When you suspend alum in dirty water, slowly mud particles accumulate at the bottom of the vessel. The process is
called:
A. decantation
B. evaporation
c. coagulation
D. sublimation


Which of the following compound is used
for the treatment of cancer?
A. potassium sulphocyanide
B. Cis-diamine dichloro platinum (II)
C. Trans-dichlorodiammine platinum (II)
\( \mathbf{D} \cdot\left[A g\left(N H_{3}\right)_{2}\right] N O_{3} \)


Which fungal disease spreads by seed and flowers?
A . Loose smut of Wheat
B. Corn stunt
c. covered smut of Barley
D. Soft rot of Potato


A block is moving in a circular path at constant speed. Which of the following statements is/are true?
I. The velocity is constant.
II. The direction of motion is constant.
III. The magnitude of velocity is constant.
A. II only
B. I and III only
c. ॥ and III only
D. I and II only
E. III only


Which letter corresponds to the
activation energy of the reaction after
the addition of a catalyst?
\( A \cdot A \)
B. B
\( c . c \)
\( D . \) D
\( E . E \)


One mole of an ideal gas u ndergoes a
process:
\( P=\frac{P_{0}}{1+\left(V_{0} / V\right)^{2}} \)
Here \( P_{0} \) and \( V_{0} \) are constants.change in temperature of the gas when volume is
changed from \( V=V_{0} \) to \( V=2 V_{0} \) is:
A. \( -\frac{2 P_{0} V_{0}}{5 R} \)
в. \( \frac{11 P_{0} V_{0}}{10 R} \)
c. \( -\frac{5 P_{0} V_{0}}{4 R} \)
D. \( P_{0} V_{0} \)


The ratio of income of two persons is 9:
7 and the ratio of their expenditure is
\( 4: 3 . \) If each of them manages to save
Rs. 2000 per month, find their monthly income.
A. \( R s .18,000, \) Rs.14, 000
B. \( R s .1,000, R s .14,000 \)
c. \( R s .18,000, \) Rs.1, 000
D. None of these


Figure shows the graph of angle of deviation \( \delta \) versus angle of incidence \( i \)
for a light ray striking a prism. The
prism angle is
A . \( 30^{\circ} \)
B. 45
\( c \cdot 60 \)
\( D .75 \)


If the surface area of a hemisphere is 'S
then express ' \( r^{\prime} \) in terms of ' \( S \) '.


An element along with its atomic
number and mass number is represented as \( _{Z} X^{A} \) where \( X \) is the symbol of the element, \( Z \) is the atomic
number and \( A \) is the mass number.

Represent elements \( A, B, C, D \) and \( E \) with its atomic number and mass number
from the given data.
of \( \begin{array}{lll}\text { Elements } & \begin{array}{l}\text { Number } \\ \text { of } \\ \text { protons }\end{array} & \begin{array}{l}\text { Number } \\ \text { of } \\ \text { electrons }\end{array}\end{array} \) \( e \)
\( B \)
\( \mathrm{m} \)
\( E \)


Approximately \( 70 \% \) of carbon-dioxide absorbed by the blood will be transported to the lungs
A. As bicarbonate ions
B. In the form of dissolved gas molecules.
c. By binding to RBC
D. As carbamino-haemoglobin.


\( \lim _{x \rightarrow 0} \frac{\sqrt{x+6}-\sqrt{6}}{x}= \)
А. \( \frac{1}{\sqrt{6}} \)
в. \( -\frac{1}{\sqrt{6}} \)
с. \( \frac{1}{2 \sqrt{6}} \)
D. \( -\frac{1}{2 \sqrt{6}} \)


A proton and an \( \alpha \) particle having equal kinetic energy are projected in a
uniform transverse electric field as
shown in figure
A. Proton trajectory is more curved
B. \( \alpha \) particle trajectory is more curve
C. Both trajectories are equally curved but in opposite direction
D. Both trajectories are equally curved and in same direction


Raphides are found in
A. Citrus
B. Colocasia
c. Both A and B
D. None of the above


The potential energy of a molecules on the surface of a liquid compared to the one inside the liquid is :
A. zero
B. Lesser
c. Equal
D. Greater


Which component of air is exhaled by the body?
A. Nitrogen
B. Oxygen
c. Carbon dioxide
D. Hydrogen


A biological catalyst is essentially:
A. a carbohydrate
B. an enzyme
c. an amino acid
D. a nitrogen molecule


How long will it take a radiowave of
frequency \( 6 \times 10^{3} s^{-1} \) to travel from one
place to other? The distance is \( 10^{14} k m \)


Coal tar is a thick
yellow) liquid with pleasing smell


The important features of genetic code
are:
a. It is universal
b. It is commaless
c. It is degenerate
d. The third base in the codon is not
always specific The correct feature(s) is(are):
A. a only
B. b, conly
c. \( b, c, d \) only
D. all of the above


Explain wurtz fitting reaction with
example


Find the cube root of 512 by prime factorisation method:


Which one of the following can utilize
molecular nitrogen \( \left(N_{2}\right) \) as nutrient for
growth?
A. Rhizobium
B. Spirogyra
c. Mucor
D. Methancoccus


If \( \sin ^{-1} x+\sin ^{-1} y+\sin ^{-1} z=\frac{3 \pi}{2} \)
then \( \frac{\sum_{k=1}^{2}\left(x^{100 k}+y^{106 k}\right)}{\sum x^{207} \cdot y^{207}} \) is
A \( \cdot \frac{1}{3} \)
B. \( \frac{4}{3} \)
\( c \cdot \frac{2}{3} \)
D. None of these


Name the refining method used to produce semiconductors.


In the following dark reaction of photosynthesis,
\( 6 C O_{2}+6 H_{2} O+A+12 N A D P H+H \)
A and B stand for
A . 18 ADP, 18 ATP
B. 12 ATP, 18 ATP
c. 18 ATP, 18 ADP
D. 12 АтР, 12 АDP


The area bounded by the curve \( y= \)
\( f(x), \) above the \( x \) -axis, between \( x=a \)
and \( \boldsymbol{x}=\boldsymbol{b} \) is:
\( ^{\mathrm{A}} \cdot \int_{f(a)}^{b} y d y \)
B. \( \int_{a}^{f(b)} x d x \)
\( ^{c} \cdot \int_{a}^{b} x d y \)
D. \( \int_{a}^{b} y d x \)


An ellipse with centre at (0,0) cuts \( x \) axis at (3,0) and \( (-3,0) . \) If its \( e=\frac{1}{2} \) then the length of the semiminor axis is:
A \( .2 \sqrt{3} \)
B. \( \sqrt{5} \)
c. \( 3 \sqrt{2} \)
D. \( \frac{3 \sqrt{3}}{2} \)


Which of the following body parts of earthworm helps in its movements?
A. Muscular rings
B. Bristles
c. slimy fluid
D. All of the above


Which among the following is incorrect
of \( _{5} B \) in normal state?
A. \begin{tabular}{|c|c|c|c|c|}
\hline \( 2 s \) & \( 2 p \) & & \\
\hline\( \uparrow \uparrow \) & & \( \uparrow \) & \\
\hline
\end{tabular}
B. \begin{tabular}{|c|c|c|c|c|}
\hline \( 2 s \) & \multicolumn{3}{|c|} {\( 2 p \)} \\
\hline\( \uparrow \) & \( \uparrow \) & \( \uparrow \) & \multicolumn{2}{|c|} { Against aufbau principle as well as Hund's rule } \\
\hline
\end{tabular}
\( c \)
\begin{tabular}{c|c|c|c|}
\( 2 s \) & \multicolumn{2}{c} {\( 2 p \)} \\
\hline\( \uparrow \uparrow \) & \( \uparrow \) & & \\
\hline
\end{tabular} Violation of Pauli's exclusion
principle and not Hund's rule
D. \( 2 p \) \( 2 s \) \( \uparrow \downarrow \) \( : \quad \) Against aufbau principle


Solve:
\( \int_{0}^{\frac{\pi}{2}} x^{2} \sin x d x \)


Write balanced equations for the following reactions.
(a) Combustion of \( C_{2} H_{10} \) in a limited
supply of oxygen to form carbon monoxide and water.
(b)The reaction of calcium carbide with
water to form acetylene.
(c)The precipitation of calcium cyanamide from calcium carbide and nitrogen.
(d)Formation of hydrogen cyanide from methane and ammonia.


What are isotopes?
A. These are the forms of the same element having the same atomic number but different atomic masses due
to different nuclear structure.
B. These are the forms of the same element having the different atomic number but different atomic masses due to different nuclear structure.
C. These are the forms of the same element having the same atomic number but same atomic masses due to different nuclear structure.
D. none of these


f \( \boldsymbol{f}: \boldsymbol{A} \rightarrow \boldsymbol{A}, \boldsymbol{g}: \boldsymbol{A} \rightarrow \boldsymbol{A} \) are two
bijections, then prove that \( f \circ g \) is an
injection.


Jupiter, Saturn, Uranus and Neptune are known as the \( _{\text {- - }-\text { - planets. }} \)
A. inner
B. cold
c. outer
D. dwarf


The coordinates of a point whose abscissa is 5 and which lies on the \( x \)
axis is
A . (5,0)
B. (0,5)
D. (5,5)


A body in uniform motion covers
A. different distances in equal intervals of time
B. equal distances in different intervals of time
C. equal distances in equal intervals of time
D. different distances in different intervals of time


Water on reaction with hydrochloric
acid forms:
A. hydronium ion and chloride ion
B. hydrogen and chlorine
c. no reaction
D. hydrogen and chloride ion


Write the structural formulae of any two
position isomers of an alcohol with
molecular formula \( C_{5} H_{12} O \)


f \( n(A)=4 \) and \( n(B)=6, \) then the
number of surjections from \( \boldsymbol{A} \) to \( \boldsymbol{B} \) is
A \( \cdot 4^{\circ} \)
B. \( 6^{\text {4 }} \)
c. 0
D. 24


In nuclei with mass number greater
than \( 20, \) the average binding energy is:
\( \mathbf{A} \cdot 8 M e V \)
в. 0.8 Ме \( V \)
\( c .80 M e V \)
D. \( 0.08 \mathrm{MeV} \)


Differentiate w.r.t. \( x \) in \( \tan ^{-1}\left(\frac{5 x}{1-6 x^{2}}\right) \)


When a group IIA atom forms an ion, what charge does it have?
\( A \cdot+2 \)
B . - -
\( c \cdot+3 \)
\( D \cdot-3 \)
E. None. It is neutral.


A substance of mass \( m_{1} \) with specific
heat capacity \( s_{1} \) and initial
temperature \( \theta_{1} \) is mixed with another
substance of mass \( m_{2}, \) specific heat
capacity \( s_{2} \) and initial temperature \( \theta_{2} \) respectively. Then, their equilibrium
temperature is \( \left.\ldots \ldots \text { (take } \boldsymbol{\theta}_{1}>\boldsymbol{\theta}_{2}\right) \)
A \( \cdot \frac{m_{1} s_{1} \theta_{1}-m_{2} s_{2} \theta_{2}}{m_{1} s_{1}-m_{2} s_{2}} \)
В \( \cdot \frac{m_{1} s_{1} \theta_{1}-m_{2} s_{2} \theta_{2}}{m_{1} s_{1}+m_{2} s_{2}} \)
c. \( \frac{m_{2} s_{2} \theta_{2}-m_{1} s_{1} \theta_{1}}{m_{1}+m_{2}} \)
D. \( \frac{m_{1} s_{1} \theta_{1}+m_{2} s_{2} \theta_{2}}{m_{1} s_{1}+m_{2} s_{2}} \)


Enzyme pepsin acts upon food at a pH of about
A. 3 to split proteins
B. 2 to split carbohydrate
C. 7 to change protein into peptones
D. 2 to change protein in amino acids


Is it a quadratic equation? \( \boldsymbol{x}+\frac{\mathbf{1}}{\boldsymbol{x}}=\boldsymbol{x}^{2}, \boldsymbol{x} \neq \mathbf{0} \)


Find the unit digit of the cube root of the following number:
\( \mathbf{1 7 5 6 1 6} \)
A . 5
B. 6
c. 8
D. 9


In solid ice, oxygen atom is surrounded
A. Tetrahedrally by 4 hydrogen atoms
B. Octahedrally by 2 oxygen and 4 hydrogen atoms
C . Tetrahedrally by 2 hydrogen and 2 oxygen atoms
D. Octahedrally by 6 hydrogen atoms


During the replication of DNA, one of the two strands is synthesized in pieces and are joined later in the presence of
enzyme called
A. RNA ligase
B. DNA ligase
c. r- RNA
D. \( m \) - RNA


The mean length of an object is \( 5 \mathrm{cm} \) Which of the following measurements is most accurate?
A \( .4 .9 \mathrm{cm} \)
B . \( 4.805 \mathrm{cm} \)
\( c .5 .25 m \)
D. \( 5.4 \mathrm{cm} \)


The odds against A solving a problem are 8 to 6 and the odds in favour of \( B \)
solving the same problem 14 to \( 12 . \) The probability of solving the problem if they both try independently is
A \( \cdot \frac{67}{91} \)
в. \( \frac{5}{21} \)
c. \( \frac{4}{21} \)
D.


\( A \)
\( A-3 \) \( E-4, F-7 \) \( \mathrm{B}-5, \mathrm{C}-1, \mathrm{D}-2 \) a \( G-6 \)
B. \( A-3, B-5, C-2, D-1, E- \)
7 \( F-4 \) \( G-6 \)
C. \( A-3, B-5, C-2, D-1, E-4, F-7, G-6 \)
D. \( A-6, B-5, C-2, D-1, E-4, F-7, G-3 \)


A bomb of mass 3.0 kg explodes in air
into two pieces of masses \( 2.0 \mathrm{kg} \) and 1.0 kg. The smaller mass goes at a speed of \( 80 \mathrm{m} / \mathrm{s} \). The total energy imparted to the two fragments is:
A. \( 1.07 \mathrm{kJ} \)
J
B . 2.14 k
c. \( 2.4 \mathrm{kJ} \)
D. \( 4.8 \mathrm{kJ} \)


The figure shows the velocity \( (v) \) of \( a \)
particle plotted against time \( (t) \)
This question has multiple correct options
A. The particle changes its direction of motion at some point
B. The acceleration of the particle remains constant
C. The displacement of the particle is zero
D. The initial and final speeds of the particle are the
\( \operatorname{san} \)


Assertion
The logic gate NOT can be built using diode
Reason
The output voltage and the input
voltage of the diode have \( 180^{\circ} \mathrm{C} \) phase difference.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The value of
\( \frac{18^{3}+7^{3}+3.18 .7 .25}{3^{6}+6.243 .2+15.81 .4+20.27 .8+15.9 .16+6.3 .32+64} \)
\( A \cdot 4 \)
\( B .3 \)
\( c \cdot 2 \)
D.


Find the I.F of \( \boldsymbol{x} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+\boldsymbol{y}(\boldsymbol{1}+\boldsymbol{x})=\mathbf{1} \)
A . \( x . e^{x} \)
в. \( e^{x} / x \)
c. \( x+\log x \)
D. xlogx


On addition of \( \operatorname{conc} . H_{2} S O_{4} \) to a
chloride salt, colourless fumes are
evolved but in case of iodide salt, violet
fumes come out. This is because:
A. \( H_{2} S O_{4} \) reduces HI to \( I_{2} \)
B. \( H I \) is of violet colour
C. \( H I \) gets oxidised to \( I_{2} \)
D. \( H I \) changes to \( H I O_{3} \)


Evaluate \( \int \frac{1+x^{-2 / 3}}{1+x} d x \)
The ans is \( =\frac{1}{2}\left[\log (t+1)^{4}\left(t^{2}-t+\right.\right. \)
1) \( ]+\sqrt{3} \cdot \tan ^{-1} \frac{2 t-1}{\sqrt{(3))}} \)
then \( t=? \)
\( \mathbf{A} \cdot x^{1 / 3} \)
B . \( x^{1 / 2} \)
\( c \)
\( \mathbf{D} \cdot x^{3} \)


f matrix \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{2} & \mathbf{- 2} \\ \mathbf{- 2} & \mathbf{2}\end{array}\right] \) and \( \boldsymbol{A}^{\mathbf{2}}=\boldsymbol{p} \boldsymbol{A} \)
then write the value of \( p \)


\( A, B, C \) are three points on a circle such
that \( A B \) is the chord and \( C P \) is the
perpendicular to \( O P, \) where \( O \) is the
centre and \( P \) is any point on \( A B . \) The
radius \( r \) of the circle is given by
A \( \cdot r^{2}=O P^{2}+A P \times C P \)
B . \( r^{2}=O P^{2}+A P \times P B \)
c. \( r^{2}=O P^{2}+P B \times P C \)
D . \( r^{2}=O P^{2}+P B^{2} \)


Prove theoretically the relation between
e.m.f. induced in a coil and rate of
change of magnetic flux in
electromagnetic induction. A paralle plate air condenser has a capacity of 20
\( \mu F . \) What will be the new capacity if
(a) the distance between the two plates is doubled?
(b) a marble slab of dielectric constant
8 is introduced between the two plates?


Components in a mixture are present in
varying proportions and not in a fixed proportion.


Equation of 251 mpu harmonic progression wave arriving at a point in the medium simultaneously \( \boldsymbol{y}_{1}=\mathbf{0 . 0 5} \sin 2 \pi\left(\mathbf{5 0 t}-\frac{\boldsymbol{x}}{\boldsymbol{\lambda}}\right) \boldsymbol{m} \)
\( \boldsymbol{y}_{2}=\mathbf{0 . 0 5} \sin 2 \pi\left(\mathbf{5 5 t}-\frac{\boldsymbol{x}}{\mathbf{2}}\right) \boldsymbol{m} \)
Calculate wavelength of first wave and beat frequency when sounded together.


The adhering of the molecules of gas on the surface of a solid is called
A. mixture
B. adsorption
c. reduction
D. none of these


A body moving at \( 2 \mathrm{m} / \mathrm{s} \) can be stopped over a distance \( x \). If its kinetic energy is
doubled, how long will it go before coming to rest, retarding force remains unchanged?
\( A \)
B . \( 2 x \)
c. \( 4 x \)
D. \( 8 x \)


Potential energy function describing the interaction between two atoms of a
diatomic molecule is \( U(r)=\frac{a}{r^{12}}-\frac{b}{r^{6}} \)
Force acting between them will be zero
when the distance between them would
be
A
B. \( \quad\left(\frac{b}{2 a}\right)^{\frac{1}{6}} \)
\( \left(\frac{a}{b}\right)^{\frac{1}{6}} \)
D. \( \quad\left(\frac{b}{a}\right)^{\frac{1}{6}} \)


Equipotential surfaces are
A. Surfaces that are perpendicular to gravitational fields
B. Surfaces that have same mass on top of it
c. surface that have same radius of curvature
D. Surfaces that have same gravitational field on it


The radius of first Bohr orbit in
hydrogen atom is \( r_{0} \) then the radius of
first orbit in helium atom will be
A \( .2 r_{0} \)
B. \( 4 r_{0} \)
c. \( \frac{r_{0}}{2} \)
D. \( r \)


Reducing agents does not include:
A. chlorine
B. carbon
c. potassium iodide
D. carbon monoxide


A electric dipole having charge \( q \) and
\( -q \) are placed at distance \( ^{\prime} d^{\prime} \) is in
equilibrium in a uniform electric filed \( \boldsymbol{E} \)
Each charge has mass ' \( m^{\prime} . \) If dipole is displayed by small angle. Then its angular frequency of oscillation is:
A \( \cdot \sqrt{\frac{3 q E}{m d}} \)
в. \( \sqrt{\frac{q E}{2 m d}} \)
c. \( \sqrt{\frac{2 q E}{m d}} \)
D. \( \sqrt{\frac{2 q E}{3 m d}} \)


Calculate, how many methane
molecules and how many hydrogen and carbon atoms are there in 25.0 g of methane?


The magnitude of crystal field stabilization energy in octahedral field
depends on
I the nature of the ligand
Il : the charge on the metal ion
III : whether the metal is in the first,
second or third row of the transition
elements.
A. \( I, \) II, III all are correct
B. I, II are correct
c. ॥, Ill are correct
D. III only correct


Which one of the following is incorrectly matched?
A. Renin- Liver
B. Ptyalin-Mouth
c. Pepsin- Stomach
D. Trypsin- - Intestine


Propyl Benzene reacts with bromine in
presence of light or heat to give:
\( A \)
B.
\( c \)
\( D \)


Product \( Q \) is:
\( A \). An amide
B. An amine
C. Nitro compound
D. Nitrite Compound


Which of the diseases is caused due to
mercury poisoning?
A. Minamata disease
B. Malaria
c. Hepatits
D. Kwashiorkar


The masses and the radii of the earth
and the moon are \( M_{1}, R_{1} \) and \( M_{2}, R_{2} \)
respectively. Their centres are at a
distance \( d \) apart. Find the minimum
speed with which a particle of mass \( \boldsymbol{m} \)
should be projected from a point
midway between the two centres so as to escape it to infinity.


There is one \( (S-S) \) bond in \( H_{2} S_{2} O_{8} \)
A. True
B. False


Solve: \( \frac{d y}{d x}+2 y \tan x=\sin x \)


Give the order of the rotational
symmetry for each figure:


A depolarizer used in dry cell is:
A. ammonium chloride
B. manganese dioxide
C . potassium oxide
D. sodium phosphate


Two object \( A \) and \( B \) weighting \( 10 g \) and 10kg respectively are dropped from the same height. Will both the objects reach the ground together or will one of them reach early?
A. Object A will reach first
B. Object B will reach first
c. Both will reach at the same time
D. Unsure


Styrene can be purified by:
A. Simple distillation
B. Fractional distillation
c. Vacuum distillation
D. Steam distillation


Staminal tube is found in
A. Nicotiana
B. Asparagus
c. Hibiscus
D. Pea


Androgens are produced by
A. Adrenals and ovaries
B. Ovaries and testes
c. Testes and adrenals
D. Adrenals only


Q Type your question
to
X). Assume that \( Y \) and \( Z \) are on the
same horizontal line, and \( z \) and \( X \) are on
the same vertical line. The area inside
the shape \( \boldsymbol{X}-\boldsymbol{Y}-\boldsymbol{Z}-\boldsymbol{X} \) is \( \mathbf{1 0 0 0} \boldsymbol{J} \)
If the heat absorbed by the gas during
process \( X-Y \) is \( 2000 J \) and the heat
released by the gas during process \( Y \)
\( Z \) is \( 3000 J \), how much heat is lost or
gained during process \( Z-X ? \)
A \( .2000 J \) is gained
B. \( 2000 \mathrm{J} \) is lost
c. \( 1000 J \) is gained
D. \( 1000 \mathrm{J} \) is lost
E. \( 5000 \mathrm{J} \) is gainec


The oxidation number of hydrogen varies from:
\( A \cdot-1+0+1 \)
B. 0 to +1
\( c \cdot-1 \) to 0
\( D \cdot 0 \) to +2


A concave lens with unequal radii of
curvature made of glass \( \left(\mu_{g}=1.5\right) \) has
a focal length of \( 40 \mathrm{cm} . \) If it is immersed
in a liquid of refractive index \( \mu_{1}=2 \) then
A. It behaves like a convex lens of \( 80 \mathrm{cm} \) focal length
B. It behaves like a convex lens of \( 20 \mathrm{cm} \) focal length
c. Its focal length becomes \( 60 \mathrm{cm} \)
D. Nothing can be said


\( \boldsymbol{R}-\boldsymbol{C O O H} \frac{N D_{3}}{\Delta}(\boldsymbol{A}) \frac{B r_{2}, \boldsymbol{K} \boldsymbol{O} \boldsymbol{H}}{\Delta} \)
\( (B) \stackrel{N a N O_{2}+H C l}{\longrightarrow}(C) \)
What is \( A, B \) and \( C ? \)
A \( \cdot(A) R C O N D_{2} ;(B) R N H_{2} ;(C) \) ROH
B . \( (A) R C O N D_{2} ;(B) R N D_{2} ;(C) R O D \)
c. \( (A) R C O N H D ;(B) R N H D ;(C) \) ROH
D. None of these


A solution of a substance containing 1.05 g per 100 mL was found to be isotonic with \( 3 \% \) glucose solution. The molecular mass of the substance is:
A . 31.5
B. 6.3
\( c .630 \)
D. 63


Given \( : f(x)=4 x^{3}-6 x^{2} \cos 2 a+ \)
\( 3 x \sin 2 a \cdot \sin 6 a+\sqrt{\ln \left(2 a-a^{2}\right)} \) then
A. \( f(x) \) is not defined at \( x=\frac{1}{2} \)
B \( \cdot f^{\prime}\left(\frac{1}{2}\right)<0 \)
C \( \cdot f^{\prime}(x) \) is not defined at \( x=\frac{1}{2} \)
D \( \cdot f^{\prime}\left(\frac{1}{2}\right)>0 \)


Consider the radiations emitted by the human body. Which of the following statements is true?
A. radiations lie in ultraviolet region
B. radiations lie in infrared region
c. radiations are emitted only during the day
D. radiations are emitted during summer and absorbed during winter


When a small mass \( m \) is suspended at
lower end of the elastic wire having upper end fixed with ceiling. There is loss in gravitational potential energy.
let it be \( x, \) due to extension of wire,
mark correct option,
A. The lost energy can be recovered
B. The lost energy can be irrecoverable
C . only \( \frac{x}{2} \) amount of energy recoverable
D. only \( \frac{x}{3} \) amount of energy recoverable


Two \( S H M \) are represented by equation
\( \boldsymbol{x}_{1}=\mathbf{4} \sin \left(\boldsymbol{\omega} \boldsymbol{t}+\mathbf{3 7}^{\boldsymbol{o}}\right) \) and \( \boldsymbol{x}_{2}= \)
\( 5 \cos (\omega t) . \) The phase difference between
them is
A \( .37^{\circ} \)
B . \( 127^{\circ} \)
\( c \cdot 53^{\circ} \)
D. \( 143^{\circ} \)


The depression produced at the end of a
\( 50 c m \) long cantilever on applying a load is 15 mm. The depression produced at a
distance of \( 30 \mathrm{cm} \) from the rigid end will
be
A. 3.24 \( \mathrm{mm} \)
B. 1.62 \( \mathrm{mm} \)
c. \( 6.48 \mathrm{mm} \)
D. 12.96 mm


Which one of the following organisms is likely to show the highest concentration of DDT, once it has been introduced into
the ecosystem?
A. Grasshopper
B. Toadd
c. snake
D. cattle


If \( \boldsymbol{y}=\boldsymbol{e}^{\log \left(1+\boldsymbol{x}+\boldsymbol{x}^{2}+\boldsymbol{x}^{3}+\cdots\right)}, \) where \( |\boldsymbol{x}|<\mathbf{1} \)
then \( \frac{d y}{d x} \) is equal to
A \( \cdot \frac{-1}{(1-x)^{2}} \)
B. \( \frac{1}{(1-x)^{2}} \)
c. \( \frac{1}{(1+x)^{2}} \)
D. None of these


In Hostel, one day reading hours of 20 students was observed, whose result is mentioned in the table below. Form the
table, find the Mode.
\[
\begin{array}{llllll}
\text { No. of } & 1- & 3- & 5- & 7- & 9- \\
\text { reading } & 3 & 5 & 7 & 9 & 11
\end{array}
\]
Student's strength in the nostel


Solve the following equation \( -4(2- \)
\( \boldsymbol{x})=\mathbf{9} \)


In the Lassaigne's test for the detection of
sulphar, the purple color is due to the
formation of :
\( \mathbf{A} \cdot N a_{4}\left[F e(C N)_{5} N O S\right] \)
B \( \cdot N a_{3}\left[F e(C N)_{5} S\right] \)
\( \mathbf{c} \cdot N a_{2}\left[F e(C N)_{5} N O S\right] \)
D. \( N a_{3}\left[F e(C N)_{6}\right] \)


The substance that triggers the fall of mature leaves and fruits from plant is
due to
A . Auxin
B. Gibberellin
c. Abscisic acid
D. Cytokinin


When the circumference of a toy balloon
is increased from \( 20 \mathrm{cm} \) to \( 25 \mathrm{cm} \), the
radius is increased by
A \( .5 \mathrm{cm} \)
B. \( 2 \frac{1}{2} c m \)
c. \( 5 / \pi c m \)
D. \( 5 / 2 \pi c m \)
E . \( \pi / 5 \mathrm{cm} \)


For a certain atom, there are energy
levels \( A, B, C \) of a certain atom
corresponds to increasing values of
energy, i.e., \( \boldsymbol{E}_{\boldsymbol{A}}<\boldsymbol{E}_{\boldsymbol{B}}<\boldsymbol{E}_{\boldsymbol{C}} . \) Choose the
correct option if \( \lambda_{1}, \lambda_{2} \) and \( \lambda_{3} \) are the
wavelengths of radiations
corresponding to the transitions \( C \) to
\( B, B \) to \( A \) and \( C \) to \( A \) respectively:
\( A \cdot \lambda_{3}=\lambda_{1}+\lambda_{2} \)
B. \( \lambda_{3}=\frac{\lambda_{1} \lambda_{2}}{\lambda_{1}+\lambda_{2}} \)
c. \( \lambda_{1}+\lambda_{2}+\lambda_{3}=0 \)
D. \( 3 \lambda_{2}=\lambda_{3}+2 \lambda_{2} \)


What is the sign of the flux through the right-end cap of the cylinder?
A. Positive
B. Negative
c. There is no flux through the right-end cap
D. cant say


A ball is thrown vertically upwards. The
positive direction is taken to be in
upward direction.

Which of the following is the correct
sign of the quantities during its
ascent?
\( \begin{array}{llll} & \text { POSITION } & \text { VELOCITY } & \text { ACCELERATIO } \\ \text { (A) } & \text { Positive } & \text { Positive } & \text { Positive } \\ \text { (B) } & \text { Positive } & \text { Positive } & \text { Negative } \\ \text { (C) } & \text { Positive } & \text { Negative } & \text { Negative } \\ \text { (D) } & \text { Negative } & \text { Positive } & \text { Negative } \\ \text { (E) } & \text { Negative } & \text { Negative } & \text { Negative }\end{array} \)
\( A \cdot A \)
B. B
\( c \cdot c \)
\( D \cdot D \)
\( E \)


Find the equation of the circle:
Centered at (3,-2) with radius 4
\( \mathbf{A} \cdot x^{2}+y^{2}+6 x-4 y=3 \)
B \( \cdot x^{2}+y^{2}-6 x+4 y=3 \)
C \( \cdot x^{2}+y^{2}-3 x+2 y=-3 \)
D. \( x^{2}+y^{2}+3 x-2 y=-3 \)


A force of \( 20 \mathrm{N} \) acting on a body of mass
\( 10 \mathrm{kg} \) is found to double its velocity in 8
s. Find its initial velocity?
\( A \cdot 6 m s^{-1} \)
B . \( 16 \mathrm{m} \mathrm{s}^{-1} \)
\( c \cdot 8 m s^{-1} \)
D. \( 10 \mathrm{m} \mathrm{s}^{-1} \)


Two free charges \( +q \) and \( +4 q \) are
placed at a distance \( ^{\prime} r^{\prime} \) between them.
A third charge is placed in between them and find the third charge when the system is in equilibrium.
A \( \cdot \frac{4 q}{3} \)
в. \( \frac{4 q}{9} \)
c. \( \frac{2 q}{9} \)
D. \( \frac{q}{9} \)


If \( \boldsymbol{v}_{1} \sin \boldsymbol{\theta}_{1}=\boldsymbol{v}_{2} \sin \theta_{2}, \) then choose the
incorrect statement
A. The time of flight of both the particles will be same
B. The maximum height attained by the particles will be same
C. The trajectory of one with respect to another will be a horizontal straight line
D. None of these


Identify the products (which can be in the form of ions \( ) \) in the following:
(a) \( \boldsymbol{K} \boldsymbol{F}+\boldsymbol{I} \boldsymbol{F}_{5} \rightarrow \)
(b) \( \boldsymbol{C s} \boldsymbol{F}+\boldsymbol{I} \boldsymbol{F}_{5} \rightarrow \)
(c) \( K C l+I C l \rightarrow \)
\( (d) C s I_{3} \triangle \)
\( (e) R b\left[I C l_{2}\right]_{\rightarrow} \)
\( (f) K[B r I C l]_{\rightarrow} \)
\( (g) I_{2}+I C l+A l C l_{3} \triangle \)


\( \mathrm{R} \) is a radius of a planet and \( \rho \) is its
density. The escape velocity on its surface will be
A \( \cdot R^{2} \sqrt{4 \pi G \rho / 3} \)
в. \( R \sqrt{4 \pi G \rho / 3} \)
c. \( R^{2} \sqrt{8 \pi G \rho / 3} \)
D. \( R \sqrt{8 \pi G \rho / 3} \)


How many chlorine atoms are present in Chloropicrin?
A . 1
B.
\( c \cdot 3 \)
\( D \)


When 60 calories of heat are supplied to \( 15 \mathrm{g} \) of water, the rise in temperature is
A \( \cdot 75^{\circ} \mathrm{C} \)
B. \( 900^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 4^{\circ} C \)
D. \( 0.25^{\circ} \mathrm{C} \)


Determine the contrapositive of the following statement:
Only If Max studies will he pass the test.


A block of mass \( 2 k g \) slides down the
face of a smooth \( 45^{\circ} \) wedge of mass
\( 9 k g \) as shown in the figure. The wedge
is placed on a frictionless horizontal
surface. Determine the acceleration of
the wedge.
\( A \cdot 2 m / s^{2} \)
B. \( \frac{11}{\sqrt{2}} \mathrm{m} / \mathrm{s}^{2} \)
\( \mathrm{c} \cdot 1 \mathrm{m} / \mathrm{s}^{2} \)
D. None of these


If \( x+\frac{1}{x}=\sqrt{3}, \) find the value of \( x^{3}+ \)
\( \frac{1}{x^{3}} \)


A wire bent in the form of a circle of
radius \( 42 \mathrm{cm} \) is cut and again bent in
the form of a square. The ratio of the
regions enclosed by the circle and the square in the two cases is given by :
A .11: 12
B. 21: 33
c. 22: 33
D. 14: 11


At what angular velocity of the rod the horizontal component of the force
acting on the lower end of the axis \( O O^{\prime} \)
is equal to zero?
A. \( 12.0 \mathrm{rad} / \mathrm{s} \)
B. \( 6.0 \mathrm{rad} / \mathrm{s} \)
c. \( 3.0 \mathrm{rad} / \mathrm{s} \)
D. \( 9.0 \mathrm{rad} / \mathrm{s} \)


A \( 0.5 m \) long straight wire in which a
current of \( 3.2 A \) is flowing is kept at right angle to a uniform magnetic field
of \( 2.0 T . \) The force acting on the wire will
be:
A \( .2 N \)
в. 2.4 и
\( c .3 .2 N \)
D. 3N


There is \( 30 \% \) chance that it rains on any particular day. Given that there is at least one rainy day in a week, what is the probability that there are at least two rainy days in the week?
A \( \frac{1-4(0.7)^{7}}{1-(0.7)^{7}} \)
В. \( \frac{4(0.7)^{7}}{1-(0.7)^{7}} \)
c. \( \frac{1-(0.7)^{7}}{1-4 .(0.7)^{7}} \)
D. \( \frac{(0.7)^{7}}{1-4 .(0.7)^{7}} \)


Define coefficient of self inductance
and write its unit.


The dimensional formula for coefficient
of thermal conductivity is:
\( \mathbf{A} \cdot[M L T K] \)
B . \( \left[M L T K^{-1}\right] \)
c. \( \left[M L T^{-1} K^{-1}\right] \)
D \cdot \( \left[M L T^{-3} k^{-1}\right] \)


Which of the following taxonomic ranks
contains organisms most similar to one
another?
A. Class
B. Genus
c. Family
D. species


Find the limits of
\( \frac{\sqrt{\boldsymbol{x}}-\sqrt{\mathbf{2 a}}+\sqrt{\boldsymbol{x}-\mathbf{2} \boldsymbol{a}}}{\sqrt{\boldsymbol{x}^{2}-\mathbf{4} \boldsymbol{a}^{2}}}, \) when \( \boldsymbol{x}=\mathbf{2} \boldsymbol{a} \)


Let \( P(2,-4) \) and \( Q(3,1) \) be two given
points. Let \( R(x, y) \) be a point such that
\( (x-2)(x-3)+(y-1)(y+4)=0 \)
area of \( \triangle P Q R \) is \( \frac{13}{2}, \) then the number
of possible positions of \( \boldsymbol{R} \) are
A .2
B. 3
\( c \cdot 4 \)
D. None of these


To receive Grade \( A \) in a course, one
must obtain an average of 90 marks or more in five examinations (each of 100
marks). If Sunitas marks in first four examinations are 87,92,94 and 95
find minimum marks that Sunita must
obtain in the fifth examination to get
grade \( A \) in the course


Assertion
(A) : The value of coefficient
of restitution is independent of the masses and velocities of the colliding bodies but depends on their materials. Reason (R) : Coefficient of restitution is
the ratio of the relative velocity of separation or the relative velocity of approach
A. Both Assertion
(A) and Reason
(R) are correct and R is the correct explanation
B. Both Assertion
(A) and Reason
(R) are correct but the reason does not give the correct explanation
c. A is true but R is false
D. A is false but R is true


In case of a virtual and erect image, the magnification created by the mirror is
A. positive
B. negative
c. unity
D. infinity


Which of the following is the incorrect character of brown algae?
A. Presence of chl a and b
B. It remain attached to substratum
c. Presence of chl a and c.
D. Presence of fucoxanthin


The recent ancestors of modern man
were
A. Java ape man and Peking man
B. Poking man and Rhodesian man
C. Rhodesian man and Cro-Magnon man
D. Cro-Magnon and Neanderthal man


Evaluate \( : \int x \tan ^{-1} x d x \)


If a function from \( R \rightarrow R \) such that
\( f(x)=x^{2} \forall x \epsilon R \) then show that \( f \) is
not one-one.


Light travels through a glass plate of
thickness 't' and refractive index 'n'. If c
is the velocity of light in vacuum, then the time taken by light to travel through the thickness of the plate will be
A \( \cdot \frac{n t}{c} \)
B. \( \frac{t}{n c} \)
c. \( \frac{t c}{n} \)
D. \( \frac{c}{n t} \)


Burette and Pipette are used to
measure mass.
A . True
B. False


Phenol is a:
A . crystalline solid
B. amorphous solid
C . volatile liquid
D. nonvolatile liquid


Domestication of silk worm or the
method of obtaining silk from silkworms is called as
A. Sericulture
B. Pisciculture
c. Apiculture
D. Horticulture


The plane \( a x+b y+c z+d=0 \) divides
the line joining \( \left(x_{1}, y_{1}, z_{1}\right) \) and
\( \left(x_{2}, y_{2}, z_{2}\right) \) in the ratio
A. \( -\frac{a x_{1}+b y_{1}+c z_{1}+d}{a x_{2}+b y_{2}+c z_{2}+d} \)
B. \( -\frac{a x_{1} \times a x_{2}+b y_{1} \times b y_{2}+c z_{1} \times c z_{2}+d^{2}}{a x_{2}+b y_{2}+c z_{2}+d} \)
c. \( -\frac{a+b+c+d}{x_{1}+x_{2}+y_{1}+y_{2}+z_{1}+z_{2}} \)
D \( \cdot \frac{a x_{1}^{2}+b y_{1}^{2}+c z_{1}^{2}+d}{a x_{2}^{2}+b y_{2}^{2}+c z_{2}^{2}+d} \)


n the following figure, the line ABCD is
perpendicular to PQ ; where P and Q are the centres of the circles. Show that:
\( A B=C D \)
ii) \( A C=B D \)


Sania, a high-board diver of mass \( 50 \mathrm{kg} \)
is diving from a height of \( 30 \mathrm{m} \) into a pool (see figure given). What is the
potential energy of Sania at point \( A \) ?
\( \left(g=10 m s^{-2}\right) \)
A . \( 5000 J \)
в. 10000 .
c. \( 15000 J \)
D. 20000


For rusting of iron to take place
are required.
\( A \cdot O_{2} \) and \( C O_{2} \)
B. \( H_{2} O \) and \( N_{2} \)
\( \mathbf{c} \cdot H_{2} O \) and \( O_{2} \)
D. \( H_{2} O \) and \( H_{2} \)


A sample of ozone gas is found to be
\( 40 \% \) dissociated into oxygen. The average mass of sample should be
\( \mathbf{A} \cdot 41.60 \)
B . 40
c. 42.35
D. 38.40


Assertion
There is a very little difference in acidic
strengths of \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4}, \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3} \) and
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{2} \)
Reason
The number of unprotonated oxygen
responsible for an increase of acidic strength due to inductive effect
remains the same
Read the above assertion and reason
and choose the correct option regarding
it.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A semiconductor \( X \) is made by doping a germanium crystal with arsenic \( (\mathrm{Z}= \)
33). A second semiconductor Y is made
by doping germanium with indium \( (z= \)
49). The two are joined end to end and
connected to a battery as shown. Which
of the following statements is correct?
A. \( x \) is \( p \) -type, \( Y \) is \( n \) -type and the junction is forward biased
B. \( x \) is \( n \) -type, \( Y \) is \( p \) -type and the junction is forward biased
c. \( x \) is \( p \) -type, \( Y \) is \( n \) -type and the junction is reverse biased
D. \( x \) is \( n \) -type, \( Y \) is \( p \) -type and the junction is reverse biased


If \( \sin \alpha+\sin \beta=a \) and \( \cos \alpha-\cos \beta= \)
\( b, \) then \( \tan \frac{\alpha-\beta}{2} \) is equal to
A. \( -\frac{a}{b} \)
в. \( -\frac{b}{a} \)
c. \( \sqrt{a^{2}-b^{2}} \)
D. None of these


Wheels reduce friction due to:
A. more area of contact
B. less area of contact
\( c \cdot \operatorname{size} \)
D. all of the above


\( \boldsymbol{O} \boldsymbol{E}=\frac{1}{2} \boldsymbol{A} \boldsymbol{B} \)


If the lines \( x+2 y+3=0, x+2 y- \)
\( \mathbf{7}=\mathbf{0} \) and \( \mathbf{2} \boldsymbol{x}-\boldsymbol{y}-\mathbf{4}=\mathbf{0} \) are the sides
of a square, then equation of the remaining sides of the square can be This question has multiple correct options
A. \( 2 x-y+6=0 \)
В. \( 2 x-y+8=0 \)
c. \( 2 x-y-10=0 \)
D. \( 2 x-y-14=0 \)


Which of the following element is purified by vapour phase refining?
A . \( F e \)
в. \( Z r \)
c. \( C u \)
D. \( A u \)


\( (-12)-(-6)= \)
\( A \cdot-6 \)
B . -18
\( c \cdot+6 \)
D. None of these


Which of the following is used for the production of oxy-acetylene flame for welding and cutting metals?
A. Ethane
B. Ethene
c. Ethyne
D. None of the above


A particle \( P \) is sliding down a frictionless hemispherical bowl. It
passes the point \( A \) at \( t=0 . \) At this
instant of time, the horizontal
component of its velocity is \( v . A \) bead \( Q \) of the same mass as \( P \) is ejected from
\( A \) at \( t=0 \) along the horizontal string
\( A B, \) with the speed \( v . \) Friction between
the bead and the string may be
neglected. Let \( t_{p} \) and \( t_{q} \) be the respective times taken by \( P \) and \( Q \) to reach the
point \( \boldsymbol{B} \). Then
\( \mathbf{A} \cdot t_{p}<t_{q} \)
B . \( t_{p}=t_{q} \)
\( c \cdot t_{p}>t_{q} \)
D. \( _{t_{p} / t_{q}}=\frac{\text {length of are } A C D}{\text {length of cord } A B} \)


Alternating voltage \( V=400 \sin (500 \Omega t) \)
is applied across the resistance
\( (0.2 K \Omega) . \) The r.m.s value of current in
ampere is
\( A \cdot 1.414 \mathrm{A} \)
B. 14.14 A
\( c \cdot 0.1414 \mathrm{A} \)
\( D \cdot 2 A \)


A plot of potential energy v/s kinetic energy of a particle executing SHM gives a straight line
A. passing through the origin
B. with positive slope
c. with intercepts on both the axes
D. parallel to either of the axes


Bleaching powder is obtained by the
interaction of \( C l_{2} \) with:
A . dilute solution of \( C a(O H)_{2} \)
B. concentrated solution of \( C a(O H)_{2} \)
c. dry Cao
D. dry slaked lime


The twentieth term of the GP \( \frac{5}{2}, \frac{5}{4}, \frac{5}{8}, \dots \) is
A \( \cdot \frac{5}{2^{19}} \)
в. \( \frac{5}{2^{20}} \)
c. \( \frac{5}{2^{10}} \)
D. \( \frac{5}{10^{11}} \)


When we enter cinema hall, we cannot
see properly for short time. This is because
A. Pupil does not open
B. Pupil does not close
c. Adjustment of pupil takes sometime
D. None


Solve:
\( \frac{a x}{b}-\frac{b y}{a}=a+b \)
\( a x-b y=2 a b \)


Uncertainity in position of a particle of \( 25 \mathrm{g} \) in space is \( 10^{-15} \mathrm{m} . \) Determine
uncertainity in velocity \( \left(\mathrm{m} \mathrm{sec}^{-1}\right) \) in it. (plank's constant, \( \boldsymbol{h}=\mathbf{6 . 6} \times \mathbf{1 0}^{-\mathbf{3 4}} \mathbf{J s} \) )
A . \( 2.1 \times 10^{-18} \)
В. \( 1.2 \times 10^{-18} \)
c. \( 1.8 \times 10^{-18} \)
D. \( 2.5 \times 10^{-18} \)


A 2-ampere current flows in a conductor which has \( 1 \times 10^{24} \) free electrons per
meter. What is their average drift velocity?
A \( .1 .25 \mathrm{m} / \mathrm{s} \)
в. \( 125000 \mathrm{m} / \mathrm{s} \)
c. \( 3 \times 10^{8} \mathrm{m} / \mathrm{s} \)
D. \( 1.25 \times 10^{-5} \mathrm{m} / \mathrm{s} \)


Find the expression that can be used to designate a linear nonpoplar molecule that contains polar bonds.
в. \( C O_{2}(g) \)
\( \mathbf{c} \cdot 2 N_{2} O(g) \)
D. \( 2 N a C l(a q) \)
E \( \cdot H_{2} S O_{4}(a q) \)


\( f(x)=\left|\begin{array}{lll}a^{-x} & e^{x \ln a} & x^{2} \\ a^{-3 x} & e^{3 x \ln a} & x^{4} \\ a^{-5 x} & e^{5 x \ln a} & 1\end{array}\right|, \) then
A. \( f(x) \cdot f(-x)=0 \)
B. \( f(x)-f(-x)=0 \)
c. \( f(x)+f(-x)=0 \)
D. None of these


The sieve tubes and companion cells are exceptional feature of
A. Gymnosperms
B. Angiosperms
c. Ferns
D. Pteridophytes


Find the value of following determinant. \( \left|\begin{array}{cc}-1 & 7 \\ 2 & 4\end{array}\right| \)


What is the first term and the common
difference of an A.P. recognised as?
A . 'a' and'f'
B. ' \( f^{\prime} \) and ' \( d^{\prime} \)
c. 'f' and 'a'
D. 'a' and 'd'


A particle of mass \( m \) moves uniformly
with a speed \( v \) along a circle of radius \( r \)
\( A \) and \( B \) are two points on the circle, such that the arc AB subtends an angle
\( \theta \) at the center of the circle. The
magnitude of change in momentum as the particle moves from \( A \) to \( B \) is given by:
A \( \cdot 2 m v \sin \left(\frac{\theta}{2}\right) \)
в. \( 2 m v \cos \left(\frac{\theta}{2}\right) \)
c. zero
D. 2 mvtan\( \left(\frac{\theta}{2}\right) \)


Seasonal movement of stem towards
light is
A. Photoperiodism
B. Heliotropism
c. Photonasty
D. Hydrotropism


Discuss the nature of the roots of the
equations \( (a+c-b) x^{2}+2 c x+(b+ \)
\( \boldsymbol{c}-\boldsymbol{a})=\mathbf{0} \)
A. Real and equal
B. Real and unequal
c. Imaginary
D. None of these


When a pressure of 100 atmosphere is applied on a spherical ball, then its volume reduces to \( 0.01 \% \). The bulk
modulus of the material of the rubber in
dyne \( / c m^{2} \) is :
\( \mathbf{A} \cdot 10 \times 10^{12} \)
B . \( 100 \times 10^{12} \)
c. \( 1 \times 10^{12} \)
D. \( 1000 \times 10^{12} \)


Which is the correct order of formation
of \( M g C l_{2} \) by Born-Haber cycle?
1. Sublimation of \( M g ; \quad \) 2. Bond
dissociation of \( C l_{2} \)
3. lonisation of \( M g \quad ; \quad \) 4. Electron
gained by \( C l \)
A .1,3,2,4
в. 1.3,4,2
c. 1,2,3,4
D. None of these.


Density is highest for:
A \( . C H_{3} C l \)
в. \( C H_{2} C l_{2} \)
c. \( C H C l_{3} \)
D. \( C C l \)


Potato chips manufacturers fill the packet of chips with nitrogen gas. Why?


Two particles \( A \) and \( B \) are revolving on two circles with time periods 4 second and 6 second respectively. Time period of particle A with respect to B will be
A. 6 seconds
B. 12 seconds
c. 18 seconds
D. 24 seconds


Identify the graph of the polynomial function \( \boldsymbol{f} \)
\( f(x)=x^{4}-2 x^{3}-x^{2}+2 x \)
A. graph a
B. graph b
c. graph c
D. graoh d


Write short notes on dispersion of light.


Assign configuration to the following?
A. \( E \)
в. \( E, E \)
\( c . E, z \)
D. \( Z, Z \)


Find the median class for the following
data given below:
\( \begin{array}{llll}\text { Number } & \mathbf{0}- & \mathbf{1 0}- & \mathbf{2 0}- \\ \text { of cars } & \mathbf{1 0} & \mathbf{2 0} & \mathbf{3 0}\end{array} \)
Frequency 7 13
A . \( 30-40 \)
в. \( 40-50 \)
c. \( 50-60 \)
D. \( 60-70 \)


The sum of square of deviations for 10
observations taken from mean 50 is
250. The coefficient of variation is
A . 10
B. 20
\( c . \) 30
D. 40


Which of the following has more
inertia. A rubber ball or a stone of the
same size?
A. rubber ball
B. stone
c. both have same intertic
D. cannot be determined


The osmotic pressure of \( 40 \% \)
(weight/volume) urea solution is 1.64 \( \operatorname{atm} \) and that of \( 3.42 \% \) (weight/volume) cane sugar is 2.46 atm. When equal volumes of the above two solutions are
mixed, the osmotic pressure of the resulting solution is:
A. 1.64 atm
B. 2.46 atm
c. 4.10 atm
D. 2.05 atm


Algae are in the same major group of plants, so are the
A. Mosses
B. Liverworts
c. Fungi
D. Ferns


Define aestivation in flowers.


\( \boldsymbol{R}^{\prime} \) is :
A. sulphanilamide
B. \( p \) -bromo sulphanilamide
c. \( o \) -bromo sulphanilic acid
D. sulphanilic acid


A photon of wavelength \( 4400 \dot{A} \) is passing through vacuum. The effective mass and momentum of the photon are
respectively?
A \( .5 \times 10^{-36} k g, 1.5 \times 10^{-27} k g-m / s \)
B . \( 5 \times 10^{-25} \mathrm{kg}^{\text {' }}, 1.5 \times 10^{-26} \mathrm{kg}-\mathrm{m} / \mathrm{s} \)
C. Zero, \( 1.5 \times 10^{-26} \mathrm{kg}-\mathrm{m} / \mathrm{s} \)
D. \( 5 \times 10^{-36} \) в \( g \), \( 1.36 \times 10^{-43} \) kg \( -m / s \)


A coil is placed in transverse magnet
field of 0.02 T. If this coil starts
shrinking at a rate of \( 1 \mathrm{mm} / \mathrm{sec}, \) while
its radius remains \( 4 \mathrm{cm}, \) then what is
the value of induced emf?
\( A \cdot 2 \mu V \)
B . \( 2.5 \mu V \)
\( c .5 \mu V \)
D. \( 8 \mu V \)


Numbers of pairs of salivary glands present in rabbit are
A. one
B. Three
c. Four
D. Five


Find the sum of first 10 terms of
the arithmetic series if \( a_{1}=2 \) and
\( a_{10}=22 \)
A. 155
в. 120
\( c .165 \)
D. 130


Aluminium hydroxide forms a positively charged sol. Which of the following ionic substances should be most effective in
coagulating the sol?
\( \mathbf{A} \cdot N a C l \)
в. \( C a C l_{2} \)
\( \mathbf{c} \cdot F e_{2}\left(S O_{4}\right)_{3} \)
D. \( K_{3} P O_{4} \)


Iron sulphide is heated in air to form \( \mathbf{A} \)
an oxide of sulphur. A is dissolved in water to give an acid. The basicity of this acid is:
\( A \cdot 2 \)
B. 3
\( c \)
D.


Heat causes-
A. change in temperature
B. chemical change
C. biological change
D. all of these


Which of the following is a Lewis acid?
A \( . H_{2} O \)
в. \( C l^{\circ} \)
\( \mathrm{c} \cdot B F_{3} \)
D. \( N H_{3} \)


It is well known that a raindrop or a small pebble falls under the influence of the downward gravitational force and the opposing resistive force. The resistive force is known to be
proportional to the speed of the drop. Consider a drop or small pebble of 1 g falling (from rest) from a diff of height \( 1.00 \mathrm{km} . \) It hits the ground with a speed
of \( 50.0 \mathrm{m} s^{-1} . \) What is the work done by
the unknown resistive force?


On reaction with unsaturated
hydrocarbons, Type \( \boldsymbol{X} \boldsymbol{Y} \) interhalogen compounds gives:
A. displacement reaction
B. addition reaction
c. substitution reaction
D. none of these


In the circuit shown, what will be the
current through the \( 6 V \) zener?
\( \mathbf{A} \cdot 6 m A, \) from \( A \) to \( B \)
B. \( 2 m A \), from A to \( B \)
\( \mathrm{c} .2 \mathrm{mA}, \) from \( \mathrm{B} \) to \( A \)
D. Zero


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


The following figures GUNS and RUNS
are parallelograms. Find \( x \) and \( y \) (Lengths are in \( \mathrm{cm} \) )


The efficiency of an enzyme to catalyse a reaction is due to its capacity to:
A. Reduce the activation energy of the reaction
B. Form strong enzyme-substrate complex
c. Decrease the bond energies of all substrate molecules
D. Alter the substrate geometry to fit into the shape of the enzyme molecule


What is the total random translational
energy of the molecules in one mole of
this gas?


Medium is necessary for sound to propagate.
A . True
B. False


A and B are two square matrices of
same order and \( A^{\prime} \) denotes the
transpose of \( A \), then
\( \mathbf{A} \cdot(A B)^{\prime}=B^{\prime} A^{\prime} \)
B. \( (A B)^{\prime}=A^{\prime} B^{\prime} \)
\( \mathbf{C} \cdot A B=0 \Rightarrow|A|=0 \) or \( |B|=0 \)
D . \( A B=0 \Rightarrow A=0 \) or \( B=0 \)


A series-parallel combination of battery consisting of a large number \( N=300 \)
of identical cells, each with an internal
resistance \( r=0.3 \Omega, \) is loaded with an
external resistance \( \boldsymbol{R}=\mathbf{1 0} \boldsymbol{\Omega} \). then, the
number \( n \) of parallel group consisting of an equal number of cells connected in
series at which the external resistance
generates highest thermal power is
A. 3
B. 4
\( c .5 \)
D. none of the above


Bohr's atomic model is based on the
following postulates:
This question has multiple correct options
A. an atom consists of nucleus.
B. an electron can rotate only in certain energy levels.
C . an electron remains moving with continuous loss of energy.
D. none of the above.


Assertion
The right-handed coordinate system is converted into left-handed coordinate
system by a plane mirror and
Reason
Plane mirror produces the reversal in the direction of normal
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 are correct


The diagram shows a venturimeter through which water is flowing. The
speed of water \( X \) is \( 2 \mathrm{cms}^{-1} . \) The speed
of water at \( Y\left(\text { taking } g=10 \mathrm{ms}^{-2}\right) \) is
A \( .23 \mathrm{cms}^{-1} \)
B. \( 32 \mathrm{cms}^{-1} \)
c. \( 101 \mathrm{cms}^{-1} \)
D. \( 1024 \mathrm{cms}^{-1} \)


The process of RNA formation from DNA is called as
A. Transition
B. Translation
c. Transversion
D. Transcription


Q Type your question.
represent the phase of the moon?
\( A \)
в.
\( c \)
\( D \)


Select the principal functional group
when the following groups are present
in the molecule:
\( \boldsymbol{O H}, \boldsymbol{C O O H},-\boldsymbol{N} \boldsymbol{O}_{2} \)


A nucleic acid is made up of which kind
of monomers?
A. Amino acids
B. Nucleotides
c. Alternating sugar.and phosphate groups
D. Monosaccharides


In the Merck's process, the reagents involved for the preparation of hydrogen peroxide are:
A. \( B a O_{2}, H C l \)
в. \( N a_{2} O_{2}, H_{2} S O_{4} \)
\( \mathbf{c} \cdot B a_{2} O_{2}, H_{2} C O_{3} \)
\( \mathrm{D} \cdot P b O_{2}, H_{2} O \)


The molecules like \( B r F_{5} \) and \( X e O F_{4} \)
are square pyramidal in shape. What is the type of hybridisation shown in these molecules?
A. \( d s p^{3} \)
B. \( d s p^{2} \)
\( \mathbf{c} \cdot s p^{3} d \)
D. \( s p^{3} d^{2} \)


Assertion
The main plant body of bryophytes is gametophyte.
Reason
Alternation of generation is absent in bryophytes
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


What is the correct relationship
between volumes of the two flask?
A. \( V_{B}=2 V_{A} \)
B . \( V_{B}=4 V_{A} \)
\( \mathbf{c} \cdot V_{B}=5 V_{A} \)
D. \( V_{B}=5.5 V_{A} \)


Cucurbits and papaya plants bear staminate and pistillate flowers.
Mention the categories they are put
under separately on the basis of the type of flowers they bear.


For the equilibrium \( N_{2}+3 H_{2} \rightleftharpoons \)
\( 2 N H_{3}, K_{c} \) at \( 1000 K \) is \( 2.37 \times 10^{-3} . \) If
at equilibrium \( \left[\boldsymbol{N}_{2}\right]=\mathbf{2} \boldsymbol{M},\left[\boldsymbol{H}_{2}\right]=\boldsymbol{3} \boldsymbol{M} \)
the concentration of \( \boldsymbol{N} \boldsymbol{H}_{3} \) is:
A . \( 0.00358 M \)
B. \( 0.0358 M \)
c. \( 0.358 M \)
D. 3.58 М


If length of a pendulum of wall clock is increased by \( 0.1 \% \), then find error in time per day.


Muscle cells engaged in vigorous activity, build up a high concentration
of
A . Lactic acid.
B. Pyruvic acid.
c. Alcohol.
D. cholesterol.


Find the sum to 20 terms in each of the
geometric progressions in
\( \mathbf{0 . 1 5}, \mathbf{0 . 0 1 5}, \mathbf{0 . 0 0 1 5}, \ldots \)


Which of the following strategy is not a
correct approach to reduce global warming?
A. Reducing the green house gas emission by limiting the use of fossil fuels.
B. Increase the vegetation cover, particularly the forest for photosynthetic utilization of \( C O_{2} \)
C. Minimizing the use of nitrogen fertilizers in agriculture for reducing \( N_{2} \) O emission.
D. Increasing the use of air conditioners, refrigeration unit and production of plastic foams and propellants in aerosal spray cans.
E. Developing substitutes for chlorofluorocarbons.


Describe Kreb's cycle. (Flow chart or
Explanation)


The pressure of a liquid is plotted on the Y-axis at a depth h in a liquid of density \( \rho \) and the value of h on the X-axis, the
graph is a straight line. The slope of the straight line is : \( (\mathrm{g}= \) acceleration due to gravity
\( \mathbf{A} \cdot \rho g \)
B. \( 1 / \rho g \)
\( \mathbf{c} \cdot \rho / g \)
D. \( g / \rho \)


Why does the increased level of
nutrients in the water affect the
survival of aquatic organisms?


IUPAC name of the above compound is :


What do you understand by temporary
hardness?


Global warming could result in wide ranging effects on:
A. rainfall patterns
B. agriculture, forests
c. plants and animals
D. All of the above


The kinetic energy of most energetic electrons emitted from a metallic
surface is doubled when the wavelength of the incident radiation is changed
from 400 nm to 310 nm. The work
function of the metal is :
A \( .0 .9 e V \)
B. 1.7 eV
c. 2.2 eV
D. 3.1 eV


In terms of basic units of mass(M),
length(L), time(T) and charge(Q), the dimensions of magnetic permeability of
vacuum \( \left(\mu_{0}\right) \) would be?
\( \mathbf{A} \cdot\left[M L Q^{-2}\right] \)
B . \( \left[L T^{-1} Q^{-1}\right] \)
\( \mathbf{c} \cdot\left[M L^{2} T^{-1} Q^{-2}\right] \)
D \( \cdot\left[L T Q^{-1}\right] \)


A block of mass \( m \) is connected to a
spring of force constant \( k . \) Initially the block is at rest and the spring has natural length. A constant force \( \boldsymbol{F} \) is applied horizontally towards right. The maximum speed of the block will be (there is no friction between block and
the surface)
A \( \cdot \frac{F}{\sqrt{2 m k}} \)
B. \( \frac{F}{\sqrt{m k}} \)
c. \( \frac{\sqrt{2} F}{\sqrt{m k}} \)
D. \( \frac{2 F}{\sqrt{m k}} \)


Which one of the following drugs prevents the interaction of histamine with its receptor?
A. Antihistamines
B. Analgesics
c. Antibiotics
D. Disinfectants


A potentiometer wire of length \( 10 m \) is connected in series with a battery. The
e.m.f. of a cell balances against \( 250 \mathrm{cm} \) length of wire. If length of potentiometer wire is increased by \( 1 m, \) the new
balancing length of wire will be
\( \mathbf{A} \cdot 2.00 m \)
B. \( 2.25 m \)
c. \( 2.50 m \)
D. \( 2.75 m \)


When the light enters from air to glass, which colour the angle of deviation maximum?
A. Red
B. Yellow
c. Blue
D. Violet


The number of isomers of \( C_{5} H_{10} \) is?
A . 10
B. 11
c. 12
D. 13


Assertion
Primary benzylic halides are more reactive than primary alkyl halides
towards \( S_{N} 1 \) reaction
Reason
Reactivity depends upon the nature of the nucleophile and the solvent
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


Assign oxidation numbers to each atom
in \( \boldsymbol{N} \boldsymbol{H}_{\mathbf{4}} \boldsymbol{N} \boldsymbol{O}_{2} \)
A. \( N=4,-4 ; H=1 ; O=-2 \)
B. \( N=-3 ; H=1 ; O=3 \)
c. \( N=-1 ; H=1 ; O=-2 \)


The enthalpy of formation of
\( \boldsymbol{C} \boldsymbol{O}_{(g)}, \boldsymbol{C} \boldsymbol{O}_{2(g)}, \boldsymbol{N}_{2} \boldsymbol{O}_{(\boldsymbol{g})} \) and \( \boldsymbol{N}_{2} \boldsymbol{O}_{4(\boldsymbol{g})} \) is
-110,-393,+811 and \( 10 k J / m o l \)
respectively. For the reaction,
\( N_{2} O_{4(g)}+3 C O_{(g)} \rightarrow N_{2} O_{(g)}+ \)
\( \mathbf{3} C O_{2(g)} \cdot \triangle \boldsymbol{H}_{r}(\boldsymbol{k} \boldsymbol{J} / \boldsymbol{m o l}) \) is
\( \mathbf{A} \cdot-212 \)
B. +212
\( \mathbf{c} \cdot+48 \)
D. -48


ENERGY OF AN ORBITING SATELLITE
The change in potential energy is:
\( ^{A} \cdot \frac{G M_{E} m}{2 R_{E}} \)
в. \( \frac{G M_{E} m}{4 R_{E}} \)
c. \( \frac{G M_{E} m}{8 R_{E}} \)
D. \( \frac{G M_{E} m}{R_{E}} \)


What happens when:
(i) magnesium is burnt in air
(ii) quick lime is heated with silica
(iii) chlorine reacts with slaked lime
(iv) calcium nitrate is heated


The correct reactivity order of alcohols towards \( \boldsymbol{H}-\boldsymbol{X} \) will be:
(I) \( \boldsymbol{C H}_{2}=\boldsymbol{C H}-\boldsymbol{O H} \)
(II) \( \boldsymbol{C H}_{2}=\boldsymbol{C H}-\boldsymbol{C H}_{2} \boldsymbol{O H} \)
(III) \( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{O H} \)
\( (\mid V) C H_{3}-C H-C H_{3} \)
a \( ^{1} \)
A \( , I I>I>I I I>I V \)
\( V \)
B. \( I V>I I I>I I>I \)
c. \( I I>I V>I>I I I \)
D. \( I I>I V>I I I>I \)


The area bounded by the \( y \) -axis, \( y= \) \( \cos x \) and \( y=\sin x \) when \( 0 \leq x \leq \frac{\pi}{2} \)
A \( \cdot 2(\sqrt{2}-1) \)
B. \( \sqrt{2}-1 \)
\( c \cdot \sqrt{2}+1 \)
D. \( \sqrt{2} \)


A pnjunction is a/an
A. Bidirectional component
B. Unidirectional Component
C. Linear component
D. None of these


In the reaction \( \boldsymbol{X} \rightarrow \boldsymbol{Y} \), the initial
concentration of \( X \) is 2.5 mol \( L^{-1} \) and
its concentration after 3 hours is 0.7
mol\( L^{-1} . \) What is the average rate of the
reaction?


When \( 1 k g \) of water is heated through
\( 1^{o} C, \) the amount of heat energy
required to do so is :
A. 1 call \( l \)
B. 1 kcal
c. 1000 cal
D. both (b) and (c)


For the reaction, \( \boldsymbol{C l}_{2}+\mathbf{2} \boldsymbol{I}^{-} \rightarrow \boldsymbol{I}_{2}+ \)
\( 2 C l^{-}, \) the initial concentration of \( I^{-} \)
was 0.20 mol \( l i t^{-1} \) and the
concentration after 20 min was
0.18 mol lit\( ^{-1} . \) Then, the rate of
formation of \( I_{2} \) in \( \operatorname{mol} l i t^{-1} \min ^{-1} \)
would be:
A \( \cdot 1 \times 10^{-3} \)
B . \( 5 \times 10^{-4} \)
c. \( 1 \times 10^{-4} \)
D . \( 5 \times 10^{-3} \)


The device in which the nuclear fission
and release of energy is controlled, is
known as:
A. thermopile
B. thermostat
c. nuclear reactor
D. cloud chamber


Which amongst the following contains a covalent bond?
A. \( M g C l_{2} \)
в. \( C a F_{2} \)
c. \( A I_{2} O_{3} \)
D. \( H C l \)


The precipitate of
\( \boldsymbol{C a} \boldsymbol{F}_{2}\left(\boldsymbol{K}_{s p}=1.7 \times 10^{-10}\right) \) is obtained
when equal volumes of the following are \( \operatorname{mixed} \)
\( \begin{array}{lll}\text { A. } 10^{-4} M & C a^{2-}+10^{-4} M & F^{-}\end{array} \)
\( \begin{array}{lll}\text { В. } 10^{-2} M & C a^{2-}+10^{-3} M & F^{-} \\ & \end{array} \)


Assertion: In man, only peripheral
nervous system is present.
Reason: The peripheral nervous system
includes nerves coursing between the
central nervous system and different
parts of the body.
A. If both the assertion and the reason are true and the reason is the correct explanation of the assertion
B. If both the assertion and the reason are true and the reason is not the correct explanation of the assertion
C. If the assertion is true and the reason is false
D. If both the assertion and the reason is false
E. If the assertion is false but the reason is true


The runs scored by Virat in 7 different matches are given as:
\[
89,91,54,66,13,97,06
\]
Calculate the mean deviation about the
median for this data.
A. 31.26
B. 30.06
c. 29.142
D. 27.85


The dimensions of \( \frac{a}{b} \) in the equation \( P=\frac{a-t^{2}}{b x}, \) where \( P \) is pressure, \( x \) is
distance and \( t \) is time, are
A \( \cdot\left[M^{2} L T^{-3}\right] \)
в. \( \left[M T^{-2}\right] \)
\( \mathbf{c} \cdot\left[L T^{-3}\right] \)
\( \mathbf{D} \cdot\left[M L^{3} T^{-1}\right] \)


An electric bulb of \( 15 \mathrm{V} \) is connected to a
battery of \( 15 \mathrm{V} \) which has negligible resistance. If the resistance offered by
the bulb is \( 5 \Omega \) the power of the bulb is
\( \ldots \) W.
A . 225
B. 75
\( c .30 \)
D. 45


The price paid by the shopkeeper.
A \( . \) Rs.2, 400
B. \( R s .2,100 \)
c. \( R s .1,890 \)
D. Rs.1,960


An \( N C C \) parade is going at a uniform
speed of \( 6 k m / h \) through a place under a berry tree on which a bird is sitting at a height of 12.1 m. At a particular
instant the bird drops a berry. Which cadet (give the distance from the tree at the instant) will receive the berry on his uniform?


The modern periodic table has been evolved through the early attempts of Dobereiner, Newland and Mendeleev.
List one advantage and one limitation of all the three attempts.


Find out the temperature at which half
of the air escapes out.


Which of the following practices involve green chemistry?
(i) Substitute CFCs by environmental friendly HFCs and other compounds.
(ii) Replace halogenated solvent by liquid \( C O_{2} \) for drycleaning.
(iii) Use of \( \boldsymbol{H}_{2} \boldsymbol{O} \) for bleaching instead of
\( C l_{2} \)
(iv) Making disposable eating utensils and storage jars of plastics.
\( A \). (i) and (ii)
B. (ii) and (iv)
c. (iii) and (iv)
D. (i), (ii) and (iii)


Gases have fixed shape and volume.
A. True
B. False


Find the square of:
607
A. 368549
B. 368449
\( c .368349 \)
D. 368249


The quantity of solute dissolved in a given mass or volume of the solution is called:
A. parameter of solution
B. concentration of solution
c. similarity of solution
D. massive mass


In meiosis I, the centromere undergoes
A. Division between anaphase a interphase
B. Division between prophase and metap
C. Division but the daughter chromosomes do not separate
D. No division


Name the first organic acid produced by microbial fermentation.


One pink solid (X) has the formula
\( \mathrm{CoCl}_{3} \cdot 5 N \mathrm{H}_{3} \cdot \mathrm{H}_{2} \mathrm{O} \cdot \mathrm{A} \) solution of this
salt (X) in water is also pink and
precipitates 3 mole \( A g C l \) on treatment with silver nitrate solution. When the
pink solid (X) is heated, it loses
1 \( \operatorname{mole} H_{2} O \) to yield a purple solid \( (Y) \)
with the same molar ratio of \( \boldsymbol{N} \boldsymbol{H}_{3} \)
\( C l: C o . \) The purple solid releases two of
its chlorides rapidly on dissolution and
after treatment with \( A g N O_{3} \) solution. The coordination number of cobalt in
complexes \( (X) \) and \( (Y) \) is six. The IUPAC
name of pink (X) and purple (Y) complexes respectively are:
A. Tetraamminechloridoaquacobalt(III) chloride and pentaamminechloridocobalt(III) chloride
B. Pentaamminechloridocobalt(III) chloride and pentaammineaquacobalt(III) chloride,
c. Pentaammineaquacobalt(III) chloride and pentaamminechloridocobalt(III) chloride
D. Pentaammineaquacobaltate(III) chloride and pentaamminechloridocobaltate(III) chloride


A mixture of toluene, benzoic acid, aniline and phenol was dissolved in diethyl ether and extracted with
\( 5 \% N a H C O_{3} \) solution. This extract
was acidified until a white crystalline compound appeared. What is the identity of this compound?
A. Toluene
B. Benzoic acid
c. Aniline
D. Phenol


Which of the following statements is
incorrect?
A. Enzymes exist in colloidal state
B. Enzymes are catalysts
c. Enzymes can catalyse any reaction
D. Urease is an enzyme


Which is an ozonide?
A. \( K O_{3} \)
B. \( N H_{4} O_{3} \)
\( \mathrm{c} \cdot \mathrm{Cr}_{2} \mathrm{O}_{3} \)
D. both (a) and (b)


What is the molarity of \( 11.2 ~ V \) of \( H_{2} O_{2} ? \)
\( A \cdot 1 M \)
в. \( 2 M \)
c. \( 5.6 M \)
D. \( 11.2 M \)


The de-Broglie wavelength of an electron travelling with \( 10 \% \) of velocity of light is equal to:
A. \( 242.4 \mathrm{pm} \)
B. 24.2pm
c. \( 2.42 \mathrm{pm} \)
D. 0.2424 pm


A reaction occurs spontaneously if
\( \mathbf{A} \cdot T \Delta S<\Delta H \) and both \( \Delta H \) and \( \Delta S \) are \( +v e \)
B. \( T \Delta S>\Delta H \) and both \( \Delta H \) and \( \Delta S \) are +ve
c. \( T \Delta S=\Delta H \) and both \( \Delta H \) and \( \Delta S \) are +ve
D. \( T \Delta S>\Delta H \) and both \( \Delta H \) and \( \Delta S \) are -ve


Find the position, velocity and acceleration at \( t=2 s \)


Work done is a \( _{--}- \) - quantity
A. vector
B. scaler
c. constant
D. fundamental


Assertion
When white light fall on the compact disc, multicolours are seen after
reflection.
Reason
CD disc behaves like a prism.
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


\( 0-x y \) lene on ozonolysis will give :
\( A \)
\( \mathrm{CHO} \)
\( \mathrm{I}_{\mathrm{CHO}}^{\mathrm{O}} \mathrm{CH}_{3}-\mathrm{C}-\mathrm{CHO} \)
\( \mathrm{NH} \)
в.
\( \begin{array}{l}\mathrm{CH}_{3}-\mathrm{C}=\mathrm{O} \quad \mathrm{O} \\ \mathrm{CH}_{3}-\mathrm{C}=\mathrm{O}\end{array} \& \mathrm{CH}_{3}-\mathrm{C}-\mathrm{CHO} \)
c.
\( \mathrm{CH}_{3}-\mathrm{C}=\mathrm{O} \)
\( \mathrm{CH}_{3}-\mathrm{C}=\mathrm{O} \)\( \& \mathrm{CHO} \)
\( \mathrm{CHO} \)
\( D \)
\( \mathrm{CH}_{3}-\mathrm{C}=\mathrm{O} \quad \) II
\( \mathrm{CH}_{3}-\mathrm{C}=\mathrm{O}, \mathrm{CH}_{3}-\mathrm{C}-\mathrm{CHO} \& \underset{\mathrm{CHO}}{\mathrm{I}} \)


For gaseous state, which of the
following is incorrect?
A. Thermal energy = Molecular attraction
B. Thermal energy >> Molecular attraction
C. Thermal energy \( << \) Molecular attraction
D. Molecular force >> attractiori in liquid


If \( k>0 \)
\( \mathbf{A}:(-\mathbf{1})(-\mathbf{2})(-\boldsymbol{k}) \)
\( \mathrm{B}:(1)(2)(k) \)
Then
A. Quantity in A is greater than B
B. Quantity in B is greater than A.
c. Both quantities are equal.
D. The relationship cannot be determined from the information given.


The first periodic law stated by
Mendeleev was:
A. there is no correlation in the properties and atomic weights of the elements
B. the properties of the elements are a periodic function of their atomic numbers
C. the properties of the elements are a periodic function of their atomic weights
D. the properties of the elements are a periodic function of their empirical formula


The Calvin cycle proceeds in three
stages.
(1) Reduction, during which carbohydrate is formed at the expense of the photochemically made ATP and NADPH.
(2) Regeneration, during which the carbon dioxide acceptor ribulose- 1,5 biphosphate is formed
(3) Carboxylation, during which carbon dioxide combines with ribulose- -1, 5biphosphate

Identify the correct sequence from the following.
A .3,1,2
в. 3, 2,
\( c \cdot 1,2,3 \)
D. 2,1,
E. None of the above


Which type of bond carbon atoms forms with other atoms?
A. Ionic bond
B. Hydrogen bond
c. Metallic bond
D. covalent bond


The condensation polymer among the following is:
A . rubber
B. protein
c. poly vinyl chloride
D. polyethene


Radiation, with wavelength \( 6561 A \) falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of \( 3 \times \)
\( 10^{-4} \mathrm{T} . \) If the radius of the largest
circular path followed by the electrons
is \( 10 \mathrm{mm} \), the work function of the metal is close to?
A \( .0 .8 \mathrm{eV} \)
B. \( 1.1 \mathrm{eV} \)
c. 1.6 ev
D. 1.8 ev


A garden is \( 90 \mathrm{m} \) long and \( 75 \mathrm{m} \) broad. \( \mathrm{A} \)
path \( 5 \mathrm{m} \) wide is to be built outside and around it. Find the area of the path. Also find the area of the garden in hectares.


In the given figure, \( \angle \mathbf{1}=\mathbf{7 0}^{\circ} . \) Find
\( 180^{\circ}-2 \angle x \)
\( A \cdot 50^{\circ} \)
B . \( 40^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 60^{\circ} \)


The work function of a metal is 4 eV. If
light of frequency \( 2.3 \times 10^{15} \mathrm{Hz} \) is
incident on metal surface, then:
A. no photoelectron will be ejected
B. 2 photoelectron of zero kinetic energy are ejected
C. 1 photoelectron of zero kinetic energy is ejected it
D. 1 photoelectron is ejected, which required the stopping potential of 5.52 volt


Let \( \boldsymbol{\alpha}, \boldsymbol{\beta} \) be the roots of \( \boldsymbol{a x}^{2}+\boldsymbol{b x}+\boldsymbol{c}= \)
\( 0 ; \gamma, \delta \) be the roots of \( p x^{2}+q x+r=0 \)
and \( D_{1}, D_{2} \) are the respective
discriminants of these equations. If the
\( \boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\gamma}, \boldsymbol{\delta} \) are in AP, then \( \boldsymbol{D}_{1}: \boldsymbol{D}_{2} \) is
equal to
\( \mathbf{A} \cdot \frac{a^{2}}{b^{2}} \)
B. \( \frac{a^{2}}{p^{2}} \)
\( ^{\mathbf{C}} \cdot \frac{b^{2}}{q^{2}} \)
D. \( \frac{c^{2}}{r^{2}} \)


If \( 2 a+3 b+6 c=0, \) then at least one
root of the equation \( \boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{b} \boldsymbol{x}+\boldsymbol{c}=\mathbf{0} \)
lies in the interval
\( \mathbf{A} \cdot(0,1) \)
B \( \cdot(1,2) \)
\( \mathbf{c} \cdot(2,3) \)
D \( \cdot(-1,0) \)


Universal gravitational constant is indepndent of the intervening medium.
A. True
B. False


The image which can be obtained on a screen is called
A. a virtual image
B. a real image
c. either a real or a virtual image
D. neither a real nor a virtual image


If three positive real numbers \( a, b, c \) are
in \( A . P . \) such that \( a b c=4, \) then the
minimum possible value of \( b \) is
\( \mathbf{A} \cdot 2^{3 / 2} \)
B. \( 2^{2 / 3} \)
\( \mathbf{c} \cdot 2^{1 / 3} \)
D. \( 2^{5 / 2} \)


How the small bulbs, which are used for
decoration purpose,are connected?
A. in parallel
B. in series
c. in mixed order
D. all of the above


For the damped oscillator shown in Fig
the mass of the block is \( 200 g, k= \)
\( 80 N m^{-1} \) and the damping constant \( b \)
is \( 40 g s^{-1} \) Calculate.
(a) The period of oscillation,
(b) Time period for its amplitude of
vibrations to drop to half of its initial
value
(c) The time for the mechanical energy
to drop to half initial value.


Q Type your question
Nưe:
points at infinite distance from the
spheres)? The diagram shows two spheres, charged uniformly as indicated. All
regions are along a line connecting the centers of the objects.

Region \( A \) is anywhere to the left of the 5.0 Coulomb charge. Region B is to the right of the 5.0 Coulomb charge and closer to the 5.0 Coulomb charge than to the 3.0 Coulomb charge. Region \( C \) is to
the right of the 5.0 Coulomb charge but closer to the 3.0 Coulomb charge than to the 5.0 Coulomb charge. Region D is anywhere to the right of the 3.0 Coulomb charge.
\( A \cdot A \)
B. B
\( c \cdot c \)
D.
E. There is no region where the electric potential could possibly be zero


Choose the correct answer from the
alternatives given
Minerals enter a plant mainly by:
A. diffusion
B. pressure flow
c. translocation
D. active transportt


The vector component of the vector \( \hat{\mathbf{i}}+ \) \( \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) perpendicular to the vector \( \boldsymbol{2} \hat{\boldsymbol{i}}- \)
\( \hat{\boldsymbol{j}}+\boldsymbol{2} \hat{\boldsymbol{k}} \) is
A \( \cdot \frac{1}{3}(\hat{i}+4 \hat{j}+\hat{k}) \)
B \( \cdot \frac{1}{4}(2 \hat{i}-2 \hat{j}-3 \hat{k}) \)
c \( \cdot \frac{1}{2}(2 \hat{i}+2 \hat{j}-\hat{k}) \)
D \( \cdot \frac{1}{4}(2 \hat{i}+2 \hat{j}-\hat{k}) \)


Find the area of the shaded segment(in
sq. units)
\( A \cdot 88.5 \)
3,90,5
\( c .86 .5 \)
88


\( A B C \) and \( A B D \) are two triangles on
the same base \( A B . \) If line-segment
\( C D \) is bisected by \( A B \) at \( O, \) show \( \operatorname{that} \boldsymbol{a r}(\boldsymbol{A B C})=\boldsymbol{a r}(\boldsymbol{A B D}) \)


Which polymer among the following does not soften on heating?
A. Bakelite
B. Polythene
c. Polystyrene
D. PVC


A string is clamped on both ends. Which of the following wave equations is valid for a stationary wave set up on this string? (Origin is at one end of string.)
A. \( y= \) Asinkx sint
B. \( y= \)Acoskx sint
c. \( y= \) Acosk \( x \) cost
D. None of the above


Electrolysis of fused \( K C l . M g C l_{2} \) gives:
A. potassium only
B. magnesium only
c. magnesium and chlorine
D. potassium, magnesium and chlorine


If \( y=\frac{5 x}{(1-x)^{2 / 3}}+\cos ^{2}(2 x+1), \) find
\( \frac{d y}{d x} \)
A. \( \frac{5}{3(1-x)^{5 / 9}}(3-x)-2 \sin (4 x+2) \)
в. \( \frac{-5}{3(1-x)^{5 / 9}}(3-x)-2 \sin (4 x+2) \)
c. \( \frac{4}{3(1-x)^{5 / 9}}(3-x)-2 \sin (4 x+2) \)
D. \( \frac{5}{3(1-x)^{5 / 9}}(3-x)-\sin (4 x+2) \)


Electrostatic precipitation of carbon from smoke is used to control what type of pollution?
1. Air
2. Soil
3. Both 1 and 2
4. None of the above


Find the value of: \( \left|\begin{array}{ll}-3 & -5 \\ -2 & -1\end{array}\right| \)


A box is 1 m long, \( 60 \mathrm{cm} \) wide and
\( 40 \mathrm{cm} \) high. Find the expenditure of colouring its all outer side without its bottom at the rate of \( R s .20 \) per square
meter.


During blood transfusion the needle is inserted in a vein where the gauge
pressure is 2000 Pa. At what height must the blood container be placed so that the blood mayjust enter the vein? Density of whole blood is 1.06
\( \times 10^{3} k g / m^{3} \)
A. \( 0.1 \mathrm{m} \)
B. 0.2 \( m \)
\( c .0 .5 \mathrm{cm} \)
D. 0.7 \( m \)


Mark the following statement is true or
false.

If a ball starts falling from the position of rest, then it travels a distance of \( 25 \mathrm{m} \)
during the third second of its fall.


Which one of the following is categorised under living fossils?
A. Moss
B. Cycas
c. saccharomyces
D. Spirogyra


Select the correct statement(s).
This question has multiple correct options
A. Surface active agents posses surface activity to lower the surface area, i.e., to reduce the surface energy.
B. Detergents possesses the property of surface activity and detergency.
C. All the surfactants are detergents.
D. Soaps are anionic class of surfactant.


Prove that potential at point on transverse (equatorial) position of electric dipole is zero.


The correct order of the spin-only magnetic moment of metal ions in the
following low spin complexes, \( \left[\boldsymbol{V}(\boldsymbol{C N})_{6}\right]^{4-},\left[\boldsymbol{F e}(\boldsymbol{C} \boldsymbol{N})_{6}\right]^{4-} \)
\( \left.\left[\boldsymbol{R u}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right]^{3+}, \text { and }\left[\boldsymbol{C r}(\boldsymbol{N} \boldsymbol{H})_{3}\right)_{6}\right]^{2+}, \) is:
A \( \cdot V^{2+}>C r^{2+}>R u^{3+}>F e^{2+} \)
B . \( V^{2+}>R u^{3+}>C r^{2+}>F e^{2+} \)
c. \( C r^{2+}>V^{2+}>R u^{3+}>F e^{2+} \)
D. \( C r^{2+}>R u^{3+}>F e^{2+}>V^{2}+ \)


Solve \( \tan ^{-1}\left(\frac{1-x}{1+x}\right)= \)
\( \frac{1}{2} \tan ^{-1} x,(0<x<1) \)


Write the first five terms of the following arthmetic progression where first term \( a=3, \) common difference \( d=4 \)


A particle moves along with x-axis. The position \( x \) of article with respect to time \( \mathrm{t} \) from origin given by \( \boldsymbol{x}=\boldsymbol{b}^{0}+\boldsymbol{b}_{1} \boldsymbol{t}+ \)
\( b_{2} t^{2} . \) The acceleration of particle is:
\( A \cdot b_{0} \)
в. \( b_{1} \)
\( c \cdot b_{2} \)
D. \( 2 b_{2} \)


Find relation between these two
compounds
A. Chain isomer
B. Position isomer
C. Functional isomer
D. None of the above


Short / Long answer type questions. Answer the following with reference to the anatomy of dicot stem:
(i) Where exactly are the cambial cells located in the vascular bundles?
What is the name given to such a bundle,
(iii) How are the xylem vessels
arranged ?
(iv) What type of cells constitute the pith?


Choose the correct answer from the
alternatives givens. In most \( \ldots \ldots . . . ., \) cells secrete fibres of
collagen and elastin:
A. epithelial tissue
B. muscle tissue
c. connective tissue
D. nervous tissue


correctmatch withA B C D is
List - I List - II
A) \( \mathrm{SO}_{3} \)
1) \( 119.5^{\circ} \), Angular
B) \( \mathrm{SO}_{2} \)
2) \( 109^{\circ} .28^{1}, \) tetrahedron
\( \mathrm{C}) \mathrm{H}_{2} \mathrm{O} \)
3) \( 120^{\circ}, \) Trigonal planar
\( \mathrm{D}) \mathrm{O}_{3} \)
4) \( 104^{\circ} .30^{\prime} \) angular
5) \( 116.5^{\circ} \) Angular
A. 2145
B. 5213
C. 3145
D. 1324


Which among the following is not
correctly matched with their colour?
Compound

Colour
\( \mathbf{A} \cdot N a_{4}\left[F e(C N)_{5} N O S\right] \quad \) purple
\( \mathbf{B} \cdot F e_{4}\left[F e(C N)_{6}\right]_{3} \)
blue
\( \mathbf{c} \cdot F e(C N S)_{3} \)
blood red
D. \( A g C l \) light yellow


A reaction:
\( \frac{1}{2} H_{2}(g)+A g C l(s) \rightleftharpoons H^{\oplus}(a q)+ \)
\( C l^{\ominus}(a q)+A g(s) \) occurs in a galvanic
cell.
The structure of the cell will be:
A \( \cdot A g, A g C l(s)|K C l(s o l)| A g N O_{3}(s o l), A g \)
B . \( P t, H_{2}(g)|H C l(s o l)| A g N O_{3}(s o l), A g \)
c. \( P t, H_{2}(g)|H C l(s o l)| A g C l(s), A g \)
D. \( P t, H_{2}(g)|K C l(s o l)| A g C l(s), A g \)


If \( T=2 \pi \sqrt{\frac{l}{g}}, \) then relative errors in \( T \) and I are in the ratio
A . \( 1 / 2 \)
B.
c. \( 1 / 2 \pi \)
D. none of these


\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \longrightarrow \boldsymbol{H}^{+}+\boldsymbol{H} \boldsymbol{S} \boldsymbol{O}_{4}^{-}(100 \% \)
ionisation)
\( \boldsymbol{H} \boldsymbol{S O}_{4}^{-} \longrightarrow \boldsymbol{H}^{+}+\boldsymbol{S} \boldsymbol{O}_{4}^{2-} \)
ionisation)
The given reaction takes place when sulphuric acid dissolves in water.
If we start with \( 0.2 ~ M \) aqueous solution
of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) then maximum
concentration is of
species.
A. \( H_{2} S O_{4} \)
в. \( H_{3} O^{+} \)
\( c \cdot s O_{4}^{2} \)
D. \( H S O_{4}^{-} \)


Partial roasting of chalcopyrite
produces
A \( \cdot \mathrm{Cu}_{2} \mathrm{S} \) and \( \mathrm{Fe} \mathrm{O} \)
B. \( \mathrm{Cu}_{2} \mathrm{O} \) and \( \mathrm{FeO} \)
c. \( \mathrm{CuS} \) and \( \mathrm{Fe}_{2} \mathrm{O}_{3} \)
D. \( \mathrm{Cu}_{2} \mathrm{O} \) and \( \mathrm{Fe}_{2} \mathrm{O}_{3} \)


In the rectangle shown below, the two
corners have charges \( q_{1}=-5 \mu C \) and
\( q_{2}=+2.0 \mu C . \) The work in moving a charge
\( +3.0 \mu C \) from \( B \) to \( A \) is:


In which of the families, the stamens are in two whorls and epiphyllous?
A. Malvaceae
B. Solanaceae
c. Liliaceae
D. Caesalpinoideae


If \( \tan ^{-1} x=\frac{\pi}{10} \) for some \( x \in R, \) then
find the value of \( \cot ^{-1} x \)


A park in the shape of a quadrilateral
\( A B C D \) has \( C=90^{0} . A B=18 m \)
\( B C=24 m, C D=10 m \) and \( A D= \)
16 \( m \). how much area does it occupy?


Mention the significance of Zeroth law
of Thermodynamics.


Two coils are Placed close to each other.
The mutual inductance of the pair of
coils depends upon
A. Relative position and orientation of the two coils
B. the materials of the wires of the coils
c. the current in the two coils
D. the rates at which currents are changing in the two coils


A coin is tossed three times. Consider
the following events:
A: No head appears
B: Exactly one head appears
C: At least two heads appear Which one of the following is correct?
A \( .(A \cup B) \cap(A \cup C)=B \cup C \)
B . \( \left(A \cap B^{\prime}\right) \cup\left(A \cap C^{\prime}\right)=B^{\prime} \cup C^{\prime} \)
C \( . A \cap B\left(B^{\prime} \cup C^{\prime}\right)=A \cup B \cup C \)
D. \( A \cap\left(B^{\prime} \cup C^{\prime}\right)=B^{\prime} \cap C^{\prime} \)


Find the equations of the straight lines which pass through (3,2) and make an
angle of \( 45^{\circ} \) with the line \( x=2 y+4 \)


Which equation represents the line that
passes through the point (1,3) and is parallel to the \( x \) -axis?
\( \mathbf{A} \cdot y=3 \)
B. \( y=1 \)
\( \mathbf{c} \cdot x=1 \)
D. \( x=3 \)


Water coming out of a horizontal tube
at a speed \( v \) strikes normally a vertically was close to the mouth of the tube and falls down vertically after impact. When the speed of water is
increased to \( 2 v \)
This question has multiple correct options
A. the thrust exerted by the water on the wall will be doubled
B. the thrust exerted by the water on the wall will be four times
c. the energy lost per second by water strikeup the wall will also be four times
D. the energy lost per second by water striking the wall will be increased eight times


Construct a triangle with perimeter
\( 12 c m \) and the ratio of their angles is 3:
4: 5


What are 'nucleic acids'?
Define complex lipids. Mention any 'two functions of lipids.


Let \( \vec{a} \) be an unit vector and \( m \) being a
scalar then find the value of \( m \) from the
equation \( |\boldsymbol{m} \overrightarrow{\boldsymbol{a}}|=\mathbf{2} \)


If \( 3 x^{2}+4 x y-7 y^{2}=0 \) Find \( (a) \frac{d y}{d x} \) and
(b) \( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}} \)


Thickening the lining of the uterus each month in female body is the function of which of the following hormone?
A . LH
B. FSH
c. Progesterone
D. Oxytocin


Benzene, ethane and ethylene are just three of a large number of
hydrocarbons-compounds that contain only carbon and hydrogen. By using law of proportions and following data, the mass ratio of carbon in benzene, ethane
and ethylene is a:b:c. Then calculate the value of \( a, b \) and \( c \)
\( A \)
\( a=6, b=2, c=3 a \)
B. \( a=5, b=2, c=1 \)
c. \( a=3, b=2, c=2 \)
D. None of these


In Newlands' table, which of the
following elements was not placed in the same group in which cobalt and
nickel were present?
A. Chlorine
B. Bromine
C. Fluorine
D. None of the above


A particle of mass 'm' and charge 'Q' is acceleration in cyclotron. if magnetic field is 'B' and radius cyclotron is \( r \) then the kinetic energy of particle.
A \( \cdot \frac{Q B r}{2 m} \)
\( ^{\text {в. }} \frac{Q^{2} B^{2} r}{2 m} \)
c. \( \frac{Q^{2} B^{2} r^{2}}{2 m} \)
D. \( \frac{Q^{2} B^{2} r^{2}}{m} \)


\( \sim p \wedge q \) is logically equivalent to
\( \mathbf{A} \cdot p \rightarrow q \)
в. \( q \rightarrow p \)
\( \mathbf{c} \cdot \sim(p \rightarrow q) \)
\( \mathbf{D} \cdot \sim(q \rightarrow p) \)


An ecosystem which can be easily ruined/damaged but can recover after some time if damaging effect stops. The ecosystem is characterised by having
A. Low and poor stability with low resilience
B. High stability and low resilience
c. Low stability and high resilience
D. High stability and high resilience


To change \( (3 x+4 y+5)-(2 x+3 y+ \)
4) \( \frac{d y}{d x}=0 \) into homogeneous equation
origin is shifted to \( (\boldsymbol{h}, \boldsymbol{k}) \) then \( \boldsymbol{h}+\boldsymbol{k}= \)
\( A \cdot 3 \)
B.
c. -2
D. -


Vacuum desiccator is used
A. for drying crystals
B. for purifying crystals
C. for separation of crystals
D. for the process of crystallisation


The solution of differential equation \( \left(x^{2}+y^{2}\right) d y=x y d x \) is \( y=y(x) . \) If
\( \boldsymbol{y}(\mathbf{1})=\mathbf{1} \) and \( \boldsymbol{y}\left(\boldsymbol{x}_{0}\right)=\boldsymbol{e}, \) then \( \boldsymbol{x}_{0} \) is:
A \( \cdot \sqrt{2\left(\mathrm{e}^{2}-1\right)} \)
B . \( \sqrt{2\left(\mathrm{e}^{2}+1\right)} \)
\( c \cdot \sqrt{3} e \)
D. \( \sqrt{\frac{e^{2}+1}{2}} \)


Toluene was synthesized by passing acetylene through red hot tube.
A. True
B. False


Which of the following is NOT an allosteric modulation of hemoglobin?
A. Carbon dioxide
в. \( H^{+} \)
c. 2,3 - Bisphosphoglycerate
D. Carbon monoxide


The maximum and minimum oxidation
states of phosphorus are:
\( A \cdot+3,-1 \)
B. +5,-1
\( \mathrm{c} \cdot+5,-3 \)
D. +6,-2


Prove \( 6 i^{50}+51^{41}-2 i^{19}+6 i^{60}=7 i \)


Which of the following is a nucleoside?
A. Adenosine
B. Adenine
c. Deoxyribose
D. Adenylic acid


What is the law of limiting factors? Explain it with an illustration.


The compound (C) is:
(D) \( \quad(\mathrm{C})+\mathrm{CO}_{2} \)
\[
\begin{array}{ll}
\left(\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{2}\right) & \left(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}\right) \\
\text { Acid } &
\end{array}
\]
\( A \)
B.
\( c \)
D.


An electron tube was sealed off during
manufacture at a pressure of \( 1.2 \times \)
\( 10^{-7} \mathrm{mm} \) of mercury at \( 27^{\circ} \mathrm{C} \). Its
volume is \( 100 \mathrm{cm}^{3} . \) The number of
molecules that remain in the tube is
A \( .2 \times 10^{16} \)
В . \( 3 \times 10^{15} \)
c. \( 3.86 \times 10^{11} \)
D. \( 5 \times 10^{11} \)


Mention the following for the complex
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4} \boldsymbol{C l}_{2}\right] \boldsymbol{N} \boldsymbol{O}_{2} \)
¡) IUPAC name
ii) Central metal ion
iii) Ligand
iv) Charge on the Co-ordination sphere
v) Co-ordination number.


Pitch of the helical path described by the particle is :
A. \( \frac{2 \pi m v_{0}}{B_{0} q} \)
В. \( \frac{\sqrt{3} \pi m v_{0}}{2 B_{0} q} \)
c. \( \frac{\pi m v_{0}}{B_{0} q} \)
D. \( \frac{2 \sqrt{3} \pi m v_{0}}{B_{0} q} \)


In a squared sheet, draw two triangles of equal area such that the triangles are congruent.comment about perimeter.


Assertion
In the phenomenon of mutual induction,
self Induction of each of the coil
persists.
Reason
Self induction arises when strength of
current in one coil changes. In mutual induction, current is changing in both
the individual coils.
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


Construct an isosceles \( \Delta A B C \) such
that:
(i) base \( A B=4.2 c m, \) base angle \( = \)
\( 30^{\circ} \)


Let \( \boldsymbol{f} \) be an injective map with domain \( \{x, y, z\} \) and range \{1,2,3\} such that exactly one of the following statements is correct and the remaining are false:
\( \boldsymbol{f}(\boldsymbol{x})=\mathbf{1}, \boldsymbol{f}(\boldsymbol{y}) \sqrt{\mathbf{1}}, \boldsymbol{f}(z) \sqrt{\mathbf{2}} . \) The value of
\( \boldsymbol{f}^{-1}(1) \) is
\( A \)
B.
\( c \cdot z \)
D. none of these


A force of \( 15 N \) increases the length of a wire by \( 1 \mathrm{mm} . \) The additional force required to increase the length by
\( 2.5 m m \) in \( N \) is
A . 22.5
в. 37.5
c. 52.5
D. 75


In a town of 10,000 families it was
found that \( 40 \% \) families buy newspaper \( A, 20 \% \) buy newspaper \( B \) and \( 10 \% \) buy newspaper \( C, 5 \% \) families buy \( A \) and \( B \) \( 3 \% \) buy \( B \) and \( C \) and \( 4 \% \) buy \( A \) and \( C . \) If
\( 2 \% \) families buy all three newspapers, find number of families which buy None
of \( \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C} \)


The two capacitors \( 2 \mu F \) and \( 6 \mu F \) are put in series, the effective capacity of
the system is \( \mu \boldsymbol{F} \) is:
\( A \cdot 8 \mu F \)
в. \( 2 \mu F \)
c. \( 3 / 2 \mu F \)
D. \( 2 / 3 \mu F \)


A snake moves
A. In a straight line
B. By making loops
C. By its scales
D. By its hollow bones


A thin uniform rod \( A B \) of mass \( m= \)
1.0 \( k g \) moves translationally with
acceleration \( \boldsymbol{w}=\mathbf{2 . 0} \boldsymbol{m} / \boldsymbol{s}^{2} \) due to two
antiparallel forces \( \boldsymbol{F}_{1} \) and \( \boldsymbol{F}_{2} \) (figure shown above). The distance between the
points at which these forces are applied is equal to \( a=20 \mathrm{cm} . \) Besides, it is
known that \( F_{2}=5.0 N . \) Find the length
of the rod in metres.


In classical theory, i.e, in Rutherford
atomic model path of the electron will
be
A. Circular
B. Straight
c. Parabolic
D. Spiral


Define the following as related to proteins:
(i) Peptide linkage
(ii) Primary structure
(iii) Denaturation


Assertion
In the reaction,
\( \left.\left.2 C u_{2} O_{(s)}+C u_{2} S_{(} s\right) \rightarrow 6 C u_{(} s\right)+ \)
\( \boldsymbol{S} \boldsymbol{O}_{2(\boldsymbol{g})} \)
copper acts as a reductant and sulphur
acts as an oxidant
Reason
The given reaction is not a redox
reaction
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


Coal, petroleum natural gas, and
propane are fossil fuels They are called
fossil fuels because
A. they are burnt to release energy and they cause air pollution
B. they were formed from the buried remains of plants and tiny animals that lived hundreds of millions of
years ago
C. they are nonrenewable and will run out
D. they are mixed with fossils to provide energy


2 tables and 3 chairs cost Rs.2000
Where as 3 tables and 2 chairs cost Rs.
2500.Find the total cost of 1 table and 5
chairs.


Chemical leaching is not useful in the concentration of:
This question has multiple correct options
A. copper pyrite
B. bauxite
c. galena
D. cassiterite


Solve the following pairs of equations by reducing them to a pair of linear equations:
\( \frac{7 x-2 y}{x y}=5 \)
\( \frac{8 x+7 y}{x y}=15 \)


If the various terms in the below-given expressions have usual meanings, the van't Hoff factor ( \( i \) ) cannot be calculated
by which of the following expression?
A \( . \pi V=\sqrt{i n R T} \)
B. \( \Delta T_{f}=i K_{f}-m \)
c. \( \Delta T_{b}=i K_{b}-m \)
\( \frac{P_{\text {solvent}}^{o}-P_{\text {solution}}}{P_{\text {solvent}}^{o}}=i\left(\frac{n}{N+n}\right) \)


Select incorrect statement about \( N_{2} O_{4} \)
\( \therefore \)
A. It self ionises as \( N O^{+}, N O_{3}^{-} \)
B. Substance containing \( N O^{+} \) is said to be acid and that
containing \( N O_{3}^{-} \) is said to be base
\( \mathrm{C} \cdot \mathrm{N}_{2} \mathrm{O}_{4} \) is paramagnetic
D. \( N O_{2} \) dimerises to \( N_{2} O_{4} \) with disappearance in paramagnetism


What is the physical state of water at
\( \mathbf{0}^{\circ} \boldsymbol{C} ? \)


Which of the following complex ions, which is diamagnetic in nature?
A \( \cdot\left[C c F_{6}\right]^{3-} \)
B. \( \left[N i C l_{4}\right]^{2-} \)
c. \( \left[N i(C N)_{4}\right]^{2} \)
\( \mathbf{D} \cdot\left[C u C l_{2}\right]^{2} \)


Statement: Detergents give scum with
hard water.

State whether the given statement is
true or false.
A. True
B. False


A negatively charged particle is moving through a magnetic field as pictured
below.
What is the direction of the force on the
particle due to the magnetic field at the instant in the picture?
West
A. North
B. west
c. East
D. Up
E. Down


Solve:6 \( +7 b-3 b^{2} \)


Find the co-ordinates of the points on the join of (-3,7,-13) and (-6,1,-10) which is nearest to the intersection of the planes: \( 3 x-y- \)
\( \mathbf{3} z+\mathbf{3 2}=\mathbf{0} \) and \( \mathbf{3} \boldsymbol{x}+\mathbf{2} \boldsymbol{y}-\mathbf{1 5 z}-\mathbf{8}= \)
0


Bond energy of \( A B, A_{2} \) and \( B_{2} \) are in the
ratio 1: 1: 0.5 and the enthalpy of
formation of \( A B \) from \( A_{2} \) and \( B_{2} \) is
\( -100 \mathrm{kJ} \mathrm{mol}^{-1} . \) Then the bond enthalpy
of \( \boldsymbol{A}_{2} \) is:
\begin{tabular}{l}
A. \( 400 \mathrm{kJ} \mathrm{mol}^{-1} \) \\
\hline
\end{tabular}
B. 200 kJ mol-
c. \( 100 \mathrm{kJ} \mathrm{mol}^{-1} \)
D. 300 kJ mol-


Calculate the geometric mean of 3 and
\( \mathbf{2 7} \)
\( \mathbf{A} \cdot \mathbf{3} \)
B. 6
\( c .9 \)
D. 12


The arrangement of the following conics in the ascending order of their eccentricities is
A) \( r(4+\cos \theta)=8 \)
B) \( \frac{1}{r}=\frac{3}{5}-\frac{3 \cos \theta}{5} \)
C) \( 8=r(1+3 \cos \theta) \)
A. \( B, C, A \)
в. \( B, A, C \)
c. \( A, B, C \)
D. \( A, C, B \)


The dimensional formula of electric
potential is given by
\( \mathbf{A} \cdot\left[M L^{2} T^{-3} A^{-1}\right] \)
B. \( \left[M L^{2} T^{-2} A^{-1}\right] \)
\( \mathbf{c} \cdot\left[M L^{2} T^{-1} A^{-1}\right] \)
D. \( \left[M L^{2} T^{-2}\right] \)


A disc of mass \( m \) and radius \( R \) moves
in the \( x \) -y plane as shown in figure. The
angular momentum of the disc about
the origin \( O \) at the instant shown is:
\( ^{\mathrm{A}} \cdot_{-}^{5}^{m R^{2} \omega \hat{k}} \)
\( ^{\mathrm{B}} \cdot \frac{7}{3}^{m R^{2} \omega \hat{k}} \)
C \( -\frac{9}{2} m R^{2} \omega \hat{k} \)
\( \stackrel{0}{2}^{m} m^{2} \omega \)


The energy required to break one mole
of hydrogen-hydrogen bonds in \( H_{2} \) is \( 436 k J . \) What is the longest wavelength
of light required to break a single hydrogen-hydrogen bond?
A \( .68 .5 \mathrm{nm} \)
в. 137 пт
\( c .274 n m \)
D. 548 пт


Give the resonating structures of \( N O_{2} \)
and \( N_{2} O_{5} \)


In figure,prove AB \( \| \mathrm{EF} \)


Let ABCD be a parallelogram. Let AP, CQ be the \( \perp \) from \( A \) and \( C \) on its diagonal
BD. Which of the following is true. This question has multiple correct options
A. \( C Q=P D \)
в. \( P D=Q B \)
c \( . A P=C Q \)
D. \( A P=B Q \)


Assertion
If \( \boldsymbol{H}_{2} \) and \( \boldsymbol{C l}_{2} \) enclosed separately in the
same vessel exert pressure of 100 and
200 mm respectively, their mixture in
the same vessel at the same
temperature will exert a pressure of
\( 300 m m \)
Reason
Dalton's law of partial pressures states that total pressure is the sum of partial
pressures.
Read the above assertion and reason
and choose the correct option regarding
¡t.
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 hardness of water due to \( H C O_{3}^{\ominus} \) is
122 ppm. Select the correct statement(s).
This question has multiple correct options
A. The hardness of water in terms of \( C a C O_{3} \) is 200 ppm.
B. The hardness of water in terms of \( C a C O_{3} \) is 100 ppm.
C. The hardness of water in terms of \( C a C l_{2} \) is 222 ppm.
D. The hardness of water in terms of \( M g C l_{2} \) is 95 ppm.


An insect sits on the end of a long board
of length 5 m. The board rests on a frictionless horizontal table. The insect
wants to jump to the opposite end of the board. What is the minimum take-off speed (in \( \mathrm{m} / \mathrm{s} \) ) of insect relative to
ground, that allows the insect to do the trick? The board and the insect have
equal masses. \( \left(\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} / \boldsymbol{s}^{2}\right) \)


Which of the following statements is
not correct about order of a reaction?
A. The order of a reaction can be a fractional number
B. Order of a reaction is experimentally determined quantity
C. The order of a reaction is always equal to the sum of the stoichiometric coefficients of reactants in the
balanced chemical equation for a reaction
D. The order of a reaction is the sum of the powers of molar concentration of the reactants in the rate law expression


What is the unit for the rate constant of
a second order reaction?
A \( \cdot s^{-1} \)
B. mol \( L^{-1} \)
c. mol \( L^{-1} s^{-1} \)
D. \( \mathrm{L} \) mol \( ^{-1} s^{-1} \)
E \( \cdot \operatorname{mol}^{2} L^{-2} s^{-2} \)


A liquid A has specific heat capacity higher than the liquid B. Which liquid can be used a heat reservoir to keep juice bottles without freezing?
\( A \cdot A \)
B. B
c. Both can be used
D. Data insufficient


Halogenation of alkene using \( B r_{2} / C C l_{4} \) is syn addition but not anti
addition.
If this is true enter 1 , else enter 0 .


How can ceramic articles be given a
colored tinge?


Charge on a body can be:
A \( .-1.3 e \)
B. \( 0.9 e \)
\( c . \pm 3 e \)
D. \( 1.5 e \)


The force applied by the archer to stretch the bow is an example of (contact, non-contact) force.


The graph of a constant function \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{k} \) is?
A. A straight line parallel to \( X \) -axis
B. A straight line parallel to \( Y \) -axis
c. A straight line passing through orgin
D. None


The frequancy of oscillation of current in the inductor is-
A \( \cdot \frac{1}{3 \sqrt{L C}} \)
B. \( \frac{1}{6 \pi \sqrt{L C}} \)
c. \( \frac{1}{\sqrt{L C}} \)
D. \( \frac{1}{2 \pi \sqrt{L C}} \)


Describe the path of ascent of sap due
to transpiration pull


\( \lim _{x \rightarrow 0} \frac{x \cos x-\log (1+x)}{x^{2}} \) is equal to
A \( \cdot \frac{1}{2} \)
B.
c. 1
D. None of these


An electron having mass ' \( m \) ' charge ' \( q^{\prime} \) and \( K . E . K \) enters a uniform magnetic
field - ' \( B \) ' perpendicularly. Then its frequency of rotation.
A \( \cdot \frac{q B}{\pi m} \)
в. \( \frac{q B}{2 \pi m} \)
с. \( \frac{q B E}{2 \pi m} \)
D. \( \frac{q B}{2 \pi} \)


The number of turns in an air core
solenoid of length \( 25 \mathrm{cm} \) and radius 4 \( \mathrm{cm} \) is \( 100 . \) Its self inductance will be
A \( \cdot 5 \times 10^{-4} H \)
в. \( 2.5 \times 10^{-4} H \)
c. \( 5.4 \times 10^{-3} H \)
D . \( 2.5 \times 10^{-3} \mathrm{H} \)


A particle moves on the curve \( y=\frac{x^{4}}{4} \)
where \( \boldsymbol{x}=\boldsymbol{t} / 2, \mathbf{x} \) and \( \mathbf{y} \) are measured in
metre and \( t \) in second. At \( t=4 s, \) find
the velocity of particle.


Object will remain at rest or in uniform motion in a straight line unless acted upon by an external force - which law is
this?
A. Newton's third law
B. Newton's first law
c. Newton's second law
D. None of these


Acids which are synthesised in the laboratory are called as:
A. inorganic acid
B. mineral acid
c. organic acid
D. both (A) and (B)


Coefficient of static friction is depends
on


Differentiate the following function with
respect to \( \boldsymbol{x} \)
\( \sin h^{-1}(\sqrt{x}) \)


Give reasons for the following:
(i) Oxygen is a gas but sulphur is a solid.
(ii) \( O_{3} \) acts as a powerful oxidising
agent.
(iii) \( B i H_{3} \) is the strongest reducing agent amongst all the hydrides of group
15 elements.


A particle with a specific charge \( \mathrm{S} \) is fired with a speed \( V \) towards a wall at a
distance d, perpendicular to the wall. The minimum magnetic field that must exist in this region for the particle to not hit the wall is :
A \( \cdot \frac{V}{s d} \)
в. \( \frac{2 V}{s d} \)
c. \( \frac{V}{2 s d} \)
D. \( \frac{V}{4 s d} \)


If \( A \) and \( B \) are two square matrix of
order \( n \) then prove that \( :(A B)^{-1}= \)
\( \boldsymbol{B}^{-1} \boldsymbol{A}^{-1} \)


The electronic configuration of \( \boldsymbol{E} \boldsymbol{u} \)
(Atomic No. 63 ), \( G d \) (Atomic No. 64 ) and
Tb (Atomic No. 65 ) are :
A \( \cdot[X e] 4 f^{7} 6 s^{2},[X e] 4 f^{8} 6 s^{2} \) and \( [X e] 4 f^{8} s d^{1} 6 s^{2} \)
B . \( [X e] 4 f^{7} 5 d^{1} 6 s^{2},[X e] 4 f^{7} 5 d^{1} 6 s^{2} \) and \( [X e] 4 f^{9} 6 s^{2} \)
C \( \cdot[X e] 4 f^{6} 5 d^{1} 6 s^{2},[X e] 4 f^{7} 5 d^{1} 6 s^{2} \) and \( [X e] 4 f^{8} 5 d^{1} 6 s^{2} \)
D \cdot \( [X e] 4 f^{7} 6 s^{2},[X e] 4 f^{7} 5 d^{1} 6 s^{2} \) and \( [X e] 4 f^{9} 6 s^{2} \)


The diameter of the moon is
approximately on fourth of the diameter of the earth. Find the ratio of their
surface areas.


Compositae is also known as
A. Asteraceae
B. Fabaceae
c. Liliaceae
D. Poaceae


Assertion
Two thin blankets put together are warmer than a single blanket of double the thickness.
Reason
Thickness increases because of air
layer enclosed between the two blankets.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of the following statement(s)
is/are correct about the modern
periodic table?

This question has multiple correct options
A. It consists of \( s, p, d \) and \( f \) blocks
B. The energy levels filling order in 6 th period is \( 6 s, 4 f, 5 d \) and \( 6 p \)
C . III \( B \) group does not contain maximum number of elements
D. It consists only metals


The higher the
temperature
A. lower the energy
B. higher the energy
C. moderate energy
D. none of above


The \( t_{1 / 2} \) for \( ^{14} \mathbf{C} \) in (i) \( ^{14} \mathrm{CO}_{2} \) (ii) \( ^{14} C_{6} \mathbf{H}_{12} \mathrm{O}_{6}(\text { iii }) \) coal containing \( ^{14} \mathbf{C}(i \boldsymbol{v}) \)
cellulose containing \( ^{14} \mathbf{C} \) is :
\( \mathbf{A} \cdot \operatorname{more} \operatorname{in}^{14} \mathrm{CO}_{2} \)
B. more in coal containing \( ^{14} \mathrm{C} \)
c. more in \( ^{14} C_{6} \mathrm{H}_{12} \mathrm{O}_{6} \)
D. same in all species


A wheel having moment of inertia
\( 4 k g m^{2} \) about its symmetrical axis, rotates at rate of 240 rpm about it. The torque which can stop the rotation of the wheel in one minute is:
\( ^{\mathbf{A}} \cdot \frac{5 \pi}{7} N m \)
в. \( \frac{8 \pi}{15} \mathrm{Nm} \)
c. \( \frac{2 \pi}{9} N m \)
D. \( \frac{3 \pi}{7} N m \)


Arrange the following compounds in increasing order of their boiling points.
I. \( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{B r} \)
II. \( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{B r} \)
III. \( \left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C H} \boldsymbol{C H}_{2} \boldsymbol{B r} \)
IV. \( \left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{C B r} \)
A. \( I I<I<I I I<I V \)
в. \( I I I<I<I V<I I \)
c. \( I V<I I I<I I<I \)
II \( I<I V<I I I<I I \)
1