Assertion
Addition of \( \boldsymbol{H} \boldsymbol{C l} \) to \( \boldsymbol{3}, \boldsymbol{3}, \boldsymbol{3} \) -trifuoro-1
propene gives 1 -chloro-3, 3,3 -trifluoro
propane as major product.
Reason
Addition follow Markownikoff's rule.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of the following cannot be the probability of an event?
A \( \cdot \frac{2}{3} \)
в. -1.5
c. \( 15 \% \)
D. 0.7


The inducer for switching on the lac operon in bacteria is
A. Presence of lactos
B. Number of bacteria
c. Presence of structural genes in the bacteria
D. Presence of sucrose
E. Presence of RNA polymerase


(A): the linear coefficients of expansion
of a crystal along three perpendicular
\( \operatorname{axes} \operatorname{are} \alpha, \frac{-\alpha}{2}, \frac{\alpha}{5} . \) its volume
coefficient is \( \frac{7 \alpha}{10} \)
(B): For an-isotropic solids
\( \boldsymbol{r}=\boldsymbol{\alpha}_{\boldsymbol{x}}+\boldsymbol{\alpha}_{\boldsymbol{y}}+\boldsymbol{\alpha}_{\boldsymbol{z}} \)
\( A \cdot A \) and \( B \) are correct and \( B \) is correct explanation for \( A \)
B. A and B are correct and B is not correct explanation for \( A \)
C. A is true and B is false
D. A and B both are wrong


Blood passes from left ventricle to right atrium. It is
A. Pulmonary circulation
B. Systemic circulation
c. Coronary circulation
D. Arterovenous circulation


Which of the following is correct order of
acidic strength for the given
compounds:
A \( . I>I I>I I I>I V \)
\( V \)
В. \( I I>I>I I I>I V \)
c. \( I I>I I I>I>I V \)
\( . I>I I I>I I>I V \)
\( V \)


Find the number of 4 letter words that
can be formed using the letters of the
word PISTON, in which at least one
letter is repeated.


Three cell, \( (A, B \& C) \) each of emf \( E \)
and internal resistance \( (r) \) are
connected in series as shown in figure.
The potential difference across the cell
\( C^{\prime} \) is
A \( \cdot \frac{E r}{R} \)
B. \( \frac{E(R+r)}{R+3 r} \)
c. \( \frac{E(R+4 r)}{R+3 r} \)
D. \( \frac{E(R+3 r)}{R+4 r} \)


An engineering student manufactured
a metal sheet from a block of metal by hammering it in his workshop. Which property of metal did he use in doing
so?
A. Ductility
B. Sonorosity
c. conductivity
D. Malleability


Perform the indicated operations:
\( (8-2 i)-(-2-6 i) \)
\( \mathbf{A} \cdot 6+4 i \)
B. \( 10+4 i \)
\( c \cdot 10+8 i \)
D. \( 10-8 i \)


Select correct statement about valence-
bond approach
A. Each bond is formed by maximum overlap for its maximum stability
B. It represents localised electron model of bonding
c. Most of the electrons retain the same orbital locations
as in a separated atoms
D. All the above are correct statements


Find the distance between the following
pair of points:
\( (a, 0) \) and \( (0, b) \)


Which of the following sequences
correctly portrays the flow of electrons
during photosynthesis?
\( \mathbf{A} \cdot H_{2} O \rightarrow \mathrm{NADPH} \rightarrow \) Calvin cycle
B. NADPH \( \rightarrow \) chlorophyll \( \rightarrow \) Calvin cycle
\( \mathrm{C} \cdot H_{2} \mathrm{O} \rightarrow \) photosystem-I \( \rightarrow \) photosystem-I
D. NADPH \( \rightarrow \) electron transport chain \( \rightarrow O_{2} \)


Which of the following graphs represents the correct variation of
inductive reactane \( X_{L} \) with frequency \( v \)
7
\( A \)
в.
c.
D.


Electric charges are distributed in a small volume. The flux of the electric
field through a spherical surface of radius \( 10 \mathrm{cm} \) surrounding the total charge is 25 V-m. The flux over
concentric sphere of radius \( 20 \mathrm{cm} \) will
be:
\( A \cdot 25 \vee m \)
B. \( 50 \mathrm{Vm} \)
\( c .100 \mathrm{vm} \)
D. \( 200 \mathrm{vm} \)


Solve \( \frac{2^{3} \times 3^{5} \times 8}{27 \times 36} \)


The given graph shows variation with
time in the source voltage and steady
state current drawn by a series RLC
circuit.

Which of the following statements
is/are correct?
This question has multiple correct options
A. Current lags the voltage
B. Resistance in the circuit is \( 250 \sqrt{3} \Omega \)
C. Reactance in the circuit is \( 250 \Omega \)
D. Average power dissipation in the circuit is \( 20 \sqrt{3} \mathrm{w} \)


Mg is present in
A . Chlorophy
B. Haemoglobin
c. Vitamin-12
D. Vitamin-B


The sum of all the solution(s) of the
equation \( \sin ^{-1} 2 x=\cos ^{-1} x \) is


Factorise:
\( x^{2}-6 x-135 \)
\( \mathbf{A} \cdot(5 x)(13 x+9) \)
B. \( (x-15)(13 x+9) \)
\( \mathbf{C} \cdot(5 x)(x+9) \)
D. \( (x-15)(x+9) \)


Between two numbers whose sum is \( \frac{13}{6} \) an even number of A.M.s are inserted,
the sum of these means exceeds their
number by unity. Find the number of
means.


\( Z S M-5 \) converts:
A. alcohol to petrol
B. benzene to toluene
c. toluene to benzene
D. heptane to toluene


Find the cube root of 125


A particle starts from the origin of coordinates at time \( t=0 \) and moves in
the \( x y \) plane with a constant
acceleration \( \alpha \) in the \( y \) -direction. Its
equation of motion is \( y=\beta x^{2} \). Its
velocity component in the x-direction is
A. variable
B. \( \sqrt{\frac{2 \alpha}{\beta}} \)
c. \( \frac{\alpha}{\beta} \)
D. \( \sqrt{\frac{\alpha}{2 \beta}} \)


Find area of circle \( 4 x^{2}+4 y^{2}=9 \) which
is interior to the parabola \( x^{2}=4 y \)


Integrate the function \( \frac{x e^{x}}{(1+x)^{2}} \)


Find the value of the following determinants. \( \left|\begin{array}{cc}\mathbf{5} & \mathbf{3} \\ -\mathbf{7} & \mathbf{0}\end{array}\right| \)


Two mirrors are inclined at an angle of
\( 45^{0}, \) an object is placed between them. Then number of images formed will be:
\( A \cdot 6 \)
B. 7
\( c .5 \)
D.


Three particles \( A, B \) and \( C \) are situated at the vertices of an equilateral triangle
of side \( r \) at \( t=0 . \) The particle \( A \) heads
towards \( B, B \) towards \( C, C \) towards \( A \)
with constant speeds \( v . \) Find the time of their meeting.


To locate the Pole Star using Ursa Major, to which direction should the imaginary line be drawn?
A. North
B. west
c. East
D. south


Assertion
Unlike cabbage, sunflower plant has long internode with leaves that are far apart.
Reason
Sunflower produces sufficient amounts of Gibberellins during its growing period.
A. If both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. If both Assertion and Reason are correct, but Reason is not the correct explanation for Assertion
c. If Assertion is correct but Reason is incorrect
D. If Assertion is incorrect but Reason is correct


The first element of the groups 1 and 2
are different from other members of the
respective groups. Their behaviour is more similar to the second element of
the following groups. What is this relationship known as?
A. Anomalous relationship
B. Periodic relationship
c. Diagonal relationship
D. Chemical relationship


Identify the correct statement about nomenclature of alkyl halide.
A. The monohalogen derivatives of alkanes are called as alkyl halides.
B. The common name of an alkyl halide is always written as two separate words
c. In IUPAC system, the monohalogen derivatives of alkanes are named as haloalkanes
D. All of above


Which of the following statements is correct regarding Poisson's ratio?
A. It is the ratio of the longitudinal strain to the lateral strain
B. Its value is independent of the nature of the material
C. It is unitless and dimensionless quantity
D. The practical value of Poisson's ratio lies between 0 and 1


Find the direction cosines of the line PQ
joining the points \( P(2,3,4) \) and \( Q(2,1,1) \)


DNA differs from RNA in having
A. cytosine but no guanine
B. Thymine but no uracil
c. Uracil but no thymine
D. Thymine but no cytosine


Chord \( A B \) of the circle \( x^{2}+y^{2}=100 \)
passes through the point (7,1) and
subtends an angle of \( 60^{\circ} \) at the
circumference of the circle. If \( m_{1} \) and
\( m_{2} \) are the slopes of two such chords
then the value of \( m_{1} m_{2} \) is
A . -1
B.
c. \( 7 / 12 \)
D. -


What happens when a copper rod is
placed in \( F e S O_{4} \) solution?


Which of the following is the correct order of consecutive the phases of
Moon?
A. Last quarter, Waxing crescent, New moon
B. Waxing crescent, New moon, Last quarter
c. New moon, Waxing crescent, Last quarter
D. New moon, Last quarter, Waxing crescent


A \( 100 d m^{3} \) flask contains 10 mole each
of \( N_{2} \) and \( H_{2} \) at 777 K.After
equilibrium was reached, partial
pressure of \( \boldsymbol{H}_{2} \) was 1 at \( \boldsymbol{m} \). At this point
5 litre of \( H_{2} O_{(I)} \) was injected and gas mixture was cooled to \( 298 \mathrm{K} \). Find out
the pressure of gaseous mixture left.


\( \boldsymbol{p} \boldsymbol{K}_{\boldsymbol{b}} \) of \( \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{O H} \) is \( \boldsymbol{4} . \boldsymbol{7} 4 . \) If the ratio of
the buffer mixture \( \left[\boldsymbol{N} \boldsymbol{H}_{\boldsymbol{4}} \boldsymbol{C l}\right]: \)
\( \left[N H_{4} O H\right] \) is \( 1: 10, \) then the \( p H \) of that
buffer is:
A .4 .74
B. 10.26
c. 9.26
D. 3.74


A rigid container of negligible heat capacity contains one mole of an ideal gas. The temperature of the gas
increase by \( 1^{\circ} \mathrm{C} \) if \( 3 \cdot 0 \) cal of heat is
added to it. The gas may be This question has multiple correct options
A. helium
B. argon
c. oxygen
D. carbon dioxide


Bundle of His' is a network of
A. Muscle fibres distributed throughout the heart walls
B. Muscle fibres found only in the ventricle wall
C. Nerve fibres distributed in ventricles
D. Nerve fibres found throughout the heart


A person has Rs.30,000 to invest.He wants to invest some amount in the
fixed deposit and remaining in savings account.The interest rates are \( 7 \% \) and
\( 5 \% \) p.a for the fixed deposit and the saving account respectively. Find how he should divide the total amount
\( R s .30000 \) in two accounts if he wants to
get the annual interest as
(i) \( R s .1800 \)
(ii) \( R s .2000 \)


A vertical board having a rough surface is accelerated horizontally with acceleration a such that a \( 5 \mathrm{Kg} \) block
pressing against it does not fall. If \( \mu \) be
the coefficient of friction, then the
maximum acceleration of board is


Find the cube root of :
\( \mathbf{2}^{\frac{10}{27}} \)
\( A \cdot 2^{\frac{1}{27}} \)
B. \( 2^{\frac{1}{50}} \)
c. \( 2^{\frac{5}{5}} \)
D. None of these


Which part of Nephron is not permeable
for water?


The human body undergoes several changes during adolescence. These changes mark the onset of
A. Puberty
B. Prematurity
c. Post adolescence
D. Ageing


A body is released from the top of an
inclined plane of inclination \( \theta . \) It
reaches the bottom with velocity \( v \). If the
length remain same and the angle of inclination is doubled, what will be the velocity of the body on reaching the ground
\( A \cdot v \)
B. \( 2 v \)
C. \( [2 \cos \theta]^{1 / 2} v \)
D. \( [2 \sin \theta]^{1 / 2} v \)


If \( 20 g \) m of water at \( 50^{\circ} \mathrm{C} \) is mixed with
\( 60 g \) of water at \( 10^{\circ} \mathrm{C} \). Then calculate the
final temperature of the mixture.


Assuming the additivity of covalent radii in the \( C-I \) bond, what would be
the iodine-iodine distance in each of the
diiodobenzene? Assume that the ring is
regular hexagon and that each \( C-I \)
bond lies on a line through the centre of the hexagon. (Take \( C-C \) bond-length \( =1.40 A \) radius of iodine atom \( =1.33 \dot{A} \) radius of carbon atom \( =0.77 \dot{A} \) )
\( \ln o-, m- \) and \( p- \) isomers, bond
angles are respectively \( 60^{\circ}, 120^{\circ} \) and
\( 180^{\circ} . \) Hence, the distance between two-
atoms is:
A . \( 3.5 \hat{A} \)
в. \( 4.0 \hat{A} \)
\( c .7 .0 \hat{A} \)
D. \( 8.0 \hat{A} \)


If the force on the surface is doubled
and the area is reduced to half,
pressure will:
A. Become 2 times
B. Become 3 times
c. Become 4 times
D. Remain unchanged


The length of the diagonal of a square is \( 8 \sqrt{2} \mathrm{cm} . \) Find the length of its side and
hence the find the area of the square.


When two objects are rubbed against
each other they
A. will loose electrons
B. will repel electrons
c. will attracts each other
D. may attract or repel each other


If the sum of 8 terms of an A.P. is 64 and
the sum of 19 terms is 361 , find the
sum of \( n \) terms.


A line makes equal angles with the coordinate axis. The direction cosines of this line are
A \( \cdot\left(\frac{1}{3}, \frac{1}{3}, \frac{1}{3}\right) \)
B \( \cdot\left(\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}\right) \)
\( ^{\mathbf{c}} \cdot\left(\frac{1}{\sqrt{3}}, \frac{1}{3}, \frac{1}{3}\right) \)
D \( \cdot\left(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right) \)


An electromagnetic wave of frequency
\( \boldsymbol{v}=\mathbf{3 . 0} \boldsymbol{M} \boldsymbol{H} \boldsymbol{z} \) passes from vacuum
into a dielectric medium with
permittivity \( \epsilon=4.0 . \) Then
A. wavelength is halved and frequency remains unchanged.
B. wavelength is doubled and frequency becomes half.
C. wavelength is doubled and frequency remains unchanged.
D. wavelength and frequency both remain unchanged.


An electron of charge \( e \) moves in a
circular orbit of radius \( r \) around a
nucleus the magnetic field due to orbit motion of the electron at the site of the
nucleus is \( B \). The angular velocity \( \omega \) of
the electron is:
A \( \cdot \omega=\frac{\mu_{0} e B}{4 \pi r} \)
B. \( \omega=\frac{\mu_{0} e B}{\pi r} \)
c. \( _{\omega=\frac{4 \pi r B}{\mu_{0} e}} \)
D. \( \omega=\frac{2 \pi r B}{\mu_{0} e} \)


In SI system, the unit of work is


Which one of the following will be most
basic?
A. Aniline
B. P-methoxyaniline
c. P-nitroaniline
D. Benzylamine


The relation between \( [\boldsymbol{E}] \) and \( [\boldsymbol{B}] \) is
\( \mathbf{A} \cdot[E]=[B][L][T] \)
B . \( [E]=[B][L]^{-1}[T] \)
c. \( [E]=[B][L][T]^{-1} \)
D・ \( [E]=[B][L]^{-1}[T]^{-1} \)


During the past century, the temperature of the earth has increased
by \( 0.6^{\circ} \mathrm{C}, \) most of it during the last few decades. Rise in temperature causes deleterious changes in the environment, thus leading to increased melting of polar ice caps as well as other places like Himalayan snow caps. Suggest any two control measures that will reduce global warming?


Evaluate :
\( \int x^{3} \sqrt{1-x^{8}} d x \)


Find counter examples to disprove the following statement

A quadrilateral with all sides are equal
is a square.


Which of the following is not a redox reaction?
A \( \cdot 2 N O+O_{2} \rightarrow 2 N O_{2} \)
в. \( C l_{2}+H_{2} O \rightarrow H C l+H C l O \)
\( \mathrm{c} \cdot 2 \mathrm{Cr} \mathrm{O}_{4}^{2-}+2 \mathrm{H}^{+} \rightarrow \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}+\mathrm{H}_{2} \mathrm{O} \)
D. \( M n O_{4}^{-}+8 H^{+} \rightarrow M n^{2+}+4 H_{2} O \)


Who established the fact of animal
electricity?
A. Van de Graaff
B. Count Alessandro Volta
c. Gustav Robert Kirchhoff
D. Hans Christian Oersted


Which of the following substance have abnormally high boiling points and why?
\( \boldsymbol{H}_{2} \boldsymbol{S}, \boldsymbol{H}_{2} \boldsymbol{O}, \boldsymbol{H} \boldsymbol{F}, \boldsymbol{H} \boldsymbol{I}, \boldsymbol{C} \boldsymbol{H}_{4}, \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O} \boldsymbol{H} \)


In a group of 15 women, 7 have nose studs, 8 have ear rings and 3 have neither. How many of these have both nose studs and ear rings?
A . 0
B . 2
\( c .3 \)
D.


The sound wave is of the type


Find the median of the following data
\( \mathbf{3}, \mathbf{1}, \mathbf{5}, \mathbf{6}, \mathbf{3}, \mathbf{4}, \mathbf{5} \)


Draw the graph of the straight line given
by the equation \( 4 x-3 y+36=0 \)
Calculate the area of the triangle formed by the line drawn and the coordinate axes.
A. Area \( =45 \) sq. units
B. Area = 54 sq. units
c. Area \( =48 \) sq. units
D. Area = 58 sq. units


Select the correct code about complex
\( \left[\boldsymbol{C r}\left(\boldsymbol{N} \boldsymbol{O}_{2}\right)\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5}\right]\left[\boldsymbol{Z} \boldsymbol{n} \boldsymbol{C l}_{4}\right] \)
(I) IUPAC name is pentaamminenitritoN-chromium(III) tetrachlorozincate (II)
(II) It does not exhibit geometrical isomerism
(III) It shows linkage isomerism
(IV) Its coordination isomerism
A. III, IV
B. I, III and IV
c. ॥, ॥ा and IV
D. I, II, III and IV


22.4 litres of a gas at S.T.P. weigh 16 \( g \). Identify the gas.
A \( \cdot C H_{4} \)
в. \( O_{2} \)
c. \( N_{2} \)
D. All of these


State five differences between mass
and weight.


If \( R \) is a relation from a set \( A \) to a set \( B \)
and \( S \) is a relation from \( B \) to a set \( C \)
then the relation \( S O R \)
A. is from \( A \) to \( C \)
B. is from \( C \) to \( A \)
c. does not exist
D. none of these


Find the mean deviation about the
mean for the data:
4,7,8,9,10,12,13,17


Which option will have a terminating decimal expansion?
A \( \cdot \frac{77}{210} \)
в. \( \frac{23}{30} \)
c. \( \frac{125}{441} \)
D. \( \frac{23}{8} \)


The angle turned by a body undergoing circular motion depends on time as
\( \boldsymbol{\theta}=\sqrt{\mathbf{2}} \boldsymbol{\theta}_{0}+\mathbf{3} \boldsymbol{\theta}_{1} \boldsymbol{t}+\boldsymbol{\theta}_{2} \boldsymbol{t}^{2} \) Then the
angular acceleration of the body is
A. \( \sqrt{\theta_{1}} \)
в. \( \sqrt{3} \theta_{2} \)
\( c \cdot 2 \theta_{1} \)
D. \( 2 \theta_{2} \)


\( \ln \) a system \( \boldsymbol{A}(\boldsymbol{s}) \rightleftharpoons 2 \boldsymbol{B}(\boldsymbol{g})+\boldsymbol{3} \boldsymbol{C}(\boldsymbol{g}) \)
the concentration of \( C \) at equilibrium is
increased by a factor \( 2, \) it will cause the equilibrium concentration of \( B \) to change to:
A. two times of its original value
B. one half of its original value
c. \( 3 \sqrt{2} \) times of its original value
D. \( \frac{1}{2 \sqrt{2}} \) times of its original value


The value of \( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}} \int_{2}^{\boldsymbol{x}^{2}}(\boldsymbol{t}-\mathbf{1}) \boldsymbol{d} \boldsymbol{t} \)
A \( \cdot\left(x^{2}-1\right) \)
В. \( x\left(x^{2}-1\right) \)
c. \( 2 x\left(x^{2}-1\right) \)
D. none of these


The moment of inertia of a flywheel is \( 0.2 k g m^{2} \) which is initially stationary. constant external torque \( 5 N m \) acts on the wheel. The work done by this torque
during 10 sec is:
A . \( 1250 J \)
B. \( 2500 J \)
c. \( 5000 J \)
D. \( 6250 J \)


\( \boldsymbol{A}=\left(\begin{array}{cc}\mathbf{3} & \mathbf{2} \\ -\mathbf{1} & \mathbf{4}\end{array}\right), \boldsymbol{B}=\left(\begin{array}{cc}-\mathbf{2} & \mathbf{5} \\ \mathbf{6} & \mathbf{7}\end{array}\right) \) and
\( C=\left(\begin{array}{cc}1 & 1 \\ -5 & 3\end{array}\right), \) then verify that
\( \boldsymbol{A}(\boldsymbol{B}+\boldsymbol{C})=\boldsymbol{A} \boldsymbol{B}+\boldsymbol{A} \boldsymbol{C} \)


If \( \frac{x^{2}+1}{x}=3 \frac{1}{3} \) and \( x>1 ; \) find the
value of
\( x-\frac{1}{x} \)
A \( \cdot 2 \frac{2}{3} \)
в. \( 1 \frac{2}{9} \)
c. \( 2 \frac{5}{7} \)
D. \( 1 \frac{1}{3} \)


Identify linear polynomial from the following.
\( \mathbf{A} \cdot x+1 \)
B . \( x^{2}+x+5 \)
c. \( x^{3}+2 x^{2}+6 x+5 \)
D. None of the above


The displacement of particle in SHM in one time period is
A . zero
B. a
c. \( 2 a \)
D. 42


15 coupons are numbered \( 1,2,3, \dots, 15 \)
respectively. 7 coupons are selected at random one at a time with replacement. The probability that the largest number appearing on a selected coupon is 9 is
\( ^{A} \cdot\left(\frac{9}{16}\right)^{6} \)
\( ^{\mathrm{B}}\left(\frac{8}{15}\right)^{7} \)
\( ^{c}\left(\frac{3}{5}\right)^{7} \)
D. \( \frac{9^{7}-8^{7}}{15^{7}} \)


A rectangular block has length, breadth and height of \( 30 \mathrm{cm}, 20 \mathrm{cm} \) and \( 10 \mathrm{cm} \) respectively.Which one ofthe following statements is correct?
A. The minimum pressure is exerted when breadth and height form the base
B. The maximum pressure is exerted when breadth and height form the base
c. The minimum pressure is exerted when length and height form the base
D. The maximum pressure is exerted when length and breadth form the base


An object projected upwards with a velocity of \( 100 \mathrm{m} / \mathrm{s} \) it will strike the ground after.


Soda water is a solution of


The combination of the gates shown
below produces where \( G_{1} \) to \( G_{4} \) are NOR
gates:
A. AND gate
B. xoR gate
c. NOR gate
D. NAND gate


Give the condensed formula of
following,
\( 2-H y d r o x y-1,2,3- \)
propanetricarboxylic acid:
A \( \cdot(H O O C) C H_{2} C(C O O H)(O H) C H_{2}(C O O H) \)
в. \( (H O O C) C H_{2} C(C O O H)(C O O H) C H_{2}(O H) \)
\( \mathrm{c} \cdot(\mathrm{HOOC}) \mathrm{CH}_{3} \mathrm{C}(\mathrm{COOH}) \mathrm{CH}_{2}(\mathrm{COOH}) \)
D. \( (H O O C) C H_{2} C H_{2} C(C O O H)(O H) C H_{2}(C O O H) \)


The air film in a Newton's ring apparatus is replaced by an oil film. The radii of the rings
A. remains the same
B. increases
c. decreases
D. none of the above


A person takes 15 breathes per
minute.The volume of air inhaled in
each breath is \( 448 \mathrm{ml} \) and contains \( 21 \% \)
oxygen by volume.The exhaled air contains \( 16 \% \) of oxygen by volume.If all the oxygen is used in the combustion of sucrose, how much of the Sucrose is
burnt in the body per day\& how much
heat is evolved. \( \triangle \boldsymbol{H}_{c o m} \) of sucrose is \( = \)
\( -6000 k j m o l^{-1} \).take temperature to be \( 300 \mathrm{K} \) throughout.[Assuming
\( \left.\boldsymbol{V}_{\text {inhaledair}}=\boldsymbol{V}_{\text {exhaledair}}, \boldsymbol{P}_{\text {atm}}=\mathbf{1} \boldsymbol{a} \boldsymbol{t m}\right] \)
A. 7.822 Mj/day evolved,460 gm
B. 7.822 Mj/day evolved,560 gm
c. 9.822 Mj/day evolved,460 gm
D. 9.822 Mj/day evolved,560 gm


Which one of the following Clements would consider to be the climax
community in a humid environment?
A. The pioneer community
B. Lichens, mosses, and ferns
c. Large plants such as shrubs and trees
D. Small native plants of the area such as grasses and herbs


A molecule has 3 bond pairs and 1 lone pairs on the central atom. Identify the
molecule.
A \( \cdot C l F_{3} \)
B. \( S F_{6} \)
\( \mathrm{c} \cdot C H_{4} \)
D. \( P C l_{3} \)


5 cards are drawn at random from a well
shuffled pack of 52 playing cards. If it is known that there will be at least 3
hearts, the probability that there are exactly 3 hearts is
A. \( \frac{13}{^{13} s_{3}+^{13} c_{4}+^{13} c_{5}} \)
в.
\( c \)
D. \( \frac{13}{^{13} s_{3} \times^{13} c_{4} \times^{13} c_{5}} \)


Split 69 late three pats such that they
are in \( A . P . \) and the product of two
smaller parts is 483
A . 21
B. 23
c. 25
D. Allofabove


The force acting on a mass of \( 1 g \) due to the gravitational pull on the earth is called 1 gw \( t . \) One \( g w t \) equals
A. \( 1 N \)
в. \( 9.8 N \)
c. 980 dyne
D. None of these


The process which helps in perpetuation of race
is
A. Nutrition
B. Photosynthesis
c. Excretion
D. Reproduction


(i) If \( \vec{a} \times \vec{b}=\vec{c} \times \vec{d} \) and \( \vec{a} \times \vec{c}=\vec{b} \times \vec{d} \)
show that \( \vec{a}-\vec{d} \) and \( \vec{b}-\vec{c} \) are paralle
(ii) Find the direction cosines of the line
joining (2,-3,1) and (3,1,-2)


A uniform disc of radius \( R \) is put over
another uniform disc of radius \( 2 R \)
made of same material having same thickness. The peripheries of the two discs touches each other. Locate the
centre of mass of the system taking
center of large disc at origin.


The difference between the lengths of the major axis and the latus-rectum of
an ellipse is
A \( . a \)
в. \( 2 a e \)
\( c \cdot a e^{2} \)
D. \( 2 a e^{2} \)


An inductor \( 200 \mathrm{mH} \), capacitor \( 500 \mu \mathrm{F} \)
and resistor \( 10 \Omega \) are connected in
series with a \( 100 \mathrm{V} \) variable frequency ac source. What is the frequency at which the power factor of the circuit is unity?
A . \( 10.22 \mathrm{Hz} \)
B. 12.4 нz
c. \( 19.2 \mathrm{Hz} \)
D. 15.9 нz


Borax bead test is used to identify the:
\( A \). anion in coloured salt
B. cation in coloured salt
C. anion in white salt
D. cation in white salt


So that the torque acting on it is maximum.


\( \int \sin ^{-1} d x \)


Which of the following changes
weather?
\begin{tabular}{|l|l|l|l|}
\hline Day & Max. & Min. & Forecast \\
\hline Sun & \( 36^{\circ} \mathrm{C} \) & \( 24^{\circ} \mathrm{C} \) & Sunny and hot \\
Mon & \( 34^{\circ} \mathrm{C} \) & \( 22^{\circ} \mathrm{C} \) & Sunny \\
Tue & \( 30^{\circ} \mathrm{C} \) & \( 20^{\circ} \mathrm{C} \) & Dry and cloudy \\
Wed & \( 32^{\circ} \mathrm{C} \) & \( 21^{\circ} \mathrm{C} \) & Cloudy \\
Thu & \( 27^{\circ} \mathrm{C} \) & \( 16^{\circ} \mathrm{C} \) & Rain \\
Fri & \( 30^{\circ} \mathrm{C} \) & \( 20^{\circ} \mathrm{C} \) & Light showers \\
Sat & \( 32^{\circ} \mathrm{C} \) & \( 21^{\circ} \mathrm{C} \) & Cloudy \\
\hline
\end{tabular}
\( 4 . \) sur
B. Man
c. wood
D. Television


The property seen in f-block elements is:
A. Lanthanide contraction
B. actinide contraction
\( c . \) both \( (A) \) and \( (B) \)
D. none of these


Lichen is pioneer in succession.
A. Hydrosere
B. Lithosere
c. xerosere
D. Both B and C


Write the following equation in ionic form.
\( M n O_{2}+4 H C l \rightarrow M n C l_{2}+2 H_{2} O+ \)
\( C l_{2} \)


Which of the following inhibits \( 0_{2} \) release in light phase?
A. PMAA
B. Zeatin
c. DCMU
D. None of the above


Cardiac output is blood
A. Received by heart per minute
B. Pumped by ventricles per sec
C. Pumped by each ventricle per minute
D. Pumped by left ventricle per hour


Differentiate \( \cos ^{-1} x \)
A \( \cdot \frac{-1}{\sqrt{\left(1-x^{2}\right)}} \)
B. \( \frac{1}{\sqrt{\left(1-x^{2}\right)}} \)
c. \( \frac{-1}{\sqrt{\left(1+x^{2}\right)}} \)
D. \( \frac{1}{\sqrt{\left(1+x^{2}\right)}} \)


At constant temperature \( N_{2} \) gas of 200
\( \mathrm{cm} \) at \( 720 \mathrm{mm} \) pressure and \( O_{2} \) gas of
\( 400 \mathrm{cm}^{3} \) at \( 750 \mathrm{mm} \) pressure. These are
mixed in 1 ltr capacity flask, than what will be the final pressure.
\( A \cdot 111 \mathrm{mm} \)
B. 222 mm
c. \( 333 \mathrm{mm} \)
D. 444 mm


Enteronephric nephridia of earthworm are connected with
A. Excretion
B. Digestion
c. osmoregulation
D. All of the above


A conductor of length I and mass m is placed along the east-west line on a table. Suddenly a certain amount of
change is passed through it and it is found to jump to a height h. The earth's
magnetic induction is B. The charge
passed through the conductor is:
A \( \cdot \frac{1}{B m g h} \)
B. \( \frac{\sqrt{2 g h}}{B / m} \)
c. \( \frac{g h}{B / m} \)
D. \( \frac{m \sqrt{2 g h}}{B l} \)


Which of the following is not a redox reaction?
A. \( C a C O_{3} \rightarrow C a O+C O_{2} \)
в. \( O_{2}+2 H_{2} \rightarrow 2 H_{2} O \)
c. \( _{N a+H_{2} O \rightarrow N a O H+\frac{1}{2} H_{2}} \)
D. \( M n C l_{3} \rightarrow M n C l_{2}+\frac{1}{2} C l_{2} \)


Ocean thermal energy is based on:
A. temperature difference across the sea.
B. temperature difference between surface and depths of sea.
C. high temperature at depth of sea water.
D. temperature rise in climate caused by sea water.


Find the number of acid(s) which are
having hypo prefix in their name from the following:
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4}, \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3}, \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{2}, \boldsymbol{H} \boldsymbol{C l O}, \boldsymbol{H}_{4} \boldsymbol{P}_{2} \)


Constructing a frequency distribution
A. is one of the most common means of summarizing data.
B. begins by recording the number of times a particular value occurs
C. is the basis for construction of a percentage distribution.
D. All of the above


Which type of muscle is found in heart?
A. Cardiac
B. Skeletal
c. smooth
D. All of the above


The following frequency table shows that the demand for a sweet and the
number of customers. Find the mode of
demand of sweet.
weight of \( \begin{array}{ll}250- & 500- \\ 500 & 750\end{array} \) sweet \( \begin{array}{ll}0- & 25 \\ 250 & 50\end{array} \) (gram)
No. of
60
25
custome


The standard solution of sodium
hydroxide cannot be prepared by direct weighing of cold sodium hydroxide because it is :
A . a solid
B. a liquid
c. deliquescent
D. none of the above


The volume of water to be added to
\( 100 \mathrm{cm}^{3} \) of \( 0.5 \mathrm{M} H_{2} \mathrm{SO}_{4} \) to get
decimolar concentration is :
A. \( 500 \mathrm{ml} \)
B. 100 \( \mathrm{ml} \)
c. \( 400 \mathrm{ml} \)
D. 300 m1


Which term of the progression 5,8,11
\( 14, \dots \) is \( 320 ? \)
A . 106 th
B. 105 th
c. 107 th
D. 104 th


A particle undergoes SHM with a time period of 2 seconds. In how much time will it travel from its mean position to a displacement equal to half of its
amplitude?
A \( \cdot(1 / 2) s \)
в. \( (1 / 3) s \)
c. \( (1 / 4) s \)
D. \( (1 / 6) s \)


Why are group I elements:
(a) univalent
(b) largely ionic
(c) strong reducing agents
(d) poor complexing agents?
(e) why do they have the lowest first
ionization energy values in their
periods?


When \( x=2, \) the value of the
expression \( 4 x^{2}+\frac{9}{x^{2}}-12 \) is:
A \( \cdot \frac{25}{4} \)
в. \( \frac{-4}{25} \)
c. \( \frac{4}{25} \)
D. \( \frac{-25}{4} \)


\( \frac{\boldsymbol{x}^{\boldsymbol{4}}-\mathbf{5} \boldsymbol{x}^{\boldsymbol{2}}+\mathbf{1}}{\left(\boldsymbol{x}^{\mathbf{2}}+\mathbf{1}\right)^{\mathbf{3}}}= \)
\( \mathbf{A} \cdot \frac{1}{\left(\mathbf{x}^{2}+1\right)}-\frac{1}{\left(\mathbf{x}^{2}+1\right)^{2}}+\frac{7}{\left(\mathbf{x}^{2}+1\right)^{3}} \)
\( \mathbf{B} \cdot \frac{1}{\left(\mathbf{x}^{2}+1\right)}-\frac{7}{\left(\mathbf{x}^{2}+1\right)^{2}}+\frac{7}{\left(\mathbf{x}^{2}+1\right)^{3}} \)
\( \mathbf{C} \cdot \frac{7}{\left(\mathbf{x}^{2}+1\right)}-\frac{7}{\left(\mathbf{x}^{2}+1\right)^{2}}+\frac{1}{\left(\mathbf{x}^{2}+1\right)^{3}} \)
\( \frac{7}{\left(\mathbf{x}^{2}+1\right)}-\frac{1}{\left(\mathbf{x}^{2}+1\right)^{2}}-\frac{1}{\left(\mathbf{x}^{2}+1\right)^{3}} \)


In a quadrilateral define the following:
Opposite angles


\( A l_{2} O_{3} \) is chemical formula of :
A . cryolite
B. corundum
c. kaolin
D. bauxite


The following table shows the marks
obtained by 48 students in a Quiz competition in Mathematics. Calculate the standard deviation.
Data x
\[
\begin{array}{cc}
\mathbf{7} & \mathbf{8}
\end{array}
\]
Frequency


A gaseous hypothetical chemical
equation \( 2 A \rightleftharpoons 4 B+C \) is carried out
in a closed vessel. The concentration of \( B \) is found to be increase by \( 5 x \)
\( 10^{3} \) mol. \( L^{-1} . \) in 10 seconds. The rate of
appearance of \( B \) is:
A \( \cdot 5 \times 10^{2} \mathrm{molL}^{-1} \mathrm{sec}^{-1} \)
B. \( 5 \times 10^{5} \mathrm{mol} \mathrm{L}^{-1} \mathrm{sec}^{-1} \)
c. \( 6 \times 10^{-5} \mathrm{mol} \mathrm{L}^{-1} \mathrm{sec}^{-1} \)
D. \( 4 \times 10^{-4} \mathrm{mol} \mathrm{L}^{-1} \mathrm{sec}^{-1} \)


The number of words that can be formed
using any number of letters of the word "KANPUR" without repeating any letter is
A . 720
в. 1956
\( c .360 \)
D. 370


Let \( \Gamma \) denote a curve \( y=f(x) \) which is
in the first quadrant and let the point
(1,0) lie on it. Let the tangent to \( \Gamma \) at a
point \( \boldsymbol{P} \) intersect the \( \mathbf{y} \) -axis at \( \boldsymbol{Y}_{\boldsymbol{P}} . \) If
\( P Y_{P} \) has length 1 for each point \( P \) on \( \Gamma \)
Then which of the following options
is/are correct?
This question has multiple correct options
A \( y=-\ln \left(\frac{1+\sqrt{1-x^{2}}}{x}\right)+\sqrt{1-x^{2}} \)
B. \( x y^{\prime}+\sqrt{1-x^{2}}=0 \)
C \( \cdot x y^{\prime}-\sqrt{1-x^{2}}=0 \)
D. \( y=\ln \left(\frac{1+\sqrt{1-x^{2}}}{x}\right)-\sqrt{1-x^{2}} \)


You spend \( 7 \frac{1}{2} \) hours out of 24 hours at school. What percentage of a day is
this?


Geeta placed three objects made of different materials as shown in the
figure. She observed a bright spot of light at (II) but (III) would not get any spot. Then,
A. (I) and (II) are made of transparent materials and (III) is made of opaque material
B. (I) is made of transparent material,
(II) is made of translucent material and (III) is made of opaque material.
c. (।) is made of transparent material
(II) is made of opaque material and (III) is made of either transparent or opaque or translucent material
D. (I) and (II) are made of opaque material and (III) is made of transparent material.


The mechanism of removing introns followed by joining of the exons in a defined order during transcription is called
A. Splicing
B. Tailing
c. Transformation
D. Capping


A cold steel spoon is dipped in a cup of hot milk. It transfer heat to its other end
by the process of


\( K_{2} S O_{4} \) does not undergo hydrolysis. If true write 1 , else write 0


The diagram of the large intestine of
man is given above. Identify the parts
labelled \( A, B, C, D, E \) and \( F \)
A. A- sigmoid colon, B- Vermiform appendix, CAscending colon, D- Transverse colon, E- Descending colon, F-Caecum.
B. A- Caecum, B- Vermiform appendix, C- sigmoid colon
D- Ascending colon, E- - Transverse colon, F- Descending colon
C. A- Caecum, B- Vermiform appendix, C- Ascending colon, D- Transverse colon, E- Descending colon, FSigmoid colon.
D. A- Sigmoid colon, B- Vermiform appendix, CDescending colon, D- - Transverse colon, E- Ascending colon, F- Caecum


The conductivity of a saturated solution of \( A g_{3} P O_{4} \) is \( 9 \times 10^{-6} S m^{-1} \) and its
equivalent conductivity is \( 1.50 \times \) \( 10^{-4} S m^{2} \) equivalent \( ^{-1} . \) The \( K_{s p} \) of
\( A g_{3} P O_{4} \) is:
A \( \cdot 4.32 \times 10^{-18} \)
B. \( 1.8 \times 10^{-9} \)
c. \( 8.64 \times 10^{-13} \)
D. None of these


Malachite is an ore of:
A. copper
B. iron
c. zinc
D. silver


Animals show locomotion but plants do
not.
"What is the reason for this?
A. Plants are autotrophs
B. Plants are heterotrophs
c. Plants have organs of defence
D. None of these


In the reaction : \( \boldsymbol{K}_{\mathbf{4}}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right]+ \)
\( K_{2} C O_{3} \rightarrow \) the product formed is :
A \( . F e C O_{3} \)
в. \( K C N \)
c. \( K F e C O_{3} \)
D. \( K_{3}\left[F e(C N)_{6}\right] \)


Examine the continuity of the function \( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{l}(\sin \boldsymbol{x}-\cos \boldsymbol{x}) \text { for } \boldsymbol{x} \neq 0 \\ -\mathbf{1} \text { for } \boldsymbol{x}=\mathbf{0}\end{array}\right. \)
at the point \( \boldsymbol{x}=\mathbf{0} \)


Explain the effect of inductive effect for reactivity of alkyl halides.


Workout the following divisions
\( \mathbf{3 6}(\boldsymbol{x}+\mathbf{4})\left(\boldsymbol{x}^{2}+\mathbf{7} \boldsymbol{x}+\mathbf{1 0}\right) \div \mathbf{9}(\boldsymbol{x}+\mathbf{4}) \)
\( \mathbf{A} \cdot\left(x^{2}+7 x+10\right) \)
B. \( 4\left(x^{2}+7 x+6\right) \)
c. \( 4\left(x^{2}+7 x+10\right) \)
D. None


If \( \boldsymbol{y}= \)
\( \sqrt{\sin x+\sqrt{\sin x+\sqrt{\sin x+\cdots \cdot t o \infty}}} \)
then \( \frac{d y}{d x} \) is
A \( \cdot \frac{\cos x}{1+2 y} \)
B. \( -\frac{\sin x}{1-2 y} \)
c. \( \frac{\cos x}{1-2 y} \)
D. \( \frac{\cos x}{2 y-1} \)


A cell having EMF E and internal resistance \( r \) is connected to a load \( R \)
Find the value of \( R \) such that power dissipated by the cell is maximum


A uniform nonconducting rod of mass \( \mathrm{m} \) and length \( l, \) with charge density \( \lambda \) as shown in figure, is burged at the midpoint at origin so that it can rotate in a horizontal plane without any friction. A uniform electric field E exists
parallel to x-axis in the entire region. Calculate the period of small oscillations of the rod


The product (B) is:
\( (\mathbf{A}) \)
\( A \)
B.
\( c \)
D.


A star has a parallax angle \( p \) of 0.723 arcseconds. What is the distance of the
star?
A . 1.38 parsecs
B. 2.38 parsecs
c. 3.38 parsecs
D. 4.38 parsecs


Give reason:
Aromatic primary amines cannot be prepared by Gabriel's phthalimide synthesis.


Two identical circular loops of metal wire are lying on a table without
touching each other. Loop - \( A \) carries a
current which increases with time. In
response, the loop-B
A. remains stationary
B. is attracted by the loop \( A \)
c. is repelled by the loop \( A \)
D. rotates about its \( C M \) with \( C M \) fixed
E. none of these


Calculate the area of the designed
region in Fig. common between the two
quadrants of circles of radius \( 8 \mathrm{cm} \)
each


A cylinder contains either ethylene or
propylene. \( 12 m l \) of gas required \( 54 m l \) of oxygen for complete combustion. The
gas is:
A. Ethylene
B. Propylene
c. 1: 1 mixture of two gases
D. 1: 2 mixture


\( A B C \) is an isosceles triangle inscribed in a circle of radius \( r . \) If \( A B=A C \) and \( h \)
is the altitude from \( A \) to BC. If the
triangle \( A B C \) has perimeter \( P \) and area
\( \Delta \) then \( \lim _{h \rightarrow 0} 512 r \frac{\Delta}{P^{3}} \) is equal to


AP and BQ are the bisectors of two
alternate interior angles formed by the
intersection of a transversal t with
parallel lines \( l \) and \( m . \) If \( \angle P A B= \)
\( \boldsymbol{x} \angle \boldsymbol{Q} \boldsymbol{B} \boldsymbol{A} . \) Find \( \boldsymbol{x} \)


Which of the following is not a unit for electric potential?
A. volt
B. Joule/coulomb
c. Erg/stat coulomb
D. None of these


Control of automobile air pollution can be done by all except:
A. use of biopetrol
B. periodic check up of pollution control for all vehicles
c. use of low sulphur diesel or CNG
D. prefering individual vehicles.


Find the area of a segment of a circle
with a central angle of 135 degrees and a radius of 2. Express answer to nearest integer.
A . 1
B . 2
\( c .3 \)
\( D \)


Solve: \( 5 x-7<3(x+3), 1-\frac{3 x}{2} \geq \)
\( x-4 \)


At certain temperature, the \( \mathrm{H}^{+} \) ion
concentration of water is \( 4 \times 10^{-7} \mathrm{M} \)
then the value of \( K_{w} \) at the same
temperature is :
A \( \cdot 10^{-14} \mathrm{M}^{2} \)
B. \( 4 \times 10^{-14} \mathrm{M}^{2} \)
c. \( 1.6 \times 10^{-13} \mathrm{M}^{2} \)
D. \( 4 \times 10^{-7} \mathrm{M}^{2} \)


A typical thermistor can easily measure a change in temperature of the order of
A \( \cdot 10^{-3} \circ \)
B. \( 10^{-2} \) о \( C \)
\( \mathrm{c} \cdot 10^{2} \circ \)
D. \( 10^{3} \circ \)


Sound and light waves both:
A. have similar wavelength
B. obey the laws of reflection
C. travel as longitudinal waves
D. travel through vacuum


The xy-plane divides the line joining the points (-1,3,4) and (2,-5,6)
A. internally in the ratio 2: 3
B. externally in the ratio 2: 3
c. internally in the ratio 3: 2
D. externally in the ratio 3: 2


The melting points of most of the solid substances increase with an increase
of pressure acting on them. However, ice melts at a temperature lower than its usual melting point, when the pressure increases. This is because:
A. ice is less denser than water
B. pressure generates heat
C. the bounds break under pressure
D. ice is not a true solid


The proper value of significant figures in \( 38.0+0.0035+0.00003 \) is:
A . 38
B. 38.0035
c. 38.00353
D. 38.0


If dimensions of length are expressed
\( \operatorname{as} G^{x} C^{y} h^{z} \) where \( G, C \) and \( h \) are
universal gravitational constant, speed of light and Planck's constant respectively. Then This question has multiple correct options
\( \mathbf{A} \cdot x=y \)
B. \( x=z \)
c. \( y=-3 / 2 \)
D. \( z=1 / 2 \)


\( f \sin \left(60^{\circ}+30^{\circ}\right)=\sin 60^{\circ} \cos 30^{\circ}+ \)
\( \sin 30^{\circ} \cos 60^{\circ} \) then what is the value of
\( \sin \left(60^{\circ}+30^{\circ}\right) .=? \)


If \( h(x)=x^{2}-2, \) then the value of \( \frac{1}{2} h\left(\frac{1}{2}\right) \) is:
\( \mathbf{A} \cdot \mathbf{0} \)
в.
\( c \cdot-\frac{7}{8} \)
D. 7 8


Which element is present in Ruby as impurity?
A. \( C u \)
в. \( C r \)
c. \( A u \)
D. \( Z n \)


Boojho wishes to contribute to reducing air pollution. Which vehicle should be
used for going to school?
A . car
B. school bus
c. auto rickshaw
D. scooter


Which of the following statements is wrong regarding Medical Termination of Pregnancy (MTP)?
A. In India it is legal up to the 2 oth week of pregnancy
B. MTPs can't be done without surgery
c. MTPs are considered to be relatively safe during the first trimester
D. It needs the assistance of qualified medical practitioners.


Which class of drugs is used in
sleeping pills?


Two parallel plane mirrors placed facing each other forms \( \infty \) images of an
object. Does this hold good, if they are placed at an angle \( \boldsymbol{\theta} \neq \mathbf{0} ? \)
A. Yes
B. No
c. only if angle is of the form \( \theta=\pi / n, n=1,2,3 \dots \)
D. only if angle is of the form \( \theta \neq \pi / n, n=1,2,3 \dots \)


Evaluate the given integral. \( \int e^{x}\left(\frac{1+x}{(2+x)^{2}}\right) d x \)


Fill in the blank with appropriate
answer:
In Young's double slit experiment, the path difference between two interfering waves at a point on the screen is \( \frac{5 \lambda}{2}, \lambda \) being wavelength of the light used. The dark fringe will lie at this point.


Find the equivalent resistance about
any branch of the base of the square pyramid shown. Assume resistance of each branch is R
A. \( \frac{7 R}{15} \)
в. \( \frac{8 R}{15} \)
c. \( \frac{R}{2} \)
D. None of these


The velocity of efflux of a liquid through an orifice in the bottom of the tank does
not depend upon:
A. size of orifice
B. height of liquid
c. acceleration due to gravity
D. density of liquid


The function \( f(x)=\frac{1}{x} ; x>0 \) on its domain is
A. increasing
B. decreasing
c. constant
D. information insufficient


Depreciation applicable to an equipment is \( 20 \% . \) By how much per cent, will the value of the equipment 3
years from now be less than the present value?
A . 60\%
B. 54\%
c. 50.8\%
D. 48.8\%


Three Mark Questions How has sex originated?


Which of the below statements prove that friction is disadvantageous?
A. Tyres of cars wear out
B. Soles of shoes wear out
c. Machine parts wear out
D. All of the above


Benzene does not undergo polymerisation due to:
A. cyclic nature
B. aromatic nature
c. resonance
D. steric effect


The shape of the chloroplast in higher
plants is
A. Discoid
B. Cup shapeddped
c. Girdle shaped
D. Reticulate


If in a \( G P \) the \( (p+q)^{t h} \) term is \( a \) and
the \( (p-q)^{t h} \) term is \( b, \) then \( p^{t h} \) term is
\( \mathbf{A} \cdot(a b)^{1 / 3} \)
B \( \cdot(a b)^{1 / 2} \)
\( \mathbf{c} \cdot(a b)^{1 / 4} \)
D. None of these


Pseudo-unipolar neurons occur in
A. Retina
B. Dorsal ganglion
C. Ventral root of spinal nerve
D. Nerve nuclei.


Suggest the aspects of reproductive
health which need to be given specia
attention in the present scenario.


An ellipse has \( O B \) as semi-minor axis, \( F \) and \( F^{\prime} \) its foci and the \( \angle F B F^{\prime} \) is a
right angle. Then, the eccentricity of the ellipse is
A \( \cdot \frac{1}{\sqrt{3}} \)
B. \( \frac{1}{4} \)
\( c \cdot \frac{1}{2} \)
D. \( \frac{1}{\sqrt{2}} \)


The compound used in Hawker's lamp and in light houses for illumination
purposes is :
A. methane
B. ethane
c. ethylene
D. acetylene


\( 6 \times 10^{22} \) gas molecules each of mass
\( 10^{-24} \mathrm{kg} \) are taken in a vessel of 10 litres. What is the pressure exerted by gas molecules if the average velocity of the gas molecules is \( 92.62 \mathrm{m} / \mathrm{sec} ? \)
A \( \cdot 2 \times 10^{5} P a \)
B. \( 20 P a \)
c. \( 2 \times 10^{6} P a \)
D. \( 2 \times 10^{4} P a \)


Potential difference across capacitor of
capacitance 3C when the current in the circuit is maximum is
\( A \cdot \frac{3 V_{0}}{4} \)
B. \( \frac{V_{0}}{4} \)
\( c \cdot \frac{5 V_{0}}{4} \)
D. none of these


\( C H_{3} C O O H \) dimerizes in benzene
when \( 1.65 g \) of \( C H_{3} C O O H \) dissolved in
\( 100 g \) of benzene the elevation of \( B p s \) of
the solution was found \( 0.36 K . \) If \( K_{b} \) for
benzene in 2.85 K.kgl mol. Then find
Vant Hoff factor and degree of
association of \( \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C O O H} \)


Which of the following substances is used as the gaseous dielectric in high voltage transformers?
A. \( S F_{4} \)
в. \( S F_{6} \)
c. \( S C l_{6} \)
D. \( T e F_{6} \)


In the figure masses \( 400 k g \) and \( 100 k g \) are fixed. How much work must be done
to move a \( 1 k g \) mass from point \( A \) to
point \( \boldsymbol{B} ? \)


If \( \mathbf{A} \) is a non-singular square matrix of order \( 3 \times 3, \) find \( |a d j A| \)


Give the structure and IUPAC name of
Di-tert-butylamine


The answer to each of the following question is a single digit integer, ranging from 0 to 9
Number of moles of \( O_{2} \) formed by 136 g of \( H_{2} O_{2}, \) on complete decomposition will be:


Addition of \( K I \) drop by drop to \( A g N O_{3} \) aqueous solution gives an impure sol of AgI. The impurities needed not to be removed by dialysis is :
A. suspended state of \( A g I \)
B. excess of \( A g N O_{3(a q .)} \)
C. excess of \( K I_{(a q .)} \)
D. excess of \( K N O_{3\left(a_{7}\right)} \)


A man wants to reach point B on the
opposite bank of river flowing at a speed as shown in figure. What
minimum speed relative to water
should the man have so that he can
reach point B?


Tripling the speed of a motor car multiplies the distance needed for
stopping it by
\( A \cdot 3 \)
B. 6
\( c \cdot 9 \)
D. some other number


When the refraction takes place
through a glass prism the emergent ray always bends towards the \( \ldots \) prism.
A. base
B. two
c. dispersion
D. deviation


The rate at which a solid dissolves in
water is increased by which of the following?
I. Crushing the solid into smaller pieces
II. Agitating the mixture
III. Placing the mixture in an ice bath
A. I only
B. II only
c. I and II only
D. I and III only


Region between elastic point and yield point is known as
A. Elastoplastic region
B. Electronegative region
c. Electro ductile region
D. Electro plating region


A glass vessel does not break when it
falls on a hard floor, but it breaks when
it falls on a carpet. State true or false.


A slab of stone area \( 3500 \mathrm{cm}^{2} \) and
thickness \( 10 \mathrm{cm} \) is exposed on the lower
surface to steam at \( 100^{\circ} \mathrm{C} \). A block of
ice at \( 0^{\circ} C \) rests on upper surface of the slab. In one hour \( 4.8 k g \) of ice of melted.
The thermal conductivity of the stone is \( J s^{-1} m^{-1} k_{-1} \) is
(Latent heat of ice \( =\mathbf{3 . 3 6} \times \mathbf{1 0}^{\mathbf{5}} \mathbf{J} / \mathbf{k g} \) )
A . 12.0
B. 10.5
c. 1.02
D. 1.24


The substrate for photorespiration is which of the following?
A. Serine
B. Glycolate
c. Indole acetic acid
D. Malic acid


There are 500 students in the school in
Dahihanda village. If 350 of them can swim, what percent of them can swim
and what percentage cannot?


The work done in carrying in point
charge from one point to the another in an electrostatic field depends on the path along which the point charge is carried
A. True
B. False


How many constellations comprise the signs of the zodiac?
\( \mathbf{A} \cdot \mathbf{6} \)
B. 9
c. 11
D. 12


Which of the following is not an application of very large molecule covalent substances?
A. Plastic development that reduces waste
B. Medicine delivery systems
c. Advancements in automotive frame structures
D. Nanotechnology


Enterogastrone is secreted by
A. Gastric mucosa
B. Oesophageal mucosa
c. Saliva
D. Duodenal mucosa


The masses of sun and earth are \( M_{s} \)
and \( M_{e}, \) respectively and the distance
between them is \( R_{e s} \) then, the distance
of a body of mass \( \mathrm{m} \), from the earth
along the line towards the sun, where the sun's gravitational pull balances that of the earth is
A \( \cdot \frac{R_{e s}}{\sqrt{M_{s} / M_{e}}+1} \)
В. \( \frac{R_{e s}}{\sqrt{M_{e} / M_{s}}+1} \)
c. \( \frac{R_{e s}}{\sqrt{M_{s} / M_{e}}-1} \)
D. \( \frac{R_{e s}}{1-\sqrt{M_{e} / M_{s}}} \)


A five-digit number divisible by 3 is to be formed using the digits 0,1,2,3,4
and \( 5, \) without repetition. The total number of ways this can be done is
A . 216
в. 240
c. 600
D. 3125


Give the oxidation state of underlined.
\( \boldsymbol{C a O C l}_{2} \)


\( \lim _{x \rightarrow 0} \frac{\sqrt{1-\sqrt{\cos x}}}{x}= \)
A \( \cdot \frac{1}{2} \)
B. \( -\frac{1}{2} \)
c. Does not exist
D. None of these


State the hybridization and magnetic
property of \( \left[\boldsymbol{F e}(\boldsymbol{C N})_{6}\right]^{3-} \) ion according
to the valence bond theory.


The characteristic feature of ovule of
gymnosperms is
A. Orthotropus
B. Unitegmic
c. Amphitropous
D. Both A and B


Which carbohydrate does not have
\( C_{x}\left(H_{2} O\right)_{y} \) general formula?
A . Melitriose
B. stachyose
C . Fructose
D. Rhamnose


Smoke is an example of:
A. solid dispersed in solid
B. solid dispersed in gas
c. solid dispersed in liquid
D. gas dispersed in solid


Assertion
The reaction in \( C a C O_{3} \) and \( H C l \) goes
to completion.
Reason
Reactions that form a precipitate go to
completion
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 man fired a bullet against a wall and
hears an echo after \( 2 s . \) He walks \( 80 m \)
towards the wall and fired bullet, such
that he hears echo after \( 1 s \). Find the
distance from wall to the second fired
place


Rubies are crystalline forms
of
A. copper oxide
B. Zinc oxide
c. Aluminium oxide
D. Iron oxide


Which of the following shows negative
deviation from Raoult's law?
A. \( C H C l_{3} \) and acetone
в. \( C_{6} H_{6} \) and \( C_{2} H_{5} O H \)
\( \mathbf{c} \cdot C_{6} H_{5} C H_{3} \) and \( C_{6} H_{6} \)
D. \( C_{6} H_{6} \) and \( C C l_{4} \)


\( \operatorname{Given}(\boldsymbol{a}-\mathbf{2}, \boldsymbol{b}+\mathbf{3})=(\mathbf{6}, \mathbf{8}), \) are equal
ordered pair. Find the value of \( a \) and \( b \)
A \( . a=8 \) and \( b=5 \)
B. \( a=8 \) and \( b=3 \)
c. \( a=5 \) and \( b=5 \)


Rate at which electric work is done is
A. Potential difference
B. Energy
c. Power
D. All


In a circuit shown, the average power dissipated in the resistor is (assume
diode to be ideal)
A \( \cdot \frac{E_{0}^{2}}{2 R} \)
в. \( \frac{E_{0}^{2}}{4 R} \)
c. \( \frac{E_{0}^{2}}{R} \)
D. zero


If \( \int \frac{1}{1+\cot x} d x=A \log \mid \sin x+\cos \)
\( \boldsymbol{x} \mid+\mathrm{Bx}+c, \) then \( \boldsymbol{A}=\ldots \ldots . ., \boldsymbol{B}= \)
A \( \cdot-\frac{1}{2}, \frac{1}{2} \)
в. -1,1
\( c \cdot \frac{1}{3}, \frac{1}{2} \)
D. \( \frac{-1}{3}, \frac{1}{2} \)


Very Short Answer Type Questions:
How is nitrogen a significant gas?


The resultant of two equal forces is
double of either of the force. The angle between them is :
A \( \cdot 0^{\circ} \)
B. 60
\( c .90^{\circ} \)
D. 120


If \( \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{0} & \mathbf{1} \\ \mathbf{0} & \mathbf{2} & \mathbf{0} \\ \mathbf{1} & \mathbf{- 1} & \mathbf{4}\end{array}\right], \boldsymbol{A}=\boldsymbol{B}+\boldsymbol{C}, \boldsymbol{B}= \)
\( \boldsymbol{B}^{\boldsymbol{T}}, \boldsymbol{C}=-\boldsymbol{C}^{\boldsymbol{T}}, \) then \( \boldsymbol{C}= \)
A. \( \left[\begin{array}{ccc}0 & 0.5 & 0 \\ -0.5 & 0 & 0 \\ 0 & 0 & 0\end{array}\right] \)
B. \( \left[\begin{array}{ccc}0 & 0 & 0 \\ 0 & 0 & 0.5 \\ 0 & -0.5 & 0\end{array}\right] \)
c. \( \left[\begin{array}{ccc}0 & -0.5 & 0.5 \\ 0.5 & 0 & 0.5 \\ -05 & 0 & 0\end{array}\right] \)
D. \( \left[\begin{array}{ccc}0 & 0.5 & 0 \\ -0.5 & 0 & 0.5 \\ 0 & -0.5 & 0\end{array}\right] \)


Find the value of \( \left(4 \cdot \sin 30^{0} \cos 30^{0}\right)^{2} \)


\( f^{n} P_{r}=^{n} P_{r+1} \) and \( ^{n} C_{r}=^{n} C_{r-1}, \) then
the values of \( n \) and \( r \) are:
A \( \cdot r, 3 \)
B. 3,2
c. 4,2
D. 3,4


Find the general term \( \left(n^{t h} \) term ) and \right.
\( 23^{t h} \) term of the sequence \( \mathbf{3}, \mathbf{1},-\mathbf{1},-\mathbf{3}, \dots \)


Which of the following functions from \( \boldsymbol{A} \)
to \( B \) are one-one and onto?
(i) \( \boldsymbol{f}_{1}=\{(\mathbf{1}, \mathbf{3}),(\mathbf{2}, \mathbf{5}),(\mathbf{3}, \mathbf{7})\} ; \boldsymbol{A}= \)
\( \{1,2,3\}, B=\{3,5,7\} \)
(ii) \( f_{2}=\{(2, a),(3, b),(4, c)\} ; A= \)
\( \{2,3,4\}, B=\{a, b, c\} \)
(iii) \( \boldsymbol{f}_{3}=\{(\boldsymbol{a}, \boldsymbol{x}),(\boldsymbol{b}, \boldsymbol{x}),(\boldsymbol{c}, \boldsymbol{z})\} ; \boldsymbol{A}= \)
\( \{a, b, c, d\} ; B=\{x, y, z\} \)


In a fuel cell, hydrogen and oxygen react to produce electricity. In the process, hydrogen gas is oxidized at anode and
oxygen at cathode. If 67.2 L of \( H_{2} \) at STP
reacts in 15 min, the average current (in \( A \) ) produced is :
Anode reaction \( : H_{2}+2 \stackrel{\ominus}{O} H \rightarrow 2 H_{2} O+ \)
\( 2 e^{-} \)
Cathode reaction \( : \boldsymbol{O}_{2}+\mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O}+ \)
\( 2 e^{-} \rightarrow 4^{\ominus} \)
(write your answer to nearest integer)


The overall reaction of a hydrogen-
oxygen fuel cell is:
A \( \cdot 2 H_{2(g)}+O_{2(g)} \rightarrow 2 H_{2} O_{(l)} \)
B \( \cdot 2 H_{2(g)}+4 O H_{(a q)}^{-} \rightarrow 4 H_{2} O_{(l)}+4 e^{-} \)
c. \( O_{2(g)}+2 H_{2} O_{(l)}+4 e^{-} \rightarrow 4 O H_{(a q)}^{-} \)
D. \( 4 O H_{(a q)}^{-}+4 e^{-} \rightarrow 2 H_{2} O_{(l)} \)


With the help of a circuit diagram
describe the method to find the value of
an unknown resistance using meter bridge arrangement.


During transcription, the DNA site at which RNA polymerase binds is called
as
A. Promoter
B. Regulator
c. Receptor
D. Enhancer


A ball P moving with a speed of \( \boldsymbol{v} \boldsymbol{m} \boldsymbol{s}^{-1} \)
collides directly with another identical
ball Q moving with a speed \( 10 \mathrm{ms}^{-1} \) in the opposite direction. P comes to rest after the collision. If the coefficient of
restitution is \( 0.6, \) the value of \( v \) is:
A \( \cdot 30 m s^{-1} \)
B. \( 40 \mathrm{ms}^{-1} \)
c. \( 50 m s^{-1} \)
D. \( 60 m s^{-1} \)


If \( y=\frac{x}{a+\frac{x}{b+y}}, \) then \( \frac{d y}{d x} \) is
\( \mathbf{A} \cdot \frac{a}{a b+2 a y} \)
B. \( \frac{b}{a b+2 b y} \)
c. \( \frac{a}{a b+2 b y} \)
D. \( \frac{b}{a b+2 a y} \)


Number of \( \sigma \) and \( \pi \) bonds in \( C_{2} \)
molecule is/are:
\( \mathbf{A} \cdot 1 \sigma \) and \( 1 \pi \)
B. \( 1 \sigma \) and \( 2 \pi \)
c. \( 2 \pi \) only
D. \( 1 \sigma \) and \( 3 \pi \)


Supplementary and complementary angles need not be
A . equal to \( 180^{\circ}, 90^{\circ} \)
B. adjacent
c. angles
D. none


If \( \boldsymbol{A}=(\mathbf{5}, \mathbf{8}), \) then area of \( \triangle \boldsymbol{A B D} \) in
square units is
A \( \cdot \frac{96 \sqrt{5}}{89} \)
в. \( \frac{960 \sqrt{5}}{89} \)
c. \( \frac{960 \sqrt{5}}{\sqrt{8} 9} \)
D. None of these


Micronutrients are needed in amounts
A. \( 8 \mathrm{m} \) mole/kg dry matter
B. \( 18 \mathrm{m} \) mole/kg dry matter
c. \( 25 \mathrm{m} \) mole/kg dry matter
D. 30m mole/kg dry matter


Represent the following families of curves by forming the corresponding differential equation.(a, b being parameters). \( x^{2}-y^{2}=a^{2} \)


The equilibrium constant for the reaction \( \boldsymbol{A} \Leftrightarrow \boldsymbol{B} \) is \( \boldsymbol{K} \). The equilibrium
constant for the reaction \( \boldsymbol{m} \boldsymbol{A} \Leftrightarrow \boldsymbol{m} \boldsymbol{B} \) is:
\( \mathbf{A} \cdot m K \)
в. \( \frac{K}{m} \)
c. \( K^{m} \)
D. \( K^{-m} \)


If \( \arg (z)<0, \) then \( \arg (-z)- \)
\( \boldsymbol{a r} \boldsymbol{g}(\boldsymbol{z})= \)
A . \( \pi \)
в. \( -\pi \)
\( c \cdot \frac{\pi}{2} \)
D. \( -\frac{\pi}{2} \)


Which of the following statement(s)
is/are correct"?
This question has multiple correct options
A. The chemical processes in the production of steel from haematite ore involve reduction followed by
oxidation.
B. In Hall-Heroult process, the electrolyte used is a molten mixture of alumina and cryolite or fluorspar.
C. Lead is extracted from its chief ore galena by both carbon reduction as well as self reduction,
D. Haematitic, cassiterite, and argentite are oxide ores.


Which one of the following factors is biotic?
A. Photoperiod
B. Carbon dioxide content of the soil
c. Texture and porosity of soil
D. Rainfall


If we double the radius of a coil keeping the current through it unchanged, then the magnetic field at any point at a large distance from the centre becomes
approximately
A. double
B. three times
c. four times
D. one-fourth


What are strong electrolytes?
A. Compounds which in fused or in the aqueous solution state are almost completely dissociated
B. Compounds which are good conductors of electricity
C. Both A and B
D. None of the above


Barometer was constructed by
A. Torricelli
B. Newton
c. Archimedes
D. None


The value of \( -5 \times-2 \times-2 \times-3 \) is
\( A \cdot 80 \)
B. 65
\( c \cdot 60 \)
D. -60


An aqueous solution of a metal bromide
\( M B r_{2}(0.05 M) \) is saturated with \( H_{2} S \)
The minimum \( p H \) at which \( M S \) will
precipitate is \( \boldsymbol{X} \) ? \( \boldsymbol{K}_{s p} \) for \( \boldsymbol{M} \boldsymbol{S}=\boldsymbol{6} . \boldsymbol{0} \times \)
\( 10^{-21} \)
Concentration of saturated \( \boldsymbol{H}_{2} \boldsymbol{S}= \)
\( \mathbf{0 . 1} M ; K_{1}=10^{-7} \) and \( K_{2}=1.3 \times \)
\( 10^{-13} \) for \( H_{2} S \)
A. 5
B. 8
\( c \)
D. 4


Which quadrant does the solution lie
in?
A . \( I \)
в. \( I I \)
\( c . I I I \)
D. \( I V \)


At a place of latitude \( 5^{\circ}, \) the angle of dip is nearly
\( A \cdot 5^{\circ} \)
B. \( 10^{\circ} \)
\( c \cdot 2.5^{\circ} \)
D. \( 7.5^{\circ} \)


Find \( K \) where
\( \lim _{x \rightarrow k}\left[\frac{x^{4}-1}{x-1}\right]=\lim _{x \rightarrow k}\left(\frac{x^{3}-k^{3}}{x^{2}-k^{2}}\right) \)


A microscope has an objective of focal length \( 1.5 \mathrm{cm} \) and an eyepiece of focal length \( 2.5 \mathrm{cm} . \) If the distance between
objective and eyepiece is \( 20.5 \mathrm{cm}, \) what
is the magnification produced when the final image is at infinite distance
away?
A . 100
B. 75
\( c .110 \)
D. 120


Evaluate:
\( \int \frac{x^{3}-4 x^{2}+6 x+5}{x^{2}-2 x+3} d x \)


Electric heaters used for cooking have the filament or the heating coil on a plate made up of clay because:
A. clay is a bad conductor of heat
B. clay is a bad conductor of electricity
c. clay is necessary for good taste
\( D \cdot \operatorname{both} A \& B \)


Assertion
Closed circulatory system is less efficient than open circulatory system.
Reason
The blood flow is slow in closed
circulatory system than in open circulatory system.
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


With the increase in size of a group:
A. metallic character decreases
B. metallic character increases
C . chemical reactivity decreases
D. chemical reactivity remains same


The oscillations of a pendulum slow
down due to:
A. the force exerted by air and the force exerted by friction at the support
B. the force exerted by air only
C. the forces exerted by friction at the support
D. they never slow down


Find \( \frac{d y}{d x}, \) if \( x=a(\theta-\sin \theta) \) and \( y= \)
\( \boldsymbol{a}(\mathbf{1}-\cos \boldsymbol{\theta}) \)


\( \boldsymbol{F}=\boldsymbol{G} \frac{\boldsymbol{m}_{1} \times \boldsymbol{m}_{2}}{\boldsymbol{R}^{2}} \) is the formula to prove
A. Newton's First law of motion
B. Newton's Second law of motion
C. Newton's Third law of motion
D. Newton's law of Gravitation


Identify the wrong sign convention.
A. The magnification for virtual image formed by a convex lens is positive
B. The magnification for real image formed by a convex lens is negative
C. The height measured normal to the principal axis upwards is positive
D. The distances measured in the direction of incident
light is positive
E. The magnification for virtual image formed by a concave lends is negative


The bond energies in \( \mathrm{NO}, N O^{+} \) and
\( N O^{-} \) follow the order:
A \( \cdot N O^{+}>N O>N O^{-} \)
В. \( N O>N O^{+}>N O^{-} \)
c. \( N O^{-}>N O>N O^{+} \)
D. \( N O^{+}>N O^{+}>N O \)


A ball of mass \( \mathrm{m} \) is thrown vertically upward from the ground and reaches a height h before momentarily coming to rest.If \( g \) is acceleration due to gravity,the impulse received by the ball due to gravity force during its flight is
\( \mathbf{A} \cdot \sqrt{2 m^{2} g h} \)
в. \( \sqrt{4 m^{2} g h} \)
\( \mathbf{c} \cdot \sqrt{8 m^{2} g h} \)
D. \( 4 \sqrt{m^{2} g h} \)


A string tied on a roof can bear a maximum weight of 50 kg wt. The minimum acceleration that can be
acquired by a man of \( 98 \mathrm{kg} \) to descend will be :
(take \( \mathfrak{g}=9.8 m / s^{2} \)
A. \( 9.8 m / s^{2} \)
В. 4.9 \( m / s^{2} \)
C \( .4 .8 m / s^{2} \)
D. \( 5 m / s^{2} \)


Which of the following is least reactive in a nucleophilic substitution reaction?
A. \( C H_{2}=C H C l \)
в. \( C H_{3} C H_{2} C l \)
c. \( C H_{2}=C H C H_{2} C l \)
D. \( \left(C H_{3}\right)_{3} C-C l \)


The figure shows four animals \( A, B, C \)
and D. Select the correct answer
regarding the characteristic feature of animals.
A. A and D have cnidoblasts for self-defence
B. c and D have true coelom
c. A and D respire mainly through gills
D. B and C show radial symmetry


First life on earth was
A. Chemoautotrophs
B. Autotrophs
c. Photoautotrophs
D. None of these


Explain why carbon generally forms compounds by covalent bonds.


Find the area of the given parallelogram


The
distance from the centre to the
circumference.
A. Sector
B. Segment
c. Diameters
D. Radius


At \( 900 \mathrm{K}, p K_{w} \) is \( 13 . \) At this temperature
an aqueous solution with \( \boldsymbol{p} \boldsymbol{H}=\mathbf{7} \) will
be:
A . acid
B. basic
c. natural
D. none of these


Draw the structure of major monohalo product in each of the following reactions.
(ii)


In Dholak sound produce due to which of the following?
A. Stretched membrane
B. Stretched strings
c. Vibration of air
D. Air column


If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of other chord


\( \mathrm{R}, \mathrm{S} \) and \( \mathrm{T}, \) respectively are?
\( \mathbf{A} \cdot S O_{2} C l_{2}, P C l_{5} \) and \( H_{3} P O_{4} \)
B. \( S O_{2} C l_{2}, P C l_{3} \) and \( H_{3} P O_{3} \)
\( \mathbf{c} \cdot S O C l_{2}, P C l_{3} \) and \( H_{3} P O_{2} \)
D \( \cdot S O C l_{2}, P C l_{5} \) and \( H_{3} P O_{4} \)


Which of the following statement(s)
is/are correct
This question has multiple correct options
A. A plane mirror cannot form real image of real object
B. A ray of light gets reflected successively from two mirrors which are mutually perpendicular net angular deviation suffered by the ray does not depend upon angle of incidence of first mirror
C. When a glass prism is completely submerged in water then its dispersive power increases
D. Refractive index of a material does not depend upon wavelength of light


Why is the switch for any electrical appliance always fitted on to the live
wire ?
A. No current flows in the neutral wire
B. There will be a short circuit if the switch is in the earth lead
c. The device can never be switched off if the switch is in the neutral lead
D. The device can only be isolated if the switch is in the live lead


How cloth is cleaned with the help of detergents?


The capacitance of a parallel plate
capacitor with air as medium is \( 3 \mu \mathrm{F} \) As a dielectric is introduced between
the plates, the capacitance becomes 15
\( \mu \mathrm{F} . \) The permittivity of the medium in
\( C^{2} N^{-1} m^{-2} \) is
A . \( 8.15 \times 10^{-11} \)
В. \( 0.44 \times 10^{-10} \)
C . \( 15.2 \times 10^{12} \)
D. \( 1.6 \times 10^{-14} \)


Select the correct alternate:
The geometry of \( H_{2} S \) and its dipole
moment are:
A. angular and non-zero
B. angular and zero
c. linear and non-zero
D. linear and zero


In kingdom animalia according to the traditional school of systematic, birds are assigned to a different group from reptiles because
A. They evolved from reptiles
B. They are quite different from reptiles
c. Feathers evolved from scales
D. All of the above


Which compound/s is/are formed when
hydrolysis of Marshall's acid take place
\( ? \)
This question has multiple correct options
A. \( H_{2} S O_{3} \)
в. \( H_{2} C O_{4} \)
c. \( H_{2} O_{2} \)
D. \( H_{2} S O_{4} \)


Two thermally insulated vessels 1 and 2
are filled with air at temperature
\( \left(\mathbf{T}_{1}, \mathbf{T}_{2}\right), \) volume \( \left(\mathbf{V}_{1}, \mathbf{V}_{2}\right) \) and pressure
\( \left(\mathbf{P}_{1}, \mathbf{P}_{2}\right) \) respectively. If the valve joining the two vessels is opened, the
temperature inside the vessel at equilibrium will be:
\( \mathbf{A} \cdot \mathbf{T}_{1}+\mathbf{T}_{2} \)
B. \( \left(\mathrm{T}_{1}+\mathrm{T}_{2}\right) / 2 \)
\( \mathrm{c} \cdot \mathrm{T}_{1} \mathrm{T}_{2}\left(\mathrm{P}_{1} \mathrm{V}_{1}+\mathrm{P}_{2} \mathrm{V}_{2}\right) \)
\( \mathrm{P}_{1} \mathrm{V}_{1} \mathrm{T}_{2}+\mathrm{P}_{2} \mathrm{V}_{2} \mathrm{T}_{1} \)
D. \( \frac{\mathrm{T}_{1} \mathrm{T}_{2}\left(\mathrm{P}_{1} \mathrm{V}_{1}+\mathrm{P}_{2} \mathrm{V}_{2}\right)}{\mathrm{P}_{1} \mathrm{V}_{1} \mathrm{T}_{1}+\mathrm{P}_{2} \mathrm{V}_{2} \mathrm{T}_{2}} \)


Express \( \sin 12 \theta+\sin 4 \theta \) as the product
of sines and cosines.


If \( f(x) \) is a polynomial of degree \( n(>2) \)
and \( f(x)=f(k-x), \) (where \( k \) is a
fixed real number), then degree of \( \boldsymbol{f}^{\prime}(\boldsymbol{x}) \)
is
\( A \)
B. \( n-1 \)
\( \mathbf{c} \cdot n-2 \)
D. None of these


What is the electronic configuration of chromium atom \( (z=24) ? \) Give a reason
for your answer.


The minimum concentration of an
electrolyte required to cause coagulation of a sol is called:
A. flocculation value
B. gold number
c. protective value
D. none of these


The radii of two cylinders are in the ratio
2: 3 and their heights are in the ratio
\( \mathbf{5}: \mathbf{3}, \) then the ratio of their volumes is
\( ? \)
A . 15: 16
B. 14: 17
c. 20: 27
D. 4: 9


To convert a pure semiconductor into \( n \)
type semi-conductor, what type of impurity is added to it?


1 V equals:
A . 1 J
B. \( 1 \mathrm{JC}^{-1} \)
\( c \cdot 1 C J^{-1} \)
D. 1 JC


At some planet, \( g=1.96 m s^{-2} . \) If it is
safe to jump from a height of \( 2 m \) on earth, then the corresponding safe height on that planet is
\( \mathbf{A} \cdot 2 m \)
B. \( 5 m \)
c. \( 10 m \)
D. \( 20 m \)


If \( \sin ^{-1} x+\sin ^{-1} y=\frac{2 \pi}{3}, \) then find the
value of \( \cos ^{-1} x+\cos ^{-1} y \)


Two capacitors connected in parallel
having the capacities \( C_{1} \) and \( C_{2} \) are
given ' \( q^{\prime} \) charge, which is distributed among them. The ratio of the charge on
\( C_{1} \) and \( C_{2} \) will be :
A \( \cdot \frac{C_{1}}{C_{2}} \)
в. \( \frac{C_{2}}{C_{1}} \)
\( \mathbf{c} \cdot C_{1} C_{2} \)
D. \( \frac{1}{C_{1} C_{2}} \)


The formula for calculating \( \bar{M}_{n} \) of a polymer is:
A. \( \frac{\sum N i M i}{\sum N i} \)
в. \( \frac{\sum N i M i}{\sum M i} \)
c. \( \frac{\sum_{N i M i}^{2}}{\sum M i} \)
D. \( \frac{\sum N i M i^{2}}{\sum N N M i} i \)


Solve: \( \sqrt{7 \sqrt{7 \sqrt{7 \sqrt{7 \sqrt{7 \ldots \ldots}}}}}=k . \) Find k.


Which of the following is considered as unit of inheritance?
A. Gene
B. Chromosome
c. Nucleotide
D. codon
E. Chromatid


The blamer series of spectral lines for
hydrogen appear in the visible region. What is the lower energy level that these electronic transitions start from, and what transitions correspond to the
spectral lines at \( 379.0 \mathrm{nm} \) and \( 430.0 \mathrm{nm} \) respectively?


Which of the following is produced by action of conc. sulphuric acid over potassium ferrocyanide?
\( A \cdot O_{2} \)
в. \( C O \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \)
D. \( N_{2} \)


Given \( \vec{A}=2 \hat{i}+3 \hat{j} \) and \( \vec{B}=\hat{i}+\hat{j} . \) The
component of vector \( \overrightarrow{\boldsymbol{A}} \) along vector \( \overrightarrow{\boldsymbol{B}} \) is:
A \( \cdot \frac{1}{\sqrt{2}} \)
B. \( \frac{3}{\sqrt{2}} \)
c. \( \frac{5}{\sqrt{2}} \)
D. \( \frac{7}{\sqrt{2}} \)


Two concentric spherical shells of radii a and 1.2 a have charges \( +\mathrm{Q} \) and \( -2 \mathrm{Q} \) respectively. At what distance from centre potential will be same as that of centre?
A . 2 a
B. 1.5 a
c. 2.5 a
D. 3a


The valency of nitrogen in \( N H_{3} \) is :
\( A \cdot 3 \)
B. 4
\( c .5 \)
D.


A ball \( A \) of mass \( 2.5 \mathrm{kg} \) moving at \( 5 \mathrm{m} / \mathrm{s} \) collides with an identical ball \( B \) at rest.
A stops and B starts moving. What is the magnitude of velocity of B after the collision?
\( A \cdot 5 m / s \)
B. 12.5 \( \mathrm{m} / \mathrm{s} \)
\( c .2 .5 \mathrm{m} / \mathrm{s} \)
D. \( 10 \mathrm{m} / \mathrm{s} \)


a polysaccharide having \( \beta-D \)
glucoside units, has a stronger and more compact physical structure than
starch which has \( \alpha \) -D-glucsoe unit
A. Cellulose
B. L-Fructose
c. D-Fructose
D. None of these


How many of the following substances
are soluble in concentrated \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) ?
\( \boldsymbol{B} \boldsymbol{a} \boldsymbol{S} \boldsymbol{O}_{4}, \boldsymbol{C} \boldsymbol{u} \boldsymbol{S}, \boldsymbol{P b} \boldsymbol{S}, \boldsymbol{H} \boldsymbol{g} \boldsymbol{S} \)
\( A \)
B. 2
\( c \cdot 3 \)
D. 4


An electron moves with a constant
speed v along a circle of radius r. The magnetic moment will be (e is the electron charge)
A . evr
B. \( \frac{e v r}{2} \)
\( \mathbf{c} \cdot \pi r^{2} e v \)
D. \( 2 \pi r e v \)


Potential difference between two points is 60 V. How much work will done on
bringing charge of \( 3 \times 10^{-5} \) Coulomb
from one point to another point.


Solution of the differential equation \( \boldsymbol{y}^{\prime}+\boldsymbol{y} \sec ^{2} \boldsymbol{x}=\sec ^{2} \boldsymbol{x} \cdot \boldsymbol{\operatorname { t a n }} \boldsymbol{x} \) is
A \( \cdot y=(\tan x+1)+c e^{-\tan x} \)
B . \( y=(\tan x-1)+c e^{-t a n x} \)
C \( \cdot y=(\tan x+1)+c e^{\tan x} \)
D. None of these


Specific heat may be defined as:
A. heat capacity at constant volume
B. heat capacity at constant pressure
c. heat capacity mol-
D. heat capacity \( g^{-1} \)


The value of angle of dip at magnetic poles of the Earth is


\( \int_{0}^{1}(\sqrt{\boldsymbol{x}}) \boldsymbol{d} \boldsymbol{x}+\int_{0}^{4 / 3}(\sqrt{\boldsymbol{4}-\boldsymbol{3} \boldsymbol{x}}) d \boldsymbol{x} \)


During the process of electrolyte refining of copper, some metals present as impurity settle as 'anode mud'. These
are:
A. Sn and Ag
B. Pb and Zn
c. \( A g \) and \( A u \)
D. Fe and Ni


The given figure shows a diagrammatic
sketch of a portion of human male
reproductive system. Identify the parts labelled as \( A, B, C \) and
D and select the correct option.
A. A-vas deferens, B-seminal vesicle, C-Prostate, DBulbourethral gland
B. A-Vas deferens, B-Seminal vesicle, C-Bulbourethral gland, D-Prostate
c. A-Ureter, B-Seminal vesicle, C-Prostate, DBulbourethral gland
D. A-Ureter, B-Prostate, C-Seminal vesicle, DBulbourethral gland


Which of following is NOT a property of red phosphorus?
A. Insoluble in carbon disulphide
B. It does not show chemiluminescence by action of air
c. It forms phosphine when treated with hot sodium hydroxide solution
D. It is non-poisonous


The pH of a solution containing
\( N H_{4} O H \) and \( N H_{4}^{+} \) is \( 9 . \) If \( \left[N H_{4}^{+}\right]=0 . \)
\( \mathrm{M} \) and \( \mathrm{Ka} \) of \( N H_{4}^{+} \) is \( 5 \times 10^{-10} \) then
what is \( \left[\boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{O} \boldsymbol{H}\right] ? \)


Which of the following statements is
correct about the reaction given below?
4 Fe \( (s)+3 O_{2}(g) \rightarrow 2 F e_{2} O_{3}(g) \)
A. The total mass of reactants \( = \) Total mass of the products. It follows the law of conservation of mass.
B. The total mass of reactants = Total mass of the products. Therefore, the law of multiple proportions is followed.
C. Amount of \( F e_{2} O_{3} \) can be increased by taking any one of the reactants (iron or oxygen) in excess.
D. Amount of \( F e_{2} O_{3} \) produced will decrease if the amount of any one of the reactants (iron or oxygen) is taken in excess.


Villi are present in the intestine and not
in the stomach. Give reasons.


Write each of the following in the form of \( a x+b y+c=0 \) and find the value of \( a, b \) and c
(i) \( x=-5 \)
(ii) \( y=2 \)
(iii) \( 2 x=3 \)
\( (i v) 5 y=-3 \)


In a simultaneous throw of a pair of
dice, if the probability of getting a total of 9 or 11 is \( \frac{1}{x} . \) Find \( x \)


The value of acceleration due to gravity on the surface of the earth depends on.
A. pressure
B. acceleration
c. gravitational force between an object and the earth
D. none of these


How many \( 3- \) digit numbers can be
formed by using the digits 0,1,3,5,7 while each digit may be repeated any number of times?


Find the measure of each exterior angle
of a regular polygon of 15 sides
A \( \cdot 24^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 36^{0} \)
D. \( 42^{\circ} \)


Identify the gas evolved and give the chemical test in each of the following
case:
(i) Dilute hydrochloric acid reacts with sodium sulphite.
(ii) Dilute hydrochloric acid reacts with
iron
(II) sulphide.


The rain mixed with sulphuric acid is called as
A. Acid rain
B. Alkaline rain
c. Neutral rain
D. None of these


Which set of teeth help in grinding food?


If \( \lim _{x \rightarrow 0}\left(\frac{\cos 4 x+a \cos 2 x+b}{x^{4}}\right) \) is finite
then the value of \( a, b \) respectively are
\( \mathbf{A} \cdot 5-4 \)
в. -5,-4
c. -4,3
D. 4,5


Major radiation of mammals, birds and pollinating insects took place in which epoch?
A. Oligocene
B. Eocene
c. Pliocene
D. Palaeocene


Consider the following decay series:
\( \boldsymbol{A} \longrightarrow \boldsymbol{B} \longrightarrow \boldsymbol{C} \longrightarrow \boldsymbol{D} \)
Where, \( A, B \) and \( C \) are radioactive
elements with half lives of 4.5 sec, 15
days and 1 sec respectively and \( D \) is
non-radioactive element. Starting with
1 mole of \( A \), the number of moles of \( A \)
\( B, C \) and \( D \) left after 30 days are:
A. One mole of \( D \) and none of \( A, B \) or \( C \)
B. \( 3 / 4 \) mol of \( B, 1 / 4 \) mol of \( D \) and none of \( A \) or \( C \)
C. \( 1 / 4 \) mol of \( B, 3 / 4 \) mol of \( D \) and none of \( A \) or \( C \)
D. \( 1 / 2 \) mol of \( B, 1 / 4 \) mol of \( C, 1 / 4 \) mol of \( D \) and none of \( A \)
E . \( 1 / 4 \) mol of each \( A, B, C \) and \( D \)


Identify the graph of the polynomial
function \( \boldsymbol{f} \)
\( f(x)=x^{4}+x^{3}-2 x^{2} \)
\begin{tabular}{|l|l|l|l|l|}
\hline 1 & 1 & & & \\
\hline & & & & \\
\hline & & & & \\
\hline & & & & \\
\hline & & & & \\
\hline & & & & \\
\hline
\end{tabular}
A. graph a
B. graph b
c. graph c
D. graph d


Find the correct co-related number.
\( \mathbf{5}: \mathbf{3 6}:: \mathbf{6}: ? \)
A . 48
B. 50
c. 49
D. 56


Find the mode for the following data:
Students \( \begin{array}{lll}\mathbf{1 0} & \mathbf{1 4} & \mathbf{2 0}\end{array} \) \( \mathbf{3 0} \)
Frequency \( \quad 2 \quad 2 \)
A . 10
B . 20
c. 60
D. 30


toppr \( t \)
Q Type your question-
\[
\underset{\mathbf{C}_{7} \mathbf{H}_{\mathbf{1} 4}}{(\mathbf{A})} \frac{\mathbf{H}_{2}+\mathbf{P} \mathbf{d}}{\left(\mathbf{C}_{7} \mathbf{H}_{16}\right)}
\]
Optically active Optically active
Optically active
This question has multiple correct options
\( A \)
(A) and (C) are the same compound which is
B.
(A) and (C) are the same compound which is
\( c \)
(B) is
\( D \)
(B) is


If \( 9 \mathrm{gm} H_{2} O \) is electrolysed completely with the current of \( 50 \% \) efficiency then?
A. 96500 charge is required
B. \( 2 \times 96500 \) C charge is required
\( \mathrm{c} \cdot 5.6 \mathrm{L} \) of \( \mathrm{O}_{2} \) at STP will be formed
D. 11.2 Lof \( O_{2} \) at STP will be formed


Site of glycolysis or EMP is
A. Mitochondria
B. Cytoplasm
\( c . \) E.R
D. Ribosomes


Compound \( \left[\boldsymbol{C o}(\boldsymbol{C N})_{2}(\boldsymbol{e n})_{2}\right] \boldsymbol{C l} \) can
show:
A. only optical isomerism
B. only geometrical and optical isomerism
c. only structural isomerism
D. structural, geometrical and optical isomerism


Two electric charges \( 12 \mu C \) and \( -6 \mu \)
electric field intensity at zero potentia
and outside the region between them
A \( \cdot 1.25 \times 10^{6} N / C \)
В. \( 3.75 \times 10^{5} N / C \)
c. \( 4.5 \times 10^{6} N / C \)
D. \( 6.75 \times 10^{5} N+C \)


Evaluate \( : \int_{-2}^{2}|2 x+3| d x \)


Hydrogen bomb is based on
A. thermochemical reaction
B. nuclear fission
c. nuclear fusion
D. none of these


The change in the oxidation number of
the underlined nitrogen atom in the following chemical reactions are :
a. Nitrous acid \( \left(H \underline{N} O_{2}\right) \) reduces
\( M n O_{4}^{\ominus} \) in acid solution
b. Nitrous acid \( \left(H \underline{N} O_{2}\right) \) oxidises \( I^{\ominus} \) to
\( I_{2} \) in acid solution.
\( A \cdot(a)+3 \) to +5
\( (b)+3 t 0+2 \)
B. (a) +3 to +6
\( (b)+3 t 0+2 \)
\( c \cdot(a)+3 t a+5 \)
\( (b)+3 t 0+1 \)
D. \( (a)+3 \) to +2
\( (b)+3 t 0+5 \)


Sample space for experiment in which two coins are tossed is
A . 8
B. 4
\( c \cdot 2 \)
D. None of these


Determine the equilibrium constant of the following reaction at \( 298 K: \) \( 2 F e^{3+}+S n^{2+} \rightarrow 2 F e^{2+}+S n^{4+} \)
(Given: \( \boldsymbol{E}_{\boldsymbol{S n}^{4+} / \boldsymbol{S n}^{2+}}^{\circ}= \)
\( \mathbf{0 . 1 5} \)volt; \( \boldsymbol{E}_{\boldsymbol{F} e^{3+} / \mathbf{F e}^{2+}}^{\circ}=\mathbf{0 . 7 7 1} \mathbf{v o l t} \mathbf{t} \)


\( K F \) combines with \( H F \) to form \( K H F_{2} \)
The compound contains the species:
A \( \cdot K^{+}, F^{-} \) and \( H^{+} \)
B. \( K^{+}, F^{-} \) and \( H F \)
c. \( K^{+} \) and \( \left[H F_{2}\right]^{-} \)
D. \( [K H F]^{+} \) and \( F_{2} \)


The compound of vanadium has
magnetic moment of \( 1.73 B \). The vanadium chloride has the formula:
A \( \cdot V C l_{2} \)
в. \( V C l_{3} \)
c. \( V C l_{4} \)
D. \( V C l_{5} \)


Assertion
BaCO \( _{3} \) is more soluble in \( H N O_{3} \) than
in plain water.
Reason
Carbonate is a weak base and reacts
with the \( H^{+} \) from the strong acid causing the barium salt to dissociate.
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


Two bad eggs are accidentally mixed up with ten good ones. Find the probability of picking good eggs.


An electron in ground state absorbs 1.5 times as much energy required to escape from H atom. The wavelength of
electron emitted in \( A^{\circ} \) is :
A \( .4 .21 A^{\circ} \)
B . \( 4.71 A^{\circ} \)
c. \( 3.52 A^{\circ} \)
D. \( 3.711 A^{\circ} \)


The IUPAC name of the following
compound is:


Proteins have primary structures. If you are given a method to know which
amino acid is at either of two termini (ends) of a protein, can you connect this information to purity or homogeneity of a protein?


Referring a-s diagram in the Fig., find the velocity after particle travel \( 250 \mathrm{m} \)
from starting. Assume \( v_{0}=0 \)


The probability that at least one of the
events \( A \) and \( B \) occurs is 0.7 and they occur simultaneously with probability
\( 0.2 . \) Then \( P(\bar{A})+P(\bar{B})= \)
A . 1.8
B. 0.6
c. \( 1 . \)
D. 1.


Let \( \mathrm{R} \) be a relation from \( \mathrm{N} \) to \( \mathrm{N} \) defined
by \( R=\left\{(a, b): a, b \in N \text { and } a=b^{2}\right\} . \) Is
the following statement is true for \( (\boldsymbol{a}, \boldsymbol{a}) \in \boldsymbol{R} \forall \boldsymbol{a} \in \boldsymbol{N} \)
A. True
B. False


Convert \( \frac{3 \pi}{7} \) in degrees.


State Flemings right hand rule. For what purpose is it used?


A current I flows in the anticlockwise
direction through a square loop of side a lying in the xoy plane with its center at the origin. The magnetic induction at the center of the square loop is
A \( \cdot \frac{2 \sqrt{2} \mu_{0} I}{\pi a} \hat{e}_{x} \)
B. \( \frac{2 \sqrt{2} \mu_{0} I}{\pi a} \hat{e}_{z} \)
\( ^{\mathrm{c}} \cdot \frac{2 \sqrt{2} \mu_{0} I}{\pi a^{2}} \hat{e}_{z} \)
D. \( \frac{2 \sqrt{2} \mu_{0} I}{\pi a^{2}} \hat{e}_{x} \)


A particle moves with constant speed \( v \) along a regular hexagon ABCDEF in the same order. Then the magnitude of the velocity for its motion from A to This question has multiple correct options
\( \mathbf{A} \cdot_{F} \) is \( \frac{v}{5} \)
B \( \cdot \) D is \( \frac{v}{3} \)
c. \( \quad \mathrm{c} \) is \( \frac{v \sqrt{3}}{2} \)
D. B is \( v \)


Two open organ pipes of fundamental
frequencies \( n_{1} \) and \( n_{2} \) are joined in series. The fundamental frequency of the new pipe so obtained will be:
A \( \cdot n_{1}+n_{2} \)
в. \( \frac{n_{1} n_{2}}{n_{1}+n_{2}} \)
c. \( n_{1}+\frac{n_{2}}{2} \)
D. None of the above


In chulhas, gaps are left between the
\( \log s \)
A. to decrease the ignition temperature of the fuel
B. to allow the air to enter and facilitate fuel burning
c. to cut off the supply of air
D. all of these


Vacuum distillation is conducted to
concentrate \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) solution
A. True
B. False


The frequency of A.C mains in India is
A. \( 30 c / s \)
B. \( 50 c / s \)
\( \mathbf{c} \cdot 60 c / s \)
D. \( 120 c / s \)


\( \mathbf{A} \)
0.1 molar solution of \( N a C l \) is found
to be isotonic with \( 1 \% \) urea solution.
Calculate
(a) Van't Hoff factor
(b)Degree of dissociation of sodium
chloride.

Assume density of \( 1 \% \) urea equal to
\( 1 g c m^{-3} \)
\( \begin{array}{ll}\text { A. }(a) & 1.667, \text { (b) } 0.667\end{array} \)
В. (а) \( 1.82, \) (b) 0.69


If \( A \) and \( B \) are independent events such that \( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B})=\mathbf{0 . 6}, \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 2}, \) find
\( P(B) \)


Solve \( \sec ^{2} x \tan y d y+\sec ^{2} y \tan x d x= \)
\( \mathbf{D} \)


A person wear normal spectacles in which the distance of glasses and eyes is approximately \( 2 \mathrm{cm}, \) then power required is \( -5 D . \) If he wears contact
lens, then the required power is?
A . -5.2 D
B. -4.54 D
c. \( +5.2 \mathrm{D} \)
D. +4.7 D


Eight identical cells each of potential and internal resistance r are connected
in series to form a closed circuit. An
ideal voltmeter connected across 2 cells
will read :-
A . 13 E
B. zero
\( c \cdot 2 E \)
D. 10 E


What loci are represented by the equations:
\( (x+y)^{2}-c^{2}=0 \)


A sample of \( H e^{+} \) ions in a gaseous
state had all ions in \( n^{t h} \) excited state.
This sample on returning to ground state emits a total of 28 spectral lines.
Value of \( n \) is:
\( A \cdot 8 \)
B. 7
\( c \cdot 6 \)
D. 5


The two curves \( x^{3}-3 x y^{2}+2=0 \) and
\( \mathbf{3} \boldsymbol{x}^{2} \boldsymbol{y}-\boldsymbol{y}^{3}-\boldsymbol{2}=\mathbf{0} \)
A. cut at right angles
B. touch each other
c. cut at an angle \( \frac{\pi}{3} \)
D. cut at an angle \( \frac{\pi}{4} \)


Consider the following reaction:
\( \boldsymbol{H} \boldsymbol{C H O}+\mathbf{2}\left[\boldsymbol{A} \boldsymbol{g}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2}\right]^{+}+\boldsymbol{3} \boldsymbol{O} \boldsymbol{H}^{-} \rightarrow \)
\( \mathbf{2 A g}+\boldsymbol{H C O O}^{-}+\mathbf{4 N H}_{\mathbf{3}}+\mathbf{2 H}_{\mathbf{2}} \boldsymbol{O} \)
Which of the following statements
regarding oxidation and reduction is
correct?
\( \mathbf{A} \cdot H C H O \) is oxidised to \( H C O O^{-} \) and \( \left[A g\left(N H_{3}\right)_{2}\right]^{+} \) is reduced to \( A g \)
B. \( H C H O \) is reduced to \( H C O O^{-} \) and \( \left[A g\left(N H_{3}\right)_{2}\right]^{+} \) is oxidised to \( A g \)
\( \mathbf{C} \cdot\left[A g\left(N H_{3}\right)_{2}\right]^{+} \) is reduced to \( A g \) while \( O H^{-} \) is oxidised to \( H C O O^{-} \)
\( \mathbf{D} \cdot\left[A g\left(N H_{3}\right)_{2}\right]^{+} \) is oxidised to \( N H_{3} \) while \( H C H O \) is reduced to \( H_{2} O \)


Is it possible to have a triangle with the
following sides \( 2 \mathrm{cm}, 3 \mathrm{cm}, 5 \mathrm{cm} \)


Given below are Matching type questions, with two columns(each
having some items) each.Each item of column \( I \) has to be matched with the
items of column \( I I \), by enclosing the
correct match.
Note:An item of column \( I \) can be
matched with more than one items of
columnII.All the items of column \( I I \)
have to be matched. The equation of conics represented by the general equation of second degree \( \boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{2 h x} \boldsymbol{y}+\boldsymbol{b} \boldsymbol{y}^{2}+\boldsymbol{2} \boldsymbol{g} \boldsymbol{x}+\boldsymbol{2} \boldsymbol{f} \boldsymbol{y}+\boldsymbol{c}= \)
0
and the discriminant of above equation is represented by \( \triangle, \) where \( \triangle=a b c+ \) \( 2 f g h-a f^{2}-b g^{2}-c h^{2} \) or \( \left(\begin{array}{lll}a & h & g \\ h & b & f \\ g & f & c\end{array}\right) \)
Now, match the entries from the
following two columns


Which of the following catalysts is/are used for partial reduction of alkyne?
A . \( N i \)
B. \( N i_{2} B \) or P-2 catalyst
c. Lindlar catalyst
D. None of these


Among the following, which is not the component of coal gas?
A. Methane
B. Hydrogen
c. oxygen
D. carbon dioxide


The Jupiter's period of revolution around the Sun is 12 times that of the

Earth. Find the ratio gravitational force exerted on Earth to that on Jupiter
A. 27.47
в. \( \frac{1}{27.47} \)
c. 16.2
D. \( \frac{1}{16.2} \)


Find the equation of the line intersecting the \( x \) -axis at a distance of
3 units to the left of origin with slope
-2


When water is cooled it contracts until
it reaches and then it
starts expanding.
A \( \cdot 37^{\circ} \mathrm{C} \)
B. \( 40^{\circ} \mathrm{C} \)
\( c \cdot 0^{\circ} \mathrm{C} \)
D. \( 4^{\circ} \mathrm{C} \)


A tall vertical cylinder filled with water is kept on a horizontal table top. Two small holes \( A \) and \( B \) are made on the
wall of the cylinder, A near the middle and B just below the free surface of
water
A. Water jet through A will have larger range
B. Water jet through B will have larger range
c. water jets through \( A \) and \( B \) will have equal range
D. There will be no water jet through B


The equation \( 16 x^{2}-3 y^{2}-32 x+ \)
\( 12 y-44=0 \) represents a hyperbola.
A. The length of whose transverse axis is \( 4 \sqrt{3} \)
B. The length of whose conjugate axis is 4
c. whose centre is (-1,2)
D. whose eccentricity is \( \sqrt{\frac{19}{3}} \)


Assertion
Static friction is a self adjusting force.
Reason

Coefficient of friction does not depend
upon mass of the body.
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


\( \sin ^{-1}\left(\sin \left(\frac{2 x^{2}+4}{1+x^{2}}\right)\right)<\pi-3 \) if
A . \( -1 \leq x \leq 0 \)
в. \( 0 \leq x \leq 1 \)
c. \( -1<x<1 \)
D. \( x>1 \)


The colour of \( C r_{2} O_{7}^{2-} \) changes from orange to blue-green when added to compound (A). The blue-green colour is due to the formation of :
A \( \cdot C r^{2} \)
в. \( C r^{3} \)
\( \mathrm{c} \cdot \mathrm{Cr} \mathrm{O}_{4}^{2} \)
D. \( C r O_{5} \)


A cilium beats
A. Asymmetrically by sweeping action
B. Symmetrically by sweeping action
C. Symmetrically by undulatory action
D. Asymmetrically by undulatory action


State true or false:
Rational number from following real
numbers \( -8.0, \sqrt{5}, \frac{5}{7},-\sqrt{18}, \sqrt{32}, 4.28, \pi, 3, \frac{8}{15} \)
\( \operatorname{are}-8.0 . \frac{5}{7}, 4.28,3, \frac{8}{15}, 0.075 \)
A. True
B. False


The vectors \( \hat{\boldsymbol{i}}+\boldsymbol{2} \hat{\boldsymbol{j}}+\boldsymbol{3} \hat{\boldsymbol{k}}, \boldsymbol{2} \hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) and
\( \mathbf{3} \hat{\mathbf{i}}+\hat{\boldsymbol{j}}+\mathbf{4} \hat{\boldsymbol{k}} \) are so placed that the end
point of one vector is the starting point of the next vector. Then the vectors are :
A. Not coplanar
B. Coplanar but cannot form a triangle
c. coplannar but can form a triangle
D. coplanar and can form a right angled triangle


A circle has the equation \( (x+1)^{2}+ \)
\( (y-3)^{2}=16 \) What are the coordinates
of its center and the length of its
radius?
A. (-1,3) and 4
B. (1,-3) and 4
c. (-1,3) and 16
D. (1,-3) and 16


\( 17.4 \% \) (w/v) \( K_{2} S O_{4} \) solution at \( 27^{0} C \) is
isotonic with \( 5.85 \% \) (w/v) NaCl solution
at \( 27^{0} C . \) If \( \mathrm{NaCl} \) is \( 100 \% \) ionised, what is
\( \% \) ionisation of \( K_{2} S O_{4} \) in aq. solution?


What is covalency?


Arrange in correct order of density:
A. \( C H_{2} C l_{2}<C H C l_{3}<C C l_{4} \)
в. \( C H_{2} C l_{2}>C C l_{4}>C H C l_{3} \)
c. \( C C l_{4}<C H_{2} C l_{2}<C H C l_{3} \)
D. \( C H_{2} C l_{2}>C C l_{4}<C H C l_{3} \)


An artillery target may be either at point
\( I \) with probability \( \frac{8}{9} \) or at point \( I I \) with
probability \( \frac{1}{9} . \) We have 21 shells each of which can be fired at point \( I \) or \( I I \). Each
shell may hit the target independently of the other shell with probability \( \frac{1}{2} . \) How
many shells must be fired at point \( I \) to hit the target with maximum
probability?
A. \( P(A) \) is maximum where \( x=11 \).
B. \( P(A) \) is maximum where \( x=12 \)
c. \( P(A) \) is maximum where \( x=14 \)
D. \( P(A) \) is maximum where \( x=15 \)


Solve \( \frac{|\boldsymbol{x}-\mathbf{3}|}{\boldsymbol{x}^{2}-\mathbf{5} \boldsymbol{x}+\mathbf{6}} \geq \mathbf{2} \)


Which one of the following is not a property of carbon?
A. It exhibits catenation
B. It forms multiple bonds
c. Its melting points and boiling points are very high
D. It is a semi-metal


(i) Prove that osmotic presser is a
colligative property
(ii) Calculate the molar concentration of
urea solution if it exerts an osmotic
pressure of 2.45 atmosphere at \( 300 \mathrm{K} \) \( \left[\mathrm{R}=0.0821 \mathrm{I} . \text { atm. } \operatorname{mol}^{1} \boldsymbol{K}^{-1}\right] \)


A gas is compressed at constant pressure \( 50 N / m^{2} \) from a volume of
\( 0 m^{3} \) to a volume \( 4 m^{3} . \) Energy \( 100 J \) is then added to the gas by heating. Its internal energy is :
A. Increased by \( 100 \mathrm{J} \)
B. Increased by 200 J
c. Decreased by \( 100 \mathrm{J} \)
D. Increased by 400 J


The mass of \( U^{234} \) of radioactivity 1 curie
is
A . 3.7 \( \times 10^{10} g \)
B. 3.7 \( \times 10^{-10} g \)
c. \( 6.25 \times 10^{-34} g \)
D . 1.438 \( \times 10^{-11} g \)


Find the value of \( z \) in the given
equation \( \frac{z}{6}\left(\frac{3}{2}\right)-7=-2(3 z-4) \)
\( A \cdot-\frac{12}{5} \)
B. \( -\frac{4}{25} \)
c. \( \frac{4}{25} \)
D. \( \frac{12}{5} \)


Which of the following represents the study of matter?
A. Chemistry
B. Biology
c. Geology
D. Physics
E. Psychology


Box-I contains 5 red and 4 white balls
while box-ll contains 4 red and 2 white
balls. A fair die is thrown. If it turns up a
multiple of \( 3, \) a ball is drawn, from boxelse a ball is drawn from box-II. The probability that the ball drawn is white is \( \frac{a}{27} . \) Find \( a \)


Prove that the angle between the straight lines joining the origin to the intersection of the straight line \( y= \)
\( 3 x+2 \) with the curve \( x^{2}+2 x y+ \)
\( 3 y^{2}+4 x+8 y-11=0 \) is \( \tan ^{-1} \frac{2 \sqrt{2}}{3} \)


Consider the functions, \( \boldsymbol{f}(\boldsymbol{x})=\mid \boldsymbol{x} \)
\( \mathbf{2}|+| \boldsymbol{x}-\mathbf{5} \mid, \boldsymbol{x} \in \boldsymbol{R} \)
Statement 1: \( \boldsymbol{f}^{\prime}(\mathbf{4})=\mathbf{0} \)
Statement \( 2: f \) is continuous in [2,5] differentiable in (2,5) and \( f(2)=f(5) \)
A. Statement 1 is false, Statement 2 is true
B. Statement 1 is true, Statement 2 is true; Statement 2 is correct explanation for Statement
c. statement 1 is true, statement 2 is true; Statement 2 is not a correct explanation for Statement 1
D. Statement 1 is true, Statement 2 is false


If \( a \) and \( b \) are the two vectors such that
\( |\boldsymbol{a}|=\mathbf{3} \sqrt{\mathbf{3}},|\boldsymbol{b}|=\mathbf{4} \) and \( |\boldsymbol{a}+\boldsymbol{b}|=\sqrt{\mathbf{7}} \)
then the angle between \( a \) and \( b \) is
\( \mathbf{A} \cdot 120^{\circ} \)
В. \( 60^{\circ} \)
\( c \cdot 30^{\circ} \)
D. \( 150^{\circ} \)


\( \mathrm{n} \Delta A B C, \mathrm{AD} \) bisects \( \angle B A C \) and \( \mathrm{AD}= \)
DC. If \( \angle A D B=100^{\circ} \), then find \( \angle A B D \).
\( A \cdot 30 \)
в. 45
\( c \cdot 60 \)
D. 90


Assertion
Molar mass of \( C a \) is not always 40 gm.
Reason

Average molar mass of \( C a \) is 40 gm and is calculated by abundance percentage of all isoptopes of \( \boldsymbol{C} \boldsymbol{a} \)
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


Out of 800 families with 4 children
each, the expected number of families having atleast one boy is
A . 550
B. 50
c. 750
D. 300


Assertion
Micelles are formed by surfactant molecules above the critical micellar
concentration (CMC).
Reason
The conductivity of solution having surfactant molecules decreases sharply at the CMC.
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


Define order of reaction.


If the length of the wire is doubled, then the specific resistance will be :-
\( \mathbf{A} \cdot \) two times
B. (1/2) times
c. four times
D. same


Metal hydrides are ionic, covalent or
molecular in nature. Among \( L i H, N a H, K H, R b H \) and \( C s H, \) the
correct order of increasing ionic character is:
A \( . L i H>N a H>C s H>K H>R b H \)
в. \( L i H<N a H<K H<R b H<C s H \)
c. \( R b H>C s H>N a H>K H>L i H \)
D. \( N a H>C s H>R b H>L i H>K H \)


Find the derivative of \( f(x)=\frac{x \cos x}{\sqrt{1+x^{2}}} \)


Find the ratio of number of \( \sigma \) -bonds and
\( \pi \) -bonds in sodium hexa
metaphosphate.


An element forms a covalently bonded compound with hydrogen, that has the
formula \( X H_{3} \), where \( X \) is the element. In which group of the periodic table would you expect to find \( \boldsymbol{X} \) ?
A. group 1
B. group 14
c. group 15
D. group 17


Which of the following expressions is the simplified form of the given
expression, given that \( m \) and \( n \) are positive? \( \sqrt{9 m^{5} n^{2}-m^{4} n^{2}} \)
A. \( 3 \sqrt{m} \)
в. \( 3 m n \)
c. \( 3 n \sqrt{m} \)
D. \( m^{2} n \sqrt{9 m-1} \)


Thin films like soap bubbles and oil
floating on water can create colorful
patterns. Which of the following explanations most accurately describes why this happens?
A. Thin films contain many different colored chemicals
B. Thin films diffract and refract light so that it sets up interference patterns
c. Thin films provide reflection from the front and back surfaces, and this creates interference patterns
D. Thin films polarize light which interferes with the unpolarized light to create colors
E. Thin films absorb some colors and allow others to reflect


Show that the vectors \( 2 \hat{i}-3 \hat{j}+4 \hat{k} \) and \( -4 \hat{i}-6 \hat{j}+-8 \hat{k} \) are collinear


In Young's double slit experiment, the two equally bright slits are coherent, but of phase difference \( \frac{\pi}{3} . \) If maximum
intensity on the screen is \( I_{0} \), the intensity
at the point on the screen equidistant from the slits is_-
A . \( I_{0} \)
в. \( \frac{I_{0}}{2} \)
c. \( \frac{I_{0}}{4} \)
D. \( \frac{3 I_{0}}{4} \)


The apoplast is located
A. Outside the plasma membrane
B. In the entire cytosol
C. On both sides of plasma mebrane
D. In the plastidial content


Equilibrium constants is given (in atm)
for the following reaction \( 0^{\circ} C \)
\( N a_{2} H P O_{4} \cdot 12 H_{2} O(s) \rightleftharpoons \)
\( N a_{2} H P O_{4} .7 H_{2} O(s)+ \)
\( \mathbf{5} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) ; \quad \boldsymbol{K}_{\boldsymbol{p}}=\mathbf{2 . 4 3} \times \mathbf{1 0}^{-\mathbf{1 3}} \)
The vapour pressure of water at \( 0^{\circ} \mathrm{C} \) is
4.56 torr
At what relative humidities will
\( N a_{2} H P O_{4} \cdot 12 H_{2} O(s) \) be efflorescent
when exposed to air at \( 0^{\circ} \mathrm{C} \) ?


Which of the following is used as fuel?
A. Gasoline
B. Ether
C. Pitch tar
D. Grease


Two equal masses attached to a rod is made to experience equal force.Force on both rod is perpendicular to it but in one rod it acts on attached mass and in
other rod it is acted on the mid point of rod. now choose the correct statement
A. Both rod has same motion
B. they have different linear acceleration
c. one of the rod shows no angular motion
D. none of the above


Yellow color of chlorine water fades
because of?
A. Form HCI \& нос
B. Chlorine gas escapes
c. \( C l O_{2}+H_{2} \)
D. \( C l_{2} O \)


Which of the following method is responsible for ATP production by green plant cells in the presence of sunlight?
A. By phosphorylation only
B. By oxidative phosphorylation only
c. By only substrate level phosphorylation
D. All of the above


A liquid of bulk modulus \( k \) is
compressed by applying an external pressure such that its density
increases by \( 0.01 \% . \) The pressure applied on the liquid is:
A \( \cdot \frac{k}{10000} \)
в. \( \frac{k}{1000} \)
c. \( 1000 k \)
D. \( 0.01 k \)


Name the adsorbent used to removal of
colouring matter from solution.


If in a wire of Young's modulus \( Y \) longitudinal strain \( X \) is produced then the potential energy stored in its unit volume will be :
\( \begin{array}{l}\text { A } .0 .5 Y X^{2} \\ ^{2}\end{array}^{.0 .5 Y X X^{2}} \)
в. \( 0.5 Y^{2} X \)
\( \mathbf{c} \cdot 2 Y X^{2} \)
D. \( Y X^{2} \)


If \( \tan ^{2} \theta=\left(1-e^{2}\right) \) then \( \sec \theta+ \)
\( \tan ^{3} \theta \operatorname{cosec} \theta \) is equal to
A \( \cdot\left(2+e^{2}\right)^{\frac{3}{2}} \)
B. \( \left(2-e^{2}\right)^{\frac{3}{2}} \)
c. \( \left(1-e^{2}\right)^{\frac{3}{2}} \)
D. \( \left(1+e^{2}\right)^{\frac{3}{2}} \)


Solve the following inequality and show
it graphically:
\( |\boldsymbol{x}+\mathbf{3}|<\mathbf{4}, \boldsymbol{x} \in \boldsymbol{R} \)
\( A \)
B.
\( c \)
D.


Find \( \sin \frac{x}{2}, \cos \frac{x}{2}, \tan \frac{x}{2} \) in second
quadrant, if \( \tan x=-\frac{4}{3} \)