are included in Lacertilia.
A . Lizards
B. Turtles
c. snakes
D. Tortoises


Find the dot product of the following vectors:
\( \vec{a}=2 \hat{i}+\hat{j}+3 \hat{k} \) and \( \vec{b}=3 \hat{i}+5 \hat{j}-2 \hat{k} \)


A man from top of a 100 meters high towers sees a car moving towards the tower at an angle of depression of \( 30^{0} \) After some time, the angle of
depression becomes \( 60^{0} . \) The distance (in meters) travelled by the car during this time is
A. \( 100 \sqrt{3} \)
3
в. \( \frac{200 \sqrt{3}}{3} \)
c. \( \frac{100 \sqrt{3}}{3} \)
D. \( 200 \sqrt{3} \)


If a body loses half of its initial velocity on permenenting \( 2 \mathrm{cm} \) in a wooden block, them how much it penetrate
more before its velocity reduces to one fourth of its initial velocity [Assume retaradation of body in uniform \( ] \)
A. \( 2 \mathrm{cm} \)
B. \( 1 \mathrm{cm} \)
\( c \cdot 0.5 \mathrm{cm} \)
D. \( 4 \mathrm{cm} \)


In the human digestive system, digestion occurs in
(a) Buccual cavity
(b) Stomach
(c) Small intestine
(d) Large intestine
A . (a) only
B. (a) and (b) only
\( c \cdot(b),(c) \) and \( (d) \) only
D. \( (a),(b) \) and (c) only


The equation of the line with inclination
\( 45^{0} \) and passing through the point (-1,2)
is
A. \( x+y+3=0 \)
в. \( x-y+3=0 \)
c. \( x-y-3=0 \)
D. \( x+y-3=0 \)


What were the two criteria used by Mendeleev in creating his Periodic Table?


The average acceleration due to gravity is \( 8.9 \mathrm{ms}^{-2} \)
A. True
B. False


Which of the following statements is
not true about enzyme inhibitors?
A. Inhibit the catalytic activity of the enzyme.
B. Prevent the binding of substrate.
C. Generally a strong covalent bond is formed between an inhibitor and an enzymes.
D. Inhibitors can be competitive or non-competitive.


The iodine atom in \( I C l_{2}^{-} \) involves:
A \( \cdot s p^{3} d \) hybridisation
B. \( s p^{3} d^{2} \) hybridisation
c. \( s p^{2} \) hybridisation
D. \( s p^{3} \) hybridisation


For an incident light ray on a mirror, If the angle between the mirror and the
incident ray is \( 30^{\circ}, \) what will be the
angle of reflection?
\( A \cdot 30 \)
B. 60
\( c .90 \)
D. 150


Fill in the blanks with appropriate
words.
The network of capillaries, enclosed in a Bowmans capsule is called


Two horizontal circular discs of
different radii are free to rotate about
their central axes. One disc is given
some angular velocity and the other is
stationary. Their rims are now brought
in contact. There is friction between the
rims. Correct statement from the
following is:
A. Force of friction between the rims will disappear when the discs rotate with same angular speed
B. Force of friction between the rims will disappear when they have equal linear velocities
C. Angular Momentum of the system is conserved
D. Rotational Kinetic Energy of the system is conserved.


Consider the principle diagonal
elements of \( B \) as \( \left(b_{1}, b_{2}, b_{3}\right) \) such that
\( b_{1}>b_{2}>b_{3}, \) then the value of \( \lambda \) for
which \( b_{1}, b_{2},\left(b_{3} \lambda\right) \) are in \( G . P \)
\( A \cdot 3 \)
B.
c. \( -\frac{1}{3} \)
D. \( \frac{81}{91} \)


Light year is the unit of
A. distance
B. time
c. speed
D. mass


A wire of radius r has resistance R. If it is stretched to a radius \( \frac{r}{2}, \) its
resistance will be
A. 16 R
в. 2 R
\( c .4 \) R
D. 0


Reagent used in Carius method is:
A \( \cdot \) fuming \( H N O_{3} \) with \( A g N O_{3} \)
B. fuming \( H N O_{3} \) with \( A g N O_{2} \)
c. fuming \( H_{2} S O_{4} \) with \( A g N O_{3} \)
D. fuming \( H_{2} S O_{4} \) with \( A g N O_{2} \)


Photo-oxidation of water in
photosynthesis is in association of
A. Cytochrome \( b_{6} \)
B. Pigment system- -
c. Pigment system- - I
D. Plastocyanin


Two towns \( A \) and \( B \) are connected by a regular bus service with a bus leaving in either direction every T minutes. A
man cycling with a speed \( 20 \mathrm{km} \mathrm{h}^{-1} \) in
the direction \( A \) to \( B \) notices that a bus
goes past him every 10 min in the direction of his motion, and every 2 min in the opposite direction. The speed of the bus on the road is:
A. \( 10 \mathrm{kmph} \)
B. 20 kmph
c. \( 40 \mathrm{kmph} \)
D. 30 kmph


Explain inconsistency of Ampere's circuital law during charging of a capacitor.


Which selection is the correct formula
for the chlorate ion?
A \( \cdot C l^{-} \)
B. \( C l O^{-} \)
\( \mathrm{c} \cdot \mathrm{ClO}_{2}^{-} \)
D. \( C l O_{3}^{-} \)
E \( \cdot C l O_{4}^{-} \)


The fractional change in intensity of the
central maximum as function of time is
A \( \cdot \frac{A \sin \omega t}{L} \)
B. \( \frac{2 A \sin \omega t}{L} \)
c. \( \frac{3 A \sin \omega t}{L} \)
D. \( \frac{4 A \sin \omega t}{L} \)


The missing term in the following equation is \( 2 F e^{3+}+S n^{2+} \rightarrow 2 F e^{2+}+ \)
\( \ldots . ? \)
\( A \cdot S n^{4} \)
в. \( S n^{3} \)
\( c \cdot s n^{2} \)
D. \( S n^{+} \)


Which one of the following sets is true set of real values of \( x \) for which the
function, \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x} \ell \boldsymbol{n} \boldsymbol{x}-\boldsymbol{x}+1 \) positive
\( ? \)
в. (0,1)
c. \( (e, \infty) \)
D. (0,1) and \( (1, \infty) \)


The amount of heat evolved on
combustion of 10 grams of benzoic acid is \( 10 K . \) Cals. The heat of combustion
of Benzoic acid is:
A. -122 K. Cals
B. -112 K Cals
c. -132 K. Cals
D. \( -92 K, \) Cals


The formula of hydride of the halogen in period 3 is:
A. \( H C l_{2} \)
в. \( H C l_{3} \)
c. \( H_{2} C l_{4} \)
D. \( H C l \)


Assertion
Statement-1: Oxyacids of group VI A
elements : \( \boldsymbol{H}_{2} \boldsymbol{S O} \boldsymbol{4}, \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{e} \boldsymbol{O}_{4}, \boldsymbol{H}_{6} \boldsymbol{T} \boldsymbol{e} \boldsymbol{O}_{6} \)
Reason
Statement-2: The lighter member
where \( \boldsymbol{O}(\boldsymbol{2} \boldsymbol{p}) \rightarrow \boldsymbol{X}(\boldsymbol{3} \boldsymbol{d}, \boldsymbol{4} \boldsymbol{d}) \boldsymbol{\pi} \) bonding
is significant forms strong \( \pi- \) bonds
to give \( \boldsymbol{X} \boldsymbol{O}_{4}^{2-} \)
A. Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-
B. Statement-1 is true, statement-2 is true and statement-2 is not the correct explanation for statement-1
c. Statement-1 is true, statement-2 is false.
D. Statement-1 is false, statement-2 is true.


Among the following, the most acidic
hydrocarbon is:
\( A \)
в.
\( c \)
\( D \)


Which of the following carbon atoms is most electronegative? \( \stackrel{I I I}{C H_{3}}-C_{I H_{2}}^{I I}-C \equiv C_{H}^{I} \)
\( A \)
B. I
\( c \)
D. All are equal electronegative


In the case of the Bohr atomic model if
\( E_{K} \) and \( U \) are the kinetic and potential
energies of an electron in an orbit then:
\( \mathbf{A} \cdot E_{K}+U=0 \)
B . \( E_{K}-U=0 \)
\( \mathbf{c} \cdot 2 E_{K}+U=0 \)
D. \( E_{K}+2 U=0 \)


Assertion
Temporary hardness in water is due to
presence of chlorides of Magnesium.
Reason

Temporary hardness is removed by
Clark's method.
Choose the correct option.
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


Which of the following are Lewis acid-
base reactions:
This question has multiple correct options
A \( \cdot C u C l_{2}+4 H_{2} O \longrightarrow\left[C u\left(H_{2} O\right)_{4}\right]^{2+}+2 C l^{-} \)
в. \( _{K I+4 S O_{2}(s) \rightarrow K^{+}\left[\left(S O_{4}\right)_{4} I^{-}\right]} \)
\( \mathbf{c} \cdot B F^{3}+N H_{3} \longrightarrow\left[H_{3} N \cdot B F_{3}\right] \)
D. \( S O_{3}^{2-}+O \longrightarrow S O_{4}^{2} \)


A particle performs linear S.H.M. At a particular instant, velocity of the
particle is \( ^{\prime} u^{\prime} \) and acceleration is \( ^{\prime} \alpha^{\prime} \)
while at another instant velocity is \( ^{\prime} v^{\prime} \)
and acceleration is \( ^{\prime} \boldsymbol{\beta}^{\prime}(\mathbf{0}<\boldsymbol{\alpha}<\boldsymbol{\beta}) . \) The
distance between the two positions is
A \( \cdot \frac{u^{2}-v^{2}}{\alpha+\beta} \)
в. \( \frac{u^{2}+v^{2}}{\alpha+\beta} \)
c. \( \frac{u^{2}-v^{2}}{\alpha-\beta} \)
D. \( \frac{u^{2}+v^{2}}{\alpha-\beta} \)


Two particles \( A \) and \( B \) start moving with velocities \( 20 m / s \) and \( 30 \sqrt{2} m / s \)
along \( x-a x i s \) and at an angle \( 45^{\circ} \) with
\( x- \) axis respectively in \( x y- \) plane from
origin. The relative velocity of \( \boldsymbol{B} \) w.r.t. \( \boldsymbol{A} \)
\( \mathbf{A} \cdot(10 \hat{i}+30 \hat{j}) m / s \)
B. \( (30 \hat{i}+10 \hat{j}) m / s \)
c. \( (30 \hat{i}-20 \sqrt{2} \hat{j}) m / s \)
D. \( (30 \sqrt{2} \hat{i}+10 \sqrt{2} \hat{j}) m / s \)


How many moles of hypophosphorous acid are involved in its thermal
decomposition reaction when one mole of each product is formed?


Write the difference between Pectoral
and Pelvic girdle.


A message signal of frequency \( 20 \mathrm{KHz} \)
and peak voltage of 20 volts is used to modulate a carrier signal of frequency 2
MHz and peak voltage of 40 volts.
Determine
(i) modulation index,
(ii) the
side bands produced. Draw the corresponding frequency spectrum of amplitude modulated signal.


In plants and animals, the ratio of \( \mathrm{C}^{14} \) to
\( C^{12} \) is


When a solution of 500 m \( L \) of \( 2 M \)
\( K O H \) is added to \( 500 m L \) of \( 2 M H C l \)
then the rise temperature \( T_{1} \) is noted. When the same experiment is repeated by mixing \( 250 m L \) of each solution, the
rise in temperature \( T_{2} \) is noted :
A \( \cdot T_{1}=T_{2} \)
В. \( T_{1}=2 T_{2} \)
\( \mathbf{c} \cdot T_{2}=2 T_{1} \)
D. \( T_{1}=4 T_{2} \)


Nitrogen is produced by heating:
This question has multiple correct options
A \( . H N O_{3} \)
в. \( N H_{4} C l \)
c. \( N H_{4} N O_{3} \)
D. \( N H_{4} C l+N a N O_{2} \)


Select the incorrectly matched pair.
A. Phragmoplast - Persistent spindle
B. Reductional division - Meiosis I
C. Equational division - Meiosis II
D. Crossing over - Non - homologous chromosomes


Which of the following is scientific name of peacock?
A. Passer domesticus
B. Pavo cristatus
c. Archaeopterx lithographica
D. Psittacula eupatrica


Evaluate: \( \tan ^{-1}(1)+\cos ^{-1}\left(\frac{1}{2}\right)+ \)
\( \sin ^{-1}\left(\frac{1}{2}\right) \) which lies in the interval
\( [\mathbf{0}, \boldsymbol{\pi}] \)


When exposed to sunlight, thin films of oil on water often exhibit brilliant
colours due to the phenomenon of
A. the dispersion
B. the interference
c. the diffraction
D. the angular acceleration


Find the maximum value of \( g(f(x)) \) if \( f(x)=x+4 \) and
\( \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{6}-\boldsymbol{x}^{2} \)
A . -6
B. -4
\( c \cdot 2 \)
D. 4
E . 6


Let, \( f(x+1)=2 x^{2}-3 x-1, \) then find
the value of \( \boldsymbol{f}(\mathbf{0}) \) and \( \boldsymbol{f}(\boldsymbol{x}+\mathbf{2}) \)


\( A \) is a \( 3 \times 3 \) matrix and \( B \) is its adjoint
matrix. If the determinant of \( B \) is 64
then the det \( A \) is
\( A \cdot 4 \)
B. ±4
\( c .\pm 8 \)
D. 8


A radioactive element has atomic
number' \( Z \) and mass number'A'. Select
the correct statements among the
following.
This question has multiple correct options
A. Both ' \( A \) ' and ' \( Z \) ' decrease in \( \alpha \) -decay
B. Both 'A' and ' \( Z \) ' remain unchanged in \( \gamma \) -decay
C . 'A' remains unchanged and' \( Z \) ' decreases by one; the
process is called \( \beta^{+} \) (positron) decay or \( K \) -electron capture
D. Both 'A' and 'Z' increase in the nuclear isomerism


Use the figure below to answer the
question that follows. Which of the four molecular structures.
I-IV, exhibits trigonal planar molecular geometry?
0
ex
\( 0=t \)
\( A \)
в.
\( c \)
\( D \)


Ammonia gas is not prepared by:
A. reduction of sodium nitrite or sodium nitrate by the reaction of zinc dust and sodium hydroxide
B. hydrolysis of calcium cyanamide
C. heating ammonium chloride with slaked lime
D. heating of \( \left(N H_{4}\right)_{2} C r_{2} O_{7} \)


Heat is transmitted from higher to lower temperature through actual motion of the molecule in
A. conduction
B. convection
c. radiation
D. all of these


In glycolysis pathway which of the following steps show reduction of \( c 0 \) enzyme?
A . 1,3 -diphosphoglycerate to 3 -phosphoglycerate
B. Glucose 6-phosphate to fructose 6-phosphate
c. Glyceraldehyde 3-phosphate to 1,3diphosphoglycerate
D. 3-phosphoglycerate to 2-phosphoglycerate


Naturally occurring boron consists of two isotopes whose atomic weights are
10.01 and 11.01. The atomic weight of natural boron is 10.81 . Calculate the
percentage of each isotope in natural boron.


When two progressive waves of
intensity \( \boldsymbol{I}_{1} \) and \( \boldsymbol{I}_{2} \) but slightly different
frequencies superpose, the resultant
intensity fluctuates between
\( \mathbf{A} \cdot(\sqrt{I_{1}}+\sqrt{I_{2}})^{2} \) and \( (\sqrt{I_{1}}-\sqrt{I_{2}})^{2} \)
B \( \cdot(\sqrt{I_{1}}-\sqrt{I_{2}}) \) and \( (\sqrt{I_{1}}+\sqrt{I_{2}}) \)
\( \mathbf{C} \cdot\left(I_{1}+I_{2}\right) \) and \( \left(I_{1}-I_{2}\right) \)
D. \( \left(I_{1}+I_{2}\right)^{2} \) and \( \left(I_{1}-I_{2}\right)^{2} \)


lamu \( =1 / 12 \) the mass of one \( C-12 \) atom
A. True
B. False


The colour of the red glass in traffic
signals is due to:
A. \( S b_{2} S_{3} \)
в. \( H g I_{2} \)
c. \( C d S \)
D. \( C d S e \)


Statement 1: The molecule \( S O_{2} \) has a net dipole. Statement 2: Oxygen has the higher electronegativity than sulfur.
A. Both Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of statement 1
B. Both Statement 1 and Statement 2 are correct, but Statement 2 is NOT the correct explanation of Statement 1.
c. Statement 1 is correct, but Statement 2 is not correct
D. Statement 1 is not correct, but Statement 2 is correct


If the cost price is \( 96 \% \) of the selling price, then what is the profit percent?
A. \( 5.72 \% \)
B. \( 3.72 \% \)
c. \( 8.92 \% \)
D. \( 4.17 \% \)


During the charging of lead storage battery, the reaction at anode is
represented by:
A \( \cdot P b^{2+}+S O_{4}^{2-} \rightarrow P b S O_{4} \)
B . \( P b S O_{4}+2 H_{2} O \rightarrow P b O_{2}+S O_{4}^{2-}+4 H^{+}+2 e \)
c. \( P b \rightarrow P b^{2+}+2 e \)
\( \mathbf{D} \cdot P b^{2+}+2 e \rightarrow P b \)


Which of the following is the right way of expressing 1 watt of power?
A. 1 watt
B. \( 1 \mathrm{w} \)
\( c \cdot 1 w \)
D. 1 wt


Real Image is always erect.
Is the above statement True or False?
A. True
B. False


The differential equation representing
the family of curves \( y=x e^{c x} \) (c is a
constant) is
A \( \cdot \frac{d y}{d x}=\frac{y}{x}\left(1-\log \frac{y}{x}\right) \)
B . \( \frac{d y}{d x}=\frac{y}{x} \log \left(\frac{y}{x}\right)+1 \)
C \( \cdot \frac{d y}{d x}=\frac{y}{x}\left(1+\log \frac{y}{x}\right) \)
D. \( \frac{d y}{d x}+1=\frac{y}{x} \log \frac{y}{x} \)


The \( K_{a} \) values of \( C a C O_{3} \) and \( C a C_{2} O_{4} \)
in water are \( 4.7 \times 10^{-9} \) and \( 1.3 \times 10^{-9} \)
respectively, at \( 25^{\circ} \mathrm{C} \). If a mixture of
two is washed with \( H_{2} O, \) what is \( C a^{2+} \)
ion concentration in water?
A \( .7 .746 \times 10^{-5} \)
В. \( 5.831 \times 10^{-5} \)
c. \( 6.856 \times 10^{-5} \)
D. \( 3.606 \times 10^{-5} \)


A cotton reel of mass \( m \) and moment of
inertia \( I \) is kept at rest on a smooth horizontal surface. The reel has inner
and outer radius \( r \) and \( R \) respectively.
horizontal force \( \boldsymbol{F} \) starts acting as
shown in figure. Find the
(a) acceleration of the centre of mass of
reel
(b) angular acceleration of the reel
(c) net acceleration of point of contact


Lymph is colourless because
A. WBC are absent
B. WBC are present
C. Haemoglobin is absent
D. \( R B C \) are absent


Improper fraction of \( 12 \frac{1}{6} \) is
\( A \cdot \frac{72}{6} \)
в. \( \frac{73}{6} \)
c. \( \frac{108}{6} \)
D. \( \frac{85}{6} \)


A cube is shifted to a depth of \( 100 m \) is
alake. The change in volume is \( 0.1 \% \). The bulk modules of the material is nearly
\( \mathbf{A} \cdot 10 P a \)
в. \( 10^{4} P a \)
\( \mathbf{c} \cdot 10^{7} P a \)
D. \( 10^{9} \mathrm{Pa} \)


The heart of which one of the following is proportionately larger than that of other vertebrates?
A. Amphibians
B. Reptiles
c. Birds
D. Man


If screening effect is not considered,
and thus effective nuclear charge is the atomic number then the larger radius out of \( L i, N a \) is 11
(consider only atomic number)


A couple always tends to produce:
A. Linear motion
B. Rotatory motion
C. Both linear and rotatory motion
D. Vibratory motion


The hybridization of boron atom in orthoboric acid is:
\( A \cdot s p \)
B \( \cdot s p^{2} \)
\( c \cdot s p^{3} \)
D. \( s p^{3} d \)


The conjugate of \( (2+i) /(3+i) \) in the
form of \( a+i b \) is
\( \mathbf{A} \cdot 13 / 2+i(15 / 2) \)
B . \( 7 / 10+i(-1 / 10) \)
c. \( 13 / 10+i(-15 / 2) \)
D. \( 13 / 10+i(9 / 10) \)


In Young's double slit experiment, separation between the slits is halved
and distance between slits and screen
is doubled. The fringe width is
A. same
B. quadrupled
c. halved
D. one-third


In a factory,the production of motor bikes was 40,000 in a particular year,which rose to 48,400 in two years. Find the rate of growth per annum ,if it was uniform during two years?


The instantaneous value of emf and
current in an A.C. circuit are; \( \boldsymbol{E}= \)
\( 1.414 \sin \left(100 \pi t-\frac{\pi}{4}\right), I= \)
\( 0.707 \sin (100 \pi t) . \) The admittance of
the circuit will be mho.
A \( \cdot \frac{1}{\sqrt{2}} \)
B. \( \sqrt{2} \)
\( c \cdot \frac{1}{2} \)
D.


Find the unit vectors perpendicular to both \( \vec{a} \) and \( \vec{b}, \) when \( \vec{a}=3 \hat{i}+\hat{j}-2 \hat{k} \) and \( \overrightarrow{\boldsymbol{b}}=\mathbf{2} \hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}-\hat{\boldsymbol{k}} \)


The harmonic mean of two numbers is
4. Their arithmetic mean is A and
geometric mean is G. If G satisfies
\( 2 A+G^{2}=27, \) the numbers are
A .1,13
в. 9,12
c. 3,6
D. 4,8


Define particular solution of a differential equation


Rewrite the following rational numbers in the simplest form:
\( \frac{25}{45} \)


Elements A and B combine to form three
different compounds:
\( 0.3 \mathrm{g} \) of \( \mathrm{A}+0.4 \mathrm{g} \) of \( \mathrm{B} \rightarrow 0.7 \mathrm{g} \) of
compound \( x \) \( 18.0 \mathrm{g} \) of \( \mathrm{A}+48.0 \mathrm{g} \) of \( \mathrm{B} \rightarrow 66.0 \mathrm{g} \) of
compound \( Y \) \( 40.0 \mathrm{g} \) of \( \mathrm{A}+159.99 \mathrm{g} \) of \( \mathrm{B} \rightarrow 199.99 \mathrm{g} \)
of compound \( \mathbf{Z} \) State the law illustrated by these chemical combinations.
A. Law of reciprocal proportion
B. Law of multiple proportion
c. Law of constant composition
D. None of the above


Calculate the electrostatic potential energy at the instant when the alpha particle stops?
A. \( 36.3 \mathrm{MeV} \)
B. 45.0 MeV
c. \( 3.63 \mathrm{MeV} \)
D. 40.0 Mev


n Figure as shown above the velocity of
the body at \( A \) is:
A. zero
B. unity
c. maximum
D. infinite


Balance the following equation by ion electron method:
\( \boldsymbol{H} \boldsymbol{g} \boldsymbol{S}+\boldsymbol{C l}^{-}+\boldsymbol{H}^{+}+\boldsymbol{N} \boldsymbol{O}_{3}^{-} \rightarrow \)
\( \boldsymbol{H} \boldsymbol{g} \boldsymbol{C l}_{4}^{2-}+\boldsymbol{S}+\boldsymbol{N} \boldsymbol{O}+\boldsymbol{H}_{2} \boldsymbol{O} \)


The number of different possible orders of matrices having 18 identical elements is
\( A \cdot 3 \)
B.
\( c \cdot 6 \)
D. 4


An object is placed on the principal axis of a concave mirror at a distance of 60
\( \mathrm{cm} . \) If the focal length of the concave mirror is \( 40 \mathrm{cm} \) then determine the magnification of the obtained image.
\( A \cdot 2 \)
B. - -
\( c \cdot 2.5 \)
D. -2.5


The cube of an odd natural number is
A. Even
B. Odd
c. May be even, May be odd
D. Prime number


From a point inside the circle how many secants can be drawn to the circle?
A . 0
B.
\( c \cdot 2 \)
D. Infinite


In which circles, angles at the centers make a equal chords?
A. concentric circles
B. eccentric circles
c. tangential circles
D. equal circles


When \( 5 x^{13}+3 x^{10}-k \) is divided by \( x+ \)
1, the remainder is 20. The value of k is
A . - 22
B . -12
\( c \cdot 8 \)
D. 28
\( E \cdot 14 \)


Cards marked with numbers 4 to 99 are
placed in a box and mixed thoughtly. One card is drawn from this box. Find
the probability that the number on the card is a prime number less than 30


In a school, there are 20 teachers who
teach mathematics or physics. Of these,
12 teach mathematics and 4 teach both
physics and Mathematics. How many teach physics?


The M.I. of a disc about an axis passing through its centre and perpendicular to plane is \( \frac{1}{2} M R^{2}, \) then its M.I. about a tangent parallel to its diameter is
\( ^{\mathbf{A}} \cdot \frac{1}{2} M R^{2} \)
в. \( \frac{4}{5} M R^{2} \)
c. \( \frac{5}{4} M R^{2} \)
D. \( \frac{3}{4} M R^{2} \)


The suffix "-oideae"' is used for
A. Tribe
B. Family
c. class
D. Subfamily


Assertion
Diabetes insipidus is marked by excessive urination and too much thirst
for water.
Reason
Anti-diuretic hormone (ADH) is
secreted by the posterior lobe of pitutiary gland.
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 \( 10 \mathrm{kg} \) block is pulled a along a frictional surface in the form of an are
of a circle of radius \( 10 \mathrm{m} \). The applied
force \( F \) is \( 200 \mathrm{N} \) as shown in figure If \( \mathrm{a} \)
block started from rest at \( \mathrm{P} \)
A. the velocity at Q would be \( 20 \mathrm{m} / \mathrm{s} \)
B. the velocity at Q would be \( 17 \mathrm{m} / \mathrm{s} \)
C. the velocity at \( Q \) would be \( 15.5 \mathrm{m} \).
D. the velocity at Q would be \( 18 \mathrm{m} / \mathrm{s} \)


Analyze the energy diagram below for a
reaction.

Which area on the graph is not directly related to the overall reaction being
exothermic or endothermic?
\( A \cdot 1 \)
B. 2
\( c .3 \)
\( D \)


In a class of 100 students, 55 students
have passed in physics and 67 students have passed in Mathematics. Find the number of students passed in Physics only.


A double convex lens, made of a
material of refractive index \( \mu_{1}, \) is
placed inside two liquids of refractive
indices \( \mu_{2} \) and \( \mu_{3} \) as shown. \( \mu_{2}>\mu_{1}>\mu_{3} \)
A wide, parallel beam of light is incident
on the lens from the left. The lens will
give rise to
A. a single convergent beam
B. two different convergent beams
c. two different divergent beams
D. a convergent and a divergent beam


Let \( S \) be a relation on \( \mathbb{R}^{+} \) defined by
\( \boldsymbol{x} \boldsymbol{S} \boldsymbol{y} \Leftrightarrow \boldsymbol{x}^{2}-\boldsymbol{y}^{2}=\boldsymbol{2}(\boldsymbol{y}-\boldsymbol{x}), \) then \( \boldsymbol{S} \) is
A. Only reflecxive
B. Only symmetric
c. only Trasitive
D. Equivalence


Mercury is generally used in thermometer because it has a
A. High fluidity
B. High density
c. High coefficient of expansion
D. High specific heat


The region having the maximum probability of finding an electron in space is known as orbital.
A. True
B. False


Identify the triangle as equiangular acute, obtuse or right.
Answer: Right angled triangle
Mark answer as 1 if true else 0 if false
\( (i) \)


Assertion
Chlorobenzene on treatment with
\( \boldsymbol{C l}_{2} / \boldsymbol{A l} \boldsymbol{C l}_{3} \) gives mainly \( \mathbf{p} \)
dichlorobenzene.
Reason
Chlorine activate the ring towards an electrophile at ortho and para positions.
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


y-axis on velocity time graph represents
A. Instantaneous velocity
B. Average velocity
c. Mean velocity
D. None of the above


Find the critical points of the following functions and test them for their
maxima and minima. \( f(x)=\frac{x^{2}}{17}-\ln \left(x^{2} 8\right) \)


Divide 56 in four parts in A.P. such that the ratio of the product of their extremes (1 st and 4 th) to the product of means \( (2 n d \text { and } 3 r d) \) is 5: 6


The nature of \( C O \) is:
A. acidic
B. basic
c. amphoteric
D. neutral


When the mains switch of the house is
put off, it disconnects:
A. live wire
B. neutral wire
c. earth wire
D. live and neutral wires


Which option of linear equation is inconsistent?
\( \mathbf{A} \cdot x+y=1 \)
\( 2 x+y=0 \)
B. \( x-y=2 \)
\( 2 x-2 y=1 \)
c. \( 2 x-3 y=0 \)
\( 2 y+x=1 \)
D. 2x - 4 \( y=19 \) \( -2 x+y=0 \)


A reaction is represented as \( 2 A+B \mapsto \)
\( 2 C+3 D . \) The concentration of \( C \) at 10 s
is 4 moles \( l^{-1} \). The concentration of \( C \) at
20 seconds is 5.2 moles \( l^{-1} . \) The rate of
reaction of \( \mathrm{B} \) in the same time interval
could be :
A. -0.12 mole \( l^{-1} S^{-1} \)
B. -0.6 mole \( l^{-1} S^{-1} \)
c. -0.06 mole \( l^{-1} S^{-1} \)
D. -1.2 mole l" \( S^{-1} \)


Passenger of a train just drops a stone from it. The train was moving with constant velocity. What is path of the stone as observed by the passenger?
A. A Parabola
B. A circle
c. A vertical straight line
D. A hyperbola


Fill in the blanks:
(i) The \( x \) -axis and \( y \) -axis taken together
determine a plane known as
(ii) The coordinates of points in the \( \boldsymbol{X} \boldsymbol{Y} \)
-plane are of the form
(iii) Coordinate planes divide the space
into octants


Find the last term of the following
sequence \( 2,4,8 \dots \dots \dots \) to 9 terms


Differentiate the following w.r.t. \( x \) \( e^{\sin ^{-1} x} \)


Why do you think there should be an
equitable distribution of resources? What forces would be working against an equitable distribution of our
resources?


In a given \( A P ., \) if the p term is 'q'and the
\( q^{t h} \) tent is 'p', then its \( n^{t h} \) term is
\( \mathbf{A} \cdot p+q-n \)
B . \( p+q+n \)
C \( . p-q+n \)
D. \( p-q-n \)


Which of the following pairs of colloidal solutions have dispersed phase as liquid and dispersed medium as gas?
A. Fog, mist
B. Butter, milk
c. Fog, smoke
D. smoke, foam


Choose the incorrect statement about
noble gas?
A. Boiling point increases with increasing atomic mass
B. Helium has least tendency to form compound
C. Noble gases have some value of electron affinity
D. Xenon has maximum number of compounds


Define Lateral inversion.


Assertion
Spectator ions are the species that are present in the solution but do not take
part in the reaction.
Reason
The phenomenon of formation of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \)
by the oxidation of \( H_{2} O \) is known as auto-oxidation.
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


Why Hydrocarbons are considered as
better fuel?


Find the area of the closed figure bounded by the following curve \( \boldsymbol{y}=\boldsymbol{x}^{2}-\boldsymbol{2} \boldsymbol{x}+\boldsymbol{3}, \boldsymbol{y}=\mathbf{3} \boldsymbol{x}-\mathbf{1} \)


Draw labelled graphs to show how
electrical resistance varies with
temperature for:
(a) A piece of carbon.


Calculate pH of solution obtained by
mixing \( 500 \mathrm{ml} \) of \( 0.4 \mathrm{M}, M_{1} O H \) and
1500ml of \( \frac{\mathbf{0 . 8}}{\mathbf{3}} \) molar \( \boldsymbol{N}_{\mathbf{2}} \boldsymbol{O} \boldsymbol{H} . \boldsymbol{K}_{\boldsymbol{b}_{1}}= \)
\( \mathbf{1 0}^{-\mathbf{7}} \boldsymbol{K}_{\boldsymbol{b}_{2}}=\mathbf{4} \times \mathbf{1 0}^{-\mathbf{7}} \)


Which of the following is the constituent of guard cell?
A. Nucleus
B. Vacuole
c. chloroplast
D. All of the above


Amount of energy transferred from one trophic level to next is
A . 1.5\%
B . 10\%
c. 15\%
D. 20\%


A hydrogen atom is excited from \( n=1 \)
to \( n=3 \) state. The amount of energy
absorbed by the atom will be
A . \( 12.1 e V \)
B. \( 25 e V \)
c. \( 13.6 e V \)
D. \( -13.6 e V \)


It is much easier for a small animal to
run uphill than for a large animal because - ?
A. small animals have lower \( O_{2} \) requirement
B. the efficiency of muscles in larger animal is less than in smaller animal
c. it's easier to carry a small body weight
D. smaller animals have higher metabolic rate


\( ^{404} \boldsymbol{C}_{4}-^{4} \boldsymbol{C}_{1}^{303} \boldsymbol{C}_{4}+^{4} \boldsymbol{C}_{2}^{202} \boldsymbol{C}_{4}- \)
\( ^{4} C_{3}^{101} C_{4} \) is equal to
\( \mathbf{A} \cdot(401)^{4} \)
B . \( (101)^{4} \)
c. 0
D. \( (201)^{4} \)


\( \operatorname{Given} \vec{A}=2 \hat{i}-\hat{j}+2 \hat{k} ; \vec{B}=-\hat{i}-2 \hat{j}+ \)
\( \mathbf{2} \hat{\boldsymbol{k}} \)
The unit vector of \( \vec{A}-\vec{B} \)
A \( \frac{\hat{k}}{\sqrt{10}} \)
в. \( \frac{3 \hat{\imath}}{\sqrt{10} \bar{\imath}} \)
c. \( \frac{3 \hat{i}+\hat{j}}{\sqrt{10}} \)
D. \( \frac{-3 \hat{i}+\hat{k}}{\sqrt{10}} \)


State the number of significant figures in the following:
\( (a) 0.007 m^{2} \)
\( (b) 2.64 \times 10^{24} k g \)
\( (c) 0.2370 g c m^{-3} \)
\( (d) 6.320 J \)
\( (e) 6.032 N m^{-2} \)
\( (f) 0.0006032 m^{2} \)


Which one of the following is most polar?
A. \( C l-C l \)
B. \( N-F \)
c. \( C-F \)
D. \( O-F \)


Which of the following statement is not true in the context of above system
A. centre of mass reference frame is an inertial frame
B. kinetic energy of the system is minimum in centre of mass frame.
c. at the instant of maximum deformation both the blocks are instantaneously at rest in centre of mass reference frame
D. acceleration of centre of mass is constant is ground frame


An ideal gas expands according to the
law \( p V^{2}= \) const. The molar heat
capacity \( C \) is
A. \( C_{v}+ \) R
в. \( C_{v}- \) R
\( c \cdot C_{v}+2 R \)
D. \( C_{v}- \) 3R


The moment of inertia of a square plate
about a diagonal is \( I_{d} \) and that about a
side in its plane is \( I_{s} \) then
A \( \cdot I_{s}=I_{d} \)
в. \( I_{s}<I_{d} \)
\( \mathrm{c} \cdot I_{s}>I_{d} \)
D. None of these


Check if the triangles are similar. If
similar, write the similarity in symbolic
form. Mention the similarity condition
used
\( \mathbf{A} \cdot A S A \)
B. \( S A S \)
\( c . A A S \)
D. NONE


Ratio of electric and magnetic field due to moving point charge if its speed is
\( 4.5 \times 10^{5} \mathrm{m} / \mathrm{s} \)
A \( .2 \times 10^{1} \)
B . \( 3 \times 10^{11} \)
\( c \cdot 2 \times 10^{8} \)
D. \( 3 \times 10^{12} \)


If \( a, b, c \) and \( d \) are real numbers such that and if \( \boldsymbol{A}=\left|\begin{array}{cc}\boldsymbol{a}+\boldsymbol{i b} & \boldsymbol{c}+\boldsymbol{i d} \\ -\boldsymbol{c}+\boldsymbol{i d} & \boldsymbol{a}-\boldsymbol{i b}\end{array}\right| \) then
\( A^{-1}= \)
\( \mathbf{A} \cdot\left|\begin{array}{ll}a+i b & -c-i d \\ c-i d & a-i b\end{array}\right| \)
B. \( \left|\begin{array}{ll}a-i b & c+i d \\ -c+i d & a+i b\end{array}\right| \)
c. \( \left|\begin{array}{cc}a-i b & -c-i d \\ c-i d & a+i b\end{array}\right| \)
D. \( \left|\begin{array}{ll}a+i b & c+i d \\ c-i d & a-i b\end{array}\right| \)


In an election between two candidates,
the candidate who gets \( 30 \% \) of the
votes polled is defeated by 15,000 votes. What is the number of votes
polled for the winning candidate?
A .37,500
B. 30,000
c. 26,250
D. 11,250


Which of the following element's allotrop is the primary absorber of UV solar radiation in Earth's atmosphere?
A. Carbon
B. Nitrogen
c. Ozone
D. Neon
E. Argon


How many molecules of glycine are
required to release one molecule of \( \mathrm{CO}_{2} \)
in photorespiration?
A. one
B. Two
c. Three
D. Four


Arrange the following metals in the order in which they displace each other from the solution of their salts.
\( A l, C u, F e, M g \) and \( Z n \)


Plants tend to grow quicker in night
than in day is:
A. Seasonal variation
B. Biennial variable
c. diurnal variation
D. annual variation


Which of the following is a wrong pair of clothes worn during a particular season
?
A. cotton clothes during summer
B. Woolen clothes during winter
c. Dark colored clothes during summer
D. Polyester raincoats during Rainy season


State true or false:
\( \frac{3}{4 x+3}=\frac{1}{4} \)
A. True
B. False


\( C l^{35} \) and \( C l^{37} \) are:
A. isomers
B. isotopes
c. isomorphous
D. isobars


A non zero polynomial with real coefficients has the property that
\( \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{g}^{\prime}(\boldsymbol{x}) \cdot \boldsymbol{g}^{\prime \prime}(\boldsymbol{x}) \cdot \) Let the leading
coefficient of \( g(x) \) be \( a \). Then \( 36 a= \)
\( A \cdot 6 \)
B. 4
\( c .3 \)
D.


Mention two advantages of the metric
system.


Where is ozone layer found?


The black body spectrum of an object
\( O_{1} \) is such that its radiant intensity (i.e. intensity per unit wavelength interval) is maximum at a wavelength of 200
nm. Another object \( O_{2} \) has the maximum radiant intensity at \( 600 \mathrm{nm} \) The ratio of power emitted per unit area by source 01 to that of source 02 is
A .1: 8
B. 1: 9
c. 9: 1
D. 81:


Differentiate the following w.r.t. \( x: \)
\( \sin \left(\tan ^{-1} e^{-x}\right) \)


A wire that obeys Hooke's law is
of length \( l_{1} \) when it is in equilibrium
under a tension \( F_{1} \). Its length becomes \( l_{2} \) when the tension is increased of \( F_{2} \)
The energy stored in the wire during this process is
B - \( \frac{1}{4}\left(F_{2}+F_{1}\right)\left(l_{2}-l_{1}\right) \)
c. \( \frac{1}{4}\left(F_{2}-F_{1}\right)\left(l_{2}-l_{1}\right) \)
D - \( \frac{1}{2}\left(F_{2}-F_{1}\right)\left(l_{2}-l_{1}\right) \)


The minimum value of the function \( f(x) \)
\( =\int_{0}^{x} \frac{d \theta}{\cos \theta}+\int_{x}^{\pi / 2} \frac{d \theta}{\sin \theta} \) where \( x \in\left[0, \frac{\pi}{2}\right], \) is
A \( .2 \ln (\sqrt{2}+1) \)
в. \( \ln (2 \sqrt{2}+2) \)
c. \( \ln (\sqrt{3}+2) \)
D. \( \ln (\sqrt{2}+3) \)


is the most abundant
element in the earth's crust.


Fill in the blanks:
Hydrogen burns with a ....... flame and sound is heard.


Which aldehyde smell like bitter
aImond?


In what time will \( R s 2750 \) amounts to
Rs 3575 , if simple interest is calculated at \( 10 \% \) per annum?


If a polynomial \( f(x)=4 x^{4}-a x^{3}+ \)
\( b x^{2}-c x+5,(a, b, c \in R) \) has four
positive real zeros \( r_{1}, r_{2}, r_{3}, r_{4} \) such that \( \frac{r_{1}}{2}+\frac{r_{2}}{4}+\frac{r_{3}}{5}+\frac{r_{4}}{8}=1, \) then value of \( a \)
is
A . 20
B. 21
c. 19
D. 22


How many orbitals are singly occupied
in \( O_{2} \) molecule?
\( A \cdot 2 \)
B.
\( c \cdot 3 \)
D. 4


Which one of the following are not essential for opening of stomata?
A. Cytokinin
B. Temperature
c. Mechanical shock
D. Rise in \( \mathrm{pH} \)


Show that the points \( \boldsymbol{A}(\mathbf{2}, \mathbf{1},-\mathbf{1}) \)
\( B(0,-1,0), C(4,0,4) \) and \( D(2,0,1) \) are
coplanar.


The value of magnetic moment of \( \boldsymbol{V}^{3+}(\boldsymbol{Z}=\mathbf{2 3}) \) is:
A \( \sqrt{2} B M \)
T
в. \( \sqrt{3} B M \)
\( \mathbf{c} \cdot 2 B M \)
D. \( \sqrt{8} B M \)


The ratio of sigma and \( \pi \) bonds in
mesitylene is:
A . 3
B. 7
\( c .5 \)
D. 6


Potassium when heated strongly in oxygen, it forms:
в. \( K O_{2} \)
\( \mathrm{c} \cdot \mathrm{K}_{2} \mathrm{O}_{2} \)
D. \( K O_{3} \)


The value of \( \sqrt{5+\sqrt{11+\sqrt{19+\sqrt{20+\sqrt{49}}}}} \)
simplifying is
\( A \)
B. 2
\( c \cdot 4 \)
\( D \)


Inductance \( L, \) capacitor \( C \) and resistor
\( R \) are joined in series with an
alternating voltage source \( V=v_{0} \sin \omega t \)
Find the formula of impedance and phase angle, drawing vector diagram of the circuit.


Put the following parts of a reflex arc in the correct order beginning with the
sensory receptor.
A. Motor neuron
B. Interneuron C.
Effector
D. Sensory neuron
E. Sensory
receptor
\( A \cdot E, D, B, A, C \)
B. E, D, A, B, C
c. А, В, С, D, Е
D. A, E, D, B, C


How is electrical conductance of a
conductor related with length and area of cross section of the conductor?
\( \mathbf{A} \cdot G=l \cdot a \cdot k^{-1} \)
B . \( G=k . l . a^{-1} \)
c. \( G=k . a . l^{-1} \)
D. \( G=k . l^{-1} . a^{-1} \)


Two dice are thrown sumiltaneously.
Find the probability that the sum of the
numbers on the faces is not divisible by 4 or divisible by 5


An object placed from a lens produces a virtual image at distance of \( 5 \mathrm{cm} \) in
front of the lens. Calculate the focal
length of lens.
A \( .6 .25 \mathrm{cm} \)
B. \( 0.16 \mathrm{cm} \)
\( c .5 \mathrm{cm} \)
D. None


Global Warming Clauses
An increase in the sea level
II. The melting of ice at mountain peaks
III. A decrease in food production by
plants
A. I only
B. I and II
c. II and III
D. I,II and III


Lenticels and its complementary cells are developed through the activity of
A. Phellogen
B. Stelar cambium
c. Dermatogen
D. Intercalary meristem


Atmospheric pressure decreases with in height.
A. increase
B. decrease
c. Both (A) and (B)
D. None


A uniform meter sticks of mass 200 g is suspended from the ceiling through two verticle strings of equal lengths fixed at the ends. A small object of 20 g is placed on the stick at a distance of 70
\( \mathrm{cm} \) from the left end. Find the tension in
the two strings.
A \( \cdot T_{1}=1.06 N, T_{2}=1.14 N \)
B . \( T_{1}=1.03 N, T_{2}=1.17 N \)
C . \( T_{1}=1.10 N, T_{2}=1.10 N \)
D. \( T_{1}=1.00 N, T_{2}=1.20 N \)


A particle is moving along the curve
\( \boldsymbol{x}=\boldsymbol{a} \boldsymbol{t}^{2}+\boldsymbol{b} \boldsymbol{t}+\boldsymbol{c} \). If \( \boldsymbol{a} \boldsymbol{c}=\boldsymbol{b}^{2}, \) then the
particle would be moving with uniform
A. rotation
B. velocity
c. acceleration
D. retardation


Which one of the following substances has highest specific heat capacity at room temperature and atmospheric pressure?
A. water
B. Ice
c. Aluminium
D. Mercury


From a water fall, water is pouring down at the rate 100 kg per see on the blade of a turbine. If the height of the fall be 100 \( \mathrm{m}, \) the power delivered to the turbine is approximately equal to
A. \( 100 \mathrm{kW} \)
B. 1 \( w \)
\( c \cdot 1 k w \)
D. 100 \( w \)


If a SHM is given by \( y=(\sin \omega t+\cos \omega t \)
\( \mathrm{m}, \) which of the following statement is
true?
A. The amplitude is \( 1 \mathrm{m} \)
B. The amplitude is \( \sqrt{2} \mathrm{m} \).
c. Time period is \( 2 \pi / \omega \)
D. Time is considered from \( y=0 \) m.


Match the Column I and Column II and
choose the correct code given below.
Column I
(A) Peroxyacetyl nitrile
(i) Waste incineration
(B) Indigo
(ii) Vat dye
(C) IR active
(iii) Global warming molecules
(D) Dioxins
(iv) Photochemical
\( \operatorname{smog} \)
\( A \cdot A-(i v) ; B-(i i) ; C-(i i i) ; D-(i) \)
B. A-(i); B-(ii); C-(iv); D-(iii)
C. \( A-(i i) ; B-(i) ; C-(i v) ; D-(i i i) \)
D. A-(iv); B-(i); C-(iii); D-(ii)


\( P \) is any point inside the triangle \( A B C \) Prove that: \( \angle B P C>\angle B A C \)


All sex hormone can work without the
help of
A. Gonadotropins
B. Placenta
c. Pituitary
D. Insulin


In the thermal decomposition of \( N_{2} O \) at
\( 830 \mathrm{K}, \) the time required to decompose half of the reactant was 263 sec at the initial pressure \( 290 \mathrm{mm} . \) It takes 212 sec to decompose half of the reactant if initial pressure was \( 360 \mathrm{mm} \). What is the order of the reaction? Also calculate
\( t_{1 / 2} \) for \( N_{2} O \) decomposition if initial
pressure of \( N_{2} O \) is 1 atm.
A. \( O . R=2 \), Half life \( =100.2 \) sec
B. \( O . R=1 \), Half life \( =10.02 \) sec
c. \( O . R=4 \), Half life \( =1.002 \)sec
D. None of these


Is the principle reaction responsible for
the energy output of the sun:
A. Gamma decay
B. Nuclear fusion
c. Alpha decay
D. Positron emission
E. Nuclear fission


Assertion
Graph between potential energy of a spring versus the extension or compression of the spring is a straight
line
Reason
Potential energy of a stretched or
compressed spring is proportional to
square of extension or compression
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


Comment on the statement given below:
In self-induction

When the current in a coil is increasing, induced emf opposes it
When the current in a coil is
decreasing, induced emf supports it
A. A is true, B is false
B. A and B are false
c. A and B are true
D. A is false, B is true


Which of the following is a self adjusted force?
A. sliding friction
B. static friction
c. limiting friction
D. dynamic friction


A beam of protons is moving horizontally towards you. As it approaches you, it passes through a magnetic field which is directed upwards. As you see it, the magnetic field will deflect the beam to the:
A. Right
B. Left
c. Top
D. Bottom


Distinguish between n type and p type
semi conductors.


Which property of light is known as rectilinear propagation of light?
A. Light does not need a material medium to trave
B. Light does not change the property of media through which it travels
c. Light always travels in a straight line
D. All of the above


The domain of the relation \( R= \)
\( \{(x, y): x, y \epsilon N \text { and } x+y \leq 3\} \)
is
\( A \cdot\{1,2,3\} \)
B. \{1,2\}
\begin{tabular}{l}
c. \( (\ldots-1,0,1,2,3] \) \\
\hline
\end{tabular}
D. None of these


The angle between tangents drawn from
the point (-1,3) to the circle \( x^{2}+ \)
\( \boldsymbol{y}^{2}=\mathbf{5} \) is
A.
в.
c.
D.


Define the following terms:
(i) Molality (m)
(ii) Abnormal molar mass


Describe the natural source of
production of Hydrocarbon.


\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}} \tan ^{-1}\left[\frac{\sqrt{\mathbf{1}+\sin \boldsymbol{x}}-\sqrt{\mathbf{1}-\sin \boldsymbol{x}}}{\sqrt{\mathbf{1}+\sin \boldsymbol{x}}-\sqrt{\mathbf{1}-\sin \boldsymbol{x}}}\right]= \)
\( A \)
B. \( -\frac{1}{2} \)
\( c \cdot \frac{1}{2} \)
\( D \)


What is Essential and Non essential
amino acid?


Statement \( A: A \| \) green plants have chlorophyll pigment.

Statement B : Without chlorophyll, photosynthesis cannot take place.
From the above statements,
Neelima concluded that the dark red
colored croton plants in her garden
cannot prepare food on its own. But
her teacher said it is not correct. Why?
A. Croton plants are green but do not contain chlorophyll
B. Croton plants are dark red in color but do not contain chlorophyll.
c. croton plants have chlorophyll but it is hidden by dark red colour.
D. Croton plants do not have chlorophyll but they can prepare their own food.


Select the coloured compound amongst the following:
(Atomic no. \( \boldsymbol{T} \boldsymbol{i}=\mathbf{2} 2, \boldsymbol{C r}=\mathbf{2 4}, \boldsymbol{C u}= \)
\( \mathbf{2 9}, \mathbf{Z n}=\mathbf{3 0} \mathbf{)} \)
A. \( T i C l_{4} \)
в. \( C r C l_{3} \)
c. \( Z n C l_{2} \)
D. \( C u C l \)


In the laboratory process of hydrogen production, we use impure zinc because:
A. pure zinc is very costly
B. there is risk of explosion with pure
c. impurity in zinc act as catalyst
D. pure zinc is not easily available


A cylindrical vessel having diameter equal to its hight is fall of water which
is poured into two identical cylindrical vessel with diameter \( 42 \mathrm{cm} \) and height \( 21 \mathrm{cm} \) which are filled compulsory. Find the cylindrical vessel


If \( a>0, b>0, c>0 \) and the minimum value
of \( \boldsymbol{a}\left(\boldsymbol{b}^{2}+\boldsymbol{c}^{2}\right)+\boldsymbol{b}\left(\boldsymbol{c}^{2}+\boldsymbol{a}^{2}\right)+\boldsymbol{c}\left(\boldsymbol{a}^{2}+\boldsymbol{b}^{2}\right) \)
is \( \lambda a b c \), then \( \lambda \) is
\( A \cdot 2 \)
в.
\( c \cdot 6 \)
D.


Name the organs that form the
excretory system in human beings.


Pyrophosphorous acid has the molecular formula:
A. \( H_{3} P O_{3} \)
в. \( H_{3} P O_{4} \)
c. \( H_{4} P_{2} O_{5} \)
D. \( H_{4} P_{2} O_{7} \)


Assertion
Assertion : If we perform an experiment in our laboratory today and repeat the
same experiment on the same objects under identical conditions after a year,
the results are found to be the same.
Reason
Reason : The laws of nature do not
change with time.
A. both assertion and reason are true and reason is the correct explanation of assertion.
B. both assertion and reason are true and reason is not the correct explanation of assertion.
c. assertion is true but reason is false.
D. both assertion and reason are false


Euclids division lemma can be used to
find the \( \ldots \ldots \ldots . . \) of any two positive integers and to show the common
properties of numbers.
A. None of the common factors
B. Lowest common factor
c. Highest common factor
D. common factor


Match the Column I with Column II
\begin{tabular}{lll|l}
& Column I & & Column II \\
& & \\
(A) & Smaller the & & If the same \\
& resistance & & voltage is \\
greater the & (p) & applied \\
current in a & & across a \\
circuit & & resistance \\
(B) & Gmaller the resistance the current is same & (q) & If the same current is passed \\
(C) & Greater the resistance smaller the power & (r) & When resistances are connected in series \\
(D) & Greater the resistance greater the power & (s) & When resistances are connected in parallel
\end{tabular}
\( A \cdot A-r \)
, B-p, C-q, D-s
B. A-p, B-r, C-q, D-s
C. A-r, B-p, C-S, D-q
D. A-s, B-r, C-p, D-


A hollow conducting sphere has a net
charge of \( +Q . \) There are four labeled
points all on the inside of the sphere, as
shown above. Points A through D are
ocated progressively closer to the
center of the sphere.
Which point has the largest magnitude
of electric field?
A. Point A
B. Point B
\( c . \) Point \( c \)
D. Point D
E. All points have the \( d \)
ie


Electric charges having same magnitude of electric charge 'q', coulombs are placed at \( x=1 \mathrm{m}, 2 \mathrm{m}, 3 \mathrm{m} \) \( 4 m, 8 m, \dots \dots \) and so on. If any two consecutive charges have opposite sign but the first charge is necessarily positive, what will be the potential at \( x= \)
O?
A \( \cdot \frac{2 h q}{3} \)
B. zero
C. \( \frac{1}{4 \pi \varepsilon_{0}}\left(\frac{2 q}{3}\right) \)
D. \( \frac{1}{4 \pi \varepsilon_{0}}(2 q) \)


Decomposition of ozone shows negative
order with respect to oxygen.
A. True
B. False


Mixed ethers are:
A. symmetrical ethers
B. unsymmetrical ethers
C . alkyl aryl ethers
D. diaryl ethers


If a particular electromagnetic wave has the highest frequencies among the other electromagnetic waves then it should have the smallest
A. wavelengths
B. speeds
c. amplitudes
D. energies
E. periods


n figure 1, \( \angle P Q R \) is :
\( \mathbf{A} \cdot 40^{\circ} \)
B \( .50^{\circ} \)
\( c \cdot 30 \)
D. 105


Calculate the equilibrium constant for the redox reaction at \( 25^{\circ} \mathrm{C}, S r_{(s)}+ \) \( M g_{(a q)}^{2+} \rightarrow S r_{(a q)}^{2+}+M g_{(s)}, \) that occurs
in a galvanic cell. \( \boldsymbol{E}_{M g^{2+} / M g}^{o}=-2.37 \mathrm{V} \)
and \( \boldsymbol{E}_{\boldsymbol{S r}^{2}+/ \boldsymbol{S} \boldsymbol{r}}^{o}=-\boldsymbol{2} . \boldsymbol{8} \boldsymbol{9} \boldsymbol{V} \)
A \( \cdot 2.69 \times 10^{15} \)
В. \( 2.69 \times 10^{17} \)
D. \( 3.69 \times 10^{15} \)


The sun emits a light with maximum wavelength \( 510 n m \) while another star
emits a light with maximum
wavelength of \( 350 n m . \) The ratio of surface temperature of sun and the star will be:
A . 0.68
B. 2.1
c. 1.45
D. 0.46


The minimum value of \( 4 \cos ^{2} x+ \)
\( 5 \sin ^{2} x \) is


Which of the following does not form Grignard reagent on reaction with \( M g \)
in the presence of ether?
A. chloroethane
B. 1-chloropropane
c. Bromobenzene
D. All of them form Grignard reagent


Which of the following statements are correct?
(i) Glucose has a high threshold value.
(ii) Urine is concentrated in Henle's
loop.
(iii) Haemodialyser removes urea, uric acid, glucose and plasma proteins.
(iv) In glomerulus, urea, uric acid, water, glucose and plasma proteins are filtered out.
A . (i), (iii) and (iv)
B. (ii), (iii) and (iv)
c. (i) and (ii)
D. (i) and (iii)


Simplify: \( 3 a^{2}\left(2 a^{2}-3\right)+ \)
\( 4 a\left(2 a^{3}+3\right)-12(a+1) \)
A \( \cdot 14 a^{4}-9 a^{2}-12 \)
B . \( 14 a^{4}+9 a^{2}-12 \)
c. \( 14 a^{4}-9 a^{2}+12 \)
D. None of these


Draw a labeled diagram of the experiment explaining Ohm's law.


\( [\boldsymbol{X}]+\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \rightarrow[\boldsymbol{Y}] \) a colourless gas
with irritating burning smell of sulphur
\( [\boldsymbol{Y}]+\boldsymbol{K}_{2} \boldsymbol{C r}_{2} \boldsymbol{O}_{7}+\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \rightarrow \operatorname{green} \)
solution.
\( [\boldsymbol{X}] \) and \( [\boldsymbol{Y}] \) are:
\( \mathbf{A} \cdot S O_{3}^{2-}, S O_{2} \)
в. \( C l^{-}, H C l \)
\( \mathbf{c} \cdot S^{2-}, H_{2} S \)
D. \( C O_{3}^{2-}, C O_{2} \)


A diatomic gas \( (\lambda=1.4) \) does 200 Jof
work when it is expanded isobarically. Find the heat given to the gas in the
process.


A piece of copper and a piece of germanium are cooled from room temperature to \( 80 K . \) Then, which one of the following is correct?
A. Resistance of each will increase
B. Resistance of each will decrease
c. Resistance of copper will decrease while that of germanium will increase
D. Resistance of copper will increase while that of germanium will decrease


Which among the following are purine derivatives among the following bases?
1. Adenine 2.Uracil 3.Guanine 4.Thymine
A \( \cdot 1,4 \) only
B. 2, 3 only
c. 1,3 only
D. 1,3,4 only


If \( \cos ^{-1}\left(\frac{1}{x}\right)=\theta \) then \( \tan \theta= \)
A \( \frac{1}{\sqrt{x^{2}-1}} \)
B. \( \sqrt{x^{2}+1} \)
c. \( \sqrt{1-x^{2}} \)
D. \( \sqrt{x^{2}-1} \)


Given below are some functions of \( x \) and
\( t \) to represent the displacement (transverse or longitudinal) of an elastic wave. State which of these
represent (i) a travelling wave (ii) a stationary wave or (iii) none at all:
(a) \( y=2 \cos (3 x) \sin (10 t) \)
(b) \( y=2 \sqrt{x-v t} \)
(c) \( y=3 \sin (5 x-0.5 t)+4 \cos (5 x- \)
\( \mathbf{0 . 5 t} \)
(d) \( y=\cos x \sin t+\cos 2 x \sin 2 t \)


Assertion
The graph between velocity and displacement for a harmonic oscillator is an ellipse.
Reason
Velocity does not change uniformly with displacement in harmonic motion.
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


Drugs which supplement (or) substitute for chemical messengers are
A. antagonists
B. agonists
c. blocking chemicalss
D. all


Electricity used by some families is shown in the following table. Find the mode for use of electricity.
use of electricity 0
20- \( \quad 40 \) 20 40 60 (unit)
No. of
\( \begin{array}{ll}\text { 13 } & \text { 50 }\end{array} \)
families


Which set is the subset of the set
containing all the whole numbers?
\( \mathbf{A} \cdot\{1,2,3,4, \dots \dots .\} \)
в. \{1\}
\( c \cdot\{0\} \)
D. All of the above


Figure shows equipotential surfaces
concentric at 'O' the magnitude of electric fields at distance r(in meter)
measured from
A \( \cdot \frac{9}{r^{2}}\left(V m^{-1}\right) \)
в. \( \frac{6}{r^{2}}\left(V m^{-1}\right) \)
c. \( \frac{2}{r^{2}}\left(V m^{-1}\right) \)
D. \( \frac{16}{r^{2}}\left(V m^{-1}\right) \)


A body is dropped from height 8 m. After
striking the surface it rises to \( 6 m \)
what is the fractional loss in kinetic
energy during impact? Assuming the frictional resistance to be negligible.
A . \( 1 / 2 \)
в. \( 1 / 4 \)
c. \( 1 / 6 \)
D. \( 1 / 8 \)


Which one of the following is a strong
electrolyte?
A. \( C H_{3} \) СООН
в. \( H C O O H \)
c. \( H_{2} C O_{3} \)
D. \( N a O H \)


A capacitor in an ideal LC circuit is fully
charged by a DC source, then it is disconnected from DC source, the
current in the circuit
A. becomes zero instantaneously
B. grows, monotonically
c. decays monotonically
D. oscillate infinitely


State True or False.
Solutions of Schrodinger equation for \( H \) -atom give the same set of values of
the energy levels as does the Bohr's theory
A. True
B. False


The time dependence of the position of a particle of mass \( m=2 \) is given by \( \vec{r}(t)=2 t \hat{i}-3 t^{2} \hat{j} . \) Its angular
momentum, with respect to the origin at time \( t=2 \) is :
\( \mathbf{A} \cdot 36 \hat{k} \)
B . \( -34(\hat{k}-\hat{i}) \)
c. \( 48(\hat{i}+\hat{j}) \)
D. \( -48 \hat{k} \)


Find the maximum value of \( f(x)=\left(\frac{1}{x}\right)^{x} \)


\( y+x^{2}=\frac{d y}{d x} \) has the solution:
A \( \cdot y+x^{2}+2 x+2=c \cdot e^{x} \)
B. \( y+x+2 x^{2}+2=c . e^{x} \)
C \( \cdot y+x+x^{2}+2=c \cdot e^{2 x} \)
D. \( y^{2}+x+x^{2}+2=c . e^{2 x} \)


A proton and an \( \alpha- \) particle (with their
masses in the ratio of 1: 4 and charges
in the ratio of 1: 2 ) are accelerated
from rest through a potential difference
V. If a uniform magnetic field (B) is set up perpendicular to their velocities, the
ratio of the radii \( r_{p}: r_{\alpha} \) of the circular
path described by them will be :
A. \( 1: \sqrt{2} \)
Th \( : \sqrt{2} \cdot \sqrt{2} \)
B. 1: 2
\( c \cdot 1: 3 \)
D. \( 1: \sqrt{3} \)


Choose the correct statement from the
following.
This question has multiple correct options
A. lonic bond takes place between the elements that have larger difference in their electro negativity.
B. Ionic compounds conduct electricity in their solid phase.
C. Covalent compounds exhibit isomerism.
D. \( S F_{6} \) is an example of ionic compound


Natural chlorine contains chlorine in
the form of the isotope \( ^{35} C l(75.5 \%) \) and
\( ^37 C l(24.5 \%) . \) Calculate the average
atomic mass of natural chlorine.
A . 35.49
B. 35
\( c .37 \)
D. 36


What is the role of gibberellins in plant growth and development?


A particle moving on straight line whose velocity-time graph is shown in the
figure. The average speed from \( t=0 \) to
\( t=6 s \) is \( v=\frac{15}{n} m s^{-1} . \) Find the value of
\( \boldsymbol{n} \)
4
B
\( c \)


The oxide of nitrogen which forms dimer
is
A. nitrogen oxide
B. nitrous oxide
c. nitrogen dioxide
D. none of the above


The value of \( \cos \left(\frac{1}{2} \cos ^{-1} \frac{1}{8}\right) \) is
A. \( \frac{3}{4} \)
в. \( -\frac{3}{4} \)
c. \( \frac{1}{16} \)
D.


Calculate the energy required to excite one litre of hydrogen gas at 1 atm pressure and \( 298 \mathrm{K} \) to the first excited
state of atomic hydrogen. The energy for the dissociation of H-H is 436 kJ \( m o l^{-1} \)
A. \( 0.585 K J \)
В. \( 5 \times 10^{23} e V \)
c. \( 80.36 K J \)
D. none of these


When potassium iodide solution is treated with ozone ,the products formed
are:
This question has multiple correct options
\( \mathbf{A} \cdot I_{2} \)
в. \( H_{2} \)
\( c \cdot O_{2} \)
D. all of these


Two number differ by 5. If their product is \( 336, \) then the sum of the two numbers
is :
A . 21
B . 28
\( c .37 \)
D. 51


The line \( P Q \) whose equation is \( x-y= \)
2 cuts the \( x- \) axis at \( P \) and \( Q \) and
passes through \( (4,2) . \) The line \( P Q \) is
rotated about \( P \) through \( 45^{\circ} \) in the
anticlockwise direction. The equation of the line \( P Q \) in the new position is
A. \( y=-\sqrt{2} \)
B. \( y=2 \)
\( \mathbf{c} \cdot x=2 \)
D. \( x=-2 \)


A lake with an inflow of domestic
sewage rich in organic waste may result in
A. Drying of the lake vary soon due to algal bloom
B. An increased growth of fishes due to lot of nutrients
c. Death of fish due to lack of oxygen
D. Increased population of aquatic food web organisms


The half cell involving the reaction \( \boldsymbol{C r}_{2} \boldsymbol{O}_{\mathbf{7}}^{2-}(\boldsymbol{a q})+\mathbf{1 4 H}^{+}(\boldsymbol{a q})+\boldsymbol{6} e \rightarrow \)
\( 2 C r^{3+}(a q)+7 H_{2} O \) can be represented
as:
A \( \cdot P t, H^{+}(a q), C r_{2} O_{7}^{2-}(a q) \)
B . \( P t, H^{+}, C r^{3}+(a q) \)
c. \( P t, H_{2}, C r_{2} O_{7}^{2-}(a q), C r^{3+}(a q) \)
D. \( P t, H^{+}, C r_{2} O_{7}^{2-}(a q), C r^{3+}(a q) \)


To reduce the light reflected by the glass surface of a camera lens, the surface is
coated with a thin layer of another material which has an index of
refraction \( (\mu=7 / 4) \) smaller than that of glass. The least thickness of the layer to ensure that light falling
perpendicularly on the surface and
having wavelengths, \( \lambda_{1}=700 \mathrm{nm} \) and \( \lambda_{2} \)
\( =420 \mathrm{nm} \) will be weekly reflected for
both wavelengths is \( 10^{-7} \mathrm{m} \). Find \( x \) ?


If \( f(x)=\frac{4 x+x^{4}}{1+4 x^{3}} \) and \( g(x)= \)
\( \ln \left(\frac{1+x}{1-x}\right), \) then what is the value of \( f \cdot g\left(\frac{e-1}{e+1}\right) \) equal to?
A .2
B. 1
c. 0
D.


A metal cube of side length \( 8.0 \mathrm{cm} \) has its upper surface displaced with
respect to the bottom by \( 0.10 \mathrm{mm} \) when a tangential force of \( 4 \times N \) is applied at the top with bottom surface fixed. The
rigidity modulus of the material of the
cube is
A \( \cdot 4 \times 10^{14} N / m^{2} \)
B . \( 5 \times 10^{9} \mathrm{N} / \mathrm{m}^{2} \)
c. \( 8 \times 10^{14} \mathrm{N} / \mathrm{m}^{2} \)
D. \( 1 \times 10^{14} \mathrm{N} / \mathrm{m}^{2} \)


If the straight line \( y=m x+c \) is
parallel to the axis of the parabola \( \boldsymbol{y}^{2}= \) \( l x \) and intersects the parabola at
\( \left(\frac{c^{2}}{8}, c\right) \) then the length of the latus rectum is
A . 2
B. 3
\( c \cdot 4 \)
D.


\( 2 \mathrm{g} \) benzoic acid \( \left(C_{6} H_{5} C O O H\right) \)
dissolved in 25 g of benzene shoes a depression in freezing point equal to 1.62 K. Molal depression constant for benzene is \( 4.9 \mathrm{K} \mathrm{kg} \) mol\( ^{-1} . \) What is the percentage association of acid if it
forms dimer in solution?


Calculate Compound interest on Rs.
1000 over a period of 1 year at \( 10 \% \) per annum if interest is compounded half
yearly.


Oxygen forms liquid hydride which is to litmus.


The following table shows the percentage of the students of a school who participated in Election and Drawing competitions.

Competition Election Drawing
Percentage of Students
Draw a Venn diagram to represent this information and use it to find the
percentage of the students who
(i) Participated in Election only
(ii) Participated in Drawing only
(iii) Did not participate in any one of the competitions.


Dual character of an electron was
explained by:
A. Bohr
B. Heisenberg
c. De Broglie
D. Pauli


Find the correct statement about the
solubility of a solution?
A. Gases decrease in solubility with an increase in temperature
B. \( N a C l \) is insoluble in water
\( \mathbf{C} \cdot P b l_{2} \) is soluble in water
D. All nitrates are insoluble in water
E. Solubility depends solely upon the amount of solvent used


n-Propyl alcohol is obtained on hydrolysis of the adduct obtained by the
reaction of:
A. EtMgX and HCHO
B. MeMgX and \( \left(C H_{2}\right)_{2} O \)
\( \mathrm{C} \cdot \mathrm{EtMgX} \) and \( \mathrm{O}_{2} \)
D. мeMgx and \( C H_{3} C H O \)


A parallel beam of light of wavelength \( 560 \mathrm{nm} \) falls on a thin of oil (refractive
index \( =1.4 \) ) What should be the
minimum thickness of the film so that
it weakly transmits the light


In the given figure, line \( l \| \) line \( m \), line
is a transversal. Write one pair of
corresponding angles and one pair of alternate interior angles.


If the current in the primary circuit is decreased,then balancing length is obtained in the potentiometer is at:
A. Lower length
B. Higher length
c. Same length
D. 1/3rd length


What is meant by galvanizing?


A steel ball of mass \( 0.5 \mathrm{kg} \) is dropped from a height of \( 4 \mathrm{m} \) on to a horizontal heavy steel slap. the strile the slap and reounds to its original height.
(a) calculate the impulse delivered to the ball during impact
(b) if the ball is in contact with the slab
for \( 0.002, \) find the average reaction
force on the ball during impact.


A rectangular loop carrying a current \( \boldsymbol{i}_{1} \) is situated near a long straight wire
carrying a steady current \( i_{2} . \) The wire is
parallel to one of the sides of the loop and is in the plane of the loop as shown in the figure. Then the current loop will
A. move away from the wire
B. move towards the wire
c. remain stationary
D. rotate about an axis parallel to the wirce


Climax community is
A. First stable community
B. Unstable
c. unstable that develops in the beginning of succession
D. The last stable community


toppr
Q Type your question
decay products of the neutron. Therefore, considering the decay of a neutron as a two-body decay process, it was predicted theoretically that the kinetic energy of the electron should be a constant. But experimentally, it was observed that the electron kinetic
energy has a continuous spectrum. Considering a three-body decay
process, i.e. \( \boldsymbol{n} \rightarrow \boldsymbol{p}+\boldsymbol{e}^{-}+\overline{\boldsymbol{v}}_{e}, \) around
1930, Pauli explained the observed electron energy spectrum. Assuming
the anti-neutrino \( \left(\bar{v}_{e}\right) \) to be massless
and possessing negligible energy, and the neutron to be at rest, momentum
and energy conservation principles are applied. From this calculation, the maximum kinetic energy of the electron
is \( 0.8 \times 10^{6} e V . \) The kinetic energy
carried by the proton is only the recoil
energy. f the anti-neutrino had a mass of 3
\( e V / c^{2}(\text { where } c \) is the speed of light) instead of zero mass, what should be
the range of the kinetic energy, \( \boldsymbol{K}, \) of the
electron?
A. \( 0 \leq K \leq 0.8 \times 10^{6} e V \)
B . \( 3.0 e V \leq K \leq 0.8 \times 10^{6} c V \)
c. \( 3.0 e V \leq K<0.8 \times 10^{6} e V \)
D. \( 0 \leq K<0.8 \times 10^{6} e V \)


Out of given reaction which show
change in hybridisation of central
atom?
This question has multiple correct options
\( \mathbf{A} \cdot H_{3} B O_{3} \) dissolve in water
B. \( H_{2} S O_{4} \) dissolve in water
\( \mathbf{C} \cdot N_{2} O_{5(g)} \rightarrow N_{2} O_{5(s)} \)
D. \( P B r_{5(g)} \rightarrow P B r_{5(s)} \)
E \( \cdot C_{2} H_{6} \frac{\text { Homolytic }}{\text { bond cleavage of } C-C \text { bond }} \)


Two long conductors, separated by a
distance d carry current \( I_{1} \) and \( I_{2} \) in the
same direction. They exert a force \( F \) on
each other. Now the current in one of
them is increased to two times and its
direction is reversed. the distance is
also increased to 3 d. The new value of
the force between them is
A \( \cdot-\frac{2 F}{3} \)
B. \( \frac{F}{3} \)
c. \( -2 F \)
D. \( -\frac{F}{3} \)


Photorespiration is a characteristic feature of plants having
\( \mathbf{A} \cdot C_{4} \) cycle
в. \( C_{3} \) cycle
c. Aerobic respiration
D. None of the above


Choose the correct observation.
This question has multiple correct options
A. The orbital diagram in which Aufbau principle is obeyed
11 11111
B. The spectra of \( H e \) and \( L i^{+} \) will be similar
C. Following is the violation of Pauli's exclusion principle
11
D. The \( d \) -orbit involved in \( s p^{3} d \) hybridisation is \( d_{x^{2}-y^{2}} \)


Reflection is the \( _{\text {十一一一一一一一一一 }} \) Ilight
off a surface.


In the extraction of nickel by Mond process, the metal is obtained by:
A. Electrochemical reduction
B. Thermal decomposition
c. Chemical reduction by aluminium
D. Reduction by carbon


In a certain reaction, \( 10 \% \) of the
reactant decomposes in one hour, \( 20 \% \) in two hours, \( 30 \% \) in three hours and so
on. Dimension of the velocity constant
are:
A . hour \( ^{-1} \)
B. mole litre \( ^{-1} \) hour \( ^{-1} \)
c. litre mol- \( ^{1} \) hour \( ^{-1} \)
D. mole sec \( ^{-1} \)


Consider the plots given below, for the
type of reaction \( \boldsymbol{n} \boldsymbol{A} \rightarrow \boldsymbol{B}+\boldsymbol{C} \). These
plots correspond to the reaction orders respectively:
A. 0,1,2
B . 1,2,0
\( c \cdot 3,2,1 \)
D. 1,0,2


Which of the following does not affect the rate of evaporation?
A. Pressure on evaporating substance
B. Exposed surface area of the evaporating substance
c. Shape of the evaporating substance
D. Temperature


State Kirchhoff's law for an electrical
network. Using these laws, deduce the
condition for balance in a Wheatstone
bridge.


The term ecosystem was coined by
A. Warming
B. Odum
c. tansley
D. Haeckel


There are n different object \( 1,2,3, \ldots n \)
distributed at random in n boxes
\( A_{1}, A_{2}, A_{3}, \cdots A_{N} . \) Find the probability
that two objects are placed in the boxes corresponding to their number.
A .
в. \( \frac{1}{2} \)
\( c \cdot \frac{1}{3} \)
D. \( \frac{2}{3} \)


Represent the following complex number in trigonometric form:
-1


Which of the following is the unit vector perpendicular to \( \vec{A} \) and \( \vec{B} \) ?
\( A \cdot \frac{\widehat{A} \times \widehat{B}}{A B \sin \theta} \)
B. \( \frac{\widehat{A} \times \widehat{B}}{A B \cos \theta} \)
c. \( \frac{\vec{A} \times \vec{B}}{A B \sin \theta} \)
D. \( \frac{\vec{A} \times \vec{B}}{A B \cos \theta} \)


Select the correct option:
Complete the given flowchart by
selecting the correct option:
A. A- Stipes; B- Hypopharynx; C- Exopodite; D- First maxillae
B. A- Stipes; B- Exopodite; C- Hypopharynx; D- First maxillae
c. A- First maxillae; B- Hypopharynx; C- Exopodite; DStipes
D. A- First maxillae; B- Exopodite; C- Hypopharynx; D Stipes


Find identical capacitor plates, each of
area \( A, \) are arranged such that adjacent
plates are at a distance \( ^{\prime} d^{\prime} \) apart, the
plates are connected to a source of emf
\( V \) as shown in figure. The charge on
plate 1 is and that on
plate 4 is


A transformer has 500 primary turns and 10 secondary turns. If the secondary has resistive load of \( 15 \Omega \), the currents
in the primary and secondary respectively, are:
B. 3.2 \( \times 10^{-3} A, \) 0.16 \( A \)
c. 0.16 А, 0.16 А
D. 3.2 \( \times 10^{-3} A, 3.2 \times 10^{-3} A \)


Fill in the blank.
Two circles are congruent if


The equation of the line passing through \( (-4,3), \) parallel to the \( 3 x+ \) \( \mathbf{7} \boldsymbol{y}+\mathbf{6}=\mathbf{0} \)
A. \( 3 x+7 y-9=0 \)
B. 3x+7y+9=0
c. \( 3 x+7 y+3=0 \)
D. 3x+7y+12=0


The relation \( R \) defined on \( \operatorname{set} A= \)
\( \{\boldsymbol{x}:|\boldsymbol{x}|<\mathbf{3}, \boldsymbol{x} \boldsymbol{\epsilon} \boldsymbol{I}\} \) by \( \boldsymbol{R}= \)
\( \{(x, y): y=|x|\} \) is
A \( \cdot\{(-2,2),(-1,1),(0,0),(1,1),(2,2)\} \)
B - \{(-2,2),(-2,2),(-1,1),(0,0),(1,-2),(2,-1),(2,-2)\}
c. \{(0,0),(1,1),(2,2)\}
D. None of the above


Which of the following statements is/are correct? \( \boldsymbol{C S}_{2}+\boldsymbol{3 C l}_{2} \stackrel{\boldsymbol{\Delta}}{\longrightarrow} \boldsymbol{C C l}_{4}+\boldsymbol{S}_{2} \boldsymbol{C l}_{2} \)
1.0 \( g \) of \( C S_{2} \) and 2.0 g of \( C l_{2} \) reacts. This question has multiple correct options
A \( \cdot 0.714 \mathrm{g} C S_{2} \) is used in the reaction
B. \( 0.286 \mathrm{g} \mathrm{CS}_{2} \) is in excess.
c. \( 1.45 \mathrm{g} \) of \( C C l_{4} \) is formed.
D. \( 0.8 \mathrm{g} / \mathrm{Cl}_{2} \) is in excess.


Henry law constant for the solubility of methane in benzene at \( 298 \mathrm{K} \) is \( 4.27 \times \)
\( 10^{5} \mathrm{mm} \) Hg then the solubility of
methane in benzene at \( 298 \mathrm{K} \) under
760mm Hg is:
A \( \cdot 7.8 \times 10^{-2} \) mole \( / \mathrm{kg} \)
B . \( 7.8 \times 10^{-3} \) mole / kg
c. \( 7.8 \times 10^{-4} \) mole \( / \mathrm{kg} \)
D. \( 1.78 \times 10^{-3} \) mole \( / \mathrm{kg} \)


If \( \boldsymbol{y}=\mathbf{3}, \) then \( \boldsymbol{y}^{3}\left(\boldsymbol{y}^{3}-\boldsymbol{y}\right)= \)
A. 300
в. 459
\( c \cdot 648 \)
D. 999
E . 1099


If a coin is tossed 3 times, then the number of outcomes will be?


A short bar magnet is placed with its south pole pointing geographic North at a
place where \( B_{H}=0.4 \) gauss. The length
of the magnet is \( 10 \mathrm{cm} \) and pole strength
is \( 16 A-m \). The distance of each null
point from the centre will be
A. \( 0.2 m \) on axial line
B. \( 0.8 \mathrm{cm} \) on axial line
c. \( 0.4 \mathrm{cm} \) on axial line
D. \( 0.2 \mathrm{cm} \) on equitorial line


If the electric field to the left of two
sheets is \( K \sigma / \varepsilon_{0} . \) Find K?


The girdling or ringing experiment
involved
A. Tying a metallic ring to a stem
B. Removal of a ring of tissue external to xylem
C. Marking a ring shaped area on the stem
D. None of the above


A figure is said to be regular if its sides are equal in length and angles are equal
in measure. Can you identity the regular quadrilateral?


Ozone layer of upper atmosphere is being destroyed by
A. Chlorofluorocarbons
в. \( S O_{2} \)
c. \( \operatorname{smog} \)
D. None of the above


You spill a bucket of soapy water on a marble floor accidentally.lt would make it \( _{\text {十一一一一一 }} \) for you to walk on the floor.
A. more difficult
B. easier
c. no change
D. cant say


The radius of an orbit in hydrogen atom is 52.9 A. The angular momentum of the electron in the orbit could be:
A \( \cdot \frac{5 h}{\pi} \)
в. \( \frac{5 h}{4 \pi} \)
\( c \cdot \frac{4 h}{2 \pi} \)
D. \( \frac{4 h}{\pi} \)


According to Werner's coordination theory, there are kinds of
valency and


Match the following two columns:
\( \begin{array}{llll} & \text { Column I } & & \text { Column II } \\ \text { A. } & \begin{array}{l}\text { Electrical } \\ \text { resistance }\end{array} & 1 . & {\left[M L^{3} T^{-3} A^{-2}\right]} \\ \text {B. } & \begin{array}{l}\text { Electrical } \\ \text { potential }\end{array} & 2 . & {\left[M L^{2} T^{-3} A^{-2}\right]} \\ \text {C. } & \begin{array}{l}\text { Specific } \\ \text { resistance }\end{array} & 3 . & {\left[M L^{2} T^{-3} A^{-1}\right]} \\ \text {D. } & \begin{array}{l}\text { Specific } \\ \text { conductance }\end{array} & 4 . & \text { None of these }\end{array} \)
\( \mathbf{A} \cdot A-2, B-3, C-1, D-4 \)
\( \mathbf{B} \cdot A-2, B-4, C-3, D-1 \)
c. \( A-1, B-2, C-3, D-3 \)
D. \( A-1, B-3, C-2, D-4 \)


Two wires of the same material and
length but diameters in the ration 1: 2
are stretched by the same force. The potential energy per unit volume for the two wires when stretched will be in the
ratio :
\( \mathbf{A} \cdot 16: 1 \)
B . 4: 1
c. 2: 1
D. 1: 1


Consider the following statements and select the correct answer using the code given below:
A.The age of the solar system is 4.6 billion years.
B.The outer planets consists of gases.
A. Only A is correct
B. Only B is correct
c. Both land 2 are correct
D. Neither 1 nor 2 is correct


Dead burnt plaster is :
A. \( \operatorname{CaSO}_{4} \)
в. \( \operatorname{CaSO}_{4} .12 \mathrm{H}_{2} \mathrm{O} \)
\( \mathrm{c} \cdot \mathrm{CaSO}_{4} \cdot \mathrm{H}_{2} \mathrm{O} \)
D. \( \operatorname{CaSO}_{4} .2 \mathrm{H}_{2} \)


If Young modulus is three times of modulus of rigidity, then Poisson ratio is equal to:
A . 0.2
B. 0.3
\( c .0 .4 \)
D. 0.5


When petrol drops from a vehicle fall over rain water on road surface, colours are seen because of:
A. dispersion of light
B. interference of light
c. scattering of light
D. absorption of light


Mond process is used in the extraction
of


The value of \( \lim _{x \rightarrow 1}\left(\frac{x^{n}+x^{n-1}+x^{n-2}+\ldots .+x^{2}+x}{x-1}\right. \)
is
A \( \cdot \frac{n(n+1)}{2} \)
B.
\( c \cdot 1 \)
\( D \)


Separation of \( H_{2} O \) and \( D_{2} O \) by fractional distillation is possible
because \( D_{2} O \) has:
A . higher density than that of \( H_{2} O \)
B. higher boiling point than that of \( H_{2} O \)
C. higher freezing point than that of \( H_{2} O \)
D. lower dielectric constant than that of \( H_{2} O \)


According to Bohr's model of the atom, atoms emit or absorb radiation only at certain wavelengths.ldentify why is it so
A. Because the protons and electrons are distributed evenly throughout the atom
B. Because electrons can orbit the nucleus at any radius
c. Because electrons orbit the nucleus only at certain discrete radii
D. Because protons orbit the nucleus only at certain discrete radii
E. Because photons can only have discrete wavelength


The value of \( \sin \frac{\theta}{2} \cdot \sin \frac{7 \theta}{2}+ \)
\( \sin \frac{3 \theta}{2} \cdot \sin \frac{11 \theta}{2}-\sin 2 \theta \cdot \sin 5 \theta \) is equal
to
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( \mathbf{c} \cdot \sin 6 \theta-\cos 5 \theta \)
\( D \cdot \sin 6 \theta+\sin 7 \theta \)


Consider the four entries below:
I. Right auricle
II. Left auricle
III. Right ventricle
IV. Left ventricle
The above are the four chambers of
human heart in which the blood
returned to the bean by great veins flows in a sequential order. What is the correct sequentional order?
A . ॥, Iv, , ॥ ॥
в . ।, ॥I, и, Iv
c. ।, ॥, ॥ा, ।v
D. ॥, II, , , Iv


Two bottles \( A \) and \( B \) have radii \( R_{A} \) and
\( R_{B} \) and heights \( h_{A} \) and \( h_{B} \) respectively
with \( R_{B}=2 R_{A} \) and \( h_{B}=2 h_{A} . \) These
are filled with hot water at \( 60^{\circ} \mathrm{C} \)

Consider that heat loss for the bottles
takes place only from side surfaces. If the time the water takes to cool down to
\( 50^{\circ} \mathrm{C} \) is \( t_{A} \) and \( t_{B} \) for bottles \( \mathrm{A} \) and \( \mathrm{B} \)
respectively, then \( t_{A} \) and \( t_{B} \) are best
related as.
A \( \cdot t_{A}=t_{B} \)
B \( \cdot t_{B}=2 t_{A} \)
\( \mathbf{c} \cdot t_{B}=4 t_{A} \)
D. \( t_{B}=t_{A} / 2 \)


Which of these is not directly connected with ascent of sap?
A. Cohesion theory
B. Root pressure
c. Apoplast and symplast
D. Capillarity


An object of height \( 2.5 \mathrm{cm} \) is placed at a
distance of \( 15 \mathrm{cm} \) from the optical centre 'O' of a convex lens of focal length
10cm. Draw a ray diagram to find the position and the size of the image formed. Mark optical center'o', principal focus \( F \) and height of the image in the diagram.


Explain, why electronegativity of Li is greater than Mg?


Two protons are moving with same velocity in magnetic field of same magnitude, then :
A. magnetic force on protons may be zero
B. magnetic force on both must be same to each other
c. magnetic force on both may or may not be same to each other
D. both \( (a) \) and \( (c) \) are correct


The vertices of a triangle are \( (2,3,5),(-1,3,2),(3,5,-2), \) then the
angles are
\( ^{\mathrm{B}} \cos ^{-1}\left(\frac{1}{\sqrt{5}}\right), 90^{\circ}, \cos ^{-1}\left(\frac{\sqrt{5}}{\sqrt{3}}\right) \)
c. \( 30^{\circ}, 60^{\circ}, 90^{\circ} \)
D \( \cdot \cos ^{-1}\left(\frac{1}{\sqrt{3}}\right), 90^{\circ}, \cos ^{-1}(\sqrt{\frac{2}{3}}) \)


Which of the following are examples of
pseudo unimolecular reactions?
\( \mathbf{A} \cdot C H_{3} C O_{2} C_{2} H_{5}+H_{2} O \rightarrow C H_{3} C O_{2} H+C_{2} H_{5} O H \)
\( \mathbf{B} \cdot C_{12} H_{22} O_{11}+H_{2} O \rightarrow C_{6} H_{12} O_{6}+C_{6} H_{12} O_{6} \)
\( \mathbf{c} \cdot C H_{3} C O C l+H_{2} O \rightarrow C H_{3} C O_{2} H+H C l \)
D. All of the above


At the Earth, a block of mass \( m \) which
rest on the frictionless table, let \( \boldsymbol{F} \) be
the force required to produce acceleration \( a \). Calculate the force at
the Moon to produce same acceleration
if \( g_{m o o n} \) is one sixth of \( g_{e a r t h} \)
A \( \cdot \frac{F}{12} \)
в. \( \frac{F}{6} \)
c. \( \frac{F}{3} \)
D. \( F \)
E . \( 6 F \)


The best reagent which can carry out this conversion is:
\[
\mathrm{ch}_{3} \frac{\mathrm{cH}_{3}}{\mathrm{C}-\mathrm{cH}_{2}-\mathrm{oH}} \frac{\mathrm{reagent}}{\mathrm{CH}_{3}} \mathrm{CH}_{3} \frac{\mathrm{CH}_{3}}{\mathrm{CH}_{3}}
\]
A. conc. \( H C l \)
в. \( H C l, Z n C l_{2} \)
\( c \cdot s O C l_{2} \)
D. aqueous KOH


A current is flowing in electricity line towards north, the direction of magnetic field at a point which is just below the line is :
A. towards north
B. towards south
c. towards east
D. towards west


Four identical cells of emf \( \boldsymbol{E} \) and
internal resistance \( r \) are to be
connected in series. Suppose if one of the cell is connected wrongly, the equivalent emf and effective internal resistance of the combination is
\( \mathbf{A} \cdot 4 E \) and \( 4 r \)
B. \( 4 E \) and \( 2 r \)
\( \mathbf{c} \cdot 2 E \) and \( 4 r \)
D. \( 2 E \) and \( 2 r \)


If earth attracts an apple with a force of
10 newton, then with what force the
apple will attract the earth.


Primary coil of a step-up transformer
has number of turns than
secondary coil.
A. more
B. less
c. same
D. cant say


In the adjoining figure find the values of
\( x \) and \( y \)


Ethylidene chloride can be prepared by
the reaction of \( H C l \) and:
A. ethane
B. ethylene
c. acetylene
D. ethylene glycol


Consider a nuclear reaction \( \boldsymbol{A}+\boldsymbol{B} \rightarrow \)
C. A nucleus A moving with kinetic
energy of 5 MeV collides with a nucleus B moving with kinetic energy of 3 MeV and forms a nucleus \( C \) is excited state.
Find the kinetic energy of nucleus \( C \) just after its formation if it is formed in a state with excitation energy \( 10 \mathrm{MeV} \) Take masses of nuclei of \( A, B, \) and \( C \) as
25.0,10.0,34.995 amu, respectively. \( \left(1 a m u=930 M e V / c^{2}\right) \)


\( 0.08 k g \) of a substance is heated from
\( 30^{\circ} \mathrm{C} \) to \( 130^{\circ} \mathrm{C}, \) when 2000 calories of
energy is supplied to it. Calculate the specific heat capacity of the substance
in
(a) calories
(b) joules.


The first and second terms of both an
A.P. and a G.P. are same \( x \) and \( y \)
respectively where both \( x \) and \( y \) are
\( +i v e \) and \( x \) is greater than \( y . \) If \( S \) be the
sum of infinite \( G . P ., \) then prove that
sum of first \( n \) terms of \( A . P . \) is given by \( \boldsymbol{n x}-\frac{\boldsymbol{n}(\boldsymbol{n}-\mathbf{1}) \boldsymbol{x}^{2}}{\boldsymbol{2} \boldsymbol{S}} \)


Match the following
List -1 List - II
Frictional
e. Zero
\( a \)
force
b. Gravitational force \( \quad \) Electromagnetic force
c. When a body on rough inclined plane is just g. \( m g \sin \theta \) to move, then the net force acting on the body is
d. The force acting on a body \( \quad \) h. conservative placed on a smooth Ion a smooth inclined plane is
The correct match is
\( \mathbf{A} \cdot a \rightarrow h ; b \rightarrow f ; c \rightarrow g ; d \rightarrow e \)
\( \mathbf{B} \cdot a \rightarrow f ; b \rightarrow h ; c \rightarrow e ; d \rightarrow g \)
\( \mathbf{C} \cdot a \rightarrow e ; b \rightarrow g ; c \rightarrow f ; d \rightarrow h \)
\( \mathbf{D} \cdot a \rightarrow g ; b \rightarrow e ; c \rightarrow h ; d \rightarrow f \)


A rocket of mass \( 4000 \mathrm{kg} \) is set for
vertical firing. How much gas must be ejected per second so that the rocket may have initial upwards acceleration of magnitude \( 19.6 ~ m / s^{2} ? \) [Exhaust speed of fuel \( =\mathbf{9 8 0 m / s} \)
A. \( 240 \mathrm{kg} / \mathrm{s} \)
в. \( 80 \mathrm{kg} / \mathrm{s} \)
c. \( 120 \mathrm{kg} / \mathrm{s} \)
D. None


A monoprotic acid in \( 1.00 M \) solution is
\( 0.001 \% \) ionised. The dissociation
constant of acid is:
A. \( 1 \times 10^{-3} \)
В. \( 1 \times 10^{-6} \)
c. \( 1 \times 10^{-8} \)
D. \( 1 \times 10^{-10} \)


The soluble complex formed during the extraction of silver from glance cyanide process is:
A \( \cdot \operatorname{Na}_{2}\left[\operatorname{Zn}(C N)_{4}\right] \)
В \( \cdot_{N a_{2}}\left[Z n(C N)_{6}\right] \)
c. \( _{N a_{4}}\left[Z n(C N)_{6}\right] \)
D. None of these


If \( x, y \) and \( z \) are positive real numbers
such that \( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}=\boldsymbol{a} \) then \( - \)
A \( \cdot \frac{1}{x}+\frac{1}{y}+\frac{1}{z} \geq \frac{9}{a} \)
B. \( \frac{1}{x}+\frac{1}{y}+\frac{1}{z}<\frac{9}{a} \)
C \( \cdot(a-x)(a-y)(a-z)>\frac{8}{27} a^{3} \)
D. \( (a-x)(a-y)(a-z)>a^{3} \)


Which of the following will be true for 'ash', that is obtained by burning wood in air?
A. The properties of ash will be similar to woodd
B. The properties of ash will be similar to air
c. The properties of ash will be different from both wood and air
D. The properties of ash will be similar to both wood and air


Show that in a right-angled triangle, the hypotenuse is the longest side.


When light passes through prism it is :
A. Deviated
B. Deviated and dispersed
C . Reflected
D. Laterally Displaced


Let \( x y=x+y \) then prove that \( \frac{d y}{d x}+ \) \( \frac{1}{(x-1)^{2}}=0 \)


The ratio of number of exchange pairs
present in \( d^{9} \) and magnetic moment of Cr in B.M. is:-
\( A \cdot \frac{2}{\sqrt{3}} \)
B. \( \frac{2 \sqrt{3}}{3} \)
c. \( \frac{2 \sqrt{3}}{4} \)
D. \( \frac{16}{\sqrt{35}} \)


What are the units for the rate of the
reaction \( : \boldsymbol{A} \rightarrow \boldsymbol{B} \) ?
\( \mathbf{A} \cdot \) mol.lit\( ^{-1} \)
B. mol.lit" \( s e c^{-1} \)
c. mol.g\( ^{-1} \) sec\( ^{-1} \)
D. mol.kg \( ^{-1} \) sec \( ^{-1} \)


Name the scientist who invented
electric cell and the scientist who
invented electric bulb.


The frequency of applied alternating voltage is 2 KHz.its time period will
be
A \( .0 .5 \times 10^{-3} \) second
B. 5 second
c. 0.5 second
D. 2 second


Explain Werner's theory of co-ordination compounds?


State whether the following statements are true or false.
Ecological succession is directional therefore a predictable process
A. True
B. False


\( \boldsymbol{H}-\boldsymbol{C} \equiv \boldsymbol{C}-\boldsymbol{H} \) is a structure of
A. acetaldehyde
B. ethanal
c. ethane
D. acetylene


Alkyl halides follow the reactivity sequence, \( \boldsymbol{R}-\boldsymbol{I}>\boldsymbol{R}-\boldsymbol{B r}>\boldsymbol{R}- \)
\( \boldsymbol{C l}>\boldsymbol{R}-\boldsymbol{F} \)
A. True
B. False


Which among the following is correct
about \( \gamma- \) rays ?
A. High energy electrons
B. Low energy electrons
c. High energy electromagnetic waves
D. High energy positrons


Two identical plates of different metals are joined to form a single plate whose thickness is double the thickness of
each plate. If the coefficients of conductivity of each plate are 2 and 3 respectively, then the conductivity of the composite plate will be
A. 5
B. 2.4
c. 1.5
D. 1.2


Persons A and B are standing on the opposite sides of a \( 3.5 \mathrm{m} \) wide water
stream which they wish to cross. Each one of them has a rigid wooden plank
whose mass can be neglected. However,
each plank is only slightly longer than 3
m. So they decide to arrange them
together as shown in the figure
schematically. With B(mass 17kg) standing, the maximum mass of \( A, \) who can walk over the plank is close to.
A . \( 17 \mathrm{kg} \)
B. \( 65 \mathrm{kg} \)
\( c .80 \mathrm{kg} \)
D. \( 105 \mathrm{kg} \)


If \( m \) be the slope of a tangent to the
curve \( e^{y}=\left(1+x^{2}\right) \) then
A \( .|m|>1 \)
B. \( m<1 \)
c. \( |m|<1 \)
D. \( |m| \leq 1 \)


Beryllium resembles Aluminium in properties. This is mainly due to:
A . equal electro negativity values of elements
B. equal atomic volumes of the elements
c. equal electron affinity
D. equal nuclear charges in their atoms


Verticillaster is a type of
A. Phyllotaxis
B. Inflorescence
C. Placentation
D. Venation


A frame \( A B C D \) is rotating with an
angular velocity \( \omega \) about an axis
passing through point \( O \) perpendicular
to the plane of paper as shown in the figure. A uniform magnetic field \( \vec{B} \) is applied into the plane of the paper in the region as in the figure. Match the following.


The slope of the tangent to the curve \( y=\int_{0}^{x} \frac{d t}{1+t^{3}} \) at the point where \( x=1 \) is.
A \( \cdot \frac{1}{4} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{1}{2} \)
D. 1


Two point charge \( Q \) and \( -3 Q \) are placed at some distance apart. If the electric field at the location of \( Q \) is \( \vec{E} \), the field at the location of \( -3 Q \) is:
A. \( \vec{E} \)
в. \( -\vec{E} \)
c. \( +\frac{\vec{E}}{3} \)
D. \( -\frac{\vec{E}}{3} \)


In a class of 50 students, \( 40 \% \) are girls.
Find the number of girls and number of
boys in the class?


Compound \( A \) has how many functional
groups?
\[
\begin{array}{l}
\text { a-Amino acid (A) } \frac{\mathrm{MeOH} / \mathrm{HCl}}{\left(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{NO}_{3}\right)} \\
\begin{array}{c}
\left.(\mathrm{D})\left(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{NO}_{2} \mathrm{Cl}\right) \quad \stackrel{\mathrm{H}_{3} \mathrm{O}^{\oplus}}{(\mathrm{Na}-\mathrm{Hg} / \mathrm{HCl}}\right) \\
& (\mathrm{D})\left(\mathrm{C}_{4} \mathrm{H}_{9} \mathrm{NO}_{2} \mathrm{Cl}_{2}\right)
\end{array}
\end{array}
\]
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c \cdot 3 \)
\( D \)


Match List-1 with list-2
\( \begin{array}{ll}\text { List-1 } & \text { List-2 } \\ \text { A. Emitter } & \text { E. Transistor } \\ \text { B. Base } & \text { F. Moderately doped } \\ \text { C. Collector } & \text { G. Lightly doped } \\ \text { D. Transfer of resistance } & \text { H. Heavily doped } \\ \text { I. largest physical size }\end{array} \)
A. A-F B-E C-H,I D-G
B. A-G B-F.I C-E D-H
c. A-HB-G C-F,I D-E
D. A-E B-H,I C-G D-F


In rabbit, the opening of post caval in the right auricle is guarded by
A. Bicuspid valve
B. Tricuspid valve
c. Eustachian valve
D. sino-auricular valve


The radius of the cylinder whose lateral surface area is \( 704 \mathrm{cm}^{2} \) and height
\( 8 c m, \) is
A. \( 6 \mathrm{cm} \)
в. 4 ст
\( c .8 c m \)
D. \( 14 \mathrm{cm} \)


In which one of the following pairs is the specific characteristic of a soil not
correctly matched?
A. Laterite - contains aluminium compound
B. Terra rossa - most suitable for roses
c. chernozems - richest soil in the world
D. Black soil- rich in calcium carbonate


Bacteria are no more classified as
plants primarily because
A. These are unicellular and prokaryotic
B. These are microscopic
C. Many of them are parasitic
D. They do not have chlorophyll


A particle having mass \( m \) and charge \( q \) is released from the origin in a region in which electric field and magnetic fields are given by \( \vec{B}=-B_{0} \hat{j} \) and \( \vec{E}=E_{0} \hat{k} \)
Find the speed of the particle as a
function of its \( z- \) coordinate.
A \( \cdot \sqrt{\frac{q E z}{m}} \)
B. \( \sqrt{\frac{2(q v B+q E) z}{m}} \)
D. \( \sqrt{\frac{2 q E z}{m}} \)


Given are the structures of cyclic \( D \)
glucoside
Moles of \( H C H O \) formed are:
\( (X) \)
A . 1,1
в. 2,2
\( \mathrm{c} \cdot 1,2 \)
D. 2,


Choose the correct answer
Property of anode rays:
A. Travel in straight lines: They cast a shadow of the objects placed in their way.
B. Produce mechanical effect: A paddle wheel placed in their path starts rotating.
C. Rays are positively charged: Anode rays are deflected towards the negative plate of an electric field.
D. All of the above


Which of the following are the properties of fuse wire?
A. Made of alloy of tin
B. Has a low melting point
c. connected in series with main supply
D. All of the above


Hydrogen peroxide is now generally prepared to industrial scale by the:
A . action of \( H_{2} S O_{4} \) on barium peroxide
B. action of \( H_{2} S O_{4} \) on sodium peroxide
C . electrolysis of \( 50 \% \mathrm{H}_{2} \mathrm{SO}_{4} \)
D. burning hydrogen in excess of oxygen


Two elements 'P' and 'Q' belong to the same period of the modern periodic table and are in Group 1 and Group 2 respectively. Compare their following characteristics in tabular form.
(a) The number of electrons in their
atoms
(b) The sizes of their atoms
(c) Their metallic character
(d) Their tendencies to lose electrons
(e) The formula of their oxides
(f) The formula of their chlorides


A uniform wire of length \( 1 ~ m \) and radius
\( 0.028 \mathrm{cm} \) is employed to raise a stone of
density \( 2500 \mathrm{kg} / \mathrm{m}^{3} \) immersed in water. Find the change in elongation of wire when the stone is raised out of
water.
\( [\text {massofstone}=\mathbf{5} k g, \) Yofmaterialo


Write down the reaction when Ammonia
reacts with atmospheric oxygen in the presence of catalyst.


A wire of length \( L \) and cross-sectional \( A \)
is made of a material of Young's
modulus. If the wire is stretched by an amount \( x, \) the work done is


Construct three tangents ( from a point outside to the circle \( ) \) to the circle of
radius \( 5 \mathrm{cm} \)


The two types of bonds present in \( B_{2} H_{6} \) are covalent and ionic bond. If true enter
1, else enter 0


By charging the metal electrodes and gas inside the cathode ray tube:
A. the electron particle were produced
B. the proton particle were produced
c. the neutron particle were produced
D. none of the above


The value of \( 1+\cot ^{2} A \) is
\( \mathbf{A} \cdot \cos ^{2} A \)
B. \( \sec ^{2} A \)
\( \mathbf{c} \cdot \tan ^{2} A \)
D. \( \operatorname{cosec}^{2} A \)


Find the value of \( \sin 22^{0} \cos 38^{0}+ \)
\( \cos 22^{0} \sin 38^{0} \)
\( A \cdot \frac{1}{2} \)
B. \( -\frac{\sqrt{3}}{2} \)
c. \( \frac{\sqrt{3}}{2} \)
D. \( \frac{1}{\sqrt{2}} \)


Four point masses are placed at the
corners of a square of side \( 2 m \) as shown
in figure. Find the centre of mass of the
system w.r.t the centre of square


Calculate mean deviation from the
median of the following data:
\( \begin{array}{llll}\text { Class } & 0- & 6- & 1 \\ \text { interval: } & 6 & 12 & 1\end{array} \)
8
一年 18
Frequency: \( \quad 4 \)
5


Choose the appropriate option:
In metals. than the insulators.
A. There are more free electrons
B. There are less free electrons
c. There are all free electrons
D. There are no free electrons


IUPAC name of the given compound is:
\[
\begin{array}{c}
\mathrm{H}_{3} \mathrm{C}-\mathrm{CH}-\mathrm{CH}_{2}-\mathrm{CH}-\mathrm{CH}-\mathrm{CH}_{2}-\mathrm{CH}_{3} \\
\mathrm{OH}
\end{array}
\]
A. 5 -ethylheptane-2.4-diol
B. 3-ethylheptane-4,6-diol
C . 4-ethyl-1-methylhexane-1,3-diol
D. none of these


A particle moves in \( x y \) plane. The position vector at any time \( t \) is \( \vec{r}= \) \( \left\{(2 t) \hat{i}+\left(2 t^{2}\right) \hat{j}\right\} m . \) The rate of change of \( \theta \) at time \( t=2 \) second (where \( \theta \) is an
angle which its velocity vector makes
with positive \( x-a x i s) \) is:
A \( \cdot \frac{2}{17} \operatorname{rad} / s \)
в. \( \frac{1}{14} r a d / s \)
c. \( \frac{4}{7} \) rad \( / \) s
D. \( \frac{6}{5} \) rad \( / \) s


On subtracting -5 from \( 0, \) we get
A . -5
B. 5
c. 50
D. 0


Nitrating mixture is :
A. Fuming nitric acid
B. Mixture of conc \( H_{2} S O_{4} \) and conc \( H N O_{3} \)
C. Mixture of nitric acid and anhydrous zinc chloride
D. None of the above


Find five numbers in Arithmetic
progression whose sum is 25 and the
sum of whose squares as 135


Irrespective of the source, pure sample of water always yields \( 88.89 \% \) mass of oxygen and \( 11.11 \% \) mass of hydrogen. This is explained by the law of:
A. conservation of mass
B. constant proportion
c. multiple proportion
D. constant volume


Which of the following organism has the highest heart rate?
A. Elephant
B. Whale
c. мап
D. Mouse


Which of the following oxides can dissolve in water to form a solution
that would turn litmus indicator red in
colour?
\( \mathbf{A} \cdot M g O \)
в. \( K_{2} \) О
c. \( \mathrm{CO}_{2} \)
D. ZnO
E. \( H_{2} O \)


Chromosome start separating at which stage of mitosis?
A. Early metaphase
B. Late metaphase
c. Early anaphase
D. Early telophase


Which of the following is the dimension of the coefficient of friction?
A \( \cdot\left[M^{2} L^{2} T\right] \)
В \( \cdot\left[M^{0} L^{0} T^{0}\right] \)
\( \mathbf{c} \cdot\left[M L^{2} T^{-2}\right] \)
D. \( \left[M^{2} L^{2} T^{-2}\right] \)


Give the IUPAC name of the following
compound


Quantity of nucleic acids in animal
cells is
A. 2-5\%
B. 5-8\%
c. \( 10-13 \% \)
D. 15-18\%


Assertion
The time of flight 'T' is the sum of time
of ascent and time of descent.
Reason
The time of ascent is equal to the time
of descent.
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 compounds act as both acid and base?
A. \( N a H C O_{3} \)
в. \( A l_{2} O_{3} \)
\( c \cdot C a O \)
D. \( M g O \)


A fighter plane of length \( 20 \mathrm{m}, \) wing span (distance from tip of one wing to the tip of the other wing) of \( 15 \mathrm{m} \) and height \( 5 \mathrm{m} \) is flying towards east over Delhi. Its speed is \( 240 m s^{-1} \). The earth's
magnetic field over Delhi is \( 5 \times 10^{-5} \mathrm{T} \)
with the declination angle \( \sim 0^{\circ} \) and dip
of \( \theta \) such that \( \sin \theta=\frac{2}{3} . \) If the voltage
developed is \( V_{B} \) between the lower and
upper side of the plane and \( V_{W} \) between
the tips of the wings then \( V_{B} \) and \( V_{W} \)
are close to
A \( \cdot V_{B}=40 m V ; V_{W}=135 \mathrm{mV} \) with left side of pilot at
higher voltage
B . \( V_{B}=45 \mathrm{mV} ; V_{W}=120 \mathrm{mV} \) with right side of pilot at
higher voltage
C. \( V_{B}=40 \mathrm{mV} ; V_{W}=135 \mathrm{mV} \) with right side of pilot at high voltage
D. \( V_{B}=45 \mathrm{mV} ; V_{W}=120 \mathrm{mV} \) with left side of pilot at
higher voltage


By selling 33 metres of cloth one gains the selling of 11 metres Find the gain percent
\( A \). \( 17.5 \% \)
в. 33.33\%
c. \( 40 \% \)
D. 50\%


The electron energy in \( H \) atom is given by \( \frac{-21.7 \times 10^{-12}}{n^{2}} \) erg. The longest wavelength (in \( \mathrm{cm} \) ) of light that can be used to cause the removal of an
electron from \( n=2 \) orbit is:
A. \( 3.66 \times 10^{-5} \)
B . \( 3.88 \times 10^{-5} \)
c. \( 3.66 \times 10^{-6} \)
D. \( 3.88 \times 10^{-6} \)


Consider a two slit interference
arrangements such that the distance of
the screen from the slits is half the
distance between the slits. Obtain the
value of \( \mathrm{D} \) in terms of \( \lambda \) such that the
first minima on the screen falls at a
distance D from the centre 0
\( A \cdot \frac{\lambda}{2.472} \)
в. \( \frac{\lambda}{2.236} \)
c. \( \frac{\lambda}{1.227} \)
D. \( \frac{\lambda}{3412} \)


Newton said that an apple falls down from a tree because
A. Apple exerts a force of attraction on the earth
B. The earth exerts a force of attraction on the apple
c. Both are true
D. None of the options are correct


A card is drawn at random from a well
shuffled card. find the probability of card drawn is a black king.
A \( \cdot \frac{1}{26} \)
B. \( \frac{2}{26} \)
c. \( \frac{4}{26} \)
D. None of the above


Which of the following nematodes are parasitic to humans?
A. Ascaris
B. Earthworm
c. Both A and B
D. Housefly


State whether true or false.
In a series circuit, all appliances work independently.
A. True
B. False


Which of the following has the highest boiling point?
A . Ne
в. не
c. \( C H_{4} \)
D. xe


If vector \( 2 \hat{i}+3 \hat{j}+8 \hat{k} \) is perpendicular to the vector \( 4 \hat{j}-4 \hat{i}+\alpha \hat{k}, \) then the
value of \( \alpha \) is :
A . -1
в. \( \frac{1}{2} \)
\( c \cdot-\frac{1}{2} \)
D.


(a) Explain why, for a charge configuration, the equipotential surface through a point is normal to the electric
field at that point?

Draw a sketch of equipotential surfaces
due to a single charge \( (-q) \) depicting the electric field lines due to the charge.
(b) Obtain an expression for the work done to dissociate the system of
three charges placed at the vertices of an equilateral triangle of side 'a' as shown in the figure.


A uniform rod of length \( 60 \mathrm{cm} \) and mass
\( 6 k g \) is acted upon by two forces as shown in the diagram. The force exerted by \( 45 \mathrm{cm} \) part of the rod on \( 15 \mathrm{cm} \) part of
the rod is
A. \( 9 N \)
N
В. \( 18 N \)
c. \( 27 N \)
D. 30N


Waste water is rich in
A. Microbes
B. Lather
c. Plastics
D. All of the above


The I.F of \( \left(x+2 y^{3}\right) \frac{d y}{d x}=y^{2} \) is
A \( \cdot e^{1 / y} \)
B . \( e^{-1 / y} \)
\( c \cdot y \)
D. \( -1 / y \)


Figure shows a long straight wire
carrying current \( l \) and a square
conducting wire loop of side \( I \), at a
distance 'a' from current wire. Both the
current wire and loop are in the plane of
paper.Find the flux of magnetic field of
current wire,passing through the loop.


Find \( : \int_{0}^{1} \frac{x}{1+x^{2}} d x \)


The largest sphere is carved out of a cube whose edge is of length \( l \) units. Find the volume of the sphere.
A \( \cdot \frac{5 \pi l^{3}}{6} \)
в. \( \frac{3 \pi l^{3}}{5} \)
с. \( \frac{\pi l^{3}}{6} \)
D. \( \frac{2 \pi l^{3}}{7} \)


Find the direction cosines (d.cs) of
directed line \( O P \) if coordinates of \( P \) is
\( (2,3,7), O \) being the origin.


If \( \zeta \) is the set of boys in your school and
\( B \) is the set of boys who play badminton Draw a Venn-diagram showing that
some of boys do not play badminton. If
\( \boldsymbol{n}(\boldsymbol{\zeta})=\mathbf{4 0} \) and \( \boldsymbol{n}\left(\boldsymbol{B}^{\prime}\right)=\mathbf{1 7} ; \) find how
many play badminton.


A real battery has an emf \( \epsilon \) and an internal resistancer. A variable resistor
\( \mathrm{R} \) is connected across the terminal of
the battery. A current I is drawn from the battery and the potential difference across the terminal on the battery is \( \mathrm{V} \) If \( R \) is slowly decreased to zero, which of the following best describes I and V?
A. I decreases to zero, V approaches
B. I approaches an infinite value, V decreases to zero
c. I approaches \( \epsilon / r, \) v approaches
D. I approaches \( \epsilon / r, \) V decreases to zer


\[
\boldsymbol{C H}_{3}-\boldsymbol{N H}_{2} \quad \boldsymbol{C H}_{3}-\boldsymbol{N H}-\boldsymbol{C H}_{3}
\]
\( \boldsymbol{C H}_{3}-\boldsymbol{N}-\boldsymbol{C H}_{3} \)
\( \boldsymbol{C H}_{3} \)
Compare boiling points of the given compounds:


Elasticity is defined as the ability of a
body to
A. Resist linear motion in a hard surface
B. Resist rolling motion in a hard surface
c. Resist a distorting influence and to return to its original size and shape when that influence or force is removed.
D. Resist electric current in a magnetic field


Express 10 months as a fraction of
year


Light enters from denser to rarer
medium. Choose the correct option.
A. Angle of refraction = Angle of incidence
B. Angle of refraction > Angle of incidence
c. Angle of refraction <Angle of incidence
D. Angle of refraction \( \geq \) Angle of incidence


State whether the given statement is true or false:
Dipositive zinc exhibits paramagnetism due to loss of two electrons from \( 3 d \) -orbitals of neutral
atom


Type your question
\( A \)
\( B \)
\( c \)
\( \boldsymbol{\beta}- \) lactone
\( D \)