During propagation of longitudinal plane wave in a medium, two particles separated by a distance equivalent to one wavelength at an instant will be/have
A. In phase, same displacement
B. In phase, different displacement
C. Different phase, same displacement
D. Different phase, different displacement


Which one of the following compounds would
undergo nitration with the greatest ease?
A. benzene
B. phenol
c. nitrobenzene
D. benzoic acid


What is residual entropy?


(i) Define mutual inductance.
(ii) A pair of adjacent coils has a
mutual inductance of 1.5 H. If the
current in one coil changes from 0 to
\( 20 A \) in \( 0.5 s, \) what is the change of flux linkage with the other coil?


Tangential acceleration of the centre of
mass is:
\( \mathbf{A} \cdot \frac{3 F}{4 m} \)
в. \( \frac{F}{m} \)
c. \( \frac{2 F}{3 m} \)
D. \( \frac{4 F}{3 m} \)


\( \lim _{x \rightarrow \infty}(\sqrt{x^{2}+x}-\sqrt{x^{2}-x}) \) equals
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \infty \)
c. 1
D.


Calculate the energy emitted by the sun
in one second. Also estimate the mass
of the sun that is converted to energy in one second.
(Take solar constant as \( 1.4 \times \)
\( 10^{3} W m^{-2}, \) distance between the earth
and the sun as \( 1.5 \times 10^{11} m \) and the
velocity of light as \( 3 \times 10^{8} m S^{-1} \) ).


A particular rocket is propelled such that its velocity increases as a function of time according to \( v(t)=A t^{\frac{1}{2}}, \) where
\( A \) is a constant.
Which of the following represents the correct acceleration function?
A \( \cdot a(t)=\frac{2}{3} A t^{3 / 2} \)
B \( \cdot a(t)=2 A t^{3 / 2} \)
c. \( a(t)=\frac{1}{2} A t^{-1 / 2} \)
D. \( a(t)=\frac{-1}{2} A t^{-1 / 2} \)
E. None of the above


If \( f(x)=\frac{2^{x}+2^{-x}}{2}, \) then \( f(x+ \)
\( y) \cdot f(x-y) \) is equal to \( ? \)
A \( \left.\cdot \frac{1}{2}[f(x+y)]+f(x-y)\right] \)
B. \( \frac{1}{2}[f(2 x)+f(2 y)] \)
c. \( \left.\frac{1}{2}[. f(x+y)]+f(x-y)\right] \)
D. None of these


In a long straight conductor carrying current, if the current is tripled and the
distance of the point from the conductor
is doubled, then the ratio of new
magnetic induction to old magnetic
induction is
A .3: 2
B . 2: 3
\( c \cdot 4: 9 \)
9: 4


Match the columns and find the correct
option.
(a) Munch
(i) Stomatal movement
(ii) Hastens fruit ripening by
(b) Darwin \( \quad \) volatiles
\( (c) \)
(iii) Growth of coleo towards light Cousins
(d) Levitt
(iv) Nature of enzymes
(v) Bidirectional traces in phloem
\( A \cdot a-i i i, b-i v, c-i, d-i i \)
B. a-iv, b-iii, c- i, d-i i
C. \( a-v, b- \) iii, c- ii, d- i
D. a- iii, b- i, c- iv, d- v


Which of the following is present at the time of cracking of hydrocarbons?
A. copper
B. Zeolite
c. Nickel
D. Molybdenum


Cycle tube when filled with an air, it swells up because of the pressure exerted by the particles of the air in the tube
A. True
B. False


cathode plate inside a vacuum tube as
shown in the figure. The work function
of the cathode surface is \( \phi \) and the
anode is a wire mesh of conducting
material kept at a distance d from the
cathode. A potential difference V is
maintained between the electrodes. If
the minimum de Broglie wavelength of
the electrons passing through the
anode is \( \lambda_{e}, \) which of the following
statement(s) is(are) true?
A \( \cdot \lambda_{e} \) increases at the same rate as \( \lambda_{p h} \) for \( \lambda_{p h}<h c / \phi \)
B. \( \lambda_{e} \) is approximately halved, if dis doubled
C. \( \lambda_{e} \) decreases with increase in \( \phi \) and \( \lambda_{p h} \)
D. For large potential difference \( (V>>\phi / e) \lambda_{e} \) is
pproximately halved if \( V \) is made four time


Degree of the polynomial \( \boldsymbol{p}(\boldsymbol{x})=-10 \)
is
A . -10
B. 10
\( c \cdot 0 \)
D.


Upon mixing equal volume of two solution of strong acids having pH values \( 2 \& 4, \) resulting solution will
have pH:
A. equal to 3
B. closer to 2 than 4
c. closer to 4 than 2
D. closer to 3 than 2


There is a sudden increase in current in
zener diode is
A. Due to rupture of bonds
B. Resistance of deplection layer becomes less
c. Due to high doping
D. Due to less doping


What is the current in the circuit shown
(Figure)
\( \mathbf{A} \cdot 1.5 A \)
B. \( 0,5 A \)
\( \mathbf{c} .2 .5 A \)
D. None of these


In the equation:
\( \boldsymbol{C u}+\boldsymbol{X} \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \rightarrow \boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{2}+ \)
\( \boldsymbol{Y} \boldsymbol{N} \boldsymbol{O}_{2}+\mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O} \)
the value of \( X \) and \( Y \) are?
A. 3 and
B. 8 and 6
c. 4 and 2
D. 7 and


State the law of conservation of angular
momentum


Calculate the following with due regard for significant figures:
\( \frac{\mathbf{1 . 5 3} \times \mathbf{0 . 9 9 9 5}}{\mathbf{1 . 5 9 2}} \)
A .0 .961
B. 0.921
c. 0.123
D. 0.913


A body rotating with uniform angular acceleration covers \( 100 \pi(\text {radian}) \) in
the first \( 5 s \) after the start. Its angular
speed at the end of \( 5 s( \) in radian/s) is
then
A . \( 40 \pi \)
B. \( 30 \pi \)
\( c \cdot 20 \pi \)
D. \( 10 \pi \)


The area bounded by the circle \( x^{2}+ \)
\( y^{2}=8, \) the parabola \( x^{2}=2 y \) and the
line \( y=x \) in \( y \geq 0 \) is
A \( \cdot \frac{2}{3}+2 \pi \)
в. \( \frac{2}{3}-2 \pi \)
c. \( \frac{2}{3}+\pi \)
D. \( \frac{2}{3}-\pi \)


Sexually transmitted diseases can be prevented by using condoms.
A. True
B. False


You are marooned on a frictionless
horizontal plane and cannot exert any
horizontal force by pushing against the
surface. How can you get off
\( \mathbf{A} \cdot \) By jumping
B. By rolling your body on the surface
C. By splitting or sneezing or throwing any object
D. By throwing an object in opposite direction


A body of mass \( 10 \mathrm{kg} \) moving with a velocity of \( 5 m s^{-1} \) hits a body of 1 gm at rest. Find the velocity of the second body after collision assuming it to be perfectly elastic?
A \( \cdot 10 m s^{-1} \)
B. \( 5 m s^{-1} \)
\( \mathbf{c} \cdot 15 m s^{-1} \)
D. \( 0.10 m s^{-1} \)


A rectangular coil of 500 turns and of
\( \operatorname{area} 6 \times 10^{-4} m^{2} \) is suspended inside a
radial magnetic field of induction
\( 10^{-4} T \) by a suspension wire of torsional constant \( 5 \times 10^{-10} N m \) per degree
Calculate the current required to
produce a deflection of \( 10^{\circ} \)


The sum of 1 st \( n \) terms of the series
\( \frac{1^{2}}{1}+\frac{1^{2}+2^{2}}{1+2}+\frac{1^{2}+2^{2}+3^{2}}{1+2+3}+\dots \dots \)
\( ^{\text {A } \cdot \frac{n+2}{3}} \)
в. \( \frac{n(n+2)}{3} \)
c. \( \frac{n(n-2)}{3} \)
D. \( \frac{n(n-2)}{6} \)


\( \mathbf{A} \)
\( 0.5 \mathrm{kg} \) block slides from the point \( \mathrm{A} \) on a horizontal track with an initial speed \( 3 \mathrm{m} / \mathrm{s} \) towards a weightless horizontal spring of length \( 1 \mathrm{m} \) and force constant
2 N/m. The part AB of the Track is frictionless and the part BC has the coefficient of static and kinetic friction
as 0.22 and 0.20 respectively. If the distance \( A B \) and \( B D \) are \( 2 m \) and 2.14 m
respectively, find the total distance through which the block moves before it comes to rest completely.
\( \left(g=10 m / s^{2}\right) \)


The electron drift speed is small and the charge of the electron is also small
but still, we obtain large current in a conductor. This is due to
A. the conducting property of the conductor
B. the resistance of the conductor is small
c. the electron number density of the conductor is small
D. the electron number density of the conductor is enormous


Sum to \( n \) terms the series:
\( \mathbf{1} \times \mathbf{2}+\mathbf{2} \times \mathbf{3}+\mathbf{3} \times \mathbf{4}+\mathbf{4} \times \mathbf{5}+\dots \)


A chord of a circle of radius \( 15 \mathrm{cm} \)
subtends an angle of \( 60^{\circ} \) at the center.
Find the of the corresponding minor and major segments of the circle. \( (U s e \pi=3.14 a n d \sqrt{3}=1.73) \)


Area of the segment cut off from the
parabola \( \boldsymbol{x}^{2}=\mathbf{8} \boldsymbol{y} \) by the line \( \boldsymbol{x}-\boldsymbol{2} \boldsymbol{y}+ \)
\( \mathbf{8}=\mathbf{0} \) is:
A . 12
B. 24
c. 48
D. 36


Which of the following is the solution set of the equation \( 2 \cos ^{-1}(x)= \)
\( \cot ^{-1}\left(\frac{2 x^{2}-1}{2 x \sqrt{1-x^{2}}}\right) ? \)
\( \mathbf{A} \cdot(0,1) \)
B . \( (-1,1)-\{0\} \)
c. (-1,0)
D \cdot [-1,1]


Very short answer type. In what form Is the food stored in green
algae?


Of the students in a college, it is known
that \( 60 \% \) reside in hostel and \( 40 \% \) are
day scholars.Previous year results report that \( 30 \% \) of all students who
reside in hostel attain 'A' grade and \( 20 \% \) of day scholars attain 'A' grade in their
annual examination. At the end of the
year, one student is chose at random
from the college and he has an 'A' grade, what is the probability that the student is a hostlier?


Assertion
An electric motor converts electrical
energy to mechanical energy.
Reason
The working of the motor is based on
mutual induction.
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


Protein rich diet brings about relatively no change in which of the following constituents of urine?
A. Urea
B. Creatinine
c. Uric acid
D. Ammonia


Which is the last step in the process?
\( A \cdot 1 \)
B. 2
\( c .3 \)
D. 4


The following statements relate to the
adsorption of gases on a solid surface.
Identify the incorrect statement among
them :
A. Enthalpy of adsorption is negative.
B. On adsorption, the residual forces on the surface are increased.
C. On adsorption, decrease in surface energy appears as heat
D. Entropy of adsorption is negative.


The solubility of a gas in a liquid is directly proportional to the pressure of the gas. This statement is:
A. Raoult's law
B. Henry's law
c. van't Hoff's law
D. None of these


Given is a representation of a type of pollution. Study the picture and answer the question. Write one measure to reduce this
pollution.


Find the slope of the line, which makes
an angle of \( 30^{\circ} \) with the positive
direction of \( y- \) axis measured
anticlockwise.


Chilli is
A. Solanum melongena
B. Atropa acuminata
C . Capsicum annuum
D. Physalis peruviana


Find the product of \( (-1) \times(-2) \times \)
\( (3) \times 4 \)


p-type crystal of p-njunction diode is
connected to a positive terminal of
battery and n-type crystal connected to
negative terminal of battery. Then
A. diode is forward biased.
B. diode is reversed biased.
C. potential barrier in depletion layer increases.
D. potential barrier in depletion layer remains unchanged.


In reduction of dichromate by \( \boldsymbol{F} \boldsymbol{e}(\boldsymbol{I} \boldsymbol{I}) \)
the number of electrons involved per
chromium atoms is:
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D.


\( \frac{1}{2.3}+\frac{1}{4.5}+\frac{1}{6.7}+\ldots \infty= \)
A \( \cdot 1+\log _{e} 2 \)
B . \( 1-\log _{\mathrm{e}} 2 \)
c. \( 2+\log _{\mathrm{e}} 2 \)
D. \( 2-\log _{\mathrm{e}} 2 \)


Construct a quadrilateral \( A B C D \) in
which \( A B=4.2 c m, B C= \)
\( 6 c m, C D=5.2 c m, D A=5 c m \) and
\( \boldsymbol{A C}=\mathbf{8 c m} \)


A process is approximately reversible. In real life scenarios, this happens only
when:
A. system variables are constant
B. the change in system variables is very fastt
c. the change in system variables is very slow
D. A or


\( \lim _{x \rightarrow 0} \frac{\sin |x|}{x} \) is equal to
\( \mathbf{A} \cdot 1 \)
B. 0
C. Positive infinity
D. Does not exist


According to Dobereiner in Triads, atomic weight of the centre element is equal to 1st and 3rd
elements in that triads.
A. Geometric Mean
B. Arithmetic Mean
c. Harmonic Mean
D. None of these


a. Which gas is dissolved in soft drinks?
What will you do to increase the solubility of this gas?


How will you bring about the following conversions?
(i) Ethanol to but-1-yne
(ii) Ethane to bromoethene
(iii) Propene to1-nitropropane
(iv) Toluene to benzyl alcohol
(v) Propene to propyne Ethanol to ethyl fluoride
(vii) Bromomethane to propanone
(viii) But-1-ene to but-2-ene
(ix) 1 -Chlorobutane to n-octane
(x) Benzene to biphenyl.


What is the number of significant figures obtained after addition of
4.523,2.3 and \( 6.24 ? \)
A. Two
B. Three
c. Four
D. Five


Verify: \( \boldsymbol{A}^{\prime} \cap \boldsymbol{B}=\boldsymbol{B}-(\boldsymbol{A} \cap \boldsymbol{B}) \)
A. True
B. False


(a) Roasting and calcination are the two processes to reduce the metal oxides to
the respective metals.
(b) Magnesium is extracted from its ore by electrolytic reduction process.
(c) Cryolite is used in metallurgy of aluminium in order to increase the
fusibility and conductivity
(d) I Hall's process bauxite is leached
with the help of \( N a_{2} C O_{3} \)
Which of the following options regarding the above statements is
correct?
\( A \cdot a, b \) and \( c \)
B. b, c and d
\( c \cdot c \) and \( d \)


Because of lanthanoid contraction
A. zrand Y have about the same radius
B. zrand Nb have similar oxidation state
c. zrand \( H f \) have about the same radius
D. zrand zn have the same oxidation state


Three roots of \( n \) are
A. 0,1,2
в. -1,1,3
\( \mathrm{c} .-2,2,3 \)
D. -3,1,5


In dinophyceae, trichocysts occur in
A. Peridinium
B. Nematodinium
c. caratium
D. Gonyaulax.


Derive the balancing condition of a
Wheatstone bridge.


The cost price of 40 Magazines is the
same as the selling price of 'P' articles. If the profit is \( 25 \% \), then find the value of
P'.


Calculate the wavelength (in nanometre) associated with a proton moving at \( 1 \times 10^{3} m s e c^{-1} \)
\( \left[\text { mass of proton }=\mathbf{1 . 6 7} \times \mathbf{1 0}^{-\mathbf{2 7}} \mathbf{k g}, \boldsymbol{h}=\right. \)
\( 6.63 \times 10^{-34} J \) sec
\( \mathbf{A} \cdot 0.032 \mathrm{nm} \)
B. \( 0.40 \mathrm{nm} \)
c. \( 2.5 \mathrm{nm} \)
D. \( 14 \mathrm{nm} \)


A gas mixture \( 3.67 L \) in volume contain
\( C_{2} H_{4} \) and \( C H_{4} \) is proportion of 2: 1 by
moles and is at \( 25^{\circ} \mathrm{C} \) and 1 atm. If the
\( \Delta H_{C}\left(C_{2} H_{4}\right) \) and \( \Delta H_{C}\left(C H_{4}\right) \) are
-1400 and \( -900 k J / m o l, \) find heat evolved on burning this mixture:
в. \( 50.88 k J \)
c. \( 201 k J \)
D. 160kJ


A steamer is heading due North with
\( 20 m s^{-1} . \) The wind is blowing \( 10 m s^{-1} \) due west. In which direction the flag on the mast flutters?
A \( \cdot \tan ^{-1} \frac{1}{2} \) west of north
B. \( \tan ^{-1} \frac{1}{2} \) east of north
c. \( \tan ^{-1} \frac{1}{2} \) north of east
D. \( \tan ^{-1} \frac{1}{2} \) north of west


A ball of mass \( 10 \mathrm{kg} \) is moving with a velocity of \( 10 \mathrm{m} / \mathrm{s} \). It strikes another ball
of mass \( 5 \mathrm{kg} \), which is moving in the same direction with a velocity of \( 4 \mathrm{m} / \mathrm{s} \) If the collision is elastic their
velocities after collision will be
respectively:
A \( \cdot 12 \mathrm{m} / \mathrm{s}, 6 \mathrm{m} / \mathrm{s} \)
B. \( 12 \mathrm{m} / \mathrm{s}, 25 \mathrm{m} / \mathrm{s} \)
\( c \cdot 6 m / s, 12 m / s \)
D. \( 8 \mathrm{m} / \mathrm{s}, 20 \mathrm{m} / \mathrm{s} \)


For AX ionic crystal to exist in bcc
structure, the ratio of
\( \left(\frac{r_{\text {cation}}}{r_{\text {anion}}}\right) \) should be
A. between 0.41 to 0.73
B. greater than 0.73
C. less then 0.41
D. None of these


A light wave can travel
This question has multiple correct options
A. In vacuum
B. In vacuum only
C . In a material medium
D. In a material medium only


Both antacids and anti allergic drugs are antihistamines hence, they can be
use in place of each other. If true enter 1 , if false enter 0 .


For a differentiable function \( \phi(x) \) find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) for \( \boldsymbol{y}=\boldsymbol{e}^{\sin \phi(\boldsymbol{x})} \)


Which of the ligands can show linkage
isomerism?
\( \mathbf{A} \cdot C N S \)
в. \( N O_{2} \)
c. \( C N \)
D. All of these


The red or orange coating that forms on the surface of iron when exposed to air
and moisture for some time is called:
A. galvanisation
B. electroplating
c. rust
D. reduction


With reference to the figure shown, if the coefficient of friction at the
surfaces is 0.42 , then the force
required to pull out the \( 6.0 k g \) block with
an acceleration of \( 1.50 m / s^{2} \) will be :
A \( .36 N \)
в. 24 N
\( c .84 N \)
D. \( 51 N \)


If you deposit Rs. 500 in an account that earns \( 5 \% \) compounded quarterly, then what would be the balance in that
account after 4 years?
A. 600
в. 610
\( c .620 \)
D. 630


Chipko movement is concerned with
A. Conservation of water resources
B. Conservation of forest
C. Conservation of tiger
D. Conservation of biodiversity


\( B e C l_{2} \) is an electrophile and has
polymeric structure in solid state. Answer whether the above statement is
true or false.
If true enter 1 , else enter 0 .


Which of the following statements is/are incorrect about lymph?
(i)Lymph is colourful as it has haemoglobin but no RBC.
(ii)lt contains specialised Iymphocytes which are responsible for immunity of the body.
(iii)Lymph is an important carrier for nutrients and hormones.
(iv)Fats are absorbed through lymph in
the lacteals present in the intestinal villi.
A. i only
B. iii and iv
c. ii and iii
D. iv only


Assertion: Atoms are not electrically
neutral
Reason: Number of protons and
electrons are different.
A. Both assertion and reason are true and the reason is a correct explanation of the assertion.
B. Both assertion and reason are true but reason is not a correct explanation of the assertion.
c. Assertion is true but reason is false
D. Both the assertion and reason are false.
E. Assertion is false but reason is true


Higher is the (mass/volume) of
solute in a solution lower is its vapour
pressure.


What is coordinate bond?


Property of all the alkaline earth metals
that increases with their atomic
number is:
A. solubility of their carbonates
B. thermal stability of their sulphates
c. ionisation energy
D. electronegativity


What is the wavelength of the most energetic photon emitted in the Balmer's series of the hydrogen atom?
A . 3694 A
в. 5756 А
c. 3333 А
D. 3669 A


suppose that a hypothetical atom gives a red, green,blue and violet line spectrum. Which jump according to figure would give off the red spectral
ine
A \( .3 \rightarrow 1 \)
В . \( 2 \rightarrow 1 \)
\( c \cdot 4 \rightarrow 1 \)
D. \( 3 \rightarrow 2 \)


Select the species which can act as an acid as well as base.
This question has multiple correct options
\( \mathbf{A} \cdot S O_{4}^{2-} \)
в. \( H S^{-} \)
\( \mathrm{c} \cdot \mathrm{H} \mathrm{CO}_{3}^{-} \)
D. \( H S O_{4} \)


Read the following statements
regarding liver:
(A)Hepatic lobules are structural and functional unit of liver.
(B)Liver secreates bile, which contains
digestive enzymes
(C) Each hepatic lobule is covered by a thin epithetial tissue, called "Glisson's capsule"
(D) Hepato-pancreatic duct is guarded by sphincter of Boyden. Correct statements regarding liver is/are:-
A. one
B. Two
c. Three
D. Four


For a reversible reaction, \( A \stackrel{\boldsymbol{K}_{1}}{\dot{\boldsymbol{K}}_{2}} \boldsymbol{B}, \) Ist
order in both the directions, the rate of
reaction is given by:
\( \mathbf{A} \cdot K_{1}[A] \)
\( \mathbf{B} \cdot-K_{2}[B] \)
\( \mathbf{c} \cdot K_{1}[A]+K_{2}[B] \)
\( \mathbf{D} \cdot K_{1}[A]-K_{2}[B] \)


If \( f(y)=e^{y} \) and \( g(y)=y, y>0 \) and
\( \boldsymbol{F}(\boldsymbol{t})=\int_{0}^{t} \boldsymbol{f}(\boldsymbol{t}-\boldsymbol{y}) \boldsymbol{g}(\boldsymbol{y}) d \boldsymbol{y} \) then
A \( \cdot F(t)=e^{t}-(1+t) \)
B \( \cdot F(t)=t e^{t} \)
\( \mathbf{c} \cdot F(t)=t e^{-t} \)
\( \mathbf{D} \cdot F(t)=1-e^{t}(1+t) \)


A ray reflected successively from two plane mirrors inclined at a certain
angle undergoes a deviation of \( 240^{\circ} \)
Then, the number of images observable is?
A . 3
B. 5
\( c \cdot 7 \)
D.


Hardness in water is expressed in
terms of ppm of \( C a C O_{3} . \) If hardness is
200 ppm \( C a C O_{3}, \) then in terms of molarity, it is:
A. \( 0.004 \mathrm{M} \)
B. \( 0.002 M \)
c. \( 0.001 M \)
D. \( 0.0005 M \)


Fluorine shows anomalous behavior in
VIIA group due to:
A. its small size
B. high electronegativity
c. absence of d-orbitals
D. All


Write the following rational numbers in
ascending order:
\( \frac{3}{4}, \frac{7}{12}, \frac{15}{11}, \frac{22}{19}, \frac{101}{100}, \frac{-4}{5}, \frac{-102}{81}, \frac{-13}{7} \)


Consider the diagram given below
Parts labelled as \( A, B, C, D, E \) and \( F \)
respectively indicate
A. Sacrum, lilum, pubis, femur, tibia and fibula
3. Ilium, pubis, sacrum, femur, fibula and tibia
c. Sacrum, pubis, ilium, femur, tibia and fibula
2. llium sacrum oubis, femur. tibia and fibula


The largest sphere is cut off from a cube of side \( 5 \mathrm{cm} . \) The volume of the sphere
will be
\( \mathbf{A} \cdot 27 \pi \mathrm{cm}^{3} \)
в. \( 30 \pi \mathrm{cm}^{3} \)
\( \mathbf{c} \cdot 108 \pi \mathrm{cm}^{3} \)
D. \( \frac{125 \pi}{6} \mathrm{cm}^{3} \)


Diagram shows an electron gun inside a
cathode ray tube. Which of the following
is true?
A. F is Filament, to heat the cathode
B. \( x \) is Cathode, to emit the electrons
C. \( Y \) is Anode, to provide kinetic energy to electrons
D. All the above


Find the modulus and amplitude of \( -2 i \)
A \( \cdot|z|=2 ; \operatorname{amp}(z)=-\frac{3 \pi}{2} \)
В \( \cdot|z|=2 i ; a m p(z)=\frac{\pi}{2} \)
c. \( |z|=2 ; a m p(z)=\frac{\pi}{2} \)
D \( \cdot|z|=2 ; \operatorname{amp}(z)=-\frac{\pi}{2} \)


What is thickness of the plate?
\( A .5 \mu m \)
В. \( 0.005 \mu m \)
\( \mathrm{c} .7 \mu \mathrm{m} \)
D. \( 0.007 \mu m \)


Hot air is blown from which side of a
rotary kiln at \( 1873 \mathrm{K} \) to manufacture
cement?
A. Mlddle
B. Lower
c. Top
D. No air is blown


In Bessemer converter, \( \boldsymbol{C} \boldsymbol{u}_{2} \boldsymbol{S} \) is converted to blister copper by:
A. self reduction
B. reduction with coke
c. reduction with coal gas
D. reduction with \( H_{2} \) gas


The velocity of sound in air is \( V \) and the
root mean square velocity of the molecules is \( c \). The \( V / c= \)
A \( \cdot \frac{\gamma}{3} \)
в. \( \quad\left[\frac{\gamma}{3}\right]^{\frac{1}{2}} \)
c. \( \frac{\gamma}{\sqrt{3}} \)
D. \( \frac{\sqrt{\gamma}}{3} \)


The number of metamers of the compound with molecular formula
\( C_{5} H_{10} O \) is
A
B. 3
\( c \cdot 8 \)
D.


Which of the following effect of auxins on plants is the basis for commercial
application?
A. Callus formation
B. Curvature of stem
c. Induction of root formation in stem cuttings
D. All of the above


The equation of lines parallel to \( 3 x- \)
\( 4 y-5=0 \) at a unit distance from it is
A. \( 3 x-4 y-10=0 \)
в. \( 5 x+3 y-5=0 \)
c. \( 3 x+4 y+10=0 \)
D. \( 6 x+2 y+4=0 \)


Pressure within the lungs is called
A. Inter-pulmonary pressure
B. Intra-pulmonary pressure
c. Interstitial pressure
D. Alveolar pressure


\( \int_{0}^{\pi} x f(\sin x) d x \) equals
\( ^{\mathbf{A}} \cdot_{2 \pi} \int_{0}^{\frac{\pi}{2}} f(\sin x) d x \)
в. \( \pi \int_{0}^{\pi} f(\sin x) d x \)
c. \( \quad \pi \int_{0}^{\frac{\pi}{2}} f(\sin x) d x \)
D. None of these


A massless rigid rod of length \( 50 \mathrm{cm} \)
whose one end is attached to the edge
of the table at point \( O \) and at the other
end of the rod is a ball of clay of mass
\( \boldsymbol{m}=\mathbf{0 . 2 k g} . \) The rod extends horizontally
from the end of the table. Find out the
torque of the gravitational force on the
clay ball about point \( O ? \)
A \( .0 .01 N-m \)
B. \( 0.1 N-m \)
c. \( 1 N-m \)
D. \( 10 N-m \)
E \( .100 N-m \)


"Sella tursica" is a
A. Depression in brain enclosing pituitary
B. Cavity of skull enclosing ears
C. Covering of testis
D. Kind of endocrine gland


Assertion
Statement-1: \( \int \frac{x^{2}-1}{\left(x^{2}+1\right) \sqrt{x^{4}+1}} d x= \)
\( \sec ^{-1}\left|\frac{x^{2}+1}{x \sqrt{2}}\right|+C \)
Reason
staement-2: \( \int \frac{\boldsymbol{d t}}{\boldsymbol{t} \sqrt{\boldsymbol{t}^{2}-\boldsymbol{a}}}= \)
\( \frac{1}{\sqrt{a}} \sec ^{-1}\left|\frac{t}{\sqrt{a}}\right|+C \)
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 parallel plate capacitor with circular
plates and a capacitance \( C \) has the
radius of each plate doubled and the
distance between the plates doubled.
What is the new capacitance?
\( ^{A} \cdot \frac{C}{2} \)
в. \( C \)
\( c \cdot 2 C \)
D. \( 4 C \)


A uniform string of length \( l \), fixed at
both ends is vibrating in its \( 2 n d \)
overtone. The maximum amplitude is 'a
and tension in string is 'T', if the energy of vibration contained between two
consecutive nodes is \( \frac{K}{8} \cdot \frac{a^{2} \pi^{2} T}{l} \) then \( ^{\prime} K \) is


A discrete random variable X has the
probability distribution given below:
\( x= \)
1 0.5 1.5
2
\( P(x): \) \( k \) \( 3 k \) \( 2 k \) The
Find the value of \( \mathrm{k} \)


The domain of \( \mathbf{f}(\mathbf{x})=\log _{\mathbf{x}}\left(\mathbf{9}-\mathbf{x}^{2}\right) \) is
A. (-3,3)
B. \( (0, \infty) \)
c. (0,1)\( \cup(1, \infty) \)
D. (0,1)\( \cup(1,3) \)


A spherical ball of radius \( r \) and relative
density 0.5 is floating in equilibrium in water with half of its immersed in
water. The work done in pushing the ball down so that whole of it is just
immersed in water is \( 1 \rho \) is the density
of water-
A. 0.25 prg
в. \( 0.5 \rho r g \)
c. \( \frac{4}{3} \pi r^{3} \rho g \)
D. \( \frac{5}{12} \pi r^{4} \rho g \)


What number corresponds to the fifth missing planet?
A . 28
B. 78
c. 32
D. 36


UAA, UAG and UGA are
A. Non overlapping codons
B. Non sense codons
C. Degenerate codons
D. Chain initiator codons


Find the smallest number by which 256 must be multiplied, so that the product is a perfect cube
\( \mathbf{A} \cdot \mathbf{0} \)
B . 2
\( c .3 \)
D.


Show that \( \boldsymbol{A}(\mathbf{1}, \mathbf{1}, \mathbf{2}), \boldsymbol{B}(\mathbf{2}, \mathbf{1}, \mathbf{3}) \) and
\( C(1,3,5) \) are not collinear.


Some vascular bundles are described
as open because these
A. are surrounded by pericycle but no endodermis
B. are capable of producing secondary xylem and phloem
c. possess conjuctive tissue between xylem and phloem
D. are not surrounded by pericycle


A bag contains \( a \) white and \( b \) black
balls. Two players, \( A \) and \( B \) alternately
draw a ball from the bag, replacing the
ball each time after the draw till on of
them draws a white ball and win the
game. \( A \) begins the game. If the
probability of \( \boldsymbol{A} \) winning the game is
three times that of \( B \), the ratio \( a: b \) is
A . 1: 1
B. 1: 2
\( c \cdot 2: 1 \)
D. None of these


When brakes are applied to a bus, the
retardation produced is \( 25 \mathrm{cm} \mathrm{s}^{-2} \) and
the bus takes 20 s to stop. Calculate the initial velocity of the bus.
A \( .500 \mathrm{m} \mathrm{s}^{-1} \)
B. \( 5 \mathrm{cm} \) s \( ^{-1} \)
c. \( 5 m s^{-1} \)
D. \( 12.5 \mathrm{m} \mathrm{s}^{-1} \)


Find the slope of the line whose
inclination is
\( \mathbf{1 0 5}^{\circ} \)


A sphere of radius \( r, \) inside a cube
touches each one of the six sides of the cube. What is the volume of the cube in
terms of \( r ? \)
\( \mathbf{A} \cdot 8 r^{3} \)
B \( .2 r^{3} \)
\( \mathbf{c} \cdot 4 r^{3} \)
D. \( \frac{4}{3} \pi r \)


Figure represents two processes, a and
b for a given sample of gas. Let \( \triangle Q_{1} \)
and \( \triangle Q_{2} \) be the heat absorbed by the
systems in the two cases respectively.
Which of the following relations is
correct?
\( \mathbf{A} \cdot \triangle Q_{1}=\triangle Q_{2} \)
B \( \cdot \triangle Q_{1}>\triangle Q_{2} \)
\( \mathbf{c} \cdot \triangle Q_{1} \leq \triangle Q_{2} \)
\( \mathbf{D} \cdot \triangle Q_{1}<\triangle Q_{2} \)


A panda with a mass of \( 90.0 k g \) lies
without moving on a ramp that is
inclined at \( 25.0^{\circ} \)
What is the coefficient of
static frictional force between the ramp
and the panda?
A . 0.25
B. 0.423
\( c \cdot 0.466 \)
D. 372
E. The coefficient of static friction cannot be determined with the information giver


A current flows in a wire of circular
cross section with the free electrons
travelling with drift velocity \( \bar{V} \). If an equal current flows in a wire of same material and twice the radius, the new
drift velocity is:
\( \mathbf{A} \cdot \bar{V} \)
B. \( \frac{\vec{v}}{2} \)
c. \( \frac{\vec{v}}{4} \)
D. 2 \( \bar{V} \)


If weight of an object in air \( W_{a} \) is
\( (10.0 \pm 0.1) g \) and its weight in water
\( W_{L} \) is \( (5.00 \pm 0.2) g, \) then percentage
error in its relative density is? \( \left(\text { Relativedensity }=\frac{W_{a}}{W_{a}-W_{L}}\right) \)
A . \( 2 \% \)
B. \( 5 \% \)
c. \( 7 \% \)
D. \( 1.5 \% \)


In a geometric progression, the sum of first \( n \) terms is \( 65535 . \) If the last term is
49152 and the common ratio is \( 4, \) then
find the value of \( n \)


\( n \) elastic balls are placed at rest on a
smooth horizontal plane which is circular at the ends with radius \( r \) as
shown in the figure. The masses of the balls are \( m, \frac{m}{2}, \frac{m}{2^{2}} \ldots \ldots \frac{m}{2^{n-1}} \)
respectively. What is the minimum velocity which should be imparted to
the first ball of mass \( m \) such that \( n^{t h} \)
ball completes the vertical circle:
A \( \cdot\left(\frac{3}{4}\right)^{n-1} \sqrt{5} g r \)
В \( \cdot\left(\frac{4}{3}\right)^{n-1} \sqrt{5 g r} \)
c. \( \left(\frac{3}{2}\right)^{n-1} \sqrt{5 g r} \)
D \( \cdot\left(\frac{2}{3}\right)^{n-1} \sqrt{5 g r} \)


As plastics and synthetic fibers consist of repeating monomer units, they are known as
A . polyesters
B. polymers
c. co-polymers
D. None of the above


If \( z_{1}, z_{2}, \ldots, z_{n} \) lie on the circle \( |z|=2 \)
then the value of \( \mid z_{1}+z_{2}+\dots+ \)
\( z_{n}|-4| \frac{1}{z_{1}}+\frac{1}{z_{2}}+\ldots+\frac{1}{z_{n}} \mid \) is
A . 0
в.
c. \( -n \)
D.


8
8
8
8


Susceptibility is small and positive for
A. para magnetic only
B. diamagnetic only
c. ferro magnetic only
D. Both 1 \& 3


Which of the following are examples of
aerosols?
This question has multiple correct options
A. Whipped cream
B. Cloudd
\( c \cdot F o g \)
D. Soap lather


Q Type your question.
figure. The ring has a narrow gap f width
\( \delta \) in its circumference. The cross-
sectional area of the solenoid is \( a \). The
solenoid has a uniform internal field of
magnitude \( B(t)=B_{0}+\beta t, \) where \( \beta> \)
0. Assume that no charge can flow
across the gap, the face(s) accumulating an excess of positive
charge is/are
\( \mathbf{A} \cdot F_{1} \)
B . \( F_{2} \)
c. \( F_{1} \) and \( F_{2} \)
D. difficult to conclude as data given are insufficient
E. answer requirec


Cells at the end of prophase, when
viewed under the microscope do not
show
A. Golgi bodies and ER
B. Nucleolus and nuclear membrane
c. Chromosome and cintromere
D. More than one option is correct


The radius of a metal sphere is \( 100 \mathrm{cm} \)
\( \operatorname{at} 0^{\circ} \mathrm{C} \) and \( 101 \mathrm{cm} \) at \( 100^{\circ} \mathrm{C} . \) The
coefficient of volume expansion of metal is :
A \( \cdot 10^{-4} /^{\circ} \mathrm{C} \)
В. \( 3 \times 10^{-4} /^{\circ} \mathrm{C} \)
c. \( 2 \times 10^{-4} /^{\circ} \mathrm{C} \)
D. \( 1.5 \times 10^{-4} /^{\circ} \mathrm{C} \)


What is the basicity of \( H_{3} P O_{2} \) acid and
why?


The cluster of species formed on Galapagos islands are clear example of
all, except
A. Species formation arising by micro-evolutionary divergence from an ancestral form occupying different habitats, of microevolution leading to macro evolution
B. Founder's effect
c. Adaptive radiation
D. Sympatric speciation


Fermentation is represented by which of
the following equation?
\( \mathbf{A} \cdot \$ \$ \mathrm{C}_{-}\{6\} \mathrm{H}_{-}\{12\} \mathrm{O}_{-}\{6\} \backslash, \) ।rightarrow \( \backslash, 6 \mathrm{CO}_{-}\{2\} \backslash,+_{-} \backslash \)
\( 6 \mathrm{H}_{-}\{2\} 01,+\backslash, 673 \mathrm{K} \backslash, \mathrm{cal} \$ \$ \)
B. \( C_{6} H_{12} O_{6} \rightarrow 2 C_{2} H_{5} O H+2 C O_{2} \)
\( \mathbf{c} \cdot 6 C O_{2}+12 H_{2} O \rightarrow C_{6} H_{12} O_{6}+6 H_{2} O+6 O_{2} \)
\( \mathrm{D} \cdot 6 \mathrm{CO}_{2}+6 \mathrm{H}_{2} \mathrm{O} \frac{\text {light}}{\text {chlorophyll}} C_{6} \mathrm{H}_{12} \mathrm{O}_{6}+6 \mathrm{O}_{2} \)


If \( \boldsymbol{A}=\left[\begin{array}{lll}1 & 1 & 1\end{array}\right], \) then \( A \) is a
A. Identity matrix
B. Null matrix
c. Diagonal matrix
D. Row matrix


In what way are decomposers like
producers?
A. Either one may be the first member of a grazing food chain
B. Both produce oxygen for other forms of life
C. Both require a source of nutrient molecules and energy
D. Both supply organic food for the biosphere


If Meena gives an interest of \( \boldsymbol{R} \boldsymbol{s} \boldsymbol{4} \boldsymbol{5} \) for
one year at \( 9 \% \) rate p.a. What is the sum
she has borrowed.


Which of the following is not a thermodynamic function?
A. Enthalpy
B. Work done
c. Gibbs energy
D. Internal energy


Given that the two numbers appearin
the probability of the event 'the sum


The compound formed when aniline reacts with benzene diazonium chloride
is:
A. p-amino azobenzene
B. anilinium chloride
c. p-hydroxy azobenzene
D. diphenyl amine


Which of these is the best description of
a Zener diode?
A. It is a constant voltage device.
B. It operates in the reverse region
c. It is a constant current device
D. It works in forward region


Diagonals \( A C \) and \( B D \) of a trapezium
\( A B C D \) with \( A B \| D C \) intersect each
other at \( O . \) Prove that \( a r(A O D)= \)
\( \boldsymbol{a} \boldsymbol{r}(\boldsymbol{B O C}) \)


Starting from rest a wheel rotates with
uniform angular acceleration \( 2 \pi r a d / s^{2} \)
After \( 4 s, \) if the angular acceleration ceases to act, its angular displacement
in the next \( 4 s \) is:
B. \( 16 \pi \) rad
\( \mathbf{c} \cdot 24 \pi \quad r a d \)
D. \( 32 \pi \) rad


A person in a moving with the velocity of train. When he jumps from the train, inertia prohibits him to come at the
state of a rest all of sudden. Type 1 for true and 0 for false


If the mean deviation about the median
of the numbers \( a, 2 a, 3 a, \dots .50 a \) is 50
then \( |a| \) equals
A .2
B. 3
\( c \cdot 4 \)
D. 5


All organic compounds contain carbon and hydrogen both.
A. True
B. False


In a metre bridge, the balancing length from the left end (standard resistance
of one ohm is in the right gap) is found
to be \( 20 \mathrm{cm} \). The value of the unknown
resistance is
A . \( 4 \Omega \)
B. \( 0.5 \Omega \)
c. \( 0.4 \Omega \)
D. \( 0.25 \Omega \)


Assertion
Metals of high impurity are obtained by zone-refining.
Reason
Impurities in the ore are more soluble in
the metal than in the pure metal
Choose the correct option.
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 plant cell shrinks when it is kept in a?
A. hypotonic solution
B. hypertonic solution
C. isotonic solution
D. pure water


Energy of an electron is specified by:
A. \( n \)
B. \( l \)
c. \( n \) and \( l \)
D.


The ratio of sum of \( m \) and \( n \) terms of an
A.P is \( m^{2}: n^{2}, \) then the ratio of \( m^{t h} \) and
\( n^{t h} \) term.


\( (-28)+(-32)=? \)
\( A \cdot+60 \)
B. -60
c. 0
D. 60


During electrolysis of an aqueous
solution of sodium sulphate, 2.4 L of oxygen at STP was liberated at anode.
The volume of hydrogen at STP,
liberated at cathode would be:
A . 1.2
B. 2.4 L
c. 2.6
D. 4.8 L


In the hydrogen atom spectrum
\( \lambda_{3-1} \) and \( \lambda_{2-1} \) represent wavelengths emitted due to transition from second
and first excited states to the ground state respectively. The value of \( \frac{\lambda_{3-1}}{\lambda_{2-1}} \) is :
\( \mathbf{A} \cdot 27 / 32 \)
в. \( 32 / 27 \)
c. \( 4 / 9 \)
D. \( 9 / 4 \)


If \( 3 x+5 y=4, \) which of the following is
equivalent to the expression \( (6 x+ \)
\( (10 y)(100 x+100 y) ? \)
A. \( 100 x+100 y \)
в. \( 200 x+200 y \)
c. \( 400 x+400 y \)
D. \( 800 x+800 y \)
E . \( 1,600 x+1,600 y \)


For a reaction to be spontaneous, the
sign of Gibbs Free Energy change \( \Delta G \) is
A. always negative
B. always positive
c. sometimes negative
D. sometimes positive
E. The sign of \( \Delta G \) has no effect on spontaneity


Assertion
Avogram is equal to 1 amu.
Reason
Avogram is reciprocal of Avogadro's
number.
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


State which statement is true
about asexual reproduction?
This question has multiple correct options
A. It is uni parental in nature.
B. It is bi parental in nature.
C. Daughter cells contain genetic material same as parent cell
D. Daughter cells do not contain genetic material same as parent cell.


1 mole of stachyose on hydrolysis yields:
A. 1 mole of glucose +1 mole of fructose +2 mole of galactose
B. 2 mole of glucose + 1 mole of fructose + 1 mole of galactose
c. 1 mole of glucose +2 mole of fructose +1 mole of galactose
D. 2 mole of glucose +2 mole of fructose


How much is \( x+3 y-4 z \) greater than \( 3 x-2 y+z ? \)


Van't Hoff factor of \( \boldsymbol{H} \boldsymbol{g}_{2} \boldsymbol{C l}_{2} \) in its
aqueous solution will be \( \left(H g_{2} C l_{2} \) is \right. \( 80 \% \) ionized in the solution):
A . 1.6
B . 2.
\( c .3 .6 \)
D. 4.6


Select the correct statement.
\( \mathbf{A} \cdot S F_{4}, C H_{4}, S i C l_{4} \) and \( C C l_{4} \) have tetrahedral structure
B. \( B F_{3}, C l F_{3} \) and \( I C l_{3} \) have trigonal planar structure
C \( . X e F_{2}, B e C l_{2} \) and \( I C l_{2}^{-} \) have linear structure
D. All are correct


\( \int e^{x} 2^{3 \log _{2} x} d x=e^{x} f(x)+c, \) then
\( \boldsymbol{f}(\boldsymbol{x})= \)
A. \( x^{3}-3 x^{2}+6 x-6 \)
B. \( x^{3}-3 x^{2}-6 x-3 \)
c. \( x^{3}-3 x^{2}+6 x+6 \)
D. \( x^{3}+3 x^{2}+6 x+6 \)


A material particle with a rest mass
\( m_{0}^{\prime} \) is moving with speed of light 'c' The de-Broglie wavelength associated is given by
\( ^{A} \cdot \frac{h}{m_{0} c} \)
в. \( \frac{m_{0}}{h} \)
c. zero
\( D \cdot \infty \)


In a cyclic heat engine operating between a source temperature of \( 600^{0} C \)
and a sink temperature of \( 20^{0} C \), the least rate of heat rejection per kW net output of the engine is,
A. \( 0.505 \mathrm{kW} \)
B. 0.49 okw
c. \( 0.333 \mathrm{kw} \)
D. none of the above


Nitrous oxide is:
A. soluble in cold water.
B. soluble in hot \( O H_{2} \)
c. acidic in nature.
D. none of these.


Write down an application of Radiocarbon?


\( A B C D \) is a trapezium with \( A B / / D C \) A line parallel to \( A C \) intersects \( A B \) at
point \( M \) and \( B C \) at point \( N . \) Prove that area of \( \triangle A D M= \) area of \( \triangle \)
\( A C N \)


Detritivores are the animals which
obtain nutrients from the
A. Dead and decomposed matter in the soil
B. Plants
c. Animals
D. None of the above


State whether true or false:
The magnetic field lines originate from the south pole and terminate at the north pole of the magnet.


A constant voltage is applied between the two ends of a uniform metallic wire
due to which some heat is developed in
it. The heat developed is doubled if:
A. both the length and radius of the wire are halved
B. both the length and radius of the wire are doubled.
c. the radius of the wire is halved
D. the length of the wire is halved.


Two balls of equal masses are projected upward simultaneously, one from the ground with speed \( 50 m / s \) and other from a \( 40 m \) high tower with initial speed \( 30 m / s . \) Find the maximum height attained by their centre of mass.
\( A \cdot 100 m \)
B. 200 \( \mathrm{m} \)
c. \( 150 \mathrm{m} \)
\( D .50 \mathrm{m} \)


\( N a C l \) is used as a food preservative and in freezing mixtures.
A. True
B. False


A car traveled the total distance of \( x \) in three equal intervals, first at a speed of \( 10 \mathrm{km} / \mathrm{h} . \) The second at a speed of 20 \( \mathrm{km} / \mathrm{h} \) and the last third at a speed of 60 km/h. Determine the average speed of the car over the entire distance \( x \)


A positively charged rod is brought near an uncharged conductor. If the rod is then suddenly withdrawn, the charge left on the conductor will be :
A. positive
B. negative
c. zero
D. data insufficient


Universe is:
A. Closed system
B. Open system
C. Receiving constant supply of energy.
D. Dissipating energy continuously.


A wire is cut into three equal parts and then connected in parallel with the
same source. How will it
(i) resistance and resistivity gets
affected?
(ii) How would the total current and the
current through the parts change?


The amount of heat required to change from solid to liquid state without rise in
its temperature is
called


\( O \) is the centre of the circle having
radius \( 5 \mathrm{cm} . O M \) is a \( \perp \) on chord \( A B \). If
\( O M=4 \mathrm{cm}, \) then the length of the
chord \( A B \) is equal to
\( A \cdot 5 \mathrm{cm} \)
B. \( 6 \mathrm{cm} \)
\( c \cdot 8 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)


A parallel plate air capacitor has
capacity' \( C^{\prime}, \) distance of separation
between plate is ' \( d^{\prime} \) and potential
difference \( ^{\prime} V^{\prime} \) is applied between the
plates. Force of attraction between the
plates of the parallel plate air capacitor is:
\( ^{\mathbf{A}} \cdot \frac{C^{2} V^{2}}{2 d^{2}} \)
B. \( \frac{C^{2} V^{2}}{2 d} \)
\( c \cdot \frac{C V^{2}}{2 d} \)
D. \( \frac{C^{2} V}{d} \)


A student is standing at a distance of
\( \mathbf{5 0} \) meters behind a bus. As soon as the
bus starts with an acceleration of
\( 1 m s^{-2}, \) the student starts running towards the bus with a uniform velocity
\( u \). Assuming the motion to be along straight road the minimum value of \( u \)
so that the student is able to catch the
bus is:
A \( .5 \mathrm{ms}^{-1} \)
B. \( 8 m s^{-1} \)
\( \mathrm{c} \cdot 10 \mathrm{ms}^{-1} \)
D. \( 12 \mathrm{ms}^{-1} \)


Identify the position where electrophilic aromatic substitution(EAS) is most
favourable.
\( A \cdot A \)
B. B
\( c \cdot c \)
D. A and C


The value of integral \( \int \tan ^{-1}\left(\frac{x^{3}}{1+x^{2}}\right)+ \)
\( \tan ^{-1}\left(\frac{1+x^{2}}{x^{3}}\right) d x \) is equal to
\( A \)
в. \( -\frac{\pi}{2}+c \)
c. \( \frac{\pi}{2}+c \)
D. \( \left(\frac{\pi}{2}\right) x+c \)


Which of the following statements is
false?
A. Kirchhoff's second law represents energy conservation.
B. Wheatstone bridge is the most sensitive when all the four resistance are of the same order of magnitude.
C. In a balanced wheatstone bridge if the cell and the galvanometer are exchanged, the null point is disturbed.
D. A rheostat can be used as a potential divider.


An artificial satellite revolves around
the earth in a circular orbit with a speed
v. If \( m \) is the mass of the satellite, its
total energy is :
A \( \cdot \frac{1}{2} m v^{2} \)
B. \( -\frac{1}{2} m v^{2} \)
\( \mathrm{c} \cdot-m v^{2} \)
D. \( \frac{3}{2} m v^{2} \)


Primary and secondary valency of platinum in the complex \( \left[\boldsymbol{P t}(\boldsymbol{e n})_{2} \boldsymbol{C l}_{2}\right] \)
are:
This question has multiple correct options
A \( \cdot 4,6 \)
в. 2,6
c. 4,4
D. 2,4


Match the List-I with List-II and select
the correct answer from the given
Codes.
\( \begin{array}{ll}\text { List-I } & \text { List-II } \\ \text { (Compound) } & \text { (Oxidation state of nitrogen) } \\ N_{2} O_{5} & -2 \\ N a N_{3} & +5 \\ \text { NO } & -1 / 3 \\ N_{2} H_{4} & +2\end{array} \)
\( \mathbf{A} \cdot A-(i i), B(\text { iii) }, C-(i v), D-(i) \)
B. A-(i), B-(ii), C-(iii), D-(iv)
C. \( A-(i v), B-(i), C-(i i), D-(i i i) \)
D. A-(iii), B-(i), C-(iv), D-(ii)


Galena is a important mineral of
A. Iead
B. germanium
c. carbon
D. tin


The supporting and nutritive cells found in the brain are
A. Ependymal cells
B. Microglia
c. Astrocytes
D. Oligodendrocytes


What are the functions of the following in breathing? Ribs


A solution containing 0.5 g of naphthalene in 50 g \( C C l_{4} \) yield a
boiling point elevation of \( 0.4 \mathrm{K}, \) while a
solution of \( 0.6 \mathrm{g} \) of an unknown solute in the same mass of the solvent gives a
boiling point elevation of 0.65 K. Find
the molar mass of the unknown solute.


Find what straight lines are represented by the following equation and determine the angles between them. \( \boldsymbol{x}^{2}+2 \boldsymbol{x} \boldsymbol{y} \sec \boldsymbol{\theta}+\boldsymbol{y}^{2}=\mathbf{0} \)


By what smallest number 29160 be
divided so that the quotient becomes a perfect cube?


Sound waves from outside are collected
by which part of the ear?
A. cochlea
B. malleus
c. pinna
D. radius


Two copper rods \( P, Q \) of thickness in the ratio 2: 5 taken. If both the rods \( P, Q \) of
lengths \( 10 \mathrm{cm} \) are heated to same temperature rise, then the ratio of the linear expansions of \( P \) to that of rod \( Q \) is:
A .2: 5
B. 5: 2
\( c \cdot 1: 1 \)
\( D \cdot 4: \)


Assertion
The dielectric constant is a number
without dimensions.
Reason
Dielectric constant is a ratio.
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


Given \( 2^{-3} \times(-7)^{-3}=-\frac{1}{m} \) Value of \( m \)
is


Find the determinant:
\( \left|\begin{array}{ccc}1 & x & x^{2} \\ 1 & y & y^{2} \\ 1 & z & z^{2}\end{array}\right| \)


The square root of \( 71 \times 72 \times 73 \times \)
\( \mathbf{7 4}+\mathbf{1} \) is :
\( A \cdot 9,375 \)
B. 9,625
\( c \cdot 5,625 \)
D. 5,255


What are the different methods applied for the purification of colloidal solutions?

This question has multiple correct options
A. Dialysis
B. Ultra filtration
c. Normal filtration
D. None of these


The potential energy function for diatomic molecule is \( U(x)=\frac{a}{x^{12}}-\frac{b}{x^{6}} \)
In a stable equilibrium, the distance between the particles is:
\( ^{A} \cdot\left(\frac{2 a}{b}\right)^{1 / 6} \)
B. \( \left(\frac{a}{b}\right)^{1 / 6} \)
\( ^{\mathrm{c}}\left(\frac{b}{2 a}\right)^{1 / 6} \)
\( \left(\frac{b}{a}\right)^{1 / 6} \)


The angle between the instantaneous velocity and acceleration of a particle executing SHM is
A. zero or \( \pi \)
В. \( \pi / 2 \)
c. zero
D.


Substances that elongate considerably and undergo plastic deformation before they break are known as
A. brittle substances
B. breakable substances
c. ductile substances
D. all of these


Which statements are correct in terms
of chemical kinetic stuides?
This question has multiple correct options
A. The quenching of a reaction can be made by cooling the reaction mixture.
B. The quenching of a reaction can be made by diluting the reaction mixture.
C. The reaction is supposed to be completed if it is kept for long time or strongly heated.
D. None of the above


Which of the following is/are not a condensation copolymer?

This question has multiple correct options
A. Nylon-
B. Nylon-6,6
c. Dacron
D. PVC


O-xylene and m-xylene are isomers
of each other.
A. chain
B. functional
c. position
D. Tautomeric


A particle is constrained to move on a straight line path. It returns to the starting point after 10 sec. The total
distance covered by the particle during this time is \( 30 m \). Which of the following
statements about the motion of the
particle is true?
A. Displacement of the particle is zero
B. Average speed of the particle is \( 3 m / s \)
c. Displacement of the particle is \( 30 m \)
D. both (a) and (b)


Write the structure of a nitrolic acid.


Nitrogen can be produced by:
This question has multiple correct options
A. liquefaction and fractional distillation of air
B. treating an aqueous solution of ammonium chloride with sodium nitrite
C. thermal decomposition of sodium azide
D. thermal decomposition of barium azide


Q Type your question
of the ray after passing through the lens
are:
\( (I) \)
(II)
\( (\mathrm{III}) \)
\( (\mathrm{IV}) \)
A. II and III only
B. I and II only
C. I, II and III
D. I, II and IV


Choose the wrong statement:
A. Penicillium is multicellular and produces antibiotics.
B. Neurospora is used in the study of biochemical genetics.
C. Morels and truffles are poisonous mushrooms.
D. Yeast is unicellular and useful in fermentation.


Assertion: Magnetic flux is a vector quantity Reason: Value of magnetic flux can be positive, negative or zero
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true


Write the correct alternatives:
According to Mendeleev's periodic law, properties of elements are periodic
function of their.
A. Atomic number
B. Atomic masses
c. Densities
D. Boiling points


If a wire is stretched by applying force at one of its ends, then the elastic
potential energy density in terms of Young's modulus Y and linear strain \( \alpha \)
will be
\( ^{A} \cdot \frac{\alpha Y^{2}}{2} \)
в. \( \frac{Y \alpha}{2} \)
c. \( \frac{\alpha^{2} Y}{2} \)
D. \( 2 \alpha^{2} Y \)


\( \boldsymbol{y}=\tan ^{-1}\left[\frac{\log \left(\frac{\boldsymbol{e}}{\boldsymbol{x}^{2}}\right)}{\log \left(\boldsymbol{e} \boldsymbol{x}^{2}\right)}\right]+ \)
\( \tan ^{-1}\left(\frac{3+2 \log x}{1-6 \log x}\right), \) then \( \frac{d^{2} y}{d x^{2}}= \)
\( A \)
в.
\( c \cdot 0 \)
D. -


Observe the diagram and fill up the
following:
a. The diagram shows ............ defect of eye.
b. ... \( . . . . . . . \) lens is used to correct this defect.


\( 0.2595 \mathrm{g} \) of an organic substance, when treated by carius method, gave 0.25 g of \( B a S O_{4} \). Calculate the percentage of sulphur in the compound.
A . \( 9.08 \% \)
в. \( 12.75 \% \) \%
c. \( 15.96 \% \)
D . 13.23\%


A ball moving with a velocity v strikes a
wall moving towards the ball with velocity u. An elastic impact lasts for seconds. Find the mean elastic force
acting on the ball


Four chambered heart is present, in which of the following reptiles?
A . Lizard
B. Snake
c. Scorpion
D. crocodile


The volume \( (V) \) of nucleus of an atom is expressed in terms of mass no. \( (A) \) of
atom as:
\( A \cdot V \propto A \)
В. \( V \propto A^{1 / 3} \)
c. \( V \propto A^{2} \)
D. \( V \propto A^{3} \)


\( \sin ^{-1}(117 / 125) \) is equal to
This question has multiple correct options
A \( .2 \alpha \)
в. \( 3 \alpha \)
c. \( \pi / 2-2 \alpha \)
D. \( \pi-3 \alpha \)


\( \mathrm{G}_{1}, \mathrm{G}_{2} \) and \( \mathrm{S} \) phases are seen in which phase of cell cycle?
A. Metaphase
B. Prophase
c. Anaphase
D. Interphase


Match the followings:


Write IUPAC name of the following
complex compound. \( K_{3}\left[F e\left(C_{2} O_{4}\right)_{3}\right. \)


In the figure, \( A P=3 \mathrm{cm}, A R= \)
\( 4.5 \mathrm{cm}, A Q=6 \mathrm{cm}, A B=5 \mathrm{cm}, \) and
\( A C=10 \mathrm{cm} . \) Find the length (in \( \mathrm{cm} \) ) of
\( \boldsymbol{A D} \)


\( \Delta H \) and \( \Delta S \) for the system
\( \boldsymbol{H}_{2} \boldsymbol{O}(l) \rightleftharpoons \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \)
at 1 atmospheric pressure are \( 40.63 k J m o l^{-1} \) and \( 108.8 J K^{-1} m o l^{-1} \)
respectively. Calculate the temperature at which the rates of forward and
backward reactions will be the same.
Predict the sign of free energy for this transformation above this temperature


Choose the correct statement
A. All mammals are viviparous
B. All cyclostomes do not possess; jaws and paired fins
C. All reptiles have a three-chambered heart
D. All Pisces have gills covered by an operculum


Two conducting charged spheres \( X \) and
\( Y \) having unequal charges are connected by the wire. Which of the following is true?
A. Charge is conserved
B. Electrostatic energy is conserved
c. Both the charge and electrostatic energy is conserved
D. Neither of these is conserved


At \( 300 \mathrm{K}, \) the density of a certain gaseous molecule at 2 bar is double to
that of dinitrogen \( \left(N_{2}\right) \) at 4 bar. The
molar mass of gaseous molecule is :
A \( \cdot 112 g \) mol \( ^{-1} \)
B . \( 224 g \) mol \( ^{-1} \)
c. \( 28 g \) mol \( ^{-1} \)
D. \( 56 g \) mol\( ^{-1} \)


Give two floral adpatations of bird pollinated plants.


The main excretory organs in man are
A. Kidneys
B. Nephridia
c. Trachea
D. Lungs


Two identical cylinders \( A \) and \( B \) with frictionless pistons contain the same
ideal gas at same temperature and the same volume \( V \). The mass of gas \( A \)
is \( m_{A} \) and that of \( B \) is \( m_{B} . \) The gas in
each cylinder is allowed to expand isothermally to the same final volume
2V. The change in the pressure in \( A \) and B are found to be \( \Delta P \) and \( 1.5 \Delta P \)
respectively. Then
\( \mathbf{A} \cdot 4 m_{A}=9 m_{B} \)
B. \( 3 m_{A}=3 m_{B} \)
\( \mathbf{c} \cdot 3 m_{A}=2 m_{B} \)
D. \( 9 m_{A}=4 m_{B} \)


Lateral root in higher plants arise from
A. Cortex
B. Pericycle
c. Epidermis
D. Endodermis


Benzene has its applications in:
A. rubber manufacturing
B. printing
c. making adhesives
D. all


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


Find the negative of middle term in the expansion of
\( \left(\frac{2 x}{3}-\frac{3}{2 x}\right)^{6} \)


A sphere of mass \( \mathrm{m}, \) moving with a speed \( v, \) strikes a wall elastically at an angle of incidence \( \theta \). If the speed of the sphere before and after collision is the same and the angle of incidence and
velocity normally towards the wall the angle of rebound is equal to the angle of incidence and velocity normally towards the wall is taken as negative then, the change in the momentum parallel to wall is :
A. mv \( \cos \theta \)
B. 2 mv \( \cos \theta \)
c. - 2 mv \( \cos \theta \)
D. zero


Which of the following is equivalent set
(i) \( \boldsymbol{A}=\{\mathbf{2}, \mathbf{3}, \mathbf{5}, \mathbf{7}\} \)
(ii) \( B=\{a, e, i, o, u\} \)
(iii) \( \boldsymbol{C}=\{-\mathbf{1},-\mathbf{9},-\mathbf{8},-\mathbf{7}\} \)
A. (i) and (ii)
B. (i) and (iii)
c. (ii) and (iii)
D. None of these


For an acute angle, \( \alpha, \sin \alpha+\cos \alpha \)
takes the
greatest value when \( \alpha \) is
A \( .30^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 60^{0} \)
D. \( 90^{\circ} \)


What is the total resistance across \( A \)
and \( \mathrm{B} \) in the circuit shown in figure
\( A \cdot 1 \Omega \)
в. \( 2 \Omega \)
\( c \cdot 1.5 \Omega \)
D. none of these


Which of the following is true regarding homospory and heterospory?
A. Homospory: one kind of spore is produced, typically resulting in a bisexual gametophyte.
B. Heterospory: two types of spores develop into separate male and female gametophytes
c. Both A and B are correct
D. Both A and B are incorrect


Which of the following is an example of taxon?
A. Genera
B. Family
c. class
D. All of the above


Find the differential equation of the family of all striaght lines passing through the origin.


Leyding cells produce a group of hormones called.
A. Androgens
B. Estrogen
c. Aldosterone
D. Gonadotropins


The value of \( \cot 16^{\circ} \cot 44^{\circ}+ \)
\( \cot 44^{\circ} \cot 76^{\circ}-\cot 76^{\circ} \cot 16^{\circ} \) is
A . 3
B. \( \frac{1}{3} \)
\( c \cdot-\frac{1}{3} \)
D. - 3


Fill in the blank:
Tendency of an object to change in its state of rest or motion is
called inertia
A. Allow
B. Assist
c. Resist
D. None of these


Photochemical smog is formed in:
A. summer during day time
B. summer during morning time
c. winter during morning time
D. winter during day time


Circular Motion can be an example of
periodic motion. State whether the given statement is
True or False.
A. True
B. False


A body is projected vertically up from a point on the ground. When it is at a height \( h \) above the ground, its kinetic
and potential energies are found to be in the ratio of \( 3: 2 . \) If the body rises to a
maximum height of \( H \) above the ground, then the ratio of \( \boldsymbol{H}: \boldsymbol{h} \) will be
A . 5: 3
B . 2: 1
c. 5: 2
D. 2: 5


The propagation of heat in vacuum takes place by
A. Conduction
B. Convection
c. Radiation
D. None of these


The characteristic of the last elements
in the periods of a periodic table:
A. orbital completely
B. zero electron affinity
c. zero tendency in accepting electrons
D. All of these


The velocity of electron will be:
A. Same in both cases
B. 1.4 times in second experiment than in first experiment
C. Double in second experiment than in first experiment
D. Four times in the second case than in first case


Energy released during movement of electrons through the photosystems in photosynthesis is used to drive protons across the membrane against concentration gradient. As a result the protons accumulate in
A. thylakoid lumen
B. stroma of chloroplast
c. matrix of mitochondrion
D. none of these


When a charged rod is brought near the disc of a negatively charged gold leaf electroscope, it is observed that the divergence of leaves decreases.What inference do you draw about the charge
on the rod?
A. Rod is positively charged
B. Rod is negatively charged
c. Rod has no charge
D. cant say


Which of the following statements are true for density?
A. It is a physical property of matter
B. It is a scalar quantity
c. It is the mass per unit volume of a substance
D. All of the above


In case of force oscillations of a body
A. driving force is constant throughout
B. driving force is to be applied only momentarily.
C . driving force has to be periodic and continuous.
D. driving force is not required.


A uniform disc of radius \( R \) is spinned to
the angular velocity \( \omega \) and then
carefully placed on a horizontal surface.
How long will the disc be rotating on the surface if the friction coefficient is
equal to \( k \) ? The pressure exerted by the
disc on the surface can be regarded as uniform.
\( \mathbf{A} \cdot_{t}=\frac{5 R \omega_{0}}{4 k g} \)
B. \( t=\frac{3 R \omega_{0}}{4 k g} \)
\( \mathbf{c} \cdot_{t}=\frac{3 R \omega_{0}}{8 k g} \)
D. None of these


Assertion
Asexual reproduction involves formation of clones of an organism.
Reason
Clones are morphologically and genetically similar individuals.
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


Which complex among the following gives a white precipitate on treatment with an aqueous solution of barium
chloride?
\( \mathbf{A} \cdot\left[P t\left(N H_{3}\right)_{4} B r_{2}\right] C l_{2} \)
B \( \cdot\left[C o\left(N H_{3}\right)_{5} S O_{4}\right] N O_{2} \)
c. \( \left[C o\left(N H_{3}\right)_{5} N O_{2}\right] S O_{4} \)
D. \( \left[P t\left(N H_{3}\right)_{4} C l_{2}\right] B r_{2} \)


Name the following halides according to IUPAC system and classify them
as alkyl, allyl, benzyl (primary, secondary, tertiary), vinyl or aryl
halides:
i) \( \left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C H C H}(\boldsymbol{C l}) \boldsymbol{C H}_{3} \)
ii) \( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right) \boldsymbol{C H}\left(\boldsymbol{C}_{2} \boldsymbol{H}_{5}\right) \boldsymbol{C l} \)
iii) \( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C}\left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C H}_{2} \boldsymbol{I} \)
iv) \( \left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{C C H}_{2} \boldsymbol{C H}(\boldsymbol{B r}) \boldsymbol{C}_{6} \boldsymbol{H}_{5} \)
v) \( \boldsymbol{C H}_{3} \boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right) \boldsymbol{C H}(\boldsymbol{B r}) \boldsymbol{C H}_{3} \)
vi) \( \boldsymbol{C H}_{3} \boldsymbol{C}\left(\boldsymbol{C}_{2} \boldsymbol{H}_{5}\right)_{2} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{B r} \)
vii) \( \boldsymbol{C H}_{3} \boldsymbol{C}(\boldsymbol{C l})\left(\boldsymbol{C}_{2} \boldsymbol{H}_{5}\right) \boldsymbol{C H}_{2} \boldsymbol{C H}_{3} \)
viii) \( \boldsymbol{C H}_{3} \boldsymbol{C H}= \)
\( \boldsymbol{C}(\boldsymbol{C l}) \boldsymbol{C H}_{2} \boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right)_{2} \)
ix) \( \boldsymbol{C H}_{3} \boldsymbol{C H}=\boldsymbol{C H C}(\boldsymbol{B r})\left(\boldsymbol{C H}_{3}\right)_{2} \)
\( \mathbf{x} \) ) \( \boldsymbol{p}-\boldsymbol{C l} \boldsymbol{C}_{6} \boldsymbol{H}_{4} \boldsymbol{C H}_{2} \boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right)_{2} \)
xi) \( \boldsymbol{m}-\boldsymbol{C l} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C}_{6} \boldsymbol{H}_{4} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C}\left(\boldsymbol{C} \boldsymbol{H}_{3}\right)_{3} \)
xii) \( o-B r- \)
\( \boldsymbol{C} \quad \mathscr{C H}\left(\boldsymbol{C H}_{3}\right) \boldsymbol{C H}_{2} \boldsymbol{C H}_{3} \)


A beautiful girl with two normal eyes wants to see full width of her face by a plane mirror. The eye to eye and ear to
ear distance of her face are 4 inch and 6
inch respectively. The minimum width of the required mirror is:


The process of
photophosphorylation was discovered
by
A. Calvin
B. Arnon
c. Priestley
D. Warburg


Which one of the following is the correct pairing of a body part and the kind of muscle tissue that moves it?
A. Heart - smooth muscles
B. Stomach - Smooth muscles
c. Urinary bladders - Striated muscles
D. Triceps - cardiac muscles


The substance which lowers the acidity
of stomach is called


In what direction does the induced
current in coil flow
\( A \cdot A \) to \( B \)
B. в to A
c. No current
D. cant say


How does sound from a sound
producing body travel through air to
reach our ears?
A. through crest and troughs
B. through compression and rarefaction
\( c \cdot \) both
D. none


dor of of se


Which of the following method can be used for the preparation of methane?
A. Wurtz reaction
B. Kolbe's reaction
c. Reduction of alkyl halide
D. Hydrogenation of alkene


Prove the following identity :
\[
\frac{1}{\sin \theta+\cos \theta}+\frac{1}{\sin \theta-\cos \theta}=\frac{2 \sin \theta}{1-2 \cos ^{2} \theta}
\]


The signs of eutrophication of water
bodies include
A. Reduced oxygen demand
B. Rapid decomposition of organic matter
c. Algal bloom
D. Fluorosis


If the specific heat of lead is \( 0.03 \frac{c a l}{g^{o} C} \)
thermal capacity of \( 500 \mathrm{g} \) of lead is.
A . \( 5 \mathrm{cal}^{\circ} C^{-1} \)
B . \( 10 \mathrm{cal}^{\circ} \mathrm{C}^{-1} \)
C . \( 15 \mathrm{cal}^{\circ} \mathrm{C}^{-1} \)
D. 20cal \( ^{\circ} C^{-1} \)


Show that the four lines \( a x \pm b y \pm c= \)
0 enclose a rhombus whose area is \( \frac{2 c^{2}}{a b} \)


What do you know about Bakelite?


A particle moving towards south in a
vertically downward magnetic field is
deflected toward the east.What is the
sign of the charge on the particle?


Person who use boolean algebra for describing the operation of logic gates first was
A . Boole
B. Shannon
c. schottky
D. zener


Plant growth in length is due to activity of
A. Apical meristem
B. Dermatogen
c. Periblem
D. Lateral meristem


A triangle has side lengths of 6 inches
and 9 inches. If the third side is an integer, calculate the minimum possible perimeter of the triangle (in inches).
A . 4
B. 15
c. 8
D. 19
E . 29


Identify the graph which correctly
represents the variation of capacitive
reactance \( X_{C} \) with frequency.
\( A \)
B.
\( c \)
D.


Outline the principles of refining of metals by the following methods:
(i) Zone refining
(ii) Vapour phase refining


For the reaction \( \boldsymbol{A}+\boldsymbol{B} \rightarrow \mathbf{3} \boldsymbol{C} ; \) at \( \mathbf{2 5}^{\boldsymbol{o}} \boldsymbol{C} \)
a \( 3 L \) vessel contains 1,2 and 4 moles of
\( A, B \) and \( C \) respectively. If reaction is in equilibrium then
A \( \cdot K_{c}=10 \)
В. \( K_{c}=12 \)
C . \( K_{c}=10.66 \)
D. \( K_{c}=9.56 \)


How will you determine the electric field
a any point along the axial line of an electric dipole.


Which of the following belongs to a fish category?
A. Star fish
B. Cuttle fish
c. Devil fish
D. Sea horse


Radioactive \( C^{14} \) is given to \( C 0_{2} \) and
released to atmosphere. This \( C 0_{2} \) is
taken by ribulose diphosphate in a \( C_{3} \)
plant. First radioactive \( C^{14} \) is seen in
which compound?
A. PGAL
B. PEP
c. RMP
D. PGAA


How does the blood come out of the
capillary and come in contact with the Bowman's capsule so as to form filtrate?


Based on solute-solvent interactions,
arrange the following in order of increasing solubility in n-octane and explain.
Cyclohexane, \( \boldsymbol{K} \boldsymbol{C l}, \boldsymbol{C H}_{3} \boldsymbol{O H}, \boldsymbol{C H}_{3} \boldsymbol{C N} \)


Construct a quadrilateral \( P Q R S, \) with
\( \boldsymbol{P Q}=\mathbf{3} \mathrm{cm}, \boldsymbol{Q} \boldsymbol{R}=\mathbf{9} \mathrm{cm}, \boldsymbol{R} \boldsymbol{S}=\mathbf{5} \mathrm{cm} \)
\( \angle Q=45^{\circ}, \angle R=60^{\circ} \)


Find the differential equation of the following. \( \tan ^{-1}\left(\frac{1-\cos x}{\sin x}\right) \)


9
\( \$ \)
\( \infty \)


Excess of \( P C l_{5} \) reacts with
concentrated \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) giving:
A. chlorosulphuric acid
B. sulphurous acid
c. sulphuryl chloride
D. thionyl chloride


Etard reaction in the following is:
A. oxidation of toluene to benzaldehyde by chromylchloride
B. oxidation of toluene to benzaldehyde by alkaline \( K M n O_{4} \)
C . dry distillation of calcium benzoate
D. reaction of benzene with \( C l_{2} \) in the presence of UV
light


In principle, longest Henle's loop should
be found in the nephrons of desert dwelling mammal feeding mainly on?
A. succulent cactus
B. Fleshy fruits
c. Leathery leaves
D. seeds


The moles of \( H C l \) required to
neutralise left \( N H_{3} \) solution after
adsorption is:
A .0 .123
B. 0.175
c. 0.145
D. 0.153


Which of the following are not units of
self inductance?
This question has multiple correct options
A. Weber / m \( ^{2} \)
B. \( O h m- \)second
c. Joule - ampere
D. Joule - ampere \( ^{-} \)


A dynamo produces an electric current.
It is based on the principle:
A. magnets have attractive property
B. conductors carrying current behave like magnets
C. electromagnetic induction
D. none of these


A.M. of \( a-2, a, a+2 \) is


Binary fission is the division of the parent body into how many parts?
A. Three
B. Four
c. Two
D. Nine


State whether True=1 or False=0
\( \int \frac{x^{2}}{\left(x^{2}+1\right)\left(x^{2}+4\right)} d x=\frac{-1}{3} \tan ^{-1} x+ \)
\( \frac{2}{3} \tan ^{-1}\left(\frac{x}{2}\right)+C \)


Which of the following statement is
correct about diborane?
A. It is used as a flux for soldering metal.
B. It is a crystalline form of silica.
C. It has banana bonds present in structure.
D. It is used as catalyst in petrochemical industries.


A compound was found to contain 5.37\% nitrogen.What is the minimum molecular weight of compound?
A . 26.07
B. 2.607
c. 260.7
D. None of these


An examples of a simple fuel cell is:
A. lead storage battery
в. \( H_{2}-O_{2} \) cell
c. daniell cell
D. lechlanche cell


The products formed by the complete
hydrolysis of \( \boldsymbol{P} \boldsymbol{C l}_{3} \) are:
A. \( H_{3} P O_{3} \) and \( H C l \)
в. \( P O C l_{3} \) and \( H C l \)
\( \mathbf{c} \cdot H_{3} P O_{4} \) and \( H C l \)
D. \( H_{4} P_{2} O_{7} \) and \( H C l \)


Assertion
A body with constant acceleration
always moves along a straight line.
Reason

A body with constant magnitude of acceleration may not speed up.
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 parallel plane capacitor \( C \) with plates
of unit area and separation \( d \) is filled
with a liquid of dielectric constant \( k= \)
2. The level of liquid is \( \frac{u}{3} \) initially.
Suppose the liquid level decreases at a
constant speed \( v \), the time constant as
a function of time \( t \) is
A \( \frac{6 \varepsilon_{0} R}{5 d+3 v} \)
B. \( \frac{(15 d+9 v t) \varepsilon_{0} R}{2 d^{2}-3 d u t-9 v^{2} t^{2}} \)
c. \( \frac{6 \pi \varepsilon_{0} R}{5 d-3 v} \)
D. \( \frac{(15 d-9 v t) \varepsilon_{0} R}{2 d^{2}+3 d v t-9 v_{2 t^{2}}} \)


The Magnetic effect of current was discovered by:
A. John Ambrose Fleming
B. Hans Christian Oersted
c. Michael Faraday
D. André-Marie Ampère


The work done in pulling up a block of
wood weighing \( 2 k N \) for a length of \( 10 m \) on a smooth plane inclined at an angle
of \( 15^{\circ} \) with the horizontal is:
\begin{tabular}{l}
A. \( 5.17 k J \) \\
\hline
\end{tabular}
в. \( 6.42 k J \)
c. \( 7.03 k J \)
D. \( 9.82 k J \)


\( f\left(\begin{array}{lll}1 & 5 & 2 \\ 1 & -3 & 4\end{array}\right), \) then find \( A^{T} \) and \( \left(A^{T}\right)^{T} \)


A linear charge having linear charge
density \( \lambda \), penetrates a cube diagonally
and then it penetrate a sphere diametrically as shown. What will be the ration of flux coming out of cube and
sphere.
\( ^{A} \cdot \frac{1}{2} \)
в. \( \frac{2}{\sqrt{3}} \)
c. \( \frac{\sqrt{3}}{2} \)
\( D \)


What is the major product (s) when 2
methyl-2-butene reacts with (i) \( O_{3} \) (ii)
\[
Z n / C H_{3} C O O H(a q) ?
\]
A. \( I+I I \)
B. \( I I+I I I \)
c. \( I I I+I V \)
D. II


How much electric charge is required to oxidise:
(a) 1 mole of \( H_{2} O \) to \( O_{2} \) and
(b) 1 mole of \( F e O \) to \( F e_{2} O_{3} \)


By corpuscular theory of light, the phenomenon which can be explained is
\( A \). refraction
B. diffraction
c. interference
D. polarisation


Estimate whether it takes more energy
to get a satellite upto \( 1600 \mathrm{km} \) above the earth than to put in orbit there
earth's radius is \( 6400 \mathrm{km} \). Does your
answer remain same for height \( 3200 \mathrm{km} \)
or for height \( 4800 \mathrm{km} ? \)


The extraction of metals from oxide
ores may involve:
This question has multiple correct options
A. reduction with carbon
B. reduction with aluminium
c. electrolyte reduction
D. reduction with \( c 0 \)


A second lens is now placed adjacent to
the first in contact with it. The new lens
is concave, with focal length \( \boldsymbol{f}=-\mathbf{3} \boldsymbol{f} \)
What is the focal length \( f_{t o t} \) of the two
lens system? Treat the lenses as thin
A \( \cdot f_{\text {tot }}=f / 2 \)
B. \( f_{\text {tot}}=2 f / 3 \)
\( c \cdot f_{t o t}=f \)
D. \( f_{\text {tot}}=3 f / 2 \)


Which of the following are not equivalence relations on I?
\( A \). a \( R b \) if \( a+b \) is an even integer
B. a R b if \( a-b \) is an even integer
\( \mathbf{c} \cdot \) a \( \mathrm{R} \mathrm{b} \) if \( a<b \)
D. a R b if \( a=b \)


The following symbol represents
A. NAND gate
B. NOT gate
c. AND gate
D. or gate


Which of the following organism is likely to have more concentration of
D.D.T in its body?
A. Herbivores
B. Carnivores
c. Top carnivores
D. Primary producers


Explain antacids with a suitable example.


The mode of the following data is 85.7
Find the missing frequency in it.
\( \begin{array}{ll}\text { Size } & \text { Frequency } \\ \text { 45-55 } & \text { 7 } \\ \text { 55-65 } & 12 \\ \text { 65-75 } & \text { 17 } \\ \text { 75-85 } & \text { f } \\ \text { 85-95 } & \text { 32 } \\ \text { 95-105 } & \text { 6 } \\ \text { 105-115 } & \text { 10 }\end{array} \)
A . 33
B. 31
\( c .30 \)
D. 32


To make 0.01 mol, which of the following
has maximum mass?
A. \( N a H C O_{3} \)
B. \( N a_{2} C O_{3} \)
\( \mathbf{c} \cdot N a_{2} S O_{4} \)
D. \( N a_{2} C_{2} O_{4} \)


What is a protective colloid?


Which of the following statement
regarding solubility of ethers in water is
true?
A. Ethers are sparingly soluble in water due to the formation of hydrogen bond with water.
B. Ethers are highly soluble in water due to the formation of hydrogen bond with water.
C. Ethers are sparingly soluble in water as they cannot form hydrogen bond with water.
D. Ethers are highly soluble in water as they are polar in nature.


An experiment is conducted to fully
oxidize a sample of magnesium ribbon.
Which factor would do the most to
make the reaction proceed more
quickly?
A. Vigorous heating of the reaction vessel
B. Addition of carbon dioxide to the reaction vessel.
C. Removal of oxygen from the reaction vessel.
D. Carefully folding the magnesium sample into a small, cubic shape.
E. Addition of nitrogen gas the the reaction vessel.


Solve \( \tan p \theta=\cot q \theta \)


Amongst the given options, the compound(s) in which all the atoms are in one plane in all the possible conformations (if any), is/are:
This question has multiple correct options
\( A \)
B.
c. \( H_{2} C=C=O \)
D. \( H_{2} C=C=C H_{2} \)


If \( n \) balls hit elastically and normally on a surface per unit time and all the balls are of mass \( m \) moving with the same
velocity \( u, \) then force on the surface is:
\( \mathbf{A} \cdot m \times u \times n \)
В . \( 2 \times m \times u \times n \)
c. \( \frac{1}{2} \times m u^{2} n \)
D. \( m u^{2} n \)


If the points \( (k, 2-2 k)(1-k, 2 k) \) and \( (-k \) \( -4,6-2 x) \) be collinear the possible values of k are
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{2} \)
\( c \)
D. - -


If \( \log x-5 \log 3=-2, \) then \( x \) equals
A . 1.25
B. 0.81
c. 2.43
D. 0.8
E. either 0.8 or 1.25


Which of the following statement(s) is/are correct:
A. The gap between the top of the valance band and the bottom of the conduction band is called energy band \( \operatorname{gap} \)
B. More band gap results in less electron transfer
c. A semiconductor is a material with a small but nonzero band gap that behaves as an insulator at absolute zero
D. All of the above


Which of the following statements is
correct about friction?
A. The coefficient of friction between a given pair of substances is largely independent of the area of contract between them.
B. The frictional force can never exceed the reaction froce
on the body from the support surface.
C. Rolling friction is only slighting smaller than sliding friction.
D. The main source of friction is the irregularity of the surface in contact.


How does the presence of double bonds in rubber molecules influence
their structure and reactivity?


If \( \boldsymbol{A}+\boldsymbol{B}+\boldsymbol{C}=\boldsymbol{\pi} \) and \( \mathbf{A}, \mathbf{B}, \mathbf{C} \) are all
greater then 0 and angle \( C \) is obtuse then
\( \mathbf{A} \cdot \tan A \tan B \geq 1 \)
B. \( \tan A \tan B<1 \)
\( \mathbf{c} \cdot \tan A \tan B=1 \)
D. None of these


All kind of matter is made up of extremely small particles called
\( A \). atom
B. molecule
\( c \cdot \) ion
D. compound


A point starts from rest and moves
along a circular path of radius \( 20 \mathrm{cm} \) with a constant tangential acceleration
of \( 5 \mathrm{cm} / \mathrm{s}^{2} . \) The time needed for the
centripal acceleration of the point to be equal to its tangential acceleration is:
A . \( 0.2 s \)
в. \( 0.5 s \)
\( c \cdot 1 s \)
D. 2 s


\( (p+q)-(p-q) \) is equal to
\( \mathbf{A} \cdot 2 p+2 q \)
в. \( 2 p \)
c. \( 2 q \)
D. 0


Which of the following is incorrect?
A. Hydrogen > Deuterium > Tritium; (\% relative abundance)
B. Hydrogen < Deuterium < Tritium; (density/gL \( ^{-1} \) )
C. Hydrogen < Deuterium < Tritium; (boiling point/K)
D. Hydrogen > Deuterium > Tritium; (melting point/K)


What would happen when a solution of
potassium chromate is treated with an excess of dilute nitric acid?
A \( \cdot C r^{3+} \) and \( C r_{2} O_{7}^{2-} \) are formed
B. \( C r_{2} O_{7}^{2-} \) and \( H_{2} O \) are formed
C. \( C r_{2} O_{4}^{2-} \) is reduced to +3 state of \( c r \)
D. \( C r_{2} O_{4}^{2-} \) oxidised to +7 state of \( c r \)


In Fig. arcs have been drawn of radius
\( 21 \mathrm{cm} \) each with vertices \( A, B, C \) and \( D \)
of the square \( A B C D \) as centres. The
area of the shaded region is
\( \mathbf{A} \cdot 693 \mathrm{cm}^{2} \)
B. \( 346.5 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 2772 \mathrm{cm}^{2} \)
D. \( 1386 \mathrm{cm}^{2} \)


Define a gene?


The electronic configuration of elements \( A, B, C, D \) and \( E \) are as follows:
\( \begin{array}{llll}A(2,8,7) & B(2,8,1) & C(2) & D(2,\end{array} \)
6) \( \quad E(2,8) \)
The element which can donate electrons in a chemical reaction is:
\( A \cdot A \)
B. B
\( c \cdot D \)
D.


If \( P Q R S \) is a square, \( A B \| S Q, A \) is
midpoint of \( S R \) and \( A C=C B, \) which
one is true?
A. \( S A=B Q \)
B. \( P C \) is the bisector of \( \angle S P Q \)
c. \( P C \) if produced will pass through \( R \)
D. All of these


Optical isomers possible for
\( \boldsymbol{C H}_{2} \boldsymbol{O H C H O H C H O H C H O} \) are:
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D.


The outer most electronic configuration of the most electronegative element is:
\( A \cdot n s^{2} n p^{3} \)
B. \( \mathrm{ns}^{2} \mathrm{np}^{4} \)
\( c \cdot n s^{2} n p^{5} \)
D. \( \mathrm{ns}^{2} \mathrm{np}^{6} \)


Laws of reflection hold good for
A. Plane mirrors
B. Concave mirrors
c. Convex mirrors
D. All


Find the smallest number which should be multiplied to 231525 to make it a
perfect cube.
A . 5
B. 3
\( c \cdot 7 \)
D. 21


Which of the following can have vacant
\( \boldsymbol{p}- \) orbital?
\( A \cdot \cdot C H_{3} \)
в. \( \stackrel{\oplus}{C H}_{3} \)
c. \( 11 \mathrm{CH}_{2} \)
D. Both (b) and (c)


\( \left(3 x^{2}-x\right) \div(-x) \) is equal to
A \( .3 x+1 \)
B. \( -3 x-1 \)
c. \( -3 x+1 \)
D. \( 3 x-1 \)


A thin bar of mass 'M' and length 'L' is
free to rotate about a fixed horizontal
axis through a point at its end.The bar is brought to a horizontal position and then released. The angular velocity when it reaches the lowest point is:
A. directly proportional to its length and inversely proportional to its mass
B. independent of mass and inversely proportional to the square root of its length
c. dependent only upon the acceleration due to gravity
D. directly proportional to its length and inversely proportional to the acceleration due to gravity.


Find the \( 12^{t h} \) term of the A.P.:
\( \mathbf{9}, \mathbf{1 3}, \mathbf{1 7}, \mathbf{2 1}, \dots . \)


Mode of the distribution
\begin{tabular}{lccccc}
Marks & 4 & 5 & 6 & 7 & 8 \\
No. of students & 3 & 5 & 10 & 6 & 1 \\
\hline
\end{tabular}
\( \mathbf{A} \cdot \mathbf{6} \)
B. 10
\( c \cdot 8 \)
\( D \cdot 4 \)


Which of the following rules should be followed which identifying parent
chain?
A. Maximum number of multiple bonds
B. Maximum length
c. Maximum number of single bonds
D. All of above


The plant hormone, which is synthesized in root and translocated to aerial
parts is
A. Auxin
B. Cytokinin
c. Traumatin
D. Morphactin


If \( \boldsymbol{A}=\{\boldsymbol{a}, \boldsymbol{b}\}, \boldsymbol{B}=\{1,2,3\}, \) find \( \mathbf{B} \times \mathbf{A} \)
A. \( B \times A=\{(1, a),(2, a),(3, a),(1, b)(2, b),(3, b)\} \)
B. \( B \times A=\{(2, a),(3, a),(1, b)(2, b),(3, b)\} \)
C. \( B \times A=\{(1, a),(2, a),(3, a),(1, b)(2, b)\} \)
D. None of these


Match the columns:
\( \begin{array}{ll}\text { i. convex lens } & \text { a. presbyopia } \\ \text { ii. concave lens } & \text { b. cataract } \\ \text { iii. Artificial lens } & \text { c. myopia } \\ \text { iv. focal lens } & \text { d. hypermetropia }\end{array} \)
\( A \cdot \) i-c,ii-d,iii-a,iv-b
B. i-d,ii-c,iii-b,iv-a
C. i-b,ii-c,iii-a,iv-d
D. i-a,ii-b-iii-d,iv-c


Explain the use of N-P-N Transistor as an amplifier in common emitter mode under the following heads.
(i) Labelled circuit diagram. (ii) Working.


If the vector \( -\hat{\mathbf{i}}+\hat{\boldsymbol{j}}-\hat{\boldsymbol{k}} \) bisects the
angle between the vector \( c \) and the vector3 \( \hat{i}+4 \hat{j}, \) then the unit vector in the direction of c,is


In the froth floatation process, for the beneficiation of ores, the ore particles
float because
A. they are light
B. their surface is not easily wetted by water
c. they bear electrostatic charge
D. they are insoluble


Compare basic strength of the above compounds:
A. \( A>B>C \)
в. \( B>A>C \)
c. \( C>A>B \)
D. \( C>B>A \)


Which of the following compounds is stable?
\( \mathbf{A} \cdot C H_{3} C H(O H)_{2} \)
B. \( \left(C H_{3}\right)_{2} C H(O H)_{2} \)
\( \mathbf{c} \cdot C C l_{3} C H(O H)_{2} \)
D. None of these


Electric charge is developed due to actual transfer of
A . electron
B. proton
c. neutron
D. none


A biparous cyme ending in uniparous cyme constitutes
A. Verticillaster
B. Panicle
c. Hypanthodium
D. Cyathium


The mass of one litre of a sample of ozonized oxygen at NTP was found to be 1.5 g. When 100 mL of this mixture at NTP were treated with turpentine oil, the
volume was reduced to \( 90 \mathrm{mL} \), hence, the molar mass (in gm) of ozone is (write the answer as the interger at
ten's digit place):


Find the component of \( \vec{r} \) in the direction of \( \vec{a}: \)
A \( \cdot \frac{(\vec{r} \cdot \vec{a}) \vec{a}}{a^{2}} \)
B. \( \frac{(\vec{r} \cdot \vec{a}) \vec{a}}{a} \)
c. \( \frac{(\vec{r} \times \vec{a}) \vec{a}}{a^{2}} \)
D. None of above


Which of the following are examples of periodic motion?
A. Oscillations of a pendulum.
B. The motion of a swing
c. Motion of the earth around the sun
D. All of the above


Name the types of following triangles:
\( \triangle A B C \) with \( A B=8.7 \mathrm{cm}, A C=7 \mathrm{cm} \)
and \( B C=6 c m \)


The formula for the coefficient of range is \( \frac{\text { Range }}{\boldsymbol{a}+\boldsymbol{b}} . \) Here, \( \boldsymbol{a} \) and \( \boldsymbol{b} \) denote
A. the mean and median of the data set
B. the maximum and the minimum value of the data set
c. the mean and mode value of the data set
D. the minimum and mean value of the data set


The hybridization of the central atom will change when:
A . \( N H_{3} \) combines with \( H^{+} \)
B. \( H_{3} B O_{3} \) combines with \( O H^{-} \)
c. \( N H_{3} \) forms \( N H^{\overline{2}} \)
D. \( H_{2} O \) combines with \( H^{+} \)


For the following reaction, \( \triangle G^{\circ}= \)
\( -163 k J m o l^{-1} \)
\( \mathbf{2} \boldsymbol{O}_{\boldsymbol{3}} \rightarrow \mathbf{3} \boldsymbol{O}_{\mathbf{2}} \)
If this reaction is spontaneous enter 1
else enter 0


The minimum number of carbon atoms
that should be present in a monosaccharide is :
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 6


When a surface is irradiated with light
of wavelength \( 4950, \) a photocurrent appears which vanishes if a retarding
potential greater than \( 0.6 ~ V \) is applied across the phototube. When different source of light is used, it is found that the critical retarding potential is changed to \( 1.1 \mathrm{V} \). Find the work function of the emitted surface and the
wavelength of the second source.


Justify the following statements with an explanation:
¡) Solubility of calcium oxide decreases with increase in temperature.
ii) What happens to the solubility in exothermic process with regard to temperature?
iii) In endothermic process, solubility increases with increase in temperature.
iv) At a given temperature, increase in pressure increases the solubility of the
gas


The area of a square field is \( 30 \frac{1}{4} m^{2} \) Calculate the length of the side of the
square.
A \( \cdot_{5} \frac{1}{3} m \)
в. \( _{5} \frac{1}{2} m \)
c. \( _{5} \frac{2}{5} m \)
D. \( _{5} \frac{1}{4} m \)


The inverse of: "If two triangle are congruent then they are similar" is
A. If two triangles are similar then they are congruent.
B. If two triangles are not congruent then they are not \( \operatorname{similar} \)
c. If two triangles are not similar then they are not congruent.
D. None


Shaving mirrors are
A. convex mirrors
B. concave mirrors
c. plane mirrors
D. none of the above


An aqueous solution of salt is
alkaline. This shows that salt is made
from:
A. a strong acid and a strong base
B. a strong acid and a weak base
c. a weak acid and a weak base
D. a weak acid and a strong base


Differentiate the function with respect
to \( x \)
\( \cos x^{3} \cdot \sin ^{2}\left(x^{5}\right) \)


A slab of stone of area \( 0.36 m^{2} \) and
thickness 0.1 is exposed on the lower surface to steam at \( 100 C \). A block
of ice at \( 0 C \) rests on the upper surface
of the slab. In one hour \( 4.8 \mathrm{kg} \) of ice is melted. The thermal
conductivity of slab is- (Given latent heat of fusion of ice \( =3.36 \times 10^{5} J k g^{-1} \)
:
A. \( 1.29 \mathrm{J} / \mathrm{m} / \mathrm{s} / \mathrm{C} \)
в. 2.05 \( J / m / s / C \)
c. \( 1.02 \mathrm{J} / \mathrm{m} / \mathrm{s} / \mathrm{C} \)
D. \( 1.24 \mathrm{J} / \mathrm{m} / \mathrm{s} / \mathrm{C} \)


What is the power produced by an appliance marked " \( 240 V, 2 A ? \)
A. \( 8.3 m W \)
в. \( 60 W \)
c. \( 120 W \)
D. \( 480 W \)


Sodium or potassium salts of higher fatty acids are termed as:
A . salt
B. base
c. acid
D. soap


A chain of mass \( \mathrm{m} \) and length Lis over hanging from the edge of a smooth horizontal table such that \( \frac{1}{n} \) of its length is lying on the table. The work done in pulling the chain completely on to the table is
A \( \cdot \frac{m g L}{2 n^{2}} \)
в. \( \frac{m g L(n-1)^{2}}{2 n^{2}} \)
c. \( \frac{m g L(n-1)^{2}}{n^{2}} \)
D. \( \frac{m g L}{n^{2}} \)


Aldehydes showing
A. Electrophilic addition
B. Electrophilic substitution
C . Nucleophilic addition
D. Nucleophilic substitution


Describe a conspicuous change
observed when:
(i) a solution of \( N a C l \) is added too
solution of hydrated ferric oxide
(ii) a beam of light is passed through a solution of \( N a C l \) and then through a
solution.


Two bodies \( A \) and \( B \) having mass \( M \)
and \( m \) respectively possesses same
kinetic energy. Given that \( \boldsymbol{M}>\boldsymbol{m} \). If \( \boldsymbol{\rho}_{\boldsymbol{A}} \)
and \( \rho_{B} \) be their momentum, then which
of the following statements is true?
\( \mathbf{A} \cdot \rho_{A}=\rho_{B} \)
В \( \cdot \rho_{A}>\rho_{B} \)
c \( \cdot \rho_{A}<\rho_{B} \)
D. It cannot be predicted


Oxygen is manufactured by the fractional evaporation of:
A. water
B. liquid air
c. hydrogen peroxide
D. liquid oxygen


In a mixture of gases, the volume
content of a gas is \( 0.06 \% \) at STP.
Calculate the number of molecules of
the gas in 1 L of the mixture.
A. \( 1.613 \times 10^{23} \)
В. \( 6.023 \times 10^{23} \)
c. \( 1.61 \times 10^{27} \)
D. \( 1.61 \times 10^{19} \)


The emergent ray in a prism bends the normal.
A. Towards
B. Away from
c. Both A and B
D. None of the above


Hydraulic jacks works on which principle from below?
A. the pressure in closed container is the same at all points
B. the pressure in closed container is not same at all points
c. the pressure in closed container is opposite at all points
D. None


Multiple Correct Answers Type
All the particles thrown with same
initial velocity would strike the ground.
This question has multiple correct options
A. With same speed
B. Simultaneously
C. Time would be least for the particle thrown with velocity v downward i.e., particle 1
D. Time would be maximum for the particle 2


What is \( \tan ^{-1}\left(\frac{1}{4}\right)+\tan ^{-1}\left(\frac{3}{5}\right) \) equal
to?
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( \frac{\pi}{4} \)
\( c \cdot \frac{\pi}{3} \)
D. \( \frac{\pi}{2} \)


The graph shows how the magnification m produced by a thin lens varies with image distance v. What is the focal
length of the lens used?
\( A \cdot b^{2} c \)
\( a \)
в. \( \frac{b^{2}}{a c} \)
\( c . a \)
\( D \)


Calculate the potential of a half cell
having reaction: \( \quad A g_{2} S(s)+2 e^{-} \rightleftharpoons \)
\( 2 A g(s)+S^{2-}(a q) \) in a solution
buffered at \( p H=3 \) and which is also
saturated with \( 0.1 M H_{2} S(a q) \)
\( \left[\text { Given: } \boldsymbol{K}_{s p}\left(\boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{S}\right)=\right. \)
\( \mathbf{1 0}^{-49}, \boldsymbol{K}_{\boldsymbol{a}_{1}} \cdot \boldsymbol{K}_{\boldsymbol{a}_{2}}=\mathbf{1 0}^{-\mathbf{2 1}} \)
A . 1.18
B. 0.19
c. \( -0.19 V \)
D. None of these


Which of the following equations corresponds to the definition of
enthalpy of formation at \( 298 K ? \)
A . \( C(\text {graphite})+2 H_{2}(g)+1 / 2 O_{2}(l) \rightarrow C H_{3} O H(g) \)
B. \( C(\text { diamond })+2 H_{2}(g)+1 / 2 O_{2}(g) \rightarrow C H_{3} O H(l) \)
c. \( 2 C(\text { graphite })+4 H_{2}(g)+O_{2}(g) \quad \rightarrow 2 C H_{3} O H(l) \)
D. \( C(\text {graphite})+2 H_{2}(g)+1 / 2 O_{2}(g) \rightarrow C H_{3} O H(l) \)


\( f(x)=\lim _{n \rightarrow \infty} \frac{\log (x+2)-x^{2 n} \sin x}{x^{2 n}+1} \)
examine the continuity of \( f(x) \) at \( x=1 \)
Write 1 if continuous and 0 if not.


\( \lim _{x \rightarrow \infty} \sin x \) equals
\( \mathbf{A} \cdot 1 \)
B. 0
\( c \cdot \infty \)
D. does not exist


The symbol of \( N a \) represents the element:
A. nitrogen
B. nickel
c. sodium
D. potassium


The point of intersection of the tangents drawn to the curve \( x^{2} y=1-y \) at the
point where it is intersected by the
curve \( x y=1-y, \) is given by
A \( .(0,1) \)
в. (1,1)
c. (0,-1)
D. none of these


Three \( 60 \mathrm{W} \), 120 \( \mathrm{V} \) light bulbs are
connected across a \( 120 \mathrm{V} \) power line as
shown in Fig. Find the voltage across
each bulb.


Graphite is a conductor of electricity because
A . it has free valence electrons
B. it is a non-metal form of Carbon.
c. it is an allotrope of Carbon.
D. Both A and B


A spatially uniform magnetic tield of
\( 0.080 T \) is directed into the plane of the
page and perpendicular to it, as shown
in the accompanying figure. A wire loop
in the plane of the page has constant
area \( 0.010 \mathrm{m}^{2} . \) The magnitude of the
magnetic field decreases at a constant
rate of \( 3.0 \times 10^{-4} \) T/s. The magnitude
and direction of the induced emf is:
A \( .3 .0 \times 10^{-6} \) V clockwise
B. \( 3.0 \times 10^{-6} \mathrm{V} \) anticlockwise
C . \( 2.4 \times 10^{-5} \mathrm{V} \) anticlockwise
D. \( 8.0 \times 10^{-4} \) V clockwise


Our body temperature cannot fall below:
\( \mathbf{A} \cdot 37^{\circ} C \)
B \( .35^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 40^{\circ} \mathrm{C} \)
D. \( 42^{\circ} \mathrm{C} \)


State whether true or false.
The direction of acceleration due to
gravity is always vertically downward.
A. True
B. False


Show that the points \( \boldsymbol{A}(\boldsymbol{3}, \boldsymbol{2},-\boldsymbol{4}), \boldsymbol{B}(\boldsymbol{5}, \boldsymbol{4},-\boldsymbol{6}) \) and
\( C(9,8,-10) \) are collinear, find the ratio in which \( B \) divides \( \overline{A C} \).


Solution of differential equation \( (x \cos x-\sin x) d x=\frac{x}{y} \sin x d y \) is
\( \mathbf{A} \cdot \sin x=\ln |x y|+c \)
B. \( \ln \left|\frac{\sin x}{x}\right|=y+c \)
\( c \cdot\left|\frac{\sin x}{x y}\right|=c \)
D. None of these


An object travel \( 10 \mathrm{km} \) at a speed of
\( 100 m / s \) and another \( 10 \mathrm{km} \) at \( 50 \mathrm{m} / \mathrm{s} \)
The average speed over the whole distance is
A . \( 75 \mathrm{m} / \mathrm{s} \)
в. \( 55 \mathrm{m} / \mathrm{s} \)
c. \( 66.7 \mathrm{m} / \mathrm{s} \)
D. \( 33.3 \mathrm{m} / \mathrm{s} \)


The angle between the incident ray and the normal is called
A. Angle of incidence
B. Angle of reflection
c. Angle of refraction
D. None of these


Hair, fingernails, hoofs are all made of:
A . fat
B. vitamins
c. proteins
D. iron


The action of bromine water(excess) on
salicylic acid results in the formation
of.
\( A \)
B.
\( c \)
\( D \)


What is the oxidation state of coloured
ion in \( \left[\boldsymbol{C o}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right]^{3+} ? \)


Two circular coils \( P \) and \( Q \) are kept
close to each other, of which coil \( \boldsymbol{P} \)
carries a current. If coil \( \boldsymbol{P} \) is moved
towards \( Q, \) will some current be
induced in coil \( Q \) ? Give the reason for
your answer and name the phenomenon involved.


The expression \( \sin 27^{\circ} \cos 57^{\circ} \sin 87^{\circ} \)
simplifies to
A \( \cdot \frac{\sin 9^{\circ}}{4} \)
B. \( \frac{\cos 9^{\circ}}{4} \)
c. \( \frac{\sin 9^{\circ}}{2} \)
D. \( \frac{\cos 9^{\circ}}{2} \)


If \( (x+i y)(2-3 i)=4+i \) then \( (x, y)= \)
A. \( \left(1, \frac{1}{13}\right) \)
B \( \cdot\left(-\frac{5}{13}, \frac{14}{13}\right) \)
c. \( \left(\frac{5}{13}, \frac{14}{13}\right) \)
D. \( \left(-\frac{5}{13},-\frac{14}{13}\right) \)


For the manufacture of Ammonia by Haber's process, write the equation and optimum conditions for maximum yield
of ammonia.


An object \( A \) is kept fixed at the point \( x=3 m \) and \( y=1.25 m \) on a plank \( P \)
raised above the ground. At time \( t= \) the plank starts moving along the positive \( x \) -direction with an acceleration
\( 1.5 m / s^{2} . \) At the same instant a stone is projected from the origin with a velocity
\( \vec{u} \) as shown in the figure. A stationary person on the ground observes the
stone hitting the object during which it makes a downwards motion at the
angle of \( 45^{\circ} \) to the horizontal. All the
motions are in \( x \) -y plane. Find \( \vec{u} \) and the time after which the stone hits the
object (Take \( \boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2} \mathbf{)} \)


In a double-slit experiment, instead of taking slits of equal width, one slit is made twice as wide as the other. Then
in the interference pattern
A. the intensities of both the maxima and the minima increase
B. the intensity of the maxima increases and the minima has zero intensity
c. the intensity of the maxima decreases and that of the minima increases
D. the intensity of the maxima decreases and the minima has zero intensity


The experiment is to randomly select a human and measure his or her length.
Identify the type of the sample space.
A. Finite sample space
B. Continuous sample space
c. Infinite discrete sample space
D. None of these


A proton and an electron are placed in a
uniform electric field.
A. The electric forces acting on them will not be equal.
B. The magnitudes of the forces will be equal.
C. Their accelerations will be equal.
D. None of the above


Why ozone is known as 'chemical weed
\( ? \)
A. Because it is formed by chemical reactions
B. Because it is harmful as well useful
C. Because it is harmful, just like weeds for mankind
D. Ozone is not designated as chemical weed


A solution is made by dissolving 49 g of \( H_{2} S O_{4} \) in \( 250 \mathrm{mL} \) of water. The molarity
of solution prepared is:
\( A \cdot 2 M \)
в. 1
\( c \cdot 4 M \)
D. 5 M


Which of the following is diamagnetic?
\( A \)
\( \left[M n\left(H_{2} O\right)_{6}\right]^{2+} \)
в. \( \left[C u\left(H_{2} O\right)_{6}\right]^{3+} \)
c. \( \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+} \)
D. \( \left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+} \)


The equation \( \sin ^{2} \theta-\frac{4}{\sin ^{3} \theta-1}=1 \)
\( \frac{4}{\sin ^{3} \theta-1} \) has
A. No root
B. One root
c. \( T w o \) roots
D. Infinite roots


Which of the following is the correct
statement about I and II?
(1)
\( (\Pi) \)
A. I is reducing sugar
B. II is reducing sugar
c. 18 II both are reducing sugar
D. None of the two is reducing sugar


Which of the following is not a peroxy acid?
A. Perphosphoric acid
B. Pernitric acid
c. Perdisulphuric acid
D. Perchloric acid


The centre of two circles are \( 41 \mathrm{cm} \)
apart: The smaller circle has a radius of 4 inches and the larger one has ab radius of \( 5 \mathrm{cm} . \) The length of the common internal tangent is :
\( \mathbf{A} \cdot 41 \mathrm{cm} \)
в. \( 39 \mathrm{cm} \)
\( \mathrm{c} .39 .8 \mathrm{cm} \)
D. \( 40 \mathrm{cm} \)


Write the structure of 1-flouropropane.
\( \mathbf{A} \cdot C H_{3} C H_{2} C H_{2} C l \)
\( \mathbf{B} \cdot C H_{3} C H_{2} C H_{3} F \)
\( \mathbf{c} \cdot C H_{2} C H_{2} C H_{2} F \)
D. \( C H_{3} C H_{2} C H_{2} F \)


Among the following which one contains valence electrons in the ground state of
the magnesium \( M g \) atom?
A . \( 1 s \)
B . \( 2 s \)
c. \( 3 s \)
D. \( 3 p \)
E . \( 3 d \)


Choose correct statements:
A. Superphosphate is \( C a H_{4} P_{2} O_{8} \)
B. triple superphosphate is \( C a\left(H_{2} P O_{4}\right)_{2} \)
C. Both (a) and (b) are correct
D. None of the above is coreect


A current of \( 2 A \) is flowing through a cell of e.m.f. \( 5 V \) and internal resistance
\( 0.5 \Omega \) from negative to positive electrode. If the potential of negative electrode is \( 10 V \), the potential of
positive electrode will be :-
A \( .5 V \)
\( V \)
B. 14 \( V \)
\( \mathrm{c} .15 \mathrm{V} \)
D. \( 16 V \)


The functional isomer of
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{O H} \)
\( \mathbf{A} \cdot C H_{3}-C H-C H_{3} \)
\( _{O H} \)
в. \( C H_{3} C O C H_{3} \)
c. \( C H_{3} O C H_{3} \)
D. \( C H_{3} O C H_{2} C H_{3} \)


When \( C a C O_{3} \) is heated to a high
temperature, it undergoes
decomposition into \( C a C O \) and \( C O_{2} \)
whereas it is quite stable at room temperature. The most likely explanation of it is:
A. The enthalpy of reaction \( (\Delta H) \) overweight the term \( T \Delta S \) at high temperature
B. The term \( T \Delta S \) overweight the enthalpy of reaction at high temperature
c. At high temperature, both enthalpy of reaction and entropy change become negative
D. None of these


Find \( \boldsymbol{f} \circ \boldsymbol{g} \) and \( \boldsymbol{g} \) o \( \boldsymbol{f}, \) if \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \boldsymbol{x}^{2}, \boldsymbol{g}(\boldsymbol{x})=\cos \boldsymbol{x} \)


If \( P=\left[\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2}\end{array}\right], A=\left[\begin{array}{cc}1 & 1 \\ 0 & 1\end{array}\right] \) and
\( Q=P A P^{\prime}, \) then \( P^{\prime} Q^{2015} P \) is:
A. \( A=\left[\begin{array}{cc}0 & 2015 \\ 0 & 0\end{array}\right] \)
B. \( A=\left[\begin{array}{cc}2015 & 0 \\ 1 & 2015\end{array}\right] \)
c. \( A=\left[\begin{array}{cc}1 & 2015 \\ 0 & 1\end{array}\right] \)
D. \( A=\left[\begin{array}{cc}2015 & 1 \\ 0 & 2015\end{array}\right] \)


The possible value of \( \boldsymbol{\theta} \in(\mathbf{0}, \boldsymbol{\pi}) \) such
\( \operatorname{that} \sin (\theta)+\sin (4 \theta)+\sin (7 \theta)=0 \) are
A \( \cdot \frac{2 \pi}{9}, \frac{\pi}{4}, \frac{4 \pi}{9}, \frac{\pi}{2}, \frac{3 \pi}{4}, \frac{8 \pi}{9} \)
В. \( \frac{\pi}{4}, \frac{5 \pi}{12}, \frac{\pi}{2}, \frac{2 \pi}{3}, \frac{3 \pi}{4}, \frac{8 \pi}{9} \)
С \( \cdot \frac{2 \pi}{9}, \frac{\pi}{4}, \frac{\pi}{2}, \frac{2 \pi}{3}, \frac{3 \pi}{4}, \frac{35 \pi}{36} \)
D. \( \frac{2 \pi}{9}, \frac{\pi}{4}, \frac{\pi}{2}, \frac{2 \pi}{3}, \frac{3 \pi}{4}, \frac{8 \pi}{9} \)