In LC oscillation resistance is \( 100 \Omega \) and
inductance and capacitance is \( 1 \mathrm{H} \) and
10 \( \mu F \). Find the half power of frequency.
\( \mathbf{A} \cdot 266.2 \)
B. 366.2
c. 166.2
D. 233.2


For the reaction:
\( \boldsymbol{I}^{-}+\boldsymbol{C l O}_{3}^{-}+\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \rightarrow \boldsymbol{C l}^{-}+ \)
\( \boldsymbol{H} \boldsymbol{S} \boldsymbol{O}_{4}^{-}+\boldsymbol{I}_{2} \)
A. stoichiometric coefficient of \( H S O_{4}^{-} \) is 6
B. iodide is oxidized
c. sulphur is reduced
D. \( H_{2} O \) is one of the products


Which of the following cannot be prepared by Gabriel phthalimide synthesis?
A. Aliphatic primary amines
B. Aromatic primary amines
c. cyclic primary amines
D. None of the above


Assertion
Thermodynamic process in nature are irreversible.
Reason
Dissipative effect cannot be eliminated.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


The dimensional formula of mobility is
\( \mathbf{A} \cdot M^{-1} L^{1} T^{2} A^{\mathbf{1}} \)
B. \( M^{1} L^{0} T^{-2} A^{-1} \)
c. \( M^{1} L^{-1} T^{-2} A^{-1} \)
D. \( M^{-1} L^{0} T^{2} A^{1} \)


Describe the structure of actin and
myosin filaments.
(The Length Sarcomere is 2.5 \( \mu \) m (.Actin \( \operatorname{rod}=1 \mu m,) \) myosin \( =1.5 \mu m \) 1Myosin
filament \& 1 Actin filament is
surrounded by 3 Myosin filament.)


If \( O \) is the centre and \( B C=O B \). Prove
that \( \boldsymbol{x}=\mathbf{3} \boldsymbol{y} \)


State the laws of reflection of light.


The role of a catalyst in a reversible
reaction is to:
A. Increase the rate of forward reaction
B. Decrease the rate of backward reaction
C. Alter the equilibrium constant of a reaction
D. Allow the equilibrium to be achieved quickly


How does doubling number of turns in a
toroidal coil affect the value of
magnetic flux density?
A. Four times
B. Eight times
c. Half
D. Double


Which of the following is used in paints
\( ? \)
A. Terylene
B. Chloroprene
c. Glyptal
D. Nylon


The correct order of solubility in water for \( \boldsymbol{H} \boldsymbol{e}, \boldsymbol{N} \boldsymbol{e}, \boldsymbol{A} \boldsymbol{r}, \boldsymbol{K} \boldsymbol{r}, \boldsymbol{X} \boldsymbol{e} \) is:
A. \( X e>K r>A r>N e>H e \)
в. \( A r>N e>H e>K r>X e \)
c. \( H e>N e>A r>K r>X e \)
D. \( N e>A r>K r>H e>X e \)


Lateral roots originate from
A. Cortex
B. Epidermis
c. Endodermis
D. Pericycle


If the mass of one particle is increased by \( 50 \% \) and the mass of another particle is decreased by \( 50 \% \), the gravitational force between them
A. decreases by 25\%
B. decreases by 75 \%
c. increases by 25\%
D. does not change


Find the amount of water displaced by a solid spherical ball of diameter \( 4.2 \mathrm{cm} \) when it is completely immersed in
water


The quantity of heat taken or given out
by unit mass of a substance when it changes from solid to liquid state or liquid to solid state at constant temperature is known as


The focal length can be expressed in:
A. metre
B. Dioptre
c. watt
D. Horse power


The degree of dissociation of \( \boldsymbol{P C l}_{5} \) of decreases with increase in pressure. If true enter \( 1, \) if false enter 0


Name the group of lines in the visible region of the hydrogen spectrum.


Which of the following acts as a ligand but does not possess any unshared pair of electrons?
A. \( C_{2} H_{4} \)
в. \( N H_{3} \)
\( c \cdot e n \)
D. \( C N^{-} \)


0.1 molal-equeous solution of an electrolyte \( \mathrm{FeCl}_{2} \) is \( 80 \% \) ionised. The
boiling point of the solution at 1 atm is:
\( \left[\mathbf{K}_{\mathbf{6}}\left(\mathbf{H}_{2} \mathbf{O}\right)=\mathbf{0 . 5 2} \mathbf{K} \mathbf{k g} \mathbf{m o l}^{-\mathbf{1}}\right] \)
A. \( 273.17 K \)
B . \( 273.19^{\circ} \mathrm{C} \)
c. \( 373.19^{\circ} \mathrm{C} \)
D. \( 100.17^{\circ} \mathrm{C} \)


Percentage of \( 0_{2} \) present in inhaled air in man is about
A . 21\%
B. 78\%
c. 1\%
D. 43\%


The plastic product which can be remoulded is
A. bakelite
B. melamine
c. polyethene
D. polycot


In the \( A l_{2} C l_{6} \) dimer:
\( \mathbf{A} \cdot \) all the \( A l-C l \) bonds are equivalent
B. three \( A l-C l \) bonds are equivalent and three are not
C. two \( A l-C l \) bonds are equivalent and four are not
D. four \( A l-C l \) bonds are equivalent and two are not


\( \boldsymbol{C}_{6} \boldsymbol{H}_{5} \boldsymbol{N} \boldsymbol{H}_{2} \frac{\boldsymbol{0}-\boldsymbol{5}^{0} \boldsymbol{C}}{N a N \boldsymbol{O}_{2}+\boldsymbol{H} C l}(\boldsymbol{A}) \frac{\boldsymbol{K} \boldsymbol{C} \boldsymbol{N}}{\boldsymbol{C u}_{2}(\boldsymbol{C H})_{2}} \)
\( (B) \stackrel{H^{+} / H_{2} O}{\longrightarrow}(C) \)
The product (C) is:
A. \( C_{6} H_{5} C H_{2} N H_{2} \)
в. \( C_{6} H_{5} \)СООН
\( \mathbf{c} \cdot C_{6} H_{5} C O \)
D. All of the above


Calculate the solubility product constant of \( A g I \) from the following
values of standard electrode potentials.
\( E_{A g^{+} / A g}^{\circ}=0.80 \) volt and \( E_{I / A g I / A g}^{\circ}= \)
-0.15 volt at \( 25^{\circ} C \)


Modern periodic table is based on the atomic number of the elements. The
experiment which proved the significance of the atomic number was:
A. Mullikan's oil drop experiment
B. Moseley's work on X-ray spectra
c. Bragg's work on X-ray diffraction
D. discovery of X-rays by Rontgen


Which term of the arithmetic
progression \( 5,15,25, \ldots \) will be 130 than its \( 31^{s t} \) term?


A group of fungi with septate mycelium in which sexual repoduction is either unknown or lacking are classified under
A. Phycomycetes
B. Deuteromycetes
c. Ascomycetes
D. Basidiomycetes


Write the S.I. unit of electric power


Globular clusters of stars rotate about
most galaxies just like planets rotate about the Sun. The mass of the galaxy needed to keep them in orbit is much greater than the known mass of the
galaxy. In fact, only few percent of the
necessary mass can be seen. The missing mass is
A. found in black hole
B. is called black matter.
c. is called dark matter.
D. is called dark mass


Microvilli of intestinal epithelium are
similar in function with
A. Typhlosole in earthworm
B. Hepatic caecum in cockroach
c. Intestinal caecum in earthworm
D. Malpighian tubules in cockroach.


In Zea mays the flowers are
A. In form of condensed inflorescence
B. Unisexual on different plants
C. Diclinous on the same plant
D. Hermaphrodite


There is a small hole near the bottom of
an open tank filled with a liquid. The speed of water ejected does not depend
on:
This question has multiple correct options
A. Area of the hole
B. Density of the liquid
c. Height of the liquid from the hole
D. Acceleration due to gravity


f \( a, b, c \) are in A.P., prove that the following are also in A.P. \( \frac{1}{\sqrt{(b)}+\sqrt{(c)}}, \frac{1}{\sqrt{(c)}+\sqrt{(a)}}, \frac{1}{\sqrt{(a)}+v} \)


A spherical ball is dropped in a long column of viscous liquid Which of the
following graphs represent the variation
of
(i) gravitational force with time
(ii) viscous force with time
(iii) net force acting on the bass with
time
A. \( Q, R, P \)
B. R, Q, P
\( c . P, Q, R \)
D. R, P, Q


A substance consisting of atoms which all have the same number of protons is called a/an
A. Element
B. Molecule
c. Mixture
D. Solution


Which of the following is not a colloid?
A. Foam
B. Cloudd
c. Rooh Afaza syrup
D. Eggg


Identify type of symmetry in the given animals \( A \) and \( B \).
A. A - Bilateral, B - Asymmetrical
B. A - Bilateral, B - Bilateral
c. A - Radial, B - Bilateral
D. A - Radial, B - Radial


You have been provided with a solenoid
\( A B \)
(i) What is the polarity at end \( A ? \)
(ii) Give one advantage of an
electromagnet over a permanent
magnet.


Find the principal value of:
\( \tan ^{-1}(-1)+\cos ^{-1}\left(-\frac{1}{\sqrt{2}}\right) \)


Give a brief description of the principles of the Crystallisation and give
examples.


In a car race, car A takes a time t less
than car \( B \) at the finish and passes the
finishing point with speed \( \mathbf{v} \) more than that of the car B. Assuming that both the cars starts from rest and travel with
constant acceleration \( a_{1} \) and \( a_{2} \)
respectively. Show that \( \boldsymbol{v}=\sqrt{\boldsymbol{a}_{1} \boldsymbol{a}_{2}} \boldsymbol{t} \)


What are artificial sweetening agents? Give two examples.


Find \( A M \) of 5 and 23


In the leaching of gold by cyanide process, the following reaction takes
place:
\( \boldsymbol{a} \boldsymbol{A} \boldsymbol{u}+\boldsymbol{b} \boldsymbol{K} \boldsymbol{C} \boldsymbol{N}+\boldsymbol{c} \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{d} \boldsymbol{O}_{2} \rightarrow \)
\( e K A u(C N)_{2}+f K O H \)
\( \boldsymbol{u} \boldsymbol{A} \boldsymbol{u}+\boldsymbol{v} \boldsymbol{K} \boldsymbol{C} \boldsymbol{N}+\boldsymbol{w} \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{x} \boldsymbol{O}_{2} \rightarrow \)
\( \boldsymbol{y} \boldsymbol{K} \boldsymbol{A} \boldsymbol{u}(\boldsymbol{C} \boldsymbol{N})_{4}+\boldsymbol{z} \boldsymbol{K} \boldsymbol{O} \boldsymbol{H} \)
Identify the correct statements with respect to the stoichiometric coefficients when these reactions are
balanced using simplest natural numbers.

This question has multiple correct options
A. \( d, c, x, u \) are in anthmetic progression
B. \( c, y, w, b \) are in arithmetic progression
c. \( f, b, z, v \) are in geometic progressinon
D. \( d, c, a, b \) are geometnic progression


Which type of motion of an object that moves in a straight line?
A. Rectilinear motion
B. Periodic motion
c. circular motion
D. None of the above


In which year did Hahn and Meitner discover the phenomenon of neutroninduced fission of uranium.?
A . 1938
в. 1950
\( c .1945 \)
D. 1928


The radius of a wooden hemisphere is
10 cm. What is its volume?

If this hemisphere is curved into a cone
of maximum size, find the volume of the
cone.


A body of mass \( 2 k g \) is projected
vertically upwards with speed of \( 3 m / s \) The maximum gravitational potential energy of the body is (in J)
A . 18
в. 4.5
c. 9
D. 2.5


A very long, straight, then wires carries \( -3.60 n C m^{-1} \) of fixed negative charge. The wire is to be surrounded by a uniform cylinder of positive charge, radius \( 1.50 \mathrm{cm} \), coaxial with the wire.
The volume charge density \( \rho \) of the cylinder is to be selected so that the net electric field outside the cylinder is zero. Calculate the required positive charge density \( \rho\left(\operatorname{in} \mu C m^{-3}\right) \)
\( A \)
в. 7
\( c .5 \)
\( D \)


The molecular electronic configuration
of \( B e_{2} \) is:
A \( \cdot \sigma 1 s^{2}, \sigma^{*} 1 s^{2}, \sigma 2 s^{2}, \sigma^{*} 2 p^{2} \)
B . \( \sigma 1 s^{2}, \sigma 2 s^{2} \)
C. \( \sigma 1 s^{2}, \sigma^{*} 1 s^{2}, \sigma 2 s^{2}, \sigma^{*} 2 s^{2} \)
D. none of the above


Which of the following is a dicotyledonous family?
A . Liliaceae
B. Solanaceae
c. Pappilionaceae
D. Both B and C


Ammonia burns with oxygen to give:
A. nitrogen and water vapour
B. nitrogen and steam
c. both a and b
D. none


\( y^{2} \)
\( \frac{2}{8} \)


Four charges \( 10^{-8} ;-2 \times 10^{-8} ;+3 \times 10^{-8} \)
and \( 2 \times 10^{-8} \) coulombs are placed at the
four corners of a square of side \( 1 \mathrm{m} \). The
potential at the centre of the square is
A . zero
B. 360volt
c. \( 180 v o l t \)
D. \( 360 \sqrt{2} \) volt


Prove that
\[
\left|\begin{array}{ccc}
\mathbf{1} & \mathbf{1} & \mathbf{1}+\mathbf{3} \boldsymbol{x} \\
\mathbf{1}+\mathbf{3} \boldsymbol{y} & \mathbf{1} & \mathbf{1} \\
\mathbf{1} & \mathbf{1}+\mathbf{3} \boldsymbol{z} & \mathbf{1}
\end{array}\right|=\mathbf{9}(\mathbf{3} \boldsymbol{x} \boldsymbol{y} \boldsymbol{z}+
\]
\( \boldsymbol{x} \boldsymbol{y}+\boldsymbol{y} \boldsymbol{z}+\boldsymbol{z} \boldsymbol{x} \)


When we wear nylon dresses during winter then there is
which gets produced due to contact with out body. Fill in the Blank.
A. Magnetic
B. Electrostatic
c. Potential
D. kinetic


Find the equivalent resistance between
A and B.


Total Electric flux at a point in an electric
field is
A. positive
B. negative
c. zero
D. positive or negtive


(a) Account for the following:
(i) \( C u^{+} \) is unstable in an aqueous
solution.
(ii) Transition metals form complex compounds.
(b) Complete the following equations:
\( \boldsymbol{C r}_{2} \boldsymbol{O}_{7}^{2-}+\boldsymbol{8} \boldsymbol{H}^{+}+\boldsymbol{3} \boldsymbol{N} \boldsymbol{O}_{\overline{2}} \rightarrow \)


Let \( \boldsymbol{X} \) be the set of all persons living in a city. Persons \( x, y \) in \( X \) are said to be
related as \( x<y \) if \( y \) is at least 5 years
older than \( x \). Which one of the following
is correct?
A. The relation is an equivalence relation on \( X \)
B. The relation is transitive but neither reflexive nor symmetric
c. The relation is reflexive but neither nor symmetric
D. The relation is symmetric but neither transitive nor reflexive


The DNA molecule has uniform
diameter due to
A. Double strandedness.
B. Presence of phosphate.
c. specific base pairing between purine and pyrimidine.
D. None of the above


Periscope is used for:
A. observation beyond the obstruction
B. watching TV more clearly
C. viewing nearby objects by persons suffering from visual deformities
D. all of these


In the given figure \( \boldsymbol{\alpha} \) and \( \boldsymbol{\beta} \) are
measured in degrees. Which one of the
following statements is not correct?
\( \mathbf{A} \cdot \beta>\alpha \)
\( \mathbf{B} \cdot \sec \beta=2 \)
\( \mathbf{C} \cdot \tan 3 \alpha=\sqrt{3} \)
D \( \cdot \sin (\beta-\alpha)=\frac{1}{\sqrt{2}} \)


Why does the probability curve become
narrower when gas particles are more
massive?
A. The gas particles can travel at higher speeds
B. The gas particles are less likely to travel at slower speeds
C. The gas particles are more likely to travel at higher speeds
D. The gas particles can not travel at higher speeds
E. There are more collisions between gas particles


Assertion
The Daniell cell becomes dead after
sometimes.
Reason
The oxidation potential of Zn anode decreases and that of Cu increases.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


The surface of the sphere
A. is an equi-potential surface
B. is a zero-potential surface
C. is an uncharged surface
D. None of these


The immediate regeneration of ATP used up during muscle contraction is facilitated by
A. Glucose
B. Glycogen
c. Lactic acid
D. Creatine phosphate


In a certain reaction, \( 10 \% \) of the reactant
decomposes in one hour, \( 20 \% \) in two hours, \( 30 \% \) in three hours, and so on.
The dimension of the velocity constant (rate constant) is:
\( \mathbf{A} \cdot H r^{-1} \)
B. \( \operatorname{Mol} L^{-1} h r^{-1} \)
c. \( L m o l^{-1} s^{-1} \)
D. Mols"


Find the value of \( x \) which satisfy
euqation \( : \tan ^{-1} 2 x+\tan ^{-1} 3 x=\pi / 4 \)
A. \( x=-1 / 6 \)
В. \( x=+1 / 6 \)
c. \( x=-1 \)
D. \( x=+1 \)


The last element of actinide series is :
A. thorium
B. cerium
c. lawrencium
D. Iutetium


A radioactive element decays by parallel path as given below:
\( \boldsymbol{A} \stackrel{\lambda_{1}}{\longrightarrow} \boldsymbol{B} \quad \boldsymbol{\lambda}_{1}=\mathbf{1 . 8} \times \mathbf{1 0}^{-2} \boldsymbol{s e c}^{-1} \)
\( \mathbf{2 A} \stackrel{\lambda_{2}}{\longrightarrow} \boldsymbol{B} \quad \boldsymbol{\lambda}_{2}=\mathbf{1 0}^{-\mathbf{3}} \boldsymbol{s e c}^{-\mathbf{1}} \)
Average life of radio-nuclide \( \boldsymbol{A} \) will be:
A .52 .63 sec
B. 500 sec
c. 50 sec
D. 120 sec


The ratio of masses of oxygen and nitrogen of a particular gaseous mixture is \( 1: 4 . \) The ratio of number of
their molecule is:
\( A \cdot 1: 4 \)
B. 7:32
\( c \cdot 1: 8 \)
D. 3:16


Which of the following statements is/are correct
(i) The distance between two consecutive compressions is called frequency of sound wave
(ii) Sound propagates as pressure variations
(iii) Compressions are narrower in a high pitched sound
\( A \cdot( \) i) only
B . (ii) only
c. (iii) only
D. (ii) and (iii)


The value of \( \lim _{x \rightarrow 1} \frac{x^{m}-1}{x^{n}-1} \) is?
\( A \cdot \frac{m}{n} \)
в. \( \frac{n}{m} \)
c. \( \frac{n^{2}}{m^{2}} \)
D. \( \frac{m^{2}}{n^{2}} \)


The equilibrium constant \( \boldsymbol{K}_{c} \) for the
reaction \( N_{2(g)}+3 H_{2} \rightleftharpoons 2 N H_{3(g)} \) is
0.286 at \( 500^{\circ} C . \) Calculate \( K_{c} \) and \( K_{p} \)
for the reaction \( \mathbf{2} \boldsymbol{N} \boldsymbol{H}_{\mathbf{3}(\boldsymbol{g})} \rightleftharpoons \boldsymbol{N}_{\mathbf{2}(\boldsymbol{g})}+ \)
\( \mathbf{3} \boldsymbol{H}_{\mathbf{2}(\boldsymbol{g})} \)


Prove that the tangent drawn at the mid-point of an arc of a circle is parallel to the chord joining the end points of
the arc.


What did Kuhne do?
A. Discovered parathyroid
B. Coined the term enzyme
C. Coined the term gene
D. Discovered enzyme


Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be defined by \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{cc}x+2 & (x \leq-1) \\ x^{2} & (-1<x<1) \text { then the value } \\ 2-x & (x \geq 1)\end{array}\right. \)
of \( \boldsymbol{f}(-1)+\boldsymbol{f}(\mathbf{0})+\boldsymbol{f}(1) \) is
\( A \cdot 0 \)
B.
\( c \cdot 2 \)
D. -


Which of the following compounds is used as drying agent?
A. Calcium Oxide
B. Gypsum
c. calcium chloride
D. None of the above


Predict which of the following reaction
(s) has a positive entropy change?
।. \( \boldsymbol{A} \boldsymbol{g}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{C l}(\boldsymbol{a} \boldsymbol{q}) \rightarrow \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l}(\boldsymbol{s}) \)
II. \( \boldsymbol{N} \boldsymbol{H}_{\boldsymbol{4}} \boldsymbol{C l}(\boldsymbol{s}) \rightarrow \boldsymbol{N} \boldsymbol{H}_{\boldsymbol{3}}(\boldsymbol{g})+\boldsymbol{H} \boldsymbol{C l}(\boldsymbol{g}) \)
III. \( 2 N H_{3}(g) \rightarrow N_{2}(g)+3 H_{2}(g) \)
A . I and II
в. ॥
c. ॥ and III
D. I


Write most favourable conditions for
the conversion of \( S O_{2} \) into \( S O_{3} \)


Consider the table of standard
reduction potentials shown below.
Half-reaction
\[
\begin{array}{ll}
C l_{2}+2 e^{-} \rightarrow 2 C l^{-} & 1.36 V \\
O_{2}+4 H^{+}+4 e^{-} \rightarrow 2 H_{2} O & 1.23 V \\
2 H_{2} O+2 e^{-} \rightarrow H_{2}+2 O H^{-} & -0.83 V \\
R b^{+}+e^{-} \rightarrow R b & -2.93 V
\end{array}
\]
Use the information from the table and
your knowledge of electrochemistry to
predict the CORRECT net ionic equation
for the reaction that will occur when an
aqueous solution of rubidium chloride
undergoes electrolysis.
\( \mathbf{A} \cdot 2 R b^{+}+2 C l^{-} \rightarrow 2 R b+C l_{2} \)
B \( \cdot 2 H_{2} O \rightarrow 2 H_{2}+O_{2} \)
\( \mathbf{c} \cdot H_{2}+2 O H^{-}+2 R b^{+} \rightarrow 2 R b+2 H_{2} O \)
\( \mathbf{D} \cdot 4 C l^{-}+O_{2}+4 H^{+} \rightarrow 2 H_{2} O+2 C l_{2} \)


Light of wavelength \( \lambda \) in the air enters a medium of refractive index \( \mu . \) Two
points in this medium, lying along the
path of this light are at a distance \( ^{\prime} x^{\prime} \) apart. The phase difference between these points is
A \( \cdot \frac{2 \pi}{\lambda}-\mu x \)
в. \( \frac{2 \pi}{\lambda} \cdot x \mu \)
c. \( (\mu-1) \cdot \frac{2 \pi}{\lambda} x \)
D. \( \frac{1}{(\mu-1)} \cdot \frac{2 \pi x}{\lambda} \)


Assertion
Critical temperature is the temperature at which the intermolecular attraction
in gas molecules vanishes.
Reason
At critical point, the density of substance in gaseous and liquid states becomes same.
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 bar magnet of magnetic moment \( 1.2 A m^{2} \) is placed in the magnetic
meridian with its south pole pointing the
north. If a neutral point is found at a
distance of \( 20 \mathrm{cm} \) from the centre of the
magnet, the value of the horizontal
component of the earth's magnetic field
is
\( \mathbf{A} \cdot 3 \times 10^{-5} T \)
B \( .3 \times 10^{-4} T \)
\( \mathbf{c} \cdot 3 \times 10^{3} T \)
D. \( 3 \times 10^{-3} T \)


If \( P\left(E_{k}\right) \propto k \) for \( 0 \leq k \leq n, \) then the
probability that \( X \) is the only student to pass the examination is
A \( \cdot \frac{3}{n(n+1)} \)
в. \( \frac{6}{n(n+1)(2 n+1)} \)
\( c \cdot \frac{1}{n} \)
D. \( \frac{1}{n(2 n+1)} \)


The enzymes ribulose biphosphate carboxylase-oxygenase and phosphenol pyruvate carboxylase are activated by
A . Mg
B. zn
c. мо
D. Mn


toppr
Q Type your ques
The cleavage of \( C-O \) bond takes place
under drastic conditions with excess of
hydrogen halide, \( \boldsymbol{R}-\boldsymbol{O}-\boldsymbol{R}+ \)
\( 2 H X \rightarrow H X \rightarrow 2 R X+H_{2} O \)
If hydrogen halide is not taken in excess, then one molecule each of
alcohol and alkyl halide are formed, \( \boldsymbol{R}-\boldsymbol{O}-\boldsymbol{R}+\boldsymbol{H} \boldsymbol{I} \stackrel{^{373} \boldsymbol{H}} \boldsymbol{R}-\boldsymbol{O} \boldsymbol{H}+\boldsymbol{R}- \)
I. The order of reactivity of hydrogen
halides towards the above mentioned
reaction depends on the bond strength of halogenated acids. Weaker is the \( \boldsymbol{H}-\boldsymbol{X} \) bond, greater is its reactivity. In
case of unsymmetrical ethers, the site of cleavage is such that the halide is formed from the alkyl group which is tertiary, so that the halide formed is tertiary halide.
Indicate whether the following statements / reactions are true or false.
The order of hydrogen halide reactivity is \( \boldsymbol{H} \boldsymbol{I}<\boldsymbol{H} \boldsymbol{B r}<\boldsymbol{H} \boldsymbol{C l} \)
A. True
B. False


Two layers of cloth of equal thickness
provide warmer covering than a single
layer of cloth of double the thickness,
because they:
A. behave like a thermos
B. have lesser thickness
C. allow heat from atmosphere to the body
D. enclose between them a layer of air


Express 60.1 cal of energy in units of joules.
A. 251 J
в. 251.5 J
c. 14.4 J
D. 14.36 J
E. 251.4


Write any two differences between a
simple microscope and a compound microscope.


is the part of a neuron where information is acquired.
A. Dendrite
B. Axon
c. Nephron
D. Medulla


Make logic symbol and write Boolean expression of NOT gate.


Solve \( \left.\boldsymbol{D}=\mid \begin{array}{ccc}\mathbf{1} & -\mathbf{2} & \mathbf{1} \\ \mathbf{2} & \mathbf{1} & -\mathbf{1} \\ \mathbf{1} & \mathbf{3} & \mathbf{1}\end{array}\right] \)


Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be defined by \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{cl}\boldsymbol{\alpha}+\frac{\sin [\boldsymbol{x}]}{\boldsymbol{x}} & \boldsymbol{i f} \boldsymbol{x}>0 \\ \boldsymbol{2} & \boldsymbol{i f} \boldsymbol{x}=\mathbf{0} \\ \boldsymbol{\beta}+\left[\frac{\sin \boldsymbol{x}-\boldsymbol{x}}{\boldsymbol{x}^{3}}\right] & \boldsymbol{i} \boldsymbol{f} \boldsymbol{x}<0\end{array}\right. \)
where \( [x] \) denotes the integral part of \( y \) If \( f \) is continuous at \( x=0, \) then \( \beta-\alpha= \)
\( A \)
B. 1
\( c \cdot 0 \)
\( D \)


What is the principle of zone refining of
metals?
A. Greater mobility of the pure metal than that of the impurity
B. Higher melting point of the impurity than that of the pure metal
c. Greater noble character of the solid metal than that of the impurity
D. Greater solubility of the impurity in the molten state than in the solid


Whend \( \approx a \) but wires are not touching
the loop, it is found that the net magnetic field on the axis of the loop is
zero at a height \( h \) above the loop. In that
case :
A. Current in wire 1 and wire 2 is in the direction PQ and RS, respectively such \( h \approx a \)
B. Current in wire 1 and wire 2 is in the direction PQ and
SR, respectively and \( h \approx a \)
c. current in wire 1 and wire 2 is in the direction PQ and SR, respectively and \( h \approx 1.2 a \)
D. Current in wire 1 and wire 2 is in the direction PQ and
RS, respectively and \( h \approx 1.2 a \)


is the maximum amount of air a
person can expel from the lungs after a maximum inhalation.
A. Tidal air volume
B. Vital capacity
c. Complemental air volume
D. Total lung capacity


A plane mirror produces a magnification of
A . -1
B. +1
c. zero
D. infinity


The atomic number of chromium is 24
Its electronic configuration in ground
state is \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{1} 3 d^{5} \)
Chromium atom by losing 3 electrons
form \( \mathrm{Cr}^{3+} \) ions. A chromium atom
contains \( 17 \% \) more neutron than the
protons. Now answer the following questions
The number of unpaired electrons in \( \mathrm{Cr} \)
\( 3+ \) ions is :
\( A \cdot 3 \)
B. 6
\( c \cdot 5 \)
D.


If \( \boldsymbol{f}(\boldsymbol{x})=\left(\frac{\boldsymbol{x}^{a}}{\boldsymbol{x}^{b}}\right)^{\boldsymbol{a}+\boldsymbol{b}} \cdot\left(\frac{\boldsymbol{x}^{b}}{\boldsymbol{x}^{c}}\right)^{b+c} \cdot\left(\frac{\boldsymbol{x}^{c}}{\boldsymbol{x}^{a}}\right)^{c+a} \)
then \( f^{\prime}(x) \) is equal to
\( \mathbf{A} \cdot \mathbf{1} \)
B.
\( \mathbf{c} \cdot x^{a+b+c} \)
D. None of these


A man has to sell pulse at a loss of \( 10 \% \)
If he increases the selling price by Rs 5 per \( \mathrm{kg}, \) he would make a profit of \( 15 \% \) Find the cost price and initial selling price per kg of pulse.
A . Rs \( 20, \) Rs 18
B. Rs 18, Rs 20
c. \( R s 15, \) Rs 18
D. Rs 18, Rs 15


A group of red beetles lives on green leaves of a tree. Beetles multiply
through sexual reproduction. One day,
some green beetles are seen among the red beetles. Green beetles breed to
produce green progeny. Crows on the
tree eat beetles. Some green beetles appear among the red beetle because
A. Beetles become green by accumulating chlorophyll from the green leaves that they eat
B. Natural variations occur during sexual reproduction
C. Red beetles mimic green colour of leaves whenever they see crows
D. Beetle change colour from red to green with change of season


The perimeter of a triangle is equal to \( \boldsymbol{K} \)
times the sum of its altitude, then \( \boldsymbol{K} \) is:
\( \mathbf{A} \cdot \mathbf{1} \)
B. any number
c. less than 1
D. greater than 1


Bose-Einstein condensate is based on
which scientific principle?
A. Magnetic confinement of plasma
B. Trapping and cooling of atoms by laser beams and magnetic fields
C. Wave nature of electrons
D. Motion of charged particles in electromagnetic fields


Find \( A M \) of divisors of 100 .
\( \mathbf{A} \cdot 24 \)
B . 25.
c. 24.11
D. 21.9


Select correct statement(s):
I) When excess \( F e C l_{3} \) solution is added
to \( \boldsymbol{K}_{\mathbf{4}}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{5}\right] \) solution, in addition to
\( \boldsymbol{F} \boldsymbol{e}^{I I I}\left[\boldsymbol{F} \boldsymbol{e}^{I I}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right]^{-}, \boldsymbol{F} \boldsymbol{e}^{I I}\left[\boldsymbol{F} \boldsymbol{e}^{I I I}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right] \)
is also formed due to side redox
reaction
(II) When \( F e C l_{2} \) is added to
\( \boldsymbol{K}_{3}\left[\boldsymbol{F} e(\boldsymbol{C} \boldsymbol{N})_{6}\right] \) solution, in addition to
\( \boldsymbol{F} \boldsymbol{e}^{I I}\left[\boldsymbol{F} \boldsymbol{e}^{I I I}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right]^{-}, \boldsymbol{F} \boldsymbol{e}^{I I I}\left[\boldsymbol{F} \boldsymbol{e}^{I I}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right] \)
is also formed due to side redox
reaction
\( (\| I) F e^{I I I}\left[F e^{I I}(C N)_{6}\right]^{-} \) is
paramagnetic while \( \boldsymbol{F} e^{I I}\left[\boldsymbol{F} e^{I I I}(\boldsymbol{C} \boldsymbol{N})_{6}\right]^{-} \) is diamagnetic
\( (\mathrm{IV}) \boldsymbol{F} \boldsymbol{e}^{I I}\left[\boldsymbol{F} \boldsymbol{e}^{I I}(\boldsymbol{C} \boldsymbol{N})_{6}\right]^{-} \) is diamagnetic
while \( \boldsymbol{F e}^{I I}\left[\boldsymbol{F} e^{I I I}(\boldsymbol{C} \boldsymbol{N})_{6}\right]^{-}, \) is
paramagnetic
A \( . \) ।, ॥
в. ॥I, Iv
c. both (a) and (b)
D. None of these


The locus of a planet orbiting around the sun is:
A. A circle
B. A straight line
c. A semicircle
D. An ellipse


If in a Young's double slit experiment, the slit width is \( 3 \mathrm{cm}, \) the separation between slits and screen is \( 70 \mathrm{cm} \) and
wavelength of light is \( 1000 \mathrm{A} \), then fringe width will be \( (\mu=1.5) \)
A \( .2 .3 \times 10^{-3} \mathrm{cm} \)
В. \( 2.3 \times 10^{-4} m \)
\( \mathbf{c} \cdot 2.3 \times 10^{-5} \mathrm{cm} \)
D . \( 2.3 \times 10^{-6} \mathrm{m} \)


Through any point, \( (x, y) \) of a curve passing through the origin, lines are drawn parallel to the coordinate axes.
The curve divides the rectangle formed by the two lines and the axes into two areas, one of which is twice the other.
Then the curve may represent a family of:
A . circles
B. parabolas
c. ellipses
D. hyperbolas


The botanical name for onion and garlic can be written as
A. Allium cepa and Asphodelus tenuifolius
B. Allium sativum and Allium cepa
C. Asphodelus tenuifolius and Allium sativum
D. Allium cepa and Allium sativum


If energy (E), force (F) and linear
momentum (P) are fundamental
quantities, then match the following
and give correct answer.
\( \mathbf{A} \) B
Physical quantity Dimensional formula
Mass \( E^{0} F^{-1} p^{1} \)
a)
d)
b) Length
e) \( E^{-1} F^{0} p^{2} \)
Time \( E^{1} F^{-1} p^{0} \)
c)
f) \( r \) 1 an
\( A \cdot a-d, b-e, c-f \)
B. a-f, b-e, c-d
\( \mathbf{C} \cdot a-e, b-f, c-d \)
D. a-e, b-d, c-f


Which one of the following is a polysaccharide?
A. sucrose
B. Cellulose
c. Maltose
D. Raffinose


Which of the following particles neutron, proton,electron and deuteron has the lowest energy if all have the same de Broglie wavelength:
A. neutron
B. proton
c. electron
D. deuteron


It is found that the speed of the earth around the sun increases when it is
close to the sun.
A. Angular velocity of the earth is constant.
B. Areal velocity of the earth is not constant.
c. Areal velocity of the earth is constant
D. None of these.


Let \( \boldsymbol{f}: \boldsymbol{Z} \rightarrow \boldsymbol{Z} \) be given by \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ll}\frac{x}{2}, & \text { if } x \text { is even } \\ 0, & \text { if } x \text { is odd }\end{array} . \text { Then, } f \) is \right.
A. onto but not one-one
B. one-one but not onto
c. one-one and onto
D. neither one-one nor onto


One mole of an ideal monatomic gas
undergoes a process described by the equation \( P V^{3} \) =constant. The heat capacity of the gas during this process is:
\( A \cdot \frac{3}{2} R \)
B . \( \frac{5}{2} R \)
\( c \cdot 2 R \)
D. R


The stress-strain graph for a metal wire is as shown in the figure. In the graph, the region in which Hooke's law is
obeyed, the ultimate strength and
fracture points are represented by
A. \( O A, C, D \)
в. \( O B, D, E \)
c. \( O A, D, E \)
D. \( O B, C, D \)


Which of the following combination is
false?
A. A-T
B. A-G
c. \( c-G \)
D. A-U


Blood-red colour in the detection of both
N and S in Lassaigne's extract is due to the formation of
\( \mathbf{A} \cdot F e(C N S)_{2} \)
в. \( F e(C N S)_{3} \)
c. \( K_{4}\left[F e(C N)_{6}\right] \)
D. \( K_{3}\left[F e(C N)_{6}\right] \)


In \( N O_{3}^{-} \) ion number of bond pair and
the lone pair of electrons on nitrogen
atom are:
A .2,2
в. 3,1
c. 1,3
D. 4,0


The heats of formation of
\( \boldsymbol{C}_{6} \boldsymbol{H}_{6}(l), \boldsymbol{H}_{2} \boldsymbol{O}(l), \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g}) \) are
11.70,-68.4 and \( -94.0 k c a l \)
respectively. Calculate the heat of combustion of benzene(l)
A . -780.9 kcal-780.9kcal
B. -680.9 kcal-780.9kcal
c. 580.9 kcal-780.9kcal
D. 480.9 kcal-780.9kcal


Let \( \boldsymbol{E}=\{1,2,3,4\} \) and \( \boldsymbol{F}=\{1,2\} \) then
the number of onto functions from E to
is
A . 14
B . 16
c. 12
D. 8


The measure of the angle between the
lines, whose direction numbers are
\( l, m, n \) and \( m-n, n-l, l-m \) is
\( ^{A} \cdot \frac{\pi}{4} \)
в.
\( c \cdot \frac{\pi}{2} \)
D.


Rajesh borrowed RS. 5,000 from a bank. He will have to pay Rs.10,000 after 5
years Find the rate of interest, if the interest is payable half yearly.


Find the slope and \( y \) -intercept of the
line \( 2 x+5 y=1 \)
A \( \cdot \) slope \( =-\frac{2}{5}, y \) -intercept \( =\frac{1}{5} \)
B. slope \( =-\frac{1}{5}, y \) -intercept \( =\frac{1}{5} \)
c. slope \( =-\frac{2}{3}, y \) -intercept \( =\frac{1}{5} \)
D. slope \( =-\frac{2}{5}, y \) -intercept \( =\frac{2}{5} \)


The line \( \frac{x}{3}+\frac{y}{4}=1 \) meets the \( y- \) axis
and \( x- \) axis at \( A \) and \( B, \) respectively. square \( A B C D \) is constructed on the
line segment \( A B \) away from the origin. the coordinates of the vertex of the
square farthest from the origin are
A \( .(7,3) \)
в. (4,7)
c. (6,4)
(年. \( 6,4,4) \)
D. (3,8)


Assertion
The back emf in a dc motor is
maximum when the motor has just been switched on.
Reason
When motor is switched on it has
maximum speed.
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


If the earth is treated as a sphere of
radius \( R \) and mass \( M, \) its angular
momentum about the axis of its
rotation with period \( \boldsymbol{T} \) is
A \( \cdot \frac{4 \pi M R^{2}}{5 T} \)
в. \( \frac{2 \pi M R^{2}}{5 T} \)
\( ^{\mathrm{c}} \cdot \frac{M R^{2} T}{T} \)
D. \( \frac{\pi M R^{3}}{T} \)


The resultant of 2 vectors \( \vec{A} \) and \( \vec{B} \) is
perpendicular to the \( \vec{A} \) and its magnitude is equal to half the magnitude of vector B. Find the angle between vector \( \vec{A} \) and \( \vec{B} \)


The capacitive reactance of \( 50 \mu \mathrm{F} \)
capacitance at a frequency of \( 2 \times 10^{3} \)
\( \mathrm{Hz} \) will be \( _{----} \Omega \)
\( A \cdot \frac{2}{\pi} \)
B. \( \frac{3}{\pi} \)
\( c \cdot \frac{4}{\pi} \)
\( D \cdot \frac{5}{5} \)


Amongst the following statements, the
correct one is :
A. The gas can not be compressed below the critical temperature
B. Below critical temperature, thermal motion of the molecules is slow enough for the intermolecular forces to come into play leading to condensation of the gas.
C. At critical temperature liquid and gaseous phase can be distinguished
D. An ideal gas has a characteristic critical temperature


Assertion
Show that the points \( (\boldsymbol{a}, \boldsymbol{a}),(-\boldsymbol{a},-\boldsymbol{a}) \)
and \( (-\sqrt{3} a, \sqrt{3} a) \) are the vertices of an
equilateral triangle.
Reason
Using the distance formula we can show that the sides are equal.
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


White light is split into a spectrum by a prism and it is seen on a screen. If we
put another identical inverted prism behind it in contact. What will be seen
on the screen?
A. Violet will appear where red was
B. The spectrum will remain the same
c. There will be no spectrum, but only the original light with no deviation.
D. There will be no spectrum, but the original light will be laterally displaced


The ratio in which the area bounded by
the curves \( y^{2}=4 x \) and \( x^{2}=4 y \)
is divided by the line \( x=1 \) is
A. 64: 49
B. 15: 34
c. 15: 49
D. None o fthese


The velocity-time diagram of a
harmonic oscillator is shown in the
adjoining figure. The frequency of
oscillation is :
\( A \cdot 25 \mathrm{Hz} \)
B. 50 Н
c. \( 12.25 \mathrm{Hz} \)
D. \( 33.3 \mathrm{Hz} \)


What is the least number of squares
that must be added, so that the line \( A B \)
becomes a line of symmetry?
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c .3 \)
D.


\( a=\operatorname{cosec} 2^{0}, b=\operatorname{cosec} 2, \) then which of
the following holds true?
\( \mathbf{A} \cdot a=b \)
В \( . a>b \)
c. \( a<b \)
D. \( a=2 b \)


The area (in sq. units) of the region \( A=\left\{(x, y): x^{2} \leq y \leq x+2\right\} \) is?
A \( \cdot \frac{10}{3} \)
B. \( \frac{9}{2} \)
c. \( \frac{31}{6} \)
D. \( \frac{13}{6} \)


If \( \tan ^{-1} \frac{1-x}{1+x}=\frac{1}{2} \tan ^{-1} x, \) then \( x= \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. \( \sqrt{3} \)
c. \( \frac{1}{\sqrt{3}} \)
D. None of these


The energy gap of silicon is 1.14 eV.The
maximum wavelength at which silicon starts energy absorption, will be \( \left(h=6.62 \times 10^{-34} J s, c=3 \times 10^{8} m / s\right) \)
A \( \cdot 10.888 \AA \)
B \( \cdot 108.88 \AA \)
\( c \cdot 1088.8 \AA \)
D \( \cdot 10888 \) 能


\( N_{2} F_{4}(g) \rightleftharpoons 2 N F_{2}(g) ; \Delta H^{o}=38.5 k J \)
Which of the following conditions will
favour the formation of \( N F_{2} ? \)
This question has multiple correct options
A. Adding He to the equilibrium mixture at constant temperature and volume
B. Increasing the temperature.
c. \( N F_{2} \) gas is removed from the reaction mixture.
D. Decreasing the pressure at constant temperature


A ray of light is incident on a medium
with angle of incidence i and refracted
into a second medium with angle of
refraction \( r . \) The graph of \( \sin (i) \vee s \) \( \sin (r) \) is as shown in the figure. Then
the velocity of light in the first medium
is \( \ldots \ldots . . . . . . . . . \) times the velocity of light in
the second medium.
\( A \cdot \sqrt{3} \)
B. \( 1 / \sqrt{3} \)
c. \( \sqrt{3} / 2 \)
D. \( 2 / \sqrt{3} \)


The adjoint of the matrix \( \boldsymbol{A}= \)
\[
\left[\begin{array}{ccc}
1 & 1 & 1 \\
2 & 1 & -3 \\
-1 & 2 & 3
\end{array}\right] \text { is }
\]
\( A \)
\[
\left.\begin{array}{l|lcc}
& 9 & -1 & -4 \\
\frac{1}{11} & -3 & 4 & 5 \\
& 5 & -3 & -1
\end{array}\right]
\]
B.
\[
\left[\begin{array}{ccc}
9 & 1 & -4 \\
3 & 4 & -5 \\
5 & 3 & -1
\end{array}\right]
\]
\( c \)
\[
\left[\begin{array}{ccc}
9 & -3 & 5 \\
-1 & 4 & -3 \\
-4 & 5 & -1
\end{array}\right]
\]
D.
\[
\left[\begin{array}{ccc}
9 & -1 & -4 \\
-3 & 4 & 5 \\
5 & -3 & -1
\end{array}\right]
\]


A coil of resistance \( 40 \Omega \) is connected to
a galvanometer of \( 160 \Omega \) resistance. The coil has radius \( 6 \mathrm{mm} \) and turns 100 .
This coil is placed between the poles of a magnet such that magnetic field is perpendicular to coil. If coil is dragged out then the charge through the galvanometer is \( 32 \mu C . \) The magnetic field is?
\( \mathbf{A} \cdot 6.55 \mathrm{T} \)
B . 5.66 न
c. 0.655 न
D. 0.566 न


In which of the following elaters are found?
A. Angiosperms
B. Bryophyta
c. Algae
D. Bacteria


Which one is chain growth polymer?
A. Teflon
B. Nylon-6
c. Nylon- 66
D. Bakelite


In cellulose, \( D- \) glucose units are joined by?
A. \( \alpha-1,4 \) glycosidic linkage
B. \( \beta-1,6 \) glycosidic linkage
c. \( \beta-1,4 \) glycosidic linkage
D. peptide linkage


Bouncing of light into the same medium, from which the light ray is incident is termed as:
\( A \). refraction
B. dispersion
c. reflection
D. scattering


The rate of the reaction \( A \rightarrow \) Products,
at the initial concentration of \( 3.24 \times \)
\( 10^{-2} M \) is 9 times its rate at another
initial concentration of \( 1.2 \times 10^{-3} M \)
The order of the reaction is:


Write any four differences between
physisorption and chemisorption


Explain Eubacterium


A spinal nerve takes nerve impulses:
A. to the CNS
B. away from the cNS
\( c . \) both to and away from the cNS
D. only inside the cNS


A rational number is such that when
you multiply it with \( \frac{5}{2} \) and add \( \frac{2}{3} \) to the
product, you get \( -\frac{7}{12} . \) What is the
number?
A \( \cdot-\frac{4}{3} \)
в. \( -\frac{1}{2} \)
\( c \cdot \frac{4}{3} \)
D. \( -\frac{5}{3} \)


Heat of conduction flows in the
direction of decreasing:
A. Temperature
B. Pressure
c. Density
D. None of these


Two identical bar magnets are held perpendicular to each other with a certain separation, as shown below. The
area around the magnets is divided into
four zones. Given that there is a neutral
point it is located in.
A. Zone I
B. Zone II
C. Zone III
D. Zone IV


Attempt the following:
The price P for demand D is given as
\( P=183+120 D-3 D^{2} . \) Find D for
which the price is increasing.


The sine of the angle between the vectors \( \hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}+\boldsymbol{2} \hat{\boldsymbol{k}} \) and \( \boldsymbol{2} \hat{\boldsymbol{i}}-\boldsymbol{4} \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) is
A \( \cdot \sqrt{\frac{155}{156}} \)
в. \( \sqrt{\frac{115}{116}} \)
c. \( \sqrt{\frac{115}{147}} \)
D. \( \sqrt{\frac{157}{158}} \)


\( \operatorname{Let} U=\{1,2,3,4,5,6,7,8,9\}, A= \)
\( \{1,2,3,4\}, B=\{2,4,6,8\} \) and \( C= \)
\( \{3,4,5,6\} . \) Find (i) \( A^{\prime}(\text { ii }) B^{\prime}(\text { iii) }(A \cup \)
\( C)^{\prime}(\text { iv })(A \cup B)^{\prime}(v)\left(A^{\prime}\right)^{\prime}\left(\text { vi) }(B-C)^{\prime}\right. \)


A small magnet is placed perpendicular to a uniform magnet field. The forces acting on the magnet will result in :
A. Rotational motion
B. Translatory motion
c. No motion at al
D. Translational and rotational motion both


What is the angular speed of the second hand of a clock? If the second hand is
10cm long, then find the linear speed of
its tip. (in \( r a d / s \text { and } m / s) \)
В. 1047,0.01047
c. 0.1047,1047
D. 0.0047,0.01047


An iron sphere of mass \( 10 \mathrm{kg} \) is dropped from a height of \( 80 \mathrm{cm} . \) If the downward
acceleration of the sphere is \( 10 m s^{-2} \)
calculate the momentum of the sphere
when it just strikes the ground
A. \( 100 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
B. \( 40 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
c. \( 60 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
D. \( 75 \mathrm{kg} \mathrm{m} / \mathrm{s} \)


Common ancestor of apes and man is
A. Porapithecus
B. Cro-Magnon
C. Dryopithecous
D. Australopithecus


An electron microscope uses electrons accelerated by a voltage of \( 50 \mathrm{kV} \) Determine the de-Broglie wavelength associated with the electrons. Taking
other factors, such as numerical
aperture etc. to be same, how does the resolving power of an electron microscope compare with what of an
optical microscope which uses yellow light?


If \( \frac{\mathbf{9}^{n} \times \mathbf{3}^{5} \times(\mathbf{2 7})^{\mathbf{3}}}{\mathbf{3} \times(\mathbf{8 1})^{4}}=\mathbf{2 7}, \) then the value
of \( n \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B . 2
\( c \cdot 3 \)
D.


In a circle with center \( O, \) a chord \( P Q \) is
such that \( \boldsymbol{O} \boldsymbol{M} \pm \boldsymbol{P} \boldsymbol{Q} \) meeting \( \boldsymbol{P} \boldsymbol{Q} \) at \( \boldsymbol{M} \)
Then
\( ^{\mathbf{A}} \cdot O Q^{2}=O M^{2}+\frac{1}{2} P Q^{2} \)
B. \( O Q^{2}=O M^{2}+\frac{1}{4} P Q^{2} \)
c. \( M Q^{2}=O M^{2}-O Q^{2} \)
D. \( O M^{2}=M Q^{2}-O Q^{2} \)


Earthworm respires by
A. Clitellum
B. Ctenidia
c. Moist skin
D. Typhlosole


An electron, moving along the \( x \) -axis with an initial energy of \( 100 e V \), enters a region of magnetic field \( \vec{B}=(1.5 \times \)
\( \left.10^{-3} T\right) \hat{k} \) at \( S(\text { See figure }) . \) The field
extends between \( x=0 \) and \( x=2 c m \)
The electron is detected at the point \( Q \) on a screen placed \( 8 \mathrm{cm} \) away from the point S. The distance d between P and Q
(on the screen) is :
(electron's charge \( =1.6 \times 10^{-19} \mathrm{C}, \) mass
of electron \( \left.=9.1 \times 10^{-31} k g\right) \)
A \( .12 .87 \mathrm{cm} \)
В. \( 1.22 \mathrm{cm} \)
c. \( 11.65 \mathrm{cm} \)
D. \( 2.25 \mathrm{cm} \)


The induced current produced in a closed coil is always in nature.
A. strength
B. alternating
c. less
D. primary


Assertion
When spinning ball is thrown it deviates from its usual path in flight.
Reason
Time of flight will remain same if axis of
rotation is vertical
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


The third member of the family of alkenynes has the molecular formula?
A \( \cdot C_{6} H_{6} \)
B. \( C_{5} H_{6} \)
\( \mathbf{c} \cdot C_{6} H_{8} \)
D. \( C_{4} H_{4} \)


The power of the heater is \( 1000 W \) at
\( 1000^{\circ} \mathrm{C} . \) What will be its power at
\( 4000^{\circ} \mathrm{C} ? \)
Given, temperature coefficient of resistance of heater-wire is \( 1.4 \times \)
\( 10^{-40} C^{-1} \)
A \( .1 .42 \times 10^{3} W \)
в. \( 1.3 \times 10^{3} \mathrm{W} \)
c. \( 9.68 \times 10^{3} W \)
D . \( 1.08 \times 10^{3} W \)


In a triangle \( A B C \), a straight line parallel to \( B C \) intersects \( A B \) and \( A C \)
at point \( D \) and \( E \) respectively. If the
area of \( A D E \) is one-fifth of the area of
\( A B C \) and \( B C=10 \mathrm{cm}, \) then \( D E \)
equals
A . \( 2 \mathrm{cm} \)
в. \( 2 \sqrt{5} \) ст
\( c .4 \mathrm{cm} \)
D. \( 4 \sqrt{5} \mathrm{cm} \)


The sum of protons, electrons and neutrons in the heaviest isotope of hydrogen is:
\( \mathbf{A} \cdot \mathbf{6} \)
B. 5
\( c \cdot 4 \)
D. 3


Which of the following contains highest number of moles?
A. 90 g of water
B. \( 130 \mathrm{g} \) of carbon dioxide
c. 89.6 L of oxygen at s.T.P.
D. \( 12 \mathrm{g} \) of hydrogen gas


Describe the phloem transport from
source to sink


Tossing a coin is an example of
A. Infinite discrete sample space
B. Finite sample space
c. continuous sample space
D. None of these


Given \( f(x) \) is a linear function and \( \boldsymbol{f}(\mathbf{2})=\mathbf{3} \) and \( \boldsymbol{f}(-\mathbf{6})=-\mathbf{1 3} . \) Find \( \boldsymbol{y} \)
intercept of \( \boldsymbol{f}(\boldsymbol{x}) \)
A . -1
B.
c. 1
D.


A particle is moving in \( x \) -y plane. At time \( t=0, \) particle is at \( (1 \mathrm{m}, 2 \mathrm{m}) \) and has velocity \( (4 \hat{i}+6 \hat{j}) \mathrm{m} / \mathrm{s}, \) At \( t=4 \mathrm{s} \)
particle reaches at \( (6 \mathrm{m}, 4 \mathrm{m}) \) and has velocity \( (2 \hat{i}+10 \hat{j}) \mathrm{m} / \mathrm{s} \). In the given time interval, find.
(a) average velocity,
(b) average acceleration and
(c) from the given data, can you find average speed?


school organized a seminar in which he invited parents and principle to discuss the serious issue of diabetes and
depression in students They all resolved
this issue by strictly banning the junk food in school and to introduce healthy snacks and drinks like soup, lassi, milk etc in school canteens. They also
decided to make compulsory half an hour physical activities for the students in the morning assembly daily After six months, Mr, Roy conducted the health survey in most of the schools and
discovered a tremendous improvement in the health of students.
After reading the above passage, answer the following:
(i) What are the values (at least two)
displayed by Mr.Roy?
(ii) As a student, how can you spread
awareness about this issue?
(iii) What are tranquilizers? Give an example.
(iv) Why is use of aspartame limited to cold foods and drinks?


When heat energy is supplied to the substance, kinetic energy of its molecules:
A. Increases
B. Decreases
c. Remains Same
D. cannot be predicted


Museum is a centre of
A. Documentation
B. Experiments
c. Communication
D. None of the above


Two cells of emf's approximately \( 5 V \) and
10V are to be accurately compared
using a potentiometer of length \( 400 \mathrm{cm} \)
A. The battery that runs the potentiometer should have voltage of \( 8 \mathrm{V} \)
B. The battery of potentiometer can have a voltage of \( 15 \mathrm{V} \) and \( R \) adjusted so that the potential drop across the wire slightly exceeds \( 10 \mathrm{V} \)
C. The first portion of \( 50 \mathrm{cm} \) of wire itself should have a potential drop of \( 10 \mathrm{v} \)
D. Potentiometer is usually used for comparing resistances and not voltages


In an isosceles triangle \( A B C, \) with
\( A B=A C, \) the bisectors of \( \angle B \) and \( \angle C \)
intersect each other \( O . \) Join \( A \) to \( O \)
Show that:
\( \boldsymbol{O} \boldsymbol{B}=\boldsymbol{O} \boldsymbol{C} \)


Which compound of oxygen is most likely to contain an \( \boldsymbol{O}-\boldsymbol{O} \) bond?
A \( \cdot C O_{2} \)
в. \( N O_{2} \)
\( c \cdot s O_{2} \)
D. \( H_{2} O_{2} \)
E \( . T i O_{2} \)


Mendel's principles are related to
A. Evolution
B. Reproduction
C. Variations
D. Heredity


\( f \frac{a_{0}}{n+1}+\frac{a_{1}}{n}+\frac{a_{2}}{n-1}+\dots+\frac{a_{n-1}}{2}+ \)
\( a_{n}=0, \) then the equation \( a_{0} x^{n}+ \)
\( a_{1} x^{n-1}+\cdots+a_{n-1} x+a_{n}=0 \) has, in
the interval \( (\mathbf{0}, \mathbf{1}) \)
A. Exactly one root
B. Atleast one root
c. Atmost one root
D. No root


The moment o inertia of a circular disc
of radius \( 2 m \) and mass \( 1 k g \) about an
axis passing through the center of
mass but perpendicular to the plane of
the disc is \( 2 k g-m^{2} . \) Its moment of
inertia about an axis parallel to this
axis but passing through the edge of
the disc is (see the given figure.)
\( \mathbf{A} \cdot 8 k g-m^{2} \)
\( \mathbf{B} \cdot 4 k g-m^{2} \)
\( \mathbf{c} \cdot 10 k g-m^{2} \)
\( \mathbf{D} \cdot 6 k g-m^{2} \)


If \( \epsilon_{0} \) and \( \mu_{0} \) are the permittivity and
permeability of free space and \( \epsilon \) and \( \mu \) are the corresponding quantities for a medium, then refractive index of the
medium is:
A. \( \sqrt{\frac{\mu_{0} \epsilon_{0}}{\mu \epsilon}} \)
в. \( \sqrt{\frac{\mu \epsilon}{\mu_{0} \epsilon_{0}}} \)
c. 1
D. Insufficient information


A transformer has an efficiency of \( 80 \% \) It works at \( 4 \mathrm{kW} \) and \( 100 \mathrm{V} \). If the
secondary voltage is \( 240 \mathrm{V} \), the current in primary coil is
\( \mathbf{A} \cdot 0.4 \mathrm{A} \)
B. 4 A
c. 10 А
D. 40 A


If no external force acts on a system
A. Velocity of centre of mass remains constant
B. Total kinetic energy of the system remains constant
C. Angular momentum of system may change
D. Total mechanical energy of the system remains constant


The length of a rectangular garden is 2 feet longer than 3 times its width. If the perimeter of the garden is 100 feet, find the width of the garden.
A . 12
B. 20
c. 40
\( D \)


ABCDE is regular pentagon. The bisector
of \( \angle A \) of the pentagon meets the side
CD in M. Then the measure \( \angle A M C \) is
A \( .54^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 90^{0} \)
D. \( 100^{\circ} \)


\( A B C D \) is a parallelogram, \( A E \) is
perpendicular to \( D C, \) If \( D C=20 \mathrm{cm} \)
\( A D=5 \mathrm{cm} \) and the area of the
parallelogram is \( 40 \mathrm{cm}^{2} \). Find \( D E \)


In ECG, P-R interval corresponds to
A. Time delay in A-V node
B. S-A nodal conduction time
C. Increased ventricular contraction
D. Time interval between onset of ventricular contraction


Find \( \mathrm{k} \) so that the function
\[
\begin{array}{cc}
\boldsymbol{f}(\boldsymbol{x})=\left\{1-\cos 2 \boldsymbol{x} / 2 \boldsymbol{x}^{2}\right. & \boldsymbol{x} \neq \mathbf{0} \\
\{\boldsymbol{k} & \boldsymbol{x}=\mathbf{0}
\end{array}
\]
is coutinous at \( x=0 \)


A parallel beam of light is incident on a
glass prism in the shape of a quarter
cylinder of radius \( R=0.05 m \) and
refractive index \( n=1.5 \) placed on a
horizontal table as shown in the figure.
Beyond the cylinder, a patch of light is
found whose nearest distance \( x \) from
the cylinder is
A \( \cdot(3 \sqrt{3}-4) \times 10^{-2} m \)
B \( \cdot(3 \sqrt{2}-2) \times 10^{-2} m \)
\( \mathbf{c} \cdot(3 \sqrt{5}-5) \times 10^{-2} m \)
D. \( (3 \sqrt{2}-3) \times 10^{-2} m \)


The depth at which the value of \( g \)
becomes \( 25 \% \) of that at the surface of
the earth is (in \( \mathrm{Km} \) )
\( A \cdot 4800 \)
B. 2400
c. 3600
D. 1200


What is minimum value of \( \sec ^{2} \theta+ \)
\( \cos ^{2} \theta ? \)


A chord \( P Q \) of a circle of radius \( 10 \mathrm{cm} \)
subtends an angle of \( 60^{\circ} \) at the centre of the circle Find the area of major and
minor segments of the circle.


In which of the following, do all the \( C \) atoms not have the same hybridisation
\( ? \)
This question has multiple correct options
\( \mathbf{A} \cdot\left(C H_{3}\right)_{3} C^{\bullet} \)
в. \( _{C H_{3}-C H}^{\text {ต่ }}-C H_{3} \)
c. \( C H_{2}=C=C H_{2} \)
D. \( _{C H_{2}}=C_{H}^{\text {of }} \)


Formalin is \( 40 \% \) aqueous solution of :
A. Methanal
B. Methanoic acid
c. Methanol
D. Methanamine


Which of the following is not true for
Nostoc?
A. Autotrophic
B. Filamentous
c. Macroscopic
D. Prokaryotic


Which of the following property is not
shown by \( \boldsymbol{H}_{2} \boldsymbol{S} \) ?
A. acidic property
B. reducing property
c. oxidising property
D. both acidic and reducing property


\( f\left(a_{1}, a_{2}, a_{3}, \dots \) from a geometric \right.
progression and \( a_{i}>0 \) for all \( i \geq 1 \)
\[
\operatorname{then}\left|\begin{array}{ccc}
\log \boldsymbol{a}_{m} & \log \boldsymbol{a}_{m+1} & \log \boldsymbol{a}_{m+2} \\
\log \boldsymbol{a}_{m+3} & \log \boldsymbol{a}_{m+4} & \log \boldsymbol{a}_{m+5} \\
\log \boldsymbol{a}_{m+\boldsymbol{6}} & \log \boldsymbol{a}_{m+\boldsymbol{7}} & \log \boldsymbol{a}_{m+8}
\end{array}\right| \text { is }
\]
equal to
\( \mathbf{A} \cdot \log a_{m+8}-\log a_{m} \)
B. \( \log a_{m} \)
\( \mathbf{c} \cdot 2 \log a_{m+1} \)
D.


The net magnetic flux through any closed surface, kept in a uniform magnetic field is?
A. zero
в. \( \frac{\mu_{o}}{4 \pi} \)
c. \( 4 \pi \mu_{o} \)
D. \( \frac{4 \mu_{o}}{\pi} \)


The A.M. of two numbers is 34 and their
G.M. is \( 16 . \) The two numbers are
A . 60,8
в. 64,4
c. 56,12
D. 52,16


The potential difference between the two plates of a parallel plate capacitor
is constant. When air between the
plates is replaced by dielectric material, the electric field intensity:
A. Decreases
B. Remains unchanged
c. Becomes zero
D. Increases


Find the multiplicative inverse of \( (\pi- \)
\( \frac{22}{7} \)


Urea was first organic compounds to be synthesised by:
A. laminar
B. wohlar
c. beryine
D. haber


Find out the current flowing through
resistor \( \boldsymbol{R}_{1} \)


If true enter 1 , else enter 0 .
The \( \pi \) -electrons in ozone \( \left(O_{3}\right) \) are
delocalised


Name any four life processes in living
things.


In an LED device, the intensity of emitted light
A. increases continuously with the forward current of the diode
B. increases continuously with the forward current of the diode, reaches a maximum and then decreases.
C. decreases continuously with the forward current of the diode.
D. decreases continuously with the forward current of the diode, reaches a minimum and then increases.


The principal argument of \( 1+\sqrt{2}+i \) is
A \( \cdot \frac{\pi}{3} \)
в.
c.
D.


The sum of the series \( 1+\frac{1}{6}+\frac{1}{18}+ \)
\( \frac{7}{324}+\ldots . \infty, \) is


In the figure shown \( X \) and \( Y \) components of acceleration of center of mass are [All
surfaces are smooth]
A \( \cdot\left(a_{C M}\right)_{X}=\frac{m_{1} m_{2} g}{m_{1}+m_{2}} \)
В. \( \left(a_{C M}\right)_{X}=\frac{m_{1} m_{2} g}{\left(m_{1}+m_{2}\right)^{2}} \)
\( ^{\mathrm{c}}\left(a_{C M}\right)_{Y}=\left(\frac{m_{2}}{m_{1}+m_{2}}\right)^{2} g \)
D. Both (B) and (C) are correct


Noble gases have a stable electronic configuration because
A. valence shell is complete
B. valence shell is incomplete
c. it has four valence electrons
D. None of the above


Which is called lazy gas?
\( A \cdot K r \)
B. Ar
c. не
D. Ne


During extraction of iron, which of the following reaction(s) exhibit development of elemental impurities in
iron?
This question has multiple correct options
A. \( C a O+S i O_{2} \rightarrow C a S i O_{3} \)
в. \( M n O_{2}+C \stackrel{\Delta}{\longrightarrow} M n+C O \)
\( \mathrm{c} \cdot \mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2} \stackrel{\Delta}{\longrightarrow} P_{4} \mathrm{O}_{10} \frac{\mathrm{C}}{\Delta} P_{4} \)
D. \( \operatorname{si} O_{2}+2 C \stackrel{\Delta}{\longrightarrow} S i+2 C O \uparrow \)


\( \sin ^{-1} x+\sin ^{-1}\left(\frac{1}{x}\right)+\cos ^{-1} x+ \)
\( \cos ^{-1}\left(\frac{1}{x}\right)= \)
\( \mathbf{A} \cdot \pi \)
\( B \cdot \frac{\pi}{2} \)
\( c \cdot \frac{3 \pi}{2} \)
D. \( 2 \pi \)


Calculate the ratio of the equivalent capacitance of the circuit when two identical capacitors are in series to that when they are in parallel?
A \( \cdot \frac{1}{4} \)
B. \( \frac{1}{2} \)
c.
D. 2
E . 4


If the eccentricity of a hyperbola is \( \frac{5}{4} \) then find the eccentricity of its conjugate hyperbola.


Cr has electronic configuration as:
A \( \cdot 3 s^{2} 3 p^{6} 3 d^{1} 4 s^{1} \)
B . \( 3 s^{2} 3 p^{6} d^{5} 4 s^{1} \)
c. \( 3 s^{2} 3 p^{6} 3 d^{6} \)
D. None of the above


A charge \( Q \) is enclosed by a Gaussian spherical surface of radius R. If the
radius is doubled, then the outward
electric flux will :
A. be doubled
B. increase four times
c. be reduced to half
D. remain the same


Q Type your question
\( \mathbf{A} \)
B.
\( \mathbf{C} \)
\( D \)


"It has not escaped our notice that the specific pairing we have postulated immediately suggests a possible copying mechanism for genetic material" - This is written by
A. Meselson and Stahl
B. Archibold Garrod
c. severo ochoa
D. watson and Crick


In which phylum, the coelom is formed by fusion of gut pouches during embryonic stage?
A. Platyhelminthes
B. Aschelminthes
c. Annelida
D. Hemichordata


A wire stretches by a certain amount under a load. If the load \( \& \) radius both
are increased to 4 time. Find the stress
cause in the wire.


In Young's double slit experiment, the
two slits act as coherent sources of
equal amplitude \( A \) and wavelength \( \lambda \). In
another experiment with the same set up the two slits are same of equal amplitude of wavelength \( \lambda \) but are
incoherent. The ratio of intensity of light at the mid point of the screen in the first to the second case is?
A . 4: 1
B . 2: 1
\( c \cdot 1: 1 \)
D. 1: 2


The value of \( \lim _{n \rightarrow \infty} \cos \frac{x}{2} \cos \frac{x}{2^{2}} \ldots \cos \frac{x}{2^{n}} \)
is
A . 1
B. \( \frac{\sin x}{x} \)
c. \( \frac{x}{\sin x} \)
D. none of these


The free path of a gas molecule is the
distance through which a molecule
moves:
A. Between the two opposite walls of the container
B. In one second
c. Between two successive collisions
D. None of these


Shell coiling in Limnaea (snail) is an example of
A. Maternal inheritance
B. Biparental inheritance
c. Dauermodification
D. None of the above


Which of the following is correct electronic configuration of argon?
A. 2,8
B. 2,8,8
c. 2,8,1
D. 8,2,8


Which statement is INCORRECT.
A. Phenol has smaller dipolemoment than methanol.
B. Haloarenes are insoluble in water but are soluble in
benzene.
C. Chloroform contains chlorine but gives no reaction with \( A g N O_{3} \) solution.
D. Ethanol has much lower pka value than phenol.


Write any three differences between enantiomers and diastereomers?


For the cell
\( \boldsymbol{T} l\left|\boldsymbol{T} \boldsymbol{l}^{+}(\boldsymbol{0} \cdot \boldsymbol{0} \boldsymbol{0} \mathbf{1} \boldsymbol{M}) \| \boldsymbol{C} \boldsymbol{u}^{2+}(\boldsymbol{0} \cdot \mathbf{1} \boldsymbol{M})\right| \boldsymbol{C} \boldsymbol{u} \)
the \( E_{\text {cell}} \) at \( 25^{\circ} \mathrm{C} \) is \( 0.83 \mathrm{V} \) which can be
increased by:
This question has multiple correct options
A . increasing \( \left[C u^{2+}\right] \)
B. increasing \( \left[T i^{+}\right] \)
c. decreasing \( \left[C u^{2+}\right] \)
D. decreasing \( \left[T l^{+}\right] \)


Two beams of light have intensities of
\( I_{0} \) and \( 4 I_{0} \) in double-slit experiment. The phase difference between the beams is \( \frac{\pi}{4} \) at point \( A \) and \( \frac{\pi}{2} \) at point \( B \) Then, difference between intensities at
\( A \) and \( B \) is
A \( \cdot 2 \sqrt{2} I_{0} \)
(i) \( \sqrt{2} I_{0} \)
в. \( I_{0} \)
c. \( 4 I_{0} \)
D. \( 5 I_{0} \)


Fool's gold is:
A \( \cdot C u_{2} S \)
в. \( F e S_{2} \)
c. \( A l_{2} O_{3} \)
D. \( C u F e S_{2} \)


Draw a circle and mark a diameter.


Name the reagent that is used in leaching of gold.
A. carbon
B. Sodium cyanide
c. Carbon monoxide
D. lodine


There are three bags \( B_{1}, B_{2} \) and \( B_{3} . \) The
bag \( \boldsymbol{B}_{1} \) contains \( \mathbf{5} \) red and \( \mathbf{5} \) green balls.
\( B_{2} \) contains 3 red and 5 green balls and
\( B_{3} \) contains 5 red and 3 green balls.
Bags \( B_{1}, B_{2} \) and \( B_{3} \) have probabilities \( \mathbf{3} / \mathbf{1 0}, \mathbf{3} / \mathbf{1 0} \) and \( \mathbf{4} / \mathbf{1 0} \) respectively of
being chosen. A bag is selected at random and a ball is chosen at
random from the bag. Then which of the following options is/are correct? This question has multiple correct options
A. Probability that the chosen ball is green, given that the selected bag is \( B_{3} \), equal \( \frac{3}{8} \)
B. Probability that the selected bag is \( B_{3} \), given that the chosen ball is green, equals \( \frac{5}{13} \)
C ' probability that the chosen ball is green equals \( \frac{39}{80} \)
D. Probability that the selected bag is \( B_{3} \), given that the chosen ball is green, equals \( \frac{3}{10} \)


The locus of the centre of the circles
which touch both the circles \( x^{2}+y^{2}= \)
\( a^{2} \) and \( x^{2}+y^{2}=4 a x \) externally has the
equation:
A \( \cdot 12(x-a)^{2}-4 y^{2}=3 a^{2} \)
B \( \cdot 9(x-a)^{2}-5 y^{2}=2 a^{2} \)
C \( \cdot 8 x^{2}-3(y-a)^{2}=9 a^{2} \)
D. None of these


Evaluate \( \left|\begin{array}{cc}\sin 60^{\circ} & \cos 60^{\circ} \\ -\sin 30^{\circ} & \cos 30^{\circ}\end{array}\right| \)


In which of the following groups all are polysaccharides?
A. Sucrose, glucose and fructose
B. Maltose, lactose and fructose
c. Glycogen, sucrose and maltose
D. Glycogen, cellulose and starch


The amount of freshwater of the earth
frozen as polar or glacial ice is
A . 0.5\%
B. 0.02\%
c. \( 0.01 \% \)
D. 1.7\%
E. 2.5\%


Which one has highest melting point?
A . \( N a C l \)
в. \( N a B r \)
\( c . N a F \)
D. Nal


Name the effect of current responsible for the glow of the bulb in an electric circuit.
A. Chemical
B. Heating
c. Magnetic


Let \( \boldsymbol{f}:\left(-\frac{\boldsymbol{\pi}}{\mathbf{2}}, \frac{\boldsymbol{\pi}}{\mathbf{2}}\right) \rightarrow \boldsymbol{A} \) be defined by
\( \boldsymbol{f}(\boldsymbol{x})=\sin \boldsymbol{x} . \) If \( \boldsymbol{f} \) is a bijection, write set
\( \boldsymbol{A} \)


The process of depositing a thin layer of desired metal on another metal by means of electricity is called:
A. electrolysis
B. dialysiss
c. electroplating
D. displacement


The value of the integer \( \int_{0}^{\pi} e^{\cos ^{2} x} \cdot \cos ^{3}(2 n+1) x d x, n \) integer
is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
c. \( 2 \pi \)
D. none of these


The enolic form of acetone contains:
A. \( 9 \sigma \) -bonds, \( 1 \pi \) -bond and 2 lone pairs
B. \( 8 \sigma \) -bonds, \( 2 \pi \) -bond and 2 lone pairs
C. \( 10 \sigma \) -bonds, \( 2 \pi \) -bond and 1 lone pairs
D. \( 10 \sigma \) -bonds, \( 1 \pi \) -bond and 2 lone pairs


\( \overrightarrow{D C} \perp \overline{A B}, \) then \( \angle C D B \) is equal to:
A \( .180^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 90 \)
D. 120


If \( \boldsymbol{A}=\{\mathbf{2}, \mathbf{4}\{\mathbf{5}, \mathbf{6}\}, \mathbf{8}\}, \) then which one of
the following statements is not correct?
\( \mathbf{A} \cdot\{5,6\} \subseteq A \)
\( \mathbf{B} \cdot\{5,6\} \in A \)
c. \{2,4,8\}\( \subseteq A \)
D. \( 2,4,8 \in A \)


The increase in the internal energy of
\( 10 g \) of water when it is heated from
\( 0^{\circ} \) to \( 100^{\circ} \) and converted into steam at
\( 100 k P a \) is given as \( x \times 10^{2} J . \) Find \( x \)
The density of steam \( =\mathbf{0 . 6} k g / m^{3} \)
Specific heat capacity of water \( = \) \( 4200 J / k g-^{\circ} C \) and the latent heat of
vaporization of water \( =2.5 \times \)
\( \mathbf{1 0}^{\mathbf{6}} \boldsymbol{J} / \boldsymbol{k} \boldsymbol{g} \)


How many maximum electrons \( f \)
subshell can accommodate?
A . 12
B. 14
\( c \cdot 8 \)
D. 10


Which of the following explains, how
progeny can possess the combinations of traits that none of the parent
possessed?
A. Chromosome theory
B. Polygenic inheritance
c. Law of segregation
D. Law of independent assortment


The lightest noble gas atom contains the following particles in its nucleus:
A. 4 protons
B. 3 neutrons
c. 3 protons and 1 neutron
D. 2 protons and 2 neutrons


An organic compound containing nitrogen, on heating strongly with
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) gives ammonium sulphate
which on treatment with excess of
NaOH liberates ammonia.
A. True
B. False


The force per unit length between two long straight conductors carrying currents 3 A each in the same direction
and separated by a distance of \( 2.0 \mathrm{cm} \) is
A \( \cdot 9 \times 10^{-7} N / m \)
В. \( 9 \times 10^{-6} N / m \)
c. \( 9 \times 10^{-5} N / m \)
D. \( 9 \times 10^{-4} N / m \)


Peptization of \( S n O_{2} \) by \( N a O H \) gives:
\( \mathbf{A} \cdot\left[\operatorname{Sn} O_{2}\right] \operatorname{Sn} O_{3}^{2-}: 2 N a^{+} \)
B \( \cdot\left[\operatorname{Sn} O_{2}\right] S n^{4+}: O^{2} \)
\( \mathbf{c} \cdot\left[\operatorname{Sn} O_{2}\right] N a: O H^{-} \)
D・ \( \left[\operatorname{Sn} O_{2}\right] S n^{4+}: O H^{-} \)


Brown glass and cement have, which element common in them:
A . \( F e \)
в. \( A l \)
\( c . N a \)
D. all of these


Select incorrect statements W.r.t.
dinoflagellates
A. Theca is absent in zooxanthellae
B. Ribbon like flagellum is present in girdlel
c. Have condensed chromosomes with histones
D. Have noncontractile vacuole


Hydrogen bond are present in:
This question has multiple correct options
\( A \cdot \) ice
B. water
C . solid carbon dioxide
D. \( H F \)


Which of the following is the characteristic feature of an isotopes?
A. Same number of electrons and protons but different number of neutrons
B. Same number of electrons but different number of protons
c. Same number of neutrons but different number of electrons
D. None of the above


Which of the following semi-conducting devices is used as voltage regulator?
A. Zener diode
B. LASER diode
c. Photo diode
D. Solar cell


The value of the determinant
\( \left|\begin{array}{lll}k a & k^{2}+a^{2} & 1 \\ k b & k^{2}+b^{2} & 1 \\ k c & k^{2}+c^{2} & 1\end{array}\right| \) is
A. \( k(a+b)(b+c)(c+a) \)
B. \( k a b c\left(a^{2}+b^{2}+c^{2}\right) \)
c. \( k(a-b)(b-c)(c-a) \)
D. \( k(a+b-c)(b+c-a)(c+a-b) \)


The surface area of a solid sphere is
increased by \( 21 \% \) without changing its shape.Find the percentage increase in its :
(i)radius
(ii)volume


The total number of \( \pi \) electrons in the
given structure are :
\( A \cdot 12 \)
B. 16
\( c \)
D


If \( A \) is a matrix of order \( 3 \times 3 \) then find
\( |\boldsymbol{a} \boldsymbol{d} \boldsymbol{j} \boldsymbol{A}| \) where \( |\boldsymbol{A}|=\boldsymbol{2} \)


A common emitter amplifier is designed with \( n \) -p-n transistor \( (\alpha= \)
0.99). The input impedance is \( 1 k \Omega \) and
load is \( 10 k \Omega . \) The voltage will be :
A . 9900
B. 99
c. 9.9
D. 990


Solve \( \int \frac{2 x \ln \left(x^{2}-1\right)}{\left(x^{2}-1\right)} d x \)


If \( a+b=5 \) and \( a^{2}+b^{2}=13, \) find ab


A biconvex lens has radii of curvature of
two faces \( 0.1 \mathrm{m} \) and 0.12 respectively. If the focal length of the lens is \( 0.1 \mathrm{m} \). Find
(i) the refractive index of the material of
lens
(ii) power of lens (iii) nature and position of the image of an object placed at a distance of \( 6 \mathrm{cm} \) from the lens.


Greater the mass, greater is the inertia of the body. Type 1 for true and 0 for false


\( \boldsymbol{C H}_{3}-\stackrel{\boldsymbol{C} \boldsymbol{H}_{3}}{\boldsymbol{C} \boldsymbol{H}}-\boldsymbol{C H}_{3}(\operatorname{excess})+\boldsymbol{B} \boldsymbol{r}_{2} \stackrel{\boldsymbol{h} \boldsymbol{v}}{\boldsymbol{C H}_{3}} \)
\( \boldsymbol{C H}_{3}-\underset{\boldsymbol{B} \boldsymbol{r}}{\boldsymbol{C}}-\boldsymbol{C H}_{3}+\boldsymbol{C H}_{3}-\boldsymbol{C} \boldsymbol{H}- \)
\( \boldsymbol{C H}_{2}-\boldsymbol{B r} \)
The relative reactivity of \( 1^{\circ} H, 2^{\circ} H \) and
\( \mathbf{3}^{o} \boldsymbol{H} \) in bromination reaction has been
found to be 1: 82: 1600 respectively. In the reaction the percentage yields of the products \( (A) \) and \( (B) \) are expected to be
A. 99.4\%, 0.6\%
B. 50\%, 50\%
c. ०.6\%, 99.4\%
D. 80\%, 20\%


If \( a_{1}, a_{2}, \dots \dots, a_{24} \) are in \( A P \) and \( a_{1}+ \)
\( \boldsymbol{a}_{\boldsymbol{5}}+\boldsymbol{a}_{\boldsymbol{1 0}}+\boldsymbol{a}_{\boldsymbol{1 5}}+\boldsymbol{a}_{\boldsymbol{2 0}}+\boldsymbol{a}_{\boldsymbol{2 4}}=\mathbf{2 2 5} \) then
the sum of 24 terms of this AP is.
A. 900
в. 450
\( c \cdot 225 \)
D. None of these


Derive an expression for mechanical
force per unit area of surface charge
density


Prove that for all complex numbers \( z \) with \( |z|=1 \) \( \sqrt{\mathbf{2}} \leq|\mathbf{1}-\boldsymbol{z}|+\left|\mathbf{1}+\boldsymbol{z}^{2}\right| \leq \mathbf{4} \)


At normal temperature, \( \boldsymbol{H}_{2} \boldsymbol{O} \) is liquid
while \( H_{2} S \) is a gas.Why?


Hexane and 3-methylpentane are examples of:
A. enantiomers
B. stereoisomers
c. diastereomers
D. none of these


The Kirchhoff's first law \( \left(\sum i=0 \) ) and \right. second law \( \left(\sum i R=\sum E\right), \) where the symbols have their usual meanings, are respectively based on:
A. Conservation of charge, conservation of \( m \)
B. Conservation of energy, conservation of charge
c. conservation of momentum, conservation of charge
D. conservation of charge, conservation of energy


Factorize :
\( 8(a+1)^{2}+2(a+1)(b+2)-15(b+ \)
2)\( ^{2} \)


\( _{19}^{39} K \) and \( _{20}^{40} C a \) are :
A. Isotopes
B. Isobars
C. Isotones
D. Isodiaphers


According to the size, identify the
correct decreasing order:
a) Original star
b) Red giant
c) White Dwarf
\( A \cdot a, b, c \)
B. b, c, a
\( c \cdot c, a, b \)
D. b, a, c


Arrange the following in the decreasing order of basic strength:
¡)Aniline
ii)p-nitroaniline
iii)p-toluidine
A. i > ii > ii
B. ii>i>iii
\( c . \) iii \( >i>i \)
D. iii > ii > i


Two point charges each of \( 1 C \)
separated by 1 m distance experience a
force of \( 5.6 \times 10^{9} N \) in vacuum. How
much force is experienced by them if they are immersed in water., keeping the distance of separation between them same?
\( \boldsymbol{K}=\mathbf{8 0} \) for water.


What is echo?Waht are the necessary
conditions for its occurence? What is
SONAR?How is it used to determine the
depth of an ocean?


Which of the following is desirable in diesel and kerosene but is undesirable
in gasoline?
A. Paraffins
B. Mercaptans
c. Aromatics
D. Naphthenic acid


Find the domain of the function \( f \)
defined by \( f(x)=s q r t\left(x^{2}+1\right)+2 \)
where sqrt is the square root
A \( . R-\{2\} \)
в. \( R \)
\( c \cdot 2 \)
D. \( R-\{1\} \)


In an equilateral triangle \( \Delta A B C \) with
sides \( 5 \mathrm{cm} . \) Angle bisectors of \( \angle A, \angle B, \angle C \) meet at point \( 0 . \) Measures of OA approximately is
A . 2.5
B. 4
\( c .3 .2 \)
D. 2.8


Find the solution set of
\( \left|\begin{array}{ccc}2+x & 2-x & 2-x \\ 2-x & 2+x & 2-x \\ 2-x & 2-x & 2+x\end{array}\right|=0 \)


DNA and RNA differs by
A. Nitrogen bases and sugars
B. Nitrogen bases and phosphate groups
c. Number of C-atoms in sugars
D. sugar and phosphate groups


The number of vibrational degrees of
freedom for a \( C O_{2} \) molecule is
\( A \cdot 4 \)
B. 5
\( c \cdot 6 \)
D.


What is reflection? Give two examples.


The correct match is :
A. A-2, B-1, C-4, D-5
B. A-3, B-2, C-5, D-1
c. \( A-4, B-3, C-1, D-2 \)
D. A-1, B-2, C-4, D-3


If \( f(x)=x^{3} \) and \( g(x)=x^{3}-4 x \) in
\( -2 \leq x \leq 2, \) then consider the
statements:
(a) \( f(x) \) and \( g(x) \) satisfy mean value theorem.
(b) \( f(x) \) and \( g(x) \) both satisfy Rolle's
theorem.
(c) Only \( g(x) \) satisfies Rolle's theorem. Of these statements
A . (a) alone is correct.
B. (a) and (c) are correct
c. (a) and (b) are correct
D. None is correct


The equation of the ellipse having
vertices at (±5,0) and foci (±4,0) is
\( ^{A} \cdot \frac{x^{2}}{25}+\frac{y^{2}}{16}=1 \)
B. \( 9 x^{2}+25 y^{2}=225 \)
c. \( \frac{x^{2}}{9}+\frac{y^{2}}{25}=1 \)
D. \( 4 x^{2}+5 y^{2}=20 \)


Describe the coil and magnet experiment to demonstrate electromagnetic induction.


For two data sets, each of size \( 5, \) the
variance are given to be 4 and 5 and the corresponding means are given to be 2 and \( 4, \) respectively. The double of the variance of the combined data set is
A . 13
B. 12
\( c .5 .5 \)
D. 10


Two digit numbers are formed using the
digits 0,1,2,3,4,5 where digits are not repeated.
\( P \) is the event that the number so
formed is even
\( Q \) is the event that the number so
formed is greater than 50
\( R \) is the event that the number so
formed is divisible by 3

Then write the sample space \( S \) and
events \( P, Q, R \) using set notation.


A secondary cell after long use has an emf of \( 1.9 V \) and a large internal
resistance of \( 380 \Omega \). What maximum
current can be drawn from the cell?
Could the cell drive the starting motor of
a car?
\( \mathbf{A} \cdot 5 m A, \) yes
B. \( <5 m A \), Yes
\( \mathbf{c} .5 m A, \) No
\( \mathbf{D} \cdot<5 m A, \) No


Find the area of the base of a box of
height \( 4 \mathrm{cm} \) and lateral surface area
\( 120 \mathrm{cm}^{2}, \) if its length is twice its
breadth.


List \( A \) List \( \mathrm{B} \)
A. Dry Cell
(P) Primary cell
B. Lead storage battery
(Q) \( 38 \% H_{2} S O_{4} \)
C. Ni-Cd cell
\( (\mathrm{R}) M n O_{2}+C \)
D. \( H_{2}-O_{2} \) fuel cell
(S) Secondary cell
A \( \cdot \) A-P,R: B-Q,S:C-S:D-S
B. A-Q,R: B-P,S:C.C-P:D-Q
c. A-P, B-S:C-P,S :D-Q,R
D. A-R: B-Q:C-Q,S:D-P


\( \frac{\mathbf{2 2}}{\boldsymbol{x}+\boldsymbol{y}}+\frac{\mathbf{1 5}}{\boldsymbol{x}-\boldsymbol{y}}=\mathbf{5} \)
\( \frac{\mathbf{5 5}}{\boldsymbol{x}+\boldsymbol{y}}+\frac{\mathbf{4 5}}{\boldsymbol{x}-\boldsymbol{y}}=\mathbf{1 4} \)
A. \( x=-8, y=3 \)
в. \( x=-3, y=8 \)
c. \( x=8, y=3 \)
D. \( x=8, y=-3 \)


lonisation potential values of noble gases decrease down the group with increase in atomic size. Xenon forms
binary fluorides by the direct reaction of elements. Identify the correct statement(s) from below.
This question has multiple correct options
A. Only the heavier noble gases form such compounds
B. It happens because the noble gases have higher ionisation energies
c. It happens because the compounds are formed with electronegative ligands
D. octet of electrons provide the stable arrangements


Write the IUPAC name of the following
compound.
\[
\begin{aligned}
\mathrm{CH}_{3}-& \mathrm{C}^{\mathrm{CH}_{3}} \\
& \mathrm{CH}_{3} \mathrm{CI}
\end{aligned}
\]


\( \lim _{x \rightarrow 0}\left(\frac{a}{b}+\frac{\cos x}{b}\right) \)


Current flow takes place across a
conductor only when a p.d in maintained across its two ends.
A. True
B. False


In fig. find the values of \( x \) and \( y \) and \( t \)
Show that \( \boldsymbol{A B} \| \boldsymbol{C D} \)
A. \( x=100 \) and \( y=130 \)
B . \( x=230 \) and \( y=130 \)
c. \( x=130 \) and \( y=130 \)
D. None of these


\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left[\frac{\boldsymbol{\operatorname} \boldsymbol{\operatorname { a n } \boldsymbol { x }}-\boldsymbol{\operatorname { c o t } \boldsymbol { x }}}{\boldsymbol{\operatorname { t a n } \boldsymbol { x }}+\boldsymbol{\operatorname { c o t } \boldsymbol { x }}}\right]= \)
\( A \cdot 2 \sin 2 x \)
B. - -2 \( \sin 2 x \)
\( c \cdot 2 \cos 2 x \)
D. \( -2 \cos 2 x \)


A bag contains some white and some black balls, all combinations of balls
being equally likely. The total number of
balls in the bag is \( 10 . \) If three balls are drawn at random without replacement and all of them are found to be black,
the probability that the bag contains 1
white and 9 black balls is
A \( \cdot \frac{14}{55} \)
B. \( \frac{12}{55} \)
c. \( \frac{2}{11} \)
D. \( \frac{8}{55} \)


The ratio of energy of photon of \( \lambda=2000 \)
\( A^{o} \) to that of \( \lambda=4000 A^{o} \) is :
\( A \cdot 2 \)
B. 1/4
\( c \cdot 4 \)
D. \( 1 / 2 \)


The vibrations of a string of length \( 60 \mathrm{cm} \) fixed at both ends are
represented by the equation \( y= \) \( 4 \sin \left(\frac{\pi x}{15}\right) \cos (96 x t) \)
where \( x \) and \( y \) are in \( \mathrm{cm} \) and in seconds
A. what is the maximum displacement of a point at \( x= \) \( 5 \mathrm{cm}^{3} \)
B. where are the nodes located along the string?
c. what is the velocity of the particle at \( x=7.5 \mathrm{cm} \) at \( t= \) 0.25 sec?
D. write down the equations of the component waves whose superposition gives the above wave


The letter 'D' in D - carbohydrates
represents:
A. Dextrorotation
B. Direct synthesis
c. configuration
D. Mutarotation
E. Optical activity


Differentiate between:
Mitosis and.meiosis II


If \( \mathbf{A}=\left[\begin{array}{ll}\mathbf{3} & -\mathbf{4} \\ \mathbf{1} & -\mathbf{1}\end{array}\right] \) then \( \boldsymbol{A}^{k}= \)
\( \left[\begin{array}{cc}\mathbf{1}+\mathbf{2} \boldsymbol{k} & -\mathbf{4} \boldsymbol{k} \\ \boldsymbol{k} & \mathbf{1}-\mathbf{2} \boldsymbol{k}\end{array}\right] \)
where \( k \) is any \( + \) ve integer


Calcium and Magnesium salts like
cause hardness of water
This question has multiple correct options
A. bicarbonates
B. chlorides
C . sulphates
D. phosphates


A planet revolves about the sun in elliptical orbit. The arial velocity \( \left(\frac{\boldsymbol{d} \boldsymbol{A}}{\boldsymbol{d} \boldsymbol{t}}\right) \)
of the planet is \( 4.0 \times 10^{16} m^{2} / s . \) The
least distance between planet and the sun is \( 2 \times 10^{12} \mathrm{m} . \) Then the maximum
speed of the planet in \( \mathrm{km} / \mathrm{s} \) is
\( A \cdot 10 \)
B. 20
\( c \cdot 40 \)
D. none of these


Which nuclide is formed as a result of
this fission reaction?
\( _{92}^{235} U+_{0}^{1} n \rightarrow 3_{0}^{1} n+_{56}^{139} B a+ \)
A \( \cdot \frac{96}{33} \mathrm{Br} \)
B. 96
36
c. 彎 \( R b \)
\( b \)
E \( \cdot \frac{90}{33} \mathrm{Sr} \)


The area of a rectangular garden, ABCD,
is \( 100 m^{2} . \) Inside the garden there is a
rectangular lawn, EFGH, whose sides
are parallel to those of the garden. Find the area of the lawn, EFGH(in sq
metres).
A \( \cdot 110-5 x-\frac{200}{x} \)
B. \( 110+5 x-\frac{200}{x} \)
c. \( _{110}+5 x+\frac{200}{x} \)
D. \( 110-5 x+\frac{200}{x} \)


If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be a differentiable
function, such that \( \boldsymbol{f}(\boldsymbol{x}+\mathbf{2} \boldsymbol{y})= \)
\( \boldsymbol{f}(\boldsymbol{x})+\boldsymbol{f}(\boldsymbol{2} \boldsymbol{y})+\boldsymbol{4} \boldsymbol{x} \boldsymbol{y} \) for all \( \boldsymbol{x}, \boldsymbol{y} \in \boldsymbol{R} \)
then
A \( \cdot f^{\prime}(1)=f^{\prime}(0)+1 \)
B . \( f^{\prime}(1)=f^{\prime}(0)-1 \)
C \( \cdot f^{\prime}(0)=f^{\prime}(1)+2 \)
D. \( f^{\prime}(1)=f^{\prime}(0)+2 \)


A closed coil with a resistance R is
placed in a magnetic field. The flux linked with the coil is \( \phi \). If the magnetic
field is suddenly reversed in direction, the charge that flows through the coil will be:
A. \( \frac{\phi}{2 R} \)
в. \( \frac{\phi}{R} \)
c. \( _{2} \frac{\phi}{R} \)
D. zero


If in mixed fraction form \( \frac{19}{6} \) is equal to \( 3 \frac{x}{6}, \) then what is the value of \( x ? \)


There are 3 men and 2 women. a
'Gramswachhatta Abhiyan' committee of two is to be formed:
\( P \) is event that the committee should
contain at least one woman.
\( Q \) is event that the committee should
contain one man and one women.
\( R \) is the event there should not be a
women in the committee.
\( S \) is the sample space.
Which of the following options is
correct?
A \( . n(S)=10, n(P)=7, n(Q)=1, n(R)=3 \)
В. \( n(S)=10, n(P)=7, n(Q)=3, n(R)=3 \)
c. \( n(S)=10, n(P)=7, n(Q)=2, n(R)=3 \)
D. \( n(S)=10, n(P)=7, n(Q)=6, n(R)=3 \)


The solid form, snow and ice, is present
as
A. Ice caps at the poles of the earth.
B. Snow-covered mountains
c. Glaciers.
D. Ice caps at the poles of the earth, snow-covered mountains and glaciers


Explain the free radical mechanism of chlorination of methane.


Evaluate the following:
\( \sin ^{-1}(\sin 10) \)


The mean free path and rms velocity of
a nitrogen molecule at a temperature \( 17 \mathrm{C} \) are \( 1.2 \times 10^{-7} \mathrm{m} \) and
\( 5 \times 10^{2} \mathrm{m} / \mathrm{s} \) respectively.The time
between two successive collisions
A . \( 2.4 \times 10^{-10} \mathrm{s} \)
B . \( 1.2 \times 10^{-10} \mathrm{s} \)
c. \( 3.4 \times 10^{-13} \) s
D. 3.4 \( \times 10^{-10} \) s


A Crane had DDT level of 5 ppm in its
body. What would happen to the population of such birds?


Three stars \( A, B, C \) have surface
temperature \( T_{A}, T_{B} \) and \( T_{C} . \) A appears
bluish, B appears reddish and C
appears yellowish. We can conclude
that
A \( \cdot T_{A}>T_{c}>T_{B} \)
В \( \cdot T_{A}>T_{B}>T_{C} \)
c. \( T_{B}>T_{c}>T_{A} \)
D. \( T_{C}>T_{B}>T_{A} \)


Point (4,0) lies on
A . \( \overrightarrow{X O} \)
в. \( \overrightarrow{Y O} \)
\( c \cdot O \vec{X} \)
D. \( \overrightarrow{O Y} \)


The dispersion through a prism when a
narrow beam of white light is incident on one of its refracting surfaces, how many numbers of colors will get in the spectrum?
A. 7
B. 6
\( c \cdot 2 \)
\( D \)


\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{B r} \stackrel{\boldsymbol{a q} \boldsymbol{K O H}}{\rightarrow} \boldsymbol{A} \stackrel{\boldsymbol{K M n O}_{4} / \boldsymbol{H}^{+}}{\rightarrow} \)
\( \boldsymbol{B} \frac{N \boldsymbol{H}_{3}}{\Delta} \boldsymbol{C} \frac{\boldsymbol{B} \boldsymbol{r}_{2}}{a l k a l i} \boldsymbol{D} \)
D is:
A \( \cdot C H_{3} B r \)
в. \( C H_{3} C O N H_{2} \)
c. \( C H_{3} N H_{2} \)
D. \( C H_{2} B r_{2} \)


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


The arithmetic mean of the first \( n \)
natural numbers is
A \( \cdot \frac{(n+1)}{2} \)
в. \( \frac{(n-1)}{2} \)
c. \( \frac{n}{2} \)
D. None of these


Consider the following Lewis
Dot structure:
What is the formal charge of right-side
\( N \) atom?
\[
\left[\because \prod_{0}^{0} \ldots\right]^{-}
\]


\begin{tabular}{lllll}
Mark & \( 25- \) & \( 35- \) & \( 45- \) & \( 55- \) \\
obtained & 35 & 45 & 55 & 65 \\
Number of students & 7 & 31 & 33 & 17 \\
\hline
\end{tabular} Find mean


The \( n \) rows each contaning in cells in
series are joined in parallel. Maximum current is taken from this combination
across an external resistance of \( 3 \Omega \). If
the total number of cells used is 24 and
internal resistance of each cell is \( 0.5 \Omega \)
then
A. \( m=8, n=3 \)
в. \( m=6, n=4 \)
c. \( m=12, n=2 \)
D. \( m=2, n=12 \)


A straight copper wire of length \( 1000 \mathrm{m} \)
and cross-sectional area \( 1.0 \mathrm{mm}^{2} \)
carries a current 4.5 A. Assuming that one free electron corresponds to each copper atom.(Density of copper \( = \) \( 8.96 \times 10^{3} \mathrm{kg} m^{-3}, \) Atomic mass of
copper \( =63.5 \mathrm{g}, \) Resistivity of copper
wire \( =1.69 \times 10^{-8} \Omega \mathrm{m} \) ).
A. The time taken by an electron to displace from one end of the wire to the other is \( 4 \times 10^{6} \mathrm{s} \)
B. The sum of electric force acting on all free electrons in the given wire is \( 1 \times 10^{6} \mathrm{N} \)
C. The time taken by an electron to displace from one end of the wire to the other is \( 3 \times 10^{6} \)
D. Both (b) and (c)


Find the area of the region bounded by
the curve \( y^{2}=4 x \) and \( x=3 ? \)


\( A \) and \( B \) are two points on the axis and the perpendicular bisector respectively of an electric dipole. A and B are far away from the dipole and at equal distances from its centre. The fields at \( A \) and \( \mathrm{B} \) i.e. \( \overrightarrow{\boldsymbol{E}_{A}} \quad \) and \( \overrightarrow{\boldsymbol{E}_{B}} \) are respectively
such that
\( \mathbf{A} \cdot \overrightarrow{E_{A}}=\overrightarrow{E_{B}} \)
B . \( \overrightarrow{E_{A}}=2 \overrightarrow{E_{B}} \)
c. \( \overrightarrow{E_{A}}=-2 \overrightarrow{E_{B}} \)
D. \( \overrightarrow{E_{A}}=\frac{1}{2} \overrightarrow{E_{B}} \)


What are the possible of \( m_{5} \) when \( m_{1} \)
have \( +1,+2,+3 ? \)


\( N_{2} O_{5} \) decomposes according to equation:
\[
\mathbf{2} N_{2} \boldsymbol{O}_{\mathbf{5}} \rightarrow \mathbf{4} \boldsymbol{N} \boldsymbol{O}_{\mathbf{2}}+\boldsymbol{O}_{\mathbf{2}}
\]
What does \( \frac{\boldsymbol{d}\left[\boldsymbol{O}_{2}\right]}{\boldsymbol{d} \boldsymbol{t}} \) denote?


In a committee of 25 member, each
member is proficient either in mathematics or in statistics or in both.
If 19 of these are proficient in mathematics. 16 in statistics, find the
probability that a person selected from the committee is proficient in both.


Which one of the following order is correct for the bond dissociation
enthalpy of halogen molecules?
A \( \cdot I_{2}>B r_{2}>C l_{2}>F_{2} \)
В \( \cdot C l_{2}>B r_{2}>F_{2}>I_{2} \)
c. \( B r_{2}>I_{2}>F_{2}>C l_{2} \)
D. \( F_{2}>C l_{2}>B r_{2}>I_{2} \)


For what value of \( A, B \) and \( C . \) The output
of \( Y=1 \)
A. 001
B. 101
\( c \cdot 100 \)
D. 010


During the 19 th century, light was considered to be a stream of particles called:
A. atoms
B. electrons
c. corpuscles
D. quantas


The mean value of velocity vector projection average over \( 3 / 8 \) th of a period after the start is
A \( \cdot \frac{2 \sqrt{2} A \omega}{\pi} \)
B. \( \frac{2 A \omega}{3 \sqrt{2 \pi}} \)
c. \( \frac{A \omega}{3 \pi} \)
D. \( \frac{2 \sqrt{2} A \omega}{3 \pi} \)


If two parallel lines are intersected by a transversal, then each pair of corresponding angles are
A. Equal
B. Unequal
c. Insufficient Data
D. None of the above


A \( 5.0 \mathrm{A} \) current is setup in an external
circuit by a \( 6.0 \mathrm{V} \) storage battery for 6.0 min. The chemical energy of the battery is reduced by
В. \( 1.08 \times 10^{-4} \) 」
c. \( 1.8 \times 10^{4} \) j
D. \( 1.8 \times 10^{-4} \mathrm{J} \)


The torque of a force \( \overrightarrow{\boldsymbol{F}}=\mathbf{2} \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\boldsymbol{4} \hat{\boldsymbol{k}} \)
acting at a point \( \vec{r}=\mathbf{7} \hat{\mathbf{i}}+\mathbf{3} \hat{\mathbf{j}}+\hat{\boldsymbol{k}} \) is
\( \mathbf{A} \cdot 14 \hat{i}+38 \hat{j}+16 \hat{k} \)
B . \( 4 \hat{i}+4 \hat{j}+6 \hat{k} \)
c. \( -14 \hat{i}+38 \hat{j}-16 \hat{k} \)
D. \( 11 \hat{i}-26 \hat{j}+\hat{k} \)


Calculate the number of light years in a
petametre. (where \( \left.1 \text { peta }=10^{15} m\right) 1 \)


Explain why
(i) The dipole moment of chlorobenzene is lower than that of cyclohexyl chloride?
(ii) Alkyl halides, though polar, are immiscible with water?
(iii) Grignard reagents should be prepared under anhydrous conditions?


Count total number of S.F. in 5.003020
\( A \cdot 3 \)
B. 20
\( c .7 \)
D.


Solution of \( \sin ^{-1}\left[\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right]=\boldsymbol{x}+\boldsymbol{y} \) is:
A \( \cdot 1+\tan \left(\frac{x+y}{2}\right)=-\frac{2}{x+c} \)
B. \( 1+\cos \left(\frac{x+y}{2}\right)=-\frac{2}{x+c} \)
c. \( 1+\sec \left(\frac{x+y}{2}\right)=-\frac{2}{x+c} \)
D. \( 1+\cos \left(\frac{x+y}{2}\right)=\frac{2}{x+c} \)


Name the gas that is produced in the following cases.

Action of cold and dilute nitric acid on
copper.


Assertion
The \( 0-0 \) bond length in \( H_{2} O_{2} \) is shorter
than that of \( O_{2} F_{2} \)
Reason
\( H_{2} O_{2} \) has an open book-type structure.
Read the above assertion and reason
and choose the correct option regarding
¡t.
A. Assertion is true, Reason is true and Reason is correct explanation for Assertion
B. Assertion is true, Reason is true and Reason is NOT the
correct explanation for Assertion
c. Assertion is true, Reason is false
D. Assertion is false, Reason is true


What is the total value of \( m \) for all
electrons in \( \mathrm{N} \) atom?


Which one of the following statement is
true for the given circle?
A \( \cdot \overline{C D} \cong \overline{A B} \)
B. \( \overline{C D} \neq \overline{A B} \)
c. \( \widehat{C D} \cong \overline{A B} \)
\( \mathbf{D} \cdot \overline{C D} \cong \overline{A B} \)


Identify the gate.


Ozone is present as a chief constituent in which region of the atmosphere?
A. Troposphere
B. Stratosphere
c. Mesosphere
D. Thermosphere


Nuclides:
A. have specific atomic number
B. have same number of protons.
C. have specific atomic number and mass number.
D. are isotopes.


The set of all values of a for which the
function \( \boldsymbol{f}(\boldsymbol{x})=\left(\boldsymbol{a}^{2}=-\boldsymbol{3} \boldsymbol{a}+\right. \)
2) \( \left(\cos ^{2} x / 4-\sin ^{2} x / 4\right)+(a-1) x+ \)
\( \sin 1 \) does not process critical points is
A. \( [1, \infty) \)
(n)
в. (0,1)\( \cup(1,4) \)
c. (-2,4)
D. (1,3)\( \cup(3,5) \)


The blood component essential for blood coagulation is
A. Albumin
B. Globulin
c. Fibrinogen
D. Vitamins


When a piece of bread is chewed it tastes sweet because
A. of the enzyme salivary amylase
B. of conversion of complex sugars into simple sugars
c. conversion of protein
D. Both A and B


ff \( x^{4}+2 x^{3}-3 x^{2}+x-1 \) is divided
by \( x-2 . \) then the remainder is
A . 12
B. 14
c. 16
D. 21


The movement of stems and roots in
response to the force of gravity is called
A. Geotropism.
B. Hydrotropism.
C. Thigmotropism.
D. chemotropism.


A square OABC is inscribed in a
quardrant OPBQ of a circle. If \( O A=21 \mathrm{cm} \) find the area of the shaded region.


\( 100 \mathrm{mL} \) of \( 0.20 M \) weak acid \( H A \) is
completely neutralized by \( 0.20 M \) NaOH. \( K_{b} \) for \( A^{-} \) is \( 10^{-5} \), the \( p H \) at
the equivalence point is
A . 1
B. 7
c. 10
D. none of these


Two strings \( A \) and \( B \) with \( \mu=2 k g / m \)
and \( \mu=8 k g / m \) respectively are joined
in series and kept on a horizontal table with both the ends fixed. The tension in
the string is \( 200 \mathrm{N} \). If a pulse of amplitude \( 1 \mathrm{cm} \) travels in \( \mathrm{A} \) towards the junction, then find the amplitude of reflected and transmitted pulse.
A \( . A_{r}=2 A_{T}=7 \)
в. \( _{A_{r}}=\frac{-1}{3} A_{T}=\frac{2}{3} \)
c. \( A_{r}=8 A_{T}=9 \)
D. \( A_{r}=3 A_{t}=4 \)


State one relevant observation for each
of the following reactions:
Action of concentrated Sulphuric acid on hydrated copper sulphate.


average velocity,


Give correct IUPAC name of:
A. 2 -hydroxypropane- 1,2,3 -tricarboxylic acid
B. 2 -hydroxypropane- 2,3 -dicarboxylic acid
c. 3 -hydroxypropane- 1,2,3 -dicarboxylic acid
D. 3 -hydroxypropane- 1,2,3 -tricarboxylic acid


The color of scattered light depends on of the scattering particles.
A. shape
B. material
c. size
D. all of the above


If a \( M \) matrix \( A \) is such that \( A A^{T}= \)
\( \boldsymbol{I}=\boldsymbol{A}^{\boldsymbol{T}} \boldsymbol{A}, \) find \( |\boldsymbol{A}|=? \)


How many \( \sigma \) and \( \pi \) bonds are presents in
each of the following molecule?
(a) \( \quad H C \equiv C-C H=C H-C H_{3} \)
\( C H_{2}=C=C H-C H_{3} \)


The internal energy of an ideal gas depends upon
A. only its pressure
B. only its volume
c. only its temperature
D. its pressure and volume


The maximum value of \( \left(\frac{1}{x}\right)^{x} \) is
A \( \cdot(1 / e)^{e} \)
B . \( e^{1 / c} \)
\( c \)
D. none of these


A dichloroderivative \( (A) \) on treating
with \( K C N \) followed by acid hydrolysis and heating gives a monobasic acid
\( (B) \) along with liberation of \( C O_{2}(B) \) on heating with liquid ammonia followed
by treating with \( B r_{2} / K O H \) gives \( (C) \)
which on treating with \( N a N O_{2} \) and
\( H C l \) at low temperature followed by
oxidation gives a monobasic acid \( (D) \) having molecular mass \( 74 . C \) in the
whole process would be:
A. ethyl amine
B. propyl amine
c. tert-butyl amine
D. cyclopentyl amine.


If a line makes \( 45^{\circ}, 60^{\circ} \) with positive
direction of axes \( x \) and \( y \) then the
angles it makes with the \( z \) -axis is
A \( \cdot 30^{\circ} \)
В. \( 90^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 60^{\circ} \)


Be and Al show diagonal relationship
and thus:
This question has multiple correct options
A. their oxides are soluble in alkali solution forming \( \left[\operatorname{Be}(O H)_{4}\right]^{3-} \)
B. they form complex anion \( B e F_{4}^{2-} \) and \( A l F_{6}^{3-} \)
C \( \cdot B e C l_{2} \) and \( A l C l_{3} \) are Lewis acid
D. oxides are basic


What replaces thymine in RNA?
A. Guanine
B. Adenine
c. Uracil
D. water


Solve the equation. \( \frac{3}{2 x}+\frac{1}{x+1}=0 \)


Naveen got an increment of \( 15 \% \) in his
salary. If his salary is \( R s .14030 \), what was his original salary?


If the speed of a motor car is doubled, how much more distance will it cover
before stopping under the same retarding force?


\( \lim _{n \rightarrow \infty} n^{2}\{\sqrt{\left.\left(1-\cos \frac{1}{n}\right) \sqrt{\left(1-\cos \frac{1}{n}\right)}\right)} \)
\( A \)
\( B \)
\( c \)
\( D \)


What are tap roots?


Match each set of hybrid orbitals from
LIST-I with complex(es) given in LIST-II.
\( \begin{array}{ll}\text { LIST-I } & \text { LIST -II } \\ \text { P. } d s p^{2} & \text { 1. }\left[F e F_{6}\right]^{4-} \\ \text { Q. } s p^{3} & \text { 2. }\left[T i\left(H_{2} O\right)_{3} C l_{3}\right] \\ \text { R. } s p^{3} d^{2} & \text { 3. }\left[\operatorname{Cr}\left(N H_{3}\right)_{6}\right]^{3+} \\ \text { s.d }^{2} s p^{3} & \text { 4. }\left[F e C l_{4}\right]^{2-} \\ & \text { 5. }\left[N i(C O)_{4}\right] \\ & \text { 6. }\left[N i(C N)_{4}\right]^{2-}\end{array} \) The correct option is:
A. \( P \rightarrow 5 ; Q \rightarrow 4,6 ; R \rightarrow 2,3 ; S \rightarrow 1 \)
в. \( P \rightarrow 5,6 ; Q \rightarrow 4 ; R \rightarrow 3 ; S \rightarrow 1,2 \)
c. \( P \rightarrow 6 ; Q \rightarrow 4,5 ; R \rightarrow 1 ; S \rightarrow 2, \),
D. \( P \rightarrow 4,6 ; Q \rightarrow 5,6 ; R \rightarrow 1,2 ; S \rightarrow 3 \)


An acid \( H A \) ionises as
\( \boldsymbol{H} \boldsymbol{A} \rightleftharpoons \boldsymbol{H}^{+}+\boldsymbol{A}^{-} \)
The pH of \( 1.0 \mathrm{M} \) solution is \( 5 . \) Its dissociation constant would be:


Ultrasonic waves produced by a
vibrating quartz crystal are:
A . only longitudinal
B. only transverse
C. both longitudinal and transverse
D. neither longitudinal nor transverse


A balloon of diameter 21 meter weight
\( 100 k g . \) Calculate its pay-load, if it is filled
with \( H e \) at 1.0 atm and \( 27^{\circ} \mathrm{C} \). Density of
air is \( 1.2 \mathrm{kgm}^{-3} \). (Given: \( R= \)
\( \left.0.082 L a t m K^{-1} m o l^{-1}\right) \)
A. \( 4952.42 \mathrm{kg} \)
B. 4932.42 kg
c. \( 493.242 \mathrm{kg} \)
D. None of these


Ecosystems may be defined as
A. A species along with environment
B. Plant found in water
C. Plants found on land
D. All plants and animal species along with environment


When an elastic material with Young's modulus \( Y \) is subjected to stretching stress \( \mathrm{S} \), elastic energy stored per unit volume of the material is
\( ^{A} \cdot \frac{Y S}{2} \)
B. \( \frac{S^{2} Y}{2} \)
c. \( \frac{s^{2}}{2 Y} \)
D. \( \frac{s}{2 Y} \)


Distinguish between : Autotrophic nutrition and heterotrophic nutrition.


Winch of the following components is a part of the pectoral girdle?
A. Sternum
B. Acetabulum
c. Glenoid cavity
D. Illium


How many students spent more than 5
hours in watching TV?
\( A \cdot 20 \)
\( B .24 \)
\( c \cdot 12 \)
0.14


Give one chemical test to distinguish between the following pairs of compounds.
(i) Methylamine and dimethylamine
(ii) Secondary and tertiary amines
(iii) Ethylamine and aniline
(iv) Aniline and benzylamine
(v) Aniline and N-methylaniline.


The reflection of the plane \( 2 x+3 y+ \)
\( 4 z-3=0 \) in the plane \( x-y+z- \)
\( \mathbf{3}=\mathbf{0} \) is the plane
A. \( 4 x-3 y+2 z-15=0 \)
B. \( x-3 y+2 z-15=0 \)
c. \( 4 x+3 y-2 z+15=0 \)
D. none of these


is present between meiosis I and meiosis II.
A. Interphse
c. Interkinesis
D. Telophase II


A block of mass \( \mathrm{m} \) is suspended by a
light thread from an elevator.The
elevator is accelerating upward with uniform acceleration a. The work done
by tension on the block during t seconds is \( (1=0) \)
A \( \cdot \frac{m}{2}(g+a) a t^{2} \)
B \( \cdot \frac{m}{2}(g-a) a t^{2} \)
c. \( \frac{m}{2} g a t^{2} \)
D.


Let \( \boldsymbol{R}=\{(\boldsymbol{x}, \boldsymbol{y}): \boldsymbol{x}+\boldsymbol{2} \boldsymbol{y}=\boldsymbol{8}\} \) be a
relation on N. Write the range of R.


The increasing order of frequencies for infrared rays, Ultraviolet rays-, X-rays and Y-rays will be-
A. y-rays, X-rays, Infrared rays, Ulterviolet rays
B. X-rays,Y-rays Infrared rays,Ultraviolet rays
C. Infrared rays, Ultraviolet rays,X-rays, Y-rays
D. Ultraviolet rays,X-rays, Y-rays Infrared rays


Select the taxon mentioned that
represents both marine and fresh water
species.
A. Echionoderms
B. Ctenophora
c. cephalochordata
D. Cnidaria


Assertion
Diaphragms, cervical caps and vaults are made of rubber and are inserted
into the female reproductive tract to cover the cervix before coitus.
Reason

These are chemical barriers of
conception which are reusable.
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


Speed of light in vacuum is \( \mathrm{m} / \mathrm{s} \)


Assertion: Sudden fall of pressure at a place indicates storm

Reason: Air flows from higher pressure
to lower pressure.
A. Both Assertion and Reason are True and Reason is correct explanation of assertion.
B. Both Assertion and Reason are true but reason is not the correct explanation of assertion.
c. Assertion is true but reason is false
D. Both assertion and reason are false


The altitudes/height of heavenly bodies appears to be greater than they actually are. This is due to
A. Vertical motion of these heavenly bodies
B. Motions of the earth
c. Atmospheric refraction
D. These are visible because of light of the sun reflected from their surface


\( 0.24 g \) of a volatile substance, upon vaporisation, gives \( 45 \mathrm{ml} \) vapour at \( \mathrm{NTP} \) What will be the vapour density of the
substance?
\( \mathbf{A} \cdot 95.93 \)
B. 59.8
c. 95.39
D. 5.993


If \( y=\ln \left(x^{e^{x}}\right) \) find \( \frac{d y}{d x} \)