In an adsorption experiment, a graph between \( \log \left(\frac{x}{m}\right) \) versus \( \log p \) is found
to be linear with slope of \( 45^{\circ} . \) The intercept on \( \log \left(\frac{\boldsymbol{x}}{\boldsymbol{m}}\right) \) axis was found to
\( 0.3010 . \) The amount of the gas adsorbed per gram of charcoal under the pressure of 0.5 atm will be:
A . 1.0
в. 2.0
c. 0.50
D. 0.25


Two waves of equal amplitude \( x_{0} \) and equal frequency travel in the same
direction in a medium. The amplitude of the resultant wave is
A . 0
B. \( x_{0} \)
\( c \cdot 2 x_{0} \)
D. Between 0 and \( 2 x_{0} \)


The oxidation potential of a hydrogen
electrode at \( p H=10 \) and \( P_{H_{2}}=1 \) atm
is:
A . \( -0.59 V \)
в. \( 0.00 V \)
\( \mathrm{c} \ldots+0.59 \mathrm{V} \)
D. \( +0.118 V \)


During upward and downwards journeys under gravity, a body passes through a point at 2 sec and 14 sec. The total height reached by the body from the ground is


If two bones of shank region are broken,
they must be
A. Femur and humerus
B. Tibia and fibula
c. Radius and ulna
D. Metacarpals


Thylakoid name was given by
A. Arnon
B. Park and Biggins
c. Park and Frotan
D. Menke


During the developing process in photography, unexposed \( A g B r \) is washed away by complexation of \( A g(I) \) by sodium thiosulphate solution. These washings are often disposed of as waste. However, metallic silver can be
recovered from them by adding cyanide, followed by zinc. What is the hybridization of zinc is the complex formed during the recovery of silver?
A \( \cdot s p^{3} d^{2} \)
B \( \cdot d^{2} s p^{3} \)
\( c \cdot s p^{3} \)
D \( \cdot d s p^{2} \)


ionizes on dissociation in
water and furnishes ions in solution.
A. Mineral acids
B. Bases
c. lonic salts
D. compounds


When sulphur (in the form of \( S_{8} \) ) is
heated at temperature \( T, \) at
equilibrium, the pressure of \( S_{8} \) falls by
\( 30 \% \) from 1.0 atm, because \( S_{8(g)} \) is
partially converted into \( S_{2(g)} \). Find the
value of \( K_{p} \) for this reaction.
A . 0.96
B. 6.14
c. 204.8
D. None of these


The number of lone pair(s) of electrons
on the central atom in \( \left[\boldsymbol{B} \boldsymbol{r} \boldsymbol{F}_{4}\right]^{-}, \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{6} \)
and \( \left[\boldsymbol{S b C l}_{\mathbf{6}}\right]^{3-} \) are respectively:
\( \mathbf{A} \cdot 2,1 \) and 1
B. 2,1 and 0
c. 2,0 and 1
D. 1,0 and 0


Find the co ordinates of the point where the line through (3,4,1) and (5,1,6) \( \operatorname{crosses} X Y- \) plane


What is Tyndall effect?


What is the IUPAC name of ferrocene?
A. bis (cyclopentadienyl) iron
B. dicyclopentadienyl iron
c. discyclopentadienyl iron
D. bis (cyclopentyI) iron


Parachute type of mechanism of seed dispersal is found in
A. Pea/ Leguminosae
B. Mustard/ Cruciferae
c. cotton/ Malvaceae
D. Taraxacum/ compositae


Which is correct relation?
\( \mathbf{A} \cdot A_{e q \cdot(K O O C \cdot C O O N a)}=\frac{1}{2} \lambda_{K^{+}}+\frac{1}{2} \lambda_{N a^{+}}+\frac{1}{2} \lambda_{O X^{2}} \)
B. \( A_{e q .(\text {KOOC} \cdot \text {COONa})}=\lambda_{K^{+}}+\lambda_{N a^{+}}+\lambda_{O X^{2-}} \)
C \( \cdot A_{\text {eq. }(\text { KOOC } \cdot \text { COON } a)}=\lambda K^{+}+\lambda_{N a^{+}}+\frac{1}{2} \lambda_{O X^{2}-} \)
D. \( A_{e q .(\text {KOOC} \cdot \text {COONa})}=\frac{1}{2} \lambda_{K^{+}}+\frac{1}{2} \lambda_{N a^{+}}+\lambda_{O X^{2}} \)


If \( P \) is (-3,4) and \( M y M x(P) \) shows the reflection ofthe point \( P \) in the \( x \) -axis and then the reflection of the image in the \( y \) -
axis, then \( M_{y} M_{x}(P) \) is
\( A \cdot(3,4) \)
B. (-3,-4)
c. (-3,4)
D. (3,-4)


Which of the following independent quantities is not used to specify the
earth's magnetic field.?
A. Magnetic declination \( (\theta) \)
B. Magnetic dip.
C. Horizontal component of earth's field \( \left(B_{H}\right) \)
D. Vertical component of earth's field \( \left(B_{V}\right) \)


\( \lim _{x \rightarrow 0} \frac{\sqrt[3]{27+x}-3}{x}= \)
A \( \cdot \frac{1}{9} \)
в. \( \frac{1}{27} \)
\( c \cdot \frac{1}{3} \)
D.


Match the following and choose the
correct option
\( \begin{array}{llll}\text { A } & \text { String vibration } & \text { 1. } & \text { Tabla } \\ \text { B } & \text { Membrane vibration } & \text { 2. } & \text { Cymbals } \\ \text { C } & \text { Vibration of air } & \text { 3. } & \text { Sitar } \\ \text { D } & \text { Vibration of plate } & \text { 4. } & \text { Flute }\end{array} \)
\( A \cdot A-1, B-2, C-3, D-4 \)
B. A-2, B-1, C-4, D-3
C. A-3, B-1, C-4, D-2
D. A-4, B-3, C-2, D-1


Assertion
The effects of charge exchange are usually only noticed when at least one
of the surfaces has a high resistance to
electrical flow.
Reason
This is because the charges that transfer to or from the highly resistive
surface are more or less trapped there for a long enough time for their effects to be observed.
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


For a reaction \( \boldsymbol{X} \longrightarrow \boldsymbol{Y}, \) the graph of
the product concentration (x) versus time (t) came out to be straight line passing through the origin. Hence the \( \operatorname{graph} \) of \( \frac{-\boldsymbol{d}[\boldsymbol{X}]}{\boldsymbol{d} \boldsymbol{t}} \) and time would be:
A. straight line with a negative slope and an intercept on y-axis
B. straight line with positive slope and an intercept on \( y \) axis
c. a straight line parallel to x-axiss
D. a hyperbola


Study the graph carefully and answer
the question given below it.

The import in 1976 was approximately how many times that of the year \( 1971 ? \)
A . 0.31
B. 1.68
\( c .2 .41 \)
D. 3.22


Find the value of \( c \) if \( L M V T \) conditions
are satisfied
\( 2 x^{2}-7 x+10 \) on [2,5]


The value of \( \cos \left(2 \cos ^{-1} 0.8\right) \) is
A . 0.48
B. 0.96
\( c .0 .6 \)
D. 0.28


The biological treatment of waste water
makes use of
A. Aerobic bacteria and fungi
B. Anaerobic bacteria and algea
c. Aerobic and anaerobic bacteia
D. Anaerobic bacteria and Eucalyptus leaves


\( \frac{(1+i)^{2011}}{(1-i)^{2009}}= \)
A . -1
B.
\( c \cdot 2 \)
D. -


\( \int_{0}^{\pi / 2} \frac{\cos 2 x}{(\sin x+\cos x)^{2}} d x=\dots \dots \)
\( ^{A} \cdot \frac{\pi}{4} \)
в. \( \frac{\pi}{2} \)
\( c \cdot 0 \)
\( D \cdot-\frac{\pi}{4} \)


A sample of wustite \( F e_{x} O \) contains one \( \boldsymbol{F} e(\boldsymbol{I} \boldsymbol{I} \boldsymbol{I}) \) for every three \( \boldsymbol{F} \boldsymbol{e}(\boldsymbol{I} \boldsymbol{I}) . \) The
value of \( x \) is:
\( \mathbf{A} \cdot 9 / 8 \)
в. \( 8 / 9 \)
c. \( 3 / 4 \)
D. \( 4 / 3 \)


An ATP molecule is structurally most similar to a molecule of
A. RNA molecule
B. Vitamin molecule
c. Amino acid
D. Fatty acid


toppr
Q Type your question
\( (\mathbf{A}) \)
COO
This question has multiple correct options
A. The products (B) and (D), respectively, are:
and
B. The products (B) and (D), respectively are:
and
c. Phenol cannot be chlorinated because the ring is
susceptible to oxidation by \( C 1_{2} \)
ation of
(C) from
(B) proceeds by Arsn addition-elimination


Jill is putting a tile floor in her kitchen She needs 52 tiles to cover the whole
floor. There are 24 tiles in a box. A box
\( \operatorname{costs} R s .23 .95 . \) Individual tiles cost \( R s \)
2.95. Sales tax is \( 5 \% \). How much will 52
tiles cost approximately, including sales tax?
A . \( R s .50 \)
B. Rs. 57
c. \( R s .60 \)
D. \( R s .63 \)


French chemist laid the
foundation to the scientific
investigation of matter by describing that substances react by following certain laws.
A. Dalton
B. Rutherford
c. Anton won leuwonhook
D. A. Lavoisier


Which of the following statements is the inverse of "If you do not understand geometry, then you do not know how to reason deductively."?
A. If you reason deductively, then you understand geometry.
B. If you understand geometry, then you reason deductively.
c. If the do not reason deductively, then you understand geometry.
D. None of these


Which of the following is not a product of fertilization.
A. Zygote in algae
B. Seeds of cycas
c. Fruits of mango
D. Endosperm of cotton


At which height from the earth's surface, acceleration due to gravity is
decreased by \( 75 \% \) of its value at earth's
surface.


A solid conducting sphere having a
charge \( Q \) is surrounded by an
uncharged concentric conducting spherical shell. Let the potential difference between the surface of the
solid sphere and that of the outer surface of the shell be \( V \). If the shell is
now given a charge of \( -3 Q . \) Find out the
new potential difference between the
two surface is:
\( \mathbf{A} \cdot V \)
B. \( 2 V \)
c. \( 4 V \)
\( \mathbf{D} \cdot-2 V \)


Differentiate the following \( x^{2}(3 x-2)^{4} \cos x \)


High quality camera lenses are often coated to prevent reflection. A lens has
an optical index of refraction of 1.72 and a coating with an optical index of refraction of \( 1.31 . \) For near normal
incidence the minimum thickness of
the coating to prevent reflection
for wavelength of \( 5.3 \times 10^{-7} m \) is :
A. \( 0.75 \mu m \)
в. \( 0.2 \mu m \)
c. \( 0.1 \mu m \)
D. \( 1.75 \mu m \)


List some ways in which friction
between two surfaces can be reduced.


A current of \( 3 A \) flows through the \( 2 \Omega \)
resistor shown in the circuit. The power dissipated in the \( 5 \Omega \) resistor is
4.44
В. 2 И
\( c \cdot 1 W \)
\( 0.5 \mathrm{W} \)


The sum of the last eight coefficients in
the expansion of \( (1+x)^{15}, \) is \( ? \)
A \( \cdot 2^{16} \)
B . \( 2^{15} \)
\( c \cdot 2^{14} \)
D. none of these


Write the argument of \( (1+\sqrt{3})(1+ \)
\( i)(\cos \theta+i \sin \theta) \)


The Young's modulus of a rubber string
\( 8 \mathrm{cm} \) long and density \( 1.5 \mathrm{kg} / \mathrm{m}^{3} \) is \( 5 \times \)
\( 10^{8} N / m^{2}, \) is suspended on the ceiling
in a room. The increase in length due to its own weight will be:-
A \( \cdot 9.6 \times 10^{-5} m \)
В. \( 9.6 \times 10^{-11} m \)
c. \( 9.6 \times 10^{-3} m \)
D. \( 9.6 \mathrm{m} \)


Why Metals form positive ions?


\( \operatorname{Given} \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{3} & \mathbf{6} \\ -\mathbf{2} & -\mathbf{8}\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{ll}\mathbf{2} & \mathbf{1 6}\end{array}\right] \)
find the matrix \( \boldsymbol{X} \) such that \( \boldsymbol{X} \boldsymbol{A}=\boldsymbol{B} \)
A \( \cdot\left[-\frac{4}{3}-3\right] \)
в. \( \left[\frac{4}{3} 3\right] \)
\( ^{\mathbf{c}} \cdot\left[\begin{array}{ll}\frac{4}{3} & -3\end{array}\right] \)
D. \( \left[-\frac{4}{3} \quad 3\right] \)


Choose the correct answer from the
alternatives given. To which of the following organ/blood is supplied by the internal carotid artery?
A. Kidney
B. Liver
c. Heart
D. Brain


Find the whole quantity if \( 12 \% \) of it is Rs
\( \mathbf{1 0 8 0} \)


The probability that at least one of the events \( A \) and \( B \) occur is \( 0.6 . \) If \( A \) and \( B \)
occur simultaneously with probability
0.2, then \( \boldsymbol{P}(\overline{\boldsymbol{A}})+\boldsymbol{P}(\overline{\boldsymbol{B}})= \)
A . 0.4
B. 0.8
c. 1.2
D. 1.


From a solid cylinder whose height is \( 2.4 \mathrm{cm} \) and diameter \( 1.4 \mathrm{cm}, \) a concial
cavity of the same height and same diameter is hollowed out. Find the total
surface area of the remaining solid to
the nearest cm.


A stone is thrown vertically upward
with an initial velocity of \( 40 m / s \)
Taking \( g=10 m / s^{2}, \) find the maximum
height reached by the stone. What's the net displacement and the total distance covered by the stone?


Two wires of same material and same
diameter have lengths in the ratio 2: 5 They are stretched by the same force. The ratio of work done in stretching them is :
A .5: 2
B. 2:5
\( c \cdot 1: 3 \)
D. 3:


\( \int_{0}^{\pi / 2} \frac{\sin x-\cos x}{1+\sin x \cos x} d x \)


The term independent of \( x \) in the expansion of \( \left(1+x+2 x^{3}\right)\left(\frac{3 x^{2}}{2}-\right. \)
\( \left.\frac{1}{3 x}\right)^{9} \) is
A \( \cdot \frac{13}{54} \)
в. \( \frac{15}{54} \)
c. \( \frac{17}{54} \)
D. \( \frac{19}{54} \)


The effect of repulsion between the two lone pairs of electrons present on oxygen in water molecule is a:
A. no change in \( H-O-H \) bond angle
B. decrease in \( H-O-H \) bond angle
c. increase in \( H--O-H \) bond angle
D. all atoms will be in one plane


A charged particle having charge \( 10^{-6} C \) and mass of \( 10^{-10} k g \) is fired
from the middle of the plate making an
angle \( 30^{\circ} \) with plane of the plate. Length
of the plate is \( 0.17 \mathrm{m} \) and it is sperated
by 0.1 m.Electric field \( E=10^{-3} N / C \) is
present between the plates.Just outside the plates magnetic field is present. Find the velocity of projection of charged particle and magnitude of the magnetic field perpendicular to the plane of the figure,if it has to graze the plate at \( C \) and \( A \) parallel to the surface of the plate .(Neglect gravity)


At \( 400 \mathrm{K} \), the root mean square (r.m.s) speed of a gas \( \mathrm{X} \) (molecular weight \( = \)
40 ) is equal to the most probable speed of gas \( Y \) at 60 K. The molecular weight of
the gas Y is:
\( A \cdot 3 \)
B. 4
c. 10
D.


A silicon piece and a silver piece are connected in series and a potential
difference is applied between their free ends. The potential difference applied
on them are \( V_{1} \) and \( V_{2} \) respectively
They are then cooled to \( 200 K . \) Now
A \( \cdot V_{1} \) increases and \( V_{2} \) decreases
B. Both increase
c. Both decrease
D. \( V_{1} \) decreases and \( V_{2} \) increases


The co-ordinates of the point of trisection of the line segment joining the points (-4,3) and (2,-1) are
A \( .(2,1) \)
в. (3,1)
\( ^{\mathbf{c}} \cdot\left(-2, \frac{5}{3}\right) \)
D. None of these


Which phylum shows bilateral
symmetry and no body cavity?
A. coelenterate
B. Platyhelminthes
c. Aschelminthes
D. Annelida


Volume is a derived quantity of
A. Length
B. Mass
c. Density
D. Relative density


Find area of parallelogram whose base
is \( 24 \mathrm{cm} \) and height is \( 5 \mathrm{cm} \)


Show that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same
ratio.


If the points (2,1),(3,-2) and \( (a, b) \) are
collinear then
\( A \cdot a+b=7 \)
B. 3a+b=7
c. a-b=7
D. 3a-b=7


Discuss the different type of teeth along
with their structures and functions.


Smoke is a colloidal system of carbon
dispersed in air. This system is termed
as aerosol.
If true enter 1 , else enter 0 .
\( A \)


State the requirements of a good unit.


Why are glass tumblers made of thin
glass?


Identify (A) To (C)


Identify the correct sequence of given steps for the conversion of calcium
carbide to methyl alcohol.
(a) Reaction with aqueous \( K O H \)
(b) Hydrolysis
(c) Reaction with soda lime
(d) Reaction with \( H a S O_{4} / H_{2} S O_{4} \)
(e) Reaction with \( \boldsymbol{H} \boldsymbol{g} \boldsymbol{S} \boldsymbol{O}_{4} \)
(f) Reaction with \( P C l_{5} \)
A. \( b d e c f a \)
B. \( b d c \) a \( f e \)
c. \( b \) f \( d \) e a \( c \)
D. \( d b c e f a \)


Which of the following is key event of
anaphase of mitotic division?
A. Chromosomes are moved to spindle equator and get aligned through spindle fibres to both poles
B. Centromeres split and chromatids separate
C. Chromosomes cluster at opposite spindle poles and their identity is lost as discrete elements
D. Both
(b) and (c)


A bouquet from 11 different flowers is to be made so that it contains not less
then three flowers. Then the number of
the different ways of selecting flowers to from the bouquet
A . 1972
в. 1952
c. 1981
D. 1947


A member of these family with positive
gradient making an angle of \( \frac{\pi}{4} \) with the line \( 3 x-4 y=2, \) is
A. \( 7 x-y-5=0 \)
B. \( 4 x-3 y+2=0 \)
c. \( x+7 y=15 \)
D. \( 5 x-3 y-4=0 \)


In a trapezium whose parallel sides measure \( 24 \mathrm{cm} \) and \( 15 \mathrm{cm} \) and the
distance between them is \( 10 \mathrm{cm} . \) Find
the area of trapezium.
A \( \cdot 215 \mathrm{cm}^{2} \)
В. \( 205 \mathrm{cm}^{2} \)
\( c \cdot 195 \mathrm{cm}^{2} \)
D. \( 295 \mathrm{cm}^{2} \)


A particle of mass mm sides. The magnitude of impulse applied at each corner of the polygon is:
A \( \cdot 2 m v \sin \frac{\pi}{2 n} \)
B. \( m v \sin \frac{\pi}{2 n} \)
\( ^{\mathrm{c}} \cdot 2 m v \cos \frac{\pi}{2 n} \)
D. \( m v \cos \frac{\pi}{2 n} \)


The correct statement is
A. The nucleus \( _{3}^{6} L i \) can emit an alpha particle
B. The nucleus 210 84 Po can emit a proton.
C. Deuteron and alpha particle can undergo complete fusion.
D. The nuclei 70
30 \( Z n \) and 82
34 \( \mathrm{Se} \) can undergo complete
fusion.


In dicot root, showing secondary growth,
cork is found
A. External to primary cortex
B. Inner to epidermis and outer to pericycle
C. Outer to endodermis and inner to primary cortex
D. Inner to endodermis and external to primary phloem


Classify the following substance in the table given below.
Ink, Soda, Water, Brass, fog, blood, aerosol, sprays, fruit salad, black coffee, oil and water, boot polish, air, nail
polish, starch solution, milk.

Solution Suspensions Emulsion


A wheel of radius \( 2 \mathrm{m} \) having 8 conducting concentric spokes is rotating about its geometrical axis with an angular velocity of 10 rad/s in a uniform magnetic field of \( 0.2 T \) perpendicular to its plane. The value of induced emf between the rim of the
wheel and centre is
A . 2
B. 6
\( c \cdot 4 \)
D. 8


Assertion
The first molecules formed for
replicating cells were most probably
RNA.
Reason
This was proved by origin of ribozyme in
1987 by T. Cech in Tetrahymena.
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


Soap solution is colloidal in nature and
remove the dust particles by which of the following process? This question has multiple correct options
A. Emulsification
B. Adsorbtion
c. Stripping
D. Distillation


Check if the sequence is an AP \( \mathbf{1}, \mathbf{3}, \mathbf{9}, \mathbf{2 7}, \dots \)
A. Yes, it is an AP
B. No
c. Data Insufficient
D. Ambiguous


Which of the following is an event which
does not occur during anaphase- \( 1 ? \)
A. Spindle fibres pull homologous chromosomes towards the opposite poles of the spindle
B. The homologous chromosomes break their connection and separate out into two haploid sets or dyads
C. One such set is present at each end of the spindle
D. The process of separation of chromosomes which take place is called disengagement


Alcohol \( +H C l \leftrightharpoons \) Alkyl halide \( +H_{2} O \)
Fo this above reaction, which is needed
to make the reaction reversible.
A. Anhydrous \( Z n C l_{2} \)
в. conc. \( H_{2} S O_{4} \)
c. \( C a C l_{2} \)
D. Excess of water


A hard water sample has 131 ppm
CaSO \( _{4} \). What fraction of the water
must be evaporated in a container
before solid \( C a S O_{4} \) begins to deposit. \( \boldsymbol{K}_{s p} \) of \( \boldsymbol{C a} \boldsymbol{S} \boldsymbol{O}_{4}=\boldsymbol{9} \cdot \boldsymbol{0} \times \boldsymbol{1} \boldsymbol{0}^{-\boldsymbol{6}} \)
\( \mathbf{A} \cdot 52 \)
B. 68
c. 85
D. 42


Find the shortest distance between the \( \operatorname{lines} \bar{r}=4 \bar{i}-\bar{j}+\lambda(\bar{i}+2 \bar{j}-5 \bar{k}) \) and
\( \overline{\boldsymbol{r}}=\overline{\boldsymbol{i}}-\overline{\boldsymbol{j}}+2 \overline{\boldsymbol{k}}+\boldsymbol{\mu}(\overline{\boldsymbol{i}}+\mathbf{2} \overline{\boldsymbol{j}}-\mathbf{5} \overline{\boldsymbol{k}}) \)
A. \( \sqrt{220} \)
B. \( \frac{\sqrt{221}}{\sqrt{30}} \)
c. 432
D. \( \sqrt{33} \)


Which among the following element has the lowest value of ionization energy?
\( A \cdot \) Mg
B. ca
c. Ва
D. sr


Consider the following:
1. \( \sin ^{-1} \frac{4}{5}+\sin ^{-1} \frac{3}{5}=\frac{\pi}{2} \)
2. \( \tan ^{-1} \sqrt{3}+\tan ^{-1} 1=-\tan ^{-1}(2+ \)
\( \sqrt{\mathbf{3}}) \)
Which of the above is/are correct?
A. 1 only
B. 2 only
c. Both 1 and 2
D. Neither 1 nor 2


Regarding the magnetic properties of
lanthanides and actinides the correct
statement is:
A. Lanthanides are weakly paramagnetic while actinides are strongly paramagnetic
B. Quenching of orbital contribution is greater in lanthanides than in actinides
C. \( 5 f \) electrons in actinides are too diffuse and are less
effectively shielded which results in considerable quenching of orbital contribution, and hence the magnetic moments of actinides are significantly less than theoretically predicted values
D. Because of diffused f electrons there is no quenching of orbital contribution towards magnetic moment


A bird moves from point \( (1 m,-2 m, 3 m) \) to \( (4 m, 2 m, 3 m) . \) If
the speed of the bird is \( 10 m / s \), then the
velocity vector of the bird in \( \boldsymbol{m} / \boldsymbol{s} \) is:
\( \mathbf{A} \cdot 5(\hat{i}-2 \hat{j}+3 \hat{k}) \)
B . \( 5(4 \hat{i}+2 \hat{j}+3 \hat{k}) \)
c. \( 0.6 \hat{i}+0.8 \hat{j} \)
D. \( 6 \hat{i}+8 \hat{j} \)


Match the following hormones with the respective disease.
(a) Insulin
(i) Addison's disease
(b) Thyroxin
(ii) Diabetes insipidus
(c) Corticoids
(iii) Acromegaly
(d) Growth Hormone
(iv) Goitre
(v) Diabetes mellitus
Select the correct option.
\( A \cdot(a)-(v),(b)-(i),(c)-(i i),(d)-(i i i) \)
B. (a)-(ii), (b)-(iv), (c)-(iii), (d)-(i)
\( c \cdot(a)-(v),(b)-(i v),(c)-(i),(d)-(i i i) \)
D. (a)-(ii), (b)-(iv), (c)-(i), (d)-(iii)


Evaluate \( \int_{0}^{1} \frac{\mathbf{1}-\boldsymbol{x}}{\mathbf{1}+\boldsymbol{x}} \cdot \frac{\boldsymbol{d} \boldsymbol{x}}{\sqrt{\boldsymbol{x}+\boldsymbol{x}^{2}+\boldsymbol{x}^{3}}} \)
A \( \cdot \frac{\pi}{3} \)
в.
c. \( \frac{\pi}{12} \)
D.


In the circuit shown, the galvanometer shows zero current.The value of
resistance R is :
\( 4.1 \Omega \)
В. \( 10 \Omega \)
\( c \cdot 4 \Omega \)
D. \( 9 \Omega \)


In the transition elements the incoming electron occupies \( [n-1] \) d sublevel in preference to
\( A \cdot n p \)
B. ns
c. [n-1]d
D. \( [n+1] s \)


sphere of radii 'a' and 'b' respectively (see figure), has volume charge density \( p=\frac{A}{r}, \) Where \( A \) is a constant and \( r \) is
the distance from the centre. At the
centre of the spheres is a point charge
Q. The value of A such that the electric
field in the region between the spheres
will be constant, is:
\( A \)
B.
\( c \cdot \frac{2 Q}{\pi a^{2} Q} \)
D. \( \frac{Q}{2 \pi a^{2}} \)


State whether given statement is True or False
A device which receives and then
transmits electromagnetic signal in an artificial satellite is called transponder.
A. True
B. False


Mean free path does not depend on
\( A \cdot \rho \)
B. T
\( c \cdot d \)
D.


Blocks A and B are connected as shown
in figure. Find the relation between
acceleration of block \( A \) and \( B \)
A \( \cdot a_{A}=2 a_{B} \)
В . \( a_{B}=2 a_{A} \)
\( c \cdot a_{4}=4 a_{B} \)


An engine draws water from a depth of \( 10 m \) with constant speed \( 2 m / s \) at the rate of \( 10 \mathrm{Kg} \) per 10 second The power
of the engine is (in \( w a t t): \) (Take: \( g= \) \( 9.8 m / s^{2} \)
A. 102
B. 98
\( c .100 \)
D. 200


Evaluate: \( \int \frac{\cos ^{3} x}{\sin ^{2} x+\sin x} \)


The correct IUPAC name of the
compound is:
\[
\begin{array}{c}
\mathbf{C H}_{3} \\
\mathbf{C H}_{3}-\mathbf{C H}_{2}-\mathbf{C}=\mathbf{C H}-\mathbf{C H}_{2}-\mathbf{C H}-\mathbf{C H}_{3} \\
\mathbf{C H}_{3}-\mathbf{C H}_{2}-\mathbf{C H}-\mathbf{C H}_{2}-\mathbf{C H}_{2}-\mathbf{C H}_{2}-\mathbf{C H}_{3}
\end{array}
\]
A. 5,6 -dimethyl-8-methyldec-6-ene
B. 5,6-Diethyl-2-methyldec-4-ene
c. 6 -butyl-5-ethyl-3-methyloct-4-ene
D. 5,6-diethyl-9-methyldec-6-ene


What are the harmful effects of
ultraviolet radiations?
A. It can cause skin cancer
B. It contributes to global warming.
c. It contributes to greenhouse effect.
D. It can cause depletion of natural resources.


What is the catalyst used in the
preparation of sulphur trioxide from sulphur dioxide?


f \( \boldsymbol{I}=\int \frac{\boldsymbol{d} \boldsymbol{x}}{(1+\sin \boldsymbol{x})^{4}}= \)
\( \frac{-\boldsymbol{A}}{\mathbf{4} \mathbf{9} \mathbf{9} \mathbf{2}}\left(\frac{\mathbf{1}}{\mathbf{7}} \boldsymbol{u}^{\mathbf{7}}+\frac{\mathbf{3}}{\mathbf{5}} \boldsymbol{u}^{\mathbf{5}}+\boldsymbol{u}^{\mathbf{3}}+\boldsymbol{u}\right)+\boldsymbol{C} \)
where \( u=\frac{1-2 \sin x}{1+\sin x} \) then \( A \) is equal


Explain the formation of ionic bond with a sutable example.


The hemispherical dome of a building
needs to be painted. If the circumference of the base of dome is
\( 17.6, \) find the cost of painting it, given the cost of painting is \( R s .5 \) per
\( 100 \mathrm{cm}^{2} \)


This S.I. unit of force is
A. Joules
B. Newton
c. watt
D. Dyne


the density of the atmosphere at sea
level is \( 1.29 \mathrm{kg} / \mathrm{m}^{2} \). Assume that it does not change with altitude. The how high would the atmosphere extend?


\( 45 \% \) of the students in a school are boys.
If the total number of students in the
school is 880 , find the number of girls
in the school.


Three charges \( -2 q, q, q \) are placed on the vertices of an equilateral triangle. At the incentre of the triangle,
A. the field is zero but the potential is non-zero.
B. the field is non-zero but the potential is zero.
c. both the field and the potential is zero.
D. both the field and the potential is non-zero


The main purpose of cellular respiration
is to
A. Convert potential energy to kinetic energy
B. Convert kinetic energy to potential energy
C . Convert energy in to cell chemical
D. Convert energy stored in the chemical bonds of glucose to an energy that the cell can use


Few isomers are given below. The correct statement regarding them are:
(i) \( \left[\boldsymbol{C r}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right] \boldsymbol{C l}_{3} \)
(ii) \( \left[\boldsymbol{C r}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{5} \boldsymbol{C l}\right] \boldsymbol{C l}_{2} \cdot \boldsymbol{H}_{2} \boldsymbol{O} \)
\( \left(\text { iii) }\left[\boldsymbol{C r}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{4} \boldsymbol{C l}_{2}\right] \boldsymbol{C l} . \boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O}\right. \)
A. (i),(ii) and (iii) are hydrate isomers
B. (i),(ii) and (iii) are coordination isomers.
\( c . \) (i),(ii) and (iii) are ionisation isomers
D. (i) and (ii) are stereo-isomers


\( Z n(O H)_{2} \) is an amphoteric hydroxide which is involved in the following two equilibria existing simultaneously in aqueous solution.
\( \boldsymbol{Z n}(\boldsymbol{O} \boldsymbol{H})_{2}(\boldsymbol{s}) \rightleftharpoons \boldsymbol{Z} \boldsymbol{n}^{2+}(\boldsymbol{a} \boldsymbol{q})+ \)
\( \mathbf{2 O H}^{-}(\boldsymbol{a q}) ; \boldsymbol{K}_{s p}=\mathbf{1 . 2} \times \mathbf{1 0}^{-\mathbf{1 7}} \)
\( \operatorname{Zn}(O H)_{2}(s)+2 O H^{-}(a q) \rightleftharpoons \)
\( \left[Z n(O H)_{4}\right]^{2-}(a q) ; K_{c}=0.12 \)
At what \( p H \) the solubility of \( Z n(O H)_{2} \) will be minimum?
A. \( p H=4.11 \)
в. \( p H=6.32 \)
c. \( p H=7.68 \)
D. \( p H=9.99 \)


Rank the following compounds in order
of decreasing acid strength (most
acidic \( \rightarrow \) least acidic)
\( \mathbf{A} \cdot 2>4>1>3 \)
B. \( 1>3>4>2 \)
\( \mathbf{c} \cdot 3>1>2>4 \)
D. \( 3>1>4>2 \)


\( A B C D \) is a rectangle inscribed in a
quadrant of a circle having radius
10cm. If \( A D=2 \sqrt{5} c m \), find the area of
\( A B C D \)
\( A \cdot 30 c m^{2} \)
3. \( 50 \mathrm{cm}^{2} \)
\( c \cdot 40 c m^{2} \)
D. \( 35 c m^{2} \)


A certain sum of money amounts to
\( R s .756 \) in 2 years and to \( R s .873 \) in \( 3 \frac{1}{2} \) years at a certain rate of simple interest. What is the rate of interest per
annum?
A. \( 11 \% \) p.a.
в. \( 12 \% \) р.а.
c. \( 13 \% \) p.a.
D. \( 14 \% \) р.а.


What is the significance of meiosis?
A. Maternal and paternal genes are exchanged
B. Leads to variation
C. Both A and B
D. similar offsprings


In a series LCR circuit \( \boldsymbol{R}=\mathbf{3 0 0 \Omega}, \boldsymbol{L}= \)
\( \mathbf{0 . 9 H}, \boldsymbol{C}=\mathbf{2} \boldsymbol{\mu} \boldsymbol{F}, \boldsymbol{\omega}=\mathbf{1 0 0} \mathbf{o} \) rad/s. The
impedance of the circuit is?
A. \( 500 \Omega \)
B. 1300\Omega
c. \( 400 \Omega \)
D. \( 900 \Omega \)


Assertion
Colloidal sol \( \boldsymbol{F e}(\boldsymbol{O H})_{3} \) formed by
peptization carries positive charge.
Reason

During the formation of positively
charged colloidal particles of \( \boldsymbol{F e}(\boldsymbol{O H})_{3} \)
the electrons are lost by the colloidal
particles of \( \boldsymbol{F e}(\boldsymbol{O H})_{3} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Which of the following sets does not belong to the same group?
A. \( L i, N a, K \)
в. \( N, O, F \$ \)
c. \( B e, M g, C a \)
D. \( H e, N e, A r \)


Match the following:
Section A \( \quad \) Section B
\( P . \) Converts electric energy in to
1. Fuse \( \quad \) mechanical energy
2 Electric
\( Q . \) Heating effect of electric current generator
3. Electric
\( R . \) Converts mechanical energy in motor \( \quad \) to electrical energy
\( \mathbf{A} \cdot 1-Q, 2-R, 3-P \)
B \( .1-Q, 2-P, 3-R \)
\( \mathbf{c} \cdot 1-P, 2-Q, 3-R \)
D. \( 1-P, 2-R, 3-Q \)


Assertion
Refining of zinc is done by distillation
under reduced pressure.
Reason

Zinc is a transition metal.
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


Who was the first scientist to estimate
the human population
A. Darwin
B. Malthus
c. Garrod
D. Vavilor


Muscular ridges at inner surface of ventricles are called
A. Chordae tendinae
B. Inter ventricular septum
c. Papillary muscle
D. Trabeculae carnae


The reactions of heavy water are slow.
The reason is :
A. heavy water is associated.
B. heavy water is dissociated.
C. heavy water is of higher mass.
D. heavy water is of lower mass.


The range of \( f(x)=\cos [x],-\frac{\pi}{4}<x< \)
\( \frac{\pi}{4}, \) where \( [ \) represent greatest integer
function less than or equal to \( x \) is
\( A \cdot\{0\} \)
B . [-1,1]
\( \mathbf{c} \cdot\{\cos 1,1\} \)
D \( \cdot\{-1,1\} \)


Alkyl halides react with dialkyl copper
reagents to give:
A. Alkenyl Halide
B. Alkanes
c. Alkyl copper halides
D. alkenes


Find the value of \( m \) for which
(i) \( 5^{m} \div 5^{-3}=5^{5} \)
(ii) \( 4^{m}=64 \)
(iii) \( 8^{m-3}=1 \)
(iv) \( \left(a^{3}\right)^{m}=a^{9} \)
(v) \( \left(5^{m}\right)^{2} \times(25)^{3} \times 125^{2}=1 \)
\( (\mathrm{vi}) 2^{m}=(8)^{\frac{1}{3}} \div\left(2^{3}\right)^{2 / 3} \)


Solve equations using substitution method:
\( 5 x-2 y=10 \) and \( 4 x-6 y=3 \)
A \( \cdot \frac{-27}{11} \) and \( \frac{25}{22} \)
B. \( \frac{27}{11} \) and \( \frac{-25}{22} \)
c. \( \frac{27}{11} \) and \( \frac{25}{22} \)
D. \( \frac{-27}{11} \) and \( \frac{-25}{22} \)


The best possible method to determine the age of a tree is
A. To find out the number of branches
B. To measure it's diameter
c. To count the number of annual rings
D. To count the number of leaves


Four rays, 1,2,3 and 4 are incident normally on the face \( P Q \) of an isosceles
prism PQR with apex angles \( \angle Q=120^{\circ} \)
The refractive indices of the material of
the prism for the above rays 1,2,3 and 4 are 1.85,1.96,2.05 and \( 2.15, \) respectively and the surrounding medium is air. Then the rays emerging from the face QR are :
A. 4 only
B. 1 and 2 only
c. 3 and 4 only
D. 1,2,3 and 4


Assertion
Tidal volume is the volume of air
inspired or expired with the normal breath.
Reason
Adult person contains 500 mL expired or inspired volumes of air with each
normal breath.
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


Slaked lime reacts with chlorine to give:
\( \mathbf{A} \cdot C a C l_{2} \)
в. \( C a O \)
\( \mathbf{c} \cdot C a(O C l)_{2} \)
D. \( C a C O_{3} \)


Which of the following statements given
about emulsions is incorrect?
A. The droplets in emulsions are often negatively charged and can be precipitated by electrolytes.
B. Emulsion can be diluted with any amount of the dispersed liquid. On the other hand, the dispersion medium when mixed, forms a separate layer.
C. Emulsions can be broken into constituent liquids by heating, freezing, centrifuging, etc.
D. Emulsions also show Brownian movement and
Tyndall effect.


The probabilities of three events \( A, B, C \) are events such that \( P(A)= \) \( \mathbf{0 . 3}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 4}, \boldsymbol{P}(\boldsymbol{C})=\mathbf{0 . 8}, \boldsymbol{P}(\boldsymbol{A} \cap \)
\( \boldsymbol{B})=\mathbf{0 . 0 8}, \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{C})=\mathbf{0 . 2 8}, \boldsymbol{P}(\boldsymbol{A} \cap \)
\( \boldsymbol{B} \cap \boldsymbol{C})=\mathbf{0 . 0 9 .} \) If \( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B} \cup \boldsymbol{C}) \geq \mathbf{0 . 7 5} \)
Show that \( P(B \cap C) \) lies in the
interval [0.23,0.48]


What does it mean when a collision is
elastic?
A. No energy is gained or lost.
B. Energy is gained
c. Energy is lost
D. The particles can stretch out.
E. The particles slow down


The probability that a leap year not to contain 53 Sundays is.


Choose the correct answers from the
alternatives given :
Which one of the following is the link between glycolysis and Krebs cycle?
A. Acetyl coenzyme A
B. Phosphoenolpyutvic acid
c. Citric acid
D. Acetyl acetic acid


Which of the following give brisk effervescence with baking soda?
A. methanoic acid
B. propanoic acid
c. ethanoic acid
D. all of these


Which of the following kinds of isomerism can nitroethane exhibit?
A. Metamerism
B. Optical isomerism
c. Tautomerism
D. Position isomerism


Sulphide ions in alkaline solution react with solid sulphur to form polyvalent
sulphide ions. The equilibrium constant for the formation of \( S_{2}^{2-} \) and \( S_{3}^{2-} \) from. \( S \)
and \( S^{2-} \) ions are 1.7 and 5.3 respectively.
Calculate equuilibrium constant for the
formation of \( S_{3}^{2-} \) from \( S_{2}^{2-} \) and \( S \)
A . 0.31
в. 3.11
c. 31.3
D. 0.0313


The negation of the boolean expression
\( \sim s \vee(\sim r \wedge s) \) is equivalent to:
\( A \)
B. \( s \wedge r \)
\( \mathrm{c} \cdot s \vee r \)
D. \( \sim s \wedge \sim r \)


Factories:
\( x^{2}+6 x+9 \)


Na Cl is dissolved in water. Which of
the following statement is correct?
A. \( N a^{+} \) is oxidised
B. \( N a^{+} \) is reduced
C. \( N a^{+} \) is hydrolysed
D. \( N a^{+} \) is hydrated


Which solutions have a concentratoin of
\( 1.0 \mathrm{M} ? \)
i. 74 grams of calcium hydroxide dissolved to make 1 liter of
Solution
ii. 74.5 grams of potassium chloride dissolved to maek 1 liter of
Solution
iii. 87 grams of lithium bromide
dissolved to make 1 liter of solution
A. i only
B. iii only
c. i and iii only
D. ii and iii only
E. i, ii and iii


Which of the following options about the
oxidizing property of \( K M n O_{4} \) in acidic
medium is incorrect?
This question has multiple correct options
A \( \cdot H_{2} S \) can be oxidised to \( S O_{4}^{2} \)
B. \( H_{2} S \) can be oxidised to \( S \)
C. \( S O_{3}^{2-} \) can be oxidised to \( S O_{4}^{2} \)
D. \( C_{2} O_{4}^{2-} \) can be oxidised to \( C O_{3}^{2} \)


Prove that:
\( \lim _{x \rightarrow 0} \frac{x^{2} \sin \frac{1}{x}}{\sin x}=0 \)


A dextrorotatory sugar, present in fruits, is:
A. glucose
B. fructose
c. cellulose
D. starch


Which of the following is NOT
calcination?
\( \mathbf{A} \cdot F e(O H)_{3} \cdot x H_{2} O \rightarrow F e_{2} O_{3}+H_{2} O \)
B. \( C u C O_{3} \cdot C u(O H)_{2} \rightarrow^{2} C u O+C O_{2}+H_{2} O \)
\( \mathbf{c} \cdot C a C O_{3} \rightarrow^{C} a O+C O_{2} \)
D. \( \left(N H_{4}\right)_{2} C O_{3} \rightarrow^{2} N H_{3}+C O_{2}+H_{2} O \)


In a DC generator, induced emf in the armature is
A. DC
B. AC
c. fluctuating DC
D. both \( A C \) and \( D C \)


Mendeleev predicted the existence of
certain elements not known at that
time and named two of them as Eka -
silicon and Eka - Aluminium.

Mention the group of these elements in
the Modern Periodic Table :
A. Group 12 and Group 13.
B. Group 14 and Group 15.
c. Group 14 and Group 13.
D. Group 15 and Group 13


Let \( \boldsymbol{A}=\{1,2,3,4\} \) and \( B=\{2,4,6,8\} \)
Then find \( \boldsymbol{A}-\boldsymbol{B} \)


The non-metal which is liquid at room
temperature is:
A. chlorine
B. fluorine
c. bromine
D. iodine


The maximum energy in the thermal radiation from a heat source occurs at a
wavelength of \( 12 \times 10^{-5} \mathrm{cm} . \) According
to Wien's displacement law, the temperature of this source will be 'n'
times the temperature of another source for which the wavelength at maximum energy is \( 6 \times 10^{-5} \mathrm{cm} . \) Then
the value of \( n \) is
A . \( 1 / 2 \)
B. 1
\( c \cdot 2 \)
D. 4


\( \operatorname{Let} \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{0} & \boldsymbol{a} \\ \mathbf{0} & \mathbf{0}\end{array}\right] \) and \( (\boldsymbol{A}+\boldsymbol{I})^{50} \)
\( \mathbf{5} \mathbf{0} \boldsymbol{A}=\left[\begin{array}{ll}\boldsymbol{a} & \boldsymbol{b} \\ \boldsymbol{c} & \boldsymbol{d}\end{array}\right] . \) Then the value of \( \boldsymbol{a}+ \)
\( \boldsymbol{b}+\boldsymbol{c}+\boldsymbol{d} \) is
A . 2
B.
\( c \cdot 4 \)
D. none of these


A zener diode, having breakdown
voltage equal to \( 15 V \), is used in a
voltage regulator circuit shown in figure. The current through the diode is :
\( A \cdot 5 m A \)
B. \( 10 \mathrm{mA} \)
\( \mathbf{c} \cdot 15 m A \)
D. \( 20 m A \)


Basic character of fluorides increases
in the order:
A \( \cdot X e F_{6}<X e F_{4}<X e F_{2} \)
B. \( X e F_{2}<X e F_{4}<X e F_{6} \)
c. \( X e F_{2}=X e F_{4}<X e F_{6} \)
D. \( X e F_{2}>X e F_{4}<X e F_{6} \)


In the atmosphere of industrial smog, copper corrodes to form:
A. basic copper carbonate and sulphate
B. copper oxide
c. copper sulphide
D. copper nitrate


Find the values of \( x, \) if
(i) \( \left|\begin{array}{ll}2 & 4 \\ 5 & 1\end{array}\right|=\left|\begin{array}{ll}2 x & 4 \\ 6 & x\end{array}\right| \)
(ii) \( \left|\begin{array}{ll}2 & 3 \\ 4 & 5\end{array}\right|= \)
\( \left|\begin{array}{ll}\boldsymbol{x} & \boldsymbol{3} \\ \boldsymbol{2} \boldsymbol{x} & \boldsymbol{5}\end{array}\right| \)


In interpreting Rutherford's experiments on the scattering of alpha particles by thin foils, one must
examine what the known factors were,
and what the experiment concluded. Which of the following are true in this context?
A. The number of electrons in the target atoms \( (i . e ., Z) \) was settled by these experiments
B. The validity of Coulomb's law for distances as small as \( 10^{-13} \) was known before these experiments.
c. The experiments settled that size of the nucleus could not be larger than a certain value
D. The experiments also settled that size of the nucleus could not be smaller than a certain value


Find a wrong statement from the given
statements.
A. oxalic acid is used for making metal polish
B. benzoic acid is used in manufacture of dyes
C. oxalic acid in form of ferrous potassium oxilate used as developer in photography
D. benzoic acid is used for making metal polish


The differential equation, which represents the family if plane curves
\( \boldsymbol{y}=\boldsymbol{e}^{c \boldsymbol{x}}, \) is
A \( \cdot y^{\prime}=c y \)
B. \( x y^{\prime}-\log y=0 \)
c. \( x \log y=y y^{\prime} \)
D. ylogy = \( x y^{\prime} \)


The growth of a pollen tube towards ovule is caused by
A. Phototropism
B. Hydrotropism
c. Gravitropism
D. chemotropism


Compounds such as alcohols and glucose also contain hydrogen, but are not categorized as acids. Describe an
activity to prove it.


Compare and contrast the chemistry of group 1 metals with that of group 2 metals with respect to oxides.


Form the differential equation from the following primitives, where constant is arbitrary. \( \boldsymbol{y}=\boldsymbol{c} \boldsymbol{x}+\boldsymbol{2} \boldsymbol{c}^{2}+\boldsymbol{c}^{\boldsymbol{3}} \)


state whether the following statement
are true:

Additive inverse of a positive integer is negative.
A. True
B. False


What does Paris code and Vienna code
refer to?
A. Nomenclature of plants
B. Nomenclature of animals
c. Both of the above
D. Anticode


Enzymes in the living systems:
A. provide energy
B. provide immunity
c. transport oxygen
D. catalyse biological reactions


If \( \tan x+2 \tan 2 x+3 \tan 3 x+ \)
\( 8 \cot 8 x=\sqrt{3} \) then the general solution
of \( \boldsymbol{x}= \)
A \( \cdot n \pi+\frac{\pi}{3}, \forall \in Z \)
В \( \cdot n \pi+\frac{\pi}{6}, \forall \in Z \)
c. \( _{n \pi+\frac{\pi}{4}, \forall \in Z} \)
D. \( n \pi, \forall \in Z \)


Evaluate: \( \int_{0}^{\frac{\pi}{2}} \frac{\sin x-\cos x}{1+\sin x \cos x} d x \)


Point (0,-9) lies
A. on the \( X \) -axis
B. In the II quadrant
c. on the Y-axis
D. In the \( I V \) quadrant


Which of the following taxon includes more similar members than the
members of a class?
A. An order
B. A phylum
c. A genus
D. A species
E. A family


The function \( y=\sqrt{2 x-x^{2}} \)
A. increases in (0,1) but decreases in (1,2)
B. decreases in (0,2)
C. increases in (1,2) but decreases in (0,1)
D. increases in (0,2)


Find the value of \( a \) for which the ellipse \( \frac{x^{2}}{y^{2}}+\frac{y^{2}}{b^{2}}=1,(a>b), \) if the extremities
of the latus rectum of the ellipse having positive ordinates lie on the parabola \( x^{2}=-2(y-2) \)


\( \lim _{n \rightarrow \infty} \frac{\left(1^{k}+2^{k}+3^{k}+\ldots . .+n\right.}{\left(1^{2}+2^{2}+\ldots . .+n^{2}\right)\left(1^{3}+2^{3}+\right.} \)
\( \boldsymbol{F}(\boldsymbol{k}), \) then \( (\boldsymbol{k} \in \boldsymbol{N}) \)
A. \( F(k) \) is finite for \( k \leq 6 \)
В. \( F(5)=0 \)
c. \( F(6)=\frac{12}{7} \)
D. \( F(6)=\frac{5}{7} \)


If value of \( x \) which satisfy \( \sin ^{-1} x \leq \) \( \cos ^{-1} x \) is \( x \epsilon\left[a, \frac{b}{\sqrt{c}}\right] \)
Find the value of \( a+b+c \)
A.
B.
\( c \cdot 2 \)
D.


Which of the following is the correct
statement for the molecule, \( \boldsymbol{C} \boldsymbol{s} \boldsymbol{I}_{3} ? \)
A. It is a covalent molecule
B. It contains \( C s^{+} \) and \( I_{3}^{-} \)
c. It contains \( C s^{3+} \) and \( I^{-} \)
D. It contains \( C s^{+}, I_{3}^{-} \) and lattice \( I_{2} \) molecule


The angles of triangle are \( 45^{\circ}, 60^{\circ} \) find the third angle.


Four cubes, each of edge \( 9 \mathrm{cm}, \) are
joined as shown below, then the volume
of the resulting cuboid is in \( c m^{3} \)


A solid cylinder of glass whose diameter
is \( 1.5 m \) and height \( 1 m \) is melted and turned into a sphere. The diameter of ths sphere is-
A. 1 metre
B. 0.75 metre
c. 1.25 metres
D. 1.5 metres


If the polynomials \( \left(2 x^{3}+a x^{2}+3 x-5\right) \)
and \( \left(x^{3}+x^{2}-4 x-a\right) \) leave the same
remainder when divided by \( (x-1), \) find
the value of \( a \)


Given below are four statements (a-d)
regarding human blood circulatory
system.
(a) Arteries are thick-walled and have
narrow lumen as compared to veins.
(b) Angina is acute chest pain when the blood circulation of the brain is
reduced.
(c) Persons with blood group \( A B \) can
donate blood to any person with any blood group under ABO system.
(d) Calcium ions play a very important
role in blood clotting.

Which two of the above statements are
correct?
\( A \cdot(c) \) and (d)
B. (a) and (d)
c. (a) and (b)
D. (b) and (c)


At a certain temperature 2 moles of
carbonmonoxide and 3 moles of
chlorinw were allowed to reach
equilibrium according to the reaction \( \boldsymbol{C O}_{(g)}+\boldsymbol{C l}_{2} \leftrightharpoons \boldsymbol{C O C l}_{2} \) in a 5 lit vessel.
At equilibrium if one mole of \( C O \) is
present then equilibrium constant for the reaction is


Show that total energy of a freely falling
body remains constant during its motion.


Which of the following is NOT a
quadratic polynomial?
\( \mathbf{A} \cdot p(x)=p x^{2}+q x+r \)
B \( \cdot p(x)=a x^{2}+b x+c \)
\( \mathbf{c} \cdot p(x)=x \cdot x^{2}+x \cdot x+x \)
D \( \cdot p(x)=m x^{2}+n x+l \)


Which of the following removes debris
from cells?
A. Blood
B. Lymph
c. Interstitial fluid
D. All of the above


On increasing temperature, the equilibrium constant of exothermic and endothermic reactions
and \( ------- \) respectively:
A. increases and decreases
B. decreases and increases
c. increases and increases
D. decreases and decreases


Pick up the correct statements:
(a) Mitosis occurs in somatic cells and
meiosis in germ cells.
(b) DNA replicates once in mitosis and twice in meiosis.
(c) Mitosis and meiosis occur both in
sexually and asexually reproducing organisms.
A. a only
B. b only
c. c only
D. a and b only
E. b and conly


A force of \( 100 N \) is applied on an area of
\( 4 m^{2} . \) the pressure being applied on the
area is
\( \mathbf{A} \cdot 50 P a \)
B. \( 25 P a \)
c. \( 12.5 P a \)
D. \( 400 P a \)


The first and the last term of an AP are
17 and 350 respectively. If the common
difference is \( 9, \) how many terms are there and what is the sum?


A planet has mass and radius both half
of earth. Acceleration due to gravity \( (g) \)
at its surface should be
A \( \cdot 29.4 m / s^{2} \)
в. \( 19.6 m / s^{2} \)
C. \( 9.8 m / s^{2} \)
D. \( 4.9 \mathrm{m} / \mathrm{s}^{2} \)


A sphere of diameter \( 10 \mathrm{cm} \) weighs 44
kg. The weight of a sphere of the same material whose diameter is \( 6 \mathrm{cm} \) is
A . \( 2.64 \mathrm{kg} \)
в. \( 1.584 \mathrm{kg} \)
c. \( 0.9504 \mathrm{kg} \)
D. \( \frac{4}{3}(0.9504) k g \)


Mention the methods used to decrease
friction


If in a transformer the number of turns
of primary coil and secondary coil are 5 and 4 respectively and \( 240 \mathrm{V} \) is applied to primary coil, then the ratio of current in primary and secondary coil is :
A .4: 5
B. 5: 4
c. 5: 10
D. 8: 12


If \( A \) and \( G \) be \( A . M \) and \( G . M, \) respectively
between two positive numbers. prove that the numbers are \( \boldsymbol{A} \pm \) \( \sqrt{(\boldsymbol{A}+\boldsymbol{G})(\boldsymbol{A}-\boldsymbol{G})} \)


\( \mathbf{A}=\left[\begin{array}{cc}\cos \alpha & \sin \alpha \\ -\sin \alpha & \cos \alpha\end{array}\right] \) then \( \mathbf{A} . \mathbf{A}^{\mathbf{T}} \)
A. Null matrix
в. А
\( c \cdot I \)
D. A


A very long straight conducting wire, lying along the z-axis, carries a current of \( 2 A . \) The integral \( \oint \vec{B} . d \vec{l} \) is computed along the straight line \( P Q \), where \( P \) has
the coordinates \( (2 c m, 0,0) \) and \( Q \) has
the coordintes \( (2 c m, 2 c m, 0) . \) The integral has the magnitude (in Sl units)
\( ^{A} \cdot \frac{\pi}{2} \times 10^{-7} \)
В . \( 8 \pi \times 10^{-7} \)
D. \( \pi \times 10^{-7} \)


Which of the following forms are the most basic in \( 0.1 \mathrm{M} \) solution?
A. \( \mathrm{NaCl} \)
в. NaOCl
c. \( \mathrm{NaClO}_{2} \)
D. \( \mathrm{NaClO}_{3} \)


Graphite is good conductor of current
but diamond is non-conductor because:
A. diamond is hard and graphite is soft
B. graphite and diamond have different atomic configuration
C. graphite is composed of positively charged carbon ions
D. graphite has hexagonal layer structure with mobile \( \pi \) electrons while diamond has continuous tetrahedra
covalent structure with no free electrons


A resistance \( (\boldsymbol{R})=12 \Omega ; \) inductance
\( (L)=2 \) henry and capacitive reactance \( C=5 m F \) are connected in series to an
ac generator, then:
A. at resonance, the circuit impedance is zero
B. at resonance, the circuit impedance is \( 12 \Omega \)
c. the resonance frequency of the circuit is \( 1 / 2 \pi \)
D. at resonance, the inductive reactance is less than the capacitive reactance


The \( p H \) of a solution which turns red
litmus blue can be:
\( \mathbf{A} \cdot \mathbf{1} \)
B. 9
\( c \cdot 4 \)
D.


The range of the function \( f(x)=x^{2}+ \)
\( \frac{1}{x^{2}+1} \) is
\( A \cdot[1,+\infty) \)
B. \( [2,+\infty) \)
\( ^{\mathbf{C}} \cdot\left[\frac{3}{2},+\infty\right) \)
D. None of these


For the reversible process, the value of \( \Delta S \) is given by the expression
A. \( \Delta H / \Delta T \)
в. \( T / q(r e v) \)
\( \mathbf{c} \cdot q(r e v) \times T \)
D. \( q(r e v) / T \)


The threshold wavelength for ejection of an electron from metal is 310 nm. The
kinetic energy of emitted photoelectron is \( 36 \times 10^{-20} J . \) Then the frequency of
incident light is:
A \( \cdot 1.5 \times 10^{15} \mathrm{Hz} \)
B . \( 2.5 \times 10^{18} \mathrm{Hz} \)
c. \( 1 \times 10^{22} H z \)
D. 2.5 \( \times 10^{12} \mathrm{Hz} \)


Braille system are based on:
A. tasting
B. hearing
c. touching
D. smelling


A man (mass \( =50 \mathrm{kg} \) ) and his son \( (\operatorname{mas} s=20 \mathrm{kg}) \) are standing on a
frictionless surface facing each other. The man pushes his son so that he
starts moving at a speed of \( 0.70 m s^{-1} \) with respect to the man. The speed of the man with respect to the surface is :
A. \( 0.20 \mathrm{ms}^{-1} \)
B . \( 0.14 m s^{-1} \)
c. \( 0.47 m s^{-1} \)
D. \( 0.28 m s^{-1} \)


The magnetic potential energy stored in a certain inductor is \( 25 \mathrm{mJ} \), when the
current in the inductor is \( 60 \mathrm{mA} \). This
inductor is of inductance.
A . 1.389 н
В. 0.138 н
c. 13.89 н
D. \( 138.88 \mathrm{H} \)


Consider three matrices \( A= \) \( \left[\begin{array}{ll}\mathbf{2} & \mathbf{1} \\ \mathbf{4} & \mathbf{1}\end{array}\right] \quad \boldsymbol{B}=\left[\begin{array}{ll}\mathbf{3} & \mathbf{4} \\ \mathbf{2} & \mathbf{3}\end{array}\right] \quad \) and \( \quad \boldsymbol{C}= \)
\( \left[\begin{array}{cc}\mathbf{3} & -\mathbf{4} \\ -\mathbf{2} & \mathbf{3}\end{array}\right] \)
The value of the sum \( t r(A)+ \) \( \operatorname{tr}\left(\frac{A B C}{2}\right)+\operatorname{tr}\left(\frac{A(B C)^{2}}{4}\right)+ \)
\( \operatorname{tr}\left(\frac{\boldsymbol{A}(\boldsymbol{B C})^{3}}{\boldsymbol{8}}\right)+\ldots \ldots \ldots .+\infty \) is
\( (\operatorname{tr}(A) \text { denotes trace of a matrix } A) \)
A . 6
B. 9
c. 12
D. none of these


Environmental pollution refers to:
A. peeling of top soil
B. dissipation of energy
C. release of toxic/undesirable materials in environment
D. None of these


A particle of mass m begins to slide down a fixed smooth sphere from the top with negligible initial velocity. What is its tangential acceleration when it breaks off the sphere?
A \( \cdot \frac{2 g}{3} \)
B. \( \frac{\sqrt{5} g}{3} \)
\( c \cdot g \)
D. \( \frac{g}{3} \)


A force of \( 5 \mathrm{N}, \) making an angle \( \theta \) with
the horizontal, acting on an object displaces it by \( 0.4 \mathrm{m} \) along the horizontal direction. If the object gains kinetic energy of 1 J, the horizontal component of the force is?
A . \( 1.5 \mathrm{N} \)
в. 2.5 N
c. 3.5 N
D. 4.5 N


When a weight \( \mathrm{W} \) is hung from one end of a wire of length \( L \) (other end being fixed), the length of the wire increases by 1. If the same wire is passed over a pulley and two weights Weach are hung at the two ends, what will be the total
elongation in the wire?


If two bodies \( A \) and \( B \) of \( 50^{0} C \) comes in
contact with each other. The heat will
flow
\( A \cdot \) Body \( A \rightarrow \) Body \( B \)
B. Body B \( \rightarrow \) Body A
c. nowhere
D. from both the bodies


Which of the following reproduces by budding?
A. Fern
B. Yeast
c. Rhizopus
D. Rose


Solid calcium oxide reacts vigorously with water to form calcium hydroxide accompanied by liberation of heat. This process is called slaking of lime. Which among the following is (are) true about slaking of lime?
(i) It is an endothermic reaction
(ii) It is an exothermic reaction
(iii) The pH of the resulting solution will be more than seven
(iv) The pH of the resulting solution will be less than seven
A \( \cdot \) (i) and (ii)
B. (ii) and (iii)
c. (i) and (iv)
D. (iii) and (iv)


For reaction \( , 2 A+B \rightleftharpoons 2 C, K=x \)
Equilibrium constant for \( \boldsymbol{C} \rightleftharpoons \boldsymbol{A}+\frac{\mathbf{1}}{\mathbf{2}} \boldsymbol{B} \)
will be:
\( A \)
в. \( \frac{x}{2} \)
c. \( \frac{1}{\sqrt{x}} \)
D. \( \sqrt{x} \)


Four particles each of mass ' \( m^{\prime} \) are
placed at the corners of a square of side
\( L^{\prime \prime} . \) The radius of gyration of the system
about an axis normal to the square and
passing through its centre.
A \( \cdot \frac{L}{2} \)
в. \( \frac{L}{\sqrt{2}} \)
\( c . L \)
\( D . \sqrt{2} L \)


If \( x \sin y=\sin (y+a) \) and \( \frac{d y}{d x}= \)
\( \frac{A}{1+x^{2}-2 x \cos a} \) then the value of \( A \) is
\( A \cdot 2 \)
B. \( \cos a \)
\( c .-\sin a \)
D. - -


The figure shows a square plate of
uniform mass distribution. \( A A^{\prime} \) and
\( B B^{\prime} \) are the two axes lying in the plane
of the plate and passing through its
centre of mass. It \( I_{0} \) is the moment of
inertia of the plate about \( A A^{\prime} \) then its
moment of inertia. about the \( B B^{\prime} \) axis
is
\( A \cdot I_{b} \)
B \( \cdot I_{6} \cos \theta \)
\( \mathbf{c} \cdot I_{\theta} \cos ^{2} \theta \)
D. None of thes


The work done in driving a liquid through a pipe against a pressure difference of \( 200 \mathrm{K} \) Pa between the
ends of a pipe at \( 20 K m^{3} \) of water
\( \begin{array}{ll}\text { A. } 2 \times 10^{9} & \text { J }\end{array} \)
В. \( 4 \times 10^{9} \) Л
\begin{tabular}{ll}
с. \( 8 \times 10^{9} \) & Л \\
\hline
\end{tabular}
D. \( 16 \times 10^{9} J \)


A horizontal circular platform of radius
\( 0.5 m \) and mass \( 0.45 k g \) is free to rotate
about its axis. Two massless spring toyguns, each carrying a steel ball of mass \( 0.05 k g \) are attached to the platform at a distance \( 0.25 m \) from the centre on its
either sides along its diameter (see figure). Each gun simultaneously fires the ball horizontally and perpendicular to the diameter in opposite directions. After leaving the platform, the ball have horizontal speed of \( 9 m s^{-1} \) with respect to the ground. The rotational speed of
the platform in \( r a d s^{-1} \) after the balls
leave the platform is :


A particle is executing SHM of period 4s.Then the time taken by it to move from thr extreme position to \( \frac{\sqrt{3}}{2} \) of the amplitude is:
A \( \cdot \frac{1}{3} s \)
в. \( \frac{2}{3} \) s
c. \( \frac{3}{4} \)
D. \( \frac{4}{3} \) s


Find the maximum intensity \( \mathrm{E}_{\max } \) and
the corresponding distance \( r_{m} \)


A cylinder is rolling without sliding over
two horizontal planks (surfaces) 1 and 2
If the velocities of the surfaces \( A \) and \( B \)
are \( -\boldsymbol{v} \hat{\boldsymbol{i}} \) and \( 2 \boldsymbol{v} \hat{\boldsymbol{i}} \) respectively. Then
This question has multiple correct options
A \( \cdot \) position of instantaneous axis of rotation is \( \frac{2 R}{3} \)
B. position of instantaneous axis of rotation is \( \frac{4 R}{3} \)
c. angular velocity of the cylinder is \( 5 v / 2 R \)
D. angular velocity of the cylinder is \( 3 v / 2 R \)


Which of the following is a state function?
\( \mathbf{A} \cdot q \times w \)
в. \( q+w \)
c. \( \frac{q^{2}}{w^{2}} \)
D. \( \sqrt{q w} \)


Calculate the amount of \( C a C l_{2} \) (molar
mass \( =111 g \) mol \( ^{-1} \) ) which must be
added to \( 500 g \) of water to lower its
freezing point by \( 2 K, \) assuming \( C a C l_{2} \)
is completely dissociated. \( \left(K_{f} \) for \right. water \( =1.86 K k g m o l^{-1} \) )


Grain of Maize is
\( \mathbf{A} \cdot \) Seed
B. Fruit
C. Neither seed nor fruit
D. Bud of flower


A reaction carried out by 1 mol of \( N_{2} \)
and 3 mol of \( H_{2} \) at equilibrium. The
mole fraction of \( N H_{3} \) as 0.012 at \( 500 C \) and 10 atm pressure.What the pressure
at which mole \( \% \) of \( N H_{3} \) in equilibrium mixture is increased to \( 10.4 ? \). (in atm)
A . 57
в. 105
\( c \cdot 200 \)
D. None of these


The direction of the force on a current
carrying conductor held perpendicular to an uniform magnetic field is given by:
A. Fleming's right hand rule
B. Ampere's swimming rule
c. Maxwell's right hand cork screw rule
D. Fleming's left hand rule


The distance between an object its doubly magnified by a concave mirror of focal length \( f \) is
A \( \cdot 3 f / 2 \)
B. \( 2 f / 3 \)
\( c \cdot 3 f \)
D. Depend on whether the image is real or virtual


Assertion
Decomposition of hydrogen peroxide is an example of disproportionation
reaction.
Reason
In a disproportionation reaction, an
element in one oxidation state is
simultaneously oxidised and reduced.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The equivalent capacitance between \( \mathrm{P} \)
and \( Q \) of the given figure is (the capacitance of each capacitor is1 \( \mu F \) ):
\( A \cdot 2 \mu F \)
B. \( 0.5 \mu F \)
\( c \cdot 5 \mu F \)
D. \( 0.2 \mu F \)


\( 12 \mathrm{gms} \) of alkaline earth metal gives
14.8 gms of its nitride. What is the atomic mass of metal?
A . 15
B. 20
c. 30
D. 40


Six positive number are in G.P., such that the \( r \) product is \( 1000 . \) If the fourth term is \( 1, \) then the last term is
A. 1000
в. 100
c. \( \frac{1}{100} \)
D. \( \frac{1}{1000} \)


0
7
\( \frac{d}{d x} \)


Calculate the fifth term of the sequence
\( a_{n}=2(n-1)^{2}-3 \)
A . 19
B . 29
c. 39
D. 49


During respiration in plants, the glucose is broken down into
A. Carbon dioxide
B. water
c. Energy
D. All of the above


Hoffmann bromamide reaction is used
to convert:
A. An organic compound into lower homologue
B. An organic compound into higher homologue
C. A lower alkane into higher alkene
D. None of these


When we boil tulsi leaves in water
water acquires a characteristic smell of leaves because
A. Smell of leaves diffuse in water
B. Leaves melt in water
c. Stored wastes in the leaves dissolve in water
D. Leaves pollute water


Identify the correct statement(s).
\( \mathbf{A} \cdot C H_{3}-C H_{2}-C H_{2}-C O-C H_{3}, C H_{3}-C H_{2}- \)
\( C O-C H_{2}-C H_{3} \) are position isomers only
B. \( C H_{3}-C H_{2}-C H_{2}-C O-C H_{3}, C H_{3}-C H_{2}- \)
\( C O-C H_{2}-C H_{3} \) are position isomers as well as
metamers.
\( \mathbf{c} \cdot C H_{3}-C O-C H\left(C H_{3}\right)-C H_{3}, C H_{3} C O-C H_{2}- \)
\( C H_{2}-C H_{3} \) are tautomers to each other
D. \( C H_{2}=C(O H)-C H_{2}-C H_{2}-C H_{3}, C H_{3}- \)
\( C(O H)=C H-C H_{2}-C H_{3} \) are tautomers as well as
position isomers


Find the maximum potential a \( \boldsymbol{C u} \) ball (isolated) can have when irradiated with a wavelength \( \lambda=140 n m \)
\( \left[\phi_{C u}=4.47 \mathrm{eV}\right] \)
A . \( 4.47 V \)
B. 8.86 \( V \)
c. \( 13.33 V \)
D. 4.39 \( V \)


Light of wave length \( 6.5 \times 10^{-7} \mathrm{m} \) is
made incident on two slits \( 1 \mathrm{mm} \) apart. The distance between third dark fringe and fifth bright fringe on a screen distant \( 1 \mathrm{m} \) from slits will be
A. \( 0.325 \mathrm{mm} \)
B. 0.65 mm
c. \( 1.625 \mathrm{mm} \)
D. 3.25 mm


Which of the following I.U.P.A.C. name is
correct?
A. 2-Methyl-3-ethyl pentane
B. 2 -ethyl- - 3-Methyl pentane
c. 3-ethyl-2-methyl pentene
D. 3-Metyl-2-ethyl pentene


The domain of the function \( f(x)=^{24-x} \)
\( \boldsymbol{C}_{3 x-1}+^{40-6 x} \boldsymbol{C}_{8 x-10} \) is
A \( \cdot\{2,3\} \)
3 \( \} \)
в. \{1,2,3\}
D. None of these


Kinetic energy of molecules is highest
in:
A. gases
B. solids
c. liquids
D. solutions


Covalency of oxygen cannot exceed 2 unlike sulphur which can show +4 or +6 because:
A. oxygen atom does not have d-orbitals
B. oxygen atom has two unpaired electrons in its valence shell
c. oxygen can form a double bond with another oxygen atom
D. electrons of oxygen atom cannot be promoted to dorbitals due to its small size


In a H-atom, an electron is in \( 2^{n d} \) excited state and its radius \( =4.75 \AA \)
Calculate de-broglie wavelength of the electron.
A \( \cdot \frac{8.5 \pi}{4} \)
B. 0
с. \( \frac{19 \pi}{3} \),
D. \( \frac{9.5 \pi}{3} \)


Fucoxanthin occurs in
A. Cyanophyceae
B. Rhodophyceae
C. Chlorophyceae
D. Phaeophyceae


A ball of mass \( m \) at rest receives an
impulse \( I_{1} \) in the direction of north.
After some time, it received another
impulse \( I_{2} \) in the direction of south. The
final kinetic energy of the ball is
A \( \cdot \frac{\left(I_{1}+I_{2}\right)^{2}}{2 m} \)
в. \( \frac{\left(I_{1}-I_{2}\right)^{2}}{2 m} \)
c. \( \frac{I_{1}^{2}+I_{2}^{2}}{2 m} \)
D. \( \frac{I_{1}^{2}-I_{2}^{2}}{2 m} \)


Mark correct option or options:
A. Electric field and magnetic field are basically independent
B. Electric field and magnetic field are two aspect of the electromagnetic field
C. Electric field and magnetic field may be produced by charge in rest
D. Both \( (a) \) and
\( (c) \) are correct


The air becomes heated by
A. Conduction
B. Convection
c. Radiation
D. Expansion
E. Diffusion


Why does sun appear reddish at sunrise
and sunset?
A. Near the horizon it passes through thick layers of atmosphere having larger particles
B. Sunlight travels longer distance at sunrise and sunset
C. Both A and B
D. None of the above


The lengths of the two tangents from an external point to a circle are
A. equal
B. different
c. both A and B
D. none of the above


Number of short periods in Mendeleev
table is :
A .2
B. 3
\( c \cdot 4 \)
\( D \)


Brittleness is a characteristic property
of:
A. gaseous non-metals
B. liquid non-metals
c. solid non-metals
D. none of the above


A plane progressive wave has frequency \( 25 H z \) and amplitude \( 2.5 \times 10^{-5} \mathrm{m} \) and
initial phase zero, propagates along the negative x-direction with a velocity of \( \mathbf{3 0 0 m} / \)s. The phase difference
between the oscillations at two points \( 6 m \) apart along the line of propagation is :
\( A \)
в. \( \frac{\pi}{2} \)
c. \( 2 \pi \)
D. \( \frac{\pi}{4} \)


Froth flotation method is used for the
concentration of :
A. oxide ores
B. sulphide ores
c. sulphate ores
D. halide ores


A pole has to be erected at a point on the boundary of a circular park of
diameter 13 meters in such a way that the difference of its distance from two
diametrically opposite fixed gates \( \boldsymbol{A} \) and \( B \) on the boundary is 7 meters. It is possible to do so? If yes, at what distances from the two gates should the
pole be erected?
A. \( 6.71 m \)
в. \( 0.71 m \)
c. \( 1.51 m \)
D. \( 5.51 \mathrm{m} \)


Find the present value of annuity
immediate of \( R s .18,000 \) p.a for 3 years at \( 9 \% \) p.a compounded annually [Given
\( \left.(\mathbf{1} . \mathbf{0 9})^{\mathbf{3}}=\mathbf{1 . 2 9}\right] \)


Why is Wurtz reaction not preferred for the preparation of alkanes containing odd number of carbon atoms? IIlustrate
your answer by taking one example.


Which of the following is correct electron dot structure of oxygen?
\( A \)
\[
\therefore \dot{0}: \therefore \dot{0}:
\]
в.
\[
\therefore \dot{0}: \stackrel{\because}{0}:
\]
\( c \)
\[
\therefore 0:: 0:
\]
D.
\[
\therefore \dot{0}:: \dot{0}
\]


Which of the following will show optical isomerism ?
\( \mathbf{A} \cdot\left[C u\left(N H_{3}\right)_{4}\right]^{2} \)
B \( \cdot\left[Z n C l_{4}\right]^{2} \)
\( \mathbf{c} \cdot\left[\operatorname{Cr}\left(C_{2} O_{4}\right)_{3}\right]^{3-} \)
D \( \cdot\left[\operatorname{Co}(C N)_{6}\right]^{3-} \)


The velocity at the maximum height of projectile is half of its initial velocity projection. The angle of projection is
A . \( 30^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 76^{\circ} \)


We have \( 2.0 \mathrm{kg} \) of a block of a
substance at its melting point. The
substance has a latent heat of fusion of
\( 1500 J \) per kilogram and a specific heat
of \( 2500 J \) per kilogram degree Celsius. How much heat is needed to change the block entirely into a liquid?
\begin{tabular}{l}
A. \( 5000 \mathrm{J} \) \\
\hline
\end{tabular}
B. \( 750 J \)
c. \( 1250 J \)
D. 3000 \( J \)
ह. \( 8000 J \)


Prove that \( \left|\begin{array}{lll}1 ! & 2 ! & 3 ! \\ 2 ! & 3 ! & 4 ! \\ 3 ! & 4 ! & 5 !\end{array}\right|=4 ! \)


Prove that
\( \frac{\cos e c A+1}{\cos e c A-1}=\frac{1+\sin A}{1-\sin A} \)


Two resistances \( 20 \Omega \) and \( 40 \Omega \) are
connected in parallel. If total current is 4.5 \( A \). Find the current through \( 20 \Omega \) resistance


If one angle of a triangle is equal to the sum of the other two angles, then the triangle is
A. an isosceles triangle
B. an obtuse triangle
c. an equilateral triangle
D. a right triangle


Oxygen is in state.
A. solid
B. liquid
c. gaseous
D. none of these


dentify the process.
A. Replication
B. Fertilisation
c. Binary fission
D. Budding


Match the entries in column I with those
in column II and choose the correct
combination from the options given.
Column I
1. Cerebrum and basal
a. Diencephalon \( \quad \) ganglia
b. Telencephalon
2. Medulla
3. Cerebellum and pons Myelencephalon
d. Metencephalon
4. Thalamus
A. \( a-4, b-3, c-1, d-2 \)
B. \( a-3, b-4, c-1, d-2 \)
c. \( a-4, b-3, c-2, d-1 \)
D. \( a-1, b-2, c-3, d-4 \)
E \( . a-4, b-1, c-2, d-3 \)


The correct order of strength of bonds is:
A. \( s-s>s-p>p-p \)
В. \( s-s<s-p<p-p \)
c. \( s-p>s-s>p-p \)
D. \( s-s>p-p>s-p \)


The solution of the equation \( \frac{d y}{d x}= \) \( \frac{x(2 \log x+1)}{\sin y+y \cos y} \) is
A \( y \sin y=x^{2} \log x+\frac{x^{2}}{y}+c \)
B \( \cdot y \cos y=x^{2}(\log x+1)+c \)
c. \( y \cos y=x^{2} \log x+\frac{x^{2}}{2}+c \)
D. \( y \sin y=x^{2} \log x+c \)


A container is filled with 20 moles of an
ideal diatomic gas at absolute temperature T. When heat is supplied to gas temperature remains constant but 8 moles dissociate into atoms. Heat
energy given to gas is
A . 4 RT
в. 6 RT
\( c .3 \) RT
D. 5 RT


Choleresis means release of
A. Gastric juice
B. Bile
c. Intestinal juice
D. Pancreatic juice


The first three terms pf A.P are
\( (3 y-1) \cdot(3 y+5) \) and \( (5 y+1) . \) Then \( Y \)
equals to


What are the direction ratios of the line
if it passes through the intersection of the planes \( x=3 z+4 \) and \( y=2 z-3 ? \)
A \( .(1,2,3) \)
в. (2,1,3)
c. (3,2,1)
D. (1,3,2)


Which of the following is a step-growth polymer?
A. Styrene
B. Nylon-6,6
c. Teflon
D. Rubber


Whipped cream is an example of:
A. Dispersion Medium-Liquid; Dispersed Phase-Gas
B. Dispersion Medium-Liquid; Dispersed Phase-Liquid
C. Dispersion Medium-Liquid; Dispersed Phase-Solid
D. Dispersion Medium-Gas; Dispersed Phase-Liquid


A circle is inscribed in a triangle whose
sides are 40,40 and \( 48 \mathrm{cm} \) respectively. A smaller circle touching two equal sides of the triangle and to the first circles, then the area of smaller circle is


Match the above given table.
A. A-3, B-1, C-4, D-5
B. \( A-2, B-3, C-5, D-4 \)
c. A-1, B-3, C-4, D-2
D. A-4, B-5, C-3, D-2


Which of the following is not used as cooking utensils even being a metal?
A. copper
B. Leadd
c. silver
D. Iron


What is the difference between
physisorption and chemisorption?


A metal ball falls from a height 1 m on a
steel plate and jumps up to a height of
\( 0.81 m . \) Find the coefficient of
restitution


Which of the following is a dicarboxylic
acid with one double bond?
A. Ethylene
B. Traumatic acid
c. Absicic acid
D. Auxins


A point object is placed at a distance of
\( 12 c m \) on the principal axis of a convex lens of focal length \( 10 \mathrm{cm} \). A convex mirror is placed coaxially on the other side of the lens at a distance of \( 10 \mathrm{cm} \). If
the final image coincides with the object, sketch the ray diagram and find the focal length of the convex mirror.


Assertion
Large intestine also shows the presence of villi, like small intestine.
Reason
Absorption of water and some salts are
done by the inner wall of the large intestine.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


The differential equation of the family of straight lines which passes through the origin is
A \( \cdot y=x \frac{d y}{d x} \)
в. \( y+x \frac{d y}{d x}=0 \)
c. \( _{x+y} \frac{d y}{d x}=0 \)
D. \( \frac{d y}{d x}=m \)


Which of the following is not a poisonous substance?
A . \( \mathrm{NH}_{3} \)
в. РНз \( _{3} \)
c. \( \mathrm{AsH}_{3} \)
D. \( \mathrm{BiH}_{3} \)


Find the continuity of \( f(x) \), If \( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{ccc}\boldsymbol{x}+\mathbf{1} & \boldsymbol{i f} & \boldsymbol{x} \geq \mathbf{1} \\ \boldsymbol{x}^{2}+\mathbf{1} & \boldsymbol{i f} & \boldsymbol{x}<\mathbf{1}\end{array}\right\} \)


The value of the definite integral \( \int_{0} \sqrt{\ln \left(\frac{\pi}{2}\right)} \cos \left(e^{x^{2}}\right) 2 x e^{x^{2}} d x \) is:
\( A \cdot 1 \)
B. \( 1+(\sin 1) \)
c. \( 1-(\sin 1) \)
D. \( (\sin 1)-1 \)


The transverse displacement \( y(x, t) \) of \( a \)
wave on a string is given by \( y(x, t)= \) \( e^{\left(a x^{2}+b t^{2}+2 \sqrt{a b} x t\right)} . \) This represents a
A \( \cdot \) wave moving in -x direction with speed \( \sqrt{\frac{b}{a}} \)
B. standing wave of frequency \( \sqrt{b} \)
C standing wave of frequency \( \sqrt{\frac{1}{\sqrt{b}}} \)
D. wave moving in + x direction with \( \sqrt{\frac{a}{b}} \)


Which of the following is true for \( N_{2} O_{5} \) ?
A. Paramagnetic
B. Anhydride of \( H N O_{2} \)
c. Brown gas
D. Exist in solid In form of \( \left[N O_{2}^{+}\right]\left[N O_{3}^{-}\right] \)


Assertion
If optical density of a substance is more than that of water then the mass
density of substance can be less than
water
Reason
Optical density and mass density are not related.
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


Assertion
Internal energy change in a cyclic
process is zero.
Reason
Internal energy is a state function.
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.


When one molecule of glucose undergoes glycolysis aerobically, last stable product will be
A. One pyruvic acid
B. Two pyruvic acid
c. Three pyruvic acid
D. Four pyruvic acid


Which of the following statements is
correct?
A. The balls will execute simple harmonic motion between the two plates
B. The balls will bounce back to the bottom plate carrying the same charge they went up with
C. The balls will stick to the top plate an remain there
D. The balls will bounce back to the bottom plate carrying the opposite charge they went up with


The conductivity of a semi conductor is:
This question has multiple correct options
A. Greater than the conductivity of metals.
B. Less than the conductivity of metals.
C. Equal to the conductivity of metals.
D. Intermediate between the conductivity of metals and insulators.


Law of constant proportion states that:
\( \mathbf{A} \cdot \) a chemical compound always contains exactly the same proportion of elements by mass.
B. mass can neither be created nor destroyed in a chemical reaction.
C. when two elements combine with each other to form
two or more than two compounds, the masses of one the element which combines with the fixed mass of
the other, bears a simple whole number ratio.
D. total mass of products is always equal to the total mass of reactants.


Integrate \( \int x . \sin 2 x d x \)


If two waves are moving in same
medium and meet at the same time
and both are in the same phase. It will
be:
A. Reflection
B. Refraction
C. Diffraction
D. Constructive interference
E. Destructive interference


The above figure shows a toroidal
solenoid whose cross-section is
rectangular. Find the magnetic flux (in \( \mu W b) \) through this cross-section if the
current through the winding equals \( I=1.7 A \) the total number of turns is
\( N=1000, \) the ratio of the outside
diameter to the inside one is \( \eta=1.6 \)
and the height is equal to \( h=5.0 \mathrm{cm} \)


Which of the following vitamins are water soluble?
This question has multiple correct options
\( A \cdot A \)
B.
\( c \cdot B \)
D.


Agar-Agar is used in salt bridge since it is:
A. an electrolyte
B. a non-electrolyte
c. an inert electrolyte
D. a solid


Internal energy per mole of gas depends
on
A. viscosity
B. density
c. temperature
D. thermal conductivity


If the decay constant of radium is
\( 4.28 \times 10^{-4} \) per year, then its half life
will be approximately be
A. 1240 years
B. 1620 years
c. 2000 years
D. 2260 years


Trace the curve \( \boldsymbol{y}=\boldsymbol{x}^{3} \)


The wave number of energy emitted when electron jumps from fourth orbit to seconds orbit in hydrohen in \( 20,497 \mathrm{cm}^{-1} . \) The wave number of
energy for the same transition in \( \boldsymbol{H} \boldsymbol{e}^{+} \)
is
A \( .5,099 \mathrm{cm}^{-1} \)
B . \( 20,497 \mathrm{cm}^{-1} \)
c. \( 40,994 \mathrm{cm}^{-1} \)
D. \( 81,988 \mathrm{cm}^{-1} \)


A mass ' \( m^{\prime} \) moves with velocity \( v= \) \( \sqrt{3} m / s \) and collides with another mass
\( 2 m \) initially at rest. After collision first mass move with velocity \( \frac{v}{\sqrt{3}} \) in the
direction perpendicular to initial
direction of motion. Speed of second mass (in \( \mathrm{m} / \mathrm{s} \) ) after collision is


All rhombuses are square.
A. True
B. False


The average weight of 39 students in a
class is \( 23 \mathrm{kgs} \). Among them Sita is the heaviest while Tina is the lightest. If
both of them are excluded from the
class still the average remains same.
The ratio of weight of Sita to Tina is 15:
8, then what is the weight of the Tina?


f \( x=3, \) then the value of \( 20 x^{7}+x^{5} 3 \)


The number of natural numbers \( n \) such
that \( \phi(n) \) is odd is
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c .3 \)
D. None


Which of the following letters will be seen without any change in a plane mirror?
A.
B. T
\( c \cdot L \)
D.


The capacitors \( C_{1}, C_{3}, C_{4}, C_{5} \) shave a
capacitance \( 4 \mu F \) each and \( C_{2} \)
has capacitance \( 10 \mu F \). The effective
capacitance between \( \mathrm{P} \) and \( \mathrm{Q} \) will be :
\( \mathbf{A} \cdot 8 \mu F \)
в. \( 6 \mu F \)
\( c .4 \mu F \)
D. \( 2 \mu F \)


The median of the series
\( 8,12,15,7, x, 19,22 \) lies in the interval
\( \mathbf{A} \cdot[12,15] \)
B . [7,15]
c. [15,17]
D. [9,12


If only \( 2 \% \) of the main current is to be
passed through a Galvanometer of resistance \( G, \) the resistance of shunt
should be :
A. \( G / 50 \)
в. \( G / 49 \)
c. \( 50 / G \)
D. \( 49 G \)


The valence bond structure of carbon
monoxide is best described as \( : C \equiv 0 \)
with a dative bond from oxygen atom to the less electronegative carbon atom. If true enter 1 else 0


\( \left|\begin{array}{ccc}\boldsymbol{a}+\boldsymbol{b} & \boldsymbol{a}+\mathbf{2} \boldsymbol{b} & \boldsymbol{a}+\boldsymbol{3} \boldsymbol{b} \\ \boldsymbol{a}+\mathbf{2} \boldsymbol{b} & \boldsymbol{a}+\boldsymbol{3} \boldsymbol{b} & \boldsymbol{a}+\boldsymbol{4} \boldsymbol{b} \\ \boldsymbol{a}+\boldsymbol{4} \boldsymbol{b} & \boldsymbol{a}+\boldsymbol{5} \boldsymbol{b} & \boldsymbol{a}+\boldsymbol{6} \boldsymbol{b}\end{array}\right|= \)
A \( \cdot a^{2}+b^{2}+c^{2}-3 a b \)
B. \( 3 a b c \)
\( c \cdot 3 a+5 b \)
\( D \)


A point charge \( +Q \) fixed in position, as shown in the diagram. Five points near
the charge and in the plane of the page are shown.
At which point will an electron experience a force directed toward the
top of the page?
\( A \cdot A \)
B. B
\( c \cdot c \)
D.
\( E . E \)


The magnetic susceptibility of a
paramagnetic material at \( -73^{0} \) is
\( 0.0075, \) its value at \( -173^{0} \mathrm{C} \) will be
A . 0.0045
B. 0.0030
c. 0.015
D. 0.0075


The fifth term of an A.P is 1 whereas its
31st term is \( -77 . \) Find sum of its first
fifteen terms. Also find which term of
the series will be -17 and sum of how
many terms will be 20


Living organisms have \( \ldots \). essential
processes.
A. 5
B. 6
\( c \cdot 7 \)
\( D \)


Botanical name of banana is
A . Musa paradisiaca
B. Calotropis procera
c. Mimosa pudica
D. Iberis amara


What are the factors on which
resistance of a conductor depends?


An electric motor is a device to convert
electrical energy into mechanical energy. The motor shown below has a rectangular coil \( (15 \mathrm{cm} \times 10 \mathrm{cm}) \) with
100 turns placed in a uniform magnetic
fleld \( B=2.5 T . \) When a current is
passed through the coil, lt completes 50 revolutions in one second. the power
output of the motor is \( 1.5 k W \). The
current rating of the coil should be
\( A \cdot 1 A \)
B. 2 A
\( c \cdot 3 A \)
\( D \cdot 4 A \)


Show that the pressure in a fluid at rest in same at all points if we ignore gravity.


The shaded shape is made of 5 congruent squares. The side of one square is \( 4 \mathrm{cm} \). Find the total area of the
shaded shape.


The purpose of using heavy water in
nuclear reactor is:
A. to cool the reactor to room temperature
B. to make the dynamo blades to work well
C. to decrease the energy of fast neutrons
D. to increase the energy released in nuclear fission


For the complex \( \left[N i C l_{4}\right]^{2-}, \) write
(i) the IUPAC name
(ii) the hybridization type (iii) the shape of the complex.
(Atomic no. of \( \boldsymbol{N} \boldsymbol{i}=\mathbf{2 8}) \)


Soap was never actually discovered but instead gradually evolved from crude mixtures of alkaline and fatty material
Up to \( 1800, \) soap was believed to be a mechanical mixture of fat and alkali,
then Chevreul, a French chemist showed that soap formation, was actually a chemical reaction.
Which one of the following follows from
the above statement?
A. Chevreul discovered the process of soap making
B. Alkaline and fatty material, both being natural material, their mixture which is used as soap is still natural materials mixture
c. Soap is a natural product, whose existence was later established
D. Crude mixing of alkaline and fatty material in early days was actually chemical process of formation of soap


ff \( l=20, d=-1, n=17, \) then the first
term is :
A . 30
B. 32
\( c .34 \)
D. 36 6


Assertion
The second law of thermodynamics
states that the entropy of a closed or isolated system always increases. This means that all available energy is used
up and there is no more potential for
further useful work.
Reason
The system becomes disordered and
also degraded
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


Number of peroxy linkage in
\( \boldsymbol{K}_{3} \boldsymbol{C r}\left(\boldsymbol{O}_{2}\right)_{x} \) having oxidation number of
\( C r \) as +5 is :


-
Whan
-
-


Which of the following polymers contains 1,3 -butadiene as one of the
monomers ?
This question has multiple correct options
A. Butyl rubber
B. Nitrile rubber
c. ABS plastic
D. sBR


The sum of the first \( n \) terms of an A.P. is
half of the sum of the next \( n \) terms. In
the usual notation, the value \( \frac{\boldsymbol{S}_{3 n}}{\boldsymbol{S}_{n}} \) is
A . 10
B. 8
\( c \cdot 6 \)
D.


Derive expression for the self-induction of solenoid. What factors affect its value
and how?


Assertion
The length of the day is slowly increasing.
Reason
The dominant effect causing a
slowdown in the rotation of the earth is
the gravitational pull of other planets in the solar system.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Bats detect the obstacle in their path
by receiving the detected
A. Infrasonic waves
B. Ultrasonic waves
c. Both
D. None


(a) Draw a ray diagram showing the image formation by a compound microscope. Hence obtain expression for total magnification when the image is formed at infinity
(b) Distinguish between myopia and hypermetropia. Show diagrammatically how these defect can be corrected.


A particle executes SHM with
amplitude \( 0.5 \mathrm{cm} \) and frequency \( 100 s^{-1} \) The maximum speed of the particle is \( (\operatorname{in} m / s) \)
\( A \)
B. 0.5
c. \( 5 \pi \times 10^{-5} \)
D. \( 100 \pi \)


Find the mean wage of the following distributions
\( \begin{array}{llllll}\text { Category } & \text { A } & \text { B } & \text { c } & \text { D } & \text { E } \\ \begin{array}{l}\text { Wages } \\ \text { per day }\end{array} & \text { 50 } & \text { 60 } & \text { 70 } & \text { 80 } & \text { 90 } \\ \begin{array}{l}\text { No. of } \\ \text { Workers }\end{array} & 2 & 4 & 8 & 12 & 10\end{array} \)


\( f(x)=\frac{x}{\log x}-\frac{\log 5}{5} \) is decreasing in
\( A \cdot(e, \infty) \)
B. (0,1) \( \mathrm{U}(1, \mathrm{e}) \)
\( c \cdot(0,1) \)
D. (1, e)


How many significant figures in \( 7.89 \times \)
\( \mathbf{1 0}^{\mathbf{1 1}} \) liters?
\( A \)
B. 3
\( c .5 \)
D. 1


How many number greater than a million can be formed with the digits
\( 2,3,0,7,7,3,7, ? \)


The value of \( \mathrm{k} \) for which polynomial
\( x^{2}-k x+4 \) has equal zeroes is
This question has multiple correct options
A .4
B . 2
\( c .-4 \)
D. -


The process of passing of a precipitate into colloidal solution, on adding an electrolyte is called:
A. dialysiss
B. peptisation
c. electrophoresis
D. electrosmosis


Assertion
Chlorine water must be stored in dark
colored bottles.
Reason
Hypochlorous acid on exposure to
sunlight decomposes to \( H_{2} \) and \( C l_{2} \)
gas.
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


NaOH can also be prepared by electrolysis of aqueous NaCl. Amount of NaOH formed when 0.445 L of \( \mathrm{NaCl} \) (aq) is electrolysed for 137 s with a current of
\( 1.08 A, \) is :
A . \( 0.09 g \)
B. \( 0.12 g \)
c. \( 0.06 g \)
D. amount of NaCl has not been given


Which of the following metals can form nitride with nitrogen?
A \( . L i \)
в. \( N a \)
\( \mathrm{c} \cdot M g \)
D. \( C a \)


Which one of the following best describes the horizontal part of a
projectile's motion?
A. It moves at a constant horizontal velocity
B. It moves at a continually changing horizontal velocity
c. It always has zero horizontal velocity
D. The answer to this question depends on whether it is fired horizontally or at an angle


In vacuum, to travel distance 'd', light takes time 't' and in medium to travel
distance \( ^{\prime} 5 d^{\prime}, \) it takes time 'T'. The
critical angle of the medium is.
A \( \cdot \sin ^{-1}\left(\frac{5 T}{t}\right) \)
в. \( \sin ^{-1}\left(\frac{5 t}{3 T}\right) \)
c. \( \sin ^{-1}\left(\frac{5 t}{T}\right) \)
D. \( \sin ^{-1}\left(\frac{3 t}{5 T}\right) \)


For the battery shown in the figure:
This question has multiple correct options
A. equivalent internal resistance R is given by:
\( \frac{1}{R}=\frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}} \)
B. if \( E_{3}=\frac{\left(E_{1} R_{2}+E_{2} R_{1}\right)}{\left(R_{1}+R_{2}\right)} \), equivalent e.m.f. of the battery
will be equal to \( E_{3} \)
C . equivalent e.m.f. of the battery is equal \( E=\left(E_{1}+\right. \)
\( E_{2}+E_{3} / 3 \)
D. equivalent e.m.f. of the battery not only depends upon values \( E_{1}, E_{2} \) and \( E_{3} \) but depends upon valiues of \( R_{1} \) and \( R_{3} \) also


For each real \( \boldsymbol{x}, \) let \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \max \left\{x, x^{2}, x^{3}, x^{4}\right\}, \) then \( f(x) \) is
A . \( x^{4} \) for \( x \leq-1 \)
B . \( x^{2} \) for \( -1<x \leq 0 \)
c. \( f\left(\frac{1}{2}\right)=\frac{1}{2} \)
D. \( f\left(\frac{1}{2}\right)=\frac{1}{4} \)


A group which deactivates the benzene ring towards EAS but which direct the
incoming group principally to the ortho and para position is:
A \( .-N H_{2} \)
в. \( -C l \)
\( c \cdot N O_{2} \)
D. \( -N H_{2} C O C H_{3} \)


A mass \( \mathrm{M} \) is broken in two parts: \( \mathrm{m} \) and \( (M-m) . \) Relation between \( m \) and \( M s o \)
that the force of gravitation between the two parts is maximum is.
\( A \cdot m M=2 \)
в. \( m=\frac{M}{2} \)
c. \( M=m^{2} \)
D. None of these


Describe the compound microscope on the following headings
(i) Labelled Ray diagram of formation of image.
(ii) Magnifying power when final image is formed at least distance of distinct
vision.


A smooth rod of mass \( 1 k g \) is in
equilibrium inside a hollow fixed spher
such that \( \angle A C B=120^{\circ} . \) Find the
normal reaction on the rod at end \( A \)


The process of propagation of new
individual from the existing one is called as
A. Fertilization
B. Syngamy
c. Reproduction
D. Propagation


In a lake an inflow domestic sewage
rich in organic waste may result in
A. Drying of the lake very soon due to algal bloom.
B. An increased production of fish due to lot of nutrients
c. Death of fish due to lack of oxygen
D. Increased population of aquatic food web organism.


Which of the following metallurgical processes does not involve heating?
A. Smelting
B. Calcination
c. Roasting
D. Leaching


The arc \( A B \) with the centre \( C \) and the
infinitely long wire having linear charge density \( \lambda \) are lying in the same plane.
The minimum amount of work to be
done to move a point charge \( q_{0} \) from
point \( A \) to \( B \) through a circular path \( A B \)
of radius \( a \) is equal to:
A \( \cdot \frac{q_{0}^{2}}{2 \pi \varepsilon_{0}} \log \left(\frac{2}{3}\right) \)
в. \( \frac{q_{0} \lambda}{2 \pi \varepsilon_{0}} \log \left(\frac{3}{2}\right) \)
c. \( \frac{q_{0} \lambda}{2 \pi \varepsilon_{0}} \log \left(\frac{2}{3}\right) \)
D. \( \frac{q_{0} \lambda}{\sqrt{2} \pi \varepsilon_{0}} \)


the value of \( \boldsymbol{x} \stackrel{\lim }{\longrightarrow} \mathbf{0} \frac{\sin \boldsymbol{x}^{\mathbf{0}}}{\boldsymbol{x}} \)


Water is liquid at room temperature but not hydrogen sulphide. Why?


For any reaction, greater the value of equilibrium constant greater is the
extent of reaction.
A. True
B. False


The lines of symmetry of the given
figure is/are
\( A \)
B.
\( c \)
\( D \)


Solve:
\( \int \frac{x^{3}+x+1}{x^{2}-1} d x \)
A \( \cdot \frac{x^{2}}{2}+\log \left(x^{2}-1\right)+\frac{1}{2} \log \frac{x-1}{x+1}+c \)
B \( \cdot \frac{x^{2}}{2}+\log \left(x^{2}-1\right)-\frac{1}{2} \log \frac{x-1}{x+1}+c \)
\( ^{\mathbf{C}} \cdot \frac{x^{2}}{2}-\log \left(x^{2}-1\right)+\frac{1}{2} \log \frac{x+1}{x-1}+c \)
D \( \cdot \frac{x^{2}}{2}-\log \left(2 x^{2}-1\right)-\frac{1}{2} \log \frac{x-1}{x+1}+c \)


\( \int \sec ^{2} x \log \left(1+\sin ^{2} x\right) d x= \)
\( \tan x \log \left(1+\sin ^{2} x\right)-2 x+ \)
\( \sqrt{k} \tan ^{-1} \sqrt{k} \tan x . \) Find the value of \( k \)


The position vector of a particle is \( r= \) \( (a \cos \omega t) \hat{i}+(a \sin \omega t) \hat{j} . \) The velocity
vector of the particle is
A. parallel to position vector
B. perpendicular to position vector
c. directed towards the origin
D. directed away from the origin


Which of the following is known as regenerated fibre?
A. Nylon - 66
B. Terylene
c. Nylon - 6
D. Rayon


For any two complex numbers \( z_{1} \) and \( z_{2} \)
prove that \( \operatorname{Re}\left(z_{1} z_{2}\right)=\operatorname{Re} z_{1} \operatorname{Re} z_{2} \)
\( \operatorname{Im} z_{1} \operatorname{Im} z_{2} \)


The cube as shown in Fig. has sides of
length \( L=10.0 \mathrm{cm} . \) The electric field is
uniform, has a magnitude \( \boldsymbol{E}=\mathbf{4 . 0 0} \times \)
\( 10^{3} N C^{-1}, \) and is parallel to the \( x y- \)
plane at an angle of \( 37^{\circ} \) measured from
the \( +x-a x i s \) towards the \( +y-a x i s \)
The total net electric flux through all faces of the cube is
\( \mathbf{A} \cdot 8 N m^{2} C^{-1} \)
B. \( -8 N m^{2} C^{-1} \)
\( \mathbf{c} \cdot 24 N m^{2} C^{-1} \)
D. zero


If the first term of GP is \( 7, \) its \( n^{t h} \) term is
448 and sum of \( n \) terms is \( 889, \) then
find the fifth term of GP


\( P, Q \) and \( R \) are partners in a business.
\( P \) whose money has been used for 4 months, claims \( \frac{1}{8} \) of the profit \( , Q \)
whose money has been used for 6 months, claims at \( \frac{1}{3} \) of the profit. \( \boldsymbol{R} \)
had invested Rs. 1560 for 8 months. How
much did \( P \) and \( Q \) contribute?


The total number of species belonging to present day gymnosperms is about
A. 2000
B. 850
c. 2500
D. 4000


You have the mixture of salt, sand and lodine. Which of these is the best
technique to separate these mixtures?
A. Evaporation
B. Distillation
c. Sublimation
D. Solvent Extraction


The resistance of an object depends on
its :
A. shape
B. material of which it is composed
\( c . \) size
D. all of the above


A quarter cylinder of radius \( \boldsymbol{R} \) and
refractive index 1.5 is placed on a table.
A point object \( P \) is kept at a distance of
\( m R \) from it. The value of \( ^{\prime} m^{\prime} \) for which a
ray from P will emerge parallel to the
table, as shown in figure, is
\( A \cdot 4 / 3 \)
B. \( 3 / 4 \)
\( c \cdot 3 / 2 \)
D. \( 2 / 3 \)


Which of the following gaseous molecules is monoatomic?
A. Chlorine
B. Helium
c. oxygen
D. Nitrogen


Which of the following has the highest
ionization energy?
A. \( C \)
в. \( N \)
\( c \cdot O \)
D. \( F \)
E . \( N e \)


Is 243 a perfect cube? If not find the
smallest number by which 243 must be multiplied to get a perfect cube


In the given figure, name the ray which
represents the correct path of light
while emerging out through a glass
blocks:
A . \( A \)
в. \( B \)
\( c . c \)
D. \( D \)


In Cockroach, wings are absent from
A. Prothorax
B. Mesothorax
c. Metathorax
D. None of the above


Antihistamines have advantage over
antacids in the treatment of acidity.
If true enter 1 , else enter 0 .


Assertion
To increase the length of a thin steel
wire of \( 0.1 \mathrm{cm}^{2} \) cross sectional area by
\( 0.1 \%, \) a force of \( 2000 N \) is required, its
\( \boldsymbol{Y}=\mathbf{2 0 0} \times \mathbf{1 0}^{\mathbf{9}} \boldsymbol{N} \boldsymbol{m}^{-\mathbf{2}} \)
Reason
It is calculated by \( Y=\frac{\boldsymbol{F} \times \boldsymbol{L}}{\boldsymbol{A} \times \boldsymbol{\Delta} \boldsymbol{L}} \)
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


IUPAC name of the following compound
is:


A data consists of \( n \) observation:
\( \boldsymbol{x}_{1}, \boldsymbol{x}_{2}, \ldots \ldots . ., \boldsymbol{x}_{n} . \) If \( \sum_{i=1}^{n}\left(\boldsymbol{x}_{i}+\mathbf{1}\right)^{2}=\mathbf{9} \boldsymbol{n} \)
and \( \sum_{i=1}^{n}\left(x_{i}-1\right)^{2}=5 n, \) then the standard deviation of this data is:
A . 5
B. \( \sqrt{5} \)
c. \( \sqrt{7} \)
\( D \)


Which of the following is a suitable example for illustrating the law of conservation of mass? (Atomic mass of
\( 0=16 ; H=1) \)
A. \( 18 g \) of water is formed by the combination of \( 16 g \) oxygen with \( 2 g \) of hydrogen
B. 18g of water in liquid state is obtained by heating 18 g of ice
c. \( 18 g \) of water is completely converted into vapour state on heating
D. \( 18 g \) of water freezes at \( 4^{\circ} C \) to give same mass of ice.


Consider the following statements A and B given below and identify the
correct answer:
A) If \( \vec{A} \) is a vector, then the magnitude of the vector is given by \( \sqrt{\overrightarrow{\boldsymbol{A}} \times \overrightarrow{\boldsymbol{A}}} \)
B) If \( \vec{a}=m \vec{b} \) where 'm' is a scalar, the
value of 'm' is equal to \( \frac{\vec{a} \cdot \vec{b}}{b^{2}} \)
A. both \( A \& B \) are correct
B. A is correct but B is wrong
c. A is wrong but B is correct
D. both A and B are wrong


If an orbiting satellite comes to a
standstill suddenly,
A. the satellite will move along the tangent.
B. the satellite will move radically towards centre of the orbit
C. the satellite will go to outer space and will be lost.
D. the satellite will continue to move in the same orbit.


Question below refers to the
overall reaction and half-reactions with
standard reduction potentials below. \( 2 F e^{2+}+C l_{2} \rightarrow 2 F e^{3+}+2 C l ? \)
\( \boldsymbol{F e}^{3+}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{F} e^{2+} ; \boldsymbol{E}_{r e d}^{o}=0.77 \) volts
\( C l_{2}+2 e^{-} \rightarrow 2 C l^{-} ; E_{r e d}^{o}=1.36 \) volts
Find the overall potential for the reaction?
A. 0.18 volt
B. 0.59 volts
c. \( 1.05 v o l t s \)
D. 2.13voolt
E. 2.90volts


A wheel has moment of inertia
\( 10^{-2} k g-m^{2} \) and is making 10 rps. The
torque required to stop it in 5 secs is
A. 12.56
B. 9.42
\( c \cdot 6.28 \)
D. 3.14


\( H B r \) fails to give addition products
with carbonyl compounds. Is the above statement true?
A. True
B. False


A \( \cdot t^{2}+3,-t^{3}-1 \)
B. \( 4 t^{2}+3,-8 t^{2}-1 \)
\( \mathbf{C} \cdot t^{2}+3, t^{3}-1 \)
D. \( 16 t^{2}+3,-64 t^{3}-1 \)


An electron is moving vertically downwards at any place. The direction of magnetic force acting on it due to horizontal component of earth's magnetic field will be
A. towards east
B. towards west
c. towards north
D. towards south


Three elastic wires, \( P Q, P R \) and \( P S \)
support a body \( P \) of mass \( M, \) as shown
in the figure. The wires. are of the same
material and cross-sectional area, the
middle one being vertical. The load carried by the middle wire is:
A \( \cdot \frac{M g}{1+2 \cos ^{2} \theta} \)
в. \( \frac{M g}{1+2 \cos ^{3} \theta} \)
\( c \)
D. \( \frac{M g}{\cos \theta+2 \cos ^{3} \theta} \)


The product of the third by the sixth term of an arithmetic progression is
406. The division of the ninth term of the
progression by the fourth term gives a quotient 2 and a remainder \( 6 . \) Find the
first term and the difference of the
progression.


One mole of any substance contains
\( 6.023 \times 10^{23} \) particles. It was
determined by
A. Berzilius
B. Avogadro
c. Dalton
D. Perin


Find the area of the fields shown in Fig. (All measurements are in metres)
A \( .2572 \mathrm{m}^{2} \)
B . \( 25070 m^{2} \)
c. \( 2472 m^{2} \)
D. \( 2470 m^{2} \)


A star is receding away from earth with
a velocity of \( 10^{5} m / s . \) If the wavelength of its spectral line is \( 5700 A \), then Doppler shift will be
\( A \cdot 200 \stackrel{\circ}{A} \)
B \( \cdot 1.9 A \)
c. \( 20 \stackrel{\circ}{A} \)
D. \( 0.2 \stackrel{\circ}{A} \)


When heated in air, brown copper
powder turns black. This black powder would turn brown again when heated
with:
A. \( C O \)
в. \( O_{2} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \)
D. \( N H_{3} \)


Lymph is more similar to
A. Blood
B. Interstitial fluid
c. Both A and B
D. None of the above


The resultant complex number when \( (4+6 i) \) is divided by \( (10-5 i) \) is
A \( \cdot \frac{2}{25}+\frac{16}{25} i \)
B \( \cdot \frac{2}{25}-\frac{16}{25} i \)
c. \( \frac{2}{5}+\frac{6}{5} \)
D. \( \frac{2}{5}-\frac{6}{5} \)


Copper has 29 electrons and 35
neutrons. Find the atomic mass.
A . 62
B. 63
\( c \cdot 54 \)
\( D \cdot 64 \)


Susceptibility of ferromagnetic substance is
\( A \cdot>1 \)
B. \( <1 \)
\( c \cdot 0 \)
\( D \)


The coordinates of a point which is equidistant from the point \( (0,0,0),(a, 0,0),(0, b, 0) \) and \( (0,0, c) \)
are given by
\( ^{\mathbf{A}} \cdot\left(\frac{a}{2}, \frac{b}{2}, \frac{c}{2}\right) \)
в. \( \left(\frac{-a}{2}, \frac{-b}{2}, \frac{c}{2}\right) \)
\( ^{\mathrm{c}}\left(\frac{a}{2}, \frac{-b}{2}, \frac{-c}{2}\right) \)
D \( \cdot\left(\frac{-a}{2}, \frac{b}{2}, \frac{-c}{2}\right) \)


The Bohr's orbit radius for the hydrogen
atom \( (n=1) \) is approximately 0.53 A. The radius for the first excited state \( (n=2) \)
orbit is:
A . \( 0.27 \mathrm{A} \)
B. 1.27 A
c. 2.12 A
D. 3.12 A


Factorize:
\( a^{6}+27 b^{3} \)
\( \mathbf{A} \cdot\left(a^{2}-3 b\right)\left(a^{4}-3 a^{2} b+9 b^{2}\right) \)
B \( \cdot\left(a^{2}+3 b\right)\left(a^{4}-3 a^{2} b+9 b^{2}\right) \)
\( \mathbf{C} \cdot\left(a^{2}+3 b\right)\left(a^{4}-a^{2} b+9 b^{2}\right) \)
D. \( \left(a^{2}+3 b\right)\left(a^{4}-a^{2} b-9 b^{2}\right) \)


ABCD is a square frame of side \( l \). The
force at B if charges as shown in figure
are placed at the corners of the square
will be:
A \( \cdot \frac{q^{2}(2 \sqrt{2}-1)}{4 \pi \varepsilon_{0} 2 l^{2}} \)
B. \( \frac{q^{2}(2 \sqrt{2}+1)}{4 \pi \varepsilon_{0} l^{2}} \)
c. \( \frac{q^{2}(2 \sqrt{2}-1)}{4 \pi \varepsilon_{0} l^{2}} \)
D. \( \frac{q^{2}(2 \sqrt{2}+1)}{4 \pi \varepsilon_{0} 2 l^{2}} \)


Which of the following is correct increasing order of molecular mass?
A. \( H_{2} O<H C l<H_{2} S<C O_{2} \)
в. \( H_{2} O<H_{2} S<H C l<C O_{2} \)
c. \( H_{2} O<C O_{2}<<H C l<H_{2} S \)
D. \( H C l<H_{2} S<H_{2} O<C O_{2} \)


Light waves can be polarised because they
A. have high frequencies
B. have short wavelength
c. are transverse
D. can be reflected


A body moves in a plane so that the displacements along the \( x \) and \( y \) axes are given by \( \boldsymbol{x}=\mathbf{3} \boldsymbol{t}^{3} \) and \( \boldsymbol{y}=\mathbf{4} \boldsymbol{t}^{3} . \) The
velocity of the body is :
A \( .10 t \)
B . 15
\( c \cdot 15 t^{2} \)
D. \( 25 t^{2} \)


Find the values of \( x \) and \( y \)
A . \( x=10.3, y=12.7 \)
B . \( x=12.9, y=15.6 \)
C. \( x=15.3, y=12.3 \)
D. \( x=19.3, y=15.4 \)


Find the approximate value of induced
current assuming the resistance to the current is confined to the square.
A \( \cdot \frac{B L \omega d t}{\rho} \)
\( ^{\text {В }} \cdot \frac{B L^{2} \omega d t}{\rho} \)
\( ^{\text {c. }} \frac{B L^{2} \omega d}{\rho} \)
\( \frac{B L \omega d^{2}}{\rho} \)


Equal weighs of \( C H_{4} \) and \( H_{2} \) are mixed
in a container at \( 25^{\circ} \mathrm{C} \). Fraction of total
pressure exerted by methane is?


Write the order and degree of the differential equation \( \boldsymbol{y}=\boldsymbol{x} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+ \)
\( \boldsymbol{a} \sqrt{1+\left(\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right)^{2}} \)