How much heat is needed to transform
a \( 1 \mathrm{kg} \) block of ice at \( 5^{\circ} \mathrm{C} \) to a puddle of
water at \( 10^{\circ} \mathrm{C} ? \)


The given graph(a) and (b) represent the variation of the opposition offered by the circuit element to the flow of
alternating current, with frequency of the applied emf. Identify the circuit element corresponding to each graph.


Find the angle in degrees through which the photon is scattered in the scattering event described.
\( \mathbf{A} \cdot\left(3 \times 10^{-3}\right) \)
B \( \cdot\left(3 \times 10^{-5}\right) \)
C \( \cdot\left(3 \times 10^{-7}\right) \)
D. \( \left(3 \times 10^{-9}\right) \)


The potential energy of a body is given by \( U=A-B x^{2} \) (where \( x \) is the
displacement). The magnitude of force acting on the particle is
A. Constant
B. Proportional to \( x \)
c. Proportional to \( x^{2} \)
D. Inversely proportional to


Evaluate: \( \int \frac{2 x^{2}+1}{x^{2}\left(x^{2}+4\right)} d x \)


A rain drop starts falling from a height of \( 2 k m . \) It falls with a continuously decreasing acceleration and attains its terminal
velocity at a height of \( 1 k m . \) The ratio of
the work done by the gravitational force in the first half to the that in the second
half to the drops journey is
A. 1: 1 and the time of fall of the drop in the two halves is \( a: 1 \text { (where } a>1) \)
B. 1: 1 and the time of fall of the drop in the two halves is
\( a: 1 \text { (where } a<1) \)
c. \( a: 1 \) (where \( a>1 \) ) and the time of fall of the drop in
the two halves is 1: 1
D. \( a: 1 \) (where \( a<1 \) ) and the time of fall of the drop in the two halves is 1: 1


All forest fires emit(s):
A. carbon monoxide
B. sulphur dioxide
C. nitrogen dioxide
D. all of the above


Which of the following is a cubic polynomial?
\( \mathbf{A} \cdot p(x)=x^{2}-16 \)
в. \( p(x)=x-16 \)
C \( \cdot p(x)=x^{3}-27 \)
D \( \cdot p(x)=27^{3} \)


Define Stalor Law.


Find the time period of the motion of the
particle shown in figure. Neglect the
small effect of the bend near the
bottom.


What is the anomalous expansion?


The screening effect of \( \boldsymbol{d} \) electrons is:
A. much less than \( s \) -electrons
B. much more than \( s \) -electrons
c. equal to \( s \) -electrons
D. equal to \( p \) -electrons


Two wires carrying
A. parallel current repel each other
B. antiparallel current attract each other.
C. antiparallel current repel each other.
D. equal magnitudes of antiparallel current attract each other.


Which of the following is incorrect?
A. Hydrogen > Deuterium > Tritium; (\% relative abundance)
B. Hydrogen < Deuterium < Tritium; (density/g \( L^{-1} \) )
C. Hydrogen < Deuterium < Tritium; (boiling point/K)
D. Hydrogen < Deuterium > Tritium; (melting point/K)


Whose experiments cracked DNA and discovered triplet nature of genetic
code?
A. Beadle and Tatum
B. Hershey and Chase
c. Morgan and Sturtevant
D. Nirenberg and Matthaei


What is the cause of friction.


Two independent monochromatic
sodium lamps can not produce interference because
A. The frequencies of the two sources are different
B. The phase difference between the two sources changes will respect to time.
c. The two sources become coherent.
D. The amplitude of two sources is different


Find the inductance of a solenoid of
length \( l_{0}, \) made of Cu windings of mass
m. The winding resistance is equal to \( R \)
The diameter of solenoid \( <<l . \rho_{0} \) is resistivity of Cu and \( \rho \) is density of the
Cu.
\( ^{\text {A }} \cdot \frac{\mu_{0} R m}{2 \pi l_{0} \rho \rho_{0}} \)
в. \( \frac{\mu_{0} R m}{4 \pi l_{0} \rho \rho_{0}} \)
c. \( \frac{\mu_{0} R m}{3 \pi l_{0} \rho \rho_{0}} \)
D. \( \frac{2 \mu_{0} R m}{3 \pi l_{0} \rho \rho_{0}} \)


\( \lim _{n \rightarrow \infty}\left[\frac{1}{n^{2}} \sec ^{2} \frac{1}{n^{2}}+\frac{2}{n^{2}} \sec ^{2} \frac{4}{n^{2}}+\frac{3}{n^{2}} \sec ^{2}\right. \)
equals
A \( \cdot \frac{1}{2} \operatorname{cosec} 1 \)
B. \( \frac{1}{2} \) sec
c. \( \frac{1}{2} \tan 1 \)
D. \( \tan 1 \)


Ethylene reacts with bromine to form:
A. chloroethane
B. ethylene dibromide
c. cyclohexane
D. 1-bromo propane


The value of \( \sin 51^{\circ}+\cos 81^{\circ} \) is
A . \( \cos 21^{\circ} \)
B. \( \sin 21^{\circ} \)
\( \mathbf{c} \cdot \cos 42^{\circ} \)
\( \mathbf{D} \cdot \sin 42^{\circ} \)


A particle having charge \( q \) and mass \( m \) is projected with velocity \( \overrightarrow{\boldsymbol{v}}=2 \hat{\mathbf{i}}-\mathbf{3} \hat{\mathbf{j}} \)
in a uniform electric field \( \overrightarrow{\boldsymbol{E}}=\boldsymbol{E}_{0} \cdot \hat{\boldsymbol{j}} \)
Change in momentum \( |\Delta \bar{p}| \) during any
time interval \( t \) is given by:
A \( \cdot \sqrt{q E_{0} t} \)
в. \( q E_{0} \)
c. \( \frac{q E_{0} t}{m} \)
D. zero


For the reaction \( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{I}_{2}(\boldsymbol{g}) \rightleftharpoons \)
\( 2 H I(g) K_{i}=66.9 \) at \( 350^{\circ} \mathrm{C} \) and \( K_{i}= \)
\( \mathbf{5 0 . 0} \) at \( 448^{\circ} \) C. The reaction has:
\( \mathbf{A} \cdot \Delta H=+v \)
в. \( \Delta H=- \) ve
c. \( \Delta H=z \) ro
D. none of the above


Which one of the following is best condition for the plane \( a x+b y+c z+ \)
\( d=0 \) to intersect the \( x \) and \( y \) axes at
equal angle
A \( \cdot|a|=|b| \)
\( b \mid \)
B . \( a=-b \)
c. \( a=b \)
D. \( a^{2}+b^{2}=1 \)


In the leaching of \( A g_{2} S \) with \( \mathrm{NaCN} \)
a stream of air is also passed. Which of the following is the correct explanation for this step?
A. Reversible nature of reaction between \( A g_{2} S \) and \( ^{N a C N} \)
B. To oxidize \( N a_{2} S \) formed into \( N a_{2} S O_{4} \) and sulphur
c. both (1) and (2)
D. both are not suitable


\( 1 A^{\circ} \) is
\( A \cdot 10^{-6} m \)
\( B \cdot 10^{-9} m \)
\( \mathbf{C} \cdot 10^{-10} \mathrm{m} \)
\( D \cdot 10^{-3} m \)


Which of the following functions from \( Z \)
to itself are bijections?
\( \mathbf{A} \cdot f(x)=x^{3} \)
B. \( f(x)=x+2 \)
c. \( f(x)=2 x+1 \)
\( \mathbf{D} \cdot f(x)=X^{2}+x \)


A person sitting in an open car moving at constant velocity throws a ball vertically up into air. Where will the ball
fall?
A. Outside the car
B. In the car ahead of the person
c. In the car to the side of the person
D. Exactly in the hand from which it was thrown up


CMC (Critical Micelle Concentration) is:
A. concentration at which micelles are destroyed
B. concentration at which micelles formation starts
C. concentration of electrolyte added to destroy the micelles
D. concentration of micelles at room temperature


toppr
Q Type your question
and \( B_{2} \) (dashed line). If \( B_{2} \) is larger than
\( B_{1} \) which of the following graphs shows
the correct variation of \( \boldsymbol{R} \) with \( \boldsymbol{T} \) in
these fields?
\( A \)
B.
\( c \)
D.


Ethanol burns to produce carbon dioxide and water and can be used as:
A . gas
B. fuel
c. antioxidant
D. free radical


The effective capacitance between \( \mathrm{P} \) and
Q of the figure below is :
\( C_{1}=C_{3}=C_{4}=C_{5}=10 \mu F \)
\( C_{2}=100 \mu F \)
A \( .10 \mu F \)
B. \( 40 \mu F \)
\( c .5 \mu F \)
D. \( 20 \mu F \)


In which bacteria, lipopolysaccharide is found as the main surface antigen?
A. Gram negative bacteria
B. Gram positive bacteria
c. cyanobacteria
D. All of the above


The shape of the top of a table in a
restaurant is that of a segment of a
circle with centre \( O \) and \( \angle B O D=90^{\circ} \)
f \( B O=O D=60 \mathrm{cm} . \) The perimeter of
the table is (Take \( \pi=\mathbf{3 . 1 4} \) )
A . \( 402 \mathrm{cm} \)
в. \( 402.6 \mathrm{cm} \)
c. \( 401 \mathrm{cm} \)
D. \( 400 \mathrm{cm} \)


The expression \( \frac{5-x}{x^{2}-x-20} \) when simplified equals
A \( \cdot \frac{1}{(x+4)} \)
в. \( \frac{1}{(x-4)} \)
c. \( -\frac{1}{(x+4)} \)
D. \( \frac{1}{(x-5)} \)


What is the length of small intestine in
an adult human being?
A. \( 3.5 \mathrm{m} \)
B. \( 6.5 \mathrm{m} \)
c. \( 4.5 \mathrm{m} \)
D. 2.5 \( m \)


What do you understand by the term Echolocation?


Write the three laws given by Kepler.


As per de Broglie's formula a
macroscopic particle of mass \( 100 g \) and
moving at a velocity of \( 100 \mathrm{cm} s^{-1} \) will have a wavelength of :
A \( \cdot 6.6 \times 10^{-29} \mathrm{cm} \)
B . \( 6.6 \times 10^{-30} \mathrm{cm} \)
c. \( 6.6 \times 10^{-31} \mathrm{cm} \)
D. \( 6.6 \times 10^{-32} \mathrm{cm} \)


Two cells of emf's \( 1.25 \mathrm{V} \) and \( 0.75 \mathrm{V} \) having equal internal resistance are connected in parallel. The effective emf is
A . \( 0.75 v \)
B. 1.25V
c. \( 2.0 v \)
D. 1.0v
E. \( 0.5 v \)


If \( f(x)=2 x-5, \) then what is the value
of \( \boldsymbol{f}(\mathbf{2})+\boldsymbol{f}(\mathbf{5}) ? \)
A .
B. 2
\( c \cdot 3 \)
D. 4
E . 5


Two small identical electrical dipoles
\( A B \) and \( C D \) each of dipole moment \( \vec{p} \)
are kept at an angle of \( 120^{\circ} \) as shown in
the figure. What is the resultant dipole moment of this combination ? If this
system is subjected to electric field \( (\vec{E}) \) directed along \( +\boldsymbol{X} \) direction, what will
be the magnitude and direction of the
torque acting on this?


A long wire carrying a current \( i \) is bent
to form a plane angle \( \alpha \). Find the
magnetic field \( B \) at point on the
bisector of this angle situated at a distance \( x \) from the vertex


Find the sum of \( 2,7,12, \ldots \) to 10 terms
A. 160
в. 245
\( c \cdot 290 \)
D. 300


Which kind of isomerism is exhibited
by octahedral \( \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Br}_{2}\right] \mathrm{Cl} \) ?
A. Geometrical and optical
B. Geometrical and ionsation
c. optical and ionisation
D. none of these


The vector equation of the line \( \frac{x-2}{2}= \) \( \frac{2 y-5}{-3}, z=-1 \) is \( \vec{r}= \)
\( \left(2 \hat{i}+\frac{5}{2} \hat{j}-\hat{k}\right)+\lambda\left(2 \hat{i}-\frac{3}{2} \hat{j}+x \hat{k}\right) \)
where \( x \) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B.
c. 2
D. 3


A \( 40 \mathrm{N} \) block is supported by two ropes. One rope is horizontal and the other
makes an angle of \( 30^{\circ} \) with the ceiling.
The tension in the rope attached to the ceiling is approximately:
A. 80 N
B. 40 N
c. \( 34.6 \mathrm{N} \)
D. 46.2 N


At \( 300 \mathrm{K} \), the vapour pressure of an ideal solution containing 3 mole of \( A \) and 2 mole of \( \mathrm{B} \) is 600 torr. At the same
temperature, if 1.5 mole of \( A \& 0.5 \) mole of \( \mathrm{B} \) (non-volatile) are added to this solution the vapour pressure of solution increases by 30 torr. What is the value
of \( P_{B}^{\circ} ? \)
A . 150
в. 405
c. 90
D. none of these


Le Chatelier's principle finds extensive
application in predicting the conditions for getting maximum yield of products in reactions of industrial importance.
If true enter 1 , if false enter 0 .


Let \( P \) and \( Q \) be two sets then what is
\( \left(\boldsymbol{P} \cap \boldsymbol{Q}^{\prime}\right) \cup(\boldsymbol{P} \cup \boldsymbol{Q})^{\prime} \) equal to \( ? \)
A \( \cdot\left(P \cap Q^{\prime}\right) \cup(P \cup Q)^{\prime}=\xi \cap Q^{\prime}=\xi \cap Q^{\prime}=\xi \)
B . \( \left(P \cup Q^{\prime}\right) \cup(P \cup Q)^{\prime}=\xi \cap Q^{\prime}=\xi \cap Q^{\prime}=\xi \)
C \( \cdot\left(P \cap Q^{\prime}\right) \cup(P \cap Q)^{\prime}=\xi \cap Q^{\prime}=\xi \cap Q^{\prime}=\xi \)
D. none of the above


At \( 25^{\circ} C, \) the solubility product of \( C u C l \)
is \( 2.0 \times 10^{-7} \) and \( E_{C l^{-}|C u C l| C u}^{\circ} \) is
\( 0.128 V . \) The value of \( E_{C u^{+} / C u}^{\circ} \) is:
\( [(\log 2=0.3),(2.303 R T / F=0.06)] \)
A. \( -0.274 V \)
в. \( -0.402 \mathrm{V} \)
\( \mathbf{c} .+0.53 V \)
D. \( +0.402 \mathrm{V} \)


Sum the following series to n terms:
\( \mathbf{3}+\mathbf{5}+\mathbf{9}+\mathbf{1 5}+\mathbf{2 3}+\dots \)
A \( \cdot \frac{n}{3}\left(n^{2}-8\right) \)
В \( \cdot \frac{n}{3}\left(n^{2}+8\right) \)
c. \( \frac{n}{2}\left(n^{3}+8\right) \)
D. None of these


Two like magnetic poles of strength 10 and \( 40 S I \) units are separated by a
distance \( 30 c m . \) The intensity of magnetic field is Zero on the line joining them.
A. At a point \( 10 \mathrm{cm} \) from stonger pole.
B. At a point \( 20 \mathrm{cm} \) from stonger pole.
c. At a mid-point.
D. At infinity.


The value of \( \cos \left(-1044^{\circ}\right) \) is \( \frac{(\sqrt{5}+1)}{4} \)
A . True
B. False


A straight line and a point not lying on it
are given on a plane. Find the set of
points which are equidistant from the given straight line and the given point.


The atmospheric pressure remains unchanged throughout the earth's atmosphere.
A. True
B. False


On which principle A.C generator
works?


By using elementary transformation find the inverse of \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{2} \\ \mathbf{2}-\mathbf{1}\end{array}\right] \)


Mark the incorrect statement:
A. The principal focus of a spherical mirror lies midway between the pole and centre of curvature
B. For spherical mirrors of small aperture, \( R=\frac{f}{2} \)
C. Centre of curvature lies outside its reflecting surface
D. All


Write notes on Brownian movement.


If \( \frac{1}{(1-2 x)(1+3 x)}=\frac{A}{1-2 x}+\frac{B}{1+3 x} \)
then \( 2 B= \)
\( A \cdot A \)
B. 2A
\( c \cdot 3 A \)
D. -3A


I.F. of \( \frac{d y}{d x}+y \tan x=x^{2} \cos ^{2} x \) is:
A . sec
B. \( \cos x \)
\( \mathbf{c} \cdot \sec ^{2} x \)
D. \( \cos ^{2} x \)


Choose the correct option about light.
A. Light requires a material medium to travel from one place to another
B. Light does not require a material medium to propagate
c. Light has mass but it is negligible
D. Light waves are longitudinal wave


What is Primary Battery? Give one
example.


Energy required to move a body of mass
\( \mathrm{m} \) from an orbit of radius \( 2 \mathrm{R} \) to \( 3 \mathrm{R} \) is:
\( ^{\mathbf{A}} \cdot \frac{G M m}{12 R^{2}} \)
в. \( \frac{G M m}{3 R^{2}} \)
c. \( \frac{G M m}{8 R} \)
D. \( \frac{G M m}{6 R} \)


Which of the following is wrong about the carbohydrate?
A. Starch is a carbohydrate
B. Carbohydrates are produced in photosynthesis
c. cellulose is not a carbohydrate
D. Carbohydrates are also called as saccharides


Proximal convoluted tubule (PCT) is
lined with
A. Cuboidal epithelium
B. Simple brush border epithelium
c. simple cuboidal brush border epithelium
D. Simple ciliated brush border epithelium
E. Columnar epithelium


The interior angles of a pentagon are in the ratio \( 4: 5: 6: 7: 5 . \) Find each angle
of the pentagon
A \( \cdot 80^{\circ}, 100^{\circ}, 120^{\circ} 140^{\circ} \) and \( 100^{\circ} \)
\( ^{\circ} \)
В. \( 100^{\circ}, 120^{\circ}, 110^{\circ}, 140^{\circ} \) and \( 100^{\circ} \)
D. none of the above


Ajit buys a motor cycle for Rs. 17,600 including sales tax. If the rate of sales \( \operatorname{tax} \) is \( 10 \%, \) then the sale price of the motor cycle is:
A . Rs. 16,000
B. Rs. 15,000
c. Rs. 14,000
D. Rs. 12,000


Uniform rod of mass \( m \), length \( l \), area of
cross-section \( \boldsymbol{A} \) has Young's modulus \( \boldsymbol{Y} \) If it is hanged vertically, elongation under its own weight will be :
\( ^{\text {A }} \cdot \frac{m g l}{2 A Y} \)
в. \( \frac{2 m g l}{A Y} \)
c. \( \frac{m g l}{A Y} \)
D. \( \frac{m g Y}{A l} \)


The area of the plane region bounded by the curves \( x+2 y^{2}=0 \) and \( x+3 y^{2}= \)
1 is equal to
A \( \cdot \frac{5}{3}^{\operatorname{sq} . u n i t} \)
в. \( \frac{1}{3} \) sq.unit
c. \( \frac{2}{3} \) squnit
D \( \cdot \frac{4}{3} \) sq.unit


Traces of molybdenum are used with finely divided iron which acts as a
catalyst during Haber's process for the synthesis of ammonia. Here molybdenum:
A. acts as a promoter to increase the activity of the catalyst
B. acts as a poison to decrease the activity of the catalyst
c. provides a new pathway to the reaction
D. forms another intermediate compound with lesser activation energy


The ratio of speed of sound in a gas to
that in water vapours at any temperature is. (when molecular weight of gas is 40 gm/mol and for water vapours is 18 gm/mol)
A . 0.75
B. 0.73
\( c \cdot 0.68 \)
D. none of these


Diffrentiate w.r.t \( x: \)
\( \boldsymbol{y}=e^{2 x}(\boldsymbol{a}+\boldsymbol{b} \boldsymbol{x}) \)


\( f \angle 2=(3 x-10)^{\circ} \) and \( \angle 8=(5 x-30)^{\circ} \)
find the measures of \( \angle 2 \) and \( \angle 8 \)
This question has multiple correct options
\( \mathbf{A} \cdot \angle 2=20^{\circ} \)
\( \mathbf{B} \cdot \angle 8=20^{\circ} \)
\( \mathbf{c} \cdot \angle 2=40^{\circ} \)
D. \( \angle 8=40^{\circ} \)


The plane of a mirror makes an angle
\( 30^{\circ} \) with borizontal. If any vertical ray is incident on the mirror, then angle made by the reflected ray on plane mirror will be-
\( A \cdot 30 \)
B . 45
\( c \cdot 60 \)
D. \( 90^{\circ} \)


An ellipse, with foci at (0,2) and (0,-2) and mirror axis of length \( 4, \) passes through which of the following points?
A \( \cdot(1,2 \sqrt{2}) \)
B. \( (2, \sqrt{2}) \)
D. \( (\sqrt{2}, 2) \)


Determine if the points (5,-1,1),(7,-4,7),(1,-8,10) and
(-1,-3,4) are the vertices of a rhombus or a square


An electric field \( \boldsymbol{E} \) and a magnetic field
\( B \) act over the same region in which an electron enters along the \( x \) -axis. The
combination of \( E \) and \( B \) which
permits the electron to go undeflected
is:
A. \( E \) along \( Y \) -axis and \( B \) along \( Y \) -axis
B. \( E \) along \( Y \) -axis and \( B \) along \( Z \) -axis
c. \( E \) along \( X \) -axis and \( B \) along \( Z \) -axis
D. \( E \) along \( Y \) -axis and \( B \) along \( X \) -axis


What is the modal class for the
following distributions?
\( \begin{array}{llll}\text { Class } & \mathbf{2 2}- & \mathbf{3 3}- & \mathbf{4 4}- \\ \text { interval } & \mathbf{3 3} & \mathbf{4 4} & \mathbf{5 5}\end{array} \)
Frequency 23 45 67
A \( .55-66 \)
в. \( 66-77 \)
c. \( 77-88 \)
D. \( 88-99 \)


In a meter bridge, the wire of length \( 1 \mathrm{m} \)
has a non-uniform cross-section such
that, the variation \( \frac{d R}{d l} \) of its resistance \( R \) with length \( l \) is \( \frac{d R}{d l} \propto \frac{1}{\sqrt{l}} . \) Two equal
resistances are connected as shown in
the figure. The galvanometer has zero deflection when the jockey is at point \( P \) What is the length \( A P: \)
\( A \cdot 0.2 m \)
В. \( 0.3 m \)
c. \( 0.25 m \)
D. \( 0.35 m \)


What indicate \( X, Y \) in the given
diagram?
A. x-cell surface membrane Y-Plasmodesma
B. X-Plasmodesma Y-Tonoplast
c. x-cell surface membrane Y-Cytoplasm
D. x-Plasmodesma Y-Cell surface membran


Non-Lanthanoid atom is:
A . La
B . Lu
\( c \cdot P r \)
D. Pm


Reciprocal of radioactive decay
constant is
A. Half life period
B. Whole life period
c. Average life period
D. Avagadro number


How many diagonals does a triangle have?
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
\( D \)


Dissociation of \( \boldsymbol{F e}(\boldsymbol{O H})_{3} \) will be least
in:
A. \( 0.1 M \) NaOH
в. \( 0.1 M \) НС\( l \)
\( \mathbf{c} \cdot 0.1 M B a(O H)_{2} \)
D. \( H_{2} O \)


All enzymes of TCA cycle are located in the mitochondrial matrix except one which is located in inner mitochondrial
membranes in eukaryotes and in the cytosol in prokaryotes. This enzyme is
A. Lactate dehydrogenase
B. Isocitrate dehydrogenase
C. Malate dehydrogenase
D. succinate dehydrogenase


Magnetic dipole moment is a:
A. Scalar quantity
B. Vector quantity
C. Constant quantity
D. None of these


A force vector is acting on a unit length
of a thin wire, carrying a current \( \boldsymbol{I}= \)
\( 80 A, \) at a point \( O . \) Find the magnitude
and direction of the force vector, if the
wire is bent as shown in figure above, the distance between the long parallel
segments of the wire being equal to \( l= \)
\( \mathbf{2 0} \boldsymbol{c m} \)
A. \( 1.3 N \)
B. \( 0.26 N \)
c. \( 2.6 N \)
D. \( 0.013 N \)


Which phenomena of light makes a pool of water appears to be less deep than it actually is?
A. Reflecion
B. Refraction
c. Diffraction
D. Lateral inversion


State True or False.
Oxides of the s-block metals are
strongly acidic and from salts with
basic oxides.


What happens to the rate of evaporation of water, if the atmospheric pressure is decreased during the extraction of colored components?
A. Increases
B. Decreases
c. Do not change
D. None


Indian Monkey is
A. Macaca
B. Gorilla
c. Ramapithecus
D. Simia


A ball of radius R carries a positive charge whose volume charge density depends only on the distance r from the ball's centre as: \( \rho=\rho_{0}\left(1-\frac{r}{R}\right) \) where
\( \rho_{0} \) is constant. Assume \( \epsilon \) as the
permittivity of the ball.
Then the magnitude of the electric field as a function of the distance r outside
the ball is given by :
A. \( \quad E=\frac{\rho_{0} R^{3}}{8 \epsilon r^{2}} \)
в. \( \quad E=\frac{\rho_{0} R^{3}}{12 r r^{2}} \)
c. \( _{E=\frac{\rho_{0} R^{3}}{16 \epsilon^{2}}} \)
D. \( \quad E=\frac{\rho_{0} R^{3}}{24 r^{2}} \)


Sublimation requires additional energy and is an:
A. endothermic change
B. exothermic change
\( c . \) both a and \( b \)
D. none of above


Which of the following is not a monosaccharide?
A. Glucose
B. Fructose
c. Glyceraldehyde
D. sucrose


What happen to the image, if a convex lens is made up of two different transparent material, as shown in
figure?


A coil of inductance 1 henry and
resistance \( 10 \Omega \) is connected to an ideal
battery of emf \( 50 \mathrm{V} \) at time \( t=0 \)

Calculate the ratio of the rate at which
magnetic energy is stored in the coil to the rate at which energy is supplied by the battery at \( t=0.1 \) sec.
A.
в. \( \frac{1}{e-1} \)
\( c \cdot_{1-\frac{1}{e}} \)
\( D \cdot \frac{1}{e} \)


\( \Delta A B C \) fig. \( 2, \angle x+\angle y+\angle z \) is equals
A \( \cdot 120^{\circ} \)
B. \( 180^{\text {? }} \)
\( c \cdot 240 \)
D. 360


Product of sexual reproduction
generally generates
A. Prolonged dormancy
B. New genetic combination leading to variation
c. Large biomass
D. Longer viability of seeds


Density of a material varies with
temperature.
A . True
B. False


Mendeleev classified elements in:
A. increasing order of atomic groups.
B. seven periods and eight groups.
C. seven periods and nine groups
D. eight periods and seven groups


If \( \cos \left(2 \sin ^{-1} x\right)=\frac{1}{9}, \) the value of \( x \)
which satify equation is \( \pm \frac{a}{b} . \) Find the value of \( a+b \)
A . 2
B. 3
\( c \cdot 4 \)
D.


When a dielectric slab of thickness \( 4 \mathrm{cm} \)
is introduced between the plates of parallel plate condenser, it is found that
the distance between the plates has to be
increased by \( 3 \mathrm{cm} \) to restore the capacity to it's original value. The dielectric
constant of the slab is
A \( \cdot \frac{1}{4} \)
B. 4
\( c .3 \)
D.


The phenomena of a electromagnetic
induction is
A. The process of charging a body
B. The process of generating magnetic field due to current passing through a coil
C. Producing induced current in a coil due to relative motion between a magnet and a coil
D. All the above


A ball thrown from point \( A \) making an
angle \( 60^{\circ} \) with the line \( O A S \) as shown
in the figure, where \( O A=\frac{R}{\sqrt{3}}(O \) is the
centre of spherical surface of \( \boldsymbol{P} \boldsymbol{Q} \boldsymbol{S} \) ). If after striking the hemispherical surface, the ball rebounds in direction
parallel to \( O A \). Find the coefficient of restitution between the ball and the
surface. (Neglect the effect of gravity and any type of frictional force


In a Wheatstone bridge \( P=10 \Omega, Q=20 \Omega \)
\( \mathrm{R}=30 \Omega \). The value of 'S' in order that no
current flows through the galvanometer
is :
A . \( 15 \Omega \)
B. \( 45 \Omega \)
\( c \cdot 30 \Omega \)
D. \( 60 \Omega \)


The treatment of a compound \( X \) with
\( H I O_{4} \) produces \( C H_{3} C H O \) and
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H O} \). The compound \( \mathbf{X} \) is :
A. \( C H_{3} C H=C H C H_{2} C H_{3} \)
в. \( C H_{3} C H(O H) C H(O H) C H_{2} C H_{3} \)
c. \( C H_{3} C H=C H C H=C H_{2} \)
D. \( C H_{3} C H(O H) C H_{2} C H O \)


If \( \boldsymbol{A}=\left[\boldsymbol{a}_{i j}\right] \) is a scalar matrix of order
\( \boldsymbol{n} \times \boldsymbol{n} \) such that \( \boldsymbol{a}_{\boldsymbol{i} i}=\boldsymbol{k} \) for all \( \boldsymbol{i}, \) then
trace of \( \boldsymbol{A} \) is equal to
\( \mathbf{A} \cdot n k \)
\( \mathbf{B} \cdot n+k \)
c. \( \frac{n}{k} \)
D. None of these


Two men enter a railway compartment
having 6 seats unoccupied. In how
many ways can they are seated?


A block of mass \( 1 \mathrm{kg} \) slides down a curved track which forms one quadrant of a circle of radius \( 1 \mathrm{m} \) as shown in
figure. The speed of the block at the
bottom of the track is \( v=2 m s^{-1} \). The
work done by the force of friction
is (Take \( \left.g=10 m s^{-2}\right) \)
\( A \cdot+4 J \)
B. - -4
\( c \cdot-8 \)
D. +83


Which of the following statement (s) differentiate between electrochemical
cell and electrolytic cell? This question has multiple correct options
A. Spontaneous or non-spontaneous nature of the chemical process.
B. Chemical reactions occurring at the electrodes
c. Positive and negative nature of anode
D. Dependence on Faraday's law


Find the value of \( \left(\frac{1-i}{1+i}\right)^{40} \)


A coil of 1200 turns and mean area of
\( 500 \mathrm{cm}^{2} \) is held perpendicular to a uniform magnetic field of induction
\( 4 \times 10^{-4} \mathrm{T} . \) The resistance of the coil is
20 ohms. When the coil is rotated
through \( 180^{0} \) in the magnetic field in 0.1
s, the average electric current (in \( \mathrm{mA} \) ) induced is :
A \( \cdot 12 \)
B. 24
\( c . \) 36
D. 48


\( \operatorname{Let} \boldsymbol{y}=\sqrt{\frac{(\boldsymbol{x}+\mathbf{1})(\boldsymbol{x}-\mathbf{3})}{\boldsymbol{x}-\mathbf{2}}} \)
Find all the real values of \( x \) for which \( y \)
takes real values.


\( \boldsymbol{H}^{+}, \boldsymbol{D}^{+}, \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \boldsymbol{T}^{+} \) differ in:
A. number of electrons
B. number of neutrons
c. number of proton
D. all are correct


Assertion
A catalyst always lowers the energy of activation.
Reason
Catalyst interact with reactant molecules to form adsorbed activated
complex with evolution of energy
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 and Reason both are incorrect


If \( \alpha, \beta, \gamma, \delta \) are in arithmetic
progression. Then which is of the following is correct
A. \( \tan (\alpha+\delta)=\tan (\beta+\gamma) \)
B. \( \tan (\alpha+\gamma)=\tan (\beta+\delta) \)
c. \( \tan (\alpha+\beta)=\tan (\gamma+\delta) \)
D. none of these


Compound \( [A] \) is an aromatic amine
which react with \( N a N O_{2}+H C l \) at
\( 273-278 K \) and form compound \( [B] \)
Compound \( [\boldsymbol{B}] \) react with \( \boldsymbol{H} \boldsymbol{B} \boldsymbol{F}_{4} \) and
the obtain product on further heating, in
the presence of \( N a N O_{2} \) and confirm
compound \( [C] . \) Compound \( [C] \) reduced
in the presence of \( \boldsymbol{S n} / \boldsymbol{H} \boldsymbol{C l} \) to reformed compound \( [\boldsymbol{A}] . \) Write general
name of \( ^{\prime} A^{\prime},^{\prime} B^{\prime} \) and \( ^{\prime} C^{\prime} \) and write
equation of all reaction involved?


A circular coil of radius \( 10 \mathrm{cm}, 500 \)
turns and resistance \( 2 \Omega \) is placed with its plane perpendicular to the horizontal component of the earth's magnetic field It is rotated about its vertical diameter
through \( 180^{\circ} \) in 0.25 s. Estimate the
magnitudes of the emf and current
induced in the coil. Horizontal
component of earth's magnetic field at the place is \( 3.0 \times 10^{-5} \mathrm{T} \)


When an AC voltage of \( 220 \mathrm{V} \) is applied to the capacitor \( C \), then
A. the maximum voltage between plates is 220 v.
B. the current is in phase with the applied voltage
c. the charge on the plate is not in phase with the applied voltage
D. power delivered to the capacitor per cycle is zero


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


Name the radiation which can be
detected by a solution of silver chloride.
A. X-ray radiation
B. ultraviolet radiation
c. infrared radiation
D. visible radiation


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


The vapor pressure of water at \( 80^{\circ} \mathrm{C} \) is
355 torr. \( A \) 100 \( m l \) vessel contained
water-saturated oxygen at \( 80^{\circ} \mathrm{C} \) the
total gas pressure being 760 torr. The contents of the vessel were pumped into a \( 50.0 \mathrm{ml} \), vessel at the same
temperature, What were the partial pressure of oxygen and of water vapor
what was the total pressure in the final equilibrated state? Neglect the volume of any water which might condense.


What is a lone pair of electrons?


\[
\begin{array}{l}
\boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{O H} \quad \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}- \\
\boldsymbol{\oplus} \boldsymbol{H}_{2} \quad \boldsymbol{C H}_{3}-\boldsymbol{O}-\boldsymbol{C H}_{3}
\end{array}
\]
\( \boldsymbol{I} \)
III
The order that has the following compounds correctly arranged with respect to increasing acidity is:
A. is iis iii
B. isilisi
\( c . \) iiciciii
D. iiisisi


Which of the following is more acidic in its aqueous solution?
A. \( H_{2} O \)
в. \( H_{2} S \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{Se} \)
D. \( H_{2} T e \)


To an \( A g_{2} C r O_{4} \) solution over its own
precipitate, \( C r O_{4}^{2-} \) ions are added. This results in:
A . increase in \( A g^{+} \) concentration
B. decrease in concentration
c. increase in the solubility product
D. decrease in the solubility product


Mercury is often used in clinical thermometers.Which one of the
following properties of mercury is not a reason for this ?
A. The coefficient of the thermal expansion is large
B. It is shiny
c. It is a liquid at room temperature
D. It has high density


Show that period of a satellite revolving around the Earth depends upon mass of
the Earth.


Find three different solution of the each
of the equation. \( 3 x+4 y=7 \)


In the fig. Straight lines \( A B \& C D \) pass
through centre \( O . \) If angle \( \angle D C E=40^{\circ} \)
\( \& \angle A O D=75^{\circ} \)
Find \( \angle C D E \& \angle O B E \)


Two waves are propagating along a taut string that coincides with the \( x \) -axis. The first wave has the wave function
\( \boldsymbol{y}_{1}=\boldsymbol{A} \cos [\boldsymbol{k}(\boldsymbol{x}-\boldsymbol{v} \boldsymbol{t})] \) and the second
has the wave function \( y_{2}=A \cos [k(x+ \)
\( \boldsymbol{v} \boldsymbol{t})+\boldsymbol{\phi}] \)
A. For constructive interference at \( x=0, \phi=\pi \)
B. For constructive interference at \( x=0, \phi=3 \pi \)
c. For destructive interference at \( x=0, \phi=\pi \)
D. For destructive interference at \( x=0, \phi=2 \pi \)


The rate law of the reaction
\( \boldsymbol{C}_{2} \boldsymbol{H}_{4} \boldsymbol{B} \boldsymbol{r}_{2}+\boldsymbol{3} \boldsymbol{l}^{-} \rightarrow \boldsymbol{C}_{2} \boldsymbol{H}_{4}+\boldsymbol{2} \boldsymbol{B} \boldsymbol{r}^{-}+ \)
\( \boldsymbol{I}_{3}^{-} \) is rate \( =\boldsymbol{k}\left[\boldsymbol{C}_{2} \boldsymbol{H}_{4} \boldsymbol{B} \boldsymbol{r}_{2}\right]\left[\boldsymbol{I}^{-}\right] . \) The rate of
reaction is found to be \( 1.1 \times 10^{-4} M / s \)
when the concentrations of \( C_{2} H_{4} B r_{2} \)
and \( I^{-} \) are \( 0.12 \mathrm{M} \) and \( 0.18 \mathrm{M} \)
respectively. Calculate the rate constant of the reaction.
\( \mathbf{A} \cdot 4.27 \times 10^{-3} M^{-1} s^{-1} \)
B . \( 1.65 \times 10^{-3} M^{-1} s^{-1} \)
C \( .5 .1 \times 10^{-3} M^{-1} s^{-1} \)
D. None of these


Which of the following statements
is/are not correct?
This question has multiple correct options
A. A catalyst always increases the speed of a reaction.
B. A catalyst does not take part in the reaction.
C. A catalyst may affect the nature of the products formed.
D. A catalyst is always an external substance added to the reaction mixture.


A 2 kg mass moving on a smooth frictionless surface with a velocity of \( 10 m s^{-1} \) hits another 2 kg mass kept at rest, in an inelastic collision. After
collision, if they move together,
A. they travel with a velocity of \( 5 m s^{-1} \) in the same direction
B. they travel with a velocity of \( 10 \mathrm{ms}^{-1} \) in the same direction
c. they travel with a velocity of \( 10 m s^{-1} \) in the opposite direction
D. they travel with a velocity of \( 5 m s^{-1} \) in the opposite direction


The sum of the coefficients in the first,
second, and third terms of the expansion of \( \left(x^{2}+\frac{1}{x}\right)^{m} \) is equal to 46 Find the term of the expansion which does not contain \( x \)


Line \( L \) passes through the points
(4,-5) and \( (3,7) . \) Find the slope of any line perpendicular to line \( \boldsymbol{L} \)
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{4} \)
\( c \cdot \frac{1}{8} \)
D. \( \frac{1}{12} \)


The sum of the co-efficients of all odd
degree terms in the expansion of \( (x+\sqrt{x^{3}-1})^{5}+(x+\sqrt{x^{3}-1})^{5} \)
\( (x>1) \) is:
A . 2
B. -
\( c \cdot 0 \)
\( D \)


Identify the metal which neither shows malleability nor ductility.
A. copper
B. Leadd
c. zinc
D. Aluminium


Which of the following gives an alkaline gas on hydrolysis?
A \( \cdot P C l_{3} \)
в. \( B i C l_{3} \)
c. \( N C l_{3} \)
D. \( P B r_{3} \)


The only requirement of an ecosystem is a constant input of energy that comes by the process of respiration
A. True
B. False


A farmer bought a cow and a calf together for Rs. \( 14000 . \) After some time, he sold the cow at a profit of \( 20 \% \) and the calf at a profit of \( 13 \% \). On the whole he got a profit of \( 17 \% \). Find the cost price of the cow and the calf.
A. Rs. 8000, Rs. 6000
B. Rs. 6000, Rs. 6000
c. Rs. 8000, Rs. 8000
D. Rs. 9000, Rs. 5000


wavelength \( 6000 A \) is placed at a very
small height h above a flat reflecting
surface \( M N \) as shown in the figure. The
intensity of the reflected light is \( 36 \% \) of the incident intensity. Inference fringes
are observed on a screen placed paralle to the reflecting surface at a very large
distance \( D \) from it. If the intensity at \( p \)
be maximum, then the minimum
distance through which the reflecting
surface \( M N \) should be displaced so
that at \( P \) again becomes maximum?
\( A \cdot 3 \times 10^{-7} \mathrm{m} \)
B . \( 6 \times 10^{-7} \mathrm{m} \)
C. \( 1.5 \times 10^{-7} \mathrm{m} \)
D. \( 12 \times 10^{-7} \mathrm{m} \)


Dimensional formula for the universal
gravitational constant \( G \) is
A \( \cdot M^{-1} L^{2} T^{-2} \)
B . \( M^{0} L^{0} T^{0} \)
c. \( M^{-1} L^{3} T^{-2} \)
D. \( M^{-1} L^{3} T^{-1} \)


Rub a glass rod with a piece of silk. What happens?
A. the glass has a slightly positive charge and the silk is also slightly positive
B. the glass has a slightly positive charge and the silk is slightly negative
C. the glass has a slightly negative charge and the silk is also slightly negative
D. the glass has a slightly negative charge and the silk is slightly positive


Which one of the following is an
artificial sweetening agent?
\( A \)
B.
\( c \)
D.


An object launched straight up into the air is said to have parabolic motion (because it goes up, reaches a maximum height, and then comes back down). The height (h) of a projectile at time \( t \) is given by the equation \( h= \) \( \frac{1}{2} g t^{2}+u t+h_{0}, \) where \( g \) is the
acceleration due to gravity and \( u \) and \( h_{0} \) are the object's initial velocity and initial height, respectively. Which of the following equations correctly represents the object's acceleration due to gravity in terms of the other variables?
A \( \cdot g=\frac{h-u t-h_{0}}{t} \)
B. \( g=\frac{h-u t-h_{0}}{2 t^{2}} \)
c. \( g=\frac{2\left(h-u t-h_{0}\right)}{t^{2}} \)
D. \( g=t \sqrt{2\left(h-u t-h_{0}\right)} \)


The magnetic moment of \( \left[N i X_{4}\right]^{2-} \) ion
is found to be zero. Then the metal of the
complex ion is \( (X= \) monodentate anionic ligand ).
A \( \cdot s p^{3} \) hybridised
B \( \cdot s p d^{2} \) hybridised
c. \( d s p^{2} \) hybridised
D. \( d^{2}^{2} p \) hybridised


An electron in hydrogen atom is excited to 'N' shell. What are the possible
transitions it can undergo? Compare the energies of transitions.
A. 3 transitions, energies goes on decreasing
B. 2 transitions, energies goes on decreasing
c. 3 transitions, energies goes on increasing
D. 2 transitions, energies goes on increasing


The figure below is the sectional view of
a part of the skull showing a sense
organ:
(i) Name the sense organ.
(ii) What are the parts labelled "m", "i"
and "s"? What do these three parts
constitute collectively?
(iii) What do you call the part shown in the form of a spiral? What is its function?
(iv) Name the part labelled "tm"? What
is its function?
TUBE


Assertio
A block of mass \( m \) starts moving on a
rough horizontal surface with a velocity
\( v . \) It stops due to friction between the
block and the surface after moving through a certain distance. The surface
is now tilted to an angle of \( 30^{\circ} \) with the horizontal and the same block is made
to go up on the surface with the same
initial velocity \( v \). The decrease in the
mechanical energy in the second situation is smaller than that in the
first situation.
Reason
The coefficient of friction between the
block and the surface decreases with
the increase in the angle of inclination
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 stone attains a momentum of
1 kg m/s when it flies with a velocity of \( 2 m / s, \) then what will be the mass of the
stone?
A. \( 500 g \)
в. \( 2 k g \)
\( c \cdot 2 g \)
D. None


Considering the state of hybridization of carbon atoms, the molecule among the following which is linear is :
A \( \cdot C H_{3}-C H \equiv C H-C H_{3} \)
в. \( C H_{3}-C H=C H-C H_{3} \)
c. \( C H_{2}=C H-C H_{2}-C \equiv C H \)
D. \( C H_{3}-C H_{2}-C H_{2}-C H_{3} \)


If an ideal gas, at constant temperature and pressure, expands, then its
A. entropy increases and then decrease
B. internal energy increases
C. internal energy remains the same
D. internal energy decreases


The value of \( x \) satisfying \( \tan \left(\sec ^{-1} x\right)=\sin \left(\cos ^{-1} \frac{1}{\sqrt{5}}\right) \) is
\( ^{A}+\frac{3}{\sqrt{5}} \)
\( ^{\mathrm{B}} \pm \frac{5}{\sqrt{3}} \)
c. \( =\frac{\sqrt{2}}{3} \)
D. \( \pm \frac{3}{5} \)


Calculate the \( p H \) of a \( 0.033 \mathrm{M} \)
ammonia solution, if \( 0.033 \mathrm{M} N H_{4} C l \) is introduced in this solution at the same
temperature. \( \left(k_{b} \text { for } N H_{3}=1.77 \times\right. \)
\( \left.10^{-5}\right) \)


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


Assertion
The earth's magnetic field is due to iron present in its core.
Reason
At a high temperature magnet losses its magnetic property or magnetism.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


State True or False.
The Schrodinger equation restricts the electron in a \( \boldsymbol{H} \) -atom to certain sharp
orbits.
A. True
B. False


If \( f(x)=3 x-7, \) then what is \( f \)
chickpea \( ) ? \)
A. \( 3 \times \) chickpea -7
B. chickpea -
c. chickpea
D. chickpea +7


Which of the following is NOT an
application of ultrasound waves?
\( A \)
в.
\( c \)
\( D \)


toppr
Q Type your question
(iii) \( \mathrm{CH}_{3} \mathrm{MgBr} \)
\( (\mathrm{iv}) \mathrm{H}_{3} \mathrm{O}^{8} \)
\( A \)
\( B \)
\( c \)
\( D \)


The unit vector perpendicular to the plane containing \( \overrightarrow{\boldsymbol{A}}, \overrightarrow{\boldsymbol{B}} \) such that \( \overrightarrow{\boldsymbol{A}}= \)
\( 4 \hat{i}-\hat{j}-\hat{k} \) and \( \vec{B}=4 \hat{i}+\hat{j}-4 \hat{k} \) is:
\( \frac{5 \hat{i}-5 \hat{j}+5 \hat{k}}{\sqrt{3}} \)
B. \( \frac{5 \hat{i}+12 \hat{j}+8 \hat{k}}{\sqrt{233}} \)
c. \( \frac{\hat{i}+3 \hat{j}+\hat{k}}{11} \)
D. \( 5 \hat{i}-5 \hat{j}+5 \hat{k} \)


In plant taxonomy, a division is the equivalent to
A. Family
B. Order
c. class
D. Phylum


For a current carrying inductor, emf associated in \( 20 m V . \) Now, current
through it changes from \( 6 A \) to \( 2 A \) in \( 2 s \) The coefficient of mutual inductance is
\( \mathbf{A} \cdot 20 m H \)
в. \( 10 m H \)
\( \mathbf{c} \cdot 1 m H \)
D. \( 2 m H \)


What is the difference of frequencies of
the intervals \( 30-40 \) and \( 40-50 ? \)
A . 5
B. 20
c. 15
D. 25


The main oxides formed on combustion
of \( L i, N a \) and \( K \) in excess of air are
respectively:
A. \( L i O_{2}, N a_{2} O_{2} \) and \( K_{2} O \)
в. \( L i_{2} O_{2}, N a_{2} O_{2} \) and \( K O_{2} \)
c. \( L i_{2} O, N a_{2} O_{2} \) and \( K O_{2} \)
D. \( L i_{2} O, N a_{2} O \) and \( K O_{2} \)


Which one of the following statements is true for ammonium ion?
A. All bonds are ionic
B. All bonds are coordinate covalent
c. \( H \) atoms are situated at the corners of a square
D. \( H \) atoms are situated at the corners of a tetrahedron


The number of ways of distributing 12 identical oranges among 4 children so
that every child gets at least one orange
and none of the child gets more than 4
is
A. 3
B. 52
\( c .35 \)
D. 42


The electrical resistance in ohms of a
certain thermometer varies with
temperature according to the
approximate law: \( \boldsymbol{R}=\boldsymbol{R}_{0}[\mathbf{1}+\mathbf{5} \times \)
\( \left.10^{-3}\left(T-T_{0}\right)\right] . \) The resistances is
\( 101.6 \Omega \) at the triple-point of water \( 273.16 \mathrm{K}, \) and \( 165.5 \Omega \) at the normal
melting point of lead \( (600.5 K) \). the temperature when the resistance is
\( 123.4 \Omega \) is \( (360+x)^{o} c \) then the value of \( x \)
is


If \( \boldsymbol{A}=\left[\begin{array}{lll}\boldsymbol{a}^{2} & \boldsymbol{a b} & \boldsymbol{a c} \\ \boldsymbol{a b} & \boldsymbol{b}^{2} & \boldsymbol{b c} \\ \boldsymbol{a c} & \boldsymbol{b c} & \boldsymbol{c}^{2}\end{array}\right] \) and \( \boldsymbol{a}^{2}+\boldsymbol{b}^{2}+ \)
\( c^{2}=1 \) then \( A^{2}= \)
A \( .2 A \)
в.
\( c .3 A \)
D. \( \frac{1}{2} \)


A dies is thrown three times and the
sum of three numbers obtained is 15
The probability of first throw being 5 is:
A \( \cdot \frac{3}{10} \)
B. \( \frac{2}{5} \)
c. \( \frac{1}{5} \)
D. \( \frac{4}{5} \)


Mirage is a phenomenon due to:
A. refraction of light
B. reflection of light
C. total internal reflection of light
D. diffraction of light


If true enter 1 , else enter 0 .
The energy of the resonance hybrid may
be more than that of any of the
individual Lewis formula.
A.


The given relation is \( (1+\tan a+ \)
\( \cos a)(\sin a-\cos a)=2 \sin a \tan a- \)
cat \( a \cos a \)
A. True
B. False


\( \lim _{n \rightarrow \infty}\left(\frac{1}{x^{2}}+\frac{2}{x^{2}}+\frac{3}{x^{2}}+\ldots+\frac{x}{x^{2}}\right) \)


Which of the following is NOT equivalent to \( \boldsymbol{p} \rightarrow \boldsymbol{q} ? \)
A. ponly if q
B. q is necessary for \( p \)
c. q only if \( p \)
D. p is sufficient for \( q \)


Find the sum of 'x' co-ordinates of the
vertices of a triangle if the mid-points of
its sides be the points (6,-1),(-1,-2) and (1,-4)


The \( \boldsymbol{K}_{s p} \) for \( \boldsymbol{C r}(\boldsymbol{O} \boldsymbol{H})_{3} \) is \( \mathbf{1 . 6} \times \mathbf{1 0}^{-\mathbf{3 0}} \)
The molar solubility of this compound in water is:


divides a circle into
two segments i.e major segment and minor segment.
A. An arc
B. A chord
c. A sector
D. A tangent


The graph below shows the "x-direction"
position of a charged particle flying
around in space and accelerating due
only to some electric field.

During which time interval is the force
on the particle in the x-direction
greatest?
\( \mathbf{A} \cdot 5 \) to 6 seconds
B. 6 to 7 seconds
\( c .7 \) to 8 seconds
D. 8 to 9 seconds
E. 10 to 11 seconds


The two amines shown differ by a factor
of about 40,000 in their ionisation constants. Which is stronger base? Explain:


Light is a form of that we
can detect with our
A. energy, ears
B. corpuscles, eyes
c. energy, eyes
D. sensation, skin


Polymerization in which two or more chemically different monomers take
part is called:
A. Addition polymerization
B. Copolymerization
c. chain polymerization
D. Homo polymerization


the values of \( I, C \) and \( R \) for a circuit are 1
\( \mathrm{H}, 9 \mathrm{F}, \) and \( 3 \Omega \). what is the quality factor for the circuit at resonance?
\( A \)
B. 9
\( c \cdot 19 \)
D. 13


The product(s) formed when \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) reacts with disodium hydrogen phosphate is:
A \( \cdot P_{2} O_{5}, N a_{3} P O_{4} \)
в. \( N a_{2} H P O_{4} \cdot H_{2} O_{2} \)
c. \( N a H_{2} P O_{4} \cdot H_{2} O \)
D. \( N a_{2} H P O_{4} \cdot H_{2} O \)


Calculate the mode
\( \begin{array}{ccccccc}\boldsymbol{x} & 3 & 6 & 9 & 12 & 15 & 18 \\ f & 6 & 8 & 11 & 4 & 10 & 7\end{array} \)
\( \mathbf{A} \cdot \mathbf{9} \)
B. 11
c. 12
D. 15


Assertion
Globular proteins are highly branched proteins usually soluble in water.
Reason
Insulin and Albumin are the common
fibrous proteins.
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


What will happen when excess of chlorine gas is reacted with ammonia
gas?


Which one of the following gives the resultant capacitor when capacitors are joined in series?
A. The sum of the individual capacitors
B. The reciprocal of the sum of the reciprocals of the individual capacitors
c. The reciprocal of the sum of the capacitors
D. The sum of the reciprocals of the individual capacitors


The figure shows a ray incident at angle
\( i=\frac{\pi}{3} . \) If the plot drawn show the
variation of \( |r-i| \) versus \( \frac{\mu_{1}}{\mu_{2}}=k,(r= \)
angle of refraction)
A \( \cdot \) the value of \( k_{1} i s \frac{2}{\sqrt{3}} \)
B. the value of \( \theta_{1}=\frac{\pi}{6} \)
C. the value of \( \theta_{2}=\frac{\pi}{3} \)
D. the value of \( k_{2} \) is 1


A. \( C . \) supply gives \( 30 V \) r.m.s. which passes through a \( 10 \Omega \) resistance. The power dissipated in it is :
B. \( 90 W \)
c. \( 45 \sqrt{2} \mathrm{W} \)
D. \( 45 W \)


The point \( P \) is the intersection of the
straight line joining the points \( Q(2,3,5) \) and \( R(1,-1,4) \) with the plane
\( 5 x-4 y-z=1 . \) If \( S \) is the foot of the
perpendicular drawn from the point
\( T(2,1,4) \) to \( Q R, \) then the length of the
line segment \( P S \) is
A \( \cdot \frac{1}{\sqrt{2}} \)
B. \( \sqrt{2} \)
\( c \cdot 2 \)
D. \( 2 \sqrt{2} \)


At a given temperature, total vapour pressure in Torr of a mixture volatile
components A and B is given by
\( \boldsymbol{P}_{\text {Total}}=\mathbf{1 2 0}-\mathbf{7 5 X}_{\boldsymbol{B}} \)
Hence, vapour pressure of pure \( A \) and \( B \) respectively (in Torr) are?
A . 120,75
в. 120, 195
\( c \cdot 120,45 \)
D. 75, 45


Which of the following has a negative temperature coefficient?
A .
B. Fe
\( c . \) мп
D. Agg


The induced voltage across a stationary conductor in a stationary magnetic field is
A. zero
B. reversed in polarity
c. increased
D. decreased


Read the given observations for four elements \( \begin{array}{l}A_{1} P A_{2} \\ Z_{1} P, Z_{2}\end{array}, \begin{array}{l}A_{3} \\ Z_{3}\end{array} \boldsymbol{R} \) and \( A_{4} \)
\( Z_{4} S \)
carefully. Here Z represents atomic
number and A represents mass number.
(i) Elements P and R shows similar
chemical properties.
(ii) Elements \( Q \) and \( S \) belong to different
groups.
(iii) For elements \( \mathrm{P} \) and \( \mathrm{R}, Z_{1}=Z_{3} \) and
\( \boldsymbol{A}_{1} \neq \boldsymbol{A}_{3} \)
(iv) For elements \( \mathrm{Q} \) and \( \mathrm{S}, Z_{2} \neq Z_{4} \) and
\( \boldsymbol{A}_{2}=\boldsymbol{A}_{4} \)
Which of the following statements is
correct?
\( A . P \) and \( R \) are isobars while \( Q \) and \( S \) are isotopes
B. P and S are isobars while Q and R are isotopes
c. \( P \) and \( Q \) are isotopes while \( R \) and \( S \) are isobar
D. \( P \) and \( R \) are isotopes while \( Q \) and \( S \) are isobar


Solve the following system of inequalities graphically \( 3 x+2 y \leq 12, x \geq 1, y \geq 2 \)


Determine the standard reduction
potential for the half reaction:
\( \boldsymbol{C l}_{2}+\boldsymbol{2} \boldsymbol{e}^{-} \longrightarrow \boldsymbol{2} \boldsymbol{C l}^{-} \)
Given: \( \boldsymbol{P} \boldsymbol{t}^{2}+\boldsymbol{2} \boldsymbol{C l} \longrightarrow \boldsymbol{P} \boldsymbol{t}+ \)
\( \boldsymbol{C l}_{2}, \boldsymbol{E}_{c e l l}^{0}=-\mathbf{0 . 1 5} \boldsymbol{V} \)
\( \boldsymbol{P t}^{2}+\boldsymbol{2} \boldsymbol{e}^{-} \longrightarrow \boldsymbol{P t}, \boldsymbol{E}^{0}=\mathbf{1 . 2 0} \boldsymbol{V} \)


Which of following can induce the maximum induced voltage?
A. 1 amp dc.
B. 1 amp 1 Н \( z \).
c. 1 amp 100 н \( z \)
D. 20 amp dc.


Cause of Addison's disease is
A. Hyposecretion of aldosterone hormone
B. Hypersecretion of aldosterone hormone
C. Hypersecretion of cortisone hormone
D. None of the above


The mean deviation about median from
the data
\( \mathbf{3 4 0}, \mathbf{1 5 0}, \mathbf{2 1 0}, \mathbf{2 4 0}, \mathbf{3 0 0}, \mathbf{3 1 0}, \mathbf{3 2 0} \) is
\( \mathbf{A} .50 \)
B. 52.8
c. 55
D. 45


Select the correct answer. The three
steps from solids to point are
A. Solids - surfaces - lines - points
B. Solids-lines - surfaces - points
C. Solids - surfaces - element - points
D. Solids - elements - surfaces - points


The sum of first 4 term of GP with \( a= \)
\( \mathbf{2}, \boldsymbol{r}=\mathbf{3} \) is
A . 80
B . 26
\( c \cdot 127 \)
D. 8


Heart wall is made up of
A. Myocardium
B. Epicardium
c. Endocardium
D. All of the above


If Earth is supposed to be a sphere of
radius \( R, \) if \( g_{30^{\circ}} \) is value of acceleration
due to gravity at latitude of \( 30^{\circ} \) and \( g \) at
the equator, the value of \( g-g_{30^{\circ}} \) is
A \( \cdot \frac{1}{4} \omega^{2} R \)
в. \( \frac{3}{4} \omega^{2} R \)
c. \( \omega^{2} R \)
D. \( \frac{1}{2} \omega^{2} R \)


Calculate the number of coulombs
required to deposit 6.75 g of \( A l \) when the electrode reaction is:
\( \boldsymbol{A l}^{3+}+\mathbf{3} e^{-} \rightarrow \boldsymbol{A l} \)


Three different coins are tossed
together find the probability of
i) Exactly two heads
ii) At least
one tails
ii) Almost two heads
iv) At most
two tails
v) At least two tails
vi) At most
one head
vii) At least one head


10 witnesses each of whose probability of speaking the truth is \( \frac{5}{6} . \) Asserts that the certain event took place, if the probability of this event before their statement is \( \frac{1}{1+5^{9}}, \) find the probability of the truth of their assertion.


Find the size of object which can be featured with \( 5 M H z \) in water.
A. \( 0.148 \mathrm{mm} \)
B. \( 0.3 \mathrm{mm} \)
\( c .0 .5 \mathrm{mm} \)
D. \( 0.1 \mathrm{mm} \)


Assertion
The value of the van der Waals' constant
\( a^{\prime} \) is larger for ammonia than for
nitrogen.
Reason
Hydrogen bonding is present in ammonia.
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


Chromium seem to be less reactive
than estimated from its standard
reduction potential value because of formation of oxide layer. If true enter 1 , else enter 0


Identify the median class.
\( \begin{array}{lllll}\mathbf{x} & \mathbf{5}- & \mathbf{9}- & \mathbf{1 3}- & \mathbf{1 7}- \\ & \mathbf{9} & \mathbf{1 3} & \mathbf{1 7} & \mathbf{2 1}\end{array} \)
F \( \quad 3 \) 8 9
A. \( 5-9 \)
B. \( 9-13 \)
D. \( 17-21 \)


The colorless species is:
A. \( V C l_{3} \)
в. \( V O S O_{4} \)
c. \( N a_{3} V O_{4} \)
D \( \cdot\left[V\left(H_{2} O\right)_{6} S O_{4}\right] . H_{2} O \)


The tendency to show inert pair effect
follows the order:
A. \( G a<A l<I n<T l<B \)
в. \( B<A l<G a<I n<T l \)
c. \( B=A l=G a<I n<T l \)
D. \( T l< \)In \( <G a<A l<B \)


After forceful inspiration, the amount of air that can be breathed out by maximum forced expiration is equal to
A. Inspiratory Reserve Volume (IRV) + Expiratory Reserve Volume (ERV) + Tidal Volume (TV) + Residual Volume \( (R V) \)
B. IRV + RV + ERV
C. \( \operatorname{IRV}+\mathrm{TV}+\mathrm{ERV} \)
D. TV + RV + ERV


How many carbon dioxide is produced by reduction of pyruvate by Kreb's cycle?
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D.


Write the full name of ISRO.


At the moment \( t=0, \) an electron leaves
one plate of a parallel-plate condenser
with a negligible velocity. An accelerating voltage varying as \( \boldsymbol{V}=\boldsymbol{a} \boldsymbol{t} \)
where \( a \) is a constant is applied between the plates. The separation
between the plates is \( l \). The velocity of
the electron at the moment it reaches
the opposite plate will be :
\( ^{\mathrm{A}}\left(\frac{2 e a l}{9 m}\right)^{\frac{1}{3}} \)
\( ^{\mathrm{B}}\left(\frac{3 e a l}{4 m}\right)^{\frac{1}{3}} \)
\( ^{\mathrm{c}}\left(\frac{4 e a l}{m}\right)^{\frac{1}{3}} \)
\( \left(\frac{9 e a l}{2 m}\right)^{\frac{1}{3}} \)


Two positively charged particles \( X \) and
\( \boldsymbol{Y} \) are initially far away from each other
and at rest. \( X \) begins to move towards
\( Y \) with some initial velocity. The total
momentum and energy of the system are \( p \) and \( E \).Then:
A. if \( Y \) is fixed, both \( p \) and \( E \) are conserved.
B. if \( Y \) is fixed, \( E \) is conserved, but not \( p \)
c. if both are free to move, \( p \) is conserved but not \( E \)
D. if both are free, \( E \) is conserved, but not \( p \)


Consider the cylindrical element as shown in the figure. Current flowing the through element is \( I \) and resistivity of
material of the cylinder is \( \rho . \) Choose the
correct option out the following
A. Power loss in first half is four times the power loss in second half
B. Voltage drop in first half is twice of voltage drop in second half
c. Current density in both halves are equal
D. Electric field in both halves is equal


Evaluate \( \int_{0}^{\pi / 2} \cos x d x \)


Solve:
\( \operatorname{cosec}^{-1}(\cos x) \) is real \( , \) if
A. \( x \in[-1,1] \)
в. \( x \in R \)
c. \( x \) is an odd multiple of \( \frac{\pi}{2} \)
D. x is a multiple of \( \pi \)


A \( 10 \mu F \) capacitor is connected across
a \( 200 V, 50 H z \) A.C. supply. The peak
current through the circuit is :
A. \( 0.6 A \)
в. \( 0.6 \sqrt{2} A \)
D. \( 0.6 \pi A \)


Due to which phenomenon of light does Tyndall effect result?
A. Dispersion
B. Refraction
c. scattering
D. Reflection


\( K_{c} \) for the reaction of decomposition of
\( \mathrm{CaCO}_{3} \) can be written as
в. \( \left[\mathrm{CO}_{3}\right] \)
\( \mathrm{c} \cdot[\mathrm{CaO}]\left[\mathrm{CO}_{2}\right] \)
D. None of these


Choose the correctly matched option.
A. Corpus luteurn - Estrogen - Supports pregnancy
B. Thyroid - Thyroxine - Regulates blood calcium level
C. Anterior pituitary - Oxytocin - Constriction of uterine muscles during child birth
D. Posterior pituitary - Vasopressin - Stimulates reabsorption of water in collecting tubules


\( \int_{0}^{1} \sqrt{\frac{\mathbf{x}}{1-\mathbf{x}^{3}}} \mathbf{d x}= \)
A \( \cdot \frac{\pi}{4} \)
в.
c.
D.


If a vector \( \bar{A}=2 \bar{i}+2 \bar{j}+3 \bar{k} \) and \( \bar{B}= \)
\( \mathbf{3} \overline{\mathbf{i}}+\mathbf{6} \overline{\mathbf{j}}+n \bar{k}, \) are perpendicular to each
other, then the value of 'n' is:
A . 4
B. 12
\( c \cdot 6 \)
D. - -


In \( \triangle A B C, A D \) is perpendicular bisector of BC (See adjacent figure). Show that \( \triangle A B C \) is an isosceles triangle in
which \( \boldsymbol{A B}=\boldsymbol{A C} \)


Dispersal of spores in fern takes place through
A. Annulus
B. Stomium
c. Both A and B
D. Indusium


What is the use of flexibility strip in a doorbell?
A. It brings back striker to its original position
B. It supports the motion of the striker
c. It completes the electric circuit flexibly
D. Its a safety precaution


A copper solid cube of \( 60 \mathrm{mm} \) side is
subjected to a compressible pressure of \( 2.5 \times 10^{7} \) Pa. If the bulk modulus of
copper is \( 1.25 \times 10^{11} \) pascals, the change in the volume of cube is
A. \( -43.2 m m^{3} \)
В. \( -43.2 m^{3} \)
c. \( -43.2 \mathrm{cm}^{3} \)
D. \( -432 m m^{3} \)


The modified cell organelle involved in the formation of cilia and flagellum
A. Golgi complex
B. Centriole
c. stigma
D. Nucleolus


One proton weighs more than:
A . 1,800 electrons
B. 1,800 neutrons
c. Above both options are correct
D. None of the above


A \( 120 V, 60 H z \) a.c. power is connected \( 800 \Omega \) non-inductive resistance and unknown capacitance in series. The voltage drop across the resistance is found to be \( 102 \mathrm{V} \), then voltage drop across capacitor is
\( A \cdot 8 v \)
B. 102v
\( c \cdot 63 v \)
D. \( 55 v \)


Nucleosome contains
\( \mathbf{A} \cdot H_{2} A, H_{2} B, H_{3}, H_{4} \)
\( \mathbf{B} \cdot H_{3}, H_{4} \)
\( \mathbf{c} \cdot H_{2} A, H_{2} B, H_{3} \)
D. \( H_{1}, H_{2} A, H_{2} B, H_{3} \)


Which of the following materials is best suited as the core of an electromagnet
A. steel
B. Iron
c. Alnico
D. Magnetite


Write the truth table for circuit given in the figure, consisting of NOR gates and identify the logic operation (OR, AND, NOT) which this circuit is performing. (Hint: \( A=0, B=1 \) then \( A \) and \( B \) inputs of
second NOR gate will be 0 and hence
\( Y=1 . \) Similarly work out the values of \( Y \) for other combinations of \( A \) and \( B \).
Compare with the truth table of OR,
AND, NOT gates and find the correct
one).


The liquid which is collected in the
cavity of Bowman's capsule is
A. concentrated urine
B. Blood plasma minus blood proteins and corpuscles
c. Glycogen and water
D. Sulphates and water


Given below (Fig. 23.11) is the bar graph
indicating the marks obtained out of 50
in mathematics paper by 100 students.
Read the bar and answer the following
questions:
What is the number of students getting
marks between 9 and \( 40 ? \)


What will be the effect, when very high intensity of light is supplied to a photosynthesis system?
A. Process will increase
B. Process will decrease
c. Process will stop due to solarization
D. None of the above


The sum of the series \( 1+\frac{1.3}{6}+ \) \( \frac{1.3 .5}{6.8}+\ldots . \infty \) is?


By which method should the domestic
garbage be disposed?


How many 3 digit even numbers can be formed using the digits \( 3,5,7,8,9, \) if the digits are not repeated?


For any two rational numbers \( x \) and \( y \) which of the following properties are correct?
\( (i) x<y(i i) x=y(\text { iii }) x>y \)
A. Only (i) and (ii) are correct
B. Only (ii) and (iii) are correct
c. only (ii) is correct
D. All (i), (ii) and (iii) are correct


Euglena contains chlorophyll, yet, it resembles animals, because it
A. Respires like animals.
B. Feeds like animals in absence of sunlight
c. Possesses a contractile vacuole
D. Reproduces like animalss


There is \( p \pi-d \pi \) multiple bonding in:
A \( \cdot C S_{2} \)
в. \( C O_{2} \)
\( c \cdot N O_{2} \)
D. \( N O \)


If you leave the saddle when it is moving upward. The magnitude of down ward acceleration of the saddle is - - - - when
you lose contact with it:
\( A \cdot 6 m s^{-2} \)
B. 7.2 \( m s^{-2} \)
c. \( 9.8 \mathrm{ms}^{-2} \)
D. 12.2 \( m s^{-2} \)


What are the basic components of a rainwater harvesting and conservation
system? This question has multiple correct options
A. Catchment areas
B. Storage units
c. Conveyance mechanism which transports the water falling
D. Sloping roof


The amplitude of the two travelling waves that make up this standing wave
is \( 2.80 \times 10^{-x} \) m. Find \( x \)


Silicon hydrides are called:
A. silicones
B. silicates
C . silicides
D. silanes


A card is thrown from a pack of 52 cards
so that each cards equally likely to be selected. In which of the following cases are the events \( A \) and \( B \) independent?
\( A= \) the card drawn is spade, \( B= \) the
card drawn in an ace.


The work done in moving a single positive charge from infinity to a point is called \( \ldots . . \) at that point
A. Electricity
B. Electric potential
c. Potential gradient
D. None of these


Ethylene reacts with \( H B r \) to form \( ^{\prime} X \) When ' \( X^{\prime} \) is reacted with alcoholic
\( K O H,^{\prime} Y^{\prime} \) is formed. Here, ' \( X^{\prime} \) and ' \( Y^{\prime} \)
are :
A \( \cdot B r C H_{2}-C H_{2} B r \) and \( C_{2} H_{2} \)
B. \( C_{2} H_{5} B r \) and \( C_{2} H_{4} \)
c. \( C_{2} H_{5} B r \) and \( C_{6} H_{6} \)
D. \( C_{2} H_{3} B r_{3} \) and \( C_{2} H_{4} \)


Why we are not able to see our image on a cardboard even though it reflects light?
A. Because cardboard does not shine like mirror
B. Because cardboard is not as durable as mirror
c. Because cardboard's surface is irregular
D. All


\( \boldsymbol{C H}_{3} \boldsymbol{O H} \frac{(i) \boldsymbol{X}}{(i i) R \boldsymbol{h}, \boldsymbol{\Delta}} \boldsymbol{C H}_{3} \boldsymbol{C O O H} \)
In the above reaction, \( \boldsymbol{X} \) is :
A \( . C O_{2} \)
в. \( C O \)
с. \( M g O \)
D. \( C \)


Which of the following represent correct blood flow pathway in pulmonary circulation?
A. Right ventricle \( \underline{\text {Aorta}} \) Lung \( \underline{\text {Pulmonary } \text {Vein}} \) Left Atrium
B. \( \frac{\text { Pulmonary Vein Left Atrium }}{\text { Pulmonary Vein }} \) Left Atrium
c. Right Ventricle Pulmonary Vein Lung Pulmonary artery Left Atrium
D. \( \frac{\text { Pulmonary Vein }}{\text { Right Atrium }} \) Right Atrium Lung Pulmonary Vein n


Show the pathway of electric impulse.
A. Dendrite \( \rightarrow \) Cell body \( \rightarrow \) Axon \( \rightarrow \) to its end
B. Cell body \( \rightarrow \) Dendrite \( \rightarrow \) Axon \( \rightarrow \) to its end
C . Axon \( \rightarrow \) Cell body \( \rightarrow \) Dendrite \( \rightarrow \) to its end
D. Dendrite \( \rightarrow \) Axon \( \rightarrow \) Cell body \( \rightarrow \) to its end


If \( A \) is a \( 3 \times 3 \) invertible matrix, then
what will be the value of \( k \) if
\( \operatorname{det}\left(A^{-1}\right)=(\operatorname{det} A)^{k} \)


Give reason for the following:
The physical properties of isotopes of the same element are not identical


When \( \Delta G \) is zero:
A. reaction moves in forward direction
B. reaction moves in backward direction
C . system is at equilibrium
D. none of these


Assertion
Replication and transcription occur in the nucleus but translation takes place
in the cytoplasm.
Reason
mRNA is transferred from the nucleus
into cytoplasm where ribsomes and amino acids are available for protein
synthesis.
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 animal has most mixing of oxygenated and deoxygenated blood in the ventricles?
A. Scoliodon
B. Rabbitt
\( c . \) Frog
D. None of the above


The absolute configuration of is?
A \( \cdot(2 S, 3 R) \)
в. \( (2 S, 3 S) \)
c. \( (2 R, 3 R) \)
D. \( (2 R, 3 S) \)


An electroplating factory should dispose-off their waste:
A. in the nearby river
B. in the nearby garbage
c. in the nearby field
D. according to guidelines of local authority


How many sides does a polygon have whose sum of the interior angles is
\( 1980^{\circ} ? \)
A . 10
B. 13
c. 11
D. None of these


Find the principal value of the following:
\( \cot ^{-1}(-1) \)


One mole of an ideal monoatomic gas
expends isothermally against constant
external pressure of 1 atm from initial
volume of \( 1 L \) to a state where its final
pressure become equal to external pressure. If initial temperature of gas is
\( 300 K \) then total entropy change of
system in the above process is:
\( \left[\boldsymbol{R}=\mathbf{0 . 0 8 2} \boldsymbol{L} \boldsymbol{a t m m o l}^{-1} \boldsymbol{K}^{-1}=\mathbf{8 . 3} \boldsymbol{J} \boldsymbol{m}\right. \)
A . 0
B . \( \operatorname{Rln}(24.6) \)
c. \( \operatorname{Ren}(2490) \)
D. \( \frac{3}{2} \operatorname{Ren}(24.6) \)


The group number of the element with
atomic number 37 is:


If there is an error of \( 0.1 \% \) in the
measurement of the radius of a sphere, find approximately the percentage error in the calculation of the volume of the
sphere


A bag contains 8 red, 6 white and 4
black balls. A ball is drawn at random
from the bag. Find the probability that the drawn ball is
(i) red or white
(ii) not black
neither white nor black


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


Write a note on properties and uses of covalent compounds.


Unit vectors \( \hat{P} \) and \( \hat{Q} \) are inclined at an angle \( \theta \), Prove that \( |\hat{P}-\hat{Q}|=2 \sin (\theta / 2) \)
is?


Which is the key intermediate
compound linking glycolysis to Kreb's cycle ?


The charcoal culture experiment is better than water culture experiment because
A. Plants get supporttt
B. Problem of aeration is removed
c. Charcoal is an inert substance
D. All of the above


f \( |\vec{a}|=7,|\vec{b}|=11,|\vec{a}+\vec{b}|=10 \sqrt{3} \)
then \( |\vec{a}-\vec{b}|= \)
A . 10
B. \( \sqrt{10} \)
c. \( 2 \sqrt{10} \)
D. 20


Metazoa is characterised by
A. Unicellular animals
B. Colonial animals
C. Multicellular animals
D. Multicellular decomposers


A rod of length L and diameter D is subjected to a tensile load P. Which of the following is sufficient to calculate the resulting change in diameter?
A. Youngs modulus
B. Shear modulus
c. Poissons ratio
D. both Youngs modulus and Shear modulus


What is the name of the element with
atomic number \( 105 ? \)
A. Dubnium
B. Holmium
c. Kurchatovium
D. Nobelium


The angle of reflection is equal to
A \( \cdot 0^{\circ} \)
B . 45
\( c .90 \)
D. 180


State whether the following statements
are true or false.
When Van Leeuwenhoek examined
scrapings of his teeth under a microscope after drinking hot coffee, he saw living germs in them.
A. True
B. False


When a pencil is partly immersed in water, the pencil appears to bend at the surface. Reason behind this is:
A . Reflection
B. Refraction
c. Total internal reflection
D. Diffraction


Simplify: \( (\boldsymbol{x}+\mathbf{5})(\boldsymbol{x}+\mathbf{4}) \)
A \( \cdot x^{2}+27 x+20 \)
B . \( x^{2}+9 x+20 \)
c. \( x^{2}+18 x+20 \)
D. \( x^{2}+x+20 \)


Predict the order of thermal stability of the group 1 and 2 metal carbonates.


f \( \boldsymbol{n}(\boldsymbol{A})=\mathbf{4}, \boldsymbol{n}(\boldsymbol{B})=\boldsymbol{3}, \boldsymbol{n}(\boldsymbol{A} \times \boldsymbol{B} \times \)
\( C)=24, \) then \( n(C)=? \)
\( A \cdot 2 \)
B.
\( c \cdot 12 \)
D. None of these


Theoritically the No. of geometrical isomers expected for octahedral
complex \( [\text {Mabcde} \boldsymbol{f}] \) is :
A. zero
B. 30
c. 15
D. 9


A body cools from \( 50^{\circ} \mathrm{C} \) to \( 40^{\circ} \mathrm{C} \) in 5
minutes. The surrounding temperature
is \( 20^{\circ} \mathrm{C} . \) By how many \( ^{\circ} \mathrm{C} \) does the temperature decrease in the next 5 minutes? Round your answer to the nearest integer.


From the above setup answer the
following:
Why could you not use this setup for
preparing \( H_{2} \) if the generator contained
\( Z n^{+} \) vinegar?
A. Hydrogen would not be produced
B. The setup of the generator is improper
C. The generator must be heated with a burner
D. The delivery tube setup is wrong
E. The gas cannot be collected over water


Mass of a body changes at different
places on earth. State whether true or false.
A. True
B. False


The half life of a radioactive substance
is 20 minutes. The approximate time
interval \( \left(\mathrm{t}_{2}-\mathrm{t}_{1}\right) \) between the time \( \mathrm{t}_{1} \)
when \( \frac{1}{3} \) of it had decayed and \( t_{2} \) when \( \frac{2}{3} \) of it had decayed is :
\( A \cdot 7 \min \)
B. 14 min
\( c .20 \mathrm{min} \)
D. 28 min


At what distance from a long straight
wire carrying a current of \( 12 A \) will the
magnetic field be equal to \( 3 \times \) \( \mathbf{1 0}^{-\mathbf{5}} \boldsymbol{W b} / \boldsymbol{m}^{2} ? \)
A. \( 8 \times 10^{-2} \mathrm{m} \)
В. \( 12 \times 10^{-2} \mathrm{m} \)
c. \( 18 \times 10^{-2} \mathrm{m} \)
D. \( 24 \times 10^{-2} \mathrm{m} \)


Atmospheric pressure at sea level is
A . \( 1.013103 \mathrm{Pa} \)
B. 1.013 104 Pa
c. 1.013 105 \( \mathrm{Pa} \)
D. 1.013 106 Ра


If the point \( A(2,4) \) is equidistant from \( P(3,8) \) and \( Q(7, y), \) find the values of \( y \)
\( \mathbf{A} \cdot 6 \& 4 \)
B. \( 12 \& 2 \)
c. \( 10 \& 4 \)
D. None of these


What is the major edible part of a brinjal (egg plant)? This question has multiple correct options
A. Pericarp
B. Thalamus
c. Placenta
D. style


are connected together by a light spring
of stiffness \( k . \) The system is lying on a
smooth horizontal surface with the
block \( A \) in contact with a fixed vertical
wall as shown in the figure. The block \( \boldsymbol{B} \)
is pressed towards the wall by a
distance \( x_{0} \) and then released. There is
no friction anywhere. If spring takes
time \( \Delta t \) to acquire its natural length
then average force on the block \( A \) by the
wall is :
A. Zero
B. \( \frac{\sqrt{2 m k}}{\Delta t} x_{0} \)
c. \( \frac{\sqrt{m k}}{\Delta t} x_{0} \)
D. \( \frac{\sqrt{3 m k}}{\Delta t} x_{0} \)


Which one of the following statements
is correct?
A \( . \quad N a C l \) is a paramagnetic salt
B. \( C u S O_{4} \) is a diamagnetic salt
C. \( M n O \) is an example of ferromagnetic substance
D. \( C r O_{2} \) is an example of antiferromagnetic substance
E. Ferrimagnetic substance like \( Z n F e_{2} O_{4} \) becomes paramagnetic on heating


In a mixture of gases, the average number of degrees of freedom per molecule is \( 6 . \) The rms speed of the molecules of the gas is \( c . \) The velocity of
sound in the gas is
A \( \cdot \frac{c}{\sqrt{2}} \)
в. \( \frac{3 c}{4} \)
c. \( \frac{2 c}{3} \)
D. \( \frac{c}{\sqrt{3}} \)


The process of budding can be seen in This question has multiple correct options
A. Flatworms
B. Amoeba
c. Yeast
D. Hydra


Tyres have treads to
friction.fill in the bank.
A. increase
B. decrease
c. neglect
D. overcome


Find the \( \left[\frac{7}{9} p^{2} q r\right] \times\left(18 p q^{2}\right)\left(-\frac{3}{14} r^{2}\right) \)


If the velocity of water near the surface
of a \( 6 \mathrm{m} \) deep river is \( 6 \mathrm{m} / \mathrm{s} \), assuming uniform velocity gradient along the depth, find the shear stress between the horizontal layers of water (coefficient of
viscosity of water \( =10^{-2} \) poise


Nucellus of gymnosperms has 64 chromosomes and its endospermic cells will have
A . 64
B. 128
\( c \cdot 192 \)
D. 32


From a point 0 in the interior of a
\( \Delta A B C, \) perpendiculars \( 0 D, O E, \& \) OF
are drawn to the sides BC, CA \& AB
respectively. Prove that
[i] \( A F^{2}+B D^{2}+C E^{2}=O A^{2}+ \)
\( O B^{2}+O C^{2}-O D^{2}-O E^{2}-O F^{2} \)
[ii] \( A F^{2}+B D^{2}+C E^{2}=A E^{2}+ \)
\( C D^{2}+B F^{2} \)


Orange rots is due to member of -
A. Phycomycetes
B. Ascomycetes
C . Basidiomycetes
D. Deuteromycetes


Show that matrix \( A+B \) is symmetric
or skew symmetric according as \( A \) and
\( B \) are symmetric of skew symmetric.


Find the coordinates of the foci, the
vertices the eccentricity and the length
of latus rectum of the hyperbola \( 16 x^{2}- \)
\( 9 y^{2}=576 \)


If \( P=a^{2}-2 a b+b^{2} \) and \( q=4 a b, \) then
\( \boldsymbol{p}+\boldsymbol{q} \boldsymbol{a} \) is:
A \( \cdot(a-b)^{2}+4 a^{2} b \)
B . \( (a-b)^{2}-4 a^{2} b \)
c. \( (a-b)^{2}-4 b a \)
D. \( (a-b)^{2}-4 b^{2} a \)


When a cross is made between tall
plant with yellow seeds (TtYy) and tall plant with green seeds (Ttyy), what
proportions of phenotype in the offspring could be expected to be
(a) tall
and green (b) dwarf and green
Parents \( \begin{array}{ccc}\text { Tall Yellow } & \times & \text { Tall Green } \\ \pi \mathrm{T} & \mathrm{Ty} & \mathrm{Tt} \text { yy }\end{array} \) Gametes
Phenotypes Tall and Green \( =3 \) Dwarfand Gree war and Yellow
Total \( =8 \) Thus
a) Prooortion
(b) Proportion


Evaluate \( \int(1-x) \sqrt{x} . d x \)


Water will be absorbed by root hair
when the
A. Concentration of solutes in the cell sap is high.
B. Plant is rapidly respiring.
C. They are separated from soil by permeable membrane.
D. Concentration of salts in the soil is high.


The radius of the locus by the point represented by \( z, \) when \( \arg \frac{z-1}{z+1}=\frac{\pi}{4} \)
is
A \( \cdot \sqrt{2} \)
B. \( \sqrt{2} \pi \)
c. \( \frac{\pi}{\sqrt{2}} \)
D. none of these


\( \operatorname{Let} f(x)=\frac{\sin \{x\}}{x^{2}+a x+b} . \) If \( f\left(5^{+}\right) \& \)
\( f\left(3^{+}\right) \) exists finitely and are not zero, then the value of
\( (a+b) \) is (where \( \{\cdot\} \) represents
fractional part function).
\( A \cdot 7 \)
B . 10
c. 11
D. 20


Which is the correct structure of Nylon-
\( 6 ? \)
\( A \)
в.
\( c \)
\( D \)


f \( (n+2) !=2550 \times n ! \), find the value
of \( n \)


Which of the following oxides of
nitrogen is solid?
A \( \cdot N O_{2} \)
в. \( N_{2} \) О
c. \( N_{2} O_{3} \)
D. \( N_{2} O_{5} \)


Is it possible to choose \( r, \) so that a is greater than \( \frac{\boldsymbol{F}}{\boldsymbol{M}} \) ? How?


The boiling point of alcohol is higher than ether due to:
A. hydrogen bonding
B. large size of alcohol
c. presence of -OH group
D. high moleculer weight


Menstruation is due to sudden
A. Reduction of FSH
B. Increase of LH
C. Reduction in estrogen and progesteron
D. None of the above


Energy per unit volume in a stretched wire is equal to
A. half of load x strain
B. loadx strain
c. stress \( \times \) strain
D. half of stress \( x \) strain


What is the function of non-histone
protein?


An automobile spring extends \( 0.2 \mathrm{m} \) for
\( 5000 \mathrm{N} \) load. The ratio of potential energy stored in this spring when it has been compressed by \( 0.2 \mathrm{m} \) to the potential energy stored in a \( 10 \mathrm{F} \) capacitor at a potential difference of \( 10000 \mathrm{V} \) will be:
A \( \cdot 1 / 4 \)
B.
\( c \cdot 1 / 2 \)
\( D \cdot 2 \)


If \( A \) and \( B \) are square matrices of order \( n \)
\( x \) n such that \( A^{2}-B^{2}= \)
\( (A-B)(A+B), \) then of the following
will always be true?
\( A \cdot A=B \)
c. either of A or B is a zero matrix
D. either of A or B is an identify matrix


Three charged particles are in equilibrium under their electrostatic forces only. Then
A. The particles must be collinear
B. All the charges cannot have the same magnitude
c. All the charges cannot have the same sign
D. The equilibrium is unstable
E. All option is correct


A solution of sodium sulphate in water is electrolysed using inert electrodes. The products at the cathode and anode are respectively:
A. \( H_{2}, O_{2} \)
в. \( O_{2}, H_{2} \)
\( \mathrm{c} \cdot O_{2}, N a \)
\( \mathrm{D} \cdot \mathrm{O}_{2}, \mathrm{SO}_{2} \)


Only two isomeric monochloro
derivatives are possible for
This question has multiple correct options
A. n-Butane
B. 2,4-Dimethyl pentane
c. Benzene
D. 2-Methyl propane


The D.E whose solution is \( y=\frac{c}{x} \) is:
A. \( y_{1}+x y=0 \)
в. \( y_{1}=x y \)
c. \( x \cdot d y+y \cdot d x=0 \)
D. \( x . d y-y . d x=0 \)


Solutes are absorbed by a plant cell through
A. Osmosis
B. Diffusion
c. Active absorption
D. Passive absorption


Order of size of \( s p, s p^{2} \) and \( s p^{3} \) orbitals
is:
A \( \cdot s p^{3}<s p^{2}<s p \)
B \( . s p<s p^{2}<s p^{3} \)
c. \( s p^{2}<s p<s p^{3} \)
D. \( s p^{2}<s p^{3}<s p \)


toppr LOGIN JOIN NOW
\( \widehat{n} \)
Q Type your question
\( - \)
\( A \cdot A-p, B-q, C-r, D-t, E-s \)
B. \( A-r, B-p, C-t, D-s, E-q \)
\( \mathbf{C} \)
1 \( \alpha \) - \( r, C-s, D-p, E-t \)
3- \( t, C-q, D-r, E-p \)
\( D \)
-1
\( E \cdot A-t, B-s, C-p, D-q, E- \)


'Botanical snakes' are
A. Fungi
B. Bryophytes
c. Pteridophytes
D. Lichens


Which set of figures will be obtained after rounding up the following upto three significant figures? 34.216,0.04597,10.4107
A . 34.3,0.0461,10.4
B. 34.2, 0.0460, 10.4
c. 34.20,0.460,10.40
D. 34.21, 4.597, 1.04


Consider following reactions:
\( \mathbf{l}: \boldsymbol{N}_{\mathbf{2}}+\boldsymbol{O}_{\mathbf{2}} \rightarrow \)
\[
\mathbf{2} \boldsymbol{N} \boldsymbol{O} \quad \triangle \boldsymbol{H}=\boldsymbol{X}_{\mathbf{1}}
\]
\( \|: 2 C O+O_{2} \rightarrow \)
\( 2 C O_{2} \)
\[
\triangle \boldsymbol{H}=\boldsymbol{X}_{2}
\]
\( \|: 2 H_{2} O+O_{2} \rightarrow \)
\[
\mathbf{2} \boldsymbol{H}_{\mathbf{2}} \boldsymbol{O}_{\mathbf{2}} \quad \triangle \boldsymbol{H}=\boldsymbol{X}_{\mathbf{3}}
\]
\( \mathrm{IV}: \boldsymbol{P} \boldsymbol{C} \boldsymbol{I}_{3}+\boldsymbol{C} \boldsymbol{I}_{2} \rightarrow \)
\[
\boldsymbol{P C I}_{5}
\]
\[
\triangle \boldsymbol{H}=\boldsymbol{X}_{4}
\]
In which case \( (s), \triangle H_{f}=\frac{\Delta H}{2} ? \)
\( \mathbf{A} \cdot \) ।, ॥,।।
B. IV
c. ॥, ॥ ॥
\( D \)


A bar magnet is hung by a thin cotton thread in a uniform horizontal magnetic field and is in equilibrium state. the
energy required to rotate it by \( 60^{\circ} \) is \( W \) Now the torque required to keep the magnet in this new position is.
A. \( \frac{2 W}{\sqrt{3}} \)
B. \( \frac{W}{\sqrt{3}} \)
c. \( \sqrt{3} W \)
D. \( \frac{\sqrt{3}}{2} W \)


The probability of an event that is certain to happen is \( _{--}-_{-} ? \)
A . 1
B. 2
\( c .3 \)
\( D \)


Give the molecular formula for
bleaching powder.


Each side of a rhombus is \( 10 \mathrm{cm} \) long
and one of its diagonals measures 16
\( \mathrm{cm} . \) Find the length of the other diagona
and hence find the area of the rhombus.


In following symbol series, some of the symbols are missing which are given in that order as one of the alternatives
below it. Choose the correct alternative.
\( \$ \$ \operatorname{ltex} t\left\{x+_{-} x x_{-}+++x x_{-}+++x\right\} \$ \$ \)
\( A \cdot x++x \)
B. \( +x x+ \)
\( c \cdot x x x+ \)
D. \( x+x+ \)
\( E \cdot x+x x \)


Evaluate the given integral. \( \int \frac{\sec ^{2} \sqrt{x}}{\sqrt{x}} d x \)


Mohit correctly answered \( 90 \% \) of the questions in a Maths test contained exactly 40 questions. How many of the questions did he answer incorrectly?
A .4
B. 10
c. 44
D. 90


Hydrogen loses its electron to form \( \boldsymbol{H}^{+} \)
In this respect, it resembles:
A. halogens
B. alkali metalss
c. transition element
D. alkaline earth metals


Which one is make a conducting solution?
A. Pure aluminium oxide
B. Coke
c. cryolite
D. All of these


The atmospheric pressure can support vertical height of water.
A . \( 13.4 m \)
в. 10.34 т
c. \( 0.76 m \)
D. \( 7.6 m \)


According to Maxwell's equation, the velocity of light in any medium is expressed as
A \( \cdot \frac{1}{\sqrt{\mu_{0} \varepsilon_{o}}} \)
в. \( \frac{1}{\sqrt{\mu \varepsilon}} \)
c. \( \sqrt{\frac{\mu}{\varepsilon}} \)
D. \( \sqrt{\frac{\mu_{0}}{\varepsilon}} \)


The mean of \( 51,81,42,65, x \) is 75 find \( x \)


A car, starting from rest, accelerates at
the rate \( f \) through a distance \( S, \) then
continues at constant speed for time \( t \)
and then decelerates at the rate \( \boldsymbol{f} / \mathbf{2} \) to come at rest. If the total distance
traversed is \( 15 S, \) then
A \( \cdot S=\frac{1}{2} f t^{2} \)
B. \( S=\frac{1}{4} f t^{2} \)
c. \( S=f t \)
D. \( s=\frac{1}{72} f t^{2} \)


Assertion
Air bubble shines in water.
Reason
Air bubble in water shines due to
refraction of light.
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 ball of mass \( 0.1 \mathrm{kg} \) strikes a wall normally with a speed of \( 30 m s^{-1} \) and
rebounds with a speed of \( 20 m s^{-1} . \) The impulse of the force exerted by the wall on the ball is
A. \( 1 N s \)
в. 5 Ns
\( c .2 N s \)
D. 3 Ns


How many loops will be seen in each
string?
A. 1 in thinner wire and three \( i n \) thicker wire
B. 3 in thinner wire and 1 in thicker wire
C. 1 each
D. 3 each


Define a scalar matrix.


Find the transpose of each of the following matrices:
\( (i)\left[\begin{array}{c}5 \\ \frac{1}{2} \\ -1\end{array}\right] \)
\( (i i)\left[\begin{array}{cc}1 & -1 \\ 2 & 3\end{array}\right] \)
\( (i i i)\left[\begin{array}{ccc}-1 & 5 & 6 \\ \sqrt{3} & 5 & 6 \\ 2 & 3 & -1\end{array}\right] \)


What type of glycoside linkage is the following?
A \( \cdot \alpha\left(1 \rightarrow 4^{\prime}\right) \)
В \( \cdot \beta\left(1 \rightarrow 4^{\prime}\right) \)
c. \( \alpha\left(1 \rightarrow 6^{\prime}\right) \)
D. \( \beta\left(1 \rightarrow 6^{\prime}\right) \)


Two equations are given below:
A) \( \oint \overline{\boldsymbol{E}} \cdot \boldsymbol{d} \overline{\boldsymbol{A}}=\frac{\boldsymbol{Q}}{\boldsymbol{E}_{0}} \)
B) \( \oint \overline{\boldsymbol{B}} \cdot \boldsymbol{d} \overline{\boldsymbol{A}}=\mathbf{0} \)
A. A - Ampere's law B - Gauss law for electricity
B. A - Gauss law for electric fields B - Gauss law for magnetic fields
C . A - Faraday law B-Gauss law for electric fields
D. Both (A) and
(B) represent Faraday law


Conversion of glucose to pyruvate is a
A. Anabolic reaction
B. Catabolic reaction
c. Anabolic and catabolic reaction
D. None of the above


Evaluate the following:
\( \left|\begin{array}{ccc}\boldsymbol{x}+\boldsymbol{\lambda} & \boldsymbol{x} & \boldsymbol{x} \\ \boldsymbol{x} & \boldsymbol{x}+\boldsymbol{\lambda} & \boldsymbol{x} \\ \boldsymbol{x} & \boldsymbol{x} & \boldsymbol{x}+\boldsymbol{\lambda}\end{array}\right| \)


An object of mass 40 kg having velocity \( 4 \hat{\text { ì }} m / s \) collides with another objects of mass 40 kg having velocity \( 3 \hat{i} \). If the collision is perfectly inelastic, then the loss of mechanical energy.
\( A \). \( 250 J \)
B. 100
c. 125
D. 35 J


Find
\( \lim _{x \rightarrow \pi / 2} \frac{\sin (\cos x) \cos x}{\sin x-\operatorname{cosec} x} \)


Net torque on the rear wheel of the
bicycle is equal to:
A. Zero
\( \mathbf{B} \cdot 16 N-m \)
c. \( 6.4 N-m \)
\( \mathbf{D} \cdot 4.8 N-m \)


\( 0.1 M \) solution of urea would be
with \( 0.1 ~ M \) solution of \( N a C l \)
A. hypotonic
B. hypertonic
c. isotonic
D. none of these


How many acres of each (wheat and rye) should the farmer plant in order to get maximum profit?
A . (5,5)
в. (4,4)
c. (4,5)
(年. (4,5)
D. (4,3)


Which of the following compounds will show the maximum enol content?
A. \( C H_{3} C O C H_{2} C O C H_{3} \)
в. \( C H_{3} \) СОСН\( _{3} \)
c. \( C H_{3} C O C H_{2} C O N H_{2} \)
D. \( C H_{3} C O C H_{2} C O O C_{2} H_{5} \)


Generally, smaller the cell
A. The larger the nuclei.
B. The smaller the nuclei.
C. It will be metabolically more active
D. It will be metabolically less active.


How many grams of carbon dioxide gas is dissolved in a 1 L bottle of carbonated
water if the manufacturer uses a
pressure of 2.4 atm in the bottling
process at \( 25^{\circ} \mathrm{C} ? \)

Given: \( K_{H} \) of \( C O_{2} \) in water \( =29.76 \)
\( \operatorname{atm} /(\operatorname{mol} / L) \) at \( 25^{\circ} \mathrm{C} \)
A. \( 3.88 \mathrm{g} \)
B. 4.90 g
c. \( 5.33 \mathrm{g} \)
D. 3.52 g


A die is thrown. Write the sample space.
If \( B \) is the event of getting an even number, write the event \( B \) using set
notation.


A steady electric current is flowing
through a cylindrical conductor
This question has multiple correct options
A. the electric field at the axis of the conductor is zero
B. the magnetic field at the axis of the conductor is zero
C. the electric field in the vicinity of the conductor is zero
D. the magnetic field in the vicinity of the conductor is zero


Prove that:
\( \sin 50^{\circ}+\sin 10^{\circ}=\cos 20^{\circ} \)


Match the following and write the order
for ABCD.
List List - II
1) Conc
A) Decarboxylating agent
\[
H_{2} S O_{4} / 170^{0} C
\]
B) Dehydrohalogenating
2) \( \mathrm{NaOH}+\mathrm{CaO} \)
agent
C) Dehalogenating agent
3) \( Z n \) dust
D) Dehydrating agent
4) aq \( K O H \)
5) alcoholic \( K O H \)
A . 1234
B. 2 4 31
\( c \cdot 2531 \)
D. 1534


A potential difference is applied across the ends of a metallic wire. If the
potential difference is doubled, the drift
velocity will
A. Be doubled
B. Be halved
c. Be quadrupled
D. Remain unchanged


Figure shows three lenses of equal radii of curvature of the curved surfaces. the
ratio of focal lengths of \( \mathrm{P}, \mathrm{Q} \) and \( \mathrm{R} \) is
A .1: 1: 1
B. 1:1:-1
\( c \)
D . - -1:2:-


The least distance of distinct vision is
\( 25 \mathrm{cm} . \) If the focal length of a convex lens is \( 10 \mathrm{cm}, \) it acts as a simple microscope with maximum magnification of
A . 2.5
B. 3
\( c .3 .5 \)
D. 5


If \( z=i-1, \) then \( \bar{z}= \)
A . \( i+1 \)
B. \( -i-1 \)
\( c \cdot-1 \)
D. none of these


\( N a C N \) is sometimes added in the forth
flotation process as a depressant when
\( Z n S \) and \( P b S \) minerals are expected
because:
A \( \cdot P b(C N)_{2} \) is precipitated while no effect as \( Z n S \)
B. \( Z n S \) forms soluble complex \( N a_{2}\left[Z n(C N)_{4}\right] \) while \( P b S \) forms froth
c. \( P b S \) forms soluble complex \( N a_{2}\left[P b(C N)_{4}\right] \) while \( Z n S \) forms froth
D. \( N a C N \) is never added in froth flotation process


Identify the odd term out and explain. Hydrogen, hydrogen peroxide, carbon dioxide, water vapour


What do you mean by angle of inclination and horizontal component of magnetic field. Establish relation between them.


Purkinje fibre is found in
\( A \). Brain
B. Kidney
\( c . \) skin
D. conduction system of heart


Which solution will conduct the
current?
A. Sugar in water
B. Sugar in ethanol
c. lodine in ethanol
D. \( M g C l_{2} \) in water


In the figure, show that perimeter of \( \triangle A B C=2(A P+B Q+C R) \)


If a monomial \( \frac{2}{5} x^{2} y^{2}, \) binomial \( 2 x+3 y \) and a trinomial \( 2 x+3 y+4 z \) are
added, then the resultant expression is
\( a \)
A. Monomial
B. Binomial
c. Multinomial
D. Trinomial


An inductor \( 2 / \pi \mathrm{F} \) and a resistor \( 100 / \pi \)
are connected in series across a source
of emf \( \mathbf{v}=\mathbf{1 0} \sin 100[\pi \mathrm{t}] . \) Here \( \mathrm{t} \) is in
second.
(a) find the impedance of the circuit find the energy dissipated in the circuit in 20 minutes.


Coenzymes NAD and NADP contain the vitamin
A. Niacin
B. Biotin
c. Thiamine
D. Vitamin \( B_{12} \)
E. Vitamin \( A \)


Select the incorrect statement.
A. Nitrous oxide supports combustion more vigorously than air
B. Phosphorus pentaoxide dehydrates nitric acid forming nitrogen pentaoxide
C. Reactivity order of various allotropic forms of phosphorus is white \( > \) red \( > \) black
D. Red phosphorus changes to white phosphorus on heating in the atmosphere of \( C O_{2} \) or coal gas at \( 573 K \)


In Carbon-Nitrogen fusion cycle protons are fused to form a helium nucleus, positrons and release some energy.The number of protons fused and the number of positrons released in this process respectively are
\( A \cdot 4,4 \)
B. 4,2
\( c \cdot 2,4 \)
D. 4,6


At which phase of meiosis, the two cells, each with separated sister chromatids move towards opposite poles?
A. Metaphase-
B. Metaphase-I
c. Anaphase-I
D. Anaphase-II


If \( x=2, y=1 \) and \( z=-3, \) then \( x^{3}+ \)
\( y^{3}+z^{3}-3 x y z \) is equal to
\( \mathbf{A} \cdot \mathbf{6} \)
B.
\( c \cdot 2 \)
D.


A vector \( C \) when added to vectors \( A= \) \( \mathbf{3} \hat{\mathbf{i}}-\mathbf{5} \hat{\mathbf{j}}+\widehat{\boldsymbol{k}} \) and \( \boldsymbol{B}=\mathbf{2} \hat{\mathbf{i}}+\mathbf{3} \widehat{\boldsymbol{j}}-\mathbf{4} \widehat{\boldsymbol{k}} \)
gives a unit vector along the y-axis.
Then, \( C \) is
\( \mathbf{A} \cdot-5 \hat{i}+3 \hat{j}+3 \widehat{k} \)
B. \( 5 \hat{i}-3 \hat{j}-3 \widehat{k} \)
\( \mathbf{c} .-5 \hat{i}+2 \hat{j}-3 \widehat{k} \)
D. \( 5 \hat{i}-2 \hat{j}-3 \hat{k} \)


if \( z=\frac{1+3 i}{1+i} \) then
This question has multiple correct options
\( \mathbf{A} \cdot \operatorname{Re}(z)=2 \operatorname{Im}(z) \)
B. \( \operatorname{Re}(z)+2 \operatorname{Im}(z)=0 \)
\( \mathbf{c} .|z|=\sqrt{5} \)
D. \( a m p z=\tan ^{-1} 2 \)


Write balanced net ionic equation for
the following reaction in acidic solution
\( \boldsymbol{H} \boldsymbol{S} \boldsymbol{O}_{4}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{A} \boldsymbol{s}_{4}(\boldsymbol{s})+\boldsymbol{P} \boldsymbol{b}_{3} \boldsymbol{O}_{4}(\boldsymbol{s}) \rightarrow \)
\( \boldsymbol{P b S O}_{4}(\boldsymbol{s})+\boldsymbol{H}_{2} \boldsymbol{A} \boldsymbol{s} \boldsymbol{O}_{4}^{-}(\boldsymbol{a} \boldsymbol{q}) \)


The charge appearing on the outer surface of extreme left plate is :
A . \( -(Q / 2) \)
B. \( (Q / 2) \)
\( c \cdot Q \)
D. -


Which of the following halogens does not form oxyacids at room
temperature?
\( A \cdot F_{2} \)
в. \( \mathrm{Cl}_{2} \)
c. \( \mathrm{Br}_{2} \)
D. \( I_{2} \)


A convex lens \( ^{\prime} L^{\prime} \) and a plane mirror
\( M^{\prime} \) are arranged as shown in figure
below. Position of object pin' \( \boldsymbol{O}^{\prime} \) is
adjusted in such a way that the inverted
image \( ^{\prime} I^{\prime} \) formed by the lens mirror combination, coincides with the object
pin ' \( O^{\prime} . \) Explain how and when this
happens:


Warmer air is:
A. Lighter than cold air
B. Heavier than cold air
C. Both have equal weights
D. We cannot say


The displacement of a particle is
represented by the equation \( y= \) \( 3 \cos \left[\frac{\pi}{4}-2 \omega t\right] \)
The motion is:
A. non- periodic
B. periodic but not simple harmonic
c. simple harmonic with period 2 piw
D. simple harmonic with period \( \left(\frac{\pi}{\omega}\right) \)


A hole is drilled along the earth's diameter and a stone is dropped into it.
When the stone is at the centre of the
earth, it has.
A. Acceleration
B. Weight
c. Mass
D. Potential energy


With forward biased mode, the p-n junction diode
A. is one in which width of depletion layer increases
B. is one in which potential barrier increases
c. acts as closed switch
D. acts as open switch


Addition of silver nitrate to hydrochloric acid, gives an insoluble precipitate of the respective chloride, This precipitate is soluble in ammonium hydroxide and insoluble in dilute nitric acid.


\( 0.092 \mathrm{g} \) of an organic compound containing phosphorous gave 0.111 g of \( M g_{2} P_{2} O_{7} \) by usual analysis.
Calculate the percentage of the phosphorous in the organic compound.
A . \( 45.95 \% \) \%
B . \( 29.65 \% \)
c. \( 37.32 \% \)
D. 33.7\%


What does \( B O D_{5} \) represent?
A. Biological oxygen demand in five days
B. Dissolved oxygem left after five days
C. Dissolved oxygen consumed in five days
D. Microorganisms killed by ozone in sewage treatment plants in five hours


\( 10 \% \) of the tools produced by a machine are defective. Find the probability distribution of the number of defective
tools when 3 tools are drawn one by one with replacement.


\( \frac{d}{d x} \csc ^{-1}\left(\frac{1+x^{2}}{2 x}\right) \) is equal to
A \( \cdot \frac{-2}{\left(1+x^{2}\right)}, x \neq 0 \)
в. \( \frac{2}{\left(1+x^{2}\right)}, x \neq 0 \)
c. \( \frac{2\left(1-x^{2}\right)}{\left(1+x^{2}\right)\left|1-x^{2}\right|}, x \neq\pm 1,0 \)
D. None of the above


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


\( \left|\frac{1}{(1-i)^{2}}-\frac{1}{(1+i)^{2}}\right|= \)
\( A \cdot 4 \)
B. 3
\( c \cdot 2 \)
D.


Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be a function defined by
\( f(x)=\frac{x^{2}-8}{x^{2}+2} . \) Then, \( f \) is
A. one-one but not onto
B. one-one and onto
c. onto but not one-one
D. neither one-one nor onto


Evaluate \( \int_{0}^{2} \frac{x}{3} d x \)


Due to slipping, points \( \$ A \$ \) and \( \$ B \$ \) on
the rim of the disc have the velocities
shown. Distance between centre of disc
and point on disc which is having zero
velocity.
A . \( 0.04 \mathrm{m} \)
B. \( 0.05 \mathrm{m} \)
c. \( 0.06 \mathrm{m} \)
D. None


What is called black gold?
A. Petroleum
B. Natural gas
c. coal tar
D. coal


A man of height \( 170 \mathrm{cm} \) wants to see his complete image in the mirror (while standing) His eyes is at a height of 160 \( \mathrm{cm} \) from the ground
A. Minimum length of the mirror =80 cm
B. Minimum length of the mirror =85 cm
c. Bottom of the mirror should be at a height \( 80 \mathrm{cm} \)
D. Bottom of the mirror should be at a height \( 85 \mathrm{cm} \)


The correct relationship between
enthalpy (in cal mol-1) of vaporisation
of liquid and its boiling points is?


State True or False :
Gravity of Earth, attracts all objects
towards the centre of Earth.
A. True
B. False


Draw labelled diagram of Laboratory method of phosphine and give chemical equation?


Identify the energy changes in the following two cases -
\( A: A \) car moving up a hill
B : Photographic film is exposed to sun-
light
A. In 'A' mechanical energy in moving car is converted to potential energy and in 'B' potential energy is converted to chemical energy
B. In'A' potential energy in moving car is converted to kinetic energy and in 'B' chemical energy is converted to light energy.
C. In'A' kinetic energy in moving car is converted to potential energy and in 'B' potential energy is converted to light energy.
D. In'A' kinetic energy is moving car is converted to potential energy and in 'B' light energy is converted to chemical energy.


Which is not true:
A. Resistance of metals increases with increasing temperature
B. Resistance of semi-conductors decreases with rise of
temperature
C. Resistance of an electrolyte increases with rise of temperature
D. None of the above


The self potential energy of hydrogen chloride whose dipole moment is \( 3.44 \times \) \( 10^{-20} \mathrm{Cm} \) and separation between
hydrogen and chlorine atoms is \( 1.01 \times \)
\( 10^{-10} \mathrm{m} \) is:
В. \( 3.2 \times 10^{5} J \)
c. \( 4.5 \times 10^{7} J \)
D. \( 1.65 \times 10^{6} J \)


Plot the graph of line \( x=5 \)


How are \( X e O_{3} \) and \( X e O F_{4} \) prepared?


Which of the following is not simple
harmonic function?
A \( \cdot y=a \sin 2 \omega t+b \cos ^{2} \omega t \)
B. \( y=a \sin \omega t+b \cos 2 \omega t \)
c. \( y=1-2 \sin ^{2} \omega t \)
D \( \cdot y=(\sqrt{a^{2}+b^{2}}) \sin \omega t \cos \omega t \)


A \( 0.01 m \) aqueous solution of
\( \boldsymbol{K}_{3}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}\right] \) freezes \( \mathbf{a t}-\mathbf{0 . 0 6 2}^{\circ} \boldsymbol{C} \)
What is the apparent percentage of
dissociation? \( \left[\boldsymbol{K}_{f} \text { for water }=\mathbf{1 . 8 6}\right] \)
[Note : write the value to the nearest integer


Under suitable
condition temperature,pressure and catalyst,methanol can be obtain by:
A. partial oxidation of hydrocarbons
B. reacting \( H_{2} \) with \( C O \)
C. reacting \( H_{2} \) with \( C O_{2} \)
D. All the above


If the uncertainty in velocities of two
particles \( A \) and \( B \) with \( \operatorname{mass} 1.0 x \) \( 10^{-27} k g \) and \( 1.0 \times 10^{-31} k g \)
respectively is same, the ratio of uncertainty in the positions of \( A \) and \( B \) is :
A . 1000:
B. 10,000:
c. 1: 1000
D. 1:10,000


If an AP, ratio of the 4 th and 9 th terms is
\( 1: 3, \) find the ratio of 12 term and 5 th
term?


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


Prove \( : \frac{\cos ^{2} \theta}{1-\tan \theta}+\frac{\sin ^{3} \theta}{\sin \theta-\cos \theta}=1+ \)
\( \sin \theta \cos \theta \)


\( 0.01 \mathrm{M} \) solution of \( \mathrm{KCl} \) and \( \mathrm{CaCl}_{2} \) are
prepared in water. The freezing point of \( K C l \) is found to be \( -2^{o} C . \) What is the
freezing point of \( C a C l_{2} \) to be
completely ionised?
\( \mathbf{A} \cdot-3^{\circ} C \)
B \( \cdot+3^{\circ} C \)
\( \mathbf{c} \cdot-2^{o} C \)
D. \( -4^{\circ} C \)


Three vectors \( \vec{P}, \vec{Q} \& \vec{R} \) are shown in
figure let \( S \) be any point on the vector \( \vec{R} \)
the dirt. Between \( P \& S \) is if \( |\vec{R}| \) find the
general equation between \( P, Q \& S \)


During muscle contraction, which of the following decreases?
A. I band
B. A band
c. Hzone
D. Both A and C


The enlargement at one end of each semicircular canal is known as
A . Lagena
B. Utriculus
c. Ampulla
D. sacculus


The total kinetic energy of 1 mole of \( N_{2} \)
at \( 27^{\circ} C \) will be approximately:
A . \( 1500 J \)
B. 1500 calorie
c. 1500 kilo calorie
D. 1500 erg


The term 'mass' is analogous to physical quantity
A. Weight
B. Inertia
c. Force
D. Acceleration


Identify the compounds \( (X),(Y) \) and
\( (Z) \) by making an appropriate choice. \( \boldsymbol{C H}_{3} \boldsymbol{B r} \frac{M \boldsymbol{g} / \text {ether}}{\boldsymbol{x}} \boldsymbol{X} \frac{(\boldsymbol{i}) C \boldsymbol{O}_{2}}{(i i) w a t e r} \)
\( \frac{C H_{3} O H, H^{+}}{\Delta} Z \)
A \( \cdot(X)=C H_{3} M g B r(Y)=C H_{3} C O O H,(Z)= \)
\( C H_{3} C O O C H_{3} \)
B . \( (X)=C H_{3} C H_{2} B r,(Y)=C H_{3} C H_{2} O H,(Z)= \)
\( C H_{3} C H_{2} C H_{2} C H_{3} \)
C \( \cdot(X)=C H_{3} C H_{2} M g B r,(Y)= \)
\( C H_{3} C H_{2} C O O H,(Z)=C H_{3} C H_{2} C O C H_{3} \)
D . \( (X)=C H_{3} C O O H,(Y)=C H_{3} C H_{2} C O C H_{3},(Z)= \)


In an isosceles triangle \( A B C \), with \( A B=A C \), the bisectors of \( \angle B \) and \( \angle C \)
interest each other at \( O \) join \( A \) to \( O \)
show that:
\( (i) O B=O C \)
(ii) \( A O \) bisects \( \angle A \)


The heat transfer in air is poor because
A. it take place mainly due to convection
B. it take place mainly due to conduction
C. it take place mainly due to radiation
D. all of the above


Factorise \( : 3 n^{2}-53 n+232 \)


How do you simplify
\( \sin x+\cot x \cdot \cos x \)


M.I of hemisphere about axis \( 2, \) which is
parallel to diameter but passing
through centre of mass, will be
\( ^{\mathrm{A}} \cdot \frac{83}{320} m R^{2} \)
\( ^{\mathbf{B}} \cdot \frac{2}{5}^{m R^{2}} \)
\( c \cdot \frac{m R^{2}}{5} \)
\( \frac{2}{3}^{m R^{2}} \)


Which of the following is not a
characteristic of chemisorption?
\( \mathbf{A} \cdot \Delta H \) is of the order of \( 400 \mathrm{kJ} \)
B. Adsorption is irreversible
C. Adsorption may be multimolecular layer
D. Adsorption is specific