Which of the following constellations resembles a big kite with a tail?
A. Ursa Major
B. Ursa Minor
c. scorpio
D. Orion


If \( a=\frac{\sin x \times \cos 3 x}{\sin 3 x \times \cos x} \) then which of the
following is wrong?
A \( \cdot a<\frac{1}{3} \)
\( \mathbf{B} \cdot a>3 \)
c. \( \frac{1}{3}<a<3 \)
D. None of these


The vapour pressure of water at \( 27^{\circ} \mathrm{C} \) is
\( 0.2463 a t m . \) Calculate the values of \( K_{p} \)
and \( K_{c} \) at \( 27^{\circ} C \) for the equilibrium
\( \boldsymbol{H}_{2} \boldsymbol{O}\left(\boldsymbol{l} \rightleftharpoons \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g})\right. \)
Using the equilibrium constant Which of the following reactions goes almost all the way to completion, and which proceeds hardly.


Evaluate the following determinant : \( = \) \( \begin{array}{|lll|}\mathbf{6 7} & \mathbf{1 9} & \mathbf{2 1} \\ \mathbf{3 9} & \mathbf{1 3} & \mathbf{1 4} \\ \mathbf{8 1} & \mathbf{2 4} & \mathbf{2 6}\end{array} \)


To find the sum of interior angles, we
multiply the number of triangles by
\( \mathbf{A} \cdot 360^{\circ} \)
B. \( 120^{\circ} \)
\( c \cdot 180^{\circ} \)
D. \( 240^{\circ} \)


Which of the following is an INCORRECT statement regarding genetic material?
A. Genes are made up of DNA
B. Chromatin is made up of DNA
C. Histones are proteins to which chromatin is bound
D. DNA is made up of genes


Noradrenaline is a/an:
A. neurotransmitter
B. antidepressant
c. antihistamine
D. antacid


The diagram given shows the green
house effect. Which of the following would have been in the absence of
greenhouse effect in the atmosphere?
A. Pollution will increase
B. Earth's surface temerature will decrease
c. Earth surface temperature will increase
D. Earth's surface temperature remains the same


Magnetic field at point \( ^{\prime} \boldsymbol{P}^{\prime} \) due to given
current distribution is:
A \( \cdot \frac{\mu_{0} I}{4 \pi r}(1+\sqrt{2}) \odot \)
В \( \cdot \frac{\mu_{0} I}{2 \pi r}(1+\sqrt{2}) \odot \)
c. \( \frac{\mu_{0} I}{4 \pi r}(1+\sqrt{2}) \otimes \)
D. \( \frac{\mu_{0} I}{2 \pi r}(1+\sqrt{2}) \otimes \)


Assertion
Archaebacteria are more similar to
eukaryotes rather than eubacteria.
Reason

Archaean genome is more similar to eukaryotic genome rather than
bacterial genome.
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 rise in temperature of a substance
depends on:
A. The quality of heat supplied
B. The mass of the substance
c. The nature of the substance
D. All the above


The point of dissimilarity between lanthanides and actinides is:
A. three outermost shells are partially filled
B. they show oxidation of \( +3( \) common)
c. they are called inner transition elements
D. they are radioactive in nature


The value of \( \left|\begin{array}{ll}\cos 15^{\circ} & \sin 15^{\circ} \\ \sin 75^{\circ} & \cos 75^{\circ}\end{array}\right| \)


What will react with \( C H_{3} M g B r \)
followed by decomposition with \( \boldsymbol{H}_{3} \boldsymbol{O}^{\oplus} \)
to give \( 2^{\circ} \) alcohol.
A. \( C H_{2}=C H O H \)
в. \( C H_{3} C H O \)
\( c \)
D. None of these


Permanent hardness of water is due the
presence of
A. calcium carbonate
B. calcium chloride
c. calcium bicarbonate
D. calcium sulphide


Polypeptides having molecular weights above 10000 are known as:
A. Amino acids
B. Hormones
c. Proteins
D. Terminal amino acids


Atomic number is denoted by
\( A \cdot A \)
B.
\( c \cdot z \)
D. M


Cork cambium produces
A. Secondary tissue
B. Lateral meristem
C. Periderm
D. All of these


is a potent vasodilator.
A. Histamine
B. Serotonin
c. codeine
D. Cimetidine


The compound, \( \left(\boldsymbol{C} \boldsymbol{H}_{3}\right)_{3} \boldsymbol{C}-\boldsymbol{N} \boldsymbol{H}_{2} \) is a :
A. primary amine
B. secondary amine
c. tertiary amine
D. quaternary ammonium salt


Find the common factors of
\( 3 x^{2} y^{3}, 10 x^{3} y^{2}, 6 x^{2} y^{2} z \)
A \( \cdot x^{2} y^{2} \)
B. \( x y^{2} \)
c. \( x^{2} y \)
D. \( x y \)


A doctor advised a person to take an
injection of insulin because
A. His blood pressure was low
B. His heart was beating slowly
c. He was suffering from goitre
D. His sugar level in blood was high


If \( f \) is a real function defined by \( f(x)= \) \( \frac{x-1}{x+1}, \) then prove that \( f(2 x)=\frac{3 f(x)+1}{f(x)+3} \)


In the figure the charge \( Q \) is at the
center of the circle. Work done is
maximum when another charge is
taken from point \( \boldsymbol{P} \) to
\( \mathbf{A} \cdot P \)
B. \( K \)
c. \( M \)
D. \( N \)


The velocity of sound in air is \( 330 \mathrm{m} / \mathrm{s} \) The r.m.s velocity of air molecules \( (\gamma= \)
1.4) is approximately equal to
A. \( 400 \mathrm{m} / \mathrm{s} \)
B. 471.4 m/s
c. \( 231 \mathrm{m} / \mathrm{s} \)
D. \( 462 \mathrm{m} / \mathrm{s} \)


List in tabular form two distinguishing features between acquired traits and inherited traits, with one example of
each.


In stomach, excess amount of which
acid causes pain and irritation?
A. \( H C l \)
в. \( C H_{3} \) СООН
\( \mathrm{c} \cdot \mathrm{H}_{3} \mathrm{PO}_{4} \)
D. \( H_{2} S O_{4} \)


Two point object of masses \( 10^{4} k g, 10^{6} k g \) are \( 1.2 \times 10^{3} m \) apart.
Find distance of point from smaller mass at which the net gravitational force due to them will be zero(in m)
A . 109
B. 1100
\( c \cdot 11 \)
D. 99


Synthetic polymer prepared by using caprolactam is known as:
A. terylene
B. teflon
c. nylon- 6
D. neoprene


If fully charged battery contains 1.5 L of
\( 5.00 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4} \) in and \( 1.5 \mathrm{mol} \) of \( \mathrm{H}_{2} \mathrm{SO}_{4} \) is
consumed, concentration of \( H_{2} S O_{4} \) after
current is drawn is:
A . 3.50
B. 2.00 M
c. \( 4.25 \mathrm{M} \)
D. 4.00 M


If the values of force and length are increased four times, then the unit of
energy will be increase by:
A. 4 times
B. 2 times
c. 8 times
D. 16 times


The point of intersection of the lines \( \frac{x-5}{3}=\frac{y-7}{-1}=\frac{z+2}{1} \) and \( \frac{x+3}{-36}= \)
\( \frac{y-3}{2}=\frac{z-6}{4} \) is
A \( \cdot\left(21, \frac{5}{3}, \frac{10}{3}\right) \)
в. (2,10,4)
c. (-3,3,6)
D. (5,7,-2)


Which of the following factors favour the formation of complexes by d-block elements?
A. Small size.
B. High nuclear charge.
C. Presence of low energy vacant orbitals to accept lone pair of electrons donated by ligands.
D. All of the above


Evaluate \( \int \frac{x^{3}+4 x^{2}-7 x+5}{x+2} d x \)


The ionization energy of a hydrogen-like atom is 9 Rydberg. The radius of first orbit of this atom, as compared to the radius of first orbit of hydrogen atom, will be
A. One-fourth
B. Half
c. One-third
D. Three times


All chemical characteristics are
common to living beings, except
A. Type of protein present in the body.
B. Similar triple code for amino acids.
C. Energy is stored by high phosphate bonds.
D. Ribosomes are the sites of protein synthesis.


What is 'diffraction of light'? Explain its
two types.


Which of the following statements are
not true for hydrogen?
This question has multiple correct options
A. It exists as diatomic molecule.
B. It has one electron in its outermost shell.
C. It can lose electron to form a cation which can exist
freely.
D. It forms a large number of ionic compounds by losing an electron


A current of 0.965 ampere is passed through \( 500 \mathrm{ml} \) of \( 0.2 \mathrm{M} \) solution of
\( Z n S O_{4} \) for 10 minutes. The molarity of
\( Z n^{2+} \) after deposition of zinc is:
A. 0.1
B. 0.5 \( M \)
c. \( 0.8 \mathrm{M} \)
D. 0.194 M


a) i) How do you convert benzoic acid to benzamide? Write the reaction.
ii) Complete the reaction : (please find above image)
b) What happens when carbony compounds are treated with hydrazine? Write the reaction.


Find out A from the given flowchart.
\( \mathbf{A} \cdot C u_{2} S \)
B. \( C u F e S_{2} \)
\( \mathbf{c} \cdot \operatorname{Fe} S_{2} \)
\( \mathrm{D} \cdot \mathrm{Fe}_{3} \mathrm{O}_{4} \)


In the periodic table as formulated by Mendeleev, which of the following
constitute an anomalous pair of elements?
\( \mathbf{A} \cdot H \) and \( H e \)
B. \( B r \) and \( N e \)
c. \( K \) and \( A r \)
D. \( N a \) and \( B \)


Find the position vectors of a point \( \boldsymbol{R} \) which divides the line joining two points \( P \) and \( Q \) whose position vectors \( \operatorname{are} 2 \vec{a}+3 \vec{b} \) and \( \vec{a}-3 \vec{b} \) respectively
externally in the ratio \( 1: 2 . \) Also, show
that \( P \) is the midpoint of the line
segment \( \boldsymbol{R} \)


State two experiences that made you
think that air exerts pressure.


Assertion
For a first order reaction, \( t_{1 / 2} \) is independent of the initial concentration
of reactants.
Reason
For a first order reaction, \( t_{1 / 2} \) is thrice
the \( t_{7 / 8} \)
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


Determine if the points (1,5)(2,3) and (-2,-11) are collinear.
A. True
B. False


Dahlia starch is used for
A. Study of digestive enzymes
B. Study of kidney function
C. Preparation of noodles
D. Manufacture of chocolates


If \( 6 \mathrm{mm} \) is the distance moved by the
thimble on the main scale for 6
rotations then pitch of the screw is :
\( \mathbf{A} \cdot 1 \mathrm{mm} \)
B. \( 1 \mathrm{cm} \)
\( c .0 .1 \mathrm{mm} \)
D. 0.01 cm


Number of \( g \) of oxygen in
\( 32.2 g N a_{2} S O_{4} 10 H_{2} O \) is:
\( [M o l . w t=322] \)
A . 16.0
B . 2.24
c. 18.0
D. 22.4


Assertion
\( \mathbf{9 2} \mathbf{U}^{\mathbf{2 3 5}}+\mathbf{o} \mathbf{n}^{\mathbf{1}} \longrightarrow \mathbf{5 6} \mathbf{B a}^{\mathbf{1 4 0}}+\mathbf{3 6} \mathbf{K e}^{\mathbf{9 3}}+ \)
\( 3 \mathrm{on}^{1} \) is a nuclear fission reaction.
Reason
Neutrons emitted do not react further.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Find the angles in a straight line


A solution containing 5 g acetic acid in 100 g \( \boldsymbol{H}_{2} \boldsymbol{O}\left(\boldsymbol{O}_{\boldsymbol{H}_{2}}^{0} \boldsymbol{O}=\mathbf{2} \boldsymbol{3} . \mathbf{7} \mathbf{5} \boldsymbol{6} \boldsymbol{m} \boldsymbol{m} \text { at } \mathbf{2} \mathbf{5}^{\boldsymbol{o}} \boldsymbol{C}\right. \)
shows a vapour pressure of \( 23.40 \mathrm{mm} \) whereas same mass of acetic acid in
\( 100 \mathrm{g} C_{6} H_{6}\left(P_{C_{6} H_{6}}^{0}=72.5 m m \text { at } 25^{\circ} C\right) \)
shows a vapour pressure of \( 70.0 \mathrm{mm} \) Assuming non-volatile nature of \( C H_{3} C O O H, \) discuss the data given to discuss hydrogen bonding:
A. acetic acid exists as a monomer
B. acetic acid exists as a dimer
c. acetic acid is dissociated
D. acetic acid exists as an anhydride


Water flows in a horizontal tube as
shown in figure. The pressure of water
changes by \( 600 N / m^{2} \) between \( x \) and \( y \)
where the areas of cross - section are 3
\( c m^{2} \) and \( 1.5 c m^{2} \) respectively. Find the
rate of flow of water through the tube.
A \( \cdot 189 \mathrm{cm}^{3} / \mathrm{s} \)
В \( \cdot 159 \mathrm{cm}^{3} / \mathrm{s} \)
c. \( 189 \mathrm{cm}^{2} / \mathrm{s} \)
D. \( 159 \mathrm{cm}^{2} / \mathrm{s} \)


The typical floral formula of disc florets
is
\( \mathbf{A} \cdot K_{\text {pappus}} C_{5} A_{0} \underline{G}_{(2)} \)
B . \( K_{\text {рарриз}} C_{(5)} A_{(5)} \bar{G}_{(2)} \)
\( \mathbf{c} \cdot K_{5} C_{5} A_{(9)+1} \underline{G}_{(2)} \)
D. \( K_{0} C_{5} A_{5} G_{(2)} \)


Find the square root of:
0.602 correct to two places of decimal


Which of the following statement is incorrect about interhalogen
compounds?
A. They are ionic in nature
B. They are diamagnetic.
C. They behave as strong oxidising agent
D. All of these


Choose the correct answers from the
alternatives given.

If a cone, a hemisphere and a cylinder stand on the same base and have
height equal to the radius of the base, find out the ratio of their volumes.
A . 1: 3: 2
B. 2:3:
c. 3: 2:
D. 1::::


Assertion
The \( S-S-S- \) bond angle in \( S_{8} \)
molecule is \( 107.8^{\circ} \)
Reason
\( S_{8} \) has a \( V \) -shape.
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 of the following has \( n s^{2} n p^{6} n d^{10} \) \( (n+1) s^{0} \) configuration?
A. \( P d \)
в. \( A g^{+} \)
c. \( C d^{+2} \)
D. All of the above


Let \( * \) be \( a \) binary operation on \( N \) given by \( a * b=H C F *(a, b) \) find \( 22 * 4 \)


Of the following statements, the one
that is incorrect is:
A. Doubling the length of a given rectangle doubles the area.
B. Doubling the altitude of a triangle doubles the area.
C. Doubling the radius of a given circle doubles the area.
D. Doubling the divisor of a fraction and dividing its numerator by 2 changes the quotient.


\( 25.0 \mathrm{cm}^{3} \) of \( 0.0497 \mathrm{M} \) solution of
\( N H_{2} O H \) was boiled with excess of
ferric alum solutuion in \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \). The
\( \mathrm{Fe}(\|) \) formed rquired \( 24.7 \mathrm{cm}^{3} \) of 0.1007
\( \left.N K_{2} C r_{2}\right)_{7} \) solution. Identify the
product formed by oxidation of
\( N H_{2} O H \)
A \( \cdot N_{2} O_{4} \)
в. \( N_{2} \) О
\( \mathrm{c} \cdot \mathrm{N}_{2} \mathrm{O}_{2} \)
D. \( N O \)


Consider occurance of the halogen family in the periodic table and choose
true statements.

Statement I. Fluorine is the most active
nonmetallic element in the periodic
table

Statement II. As you move down the family the state of the halogens is from a solid to a gaseous state. Statement III. By filling the outermost d orbital, the halogen elements can be converted to ions.
A. I and III
B. II only
c. I and ॥
D. I only
E. Il and III


How many angles in the given figure are less than a right angle?
\( k \)
A .2
B. 3
\( c \cdot 4 \)
D. 5


\( O_{3}(g) \) is a powerful oxidising agent. The given equations,
\( \boldsymbol{S}+\mathbf{3} \boldsymbol{O}_{3}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}+\boldsymbol{3} \boldsymbol{O}_{2} \)
represent oxidation of \( S \) in the
presence of moisture to \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)


State which of the following variables are continuous and which are discrete:
a)number of children in your class
b) distance traveled by a car
c) sizes of shoes
d) time
e) number of patients in a hospital


Which one will liberate \( B r_{2} \) from \( K B r ? \)
A \( \cdot I_{2} \)
в. \( S O_{2} \)
c. \( H I \)
D. \( C l_{2} \)


Which of these is mismatched?
A. Phaneros -Visible
B. Kryptos -Concealed
c. Gymno - Naked
D. Bryon-Liverworts
E. Trachea - windpipe


Catalytic converter used for controlling pollution is used in
A. Thermal plants
B. Chimneys
c. Brick kilns
D. Motor vehicles


The actinoids which shows +7 oxidation
state are:
A. U, NP
B. Pu, Am
c. Np, Pu
D. \( A m, C m \)


Light year is a unit of
A. time
B. speedd
c. distance
D. none of these


During lactic acid fermentation
A. \( O_{2} \) is used and \( C O_{2} \) is liberated
B. Neither \( O_{2} \) is used, nor \( C O_{2} \) is liberated
\( \mathrm{c} \cdot O_{2} \) is used, but \( C O_{2} \) is not liberated
D. None of the above


\( \ln N a F \) or \( M g F_{3}, \) which is formed more
easily?
\( \mathbf{A} \cdot M g F_{3} \)
в. NaF
c. Both are easily formed
D. Can't say


(where \( P \) is the pressure and \( T \) is the
temperature) for two solvents \( \boldsymbol{X} \) and \( \boldsymbol{Y} \)
and isomolal solutions of \( N a C l \) in
these solvents. Na Cl completely
dissociates in both the solvents.
On addition of an equal number of
moles a non-volatile solute \( S \) is equal
amount (in kg) of these solvents, the
elevation of the boiling point of solvent
\( X \) is three times that of solvent \( Y \)
Solute \( S \) is known to undergo dimerization in these solvents. If the
degree of dimerization is 0.7 in solvent
\( Y, \) the degree of dimerization in solvent
\( \boldsymbol{X} \) is:


If \( \mathbf{W}_{1}, \mathbf{W}_{2} \) and \( \mathbf{W}_{3} \) represent the work
done in moving a particle from \( A \) to \( B \) along three different paths 1,2 and 3 respectively (as shown) in the
gravitational field of a point mass \( \mathbf{m} \)
find the correct relation between
\( \mathbf{W}_{1}, \mathbf{W}_{2} \) and \( \mathbf{W}_{3} \)
A. \( \mathrm{W}_{1}>\mathrm{W}_{2}>\mathrm{W}_{3} \)
B. \( \mathrm{W}_{1}=\mathrm{W}_{2}=\mathrm{W}_{3} \)
c. \( \mathrm{w}_{1}<\mathrm{W}_{2}<\mathrm{W}_{3} \)
D. \( \mathrm{W}_{2}>\mathrm{W}_{1}>\mathrm{W}_{3} \)


An electron is moving in 4 th orbit and its de-Broglie wavelength is \( \lambda \). What is the circumference of the fourth orbit?
\( A \cdot 2 / \lambda \)
B. \( 2 \lambda \)
c. \( 4 \lambda \)
D. \( 4 / \lambda \)


Imagine a new planet having the same density as that of the earth but it is 3 times bigger than the earth is size. If
the acceleration due to gravity on the surface of the earth is \( g \) and that on the
new planet is \( g^{\prime} \), then what is the value of g'lg?
\( A \cdot 3 \)
B. 4
\( c \cdot 5 \)
D. 6


If \( a, b, c, d \) are non-negative real numbers where \( a+b+c+d=1, \) then
the maximum value of \( a b+b c+c d+ \)
\( a d \) is
A \( \cdot \frac{1}{4} \)
B. 3
\( c \cdot 4 \)
D. none of these


Generally, polyamides are
A. fiberes
B. thermoplatics
c. thermosetting
D. elastomeres


Two parallel beams of positron moving
in the same direction will :
A. not interact with each other
B. repel each other
c. attract each other
D. be deflected normal to the plane containing the two beams


Which of the following \( \beta \) -keto carboxylic acid does not undergo decarboxylation on heating?
\( A \)
в.
\( c \)
D. None of these


Match the following:
A) \( 1.008 \mathrm{g} \)
2
1) 0.1 gram atom 8 gof \( \boldsymbol{H}_{2} \) What is
\( \mathrm{B}) \)
\( C) \)
\( \begin{array}{ll}245 \mathrm{g} \text { of } \mathrm{KClO}_{3} & \text { 2) } 22.4 \mathrm{L} \text { at S.T.P } \\ 71 \mathrm{g} \text { of } \mathrm{Cl}_{2} & \text { 3) } 12.046 \times 10^{23} \\ & \text { 4) } 3.0115 \times 10^{23} \\ \text { 10.8 grams of Ag } & \text { (i) }\end{array} \)
D)
\( A \cdot A-4, B-3, C-2, D-1 \)
B. \( A-2, B-3, C-4, D-1 \)
\( C \cdot A-1, B-2, C-3, D-4 \)
D. \( A-3, B-2, C-4, D-1 \)


Which of the following molecule have zero dipole moment?
\( (a) C_{6} H_{6}(b) X e F_{2} \)
\( (c) S O_{2} \)
\( (d) S F_{4}(e) \)
\( \boldsymbol{S} \boldsymbol{F}_{\boldsymbol{6}} \)
\( A \cdot(b) \) and \( (d) \)
B. (a), (b) and (e)
c. (a) and (e)
D. (c) and (d)


Which one of these is a real life
application of the third law of motion?
A. Working of pulleys
B. Use of airbags in cars for safety
C. Helicopters creating lift by pushing air down
D. Cricketers pulling their hands down while taking a catch


While travelling back to his residence in the car, Dr. Pathak was caught up in a thunderstorm. It became very dark. He stopped driving the car and waited for thunderstorm to stop. Suddenly he noticed a child walking alone on the road. He asked the boy to come inside the car till the thunderstorm stopped.
Dr. Pathak dropped the boy at his residence. The boy insisted that Dr. Pathak should meet his parents. The parents expressed their gratitude to Dr. Pathak for his concern for safety of the child.

Answer the following questions based on the above information:
(a) Why is it safer to sit inside a car during a thunderstorm?
(b) Which two values are displayed by
Dr. Pathak in his action?
(c) Which values are reflected in
parents' response to Dr. Pathak?
(d) Give an example of similar action on your part from your everyday life?


\( " P C l_{3} \) has a tetrahedral structure."
Answer whether the above statement is
true or false.
If true enter 1 , else enter 0 .


Chromium metal can be plated out from an acidic solution containing \( \boldsymbol{C r} \boldsymbol{O}_{3} \) according to the following equation.
\[
\begin{array}{c}
\boldsymbol{C r} \boldsymbol{O}_{3}(\boldsymbol{a q})+\boldsymbol{6} \boldsymbol{H}^{+}+\boldsymbol{6} \boldsymbol{e}^{-} \rightarrow \\
\boldsymbol{C r}(\boldsymbol{s})+\boldsymbol{3} \boldsymbol{H}_{2} \boldsymbol{O}
\end{array}
\]
How many grams of chromium will be plated out by 24000 coulombs?
A. \( 0.78 g \)
B. \( 0.45 g \)
c. \( 1.2 g \)
D. None of these


Draw the schematic diagram of an electric circuit consisting of a battery of two cells of \( 1.5 \mathrm{V} \) each, three resistance
of 5 ohm, 10 ohm and 15 ohm
respectively and a plug key all connected in series.


Which of the above two graphs (a) and
(b) representing the human voice is
likely to be the male voice ? Give a
reason for your answer.
\( A \)
B. B
\( c \cdot c \)
\( D \)


Find the cube of \( 3 a-2 b \)
B . \( a^{3}-54 a^{2} b+6 a b^{2}-b^{3} \)
\( \mathbf{c} \cdot 27 a^{3}-54 a^{2} b+6 a b^{2}-8 b^{3} \)
D. \( a^{3}-54 a^{2} b-36 a b^{2}-8 b^{3} \)


A \( 5 ~ k g \) stone falls from a height of
\( 1000 m \) and penetrates \( 2 m \) in a layer of
sand. The time of penetration is
A . 14.285 s
B. 0.0285 s
c. \( 7.146 \mathrm{s} \)
D. 0.285 s


\( A B=6.3 \mathrm{cm}, \mathrm{EC}=11.0 \mathrm{cm}, \mathrm{AD}=0.8 \mathrm{cm} \) and
\( A E=1.6 \mathrm{cm} \)
Enter 1 if true or 0 if false.


The function 'g' defined by \( g(x)= \) \( \sin \alpha+\cos \alpha-1 \) where \( \alpha= \)
\( \sin ^{-1} \sqrt{\{x\}} \) is (where \{\} denotes
fractional part function)


Chemical changes are
A. temporary, reversible and a new substance is produced
B. always accompanied by exchange of light
C . permanent, irreversible and a new substance is produced
D. never accompanied by exchange of light and heat energy


What will happen to two soap bubbles of
different radii which are in contact with
each other?


The total pressure or a mixture of
oxygen and hydrogen is 1.0 atm. The mixture is ignited and the water is removed. The remaining gas is pure hydrogen and exerts a pressure of 0.40 when measured at the same values of \( T \)
and \( \mathrm{V} \) as the original mixture. What was
the composition of the original mixture in mole per cent?
A \( \cdot x_{O_{2}}=0.2 ; x_{H_{2}}=0.8 \)
в. \( x_{0}_{0}=0.4 ; x_{H_{2}}=0.6 \)
c. \( x_{o_{2}}=0.6 ; x_{H_{2}}=0.4 \)
D. \( x_{O_{2}}=0.8 ; x_{H_{2}}=0.2 \)


If \( f(x)=x \cdot\left(\frac{a^{1 / x}-a^{-1 / x}}{a^{1 / x}+a^{-1 / x}}\right), x \neq \)
\( \mathbf{0}(\boldsymbol{a}>\mathbf{0},) \boldsymbol{f}(\mathbf{0})=\mathbf{0} \) then
A . fis differentiable at \( x=0 \)
B. fis not differentiable at \( x=0 \)
c. \( f \) is not continuous at \( x=0 \)
D. None of these


Evaluate the integral \( \int_{1}^{2}\left(\frac{1}{x}-\frac{1}{2 x^{2}}\right) e^{2 x} d x \) using
substitution.


Which square must be shaded so that
the figure has a line of symmetry?
\begin{tabular}{|l|l|l|l|}
\hline & & & \\
\hline & \( \mathbf{R} \) & & \\
\hline & \( \mathbf{P} \) & & \( \mathbf{Q} \) \\
\hline & & & \( \mathbf{S} \) \\
\hline
\end{tabular}
\( A \cdot P \)
в. \( Q \)
\( c . R \)
D.


Caterpillar changes into a pupa inside
nest.
A . True
B. False


The chyle contains
A. Proteins, starch, fats.
B. Peptones, starches, fats and HCI.
C. Amino acids, HCl, fats and starch.
D. Sugars, fatty acids, glycerol and amino acids.


Given \( f^{2}(x)+g^{2}(x)+h^{2}(x) \leq 9 \) and
\( \boldsymbol{U}(\boldsymbol{x})=\boldsymbol{3} \boldsymbol{f}(\boldsymbol{x})+\mathbf{4} \boldsymbol{g}(\boldsymbol{x})+\mathbf{1 0 h}(\boldsymbol{x}), \) where
\( f(x) \cdot g(x) \) and \( h(x) \) are continuous \( \forall x \in \)
R. If maximum value of \( U(x) \) is \( \sqrt{N} \)
Then find \( N \)


Find the inclination of the line whose
slope is \( \frac{\mathbf{1}}{\sqrt{\mathbf{3}}} \)


Two molecules collide and a reaction
not occur. Which of the following is not a
valid explanation for this?
A. The molecules were not in the proper states of matter.
B. The molecules did not have enough kinetic energy.
C. The molecules were not oriented correctly when they struck each other
D. The temperature of the reaction mixture was not high enough.


f \( \boldsymbol{P Q} \| \boldsymbol{S T}, \angle \boldsymbol{P Q R}=\mathbf{1 1 0}^{\boldsymbol{o}} \) and
\( \angle R S T=130^{\circ}, \) find \( \angle Q R S(\text { Indegrees }) \)


What happens when steam is passed
over red hot carbon?
A. \( C O_{2}+H_{2} \) are formed
B. \( C O+H_{2} \) are formed
c. \( H_{2}+O_{2}+ \) steam are formed
D. None of the above


Calculate the change in enthalpy for the
following process at 1 atm \( \boldsymbol{H}_{2} \boldsymbol{O}\left(\boldsymbol{l}, \mathbf{5} \boldsymbol{0}^{o} \boldsymbol{C}\right) \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}\left(\boldsymbol{g}, \mathbf{1 5 0}^{\boldsymbol{o}} \boldsymbol{C}\right) \)
given that \( \Delta H_{v} \) at \( 100^{\circ} \mathrm{C} \) is
\( 40.7 k J m o l^{-1} \)
\( C_{P}\left(H_{2} O, l\right)=75.0 J m o l^{-1} K^{-1} \)
\( \boldsymbol{C}_{\boldsymbol{P}}\left(\boldsymbol{H}_{2} \boldsymbol{O}, \boldsymbol{g}\right)=\mathbf{3 3} . \boldsymbol{3} \boldsymbol{J} \boldsymbol{m o l}^{-1} \boldsymbol{K}^{-1} \)
A \( .64 .8 K J \)
в. \( 52.5 K J \)
c. \( 48.6 K J \)
D. \( 46.1 K J \)


receives oxygenated blood from the lungs.
A. Right auricle
B. Right ventricle
c. Left auricle
D. Left ventricle


A polished metal plate with a rough black spot on it is heated to about \( 1400 K \) and quickly taken into a dark
room. Then
A. The spotwill appear brighter than the plate
B. The spot will appear darker than the plate
c. Heat conduction is easier downward
D. It is easier and more convenient to do so


The coefficient of range of the following distribution 10,14,11,9,8,12,6
A . 0.4
B . 2.
c. 8
D. 0.9


The water stored in the dam on a river
has
A. Kinetic energy
B. Potential energy
c. Electrical energy
D. Biomass energy


Drinking mineral water/aerated drink with low levels \( (\sim 0.02 \) ppm ) of pesticide for long period would
A. Cause cancer of intestine
B. Pesticide accumulation in the body
c. Cause leukaemia
D. Produce immunity against mosquito


Identify the part which vibrates to
produce sound in the following instruments:
(a) Dholak
(b) Sitar
(c) Flute


\( \boldsymbol{F} \boldsymbol{e} \boldsymbol{C l}_{3} \) on reaction with \( \boldsymbol{K}_{\boldsymbol{4}}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right] \)
in aqueous solution gives blue colour. These are separated by a
semipermeable membrane \( A B \) as
shown. Due to osmosis there is:
A. blue colour formation in side \( X \)
B. blue colour formation in side \( Y \).
c. blue colour formation in both of the sides \( X \) and \( Y \).
D. no blue colour formation


Number of moles of MeMgBr consumed
in the above reaction is :
\( A \)
B.
\( c \)
\( D \)


A plant which does not have roots is?
A . Utricularia
B. Nelumbo
c. Trapa
D. Avicennia


When negatively charged colloid like
\( A s_{2} S_{3} \) sol is added to positively
charged \( F e(O H)_{3} \) sol in suitable
amounts, then :

This question has multiple correct options
A. both the sols are precipitated simultaneously
B. this process is called mutual coagulation
c. they becomes positively charged colloid
D. they become negatively charged colloid


A larger number of oxidation states are exhibited by the actinides than those by the lanthanides.
The main reason being:
A. more reactive nature of the actinides than the lanthanides
B. \( 4 f \) orbitals are more diffused than the \( 5 f \) orbital
c. lesser energy difference between \( 5 f \) and \( 6 d \) orbitals than between \( 4 f \) and \( 5 d \) orbital
D. more energy difference between \( 5 f \) and \( 6 d \) orbitals than between \( 4 f \) and \( 5 d \) orbitals


In Young's double slit experiment two coherent sources of intensity ratio of
64: 1 produce interference fringes.
Calculate the ratio of maximum and
minimum intensities.


Displacement time equation of a
particle executing SHM is \( \boldsymbol{x}= \) \( 10 \sin \left(\frac{\pi}{3} t+\frac{\pi}{6}\right) c m . \) The distance
covered by particle in 3 seconds is
A. \( 5 \mathrm{cm} \)
B. 20 cm
c. \( 10 \mathrm{cm} \)
D. \( 15 \mathrm{cm} \)


Which one of the following species has maximum conductance in their
aqueous solutions?
A \( \cdot K_{2} P t C l_{6} \)
в. \( P t C l_{4} \cdot 2 N H_{3} \)
c. \( P t C l_{4} \cdot 3 N H_{3} \)
D. \( P t C l_{4} \cdot 5 N H_{3} \)


Classify the numbers are rational or irrational
¡) \( 2-\sqrt{3} \)
ii) \( (3+\sqrt{2})-\sqrt{23} \)
iii) \( \frac{2 \sqrt{2}}{7 \sqrt{7}} \)


Electrophile \( \oplus N O_{2} \) attacks the following: In which cases \( \oplus N O_{2} \) will attack at meta position.
(l)
(ll)
(III)
(lV)
A. Il and IV
c. ॥ and ।
D. I only


A Particle \( A \) having a charge of \( 5 \cdot 0 x \)
\( 10^{-7} C \) is fixed in a vertical wall. \( A \)
second particle \( B \) of mass \( 100 g \) and having equal charge is suspended by a silk thread of length \( 30 \mathrm{cm} \) from the
wall. The point of suspension is \( 30 \mathrm{cm} \)
above the particle \( A \). Find the angle of the thread with the vertical when it
stays in equilibrium.


A bullet of mass \( 40 g \) is fired from a gun
of mass \( 10 \mathrm{kg} \). If velocity of bullet is \( 400 m / s, \) then the recoil velocity of the gun will be
A. \( 1.6 \mathrm{m} / \mathrm{s} \) in the direction of the bullet
B. \( 1.6 \mathrm{m} / \mathrm{s} \) opposite to the direction of the bullet
c. \( 1.8 m / s \) in the direction of the bullet
D. \( 1.8 \mathrm{m} / \mathrm{s} \) opposite to the direction of the bullet


0.43 is rational and it can be written as
A \( \cdot \frac{43}{100} \)
в. \( \frac{43}{10} \)
\( c \cdot \frac{4}{3} \)
D. \( \frac{34}{10} \)


Calculate the solubility of \( A g C N \) in a
buffer solution of \( \boldsymbol{p} \boldsymbol{H}=\mathbf{3}, \boldsymbol{K}_{s p} \) of
\( A g C N=1.2 \times 10^{-15} \) and \( K a \) of
\( \boldsymbol{H C N}=\mathbf{4 . 8} \times \mathbf{1 0}^{-\mathbf{1 0}} \)
A \( \cdot 4 \times 10^{-5} M \)
В. \( 4.5 \times 10^{-6} M \)
c. \( 5 \times 10^{-5} M \)
D. \( 5.5 \times 10^{-3} M \)


If \( \log _{e}\left(\frac{1}{\left(1+x+x^{2}+x^{3}\right)}\right) \) be
expanded in a series of ascending
powers of \( \boldsymbol{x} \) the coefficient of \( x^{n} \) is \( -\frac{b}{n} \) if \( n \) be odd or of the form \( 4 m+2 \) and \( \frac{a}{n} \) if \( n \) be of the
form \( 4 m . \) Find the value of \( a+b^{2} \)


The current in the shown circuit is found to be \( 4 \sin \left(314 t-\frac{\pi}{4}\right) A \). Find the value of inductance


What is molar conductivity? How is it
related to the concentration of
electrolyte?


The motion of a particle executing SHM is given by \( \boldsymbol{x}=\mathbf{0 . 0 1} \sin 100 \pi(\boldsymbol{t}+\mathbf{0 . 0 5}) \)
where \( x \) is in metre and \( t \) in second. The
time period of motion(in second) is:
A . 0.01
B. 0.02
c. \( 0 . \)
D. 0.2


A block of mass of a 2 kg with
dimensions \( 5 c m \times 20 c m \times 10 c m \)
respectively. The ratio of maximum to
minimum pressure it exerts on the change in orientation is :
A . 1:
B. 1: 2
\( c \cdot 1: 4 \)
D. 4: 1


The least value of \( \frac{1}{2}+\frac{2}{3} \operatorname{cosec}^{2} \theta+ \)
\( \frac{3}{8} \sec ^{2} \theta \) is
A \( \cdot \frac{13}{24} \)
в. \( \frac{61}{48} \)
c. \( \frac{61}{25} \)
D. \( \frac{61}{24} \)


In a culture, the bacteria count is \( 1,00,000 . \) The number is increased by \( 10 \% \) in 2 hours. In how many hours will
the count reach \( 2,00,000, \) if the rate of growth of bacteria is proportional to the
number present?


In the circuit shown here, the cell is
ideal with emf of 2 volt. Then
This question has multiple correct options
A. no current flows in the galvanometer
B. a current of \( 0.2 A \) flows through galvanometer
c. potential difference across \( C_{1} \) is \( 1.2 V \)
D. potential difference across \( C_{2} \) is \( 1.0 \% \).


Soft iron is used for the construction of
electromagnets because for iron
A. the area of hysteresis loops is more
B. coersive force is high.
C. retentivity is high
D. magnetic saturation limits is high and coercivity is low


A Ge specimen is doped with Al. The
concentration of acceptor atom is \( \sim \)
\( 10^{21} \) atoms \( / m^{3} . \) Given that the intrinsic
concentration of electron hole pairs is \( \sim 10^{19} / m^{3} . \) The concentration of
electrons in the specimen is??
\( \mathbf{A} \cdot 10^{17} / m^{3} \)
B . \( 10^{15} / m^{3} \)
c. \( 10^{4} / m^{3} \)
D. \( 10^{2} / m^{3} \)


If \( x \) is very large, then \( \frac{2 x}{1+x} \) is
A. close to 0
B. arbitrarily large
c. lie between 2 and 3
D. close to 2


A circuit consists of three batteries of
\( \operatorname{emf} \boldsymbol{E}_{1}=\mathbf{1} \boldsymbol{V}, \boldsymbol{E}_{2}=\mathbf{2} \boldsymbol{V} \) and \( \boldsymbol{E}_{3}=\mathbf{3} \boldsymbol{V} \)
and internal resistances \( 1 \Omega, 2 \Omega \) and
1 \( \Omega \) respectively which are connected in parallel as shown in the figure. The
potential difference between points \( \boldsymbol{P} \)
and \( Q \) is:
A \( .1 .0 V \)
B. \( 2.0 V \)
c. \( 2.2 V \)
D. 3.0 \( V \)


Which of the following statement is wrong?
A. The stability of hydrides increases from \( N H_{3} \) to \( B i H_{3} \) in group 15 of the periodic table
B. Nitrogen cannot form \( d \pi-p \pi \) bond
c. single \( N-N \) bond is weaker than the single \( P-P \)
bond
D. \( N_{2} O_{4} \) has two resonance structures


A vessel containing 9 litres of an ideal gas at \( 760 \mathrm{mm} \) pressure is connected to an evacuated 9 litre vessel. The resultant
pressure is
\( A \cdot 380 \mathrm{mm} \)
B. 760 mm
c. \( 190 \mathrm{mm} \)
D. 1140 mm


\( \boldsymbol{F} \boldsymbol{e}_{\boldsymbol{x}} \boldsymbol{O}_{3}(\boldsymbol{s})+\boldsymbol{2} \boldsymbol{A} \boldsymbol{l}(\boldsymbol{s}) \rightarrow \boldsymbol{2} \boldsymbol{F} \boldsymbol{e}(\boldsymbol{l})+ \)
\( \boldsymbol{A l}_{2} \boldsymbol{O}_{\boldsymbol{y}}(\boldsymbol{s})+\boldsymbol{H} \boldsymbol{e} \boldsymbol{a} \boldsymbol{t} \)
Find the value of \( x \) and \( y \)
A. \( x=2, y=3 \)
в. \( x=3, y=2 \)
c. \( x=2, y=2 \)
D. \( x=3, y=3 \)


Which of the following is/are true for
Thomson's model of atom?
This question has multiple correct options
A. The radius of an electron can be calculated by using this model
B. In an undisturbed atom, the electron will be at their equilibrium position within the sphere
C. The cloud of positive charge and the electrons balances their mutual charge
D. None of the above


Which of the following is found only RNA and not in DNA?
A. Adenine
B. Thymine
c. Guanine
D. Uracil


ff both \( (x-2) \) and \( \left(x-\frac{1}{2}\right) \) are factors of \( p x^{2}+5 x+r, \) show that \( p=r \)


Assertion:
\( \bar{M}_{n} \) value is always greater than \( \bar{M}_{w} \) value for synthetic polymers.
Reason:
The mass average molecular weight of the polymer is equal to \( \bar{M}_{w} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


The organisms dwelling at the bottom of a lake are called
A. Phytoplanktons
B. Zooplanktons
c. Nektons
D. Benthos


Select the correct option for the graph
above.
\( A \cdot T_{1}>T_{2}>T_{3} \)
в. \( T_{1}=T_{2}=T_{3} \)
c. \( T_{1}<T_{2}<T_{3} \)
\( . T_{1}>T_{2}<T_{3} \)


The range of the data 7,9,7,5,9,9,18,6,8,9
is:
A. 7
B. 8
\( c \cdot 9 \)
D. 13


If in any plant, pith is absent, xylem surrounds the phloem or phloem surrounds the xylem. It is called as
A. Radial
B. Conjoint
c. collateral
D. concentric


The sum of the series \( 10-5+2.5 \)
\( 1.25 \ldots . . \) is called
A . finite geometric sequence
B. finite arithmetic sequence
C. infinite geometric sequence
D. infinite harmonic sequence


Two candidates attempt to solve a
quadratic equation of the \( a x^{2}+b x+ \)
\( c=0 \) One starts with a wrong value of \( b \)
and find the roots to be 2 and 6 . The
other starts with the wrong values of \( c \)
and find the roots to be \( +2,-9 . \) The correct roots of the equation are


Helium gas is used in observatory
balloon.
A . True
B. False


In figure,the cube is \( 40.0 \mathrm{cm} \) on each
edge.Four straight segments of wire \( a b, b c, c d \) and \( d a \) form a closed loop that
carries a current \( \mathrm{I}=5.00 \mathrm{A}, \) in the
direction shown.A uniform magnetic
field of magnitude \( B=0.020 \mathrm{T} \) is in the
positive y-direction.Determine the magnitude and direction of the
magnetic force on each segment


Cellulose is straight-chain
polysaccharide compound of only:
A. D-Glucose units joined by \( \alpha \) -glycosidic linkage
B. D-Glucose units joined by \( \beta \) -glycosidic linkage
C. D-Galactose units joined by \( \alpha \) -glycosidic linkage
D. D-Galactose units joined by \( \beta \) -glycosidic linkage


Which of the following solution of \( N a C l \) has the higher specific conductance?
A. \( 1 N \)
B. \( 0.01 N \)
\( c \cdot 0.1 N \)
D. \( 0.001 N \)


A particle is projected upwards. The times corresponding to height \( h \) while
ascending and while descending are \( t_{1} \)
and \( t_{2} \) respectively. The velocity of
projection will be
A \( \cdot g t \)
B. \( g t_{2} \)
c. \( g t\left(t_{1}+t_{2}\right) \)
D. \( \frac{g\left(t_{1}+t_{2}\right)}{2} \)


At a given place where acceleration due
to gravity is \( g m / s e c^{2}, \) a sphere of lead
of density \( d k g / m^{3} \) is gently released in
a column of liquid of density \( \rho k g / m^{3} . \). \( \boldsymbol{d}>\boldsymbol{\rho}, \) then immediately after the
sphere is released inside the liquid,
¡t will:
A . fall vertically with an acceleration of \( g \) m/ sec\( ^{2} \)
B. fall vertically with no acceleration
c. fall vertically with an acceleration \( g\left(\frac{d-\rho}{d}\right) \)
D. fall vertically with an acceleration \( (g \rho) / d \)


The high concentration of uric acid in the blood will eventually lead to
A. Arthritis
B. Rheumatism
c. Gout
D. Rheumatic heart


Arrange the following \( (\mathbf{w}, \mathbf{x}, \mathbf{y}, \mathbf{z}, \mathbf{)} \) in
decreasing order of their boiling points:
\( \mathbf{A} \cdot w>x>z>y \)
в. \( w>x>y>z \)
с. \( w>z>y>x \)
D. \( w>z>x>y \)


Can we use a screen coated with
barium platinocyanide in a cathode ray
tube? If so what effects do we observe
on the screen?


A constant torque of \( 1000 N \) m turns a wheel of moment of inertia \( 200 k g m^{2} \) about an axis through its centre. The wheel is at rest initially. Its angular velocity after \( 3 s \) is :
A \( \cdot 15 \) rads\( ^{-1} \)
B. 0.6 rads\( ^{-1} \)
c. 6000 rads\( ^{-1} \)
D. 5 rads\( ^{-1} \)


Write the scientific name of human
being.


f \( p \) and \( q \) are positive then the roots of the equation \( x^{2}-p x-q=0 \) are
A. imaginary
B. real \& both positive
c. real \& both negative
D. real \& of opposite sign


The Young's modulus for steel is \( Y= \) \( 2 \times 10^{11} N / m^{2} . \) If the inter-atomic
distance is \( 3.2 A \) the inter atomic force
constant in N/A will be
A \( .6 .4 \times 10^{9} \)
B. \( 6.4 \times 10^{-9} \)
c. \( 3.2 \times 10^{9} \)
D. \( 3.2 \times 10^{-9} \)


How do you account for the larger size of lanthanum than hafnium though they are successive elements?


If \( \sin x+i \cos 2 x, \cos x-i \sin 2 x \) are
conjugate to each other, then \( \mathbf{x}= \)
\( \mathbf{A} \cdot n \pi \)
B. \( (n+1) \frac{\pi}{2} \)
\( c \cdot \phi \)
D. \( (n+1) \pi \)


A particle is moving along a circle with uniform speed. The physical quantity which is constant both in magnitude and direction, is
A. velocity
B. centripetal acceleration
c. centripetal force
D. angular velocity


Which of the following statement is incorrect?
A. All algae are microscopic.
B. All algae are thalloid in nature.
C. Algae are most primitive plants.
D. Algae possess both unicellular and multicellular eukaryotes.


If the concentration of reactants is
increased by 'X', the rate constant \( \mathrm{K} \) becomes:
\( \mathbf{A} \cdot e^{\left(\frac{K}{X}\right)} \)
B . \( \frac{K}{X} \)
c. \( K \)
D. \( \frac{x}{K} \)


\( |\vec{a}+\vec{b}|^{2}-|\vec{a}-\vec{b}|^{2} \) is equal to
A . \( 4 \vec{a} . \vec{b} \)
B.
c. \( 4|\vec{a} \cdot \vec{b}| \)
D. None of these


\( \boldsymbol{C H}_{3} \boldsymbol{C H O H C H}_{2} \boldsymbol{C H O H C H}_{3} \)


Which of the following is different from
the rest?
A. bar
B. torr
c. kg-wt
D. Pa


(a) What is the structure of an optical
fiber?
(b) What is the principle used for transmitting audio and video signals using optical fiber? Explain the principle.


The strength of bonds by \( 2 s-2 s, 2 p- \)
\( 2 p, 2 s-2 p, 1 s-1 s \) overlap has the
order:
A. \( 1 s-1 s>2 s-2 s>2 s-2 p>2 p-2 p \)
В. \( 2 p-2 p>2 s-2 p>2 s-2 s>1 s-1 s \)
c. \( 2 s-2 s>1 s-1 s>2 s-2 p>2 p-2 p \)
D. \( 2 s-2 p>2 s-2 s>2 p-2 p>1 s-1 s \)


Insulin contains \( 3.4 \% \) sulphur by mass. What will be minimum molecular
weight of insulin?
A . 94.117
в. 1884
c. 941
D. 976


Solve:
\( \int_{1}^{2} \frac{2}{x} d x \)


Construct a triangle similar to a given triangle \( A B C \) with its side equal to \( \frac{5}{3} \) of
corresponding side of triangle \( \boldsymbol{A B C} \) (i.e., of scale factor \( \frac{5}{3} \) ).


Write the length of the perpendicular drawn from the point \( P(3,5,12) \) on \( x \)
axis.


A die having six faces is tossed 80 times and the data is as below:
outcome
\[
\begin{array}{ccc}
3 & 4 \\
& \\
& \\
& \\
10 & 28
\end{array}
\]
Frequency
\( \begin{array}{ll}20 & 0 \\ 0 & 10 \\ 2 & 0\end{array} \)
Find \( P(1) \)
A. 0.175
в. 0.135
\( c \cdot 0.145 \)
D. 0.125


The number of radial nodes in 3p orbital
is :


The value of \( \frac{-18 \times 5}{3 \times(-10)} \) is
A. 3
B. 6
\( c \cdot 4 \)
\( D \cdot-3 \)


Which is used as an anaesthetic during
surgery?
A. Chloroquine
B. Thyroxine
c. Halothane
D. chloramphenicol


f the following ion is coloured enter 1
else enter 0
\( M n^{2+} \)


Given: \( \vec{a} \) and \( \vec{b} \) are unit vector, and \( \theta \) be
the angle between them. Then \( \frac{1-\vec{a} \cdot \vec{b}}{1+\vec{a} \cdot \vec{b}}= \)
A \( \cdot \sin ^{2} \frac{\theta}{2} \)
в. \( \cos ^{2} \frac{\theta}{2} \)
c. \( \tan ^{2} \frac{\theta}{2} \)
D. \( \cot ^{2} \frac{\theta}{2} \)


Ammonium hydroxide is found in:
A . lime water
B. window cleaner
c. soap
D. milk of magnesia


In steel, the Young's modulus and the strain at the breaking point are \( 2 \times \) \( 10^{11} N / m^{2} \) and 0.15 respectively. The
stress at the breaking point for steel is therefore:
A \( \cdot 1.33 \times 10^{11} \mathrm{Nm}^{-2} \)
В. \( 1.33 \times 10^{12} \mathrm{Nm}^{-2} \)
c. \( 7.5 \times 10^{-13} \mathrm{Nm}^{-2} \)
D. \( 3 \times 10^{10} \mathrm{Nm}^{-2} \)


A person \( 1.6 m \) tall is standing at the centre between two walls three metre
high. What is the minimum size of a plane mirror fixed on the wall in front of
him, if he is to see the full height of the
wall behind him?


1 mole aqueous solution of \( S O_{2} C l_{2} \) is
neutralised by :
This question has multiple correct options
A \( \cdot 2 \) mol of \( C a(O H)_{2} \)
B. 1 mol of \( C a(O H)_{2} \)
c. 2 mol of \( K O H \)
D. 4 mol of \( K O H \)


Equipotential surface associated with an electric field which is increasing in
magnitude along the y-direction, are
A. parallel to \( X Y \) plane
B. parallel to \( X Z \) plane
C. parallel to \( Y Z \) plane
D. coaxial cylinders of increasing radii around the the \( x \) axis


Which one of the following on oxidation gives a ketone?
A. Primary alcohol
B. Secondary alcohol
c. Tertiary alcohol
D. All of these


What is the equation of motion for the
rocket, if \( m \) is the mass of the rocket at
a given moment, \( \vec{w} \) is its acceleration, and \( \overrightarrow{\boldsymbol{F}} \) is the external force.
\( \mathbf{A} \cdot m \vec{w}=\vec{F}-2 \mu \vec{u} \)
в. \( m \vec{w}=\vec{F}+\mu \vec{u} \)
C \( . m \vec{w}=\vec{F}-3 \mu \vec{u} \)
D \( \cdot m \vec{w}=\vec{F}-\mu \vec{u} \)


What is the Cartesian product of \( \boldsymbol{A}= \)
\{1,2\} and \( B=\{a, b\} ? \)
A \( \cdot\{(1, a),(1, b),(2, a),(b, b)\} \)
B - \( \{(1,1),(2,2),(a, a),(b, b)\} \)
c. \( \{(1, a),(2, a),(1, b),(2, b)\} \)
D \cdot \( \{(1,1),(a, a),(2, a),(1, b)\} \)


A filler is a substance added to make a
material less expensive, or for:
A. Changing its acidity
B. Changing its physical properties
c. Reducing its chemical activity
D. Increasing its anti-rusting power


Evaluate the following:
\( \sin ^{-1}(\sin 2) \)


Excess of \( K I \) and dil. \( H_{2} S O_{4}, \) were
\( \operatorname{mixed} \operatorname{in} 50 \mathrm{ml} H_{2} O_{2} . \) The \( I_{2} \) liberated
required \( 20 \mathrm{ml} \) of \( 0.1 \mathrm{N} \mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{3} \). Find
out the strength of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) in \( \boldsymbol{g} / \boldsymbol{l} \boldsymbol{i} \boldsymbol{t}^{-1} \) ?
A. \( 0.17 g / \)lit
B. \( 0.34 g / \)lit
c. \( 0.68 g / l i t \)
D. \( 1.36 g / l i t \)


A hydrogen atom of mass ' \( m^{\prime} \) being at
rest, makes a transition from its first
excited state to ground state. As a
result a photon of wavelength \( ^{\prime} \lambda^{\prime} \) is
emitted and the hydrogen atom recoils.
If \( ^{\prime} \boldsymbol{E}_{0}^{\prime} \) is the ionization energy of \( \mathbf{a} \) hydrogen atom, the Planck's constant is \( h \) and \( c \) is the speed of light in vacuum,
the recoil speed is This question has multiple correct options
A \( \cdot \frac{3 E_{0}}{4 m_{c}} \)
в. \( \frac{3 E_{0}}{m c} \)
c. \( \frac{h}{2 m \lambda} \)
D. \( \frac{h}{m \lambda} \)


is a property that resists the flow of electrons in a conductor.
A. Capacitance
B. Inductance
c. Resistance
D. None of above


A convex glass lens is immersed in
water. Compared to the power in air, its power in water will :
A. increase
B. decrease
c. not change
D. decrease for red light and increase for violet light


Find the equation of the ellipse whose
vertices are \( (\pm \mathbf{5}, \mathbf{0}) \) and foci are
(±1,0)


If the valence electron configuration of this element is \( x s^{2} 6 f^{y} \) and \( 7 d^{z}, \) then find out the value of \( x, y \) and \( z \)
A. \( x=8, y=14, z=10 \)
B . \( x=7, y=12, z=10 \)
c. \( x=9, y=10, z=10 \)
D. None of the above


(a) How does an unpolarized light incident on a Polaroid get polarized? Describe briefly, with the help of a necessary diagram, the polarization of light by reflection form a transparent medium.
(b) Two polaroids \( ^{\prime} A^{\prime} \) and \( ^{\prime} B^{\prime} \) are kept in crossed position. How should a third
Polaroid ' \( C^{\prime} \) be placed between them so that the intensity of polarized light transmitted by Polaroid \( B \) reduces to 1/8th of the intensity of unpolarized light incident of \( \boldsymbol{A} \) ?


Let \( a, b \) and \( c \) be non-zero vectors such
that no two are collinear and \( (a \times b) \times \) \( c=\frac{1}{3}|b||c| a . \) If \( \theta \) is the acute angle
between the vectors b and \( c, \) then \( \sin \theta \)
equals
A \( \cdot \frac{2 \sqrt{2}}{3} \)
B. \( \frac{\sqrt{2}}{3} \)
\( c \cdot \frac{2}{3} \)
D.


Give examples of polynomials \( \boldsymbol{p}(\boldsymbol{x}), \boldsymbol{g}(\boldsymbol{x}), \boldsymbol{q}(\boldsymbol{x}) \) and \( \boldsymbol{r}(\boldsymbol{x}), \) which satisfy
the division algorithm and
(i) \( \operatorname{deg} p(x)=\operatorname{deg} q(x) \)
(ii) \( \operatorname{deg} \boldsymbol{q}(\boldsymbol{x})= \)
\( \operatorname{deg} r(x) \) (iii) \( \operatorname{deg} r(x)=0 \)


The earth's radius is \( \mathrm{R} \) and acceleration
due to gravity at its surface is g. If a
body of mass \( m \) is sent to a height \( h= \) \( \boldsymbol{R} \)
\( \frac{i}{5} \) from the earth's surface, the
potential energy increases by
A . mgh
в. \( \frac{4}{5} m g h \)
c. \( \frac{5}{6} \) mgh
D. \( \frac{6}{7} \) mgh


Plum pudding' model of an atom was proposed by:
A. C.V.Raman
B. N.Bohr
c. E.Rutherford
D. J.J.Thomson


Write electronic configurations of the elements with atomic number 17.


\( \operatorname{Let} y=\sec \left(\frac{\theta}{2}-1\right) \) then find \( \frac{d y}{d \theta} \)


The correct order of following
compounds for increasing reactivity
towards electrophilic substitution is:
B. \( \|I|<\|<|<\mid V \)
C. \( |<| V<|| \mid<\| \)
D. \( \|<\| 1<1<I V \)


For the decomposition,
\( N H_{2} C O O N H_{4}(s) \rightleftharpoons 2 N H_{3}(g)+ \)
\( \boldsymbol{C O}_{2}(\boldsymbol{g}) ; \boldsymbol{K}_{\boldsymbol{p}}=\boldsymbol{2} \cdot \boldsymbol{9} \times 10^{-5} \boldsymbol{a} \boldsymbol{t m}^{3} \)
The total pressure of gases at equilibrium when 1.0 mol of
\( N H_{2} C O O N H_{4}(s) \) was taken to start
with, would be :
A. 0.0194 atm
B. 0.0388 atm
c. 0.0582 atm
D. 0.0776 atm


When an electron makes a transition
from \( (n+1) \) state to \( n \) state, the
frequency of emitted radiations is related to n according to \( (n>>1) \)
\( A \cdot v \alpha n^{-3} \)
B. \( v \alpha n^{2} \)
c. \( v \alpha n^{3} \)
D. \( v \alpha \) n \( ^{\frac{2}{3}} \)


Which of the following products
predominates(major produt) in the
following reaction?
A. 2 -Chloronitrobenzene
B. 3 -Chloronitrobenzene
c. 4 -Chloronitrobenzene
\( D \cdot A, C \)


When \( H_{2} O_{2} \) reacts with chlorine, the
product obtained is:
\( A \cdot O_{2} \)
в. \( H_{2} \)
c. \( C l O_{2} \)
D. НОС l


Differentiate: \( \left(\sin ^{-1} x+\frac{1}{2} \log \frac{1+x}{1-x}\right) \)


For the principal value:
\( \sin ^{-1}\left(-\frac{1}{2}\right)+2 \cos ^{-1}\left(-\frac{\sqrt{3}}{2}\right) \)


Rhynia was discovered from
A. Rhynie chert valley
B. India
c. Pakistan
D. Bihar


Choose the correct answer from the
alternatives given Which of the following is not a secretion of the adrenal glands?
A. Glucocorticoids
B. Androgens
c. Melatonin
D. Aldosterone


Area of coming together of two neuron
ends or between a dendron and axon
ends is?
A. Junction
B. Synapsis
c. synapses
D. synapticula


\( A B C D \) is a parallelogram. \( L \) is a point on \( B C \) which divides \( B C \) in the ratio
\( \mathbf{1}: \mathbf{2} . \boldsymbol{A} \boldsymbol{L} \) intersects \( \boldsymbol{B} \boldsymbol{D} \) at \( \boldsymbol{P} . \boldsymbol{M} \) is a
point on \( D C \) which divides \( D C \) in the
ratio 1: 2 and \( A M \) intersects \( B D \) in \( Q \)
Point \( P \) divides \( A L \) in the ratio
A . 1: 2
B. 1: 3
c. 3: 1
D. 2: 1


Assertion: Smaller drops of liquid resist deforming forces better than the larger
drops

Reason: Excess pressure inside a drop is directly proportional to its surface
area.
A. If both assertion and reason are true but the reason is the correct explanation of assertion.
B. If both assertion and reason are true but the reason is not the correct explanation of assertion
c. If assertion is true but reason is false
D. If both the assertion and reason are false.
E . If reason is true but assertion is false


toppr
Q Type your question
heat changes in physical and chemical processes are measured with an instrument called Calorimeter. Heat
change in the process is calculated as \( \boldsymbol{q}=\boldsymbol{m} \boldsymbol{s} \boldsymbol{\Delta} \boldsymbol{T} \ldots \ldots \ldots \boldsymbol{s}=\boldsymbol{s} \boldsymbol{p} e c i f i \boldsymbol{c} \quad \boldsymbol{h} e \boldsymbol{a} \boldsymbol{t} \)
\( =c \Delta T_{\ldots \ldots . .} c=h e a t \quad \) capacity
Heat of reaction at constant volume is
measured using bomb Calorimeter.
\( \boldsymbol{q}_{V}=\boldsymbol{\Delta} \boldsymbol{U}= \)
internal energy change
Heat of reaction at constant pressure is measured using bomb Calorimeter.
\( \boldsymbol{q}_{\boldsymbol{P}}=\boldsymbol{\Delta} \boldsymbol{H} \)
\( \boldsymbol{q}_{\boldsymbol{P}}=\boldsymbol{q}_{\boldsymbol{V}}+\boldsymbol{P} \boldsymbol{\Delta} \boldsymbol{V} \)
\( \boldsymbol{\Delta} \boldsymbol{H}=\boldsymbol{\Delta} \boldsymbol{U}+\boldsymbol{\Delta} \boldsymbol{n} \boldsymbol{R} \)
The enthalpy of fusion of ice is
\( 6.02 k J m o l^{-1} . \) The heat capacity of
water is \( 4.18 J g^{-1} C^{-1} \)
What is the smallest number of ice
cubes at \( 0^{\circ} \mathrm{C} \), each containing one mole
of water, that is needed to cool \( 500 g \) of
liquid water from \( 20^{\circ} C \) to \( 0^{\circ} C \)
\( A \cdot 8 \)
B. 7
c. 140
D. 120


\( P \) in \( P C l_{5} \) has \( s p^{3} d \) hybridisation which of the following statement is wrong
about \( \boldsymbol{P C l}_{5} \) structure?
A. Two \( P-C l \) bonds are stronger and three \( P-C l \) bonds are weaker
B. Two \( P-C l \) bonds are axial and larger than three \( P \) Cl equatorial bonds
C . \( P C l_{5} \) has trigonal bipyramidal geometry with nonpolar nature
D. All of these


Which of the following statements are
not true?
This question has multiple correct options
A. Heat is a macroscopic physical property
B. Heat is an intrinsic property of a body
C. Heat is stored in a body as internal energy
D. Heat is path independent


A solid sphere of radius \( R_{1} \) and volume charge density \( \rho=\frac{\rho_{0}}{r} \) is enclosed by a
hollow sphere of radius \( R_{2} \) with
negative surface charge density \( \sigma \), such
that the total charge in the system is
zero, \( \rho_{0} \) is positive constant and \( r \) is the
distance from the centre of the sphere. The ratio \( \frac{R_{2}}{R_{1}} \) is
A \( \cdot \frac{\sigma}{\rho_{0}} \)
В. \( \sqrt{2 \sigma / \rho_{0}} \)
C \( \cdot \sqrt{\rho_{0} / 2 \sigma} \)
D. \( \frac{\rho_{0}}{\sigma} \)


Zoodiogamy takes place in
A. Lower gymnosperms
B. Higher gymnosperms
c. Angiosperms
D. All of the above


The angle of elevation of the top of a vertical tower from a point A due east of
it is \( 45^{\circ} . \) The angle of elevation of the top of the same tower from a point B due south of \( A \) is \( 30^{\circ} \) If the distance
between \( A \) and \( B \) is \( 54 \sqrt{2} m \),then the
height of the tower (in metres),is
A. \( 18 \sqrt{3} \)
is
B . 54
c. \( 27 \sqrt{2} \)
D. 108


Which has a greater momentum, an
elephant at rest or an ant in motion?
A. Elephant
B. Ant
c. Neither has momentum
D. Same


Which statement(s) is/are correct?
This question has multiple correct options
A. Physical adsorption is multilayer non-directional and non specific.
B. Chemical adsorption is generally monolayer and specific in nature
C. Physical adsorption is due to free valence of atoms.
D. Chemical adsorption is stronger than physical adsorption.


Thin layer chromatography is :
A. Partition chromatography
B. Electrical mobility of ionic species
c. Adsorption chromatography
D. None of the above


\( (+132) \div(-12) \)
A \( .+101 \)
в. -10
\( c \cdot+11 \)
D. -11


Which of the following forms gives
osazones different from the other three?
A . Fructose
B. Glucose
c. Galactose
D. Mannose


Mass of proton \( =1.00760 a m u, \) mass
of neutron \( =1.00899 a m u, \) mass of
deuterium nucleus \( =2.0147 a m u . \) Then
binding energy is :
в. \( 1.76 a m u \)
c. \( 1.76 M e V \)
D. \( 10^{15} \) joules


The density of water is \( 1 g m / c m^{3} . \) What is its value in SI units?


Which of the following is not an actinide
\( ? \)
A. Curium
B. Californium
c. Uranium
D. Terbium


Read the following four (A-D) statements:
(a) The cranial capacity of Homo habilis was \( 650-800 \) c.c
(b) The cranial capacity of Homo erectus was about \( 900 \mathrm{c.c} \)
(c) Around two mya Australopithecus probably lived in east african grasslands.
(d) During the ice age, Homo sapiens
arose.
How many of the above statements are
not incorrect:
A. Four
B. Three
\( c . \) Two
D. one


Which of the following statement
is false?
\( \mathbf{A} \cdot H_{2} \) has just one sigma bond
B. \( H C l \) has just one sigma bond
\( \mathbf{c} \cdot H-C \equiv C-H \) has four pi bonds and three sigma bonds
D. \( C H_{2}=C H_{2} \) has five sigma bonds and one pi bond
\( \mathrm{E} \cdot H_{2} \mathrm{O} \) has two sigma bonds and two lone pairs


A wire carrying a current of \( 5 \mathrm{A} \) is placed perpendicular to a magnetic induction of 2T.The force on each centimeter of the
wire is
A . \( 0.1 \mathrm{N} \)
B. 10 N
\( c \cdot 100 N \)
D. 1 N


A fringe width of a certain interference
pattern is \( \beta=0.002 \mathrm{cm} . \) What is the
distance of \( 5^{t h} \) dark fringe from centre?
\( \mathbf{A} \cdot 1 \times 10^{-2} \mathrm{cm} \)
B. \( 11 \times 10^{-2} \mathrm{cm} \)
\( \mathrm{c} \cdot 1.1 \times 10^{-2} \mathrm{cm} \)
D. \( 3.28 \times 10^{6} \mathrm{cm} \)


Metals conduct electricity due to Presence of mobile electrons.
A. True
B. False


State whether true or false:
A boy throws a ball down from the second floor of a building. In this case, electrostatic force is acting on the ball.
A. True
B. False


Express the speed \( 36 k m h^{-1} \) in \( m s^{-1} \)
\( \mathbf{A} \cdot 3600 m s^{-1} \)
B. \( 10 m s^{-1} \)
\( \mathrm{c} \cdot 0.6 \mathrm{ms}^{-1} \)
D. \( 36 m s^{-1} \)


\( \ln \) a rhombus \( \boldsymbol{A B C D}, \angle \boldsymbol{A}=\mathbf{6 0}^{\circ} \) and
\( A B=6 \mathrm{cm} . \) Then the diagonal \( B D \) is
A \( \cdot 2 \sqrt{3} c m \)
в. 6 ст
c. \( 12 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)


Acetyl CoA reacts with OAA to form
A. Formaldehyde
B. Acetate
c. Isocitrate
D. citrate


The acceleration of a particle is increasing linearly with time \( t \) as \( b t \). The particle starts from the origin with an
initial velocity \( v_{0} . \) The distance travelled by the particle in time \( t \) will be
A \( \cdot v_{0} t+\frac{1}{3} b t^{2} \)
B. \( v_{0} t+\frac{1}{3} b t^{3} \)
c. \( v_{0} t+\frac{1}{6} b t^{3} \)
D. \( v_{0} t+\frac{1}{2} b t^{2} \)


The escape velocity of a particle of mass \( m \) varies as:
\( \mathbf{A} \cdot m^{2} \)
в. \( m \)
c. \( m^{0} \)
D. \( m^{-1} \)


At yield point, Hooke's law doesn't hold
good
A. True
B. False


If \( A=\{a, b, c, d\}, B=\{1,2,3\}, \) find whether
or not the following sets of ordered pairs are relations from \( A \) to \( B \) or not
(a) \( R_{1}=\{(a, 1),(a, 3)\} \)
(b) \( R_{2}=\{(b, 1),(c, 2),(d, 1)\} \)
\( (c) R_{3}=\{(a, 1),(b, 2),(3, c)\} \)


A Zener diode is connected to a battery
and a load as shown. The currents \( \boldsymbol{I}, \boldsymbol{I}_{\boldsymbol{Z}} \)
and \( I_{L} \) are respectively
\( \mathbf{A} \cdot 12.5 m A, 5 m A, 7.5 m A \)
B. \( 15 \mathrm{mA}, 7.5 \mathrm{mA}, 7.5 \mathrm{mA} \)
c. \( 15 \mathrm{mA}, 7.5 \mathrm{mA}, 5 \mathrm{mA} \)
D. \( 12.5 \mathrm{mA}, 7.5 \mathrm{mA}, 5 \mathrm{mA} \)


In \( \triangle A B C, P Q \) is a line segment intersecting \( A B \) at \( P \) and \( A C \) at \( Q \) such that \( \mathrm{PQ} \| \mathrm{BC} \) and \( \mathrm{PQ} \) divides \( \triangle \mathrm{ABC} \) into two parts equal in area. Find \( \frac{B P}{A B} \)


A lens forms a diminished and erect
image of an object. The magnification is
\( \frac{1}{4} . \) Find ratio of distance between object and focus and focus and image
A .4:
B. 1:
\( c .8: \)
D. 2:


\( \boldsymbol{X}+\boldsymbol{K}_{2} \boldsymbol{C O}_{3}+ \) Air \( \stackrel{\text {heat}}{\longrightarrow}(\boldsymbol{Y}) \)
\( \boldsymbol{Y}+\boldsymbol{C l}_{2} \rightarrow \boldsymbol{Z}(\text { pink }) \)
Which of the following is correct?
A. \( X= \)Black,MnO\( _{2} ; Y= \)Blue,K\( _{2} \)Cr\( O_{4} ; Z=K M n O_{4} \)
B. \( X= \)Green, \( C r_{2} O_{3} ; Y= \)Yellow,K\( _{2} C r O_{4} ; Z= \)
\( K_{2} C r_{2} O_{7} \)
c. \( X= \)Black,MnO\( _{2} ; Y= \)Green, \( K_{2} \) Mn \( O_{4} ; Z= \)
\( K M n O_{4} \)
D. \( X= \)Black, Bi\( _{2} \) O\( _{3} ; Y= \)Colourless, KBiO\( _{2} ; Z= \)
\( K B i O_{3} \)


Derive the expression for the intensity at a point where interference of light occurs. Arrive at the conditions for the
maximum and zero intensity.


An inorganic mixture gives yellow
precipitate on boiling with conc. \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \)
and ammonium molybdate
\( \left.\left(\left(N H_{4}\right)\right)_{2} M o O_{4}\right) . \) Thus, inorganic
mixture can be :
This question has multiple correct options
A \( \cdot\left(N H_{4}\right)_{3} P O_{4} \)
B. \( \left(N H_{4}\right)_{3} A s O_{4} \)
\( \mathbf{c} \cdot p b\left(N O_{3}\right)_{2} \)
D. \( \left(N H_{4}\right)_{3} C_{2} O_{4} \)
E. None of the above


When ethyl alcohol reacts with \( B r_{2} \) in
presence of red phosphorus, the compound formed is:
A \( \cdot C_{2} H_{6} \)
в. \( P B r_{3} \)
c. \( C H_{3} B r \)
D. \( C_{2} H_{5} B r \)


Solve for \( x: \)
\( \left(\tan ^{-1} x\right)^{2}+\left(\cos ^{-1} x\right)^{2}=\frac{5 \pi^{2}}{8} \)


Prokaryotic cells are characterised by
A. A distinct nuclear membrane
B. Distinct chromosomes
C. Absence of chromatin material
D. Absence of nuclear membrane


\( \left(N H_{4}\right)_{2} C r_{2} O_{7} \) (Ammonium
dichromate) is used in fire works. The
green coloured powder blown in air is :
A. \( C r_{2} O_{3} \)
в. \( C r O_{2} \)
\( \mathrm{c} \cdot \mathrm{Cr}_{2} \mathrm{O}_{4} \)
D. \( \operatorname{Cr} \mathrm{O}_{3} \)


Find the co-ordinate of points on \( x \) -axis
which are at a distance of 5 units form
the point \( (\mathbf{6},-\mathbf{3}) \)


The resistances of the four arms \( P, Q, R \) and \( \sin \) a Wheatstone's bridge are 10
ohm, 30 ohm, 30 ohm and 90 ohm, respectively. The e.m.f. and internal resistance of the cell are 7 volt and 5 ohm respectively. If the galvanometer
resistance is 50 ohm, the current drawn
from the cell will be
A . \( 1.0 \mathrm{A} \)
B. 0.2 A
\( c \cdot 0.1 \mathrm{A} \)
D. 2.0 A


Not all snakes kill be poisoning their victim through venom. Some kill by suffocating their prey by constriction. Which of the following is a constrictor?
A. Rat snake
B. King cobra
c. Rock python
D. Russell's viper


A rod of length \( 10 \mathrm{cm} \) lies along the principal axis of concave mirror of focal length \( 10 \mathrm{cm} \) in such a way thatits end closer to the pole is \( 20 \mathrm{cm} \) away from the mirror. The length of the image is
then -
\( \mathbf{A} \cdot 15 \mathrm{cm} \)
B. 2.5 \( \mathrm{cm} \)
\( c \cdot 5 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)


A \( 10 \% \) (w/w) solution of cane sugar has
undergone partial inversion according
to the reaction:
sucrose \( + \) water \( \rightarrow \) glucose \( + \) fructose The boiling point of the solution is
\( 100.7^{\circ} \mathrm{C} . \) What fraction of sugar has
inverted? \( \left[\boldsymbol{K}_{\boldsymbol{b}}\left(\boldsymbol{H}_{\mathbf{2}} \boldsymbol{O}\right)=\mathbf{1 . 8} \boldsymbol{K} \boldsymbol{g} \boldsymbol{K} \boldsymbol{m o l}^{-1}\right] \)
A. 0.5
B. 0.2
\( c \cdot 0.3 \)
D. 0.4


The number of \( \pi \) and \( \sigma \) bond in the
following structure respectively are:
\( A \cdot 8,5 \)
B. 8,6
c. 3,8
D. 5,13


If \( \lim _{n \rightarrow \infty} \frac{1^{a}+2^{a}+3^{a}+\dots+n^{a}}{n^{a+1}}=\frac{1}{5} \)
\( (w h e r e a>-1) \) then the value of \( a \) is
A .2
B. 3
\( c \cdot 4 \)
D. 5


Name the area of the retina which
contains only cones and no rods.


Which of the following shows highest magnetic moment?
A \( \cdot C o^{+3} \)
B. \( C r^{+} \)
\( \mathbf{c} \cdot F e^{+3} \)
D. \( N i^{+2} \)


In the following reaction \( \boldsymbol{C H}_{3} \boldsymbol{C H O}+\boldsymbol{N H}_{2} \cdot \boldsymbol{N} \boldsymbol{H}_{2} \rightarrow \boldsymbol{A} \stackrel{\boldsymbol{B}}{\longrightarrow} \)
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{3}+\boldsymbol{N}_{2} \)
Identify \( A \) and \( B \)
A. \( C H_{3} C H=N N H_{2} \) and \( C_{2} H_{5} O N a \)
B. \( C H_{3} C H_{2}-N H_{2} \) and \( C_{2} H_{5} O N a \)
c. \( C H_{3}-N H-N H-C H_{3} \) and \( C_{2} H_{5} O H \)
D. \( C H_{3} C H_{2} N H_{2} \) and \( C_{2} H_{5} O H \)


If \( \hat{i}+p \hat{j}+\hat{k}, 2 \hat{i}+3 \hat{j}+q \hat{k} \) are parallel
vectors then \( (p, q)=? \)
A \( \cdot\left(2, \frac{3}{2}\right) \)
в. (2,2)
c. \( \left(\frac{3}{2}, \frac{3}{2}\right) \)
D. \( \left(\frac{3}{2}, 2\right) \)


Write the definition of fossils and
explain the process of dating of fossil.


The active species in the nitration of
benzene is:
A \( . N O_{2}^{+} \)
в. \( H N O_{3} \)
c. \( N O_{3} \)
D. \( N O_{2}^{-} \)


A body is moving with velocity \( 30 m s^{-1} \)
towards east. After \( 10 s \) its velocity
becomes \( 40 m s^{-1} \) towards north. the
average acceleration of the body is
A \( .7 \mathrm{ms}^{-2} \)
В. \( \sqrt{7} \mathrm{ms}^{-2} \)
\( \mathrm{c} \cdot 5 \mathrm{ms}^{-2} \)
D. \( 1 \mathrm{ms}^{-2} \)


A transparent cube of side \( \boldsymbol{d}, \) made ot a
material of refractive index \( \mu_{2}, \) is
immersed in a liquid of refractive index
\( \mu_{1}\left(\mu_{1}<\mu_{2}\right) . \) A ray is incident on the
face \( A B \) at an angle \( \theta \) (shown in the
figure). Total internal reflection takes
place at point \( \boldsymbol{E} \) on the face \( \boldsymbol{B} \boldsymbol{C} \)
The \( \theta \) must satisfy:
\( \mathbf{A} \cdot \theta<\sin ^{-1} \frac{\mu_{1}}{\mu_{2}} \)
B \( \cdot \quad \theta<\sin ^{-1} \sqrt{\frac{\mu_{2}^{2}}{\mu_{1}^{2}}-1} \)
c. \( \theta>\sin ^{-1} \frac{\mu_{1}}{\mu_{2}} \)
\( ^{\mathrm{D}} \theta>\sin ^{-1} \sqrt{\frac{\mu_{2}^{2}}{\mu_{1}^{2}}-1} \)


Given below are the symbols of a few
electronic components. Which of these
components denote a variable inductor
7
\( A \)
B.
\( c \)
D.


\( O \) is the centre of the circle. \( A B \) is a
chord of the circle. \( \boldsymbol{O} \boldsymbol{M} \perp \boldsymbol{A B} . \) If \( \boldsymbol{A B}= \)
\( 20 \mathrm{cm}, O M=2 \sqrt{11} \mathrm{cm}, \) then radius of
the circle is
A. \( 15 \mathrm{cm} \)
B. \( 12 \mathrm{cm} \)
\( c .10 \mathrm{cm} \)
D. \( 11 \mathrm{cm} \)


A spherical shell first rolls and then slips down an inclined plane. The ratio of its acceleration in two cases will be :
A \( \cdot \frac{5}{3} \)
B. \( \frac{3}{5} \)
c. \( \frac{15}{13} \)
D. \( \frac{13}{15} \)


The line \( (a+2 b) x+(a-3 b) y=a-b \)
for different values of \( a \) and \( b \) passes through the fixed point
\( ^{\mathrm{A}} \cdot\left(\frac{3}{5}, \frac{7}{5}\right) \)
в. \( \left(\frac{7}{2}, \frac{5}{2}\right) \)
\( ^{\mathrm{c}} \cdot\left(\frac{6}{5}, \frac{6}{5}\right) \)
D \( \cdot\left(\frac{2}{5}, \frac{3}{5}\right) \)


Choose the correct answer from the
alternatives given Which of the following is not a physiological change related to photoperiodism?
A. Seed germination
B. Root branching
c. Breaking bud dormancy
D. Onset of senescence


Identify whether the following sequence is a geometric sequence or not \( \frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5} \)


A spring block system is placed on a horizontal surface so as to just fit within two vertical walls. The spring is initially unstretched. The coefficient of restitution for collison is \( e=\frac{1}{2} . \) The block is pulled to the left by a distance \( x=1 c m \) and released from rest. The
time between second and third collision
of the block with the
wall is
A \( \cdot 2 \pi \sqrt{\frac{m}{k}} \)
В. \( \pi \sqrt{\frac{m}{k}} \)
c. \( \frac{\pi}{2} \sqrt{\frac{m}{k}} \)
D. \( \frac{\pi}{4} \sqrt{\frac{m}{k}} \)


Two radioactive substances \( A \) and \( B \)
have decay constants \( 5 \lambda \) and \( \lambda \)
respectively.At \( t=0, \) they have the same number of nuclei. The ratio of
number of nuclei of \( A \) to those of \( B \) will
be \( \left(1 / e^{2}\right) \) after a time:
A \( .4 \lambda \)
B. 2\lambda
c. \( \frac{1}{2 \lambda} \)
D. \( \frac{1}{4 \lambda} \)


In changing the state of thermodynamics from A to B state, the heat required is \( Q \) and the work done by
the system is \( W \). The change in its internal energy is
A. \( Q+W \)
в. \( Q-W \)
\( c \cdot Q \)
D. \( \frac{Q-W}{2} \)


Human eye forms the image of an
object at :
A. cornea
B. iriss
c. pupil
D. retina


Which of the following cells secretes calcium carbonate and calcium
phosphate?
A. Adipocyte
B. osteocyte
c. Monocyte
D. Thrombocyte


When metals corrodes, it is being:
A. dissolved into surrounding moisture
B. weakened structurally
C. chemically combined with another metal
D. reacted with oxygen


Which of the following is the inverse of the proposition "If a number is prime, then it is odd"?
A. If a number is not prime, then it is odd.
B. If a number is not a prime, then it is not odd.
c. If a number is not odd, then it is not a prime.
D. If a number is not odd, then it is a prime.


The angle between the lines \( x \cos 30^{\circ}+ \)
\( y \sin 30^{\circ}=3 \)
\( x \cos 60^{\circ}+y \sin 60^{\circ}=5 \) is
A \( \cdot 90^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 60^{\circ} \)
D. None of these


A \( 30 g \) bullet initially travelling at \( 120 m / s \) penetrates \( 12 c m \) into a
wooden block. The average resistance by the wooden block is
A \( .2850 N \)
в. 22000N
c. \( 2000 N \)
D. 1800N


The splitting of a heavy nucleus with neutron into two smaller nuclei along
with the release of a large amount of energy is known as
A. nuclear fusion
B. nuclear fission
c. radioactive decay
D. none of the above


The circumference of the circle is
calculated by the formula
\( \mathbf{A} \cdot 4 \pi r \)
В. \( 2 \pi r^{2} \)
c. \( 2 \pi r \)
D. \( \pi r^{2} \)


If the temperature of a wire of length
\( 2 m \) and area of cross section \( 1 \mathrm{cm}^{2} \) is
increased from \( 0^{0} C \) to \( 80^{0} C \) and is not
allowed to increase in length, then required for it is \( \boldsymbol{Y}=\mathbf{1 0}^{\mathbf{1 0}} \boldsymbol{N} / \boldsymbol{m}^{\mathbf{2}} \)
A. \( 0.008 N \)
B. \( 1.06 N \)
\( c \cdot 2 \cdot 4 N \)
D. \( 3.2 N \)


Change in colour of algae, according to depth in sea is called as
A. Bohr's effect
B. Gaudikov's effect
c. Fogg's effect
D. Pasteur's effect


Three vertices of a tetrahedron are
(0,0,0),(6,-5,-1) and \( (-4,1,3) . \) If the centroid of the tetrahedron be (1,-2,5)
then the fourth vertex is
A. (2,-4,18)
в. (2,-4,-18)
\( ^{c} \cdot\left(\frac{3}{4}, \frac{-3}{2}, \frac{7}{4}\right) \)
D. none of these


Which of these are present only in male cockroach Anal cerci, Anal styles or Anal places?


Product formed is :
\( A \)
B.
\( \mathbf{c} \cdot C H_{3}-C H(O H)-C H_{2}-C H_{3} \)
D. \( H O-C H_{2}-C H_{2}-C H_{2}-O H \)


\( f(x)=2 x+1, \) then \( f\left(\frac{x}{2}\right)=? \)


A dielectric in the form of a sphere is
introduced into a homogeneous electric
field. \( A, B \) and \( C \) are three points as
shown in Fig. Then
A. Intensity at \( A \) increases while that at \( B \) and \( C \) decreases
B. Intensity at \( A \) and \( B \) decreases whereas intensity at \( C \) increases
c. Intensity at \( A \) and \( C \) increases and that at \( B \) decreases
D. Intensity at \( A, B \) and \( C \) decreases


A T-shaped object with dimensions shown in the figure is lying on a smooth floor. A force \( \vec{F} \) is applied at the point \( \mathrm{P} \)
parallel to \( A B, \) such that the object has only the translational motion without
rotation. Find the location of P with
respect to \( \mathbf{C} \)


The magnetic flux linked with a coil,in webers,is given by the equations \( \phi= \)
\( 3 t^{2}+4 t+9 . \) Then the magnitude of
induced e. \( \mathrm{m} \). \( \mathrm{f} \). at \( \mathrm{t}=2 \) second will be:
A . 2 volt
B. 4 volt
c. 8 volt
D. 16 volt


Toadstools cannot manufacture their
food because they
A. Possess haustoria
B. Lack chlorophyll
c. Live in dark places
D. Do not have leaves


When 229 J of energy is supplied as heat at constant pressure to 3 mol \( A r(g), \) the temperature of the sample is increased by \( 2.55 \mathrm{K} \). Calculate the motor heat capacity at constant volume:
A. 30 KJ \( K^{-1} \) mol \( ^{-1} \) -
B. 30 J K \( ^{-1} \) mol \( ^{-1} \)
C . 21.7 J K \( ^{-1} \) mol \( ^{-1} \)
D. 21.7 KJ K \( ^{-1} \) mol \( ^{-1} \)


How many of the following are sources of Vitamin K?
Green Leafy vegetables, Fish, Meat, Cereals, milk, Kidney Beans, Cottonseed oil


What is Glycosuria and Ketonuria? Explain.


The value of \( \int e^{\ln \sqrt{x}} d x \) is


Bhawna took a pale green substance \( \boldsymbol{A} \) in a test tube and heated it over the
flame of a burner. A brown coloured
residue \( \boldsymbol{B} \) was formed along with the evolution of two gases with buring smell of sulphur. Identify \( \boldsymbol{A} \) and \( \boldsymbol{B} \)
Write the chemical reaction involved.


A solution contain \( 36 \% \) water and \( 64 \% \)
acetaldehyde \( \left(C H_{2} C H O\right) \) by mass. The mole fraction of acetaldehyde is:
A . 0.42
B. 0.2
c. 4.2
D. 2.1


Assertion
Specific heat of a body is always greater than its thermal capacity.
Reason
Thermal capacity is the heat required for raising temperature of unit mass of the body through unit degree.
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 mean deviation of the data
2,9,9,3,6,9,4 from the mean is
A .2 .23
в. 3.23
c. 2.57
D. 3.57
E . 1.03


ntegrate the function \( \frac{\sec ^{2} x}{\sqrt{\tan ^{2} x+4}} \)


Which of the following statements is true for Algae?
A. Algae have root, stem and leaves.
B. Algae have true roots but lack leaves.
c. Algae have rhizoids and leaves.
D. Body of Algae is thallus.


Q Type your question
thin-walled hollow sphere of radius \( \mathrm{R} \)
and mass M as shown. The hollow
sphere is fixed in position and the only
force on the point mass is the
gravitational attraction of the hollow
sphere. There is a very small hole in the
hollow sphere through which the point mass falls as shown. The velocity of a
point mass when it passes through point \( P \) at a distance \( R / 2 \) from the
centre of the sphere is?
A \( \cdot \sqrt{\frac{2 G M}{3 R}} \)
в. \( \sqrt{\frac{5 G M}{3 R}} \)
c. \( \sqrt{\frac{25 G M}{24 R}} \)


Fig. shows the time acceleration graph for a particle in rectilinear motion. The
average acceleration in first twenty
seconds is
\( A \cdot 45 \mathrm{m} / \mathrm{s}^{2} \)
\( 3 \cdot 40 \mathrm{m} / \mathrm{s}^{2} \)
\( c \cdot 30 m / s^{2} \)
20


Match the items in List 1 with those in
List 2
List 1:Electronic configuration List 2: Total spin


Two identical straight wires are stretched so as to produce 6 beats per second when vibrating simultaneously. On changing the tension slightly in one of them, the beat frequency remains
unchanged. Denoting by \( \mathrm{T}_{1} \) and \( \mathrm{T}_{2}, \) the higher and the lower initial tension in
the strings, then it could be said that
while making the above changes in tension:
This question has multiple correct options
\( \mathbf{A} \cdot \mathbf{T}_{2} \) was decreased
B. \( \mathrm{T}_{2} \) was increased
\( \mathrm{c} \cdot \mathrm{T}_{1} \) was decreased
D. \( T_{1} \) was increased


The gap between the plates of a parallel
plate capacitor of area \( A \) and distance
between plates \( d \), is filled with a
dielectric whose permittivity varies
linearly from \( \epsilon_{1} \) at one plate to \( \epsilon_{2} \) at the
other. The capacitance of capacitor is :
\( \mathbf{A} \cdot \epsilon_{0}\left(\epsilon_{1}+\epsilon_{2}\right) A / d \)
В \( \cdot \epsilon_{0}\left(\epsilon_{2}+\epsilon_{1}\right) A / 2 d \)
\( \mathbf{c} \cdot \epsilon_{A} / d\left[d \ln \left(\epsilon_{2} / \epsilon_{1}\right)\right] \)
D. \( \epsilon_{0}\left(\epsilon_{2}-\epsilon_{1}\right) A /\left[d l n\left(\epsilon_{2} / \epsilon_{1}\right)\right] \)


Oil yielding plants are abundant in the family
A. Solanaceae
B. Ranunculaceae
c. cruciferae
D. Curcurbitaceae


The phenomenon involved in sea breeze and land breeze is
A. Convection
B. Conduction
c. Radiation
D. None


is equal to the work done by an external agent in carrying a unit of positive charge from the arbitrarily chosen reference point (usually infinity) to that point without any acceleration.
A. Electric potential energy
B. Electric field
C. Electric potential
D. Electric potential difference


The nodal plane in the \( \pi \) bond of ethene
is located in:
A. the molecular plane.
B. a plane parallel to the molecular plane.
C . a plane perpendicular to the molecular plane, which bisects the carbon-carbon sigma bond at right angle.
D. a plane perpendicular to the molecular plane, which contains the carbon - carbon s-bond.


Find the term independent of \( x \) in \( \left(\frac{3}{2} x^{2}-\frac{1}{3 x}\right)^{9} \)
\( A \cdot \frac{6}{15} \)
в. \( \frac{7}{18} \)
\( c \cdot \frac{7}{8} \)
D.


Circumference of a circle is equal to
A . \( \pi r \)
в. \( 2 \pi r \)
c. \( \frac{\pi r}{2} \)
D. \( 2+\frac{\pi r}{2} r \)


If \( f(a)=2, f^{\prime}(a)=1, g(a)=-1 \) and
\( g^{\prime}(a)=2, \) the value of
\( \lim _{x \rightarrow a} \frac{g(x) f(a)-g(a) f(x)}{x-a} \) is
A . -5
B. \( \frac{1}{5} \)
\( c .5 \)
D. none of these


Zener diode acts as a/an
A . oscillator
B. regulator
c. rectifier
D. fliter


\( 2 n d \) equation of motion \( (s=u t+ \)
\( \left.\frac{1}{2} a t^{2}\right) \) can be derived graphically form
\( \boldsymbol{v}-\boldsymbol{t} \) graph by finding
A. Slope
в. Area
c. Either(A) or (B)
D. Insufficient data


In a triangle \( \triangle A B C, \) points \( P, Q \) and \( R \) are the mid-points of the sides \( A B, B C \) and CA respectively. If the area of the triangle \( A B C \) is 20 sq.units, then area of the triangle PQR equal to:
A . 10 sq. units
B. \( 5 \sqrt{3} \) sq. units
c. 5 sq. units
D. 5.5 sq. units


The HCF of 455 and 42 using Euclid algorithm is
A. 7
B. 6
c. 5
\( D \)


1 \( g \) of \( N a C l \) dissolved in \( 100 g \) of water to prepare a mixture. What is the mass percentage of sodium chloride?


A capacitor of capacitance \( C \) is charged to a potential difference V from a cell and
then disconnected from it. A charge +Q is now given to its positive plate. The potential difference across the capacitor
is now:
A. \( V \)
B. \( V+\frac{Q}{C} \)
\( c \cdot V+\frac{Q}{2 C} \)
D. \( V-\frac{Q}{C}, \) if \( V<C V \)


Inverse circular functions,Principal
values of \( \sin ^{-1} x, \cos ^{-1} x, \tan ^{-1} x \)
\[
\begin{array}{l}
\tan ^{-1} x+\tan ^{-1} y=\tan ^{-1} \frac{x+y}{1-x y} \\
x y<1 \\
\quad \pi+\tan ^{-1} \frac{x+y}{1-x y}, \quad x y>1
\end{array}
\]
Prove that
\[
\tan ^{-1} \frac{1-x}{1+x} \tan ^{-1} \frac{1-y}{1+y}=
\]
\[
\sin ^{-1} \frac{\boldsymbol{y}-\boldsymbol{x}}{\sqrt{1+\boldsymbol{x}^{2}} \sqrt{1+\boldsymbol{y}^{2}}}
\]


A conductor of length / is connected to
a \( D C \) source of potential \( V \). If the length of the conductor is tripled by gradually stretching it, keeping \( V \) constant, how will
(i) drift speed of electrons and
(ii) resistance of the conductor be
affected? Justify your answer.


Prove \( : \boldsymbol{a}^{2}-\boldsymbol{b}^{2}=(\boldsymbol{a}+\boldsymbol{b})(\boldsymbol{a}-\boldsymbol{b}) \)


A current of \( 0.2 A \) flows through a wire whose ends are at a potential difference
of \( 15 V . \) The heat energy produced in 1
minute will be
\( \mathbf{A} \cdot 60 J \)
в. \( 120 J \)
\( c .180 J \)
D. \( 90 J \)


During passage of electron over ETC
A. Electron undergoes resonance
B. Electron undergoes fluorescence
c. Electron undergoes active transport
D. pH of matrix increases


Which amongst the following is true for
İike vectors?
A. Like vectors are those vectors which have the same
direction irrespective of their magnitudes.
B. Like vectors are those vectors which have the same magnitude irrespective of their directions
C. Like vectors are those vectors which have the same magnitude as well as the directions
D. None of the above


The ion which is not tetrahedral in
shape is:
A. \( B F_{4}^{-} \)
B. \( N H_{4}^{+} \)
\( \mathbf{c} \cdot X e O_{4} \)
D. \( I C l_{4} \)


Number of Faraday required to get \( 1 g \)
atom of \( M g \) from \( M g C l_{2} \) is:
A. \( 0.0035 F \)
в. \( 2 F \)
\( c .1 F \)
D. \( 0.2 F \)


Match Column-I with Column-II for
housefly classification and select the
correct option using the codes given below


From the position time graph for two particles and B is shown below. Graph and particles A making angles \( 60^{\circ} \) and
\( 30^{\circ} \) with the time axis. The ratio of
velocities \( \boldsymbol{v}_{A}: \boldsymbol{v}_{B} \) is
\( A \cdot 1: 1 \)
в. 4: 1
c. \( \sqrt{2}: 1 \)
D. 1: 3


What are the characteristics
associated with the flower?
A. Green leaves
B. Colourful petals
c. Green sepals
D. Both B and C


Iron pipes are often coated with a layer
of Zinc in order to prevent them from corrosion. This process is termed as:
A. electroplating
B. annealing
c. galvanization
D. vulcanization


The maximum and minimum
magnitudes of the resultant of two
forces are 17 newton and 7 newton
respectively, if these two forces are acting at right angle to each other, then the value of resultant of these forces in
newton will be:
A . 10
B. 12
\( c \cdot 13 \)
D. 24


The grinding stone of a flour mill is
rotating at 600 rad/sec. for this power of \( 1.2 k \) watt is used. The effective
torque on stone in \( N-m \) will be
\( A \)
B. 2
\( c \cdot 3 \)
D. 4


The domain of \( f(x)=\cos (\log x) \) is
\( A \cdot(-\infty, \infty) \)
в. (-1,1)
c. \( (0, \infty) \)
D. \( (1, \infty) \)


The weight of an object is zero at:
A. a height equal to half of the radius of earth
B. the center of the earth
C . the equator
D. both (1) and (2)


A car is moving in a circular horizontal
track of radius \( 10 m \) with a constant
speed of \( 10 m / s . \) A plumb bob is suspended from the roof of the car by a light rigid rod of length 1 m. The angle
made by the rod with track is
A . zero
B . \( 30^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 60^{\circ} \)


Ethyne is not prepared by:
A. heating iodoform with \( A g \) powder
B. hydrolysis of calcium carbide
C . heating \( C_{2} H_{2} C l_{4} \) with zinc dust
D. heating iodoform with \( N a \)


Which of the following statements
is/are not correct?
A. Antipyretics are substances which are used to reduce the body temperature
B. Analgesics are substance which are used to relieve pain.
C. Antiseptics and disinfectants can be used for the same
purposes.
D. Antiseptics can be safely applied on living tissues.


The density of coal is when
compared to coke.
A. more
B. less
c. same
D. can't say anything


Find the measure of the angles of a
triangle in each of the following cases:
One of the acute angles of a
right triangle is \( 63^{\circ} . \) Find the other angle.


Gastrocnemius muscles are found in
\( \mathbf{A} \). Fore arm
B. chest
c. Thigh
D. shank


An organic compound contains \( 66 \% \)
\( 13.3 \% H \) and the remaining is \( 0 . \) Its
vapour density is 37. The possible number of isomers of all types for the compound is:
A. 6
B. 7
\( c \cdot 5 \)
D. 8


A trader buys an unfinished article for
Rs. 1,800 and spends Rs. 600 on its finishing, parking transportation, etc. He marks the article at such a price that will give him \( 20 \% \) profit. How much will a customer pay for he article including \( 12 \% \) sales tax.
A . \( R s .3,165.60 \)
в. \( R s .3,788.60 \)
c. \( R s .3,225.60 \)
D. Rs.3, 338.60


Find the frequency of photon.
A \( \cdot 2.71 \times 10^{14} \mathrm{Hz} \)
в. 2.01 \( \times 10^{14} \mathrm{Hz} \)
c. \( 2.5 \times 10^{14} H z \)
D. 20.1 \( \times 10^{14} \mathrm{Hz} \)


Two point charges \( q \) and \( -q \) are separated by a distance 2l, Find the flux of electric field strength vector across the circle of radius \( \mathrm{R} \) placed with its centre coinciding with the midpoint of line joining the two charges in the perpendicular plane.


Prove that \( :\left|\begin{array}{ccc}\boldsymbol{a} & \boldsymbol{c} & \boldsymbol{a}+\boldsymbol{c} \\ \boldsymbol{a}+\boldsymbol{b} & \boldsymbol{b} & \boldsymbol{a} \\ \boldsymbol{b} & \boldsymbol{b}+\boldsymbol{c} & \boldsymbol{c}\end{array}\right|= \)
\( 4 a b c \)


If \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{2} \\ \mathbf{3} & \mathbf{4}\end{array}\right], \) such that \( \boldsymbol{A} \boldsymbol{X}=\boldsymbol{I}, \) then
find \( \boldsymbol{X} \)


\( A B \) is divided into maximum
equal parts
4
3
\( c \)
D. 10


wavefront and \( A O \) and \( B P \) the
corresponding extreme rays of
monochromatic light of wavelength ' \( \lambda \).
The value of angle \( \theta \) for which the ray \( \mathrm{BP} \)
and the reflected ray OP interfere
constructively is given by:
A \( \cdot \cos \theta=\frac{3 \lambda}{4 d} \)
B. \( \cos \theta=\frac{\lambda}{4 d} \)
\( \mathrm{c} \cdot \sec \theta=\frac{\lambda}{3 d} \)
D \( \sec \theta=\frac{2 \lambda}{3 d} \)


Of the following, which best
approximates the percent decrease in
consumption of wood power in the
United States from 2000 to \( 2010 ? \)
Renewable Energy Consumption
\( A \)
B. 11
\( c .21 \)
\( D \cdot 26 \)


Total mechanical energy \( \boldsymbol{E} \) of an object
of mass \( m \), at a height \( h \) above the
ground is given by the relation \( \boldsymbol{E}=\boldsymbol{m} \boldsymbol{g} \boldsymbol{h}+\frac{\boldsymbol{p}^{2}}{2 \boldsymbol{m}} \)
Find the dimension of \( \mathrm{p} .(g= \) acceleration due to gravity)


Sketch the region
\( \left\{(x, y): 9 x^{2}+4 y^{2}=36\right\} \) and find the
area of the region enclosed by it, using integration.


If \( \boldsymbol{y} \sqrt{\boldsymbol{x}^{2}+\mathbf{1}}=\log (\sqrt{\boldsymbol{x}^{2}+\mathbf{1}}-\boldsymbol{x}) \)
show that \( ,\left(\boldsymbol{x}^{2}+\mathbf{1}\right) \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+\boldsymbol{x} \boldsymbol{y}+\mathbf{1}=\mathbf{0} \)


Dispersive power of a prism decreases with the increase in prism angle.
A. True
B. False


The compound IF \( _{7} \) is named as
A. iodine heptafluorine
B. iodine septafluoride
C. iodine fluoride
D. none of these


State whether given statement is True or False
Yellow spot on the retina is highly sensitive to light.
A. True
B. False


State True or False \( \sin ^{-1} 2+\cos ^{-1} 2=\frac{\pi}{2} \)
A. True
B. False


Let \( A=Q \times Q \) and let \( ^{\star} \) be a binary
operation on A defined by \( (a, b) * \)
\( (c, d)= \)
\( (a c, b+a d) \) for \( (a, b),(c, d) \epsilon A \)
Determine, whether \( ^{*} \) is commutative and associative. Then, with respect to
on \( A \)
Find the invertible elements of \( A \)


For the following compounds, write structural formulas and IUPAC names
for all possible isomers having the number of the double or triple bond as indicated :
(a) \( C_{4} H_{8} \) (one double bond)
\( (b) C_{5} H_{8}(\text { one triple bond }) \)


Three hydrocarbons \( A, B \) and \( C \) haev melting points- \( 183 \mathrm{C},-138 \mathrm{C} \) and 95.3
respectively. which one has minimum number of carbon atoms in molecule?


Binding energy per nucleon versus
mass number curve for nuclei is
shown in the figure. \( A, B, C \) and \( D \) are
four muclei indicated on the curve. The
process that would release energy is
he process that
\( \mathbf{A} \cdot C \rightarrow 2 D \)
B . \( A \rightarrow C+D \)
\( \mathbf{c} \cdot A \rightarrow 2 C \)
D. \( B \rightarrow C+D \)


Under what conditions can path
difference and phase difference are
equal
A . \( p i \)
B. \( 2 p i \)
c. \( p i / 2 \)
D. \( 2 p i / 3 \)


Concentrated Sulphuric acid reacts with Sodium hydroxide forming
A. Potassium sulphate and Potassium sulphate
B. \( H_{2} S O_{3}+N a H_{2} S O_{4} \)
c. \( N a H S O_{4}+N a_{2} H S O_{4} \)
D. All


A substance is completely trimerized on dissolution in a solvent. The Van't
Hoff factor \( (i) \) for such change is:
A . 1
B . 2
\( c .3 \)
D. \( 1 / 3 \)


Ageing is characterised by
A. Decline in metabolic activity
B. Increased metabolic activity
C. Increased anabolism
D. Increased catabolism


Anhydrone is a common name given to:
\( \mathbf{A} \cdot M g\left(O H_{2}\right) \cdot 6 H_{2} O \)
B. \( M g S O_{4} .7 H_{2} O \)
\( \mathrm{c} \cdot M g(O H) \cdot 7 \mathrm{H}_{2} \mathrm{O} \)
D \( \cdot_{M g}\left(C l O_{4}\right)_{2} \)


Allosteric sites on an enzyme are:
This question has multiple correct options
A. those other than drug-active sites
B. those which change the shape of active sites
C. those which don't change the shape of active sites
D. all of the above


In figure \( \angle \mathbf{1}=\angle \mathbf{2} \) and \( \Delta \boldsymbol{N} \boldsymbol{S} \boldsymbol{Q} \cong \)
\( \Delta M T R, \) then prove that \( \Delta P T S \sim \)
\( \Delta P R Q \)


In the given diagram(not drawn to scale), if \( A B \| C D, A F|| B D \) and
\( \angle F C D=58^{\circ}, \) then \( \angle A F C= \)
A \( \cdot 108^{\circ} \)
B \( .126^{\circ} \)
\( c \cdot 162^{\circ} \)
D. \( 98^{\circ} \)


First menstrual cycle is
A. Parturition
B. Menopause
c. Menarche
D. Implantation


Match the given pairs.


Which is distilled first??
A . Liquid \( H_{2} \)
B . Liquid \( C O_{2} \)
c. Liquid \( O_{2} \)
D. Liquid \( N_{2} \)


State whether true or false:
Objects with the same type of charges attract each other.
A. True
B. False


Which of the following is an intensive
property?
A. temperature
B. pressure
c. density
D. all of the above


\( \boldsymbol{E}^{o} \) value of \( \boldsymbol{N} \boldsymbol{i}^{2+} / \boldsymbol{N} \boldsymbol{i} \) is \( -\mathbf{0 . 2 5} \) V and
\( A g^{+} / A g \) is \( +0.80 V . \) If a cell is made by taking the two electrodes what is the feasibility of the reaction?
A. since \( E^{\circ} \) value for the cell will be positive, redox reaction is feasible
B. since \( E^{o} \) value for the cell will be negative, redox reaction is not feasible
c. Ni cannot reduce \( A g^{+} \) to Ag hence reaction is not feasible
D. Ag can reduce \( N i^{2+} \) to Ni hence reaction is feasible


Where are radiowaves used?
A. Radar, radio and tv communications
B. Microwave ovens
C. Photographic films
D. sterilizing purpose


Mark the correct statement for algae.
A. Chlorophyllous, thalloid and complex body
B. Algae shows limited size and forms
C. Reproduce by fragmentation. Each fragment develops into a thallus
D. Most common spores produced are the zoospores that are non-flagellated.


Three distinct points \( A, B \) and \( C \) are given in the 2 -dimensional coordinate plane such that the ratio of the distance
of any one of them from the point (1,0) to the distance from the point (-1,0) is equal to \( \frac{1}{3} . \) Then the circumcentre of the triangle \( A B C \) is at the point:
\( ^{\text {A }} \cdot\left(\frac{5}{2}, 0\right) \)
в. \( \left(\frac{5}{3}, 0\right) \)
c. (0,0)
D. \( \left(\frac{5}{8}, 0\right) \)


Digestion in Periplaneta begins in
A . crop
B. Preoral cavity
c. Midgut
D. Pharynx


If there is increase in temperature of
about more than \( 35^{0} \mathrm{C} \)
A. Rate of decline of respiration will be earlier than decline of photosynthesis
B. Rate of decline of photosynthesis will be earlier than decline of respiration.
C. Both decline together
D. Both show no fixed variations.


Draw the graphs showing variation of Inductive reactance and Capacitive
reactance with frequency of applied A.C
source.


Best method of form aromatic iodide is:
\( \mathbf{A} \cdot A r N_{2}^{+}+H I \rightarrow \)
B. \( R N H_{2}+I_{2} \rightarrow \)
\( \mathbf{c} \cdot A r N_{2}^{+}+K I \rightarrow \)
D. \( A r N_{2}^{+}+P I_{3} \rightarrow \)


The chemical reaction given below:
\( \boldsymbol{C l}_{2}(\boldsymbol{g})+\boldsymbol{S} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O}(l) \rightarrow \)
\( 2 C l^{-}(a q .)+3 H^{+}(a q .)+H S O_{4}^{-}(a q .) \)
proceeds readily in aqueous acid solution.
(i) Give the half-cell reactions.
(ii) If a fully charged cell initially held 1
mole of \( C l_{2} \), for how many days could it
sustain a current of 0.05 ampere,
assuming the cell becomes non-
operative when \( 90 \% \) of initial \( C l_{2} \) has
been used up?


ABCD is parallelogram. If Land M are the middle points of \( \mathrm{BC} \) and \( \mathrm{CD} \), then \( \boldsymbol{A L}+\overline{\boldsymbol{A} \boldsymbol{M}} \) equals?
A \( \cdot \frac{1}{2} \overline{A C} \)
в. \( \frac{3}{2} \overline{A C} \)
c. \( \overline{A C} \)
D. \( \frac{2}{3} \overline{A C} \)


Three identical dice are rolled. The
probability that the same number will appear on each of them is
A \( \cdot \frac{1}{6} \)
B. \( \frac{1}{18} \)
c. \( \frac{1}{36} \)
D. None of these


A reversible chemical reaction having two reactants in equilibrium. If the
concentrations of the reactants are
doubled, then the equilibrium constant will
A. Be halved
B. Also be doubled
c. Remains the same
D. None of these


A line drawn through the midpoint of one side of a triangle is parallel to another side, so it divides the third side
in the ratio:
A . 1: 1
B . 2: 1
\( c \cdot 1: 2 \)
D. 3: 1


Draw a circle of radius \( 3 \mathrm{cm} \). Take a
point outside the circle at a distance of
\( 6 \mathrm{cm} \) from the centre of the circle.
Construct tangents from this point to the circle. Measure the angle between
the tangents and select the correct value from below.
\( \mathbf{A} \cdot 60 \)
B. 30
\( c \cdot 45 \)
D. \( 90^{\circ} \)


An electron with kinetic energy \( 5 e V \) is
incident on a hydrogen atom in its ground state. The collision
A. must be elastic
B. may be partially elastic
c. must be completely inelastic
D. may be completely inelastic


Which of the following pairs of nitrates gives the same gaseous products on thermal decomposition? This question has multiple correct options
A. \( K N O_{3} \) and \( P b\left(N O_{3}\right)_{2} \)
B. \( K N O_{3} \) and \( N a N O_{3} \)
c. \( P b\left(N O_{3}\right)_{2} \) and \( C u\left(N O_{3}\right)_{2} \)
D. \( \operatorname{NaNO}_{3} \) and \( C u\left(N O_{3}\right)_{2} \)


A particle of mass \( \mathrm{M} \) at rest decays into
two particles of masses \( m_{1} \) and \( m_{2} \)
having non zero velocities. The ratio of the de Broglie wavelengths of the
particles, \( \lambda_{1} / \lambda_{2} \) is?


Femto is \( =10^{-x}, \) then \( x=? \)


\( 9.2 \mathrm{g} N_{2} \mathrm{O}_{4} \) is heated in a \( 1 \mathrm{L} \) vessel till equilibrium state is established
\( N_{2} O_{4}(g) \rightleftharpoons 2 N O_{2}(g) \)
In equilibrium state \( 50 \% N_{2} O_{4} \) was dissociated, equilibrium constant will be
A . \( 0 . \)
B. 0.4
\( c .0 .3 \)
D. 0.2


The group number of the element with
atomic number 96 is 3
If true enter 1 , else enter 0 .


If \( \boldsymbol{x}=\tan \boldsymbol{\theta}+\cot \boldsymbol{\theta}, \boldsymbol{y}=\cos \boldsymbol{\theta}-\sin \theta \)
then
A. \( x=y \)
B. \( \frac{1-y^{2}}{2}=\frac{1}{x} \)
\( ^{\mathbf{c}} \cdot \frac{y^{2}-1}{2}=\frac{1}{x} \)
D. \( \frac{1+y^{2}}{2}=\frac{1}{x} \)


Which of the following homologous series has incorrect general formula?
A. Alkyne \( C_{n} H_{2 n-2} \)
B. Alkanol \( C_{n} H_{2 n+2} O \)
c. Alkanal \( C_{n} H_{2 n+1} O \)
D. carboxylic acid \( C_{n} H_{2 n} O_{2} \)


What is the value of electron gain
enthalpy of \( N a^{+} \) if \( I E_{1} \) of \( N A=5.1 e V \)
\( ? \)
A. \( -5.1 e V \)
В. \( -10.2 e V \)
\( \mathbf{c} .+2.55 e V \)
D. \( +10.2 e V \)


Figure below shows a portion of an
electric circuit with the currents in
amperes and their directions. The
magnitude and direction of the current
in the portion \( P Q \) is
\( \mathbf{A} \cdot 0 A \)
B. \( 3 A \) from \( P \) to \( Q \)
c. \( 4 A \) from \( Q \) to \( P \)
D. \( 6 A \) from \( Q \) to \( P \)


Find the inverse of the following matrix by using elementary row transformation
\( \left[\begin{array}{lll}0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1\end{array}\right] \)


On treating roll sulphur with an
aqueous solution of calcium hydroxide:
A. plastic sulphur is prepared
B. milk of sulphur is prepared
C . rhombic sulphur is prepared
D. roll is prepared


State Ohm's law.


If a compound statement is made up of three simple statements, then the number of rows in the truth table is
\( \mathbf{A} \cdot \mathbf{8} \)
B. 6
\( c \cdot 4 \)
D.


Arrange the fractions \( \frac{4}{5}, \frac{9}{11}, \frac{3}{5}, \frac{7}{12} \) in descending order.
A \( \cdot \frac{7}{12}, \frac{9}{11}, \frac{4}{5}, \frac{3}{5} \)
В. \( \frac{7}{12}, \frac{4}{5}, \frac{3}{5}, \frac{9}{11} \)
c. \( \frac{9}{11}, \frac{4}{5}, \frac{3}{5}, \frac{7}{12} \)
D. None of these


What is the range between \( f_{1} \) and \( f_{2} \) of
an RLC circuit that resonates at
\( 150 k H z \) and has a \( Q \) of \( 30 ? \)
A . \( 100.0 k H z \) to \( 155.0 k H z \)
B. \( 147.5 k H z \) to \( 152.5 k H z \)
c. \( 4500 k H z \) to \( 295.5 k H z \)
D. \( 149970 H z \) to \( 150030 H z \)


The image of an object formed by a
convex lens is of the same size as the
object. If the image is formed at a distance \( 50 \mathrm{cm} \) from the lens at what distance from the lens is the object
placed? Find the focal length and power
of the used.


The time period of a particle in SHM is
12 sec. At \( t=0, \) it is at mean position. The ratio of the distance travelled in the
second and sixth second is.
A \( \cdot(\sqrt{3-1}) \)
B. \( (\sqrt{2-1}) \)
c. \( \frac{1}{(\sqrt{2}-1)} \)
D. \( \frac{1}{\sqrt{2}} \)


What is the de Broglie wavelength of
(a) a bullet of mass \( 0.040 \mathrm{kg} \) travelling at the speed of \( 1.0 \mathrm{km} / \mathrm{s} \)
(b) a ball of mass \( 0.060 \mathrm{kg} \) moving at a speed of \( 1.0 \mathrm{m} / \mathrm{s}, \) and
(c) a dust particle of mass \( 1.0 \times 10^{9} k g \)
drifting with a speed of \( 2.2 \mathrm{m} / \mathrm{s} ? \)


Define alternating current and explain
working of the device which produces it. Draw labelled diagram. Describe the change in direction of current.


A glass prism with a refracting angle
of \( 60^{0} \) has a refractive index 1.52 for red
and 1.6 for voilet light.A parallel beam of white light is incident on one face at an angle of incidence, which gives minimum deviation for red light. Find:
\( \left[\boldsymbol{U} \boldsymbol{s} \boldsymbol{e}: \sin \left(\mathbf{5 0}^{0}\right)=\mathbf{0 . 7 6 0} ; \sin \left(\mathbf{3 1 . 6}^{\mathbf{0}}\right)=\mathbf{0}\right. \)
2.The angular width of the spectrum is;
A \( .6^{\circ} \)
B . \( 4.8^{\circ} \)
c \( \cdot 9.6^{\circ} \)
D. \( 12^{\circ} \)


The distance traveled by a body in \( I V^{t h} \) second is twice the distance traveled in
\( I I^{n d} \) second. If the acceleration of the
body is \( 3 m / s^{2}, \) then its initial velocity
is
\( ^{\mathrm{A}} \cdot \frac{3}{2}^{m / s} \)
в. \( \frac{5}{2} m / s \)
c. \( \frac{7}{2}^{m / s} \)
D. \( \frac{9}{2} \) m \( / \) s


The aufbau principle is violated in
\( 2 s \)
\[
2 p x \quad 2 p y \quad 2 p z
\]
This question has multiple correct options
\( \mathbf{A} \)
\( \uparrow \downarrow \quad \uparrow \downarrow \)
B.
\( \uparrow \)
\( \uparrow \downarrow \)
\[
\uparrow
\]
c.
\( \uparrow \downarrow \)
\( \uparrow \)
\( \uparrow \)
D.
\( \uparrow \downarrow \quad \uparrow \downarrow \)


In the circuit shown, the thermal power
dissipated in \( R_{1} \) is \( P . \) The thermal
power dissipated in \( \boldsymbol{R}_{2} \) is
A. \( P \)
в. \( \frac{4 P}{9} \)
c. \( \frac{2 P}{3} \)
D. \( \frac{P}{9} \)