In stationary waves, nodes are the
points where there is:
A. maximum displacement and minimum pressure change
B. minimum displacement and maximum pressure change
C. minimum displacement and minimum pressure change
D. maximum displacement and maximum pressure change


Aldol condensation will not take place in:
A. \( H C H O \)
в. \( C H_{3} C H_{2} C H O \)
\( \mathbf{c} \cdot C H_{3} C H O \)
D. \( C H_{3} \) COCH\( _{3} \)


The momentum of a system is
conserved
A. always
B. never
\( \mathrm{C} \). in the absence of external forces in the system
D. in presence of external forces in the system


What is famous for the constructive
and functional unit?
A. Ecosystem
B. Food chain
c. Food web
D. None of these


Which one of the following pairs do not impart colour to the flame?
A. \( B e C l_{2} \) and \( S r C l_{2} \)
в. \( B e C l_{2} \) and \( M g C l_{2} \)
c. \( C a C l_{2} \) and \( B a C l_{2} \)
D. \( B a C l_{2} \) and \( S r C l_{2} \)


Find whether the following functions are
one-one, onto or not:
\( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) defined by \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}+\boldsymbol{3} \) for
all \( \boldsymbol{x} \epsilon \boldsymbol{R} \)


Find the distance between the following pair of points:
(-6,7) and (-1,-5)


Write the domain of the function
\( \boldsymbol{f}(\boldsymbol{x})=\log _{4}(1+\boldsymbol{x}) \)
\( A \cdot(-1, \infty) \)
B. \( (1, \infty) \)
c. \( (2, \infty) \)
D. None of these


Name the device used for measuring the pressure exerted by liquids. Also, state its working principle.


Assume that the chances of a patient having a heart attack is \( 40 \% \). It is also assumed that a meditation and yoga
course reduce the risk of heart attack by \( 30 \% \) and prescription of certain drug reduces its chances by \( 25 \% \). At a time a
patient can choose any one of the two options with equal probabilities. It is given that after going through one of the two options the patient selected at random suffers a heart attack. Find the
probability that the patient followed a course of meditation and yoga?


\( p- \) orbitals of an atom in presence of magnetic field are:
A. three fold degenerate
B. two fold degenerate
c. non-degenerate
D. none of these


Find the slopes of the tangent and the normal to the following curves at the
indicated points.
\( \boldsymbol{x}^{2}+\mathbf{3} \boldsymbol{y}+\boldsymbol{y}^{2}=\mathbf{5} \) at \( (\mathbf{1}, \mathbf{1}) \)


Which one of the following is not a photosynthetic diazotroph.
A. Nostoc
B. Frankia
c. Anabaena
D. Rhodospirillum


Identify the rate of decarboxylation of isomeric pyridine acetic acids by the similar mechanism.
\( A \cdot 1>2>3 \)
B. \( 1>3>2 \)
c. \( 3>2>1 \)
D. \( 2>1>3 \)


The figure above shows the eye
suffering from:
A. hypermetropia
B. myopia
C . astigmatism
D. far-sightedness


Assertion
Alkali metals dissolves in liquid ammonia to give blue solution
Reason
Alkali metals in liquid ammonia give solvated species of the type \( \left[\mathbf{M}\left(\mathbf{N} \mathbf{H}_{3}\right)_{\mathbf{n}}\right]^{+}(\mathbf{M}= \) alkali metals)
A. Both Assertion and Reason are correct and the Reason is the correct explanation of the Assertion
B. Both Assertion and Reason are correct but the Reason is not the correct explanation of the Assertion
c. The Assertion is correct but the Reason is incorrect
D. The Assertion is incorrect but the Reason is correct


Find the possible value of \( \cos x, \) if \( \cot x \)
\( +\operatorname{cosec} x=5 \)


Describe the manufacture of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) by
contact process?


particle moves uniform in a circle of
radius \( 10 \mathrm{cm}, \) converting a linear distance of \( \mathrm{cm} \) in a time 2.5 sec. Find
the time taken for 10 revolutions,
A \( .0 .2 s e c \)
B. 18.34 sec
c. 79.12 sec
D. 50 sec


Which of the following product is formed by the reaction of sulphur dioxide with chlorine in presence of
sunlight?
\( A \cdot S O_{2} C l \)
в. \( S O_{2} C l_{2} \)
c. \( \operatorname{socl}_{2} \)
D. \( S O_{3} C l \)


A body can throw a stone up a
maximum height of \( 10 \mathrm{cm} \) The maximum horizontal distance that the
boy can throw the same stone up to will
be:-
A . 40
B. \( 20 \sqrt{2} m \)
c. 10
D. \( 10 \sqrt{2} \mathrm{m} \)


The elements \( ^{30} \boldsymbol{S} \boldsymbol{i}_{14},^{31} \boldsymbol{P}_{15} \) and \( ^{32} \boldsymbol{S}_{16} \) are
called :
\( A \). isotones
B. isobars
c. isotopes
D. mirror nuclei


Find the curve which passes through the point (2,0) such that segment of
the tangent between the point of tangency \( \& \) the \( y \) - axis has a constant length equal to 2


Among mammals, the efficiency of ventilation of lungs as compared to reptiles and birds is better developed by the presence of
A. Ribs and costal muscles
B. Only ribs
c. only costal muscles
D. Diaphragm


A lens is made of flint glass (refractive index \( =1.5 \) ). When the lens is immersed in a liquid of refractive index 1.25, the focal length:
A. Increases to a factor of 1.25
B. Increases to a factor of 2.5
c. Increases to a factor of 1.2
D. Decreases to a factor of 1.2


Assertion
Chlorine reacts with freshly prepared calcium hydroxide to produce bleaching powder.
Reason
Chlorine has a great affinity for
hydrogen.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Find the total surface of cuboid whose
length is \( 8 c m \) breadth is \( 6 \mathrm{cm} \) and
height is \( 5 c m \)


If the product of two numbers is 21 and their difference is \( 4, \) then the ratio of the sum of their cubes to the difference of
their cubes is
\( \mathbf{A} \cdot 185: 165 \)
B . 165: 158
c. 185: 158
D. 158: 145


Maria invested \( R s 8,000 \) in a business. She would be paid interest at \( 5 \% \) per
annum compounded annually. Find
(i) The amount credited against her
name at the end of the second year.
(ii) The interest for the 3 rd year


A wave of angular frequency \( \omega \) propagates so that a certain phase of oscillation moves along x-axis, y-axis
and z-axis with speeds \( c_{1}, c_{2} \) and \( c_{3} \)
respectively. The propagation constant \( \boldsymbol{k} \) is
A \( \cdot \frac{\omega}{\sqrt{c_{1}^{2}+c_{2}^{2}+c_{3}^{2}}}(\hat{i}+\hat{j}+\hat{k}) \)
B. \( \frac{\omega_{\hat{i}}}{c_{1}}+\frac{\omega_{\hat{\jmath}}}{c_{2}}+\frac{\omega}{c_{3}} \hat{k} \)
c. \( (\omega \hat{i}+\omega \hat{j}+\omega \hat{k}) \frac{1}{c} \)
D. \( \frac{\omega}{\left(c_{1}+c_{2}+c_{3}\right)}(\hat{i}+\hat{j}+\hat{k}) \)


Find the correct statement pertaining to the functions \( f(x)=(x-3)^{2}+2 \) and
\( g(x)=\frac{1}{2} x+1 \) graphed above
A \( \cdot f(x)=g(x) \) for exactly 2 values of \( x \)
B . \( f(x)=g(x) \) for exactly 1 values of \( x \)
c. \( f(x) \) is the inverse of \( g(x) \)
\( \mathbf{D} \cdot f(x)>g(x) \) for all \( x \)


The solution of \( \frac{d y}{d x}=\frac{\sqrt{x^{2}-y^{2}}+y}{x} \) is:
\( \mathbf{A} \cdot \tan ^{-1}\left(\frac{y}{x}\right)=\log (c x) \)
B・sin \( ^{-1}\left(\frac{y}{x}\right)=\log (c x) \)
c. \( \cos ^{-1}\left(\frac{y}{x}\right)=\log (c y) \)
D \( \cdot \sec ^{-1}\left(\frac{y}{x}\right)=\log (c y) \)


SBR (GRS, Buna-S, Cold Rubber) is
obtained by free radical copolymerisation of :
A. \( 70 \% \) Buta -1,3 - diene and \( 30 \% \) phenly ethene (styrene)
B. chloroprene and styrene
c. vinly-acetylene and styrene
D. isoprene and 1,3 - butadiene


The volume of anatomical dead space
air is normally
A. 230 \( \mathrm{ml} \)
B. 210 m1
c. \( 190 \mathrm{ml} \)
D. 150 \( \mathrm{m} \)


Find the equivalent capacitance across A and B for the arrangement shown in figure. All the capacitors are of
capacitance \( \mathbf{C}: \)
A \( \cdot \frac{3 C}{14} \)
в. \( \frac{C}{8} \)
c. \( \frac{3 C}{16} \)
D. none of these


Which of the following is not the source of hydrocarbon as a pollutant?
A. Man-made sources
B. Sources of methane
c. Fly ash
D. oxide of sulphur


Which one of the following does not match in biological category of chemical substance?
A. Gastrin
B. Thyroxine
c. oxytocin
D. Creatinine


A pith ball of mass \( 9 \times 10^{-5} k g \) carries a
charge of \( 5 \mu C \). What must be charge on
another pith ball placed directly \( 2 \mathrm{cm} \) above the pith ball such that they are held in equilibrium?
A . \( 3.2 \times 10^{-11} C \)
B . \( 7.84 \times 10^{-12} C \)
c. \( 1.2 \times 10^{-13} C \)
D. \( 1.6 \times 10^{-19} C \)


Convert the given decimal function to
percents.
\( \mathbf{0 . 0 2} \)


Which of the following are the source for hydrocarbons as pollutants?
A. Anaerobic bacterial decomposition of organic matter
B. Forest fires and trees
c. combustion of Fuels
D. All of the above


In plants, micronutrients are those
which are needed less than or equal to the following amount per gram of dry matter is
A . \( 0.1 \mathrm{mg} \)
B. \( 0.1 \mathrm{g} \)
c. \( 0.1 \mu \mathrm{g} \)
D. \( 1 \mu g \)


\( \mathbf{f} \boldsymbol{y}=\cot ^{-1} \sqrt{\frac{1-\sin x}{1+\sin x}}, \) find \( \frac{d x}{d y} \)


Which plastic is called a fire proof
plastic?
A. Melamine
B. Bakelite
c. Teflon
D. Acrylic


Choose the correct answer from the
alternatives given:

Directions for questions 71 to 75: The
graph shows the production of wheat in different years of a particular State
The year in which the production
reached maximum is
\( \mathbf{A} \cdot 1995 \)
B. 1997
\( \mathbf{c} .1999 \)
D. 2000


What is the potential difference across
a 64.0 microfarad capacitor if the
charge on the positive plate is +16.0 microcoulombs?
A. \( 4.0 V \)
B. \( 0.25 V \)
\( c .1024 V \)
D. \( 2.0 V \)
E . \( 32.0 V \)


If two bodies \( A \) and \( B \) (A bigger in size than \( \mathrm{B} \) ) are rubbed together, then :
A. A and B get equal and opposite charges
B. A and B get equal and similar charges
c. A gets more charge than B, but of opposite kind
D. A gets less charge than B, but of same kind


10g fairly concentrated solution of
\( \boldsymbol{C u} \boldsymbol{S O}_{4} \) is electrolysed using \( \mathbf{0 . 0 1} \)
faraday of electricity. The mass of resulting solution is :
A. \( 9.6025 \mathrm{g} \)
B. \( 10.6005 \mathrm{g} \)
c. \( 6.6025 \mathrm{g} \)
D. None of these


Integrate \( \frac{x^{2}+5 x+5}{x^{2}+3 x+2} \) with respect to \( x \)


A rectangular paper of length \( 45 \mathrm{cm} \) and
breadth \( 5 \mathrm{cm} \) is cut to form a square with the same area. What is the side of
the square?


The atomic theory of matter was
proposed by :
A. John Kennedy
B. Lavoisier
c. Proust
D. John Dalton


Prove that the points \( (0,0),\left(3, \frac{\pi}{2}\right), \) and \( \left(3, \frac{\pi}{6}\right) \) form an equilateral triangle.


Figure shows the circular motion of a
particle. The radius of the circle, the
period, sense of revolution and the initial position are indicated in the
figure. The simple harmonic motion of
the \( x \) - projection of the radius vector of the rotating particle P is
A \( \cdot x=2 \cos \left[2 \pi t+\frac{\pi}{4}\right. \)
B・ \( x=2 \sin \left[2 \pi t+\frac{\pi}{4}\right] \)
c. \( x=2 \sin \left[2 \pi t-\frac{\pi}{4}\right] \)
D. \( x=2 \cos \left[2 \pi t-\frac{\pi}{4}\right] \)


Distinguish between regular and
diffused reflection. Does diffused
refection mean the failure of the laws of
reflection?


Why does the sky appear dark instead
of blue to an astronaut?


Hydrogen is the element
on the earth.
A. most abundant
B. heaviest
c. lightest
D. none of these


Evaluate the following:
\( \left|\begin{array}{ccc}\boldsymbol{x} & \mathbf{1} & \mathbf{1} \\ \mathbf{1} & \boldsymbol{x} & \mathbf{1} \\ \mathbf{1} & \mathbf{1} & \boldsymbol{x}\end{array}\right| \)


The distance of the point \( ,(-1,-5,-10) \) from the point intersection of the line,
\( \frac{x-2}{3}=\frac{y+1}{4}=\frac{z-2}{12} \) and the plane \( x- \)
\( \boldsymbol{y}+\boldsymbol{z}=\mathbf{5}, \) is
\( A \cdot 13 \)
B. 1
c. 12
D. none of these


A body is thrown up with an initial velocity \( u \) and covers a maximum
height of \( h, \) then h is equal to
\( ^{\mathrm{A}} \cdot \frac{u^{2}}{2 g} \)
в. \( \frac{u}{2 g g} \)
c. 2 ug
D. none of these


How is ore of aluminium concentrated?
A. Roasting
B. Leaching
C. Froth floatation
D. Using Wilfley table


The self ionisation constant for
HCOOH is \( 10 \%-6 \) what percentage
of \( H C O O H \) are converted to \( H C O O \)
ion. The density of \( H C O O H \) is \( 1.22 g \) \( \boldsymbol{m} \boldsymbol{L}^{-1} \)


If \( x \sqrt{1+y}+y \sqrt{1+x}=0, \) then \( \frac{d y}{d x} \) is
equal to
\( ^{A} \cdot \frac{1}{(1+x)^{2}} \)
B. \( \frac{-1}{(1+x)^{2}} \)
c. \( \frac{1}{(1-x)^{2}} \)
D. None of these


If the work done by the actor is \( y \mathrm{kJ} \), find
\( 2 y \)


Who among the following are associated with SONAR?
A. Sonograph
B. Engineers
c. Astronauts
D. Navigators


The enzyme involved in alcoholic
fermentation is
A. Pyruvate decarboxylase.
B. Alcohol dehydrogenase.
c. Lactate dehydrogenase.
D. Both A and B


Find the sum of \( C_{0}+3 C_{1}+3^{2} C_{2}+ \)
\( \ldots+3^{n} C_{n} \)


\( H-\operatorname{atom} \) is of \( _{-}-_{-}----k g \)
\( \mathbf{A} \cdot 1.675 \times 10^{-27} \)
B . \( 1.673 \times 10^{-27} \)
C \( \cdot 9.109 \times 10^{-31} \)
D. \( 3.348 \times 10^{-27} \)


Which of the following would you consider to prove that a plant is a
monocot?
A. Leaves with reticulate venation
B. Taproot system
c. Vascular bundles are closed
D. Presence of cambium


Eucalyptus plant possesses twiners.
A. True
B. False


In Rutherford's experiment, most of the alpha particles are observed to
A. Pass undeflecgtedd
B. Be deflected
c. Be thrown back
D. Be absorbed


Unpolarized light passes through two
polaroids, the axis of one is vertical and
that of the other is \( 30^{\circ} \) to the vertical.
What is the orientation and intensity of
the transmitted light?
A. Plane polarized at \( 60^{\circ} \) to the vertical and having intensity \( \frac{l_{0}}{4} \)
B. Plane polarized at \( 30^{\circ} \) to the vertical and having intensity of \( \frac{3 l_{0}}{8} \)
C. Plane polarized at \( 30^{\circ} \) to the vertical and having intensity \( \frac{l_{0}}{2} \)
D. No light passes


A catalyst can change the:
A. heat of reaction and the potential energy of the reactants
B. heat of reaction and the time it takes the reaction to
proceed
C . activation energy of the reverse reaction and the potential energy of the activated complex
D. potential energy of the reactants and the time it takes the reaction to proceed
E . activation energy of the forward reaction and the potential energy of the products


Check which function is bijective from \( Z \rightarrow Z \)
(A) \( f(x)=x^{3} \)
(B) \( f(x)=2 x+1 \)


For which of the following equations is
the change in enthalpy at \( 25^{\circ} \mathrm{C} \) and 1
atm equal to \( \Delta H_{f}^{o} \) of \( C H_{2} O(l) \)
A \( \cdot C(s)+H_{2}(g)+1 / 2 O_{2}(g) \rightarrow C H_{2} O(l) \)
B. \( C(s)+2 H_{2}(g)+1 / 2 O_{2}(g) \rightarrow 2 C H_{2} O(l) \)
c. \( C(g)+2 H_{2}(g)+O(g) \rightarrow C H_{2} O(l) \)
D. \( C O(g)+2 H_{2}(g) \rightarrow C H_{2} O(l) \)


Soda water contains:
A. carbonic acid
B. sulphuric acid
C. carboxylic acid
D. nitrous acid


Find the ratio of the following: \( (\operatorname{Max}(\mathrm{M}) \) \( +\operatorname{Max}(\mathrm{N})) /(\operatorname{Max}(\mathrm{K})+\operatorname{Max}(\mathrm{L})) \) where
Max denotes the maximum number of
electrons. \( K, L, M, N \) represent the shells.
A . 4
B. 5
\( c .6 \)
\( D .7 \)


In a fission process, nucleus A divides into two nuclei B and C, their binding
energies being \( \mathbf{E}_{\mathbf{a}^{*}} \quad \boldsymbol{E}_{\boldsymbol{b}} \) and \( \boldsymbol{E}_{\boldsymbol{c}} \)
respectively. Ihen
A \( \cdot \mathbf{E}_{\mathrm{b}}+\mathrm{E}_{\mathrm{c}}=\mathrm{E}_{\mathrm{a}} \)
в. \( \mathrm{E}_{\mathrm{b}}+\mathrm{E}_{\mathrm{c}}>\mathrm{E}_{\mathrm{a}} \)
c. \( \mathrm{E}_{\mathrm{b}}+\mathrm{E}_{\mathrm{e}}<\mathrm{E}_{\mathrm{a}} \)
D. \( \mathrm{E}_{\mathrm{b}} \mathrm{E}_{\mathrm{c}}=\mathrm{E}_{\mathrm{a}} \)


Prove that
\( n_{r+1}+2^{n} C_{r}+^{n} C_{r-1}= \)


Generally semiconductor can be used safely between the temperatures:
A . -75 and 200
B. 0 and 75
c. -25 and 300
D. -40 and 1000


Name the following compound. A salt which is used in the manufacture
of glass and detergent.


Find the time period of disc?


Which of the following is not a colligative property?
A. Osmotic pressure
B. Optical activity
c. Depression in Freezing point
D. Elevation in Boiling point


Which among the following represent the conjugate acid/base pairs? This question has multiple correct options
A \( \cdot H_{3} O^{+} / H_{2} O \)
в. \( H_{2} S O_{4} / S O_{4}^{2} \)
c. \( H C O_{3}^{-} / C O_{3}^{2} \)
D. All are conjugate acid/ base pairs


A ball of mass \( \mathrm{m} \) is thrown vertically upward from the ground and reaches a height h before momentarily coming to rest.If \( g \) is acceleration due to gravity,the impulse received by the ball due to gravity force during its flight is
\( \mathbf{A} \cdot \sqrt{2 m^{2} g h} \)
в. \( \sqrt{4 m^{2} g h} \)
\( \mathbf{c} \cdot \sqrt{8 m^{2} g h} \)
D. \( 4 \sqrt{m^{2} g h} \)


'Ozone layer' is located in
A. Troposphere
B. Hydrosphere
c. stratosphere
D. Lithosphere


At a particular temperature, the
equilibrium concentrations of the substances in the previous question
are as follows: \( \left[N O_{2} C l\right]=0.5 \mathrm{M},\left[C l_{2}\right]= \)
\( 0.3 \mathrm{M},\left[N O_{2}\right]=0.2 \mathrm{M} . \) What is the value
of the equilibrium constant for this reaction?
A . 2.
B. 0.48
c. 0.0357
D. 20.83
E. 208.83


Solve the equation:\( 9(2 x-y)^{2}-4(2 x-y)-13 \)


Assertion
\( \overrightarrow{\boldsymbol{E}}=\boldsymbol{E}_{\boldsymbol{x}} \hat{\boldsymbol{i}}+\boldsymbol{E}_{\boldsymbol{y}} \hat{\boldsymbol{j}}+\boldsymbol{E}_{z} \hat{\boldsymbol{k}}, \vec{\nabla} \times \overrightarrow{\boldsymbol{E}}=\mathbf{0} \)
Reason
\( E_{x}, E_{y}, E_{z} \) is independent.
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


What do you understand by isotopes? Given one example.


Fibrous and globular shapes comes under which structure of proteins?
A. Primary
B. Secondary
c. Tertiary
D. Quaternary


Calculate the torque developed (in \( \mathrm{Nm} \) by an airplane engine whose
output is \( 2000 H P \) at an angular
velocity of 2400 rev / min.


Which one is used for the formation of
nylon - 6, 6?
A. Sulphurous acid
B. Adipic acid
c. sulphur hexafluoride
D. Phthalic acid


Solve \( \int \frac{1}{\sin x \cos ^{3} x} d x \)


Identify phase in mitosis shown by :
centromeres split and thereby sister chromatids of each chromosome
separates and they are pulled apart in opposite direction.
A. Telophase
B. Prophase
c. Metaphase
D. Anaphase


The nuclear fission chain reaction is
initiated by the particle.
A. Proton
B. Neutron
c. Electron
D. Positron


Which of the following is correct?
A. Adsorption is always exothermic.
B. Adsorption is always endothermic.
C. Physical adsorption is endothermic whereas chemisorption is exothermic.
D. Chemical adsorption is endothermic whereas physical adsorption is exothermic.


The internal resistance of a dry cell is of the order of:
A. 0.2 to 0.4 ohm.
B. 1 to 1.4 Ohm.
c. 2 to 5 ohm.
D. 1 to 15 Ohm.


A line passes through (5,-6) and it is
parallel to \( y- \) axis.Find its equation.


By the action of conc. \( \boldsymbol{H} \boldsymbol{N O}_{3} \)
phosphorus changes to:
A. phosphorus acid
B. metaphosphoric acid
c. orthophosphoric acid
D. pyrophosphoric acid


In an equilibrium, the positive catalyst increases the rate of the forward
reaction while decreases the rate of the
backward reaction.
A. True
B. False


Assertion
White phosphorus is more reactive than
red phosphorus.
Reason
It readily catches fire in air to give
dense white fumes of \( \boldsymbol{P}_{4} \boldsymbol{O}_{10} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The number of moles of \( K M n O_{4} \) that will be needed to react completely with
one mole of ferrour oxalate \( F e\left(C_{2} O_{4}\right) \) in acidic solution is :
\( \mathbf{A} \cdot \mathbf{1} \)
B. \( \frac{2}{5} \)
\( c \cdot \frac{3}{5} \)
D.


During \( \beta- \) decay (beta minus), the
emission of antineutrino particle is supported by which of the following statement(s)?
This question has multiple correct options
A. Angular momentum conservation holds good in any nuclear reaction
B. Linear momentum conservation holds good in any nuclear reaction
C. The KE of emitted \( \beta- \)particle is varying continuously
to a maximum value
D. None of the above


Solve \( : \int_{0}^{2} x \sqrt{x+2} d x \)


State the whether given statement is true or false
Prove that the coefficient of xnxn
A. True
B. False


If a body is in equilibrium under a set of non-collinear forces, then the minimum
number of forces has to be:
A. Four
B. Three
c. Two
D. Five


Which product will obtained in the
following reaction?
Reaction: \( \boldsymbol{P}_{4_{(a)}}+\mathbf{3} \boldsymbol{N a O H}_{(a q)}+ \)
\( \mathbf{3} \boldsymbol{H}_{2} \boldsymbol{O}_{(l)} \longrightarrow \)
\( \mathbf{A} \cdot P H_{3_{(a)}}+3 N a_{2} H P O_{2_{(a)}} \)
B. \( P H_{3_{(a)}}+3 N a H_{2} P O_{2_{l a q}} \)
C. \( 2 P H_{3_{(l)}}+3 N a_{2} H P O_{2_{l a}} \)
D. \( 2 P H_{3_{(l)}}+3 N a H_{2} P O_{2_{l a}} \)


\( \mathbf{A} \)
\( 2 m \) long rod of radius \( 1 c m \) which is
fixed from one end is given a twist of 0.8 radian. The shear strain developed will
be
\( \mathbf{A} \cdot 0.002 \)
B. 0.004
c. 0.008
D. 0.016


\( \boldsymbol{C H}_{3}-\boldsymbol{C} \equiv \boldsymbol{C H} \)
The IUPAC name of the compound is:
A. propane
B. propene
c. propyne
D. 1-methyl-propane


State whether given statement is True or False.
Electric potential at a point in an electric field is defined as the work done
in moving a unit positive charge from infinity to that point.
A. True
B. False


Total number of bones in appendicular skeleton of rabbit is
A . 128
B. 120
\( c \cdot 80 \)
D. 37


It is found in phosphorus and nitrogen
A. inorganic impurities
B. bacteria
c. nutrients
D. other microbes


Let \( \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{y})=\boldsymbol{f}(\boldsymbol{x}) \cdot \boldsymbol{f}(\boldsymbol{y}), \forall \boldsymbol{x}, \boldsymbol{y} \in \boldsymbol{R} \)
suppose that \( \boldsymbol{f}(\mathbf{3})=\mathbf{3}, \boldsymbol{f}^{\prime}(\mathbf{0})=\mathbf{1 1}, \) then
\( f^{\prime}(3) \) is given by
A .22
B. 44
c. 28
D. 33


What is best pH of soil for cultivation?
A. 3.4 to 5.44
B. 5 to 5.5
c. 5.5 to 6.5
D. 6.5 to 7.5


If positively charged pendulum is oscillating in a uniform electric field as shown in figure. Its time period as compared to that when it was
uncharged:
A. will increase
B. will decreas
c. will not change
D. will first increase then decreas


\( \int \tan ^{-1} x d x=-1 \)
A. \( x \tan ^{-1} x+\frac{1}{2} \log \left|\frac{\tan ^{-1} x}{x^{2}+1}\right| \)
S. \( x \tan ^{-1} x-\frac{1}{2} \log \left|x^{2}+1\right| \)
C. \( x \tan ^{-1} x+\frac{1}{2} \log \left|x^{2}+1\right| \)


If \( 3 x^{2}+4 k x+1>0 \) for all real values
of \( x, \) then \( k \) lies in the interval.
A \( \cdot\left(\frac{-\sqrt{3}}{2}, \frac{\sqrt{3}}{2}\right) \)
в. \( \left(\frac{-1}{4}, \frac{1}{4}\right) \)
\( ^{c} \cdot\left[\frac{-\sqrt{3}}{2}, \frac{\sqrt{3}}{2}\right] \)
D. \( \left(\frac{-1}{2}, \frac{1}{2}\right) \)


\( \int \frac{d x}{9+16 \sin ^{2} x} \) is equal to
A \( \cdot \frac{1}{3} \tan ^{-1}\left(\frac{3 \tan x}{5}\right)+c \)
B \( \cdot \frac{1}{5} \tan ^{-1}\left(\frac{\tan x}{15}\right)+c \)
c. \( \frac{1}{15} \tan ^{-1}\left(\frac{\tan x}{5}\right)+c \)
D. \( \frac{1}{15} \tan ^{-1}\left(\frac{5 \tan x}{3}\right)+c \)


Identify the electronic configuration of an element whose atomic radii is determined by taking half the internuclear distance between like
atoms.
\( \mathbf{A} \cdot[H e] 2 s^{2} 2 p^{5} \)
B . \( [A r] 4 s^{2} \)
c. \( [N e] 3 s^{2} \)
D \( \cdot[K r] 4 d^{5} 5 s^{2} \)


The vectors \( \bar{a}, \bar{b}, \bar{c} \) are of the same length and taken pair wise, they form equal angles. If \( \bar{a}=\bar{i}+\bar{j} \) and \( \bar{b}=\bar{j}+\bar{k} \)
then the components of \( \bar{c} \) are?
A. (1,0,1)
в. (1,2,3)
c. (-1,1,2)
D. (-1,4,1)


What are the differences between
inherited and acquired characters?
A. Inherited characters- characters that are passed on from parents to offspring. Acquired characters- characters appearing in an individual's lifetime but cannot be transmitted to next
generation.
B. Inherited characters- characters appearing in an individual's lifetime but cannot be transmitted to next
generation. Acquired characters- characters that are passed on from parents to offspring.
C. Inherited characters- characters that are passed on from offspring to parents. Acquired characters- characters appearing in an individual's lifetime but cannot be transmitted to next generation.
D. Inherited characters- characters that are passed on from offspring to parents. Acquired characters- characters appearing in an individual's lifetime and can be transmitted to next
generation.


Find \( \frac{d y}{d x} \) if \( x=a(\cos \theta+\theta \sin \theta) \). and
\( \boldsymbol{y}=\boldsymbol{a}(\sin \theta-\boldsymbol{\theta} \cos \boldsymbol{\theta}) \)


Electrochemical equivalent is the amount of substance which gets deposited from its solution on passing
electrical charge equal to :
A. 96,500 coulomb
B. 1 coulomb
c. 60 coulomb
D. 965 coulomb


Because they have different boiling points, the substances in crude oil can
be separated using:
A. chromatography
B. fractional distillation
c. sublimation
D. vacuum distillation


At sea level, atmospheric pressure is:
A. 76 cm of Hg column
B. 760 cm of Hg column
c. \( 0.76 \mathrm{cm} \) of \( \mathrm{Hg} \) column
D. 76 cm of water column


Choose the correct answers from the
alternatives given Which of the following archaea would live at a deep-sea vent?
A. Thermoacidophile
B. Halophile
c. Methanogen
D. Parasitic forms


Check the distributive property for the
stated triples of rational numbers:
\( \frac{1}{8}, \frac{1}{9}, \frac{1}{10} \)


\( \boldsymbol{I}=\int \frac{1}{\boldsymbol{x}(1+\log \boldsymbol{x})} \cdot \boldsymbol{d} \boldsymbol{x} \)


\( \boldsymbol{R}=\frac{\boldsymbol{x}}{\boldsymbol{3}} \frac{\boldsymbol{P}_{c} \boldsymbol{V}_{c}}{\boldsymbol{T}_{c}} \)
Value of \( x \) is


In the following graphical
representation for the reaction \( \boldsymbol{A} \rightarrow \boldsymbol{B} \)
there are two types of regions:
A. I and II both represent kinetic region at different interva
B. I and II both represent equilibrium regions at different time interval
c. I represents kinetic while I I represents equilibrium region
D. I represents equilibrium while II represents kinetic region


The standard reduction potential at \( 25^{\circ} \)
\( \mathrm{C} \) for the reduction of water
\( 2 H_{2} O+2 e^{-} \rightleftharpoons H_{2}+2 O H^{-} \) is -0.8277
volt. Calculate the equlibrium constant for the reaction \( 2 H_{2} O \rightleftharpoons H_{3} O^{+}+ \)
\( O H^{-} \) at \( 25^{0} C \)


If the length of DNA strand is \( 68 A^{\circ} \) then, what will be the number of nucleotides
present in DNA molecule
A . 20
B. 40
\( c \cdot 60 \)
D. 80


Suppose elements \( X \) and \( Y \) combine to
form two compounds \( X Y_{2} \) and \( X_{3} Y_{2} \)
when 0.1 mole of former weight \( 10 g \)
while 0.05 mole of the latter weighs \( 9 g \)
What are the atomic weights of \( X \) and
\( Y ? \)
A. 40,30
B. 60,40
c. 20,30
D. 30,20


The major product obtained in the photo catalysed bromination of 2 methylbutane is:
A. 1-bromo-2-methylbutane
B. 1-bromo-3-methylbutane
c. 2 -bromo- -s-methylbutane
D. 2-bromo-2-methylbutane


In a town of 10,000 families it was found that \( 40 \% \) families buy newspaper A, \( 20 \% \) families buy newspaper \( B \) and 10
\( \% \) families buy newspaper \( C .5 \% \) families buy A and B, 3\% buy B and C
and \( 4 \% \) buy \( A \) and \( C . \) If \( 2 \% \) families buy
all the three newspaper, the member of families which buy A only is


The moment of inertia of a uniform
semicircular disc of mass \( M \) and
radius \( R \) about a line perpendicular to the plane of disc and passing through the centre is :
\( ^{\mathrm{A}} \cdot \frac{M R^{4}}{4} \)
в. \( \frac{2}{5} M R^{2} \)
c. \( M R^{2} \)
D. \( \frac{M R^{2}}{2} \)


The difference in angular momentums associated with an electronic transition
in hydrogen atom is equal to \( 3 h / 2 \pi . \) The atom contains only \( \mathrm{K}, \mathrm{L}, \mathrm{M} \) and \( \mathrm{N} \) shells. Calculate the energies and radii associated with the orbits.
A. -13.6 ev and 0.314 Angstrom, 0.08 eV and 8.48 Angstrom
B. -13.6 eV and 0.529 Angstrom, - 0.08 eV and 8.48 Angstrom
c. 13.6 ev and 0.529 Angstrom, 0.08 eV and 8.48 Angstromm
D. 27.2 eV and 0.529 Angstrom, 0.08 eV and 8.48 Angstrom


The moment of inertia of a solid cylinder
about its own axis is the same as its
moment of inertia about an axis
passing through its centre of gravity and perpendicular to its length.The relation between its length \( L \)
and radius \( \boldsymbol{R} \) is:
A. \( L=\sqrt{2} R \)
В. \( L=\sqrt{3} R \)
c. \( L=3 R \)
D. \( L=R \)


Which formulae does not correctly
represents the bonding capacity of the
atom involved?
This question has multiple correct options
\( A \)
\( \mathrm{CH}_{3} \mathrm{C}=\mathrm{CCH}_{3} \)
B.
\( c \)
\( D \)


\( A, B \) and \( C \) are parallel conductors of
equal lengths carrying currents \( \boldsymbol{I}, \boldsymbol{I} \) and
\( 2 I \) respectively. Distance between \( A \)
and \( B \) is \( x . \) Distance between \( B \) and \( C \)
is also \( x . F_{1} \) is the force exerted by \( B \) on
\( A . F_{2} \) is the force exerted by \( C \) on \( A \)
Choose the correct answer.
\( \mathbf{A} \cdot F_{1}=2 F_{2} \)
B . \( F_{2}=2 F_{1} \)
\( \mathbf{c} \cdot F_{1}=F_{2} \)
D. \( F_{1}=-F_{2} \)


Organic compounds can be formed by :
A. Plants only
B. Animals only
c. Plants and Animals
D. Plants, animals and can be synthesized in laboratory


By what smallest number should we
divide 9000 so that the quotient
becomes a perfect cube. Find the cube
root of the quotient
A . 9,10
B. 9,
\( c \cdot 19,10 \)
D. 19, 5


\( P \) is a point on side \( B C \) of \( a \) parallelogram ABCD. If DP produced meets \( A B \) produced at point \( L \), then \( D L: D P=A L: B C \)
If the above statement is true then
mention answer as 1 , else mention 0 if
false


If \( \alpha, \beta \) are zeroes of polynomial \( f(x)= \) \( x^{2}+p x+q \) then polynomial having \( \frac{1}{\alpha} \) and \( \frac{1}{\beta} \) as its zeroes is:
A \( \cdot x^{2}+q x+p \)
B. \( x^{2}-p x+q \)
c. \( q x^{2}+p x+1 \)
D. \( p x^{2}+q x+1 \)


If \( \vec{a}, \vec{b}, \vec{c} \) are three vectors such that \( \vec{a}, \vec{b}, \vec{c}, \) then prove that \( \vec{a} \times \vec{b}=\vec{b} \times \vec{c}= \)
\( \vec{c} \times \vec{a}, \) and hence show that \( [\overrightarrow{\boldsymbol{a}} \overrightarrow{\boldsymbol{b}} \overrightarrow{\boldsymbol{c}}]=\mathbf{0} \)


Negation of "A is in Class \( X^{t h} \) or \( \mathrm{B} \) is in
\( X I I^{t h \prime \prime} \) is
A. A is not in class \( X^{t h} \) but \( B \) is in \( X I I^{t h}^{h} \)
C. Either A is not in class \( X^{t h} \) or \( B \) is not in \( X I I^{t^{t}} \)
D. None of these.


Find Square of : 46


Eka-aluminium forms oxide of the type :
\( A \cdot E_{2} O \)
B. \( E O \)
\( \mathrm{c} \cdot E_{2} \mathrm{O}_{3} \)
D. \( E_{3} O_{4} \)


Which of the following statement(s)
is/are correct?
A. Reversible isothermal compression of an ideal gas represents the limiting minimum value of workdone \( (|w|) \) by the surrounding on the system.
B. In an irreversible process, the cyclic integral of work is not zero
C. For thermodynamic changes in adiabatic process \( T \frac{C_{p . m}}{R} . P=\mathrm{constant} \)
D. Work done by 1 mole of a real (vander waals) gas \( W=-R T / n \frac{V_{2}-b}{V_{1}-b}-a\left[\frac{V_{1} \times V_{2}}{V_{2}-V_{1}}\right] \)


Why is mercury used as a barometer
liquid. Give three reasons.


Movement of minerals in plant roots
through diffusion is
A. Endosmosis
B. Osmosis
c. Active absorption
D. Passive absorption


A particle is dropped from top tower.During its motion its covers \( \frac{\mathbf{9}}{\mathbf{2 5}} \) part of height of tower in last \( 1 . \) then height of tower?
\( \mathbf{A} \cdot 100 m \)
B. \( 125 m \)
c. \( 175 m \)
D. \( 120 m \)


A ray of light incident normally on the
horizontal face of the slab and just fail
to emerge from the diagonal face of the
prism. If prism angle is \( 30^{\circ} \) then
refractive index of the prism can be
\( A \cdot \sqrt{2} \)
B. \( \sqrt{3} \)
c. slightly greater than 2
D. slightly less than 2


Show that the current leads the voltage by an angle \( \frac{\pi}{2} \) in an ac circuit containing a pure capacitor.


If \( a \) is inversely proportional to \( b \) and \( b \)
is inversely proportional to \( c \) then what
is proportionality between \( a \) and \( c ? \)
A. Direct
B. Inverse
c. No proportionality
D. can't be determinal


If one of the zeroes of the quadratic
polynomial \( (k-1) x^{2}+k x+1 \) is -3
then the value of \( k \) is.
A \( \cdot \frac{4}{3} \)
в. \( \frac{-4}{3} \)
\( c \cdot \frac{2}{3} \)
D. \( \frac{-2}{3} \)


A rod \( 100 \mathrm{cm} \) long and of \( 2 \mathrm{cm} \times 2 \mathrm{cm} \)
cross-section is subjected to a pull of 1000kg force. Modulus of elasticity of
the material is \( 2.0 \times 10^{6} k g / c m^{2} . \) If the
elongation of the rod is \( x \mathrm{mm} \), find the
value of \( 40 x \)


Select the correct statement.
A. Heterotrophs do not synthesise their own food.
B. Heterotrophs utilise solar energy for photosynthesis.
C. Heterotrophs synthesise their own food.
D. Heterotrophs are capable of converting carbon dioxide and water into carbohydrates.


Which of the following substituents will decrease the acidic strength of phenol?
A. \( -N O_{2} \)
B. \( -C N \)
\( \mathrm{c} \cdot-C H_{3} \)
D. - \( C H O \)


Which of the following compounds has
zero dipole moment?
\( A \)
B.
\( c \)
D


Four particles of masses \( m, m, 2 m \) and
\( 2 m \) are placed at the four corners of a
square of side \( a \) as shown in the figure.
The magnitude of the gravitational
force acting on a particle of mass \( \boldsymbol{m} \)
placed at the centre of the square is
\( ^{\mathbf{A}} \cdot \frac{2 G m^{2}}{a^{2}} \)
в. \( \frac{G m^{2}}{\sqrt{2} a^{2}} \)
c. \( \frac{G m^{2}}{2 a^{2}} \)
\( D \)


Use Euclid's division lemma to find the
HCF of the following
16 and 176
A . 16
B. 14
c. 10
D. 12


From the following information, find the equation of Hyperbola and the equation of its Transverse Axis:
Focus \( :(-2,1), \) Directrix \( : 2 x-3 y+ \) \( \mathbf{1}, \boldsymbol{e}=\frac{\mathbf{2}}{\sqrt{\mathbf{3}}} \)


In Youngs expt., the distance between two slits is \( \mathrm{d} / 3 \) and the distance
between the screen and the slits is \( 3 D \)
The number of fringes in \( 1 / 3 \) m on the screen, formed by monochromatic light of wavelength \( 3 \lambda, \) will be?
A \( \cdot \frac{d}{9 D \lambda} \)
B. \( \frac{d}{27 D \lambda} \)
c. \( \frac{d}{81 D \lambda} \)
\( D \cdot \frac{d}{D \lambda} \)


Specific heat depends on........................
and


If some or all of \( n \) things be taken at a
time, prove that the number of
combinations is \( 2^{n}-1 \)


The area of a circle is \( 24.64 . m^{2} \) What is
the circumference of the circle?
A . \( 14.64 m \)
B. 16.36 m
c. \( 17.60 m \)
D. \( 18.40 m \)


Allyl chloride is a ............... compound while vinyl chloride is inert towards
nucleophilic substitution.
A. reactive
B. mildly reactive
c. not reactive
D. netural


A body is thrown vertically upwards and rises to a height of \( 10 \mathrm{m} \). The time taken
by the body to reach the highest point is
A. 1.43 s
B. 4.1 s
c. 1.24 s
D. 2.86 s


A sample of 0.50 g of an organic compound was treated according to Kjeldahl's method. The ammonia evolved was absorbed in \( 50 \mathrm{mL} \) of \( 0.5 \mathrm{M} \)
\( H_{2} S O_{4} \).The residue acid required \( 60 \mathrm{mL} \)
of 0.5 M solution of \( N a O H \) for
neutralisation. What would be the
percentage composition of nitrogen in the compound?
A. 50
B. 60
c. 56
D. 44


If \( \boldsymbol{A}=\left(\begin{array}{ccc}\mathbf{8} & \mathbf{5} & \mathbf{2} \\ \mathbf{1} & \mathbf{- 3} & \mathbf{4}\end{array}\right), \) then find \( \boldsymbol{A}^{\boldsymbol{T}} \) and
\( \left(A^{T}\right)^{T} \)


Chemical pollution is mainly due to the discharge of organic \( \& \) inorganic substances released into the water.
Is the above statement correct?
A . True
B. False


A slender uniform rod of mass \( \mathrm{M} \) and
length l is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The
angular acceleration of the rod when it
makes an angle \( \theta \) with vertical is
A \( \cdot \frac{3 g}{2 l} \cos \theta \)
в. \( \frac{2 g}{3 l} \cos \theta \)
\( c \)
D.


Which of the following undergoes nucleophilic substitution exclusively by
\( \boldsymbol{S}_{N} 1 \) mechanism?
A. Ethyl chloride
B. Isopropyl chloride
c. Benzyl chloride
D. Chloro benzene


If \( \sum_{i=1}^{10}\left(x_{1}-15\right)=12 \) and \( \sum_{i=1}^{10}\left(x_{i}-\right. \)
15)\( ^{2}=18, \) then the S.D. of observations
\( \boldsymbol{x}_{1}, \boldsymbol{x}_{2} \ldots \ldots \ldots \ldots \boldsymbol{x}_{\mathbf{1 0}} \) is
A \( \cdot \frac{2}{5} \)
B. \( \frac{3}{5} \)
\( c \cdot \frac{4}{5} \)
D. none of these


\( 9.2 \mathrm{gm} \) of \( N_{2} O_{4}(g) \) is taken in a closed
one-litre vessel and heated till the
following equilibrium is reached
\( N_{2} O_{4}(g) \rightleftharpoons 2 N O_{2}(g) \)
At equilibrium \( 50 \% \) of \( N_{2} O_{4}(g) \) is dissociated. What is the
equilibrium constant?
[in mole lit \( ^{-1} \) ] [M.wt. of \( N_{2} O_{4} \) is 92]
A. \( 0 . \)
в. 0.2
\( c \cdot 0.4 \)
D. 2


Battery charging equipment is generally installed:
A . in well ventilated location
B. in clean and dry place.
c. as near as practical to the battery being charged
D. in location having all above features


Solve:
\( \int \frac{\log x}{x^{2}} d x \)


If \( S \) identical rain drops each falling with terminal velocity v combine to form a big drop during their fall the terminal velocity of big drop formed is :
\( A \)
B. \( \frac{v}{8} \)
\( c \cdot 4 v \)
D. 2v


A long straight horizontal cable carries a current of \( 2.5 \mathrm{A} \) in the direction \( 10^{0} \)
south of west to \( 10^{0} \) north of east. The
magnetic meridian of the place
happens to be \( 10^{0} \) west of the
geographic meridian. The earth's magnetic field at the location is \( 0.33 \mathrm{G} \) and the angle of dip is zero. Locate the line of neutral points (ignore the thickness of the cable). (At neutral points, magnetic field due to a current carrying cable is equal and opposite to the horizontal component of earth's magnetic field.)
A. \( 15.15 \mathrm{mm} \)
B. \( 30.15 \mathrm{mm} \)
c. \( 35.15 \mathrm{mm} \)
D. \( 40.15 \mathrm{mm} \)


Assertion
During apoplastic movement of water,
water travels through the cells and their
cytoplasm.
Reason
The symplastic movement of water
occurs exclusively through the
intercellular spaces and the walls of the cells.
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


Chemically, diamond is:
A. a mixture of metal carbonates
B. pure carbon
C . a pure form of sand
D. a mixture of calcium and magnesium phosphates


Velocity at mean position of a particle executing SHM is \( v \), then velocity of the particle at a distance equal to half of the amplitude is
\( A \cdot \frac{\sqrt{3}}{2} v \)
B. \( \frac{2}{\sqrt{3}} v \)
\( c \cdot 2 v \)
D. \( v \)


Rakesh took a loan of Rs. 80,000 from a
bank. If the rate of interest is \( 10 \% \) per annum. Find the difference in amounts he would be paying after \( \frac{3}{2} \) years, if the interest is compounded semi-annually.
A. 92,610
00 0,610 ?
B. 92,510
c. 8945
D. 7845


Which of the following are used as an antacid to reduce acidity in stomach?
A. Sodium carbonate and magnesium hydroxide
B. Magnesium hydroxide and sodium hydroxide
c. Sodium bicarbonate and calcium hydroxide
D. Sodium bicarbonate and magnesium hydroxide


Of these, the most ductile metal is:
A . \( A l \)
в. \( A u \)
c. \( C u \)
D. \( A g \)


Which metal is used as a catalyst in the
hydrogenation of oils?
A. Iron
B. Sodium
c. Nickel
D. Gold


A rubber ball is brought into \( 200 \mathrm{m} \) deep water, its volume is decreased by \( 0.1 \% \) then volume elasticity coefficient of the material of ball will be:
\( \left(\text {Given } \rho=10^{3} k g / m^{3} \text { and } g=\right. \)
\( \left.9.8 m s^{-2}\right) \)
A \( \cdot 19.6 \times 10^{8} N / m^{2} \)
В. \( 19.6 \times 10^{-10} N / m^{2} \)
c. \( 19.6 \times 10^{10} N / m^{2} \)
D. \( 19.6 \times 10^{-8} N / m^{2} \)


When \( 20 g m \) of a compound
\( (A)\left(M . F .=C_{4} H_{10} O_{4}\right) \) reacts with
excess of \( C H_{3} M g B r, 14.6 L \) of \( C H_{4} \) is
obtained at STP. What is structural
formula of \( (\boldsymbol{A}) \) ?
\( A \)
B.
\( c \)
D. Both (a) \& (b)


ff \( C=\left[\begin{array}{cc}3 & -6 \\ 0 & 9\end{array}\right] \) find
¡) 2C
ii) \( \frac{1}{3} C \)
iii) -


Positive and negative point charges of equal magnitude are kept at \( \left(0,0 \frac{a}{2}\right) \) and \( \left(0,0 \frac{-a}{2}\right), \) respectively. The work done by the electric field when another
positive point charge is moved from \( (-a, 0,0) \) to \( (0, a, 0) \) is:
A. positive
B. negative
c. zero
D. depends on the path connecting the initial and final positions


Visual purple is found in
A. cornea
B. Cones
c. Rods
D. Retina


A surface has work function \( 3.3 e V \)
Which of the following will cause
emission?
A. \( 100 W \) incandascent lamp
B. 40 \( W \) flouroscent lamp
c. \( 20 W \) sodium lamp
D. 20 \( W \) Hg lamp


The highest temperatures recorded in 4 different countries are listed below
What is the highest temperature listed
above?
A \( \cdot 127.6^{\circ} \)
B. \( 114.8^{\circ} \mathrm{F} \)
c. \( 136.4^{\circ} \mathrm{F} \)
D . 134.0 \( ^{\circ} \)


\( = \)
\( b \)
\( b \)
\( b \)


At \( 80 C, \) the vapour pressure of pure benzene is \( 753 \mathrm{mm} \) Hg and of pure toluene \( 290 \mathrm{mm} \) Hg. Calculate the composition of a liquid in mole per cent which at \( 80 C \) is in equilibrium with the vapour containing 30 mole per cent of
benzene.


By selling 45 mangoes for Rs. \( 40, \) a man loses \( 20 \% \). How many should he sell for Rs. 24 so as to gain \( 20 \% \) in the transaction?
A . 18
B. 24
\( c \cdot 48 \)
D. 72


A parallel plate capacitor has a
capacity \( 80 \times 10^{-6} F \) when air is
present between the plates. The volume between the plates is then completely
filled with a dielectric slab of dielectric
constant \( 20 . \) The capacitor is now connected to a battery of \( 30 \mathrm{V} \) by wires. The dielectric slab is then removed.
Then, the charge that passes now through the wire is :
A \( \cdot 45.6 \times 10^{-3} C \)
B . \( 25.3 \times 10^{-3} C \)
C. \( 120 \times 10^{-3} C \)
D. \( 12 \times 10^{-3} C \)


If the kinetic energy of the particle is increased to 16 times previous the percentage change in the deBrogille wavelength of the particle is


Name the hormones which promotes growth and flowering in plants.


If \( \boldsymbol{f}(1)=\mathbf{1} \) and \( \boldsymbol{f}(\boldsymbol{x}+\mathbf{1})=\boldsymbol{2} \boldsymbol{f}(\boldsymbol{x})+\mathbf{1} \)
for \( \boldsymbol{x} \geq 1, \) then find the range of \( \boldsymbol{f}(\boldsymbol{x}) \)
A. \( R \)
B. A series like \( 1,3,5,7,9, \ldots \)
C. A series like \( 1,3,7,15, \ldots \)
D. \( R-\{1,3,7,15, \ldots\} \)


A small steel ball falls through a syrup
at a constant speed of \( 10 \mathrm{m} / \mathrm{s} \). If the steel ball is pulled upwards with a force equal to twice its effective weight, how fast will it move upwards?
\( A \cdot 10 \mathrm{cm} / \mathrm{s} \)
B. 20 cm/s
\( c \cdot 5 \mathrm{cm} / \mathrm{s} \)
D. \( -5 \mathrm{cm} / \mathrm{s} \)


Assertion
The ratio of radius of first orbit to
second orbit of hydrogen atom is 1: 4
Reason
Radius for each circular orbit \( = \)
\( \mathbf{0 . 5 2 9} \boldsymbol{n ^ { 2 }} \boldsymbol{\hat { A }} \)
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 refrigerator placed in a room at \( 300 \mathrm{K} \) has inside temperature at \( 264 \mathrm{K} \). How many calories of heat shall be delivered
to the room for each 1 kcal of energy consumed by the refrigerator ideally
A . 7.2 kcal
B. 7.83 kcal
c. 8.33 kcal
D. 8.94 kcal


Conversion of light energy into chemical energy within the plant body was first stated by?
A. Mayer and Anderson
B. Calvin
c. Robert Mayer
D. Willstatter and Stoll


A particle executing SHM according to
the equation \( \boldsymbol{x}=\mathbf{5} \cos \left[\mathbf{2} \boldsymbol{\pi} \boldsymbol{t}+\frac{\pi}{4}\right] \) in \( \mathbf{S} \)
units. The displacement and acceleration of the particle at \( t=1.5 \) s is:
A \( .-3.0 m, 100 m s^{-2} \)
B . \( +2.54 m, 200 m s^{-2} \)
c. \( -3.54 m, 140 m s^{-2} \)
D. \( -3.55 m, 120 m s^{-2} \)


A solid copper sphere has a charge of
\( +Q \) on it. Identify the correct statement
about the charge distribution of solid
sphere?
A. \( +Q \) at the center of the sphere
B. \( Q / 2 \) at the center of the sphere and \( Q / 2 \) on the outer surface
c. \( -Q \) at the center of the sphere and \( +2 Q \) on the outer surface
D. \( +Q \) on the outer surface
E. The charge is spread evenly throughout the sphere


By what smallest number 5184 be
divided, so what the resulting number becomes a perfect cube?


Re. 1 and \( R \) s. 5 coins are available \( ( \) as
many required). Find the smallest
payment which cannot be made by these coins, if not more than 5 coins are
allowed.
\( A \cdot 3 \)
B. 12
\( c \cdot 14 \)
D. 18


If a gas is compressed adiabatically by doing work of \( 150 \mathrm{J} \), the change in the internal energy of the gas is:
A . 100 J
в. 150
c. 200 J
D. 250 J


The animals that consume plants as
food are called as
A. Herbivores
B. Saprophytes.
c. carnivores.
D. Omnivores


Potential energy increases with the
increase in :
A. work
B. Force
c. speed
D. Position


(1) Latent heat of steam is 540 cal/gm. Express this in Sl units.
(2) A liquid has a mass of \( 200 \mathrm{gm} \) and a
specific heat capacity of \( 0.8 c a l / g m / C^{o} \) Find water equivalent of the liquid.


How much should a sum of Rs. 16000
approximately amount to in 2 years at \( 10 \% \) p.a compounded half yearly?
A. Rs. 17423
B. Rs. 18973
c. Rs. 19448
D. Rs. 19880


The least length of the thread required to construct a rectangle of area 256 \( c m^{2} \) is
A . 32
B. 64
\( c \cdot 40 \)
D. 58


The angles of a quadrilateral are in \( \boldsymbol{A} . \boldsymbol{P} \)
whose common difference is \( 10^{0}, \) then
the first angle in \( A . P . \) is


What are the different types of graphs?


How many chromosomes will be in cells of human, produced by meiosis?
A . 46
B. 69
\( c \cdot 23 \)
D. 100


Express the following angle in degree \( \left(-\frac{7 \pi}{12}\right)^{c} \)


When electric current is passed through a conducting solution, there is a change of colour of the solution. This indicates
A. the chemical effect of current
B. the heating effect of current.
c. the magnetic effect of current
D. the lightning effect of current


\( 4 d, 5 p, 5 f \) and \( 6 p \) orbitals are arranged in the order of decreasing energy.The correct option is:
A \( .5 f>6 p>5 p>4 d \)
в. \( 6 p>5 f>5 p>4 d \)
c. \( 6 p>5 f>4 d>5 p \)
D. \( 5 f>6 p>4 d>5 p \)


Assertion
Statement-1: \( \left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{S i}-\boldsymbol{O H} \) is more
acidic than \( \left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{C}-\boldsymbol{O H} \)
Reason
Statement-2: \( \left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{S i}-\boldsymbol{O H} \) has
back bonding.
A. Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-
B. Statement-1 is true, statement-2 is true and statement-2 is not the correct explanation for statement-1.
c. Statement- 1 is true, statement- 2 is false
D. Statement-1 is false, statement-2 is true.


The position of a particle moving along \( \mathbf{x} \) -axis given by \( \boldsymbol{x}=\left(-\mathbf{2} \boldsymbol{t}^{3}+\mathbf{3} \boldsymbol{t}^{2}+\mathbf{5}\right) \boldsymbol{m} \)
The acceleration of particle at the instant its velocity becomes zero is
A \( \cdot 12 \mathrm{m} / \mathrm{s}^{2} \)
B . \( -12 \mathrm{m} / \mathrm{s}^{2} \)
c. \( -6 m / s^{2} \)
D. zero


Assertion
Work done by friction depends upon
displacement of the body.
Reason
Frictional force is non-conservative.
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


Assertion
The largest term in the sequence \( a_{n}= \) \( \frac{n^{2}}{n^{3}+200}, n \in N \) is the 7 th term.
Reason
The function \( f(x)=\frac{x^{2}}{x^{3}+200} \) attains
local maxima at \( x=7 \)
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


Who named positive and negative charges?
A. Faraday
B. Gauss
c. Benjamin Franklin
D. Curie


In a collinear collision, a particular with
an initial speed \( v_{0} \) strikes a stationary
particle of the same mass. If the final
total kinetic energy is \( 50 \% \) greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after collision, is?
\( A \cdot \frac{v_{0}}{2} \)
в. \( \frac{v_{0}}{\sqrt{2}} \)
c. \( \frac{v_{0}}{4} \)
\( D \cdot \sqrt{2} v_{0} \)


\( f\left(\begin{array}{cc}4 & 8 \\ -2 & -4\end{array}\right] \) find \( A^{2} \)


An ideal gas is enclosed in a cylinder with a movable piston on top of it. The
piston has a mass of \( 8000 g \) and an
area of \( 5.00 \mathrm{cm}^{2} \) and is free to slide up
and down, keeping the pressure of the gas constant. How much work in
Joules is done on the gas as the
temperature of 0.200 mol of the gas is
raised from \( 20.0^{\circ} \mathrm{C} \) to \( 300^{\circ} \mathrm{C} ? \)


Property of the alkaline earth metals
that increases with their atomic
number:
A. solubility of their hydroxides in water
B. solubility of their sulphates in water
c. ionization energy
D. electronegativity


what is the proauct or the rollowıng
reaction?
\( c \)
2


During the preparation of phenol from benzene sulfonic acid, which of the
following reagents is be used?
A . \( N a O H \)
в. \( \operatorname{NaHSO}_{4} \)
c. \( N a_{2} S O_{4} \)
D. \( N a C l \)


Show that volume expansion coefficient is three times the linear
expansion coefficient for a solid.


Define the following terms with an example in each case:
(i) Macromolecular sol
(ii) Peptization
(iii) Emuslion


A lilac-coloured flame is produced on heating.
A. Potassium in a flame
B. Cobalt in a flame
c. Sodium in a flame
D. Methane in oxygen


Sum the following series to n terms and to infinity \( \frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\dots . \)


A ray of light from a denser medium strikes a rarer medium at an angle of incidence \( i . \) If the reflected and
refracted rays are mutually perpendicular to each other then the critical angle is :
\( A \cdot \sin ^{-1}(\tan i) \)
B. \( \cos ^{-1}(\tan i) \)
\( c \cdot \cot ^{-1}(\tan i) \)
D. \( \operatorname{cosec}^{-1}(\tan i) \)


Atoms combine to form:
A. large atoms
B. molecules
c. mixtures
D. none of the above


Give example to prove that microbes release gases during metabolism.


For a first order reaction, \( \boldsymbol{A} \rightarrow \) Product
the rate of reaction at \( [\boldsymbol{A}]=\mathbf{0 . 2} \) mol \( \boldsymbol{L}^{-1} \)
is \( 1.0 \times 10^{-2} \) mol \( L^{-1} \) min \( ^{-1} . \) The half-
life period for the reaction is:
A \( \cdot 832 \) s
B. 440 s
\( \mathbf{c} \cdot 416 \mathrm{s} \)
D. 14 s


Evaluate the following integrals:
\( \int \cot ^{5} x \operatorname{cosec}^{4} x d x \)


Write the periodic properties which always increases along the periodic table in moving from left to right?


Find the sum of minimum and
maximum values of \( y \) in \( 4 x^{2}+12 x y+ \)
\( \mathbf{1 0 y}^{2}-\mathbf{4 y}+\mathbf{3}=\mathbf{0} \)


In this diol:
\( \mathbf{A} \cdot O H^{-} \) at \( C_{2} \) is more basic than that of at \( C_{5} \)
B. \( O H^{-} \) at \( C_{2} \) is more acidic than at \( C_{5} \)
C. both have same basicity
D. both have same acidic strength


For the differential equation
\( \left(1+y+x^{2} y\right) d x+\left(x+x^{3}\right) d y=0 \)
\( y\left(\frac{\pi}{4}\right)=0 \) then find the absolute value
of the constant.


Function \( f(x)=|x-2|-2|x-4| \) is
discontinous at:
A . \( x=2,4 \)
B. \( x=2 \)
C. No where
D. Except \( x=2 \)


An element \( A \) decays into element \( C \) by
the following two step processes:
\( \boldsymbol{A} \longrightarrow_{2} \boldsymbol{H} \boldsymbol{e}^{\boldsymbol{4}}+\boldsymbol{B} \)
\( \boldsymbol{B} \longrightarrow \mathbf{2}\left(_{-1} \boldsymbol{e}^{0}\right)+\boldsymbol{C} \)
Select pair for isobars from elements
\( A, B \) and \( C \)


Evaluate \( \lim _{x \rightarrow 8} \frac{\sqrt{1+\sqrt{1+x}-2}}{x-8} \)
A \( \cdot \frac{3}{2} \)
B. \( \frac{1}{4} \)
c. \( \frac{1}{24} \)
D. None of these


Isopleth for depth is
A. Isobaths
B. Isohaline
c. Isohyet
D. None of these


Solve
\( |\mathbf{7}| \times|-\mathbf{4}| \)


When a person is exposed to cold
surrounding, which of the following
does not occur?
A. Secretion of adrenal medulla and thyroid increases
B. Shivering occurs
C. Vasoconstriction occurs in the skin vessels, supplying blood to hair
D. Heart beat and volume of blood per stroke increases


In the following figures, \( A B C D \) is a
rhombus. Find the values of \( x \) and \( y \)
\( \mathbf{A} \cdot 50^{\circ}, 50^{\circ} \)
B \( \cdot 30^{\circ}, 50^{\circ} \)
c. \( 20^{\circ}, 50 \)
D. None of these


An organic compound of molecular
formula \( C_{4} H_{10} O \) does not react with
sodium. In excess of \( \boldsymbol{H} \boldsymbol{I} \), it gives only
one type of alkyl iodide. The compound
is:
A. ethoxy ethane
B. 2-methoxy propan
c. 1-methoxy propane
D. 1-butanol


Which of the following is true regarding
sign of heat and work?
A. Heat absorbed by the system has positive sign. Heat released to the surrounding has negative sign. Work done on the system has positive sign. Work done by the system has negative sign.
B. Heat absorbed by the system has negative sign. Heat released to the surrounding has positive sign. Work done on the system has positive sign. Work done by the system has negative sign.
C. Heat absorbed by the system has negative sign. Heat released to the surrounding has positive sign. Work done on the system has negative sign. Work done by the system has positive sign.
D. Heat absorbed by the system has positive sign. Heat released to the surrounding has negative sign. Work done on the system has negative sign. Work done by the system has positive sign.


For water at \( 25^{\circ} \mathrm{C}, 2 \times 10^{-7} \) moles per
litre is the correct answer for which one
of the following?
\( \mathbf{A} \cdot\left[H^{+}\right]+\left[O H^{-}\right] \)
B . \( \left[H^{+}\right]^{2} \)
c. \( \left[O H^{-}\right]^{2} \)
\( \mathbf{D} \cdot\left[H^{+}\right]-\left[O H^{-}\right] \)


Which of the following will not give halo benzene by reacting with benzene diazonium chloride?
\( \mathbf{A} \cdot C u_{2} B r_{2} / H B r \)
в. \( K I \)
c. \( S n C l_{2}+H C l \)
D. \( C u \) powder \( +H C l \)


In a certain hypothetical radioactive decay process, species A decays into species B and species B decays into species \( C \) according to the reactions \( \boldsymbol{A} \rightarrow 2 \boldsymbol{B}+ \) particles \( + \)energy
\( \boldsymbol{B} \rightarrow \mathbf{2} \boldsymbol{C}+\boldsymbol{\text {particles}}+ \)energy
The decay constant for species A is \( \lambda_{1}=1 s^{-1} \) and that for species B is
\( \lambda_{2}=100 s^{-1} . \) Initially, \( 10^{4} \) moles of
species of A were present while there was none of \( \mathrm{B} \) and \( \mathrm{C} \). It was found that
while there was none of \( B \) and \( C \). It was
found that species B reaches its
maximum number at a time \( t_{0}= \) \( 2 \ln (10) s . \) Calculate the value of
maximum number of moles of B


Can we separate the compounds of azeotropic mixture by fractional distillation? Explain


The number of solutions of the
equation \( \sin ^{-1}\left(\frac{1+x^{2}}{2 x}\right)=\frac{\pi}{2} \sec (x- \)
1) is


Which one of the following is not correctly matched?
A. Flame cells-platyhelminthes
B. stinging cells-coelenterates
c. Metameric segmentation-molluscs
D. Gill slits-chordates


What features of cockroach are
adaptations for its terrestrial and
nocturnal life?


Why ice is lighter than water?


If \( m \) arithmetic means are inserted
between 1 and 31 so that the ratio of the
\( 7 t h \) and \( (m-1) t h \) means is \( 5: 9, \) then
the value of \( m \) is
\( \mathbf{A} \cdot \mathbf{9} \)
B. 11
c. 13
D. 14


A body cools from \( 62^{\circ} \mathrm{C} \) to \( 50^{\circ} \mathrm{C} \) in 10
minutes. If the temperature of the
surroundings is \( 26^{\circ} \mathrm{C} \), then the
temperature of the body after next 10 minutes will be:
A \( \cdot 41^{\circ} \mathrm{C} \)
B . \( 44^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 46^{\circ} C \)
D. \( 48^{\circ} \mathrm{C} \)


Fusion reactions take lace at high
temperature because
A. atoms are ionized at high temperature
B. molecules break up at high temperature
C . nuclei break up at high temperature
D. kinetic energy is high enough to overcome repulsion between nuclei


Define translocation.


A dealer marks his goods at \( 30 \% \) above the cost price and allows a discount of
\( 20 \% \) on the marked price. Find his gain
or loss per cent.


A solution of \( K M n O_{4} \) is reduced to
\( M n O_{2} . \) The normality of solution is 0.6
The molarity is:
A. 1.8 m
в. 0.6 м
\( c .0 .1 \mathrm{M} \)
D. 0.2M


Antoine bought a new electric guitar
that \( \operatorname{cost} \$ 588.60 \) after \( 9 \% \) sales tax
was added. What was the price of the guitar without tax?
\( A \cdot \$ 536 \)
B. \( \$ 540 \)
\( c . \$ 542 \)
D. \( \$ 545 \)
E. \( \$ 548 \)


Inspiration occurs when
A. Pressure inside lungs is lower than atmospheric
pressure
B. Pressure inside lungs is higher than atmospheric
pressure
C. Pressure inside lungs is same as atmospheric pressure
D. Pressure has no effect


Two liquids \( A \) and \( B \) form type II non ideal solution which shows a minimum
in its temperature-mole fraction plot \( T-\chi \text { diagram }) . \) Can the two liquids be
completely separated by fractional distillation?


The life cycle of mulberry silk worm is completed within
A. 20 days
B. 30 days
c. 35 days
D. 45 days


Examples of three detergents are given
below. Mark the correct statements
following the examples.
(I) \( \quad \mathbf{C H}_{3}\left(\mathbf{C H}_{2}\right)_{10} \mathbf{C H}_{2} \mathbf{O S O}_{3}^{-} \mathbf{N a}^{+} \)
\( \left.(\mathrm{II}) \mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{\mathrm{Il}} \sqrt{\bigcirc}\right\rangle-\mathrm{so}_{3}^{-} \mathrm{Na}^{+} \)
\( \mathrm{CH}_{3} \)
\( \left.(\mathrm{III}) \mathrm{CH}_{3}+\mathrm{CH}-\mathrm{CH}_{2}\right)_{3}-\mathrm{CH}-\langle\Theta\rangle-\mathrm{SO}_{3}^{-} \mathrm{Na}^{+} \)
A. I and II are non-diodegradable detergents and III is biodegradable.
B. I and II are biodegradable detergents and III is nonbiodegradable.
C. \( 1, \) II and III are non-biodegradable detergebts
D. I is biodegradable and II, III are non-biogegradable


If \( l, m \) and \( n \) are the directional cosines
of a vector, then:
A. \( l+m+n=1 \)
B. \( l^{2}+\mathrm{m}^{2}+\mathrm{n}^{2}=1 \)
c. \( l^{2}+\mathrm{m}^{2}+\mathrm{n}^{2}=0 \)
D. \( l+\mathrm{m}+\mathrm{n}=0 \)


Find the approximate value of mode for
the following data:
\( \begin{array}{lllll}\text { Marks } & 50- & 60- & 70- & 80 \\ & 60 & 70 & 80 & 900\end{array} \)
Students 24 12
\( \mathbf{A} \cdot 71 \)
B. 72
\( c \cdot 73 \)
D. 74


Why do we see only one side of the moon
always?


Find the discriminant for the given equation:
\( \mathbf{3} \boldsymbol{x}^{2}+\mathbf{2} \boldsymbol{x}-\mathbf{1}=\mathbf{0} \)
A . 11
B. 13
c. 15
D. 16


The ratio of inversion temperature and Boyle's temperature for a real gas is


A conducting rod of length \( l \) is hinged at
point \( 0 . \) It is free to rotate in a vertical
plane. There exists a uniform magnetic field \( \vec{B} \) in horizontal direction. The rod is
released from the position shown. The potential difference between the two
ends of the rod is proportional to:
This question has multiple correct options
\( A \cdot l^{3 / 2} \)
B \( \cdot l^{2} \)
\( c \cdot \sin \theta \)
D. \( (\sin \theta)^{1 / 2} \)


Describe any four occupational respiratory disorders


Find \( p \in R \) for \( x^{2}-p x+p+3=0 \) has
A. One positive and one negative root.
B. Both roots are negative
c. one root \( >2 \) and the other root \( <2 \)
D. None of the above


Q Type your question
\( \mathbf{U}_{\mathbf{2}} \perp \mathbf{v}_{\mathbf{2}} \overrightarrow{\mathbf{\Delta}}^{\mathbf{\lambda}} \mathbf{A} \)
A can be
This question has multiple correct options
\( \mathbf{A} \)
\( B \)
\( C \)
D.


The density of a \( 10.0 \% \) by mass of \( \mathrm{KCl} \) solution in water \( 1.06 \mathrm{g} / \mathrm{mL} \). Calculate molarity, molality and mole fraction of KCl in this solution respectively.
A. \( 3.42 \mathrm{M} ; 1.489 \mathrm{m} ; 0.046 \)
B. 2.42 М; \( 1.489 \mathrm{m} ; 0.026 \)
c. 1.42 М; \( 1.489 \mathrm{m} ; 0.026 \)
D. none


Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}+\boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{b} \boldsymbol{x}+\boldsymbol{5} \sin ^{2} \boldsymbol{x} \) be
an increasing function on the set \( R \)
Then, \( a \) and \( b \) satisfy
A \( \cdot a^{2}-3 b-15>0 \)
B . \( a^{2}-3 b+15>0 \)
c. \( a^{2}-3 b+15<0 \)
D. \( a>0 \) and \( b>0 \)
0


The least count of a stop-watch is
\( (1 / 5) s . \) The time of 20 oscillations of a pendulum is measured to be 25 s. What is the maximum percentage error in this measurement?
\( A \cdot 8 \% \)
B. 1\%
c. \( 4 \% \)
D. \( 16 \% \)


羊 里 月 卓


The separation of colloidal particles from those molecular dimension is
known as:
A. dialysiss
B. electrophoresis
c. peptization
D. pyrolysis


A barometer tube, containing mercury, is lowered in a vessel containing mercury until only \( 50 \mathrm{cm} \) of the tube is
above the level of mercury in the vessel.
If the atmospheric pressure is \( 75 \mathrm{cm} \) of
mercury, what is the pressure at the top of the tube
A. \( 33.3 k P a \)
в. \( 66.7 k P a \)
c . 3.33 M \( P a \)
D. \( 6.67 M P a \)


The equilibrium constant for the given reaction is 81 at a certain temperature
If the concentrations of \( \boldsymbol{H}_{2} \) and \( \boldsymbol{I}_{2} \) are 3
moles/lit each at equilibrium, the equilibrium concentration of HI is:
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{I}_{2}(\boldsymbol{g}) \leftrightharpoons 2 \boldsymbol{H} \boldsymbol{I}(\boldsymbol{g}) \)
A. 3 mole / lit
B. 27 mole / lit
c. 9 mole / lit
D. 13.5 mole / lit


occurs when a light ray bounces back from a barrier.
A. Refraction
B. Reflection
c. Dispersion
D. Scattering


Which sugar is known as milk sugar?
A. Maltose
B. Lactose
c. Glucose
D. Fructose


Arrange the following compounds in increasing order of their property as indicated:
(i) \( \boldsymbol{F}-\boldsymbol{C H}_{2} \boldsymbol{C O O H}, \boldsymbol{O}_{2} \boldsymbol{N}- \)
\( \boldsymbol{C H}_{2} \boldsymbol{C O O H}, \boldsymbol{C H}_{3} \boldsymbol{C O O H}, \boldsymbol{H C O O H}- \)
acid character
(ii) Acetone, Acetaldehyde, Benzaldehyde, Acetophenone reactivity towards addition of \( \boldsymbol{H} \boldsymbol{C} \boldsymbol{N} \)


A uniform bar of mass \( M \) and length \( L \)
collides with a horizontal surface.
Before collision, velocity of centre
of mass was \( v_{0} \) and no angular velocity. Just after collision, velocity of centre of
mass of bar becomes \( \boldsymbol{v} \) in upward
direction as shown. Angular velocity \( \omega \)
of the bar just after impact is:
\( A \)
в.
c. \( \frac{\left(v_{0}+v\right) \cos \theta}{L} \)
\( D \)


When \( 1 g \) of water \( \operatorname{at} 0^{\circ} C \) and \( 1 \times \) \( 10^{5} N / m^{2} \) pressure is converted into
ice of volume \( 1.091 \mathrm{cm}^{3} \), the external
work done will be:
A. 0.0091 joule
B. 0.0182 joule
c. -0.0091 joule
D. - 0.0182 joule


A car covers first \( 100 \mathrm{km} \) in \( 2 \frac{1}{2} \) hours and then travels at a speed of
\( 60 \mathrm{km} / \mathrm{hr} \) for \( 1 \frac{1}{2} \) hours. Find the
average speed of the car for the whole
journey


Why is \( B F_{3} \) used as a catalyst in several industrial processes?


Given, \( \boldsymbol{f}(\boldsymbol{x})=\mathbf{2} \boldsymbol{x}^{2}+\boldsymbol{a} \)
If \( a \) is a constant and \( f(2)+f(3)= \)
\( f(5), \) calculate the value of \( a \)
\( A \cdot 6 \)
B. 12
\( c \cdot 24 \)
D. 48


State whether given statement is True or False.
Science is Classified into various
branches like physics, chemistry, biology, medical science, agriculture
science ?
A. True
B. False


When a glass rod is rubbed with silk
cloth, it acquires positive charge because:
A. electrons are added to it
B. electrons are removed from it
c. protons are added to it
D. protons are removed from it


Which of the following is correct about chemical reaction?
A. Mass of catalyst remain unchanged
B. Physical state of catalyst remain unchanged
c. changes in chemical composition of catalyst may be observedd
D. None of the above


A monoprotic acid in \( 100 M \) solution is \( 0.001 \% \) ionized. The dissociation
constant of this acid is:
A \( \cdot 1.0 \times 10^{-3} \)
B. \( 1.0 \times 10^{3} \)
c. \( 1.0 \times 10^{-8} \)
D. \( 1.0 \times 10^{-10} \)


In electrolytic solutions, carrier of
charge is
A. proton
B. electron
c. neutron
\( D \cdot \) ion


Several scientist gave different definition of species. One of those
definitions, a population or group of populations whose members have the potential in nature to interbreed and produce fertile offspring. Which of the statement is related to this definition?
A. Species that reproduce sexually
B. Species that reproduce asexually only
c. specie that form sterile hybrids upon mating
D. Extinct forms of life, based on fossil evidence
E. Species living on separate continents


A rectangular loop carrying a current \( i \) is placed in a uniform magnetic field \( B \). The area enclosed by the loop is \( A \). If there are \( n \) turns in the loop, the torque acting on the loop is given by
\( \mathbf{A} \cdot n i(\bar{A} \times \bar{B}) \)
в. \( n i(\overline{A . \bar{B}}) \)
\( \frac{i(\bar{A} \times \bar{B})}{n} \)
D. \( \frac{i(\bar{A} . \bar{B})}{n} \)


Electronic configuration of chlorine is :
A \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{1} 3 p^{6} \)
B . \( 1 s^{2} 2 s^{2} 2 p^{5} 3 s^{2} 3 p^{6} \)
c. \( 1 s^{2} 2 s^{2} 2 p^{6} 4 s^{2} 4 p^{5} \)
D. \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{5} \)


The figure shows three concentric metallic spherical shells. The outermost
shell has charged \( q_{2}, \) the innermost
shell has charged \( q_{1} \), and the middle shell is undercharged. The charge
appearing on the inner surface of the outermost shell is
A \( \cdot(a) q_{1}+q \)
\[
q
\]
B. \( (b) \frac{q}{2} \)
\( c \cdot(c)-q \)
\( D \cdot(d) \) Zero


Peptization is a reverse of coagulation.
A. True
B. False


In which of the following reactions, the product obtained is tert-butyl methyl ether?
B. \( \quad H_{3} C-\underset{C}{C}^{C H_{3}}-B r+C H_{3} O H \stackrel{O H^{-} N a}{\rightarrow} \)
c.
\[
C H_{3} B r+N a^{+} O^{-}-\underset{C_{3}}{C_{3}}^{C H_{3}}-C H_{3} \rightarrow
\]
D. \( C H_{3}-O^{-} N a^{+}+C H_{3}-C_{C}-B r \rightarrow \)
\[
_{C H_{3}}^{-}
\]


If paintbrushes cost \( \$ 1.50 \) each and canvases cost 6 times that much, which of the following represents the cost, in dollars, of p paintbrushes and c
canvases?
A. 7.5pc
B. 10.5pc
c. \( 9 c+1.5 p \)
D. \( 10.5(p+c) \)


A current carrying small loop of one turn behaves like a small magnet. If \( A \) be its
area, \( M \) its magnetic moment, the current in the loop will be
A \( \cdot \frac{M}{A} \)
в. \( \frac{A}{M} \)
c. \( M A \)
D. \( A^{2} M \)


Find the derivative by first principle
\( \cos 5 x \)


Assume the cell has a diploid number of
4. If the above chromosomes are in the
tetrad or bivalent stage of meiosis, which statement below is correct about
the events of anaphase I?
A. Two of the tetrads will go to one cell, and two will go to the other
B. Sister chromatids will break apart and each will go in one of four cells
c. one member of each homologous pair will go into each of the two cells
D. The tetrads will separate but each new cell will still be diploid since each chromosome has two chromatids


State, whether the following statement
is True or False:

In homologous series, all members have the same physical properties.


\( f(R=1 \Omega, \text { the current in the branch } x \) is


\( C_{6} H_{5} C H_{3} \frac{C r O_{2} C l_{2}}{\longrightarrow} A \stackrel{H_{2} O}{\longrightarrow} B \)
The functional group present in \( \mathrm{B} \) and name of the reaction would be :
A. \( -C H O \), Gattermann aldehyde synthesis
B. \( -C H O \), Etard reaction
c. \( -C O C H_{3} \), Friedel Crafts reaction
D. \( -C H O \), Oxo reaction


Explain how square is a quadrilateral.
A. All angles are equal
B. Because it is four sided
c. Two sides are equal
D. None of these


Incomplete loop of Henle is found in
\( \mathbf{A} \)
Frog
\( \mathbf{B} \)
Human
\( \mathbf{c} \)
Bird
D.
Mammal


A concave mirror produces 10 times enlarged image (real) of an object
placed \( 1 c m \) in front of it. Where is the
image located?
A \( .5 \mathrm{cm} \)
B. \( -10 \mathrm{cm} \)
c. \( -5 c m \)
D. \( 10 \mathrm{cm} \)


If it rains on Republic Day parade an
Auto Riksha earns Rs. \( 240, \) on the other
hand it does not rain he loses Rs. \( 60 . \) The
probability of rain on Republic Day parade is \( 0.6 . \) What is the value of expected income of an Auto Riksha on
Republic Day parade?
A . Rs. 150
B. Rs. 45
c. Rs. 120
D. Rs. 10


If \( \boldsymbol{P}(\boldsymbol{A} / \boldsymbol{B})=\boldsymbol{P}(\boldsymbol{B} / \boldsymbol{A}) . \boldsymbol{A} \) and \( \boldsymbol{B} \) are two
non-mutually exclusive events then
A. \( A \) and \( B \) are necessarily same events
в. \( P(A)=P(B) \)
c. \( P(A \cap B)=P(A) P(B) \)
D. all the above


The bright colours of ripe fruits are due
to
A. Leucoplasts
B. Chloroplasts
c. Amyloplasts
D. Chromoplasts


The molecularity of a reaction will be:
A . fractional
B. zero
c. positive whole number
D. negative


Change the following degree measures
to radian measure: \( 45^{\circ} \)
\( ^{\mathbf{A}} \cdot \frac{\pi}{6} \) radians
B \( \cdot \frac{\pi}{3} \) radians
c. \( \frac{\pi}{4} \) radians
D \( \cdot \frac{\pi}{2} \) radians


The wire having a black plastic covering
is a
A. live wire
B. neutral wire
c. earth wire
D. none of these


fa minima is formed at the detector, then the magnitude of wavelength \( \lambda \) of the wave produced is given by
A \( .2 \pi R \)
в. \( \frac{3}{2} \pi R \)
c. \( \frac{5}{2} \pi \)
D. none of these


The ratio of specific charge \( e / m \) of an electron to that of a hydrogen ion is
A . 1: 1
B. 1840: 1
c. 1: 1840
D. 2: 1


Tert-butyl methyl ether on treatment
with hydrogen iodide in cold gives:
A. tert-butyl iodide and methyl iodide
B. tert-butyl alcohol and methyl alcohol
C. tert-butyl alcohol and methyl iodide
D. tert-butyl iodide and methyl alcohol


How should people wearing spectacles
work with a microscope?
A. They should keep on wearing their spectacles
B. They should never use the microscope
C. They should take off their spectacles
D. They may either put on their spectacles or they may take off their spectacles


In the following increasing function is
A \( \cdot e^{x^{2}}^{2} \)
B \cdot \( e^{x^{3}} \)
\( c \cdot e^{0} \)
D. all the above


Among the following which is chemically inert?
A . Alkali metal
B. Alkaline earth metal
c. Transition metal
D. Halogen
E. Noble gas


Sketch the graph for \( y=\tan ^{-1}(\tan x) \)


Which of the following is not true for \( \mathbf{1} \boldsymbol{H}^{1}, \mathbf{1} \boldsymbol{H}^{2}, \mathbf{1} \boldsymbol{H}^{3} \mathbf{?} \)
A. They are isotopes of each other
B. They have similar electronic configurations
c. They exist in the nature in the ratio of 1: 2: 3
D. Their atomic masses are in the ratio of 1: 2: 3


Will geographical isolation be a major factor in the speciation of self pollinating plant species?Why or why not?


\( \boldsymbol{A} \cap \boldsymbol{X}=\boldsymbol{B} \cap \boldsymbol{X}=\boldsymbol{\phi} \& \boldsymbol{A} \cup \boldsymbol{X}=\boldsymbol{B} \cup \boldsymbol{X} \)
prove that \( \boldsymbol{A}=\boldsymbol{B} \)


Explain the concept of a parallel plate capacitor. State its any 'two' applications.


Solve: \( \boldsymbol{x}+\frac{\mathbf{1}}{\boldsymbol{x}}=\mathbf{5} \)


Suppose the cubic \( x^{3}-p x+q=0 \) has
three distinct real roots where \( p>0 \)
and \( \boldsymbol{q}>0 . \) Then,which one of the
following holds?
A. Minima at \( \sqrt{\frac{P}{3}} \) and maxima at \( -\sqrt{\frac{p}{3}} \)
B. Minima at \( -\sqrt{\frac{P}{3}} \) and maxima at \( \sqrt{\frac{p}{3}} \)
C. minima at both \( \sqrt{\frac{p}{3}} \) and \( -\sqrt{\frac{p}{3}} \)
D. Mixima at both \( \sqrt{\frac{P}{3}} \) and \( -\sqrt{\frac{P}{3}} \)


When all the parallel rays reflected from a plane surface are parallel, the reflection is known as:
A . regular reflection
B. irregular reflection
c. diffused reflection
D. none of these


Evaluate the following: \( \int(1+x) e^{x} d x \)


For a sparingle soluble salt \( A_{p} B_{q} \). the relationship of its solubility product
\( \left(L_{s}\right) \) with its solubility (S) is:
A \( \cdot L_{s}=S^{p+q} p^{p} q^{q} \)
B \( \cdot L_{s}=S^{p+q} p^{q} q^{p} \)
c. \( L_{s}=S^{p q} p^{p} q^{q} \)
D. \( L_{s}=S^{p q}(p q)^{p+q} \)


What are the two properties of carbon which lead to the formation of a large
number?


Find the electric field both inside the
shell at a distance \( r \) from the centre.
\( ^{A} \cdot \frac{Q}{4 \pi \epsilon_{0} a^{2}} \)
в. \( \frac{Q r}{4 \pi \epsilon_{0} a^{2}} \)
c. \( \frac{Q}{4 \pi \epsilon_{0} a^{3}} \)
D. \( \frac{Q r}{4 \pi \epsilon_{0} a^{3}} \)


The decrease in potential energy between top position \( A \) and bottom position B is,
\( =\boldsymbol{m} \boldsymbol{g} \boldsymbol{r}-(-\boldsymbol{m} \boldsymbol{g} \boldsymbol{r})=\boldsymbol{2 m} \boldsymbol{g} \boldsymbol{r} \quad \ldots \)
This must be equal to the increase in kinetic energy, when particle move from \( A \) to \( B \)
i.e. \( \frac{1}{2} \boldsymbol{m} \boldsymbol{v}_{2}^{2}-\frac{1}{2} \boldsymbol{m} \boldsymbol{v}_{1}^{2} \)


A sample of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) solution labelled as
28 volume has density of 265 g/L. Mark the correct option(s) representing concentration of same solution in other
units.
This question has multiple correct options
A. Molarity of \( H_{2} O_{2}=2.5 \)
B. Percentage \( w / v=17 \)
C. Mole fraction of \( H_{2} O_{2}=0.2 \)
D. Molality of \( H_{2} O_{2}=13.88 \)


The ratio of the area's bounded by the curves \( y^{2}=12 x \) and \( x^{2}=12 y \) is
divided by the line \( x=3 \) is
A .15: 49
B. 9: 15
\( c \cdot 7: 15 \)
D. 7:5


The first noble gas compound prepared by Bartlett is :
A \( \cdot \mathrm{xeF}_{2} \)
в. КrF \( _{2} \)
c. \( \mathrm{xePtF}_{6} \)
D. \( \mathrm{xeO}_{3} \)


R.Q. is less than one at the time of respiration of
A. Starch
B. Sugarcane
c. Glucose
D. Groundnut


An atom is initially at an energy level \( \boldsymbol{E}=-\mathbf{6 . 5 2} e \boldsymbol{V} . \) It absorbs a photon of
wavelength \( 860 n m . \) The internal energy
of atom after absorbing photon is
A . \( 5.08 e V \)
B. \( 1.44 e V \)
c. \( -1.44 e V \)
D. \( -5.08 e V \)


Describe in brief what is observed when
moving electrons are allowed to fall on a thin graphite film and the emergent beam falls on a fluorescent screen.


The reverse saturation current of a
silicon diode
A. doubles for every \( 10^{\circ} \mathrm{C} \) increase in temperature
B. does not change with temperature
C. halves for every \( 1^{\circ} \mathrm{C} \) decrease in temperature
D. increases by 1.5 times for every \( 2^{\circ} C \) increment in temperature


If \( \sin ^{-1} x=\frac{\pi}{5} \) for \( \operatorname{somex} \in[-1,1] \) then
find the value of \( \cos ^{-1} x \)


Select correct statement.
A. Based on reactivity series, occurrence of certain elements takes place in native state
B. Due to basic nature of oxides of alkaline earth elements, they combine with atmospheric acidic oxides giving salts
c. Both
(a) and (b) are correct
D. None of the above is correct


A diamagnetic material in a magnetic
field moves
A. perpendicular to field
B. from stronger to weaker parts of the field
c. from weaker to stronger parts of field
D. None of these


Match the column.


A hoop rolls down an inclined plane. The
fraction of its total kinetic energy that is associated with rotational motion is
A .1: 2
B. 1: 3
c. 1: 4
D. 2: 3


In how many ways can 6 persons stand in a queue?


Number of intersecting points of the
\( \operatorname{conic} 4 x^{2}+9 y^{2}=1 \) and \( 4 x^{2}+y^{2}=4 \)
is
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
D. 0 (zero)


Muscular force is a type of
A. mechanical force
B. magnetic force
c. electrostatic force
D. gravitational force


\( \boldsymbol{n} \) small balls each of mass \( \boldsymbol{m} \) impinge elastically each second on a surface
with velocity \( v \). The force experienced by
the surface will be :
A \( \cdot \frac{1}{2} m n v \)
B. \( 2 m n v \)
c. \( m n v \)
D. \( 4 m n v \)


In which of the following reactions hydrogen gas is not liberated?
\( A \cdot 1,1 \)
в. ॥, ॥ I
c. I only
D. III only


At the time of maximum deflection of
the thread with vertical, the trolley will
move with velocity
\( A \cdot 2 m / s \)
в. \( 3 m / s \)
\( \mathrm{c} \cdot 1 \mathrm{m} / \mathrm{s} \)
D. \( 4 m / s \)


The term independent of \( x \) in the expansion of \( \left(x^{2}-\frac{3 \sqrt{3}}{x^{3}}\right)^{10} \)


If \( A, B \) are square matrices of order \( 3, A \) is non-singular and \( A B=O \), then \( B \) is
\( a \)
A. Null matrix
B. singular matrix
c. Unit matrix
D. Non-singular matrix


A gun recoils backward after firing a
bullet
A. To follow the law of inertia
B. To conserve momentum
c. To conserve mass
D. The statement is wrong


The amount of charges that passes any section of the conductors in one second
is called:
A. current
B. power dissipation
c. electromotive force
D. internal resistance


If the matrix \( \left[\begin{array}{ccc}\mathbf{0} & \boldsymbol{a} & \mathbf{3} \\ \mathbf{2} & \boldsymbol{b} & \mathbf{- 1} \\ \boldsymbol{c} & \mathbf{1} & \mathbf{0}\end{array}\right] \) is a skew
symmetric matrix, find \( a, b \) and \( c \)


One of the most widely used drug in
medicine, iodex is:
A. Methyl salicylate
B. Ethyl salicylate
c. Acetyl salicylic acid
D. O-hydroxybenzoic acid


A stone is thrown in vertically upward direction with a velocity of \( 5 m s^{-1} \). If the acceleration of the stone during its
motion is \( 10 \mathrm{ms}^{-2} \) in the downward direction, what will be the height
attained by the stone and how much time will it take to reach there?
A. Height=1.25 \( m \) and time \( =0.5 \) s
B. Height= 2.5 \( m \) and time \( =0.5 \) s
c. Height= \( 2.5 \mathrm{m} \) and time \( =0.05 \mathrm{s} \)
D. Height=1.25 \( m \) and time \( =0.05 \) s


If \( \boldsymbol{x}^{\boldsymbol{y}}=\boldsymbol{a}^{\boldsymbol{x}}, \) prove that \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{\boldsymbol{x} \log _{e} \boldsymbol{a}-\boldsymbol{y}}{\boldsymbol{x} \log _{e} \boldsymbol{x}} \)


Select the correct combination of the statements (i - iv) regarding the characteristics of certain organisms.
(i) Methanogens are archaebacterial which produces methane in marshy
areas
(ii) Nostoc is a filamentous blue-green alga which fixed atmospheric nitrogen.
(iii) Chemosynthetic autotrophic bacteria synthesize cellulose from glucose.
(iv) Mycoplasma lacks a cell wall and can survive without oxygen.
A . (ii) and (iii)
B. (i), (ii) and (iii)
c. (ii), (iii) and (iv)
D. (i), (ii) and (iv)


When a base combine with metal it
forms metal salt/base and releases:
A. oxygen
B. hydrogen
c. carbon dioxide
D. nitrogen


What is empirical formula give an example ? For a compound whose empirical formula and molecular formula are same, give an example.


What is the \( Q- \) value of the reaction?
\( \boldsymbol{P}+^{7} \boldsymbol{L i} \rightarrow^{4} \boldsymbol{H} \boldsymbol{e}+^{4} \boldsymbol{H} \boldsymbol{e} \)
The atomic masses of \( ^{1} \boldsymbol{H},^{4} \boldsymbol{H} \boldsymbol{e} \) and \( ^{7} \boldsymbol{L} \boldsymbol{i} \)
are \( 1.007825 u, 4.0026034 u \) and
\( 7.016004 u \) respectively
A . 17.35 MeV
в. \( 18.06 \mathrm{MeV} \)
c. 177.35 МеV
D. 170.35 MeV


Find out the approximate amount of polythene formed from 20kg of calcium carbide from the following reactions.
\( \boldsymbol{C a} \boldsymbol{C}_{2}+\mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{C a}(\boldsymbol{O H})_{2}+\boldsymbol{C}_{2} \boldsymbol{H}_{2} \)
\( \boldsymbol{H} \boldsymbol{C} \equiv \boldsymbol{C H}+\boldsymbol{H}_{2} \frac{\boldsymbol{P d} \cdot \boldsymbol{B a S O}_{4}}{\longrightarrow} \boldsymbol{C H}_{2}= \)
\( \boldsymbol{C H}_{2} \)
\( \boldsymbol{n} \boldsymbol{C} \boldsymbol{H}_{2}=\boldsymbol{C H}_{2} \rightarrow\left(-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\right)_{n} \)
\( A \cdot 6 g \)
B. \( 9 \mathrm{kg} \)
\( \mathrm{c} .26 \mathrm{kg} \)
D. \( 29 \mathrm{kg} \)


Compound \( A_{(l)} \) and \( B_{(l)} \) function as a weak acid and weak base respectively
when dissolved in water. When pure \( A_{(l)} \)
is dissolved in anhydrous B \( _{(l)}, \) A will function as:
This question has multiple correct options
A. an acid
B. a base
c. a stronger acid than when dissolved in \( H_{2} \) O
D. a stronger base than when it is dissolved in \( H_{2} \) O


The gravitational force between two bodies is
A. repulsive at large distances
B. attractive at all places
c. attractive at short distances
D. repulsive at short distances


The weight of an object at the centre of
the earth of radius R is
A. zero
B. infinite
C . \( R \) times the weight at the surface of the earth
D. \( 1 / R^{2} \) times the weight at surface of the earth


A certain current liberated 0.504 gm of hydrogen in 2 hrs. How many grams of copper can be liberated by the same current flowing for the same time in a copper sulphate solution?
A. \( 12.7 \mathrm{gms} \)
B. 15.9 gms
c. \( 31.8 \mathrm{gms} \)
D. \( 63.5 \mathrm{gms} \)


Value based questions. Name the tissues where the following
structures occur:
Nissis granules


Permanganate ion reacts with bromide
ion in basic medium to give
magnesium dioxide and bromate ion.Write the balanced ionic equation
for the reaction.


John Newlands arranged the known elements in a/an order of
their atomic
A. increasing, masses
B. decreasing, masses
c. increasing, numbers
D. decreasing, numbers


Which of the following is affected by acid rains?
A. Infrastructure
B. Aquatic life
c. Plants
D. All of the above


\( \operatorname{Let} \mathbf{f}(\boldsymbol{x})=\left\{\begin{array}{ll}\frac{3 x+4 \tan x}{x} & \text { for } x \neq 0 \\ 7 & \text { for } x=0\end{array}\right. \)
\( \operatorname{then} f(x) \) is
A. continuous at \( x=0 \)
B. not continuous at \( x=0 \)
c. not determined at \( x=0 \)
D. \( L t_{x \rightarrow 0} f(x)=8 \)


For the reaction: \( \boldsymbol{P} \boldsymbol{C l} \boldsymbol{l}_{5}(\boldsymbol{g}) \rightarrow \boldsymbol{P} \boldsymbol{C l}_{3}(\boldsymbol{g})+ \)
\( \boldsymbol{C l}_{2}(\boldsymbol{g}) \)
\( \mathbf{A} \cdot \Delta H=\Delta E \)
B. \( \Delta H>\Delta E \)
c. \( \Delta H<\Delta E \)
D. Can't predicted


Adsorption of gases on solid surface is generally exothermic because:
A. enthalpy is positive
B. entropy decreases
c. entropy increases
D. free energy increases


Osteoporosis, an age-related disease of
skeleton system, may occur due to
A. Decreased level of estrogen
B. Accumulation of uric acid leading to inflammation of joints
C. Immune disorder affecting neuro-muscular junction leading to fatigue
D. High concentration of \( \mathrm{Ca}^{++} \) and \( \mathrm{Na}^{+} \)


Area bounded by the region \( \boldsymbol{R} \equiv \)
\( \left\{(x, y): y^{2} \leq x \leq|y|\right\} \) is
A \( \cdot \frac{4}{3} \)
B. \( \frac{3}{4} \)
c. \( \frac{1}{3} \)
D.


Name the product formed when chlorine
reacts with water.


In a container a mixture is prepared by mixing of three samples of hydrogen, helium ion \( \left(H e^{+}\right) \) and lithium ion
\( \left(L i^{2+}\right) \) In sample all the hydrogen atoms are in 1 st excited state and al
the He ions are in third excited state
and all the \( \left(L i^{2+}\right) \) ions are in fifth
excited state Find the total number of
spectral lines observed in the emission
spectrum of such a sample, when the electrons return back upto the ground
state


Rahim takes out all the hearts from the
cards. What is the probability of Picking out a diamonds.


What is the smallest positive integer \( \boldsymbol{K} \) such that \( 2000 \times 2001 \times K \) is a perfect
cube?
A \( \cdot 2^{3} \times 3^{3} \times 23^{3} \times 29^{3} \)
B . \( 2 \times 3 \times 23 \times 29 \)
c. \( 2 \times 3^{2} \times 23^{3} \times 29^{4} \)
D . \( 2^{2} \times 3^{2} \times 23^{2} \times 29^{2} \)


Consider the following statements and arrange in the order of true/false as
given in the codes.
\( S_{1}: \) In extraction of iron from haematite
ore, the reduction reactions take place
in the lower temperature range and in
the higher temperature range, in the blast furnace.
\( S_{2}: \) Sphalerite is a carbonate ore of zinc.
\( S_{3}: \) The principal ore of aluminium,
bauxite, usually contains silica, iron oxides and titanium oxide as
impurities
\( S_{4}: \) Solified copper obtained from silica lined convertor (Bessemer converter)
has blistered appearance due to the
evolution of \( \boldsymbol{S O}_{2} \)
\( \mathbf{A} \cdot \) Т \( F T T \)
B. FTFF
c. F FTT
D. TF F T


Rationalising the denominator of \( \frac{5}{\sqrt{3}-\sqrt{5}} \) is -
A \( \cdot\left(\frac{5}{2}(\sqrt{3}+\sqrt{5})\right. \)
B \( \cdot\left(-\frac{5}{2}(\sqrt{3}+\sqrt{5})\right. \)
c. \( \left(\frac{5}{2}(\sqrt{3}-\sqrt{5})\right. \)
D \( \cdot\left(-\frac{5}{2}(\sqrt{3}-\sqrt{5})\right. \)


Why does benzene undergo electrophilic substitution reactions easily and nucleophilic substitutions difficulty?


"The Castners process is the process
used for extraction of sodium in solid
state."

Answer whether the above statement is
true or false.
If true enter 1 , else enter 0


The linear momentum of a particle is given by \( \boldsymbol{P}=(\boldsymbol{a} \sin \boldsymbol{t} \hat{\boldsymbol{i}}-\boldsymbol{a} \cos \boldsymbol{t} \hat{\boldsymbol{j}}) \) kg-
\( \mathrm{m} / \mathrm{s} \) A force \( \overrightarrow{\boldsymbol{F}} \) is acting on the particle Select correct alternative/s
A. Linear momentum \( \vec{P} \) of particle is always parallel to
B. Linear momentum \( \vec{P} \) of particle is always perpendicular to \( \vec{F} \)
c. Linear momentum \( \vec{P} \) is always constant
D. Magnitude of linear momentum is constant with respect to time


Consider the reaction:
\( \boldsymbol{N} \boldsymbol{O}_{2} \rightleftharpoons \frac{1}{2} \boldsymbol{N}_{2}+\boldsymbol{O}_{2}, \boldsymbol{K}_{1} \)
\( N_{2} O_{4} \rightleftharpoons 2 N O_{2}, K_{2} \)
Give the equilibrium constant for the
formation of \( N_{2} O_{4} \) from \( N_{2} \) and \( O_{2} \)
A \( \cdot \frac{1}{K_{1}^{2}} \frac{1}{K_{2}} \)
в. \( \frac{1}{K_{1} K_{2}} \)
c. \( \sqrt{\frac{1}{K_{1} K_{2}}} \)
D. \( \frac{K_{2}}{K_{1}} \)


f \( \boldsymbol{y}=\boldsymbol{x}^{2}+\boldsymbol{x}, \) then find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \)


A magnetic needle suspended horizontally by an unspun silk fibre oscillates in the horizontal plane,
because of the restoring force originating mainly from
A. the torsion of the silk fibre
B. the horizontal component of earth's magnetic field
c. the force of gravity
D. all of the above


Immature gular fruit is
A. Berry
B. Samara fruit
c. Hypanthodium inflorescence
D. Swollen twig tip


In what ratio does (-4,6) divides the line segment joining the point \( \boldsymbol{A}(-\mathbf{6}, \mathbf{4}) \)
and \( B(3,-8) \)


What do you mean by "Rectilinear
Propagation" of Light?
A. Light travels in a straight line
B. Light travels in a curved path
C. Light exhibits dual nature of particle and wave
D. Light gets deviated when it moves in another medium


\( R-C H_{2}-C H_{2} O H \) can be converted
into \( R C H_{2} C H_{2} C O O H \) by the following
sequence of steps:
\( \mathbf{A} \cdot P B r_{3}, K C N, H_{2} / P t \)
B. \( P B r_{3}, K C N, H_{3} O^{+} \)
c. \( H C N, P B r_{3}, H_{3} O^{+} \)
D. \( K C N, H_{3} O^{+} \)


A ray of light, after refraction through a
convex lens emerges parallel to the
principal axis. The incident ray when produced appear to come from a point on principal axis. Name the point :
A. first focus
B. first centre
c. last focus
D. last centre


Draw a triangle \( A B C \) with side \( B C= \)
\( \mathbf{7} c \boldsymbol{m}, \angle \boldsymbol{B}=\mathbf{4 5}^{o}, \angle \boldsymbol{A}=\mathbf{1 0 5}^{\circ} . \) Then
construct a triangle whose side are \( \frac{4}{3} \)
times the corresponding sides of \( \triangle A B C . \) Write the construction.


Gametophytic generation is dominant
in
B. Bryophyta
c. Angiosperms
D. Gymnosperms


\( \boldsymbol{C F}_{2}=\boldsymbol{C F}_{2} \) is a monomer of:
A. Teflon
B. Orlon
c. Polythene
D. Nylon-6


Find the smallest number which should
be multiplied to 1352 to get a perfect
cube.
\( \mathbf{A} \cdot 12 \)
B . 13
c. 61
D. 21


A resistor of resistance \( 100 \Omega \) is
connected to an AC source \( \varepsilon= \)
\( (12 V) \sin \left(250 \pi s^{-1}\right) t . \) Find the energy
dissipated as heat during \( t=0 \) to \( t= \)
1.0 ms.


If \( f(x)=(x-1)(x-2) \) and interval
given was \( (0,4), \) find 'c' using Langrange's mean value theorem.
A \( \cdot 2+\frac{2}{\sqrt{3}} \)
B. \( 2-\frac{2}{\sqrt{3}} \)
c. 2
D. Both A and B


The observed osmotic pressure for a
\( 0.10 M \) solution of \( F e\left(N H_{4}\right)_{2}\left(S O_{4}\right)_{2} \) at
\( 25^{\circ} C \) is 10.8 atm. The expected and experimental (observed) values of Van't Hoff factor (i) will be respectively:
\( \left(\boldsymbol{R}=\mathbf{0 . 0 8 2} \quad \boldsymbol{L} \quad \boldsymbol{a t m} \quad \boldsymbol{k}^{-} \boldsymbol{m o l}^{-1}\right) \)
A. 5 and 4.42
B. 4 and 4.00
c. 5 and 3.42
D. 3 and 5.42


Discuss the continuity of the following
function at \( x=0 . \) If the function has a
removable discontinuity, redefine the
function so as to remove the
discontinuity
\( f(x)=\left\{\begin{array}{ll}\frac{4^{x}-e^{x}}{6^{x}}-1 & \text { for } x \neq 0 \\ \log \left(\frac{2}{3}\right) & \text { for } x=0\end{array}\right. \)


f \( a, b, c \) be positive and \( a b(a+b)+ \)
\( \boldsymbol{b} \boldsymbol{c}(\boldsymbol{b}+\boldsymbol{c})+\boldsymbol{c} \boldsymbol{a}(\boldsymbol{c}+\boldsymbol{a}) \geq \boldsymbol{\lambda} \boldsymbol{a} \boldsymbol{b} \boldsymbol{c}, \) then
value of \( \lambda \) is


A mixture of haematite, coke and limestone, on heating in blast furnace, gives molten iron metal. This is known
as:
A. Smelting
B. Calcination
c. Roasting
D. Liquation


The first stable product of
photosynthesis in \( C_{3} \) plants is
A. 3- phosphoglyceric acid
B. Dihydroxyacetone phosphate
c. Fructose- - 6 - diphosphate
D. Ribulose-1, 5- diphosphate


The developmental stages in a community are called as
A. Climax changes
B. Biological changess
c. Seral changes
D. Climatic changes


If a resistance \( R \) is melted and
recasted to half of its length, then the new resistance of the wire will be
A \( \cdot \frac{R}{2} \)
в. \( 2 R \)
c. \( R \)
D. \( \frac{R}{4} \)


\( m \)


If \( X \) follows a binomial distribution
with parameters \( n=8 \) and \( P=\frac{1}{2}, \) than
\( \boldsymbol{P}(|\boldsymbol{x}-\mathbf{4}| \leq \mathbf{2})= \)
A \( \cdot \frac{119}{128} \)
в. \( \frac{9}{128} \)
c. \( \frac{101}{128} \)
D. \( \frac{11}{128} \)


The sum of 'n' terms of two A.P.'s are in the ratio of \( \frac{5 n+2}{11 n-7} . \) Find the ratio of their sixth terms.
A . 32: 59
B. 1: 1
c. 2: 1
D. 1: 2


The device used for producing current is
called a


\( \ln a \triangle w i t h \) sides \( a, b \) and \( c, a \)
semicircle touching the sides \( A C \) and
\( C B \) is inscribed whose diameter lies on
\( A B . \) Then, the radius of the semicircle
is :
A \( \cdot \frac{a}{2} \)
в. \( \frac{\Delta}{s} \)
c. \( \frac{\Delta}{a+b} \)
D. \( \frac{2 \Delta}{a+b} \)


Rate constant for the decomposition of
ethylene oxide into \( C H_{4} \) and \( C O \) may
be described by the equation, \( \log \left[k\left(s^{-1}\right)\right]=14.34-\frac{1.25 \times 10^{4}}{T} \)
(a) What is the energy of activation of this reaction?
(b) What is the value of \( k \) at \( 670 K ? \)


Assertion
When an object is placed between two plane parallel mirrors, then all the images found are of equal intensity.
Reason

In case of plane parallel mirrors, only two images are possible.
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


In a meter bridge circuit, resistance in
the left hand gap is \( 2 \Omega \) and an unknown resistance \( X \) is in the right hand gap as shown in Figure. The null point is found
to be \( 40 \mathrm{cm} \) from the left end of the wire.
What resistance should be connected to
\( x \) so that the new null point is \( 50 \mathrm{cm} \)
from the left end of the wire?


Which of the followings are Lewis
acids?
\( \boldsymbol{H}_{2} \boldsymbol{O}, \boldsymbol{B} \boldsymbol{F}_{3}, \boldsymbol{H}^{+}, \) and \( \boldsymbol{N} \boldsymbol{H}_{4}^{+} \)


The diagram alongside shows the
refraction of a ray of light from air to a
liquid. Angle of refraction is:
A \( \cdot 60^{\circ} \)
B . \( 15^{\circ} \)
\( c .30^{\circ} \)
D. \( 45^{\circ} \)


Molar heat capacity of water in equilibrium with ice at constant
pressure is :
A. zero
B. inifinity
c. \( 40.05 k J K^{-1} \) mol \( ^{-1} \)
D. \( 75.48 k J K^{-1} m o l^{-1} \)


The intensity at the maximum in a
Young's double slit experiment is \( \boldsymbol{I}_{\mathbf{0}} \)
Distance between two slits is \( d=5 \lambda \)
,where \( \lambda \) is the wavelength of light used in the experiment. What will be the intensity in front of one the slits on the
screen place at a distance \( \mathrm{D}=2 \mathrm{m} \)


Why nascent hydrogen is more reactive
than molecular hydrogen?
A. The production of nascent hydrogen is associated with the release of high energy. This released energy activates the nascent hydrogen and makes it more energy rich than that of ordinary occurring molecular hydrogen. Because more energy means more reactivity, nascent hydrogen is more reactive than molecular hydrogen.
B. In the time of formation nascent hydrogen is in the form of minute bubbles with high internal pressure which makes it more reactive.
C. both \( A \) and \( B \)
D. none of these


A system in thermodynamic equilibrium will have the following equilibrium(s):-
A. Thermal equilibrium
B. Mechanical equilibrium
c. chemical equilibrium
D. All of these


\( P I_{3} \) upon hydrolysis give:
A. monobsic acid and dibasic acid.
B. monobasic acid and tribasic acid.
C. monobasic acid and a salt.
D. dibasic acid and tribasic acid.


The IUPAC name of sec. butyl alcohol is:
A. 1-butanol
B. 2-butanol
c. 2-methyl-1-butanol
D. 2-methyl-2-butanol


\( \Delta S^{\ominus} \) for the cell reaction assuming
that these quantities remain
unchanged in the range \( 15^{\circ} C \) to \( 35^{\circ} C \) is:
A \( \cdot 193 J K^{-1} \)
B. -193 Л \( K^{-1} \)
\( \mathbf{c} \cdot 1930 J K^{-1} \)
D. \( -1930 J K^{-1} \)


The sum of the series \( 1+\frac{\log _{e} x}{1 !}+ \)
\( \frac{\left(\log _{e} x\right)^{2}}{2 !}+\dots \dots . . \) is
A . \( x \)
B . \( x^{2} \)
c. \( x^{3} \)
D. none of these


limiting friction is slightly greater than friction.


How many molecules of glycine is
required to release one \( C O_{2} \) molecule in
photorespiration?
A. one
B. Two
c. Three
D. Four


The ion which shows maximum
paramagnetic character among the bivalent ions of the first transition
metal series is :
\( A \cdot C_{0}^{2} \)
B. \( c u^{2} \)
\( c \cdot c r^{2} \)
D. \( \mathrm{Fe}^{2} \)
\( E \cdot M n^{2} \)


(i) Write IUPAC name of \( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{N H}_{2} \)
(ii) Arrange the following amines in the order of their increasing basic strength in aqueous solution.
\( \left(\boldsymbol{C} \boldsymbol{H}_{3}\right)_{3} \boldsymbol{N}_{1}\left(\boldsymbol{C} \boldsymbol{H}_{3}\right)_{2} \boldsymbol{N} \boldsymbol{H}_{1} \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{N} \boldsymbol{H}_{2} \)


Evaluate \( \int_{0}^{2}|1-x| d x \)


In a uniform circular motion, radial
acceleration is due to
A. Change in position of the particle along \( X \) axis
B. Change in position of the particle along Y axis
C. Change in direction of tangential velocity
D. Change in magnitude of tangential velocity


A ball is thrown vertically up. If the ball reached at maximum height in \( 3 s \) Assume air resistance is negligible. The maximum height of the ball is most nearly :
A . \( 10 m \)
B. \( 15 \mathrm{m} \)
c. \( 30 m \)
D. \( 45 m \)
E . \( 60 m \)