Value of quantum numbers is \( \boldsymbol{n}= \) \( \mathbf{4}, \boldsymbol{I}=\mathbf{1}, \boldsymbol{m}=+\mathbf{1}, \) and \( \boldsymbol{s}=-\frac{\mathbf{1}}{\mathbf{2}} \) find
atomic numbers.
A .22
B. 34
\( c .33 \)
D. 36


What is the degree of the polynomial
\( 2 a^{2}+4 b^{8} ? \)
\( A \cdot 2 \)
B. 10
c. 8
D.


f \( a=2 \) and \( b=3, \) then find the values
of each of the following: \( (a+b)^{a} \)


What are the coordinates of the center
of this circle?
\( \boldsymbol{x}^{2}+(\boldsymbol{y}+\mathbf{7})^{2}=\mathbf{1 1} \)
\( A \cdot(7,7) \)
B. (0,7)
c. (-7,-7)
D. (0,-7)


The phenomenon of rotation of plane polarized light is called
A. Kerr effect
B. Double refraction
c. optical activity
D. Dichroism


The frequency of a particle performing SHM is 12 Hz. Its amplitude is \( 4 \mathrm{cm} \). Its initial displacement is \( 2 \mathrm{cm} \) towards positive extreme position. Its equation for displacement is
A. \( x=0.04 \cos (24 \pi t+\pi / 6) \)
В. \( x=0.04 \sin (24 \pi t) \)
c. \( x=0.04 \sin (24 \pi t+\pi / 6) \)
D. \( x=0.04 \cos (24 \pi t) \)


Find: \( \int \frac{e^{x}(x-3)}{(x-1)^{3}} d x \)


A compound has carbon, hydrogen, and oxygen in 3: 3: 1 atomic ratio. If the
number of moles in \( 1 g \) of the compound is \( 6.06 \times 10^{-3} \), the molecular formula of
the compound will be
\( A \cdot C_{3} H_{3} O \)
в. \( C_{6} H_{6} O_{2} \)
\( \mathbf{c} \cdot C_{9} H_{9} O_{3} \)
D. \( C_{12} H_{12} O_{4} \)


How many terms of the given G.P. \( 3, \frac{3}{2}, \frac{3}{4},, . \) be taken together to get \( \frac{3069}{512} \)
\( ? \)


The products formed when chlorine dissolves in water?
A. \( \mathrm{HCl}+\mathrm{Cl}_{2} \)
B. HCl+ HOCl
c. \( \mathrm{HOCl}+\mathrm{Cl}_{2} \)
D. HCl only


Find the equivalent capacitance
between the point \( A \) and \( B \) in given
figure where \( \boldsymbol{C}=\mathbf{5} \boldsymbol{\mu} \boldsymbol{F} \)


Green plants are known as


Explain why a rectangle is a convex quadrilateral.


Subtract.
\( 5 a^{2}-7 a b+5 b^{2} \) from \( 3 a b-2 a^{2}-2 b^{2} \)


\( \mathbf{n}[\mathbf{0}, \mathbf{1}] \) Lagranges Mean Value theorem is NOT applicable to
A. \( f(x)=x|x| \)
B . \( f(x)=|x| \)
c. \( f(x)=x \)
D. none of these


Kidney of mammals is
A. Pronephric
B. Mesonephric
C . Metanephric
D. None of the above


Write the reactions of (i) aromatic and
(ii) aliphatic primary amines with nitrous acid.


At 1 atm pressure, for a reaction \( \Delta H=+30.558 \mathrm{kJ} \mathrm{mol}-1 \) and \( \Delta \mathrm{S}=0.066 \mathrm{kJ} \)
mol-1. The temperature at which free
energy is equal to zero and the nature of the reaction below this temperature is:
A. \( 483 \mathrm{K} \), spontaneous
B. 443 K, non-spontaneous
c. \( 443 \mathrm{K}, \) spontaneous
D. 463 K, non-spontaneous


Which species has the maximum number of lone pair of electrons on the
central atom?
A \( \cdot\left[C l O_{3}\right] \)
в. \( X e F_{4} \)
c. \( S F_{4} \)
D. \( \left[I_{3}\right] \)


Fungi:
A. Are mostly multicellular
B. Are mostly unicellular
C. Prefer to grown in warm and dry places
D. May be autotrophs


The mean lives for \( \alpha \) and \( \beta \) decay of a
radioactive substance are 1620 years
and 405 years respectively. The time in which \( \frac{3}{4} t h \) of the material will decay, if it simultaneously emits \( \alpha \) and \( \beta \)
particles is
A. 449 years
B. 199 years
\( c \cdot \alpha \)
D. 99 years


The energy required to break one mole
of \( C l-C l \) bond in \( C l_{2} \) in
\( 242 k J \) mol \( ^{-1} . \) The longest wavelength
of light capable of breaking a single \( C l-C l \) bond is:
\( \left[c=3 \times 10^{4} m s^{-1} \text {and } N_{A}=6.02 \times\right. \)
\( \left.10^{23} m o l^{-1}\right] \)
A. 594 nm
B. 640 nm
c. 700 nm
D. 494 nm


A sliding rod \( A B \) of resistance \( R \) is shown in the figure. Here magnetic field \( B \) is constant and is Out of the
paper. Parallel wires have no resistance and the rod is moving with Constant velocity v. The current in the sliding rod AB in the function of \( t, \) when
switch \( \mathrm{S} \) is closed at time \( \mathrm{t}=0 \) is
\( ^{A} \cdot\left(\frac{v B d}{R}\right) e^{-t / c} \)
\( ^{\mathbf{B}} \cdot\left(\frac{v B d}{R}\right) e^{-t / R C} \)
\( ^{\mathrm{c}} \cdot\left(\frac{v B d}{R}\right) e^{R t C} \)
D. \( \left(\frac{v B d}{R}\right) e^{t / R C} \)


The volume of sphere is \( \frac{4}{3} \pi c m^{3} . \) Then the radius is
\( A \)
B. 0.02
c. 0.01
D. 2


Let \( \boldsymbol{f}: \boldsymbol{R}-\{\boldsymbol{n}\} \rightarrow \boldsymbol{R} \) be a function
defined by \( f(x)=\frac{x-m}{x-n} \) such that
\( \boldsymbol{m} \neq \boldsymbol{n}, \) then
A. \( f \) is one one into function
B. \( f \) is one one onto function
c. \( f \) is many one into function
D. \( f \) is many one onto function


The number of subsets of the set
\{10,11,12\} is
\( A \cdot 3 \)
B. 8
\( c \cdot 6 \)
D. 7


If \( \sin \theta=-0.6, \) the find the quadrant
from which the terminal arm making an
angle of \( \theta^{\circ} \) passes.
A . I quadrant
B. II quadrant
c. III quadrant
D. IV quadrant


Show that every positive integer is of
the form \( 2 q \), and that every positive odd
integer is of the form \( 2 q+1 \), where \( q \) is
some integer.


The molality of an aqueous dilute solution containing non-volatile solute is 0.1 m. What is the boiling
temperature (in \( ^{\circ} \boldsymbol{C} \) ) of solution?
(Boiling point elevation constant, \( \boldsymbol{K}_{\boldsymbol{b}}= \) \( 0.52 k g m o l^{-1} K ; \) boiling temperature
of water \( =100^{\circ} \mathrm{C} \) )
A. 100.0052
в. 100.052
c. 100.0
D. 100.52


The pathogen, Microsporum causes ringworm disease in humans and belongs to the same kingdom as which one of the following?
A. Wuchereria, a filarial worm
B. Ascaris, a round worm
c. Taenia, a tapeworm
D. Rhizopus, a mould


A sparkless current is passed through
oxygen to prepare ozone. Why?


A cyclist is riding with a speed of 27 \( \mathrm{km} / \mathrm{h} \). As he approaches a circular turn on the road of radius \( 80 \mathrm{m}, \) he applies brakes and reduces his speed at the constant rate of \( 0.50 \mathrm{m} / \mathrm{s} \) every second.
What is the magnitude and direction of the net acceleration of the cyclist on the
circular turn?


Which of the following phenomena take place when the top layer of soil is exposed?
A. Soil erosion
B. Infertile soil
c. Both A and B
D. Good quality new soil


Which of the following substances yield less than \( 4 K c a l / \) mol, when its
phosphate bond is hydrolysed?
A. Creatine phosphate
B. ADP
c. Glucose-6-phosphate
D. ATP


Bauxite containing impurities of iron oxide is purified by :
A. Hoop's process
B. Serpeck's process
c. Bayer's process
D. Electrolytic process


\( A B, A_{2} \) and \( B_{2} \) are diatomic molecules. If
the bond enthalpies of \( A_{2}, A B \) and \( B_{2} \) are
in the ratio1:1:0.5 enthalpy of formation of \( A B \) from \( A_{2} \) and \( B_{2} \) is \( -100 K J \mathrm{mol}^{-1} . \) What
is the bond energy of \( A_{2} ? \)
B. 100 KJmol-
c. 300 KJmol \( ^{-1} \)
D. 400 KJmol-


The internal energy of an ideal gas increases during an isothermal process when the gas is
A. Expanded by adding more molecules to it
B. Expanded by adding more heat to it
c. Expanded against zero pressure
D. Compressed by doing work on it


State True or False.
Nucleus always contains proton.
A. True
B. False


Grandpa lost his teeth that could never be replaced naturally because they were
A. Permanent teeth
B. Milk teeth
c. Both A and B
D. None of the above


The observer
candle because light always takes path.
A. Can; straight line
B. Can; curved
c. cannot; straight line
D. Cannot; curved


What will be the molarity of the solution in which 0.365 g of HCl gas is dissolved in \( 100 \mathrm{mL} \) of solution?
A. 2 M
B. 0.2 \( M \)
\( c \cdot 1 M \)
D. 0.1 M


Probability of an event is always less than or equal to
A. 0
B. 1
\( c \cdot> \)
D. None of these


Whcih one of the following is used as an acidic flux in metallurgy?
A. \( C a O \)
в. \( \operatorname{si} 0_{2} \)
c. \( N a_{2} C O_{3} \)
\( \mathrm{D} \cdot \mathrm{SO}_{2} \)


When sodium acetate \( \left(\boldsymbol{C H}_{3} \boldsymbol{C O O N} \boldsymbol{a}\right) \)
is added to aqueous solution of acetic
\( \operatorname{acid}\left(\boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C O O H}\right) \)
A. the pH value become zero
B. pH value reamains unchanged
c. pH value deacreases
D. pH value increases


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


Find the value of \( 2 i^{2}+6 i^{3}+3 i^{16}- \)
\( \mathbf{6} i^{19}+4 i^{25} \)


A long copper wire contains a current
of I ampere. The magnetic flux per
metre of the wire for a plane surface inside the wire as shown in figure.
\( ^{A} \cdot \frac{\mu_{0}}{2 \pi} \)
В \( \frac{\mu_{0}}{4 \pi} \)
c. \( \frac{\mu_{0}}{\pi} \)
D. \( \frac{\mu_{0}}{6 \pi} \)


BOD stands for
A. Biological oxygen demand
B. Chemical oxygen demand
C . Bio degradation
D. Biotic community


The type of elements present in group 18[0] are :
A . alkal
B. alkaline
c. transition
D. noble gases


Noble gas do not react with other
elements because:
A. they have completely paired up and stable electronic configuration.
B. their size is very small.
C. they are monoatomic.
D. none of these


What willl be the mass of oxygen
liberated by decomposition of \( 200 \mathrm{mL} \) hydrogen peroxide solution with a strength of 34 g per litre?
A. 25.5g
B. 3.0g
c. \( 3.2 g \)
D. 4.28


Explain why:
Transition elements usually form
coloured ions.


The molecules shown are:
A. enantiomers
B. diastereomers
C . identical.
D. constitutional isomers


Two Circular cells can be arranged in any of the three following situations as shown in figure. Their mutual inductance will be Maximum in which
arrangement ?
\( A \cdot(A) \)
B. (B)
\( c \cdot(c) \)
D. Same in all conditions


I. Pars interedia secretes MSH
II. Leydig's cell secreted progesterone
III. Melatonin is secreted by pineal gland IV.Myxoedema os a thyroid disorder
V. Neurohypophysis secreted ACTH
\( A \cdot \) ।, IV nad \( v \)
B. II, IV and
c. \( \| \), Il and \( v \)
D. I, III and IV


The equation of one of the tangents to the curve \( \boldsymbol{y}=\cos (\boldsymbol{x}+\boldsymbol{y}),-2 \boldsymbol{\pi} \leq \boldsymbol{x} \leq \)
\( 2 \pi ; \) that is parallel to the line \( x+2 y= \)
\( 0, \) is
A. \( x+2 y=1 \)
B. \( x+2 y=\frac{\pi}{2} \)
c. \( x+2 y=\frac{\pi}{4} \)
D. None of these


(i) What is main difference between
electromagnetic waves theory and Planck's quantum theory.
(ii) Which rule is violated in the
following orbital diagram:


Increased \( C O_{2} \) concentration in the
atmosphere leads to
A. Global warming
B. Eutrophication of lakes
c. Depletion of the ozone layer
D. Magnification in the food chain
E. Acid rain


The most abundant lipid in cell membrane is
A. Phospholipid
B. Starch
c. oil
D. Sulpholipid


Consider the following four statements
(1) Benzene does not favour the attack
of \( N u^{-} \) on itself.
(2) On benzene ring \( \boldsymbol{E}^{+} \) can attacks
easily because benzene ring is electron
rich
(3) Benzene ring does not undergo addition reaction readily because after addition reaction benzene ring loses its aromatically.
(4) When electron withdrawing groups are present on benzene ring, attack of
\( N u- \) on benzene nucleolus becomes
easy.
Out of these statements, correct
statements are-
\( A \cdot 1,3 \) and 4
B. 1,2 and 4
c. 2 and 4
D. All are correct


A long solenoid of length \( L \) has a mean
diameter \( D . \) It has \( n \) layers of winding of
\( N \) turns each. If it carries a current \( I \)
the magnetic field at its centre will be.
A. Proportional to \( D \)
B. Inversely proportional to \( D \)
c. Independent of \( D \)
D. Proportional to L.


Which of the following are in inverse
proportion?
This question has multiple correct options
A. The number of workers on a job and the time to complete the job.
B. The time taken for a journey and the distance travelled in a uniform speed.
C. Area of cultivated land and the crop harvested.
D. The time taken for a fixed journey and the speed of the vehicle.
E. The population of a country and the area of land per person.


Which would quickly absorb oxygen?
A. Alkaline solution of payrogallol
в. \( \operatorname{conc.H}_{2} S O_{4} \)
c. lime water
D. Alkaline solution of \( C u S O_{4} \)


RQ in anaerobic respiration is?
A . 0.7
B. 0.9
c. Unity
D. Infinity


The number of \( s p^{2}-p^{2} \) hybrid omega
bonds in the following compound is:
4
B.
\( c \)
2


Find out the total power supplied by the \( 60-V \) source in the circuit shown in
figure.
A. 360 \( \mathrm{w} \)
B. 200 \( w \)
\( c \cdot 400 w \)
\( D .180 \mathrm{w} \)


A vertical rod of length \( l \) is moved with
constant velocity \( v \) towards east. The
vertical component of earth's magnetic
field is \( \mathrm{B} \) and angle of dip is \( \theta . \) The induced e.m.f. in rod is:
A. \( B l v \cot \theta \)
B. \( B l v \sin \theta \)
c. \( B l v \tan \theta \)
D. \( B l v \cos \theta \)


Assertion
Odd in favour of an event \( A \) are \( 2: 1 \& \)
odd in favour of \( A \cup B \) are 3: 1 then
\( \frac{1}{12} \leq P(B) \leq \frac{3}{4} \)
Reason
If \( \boldsymbol{A} \cap \boldsymbol{B} \subset \boldsymbol{A} \) then \( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B}) \leq \boldsymbol{P}(\boldsymbol{A}) \)
A. Both Assertion \& Reason are individually true \& Reason is correct explanation of Assertion
B. Both Assertion \& Reason are individually true but Reason is not the , correct (proper) explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true


The e.m.f. of a cell is \( _{--}-_{-}- \) the voltage across its terminals when no current
flows. Fill in the blank.
A. more than
B. less than
c. equal to
D. none of these


A body of mass 5 kg moving with a speed of \( 3 m s^{-1} \) collides head on with a
body of mass \( 3 \mathrm{kg} \) moving in the
opposite direction at a speed of \( 2 m s^{-1} \) The first body stops after the collision. Find the final velocity of the second
body.
\( \mathbf{A} \cdot 3 m s^{-1} \)
B . \( 5 \mathrm{ms}^{-1} \)
\( \mathrm{c} \cdot-9 \mathrm{ms}^{-1} \)
D. \( 30 m s^{-1} \)


The amplitude of the electric field in a parallel beam of light of intensity \( 2.0 \mathrm{Wm}^{-2} \) is:
A. \( 19.4 \mathrm{N} / \mathrm{C} \)
B. 38.8 N/C
c. \( 4.85 \mathrm{N} / \mathrm{c} \)
D. 77.9 N/C


The diameter of a circle whose area is
equal to the sum of the areas of the two
circles of radii \( 24 \mathrm{cm} \) and \( 7 \mathrm{cm} \) is
\( \mathbf{A} \cdot 31 \mathrm{cm} \)
B. \( 25 \mathrm{cm} \)
\( c \cdot 62 \mathrm{cm} \)
D. \( 50 \mathrm{cm} \)


TMV contains
\( A \cdot D N A \)
B. RNA + protein
C. DNA + RNA
D. DNA + protein


Which moon is after the waxing
crescent?
A. Third Quater
B. First Quarter
c. waxing Gibbous
D. New moon


Select the correct IUPAC name for the
compound shown.
A. 5-methyl-5-ethyloctane
B. 5-methyl-5-propylheptane
C. 3-ethyl-4-methyloctane
D. 3-methyl-3-propylheptane


What is Mechanical equilibrium?
A. When no mechanical work is done by one part of the system on any other part of the system.
B. When no chemical work is done by one part of the system on any other part of the system.
C. When mechanical work is done by one part of the system on any other part of the system.
D. None of these


A body is projected up with velocity \( u \). It
reaches the same point in its path at \( t_{1} \)
and \( t_{2} \) from the time of projection. Then
\( \boldsymbol{t}_{1}+\boldsymbol{t}_{2} \) is:
A \( \cdot \frac{2 u}{g} \)
в. \( \frac{u}{g} \)
c. \( \sqrt{\frac{2 u}{g}} \)
D. \( \sqrt{\frac{u}{g}} \)


A solution of 0.2 mole \( \mathrm{Kl}(\alpha=100 \%) \) in
1000 g water freezes at \( T_{1}^{\circ} \) C. Now to
this solution 0.1 mole \( H g I_{2} \) is added
and the resulting solution freezes at
\( T_{2}^{\circ} \mathrm{C} . \) Which of the following is correct?
A \( \cdot T_{1}=T_{2} \)
в. \( T_{1}>T_{2} \)
c. \( T_{1}<T_{2} \)
D. can't be prediced


0
0
0
0
0


A monoprotic acid in a \( 0.1 \mathrm{M} \) solution
ionizes to \( 0.001 \% \). Its ionization
constant is:
A \( \cdot 1.0 \times 10^{-3} \)
В. \( 1.0 \times 10^{-6} \)
c. \( 1.0 \times 10^{-8} \)
D. \( 1.0 \times 10^{-1} \)


Which of the following is isoelectronic
pair?
A. \( C N^{-}, O_{3} \)
в. \( C l O_{2}, B r F_{2} \)
\( \mathrm{c} \cdot \mathrm{BrO}_{2}^{-}, \mathrm{BrF}_{2}^{+} \)
D. \( I C l_{2}, C l O_{3} \)


The mass of a body is can be zero
whereas the weight of a body can never be zero. True or false.
A. True
B. False


Which among the following metals is employed to provide cathodic protection to iron?
A. zinc
B. Nickel
\( c . \) Tin
D. Lead


Chlorine is passed into dilute cold KOH solution. What are the oxidation
numbers of chlorine in the products formed?
A \( .-1,+5 \)
B. -1,+3
\( \mathrm{c} \cdot+1,+7 \)
D. +1,-1


Once a choice made regarding zero potential energy reference state, the change in potential energy is :
A . same
B. different
c. depend strictly on the choice of zero potential
D. become indetermine


Compound which is used for separation
of acetone and acetophenone:
A. Sodium bisulphite.
B. Girgnard reagent.
c. Sodium sulphate
D. Ammonium chloride


If \( \sin ^{-1} \frac{3}{x}+\sin ^{-1} \frac{4}{x}=\frac{\pi}{2}, \) then \( x \) is
equal to
\( A \cdot 3 \)
B. 5
\( c \cdot 7 \)
D. 11


\( \left(\frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}\right)^{2}+\cos \left(\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right)=\mathbf{0} \)


The sum of three consecutive odd
numbers is \( 57 . \) Find the numbers.
A. 17,19 and 21
B. 19,15 and 25
c. 13,17 and 26
D. 21,13 and 29


Q Type your question
the graph between the temperature \( T \) of
the metal and time \( t \) will be closest to:
\( A \)
B.
\( c \)
\( D \)


Inflorescence with unbranched axis is
called
A. Compound racemose
B. Compound corymb
c. simple racemose
D. Verticillaster


If \( \boldsymbol{x}-\boldsymbol{y}=-\boldsymbol{6} \) and \( \boldsymbol{x} \boldsymbol{y}=\mathbf{4}, \) find the
value of \( \boldsymbol{x}^{\mathbf{3}}-\boldsymbol{y}^{\mathbf{3}} \)
\( \mathbf{A} \cdot-288 \)
в. 288
\( c \cdot-28 \)
D. None of these


A hydrocarbon compound burns with a
non-luminous flame. Which
hydrocarbon type does it indicate?
A. Alicyclic hydrocarbon
B. Aromatic hydrocarbon
c. Unsaturated hydrocarbon
D. Acyclic hydrocarbon


The theory that can completely/properly explain the nature of bonding in
\( \left[N i(C O)_{4}\right] \) is :
A. Valence bond theory
B. Crystal field theory
c. Molecular orbital theory
D. Werner's theory


Allegra, a common prescription drug with the structure shown below., is given for treatment of seasonal allergies. How many stereogenic carbon does Allegra possess?


Here is the diagram of prothallus. Identify \( A, B \) and \( C \)
A. A - archegonia, B - antheridia, C - rhizoids
B. A - antheridia, B - archegonia, C - rhizoids
c. A - archegonia, B - antheridia, C- roots
D. A - antheridia, B - archegonia, C - roots


Assertion
Pure water obtained from different
states of India always contains
hydrogen and oxygen in the ratio of 1: 8
by mass.
Reason
Total mass of reactants and products
during chemical change is always the
same.
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


Two blocks of same mass \( (4 \mathrm{kg}) \) are placed according to diagram. Initial velocities of bodies are \( 4 \mathrm{m} / \mathrm{s} \) and \( 2 \mathrm{m} / \mathrm{s} \)
and the string is taut. Find the impulse
on 4 kg when the string again becomes
taut.
A \( .24 \mathrm{N}-\mathrm{s} \)
B. \( 6 N- \) s
\( c \cdot 4 N-s \)
D. 2 N-s


Acceleration due to gravity as a
function of \( r \) is given by :
A \( \cdot \frac{4}{3} \pi G r(A-B r) \)
B . \( 4 \pi G r(A-B r) \)
c. \( \frac{4}{3} \pi G r\left(A-\frac{3}{4} B r\right) \)
D \( \cdot \frac{4}{3} \pi G r\left(A-\frac{3}{2} B r\right) \)


If tangents \( \boldsymbol{T} \boldsymbol{A} \) and \( \boldsymbol{T} \boldsymbol{B} \) from a point \( \boldsymbol{T} \)
to a circle with centre \( O \) are inclined to
each other at an angle of \( 70^{\circ}, \) then find
\( \angle A O B \) (in degrees)


A system which cannot exchange matter and energy with the surroundings called isolated.
A. True
B. False
c. Ambiguous
D. None of these


Which of the following is nonpermissible?
A \( \cdot n=4,1=3, m=0 \)
B. \( n=4,1=2, m=1 \)
c. \( n=4,1=4, m=1 \)
D. \( n=4,1=0, m=0 \)


\( \underbrace{E} \)


The sodium phenoxide ion formed during the preparation of phenol from benzene suphonic hydrolysed in prasence of acid to:
A. neutralize the basic phenoxide ion.
B. to increase the basic nature of reaction mixture
c. to acidify the reaction mixture so as to get phenol.
D. both \( A \) and \( C \).


Which of the following is a mode of asexual reproduction?
A. Gamete formation
B. Binary fission
c. Digestion
D. organogenesis


Select the correct statement at all
conditions
A. Total number of moles in a closed system at new equilibrium is less than the old equilibrium if some amount bf a substance is removed from a system.
B. In exothermic reaction, concentration of products dominate that of reactant
C. Change in Entropy of a reversible reaction is zero
D. \( A B \) and \( C \) are incorrect statements


A body moving with a constant acceleration travels the distances \( 3 m \)
and 8 m respectively in \( 1 ~ s \) and \( 2 s \)
Calculate the acceleration of the body.
\( \mathbf{A} \cdot 2 m s^{-2} \)
B. \( 3 m s^{-2} \)
c. \( 4 m s^{-2} \)
D. \( 5 m s^{-2} \)


Two metallic spheres \( S 1 \) and \( S 2 \) are
made of the same material and have
got identical surface finish. The mass of
S1 is thrice that of \( S 2 . \) Both the spheres
are heated to the same high temperature and placed in the same room having lower temperature but are thermally insulated from each other. The rate of the initial rate of cooling of
S1 to that of \( S 2 \) is?
A \( \cdot \frac{1}{3} \)
в. \( \frac{1}{\sqrt{3}} \)
\( c \cdot \sqrt{3} \)
D. \( \frac{3}{1} \)


What is the resistance, under normal working conditions, of an electric lamp rated '240 \( V, 60 \mathrm{W} \) ? If two such lamps are connected in series across a \( 240 \mathrm{V} \)
mains supply, explain why each one appears less bright.


Both the nucleus and the atom of some
element are in their respective first excited states. They get de-excited by
emitting photons of wavelengths \( \boldsymbol{\lambda}_{N}, \boldsymbol{\lambda}_{\boldsymbol{A}} \)
respectively. The ratio \( \frac{\lambda_{N}}{\lambda_{A}} \) is closest to:
A \( \cdot 10^{-6} \)
B . 10
\( c \cdot 10^{-1} \)
D. \( 10^{-10} \)


Thallophyta, Bryophyta and Pteridophyta are called as
A. Phanerogams
B. Cryptogams
c. None of the above
D. All of the above


An ac voltmeter reads \( 220 \mathrm{V} \). If the line
frequency is \( 50 H z, \) then the equation
for the line voltage is
A. \( V=220 \sin 50 t \)
B. \( V=220 \sin 100 t \)
c. \( V=311 \sin 50 \pi t \)
D. \( V=311 \sin 100 \pi t \)


Find \( x \) in the following figure \( (A B \| C D) \)


Term 'epithelium' was coined by
A. Ruysch
B. Mayer
c. Bichat
D. Marcello Malpighi


You want to show that \( \Delta \mathrm{ART} \cong \Delta \mathrm{PEN} \)
If it is given that \( \angle \mathrm{T}=\angle \mathrm{N} \) and you are to
use SAS criterion, you need to have PN=
?


Which compound is used for bleaching cloths in laundry?
A. Bleaching powder
B. Washing powder
c. Baking powder
D. Plaster of Paris


Lowest part of mantle is known as:
A. A-layer
B. B-layer
c. M-layer
D. D-layer


Mark the column I with column II and
mark the appropriate choice.
Column I
(A)
\[
R C O C H_{3} \frac{Z n-H g}{H C l}
\]
\[
R C H_{2} C H_{3}
\]
\( 2 C_{6} H_{5} C H O \stackrel{N a O H}{\longrightarrow} \)
(B)
\[
C_{6} H_{5} C O O N a+
\]
\( (C) \)
\[
\begin{array}{l}
C_{6} H_{5} C H_{2} O H \\
C_{6} H_{6}+C H_{3} C O C l \frac{A n h}{A l C l_{3}}
\end{array}
\]
(iii)
(D)
\[
\begin{array}{l}
C_{6} H_{5} C O C H_{3} \\
C_{6} H_{10} O \frac{(i) N H_{2} N H_{2}}{K O H / e t h y l e n e g l y c o l, \Delta}
\end{array}
\]
(iv)
\[
C_{6} H_{12}+N_{2}
\]
\( A \cdot(A)-(i i),(B)-(i v),(C)-(i i i),(D)-(i) \)
B. (A) - (i), (B) - (iii), (C) - (ii), (D) - (iv)
C \( \cdot(A)-(\text { iii }),(B)-(i i),(C)-(i),(D)-(i v) \)
D. \( (A)-(i v),(B)-(i),(C)-(i i),(D)-(i i i) \)


Bromine vapours are passed into a soln.
of ethyne in carbon tetrachloride gives:
A. \( C H B r_{2}-C H B r_{2} \)
в. \( C H_{2} B r-C H B r_{2} \)
c. \( C H_{2} B r-C H_{2} B r \)
D. \( C H_{3}-C H_{3} \)


What energy conversion takes place in
a generator?
A. mechanical energy into magnetic energy.
B. mechanical energy into chemical energy.
C. mechanical energy into electric energy.
D. electrical energy into mechanical energy


Pankaj wants to create tests for SAT
students. He wants to make some
calculator and non calculator tests. He
figures that each non-calculator test
will take him 3 hours to create, and
each calculator test will take 4 hours to
create. Because of his time constraint,
he can at most devote at most 6 hours
per week of his time for the next 5
weeks to create the practice and he
wants to provide at least 8 practice
tests, which of the system of inequality represent how many of each type of test
he can create?
\( \mathbf{A} \cdot n+c \geq 8 \)
\( 3 n+4 c \leq 6 \)
B \( . n+c \geq 8 \)
\( 3 n+4 c \leq 30 \)
c. \( n+c \leq 8 \)
\( 3 n+4 c \geq 30 \)
D. \( n+c \geq 6 \)
\( 3 n+4 c \leq 8 \)


What is the sum of oxidation numbers
of all the carbon atoms except that
attached to \( -C H O \) group in
\( \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{5}} \boldsymbol{C} \boldsymbol{H} \boldsymbol{O} ? \)
A . -6
B. -5
c. -4
D. - -


Dip circle is not set into magnetic meridian and the angle at which it is inclined to the magnetic meridian is
unknown. \( \delta^{\prime} \) and \( \delta^{\prime \prime} \) are apparent dips at a place in which dip circle is kept in transverse positions. The dip is:
\( \mathbf{A} \cdot \cot \delta=\cot \delta^{\prime}+\cos \delta^{\prime \prime} \)
B. \( \tan ^{2} \delta^{\prime}=\tan \delta^{\prime}+\tan ^{2} \delta^{\prime \prime} \)
\( \mathbf{c} \cdot \cos ^{2} \delta=\cos ^{2} \delta^{\prime}+\cos ^{2} \delta^{\prime \prime} \)
D. \( \cot ^{2} \delta=\cot ^{2} \delta^{\prime}+\cot ^{2} \delta^{\prime \prime} \)


The end \( B \) of uniform rod \( A B \) which
makes angle \( \theta \) with the floor is being
pulled with a velocity \( v_{0} \) as shown
Taking the length of rod as \( l \), calculate
the following at the instant when \( \boldsymbol{\theta}= \)
\( 37^{\circ} \)
(a) The velocity of end \( \boldsymbol{A} \)
(b) The angular velocity of rod
(c) Velocity of \( C M \) of the rod.


A boy of mass \( 50 \mathrm{kg} \) runs up a staircase of 45 steps in 9 s. If the height of each step of the staircase is \( 15 \mathrm{cm} \), find the
power of the boy.
\( \mathbf{A} \cdot 375 W \)
в. \( 480 \mathrm{W} \)
c. \( 550 W \)
D. \( 5390 W \)


If the projection of a line segment on
\( x, y \) and \( z \) axes are respectively 3,4 and
\( 5, \) then the length of the line segment is
\begin{tabular}{l}
A \( 3 \sqrt{2} \) \\
\hline
\end{tabular}
B. \( 5 \sqrt{2} \)
c. \( 6 \sqrt{2} \)
D. None of these


Assertion
A convex lens of glass \( (\mu=1.5) \) behave as a diverging lens when immersed in carbon disulphide of higher refractive index \( (\mu=1.65) \)
Reason
A diverging lens is thinner in the middle
and thicker at the edges.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If \( \boldsymbol{A}=\left(\boldsymbol{a}_{\boldsymbol{i} j}\right)_{\mathbf{2} \times \mathbf{2}}, \) where \( \boldsymbol{a}_{\boldsymbol{i} j}=\boldsymbol{i}+\boldsymbol{j}, \) then
\( A \) is equal to:
A. \( \left[\begin{array}{ll}1 & 2 \\ 2 & 3\end{array}\right] \)
B. \( \left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right] \)
\( \mathbf{c} \cdot\left[\begin{array}{ll}2 & 3 \\ 3 & 4\end{array}\right] \)
D. \( \left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right] \)


Which of the following phenomena support the wave theory of light?
(a) Scattering
(b) Interference
\( (c) \)
Diffraction
Velocity of light in a denser medium is less
(d) than the velocity of light in the rarer medium.
\( A \cdot A, B, C \)
B. A, B, D
\( c \cdot B, C, D \)
D. \( A, C, \)


Find the value of \( \left(\frac{a}{b-1}\right)+ \) \( \left(\frac{a}{b-1}\right)^{2}+\left(\frac{a}{b-1}\right)^{3} \) if \( a+2 b=2 \)
A . -6
B. 8
c. 10
D. -12
E . 14


Fischer Ringe's method makes use of :
A \( \cdot \mathrm{CaC}_{2} \)
B. \( \mathrm{Ca}(\mathrm{CN})_{2} \)
\( c \cdot \mathrm{CaC}_{2}+\mathrm{CaCl} \)
\( \mathrm{D} \cdot \mathrm{CaCN}_{2}+\mathrm{CaCl}_{2} \)


Is parallelogram a rectangle? Can you call a rectangle a parallelogram?


State True or False.
Almost every liquid is either an acid or a base.
A. True
B. False


The set \( S:\{1,2,3, \ldots ., 12\} \) is to be
partitioned into three sets \( A, B, C \) of equal size. Thus, \( \boldsymbol{A} \cup \boldsymbol{B} \cup \boldsymbol{C}=\boldsymbol{S}, \boldsymbol{A} \cap \)
\( \boldsymbol{B}=\boldsymbol{B} \cap \boldsymbol{C}=\boldsymbol{A} \cap \boldsymbol{C}=\boldsymbol{\phi} . \) The number
of ways to partition \( S \) is
A \( \cdot \frac{12 !}{3 !(4 !)^{3}} \)
в. \( \frac{12 !}{3 !(3 !)^{4}} \)
c. \( \frac{12 !}{(4 ! !)^{3}} \)
D. \( \frac{12 !}{(3 !)^{4}} \)


Number of isomeric primary amines
obtained from \( C_{4} H_{11} N \) are :
\( A \cdot 3 \)
B. 4
\( c \cdot 5 \)
D.


Q Type your question
experimentally verified by Davisson and Germer by diffraction experiment. Wave character of matter
has significance only for microscopic particles. de Broglie wavelength or wavelength of matter wave can be calculated using
the following relation:
\( \lambda=\frac{h}{m v} \)
where, ' \( m \) ' and ' \( v \) ' are the mass and
velocity of the particle. de Broglie hypothesis suggested that
electron waves were being
diffracted by the target, much as \( X \)
rays are diffracted by planes of atoms in the crystals.

The wavelength of matter waves
associated with a body of mass \( 1000 g \)
moving with a velocity of \( 100 m / \)sec is:
A \( \cdot 6.62 \times 10^{-39} \mathrm{cm} \)
B . \( 6.62 \times 10^{-36} \mathrm{cm} \)
C \( .6 .626 \times 10^{-36} m \)
D. \( 3.31 \times 10^{-32} m \)


What is the angular velocity \( (\omega) \) of an
electron occupying second orbit of \( L i^{2+} \)
ion?
\( ^{\mathrm{A}} \cdot \frac{8 \pi^{3} m e^{4}}{h^{3}} K^{2} \)
в. \( \frac{8 \pi^{3} m e^{4}}{9 h^{3}} K^{2} \)
\( ^{\mathbf{C}} \cdot \frac{64}{9} \times \frac{\pi^{3} m e^{4}}{h^{3}} K^{2} \)
D. \( \frac{9 \pi^{3} m e^{4}}{h^{3}} K^{2} \)


The bulk modulus of elasticity for monoatomic ideal gas during an isothermal process is \( (\mathrm{P}= \) pressure of the gas)
A. \( P \)
в. \( \frac{2 P}{3} \)
c. \( \frac{5 P}{3} \)
D. \( \frac{7 P}{3} \)


The scientist who is credited with the
discovery of 'nucleus' in an atom is
A. Niels Bohr
B. Ruther ford
c. J.J. Thomson
D. Balmer


The value of R.Q. of a succulent plant at night is
\( A \cdot<1 \)
B \( .>1 \)
c. zero.
D. Infinite.


One litre hard water contains \( 1 \mathrm{mg} \)
\( \mathrm{CaCl}_{2} \) and \( 1 \mathrm{mg} M \mathrm{g} S \mathrm{O}_{4} \). The hardness
of water is:
A . 1.743 ppm
в. 1.745 ppm
c. 1.734 ppm
D. none of the above


The number of electrons present in
\( -1 C \) of charge is:
A \( \cdot 6 \times 10^{18} \)
B . \( 1.6 \times 10^{19} \)
\( c \cdot 6 \times 10^{19} \)
D. \( 1.6 \times 10^{18} \)


Answer the following question:
1. Write Haworth projection formula of \( \boldsymbol{\alpha}-\boldsymbol{D}-(+)- \) glycopyranose
2. Define hormones.


Prove that the bisectors of opposite angles of a parallelogram are parallel.


\( C O_{2} \) goes to air, causes green house effect and gets dissolved in water. What
will be the effect on soil fertility and \( p H \)
of the water?
A. Increase
B. Decrease
c. Remain same
D. None of these


Which one of the following is not a device used to control a particulate
matter?
A. Arresters
B. Scrubbers
c. Filters
D. Electrostatic precipitator
E. Incinerator


The number of neutrons in \( _{92} U^{235} \)
nucleus is:
A . 327
в. 235
c. 143
D. 92


For two sets \( A \) and \( B, A \times B=B \times A \)
A. True
B. False


\( R_{1} \) and \( R_{2} \) are the reminders when the
polynomial \( a x^{3}+3 x^{2}-3 \) and \( 2 x^{3}- \)
\( 5 x+2 a \) are divided by \( (x-4) \)
respectively. If \( 2 R_{1}-R_{2}=0, \) then find
the value of a
A \( \cdot a=\frac{1}{6} \)
в. \( _{a=\frac{1}{3}} \)
c. \( _{a=\frac{1}{7}} \)
D. \( a=\frac{1}{5} \)


A circular loop of radius \( 3 \mathrm{cm} \) is having a current of 12.5 A. The magnitude of magnetic field at a distance of \( 4 \mathrm{cm} \) on its axis is
В \( \cdot 5.27 \times 10^{-5} T \)
\( \mathrm{c} \cdot 6.54 \times 10^{-5} T \)
D. \( 9.20 \times 10^{-5} T \)


The wavelength range of the visible spectrum extends from violet \( (400 n m) \) to red \( (750 n m) . \) Express these wavelengths in frequencies \( (\boldsymbol{H} \boldsymbol{z}) \) \( \left(1 n m=10^{-9} m\right) \)


Gutta Percha is
A. trans-polyisoprene
B. non-elastic and softens to a plastic-like material on heating
C. used in underwater cables and golf balls
D. All of the above


According to Molecular Orbital Theory:
This question has multiple correct options
A \( \cdot C_{2}^{2-} \) is expected to be diamagnetic
B. \( O_{2}^{2+} \) is expected to have a longer bond length than \( O_{2} \)
C. \( N_{2}^{+} \) and \( N_{2}^{-} \) have the same bond order
D. \( H e_{2}^{+} \) has the same energy as two isolated He atoms


We use copper wire instead of silver for electrical applications because:
A. copper is more ductile than silver
B. copper is cheaper than silver
c. of more availability of copper than silver
D. all of these


Flux density under trailing pole tips in
case of generator will :
A. increase
B. decrease
c. either increase or decrease
D. none of the above


Which of the following statements
about the monomer and dimer of \( N O_{2} \)
are not true?
This question has multiple correct options
A. Both are diamagnetic
B. Both are paramagnetic
C. The monomer is paramagnetic and the dimer is not
D. The dimer is paramagnetic and the monomer is not


The name of the metal which is
extracted from the ore is given below
Mark the example which is not correct.
A. Malachite - \( C u \)
B. Calamine - \( Z n \)
c. chlornite - \( C r \)
D. Dolomite - \( A l \)


A boy playing on the roof of a \( 10 \mathrm{m} \) high building throws a ball with a speed of
\( 10 \mathrm{m} \mathrm{s}^{-1} \) at an angle of \( 30^{\circ} \) with the horizontal. How far from the throwing point will the ball he at the height of 10 \( \mathrm{m} \) from the ground \( (\boldsymbol{g}= \) \( \left.10 m s^{-2}, s i n 30^{\circ}=\frac{1}{2}, \cos 30^{\circ}=\frac{\sqrt{3}}{2}\right) \)
\( A \cdot 8.6 m \)
B. \( 9.6 \mathrm{m} \)
c. \( 10.6 \mathrm{m} \)
D. \( 11.6 \mathrm{m} \)


Which of the following might be the
reason that the current in the circuit is
weak?
A. Circuit of the tester might not be complete
B. The material may not be able to conduct electricity as easily as metals.
c. The circuit of the tester is complete but still the bulb does not glow.
D. Both A and B


The number of distinct real roots of the
quation \( \left|\begin{array}{ccc}\cos x & \sin x & \sin x \\ \sin x & \cos x & \sin x \\ \sin x & \sin x & \cos x\end{array}\right|=0 \) in
the interval \( \left[-\frac{\pi}{4}, \frac{\pi}{4}\right] \) is
\( A \)
B. 4
\( c \cdot 2 \)
\( D \)


Consider the following statements and arrange in the order of true/ false as
given in the codes
\( S_{1}: \) Argon is used in arc welding of metals or alloys to provide an inert atmosphere.
\( S_{2}: X e F_{2}, X e F_{4} \) and \( X e F_{6} \) are
colourless crystalline solids and sublime readily at \( 298 \mathrm{K} \)
\( \boldsymbol{S}_{3}: \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{2}, \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{4} \) and \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{6} \) are readily
hydrolysed.
\( S_{4}: \) Xenon fluorides react with fluoride
ion acceptor to form cationic species and fluoride ion donors to form fluoro
anions.
\( A \). FFFF
В. TFTF
c. \( \pi \pi \)
D. FTFT


Draw a diagram of the arrangement


A charge 3 coulomb experiences a force \( 3000 N \) when placed in a uniform electric field. The potential difference between two points seperated by a
distance of \( 1 \mathrm{cm} \) along the field lines is :
A. \( 10 V \)
в. \( 90 V \)
c. \( 1000 V \)
D. \( 9000 V \)


A certain amount of a reducing agent
reduces x mole of \( K M n O_{4} \) and y mole
of \( K_{2} C r_{2} O_{7} \) in different experiments in acidic medium. If the change in oxidation state in reducing agent is same in both experiments, \( \boldsymbol{x}: \boldsymbol{y} \)
A . 5: 3
B. 3: 5
\( c .5: 6 \)
D. 6: 5


Simone and her three friends were
deciding how to pick the song they will \( \operatorname{sing} \) for their school's talent show. They
decide to roll a number cube.
The person with the lowest number chooses the song. If her friends rolled a
\( 6,5, \) and \( 2, \) what is the probability that Simone will get to choose the song?
A. \( \frac{1}{6} \)
B.
c. 0
D.


In an equilateral glass prism, for two
angles of incidence, differing by \( 10^{\circ}, \) the
angle of deviation is found to be \( 40^{\circ} \) find these angles of incidence.


The standard reduction potential of the \( A g^{+} \mid A g \) electrode at \( 298 \mathrm{K} \) is \( 0.80 \mathrm{V} \)
The solubility product of \( A g l \) is \( 6.4 \times \) \( 10^{-17} \) at \( 298 \mathrm{K} .(2.303 \mathrm{RT} / \mathrm{F}=0.06) \)
The potential of \( A g^{+} \mid A g \) electrode in a saturated solution of Agl at \( 298 \mathrm{K} \) is
\( \mathbf{A} \cdot-0.314 V \)
B . \( +0.314 V \)
c. \( -0.172 V \)
D. \( +0.172 \mathrm{V} \)


Find four numbers forming a geometric progression in which the sum of the
extreme terms is 112 and the sum of
the middle terms is 48 .


Which group shares most common characters with each other?
A. Members of the same kingdom
B. Members of the same genus
c. Members of the same phylum
D. Members of the same class
E. Members of the same family


Using determinent, if area of triangle is 4, whose vertices are \( (2,2),(6,6),(5, k) \)
then \( \mathrm{k}= \)
A . 5
B.
\( c \cdot 7 \)
D. 3


Two people carry a heavy electric motor
(M) by placing it on a board \( 2.0 \mathrm{m} \) long
that weighs 200 N. one person A lifts at one end with a force of \( 400 \mathrm{N} \). and the
other \( \mathrm{B} \) lifts the opposite end with a force of 600 N. The distance from \( A \)
where the centre of gravity of the motor
is located is
\( A \cdot 1 m \)
B. 1.25 m
\( c \cdot 0.8 m \)
D. \( 0.75 \mathrm{m} \)


Give the number of lone pairs in the central atoms of the following inter
halogen compounds \( \boldsymbol{A} \boldsymbol{X}, \boldsymbol{A} \boldsymbol{X}_{3}, \boldsymbol{A} \boldsymbol{X}_{5} \)
\( \boldsymbol{A} \boldsymbol{X}_{\mathbf{7}} \)
A . 3, 2, 1,
в. \( 3,2,1, \) о
c. 3,1,2,0
D. 3, 2, 2, 0


Identify the gas \( (C) \)
A \( . C O \)
в. \( C O_{2} \)
\( \mathrm{c} \cdot^{14} \mathrm{CO}_{2} \)
D. A mixture of \( ^{14} \mathrm{CO}_{2} \) and \( \mathrm{CO}_{2} \)


If \( \boldsymbol{y}(\boldsymbol{x}) \) satisfies the differential equation \( \cos x \frac{d y}{d x}-y \sin x=6 x \) and
\( \boldsymbol{y}\left(\frac{\boldsymbol{\pi}}{\mathbf{3}}\right)=\mathbf{0 .} \) Then value of \( \boldsymbol{y}\left(\frac{\boldsymbol{\pi}}{\boldsymbol{6}}\right) \) is
A \( \cdot \frac{\pi^{2}}{3 \sqrt{2}} \)
в. \( \frac{-\pi^{2}}{3 \sqrt{2}} \)
c. \( \frac{\pi^{2}}{2 \sqrt{3}} \)
D. \( \frac{\pi^{2}}{4} \)


In a building programme the event that all the materials will be delivered at the
correct time is \( M \) and the event that
the building programme will be completed on time is \( F . \) Given that \( \boldsymbol{P}(M)=\mathbf{0 . 8} \) and \( \boldsymbol{P}(\boldsymbol{M} \cap \boldsymbol{F})=\mathbf{0 . 6 5} \)
find \( \boldsymbol{P}(\boldsymbol{F} / \boldsymbol{M}) . \) If \( \boldsymbol{P}(\boldsymbol{F})=\mathbf{0 . 7}, \) find the
probability that the building programme will be completed on time if all the materials are not delivered at the
correct time.
\( ^{\mathbf{A}} \cdot P(F / M)=\frac{11}{16} ; P(F / \bar{M})=\frac{1}{6} \)
B. \( P(F / M)=\frac{15}{16} ; P(F / \bar{M})=\frac{1}{8} \)
\( ^{\mathbf{c}} \cdot P(F / M)=\frac{13}{16} ; P(F / \bar{M})=\frac{1}{4} \)
D. None of these


If the constant term of the binomial zpansion \( \left(2 x-\frac{1}{x}\right)^{n} \) is -160 , then \( n \) is equal to
A .4
B. 6
\( c \cdot 8 \)
D. 10


The momentum of a system is defined
A. As the product of mass of the system and the velocity of centre of mass
B. As the vector sum of the momentum of individual
particles
C. For bodies undergoing translational, rotational and oscillatory motion
D. All of the above


A student places a strip of solid magnesium metal into a beaker full of
\( 100 . m L \) of \( 3.0 \mathrm{M} \) hydrochloric acid
solution. The student observes bubbling and the disappearance of the magnesium metal.
Which species is being oxidized and which species is being reduced in this
reaction?
A. Magnesium being oxidized and the chloride ion is being reduced.
B. Magnesium being oxidized and the hydrogen ion is being reduced.
c. Magnesium being reduced and the chloride ion is being oxidized.
D. Magnesium being reduced and the hydrogen ion is being oxidized.


Which of the following is not a disproportionation reaction?
\( \mathbf{A} \cdot \stackrel{\ominus}{O} H+B r_{2} \longrightarrow B r^{\ominus}+B r O_{3}^{\mathbf{j}} \)
в. \( C u_{2} O+2 H^{\oplus} \rightarrow C u+C u^{2+}+H_{2} O \)
\( \mathrm{c} \cdot(C N)^{\ominus} \rightarrow C O_{3}^{2-}+N O_{3}^{\circ} \)
D \( \cdot(C N)_{2}+2 \hat{O} H \rightarrow C N^{\ominus}+C N O^{\ominus}+H_{2} O \)


Copy the diagram and label any two
parts from the given options in the
bracket
(Cyton, Axon, Dendron, and Plate)


For a sparingly soluble salt \( \boldsymbol{A}_{\boldsymbol{p}} \boldsymbol{B}_{\boldsymbol{q}} \)
the relationship between its solubility
product \( \boldsymbol{K}_{s p} \) and its solubility \( (s) \) is:
\( \mathbf{A} \cdot K_{s p}=s^{p+q} \cdot p^{p} \cdot q^{q} \)
B . \( K_{s p}=s^{p+q} . p^{q} . q^{p} \)
\( \mathbf{c} \cdot K_{s p}=s^{p q} \cdot p^{p} \cdot q^{q} \)
D・ \( K_{s p}=s^{p q} .(p q)^{p+q} \)


Suppose that \( f(0)=-3 \) and \( f^{\prime}(x) \leq 5 \)
for all values of \( x \). Then the largest value
which \( f(2) \) can assume is \( \ldots . \)
A . 5
B. 6
\( c \cdot 7 \)
D.


The maximum amount of solute that will
saturate \( 100 \mathrm{g} \) of solvent at that temperature is known as:
A. solubility
B. soluble
c. solution
D. none of the above


Give reasons:
A simple microscope is used by watch repairers.


Find the magnetic induction at the
point \( O . \) If the wire carrying a current
\( I=8.0 A \) has the shape shown in the
figure.


A boy in front of mirror throws ball from right hand and catches with left hand.
The direction of image of ball as seen from image of boy is:
A. Right hand to left hand
B. Left hand to Right Hand
c. Right hand to Right Hand
D. Left Hand to Left Hand


The IUPAC name of the compound is:
A. 2 - Methyl -4 - hexanamine
B. 5- Methyl - 3 - hexanamine
C .2 - Methyl -4 - amino hexane
D. \( 5- \) Methyl -3 - amino hexane


If \( \boldsymbol{x}=\mathbf{1}+\mathbf{2} \boldsymbol{i} \) and \( \boldsymbol{A}=\boldsymbol{x}^{\mathbf{3}}+\mathbf{7} \boldsymbol{x}^{\mathbf{2}}-\boldsymbol{x}+ \)
\( 26, \) then one of the value of \( \sqrt{A} \) equals
A \( .4-3 i \)
B. \( 3-4 i \)
\( c .-3+4 i \)
D. \( 3+4 i \)


Which of the following statements is
true?
A. Sound and light both require medium for propogation.
B. Sound can travel through vacuum, but light cannot.
C. Sound needs medium, but light doesn't need medium for its propogation.
D. Sound and light both can not travel in medium.


The mass of a planet is 4 times while its radius is 8 times that of the earth. If the weight of an object is \( 640 \mathrm{N} \) on earth, what will be its weight on the planet?
A. \( 40 \mathrm{N} \)
в. 80 N
\( c \cdot 160 N \)
D. 120 N


Haploid parthenogenesis among insects is shown by order
A. Hymenopterara
B. Homoptera
c. coleoptera
D. All of the above


Which of the following is not correctly paired?
A. Fabaceae: Legume family
B. Solanaceae: Potato family
c. Liliaceae: Sunflower family
D. Brassicaceae: Mustard family


\( \boldsymbol{S}_{N} 1 \) reaction on optically active substrates mainly gives:
A. retention in configuration
B. inversion in configuration
c. racemic product
D. no product


If \( G \) is the centroid of the triangle \( A B C \) then \( \overrightarrow{G A}+\overrightarrow{G B}+\overrightarrow{G C} \) is equal to
\( \mathbf{A} \cdot \overrightarrow{A B} \)
в. \( \overrightarrow{B C} \)
\( c \cdot 4 \overrightarrow{G A} \)
D.


Assertion
Bimetallic strip is used in fire alarms.
Reason

Wires on electric poles are mounted tightly, in winter
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 correct name of the following
polymer is :
A. Polyisoprene
B. Polytert-butylene
c. Polisobutane
D. Polyisobutylene


The areas of cross section of two wires
of the same material are in the ratio 1:
2 and their lengths are in the ratio 2: 1
If their ends have the same potential differences then currents through
them will be in the ratio of
A .1: 2
B . 2: 1
c. 1: 4
D. 4: 1


lonization is lare shown by:
This question has multiple correct options
A. metals
B. non-polar covalent compounds
C. polar covalent compounds
D. salts


The probability of drawing a red 9 from a standard pack of 52 playing cards is
A \( \cdot \frac{1}{13} \)
в. \( \frac{1}{26} \)
\( c \cdot \frac{1}{2} \)
D. \( \frac{1}{4} \)


In a sweet pea, tendrils are modified
A. Stipule
B. Stem
c. Leaf
D. Leaflet


Let \( \boldsymbol{O}= \) Set of odd natural numbers \( = \)
\( \{1,3,5,7,9, \dots\} \) and \( E=\operatorname{set} \) of even
natural numbers \( =\{2,4,6,8,10, \dots \dots .\} \)
Then show that \( 0.1 \notin E \)


Using differentials, find the sum of digits approximate value of the
following up to 3 places of decimal. \( (0.999)^{\frac{1}{10}} \)


Fill in the blanks:
The period between two consecutive
new moon days is and is
called a
A. 31 days, month
B. 7 days, week
c. 15 days, fortnight
D. slightly longer than 29 days, month


Let two vectors \( \vec{x} \) and \( \vec{y} \) satisfy the following conditions \( : \vec{x}+\vec{y}=\vec{a} ; \vec{x} \times \)
\( \vec{y}=\vec{b} \times \vec{a}, \vec{x} \cdot \vec{a}=1 \) where \( \vec{a} \) and \( \vec{b} \)
are non-zero perpendicular vectors,
then
\( ^{\mathrm{A}} \cdot_{\vec{x}}=\frac{|\vec{a}|^{2} \vec{b}+\vec{a}}{|\vec{a}|^{2}} \)
\( ^{\mathrm{B}} \cdot_{\vec{x}}=\frac{|\vec{a}|^{2} \vec{b}-\vec{a}}{|\vec{a}|^{2}} \)
\( \stackrel{\mathrm{C}}{*} \vec{y}=\frac{|\vec{a}|^{2}(\vec{a}-\vec{b})-\vec{a}}{|\vec{a}|^{2}} \)
\( \vec{y}=\frac{\vec{a}(\vec{a} \cdot \vec{y})-|\vec{a}|^{2} \vec{b}}{|\vec{a}|^{2}} \)


The \( \Delta H \) value at \( 360 \mathrm{K} \) for the reaction:
\( \boldsymbol{F} \boldsymbol{e}_{2} \boldsymbol{O}_{3(s)}+\boldsymbol{3} \boldsymbol{H}_{2(\boldsymbol{g})} \rightarrow \boldsymbol{2} \boldsymbol{F} \boldsymbol{e}_{(s)}+\boldsymbol{3} \boldsymbol{H}_{2} \boldsymbol{O}_{(l)} \)
given that \( \Delta \boldsymbol{H}_{300}=-33.29 k J m o l^{-1} \)
and \( C_{p} \) for \( F e_{2} O_{3(s)}, F e_{(s)}, H_{2} O(l) \) and \( \boldsymbol{H}_{2(\boldsymbol{g})} \) are \( \mathbf{1 0 3 . 8}, \mathbf{2 5 . 1}, \mathbf{7 5 . 3} \) and \( \mathbf{2 8 . 8} \)
\( \boldsymbol{J} \boldsymbol{K}^{-1} \boldsymbol{m} \boldsymbol{o l}^{-1}, \) is:
A \( .-28.1 k J m o l^{-1} \)
B. 28.1 kJmol-
\( \mathbf{c} .85 .9 k J m o l^{-1} \)
D. \( -85.9 ~ k J m o l^{-1} \)


In each of the following find the value of
\( ^{\prime} k^{\prime}, \) for which the points are collinear. \( (7,-2),(5,1),(3, k) \)


Calculate the energy spent in spraying a
drop of mercury of \( r=1 \mathrm{cm} \) radius into
\( N=10^{6} \) droplets all of same size. If the
surface tension of mercury is \( \boldsymbol{T}=\mathbf{3 5} \times \)
\( \mathbf{1 0}^{-\mathbf{3}} \mathbf{N} / \boldsymbol{m} \)


Which of the following plant form seed and have pollen tube?
A. Angiosperm
B. Pteridophytes
c. Gymnosperm
D. siphonogama


State whether true or false.
Self balancing toys have curved and heavy bases.
A. True
B. False


An object of mass 5 kg falls from rest through a vertical distance of \( 20 \mathrm{m} \) and reaches a velocity of \( 10 \mathrm{m} / \mathrm{s} \). How much work is done by the push of the air on the object?
A . -740 J
B. -750 J
c. -760 J
D. -770 J


Three charges \( \mathbf{q}_{1}=\mathbf{3} \mathbf{m} \mathbf{C}, \mathbf{q}_{2}=-\mathbf{3} \mathbf{m} \mathbf{C} \)
and \( q_{3} \) are kept at the vertices of a
triangle as shown in the figure. If the net
force acting on \( q_{1} \) is \( \bar{F} \), the charge \( q_{3} \) would have the magnitude \( \left(1+\frac{1}{n}\right)^{2} m C \)
So, \( n \) is:
\( \mathbf{A} \cdot \mathbf{8} \)
B. 4
\( c \cdot 1 \)
D. 16


The value of \( x \) that satisfies the relation
\( \boldsymbol{x}=\mathbf{1}-\boldsymbol{x}+\boldsymbol{x}^{2}-\boldsymbol{x}^{\mathbf{3}}+\boldsymbol{x}^{4}-\boldsymbol{x}^{\mathbf{5}}+. \infty \) if
\( |\boldsymbol{x}|<\mathbf{1} \)
A \( \cdot \frac{-1 \pm \sqrt{5}}{2} \)
B. \( \frac{-1 \pm 3 i}{2} \)
\( c \)
D. none


A box is placed on an inclined plane and has to be pushed down. The angle of inclination will satisfy which options among the following:
This question has multiple correct options
A. Equal to angle of friction
B. More than angle of friction
c. Less than the angle of friction
D. Greater than angle of repose


Calculate the atomic number of the
element that has 12 neutrons and a
mass number of 23


Heat of formation of \( \boldsymbol{H}_{2} \boldsymbol{O}(g) \) at \( \boldsymbol{2} \boldsymbol{5}^{0} \boldsymbol{C} \) is
\( -243 \mathrm{KJ} . \Delta U \) for the reaction \( \boldsymbol{H}_{2}(\boldsymbol{g})+ \)
\( \frac{1}{2} O_{2}(g) \rightarrow H_{2} O(g) \) at \( 25^{0} C \) is:
A. 241.8 KJ
B . -241.8 KJ
c. -243 к
D. 243 KJ


The pole is pieces of a horse-shoe magnet are made cylindrical so that the deflection of the coil is proportional to
A. the current flowing in the coil
в. \( \frac{1}{\text { current flowing in the coil }} \)
c. the magnetic field
D. the square of current flowing in the coil


The maximum number of electrons in a
shell is
A \( \cdot n^{2} \)
B \( \cdot 2 n^{2} \)
\( c \cdot 2 n \)
D. \( n \)


Which of the following differential equation is linear?
A \( \cdot \frac{d^{2} y}{d x^{2}}+x \frac{d y}{d x}+2 y=0 \)
B. \( \frac{d^{2} y}{d x^{2}}+y \frac{d y}{d x}+x=0 \)
c. \( \frac{d^{2} y}{d x^{2}}+\frac{y}{x}+\sin y=x^{2} \)
D. \( (1+x) \frac{d y}{d x}-x y=1 \)


Why is it safer to be inside a car than
standing under a tree during lightening?


\( 200 \mathrm{mL} \) of an aqueous solution of a protein contains its 1.26 g. The osmotic pressure of this solution at \( 300 \mathrm{K} \) is
found to be \( 2.57 \times 10^{-3} \) bar. The molar
mass of protein will be:
\( \left(\boldsymbol{R}=\mathbf{0 . 0 8 3} \boldsymbol{L} \boldsymbol{b a r} \boldsymbol{m o l}^{-1} \boldsymbol{K}^{-1}\right) \)
\( A \cdot 61038 \) g mol \( ^{-1} \)
B. 51022 g mol-1
C. \( 122044 \mathrm{g} \mathrm{mol}^{-1} \)
D. 31011 g mol-


Which of the following is/are linear polynomial?
A. \( x^{2}+2 \)
B. \( x+5 \)
c. \( x^{3}+x^{2}+9 \)
D. None of the above


Bleaching powder is used for sterilizing
water
A . True
B. False


\( \boldsymbol{P C l}_{5} \) molecule has:
A. three fold axis of symmetry
B. two fold axis of symmetry
c. both \( A \) and \( B \)
D. none of these


1 g of hydrogen is converted into 0.993 g of helium in a thermonuclear reaction.
The energy released is :
A \( \cdot 63 \times 10^{7} \) J
В. \( 63 \times 10^{10} \) 」
D. \( 63 \times 10^{20} \) 」


Which oxides has three dimensional
structure ?
A. \( c o \)
в. \( C O_{2} \)
\( \mathrm{c} \cdot \operatorname{si} 0_{2} \)
\( \mathrm{D} \cdot \mathrm{SO}_{2} \)


Three bodies a ring \( (R), \) a solid cylinder
\( (C) \) and a solid sphere \( (S) \) having same
mass and same radius roll down the
inclined plane without slipping. They
start from rest, if \( v_{R}, v_{C} \) and \( v_{S} \) are
velocities of respective bodies on reaching the bottom of the plane, then:
A \( \cdot v_{R}=v_{C}=v_{S} \)
в. \( v_{R}>v_{C}>v_{S} \)
c. \( v_{R}<v_{C}<v_{S} \)
D. \( v_{R}=v_{C}>v_{S} \)


If the points \( \boldsymbol{P}(\mathbf{2}, \mathbf{1},-\mathbf{3}), \boldsymbol{Q}(\mathbf{5}, \mathbf{4}, \mathbf{3}) \) and
\( R(1,4,7) \) are three vertices of a parallelogram \( P Q R S \) then the other
vertex is
A. (1,0,0)
В . (-2,1,1)
c. (-2,2,1)
D. (2,1,2)


The area of the region bounded by the
curve \( \boldsymbol{y}=\boldsymbol{x}^{2}+\mathbf{1} \) and \( \boldsymbol{y}=\mathbf{2} \boldsymbol{x}-\mathbf{2} \)
between \( x=-1 \) and \( x=2 \) is:
A. 9 sq . units
B. 12sq. units
c. 15 sq. units
D. 14sq. units


Hydrates of helium and neon have not been prepared because of :
A. low polarisability
B. small size
c. low boiling point
D. all of the above


What is Brownian movement?


Answer the following Questions:
Name and state the rule to determine
the direction of a force experienced by a straight conductor carrying placed in a magnetic field which is perpendicular to it.


Which one is more permanent
ecosystem?
A. Forest
B. Mountain
c. Desert
D. Sea


In the hydrolysis of ICI, the products are:
A. HI + HC
B. HI + HOCI
C. \( \mathrm{HCl}+\mathrm{HOl} \)
D. HOCI + HOI


8
0
\( \infty \)
\( \infty \)


A dilute solution of KCl was placed
between two Pt electrodes \( 10.0 \mathrm{cm} \)
a part, cross which a potential
difference of 6.0 volt was applied. \( \boldsymbol{K}^{+} \)
ions move \( x \mathrm{cm} \) in 2 hour at \( 25^{\circ} \mathrm{C} \), then
\( x \) is \( _{-}-------- \) (nearest integer)
lonic conductivity of \( \boldsymbol{K}^{+} \) at infinite dilution is \( 73.52 S c m^{2} m o l^{-1} \) at \( 25^{\circ} C \)


The cube root of any multiple of 8 is always divisible by:
A . 2
B. 4
c. 8
D. 16


Explain the following terms giving one example for each.
(i) Miscelles
(ii) Aerosol


A positive charge is at rest in a uniform magnetic field directed to the right. What force does the positive charge feel, due to the magnetic field?
A. An upward force
B. A downward force
c. A force to the left
D. No force is felt.


If a dipole of dipole moment \( \vec{p} \) is placed in a uniform electric field \( \vec{E} \), then
torque acting on it is given by :
\( \mathbf{A} \cdot \vec{\tau}=\vec{p} \cdot \vec{E} \)
В . \( \vec{\tau}=\vec{p} \times \vec{E} \)
C \( \cdot \vec{\tau}=\vec{p}+\vec{E} \)
D . \( \vec{\tau}=\vec{p}-\vec{E} \)


If \( \boldsymbol{A}=\left[\begin{array}{ll}\boldsymbol{a} & \boldsymbol{b} \\ \boldsymbol{0} & \boldsymbol{a}\end{array}\right] \) is \( \boldsymbol{n} \boldsymbol{t} \boldsymbol{h} \) root of \( \boldsymbol{I}_{2}, \) then
choose the correct statements.
(i) if \( n \) is odd, \( a=1, b=0 \)
(ii) if \( n \) is odd, \( a=-1, b=0 \)
(iii) if \( n \) is even, \( a=1, b=0 \)
(iv) if \( n \) is even, \( a=-1, b=0 \)
\( \mathbf{A} \cdot i, i i, i i i \)
B. \( i i, \) ii i \( i v \)
\( \mathbf{c} \cdot i, i i, i i i, i v \)
D. \( i, i i i, i v \)


1 kgf
\( \mathbf{A} \cdot 1 g f \)
в. \( 10 g f \)
c. \( 100 g f \)
D. \( 1000 g f \)


Evaluate \( \int \frac{e^{x-1}+x^{e-1}}{e^{x}+x^{e}} d x \)


Which of the following lanthanoid ions is diamagnetic ? (At. No. \( C e= \)
\( \mathbf{5 8}, \boldsymbol{S m}=\mathbf{6 2}, \boldsymbol{E u}=\mathbf{6 3}, \boldsymbol{Y b}=\mathbf{7 0}) \)
A \( \cdot C e^{2} \)
B . \( S m^{2+} \)
c. \( E u^{2+} \)
D. \( Y b^{2} \)


A bottle can hold \( 100 g \) of water at \( 40^{\circ} \mathrm{C} \)
What mass of sea water (Density \( = \) \( \left.1030 k g / m^{2}\right) \) can it hold?


Which of the following pairs is pair of interior formed by two parallel lines and on the same side of the transversal?
A \( \cdot 30^{\circ}, 60^{\circ} \)
\( ^{0}, 66,6^{\circ} \)
В. \( 30^{0}, 150^{0} \)
c. \( 60^{\circ}, 130^{\circ} \)
D. \( 50^{\circ}, 120^{0} \)


Shown in the figure is a very long semicylindrical conducting shell of radius \( \mathrm{R} \) and carrying a current i. An infinitely
long straight current carrying conductor lies along the axis of the semi - cylinder. If the current flowing
through the straight wire be \( i_{0} \), then the
force per unit length on the conducting
wire is :
A \( \cdot \frac{\mu_{0} i \times i_{0}}{\pi^{2} R} \)
В \( \cdot \frac{\mu_{0} i \times i_{0}}{\pi R^{2}} \)
c. \( \frac{\mu_{0} i_{o}^{2} \times i}{\pi^{2} R} \)
D. None of these


Choose the correct answers from the
alternatives given :
Meiosis involves:
A. two nuclear divisions with chromosomes dividing only once
B. two nuclear divisions with chromosomes dividing twice
c. two nuclear divisions with chromosomes dividing four times
D. one nuclear division with chromosomes dividing only once


The standard reduction potential at
\( 25^{\circ} \mathrm{C} \) of the reaction \( 2 H_{2} O+2 e^{-} \rightleftharpoons \)
\( H_{2}+2 \stackrel{\ominus}{O} H \) is \( -0.8277 \mathrm{V} . \) The
equilibrium constant for the reaction \( 2 H_{2} O \rightleftharpoons H_{3} O^{\oplus}+\stackrel{\ominus}{O} \) at \( 25^{\circ} C \) is:
A \( \cdot K_{w}=9.35 \times 10^{-15} \)
В. \( K_{w}=9.83 \times 10^{-15} \)
C . \( K_{w}=9.14 \times 10^{-15} \)
D. None of these


In an adult human, the length of the
small intestine is about
\( A \cdot 8.5 m \)
B. 3.5 \( m \)
c. \( 6.5 \mathrm{m} \)
D. 2.5 \( m \)


Kepler's third law states that square of
period of revolution \( (\boldsymbol{T}) \) of a planet
around the sun, is proportional to third
power of average distance \( r \) between
sun and planet
i.e \( T^{2}=K r^{3} \) here \( K \) is constant.
If the masses of sun and planet are \( \boldsymbol{M} \)
and \( m \) respectively than as per
Newton's law of gravitation force of attraction between them is \( \boldsymbol{F}=\frac{\boldsymbol{G} \boldsymbol{M} \boldsymbol{m}}{\boldsymbol{r}^{2}}, \) here \( \boldsymbol{G} \) is gravitational
constant The relation between \( G \) and \( K \)
is described as
A. \( K=G \)
B. \( \quad K=\frac{1}{G} \)
c. \( G K=4 \pi^{2} \)
D. \( G M K=4 \pi^{2} \)


\( \boldsymbol{8} \boldsymbol{p}(\boldsymbol{A} \cap \overline{\boldsymbol{B}}) \)


The solution of \( H_{2} O_{2} \) can be stored for a
long time at room temperature. However, bubbles of oxygen form as soon as a drop of bromine is added. The role of bromine for the reaction
\( 2 H_{2} O_{2}(a q) \rightarrow 2 H_{2} O(l)+O_{2}(g) \) is :
This question has multiple correct options
A. to act as a positive catalyst
B. to form an intermediate \( \left(B r^{-}\right) \) on reacting with \( H_{2} O_{2} \) following reduction of bromine and then to show oxidation of \( B r^{-} \) to \( B r_{2} \) by \( H_{2} O_{2} \)
c. to act as heterogeneous catalyst
D. to act as negative catalyst


Find the work done by the gas.


A geostationary satellite is moving in a circular orbit at a height \( 36000 k m \) from
the surface of earth. calculate its speed
if it takes 24 hours to revolve around the
earth?
(give radius of earth equal \( 6400 k m) \)


Explain the term species and hierarchical classification


Find the value of \( k \) for which \( k, 2 k-1 \)
and \( 2 k+1 \) are in \( A . P \)


At the metaphase plate during metaphase I of meiosis, there are
A. single chromosomes
B. always twenty-three chromosomes
c. bivalents
D. unpaired duplicated chromosomes


\( \ln \Delta A B C, \) if \( A B=B C \) and \( \angle B= \)
\( 80^{\circ}, \) then \( \angle C= \)
A . \( 50^{\circ} \)
B. 100
\( c \cdot 130^{\circ} \)
D. None


Water comes out more slowly from an
upstairs tap than from a similar tap downstairs.


Assertion (A): Ductile metals are used
to prepare thin wires. Reason (R) : In the stress-strain curve
of ductile metals, the length between the points representing elastic limit and breaking point is very small.
A. Both (A) and ( \( R \) ) are true and ( \( R \) ) is the correct explanation of (A)
B. Both (A) and (R) are true and (R) is not correct explanation of (A)
c. (A) is true but (R) is false.
D. (A) is false but (R ) is true


Who is called the father of modern
chemistry?
A. Faraday
B. Pristley
c. Rutherford
D. Lavoisier


On moving from left to right in a period what is the order of acidic character of
hydrides?
A. \( N H_{3}<H_{2} O<H F \)
в. \( H F<H_{2} O<N H_{3} \)
c. \( H_{2} O<H F<N H_{3} \)
D. \( H_{2} O<N H_{3}<H F \)


\( \mathbf{a} \)
b
\( d \)
As
\( \mathrm{Sn} \)
\( e \) Te What are a, b, c, d and e in the given
figure ?
\( A \cdot a=S i b=P c=S d=G e e=S b \)
\( B \cdot a=\sin b=P c=S d=S b e=G e \)
\( \mathbf{C} \cdot a=\mathrm{Si} \mathrm{b}=\mathrm{P} \mathrm{c}=\mathrm{Sb} \mathrm{d}=\mathrm{S} \mathrm{e}=\mathrm{Ge} \)
D. \( a=P b=S c=S i d=G e e=S b \)


A plant shows rhizoids and is haploid. It needs water to complete its lifecycle because the male gametes are motile.
Identify the group to which it belongs.
A. Pteridophyte
B. Gymnosperm
c. Monocot
D. Bryophytes


Study the following figures and select
the correct statements regarding these.
(i) A shows mode of asexual
reproduction in sponges through internal buds.
(ii) B shows sexual reproduction
through zoospores in Chlamydomonas.
(iii) \( \mathrm{C} \) shows asexual reproduction through conidiospores in Penicillium.
(iv) D shows external budding in Sycon.
A. (i) and (ii)
B. (i) and (iii)
c. (ii), (iii), and (iv)
D. (i), (iii) and (iv)


in the given diagram, with what force must be man pull the rope the hold the
plank in position? Weight of the man is
60 kg. Neglect the weights of plank, rope
and pulley:
A. \( 15 k g f \)
в. \( 20 k g f \)
c. \( 25 k g f \)
D. \( 30 k g f \)


A shopkeeper bought 1000 coconuts for
Rs. \( 8500, \) out of which 50 coconuts were
spoiled. He sold the remaining coconuts for Rs. 12 each. Find the profit and profit percentage earned by the shopkeeper.


In all depressions, it is likely that the transmission of
reduced.
A. serotonin
B. brompheniramine
c. terfenadine
D. cimetidine


A force can change the shape and volume of an object
A . True
B. False


Vapour pressure of chloroform
\( \left(C H C l_{3}\right) \) and dichloromethane
\( \left(C H_{2} C l_{2}\right) \) at \( 298 K \) are \( 200 m m H g \)
and 415 mm \( H g \) respectively.
(i) Calculate the vapour pressure of the solution prepared by mixing \( 25.5 g \) of
\( \boldsymbol{C H} \boldsymbol{C l}_{3} \) and \( \mathbf{4 0} \boldsymbol{g} \) of \( \boldsymbol{C H}_{2} \boldsymbol{C l}_{2} \) at \( \boldsymbol{2} \boldsymbol{9 0} \boldsymbol{K} \)
and
(ii) Mole fraction of each component in solution.


Evaluate the following integral:
\( \int \frac{\sin ^{2} x}{1+\cos x} d x \)


Pick out correct statement from the
following regarding photons:
A. Zero rest mass and zero spin
B. Zero rest mass and half integral spin
c. zero rest mass and spin of unity
D. Unit rest mass and spin of unity


If \( x, y \) and \( z \) are three unit vectors in
three-dimensional space, then the minimum value of \( |\hat{\boldsymbol{x}}+\hat{\boldsymbol{y}}|^{2}+\mid \hat{\boldsymbol{y}}+ \)
\( \left.\hat{z}\right|^{2}+|\hat{z}+\hat{x}|^{2} \) is :
A \( \cdot \frac{3}{2} \)
B. 3
c. \( 3 \sqrt{3} \)
D. 6


Reactions are listed in List-I. Match the
result of the respective reactions with the appropriate options listed in List-II.


Determine the order and degree(if defined) of the following differential equation. \( \boldsymbol{y}^{\prime \prime}+\left(\boldsymbol{y}^{\prime}\right)^{2}+\mathbf{2} \boldsymbol{y}=\mathbf{0} \)


Assertion
The coil in the resistance boxes are
made by doubling the wire.
Reason
Thick wire is required in resistance box.
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


Factorise:
\( \frac{a^{3}}{8}+1 \)


Calculate the values of the
determinants:
\( \left|\begin{array}{cccc}\mathbf{0} & \mathbf{1} & \mathbf{1} & \mathbf{1} \\ \mathbf{1} & \boldsymbol{b}+\boldsymbol{c} & \boldsymbol{a} & \boldsymbol{a} \\ \mathbf{1} & \boldsymbol{b} & \boldsymbol{c}+\boldsymbol{a} & \boldsymbol{b} \\ \mathbf{1} & \boldsymbol{c} & \boldsymbol{c} & \boldsymbol{a}+\boldsymbol{b}\end{array}\right| \)


As long as an electron is in a particular orbit, the electron can never lose its
energy on its own.
A. True
B. False


Cytokinin was first synthesized by
A. Skoog and Miller
B. Letham
c. Bensan and Calvin
D. Thimman and Went


If the tangents \( P A \) and \( P B \) are drawn from the point \( \mathbf{P}(-1,2) \) to the circles \( x^{2}+y^{2}+x-2 y-3=0 \) and \( C \) is the
centre of the circle, then the area of the
quadrilateral PACB is
A .4
B. 16
c. does not exist
D. 12


Glowing of an electric bulb is a
change.
A. physical
B. chemical
c. both physical and chemical changes
D. none of these


Arrange the following in decreasing order of their Band gaps
A. conductors, , Insulators, Semiconductors
B. Insulators, Semiconductors, Conductors
c. Insulators, Conductors, Semiconductors
D. conductors, Semiconductors, Insulators


The mass number is same as
A. atomic mass number
B. molecular mass number
\( c . \) both a and \( b \)
D. None of the above


A charge \( q_{o} \) is distributed uniformly on a ring of radius R. A sphere of equal
radius R isconstructed with its centre
on the circumference of the ring. Find the electric flux through the surface of
the sphere.
A \( \cdot \frac{q_{0}}{3 \varepsilon_{0}} \)
в. \( \frac{q_{0}}{2 \varepsilon_{0}} \)
c. \( \frac{2 q_{0}}{\varepsilon_{0}} \)
D. \( \frac{4 q_{0}}{3 \varepsilon_{0}} \)


The branches of physics and engineering that involve the study of very low temperatures, how to produce
them, and how materials behave at
those temperatures is called:
A. Cryotronics
B. Cryogenics
c. cryonics
D. cryobiology


A spaceship rotating around earth with a constant speed experiences
acceleration towards
A. against the instantaneous direction of velocity of spaceship
B. in the instantaneous direction of velocity of spaceship
c. center of the earth
D. away from the center of the earth


We should look at sun or a powerful light directly. Is the statement True or
False
A. True
B. False


Assertion
An astronaut in an orbiting space
station above the earth experience
weightlessness.
Reason
An object moving around the earth
under the influence of earth's
gravitational force is in a state of 'free
fall'.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A stream of electrons from a heated
filament was passed between two charged plates kept at a potential difference V esu. If e and m are charge and mass of an electron, respectively, then the value of \( h / \lambda \) (where \( \lambda \) is wavelength associated with electron wave) is given by :
\( \mathbf{A} \cdot 2 m e V \)
в. \( \sqrt{m e V} \)
c. \( \sqrt{2 m e V} \)
D. mev


Velocity of a particle of mass \( 2 \mathrm{kg} \) changes from \( \overrightarrow{\boldsymbol{v}}_{1}=-2 \widehat{\boldsymbol{i}}-\widehat{\boldsymbol{2}} \hat{\boldsymbol{j}} \boldsymbol{m} / \boldsymbol{s} \) to
\( \overrightarrow{\boldsymbol{v}}_{2}=(\widehat{\boldsymbol{i}}-\widehat{\boldsymbol{j}}) \boldsymbol{m} / \boldsymbol{s} \) after colliding with a
plane surface
This question has multiple correct options
A. the angle made by the plane surface with the positive \( x \) -axis is \( 90^{\circ}+\tan ^{-1}\left(\frac{1}{3}\right) \)
B. the angle made by the plane surface with the positive x-axis is \( \tan ^{-1}\left(\frac{1}{3}\right) \)
C. the direction of change in momentum makes an angle \( \tan ^{-1}\left(\frac{1}{3}\right) \) with the positive \( x \) -axis.
D. the direction of the change in momentum makes an angle \( 90^{\circ}+\tan ^{-1}\left(\frac{1}{3}\right) \) with the plane surface.


\( C_{2} D_{2} \stackrel{?}{\longrightarrow} C_{2} D_{2} H_{2}(\text { trans }) \)
Give the best reagent for this conversion.
A . \( L i /(a q .) N H_{3} \)
в. \( H_{2} / P d \)
c. \( H_{2} / N i \)
D. None of these


The coordinates of the foot of the
perpendicular from the point (1,-2,1) on the plane containing the lines, \( \frac{x+1}{6}=\frac{y-1}{7}=\frac{z-3}{8} \) and \( \frac{x-1}{3}= \)
\( \frac{\boldsymbol{y}-\boldsymbol{2}}{\mathbf{5}}=\frac{\boldsymbol{z}-\boldsymbol{3}}{\boldsymbol{7}}, \) is :
A \( \cdot(2,-4,2) \)
в. (-1,2,-1
c. (0,0,0)
D. (1,1,1)


For every single amino acid incorporated in peptide chain
ATP and GTP molecules are
used.
A \( \cdot 1,4 \)
B. 1,6
\( c \cdot 1,2 \)
D. 1, 3


When a body remains in the same state of motion (translational or rotational)
under the influence of the applied forces, the body is said to be
A. Static equilibrium
B. Dynamic equilibrium
\( c . \) Both
D. None


Can \( P C l_{5} \) act as an oxidising as well as
a reducing agent? Justify.


How does the bile help in the digestion
of fat?


Information about four hydrocarbons is
Shown.
number of \( \quad \) reaction carbon \( \quad \) with hydrocarbon atoms in the \( \quad \) water molecules
'D reaction
\( 2 \quad \) no reaction
decolourises 3
4 decolourises
\( z \)
it
Which statement is correct?
A. Hydrocarbon W has the formula \( C H_{4} \) and can be polymerised
B. Hydrocarbon x has the formula \( C_{2} H_{4} \) and can be polymerised
C. Hydrocarbon Y has the formula \( C_{3} H_{6} \) and can be polymerised
D. Hydrocarbon Y has the formula \( C_{4} H_{10} \) and can be polymerised


What is the current through an electrical appliance of rating \( 5 \mathrm{kW}, 200 \) V and can you use a fuse which is rated
\( 8 \mathrm{A} ? \)
A. 25 A, yes
B. 2.5 A, yes
\( c \cdot 25 \) A, no
D. 2.5 A, no


If \( I=\int e^{x}\left(\frac{x+2}{x+4}\right)^{2} d x, \) then I equals
A \( \cdot \frac{x}{x+4} e^{x}+C \)
в. \( \frac{x-2}{x+4} e^{x}+C \)
c. \( \frac{x+1}{x+4} e^{x}+C \)
D. \( \frac{x-1}{x+4} e^{x}+C \)


The tarnishing of silver ornaments in
atmosphere is due to:
This question has multiple correct options
A. \( A g_{2} O \)
в. \( A g_{2} S \)
c. \( A g_{2} C O_{3} \)
D. \( A g_{2} S O_{4} \)


In the adjacent, \( C P \) represents a
wavefront and \( A O \& B P, \) the
corresponding two rays. Find the
condition on \( \theta \) for constructive
interference at \( \boldsymbol{P} \) between the ray \( \boldsymbol{B P} \)
and reflected ray \( \boldsymbol{O P} \)
\( A \cdot \cos \theta=3 \lambda / 2 d \)
B. \( \cos \theta=\lambda / 4 d \)
\( \mathbf{c} \cdot \sec \theta-\cos \theta=\lambda d \)
\( \mathbf{D} \cdot \sec \theta-\cos \theta=4 \lambda d \)


Four electric charges \( +\boldsymbol{q},+\boldsymbol{q},-\boldsymbol{q} \) and
\( -q \) are placed at the corners of a square
of side \( 2 L \) (see figure). The electric
potential at point \( A, \) midway between
the two charges \( +\boldsymbol{q} \) and \( +\boldsymbol{q} \), is
A \( \cdot \frac{1}{4 \pi \epsilon_{0}} \frac{2 q}{L}(1+\sqrt{5}) \)
в. \( \frac{1}{4 \pi \epsilon_{0}} \frac{2 q}{L}\left(1+\frac{1}{\sqrt{5}}\right) \)
c. \( \frac{1}{4 \pi \epsilon_{0}} \frac{2 q}{L}\left(1-\frac{1}{\sqrt{5}}\right) \)
D. zero


A particle is moving in a straight line with constant acceleration. If \( x, y \) and \( z \) be the distances described by a particle during the pth, qth and rth second
respectively, prove that \( (\boldsymbol{q}-\boldsymbol{r}) \boldsymbol{x}+ \)
\( (r-p) y+(p-q) z=0 \)


A sphere of mass \( m \) moving with a
uniform velocity \( v \) hits another identical
sphere at rest. If the coefficient of
restitution is \( e, \) the ratio of the
velocities of the two spheres after the
collision is \( \frac{e-1}{e+1} \)
A. True
B. False


Algae attached to stone surfaces are
called
A. Epiploic
B. coenolithic
c. Epilithic
D. None of the above


Let \( \boldsymbol{f}:(\boldsymbol{a}, \boldsymbol{b}) \rightarrow \boldsymbol{R} \) be a differentiable
function. Which of the following statements is/are true:
A \( \cdot \lim _{x \rightarrow a} f(x)=\infty \Rightarrow \lim _{x \rightarrow a}\left|f^{\prime}(x)\right|=\infty \)
B \( \cdot \lim _{x \rightarrow a} f^{\prime}(x)=\infty \Longrightarrow \lim _{x \rightarrow a} f(x)=\infty \)
c. \( \lim _{x \rightarrow a} f(x)=\infty \neq \lim _{x \rightarrow a}\left|f^{\prime}(x)\right|=\infty \)
D. \( \lim _{x \rightarrow a} f^{\prime}(x)=\infty \neq \lim _{x \rightarrow a} f(x)=\infty \)


If the second term in the expansion \( \left[a^{\frac{1}{13}}+\frac{a}{\sqrt{a^{-1}}}\right]^{n} \) is \( 14 a^{5 / 2} \), then the
value of \( \frac{n C_{3}}{n C_{2}} \) is
\( \mathbf{A} \cdot \mathbf{4} \)
B. 3
c. 12
D. 6


The value of the determinant
\( \left|\begin{array}{ccc}\cos \alpha & -\sin \alpha & 1 \\ \sin \alpha & \cos \alpha & 1 \\ \cos (\alpha+\beta) & -\sin (\alpha+\beta) & 1\end{array}\right| \)
A. Independent of \( \alpha \)
B. Independent of \( \beta \)
c. Independent of \( \alpha \) and \( \beta \)
D. None of the above


Which one of the following statements is/are not true for meiosis?
A. It occur in reproductive tissue only
B. Chromosome undergo pairing in early prophase
c. chromosome do not exchange their segments
D. centromere do not divide during anaphase


All terpenes have carbon skeletons made up of
A. isoprene units
B. vinyl units
c. alkenes
D. ethylenes units


The galvanometer deflection, when key
\( K_{1} \) is closed but \( K_{2} \) is open, equals \( \theta_{0} \)
(see figure). On closing \( K_{2} \) also and
adjusting \( R_{2} \) to5 \( \Omega, \) the deflection in
galvanometer becomes \( \frac{\theta_{0}}{5} \). The
resistance of the galvanometer is, then, given by [Neglect the internal resistance of battery \( ] \)
A . \( 12 \Omega \)
B . \( 25 \Omega \)
\( c .5 \Omega \)
D. \( 22 \Omega \)


A pebble is thrown vertically upwards from a bridge with an initial velocity of \( 4.9 m s^{-1} . \) It strikes the water after \( 2 s \)
Height of the bridge is:
A . \( 19.6 \mathrm{m} \)
в. \( 14.7 \mathrm{m} \)
c. \( 9.8 \mathrm{m} \)
D. \( 4.9 \mathrm{m} \)


The correct statement with regard to
\( \boldsymbol{H}_{2}^{+} \) and \( \boldsymbol{H}_{2}^{-} \) is:
\( \mathbf{A} \cdot \) both \( H_{2}^{+} \) and \( H_{2}^{-} \) are equally stable
B. both \( H_{2}^{+} \) and \( H_{2}^{-} \) do not exist
\( \mathbf{C} \cdot H_{2}^{-} \) is more stable than \( H_{2}^{+} \)
D. \( H_{2}^{+} \) is more stable than \( H_{2}^{-} \)


The waves propagating on water
surface are

This question has multiple correct options
A. ultrasonic
B. Iongitudinal
c. unaudible
D. transverse


In protein synthesis, the codon used as a start signal is
A. UAA
в. ссА
c. AUG
D. GCA


If for an A.P. \( S_{16}=784, a=4 \) find \( d=? \)


Which of the following is not colloid?
A. Milk
B. Blood
c. Ice-Cream
D. Urea solution


In the given figure, the radius of
curvature of a curved surface for both
the piano-convex and plano-concave
lens is \( 10 \mathrm{cm} \) and refractive index for
both is \( 1.5 . \) The location of the final
image after all the refractions through
lenses is:
\( \mathbf{A} \cdot 15 \mathrm{cm} \)
B. \( 20 \mathrm{cm} \)
\( \mathbf{c} \cdot 25 c m \)
D. \( 40 \mathrm{cm} \)


Differentiate with respect to 't' \( e^{-w t} \)


The power of a lens whose focal length
is one metre is \( _{-}-_{-}-_{-}- \) dioptre
A. one
B. ten
c. hundred
D. two


Assertion
If we bend an insulated conducting wire, the resistance of the wire
increases.
Reason
The drift velocity of electrons in bent
wire decreases.
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 area of a square playground is
256.6404 square metres. Find the length of one side of the playground.
A. 16.04 metres
B. 16.02 metres
c. 16.06 metres
D. 16.08 metres


Which of the following order regarding acidity of the following compounds is correct?
A. \( R O H>H C \equiv C H>N H_{3} \)
B. \( R O H<H C \equiv C H<N H_{3} \)
c. \( R O H>H C \equiv C H<N H_{3} \)
D. \( R O H<H C \equiv C H>N H_{3} \)


During running or cycling, Which of the following organs have to increase their activity
A . Heart
B. Lungs
c. Both (1) and (2)
D. Kidneys


What is the potential energy of an electron present in N-shell of the
\( B e^{3+} \)ion?
A. \( -3.4 e V \)
B. - \( 6.8 e V \)
c. \( -13.6 e V \)
D. \( -27.2 e V \)


Assertion
pH of 10 M H Cl aqueous solution is
less than 1.
Reason
pH is negative logarithm of \( \boldsymbol{H}^{+} \)
concentration.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which type of bonding is present in liquid oxygen?
A. Hydrogen bonding
B. lonic bonding
c. Network bonding
D. London dispersion force
E. Metallic bonding


A study was conducted to find out the
concentration of sulphur dioxide in the air in parts per million (ppm) of a certain city. The data obtained for 30 days is as follows:
\( \begin{array}{cccccc}0.03 & 0.08 & 0.08 & 0.09 & 0.04 & 0.17 \\ 0.16 & 0.05 & 0.02 & 0.06 & 0.18 & 0.20 \\ 0.11 & 0.08 & 0.12 & 0.13 & 0.22 & 0.07 \\ 0.08 & 0.01 & 0.10 & 0.06 & 0.09 & 0.18 \\ 0.11 & 0.07 & 0.05 & 0.07 & 0.01 & 0.04\end{array} \) Using this table, find the probability of the concentration of sulphur dioxide in
the interval \( 0.12-0.16 \) on any of these
days.


The correct sequence of plants in a
hydrosere is?
\( \mathbf{A} \cdot \) Volvox \( \rightarrow \) Hydrilla \( \rightarrow \) Pistia \( \rightarrow \) Scirpus \( \rightarrow \) Carex \( \rightarrow \) Quercus
B. Pistia \( \rightarrow \) Volvox \( \rightarrow \) Scirpus \( \rightarrow \) Hydrilla \( \rightarrow \) Quercus \( \rightarrow \) Carex
C. Quercus \( \rightarrow \) Carex \( \rightarrow \) Volvox \( \rightarrow \) Hydrilla \( \rightarrow \) Pistia \( \rightarrow \) Scirpus
D. Quercus \( \rightarrow \) Carex \( \rightarrow \) Scirpus \( \rightarrow \) Pistia \( \rightarrow \) Hydrilla \( \rightarrow \) Volvox


How many lone pairs of electrons are in
resonance of the given compound?
\( A \cdot 4 \)
B. 2
\( c \cdot 3 \)
D. 6


Write the names of monomers of the
following polymers:
(a) Bakelite
(b) Terylene


A ball is projected on smooth inclined
plane in direction perpendicular to line of greatest slope with velocity of \( 8 \boldsymbol{m} / \boldsymbol{s} \)
t's speed after \( \left.1 s \text { is (take } g=10 \mathrm{m} / \mathrm{s}^{2}\right) \)
\( A \cdot 10 \mathrm{m} / \mathrm{s} \)
B. \( 15 \mathrm{m} / \mathrm{s} \)
\( c \cdot 12 m / s \)
\( D \cdot 16 \mathrm{m} / \mathrm{s} \)


The quantity of heat required to raise the temperature of 2000 g of water from
\( 10^{\circ} \mathrm{C} \) to \( 50^{\circ} \mathrm{C} \) is
A. 80 cal
B. 80,000 cal
c. 8000 cal
D. none of these


Suppose that a reaction has \( \Delta \boldsymbol{H}= \)
\( 40 k J \) and \( \Delta S=50 k J / K . \) At what
temperature range will it change from spontaneous to non-spontaneous?
B. \( 799 K \) to \( 800 K \)
c. \( 800 K \) to \( 801 K \)
D. \( 799 K \) to \( 801 K \)


If the first three terms in the expansion
of \( (1+a x)^{n} \) are \( 1,8 x, 24 x^{2} \)
respectively, then \( a= \)
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c \cdot 4 \)
D.


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


Gases exert pressure on the walls of the container, because the gas molecules
A. Have finite volume
B. Obey Boyle's law
c. Possess momentum
D. collide with one another


Value Based Questions
Which of the following statements is associated with A. prophase, B. meraphase, \( C . \) anaphasc, \( D \). telophase, and E. interphase of mitosis? Each chromosome consists of two
chromatids.


What are monodentate ligands? Write
one example.


A stream lined body falls through air from a height on the surface of a liquid.
Let \( d \) and \( D \) denote the densities of the
materials of the body and the liquid
respectively. If \( D>d \), then the time
after which the body will be
instantaneously at rest is:
A \( \cdot \sqrt{\frac{2 h}{g}} \)
B. \( \sqrt{\frac{2 h}{g} \frac{D}{d}} \)
c. \( \sqrt{\frac{2 h}{g} \frac{d}{D}} \)
D. \( \frac{d}{(D-d)} \sqrt{\frac{2 h}{g}} \)


Two long parallel wires are at a distance of 1 metre. Both of them carry one
ampere of current. the force of
attraction per unit length between the two wires is
A \( \cdot 2 \times 10^{-7} \mathrm{Nm}^{-1} \)
В. \( 2 \times 10^{-8} N m^{-1} \)
c. \( 5 \times 10^{-8} \mathrm{Nm}^{-1} \)
D. \( 10^{-7} N m^{-1} \)


The equations of the lines through
(1,1) and making angles of \( 45^{\circ} \) with
the line \( \boldsymbol{x}+\boldsymbol{y}=\mathbf{0} \) are
A \( . x-1=0, x-y=0 \)
В. \( x-y=0, y-1=0 \)
c. \( x+y-2=0, y-1=0 \)
D. \( x-1=0, y-1=0 \)


Two points \( A \& B \) on a disc have
velocities \( v_{1} \& v_{2} \) at some moment
Their directions make angles \( 60^{\circ} \) and
\( 30^{\circ} \) respectively with the line of
separation as shown in the figure. The
angular velocity of the disc is:
A \( \cdot \frac{\sqrt{3} v_{1}}{d} \)
B. \( \frac{v_{2}}{\sqrt{3}} \)
c. \( \frac{v_{2}-v_{2}}{d} \)
D. \( \frac{v_{2}}{d} \)


Give balanced equations for the
following named reactions:
(i) Reimer-Tiemann reaction
(ii) Rosenmund reaction
(iii) Hoffmann's degradation reaction


A first order gaseous reactions has \( K=1.5 \times 10^{-6} \mathrm{sec}^{-1} \) at \( 200^{\circ} \mathrm{C} . \) If the
reaction is allowed to run for 10 hour,
what percentage of initial concentration
would have changed into products. What is the half life period of reaction?


A generator at a utility company produces \( 100 A \) of current at \( 4000 V \)
The voltage is stepped up to \( 240000 V \) by a transformer before it is sent on a high voltage transmission line. The current in transmission line is
A \( .3 .67 A \)
в. \( 2.67 A \)
c. \( 1.67 A \)
D. \( 2.40 A \)


\( \mathbf{1 0} \)
\( \mathbf{2 0} \)
\( \mathbf{3 0} \)
40
\( f \quad 5 \quad 7 \quad 15 \quad 13 \)
From the given distribution, calculate
mean deviation about mean.
A .1 .021
B. 11.231
c. 10.256
D. 12.214


The \( p H \) of a buffer solution is \( 5 . p K a \) of
the acid present in it is 4. What is the ratio of acid and salt present in the solution?
A . 1:
B. 1:10
\( c \cdot 10: \)
D. 1: 2


In a hydroelectric power station water is allowed to fall at the rate of 2000 kg per
second on a turbine kept \( 100 \mathrm{m} \) below the water level. Calculate the potential energy of water falling every one second at the highest point.
A \( .2 \times 10^{6} J^{2} \)
В. \( 2 \times 10^{8} J \)
c. \( 2 \times 10^{7} J \)
D. \( 2 \times 10^{6} J \)


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toppr JolN Now 5
Q Type your question 0 scraiacu
\( A \)
1) c) ii)
2) a) i)
B. 1 c) ii)
2) b) i
3) a) iii) ) is in is
2) a) iii) ) is in is
3) \( b) \) i)
D. \( 1) \) a) ii)
2) c) i)


Draw the diagram of induction coil and label the following:
a. Primary coil
b. Make and break arrangement.


Two blocks each of mass m is
connected to the spring of spring constant \( \mathrm{k} \) as shown in the figure.
If the blocks are displaced slightly in opposite directions and released, they
will execute simple harmonic motion.
The time period of oscillation is
A. \( 2 \pi \sqrt{\frac{m}{k}} \)
В \( .2 \pi \sqrt{\frac{m}{2 k}} \)
\( \mathbf{c} \cdot 2 \pi \sqrt{\frac{m}{4 k}} \)
D. \( 2 \pi \sqrt{\frac{2 m}{k}} \)


Differentiate the following function with
respect to \( x \)
\( \boldsymbol{x}^{-3}(\mathbf{5}+\mathbf{3} \boldsymbol{x}) \)


Find the value of \( (2 x+5)(2 x-5) \)
A. \( 4 x-25 \)
B . \( 4 x^{2}-25 \)
c. \( 2 x^{2}-25 \)
D. \( 4 x^{2}-5 \)


The correct IUPAC name of the following compound is:
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C O}-\boldsymbol{N H}-\boldsymbol{C H}_{3} \)
A. \( N \) - ethyl ethanamide
B. N - methyl ethanamide
c. N - Methyl propanamide
D. N - ethyl methanamide


In what time will \( R s .7500 \) amount to
\( R s .8625, \) if simple interest is reckoned \( \operatorname{at} 7 \frac{1}{2} \% \) per annum?


In Pteridophytes, phloem is without
A. Sieve cells
B. Sieve tubes
c. companion cells
D. Bast fibres


The cell reaction \( \boldsymbol{C r}_{2} \boldsymbol{O}_{\mathbf{7}}^{2+}(\boldsymbol{a q})+ \)
\( \mathbf{1 4} \boldsymbol{H}^{+}(\boldsymbol{a q})+\boldsymbol{6} \boldsymbol{F} \boldsymbol{e}^{2+}(\boldsymbol{a q}) \rightarrow \)
\( \mathbf{6} F e^{3+}(\boldsymbol{a} \boldsymbol{q})+\mathbf{2} \boldsymbol{C} \boldsymbol{r}^{3+}(\boldsymbol{a} \boldsymbol{q})+\mathbf{7} \boldsymbol{H}_{2} \boldsymbol{O}(l) \)
best represented by:
A \( \cdot P t(s)\left|F e^{2+}(a q), F e^{3+}(a q) \| C r_{2} O_{7}^{2+}(a q), C r^{3+}(a q)\right| P t(s) \)
B . \( P t(s)\left|C r_{2} O_{7}^{2+}(a q), C r^{3+}(a q) \| F e^{3+}(a q), F e^{2+}(a q)\right| P t(s) \)
C. \( F e^{2+}(a q)\left|F e^{3+}(a q) \| C r_{2} O_{7}^{2+}(a q)\right| C r^{3+}(a q) \)
D. \( C r_{2} O_{7}^{2+}(a q)\left|C r^{3+}(a q) \| F e^{3+}(a q)\right| F e^{2+}(a q) \)


Which of the following compounds undergoes haloform reaction?
A. \( C H_{3} C O C H_{3} \)
в. \( H C H O \)
c. \( C H_{3} C H_{2} B r \)
D. \( C H_{3}-O-C H_{3} \)


How much money does Trishika have?
A . \( R s .125 \)
B. Rs.110
c. \( R s .115 \)
D. Rs.120


A wire of length \( 60 \mathrm{cm} \) is bent into a
circle with a gap of \( 1 \mathrm{cm} . \) At its ends, on heating it by \( 100^{\circ} \mathrm{C} \), the length of the gap increases to \( 1) 02 \mathrm{cm} . \alpha \) of material
of wire is
A \( \cdot 2 \times 10^{-4} /^{\circ} \mathrm{C} \)
B . \( 4 \times 10^{-4} /^{\circ} \mathrm{C} \)
c. \( 6 \times 10^{-4} /^{\circ} \mathrm{C} \)
D. \( 1 \times 10^{-4} /^{\circ} \mathrm{C} \)


Which of the following forms ideal solution?

This question has multiple correct options
A \( \cdot C_{6} H_{5} C l-C_{6} H_{5} B r \)
в. \( C_{6} H_{6}-C_{6} H_{5} C H_{3} \)
c. Hexane-heptane
D. none of these


If \( a+b+2 c=0, \) then the value of \( a^{3}+ \)
\( b^{3}+8 c^{3} \) is equal to
A . \( 3 a b c \)
B. \( 4 a b c \)
\( c \cdot a b c \)
D. \( 6 a b c \)


Centre of human evolution was
A. Ethiopian realm
B. Oriental realm
c. Palaeoarctic realm
D. Neotropical realm


Formation of \( C l F_{3} \) from \( C l_{2} \) and \( F_{2} \) is an
exothermic process. The equilibrium
system can be represented as:
\( \boldsymbol{C l}_{2(\boldsymbol{g})}+\boldsymbol{3} \boldsymbol{F}_{2} \rightleftharpoons \boldsymbol{2} \boldsymbol{C l} \boldsymbol{F}_{3} ; \boldsymbol{\Delta} \boldsymbol{H}=-\boldsymbol{3} \boldsymbol{2} \boldsymbol{9} \mathbf{k} \mathbf{J} \)
Which of the following will increase
quantity of \( C l F_{3} \) in the equilibrium
mixture?
A. Increase in temperature, decrease in pressure, addition of \( C l_{2} \)
B. Decrease in temperature and pressure, addition of \( C l F_{3} \)
C. Increase in temperature and pressure, removal of \( C l_{2} \)
D. Decrease in temperature, increase in pressure addition of \( F_{2} \)


By which reaction, formation of hard
water takes place?
(a)
(b)
\( (c) \)
\( (d) \)
A. by only \( d \)
B. by only \( a \)
c. by \( a, b, c \)
D. by all processes


One liquid contains \( 22 \frac{1}{2} \% \) of water, another \( 27 \% \). A glass is filled with 5 parts of one liquid and 7 parts off the
other. What is the percentage of water
in the glass?
A \( \cdot 22 \frac{1}{8} \% \)
B. 25.75 \%
c. \( 25.25 \% \)
D. \( 25 \frac{1}{8} \% \)


Match the following.
Order of rotational
symmetry
\( (P) \)
(i) 5
\( (\mathrm{Q}) \)
(ii) 2
\( (\mathbf{R}) \)
(iii) 3
\( (\mathbf{S}) \)
(iv) 4
\( \mathbf{A} \cdot(\mathrm{P}) \rightarrow(\mathrm{iv}),(\mathrm{Q}) \rightarrow(\mathrm{i}),(\mathrm{R}) \rightarrow(\mathrm{i}),(\mathrm{S}) \rightarrow(\mathrm{iii}) \)
B. \( (P) \rightarrow(\text { iv) },(Q) \rightarrow(\text { iii) },(R) \rightarrow(\text { ii) },(S) \rightarrow\text { (i) } \)
C. \( (P) \rightarrow(\text { ii) },(Q) \rightarrow(\text { iv }),(R) \rightarrow(\text { iii) },(S) \rightarrow(i) \)
\( \mathbf{D} \cdot(\mathbf{P}) \rightarrow(\mathbf{i} \mathbf{i}),(Q) \rightarrow(\mathbf{i}),(R) \rightarrow(i \mathbf{v}),(S) \rightarrow(\text { iii }) \)


Pyruvate undergoes oxidative decarboxylation to produce
A . 2-PGA.
B. \( \alpha \) -Ketone
c. succinyl Co-A.
D. Acetyl Co-A


Balance the following reactions:
\( \boldsymbol{F} \boldsymbol{e}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{F} \boldsymbol{e}_{3} \boldsymbol{O}_{4}+\boldsymbol{H}_{2} \uparrow \)


\( \int_{-a}^{a} \frac{x^{4} d x}{\sqrt{a^{2}-x^{2}}}= \)
A \( \cdot \frac{3 \pi a^{4}}{8} \)
в. \( \frac{\pi a^{4}}{8} \)
c. \( \frac{-\pi a^{4}}{8} \)
D. \( \frac{5 \pi \mathrm{a}^{4}}{8} \)


Solve the following pair of linear equations by the substitution method.
(i) \( \boldsymbol{x}+\boldsymbol{y}=\mathbf{1 4} ; \boldsymbol{x}-\boldsymbol{y}=\mathbf{4} \)
(ii) \( s-\boldsymbol{t}=\mathbf{3} ; \frac{\boldsymbol{s}}{\mathbf{3}}+\frac{\boldsymbol{t}}{\mathbf{2}}=\mathbf{6} \)
(iii) \( 3 x-y=3 ; 9 x-3 y=9 \)
(iv) \( 0.2 x+0.3 y=1.3 ; 0.4 x+0.5 y= \)
\( \mathbf{2 . 3} \)
(v) \( \sqrt{\mathbf{2}} \boldsymbol{x}+\sqrt{\mathbf{3}} \boldsymbol{y}=\mathbf{0} ; \sqrt{\mathbf{3}} \boldsymbol{x}-\sqrt{\mathbf{8}} \boldsymbol{y}=\mathbf{0} \)
(vi) \( \frac{\mathbf{3} \boldsymbol{x}}{\mathbf{2}}-\frac{\mathbf{5} \boldsymbol{y}}{\mathbf{3}}=-\mathbf{2} ; \frac{\boldsymbol{x}}{\mathbf{3}}+\frac{\boldsymbol{y}}{\mathbf{2}}=\frac{\mathbf{1 3}}{\mathbf{6}} \)


A faulty thermometer has its fixed
points marked as \( 3^{\circ} \) and \( 120^{\circ} . \) The
temperature of a body measured by the
faulty thermometer is \( 80^{\circ}, \) Find the
correct temperature of the body on Celsius scale:
A \( .36 .5^{\circ} \mathrm{C} \)
B. \( 77.8^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 25.8^{\circ} \mathrm{C} \)
D. \( 66.8^{\circ} \mathrm{C} \)


Gnawing teeth occur in
A. Rodentia
B. Lagomorpha
C. Both A and B
D. Pholidota


A heater coil connected across a given potential difference has power \( \boldsymbol{P} \). Now the coil is cut into two equal halves and joined in parallel. Across the same potential difference, this combination
has power.
A . \( P \)
в. \( 4 P \)
c. \( \frac{P}{4} \)
D. \( 2 P \)


Construct triangle \( A B C \) having given
\( B C=7 c m, A B-A C=1 \mathrm{cm} \) and
\( \angle A B C=45^{\circ} \)


Electrolytic reduction of alumina to aluminium by Hall-Heroult process is carried out
A. in the presence of Naç
B. in the presence of fluorite
C. in the presence of cryolite which forms a melt with lower melting temperature
D. in the presence of cryolite which forms a melt with higher melting temperature


In the displacement method, a convex lens is placed in between an object and a screen. If one of the magnification is 3 and the displacement of the lens between the two positions is \( 24 \mathrm{cm}, \) then the focal length of the lens is:
A . \( 10 \mathrm{cm} \)
B. \( 9 \mathrm{cm} \)
\( c \cdot 6 \mathrm{cm} \)
D. \( 16 / 3 \mathrm{cm} \)


Evaluate and write in standard form:
\( (-3+2 i)^{2}-3(3-i)(-2+2 i), \) where
\( i^{2}=-1 \)
A \( .17+36 \)
B. \( 17-36 i \)
c. \( -17-36 i \)
D. \( -17+36 i \)


Construct a triangle of sides \( 4 \mathrm{cm}, 5 \mathrm{cm} \)
and \( 6 \mathrm{cm} \) and then a triangle similar to it whose sides are \( \frac{2}{3} \) of the
corresponding sides of the first
triangle. The length of side \( A^{\prime} C^{\prime} \) (in \( c m \)
is:


A river is flowing from west to east at a speed of \( 5 \mathrm{m} / \mathrm{minute} . \) In what direction
should a man on the south bank of the
river capable of swimming at \( 10 \mathrm{m} / \mathrm{min} \) in still water should swim to cross the
water in shortest time?
A. East
B. west
c. south
D. North


A uniform meter scale balances
horizontally on a knife-edge placed at \( 55 \mathrm{cm} \) mark, when a mass of \( 25 \mathrm{g} \) is supported from one end, then the mass of the scale is:
A. \( 200 \mathrm{g} \)
B. 225 g
c. \( 350 \mathrm{g} \)
D. 275 g


Match the elements of the List-I to the
elements of List-II.
List - List - II
a) static friction
e) less friction
b) angle of repose
f) self-adjusting force
c) lubrication
g) non-conservative force
d) frictional force
h) angle of friction
\( A \cdot a-f ; b-h ; c-e ; d-g \)
B. a-e;b-g;c-h;d-f
c. \( a-g ; b-h ; c-e ; d-f \)
D. a-g ;b-h;c-f;d-e


Q Type your question
at the bottom.lnitially the holes are closed and water is filled into
the container. Now the container is
rotated about its axis with an angular velocity \( \omega=\sqrt{12} r a d / s e c . \) As seen from
the rotating frame of the container. The initial velocity of efflux after opening
the holes will be: \( \left(\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}, \boldsymbol{h}=\right. \)
\( 5 m) \)
A \( \cdot 10 \frac{m}{s} \)
В \( \cdot 10 \sqrt{2} \frac{m}{s} \)
\( \mathrm{c} \cdot_{20} \frac{m}{s} \)
D. \( 20 \sqrt{2} \frac{m}{s} \)


"Secondary messenger" is
A. Cyclic AMP
в. Атр
c. ADP
D. DNA


If \( \boldsymbol{A}=(\mathbf{5},-\mathbf{1}, \mathbf{1}), \boldsymbol{B}=(\mathbf{7},-\mathbf{4}, \mathbf{7}), \boldsymbol{C}= \)
\( (1,-6,10), D=(-1,-3,4) . \) Then
\( A B C D \) is a
A . square
B. rectangle
c. rhombus
D. none of these


A person runs \( 40 m \) to the north in \( 6.0 s \)
and then \( 30 m \) to the east in 4.0 s. Find
out the average velocity of the person?
A \( .5 .0 m / s \)
в. \( 6.0 m / s \)
c. \( 6.7 m / s \)
D. \( 7.0 m / s \)
E \( .7 .5 \mathrm{m} / \mathrm{s} \)


Give reasons:
When the gas formed on heating limstone is passed through freshly prepared lime water, the lime water turns milky.


Evaluate :-
ff \( (x)=2 x+1 \) then, \( f(2 x-3)=? \)


\( \lim _{n \rightarrow \infty} \frac{1^{3}+2^{3}+\ldots+n^{3}}{n^{4}}=\frac{1}{4} l . \) Find


Find the two digit number which is a square number and also a cubic
number.


Differentiate between algae and fungi


Assign the IUPAC names for the given
compounds:


Nisha swims in a \( 90 \mathrm{m} \) long pool. She covers \( 180 \mathrm{m} \) in one minute by swimming from one end to the other and back along the same straight path. Find the average velocity of Nisha.
\( A \cdot O m / s \)
B. 3 \( \mathrm{m} / \mathrm{s} \)
\( c \cdot 6 m / s \)
D. None of these


Removal of soil by the action of wind and water is known as
A. Soil erosion
B. Soil conservation
c. Salination
D. Calcification


The electrode potentials for \( \boldsymbol{C u}^{2+}(\boldsymbol{a q})+\boldsymbol{e}^{-} \rightarrow \)
\( \boldsymbol{C u}^{+}(\boldsymbol{a q}) \) and \( \boldsymbol{C u}^{+}(\boldsymbol{a q})+\boldsymbol{e}^{-} \rightarrow \boldsymbol{C u}(\boldsymbol{s}) \)
are \( +0.15 \mathrm{V} \) and +0.50 respectively. The value of \( \boldsymbol{E}^{0} \boldsymbol{C u}^{2+} \mid \boldsymbol{C u} \) will be :
A . \( 0.500 \mathrm{v} \)
B. 0.325
\( c .0 .650 v \)
D. 0.150


One of the rectangular components of a
force of \( 40 N \) is \( 20 N . \) Find the angle it
makes with this component and
magnitude of other component.


State whether given statement is True or False
MRI uses radio-waves.
A. True
B. False


As proved by many studies, the
greenhouse effect is rapidly increasing
because of increase in the
concentration of carbon dioxide. In the
given graph, the increase in carbon
dioxide concentration is shown.What
could be \( X \) corresponding to it?
(i) Rate of photosynthesis in plants
(ii) \( p H \) of the oceans
(iii) Water level of ocean
(iv) Average global temperature of earth
A. (i) and (iii)
B. (ii) and (iv)
C . (ii) only
D. (iv) only


The binding energy per nucleon of deuteron \( \left(_{1} H^{2}\right) \) and helium \( \left(_{2} H e^{4}\right) \) are
1.1 \( M e V \) and \( 7.0 \mathrm{MeV} \), respectively. The energy released when two deuterons fuse to form a helium
nucleus is
A. \( 36.2 \mathrm{MeV} \)
B. 23.6 MeV
c. \( 47.2 \mathrm{MeV} \)
D. \( 11.8 \mathrm{MeV} \)
E. \( 9.31 \mathrm{MeV} \)


A cycle is sold for Rs. 880 at a loss of
20\%. For how much should it be sold to
gain \( 10 \% ? \)
A . Rs.1400
B. Rs. 1210
c. Rs. 1100
D. Rs. 1000


Find the minimum uncertainty in the
position of proton when \( u_{p r o t o n}=0.01 \times \) speed of light.
A \( \cdot 3.15 \times 10^{3} m \)
В. \( 13.2 \times 10^{-14} \mathrm{m} \)
c. \( 6.6 \times 10^{-14} m \)
D. \( 1.05 \times 10^{-14} m \)


The transcription product responsible for encoding proteins to be translated is
\( A . \) mRNA
B. rRNA
c. tRNA
D. DNA
E. Nucleolus


The removal of 'Keystone' species will effect
A. The producers
B. The consumers
c. The ecosystem
D. The decomposers


In peritoneal dialysis
A. Blood is removed from the body and a natural filter is employed
B. Blood is not removed from the body and a natural filter is employed
C. Blood is not removed from the body and an artificial filter is used
D. Blood is removed from the body and an artificial filter is employed


The correct order of reactivity among the following is
I) atomic hydrogen
II) dihydrogen
III) nascent hydrogen
c. ॥>॥|>1
D. III>II>


As a planet moves around the sun it
sweeps equal areas in equal intervals of time.
A. True
B. False


The process used in purifying metals by electrolysis is called:
A. electroplating
B. electrometallurgy
c. electrorefining
D. electrodeposition


Evaluate \( \int \frac{d x}{9 x^{2}+6 x+5} \)


Diplostemonous androecium occurs in
A. silene
B. Murraya
c. Asparagus
D. Brassica


Determine the number of revolutions
made by an electron in one second in the 2 nd Bohr orbit of \( \boldsymbol{H} \) -atom.


The following figures \( G U N S \)
Find \( x \text { and } y \text { .(Lengths are in } c m) \)


In the native state, gold is present:
A. as a mixture with a metal
B. in free state
C. as a mixture with a non metal
D. as a mixture with a compound


The ratio of primary voltage to secondary voltage in a transformer is
'n'. The ratio of the primary current to secondary current in the transformer is
\( A \)
B. \( 1 / n \)
c. \( n^{2} \)
D. \( 1 / n^{2} \)


The standard quantity, used for comparison, is called fundamental
quantity.
A. True
B. False


Derivative of \( \tan ^{-1}\left(\frac{x}{\sqrt{1-x^{2}}}\right) \) with
respect to \( \sin ^{-1}\left(3 x-4 x^{3}\right) \) is
A \( \cdot \frac{1}{\sqrt{1-x^{2}}} \)
в. \( \frac{3}{\sqrt{1-x^{2}}} \)
\( c .3 \)
D.


Which of the following is not a property of aluminium?
A. Good conductor of heat and electricity
B. It is malleable
c. It is heavy
D. It is ductile