Draw a right triangle \( A B C \) in which \( B C=12 \mathrm{cm}, A B=5 \mathrm{cm} \) and \( \angle B= \)
\( 90^{0} . \) Construct a triangle similar to it and of scale factor \( \frac{2}{3} . \) Is the new triangle also a right triangle?
A. Yes
B. No
c. can't say
D. Data insufficient


In the structure of \( \boldsymbol{H}_{2} \boldsymbol{C S} \boldsymbol{F}_{4}, \) which of
the following statement(s) is/are
correct?

This question has multiple correct options
A. Two \( C-H \) bonds are in the same plane of axial \( S-F \) bonds
B. Two \( C-H \) bonds are in the same plane of equitoria \( S-F \) bonds.
c. Total six atoms are in the same plane.
D. Equitorial \( S-F \) plane is perpendicular to nodal plane
of \( \pi- \) bond


Eutrophication results in the reduction
of
A. Dissolved hydrogen
B. Dissolved oxygen
c. Mineral salts
D. None of the above


The last or terminal cytochrome in respiratory chain is
A. cyt b
B. Cyt \( a_{3} \)
c. cyt a
D. cytc


Column I contains some terms and
column II contains their meanings.
Match the properly and choose the right
answer.
Colum Column II
1. Conversion of glycogen to
A. Glycogenesis
2. Conversion of glucose to
B. Glycosuria \( \quad \) glycogen
C. \( \quad \) 3. Excretion of glucose in urine Glyconeogenesis
4. Conversion of non-
D. \( \quad \) carbohydrate sources to Glycogenolysis
5. Conversion of glucose to starch
\( A \cdot A-1, B-2, C-3, D-4 \)
B. A-2, B-3, C-4, D-1
C \( . \) A- \( 2, \) B-1, C-3, D-4
D. \( A-1, B-5, C-2, D-4 \)


A neutral organic compound A has
formula \( C_{9} H_{16} O_{3} \) and rotates plane
polarized light. A on acid hydrolysis
produces \( \mathrm{B} \) and \( C\left(C_{3} H_{8} O\right) . \) C on partial
oxidation with PCC gives \( D\left(C_{3} H_{6} O\right) \) which does not give iodoform test. D on treatment with dilute solution of
\( N a O H \operatorname{gives} E\left(C_{6} H_{12} O_{2}\right) \) which is
diastereomeric. E on treatment with the
acidic solution of \( K M n O_{4} \) produces \( B \)
Deduce structures of A to E.


Internal energy of \( n_{1} \) moles of hydrogen at temperature \( T \) is equal to the internal
energy of \( n_{2} \) moles of helium at
temperature 2T. Then the ratio \( n_{1} / n_{2} \) is:
A
B. \( \frac{2}{3} \)
\( c \cdot \frac{6}{5} \)
D. \( \frac{3}{7} \)


Find the multiplicative inverse of the complex number \( \sqrt{5}+3 i \)


Give reason
It is different to demonstrate
respiration in plants.


\( 3 \mathrm{mL}, \) of ethanol is taken in a test tube
and warmed gently in a water bath. A \( 5 \% \) solution of alkaline potassium
permanganate is added first drop by drop to this solution, then in excess.
Write chemical equation of this
reaction.


If the object is not grounded while performing electrostatic induction, the nearby charge will
A. induce equal and opposite charges in the object.
B. induce equal charges in the object.
c. induce opposite charges in the object
D. None of the above


In a fuel cell the fuel is fed to which
compartment?
A. Anode compartment
B. Cathode compartment
c. Both the compartments
D. None of the above


Three forces \( A, B \) and \( C \) acting at a point are in equilibrium. The ratio of angles between \( A \) and \( B ; B \) and \( C ; \) and
\( A \) and \( C \) is \( 1: 2: 3 . \) Then, \( A: B: C \) is
A. \( 1: \frac{\sqrt{3}}{2}: \frac{1}{2} \)
B. \( \frac{1}{2}: \frac{\sqrt{3}}{2}: 1 \)
c. \( _{1: \frac{1}{2}: \frac{1}{3}} \)
D. \( 1: \frac{1}{\sqrt{2}}: \frac{1}{\sqrt{3}} \)
E. None of these


Excess of KI reacts with \( C u S O_{4} \)
solution and then \( N a_{2} S_{2} O_{3} \) solution is
added to it. Which of the statement is
incorrect for this reaction?
A \( \cdot C u_{2} I_{2} \) is formed
B. \( C u I_{2} \) is formed
c. \( N a_{2} S_{2} O_{3} \) is oxidised
D. Evolved \( I_{2} \) is reduced


The relative formula mass, \( M_{r}, \) of
calcium carbonate, \( C a C O_{3}, \) is 100
What is the mass of carbon present in \( 100 g \) of calcium carbonate?
A \( .12 g \)
B. \( 36 g \)
c. \( 40 g \)
D. \( 60 g \)


Find the radius of the wire of length
\( 25 m \) needed to prepare a coil of
resistence \( 25 \Omega \) (Resistivity of material of wire is \( \left.3.142 \times 10^{-7} \Omega m\right) \)


Find the maximum value of current
when inductance of two henry is connected to \( 150 V, 50 \) cycle supply
\( ^{\mathrm{A}} \cdot \frac{3}{2 \sqrt{2} A} \)
B. \( \frac{5}{2 \sqrt{2} A} \)
c. \( \frac{6}{2 \sqrt{2} A} \)
D. \( \frac{7}{2 \sqrt{2} A} \)


The diameter of the moon is about 3500
km. What will be the diameter of the
image formed by a concave mirror of radius 3 m? Assume that the distance
of the moon is about \( 3 \cdot 5 \times 105 k m \)
\( A \cdot 5 \mathrm{mm} \)
B. 10 \( \mathrm{mm} \)
\( c \cdot 15 \mathrm{mm} \)
D. 20 mm


The sum of an integer and its additive inverse is always
A .
B. - -
c. 0
\( D \)


Where will the hand of a clock stop if it:
Start at 4 and makes \( \frac{3}{4} \) of a revolution, clockwise?


A ball is tossed in the air in such a way
that the path of the ball is modeled by
the equation \( y=-x^{2}+6 x \) where \( y \)
represents the height of the ball in feet
and \( x \) is the time in seconds. At what
time \( x \) will the ball reach the ground
again?
\( \mathbf{A} \cdot \mathbf{6} \)
B. 2
\( c \cdot 3 \)
D. 4
E .


The angular speed of the electron in the
\( \boldsymbol{n}^{t h} \) Bohr orbit of the hydrogen at om is
proportional to
\( A \cdot n \)
B \( \cdot n^{3} \)
c. \( \frac{1}{n} \)
D. \( \frac{1}{n^{3}} \)


Three groups \( A, B, C \) are contesting for positions on the Board of Directors of a company. The probabilities of their
winning are 0.5,0.3,0.2 respectively. If
the group \( A \) wins, the probability of
introducing a new product is 0.7 and the corresponding probabilities for groups \( B \) and \( C \) are 0.6 and 0.5
respectively. The probability that the new product will be introduced is given
by
A . 0.36
в. 0.35
c. 0.63
D. 0.53


Statement: Chloramphenicol is board spectrum antibiotic.

State whether the given statement is true or false.
A. True
B. False


Two identical containers each of volume \( V \)
0 are joined by a small pipe. The containers contain identical gases at
temperature \( T_{0} \) and pressure \( P_{0} . \) One
container is heated to temperature \( 2 \mathrm{T}_{0} \)
while maintaining the other at the
same temperature. The common pressure of the gas is \( \mathrm{P} \) and \( \mathrm{n} \) is the number of moles of gas in container at
temperature \( 2 T_{0} \)
\( \mathbf{A} \cdot P=2 P_{0} \)
в. \( \quad P=\frac{4}{3} P_{0} \)
c. \( _{n}=\frac{2 P_{0} V_{0}}{3 R T_{0}} \)
D. \( n=\frac{3 P_{0} V_{0}}{2 R T_{0}} \)


For the reaction, \( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{I}_{2}(\boldsymbol{g}) \rightleftharpoons \)
\( 2 H I(g), \) the equilibrium constant \( K_{p} \)
changes with:
A. total pressure
B. catalyst
C. the amounts of \( H_{2} \) and \( I_{2} \) present
D. temperature


Consider the motion of a positive point charge in a region where there are simultaneous uniform electric and
magnetic fields \( \mathrm{E}=\mathrm{EO} \mathrm{j} \) and \( \mathrm{B}=\mathrm{BO} \mathrm{j}, \mathrm{At} \)
time \( t=0, \) this charge has velocity \( v \) in the \( x \) -y plane, making an angle 0 with the \( x \) -axis. Which of the following option(s) is(are) correct for time \( t>0 ? \)


Which of the following hydrogen bonds are strongest in vapour phase?
A. HF \( \ldots \). HF. HF
B. HF ................ HCl
c. нс।................ нс।
D. HF ................ H


Which of the following constitute
sodium chloride crystal?
A. Sodium and chlorine atoms
B. \( N a C l \) molecules
c. Sodium ions and chloride ions
D. Sodium atoms and chlorine molecules


Divide \( (24 x-42) \) by \( (4 x-7) \)
A \( .4 x-7 \)
B. 3
\( c \cdot 6 \)
D. 7


Arrange the following stages of the human evolution in the order of their
increasing cranial capacity?
a) Neanderthal man
b) Cro-magnon
man
c) Homo erectus
d) Homo habilis


The bond order depends on the number of electrons in the bonding and non bonding orbitals. Which of the following statements is /are correct about bond
order?
A. Bond order cannot have a negative value.
B. It always has an integral value
c. It is a nonzero quantity.
D. It can assume any value-positive or negative, integral or fractional, including zero.


A block of mass \( 10 \mathrm{kg} \) is pulled by a constant horizontal force of \( 19 \mathrm{N} \) and it
is displaced by \( 15 \mathrm{m} \) across the floor. Calculate the work done.
A . 1.3
в. 30 J
c. 285 J
D. 5586 J
E. 1


The colour of \( C r O_{4}^{2-} \) is due to:
A. charge tranfer.
B. d-d transition.
c. it does not shows colour.
D. none of the above


Do plant need oxygen? If so, what is its
source?


150 spherical marbles, each of diameter \( 1.4 \mathrm{cm}, \) are dropped in a
cylindrical vessel of diameter \( 7 \mathrm{cm} \)
containing some water, which are completely immersed in water. Find the rise in the level of water in the vessel


On a Fahrenheit scale:
A. boiling point of water is \( 212^{\circ} F \)
B. the temperature will be equal to that on the Celsius
scale \( a t-40^{\circ} C \)
C. the difference between the upper fixed point and the lower fixed point is divided into 180 equal parts
D. all the above


Solve the differential equation \( \frac{d y}{d x}+ \)
\( \boldsymbol{y}=\boldsymbol{e}^{-\boldsymbol{x}} \)


Assertion
Hybridization of \( \left[\boldsymbol{A u C l}_{4}\right]^{\Theta} \) is \( \boldsymbol{s p}^{3} \)
Reason
Hybridization of Au in above complex
compound does not depend upon nature
of ligand.
A. Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.
B. Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1
C. Statement-1 is true, statement-2 is false.
D. Statement-1 is false, statement-2 is true.


When the electric current is passed
through a cell having an electrolyte, the positive ions move towards cathode and negative ions towards the anode. If the cathode is pulled out of the solution
then
A. the positive and negative ions will be move towards anode
B. the positive ions will start moving towards the anode and while negative ions will stop moving
c. the negative ions will continue to move towards and while positive ions will stop moving
D. the positive and negative ions will start moving random


Inorganic cofactor is often called
A. Coenzyme
B. Prosthetic group
c. Modulator
D. Activator


Assertion
Paramagnetic substances get poorly attracted in magnetic field.
Reason
Because magnetic dipoles are aligned along external magnetic field weakly.
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


Evaluate: \( \int_{0}^{\pi / 2} \frac{\sin ^{2} x}{\sin x+\cos x} d x \)


In benzene, each carbon atom
undergoes:
A. sp hybridization
B . \( s p^{2} \) hybridization
c. \( s p^{3} \) hybridization
D. \( d s p^{2} \) hybridization


If an A.P is given by \( 17,14, \ldots \ldots-40 \)
then 6 th term from the end is
A \( .-22 \)
B. -28
c. -25
D. 26


Assertion
When current through a bulb decreases by \( 0.5 \%, \) the glow of bulb decreases by
\( 1 \% \)
Reason
Glow (Power) which is directly proportional to square of current.
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


Consider a sample of helium and a
sample of neon, both \( a t 30^{0} C \) and
1.5 atm. Both samples have a volume of
5.0 \( L \). Which statement concerning these samples is not true?
A. Each sample contains the same number of atoms of gas
B. Each sample weighs the same amount
c. Each sample contains the same number of moles of gas
D. The density of the neon is greater than the density of the helium


Teflon is an example of polymer which is a/an
A. polyamide
B. addition Ploymer
c. polyster
D. formaldehyderesin


On adding \( 0.1 M \) solution each of
\( \left[\boldsymbol{A} \boldsymbol{g}^{+}\right],\left[\boldsymbol{B} \boldsymbol{a}^{2+}\right],\left[\boldsymbol{C} \boldsymbol{a}^{2+}\right] \) in \( \boldsymbol{N} \boldsymbol{a}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
solution, species first precipitated is:
\( \left[\boldsymbol{K}_{s p}\left(\boldsymbol{B} \boldsymbol{a} \boldsymbol{S} \boldsymbol{O}_{4}\right)=\mathbf{1 0}^{-11}, \boldsymbol{K}_{s p}\left(\boldsymbol{C a} \boldsymbol{S O}_{4}\right)=\right. \)
A \( \cdot A g_{2} S O_{4} \)
в. Ва а S О\( _{4} \)
\( c \cdot \operatorname{cas} O_{4} \)
D. All of these


The value of \( \int_{0}^{\infty} \frac{d x}{\left(x^{2}+4\right)\left(x^{2}+9\right)} \) is
A \( \cdot \frac{\pi}{60} \)
в. \( \frac{\pi}{20} \)
c. \( \frac{\pi}{40} \)
D. \( \frac{\pi}{80} \)


The volume(V) of a monatomic gas
varies with its temperature (T), as
shown in the graph. The ratio of work
done by the gas, to the heat absorbed by
it, when it undergoes a change from
state \( A \) to state \( B \), is?
A \( \cdot \frac{1}{3} \)
B. 2 \( \overline{5} \)
\( c \cdot 2 \)
7
D. 2
3


The law that describes the force as
directly proportional to magnitude of charges and inversely proportional to the distance between the charges is
known as:
A. Newton's law
B. Coulomb's law
c. Gauss's law
D. Ohm's law


Wurtz reaction of methyl iodide yields an organic compound \( X . \) Which one of
the following reactions also yields \( X ? \)
A \( \cdot C_{2} H_{5} C l+M g \stackrel{\text { Dry ether }}{\longrightarrow} \)
B . \( C_{2} H_{5} C l+L i A l H_{4} \rightarrow \)
c. \( C_{2} H_{5} C l+C_{2} H_{5} O N a \rightarrow \)
D. \( C H C l_{3} \frac{A g \text { powder }}{\wedge} \)


Which among the following is a traquilizer?
A. Aspirin
B. Valium
c. Pencillin
D. Sulphanilamide


If \( \vec{a}, \vec{b} \) and \( \vec{c} \) are three non-zero vectors such that \( \vec{a} \cdot \vec{b}=\vec{a} \cdot \vec{c}, \) then
\( A \cdot \vec{b}=\vec{c} \)
В . \( \vec{a} \perp \vec{b}, \vec{c} \)
c. \( \vec{a} \perp \vec{b}-\vec{c} \)
D. either \( \vec{a} \perp(\vec{b}-\vec{c}) \) or \( \vec{b}=\vec{c} \)


If \( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{cl}\frac{\sin \{\cos \boldsymbol{x}\}}{\boldsymbol{x}-\frac{\pi}{2}}, & \boldsymbol{x} \neq \frac{\boldsymbol{\pi}}{2} \\ \mathbf{1}, & \boldsymbol{x}=\frac{\boldsymbol{\pi}}{2}\end{array}\right. \)
(.) represents the fractional part function,
then \( \lim _{x \rightarrow \pi / 2} f(x) \) is?
\( A \)
B.
c. Does not exist
D.


Write the complete chemical reaction of rusting of iron.


Pollution of lakes and rivers affects
aquatic life. Fish cannot live in water
that has oxygen less than 4 milligrams per liter. Other freshwater aquatic life (including anaerobic bacteria) also cannot survive without adequate oxygen.'BOD' stands for:
A. Biological oxygen demand
B. Bacterial oxygen deficit
c. Basic oxygen demand
D. Building oxygen deposits


Suppose a continuous function \( \boldsymbol{f} \) \( [0, \infty) \rightarrow R \) satisfies \( f(x)= \)
\( 2 \int_{0}^{x} t f(t) d t+1 \) for all \( x \geq 0 \)
Then \( \boldsymbol{f}(\mathbf{1}) \) equals
\( A \)
B \( \cdot e^{2} \)
\( c \cdot e^{4} \)
D. \( e^{6} \)


If sum of \( n \) terms of a sequence is given
by \( S_{n}=2 n^{2}+3 n, \) find its \( 50^{t h} \) term.


Four wires of the same diameter are
connected, in turn, between two points maintained at a constant potential difference. Their resistivity's and lengths are; \( \rho \) and \( L(\text { wire } 1), 1.2 \rho \) and 1.2L (wire 2), \( 0.9 \rho \) and 0.9L (wire 3) and
\( \rho \) and \( 1.5 \mathrm{L} \) (wire 4 ). Rank the wires
according to the rates at which energy is dissipated as heat, greatest first.
A \( .4>3>1>2 \)
в. \( 4>2>1>3 \)
c. \( 1>2>3>4 \)
D. \( 3>1>2>4 \)


Match the columns and choose the
correct option.
\( \begin{array}{lllll} & \text { Column-I } & & \text { Column-II } & \\ \text { A. } & \text { Adrenaline } & \text { 1. } & \begin{array}{l}\text { Anger, fear, } \\ \text { danger }\end{array} \\ \text { B. } & \text { Oestrogen } & \text { 2. } & \begin{array}{l}\text { partnerting } \\ \text { through sense of } \\ \text { smell }\end{array} \\ \text { D. } & \text { Pheromones } & \text { 4. } & \text { Glucose }\end{array} \)
\( A \cdot A-3, B-1, C-4, D-2 \)
B. A-1,B-3,C-2,D-4
C. \( A-1, B-3, C-4, D-2 \)
D. \( A-3 . B-1 . C-2 . D- \)


The number of electrons that are
involved in the reduction of
permanganate to manganese (II) salt, manganate and manganese dioxide respectively are
A. 5,1,3
B. 5,3,1
c. 2,7,1
\( \mathbf{D} \cdot 5,2,3 \)
E .2,3,1


Several spherical drops of a liquid of radius coalesce to form a single drop to
radius \( R \). If the surface tension and \( V \) is
volume and \( r \) consideration, then the
release of energy is :
\( ^{\mathbf{A}} \cdot_{3 V T}\left(\frac{1}{r}+\frac{1}{R}\right) \)
B. \( \quad 3 V T\left(\frac{1}{r}-\frac{1}{R}\right) \)
\( ^{\mathrm{c}} \cdot_{V T}\left(\frac{1}{r}-\frac{1}{R}\right) \)
D. \( V T\left(\frac{1}{r^{2}}+\frac{1}{R^{2}}\right) \)


Find the range of the following
functions
\( \sqrt{x-5} \)


Metallic sodium is used as a drying
agent for:
This question has multiple correct options
A. chloroform
B. cyclohexane
c. diispropyl ether
D. diethylamine


Assertion: If a man with a wrist watch
on his hand falls from the top of a tower, its watch gives correct time during the
free fall.
Reason :The working of the wrist
watch depends on spring action and it has nothing to do with gravity.
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


1 m is equal to
\( \mathbf{A} \cdot 10^{-6} \) micron
B. \( 10^{6} \) micron
C \( \cdot 10^{-3} \) micron
D. \( 10^{3} \) micron


The units of conductivity are:
A. siemens \( ^{-1} \mathrm{cm}^{-1} \)
B. siemens cm
c. siemens \( c m^{-1} \)
D. siemens \( c m^{-1} m o l^{-1} \)


Define energy density of the median surrounding a charged conductor and state its formula.


Write the equations involved in the following reactions:
(i) Reimer - Tietmann reaction
(ii) Williamson synthesis


Point out the correct floral formula of
cruciferae
\( \mathbf{A} \cdot K_{2+2} C_{4 x} A_{2+4} G_{(2)} \)
B . \( K_{5} C_{6} A_{3} G_{(2)} \)
C. \( K_{2+2} C_{4} A_{2+4} G_{(2)} \)
D. \( K_{4} C_{4} A_{2} G_{(2)} \)


The structure of the \( S O_{3} \) molecule in
the gaseous phase contains:
B. \( \sigma \) -bonds and a (p\pi-p \( \pi \) ) bonds between sulphur and oxygen
c. \( \sigma \) -bonds and a (d \( \pi \) -p \( \pi \) ) bonds between sulphur and oxygen
D. \( \sigma \) -bonds, and a (p\pi-p \( \pi \) ) and a (p \( \pi \) -d \( \pi \) ) bonds between sulphur and oxygen


Molecular scissors which cut DNA at
specific site is known as
A. Pectinase
B. Polymerase
c. Restriction endonuclease
D. Ligase


In Greece and Italy, marble statues were damaged by:
\( A \cdot \operatorname{smog} \)
B. acid rains
c. eutrophication
D. leakage of \( C l_{2} \)


Bones glow in the dark because:
A. they contain shining material.
B. they contain red phosphorus.
C. white phosphorus undergoes slow combustion in contact with air.
D. white phosphorus changes into red form.


ff \( \boldsymbol{y}=\boldsymbol{y}(\boldsymbol{x}) \) satisfies the differential equation \( 8 \sqrt{x}(\sqrt{9+\sqrt{x}}) d y= \)
\( (\sqrt{4+\sqrt{9+\sqrt{x}}})^{-1} d x, x>0 \) and
\( \boldsymbol{y}(\mathbf{0})=\sqrt{\mathbf{7}}, \) then \( \boldsymbol{y}(\mathbf{2 5 6})= \)
\( A \)
B.
c. 16
D. 80


Find the domain of the following
function:
\( \boldsymbol{f}(\boldsymbol{x})=\cos ^{-1} \sqrt{\log [\boldsymbol{x}] \frac{|\boldsymbol{x}|}{\boldsymbol{x}}}, \) where, \( [\cdot] \)
denotes the greatest integer function.


The wrong option among the following
statements is :
A. The decreasing order of the value of the heat of combustion is :
B. cycloalakanes are planar
C. cyclopropane has a higher heat of combustion per methylene group \( \left(C H_{2}\right) \) than that of cyclobutane.
D. with the exception of cyclopropane, cycloalkanes are non-planar


A transformer with a \( 110 V \) primary has
a 15: 1 turns ratio. The load resistance,
\( R_{L}, \) is \( 120 . \) What is the approximate voltage across the load?
A . \( 7.3 V \)
B. \( 73 V \)
\( c .88 V \)
D. \( 880 V \)


The rate constants of a reaction at
\( 500 K \) and \( 700 K \) are \( 0.02 s^{-1} \) and
\( 0.07 s^{-1} \) respectively.

Calculate the values of \( \boldsymbol{E} \boldsymbol{a} \) and \( \boldsymbol{A} \) :


External protective tissues of plants
are
A. Cortex and Epidermis
B. Pericycle and Cortex
c. Epidermis and cork
D. Pericycle and Cork


A committee of two persons is selected from two men and two women. What is
the probability that the committee will
have no man?


A wire elengates by Imm when a weight w is hanged than it. If wire goes over a pulley and 2 weights W each are huge at two ends. What will be elongations of wire is mm?


Cathode rays have:
A. mass only
B. charge only
C. both mass and charge
D. neither mass nor charge


The removal of topsoil by water and wind is called as
A. Soil tilling
B. Soil erosion
c. soil mulching
D. Weathering


The perimeter of a sector is \( P . \) The area of the sector is maximum when its radius is
\( A \cdot 1 / \sqrt{P} \)
B. \( P / 2 \)
c. \( P / 4 \)
D. \( \sqrt{P} \)


An open flask contains air at \( 27^{\circ} \mathrm{C} \). At
what temperature should it be heated so that \( 1 / 3 r d \) of air present in it goes
out?
A \( \cdot 177^{\circ} \mathrm{C} \)
B. \( 100^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 300^{\circ} \mathrm{C} \)
D. \( 150^{\circ} \mathrm{C} \)


Two point size bodies of masses \( 20 g \)
\( 30 g \) are fixed at two ends of a light rod
of length \( 1.5 m . \) The moment of inertia of these two bodies about an axis
perpendicular to the length of rod and
passing through their center of mass is:
A. \( 1.8 \times 10^{-2} k g m^{2} \)
В. \( 2.7 \times 10^{-2} k g m^{2} \)
c. \( 4.5 \times 10^{-2} k g m^{2} \)
D. \( 6 \times 10^{-2} k g m^{2} \)


Write the simplest form of \( \tan ^{-1}[\sqrt{\frac{1-\cos x}{1+\cos x}}] \)


It is evident that, it is the genetic make up of the sperm that determine the sex of the child in human beings.
Substantiate.


The Sl unit of linear momentum is
\( \boldsymbol{k} \boldsymbol{g} \boldsymbol{m} / \boldsymbol{s}^{-1} \)
A. True
B. False


Solve: \( \frac{d y}{d x}+2 y=\sin x \)


The intensity of light beyond a particular limit is unable to increase the rate of photosynthesis. The phenomena is known as
A. Light compensation point.
B. Light saturation intensity
c. Solarization
D. None of the above


A dilute ferrous sulphate solution was
gradually added to the beaker
containing acidified potassium
permanganate solution. The light purple colour of the solution fades and finally disappears. Which of the following is the correct explanation for the observation?
A \( \cdot K M n O_{4} \) is an oxidising agent, and it oxidies \( F e S O_{4} \)
B. \( F e S O_{4} \) acts as an oxidising agent and oxidises
\( K M n O_{4} \)
C. The colour disappear due to dilution; no reaction is involved
D. \( K M n O_{4} \) is an unstable compound and decomposes is presence of \( F e S O_{4} \) to a colourless compound


A \( 4 \mathrm{cm} \) tall object is placed perpendicular to the principal axis of a convex lens of focal length \( 24 \mathrm{cm} . \) The distance of the object from the lens is 16 cm. Find the position, size and nature of the image formed, using the lens formula.


valuate: \( \left|\begin{array}{cccc}1 & a & a^{2} & a^{3}+b c d \\ 1 & b & b^{2} & b^{3}+c d a \\ 1 & c & c^{2} & c^{3}+a b d \\ 1 & d & d^{2} & d^{3}+a b c\end{array}\right| \)


For a reversible reaction, \( \boldsymbol{A}+\boldsymbol{B} \rightleftharpoons \boldsymbol{C}+ \)
\( D, \) the graph for rate of reaction with
time is given below. Mark the terms \( (p),(q) \) and \( (r) \)
A \( \cdot(p)- \) rate of backward reaction
(q) - rate of forward reaction
(r) - equilibrium
B. (p) - rate of forward reaction,
(q) - rate of backward reaction, (r) - equilibrium
c. (p) - concentration of products
(q) - concentration of reactants, (r) - rate of reaction
D. (p) - instantaneous rate of reaction,
(q) - variation of rate, (r) - average rate of reaction


Assertion
Every biological system resist a change and wants to remain in state of
equilibrium.
Reason
Climax communities of an ecosystem are produced after several changes it has gone through succession.
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


Diodes \( D-1 \) and \( D_{2} \) shown in circuit
are silicon diodes.The voltage drop (V)
across the diode \( D_{2} \) and the power
dissipated (P) by this diode \( \left(D_{2}\right) \) are
\( \mathbf{A} \cdot V_{D_{2}}=0.7 V \) and \( P_{D_{2}}=0 W \)
B. \( V_{D_{2}}=5 V \) and \( P_{D_{2}}=0 W \)
\( \mathbf{C} \cdot V_{D_{2}}=0.7 V \) and \( P_{D_{2}}=0.7 W \)
D. \( V_{D_{2}}=5.0 V \) and \( P_{D_{2}}=5 W \)


(a) What is shunt?
(b) State Ampere's circuital law. Using the law, obtain an expression for the
magnetic field well aside the solenoid of finite length.


In which of the following is true bacteria?
A. Archea Bacteria
B. Cyano Bacteria
c. Eu bacteria
D. Both B and C


\( \left(\boldsymbol{C} \boldsymbol{H}_{3}\right)_{2} \boldsymbol{C B r} \boldsymbol{C H}_{2} \boldsymbol{C H}_{3} \)
Give IUPAC name of the compound.


Mass \( \% \) of carbon in ethanol is:
A . 52
B. 13
c. 34
D. 90
E . 80


The correct arrangement for taking
temperature in the study of the
temperature-time graph is shown in
figure
A . \( A \)
B. \( B \)
\( c . c \)
D. \( D \)


Which of the following will produce a buffer solution when mixed in equal
volumes?
A. 0.1 mol \( d m^{-3} N H_{4} O H \) and 0.1 mol \( d m^{-3} H C l \)
B. 0.05 mol \( d m^{-3} N H_{4} O H \) and 0.1 mol \( d m^{-3} \) HCl
c. 0.1 mol \( d m^{-3} N H_{4} O H \) and 0.05 mol \( d m^{-3} H C l \)
D. 0.1 mol \( d m^{-3} C H_{3} C O O N a \) and 0.1 mol \( d m^{-3} \) NaOH


Give two examples of the fundamenta physical quantities along with their S.
units.


Two thin lenses of focal lengths \( 20 \mathrm{cm} \)
and \( 25 c m \) are placed in contact. The effective power of the combination is
A \( \cdot \frac{1}{9} D \)
B. \( 45 D \)
\( c . \$ \$ 6 D \$ \)
D. \( 9 D \)


The experiment value for the molar mass of a non-volatile solute is twice
the theoretic value. What is Vant Hoff
factor for the solute?


A wire elongates by I mm when a load \( \mathbf{W} \) is hanged from it. If the wire goes over a pulley and two weights Weach are hung at the two ends,the elongation of the wire will be (in mm)
A. zero
B. I / 2
\( c \)
D. 2


Find the middle term of \( \left(\frac{a}{x}+\frac{x}{a}\right)^{10} \)


The mass of hydrogen at STP, that is present in a vessel which can hold 4
grams of oxygen under similar conditions, is:
\( A \cdot 1 g m \)
B. \( 0.5 \mathrm{gm} \)
c. \( 0.25 \mathrm{gm} \)
D. 0.125 gm


A ray of light strikes a glass plate at an angle of \( 60^{0} . \) If the reflected and
refracted rays are perpendicular to each other the index of refraction of glass is
A \( \cdot \frac{1}{2} \)
B. \( \frac{\sqrt{3}}{2} \)
\( c \cdot \frac{3}{2} \)
D. 1.732


A die is thrown. Write the sample space.
If \( A \) is the event that the number is a
perfect square, write the event \( \boldsymbol{A} \) using set notation.


Isotopes differ in:
A. no. of electrons
B. no. of protons
C. no. of neutrons
D. chemical reactivity


A true solution (or simply a solution) is a homogeneous mixture, in which the solute and solvent molecules cannot be
distinguished even under a microscope.
A. True
B. False


Versatile anthers occur in
A. Helianthus annuus
B. Oryza sativa
c. solanum tuberosum
D. Hibiscus esculentus


The volume of spherical ball is increasing at the rate of \( 4 \pi c c / \) sec. Then rate of surface area when volume is
\( 288 \pi c c \) is
\( ^{\mathbf{A}} \cdot \frac{3 \pi}{4} c m^{2} / s e c \)
B. \( \frac{4}{3} c m^{2} / \) sec
c. \( \frac{4 \pi}{3} \mathrm{cm}^{2} / \mathrm{sec} \)
D. \( \frac{3}{4} c m^{2} / \) sec


Evaluate \( \sum_{n=1}^{N} U_{n} \) if
\[
\boldsymbol{U}_{\boldsymbol{n}}=\mid \begin{array}{ccc}\boldsymbol{n} & \mathbf{1} & \mathbf{5} \\ \boldsymbol{n}^{2} & \boldsymbol{2} \boldsymbol{N}+\mathbf{1} & \boldsymbol{2} \boldsymbol{N}+\mathbf{1} \\ \boldsymbol{n}^{\boldsymbol{3}} & \boldsymbol{3} \boldsymbol{N}^{2} & \boldsymbol{3} \boldsymbol{N}\end{array}
\]


Two cells of equal emf and of internal
resistances \( r_{1} \) and \( r_{2}\left(r_{1}>r_{2}\right) \) are
connected in series. On connecting this combination to an external resistance
\( \mathrm{R}, \) it is observed that the potential difference across the first cell becomes
zero. The value of R will be.
\( \mathbf{A} \cdot r_{1}+r_{2} \)
В. \( r_{1}-r_{2} \)
c. \( \frac{r_{1}+r_{2}}{2} \)
D. \( \frac{r_{1}-r_{2}}{2} \)


Find the value of \( k \) for which the
equation \( 3 x^{2}-6 x+k=0 \) has distinct
and real root.


Which of the following statement(s)
is/are correct?
This question has multiple correct options
A. Rhombic sulphur is stable at room temperature.
B. Monoclinic sulphur is stable at room temperature.
C. Both rhombic and monoclinic sulphur has the molecular formula \( S_{8} \)
D. Both rhombic and monoclinic sulphur are soluble in \( C S_{2} \)


If \( f(x)=l x \) and \( a, b, c \) are in A.P. \( k, l \) are
constants. Then \( \boldsymbol{f}(\boldsymbol{a}-\boldsymbol{k}), \boldsymbol{f}(\boldsymbol{b}-\boldsymbol{k}), \) and
\( f(c-k) \) are in
A . A.
в. с.
c. н.
D. A.G.P


(A) Draw a diagram showing the path of a monochromatic light through a triangular prism.
(B) Using this diagram obtain the relation \( n_{21}=\frac{\sin \left(\frac{A+D_{m}}{2}\right)}{\sin \left(\frac{A}{2}\right)} \)


The advantage/s associated with water harvesting at the community level is/are
A. The ground water level increases due to recharging of wells
B. Ground water keeps the layers of soil above it moist and prevents loss of water by evaporation.
c. Ground water keeps the layers of soil above it dry and prevents loss of water by evaporation
D. Both A and B


A ball is dropped from a height of \( 1 m \) The coefficient of restitution between the ground and the ball is \( 1 / 3 . \) The height to which the ball will rebound after two collisions with ground is :
A. \( 9 m \)
в. \( 1 / 9 m \)
c. \( 1 / 81 m \)
D. \( 81 m \)


The phenomenon by which the incident light falling on a surface is sent back into the same medium is known as
A. Reflection
B. Refraction
c. Dispersion
D. None


The graph of the equation \( x^{2}+\frac{y^{2}}{4}=1 \)
is
A. an ellipse
B. a circle
c. a hyperbola
D. a parabola
E. two straight lines


For making distinction between 2
pentanone and 3-pentanone the reagent to be employed is :
A \( \cdot K_{2} C r_{2} O_{7} / H_{2} S O_{4} \)
в. \( Z n-H g / H C l \)
\( \mathrm{c} \cdot \operatorname{Se} \mathrm{O}_{2} \)
D \( \cdot I_{2} / N a O H \)


A current of 5 A is flowing at 220 V in the primary coil of a transformer. if the voltage produced in the secondary coil
is \( 2200 \mathrm{V} \) anf \( 50 \% \) of power is lost, then the current in secondary will be


Show that between any two roots of the
equation \( e^{x} \cos x=1 \) there exists
atleast one root of \( e^{x} \sin x-1=0 \) by continuity and differentiability.


The mass number of a nucleus is:
A. Always less than atomic number
B. Always more than atomic number
C. Equal to atomic number
D. More than or equal to atomic number


Four resistance \( 5 \Omega, 10 \Omega, 15 \Omega \) and an unknown \( X \Omega \) are connected in series
so as to form Wheatsones network.
Determine the unknown resistance \( \boldsymbol{X} \)
if the network is balance with these
numerical values of resistances.


Write definition of molecularity of
reaction.


When two infinitely long parallel wires
separated by a distance of \( 1 m, \) each carry a current of \( 3 A \), the force in newton/metre length experienced by each will be, \( \left(\operatorname{given} \mu_{0}=4 \pi \times 10^{-7} \mathrm{S.I}\right. \)
Units).
A. \( 2 \times 10^{-7} \)
B. \( 3 \times 10^{-7} \)
c \( .6 \times 10^{-7} \)
D. \( 18 \times 10^{-7} \)


Comment on the dual position of hydrogen in the periodic table


Which of the following complexes is(are) paramagnetic? This question has multiple correct options
A \( \cdot\left[M n\left(C N_{6}\right)\right]^{3-} \)
B . \( \left[C r\left(N H_{3}\right)_{6}\right]^{3} \)
c. \( \left[F e(C N)_{6}\right]^{4+} \)
D. \( \left[C o(C N)_{6}\right]^{3} \)


If the surface area of a sphere is \( 324 \pi c m^{2} \) then its volume is
\( \mathbf{A} \cdot 950 \pi \mathrm{cm}^{3} \)
В. \( 972 \pi \mathrm{cm}^{3} \)
\( \mathbf{c} \cdot 975 \pi \mathrm{cm}^{3} \)
D. \( 980 \pi \mathrm{cm}^{3} \)


In an aquatic environment, microscopic animals and plants are collectively known as
A. Commensals
B. Herbivores
c. Fauna and flora
D. Planktons


In the reaction, \( \boldsymbol{F e}+\mathbf{2 H C l} \rightarrow \)
\( F e C l_{2}+H_{2} . \) what is the oxidation state
of Fe in \( \boldsymbol{F e C l}_{2} \) ?
\( A \cdot+2 \)
\( B \cdot+3 \)
\( c \cdot+4 \)
D. +5


The ions responsible for the bleaching action of bleaching powder and the ions responsible for loss of bleaching action of bleaching powder due to the storage for long time respectively are:
A \( \cdot C l^{-}, O C l \)
в. \( O C l^{-}, C l \)
c. \( O C l^{-}, C l O_{3} \)
D. \( C l^{-}, C l O^{-} \)


Two particles of equal mass m have respective initial velocties \( u \hat{i} \) and \( u\left(\frac{\hat{i}+\hat{j}}{2}\right) . \) They collide completely inelastically. The energy lost in the
process is?
A \( \cdot \frac{1}{3} m u^{2} \)
B. \( \sqrt{\frac{2}{3}} m u^{2} \)
c. \( \frac{3}{4} m u^{2} \)
D. \( \frac{1}{8} m u^{2} \)


A circus is climbing a \( 20 m \) long rope, which is tightly stretched and tied from the top of vertical pole to the ground. Find the height of the pole if the angle made by the rope with the ground level
is \( 30^{\circ} \)
A \( .24 m \)
в. 18 т
c. \( 28 m \)
D. \( 10 m \)


\( \int \frac{(\mathbf{2} \boldsymbol{x}+\mathbf{1})}{\left(\boldsymbol{x}^{2}+\mathbf{4} \boldsymbol{x}+\mathbf{1}\right)^{\frac{\mathbf{3}}{\mathbf{2}}}} \boldsymbol{d} \boldsymbol{x} \)
A. \( \frac{x^{3}}{\left(x^{2}+4 x+1\right)^{\frac{1}{2}}}+C \)
в. \( \frac{x}{\left(x^{2}+4 x+1\right)^{\frac{1}{2}}}+C \)
c. \( \frac{x^{2}}{\left(x^{2}+4 x+1\right)^{\frac{1}{2}}}+C \)
D. \( \frac{1}{\left(x^{2}+4 x+1\right)^{\frac{1}{2}}}+C \)


Pure water, cooled to \( -15^{\circ} \mathrm{C} \), is kept in an
insulated flask. Some ice is dropped
into the flask. The fraction of water
frozen into ice is (specific heat of ice =
\( 0.5 \mathrm{cal} / \mathrm{g}^{-0} \mathrm{C}, \) specific heat of water \( =1 \)
\( \left.\operatorname{cal} / g^{-o} C\right) \)
A \( .6 / 29 \)
B. 3/35
\( c \cdot 6 / 35 \)
D. 2/35


Explain with the help of suitable example polar convalent bond.


Why bakelite does not become soft on
heating?


The bond angle in ammonia is \( 109^{\circ} 28^{\prime} \)
A. True
B. False


In the given elements, which element does not have 2 valence electrons?
A. Ba
B. zn
c. Na
D. ca


Which of the following charges is/are impossible?
A \( \cdot 4.8 \times 10^{-18} \mathrm{C} \)
B . \( 5.8 \times 10^{-18} \mathrm{C} \)
c. \( 12.8 \times 10^{-18} \mathrm{C} \)
D . \( 20.8 \times 10^{-18} \mathrm{C} \)


A jet of a liquid of density \( \rho \) with a cross-sectional area A is incident at an
angle \( \theta \) on a wall with a velocity \( v \) and
bounces with no loss of energy. The angle \( \theta \) is measured with respect to the
wall. The force in a direction normal
to the surface of the wall is:
A \( \cdot 2 \rho A v^{2} \cos \theta \)
B. \( 2 \rho A v^{2} \sin \theta \)
\( \mathbf{c} \cdot 2 \rho A v^{2} \cos ^{2} \theta \)
D. \( 2 \rho A v^{2} \sin ^{2} \theta \)


\( y=\sin ^{2} x+4 \sin x+5 . \) Then which of
the following statements is correct? \( (D: \text { Domain, } R: \text { Range }) \)
A \( D=R \)
\( R \)
B . \( D:[2,10] \)
c. \( D:[2,10]-\{0\} \)
D. \( R:[2,10] \)


toppr
\( Q \) тур
the photosphere) of the star emits radiations of all wavelengths, producing continuous spectrum. When these radiations pass through the outer, relatively cooler, layer of the star, the radiations of certain wavelengths are selectively absorbed by this layer. This explains the dark lines in the spectrum of a star. The dark lines are
characteristic of the substances
present in the outer layer of the star. The surface temperature T of a star can be estimated by measuring the
wavelengths \( \lambda_{m} \) at which the intensity of the emitted radiation is maximum and then using Wien's displacement
law which states that \( \lambda_{m} \times \mathrm{T}=\mathrm{b} \) where
b is a constant called Wien's constant
and the above relation is called Wien's
Displacement Law which states that as the temperature increases, the maximum intensity of emission shifts (or is displaced) towards the shorter wavelengths. The value of constant has been found experimentally to be
\( 2.89 \times 10^{-3} \mathrm{mK} \)
Which one of the curves shown in Fig represents the spectral distribution of
energy \( E_{\lambda} \) of black body radiations
where \( \lambda \) is the wavelength?
4
B.
\( c \)
D.


The products \( (A) \) and \( (B) \) are :
\( A \)
\( B \)
C. both A and B
D. none of the above


A saturated solution of silver benzoate
has a \( p H \) of \( 8.63 . K_{a} \) for benzoic acid is
\( 6.5 \times 10^{-5} . K_{s p} \) of silver benzoate will
be
A. \( 1.4 \times 10^{-2} \) mol \( ^{2} \) litre \( ^{-2} \)
B . \( 1.9 \times 10^{-2} \) mol \( ^{2} \) litre \( ^{-2} \)
c. \( 2.4 \times 10^{-2} \) mol \( ^{2} \) litre \( ^{-2} \)
D. none of these


A body of mass \( \mathrm{M} \) is resting on a rough horizontal plane surface, the coefficient
of friction being equal to \( \mu . A t t=0, a \)
horizontal force \( \boldsymbol{F}=\boldsymbol{F}_{0} \boldsymbol{t} \) starts acting
on it, where \( F_{0} \) is a constant. Find the
time \( T \) at which the motion starts?
A. \( \mu M g / F_{0} \)
\( \mathbf{B} \cdot M g / \mu F_{0} \)
\( \mathbf{c} \cdot \mu F_{0} / M g \)
D. None of these


Solve:
\( \left[\begin{array}{ccc}1 & 5 & -2 \\ 3 x & 2 & 4 \\ 5 & -1 & 0\end{array}\right]=0 \)


If both the mass and radius of the earth
decrease by \( 1 \% \) the acceleration due to gravity on the surface of the earth will
A. decrease by \( 1 \% \)
B. increase by \( 1 \% \)
c. increase by \( 2 \% \)
D. remain unchanged


If \( \frac{b+c-a}{a}, \frac{c+a-b}{b}, \frac{a+b-c}{c} \) are in
\( A . P ., \) then which of the following is in
A.P.?
This question has multiple correct options
A. \( a, b, c \)
B \( \cdot a^{2}, b^{2}, c^{2} \)
c. \( \frac{1}{a}, \frac{1}{b}, \frac{1}{c} \)
D. \( b c, a c, a b \)


Which of the following species has a molecular shape similar to that of
ammonia, \( N H_{3} ? \)
\( A \cdot B H_{3} \)
в. \( H_{2} O \)
\( \mathrm{c} \cdot \mathrm{H}_{3} \mathrm{O}^{+} \)
D. \( C H_{4} \)
E \( . N H_{4}^{+} \)


State whether true or false.
A freely falling body means a body whose acceleration is equal to the
acceleration due to gravity but its initial velocity may or may not be zero.
A. True
B. False


\( f(x)=x+\sin x \) is decreasing when \( x \)
lies in the interval
A \( \cdot[-1,1] \)
B. [2,3]
c. [3,4]
D. No value of \( x \)


The correct relationship between \( T_{c}, T_{b} \)
and \( \boldsymbol{T}_{\boldsymbol{i}} \) is:


The term vitamin was introduced by
A. Dr. Funk
B. Dr Edwards
c. Dr.Strepto
D. Dr Indira Hinduja


\( \boldsymbol{C H}_{3} \boldsymbol{M} \boldsymbol{g} \boldsymbol{X}^{C \boldsymbol{H}_{3}} \stackrel{C O O C_{2} \boldsymbol{H}_{5}}{\boldsymbol{A}} \stackrel{N a}{\rightarrow} \boldsymbol{B}^{C_{2}} \frac{\boldsymbol{H}_{5} \boldsymbol{O H}}{\longrightarrow} \)
\( C \)
Here, \( C \) is :
A \( \cdot C_{2} H_{5} O C_{2} H_{5} \)
в. \( C H_{3} \) СООС\( _{2} \) Нь
c. \( C H_{3} C O O C H_{3} \)
D. \( \left(C H_{3}\right)_{3} C O C_{2} H_{5} \)


Nitrogen molecule is a non polar
covalent compound.
A. True
B. False


molecular formula \( C_{4} H_{8} O_{3} . \) It evolves
\( C O_{2} \) with \( N a H C O_{3} .^{\prime} X^{\prime} \) on reaction with
Li \( A l H_{4} \) give achiral compound 'X' is:
\( A \)
B
\( c \)
D.


As the succession proceeds number and types of \( _{\text {一一一一一一一一一 }} \) change.
A. Vegetation
B. Animals
c. Vegetation and animals
D. Vegetation, animals and decomposers


If \( \Delta E \) is the heat of reaction for
\( \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O} \boldsymbol{H}(\boldsymbol{l})+\boldsymbol{3} \boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \)
\( 2 C O_{2}(g)+3 H_{2} O(l) \)
at constant volume, the \( \Delta \boldsymbol{H} \) (heat of
reaction at constant pressure), at constant temperature is:
A. \( \Delta H=\Delta E+R T \)
B. \( \Delta H=\Delta E-R T \)
c. \( \Delta H=\Delta E-2 R T \)
D. \( \Delta H=\Delta E+2 R T \)


toppr
Q Type your question
\( r, \) as seen in the picture.
If each of the diagrams among the
possible answers shows flies with the same acceleration as the one pictured
directly below, which fly has a speed that is twice the speed of the fly pictured directly below?
\( A \)
B.
\( c \)
radius \( =r / 2 \)
D.
radius \( =r / 4 \)
E. None of the objects in this question are accelerating
since thev al speed


de-Broglie wavelength associated with
an electron revolving in the \( n^{t h} \) state of hydrogen atom is directly proportional
to
A \( . n \)
в. \( \frac{1}{n} \)
c. \( n^{2} \)
D. \( \frac{1}{n^{2}} \)


The surface density on the copper
sphere is \( \sigma . \) The electric field strength
on the surface of the sphere is:
\( A \)
B . \( \sigma / 2 \)
c. \( \sigma / 2 \varepsilon_{0} \)
D. \( \sigma / \varepsilon_{0} \)


The formula of trimethylaluminium is:
A \( . A l_{2}\left(C H_{3}\right)_{6} \)
B \( . A l\left(C H_{6}\right)_{3} \)
\( \mathbf{c} \cdot A l\left(C H_{2}\right)_{6} \)
D. None of the above


The first satellite to put into space by India is:
A . INSAT
B. Aryabhatta
c. Rohini
D. Bhaskara


In the group \( G=\{1,5,7,11\} \) under \( \otimes_{12} \)
the value of \( 7 \otimes_{12} 11^{-1} \) is equal to
\( \left(\otimes_{12}: \text { under multiplication modulo } 12\right) \)
A . 5
B. 7
c. 11
D.


State True or False.
On hills, water boils quickly.
A. True
B. False


Explain in brief criteria for animal classification.


If the sum of first \( p \) terms of an \( A . P . \) is
equal to the sum of the first \( q \) terms,
then find the sum of the first \( (\boldsymbol{p}+\boldsymbol{q}) \)
terms.


Number of coulombs required to
liberate 0.5 mol of \( \boldsymbol{O}_{2} \) is:
A . 19300
B. 193000
c. 96500
D. 9650


Cradle of human evolution is
A. Grassland of South Africa
B. Savannah of Central Africa
C. Subarctic Europe
D. Arabia


From the stress against strain graph, the behavior of the wire between elastic
limit and yield point is :
A. Perfectly elastic
B. Formation of neck
c. Perfectly plastic
D. Elastic but with permanent deformation


The following circular diagrams represents the yield of gram. If the yield
in field-A is 400 kg, then the yield in field-B will be
A. \( 600 \mathrm{kg} \)
в. \( 800 \mathrm{kg} \)
c. 900 kg
D. 1200kg


Find the length of a chord which is at a distance of \( 3 \mathrm{cm} \) from the centre of a
circle of radius \( 5 \mathrm{cm} \)
A . \( 2 \mathrm{cm} \)
B. \( 6 \mathrm{cm} \)
\( c \cdot 8 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)


The following tripeptide can be
represented as.
\( \mathbf{A} \cdot \operatorname{Tyr}-V a l-T h r \)
B. Phe \( -A l a- \)Ser
c. \( P h e- \)Leu\( - \)Cys
D. \( L y s-A l a-S e r \)


Which of the following oxides of nitrogen is used as an anaesthetic?
A . \( N O \)
в. \( N O_{2} \)
\( \mathrm{c} \cdot \mathrm{N}_{2} \mathrm{O} \)
D. \( N_{2} O_{5} \)


Two gases, carbon monoxide \( (C O) \) and
nitrogen \( \left(N_{2}\right) \) at the same temperature
have kinetic energies \( \boldsymbol{E}_{1} \) and \( \boldsymbol{E}_{2} \)
respectively. Then
A \( . E_{1}=E_{2} \)
в. \( E_{1}>E_{2} \)
\( \mathbf{c} \cdot E_{1}<E_{2} \)
D. \( E_{1} \) and \( E_{2} \) cannot be compared


The angle of inclination of a straight line parallel to \( x \) -axis is equal to
A \( \cdot 0^{\circ} \)
В. \( 60^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 90^{\circ} \)


The inert gas present in the second long period is:
A. \( K r \)
в. \( X e \)
\( c . A r \)
D. Rn


The moon's radius is \( \frac{1}{4} \) that of the earth and its mass is \( \frac{1}{80} \) times that of the earth. If \( g \) represents the acceleration due to gravity on the surface of the earth, that on the surface of the moon
is
A. \( \frac{g}{4} \)
в. \( \frac{g}{5} \)
c. \( \frac{g}{6} \)
D. \( \frac{g}{8} \)


What is radioactivity? Show that radioactive decay is exponential in nature. The half-life of a certain
substance is 5 days. How many days does this substance take for \( 31 / 32^{t h} \) of the initial mass of disintegrate?


A solution prepared by dissolving 2.8 \( \mathrm{gm} \) of lime. \( \mathrm{CaO} \) in enough water to make 100 L of lime water
\( \left(\operatorname{Ca}(O H)_{2}(a q .)\right) . \) If solubility of
\( \boldsymbol{C a}(\boldsymbol{O} \boldsymbol{H})_{2} \) in water is 148 gm. The \( \boldsymbol{p} \boldsymbol{H} \)
of the solution obtained will be:
\( [\log 2=0.3, \text { Atomic masses are } C a= \) \( \mathbf{4 0}, \boldsymbol{O}=\mathbf{1 6}, \boldsymbol{H}=\mathbf{1 1}] \)
A . 12.3
B. 1.3
c. 12.6
D. 13


A man wearing a wingsuit glides through the air with a constant velocity
of \( 47 ~ m s^{-1} \) at an angle of \( 24^{\circ} \) to the horizontal. The path of the man is shown
in Fig.
The total mass of the man and the
wingsuit is 85 kg. The man takes a time
of 2.8 minutes to glide from point \( A \) to
point \( \boldsymbol{B} \)

For the movement of the man from \( A \) to
\( B, \) determine:
the magnitude of the force on the man
due to air resistance.


Assertion
All the isotopes of a given element show same chemical behaviour.
Reason
Isotopes have different number of
neutrons present in the nucleus.
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


Evaluate \( \int_{-\pi / 4}^{\pi / 4}|\sin x| d x \)


The function \( f(x)=\sin ^{-1}(\tan x) \) is not
differentiable at-
A \( . x=0 \)
В. \( x=-\pi / 6 \)
c. \( x=\pi / 6 \)
D. \( x=\pi / 4 \)


f \( y=\log \sqrt{\frac{1+\tan x}{1-\tan x}}, \) prove that \( \frac{d y}{d x}= \)
\( \sec 2 x \)


Resonance is an example of
A. Tuning fork
B. Forced vibration
C. Free vibration
D. Damped vibration


\( A 25 \mathrm{cm} \) long solenoid has radius \( 2 \mathrm{cm} \) and 500 total number of turns. It carries
a current of 15 A. If it is equivalent to magnet of the same size and magnetization \( \vec{M} \) Magnetic moment vloume), then \( \overrightarrow{|M|} \) is.
B. 30000Am"
c. \( 30000 \pi A m^{-1} \)
D. \( 3 \pi A m^{-1} \)


The colour of dye formed in the reaction between benzene diazonium chloride
and phenol is:
A . yellow
B. orange
c. purple
D. blue


If \( \boldsymbol{A}=\{\mathbf{1}, \mathbf{2}, \mathbf{3}\}, \boldsymbol{B}=\{\mathbf{3}, \mathbf{4}\} \)
find \( (A \times B) \cup(B \times A) \)
\( \mathbf{A} \)
\[
\{(1,3),(2,3),(3,3),(1,4),(2,4),(3,4),(3,1),(4,1),(3,2)
\]
B.
\[
\{(2,3),(3,3),(1,4),(2,4),(3,4),(3,1),(4,1),(3,2),(4,2)
\]
\( \mathbf{c} \)
\{(1,3),(2,3),(3,3),(1,4),(2,4),(3,4),(3,1),(4,1),(4,2)
D. None of these


The electric potential at any point
inside the first shell is:
\( \mathbf{A} \cdot 18 \times 10^{4} V \)
B. \( 9 \times 10^{4} V \)
c. \( 4.5 \times 10^{4} V \)
D . \( 1.8 \times 10^{4} V \)


Construct the graphs of the following
function.
\( \boldsymbol{y}=\boldsymbol{x}|\boldsymbol{x}-\mathbf{3}| \)


The smog is essentially caused by the
presence of


Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{4}+\boldsymbol{3} \boldsymbol{x}+1,[-\boldsymbol{2},-1] \) then
\( A \cdot f \) has exactly two zeros in [-2,-1]
B. f has exactly one zero in [-2,-1
C \( \cdot \) f has at least one zero in [-2,-1]
D. f has no zero in [-2,-1]


The IUPAC name of \( C_{6} H_{5} \) COCl is :
A. benzoyl chloride
B. benzene chloro ketone
c. oxochloro benzene
D. chlorophenyl ketone


Which one of the following is correctly
matched ?
A. Aerosol-smoke
B. Foam-mist
c. Emulsion-curd
D. All of these


A steel rope has length \( L \), area of cross-
section \( A \), Young's modulus \( Y \). Density \( =d \) ]. If the steel rope is
vertical and moving with the force acting vertically up at the upper end, find the strain at a point \( \frac{L}{3} \) from lower
end.
\( \mathbf{A} \cdot(d g L) / 2 Y \)
в. \( (d g L) / 4 Y \)
\( \mathbf{c} \cdot(d g L) / 6 Y \)
D. \( (d g L) / 8 Y \)


According to Bohr's model, the angular
momentum of an electron in 4th orbit
is:
\( \mathbf{A} \cdot h / 3 \)
B. \( h / 2 \)
c. \( 2 h / \pi \)
D. none of these


ff \( x_{1}, y_{1} \) are the roots of \( x^{2}+8 x-20= \)
0 and \( x_{2}, y_{2} \) are the roots of \( 4 x^{2}+ \)
\( 32 x-57=0 \) and \( x_{3}, y_{3} \) are the roots of
\( 9 x^{2}+72 x-112=0 \) such that \( y_{i}<0 \)
then the points \( \left(x_{1}, y_{1}\right),\left(x_{2}, y_{2}\right) \) and
\( \left(x_{3}, y_{3}\right) \)
A. are collinear
B. form an equilateral triangle
c. form a right angled isosceles triangle
D. are concyclic


Zinc can displace copper from copper
sulfate solution because zinc is
A. more reactive than copper
B. less reactive than copper
c. more stable than copper
D. less stable than copper


Evaluate \( \int x^{2} e^{x} d x= \)
A \( \cdot e^{x}\left(x^{2}-2 x+2\right)+c \)
B . \( e^{x}\left(x^{2}+2 x+2\right)+c \)
c. \( x^{2}+e x+c \)
D. \( e^{x}\left(x^{2}+x+2\right)+c \)


Average kinetic energy in one time
period of a simple harmonic oscillator whose amplitude is \( A, \) angular velocity \( \omega \) and mass \( m, \) is
A \( \cdot \frac{1}{4} m \omega^{2} A^{2} \)
B \( \cdot \frac{1}{2} m \omega^{2} A^{2} \)
\( \mathrm{c} \cdot m \omega^{2} A^{2} \)
D. Zero


How many order of magnitude are there in one million?
A. 5
B. 4
\( c \cdot 6 \)
D. None of above


Which of the following ion will give colourless aqueous solution?
A \( . N i^{2} \)
B. \( S c^{3} \)
\( c \cdot C u^{2} \)
D. \( M n^{3+} \)


Which of the following are fleece and wool-bearing animals?
A. Sheep and goat
B. Camel and Yak
c. Both A and B
D. none of them


Condensation of phenol with acetone
gives:
A. bisphenol-A
B. catechol
c. resorcinol
D. hydroquinone


An unknown compound has molecular
formula \( C_{7} H_{12} \).It gives two aldehydes shown below upon ozonolysis followed
by workup with \( Z n-H_{2} O . \) What is the
the structure of the original compound?
and
\( A \)
B.
\( c \)
D. None of the above


In an isolated parallel plate capacitor of
capacitance \( C, \) the four surfaces have
charges \( Q_{1}, Q_{2}, Q_{3} \) and \( Q_{4} \) as shown.
The potential difference between the
plates is:
\( A \)
в. \( \frac{Q_{2}+Q_{3}}{2 C} \)
c. \( \frac{Q_{2}-Q_{3}}{2 C} \)
D. \( \frac{Q_{1}+Q_{4}}{2 C} \)


Q Type your question.
and \( T_{2}\left(T_{2}>T_{1}\right) . \) Which of the
following plots is correct?
\( A \)
B.
\( c \)
\( D \)


If \( \cos ^{-1} x+\cos ^{-1} y+\cos ^{-1} z=3 \pi \)
then \( x y+y x+z x \) is equal to
A . 1
B.
\( c .-3 \)
D. 3


What are the IUPAC rules for naming
alkyl halides?


Which of the following is the strongest base?
A. Aniline
B. N-methylaniline
c. o-methylaniline
D. Benzylamine


Out of the following options, which is the base to define the formation place
of cell plate at the end of nuclear
division?
A. Microtubules
B. Vesicles
c. Endoplasmic reticulum
D. Golgi body


Out of \( N O, N O_{2}, N_{2} O, N_{2} O_{4} \) and \( N_{2} O_{2} \)
the paramagnetic species
are
A. \( N_{2} O_{2} \) and \( N_{2} O_{4} \)
B. \( N O_{2} \) and \( N_{2} O_{4} \)
\( \mathrm{c} \cdot \mathrm{N}_{2} \mathrm{O}_{2} \) and \( \mathrm{NO}_{2} \)
D. \( N O \) and \( N O_{2} \)


The velocity with which particle strikes the plane \( \boldsymbol{O B} \)
A \( \cdot 15 \mathrm{ms}^{-1} \)
B. \( 30 m s^{-1} \)
\( c \cdot 20 m s^{-1} \)
D. \( 10 \mathrm{ms}^{-1} \)


By which method can ammonium
chloride be separated from sand?
A. By hand picking
B. By filtration
c. By sublimation
D. By diffusion


One mole of acidified \( \boldsymbol{K}_{2} \boldsymbol{C r}_{2} \boldsymbol{O}_{7} \) on
reaction with excess \( \boldsymbol{K} \boldsymbol{I} \) will
liberate \( _{\text {一一一一一一一一一 }} \) mole \( (s) \) of \( I_{2} \)
\( A \cdot 3 \)
B. 1
c. 7
D. 2


in a certain region of free space a non-
uniform electric field which depends on
X-coordinates is given by \( \overrightarrow{\boldsymbol{E}}=\boldsymbol{E}_{0} \boldsymbol{x} \hat{\boldsymbol{i}} \)
What is the total amount of electric
potential energy contained within the
cube of sides of length L as shown
below?
A \( \cdot \frac{1}{5} \varepsilon_{0} E_{0}^{2} L^{5} \)
B \( \cdot \frac{1}{5} \varepsilon_{0} E_{0}^{2} L^{6} \)
C \( \cdot \frac{1}{6} \varepsilon_{0} E_{0}^{2} L^{6} \)
D \( \cdot \frac{1}{2} \varepsilon_{0} E_{0}^{2} L^{5} \)


If true enter 1 , else enter 0 .
Following reaction is disproportionation
reaction:
\( N H_{4}^{+}+N O_{3}^{-} \longrightarrow N_{2} O+2 H_{2} O \)
\( A \)


The diagram given below represents the location and structure of an endocrine
gland. Study the same and answer the questions that follow:
Name the endocrine gland shown in the diagram.


Value of \( \int \frac{d x}{x^{2}\left(x^{4}+1\right)^{3 / 4}} \) is :
A \( -\left(1+\frac{1}{x^{4}}\right)^{\frac{1}{4}}+c \)
B. \( \quad\left(1+\frac{1}{x^{4}}\right)^{\frac{1}{4}}+c \)
c. \( \quad-\left(1-\frac{1}{x^{4}}\right)^{\frac{1}{4}}+c \)
D. None of these


Which of the following is an assumption of Kinetic theory of matter?
A. Molecules are in a state of continuous motion and possess kinetic energy
B. The kinetic energy of molecules increases with increase in temperature.
c. The molecules of matter always attract each other due to forces of cohesion and adhesion
D. All of the above


Ethyl alcohol on distillation with \( \boldsymbol{X} \)
gives chloroform, \( \boldsymbol{X} \) is:
A. a paste of bleaching powder
B. chlorine
c. methyl chloride
D. \( C a(O H)_{2} \)


The side of a cube is 2.5 metre, the volume of the cube to the correct
significant figures is :
A . 15
B. 16
\( c \cdot 1.5 \)
D. 1.6


The range of the function \( f(x)= \)
\( \left(8^{x}+4^{x}+8^{-x}+4^{-x}+5\right) \) is
\( A \cdot\left(\frac{7}{4}, \infty\right) \)
B. \( \left[\frac{7}{4}, \infty\right) \)
c. \( (9, \infty) \)
D \( \cdot[9, \infty) \)


The rate of the reaction starting with
initial concentrations \( 2 \times 10^{3} M \) and
\( 1 \times 10^{3} M \) are equal to \( 2.40 \times \)
\( 10^{4} M s^{1} \) and \( 0.60 \times 10^{4} M s^{1} \)
respectively. Calculate the order of reaction with respect to reactant:


A half cell reaction is one which:
A. involves only half a mole of electrolyte
B. goes only half way to completion
C. takes place at one electrode
D. consumes half a unit of electricity


Given that \( \vec{A} \) and \( \vec{B} \) are greater than one, then the magnitude of \( (\vec{A} \times \vec{B}) \) can not be
A . equal to \( \overrightarrow{A B} \)
B. less than \( \vec{B} \)
c. more than \( |\vec{A}||\vec{B}| \)
D. equal to \( \vec{A} / \vec{B} \)


Peptization denotes:
A. digestion of food
B. hydrolysis of proteins
C. breaking of dispersion into colloidal state
D. precipitation of a solid from colloidal state


The average human eye sees colors with
wavelength between \( 430 n m \) to \( 680 n m \)
For what visible wavelength(s) will a \( 350 n m \) thick \( (n=1.35) \) soap film
produce maximum destructive
interference?
A. \( 945 n m \)
В. \( 473 n m \)
\( c .315 n m \)
D. None of these


In Colon, constrictions of the wall form a series of small pockets called
A. Haustra
B. Crypts of lieberkuhn
c. zymogen cells
D. Taenial


sets of students who have opted for
Mathematics (M) physics (P) Chemistry
(C) and Electronics (E)
What does the shaded region represent
A. Students who oped for Physic, Chemistry and Electronics
B. Students who oped for Mathematics, Physics
Chemistry
c. Students who opted for Mathematics, Physics and Electronics
D. Students who opted for Mathematics, Chemistry and ectron


If \( f \) be a continuous function on \( [\mathbf{0}, \mathbf{1}] \)
differentiable in (0,1) such that
\( f(1)=0, \) then there exists some \( c \in \)
(0,1) such that
A \( \cdot c f^{\prime}(c)-f(c)=0 \)
B. \( f^{\prime}(c)+c f(c)=0 \)
c. \( f^{\prime}(c)-c f(c)=0 \)
D. \( c f^{\prime}(c)+f(c)=0 \)


Sewage purification is performed by
A. Microbes
B. Fertilisers
C. Antibiotics
D. Antiseptics


Cell division can not be stopped in phase of the cell cycle.
A. Gi phase
B. Ga phase
c. s phase
D. Prophase


Boiling does not occur in a closed vessel. Give reason.


Find the \( x \) in terms of \( a, b, c \)


Factorise \( (x-2 y)^{2}+7(x-2 y)+12 \)


A litre of dry air at STP expands adiabatically to a volume of 3 litres. If
\( \gamma=1.40, \) the work done by air is:
\( \left(3^{1.4}=4.6555\right) \) [Take air to be an ideal gas \( ] \)
A . \( 48 \mathrm{J} \)
в. \( 100.8 \mathrm{J} \)
c. \( 60.7 J \)
D. \( 90.5 J \)


If \( \frac{\sin ^{-1} x}{\sqrt{1-x^{2}}}=y, \) show that \( (1- \)
\( \left.x^{2}\right) \frac{d^{2} y}{d x^{2}}-3 x \frac{d y}{d x}-y=0 \)


Carbon belongs to second period and 14
group. Silicon belongs to third period and group 14. If atomic number of carbon is \( 6, \) the atomic number of
silicon is :
A. 7
B. 14
\( c \cdot 24 \)
D. 16


The dimension of the ratio of angular
momentum to linear momentum is
\( \mathbf{A} \cdot L^{0} \)
B . \( L^{1} \)
c. \( L^{2} \)
D. \( M L T \)


In \( N_{2} \) molecule, the atoms are bonded
by:
A . one \( \sigma, \) two \( \pi \) bonds
в. one \( \sigma \), one \( \pi \) bonds
c. \( t w o \sigma, \) one \( \pi \) bonds
D. three \( \sigma \), one \( \pi \) bonds


\( 2^{n} d \) separation energy of an electron in
H atom?
A. 27.2 ev
B. 1.51 ev
c. 3.4 ev
D. 13.6 ev


Derive the formula \( \omega=\frac{D \lambda}{2} \) for fringe width in Young's double slit experiment
The symbols used have their usual meanings.


A swimming pool is \( 100 \mathrm{m} \) long and \( 15 \mathrm{m} \) wide its deep and \( 24 \mathrm{m} \) height
respectively. Find the capacity of the
pool
A. \( 36,000 \mathrm{m} \)
в. \( 36,000 m^{3} \)
c. \( 36,000 m^{2} \)
D. 36,000 \( c m \)


Factorise the following expression by finding common factor. \( \boldsymbol{p}^{3}-\mathbf{1 6} \boldsymbol{p}^{2}=\mathbf{0} \)


\( A \& B \) are two separate reservoirs of water. The capacity of reservoir A is double the capacity of reservoir B. Both the reservoirs are filled completely with water, their inlets are closed and then
the water is released simultaneously
from both the reservoirs. The rate of flow
of water out of each reservoir at any
instant of time is proportional to the quantity of water in the reservoir at that time. One hour after the water is
released, the quantity of water in reservoir A is 1.5 times the quantity of water in reservoir B. After how many hours do both the reservoirs have the
same quantity of water? (Enter \( n \) if the answer is \( T=\log _{4 / 3} n \) )


What is the IUPAC name of
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5}(\boldsymbol{O} \boldsymbol{N} \boldsymbol{O})\right] \boldsymbol{S} \boldsymbol{O}_{4} ? \)
A. pentaammine nitrito-0-cobalt
(III) sulphate
B. pentaammine nitro-N-cobalt (III) sulphate
c. pentaamine nitro-0-cobalt (III) sulphate
D. pentaammonia nitro-0-cobalt
(III) sulphate


Name a moneran which shows
pendulum like movements


A reaction is spontaneous at all
temperature when
A. \( \Delta H \) is -ve and \( \Delta S \) is +ve
B. \( \Delta H \) is +ve and \( \Delta S \) is -ve
C. Both \( \Delta H \& \Delta S \) are -ve
D. Both \( \Delta H \) \& \( \Delta S \) are +ve


\( \mu=\{a, b, c, d, e, f, g, h, i, j\} \)
\( P=\{a, b, c, e\} \)
\( Q=\{b, c, d, f\} \) and
\( R=\{c, f, h, i, j\} \)
Number of elements of the set
\( \boldsymbol{P} \cup \boldsymbol{Q} \cup \boldsymbol{R} \) is:
A \( \cdot 12 \)
B. 11
c. 10
\( D \)


Elemental analysis results obtained for cortisone, an anti-inflammatory agent,
are \( 69.98 \% \) C, \( 7.83 \mathrm{H} \) and \( 22.19 \% \) 0. What
is the empirical formula of cortisone?
A \( \cdot C_{4} H_{6} O \)
в. \( C_{18} \mathrm{H}_{22} \mathrm{O}_{3} \)
\( \mathbf{c} \cdot C_{20} H_{25} O_{4} \)
D. \( C_{12} H_{28} O_{5} \)


Calculate the normal temperature of
human body in celsius scale if it is
\( \mathbf{9 8 . 4}^{\circ} \boldsymbol{F} \) in Fahrenheit scale


Let \( \boldsymbol{f}:(-\mathbf{1}, \mathbf{1}) \rightarrow \boldsymbol{R} \) be a differentiable
function satisfying
\[
\begin{array}{c}
\left(f^{\prime}(x)\right)^{4}=16(f(x))^{2} \text { for all } x \in \\
(-1,1) \\
f(0)=0
\end{array}
\]
The number of such functions is
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. more than 4


Moist iodine reacts with ozone to form :
A. \( H I \)
в. \( H I O_{3} \)
\( c \cdot I_{2} O_{3} \)
D. \( I_{2} O_{7} \)


Assertion
\( L i^{+} \) forms series of trihydrates \( L i X \)
\( \mathbf{3} \boldsymbol{H}_{\mathbf{2}} \boldsymbol{O}[\boldsymbol{X}= \)
\( \boldsymbol{C l}, \boldsymbol{B r}, \boldsymbol{I}, \boldsymbol{C l O}_{2}, \boldsymbol{C l o}_{4}, \boldsymbol{M n O}_{4}, \boldsymbol{N O}_{3}, \boldsymbol{b} \)
Reason
This is due to its smaller size \( \left(L i^{+}\right) \) and highest ion dipole interaction.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


The frequency of a sound wave is \( 256 \mathrm{Hz} \) and its wavelength is \( 1.2 \mathrm{m} \). Calculate its wave velocity.


Radium disappears at a rate
proportional to the amount present. If \( 5 \% \) of the original amount disappears
in 50 years, how much will remain at
the end of 100 years. \( \left[\text { Take } A_{0} \) as the \right. initial amount].


Which one of the following differential equations represents the family of straight lines which are at unit distance from the origin?
\( ^{A} \cdot\left(y-x \frac{d y}{d x}\right)^{2}=1-\left(\frac{d y}{d x}\right)^{2} \)
\( ^{\mathrm{B}}\left(y+x \frac{d y}{d x}\right)^{2}=1+\left(\frac{d y}{d x}\right)^{2} \)
\( ^{\mathrm{c}}\left(y-x \frac{d y}{d x}\right)^{2}=1+\left(\frac{d y}{d x}\right)^{2} \)
\( ^{\mathrm{D} \cdot}\left(y+x \frac{d y}{d x}\right)^{2}=1-\left(\frac{d y}{d x}\right)^{2} \)


Area of circle in which a chord of length
\( 2 \sqrt{3} \) units, subtends angle \( 120^{\circ} \) at its
centre is :
A . \( \pi \) sq units
B. 2 \( \pi \) sq units
c. \( 4 \pi \) sq units
D. \( 5 \pi \) sq units


Given that \( A+B+C=0 . \) Out of three
vectors, two are equal in magnitude and the magnitude of third vector is \( \sqrt{2} \) times that of either of the two having equal magnitude. Then, the angles between the vectors are given by.
A . \( 30^{\circ}, 60^{\circ}, 90^{\circ} \)
в. \( 45^{\circ}, 45^{\circ} \), \( 90^{\circ} \)
c. \( 45^{\circ}, 60^{\circ}, 90^{\circ} \)
D. \( 90^{\circ}, 135^{\circ}, 135^{\circ} \)


What are the expected products of
hydrolysis of lactose?


Hardness of water is estimated by the simplest complex formation titration Complex formed by cation in hard water during estimation of hardness is:
\( \mathbf{A} \cdot N a_{2}\left[C a\left(P O_{3}\right)_{6}\right] \)
B . \( N a_{2}[M g(E D T A)] \)
c. \( N a_{2}[P b(E D T A)] \)
D. \( \left[C a\left(S O_{4}\right)_{2}\right]^{2} \)


Order of decreasing basic strength of halides is:
A \( \cdot F^{-}>C l^{-}>I^{-}>B r^{-} \)
B . \( F^{-}>C l^{-}>B r^{-}>I^{-} \)
c. \( I^{-}>B r^{-}>C I^{-}>F^{-} \)
D. \( I^{-}>C l^{-}>B r^{-}>F^{-} \)


Which of the following is minimum at the equator?
A. Angle of dip
B. Horizontal component of earth's magnetic field
c. Angle of declination
D. Intensity of the earth's field


Each step in a food chain is called a
A. trophical level.
B. consumer level.
\( c . \) food web.
D. producer.


Pick the group which does not contain a neutral oxide.
A. \( N O_{2}, P_{4} O_{10}, A l_{2} O_{3}, N O \)
в. \( M g O, N_{2} O_{5}, S O_{3}, N_{2} O \)
\( \mathrm{c} \cdot \mathrm{CO}_{2}, \mathrm{SO}_{3}, \mathrm{CaO}, \mathrm{XeO}_{3} \)
D. \( C O, S i O_{2}, S n O_{2}, N a_{2} O_{3} \)


open end of a cylindrical vessel of
radius \( R \) and height \( 2 R \) as shown in figure. the flux of the electric field
through the surface (curved surface \( + \)
base ) of the vessel is
\( \mathbf{A} \cdot \frac{Q}{\varepsilon_{0}} \)
B. \( \frac{Q}{2 \varepsilon_{\text {d }}} \)
\( c \cdot \frac{Q}{4 \varepsilon_{0}} \)
D. \( \frac{Q}{\sqrt{5} \varepsilon_{0}} \)


When an ebonite rod is rubbed with
wool, they get oppositely charged due to conduction. Explain


The same ratio of corresponding sides is referred to as the factor for
polygons.
\( A \). scale
B. vernier
c. similar
D. congruence


Production of zoospores is characteristic of members of :
A. Ascomycetes
B. Phycomycetes
c. Basidiomycetes
D. Deuteromycetes


A particle is projected from horizontal
making an angle \( 60^{\circ} \) with initial
velocity \( 40 m s^{-1} . \) Find the time taken by
the particle to make angle \( 45^{\circ} \) from
horizontal.
A . \( 1.5 s \)
в. 2.5 \( s \)
\( c .3 .5 s \)
D. 4.5


Plasma has water to the extent of
A. \( 80 \% \)
в. \( 60 \% \)
c. \( 70 \% \)
D. \( 90 \% \) or more


The measure of angle \( y \) in the given
figure is
A. \( \angle y=65^{\circ} \)
B . \( \angle y=85^{\circ} \)
c. \( \angle y=75^{\circ} \)
D. \( \angle y=80^{\circ} \)


If \( N \) is the number of positive integral
solutions of \( \boldsymbol{x}_{1} \times \boldsymbol{x}_{2} \times \boldsymbol{x}_{3} \times \boldsymbol{x}_{4}=\mathbf{7 7 0} \)
then:
This question has multiple correct options
A. \( N \) is divisible by 4 district primes
B. \( N \) is a perfect square
C. \( N \) is a perfect fourth power
D. \( N \) is a perfect \( 8^{t h} \) power


Match the Column-I with Column-II:


Can lighting occur thunder? Justify
your answer.


The figure shows cross section of a
hollow glass tube of internal radius \( r \)
external radius \( \boldsymbol{R} \) and index of
refraction \( n . \) For two rays DE and \( A B C \) (in
which DE lies on ODE and DE is parallel
to BC), the separation \( r_{1} \) will be :
A \( \cdot r_{1}=(n-1) R \)
\( \mathbf{B} \cdot r_{1}=n^{2} R \)
\( \mathbf{c} \cdot r_{1}=n r \)
\( \mathbf{D} \cdot r_{1}=n^{2} r \)


The two molecules indicated are
capable of intramolecular hydrogen
bonding which is likely to form more
stable hydrogen bonds. Select the
correct statement
A. A has higher H-bonding
B. B has higher H-bonding
C. Both A and B have equal H-bonding
D. None of these


The surface energy of a liquid drop is \( \boldsymbol{E} \)
It is sprayed into 1000 equal droplets.
The work done in spraying is
\( \mathbf{A} \cdot 999 E \)
в. \( 99 E \)
\( \mathrm{c} .9 \mathrm{E} \)
D. \( E \)


State the nature of the given quadratic
equation \( 3 x^{2}+4 x+1=0 \)
A. Real and Distinct Roots
B. Real and Equal Roots
c. Imaginary Roots
D. None of the above


An ideal gas is initially at \( P_{l}, V_{1} \) is
expanded to \( P_{2}, V_{2} \) and then compressed adiabatically to the same
volume \( V_{l} \) and pressure \( P_{3} \).If \( W \) is the
net work done by the gas in complete process which of the
A. \( W>0 ; P_{3}>P_{1} \)
В. \( W<0 ; P_{3}>P_{1} \)
c. \( W<0 ; P_{3} \)
D. \( P_{2}>P_{1} ; W<0 \)


A scientist took 8 molecules of cytosoic aldolase into an enzyme reaction mixture to study its activity. After ten minutes of enzyme reaction, \( 60 \% \) of its
substrate was found converted into
2400 molecules of products. Then what is the TON of aldolase and number of
substrate molecules left over in the
reaction mixture?
A . 30,1440
B. 30,960
\( c .15,1280 \)
D. 15,800


Choose the correct answer from the
alternatives given. The \( _{--} \) produces red blood cells, which transport \( _{--} \) and some
A. liver, oxygen, mineral ions
B. liver, oxygen, carbon dioxide
c. bone marrow; oxygen; hormones
D. bone marrow; oxygen; carbon dioxide


A stone is tied to the middle of a string
and suspended from one end as shown
in the given figure. Here \( S \) is the stone and 0 is the point of suspension. If you
give a sharp jerk at \( P, \) the string will break:
A. below the stone
B. at the point P itself
c. from above the stone
D. nothing can be decided


In the conversion of \( B r O_{3}- \) to \( B r O_{4}^{-} \)
A. there is no change in oxidation number
B. reduction takes place in basic solution
C. reduction also takes place by \( X e F_{2} \)
D. equivalent mass of \( B r O_{3}^{-} \) is one-half of ionic mass


The roots of the equation \( x^{2}+2 \sqrt{3} x+ \)
\( \mathbf{3}=\mathbf{0} \) are
A . real and unequal
B. rational and equal
c. irrational and equal
D. irrational and unequal


In A.C circuit having only capacitor, the current
A ' lags behind the voltage by \( \frac{\pi}{2} \) in phase
B. Ieads the voltage by \( \frac{\pi}{2} \) in phase
c. leads the voltage by \( \pi \) in phase
D. lags behind the voltage by \( \pi \) in phase


Find values of \( k \) if area of triangle is 4
sq. units and vertices are
(i) \( (k, 0),(4,0),(0,2) \)
(ii) \( (2,0),(0,4),(0, k) \)


\( \int_{1}^{2} \frac{1-x}{1+x} d x \) equals
\( \left(\frac{1}{2}\right) \log \left(\frac{3}{2}\right)-1 \)
B \( \cdot 2 \log \left(\frac{3}{2}\right)-1 \)
\( ^{\mathbf{C}} \cdot \log \left(\frac{3}{2}\right)-1 \)
D. None of these


A circular loop of radius \( \boldsymbol{R} \), carrying
current \( I \), lies in \( x-y \) plane with its
center at the origin. The total magnetic
flux through \( x-y \) plane is
This question has multiple correct options
A. directly proportional to \( l \)
B. directly proportional to \( R \)
c. inversely proportional to \( R \)
D. zero


Assertion
No net force acts on a rectangular coil
carrying a steady current when
suspended freely in a uniform magnetic
field.
Reason
Force on coil in magnetic field is always
non-zero.
A. If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
B. If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
C. If Assertion is correct but Reason is incorrect.
D. If Assertion is incorrect but Reason is correct.


The differential equation of the family of
curves \( r^{2}=a^{2} \cos 2 \theta \) where 'a' is
arbitrary constant is:
This question has multiple correct options
A \( \cdot \frac{d r}{d \theta}=-r \tan 2 \theta \)
B. \( \frac{d r}{d \theta}=r \cot 2 \theta \)
c. \( \frac{d r}{d \theta} \cos 2 \theta+r \sin 2 \theta=0 \)
D. \( \frac{d r}{d \theta}=0 \)


Sum of all the rational terms in the
expansion of \( \left(2^{1 / 3}+3^{1 / 2}\right)^{6} \) is
A . 31
B. 83
c. 27
D. 91


The \( x \) and \( y \) coordinates of the particle
at any time are \( x=5 t-2 t^{2} \) and \( y= \)
10t respectively, where \( x \) and \( y \) are in
meters and \( t \) in seconds. The
acceleration of the particle at \( t=2 s \) is:
\( A \cdot 0 \)
В. \( 5 m / s^{2} \)
c. \( -4 m / s^{2} \)
D. \( -8 m / s^{2} \)


A ray of light is incident at the glass-
water interface at an angle i. It merges
finally parallel to the surface of water.
Then, the value of \( \mu_{g} \) would be :
A \( \cdot(4 / 3) \sin i \)
B. \( 1 / \)sini
c. \( 4 / 3 \)
\( D \)


Enzymes are also called biocatalyst?
A. True
B. False


A cold, green flame can be made by passing carbon dioxide over warm.
A. Grey tin
B. White phosphorous
c. Bronze
D. Green candles


Convert the following ratios into
percentage:
47: 50:


Assertion
Aluminium containers can be used for
\( \operatorname{storing} \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \)
Reason
Nitric acid cannot oxidize aluminium at
all.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The number of coordinate bonds
presents in \( S O_{3} \) molecule are:
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
D. none of these


A light circular cone buoy is pressed by
a \( 500 N \) force as shown in figure then
the path depth upto which it will
submerge is
A \( .1 .7 \mathrm{m} \)
3. 2.0 .
\( c .2 .1 m \)
D. 3.0


Vector \( \vec{A} \) is \( 2 c m \) long and is \( 60^{\circ} \) above
the \( x \) -axis in the first quadrant. Vector
\( \vec{B} \) is \( 2 c m \) long and is \( 60^{\circ} \) below the \( x \) axis in the fourth quadrant. The sum \( \vec{A}+\vec{B} \) is a vector of magnitude
A. \( 2 c m \) along positive y-axis
B. 2cm along positive x-axis
c. \( 2 c m \) along negative y-axis
D. \( 2 c m \) along negative x-axis


A student is asked to connected four
cells of e.m.f of \( 1 \mathrm{V} \) and internal
resistance 0.5 ohm in series with an
external resistance of 1 ohm. But one
cell is wrongly connected by him with its terminal reversed. the current in the
circuit is
A \( \cdot \frac{1}{3} A \)
в. \( \frac{2}{3} A \)
c. \( \frac{3}{4} \)
D. \( \frac{4}{3} \)


Wrote the following as mixed fraction \( \frac{7}{2}, \frac{8}{5} \)


Which of the following statements is
true about RBCs in humans?
A. They carry about \( 20-25 \) per cent of \( C O_{2} \)
B. They transport 99.5 per cent of \( O_{2} \)
C. They transport about 80 per cent oxygen only and the rest 20 per cent of it is transported in dissolved state in blood-plasma.
D. They do not carry \( C O_{2} \) at all.


Persistent calyx is characteristics of
A. Allium / Liliaceae
B. Hibiscus / Malvaceae
C. Dalbergia / Papionatae
D. Solanum / Solanaceae


Which step in the following problem is wrong? \( \boldsymbol{a}=\boldsymbol{b}=\mathbf{1} \)
\( \boldsymbol{a}=\boldsymbol{b} \)
step-1: \( a^{2}=a b \)
step-2: \( a^{2}-b^{2}=a b-b^{2} \)
step-3: \( (\boldsymbol{a}+\boldsymbol{b})(\boldsymbol{a}-\boldsymbol{b})=\boldsymbol{b}(\boldsymbol{a}-\boldsymbol{b}) \)
step- \( 4: a+b=\frac{b(a-b)}{a-b} \)
\( \boldsymbol{a}+\boldsymbol{b}=\boldsymbol{b} \)
\( \mathbf{1}+\mathbf{1}=\mathbf{1} \)
\( \mathbf{2}=\mathbf{1} \)
A. Step-4
B. Step-3
c. step- -
D. Step- -


Find the area of the Parallelogram ABCD
and hence find the value of \( x \)


2011 is the international year of
chemistry. "Chemistry is our life, our
future", is the motto.
"Chemistry is not a problem but a solution" is the message of green chemistry. Explain the relevance of this message.


Which of the following arrangments does not represent the correct order of
the property stated against it?
(1) \( V^{2+}<C r^{2+}<M n^{2}<F e^{2+} \)
paramagnetic behaviour
(2) \( N i^{2+}<C o^{2+}<F e^{2+}<M n^{2+} \)
ionic size
(3) \( C o^{3+}<F e^{3+}<C r^{3+}<S c^{3+} \)
stability in aqueous solution
(4) \( S c<T i<C r<M n: \) number of
oxidation states


What describes a spontaneous
reaction?
A. Positive \( \Delta H \)
B. Negative \( \Delta H \)
c. Positive \( \Delta G \)
D. Negative \( \Delta G \)


Which of the following is planar?
A. \( X e F_{2} \)
в. \( X e O_{3} F \)
c. \( X e O_{2} F_{2} \)
D. \( X e F_{4} \)


Prussian blue colour is obtained by mixing together an aqueous solution of \( \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+} \) salt with:
A. ferricyanide
B. ferrocyanide
c. hydrogen cyanide
D. sodium cyanide


The value of magnetic susceptibility for para-magnetic substance is
A . infinity
B. low positive
c. low negative
D. zero


Mechanical waves transport
A. Energy only
B. Energy and mass
C. Mass only
D. Neither energy not mass


The audible frequency for a normal human being is \( 20 \mathrm{Hz} \) to \( 20 \mathrm{kHz} \). Find
the corresponding wavelengths if the speed of sound in air \( 320 \mathrm{m} / \mathrm{s} \)


A solution at \( 20^{\circ} \mathrm{C} \) is composed of 1.5
mol of benzene and 3.5 mol of toluene. If
the vapour pressure of pure benzene of
pure benzene and pure toluene at this temperature are 74.7 torr and 22.3 torr. respectively, then the total vapour pressure of the solution and the benzene mole fraction in equilibrium with it will be, respectively.
A. 38.0 torr and 0.589
B. 30.5 torr and 0.389
c. 35.8 torr and 0.280
D. 35.0 torr and 0.480


Two bodies are in thermal equilibrium if they have the same:
A. temperatures
B. amount of heat
c. specific heat
D. thermal capacity


Explain the formation of \( \boldsymbol{O}_{2} \) molecule
using molecular orbital theory.


It is assumed that a photon takes \( 10^{6} \) years to reduce travel from core to the
surface of the sun. Find the average distance that light can travel within the
interior of the sun without being scattered.
\( \mathbf{A} \cdot 2 m m \)
в. \( 0.1 \mathrm{mm} \)
\( \mathrm{c} .0 .4 \mathrm{mm} \)
D. \( 0.6 \mathrm{mm} \)


The glittering nature of diamond is due
to?
A. Giant polymer structure
B. High refractive index
C. High IP value of carbon
D. High electro negativity of carbon


The value of \( \wedge_{m}^{\infty} \) for \( K C l \) and \( K N O_{3} \) are
149.86 and \( 154.96 \Omega^{-1} c m^{2} m o l^{-1} \)
respectively. Also \( \lambda_{C l^{-}}^{\infty} \) is 71.44 ohm \( ^{-1} \mathrm{cm}^{2} \) mol \( ^{-1} \). The value of
\( \lambda_{N O_{3}^{-}}^{\infty} \) is :
A \( \cdot 76.54 \) ohm \( ^{-1} \mathrm{cm}^{2} \) mol \( ^{-1} \)
в. 133.08 ohm \( ^{-1} \mathrm{cm}^{2} \mathrm{mol}^{-1} \)
c. 37.7 ohm \( ^{-1} \mathrm{cm}^{2} \) mol \( ^{-1} \)
D. none of the above


\( -40^{\circ} \) on absolute scale is equal to
\( A \cdot \) ok
в. \( 233 k \)
\( c \cdot 273 k \)
D. 313K


Which of the following is the only nonmetal that appears as a liquid in its elemental form under standard
conditions?
A . \( C l \)
в. \( F \)
\( c . B r \)
\( D \)


\( A(-a, 0) ; B(a, 0) \) are fixed points. \( C \) is a point which divides internally \( A B \) in a constantly ration \( \tan \alpha . \) If \( A C \& C B \)
subtend equal angles at \( P, \) that the
equation of the locus of \( \boldsymbol{P} \) is \( \boldsymbol{x}^{2}+\boldsymbol{y}^{2}+ \)
\( 2 a x \sec 2 \alpha+a^{2}=0 \)


Draw structures of the following
derivatives.
(i) The 2,4 -dinitrophenylhydrazone of benzaldehyde
(ii) Cyclopropanone oxime
(iii) Acetaldehydedimethylacetal
(iv) The semicarbazone of
cyclobutanone
(v) The ethylene ketal of hexan-3-one
(vi) The methyl hemiacetal of formaldehyde


\( \mathbf{3} \times \mathbf{8}+\mathbf{6} \times \mathbf{1 1}+\mathbf{9} \times \mathbf{1 4}+\dots \)


Why are gaseous fuels better than the
solid and liquid ones?


Two identical particles each of mass \( M \)
and charge \( Q \) are placed a certain distance part. If they are in equilibrium under mutual gravitational and electric force then calculate the order of \( \frac{Q}{M} \) in
SI units.


Ferromagnetic ore properties are due to
A. filled inner sub-shells
B. vacant inner sub-shells
C . partially filled inner sub-shells
D. all the sub-shells equally filled


Examine if Mean value Theorem applies
to \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}+\mathbf{3} \boldsymbol{x}^{2}-\mathbf{5} \boldsymbol{x} \) in the interval
[1,2]. If it does, then find the intermediate point whose existence is asserted by theorem.
A. Mean Value theorem is applicable and intermediate points are \( c=-3.55,1.55 \)
B. Mean Value theorem is not applicable
c. Mean Value theorem is applicable and intermediate points are \( c=3.55,-1.55 \)
D. none of these


If \( 2(a-8 \times 5)-2 \times 7=3 \times 1 \times a+ \)
\( \mathbf{7} \times \mathbf{4}-(\mathbf{8} \times \mathbf{1} \times \mathbf{a}-\mathbf{1}), \) find \( \boldsymbol{a} \)
A \( \cdot \frac{123}{8} \)
B. \( \frac{123}{7} \)
c. \( \frac{8}{123} \)
D. \( \frac{7}{123} \)


The velocity of water in river is
180kmh \( ^{-1} \) near the surface. If the river
is \( 5 \mathrm{m} \) deep, then the Shearing stress between the surface layer and the bottom layer is then(coefficient of
viscosity of water, \( \boldsymbol{\eta}=\mathbf{1 0}^{-\mathbf{3}} \boldsymbol{P a} \boldsymbol{s} \)
\( \mathbf{A} \cdot 10^{-2} N m^{-2} \)
B. \( 10^{-3} N m^{-2} \)
c. \( 10^{-4} N m^{-2} \)
D. \( 10^{-5} N m^{-2} \)


Calculate the standard oxidation
potentials of zinc electrode form the
following data. The EMF of the cell :
\( \boldsymbol{L} \boldsymbol{i}|\boldsymbol{L} \boldsymbol{i} \oplus(\mathbf{0 . 0 5} \boldsymbol{M}) \| \boldsymbol{A} \boldsymbol{n}| \boldsymbol{Z} \boldsymbol{n}^{2+}(\boldsymbol{0} . \boldsymbol{5} \boldsymbol{M}), \boldsymbol{E} \)
\( -3.045 V, \) is \( 2.35 \mathrm{V} \) at \( 25^{\circ} \mathrm{C} \)


The botanical term used for the
androecium in a flower of China rose
(Hibiscus rosa sinensis) is
A. Polyadelphous
B. Monadelphous
c. Diadelphous
D. Polyandrous


Acid buffer can be prepared by mixing solutions of:
A \( . \quad N a C l+N a O H \)
в. \( H_{2} S O_{4}+N a_{2} S O_{4} \)
c. \( N H_{4} O H+N H_{4} C l \)
D. \( C H_{3} C O O N a+C H_{3} C O O H \)


The distance between the parallel lines \( 3 \cos \theta+4 \sin \theta+\frac{5}{r}=0 \) and \( 6 \cos \theta+ \)
\( 8 \sin \theta+\frac{7}{r}=0 \) is
\( A \cdot \frac{3}{5} \)
в. \( \frac{3}{10} \)
\( c \cdot \frac{3}{20} \)
D.


A vessel of \( 125 \mathrm{cc} \) contains \( _{1}^{3} \mathrm{H}\left(t_{1 / 2}=\right. \) 12.3 \( y \) ) at \( 500 \mathrm{kPa} \) and \( 300 \mathrm{K} \). Find the
activity of the gas
A. \( 0.754 \mathrm{Ci} \)
в. 7.24 Сг
c. \( 72.4 \mathrm{Ci} \)
D. 724 С\( i \)


What is \( p K \) value of the complex
\( \left[\boldsymbol{P t C l}_{4}\right] \) if
\( \boldsymbol{P t}^{4+}+\boldsymbol{C l}^{-} \rightarrow[\boldsymbol{P t C l}]^{3+} \)
\( \boldsymbol{K}_{\mathbf{1}}=\mathbf{1 0}^{-\mathbf{2}} \)
\( [\boldsymbol{P t C l}]^{3+}+\boldsymbol{C l}^{-} \rightarrow\left[\boldsymbol{P t} C l_{2}\right]^{2+} \)
\( \boldsymbol{K}_{2}=\mathbf{1 0}^{-3} \)
\( \left[\boldsymbol{P t C l}_{2}\right]^{2+}+\boldsymbol{C l}^{-} \rightarrow\left[\boldsymbol{P t C l}_{3}\right]^{+} \)
\( \boldsymbol{K}_{3}=\mathbf{1 0}^{-4} \)
\( \left[\boldsymbol{P t C l}_{3}\right]^{+}+\boldsymbol{C l}^{-} \rightarrow\left[\boldsymbol{P t} \boldsymbol{C l}_{4}\right] \)
\( \boldsymbol{K}_{4}=\mathbf{1 0}^{-4} \)


A considerable part of the harmful \( \boldsymbol{U} \boldsymbol{V} \)
rays of the sum does not reach the
surface of the earth. This is because
high above the earth's atmosphere, there is a layer of
\( A \cdot O_{3} \)
в. \( C O_{2} \)
\( c \cdot S O_{2} \)
D. \( N O \)


An electric bulb of \( 250 c c \) was sealed off at
a pressure \( 10^{-3} \mathrm{mm} \) of \( \mathrm{Hg} \) and
temperature \( \$ \$ 27^{\wedge}\{0\} \$ \$ \) C. The number
of molecules present in the gas is
A \( \cdot 8.02 \times 10^{15} \)
В. \( 6.023 \times 10^{23} \)
c. \( 8.021 \times 10^{23} \)
D. \( 6 \times 10^{22} \)


Which of the following biologists is responsible for the binomial system for naming organisms that we use today?
A. Carolus Linnaeus
B. Whittaker
c. Theophrastus
D. Aristotle


In induction the charge induced in the near surface of a dielectric is:
A. equal and similar
B. greater and dissimilar
c. lesser and dissimilar
D. equal and dissimilar


The quantities \( A \) and \( B \) are related by
the relation \( \boldsymbol{A} / \boldsymbol{B}=\boldsymbol{m}, \) where \( \boldsymbol{m} \) is the
linear mass density and \( A \) is the force, the dimensions of \( B \) will be :
A. Same as that of pressure
B. Same as that of work
c. Same as that of momentum
D. Same as that of latent heat


Turpentine oil can be purified by:
A. steam distillation
B. vaccum distillation
C. fractional distillation
D. sublimation


A leakage begins in water tank at
position \( P \) as shown in the figure. The
initial gauge pressure pressure above
that of the atmosphere) at \( P \) was \( 5 x \)
\( 10^{5} N / m^{2} \). If the density of water is
1000kg/ \( m^{3} \) the initial velocity with
which water gushes out is:
A \( .3 .2 m s^{-1} \)
B. \( 32 m s^{-1} \)
\( \mathbf{c} \cdot 28 m s^{-1} \)
D. \( 2.8 m s^{-1} \)


Then equilibrium constant for the
reaction is:
For the following reactions, equilibrium constants are indicated on the arrow
\[
\begin{array}{l}
\mathrm{H}_{3} \mathrm{PO}_{4} \stackrel{K_{1}}{\Leftrightarrow} \mathrm{H}^{+}+\mathrm{H}_{2} \mathrm{PO}_{4} \\
\mathrm{H}_{2} \mathrm{PO}_{4}^{*} \Leftrightarrow \mathrm{H}^{*}+\mathrm{HPO}_{4}^{-2} \\
\mathrm{HPO}_{4}^{-2} \stackrel{K_{3}}{\Leftrightarrow} \mathrm{H}^{+}+\mathrm{PO}_{4}^{-3}
\end{array}
\]
Then equilibrium constant for the reaction
\[
\mathrm{H}_{3} \mathrm{PO}_{4} \Leftrightarrow \quad 3 \mathrm{H}^{+}+\mathrm{PO}_{4}^{3} \text { will be }
\]
\( \mathbf{A} \cdot K_{1}+K_{2}+K_{3} \)
B . \( \sqrt{K_{1} K_{2} K_{3}} \)
\( \mathbf{c} \cdot K_{1} \times K_{2} \times K_{3} \)
D. \( \frac{1}{K_{1} K_{2} K_{3}} \)


Which one of the following is the main cause of land degradation in Punjab?
A. Intensive cultivation
B. Deforestation
c. over irrigation
D. Overgrazing


A charge \( q \) is moving with a velocity \( (v) \) parallel to a magnetic field \( (B) \). Force on the charge due to magnetic field is:
A \( . q v B \)
в. \( q B / v \)
c. zero
D. \( B v / q \)


Milk of magnesia \( M g(O H)_{2} \) is a/an:
A . acid
B. antacid
c. alkal
D. rock salt


What is ratio of time periods \( \left(T_{1} / T_{2}\right) \) in
second orbit of hydrogen atom to third orbit of \( \boldsymbol{H} \boldsymbol{e}^{+} \) ion?
\( A \cdot \frac{8}{27} \)
в. \( \frac{32}{27} \)
c. \( \frac{27}{32} \)
D. \( \frac{27}{8} \)


The input AC voltage to the transformer
is \( 3 \mathrm{kV} \) and output is \( 100 \mathrm{V} \). Then:
A. The ratio of number of turns in the primary to secondary coil is 30: 1
B. The transformer is a step down transformer
c. The transformer is a step up transformert
D. Both 1 and 2


f \( x y=6, \) then minimum value of \( 2 x+ \)
\( 3 y \) is


Light with energy flux of \( 24 W m^{-2} \) is incident on a well polished disc of radius \( 3.5 \mathrm{cm} \) for one hour. The
momentum transferred to the disc is
A \( \cdot 1.1 \mu \mathrm{kgms}^{-1} \)
B. 2.2 \( \mu \mathrm{kgms}^{-1} \)
c. \( 3.3 \mu \mathrm{kgms}^{-1} \)
D. \( 4.4 \mu \mathrm{kgms}^{-1} \)


In electrtolysis of \( A l_{2} O_{3} \) by Hall-
Heroult process:
A. cryolite \( N a_{3}\left[A I F_{6}\right] \) lowers the melting point of \( A l_{2} O_{3} \) and increases its electrical conductivity
B. \( A l \) is obtained at cathode and probably \( C O_{2} \) at anode
c. both (a) and (b) are correct
D. none of the above is correct


A metal ball falls from a height of \( 1 \mathrm{m} \) on to a steel plate and jumps upto a height of \( 81 \mathrm{cm} . \) Find the coefficient of
restitution of the ball material.
A. 0.2
B. 9
\( c \cdot 0.9 \)
D. 90


Which of the following is not a polymer?
A . Ice
B. Starch
c. Protein
D. Cellulose


By the principle of Mathematical induction, prove that, for \( n \geq 1 \)
\[
\mathbf{1}^{2}+\mathbf{2}^{2}+\mathbf{3}^{2}+\cdots+\boldsymbol{n}^{2}>\frac{\boldsymbol{n}^{\mathbf{3}}}{\mathbf{3}}
\]


If \( a=-6 \) and \( b=7, \) then \( 4 a(3 b+5)+ \)
\( \mathbf{2 b}=\mathbf{?} \)
A . 638
в. 624
\( c .610 \)
D. -610
E . -638


What is interstitial fluid?
A. Fluid which removes waste
B. Fluid which dissolves nutrients
C. Fluid which occupies spaces between the cells
D. All of the above


Differentiate between veins and
arteries?


Male and female Cockroaches can be
distinguished externally through
A. Anal styles in male
B. Anal cerci in female
c. Anal style and antennae in females
D. Both B and C


Riya performs two set of experiments to
study the length of the foam formed which follows
Set \( I: \) She takes 10 ml of distilled water
in test tube " \( A^{\prime \prime} \) and adds \( 5-6 \) drops of
liquid soap in it and shakes the test tube vigorously. Set \( I I: \) She takes 10 ml of distilled
water in a test tube \( ^{\prime \prime} A^{\prime \prime} \) and adds \( 5-6 \)
drops of liquid soap with half spoonful
of \( C a S O 4 \) in it and shakes the tube.
Write your observation and reason


The binding energy of electrons in a metal is \( 193 \mathrm{kJ} \mathrm{mol}^{-1} \). The threshold
frequency of the metal is:
A. \( 8.83 \times 10^{14} \mathrm{s}^{-1} \)
B. 4.83 \( \times 10^{14} \mathrm{s}^{-1} \)
c. \( 5.83 \times 10^{14} \mathrm{s}^{-1} \)
D. 6.83 \( \times 10^{14} \mathrm{s}^{-1} \)


By selling a watch for \( R s .1275 \), Javed
lost \( 15 \% \). At what price should he sell to
make a profit of \( 10 \% ? \)


Write a value of
\( \int \sqrt{9+x^{2}} d x \)


Who discovered X-rays?
A. Michael Faraday
B. Albert Einstein
C. W.K. Roentgen
D. J.J. Thomson


Consider the plane \( (\boldsymbol{x}, \boldsymbol{y}, \boldsymbol{z})= \)
\( (0,1,1)+\lambda(1,-1,1)+\mu(2,-1,0) . \) The
distance of this plane from the origin is:
A \( \cdot \frac{1}{3} \)
B. \( \frac{\sqrt{3}}{2} \)
\( c \cdot \sqrt{\frac{3}{2}} \)
D. \( \frac{2}{\sqrt{3}} \)


In photosynthesis in plants, \( \boldsymbol{H}_{2} \boldsymbol{O} \) and
\( C O_{2} \) react in presence of light and chlorophyll to give carbohydrate and oxygen.When the carbohydrate is burnt in air, the gases produced are:
A. \( C O_{2}+H_{2} \)
в. \( C O_{2}+C O \)
c. \( C O_{2}+H_{2} O \)
D. \( C O_{2}+O_{2} \)


A nucleus \( X \) initially at rest, undergoes alpha decay according to the equation
\[
\mathbf{9 2}^{\boldsymbol{X}^{A}} \rightarrow \boldsymbol{Z}^{Y^{228}}+\boldsymbol{\alpha}
\]
Then, the values of \( A \) and \( Z \) are
A .94,230
в. 232,90
c. 190,32
D. 230,94


In a cathode ray oscillograph, the focusing of beam on the screen is achieved by
A. Convex lens
B. Magnetic field
c. Electric potential
D. All of these


Argon and calcium are isobar. Why?
A. Both have same atomic number equal to 40
B. Both have different atomic mass
C. Both have same atomic mass equal to 40
D. None of above


An iron block of mass \( 2 k g \), falls from a
height of \( 10 m . \) After colliding with the ground it loses \( 25 \% \) energy to surroundings and rest is gained as heat. Then find the temperature rise of the block. (Take sp. heat of iron
\( \left.470 J / k g^{\circ} C\right) \)
A. \( 0.53^{\circ} \) C C \( C \) ?
B. \( 0.053^{\circ} \mathrm{C} \)
c. \( 0.159^{\circ} \mathrm{C} \)
D. \( 0.212^{\circ} \mathrm{C} \)


The sum of the measures of interior
angles of a polygon of \( n \) sides is equal to
A. \( 2 n \) right angles
B. \( (2 n-2) \) right angles
c. \( 2(n-2) \) right angles
D. \( 2(n-4) \) right angles


Figure shows a full wave bridge rectifier
circuit. The input a.c. is connected
across
\( A \cdot A \) and \( B \)
B. A and C
C. \( B \) and \( D \)
D. \( B \) and \( C \)


The correct order of increasing \( s \) character (in percentage) in the hybrid orbitals of the given molecules/ions is (assume all hybrid orbitals are exactly equivalent):
\( \boldsymbol{C H}_{2} \quad \boldsymbol{X} \boldsymbol{e F}_{4} \quad \boldsymbol{B r} \boldsymbol{F}_{3} \quad \boldsymbol{N C l}_{3} \quad: \boldsymbol{C C l}_{2} \)
\( \mathbf{A} \cdot\|<\| \mathbf{I}<\mid V<1=\mathbf{V} \)
B. \( |>V>|||>|V>| \mid \)
\( c \cdot\|1<\|<1<V<1 V \)
D. \( \|<I V<\| 1<1<V \)


What are micronutrients? Write two
examples of it?


If \( a, b \) are nonzero vectors and \( a \) is
perpendicular to \( b \), then \( a \) has nonzero
vector \( r \) satisfying \( r \cdot a=\alpha, \) for some
scalar \( \boldsymbol{\alpha}, \boldsymbol{a} \times \boldsymbol{r}=\boldsymbol{b} \) is
A \( \cdot \frac{\alpha a+(a+b)}{|a|^{2}} \)
в. \( \frac{\alpha a+a \times b}{|b|^{2}} \)
c. \( \frac{\alpha a-(a \times b)}{|a|^{2}} \)
D. \( \frac{\alpha a-(a \times b)}{|b|^{2}} \)


Which of the following is not a genetic material?
A. ds DNA
B. ss DNA
c. \( d s \) RNA
D. None of the above


The value of \( \int_{0}^{\pi / 2} \frac{f(x) d x}{f(x)+f(\pi / 2-x)} \)
is equal to
A . \( \pi / 4 \)
B . \( \pi / 2 \)
\( c . \pi \)
D. None


Set the following vectors in the increasing order of their magnitudes.
a) \( 3 \hat{i}+4 \hat{j} \)
b) \( 2 \hat{i}+4 \hat{j}+6 \hat{k} \)
c) \( 2 \hat{i}+2 \hat{j}+2 \hat{k} \)
\( A \cdot b, a, c \)
B. \( c, a, b \)
\( c \cdot a, c, b \)
D. a, b, c


Conversion of benzene diazonium
chloride to chlorobenzene is:
A. Sandmeyer's reaction
B. Stephen's reaction
c. Gomberg reaction
D. Schotten-Baumann reaction


Symbols in (I) and (II) represent
standard transistors. Then
A. both represents p-n-p transistors
B. both represents n-p-n transistors
c. (I) represents n-p-n and (II) represents \( p \) -n-p.
D. (I) represents p-n-p and (II) represents n-p-n-


Which of the following is used as an acid bath in dyeing cotton and wool?
A. Methanoic acid
B. Acetic acid
c. Benzoic acid
D. Sulphuric acid


The quantity \( \boldsymbol{X}=\frac{\boldsymbol{\epsilon}_{0} \boldsymbol{L} \boldsymbol{V}}{\boldsymbol{t}}: \boldsymbol{\epsilon}_{0} \) is the
permittivity of free space, \( \boldsymbol{L} \) is length, \( \boldsymbol{V} \)
is potential difference and \( t \) is time. The
dimensions of \( X \) are same as that of
A . Resistance
B. Charge
c. voltage
D. current


Barometric height used as a unit to express the atmospheric pressure because atmospheric pressure holds the mercury in the tube, so the height of mercury is used as a unit to express the atmospheric pressure.Type 1 for true and 0 for false


Compound \( A \) and \( B \) are two oxides of
sulfur. Compound A is 50\% sulfur by
mass, while Compound B is \( 40 \% \) sulfur
by mass.

Given the atomic masses of sulfur and
oxygen are 32 amu and 16 am \( u \) respectively, which of the following statements is NOT a valid
interpretation of these data? This question has multiple correct options
A. Compound A could have the formula, \( S O_{2} \)
B. Compound B could have the formula, \( S O_{2} \)
C. Compound A and B illustrate Dalton's law of multiple proportions.
D. Compound A could have the formula, \( S O \).


A force of \( 10 \mathrm{N} \) inclined to the horizontal
at an angle of 60 acts on a body can move in horizontal direction only find its
acceleration.


The experiment given shows that light:
A. Can be reflected
B. Is a form enrgy
C. Travels in straight line
D. Can pass through all objects


Find the area of the quadrilateral ABCD whose vertices are \( A(-3,-1), B(-2,-4) \)
\( C(4,-1) \) and \( D(3,4) \)


The pressure required to liquefy a gas at the critical temperature is called
A. reduced pressure
B. critical pressure
c. vapour pressure
D. atmospheric pressure


Momentum is a measure of quantity of
A. motion
B. friction
c. gravitation
D. electric force


The total number of chromosomes in an
organism with haploid number of 18 would be
\( A \cdot 18 \)
B. 16
\( c \cdot 26 \)
D. 36
E. 46


Reabsorption of water in the nephron is controlled by ADH and aldosterone hormone.
A. True
B. False


The correct statement(s) about the
oxoacids, \( H C l O_{4} \) and \( H C l O, \) is (are):
This question has multiple correct options
A. the central atom in both \( H C l O_{4} \) and \( H C l O \) is \( s p^{3} \)
hybridized
B. the conjugate base of \( H C l O_{4} \) is weaker base than \( H_{2} O \)
C \( \cdot H C l O_{4} \) is formed in the reaction between \( C l_{2} \) and \( H_{2} O \)
D. \( H C l O_{4} \) is more acidic than \( H C l O \) because of the resonance stabilization of its anion


Very short answer type. Name any two macronutrients and
state their importance in plant nutrition.


A lamp is marked \( 60 \mathrm{W}, 220 \mathrm{V} \). If it
operates at \( 200 \mathrm{V} \), the rate of consumption of energy will
A. decrease
B. increase
c. remain unchanged
D. first increase then decrease


The stable oxidation states of Cr are:
\( A \cdot+3,+6 \)
\( B \cdot+3,+4 \)
\( c \cdot+1,+4 \)
\( D \cdot+2,+5 \)


Potassium ferrocyanide is stored in dark coloured bottles and kept away
from sunlight because:
This question has multiple correct options
A. undergoes displacement in sunlight
B. dark colors of the bottles absorb a lot of energy from light
c. undergoes decomposition in sunlight
D. evaporates in sunlight


\( C S_{2} \) burns in excess air to produce :
A. \( C O_{2} \& S O_{2} \)
в. \( C O_{2} \& S O_{3} \)
c. \( \cos S O_{2} \)
D. \( \operatorname{co~} \& \mathrm{SO}_{3} \)


Number of pollen grains produced per pollen mother cell is gymnosperms is
A . 4
B. 2
\( c \cdot 6 \)
D. 10


What do you mean by Corrosion?


The angle between particle velocity and wave velocity in a transverse wave is:
A. zero
в. \( \pi / 4 \)
c. \( \pi / 2 \)
D.


If \( \cos 2 B=\frac{\cos (A+C)}{\cos (A-C)}, \) then
\( \tan A, \tan B, \tan C \) are in
A. \( A . P . \)
в. \( G . P \)
c. \( H . P \)
D. None of these


If brakes are applied all of a sudden in a moving car, passengers automatically lean forward is an example of inertia in motion: Type 1 for true and 0 for false


The principal is Rs. \( 1000, \) so if you pay off Rs. \( 500, \) the remaining Rs. 500 left to repay is also called the
A. interest
B. Ioan
c. principal
D. rate


The inductive reactance of a choke coil
of \( 1 / 4 \pi m H \) in an \( A C \) circuit of \( 50 H z \) will be
A. 25 ohm
B. 0.25 ohm
c. 0.025 ohm
D. 2.5 ohm


Which one of the following is a
matching pair?
A. Lub-sharp closure of AV valves at the begining of ventricular systole
B. Dup-sudden opening of semilunar valves at the begining of ventricular diastole
C. Pulsation of the radial artery-valves in the blood vessels
D. Initiation of the heart beat-Purkinje fibres


Find the total number of possible structural isomers of the compound \( \left[\boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right]\left[\boldsymbol{P t} C l_{4}\right] \)


If three sides of a triangle are respectively equal to three sides of
another triangle, then the triangles are:
A. unequal
B. equilateral
c. congruent
D. none of these


The valency of an atom is equal to its combining capacity.
A. True
B. False


In the middle of the depletion layer of a reverse biased \( p-n \) junction, the
A. Potential is zero
B. Potential is maximum
c. Electric field is maximum
D. Electric field is zero


In which stage DNA replication takes place?
A. Metaphase
B. \( G_{1} \) -phase
c. \( S \) - phase
D. \( G_{2} \) -phase


A heavy block of length \( b \) and height \( h \) is
placed at rest on a rough inclined plane of inclination \( \theta \) with the horizontal, as
shown in figure.
(a) The normal reaction from the
surface cannot pass through the centre
mass.Why?
(b) If \( \mu \) is the coefficient of friction
between the block and the inclined
plane, then discuss the conditions of
translational and rational equilibrium of the block.
A heavy block is placed at rest on a rough inclined plane.


Rod-shaped elongated sclereids found in the seed coats of pulses are known as
A. Astrosclereids
B. Macrosclereids
c. Trichosclereids
D. Brachysclereids


\( C_{2} H_{4}+H_{2} \stackrel{N i / P d}{\longrightarrow} C_{2} H_{6} \)
name of this reaction is:
A. substitution
B. hydrogenation
c. alkanes formation
D. dehydrohalogenation