Combine three resistors \( 5 \Omega, 4.5 \Omega \) and
\( 3 \Omega \) in such a way that the total resistance of this combination is
maximum:
A . \( 12.5 \Omega \)
B. \( 13.5 \Omega \)
c. \( 14.5 \Omega \)
D. \( 16.5 \Omega \)


\( \mathbf{A} \)
is the interval from one
noon to the next noon
A. mean solar day
B. solar day
c. lunar day
D. day


Which of the following is true for a toroid?
A. low inductance and \( Q \) factor
B. high inductance and Q factor
c. high inductance and low \( \mathrm{Q} \) -factor
D. low inductance and high \( \mathrm{Q} \) -factor


Assertion
Dil. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) can convert into a normal
salt.
Reason
Sulphuric acid is dibasic acid. On neutralizing with a base it forms acid salt and normal salt
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Assertion
The driving force for passive absorption is non metabolic in origin.
Reason
The driving force for active absorption is energy derived from metabolic
processes.
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


Amino acids are :-
A. As basic as a typical amine and as acidic as a carboxylic acid.
B. Less basic than a typical amine and less acidic than a
-СООН
C. More basic than atypical amine and more acidic than \( a-c O O H \)
D. Nothing is certain


Two wires are made of the same
material and have the same volume.
The first wire has cross-sectional area \( A \) and the second wire has cross-sectional
area 3 A. If the length of the first wire is
increased by \( \Delta l \) on applying a force \( F \) how much force is needed to stretch the
second wire by the same amount?
A . 4 F
B. 9 F
\( c . F \)
D. 6 F


If the thermal capacity of a body is infinity, then which of the following
statements are correct?
A. Heat can never be added to it
B. Heat can never be extracted from it
c. The temperature of the body cannot be altered by adding or extracting any amount of heat
D. It has infinite amount of heat


What product is formed on heating two molecules of urea?
A. Uric Acid
B. Biuret
c. Nitrogen
D. carbon dioxide


The structure of \( \mathbf{X e O}_{2} \mathbf{F}_{2} \) is:
A. square pyramidal
B. trigonal bipyramidal
c. octahedral
D. tetrahedral


are found in
nitrates, phosphates of metals.
A. Inorganic impurities
B. organic impurities
c. Nutrients
D. Bacteria


The measure of an angle in degrees,
grades and radians be \( \mathrm{D}, \mathrm{G} \) and \( \mathrm{C} \)
respectively, then relation between them \( \frac{\boldsymbol{D}}{\mathbf{9 0}}=\frac{\boldsymbol{G}}{\mathbf{1 0 0}}=\frac{\boldsymbol{2} \boldsymbol{C}}{\boldsymbol{\pi}} \) but \( \mathbf{1}^{\circ}= \)
\( \left(\frac{180}{\pi}\right)^{0} \simeq 57^{\circ}, 17^{\prime}, 44.8^{\prime \prime} \) and sum of
interior angles of a \( n \) -sided regular polygon is \( (2 n-4) \frac{\pi}{2} . \) On the basis of above information, answer the following questions:One angle of a triangle is \( \frac{4 x}{3} \)
grades and another is \( 3 x \) degrees, while the third is \( \frac{2 \pi x}{75} \) radians. Then the angles in degrees are -
A \( \cdot 20^{\circ}, 60^{\circ}, 100^{\circ} \)
B . 24 ' , 60 \( ^{\circ}, 96^{\circ} \)
c. \( 36^{\circ}, 60^{\circ}, 84^{\circ} \)
D. \( 20^{\circ}, 40^{\circ}, 120^{\circ} \)


\( \frac{0.86 \times 0.86 \times 0.86+0.14 \times 0.14 \times 0.1}{0.86 \times 0.86-0.86-0.14+0.14 \times 0.1} \)
is equal to
A . 1
B. 0
c. 2
D. 10


In a container water is filled upto
certain height with a hole at its bottom.
A bird is coming towards free surface of the liquid with velocity \( \vec{V}_{b}=(12 \hat{i}- \) \( \mathbf{1 0} \hat{\boldsymbol{j}}) \boldsymbol{m} / \boldsymbol{s} \) and fish is rising upwards
with velocity \( \vec{V}_{f i s h}(3 \hat{j}) m / s \)
The speed of bird as seen by fish under normal incidence condition at the
moment when water level in container
is \( 20 m \) from its bottom is: (given hole
area \( =1 c m^{2} ; \) surface area of liquid \( = \)
\( \left.20 c m^{2}\right) \)
A \( .20 m / s \)
B. \( 40 \mathrm{m} / \mathrm{s} \)
c. \( 10 \mathrm{m} / \mathrm{s} \)
D. \( 12 m / s \)


The range of the function \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}-[\boldsymbol{x}] \)
where \( [x] \) represents the greatest
integer less than or equal to \( x \) is
\( A \cdot\{0\} \)
в. [0,1]
c. (0,1)
()
D. [0,1]


\( A \) and \( B \) are two hollow metal spheres
of radii \( 50 c m \) and \( 1 m \) carrying charges
\( 0.6 \mu C \) and \( 1 \mu C \) respectively. They are connected externally by a conducting wire. Now the charge flows from :
A. \( A \) to \( B \) till the charges become equal
B. \( A \) to \( B \) till the potentials become equal
c. \( B \) to \( A \) till the charges become equal
D. \( B \) to \( A \) till the potentials become equal


In the expansion of \( (a+b)^{n}, \) the ratio of
the binomial coefficients of \( 2^{n d} \) and \( 3^{r d} \)
terms is equal to the ratio of the binomial coefficients of \( 5^{t h} \) and \( 4^{t h} \)
terms, then \( n= \)
A . 4
B. 5
\( c .6 \)
D.


The wavelength of the radiation emitted
when an electron falls from Bohr orbit 4
to 2 in hydrogen atom is:
A . 243 nm
В. 972 пт
c. 486 пт
D. 182 nm


How are clones produced in plants?


Ethane, with the molecular formula
\( C_{2} H_{6} \) has:
A. 6 covalent bonds
B. 7 covalent bonds
c. 8 covalent bonds
D. 9 covalent bonds


Assertion
In electrolyte refining of metal, impure metal is made cathode while a strip of
pure metal is used as anode.
Reason
The pure metal gets deposited at anode as anode mud.
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


Chemistry involves the qualitative and quantitative determination of the
chemical components of substances
A. Analytical chemistry
B. Chromatography
c. spectroscopy
D. Qualitative chemistry


The equivalent resistance of network of
three \( 2 \Omega \) resistors can not be
A . 0.67
B. 2\Omega
\( c .3 \Omega \)
D. \( 6 \Omega \)


Find the area of a rhombus whose side
is \( 5 c m \) and whose altitude is 4.8 cm. If
one of its diagonal is \( 8 \mathrm{cm} \) long, find the
length of the other diagonal


Obtain the equations of the lines
passing through the intersection of \( \operatorname{lines} 4 x-3 y-1=0 \) and \( 2 x-5 y+ \)
\( \mathbf{3}=\mathbf{0} \) and equally inclined to the axes


Increasing order of metallic characteristic of \( \mathrm{C}, \mathrm{Sb}, \mathrm{As}, \mathrm{Bi}, \) Si is
shown by :
A. \( c, \) si, \( A s, \) sb, Bi
B. \( C, \) Si, Bi, Sb, As
c. \( c, \) si \( , \) sb, Bi, As
D. \( c, \) si, As, Bi, Sb


Two plane mirrors, each of length \( 2 \sqrt{3 m}, \) are placed parallel to each other at a dist of \( 0.2 m . \) A light ray is incident
on 1 mirror at an angle of \( 30^{\circ} \) as shown, then after how many reflections, the light ray will emerge out of mirror?


A dynamo consists of
A. a horse-shoe magnet
B. an armature coil
C . two slip rings
D. all of these


Water falls from a height of \( 50 \mathrm{cm} \) Calculate the rise in temperature of water when it strikes the bottom. \( (g= \)
\( 10 m s^{-2}, \) sp. heat capacity of water \( = \)
\( \left.4200 J / k g^{o} C\right) \)


If \( \angle B \) and \( \angle Q \) are acute angels such
that \( \sin B-\sin Q, \) then prove that
\( \angle B=\angle Q \)


(a) How will you obtain following from phenol?
(i) 2,4,6 Tribromophenol
(ii) Picric-Acid
(b) What is the reaction of Diethyl ether
with \( \boldsymbol{H} \boldsymbol{I} \) -Acid?


Find the 7 th term from the end in the
expansion of \( \left(9 x-\frac{1}{3 \sqrt{x}}\right)^{18}, x \neq 0 \)


An object shaped as \( L \) is placed
between two parallel plane mirrors as
shown. In the first seven closest images,
how many laterally inverted images are formed?
\( A \)
B. 2
\( c \)
\( D \)


Slime moulds are
A. photosynthetic protists
B. saprophytic protists
\( c . \) both (a) and (b)
D. none of these.


If combining atoms of a compound have nearly similar electronegativities the bond between them is
A . electrovalent
B. covalent
c. metallic
D. ionic


In presence of \( \boldsymbol{H}_{2} \boldsymbol{S}, \boldsymbol{S} \boldsymbol{O}_{2} \) acts as :
A. An oxidising agentt
B. A reducing agent
c. A hydrolysis agentt
D. A redox reagent


If blood cells are eliminated from the
blood, the liquid left is
A. Serum
B. Plasma
c. Lymph
D. synovial fluid


If \( f(x) \) is a function such that \( f^{\prime \prime}(x)+ \)
\( \boldsymbol{f}(\boldsymbol{x})=\mathbf{0} \) and \( \boldsymbol{g}(\boldsymbol{x})=[\boldsymbol{f}(\boldsymbol{x})]^{2}+\left[\boldsymbol{f}^{\prime}(\boldsymbol{x})\right]^{2} \)
and \( g(3)=8, \) then \( g(8)= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. 3
\( c .5 \)
D. 8


Fill in the blanks:
The force resulting due to the action of muscles is known as the
force.
A. contact
B. muscular
c. friction
D. magnetic


Suppose elements \( X \) and \( Y \) combine to
form two compounds, \( \boldsymbol{X} \boldsymbol{Y}_{2} \) and \( \boldsymbol{X}_{3} \boldsymbol{Y}_{2} \)
where 0.1 mol of former weigh 10 g while 0.05 mol of the latter weigh 9 g. What are the atomic weights of \( X \) and
\( \boldsymbol{Y} \) respectively?
A . 40,30
B. 60,40
c. 20,30
D. 30,20


The volume of blood that enters into the
aorta with each ventricular systole is called
A. Cardiac cycle
B. Stroke volume
c. cardiac output
D. Vital capacity


Solid substances constitute \( _{-}-1 \% \)
the non-cellular part of Iymph.
A . \( 34 \% \)
B. 6\%
c. \( 12 \% \)
D. 82\%


There are \( n \) points in a plane out of these points no three are in the same straight line except \( p \) points which are
collinear. Let " \( k \) " be the number of
straight lines and "m" be the number of
triangles.Then find \( m-k \) ?(Assume
\( \boldsymbol{n}=\boldsymbol{7} \boldsymbol{p}=\mathbf{5}) \)


One gram mole of glucose on complete
oxidation to \( C O_{2} \) and \( H_{2} O \) produces
about
A .6,86,000 Cal
B. 6,860 Cal
c. 68,600 Cal
D. 68,60,000 Cal


Which one is removed from substrate
during glycolysis
A. Hydrogen
B. Electrons
c. Both A and B
D. oxygen


Write a short note on Catenation


The spark seen inside a switch is:
A. electrical discharge
B. due to heating effect of current
C . an indicator glowing
D. a sudden fire


\( \lim _{x \rightarrow 0} \frac{\sqrt{\frac{1}{2}(1-\cos x)}}{x}= \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. -
\( c \cdot 0 \)
D. does not exist


According to the Newton's third law of
motion, action and reaction pair:
A. always act on the same body
B. always act on different bodies in opposite directions
C. have same magnitude and directions
D. act on either body at normal to each other


if \( \boldsymbol{\alpha} \) and \( \beta \) are complex cube root of
unity then find the value of \( \boldsymbol{\alpha}^{2}+\boldsymbol{\beta}^{2}+ \)
\( \boldsymbol{\alpha} \boldsymbol{\beta} \)


Which of the following phenomenon can
be related to electric current
A. Magentism
B. Gravitation
c. Nuclear Fission
D. chemical Bonding


Find the general expressions for two positive integers which are such that if their product is taken from the sum of
their squares the difference is a perfect
square


Let \( \boldsymbol{E}=\left\{\boldsymbol{x}: \boldsymbol{x}^{2}+\mathbf{5} \boldsymbol{x}-\boldsymbol{6}=\boldsymbol{0}\right\} \) and
\( \boldsymbol{F}=\{-\mathbf{6}, \mathbf{1}\} . \) Then
A \( . E=F \)
в. \( E \neq F \)
c. \( E \subset F \)
D. \( F \subset E \)


The magnetic tield at the centre ot a
circular coil of radius \( r \) is \( \pi \) times that
due to a long straight wire at a distance
r from it, for equal currents. Figure
shows three cases. In all cases the
circular path has radius r and straight
ones are infinitely long. For same
current the \( \mathrm{B} \) field at the centre \( \mathrm{P} \) in
cases 1,2,3 has the ratio:
\( ^{\mathbf{A}} \cdot-\left(\frac{\pi}{4}+\frac{1}{2}\right):\left(\frac{\pi}{2}\right):\left(\frac{3 \pi}{4}-\frac{1}{2}\right) \)
B \( \cdot\left(-\frac{\pi}{2}+1\right):\left(\frac{\pi}{2}+1\right):\left(\frac{3 \pi}{4}+\frac{1}{2}\right) \)
\( \mathbf{C} \cdot-\frac{\pi}{2}: \frac{\pi}{2}: \frac{3 \pi}{4} \)
D \( \cdot\left(-\frac{\pi}{2}-1\right):\left(\frac{\pi}{2}-\frac{1}{4}\right):\left(\frac{3 \pi}{4}+\frac{1}{2}\right) \)


Devendra, a computer accessories
vendor gave a discount of \( 20 \% \) on a pen-
drive and his profit reduced from Rs.
200 to Rs. \( 100 . \) What is Devendra's cost
price?
A . Rs. 300
B. Rs. 200
c. Rs. 400
D. None of these


Nearly \( 76 \% \) fresh water is confined in
A . Ice caps and glaciers
B. Soil water
c. Ground water
D. Surface water


Write three rational numbers that lie
between the two given numbers. \( \frac{7}{9},-\frac{5}{9} \)


\( A, B, C \) try to hit a target simultaneously but inside- - target are \( \frac{3}{4}, \frac{1}{2}, \frac{5}{8}, \) the probability that target is bur by \( \boldsymbol{A} \) or \( \boldsymbol{B} \) but not by \( \boldsymbol{C} \) is
A \( \cdot \frac{21}{64} \)
B. \( \frac{7}{8} \)
c. \( \frac{7}{32} \)
D. \( \frac{9}{64} \)


A virtual image is one which:
A. can be taken on a screen
B. cannot be taken on a screen
c. sometimes can be and sometimes cannot be taken on
a screen
D. is formed only by a concave mirror


The heart of which animal is myogenic in nature?
A. cockroach
B. Leech
c. Elephant
D. All of the above


The distance between the focus and the
pole of the mirror is called:
A. Focal length
B. Radius of curvature
c. Principal axis
D. Diameter of curvature


Energy possessed by a body due to its motion is:
A. kinetic energy
B. nuclear energy
c. potential energy
D. thermal energy


Identify the parameter which measures
the time it takes to complete one cycle?
A . period
B. wavelength
c. frequency
D. amplitude
E. speed


Simplify:
\( \frac{1-\cos x}{1+\cos x} \)


A sphere of aluminium of mass 0.047 kg placed for sufficient time in a vessel containing boiling water, so that the
sphere is at \( 100^{\circ} \mathrm{C} \).It is then immediately transferred to \( 0.14 \mathrm{kg} \) copper calorimeter containing \( 0.25 \mathrm{kg} \) of water at \( 20^{\circ} \mathrm{C} \). The temperature of water rises and attains a steady state
at \( 23^{\circ} C \). Calculate the specific \( h \) capacity of aluminium. Given :specific heat capacity of water is 4186 \( J k g^{-1} K^{-1} \) specific heat capacity of copper calorimeter is 385 Jkg\( ^{-1} \boldsymbol{K}^{-1} \)


A bob of mass \( m \) hangs from the ceiling
of a smooth trolley car which is moving
with a constant acceleration \( a \). If the
Young's modulus, radius and length of
the string are \( Y, r \) and \( l \) respectively
f the stress in the string is \( \frac{2 m \sqrt{g^{2}+d^{2}}}{x \pi r^{2}} . \) Find \( x \)


Write a balanced equation using the correct symbols for these chemical
reactions:
i) Action of hydrogen on ethene in the presence of nickel catalyst.
ii) Combustion of methane evolving carbondioxide and water.
iii) Dehydrogenation of ethanol.
iv) Decarboxylation of Sodium salt of ethanoic acid.


Consider a 'beam expander' which
consists of two converging lenses of focal lengths \( 40 \mathrm{cm} \) and \( 100 \mathrm{cm} \) having a common optical axis. A laser beam of diameter \( 2 \mathrm{mm} \) is incident on the \( 40 \mathrm{cm} \)
focal length lens. Then what is the
diameter (in mm) of the final beam (see
figure)?


Let \( 0<\theta<\pi / 2 \) and
\( \boldsymbol{\Delta}(\boldsymbol{x}, \boldsymbol{\theta})=\left|\begin{array}{ccc}\boldsymbol{x} & \tan \boldsymbol{\theta} & \cot \boldsymbol{\theta} \\ -\tan \boldsymbol{\theta} & -\boldsymbol{x} & \mathbf{1} \\ \cot \boldsymbol{\theta} & \boldsymbol{1} & \boldsymbol{x}\end{array}\right| \)
then
This question has multiple correct options
A \( \cdot \Delta(0, \theta)=0 \)
B. \( \Delta\left(x, \frac{\pi}{4}\right)=x-x^{3} \)
c. \( \operatorname{Min}_{0<\theta<\pi / 2} \Delta(1, \theta)=0 \)
D. \( \Delta(x, \theta) \) is independent of \( x \)


Conductivity of metal decreases with
temperature while conductivity of electrolytic conductors increases with temperature. Why?


Which compound is mainly responsible for the depletion of ozone layer?
A. \( C O_{2} \)
в. \( C H_{4} \)
c. \( C H_{3} \) ОН
D. \( C F_{2} C l_{2} \)


Which is not a colloid?
A. Egg white
B. Chlorophyll
c. Ruby glass
D. Milk


In circular motion of a particle,
This question has multiple correct options
A. particle cannot have uniform motion
B. particle cannot have uniformly accelerated motion
C . particle cannot have net force equal to zero
D. particle cannot have any force in tangential direction


Ribozymes are
A. RNA acting as enzymes.
B. Antibody acting as enzymes.
C. Ribosomes acting as enzymes.
D. None of the above.


toppr
Q Type your question
following combination(s) shown below
will archive the desired result?
\( A \)
B. 2
\( c \cdot 3 \)
\( D \cdot 4 \)


In a reaction \( 5 g \) ethyl acetate is hydrolysed per litre in presence of
dilute \( H C l \) in 300 min. If the reaction
is of the first order and initial
concentration is \( 22 g / L, \) calculate the
rate constant for the reaction.


If \( A, B, C \) are three independent events
of an experiment such that, \( \boldsymbol{P}(\boldsymbol{A} \cap \) \( \left.\boldsymbol{B}^{C} \cap \boldsymbol{C}^{C}\right)=\frac{1}{4}, \boldsymbol{P}\left(\boldsymbol{A}^{C} \cap \boldsymbol{B} \cap \boldsymbol{C}^{C}\right)= \)
\( \frac{1}{8}, P\left(A^{C} \cap B^{C} \cap C^{C}\right)=\frac{1}{4}, \) then find
\( \boldsymbol{P}(\boldsymbol{A}), \boldsymbol{P}(\boldsymbol{B}), \boldsymbol{P}(\boldsymbol{C}) \)


In Galapagos islands, Darwin observed variations in structure in
A. Elephants
B. Giraffes
c. Rats
D. Finch birds


A \( H e^{2+} \) ion travels at right angles to a magnetic field of \( 0.80 \mathrm{T} \) with a velocity of \( 10^{5} m / s . \) If \( \mathrm{M} \) is the magnitude of the
magnetic force on the ion, find \( x \) such that \( \boldsymbol{x}=\boldsymbol{M} \times \mathbf{1 0}^{\mathbf{1 6}} \)


Fundamental building blocks of proteins containing an amino group
\( \left(N H_{2}\right) \) and a carboxyl group (COOH) at the alpha carbon atom


From a unifrom disc of radius \( R \) an
equilateral triangle of side \( \sqrt{3} R \) is cut
as shown. The new position of centre of mass is
A \( \cdot(0,0) \)
в. \( (0 . R) \)
c. \( (R, 0) \)
\( 0 . \frac{\sqrt{3}}{28} \)


The acceleration of a moving body can be found from the area under velocitytime graph.
A. True
B. False


In the figure, \( M N S \) is tangent to the
circle with centre \( O \) at \( N \)
\( A B \) is chord parallel to \( M N S . \) find
\( \angle A N C \)
A . 50
B. \( 90^{\circ} \)
\( c \cdot 40 \)
D. 20


Select the option where the property describing muscle fibres is not associated with wall of stomach.
A. Presence of actin and myosin fibrils
B. Branched, multinucleated appearance
c. Presence of cell junctions
D. Involuntary nature


Assertion
lonic radii of Ta and Nb are same
Reason
The lanthanide contraction cancels
almost exactly the normal size increase on descending a group of transition
elements
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 \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{3} & \mathbf{1} \\ -\mathbf{1} & \mathbf{2}\end{array}\right], \) show that \( \boldsymbol{A}^{2}-\mathbf{5} \boldsymbol{A}+ \)
\( \mathbf{7} \boldsymbol{I}=\boldsymbol{O} . \) Hence find \( \boldsymbol{A}^{-1} \)


Find the \( n^{t h} \) term of
\( 6,11,16,21, \dots \dots \)


In a class, 54 students are good in Hindi only, 63 students are good in Mathematics only and 41 students are good in English only. There are 18 students who are good in both Hindi and Mathematics. 10 students are good
in all three subjects. What is the number of students who are good in either Hindi or Mathematics but not in
English?
A . 99
в. 107
c. 125
D. 130


f Hund's rule is not applicable, then how many unpaired electrons are present in \( N O \) molecule?


Write the IUPAC name of the given
compound:


Phosphorus has valencies of 3 and 5
What is the formula of the two oxides of
phosphorus?


In which of the following compounds transition metal has zero oxidation
state?
A. \( \mathrm{CrO}_{5} \)
B. \( \mathrm{NH}_{2} \cdot \mathrm{NH}_{2} \)
c. \( \mathrm{NOClO}_{4} \)
D \( \cdot\left[F e(C O)_{5}\right] \)


The following two compounds are:
A. identical
B. conformational isomers
c. geometrical isomers
D. structural isomers


Which soil is used in cosmetics?
A. Multani soil
B. Terracotta soil
c. Shadu soil
D. Kaolin


A charge of \( 10 \mathrm{C} \) is brought from infinity to a point near a charged body and in
this process, 200 J of work is done
Calculate the electric potential at that point near the charged body
A . \( 20 \mathrm{v} \)
B. \( 10 \mathrm{v} \)
\( c .5 v \)
D. 15 v


Assertion
Acceleration of charged particle in nonuniform electric field does not depend on velocity of charge particle.
Reason
Charge is an invariant quantity. That is amount of charge on particle does not depend on frame of reference.
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


Check whether \( 5-6 x=\frac{2}{5} x^{2} \) is
a quadratic equation.


A modern 200 W sodium street lamp
emits yellow light of wavelength \( 0.6 \mu m \) Assuming it to be \( 25 \% \) efficient in converting electrical energy to light, the number of photons of yellow light it emits per second is :
A \( \cdot 62 \times 10^{20} \)
B . \( 3 \times 10^{19} \)
c. \( 1.5 \times 10^{20} \)
D. \( 6 \times 10^{18} \)


Number of rod cells in eye is
A . 120 million
B. 80 million
c. 60 million
D. 180 million


A body moving in a circular path with constant speed is an accelerated
motion. Why?


Which of the following is not a good method to make \( 2,2- \)
dimethylpropanoic acid?
A \( \cdot\left(C H_{3}\right)_{3} C C H_{2} O H^{K_{2} C r_{2} O_{7}, H_{2} S O_{4}} \)
B. \( \left(C H_{3}\right)_{3} C B r_{\text {Diethylether }(i)} \stackrel{M g}{\stackrel{(i)}{H_{2} O}, H} \)
\( ^{\mathbf{c}} \cdot\left(C H_{3}\right)_{3} C B r \stackrel{N a C N}{\longrightarrow} \frac{H_{3} \bar{\phi}}{H e a t} \)
D. \( \left(C H_{3}\right)_{3} C C=C H \stackrel{O_{3}}{\longrightarrow} \stackrel{O H_{2}}{\longrightarrow} \)


If
\( \sin ^{-1} \frac{2 x}{1+x^{2}} ; \cos ^{-1} \frac{1-x^{2}}{1+x^{2}} ; \tan ^{-1} \frac{2 x}{1-x^{2}} \)
each is equal to \( 2 \tan ^{-1} x . \),then show that \( \int 2 \tan ^{-1} x= \)
\( 2\left[x \tan ^{-1} x-\frac{1}{2} \log \left(1+x^{2}\right)\right] \)


Which of the following alkene on
catalytic hydrogenation given cis and
trans isomer?
\( A \)
B. 4,1-Dimethyl cyclohexene
\( c \)
D. All of the above


Find the distances between the
following pair of points. \( \$ \$(4,-7) \) and \( (-1, \)
5)\( \$ \$ \)


Select the option which
describes the best definition of heat in
the context of thermal energy?
A. energy possessed by a system due to movement of particles within the system
B. the measure of thermal energy
C. thermal energy transferred from one object to another
D. energy possessed by an object due to the temperature of the object
E . potential energy


Observe the diagram carefully and answer the following.
a) Name the type of transport.
b) Define the process.


Benzene and toluene form an ideal
solution over the entire range of
composition. The vapour pressure of pure benzene and toluene at \( 300 K \) are
\( 50.71 m m H g \) and \( 32.06 m m H g \)
respectively. Calculate the mole fraction
of benzene in vapour phase if \( 80 g \) of
benzene is mixed with \( 100 g \) of toluene.


Consider the statements given below regarding contraception and answer as directed thereafter
(a) Medical Termination of Pregnancy (MTP) during first trimester is generally safe.
(b) Generally chances of conception are nil until mother breast-feeds the infant
upto two years.
(c) Intrauterine devices like copper \( T \)
are effective contraceptives.
(d) Contraception pills may be taken upto one week after coitus to prevent conception. Which two of the above statements are
correct?
A. a and c
B. a and b
\( \mathbf{C} \cdot \mathbf{b} \) and \( c \)
D. \( c \) and \( d \)


A mixture of ethanol and \( C C l_{4} \) has \( 30 \% \)
\( C C l_{4} \) by weight, what is mole fraction of
\( \boldsymbol{C C l}_{4} \) in the mixture?
A . 0.11
B. 0.89
c. 0.25
D. 0.67


Lithium exists in nature in the form of
two isotopes, Li-6 and Li-7 with atomic
masses \( 6.0151 \mathrm{u} \) and \( 7.0160 \mathrm{u} \) and the
percentages 8.24 and 91.76 respectively Calculate average atomic mass.


When one acute angle of a triangle is equal to one acute angle of other triangle, and the triangles are right angles, do you think the triangles are similar?
A. Not sure
B. Similar
c. Not similar
D. cannot be possible


The maximum number of hydrogen
bonds that a molecule of water can have
is:
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c .3 \)
D. 4


A drilling machine of \( 10 k W \) power is
used to drill a bore in a small
aluminium block of mass \( 8 k g . \) If \( 50 \% \) of
power is used up in heating the machine itself or lost to the
surroundings then how much is the rise in temperature of the block in
2.5 minutes?
Given: specific heat of aluminium \( = \)
\( \mathbf{0 . 9 1} \boldsymbol{J} / \boldsymbol{g}^{\boldsymbol{o}} \boldsymbol{C} \boldsymbol{)} \)
\( \mathbf{A} \cdot 103^{\circ} C \)
B . \( 130^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 105^{\circ} \mathrm{C} \)
D. \( 30^{\circ} \mathrm{C} \)


\( \boldsymbol{f}(\boldsymbol{x})=\mathbf{1} /\left(\mathbf{1}-\boldsymbol{e}^{-\mathbf{1} / \boldsymbol{x}}\right), \boldsymbol{x} \neq \mathbf{0} \) If \( \mathbf{f} \) is
continuous at \( x=0 \) then, Find \( f(0) \)


Mathematically, specific heat is related
as:
A. \( c=Q m \Delta t \)
B. \( c=\frac{Q}{m \Delta t} \)
c. \( c=\frac{m \Delta t}{Q} \)
D. \( c=\frac{m}{Q \Delta t} \)


Which of the set of oxides are arranged in the proper order of basic, amphoteric, acidic?
A. \( S O_{2}, P_{2} O_{5}, C O \)
\( \mathrm{c} \cdot \operatorname{Si} \mathrm{O}_{2}, \mathrm{CaO}, \mathrm{Al}_{2} \mathrm{O}_{3} \)
D. \( C O_{2}, A l_{2} O_{3}, C O \)


\( f S_{n} \) denotes the sum of \( n \) terms of an
AP whose common differences is \( d \)
show that \( \boldsymbol{d}=\boldsymbol{S}_{\boldsymbol{n}}-\boldsymbol{2} \boldsymbol{S}_{\boldsymbol{n}-1}+\boldsymbol{S}_{\boldsymbol{n}-\boldsymbol{2}} \)


The process of increasing the percentage of fissionable \( U-235 \) in
naturally occurring Uranium is called
A. controlled fission
B. artificial transmutation
c. chemical process
D. enrichment


Let \( S \) be a relation on the set \( R \) of all
real numbers defined by \( \boldsymbol{S}= \)
\( \left\{(a, b) \in R \times R: a^{2}+b^{2}=1\right\} . \) Prove
that \( S \) is not an equivalence relation on
\( \boldsymbol{R} \)


A solution containing \( \boldsymbol{N} \boldsymbol{a}^{\oplus}, \boldsymbol{N} \boldsymbol{O}_{3}^{\ominus}, \boldsymbol{C l}^{\ominus} \)
and \( S O_{4}^{2-} \) ions, all at unit concentrations, is electrolyzed between nickel anode and plantinum cathode. As the current is passed through the cell :
This question has multiple correct options
A. pH of the cathode increases
B. Oxygen is the major product at anode
c. Nickel is deposited at cathode
D. Chlorine is the maior product at anode


Which of the following is an acidic salt?
A. \( N a H_{2} P O_{2} \)
в. \( \operatorname{NaH}_{2} \mathrm{PO}_{3} \)
\( \mathbf{c} \cdot N a_{2} H P O_{3} \)
D. \( N a_{3} P O_{4} \)


The distance between them at time \( t \) is:
A \( \cdot \sqrt{(200)^{2}+(100)^{2}} m \)
B. \( \sqrt{(200-4 t)^{2}+(100-2 t)^{2}} m \)
c. \( [(200-4 t)+(100-2 t)] m \)
D. \( \sqrt{(200-2 t)^{2}+(100-4 t)^{2}} m \)


In the propagation of polarised light waves, the angle between the plane of vibration and the plane of polarization
is
A \( \cdot 0^{\circ} \)
B. 90
c. 45
D. \( 180^{\circ} \)


The total number of moles of valence
electrons in \( 4.2 \mathrm{g} \) of \( N_{3}^{-} \) ion are:
A \( .2 .2 N_{A} \)
в. \( 4.2 N_{A} \)
c. \( 1.6 N_{A} \)
D. \( 3.2 N_{A} \)


\( C_{5} H_{12} \) has a symmetrical structure
with one quaternary carbon. Its IUPAC name is :
A. n-pentane
B. 2-methylbutane
c. 2,2-dimethylpropane
D. 3-methylbutane


Phosphorous can form two types of halides whereas nitrogen can form only one type of halide. Give reason(s).


When a metal conductor connected to
left gap of a meter bridge is heated, the balancing point.
A. Shifts towards right
B. Shifts towards left
c. Remains unchanged
D. Remains at zero


Myocardial infarction is due to
A. Infection of heart muscles
B. Weakening of heart muscles
c. clot in blood vessels of heart
D. Breakage of coronary vessel


If the shortest wavelength in Lyman series of hydrogen atom is \( A \), then the longest wavelength in Paschen series of
\( \boldsymbol{H} \boldsymbol{e}^{+} \) is :
A \( \cdot \frac{36 A}{7} \)
в. \( \frac{5 A}{9} \)
c. \( \frac{36 A}{5} \)
D. \( \frac{9 A}{5} \)


Given a function \( f \) such that \( f(4)=5 \)
then which of the following is/are true
for \( \boldsymbol{f} ? \)
A \( . f(x) \neq x+1 \)
в. \( f(x) \neq 2 x-3 \)
c. \( f(x) \neq 3 x-2 \)
D. \( f(x) \neq 4 x-11 \)


Differentiate between
Ureter and urethra


Air pollution is caused because of the high proportion of undesirable gases
such as
A. Methane
B. Carbon dioxide
c. Sulphur dioxide
D. All of the above


The velocity of electron of H-atom in its
ground state is \( 2.2 \times 10^{-6} m / s . \) The de-
Broglie wavelength of this electron would be:
A. 0.33 nm
B. 23.3 nm
c. 45.6 nm
D. \( 100 \mathrm{nm} \)


When a current flows through a conductor its temperature
A. May increase or decrease
B. Remains same
c. Decreases
D. Increases


Expand the following binomial \( \left(1-3 a^{2}\right)^{6} \)


A plane flying horizontally at a height of
\( 1500 \mathrm{m} \) with a velocity of \( 200 \mathrm{m} s^{-1} \)
passes directly overhead an antiaircraft gun. Then the angle with the horizontal at which the gun should be fired for the shell with a
muzzle velocity of \( 400 \mathrm{ms}^{-1} \) to hit the
plane is:
A \( .90^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 30 \)
D. \( 45^{\circ} \)


Fats \( +\mathrm{NaOH} \rightarrow \)
+ Glycerol.
One of the products formed in this
reaction is :
A. Soap
B. cloth
c. Paper
D. woodd


The vibrations of a body which take place under the influence of an external
periodic force acting on it are called
A. Forced vibrations
B. Free vibration
c. Damped vibrations
D. All


Sama and Imran visit a shop to bay books. If each book cost \( \frac{21}{2}, \) find the \( \operatorname{cost} \) of 20 books. If \( \operatorname{Sam} \) paid \( \frac{1}{3} \) of the amount, how much should Imran pay?


Describe the extraction of three
different elements using carbon as the reducing agent.


The binary operation \( *: \boldsymbol{R} \times \boldsymbol{R} \rightarrow \boldsymbol{R} \) is
defined as \( a * b=2 a+b . \) Find \( (2 * 3) * \)
4


The value of admittance at resonance in
antiresonant
A \( \cdot \sqrt{G^{2}-S^{2}} \)
B . \( G^{2}+S^{2} \)
c. \( \sqrt{G^{2}+S^{2}} \)
D. \( \frac{G^{2}}{S^{2}} \)


What is \( X \), in the following reaction?
\( \boldsymbol{K} \boldsymbol{H} \boldsymbol{S} \boldsymbol{O}_{4}+\boldsymbol{F}_{2} \rightarrow \boldsymbol{H} \boldsymbol{F}+\boldsymbol{X} \)
A. \( K_{2} S O_{4} \)
в. \( K_{2} S_{2} O_{4} \)
\( \mathbf{c} \cdot K_{2} S_{2} O_{3} \)
D. \( K_{2} S_{2} O_{8} \)


If \( \sqrt{\boldsymbol{x}}-\sqrt{\mathbf{1 2}}=\sqrt{\mathbf{4}}-\sqrt{\boldsymbol{x}}, \) then find \( \boldsymbol{x} \)
A. \( 1+\sqrt{3} \)
B. \( 2+2 \sqrt{3} \)
c. \( 4+\sqrt{3} \)
D. \( 4+2 \sqrt{3} \)


A good lubricant should be highly
A. viscous and volatile
B. non-viscous and non-volatile
c. viscous and non-volatile
D. transparent


In the following reaction \( 2 H_{2} O_{2}(a q) \rightarrow \)
\( 2 H_{2} O(\ell)+O_{2}(g) \) rate of formation of
\( O_{2} \) is \( 36 g \min ^{-1} \)
(a) What is the rate of formation of \( H_{2} O \)
(b) What is the rate of disappearance of
\( \boldsymbol{H}_{2} \boldsymbol{O} \)


Mention any two reasons for the anomalous behaviour of oxygen.


\( \sigma_{0} \)
\( @_{0} \)
\( \sigma_{0} \)
\( \sigma_{0} \)


The breaking strength of the string connecting wall an block B is 175 N Find the maximum magnitude of weight of block A for which the system will be stationary The block B is weighs 700 N (neglect friction)
\( \left(g=10 m / s^{2}\right) \)
A \( \cdot \frac{175}{\sqrt{3}} N \)
B. \( \frac{175 \sqrt{3}}{2} N \)
\( c \cdot 175 \sqrt{3} N \)
\( N \)
D. None of thes


Consider the following two statements:
(A) Kirchhoff's Junction Law follows
from conservation of charge.
(B) Kirchhoff's Loop Law follows from conservative nature of electric field
A. Both A and B are correct
B. A is correct but B is wrong
c. A is correct but A is wrong
D. Both A and B are wrongg


Two metallic oxides contain \( 27.6 \% \) and
\( 30 \% \) oxygen respectively. If the formula
of the first oxide is \( X_{3} O_{4}, \) that of the
second will be:


Sum of two mechanical waves
travelling in any direction (having the same frequency)
A. can be summed up to give a stationary wave
B. is added using the phasor diagramm
c. can have graphical representation with no troughs and elevations
D. none of the above


Discuss why wearing more layers of
clothing during winter keeps us warmer
than wearing just one thick piece of clothing?


Find the number of waves made by a
Bohr electron in one complete revolution
in the 3 rd orbit.


IUDs which are used by females
A. Act as spermicidal jellies
B. Block the entry of sperms into vagina
C. Are implanted under the skin and they release progestron and estrogen
D. Release copper ions in the uterus that increase phagocytosis of sperms


Q Type your question
Nư.
between the plates. The battery is then
disconnected and a dielectric slab of
dielectric constant \( K \) is placed in between the plates of the capacitor as
shown.

Now, answer the following questions based on above information. The
electric field in the gaps between the
plates and the dielectric slab will is :
A \( \cdot \frac{\varepsilon A V}{d} \)
в. \( \frac{V}{d} \)
\( c \cdot \frac{K V}{d} \)
D. \( \frac{V}{d-t} \)


(Molarity/Molality) is the number of moles of solute dissolved
per kg of solvent.


Out of aldehyde and ketones, which is more reactive towards nucleophilic
addition?
A. Aldehyde
B. Ketone
c. Equally reactive
D. cannot be predicted


State whether the following statements
are true or false.

The knowledge of systematics helps in various branches of basic and applied biology
A. True
B. False


The main factors which affect corrosion
are :
A. Position of metal in electrochemical series
B. Presence of \( C O_{2} \) in water
c. Presence of impurities coating
D. All are correct


\( \ln \triangle A B C \) the \( \angle B=60^{\circ}, \angle C=45^{\circ} \)
Find \( \angle A \)


Pnicogens are the elements of group:
A . 15
B. 13
c. vıl
D. zero


Round 984 liters to 2 significant digits.
A. \( 1.00 \times 10^{3} \) liters
B. 1000 liters
c. 900 liters
D. 980 liters


Which of the following is the most precise instrument for measuring length?
A. Metre rod of least count \( 0.1 \mathrm{cm} \)
B. Vernier calipers of least count \( 0.01 \mathrm{cm} \)
c. Screw gauge of least count \( 0.001 \mathrm{cm} \)
D. None of these


Fill in the blanks:
\( \mathbf{1 5} \times(-\mathbf{3})=\dots \dots \dots \)


A vertical tower OP stands at the centre
O of a square ABCD. Let h and b denote the length OP and AB respectively.
Suppose \( \angle A P B=60^{\circ}, \) then the
relationship between h and b can be
expressed as:
\( \mathbf{A} \cdot 2 b^{2}=h^{2} \)
B \( \cdot 2 h^{2}=b^{2} \)
\( \mathbf{c} \cdot 3 b^{2}=2 h^{2} \)
D. \( 3 h^{2}=2 b^{2} \)


Tree ecosystem is an example of :-
A. Grazing Food chain
B. Detritus Food Chain
C. Both 1 and 2 above
D. Parasitic Food chain


9650 charge is passed through an aqueous solution of metal nitrate \( \mathrm{M}(\mathrm{N} \mathrm{O} \)
\( 3 x \) to obtain 2 g metal (at. mass 180 ). What is the valence of metal?
A. 7
B. 3
\( c \cdot 4 \)
\( D \cdot 9 \)


What should be the initial downward
speed of the racketeer so that he
catches the student at the top of 100 th
floor for safe landing?
A. It can have many values
B . \( 180 \mathrm{ms}^{-1} \)
c. \( 137.1 \mathrm{ms}^{-1} \)
D. cannot be determined


Industrial preparations of \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) by Ostwald's process involves:
A . reduction of \( N H_{3} \)
B. oxidation of \( N H_{3} \)
C. hydrogenation of \( N H_{3} \)
D. hydrolysis of \( N H_{3} \)


Why does a straw get attracted towards another straw which is rubbed with a
sheet of paper?
A. Due to friction force
B. Due to electrostatic force
c. Due to magnetic force
D. Due to gravitational force


Write short note on the functions of the
thyroid hormones.


State Ohm's law. Suggest an
experiment to verify it and explain the
procedure.


D-glucose \( \& \) D-fructose can be differentiated by:
A. Fehling solution
B. Tollens reagent
c. Benedict test
D. \( B r_{2} / H_{2} O \)


Work done in forming a liquid drop of
radius \( R \) is \( W_{1} \) and that of radius \( 3 R \) is
\( W_{2} . \) The ratio of work done is:
A .1: 3
B. 1: 2
c. 1: 4
D. 1: 9


The volume of dry \( N_{2} O \) produced at this point measured at STP is
L)


The Cartesian equation of a line is
\( \frac{\boldsymbol{x}-\mathbf{5}}{\mathbf{3}}=\frac{\boldsymbol{y}+\mathbf{4}}{\mathbf{7}}=\frac{\boldsymbol{z}-\mathbf{6}}{\mathbf{2}} . \) Write its vector
form.


Dry ice is used in fire extinguishers. The dry ice is stored in the cylinder in a solid form. When sprayed on a fire it quickly changes into the gas known as carbon
dioxide \( \left(C O_{2}\right) . \) What is this change of
state called?
A. Sublimation
B. Condensation
c. Distillation
D. Evaporation


The length of a metal wire is \( l_{1} \) when the tension in it is \( F_{1} \) and \( l_{2} \) when the
tension is \( F_{2} \). Then original length of the wire is:
A. \( \frac{l_{1} F_{1}+l_{2} F_{2}}{F_{1}+F_{2}} \)
в. \( \frac{l_{2}-l_{1}}{F_{2}-F_{1}} \)
c. \( \frac{l_{1} F_{2}-l_{2} F_{1}}{F_{1}-F_{2}} \)
D. \( \frac{l_{1} F_{1}-l_{2} F_{2}}{F_{2}-F_{1}} \)


Match the above lists and choose the
correct option.
\( A \cdot A-2, B-3, C-4, D-1 \)
B. \( A-3, B-2, C-4, D-1 \)
\( C \cdot A-2, B-4, C-3, D-1 \)
D. \( A-2, B-3, C-1, D-4 \)


Typical lub-dub sounds heard in heartbeat are due to
A. closing of bicuspid and tricuspid valves
B. closing of semilunar valves
c. closure of bicuspid-tricuspid valves followed by semilunar valves
D. Blood under pressure through aorta


The linear magnification for a mirror is the ratio of the size of the image to the
size of the object, and is denoted by \( ^{\prime} \boldsymbol{m}^{\prime} \)
Then \( m \) is equal to (symbols have their usual meanings)
A. True
B. False


The correct relationship between free energy change in a reaction and the
corresponding equilibrium constant,
\( K_{c} \) is :
A \( . \triangle G=R T \ln K_{c} \)
B. \( -\triangle G=R T \ln K_{c} \)
c. \( \triangle G^{0}=R T l n K_{c} \)
D. \( -\triangle G^{0}=R T \ln K_{c} \)


A solid sphere hung at the lower end of a wire is suspended from a fixed point so
as to give an elongation of \( 0.4 m m \) When the first solid sphere is replaced by another one made of same material
but twice the radius, the new
elongation is
A . \( 0.8 m m \)
в. \( 1.6 m m \)
\( \mathrm{c} .3 .2 \mathrm{mm} \)
D. \( 1.2 m m \)


Let \( \boldsymbol{f}(\boldsymbol{x})=|\sin \boldsymbol{x}|, \) then \( \boldsymbol{f}(\boldsymbol{x}) \) is?
A. continuous every where
B. non-differentiable at odd and even multiple of \( \pi \)
C . everywhere continuous but non-differentiable at \( x= \) \( n \pi, n \in I \)
D. All of these


ABCD is a flower bed. If \( O A=21 c m \) and
\( O C=14 m, \) find the area of the bed.
[Use \( \left.\pi=\frac{22}{7}\right] \)
\( A \cdot 161.4 m^{2} \)
в. \( 192.5 m^{2} \)
c. \( 212.6 m^{2} \)
D. \( 257.2 .5 m^{2} \)


Slip of a reciprocating pump is defined
as
A. Difference of theoretical discharge and actual discharge
B. ratio of actual discharge to theoretical discharge
C. ratio of theoretical discharge to actual discharge
D. None


If the distance between the plane,
\( 23 x-10 y-2 z+48=0 \) and the plane containing the lines \( \frac{\boldsymbol{x}+\mathbf{1}}{\mathbf{2}}=\frac{\boldsymbol{y}-\boldsymbol{3}}{\boldsymbol{4}}= \)
\( \frac{z+1}{3} \) and \( \frac{x+3}{2}=\frac{y+2}{6}= \)
\( \frac{z-1}{\lambda}(\lambda \epsilon R) \) is equal to \( \frac{k}{\sqrt{633}} \) then \( k \) is
equal to


Heart of fish receive
A. Oxygenated bloodd
B. Deoxygenated blood
c. Both A and B
D. None of the above


The long form of the periodic table is
based on :
A. number of electrons
B. mass of the atoms
c. electronegativity
D. shape of the atom


The longest phase of mitosis is
A. Prophase
B. Metaphase
c. Anaphase
D. Telophase


Refraction of the light from the air to glass and from air to water are shown in
the figure (i) and figure (ii) below. The
value of an angle \( \theta \) in the case of
refraction as shown in the figure (iii) will be
A . 30
B. 35 5
\( c \cdot 60 \)
\( D \cdot 4 \)


is an action where the result
is uncertain.
A. Space
B. Sample
c. Experiment
D. Event


State true or false:
In parallelogram \( A B C D . E \) is the mid-
point of \( A B \) and \( A P \) is parallel to \( E C \)
which meets \( D C \) at point \( O \) and \( B C \)
produced at \( \boldsymbol{P} \). Hence
\( O \) is mid-point of \( \boldsymbol{A} \boldsymbol{P} \)
A. True
B. False


Explain the different types of spectral series in a hydrogen atom.


A covalent compound which behaves like an ionic compound in aqueous solution is :
A. sulphate
B. sulphur
c. hydrogen chloride
D. graphite


Name the reagent used for Bromination of phenol to 2,4,6 -tribromophenol:
\( \mathbf{A} \cdot H B r \)
B. \( N B S \)
c. \( B r_{2} / H_{2} O_{2} \)
D. \( B r_{2} / H_{2} O \)


The value of \( \cos ^{2} 45^{\circ}-\sin ^{2} 15^{\circ} \) is
\( A \cdot \frac{3}{4} \)
B. \( \frac{\sqrt{5}}{4} \)
\( c \cdot \frac{\sqrt{3}}{4} \)
D. \( \frac{\sqrt{5}+1}{4} \)


A woman has only daughters, analyse the situation genetically and provide a suitable explanation.


The first and second dissociation
constants of an acid \( \boldsymbol{H}_{2} \boldsymbol{A} \) are \( \mathbf{1 . 0} \times \)
\( 10^{-5} \) and \( 5.0 \times 10^{-10} \) respectively. The
overall dissociation constant of the acid
will be:
A \( .5 .0 \times 10^{-5} \)
В. \( 5.0 \times 10^{15} \)
c. \( 5.0 \times 10^{-15} \)
D. \( 2.0 \times 10^{5} \)


In a \( \triangle A B C, \) if \( 2 \angle A=3 \angle B=6 \angle C \)
calculate the measures of \( \angle B \) (in
degrees)


opp


Lead storage battery is most widely used in automobiles.
A. True
B. False


Seven white balls and three black balls
are randomly placed in a row. The probability that no two black balls are placed adjacently, equals?
A \( \cdot \frac{1}{2} \)
в. \( \frac{7}{15} \)
c. \( \frac{2}{15} \)
D.


Chemical name of \( N a_{3} P O_{4} \) is :
A. Sodium phosphate
B. Sodium phosphite
c. sodium hypo-phosphate
D. none of these


The chemical substances, which relieve the pain either completely or partially, are called:
A. tranquilizers
B. steroids
c. analgesics
D. antihistamines


2
2
8
8


The value of time when the current
reverse its sign for the first time will be
A. T/2
B. T/4
c. \( T / 6 \)
D. \( T / 8 \)


The gases associated with the green
house effect is:
A. \( C O_{2} \)
в. \( O_{2} \)
c. methene
D. \( C O \)


An aqueous solution of methanol in
water has vapour pressure:
A. equal to that of water
B. equal to that of methanol
c. more than that of water
D. less than that of water


Drinking aerated drink with low levels
(0.02 ppm) of pesticide for long period would cause
A. cancer of intestine
B. Accumulation in the body
c. Leukaemia
D. Immunity against mosquito


A body dropped from a height \( h \) with an
initial speed zero reaches the ground with a velocity of \( 3 k m / h \). Another body of the same mass was dropped from the same height \( h \) with an initial speed \( 4 k m / h \) will reach the ground with a
velocity of
\( \mathbf{A} \cdot 3 k m / h \)
в. \( 4 k m / h \)
c. \( 5 k m / h \)
D. \( 12 k m / h \)


"Like begets like" an important and universal phenomenon of life is due to
A. Eugenics
B. Inheritance
c. Dominance
D. crossing-over


In which of the following process, threads are taken out from the
cocoons?
A. Spinning
B. Scorching
c. shearing
D. None of the above


The degree of the differential equation \( \left(\frac{d^{2} y}{d x^{2}}\right)^{2}+\left(\frac{d y}{d x}\right)^{2}=x \sin \left(\frac{d^{2} y}{d x^{2}}\right) \)
\( A \cdot 1 \)
B. 2
\( c .3 \)
D. None of these


Five isomeric alkenes (all positional
isomers) \( A \) to \( E, \) all on catalytic
hydrogenation with \( \boldsymbol{H}_{2} / \boldsymbol{P} \boldsymbol{t} \) gives the
same optically active alkane \( \boldsymbol{F} \). Only \( \mathbf{A} \)
and \( \mathrm{B} \) are optically active and \( A \) liberate
more heat on hydrogenation than \( \boldsymbol{B} . \boldsymbol{C} \) show geometrical isomerism. \( \boldsymbol{E} \) evolves
more heat on hydrogenation than \( D \)
Alkene liberating least heat on hydrogenation is:
\( \mathbf{A} \cdot B \)
B. \( C \)
c. \( D \)
D. \( E \)


\( K_{3} C o F_{6} \) is a high spin complex. What
is the hybridisation of \( C o \) atom in this
complex?
\( A \cdot s p^{3} d \)
B \( \cdot s p^{3} d^{2} \)
c. \( d^{2} s p^{3} \)
D. \( d s p^{2} \)


Kjeldahl's method cannot be used for:
This question has multiple correct options
A \( . P h N O_{2} \)
в. \( P h N H C O P h \)
c. Azobenzene
D. Pyridine


The IUPAC name of above structure is :
A. phenyl ethanone
B. methyl phenyl ketone
\( c . \) acetophenone
D. phenyl methyl ketone


Give plausible explanation for each of the following:
i. Why are amines less acidic than alcohols of comparable molecular
masses?
ii. Why do priomary amines have higher boiling points than tertiary amines?
iii. Why are aliphatic amines stronger bases than aromatic amines?


When an atom undergoes \( \beta \) -decay, its
atomic number
A. Does not change
B. Increases by 1
c. Decreases by 1
D. Increases by 2


Find the square of 86 without multiplication.


f \( x+i y=\frac{-1+\sqrt{3} i}{1+i}, \) then find \( x \) and \( y \)


Ice of mass 200 g at \( 0^{\circ} \mathrm{C} \) is converted to
water at \( 0^{\circ} \mathrm{C} \) in 8 minutes supplying
heat to it at a constant rate. Calculate
the time taken to raise the temperature of water to \( 100^{\circ} \mathrm{C} \) with heat provided at the same rate. (take the latent heat of
fusion of ice \( =336 J g^{-1 \circ} C^{-1} \) and
specific heat capacity of water \( = \) \( \left.4.2 J g^{-1 \circ} C^{-1}\right) \)


A ball of mass M moving with a velocity V collides head on elastically with
another of same mass but moving with a velocity v in the opposite direction After collision,
A. the velocities are exchanged between the two balls
B. both the balls come to rest
c. both of them move at right angles to the original line of motion
D. one ball comes to rest and another ball travels back with velocity \( 2 v \)


Discuss the principle and method of softening of hard water by synthetic ion exchange resins.


"Nitride ion is a strong Bronsted Lowry acid."

Answer whether the above statement is
true or false.
If true enter 1 , else enter 0


Find the value of the unknown interior
angle \( x \) in the following figure.


Vinegar contains which organic acid?
A. Vanillic acid
B. Lactic acid
c. Oxalic acid
D. Acetic acid


acts as the
cathode.
\( \mathbf{A} \cdot Z n(s) \)
B. \( C u^{2+}(a q) \)
\( \mathbf{c} \cdot Z n^{2+}(a q) \)
\( \mathbf{D} \cdot C u(s) \)
E \( . H_{2} O \)


A piece of lead falls from a height of 100m on a fixed non-conducting slab which brings it to rest. The temperature of the lead piece immediately after collision increases by (Sp.heat of lead
is \( 30.6 \mathrm{cal} / \mathrm{kg} /^{0} C \) and \( g=9.8 m / s e c^{2} . \)
\( A \cdot \) ок
в. \( 27^{\circ} \mathrm{C} \)
c. \( 7.62 k \)
D. 4.2k


A particle of mass \( 5 \mathrm{kg} \) is free to slide on a smooth ring of radius \( r=20 \mathrm{cm} \) fixed in a vertical plane. The particle is attached to one end of a spring whose other end is fixed to the top point 0 of the ring. Initially the particle is at rest at a point \( A \) of the ring such that \( \angle O C A \) \( =60^{\circ}, \mathrm{C} \) being the centre of the ring.
The natural length of the spring is also equal to \( r=20 \mathrm{cm} . \) After the particle is released, it slides down the ring, the contact force between the particle \( \& \) the ring becomes zero when it reaches the lowest position B. Determine the force constant of the spring.


A solution containing 4 g of a nonvolatile organic solute per \( 100 \mathrm{mL} \) was found to have an osmotic pressure
equal to \( 500 \mathrm{cm} \) of mercury at \( 27^{\circ} \mathrm{C.The} \) molecular weight of solute is:
A . 14.97
B. 149.7
c. 1697
D. 1.497


Which of the following is used for metal cleaning and finishing?
A. \( C H C l_{3} \)
в. \( C H I_{3} \)
c. \( C H_{2} C l_{2} \)
D. \( C_{6} H_{6} \)


Assertion: K-shell electron capture is detected by analyzing the wavelength of X-ray emitted. Reason: The wavelength of the X-ray is characteristic of the daughter element and not the parent element.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false


\( 2 H_{2} O_{2}(l) \rightarrow 2 H_{2} O(l)+O_{2}(g) \)
\( 100 \mathrm{mL} \) of \( X \) molar \( H_{2} O_{2} \) gives \( 3 \mathrm{L} \) of \( O_{2} \) gas under the condition when 1 mol
occupies 24 L. The value of \( X \) is :
A . 2.5
B. 1.0
\( c \cdot 0.5 \)
D. 0.25


Fill in the blanks:
The diameter of a circle are


The minimum number of vectors of
unequal magnitude required to produce a zero resultant is :
A .2
B. 3
\( c \cdot 4 \)
D. more than 4


Find mean of the following for example distribution
Marks \( \quad \begin{array}{cccc}0 & 20- & 40- & 60- \\ 20 & 40 & 60 & 80\end{array} \)
No.of
students 10 8


Transfer of information from molecule of
DNA to mRNA is called as
A. Transcription
B. Translation
c. Replication
D. None of the above


Charges \( 2 \mu C \) and \( 1 \mu C \) are placed at
corners \( A \) and \( B \) of square of side \( 5 \mathrm{cm} \)
as shown in figure. The amount of work to be done against the electric field in moving a charge of \( 1.0 \times 10^{-6} C \) from \( C \)
to \( D \) is :
B. 0.053 J
c. \( 0.017 J \)
\begin{tabular}{l}
.0 .035 \\
\hline
\end{tabular}


Using elementary tansormations, find
the inverse of each of the matrices, if it
exists in \( \left[\begin{array}{ll}2 & 3 \\ 5 & 7\end{array}\right] \)


Find the seventh term of the G.P.: \( \sqrt{3}+ \)
\( 1,1, \frac{\sqrt{3}-1}{2} \)


Gaseous \( N_{2} O_{4} \) dissociates into
gaseous \( N O_{2} \) according to the reaction
\( N_{2} O_{4}(g) \rightleftharpoons 2 N O_{2}(g) \) at \( 300 \mathrm{K} \) and 1
atm pressure, the degree of
dissociation of \( N_{2} O_{4} \) is \( 0.2 . \) If one mole
of \( N_{2} O_{4} \) gas is contained in a vessel then the density of the equilibrium mixture is :
A. \( 3.11 \mathrm{g} / \mathrm{L} \)
B. 4.56 g/L
c. \( 1.56 g / L \)
D. \( 6.22 \mathrm{g} / \mathrm{L} \)


\( \boldsymbol{H} \boldsymbol{C} \boldsymbol{H} \boldsymbol{O} \stackrel{\text {Reduction}}{\longrightarrow} \boldsymbol{A} \stackrel{\boldsymbol{P}}{\longrightarrow} \)and\( \quad \boldsymbol{I}_{2} \)
\( \boldsymbol{B} \stackrel{\boldsymbol{K C N}}{\longrightarrow} \boldsymbol{C} \stackrel{\boldsymbol{H y d r o l y s i s}}{\boldsymbol{D}} \)
What is \( D ? \)
A . Acetic acid
B. Ethylamine
c. Acetamide
D. None of these


At which point is the centre of gravity
situated in: A triangular lamina
A. At the point of intersection of its perpendicular bisectors
B. At the point of intersection of its angular bisectors.
c. At the point of intersection of its sides
D. At the point of intersection of its medians.


In a series resonant \( L C R \) circuit, the
voltage across \( \boldsymbol{R} \) is 100 volts and \( \boldsymbol{R}= \)
\( 1 k \Omega \) with \( C=2 \mu F . \) The resonant
frequency is 200 rad/s. At resonance
the voltage across \( L \) is
A. \( 4 \times 10^{-3} V \)
В. \( 2.5 \times 10^{-2} V \)
c. \( 40 V \)
D. 250 V


0.34 can be represented as
A \( \cdot \frac{34}{100} \)
в. \( \frac{34}{1000} \)
\( c \cdot \frac{34}{10} \)
D. None of the above


A zero vector has
This question has multiple correct options
A. Any direction
B. Many directions
C. No direction
D. None of these


\( \mathbf{A}-\mathbf{4} . \mathbf{8 0} \mu \mathbf{C} \) charge is moving at a
constant velocity of \( 6.80 \times 10^{5} m / s \) in
the \( +x \) direction relative to a reference frame.At the instant when the point
charge is at the origin,what is the magnetic field vector it produces at the following points \( x=0, y=0.500 \mathrm{m}, z=0 ? \)


A solid sphere is rolling on a rough surface, whose centre of mass is at \( C \) at
a certain instant. Find at that instant it
has angular velocity \( \omega \) Its radius is \( \mathrm{R} \). Find the angular acceleration at that instant mass of sphere is \( \mathrm{m} \)
A \( \frac{5}{2} \frac{g d}{R^{2}} \)
В \( \frac{5}{7} \frac{g d}{R^{2}} \)
c. \( \frac{5}{2} \frac{d\left(g+\omega^{2} R\right)}{R^{2}} \)
\( D \)


The empirical formula of a compound containing 47.9 \% potassium, 5.5 \% beryllium and \( 46.6 \% \) fluorine by mass is
[At. weight of \( \mathrm{Be}=9 ; \mathrm{F}=19 ; \mathrm{K}=39] \)
A. \( K_{2} B e F_{2} \)
в. \( K B e F_{4} \)
\( \mathrm{c} \cdot K_{2} B e_{2} F_{4} \)
D. \( K_{2} B e F_{4} \)


State True or False.
The mass of a substance deposited on
the cathode or anode during electrolysis is given by \( \mathbf{w}=\frac{\boldsymbol{E} \boldsymbol{i} \boldsymbol{t}}{\boldsymbol{F}} \)
A. True
B. False


Two particles of equal mass go around in a circle of radius \( r \) under the action
of their mutual gravitational attraction. If the mass of each particle is \( m \), the
speed of each particle is
A \( \cdot \sqrt{\frac{G m}{r}} \)
в. \( \sqrt{\frac{G m}{2 r}} \)
c. \( \sqrt{\frac{G m}{4 r}} \)
D. \( \sqrt{\frac{2 G m}{r}} \)


Demonstrates the relationship between pressure \( (x \text { -axis ) and volume }(y \text { -axis }) \)
in Boyle's Law.
\( A \)
B.
\( c \)
D.
\( E \)


Ecosystem creates
A. Food chains and food web
B. Food web
c. Habitats
D. None of the above


The energy equivalent to a substance of
mass \( 1 \mathrm{g} \) is?
A \( \cdot 18 \times 10^{13} \) 」
В. \( 9 \times 10^{13} \) j
C \( .18 \times 10^{6} \mathrm{J} \)
D. \( 9 \times 10^{6} \),


Two coils have self-inductance \( \boldsymbol{L}_{\mathbf{1}}=\mathbf{4} \)
\( \boldsymbol{m} \boldsymbol{H} \) and \( \boldsymbol{L}_{2}=\mathbf{1} \boldsymbol{m} \boldsymbol{H} \) respectively. The
currents in the two coils are increased
at the same rate. At a certain instant of
time both coils are given the
same power. If \( i_{1} \) and \( i_{2} \) are the currents
in the two coils, at that instant of time
respectively, then the value of \( \left(i_{1} / i_{2}\right) \) is
A \( \cdot \frac{1}{8} \)
в. \( \frac{1}{4} \)
\( c \cdot \frac{1}{2} \)
D.


The following consecutive terms \( \frac{1}{1+\sqrt{x}}, \frac{2}{1-x}, \frac{1}{1-\sqrt{x}} \) of a series are
in
A. H.P
в. G.P.
c. A.P.
D. None


If \( a-b=5 \) and \( a^{2}+b^{2}=53, \) find the
value of \( a b \)


The size of isoelectronic species \( -F, N a^{+} \) and \( M g^{2+} \) is effected by:
A. Nuclear charge.
B. Valence principal quantum number (n)
c. Electron-electron interaction in the outer orbitals
D. Atomic mass


Long answer type question:
Explain the mechanism of reflex action
with the help of an example.


Statement 1: Electric current (flow of
electrons) creates heat in the resistor.
Statement 2: Heat in the resistor is
created according to the rule of energy conservation.
Explain Statement 1 with the help of
Statement 2.


Mention two cases in which it is useful
to decrease the pressure exerted by a force and two cases in which it is useful
to increase the pressure exerted by a force.


Write a value of
\( \int \frac{\sin x-\cos x}{\sqrt{1+\sin 2 x}} d x \)


Find \( (x, y) \) if \( (3,2),(6,3),(x, y) \) and (6,5) are the vertices of a parallelogram
A . (9,6)
B. (6,6)
\( c .(9,9) \)
D. None of these


Which of the following is a correct
statement regarding the pressure due
to fluids?
A. Force acting on the wall due to pressure is always perpendicular to it because of collision between the molecules takes place perpendicular to it.
B. Force acting on the wall due to pressure is always perpendicular to it because of collision between the molecules takes place oblique to it.
C. Force acting on the wall due to pressure is always oblique to it because of collision between the molecules takes place perpendicular to it.
D. Force acting on the wall due to pressure is always perpendicular to it because of collision between the molecules takes place at any direction to it but its normal reaction on the wall is always perpendicular to it.


The general form of A.P. is \( a, a+d \)
\( \mathbf{A} \cdot a+2 d \)
B. \( a-2 d \)
\( \mathbf{c} \cdot a+d \)
\( \mathbf{D} \cdot a-d \)


Orbit is a region of space around the nucleus where the probability of finding an electron is maximum.
A. True
B. False


An ecosystem is characterized by which of the following
A. Energy flow
B. Autotrophs converting solar energy to organic compounds
c. Decomposers recycling organic matter to inorganic compounds
D. All of the above


Fill in the blank:
The angle of incidence, in a plane mirror, is \( _{--}-_{-}-_{-}- \) the angle of reflection.
A. equal to
B. greater than
c. less than
D. twice


If the unit of tension is divided by the unit of surface tension the derived unit
will be same as that of
A . mass
B. length
c. area
D. work


Biotic components include
A. Only producers
B. Producers, consumers and decomposers
c. Only consumers
D. only producers and consumers


The focal length of a lens of glass \( \left(_{a} \mu_{g}=\frac{3}{2}\right) \) air is \( 10 \mathrm{cm} . \) The focal length
of the lens when it is immersed in water \( \left(_{a} \mu_{w}=\frac{4}{3}\right) \) will be
A. \( 40 \mathrm{cm} \)
B. 50 \( \mathrm{cm} \)
\( c \cdot 60 \mathrm{cm} \)
D. 80 cm


Botanical names of jowar and rice are respectively
A. Oryza sativa and Pennisetum typhoides
B. Sorghum vulgare and Oryza sativa
C. Triticum aesativum and Pennisetum typhoides
D. Oryza sativa and Sorghum vulgare


The mean and variance of a binomial
distribution are 4 and 3 respectively. Fix the distribution and find \( P(X \geq 1) \)


You measure the capacitor and inductor voltages in a driven RLC circuit, and find 10V for the rms capacitor voltage and \( 15 V \) for the \( r m s \) inductor voltage.
A \( \cdot \omega=\omega_{r e s} \)
В. \( \omega<\omega_{r e s} \)
\( \mathbf{c} \cdot \omega>\omega_{r e s} \)
D. can't be said


A uniform thin bar of mass \( 6 \mathrm{m} \) and length 12L is bent to make a regular hexagon. Its moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of a hexagon is
A \( .20 m L^{2} \)
\( \mathbf{B} \cdot 6 m L^{2} \)
c. \( \frac{12}{5} m L^{2} \)
D. \( 30 m L^{2} \)


A nearsighted person cannot be see beyond \( 25 \mathrm{cm} . \) Assuming that the separation of the glass from the eye is
\( \mathbf{1} c m, \) find the power of lens needed to see distant objects.


Which of the following is NOT produced by kidneys?
A. Calcitriol
B. Erythropoietin
c. Angiotensinogen
D. Renin


What is the distance of closest
approach to the nucleus of an \( \alpha \) particle which undergoes scattering by
\( 180^{\circ} \) in Geiger-Marsden experiment?


What is the shape of d-orbital?
A. spherical
B. dumb bell
c. double dumb bell
D. no definite shape


A merchant marks his goods in such a
way that the profit on sale of 50 articles is equal to the selling price of 25 articles. What is his profit margin?
A . \( 25 \% \)
B. \( 50 \% \)
c. \( 100 \% \)
D. \( 66.67 \% \)


When air is replaced by a dielectric
medium of constant \( K \), the capacity of
the condenser:
A. increases \( K \) times
B. increases \( K^{2} \) times
C . remains unchanged
D. decreases \( K \) times


In a clockwise system, which of the following is true?
в. \( \hat{i} \hat{.}=0 \)
\( \mathbf{c} \cdot \hat{j} \times \hat{j}=1 \)
D. \( \hat{k} . \hat{.}=1 \)


Mention any one hydrolytic product of lecithin.


Assertion
Chemical messengers are chemicals that enable communication of a
message between two neurons or
between neurons and muscles.
Reason

Chemicals enter the cell through receptor.
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


Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) where \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{2}^{|\boldsymbol{x}|}-\boldsymbol{2}^{-\boldsymbol{x}} \)
then \( f(x) \) is
A. periodic function
B. one one function
c. many one function
D. None of these


Consider the function \( \boldsymbol{f}(\boldsymbol{x})= \) \( \left\{\begin{array}{cl}\frac{x+5}{x-2} & \text { if } x \neq 2 \\ 1 & \text { if } x=2\end{array} . \text { Then } f(f(x)) \) is \right.
discontinuous.
A. At all real numbers
B. At exactly two values of \( x \)
c. At exactly one value of \( x \)
D. At exactly three values of \( x \)


The middle term in the expansion of
\( \left(\frac{10}{x}+\frac{x}{10}\right)^{10} \)
A . \( ^{10} C_{5} \)
в. \( ^{10} C_{6} \)
c. \( _{10} \mathrm{C}_{5} \frac{1}{x^{10}} \)
D. \( ^{10} C_{5} x^{10} \)
E . \( ^{10} C_{5} 10^{10} \)


A 100 millihenry coil carries a current of ampere. Energy stored in its magnetic field is
A . 0.5
B . 1 J
c. 0.05
D. 0.1


Two conductors \( A \) and \( B \) of the same
length and diameter are connected across the same battery. The resistivity of \( A \) is twice that of \( B \). If
\( P_{A} \) and \( P_{B} \) be the powers dissipated
\( \operatorname{across} A \) and \( B, \) respectively, then
A \( \cdot P_{A}=P_{B} \)
В. \( P_{A}>P_{B} \)
c. \( P_{A}<P_{B} \)
D. \( P_{A}=P_{B}=1 \)


The bulk modulus of water is \( 2.0 \times \)
\( 10^{9} N / m^{2} \) The pressure required to
increase the density of water by \( 0.1 \% \) is
A \( \cdot 2.0 \times 10^{3} N / m^{2} \)
B . \( 2.0 \times 10^{6} N / m^{2} \)
C \( \cdot 2.0 \times 10^{5} \mathrm{N} / \mathrm{m}^{2} \)
D. \( 2.0 \times 10^{7} N / m^{2} \)


Nucleic acids are?
A. small molecules
B. dipeptides
C. long chain polymers of nucleotides
D. polypeptides


\( \lim _{x \rightarrow 1} \frac{\sqrt[3]{x^{2}}-2 \sqrt[3]{x}+1}{(x-1)^{2}} \) is equal to
A \( \cdot \frac{1}{9} \)
B.
\( c \cdot \frac{1}{3} \)
D. none of these


Two capacitors are connected as shown
in figure below. If the equivalent
capacitance of the combination is \( 4 \mu F \)
(i) Calculate the value of \( C \)
(ii) Calculate the charge on each
capacitor.
(iii) What will be the potential drop
across each capacitor?


The ratio of a specific heats of a gas is \( 9 / 7, \) then the number of degrees of
freedom of the gas molecules for translation motion is:


For what value(s) of a will the two points \( (1, a, 1) \) and \( (-3,0, a) \) lie on opposite
sides of the plane \( 3 x+4 y-12 z+ \)
\( \mathbf{1 3}=\mathbf{0} ? \)
A \( . a<-1 \) or \( a>1 / 3 \)
B. \( a=0 \) only
\( c \cdot 0<a<1 \)
D. \( -1<a<1 \)


Simplify the following expression. \( 6 x-20 y+7 z-8 x+25 y-11 z \)


A particle of mass \( m \) is in UCM of
radius \( r \) and has momentum equal to
\( P . \) Its \( \mathrm{KE} \) is equal to:
\( ^{\mathrm{A}} \cdot \frac{P^{2}}{2 m} \)
в. \( \frac{P^{2}}{m} \)
c. \( \frac{P}{2 m} \)
D. \( \frac{P}{m} \)


Where are the enzymes of the electron
transport system found?


In the structure of DNA, one-nucleotide
purine base joins with pyramid type by which bond?
A. Aster
B. Weak hydrogen
c. Glycosidic
D. Peptide


The magnitude of the force required to
move the conducting rod at constant
speed \( 5 c m / s \) at the same instant \( t= \)
\( 2 s, \) is equal to
B. \( 0.12 N \)
c. \( 0.08 N \)
D. \( 0.64 N \)


Use the bond energies to estimate \( \Delta \boldsymbol{H} \) for this reaction:
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{H}_{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \)
\begin{tabular}{|c|c|}
\hline Bond & Bond energy \\
\hline \( \mathrm{H}-\mathrm{H} \) & \( 436 \mathrm{kJ} \mathrm{mol}^{-1} \) \\
\hline \( 0-0 \) & \( 142 \mathrm{kJ} \mathrm{mol}^{-1} \) \\
\hline \( 0=0 \) & \( 499 \mathrm{kJ} \mathrm{mol}^{-1} \) \\
\hline \( \mathrm{H}-0 \) & \( 460 \mathrm{k} \mathrm{mol}^{-1} \) \\
\hline
\end{tabular}
A. \( -127 k J \)
\( J \)
в. \( -109 k J \)
c. \( -400 k J \)
D. \( -800 k J \)


Three identical blocks each having a
mass \( \mathrm{m} \) are pushed by a force \( \mathrm{F} \) on a
friction less table. what is the
acceleration of the blocks? what is the
net force on the block P? hat force does
p apply on \( Q . \) what forces \( Q \) apply on \( R ? \)
\( A \cdot \frac{3 F}{8} \)
B. \( \frac{F}{7} \)
\( \mathbf{c} \cdot \frac{F}{3} \)
D. \( \frac{2 F}{4} \)


If a polynomial \( f(x)=4 x^{4}-a x^{3}+ \)
\( b x^{2}-c x+5,(a, b, c \epsilon R) \) has four
positive real roots \( r_{1}, r_{2}, r_{3}, r_{4} \) such that
\( \frac{r_{1}}{2}+\frac{r_{2}}{4}+\frac{r_{3}}{5}+\frac{r_{4}}{8}=1 \) Then value of \( a \)
will be
A . 20
B . 21
\( c \cdot 19 \)
D. 22


Assertion
Small liquid drops assume spherical
shape.
Reason
Due to surface tension liquid drops tend to have minimum surface area.
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 maximum electric field intensity
inside the ball is:
A \( \cdot \frac{\rho_{0} R}{9 \epsilon} \)
B. \( \frac{\rho o}{9 R} \)
\( \mathbf{c} \cdot \frac{\rho_{0} R}{3 \epsilon} \)
D. \( \frac{\rho_{0} R}{6 \epsilon} \)


The meteors seldom reach the earth
because of :
A. freezing caused when they pass through the atmosphere
B. vapourization caused when they pass through the atmosphere
c. greater force of attraction towards sun
D. greater force of attraction towards moon


Determine the A.P. whose fifth tern is 19
and different one of the eight term from the thirteenth term is 20


The hydrolysis of sodium carbonate
involves the reaction between:
A. sodium ion and water
B. \( N a^{+} \) and \( O H^{-} \)
\( \mathrm{c} \cdot \mathrm{CO}_{3}^{2-} \) and water
D. \( C O_{3}^{2-} \) and \( H^{+} \)


The air we breathe out contains more
A. Oxygen
B. Carbon dioxide
c. water
D. chlorophyll


Assertion
A body on an inclined plane just tends to slide down if the angle of inclination is equal to angle of friction.
Reason
When the angle of inclination is equal
to the angle of friction, the component of weight parallel to the plane is just sufficient to overcome the frictional
force.
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


Meso isomers are possible when the organic compound contains:
A. one asymmetric carbon
B. two or more dissimilar asymmetric carbons
c. similar asymmetric carbons
D. unsaturation


Energy of electron in first excited state
of \( H \) -atom is:
A. \( -13.12 \times 10^{5} \mathrm{J} / \mathrm{mol} \)
B. \( -3.28 \times 10^{5} \mathrm{J} / \mathrm{mol} \)
c. \( 13.12 \times 10^{3} J / \) mol
D. \( 3.28 \times 10^{2} J / \) mol


Solar radiation emitted by sun
resembles that emitted by a black body
at a temperature of \( 6000 K . \) Maximum
intensity is emitted at a wavelength of about \( 4800 A \). If the sun was
cooled down from \( 6000 K \) to \( 3000 K \)
then the peak intensity would occur at a
wavelength of :
A. 4800 A
в. 9600 \( \dot{A} \)
c. 2400 月
D. \( 19200 \dot{A} \)


Which of the following polymers can be
formed by using the following monomer
unit??
A . Nylon-6,6
B. Nylon-2-nylon-6
c. Melamine polymer
D. Nylon-6


Find the sum of the first 6 terms of the
geometric series \( 80-20+5+\dots . \)
A .63 .984
B. 32.451
c. 54.876
D . 25.458


Classification
\( \mathbf{i} \)
A. Only study about classes
B. Arrangement of organisms into groups or sets on the basis of similarities, differences and their relationship
C. Only study about species
D. Rearrangement of organisms into groups or sets on the basis of only their differences


Geometric mean of 3,9 and 27 is
A . 18
B. 6
\( c .9 \)
D. None of these


In ground state of chromium atom \( (Z=24) \) the total number of orbitals
populated by one or more electrons is??
A . 15
B . 16
c. 20
D. 14


The C. M. of a uniform card board cut in
T shape as shown in figure is:
4. \( 4 \mathrm{cm} \) from A towards
B. \( 4 \mathrm{cm} \) from B towards
\( \mathrm{c} .3 \mathrm{cm} \) from \( \mathrm{B} \) towards \( \mathrm{A} \)
D. 3 cm from A towards


A piece of copper weighing 500 g is heated to \( 100^{\circ} \mathrm{C} \) and dropped into \( 200 \mathrm{g} \)
of water at \( 25^{\circ} \mathrm{C} \). Find the temperature of the mixture. The specific heat of Cu is \( 0.42 J g^{-1} o C^{-1} \)
A \( \cdot 30^{\circ} \mathrm{C} \)
B . \( 40^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 50^{\circ} C \)
D. \( 60^{\circ} \mathrm{C} \)


Of the adult population in a certain city \( 45 \% \) of men and \( 25 \% \) of women are
married. Assuming that no man marries more than one women, and
vice versa, the percentage of total population of adults who are married is:
A . 31.1
B . 30
c. 33.33
D . 32.14


Three integers are chosen at random without replacement from the 1st 20 integers. The probability that their
product is even is
A \( \cdot \frac{16}{19} \)
в. \( \frac{17}{19} \)
c. \( \frac{18}{19} \)
D. \( \frac{15}{19} \)


Which of the following is not an application of orthoboric acid?
A. As an antiseptic and eye wash
B. In glass industry
c. In glazes for pottery
D. In borax-bead test


The heights of two cylinders are in the ratio of \( 3: 1 . \) If the volumes of two
cylinders be same, then find the ratio of their respective radii.
A \( \cdot 1: \sqrt{3} \)
в. \( 2: \sqrt{3} \)
c. \( \sqrt{3}: 1 \)
D. None of these


Given \( k_{1}=1500 N m^{-1}, k_{2}= \)
\( \mathbf{5 0 0} N \boldsymbol{m}^{-1}, \boldsymbol{m}_{1}=\mathbf{2 k g}, \boldsymbol{m}_{2}=\mathbf{1 k g} . \) Find:
a. Potential energy stored in the springs in equilibrium, and
b. work done in slowly pulling down \( m_{2} \)
by \( 8 \mathrm{cm} \)


Count total number of S.F. in \( 6.020 \times \)
\( 10^{23} \)
A .4
B. 3
\( c \cdot 6 \)
D. 7


Divide:
\( x^{7}-y^{7} \) by \( x-y \)


\( \boldsymbol{C a} \boldsymbol{C O}_{3}+\boldsymbol{S i O}_{2} \rightarrow \)
A \( \cdot C a O+\operatorname{Si} C O_{3} \)
в. \( \mathrm{CaSiO}_{3}+\mathrm{SiO}_{2} \)
c. \( C a S i O_{3}+C a O \)
D. \( \mathrm{CaSiO}_{3}+\mathrm{CO}_{2} \)


Balance the following in basic medium:
\( \boldsymbol{F} \boldsymbol{e}_{3} \boldsymbol{O}_{4}+\boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4}^{-} \rightarrow \boldsymbol{F} \boldsymbol{e}_{2} \boldsymbol{O}_{3}+\boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{2} \)
A \( \cdot 6 F e_{3} O_{4}+2 M n O_{4}^{-}+H_{2} O \rightarrow 9 F e_{2} O_{3}+2 M n O_{2} \)
\( 2 O H^{-} \)
B. \( 6 F e_{3} O_{4}+4 M n O_{4}^{-}+H_{2} O \rightarrow 9 F e_{2} O_{3}+5 M n O_{2}+ \)
\( O H^{-} \)
\( \mathrm{c} \cdot 6 \mathrm{Fe}_{3} \mathrm{O}_{4}+\mathrm{MnO}_{4}^{-}+\mathrm{H}_{2} \mathrm{O} \rightarrow 9 \mathrm{Fe}_{2} \mathrm{O}_{3}+3 \mathrm{MnO}_{2}+ \)
\( 2 O H^{-} \)
D. None of these


\( n \) resistors each of resistance \( R \) first
combine to give maximum effective resistance and then combine to given
minimum effective resistance. The ratio
of the maximum to minimum
resistance is:
A . \( n \)
B \( \cdot n^{2} \)
c. \( n^{2}-1 \)
\( \mathbf{D} \cdot n^{3} \)


Substance \( X \) has three common
isotopes: \( X-48, X-49 \) and \( X-51 \)
If the relative abundances of these three
isotopes are \( 42 \%, 38 \% \) and \( 20 \% \)
respectively, what is the atomic mass of substance \( \boldsymbol{X} \) ?
A . 49.33 amu
B. 48.62 amu
c. 50.67 amu
D. 48.98 amu
E . 49.67 amu


Joining of repeating units to form a macromolecule is called
A. Polymerisation
B. Aggregation
c. Polymorphism
D. Condensation


The number of \( \pi- \) bonds present in
the monomer of polyacrylonitrile is:
A . 2
B.
\( c .3 \)
D. 4


Find the mismatch
A. Sky wave communication: Frequency upto 30 MHz
B. Line-of-sight communication: Frequency greater than \( 40 \mathrm{MHz} \)
C. Mobile telephony : Frequency range \( 800-950 \mathrm{kHz} \)
D. Facsimile : Static document
E. Ground wave propagation: Frequency less than a few МНz


Assertion: The properties of paramagnetic and ferromagnetic substances are not affected by heating.
Reason: As temperature rises, the alignment of molecular magnets gradually decreases
A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true and R is not correct explanation of A
c. A is true, but R is false
D. A is false, but R is true


The term 'feed back' refers to the effect
of
A. Substrate on the rate of enzymatic reaction
B. End products on the rate of enzymatic reaction
C. Enzyme concentration on its rate of reaction
D. An external compound on the rate of enzymatic reactions


Astigmatism for a human eye can be
removed by using an additional:
A. concave lens
B. convex lens
c. cylindrical lens
D. prismatic lens


Which of the following is the monomer of cellulose?
A. \( \beta-D \) -glucose
B. Amylose
c. Amylopectin
D. Glycogen


Link between glycolysis, Krebs cycle and beta-oxidation of fatty acid is
A. Pyruvic acid
B. Acetyl CoA
c. Acetaldehyde
D. Citric acid


Two thermometers are used to record
the temperature of a room and the bulb
of one is wrapped in wet hanky.
A. The temperature recorded by both will be same
B. The temperature recorded by the wet-bulb thermometer will be greater than that recorded by the other
C. The temperature recorded by dry-bulb thermometer will be greater than that recorded by the other
D. None of the above


For the following statements, write T for
True and \( F \) for False.
The mass of an electron is \( 1 / 2000 \)
times that of proton.


The set representing the correct order of first ionisation potential is :
A. \( K>N a>L i \)
в. \( B e>M g>C a \)
c. \( B>C>N \)
D. \( G e>S i>C \)


For \( \boldsymbol{a}>\mathbf{0}, \) arg \( (\boldsymbol{i} \boldsymbol{a})= \)
A \( \cdot \frac{\pi}{2} \)
B. \( -\frac{\pi}{2} \)
\( c . \pi \)
D. - \( \pi \)


Under 3 at \( m, 12.5 \) litres of a certain gas
weighs 15 g. The average speed of gaseous molecules is \( x \times 10^{4} \mathrm{cm} \) sec \( ^{-1} \)
Value of \( x \) is...... (only integer part)


A ball is thrown vertically upwards. It
has a speed of \( 10 m s^{-1}, \) when it has
reached on half of its maximum height. How high does the ball rise? (Take \( g= \)
\( \left.10 m s^{-2}\right) \)
A . \( 10 \mathrm{m} \)
B. \( 5 \mathrm{m} \)
\( c \cdot 15 m \)
D. 20 \( m \)


Iron bacterium is
A. Beggiotoa
B. Geobacillus
c. Thiobacillus
D. None of the above


Show that the right circular cylinder of given surface and maximum volume is
such that its height is equal to the diameter of the base.


The equilibrium constant \( K_{C} \) for the reaction,
\( A(g)+2 B(g) \rightleftharpoons 3 C(g) \) is \( 2 \times 10^{-3} \)
What would be the equilibrium partial
pressure of gas \( C \) if initial pressure of \( \operatorname{gas} A \) and \( B \) are 1 and 2


toppr
Q Type your question-
molecules reacts with \( H_{2} O \) to form
\( N H_{4} O H \) molecules. \( N H_{4} O H \) again
dissociates into \( N H_{4}^{+} \) and \( O H^{-} \) ions.
In solution therefore, we have \( \boldsymbol{N} \boldsymbol{H}_{3} \)
molecules, \( N H_{4} O H \) molecules and
\( N H_{4}^{+} \) ions and the following equilibrium exist:
\( N H_{3}(g) \rightleftharpoons N H_{3}(l)+H_{2} O(l) \rightleftharpoons \)
\( N H_{4} O H(a q) \rightleftharpoons N H_{4}^{+}(a q)+ \)
\( \boldsymbol{O} \boldsymbol{H}^{-}(\boldsymbol{a} \boldsymbol{q}) \)
Let, \( c_{1}(\text { mol } / L) \) of \( N H_{3} \) pass in liquid
state which on dissolution in water
forms \( c_{2}(m o l / L) \) of \( N H_{4} O H . \) The
solution contains \( c_{3}(m o l / L) \) of \( N H_{4}^{+} \) ions.
Concentration of undissociated
ammonium hydroxide is
\( \mathbf{A} \cdot c_{1}+c_{2} \)
в. \( c_{2}-c_{3} \)
\( \mathbf{c} \cdot c_{1}+c_{3} \)
D. \( c_{1}-c_{2} \)


Find the sum of the following arithmetic progressions:
\( a+b, a-b, a-3 b, \ldots . . \) to 22 terms.


Which type of ores are concentrated by froth flotation process?
A. Carbonates
B. Sulphides
c. oxides
D. Phosphates


topp 5
\( Q \) туре уочт question
(B)
\( (\mathrm{C}) \)
\( (D) \)
(E)


A negatively charged body has
A. an excess of protons
B. an excess of electrons
C . an excess of photons
D. an deficiency of electrons


\( \frac{\boldsymbol{x}+\mathbf{2}}{\boldsymbol{x}^{\boldsymbol{3}}-\boldsymbol{x}}= \)
A. \( \frac{1}{2(x+1)}+\frac{3}{2(x-1)}-\frac{2}{x} \)
B. \( \frac{1}{2(x+1)}-\frac{3}{2(x-1)}-\frac{2}{x} \)
c. \( \frac{1}{2(x+1)}-\frac{3}{2(x-1)}+\frac{2}{x} \)
D. \( \frac{1}{2(x+1)}+\frac{3}{2(x-1)}+\frac{2}{x} \)


\( \frac{\pi}{8} \)
of
of
se


Positive slope of a velocity-time graph implies
A. accelerated motion
B. retarded motion
c. uniform motion
D. no motion


Pollen drop of gymnosperms is
\( A \cdot \operatorname{Red} d r o p \)
B. Pollen dropped by wind
C. Nucellus secretions
D. Malic acid drop


Two particles \( A \) and \( B \) are shot from the same height at \( t=0 \) in opposite
directions with horizontal velocities
\( 3 m / s \) and \( 4 m / s \) respectively. If they are subjected to the same vertical acceleration due to gravity \( (\boldsymbol{g}= \)
\( 9.8 m / s^{2} \) ). the distance between them
when their velocity vectors become mutually perpendicular is:
A . \( 1.059 m \)
в. \( 1.412 m \)
c. \( 2.474 m \)
D. \( 9.8 m \)


Which of the following is an oxide ore? This question has multiple correct options
A. bauxite
B. cuprite
c. haematite
D. galena


Form the differential equation
corresponding to \( y^{2}-2 a y+x^{2}=a^{2} b y \)
eliminating a.


The time period of the variation of potential energy of a particle executing \( \boldsymbol{S H} \boldsymbol{M} \) with period \( \boldsymbol{T} \) is
\( \mathbf{A} \cdot T / 4 \)
в. \( T \)
c. \( 2 T \)
D. \( T / 2 \)
E . \( T / 3 \)


What are the advantages of sexual
reproduction over asexual
reproduction?


The boiling point of alkyl halide are higher than those of corresponding alkanes because of:
A. dipole-dipole interaction
B. dipole-induced dipole interaction
c. \( H \) -bonding
D. none of the above


The silvering on the back surface of a mirror can be done by
A . Silver
B. Mercury
c. None
D. All kind of shiny materials


A given object takes \( n \) times more time
to slide down \( 45^{\circ} \) rough inclined plane
as it takes to slide down a perfectly
\( \operatorname{smooth} 45^{\circ} \) incline. The coefficient of
kinetic friction between the object and
the incline is:
A \( \cdot \frac{1}{2-n^{2}} \)
B. \( 1-\frac{1}{n^{2}} \)
c. \( \sqrt{1-\frac{1}{n^{2}}} \)
D. \( \sqrt{\frac{1}{1-n^{2}}} \)


1 Parsec is equivalent to how much AU?
A . 206
B. 206264000
\( c \cdot 206264 \)
D. 20600


Which of the following is whole number?
A. Atomic mass
B. Atomic number
c. Atomic volume
D. Atomic radius


For the situation shown in the figure,
flux through the square loop is
\( \mathbf{A} \cdot\left(\frac{\mu_{0} i a}{2 \pi}\right) \ln \left(\frac{a}{2 a-b}\right) \)
B \( \cdot\left(\frac{\mu_{0} i b}{2 \pi}\right) \ln \left(\frac{a}{2 b-b}\right) \)
\( \left(\frac{\mu_{0} i b}{2 \pi}\right) \ln \left(\frac{a}{b-a}\right) \)
\( \left(\frac{\mu_{0} i a}{2 \pi}\right) \ln \left(\frac{2 a}{b-a}\right) \)


A wound-up watch spring possesses
A. kinetic energy
B. elastic potential energy
c. nuclear energy
D. sound energy


How many molecules
of oxygen are bound to one molecule of haemoglobin
\( A \)
B. 2
\( c \cdot 3 \)
D. 4


Assertion
When super charged particles enter the earth's atmosphere from the solar wind they tend to be channeled toward the
poles.
Reason
This is due to magnetic forces causing
them to spiral around the magnetic
field lines of the earth.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Evaluate \( \int_{0}^{\pi} \frac{x}{a^{2} \cos ^{2} x+b^{2} \sin ^{2} x} d x \)


In a young's double-slit experiment, the
slits are separated by \( 0.5 m m, \) and the
screen is placed \( 150 c m \) away. A beam of light consisting of two wavelengths,
\( 650 n m, \) and \( 520 n m, \) is used to obtain
interference fringes on the screen. The
least distance from the common central
maxima to the point where the bright
fringes due to both the wavelengths
coincide is:
\( \mathbf{A} \cdot 9.75 m m \)
B. \( 15.6 m m \)
c. \( 1.56 m m \)
D. \( 7.8 m m \)


If \( V \) ml of the vapours of substance at NTP weighs \( W \) g. Then, molecular weight of substance is :
A \( \cdot \frac{W}{V} \times 22400 \)
в. \( \frac{V}{W} \times 22.4 \)
C \( \cdot(W-V) \times 22400 \)
D. \( \frac{W \times 1}{V \times 22400} \)


If the difference between \( (\boldsymbol{n}+\mathbf{1})^{t h} \) Bohr
radius and \( n^{t h} \) Bohr radius is equal to
the \( (\boldsymbol{n}-\mathbf{1})^{t h} \) Bohr radius then find the
value of \( n \)
A . 4
B. 3
c. 2
D.


Prove that the line segments joining the midpoints of the sides of a triangle from
four triangles each of which is similar
to the original triangle.


The speed of electron revolving in the 4
th orbit of a hydrogen like atom or ion is \( 1094 \mathrm{km} / \mathrm{s} . \) The atom or ions is:
A. \( H \)
в. \( H e^{+} \)
\( \mathrm{c} \cdot L i^{2} \)
\( D \cdot B e^{3} \)


The diagram given below show the cross
section of two kinds of blood vessels:
i) Identify the blood vessels \( A \) and \( B \). In
each case give a reason to support your
answer.
ii) Name the parts numbered 1 and 2
iii) When are the sound "LUB" and "DUP"
produced during a heartbeat?
iv) Name the blood vessel that:
Begins and ends in capillaries
2. Supplies blood to the walls of the
heart.


Bredig's arc method cannot be used for the preparation of colloidal sol of ? This question has multiple correct options
A. copper
B. Gold
c. Silver
D. Sodium


The arithmetic mean of the series
\( 1,2,2^{2}, \dots 2^{n-1} \) is
A \( \cdot \frac{2^{n}}{n} \)
B. \( \frac{\left(2^{n}-1\right)}{n} \)
\( ^{\mathrm{C}} \cdot \frac{\left(2^{n+1}\right)}{n} \)
D. None of these


The value of \( K \) in order that \( f(x)= \)
\( \sin x-\cos x-K x+5 \) decreases for all
positive real values of \( x \) is given by
A \( . K<1 \)
в. \( K \geq 1 \)
c. \( K>\sqrt{2} \)
D. \( K<\sqrt{2} \)


A steel rope has length \( L \), area of cross-
section \( A \), Young's modulus \( Y \) and density as \( d \). It is pulled on a horizontal
frictionless floor with a constant horizontal force \( F=\frac{d A L g}{2} \) applied at one
end. Find the strain at the midpoint.
\( \mathbf{A} \cdot \frac{d g L}{2 Y} \)
B. \( \frac{d g L}{4 Y} \)
\( \mathbf{c} \cdot \frac{d g L}{6 Y} \)
D. \( \frac{d g L}{8 Y} \)


The motion of a body is given by the equation \( \frac{d v}{d t}=6-3 v \) where v is the speed in \( m s^{-1} \) and \( t \) is time in s. The
body is at rest at \( t=0 . \) The speed varies with time as
A \( \cdot v=\left(1-e^{-3 t}\right) \)
B . \( v=2\left(1-e^{-3 t}\right) \)
c. \( v=\left(1+e^{-2 t}\right) \)
D \( \cdot v=2\left(1+e^{-2 t}\right) \)


Let \( \boldsymbol{f}(\boldsymbol{x})=\sqrt{\mathbf{2} \boldsymbol{x}+\mathbf{1}} \) and let \( \boldsymbol{c} \) be the
number that satisfies the Mean value
theorem for \( f \) on the interval [4,12]
What is \( c \) ?
\( \mathbf{A} \cdot \mathbf{0} \)
в. 1.5
\( c \cdot 4 \)
D. 7.5


\( \begin{array}{lll}\text { Element } & \text { Reaction with water } & \triangle \boldsymbol{T}\left(^{\circ} \boldsymbol{C}\right) \\ \mathrm{A} & \text { small bubbles formed } & -2 \\ \mathrm{B} & \text { vigorous bubbling } & +10 \\ \mathrm{C} & \text { dissolves, no bubbles } & 0 \\ \mathrm{D} & \text { small bubbles formed } & 0\end{array} \) Which electron configuration would
match the laboratory data for Element
\( \mathrm{B} ? \)
\( \mathbf{A} \cdot[N e] 3 s^{2} \)
\( \mathbf{B} \cdot[X e] 6 s^{2} \)
\( \mathbf{C} \cdot[A r] 4 s^{2} 3 d^{10} \)
D. \( [N e] 3 s^{2} 3 p^{3} \)


State True or False.
Pressure at a point in a liquid is inversely proportional to the height of the liquid column.
A. True
B. False


Write the process of making ethyl acetate by esterification with equation.


Which is the fish that give birth to
young ones?
A. Scoliodon
B. Anabas
c. Heteropneustes
D. catla catla


Find the length of edge of a cube with following surface area
\( 1944 \mathrm{cm}^{2} \)
\( 2646 \mathrm{cm}^{2} \)
A. \( 28 \mathrm{cm} ; 21 \mathrm{cm} \)
в. \( 17 \mathrm{cm} ; 21 \mathrm{cm} \)
\( \mathrm{c} .18 \mathrm{cm} ; 21 \mathrm{cm} \)
D. \( 18 \mathrm{cm} ; 20 \mathrm{cm} \)


Acrolyn is the starting material for
certain plastics. CH and CO bonds are
polar. If true enter 1 , else 0


The time period of a simple pendulum at the center of the earth is:
A . zero
B. infinite
c. less than zero
D. none of these


The ticking of a watch sounds louder when heard through water than through a metal. True or false.
A. True
B. False


Find the total surface area of a
hemisphere of radius \( 3.5 \mathrm{cm} \)


Find the arithmetic mean between 9
and 19


During any collision
A. Momentum is conserved
B. Linetic energy is conserved
c. Both conserved
D. All


\( " \boldsymbol{I} \boldsymbol{F}_{7} \) has pentagonal bipyramidal
structure."
Answer whether the above statement is
true or false.
If true enter 1 , else enter 0 .


Leaves of submerged hydrophytes are
A. Epistomatic
B. Hypostomatic
c. Astomatic
D. Both A and B


The girth of the roller is \( 75 \mathrm{cm} \) and its
width is 2 metres. How many
revolutions must it make to roll a field
whose area is 3 hectare?
A . 2000
B. 20000
\( c \cdot 200 \)
D. NONE OF THESE


Construct a triangle with sides \( 5 \mathrm{cm}, 6 \mathrm{cm} \) and \( 7 \mathrm{cm} \) and then another triangle whose sides are \( \frac{7}{5} \) times of the corresponding sides of the first triangle. Write down the steps of construction.


When diamond is heated to \( 1500^{\circ} \mathrm{C} \), in
the absence of air, it forms:
A. graphite
B. carbon black
\( c . \) soot
D. coke


The proton is heavier than an electron by
A. 1835 times
B. 18000 times
c. 1000 times
D. 100 times


Find a quadratic polynomial with \( \frac{1}{4},-1 \) as the sum and product of its zeroes respectively.


Two reactions \( R_{1} \) and \( R_{2} \) have identical
pre-exponential factors. Actiation
energy of \( R_{1} \) exceeds that of \( R_{2} \) by
\( \mathbf{1 0 k J}^{-1 . \text { If }} \boldsymbol{K}_{1} \) and \( \boldsymbol{K}_{2} \) are rate
constants for reactions \( \boldsymbol{R}_{1} \) and \( \boldsymbol{R}_{1} \)
respectively at \( 300 \mathrm{K}, \) then \( \ln \left(K_{1} / K_{2}\right) \) is
equal to :\( \boldsymbol{R}=\mathbf{8 . 3 1 4} \boldsymbol{J}^{-1} \boldsymbol{K}^{-1} \)
\( A \cdot 8 \)
B. 12
\( c \cdot 6 \)
D. 4


\( P \) is point in the interior of an equilateral triangle with side a units. If \( P_{1}, P_{2} \) and \( P_{3} \) are the distance of \( P \) from
the three sides of the triangle, then
\( \boldsymbol{P}_{1},+\boldsymbol{P}_{2}+\boldsymbol{P}_{3} \) is?
A \( \cdot \) equals \( \frac{2 a}{3} \) units
в. \( _{\text {equals }} \frac{a \sqrt{3}}{2} \)
\( c . \) is more than a unit
D. cannot be determined unless the location of P is specified.


The binding energy per nucleon for \( C^{12} \) is \( 7.68 M e V \) and that for \( C^{13} \) is
7.5 \( M e V \). How much energy is required
to remove a neutron from \( C^{13} \) ?
A. \( 5.34 \mathrm{MeV} \)
B. \( 5.5 \mathrm{MeV} \)
c. \( 9.5 \mathrm{MeV} \)
D. \( 9.34 \mathrm{MeV} \)


Among the following, the couple with most positive reduction potential is :
A. \( M n^{+3} / M n^{+2} \)
B. \( C r^{+3} / C r^{+2} \)
c. \( F e^{+3} / F e^{+2} \)
D. \( C o^{+3} / C o^{+2} \)


A triangle with all 3 equal sides is called as:
A. isosceles
B. equilateral
c. scalene
D. none of these


The current in the forward bias is known
to be more \( (\sim \boldsymbol{m} \boldsymbol{A}) \) than the current in
the reverse bias \( (\sim \mu A) . \) What is the
reason, then, to operate the photodiode in reverse bias?


The points \( A(-1,3,0), B(2,2,1) \) and
\( C(1,1,3) \) determine a plane. The distance of the plane \( A, B, C \) from the
point \( D(5,7,8) \) is
A . \( \sqrt{66} \)
B. \( \sqrt{71} \)
c. \( \sqrt{73} \)
D. \( \sqrt{76} \)


Which of the major sources of air pollution contributes pollutants like chlorofluorohydrocarbons?
A. Industrial effluents
B. Aerosols
c. sewage pollutants
D. All of the above


The IUPAC name of the following compound is ethyl \( 4- \) bromo -3
chlorobenzoate
A. True
B. False


\( H_{2} O_{2} \) is always stored in black bottles
because:
A . it is highly unstable
B. it has high enthalpy of decomposition
c. it undergoes auto oxidation on prolonged standing
D. none of the above


Find the second derivative of the
function \( \boldsymbol{x}^{\mathbf{2 0}} \)


Find the area under the curve \( \boldsymbol{y}= \)
\( \left(x^{2}+2\right)^{2}+2 x \) between the lines \( x=0 \)
\( x=2 \) and the \( X \) -axis


Valli took some common salt,
naphthalene balls, camphor, baking
soda and washing soda. She attempted
to dissolve these substances either in
water or in acetone.

Complete the table with the expected results.
MEDIUM IN SUBSTANCE WHICH ITIS SOLUBLE
a. Common salt
\( b \)
Naphthalene balls
c. Camphor
d. Baking soda
e. Washing soda


Which of the following bonds is the most ionic?
A. \( C s-C l \)
в. \( A l-C l \)
c. \( C-C l \)
D. \( H-C l \)


An urn contains 2 white and 2 black
balls. A ball is drawn at random. If it is
white it is not replaced into the urn. Otherwise it is replaced along with another ball of same colour. The process
is repeated. The probability that the third ball drawn is black is1 \( -\frac{k}{30} \). Find
the value of \( k \) ?


Using the ahove approximation, the value \( \sqrt{104} \) is
\( \mathbf{A} \cdot 10.18 \)
B. 10.49
c. 10.2
D. 10.28


Which statements are correct about the
following compounds?

Bicyclo[2.2.1] hept-l-ene Bicyclo[4.4.0] dec-1-ene
This question has multiple correct options
A . (I) is not isolable because trans-cyclohexane is too strained.
B. (II) is isolable because trans-unit can be bridged by six C atoms. Eight-membered and larger rings can have a trans-substituted (C=C)in the ring
C. (III) is not isolable, exocyclic double bonds (double bond at the bridgehead) are unstable because of high strain (due to ring and double bond joining the two rings)
D. (IV) is isolablem, although there is a double bond at a bridgehead (joining two rings) but one of the bridgeheads has no C atom and bridgehead C atoms can flatten without ring strain.


Find \( \frac{d y}{d x}, \) when \( y=x^{x}-2^{\sin x} \)


For a common emitter amplifier, the current gain is \( 70 . \) If the emitter current
is \( 8.8 \mathrm{mA} \), then the collector current is:
\( \mathbf{A} \cdot 0.124 m A \)
в. \( 4.34 m A \)
\( c .8 .68 m A \)
D. \( 1.72 m A \)


Solution:
\( 10 a^{2}(0.1 a-0.5 b) \)


Column II gives name of material use for device given in column I:


An LED operates under which biasing condition?
A. Forward bias
B. Reverse bias
c. can operate both in forward and reverse bias
D. No biasing is required


The complete set of values of \( x \)
satisfying equation \( \cot x-\cos x= \)
\( 1-\cot x \cos x \) is
A \( \cdot\left\{x: x=(4 n \pi+1) \frac{\pi}{4}, n \in I\right\} \)
в. \( \left\{x: x=2 n \pi+\frac{\pi}{4}, n \in I\right\} \)
C \( \cdot\{x: x=2 n \pi \pm \pi, n \in I\} \)
D \( \cdot\{x: x=2 n \pi+\pi, n \in I\} \cup\left\{x: x=n \pi+\frac{\pi}{4}, n \in I\right\} \)


The number of real solutions of
\( \tan ^{-1}(\sqrt{x(x+1)}+ \)
\( \sin ^{-1} \sqrt{\left(x^{2}+x+1\right)}=\frac{\pi}{2} \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. infinite


A value of \( k \) such that the straight lines \( \boldsymbol{y}-\boldsymbol{3} \boldsymbol{x}+\boldsymbol{4}=\boldsymbol{0} \) and \( (\boldsymbol{2} \boldsymbol{k}-\mathbf{1}) \boldsymbol{x}-(\boldsymbol{8} \boldsymbol{k}- \)
1) \( y-6=0 \) are perpendicular is
A \( \cdot \frac{2}{7} \)
B. \( -\frac{2}{7} \)
c.
D.


Current \( i \) is flowing in a coil of area \( A \& \)
number of turns \( N, \) then magnetic
moment of the coil is \( M \) is equal to
A. \( N i A \)
в. \( \frac{N i}{A} \)
c. \( \frac{N i}{\sqrt{A}} \)
D. \( N^{2} A i \)


The kinetic energy possessed by a body with mass \( m \) and moving with a velocity \( v \) at a height \( h \) is given by
\( A \cdot m g h \)
B. \( m v^{2} \)
c. \( \frac{1}{2} m g h \)
D. \( \frac{1}{2} m v^{2} \)


The arrangement of elements in a group of three is known as


\( \mathbf{f}|z+\mathbf{1}|=z+\mathbf{2}(\mathbf{1}+i), \) then find \( z \)


Suggest reasons for the phenomenon associated with the following.
(i) The sky appearing blue
(ii) Twinkling of stars


The commercial cryogenic processing industry was founded in \( 1966 \mathrm{by} \)
A. James William
B. Ed Busch
C. Robert Henry
D. None of the above


The isotope of hydrogen, \( D_{2} \) forms
heavy water, \( D_{2} O . \) It is qualified as \( D_{2} O \) because it is:
A. a heavy liquid
B. an oxide of heavier isotope of oxygen
c. an oxide of deuterium
D. denser than water


If the square root of a number is
between 6 and \( 7, \) then its cube root lies between
\( \mathbf{A} \cdot 2,3 \)
в. 2.5,3
\( c .3,4 \)
D. 4,4.5


If the temperature of a body is raised by
\( 5 \% \) then the heat energy radiated would increases by
A . \( 5 \% \)
B . 10\%
c. \( 11.65 \% \)
D. 21.55


Select the correct statements about
adsorption
This question has multiple correct options
\( \mathbf{A} \cdot \Delta G=-v e \)
B. \( \Delta H=-v e \)
c. \( \Delta S=-v e \)
D. \( \Delta G>T \Delta S \)


How many carbon atoms are present in a molecule of pentane?
A .
B. 2
\( c .5 \)
D. 3
E. 7


A line separates a plane into three parts namely the two half-planes and the line itself
A. True
B. False


The surface in the figure (b) would be like which of the following?
A. A mirror
B. A sheet of paper
c. A waxed paper
D. A painted wall


8.8
8.8
8.8


A resistance \( \boldsymbol{R} \) and a capacitor \( \boldsymbol{C} \) are
joined to a source of \( \boldsymbol{A} \boldsymbol{C} \) of constant
e.m.f and variable frequency.
The potential difference across \( C \) is \( V \)
If the frequency of \( \boldsymbol{A} \boldsymbol{C} \) is gradually increased, \( \boldsymbol{V} \) will
A. increase
B. decrease
c. remain constant
D. first increase and then decreas


For a homogeneous gaseous reaction, \( \boldsymbol{A} \longrightarrow \boldsymbol{B}+\boldsymbol{C}+\boldsymbol{D}, \) the initial pressure
was \( P_{0} \) while pressure at time \( t \) was \( P \) Derive an expression for rate constant
\( K \) in terms of \( P_{0}, P \) and \( t \) [Assume first-order reaction]


The value of \( 9 \tan ^{2} \theta-9 \sec ^{2} \theta \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B. 0
\( c .9 \)
D. - -


Identify \( X, Y \) and \( Z \) in the given
reaction
\( \boldsymbol{C H}_{2}=\boldsymbol{C H}_{2} \frac{\boldsymbol{B r}_{2}}{\boldsymbol{C C l}_{4}} \boldsymbol{X} \frac{\boldsymbol{N a C N}}{(\boldsymbol{2} \text { moles })} \)
\( Y \stackrel{\boldsymbol{L i A l H}_{4}}{\longrightarrow} \boldsymbol{Z} \)
\( \mathbf{A} \cdot X=C H_{2} B r C H_{2} B r, Y=C H_{3} C H_{2} C H_{2} C N \)
B . \( X=C H_{2} B r C H_{2} B r, Y=C H_{3} C H_{2} C N \)
\( \mathbf{c} \cdot X=C H_{3} C H_{2} B r, Y=C H_{3} C H_{2} C N \)
D. \( X=C H_{2} B r C H_{2} B r, Y=N C C H_{2} C H_{2} C N \)


Number of \( \boldsymbol{H} \boldsymbol{C O}_{3}^{-} \) ions joined by \( \boldsymbol{H}- \)
bonding in \( \boldsymbol{K} \boldsymbol{H} \boldsymbol{C O}_{3} \) is:
A. 5
B.
\( c \cdot 3 \)
D.


Who is called as 'father of plant
physiology'?
A. K. V Thimann
B. Stephen Hales
c. M. Calvin
D. E. Rabinowitch


How many ATP molecules are obtained
from fermentation of 1 molecule of
glucose?
\( A \cdot 2 \)
B. 4
\( c \cdot 3 \)
D. 5


The negative Zn pole of a Daniel cell, sending a constant current through a circuit, decreases in mass by 0.13 g in 30 minutes. If the electrochemical
equivalent of Zn and Cu are 32.5 and
31.5 respectively, the increase in the mass of the positive Cu pole in this time is:
A. 0.180 g
B. 0.141 g
c. \( 0.126 \mathrm{g} \)
D. 0.242


What is refraction?
A. Phenomenon in which ray of light deviates from its path at the surface of separation of two media.
B. Phenomenon in which ray of light reflects from its path at the surface of separation of two media.
C. Phenomenon in which ray of light deviates from its path at the surface of 1st media
D. None


Ideal fuel has a
calorific value.
A. low
B. highh
c. moderate
D. zero


A gas has a volume of \( \mathrm{V} \mathrm{cm}^{3} \) at \( 10^{\circ} \mathrm{C} \). If
the pressure is doubled, at what temperature will the volume still be \( \mathbf{V} \)
\( c m^{3} ? \)
A \( \cdot 273^{\circ} \mathrm{C} \)
B. \( 300^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 283^{\circ} \mathrm{C} \)
D. \( 293^{\circ} \mathrm{C} \)


Doping of intrinsic semiconductor is
done
A. To neutralize charge carriers
B. To increase the concentration of majority charge carriers
C. To make it neutral before disposal
D. To carry out further purification


If \( a^{2}+b^{2}=29 \) and \( a b=10, \) then find
\( a-b \)
A . 10
B. 3
\( c \cdot 9 \)
D. 19


Explain the terms:
(a) Leaching (b) Roasting.