A person has a \( 15 \mathrm{cm} \) wide face and his
two eyes are separated by \( 9 \mathrm{cm} . \) The minimum width of a mirror required for
the person to view his complete face literally is
\( \mathbf{A} \cdot 15 \mathrm{cm} \)
в. 9 ст
\( c .6 c m \)
D. 3 cm


A buffer solution of \( p H=9 \) can be
prepared by mixing:
A. \( C H_{3} C O O N a \) and \( C H_{3} C O O O H \)
B. \( N a C l \) and \( N a O H \)
c. \( N H_{4} C l \) and \( N H_{4} O H \)
D. \( K H_{2} P O_{4} \) and \( K_{2} H P O_{4} \)


Give reasons.
In old age bifocal lens is necessary
for person.


State whether the following statement is true or false. Give reason to support
your answer. \( \{a, b, a, b, a, b, \ldots . .\} \) is an infinite set
A. True
B. False


If value of \( x \) which satisfy equation \( \sin ^{-1} \frac{2 x}{1+x^{2}}=\tan ^{-1} \frac{2 x}{1-x^{2}}, \) is \( -a< \)
\( \boldsymbol{x}<\boldsymbol{b} \)
Find the value of \( a+b \)
A . -1
B.
c. 1
D.


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


The term \( \frac{d c}{d t} \) in a rate equation refers to:
A. concentration of reactants
B. change in concentration of reactants or products with time
C. velocity constant of the reaction
D. concentration of products


Spin multiplicity is zero for:
\( A \)
\begin{tabular}{|l|l|l|}
\hline \( \mathbf{1} \) & \( \mathbf{1} \) & \( \mathbf{1} \) \\
\hline
\end{tabular}
в. \begin{tabular}{|l|l|l|}
\hline \( \mathbf{1} \) & \( \mathbf{1} \) & \( \mathbf{j} \) \\
\hline
\end{tabular}
\( c \)
\( \left|\begin{array}{ll}\hline \mid & \downarrow & \downarrow\end{array}\right| \)
D. \( \sqrt{ }|V| \)


Two short magnets placed along the same axis with their like poles facing each other will repel each other with a
force which varies inversely as
A. Distance
B. Square of distance
c. cube of distance
D. Fourth power of distance


When 2 moles of \( C_{2} H_{6} \) are completely
burnt, \( 3120 k J \) of heat is liberated.
Calculate the heat of formation \( \Delta \boldsymbol{H}_{f}^{o} \)
for \( \boldsymbol{C}_{2} \boldsymbol{H}_{\mathbf{6}} \)
Given: \( \Delta H_{f}^{o} \) for \( C O_{2}(g) \) and \( H_{2} O(l) \) are
-395 and \( -286 k J \) respectively.
A . \( -88 k J / m o l \)
в. \( +88 k J / m o l \)
c. \( -58 k J / m o l \)
D. None of the above


How many zeros in \( 100 ! ? \)


Explain electron transport system


Density of water is
\( \mathbf{A} \cdot 1000 k g / m^{3} \)
B . \( 1 k g / m^{3} \)
\( \mathbf{c} \cdot 1000 g / \mathrm{cm}^{2} \)
D. \( 100 k g / m^{3} \)


Distance travelled by sound in year is called AU?
A . True
B. False


A diamagnetic substance produces a
A. Strong magnetic field in opposition of an externally applied magnetic field
B. Weak magnetic field in the direction of an externally applied magnetic field
C. Weak magnetic field in opposition of an externally applied magnetic field
D. Strong magnetic field in the direction of an externally applied magnetic field


Which is not a mineral of aluminium?
A. Anhydrite
B. Bauxite
c. corundum
D. Diaspore


Two identical heater wires are first
connected in series and then in parallel with a source of electricity. The ratio of heat produced in the two cases is
A. 2:
B. 1: 2
\( c \cdot 4: \)
\( D \cdot 1: 4 \)


ray is the ray of light striking a
surface.
A. Incident
B. refracted
c. reflected
D. All the above


Two point charges \( 2 C \) and \( -1 C \) are
placed at \( \boldsymbol{x}=\mathbf{0} \) and \( \boldsymbol{x}=\boldsymbol{6} \) respectively.
The potential will be zero at points:
A. \( x=2,-2 \)
в. \( x=1,5 \)
c. \( x=4,12 \)
D. \( x=2,9 \)


Evaluate \( \int x^{2} \log x d x \)


Let \( \boldsymbol{f}(\boldsymbol{x})=[\boldsymbol{x}] \) and \( \boldsymbol{g}(\boldsymbol{x})=|\boldsymbol{x}| . \) Find
\( (\boldsymbol{g} \boldsymbol{o} \boldsymbol{f})\left(-\frac{\boldsymbol{5}}{\boldsymbol{3}}\right)-(\boldsymbol{f o g})\left(-\frac{\boldsymbol{5}}{\boldsymbol{3}}\right) \)
\( A \)
B . 2
\( c .3 \)
\( D \)


A box contains x molecules of a gas. How
will the pressure of the gas be affected if the number of molecules is made \( 2 x ? \)
A. Pressure will decrease
B. Pressure will remain unchanged.
c. Pressure will be doubled
D. Pressure will become three times.


A string is stretched between fixed points separated by \( 75.0 \mathrm{cm} \). It is observed to have resonant frequencies
of \( 420 H z \) and \( 315 H z . \) There are no
other resonant frequencies between these two. Then, the lowest resonant
frequency for this string is
\( \mathbf{A} \cdot 105 H z \)
в. \( 1.05 \mathrm{Hz} \)
\( \mathrm{c} .1050 \mathrm{Hz} \)
D. \( 10.5 \mathrm{Hz} \)


Solve \( \int x^{3} \log x d x \)
A \( \frac{x^{4} \log x}{4}+C \)
B. \( I=\frac{x^{4}}{4} \log x-\frac{x^{4}}{16}+C \)
c. \( \frac{1}{8}\left[x^{4} \log x-4 x^{2}\right]+C \)
D \( \cdot \frac{1}{16}\left[4 x^{4} \log x+x^{4}\right]+C \)


Continuous sewage flow into a stream would lead to
A. Eutrophication
B. Algal bloom
c. Depletion of oxygen
D. Increase in temperature


The most fundamental characteristic of
living being is
A. Locomotion
B. Regeneration
c. Fragmentation
D. Reproduction


Which of the following statements can be related to sexual reproduction?
A. Gametes are usually haploid.
B. Gametes are usually diploid.
c. The zygote is usually haploid.
D. The chromosome number is reduced during mitosis


Which one is not a constituent of
nucleic acid?
A . Uraci
B. Guanidine
c. Phosphoric acid
D. Ribose sugar


A chain is held on friction-less
horizontal table with one-fourth of its
length hanging over the edge. If the chain gas a length I and a mass \( \mathrm{M} \) what is the work required to pull the hanging part back on the table?


The statement written as value of \( x \) is
less than 50 is represented as
A \( .50<x \)
в. \( x>50 \)
c. \( x<50 \)
D. None of these


The following graph illustrates:
A. Dalton's law
B. Charles'law
c. Boyle's law
D. Gay-Lussac's law


The probability that certain electronic component fails when first used is 0.10 If it does not fail immediately, the probability that is lasts for one year is 0.99. The probability that a new component will last for one year is
A. 0.891
1
B. 0.692
\( c \cdot 0.92 \)
D. None of these


The d.rs of the lines \( \boldsymbol{x}=\boldsymbol{a} \boldsymbol{y}+\boldsymbol{b}, \boldsymbol{z}= \)
\( \boldsymbol{c} \boldsymbol{y}+\boldsymbol{d} \) are:
A. \( 1, a, c \)
B. \( a, 1, c \)
c. \( b, 1, c \)
D. \( c, a, 1 \)


An equilibrium expression may
be forced to completion by:
A. adding a catalyst
B. increasing the pressure
C. increasing the temperature
D. removing the products from the reaction mixture as they are formed
E. decreasing the reactant concentration


2 moles of \( A \& 3 \) moles of \( B \) are mixed in
litre vessel and the reaction is carried
at \( 400^{\circ} \mathrm{C} \) according to the equation; \( A+B \rightleftharpoons 2 C . \) The equilibrium constant
of the reaction is \( 4 . \) Find the number of
moles of \( C \) at equilibrium.
A. 2.4 mole
B. 2.8 mole
c. 3.2 mole
D. 3.7 mole


The range of \( \boldsymbol{f}(\boldsymbol{x})= \)
\( -3 \cos \sqrt{3+x+x^{2}} \) is
A. [-1,1]
в. [-2,2]
c. [-3,3]
D. [-4,4]


Explain the terms papilionaceous
corolla.


The value of \( x \) at which tangent to the
curve \( \boldsymbol{y}=\boldsymbol{x}^{3}-\boldsymbol{6} \boldsymbol{x}^{2}+\boldsymbol{9} \boldsymbol{x}+\boldsymbol{4}, \boldsymbol{0} \leq \boldsymbol{x} \leq \)
5 has maximum slope is
\( \mathbf{A} \cdot \mathbf{0} \)
B. 2
\( c \cdot \frac{5}{2} \)
\( D \)


In the reaction,
\( \boldsymbol{X}+\boldsymbol{I}_{2}+\mathbf{2} \boldsymbol{H} \boldsymbol{C l} \rightarrow \boldsymbol{S} \boldsymbol{n} \boldsymbol{C l}_{4}+\mathbf{2 H I} \)
The correct option regarding \( X \) is/are:
A. It is an strong reducing agent
B. It is an angular molecule
C. It is used as a reagent in test of \( H g^{2+} \) radical
D. All of the above


The differential equation of the family of lines which pass through (1,-1) is:
A \( \cdot y=(x+1) \frac{d y}{d x}+1 \)
B. \( y=(x+1) \frac{d y}{d x}-1 \)
c. \( y=(x-1) \frac{d y}{d x}+1 \)
D. \( y=(x-1) \frac{d y}{d x}-1 \)


In the given triangle \( A B C, \) find the
measure of \( \angle \boldsymbol{A B C} \)


The common difference of
\( -2,-4,-6,-8, \dots \dots \dots . . \) is :
A . -2
B. -
\( c \cdot 2 \)
\( D \)


Which of the following acids contain \( \boldsymbol{P} \)
in \( 5+ \) oxidation state \( ? \)
This question has multiple correct options
A. orthophosphoric acid.
B. Metaphosphoric acid
c. Phosphorus acid.
D. Pyrophosphoric acid.


Russell bodies are found in
A. Eosinophils
B. Monocytes
c. Mast cells
D. Plasma


The speed of light in two media I and I
are \( 2.2 \times 10^{8} m / s \) and \( 2.4 \times 10^{8} m / s \)
respectively. The critical angle for light refracting from I to II medium will be
A \( \sin ^{-1}\left(\frac{12}{11}\right) \)
(i) \( \left(\frac{1}{1}\right)(1)^{\frac{1}{11}} \)
\( \mathbf{B} \cdot \sin ^{-1}\left(\frac{11}{12}\right) \)
\( \mathbf{c} \cdot \sin ^{-1}\left(\frac{12}{24}\right) \)
\( \mathbf{D} \cdot \sin ^{-1}\left(\frac{12}{21}\right) \)


The molecular mass of a non-volatile
organic compound is determined either by the Victor Meyer's. method or Duma's method.
A. True
B. False


Efficiency of a heat engine whose sink is at a temperature of \( 300 K \) is \( 40 \% \). To
increase the efficiency to \( 60 \% \), keeping the sink temperature constant, the source temperature must be increased
by :
\( \mathbf{A} \cdot 750 K \)
B. \( 500 K \)
c. \( 250 K \)
D. \( 1000 K \)


Name the rays or waves produced by the changes in the nucleus of an atom.
A. X-rays
B. UV rays
c. Gamma rays
D. IR rays


Which of the following imparts violet colouration to the Bunsen burner non-
luminous flame?
\( \mathbf{A} \cdot N a C l \)
в. \( B a C l_{2} \)
c. \( C a C l_{2} \)
D. KCl


A heavy block kept on a frictionless
surface and being pulled by two ropes of
equal mass \( m \) as shown in the figure. At
\( t=0, \) the force on the left rope is
withdraw but the force on the right end
continues to act, Let \( F_{1} \) and \( F_{2} \) be the
magnitudes of the force by the right
rope and the left rope on the block respectively.
\( \mathbf{A} \cdot F_{1}=F_{2}=F \quad \) for \( t<0 \)
B . \( F_{1}=F_{2}=F+m g \quad \) for \( t<0 \)
C \( \cdot F_{1}=F_{1} \quad F_{2}=F \) for \( t>0 \)
D. \( F_{1}<F_{1} \quad F_{2}=F \) for \( t>0 \)


The slope and y-intercept of the following line are respectively
\( 8 x-4 y-1=0 \)
A \( \cdot \)slope\( =m=\frac{-1}{2} \) and \( y- \) intercept \( =\frac{1}{4} \)
B . slope \( =m=2 \) and \( y- \) intercept \( =-\frac{1}{4} \)
c. slope \( =m=-\frac{1}{2} \) and \( y- \) intercept \( =-\frac{1}{4} \)
D. slope \( =m=\frac{1}{2} \) and \( y- \) intercept \( =\frac{1}{4} \)


For the following cell having a hydrogen
electrode and a normal calomel
electrode, the electromotive force (EMF)
is \( 0.634 \mathrm{V} \) at \( 298 \mathrm{K} \)
\( \boldsymbol{P t}\left[\boldsymbol{H}_{2}(\boldsymbol{1} \boldsymbol{a} \boldsymbol{t m}) \mid \boldsymbol{H}^{+}(\boldsymbol{p} \boldsymbol{H}=\boldsymbol{x}) \|\right. \)
\( \boldsymbol{K} \boldsymbol{C l}(\mathbf{1} \boldsymbol{N})\left|\boldsymbol{H} \boldsymbol{g}_{2} \boldsymbol{C l}_{2}(\boldsymbol{s})\right| \boldsymbol{H} \boldsymbol{g}(l) \)
If \( E^{o} \) of \( C l^{-}\left|H g_{2} C l_{2}\right| H g \) is \( 0.28 \mathrm{V} \), then
select the incorrect statements.
This question has multiple correct options
A. The cell reaction is \( H_{2}(s)+2 H g(l)+2 C l^{-}(g) \rightarrow \)
\( 2 H^{+}(l)+H g_{2} C l_{2}(s) \)
B. The value of \( x \) is 5
c. The value of \( x \) is 6
D. If semi-normal calomel cathode is used in place of normal cathode cell, then the emf will decrease


The length of a potentiometer wire is \( 1200 \mathrm{cm} \) and it carries a current of
\( 60 m A . \) For cell of emf \( 5 V \) and internal
resistance of \( 20 \Omega \), the null point on it is
found to be at \( 1000 \mathrm{cm} . \) The resistance
of whole wire is:
A . \( 60 \Omega \)
в. \( 100 \Omega \)
\( c .80 \Omega \)
D. \( 120 \Omega \)


The following are the marks of 9 students in a class:
19,26,29,28,31,35,36,37,48
Find the median of these marks.


Two vessels \( A \) and \( B \) have same base
area. Equal volumes of a liquid are poured in the two vessels to different
heights \( h_{A} \) and \( h_{B}\left(>h_{A}\right) . \) In which
vessel, the force on the base of vessel will be more.


The value of \( \sqrt{2} \) in correct significant
digits is :
A .1 .414
B. 1.4
\( c \cdot 1.0 \)
\( D \)


A peptide hormone is:
A. estrone
B. testosterone
c. insulin
D. corticoid


Two coils have a mutual inductance
\( 0.55 H . \) The current changes in the first
coil according to equation \( \boldsymbol{I}=\boldsymbol{I}_{0} \sin \omega \boldsymbol{t} \)
where, \( I_{0}=10 A \) and \( \omega=100 \pi r a d / s \)
The maximum value of emf in the
second coil is
A . \( 2 \pi \)
в. \( 5 \pi \)
c. \( \pi \)
D. \( 4 \pi \)


Which of the following is one of the postulates of Rutherford's theory?
A. Electrons continuously lose energy
B. Electrons move in a spiral path around the nucleus
c. Electrons revolve in a specific path around the nucleus
D. Electrons revolve in a stationary orbit


In fructofuranose, OH group of which
carbon adds to \( >\boldsymbol{C}=\boldsymbol{O} \) group?
A. \( C_{3} \)
в. \( C_{4} \)
c. \( C_{5} \)
D. \( C_{2} \)


A substance which decomposes at or below its boiling point cannot be purified by? This question has multiple correct options
A. Steam distillation
B. Simple distillation
c. Fractional distillation
D. Distillation under reduced pressure


A qualitative analysis test for \( M n^{2+} \)
involves its oxidation to \( M n O_{4}^{-} \) in
acidic solution by sodium bismuthate,
\( N a B i O_{3} . \) The bisulphate ion is reduced
to \( B i^{3 i} . \) What is a balanced equation for
this test?
A \( \cdot B i O_{3}^{-2}+M n^{2+}+H^{+} \rightarrow M n O_{4}^{-}+B i^{3+}+H_{2} O \)
B. \( 5 B i O_{3}^{-}+2 M n^{2+}+7 H^{+} \rightarrow 2 M n O_{4}^{-}+5 B i^{3+}+7 O H \)
C. \( 5 B i O_{3}^{-}+2 M n^{2+}+14 H^{+} \rightarrow 2 M n O_{4}^{-}+5 B i^{3+}+7 H_{2} O \)
D. None of these


The most suitable method of separation of equal \( (1: 1) \) mixture of ortho-
nitrophenol and para-nitrophenol is:
A. Crystallisation
B. Distillation
c. Sublimation
D. chromatography


If the pressure in a closed vessle is
reduced by drawing out some gas the mean-free path of molecules
A. losing their kinetic energy
B. sticking to the walls
c. changing their momenta due to collision with the walls
D. getting accelerated towards the wall


If the roots of \( a x^{3}+b x^{2}+c x+d=0 \)
are in H.P., then the roots of \( d x^{3}-c x^{2}+ \)
\( b x-a=0 \) are in
A. A.P
в. с.
c. н.
D. A.G.P


If equal volume of \( B a C l_{2} \) and \( N a F \) solutions are mixed, which of these
combination will give a precipitate? \( \boldsymbol{K}_{s p} \) of \( \boldsymbol{B a} \boldsymbol{F}_{2}=\mathbf{1 . 7} \times \mathbf{1 0}^{-\mathbf{7}} \)


Points \( X \& Y \) are taken on the sides QR
\& RS respectively of a parallelogram \( \mathrm{PQRS}, \) so that \( \boldsymbol{Q} \overrightarrow{\boldsymbol{X}}=4 \overrightarrow{\boldsymbol{X}} \boldsymbol{R} \& \overrightarrow{\boldsymbol{R} \boldsymbol{Y}}= \)
\( 4 \vec{Y} \) S. The line \( X Y \) cuts the line \( P R \) at \( Z \) Prove that \( \overrightarrow{P Z}=\left(\frac{21}{25}\right) \overrightarrow{P R} \)


Complete the following statement. All İsotopes of Uranium have
A. the same atomic number and the same mass number.
B. different atomic numbers but the same mass number.
c. different atomic numbers and different mass
numbers.
D. the same atomic number but different mass numbers.
E. no electrons.


\( E_{1}, E_{2}, E_{3} \) are the emf values of the
three galvanic cells respectively.
(i) \( Z n\left|Z n_{1 M}^{2+}\right|\left|C u_{0.1 M}^{2+}\right| C u \)
\( (\text { ii }) Z n\left|Z n_{1 M}^{2+}\right|\left|C u_{1 M}^{2+}\right| C u \)
(iii) \( Z n\left|Z n_{0.1 M}^{2+} \| C u_{1 M}^{2+}\right| C u \)
Which one of the following is true?
A \( . E_{2}>E_{3}>E_{1} \)
в. \( E_{3}>E_{2}>E_{1} \)
c. \( E_{1}>E_{2}>E_{3} \)
D. \( E_{1}>E_{3}>E_{2} \)


\( \operatorname{Let} D_{1}=\left|\begin{array}{ccc}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{a}+\boldsymbol{b} \\ \boldsymbol{c} & \boldsymbol{d} & \boldsymbol{c}+\boldsymbol{d} \\ \boldsymbol{a} & \boldsymbol{b} & \boldsymbol{a}-\boldsymbol{b}\end{array}\right| \) and \( D_{2}= \)
\( \left|\begin{array}{ccc}\boldsymbol{a} & \boldsymbol{c} & \boldsymbol{a}+\boldsymbol{c} \\ \boldsymbol{b} & \boldsymbol{d} & \boldsymbol{b}+\boldsymbol{d} \\ \boldsymbol{a} & \boldsymbol{c} & \boldsymbol{a}+\boldsymbol{b}+\boldsymbol{c}\end{array}\right| \) then the value of \( \frac{D_{1}}{D_{2}} \)
where \( b \neq 0 \) and \( a d \neq b c, \) is
A . -2
B. 0
\( c \cdot-2 b \)
D. \( 2 b \)


A beam of light of wavelength 600 nm
from a distant source falls on a single slit \( 1 \mathrm{mm} \) wide and the resulting diffraction pattern is observed on a screen \( 2 \mathrm{m} \) away. The distance between the first dark fringes on either side of the central bright fringe is?
A . \( 1.2 \mathrm{cm} \)
B. \( 1.2 \mathrm{mm} \)
\( c .2 .4 \mathrm{cm} \)
D. \( 2.4 \mathrm{mm} \)


What is magnus effect?


A rifle bullet loses \( 1 / 20 \) th of its velocity in passing through a plank. What will be the least number of such planks required to just stop the bullet?


If the function \( f(x)=x^{3}-6 a x^{2}+5 x \)
satisfies the conditions of Lagrange's mean theorem for the interval [1,2] and the tangent to the curve \( y=f(x) \) at
\( \boldsymbol{x}=\mathbf{7} / \mathbf{4} \) is parallel to the chord joining
the points of intersection of the curve
with the ordinates \( x=1 \) and \( x=2 \)
Then the value of a is?
\( \mathbf{A} \cdot 35 / 16 \)
B. \( 35 / 48 \)
c. \( 7 / 16 \)
D. \( 5 / 16 \)


Pulling of a cart/tram is an example of
A . Resultant force
B. Gravitational force
c. contact force
D. Action at a distance force


\( \frac{\sin A}{1+\cos A}+\frac{\sin A}{1-\cos A} \) is equal to
\( A \cdot \sin A \)
B. \( 2 \operatorname{cosec} A \)
\( c \cdot \cos A \)
D. None of these


At a given instant of time the position vector of a particle moving in a circle with a velocity \( 3 \hat{i}-4 \hat{j}+5 \hat{k} \) is \( \hat{i}+9 \hat{j}- \)
8 \( \hat{k} \). It's angular velocity at that time is
A \( \cdot \frac{(13 \hat{i}-29 \hat{j}-31 \hat{k})}{\sqrt{146}} \)
B. \( \frac{(13 \hat{i}-29 \hat{j}-31 \hat{k})}{146} \)
\( \frac{(13 \hat{i}+29 \hat{j}-31 \hat{k})}{\sqrt{146}} \)
D. \( \frac{(13 \hat{i}+29 \hat{j}+31 \hat{k})}{146} \)


Find the value of the following modulus:
\( |-11|-|3| \)


Two players \( A \) and \( B \) are competing at a trivia quiz game involving a series of questions. On any individual question,
the probabilities that \( A \) and \( B \) give the correct answer are \( \alpha \) and \( \beta \) respectively,
for all questions, with outcomes for different questions being independent. The game finishes when a player wins by answering a question correctly. Compute the probability that A wins if B answers the first question.
A \( \cdot \frac{\alpha}{1-(1-\alpha)(1-\beta)} \)
в. \( \frac{(1-\beta)}{1-(\alpha)(\beta)} \)
c. \( \frac{(1-\beta) \alpha}{1-(1-\alpha)(1-\beta)} \)
D. none of these


The angle subtended at the point (1,2,3) by the points \( P(2,4,5) \) and \( Q(3,3,1) \) is
A \( \cdot 90^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 30^{\circ} \)
D. \( 0^{\circ} \)
\( E \cdot 45^{\circ} \)


Assertion
The Sl unit of weight is newton.
Reason
Weight is the force of gravity with which
a body is attracted towards the earth.
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 iodide content of a solution was
determined by titration with cerium (IV) sulphate in the presence of \( \boldsymbol{H} \boldsymbol{C l} \), in
which \( I^{-} \) is converted to \( I_{2} . A 250 \mathrm{ml} \)
sample of the solution required \( 20 \mathrm{ml} \) of
\( 0.05 N C e^{4+} \) solution. What is the
iodide concentration in the original solution in \( g / L ? \)
A. 0.508
B. 2.032
c. 0.762
D. 0.127


A current of \( 300 \mathrm{mA} \) is made to flow
through a \( 6 k \Omega \) resistor. What is the potential difference across the resistor?
A . \( 1800 v \)
B. 50v
c. \( 0.02 v \)
D. 500v


Nitric acid is manufactured by the Ostwald process in which nitrogen dioxide reacts with water. The reaction
is as follows:
\( \boldsymbol{p} \boldsymbol{N} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \rightarrow \)
\( \boldsymbol{q} \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{N} \boldsymbol{O} \)
Find the value of \( \boldsymbol{p}+\boldsymbol{q} \)
A . 8
B. 4
\( c .5 \)
D.


Simplify: \( \sin ^{-1}(2 x \sqrt{1-x^{2}})= \)
\( \dots . .\left(|x|<\frac{1}{\sqrt{2}}\right) \)


A polygon which has no diagonal.
A. Quadrilateral
B. Heptagon
c. Triangle
D. Pentagon


Which of the following is mostly easily
cleaved by \( \boldsymbol{H} \boldsymbol{B r} \) ?
\( A \)
\( B \)
\( c \)
D.


Write the number of decimal place in
\( \mathbf{8 2 3 5 . 4 0 3} \)


A coil of inductance \( 0.50 H \) and
resistance \( 100 \Omega \) is connected to a
\( 240 V, 50 H z \) ac supply. The maximum current in the coil is given as \( \frac{x}{100} A \) Find \( x \)


Meenakshi gets \( 16 \frac{2}{3} \% \) simple interest on her fixed deposits. Her interest will be equal to the deposit in
years
\( A \cdot 8 \)
B. 8.5
\( c \cdot 6 \)
D. 6.25


Significance of classification is
A. It makes the study of such a wide variety of organisms
easy
B. It projects before us a good picture of all life forms at a glance
C. It helps us understand the inter-relationship among different groups of organisms
D. All of the above


The balanced equation in basic
medium is :
\( \boldsymbol{C l O}_{2}+\boldsymbol{S b O}_{2}^{-} \rightarrow \boldsymbol{C l O}_{2}^{-}+\boldsymbol{S b}(\boldsymbol{O H})_{6}^{-} \)
A \( \cdot 2 C l O_{2}+S b O_{2}^{-}+2 O H^{-}+2 H_{2} O \rightarrow 2 C l O_{2}^{-}+ \)
\( S b(O H)_{6} \)
B . \( 2 C l O_{2}+5 S b O_{2}^{-}+2 O H^{-}+3 H_{2} O \rightarrow 2 C l O_{2}^{-}+ \)
\( 2 S b(O H)_{6} \)
\( \mathrm{c} \cdot 2 \mathrm{ClO}_{2}+\mathrm{SbO}_{2}^{-}+3 \mathrm{OH}^{-}+4 \mathrm{H}_{2} \mathrm{O} \rightarrow 2 \mathrm{ClO}_{2}^{-}+ \)
\( 3 S b(O H)_{6} \)
D. None of these


Solve: \( \boldsymbol{x} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}-\boldsymbol{y}+\boldsymbol{x} \sin \left(\frac{\boldsymbol{y}}{\boldsymbol{x}}\right)=\mathbf{0} \)


The power generated in a windmill:
A. is more in rainy season since damp air would make more air mass hitting the blades
B. depends on the height of the tower
C. depends on wind velocity
D. can be increased by planting tall trees close to the tower


Write about what a prokaryotic cell lacks?


Statement A: Density of nucleus is independent of its mass number Statement B: Beryllium is used as a
moderator in nuclear reactors
A. Both A and B are correct
B. Both A and B are wrong
C. A is correct,B is wrong
D. A is wrong,B is correct


Assertion:Presently, the global atmosphe
re is warming up.

Reason :The depletion of stratospheric oz
one layer has resulted in increase in ultra
violet radiations reaching the earth.
A. If both the assertion and the reason are true and the
reason is a correct explanation of the assertion
B. If both the assertion and reason are true but the reason is not a correct explanation of the assertion
C. If the assertion is true but the reason is false
D. If both the assertion and reason are false
E. If the assertion is false but reason is true


For a system \( C(s)+O_{2}(g)=C O_{2}(g) \)
which of the following is correct?
\( \mathbf{A} \cdot \Delta H=\triangle E \)
в. \( \triangle H>\triangle E \)
c. \( \triangle H<\triangle E \)
D. \( \triangle H=0 \)


In the reaction, \( X \) is:
\( \mathrm{CH}_{3} \mathrm{C}=\mathrm{C}-\mathrm{CH}_{3} \frac{(\mathrm{i}) X}{(\mathrm{ij}) 2 \mathrm{o} / \mathrm{H}_{2} \mathrm{O}} \rightarrow \mathrm{CH}_{3}-\underset{\mathrm{O}}{\mathrm{I}}-\mathrm{C}_{\mathrm{O}}-\mathrm{CH}_{3} \)
A \( . H N O_{3} \)
в. \( O_{2} \)
\( c \cdot O_{3} \)
D. \( K M n O_{4} \)


(i) On what factor does the position of the centre of gravity of a body depend?
(ii) What is the S.l.unit of the moment
of force?


Set up an experiment to demonstrate
root pressure.


n the figure \( \angle B A C=75^{\circ}, \angle A B C= \)
\( 35^{\circ} . \) Find the measures of \( \angle B A Z \)


For \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3} \) and \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4}, \) the correct
choice is:
A \( \cdot H_{3} P O_{3} \) is dibasic and reducing
B. \( H_{3} P O_{3} \) is dibasic and non-reducing
\( \mathrm{c} \cdot H_{3} P O_{4} \) is tribasic and reducing
D. \( H_{3} P O_{3} \) is tribasic and non-reducing


The dot product of a vector with vectors \( \hat{\mathbf{i}}+\hat{\mathbf{j}}-\mathbf{3} \hat{\mathbf{k}}, \hat{\mathbf{i}}+\mathbf{3} \hat{\mathbf{j}}-\mathbf{2} \hat{\mathbf{k}}, \mathbf{2} \hat{\mathbf{i}}+\hat{\mathbf{j}}+\mathbf{4} k \) are
0,5 and 8 respectively. Find the vector


Using differentials, find the sum of digits approximate value of the following up to 3 places of decimal. \( \sqrt{0.6} \)


Sieve tube is component of
A. Xylem
B. Cortex
c. Phloem
D. Both of xylem and phloem


\( \operatorname{et} \Delta_{1}=\left|\begin{array}{ccc}x & y & x+y \\ y & x+y & x \\ x+y & x & y\end{array}\right| \)
\( \boldsymbol{\Delta}_{2}=\left|\begin{array}{ccc}\mathbf{1} & \boldsymbol{x} & \boldsymbol{y} \\ \mathbf{1} & \boldsymbol{x}+\boldsymbol{y} & \boldsymbol{y} \\ \mathbf{1} & \boldsymbol{x} & \boldsymbol{x}+\boldsymbol{y}\end{array}\right| \)
\( \boldsymbol{\Delta}_{3}=\left|\begin{array}{ccc}\boldsymbol{x} & \boldsymbol{x}+\boldsymbol{y} & \boldsymbol{x}+\boldsymbol{2} \boldsymbol{y} \\ -\boldsymbol{x} & \boldsymbol{x} & \boldsymbol{0} \\ \boldsymbol{0} & -\boldsymbol{x} & \boldsymbol{x}\end{array}\right| \)
\( \boldsymbol{\Delta}_{4}=\left|\begin{array}{lll}1 & \boldsymbol{x} & \boldsymbol{x}^{2} \\ \mathbf{1} & \boldsymbol{y} & \boldsymbol{y}^{2} \\ \mathbf{1} & \mathbf{1} & \mathbf{1}\end{array}\right| \)
then


Statement - I: The mixing of two completely miscible liquid. A and B showing positive deviation from Raoult's law is followed by an
absorption of heat Statement - ll: The A- B molecular
interaction forces are stronger than the
A-A or B-B molecular interaction forces.
A. Statement-lis true, Statement- - 2 is true; Statement 2 is a correct explanation for Statement- -
B. Statement-1 is true, Statement - 2 is true; Statement 2 is not a correct explanation for Statement - -
c. statement-lis true, Statement- - 2 is false
D. Statement-lis false, Statement- - 2 is true


The tension in a string holding a solid block below the surface of a liquid
(where \( \rho_{\text {liquid}}>\rho_{\text {block}} \) ) as in shown in
the figure is \( \boldsymbol{T} \) when the system is at rest.Then what will be the tension in the
string if the system has upward acceleration \( a \) ?
\( ^{\mathbf{A}} \cdot T\left(1-\frac{a}{g}\right) \)
в. \( T\left(1+\frac{a}{g}\right) \)
\( ^{\mathbf{c}} \cdot T\left(\frac{a}{g}-1\right) \)
D. \( \frac{a}{a} \)


The degree of a polynomial \( 2 x^{5}-5 x^{3}- \)
\( 10 x+9 \) is
A . 5
B. 3
c. 1
D.


An electric current can produce
A. heating effect only.
B. chemical effect only.
C . magnetic effect only.
D. chemical, heating, and magnetic effects.


Acid rain is caused by
A. emission of gases from industries
B. air pollutants
C. both (A) and (B)
D. none of above


If \( x^{m} \cdot y^{n}=(x+y)^{m+n}, \) then \( \frac{d y}{d x} \) is \( ? \)
A. \( \frac{y}{x} \)
в. \( \frac{x+y}{x y} \)
c. \( x y \)
D. \( \frac{x}{y} \)


Which of the following compounds
cannot be prepared singly by the Wurtz
reaction?
\( \mathbf{A} \cdot C_{2} H_{6} \)
B. \( \left(C H_{3}\right)_{2} C H C H_{3} \)
\( \mathbf{c} \cdot C H_{3} C H_{2} C H_{2} C H_{3} \)
D. All of the above can be prepared


Number of ways in which 3 boys and 3 girls can be seated on a line where two
particular girls do not want to sit adjacent to a particular boy is equal to
A . 36
B. 72
c. 144
D. 288


Number of one-one functions from A to
B where \( n(A)=4, n(B)=5 \)
A .4
B. 5
\( c \cdot 120 \)
D. 90


A steel wire can support a maximum
load of \( W \) before reaching its elastic limit. How much load can another wire,
made out of identical steel, but with a
radius one half the radius of the first wire, support before reaching its elastic limit.?
\( \mathbf{A} \cdot W \)
в. \( \frac{W}{2} \)
c. \( \frac{w}{4} \)
D. \( 4 W \)


Among the following hydroxides, the one
which has the lowest value of \( \boldsymbol{K}_{s p} \) at
ordinary temperature (about \( 25^{\circ} C \) ) is:
\( \mathbf{A} \cdot M g(O H)_{2} \)
\( \mathbf{B} \cdot C a(O H)_{2} \)
\( \mathbf{c} \cdot B a(O H)_{2} \)
D. \( B e(O H)_{2} \)


Find the acute angle between the lines \( 3 x+y-7=0 \) and \( x+2 y-9=0 \)
A \( \cdot 45^{\circ} \)
B . \( 135^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 120^{\circ} \)


Three closed vessels \( A, B \) and \( C \) are at the
same temperature T and contain gases which obey Maxwell distribution law of
velocities. Vessel A contains \( O_{2}, \) B only \( N_{2} \)
and \( \mathrm{C} \) mixture of equal quantities of \( \mathrm{O}_{2} \)
and \( N_{2} \). If the average speed of \( O_{2} \)
molecules in vessel \( \mathrm{A} \) is \( V_{1} \) and that of \( N_{1} \)
molecules in vessel B is \( V_{2} \), then the
average speed of the \( O_{2} \) molecules in
vessel C is
A \( \cdot \frac{\left(v_{1}+v_{2}\right)}{2} \)
B. \( V_{1} \)
c. \( \sqrt{v_{1} v_{2}} \)
D. None of these


If \( f(x)=x^{2}+2 b x+2 c^{2} \) and \( g(x)= \)
\( -x^{2}-2 c x+b^{2} \) are such that min
\( f(x)>\max g(x), \) then the relation
between \( b \) and \( c \) is
A. no relation
в. \( 0<c<b / 2 \)
C \( \cdot|c|<|b| \sqrt{2} \)
D \( \cdot|c|>|b| \sqrt{2} \)


During binary fusion in Amoeba which of the following organelles is duplicated?
A. Plasma membrane
B. Nucleus
c. Centriole
D. All of these


\( N \) conducting plares are placed face to face as shown in figure. Distance
between any two plates is \( d \). Area of the plates is \( A, \frac{A}{2}, \frac{A}{4}, \frac{A}{8} \dots \frac{A}{2(n-1)} . \) The
equivalent capacitance of the system is


\( \sum_{k=1}^{k=n} \tan ^{-1} \frac{2 k}{2+k^{2}+k^{4}}=\tan ^{-1}\left(\frac{6}{7}\right) \)
then the value of ' \( n \) ' is equal to
A . 2
B. 3
\( c \cdot 4 \)
D. 5


The mineralization of nutrients for
plants can be done by
A. Virus
B. Protozoa
c. Phytoplankton
D. None of the above


The volume of cube is \( 36 \mathrm{cm}^{3} . \) Its
surface area is
A \( \cdot 6(36)^{\frac{3}{2}} \)
B. \( (36)^{\frac{3}{2}} \)
c. \( 6(36)^{\frac{2}{5}} \)
D. None


Reproductive cells (germinal epithelium) are made up of which of the following epithelial tissue?
A. Cuboidal
B. Columnar
c. Squamous
D. Sensory


Percentage of water left in the soil when
a plant begins to wilt is known as
A. Wilting coefficient
B. pH value of soil
c. Field capacity
D. Water holding cpacity


Name the state of matter in which
particles just move randomly because of a very weak force of attraction.


If \( \mathbf{Y}=(x+\sqrt{x^{2}-1})^{m} \) show that
\( \left(x^{2}-1\right) \frac{d^{2} y}{d x^{2}}+x \frac{d y}{d x}=m^{2} y \)


The expression gynoecium is
apocarpous implies that the
A. Gynoecium comprises only one pistil which is fused with the stamen
B. Gynoecium comprises more than one carpel, all of which are free
C. Gynoecium comprises only one carpel which is free
D. Gynoecium comprises more than one carpel which are fused


State whether true or false.
Magnetic lines of force are imaginary lines.
A. True
B. False


In the above reaction if \( A \) is \( N H_{4} C l \) and
\( D \) is \( C O_{2} \) then \( B \& C \) respectively are:
\( (A)+N a O H \rightarrow N a C l+N H_{3}+H_{2} O \)
\( N H_{3}+C O_{2}+H_{2} O \rightarrow(B) \)
(B) \( +N a C l \rightarrow(C)+N H_{4} C l \)
\( (\mathrm{C}) \rightarrow N a_{2} C O_{3}+H_{2} O+(D) \)
A. \( N H_{4} H C O_{3}, N a H C O_{3} \)
в. \( \operatorname{NaHCO}_{3, N H_{4} H C O_{3}} \)
\( \mathrm{c} \cdot_{\left(N H_{4}\right)_{2}} C O_{3}, N a_{2} C O_{3} \)
D. \( \operatorname{Na}_{2} \operatorname{CO}_{3},\left(N H_{4}\right)_{2} C O_{3} \)


Evaluate: \( \sec ^{-1}(-2) \)


The given compound is:
A. 3 -Ethylpent-1, 3-diene
B. 2-Ethylpent-2, 3-diene
c. Pentadiene
D. None of these


Differentiate the given function w.r.t. \( x \)
\( \cos \left(\log x+e^{x}\right), x>0 \)


Evaluate \( : \int_{-x}^{x}(\cos a x-\sin b x)^{2} d x \)


Which of the following utilizes Newton's third law of motion?
A. Archery
B. space rocket
c. venturimeter
D. Internal combustion engine
E. Kite flying


The most stable oxidation state of
Thallium is:
\( A \cdot+1 \)
B. +3
\( c \cdot+4 \)
D. +6


Which shape has the verties (3,2),(0,5),(-3,2) and (0,-1)\( ? \)
A. Rectangle
B. Square
c. Trapezium
D. Rhombus


The isotopic masses of \( _{1}^{2} \mathbf{H} \) and \( _{2}^{4} \mathbf{H e} \) are
\( \mathbf{2 . 0 1 4 1} \) and \( \mathbf{4 . 0 0 2 6} \) amu
respectively. The velocity of light in
vacuum is \( 2.998 \times 10^{8} m / \) sec. The
quantity of energy liberated when two mole of \( _{1}^{2} \mathbf{H} \) undergo fusion to form 1
mole of \( _{2}^{4} \) He is :
A \( \cdot 2.3 \times 10^{12} J \)
В. \( 4.3 \times 10^{12} J \)
c. \( 6.6 \times 10^{12} J \)
D. none of these


Evaluate \( \int \frac{\cos 2 x}{\sqrt{1+\sin 2 x}} d x \)


Which of the following are countably
infinite and uncountably infinte.
(i) Set of natural numbers
(ii) Set of real numbers
A. Both \( (i) \) and \( (i i) \) are uncountably infinite
B. ( \( i \) ) uncountably infinite and
\( (i i) \) countably infinite
C. \( (i) \) countably infinite and \( (i i) \) uncountably infinite
D. Both \( (i) \) and \( (i i) \) are countably infinite


The points \( P, Q, R \) have regular cartesian coordinates
(1,1,-1),(4,1,2) and (-2,1,2)
respectively. Which of the following is
true for the triangle \( P Q R ? \)
A. All the sides have the same length.
в. \( Q R=2 P Q \)
c. Angle \( P Q R \) is a right angle.
D. The area of the triangle is 18 square units.


The sum of \( n \) terms of an \( A P \) is \( 2 n^{2}+n \)
Then 8 th term of the A.P is
A. 31
B. 27
c. 35
D. 39


\( 25 \mathrm{cm}^{3} \) of oxalic acid completely
neutralised \( 0.064 g \) of sodium
hydroxide. Molarity of the oxalic acid solution is :
в. 0.032 м
c. 0.064 м
D. 0.015 М


If \( N \) denote the set of all natural
numbers and \( R \) be the relation on \( N \times \)
\( N \) defined by \( (a, b) R(c, d) . \) if \( a d(b+ \)
\( c)=b c(a+d), \) then \( R \) is
A. Symmetric only
B. Reflexive only
c. Transitive only
D. An equivalence relation


toppr 5
Q Type your question
\( B \)
\( c \)
\( D \)


Assertion STATEMENT-1: If \( \vec{a}, \vec{b}, \vec{c} \) are non coplanar unit vectors equally inclined to one
another at an angle \( \theta, \) then there will
exist three scalar \( p, q, r \) such that \( \vec{a} \times \) \( \overrightarrow{\boldsymbol{b}}+\overrightarrow{\boldsymbol{b}} \times \overrightarrow{\boldsymbol{c}}=\boldsymbol{p} \overrightarrow{\boldsymbol{a}}+\boldsymbol{q} \overrightarrow{\boldsymbol{b}}+\boldsymbol{r} \overrightarrow{\boldsymbol{c}} \)
Reason STATEMENT-2 : \( \overrightarrow{\boldsymbol{a}} \times \overrightarrow{\boldsymbol{b}} \) is a vector
perpendicular to plane containing \( \vec{a} \) and \( \vec{b} \) and \( \vec{b} \times \vec{c} \) is a vector perpendicular to plane containing \( \overrightarrow{\boldsymbol{b}} \) and \( \overrightarrow{\boldsymbol{c}} \) so \( \overrightarrow{\boldsymbol{a}} \times \overrightarrow{\boldsymbol{b}}+\overrightarrow{\boldsymbol{b}} \times \)
\( \vec{c} \) will be non-zero only if \( \vec{a}, \vec{b}, \vec{c} \) are
coplanar.
A. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-
B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
c. Statement-1 is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is True


Primary winding and secondary winding of a transformer has
100 and 300 turns respectively. If its
input power is \( 60 \mathrm{W} \) then output power of the transformer will be
A . 240 \( w \)
B. 180 \( w \)
\( c \cdot 60 w \)
D. 20 W


Find the height of a parallelogram
whose area is \( 54 \mathrm{cm}^{2} \) and the base is
\( 15 \mathrm{cm} \)


\( " F e^{3+} \) is more stable than \( F e^{2+} \)
Answer whether the above statement is
true or false.
If true enter 1 , else enter 0 .


The starting and ending elements of actinides are respectively:
\( \mathbf{A} \cdot T h \) and \( L u \)
B. \( T h \) and \( L r \)
c. \( A c \) and \( L u \)
D. \( A c \) and \( L r \)


Convert the given fractional numbers to
percentage. \( \frac{5}{4} \)


The cost of setting up the type of a magazine is Rs. 1000 , the cost of running the printing machine is Rs. 120 per 100 copies, the cost of paper, ink and so on is 60 paise per copy. The magazines are sold at Rs. 2.75 each.
900 copies are printed, but only 784 copies are sole. What is the sum to be obtained from advertisements to give a
profit of \( 10 \% \) on the cost?
A. Rs. 730
B. Rs. 720
c. Rs. 726
D. Rs. 736


The product of \( -3 x y z, 6 x^{2} y z^{3}, \) and
\( -4 x^{3} z^{2} \) is
\( \mathbf{A} \cdot 64 x^{6} y^{2} z^{6} \)
B. \( -64 x^{6} y^{2} z^{6} \)
C \( .-42 x^{6} y^{2} z^{6} \)
D. \( 72 x^{6} y^{2} z^{6} \)


Calculate oxidation number of central
\( \operatorname{atom} \operatorname{in}\left[\boldsymbol{K}_{4}\left[\boldsymbol{F} e(\boldsymbol{C} \boldsymbol{N})_{6}\right]\right. \)


Assertion
The excess pressure above atmospheric
pressure is usually called as gauge
pressure.
Reason
Gauge pressure = (Total pressure) (atmospheric pressure)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The standard Gibbs energy change at \( 300 K \) for the reaction \( 2 A \leftrightharpoons B+C \) is
\( 2494.2 J . \) At a given time, the composition of the reaction mixture is \( [A]=\frac{1}{2},[B]=2 \) and \( [C]=\frac{1}{2} . \) The reaction
proceeds in the \( :[R= \) \( \mathbf{8 . 3 1 4 J} / \mathbf{K} / \mathbf{m o l}, e=\mathbf{2 . 7 1 8} \)
A . forward direction because \( Q>K_{e} \)
B. reverse direction because \( Q>K_{e} \)
C. forward direction because \( Q<K_{e} \)
D. reverse direction because \( Q<K_{e} \)


Assertion
Heterophylly is seen in many aquatic
plants
Reason
Aquatic plants survive in two different
conditions of the environment
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


\( \frac{1^{2}}{1}+\frac{1^{2}+2^{2}}{1+2}+\frac{1^{2}+2^{2}+3^{2}}{1+2+3}+\ldots+n \)
terms \( = \)
A. \( \frac{n(n+3)}{4} \)
в. \( \frac{n(n+3)}{5} \)
c. \( \frac{n(n+2)}{3} \)
D. \( \frac{n(n+5)}{6} \)


Its basic strength is \( 10^{10} \) more than 1
dimethyl amino naphthalene due to:
A. resonance
B. steric inhibitation of resonance
c. ortho effect
D. hyperconjugation


What is true regarding the following
acid catalyzed esterification (Fischer)
reaction ?
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C O O H}+\boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{O H} \stackrel{\boldsymbol{H}^{+}}{\longrightarrow} \)
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C O O C}_{2} \boldsymbol{H}_{5} \)
This question has multiple correct options
A. The reaction involves production on \( s p^{3} \) -oxygen of acid in the first step
B. The reaction involves protonation on \( s p^{2} \) -oxygen of acid followed by formation of acylium ion \( \left(R O C^{+}\right) \) in the first step
C. The slowest step of reaction is the nucleophilic attack of alcohol on \( s p^{2} \) carbon of acid
D. Alcohol undergoes protonation in the first step


A condenser of \( 250 \mu F \) is connected in
parallel to a cell of inductance \( 0.16 \mathrm{mH} \) while its effective resistance is while
its. Determine the resonant frequency.
A \( \cdot 9 \times 10^{4} \mathrm{Hz} \)
B . \( 16 \times 10^{7} \) Н \( _{2} \)
c. \( 8 \times 10^{5} \) Н \( z \)
\( \mathbf{D} \cdot 9 \times 10^{3} \mathrm{Hz} \)


Mesophyll development in leaves is stimulated by
A. Rhizocaline
B. Caulocaline
c. Phyllocaline
D. All of the above


A dealer makes a profit of \( 9 \% \) by
selling a camera for \( R s .3379 . \) Find the
cost price of the camera?


Five cells each of internal resistance
\( 0.2 \Omega \) and \( \mathrm{emf} 2 V \) are connected in
series with a resistance of \( 4 \Omega \).The
current through the external resistance
is
A. \( 4 A \)
в. \( 2 A \)
\( c \cdot 1 A \)
D. \( 0.5 A \)


Which one of the following is an example of hydrosol?
A. starch sol
B. Gold sol
c. Both (a) and (b)
D. None of these


The ionization energy of the ground state of hydrogen atom is \( 2.18 \times 10^{-18} \)
J. The energy of an electron in its second orbit would be:
В. \( -2.18 \times 10^{-18} \mathrm{J} \)
c. \( -4.36 \times 10^{-18} \mathrm{J} \)
D. \( -5.45 \times 10^{-19} \mathrm{J} \)


If the sum of the lengths of the hypothesis and another side of a right angle is given, show that the area of the triangle is maximum when the angle
between these sides is \( \frac{\pi}{3} \)


Conifers differ from grasses, in the
A. Formation of endosperm before fertilization
B. Production of seeds from ovules
C. Lack of xylem tracheids
D. Absence of pollen tubes


A stationary ball weighing \( 0.25 k g \) acquires a speed of \( 10 m / s \) when hit by a hockey stick. The impulse imparted to the ball is
\( \mathbf{A} \cdot 2.5 N s \)
B. \( 2.0 N s \)
c. \( 1.5 N s \)
D. \( 0.5 N s \)


The stability of the hydrides follows the
order.
A. \( N H_{3}>P H_{3}>A s H_{3}>S b H_{3} \)
B. \( N H_{3}<P H_{3}<S b H_{3}<A s H_{3} \)
c. \( P H_{3}>N H_{3}>A s H_{3}>S b H_{3} \)
D. \( A s H_{3}>N H_{3}>P H_{3}>S b H_{3} \)


Which one of the following is the most durable wood?
A. Shorea robusta
B. Cedrus deodara
c. Dalbergia sisso
D. Tectona grandis


Choose the correct answers from the
alternatives given :
An exergonic reaction is
A. a spontaneous reaction in which energy is given off
B. an uphill reaction requiring input of energy
c. an anaerobic reaction
D. an oxidation reaction


Which of the following is a quadratic
equation?
\( \mathbf{A} \cdot x^{\frac{1}{2}}+2 x+3=0 \)
B. \( \left(x^{2}-1\right)(x+4)=x^{2}+1 \)
C \( \cdot x^{2}-3 x+5=0 \)
D. \( \left(2 x^{2}+1\right)(3 x-4)=6 x^{2}+3 \)


What happens when calcium carbide is treated with water?
A. Ethane is formed
B. Methane and ethane are formed.
c. Ethyne is formed.
D. Ethene and ethyne are formed


Two small spheres of masses \( 10 \mathrm{kg} \) and \( 30 \mathrm{kg} \) are joined by a rod of length \( 0.5 \mathrm{m} \) and of negligible mass. The M.I. of the system about a normal axis through centre of mass of the system is
A \( \cdot 1.875 \mathrm{kgm}^{2} \)
B. 2.45 \( k g m^{2} \)
c. \( 0.75 \mathrm{kgm}^{2} \)
D. \( 1.75 \mathrm{kgm}^{2} \)


A device used for measuring small
currents due to changing magnetic field is known as:
A. galvanometer
B. ammeter
c. potentiometer
D. voltmeter


For the reaction \( 2 A+B \rightarrow C+ \)
\( D,-\frac{\boldsymbol{d}[\boldsymbol{A}]}{\boldsymbol{d} \boldsymbol{t}}=\boldsymbol{k}[\boldsymbol{A}]^{2}[\boldsymbol{B}] . \) The expression
for \( \frac{-\boldsymbol{d}[\boldsymbol{B}]}{\boldsymbol{d} \boldsymbol{t}} \) will be:
\( \mathbf{A} \cdot K[A]^{2}[B] \)
B . \( 1 / 2 K[A]^{2}[B] \)
\( \mathbf{c} \cdot K[A]^{2}[2 B] \)
D. \( K[2 A]^{2}[B] \)


Match the List I and List
List I
(i)
(A)The limits of pH values of buffer 0
solution 10
(B) Concentration of \( \left[H_{3} O^{+}\right] \) in \( 0.001 M \)
\( B a(O H)_{2} \) Equal
(C) The buffer capacity of a solution is maximum when concentration of salt to 10 that of acid is
(D) Ionic product of water is \( p K_{a} \pm \) 1
A \( . A-(i v) ; B-(i i) ; C-(i) ; D-(i i i) \)
B. A-(iv); B-(i); C-(iii); D-(ii)
C \( . A-(i) ; B-(i v) ; C-(i i) ; D-(i i i) \)
D. A-(iv); B-(i); C-(ii); D-(iii)


Quinaine is obtained from-
A. Bark
B. Fruit
c. Leaves
D. Roots


What is self inductance? Name the
factors on which self inductance
depends.


Which one of the following character dif ferentiate man from other mammals?
A. Superior intelligence
B. Power of speech
c. social life
D. Greater cranial capacity


\( 0.16 g \) of \( N_{2} H_{4} \) are dissolved in water
and the total volume made up to
500 \( m L \). Calculate the percentage of
\( N_{2} H_{4} \) that has reached with water at
this dilution. The \( K_{b} \) for \( N_{2} H_{4} \) is \( 4.0 \times \)
\( \mathbf{1 0}^{-6} \boldsymbol{M} \)


In the figure shown a planet moves in an
elliptical orbit around the sun. Compare
the speeds, linear and angular
momenta at the points \( A \) and \( B \)


Lanthanoids contraction is due to
increase in:
A. shielding by \( f \) -electrons
B. atomic number.
c. effective nuclear charge
D. size of 4 f-orbital.


The BOD value of municipal sewage is:
A. \( 1-5 \) ppm
B. 5-10 ppm
c. \( 50-100 \) ppm
D. 100-4000 ppm


One of the rectangular components of a force of \( 50 N \) is \( 30 N . \) The other
rectangular component will be
A . \( 40 N \)
в. \( 30 N \)
\( c .35 N \)
D. \( 45 N \)


If the emf of the battery in primary circuit of a potetimeter is doubled the value of potential gradient will:-
A. Remain Uncharged
B. Be halved
c. Be doubled
D. None of these


When the polynomial \( \left[6 x^{4}+8 x^{3}+\right. \)
\( \left.29 x^{2}+21 x+7\right] \) is divided by another
polynomial \( \left[3 x^{2}+4 x+1\right] \) the
remainder is in the form of \( (a x+b) \)
Find \( a \) and \( b \)


There are 2 brothers \( A \) and
B. Probability that \( A \) will pass in exam is \( 3 / 5 \) and that
B will pass in exam is \( 5 / 8 . \) What will be
the probability that only one will pass in the exam?


A body of 0.5 kg moves along the positive x-axis under the influence of a
varying force \( F \) (in Newtons) as shown
below.
f the speed of the object at \( x=4 \) m is
\( 3.16 \mathrm{m} . \mathrm{s}^{-1} \) then its speed at \( \mathrm{x}=8 \mathrm{m} \) is
A. \( 3.16 m \cdot s^{-1} \)
B. \( 9.3 m \cdot s^{-1} \)
\( c \cdot 8 m \cdot s^{-1} \)
D. \( 6.8 m \cdot s^{-1} \)


A circular coil of 100 turns has an
effective radius of \( 0.05 \mathrm{m} \) and carries a
current of 0.1 A. How much work is
required to turn it in an external magnetic field of \( 1.5 W b m^{-2} \) through
\( 180^{\circ} \) about an axis perpendicular to the magnetic field?


Which of the following two substances react to produce blister copper?
\( \mathbf{A} \cdot C u_{2} S_{(s)} \) and \( C u_{2} O_{(s)} \)
B. \( C u_{2} O_{(s)} \) and \( F e S_{S_{s}} \)
c. \( C u_{2} S_{(s)} \) and \( O_{2(g)} \)
D. \( C u_{2} S_{(s)} \) and \( F e S_{2(s)} \)


The, sum of the radius of the base and
the height of a solid cylinder is 37 metres. If the total surface area of the
cylinder be 1628 sq. metres, its volume is :
A \( .3180 m^{3} \)
в. \( 4620 m^{3} \)
\( c .5240 m^{3} \)
D. None of these


Assertion
\( P_{4} O_{10} \) is not used to dry \( N H_{3} \)
Reason
\( P_{4} O_{10} \) is acidic and \( N H_{3} \) is basic.
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


Find whether the following statement
are true or false.
In a rational number of the form \( \frac{\boldsymbol{p}}{\boldsymbol{q}}, \boldsymbol{q} \)
must be a non zero integer.
A. True
B. False


How many neutrons result from the
following fission reaction?
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
D. 4
\( E .5 \)


2-Methyl propane on monochlorination under photochemical condition give:
A. 2 -chloro-2-methylpropane as major product
B. (1:1) mixture of 1-chloro-2-methylpropane and 2chloro-2-methylpropane
C. 1 -chloro-2-methylpropane as a major product
D. \( (1: 9) \) mixture of 1 -chloro- 2 -methylpropane


When will the quadratic equation
\( \boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{b} \boldsymbol{x}+\boldsymbol{c}=\boldsymbol{0} \) NOT have Real Roots?
A. \( b^{2}-4 a c \geq 0 \)
B . \( b^{2}-4 a c>0 \)
c. \( b^{2}-4 a c<0 \)
D. None of these


A motorcyclist executes a horizontal loop at a speed of \( 65 k m / h \) while
himself making an angle of \( 12^{\circ} \) with the
horizontal. What is the radius of the
\( \operatorname{loop} ?(\operatorname{in} m) \)
\( \mathbf{A} \cdot 123.6 \)
B. 156.6
c. 156.3
D. 174.3


Enthalpy change during a reaction does
not depend upon
A. conditions of a reaction
B. initial and final concentration
C . physical states of reactants and products
D. number of steps in the reaction


If \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{4} & \mathbf{2} \\ \mathbf{- 1} & \mathbf{1}\end{array}\right], \) then \( (\boldsymbol{A}-\mathbf{2} \boldsymbol{I})(\boldsymbol{A}-\mathbf{3} \boldsymbol{I}) \)
equals-
\( \mathbf{A} \cdot \mathbf{0} \)
в.
c. \( I \)
D. \( 5 I \)


If the equation to the locus of points equidistant from the points (-2,3),(6,-5) is \( a x+b y+c=0 \)
where \( a>0 \) then, the ascending order
of \( a, b, c \) is
A. \( a, b, c \)
в. \( c, b, a \)
c. \( b, c, a \)
D. \( a, c, b \)


The decreasing order for acidic strength
¡s:
\( \mathbf{A} \cdot N O_{2} C H_{2} C O O H>N C C H_{2} C O O H> \)
\( F C H_{2} C O O H>C l C H_{2} C O O H \)
B \( \cdot F C H_{2} C O O H>N C C H_{2} C O O H> \)
\( N O_{2} C H C O O H>C l C H_{2} C O O H \)
\( \mathrm{c} \cdot \mathrm{N} \mathrm{O}_{2} \mathrm{CH}_{2} \mathrm{COOH}>\mathrm{FCH}_{2} \mathrm{COOH}> \)
\( C N C H_{2} C O O H>C l C H_{2} C O O H \)
D. \( C N C H_{2} C O O H>O_{2} N C H_{2} C O O H> \)
\( F C H_{2} C O O H>C l C H_{2} C O O H \)


Which of the following are governed by
emulsion formation?
This question has multiple correct options
A. Preparation of food stuffs.
B. Food digestion in intestine
c. Preparation of many cosmetic products.
D. Process of cementation


Write any two uses and two properties
of covalent compounds.


\( \operatorname{Let} \cos ^{-1}\left(4 x^{3}-3 x\right)=a+b \cos ^{-1} x \)
\( x \in\left[-\frac{1}{2}, \frac{1}{2}\right], \) then the principal value of \( \sin ^{-1}\left(\sin \frac{a}{b}\right) \) is
\( A \cdot-\frac{\pi}{3} \)
в.
\( c \cdot-\frac{\pi}{6} \)
D. None of these


Which of the followings are intensive
properties? Temperature, Mass, Volume, Boiling point


Let \( P(2,-4) \) and \( Q(3,1) \) be two given points. Let \( R(x, y) \) be a point such that \( (x-2)(x-3)+(y-1)(y+4)=0 \)
area of \( \Delta P Q R \) is \( \frac{13}{2}, \) then the number
of possible positions of \( \boldsymbol{R} \) are
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
\( D \)


\( |f| Z \mid=2 \) and \( \arg (Z)=\frac{\pi}{4} \) then write \( Z \)


Hair cream is an example of
A . gel
B. sol
c. aeroso
D. emulsion


What types of bonds is/are present in each of the following molecule(s)? Calcium chloride
A. Covalent
B. lonic
c. Both \( A \& B \)
D. Neither A nor B


If \( \overrightarrow{\boldsymbol{A}}=\boldsymbol{i}-\boldsymbol{j}, \overrightarrow{\boldsymbol{B}}=\boldsymbol{i}+\boldsymbol{j}+\boldsymbol{k} \) are two
vectors and \( \vec{C} \) is another vector such that \( \vec{A} \times \vec{C}+\vec{B}=\overrightarrow{0} \) and \( \vec{A} \cdot \vec{C}=0, \) then
\( |\vec{C}|^{2}= \)
A \( \cdot \frac{3}{2} \)
в. 8
c. \( \frac{19}{2} \)
D. \( \frac{17}{2} \)


Ray optics is valid when characteristic dimensions are
A. of the same order as the wavelength of light
B. much smaller than the wavelength of light
c. much larger than the wavelength of light
D. of the order of \( 1 \mathrm{mm} \)


The graph between velocity and position
for a damped oscillation will be?
A. Straight line
B. Circle
C . Ellipse
D. Spiral


0.1 normal solution of \( N a C l \) is found to
be isotonic with \( 1.1 \% \) solution of Urea.
Calculate the apparent degree of
ionisation of \( N a C l \)
\( \mathbf{A} \cdot 0.083 \)
B. 8.3
c. 0.83
D. 0.42


With an object between those, if the angle between two plane mirrors is acute, the number of images formed will be:
\( A . \) more than 3
B. less than 3
c. more than 1
D. equal to zero


Phosphate pollution is brought about by
A. Phosphate rocks
B. Automobile exhausts
c. sewage and phosphate rocks
D. Sewage and agricultural fertilisers


The angle which the tangent to a curve at any point \( (x, y) \) on it makes with axis
of \( x \) is \( \tan ^{-1}\left(x^{2}-2 x\right) \) for all values of \( x \)
and it passes through the point (2,0) Determine the point on it whose
ordinate is maximum.
A \( .(2,8 / 3) \)
в. \( (0,4 / 3) \)
c. \( (1,2 / 3) \)
D. \( (-1,4 / 3) \)


Write any one cause of uncontrolled
population growth.


Blood vessels do not pierce
A. Dermis
B. Endodermis
c. Epidermis
D. None of the above


Which one of the following occurs by an
addition elimination mechanism?
A. Toluene, \( \mathrm{Br}_{2}, \mathrm{FeBr}_{3} \rightarrow \rho \) -bromotoluene
B. Benzene, HNO \( _{3}, \mathrm{H}_{2} \mathrm{SO}_{4} \rightarrow \) nitrobenzene
C. Benzene, \( \mathrm{CO}, \mathrm{HCl} \), AlCl \( _{3} \), \( \mathrm{CuCl} \rightarrow \) benzaldehyde
D. 2, 4-dinitrochlorobenzene, NaOH, heat, then H \( ^{+} \rightarrow 2,4- \) dinitrophenol


The value of current \( i \) in the given
circuit is:
A. zero
B. 5 Amp.
c. 7 Amp
D. 11 Amp


Which of the compound does not has
electron linkage?
\( \mathbf{A} \cdot K C N \)
в. \( N H_{4} C l \)
\( \mathbf{c} \cdot C a C_{2} \)
D. \( N H_{3} \rightarrow B F_{3} \)


Arrange the following elements in order of decreasing non-metallic character \( \boldsymbol{G} \boldsymbol{e}, \boldsymbol{S} \boldsymbol{n}, \boldsymbol{P} \boldsymbol{b}, \boldsymbol{S} \boldsymbol{i} \)
A. \( P b,>S n,>G e,>S i \)
в. \( P b,>G e,>S n>S i \)
\( \mathbf{c} \cdot S i,>G e>S n>P b \)
D. Equal non-metallic character
E. None of the above


\( \boldsymbol{f}=\{(\boldsymbol{3}, \boldsymbol{4}),(\boldsymbol{4}, \boldsymbol{3})\} \boldsymbol{g}=\{(\boldsymbol{3}, \boldsymbol{7}),(\boldsymbol{4}, \boldsymbol{8})\} \)
Find \( \boldsymbol{f}-\boldsymbol{g} \)


The solubility of the gas in a liquid solution with an increase in
temperature.
A . decreases
B. increases
c. remains same
D. none of these


Biological species are kept separate from closely related species inhabiting the same geographical region by reproductive isolating mechanism, which is called as
A. Phenetic concept
B. Phylogenetic concept
c. Biological species concept
D. None of these


Find the inverse of the following matrix using transformation method. \( \left[\begin{array}{cc}\mathbf{1} & \mathbf{2} \\ \mathbf{2} & -\mathbf{1}\end{array}\right] \)


(a) Silicone is a polymeric organo silicon compound which is chemically inert and thermally stable
(b) Silicon carbide can be used as a
lubricant.
(c) Silicon dioxide is the raw material
for the manufacture of cement as well
as glass.
(d) Hardness of \( S i O_{2} \) and \( S i C \) is due to
their regular tetrahedral structure.
Which of the following regarding silicon and its compounds is correct?
A. a and
B. b and c
\( c \cdot a, c \) and \( d \)
D. only d


A muscular transverse partition in mammals that separates thorax from abdomen is
A. Diaphragm
B. Pharynx
c. stomach
D. Duodenum


Which of the following does not
represent resonating structures?
A. \( C H_{3}-C O-C H_{3} \) and \( C H_{3}-C(O H)=C H_{2} \)
в.
and
\( c \)
\( C H_{3}-C-C H_{3} \) and
D. \( C H_{2}=C=O \) and \( \stackrel{(-)}{C} H_{2}-C \equiv O^{(+)} \)


The slope of one of the lines given by \( a x^{2}+2 h x y+b y^{2}=0 \) is \( k \) times the
other, then
A \( \cdot 4 k^{2} h=a b(1+k) \)
B . \( k h^{2}=4 a b(1+k)^{2} \)
C. \( k h^{2}=2 a b(1+k)^{2} \)
D. \( 4 k h^{2}=a b(1+k)^{2} \)


When a beam of light, from an object,
appears to meet at a point after reflection from a mirror, then the image formed is known as:
A . real image
B. virtual image
c. incident image
D. all of the above


Three rods of material \( X \) and three rods
of material \( Y \) are connected as shown
in figure. All the rods are identical in length and cross-sectional area. If the
end \( A \) is maintained at \( 60^{\circ} \mathrm{C} \) and the
junction \( E \) at \( 10^{\circ} \mathrm{C} \), calculate the
temperatures of the junctions \( B, C, D \)
The thermal conductivity of \( X \) is 0.92
\( C G S \) units and that of \( Y \) is \( 0.46 C G S \)
units.


With increase in frequency of an ac
supply, the impedance of an \( L-C-R \)
series circuit
A. remains constant
B. increases
C . decreases
D. decrease at first becomes minimum and then
increases.


A pair of dice is thrown. What is the probability of getting an even number on the first die or a total of \( 8 ? \)


Express the given complex number in
the form \( a+i b: \)
\( (1-i)^{4} \)


if \( \alpha \) and \( \beta \) are sum and product of roots of the given equation respectively, then
\( (-\boldsymbol{\alpha} \boldsymbol{\beta}) \) is
A. always a prime number
B. always an odd integer
c. always an irrational number
D. dependent on value of a


Draw the structure of Phenol
formaldehide polymer


A tissue is a grouping of cells similar in
A. Function
B. Structure
c. Heredity
D. origin and function


Find the value of \( x \).
\( \sqrt{\mathbf{3}} \boldsymbol{x}-\mathbf{2}=\mathbf{2} \sqrt{\mathbf{3}}+\mathbf{4} \)
\( \mathbf{A} \cdot x=2(1+\sqrt{3}) \)
в. \( x=(1+2 \sqrt{3} \)
c. \( x=3(2+\sqrt{2}) \)
D. \( x=-2(3+\sqrt{3}) \)


The magnetic needle of a tangent galvanometer is deflected at an angle 30 due to a magnet. The horizontal component of earth's magnetic field
\( 0.34 \times 10^{-4} T \) is along the plane of the
coil. The magnetic intensity is:
A . \( 1.96 \times 10^{-4} T \)
B . \( 1.96 \times 10^{-5} T \)
c. \( 1.96 \times 10^{4} T \)
D. \( 1.96 \times 10^{5} T \)


State whether the given statement is true or false:

With the increase in distance from the
nucleus, energy of electron increases and the velocity of electron decreases.
A. True
B. False


A certain weak acid has \( \boldsymbol{K}_{\boldsymbol{a}}=\mathbf{1 . 0} \times \)
\( 10^{-4} . \) The equilibrium constant for tis
reaction with a strong base is \( \boldsymbol{K}_{e q}= \) \( 10^{5 X} . \) Value of \( X \) is


In a diffraction(single slit experiment), the slit is exposed by white light. The fringe surrounding the central fringe is
A. Red
B. Yellow
c. violet
D. Green


If \( \alpha, \beta \) are two different values of \( \theta \) lying
between 0 and \( 2 \pi \) which satisfy the
equation \( 6 \cos \theta+8 \sin \theta=9 \) Find
\( \cos (\alpha+\beta) \)


The number of bridging ligands and the number of bromine atoms present per molecule of the compound decaammine- \( \mu^{-} \) hydroxodichromium(III) bromide are respectively:
A . 1,5
в. 2,6
c. 1,4
D. 1,3


Phoshphorus content in an organic compound can be detected by:
A. sesquioxide
B. superoxide
c. peroxide
D. suboxide


The absolute temperature T of a gas is
plotted against its pressure \( \mathrm{P} \) for two
different constant volumes \( V_{1} \) and \( V_{2} \)
where \( V_{1}>V_{2} . \) T is plotted along \( x \) -axis
and \( \mathrm{P} \) along \( \mathrm{y} \) -axis.
A. Slope for curve corresponding to volume \( V_{1} \) is greater
than that corresponding to volume \( V_{2} \)
B. Slope for curve corresponding to volume \( V_{2} \) is greater than that corresponding to volume \( V_{1} \)
C. Slope for both curves are equal
D. Slope for both curves are unequal such that they intersect at \( T=0 \)


f \( x, y \) and \( z \) are all distinct and \( \left|\begin{array}{lll}\boldsymbol{x} & \boldsymbol{x}^{2} & \boldsymbol{1}+\boldsymbol{x}^{3} \\ \boldsymbol{y} & \boldsymbol{y}^{2} & \boldsymbol{1}+\boldsymbol{y}^{3} \\ \boldsymbol{z} & \boldsymbol{z}^{2} & \boldsymbol{1}+\boldsymbol{z}^{3}\end{array}\right|=\mathbf{0}, \) then the value of
\( x y z \) is.
A . -4
B. -
\( c .-2 \)
D. - -


Consider a circuit which contains a
resistance free battery and a single
resistance \( R . \) If a second resistance is
added in parallel with \( \boldsymbol{R} \)
A. The voltage across \( R \) will decrease
B. The current through \( R \) will increase
C. The total current drawn from the battery will increases
D. The power dissipated in \( R \) will decrease current drawn from battery will increase


Which term of the sequence \( 20,19 \frac{1}{4}, 18 \frac{1}{2}, 17 \frac{3}{4}, \ldots . . \) is the first
negative term?


\( \boldsymbol{E} \) is kinetic energy of a simple harmonic oscillator at its mean
position. The phase angle from mean position at which its kinetic energy is \( \boldsymbol{E} / 2 \) is :
A . \( \pi / 5 \) rad
в. \( \pi / 4 \) rad
c. \( \pi / 3 \) rad
D. None of the above


Express the following in a recurring decimal form.
\( 2 \frac{1}{6} \)
A \( .2 .1 \overline{6} \)
B. \( 2.1 \overline{8} \)
c. \( 2.1 \overline{4} \)
D. 2.19


State whether the given statement is True or False :

The plates of the outermost layer of the Earth are always in continuous motion
A. True
B. False


The increasing order of acidic strength in the following acids.
\( \boldsymbol{C l C H}_{2} \boldsymbol{C O O H}, \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C O O H}, \boldsymbol{C l C} \)
and \( C H_{3} C O O H \) is:
A \( \cdot\left(C H_{3}\right)_{2} C H C O O H<C H_{3} C H_{2} C O O H< \)
\( \mathrm{ClCH}_{2} \mathrm{CH}_{2} \mathrm{COOH}<\mathrm{CH}_{3} \mathrm{COOH}<\mathrm{ClCH}_{2} \mathrm{COOH} \)
в. \( C H_{3} C H_{2} C O O H<\left(C H_{3}\right)_{2} C H C O O H< \)
\( \mathrm{ClCH}_{2} \mathrm{CH}_{2} \mathrm{COOH}<\mathrm{CH}_{3} \mathrm{COOH}<\mathrm{ClCH}_{2} \mathrm{COOH} \)
c. \( \left(C H_{3}\right)_{2} C H C O O H<C H_{3} C H_{2} \) СООН\( < \)
\( \mathrm{ClCH}_{2} \mathrm{CH}_{2} \mathrm{COOH}<\mathrm{ClCH}_{2} \mathrm{COOH}<\mathrm{CH}_{3} \mathrm{COOH} \)
D. \( \left(C H_{3}\right)_{2} C H C O O H<C l C H_{2} C H_{2} C O O H< \)
\( C H_{3} C H_{2} C O O H<C H_{3} C O O H<C l C H_{2} C O O H \)


Which of the following is a nondirectional bond?
A . covalent
B. electrovalent
c. coordinate-covalent
D. none of these


The appropriate value is \( \cos 61^{\circ} \) is
A . 0.4848
B. 0.4849
c. 0.4948
D. 0.5059


Find the general solution:
\( \sin x+\sin 3 x+\sin 5 x=0 \)


Calculate the sum of ratios of \( \sigma \)
bonding electrons and \( \pi \) bonding
electrons in \( C_{2} \) molecule


A graph between kinetic energy and
momentum of a particle is plotted as shown in the figure. The mass of the
moving particle is:-
\( A \cdot 1 \mathrm{kg} \)
B. 2 kg
\( c \cdot 3 k g \)
\( D \cdot 4 \mathrm{kg} \)


\( \phi^{-} \)
\( p \)
\( \dot{\theta} \)
\( \phi \)


A resistance of \( R \Omega \) draws current from
a potentiometer. The potentiometer wire, \( A B, \) has a total resistance of \( R_{0} \Omega \)
A voltage \( \boldsymbol{V} \) is supplied to the
potentiometer. Derive an expression for
the voltage across \( R \) when the sliding
contact is in the middle of the
potentiometer wire.


Equation of the ellipse in its standard form is \( \frac{\boldsymbol{x}^{2}}{\boldsymbol{a}^{2}}-\frac{\boldsymbol{y}^{2}}{\boldsymbol{b}^{2}}=\mathbf{1} \)
A. True
B. False
c. Nither
D. Either


Na, Mg and Al are the elements having one, two and three valence electrons
respectively. Which of these elements
(i) has the largest atomic radius, (ii) is least reactive? Justify your answer
stating reason for each.


Correct order of boiling point for the given compounds is:
a) \( 1- \) chloropropane
b) isopropyl chloride
c) 1-chlorobutane
\( A \cdot a<b<c \)
в. \( b>a>c \)
\( c \cdot b<a<c \)
D. \( a>b>c \)


A body of mass \( m \) is projected with
initial speed \( u \) at an angle \( \theta \) with the
horizontal. The change in momentum of body after time \( t \) is
A \( . m u \sin \theta \)
B . \( 2 m u \sin \theta \)
\( \mathrm{c} \cdot m g t \)
D. zero


More energetic molecules of a body transfer some of their energy to other molecules, without any change in their
position in:
A. conduction
B. convection
c. radiation
D. none of these


When the two surfaces are coated with
the lubricant, then they will:
A. slide upon each other
B. stick to each other
C. roll upon each other
D. jump on each other


The value of \( \tan \left(2 \tan ^{-1} 1 / 5-\pi / 4\right) \) is?
A. \( -7 / 17 \)
в. \( +7 / 17 \)
c. \( -12 / 17 \)
D. \( -+2 / 17 \)


The stabilities of coordination
compounds containing the ions \( \boldsymbol{C u}^{2+}, \boldsymbol{N i}^{2+}, \boldsymbol{C o}^{2+}, \boldsymbol{F} \boldsymbol{e}^{2+} \) and \( \boldsymbol{M} \boldsymbol{n}^{2+} \)
follow the order:
A \( \cdot M n^{2+}>F e^{2+}>C o^{2+}>N i^{2+}+C u^{2+} \)
B . \( N i^{2+}>C u^{2+}>F e^{2+}>C o^{2+}+M n^{2+} \)
c. \( C u^{2+}>N i^{2+}>C o^{2+}>F e^{2+}+M n^{2+} \)
D. \( F e^{2+}>M n^{2+}>N i^{2+}>C o^{2+}+C u^{2} \)


Calculate approximately how much current is necessary to produce oxygen
gas at the rate of \( 1 ~ m L \) per second?


If \( A=5 \) units, \( B=6 \) units and \( |\vec{A} \times \vec{B}|= \) 15 units, then the angle between \( \vec{A} \) and \( \vec{B} \)
is:
This question has multiple correct options
\( A \cdot 30^{\circ} \)
B. \( 60^{\circ} \)
c. \( 90^{\circ} \)
D. \( 150^{\circ} \)


Identify odd term related with reproduction in living organisms.
A. Zygote formation
B. Fragmentation
c. Regeneration
D. Budding


The maximum number of electrons in a
sub-shell is
A. \( 2(2 l+1) \)
B. \( 2 l+1 \)
\( c \cdot 2 l \)
D. \( 2 l-1 \)


The area of a square and a
parallelogram is the same. If the side of the square is \( 60 \mathrm{cm} \) and base of the
parallelogram is \( 120 \mathrm{cm} \), find the
corresponding height of the parallelogram.


Arrange the following molecules in the
increasing order of \( \alpha \) to \( \pi \) bond ratio?
(1)
(2)
(3)
(4)
\( A \cdot(2)<(3)<(4)<(1) \)
B. \( (2)<(4)<(3)<(1) \)
\( c \cdot(3)<(2)<(1)<(4) \)
\( D \cdot(2)<(3)<(1)<(4) \)


If magnification is positive, the nature of the image is:
A. real and inverted
B. virtual and erect
c. real
D. none of these


Suppose \( A=\frac{d y}{d x} \) when \( x^{2}+y^{2}=4 \) at \( (\sqrt{2}, \sqrt{2}), B=\frac{d y}{d x} \) when \( \sin y+\sin x= \)
\( \sin x-\sin y \) at \( (\pi, \pi) \) and \( C=\frac{d y}{d x} \) when
\( 2 e^{x y}+e^{x} e^{y}-e^{x}-e^{y}=e^{x y+1} \operatorname{at}(1,1) \)
then \( (A+B+C) \) has the value equal
to
\( A \)
в.
\( c \cdot-3 \)
D.


Assertion
If two triangles have same perimeter, then they are congruent.
Reason
If under a given correspondence, the three sides of one triangle are equal to the three sides of the other triangle,
then the two triangles are congruent.
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 are correct


Ice at \( -20^{\circ} \mathrm{C} \) is filled upto height \( h= \)
\( 10 \mathrm{cm} \) in a uniform cylindrical vessel
Water at temperature \( \theta^{\circ} C \) is filled in
another identical vessel up to the same
height \( h=10 \mathrm{cm} . \) Now, water from
second vessel is poured into first vessel and it is found that level of upper surface
falls through \( \Delta h=0.5 \mathrm{cm} \) when
thermal equilibrium is reached. Neglecting thermal capacity of vessels, change in density of water due to change in temperature and loss of heat due to radiation, calculate initial
temperature \( \theta \) of water in \( ^{o} C \) Given, Density of water, \( \rho_{w}=1 g \mathrm{cm}^{-3} \)
Density of ice, \( \rho_{i}=0.9 g \mathrm{cm}^{-3} \)
Specific heat of water, \( s_{w}=1 \mathrm{cal} / \mathrm{g}^{\circ} \mathrm{C} \)
Specific heat of ice, \( s_{i}=0.5 \mathrm{cal} / \mathrm{g}^{\circ} \mathrm{C} \)
Specific latent heat of ice, \( L=80 \) cal \( / g \)


Mechanism of aerobic respiration / tricarboxylic acid pathway was discovered by
A. Calvin
B. Krebs
c. Pasteur.
D. Hatch and Slack


Subtracting two positive/negative integers with same
sign or opposite sign is same as:
A. Subtracting one positive and one negative integer
B. Adding two positive integers
c. Adding two negative integers
D. Adding one positive and one negative integer


Which of the following has smell resembling to bleaching powder?
A \( \cdot N O_{2} \)
в. \( H N O_{4} \)
c. \( H N O_{3} \)
D. None of these


If \( \operatorname{cosec} \theta=2 x \) and \( y \cot \theta=2, \) then the
value of \( 4\left(x^{2}-\frac{1}{y^{2}}\right) \) is :
\( A \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{1}{3} \)
D.


The higher values of specific heat of water than other liquids has been accounted in terms of :
A. High dielectric constant
B. Polarity
c. H-bonding
D. None of these


Refer to the given figure showing a typical plant with its parts labelled as U, \( V, W \) and \( X \) and read the following paragraph. P is a plant where part U is edible, plant \( Q \) has edible part \( W \), plant R has edible part \( X \) whereas plant \( S \) has
edible part \( V \)
Select the option that correctly identifies these plants.
A. P-Clove, Q-Mustard, R-Cumin, S-Ginger
c. P-Pomegranate, Q-Spinach, R-Clove, S-Radish
D. P-cumin, Q-Rose, R-spinach, S-Potato


Consider the given organometallic compound.
\( (\mathrm{I})\left(\boldsymbol{C} \boldsymbol{H}_{3}\right)_{2} \boldsymbol{H} \boldsymbol{g} \)
(II) \( \left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{Z} \boldsymbol{n} \)
\( \left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{M} \boldsymbol{g} \)
\( (\mid V) C H_{3} L i \)
The correct decreasing order of ionic character is :
A. \( I>I I>I I I>I V \)
В. \( I I>I>I I I>I V \)
c. \( I>I I I>I I>I V \)
D. \( I V>I I I>I I>I \)


Which of the following has a square planar structure?
\( A \)
\( \left[N i(C O)_{4}\right] \)
в.
c. \( \left[N i(C N)_{4}\right]^{2} \)
D. All of the above


Statement I: Under the conditions of low
pressure and high temperature, the
ideal gas laws are inaccurate.

Statement II: The deviation from the
ideal gas law is due to non-negligible
volume of the molecules and the
interactions between molecules.
A. Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1
B. Both the Statement 1 and Statement 2 are correct and Statement 2 is NOT the correct explanation of Statement 1
C. Statement 1 is correct but Statement 2 is not correct
D. Statement 1 is not correct but Statement 2 is correct
E. Both the Statement 1 and Statement 2 are not correct


State Faraday's first law of electrolysis. Write any 'two' uses of each of the following
(a) \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
(b) Chlorine
Distinguish between crystalline solids and amorphous solids. A solution of a substance having mass \( 1.8 \times 10^{-3} k g \) has the osmotic pressure
of 0.52 atm at \( 280 \mathrm{K} \). Calculate the
molar mass of the substance used.
[Volume \( =1 d m^{3}, R= \)
\( \left.8.314 J K^{-1} m o l^{-1}\right] \)


Magnetic equator is
A. Isoclinic line
B. Aclinic line
C. Isogonic line
D. Agonic line


Match and find the correct combination
\( \mathbf{A} \)
\( A-4, B-3, C-2, D-1 \)
B. \( A-3, B-4, C-1, D-2 \)
C \( \cdot A-4, B-2, C-1, D-3 \)
D. \( A-1, B-2, C-4, D-3 \)


Assertion: According to the principle of common ion effect, the solubility of
\( H g C l_{2} \) is expected to be less in an
aqueous solution of \( K I \) than in water.
\( H g I_{2} \) dissolves in an aqueous
solution of \( K I \) to form a clear solution.
Reason: lodide ion, \( \boldsymbol{I}^{-} \) is highly
polarizable.
A. Both Assertion and Reason are correct and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion
c. Assertion is correct but Reason is not correct
D. Assertion is not correct but Reason is correct
E. Both Assertion and Reason are not correct


In an examination there were 640 boys
and 360 girls. \( 60 \% \) of the boys and \( 80 \% \) of the girls were successful. The percentage of failures was:
A . 20
B. 60
c. 30.5
D. 32.8


In the figure 7.31 , radius of the circle is
\( \mathbf{7} \boldsymbol{c m} \) and \( \boldsymbol{m}(\boldsymbol{a} \boldsymbol{r} \boldsymbol{c} \boldsymbol{M} \boldsymbol{B} \boldsymbol{N})=\boldsymbol{6} \boldsymbol{0}^{o} \)
find Area of the circle.
A . 45
B . 42.96
c. 43.96
D. 44


Match column -I with column-II and
select the correct answer using the codes given below:
Column-I Colum -
\( \| \)
(A) Global warming Eutrophication
(B) Algal bloom
\( (q) C O \)
\( \mathbf{C O}_{\mathbf{2}} \)
(C) Nitrogen fixation Rhizobium
(D) Pseudomonas
(s) Fossil
Fuel
(E) Non-renewable resource
Denitrification
\( A \cdot(A)-p,(B)-q,(C)-r,(D)-t,(E)-s \)
B. (A)- q, (B)- \( p,(C)-r,(D)-t,(E)-s \)
C. \( (A)-q,(B)-p,(C)-r,(D)-s,(E)-s \)
D. \( (A)-q,(B)-p,(C)-s,(D)-r,(E)-t \)


\( A 30 g \) of ice that is at a temperature
\( 0^{\circ} \mathrm{C} \) falls 6 meters from the eaves of a
house to the ground below. If \( 5 \% \) of the kinetic energy that the ice possesses when it strikes the ground converts into heat, Identify the correct statement?
(Note: \( \left.\boldsymbol{H}_{f} \boldsymbol{w} \boldsymbol{a} \boldsymbol{t} \boldsymbol{e} \boldsymbol{r} \boldsymbol{0} . \boldsymbol{3} \boldsymbol{3} \boldsymbol{5} \boldsymbol{J} / \boldsymbol{g}\right) \)
A. The ice would become colder during the fall; therefore, no ice would melt
B. This would not happen because it would break the law of conservation of mass
c. Less than \( .3 g \) of the ice would melt
D. The frictional work done to stop the icicle's fall would use up all the energy and leave none for anything else
E. The icicle would shatter and the energy would convert into momentum


The area of the region, bounded by the curves \( \boldsymbol{y}=\sin ^{-1} \boldsymbol{x}+\boldsymbol{x}(\mathbf{1}-\boldsymbol{x}) \) and \( \boldsymbol{y}= \)
\( \sin ^{-1} x-x(1-x) \) in the first quadrant
is
\( A \cdot 1 \)
в. \( \frac{1}{2} \)
\( c \cdot \frac{1}{3} \)
D.


Fill in the blanks:
The perpendicular distance of a point (5,12,13) from \( Y \) -axis is


Which of the following is known as excretory organs of earthworm?
A. Coelom
B. Flame cells
c. Nephridia
D. Gizzardd


The earth's magnetic field at a certain place has a horizontal component of \( 0.3 G \) and total strength \( 0.5 G . \) Find
angle of dip in \( \tan ^{-1} \)
A \( \cdot \delta=\tan ^{-1} \frac{4}{3} \)
B. \( \delta=\tan ^{-1} \frac{3}{4} \)
c. \( \delta=\tan ^{-1} \frac{5}{3} \)
D. \( \delta=\tan ^{-1} \frac{3}{5} \)


The moment of inertia of a disc of
radius \( 0.5 \mathrm{m} \) about its geometric axis is \( 2 \mathrm{kg}-m^{2} . \) If a string is tied to its circumference and a force of 10 Newton is applied, the value of torque with respect to this axis will be :-
A. 2.5 N-m
B. 5 N-m
\( c \cdot 10 N-m \)
D. 20 N-m


In the figure above, point \( A \) and \( B \) lie on
the circle with center \( O . \) If \( x=80, \) what
is the value of \( z ? \)
A . \( 80^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 50^{\circ} \)
D. \( 40^{\circ} \)
E .10


What would you predict for the atomic number of the noble gas beyond \( \boldsymbol{R} \boldsymbol{n} \), if
such an element has sufficient stability to be prepared or observed? Assume
that \( g- \) orbitals are still not occupied in the ground state of preceding elements.


Paramecium is a protist because of its
A. Eukaryotic unicellular structure
B. Prokaryotic unicellular structure
c. Mesokaryotic unicellular structure
D. None of these


Describe the internal structure of
human heart.


Calculate
(a) frequency and (b) wave-
number of yellow radiation having
wavelength \( 5800 A \)


IUPAC name of the compound is:


A positive charge 'q' of mass 'm' is moving along the +x axis. We wish to apply a uniform magnetic field \( B \) for
time \( \Delta t, \) so that the charge reverses its
direction, crossing the y axis at a distance \( d \). Then:
A \( \cdot B=\frac{m v}{q d} \) and \( \Delta t=\frac{\pi d}{v} \)
B. \( B=\frac{m v}{2 q d} \) and \( \Delta t=\frac{\pi d}{2 v} \)
c. \( _{B}=\frac{2 m v}{q d} \) and \( \Delta t=\frac{\pi d}{2 v} \)
D. \( B=\frac{2 m v}{q d} \) and \( \Delta t=\frac{\pi d}{v} \)


Consider the statements about
cellulose.

The correct statements is/are:
This question has multiple correct options
A. Cellulose is a colourless crystalline solid
B. It is mainly branched chain polysaccharideonly I
c. Its individual strands align with each other through a number of hydrogen bonds
D. It is rigid and acts as cell wall material


Order and degree of \( \left(1+y_{1}^{2}\right) y_{3}= \)
\( \mathbf{3} \boldsymbol{y}_{2} \boldsymbol{y}_{1}^{2} \) are:
A . 2,3
B. 2,
\( c \cdot 3, \)
D. 3,2


NAND and NOR gates are called universal gates primarily because they
A. are available universally
B. can be combined to produce OR, AND and NOT gates
c. are widely used in Integrated circuit packages
D. are easiest to manufacture


Find the dimensions of \( G \varepsilon_{0} .(G= \)
Universal Gravitational constant \( , \varepsilon_{0}= \)
permittivity in vacuum)


Find the value \( f(0) \) so that the function
\( \boldsymbol{f}(\boldsymbol{x})=\frac{1}{x}-\frac{2}{e^{2 x}-1}, \boldsymbol{x} \neq 0 \) is continuous
at \( x=0 \& \) examine the differentiability
of \( f(x) \) at \( x=0 \)
A \( \cdot f(0)=0, \) differentiable at \( x=0 \)
B. \( f(0)=0, \) not differentiable at \( x=0 \)
\( \mathrm{c} . f(0)=1, \) differentiable at \( x=0 \)
D. \( f(0)=1, \) not differentiable at \( x=0 \)


The equilibrium constant \( \boldsymbol{K}_{c} \) for the
reaction \( P_{4}(g) \rightleftharpoons 2 P_{2}(g) \)
is 1.4 at \( 400^{\circ} \mathrm{C} . \) Suppose that 3 moles of
\( P_{4}(g) \) and 2 moles of \( P_{2}(g) \) are mixed in
2 litre container at \( 400^{\circ} \mathrm{C} \). What is the
value of reaction quotient \( \left(Q_{c}\right) ? \)
\( A \cdot \frac{3}{2} \)
B. \( \frac{2}{3} \)
c. 1
D. None of these


A block is constrained to move along \( x \)
axis under a force \( F=-2 x \). Here, \( F \) is in
newton and \( x \) in metre. Find the work
done by this force when the block is displaced from \( x=2 m \) to \( x=-4 \) m.
A . -4 J
B. -8J
c. -12
D. -16


The minimum number of elements that
must be added to the relation \( \boldsymbol{R}= \)
\( \{(1,2)(2,3)\} \) on the set of natural
numbers so that it is an equivalence is
A . 4
B. 7
\( c .6 \)
D.


The force acting on a mass of 1g due to the gravitational pull on the earth is called lgwt. One gwt equals:
\( A \cdot 1 N \)
B. \( 9.8 \mathrm{N} \)
c. 980 dyne
D. none of these


Three charges \( 1 \mu C, 2 \mu C, \) and \( 3 \mu C \) are kept at vertices of an equilateral triangle of side \( 1 \mathrm{m} \). If they are brought nearer, so that they now form an
equilateral triangle of side \( 0.5 m, \) then
work done is :
A. \( 0.11 J \)
\( J \)
в. \( 11 J \)
c. \( 0.01 J \)
D. \( 1.1 \mathrm{J} \)


A stress strain curve plotted for two
wires are as shown. The labels 1 is the
elastic point, 2 and 3 are the yield
points wires \( A \) and \( B \). Which one is more
ductile
4.4
B. B
c. Both are brittle
D. Both are ductile


The minimum value of \( 2 x^{3}-9 x^{2}+ \)
\( 12 x+4 \) is
A . 4
B. 5
\( c .6 \)
D.
E. 8


Solubility of a substance depends on:
A. nature of solute
B. nature of solvent
c. temperature
D. all of the above


A solution of \( S O_{2} \) in water reacts with
\( \boldsymbol{H}_{2} \boldsymbol{S} \) precipitating sulphur. Here \( \boldsymbol{S O}_{2} \)
acts as:
A. Oxidising agent
B. Reducing agent
c. Acid
D. catalyst


Two point charges \( A=+3 \) nC and \( B= \)
+1 nC are placed \( 5 c m \) apart in air. The
work done to move charge \( B \) towards \( A \)
by \( 1 \mathrm{cm} \) is :
A \( \cdot 2.0 \times 10^{-7} J \)
В. \( 1.35 \times 10^{-7} J \)
c. \( 2.7 \times 10^{-7} J \)
D. \( 12.1 \times 10^{-7} \mathrm{J} \)


Construct a triangle \( M N P, \) whose
perimeter is \( 15 \mathrm{cm} \) and whose sides are
in the ratio 2: 3: 4


A sphere of mass \( m \) is moving with a velocity \( (4 \hat{i}-\hat{j}) m / s \) hits a surface and rebounds with a velocity \( (\hat{i}+3 \hat{j}) m / s . \) The coefficient of restitution between the sphere and the
surface is \( k / 16 . \) find the value of \( k \)
\( A \cdot 9 \)
B. 8
\( c \cdot 7 \)
D. 6


The angle between the lines \( x+y- \)
\( \mathbf{3}=\mathbf{0} \) and \( \boldsymbol{x}-\boldsymbol{y}+\mathbf{3}=\mathbf{0} \) is \( \boldsymbol{\alpha} \) and the
acute angle between the lines \( x- \) \( \sqrt{3 y}+2 \sqrt{3}=0 \) and \( \sqrt{3 x}-y+1=0 \)
is
\( \beta . \) Which one of the following is
correct?
A. \( \alpha=\beta \)
в. \( \alpha>\beta \)
c. \( \alpha<\beta \)
D. \( \alpha=2 \beta \)


Which part of the solar system is farthest from the sun?
A. Pluto
B. The Oort cloud
c. The asteroid belt
D. The milky way
E. The Kuiper belt


Evaluate the following limits. \( \lim _{x \rightarrow 1} \frac{1+(x-1)^{2}}{1+x^{2}} \)


Two particles are projected in air with
speed \( u \) at angles \( \theta_{1} \) and \( \theta_{2} \) (both acute) to the horizontal, respectively. If the height reached by the first particle is greater than that of the second, then
which one of the following is correct?
(where \( T_{1} \) and \( T_{2} \) are the time of flight.)
A. \( \theta_{1}>\theta_{2} \)
a
B \( \cdot \theta_{1}=\theta_{2} \)
c. \( T_{1}<T_{2} \)
D. \( T_{1}=T_{2} \)


Elastic waves in solid are:
A. Transverse Only
B. Longitudinal Only
C. Either transverse or longitudinal
D. Neither transverse nor longitudinal


A 1 m long uniform beam is balanced
as shown. Calculate the force \( F \)
\( A \cdot 2 N \)
B. 3 N
\( c \cdot 7 N \)
D. \( 11 N \)


Identify the correct statement for
change of Gibbs energy for a system \( (\Delta \)
\( \left.\mathrm{G}_{\text {system}}\right) \) at constant temperature and
pressure:
\( \mathbf{A} \cdot \) If \( \Delta \mathrm{G}_{\text {system}}>0, \) the process is spontaneous
B. If \( \Delta G_{s y s t e m}=0, \) the system has attained equilibrium
C. If \( \Delta G_{\text {system}}=0, \) the system is still moving in a particular direction
D. If \( \Delta \mathrm{G}_{\text {system}}<0 \), the process is not spontaneous


Fermentation is a type of anaerobic respiration that occurs in yeast and bacteria.What is the function of
fermentation?
I. Regenerate \( \boldsymbol{N} \boldsymbol{A} \boldsymbol{D}^{+} \) from \( \mathrm{NADH} \)
II. Produce oxygen as a waste product
III. Produce ATP
A. I only
B. II only
c. ॥ only
D. I and II only
E. I and III only


A sphere of mass \( \mathrm{m} \) and radius \( r \) is
projected in a gravity free space with speed \( v . \) If coefficient of viscosity of the medium in which, it moves is \( \frac{1}{6 \pi}, \) then the distance travelled by the body before it stops, is:
A \( \cdot \frac{m v}{2 r} \)
в. \( \frac{2 m v}{r} \)
c. \( \frac{m v}{r} \)
D. \( \frac{m v}{4 r} \)


Which of the following is an acid-base
neutralization reaction?
\( \mathbf{A} \cdot A g^{+}(a q)+C l^{-} \rightarrow A g C l(a q) \)
B \( \cdot C_{5} H_{12}(s)+8 O_{2}(g) \rightarrow 5 C O_{2}(g)+6 H_{2} O(l) \)
\( \mathbf{C} \cdot N H_{3}(s)+H_{2} O(s) \leftrightharpoons N H_{4}^{+}(s)+O H^{-}(s) \)
D. \( H C_{2} H_{3} O_{2}(l)+O H^{-}(a q) \rightarrow H_{2} O(O)+C_{2} H_{3} O_{2}^{-}(a q) \)
E \( \cdot C a C O_{3}(s) \rightarrow C a O(s)+C O_{2}(g) \)


Rank the following compounds with respect to increasing acidity:
\( A \cdot D<C<A<B \)
B. \( B<A<D<C \)
\( c \cdot B<A<C<D \)
\( D \cdot B<C<A<D \)


A resistor of \( 6 k \Omega \) with tolerance \( 10 \% \)
and another of \( 4 k \Omega \) with tolerance \( 10 \% \)
are connected in series.The tolerance of
combination is about
\( A \cdot 5 \% \)
B. \( 10 \% \)
\( c \cdot 12 \% \)
D. \( 15 \% \)


Inelastic collisions occur in :
I. Real gases
II. Ideal gases
III. Fusion reactions
Which of the following is correct option about the above problem?
A . I and II
B. II and III
c. I and III
D. I only
E. II only


a. Calculate e.m.f of cell for the reaction:
\( M g_{(s)}+C u^{2+}(0.0001 M) \rightarrow \)
\( M g^{2+}(0.001 M)+C u_{(s)} \)
Given that: \( E_{M g^{2+} / M g}^{o}=-2.37 \mathrm{V} \)
\( E_{C u^{2+} / C u}^{o}=+0.34 v \)
b. i) State Kohlrausch law.
ii) What is meant by limiting molar
conductance.


In an exothermic reaction, \( \Delta \boldsymbol{H} \) is:
A . positive
B. negative
c. zero
D. may be positive or negative


The number of capital letters of the English alphabets having both horizontal and vertical lines of
symmetry is -
A. 0
B.
\( c \cdot 4 \)
D.


A catalyst is a substance which:
A. Increases the equilibrium concentration of the product
B. Changes the equilibrium constant of the reaction
C. Shortens the time to reach equilibrium
D. Supplies energy to the reaction


If the points (1,0),(0,1) and \( (x, 8) \) are collinear, then the value of \( x \) is equal to
\( \mathbf{A} \cdot \mathbf{5} \)
B. -6
\( c \cdot 6 \)
D. -


Assertion
A disc rolls without slipping on a horizontal ground with uniform speed has 0 acceleration of lowest point.
Reason
velocity of the lowest point of the same
disc is zero
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 incorrect but Reason is correct
D. Both Assertion and Reason are incorrect


A real object is placed at a distance \( \frac{\boldsymbol{f}}{\mathbf{2}} \) in front of a concave mirror having focal length \( f . \) If object is shifted by a distance \( \frac{f}{4} \) away from the mirror. Find the ratio of final magnification to initial magnification.
A .4
B.
\( c \cdot \frac{1}{2} \)
D. 2


Assertion
An orbital cannot have more than two
electrons.
Reason
The two electrons in an orbital create
opposite magnetic field.
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 point \( P \) lies on a line whose ends are \( A(1,2,3) \) and \( B(2,10,1) . \) If \( z \)
component of \( \boldsymbol{P} \) is \( \boldsymbol{7}, \) then the
coordinates of \( \boldsymbol{P} \) are
A \( \cdot(-1,-14,7) \)
B. (1,-14,7)
c. (-1,14,7)
D. (1,14,7)


Why is boiling point of ethyl bromide higher that that of ethyl chloride?


In certain parts of India muscular distrophy is commonly found among the poor people because they eat cheap
pulses of
A. Phaseolus mungo
B. Pisum sativum
c. Lathyrus sativus
D. Cicer


A body of mass 5 kg undergoes a change in speed from 30 to \( 40 \mathrm{m} / \mathrm{s} \). Its momentum would increase by :
A. \( 50 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
B. 75 kg m/s
c. \( 150 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
D. 350 kg m/s


If \( \sqrt{\sqrt{\mathbf{2 5 0 0}}+\sqrt{\mathbf{9 6 1}}}=(x)^{2}, \) then \( \boldsymbol{x} \)
equals
\( \mathbf{A} \cdot 81 \)
в.
c. 6561
\( D \)


Find the area of square with Perimeter
\( \mathbf{1 0 0 c m} \)


In volcanic eruptions, Sulphur undergoes following reaction:
\( \mathbf{2} \boldsymbol{H}_{2} \boldsymbol{S}(\boldsymbol{g})+\boldsymbol{S} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{3} \boldsymbol{S}(\boldsymbol{s})+\mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O} \)
A. Disproportionation
B. Comproportionation
c. Neutralisation
D. Displacement


The hypothetical complex chloro
diaquatriamminecobalt(III) chloride can be represented as:
A \( \cdot\left[\operatorname{CoCl}\left(N H_{3}\right)_{3}\left(H_{2} O\right)_{2}\right] C l_{2} \)
в. \( \left[\operatorname{CoCl}\left(N H_{3}\right)_{3}\left(H_{2} O\right) C l_{3}\right] \)
c. \( \left[\operatorname{CoCl}\left(N H_{3}\right)_{3}\left(H_{2} O\right)_{2} C l\right. \)
D \( \cdot\left[\operatorname{CoCl}\left(N H_{3}\right)_{3}\left(H_{2} O\right)_{3} C l_{3}\right] \)


A circle touches the \( y \) -axis at (0,2) and has an intercept of 4 units on the positive side of the \( x \) -axis. Then the equation of the circle is?
A \( \cdot x^{2}+y^{2}-4(\sqrt{2} x+y)+4=0 \)
B . \( x^{2}+y^{2}-4(x+\sqrt{2} y)+4=0 \)
C \( \cdot x^{2}+y^{2}-2(\sqrt{2} x+y)+4=0 \)
D. none of these


Is the function defined by \( f(x)=|x|, \) a
continuous function?


Find the equation of the plane passing through the point (2,-1,1) and through the line of intersection of the planes \( \vec{r} \). \( (2 \hat{i}-3 \hat{j}+\hat{k})=3 \) and \( \vec{r} \cdot(\hat{i}+5 \hat{j}- \)
\( \hat{\boldsymbol{k}})=\mathbf{4 . 4} \)


At CMC, the surfactant molecules
undergoes:
A. association
B. aggregation
c. micelle formation
D. all of the above


The IUPAC name is: \( \boldsymbol{H}-\stackrel{\boldsymbol{C}}{\boldsymbol{C}}-\dot{\boldsymbol{C}}-\boldsymbol{C l} \)
A. 1,2 - dichoroethane
B. 2, 2 - dichloroethane
c. 1,1 - Dichloroethane
D. dichloroethane


In what ratio \( \mathrm{Cl}_{17}^{37} \) and \( \mathrm{Cl}_{17}^{35} \) be present so
as to obtain \( \mathrm{Cl}_{17}^{35.5} ? \)
A .1: 2
B. 1:
\( c \cdot 1: 3 \)
D. 3:


When \( H_{2} O_{2} \) is added to ice cold
solution of acidified potassium
dichromate in ether and the contents
are shaken and allowed to stand:
A. a blue colour is obtained in ether because of formation of \( C r O_{5} \)
B. a blue colour is obtained in ether because of formation of \( \mathrm{CrO}_{3} \)
c. a blue colour is obtained in ether because of formation \( \operatorname{of} C r_{2}\left(S O_{4}\right)_{3} \)
D. chromyl chloride is formed


How many moles of the iodine remain unreacted at equilibrium?
A . 0.388
в. 0.112
c. 0.25
D. 0.125


A cylindrical tube of uniform crosssectional area A is filled with two air
tight frictionless pistons. The pistons are connected to each other by a
metallic wire. Initially, the pressure of
the gas is \( p_{o} \) and temperature is \( T_{o} \)
atmospheric pressure is also \( p_{o} \$ . \) Now, the temperature of the gas is increased
to \( 2 T_{0}, \) the tension of wire will be.
A \( \cdot 2 p_{o} \)
в. \( p_{o} A \)
c. \( \frac{p_{o} A}{2} \)
D. \( 4 p_{o} A \)


Mark the true statement among the following with reference to normal
breathing.
A. Inspiration is a passive process whereas expiration is active
B. Inspiration is an active process whereas expiration is passive
C. Inspiration and expiration are active processes.
D. Inspiration and expiration are passive processes.


The study of chemical reactions at
surfaces of substances is called:
A. Photo chemistry
B. Surface chemistry
c. Thermo chemistry
D. None


Two sitar strings, \( A \) and \( B \), playing the
note 'Dha' are slightly out of tune and
produce beats and frequency 5 Hz.The tension of the string \( B \) is slightly increased and the beat frequency is
found to decrease by \( 3 H z \). If the frequency of \( \boldsymbol{A} \) is \( \mathbf{4 2 5} \boldsymbol{H} \boldsymbol{z}, \) the original frequency of \( \boldsymbol{B} \) is
A \( .430 H z \)
в. 428 Н \( z \)
c. \( 422 \mathrm{Hz} \)
D. \( 420 \mathrm{Hz} \)


The pyruvic acid formed during
glycolysis is oxidised to \( C O_{2} \) and \( H_{2} O \)
in a cycle called
A. Calvin cycle
B. Nitrogen cycle
c. Hill reaction
D. Krebs' cycle


Write balanced chemical equations for the following reactions:
Oxalic acid is treated with acidified
potassium permanganate solution


The energy stored per unit volume in copper wire, which produces longitudinal strain of \( 0.1 \% \) is:
\( \left(\boldsymbol{Y}=\mathbf{1 . 1} \times \mathbf{1 0}^{\mathbf{1 1}} \boldsymbol{N} / \boldsymbol{m}^{2}\right) \)
A \( \cdot 11 \times 10^{3} \mathrm{J} / \mathrm{m}^{3} \)
В . \( 5.5 \times 10^{3} J / m^{3} \)
\( \mathbf{c} \cdot 5.5 \times 10^{4} J / m^{3} \)
D. \( 11 \times 10^{4} J / m^{3} \)


The rate law for a reaction between the
substances \( A \) and \( B \) is given by:
Rate \( =\boldsymbol{K}[\boldsymbol{A}]^{n}[\boldsymbol{B}]^{m} . \) On doubling the
concentration of \( A \) and having concentration of \( B \) the ratio of new rate
law to the earlier rate of the reaction will
be as
\( \mathbf{A} \cdot n-m \)
B \( \cdot 2^{(n-m)} \)
c. \( \frac{1}{2^{m+n}} \)
D. \( m+n \)


If \( (1+a x)^{n}=1+8 x+24 x^{2}+\dots \) then
\( \boldsymbol{a} \times \boldsymbol{n} \) is:
\( \mathbf{A} \cdot \mathbf{8} \)
B. 12
c. 16
D . 24


Evaluate \( : \int \frac{1}{\sqrt{(x-1)(x-2)}} d x \)
A.
\[
\begin{array}{l}\text { B. } \log \left|\left(x-\frac{3}{2}\right)+\sqrt{x^{2}-3 x+2}\right|+C \\ \text { c. } \log \left(\left(x-\frac{3}{2}\right)+\sqrt{x^{2}-3 x+2}\right)+C \\ \text { D. } & =\log \left|\left(x-\frac{3}{2}\right)+\sqrt{x^{2}+3 x+2}\right|+C\end{array}
\]


Only RNA contains which of the
following base?
A. Thymine
B. Uraci
c. Adenine
D. Cytosine


A uniform but time-varying magnetic
field \( B_{(t)} \) exists in a circular region of radius a and is direction into the plane
of the paper, as shown in the figure. The magnitude of the electric field at point \( P \) at a distance \( r \) from the centre of the
circular region
\( A \). is zero
B. decreases as \( 1 / r \)
c. increases as
D. decrease as \( 1 / r^{2} \)


\( \frac{7 x^{3}+3 x^{2}-x+1}{x+1}=\left(a x^{2}+b x+c\right) \)
\( \frac{2}{x+1} \) then \( a= \)
A . 3
B. 7
\( c \cdot 1 \)
D.


The product formed in the given
reaction will react with \( x \) molecules of
\( C H_{3} M g B r . \) What is \( x ? \)


Assertion
The angular momentum of an electron in an atom is quantized.
Reason
In an atom only those orbits are permitted in which angular momentum of the electron is integral multiple of \( \frac{h}{2 \pi} \) where \( h \) is a plank's constant.
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


The first attempt to classify elements systemically was made by :
A. Mendeleev
B. Newland
c. Lother Meyer
D. Dobereiner


Which of the following best illustrates malleability?
A. Flow of thick fluid
B. Burning of glass
c. Hammering of steel
D. All of these


Define spring balance.


Starch is:
\( \mathbf{A} \cdot C_{12} H_{22} O_{11} \)
B. \( C_{6} H_{10} O_{5} \)
\( \mathbf{c} \cdot\left(C_{6} H_{10} O_{5}\right)_{n} \)
\( \mathbf{D} \cdot\left(C_{6} H_{12} O_{6}\right)_{n} \)


Let the potential energy of a hydrogen atom in the ground state be zero. Then its energy in the first excited state will
be
A. 10.2 eV
в. 13.6 еV
c. 23.8 eV
D. \( 27.2 \mathrm{eV} \)


Root pressure is measured by
A. Potometer
B. Barometer
c. Manometer
D. Auxanometer


The resultant of two vectors \( \vec{P} \) and \( \vec{Q} \) is
\( \vec{R} \). If the magnitude of \( \vec{Q} \) is doubled, the new resultant vector becomes
perpendicular to \( \vec{P} \). Then, the magnitude of \( \overrightarrow{\boldsymbol{R}} \) is equal to
\( A \cdot P+Q \)
в. \( P \)
c. \( P-Q \)
D. \( Q \)


Choose the correct combination
\begin{tabular}{cccc}
Hormone & Source & Functic \\
A. & Vasopressin & Posterior pituitary & Increas of wate through \\
B. & Norepinephrine & Adrenal medulla & Increas heart be respirat and ale \\
C. & Glucagon & \( \beta \) -cells of islet of Langerhans & Stimula glycoge \\
D. & Prolactin & Posterior pituitary & Regulat growth mamm glands milk formati females \\
\hline
\end{tabular}
\( A \cdot A \)
\( B . \quad B \)
\( c \cdot c \)
D.


Which one of the following statement(s)
is/are correct?
A. Brownian movement is more pronounced for smaller particles than for bigger ones.
B. Sols of metal sulphides are lyophilic.
C. According to the Schulze-Hardy law, the bigger the size of the ion, the greater is its coagulating power.
D. One would expect charcoal to adsorb chlorine more strongly than hydrogen sulphide.


Haemocoel is found in
A. Hydra
B. Ascaris
c. Earthworm
D. cockroach


The reaction \( \boldsymbol{C} \boldsymbol{H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{N} \boldsymbol{O}_{2}+ \)
\( \boldsymbol{O H}^{-} \longrightarrow \boldsymbol{C H}_{3}-\stackrel{\oplus}{\boldsymbol{C} \boldsymbol{H}}-\boldsymbol{N} \boldsymbol{O}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \)
obeys the rate law for pseudo first order
kinetics in the presence of a large excess of hydroxide ion. If \( 1 \% \) of nitro ethane undergoes reaction is half a minute when the reactant
concentration is \( 0.002 M . \) What is the
pseudo first order rate constant? \( (\log 99=1.996) \)


Identify the type of set \( \boldsymbol{B}=\{\boldsymbol{x}: \boldsymbol{x} \boldsymbol{\epsilon} \boldsymbol{W}, \boldsymbol{x}=\boldsymbol{2} \boldsymbol{n}\} \)
A. Finite Set
B. Null Set
c. Infinite Set
D. singleton set


In which year Robert Hooke presented his law of elasticity?
A . 1672
в. 1674
c. 1676
D. 1678


List 1 and List 2 contains four entries
each. Entries of List 1 are to be matched
with some entries of List 2. One or more
than one entries of List 1 may have the matching with the same entries of List
2


An electricity bulb of 100 watt is connected to supply of electricity of 220V. Resistance of filament is
A . \( 484 \Omega \)
в. \( 100 \Omega \)
c. \( 22000 \Omega \)
D. 242\Omega


The viscous force acting on a body falling under gravity in a viscous fluid will be
A \( \cdot \frac{6 \pi V}{\eta r} \)
в. \( \frac{6 \pi \eta r}{V} \)
c. \( 6 \pi \eta r V \)
D. \( \frac{r V}{6 \pi \eta} \)


If an edge of a cube measure \( 2 \mathrm{m} \) with a
possible error of \( 0.5 \mathrm{cm} . \) Find the corresponding error in the calculated volume of the cube.
\( \mathbf{A} \cdot 0.6 m^{3} \)
В. \( 0.06 m^{3} \)
c. \( 0.006 m^{3} \)
D. \( 0.0006 \mathrm{m}^{3} \)


Fill in the blanks:
(a) Phosphorus is very \( _{-}---- \) non-
metal.
(b) Metals are conductors of heat
and
(c) Iron is \( _{-1-} \) reactive than
copper.
(d) Metals react with acids to produce
gas.


Geeta purchased a face-cream for Rs. 79.10 including Sales Tax. If the printed price of the face-cream is Rs. \( 70 ; \) find the rate of Sales Tax.
A . \( 2 \% \)
B. \( 7 \% \)
c. \( 11 \% \)
D. \( 13 \% \)


If the length of the common chord of two intersecting equal circles be \( 6 \mathrm{cm} \) and
if the radius of each circle be \( 5 \mathrm{cm} \) then
the distance between the centers of the
circle is
A. \( 7 \mathrm{cm} \)
B. \( 8 \mathrm{cm} \)
\( c .9 \mathrm{cm} \)
D. none


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


Toluidine blue specifically stains
A. DNA
B. RNAA
c. chitin
D. Lignin


The chronological order of human
evolution from early to the recent is
A. Ramapithecus \( \rightarrow \) Homo habilis \( \rightarrow \) Australopithceus \( \rightarrow \) Homo erectus
B. Australopithecus \( \rightarrow \) Homo habilis \( \rightarrow \) Ramapithecus \( \rightarrow \) Homo erectus
C. Australopithecus \( \rightarrow \) Ramapithecus \( \rightarrow \) Homo habilis \( \rightarrow \) Homo erectus
D. Ramapithecus \( \rightarrow \) Australopithceus \( \rightarrow \) Homo habilis \( \rightarrow \) Homo erectus