3) \)
B. (2,3)
c. (2,-3)
D. (-2,-3)


Identify the reason for water scarcity.
A. Increasing rate of population
B. Increasing rate of industries
C. Both A and B
D. None of the above


In modern periodic table, Hf is alphabetical symbol for:
A. Hafnium
B. Hassium
c. Hellium
D. Hafnum


An infinitely long wire is kept along z-
axis from \( z=-\infty \) to \( z=+\infty, \) having
uniform linear charge density \( \frac{10}{9} n C / m . \) The electric field \( \vec{E} \) at point \( (6 \mathrm{cm}, 8 \mathrm{cm}, 10 \mathrm{cm}) \) will be:
\( A \cdot(160 i+120 j+200 k) N / C \)
B. (200 k) N/C
\( c \cdot(160 i+120 j) N / c \)
D. \( (120 \mathrm{i}+160 \mathrm{j}) \mathrm{N} / \mathrm{C} \)


The compound which has the lowest
boiling point is:
A \( \cdot H_{2} O \)
В \( \cdot C_{2} H_{5} O H \)
\( \mathbf{c} \cdot C H_{3} O H \)
D. \( C H_{3} O C H_{3} \)


A centre tapped transformer is rated 12
0-12 V. The peak voltage obtained is
A . 12 v
B. \( \frac{12}{\sqrt{2}} V \)
\( \mathrm{c} \cdot 12 \sqrt{2} V \)
D. \( 24 V \)
E \( .24 \sqrt{2} V \)


A steady current is set up in a metallic wire of non-uniform cross section. Then
the drift velocity is related to the area of \( \operatorname{cross} \operatorname{section}(A) \) as:
A. \( V_{d} \propto A^{-1} \)
B. \( V_{d} \propto A \)
\( \mathbf{C} \cdot V_{d} \propto A^{2} \)
D. \( V_{d} \) is independent of \( A \)


A spherical soap bubble has a radius \( ^{\prime} \boldsymbol{r}^{\prime} \)
The surface tension of the soap film is
T.The energy needed to double the
diameter of the bubble at the same
temperature is:
A \( .24 \pi r^{2} \sigma \)
В. \( 4 \pi r^{2} \sigma \)
\( \mathbf{c} \cdot 2 \pi r^{2} T \sigma \)
D. \( 12 \pi r^{2} T \sigma \)


Simplify the expression and find the
value if \( x \) is equal to 2
\( 3(x+2)+5 x-7 \)


The function \( \frac{|\boldsymbol{x}|}{\boldsymbol{x}^{2}+\mathbf{2} \boldsymbol{x}}, \boldsymbol{x} \neq \mathbf{0} \) and
\( \boldsymbol{f}(\mathbf{0})=\mathbf{0} \) is not continuous at \( \boldsymbol{x}=\mathbf{0} \)
because-
A \( \cdot \lim _{x \rightarrow 0} f(x) \neq f(0) \)
B. \( \lim _{x \rightarrow 0^{+}} f(x) \) does not exist
c. \( \lim _{x \rightarrow 0^{-}} f(x) \) does not exist
D. \( \lim _{x \rightarrow 0} f(x) \) does not exist


Four simılar prism or same materıal having same angle of prism are arranged. Which of the following
arrangements given no net angular deviation?
\( A \)
B.
\( c \)
D.


A contractile mid-body forms during cytokinesis in
A. Animal
B. Higher plants
c. Fungi
D. Algae


The process of formation of mRNA from
DNA is known as
A. Transformation
B. Translation
c. Transcription
D. Translocation
E. Relication


A yellow substance oozing out from
wound has
\( \mathbf{A} \cdot \) Lymph \( +\mathrm{RBC}+\mathrm{WBC} \)
B. Lymph + RBC + dead bacteria
C. Dead WBC+ bacteria + tissue debris
D. Lymph + dead leucocytes


Explain how the skeletal systems performs the following.
Support.


A point object is placed on the axis of a
thin convex lens of focal length \( 0.05 m \)
at a distance of \( 0.2 m \) from the lens and
its image is formed on the axis. If the object is now made to oscillate along the axis with a small amplitude of \( \boldsymbol{A} \) \( \mathrm{cm}, \) then what is the amplitude of oscillation of the image? [you may assume \( \frac{1}{1+x} \approx 1-x, \) where \( x<<1 \)
A \( \cdot \frac{4 A}{9} \times 10^{-2} m \)
в. \( \frac{5 A}{9} \times 10^{-2} m \)
c. \( \frac{A}{3} \times 10^{-2} m \)
D. \( \frac{A}{9} \times 10^{-2} m \)


The enthalpy of formation of water from hydrogen and oxygen is \( -286.0 k J \)
mol \( ^{-1} \). The enthalpy of decomposition
of water into hydrogen and oxygen is
\( k J m o l^{-1}: \)
A . -286.0
в. -143.0
c. 286.0
D. 143.0


The marks scored by two students
\( M, N \) in a class are given below. Find
the mean using direct method.
\begin{tabular}{|l|l|l|l|l|l|}
\hline\( M \) & 98 & 88 & 87 & 90 & 70 \\
\hline\( N \) & 50 & 65 & 80 & 95 & 100 \\
\hline
\end{tabular}
A. 65 marks
B. 70 marks
C. 85 marks
D. 90 marks


\( 233 \mathrm{K} \) is equal to
A \( \cdot 40 \)
B . \( -40^{\circ} \)
\( c \cdot 172^{\circ} \)
D. - 172


What is the p.d. across the terminals
\( \left(V_{T}\right) \) of a cell with emf \( E \) for open circuit
\( ? \)
A \( \cdot V_{T}<E \)
в. \( V_{T}>E \)
c. \( V_{T}=0 \)
D. \( V_{T}=E \)


Differentiate \( \boldsymbol{x}=\boldsymbol{y}+ \)


'Vasa-vasorum' refers to
A. Jugular anastomosis
B. A network of blood vessels in an organ
C. Vessels of vessels
D. Carotid labyrinth regulating pressure of blood vessels


State whether given statement is True or False
Black bodies are good absorbers of radiant heat.
A. True
B. False


Assertion
The ground state electron configuration
orbitals of elemental \( \boldsymbol{C u} \) is \( [\boldsymbol{A} \boldsymbol{r}] \boldsymbol{4} \boldsymbol{s}^{1} \boldsymbol{3} \boldsymbol{d}^{1} \)
Reason
Completely half-filled and filled dorbital best show special electronic
stabilization
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


At a depth of \( 1000 \mathrm{m} \) in the ocean,what
is the gauge pressure when density of sea water is given \( 1.03 \times 10^{3} \mathrm{kgm}^{-3} \) ?
Take \( \boldsymbol{g}=\mathbf{1 0 m s}^{-\mathbf{2}} \)
A. 675 atm
B. 103 atm
c. 203 atm
D. 244 atm


Compare the solubility and thermal stability of the following compounds of the alkali metals with those of the
alkaline earth metals.
\( \mathbf{A} \cdot \) Nitrates
B. Carbonates
c. Sulphates
D. none of these


Which combination cannot be used for
the preparation of hydrogen gas in the laboratory?
I. \( Z n / \) conc. \( H_{2} S O_{4} \)
II. \( Z n / d i l . H N O_{3} \)
III. \( Z n / d i l . H_{2} S O_{4} \)
Zinc in I and II is not very pure while in
III, it is very pure.
A. I and II
B. I, II and III
c. ॥ा only
D. I and III


Which clotting factor has been rejected
now?
A. VIII
B. VII
\( c \cdot v \)
\( D \)


How much electricity in terms of Faraday is required to produce 40.0 g of
\( A l \) from molten \( A l_{2} O_{3} ? \)
A. 1 Faraday
B. 2 Faraday
c. 3.2 Faraday
D. 4.44 Faraday


The metal which can form a
predominantly stable covalent halide of the formula MX (X=halogen)?


Fundamental theorem of arithmetic is
basically used for
A. proving the irrationality of numbers.
B. to explore when exactly the decimal expansion of a rational number is terminating or non-terminating repeating.
c. prime numbers.
D. both A and B.


How is ethanol prepared from the following compounds:
1. Ethene


Figure shows a copper rod joined to a steel rod. The rods have equal length and equal cross sectional area.The free
and of the copper rod is kept at \( 0^{\circ} \mathrm{C} \) and
that of the steeel rod is kept at \( 100^{\circ} \mathrm{C} \) Find the temperature at the junction of the rods. Conductivity of copper =
\( 390 W / m^{\circ} C \) and that of steel =
\( 46 W / m^{\circ} C \)
\( 0^{\circ} \mathrm{C}\left[\begin{array}{ll}\text { Copper } & \text { Steel }\end{array}\right. \)
\( \mathbf{A} \cdot 5.3^{\circ} \mathrm{C} \)
B . \( 10.6^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 15.6^{\circ} \mathrm{C} \)
D. None of these


Find the values of \( x \), if
\( \left|\begin{array}{ll}2 & 4 \\ 5 & 1\end{array}\right|=\left|\begin{array}{cc}2 x & 4 \\ 6 & x\end{array}\right| \)


The excess energy of electron is used in
the synthesis of
A. Organic compounds
B. ATP from ADP and iP
c. \( N A D P H_{2} \) from \( N A D P \)
D. None of the above


The ionization energy of \( L i^{2+} \) is equal to
\( \mathbf{A} \cdot 9 h c R \)
B. \( 6 h c R \)
\( \mathbf{c} \cdot 2 h c R \)
D. hcR


Calcium lactate is a salt of a weak
organic acid and represented as
\( \boldsymbol{C} \boldsymbol{a}(\boldsymbol{L} \boldsymbol{a} \boldsymbol{c})_{2} \cdot \boldsymbol{A} \) saturated solution of
\( C a(L a c)_{2} \) contains 0.13 mole of this
salt in 0.50 l litre solution. The pOH of
this solution is \( 5.60 . \) Assuming a complete dissociation of salt, calculate
\( K_{a} \) of the lactic acid.


Which has thin and thick segments?
A. DL of loop of Henle
B. AL of loop of Henle
c. РСТ
D. DCT


In quiescent zone, DNA content is
A . High
B. Low
c. Very high
D. Balanced


The diameter of base of a cylinder is
\( 14 \mathrm{cm} \) and its height is \( 20 \mathrm{cm} . \) Find the
whole surface area and volume.


When a force acts on a large area, the
pressure it exerts is more.
A. True
B. False
c. Ambiguous
D. Data insufficient


\( A D=B E \)
4 . True
3. False


The electron configuration for potassium in the ground state:
A \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} \)
B . \( 1 s^{2} 2 s^{2} p^{6} 3 s^{2} 3 p^{6} 4 s^{2} \)
C \( \cdot 1 s^{2} 2 s^{2} p^{6} 3 s^{2} 3 p^{6} 4 s^{1} \)
D. \( 1 s^{2} \)
E \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 p^{1} \)


The sum of the first \( n \) terms of an \( A P \) is
\( 3 n^{2}+6 n . \) Find the \( n^{t h} \) term of this \( A . P \)


The volume of a sphere is 38808 cu.cm.
The curved surface area of the sphere \( \left(\operatorname{in} c m^{2}\right) \) is:
A .5544
в. 1386
\( c .8316 \)
D. 4158


Consider two concentric spherical
metal shells of radii 'a' and b> a. The
outer shell has charge \( Q, \) but the inner shell has no charge,Now,the inner shell is grounded. This means that the inner
shell will come at zero potential and that electric fields lines leave the outer
hell and end on the inner shell.


Which of the following statement proves that guard cell is a living cell?
A. It has a nucleus
B. It has chloroplast.
c. It is a bean shaped cell.
D. Both A and B


The volume of a sphere is \( \frac{4}{3} \pi r^{3} c . c . \) What is the ratio of the volume of a
cube to that of a sphere which will fit inside the cube?
\( \mathbf{A} \cdot 4: 3 \pi \)
в. \( 2: \pi \)
\( c \cdot 8: \pi \)
D. \( 6: \pi \)


The name of the figure formed by the points (-1,-3,4),(5,-1,1),(7,-4,7)
and (1,-6,10) is a
A. square
B. rhombus
c. parallelogram
D. rectangle


In the experiment of half deflection method the resistance \( R \) should be
\( A \cdot>S \)
B. \( \approx \) s
\( c \cdot<s \)
\( \mathrm{D} \cdot \approx \mathrm{G} \)


The property of inertia is more in:
\( A \cdot \) a car
B. a truck
\( c . \) a cart
D. a toy car


The angle of crown glass \( (\mu=1.52) \)
prism is \( 5^{\circ} . \) What should be the angle of flint glass \( (\mu=1.63) \) prism so that the
two prisms together may be used in a direct vision spectroscope?
A . \( -2.14^{\circ} \)
B. \( +2.14^{\circ} \)
c. \( -4.12^{\circ} \)
D. \( +4.12^{\circ} \)


Write Biot-Savart law.
Write the path of motion of an electron
when it enters in magnetic field at
(a) perpendicular
(b) an angle \( \boldsymbol{\theta} \)


Factorise :
\( 121 a c-16 a^{2} b^{2} \)
A \( \cdot a\left(121 c-16 a b^{2}\right) \)
В . \( a\left(121 c+16 a b^{2}\right) \)
\( \mathbf{c} \cdot a\left(121 c-16 a c^{2}\right) \)
D. none of these


Shade the region that represents the set
\( \boldsymbol{P} \cap \boldsymbol{Q}^{\prime} \) in figure


Which of the following will show Tyndal
effect ?
(I) Salt solution
(II) Milk
(III) Starch solution
A . ।, ॥।, ॥।
B. ।, ॥
c. ॥, ॥ ॥
D. I, III


The animals in which coelom originates as a space in the mesoderm are termed
as
A. Acoelomates
B. Pseudocoelomates
c. Schizocoelic and enterocoelic
D. All of the above


Which of the following statements
about anhydrous aluminium chloride is
correct?
A. It conducts electricity in aqueous solutions
B. It exists as dimer both in the vapour state below \( 350^{\circ} \mathrm{C} \)
and in non-polar solvents
C. It is prepared by heating \( A l_{2} O_{3} \) in a stream of sulphur
chloride \( \left(S_{2} C l_{2}\right) \) vapour and chlorine
D. All of these


At what temperature does water boil?


A current of 2 ampere passing for 5 hours deposits \( 22.2 \mathrm{g} \) of tin, the oxidation state of tin is:
[At. wt. \( =119] \)
A. 0
B. 3
\( c \cdot 2 \)
D. 4


Short / Long answer type questions. On what basis are fungi classified?


nuclear fusion produces:
\( A \cdot \) argon
B. duterium
c. helium
D. protium


The element with electronic
configuration 2,8,6 is
A. metallic
B. non-metallic
c. metalloid
D. None of these


In a Daniell cell, current flows from
cathode to anode outside the cell.
If the statement is true enter 1 , else
enter 0


While sieving grains, small pieces fall down. Which force pulls them down?
A. Coulomb force
B. Gravitational force
c. Nuclear force
D. Electrostatic force


Find the remainder when \( p(x)= \)
\( -3 x^{3}-4 x^{2}+10 x-7 \) is divided by
\( \boldsymbol{x}-\mathbf{2} \)
A . -26
в. -27
c. 26
D. 27


Iron articles rust readily whereas steel
which is also mainly made of iron will
not undergo corrosion.
A. True
B. False


A circuit has a self-inductance of \( 1 \boldsymbol{H} \)
and carries a current of \( 2 A . \) To prevent sparking, when the circuit is switched off, a capacitor which can withstand
\( 400 V \) is used. The least capacitance of
the capacitor connected across the
switch must be equal to
A. \( 50 \mu F \)
B. \( 25 \mu F \)
c. \( 100 \mu F \)
D. \( 12.5 \mu F \)


two equal drops of water each of radius
\( \boldsymbol{r} \) are falling through air with a steady velocity \( 8 c m / s \). the two drops combine
to form a big drop. The terminal velocity of big drop will be:
A \( \cdot \quad_{8(2)} \frac{2}{3} \mathrm{cm} / \mathrm{s} \)
в. \( \quad \frac{2}{3} \mathrm{cm} \)
c. \( \quad 4(2)^{\frac{2}{3}} c m \)
D. 32 cm / \( s \)


Following are the five rational numbers
which are smaller than \( 2 \Rightarrow \) \( 1, \frac{1}{2}, 0,-1, \frac{-1}{2} \)
If true then enter 1 and if false then
enter \( \mathbf{0} \)


The Henry law constant for dissolution of a gas in an aqueous medium is \( 3 \times \) \( 10^{2} \) atm. At what partial pressure of the
gas (in atm), the molality of gas in aqueous solution will be \( \frac{5}{9} M ? \)
A . 2.2 M
в. 9 м
\( c .3 \) м
D. none


One litre of a buffer solution is prepared
by dissolving 0.6 mole of \( N H_{3} \) and 0.4
mole of \( N H_{4} C l . \) What is the pH of the
solution? for \( \boldsymbol{N} \boldsymbol{H}_{3}, \boldsymbol{K}_{\boldsymbol{b}}=\mathbf{1 . 8 5} \times \mathbf{1 0}^{-\mathbf{5}} \)
(i) What is the pH of the buffer after addition of 0.1 mole of \( H C l \)
(ii) What is the pH of the buffer after
addition of 0.1 mole of \( N a O H \)


If \( \vec{A} \times \vec{B}=0, \vec{B} \times \vec{C}=0, \) then \( \vec{A} \times \)
\( \vec{C}= \)
A. \( A C \)
в. \( \frac{A B^{2}}{C} \)
c. \( Z \) ero
D. Noneofthese


A particle is projected at \( 60^{\circ} \) to the horizontal with a kinetic energy K. The kinetic energy at the highest point is?
\( A \cdot K \)
B. zero
c. \( K / 4 \)
D. \( K / 2 \)


Fill in the blank:
Ursa Major appears like
A . a ladle
B. a quadrilateral
c. the letter'M
D. a huntter


State whether the given list of numbers is an arithmetic progression or not.
\( a) 13,20,27,34, \dots \)
\( \boldsymbol{b}) \boldsymbol{6}, \boldsymbol{1} \boldsymbol{6}, \boldsymbol{2} \boldsymbol{6}, \boldsymbol{3} 5, \ldots \)


Write any four benefits of using solar
cooker.


is a greenish yellow gas
having an irritating choking and unpleasant odour.
A. Fluorine
B. Bromine
c. Chlorine
D. Hydrogen sulphide


State whether the given statement is true or false:

The mixture of hydrazine and hydrogen peroxide with a copper
(II) catalyst is used as a rocket propellant.


Who discovered lacteal?
A. Franklin
B. Priestley
C. Benda
D. Gaspare Aselli


On selling an article at a discount of
\( 20 \% \) the profit is \( 20 \% . \) Find the profit percent if the article is sold at a
discount of \( 10 \% \)
A . 25\%
B. 30\%
c. 15\%
D. 35\%


Which of the following factors are equal in a reversible chemical reaction at
equilibrium?
A. The number of moles of the reactants and products
B. The potential energies of the reactants and products
c. The activation energies of the forward and reverse reactions
D. The rates of reaction for the forward and reverse reactions
E. The concentrations of the reactants and products.


Two closed vessels of an equal volume
containing air at pressure \( P_{1} \) and
temperature \( T_{1} \) are connected to each
other through a narrow tube. If the temperature in one of the vessels is now
maintained at \( T_{1} \) and that in the other
at \( T_{2}, \) what will be the pressure in the
vessels?
A \( \cdot \frac{2 P_{1} T_{1}}{T_{1}+T_{2}} \)
в. \( \frac{T_{1}}{2 P_{1} T_{2}} \)
c. \( \frac{2 P_{1} T_{2}}{T_{1}+T_{2}} \)
D. \( \frac{2 P_{1}}{T_{1}+T_{2}} \)


Let \( a, b, c \) be non-zero real numbers
such the :
\( \int_{0}^{1}\left(1+\cos ^{8} x\right)\left(a x^{2}+b x+c\right) d x= \)
\( \int_{0}^{2}\left(1+\cos ^{8} x\right)\left(a x^{2}+b x+c\right) d x, \) then
the quadratic equation \( a x^{2}+b x+c= \)
0 has
\( A \cdot \) no root in (0,2)
B. atleast one root in (0,2)
C \( . \) a double root in (0,2)
D. none


is a fuel made by compressing natural gas.
A . LPG
в. смG
c. Both a and \( b \)
D. None of above


Study the following statements about chordate.
A) Columella auris present in the middle ear of amphibians is modified hyomandibula of fishes.
B) Reptiles lay cledoic egg.
C) Sphenodon is a connecting link between amphibians and reptiles.
D) Panthera tigris is an extinct animal of
India.
From the above identify the incorrect
statement or statements.
\( A \cdot A, C \)
B. Only A
c. only D
D. B,


Should the handle and bristles of a
tooth brush be made of the same
material? Explain your answer.


\( f\left(\frac{1+i}{1-i}\right)^{3}-\left(\frac{1-i}{1+i}\right)^{3}=A+i B \)
\( \operatorname{then} A, B= \)
A . 0,2
B. 0,-2
\( c .2,0 \)
D. -2,0


Fill any one of the following am a hibiscus plant
have \( _{\text {- }}--_{\text {- }}--_{\text {ype of rootsystem }} \) My leaves have venation
My flowers are_ \( -\ldots-\ldots \) merous Therefore I belong to the Division and subdivision


\( \left(\tan ^{-1} x\right)^{2}+\left(\cot ^{-1} x\right)^{2}=\frac{5 \pi^{2}}{8} \Rightarrow x= \)
\( A \cdot-1 \)
B.
\( c \cdot c \)
D. \( \pi \sqrt{\frac{5}{8}} \)


Simplify:
\( (1+i)^{(-1+i)} \)


What are micro-consumers?


An aqueous solution of a gas \( (\boldsymbol{X}) \) shows the following reactions.
(i) It turns red litmus blue.
(ii) When added in excess to a \( C u S O_{4} \)
solution, a deep blue colour is obtained.
(iii) On addition of \( F e C l_{3} \) solution, a
brown precipitate soluble in dilute
\( H N O_{3} \) is obtained
Then the gas \( (\boldsymbol{X}) \) will be :
\( A \cdot S O_{2} \)
в. \( N H_{3} \)
\( c \cdot N O_{2} \)
D. \( N_{2} \) O


With respect to halogens, four
statements are given below. Which of
them is correct?
A. The bond dissociation energies for halogens is in the order \( : I_{2}<F_{2}<B r_{2}<C l_{2} \)
B. The only oxidation state is -1
C. The amount of energy required for the excitation of electrons to first excited state decreases progressively as we move from F to 1
D. They form \( H X_{2}^{-} \) species in their aqueous solutions (X=halogen)


If \( K_{a 1} \) and \( K_{a 2} \) are the ionization constants of \( \boldsymbol{H}_{3} \stackrel{+}{\boldsymbol{N}} \boldsymbol{C} \boldsymbol{H} \boldsymbol{R} \boldsymbol{C O O} \boldsymbol{H} \) and
\( \boldsymbol{H}_{3}^{+} \boldsymbol{N} \boldsymbol{C} \boldsymbol{H} \boldsymbol{R} \boldsymbol{C O O}^{-}, \) respectively, the \( \boldsymbol{p} \boldsymbol{H} \)
of the solution at the isoelectric point
is:
A \( \cdot p H=p K_{a 1}^{\circ}+p K_{a 2}^{\circ} \)
в.
\[
p H=\left(p K_{a 1}^{\circ} p K_{a 2}^{\circ}\right)^{\frac{1}{2}}
\]
c.
\[
p H=\left(p K_{a_{1}}^{\circ}+p K_{a 2}^{\circ}\right)^{\frac{1}{2}}
\]
D. \( _{p H}=\frac{\left(p K_{a 1}^{\circ}+p K_{a 2}^{\circ}\right)}{2} \)


Assertion
Two coaxial conducting rings of different radii are placed in space. The mutual inductance of both the rings is
maximum if the rings are also coplanar
Reason
For two coaxial conducting rings of different radii, the magnitude of
magnetic flux in one ring due to current in the other is maximum when both the
rings are coplanar.
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


Derive the expression for the voltage gain of a transistor amplifier in \( \mathrm{CE} \) configuration terms of the load
resistance \( \boldsymbol{R}_{\boldsymbol{L}} \). current gain \( \boldsymbol{\beta}_{\boldsymbol{a}} \) and input resistance. Explain why input and output voltages are in opposite phase.


How many electrons in an atom with z=
104 can have \( (\boldsymbol{n}+\boldsymbol{l})=\mathbf{8} \) ?
A . 18
B. 16
\( c \cdot 3 \)
D.


Silicon is not suitable for fabrication of
light emitting diodes because it is:
A. an indirect band gap semiconductor
B. a direct band gap semiconductor
c. a wide band gap semiconductor
D. none of the above


If \( \vec{a} \cdot \hat{i}=4, \) then \( (\vec{a} \times \hat{j}) \cdot(2 \hat{j}-3 \hat{k}) \) is
equal to
A . 12
B . 2
c. 0
D. -12


The position vectors of \( \boldsymbol{P} \) and \( \boldsymbol{Q} \) are
respectively \( a \) and \( b \). If \( R \) is a point on
\( P Q, P Q \) such that \( P R=5 P Q, \) then the
position vector of \( \boldsymbol{R} \) is
A \( .5 b-4 a \)
B. \( 5 b+4 a \)
c. \( 4 b-5 a \)
D. \( 4 b+5 a \)


A dividing diploid cell supplied with colchicine will become
A. haploid
B. tetraploid
c. triploid
D. remain diploid


How is propyne prepared from an:
(i) alkylene dihalide
\( (i i) \) alkylidene dihalide and
(iiii) Tetrahaloalkane


Function of transmitter in a SONAR is to
A. produce infrasonic waves
B. convert the reflects ultrasonic waves into electrical signals
c. produce and transmits ultrasonic waves
D. do all the above


If the lines \( \frac{x-4}{2}=\frac{y+5}{4}=\frac{z-1}{-3} \) and
\( \frac{x-2}{1}=\frac{y+1}{3}=\frac{z}{2} \) intersects, find
their point of intersection.


The term independent of \( x \) in \( (1+ \)
\( x)^{n}\left(1+\frac{1}{x}\right)^{n} \) is
A \( \cdot C_{0}^{2}+2 \cdot C_{1}^{2}+3 \cdot C_{2}^{2}+\ldots \ldots \ldots+(n+1) \cdot C_{n}^{2} \)
B. \( \left(C_{0}+C_{1}+C_{2}+\ldots \ldots . .+C_{n}\right)^{2} \)
c. \( C_{0}^{2}+C_{1}^{1}+C_{2}^{2}+\ldots \ldots . .+C_{n}^{2} \)
D. None


In the graph (1), the equilibrium state is
reached at:
\( A \cdot t \)
B \( \cdot t_{2} \)
\( c \cdot t_{3} \)
\( D \cdot t_{4} \)


Sensitivity of a moving coil
galvanometer can be increased by
Fill in the blank.
A. decreasing number of turns in rectangular coil
B. decreasing magnetic induction of magnetic field
C. increasing area of rectangular coil
D. increasing twist constant of phosphor bronze fiber


NAND and NOR gates are called universal gates because they
A. are universally available
B. can be combined to produce OR, AND and NOT gates.
c. are widely used in the integrated circuits.
D. can be easily manufactured


Tyndall effect is not observed in :
A. suspension
B. true solution
c. emulsions
D. collodial solution


By using the above informations define the electronic configuration of \( S \) atom.
A \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{4} \)
B . \( 1 s^{2} 1 p^{6} d^{6} 2 s^{2} \)
c. \( 1 s^{2} 1 p^{6} 1 d^{10} \)
D. \( 1 s^{2} 1 p^{6} 2 p^{6} 2 d^{2} \)


The acceleration of a particle starting from rest moving in a straight line with uniform acceleration is \( 8 m / s^{2} . \) The
time taken by the particle to move the second metre is
A \( \cdot \frac{\sqrt{2}-1}{2} s \)
B. \( \frac{\sqrt{2}+1}{2} s \)
\( \mathbf{c} \cdot(1+\sqrt{2}) s \)
D. \( (\sqrt{2}-1) s \)


The main reasons for deforestation are:
A. rapid increase in the population of human beings and their livestock
B. urbanization and human settlements
c. cutting down of trees for obtaining fuel
D. All of the above


Two angles of a polygon are right
angles and the remaining are \( 120^{\circ} \)
each. Find the number of sides in it.


Find the converse of the statement,"If
ABCD is square, then it is a rectangle".
\( A . \) If \( A B C D \) is a square, then it is .not a rectangle.
B. If \( A B C D \) is not a square, then i is a rectangle.
C. if ABCD is a rectangle, then it is square.
D. If \( A B C D \) is not a square, then it is not a rectangle.


If a uniform beam of \( 1 \mathrm{m} \) is balanced as
shown above, what would be the
moment of force \( F \) about point \( W ? \)
\( \mathbf{A} \cdot 110 N \mathrm{cm} \)
в. \( 40 \mathrm{N} \mathrm{cm} \)
c. \( 220 \mathrm{N} \mathrm{cm} \)
D. \( 80 \mathrm{N} \) cm


Factorise: \( 7 \sqrt{2} y^{2}-10 y-4 \sqrt{2} \)


How is the following derived unit related to the fundamental units?
1) joule
A . \( N m s^{-1} \)
в. \( N m \)
c. \( k g m^{2} s^{-1} \)
D. \( k g m^{2} s^{-2} \)


Which one of the following does not
correctly represent the correct order of
the property indicated against it?
\( \mathbf{A} \cdot T i^{3+}<V^{3+}<C r^{3+}<M n^{3+} ; \) increasing magnetic
moment
B. \( T i<V<C r<M n \); increasing melting point
C \( . T i<V<M n<C r ; \) increasing 2nd ionization enthalpy
D. \( T i<V<C r<M n \); increasing number of oxidation
states


(A) What do you mean by barrier
potential of diode?
(B) With help of a diagram explain the working of a full wave rectifier.


The record of a weather station shows
that out of the past 250 consecutive days, its weather forecasts were correct 175
times. What is the probability that on a given day it was correct?
A . 0.9
B. 0.8
\( c .0 .7 \)
D. 0.6


The needle of the dip circle of a place
stay at \( 30^{0} . \) The dip circle is inclined at
an angle towards \( 30^{0} \) with the magnetic
meridian. The true dip at the place is:
A \( \cdot \tan ^{-1} \sqrt{3} \)
B. \( \tan ^{-1} \frac{\sqrt{3}}{2} \)
c. \( \tan ^{-1} \frac{1}{2} \)
D. \( \tan ^{-1} \frac{3}{2} \)


The IUPAC name of tertiary butyl chloride is ?
A. 2-chloro-2-methylpropane
B. 3-chlorobutane
c. 4 -chlorobutane
D. 1, 2-chloro-3-methylpropane.


A flow of liquid is streamline if the Reynold number is
A. Less than 1000
B. Greater than 1000
c. Between 2000 to 3000
D. Between 4000 to 5000


A coil of wire of a certain radius has 100
turn and a self-inductance of 15 mH. The
self-inductance of a second similar coil
of 500 turns will be :
\( \mathbf{A} \cdot 75 m H \)
в. 375 тН
c. \( 15 m H \)
D. none of these


A square non-singular matrix A satisfies \( \boldsymbol{A}^{2}-\boldsymbol{A}+\boldsymbol{2} \boldsymbol{I}=\boldsymbol{0}, \) then \( \boldsymbol{A}^{-1}= \)
\( \mathbf{A} \cdot I-A \)
B \( \cdot \frac{1}{2}(I-A) \)
c. \( I+A \)
D \( \cdot \frac{1}{2}(I+A) \)


Assertion
If a gas container is placed in a moving
train, the temperature of gas will increase.
Reason
Kinetic energy of gas molecules will increase.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


A motor car moving at a speed of
\( 72 k m / h \) can not come to a stop in less
than \( 3.0 s \) while for a truck this time
interval is \( 5.0 s . \) On a higway the car is behind the truck both moving at
\( 72 k m / h . \) The truck gives a signal that
it is going to stop at emergency. At what
distance the car should be from the
truck so that it does not bump onto (collide with) the truck. Human
response time is \( 0.5 s \)
\( \mathbf{A} \cdot 1.25 m \)
в. \( 1.5 m \)
c. \( 1 m \)
D. \( 0.5 m \)


If a man is exposed to an environment of \( 100 \% \) oxygen, then the concentration of which of the following enzyme is increased in lungs?
A. Superoxide dismutase
B. Catalase
c. carbonic anhydrase
D. All of the above


Draw a curve for showing variation in alternating current with frequency in LCR resonant circuit. Hence obtain an
expression of bandwidth.


Define the angle of reflection.


When a sphere of radius \( r_{1}=1.2 \mathrm{mm} \)
moves in glycerin, the laminar flow is observed if the velocity of the sphere
does not exceed \( v_{1}=23 \mathrm{cm} / \mathrm{s} . \) At what
minimum velocity \( v_{2}(\text { in } \mu \mathrm{m} / \mathrm{s}) \) of \( \mathrm{a} \)
sphere of radius \( r_{2}=5.5 \mathrm{cm} \) will the
flow in water become turbulent? The
viscosities of glycerin and water are
equal to \( \eta_{1}=13.9 P \) and \( \eta_{2}=0.011 P \)
respectively.


Factorise \( 8 x^{3}+27 y^{3}+36 x^{3} y+54 x y^{2} \)


Number of solutions of the equation \( (\sqrt{3}+1)^{2 x}+(\sqrt{3}-1)^{2 x}=2^{3 x} \) is


A metal wire of resistivity \( 64 \times 10^{-6} \Omega \)
and length \( 198 \mathrm{cm} \) has a resistance of 7
\Omega. Calculate its radius.


Find the number of peroxide molecule(s) in the following:
\( M g O, C a O, L i_{2} O, B a O_{2} \)


Choose the false statement
A. In a perfect elastic collision, the relative velocity of approach is equal to the relative velocity of separation
B. In an inelastic collision the relative velocity of approach is less than the relative velocity of separation
C. In an inelastic collision, the relative velocity of separation is less than the relative velocity of approach
D. In perfect inelastic collision relative velocity of separation is zero


A moving electron enters a uniform
magnetic field perpendicularly. Inside the magnetic field, the electron travels along:
A. a straight line
B. a parabola
c. a circle
D. a hyperbola


Avalanche breakdown is primarily dependent on the phenomenon of :
A . Collision
B. Ionisation
c. Doping
D. Recombination


Events \( E_{1}, E_{2}, E_{3} \) are possible events of an experiment and their probabilities are recorded.Mark the possible correct
answers.
This question has multiple correct options
\( \begin{array}{ll}\text { A } \cdot P\left(E_{1}\right)=0.3, & P\left(E_{2}\right)=0.4, \quad P\left(E_{3}\right)=0.3\end{array} \)
B - \( P\left(E_{1}\right)=0.1, \quad P\left(E_{2}\right)=0.4, \quad P\left(E_{3}\right)=0.5 \)
C \( \cdot P\left(E_{1}\right)=0.6, \quad P\left(E_{2}\right)=-0.3, \quad P\left(E_{3}\right)=0.7 \)
D \( \cdot P\left(E_{1}\right)=0.4, \quad P\left(E_{2}\right)=0.2, \quad P\left(E_{3}\right)=0.3 \)


If the rate of change in the circumference of a circle of \( 0.3 \mathrm{cm} / \mathrm{s} \) then the rate of change in the area of the circle when the radius is \( 5 \mathrm{cm}, \) is:
A. \( 1.5 \mathrm{sq} \mathrm{cm} / \mathrm{s} \)
B. \( 0.5 \mathrm{sq} \mathrm{cm} / \mathrm{s} \)
c. \( 5 \mathrm{sq} \mathrm{cm} / \mathrm{s} \)
D. 3 sq cm/s


Find number of protons and neutrons
for \( (a),(b) \) and \( (c) \) respectively.
(a) \( _{17}^{35} C l(b)_{6}^{12} C(c)_{35}^{81} B r \)
\( A \cdot n_{p}=17,6,35 \)
\( n_{n}=18,6,46 \)
B . \( n_{p}=16,6,35 \)
\( n_{n}=18,6,46 \)
\( c \cdot n_{p}=17,6,35 \)
\( n_{n}=18,6,45 \)
D \( . n_{p}=16,6,35 \)
\( n_{n}=18,6,45 \)


If \( \boldsymbol{A}=\left\{\boldsymbol{x} \epsilon \boldsymbol{R} / \frac{\boldsymbol{\pi}}{\boldsymbol{4}} \leq \boldsymbol{x} \leq \frac{\boldsymbol{\pi}}{\boldsymbol{3}}\right\} \) and \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \sin x-x, \) then \( f(A)=: \)
A. \( \left[\frac{\sqrt{3}}{2}-\frac{\pi}{3}, \frac{1}{\sqrt{2}}-\frac{\pi}{4}\right] \)
B. \( \left[-\frac{1}{\sqrt{2}}-\frac{\pi}{4}, \frac{\sqrt{3}}{2}-\frac{\pi}{3}\right] \)
\( ^{\mathbf{C}} \cdot\left[-\frac{\pi}{3}, \frac{-\pi}{4}\right] \)
D. \( \left[\frac{\pi}{4}, \frac{\pi}{3}\right] \)


Assertion
Cryolite is used in electrolytic
extraction of \( A l \) from alumina.
Reason
It dissolves alumina.
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 and Reason is correct


If a electric flux leaving and entering
from closed surface are \( \phi \) and \( \phi \)
respectively, then the charge associated with closed surface will be
A \( \cdot \frac{\phi_{2}-\phi_{1}}{\varepsilon_{0}} \)
B. \( \frac{\phi_{1}+\phi_{2}}{\varepsilon_{0}} \)
c. \( \frac{\phi_{1}-\phi_{2}}{\varepsilon_{0}} \)
D \( \cdot \varepsilon_{0}\left(\phi_{2}-\phi_{1}\right) \)


Electric potential due to a point charge \( q \) at a distance \( r \) from is given by
A \( \cdot V=\frac{q}{4 \pi \epsilon_{0}} \)
B. \( V=\frac{q}{4 \pi \epsilon_{0} r^{2}} \)
\( \mathbf{c} \cdot v=\frac{q}{4 \pi \epsilon_{0} r} \)
D. \( v=\frac{q^{2}}{4 \pi \epsilon_{6} r} \)


(A) is 2,3 -diabromobutan-1, 4 -dioic
acid. Which stereochemical reactant is
\( (A) ? \)
\( (\mathbf{A}) \)
A. Erythro
B. Meso-
c. Threo-
D. Both (a) and (b)


A solenoid of length \( 50 \mathrm{cm}, \) having 100 turns carries a current of 2.5 A. The
magnetic field at one end of the solenoid is:
A. 3.14 \( \times 10^{4} \) न
B. 6.28 \( \times 10^{4} \) Т
c. \( 1.57 \times 10^{4} \) न
D. 9.42 \( \times 10^{4} \) न


Which of the following is correct:
\( A \cdot \sin 1^{\circ}>\sin 1 \)
B. \( \sin 1^{\circ}<\sin 1 \)
\( \mathbf{c} \cdot \cos 1^{\circ}<\sin 1 \)
D. None of these


We want a mirror that will make an
object look larger. What combination of image and object distances (from the
mirror) will accomplish this?
A. Image Distance \( 3.0 \mathrm{cm} \), Object Distance \( 3.0 \mathrm{cm} \)
B. Image Distance \( 2.0 \mathrm{cm} \), Object Distance \( 3.0 \mathrm{cm} \)
C. Image Distance \( 3.0 \mathrm{cm} \), Object Distance \( 5.0 \mathrm{cm} \)
D. Image Distance \( 3.0 \mathrm{cm} \), Object Distance \( 2.0 \mathrm{cm} \)
E. Image Distance \( 3.0 \mathrm{cm}, \) Object Distance \( 10.0 \mathrm{cm} \)


Each surface area of a cube is \( 100 \mathrm{cm}^{2} \)
If parallel surface of base cut the cube
in two equal parts then total surface area of each equal part.


Assertion
If \( a>0 \) and \( b^{2}-4 a c<0 . \) then the
value of the integral \( \int \frac{d x}{a x^{2}+b x+c} \) will be of the type \( \mu \tan ^{-1}\left(\frac{x+A}{B}\right)+ \)
\( C ; \) where \( A, B, C, \mu \) are constant.
Reason
\( f\left(a>0, b^{2}-4 a c<0, \text { then } a x^{2}+b x+\right. \)
\( c \) can be written as sum of two squares.
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


A body moving with uniform acceleration \( 8 m s^{-2} \) starts from rest.
The distance covered by it in fifth second will be
\( \mathbf{A} \cdot 8 m \)
в. 64 т
c. \( 4 m \)
D. 36 \( m \)


The de-Broglie's wavelength of electron present in first Bohr orbit of 'H' atom is :
A \( \cdot 0.529 \) a
B \( \cdot 4 \times 0.529 \)
c. \( 2 \pi \times 0.529 \) 能
D. \( \frac{0.529}{2 \pi} \stackrel{\circ}{A} \)


If the wire in the experiment to determine the resistivity of a material using metre bridge is replaced by copper or hollow wire the balance point
i.e. null point shifts
A. to right
B. to left
c. at same point
D. None of these


A certain mass of an ideal gas
undergoes a reversible isothermal compression. Its molecules, compared
with the initial state, will then have the
same
(i) root mean square velocity
(ii) mean momentum
(iii) mean kinetic energy
\( A \cdot(i),(\text { ii) },( \text { iii) } \)
B. (i), (ii)
c. (ii), (iii)
D. (i)


If \( (1-i) x+(1+i) y=1-3 i, \) then
\( (x, y)= \)
A. (2,-1)
в. (-2,-1)
c. (-2,1)
D. (2,1)


Bithionol is generally added to the soaps as an additive to function as
a/an:
A. buffering agent
B. antiseptic
c. softener
D. dryer


There is an isolated planet having mass 2M and radius 2R, where M and R are
the mass and radius of the earth.
simple pendulum having mass \( \mathrm{m} \) and length \( \mathrm{R} \) is made to small oscillations on the planet. Find the time period of SHM of the pendulum in second. (Take \( \left.\pi=3.00, \mathrm{g}=10 \mathrm{m} / \mathrm{s}^{2}, \sqrt{2}=1.41\right) \)
A. 8000
B. 6768 s
c. 9000 s
D. 7968 s


Assertion
\( X e F_{6} \) can be used as an oxidising
agent.
Reason
Oxidation state of \( \mathrm{Xe} \) in \( X e F_{6} \) is +6
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 true but Reason is false
D. Assertion is false but Reason is true


Find derivative of \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x} \cos \boldsymbol{x} \)


Identify without plotting, the lines parallel to the \( x \) or \( y \) axis: \( 3-7 y=0 \)


The displacement \( (x) \) - time \( (t) \) graph of
a particle in one dimension motion is as
shown in the figure, the average speed
is greatest in the interval:
\( A \)
B.
\( c \)
\( D \)


A stream of a liquid of density \( \rho \) flowing
horizontally with speed v rushes out of a tube of radius r and hits a vertical wall
nearly normally. Assuming that the liquid does not rebound from the wall,
the force exerted on the wall by the impact of the liquid is given by.
A . \( \pi r \rho v \)
B . \( \pi r \rho v^{2} \)
c. \( \pi r^{2} \rho v \)
D・ \( \pi r^{2} \rho v^{2} \)


A virtual image larger than the object can be produced by a :
A. concave lens
B. concave mirror
c. convex mirror
D. plane mirror


According to the remainder theorem when we divide a polynomial \( f(x) \) by
\( (x-c), \) the remainder equals
A \( . f(c) \)
в. \( f(-c) \)
c. 0
D. None of the above


Addition of water to this solution will
not change \( \left[\boldsymbol{H}_{3} \boldsymbol{O}^{+}\right] \)
A. Chemical pH indicator
B. Acid/base buffer
c. Anhydrous solution
D. Hypotonic solution


A letter is known to have come either
from \( \boldsymbol{T} \boldsymbol{A} \boldsymbol{T} \boldsymbol{A} \boldsymbol{N} \boldsymbol{A} \boldsymbol{G} \boldsymbol{A} \boldsymbol{R} \) or \( \boldsymbol{C A L} \boldsymbol{C U T T A} \)
On the envelope just two consecutive
letters \( T A \) are visible. What is the
probability that the letter came from \( \boldsymbol{T} \boldsymbol{A} \boldsymbol{T} \boldsymbol{A} \boldsymbol{N} \boldsymbol{A} \boldsymbol{G} \boldsymbol{R} ? \)
A \( .1 / 11 \)
в. \( 7 / 9 \)
c. \( 4 / 11 \)
D. \( 7 / 11 \)


A particle starts from the point \( 0.8 \mathrm{m} \) and moves with a uniform velocity of 3 \( \mathrm{m} / \mathrm{s} . \) what is the angular momentum of the particle after 5 seconds about origin.mass of the particle is \( 1 \mathrm{kg} \)
A \( \cdot 12 k g m^{2} / \mathrm{s} \)
B. \( 24 k g m^{2} / s \)
\( \mathbf{c} \cdot 32 k g m^{2} / s \)
D. \( 44 \mathrm{kgm}^{2} / \mathrm{s} \)


Which one of the following is not a fundamental SI unit?
A. Ampere
B. Candela
c. Newton
D. Kelvin


\( 0.003 m \) is dropped into a tube containing a viscous fluid filled up to
the \( 0 \mathrm{cm} \) mark as shown in the figure.
Viscosity of the fluid \( =1.2160 N . m^{-2} \)
and its density \( \rho_{L}=\rho / 2= \)
\( 1260 k g . m^{-3} . \) Assume the ball reaches
terminal speed by the \( 10 c m \) mark. Find the time taken (in sec) by the ball to
traverse the distance between the \( 10 \mathrm{cm} \)
and \( 20 c m \) mark. ( \( g \) =acceleration due to
gravity \( =10 m s^{-2} \)


Whenever a hydrogen atom emits a
photon in the Balmer series, This question has multiple correct options
A. it may emit another photon in the Balmer series.
B. it must emit another photon in the Lyman series.
C. the second photon, it emitted, will have a wavelength of about \( 122 \mathrm{nm} \)
D. it may emit a second photon, but the wavelength of this photon cannot be predicted.


The net force is zero at which point on
the graph?
\( A \cdot A \)
\( B . \quad B \)
\( \mathrm{c} \cdot \mathrm{C} \)
\( D, D \)
\( E . \)


In the Argand's plane, the locus of \( z(\neq \)
1) such that
\( \arg \left\{\frac{3}{2}\left(\frac{2 z^{2}-5 z+3}{3 z^{2}-z-2}\right)\right\}=\frac{2 \pi}{3} i s \)
A. a hyperbola with the directrices at \( z=-3 / 2 \) and \( z= \)
\( -2 / 3 \)
B. an ellipse with the directrices at \( z=3 / 2 \) and \( z=2 / 3 \)
c. a segment of a circle subtending angle \( \frac{2 \pi}{3} \) on arc between points \( z=-3 / 2 \) and \( z=2 / 3 \) lying below real axis.
D. a segment of a circle subtending angle \( \frac{2 \pi}{3} \) on arc
between points \( z=3 / 2 \) and \( z=-2 / 3 \) lying above real axis.


The equation of the circle passing through the point (-1,2) and having two diameters along the pair of lines \( x^{2}-y^{2}-4 x+2 y+3=0 \) is
A \( \cdot x^{2}+y^{2}-4 x-2 y+5=0 \)
B \( \cdot x^{2}+y^{2}+4 x+2 y-5=0 \)
c. \( x^{2}+y^{2}-4 x-2 y-5=0 \)
D. \( x^{2}+y^{2}+4 x+2 y+5=0 \)


Find the points of local maxima or local minima and corresponding local maxima and local minimum value of
the following functions. Also, find the points of inflection, if any. \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}-\boldsymbol{2} \boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{a}^{2} \boldsymbol{x}, \boldsymbol{a}>\boldsymbol{0}, \boldsymbol{x} \in \boldsymbol{R} \)


In the given figure, 0 is the centre of the
circle. If \( \angle A O D=140^{\circ} \) and \( \angle C A B= \)
\( 50^{\circ}, \) Then
(i) \( \angle \boldsymbol{E} \boldsymbol{D} \boldsymbol{B} \) (ii) \( \angle \boldsymbol{E} \boldsymbol{B} \boldsymbol{D} \) are
respectively
\( \begin{array}{lll}A & -70^{\circ} & \ & 50\end{array} \)
\( \begin{array}{lll}\text { B } \cdot 50^{\circ} & 110^{\circ}\end{array} \)
\( \begin{array}{lll}c \cdot 30^{\circ} & \ & 70^{\circ}\end{array} \)
\( \begin{array}{lll}\text { D. } 120^{\circ} & \text { \& } 130^{\circ}\end{array} \)


If \( y=5^{x} x^{5}, \) then \( \frac{d y}{d x} \) is
A \( \cdot 5^{x}\left(x^{5} \log 5-5 x^{4}\right) \)
B . \( x^{5} \log 5-5 x^{4} \)
c. \( x^{5} \log 5+5 x^{4} \)
D. \( 5^{x}\left(x^{5} \log 5+5 x^{4}\right) \)


Sign of the product of 231 negative integer and 9 positive integer is
A. Negative
B. Positive
\( c \cdot 0 \)
D. None of these


The biggest diamond ever found is:
A. cullinan
B. kohinoor
c. bituminous
D. peat


The hybridised state of \( C u \) in
\( \left[\boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right]^{2+} \) is:
\( \mathbf{A} \cdot s p \)
B \( \cdot s p^{2} \)
\( c \cdot s p^{3} \)
D. \( d s p^{2} \)


Resonance is not shown by-
A \( \cdot(a) C_{6} H_{6} \)
в. \( (b) C O_{2} \)
\( c \cdot(c) C O_{3}^{2} \)
D \( \cdot(d) \operatorname{Si} O_{2} \)


If the ratio of the angles of a triangle is
2: 3: 5 then angles are
A \( \cdot 36^{\circ}, 54^{\circ}, 90^{\circ} \)
В . \( 18^{\circ}, 36^{\circ}, 126^{\circ} \)
c. \( 20^{\circ}, 60^{\circ}, 180^{\circ} \)
D. \( 18^{\circ}, 60^{\circ}, 102^{\circ} \)


For a reaction
\( 2 A+B \rightarrow C+D, \) the active mass of \( B \)
is kept constant but that of \( \boldsymbol{A} \) is tripled.
The rate of reaction will -
A. Decrease by 3 times
B. Increased by 9 times
C. Increase by 3 times
D. Unpredictable


What will happen if the diaphragm of a person gets ruptured in an accident?


Which of the following solution cannot act as a buffer?
A. \( N a H_{2} P O_{4}+H_{3} P O_{4} \)
в. \( C H_{3} \) СООН \( +C H_{3} \) СОО Na
c. \( H C l+N H_{4} C l \)
D. \( H_{3} P O_{4}+N a_{2} H P O_{4} \)


According to Hooke's law of elasticity, if stress is increased, then the ratio of
stress to strain :
A. becomes zero
B. remains costant
c. decreases
D. increases


Which of the following elements follow Dobereiner's law of Triads?
A. \( \mathrm{Na}=23, \mathrm{Li}=7 \) and \( \mathrm{K}=39 \)
B. Cl = \( 35, \mathrm{Br}=80 \) and \( \mathrm{F}=19 \)
c. \( \mathrm{ca}=40, \mathrm{Mg}=24 \) and \( \mathrm{Sr}=88 \)
D. \( \mathrm{Na}=23, \mathrm{K}=39 \) and \( \mathrm{Rb}=85 \)


In the given (a) calculate the effective
resistance of the circuit and (b)
calculate the reading of the ammeters
\( A_{1} A_{2} \) and \( A_{1} \) If \( R_{1}=10 \Omega \) and \( R_{2}=6 \Omega \)
and \( \boldsymbol{E}=\mathbf{1 0} \boldsymbol{V} \)


The vertical plane which passes through the magnetic axis of a freely suspended magnetic at rest is called
A. Magnetic meridian
B. Geographical meridian
c. North meridian
D. South meridian


If \( 1.0 \mathrm{g} \) body is traveling along the \( \mathrm{x} \) -axis at \( 100 \mathrm{cm} \mathrm{s}^{-1} \) within error limits of ±1
\( \mathrm{cm} \mathrm{s}^{-1}, \) what is the uncertainty in its
position?
\( \mathbf{A} \cdot 5 \times 10^{-30} \mathrm{m} \)
B. \( 5 \times 10^{-31} \mathrm{m} \)
c. \( 5 \times 10^{-20} \mathrm{m} \)
D. \( 5 \times 10^{-10} \mathrm{m} \)


The pressure inside a soap bubble of
radius \( 1 c m \) balances \( 1 m m \) of a column
of oil of specific gravity \( 0.8 . \) If the surface tension of the soap solution (in \( N / m \) ) is \( \mathbf{T}=\mathbf{n} \times \mathbf{1 0}^{-2}, \) find \( n . \) (Take
acceleration due to gravity to be
\( \left.10 m / s^{2}\right) \)


An electromagnet:
A. has its own persistent magnetic field
B. acts as a magnet when an electric current passes through it
C. both \( A \) and \( B \)
D. none of the above


If \( \boldsymbol{x}+\boldsymbol{i} \boldsymbol{y}=\frac{\boldsymbol{3}}{\boldsymbol{2}+\cos \boldsymbol{\theta}+\boldsymbol{i} \sin \boldsymbol{\theta}} \) then the
value of \( (x-3)(x-1)+y^{2}= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c .-1 \)
D.


Let \( \boldsymbol{f}(\boldsymbol{x}) \) be a polynomial of degree three
satisfying \( \boldsymbol{f}(\mathbf{0})=-\mathbf{1} \) and \( \boldsymbol{f}(\mathbf{1})=\mathbf{0} \)
Also, 0 is a stationary point of \( f(x) \). If
\( f(x) \) does not have an extremum at \( x=0, \) then \( \int \frac{f(x)}{x^{3}-1} d x \) is equal to
A \( \cdot \frac{x^{2}}{2}+c \)
B. \( x+c \)
c. \( \frac{x^{3}}{6}+c \)
D. None of these


Determine the oxidation state of Cr in
\( \left[\boldsymbol{C r}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4} \boldsymbol{C l}_{2}\right] \boldsymbol{C l} \)
\( A \cdot+3 \)
B . - -
\( c \cdot+2 \)
\( D \cdot+4 \)


Assertion
Potential is work done to bring a point charge from infinity to to required point under the influence of electric field.
Reason
Gravitational potential is analogous to electric potential and have same dimensions.
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


Determine range \( \boldsymbol{y}=\mathbf{3} \sin \boldsymbol{x}+ \)
\( 4 \cos (x+\pi / 3)+7 \)
A \( \cdot 7-\sqrt{5-3 \sqrt{3}}, 7+\sqrt{5-3 \sqrt{3}} \)
B・ \( 7-\sqrt{10-3 \sqrt{3}}, 7+\sqrt{10-3 \sqrt{3}} \)
c. \( _{7}-\sqrt{10+3 \sqrt{3}}, 7+\sqrt{10-3 \sqrt{3}} \)
D \( \cdot 7-\sqrt{10+3 \sqrt{3}}, 7-\sqrt{10-3 \sqrt{3}} \)


The value of the resistance \( R \) in figure
is adjusted such that power dissipated
in the \( 2 \Omega \) resistor is maximum. Under
this condition
This question has multiple correct options
A \( . R=0 \)
в. \( R=8 \Omega \)
c. power dissipated in the \( 2 \Omega \) resistor is \( 72 ~ W \)
D. power dissipated in the \( 2 \Omega \) resistor is \( 8 W \)