A water film having a refractive index of 1.33 in air is 320 nm thick. If it is illuminated with white light at normal incidence, the light of what wavelength (in \( \mathrm{nm} \) ) will appear to be in reflected light?


Explain the bond formation in sodium chloride.


Rainbow is produced when sunlight falls on drops of rain. Which of the
following physical phenomena is/are responsible for this?
A. Diffusion
B. Dispersion and total internal reflection
c. only refraction
D. Diffusion, refraction and total internal reflection.


Sum of the series \( 1+(1+2)+ \)
\( (1+2+3)+(1+2+3+4)+\ldots \) to \( n \)
terms be \( \frac{1}{m} n(n+1)\left[\frac{2 n+1}{k}+1\right] \)
Find the value of \( \mathrm{k}+\mathrm{m} \)


What type of organisms were included
in Kingdom Animalia by Whittaker
(1969) in his Five Kingdom system of classification?


Mycelium of Mucor/Rhizopus is
A. Aseptate and unicellular
B. Septate and unicellular
C . Septate and multicellular
D. Coenocytic


Moss protonema can be differentiated from filamentous alga in
A. Long rhizoids
B. Coenocytic nature
c. oblique septa
D. Absence of chloroplasts


Substraction of rational numbers is
associative.

If true then enter 1 and if false then
enter 0


The magnetic field intensity due to a bar
magnet is \( 100 \mathrm{Am}^{-1} \). The magnetic
induction field strength due to it is:
A \( \cdot \frac{4 \pi}{10^{7}} T \)
B. \( \frac{4 \pi}{10^{5} T} \)
\( ^{\mathbf{C}} \cdot \frac{10^{3}}{4 \pi} T \)
D. \( \frac{10^{5}}{4 \pi} T \)


If the speed of light (c), acceleration due to gravity (g) and pressure (p) are taken as fundamental units, the dimensions
of gravitational constant (G) are:
A \( \cdot c^{0} g p^{-3} \)
B \( \cdot c^{2} g^{3} p^{-2} \)
C. \( c^{0} g^{2} p^{-1} \)
D \cdot \( c^{2} g^{2} p^{-2} \)


Anaerobic synthesis is found in bacteria which is
A. Endergonic
B. Exergonic
c. Isothermal
D. None of the above


In a circle of radius \( 21 \mathrm{cm}, \) an arc
subtends an angle of \( 60^{\circ} \) at the centre.
The area of the segment formed by the corresponding chord of the arc is :
A \( .42 \mathrm{cm}^{2} \)
В. 421.73 \( c m^{2} \)
c. \( 429.43 \mathrm{cm}^{2} \)
D. \( 40 \mathrm{cm}^{2} \)


The fuel obtained by decomposing sludge is:
A. biogas
B. petrol
c. diesel
D. kerosene


There are two small boxes \( A \) and \( B \). \( \ln A \)
there are 9 white beads and 8 black
beads.
\( \ln B \) there are 7 white and 8 black
beads. We want to take a bead from a
box.
(a) What is the probability of getting a white bead from each box?
(b) \( A \) white bead and a black bead are
added to box \( B \) an then a bead is taken
from it.

What is probability of getting a white bead from it.


An organic compound was used with sodium metal and extracted with
distilled water. On adding freshly
prepared \( F e S O_{4} \) solution followed by
the addition of \( F e C l_{3} \) and dil. \( H C l \)
produced greenish blue solution. \( 0.30 \mathrm{g} \) of the organic compound after kjeldahlisation evolved a gas (X) which
was passed on \( 100 \mathrm{ml} \) of \( 0.1 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4} \)
The excess of acid required \( 20 \mathrm{ml} \) of 0.5
M \( N a O H \) for neutralisation.
Dil. \( H C l \) is added to the solution in the
above test to:
A. make the solution acidic
B. to dissolve \( F e S O_{4} \)
c. to dissolve \( F e(O H) \) )
D. to change \( F e S O_{4} \) to \( F e C l_{2} \)


Current in a circuit falls from \( 5.0 A \) to
\( 0.0 A \) in 0.1 sec. If an average emf of
\( 200 V \) is induced, give an estimate of the self-inductance of the circuit.


Name the gas in each of the following:
The gas produced on reaction of dilute sulphuric acid with a metallic sulphide


Calculate the electrode potential at a copper electrode dipped in a \( 0.1 M \)
solution of copper sulphate at \( 25^{\circ} \mathrm{C} \). The standard electrode potential of \( C u^{2+} / C u \) system is 0.34 volt at \( 298 K \)


Oxidation numbers of \( M n \) in its
compounds \( M n C l_{2}, M n(O H)_{3} \)
\( M n O_{2} \) and \( K M n O_{4} \) respectively are:
\( A \cdot+2,+4,+7,+3 \)
B. +2,+3,+4,+7
\( c \cdot+7,+3,+2,+4 \)
\( D \cdot+7,+4,+3,+2 \)


If \( A \) and \( B \) are square matrices of the same order such that \( (\boldsymbol{A}+\boldsymbol{B})(\boldsymbol{A}- \)
\( B)=A^{2}-B^{2} \) then \( \left(A B A^{-1}\right)^{2} \) is equal
to
\( \mathbf{A} \cdot B^{2} \)
B. \( I \)
c. \( A^{2} B^{2} \)
D. \( A^{2} \)


The north pole of a bar magnet is moved towards a coil along the axis passing through the centre of the coil when viewed in the direction of the motion of
the magnet direction of induced current
is:
A. clockwise
B. Anti - Clockwise
c. No current in the coil
D. Either clockwise or anti-clockwise


In the given Haworth Projection, which
group is above the plane of the ring?
A. propy
B. ethy
c. methy
D. hydroxy


When the polynomial \( a^{3}+2 a^{2}- \)
\( 5 a x-7 \) is divided by \( a+1, \) the
remainder is \( R_{1} . \) If \( R_{1}=14 \), find the
value of \( \boldsymbol{x} \)
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D.


Matrices \( A \) and \( B \) satisfy \( A B=B^{-1} \) where \( \boldsymbol{B}=\left[\begin{array}{cc}2 & -1 \\ 2 & 0\end{array}\right], \) then
find without finding \( A^{-1}, \) the matrix \( X \)
satisfying \( \boldsymbol{A}^{-1} \boldsymbol{X} \boldsymbol{A}=? \)
A. \( B \)
в. \( B^{2} \)
c. \( A \)
D. None of these


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. \( \sin ^{-1}\left(\frac{3 t}{5 T}\right) \)


A vibrating body:
A. Will always produce sound
B. May or may not produce sound if the amplitude of vibration is low
C. Will produce sound which is audible to humans.
D. None of the above


The motion in which all points of a moving body move uniformly in the same line or direction is known as
A. Rolling
B. Rotatory
c. Both A and B
D. Translational


A particle is thrown upwards from the ground. It experiences a constant resistance force which can produce
retardation \( 2 \frac{m}{s^{2}} . \) The ratio of time of
ascent to the time of descent is? \( [\boldsymbol{g}= \)
\( \left.\mathbf{1 0 m} / \boldsymbol{s}^{\mathbf{2}}\right] \)
A . 1:
B. \( \sqrt{\frac{2}{3}} \)
\( c \cdot \frac{2}{3} \)
D. \( \sqrt{\frac{3}{2}} \)


In a GP the sum of three numbers is 14
if 1 is added to first two numbers and
the third number is decreased by \( 1, \) the series becomes \( A P, \) find the geometric
sequence. This question has multiple correct options
\( \mathbf{A} \cdot 2,4,8 \)
в. 8,4,2
\( c .6,18,54 \)
D. 8,16,32


In the statement of Fleming's left hand rule, magnetic field is represented by
A. thumb
B. fore finger
c. middle finger
D. none


A balloon is blown up to a radius \( R \). It is
then has a positive charge \( +Q \) added to it. Air is then let out so that the radius
reduces to \( R / 2 \), however, the net charge remains the same.
How is the charge density affected by the reducing of the radius?
A. The charge density increases.
B. The charge density is unaffected.
c. The charge density decreases.
D. There is not enough information to answer the question


Consider the given structures \( (A),(B),(C) \) and \( (D) \)
Which of the following statements is
not correct?
\( (\mathbf{A}) \)
\( \mathbf{B} \)
\( A . B \) and \( C \) are identical
B. \( A \) and \( B \) are enantiomers
\( \mathrm{c} . A \) and \( C \) are enantiomers
D. \( B \) and \( D \) are enantiomers


Is \( \pi \) a rational number? Justify your
answer


Given two mutually exclusive events \( \boldsymbol{A} \) and \( B \) such that \( P(A)=\frac{1}{2} \) and \( P(B)=\frac{1}{3}, \) find \( P(A \text { or } B) \)
A \( \cdot \frac{3}{5} \)
в. \( \frac{5}{6} \)
\( c \cdot \frac{4}{5} \)
D. None of these


Find the mean salary of 80 workers of a
factory from the following tables:
\( \begin{array}{ll}\text { Salary (in Rs) } & \text { Numbers of workers } \\ 5000 & 22 \\ 6000 & 18 \\ 7000 & 15 \\ 8000 & 10 \\ 9000 & 8 \\ 10000 & 7\end{array} \)


The mean of \( 12,65,84,75, a \) is 50 Find a


If the total binding energies of \( _{1}^{2} \boldsymbol{H},_{2}^{4} \boldsymbol{H} \boldsymbol{e} \)
\( _{26}^{56} F e \&_{92}^{235} U \) are 2.22,28.3,492 and
\( 1786 M e V \) respectively, identify the most stable nucleus of the following
\( \mathbf{A} \cdot_{26}^{56} F e \)
в. \( _{1}^{2} \mathrm{H} \)
\( \mathrm{C} \cdot \frac{235}{922} \mathrm{U} \)
\( \mathbf{D} \cdot_{4}^{2} H e \)


Given that \( 5 x-2(6+7 x)=15, \) the
value of \( x \) is
A \( \cdot 1 \frac{13}{14} \)
B. \( 1 \frac{8}{19} \)
\( c \cdot \frac{1}{3} \)
D. - 3


Area lying in the first quadrant and bounded by the circle \( x^{2}+y^{2}=4 \) and
the line \( \boldsymbol{x}=\boldsymbol{y} \sqrt{\mathbf{3}} \) is:
A . \( \pi \)
в. \( \frac{\pi}{2} \)
c. \( \frac{\pi}{3} \)
D. None of these


The general value of \( x \) for the equation
\( 9^{\cos x}-2.3^{\cos x}+1=0 \)
A \( . n \pi \)
в. \( \frac{n \pi}{2} \)
\( c \cdot 2 n \pi \)
D. \( (2 n+1) \frac{\pi}{2} \)


\( " N_{2} H_{4} \) (hydrazine) reduces iodine to \( I^{-} \)
and in the process, is oxidised to \( N_{2} \)
gas." Answer whether the above statement is
true or false.
If true enter 1 , else enter 0 .


results in division of a cell into four
cells.
A. Mitosis
B. Interphase
c. Prophase
D. Meiosis


A rectangular tank is placed on a horizontal ground end is filled with water to a height \( H \) above the base. \( A \)
small hole is made on one vertical side
at a depth \( D \) below the level of water in
the tank. The distance \( x \) from the
bottom of the tank, at which the water jet from the tank will hit the ground is,
\( \mathbf{A} \cdot 2[D(H-D)]]^{1 / 2} \)
в. \( 2(g D)^{\frac{1}{2}} \)
C \( \cdot 2[D(H+D)]]^{1 / 2} \)
D \( \frac{1}{2}(D H)^{\frac{1}{2}} \)


Boyle's law may be expressed as:
This question has multiple correct options
\( \mathbf{A} \cdot(d P / d V)_{T}=K / V \)
\( \mathbf{B} \cdot(d P / d V)_{T}=-K / V^{2} \)
\( \mathbf{c} \cdot(d P / d V)_{T}=-K / V \)
D. \( V \propto 1 / P \)


Calculate the \( \% \) composition of Carbon
in \( C O_{2} . \) Molar mass is 44.01
A . \( 40 \% \)
B. 67\%
c. 30\%
D. 27\%


Two balls of the same size but of
different materials, rubber and iron are
kept on the smooth floor of a moving train. The brakes are applied suddenly to stop the train. Will the balls start
rolling? If so, in which direction? Will they move with the same speed?
A. Iron ball is faster than rubber ball
B. Rubber ball is faster than iron bal
c. Both move at the same speed
D. None of them move


What constitutes smog?


\( f(x+2) \) is a factor of \( \left(x^{4}-x^{2}-a\right) \)
then find \( a \)


The de Broglie wavelength of electron accelerated through \( V \) volt is nearly given by:
\( \underset{(i n A)}{\lambda}=\left[\frac{x}{V}\right]^{1 / 2} . \) Find the value of \( \frac{x}{75} \)


An element with atomic number 21 is
a/an:
A. Halogen
B. Representative element
c. Transition element
D. Alkali metal


The speed-time graph of a particle
moving along a solid cover is shown
below. The distance traversed by the
particle from \( t=0 \) to \( t=3 \) is:
(second)
\( A \)
\( B \)
c. \( \frac{10}{3} \) m
D. \( \frac{10}{5} \) m


\( \int \frac{x+3}{(x-1)(x-2)(x-3)} d x \)


Find the next term of the sequence:
\( \mathbf{3}, \mathbf{6}, \mathbf{1 2}, \mathbf{2 4}, \dots \dots \dots \)
A . 32
B. 48
c. 54
D. 64


An ideal gas \( \left(\frac{C_{p}}{C_{v}}=\gamma\right) \) is taken through a process in which the pressure and the volume vary as \( P=a V^{b} \). The
value of b for specific heat capacity as zero is
A. \( 2 \gamma \)
B.
c. \( -\gamma \)
D. -


The range of \( \tan ^{-1}\left(\log _{2}\left(x^{2}-2 x+2\right)\right) \)
is


A passenger train takes 2 hours more
than an express train to travel a
distance of \( 240 k m . \) The speed of the
express train is more than that of
passenger train by \( 20 k m / h \). Find the speed of both the trains.


Which of the following will not give an
alkyne?
\( A \)
B
\( c \)
\( \mathrm{D} \cdot \mathrm{CH}_{3} \mathrm{CCl}_{3} \frac{\mathrm{Ag}-\text {powder}}{\mathrm{Het}} \)


Find the volume of a cube if its total
surface area is 294 sq \( c m \)


Assertion
\( \operatorname{Let} \boldsymbol{A}=\{1,2,3,4,5\} \rightarrow B= \)
\{1,2,3,4,5\} then number of one-one
mapping from \( \boldsymbol{A} \) to \( \boldsymbol{B} \) such that \( \boldsymbol{f}(\boldsymbol{i}) \neq \)
\( j \) is equal to \( 44(1 \leq i \leq 5,1 \leq j \leq 5) \)
Reason
The number of dearrengement of \( n \) object is given by
\( n !\left\{1-\frac{1}{1 !}+\frac{1}{2 !}-\frac{1}{3 !}+\ldots+\frac{(-1)^{n}}{1 !}\right\} \)
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


Express in radians \( 345^{\circ} 25^{\prime} 36^{\prime \prime} \)
A . \( 1.726268 \pi^{c} \)
B . \( 1.3465338 \pi^{c} \)
\( \mathbf{c} \cdot 1.91903 \pi^{c} \)
D. \( 1.1978258 \pi^{c} \)


lime water is a solution of:
A \( \cdot C a(O H)_{2} \) in water
B. \( C a C l_{2} \) in water
c. NaOH in water
D. NaCl in water


The oxidation state of \( C u \) and \( F e \) in
Chalcopyrite is, respectively +1 and +3
A . True
B. False


The diameter of a wheel is 1.26 m. How
far will it travel in 500 revolutions?
\( \mathbf{A} \cdot 1980 m \)
B. 2000m
\( c .2420 m \)
D. \( 1890 m \)


In the bell jar experiment, after vacuum pump is started
A. the sound of the bell disappears suddenly
B. the sound becomes fainter gradually
c. the sound is heard with the same loudness
D. unpredictable


Thermal capacity \( =M a s s \times \)
Heat capacity
A. True
B. False


Name the following:
Distinctive reaction that takes place
when ethanol is treated with acetic
acid.


Nickel is purified by thermal decomposition of its:
A. Hydride
B. Chloride
c. Azide
D. carbony!


The velocity of all electromagnetic
radiation is \( x \times 10^{8} \mathrm{m} \mathrm{s}^{-1} \)
Value of \( x \) is :


Of 30 snakes at the reptile house, 10 have stripes, 21 are poisonous, and 5 have no stripes and are not poisonous. How many of the snakes have stripes AND are poisonous?
A . 5
B. 6
c. 10
D.


For positive numbers \( \boldsymbol{x}, \boldsymbol{y}, \boldsymbol{z} \) the
numerical value of the determinant \( \left|\begin{array}{ccc}\mathbf{1} & \log _{x} \boldsymbol{y} & \log _{\boldsymbol{x}} \boldsymbol{z} \\ \log _{\boldsymbol{y}} \boldsymbol{x} & \boldsymbol{3} & \log _{\boldsymbol{y}} \boldsymbol{z} \\ \log _{\boldsymbol{z}} \boldsymbol{x} & \log _{\boldsymbol{z}} \boldsymbol{y} & \boldsymbol{5}\end{array}\right| \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \log x \log y \log z \)
\( c .1 \)
D. 8


With a mixture of conc. \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) and
conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) anisole
gives
A. ortho nitro anisole
B. para nitro anisole
c. ortho and para nitro anisole
D. meta nitro anisole


An experiment requires minimum \( \beta \)
activity produced at the rate of \( 346 \beta \)
particles per minute. The half-life period of \( _{42}^{99} \) Mo which is a \( \beta \) -emitter is 66.6 hr. The minimum amount of \( _{42}^{99} \) Mo required to carry out the experiment in 6.909 hour is :
A \( \cdot 6.78 \times 10^{-16} g \)
В. \( 3.52 \times 10^{-16} g \)
c. \( 5.21 \times 10^{-16} g \)
D. none of these


The image of an object formed by a convex lens when the object is placed between the lens and the focal point is -
A. Virtual and inverted
B. Real and magnified
c. Real and diminished
D. Virtual and magnified


Which of the following waste is present in coolant water from atomic reactors?
A. Solid municipal waste
B. Low-level radioactive waste
c. High-level radioactive waste
D. None of the above


Number of partial fractions obtained
\( \frac{3 x-5}{(x+1)^{3}\left(x^{2}+1\right)^{2}} \)
A. 5
B. 4
\( c \cdot 6 \)
D. 3


Evaluate: \( \int_{-a}^{a} \frac{\sqrt{a-x}}{\sqrt{a+x}} d x \)


0 0
0
0
0


Elements with atomic numbers 9,17,35
53 are collectively known as:
A. chalcogens
B. halogens
c. lanthanides
D. rare gases


Fill in the blanks in the following so that each of the following statements is true. \( \ln a \Delta B C \) if \( \angle A=\angle C, \) then \( A B=\dots \)


In Drosophila, the Y-chromosome does
not determine maleness but is
necessary for fertility.
A. True
B. False


State the position of the object in case of image formed by a concave mirror with the following characteristics : image is virtual and
upright


Taiga refers to
A. Temperate deciduous forest
B. subtropical semi-deciduous forest
C . Evergreen forest
D. North temperate coniferous forest


For two \( 3 \times 3 \) matrices \( A \) and \( B \), let
\( A+B=2 B^{\prime} \) and \( 3 A+2 B=I_{3}, \) where
\( B^{\prime} \) is the transpose of \( B \) and \( I_{3} \) is \( 3 \times 3 \)
identify matrix. Then :
A. \( 5 A+10 B=2 I_{3} \)
В . \( 3 A+6 B=2 I_{3} \)
c. \( 10 A+5 B=3 I_{3} \)
D. \( B+2 A=I_{3} \)


The line of action of a force \( \overrightarrow{\boldsymbol{F}}= \)
\( (-3 \hat{i}+\hat{j}+5 \hat{k}) N \) passes through \( a \)
point \( (7,3,1) . \) The moment of force \( (\vec{\tau}=\vec{r} \times \vec{F}) \) about the origin is given by
\( \mathbf{A} \cdot 14 \hat{i}+38 \hat{j}+16 \hat{k} \)
B . \( 14 \hat{i}+38 \hat{j}-16 \hat{k} \)
c. \( 14 \hat{i}-38 \hat{j}+16 \hat{k} \)
D. \( 14 \hat{i}-38 \hat{j}-16 \hat{k} \)


\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left(\boldsymbol{x}^{2} \boldsymbol{e}^{\boldsymbol{a} \boldsymbol{x}}\right) \)
A \( \cdot e^{a x}\left(a x^{2}+2 x\right) \)
B \( \cdot e^{a x}\left(2 a x^{2}+2 x\right) \)
C \( \cdot e^{a x}\left(a x^{2}+2 a x\right) \)
D. \( e^{a x}\left(a x^{2}-2 a x\right) \)


Total energy of an electron in the ground state of hydrogen atom is \( -13.6 e V \). Its
total energy, when hydrogen atom is in the first excited state, is:
\( \mathbf{A} \cdot+13.6 \mathrm{eV} \)
B. \( +3.4 e V \)
c. \( -3.4 e V \)
D. \( -54.4 e V \)


State the type of chemical reaction involved in given reaction,
a] Calcium + oxygen \( \rightarrow \) Calcium oxide
A. Displacement Reactions
B. Decomposition Reactions
c. combination Reactions
D. Neutralization Reactions


Evaluate \( \int \frac{(\sin x)^{2018}}{(\cos x)^{2020}} d x \)
A. \( \frac{(\tan x)^{2019}}{2019}+c \)
B. \( \frac{(\sin x)^{2019}}{2019}+c \)
c. \( \frac{(\cos x)^{2019}}{2019}+c \)
D. \( \frac{(\tan x)^{2019} \sec ^{2} x}{2019}+c \)


The points \( (\boldsymbol{k}-\mathbf{1}, \boldsymbol{k}+\mathbf{2}),(\boldsymbol{k}, \boldsymbol{k}+ \)
1) \( ,(k+1, k) \) are collinear for
A. any value of \( k \)
B. \( k=-\frac{1}{2} \) only
c. no value of \( k \)
D. integral values of \( k \) only


The time \( t \) (after entering in rough
surface) after which ring starts pure
rolling
A. \( \frac{v_{0}}{2 \mu_{0}} \)
в. \( \underline{v_{0}} \)
\( g \)
c. \( \frac{v_{0}}{\mu g g g g} \)
D. None of these


The value of
\( A \cdot O \)
B. \( 30^{\text {th }} \)
\( c \cdot 30^{-x} \)
D. None of these


Which of the following sequences would yield m-nitro chlorobenzene \( (Z) \) from benzene?
A. Benzene \( \frac{C l_{2} / F e C l_{3}}{\longrightarrow}(X) \frac{H N O_{3}}{H_{2} S O_{4}}(Z) \)
B. Benzene \( \frac{H_{2} S O_{4} / H N O_{3}}{\longrightarrow}(Z) \)
c. Benzene \( \frac{H_{2} S O_{4} / H N O_{3}}{\rightarrow}(X) \frac{C_{l 2} / F e C l_{3}}{\longrightarrow}(Z) \)
D. All of these


Assertion
At high temperature, a ferromagnet
becomes a paramagnet.
Reason
The ferromagnetic property depends on
temperature.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Two balls of mass \( m_{1} \) and \( m_{2} \) where
\( m_{2}=0.5 m_{1}, \) undergo head on collision
as shown in figure.
If \( \boldsymbol{v}_{3}=\mathbf{0 . 5} \boldsymbol{v}_{1} \) value of \( \boldsymbol{v}_{4} \) is
fter collision
A \( \cdot v_{4}=v_{1}+v_{2} \)
B \( \cdot v_{4}=v_{1}+2 v_{2} \)
\( \mathbf{c} \cdot v_{4}=2 v_{1}+v_{2} \)
\( \mathbf{D} \cdot v_{4}=2 v_{1}+3 v_{2} \)


By imparting heat to a body, its
temperature rises by \( 15^{\circ} \mathrm{C} \). What is the corresponding rise in temperature on kelvin scale?
\( \mathbf{A} \cdot 288 K \)
в. \( 15 K \)
\( c .30 K \)
D. \( 7.5 K \)


The base of a right prism is a Trapezium whose lengths of two Parallel sides are
\( 10 c m \) and \( 6 \mathrm{cm} \) and distance between
them is \( 5 \mathrm{cm} . \) If the height of the prism
is \( 8 \mathrm{cm}, \) its volume is
A \( \cdot 320 \mathrm{cm}^{3} \)
B. \( 300.5 \mathrm{cm}^{3} \)
\( c \cdot 310 c m^{3} \)
D. \( 300 \mathrm{cm}^{3} \)


Find the value of \( s, \) if \( 3 s^{2}+8 s+3 \)


Side of a square is \( 5 \mathrm{cm} \). What is the
length of its diagonal.


A dipole with a dipole moment of magnitude \( p \) is in stable equilibrium in an electrostatic field of magnitude E. Find the work done in rotating this dipole to its position of unstable equilibrium.
A. 2pE
B. 4pE
c. pE
D. 9pE


Find the perimeter of
(i) \( \Delta \mathrm{ABC} \)
(ii) rectangle BCDE.
\( \mathbf{A} \)
(i) \( -8 \frac{1}{60} \mathrm{cm}, \) (ii)- \( 5 \mathrm{cm} \)
3
(i) \( -5 c m, \) (ii) \( -10 \frac{1}{6} \mathrm{cm} \)
c. \( \left(\text { i) }-8 \frac{1}{60} \text { cm, (ii) }-10 \frac{1}{5} \) cm \right.
) . (i)- \( 8 \mathrm{cm}, \) (ii) \( -23 \mathrm{cm} \)


Find the change in velocity of the tip of the minute hand (radius \( =10 \mathrm{cm} \) ) of a
clock in 45 minutes. \( (\text { in } \mathrm{cm} / \mathrm{min}) \)
A \( \cdot \frac{\sqrt{2}}{3} \)
B. \( \pi \frac{\sqrt{2}}{2} \)
c. \( \pi \frac{\sqrt{3}}{3} \)
D. \( \pi \frac{2}{3} \)


A body starts from rest with uniform acceleration and acquires a velocity \( \boldsymbol{v} \)
in time \( T . \) The instantaneous kinetic
energy of the body at time \( t \) is
proportional to:
\( \mathbf{A} \cdot(v / T) t \)
B \( \cdot\left(v^{2} / T\right) t^{2} \)
C \( \cdot\left(v^{2} / T^{2}\right) t \)
D. \( \left(v^{2} / T^{2}\right) t^{2} \)


Which of the following has no reaction
with water?
A. Ba
B. sr
\( c . \) Ве
D. Mg


Opinion No. of students
135
dislike
To know the opinion of the students about the subject statistics, a survey of
200 students was conducted. The data
is recorded in the following table.
Find the probability that a student
chosen at random
(i) likes statistics
(ii) does not like it.


angled isosceles triangle of height
\( 10 \mathrm{cm} \) is kept such that the \( 90^{\circ} \) vertex
is very close to an infinitely long
conducting wire (see the figure). The
wire is electricity insulted from the loop
The hypotenuse of the triangle is parallel to the wire. The current in the
triangle loop is in counterclockwise
direction and increased at a constant
rate of \( 10 A s^{-1} . \) Which of the following
statement(s) is(are) true?
This question has multiple correct options
A \cdot The magnitude of induced emf in the wire is \( \left(\frac{\mu_{0}}{\pi}\right) \) volt
B. If the loop is rotated at a constant angular speed about the wire, an additional emf of \( \left(\frac{\mu_{0}}{\pi}\right) \)
C. The induced current in the wire is in opposite direction to the current along the hypotenuse
D. There is a repulsive force between the wire and the loop


Spraying of DDT on crops produces pollution of
A. Soil and water only
B. Air and soil only
c. Air, soil and water
D. Air and water only


Why is \( K O_{2} \) paramagnetic?


Assertion
Bond angle of \( \boldsymbol{P} \boldsymbol{F}_{3}>\boldsymbol{P} \boldsymbol{C l}_{3} \) but bond
angle of \( \boldsymbol{P C l}_{3}<\boldsymbol{P B r}_{3} \)
Reason
The bond angles show an increase on decreasing electronegativity of attached other atom on central atom
but in \( P F_{3} p \pi-d \pi \) bonding results in
an increase in bond angle.
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


A given sample of an ideal gas occupies a volume \( V \) at a pressure \( P \) and absolute temperature T. The mass of each
molecule of the gas is m. which of the following gives the density of the gas?
A. mKT
B. P/(kT)
\( \mathbf{c} \cdot \operatorname{Pm} /(\mathrm{k} \mathrm{T}) \)
D. P/(KTV)


What is correct order of rate of nitration
of the following compounds?
\( \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{5}} \boldsymbol{N} \boldsymbol{R}_{\boldsymbol{3}} \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{5}} \boldsymbol{N} \boldsymbol{M} \boldsymbol{e}_{\boldsymbol{2}} \)
\( \boldsymbol{F} \)
\( A \cdot G>A>B>C>D>E>F \)
B. \( G>B>C>D>A>F \)
\( \mathrm{c} \cdot \mathrm{G}>\mathrm{A}>\mathrm{B}=\mathrm{C}=\mathrm{D}>\mathrm{E}>\mathrm{F} \)
D. \( G>A>B>C=D>E>F \)


What is leaf venation?


If two balls each of mass \( 0.06 \mathrm{kg} \) moving
in opposite directions with same speed \( 4 m / s \) collide and rebound with the same speed, then the impulse imparted to each ball due to other is
\( \mathbf{A} \cdot 0.48 k g-m / s \)
в. \( 0.24 \mathrm{kg}-\mathrm{m} / \mathrm{s} \)
c. \( 0.81 \mathrm{kg}-\mathrm{m} / \mathrm{s} \)
D. Zero


Write structural formula for the \( I U P A C \)
name:
2-Chlorobutane


Which description of ethanoic acid is
correct?
A. A clear, colourless and odourless liquid
B. A colourless liquid with a distinctive odour
c. A soft white solid with a distinctive odour
D. A transparent solid with a low melting point


(i) Quadrilateral \( A B C D \)
\( A B=4.5 c m \)
\( B C=5.5 \mathrm{cm} \)
\( C D=4 c m \)
\( A D=6 \mathrm{cm} \)
\( A C=7 c m \)
(ii) Quadrilateral \( J U M P \)
\( J U=3.5 c m \)
\( \boldsymbol{U} \boldsymbol{M}=\boldsymbol{4} \boldsymbol{c} \boldsymbol{m} \)
\( M P=5 c m \)
\( \boldsymbol{P J}=\mathbf{4 . 5 c m} \)
\( \boldsymbol{P U}=\mathbf{6 . 5 c m} \)
(iii) Parallelogram \( M O R E \)
\( \boldsymbol{O} \boldsymbol{R}=\boldsymbol{6} \boldsymbol{c m} \)
\( \boldsymbol{R} \boldsymbol{E}=\mathbf{4 . 5 c m} \)
\( E O=7.5 \mathrm{cm} \)
(iv) Rhombus \( B E S T \)
\( B E=4.5 c m \)
\( \boldsymbol{E T}=\mathbf{6} \boldsymbol{c m} \)


If \( \boldsymbol{A}=\left[\begin{array}{ll}\boldsymbol{\alpha} & \boldsymbol{2} \\ \boldsymbol{2} & \boldsymbol{\alpha}\end{array}\right] \) and \( \left|\boldsymbol{A}^{3}\right|=\mathbf{1 2 5}, \) then the
value of \( \alpha \) is
\( A \cdot \pm 1 \)
\( B \cdot \pm 2 \)
\( c \cdot \pm 3 \)
\( D .\pm 5 \)


Choose the correct answer from the
alternatives given Which of the following is the bodys
largest blood vessel?
A. Aorta
B. Capillaries
c. Pulmonary vein
D. Heart


Two particles of mass \( m \), constrained to move along the circumference of a smooth circular hoop of equal mass \( m \)
are initially located at opposite ends of
a diameter and given equal velocities \( v_{0} \)
shown in the figure. The entire
arrangement is located in gravity free space. Their velocityjust before collision is?
\( A \)
в. \( \frac{\sqrt{3}}{2} v_{0} \)
c. \( \frac{2}{\sqrt{3}} v \)
D. \( \frac{\sqrt{7}}{3} v_{0} \)


The value of \( \left(9 x^{2}+18 x+27\right) \div 9 \) is
equal to
\( \mathbf{A} \cdot x+2 \)
B. \( x^{2}+2 x+2 \)
c. \( x^{2}+2 x+3 \)
D. \( x^{2}+2 x+1 \)


Equivalent resistance of the system and potential difference across the external resistance in the figure.
A \( . r, \)
в. \( r, E \)
\( c \cdot o, E \)
' \( r, \frac{E R}{R+r} \)


Let \( \vec{a} \) and \( \vec{b} \) be two unit vectors if the vectors \( \vec{c}=\vec{a}+2 \vec{b} \) and \( \vec{d}=2 \vec{a}- \)
\( 4 \vec{b} \) are perpendicular to each other Then the angle between \( \vec{a} \) and \( \vec{b} \) is:
A \( \cdot \frac{\pi}{6} \)
в. \( \frac{\pi}{2} \)
\( c \cdot \frac{\pi}{3} \)
D.


Number of ordered pair(s) \( (a, b) \) of real numbers such that \( (\boldsymbol{a}+\boldsymbol{i} \boldsymbol{b})^{2008}=\boldsymbol{a}- \)
ib holds good, is?
A . 2008
B. 2009
\( c .2010 \)
D. 2011


Evaluate the integral \( \int_{0}^{\frac{\pi}{2}} \frac{\sin ^{\frac{3}{2} x} d x}{\sin ^{\frac{3}{2}} x+\cos ^{\frac{3}{2}} x} \)
A \( \cdot \frac{\pi}{2} \)
в. \( \frac{\pi}{4} \)
c. \( \pi \)
D.


Ethanol is separated form water by:
A. Crystallisation
B. Chromatography
C. Fractional distillation
D. Adding methyl alcohol


Among ethanol, dimethyl ether, methanol and propanal, the isomers are
A. ethanol, dimethyl ether, methanol and propanal
B. ethanol and methanol
c. ethanol, dimethyl ether, and methanol
D. ethanol and dimethyl ether


The equilibrium constant of a reaction
is 10. What will be the value of \( \Delta G^{0} \) at
300 K?
\( A \). \( -5.74 k J \)
B. - 574 k
c. +11.48 k
D. +5.74 kJ


Choose the correct answers from the
alternatives given :
Which of the following regarding DNA is
not true?
A. Complementary base pairs consist of one purine and one pyrimidine
B. Side rails of the DNA double helix are made of alternating molecules of phosphate and ribose
c. complementary base pairs are joined by hydrogen bonds
D. Amount of thymine equals the amount of adening


A horse is tied to a peg at one corner of
a square shaped grass field of side \( 15 m \)
by means of a \( 5 m \) long rope. Find
(i) the area of that part of the field in
which the horse can graze.
(ii) The increase in the grazing area if
the rope were \( 10 m \) long instead of \( 5 m \)
(Use \( \boldsymbol{\pi}=\mathbf{3 . 1 4}) \)


How are carboxylic acids prepared using Grignard reagent?


High value of BOD (Biochemical Oxygen Demand) indicates
A. Water is less polluted
B. Consumption of organic matter in the water is higher by the microbes
c. water is pure
D. None of these


For which of the following substances the resistance decreases with the
decrease in temperature:
A. Germanium
B. Silicon
c. silver
D. None


Which is common to kidney and skeleton in mammals?
A. cortex
B. Medulla
c. Pelvis
D. Radius


Write the value of \( \sin ^{-1}\left(\frac{1}{3}\right)- \)
\( \cos ^{-1}\left(-\frac{1}{3}\right) \)


Which of the following is a path function?
A. Internal Energy
B. Enthalpy
c. work
D. All of the above


If the \( 10^{t h} \) term and the \( 18^{t h} \) term of an
A.P are 25 and 41 respectively then
find the following ( \( a \) ) the \( 1^{s t} \) term and
the common difference
(b) the \( 38^{t h} \)
term.


A cup of water was heated for eight minutes. The thermometers show the
temperature readings during different times of heating.What can be the
temperature when it is heated for three
minutes?
\( A, 2 \)
в. 28
\( c \cdot 28 \)
D. 30


Integrate:
\( \int x \sqrt{x^{2}+2} d x \)


Find the minimum value of \( |z-1| \) if
||\( z-3|-| z+||1=2 \)
A \( \cdot|z-1| \geq 0 \)
B \( \cdot|z-1| \geq 1 \)
c. \( |z-1| \geq 2 \)
D. \( |z-1| \geq 3 \)


The radius of a black hole \( \left(R_{B}\right) \) and its
Schwarzschild radius \( \left(R_{S}\right) \) are related
as:
A \( \cdot R_{B}>R_{S} \)
B \( . R_{B} \geq R_{S} \)
\( \mathbf{c} \cdot R_{B} \leq R_{S} \)
D. \( R_{B}=R_{S}=\infty \)


Probability of hitting a target independently of 4 persons are \( \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{8} . \) Then the probability that
target is hit, is?
A \( \cdot \frac{1}{192} \)
в. \( \frac{5}{192} \)
c. \( \frac{25}{32} \)
D. \( \frac{7}{32} \)


Which of the following statements(s)
is(are) true?
This question has multiple correct options
A. The two six-membered cyclic hemiacetal forms of \( D-(+)-g l u c o s e \) are called anomers
B. Hydrolysis of sucrose gives dextrorotatory glucose and laevorotatory fructose
C. Monosaccharides cannot be hydrolysed to give polyhydroxy aldehydes and ketones
D. Oxidation of glucose with bromine water gives glutamic acid


\( \frac{\sin i}{\sin r}=\dots \dots \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
c. constant
D. Variable


No. of meiotic divisions required for the
formation of 200 seeds of Capsella will
be?
A . 200
в. 400
c. 250
D. 300


Two cars are moving in the same
direction with the same speed of
\( 30 k m / h r . \) They are separated by \( 5 k m \) What is the speed of car moving in the opposite direction if it meets the two
cars at an interval of 4 minute:
A. \( 45 k m / h r \)
в. \( 60 k m / h r \)
c. \( 105 k m / h r \)
D. None


Construct a quadrilateral \( A B C D, \) when
\( A B=6.3 \mathrm{cm}, B C=C D=4.2 \mathrm{cm} \) and
\( \angle A B C=\angle B C D=90^{\circ} \)
Find the length of side \( A D \) and
\( \boldsymbol{m} \angle \boldsymbol{B} \boldsymbol{A} \boldsymbol{D} \)
A. \( A D=3.5 \mathrm{cm}, 70^{\circ} \)
B. \( A D=4.7 \mathrm{cm}, 65 \)
C . \( A D=4.5 \mathrm{cm}, 70^{\circ} \)
D. \( A D=3.5 \mathrm{cm}, 65 \)


Identify the logic operation of the following logic circuit:
A. NAND
B. AND
c. Non
D. on


Examine the continuity of the following function at given points:
(i) \( \boldsymbol{f}(\boldsymbol{x})= \)
\[
\begin{array}{ll}
\frac{e^{5 x}-e^{2 x}}{\sin 3 x}, & \text { for } x \neq 0 \\
= & \text { for } x \neq 0
\end{array}
\]


Distinguish between electric motor and electric generator


\( \lim _{x \rightarrow 0} \frac{(1-\cos 2 x)^{2}}{2 x \tan x-x \tan 2 x} \) is
\( A \cdot 2 \)
B. \( -\frac{1}{2} \)
\( c \cdot \frac{1}{2} \)
\( D \ldots-2 \)


Element \( A \) reacts with oxygen to form a
compound \( A_{2} O_{3} \). If 0.359 gram of \( A \) reacts to give 0.559 gram of the compound, then atomic weight of \( \boldsymbol{A} \) will
be:
A. 5
B. 43.08
c. 49.7
D. 47.9


Two identical lights sources \( S_{1} \) and \( S_{2} \)
emit the light of same wavelength \( \lambda \)
These light rays will exhibit interference ¡f
A. their phase difference remain constant
B. their phase difference is distributed randomly
c. their light intensities remain constant.
D. theirlight intensities change continuously


Which one of the following is not applicable to the phenomenon of adsorption?
A. \( \Delta H>0 \)
в. \( \Delta G<0 \)
\( c \cdot \Delta S<0 \)
\( \mathbf{D} \cdot \Delta H<0 \)


Elastic waves in solid are
A. Transverse
B. Longitudinal
c. Either transverse or longitudinal
D. Neither transverse nor longitudinal


Sketch top, front and side view for the following diagram.


f the determinant \( D= \)
\[
\left|\begin{array}{ccc}
\mathbf{1} & \mathbf{1} & \mathbf{1} \\
\boldsymbol{\alpha}+\boldsymbol{\beta} & \boldsymbol{\alpha}^{2}+\boldsymbol{\beta}^{2} & \mathbf{2} \boldsymbol{\alpha} \boldsymbol{\beta} \\
\boldsymbol{\alpha}+\boldsymbol{\beta} & \mathbf{2} \boldsymbol{\alpha} \boldsymbol{\beta} & \boldsymbol{\alpha}^{2}+\boldsymbol{\beta}^{2}
\end{array}\right| \text { and }
\]
\( \boldsymbol{D}_{1}=\left|\begin{array}{ccc}\mathbf{1} & \mathbf{0} & \mathbf{0} \\ \mathbf{0} & \boldsymbol{\alpha} & \boldsymbol{\beta} \\ \mathbf{0} & \boldsymbol{\beta} & \boldsymbol{\alpha}\end{array}\right|, \) then find the
determinant of \( D_{2} \) such that \( D_{2}=\frac{D}{D_{1}} \)


A box weighing \( 2000 N \) is to be slowly
slid through \( 20 m \) on a straight track having friction coefficient 0.2 with the
box. Find the work done by the person pulling the box with a chain at an angle \( \theta \) with the horizontal.


\( \mathrm{cm} \) make \( 3.25 \mathrm{km} \)


Explain the inconsistency of Ampere's circuital law during charging of a capacitor. Define displacement current


The sum of the first q terms of A.P is \( 63 q-3 q^{2} . \) If its pth term is -60, Find the
value of \( p . \) Also, find the 11 th term of this
A.P.


Initially car \( A \) is \( 21 \mathrm{m} \) ahead of car \( B \).
Both start moving at time \( t=0 \) in same direction along straight line. if \( A \) is moving with constant velocity \( 20 \mathrm{m} / \mathrm{s} \) and B starts from rest with an
acceleration \( 2 m / s^{2} \) towards \( A, \) then the
time when car \( B \) will catch the car \( A \) is
A . \( 21 s \)
в. \( 22 s \)
\( c .10 s \)
D. Can never catch \( A \)


Which acid is used in rubber industry as a coagulating agent?
A. Methanoic acid
B. Ethanoic acid
c. Propanoic acid
D. Butanoic acid


The number 0 is not the reciprocal of
any number.
A. True
B. False
c. Ambiguous.
D. None


The efficiency of an enzyme in
catalyzing a reaction is due to its
capacity
A. To form a strong enzyme-substrate complex
B. To decrease the bond energy of all substrate molecules
C. To change the shape of the substrate molecule
D. To lower the activation energy of the reaction


A unit vector \( \boldsymbol{d} \) is equally inclined at an angle \( \alpha \) with the vectors \( a=\cos \theta . i+ \)
\( \sin \theta . j, b=-\sin \theta . i+\cos =\theta . j \) and
\( c=k . \) Then \( \alpha \) is equal to
A \( \cdot \cos ^{-1}\left(\frac{1}{\sqrt{2}}\right) \)
B. \( \cos ^{-1}\left(\frac{1}{\sqrt{3}}\right) \)
c. \( \cos ^{-1} \frac{1}{3} \)
D.


Very short answer type:
Classify the following fruits into two categories, dehiscent and indehiscent fruits samara, nut, follicle pod,
caryopsis, achene, capsule


The ratio of dimensions electric field
and magnetic field is,
A \( . M T^{1} L^{-1} \)
B. \( M T^{-1} L^{-2} \)
\( \mathbf{c} \cdot M T^{2} L^{-1} \)
D. \( L T^{-1} \)


Choose the right from the following.
(i) In light, hormone auxin, helps the cells to grow longer in plants.
(ii) Plant hormone gibberellins help in growth of a stem.
(iii) Cytokinin inhibits cell division.
(iv) Abscisic acid promotes growth in plants.
A . (I) and (iii) are correct
B. (ii) and (iv) are correct.
c. (i) and (ii) are correct.
D. (i) and (iv) are correct.


The length of each side of the cubical
box is \( 2.4 m . \) Its volume is:
A . 13.824 cu. \( m \)
в. 13.824 си. ст
c. \( 13.824 \mathrm{m}^{2} \)
D. 13.824 sq. \( \mathrm{cm} \)


The net force acting is not zero on
A. a retarding train
B. a ball falling with terminal velocity
C . a kite held stationary
D. a truck moving with constant velocity
\( \mathrm{E} \cdot \) a book placed on a table


Bond dissociation enthalpy of EH (E =
element) bonds is given below. Which of
the compounds will act as strongest reducing agent?
\[
\begin{array}{llll}
\text { Compound } & \boldsymbol{N H}_{3} & \boldsymbol{P H}_{\boldsymbol{3}} & \boldsymbol{A} \boldsymbol{s} \boldsymbol{H}_{\boldsymbol{3}} \\
\boldsymbol{\Delta}_{\text {diss}}(E- & & & \\
& & \\
& & \\
& &
\end{array}
\]
\[
389
\]
322
\[
H) / k J m o l^{-1}
\]
\( \mathbf{A} \cdot N H_{3} \)
B \( . P H_{3} \)
\( \mathbf{c} \cdot A s H_{3} \)
D. \( S b H_{3} \)


Which of the following point is not
shown by Rutherford alpha scattering experiment?
A. \( \alpha \) - particle can come within a distance of the order of \( 10^{-14} \mathrm{m} \) of the nucleus
B. The radius of the nucleus is less than \( 10^{-14} m \)
C. Sattering follows coulombs law
D. The positively charged parts of an atom move with extremely high velocities


Select correct statement(s):
This question has multiple correct options
A. In \( \alpha \) -graphite, the layers are arranged in the sequence \( A B A B \)
B. \( \ln \beta \) -graphite, the layers are arranged in the sequence \( A B C A B C \)
C. In \( \alpha \) -graphite, the layers are arranged in the sequence \( A B C A B C \)
D. \( \ln \beta \) -graphite, the layers are arranged in the sequence \( A B A B \)


If the attractive force between two
bodies of mass \( M_{1} \) and \( M_{2} \) and
situated at a distance \( \mathrm{R} \) is \( \mathrm{F} \), then find
the force \( F^{\prime} \) between them at distance
\( (R+d) \) in terms of \( F \)


The molecular weight of heavy water is than ordinary water


Assertion
Darwin's finches of Galapagos islands have different types of modified beaks according to their food habits.
Reason
Adaptive radiation, leads to
development of different functional
structure from a common ancestral
form.
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


Evaluate: \( \int \frac{\sin x}{\sin 4 x} d x \)


Identify the stage of cell division.
A. Prophase II of meiosis
B. Both prophase and metaphase of mitosis
C. Prophse I during meiosis
D. Prophase of mitosis


We have two solutions, one is 1 L of 0.1 M
NaCl and the other is 2 L of 0.2 M
\( \mathrm{CaCl}_{2} . \) Using only these two solutions,
a solution of \( 2.5 L \) volume can be
prepared which has \( \left[\boldsymbol{C l}^{-}\right]=\mathbf{0 . 3 4} \boldsymbol{M} \)
Calculate the osmotic pressure of the
solution prepared. Given: \( \boldsymbol{t}=\mathbf{3 0 0} \boldsymbol{K},(\boldsymbol{R}= \)
\( \left.\mathbf{0 . 0 8 2} \boldsymbol{L} \boldsymbol{a t m} \boldsymbol{m o l}^{-1} \boldsymbol{K}^{-1}\right) \)
A. 10.8 atm
B. 12.8 atm
\( c .5 .6 \) atm
D. None of these


Two particles move parallel to \( x \) -axis about the origin with same amplitude and frequency. At a certain instant they are found at a distance \( \frac{a}{3} \) from the origin on opposite sides but their
velocities are found to be in same
direction.Then the phase difference between two particles will be
A \( \cdot \cos ^{-1}\left(\frac{7}{9}\right) \)
В. \( 180^{\circ} \)
c. \( 45^{\circ} \)
D. None of the above


The three domain system with six kingdom is the latest classification based on
A. Mitochondrial genes
B. Nuclear genes
C. 16 S rRNA gene
D. chloroplast genes


Which of the following conducts the impulse from AV node to the ventricles?
A. Purkinji fibres
B. SA node
c. Right atrium
D. None of the above


A body is thrown vertically upwards
from the top \( A \) of a tower. It reaches the
ground in \( t_{1} \) seconds. If it thrown
vertically downwards from A with same
speed it reaches the ground in \( t_{2} \)
seconds. If it is allowed to fall freely
from \( A, \) then the time it takes to reach
the ground is given by:
A \( \cdot t=\frac{t_{1}+t_{2}}{2} \)
B. \( t=\sqrt{\frac{t_{1}^{2}+t_{2}^{2}}{2}} \)
C \( . t=\sqrt{t_{1} t_{2}} \)
D. \( t=t_{1}+t_{2} \)


Which of the following is a compound?
A. Iron
B. Gold
C. Platinum
D. Camphor


Which of the following statement is
true?
A. All living member of class Cyclostomata are parasites of some fish
B. There are about 2000 species in class Osteichthyes
C. Ciona belongs to subphylum Cephalochordata
D. Arthropods are diploblastic animals
E. Ascaris lumbricoides is a flat worm


One type of liquid contains \( 25 \% \) of benzene, the other contains \( 30 \% \) of benzene. A can is filled with 6 parts of
the first liquid and 4 parts of the second liquid. Find the percentage of benzene in the new mixture.


Find the number of permutations that can be made with the letters of the word
\( ' M O U S E^{\prime} \)
This question has multiple correct options
A . \( 5 ! \)
B. 5
c. 720
D. 120


Find the number of moles of sodium
nitrate which contains 1.5 moles of
oxygen atoms.
A . 0.5
в. 1.5
c. \( 2 . \)
D. 1.0


For the reaction \( \boldsymbol{A}+\boldsymbol{B} \rightarrow \) product, it is
found that the order of \( A \) is 1 and the order of \( B \) is \( \frac{1}{2}, \) the concentration of both \( A \) and \( B \) are increased four times,
the rate will increase by a factor of
\( A \cdot 16 \)
B. 8
\( c \cdot 6 \)
D. 4


Percolation tank is the storage of water for
A. Domestic pupose
B. Industrial use
c. Irrigation
D. Both A and C


Reagent (C) is:
\( \mathbf{A} \cdot O_{3} / P h_{3} P \)
\( \mathbf{B} \cdot O_{3} / N a B H_{4} \)
\( \mathbf{c} \cdot O_{3} / H_{2} O_{2} \)
D. \( K M n O_{4} / \) O \( H \)


In a circuit, the current lags behind the voltage by a phase difference of \( \pi / 2 \) the circuit will contain which of the
following:
A . Only R
B. Only c
c. \( R \) and \( c \)
D. only L


The length of two sides of a triangle are
\( 20 \mathrm{mm} \) and \( 29 \mathrm{mm} . \) Which of the
following can be the value of third side to form the triangle?
\( A \cdot 6 \mathrm{mm} \)
B. \( 7 \mathrm{mm} \)
\( c .23 \mathrm{mm} \)
D. \( 8 \mathrm{mm} \)


How are 0.50 mol \( N a_{2} C O_{3} \) and \( 0.50 \mathrm{M} \)
\( N a_{2} C O_{3} ? \)


A man mixes two types of rice \( (X \text { and } Y) \) and sells the mixture at the rate of

Rs.17 per kg. Find his profit percentage.
\( P: \) Rate of \( X \) is Rs.20 per \( \mathrm{kg} \)
\( Q: \) Rate of \( Y \) is Rs.13 per \( \mathrm{kg} \)
A. Only P is sufficient to answer
B. Only Q is sufficient to answer
c. Both are sufficient to answer
D. None of them are sufficient to answer


One mole of ethanol is treated with one
mole of ethanoic acid at \( 25 . \) One-forth of the acid changes into ester at equilibrium. The equilibrium constant for the reaction will be:
A . \( 1 / 9 \)
B. \( 4 / 9 \)
c. 9
D. \( 9 / 4 \)


Two blocks of masses \( 6 \mathrm{kg} \) and \( 4 \mathrm{kg} \) are attached to the two ends of a massless
string passing over a smooth fixed pulley. If the system is released, the acceleration of the centre of mass of the
system will be :
A . g, vertical downwards
B. g/5, vertical downwards
c. g/25, vertical downwards
D. zero


A candle is burnt in a beaker until it
extinguishes itself. A sample of gaseous mixture in the beaker contains \( 6.08 \times 10^{20} \) molecules of \( N_{2}, 0.76 \times \)
\( 10^{20} \) molecules of \( O_{2}, \) and \( 0.50 \times 10^{20} \)
molecules of \( C O_{2} . \) The total pressure is
\( 734 \mathrm{mm} \) of Hg. The partial pressure of
\( O_{2} \) would be:
A. \( 760.0 \mathrm{mm} \) of \( \mathrm{Hg} \)
B. 76.0 mm of Hg
c. \( 7.6 \mathrm{mm} \) of \( \mathrm{Hg} \)
D. \( 0.76 \mathrm{mm} \) of \( \mathrm{Hg} \)


In an expt, a beam of electron passes
undeviated through mutually perpendicular elec. and mag fields of
respective strength \( \boldsymbol{E}=\mathbf{7 . 2} \times \)
\( 10^{6} N C^{-1} \) and \( B=2.4 \) T. The velocity of
the electron is
\( \mathbf{A} \cdot 17.3 \times 10^{7} m s^{-1} \)
B . \( 3 \times 10^{6} m s^{-1} \)
c. \( 2 \times 10^{6} m s^{-1} \)
D. \( 6 \times 10^{6} \mathrm{ms}^{-1} \)


If the angle between the planes \( \boldsymbol{r} \cdot(\boldsymbol{m} \hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}+\boldsymbol{2} \hat{\boldsymbol{k}})+\boldsymbol{3}=\boldsymbol{0} \) and \( \overline{\boldsymbol{r}} \cdot(\boldsymbol{2} \hat{\boldsymbol{i}}- \)
\( m \hat{j}-\hat{k})-5=0 \) is \( \frac{\pi}{3} \) then \( m= \)
\( A \cdot 2 \)
B. ±3
\( c \cdot 3 \)
D. - -


For a body in circular motion with a constant angular velocity, the magnitude of the average acceleration over a period of half a revolution is..... times the magnitude of its instantaneous acceleration
A \( \cdot \frac{2}{\pi} \)
в. \( \frac{\pi}{2} \)
c. \( \pi \)
D.


When electricity is passed through
molten \( A l C l_{3}, 13.5 g \) of \( A l \) is deposited. The number of Faraday's must be:
A . 0.5
в. 1.0
c. 1.5
D. 2.0


In the given figure, \( \boldsymbol{T} \boldsymbol{T}^{\prime} \) is the tangent
line. Which one of the following
relationship is true?
\( \mathbf{A} \cdot x+y=2 z \)
B . \( x+y=z \)
c. \( z-3 x=y \)
D. \( z-2 x=y \)


The quantum number n of the state
finally populated in \( \mathbf{H e}^{+} \) ions is:
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5


Turn ratio in a setup transformer is \( 1: 2.1 \mathrm{f} \) a lechlanche cell of \( 1.5 \mathrm{V} \) is connected
across the input, what is the voltage across the output?
A . \( 1.5 v \)
B. 0.0
\( c \cdot 3 v \)
D. 0.75 \( v \)


A simple microscope is used by watchmakers. Given reason.


Fill in the blank:
Inner transition elements exhibit
different coloured compounds on
account of unfilled orbitals.
\( A \)
B. f
\( c \cdot d \)
\( D \)


The kinetic energy of an electron get tripled then the de-Broglie wavelength associated with electron changes by a
factor of
A \( \cdot \frac{1}{3} \)
B. \( \sqrt{3} \)
c. \( \frac{1}{\sqrt{3}} \)
D. 3


A particle starts moving rectilinearly at time \( t=0 \) such that its velocity \( v \)
changes with time \( t \) according to the equation \( \boldsymbol{v}=\boldsymbol{t}^{2}-\boldsymbol{t}, \) where \( \boldsymbol{t} \) is in
seconds and \( v \) is in \( m s^{-1} \). The time
interval for which the particle retards (i.e., magnitude of velocity decreases) is:
A. \( t<1 / 2 \)
B. \( 1 / 2<t<1 \)
\( c \cdot t>1 \)
D. \( t<1 / 2 \) and \( t>1 \)


The order and degree of the differential
equation. \( \left(\frac{d^{2} y}{d x^{2}}\right)^{3}+\left(\frac{d y}{d x}\right)=\int y d x \) are
respectively.
A . 2 and 3
B. 2 and 2
\( c .3 \) and 1
D. 3 and 2


The rating of an electrical appliance is \( 60 W, 220 V . \) What is the safe limit of
current in it, while in use?
\( \mathbf{A} \cdot 0.20 A \)
B. \( 0.27 A \)
c. \( 0.50 A \)
D. \( 1.2 A \)


A certain weight is attached to a spring It is pulled down and then released. It oscillates up and down. Its K.E. will be.
A. maximum at the middle of the movement
B. maximum at the bottom
c. maximum just before it is released
D. constant


Describe the experiment performed by
Griffith. What conclusions did he infer
from his observations?


An ideal transformer is used on 220 V
line to deliver 2 A at 110 V. The current
through the primary is :
\( A \cdot 10 A \)
B. 5 A
\( c \cdot 1 A \)
D. 0.1 A


A student pulls a wooden box along a rough horizontal floor (without the block
loosing contact with the floor) at
constant speed by means of a force \( P \)
as shown, to the right. \( (W \) is weight of
block, \( N \) is normal reaction on the
block, \( f \) is force of friction on the block).
Which of the following must be true?
A \( . P>f \) and \( N<W \)
B. \( P>f \) and \( N=W \)
c. \( P=f \) and \( N>W \)
\( D<f \) and \( N=W \)


Which of the following is correct regarding buffer solution?
A. It contains weak acid and its conjugate base.
B. It shows low change in pH on adding small amount of acid or base.
c. (A) and (B) both
D. None of these


When \( y=3 \) which of the following is
FALSE?
A. \( y \) is prime and \( y \) is odd
B. \( y \) is odd or \( y \) is even
c. \( y \) is not prime and \( y \) is odd
D. \( y \) is odd and \( 2 y \) is even


What is \( F \) ?
\[
\mathrm{F} \frac{\mathrm{H}^{\oplus} / \mathrm{KMnO}_{4}}{\Delta} \geq \text { acetone }+\text { ethanoic acid }
\]


Let \( f(x)=x^{3}+6 x^{2}+6 x \) and let \( c \) be
the number that satisfies the Mean
value theorem for \( f \) on the interval
\( [-6,0] . \) What is \( c ? \)
A. -5
B. -4
c. -3
D. -


Assertion (A):The derivative of \( (\log x)^{x} \)
w.r.t \( \boldsymbol{x} \) is \( (\log \boldsymbol{x})^{x-1}[\mathbf{1}+\log \boldsymbol{x} \log (\log \boldsymbol{x})] \)
Reason
\( (\mathrm{R}): \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left\{\boldsymbol{f}(\boldsymbol{x})^{g(\boldsymbol{x})}\right\}=\boldsymbol{f}(\boldsymbol{x})^{g(\boldsymbol{x})} \)
\( \left(g(x) \frac{f^{\prime}(x)}{f(x)}+g^{\prime}(x) \log (f(x))\right) \)
A. Both A and R are true R is correct reason of A
B. Both A and R are true R is not correct reason of
c. A is true but R is false
D. A is false but R is true


If \( \alpha, \beta \) and \( \gamma \) are the roots of the
equation \( x^{3}+p x+q=0 \) then the value of the determinant \( \left|\begin{array}{lll}\boldsymbol{\alpha} & \boldsymbol{\beta} & \gamma \\ \boldsymbol{\beta} & \gamma & \boldsymbol{\alpha} \\ \boldsymbol{\gamma} & \boldsymbol{\alpha} & \boldsymbol{\beta}\end{array}\right| \) is
2
\( \mathbf{A} \cdot \underline{p} \)
B. \( q \)
c. \( p^{2}-2 q \)
\( D \)


The expression of electric power \( (\boldsymbol{P})= \)
A \( \cdot I R^{2} \)
в. \( V I \)
c. \( I R \)
D. \( V R^{2} \)


In the set of all positive integers show
that the relation '>' is not an
equivalence relation.


Polyethene is a resin obtained by polymerisation of
A. butadiene
B. ethylene
c. isoprene
D. propylene


When \( H_{2} S \) is passed into aqueous \( S O_{2} \)
\( \mathbf{A} \cdot H_{2} S \) is converted to yellow precipitate of sulphur.
B. \( S O_{2} \) is converted to yellow precipitate of sulphur.
C . a clear solution of \( H_{2} S O_{4} \) is formed.
D. \( S O_{2} \) as well as \( H_{2} S \) are converted into a yellow precipitate of sulphur


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


The noble gas mixture is cooled in a coconut bulb at \( 173 K . \) The gases that
are not adsorbed are:
A. Helium and Neon
B. Helium and Xenon
c. xenon and Neon
D. none of these


Hydrogen molecules are:
A. monoatomic and form \( X_{2}^{2-} \) type ions
B. diatomic and form \( X_{2}^{-} \) type ions
C . diatomic and form \( X^{-} \) as well as \( X^{+} \) type ions
D. monoatomic and form \( X^{-} \) type ions


The trend in non metallic character
across a period:
A. decreases
B. increases
c. constant
D. none of these


Charge on an electron is :
\( \mathbf{A} \cdot+e \)
в. \( -e \)
\( c . \pm e \)
D. All


Fifteen coupons are numbered \( 1,2, \ldots . .15 \)
respectively. Three coupons are selected at random without replacement. The probability that the maximum number on the selected coupon is \( 9, \) is
A \( \cdot 4 / 65 \)
в. \( 3 / 65 \)
\( \mathrm{c} \cdot 1 / 13 \)
D. None of these


Write differences between primary
metabolism and secondary metabolism.


The movement of free atoms from
higher concentration to lower
concentration is called:
A. Osmosis
B. Diffusion
c. Endosmosis
D. Exosmosis


Prove that the sum of two successive
odd numbers is divisible by 4


\( \infty \)
80
\( \frac{80}{00} \)
900


The energy required for the electron to jump from \( n=2 \) to \( n=3 \) will be:
\( \mathbf{A} \cdot 5 x k J \)
в. \( \frac{36 x}{5} k J \)
c. \( \frac{5 x}{36} k J \)
D. \( \frac{9 x}{4} k J \)


If coil is placed perpendicular to field lines then number of lines passing
through coil are :
\( A \). minimum
B. maximum
c. zero
D. may be max. or min


State the role of citizens in pollution control. Give three efforts taken in order
to reduce pollution.


Jacob and Monad named those enzymes
allosteric whose activity is regulated by
A. Substrate
B. End product
c. coenzymes
D. Prosthetic groups


The number of molecules present in 4.4
gof \( C O_{2} \) gas is:
A \( \cdot 6.023 \times 10^{23} \)
В. \( 5.023 \times 10^{23} \)
c. \( 6.023 \times 10^{24} \)
D. \( 6.023 \times 10^{2} \)


Consider an expanding sphere of instantaneous radius \( R \) whose total
mass remains constant. The expansion is such that the instantaneous density
\( \rho \) remains uniform throughout the
volume. The rate of fractional change in density \( \left(\frac{1}{\rho} \frac{d p}{d t}\right) \) is constant. The
velocity \( v \) of any point on the surface of
the expanding sphere is proportional to
A \( \cdot R^{2 / 3} \)
в. \( R \)
c. \( R^{3} \)
D. \( \frac{1}{R} \)


\( \frac{3^{x} \times 3}{3^{2 x-2}}=9^{-2}, \) find \( x \)


The reserve food of brown algae is
A. Fucoxanthin
B. Volutin
c. Laminarin
D. Paramylum


Free energy change for the process \( \boldsymbol{A}(\boldsymbol{s}) \rightleftharpoons \boldsymbol{B}(l) \) will be:
A .
B. 1
\( c \cdot 2 \)
D.


State whether the given statement is
true or false:
Combination is the reverse of
decomposition reaction
A. True
B. False


When the leaves occur on................, trees
are called as columnar.
A. All branches
B. Only at the top of the trunk
c. only on the lower branches
D. only on the middle portion of the trunk


The pressure coefficient of a gas is \( \operatorname{(in} /^{0} C \)
):
A. 0.00367
в. - -27
\( c . \) 98
D. 3.14


Lanthanoids are also called as
A. Transition elements
B. Rare earth elements
c. Both A and B
D. None of these


From the given reactions which is a
redox reaction?
This question has multiple correct options
\( \mathbf{A} \cdot C u O(s)+H_{2}(g) \rightarrow C u(s)+H_{2} O(l) \)
B \( \cdot 2 C u(s)+O_{2}(g) \rightarrow 2 C u O(s) \)
\( \mathbf{c} \cdot C(s)+2 H_{2}(g) \rightarrow C H_{4}(g) \)
D. \( 4 A l(s)+3 O_{2}(g) \rightarrow 2 A l_{2} O_{3}(s) \)


Albert is riding his scooter at a velocity of \( 80 k m / h \) when he sees an old woman crossing the road \( 45 m \) away he immediately steps hard on the break to get the maximum deceleration of
\( 7.5 m / s^{2} . \) How far will he go before stopping, will he hit the old woman? (in
\( m) \)
A. \( 36.4, \) Yes
B. \( 35, \) No
c. \( 54.2, \) Yes
D. \( 32.9, \) No


The area of a square is \( 5.29 \mathrm{cm}^{2} \). The
area of 7 such squares taking into account the significant figures is?
\( \mathbf{A} \cdot 37 \mathrm{cm}^{2} \)
в. \( 37.0 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 37.03 \mathrm{cm}^{2} \)
D. \( 37.030 \mathrm{cm}^{2} \)


\( K_{a} \) for \( C H_{3} C O O H \) is \( 1.8 \times 10^{-5} \) and
\( K_{b} \) for \( N H_{4} O H \) is \( 1.8 \times 10^{-5} . \) The pH of
ammonium acetate will be:
\( \mathbf{A} \cdot 7.005 \)
в. 4.75
\( c .7 .0 \)
D. between 6 and 7


In a common emitter (CE) amplifier having a voltage gain \( G, \) the transistor
used has transconductance 0.03 mho
and current gain \( 25 . \) If the above transistor is replaced with another one with transconductance 0.02 mho and
current gain \( 20, \) the voltage gain will be
A \( \cdot \frac{2}{3} G \)
в. \( 1.5 G \)
c. \( \frac{1}{3} G \)
D. \( \frac{5}{4} G \)


The area bounded by two branches of the curve \( (\boldsymbol{y}-\boldsymbol{x})^{2}=\boldsymbol{x}^{3} \& \boldsymbol{x}=\mathbf{1} \) equals
A . \( 3 / 5 \)
B. \( 5 / 4 \)
\( c \cdot 6 / 5 \)
D. \( 4 / 5 \)


The reaction \( \mathbf{2} \boldsymbol{S} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{O}_{2} \stackrel{N O(\boldsymbol{g})}{\boldsymbol{\lambda}} \boldsymbol{2} \boldsymbol{S} \boldsymbol{O}_{3}(\boldsymbol{g}) \)
A. Heterogeneous catalysiss
B. Homogegenous catalysiss
c. Enzyme catalysis
D. None of them


Which one of the following is a vascular cryptogam?
A. Equisetum
B. Ginkgo
c. Marchantia
D. Cedrus


What happens in a negative beta decay
\( ? \)
A. an atomic electron is ejected
B. an electron which is already present within the nucleus is ejected
c. a neutron in the nucleus decays emitting an electron
D. a proton in the nucleus decays emitting an electron


f \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 4}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 8}, \boldsymbol{P}(\boldsymbol{B} / \boldsymbol{A})= \)
0.6. Find \( P(A / B) \)


Hydrogen readily combines with these elements?
This question has multiple correct options
A. Na a
B.
\( c \cdot c a \)
D. zn


An LCR series circuit is connected to ac
source. At resonance, the applied voltage and the current flowing through
the circuit will have a phase difference
of:
\( \mathbf{A} \cdot \pi / 4 \)
B. zero
\( c \)
D. \( \pi / 2 \)


Which of the following statements is
not true?
A. A heart murmur usually indicates a fatal heart defect
B. Angina pectoris may occur when doing strenuous activity after eating a heavy meal
C. An incompetent valve can permit a backflow of blood
D. A coronary artery spasm can cause an obstruction of blood flow


A box has tokens numbered 3 to 100 . If a
token is taken out at random the
chance that the number is divisible by 7
is
A \( \cdot 1 / 4 \)
B. 1/5
\( c \cdot 1 / 6 \)
D. 1/


A survey conducted on 20 households in a locality by a group of students resulted in the following frequency table for the number of family members in a household.
\[
\begin{array}{llllll}
\text { Family } & 1- & 3- & 5- & 7- & 9- \\
\text { size } & 3 & 5 & 7 & 9 & 11
\end{array}
\]
Numbe of 7 familie
The mode of this data 3.286
A. True
B. False


Newton's formula for the velocity of
sound in gas is
\( ^{\mathrm{A}} \cdot_{v}=\sqrt{\frac{P}{\rho}} \)
в. \( _{v}=\frac{2}{3} \sqrt{\frac{P}{\rho}} \)
c. \( v=\sqrt{\frac{\rho}{P}} \)
D. \( v=\sqrt{\frac{2 P}{\rho}} \)


Which of the following is one of the most common application of chemical effects of electric current?
A. Electrophoresis
B. Electroplating
c. Galvanization
D. Mineralization


Solve the equations \( \frac{5}{x-1}+\frac{1}{y-2}=2 \) and \( \frac{6}{x-1}- \)
\( \frac{3}{y-2}=1 \)


If \( A \) and \( B \) are mutually exclusive such
that \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 3 5} \) and \( \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 4 5} \)
find
\( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B}) \)


In formulating the theory of evolution by natural selection, Charles Darwin
was greatly influenced by
A. environmental factors
B. mutations
c. Maithus idea on population control
D. all of these


Inertia of a body depends on:
A. Mass of the body
B. Velocity of the body
c. Acceleration of the body
D. Energy of the body


The mass equivalent of 931.5 Mev energy is
A \( \cdot 1.66 \times 10^{-27} k g \)
B. \( 6.02 \times 10^{-24} k g \)
C \( .1 .66 \times 10^{-20} \mathrm{kg} \)
D. \( 6.02 \times 10^{-27} k g \)


Largest difference in radii is found in
which of the following pair?
A. \( L i, N a \)
в. \( N a, K \)
c. \( K, R b \)
D. \( R b, C s \)


(a) Describe briefly, with the help of a diagram, the role of the two important processes involved in the formation of a
\( p-n \) junction
(b) Name the device which is used as a
voltage regulator. Draw the necessary circuit diagram and explain its working.


If \( \quad z_{r}=\cos \frac{r \alpha}{n^{2}}+i \sin \frac{r \alpha}{n^{2}}, \) where \( r= \)
\( 1,2,3, \dots, n, \) then \( \lim _{n \rightarrow \infty}\left(z_{1}, z_{2} \dots \dots, z_{n}\right) \) is
equal to
A \( \cdot \cos \alpha+i \sin \alpha \)
B・sin \( \frac{\alpha}{2}+i \cos \frac{\alpha}{2} \)
\( \mathbf{c} \cdot e^{i \alpha / 2} \)
D. \( \sqrt{e^{i}} \)


Photoperiodism phenomena was first discovered by
A. Garnet and Allardardand
B. Haberlandt
c. wickson and Thimann
D. Osborne


Short/long answer type questions. Most fungi resemble protists or even plants. What is the justification for placing fungi in a separate kingdom?


Assertion: Emitted radiations lie in
visible region when electrons jump from higher level to \( n=2 \) in hydrogen. Reason: Balmer series radiations
belong to visible range in H-atoms.
A. Both Reason and Assertion are true and reason is the correct explanation of assertion
B. Both Reason and Assertion are true but reason is not correct explanation of assertion
c. Assertion is true but reason is false
D. Assertion and reason both are false
E. Assertion is false but reason is true


If two tangents are drawn at the end points of two radii that are inclined at
an angle of \( 110^{\circ} . \) Find the angle between
the tangents.
\( \mathbf{A} \cdot 110^{\circ} \)
B. 55
\( c \cdot 70^{\circ} \)
D. \( 20^{\circ} \)


The area of parallegram represented by the vectors. \( \overrightarrow{\boldsymbol{A}}=\boldsymbol{2} \hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}} \) and \( \overrightarrow{\boldsymbol{B}}=\hat{\boldsymbol{i}}+ \)
\( 4 \hat{j} \) is :-
A. 14 units
B. 7.5 units
c. 10 units
D. 5 units


A stretched rope having linear mass density \( 5 \times 10^{-2} k g m^{-1} \) is under a
tension of \( 80 N . \) The power that has to be supplied to the rope to generate harmonic waves at a frequency of \( 60 H z \)
and an amplitude of \( 6 \mathrm{cm} \) is
\( \mathbf{A} \cdot 215 W \)
B. \( 251 W \)
\( \mathbf{c} .512 W \)
D. \( 521 W \)


A charged particle of specific charge (charge/mass) \( \alpha \) is released from
origin at time \( t=0 \) with velocity \( \vec{v}= \)
\( v_{0}(\hat{i}+\hat{j}) \) in a uniform magnetic field
\( \vec{B}=B_{0} \hat{i} . \) Coordinates of the particle at
time \( t=\frac{\pi}{B_{0} \alpha} \) are
A \( \cdot\left(\frac{v_{0}}{2 B_{0} \alpha}, \frac{\sqrt{2} v_{0}}{\alpha B_{0}}, \frac{-v_{0}}{B_{0} \alpha}\right) \)
В \( \cdot\left(\frac{-v_{0}}{2 B_{0} \alpha}, 0,0\right) \)
\( ^{\mathbf{C}} \cdot\left(0, \frac{2 v_{0}}{B_{0} \alpha}, \frac{v_{0} \pi}{2 B_{0} \alpha}\right) \)
D \( \cdot\left(\frac{v_{0} \pi}{B_{0} \alpha}, 0, \frac{-2 v_{0}}{B_{0} \alpha}\right) \)


Which teeth of human are shovel-
shaped and used for nibbling, cutting and tearing?
A. Canines
B. Premolars
c. Molars
D. Incisors


Hydrolith, a source of hydrogen is :
A. \( N a H \)
в. \( C a H_{2} \)
c. \( L i H \)
D. \( B a H_{2} \)


The capacity of a parallel plate condenser
consisting of two plates each of \( 10 \mathrm{cm}^{2} \)
separated by a distance of \( 2 \mathrm{mm} \) is:
(Take air as the medium between the
plates
A \( \cdot 8.85 \times 10^{-13} F \)
В. \( 4.42 \times 10^{-12} \mathrm{F} \)
c. \( 44.25 \times 10^{-12} F \)
D. \( 88.5 \times 10^{-13} F \)


Why is foundry coke used in boilers and furnaces?
A. Excellent insulator
B. Excellent source of light
c. Excellent source of heat
D. None of above


Represented \( \frac{-3}{4} \& \frac{1}{8} \) on the number line


The equilibrium constants \( \boldsymbol{K}_{\boldsymbol{p}_{1}} \) and \( \boldsymbol{K}_{\boldsymbol{p}_{2}} \)
for the reactions, \( \boldsymbol{X} \rightleftharpoons 2 \boldsymbol{Y} \) and \( \boldsymbol{Z} \rightleftharpoons \)
\( P+Q, \) respectively are in the ratio of
1 : 9. If the degree of dissociation of \( \boldsymbol{X} \)
and \( Z \) be equal then the ratio of total
pressures at the equilibrium is:
A . 1: 9
B. 1: 36
c. 1: 1
D. 1: 3


A current of \( 4.0 A \) is passed for 5 hours through \( 1 L \) of \( 2 M \) solution of nickel
nitrate using two nickel electrodes. The molarity of the solution at the end of the electrolysis will be:
\( \mathbf{A} \cdot 1.6 M \)
в. \( 1.2 M \)
c. \( 2.5 M \)
D. \( 2.0 M \)


Starting with sodium chloride how would you proceed to prepare (i) sodium metal,
(ii) sodium hydroxide,
(iii) sodium peroxide,
(iv) sodium
carbonate?


A copper rod of length 'I' rotates at an
angular velocity ' \( \omega^{\prime} \) in a uniform magnetic field B as shown in figure. What is the induced emf across its
ends?


Origin of gymnosperms occured in
era.
A. Coenozoic
B. Paeleozoic
c. Mesozoic
D. Precambrian


The dimensional formula for impulse is:
A \( . M L T^{-2} \)
в. \( M L T^{-1} \)
\( \mathbf{c} \cdot M L^{2} T^{-1} \)
D. \( M^{2} L T^{-1} \)


A wire is subjected to a tensile stress. If
A represents area of cross-section,
represents original length, I represents extension and Y is Young's modulus of elasticity, then elastic potential energy of the stretched wire is
\( \mathbf{A} \cdot U=\frac{2 L}{A Y} I^{2} \)
B \( \cdot U=\frac{A L}{2 Y} I^{2} \)
\( \mathbf{c} \cdot U=\frac{A Y}{2 L} I^{2} \)
D. \( U=\frac{1}{4} \frac{A Y}{L} I^{2} \)


Evaluate the given integral: \( \int_{0}^{5} x^{4} d x \)


Fill in the blank.
In uniform circular motion
remains constant.
A. Acceleration
B. Time
c. speed
D. Direction


A current of \( 2 A \) is passed through a coil
of 1000 turns to produce a flux of
\( 0.5 \mu W b . \) Self inductance of the coil
A \( .2 .5 \times 10^{-4} H \)
В. \( 2.5 \times 10^{-5} H \)
c. \( 2.5 \times 10^{-6} H \)
D. \( 2.5 \times 10^{-7} H \)


\( \sqrt[4]{0} x+\cos (\infty) \)
.700
\( \$ \)
\( \$ 0 \)
\( \tan \)


Mark the incorrect reason why plants
need water and minerals
A. Transportation
B. cooling
c. Bleeding
D. All


If the values of \( \wedge_{\infty} \) of \( \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{C l}, \boldsymbol{N} \boldsymbol{a} \boldsymbol{O H} \)
and \( N a C l \) are 130,217 and
109 ohm \( ^{-1} \cdot c m^{2} \cdot e q u i v^{-1} \)
respectively, the \( \wedge_{\infty} \) of \( N H_{4} O H \) in
\( o h m^{-1} \cdot c m^{2} \cdot e q u i v^{-1} \) is:
A .238
в. 198
c. 22
D. 456


If \( f \) be the differentiable for \( \forall x \). If
\( \boldsymbol{f}(1)=-2 \) and \( \boldsymbol{f}^{\prime}(\boldsymbol{x}) \geq 2 \) for \( [\mathbf{1}, \boldsymbol{6}] \) then
A. \( f(6)<8 \)
В. \( f(6)=5 \)
\( \mathbf{c} \cdot f(6) \geq 8 \)
D. \( f(6)<5 \)


Draw the graph for the linear equation
\( \boldsymbol{x}=-2 \boldsymbol{y} \)
A. passes through (0,0) and \( m=2 \)
B. passes through (0,0) and \( m=-2 \)
c. passes through (1,2) and \( m=-\frac{1}{2} \)
D. passes through (0,0) and \( m=-\frac{1}{2} \)


A student performs an experiment to determine the Young's modulus of a wire, exactly \( 2 \mathrm{m} \) long, by Searle's method. In a particular reading, the student measures the extension in the
length of the wire to be \( 0.8 m m \) with an
uncertainty of \( \pm 0.05 \mathrm{mm} \) at a load of exactly \( 1.0 k g . \) The student also
measures the diameter of the wire to be
\( 0.4 m m \) with an uncertainty of ±0.01
\( \mathrm{mm} . \) Take \( \mathrm{g}=9.8 \mathrm{m} / \mathrm{s}^{2} \) (exact). The
Young's modulus obtained from the reading is
в. \( (2.0 \pm 0.2) \times 10^{11} \mathrm{N} / \mathrm{m}^{2} \)
c. \( (2.0 \pm 0.1) \times 10^{11} \mathrm{N} / \mathrm{m}^{2} \)
D. \( (2.0 \pm 0.05) \times 10^{11} \mathrm{N} / \mathrm{m}^{2} \)


The direct change from solid to gaseous state is referred to as:
A. dissociation
B. decomposition
c. sublimation
D. deliquescence


The long form of the periodic table
consists of \( _{-} \) horizontal rows and
vertical columns
A. 6 and 17
B. 7 and 7
c. 5 and 7
D. 7 and 18


Magnesium reacts with an element \( (\boldsymbol{X}) \)
to form an ionic compound. If the ground state electronic configuration of
\( (X) \) is \( 1 s^{2} 2 s^{2} 2 p^{3}, \) the simplest formula for this compound is:
A. \( M g_{2} X \)
в. \( M g_{2} X_{3} \)
с. \( M g_{3} X_{2} \)
D. \( M g X_{2} \)


Name the plastic used for making non-
stick pans:
A. PVC
B. Teflon
c. Bakelite
D. Melamine


The area of a rectangle and square are
same. If the side of a square is \( 80 m \) and length of rectangular park is \( 200 m \) Find breadth of the rectangle.


WEIGHTLESSNESS
An astronaut experiences weightlessness in a space satellite. It is because
A. the gravitational force is small at that location in space
B. the gravitational force is large at that location in space
c. the astronaut experiences no gravity.
D. the gravitational force is infinitely large at that location in space


f \( a, b, c \) are real numbers such that \( \left|\begin{array}{ccc}\boldsymbol{b}+\boldsymbol{c} & \boldsymbol{c}+\boldsymbol{a} & \boldsymbol{a}+\boldsymbol{b} \\ \boldsymbol{c}+\boldsymbol{a} & \boldsymbol{a}+\boldsymbol{b} & \boldsymbol{b}+\boldsymbol{c} \\ \boldsymbol{a}+\boldsymbol{b} & \boldsymbol{b}+\boldsymbol{c} & \boldsymbol{c}+\boldsymbol{a}\end{array}\right|=0, \) then show
that either \( \boldsymbol{a}+\boldsymbol{b}+\boldsymbol{c}=\boldsymbol{0} \) or, \( \boldsymbol{a}=\boldsymbol{b}=\boldsymbol{c} \)


Plants take in air through tiny openings called........... which are present on
A . Leaves, stomata
B. Hydathodes, leaves
c. Stomata, stem
D. Stomata, leaves


Let \( \boldsymbol{f}:[\boldsymbol{a}, \boldsymbol{b}] \rightarrow[\mathbf{1}, \infty) \) be a continuous
function and let \( g: R \rightarrow R \) be defined
\( \operatorname{as} g(x)=\left\{\begin{array}{ccc}0 & \text { if } & x<a \\ \int_{a}^{x} f(t) d t & \text { if } & a \leq x \leq b \\ \int_{a}^{b} f(t) d t & \text { if } & x>b\end{array}\right. \)
Then
This question has multiple correct options
\( \mathbf{A} \cdot g(x) \) is continuous but not differentiable at \( a \)
B. \( g(x) \) is differentiable on \( R \)
C \( \cdot g(x) \) is continuous but not differentiable at \( b \)
D. \( g(x) \) is continuous and differentiable at either \( a \) or \( b \) but not both


In the following reaction:
\( 2 S O_{2}(g)+O_{2}(g) \rightleftharpoons 2 S O_{3}(g) \) the
equilibrium is not attained. The rate of forward reaction is greater than that of backward reaction. Thus, which of the following is the correct relation between
\( \boldsymbol{K}_{\boldsymbol{p}} \) and \( \boldsymbol{Q}_{\boldsymbol{p}} ? \)
\( \mathbf{A} \cdot K_{p}=Q_{p} \)
B \( \cdot Q_{p}>K_{p} \)
\( \mathbf{c} \cdot Q_{p}<K_{p} \)
D. \( K_{p}=Q_{p}=1 \)


The laws of reflection hold good for:
A. plane mirror only
B. concave mirror only
C. convex mirror only
D. all mirrors irrespective of their shape


A satellite has a kinetic energy \( X \) potential energy \( Y \) and total energy \( z \) in a given orbit. How are they related
A. \( Z=Y=-2 X \)
в. \( Z=Y / 2=-X \)
c. \( Z=2 Y=-2 X \)
D. \( 2 Z=Y=-2 X \)
\( X \)


In a one-dimensional collision between
two particles, their relative velocity is \( \bar{v}_{1} \)
before the collision and \( \bar{v}_{2} \) and the
collision.

This question has multiple correct options
A \( . \overline{v_{1}}=\overline{v_{2}} \) if the collision is elastic.
B. \( \overline{v_{1}}=-\overline{v_{2}} \) if the collision is elastic.
\begin{tabular}{l|l}
c. \( |\overline{v_{2}}|=\left|v_{1}\right| \) in all cases.
\end{tabular}
D. \( v_{1}=-k \bar{v}_{2} \) in all cases, where \( k \geq 1 \)


The example of nuclear fusion is:
A. Formation of barium and krypton from uranium
B. Formation of helium from hydrogen
C. Formation of plutonium - 235 from uranium -235
D. Formation of water from hydrogen and oxygen


Calculate the maximum work when 24
g of oxygen are expanded isothermally
and reversibly from a pressure of \( 1.6 \times \) \( 10^{5} \) Pa to 100 kPa at \( 298 \mathrm{K} \)


There are 4 candidates for a Natural
science scholarship, 2 for a Classical and 6 for a Mathematical
scholarship,then find No. of ways these scholarships can be awarded is,
A . 48
B. 12
c. 24
D. 8


The value of the determinant \( \Delta= \)
A \( a_{1} a_{2}+b_{1} b_{2} \)
a
В \( \cdot\left(a_{1} a_{2} a_{3}\right)+\left(b_{1} b_{2} b_{3}\right) \)
c. \( a_{1} a_{2} b_{1} b_{2}+a_{2} a_{3} b_{2} b_{3}+a_{3} a_{1} b_{3} b_{1} \)
D. none of these


Refraction of light occurs when:
A. light passes through a narrow opening.
B. light passes into a new transparent material (not head on) in which it travels at a new speed.
C . light strikes the edge of an object.
D. light becomes polarized.
E. light passes through a diffraction grating.


How much below the surface of the
earth does the acceleration due to
gravity become \( 70 \% \) of its value at the surface of earth? (Take \( \boldsymbol{R}=\mathbf{6 4 0 0 k m} \) )


State Le Chatelier's principle?


Assertion
Ortho and para-nitrophenols can be separated by steam distillation.
Reason

Ortho isomer associates through intermolecular hydrogen bonding while Para isomer associates through
intramolecular hydrogen bonding.
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


8
cylinder to be negligible, find the time dependence of the kinetic energy of the
whole system.
\( ^{\mathbf{A}} \cdot_{T}=\frac{m g^{2} t^{2}}{2\left(1+\frac{2 M}{m}\right)} \)
\( ^{\mathbf{B}} \cdot_{T}=\frac{m g^{2} t^{2}}{2\left(1+\frac{M}{2 m}\right)} \)
\( ^{\mathbf{C}} T=\frac{m g^{2} t^{2}}{2\left(1+\frac{M}{m}\right)} \)
\( ^{\mathrm{D}} T=\frac{2 m g^{2} t^{2}}{2\left(1+\frac{M}{2 m}\right)} \)


A point mass oscillates along the \( x \) axis according to the law \( \boldsymbol{x}= \)
\( x_{0} \cos (\omega t-\pi / 4) . \) If the acceleration of
the particle is written as \( a= \)
\( A \cos (\omega t+\delta) \) then:
A \( . A=x_{0}, \delta=-\pi / 4 \)
B . \( A=x_{0} \omega^{2}, \delta=-\pi / 4 \)
C \( . A=x_{0} \omega^{2}, \delta=-\pi / 8 \)
D. \( A=x_{0} \omega^{2}, \delta=3 \pi / 4 \)


In a triangle \( A B C, \) a line \( P Q \) is drawn
parallel to \( B C \), points \( P \), Q being on \( A B \)
and \( A C \) respectively. If \( A B=3 A P \)
then what is the ratio of the area of
triangle \( A P Q \) to the area of triangle
\( A B C ? \)
A .1: 3
B. 1: 5
c. 1: 7
D. 1: 9


\( \mathbf{0 . 1} \boldsymbol{M} \boldsymbol{K}_{4}\left[\boldsymbol{F} e(\boldsymbol{C} \boldsymbol{N})_{6}\right] \) is \( 60 \% \) ionized
What will be its Van't Hoff factor?
A . 1.4
в. 3.4
c. 2.4
D. 4.


When a liquid in a heat insulated closed vessel is stirred using a peddle then the
temperature of the liquid:
A. Increases
B. Decreases
c. Remains constant
D. Becomes \( 0^{\circ} \mathrm{C} \)


if \( [\mathrm{x}] \) is the integral part of \( \mathrm{x} \), then solve \( \left[\mathbf{4}-[\boldsymbol{x}]^{2}\right]-[\boldsymbol{x}]^{2}=\mathbf{2} \)
find the number of integers satisfying
the equation.


Origin of lateral roots is
A. Endogenous
B. Axillary
c. Exogenous
D. Peripheral


Which of the following is miscible with
water?
A. \( C S_{2} \)
В . \( C_{2} H_{5} O H \)
c. \( C C l_{4} \)
D. \( C H C l_{3} \)


Identify the products \( A, B \) and \( C \)


If in a solvent, n simple molecules of solute combine to form an associated
molecule, \( \alpha \) is the degree of association, the van't Hoff's factor is
equal to:
A. \( \frac{1}{1-n \alpha} \)
B. \( 1-\alpha+n \alpha \)
\( c \cdot_{1-\alpha+\frac{\alpha}{n}} \)
D. \( \frac{\alpha}{n}-1+\alpha \)


Find the domain of definition of the
following function. \( \boldsymbol{f}(\boldsymbol{x}),=\sqrt{\mathbf{2}-\boldsymbol{x}}+\sqrt{\mathbf{1}+\boldsymbol{x}} \)


The dimensional formula of arial
velocity is
\( \mathbf{A} \cdot\left[M^{0} L^{-2} T^{1}\right] \)
B . \( \left[M^{0} L^{-2} T^{-1}\right] \)
C . \( \left[M^{0} L^{2} T^{-1}\right] \)
\( \mathbf{D} \cdot\left[M^{0} L^{2} T^{1}\right] \)


To carry out the so-called electrolysis of
water, sulphuric acid is added to water. How does the addition of sulphuric acid produce a conducting solution?


\( \frac{-}{k} \)


Ram purchases a chair at \( R s .70 \) and
spent \( R s .17 \) on its repair and 50 paise
on cartage. If he sold the chair at

Rs.100 then his approximate margin of profit will be ?
A . \( 13.30 \% \)
B . \( 11.25 \% \)
c. \( 12.5 \% \)
D. 14.3\%


In a hydrogen atom, if energy of an electron in the ground state is \( 13.6 \mathrm{eV} \) then that in the 2 nd excited state is:
A . \( 1.51 \mathrm{eV} \)
B. 3.4 ev
\( c \cdot 6.04 \mathrm{ev} \)
D. 13.6 ev


A first-order reaction is \( 50 \% \) completed
in 20 minutes at \( 27^{0} \) C and in 5 min at
\( 47^{0} \mathrm{C} . \) The energy of activation of the reaction is :
A. \( 43.85 k J / \) mol
в. \( 55.33 k J / \) mol
c. \( 11.97 k J / \) mol
D. \( 6.65 k J / \) mol


If \( D \) be subset of the set of all rational
numbers, then \( D \) is closed under the
binary operations of
A. addition, subtraction and division
B. addition, multiplication and division
c. addition, subtraction and multiplication.
D. subtraction, multiplication and division


Units of \( K_{c} \) for the reaction of formation
of \( S O_{3} \) from \( S O_{2} \) and \( O_{2} \) are \( g \) mol \( ^{-1} \)
A. True
B. False


The advantage(s) of using carbon to reduced a number of oxides and other
compounds are:
This question has multiple correct options
A. easy availability of coke
B. low cost of carbon
c. tendency of carbon to show catenation.
D. presence of carbon lowers the melting point of the oxide


The correct order of covalent nature is:
A. \( B e C l_{2}> \) LiCl
в. \( B e C l_{2}<L i C l \)
c. \( B e C l_{2}=L i C l \)
D. None of these


Fungal cell wall is formed of :
A. Pectin
B. Hemicellulose
c. chitin and cellulose
D. Chitin and pectin


Three capacitors, \( 3 \mu F, 6 \mu F \) and \( 6 \mu F \) are connected in series to a source of
120V. The potential difference, in
volts, across the \( 3 \mu F \) capacitor will be
A . 24
B. 30
\( c \cdot 40 \)
\( D \cdot 60 \)


Assertion: \( F \) is more electronegative
than \( C l \)
Reason: \( F \) has high electron affinity than
\( C l \)
A. If both assertion and reason are true and the reason is a correct explanation of the assertion
B. If both assertion and reason are true but reason is not a correct explanation of the assertion
C. If the assertion is true but reason is false
D. If both the assertion and reason are false
E. If the assertion is false but the reason is true


A gas is enclosed in a cylinder with a movable friction less piston. Its initial
thermodynamic state at pressure \( \boldsymbol{P}_{i}= \) \( 10^{5} P a \) and volume \( V_{i}=10^{-3} m^{3} \)
changes to a final state at \( \boldsymbol{P}_{f}= \) \( (1 / 32) \times 10^{5} P a \) and \( V_{f}=8 \times 10^{-3} m^{3} \)
in an adiabatic quasi-static process, such that \( P^{3} V^{5} \) =constant. Consider
another thermodynamic process that brings the system from the same initial state to the same final state in two
steps: an isobaric expansion at \( \boldsymbol{P}_{i} \) followed by an isochoric (isovolumetric)
process at volume \( V_{f} . \) The amount of heat supplied to the system in the twostep process is approximately:
\( \mathbf{A} \cdot 112 J \)
в. 294 Л
c. \( 588 J \)
D. \( 813 J \)


The probability that a two digit number selected at random will be a multiple of
'3' and not a multiple of '5' is
A \( \cdot \frac{2}{15} \)
в. \( \frac{4}{15} \)
c. \( \frac{1}{15} \)
D. \( \frac{4}{90} \)


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}, \boldsymbol{i f} \boldsymbol{x}^{\frac{2}{3}}+\boldsymbol{y}^{\frac{\boldsymbol{2}}{3}}=\boldsymbol{a}^{\frac{\boldsymbol{2}}{3}} \)


A body is first displaced by \( 5 \mathrm{m} \) and the n by \( 12 \mathrm{m} \) in different directions. The mi nimum displacement it can have is
\( \mathrm{m} \)
A. 0
B. 5
\( c \cdot 7 \)
D. 12


Write the name and formula of the first
member of the carbon compounds having functional group - COOH .


When sugar is dissolved in water, the
level of water
A. increases
B. decreases
c. remains same
D. data insufficient


The following table shows the number of workers in a factory and their daily wages. Find the median of the daily
wages.
\( \begin{array}{llll}\text { Daily } & \mathbf{1 0 0}- & \mathbf{1 1 0}- & \mathbf{1 2 0}- \\ \text { wages(Rupees) } & \mathbf{1 1 0} & \mathbf{1 2 0} & \mathbf{1 3 0}\end{array} \)
No. of workers 37
38


Write any two difference between
addition and condensation
polymerisation.


A tester is used to check the conduction
of electricity through two liquids, labelled \( A \) and \( B \). It is found that the
bulb of the tester glows brightly for liquid A while it glows very dim for liquid B. You would conclude that:
A. liquid \( A \) is a better conductor than liquid \( B \)
B. liquid \( B \) is a better conductor than liquid \( A \)
c. both liquids are equally conducting
D. conducting properties of liquid cannot be compared in this manner.


For a valid Bohr orbit, its circumfrence
should be :
\( \mathbf{A} \cdot=n \lambda \)
B. \( =(n-1) \lambda \)
\( \mathbf{c} \cdot>n \lambda \)
\( \mathbf{D} \cdot<n \lambda \)


Find the inverse of the following matrices by the adjoining method \( \left[\begin{array}{cc}-1 & 5 \\ -3 & 2\end{array}\right] \)


Provide the systematic name of the
compounds shown.
\( \mathbf{A} \cdot 4-b u t y l-2-e t h y l-1- \)methylcycloheptane
B. \( 1-b u t y l-4- \) ethyl \( -3- \) methylcycloheptane
c. \( 2-b u t y l-4- \) ethyl \( -1- \) methylcycloheptane
D. \( 4-b u t y l-1- \) ethyl \( -2- \) methylcycloheptane


For which of the following solutes the
van't Hoff factor is not greater than one?
A. \( N a N O_{3} \)
в. \( B a C l_{2} \)
\( \mathbf{c} \cdot_{K_{4}}\left[F e(C N)_{6}\right] \)
D. \( N H_{2} C O N H_{2} \)


\( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{c}x \\ \frac{a e^{|x|}+3 . e^{\frac{-1}{x}}}{1} \\ (a+2) e^{\frac{1}{|x|}-e^{\frac{-1}{x}}}\end{array}\right) \begin{array}{l}x \neq 0 \\ 0\end{array} \)
differentiable at \( \boldsymbol{x}=\mathbf{0} \) then \( [\boldsymbol{a}]=_{--}(\mathbb{D} \)
denotes greatest integers function
4
B. -1
\( c \cdot 2 \)
\( 0 .-3 \)


The rest energy of an electron is:
A. \( 510 \mathrm{KeV} \)
в. \( 931 \mathrm{KeV} \)
c. \( 510 \mathrm{MeV} \)
D. \( 931 \mathrm{MeV} \)


The ground state energy of hydrogen atom is \( -13.6 e V \)
(i) What is the kinetic energy of an
electron in the \( 2^{n d} \) excited state?


Evaluate \( \int_{-6}^{0}|x+3| d x . \) What does this integral represent on the graph?


let \( \boldsymbol{f}(\boldsymbol{\theta})=\frac{1}{1+(\tan \theta)^{2013}} \) then value of
\( \sum_{\theta=1^{0}}^{89^{\circ}} f(\theta) \) equals
A . 45
B. 44
c. \( 89 / 2 \)
D. \( 91 / 2 \)


A uniform electric field and a uniform
magnetic field are acting along the same direction in a certain region. If an electron is projected along the direction of the fields with a certain velocity then
A. its velocity will increase
B. its velocity will decrease
c. it will turn towards left of direction of motion
D. it will turn towards right of direction of motion


The molecular formula of dithionic acid
is:
A \( \cdot H_{2} S_{2} O_{7} \)
в. \( H_{2} S_{2} O_{6} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{S}_{2} \mathrm{O}_{5} \)
D. \( H_{2} S O_{5} \)


The blood pressure is high in
A. Arteries
B. Vein
c. capillaries
D. Veins portal system


Discuss the motion of an object under
free fall


\( \frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+. . n \) terms \( = \)
A \( \cdot \frac{3 n}{2(3 n+2)} \)
B. \( \frac{3 n}{3 n+2} \)
c. \( \frac{n}{2(3 n+2)} \)
D. \( \frac{n}{3 n+2} \)


Figure below shows two paths that may
be taken by a gas to go from a state \( \boldsymbol{A} \)
to a state \( c \)
In process \( A B, 400 J \) of heat is added to
the system and in process \( B C, 100 J \) of
heat is added to the system. The heatt
absorbed by the system in the process
\( A C \) will be
A . \( 500 J \)
B . \( 460 J \)
c. \( 300 J \)
D. \( 380 J \)


The values of 'a' for which \( y=x^{2}+ \)
\( a x+25 \) touches \( x \) -axis are
\( \mathbf{A} \cdot \pm 10 \)
B. ±2
\( c .\pm 1 \)
D.


000
灣 8
What


A company has 450 employees. It needs
to hire \( 18 \% \) more employees, how many more employees will it hire?


Prove that points \( A, B, C \) having positions vectors \( \vec{a}, \vec{b}, \vec{c} \) are collinear, if \( [\overrightarrow{\boldsymbol{b}} \times \overrightarrow{\boldsymbol{c}}+\overrightarrow{\boldsymbol{c}} \times \overrightarrow{\boldsymbol{a}}+\overrightarrow{\boldsymbol{a}} \times \overrightarrow{\boldsymbol{b}}]=\overrightarrow{\mathbf{0}} \)


What would be the molar concentration
of human DNA in a human cell? Consult
your teacher.


Assertion
The greatest value of the moduli of
complex numbers \( z \) satisfying the equation \( \left|z-\frac{4}{z}\right|=2 \) is \( \sqrt{5}+1 \)
Reason
For any two complex number \( z_{1} \) and \( z_{2} \)
\( \left|z_{1}-z_{2}\right| \geq\left|z_{1}\right|-\left|z_{2}\right| \)
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 number of specific heat for a gas
system is
A . 1
B. 2
\( c .3 \)
D.


State three advantages of alcohol over mercury for using it as a thermometric liquid


Evaluate the following integral
\( \int \frac{e^{x}+1}{e^{x}+x} d x \)


Mark the following rational numbers on
the number line.
\( \frac{3}{4} \)


A source of constant potential
difference is connected across a
conductor having irregular cross section as shown,then
A. Electric field intensity at \( P \) is greater than that at \( Q \)
B. rate of electrons crossing per unit area of cross section at \( P \) is less than that at \( Q \)
c. the rate of generation of heat per unit length at \( P \) is greater than at \( Q \)
D. mean kinetic energy of free electrons at \( P \) is greater than that at \( Q \)


State whether the given statement is
true or false:
First law of thermodynamics is applicable to all processes irrespective to whether they are reversible or
irreversible.
A. True
B. False


Choose the correct option.
This question has multiple correct options
\( \mathbf{A} \cdot T_{n+2}-T_{n-1} \) is divisible by 2
\( ^{\mathbf{B}} \cdot \frac{T_{n+1}+T_{n-1}}{T_{n}}=2 r \)
C. Neither (A) nor (B)
D. None of the above


Explain the main functions of leaf.


Write the IUPAC name of following ketone or aldehyde. If possible, give the
common name(s) also.
\( \boldsymbol{C H}_{3} \boldsymbol{C O}\left(\boldsymbol{C H}_{2}\right) \boldsymbol{C H}_{3} \)


The vapour pressure of a solvent at 293
K is 100 mm Hg. Then the vapour pressure of a solution containing 1 mole of a strong electrolyte \( \left(A B_{2}\right) \) in 99 moles of the solvent at \( 293 \mathrm{K} \) is:
(Assume complete dissociation of solute)
A. \( 103 \mathrm{mm} \) Hg
в. \( 99 \mathrm{mm} \) Нв
\( \mathbf{c} .97 \mathrm{mm} \mathrm{Hg} \)
D. \( 101 \mathrm{mm} \) Н


Which of the following is NOT true?
A. A sharp knife can easily cut due to its small cutting surface.
B. It is easier to walk in sand than on road.
C. A battle tank can move easily on soft ground because its tracks have bigger surface.
D. The pressure exerted by a needle is much more than the foot of an elephant.


If two events \( A \) and \( B \) such that
\( \boldsymbol{P}\left(\boldsymbol{A}^{\prime}\right)=\mathbf{0 . 3}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 5} \) and \( \boldsymbol{P}(\boldsymbol{A} \cap \)
\( B)=0.3, \) then \( P\left(B \mid A \cup B^{\prime}\right) \) is
A . \( 3 / 8 \)
B. 2 /
c. \( 5 / 6 \)
D. \( 1 / 4 \)


Two substances \( P \) and \( Q \) when brought
together, form substance R with the evolution of heat. The properties of R are
different from both \( \mathrm{P} \) and \( \mathrm{Q} \). What is
substance R?
A. A compound
B. An element
c. A metal
D. A mixture


Name the new antacid which prevents
formation of acid in stomach.
A. Omeprazole
B. Pantaprazole
c. Hemoprazole
D. none of these


If \( \bar{a}, \bar{b}, \bar{c} \) are position vectors of the noncollinear points \( A, B, C \) respectively, the shortest distance of \( A \) and \( B C \) is?
A. \( \bar{a} \cdot(\bar{b}-\bar{c}) \)
a)
в. \( \bar{b} \cdot(\bar{c}-\bar{a}) \)
c. \( |\bar{b}-\bar{a}| \)
D \( \cdot \sqrt{|\vec{b}-\vec{a}|^{2}-\left[\frac{(\vec{a}-\vec{b} \cdot(\vec{b}-\vec{c})}{|\vec{b}-\vec{c}|}\right)^{2}} \)


Range of nuclear force is approximately
A \( \cdot 2 \times 10^{-15} m \)
B . \( 1.5 \times 10^{-20} m \)
c. \( 7.2 \times 10^{-4} m \)
D. \( 1.4 \times 10^{-15} \mathrm{m} \)


An important step in the manufacture of pulp in paper industry from woody
tissues of plants is
A. Preparation of pure cellulose by removing lignin.
B. Treatment of wood with chemicals for breakdown of
cellulose.
C. Removal of oil by suitable chemicals
D. Removal of water from wood by prolonged heating at \( 50^{\circ} \mathrm{C} \)


The phosphorus in a 4.258 g sample of a plant food was converted to \( P O_{4}^{3-} \) and
precipitated as \( A g_{3} P O_{4} \) through the
addition of \( 50.0 \mathrm{mL} \) of \( 0.082 M A g N O_{3} \)
The excess of \( A g N O_{3} \) was back titrated with \( 4.86 \mathrm{mL} \) of \( 0.0625 M \)
\( K S C N . \) Express the results of this
analysis in terms of \( P_{2} O_{5} \) as nearest
integer \%. \( P_{2} O_{5}+9 H_{2} O \rightarrow 2 P O_{4}^{3-}+6 H_{3} O^{+} \)
\( 2 P O_{4}^{3-}+6 A g^{+} \rightarrow 2 A g_{3} P O_{4} \)
\( \boldsymbol{A} \boldsymbol{g}^{+}+\boldsymbol{S C N}^{-} \rightarrow \boldsymbol{A} \boldsymbol{g} \boldsymbol{S} \boldsymbol{C} \boldsymbol{N}(\boldsymbol{s}) \)


What is the best reagent would you choose to convert \( M n O_{4}^{2-} \) to \( M n O_{4}^{-} ? \)
A \( \cdot C l_{2} \) water
в. \( O_{3} \)
c. Both \( A \) and \( B \)
D. None of these


(a) State briefly the processes involved in the formation of p-njunction explaining clearly how the depletion region is formed.
(b) Using the necessary circuit diagram, show how the \( V-1 \) characteristics of a p-njunction are
obtained in
(i) Forward biasing
(ii) Reverse biasing How are these characteristics made
use of in rectification?


What will be the pH of solution when 'A'
and 'C' solutions are mixed completely?
A. 9.5
B. 5
c. 10.15
D. 8.85


What is the colour corresponding to the wavelength of light emitted when the electron in a hydrogen atom undergoes transition from \( n=4 \) to \( n=2 ? \)
A. Blue
B. Red
c. Yellow
D. Green


State how de-Broglie wavelength \( (\lambda) \) of
moving particles varies with their linear momentum (p).


The diffusion current in a p-njunction
is greater than the drift current when the junction is
A. forward biased.
B. reverse biased
c. unbiased.
D. both forward and reverse biased


Which of the following ion is more paramagnetic?
A \( \cdot L a^{3+}(Z=57) \)
B . \( L u^{3+}(Z=71) \)
\( \mathbf{c} \cdot Y b^{3+}(Z=70) \)
D. \( S m^{3+}(Z=62) \)


Mycorrhizae are associated with angiosperms.
A. Anacardiaceae
B. Orchidaceae
c. Both of the above
D. None of the above


Find the foci of the curve \( 16 x^{2}- \)
\( \mathbf{2 4 x y}+\mathbf{9 y}^{2}+\mathbf{2 8 x + 1 4 y}+\mathbf{2 1}=\mathbf{0} \)


In the dissociation of bicarbonate ion,
the conjugate base involved is:
\( \mathbf{A} \cdot C O_{3}^{2-} \)
в. \( C O_{2} \)
c. \( H_{2} C O_{3} \)
D. \( C O \)


ZnS and PbS are separated by using?


Calculate the probability that a donor
state in the doped material is
occupied?
A. 0.824
B. 0.08
c. 0.008
D. 8.2


Find the sum of given series
\( 31+32+33+\ldots .+50 \)


Density of ice is less than that of water because of:
A. absence of hydrogen bonding
B. crystal modification of ice
c. open porous structure of ice due to hydrogen bonding
D. different physical states of these


Which of the following statements is
not true about RNA ?
A. It has always double stranded \( \alpha \) -helix structure.
B. It usually does not replicate.
C. It is present in the nucleus of the cell.
D. It controls the synthesis of protein.


Factorise the polynomial: \( a x^{2}+b x^{2}+ \)
\( a y^{2}+b y^{2} \)


\( \boldsymbol{H}_{2} \boldsymbol{S} \) react with \( \boldsymbol{O}_{2} \) in restricted supply
of \( \boldsymbol{O}_{2} \) to form:
A \( \cdot H_{2} S+S \)
в. \( H_{2} S+S O_{2} \)
c. \( H_{2} S+S O_{3} \)
D. \( H_{2} S O_{4}+S \)


Calculate the arithmetic mean for the
following data using step deviation method.
\( \begin{array}{lllll}\text { Marks } & 0- & 10- & 20- & 30- \\ & 10 & 20 & 30 & 40\end{array} \)
No. of
students 15 22 8


The number of stomatal pores per \( c m^{2} \) of leaf surface are in the range of
A \( .1000-60,000 \)
B. 10 - 1000
c. \( 50,000-100,000 \)
D. 50-100


If the initial concentrations in a particular mixture of reactants and
products are \( \left[\boldsymbol{P C l}_{5}\right]=\mathbf{0 . 5} \boldsymbol{M},\left[\boldsymbol{P C l}_{3}\right]= \)
\( 0.15 M, \) and \( \left[C l_{2}\right]=0.6 M, \) the direction
in which the reaction proceed to reach equilibrium is:
A \( \cdot \) to the left \( \left[P C l_{5}\right]=0.325 M ;\left[P C l_{3}\right]=0.295 M ;\left[C l_{2}\right]= \)
\( 0.735 M \)
B. to the left, \( \left[P C l_{5}\right]=0.315 M ;\left[P C l_{3}\right]=0.245 M ;\left[C l_{2}\right]= \)
\( 0.735 M \)
c. to the right, \( \left[P C l_{5}\right]=0.365 M ;\left[P C l_{3}\right]= \) \( 0.285 M ;\left[C l_{2}\right]=0.735 M \)
D. None of these


In a chemical reaction, oxidation is
always accompanied by reduction
If true enter 1 , else enter 0 .
\( A \)


If the potential energy between electron and proton at a distance \( r \) is given by \( U=-\left(\frac{k e^{2}}{3 r^{3}}\right) . \) The force is :
A \( \cdot_{F}=\frac{k e^{2}}{r^{2}} \)
B. \( _{F}=-\frac{3}{4} \frac{k e^{2}}{r^{4}} \)
\( ^{\mathrm{c}} \cdot_{F}=\frac{k e^{2}}{r^{4}} \)
D. \( _{F}=\frac{k e^{2}}{r} \)


If \( x^{5}-9 x^{2}+12 x-14 \) is divisible by
\( (x-3), \) what is the remainder?
\( A \cdot 0 \)
B.
\( c .56 \)
D. 184


The term reflection refers to the bending of light rays:
A. when they strike a mirror
B. when they enter a different medium
c. around a sharp edge
D. around the boundary of a narrow aperture


Assertion
Ratio of maximum intensity and minimum intensity in interference is 25
1. Hence amplitude ratio of two waves should be 3: 2
Reason
\( \frac{\boldsymbol{I}_{m a x}}{\boldsymbol{I}_{m i n}}=\left(\frac{\boldsymbol{A}_{1}+\boldsymbol{A}_{2}}{\boldsymbol{A}_{1}-\boldsymbol{A}_{2}}\right)^{2} \)
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


What is the area of the triangle formed by the points \( (a, c+a),(a, c) \) and
\( (-a, c-a) ? \)
A. \( -a^{2} \)
B. \( \frac{1}{a^{2}} \)
c. \( a^{2}+a \)
D. zero


Mole fraction =
A. \( \frac{\text { Number of moles of constituent }}{\text { Number of moles of all constituents }} \)
B. Number of molecule of constituent + Total number of
moles of all constituents
C. Both (A) and (B) above
D. None of the above


Classify the following function as injection, surjection or bijection:
\( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R}, \) defined by \( \boldsymbol{f}(\boldsymbol{x})=\mathbf{1}+\boldsymbol{x}^{2} \)


A sphere of radius \( 1 m \) is rolling on a
rough horizontal surface. The magnitude of velocity of \( A \) w.r.t. \( B \) is
A . \( v_{c m} \)
B . \( v_{c m} / 2 \)
c. \( 1.73 v_{c m} \)
D. zero


The \( _{\text {一一一一一一 }} \) product rule says that when the product of two terms is zero,
then either of the terms is equal to zero.
A. one
B. two
c. three
D. zero


A ray of light in a liquid of refractive
index 1.4 approaches the boundary surface between the liquid and air at an
angle of incidence whose sine is 0.8 Which of the following statement is correct about the behaviour of the light?
A. It is impossible to predict the behaviour of the light ray on the basis of the information supplied
B. The sine of the angle of refraction of the emergent ray will be less than 0.8
C. The ray will be internally reflected
D. The sine of the angle of refraction of the emergent ray will be greater than 0.8


Find the distances between the
following pair of parallel lines:
\( \mathbf{3} \boldsymbol{x}+\mathbf{4} \boldsymbol{y}+\mathbf{9}=\mathbf{0}, \mathbf{6} \boldsymbol{x}+\mathbf{8} \boldsymbol{y}+\mathbf{1 5}=\mathbf{0} \)
A \( \cdot \frac{3}{10} \)
B. \( \frac{3}{5} \)
c. \( \frac{33}{10} \)
D. \( \frac{24}{5} \)


In Reimer-Tiemann reaction, reactants
are:
A. phenol, \( C H C l_{3} \) and alkal
B. phenol, \( C C l_{4} \) and alkali
c. aniline, \( C H C l_{3} \) and alkal
D. both Phenol, \( C H C l_{3} \) and alkali and phenol, \( C C l_{4} \) and alkal


Number of hydrogen bonds between adenine and cytosine is:
A. 0
B.
\( c \cdot 2 \)
\( D \)


Evaluate \( \int_{0}^{\pi / 4} \sin ^{3} 2 t \cos 2 t d t \)


The resultant of two forces which
are equal in magnitude is equal to either of two vectors in magnitude. Find
the angle between the forces.
A .60
B . 45
\( c \cdot 90 \)
D. \( 120^{\circ} \)


In which case hydrolysis is faster
\( A \)
B.
c. at equal rate
D. no hydrolysis


Under what conditions permanent
electromagnet is obtained if a current carrying solenoid is used? Support your answer with the help of a labelled circuit diagram.


The heat of combustion of napthalene,
\( C_{10} H_{8}, \) at constant volume at \( 25^{\circ} \mathrm{C} \) was
found to be \( -5133 k J \) mol \( ^{-1} \)

Calaculate the value of enthalpy change
at constant pressure at the same temperature


In an experiment, 2.4 g of iron oxide on reduction with hydrogen gave 1.68 g of iron. In another experiment, 2.9 g of iron oxide gave 2.09 g of iron on reduction. Which law is illustrated from the above
data?
A. Law of constant proportions
B. Law of multiple proportions
c. Law of reciprocal proportions
D. Law of conservation of mass


Find the cube root of the following number by prime factorization method:
2744


If the equation \( a x^{2}+b x+c=0 \)
\( a, b, c \in R \) have non-real roots, then
This question has multiple correct options
A \( \cdot c(a-b+c)>0 \)
B. \( c(a+b+c)>0 \)
c. \( c(4 a-2 b+c)>0 \)
D. None of the above