An organic compound answers Molisch's test as well as Benedict's test.
But it does not answer Scliwanoff's test.
Most probably, it is :
A. sucrose
B. Protein
c. Fructose
D. Maltose


\[
\begin{array}{c}
\text { Given: } S+\frac{3}{2} O_{2} \longrightarrow S O_{3}+2 x k c a l \\
S O_{2}+\frac{1}{2} O_{2} \longrightarrow S O_{3}+y k c a l
\end{array}
\]
With the help of the above reactions,
find out the heat of formation of \( \boldsymbol{S O}_{2} \)
A \( \cdot(2 x-y) \)
B . \( (x+y) \)
\( \mathbf{c} \cdot(2 x+y) \)
D \( \cdot(2 x / y) \)


A mixture of benzene and toluene forms
A. An ideal solution
B. Non-ideal solution
c. suspension
D. Emulsion


Solve: \( \int \frac{x+\sqrt{1-x^{2}}}{x \sqrt{1-x^{2}}} d x=? \)


In the given equation
\( a=\frac{2}{3} b+5 . \) If \( b=6, \) then \( a=? \)
\( A \cdot 7 \)
B. 9
c. 11
D. 13


If the radius of the earth be increased by
a factor of 5 by what factor its density be changed to keep the value of \( g \) the
same?
A \( \cdot \frac{1}{25} \)
B. \( \frac{1}{5} \)
c. \( \frac{1}{\sqrt{5}} \)
\( D \)


Find the multiplicative inverse of the complex numbers given. \( \sqrt{5}+3 i \)


In which of the following process convection does not take place primarily?
A. Sea and land breeze
B. Trade wind
c. Boiling of water
D. Warming of glass of bulb due to filament


Which of the following has peritrichous flagella?
A. Pseudomonas
B. Bacillus typhosus
c. spirillium
D. Vibrio


Statement - I : Every collision of
reactant molecule is not successful
Statement - II: Every collision of reactant molecule with proper
orientation is successful one.
A. Both statements are true Statement- - II is correct explanation of Statement- -
B. Both statements are true but statement- -II is not correct explanation of Statement- -
c. statement-lis true but statement- - II is false
D. Statement- - lis false but Statement - || is true


Choose the correct answer among the
alternatives given :
In the following pairs of halogen
compounds, which compound
undergoes faster \( \boldsymbol{S}_{N} 1 \) reaction?
\( (\mathrm{i}) \)
\( A \)
(i)
(ii)
B.
(i)
(ii)
\( c \)
(i)
(ii)
\( D \)
(i)
(ii)


A needle placed \( 45 c m \) from a lens forms
an image on a screen placed \( 90 \mathrm{cm} \) on
the other side of the lens. Identify the type of the lens and determine its focal
length. What is the size of the image if the size of the needle is \( 5.0 \mathrm{cm} \) ?


The vapour pressure of two miscible
liquids \( (A) \) and \( (B) \) are 300 and
\( 500 m m \) of \( H g \) respectively. In a flask 10 mole of \( (A) \) is mixed with 12 mole
of \( (B) . \) However, as soon as \( (B) \) is added, \( (A) \) starts polymerising into a completely insoluble solid. The polymerisation follows first-order kinetics. After 100 minute, 0.525 mole of a solute is dissolved which arrests
the polymerisation completely. The final vapour pressure of the solution is
400 mm of \( H g . \) Estimate the rate
constant of the polymerisation reaction. Assume negligible volume change on mixing and polymerisation and ideal behaviour for the final solution.
A . \( 1.3 \times 10^{-2} \)
B . \( 15 \times 10^{-3} \)
c. \( 2.0 \times 10^{-4} \)
D. \( 1.0 \times 10^{-4} \)


A man takes a step forward with probability 0.4 and backward with probability 0.6. Suppose the man takes
11 steps and \( p_{r} \) denotes the probability
that the man is \( r \) steps away from his initial position, then value of


The total no. of solution of equation \( |\cot x|=\cot x+\frac{1}{\sin x}, x \in[0,3 \pi] \) is
equal to
\( A \cdot 3 \)
B . 2
\( c \cdot 1 \)
\( D \)


\( \sum_{r=0}^{n} r^{2} .^{n} C_{r} p^{r} q^{n-r}, \) where \( p+q=1 \)
is simplified to:
A \( \cdot n p q+n^{2} p^{2} \)
B . \( n^{2} p^{2} q^{2}+n p \)
c. \( n p(p+q) \)
D. \( \frac{p(q+1)}{2} \)


For \( B F_{3} \) molecule, which of the
following is/are true?

This question has multiple correct options
\( A \cdot B \) -atom is \( s p^{2} \) hybridised.
B. There is a \( p \pi-p \pi \) back bonding in this molecule.
C. Observed B-F bond length is found to be less than the expected bond length.
D. There is a \( p \pi-d \pi \) back bonding in this molecule.


a. A cylinder of gas is assumed to contain \( 11.2 k g \) of butane. If a normal
family needs \( 20000 k J \) of energy per day for cooking, how long will the cylinder last? Given that the heat of combustion
of butane is \( 2658 k J \quad m o l^{-1} \)
b. If the air supply of the burner is insufficient (i.e. you have a yellow instead of blue flame), a portion of the
gas escapes without combustion.
Assuming that \( 30 \% \) of the gas is wasted due to this inefficiency, how
long would the cylinder last?
A. a. 26 days, b. 18 days
B. a. 17 days, b. 26 days
c. a. 16 days, b. 17 days
D. None of these


vertically varies with time. It the ettect
of air resistance is neglected which
graph correctly describes this behavior?
\( A \)
B.
\( c \)
D. None of them


\( H_{2} O \) is a liquid but \( H_{2} S \) is a gas.
Explain why?


A dip needle on a plane perpendicular to magnetic meridians will remain
A. horizontal
B. vertical
c. inclined at \( 45^{\circ} \) with horizontal
D. in any direction


Which of the following is a sessile?
A. Rice
B. Mango
c. Neem
D. Sunflower


The total number of electrons that take
part in forming bonds in \( N_{2} \) is:
\( A \cdot 2 \)
B. 4
\( c \cdot 6 \)
D. 10


Assertion
Two distinct lines cannot have more
than one point in common.
Reason
Any number of lines can be drawn
through one point.
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


Illustrate how copper metal can give different products on reaction with
\( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \)


Sodium benzoate has it's application in:
This question has multiple correct options
A. food preservation
B. pharmacy
c. fireworks
D. fuel in whistle mix


The width of the depleted region of a p-n junction is of the order of a few tenth of
\( \mathbf{a} \)
A. millimeter
B. micrometer
c. metre
D. nanometre


Write IUPAC name of the compound
above
A. 2-Amino-4-hydroxybenzoic acid
B. 6-Amino-4-hydroxybenzoic acid
c. 3-Amino-4-carboxyphenol
D. 2-Carboxy-5-hydroxyaniline


If the sum of three numbers in A.P., is 24
and their product is \( 440, \) find the
numbers.


A sum becomes \( R s .4800 \) after two
years and \( R s .6400 \) after four years at
compound interest per annum compounded annually. Find the
sum.


ff \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) is given by \( \boldsymbol{f}(\boldsymbol{x})=(\boldsymbol{3}- \)
\( \left.\boldsymbol{x}^{3}\right)^{1 / 3}, \) find \( \boldsymbol{f} \boldsymbol{o} \boldsymbol{f}(\boldsymbol{x}) \)


The species name
A. Can be same as of genus
B. Cannot be used for another genus
C. Cannot be used for the same or another genus again
D. None of these


Some of the batteries are rechargeable :
I bry cell battery
II : Lead-storage (acid) battery
III : Nickel-cadmium battery
IV: Lithium battery
V: Fuel cell
Select correct alternates:
\( \mathbf{A} \cdot \) ।, ॥।, ॥ ।
в. ॥, ॥I, IV
c. ॥ा, ।v, \( v \)
D. ॥, III, v


Which of the following reaction is a part
of Hall's process?
\( \mathbf{A} \cdot A l_{2} O_{3}+2 N a O H \rightarrow 2 N a A l O_{2}+H_{2} O \)
B \( \cdot F e_{2} O_{3}+2 A l \rightarrow 2 F e+A l_{2} O_{3} \)
\( \mathbf{c} \cdot A l N+3 H_{2} O \rightarrow A l(O H)_{3}+N H_{3} \)
D. \( A l_{2} O_{3} .2 H_{2} O+2 N a_{2} C O_{3} \rightarrow 2 N a A l O_{2}+C O_{2}+2 H_{2} O \)


What are the catalytic amino acids of chymotrypsin?


Which of the following has the highest oxidation potential?
A. \( N a \)
в. \( A g \)
c. \( A l \)
D. \( Z \) n


The median of a set of 9 distinct
observations is \( 20.5 . \) If each of the
largest 4 observations of the set is
increased by \( 2, \) then the median of new
set :
A. is increased by 2 .
B. is decreased by 2.
c. is two times the original median.
D. remains the same as that of the original set.


Ribonucleic acid occurs in
A. Nucleus
B. Cytoplasm
C. Both A and B
D. Mitochondria and chloroplast


A solid sphere, a hollow sphere and a ring, all having equal mass and radius, are placed at the top of an incline and
released. The friction coefficients
between the objects and the incline are equal but not sufficient to allow pure rolling. The greatest kinetic energy at the bottom of the incline will be
achieved by:
A. The solid sphere
B. The hollow sphere
c. The ring
D. All will achieve same kinetic energy


Current is flowing with a current density \( J=480 \) amp \( / \mathrm{cm}^{2} \) in a copper
wire. Assuming that each copper atom contribution one free electron and gives that Avogadro number \( =\mathbf{6 . 0} \times \)
\( 10^{23} \) atoms/mole Density of copper \( = \)
\( 9.0 g / c m^{3} . \) Atomic weight of copper \( = \)
\( 64 g / \) mole Electronic charge \( =1.6 \times \)
\( 10^{-19} \) coulomb. The drift velocity of
electrons is:
\( \mathbf{A} \cdot 1 \mathrm{mm} / \mathrm{s} \)
B. \( 2 \mathrm{mm} / \mathrm{s} \)
c. \( 0.5 \mathrm{mm} / \mathrm{s} \)
D. \( 0.36 \mathrm{mm} / \mathrm{s} \)


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


A salt is made of bivalent ions \( X \) and \( Y \)
each of which is capable of decolorizing
acidified \( K M n O_{4} \) solution. The salt is
likely to be:
A. stannic chloride
B. ferric sulphate.
c. ferrous sulphate.
D. ferrous oxalate


Let \( A \) and \( B \) be two events such that
\( \boldsymbol{P}(\overline{\boldsymbol{A} \cup \boldsymbol{B}})=\frac{1}{6}, \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})=\frac{1}{4} \) and
\( P(\bar{A})=\frac{1}{4}, \) where \( \bar{A} \) stands for the
complement of the event A. Then, the
events \( A \) and \( B \) are
A. Independent but not equally likely
B. Independent and equally likely
c. Mutually exclusive and independent
D. Equally likely but not independent


Which of the following is/ are thermoplastic polymers?
A. Nylon - 6,6
B. Bakelite
c. Polystyrene
D. Terylene


Which of the following reaction is
feasible for the preparation of 1 -propoxy
2 methyl propane?
This question has multiple correct options
A. Williamson's synthesis of
\( \left(M e_{2} C H C H_{2} O N a+M e C H_{2} C H_{2} C l\right) \)
B. Williamson's synthesis of
\( \left(M e_{2} C H C H_{2} C l+M e C H_{2} C H_{2} O N a\right) \)
C. Alkoxymercuration-demercuration of
\( \left(M e_{2} C=C H_{2}+M e C H_{2} C H_{2} O H\right) \)
D. Alkoxy mercuration demercuration of propene with \( M e_{2} C H C H_{2} O H \)


\( F e S_{2} \) is also called because it
has been mistaken for gold.
A. Pure gold
B. Fool's gold
c. Ferric
D. None of these


In human females, the ovarian cycle
begins when the
A. levels of oestrogen reach their maximum
B. hypothalamus stimulates the anterior pituitary to increase its output of FSH and LH
C. level of progesterone drops precipitously
D. hypothalamus increases its release of FSH and LH.


If the displacement, velocity and acceleration of particle in \( S H M \) are
\( \mathbf{1} \boldsymbol{c m}, \mathbf{1} \boldsymbol{c m} / \boldsymbol{s e c} \) and \( \mathbf{1} \boldsymbol{c m} / \boldsymbol{s e c}^{\mathbf{2}} \)
respectively its time period (in secs) will be:
A . \( \pi \)
B. \( 0.5 \pi \)
\( c .2 \pi \)
D. \( 1.5 \pi \)


What chemical process is used for obtaining a metal from its oxide?


The modern periodic table is ordered on the basis of:
A. atomic mass
B. atomic radius
c. atomic charge
D. atomic number


Which of the following has been arranged in order of increasing bond strength:
A \( \cdot Z n_{2}^{2+}<H g_{2}^{2+}<C d_{2}^{2} \)
B \( \cdot C d_{2}^{2+}<H g_{2}^{2+}<Z n_{2}^{2} \)
c. \( Z n_{2}^{2+}<C d_{2}^{2+}<H g_{2}^{2} \)
D. \( H g_{2}^{2+}<C d_{2}^{2+}<Z n_{2}^{2+} \)


If the diameter of the sphere is doubled, the surface area of the resultant sphere
becomes \( x \) times that of the original
one. Then, \( x \) would be
A . 2
B. 3
\( c \cdot 4 \)
\( D \)


What is the IUPAC name of \( K_{2}\left[P t C l_{6}\right] ? \)
A. Potassium hexachloro platinum
B. Potassium hexachloro platinum (IV)
C. Potassium hexa chloro platinate (IV)
D. Dipotassium hexa chloro platinum


When a sound wave of frequency \( 300 \mathrm{Hz} \) passes through medium, the maximum displacement of a particle of the
medium is \( 0.1 \mathrm{cm} . \) The maximum
velocity of the particle is equal to.
\( \mathbf{A} \cdot 60 \pi \mathrm{cm} / \mathrm{s} \)
B. \( 30 \pi \mathrm{cm} / \mathrm{s} \)
\( \mathrm{c} \cdot 60 \mathrm{cm} / \mathrm{s} \)
D. \( 30 \mathrm{cm} / \mathrm{s} \)


Which of the following is a statement?
\( A \). I am Lion.
B. Logic is an interesting subject
C. A triangle is a circle and 10 is a prime number
D. None of these.


will have the most kinetic energy when
each balls is released from the top of
the ramp?
\( A \)
B.
\( c \)
\( D \)


A monoprotic acid in \( 1.00 M \) solution is
\( 0.001 \% \) ionised. The dissociation
constant of acid is:
A \( \cdot \alpha^{2} C+\alpha K-K=0 \)
B . \( \alpha^{2} C-\alpha K-K=0 \)
c. \( \alpha^{2} C-\alpha K+K=0 \)
D \( \cdot \alpha^{2} C+\alpha K+K=0 \)


One integer is two more than a second integer. The first integer added to four times the second is equal to \( 17 . \) Find the values of the two integers.
A .2 and 4
B. 3 and 5
c. 4 and 6
D. 1 and 3


f the tension in the string in the figure
is \( 16 \mathrm{N} \) and the acceleration of each
bock is \( 0.5 m / s^{2}, \) find the friction
coefficients at the to contacts with the
blocks.


\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}} \sec \boldsymbol{x}= \)
\( \mathbf{A} \cdot \sec x \tan x \)
\( \mathbf{B} \cdot \cos x \tan x \)
\( c \cdot \sin x \tan x \)
\( \mathbf{D} \cdot \sec x \cot x \)


If \( \boldsymbol{a}=\boldsymbol{e}^{\boldsymbol{i} \boldsymbol{\alpha}}, \boldsymbol{b}=\boldsymbol{e}^{\boldsymbol{i} \boldsymbol{\beta}}, \boldsymbol{c}=\boldsymbol{e}^{\boldsymbol{i} \gamma} \) and \( \cos \boldsymbol{\alpha}+ \)
\( \cos \beta+\cos \gamma=0=\sin \alpha+\sin \beta+ \)
\( \sin \gamma, \) then prove the following
\( \sum \cos 2 \alpha=0=\sum \sin 2 \alpha \)


Mendeleev arranged the elements in increasing order of their atomic masses and according to their physical properties.
A. True
B. False


Define: Atomic radius, lonic radius, lonisation Enthalpy, Electron Gain enthalpy, Electronegativity.


Which of the following element(s) is/are not react directly with nitrogen to form nitride ?
This question has multiple correct options
A . Na
B. Li
\( c \cdot k \)
D. Rb


The ratio of lateral strain to the linear
strain within elastic limit is known as:
A. Young's modulus
B. Bulk's modulus
c. Rigidity modulus
D. Poisson's ratio


What is the name of joint between ribs
and sternum?
A. cartilaginous joint
B. Angularjoint
c. Gliding joint
D. Fibrous joint


An ice cream cone is the union of a right circular cone and a hemisphere that has the same circular base as the cone.
Find the volume of the ice cream, if the
height of the cone is \( 9 \mathrm{cm} \) and the
radius of its base is \( 2.5 \mathrm{cm} \)


The major excretory product in humans
is
A. Urea
B. Ammonia
c. Uric acid
D. All of the above


A mixture of sodium oxide and calcium
oxide are dissolved in water and
saturated with excess carbon dioxide
gas. The resulting solution is and
it contains
\( \mathbf{A} \cdot \operatorname{Basic} N a O H \) and \( C a(O H)_{2} \)
B. Neutral \( N a_{2} C O_{3} \) and \( C a C O_{3} \)
\( \mathbf{c} . \) Ваsic \( N a_{2} C O_{3} \) and \( C a C O_{3} \)
D. Acidic \( N a O H \) and \( C a C O_{3} \)


From a square metal sheet of side \( 28 \mathrm{cm}, \) a circular sheet is cut off. Find the radius of the largest possible
circular sheet that can be cut. Also find
the area of the remaining sheet.
A \( .14 \mathrm{cm}, 148 \mathrm{cm}^{2} \)
B. \( 14 \mathrm{cm}, 168 \mathrm{cm}^{2} \)
c. \( 12 \mathrm{cm}, 168 \mathrm{cm}^{2} \)
D. \( 14 \mathrm{cm}, 164 \mathrm{cm}^{2} \)


Steam at \( 100^{\circ} \mathrm{C} \) is passed into \( 1.1 \mathrm{kg} \) of water contained in a calorimeter of
water equivalent \( 0.02 \mathrm{kg} \) at \( 15^{\circ} \mathrm{C} \) till the temperature of the calorimeter and its
contents rises to \( 80^{\circ} \mathrm{C} \). The mass of the
steam condensed in kilograms is
A. 0.130
B. 0.065
c. 0.260
D. 0.135


Draw a structure of \( B e C l_{2} \) in vapour
phase.


A triangle can have:
A. one right angle
B. two right angles
C . three obtuse angles
D. none of these


The gas displaced in Victor Meyer's method is air.
A . True
B. False


Hess's law is based on:
A. law if conservation of mass
B. law of conservation of energy
C. first law of thermodynamics
D. None of the above


toppr
Q Type your question_
\( A \)
B.
\( c \)
\( D \)


A sphere is projected up an inclined
plane with a velocity \( v_{0} \) and zero angular velocity as shown. The coefficient of friction between the
sphere and the plane is \( \mu=\tan \theta . \) If
the total time of rise of the sphere is
\( \frac{\boldsymbol{x} \boldsymbol{v}_{0}}{\boldsymbol{g} \sin \theta}, \) find the value of \( \boldsymbol{2} \boldsymbol{x} \)


Maltose is hydrolysed to:
A. Glucose
B. Glucose and Fructose
c. Glucose and Galactose
D. Fructose


Which of the following is not true?
A. Ordinary water is electrolysed more rapidly than \( D_{2} O \)
B. Reaction between \( H_{2} \) and \( C l_{2} \) is much faster than
\( D_{2} \) and \( C l_{2} \)
\( \mathrm{C} \cdot D_{2} \mathrm{O} \) freezes at lower temperture than \( \mathrm{H}_{2} \mathrm{O} \)
D. Bond dissociation energy for \( D_{2} \) is greater than \( H_{2} 1 \)


Which of the following will not change the concentration of ammonia in the
equilibrium?
\( N_{2}(g)+3 H_{2}(g) \rightleftharpoons 2 N H_{3}(g) ; \Delta H= \)
\( -\boldsymbol{x} \boldsymbol{k} \boldsymbol{J} \)
A. increase of pressure
B. increase of temperature
c. decrease of volume
D. addition of catalyst


Species having \( p \pi-p \pi \) overlapping is:
A \( \cdot C H_{4} \)
в. \( H_{3} O^{+} \)
c. \( C O_{2} \)
D. \( H_{2} \)


Let \( X \) denote the number of hours you
study during a randomly selected school day. The probability that \( X \) can
take the values of \( x, \) has the following
form, where \( k \) is some constant \( \boldsymbol{P}(\boldsymbol{X}=\boldsymbol{x})=\left\{\begin{array}{ll}\mathbf{0}, \mathbf{1} & \text { if } \boldsymbol{x}=\mathbf{0} \\ \boldsymbol{K} \boldsymbol{x} & \text { if } \boldsymbol{x}=\mathbf{1} \text { or } \mathbf{2} \\ \boldsymbol{K}(\mathbf{5}-\boldsymbol{x}) & \text { if } \boldsymbol{x}=\mathbf{3} \text { or } \mathbf{4} \\ \mathbf{0} & \text { otherwise }\end{array}\right. \)
What is the probability that you study.
For at least two hour.


Washing soda soften both temporal and
permanent hardness by :
A. Dissolving salts
B. Forming precipitate
c. Forming soluble salts
D. None of the above


What is corrosion? Do gold ornaments
corrode? Justify.


The unit vector perpendicular to \( \vec{A}= \) \( \mathbf{2} \hat{\mathbf{i}}+\mathbf{3} \hat{\mathbf{j}}+\hat{\boldsymbol{k}} \) and \( \overrightarrow{\boldsymbol{B}}=\hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) is:
A \( \cdot \frac{4 \hat{i}-\hat{j}-5 \hat{k}}{\sqrt{42}} \)
B. \( \frac{4 \hat{i}-\hat{j}+5 \hat{k}}{\sqrt{42}} \)
c. \( \frac{4 \hat{i}+\hat{j}+5 \hat{k}}{\sqrt{42}} \)
\( \frac{4 \hat{i}+\hat{j}-5 \hat{k} \hat{k}}{\sqrt{42}} \)


Is 53240 a perfect cube? If not then by which smallest natural numbers should
be divided so that the quotient is a perfect cube?


Find the value of \( a, \) so that the following
system of equations bears no solution \( 2 y-6 x=28 \)
\( 4 y-a x=28 \)
A . -12
B. - -
\( c \cdot 3 \)
D. 6
\( E \cdot 12 \)


The electric field in a certain region is acting radially outward and is given by \( E=A r . A \) charge contained in a sphere
of radius 'a' centered at the origin of the
field, will be given by :
A \( \cdot 4 \pi \epsilon_{0} A a^{3} \)
В \( \cdot \epsilon_{0} A a^{3} \)
\( \mathbf{c} \cdot 4 \pi \epsilon_{0} A a^{2} \)
D. \( A \epsilon_{0} a^{2} \)


Artificial rain based on the principle of :
A. coagulation
B. electrophoretic effect
C. emulsification
D. Tyndall effect


What is value of
\( 1+x+x^{2}+x^{3}+x^{4}+\dots \)
where \( \boldsymbol{x} \neq \mathbf{1} \)


The \( R M S \) velocity of an ideal gas at
\( 27^{0} C \) is \( 0.3 m / \)sec. Its \( R M S \) velocity at
\( 927^{\circ} \mathrm{C} \) is :
A. \( 6 \mathrm{m} / \mathrm{sec} \)
в. \( 0.3 \mathrm{m} / \mathrm{sec} \)
c. \( 0.6 m / s e c \)
D. 3 \( m / \)sec


The value of \( \sin ^{2} 30^{\circ}-\cos ^{2} 30^{\circ} \) is:
A. \( -\frac{1}{2} \)
B. \( \frac{\sqrt{3}}{2} \)
\( c \cdot \frac{3}{2} \)
D. \( \frac{2}{3} \)


If for a sequence \( \left(\boldsymbol{t}_{n}\right), \boldsymbol{S}_{n}=\mathbf{4} \boldsymbol{n}^{2}-\boldsymbol{3} \boldsymbol{n} \)
show that the sequence is an \( A . P \)


Which is least soluble?
A \( \cdot N a_{2} S \)
в. \( M g S \)
c. \( M g C l_{2} \)
D. \( N a C l \)


Give the balanced equations for the
conversion of argentite \( \left(\boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{S}\right) \) to
metallic silver.


In the following properties of a wave, the one which is independent of the other is
A. amplitude
B. velocity
c. wavelength
D. frequency


The major organic product(s) in the reaction given below is/are:
\( \boldsymbol{C H}_{3} \boldsymbol{O C H}\left(\boldsymbol{C H}_{3}\right)_{2}+\boldsymbol{H I} \rightarrow \)
Product\( (s) \)
A \( \cdot I C H_{2} O C H\left(C H_{3}\right)_{2} \)
в. \( C H_{3} O C(I)\left(C H_{3}\right)_{2} \)
c. \( C H_{3} O H+\left(C H_{3}\right)_{2} C H I \)
D. \( C H_{3} I+\left(C H_{3}\right)_{2} C H O H \)


With \( M n O \), colour of the bead in
sodium carbonate-bead test is:
\( A \cdot \) pink
B. black
c. yellow
D. green


Of the following instruments, which instruments is most suitable for
measuring a temperature of \( 400^{\circ} \mathrm{C} ? \)
A. Mercury thermometer
B. Alcohol thermometer
c. Radiation thermometer
D. Thermo-couple thermometer


Which of the following does not comes under microscopic forces?
A. Normal force
B. Tension force
c. Frictional force
D. All of these


The temperature coefficient of the e.m.f. of cell, \( \left(\frac{d E}{d T}\right)_{p} \) is given by:
A \( \cdot \frac{n F}{\Delta S} \)
в. \( \frac{\Delta S}{n F} \)
c. \( \frac{\Delta S}{n F T} \)
D. \( -n F E \)


Lead obtained from galena ore (PbS) by air reduction or carbon reduction
process contains base metal (Cu, Bi, As, Sn, \( Z n \) ) as impurities. Which of the following electrolyte is used for electrolysis of Pb?
\( \mathbf{A} \cdot P b S O_{4}+H_{2} S O_{4} \)
в. \( P b C l_{2}+H C l \)
\( \mathbf{c} \cdot P b S i F_{6}+H_{2} S i F_{6} \)
D. none of these


A star's distance \( (d) \) and its parallax angle \( (p) \) are related to each other as:
A \( \cdot d=\frac{1}{p} \)
в. \( d=\frac{1}{p^{2}} \)
c. \( _{p}=\frac{1}{d^{2}} \)
D. none of these


If \( f:[0, \infty) \rightarrow[0, \infty), \) and \( f(x)=\frac{x}{1+x} \)
then \( f \) is
A. one - one and onto
B. one - one but not onto
c. onto but not one-one
D. nether one-one nor onto


From the top of a cliff \( 24 \mathrm{mt} \) height, a man observes the angle of depression of
a boat is to be \( 60^{\circ} . \) The distance of the
boat from the foot of the cliff is
A. \( 8 \sqrt{3} \mathrm{mt} \)
t
B. \( 8 \sqrt{2} \mathrm{mt} \)
c. \( 8 \sqrt{5} \mathrm{m} \) t
D. \( 8 \mathrm{m} \)


Starch is converted into maltose by an
enzyme:
A. maltase
B. zymase
c. diastase
D. invertage


For the set of reactions, \( \boldsymbol{k}_{1} \)
(i) \( \boldsymbol{A}+\boldsymbol{B} \rightleftharpoons \boldsymbol{C}, \quad(\mathrm{ii}) \boldsymbol{C}+\boldsymbol{B} \quad \stackrel{k_{3}}{\rightarrow} \boldsymbol{D} \)
\( \boldsymbol{k}_{2} \)
\( \boldsymbol{k}_{1}[\boldsymbol{A}][\boldsymbol{B}]-\boldsymbol{k}_{2}[\boldsymbol{C}]-\boldsymbol{k}_{3}[\boldsymbol{C}][\boldsymbol{B}] \) is equal
to:
\( ^{\mathbf{A}} \cdot \frac{-d[A]}{d t} \)
в. \( \frac{-d[B]}{d t} \)
c. \( \frac{d[C]}{d t} \)
D. \( \frac{d[D]}{d t} \)


The radius of gyration of a rotating
circular ring is maximum about which
of the following axis of rotation:
A. neutral axis
B. axis passing through diameter of ring
c. axis passing through tangent of ring in its plane
D. axis passing through tangent of ring perpendicular to plane of ring.


Assertion
The world population was around 2
billion in 1900 which has rocketed to
about 6 billion by 2000
Reason
Increase in longevity due to decline in
death rate, maternal mortality rate and infant mortality rate has been some
major causes of population explosion
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 radius of the shortest orbit in a one-
electron system is 18 pm. It may be
A. hydrogen
B. deuterium
\( \mathrm{c} \cdot H^{+} \)
D. \( L^{++} \)


A slightly divergent beam of charged particles accelerated by a Potential difference B propagates from a point \( \mathbf{A} \) along the axis of solenoid. The beam is brought into focus at a distance I from the point \( A \) at two successive values of
magnetic induction \( B_{1} \) and \( B_{2} \). If the
specific charge \( \mathrm{q} / \mathrm{m} \) of the particles is \( \frac{\boldsymbol{q}}{\boldsymbol{m}}=\frac{\boldsymbol{x} \boldsymbol{\pi}^{2} \boldsymbol{V}}{\boldsymbol{l}^{2}\left(\boldsymbol{B}_{2}-\boldsymbol{B}_{1}\right)^{2}} \cdot \) Find \( \boldsymbol{x} \)


Find the unit vector perpendicular to the plane of given vectors. \( \vec{P}=i-2 j+\hat{k} \)
\( \vec{Q}=2 i+j-\hat{k} \)


The crossopterygians possess scales called as
A. Placoid
B. Cycloid
c. Ganoid
D. cosmoid


A lightning conductor installed in a
building
A. does not allow the lightning to fall on the building
B. repels the lightning
C. forces the lightning to fall in an area where there are no buildings
D. conducts electric charge to the ground when lightning strikes the building


The number of subunits present in haemoglobin are:
A . 2
B. 3
\( c \cdot 4 \)
\( D \)


Let \( A=\{1,2,3,4\} \) and \( R \) is a relation
on \( A \) such that \( R=\{(a, b): a=2 b\} \)


The rate of chemical reaction depends
on the nature of reactants because:
A. the number of bonds broken in the reactant molecules and the number of bonds formed in product molecules changes
B. some of the reactants are solids at the room
temperature
C. some of the reactants are coloured
D. some of rectants are liquid at room temperature


(i) It is used in making leads of pencils.
(ii) It is used as dry lubricant.
(iii) It is used in making black paint and printers ink.
(iv) It is used in nuclear reactors as
moderator.
Which is this substance?
A. Diamond
B. Buckminister fullerene
c. Lampblack
D. Graphite


If \( \int \frac{(4 x+3)}{\sqrt{2 x^{2}+2 x-3}}= \)
\( 2 \sqrt{2 x^{2}+2 x-3}+ \)
\( \frac{1}{\sqrt{\boldsymbol{k}}} \log \left|\boldsymbol{x}+\frac{1}{2}+\sqrt{\boldsymbol{x}^{2}+\boldsymbol{x}-\frac{\boldsymbol{3}}{2}}\right|+\boldsymbol{C} \)
then value of \( k \) is


The value of \( 2^{n}\{1.3 .5 \ldots \ldots .(2 n- \)
\( \mathbf{3})(\mathbf{2 n - 1})\} \) is
A \( \cdot \frac{(2 n) !}{n !} \)
B. \( \frac{(2 n) !}{2^{n}} \)
c. \( \frac{n !}{(2 n !) !} \)
D. None of these


Prove that \( \sqrt{2} \) is an irrational number.


Find the number of atoms present in 0.25 moles of hydrogen.


f maximum energy is stored in
capacitor at \( t=0 \) then find the time
after which current in the circuit will be
maximum.
\[
\mathrm{L}=25 \mathrm{mH}
\]
A. \( \frac{\pi}{2} m s \)
в. \( \frac{\pi}{4} m s \)
\( c . \pi m s \)
D. \( 2 m \)


Read the following statements and find out the incorrect statement.
A) Genetics deals with the inheritance
as well as variation of characters from
parents to offspring
B) Variation is the process by which characters are passed on from parent to
progeny
C) Inheritance is the basis of heredity
D) Inheritance is the degree by which
progeny differ from their parents
E) Human knew from as early as
\( 8000-10000 B . C . \) that one of the
causes of variation was hidden in
sexual reproduction
\( A \cdot B, D \) and \( E \) only
B. A, C and E only
C. B and D only
D. E only


Following are the misconceptions about
root hydrotropism. State whether they
are correct or not.
i. The greater growth of roots in moist
soil zones than in dry soil zones is not
usually a result of hydrotropism. Hydrotropism requires a root to bend
from a drier to a wetter soil zone. Roots
require water to grow so roots that happen to be in moist soil will grow and branch much more than those in dry
soil.
ii. Roots cannot sense water inside
intact pipes via hydrotropism and break the pipes to obtain the water.
iii. Roots cannot sense water several
feet away via hydrotropism and grow toward it. At best hydrotropism probably
operates over distances of a couple millimeters.
A. (i) and (iii) are correct.
B. (i) and
(ii) are correct
C. All are correct.
D. None of the above are correct.


If " \( n " \) number of \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \) molecules are
polymerized to produce chain molecule and ring molecule separately, then the number of \( \boldsymbol{P}-\boldsymbol{O}-\boldsymbol{P} \) linkages formed
is, respectively:
A \( . n \) and \( (n-1) \)
в. \( (n-1) \) and \( (n-1) \)
c. \( (n-1) \) and \( n \)
D. \( n \) and \( n \)


An inductor of inductance 100 m \( H \) is
connected in series with a resistance, a variable capacitance and an AC source of frequency \( 2.0 \mathrm{kHz} \); The value of the
capacitance so that maximum current
may be drawn into the circuit.
\( A \cdot 50 \mathrm{nF} \)
B. 60 nF
\( c \cdot 63 \) nf
D. 79 nf


A car of mass \( 1000 \mathrm{kg} \) moving with a
speed \( 18 k m h^{-1} \) on a smooth road and
colliding with a horizontally mounted
spring of spring constnat \( 6.25 \times \)
\( 10^{3} N m^{-1} . \) The maximum compression
of the spring is
A . \( 1 m \)
B. \( 2 m \)
\( c .3 m \)
D. \( 4 m \)


In a nuclear reaction,
\( _{1}^{2} \boldsymbol{H}+_{1}^{2} \boldsymbol{H} \longrightarrow_{2}^{3} \boldsymbol{H} \boldsymbol{e}+_{0}^{1} \boldsymbol{n} \)
if the masses of \( _{1}^{2} H \) and \( _{2}^{3} H e \) are
\( \mathbf{2 . 0 1 4 7 4 1} \) amu and \( \mathbf{3 . 0 1 6 9 7 7} \) amu
respectively, then the \( Q \) -value of the
reaction is nearly:
B. 3.57 Mev
c. 0.82 Mev
D. 2.45 MeV


Which of the following is not an
intermolecular redox reaction?
\( \mathbf{A} \cdot M g C O_{3} \longrightarrow M g O+C O_{2} \)
B. \( O_{2}+2 H_{2} \longrightarrow 2 H_{2} O \)
\( \mathbf{c} \cdot K+H_{2} O \longrightarrow K O H+(1 / 2) H_{2} \)
D. \( M n B r_{3} \longrightarrow M n B r_{2}+(1 / 2) B r_{2} \)


Planets A and B have same average density. Radius of \( A \) is twice that of \( B \) The ratio of acceleration due to gravity
on the surface of \( A \) and \( B \) is
A . 2:
B. 1:
\( c \cdot 1: 4 \)
D. 4:


A copper wire of length \( 2.2 \mathrm{m} \) and a steel wire of length \( 1.6 \mathrm{m}, \) both of diameter 3.0 \( \mathrm{mm} \) are connected end to end. When
stretched by a force, the elonation in length \( 0.50 \mathrm{mm} \) is produced in the copper wire. The stretching force is \( \left(Y_{c u}=1.1 \times 10^{11} N / m^{2}, Y_{\text {steel}}=2.0 \times\right. \)
\( \left.\mathbf{1 0}^{\mathbf{1 1}} \mathbf{N} / \boldsymbol{m}^{\mathbf{2}}\right) \)
A \( \cdot 5.4 \times 10^{2} N \)
B . \( 3.6 \times 10^{2} N \)
c. \( 2.4 \times 10^{2} N \)
D. \( 1.8 \times 10^{2} N \)


Suggest one way to strengthen the magnetic field in the electromagnet.


State True or False.
Corrosion of iron is a redox process.
A. True
B. False


Angle of reflection is the angle between
and the


Draw electron dot representation for the
formation of \( \boldsymbol{C}_{2} \boldsymbol{H}_{2} \)


Two magnetic poles one of which is three
times as strong as the other exert on each other, a force equal to \( 3 \times 10^{-3} \) when
separated by a distance of \( 10 \mathrm{cm} \). The
strength of the each pole is
\( \mathbf{A} .5 \mathrm{Am}, 15 \mathrm{Am} \)
В. 30 Ат, 10 Ат
\( \mathbf{c} .20 \mathrm{Am}, 60 \mathrm{Am} \)
D. \( 50 A m, 150 A m \)


Colour of black soil is due to
A. Iron, Aluminium, Humus content
B. Presence of zinc, Sulphur, Potassium content
C. Litter content
D. All of the above


Consider the curve \( y=e^{2 x} . \) What is the
slope of the tangent to the curve at (0,1)
\( ? \)
A .
B. 1
\( c \cdot 2 \)
D. 4


The chemical reaction which proceed with the absorption of heat energy are:
A. exothermic reaction
B. endothermic reaction
c. both \( A \) and \( B \)
D. none of the above


The slope of kinetic energy and displacement curve for a particle in motion will be
A. Equal to the acceleration of the particle
B. Directly proportional to the acceleration of the particl
C . Inversely proportional to the acceleration of the particle
D. None of the above


Let \( z_{1}=2-i, z_{2}=-2+i \)
Find
(i) \( \operatorname{Re}\left(\frac{z_{1} z_{2}}{\overline{z_{1}}}\right) \)
(ii) \( \operatorname{Im}\left(\frac{1}{z_{1} \overline{z_{1}}}\right) \)


In Bernoulli's theorem which of the
following is conserved?
A. mass
B. energy
c. liner momentum
D. all the above


The Sl unit of thermal capacity is.
A. Joule
B. Joule \( k g^{-1} \)
c. Joule \( k g-1 K-1 \)
D. Joule \( K^{-1} \)


The simplest formula of a compound containing \( 50 \% \) of an element \( X \)
(Atomic weight 10 ) and \( 50 \% \) of element
\( Y \) (Atomic weight 20 ) is :
A . \( X Y \)
в. \( X_{2} Y \)
c. \( x Y_{2} \)
D. \( X_{2} Y_{3} \)


Which compound is produced by the action of chlorine on dry slaked lime?


Passive absorption of mineral salts is not dependent on
A. Diffusion
B. Osmosis
c. Donnan equilibrium
D. Ionic exchange


Which of the following is not correct?
A \( \cdot N a^{+}+C l^{-} \rightarrow N a C l \)
B. \( N a^{+2}+2 F^{-} \rightarrow C a F_{2} \)
\( \mathbf{c} \cdot N a^{+}+F^{-} \rightarrow N a F \)
D. \( C a^{2+}+2 N a^{+} \rightarrow C a N a_{2} \)


With the decrease in the wave length of the incident radiation the velocity of the photoelectrons emitted from a given metal
A. Remains same
B. Increases
c. Decreases
D. Increases first and then decreases


Given is a diagram of a human blood
smear.

Study the diagram and answer the question that follow. Mention two structural differences
between the parts \( ^{\prime} 1^{\prime} \) and \( ^{\prime} 2^{\prime} \)


By the statement 'survival of the fittest',
Darwin meant that
A. The strongest of all species survives
B. The most intelligent of the species survives
C. The cleverest of the species survives
D. The species most adaptable to changes survives


\( \lim _{x \rightarrow 0} \frac{\sin ^{2} x}{\sqrt{2}-\sqrt{1+\cos x}} \) equals:
A \( .2 \sqrt{2} \)
B. \( 4 \sqrt{2} \)
\( c \cdot \sqrt{2} \)
\( D \)


Give two examples of unicellular
organisms.
A. Hydra, Chara
B. Amoeba, Paramecium
c. Marchantia, Riccia
D. None of these


If first, second and last terms of an A.P.
are \( a, b \) and \( c \)
respectively. Then the number of terms =
A \( \cdot \frac{a+b-2 c}{a-c} \)
в. \( \frac{c+a-2 b}{c-b} \)
c. \( \frac{b+c-2 a}{b-a} \)
D. \( \frac{a+b+2 c}{2(b-c)} \)


Identify the state quantity among the following
This question has multiple correct options
\( A \cdot q \)
B. \( 9-w \)
\( c \cdot q+w \)
D. q/w


Bleaching action of chlorine is by:
A. oxidation
B. reduction
c. neutralization
D. displacement


Velocity-time graph, for a body, being a curve implies
A. that the body is moving with uniform acceleration
B. that the body is moving with variable acceleration
C. that the body is moving with zero acceleration
D. that the body is at rest


A bag contains 8 red and 5 white balls.
Two successive draws of 3 balls are
made at random from the bag without replacements. Find the probability that the first draw yields 3 white balls and the second draw 3 red balls.


Methyl amine with nitrous acid gives
A. methyl alcohol
B. methyl nitrite
c. dimethyl ether
D. methyl nitrite and dimethyl ether


The work done in rotating the magnet from the direction of uniform field to the
opposite direction to the field is \( W \). The
work done in rotating the magnet from the field direction to half the maximum
couple position is :
A \( .2 ~ W \)
B. \( \frac{\sqrt{3} W}{2} \)
c. \( \frac{W}{4}(2-\sqrt{3}) \)
D. \( \frac{W}{4}(1-\sqrt{3}) \)


Which among the following sequences is correct about the bond energy of \( C- \) \( C, C=C \) and \( C \equiv C \) bonds?
A. \( C \equiv C>C=C>C-C \)
в. \( C \equiv C<C=C<C-C \)
c. \( C=C>C \equiv C>C-C \)
D. \( C \equiv C>C-C>C=C \)
\( C \)


Metals are usually not found as nitrates
in their ores. Out of the following two \( (a \) and \( b \) ) reasons which is /are true for the
above observation?
(a) Metal nitrates are highly unstable
(b) Metal nitrates are highly soluble in
water
\( \mathbf{A} \cdot a \) is false but \( b \) is true
B. \( a \) is true but \( b \) is false
c. \( a \) and \( b \) are true
D. \( a \) and \( b \) are false


An object of mass \( m_{1} \) moving with speed v collides with another object of
mass \( m_{2} \) at rest and stick to it. Find the
impulse to the second object.


ff \( x, 2 x+2,3 x+3, \ldots \ldots \) are in G.P., then
the fourth term is
A . -13.
B. 25.1
\( c .-12.6 \)
D. 17.6


Which of the following oxidation state is common for all lanthanides?
\( A \cdot+2 \)
B. +3
\( c \cdot+4 \)
D. +5


Find the slope and \( y \) -intercept of the line given by the equation \( 2 y+3 x=-2 \)


\( \frac{x}{x} \)


How is sinus venosus formed in
Amphibia?


Assertion
Ecosystem is the structural and
functional unit of biosphere consisting of abiotic and biotic components which
interact with each other and maintain a
balance in nature.
Reason
In an ecosystem, energy and matter are continuously exchanged between living and non-living components.
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.


Neurospora crassa is widely used in genetical studies because of all the
following except one.
A. It is a haploid plant and mutations can be easily detected
B. It can be easily cultured
c. Life-cycle short
D. spores are not affected by mutagens


A fire work gave bright crimson light. It probably contained a salt of
A . \( \mathrm{ca} \)
B. sr
c. Ва
D. Mg


Molecular mass of a non-volatile solute
can be determined by which of the following method?
A. cryoscopic method
B. Victor-Meyer's method
c. Graham's method
D. Duma's method


A thin disc of radius \( \mathrm{R} \) and mass \( \mathrm{M} \) has
charge q uniformly distributed on it. It rotates with angular velocity \( \omega . \) The ratio of magnetic moment and angular momentum for the disc is?
A \( \cdot \frac{q}{2 M} \)
в. \( \frac{R}{2 M} \)
c. \( \frac{q^{2}}{2 M} \)
D. \( \frac{2 M}{q} \)


Which of the following is not dimension less
A. Poission ratio
B. Sharing strain
c. Longitudinal strain
D. Volume stress


Differentiate with respect to \( x \) \( \sin \left(m \sin ^{-1} x\right) \)
\( A \cdot \cos \left(m \cos ^{-1} x\right) \)
B . \( \sin \left(m \sin ^{-1} x\right) \)
\( \mathrm{c} \cdot m^{2} \sin x \)
D. none of these


In Rutherford experiment, a 5.3 MeV
\( \alpha- \) particle moves towards the gold nucleus \( (Z=79) . \) How close does the
\( \alpha- \) particle to get the centre of the nucleus,before it comes momentarily to
rest and reverses its motion? \( \left(\boldsymbol{E}_{\mathbf{0}}=\right. \) \( \left.\mathbf{8 . 0} \times \mathbf{1 0}^{-\mathbf{1 2}} \mathbf{F} / \boldsymbol{m}\right) \)
A \( \cdot 3.4 \times 10^{-15} \mathrm{m} \)
B. \( 8.6 \times 10^{-14} \) m
c. \( 4.3 \times 10^{-14} \) и
D. \( 1.6 \times 10^{-14} \mathrm{m} \)


In an ellipse the length of major axis is 10 and the distance between the foci is
8. Then the length of minor axis is:
A . 5
B. 7
\( c \cdot 4 \)
D. 6


A vein differ from an artery in having
A. Strong muscular walls
B. Narrow lumen
C. Valves that control direction of blood flow opposite to heart
D. Valves that control direction of blood flow towards
heart


toppr
Q Type your question.
radicals with almost equal ease, whereas bromine free radicals have a
clear preference for the formation of tertiary free radicals. So, bromine is
less reactive, and more selective
whereas chlorine is less selective and
more effective.
The relative rate of abstraction of
hydrogen by Br is \( \underset{(1600)}{3^{\circ}}>\underset{(82)}{2^{\circ}}>1^{\circ} \)
The relative rate of abstraction of
hydrogen by Cl is \( \mathbf{3}^{\circ}>\underset{(3.8)}{\mathbf{2}}^{\circ}>\mathbf{1}_{(1)}^{\circ} \)
\( (\mathbf{5}) \)
F. What would be the product ratio \( x / y \) in the chlorination of propane if all the
hydrogen were abstracted at equal rate
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{3} \frac{C l_{2}}{h v} \boldsymbol{C H}_{3}- \)
\( \boldsymbol{C H}_{3} \)
\( A \cdot 1 \)
3
B. 3 \( \overline{1} \)
\( c .9 \)
\( \overline{1} \)
\( D \)


In the given circuit, initially \( \boldsymbol{K}_{\mathbf{1}} \) is
closed and \( K_{2} \) is open. Then \( K_{1} \) is
opened and \( K_{2} \) is closed. If \( q_{1}^{\prime} \) and \( q_{2}^{\prime} \) are
charges on \( C_{1} \) and \( C_{2} \) and \( V_{1} \) and \( V_{1} \)
are the voltage respectively, then
A. charge on \( C_{1} \) gets redistributed such that \( V_{1}=V_{2} \)
B. charge on \( C_{1} \) gets redistributed such that \( q_{1}^{\prime}=q_{2}^{\prime} \)
C. charge on \( C_{1} \) gets redistributed such that \( C_{1} V_{1}= \) \( C_{2} V_{2}=C_{1} V \)
D. charge on \( C_{1} \) gets redistributed such that \( q_{1}^{\prime}+q_{2}^{\prime}=2 q \)


If \( \overline{\boldsymbol{a}}=(2 \overline{\boldsymbol{i}}-\mathbf{1 0} \overline{\boldsymbol{j}}+\mathbf{6} \overline{\boldsymbol{k}}) ; \overline{\boldsymbol{b}}= \)
\( (5 \bar{i}-3 \bar{j}+\bar{k}) . \) The ratio of projection of
\( \bar{a} \) on \( \bar{b} \) to projection of \( \bar{b} \) on \( \bar{a} \) is
A . 2: 1
B. 1: 2
\( c \cdot 2: 3 \)
D. 3: 2


What is dielectric substance?


There are two unknown charges, \( Q_{1} \) and
\( Q_{2} . \) A positive charge is placed at P.P is
closer to \( Q_{2} \) than \( Q_{1} \). If the net electric
force acting on the charge at P is zero, then conclusion is :
\[
\frac{\boldsymbol{\rho}_{1}}{\mathbf{0}} \quad \boldsymbol{P} \quad \underline{\boldsymbol{Q}}_{2}
\]
A. Both \( Q_{1} \) and \( Q_{2} \) are positive
B. Both \( Q_{1} \) and \( Q_{2} \) are negative
C. Both \( Q_{1} \) and \( Q_{2} \) have opposite signs
D. Both \( Q_{1} \) and \( Q_{2} \) have the same sign, but the
magnitude of \( Q_{1} \) is greater than the magnitude of \( Q_{2} \)
E. \( Q_{1} \) and \( Q_{2} \) have same sign, but the magnitude of \( Q_{2} \) is greater than the magnitude of \( Q_{1} \)


The probability of a sure event (or certain event) is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
\( D \)


The reduction of phenol to benzene is carried out with sodium borohydride.
A. True
B. False


Establish the formula \( \frac{1}{\boldsymbol{f}}=\frac{1}{\boldsymbol{u}}+\frac{1}{\boldsymbol{v}} \) for \( \mathbf{a} \)
concave mirror, where symbols have their usual meanings.


Assertion
The direction of induced emf is always
such as to oppose the change that causes it.
Reason
Conservation of energy applies to know the direction of induced emf.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If \( A \) is a symmetric and \( B \) skew
symmetric matrix and \( (\boldsymbol{A}+\boldsymbol{B}) \) is non-
singular and \( C=(A+B)^{-1}(A-B) \)
\( \operatorname{then} C^{T}(A+B) C=A+B \)
A. True
B. False


How is oxygen prepared from the following compound?
\( P b O_{2} \)


If \( \sec A+\tan A=m \) and \( \sec A- \)
\( \tan A=n, \) find the value of \( \sqrt{m n} \)
\( A \cdot 0 \)
B. ±1
\( c .\pm 2 \)
\( D \ldots 3 \)


Diatomic molecule which contains two
pi bonds is
в. \( C_{2} \)
\( c \cdot O_{2} \)
D. \( H_{2} \)


The mean deviation of the following data from mean is :
\( \begin{array}{llllll}\text { Class } & 0- & 5- & 10- & 15- & 20 \\ \text { interval } & 5 & 10 & 15 & 20 & 25\end{array} \) Frequency \( \quad 3 \quad 4 \quad 8 \quad 10 \)
\( \mathbf{A} \cdot \mathbf{5} \)
B. 4
\( c \cdot 6 \)
D. 3


Dioxane used as a solvent is obtained
by distilling with
\( \mathbf{A} \cdot \) glycerol, conc. \( H_{2} S O_{4} \)
B. glycerol, conc. \( H_{3} P O_{4} \)
C . glycol, conc. \( H_{2} S O_{4} \)
D. glycol, conc. \( H_{3} P O_{4} \)


\( \mathbf{4} \boldsymbol{H}^{+}+\boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4}^{-}+\boldsymbol{C}_{2} \boldsymbol{O}_{4}^{2-} \rightarrow \boldsymbol{M} \boldsymbol{n}^{2+}+ \)
\( 2 C O_{2}+4 O H^{-} \)
For the preceding reaction, which of the following statements is not always true based on the knowledge that oxalate reacts slowly at room temperature causing a fade in the purple colour due to the manganate ion?
A. Using an acid-base catalyst will increase the overal rate of the reaction
B. There are multiple steps in the reaction mechanism.
c. The reaction is carried out at elevated temperatures to make the procedure practical in terms of time
D. Use of a spectrophotometer and a Beer's Law plot will help determine the rate for the overall reaction mechanism.


Optimum pH for enzyme trypsin is
\( \mathbf{A} \cdot 5 \cdot 9 \)
в. \( 4 \cdot 6 \)
c. 8
D.


A certain current on passing through a galvanometer produces a deflection of 100 divisions. When a shunt of one ohm
is connected, the deflection reduces to
1 division. The galvanometer resistance is
A. \( 100 \Omega \)
B. \( 99 \Omega \)
\( c .10 \Omega \)
D. \( 9.9 \Omega \)


\( \operatorname{Given} f(x)=\frac{[\{|x|\}] e^{x^{2}}\{[|x+\{x\}|]\}}{\left(e^{1 / x^{2}}-1\right) \operatorname{sgn}(\sin x)} \)
for \( \boldsymbol{x} \neq \mathbf{0} \)
\( =0, \) for \( x=0 \)
Where \( \{x\} \) is the fractional part
function; \( [x] \) is the step up function and
\( \operatorname{sgn}(x) \) is the signum function of \( x \) then,
\( \boldsymbol{f}(\boldsymbol{x}) \)
A. is continuous at \( x=0 \)
B. is discontinuous at \( x=1 \)
C. has a removable discontinuity at \( x=0 \)
D. has an irremovable discontinuity at \( x=0 \)


The number of ways of arraigning 6 players to throw the cricket ball so that the oldest player may not throw first is
A .120
в. 600
\( c .720 \)
D. 715


The electric field of certain radiation is
given by the equation \( \boldsymbol{E}= \)
\( 200\left[\sin \left(4 \pi \times 10^{10}\right) t+\sin (4 \pi x\right. \)
\( \left.\left.\mathbf{1 0}^{\mathbf{1 5}}\right) \boldsymbol{t}\right] \) falls in a metal surface having
work function \( 2.0 e V . \) The maximum
kinetic energy ( in eV) of the photoelectrons is [use Planck's
constant \( (h)=6.63 \times 10^{-34} J-s \) and
electron charge \( \left(\boldsymbol{E}=\mathbf{1 . 6} \times \mathbf{1 0}^{-\mathbf{1 9}} \boldsymbol{C}\right) \)
A. 3.3
B. 4.3
c. 5.3
D. 6.3
E. 7.3


State whether the given statement is
True or False.

A concave lens is always tapering at edges and thicker in the middle.


Egg shell is made up of a chemical. In
which of the two ores this chemical is
present?
A. lime stone: \( C a C O_{3} \), Dolomite \( : C a C O_{3} . M g C O_{3} \)
B. lime stone: \( C a C O_{3} . M g C O_{3} \), Dolomite \( : C a C O_{3} \)
c. lime stone \( : C a_{2} C O_{3} \), Dolomite \( : C a_{2} C O_{3} . M g C O_{3} \)
D. None of these


The displacement of a particle is
described by \( \boldsymbol{x}=\boldsymbol{t}+\mathbf{2} \boldsymbol{t}^{2}+\mathbf{3} \boldsymbol{t}^{3}-\boldsymbol{4} \boldsymbol{t}^{4} \)
The acceleration at \( t=3 \sec \) is
A . +378 units
B. +374 units
c. -378 units
D. -374 units


\( 1,2,3, \) butanetriol undergoes oxidative
cleavage of \( H I O_{4} . \) During this process
This question has multiple correct options
\( A \)
equivalent of \( \mathrm{HIO}_{4} \) consumed \( \& \mathrm{HCO}_{2} \mathrm{H} \)
\( \& \mathrm{H}_{3} \mathrm{C}-\mathrm{C}-\mathrm{CO}_{2} \mathrm{H} \) are formed
\( \| \)
B. 2 equivalents of \( H I O_{4} \) consumed \& \( H C O_{2} H \) \( H C H=O \& C H_{3}-C H=O \) are formed
C .3 equivalents of \( H I O_{4} \) consumed \& \( H C O_{2} H \) (2 eq.) \&
1 eq. of \( C H_{3} C O_{2} H \) are formed
D. 2 equivalents of \( H I O_{4} \) consumed \& 2 eq. of \( H C O_{2} H \)
\& 1 eq. of \( C H_{3} C H=O \) is formed.


Solve the inequalities for real \( x \) \( \frac{x}{4}<\frac{(5 x-2)}{3}-\frac{(7 x-3)}{5} \)


Name the type of lens which is used to
correct?
i) Myopia
ii) Hypermetropia.


Reduction of acetyl chloride with \( H_{2} \) in
presence of Pd and \( B a S O_{4} \) gives :
A. \( C H_{3} C O C H_{3} \)
в. \( C_{2} H_{5} O H \)
с. \( C H_{2} \) СООН
D. \( C H_{3} C H O \)


U-r graph of a particle performance SHM is as shown in figure. What
conclusion cannot be drawn from the
graph?
A. Mean position of the particle is at \( r=2 \mathrm{m} \)
B. Potential energy of the particle at mean position is 10 .
C. Amplitude of oscillation is \( 1 \mathrm{m} \)
D. None of these


The reaction: \( \boldsymbol{P} \boldsymbol{C l}_{3}+\boldsymbol{3} \boldsymbol{H}_{2} \boldsymbol{C}_{2} \boldsymbol{O}_{4} \rightarrow \)
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3}+\boldsymbol{3} \boldsymbol{C} \boldsymbol{O}+\boldsymbol{3} \boldsymbol{C} \boldsymbol{O}_{2}+\boldsymbol{3} \boldsymbol{H} \boldsymbol{C l} \) is a
disproportionation reaction
If true enter 1 , else enter 0 .
\( A \)


Which of the following statements are true about the dilute solutions of alkali
metals in liquid ammonia? This question has multiple correct options
A. They are deep blue coloured solutions
B. They are highly conducting in nature
c. They are diamagnetic in nature
D. Ammoniated cations and ammoniated anions are formed in the solution


An underground specialised shoot with reduced disc like stem covered by
fleshy leaves is
A. Bulb
B. Bulbil
C. Rhizome
D. Rhizophore


Which of the following amino acid has hydroxyl methyl group as its R group?
A. Serine
B. Proline
c. Alanine
D. Arginine


The sodium extract of an organic
compound on boiling with \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) and
on subsequent treatment with ammonium molybdate solution gives a yellow precipitate. Which of the following elements may be present in the compound?
A. Nitrogen
B. Sulphur
c. Phosphorus
D. Halogen


Blood pressure is measured with an
instrument called as
A. Spirometer
B. Sphygmomanometer
c. Perometer
D. None of the above


Assertion
If a point charge \( q \) is placed in front of an infinite grounded conducting plane surface, the point charge will experience a force.
Reason
This force is due to the induced charge
on the conducting surface which is at zero potential.
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 sum of the real roots of the
equation \( |\boldsymbol{x}-\mathbf{2}|^{2}+|\boldsymbol{x}-\mathbf{2}|-\mathbf{2}=\mathbf{0} \)
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D.


\( \Delta H_{f}=-98.2 \mathrm{K} . \mathrm{Cal} / \mathrm{mole} \)
\( \boldsymbol{S}_{N a}=36 \mathrm{K.Cal} / \mathrm{mole} \)
\( \boldsymbol{I}_{N a}=118.5 \mathrm{K} . \mathrm{Cal} / \mathrm{mole} \)
\( \frac{1}{2} D_{C l_{2}}=29 \mathrm{K} . \mathrm{Cal} / \mathrm{mole} \)
\( \boldsymbol{U}_{N a C l}=-184.2 \mathrm{K} . \mathrm{Cal} / \mathrm{mole} \)
From the data given below for \( N a C l \)
the electron affinity of chlorine \( \left[-\boldsymbol{E}_{\boldsymbol{a}}\right] \) is:
A . -97.5 K.cal/ mole
B. -108 K.cal/mole
c. -75 K.cal/mole
D. -128 K.cal/mole


Evaluate: \( \int \frac{1}{9 x^{2}+49} d x \)


What is the maximum number of
orbitals that can be identified with the
following quantum numbers?
\( \left[n=3 ; l=1 ; m_{l}=0\right] \)
\( A \)
B. 2
\( c \cdot 3 \)
D.


Which of the following characteristics is not correct for physical adsorption?
A. Adsorption is spontaneous
B. \( \Delta H \) and \( \Delta S \) are negative
c. It is reversible in nature
D. Degree of adsorption increa ture


Assertion
In a sinusoidal travelling wave on a string potential energy of deformation of string element at extreme position in maximum.
Reason
The particles in sinusoidal travelling wave perform SHM.
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


If a newton's colour disc composed of seven colours is rotated at high speed, it appears as
A. Seven coloured disc rotating
B. Few colours merge and only three dominant colours are visible
c. Colours mix and it appears white
D. colours mix giving a sparkling effect


In \( \triangle A B C, \overline{X Y} \) is paralled to \( \overline{A C} \) and
divides the triangle into two parts of equal area, Then the \( \frac{A X}{A B} \) equals
A \( \cdot \frac{\sqrt{2}+1}{2} \)
B. \( \frac{2-\sqrt{2}}{2} \)
c. \( \frac{2+\sqrt{2}}{2} \)
D. \( \frac{\sqrt{2}-1}{2} \)


The general solution of \( \sin \theta=0 \) is
A \( \cdot\left(n+\frac{1}{2}\right) \pi \)
в. \( n \pi+(-1)^{n} \frac{\pi}{2} \)
\( c . n \pi \)
D. none


Let \( A=\{1,2,3, \ldots, 14\} . \) Define a relation \( \boldsymbol{R} \) from \( \boldsymbol{A} \) to \( \boldsymbol{A} \) by \( \boldsymbol{R}=\{(\boldsymbol{x}, \boldsymbol{y}) \)
\( \mathbf{3} \boldsymbol{x}-\boldsymbol{y}=\mathbf{0} \text { where } \boldsymbol{x}, \boldsymbol{y} \in \boldsymbol{A}\} . \) Write down
its domain, co-domain and range.


Which is not the renewable source of
energy?
A. wind
B. water
c. natural gas
D. tides


Which of the following is a feature of physical change?
A. It is reversible
B. It is temporary
c. No new substance is formed
D. All of the above


Find the resultant magnetic moment
when \( \boldsymbol{\theta}=\mathbf{2 4 0}^{\circ} \)
\( \mathbf{A} \cdot M / 4 \pi \)
в. \( 2 M / \pi \)
c. \( 3 M / \pi \)
D. \( 3 \sqrt{3} M / 4 \pi \)


Which of following is unary operation?
A. addition
B. multiplication
c. square root
D. None of Above


Write a short note on Cellulose.


Find the number of compounds from the list below that will be oxidised by
Tollens reagent (Ammonical silver nitrate solution)
\( \boldsymbol{H}_{3} \boldsymbol{C}-\boldsymbol{C H O} \quad \boldsymbol{H}_{3} \boldsymbol{C}-\stackrel{\stackrel{O}{\|}}{\boldsymbol{C}-} \)
\( \boldsymbol{C H}_{3} \quad \boldsymbol{H}_{3} \underset{_{O H}^{\boldsymbol{I}}}{\boldsymbol{C}-\boldsymbol{C}}-\boldsymbol{C H}_{3} \)
\( \boldsymbol{H}_{3} \boldsymbol{C}-\boldsymbol{C H}_{2} \boldsymbol{C} \equiv \)
\( \boldsymbol{C H} \quad \boldsymbol{H}_{3} \boldsymbol{C}-\boldsymbol{C} \equiv \boldsymbol{C}- \)
\( \boldsymbol{C H}_{3} \quad \) Fructose


When a source moves away from stationary observer with velocity v then
apparent change in frequency is \( \Delta n_{1} \)
When an observer approaches the stationary source with same velocity
then change in frequency is \( \Delta n_{2} \) then :
A \( \cdot \Delta n_{1}=\Delta n_{2} \)
в. \( \Delta n_{1}>\Delta n_{2} \)
c. \( \Delta n_{1}<\Delta n_{2} \)
D. \( \Delta n_{1}=2 \Delta n_{2} \)


If the simple interest on 3000 rupees is 600 rupees at a certain rate for a certain number of years, what would the
interest be on 1500 rupees under the
same condition?
A. 300 rupees
в. 1000 rupees
c. 700 rupees
D. 500 rupees


Which of the following eliminates the species from a particular area?
I. Use of insecticides
II. Hunting of the species as prey
III. Habitat destruction
A. True
B. False


The mass of the moon is \( \frac{1}{81} \) of the earth
but the gravitational pull is \( \frac{1}{6} \) of the
earth. It is due to the fact that
A the radius of earth is \( \frac{9}{\sqrt{6}} \) of the moon
B. The radius of moon is \( \frac{81}{6} \) of the eartt
c. Moon is the satellite of the earth
D. None of the above


How many terms in the column is
associated to stonewort?
Protandrous, Gynandrous, shield cells, coronary cells, Tube cells, Archegoniophore, Globule, Monoecious
A. 5
B. 6
\( c \cdot 7 \)
\( D \)


Take a circle with centre \( C \) and
construct a tangent to a circle from an
external point \( \boldsymbol{P} \)


Two resistances are expressed as
\( \boldsymbol{R}_{1}(\mathbf{4} \pm \mathbf{0 . 5} \%) \boldsymbol{\Omega} \) and \( \boldsymbol{R}_{2}(\mathbf{1 2} \pm \mathbf{0 . 5} \%) \boldsymbol{\Omega} \)
The net resistance when they are
connected in series with percentage
error is:
(In series \( \left.\boldsymbol{R}=\boldsymbol{R}_{1}+\boldsymbol{R}_{2}\right) \)
A . \( (16 \pm 0.5 \%) \Omega \)
B. \( (16 \pm 6.25 \%) \Omega \)
c. \( (16 \pm 22 \%) \Omega \)
D. \( (16 \pm 2.2 \%) \Omega \)


Heat is added to an ideal gas, and the
gas expands. In such a process the
temperature
A. must always increase
B. will remain the same if the work done equals the heat added
C. must always decrease
D. will remains the same If change in internal energy equals the heat added.


Why are metals lustrous?
A. Light is transmitted through delocalized electrons
B. They have a high boiling point
C. Light is reflected through delocalized electrons
D. Light does not travel through metals at all


Sequence the life cycle of a silkworm
with pupa, larva, egg and adult stages.


The intensity at the central maximum
(0) in a Yong's double slit experimental
set-up shown in the figure is \( I_{O} \). If the
distance \( O P \) equals one-third of the
fringe width of the pattern. show that
the intensity at point P.would equal \( \frac{I_{O}}{4} \)


Fill up the table on finding complementary angle of given angle:
\( \begin{array}{ll}\text { Angle }-1 & \text { Angle }-2 \\ \text { 500 }\end{array} \)
(1)
\( 50^{\circ} \) 1
一较 - (1) and
(2) , a \( - \) \( - \) \( 63^{\circ} \)
(3) an \( 47^{\circ} \) and \( - \) (4) (i)
(5)
(6) " \begin{tabular}{ll}
\( 47^{\circ} \) & \( - \) \\
\( 56^{\circ} \) & \( 12^{\circ} \) \\
\hline & \\
\( 67^{\circ} \) & \\
\hline
\end{tabular} "of


According to kinetic theory of gasses at
Zero kelvin
a) Pressure of ideal gas is zero
b) Volume of ideal gas is zero
c) Internal energy of ideal gas is zero
d) Matter exists in gaseous state only
A . a \& dare true
B. a,b \& d are true
c. a,b \& c are true
D. All are true


Find the equation of the hyperbola satisfying the give conditions: Vertices
\( (\pm \mathbf{7}, \mathbf{0}) \)
\( e=\frac{4}{3} \)


Which of the following compounds will be dissociated into its constituent
ions?
This question has multiple correct options
A. Solid \( N a C l \)
B. Molten NaCl
c. solid \( C a C l_{2} \)
D. Molten \( C a C l \)


Assertion
(A): Hydrogen shows resemblance with alkali metals as well
as halogens. Reason
(R): Hydrogen exists in atomic form only at high temperature.
A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true but R is not a correct explanation of
c. \( A \) is true but \( R \) is false
D. A is false but R is true


A prokaryotic autotrophic nitrogen fixing symbiont roots are found in
A. Plsum
B. Alnus
c. cycas
D. cicer


The wave number of the first line of
Balmer series of H atom is \( 15200 \mathrm{Cm}^{-1} \)
What is the wave number of the first
line of Balmer series of \( L i^{2+} \) ion?
A. \( 15200 \mathrm{Cm}^{-1} \)
B. \( 6080 \mathrm{Cm}^{-1} \)
c. \( 76000 C m^{-1} \)
D. \( 136800 C m^{-1} \)


Gasoline combusts in the presence of
oxygen:
A. There is not enough information to tell if this is a physical or chemical property.
B. This is neither a physical nor a chemical property.
C. This is both a physical and chemical property.
D. This is a physical property.
E. This is a chemical property


The radius of curvature of the curvedd
surface of a plano-convex lens is \( 20 \mathrm{cm} \) If the refractive index of the material of
the lens be \( 1.5, \) it will
A. act as convex lens only for the objects that lie on its curved side
B. act as a concave lens for the objects that lie on its curved side
c. act as a convex lens irrespective of the side on which the object lies.
D. act as a concave lens irrespective of side on which the object lies


Two vectors \( A \) and \( B \) have equal
magnitudes. If magnitude of \( A+B \) is equal to \( n \) times the magnitude of \( A-B \)
then the angle between \( A \) and \( B \) is
A \( \cdot \cos ^{-1}\left(\frac{n-1}{n+1}\right) \)
B. \( \cos ^{-1}\left(\frac{n^{2}-1}{n^{2}+1}\right) \)
c. \( \sin ^{-1}\left(\frac{n-1}{n+1}\right) \)
D. \( \sin ^{-1}\left(\frac{n^{2}-1}{n^{2}+1}\right) \)


The figure shows a circuit consisting of four capacitors. Find the effective
capacitance between \( \boldsymbol{X} \) and \( \boldsymbol{Y} \)


The displacement of a particle is
represented by the equation \( y= \)
\( \sin ^{3}(\omega t) . \) The motion is
A. non-periodic
B. periodic but not simple harmonic
c. simple harmonic with period \( \frac{2 \pi}{\omega} \)
D. simple harmonic with period \( \frac{\pi}{\omega} \)


In a periodic motion the repetition
pattern repeats:
A. over a fixed interval of time
B. over a fixed interval of distance
C. over a fixed change in velocity
D. over a fixed change in acceleration


Simplify: \( \frac{(-33) \times(96)}{(11) \times(-24)} \)
A. -14
B. 12
c. 10
D. -12


The multiplicative identity for integers
is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
c. \( 0 . \)
\( D \)


The coefficient of linear expansion \( \alpha \) is that of the coefficient of real
expansion.
A. double
B. one third
c. half
D. equal to


Two spheres of radii \( r_{1} \) and \( r_{2}\left(r_{1}>r_{2}\right) \)
is dropped through a tube full of
glycerine. Their terminal velocities \( \boldsymbol{v}_{1} \)
and \( v_{2} \) are calculated in the experiment.
Which of the following is true?
A \( \cdot v_{1}=v_{2} \)
В. \( v_{1}>v_{2} \)
c. \( v_{1}<v_{2} \)
D. \( v_{1} \) and \( v_{2} \) are independent of \( r_{1} \) and \( r_{2} \)


Find the sum of period number and group number of phosphorous?
A . 16
B. 17
c. 18
D. 19


A ball is thrown upwards. It returns to ground describing a parabolic path.Which of the following remains constant.
A. Speed of the ball
B. Kinetic energy of the ball
c. vertical component of velocity
D. Horizontal component of velocity


The mass of oxygen gas (in Kilo grams) occupying a volume of 11.2 litre at a temperature \( 27^{0} \mathrm{C} \) and a pressure of \( 76 \mathrm{cm} \)
of mercury is :
(Molecular weight of oxygen \( =32 \) )
A. 0.001456
B. 0.01456
c. 0.1456
D. 1.1456


Give two examples of Colloid.


Factors of \( 6 p-12 q \) are
This question has multiple correct options
\( \mathbf{A} \cdot(p-2 q) \)
B. 2
\( \mathbf{c} \cdot(2 q-p) \)
D. 3


Calculate the mass of compound (molar mass \( =256 g m o l^{-1} \) ) to be dissolved in
\( 75 g \) of benzene to lower its freezing
point by \( 0.48 K\left(K_{f}=5.12 K k g m o l^{-1}\right) \)


The chemistry of the actinoids is not so smooth as that of the lanthanoids.
Justify this statement by giving some examples from the oxidation state of these elements.


If \( \boldsymbol{y}=\cot ^{-1}\left[\frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}}\right] \)
where \( 0<x<\frac{\pi}{2}, \) then \( \frac{d y}{d x} \) is equal to
A. \( -\frac{1}{2} \)
B. 2
\( c \cdot \sin x+\cos x \)
\( \mathbf{D} \cdot \sin x-\cos x \)


If \( \vec{a}=\hat{i}-2 \hat{j}+3 \hat{k}, \vec{b}=2 \hat{i}+3 \hat{j}-\hat{k} \) and
\( \overrightarrow{\boldsymbol{c}}=\boldsymbol{r} \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+(\boldsymbol{2} \boldsymbol{r}-\boldsymbol{1}) \hat{\boldsymbol{k}} \) are three
vectors such that \( \vec{c} \) is parallel to the plane of \( \vec{a} \) and \( \vec{b}, \) then \( r \) is equal to?
\( \mathbf{A} \cdot \mathbf{0} \)
B . 2
c. -1
\( D \)


Which of the following elements in an
organic compound cannot be detected
by Lassaigne's test?
A. Nitrogen
B. Sulphur
c. Chlorine
D. Hydrogen


The area bounded by the curves \( y= \)
\( -\sqrt{-x} \) and \( x=-\sqrt{-y} \) were \( x, y \leq 0 \)
This question has multiple correct options
A. Can not be determined
B. is \( 1 / 3 \)
\( c \cdot \) is \( 2 / 3 \)
D. is same as that of the figure by the curves \( y= \) \( \sqrt{-x} ; x \leq 0 \) and \( x=\sqrt{-y} ; y \leq 0 \)


Suppose \( A \) is a matrix such that \( A^{2}= \)
\( \boldsymbol{A} \) and \( (\boldsymbol{I}+\boldsymbol{A})^{10}=\boldsymbol{I}+\boldsymbol{k} \boldsymbol{A}, \) find \( \boldsymbol{k} \)


The charge on the colloidal particles does not account for the stability of solutions.
A. True
B. False


The threshold frequency of a metal corresponds to the wavelength of \( x n m \) In two separate experiments \( A \) and \( B \), incident radiations of wavelengths \( 1 / 2 x \) nm and \( 1 / 4 \times \) nm respectively are used. The ratio of kinetic energy of the released electrons in experiment B to that in experiment \( A \) is:
\( A \cdot 1 / 3 \)
B. 2
\( c \cdot 4 \)
\( D .3 \)
E. \( 1 / 2 \)


What is the quantity of heat released
per kg of water per \( 1^{\circ} \mathrm{C} \) fall in temperature?


State True or False.
Bond order is the measurement of bond
strength.
A. True
B. False


The annual maintenance cost of a
machine in a factory over a seven years period is represented in the histogram.
In which year the maintenance is very
low?
A . \( 1995-1996 \)
B. \( 1996-1997 \)
\( \mathbf{c} .1997-1998 \)
D. \( 1998-1999 \)


The number of moles of \( K M n O_{4} \) that will be needed to react with one mole of
sulphite ion in acidic solution is :
A \( \cdot \frac{2}{5} \)
B. \( \frac{3}{5} \)
\( c \cdot \frac{4}{5} \)
D.


In the sodium fusion test of organic compounds, the nitrogen of an organic compound is converted to:
A. sodium cyanide
B. sod-amide
c. sodium nitrite
D. sodium nitrate


A cart of mass M has a vlock of mass \( \mathrm{m} \)
in contact with it as shown in fig. The
coefficient of friction between the block
and the cart is \( \mu . \) What should be the
minimum acceleration of the cart so
that the block of mass \( \mathrm{m} \) does not fall?


Which of the following statements are
correct?
This question has multiple correct options
A. An activating group is an electron-releasing group
B. An activating group activates all positions of the benzene ring
C. The effect of any group-whether activating or deactivating - is the strongest at the ortho-and parapositions in the benzene ring
D. An activating group activates only the ortho-and parapositions in the benzene ring


If \( \frac{1}{2}, \frac{1}{2}, n(n<0) \) are the dos of a line,
then the angle made by that line with \( \boldsymbol{O} \boldsymbol{Z} \) where \( \boldsymbol{O}=(\mathbf{0}, \mathbf{0}, \mathbf{0}) \) is
A \( \cdot \frac{-1}{\sqrt{2}} \)
B . \( 45^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 135^{\circ} \)


Position of a particle in a rectangular coordinate system is (3,2,5) . Then its position vector will be
A \( \cdot 3 \hat{i}+5 \hat{j}+\hat{k} \)
B \( \cdot 3 \hat{i}+2 \hat{j}+5 \hat{k} \)
c. \( 5 \hat{i}+3 j+2 \hat{k} \)
D. None of tese


You have to show that \( \Delta A M P \cong \Delta A M Q \)
In the following proof, supply the
missing reasons
steps Reasons
(i) PM=QM
(i)
\( \angle \mathrm{PMA}=\angle \mathrm{QMA} \)
(i)
(ii) AM =AM
(iii)
(iv) \( \Delta \mathrm{AMP} \cong \Delta \mathrm{AMQ} \)
(iv)


State True or False.
The electrical energy released from an electrochemical cell can do useful work.
A. True
B. False


The internal resistance of a cell is the
resistance of
A. Electrolyte not in the cell
B. Electrolyte of the cell
c. vessel of the cell
D. None of these


The stress \( (y) \) and the strain \( (x) \) are measured for a wire by adding loads to one end of the wire and the other end suspended. They follow an equation \( y=3 x+1 \) from \( x=0 \) to 3 and \( y=-4(x- \)
3) \( ^{2}+10 \) for \( x>3 \). In which region is
Hooke's law valid
A \( . x=0 \) to 3
B. \( x=3 \)
\( c \cdot x>3 \)
D. for all values of \( x \)


How many lines of symmetry does this star have?
\( A \cdot 2 \)
B. 5
\( c \cdot 4 \)
\( D \)


A 5 metre long wire is fixed to the
ceiling. A weight of \( 10 k g \) is hung at the
lower end and is 1 metre above the floor.
The wire was elongated by 1 mm. The energy stored in the wire due to stretched is
A . zero
B. 0.05joule
c. 100 joule
D. 500 joule


For a given alkyl group, the boiling points of alkyl halides follow the order:
A \( . R I>R B r>R C l \)
в. \( R C l>R B r>R I \)
c. \( R I>R C l>R B r \)
D. \( R B r>R I>R C l \)


\( \int_{0}^{\frac{\pi}{2}} \frac{200 \sin x+100 \cos x}{\sin x+\cos x} d x= \)
A \( .50 \pi \)
B . \( 25 \pi \)
\( c .75 \pi \)
D. \( 150 \pi \)


A particle starting from a point \( A \) and
moving with a positive constant
acceleration along a straight line reaches another point \( B \) in time \( T \)
Suppose that the initial velocity of the particle is \( u>0 \) and \( P \) is the mid-point
of the line \( A B . \) If the velocity of the
particle at point \( \boldsymbol{P} \) is \( \boldsymbol{v}_{1} \) and if the velocity at time \( \frac{T}{2} \) is \( v_{2}, \) then
\( \mathbf{A} \cdot v_{1}=v_{2} \)
B \( . v_{1}>v_{2} \)
\( \mathbf{c} \cdot v_{1}<v_{2} \)
D. \( v_{1}=\frac{1}{2} v_{2} \)


If \( \tan \theta_{1}=k \cot \theta_{2}, \) then \( \frac{\cos \left(\theta_{1}+\theta_{2}\right)}{\cos \left(\theta_{1}-\theta_{2}\right)}= \)
A. \( \frac{1+k}{1-k} \)
B \( \cdot \frac{1-k}{1+k} \)
c. \( \frac{k+1}{k-1} \)
D. \( \frac{k-1}{k+1} \)


Solve: \( \frac{3 x+5}{2 x+7}=5 \)


Which of the following reasons make
nuclear waste an extremely potent
pollutant?
This question has multiple correct options
A. It causes mutations at a very high rate
B. It is responsible for heating of Earths surface and atmosphere
C. It is a very challenging task to provide safe disposal of radioactive wastes
D. All of the above


If this solution were diluted to 10 times
its volume, what would be the \( p H \)
? (write the value to the nearest integer)


Solve for \( \boldsymbol{x}, \boldsymbol{y} \)
\( (a+2 b) x+(2 a-b) y=2,(a- \)
2b) \( x+(2 a+b) y=3 \)
A. \( x=(5 b-2 a), y=10 a b \)
в. \( x=\frac{5 b-2 a}{10 a b}, y=\frac{a+10 b}{10 a b} \)
c. \( x=\frac{5 b-2 a}{10 a b}, y=\frac{5 a+10 b}{10 a b} \)
D. \( x=\frac{5 b+2 a}{10 a b}, y=\frac{a+10 b}{10 a b} \)


What is the Specific Heat capacity of water in \( \mathrm{Jkg}^{-1} \boldsymbol{K}^{-1} \) ?
A . 4.12
B. 4200
c. 4.2
D. 420


The decreasing order of bond angle is:
A \( \cdot N O_{2}>N O_{2}^{+}>N O_{2}^{-} \)
B . \( N O_{2}^{-}>N O_{2}>N O_{2}^{+} \)
\( \mathbf{c} \cdot N O_{2}^{+}>N O_{2}>N O_{2}^{-} \)
D. \( N O_{2}^{+}>N O_{2}^{-}>N O_{2} \)


n Fig. if \( \boldsymbol{A B} \| \boldsymbol{D} \boldsymbol{E}, \angle \boldsymbol{B A C}=\mathbf{3 5}^{\circ} \) and
angleC \( D E=53^{\circ}, \) find \( \angle D C E \)


Plants take nitrogen from the soil by absorption through their roots as This question has multiple correct options
A. Nitrate ions
B. Nitrite ions
c. Ammonium ions
D. All of the above


Mendelism is genetics of
A. Haploids
B. Diploids
c. Prokaryotes
D. All of the above


The sum of lengths of any two sides of a triangle is always the
third side.
A. greater than
B. less than
c. equal to
D. none of these


Why are \( M n^{2+} \) compounds more stable
than \( F e^{2+} \) towards oxidation to their
+3 state?


In the given complexes \( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)\right]^{3+} \ldots \)
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5} \boldsymbol{C l}\right]^{2+} \ldots .2 \)
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right]^{3+} \ldots . .3 \)
The decreasing order of \( \lambda \) absorbed is:
A. \( (i i i)>(i i)>(i) \)
B. \( (i i i)>(i)>(i i) \)
c. \( (i i)>(i)>(i i i) \)
D. \( (i i)>(i i i)>(i) \)


Hydrogen is not found free in the
nature because hydrogen is a/an:
A. reactive element
B. non-reactive element
c. electropositive element
D. none of the above


The terminals of a \( 18 V \) battery with an
internal resistance of \( 1.5 \Omega \) are
connected to a circular wire of
resistance \( 24 \Omega \) at two points distant at
one quarter of the circumference of a
circular wire. The current through the bigger arc of the circle will be
\( \mathbf{A} \cdot 0.75 A \)
в. \( 1.5 A \)
c. \( 2.25 A \)
D. \( 3 A \)


Assertion
There is a decrease in photosynthesis if the photosynthetic cells are illuminated
by light of \( P_{680} \) nm or more wavelength
Reason
In red drop phenomenon the rate of photosynthesis decrease
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 hormone is not translocated?
A. Auxin
B. Gibberellins
c. ABA
D. Cytokinin
E. Ethylene


If \( A \) is the area of the figure bounded by
the straight lines \( x=0 \) and \( x=2, \) and
the curves \( y=2^{x} \) and \( y=2 x-x^{2} \) then the value of \( 672\left(\frac{3}{\log 2}-A\right) \) is


If the length of the second's hand in a stop-clock is \( 3 \mathrm{cm} \) angular velocity linear velocity of the tip is:
A \( \cdot 0.2047 r a d s^{-1}, 0.0314 m s^{-1} \)
B. 0.2547 rads \( ^{-1}, 0.0314 \mathrm{ms}^{-1} \)
c. \( 0.10472 r a d s^{-1}, 0.06314 m s^{-1} \)
D. 0.1047 rads \( ^{-1}, 0.00314 \mathrm{ms}^{-1} \)


Four couples (husband and wife) decido
to form a committee of four members.
The number of different committees
that can be formed in which no couple
finds a place Is


The quantityjerk, \( j, \) is defined as the
time derivative of an objects acceleration, \( \boldsymbol{J}=\frac{\boldsymbol{d} \boldsymbol{a}}{\boldsymbol{d} \boldsymbol{t}}=\frac{\boldsymbol{d}^{\boldsymbol{3}} \boldsymbol{x}}{\boldsymbol{d} \boldsymbol{t}^{3}} \)
What is the physical meaning of the area under a graph of jerk versus time?
A. The area represents the object's change in acceleration.
B. The area represents the object's acceleration.
c. The area represents the object's change in velocity.
D. The area represents the object's velocity.


If \( \boldsymbol{w}=\frac{\boldsymbol{z}}{\boldsymbol{z}-\frac{1}{\mathbf{3}} \boldsymbol{i}} \) and \( |\boldsymbol{w}|=1 \) then \( \boldsymbol{z} \)
lies on
A . a circle
B. an ellipse
c. a parabola
D. a straight line


Assertion
Systematics is defined as the science of diversity of organisms in evolutionary
context
Reason
Systematics include interrelationship
between organisms
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 is not the function of a NOT gate?
A. Stop a signal.
B. Invert an input signal
c. complement a signal.
D. change the logic in a digital circuit


Find the smallest number by which 243 must be multiplied to obtain a perfect
cube.


When an input signal 1 is applied to a NOT gate, its output is
\( \mathbf{A} \cdot \mathbf{1} \)
B. 0
c. either 0 or 1
D. both 0 and 1


Match the follwoing


a. Complete the table
A
n Atoms \( \begin{array}{ll}\text { Atomic } & \text { Electronic } \\ \text { Number } & \text { Distribution }\end{array} \)
11
12 \( \mathrm{Mg} \) 1
2,8,7
b. Draw the structure of \( H_{2} O \) and \( N H_{3} \)
molecules.


The mammal that does not possess 7 cervical vertebrae is
A . Horse
B. Giraffe
c. Elephant
D. Manatee


Mac Arthur process is used for the extraction of :
A . Au
\( c \cdot c u \)
D. zn


Very short answer type.
Name the source gland and give one main action of the following hormones:
estrogen


Light of wavelength \( \lambda_{0} \) in air enters a
medium of refractive index \( n . \) If two
points \( A \) and \( B \) in this medium lid
along the path of this light at a distance
\( x, \) then phase difference \( \phi_{0} \) between
these two points is
\( ^{\mathbf{A}} \cdot_{0}=\frac{1}{n}\left(\frac{2 \pi}{\lambda_{0}}\right) x \)
B \( \cdot_{\phi_{0}}=n\left(\frac{2 \pi}{\lambda_{0}}\right) x \)
\( ^{\mathbf{c}} \cdot_{\phi_{0}}=(n-1)\left(\frac{2 \pi}{\lambda_{0}}\right) x \)
D \( , \quad \phi_{0}=\frac{1}{(n-1)}\left(\frac{2 \pi}{\lambda_{0}}\right) x \)


The cutting edges of tools like knives, blades etc are provided with sharp edges. Explain why?


For the following three reactions \( a, b, c \) equilibrium constants are given:
1. \( \boldsymbol{C O}(\mathbf{g})+\mathbf{H}_{2} \mathbf{O}(\mathbf{g}) \rightleftharpoons \mathbf{C} \mathbf{O}_{2}(\mathbf{g})+\mathbf{H}_{2}(\mathbf{g}) \)
\( ; \mathbf{K}_{\mathbf{1}} \)
2. \( \mathbf{C H}_{4}(\mathbf{g})+\mathbf{H}_{2} \mathbf{O}(\mathbf{g}) \rightleftharpoons \mathbf{C O}(\mathbf{g})+ \)
\( \mathbf{3} \mathbf{H}_{\mathbf{2}}(\mathbf{g}) ; \mathbf{K}_{\mathbf{2}} \)
3. \( \mathbf{C H}_{4}(\mathbf{g})+\mathbf{2} \mathbf{H}_{\mathbf{2}} \mathbf{O}(\mathbf{g}) \rightleftharpoons \mathbf{C} \mathbf{O}_{\mathbf{2}}(\mathbf{g})+ \)
\( \mathbf{4} \mathbf{H}_{\mathbf{2}}(\mathbf{g}) ; \mathbf{K}_{\mathbf{3}} \)
Which of the following relations is
correct?
A \( \cdot \mathrm{K}_{3}=\mathrm{K}_{1} \mathrm{K}_{2} \)
в. \( \mathrm{K}_{3} \cdot \mathrm{K}_{2}^{3}=\mathrm{K}_{1}^{2} \)
c. \( \mathrm{K}_{1} \sqrt{\mathrm{K}_{2}}=\mathrm{K}_{3} \)
D. \( \mathrm{K}_{2} \mathrm{K}_{3}=\mathrm{K}_{1} \)


If Hunds rule is not obeyed by some elements given below then which atom has maximum magnetic moment?
\( A \cdot F e \)
B. zn
c. \( c r \)
D. Mn


The compounds
\( \left[\boldsymbol{C r}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right] \boldsymbol{C l}_{3},\left[\boldsymbol{C r}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{5}\right] \boldsymbol{C l} \cdot \boldsymbol{H}_{2} \boldsymbol{O} \)
and \( \left[\boldsymbol{C r}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{4} \boldsymbol{C l}_{2}\right] \boldsymbol{C l} \cdot \boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O} \) exhibits:
A . linkage isomerism
B. geometrical isomerism.
c. ionization isomerism.
D. hydrate isomerism.


Sodium when burnt in excess of oxygen
gives sodium oxide. If true enter 1 , else
enter 0


STATEMENT 1: In a \( \Delta A B C, \) if \( A, B, C \)
are in \( A . P . \) and triangle is equilateral,
then \( \cos A+2 \cos B+\cos C=2 \)
STATEMENT 2: In a \( \Delta A B C, \) if \( A, B, C \)
\( \operatorname{are} \operatorname{in} A \cdot P \cdot \) and \( \cos A+\cos B+ \)
\( \cos C=2, \) then the triangle
is isosceles.
A. Statement-1 is true, Statement-2 is true, Statementis correct explanation of Statement-
B. statement-1 is true, statement-2 is true, statement- is not correct explanation for Statement-
c. statement-1 is true, statement-2 is false
D. statement-1 is false, Statement-2 is true


Cerium (atomic number \( =58 \) ) is an
important member of the lanthanoids Which of the following statements about cerium is incorrect?
A. The +4 oxidation state of cerium is not known in solutions
B. The +3 oxidation state of cerium is more stable than the +4 oxidation state
c. The common oxidation states of cerium are +3 and +4
D. Cerium (IV) acts as an oxidising agentt


At mid day hours, the xylem sap is in
state of
A. compression
B. Tension
c. Relaxation
D. Adhesion


A ball is dropped downwards, after 1 sec another ball is dropped downwards from the same point. What is the distance between them after 3 sec? (Take \( g= \)
\( \left.10 m s^{-2}\right) \)
A \( .20 m \)
B. \( 25 m \)
\( c .50 m \)
D. \( 9.8 m \)


The sequence from \( (\boldsymbol{A}) \) to \( (\boldsymbol{D}+\boldsymbol{E}) \) is
called:
A. Wohl's method
B. Ruff method
c. Kiliani's method
D. Ekenstein method


The light beams of intensities in the
ratio of 9: 1 are allowed to interfere.
What will be the ratio of the intensities
of maxima and minima?
A . 3: 1
B. 4: 1
c. 25: 9
D. 81: 1


Which of the following helps in coal formation?
A. Bacteria
B. Gymnosperm
c. Pteridophytes
D. Archaebacteria


Which of the following is incorrect?
A. Fructose is reducing sugar
B. Cellulose has \( \beta \) -D Glucose units
c. DNA has D-ribose
D. Amylopectin is insoluble in water


Which of the following statements is
the contrapositive of the statement, You
win the game if you know the rules but
are not overconfident.
A. If you lose the game then you dont know the rules or you are overconfident
B. A sufficient condition that you win the game is that you know the rules or you are not overconfident
c. If you dont know the rules or are overconfident you lose the game
D. If you know the rules and are overconfident then you win the game


An object is moving in a circular path of
radius \( 3.5 \mathrm{m} \). If it completes one full cycle, what will be the displacement and what is the distance traveled?


"Sexual reproduction is more advance than asexual reproduction" Why?


If 0 is the origin and the coordinates of \( P \) is \( (1,2,-3), \) then find the equation of the plane passing through P and perpendicular to OP.
A. \( x-2 y-3 z=-15 \)
в. \( x+2 y-3 z=14 \)
c. \( x-2 y+3 z=15 \)
D. \( x-2 y-3 z=15 \)


Which halogen has the highest value of negative electron gain enthalpy?
A. Fluorine
B. Chlorine
c. Bromine
D. lodine


An enzyme accelerates a biochemica
reaction by
A. Increasing substrate movements
B. Changing free enzyme
c. Production of heat
D. Lowering energy of activation


In which of the following, all bond length are not equal?
\( \boldsymbol{P C l}_{5}, \boldsymbol{S F}_{4}, \boldsymbol{C l F}_{3}, \boldsymbol{X} \boldsymbol{e F}_{2},\left[\boldsymbol{S F}_{5}\right]^{+},\left[\boldsymbol{C l} \boldsymbol{F}_{4}\right]^{+} \)
\( A \cdot 6 \)
B. 7
\( c \cdot 5 \)
D.


Arrange \( s, p \) and \( d \) sub-shells of a shell in the increasing order to effective
nuclear charge \( \left(Z_{e f f}\right) \) experienced by the electron present in them.
\( A \cdot s>p>d \)
B. p>s>dd
\( c \cdot d>p>s \)
D. none of the above


If the ceiling of a cinema is made flat,
what will happen?
A. No sound will be audible at all
B. Picture will vanish
c. Sound will not reach properly to every person
D. Pictures will not be clear to everyone


Which of the following feature makes chromium suitable for electroplating?
A. Shiny appearance
B. Does not corrode
c. Resistance to scratch
D. All of the above


Derive the expression for magnetic field at a point on the axis of a circular
current carrying loop.


In the uranium radioactive series the
initial nucleus is \( _{92}^{238} \mathrm{U} \) and the final nucleus is \( _{82}^{206} \) Pb. When the uranium nucleus decays to lead, number of \( \alpha \)
particles emitted is and the
number of \( \beta \) -particles emitted is


in Mendeleev's
periodic table was not possible.


State whether given statement is True or False

Iron is a better conductor of heat than
copper
A. True
B. False


Hydrazine is not:
A . a reducing agent
B. an oxidising agent
\( c . \) an acid
D. a base


Which of the following is an additive property?
A. conductance
B. Viscosity
c. Surface tension
D. None of these


The sum of three consecutive odd
numbers is \( 51 . \) Find the numbers.


A copper block of mass \( 50 \mathrm{g} \) is heated to
\( 100^{\circ} \) and placed on a block of ice at \( 0^{\circ} \mathrm{C} \)
The specific heat of copper is \( 0.1 \mathrm{cal} \)
\( g^{-1} \cdot C^{-1} \) and latent heat of ice is
\( 80 c a l g^{-1} . \) The amount of ice melted is
A. \( 6.15 \mathrm{g} \)
B. \( 6.2 \mathrm{g} \)
c. \( 6.25 \mathrm{g} \)
D. \( 6.3 \mathrm{g} \)


What is the action of chlorine on Excess
\( N H_{3} \)


Frame a formula for the following
statement:
The Fahrenheit temperature \( F \) decreased by 32 is equal to nine-fifths of the centigrade temperature \( C \)
A \( \cdot F+32=\frac{9}{5} C \)
в. \( F-32=\frac{5}{9} C \)
c. \( \quad F-32=\frac{9}{5} C \)
D. none of the above


Mica is used in electrical appliances
such as electric iron because mica is
A. a good conductor of heat but a bad conductor of electricity
B. a bad conductor of heat but a good conductor of electricity
C. a good conductor of heat as well as electricity
D. a bad conductor of heat as well as electricity


Which of the following fibres is said to be very harmful for health?
A. Sawdust
B. Asbestos
c. нау
D. Cellulose


Diagonals \( A C \) and \( B D \) of a trapezium
\( A B C D \) with \( A B \| D C \) intersect each
other at the point \( 0, \frac{O A}{O C}=? \)
A \( \cdot \frac{B D}{O B} \)
в. \( \frac{B O}{O D} \)
c. \( \frac{A O}{O B} \)
D. \( \frac{c o}{O D} \)


If the solubility of the salt
\( \boldsymbol{L} \boldsymbol{i}_{3} \boldsymbol{N} \boldsymbol{a}_{3}\left(\boldsymbol{A l} \boldsymbol{F}_{6}\right)_{2} \) is \( \boldsymbol{x}, \) then its solubility
product would be:
A \( \cdot 26 x^{8} \)
B . \( 2916 x^{8} \)
\( \mathbf{c} \cdot 256 x^{6} \)
D. none of these


Inverse of a statement can be explained
as
A. Negating both the hypothesis and conclusion of a conditional statement
B. Antecedent is the negation of the original antecedent and whose consequent is the negation of the original consequent.
c. both are correct
D. none is correct


At what maximum width \( \delta_{\max }, \) of the
slit are the interference fringes on the
screen observed still sharp?
\( \mathbf{A} \cdot 42 \mu m \)
B. \( 36 \mu m \)
\( \mathrm{c} .64 \mu \mathrm{m} \)
D. none of these


State True or False.
There is no difference between one mole
and one gram molecule
A. True
B. False


Conjugate double bond is present in
A . 1,3-butadiene
B. Butylene
c. Isobutylene
D. Propylene


In a shooting competition a marksman receives 50 paise if he hits the mark and pays 20 paise if he misses it. He tried 60 shots and was paid Rs. 1.30 How many times did he hit the mark?
A . 19
B. 22
\( c \cdot 18 \)
D. 21


Write the differences between
physisorption and chemisorption with respect to the following:
(i) Specificity
(ii) Temperature
dependence
(iii) Reversibility and (iv)
Enthalpy change


Why is that the urine excreted during
summer months is hypertonic?


In forward bias of p-njunction, the potential barrier
A. increases
B. decreases
c. remains unchanged
D. becomes zero


Boron rods are used in nuclear reactor
as
A. moderator
B. control rods
c. coolant
D. protective shield


The hypothetical complex
chlorodiaquatriamminecobalt(III) chloride can be represented as:
A \( \cdot\left[\operatorname{CoCl}\left(N H_{3}\right)_{3}\left(H_{2} O\right)_{2}\right] C l_{2} \)
B. \( \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{3}\left(\mathrm{H}_{2} \mathrm{O}\right) \mathrm{Cl}_{3}\right] \)
c. \( \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{3}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2} \mathrm{Cl}\right. \)
D \( \left[\operatorname{Co}\left(N H_{3}\right)_{3}\left(H_{2} O\right)_{3}\right] C l_{3} \)


Seed having the longest viability is
A. chenopodium
B. Quercus
C. Nelumbo
D. Eucalyptus


Define coagulating value of solution?


Why is it not advisable to separate
two species on the basis of
gross morphology alone? What other
criteria should be taken into
consideration?


\( \boldsymbol{x}, \mathbf{2} \boldsymbol{x}, \mathbf{4} \boldsymbol{x}, \dots \)
The first term in the sequence above is
\( x, \) and each term thereafter is equal to twice the previous term. Find the sum of the first five terms of this sequence.
A . \( 10 x \)
в. \( 15 x \)
c. \( 30 x \)
D. \( 31 x \)
E. \( 32 x \)


The electrical potential on the surface of a
sphere of radius \( ^{\prime} r^{\prime} \) due to a charge \( 3 \times \)
\( 10^{-6} \) is \( 500 V \). The intensity of electric field
on the surface of the sphere is \( \left[\frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9} N m^{2} C^{-2}\right]\left(i n N C^{-1}\right) \)
A \( .250 / 27 \)
B. \( 27 / 250 \)
\( c .250 \)
D. 27


Every planet revolves around the sun in a/an orbit.
A. elliptical
B. circular
c. parabolic
D. none of these


A potentiometer is connected between and B and the balance point is obtained
at \( 203.6 \mathrm{cm} . \) When the end of the
potentiometer connected to B is shifted to \( C, \) then the balance point is obtained
at \( 24.6 \mathrm{cm} . \) If now the potentiometer be connected between \( \mathrm{B} \) and \( \mathrm{C} \), the balance
point will be at:
A. \( 179.0 \mathrm{cm} \)
В. \( 197.2 \mathrm{cm} \)
c. \( 212.0 \mathrm{cm} \)
D. \( 228.0 \mathrm{cm} \)


What are the units of rate constant of a
pseudo unimolecular reaction?


Horned toad, Phrynosoma has
keratinized horns on its head. It is a or
an
A . Lizard
B. Amphibian
c. chelonian reptile
D. Mammal


A system is taken along paths \( A \) and \( B \) as shown. If amounts of heat given in these processes are respectively \( Q A \) and
\( \mathrm{QB}, \) then:
A \( \cdot \mathrm{QA}=\mathrm{Q} \)
B. QA>QB
c. \( Q B<Q A \)
D. none of these


Which of the following process is responsible for the digestion of fat in
out intestine?
A. Electrophoresis
B. Demulsification
c. Emulsification
D. Peptization


Find the following set is singleton set or
not.
\( \mathrm{B}=\{\boldsymbol{y}: 2 \boldsymbol{y}+1<3 \text { and } \boldsymbol{Y} \boldsymbol{\epsilon} \boldsymbol{W}\} \)


Tubectomy is a population control method performed in
A . Males
B. Females
c. Both A and B
D. None of the above


Assertion
Slime moulds are advanced protista.
Reason
They form hard resting bodies like fungi
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.


Write the general term in the expansion
of \( \left(x^{2}-y\right)^{6} \)


Describe the working of an AC generator with the help of a labelled circuit
diagram. What changes must be made in the arrangement to convert it to a DC generator?


Draw the electron dot stucture
of Acetylene
\( A \)
B.
and
c. both A and B
D. none of these


The IUPAC name of the given structure
is:
A. N-methyl-N-ethyl ethanamine
B. diethyl methanamine
c. N-ethyl-N-methyl ethanamine.
D. methyl diethyl ethanamine


Full form of GFC is?
A. Grazing food chain
B. Grazing fish chain
C. Gross food chain
D. Green forest conservation


Can a body have acceleration without
having velocity?


A cube has \( _{\text {the }} \) egdes
vertices


During conductometric titration of \( 0.1 \mathrm{M} \)
HCl with \( 1.0 \mathrm{M} \mathrm{KOH} \), which of the following
will be observed?
A. Resistance of the solution decreases upto equivalence point and then increases
B. Resistance of the solution increases upto equivalence point and then decreases
C. Conductance increases upto equivalence point and then decreases
D. Conductance decreases upto equivalence point and then becomes almost constant


Three point charges of \( +2 q,+2 q \) and
\( -4 q \) are placed at the corners \( A, B \) and \( C \) of an equilateral triangle \( A B C \) of side ' \( x \) '. The magnitude of the electric
dipole moment of this system is :
A \( \cdot 2 \sqrt{3} q x \)
в. \( 2 q x \)
\( \mathbf{c} \cdot 3 q x \)
D. \( 3 \sqrt{2} q x \)


Find the mean of the following data
using shortcut method.
\begin{tabular}{|c|c|c|c|c|}
\hline Class interval & \( 10-15 \) & \( 15-20 \) & \( 20-25 \) & \( 25-30 \) \\
\hline Frequenuy & 7 & 12 & 8 & 10 \\
\hline
\end{tabular}
A. 19.781
B . 20.836
c. 20.337
D. 21.005


The oxidation of \( S O_{2} \) by \( O_{2} \) to \( S O_{3} \) is an
exothermic reaction. The yield of \( \boldsymbol{S O}_{3} \)
will be increased for the exothermic
reaction if:
A. temperature is increases and pressure is kept constant
B. temperature is reduced and pressure is increased
c. both temperature and pressure are increses
D. both temperature and pressure are decreased


When the soil of the greenhouse nurseries is sterilized with methyl
bromide gas, it leads to a deficiency of:
A. cellulose in roots
B. chlorophyll in green leaves
c. zinc in plants
D. iron in red flowers


Which of the following statement is
true?
A. Metals are bad conductors of heat
B. In gases, heat is transferred by conduction
c. In conduction, molecules move from hotter to colder parts transmitting energy
D. Metals conduct heat better than the gases


Assertion
Statement \( -1: N F_{3} \) is a weaker ligand
\( \operatorname{than} N\left(C H_{3}\right)_{3} \)
Reason
Statement \( -2: N F_{3} \) ionizes to give \( F^{-} \)
ion in aqueous solution.
A. Statement -1 is true, Statement -2 is true and Statement - 2 is correct explanation for Statement -
1.
B. Statement -1 is true, Statement -2 is true and Statement - 2 is NOT the correct explanation for Statement - 1
c. Statement -1 is true, Statement -2 is false
D. Statement -1 is false, Statement -2 is true


Which has highest bond energy and stronger bond?
\( \mathbf{A} \cdot F_{2} \)
B. \( C l_{2} \)
c. \( B r_{2} \)
D. \( I_{2} \)


Hydrogen has:
This question has multiple correct options
A. half filled subshell
B. half filled shell
C. one electron in valence shell
D. half filled orbital


Electromagnets are made of soft iron,
because soft iron has
A. High susceptibility and low retentivity
B. Low susceptibility and high retentivity
c. Low susceptibility and low retentivityy
D. High susceptibility and high retentivity


Consider the cubic \( f(x)=8 x^{3}+ \)
\( 4 a x^{2}+2 b x+a, \) where \( a, b, \in R \)
For \( \boldsymbol{a}=\mathbf{1}, \) if \( \boldsymbol{y}=\boldsymbol{f}(\boldsymbol{x}) \) is strictly
increasing \( \forall x \in R, \) then maximum
range of values of \( b \) is
\( ^{\mathbf{A}} \cdot\left(-\infty, \frac{1}{3}\right) \)
B. \( \left(\frac{1}{3}, \infty\right) \)
\( ^{c} \cdot\left[\frac{1}{3}, \infty\right) \)
\( D \cdot(-\infty, \infty) \)


On which of the following factors, does
the molecular arrangement of a
substance depend?
A. Temperature and pressure
B. Concentration and temperature
c. Temperature, pressure and concentration
D. Volume and pressure


In the arrangement shown in fig. plate has a charge equal to \( 60 \mu C \) The ratio
\( d_{1} / d_{2} \) is \( 2 . \) Then
\( q_{1}=_{-} \)
\( q_{2}=_{-}-- \)
\( \mathbf{q}_{3}=_{-}- \)
\( \boldsymbol{q}_{4}=_{-}-- \)
\( \boldsymbol{q}_{5}=-- \)
\( \boldsymbol{q}_{6}=_{-}- \)


Why does water vapour condense when
it reaches high up in the atmosphere?


toppr 5
Q Type your question-
1. \( \boldsymbol{C} \boldsymbol{l}_{2}, \boldsymbol{F} \boldsymbol{e} \boldsymbol{l}_{3} \)
III. \( \boldsymbol{H} \boldsymbol{B} \boldsymbol{r}, \) Heat
\( A \)
B.
\( c \)
\( D \)


What should be added to \( 5 x^{2}+2 x y+ \)
\( y^{2} \) to get \( 3 x^{2}+4 x y ? \)
A. \( -2 x^{2}+2 x y-y^{2} \)
B . \( x^{2}+2 y-y^{2} \)
C \( .-2 x^{2}+2 y-x y^{2} \)
D. \( x^{2}+2 x y-y^{2} \)


\( |f| A \mid=47, \) then find \( \left|A^{T}\right| \)


The IUPAC name of the compound is
A. 2,4-dimethylpentanoic acid
B. 2,3-dimethylpentanoic acid
C. 1,4 -dimethylpentanoic acid
D. 3,4-dimethylpentanoic acio


Twenty persons arrive in a town having
3 hotels \( x, y \) and \( z . \) If each person randomly chooses one of these hotels, then what is the probability that aleast 2 of them goes in hotel \( x, \) atleast 1 in hotel \( y \) and atleast 1 in hotel \( z ?( \) each
hotel has capacity for more than 20 guests).
\( ^{\mathbf{A}} \cdot \frac{^{18} C_{2}}{^{22} C_{2}} \)
B. \( \frac{20 C_{2} \cdot^{18} C_{1} \cdot^{17} C_{1} \cdot 3^{16}}{3^{20}} \)
C. \( \frac{^{20} C_{9}}{3^{9}} \)
D. \( \frac{3^{20}-13.2^{20}+43}{3^{20}} \)


Two coils each of self-inductance \( L \) are
connected in parallel. It they are separated by a large distance, then what will be the self-inductance of
combination?
A \( \cdot \frac{L}{4} \)
в. \( \frac{L}{2} \)
\( c . L \)
D. \( 2 L \)


What is the momentum of a \( 6.0 k g \)
bowling ball with a velocity of \( 2.2 m / s ? \)
A . 11.2
B. 17.2
c. 15.2
D. 13.2


(D) and (C) are:
A. Isomeric alkane
B. Isomeric alkene
C. Not isomers
D. \( (C) \) is an alkene and (D) is salt


In a hydro power plant:
A. Potential energy possessed by stored water is converted into electricity
B. Kinetic energy possessed by stored water is converted into potential energy
C. Water is heated to produce electricity
D. Water is converted into steam to produce electricity


In the expansion of \( \left[7^{1 / 3}+11^{1 / 9}\right]^{6561} \) the number of terms free from radicals
is
A . 730
в. 729
c. 725
D. 750


Which of the following entities are closely associated to each other
A. Gravitation and nuclear fusion
B. Electricity and magnetism
c. Chemical Bonding and Planetary motion
D. None


Which of the following represents a correctly balanced half-reaction?
A \( \cdot C l_{2}+2 e^{-} \rightarrow C l^{-} \)
B \( \cdot 2 e+F e \rightarrow F e^{2+} \)
c. \( O_{2} \rightarrow 2 e^{-}+2 O^{2} \)
D. \( A l^{3+} \rightarrow A l+3 e^{-} \)
E \( \cdot 2 H^{+}+2 e^{-} \rightarrow H_{2} \)


Solve: \( \int \frac{\cos x}{x} d x \)


The ratio of the angular node of a \( 3 s \)
orbital to the spherical node of a \( 4 p \)
orbital is:


Calculate the value of current \( i \), in the
given electric circuit:


Calculate the \( H^{+} \) ion concentration in
\( \mathbf{0 . 1 0} \boldsymbol{M} \) acetic acid solution. Given that
the dissociation constant of acetic acid
in water is \( 1.8 \times 10^{-6} \)


A solenoid has 2000 turns wound over a
length of \( 0.3 m . \) Its cross-sectional area is equal to \( 1.2 \times 10^{-3} m^{2} \). Around its
central cross-section, a coil of 300
turns is wound. If an initial current of
\( 2 A \) flowing in the solenoid is reversed in
\( 0.25 s, \) the emf induced in the coil is
A \( .0 .6 m V \)
B. \( 60 m V \)
c. \( 40.2 m V \)
D. \( 0.48 m V \)


A current carrying conducting square frame of side I carrying current lis
placed in a uniform transverse magnetic field \( \vec{B} \) as shown in the figure.
Choose the incorrect statement.
A. Magnitude of force on the frame is \( 4 I B l \)
B. Magnitude of torque on the frame \( I l^{2} B \)
C. Torque on the frame is zero
D. Both (1) and (2)


\( \boldsymbol{C N}^{-} \longrightarrow \boldsymbol{C N O}^{-} \)
The number of electrons that must be
added in balancing the half reaction is:
\( \mathbf{A} \cdot \mathbf{0} \)
B. 1 on the right
c. 1 on the left
D. 2 on the right


Which adsorption does note take place at very low temperature?
A. Physical adsorption
B. Chemical adsorption
c. Biological adsorption
D. None of the above


When the load on a wire is slowly increased from 3 to \( 5 k g w t \), the
elongation increases from 0.61 to 1.02 \( m m \). The work done during the extension of wire is
\( \mathbf{A} \cdot 0.16 J \)
в. \( 0.016 J \)
c. 1.6 .5
D. 16.5


toppr
Q Type your question.
cnargea partıcies. wıth a rıela b resia,
is found that the filter transmits \( \alpha \) -
particles each of energy \( 5.3 \mathrm{MeV} \). The magnetic field is increased to \( 2.3 \mathrm{B} \)
Tesla and deuterons are passed into the filter. The energy of each deuteron
transmitted by the filter is MeV.
A . 28 Mev
B. 14Mev
c. 7 Mev
D. 18Me


Unpaired electron(s) in superoxide ion


If the sum of first \( 2 n \) terms of \( A . P .2,5 \)
\( 8, \ldots \) is equal to the sum of the first \( n \) terms of the A.P.57,59, 61, ...., then n
equals-
A . 10
B. 12
\( c \cdot 11 \)
D. 13