Assertion
Oxidation is the gain of oxygen.
Reason

Reduction is the loss of oxygen.
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


(i) Define rectification.
(ii) Draw a circuit diagram of a full-
wave rectifier.
(iii) Semi-conductor related to given
energy band diagram is:
n-type semi-conductor, p-type semiconductor or intrinsic semi-conductor.


In the Arrhenius equation \( k=A e^{E / R T} \)
rate will be constant at:
A . infinite \( T \) or zero \( E_{a} \)
B. infinite \( E_{a} \) or zero \( T \)
C. infinite \( E_{a} \) and zero \( T \)
D. none of these


The height of an individual depends on the genes inherited from the parents.
A. True
B. False


The time after which bolt hit the floor of
the elevator


The charge stored in a capacitor is \( 20 \mu C \) and the potential difference across the plates is \( 500 \mathrm{V} \). Its capacity is :
A. \( 0.04 \mu F \)
B . \( 10^{-2} \mu F \)
c. \( 2 \times 10^{-6} \mu F \)
D. 250 \muF


Construct a right angle triangle whose
hypotenuse is \( 6 \mathrm{cm} \) long and one of the
legs is \( 4 \mathrm{cm} \) long.


Bromine reacts with the hot aqueous
alkali to give bromide and bromate. What is the change that is brought
about in the oxidation state of bromine
to bromate?
A \( .-1 \) to +5
B. 0 to +5
\( c \cdot 0 \) to +7
D. None of these


An electron moves at right angle to a magnetic field of \( 15 \times 10^{-2} T \) with a
speed of \( 6 \times 10^{7} m / s . \) If the specific
charge of the electron is \( 1.7 \times \) \( 10^{11} C / k g . \) The radius of the circular
path will be
\( \mathbf{A} \cdot 2.9 \mathrm{cm} \)
в. \( 3.9 \mathrm{cm} \)
\( c .2 .35 \mathrm{cm} \)
D. \( 2 c m \)


Which of the following is not a target molecule for drug function in body?
A. Carbohydrates
B. Lipids
c. Vitamins
D. Proteins


For the reaction between \( M n O_{4}^{-} \) and
\( C_{2} O_{4}^{-} \) in basic solution, the unbalanced equation is as follows:
\( M n O_{4}^{-}+C_{2} O_{4}^{2-} \longrightarrow M n O_{2}(s)+ \)
\( \boldsymbol{C O}_{3}^{2-} \)
In a balanced equation, the number of
\( O H^{-} \) ions on the right is :


Write electronic configurations of the elements with atomic number 14.


If \( \boldsymbol{y}=\frac{\boldsymbol{x}^{2}}{\mathbf{2}}+\frac{\mathbf{1}}{\mathbf{2}} \boldsymbol{x} \sqrt{\boldsymbol{x}^{2}+\mathbf{1}}+ \)
\( \ln \sqrt{x+\sqrt{x^{2}+1}} \), then the value of
\( \boldsymbol{x} \boldsymbol{y}^{\prime}+\log \boldsymbol{y}^{\prime} \) is
\( \mathbf{A} \cdot \underline{y} \)
B. \( 2 y \)
c. 0
D. \( -2 y \)


In which case there is change in
oxidation number:
A . Aqueous solution of \( C r O_{4}^{2-\text { - - is acidified }} \)
B. \( S O_{2} \) gas is passed into \( C r_{2} O_{7}^{2} \)
c. \( C r_{2} O_{7}^{2-} \) solution is made alkaline
D. \( C r O_{2} C l_{2} \) is dissolved in \( N N a O H \)


Two identical smooth balls are
projected from points 0 and \( A \) on the horizontal ground with same speed of projection. the angle of projection in
each case is \( 30^{\circ} \) (see figure). The distance between 0 and \( A \) is 100 m. The
balls collide in mid-air and return to
their respective points of projection. If the coefficient of restitution is \( 0.7, \) find
the speed of projection of either ball (in
\( \mathrm{m} / \mathrm{s}) \) correct to nearest integer. (Take
\( \left.g=10 m s^{-2} \text {and } \sqrt{3}=1.7\right) \)


The cartesian product \( \boldsymbol{A} \times \boldsymbol{A} \) has \( \mathbf{9} \)
elements among which are found (-1,0) and \( (0,1) . \) Find the set \( A \) and
the remaining elements of \( \boldsymbol{A} \times \boldsymbol{A} \)


The ratio of the speed of light in a vacuum to the speed of light in a particular material is called what?
A. the coefficient of diffraction of the material.
B. the index of refraction of the material
c. the coefficient of refraction to the material
D. the index of diffraction of the material.
E. the modulus of diffraction of the material.


Which one of the following is the correct percentage of (the two out of
four) greenhouse gases that contribute to the total globa
warming?
A \( \cdot \mathrm{N}_{2} \mathrm{O} 6 \%, \mathrm{CO}_{2} 86 \% \)
B. Methane 20\%, N_0 18\%\%
c. СFC 14\%, Methane 20\%
D. \( \operatorname{co}_{2} \) 40\%, сFС \( 30 \% \)


\( f(a+b+c=27, \) then what is the value
of \( (a-7)^{3}+(b-9)^{3}+(c-11)^{3}- \)
\( \mathbf{3}(\boldsymbol{a}-\mathbf{7})(\boldsymbol{b}-\mathbf{9})(\boldsymbol{c}-\mathbf{1 1}) ? \)
A . 0
B. 9
c. 27
D. 81


The number of different ways of
distributing 10 marks among 3 questions, each carrying at least 1 mark, is
A . 72
B. 71
\( c .36 \)
D. none of these


The differential equation for the family of curves \( x^{2}-y^{2}+2 a x=0, \) where \( a \) is
an arbitrary constant is:
A \( \cdot\left(x^{2}-y^{2}\right)=2 x y y^{\prime} \)
B . \( x^{2}-y^{2}=-2 x y . y^{\prime} \)
c. \( \left(x^{2}+y^{2}\right) y^{\prime}=2 x y \)
D. \( x^{2}+y^{2}=2 x y . y^{\prime} \)


\( f\left|\begin{array}{ccc}\boldsymbol{x}+\mathbf{1} & \mathbf{3} & \mathbf{5} \\ \mathbf{2} & \boldsymbol{x}+\mathbf{2} & \mathbf{5} \\ \mathbf{2} & \mathbf{3} & \boldsymbol{x}+\mathbf{4}\end{array}\right|=\mathbf{0}, \) then \( \boldsymbol{x}=? \)
A . 1,9
В. -1,9
c. -1,-9
D. 1,-9


Storms, cyclones, earthquake, lightning etc. are \( \ldots \ldots . . . . . . . \) natural phenomena:
A. constructive
B. destructive
c. simple
D. complex


In a certain oscillatory system, the amplitude of motion is \( 5 \mathrm{m} \) and the time
period is 4 s. The time taken by the particle for passing between points which are at distance of \( 4 \mathrm{m} \) and \( 2 \mathrm{m} \)
from the centre and on the same side of
it will be
A. 0.30 s
B. 0.32
c. 0.33
D. 0.35


An \( \alpha \) -particle captures two electrons.
What does it change to?
A. Hydrogen atom
B. Helium atom
c. Lithium atom
D. Berrylium atom


Which of the following statement/s is/are correct with regard to ozone depletion:
1. The ozone hole is measured in terms
of ozone concentrations, which is
expressed in Dobson units.
2. The major cause for ozone depletion is the presence of CFCs in the stratosphere - CFCs are entirely manmade and not found naturally.
A. only
B. Only 2
c. Both A and B
D. None of the above


Distinguish between DNA and RNA.


Solve:
\( \frac{x \cos ^{-1} x}{\sqrt{1-x^{2}}} d x \)


If the angle of incidence is \( 45^{\circ} \) then the angle of reflection is -
A \( .90^{\circ} \)
B . \( 221 / 2^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 30^{\circ} \)


Addition of mercuric acetate in the
presence of water is called as
oxymercuration. The adduct obtained
gives alcohol on reduction with \( N a B H_{4} \) in alkaline medium. This is known as
demercuration. Oxymercurationdemercuration allows Markownikoff's
addition of \( \mathrm{H}, \mathrm{OH} \) without
rearrangement. The net result is the
addition of \( H_{2} O . \) Answer the following
question:
The product 'C' formation from B occurs through:
A. Enol formation.
B. \( S_{N} 1 \) mechanism.
c. Neighbouring group particitation.
D. \( S_{N} A E \) mechanism.


Molecules of benzoic acid
\( \left(C_{6} H_{5} C O O H\right) \) dimerise in benzene. g of the acid dissolved in 30 g of benzene
shows a depression in freezing point
equal to \( 2 \mathrm{K} \). If the percentage association of the acid to form a dimer
in the solution is \( 80, \) then \( w \) is:
(Given that \( \boldsymbol{K}_{f}=\mathbf{5} \mathrm{K} \) kg \( \boldsymbol{m o l}^{-1} \), Molar
mass of benzoic acid \( =122 \) g \( m o l^{-1} \)
A . \( 1.8 g \)
в. 2.4g
c. \( 1.0 g \)
D. \( 1.5 \mathrm{g} \)


Assertion
Gemmae formation in Funaria occurs in
favourable condition
Reason
The gemmed form on the stern and
leaves
A. If both the assertion and the reason are true and the
reason is a correct explanation of the assertion
B. If both the assertion and reason are true but the reason is not a correct explanation of the assertion
C. If the assertion is true but the reason is false
D. If both the assertion and reason are false


Which of the following comes under indirect tax?
A. Wealth Tax
B. House Tax
c. Sales \( \operatorname{tax} \)
D. All of these


A cloth merchant says that due to slump in the market, he sells the cloth at \( 10 \% \) loss, but he uses a false metre
scale and actually gain \( 20 \% \). Find the actual length of the scale.
\( A \cdot 80 \mathrm{cm} \)
B. 75 cm
c. \( 70 \mathrm{cm} \)
D. 60 \( m \)


The density of a gas \( A \) is twice that of \( B \)
Molar mass of \( A \) is half that of \( B \). The
ratio of partial pressure of \( \boldsymbol{A} \) to \( \boldsymbol{B} \) is:
A. \( 1 / 4 \)
B. \( 1 / 2 \)
\( c \cdot 4 / 1 \)
D. 2/1


List I and List II contains four entries
each. Entries of Column I are to be
matched some entries of List II. One or
more than one entries of List I may
match with the same entry of List II


Which of the following species are oxidised and reduced in the following (unbalanced) reaction?
\( \boldsymbol{C N}^{-}+\boldsymbol{O C l}^{-} \longrightarrow \boldsymbol{N}_{2}+\boldsymbol{H} \boldsymbol{C O}_{3}^{-}+ \)
\( C l^{-} \)
A. oxidized- \( C, N \) in \( C N^{-} \) ", reduced \( -O C l^{-} \)
B. Oxidized- \( N, C N^{-}, H C O_{3}^{-} ; N_{2} \) reduced \( -C O C l^{-} \)
C. oxidized- \( C, N, H C O_{3}^{-} ; N_{2} \) reduced \( -O C l^{-}, C N^{-} \)
D. None of these


The point which does not belong to the feasible region of the LPP:
Minimize: \( Z=60 x+10 y \)
subject to \( 3 x+y \geq 18 \)
\( 2 x+2 y \geq 12 \)
\( x+2 y \geq 10 \)
\( x, y \geq 0 \) is
в. (4,2)
D. (10,0)


Shikha's income is \( 60 \% \) more than that
of Shalu. By what percent is Shalu's income is less than Shikha's?


\( \sin ^{-1}\left(\frac{x}{5}\right)+\operatorname{cosec}^{-1}\left(\frac{5}{4}\right)=\frac{\pi}{2} \) then
value of \( x \) is


How many terms are there in the
sequence \( 9,12,15, \dots \dots 66 ? \)
A . 18
B. 19
c. 20
D. 21


Observe the circuit and answer the
question given below. Are resistors 3
and 4 in series??


\( \boldsymbol{S}=\boldsymbol{3}^{10}+\boldsymbol{3}^{9}+\frac{3^{9}}{4}+\frac{3^{7}}{2}+\frac{5.3^{6}}{16}+\frac{3^{2}}{16}+ \)
\( \frac{7.3^{4}}{64}+\ldots \ldots \ldots \) upto infinite terms, then
\( \left(\frac{25}{36}\right) S \) equal to
A \( \cdot 6^{\text {? }} \)
B. \( 3^{10} \)
\( c \cdot 3^{1} \)
D. \( 2.3^{10} \)


Which of the following is monomer of
the given polymer?
\( A \)
\( \mathbf{B} \)
\( c \)
\( D \)


The value of \( ^{\prime} a^{\prime} \) for which the area of the
triangle included between the axes and
any tangent to the curve \( x^{a} y=\lambda^{a} \) is
constant, is/are
This question has multiple correct options
A \( -\frac{1}{2} \)
в. - 1
\( c \cdot \frac{1}{2} \)
D.


If there is only one type of charge in the
universe, then what is the flux to the
entire universe.
\( (\vec{E} \rightarrow \text { Electric field, } \overrightarrow{d s} \rightarrow \) Area vector)
\( \mathbf{A} \cdot \oint \vec{E} \cdot \overrightarrow{d s} \neq 0 \) on any surface
B. \( \oint \vec{E} \cdot \overrightarrow{d s} \) could not be defined
\( \mathbf{c} \cdot \oint \vec{E} \cdot \overrightarrow{d s}=\infty \) if charge is inside
D \( \cdot \oint \vec{E} \cdot \overrightarrow{d s}=0 \) if charge is outside, \( =\frac{q}{\epsilon_{0}} \) if charge is
inside


Describe with the help of a diagram the
structure of Golgi body and state its
function.


f the solution set for the system
is given by the above
figure, then which of the following is
NOT a solution to the system?
A \( \cdot(0,3) \)
B. (1,2)
c. (2,4)
D. (3,3)


The side of an equilateral triangle expands at the rate of \( \sqrt{3} \mathrm{cm} / \) sec.When
the side is \( 12 \mathrm{cm}, \) the rate of increase of
its area is
A \( \cdot 12 \mathrm{cm}^{2} / \mathrm{sec} \)
B. \( 18 \mathrm{cm}^{2} / \mathrm{sec} \)
c. \( 3 \sqrt{3} \mathrm{cm}^{2} / \mathrm{sec} \)
D. \( 10 \mathrm{cm}^{2} / \mathrm{sec} \)


Lactose on hydrolysis produces a mixture of:
A. glucose only
B. glucose and fructose
c. glucose and galactose
D. fructose and galactose


Which of the following explains the increase of the reaction rate by catalyst
\( ? \)
A. Catalyst decreases the rate of backward reaction so that the rate of forward reaction increases.
B. Catalyst provides extra energy to reacting molecules so that they may produce effective collisions.
c. catalyst provides an alternative path o lower activation energy to the reactants
D. Catalyst increases the number of collisions between the reacting molecules.


Given planes are \( \boldsymbol{P}_{1}: \boldsymbol{c} \boldsymbol{y}+\boldsymbol{b} \boldsymbol{z}=\boldsymbol{x} \quad \boldsymbol{P}_{2}: \boldsymbol{a} \boldsymbol{z}+\boldsymbol{c} \boldsymbol{x}=\boldsymbol{y} \quad \boldsymbol{P}_{3} \)
\( P_{1}, P_{2} \) and \( P_{3} \) pass through one line, if
A \( \cdot a^{2}+b^{2}+c^{2}=a b+b c+c a \)
B . \( a^{2}+b^{2}+c^{2}+2 a b c=1 \)
\( \mathbf{c} \cdot a^{2}+b^{2}+c^{2}=1 \)
D. \( a^{2}+b^{2}+c^{2}+2 a b+2 b c+2 c a+2 a b c=1 \)


The period of element with atomic number 20 in the periodic table is :
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
\( D \)


Let \( X \) and \( Y \) be two events such that
\( P(X)=\frac{1}{3}, P(X / Y)=\frac{1}{2} \) and
\( \boldsymbol{P}(\boldsymbol{Y} / \boldsymbol{X})=\frac{2}{5} \cdot \) Then
This question has multiple correct options
\( ^{\mathbf{A}} \cdot P(X \cup Y)=\frac{2}{5} \)
В \( \cdot P(Y)=\frac{4}{15} \)
\( c \cdot P\left(X^{\prime} \mid Y\right)=\frac{1}{2} \)
D. \( P(X \cap Y)=\frac{1}{5} \)


What is the function for the arithmetic
sequence \( 3,4,5,6,7 \dots ? \)
\( \mathbf{A} \cdot n+2 \)
в. \( n-1 \)
c. \( 2 n+1 \)
D. \( 2 n-1 \)


If lies in the second quadrant, then the value of \( \sqrt{\left(\frac{1-\sin \theta}{1+\sin \theta}\right)}+\sqrt{\left(\frac{1+\sin \theta}{1-\sin \theta}\right)} \) is
\( \mathbf{A} \cdot 2 \sec \theta \)
в. \( -2 \sec \theta \)
\( c .2 \operatorname{cosec} \theta \)
D. noneofthese


Find the total numbers of isomers of
\( C_{7} H_{14}(\text { only } 5-\text { membered ring }) \)


The gas that is not considered as a
green house gas' is:
A. \( C O_{2} \)
в. \( C H_{4} \)
\( c \cdot O_{2} \)
D. \( O_{3} \)


The limiting value of static friction is
A. Equal to the dynamic friction
B. Always less than the dynamic friction
c. Always greater than dynamic friction
D. Less than the rolling friction


Which of the following statement is not true for halogens?
A. All form monobasic oxyacids.
B. All but fluorine show positive oxidation states
c. All are oxidizing agents
D. chlorine has the highest electron-gain enthalpy


A student uses a simple pendulum of
exactly 1 m length to determine \( g \), the
acceleration due to gravity. He uses a
stopwatch with the least count of 1 sec
for this and records 40 seconds for 20
oscillations. For this observation, which
of the following statements is(are)
true?
This question has multiple correct options
A. Error \( \Delta T \) in measuring \( T \), the time period, is 0.05 seconds.
B. Error \( \Delta T \) in measuring \( T \), the time period, is 1 second.
C. Percentage error in the determination of \( g \) is \( 5 \% \)
D. Percentage error in the determination of \( g \) is \( 2.5 \% \)


Isotopes have same but
different
A. atomic number, mass number
B. atomic mass number, atomic number
C. number of neutrons, atomic number
D. None of these


Give chemical equations for the following conversions:
(i) Ethylene into polythene
(ii) Ethyl alcohol into iodoform


The form of \( S i O_{2} \) used as piezoelectric
material :
A . cristobalite
B. quartz
c. kiesulguhr
D. silica gel


What is emulsifying agent? Give one example?


The atomic number of an element is 7
This implies that its nucleus contains:
A. 7 electrons
B. 7 protons
c. 7 neutrons
D. 7 protons and 7 electrons


p-nitrophenol and o-nitrophenol are
separated by
A. Crystallisation
B. Fractional distillation
c. Distillation
D. Steam distillation


In the Watson and Crick model of DNA,
the steps of the ladder are composed of
A . sugars
B. a purine and a pyrimidine
c. two purines
D. a sugar and a phosphate molecule


Which one of the following is an example of co-polymer?
A. Buna - s
B. Teflon
c. PVC
D. Polypropylrnr


An inductor L of inductance \( \boldsymbol{X}_{\boldsymbol{L}} \) is
connected in series with a bulb \( \mathrm{B} \) and
an ac source. How would brightness of the bulb change when (i) number of turn in the inductor is reduced, (ii) an
iron rod is inserted in the inductor and
(iii) a capacitor of reactance \( \boldsymbol{X}_{\boldsymbol{C}}=\boldsymbol{X}_{\boldsymbol{L}} \)
is inserted in series in the circuit.
Justify your answer in each case.


Family planning programme was invented in
A . 1981
B. 1972
\( c \cdot 1962 \)
D. 195


During decarboxylation of ethanoic acid
with soda lime \( (N a O H+C a O), C O_{2} \)
is removed as:
A. \( C O_{2} \)
в. \( C O \)
c. \( N a_{2} C O_{3} \)
D. \( C a C O_{3} \)


The points \( \boldsymbol{A}(-4,1) \)
\( B(-2,-2), C(4,0), D(2,3) \) are the
vertices of
A. parallelogram
B. rectangle
c. rhombus
D. None of these


\( \ln \triangle A B C, P, Q \) and \( R \) are the midpoints of the sides \( A B, B C \) and \( C A \)
respectively. If \( D \) is any point
(i) then express \( D A+D B+D C \)
interms of \( D P, D Q \) and \( D R \)
(ii) if \( \boldsymbol{P A}+\boldsymbol{Q B}+\boldsymbol{R C}=\boldsymbol{a}, \) then find \( \boldsymbol{a} \)


Assertion
Newland's law of octaves of elements is
a function of their state that the
property of every eighth element is the repetition of the first.
Reason
The maximum of 8 electrons can be
accommodated in valence shell.
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


During adolescence, several changes occur in the human body. Out of the following, which change is associated with sexual maturation in boys?
A. Loss of milk teeth
B. Increase in height
c. cracking of voice
D. weight gain


Find the total surface area of a hollow
cylinder of internal radius \( 3 \mathrm{cm} \) thickness \( 1 \mathrm{cm} \) and height \( 14 \mathrm{cm} \)
\( A \cdot 330 \mathrm{cm}^{3} \)
B. \( 660 \mathrm{cm}^{2} \)
c. \( 990 \mathrm{cm}^{2} \)
D. \( 1320 \mathrm{cm}^{2} \)


The sum of three number is \( 15 . \) If the
second number is subtracted from the
sum of first and third number then we
get 5 an if twice of first number is added to second and if the third number
is subtracted from the sum we get 4


The nucleus of deuterium, called a
deuteron, contains:
A. one proton and no neutron
B. one proton and one electron
c. one proton and one neutron
D. one proton and two neutron


Figure shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges.Which particle has the highest charge to mass ratio?


The heat of neutralization of HCl by NaOH is \( -55.9 \mathrm{kJ} / \mathrm{mol} \). If the heat of
neutralization of HCN by NaOH is -12.1 kJ/ mol.

The energy of dissociation of HCN is :
A. -43.8 kJ
B. 43.8 kJ
c. 68 kJ
D . -68kJ


A particle is executing SHM of amplitude \( A, \) about the mean position \( x=0 . \) Which of the following is a
possible phase difference between the positions of the particle at \( x=+\frac{A}{2} \) and \( \boldsymbol{x}=-\frac{\boldsymbol{A}}{\sqrt{\mathbf{2}}} \)
This question has multiple correct options
A . 75
B . \( 165^{\circ} \)
\( \mathbf{c} \cdot 135^{\circ} \)
D. 195


Solve \( \frac{3 a-2}{3}+\frac{2 a+3}{2}=a+\frac{7}{6} \)


A given ray of light suffers minimum deviation in an equilateral prism \( P \) Additional prisms \( Q \) and \( R \) of identical shape and material are now added to \( P \) as shown in the figure. The ray will
suffer:
A. same deviation
B. greater deviation
c. total internal reflection
D. no deviation


Radius of curvature is found to be equal
to twice the focal length for:
A. Plane mirror of small aperture
B. Spherical mirrors of small aperture
c. Plane mirrors of large aperture
D. Spherical mirrors of large aperture


A charged particle enters into a uniform magnetic field with velocity vector at an
angle of \( 45^{\circ} \) with the magnetic field. The pitch of the helical path followed by the particle is \( p . \) The radius of the helix will
be
A \( \cdot \frac{p}{\sqrt{2} \pi} \)
B. \( \sqrt{2 p} \)
c. \( \frac{p}{2 \pi} \)
D. \( \frac{\sqrt{2 p}}{\pi} \)


Let \( A \) be a \( 3 \times 3 \) matrix such that \( a_{11}= \)
\( a_{33}=2 \) and all the other \( a_{i j}=1 . \) Let
\( \boldsymbol{A}^{-1}=\boldsymbol{x} \boldsymbol{A}^{2}+\boldsymbol{y} \boldsymbol{A}-\boldsymbol{z} \boldsymbol{I}, \) then find the
value of \( (x+y+z) \) where \( I \) is a unit of
matrix of order 3
A . -9
B. 9
c. 1
D. -


The acceleration due to gravity:
A. has the same value everywhere is space
B. has the same value everywhere on the earth
C. varies with the latitude on the earth
D. is greater on the moon due to its smaller diameter


State whether true or false:
The hollow shaft is much stronger than a solid shaft of same mass, same
length and same material
A. True
B. False


Derivative of \( \left(\tan ^{-1} x\right)^{2} \) wrt to \( x \)


Fill in the blanks:
The first kinematic equation gives relation between \( \ldots \ldots . . . \) and time.


An astronaut, orbiting in a spaceship round the earth, has a centripetal
acceleration of \( 6.67 m / s^{2} . \) Find the
height of the spaceship above the surface of the earth.
\( \left(G=6.67 \times 10^{11} N m^{2} / k g^{2}, \) radius of \right.
the earth \( =6400 \mathrm{km} \)


The hybridization of atomic orbitals
of nitrogen in \( N O_{2}^{+}, N O_{2}^{-} \) and \( N H_{4}^{+} \) is:
A \( \cdot s p^{2}, s p^{3} \) and \( s p^{2} \) respectively
B. \( s p, s p^{2} \) and \( s p^{3} \) respectively
C. \( s p^{2}, s p \) and \( s p^{3} \) respectively
D. \( s p^{2}, s p^{3} \) and \( s p \) respectively


The waves produced by simple
pendulum (having time period 2 seconds) are.
A. Infrasonics
B. Audible
c. Ultrasonic
D. None of these


Epidermis is specialized for
A. Respiration
B. Absorption
c. Protection
D. All of the above


In conducting wire of radius \( 5 m m \)
resistivity \( \rho=1.1 \times 10^{-8} \Omega / m \) and
current of \( 5 A \) is flowing. Drift velocity of
free electron is \( 1.1 \times 10^{-3} \mathrm{m} / \mathrm{s} \) find out
mobility of free electron.
A . \( 1.57 \mathrm{m}^{2} \) volt/sec
B . \( 1.25 \mathrm{m}^{2} \) volt/sec
c. \( 1.2 m^{2} \) volt/sec
D. \( 2 m^{2} \) volt/sec


A wire loop is rotated in a magnetic field. The frequency of change of direction of the induced e.m.f. is
A. once per revolution
B. Twice per revolution
c. Four times per revolution
D. Six times per revolution


A vibrator makes \( 150 \mathrm{cm} \) of a string to vibrate in 6 loops in the longitudinal arrangement when it is stretched by 150
N. The entire length of the string is then weighed and is found to weigh \( 400 \mathrm{mg} \)
Then
This question has multiple correct options
A. Frequency of the vibrator is 3 \( \mathrm{kHz} \)
B. Frequency of the vibrator is \( 1.5 \mathrm{kHz} \)
c. Distance between two nodes is \( 25 \mathrm{cm} \)
D. Distance between two nodes is 33 cm


A leaf which possesses stomata exclusively on its upper surface is called as
A. Oat type
B. Mulberry type
c. Lotus type
D. cactus type


The centripetal acceleration of a particle varies inversely with the square of the radius \( r \) of the circular path. The
KE of this particle varies directly as:
\( A \)
B \( \cdot r^{2} \)
c. \( r^{-} 2 \)
D. \( r^{-1} \)


During the adiabatic change of ideal gas, The relation between the pressure and the density will be -
\( ^{A} \cdot \frac{p_{1}}{P_{2}}=\left(\frac{d_{2}}{d_{1}}\right)^{1 / \gamma} \)
B . \( p_{1} d_{1}^{\prime \prime}=p_{2} d_{2} \gamma \)
c. \( p_{1} d_{1}^{\gamma}=p_{2} d_{2}^{-} \)
D. \( \frac{p_{1}}{P_{2}}=\left(\frac{d_{2}}{d_{1}}\right)^{2} \)


In which compounds does vanadium
have an oxidation number of \( +4 ? \)
A. \( N H_{4} V O_{2} \)
B . \( K_{4}\left[V(C N)_{6}\right] \)
\( c \cdot v o s O_{4} \)
D. \( \operatorname{Cr} \mathrm{O}_{2} \mathrm{Cl}_{2} \)


You are given two circuits as shown in Fig., which consist of NAND gates. Identify the logic operation carried out by the two circuits.


What are heterotrophs?


An electron having charge \( 1.6 \times 10^{-19} \mathrm{C} \)
and mass \( 9 \times 10^{-31} \mathrm{kg} \) is moving with
\( 4 \times 10^{6} \mathrm{m} / \mathrm{s} \) speed in a magnetic field
of \( 2 \times 10^{-1} \) tesla in a circular orbit. The
force acting on an electron and the radius of circular orbit will be:
A \( \cdot 1.28 \times 10^{-14} N, 1.1 \times 10^{-3} m \)
B . \( 1.28 \times 10^{15} N, 1.2 \times 10^{-12} m \)
C . \( 1.28 \times 10^{-13} N, 1.2 \times 10^{-4} \mathrm{m} \)
D. none of these


\( \left[\boldsymbol{F} \boldsymbol{e} \boldsymbol{F}_{6}\right]^{3-} \) has Fe atom
hybridised with unpaired electrons.
A \( \cdot d^{2} s p^{3}, 4 \)
B \( \cdot d^{2} s p^{3}, 5 \)
\( \mathrm{c} \cdot s p^{3} d^{2}, \)
D. \( s p^{3} d^{2}, 3 \)


The value of a machine depreciates by 5
\( \% \) each year. A man pays Rs. 30, 000 for the machine. Find its value after three
years


\( \ln a \Delta A B C, \) BD is the median to the side
\( A C, B D \) is produced to \( E \) such that \( B D=D E \) Hence, AE parallel to BC. State whether the above statement is
true or false.
A. True
B. False


Which of the following is NOT a type of force?
A. muscular
B. magnetic
c. chemical
D. pulling a bucket of water from a well


Which of the following reactions will not
produce \( H_{2} \) gas?
(a) Fe+dil. HCI
(b) \( \mathrm{Zn}+ \) dil. HCl
(c) \( \mathrm{Cu}+ \) dil. \( \mathrm{HCl} \)
(d) \( A g+d i l . H C l \)
\( A \cdot a, c, d \)
B. \( c, d \)
\( c \cdot a, d \)
\( D \cdot b, d \)


A physical quantity \( \times \) is calculated from the relation \( \boldsymbol{x}=\frac{\boldsymbol{a}^{2} \boldsymbol{b}^{3}}{\boldsymbol{c} \sqrt{\boldsymbol{d}}} \)
percentage error in \( a, b, c \) and \( d \) are \( 2 \%, 1 \%, 3 \% \) and \( 4 \% \) respectively. What
is the percentage error in \( x ? \)


Which of the following show non-zero multiple oxidation state?
A . \( S \)
B. \( O \)
\( c \cdot Z n \)
D. \( H \)


Which of the following species are hypervalent? \( 1 . C l O_{4}^{-}, 2 . B F_{3}, 3 . S O_{4}^{2-}, 4 . C O_{3}^{2-} \)
\( \mathbf{A} \cdot 1,2,3 \)
в. 1,3
\( c .3,4 \)
D. 1,2


Which of the following represents the
floral characters of Liliaceae?
A. Six sepals, zygomorphic, six stamens, bilocular ovary, axile placentation
B. Tetramerous, actinomorphic, polyphyllous, unilocular ovary, axile placentation
C. Trimerous, actinomorphic, polyandrous, superior ovary, axile placentation
D. Bisexual. zygomorphic, gamophyllous, inferior ovary, marginal placentation
E. Unisexual, actinomorphic, trilocular, inferior ovary, axile placentation


Let \( \boldsymbol{A}=\{1,2\}, \boldsymbol{B}=\{1,2,3,4\}, C= \)
\{5,6\} and \( D=\{5,6,7,8\} \) Verify that
(i) \( \boldsymbol{A} \times(\boldsymbol{B} \cap \boldsymbol{C})=(\boldsymbol{A} \times \boldsymbol{B}) \cap(\boldsymbol{A} \times \boldsymbol{C}) \)
(ii) \( A \times C \) is a subset of \( B \times D \)


In which one of the following regions of the electromagnetic specturm will the vibration motion of molecules give rise
to absorption?
A . Ultraviolet
B. Microwave
c. Infrared
D. Radio wave


Find the area of the region bounded by the ellipse \( \frac{x^{2}}{9}+\frac{y^{2}}{5}=1 \) between the
two latus rectums.


The Boolean expression \( ((\boldsymbol{p} \wedge \boldsymbol{q}) \vee \)
\( (p \vee \sim q)) \wedge(\sim p \wedge \sim q) \) is equivalent
to :
\( \mathbf{A} \cdot p \wedge(\sim q) \)
B . \( p \vee(\sim q) \)
c. \( (\sim p) \wedge(\sim q) \)
D. \( p \wedge q \)


Find the differential equation of the family of curve represented by
\( c(y+c)^{2}+x^{3}=0 \)


Which of the following is eco friendly combustible substance?
A . Diesel
B. Petrol
c. c. N.G
D. cow dung


Two billiard balls are rolling on a flat table. One has velocity components \( \boldsymbol{V}_{\boldsymbol{x}}=\mathbf{1} \boldsymbol{m} / \boldsymbol{s}, \boldsymbol{V}_{\boldsymbol{y}}=\sqrt{\mathbf{3}} \boldsymbol{m} / \boldsymbol{s} \) and the
other has component \( V_{x}=2 m / s \) and
\( V_{y}=2 m / s . \) If both the balls start moving from the same point the angle between their path is:
A \( .60^{\circ} \)
B . 45
\( c \cdot 22.5 \)
D. \( 15^{\circ} \)


Which of the following compounds are toxic?
A. Benzene
B. Toluene
c. Carbon tetrachloride
D. All of the above


Consider the following statements:
1. If \( A \) and \( B \) are exhaustive events, then
their union is the sample space.
2. If \( A \) and \( B \) are exhaustive events,
then their intersection must be an
empty event. Which of the above statements is/are
correct?
A. 1 only
B. 2 only
c. Both 1 and 2
D. Neither 1 nor 2


explain \( N O \) and \( N O_{2} \) follow the law
of multiple proportion or not


A bullet moving with a velocity of \( 200 \mathrm{cm} / \mathrm{s} \) penetrates a wooden block and comes to rest after traversing \( 4 \mathrm{cm} \) inside it. What velocity is needed for travelling distance of \( 9 \mathrm{cm} \) in same
block
A. \( 100 \mathrm{cm} / \mathrm{s} \)
B. \( 136.2 \mathrm{cm} / \mathrm{s} \)
c. \( 300 \mathrm{cm} / \mathrm{s} \)
D. \( 250 \mathrm{cm} / \mathrm{s} \)


The equilibrium concentration of \( C_{2} H_{4} \)
in the following gas phase reaction can be increased by:
\( \boldsymbol{C}_{2} \boldsymbol{H}_{4}(\boldsymbol{g})+\boldsymbol{H}_{2}(\boldsymbol{g}) \rightleftharpoons \)
\( \boldsymbol{C}_{2} \boldsymbol{H}_{6}(\boldsymbol{g}), \quad \boldsymbol{\Delta} \boldsymbol{H}=-\mathbf{3 2 . 7} \boldsymbol{k} \boldsymbol{c a l} \)
A \( \cdot \) removal of \( C_{2} H_{6} \)
B. removing \( H_{2} \)
c. decrease in temperature
D. increase in pressure


A stone tied to the end of a string \( 80 \mathrm{cm} \) long is whirled in a horizontal circle
with a constant speed. If the stone makes 14 revolutions in 25 s, the magnitude of acceleration is :
A \( \cdot 20 m s^{-2} \)
В \( \cdot 12 m / s^{2} \)
c. \( 27.53 m s^{-2} \)
\( \mathbf{D} \cdot 8 m s^{-2} \)


What is Juxtaglomerular apparatus?


If the potential difference \( V_{A}-V_{B} \) for
the circuit shown in the figure is given \( \operatorname{as}\left(-\frac{20+x}{9} V\right) n . \) Find \( x \)


The value of \( c \) in Lagrange's theorem for
the function \( f(x)=|x| \) in the interval
[-1,1] is
A. 0
B. \( 1 / 2 \)
c. \( -1 / 2 \)
D. non-existent in the interval


Find \( g \circ f \) and \( f \circ g \) when \( f: R \rightarrow R \) and \( g: R \rightarrow R \) are defined by \( f(x)= \)
\( \mathbf{2} \boldsymbol{x}+\boldsymbol{x}^{2} \) and \( \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{x}^{3} \)


The magnetic field lines inside the solenoid are in the form of
A. parallel straight lines.
B. circular lines.
c. anticlockwise lines.
D. all


Quantitative analysis of an organic compound gave the following results.
Percentage of carbon \( =92.3 \) and percentage of hydrogen \( =7.7 \) If the molecular weight of the compound is \( 78 . \) Calculate its molecular formula.


Among the following, the false
statements is:
A. latex is a colloidal solution of rubber particles which are positively charged
B. tyndall effect can be used to distinguish between a colloidal solution and a true solution
C. it is possible to cause artificial rain by throwing electrified sand carrying charge opposite to the one on clouds from an aeroplane
D. Iyophilic sol can be coagulated by adding an electrolyte


A capacitor of capacitance \( C=4 \mu F \) is
connected as shown in figure. If internal resistance of the cell is \( 0.5 . \) The charge
on the capacitor plates is
A. zero
3. \( 8 \mu \) C
\( c \cdot 4 \mu C \)
\( D \cdot 6 \mu C \)


AB is a wire of potentiometer with the increase in the value of resistance \( \mathrm{R} \),
the shift in the balance point J will be.
A. Towards B
B. Towards A
c. Remains constant
D. First towards B then back towards


A river with high BOD value is
A. Highly polluted
B. Highly clean
c. Highly productive
D. Highly conducive for pisciculture


Solve the following pair of equation by
the elimination method.
\( \boldsymbol{x}+\boldsymbol{y}=\mathbf{1 4}, \boldsymbol{x}-\boldsymbol{y}=\mathbf{4} \)


How many diagonals are there in a
hexagon?
A. 6
B. 4
\( c \cdot 11 \)
\( D \)


Which molecule is only electron donor?
A . \( N H_{3} \)
в. \( B F_{3} \)
c. \( P F_{3} \)
D. \( A s F_{5} \)


Ray optics fail when the size of the obstacle is :
A . 5
B. 3
c. less than the wavelength of light
D. \( (a) \) and
\( (b) \) both


Two solid balls of rubber \( A \) and \( B \) whose
masses are \( 200 g m \) and \( 400 g m \) respectively, are moving in mutually opposite directions. if the velocity of bal \( A \) is \( 0.3 m / s \) and both the ball come to rest after collision, then the velocity of
ball \( B \) is :
A. \( 0.15 \mathrm{m} / \mathrm{s} \)
в. \( -0.15 \mathrm{m} / \mathrm{s} \)
c. \( 1.5 \mathrm{m} / \mathrm{s} \)
D. None of these


The value of ' \( b^{\prime} \) such that the equation \( \frac{b \cos x}{2 \cos 2 x-1}=\frac{b+\sin x}{\left(\cos ^{2} x-3 \sin ^{2} x\right) \tan x} \)
possess solution, then prove that belongs to the set \( \left(-\infty, \frac{1}{2}\right) \)


In the figure, a point source \( ^{\prime} \boldsymbol{P}^{\prime} \) is
placed at a height \( h \) above the plane
mirror in a medium of refractive index
An observer \( O \), vertically above \( P \) outside the liquid, sees \( P \) and it image in the mirror. The apparent distance between these two is :
\( A \cdot 2 \mu h \)
B. \( 2 h \) \( \mu \)
c. \( \frac{2 h}{\mu-1} \)
' \( \quad h\left(1+\frac{1}{\mu}\right) \)


Which minimum measurements do you
require to check if the given figures are
congruent:
Two rhombuses


Assertion
When diamagnetic material is placed in a non-uniform magnetic field, it tends to move from stronger to the weaker part of the magnetic field.
Reason
Diamagnetic materials posses string magnetism.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A uniform wire of resistance \( 100 \Omega \) its
melted and made in the form of uniform
wire, whose length is double that of the original. The resistance of the new wire
is
A \( .200 \sqrt{2} \Omega \)
B. \( 800 \Omega \)
c. \( 200 \Omega \)
D. \( 400 \Omega \)


Friction is a force that opposes motion.
A. True
B. False
c. Ambiguous
D. Data insufficient


The wavelength associated with a golf ball weighing 200 g and moving at a speed of \( 5 \mathrm{m} / \mathrm{h} \) is of the order:
A \( \cdot 10^{-10} m \)
В. \( 10^{-20} m \)
\( \mathbf{c} \cdot 10^{-30} m \)
D. \( 10^{-40} m \)


What names apply to chemical species
corresponding to locations 1 and 2 on
this reaction coordinate diagram?
Location 1

Location 2
A. Activated complex Activated complex
B. Reaction intermediate Activated complex
c. Activated complex Intermediate
D. Reaction intermediate Intermediate


Value of electric potential at the center of uniformly charged non conducting sphere is 30 volt then what will be value of potential at surface.


Charge \( 5 \mu C,-2 \mu C, 3 \mu C \) and \( -9 \mu C \)
are placed on a square ABCD of side 1 cm. The net electric potential at the centre is:
A. \( -27 K V \)
В. \( -27 \sqrt{2} \times 10^{5} V \)
\( \mathrm{c} .-9 \mathrm{KV} \)
D. \( 0 V \)


Two non-reactive monoatomic ideal
gases have their atomic masses in the
ratio 2:3. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature, is 4: 3 The ratio of their densities is
\( A \cdot 1: 4 \)
B. 1: 2
\( c \cdot 6: 9 \)
D. 8: 9


Choose the correct answers from the
alternatives given Which of the following archaea would live at a deep-sea vent?
A. Heterotrophic nutrition
B. Prokaryotic organisation
c. Presence of flagella
D. Rigid cell wall


The magnetic moment associated with
a circular coil of 35 turns and radius 25
\( \mathrm{cm}, \) if it carries a current of \( 11 \mathrm{A} \) is:
A \( .72 .2 A m^{2} \)
B . \( 70.5 A m^{2} \)
c. \( 74.56 A m 2 \)
D. \( 75.56 A m^{2} \)


Q Type your question
4
\( B \)
\( c \)
\( D \)


ABCD is a rhombus whose diagonals AC
and BD intersect at a point \( 0 . \) If side \( A B \) \( =10 \mathrm{cm} \) and diagonal \( \mathrm{BD}=16 \mathrm{cm}, \) find
the length of diagonal AC.


A green plant starts evolving carbon
dioxide instead of oxygen on a hot
summer day. Explain.


The EMF of an \( \boldsymbol{H}_{2}-\boldsymbol{O}_{2} \) fuel cell:
\( A \cdot \) is independent of partial pressures of \( H_{2} \) and \( O_{2} \)
B. decreases on increasing \( P_{H_{2}} \) and \( P_{O_{2}} \)
C. increases on increasing \( P_{H_{2}} \) and \( P_{O_{2}} \)
D. varies with the concentration of \( O H^{-} \) ions in the
cathodic and anodic compartments


According to the Bohr's atomic model, the relation between principal quantum number (n) and radius of orbit(r) is?
\( \mathbf{A} \cdot r \propto n^{2} \)
B. \( r \propto \frac{1}{n^{2}} \)
c. \( _{r} \propto \frac{1}{n} \)
D. \( r \propto n \)


Which of the following complex shows
ionization isomerism :
\( ^{\mathbf{A}} \cdot\left[C r\left(N H_{3}\right)_{6}\right] C l_{3} \)
в. \( \left[C r(e n)_{2}\right] C l_{2} \)
\( c \)
\( \left[\mathrm{Cr}(e n)_{3}\right] \mathrm{Cl}_{3} \)
D. \( \left[\operatorname{CoBr}\left(N H_{3}\right)_{5}\right] S O_{4} \)


Soil salinity is measured by
A. Porometer
B. Potometer
c. conductivity meter
D. Calorimeter


Simplify :
\( [\mathbf{0 . 9}-\{\mathbf{2 . 3}-\mathbf{3 . 2}-(\mathbf{7 . 1}-\mathbf{5 . 4}-\mathbf{3 . 5})\}] \)
\( A \)
B. 0.9
\( c .0 .8 \)
\( D \)


A woman weighs 500 N earth. With how much forces her body pulling up on the
earth?
A. O newton
B. Between O and 500 newton
c. 500 newton
D. between 500 and 1000 newton
E. greater than 1000 newton


\[
\begin{array}{l}
\boldsymbol{8 H}^{+}+\mathbf{4 C l}^{-}+\boldsymbol{M n O}_{\boldsymbol{4}}^{-} \rightarrow \mathbf{2} \boldsymbol{C l}_{\mathbf{2}}+ \\
\boldsymbol{M n}^{\mathbf{2}+}+\mathbf{4} \boldsymbol{H}_{\mathbf{2}} \boldsymbol{O}
\end{array}
\]
Trial
\( \left[C l^{-}\right] \quad\left[M n O_{4}^{-}\right] \quad \) Rate
\( 0.0104 \quad 0.00800 \)
\[
2.25 \times
\]
0.0312 0.00800
03
10
.031
12 0.00400
\[
02 \times 1
\]
Based on the above information,
determine the overall rate law for the
reaction given that the reaction is third
order with respect to the hydrogen ion.
A \( . \) Rate \( =k\left[C l^{-}\right]^{2}\left[M n O_{4}^{-}\right]\left[H^{+}\right]^{3} \)
B. Rate\( =k\left[\mathrm{Cl}^{-}\right]^{2}\left[\mathrm{MnO}_{4}^{-}\right]^{3}\left[\mathrm{H}^{+}\right]^{3} \)
c. \( R a t e=k\left[C l^{-}\right]\left[M n O_{4}^{-}\right]^{3}\left[H^{+}\right]^{3} \)
D. Rate\( =k\left[C l^{-}\right]^{3}\left[M n O_{4}^{-}\right]\left[H^{+}\right]^{3} \)


IUPAC name is 1-phenyl propan-3-ol Is the above statement correct?
A. True
B. False


How many molecules of water are
needed by a green plant to produce one molecule of hexose/reduce 6 molecules
of \( C O_{2} ? \)
\( A \cdot 6 \)
B. 12
\( c \cdot 24 \)
\( D \)


In a closed cylinder of capacity \( 24.6 L \)
the following reaction occurs at \( 27^{\circ} \mathrm{C} \)
\( \boldsymbol{A}_{2}(s) \rightleftharpoons \boldsymbol{B}_{2}(s)+2 C(\boldsymbol{g}) \)
At equilibrium, \( 1 g \) of \( B_{2}(s) \) (molar
mass \( =50 g m o l^{-1} \) ) is present. The
equilibrium constant \( \boldsymbol{K}_{\boldsymbol{p}} \) for the
equilibrium in \( a t m^{2} \) unit is:
\( \left[\boldsymbol{R}=\mathbf{0 . 0 8 2} \boldsymbol{L} \boldsymbol{a t m} \boldsymbol{K}^{-1} \boldsymbol{m o l}^{-1}\right] \)
A \( \cdot 1.6 \times 10^{-2} \)
в. \( 1.6 \times 10^{-5} \)
c. \( 1.6 \times 10^{-3} \)
D. \( 1.6 \times 10^{-4} \)
E . \( 1.6 \times 10^{-1} \)


State true or false:
In an acute-angled \( \triangle A B C, A D \) is
perpendicular to side \( B C, \) then \( A C^{2}= \)
\( A B^{2}+B C^{2}-2 B C \times B D \)
A. True
B. False


is an environment-friendly product and better than halons which
are used to extinguish fire.
A. Ibuprofen
B. Pyrocool
c. Carcinogen
D. Carbon-dioxide


Which of the following substituents will decrease the basicity of the aniline when attached to its para position:
A \( .-O H \)
в. \( -N O_{2} \)
\( \mathbf{c} \cdot-O C H_{3} \)
D. All of these


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

In case of plane parallel mirrors, only two images are possible.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Method used for obtained highly pure silicon, used as a semiconductor
material, is
A. oxidation
B. electrochemical
c. crystallization
D. zone refining


How many more co-ordination isomers
are possible of the compoun \( \left[\boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right]\left[\boldsymbol{P t} \boldsymbol{C l}_{4}\right] ? \)
\( A \cdot 3 \)
B. 4
\( c \cdot 6 \)
D. 8


Topaz, opal, agate, and onyx are precious and beautiful stones found in
nature. All these are different forms of:
\( A \). silica
B. soda
c. carbon
D. lime


Show that \( \left(\boldsymbol{m}^{2}-\mathbf{1}\right),(\boldsymbol{2 m}), \boldsymbol{m}^{2}+\mathbf{1} \)
always form a pythagoran triplet.


Earthworm is
A . Nocturnal
B. Diurnal
c. Aquatic
D. All the above


Give an example of fixed joint.


Which is not the function of lymph?
A. Transport RBCs
B. Drain excess tissue fluid
C. Transport lymphocyte and antibodies
D. Transport absorbed fat


Formic acid is considered as resonance
hybrid of the four resonating
structures
\[
\begin{array}{cc}
\mathbf{0} & \mathbf{O}^{\mathbf{\theta}} \\
\mathbf{H}-\mathbf{C}-\mathbf{O} \mathbf{H} & \longrightarrow \mathbf{H}-\mathbf{C}-\stackrel{\oplus}{\mathbf{O} \mathbf{H}} \\
\mathbf{I} & \mathbf{O}^{\oplus} \\
\mathbf{H}-\mathbf{C}-\mathbf{O}-\mathbf{H} & \mathbf{O}^{\mathbf{\theta}} \\
\mathbf{I V} & \mathbf{I}
\end{array}
\]


In a hydraulic lift, used at a service station the radius of the large and small piston are in the ratio of \( 20: 1 . \) What
weight placed on the small piston will be sufficient to lift a car of mass 1500
kg?
A. \( 3.75 \mathrm{kg} \)
B. 37.5 kgg \( g \)
c. \( 7.5 \mathrm{kg} \)
D. 75 kg


The Vanderwaal's equation for a gas is \( \left(p+\frac{a}{V^{2}}\right)(V-b)=n R T, \) where \( P, v \)
R, \( T \) and \( n \) represent the pressure, volume, universal gas constant, absolute temperature, and number of moles of a gas respectively and 'a' and 'b' are constants. The ratio \( \frac{b}{a} \) will have the following dimensional formula:
\( \mathbf{A} \cdot M^{-1} L^{-2} T^{2} \)
В. \( M^{1} L^{-1} T^{-1} \)
c. \( M L^{2} T^{2} \)
D. \( M L T^{-2} \)


Restoring force in the SHM is
A. conservative
B. nonconservative
C . frictional
D. centripetal


An observer on the sea shore observes
54 waves reaching the coast per minute. If the wavelength is \( 10 m \), the
velocity is
A \( .9 \mathrm{ms}^{-1} \)
В. \( 54 m s^{-1} \)
c. \( 18 \mathrm{ms}^{-1} \)
D. \( 36 m s^{-1} \)


If \( \boldsymbol{A}=\tan ^{-1}\left(\frac{1}{7}\right) \) and \( \boldsymbol{B}=\boldsymbol{t a n}^{-1}\left(\frac{1}{3}\right) \)
then
This question has multiple correct options
\( ^{\mathbf{A}} \cdot \cos 2 A=\frac{24}{25} \)
В. \( \cos 2 B=\frac{4}{5} \)
c. \( \cos 2 A=\sin 4 B \)
D. \( \tan 2 B=\frac{3}{4} \)


The average power dissipated in a pure inductance is
\( ^{\mathbf{A}} \cdot \frac{1}{2}^{L I^{2}} \)
B . \( L I^{2} \)
c. \( L I^{2} / 4 \)
D. zero


A stretched string is in unison with a
tuning fork of frequency \( 392 \mathrm{Hz} \). If the length of the string is decreased by \( 2 \% \) the number of beats heard per second is nearly
\( A \cdot 2 \)
B. 4
\( c \cdot 8 \)
D. 16


In what cases, does a light ray not deviate at the interface of two media?


The projection of the vector \( A=\hat{i}-2 \hat{j}+ \) \( \hat{k} \) on the vector \( \mathrm{B}=4 \hat{i}-4 \hat{j}+7 \hat{k} \) is:
A . \( 19 / 9 \)
в. 38/9
\( c \cdot 8 / 9 \)
\( D \cdot 4 / 9 \)


Increasing order of sizes of hybrid
orbitals is:
В \( \cdot s p^{3}, s p^{2}, s p \)
\( \mathbf{c} \cdot s p^{2}, s p^{3}, s p \)
D. \( s p^{2}, s p, s p^{3} \)


Rutherford's alpha-particle scattering experiment was responsible for the discovery of:
A. atomic nucleus
B. electron.
c. proton
D. neutron.


On the basis of information available for
the reaction:
\( \frac{4}{3} A l+O_{2} \rightarrow \frac{2}{3} A l_{2} O_{3} ; \triangle G= \)
\( -827 k J / m o l \) of \( O_{2} \)
the minimum emf required to carry out
an electrolysis of \( A l_{2} O_{3} \) is:
(Given: \( 1 \boldsymbol{F}=\mathbf{9 6 5 0 0} \boldsymbol{C}) \)
A \( .2 .14 V \)
в. \( 4.28 \mathrm{V} \)
c. \( 6.42 V \)
D. \( 8.56 V \)


Which of the following oxides reacts
with
Both \( H C l \) and \( N a O H ? \)
A. \( \mathrm{CaO} \)
в. ZnO
c. \( N_{2} O_{5} \)
D. \( C O_{2} \)


A light weight boy holds two heavy dumbbells of equal masses with outstretched arms while standing on a
turn-table which is rotating at an
angular frequency \( \omega_{1} \) when the
dumbbells are at distance \( r_{1} \) from the
axis of rotation. The boy suddenly pulls
the dumbbells towards his chest until
they are at distance \( r_{2} \) from the axis of rotation. The new angular frequency of
rotation \( \omega_{2} \) of the turn-table will be
equal to
A \( \cdot \omega_{1} \frac{r_{2}}{r_{1}} \)
В. \( _{\omega_{1}} \frac{r_{1}^{2}}{r_{2}^{2}} \)
c. \( _{\omega_{1}} \frac{r_{1}}{r_{2}} \)
D. \( _{\omega_{1}} \frac{r_{2}^{2}}{r_{1}^{2}} \)


If \( z=\frac{\sqrt{3}+i}{2}, \) then the value of \( z^{69} \) is
A . \( -i \)
B.
\( c \)
D.


Two block of equal mass are tied with a
light which passes over a masseless pulley as shown in figure. The magnitude of acceleration of centre of
mass of both the block is (neglect
friction everywhere)
A \( \cdot \frac{\sqrt{3}-1}{2} g \)
B \( \cdot(\sqrt{3}-1) g \)
c. \( \frac{g}{2} \)
D. None of these


A ball of mass \( 50 g m \) is dropped from a height \( h=10 m . \) It rebounds losing 75
percent of its kinetic energy. If it remains in contact with the ground for \( \Delta t=0.01 \) sec., the impulse of the
impact force is:
A. \( 1.3 N-s \)
B. \( 1.05 N-s \)
c. \( 1300 N-s \)
D. \( 015 N-s \)


A train at rest has a length of \( 100 \mathrm{m} . \) At what speed must it approach a tunnel of length \( 80 \mathrm{m} \) so that an observer at rest with respect to the tunnel will see
that the entire train is in the tunnel at
one time?
A . 1.25c
B. 0.8ç
c. \( 0.64 c \)
D. 0.6c
E . \( 0.36 c \)


Two thin, long,parallel wires,seperated by a distance 'd' carry a current of 'i'A in the same direction.They will:
A. Attract each other
B. Repel,each other
c. Depend upon the material of wire
D. Can't say


Elongation of peptide chain involves all
except
\( A . \) mRNA
B. GTP and peptidyl tranferase
c. Tu, Ts and G factors
D. Formyl met-tRNA


Chemically, detergent is:
A. sodium lauryl sulphate
B. sodium stearate
c. sodium carbonate
D. sodium acetate


The conductivity of \( 0.2 \mathrm{M} \) KCl solution is
\( 3 \times 10^{-2} \) oh \( m^{-1} c m^{-1} . \) Calculate its
molar conductance


If the number of \( 1^{\circ} \) and \( 2^{\circ} \) alcoholic
groups in sucrose are \( x \) and \( y, \) then
the value of \( y-x \) is:


Which one of the following is not a green-house gas?
A. \( C O_{2} \)
в. \( N_{2} \) О
\( c \cdot O_{3} \)
D. \( N_{2} \)


Write balanced equations for the
formation of \( N C l_{3} \) and \( P C l_{3} . \) Given
equations for hydrolysis reactions of
\( N C l_{3} \) and \( P C l_{3} \)


Draw a neat diagram of the following
and label the parts.
DC dynamo


Compare how the magnitude of the electric field decreases with distance
from a uniform charged sphere and a uniform charged wire.
A. Both decrease with a one over the square of the distance relationship.
B. From the sphere, the electric field decreases with a one over the distance relationship. From the wire, the electric field decreases with a one over the distance squared relationship
c. Both decrease with a one over the distance relationship.
D. From the wire, the electric field decreases with a one over the distance relationship. From the sphere, the electric field decreases with a one over the distance squared relationship


Which of the following are equally likely outcomes?
A. Tossing a coin getting head or tail
B. While throwing a die getting any one of 6 numbers
c. Both A and B
D. None of these


Phenelzine is used as an:
A. analgesic
B. antiseptic
c. antipyretic
D. antidepressant


Given that, \( \boldsymbol{t}=\mathbf{5} \boldsymbol{s}, \boldsymbol{u}=\mathbf{0} \boldsymbol{m} / \boldsymbol{s}, \boldsymbol{s}= \)
\( 110 m \)
find the acceleration


Match List I with List II.
List I
List II
A) Greenhouse effect
1. Respiration
B) Oxygen
2. Keeping food items fresh
C) Nitrogen
3. Nitric acid and sulphuric acid
D) Acid Rain
4. Carbon dioxide
A. \( A-4, B-1, C-2, D-3 \)
B. \( A-1, B-2, C-3, D-4 \)
C. \( A-2, B-3, C-4, D-1 \)
D. \( A-3, B-2, C-1, D-4 \)


A bullet of mass 10 g moving with velocity of \( 1.5 \mathrm{m} / \mathrm{s} \) hits a thick wooden plank of mass 90 g. The plank is initially at rest, but when it gets hit by the bullet, the bullet remains in the plank and both move with a certain speed. Calculate the speed with which plank containing the bullet moves?
A. \( 0.15 \mathrm{m} / \mathrm{s} \)
B. \( 0.5 \mathrm{m} / \mathrm{s} \)
\( c \cdot 1.5 \mathrm{m} / \mathrm{s} \)
D. \( 2 \mathrm{m} / \mathrm{s} \)


Calculate the mole fraction of glucose in an aqueous solution that contains 45 g of glucose in 45 g of water. Find out the weight of NaOH required to be disolved in 90 g of water in order to get a solution of the same mole fraction.
A \( \cdot \frac{1}{11}, 20 g \)
в. \( \frac{1}{11}, 10 g \)
c. \( \frac{1}{10}, 10 g \)
D. \( \frac{1}{10}, 20 g \)


Which help us to recognize sound?


Evaluate the following:
\( 46^{3}+34^{3} \)


\( 0.2 \mathrm{L} \) of aqueous solution of a protein contains \( 1.26 \mathrm{g} \) of the protein. The osmotic pressure of such a solution at
\( 300 \mathrm{K} \) is found to be \( 2.57 \times 10^{-3} \) bar.
Calculate the molar mass of the protein.
\( \left(\boldsymbol{R}=\mathbf{0 . 0 8 3} \boldsymbol{L} \text { bar } \boldsymbol{m o l}^{-1} \boldsymbol{K}^{-1}\right) \)


Two electrons are entering
perpendicularly to the magnetic field. The velocity of one of the electrons is
three times greater than the velocity of
the other electron. Calculate the ratio of
the circular radii of the path followed by
the two electrons?
A. The faster electron has a radius two times larger than the slower electron
B. The faster electron has a radius three times larger than the slower electron
C. The faster electron has a radius eight times larger than the slower electron
D. The faster electron has a radius sixteen times larger than the slower electron
E. The faster electron has a radius sixty-four times larger than the slower electron


Solve :
\( x+\frac{1}{x} \geq 2 \)
в. \( R \)
\( c \cdot \phi \)
D. \( [0, \infty) \)


A smooth uniform string of natural length \( l \),cross-sectional area \( A \) and
Young's modulus \( Y \) is pulled aling its
length by a force \( \boldsymbol{F} \) on a horizontal
surface. If the elastic potential energy stored in the string is \( U=\frac{F^{2} l}{x A Y} . \) Find \( x \)


Select the correct statement(s) about
the following This question has multiple correct options
A \( \cdot O_{3} \) is used as germicide for purification of air
B. \( \ln O_{3} \), 0 -o bond length is identical with that of molecular oxygen
\( \mathrm{c} \cdot O_{3} \) molecule is angular in shape
D. \( O_{3} \) is an oxidizing agent


Find the decreased maintenance cost in
the year \( 2000-2001 \) when compared
to 1999 to 2000
listopran
\( A .100 \)
в. 120
\( c .1500 \)
D. 150


Which of the following is/are the secretion/s of Adrenal gland?
A. Cortisone
B. Nor-epinephrine
c. Adrenaline
D. All of the above


Statement I: Radiation and
radioisotopes can have beneficial uses Because
Statement II: Radioisotopes and radiation can be used for radio dating,
radiotracers, and food preservation
A. Both statements are true and Statement II is the correct explanation of statement
B. Both statements are true but Statement II is not the correct explanation of statement
c. statement lis true and Statement II is false
D. Statement lis false and Statement II is true
E. Both statements are false


Assume that a neutron breaks into a
proton and an electron. The energy released during this process is : (mass of neutron \( =1.6725 \times 10^{-27} k g, \) mass
of proton \( =1.6725 \times 10^{-27} k g, \) mass of
electron \( \left.=9 \times 10^{-31} k g\right) \)
\( \mathbf{A} .5 .4 \mathrm{MeV} \)
в. \( 0.73 \mathrm{MeV} \)
c. \( 7.10 M e V \)
D. \( 6.30 \mathrm{MeV} \)


Construct a triangle of sides \( 4 \mathrm{cm}, 5 \mathrm{cm} \)
and \( 6 \mathrm{cm} \) and then a triangle similar to it whose sides are \( \frac{2}{3} \) of the corresponding sides of the first triangle.


During glycolysis, fructose 1,6 biphosphate is split into
A. Dihydroxyacetone phosphate and 2 phosphoglyceraldehyde
B. Dihydroxyacetone phosphate and 1 phosphoglyceraldehyde
c. Dihydroxyacetone phosphate and 4 phosphoglyceraldehyde
D. Dihydroxyacetone phosphate and 3phosphoglyceraldehyde


A major constituent of natural gas is:
A \( . \quad \) NaH \( \mathrm{CO}_{3} \)
в. \( H_{2} S O_{4} \)
\( \mathrm{c} \cdot \mathrm{CH}_{4} \)
D. \( C a(O H)_{2} \)


Check whether given series is \( A P s ? \) If
they form an \( A P \), find the common
difference \( d \) and write three more terms.
\( -1.2,-3.2,-5.2,-7.2, \dots . \)


Why does colloidal particle show Tyndall
effect?


The number of redox reactions from the
following equations are:
a. \( \boldsymbol{H}_{2} \boldsymbol{S}+\boldsymbol{F} \boldsymbol{e}^{3+} \longrightarrow \boldsymbol{F} \boldsymbol{e}^{2+}+\boldsymbol{S} \downarrow+\boldsymbol{H}^{\oplus} \)
b. \( \boldsymbol{I}^{\ominus}+\boldsymbol{I} \boldsymbol{O}_{3}^{\ominus}+\boldsymbol{H}^{\oplus} \longrightarrow \boldsymbol{I}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \)
c. \( \boldsymbol{B} \boldsymbol{i}(\boldsymbol{s})+\boldsymbol{N} \boldsymbol{O}_{3}^{\ominus}+\boldsymbol{H}^{\oplus} \longrightarrow \boldsymbol{N} \boldsymbol{O}_{2}+ \)
\( B i^{3+}+H_{2} O \)
\( \mathbf{d .} \boldsymbol{I}^{\ominus}+\boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O} \longrightarrow \boldsymbol{I}_{2}+\stackrel{\ominus}{\boldsymbol{O}} \boldsymbol{H} \)
e. \( \boldsymbol{C u}(\boldsymbol{s})+\boldsymbol{A} \boldsymbol{u}^{\oplus} \longrightarrow \boldsymbol{A} \boldsymbol{u}(\boldsymbol{s})+\boldsymbol{C} \boldsymbol{u}^{2+} \)


In Solvay ammonia process, sodium
bicarbonate is precipitated due to
A . presence of \( N H_{3} \)
B. reaction with \( C O_{2} \)
C. reaction with brine solution
D. reaction with NaOH


\( f\left(\begin{array}{cc}x+y & x-y \\ 2 x+z & x+z\end{array}\right)=\left(\begin{array}{cc}0 & 0 \\ 1 & 1\end{array}\right), \) then
the values of \( x, y \) and \( z \) are respectively
\( \mathbf{A} \cdot 0,0,1 \)
в. 1,1,0
\( \mathrm{c} \cdot-1,0,0 \)
\( \mathbf{D} \cdot 0,0,0 \)


For strong electrolytes, van't Hoff factor i' equals to total number of
(ions/atoms) in the formula unit


A student appears for tests, I, II and III The student is successful if he passes in
tests I, Il or I, Ill. The probabilities of the student passing in tests I, II and III are espectively \( \mathrm{p}, \mathrm{q} \) and \( \frac{1}{2} . \) If the probability of the student to be successful is \( \frac{1}{2} \) then
A \( \cdot p(1+q)=1 \)
B. \( q(1+p)=1 \)
c. \( p q=1 \)
D. \( \frac{1}{p}+\frac{1}{q}=1 \)


Example of Invention in field of communication is
A. Telephone
B. Fax
c. Internet
D. All of these


Preserved traces of living organisms are
called as fossils. What type of fossil is
shown in the figure?
A. Fossil of a tree trunk
B. Fossil of trilobite
C. Fossil of ammonite
D. Fossil of Knightia


When a solid is converted into a gas, directly by heating then this process is known as:
A. Sublimation
B. Vaporization
c. condensation
D. Boiling


What would be the percentage of thymine (T) and cytosine (C) in a molecule of DNA composed of approximately \( 16.2 \% \) adenine \( (A) \) and 33.4\% guanine (G)?
A . 16.3\% T and 16.3\% C
B. 34.1\% T and 34.1\% C
c. \( 34.1 \% \) T and \( 16.3 \% \) C
D. 16.3\% T and 34.1\% C
E. 33.4\% T and 16.2\% C


Which is the correct order of increasing energy of the listed orbitals in the atom
of titanium?
(At. no. \( Z=22) \)
\( \mathbf{A} \cdot 3 s 3 p 3 d 4 s \)
B. 3s 3p 4s 3d
c. \( 3 s \) 4s \( 3 p 3 d \)
D. \( 4 s 3 s 3 p 3 d \)


In the pictorial representation of an orbital, the role of different intensity of shading is to find the maximum probability of an electron.
A . True
B. False


Re-arrange suitably and find the sum in
each of the following:
\( \frac{-6}{7}+\frac{-5}{6}+\frac{-4}{9}+\frac{-15}{7} \)


How should the electric lamps in a
building be connected?


The length of one side of a
parallelogram is \( 17 \mathrm{cm} \). If the length of its diagonals are \( 12 \mathrm{cm} 26 \mathrm{cm} \), then find
the length of the other side of a
parallelogram.


Write reactions involved in extraction of
silver from it's ore by leaching process. 0-nitrophenol is more acidic than 0 cresol; Explain.


Equal weights of methane and oxygen are mixed in an empty container at
\( 25^{\circ} \mathrm{C} . \) The fraction of the total pressure
exerted by oxygen is:
A \( \cdot \frac{1}{3} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{2}{3} \)
D.


A wire of length \( 44 \mathrm{cm} \) is bent into a
circle and a current of \( 9.8 A \) is passed through it. The intensity of magnetic induction at the centre of the circle is
\( \mathbf{A} \cdot 8.8 \times 10^{-6} T \)
B . \( 8.8 \times 10^{-5} T \)
c. \( 8.4 \times 10^{-6} T \)
D. \( 61.5 \times 10^{-5} T \)


Construct a \( 2 \times 3 \) matrix \( A=\left[a_{i j}\right] \)
whose element \( a_{i j} \) is \( a_{i j}=2 i-j \)


Name the two parts of the alimentary canal where fat is digested.


When phenol reacts with chloroform and an alkali like \( N a O H, \) the
compound formed is salicylaldehyde. If
we use carbon tetrachloride in place of
chloroform, the product obtained is:
A. salicylic acid
B. cyclohexanol
c. phenolphthalein
D. salicylaldehyde


A plane mirror is used as a magnifying
glass. This statement is:
A. True
B. False


The primary of a transformer has 400
turns while the secondary has 2000 turns. If the power output from the secondary at \( 1000 V \) is \( 12 k W, \) what is
the primary voltage?
\( \mathbf{A} \cdot 200 V \)
B. \( 300 V \)
c. \( 400 V \)
D. \( 500 V \)


If the ratio of the concentration of
electrons to that of hole in a semiconductor is \( \frac{7}{5} \) and the ratio of currents is \( \frac{7}{4} . \) Then, the ratio of their drift velocities is :
A \( \cdot \frac{4}{7} \)
B. \( \frac{4}{5} \)
\( c \cdot \frac{5}{8} \)
D.


A uniform rope of mass \( 0.1 \mathrm{kg} \) and length 2.5 m. hangs from ceiling. The speed of transverse wave in the rope at upper end and at a point \( 0.5 \mathrm{m} \) distance from lower end will be:
\( A \cdot 5 \mathrm{m} / \mathrm{s}, 2.24 \mathrm{m} / \mathrm{s} \)
B. \( 10 \mathrm{m} / \mathrm{s}, 3.23 \mathrm{m} / \mathrm{s} \)
c. \( 1.5 \mathrm{m} / \mathrm{s}, 1.2 \mathrm{m} / \mathrm{s} \)
D. none of these


A cube at temperature \( 0^{\circ} C \) is
compressed equally from all sides by an
external pressure \( P . \) By what amount should its temperature be raised to bring it back to the size it had before
the external pressure was applied. The bulk modulus of the material of the
cube is \( B \) and the coefficient of linear
expansion is \( \alpha \)
\( \mathbf{A} \cdot P / B a \)
в. \( P / 3 B \alpha \)
c. \( 3 \pi \alpha / B \)
D. \( 3 B / P \)


Predict which of the following will be coloured in aqueous solution? \( \boldsymbol{T} \boldsymbol{i}^{3+}, \boldsymbol{V}^{3+}, \boldsymbol{C} \boldsymbol{u}^{+}, \boldsymbol{S} \boldsymbol{c}^{3+}, \boldsymbol{M} \boldsymbol{n}^{2+}, \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+} \) and
\( C o^{2+} . \) Give reasons for each


If \( \sqrt{1-x^{2}}+\sqrt{1-y^{2}}=a \) find \( \frac{d y}{d x} \)


A ball reaches a racket at \( 60 \mathrm{m} / \mathrm{s} \) along \( +X \) direction, and leaves the rocket in
the opposite direction with the same speed. Assuming that the mass of the ball as \( 50 \mathrm{gm} \) and the contact time is 0.02 second, the force exerted by the racket on the ball is
A. 300 N along + X direction
B. 300 N along - X direction
c. \( 3,00,000 \mathrm{N} \) along \( +\mathrm{x} \) direction
D. 3,00,000 N along - X direction


An energy of 68 eV is required to excite a hydrogen-like atom from its second Bohr orbit to the third. The nuclear
charge is Ze. The value of \( Z \) is:
\( A \cdot 6 \)
B. 4
\( c \cdot 3 \)
D.


Hydrogen can be produced by:
This question has multiple correct options
A . electrolysis of water
B. distillation of air
C . steam methane reforming process
D. evaporation of water


ATP molecules produced respectively by
\( N A D H\left(H^{+}\right) \) and \( F A D H_{2} \) during
electron transport are
A. 3 and 2
B. 1 and 1
\( c \cdot 2 \) and3
D. 3 and 3


A 2 -dimensional bent rod is made out of
a material with uniform density.
Its center of mass is located at which
position coordinate? Refer to the
diagram of the bent rod and ignore the
rod's thickness in your calculations.
\( \mathbf{A} \cdot(0,0) \)
B \( \cdot\left(\frac{w}{4}, \frac{l}{4}\right) \)
c. \( \left(\frac{w}{3}, \frac{l}{3}\right) \)
D \( \cdot\left(\frac{w}{2}, \frac{l}{2}\right) \)
E \( \cdot\left(\frac{w^{2}}{2(l+w)}, \frac{l^{2}}{2(l+w)}\right) \)


Identify the part "E" from the shown
figure of human eye :
A. Retina
B. Optic nerve
C. Cornea
D. Pupil


Equal volume of two immiscible liquids
of densities \( \rho \) and \( 2 \rho \) are filled in a
vessels as shown in the figure. Two
small holes are punched at depths \( h / 2 \) and \( 3 h / 2 \) from the surface of lighter
liquid. if \( v_{1} \) and \( v_{2} \) are the velocities of
efflux at these two holes, then \( \frac{\mathrm{v}_{1}}{\mathrm{r}} \) is
\( A \cdot \frac{1}{2 \sqrt{2}} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{1}{4} \)
D. \( \frac{1}{\sqrt{2}} \)


Nitrogen containing organic compound when fused with sodium metal forms:
A. \( N a N O_{2} \)
в. \( N a C N \)
c. \( N a N H_{2} \)
D. NaNC


Which compound is prepared by the following reaction? \( X e+F_{2}\left(2: 1 \text { volume ratio) } \frac{N i}{\rightarrow} \text { at } 673 \mathrm{K}\right. \)
\( \mathbf{A} \cdot X e F_{4} \)
B . \( X e F_{2} \)
с. \( X e F_{6} \)
D. None of these


Value of planck's constant is
\( \mathbf{A} \cdot 6.6 \times 10^{-34} J s \)
B . \( 6.4 \times 10^{-26} \mathrm{Js} \)
C \( \cdot 6.8 \times 10^{-27} \mathrm{Js} \)
D. \( 6.6 \times 10^{-28} \mathrm{Js} \)


Which of the following is not a unit of charge?
A. coulomb
B. ampere-second
c. microcoulomb
D. ampere/second


A solution having \( \Delta \boldsymbol{H}_{m i x}=+ \) ve will
exhibit deviation from
ideal behaviour
A. negative
B. positive
\( c \cdot \) no
D. depends upon the properties of the mixing components


What is meant by feedback? Derive an expression for voltage gain of an amplifier with negative feedback.


Write the rate law for -Reaction is zero
order in \( A \) and second order in \( B \).


Which of the following statements is/are correct?
This question has multiple correct options
A \( \cdot N O_{2} \) is a paramagnetic substance
B. Solid is brown in colour
c. \( N O_{2} \) dimerizes about \( N_{2} O_{4} \)
D. \( N O_{2} \) is a mixed anhydride


The root mean square speed at \( N T P \)
for the \( \operatorname{gases} C H_{4}, H_{2}, H e \) and \( F_{2} \) are
in the order
A \( \cdot C H_{4}<H_{2}<H e<F_{2} \)
B. \( H_{2}<H e<C H_{4}<F_{2} \)
c. \( H_{2}<H e<F_{2}<C H_{4} \)
D. \( F_{2}<C H_{4}<H_{2}<H e \)


The shaded region in the figure is the
solution set of the inequations.
\( \mathbf{A} \cdot 5 x+4 y \geq 20, x \leq 6, y \geq 3, x \geq 0, y \geq 2 \)
B. \( 5 x+4 y \geq 20, x \geq 6, y \leq 3, x \geq 0, y \geq 2 \)
c. \( 5 x+4 y \geq 20, x \leq 6, y \leq 3, x \geq 0, y \geq 0 \)
D. \( 5 x+4 y \leq 20, x \leq 6, y \leq 3, x \geq 0, y \geq 2 \)


If 8 G.M.'s are inserted between 2 and 3
then the product of the 8 G.M.'s is
\( \mathbf{A} \cdot \mathbf{6} \)
B. 36
c. 216
D. 1296


What is the time required to empty the tank through the orifice at the bottom?


is soluble in water, ethanol
and methanol.
A . \( N a O H \)
в. \( N a H \)
\( c . N a O \)
D. None of these


If a charge is moved against the coulomb force of an electric field, then :
A. work is done by the electric field
B. energy is used from some outside source
c. the strength of the field is decreased
D. the energy of the system is decreased


In a compound \( C, H \) and \( N \) are present
in 9: 1: 3.5 by weight. If the molecular mass of the compound is \( 108, \) what is
the molecular formula?
A \( \cdot C_{6} H_{8} N_{2} \)
в. \( C_{6} H_{7} N \)
c. \( C_{2} H_{8} N_{2} \)
D. \( C_{6} H_{5} N_{2} \)


Two heater coils 1 and 2 made of the
same material are connected in parallel across the mains. The length and
diameter of the wire of coil 2 are
doubled of that coil \( 1 . \) Find the ratio of
heat generated between coil land 2
A .1: 2
B. 1: 1
c. 2: 1
D. 3: 2


The process of conversion of dead vegetation into coal is termed as:
A. precipitation
B. reduction
c. oxidation
D. carbonization


the general solution of differential
equation \( \boldsymbol{x}^{4} \frac{d y}{d x}+\boldsymbol{x}^{3} \boldsymbol{y}+\operatorname{cosec} \boldsymbol{x} \boldsymbol{y}=\mathbf{0} \)
is
A \( \cdot 2 \cos (x y)+\frac{1}{x^{2}}=0 \)
B. \( 2 \cos (x y)+\frac{1}{y^{2}}=0 \)
\( c \cdot 2 \sin y+\frac{1}{x^{2}}=c \)
D. \( 2 \sin (x y)+\frac{1}{y^{2}}=c \)


Complete the following:
\[
\boldsymbol{F} \boldsymbol{e} \boldsymbol{S} \boldsymbol{O}_{4}+\boldsymbol{6} \boldsymbol{N} \boldsymbol{a} \boldsymbol{C} \boldsymbol{\longrightarrow}
\]


S-character in \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{O}_{4} \) is \( 1 / \)
of
total hybrid orbitals.


On changing of medium, remains same.
A. Wavelength
B. Frequecy
c. speed
D. None


If the system of equations \( : x-k y-z= \)
\( \mathbf{0}, \boldsymbol{k} \boldsymbol{x}-\boldsymbol{y}-\boldsymbol{z}=\mathbf{0}, \boldsymbol{x}+\boldsymbol{y}-\boldsymbol{z}=\mathbf{0} \) has a non
zero solutions then find the possible
value of \( k \)


How many hydrate isomers of
\( \left[\boldsymbol{F} \boldsymbol{e}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right] \boldsymbol{C l}_{3} \) are possible?


If a ball of steel (density \( \rho=7.8 g c m^{-3} \)
attains a terminal velocity of \( 10 \mathrm{cm} s^{-1} \) when falling in a tank of water (coefficient of viscosity \( \eta_{w a t e r}= \)
\( \left.8.5 \times 10^{-4} \text {Pa.s }\right) \) then its terminal
velocity in glycerine \( (\rho= \) \( \left.12 g c m^{-3}, \eta=13.2 \text { pa.s }\right) \) would be
nearly:-
A. \( 1.6 \times 10^{-5} \mathrm{cm} \mathrm{s}^{-1} \)
в. \( 6.25 \times 10^{-4} \mathrm{cm} \mathrm{s}^{-1} \)
c. \( 6.45 \times 10^{-4} \mathrm{cm} s^{-1} \)
D. \( 1.5 \times 10^{-5} \mathrm{cm} \mathrm{s}^{-1} \)


A wire of resistance \( 10 \Omega \) is bent to form
a complete circle. Find its resistance
between two diametrically opposite
point
A . \( 5 \Omega \)
В. \( 2.5 \Omega \)
c. \( 1.25 \Omega \)
\( D \cdot \frac{10}{0} s \)


(i) Gas (A) is more soluble in water than
gas
(B) at the same temperature. Which
one of the two gases will have the higher
value of \( \boldsymbol{K}_{\boldsymbol{H}} \) (Henry's constant) and
why?
(ii) In non-ideal solution, what type of
deviation shows the formation
of maximum boiling azeotropes?


\( \operatorname{Let} A=\{1,2,3\} \) and \( B=\{3,4\} \) then
find \( A \cap B \) and then find \( A \times(A \cap B) \)


A particle executes SHM with a time
period of 16 s. \( A t \) time \( t=2 s, \) the
particle crosses the mean position
while at \( t=4 s, \) its velocity is \( 4 m s^{-1} \)
The amplitude of motion in metre is?
A \( \cdot \sqrt{2} \pi \)
В. \( 16 \sqrt{2} \pi \)
c. \( 32 \sqrt{2} / \pi \)
D. \( 4 / \pi \)


The book 'Systema Naturae' was written
by
A. Linnaeus
в. Haeckel
c. whittaker
D. Brown


Match the sugars in column I with their
types given in column II and mark the appropriate choice.
Column I
(A) Glucose
(i) Ketohexose
(B) Fructose
(ii) Aldohexose
(C) Ribose
(iii) Aldotetrose
(D) Erythrose
(iv) Aldopentose
\( A \cdot(A) \rightarrow(i v),(B) \rightarrow(i),(C) \rightarrow(i i i),(D) \rightarrow(\text { ii }) \)
B. (A) \( \rightarrow \) (iii), (B) \( \rightarrow \) (iv), (C) \( \rightarrow \) (i), (D) \( \rightarrow \) (ii)
C \( \cdot(A) \rightarrow(i),(B) \rightarrow(\text { ii) },(C) \rightarrow(\text { iii) },(D) \rightarrow\text { (ii) } \)
D. (A) \( \rightarrow \) (ii), (B) \( \rightarrow \) (i), (C) \( \rightarrow \) (iv), (D) \( \rightarrow \) (iii)


If air drag is not neglected, then which is greater time of ascent or time of descent?


The propulsion of rocket illustrates that
This question has multiple correct options
A. Linear momentum is conserved
B. Angular momentum is not conserved
C. Newton's third law is applicable
D. Linear momentum is not conserved


Consider the arrangement shown in Fig
29.15(a). The distance \( D \) is large,
compared to \( d \). Find minimum value of
\( d \) so that there is a dark fringe at \( O . \) For
the same value of \( d \) find \( x \) at which next
bright fringes is formed.


The wave that propagates as an oscillation of matter, and therefore
transfers energy through a medium is
A. Mechanical wave
B. Ultrasonic wave
c. Infrared wave
D. None


Which among the following properties are not shown by the roots?
A. Distinction of primary and secondary roots
B. Distinction of nodes and internodes
c. Tertiary roots and rootlets
D. Endogenous branches


Assertion
Methane is a component of greenhouse gases and contributing to global warming about 20 percent.
Reason
Introduction of multi-point fuel
injection engines in automobiles has decreased methane content in the
exhausts.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect.
D. Both Assertion and Reason are incorrect.


A electric dipole moment \( \overrightarrow{\boldsymbol{p}}= \) \( (2.0 \hat{i}+3.0 \hat{j}) \mu C . m \) is placed in a
uniform electric field \( \overrightarrow{\boldsymbol{E}}= \) \( (3.0 \hat{i}+2.0 \hat{k}) \times 10^{5} N C^{-1} \)
This question has multiple correct options
A. The torque that \( \vec{E} \) exerts on \( \vec{p} \) is \( (0.6 \hat{i}-0.4 \hat{j}-0.9 \hat{k}) N m \)
B. The potential energy of the dipole is -0.65
c. The potential energy of the dipole is \( 0.6 J \)
D. If the dipole is free to rotate in the electric field, the maximum magnitude of potential energy of the dipole during the rotation is 1.3 .5


toppr
Q Type your question
are taken in \( A \) and \( B \). How many of the following statement(s) is/are correct?
\( \mathbf{P}_{X}^{0}=\mathbf{2 0 0} \) tor \( r \)
\( \mathbf{P}_{Y}^{0}=\mathbf{5 0} \) tor \( r \)
(i) If \( \mathrm{NaCl} \) is added to vessel \( \mathrm{B} \), the
lowering of vapour pressure takes place.
(ii) If glucose is added to vessel \( A, \) the boiling point of the solution increases.
(iii) If the valve connecting \( A \) and \( B \) is
opened, then \( \mathbf{P}_{T} \) in both the vessel
becomes equal and is given by Raoult's law.
(iv) After opening the valve, the level of liquid in both the container decreases (even a slight decrease is to be considered)
(v) After opening the valve, the final pressure in vessel B is more than 50
torr.
(vi) After opening the valve, the final pressure in vessel \( A \) is more than 200
torr
\( A \cdot 2 \)
B. 3
\( c \)
\( D \)


Verify Rolle's theorem for each of the following functions on the indicated intervals:
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{e}^{\boldsymbol{x}} \sin \boldsymbol{x} \) on \( [\mathbf{0}, \boldsymbol{\pi}] \)


Crystals are formed by ions, atoms, and molecules having an internal pattern that is
A. irregular, non-repeating
B. regular, repeating
c. regular, non-repeating
D. none of the above


Liquids generally have lower density as
compared to solids but ice floats on water. Why?


The group that has \( +R \) and \( -I \) effects
is:
A. \( -C H O \)
в. \( -O H \)
c. \( C=O \)
D. \( C N \)


The number of \( 1^{\circ} \) alkyl halides are
formed with the formula \( C_{5} H_{11} C l \) is:
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5


An example for anionic detergent is:
A. NaLs
B. СТАВ
c. trimethyl phosphate
D. all


If \( f(x)=x+\frac{1}{x} \) find \( f(5) \)


The uncertainties in the velocities of
two particles, \( A \) and \( B \) are 0.05 and
\( 0.02 m s^{-1} \) respectively. The mass of \( B \)
is five times to that of the mass of \( \boldsymbol{A} \) What is the ratio of uncertainties \( \frac{\Delta x_{A}}{\Delta x_{B}} \) in their positions?
A . 2
B. 0.25
\( c \cdot 4 \)
\( D \)


Fill in the blanks.
a) For a motor: a permanent magnet, then for a commercial motor:
b) Focal length of a lens: metre, then for
power of a lens:


Consider the circular loop having
current \( i \) and with central point \( O . \) The
magnetic field at the central point \( \boldsymbol{O} \) is
A \( \cdot \frac{2 \mu_{0} i}{3 \pi R} \) acting downward
B. \( \frac{5 \mu_{0} i}{12 R} \) acting downwaro
c. \( \frac{6 \mu_{0} i}{11 R} \) acting downwar
D. \( \frac{3 \mu_{0} i}{7 R} \) acting downwar


Match the terms to these definitions.
adipose tissue, blood, cardiac muscle, compact bone, connective tissue,
endocrine gland, epidermis, epithelial tissue, exocrine gland, fibroblast, homeostasis, lacuna, ligament, organ system, skeletal muscle, spongy bone, tendon tissue, nervous tissue, striated muscle.
A firm, white, fibrous inelastic cord
which attaches muscle to bone.


Consider the following iodides:
\( \boldsymbol{P I}_{3} \quad \boldsymbol{A} \boldsymbol{s} \boldsymbol{I}_{3} \quad \boldsymbol{S} \boldsymbol{b} \boldsymbol{I}_{3} \)
\( \mathbf{1 0 2}^{\circ} \quad \mathbf{1 0 0 . 2}^{\circ} \quad \mathbf{9 9}^{\circ} \)
The bond angle is maximum in \( \boldsymbol{P I}_{3} \)
which is :
A. due to small size of phosphorus
B. due to more bond pair-bond pair repulsion in \( P I_{3} \)
c. due to less electronegativity of \( \mathrm{P} \)
D. none of these


The asymptotes of a hyperbola having centre at the point (1,2) are parallel to the lines \( 3 x+4 y=0 \) and \( 4 x+5 y=0 \)
If the hyperbola passes through the point \( (3,5), \) Find the equation of the hyperbola.


Which of the following is disproposination reaction?
A \( \cdot C a C O_{3}+2 H^{+} \rightarrow C a^{2+}+H_{2} O+C O_{2} \)
B . \( 2 \mathrm{CrO}_{4}^{2-}+2 \mathrm{H}^{+} \rightarrow \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}+\mathrm{H}_{2} \mathrm{O} \)
c. \( C r_{2} O_{7}^{2-}+2 O H^{-} \rightarrow 2 C r O_{4}^{2-}+H_{2} O \)
D. \( C u_{2} O+2 H^{+} \rightarrow C u+C u^{2+}+H_{2} O \)


The function \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) defined by
\( f(x)=\frac{x^{2}}{1+x^{2}} \forall x \in R \) is
A. one one but not onto
B. onto but not one one
c. a bijection
D. neither one one nor onto


The hardness of water caused by 0.25
moles of \( M g C l_{2} \) is equal to :
1) the hardness of water caused by 25
grams of \( \boldsymbol{C a} \boldsymbol{C O}_{3} \)
II) the hardness of water caused by 0.25
moles of \( \boldsymbol{C a C O}_{3} \)
III) the hardness of water caused by 1
moles of \( \boldsymbol{C a} \boldsymbol{C O}_{3} \)
A. only II is correct.
B. I and II are correct.
c. I and III are correct.
D. only I is correct.


Leptothrix is a
A. Nitrifying bacteria
B. Sulphur bacteria
C. Iron bacteria
D. Hydrogen bacteria


The species that can have a transisomer is:
\( (e n=\text { ethane }-1,2-\text { diamine, ox }= \) oxalate)
A \( \cdot\left(P t(e n) C l_{2}\right] \)
\( \mathbf{B} \cdot\left[C r(e n)_{2}(o x)\right]^{+} \)
c. \( \left[\left[Z n(e n) C l_{2}\right]\right. \)
D. \( \left[P t(e n)_{2} C l_{2}\right]^{2+} \)


If long hollow copper pipe carries a direct current, the magnetic field associated with the current will be:
A. only inside the pipe
B. only outside the pipe
c. neither inside nor outside the pipe
D. both inside and outside the pipe


Find the circumference of the inner and
the outer circles, shown in the adjoining
figure. (Take \( \boldsymbol{\pi}=\mathbf{3 . 1 4}) \)


The earth pulls a stone downwards due to gravity. The stone exerts:
A. an equal and opposite force on the earth
B. a greater force on the earth
c. a lesser force on the earth
D. no force on the earth


Hydrogen could well be a fuel for the future. Which of the following statement is true about the potential use of hydrogen as a fuel?
A. Easily liquefiable
B. Produces lots of green house gases on combustion
c. Explosive when mixed with air
D. All of the above


A bullet of mass \( 20 g \) has an initia
speed of \( 1 m s^{-1} \),just before it starts penetrating a mud wall of thickness \( 20 c m . \) if the wall offers a mean
resistance of \( 2.5 \times 10^{-2} N, \) the speed of
the bullet after emerging from the other
side of the wall is close to :
A \( \cdot 0.4 m s^{-1} \)
В. \( 0.1 m s^{-1} \)
\( \mathbf{c} \cdot 0.3 m s^{-1} \)
D. \( 0.7 m s^{-1} \)


Assertion
Reversible systems are difficult to find
in the real world.
Reason
Most processes are dissipative in
nature.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A transformer having efficiency of \( 75 \% \) is working on \( 220 V \) and \( 4.4 k W \) power supply. If the current in the secondary coil is \( 5 A . \) What will be the voltage
across secondary coil and the current in primary coil?
\( \mathbf{A} \cdot V_{s}=220 V, i_{p}=20 A \)
B. \( V_{s}=660 V, i_{p}=15 A \)
C . \( V_{s}=660 V, i_{p}=20 A \)
D. \( V_{s}=220 V, i_{p}=15 A \)


A train blowing its whistle moves with a constant velocity v away from an observer on the ground. The ratio of the
natural frequency of the whistle to that measured by the observer is found to be
1.2. If the train is at rest and the observer
moves away from it at the same velocity, this ratio would be given by
A . 0.5
B. 1.25
\( c \cdot 1.52 \)
D. 2.05


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


Write the formula for the sum of first \( n \)
positive integers.


An electric current predominantly produce.................. field around it.
A. magnetic
B. electric
c. gravitational
D. all the above


The average distance between Earth and the Sun is \( 1.496 \times 10^{8} k m \) and the
speed of light coming from the Sun is \( 3 \times 10^{8} m / s . \) How much time will it
take for Sun's rays to reach Earth?
A. 3 min
B. \( 498.66 s \)
c. \( 8 \min 30 s \)
D. \( 554 s \)


A particle is projected with a speed u at
an angle \( \theta \) with the horizontal. What is the radius of curvature of the parabola traced out by the projectile at a point where the particle velocity makes an \( \boldsymbol{\theta} \)
angle \( \frac{-}{2} \) with the horizontal


The kidneys in the human body
A. Excrete waste products and any excess of salts
B. Regulate the concentration of the salts in the blood and of the reaction (acid-base balance) of the blood
C. Regulate the water balance in the body
D. All of the above


If the frequency of an alternating e.m.f.
is \( f \) in \( L-C-R \) circuit, then the value of
impedance \( \mathbf{Z} \) as log(frequency)
increases:
A. increases
B. increases and then becomes equal to resistance, then it will start decreasing
c. decreases and when it becomes minimum, equal to the resistance then it will start increasing
D. go on decreasing


Which of the following substances will lose its solutbility with increase in temperature?
A . \( N a O H \)
в. \( N a_{2} C O_{3} \)
c. \( N a_{2} S O_{4} \)
D. All


Determine the reaction at support \( A \) ad
B of loaded beam shown in Fig.1


A current of 3 amp. flows through the 2
ohm resistor shown in the circuit. The
power dissipated in the 5 ohm resistor
is:
A . 1 watt
B. 5 watt
\( c .4 \) watt
D. 2 watt


In fungi, the reserved food is in the form
of ?


Which of the following do not exist as stable molecules?
This question has multiple correct options
A. \( H_{3} \)
B. \( H-H e \)
c. \( H e_{2} \)
D. \( H_{3} O \)


\( \mathbf{A}=\left[\begin{array}{ccc}\mathbf{1}^{2} & \mathbf{2}^{\mathbf{2}} & \mathbf{3}^{2} \\ \mathbf{2}^{\mathbf{2}} & \mathbf{3}^{2} & \mathbf{4}^{2} \\ \mathbf{3}^{\mathbf{2}} & \mathbf{4}^{\mathbf{2}} & \mathbf{5}^{\mathbf{2}}\end{array}\right], \) then \( |\boldsymbol{A} \boldsymbol{d} \boldsymbol{j} \boldsymbol{A}|= \)
\( A \)
B . 16
\( c \cdot 64 \)
D. 128


Who is called father of modern
chemistry?
A. Antoine Lavoisier
B. Gilbert Lewis
c. Gibbs
D. Otto Hahn


Determine whether the equation \( 5 x^{2}= \)
\( 5 x \) is quadratic or not.
A. Yes
B. No
c. complex equation
D. None


Carbon dioxide is carried in the blood,
mainly as
A. Sodium bicarbonate
B. Potassium bicarbonate
C. Carbamino-haemoglobin
D. Dissolved gas in plasma


How will the image formed by a convex
lens be affected if the central portion of lens is wrapped in black paper?
A. No image is formed by the remaining portion of lens
B. There will be no effect
c. The full image will be formed but it will be less bright
D. The central portion of the image will be absent


If \( \lim _{x \rightarrow 2^{+}} \frac{x-3}{x^{2}-4}=a \) then \( \frac{1}{a} \) is equal
to


Bleaching powder is obtained by the interaction of \( C l_{2} \) with a:
A. dilute solution of \( C a(O H)_{2} \)
B. concentrated solution of \( C a(O H)_{2} \)
c. dry \( C a O \)
D. dry slaked lime


An ellipse \( \frac{x^{z}}{4}+\frac{y^{z}}{3}=1 \) confocal with
hyperbola \( \frac{x^{2}}{\cos ^{2} \theta}-\frac{y^{2}}{\sin ^{2} \theta}=1 \) then the
set of value of \( ^{\prime} \mathbf{0}^{\prime} \)
A. \( R \)
В . \( R-\{n \pi, n \epsilon z\} \)
\( ^{\mathrm{c}} \cdot_{R}-\left\{(2 n+1) \frac{\pi}{2}, n \epsilon z\right\} \)
D. \( _{R-}\left\{\frac{n \pi}{2}, n \epsilon z\right\} \)


Which plant shows distinct
development from juvenile to adult
phase?
A. Triticum vulgare
B. Hedera Helix
c. Solanum tuberosum
D. Petunia


A cell contains two hydrogen electrode.
The negative electrode is in contact with a solution of \( 10^{-6} M \) hydrogen ions
The emf of the cell is 0.118 volt \( \operatorname{at} 25^{\circ} C \)
Calculate the concentration of hydrogen ions at the positive electrode.


The charge/size ratio of a cation determines its polarizing power. Which one of the following sequences represents the increasing order of the polarizing power of the cationic species,
\( \mathrm{K}^{+}, \mathrm{Ca}^{2+}, \mathrm{Mg}^{2+}, \mathrm{Be}^{2+} ? \)
\( A \cdot M g^{2+}<B e^{2+}<K^{+}<C a^{2+} \)
B. \( B e^{2+}<K^{+}<C a^{2+}<M g^{2} \)
C \( \cdot \mathrm{k}^{+}<\mathrm{Ca}^{2+}<\mathrm{Mg}^{2+}<\mathrm{Be}^{2+} \)
D. \( \mathrm{Ca}^{2+}<\mathrm{Mg}^{2+}<\mathrm{Be}^{2+}<\mathrm{K}^{+} \)


Q Type your question
performed the above experiment with two different solutions (Y). If in the case
of Nikita, solution(Y) is dilute
hydrochloric acid and in case of
Tarun, solution (Y) is sodium hydroxide
then compounds formed are
and \( _{--}-_{-} \) respectively
A. \( N a_{2} Z n O_{2} \) and \( Z n C l_{2} \)
в. \( Z n C l_{2} \) and \( N a_{2} Z n O_{2} \)
c. \( Z n S O_{4} \) and \( N a_{2} Z n O_{2} \)
D. \( Z n C l_{2} \) and \( Z n O \)


If \( \boldsymbol{x}, \boldsymbol{y}, \boldsymbol{z}>\mathbf{0} \) and \( \boldsymbol{x} \boldsymbol{y} \boldsymbol{z}=\mathbf{1} \)
Then
This question has multiple correct options
\( \mathbf{A} \cdot x^{2}+y^{2}+z^{2} \leq x^{3}+y^{3}+z^{3} \)
B . \( x^{2}+y^{2}+z^{2} \geq x^{3}+y^{3}+z^{3} \)
\( \mathbf{c} \cdot\left(x^{4}+y^{4}+z^{4}\right) \geq\left(x^{3}+y^{3}+z^{3}\right) \)
D. \( \left(x^{4}+y^{4}+z^{4}\right) \leq\left(x^{3}+y^{3}+z^{3}\right) \)


A physical quanity \( P \) is releated to four
observation \( a, b, c \) and \( d \) as follows \( P= \)
\( a^{3} b^{3} / \sqrt{c d T h e} \) percentage errors of
measurement in \( a, b, c \) and \( 1 \%, 3 \%, 4 \% \)
and \( 2 \% \) repectively. What is the
percentage erros in quanity \( P \) ? If the
value of \( \boldsymbol{P} \). Calculated using the above
relations turns out to +ve \( 3.763, \) to what value you should round off the result?


Sulphide ore of zinc/copper is concentrated by:
A. forth floatation
B. electromagnetic process
c. gravity process
D. distillation


When a \( 4 k g \) mass is hung vertically on a light spring that obeys Hooke's law,
the spring stretches by 2 cms. The work required to be done by an external agent in stretching this spring by \( 5 c m s \) will
be \( \left(\boldsymbol{g}=\mathbf{9 . 8 m} / \boldsymbol{s e c}^{2}\right) \)
A. 4.900 joule
B . 2.450 joule
c. 0.495 joule
D. 0.245 joule


Out of gravitational, electrostatic, vander waal and nuclear forces, which
are able to provide attractive force
between two neutrons?
A. Electrostatic and gravitational
B. Electrostatic and nuclear
c. vander waal and nuclear
D. Nuclear and gravitational


Calculate the amount of heat energy
required to raise the temperature of \( 2 g \) of mercury (Specific heat Capacity
\( \left.0.12 J g^{-1} o C^{-1}\right) \) from \( 10^{\circ} C \) to \( 30^{\circ} C \)
A . \( 1.2 J \)
в. 2.4
c. \( 4.8 J \)
D. 9.6 .5


How many maximum number of atoms
are coplanar in \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{O} \boldsymbol{F}_{4} ? \)


Two bar magnets are placed on a piece of cork which floats on water. The magnets
are so placed that their axis are mutually
perpendicular. Then the cork
A. rotates
B. moves a side
c. oscillates
D. neither rotates nor oscillates


Thin filament is made up of
A. Actin, troponin and tropomyosin
B. Actin and troponin
C. Myosin and troponin
D. Actin and tropomyosin


A ferromagnetic material heated above its curie temperature. Which one is a
correct statement?
A. Ferromagnetic domains are perfectly arranged
B. Ferromagnetic domains become random
c. Ferromagnetic domains are not influenced
D. Ferromagnetic material changes into diamagnetic materia


From Delhi station, if we buy 2 ticket for
station \( A \) and 3 tickets for station \( B \), the
total cost is Rs.77. But if we buy 3 tickets for station \( A \) and 5 tickets for
station \( \mathrm{B} \), the total cost is Rs. 124. What
are the fares from Delhi to station \( A \) and
to station B ?
A. \( A=R s .12 ; B=R s .17 \)
в. \( A=R s .13 ; B=R s .17 \)
c. \( A=R s .18 ; B=R s .17 \)
D. \( A=R s .19 ; B=R s .17 \)


The males of bees and wasps are
A. Haploid
B. Polyploid
\( c \cdot x x \)
D. xo


Which of the following can conduct electricity in the solid state?
A. sucrose, \( C_{12} H_{22} O_{11}(s) \)
B. Graphite, C(s)
C. Sodium hydroxide, NaOH(s)
D. Iron(III) chloride, \( F e C l^{3}(s) \)
E . lodine, \( I_{2}(s) \)


A catalyst lower the activation energy of
a reaction from \( 20 \mathrm{kJ} \) mole \( ^{-1} \) to \( 10 \mathrm{kJ} \)
mol \( ^{-1} \). The temperature at which the uncatalysed reaction will have the same rate as that of the catalyzed at 27
\( o C \) is:
A \( \cdot-123^{\circ} C \)
B. \( 327^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 150^{\circ} \mathrm{C} \)
\( \mathrm{D} \cdot+23^{\circ} \mathrm{C} \)


How much \( N a F \) should be added to 100
mL of solution having \( 0.016 M \) in \( S r^{2}+ \)
ions to reduce its concentration to
\( 2.5 \times 10^{-3} M ?\left(K_{s p} S r F_{2}=8 \times 10^{-10}\right) \)
A. 0.098 g
ggg \( . . .998 \)
B. 0.168 g
c. 0.177 g
D. 0.118 g


Clay soil is obtained
A. In desert
B. Around ponds
c. on seashore
D. on rocks


A geostationary satellite appears to remain stationary with respect to
earth's surface because.
A. It moves with the Moon
B. It moves with a very slow speed
c. It does not move
D. Its period of rotation is identical to the spin of the earth


A terrestrial telescope is made by introducing an erecting lens of focal length, \( f \), between the objective and eyepiece lens of an astronomical telescope. This causes the length of telescope tube to increase by an
amount equal to
\( A \cdot f \)
B . \( 2 f \)
\( c \cdot 3 f \)
D. \( 4 f \)


Radius of the nucleus is about
times less than the radius of the atom.
A \( \cdot 10^{3} \)
B. \( 10^{\text {। }} \)
\( c \cdot 10^{5} \)
D. \( 10^{2} \)


The initial rate of zero-order reaction of
the gaseous equation \( A(g) \rightarrow 2 B(g) \) is \( 10^{-2} \mathrm{M} \min ^{-1} \) if the initial
concentration of \( A \) is 0.1 M. What would
be a concentration of \( B \) after 60
seconds?
\( \mathbf{A} \cdot 0.09 M \)
в. \( 0.01 M \)
c. \( 0.02 M \)
D. \( 0.03 M \)


If \( f(x) \) satisfies Rolles theorem for \( f(x) \) in \( [\boldsymbol{a}, \boldsymbol{b}] \) then \( \int_{a}^{\boldsymbol{b}} \boldsymbol{f}^{\prime}(\boldsymbol{x}) \boldsymbol{d} \boldsymbol{x}= \)
\( \mathbf{A} \cdot f(b)+f(a) \)
B . \( f(a) \)
\( c \cdot f(b) \)
D.


Find the time period and the
wavelength.


Name the ear ossicles in the order
of arrangement in humans.


\( \boldsymbol{O}=\boldsymbol{C}=\boldsymbol{O} \)
How many pi bonds does given compound have?
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5


In an experiment to determine the focal length \( (f) \) of a concave mirror by the
\( u-v \) method, a student places the
object pin \( A \) on the principal axis at a distance \( x \) from the pole \( P . \) The student
looks at the pin and its inverted image from a distance keeping the eye in line with \( P A . \) When the student shifts the
eye towards left, the image appears to
the right of the object pin. Then:
A. \( x<f \)
B. \( f<x<2 f \)
c. \( x=2 f \)
D. \( x>2 f \)


\( K O_{2} \) is used in life supports in space
create submarines and emergency
breath apparatus since it:
A. absorbs \( C O_{2} \)
B. release \( O_{2} \)
c. release \( C O_{2} \)
D. absorbs \( C O_{2} \) and releases \( O_{2} \)


Prokaryotes are
A. Unicellular
B. Multicellular
C. Both A and B
D. None of the above


Ferrous sulphate heptahydrate is used to fortify foods with iron. The amount (in grams) of the salt required to achieve 10 ppm of iron in 100 kg of wheat is
[Atomic weight \( : \mathrm{Fe}=\mathbf{5 5 . 8 5} \mathrm{S}=\mathbf{3 2 . 0 0} \mathrm{O} \)
\( =\mathbf{1 6 . 0 0}] \)


Find the value of :
\( (\mathbf{5} i)\left(-\frac{\mathbf{3}}{\mathbf{5}} i\right) \)


Which of the following is not a type of an
IC?
A. Analog IC
B. Digital IC
c. Mixed IC
D. compound IC


In a p-njunction having depletion layer
of thickness \( 10^{-6} m \), the potential
across it is \( 0.1 \mathrm{V} \). The electric field is
A \( \cdot 10^{7} V / m \)
В \( \cdot 10^{-6} V / m \)
c. \( 10^{5} V / m \)
D. \( 10^{-5} V / m \)


Assertion
Aqueous solution of \( N a O X \) is alkaline.
Reason
It is a salt of weak acid \( (\boldsymbol{H} \boldsymbol{O} \boldsymbol{X}) \) are
strong base \( (N a O H) \)
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 lanthanides contraction refers to:
A. ionic radius of the series
B. valence electrons of the series
c. the density of the series
D. electronegativity


State and prove principle of conservation of angular momentum.


A resistor with the color coded value of
1000 ohms and \( 10 \% \) tolerance can have
an actual resistance between
A. 900 ohm and 1100 ohm
B. 900 ohm and 1010 ohm
c. 990 ohm and 1010 ohm
D. 900 ohm and 1000 ohm


What is \( \sin ^{-1} \sin \frac{3 \pi}{5} \) equal to \( ? \)
\( \mathbf{A} \cdot \frac{3 \pi}{5} \)
B. \( \frac{2 \pi}{5} \)
\( c \cdot \frac{\pi}{5} \)
D. None of the above


The length of minute hand of a clock is
14cm. Find the area swept by this minute hand in 10 minutes. \( \left(\pi=\frac{22}{7}\right) \)


The value of \( \sqrt[3]{-125 \times(-1000)} \) is
A. 50
B. - -50
c. 55
D . -55


If \( z=x+i y \) is a complex number such
that \( \bar{z}^{\frac{1}{3}}=a+i b, \) then the value of \( \frac{1}{a^{2}+b^{2}}\left(\frac{x}{a}+\frac{y}{b}\right)= \)
A . -1
B. -
\( c \cdot 0 \)
D.


toppr LoGın
Q Type your question
enthalpy \( \left(\text { in } \mathrm{kJ} \mathrm{mol}^{-1}\right) \) of a few elements
are given below:
\begin{tabular}{llll}
Elements & \( \boldsymbol{\Delta} \boldsymbol{H}_{1} \) & \( \boldsymbol{\Delta} \boldsymbol{H}_{2} \) & \( \boldsymbol{\Delta}_{e g} \mathbf{H} \) \\
1 & 520 & 7300 & -60 \\
11 & 419 & 3051 & -48 \\
\hline 111 & 1681 & 3374 & -328 \\
\hline \( \mathrm{IV} \) & 1008 & 1846 & -295 \\
\( \mathrm{V} \) & 2372 & 5251 & +48 \\
\hline \( \mathrm{V} \) & 738 & 1451 & -40
\end{tabular} Which of the above elements is likely to
be:
(a) the least reactive element,
(b) the most reactive metal,
(c) the most reactive non-metal,
(d) the least reactive non-metal,
(e) the metal which can form a stable
binary halide of the formula \( \mathrm{M} \mathrm{X}_{2} \)
(X=halogen) and
(f) the metal which can form a
predominantly stable covalent halide of
th \( \cdot \) mula MX (X=halogen)?


Among the following the species having same geometry for central atom are
(i) \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{\mathbf{4}} \)
(ii) \( \boldsymbol{S} \boldsymbol{F}_{\mathbf{4}} \)
(iii) \( \left[N i C l_{4}\right]^{2-} \)
(iv) \( \left[\boldsymbol{P d C l}_{4}\right]^{2-} \)
A. (i) and (iv)
B. (i), (iii) and (iv)
c. (ii) and (iii)
D. (iii) and (iv)


Which of the following is correct in
regards to photorespiration?
A. In mitochondria, serine in converted into hydroxypyruvate
B. In mitochondria, two glycine molecules unite to form serine
C. In mitochondria, glycolate is oxidised to form glyoxylate
D. In peroxisomes, three molecules of glycine unite to form serine


If \( \boldsymbol{A}=(\boldsymbol{6}, \boldsymbol{7}, \boldsymbol{8}, \boldsymbol{9}), \boldsymbol{B}=(\boldsymbol{4}, \boldsymbol{6}, \boldsymbol{8}, \boldsymbol{1} \boldsymbol{0}) \) and
\( \boldsymbol{C}=\{\boldsymbol{x}: \boldsymbol{x} \boldsymbol{\epsilon} \boldsymbol{N}: \boldsymbol{2}<\boldsymbol{x} \leq \mathbf{7}\} ; \) find :
\( \boldsymbol{n}(\boldsymbol{B}-(\boldsymbol{A}-\boldsymbol{C})) \)


The metal which gives hydrogen on treatment with hydrochloric acid as wel as sodium hydroxide is:
A. \( F e \)
в. \( Z \) и
c. \( C u \)
D. All of the above


According to molecular orbital theory, which of the following will not exist?
A \( \cdot H_{2}^{+} \)
в. \( B e_{2} \)
c. \( B_{2} \)
D. \( C_{2} \)


If sum of the distances of a point from
two perpendicular lines in a plane is 1 then its locus is
A. a square
B. a circle
c. a straight line
D. two intersecting lines


Amines are the derivatives of:
\( A \). acids
B. ammonia
c. alkanes
D. esters


The pressure of moist gas at a given temperature is \( 10 \mathrm{mm} \) Hg at volume \( V \)
Aqueous tension at this temperature is \( 3 \mathrm{mm} \) Hg point the final pressure of gas at the same temperature if the volume is reduced to \( 1 / 3 \) original volume is:
A. 30mm Hg
B. 27mm Hg
c. \( 24 \mathrm{mm} \) ну
D. \( 21 \mathrm{mm} \) Hg


Represent the following complex number in trigonometric form:
\( (-\sqrt{3}+i)^{3} \)


Select the correct Rh-blood groups of the parents, whose child is affected with erythroblastosis foetalis.
A. Both Father and Mother are Rh +ve
B. Mother is Rh \( + \) ve and Father is Rh-ve
c. Both Father and Mother are Rh -ve
D. Father is Rh +ve and Mother is Rh-ve


(a) What is addition polymer? Give
example.
(b) What is PHBV? How is it useful to
man?


Which among the following is not a types of muscular tissues?
A. Cardiac muscles
B. Skeletal muscles
c. smooth muscles
D. None of the above


If \( \boldsymbol{A}=\left[\begin{array}{ccc}\boldsymbol{x} & \mathbf{1} & -\boldsymbol{x} \\ \mathbf{0} & \mathbf{1} & -\mathbf{1} \\ \boldsymbol{x} & \mathbf{0} & \mathbf{7}\end{array}\right] \) and \( \operatorname{det}(\boldsymbol{A})= \)
\( \left|\begin{array}{ccc}\mathbf{3} & \mathbf{0} & \mathbf{1} \\ \mathbf{2} & \mathbf{- 1} & \mathbf{0} \\ \mathbf{0} & \mathbf{6} & \mathbf{7}\end{array}\right| \) then the value of \( \boldsymbol{x} \) is
A . -3
B. 3
\( c \cdot 2 \)
D. -8
E. -2


The Schrodinger wave equation for hydrogen atom is:
\( \mathbf{\Psi}_{2 s}=\frac{1}{4 \sqrt{2} \pi}\left(\frac{1}{a_{0}}\right)^{3 / 2}\left[2-\frac{r_{0}}{a_{0}}\right] e^{-r / a_{0}} \)
where \( a_{0} \) is Bohr radius. If the radial
node in \( 2 s \) be at \( r_{0}, \) then find \( r \) in terms
of \( a_{0} \)
A \( \cdot \frac{a_{0}}{2} \)
В. \( 2 a_{0} \)
c. \( \sqrt{2} a_{0} \)
D. \( \frac{a_{0}}{\sqrt{2}} \)


The first true angiosperm evolved from
an ancestor is
A. Arceuthobium
B. Gnetum
c. cycas
D. Taxus


Which of the following statements is
false?
A. Some desert plants do not have leaves.
B. Thick skin protects animals from the blazing heat of
sun
C. In cold regions, plants grow new leaves during winter.
D. Bears have thick fur as a protection against the cold.


Heliocentric theory was proposed by
A. Copernicus
B. Ptolemy
c. Newton
D. Tychobrahe


Find area enclosed by \( |x|+|y| \leq 3 \) and
\( x y \geq 2 \)
\( \mathbf{A} .5-2 \log 4 \)
B. \( 3-2 \log 4 \)
c. \( 3-\log 4 \)
D. \( 3-2 \log 7 \)


A camera is an optical instrument which makes use of a :
A. convex lens
B. concave lens
c. cylindrical lens
D. planar lens


Two point objects of masses 1.5 g and 2.5 g respectively are at a distance of 16 \( \mathrm{cm} \) apart, the centre of gravity is at a distance \( x \) from the object of mass 1.5 g where \( x \) is:
\( A \cdot 10 \mathrm{cm} \)
B. \( 6 \mathrm{cm} \)
\( c \cdot 13 \mathrm{cm} \)
D. 3 cm


Find :
\( \int \log x d x \)


The bulk modulus of a liquid of density
\( 8000 k g m^{-3} \) is \( 2 \times 10^{9} N m^{-2} . \) The
speed of sound in that liquid is (in
\( \left.m s^{-1}\right) \)
A . 200
B. 250
\( c \cdot 100 \)
D. 350
E. 500


A redistribution of electrical charge in an object, caused by the influence of nearby charges is termed as
A. electric conduction
B. ionisation
c. electrostatic induction
D. electromagnetic induction


A square garden has area 24686.6944
\( m^{2} . \) A trench of one meter wide has to be
dug along the boundary inside the garden. After digging the trench, what will be the area of the left out garden?


A body enters in MRI machine in 10 sec
If the magnetic field is \( 1.5 T \) and
circumference of MRI machine is \( 0.9 m \)
then find out emf induced in the body.
A . \( 0.96 V \)
B. \( 9.6 V \)
c. \( 9.6 m V \)
D. \( 96 m V \)