of Helianthus leaf passing through the
midrib, certain parts have been
indicated by alphabets, choose the
answer in which these alphabets have been correctly matched with the parts
which they indicate.
A. A- Epidermis, B- Spongy parenchyma, C- Palisade parenchyma, D- Stomata, F - Phloem, G- Metaxylem, H Protoxylem
B. A- Epidermis, B- Palisade parenchyma, C- Spongy Parenchyma, D- Sub stomatal cavity, F- Phloem, GMetaxylem, H- Protoxylem
C. A- Epidermis, B- Palisade parenchyma, C- Spongy parenchyma, D- Stomata, F- Endodermis, G- Xylem, HPhloem
D. A- Epidermis, B- Palisade parenchyma, C- Spongy parenchyma, D- Stomata, F- Phloem, G- Metaxylem, HProtoxylem


\( (+/-) \) Tartaric acid and meso-tartaric
acid are :
A. Enantiomers
B. Diastereomers
c. geometric isomers
D. None of these


The term karyokinesis is used for
A. Disappearance of nuclear membrane during metaphase
B. Changes occurring at anaphase, when chromosomes move to the opposite poles
C. Event occurring during interphase
D. Over all changes occurring in nucleus during the cell division


Let \( \Delta(x)= \)
\( \left|\begin{array}{ccc}(\boldsymbol{x}-\mathbf{2}) & (\boldsymbol{x}-\mathbf{1})^{2} & \boldsymbol{x}^{\mathbf{3}} \\ (\boldsymbol{x}-\mathbf{1}) & \boldsymbol{x}^{2} & (\boldsymbol{x}+\mathbf{1})^{3} \\ \boldsymbol{x} & (\boldsymbol{x}+\mathbf{1})^{2} & (\boldsymbol{x}+\mathbf{2})^{3}\end{array}\right| \) Then the
coefficient of \( x \) in \( \Delta(x) \) is \( -k . \) Find \( k \)
\( A \cdot-1 \)
B. 2
\( c \cdot-2 \)
\( D \)


When one drop of a liquid is broken into number of droplets, which of the statement is correct?
A. Surface area decreases
B. Surface energy decreases
c. Temperature of liquid increases
D. Surface area increases


Find \( 6 y^{5}-y^{4}+4 y^{3}-5 y^{2}-y-15 \) if
\( y=3 \)


Which of the following countries suffer from the acid rains?
1. Canada
2. France
3. Norway
4. Germany Select the correct answers from the
codes given below:
A . 1 and 2
B. 1 and 3
\( c \cdot 2 \) and 3
D. 3 and 4


How is the food taken and digested in Amoeba and Paramecium?


Evaluate:
\( \left(\frac{a}{2 b}+\frac{2 b}{a}\right)^{2}-\left(\frac{a}{2 b}-\frac{2 b}{a}\right)^{2}-4 \)


If \( 6 x-x^{2}=1, \) then the value of \( (\sqrt{x}- \)
\( \left.\frac{1}{\sqrt{x}}\right) \) is
\( A \cdot 2 \)
B. 3
c. 1
D. -


Select the IUPAC name for the following
complex.
A. Tetraamminecobalt (III)- \( \mu \) dihydroxidobis(ethylenediamine) cobalt (III) chloride
B. \( \mu \) -Dihydroxidotetraamminebis(ethylenediamine) dicobalt(III) chloride
c. Tetraammine cobaltate (III)- \( \mu \) -dihydroxidobis(ethane-
1, 2-diamine) cobalt
(III) chloride
D. Tetraamminecobalt (III)- \( \mu \) dihydroxidobis(ethylenediamine) cobalt(II) tetrachloride


Refer to teh circuit shown. What will be
the total power dissipation in the
circuit if \( \boldsymbol{P} \) is the power dissipated in
\( R_{1} ? \) It is given that \( R_{2}=4 R_{1} \) and \( R_{3}= \)
\( 12 R_{1} \)
A \( .4 P \)
в. \( 7 P \)
c. \( 13 P \)
D. \( 17 P \)


Identity the element which can't conduct electricity:
A. graphite
B. iron
c. phosphorus
D. copper


A normal to the plane \( x=2 \) is...
A \( .(0,1,1) \)
в. (2,0,2)
c. (1,0,0)
D. (0,1,0)


A solenoid of length 1 m, area of crosssection \( 4.0 \mathrm{cm}^{2} \) and having 4000 turns is placed inside another solenoid of 2000 turns having a cross-sectional \( \operatorname{area} 6 \mathrm{cm}^{2} \) and length 2 m. The mutual
inductance between the solenoids is
\( x \pi \times 10^{-5} H . \) Findout the value of \( x \)


Which of the following is a consequence of total internal reflection?
A. Optical fibre
B. Mirage
c. Looming
D. All


Which of the following is the correct ord
er of evolutionary history of man?
A. Peking man, Heidelberg man, Neanderthal, CroMagnon
B. Peking man, Homo sapiens, Cro-Magnon, Neanderthal
C. Peking man, Neanderthal, Homo sapiens, Heidelberg
D. Peking man, Cro-Magnon, Homo sapiens, Neanderthal


An elastic material of Young's modulus \( Y \) is subjected to a stress \( S \). The elastic energy stored per unit volume of the material is :
A \( \cdot \frac{S Y}{2} \)
B. \( \frac{s^{2}}{2 Y} \)
c. \( \frac{s}{2 Y} \)
D. \( \frac{2 S}{Y} \)


For the reaction, \( A \rightarrow B \), the rate law is,
rate \( =\boldsymbol{k}[\boldsymbol{A}] . \) Which of the following
statements is incorrect?
A. The reaction follows first order kinetics
B. The \( t_{1 / 2} \) of the reaction depends on initial concentration
c. \( k \) is constant for the reaction at a constant temperature.
D. The rate law provides a simple way of predicting the
of the reaction


When light propagates in vacuum there is an electric field and a magnetic field. These fields
This question has multiple correct options
A. are constant in time
B. have zero average value
c. are perpendicular to the direction of propagation of light
D. are mutually perpendicular


In the given figure, if line \( A B \| \) line \( C F \)
and line BC || line ED then prove that
\( \angle A B C=\angle F D E \)


The escape velocity of a projectile from the earth's surface is approximately.
A. \( 7 \mathrm{km} / \mathrm{s} \)
В. \( 112 \mathrm{km} / \mathrm{s} \)
c. \( 11.2 \mathrm{km} / \mathrm{s} \)
D. \( 1.1 \mathrm{km} / \mathrm{s} \)


When a \( U^{238} \) nucleus originally at rest,
decay by emitting an alpha particle having a speed \( 1.5 \times 10^{7} m^{-1} . \) Then
calculate the kinetic energy of the residual nucleus.


The percentage of mass lost during nuclear fusion is
A . 0.1\%
B. 0.4\%
c. 0.5\%
D . 0.65\%


Match the two lists. Choose the choice
which gives the correct combination of
the alphabets of the two columns.
List II
(Secretions) List I (Type of
cells) Lysozyme \( A \) \begin{tabular}{c|c}
\( ^{A} \) & \( B \) eta cells \\
\hline\( B \) & \( M \) astcells \\
\hline C & Paneth cells \\
\hline Acinarcells \\
\hline
\end{tabular} Mucus
\( r \) Histamine s \( \quad \) Insulin \( t \quad \) Pancreatic
enzymes
A. \( A-q, B-r, C-p, D-t \)
B. A-s, B-r, C- p, D-t
C. \( A-t, B-q, C-r, D-s \)
D. \( A-s, B-q, C-p, D-t \)


An ideal gas is allowed to expand from
\( 5 L \) to \( 15 L \) once rapidly and once very slowly. The magnitude of work done in
two processes are \( W_{1} \) and \( W_{2} \), they are
related as:
A. \( W_{1}=W_{2} \)
в. \( W_{1}>W_{2} \)
c. \( W_{1}<W_{2} \)
D. data is insufficient


The depletion region is
A. region of opposite charges.
B. neutral region.
C . region of infinite energy.
D. region free of charge carriers.


One gram of a radioactive substance
disintegrates at the rate of \( 3.7 \times 10^{10} \)
disintegrations per second. The atomic mass of the substance is \( 226 . \) Calculate
its mean life:


The product is more stable than reactants in reaction having large value
of K.
If true enter 1 , else enter 0 .
A.


If \( \cot ^{-1}\left(\frac{1}{x+1}\right)+\cot ^{-1}\left(\frac{1}{x-1}\right)= \)
\( \tan ^{-1} 3 x-\tan ^{-1} x \)
then \( \boldsymbol{x}= \)
A. \( \pm 1 / 2 \)
B. \( -1, \pm 1 / 3 \)
c. 2,±1
D. \( -1 . \pm 1 / 2 \)


Find the principal value:
\( \sin ^{-1}\left(\tan \frac{5 \pi}{4}\right) \)


Which one of the following hydrolyze internal phosphodiester bonds in a polynucleotide chain?
A . Lipase
B. Protease
c. Exonuclease
D. Endonuclease


Two point charges exert force of \( \boldsymbol{F} \) Newton when separated by a distance of \( 10 \mathrm{cm} \) in air. The distance for which the
force between them will be same if the
medium them has \( \varepsilon_{r}=4, \) is:-
\( A \cdot 10 \mathrm{cm} \)
B. 20 cm
\( c \cdot 5 \mathrm{cm} \)
D. 2.5 cm


The acidity of ortho-nitrophenol is that of orthomethoxyphenol
A. more than
B. similar
c. less than
D. none of these


The dimensions of torque are same as
that of
A. Moment of force
B. Pressure
c. Acceleration
D. Impulse


(a) What does by magnifying power of a Microscope?
(b) An object is placed ar \( 20 \mathrm{cm} \) from a
convex lens. If 3 times magnified real image is formed by the lens then find the focal length of lens.


The number of rotational symmetry of an equilateral triangle is/are:
A .
B.
\( c \cdot 3 \)
\( D \)


Ideal fluid flows along a flat tube of constant cross-section, located in a
horizontal plane and bent as shown in figure above (top view). The flow is steady. Are the velocities of the
fluid equal at points 1 and \( 2 ? \)
A. Velocity at point 1 is less than velocity at point 2
B. Velocity at point 1 is more than velocity at point 2
c. velocity at point 1 is equal to velocity at point 2
D. can't be determined


Use Huygen's principle to show how a plane wavelength propagates from a denser to rarer medium. Hence verify
Snell's law of refraction


Which type of polynomial is \( 3 x^{3} ? \)
A. Cubic Polynomial
B. Linear Polynomial
c. square Polynomial
D. None of These


\( S_{1} \) and \( S_{2} \) are two equipotential
surfaces on which the potentials are not equal. Then-
This question has multiple correct options
A. \( S_{1} \) and \( S_{2} \) both cannot intersect.
B. \( S_{1} \) and \( S_{2} \) both cannot be plane surfaces.
c. In the region between \( S_{1} \) and \( S_{2} \), the field is maximumm where they are closed to each other
D. A line of force from \( S_{1} \) and \( S_{2} \) must be perpendicular to both


Assertion
Treatment of 2 -methyl-2-pentene with
NBS in \( C C I_{4} \) gives 4 -bromo-2-methyl-2-
pentene as major product.
Reason
NBS brings about free radical abomination at acrylic position.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A stretched string is vibrating
according to the equation \( \boldsymbol{y}= \)
\( 5 \sin \left(\frac{\pi x}{3}\right) \cos 400 \pi t, \) where \( y \) and a are
in \( \mathrm{cm} \) and \( t \) is second. Potential energy
will be zero at time t:-
A . 2 s
B. 4 s
\( c \cdot 8 s \)
D. 16 s


The dimensions of torque are
\( \mathbf{A} \cdot\left[M L^{3} T^{-3}\right] \)
В \( \cdot\left[M L^{-1} T^{-1}\right] \)
c. \( \left[M L^{2} T^{-2}\right] \)
D \( \cdot\left[M T^{-2}\right] \)


If the middle term in the expansion of \( \left(x^{2}+\frac{1}{x}\right)^{n} \) is \( 924 x^{6}, \) then \( n= \)
A . 10
B. 12
c. 14
D. none of these


A solution of which substance can best
be used as both titrant and its own
indicator in an oxidation-reduction
titration?
\( \mathbf{A} \cdot I_{2} \)
в. NaOCl
c. \( K_{2} C r_{2} O_{7} \)
D. \( K M n O_{4} \)


A non-uniform bar of weight \( W \) is
suspended at rest by two strings of
negligible weight as shown in fig. The angles made by the strings with the
vertical are \( 36.9^{\circ} \) and \( 53.1^{\circ} \)
respectively. The bar is \( 2 m \) long.
Calculate the distance d of the center of
gravity of the bar from its left end


The resistance of wire in a heater at
room temperature is \( 65 \Omega \). When the heater is connected to a 220 V supply
the current settles after a few seconds
to \( 2.8 \mathrm{A} \). What is the steady temperature of the wire. (Temperature coefficient of
resistance \( \boldsymbol{\alpha}=\mathbf{1 . 7 0} \times \mathbf{1 0}^{-\mathbf{4} \circ} \boldsymbol{C}^{-\mathbf{1}} \mathbf{)} \)
A \( .955^{\circ} \mathrm{C} \)
B. \( 1055^{\circ} \mathrm{C} \)
\( \mathrm{c} \cdot 1155^{\circ} \mathrm{C} \)
D. \( 1258^{\circ} \mathrm{C} \)


What is the bond order of \( N O^{+} ? \)


In. triangle \( A B C, \angle A+\angle B=144 \) and \( \angle A+ \)
\( \angle C=124 \)
Calculate smallest angle of the triangle.
\( A \cdot 36^{\circ} \)
B. \( 56^{\circ} \)
\( c \cdot 46^{\circ} \)
D. none of these


Related species which are reproductively isolated but morphologically similar are called
A. Allopatric
B. Sympatric
c. sibling
D. Morphospecies


f \( A(3,2,6), B(1,4,5) \) and \( C(3,5,5) \) are
the vertices of \( \Delta A B C, \) then find
\( \boldsymbol{m} \angle \boldsymbol{A} \boldsymbol{B} \boldsymbol{C} \)


A rod of length L, along East west direction is dropped from a height H. If B
be the magnetic field due to earth at that place and angle of dip is \( \theta \), then what is the magnitude of induced emf
across two ends of the rod when the rod
reaches the earth.


Classify the following set as 'singleton'
or 'empty': \( B=\{y \mid y \) is an odd prime
number \( <4\} \)
A. singleton
B. Empty
c. Data insufficient
D. None of these


PQR is a right-angle triangle right angled at Q. XY is parallel to QR. PQ = 6 cm and \( \mathrm{PX}: \mathrm{XQ}=1: 2 . \) Calculate the lengths of PR
and QR.


A coil of area \( 5 \mathrm{cm}^{2} \) with 20 turns is
kept under the magnetic field of \( 10^{3} \) Gauss. Normal to the plane of coil
makes an angle \( 30^{\circ} \) with the magnetic field. The flux through the coil is
A \( \cdot 6.67 \times 10^{-4} \mathrm{Wb} \)
B. \( 3.2 \times 10^{-5} \mathrm{Wb} \)
\( \mathbf{c} \cdot 5.9 \times 10^{-4} W b \)
D. \( 8.65 \times 10^{-4} W b \)


Suppose \( g(x)=2 x+1 \) and \( h(x)= \)
\( 4 x^{2}+4 x+5 \) and \( h(x)=(f o g)(x) \) The
area enclosed by the graph of the function \( \boldsymbol{y}=\boldsymbol{f}(\boldsymbol{x}) \) and the pair of
tangents drawn to it from the origin is
\( A \cdot 8 / 3 \)
B. \( 16 / 3 \)
c. \( 32 / 3 \)
D. none


Whether a child died after normal birth
or died before birth can be confirmed
measuring
A. The weight of the child
B. The dead space air
c. Tidal volume of air
D. Residual volume of air


Distinguish between Water pollution and land pollution.


The chemical name of melamine
is
A. 2,4 -Diamino-1, 3,5 -triazine
B. 2-Amino-1,3, 5-triazine
c. 2,4,6 -Triamino- 1,3,5 -triazine
D. 1,3,5 -Triamino- 2,4,6 -triazine


Assuming \( (2 s-2 p) \) mixing is not
operative, the paramagnetic species among the following is :
\( \mathbf{A} \cdot B e_{2} \)
в. \( B_{2} \)
c. \( C_{2} \)
D. \( N_{2} \)


A hollow conducting sphere is placed in
an electric field produced by a point
charge as shown. Let \( V_{A}, V_{B}, V_{C} \) be the
electric potentials at points \( A, B, C \)
respectively and \( V_{0} \) is the potential at
centre 0 due to induced charge on shell.
This question has multiple correct options
A \( . V_{0}=0 \)
В. \( V_{A}>V_{B}>V_{C} \)
\( \mathbf{c} \cdot V_{4}=V_{B}=V_{O} \)
\( \mathbf{D} \cdot V_{A}<V_{B}<V_{C} \)


The radius of the given figure below is 21 mi. Find its volume. (use \( \pi=\frac{22}{7} \) ).
A \( .19,504 \mathrm{mi}^{3} \)
в. \( 19,404 \mathrm{mi} \)
C. \( 19,404 \mathrm{mi}^{3} \)
D. \( 29,504 \mathrm{mi}^{3} \)


The cytoplasm divides at
A. Mitosis
B. Prophase
c. Cytokinesis
D. Interphase
E. Metaphase


A symmetrical die is thrown 6 times. If getting an odd number is a success, the probability of at the most 5 successes
is
A \( \cdot \frac{5}{64} \)
в. \( \frac{15}{64} \)
c. \( \frac{63}{64} \)
D. \( \frac{36}{64} \)


Suppose \( x \) and \( y \) are real numbers such that \( \tan x+\tan y=42 \) and \( \cot x+ \)
\( \cot y=49, \) then the single digit prime
number by which the value of
\( \tan (x+y) \) is not divisible is


Three identical large metal plates of
area \( A \) are small at distances \( d \) and \( 2 d \)
from each other. Top metal plate is
uncharged, while the other metal plates
have charges \( +Q \) and \( -Q . \) Top and
bottom metal plates are connected by
switch \( S \) through a resistor of unknown
resistance. What energy (in mJ) is dissipated in the resistor when switch
is closed?
(given: \( \left.\frac{\epsilon_{0} A}{d}=6 \mu F, Q=60 \mu C\right) \)


Which of the following best describe about the statement "An object slides on a horizontal, frictionless surface".
A. Inertia
B. Unbalanced forces
C. Action and reaction force pairs
D. Universal gravitation
E. simple harmonic motion


Check whether the following is Quadratic equations:
\( (x+1)^{2}=2(x-3) \)


The oxidation states of metal in the
compounds \( F e_{0.94} O \) and
\( \left[\boldsymbol{C r}\left(\boldsymbol{P P h}_{3}\right)_{3}(\boldsymbol{C O})_{3}\right] \) respectively are:
A \( \cdot \frac{200}{94}, 0 \)
в. \( 0, \frac{94}{200} \)
\( c \cdot 2,1 \)
D. \( 1, \frac{200}{94} \)


Using
(i) or \( (i i) \) above the best upper bound of \( \int_{0}^{1} \sqrt{1+x^{4}} d x \) is
A. \( 1+\sqrt{2} \)
B. \( \frac{1+\sqrt{2}}{2} \)
c. \( \frac{\sqrt{2}-1}{2} \)
D. \( 2(\sqrt{2}-1) \)


At what temperature liquid water will be in equilibrium with water vapour? \( \boldsymbol{\Delta} \boldsymbol{H}_{\boldsymbol{v a p}}=\mathbf{4 0 . 7 3} \boldsymbol{k J} \boldsymbol{m o l}^{-1}, \boldsymbol{\Delta} \boldsymbol{S}_{\boldsymbol{v a p}}= \)
\( \mathbf{0 . 1 0 9} \boldsymbol{k J} \boldsymbol{K}^{-\mathbf{1}} \boldsymbol{m o l}^{-1} \)
A. \( 282.4 \mathrm{k} \)
в. 373.6 к
\( c \cdot 100 k \)
D. 400


Figure as shown a rod \( P Q \) of length
\( 20.0 \mathrm{cm} \) and mass \( 200 \mathrm{g} \) suspended through a fixed point \( O \) by two threads
of length \( 20.0 \mathrm{cm} \) each. A magnetic field
of strength \( 0.500 T \) exists in the vicinity
of the wire \( P Q \) as shown in the figure.
The wires connecting with \( P Q \) with the battery are loose and exert no force on
\( P Q \)
(a) Find the tension in the threads when
the switch \( S \) is open.(b) A current of
\( 2.0 A \) is established when the switch \( S \)
is closed. Find the tension in the thread.


Find the focal length of convex mirror whose radius of curvature is \( 32 \mathrm{cm} \)
A . \( 16 \mathrm{cm} \)
B. \( 32 \mathrm{cm} \)
\( c \cdot 8 c m \)
D. \( 64 \mathrm{cm} \)


Solve linear equation:
\( \frac{n}{2}-\frac{3 n}{4}+\frac{5 n}{6}=21 \)


\( 32 g \) of \( O_{2} \) is contained in a cubical
container of side \( 1 m \) and maintained
at a temperature of \( 127^{0} C . \) The isothermal bulk modulus of elasticity of
the gas in terms of universal gas constant \( \boldsymbol{R} \) is
\( \mathbf{A} \cdot 127 R \)
B. \( 400 R \)
\( c \cdot 200 R \)
D. \( 560 R \)


A free electron in an electric field
A. remains stationary
B. moves from the higher potential to the lower potential
C. moves from the lower potential to the higher potential
D. None


Heart beat originates from
A. Pacemaker
B. Cardiac muscles
c. Left atrium
D. Right ventricle


A body freely falls from a certain height
on to the ground in a time \( t . \) During the
first one third of the time interval it
gains a kinetic energy \( \Delta k_{1} \) and during the last one-third of the interval, it gains
a kinetic energy \( \Delta k_{2} \). The ratio \( \Delta k_{1} \)
\( \boldsymbol{\Delta} \boldsymbol{k}_{2} \) is:
A . 1: 1
B. 1: 3
c. 1: 4
D. 1: 5


Rhombic sulphur consists of:
A. \( \mathrm{S}_{8} \) chains
B. \( \mathrm{S}_{2} \) molecules
c. \( \mathrm{s}_{4} \) rings
D. \( S_{8} \) rings


Three vectors \( \overrightarrow{\boldsymbol{A}}=\boldsymbol{a} \overrightarrow{\boldsymbol{i}}+\overrightarrow{\boldsymbol{j}}+\overrightarrow{\boldsymbol{k}}, \overrightarrow{\boldsymbol{B}}=\overrightarrow{\boldsymbol{i}}+ \)
\( \boldsymbol{b} \overrightarrow{\boldsymbol{j}}+\overrightarrow{\boldsymbol{k}}, \overrightarrow{\boldsymbol{C}}=\overrightarrow{\boldsymbol{i}}+\overrightarrow{\boldsymbol{j}}+\boldsymbol{c} \overrightarrow{\boldsymbol{k}} \) are mutually
perpendicular \( (\vec{i}, \vec{j}, \vec{k} \) are unit vectors along \( X, Y, Z \) axis respectively. The respective values of \( a, b \) and \( c \) are
\( \mathbf{A} \cdot 0,0,0 \)
B. \( -\frac{1}{2},-\frac{1}{2},-\frac{1}{2} \)
c. 1,-1,1
D. \( \frac{1}{2}, \frac{1}{2}, \frac{1}{2} \)


Calculate mean deviation about mean
for the given data.
Score \( (x) \quad 6 \quad 20 \) 3. 8
11 Frequency
\( \begin{array}{ll}\text { (f) } & \text { (f) } 7\end{array} \) 27
A. 3.117
B. 3.217
c. 4.212
D. 6.21


\( \boldsymbol{P Q} \| \boldsymbol{R} \boldsymbol{S}, \) find the measure of \( \boldsymbol{m} \)
กก
90
137


Equanil is an example of:
A. artificial sweeteners
B. tranquilisers
C. antihistamines
D. antifertility drugs


A hollow cylindrical box of length 1 m
and area of cross-section \( 25 \mathrm{cm}^{2} \) is
placed in a three dimensional coordinate system as shown in the
figure. The electric field in the region is \( \operatorname{given} \) by \( \vec{E}=50 x \hat{i}, \) where \( E \) is in \( N C^{-1} \)
and \( x \) is in metres.
Find
(i) Net flux through the cylinder
(ii) Charge enclosed by the cylinder.


At \( 30^{\circ} C, \) the solubility of
\( A g_{2} C O_{3}\left(K_{s p}=8 \times 10^{-2}\right) \) will be
maximum in:
A. 0.05 M \( \mathrm{Na}_{2} \mathrm{CO}_{3} \)
B. \( 0.05 M A g N O_{3} \)
c. Pure water
D. \( 0.05 N H_{3} \)


If current \( I_{1}=3 A \) sinwt and \( I_{2}= \)
4 Acos\( \omega t, \) then \( I_{3} \) is
A \( .5 A \sin \left(\omega t+53^{\circ}\right) \)
B. \( 5 A \sin \left(\omega t+37^{\circ}\right) \)
c. \( 5 A \sin \left(\omega t+45^{\circ}\right) \)
D. 5 Asin \( \left(\omega t+30^{\circ}\right) \)


\( \boldsymbol{E}_{\text {Cell }}^{\ominus} \) of \( \boldsymbol{Z} \boldsymbol{n} / \boldsymbol{Z} \boldsymbol{n}^{2+} \| \boldsymbol{C} \boldsymbol{u}^{2+} / \boldsymbol{C u} \) is \( \mathbf{1 . 1 0} \mathbf{v} \)
at \( 25^{\circ} \mathrm{C}, \) the equilibrium constant for
the reaction, \( Z n+C u^{2+} \rightleftharpoons C u+ \)
\( Z n^{2+} \) is approximately of the order of:
\( \mathbf{A} \cdot 10^{-28} \)
B . \( 10^{+37} \)
\( \mathbf{c} \cdot 10^{-18} \)
D. \( 10^{17} \)


Among the following, the correct
statement is:
A. Phosphates have no biological significance in humans
B. Between nitrates and phosphates, phosphates are less abundant in earths crust
C. Between nitrates and phosphates, nitrates are less abundant in earths crust
D. Oxidation of nitrates is possible in soil


\( 14 \mathrm{g} \) of an element \( \mathrm{X} \) combines with 16 g of oxygen. On the basis of this, which of the following statement is correct?
[At.wt of oxygen \( =16] \)
A. The element \( x \) could have an atomic weight 7 and its oxide formula is \( X O \)
B. The element X could have an atomic weight 14 and its oxide formula is \( X_{2} O_{3} \)
c. The element \( x \) could have an atomic weight 7 and its oxide formula is \( X_{2} O \)
D. The element x could have an atomic weight 14 and its oxide formula is \( X O_{2} \)


Evaluate \( \int_{0}^{6}(x+2) d x \)


Verify the applicability of LMV theorem for \( \boldsymbol{f}(\boldsymbol{x})=\frac{\mathbf{1}}{\mathbf{1}+\boldsymbol{x}} \) in \( [\mathbf{1}, \mathbf{0}] \)


The interfering fringes formed by a thin oil film on water are seen in yellow light of sodium lamp. We find the fringes
A . coloured
B. black and white
c. yellow and black
D. coloured white yellow


Find the value of \( x: \)
\( \boldsymbol{x}^{2}+\boldsymbol{p}^{2}=(\boldsymbol{q}-\boldsymbol{x})^{2} \)
\( ^{\mathbf{A}} \cdot \frac{q^{2}-p^{2}}{2 q} \)
в. \( \frac{q^{2}-p^{2}}{2} \)
\( ^{\mathrm{C}} \cdot \frac{q^{2}-p^{2}}{2 p} \)
D. \( \frac{p^{2}-q^{2}}{2 p} \)


Active transport is characterised by
A. Requires special membrane proteins
B. Highly selective
c. Requires ATP energy
D. All of the above


Degree of dissociation refers to the ratio
of the concentration of charged ions to the concentration of ionic compound.
A. True
B. False


A condenser is charged to a potential difference of \( 120 \mathrm{V} \). It's energy is \( 1 \times \)
\( 10^{-5} J . \) If battery is there and the space
between plates is filled up with a
dielectric medium \( \left(\varepsilon_{r}=5\right) . \) Its new energy
is
\( \mathbf{A} \cdot 10^{-5} J \)
В. \( 2 \times 10^{-5} J \)
c. \( 3 \times 10^{-5} J \)
D . \( 5 \times 10^{-5} J \)


\( \boldsymbol{H}-\boldsymbol{O}-\boldsymbol{E} \boldsymbol{I}=\boldsymbol{O} \)
Statement: In the given structure El denotes Nitrogen (N) atom.
If true enter 1 , else enter 0 .


Find the Quotient and the Remainder
when the first polynomial is divided by
the second.
\( \left(x^{4}-2 x^{3}+2 x^{2}+x+4\right) \) by \( \left(x^{2}+x+\right. \)
1)
A. Quotient \( =x^{2}+3 x+4 \), Remainder \( =0 \)
B. Quotient= \( x^{2}-3 x-4 \), Remainder \( =0 \)
c. Quotient \( =-x^{2}-3 x+4 \), Remainder \( =0 \)
D. Quotient \( =x^{2}-3 x+4 \), Remainder \( =0 \)


Longest fibers are found in
A. Jute
B. cotton
c. Sunn hemp
D. coir


For the reaction \( 2 S O_{2}+O_{2} \rightleftharpoons 2 S O_{3} \)
the units of \( \boldsymbol{K}_{c} \) is:
A. litre/mole
B . mole /litre
c. \( \left(\text {mol litre}^{-1} \text {) }^{2}\right. \)
D. (liter mole \( ^{-1} \) ) \( ^{2} \)


\( X \) follows a binomial distribution with
parameters \( \boldsymbol{n}=\boldsymbol{6} \) and \( \boldsymbol{P} . \) If \( \boldsymbol{4} \boldsymbol{P}(\boldsymbol{x}= \)
\( \mathbf{4})=\boldsymbol{P}(\boldsymbol{x}=\mathbf{2}), \) then \( \boldsymbol{P}= \)
A \( \cdot \frac{1}{2} \)
в.
\( c \cdot \frac{1}{6} \)
D.


Vitamin \( B_{12} \) is a complex of cobalt. If
true enter 1 , else enter 0


Evaluate \( \int \frac{2 \cos x-3 \sin x}{6 \cos x+4 \sin x} d x \)


Column
(order of magnitude in Pa)


The price of wheat falls by \( 16 \% \) By what
percentage a person can increase the consumption of wheat so that his
overall budget does not change?
A . 16\%
B . 18\%
c. \( 18.5 \% \)
D. 19\%


Biomass can be defined or described
as:
A. petroleum
B. organic matter which can be converted to fuel
c. inorganic matter which can be converted to fuel
D. massive living things


In the figures given, identify the type of zero error and also suggest the correction to be made, by reasoning it
outt


What is a pure substance?


If a body starts from rest and moves with uniform acceleration, the
displacements of the body in \( 1 s, 2 s, 3 s \) etc., are in the ratio of \( 1: 4: 9, \) etc. (True/False)


Find the sum of the following geometric series \( 1+\frac{1}{3}+\frac{1}{9}+\ldots \ldots \ldots . \) upto \( \infty \)


Area of a rhombus is \( 850 \mathrm{cm}^{2} \) If one of
its diagonal is \( 34 \mathrm{cm} \). Find the length of the other diagonal.


Evaluate the following integral
\( \int \frac{\sec x \operatorname{cosec} x}{\log (\tan x)} d x \)


In a region, steady and uniform electric and magnetic fields are present. These two fields are parallel to each other. A charged particle is released from rest in this region. The path of the particle will
be a
A. helix
B. straight line
c. ellipse
D. circle


The \( x \) and \( y \) components of vector \( \vec{A} \) are
\( 4 m \) and \( 6 m \) respectively. The \( x \) and \( y \) components of vector \( \overrightarrow{\boldsymbol{A}}+\overrightarrow{\boldsymbol{B}} \) are \( \mathbf{1 0} \boldsymbol{m} \)
and 9 m respectively. For the vector \( \vec{B} \) calculate the following
(i) \( x \) and \( y \) components
(ii) length and
(iii) the angle it makes with \( x \) -axis
A. (i) \( 6 m, 3 m \)
(ii) \( \sqrt{45} m \)
(iii) \( \tan ^{-1}\left(\frac{1}{2}\right) \)
B.
(i) \( 4 m, 2 m \) (ii) \( \sqrt{90} m \) (iii) \( \tan ^{-1}\left(\frac{1}{2}\right) \)
c. \( \left(\text { i) } 3 m, 6 m \text { (ii) } \sqrt{45} m \text { (iii) } \tan ^{-1}\left(\frac{3}{2}\right)\right. \)
\( D \)
(i) \( 4 m, 3 m \) (ii) \( \sqrt{60} m \) (iii) \( \tan ^{-1}\left(\frac{5}{2}\right) \)


What is a cathode?
A. Electrode where reduction takes place and electrons are gained.
B. Electrode where oxidation takes place and electrons are lost.
C. Electrode where reduction takes place and electrons are lost.
D. A fluid that conducts electricity.
E. Electrode where oxidation takes place and electrons a re gained.


Sum of \( n \) terms: \( 5+9+13+17+ \)
\( \mathbf{2 1}+\mathbf{2 5}+\dots \)


A hemisphere bowl is made of steel of \( 0.25 \mathrm{cm} \) thickness. The inner radius of
the bowl is \( 5 \mathrm{cm} . \) The volume of steel
used is \( _{-}-_{-}-_{-}-_{-}-_{-} \cdot(\pi=\mathbf{3 . 1 4 1}) \)
\( \mathbf{A} \cdot 42.15 \mathrm{cm}^{3} \)
B . \( 41.52 \mathrm{cm}^{3} \)
c. \( 41.24 \mathrm{cm}^{3} \)
D. \( 40 \mathrm{cm}^{3} \)


Which of the following having a square planar structure is:
\( \mathbf{A} \cdot N H_{4}^{+} \)
в. \( B F_{4} \)
c. \( x e F_{4} \)
D. \( C C l_{4} \)


Alternating current is transmitted to
distant places at
A. high voltage and low current.
B. high voltage and high current
c. low voltage and low current.
D. low voltage and high current.


The nature of positive rays produced in a vacuum discharge tube depends
upon:
A. the nature of the gas filled
B. nature of the material of cathode
c. nature of the material of anode
D. the potential applied across the electrodes


Which one is not correct for oxidation of
food?
A. It is multiple process
B. All released energy is traped in form of ATP
C. Traped energy is further used for bio synthesis of other molecules
D. Oxidisable compound is known as respiratory substrate


A neutron moving with a certain kinetic energy collides head on with an atom of mass number A. The fractional kinetic
energy retained by it is
A \( \frac{A-1}{A+1} \)
\( ^{\mathrm{B}}\left(\frac{A+1}{A-1}\right)^{2} \)
c. \( \frac{A+1}{A-1} \)
\( ^{D \cdot}\left(\frac{A-1}{A+1}\right)^{2} \)


The value of \( \left(1+\frac{1}{a}\right)\left(1+\frac{1}{a-1}\right)\left(1+\frac{1}{a-2}\right) \)
A. \( \frac{a-3}{a} \)
B. \( \frac{a+1}{a-4} \)
c. \( \frac{a+1}{a-1} \)
D. \( \frac{a-1}{a-4} \)


What is the disintegration constant of a radioactive element, if the number of its
atoms diminishes by \( 18 \% \) in 24 h?
A. \( 2.1 \times 10^{-3} / s \)
в. \( 2.1 \times 10^{5} / s \)
C \( .22 \times 10^{6} / s \)
D. \( 22 \times 10^{-6} / s \)


How many species out of the following have reducing properties?
\( N H_{3}, P H_{3}, H_{3} P O_{2}, H_{3} P O_{3}, H_{3} P O_{4} \)


Power losses in case of ac (in W) is


How does the average kinetic energy of a gas molecule depend on the absolute
temperature of the gas?


Derive an expression for work done in adiabatic expansion


Object is placed between infinity and a device. Image formed is diminished and between pole and focus, behind it. If the image is virtual and erect, identify the device.
A. Convex mirror
B. Concave mirror
c. Spherical mirror
D. Plane mirror


The temperature maintained in contact
tower during the manufacture of sulphuric acid is :
A \( \cdot 450-500^{\circ} \mathrm{C} \)
в. \( 350-400^{\circ} \mathrm{C} \)
c. \( 300-350^{\circ} \mathrm{C} \)
D. \( 250-300^{\circ} \mathrm{C} \)


The interference pattern with two
coherent light sources of density ratio \( n \) In the interference pattern, the ratio \( \frac{\boldsymbol{I}_{m a x}-\boldsymbol{I}_{m i n}}{\boldsymbol{I}_{m a x}+\boldsymbol{I}_{m i n}} \) will be:
A. \( \frac{\sqrt{n}}{n+1} \)
B. \( \frac{2 \sqrt{n}}{n+1} \)
c. \( \frac{\sqrt{n}}{(n+1)^{2}} \)
D. \( \frac{2 \sqrt{n}}{(n+1)^{2}} \)


Geometrical configuration of \( B F_{3} \) and
\( N F_{3} \) molecules is:
A. The same because of same covalency of the central atom
B. Different because BF3 is non-polar
c. Different because BF3 is polar
D. None of the above is correct


If the distance travelled by a body in the
\( n^{t h} \) second is given by \( (4+6 n) m, \) then find the initial velocity and acceleration of the body respectively.


Growth is primarily affected by two climatic factors
A. Light and temperature
B. Temperature and relative humidity
c. Light and wind
D. Rainfall and temperature


A particle of mass \( 0.5 \mathrm{kg} \) is executing SHM along a straight line. Its path length is \( 10 \mathrm{cm} \) and time period is 8s. TE
when its phase angle is \( \frac{\pi}{6} \) radian is
B. 0.964x10-4 J
c. \( 3.856 \times 10^{-4} \) j
D. 4.324x10-4 J


The terminal velocity of a steel ball 2 \( \mathrm{mm} \) in diameter falling through glycerin
is \( 44 \times 10^{-2} \mathrm{cm} / \mathrm{s} \) (Given that specific
gravity of steel \( =8, \) specific gravity of steel =8, specific gravity of glycerin a
1.3, viscosity of glycerine 8.3 poise.)


Which of the following cannot exists on the basis of M.O. theory?
A. \( C_{2} \)
в. \( H e_{2}^{+} \)
c. \( H_{2}^{+} \)
D. \( H e_{2} \)


The ratio of angular frequency and angular wave number is
A. particle velocity
B. wave velocity
c. energy
D. wavelength per unit oscillation


(a) What product is released after the first step of glucose breakdown? Where does it take place?
(b) How are the small intestines
designed to perform absorption of food?


Which polymer is obtained from \( 2- \)
chlorobuta-1,3-diene?


Ethyl alcohol is the end product of
respiration.


The peroxide linkage \( (-O-O-) \) is not
present in:
A \( . H_{2} S O_{5} \)
в. \( C r O_{5} \)
c. \( H N O_{4} \)
D. \( H C l O_{4} \)


Which Lewis structure would produce a
molecule with a linear geometry?
A \( . A X_{2} \)
в. \( A X_{2} E_{2} \)
\( \mathrm{c} \cdot A X_{3} \)
D. \( A X_{3} E \)


Which of the following would happen in the presence of greenhouse effect in the atmosphere?
A. Pollution will increase
B. The earth's surface temperature will increase
c. The earth's surface temperature remains the same,
D. The depleted ozone layer will decrease the earth's temperature.


The radius of earth is about \( 6400 \mathrm{km} \)
and that ofmars is \( 3200 \mathrm{km} \). The mass
of the earth is 10 times the mass of
mars. An object weight \( 200 \mathrm{N} \) on the surface of earth. Its weight on the
surface of mars will be.
A. 80 N
B. 40 N
\( c . \) 20
\( D \cdot 8 N \)


When a co-ordination compound
\( C r C l_{3} \cdot 6 H_{2} O \) is mixed with \( A g N O_{3}, 2 \)
moles of \( A g C l \) are precipitated per mole of the compound. Write
(i) Structural formula of the complex.
(ii) IUPAC name of the complex.


The series of natural numbers is
divided into groups (1),(2,3,4),(3,4,5,6,7),(4,5,6,7,8,9
Let the sum of the numbers in \( n t h \)
group be \( =[k n-m]^{2} \).FInd \( k+m ? \)


A rubber ball drops from a height h. If the ball rises to h / 2 after rebounding three times coefficient of restitution \( e \)
is
A \( \cdot \frac{1}{2} \)
в. \( \quad\left(\frac{1}{2}\right)^{\frac{1}{2}} \)
c. \( \quad\left(\frac{1}{2}\right)^{\frac{1}{4}} \)
D.


Check the distributive property for the stated triples of rational numbers:
\( \frac{-4}{9}, \frac{6}{5}, \frac{11}{10} \)


Which of the following compounds undergoes hydrolysis?
A. \( S F_{6} \)
в. \( S C l_{6} \)
c. \( \operatorname{se} F_{6} \)
D. \( T e F_{6} \)


What is observed when excess of
ammonia passed through an aqueous solution of lead nitrate?
A. Red precipitate of lead hydroxide is formed
B. Chalky white precipitate of lead phosphate formed
c. chalky white precipitate of lead hydroxide is formed
D. None of these


The types of chains formed by carbon
are :
A. straight
B. closed
c. branched
D. all of the above


A gramophone turntable rotating at an angular velocity of 3 rad\( / \)s stops after one revolution. Find the angular
retardation. (in \( \left.r a d / s^{2}\right) \)
\( \mathbf{A} \cdot 0.698 \)
B. 0.125
c. 0.569
D. 0.716


"Hyponitrous acid and nitramide both
have the formula \( H_{2} N_{2} O_{2} \). Hyponitrous
acid is a weak diprotic acid while nitramide contains the amide group
\( \left(-N H_{2}\right) \)
Answer whether the above statement is
true or false.
If true enter 1 , else enter 0 .


n \( \triangle A B C \) what is sum of the angles a \( + \)
\( b+c+d+e+f+g+h+i ? \)
\( 4 \cdot 360 \)
3.540
\( c \cdot 600 \)
cannot be determine


Find whether it is a terminating or a non-terminating decimal
\( 2.4 \div 0.072 \)
A. Terminating
B. Non-terminating
c. Ambiguous
D. Data insufficient


The cost of \( 1 \mathrm{kg} \) wheat is Rs.58. What is
the cost of \( 4 \frac{1}{8} \) kg wheat?


Which Indian scientist is known for his
crucial role in the development of Indias missile and nuclear weapons
programmes?
A. A. P. J. Abdul Kalam
B. c. v. Raman
c. Jagadish Chandra Bose
D. Har Gobind Khorana


If \( f(x)=\frac{1-\cos a x}{1-\cos b x} \) for \( x \neq 0, \) is
continuous at \( \boldsymbol{x}=\mathbf{0} \) then \( \boldsymbol{f}(\mathbf{0})= \)
A \( \cdot \frac{a^{2}}{2} \)
B. \( \frac{a}{b^{2}} \)
c. \( \frac{a}{b} \)
D. \( \frac{a^{2}}{b^{2}} \)


Hexane has more number of isomers
than heptane.
A. True
B. False


A coin is tossed 5 times. The probability of 2 heads and 3 tails is:
A \( \cdot \frac{11}{16} \)
B. \( \frac{5}{16} \)
c. \( \frac{11}{32} \)
D. \( \frac{5}{32} \)


The specific heat capacity of solid is
\( A \cdot R \)
в. 3 R
c. 5 R
D. 9 R


In the reaction \( M+O_{2} \longrightarrow M O_{2} \)
(super oxide) the metal is :
A \( . L i \)
в. \( N a \)
\( c . K \)
D. \( B a \)


pH of stomach in rabbit is about
A. 7
B. 2
\( c \cdot 8 \)
D. 11


In a potentiometer of wire length \( l \), a cell of emf \( V \) is balanced at a length \( \frac{l}{3} \) from the positive of the wire. For another cell
of emf \( 1.5 V, \) the balancing length
becomes
A \( \cdot \frac{l}{6} \)
B. \( \frac{l}{2} \)
c. \( \frac{l}{3} \)
D. \( \frac{2 l}{3} \)
E \( \cdot \frac{4 l}{3} \)


Calculate the \( p H \) of the resulting
solution formed by mixing the following solutions.
\( 10 m L \) of \( 0.1 M H_{2} S O_{4}+10 m L \) of
\( \mathbf{0 . 0 1} M K O H \)


Predict the product
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C N}+\boldsymbol{H}_{2} / \boldsymbol{N i} \rightarrow ? \)
A \( \cdot C H_{3}-C H_{2}-C H_{2}-N H_{2} \)
в. \( C H_{3}-C H_{2}-N H_{2} \)
\( c . \) both a and \( b \)
D. none of these


Assertion
\( E_{c e l l}^{0} \) is negative for electrolytic cell.
Reason
\( \triangle G^{0} \) is positive for electrolytic cell.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The number of significant figures in
\( \mathbf{0 . 0 0 2 1 0} \) is
A . five
B. six
c. four
D. three


In which of the following reactions,
\( H_{2} O_{2} \) acts as a reducing reagent?
A \( \cdot P b O_{2(s)}+H_{2} O_{2(a q)} \rightarrow P b O_{(s)}+H_{2} O_{(l)}+O_{2(g)} \)
B . \( N a_{2} S O_{3(a q)}+H_{2} O_{2(a q)} \rightarrow N a_{2} S O_{4(a q)}+H_{2} O_{(l)} \)
\( \mathbf{c} \cdot 2 K I_{(a q)}+H_{2} O_{2(a q)} \rightarrow 2 K O H_{(a q)}+I_{2(s)} \)
D. None of these


Positive slope of displacement time graph implies
A. that the body is moving away from the reference point
B. that the body is moving towards the reference point
c. that the body is at rest
D. nothing as particular


Two isolated point poles of strength \( 30 A m \) and \( 60 A m \) are placed at a
distance of \( 0.3 m . \) The force of repulsion
is:
A \( \cdot 2 \times 10^{-3} N \)
B . \( 2 \times 10^{-4} N \)
c. \( 2 \times 10^{5} N \)
D. \( 2 \times 10^{-5} N \)


f a piece of metal is heated to an absolute temperature \( T \) and then put in
an enclosure at absolute temperature \( t \)
then the heat generated in the atmosphere will be proportional to
A \( \cdot(T-t)^{4} \)
B . \( T^{4}-t^{4} \)
\( c \cdot T^{2}-t^{2} \)
D. \( T^{3}-t^{3} \)


How many quantum numbers are rquired to specify the position of eletron:-
\( A \)
B. 2
\( c \cdot 3 \)
D. 4


Find the distance between the points (0,8) and (6,0)


Photon having the energy equivalent to the binding energy of 4th state of \( \boldsymbol{H} \boldsymbol{e}^{+} \) atom is used to eject an electron from the metal surface of work function 1.4
eV. If electrons are further accelerated
through the potential difference of \( 4 \mathrm{V} \) then determine the minimum value of
de-Broglie wavelength associated with the electron.
в. 2.5 А \( ^{\text {о }} \)
\( c \cdot 7.6 A^{\circ} \)
D. \( 10 A^{\circ} \)


If \( \boldsymbol{A}=\{\boldsymbol{x}, \boldsymbol{y}\} \) and \( \boldsymbol{B}=\{\boldsymbol{y}, \boldsymbol{x}\} ; \) then
\( \boldsymbol{A} \times \boldsymbol{B}=? \)
What are the number of elements of
such set?


The greater the number of chloroplast greater is the turgidity of guard cell.
A. True
B. False


\( \boldsymbol{H} \boldsymbol{F}+\boldsymbol{H}_{3} \boldsymbol{O}^{+} \rightarrow \boldsymbol{H}_{2} \boldsymbol{F}^{+}+\boldsymbol{H}_{2} \boldsymbol{O} \)
In the above reaction, Bronsted bases
are:
A. \( H_{3} O^{+}, H_{2} O \)
в. \( H F, H_{3} O^{+} \)
c. \( H_{2} F^{+}, H_{2} O \)
D. \( H F, H_{2} O \)


A choke is preferred to a resistance for limiting current in AC circuit because:
A. Choke is cheap
B. There is no wastage of power
c. choke is compact in size
D. Choke is a good absorber of heat


First cloned animal was
A. Dolly sheep
B. Polly sheep
C. Molly sheep
D. Dog


Centriole/centrosome replication
occurs in
A. Early prophase
B. \( G_{1} \) -phase
c. S-phase
D. \( G_{0} \) -phase


Find the area between the two
parabolas \( \boldsymbol{y}^{2}=\boldsymbol{x}, \boldsymbol{X}^{2}=\boldsymbol{y} \)


When acetone is condensed into a ketol
the reagent used is :
\( \mathbf{A} \cdot B a(O H)_{2} \)
в. \( N a H C O_{3} \)
c. \( B r_{2} \) water
D. \( C l_{2} \)


When a brown compound of \( \mathrm{Mn}(\mathrm{A}) \) is treated with \( H C l, \) it gives a gas B. The
gas B taken in excess reacts with \( N H_{3} \) to give an explosive compound C. The compounds \( A, B \) and \( C \) are :
A. \( A=M n O_{2}, B=C l_{2}, C=N C l_{3} \)
В. \( A=M n O, B=C l_{2}, C=N H_{4} C l \)
c. \( A=M n_{3} O_{4}, B=C l_{2}, C=N C l_{3} \)
D. \( A=M n O_{3}, B=C l_{2}, C=N C l_{2} \)


Write an expression for the magnitude
of the resultant vector 'R' of two vectors
\( \vec{A} \) and \( \vec{B} \) acting at a point. When will this resultant vector 'R' be maximum?


The north-south polarities of an electromagnet can be determined with the help of
A. Maxwell's corkscrew rule
B. right hand thumb rule
c. clock face rule
D. Fleming's left-hand rule


The equation of the base of an equilateral triangle is \( \mathbf{x}+\mathbf{y}-\mathbf{2}=\mathbf{0} \)
and the vertex is \( (2,-1), \) then the
length of side is
A . 1
в. 2
\( c .3 \)
D. \( \sqrt{\frac{2}{3}} \)


The electronic configuration of cerium
is:
в. \( [X e] 4 f^{1} 5 d^{1} 6 s^{2} \)
\( \mathbf{c} \cdot[X e] 4 f^{2} 5 d^{0} 6 s^{2} \)
D. Both A and B


Find the value of I?
\( A \cdot-1.4 A \)
3. - -२.।
\( c \cdot 2 A \)
D. \( -4.2 \mathrm{A} \)


Match the column.


Give Reason:
A square can be thought of as a special
rhombus.


Identify the pair of substances having the same formula unit mass.
A. Calcium chloride, potassium carbonate
B. Calcium oxide, hydrochloric acid
c. carbon monoxide, ammonia
D. Carbon dioxide, nitrous oxide


What is latent heat of fusion?


Why is ice at \( 0^{\circ} \mathrm{C} \) more effective in
cooling than water at \( 0^{\circ} \mathrm{C} ? \)


The expression \( \frac{3-4 i}{5+3 i} \) is equivalent to
A \( \cdot \frac{27-29 i}{34} \)
в. \( \frac{27-29 i}{16} \)
c. \( \frac{3-29 i}{34} \)
D. \( \frac{1}{8} \)
E . \( 15-8 i \)


In solving a problem, one student makes a mistake in the coefficient of
the first degree term and obtains -9
and -1 for the roots. Another student
makes a mistake in the constant term
of the equation and obtains 8 and 2 for the roots. The correct equation was?
A. \( x^{2}+10 x+9=0 \)
B . \( x^{2}-10 x+16=0 \)
c. \( x^{2}-10 x+9=0 \)
D. None of the above


Copper is generally used for making
calori-meters because it
A. Does not get rusted
B. Is cheap and easily available
C. Is easy to mould it in the required shape
D. Quickly attains the temperature of the liquid contained in it


Which one of the following does not
represent a travelling wave?
\( \mathbf{A} \cdot y=f(x-v t) \)
B \( \cdot y=y_{\max } \sin k(x+v t) \)
\( \mathbf{c} \cdot y=y_{\max } \log (x-v t) \)
D. \( y=f\left(x^{2}-v t^{2}\right) \)


Assertion
Each of the plates of a parallel-plate
capacitor is given equal positive charge
Q. The charges on the facing surfaces
will be same.
Reason
A negative charge \( (-Q) \) will be induced
on each of the facing surfaces.
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


Q Type your question
positioned al poinis 1 and \( 4, \) ine \( 11 € \) id
intensity to the right of the charge \( Q_{2} \)
on the line that passes through the two
charges varies according to a law that is represented schematically in the figure.

The field intensity is assumed to be positive if its direction coincides with
the positive direction on the \( x-a x i s \)
The distance between the charges is \( l \)
Find the sign of each charge.
A. \( Q_{2} \) is positive and \( Q_{1} \) is negative
B. \( Q_{2} \) is positive and \( Q_{1} \) is positive
\( \mathrm{C} \cdot Q_{2} \) is negative and \( Q_{1} \) is negative
D. \( Q_{2} \) is negative and \( Q_{1} \) is positive


A card is draw from a well-shuffled pack
of 52 cards. What is the probability that a card will be a king?


Striped muscles are
A. Syncytial
B. Uninucleate
c. Binucleate
D. Anucleate


The tendency of a bonded atom in a molecule to lose or repel the electron density of a shared pair of electrons is
called:
A. electro negativity
B. electropositivity
c. electroneutrality
D. none of these


Area of the region bounded by the curve
\( \boldsymbol{y}=\mathbf{2 5}^{\boldsymbol{x}}+\mathbf{1 6} \) and curve \( \boldsymbol{y}=\boldsymbol{b} . \mathbf{5}^{\boldsymbol{x}}+\mathbf{4} \)
whose tangent at the point \( \boldsymbol{x}=\mathbf{1} \)
makes an angle \( \tan ^{-1}(40 \log 5) \) with
the \( x- \) axis is:
\( ^{\mathbf{A}} \cdot_{2 \log _{5}}\left(\frac{e^{4}}{27}\right) \)
\( ^{\mathbf{B}} \cdot_{4 \log _{5}}\left(\frac{e^{4}}{27}\right) \)
\( \mathbf{c} \cdot_{3 \log _{5}}\left(\frac{e^{4}}{27}\right) \)
D. None of these


Vertebrae are absent is
A. Duck-billed platypus
B. Turtle
C. Amphioxus
D. Trout
E . Rabbit


\( 2 \tan ^{-1}\left(\frac{\sqrt{a-b}}{a+b} \tan \frac{x}{2}\right)= \)
A \( \cdot \cos ^{-1}\left(\frac{b+a \cos x}{a+b \cos x}\right) \)
B. \( \cos ^{-1}\left(\frac{b+a \cos x}{a-b \cos x}\right) \)
c. \( \cos ^{-1}\left(\frac{b-a \cos x}{a+b \cos x}\right) \)
D. \( \cos ^{-1}\left(\frac{b-a \cos x}{a-b \cos x}\right) \)


Heights of the pupils of a particular school are given. Draw greater than cumulative curve and find the median
height from it.
\( 110-\quad 120 \)
\( \begin{array}{ll}90- & 100- \\ 100 & 110\end{array} \) Height
(in \( \mathrm{cm} \) ) 120 13.
Number of pupils


The inital velocity of a particle is \( u \) (at
\( t=0 \) ) and the acceleration \( a \) is given by
\( \alpha t^{3 / 2} . \) Which of the following relations is vaild?
A \( \cdot v=u+\alpha t^{3 / 2} \)
B. \( v=u+\frac{3 \alpha t^{3}}{2} \)
c. \( v=u+\frac{2}{5} \alpha t^{5 / 2} \)
D . \( v=u+\alpha t^{-5 / 2} \)


A body covers 26,28,30 and 32 meters in \( 10^{t h}, 11^{t h}, 12^{t h} \) and \( 13^{t h} \) seconds
respectively. The body starts
A. from rest and moves with uniform velocity
B. from rest and moves with uniform acceleration
c. with an initial velocity and moves with uniform acceleration
D. with an initial velocity and moves with uniform velocity


From the sum of \( 3 x-y+11 \) and \( -y- \)
11, subtract the sum of \( 3 x^{2}-5 x \) and
\( -x^{2}+2 x+5 \)


The grittiness of pulp of wood apple is due to
A. Macrosclereids
B. Brachysclereids
c. osteosclereids
D. Astrosclereids


A loaded spring gun of mass \( M \) fires a bullet of mass \( m \) with a velocity \( v \) at an
angle of elevation \( \theta \). The gun is initially at rest on a horizontal smooth surface.
After firing, the centre of mass of the
gun and bullet system
A . Moves with velocity \( \frac{v}{M} \) m
B. Moves with velocity \( \frac{v m}{M \cos \theta} \) in the horizontal direction
c. Does not move in horizontal direction
D. Moves with velocity \( \frac{v(M-m)}{M+m} \) in the horizonta direction


Trophic movements are growth
movements of plants in response to a stimulus from a specific direction.
A. True
B. False


In Ginkgoales, the male gametes are
A. Motile
B. Non-motile
C. Amoeboid
D. Absent


A boat is streamlined to reduce the
resistance to motion offered by
A. True
B. False


Among the following industrial waste can be managed by :
A. recycling
B. burning of combustible waste material
c. dumping
D. all of the above


If the sum \( 1+2+3+\ldots .+K \) is a
perfect square \( N^{2} \) and if \( N \) is less than
\( 100, \) then the possible values for \( K \) are:
A. only 1
B. 1 and 8
c. only 8
D. 8 and 49
E. \( 1,8, \) and 49


Statement- 1: Alkanes participate in
substitution reactions.

Statement- 2: Alkanes are saturated
hydrocarbons.
A. Both statement- 1 and statement-2 are correct statement-2 is a correct explanation of statement-1.
B. Both statement-1 and statement-2 are correct statement-2 is not a correct explanation of statement-
1.
C. Statement-1 is correct, statement-2 is incorrect.
D. Statement-1 is incorrect, statement-2 is correct.


The nuclear reactor of the power plant must be shielded with \( _{-}-_{-}-_{-} \) walls.
A. Leadd
B. steel
c. Both
D. None


Physical treatment for the industrial wastes include sedimentation and
filtration.
A. True
B. False


toppr
Q Type your question.
mirrors, then 5 images of the object will be formed.

Reason: For a given system of mirrors the total number of images formed due to successive reflection is equal to either \( \frac{360^{\circ}}{\theta} \) or \( \frac{360^{\circ}}{\theta}-1 \) accordingly as \( \frac{360^{\circ}}{\theta} \) is odd or even respectively.
A. If both Assertion 'and Reason are correct and Reason
is the correct explanation
B. If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion
c. If Assertion is correct but Reason is incorrect
D. If Assertion is incorrect but Reaso


A geometry box is marked for \( R s .325 . \) If
the rate of tax is \( 12 \% \), find the amount a
customer has to pay for it.


Based on the following reaction and
rate data:
\( \boldsymbol{A}(\boldsymbol{g})+\boldsymbol{B}(\boldsymbol{g}) \rightarrow \) products
and ) Experiment \( \quad \begin{array}{lll}{[A]} & {[B]} & \text { Initial } \\ \mathrm{mol} / \mathrm{L} & \mathrm{mol} / \mathrm{L} & \begin{array}{l}\text { Rate } \\ (\mathrm{M} / \mathrm{s})\end{array}\end{array} \) 0.040 \( \begin{array}{ccc}1 & 0.060 & 0.010 \\ 2 & 0.030 & 0.010 \\ 3 & 0.030 & 0.020\end{array} \) 0.040 0.080
What is the order of the reaction with
respect to \( \boldsymbol{B} ? \)
\( A \cdot O \)
B.
\( c \cdot 2 \)
D. 3
\( E \cdot 4 \)


If density of the earth is doubled keeping its radius constant, then acceleration due to gravity (present
value \( 9.8 m / s^{2} \) ) will be:
A \( \cdot 2.45 \mathrm{m} / \mathrm{s}^{2} \)
B . \( 4.9 \mathrm{m} / \mathrm{s}^{2} \)
c. \( 9.8 \mathrm{m} / \mathrm{s}^{2} \)
D. \( 19.6 \mathrm{m} / \mathrm{s}^{2} \)


In reality, a spring won't oscillate for
ever. will \( \quad \) the amplitude of oscillation until eventually the system is at rest.
A. Frictional force, increase
B. Viscous force, decrease
c. Frictional force, decrease
D. Viscous force, increase


Two closed vessels of the equal volume
contain air at \( 105 \mathrm{kPa} \) at \( 300 \mathrm{K} \) and are
connected through a narrow tube. If one
of the vessels is now maintained at \( 300 \mathrm{K} \)
and the other at \( 400 \mathrm{K} \) then the pressure
becomes.
A . 120kPa
B. 105kPa
c. \( 150 k P a \)
D. 300kPa


For a random experiment, all possible outcomes are called
A. numerical space.
B. event space
c. sample space.
D. both b and c


Select the correct option:
Identify the figures \( A, B, C \) showing
different types of muscle and select the correct option:
A. A- smooth muscle; B- Striated muscle; C- Cardiaç muscle
B. A-Cardiac muscle; B- - Smooth muscle; Striated muscle
c. A- striated muscle; B- Smooth muscle; C- Cardiaç muscle
D. A- Involuntary muscle; B- Voluntary muscle; C- Heat muscle


Metals more reactive than carbon are
usually extracted by
A. Pyrolysis
B. Electrolysis
c. Fractional distillation
D. Filteration


A metal sphere of radius \( 1 \mathrm{cm} \) is given a charge of \( 3.14 \mu C . \) Find the electric
intensity at a point \( 1 \mathrm{m} \) from the center
of the sphere.


Evaluate : \( \int \frac{(4 x+1) d x}{x^{2}+3 x+2} \)
A.
\[
\begin{array}{l}\text { s. } \\ \begin{array}{l}\text { s. } 2 \log \left|x^{2}+5 x+2\right|-5 \log \left|\frac{x+1}{x+2}\right|+C \\ =2 \log \left|x^{2}+3 x+2\right|-5 \log \left|\frac{x+3}{x+2}\right|+C\end{array} \\ \text { 0. }=2 \log \left|x^{2}+3 x+2\right|-5 \log \left|\frac{x+1}{x+2}\right|+C\end{array}
\]


Evaluate :
\[
\boldsymbol{\Delta}=\left|\begin{array}{ccc}
\cos \alpha \cos \beta & \cos \alpha \sin \beta & -\sin \alpha \\
-\sin \beta & \cos \beta & 0 \\
\sin \alpha \cos \beta & \sin \alpha \sin \beta & \cos \alpha
\end{array}\right|
\]


Bohr proposed his atomic model based
on:
A. oil drop experiment
B. planck's quantum theory
c. \( \alpha \) -ray scattering experiment
D. experiments on conduction of gases


Inner darker, harder portion of secondary xylem that cannot conduct water in older dicot stem is called?
A. Alburnum
B. Bast
c. Duramen
D. woodd


In the adsorption of a gas on solid, Freundlich isotherm is obeyed. Thus, if
the slope of the plot is zero, then the extent of adsorption is:
A. directly proportional to the pressure of gas
B. inversely proportional to the pressure of the gas
c. independent of the pressure of the gas
D. proportional to the square of the pressure of the ga:


A constant electric current flows for 4
hours through two electrolytic cells connected in series. One contains
\( \mathrm{AgNO}_{3} \) solution and second contains
\( \mathrm{CuCl}_{2} \) solution. During this time 4 grams of Ag are deposited in the first cell.
(a) How many grams of Cu are deposited in the second cell?
(b) What is the current flowing in amperes?


In the following distribution calculate
mean \( \bar{x} \) from assumed mean
Class-
interval \( \begin{array}{lll}10- & 25- & 4 \\ 25 & 40 & 5\end{array} \) 7.
7 7 55 70
Frequency 2
If \( \bar{x}=a b, \) then \( a+b \) is :


Which of the following statement(s)
is/are wrong?
A. The malting point of trans-but-2-ene is greater than that of the cis-isomer due to symmetrical packing in the crystal lattice of the trans-form.
B. The boiling point of cis-but-2-ene is greater than that of the trans-isomer due to steric strain in the cisisomer because of van der Waals repulsion force of large group on the same side of the double bond and the cis-isomer becomes less stable because of the increasing repulsive force
C. The boiling point of the cis-isomer is greater than that of the trans-isomer due to the relatively high polarity of the cis-isomer compared to its trans-isomer
D. Refer Image
The boiling point of
is greter than that


In the expansion of \( \left(7^{1 / 3}+11^{1 / 9}\right)^{6561} \) prove that there will be only 730 terms which are free from radicals.


\( \int \frac{\sin (2 x)}{1+\cos ^{2} x} d x \) is equal to
A \( \cdot-\frac{1}{2} \log \left(1+\cos ^{2} x\right)+c \)
B . \( 2 \log \left(1+\cos ^{2} x\right)+c \)
c. \( \frac{1}{2} \log (1+\cos 2 x)+c \)
D. \( c-\log \left(1+\cos ^{2} x\right) \)


\( \operatorname{Let} f^{\prime}(x)=e^{x^{2}} \) and \( f(0)=10 . \) If \( A< \)
\( f(1)<B \) can be concluded from the
mean value theorm, then the largest value of \( (\boldsymbol{A}-\boldsymbol{B}) \) equals
\( A \)
B. \( 1-e \)
\( \mathbf{c} \cdot e-1 \)
D. \( 1+e \)


An object shaped as ' \( L^{\prime} \) is placed between two parallel plane mirrors as shown. In the first seven closest images
that are formed, how many laterally inverted images are formed?
\( A \)
B. 2
\( c \cdot 3 \)
\( D \cdot 4 \)


For the reaction; \( N_{2} O_{5} \rightarrow 2 N O_{2}+\frac{1}{2} O_{2} \)
Given:
\( -\frac{\boldsymbol{d}\left[\boldsymbol{N}_{2} \boldsymbol{O}_{5}\right]}{\boldsymbol{d} \boldsymbol{t}}=\boldsymbol{K}_{1}\left[\boldsymbol{N}_{2} \boldsymbol{O}_{5}\right], \frac{\boldsymbol{d}\left[\boldsymbol{N} \boldsymbol{O}_{2}\right]}{\boldsymbol{d} \boldsymbol{t}}= \)
\( \boldsymbol{K}_{2}\left[\boldsymbol{N}_{2} \boldsymbol{O}_{5}\right], \frac{\boldsymbol{d}\left[\boldsymbol{O}_{2}\right]}{\boldsymbol{d} \boldsymbol{t}}=\boldsymbol{K}_{3}\left[\boldsymbol{N}_{2} \boldsymbol{O}_{5}\right] \)
The relation between \( \boldsymbol{K}_{1}, \boldsymbol{K}_{2} \) and \( \boldsymbol{K}_{3} \) is:
\( \mathbf{A} \cdot 2 K_{1}=K_{2}=4 K_{3} \)
в. \( K_{1}=K_{2}=K_{3} \)
\( \mathbf{c} \cdot 2 K_{1}=4 K_{2}=K_{3} \)
D. none of the above


A wire of length \( L \) and cross sectional
area \( A \) is made of a material of Young's
modulus \( Y \). If the wire is stretched by
an amount \( x, \) the work done is
A \( \cdot \frac{Y A x^{2}}{3 L} \)
в. \( \frac{Y A x^{2}}{4 L} \)
c. \( \frac{Y A x^{2}}{L} \)
D. \( \frac{Y A x^{2}}{2 L} \)


The dedifferentiated cells mature to
form some specific cells to perform specific functions, this is referred to as
A. Differentiation
B. Dedifferentiation
c. Redifferentiation
D. Development


A meter stick of mass 400 g is pivoted at one end and displaced through an angle \( 60^{0} . \) The increase in its potential energy is


the central bright maxima is twice as wide as the other maxima.


Imagine a cannon being fired on the
surface of the moon. Then the sound will
This question has multiple correct options
A. Be heard at the surface of the earth during all seasons
B. Not be heard at the surface of the earth
\( \mathrm{C} . \) Be heard at the surface of the earth during the rainy season
D. Not be heard on the earth or on the moon


The range of \( f(x)=\operatorname{cosec}^{2} x+ \)
\( 25 \sec ^{2} x \) is \( (a, \infty] \) Find \( a \)


Calculate the coefficient of range for the following data:
\( \begin{array}{llll}\text { Heights } & 120- & 125- & 130- \\ \text { in cm. } & 124 & 129 & 134\end{array} \)
No. of
students 9


\( \int\left(\frac{2 x-1}{3 \sqrt{x}}\right)^{2} d x \) on \( (0, \infty) \)


If the image formed by a spherical mirror for all positions of the object placed in front of it is always erect and diminished, what type of mirror is it? Draw a labelled ray diagram to support
your answer.


Find the intervals in which the function
\( f(x)=\frac{x^{4}}{4}-x^{3}-5 x^{2}+24 x+12 \) is
(a) strictly increasing,
(b) strictly decreasing.


What are the assumptions made during
the calculation of net gain of ATP in
respiration?


A plant with both male and female
flowers borne over it is
A. Monoecious
B. Dioecious
c. Unisexual
D. Bisexual


Which of the following substance consists of only one element?
A. Diamond
B. Glass
c. Marble
D. sand


In vascular plants, light promotes
A. Growth
B. Development
C. Differentiation
D. All of the above


In the reaction \( C(s)+C O_{2} \rightleftharpoons 2 C O(g) \)
the equilibrium pressure is 12 atm. If
\( 50 \% C O_{2} \) reacts, calculate
\( \boldsymbol{K}_{\boldsymbol{P}}: \)
A \( \cdot_{K_{P}}=0.25 \) atm
В \( \cdot_{K_{P}}=4 \quad \) atm
\( \mathbf{c} \cdot_{K_{P}=16} \) atm
D. \( _{K_{P}}=8 \) atm


is the respiratory pigment which
carry oxygen in the blood.
A. Myoglobin
B. Bilirubin
c. Biliverdin
D. Haemoglobin


What are the postulates of valence bond theory?


The effective resistance between points
P and Q of the electrical circuit shown in
the figure is
A \( \cdot \frac{2 R r}{R+r} \)
B. \( \frac{8 R(R+r)}{3 R+r} \)
\( c \cdot 2 r+4 R \)
D. \( \frac{5 R}{2}+2 \)


Evaluate the following:
\( \cos ^{-1}(\cos 12) \)


A parallel plate air condenser has capacity of \( 20 \mu F \). If the distance between two plates is doubled, then new
capacity will be
A \( .5 \mu F \)
B. \( 10 \mu F \)
\( \mathbf{c} \cdot 15 \mu F \)
D. \( 20 \mu F \)


Give the MKS units for the following
quantities.
Power of lens.
A. hertz
B. Dioptre
c. ohms
D. unit less


The velocity-position graph of a particle is shown in figure. Write the relation
between \( v \) and \( x \)


If the four letter words(need not be meaningful) are to be formed using the
letters from the word "MEDI

TERRANEAN" such that the first letter is
\( \mathrm{R} \) and the fourth letter is \( \mathrm{E} \), then the
total number of such words, is?
A \( \cdot \frac{11 !}{(2 !)^{3}} \)
B . 59
c. 110
D. 56


A force \( F=5 t \) is applied on a block of
mass \( 10 \mathrm{kg} \) kept on rough horizontal surface \( (\mu=0.5), \) in rest what is speed of the block at \( t=20 \) s?
\( A \cdot 15 \mathrm{m} / \mathrm{s} \)
B. \( 18 \mathrm{m} / \mathrm{s} \)
\( c \cdot 2.5 \mathrm{m} / \mathrm{s} \)
D. cannot be calculated


A copper rod of \( 88 \mathrm{cm} \) and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of aluminium rod is :
\( \left(\alpha_{C u}=1.7 \times 10^{-5} K^{-1} \text {and } \alpha_{A l}=\right. \)
\( \left.2.2 \times 10^{-5} K^{-1}\right) \)
\( \mathbf{A} \cdot 6.8 \mathrm{cm} \)
B. \( 113.9 \mathrm{cm} \)
\( \mathbf{c} .88 \mathrm{cm} \)
D. \( 68 \mathrm{cm} \)


What is LED? Show its \( (\boldsymbol{v}-\boldsymbol{i}) \)
characteristics drawing circuit diagram.


The average depth of Indian Ocean is about \( 3000 m \). The fractional
compression, \( \frac{\Delta V}{V} \) of water at the
bottom of the ocean is then
(Given: Bulk modulus of the water=
\( 2.2 \times 10^{9} N m^{-2} \) and \( g=10 m s^{-2} \)
\( \mathbf{A} \cdot 0.82 \% \)
B . \( 0.91 \% \)
c. \( 1.36 \% \)
D. 1.24\%


The values of \( n_{1} \) and \( n_{2} \) for Pfund's
series are
A \( \cdot n_{1}=5, n_{2}=6,7 \)
В . \( n_{1}=4, n_{2}=5,6,7 . . . \)
C \( . n_{1}=3, n_{2}=4,5,6 \dots \)
D. \( n_{1}=2, n_{2}=3,4,5 \dots \)


Rayon is chemically known as:
A. cellulose nitrate
B. cellulose
c. cellulose acetate
D. resins


\( x \)
Liquid sodium \( \quad \) Breathing apparatus metal \( \quad \) submarine
Potassium \( \quad \) Explosive
Potassium nitrate Coolant in nuclear reaction
Potassium
superoxide Soft soap
Match the compounds/metal in(X) with
their used in (Y). hence correct order is.
A . A-l, B-III, C-II, D-IV
B. A-III, B-IV, C-II, D-I
C . A-II, B-I, C-III, D-IV
D. A-IV, B-II, C-III, D-1


Two systems, \( \boldsymbol{P C l}_{5(g)} \rightleftharpoons \boldsymbol{P C l}_{3(g)}+ \)
\( \boldsymbol{C l}_{2(\boldsymbol{g})} \) and \( \boldsymbol{C O C l}_{2(\boldsymbol{g})} \rightleftharpoons \boldsymbol{C O}_{(g)}+\boldsymbol{C l}_{2(\boldsymbol{g})} \)
are simultaneously in equilibrium in a vessel at constant volume. If some \( C O \)
is introduced into the vessel then at the
new equilibrium, the concentration of :
A . \( P C l_{5} \) is increased
B. \( P C l_{3} \) remains unchanged
c. \( P C l_{5} \) is decreased
D. \( C l_{2} \) is increased


A toy rocket is launched straight up. At the exact top of its flight path, which of the following is true?
A. Its velocity and acceleration are zero
B. Its velocity is zero and acceleration is \( 9.8 \mathrm{m} / \mathrm{s}^{2} \)
C . It velocity is \( 9.8 \mathrm{m} / \mathrm{s} \) and acceleration is \( 9.8 \mathrm{m} / \mathrm{s}^{2} \)
D. It velocity is \( 9.8 m / s \) and acceleration is zero
E. It velocity is \( 9.8 \mathrm{m} / \mathrm{s} \) and displacement is \( 9.8 \mathrm{m} \)


Which among the following sets of atomic numbers is/are associated with
the increasing order of the number of
unpaired electrons?
\( (a) z=29 ; z=20 ; Z=25 ; Z=27 ; Z=24 \)
\( (b) z=20 ; z=29 ; z=22 ; z=27 ; z=25 \)
\( (c) z=19 ; z=22 ; z=24 ; z=26 ; z=25 \)
\( (d) Z=19 ; Z=22 ; Z=26 ; Z=25 ; Z=24 \)
\( A \cdot \) a and \( c \)
B. b and
\( c \cdot a \) and \( d \)
D. b and c


\( \cos 1^{\circ} \cos 2^{\circ} \cos 3^{\circ} \dots \dots \dots \dots \dots \cos 90^{\circ} \)
\( \mathbf{A} \cdot \mathbf{0} \)
B . -1
\( \mathbf{c} \cdot 1 \)
D. None of these


\( \int x^{2} e^{x} d x=? \)


Washing soda \( \left(N a_{2} C O_{3} .10 H_{2} O\right) \) is widely used in softening of hard water. If 1 L of hard water requires 0.0286 g of
washing soda, the hardness of \( C a C O_{3} \) in ppm is :
A . 10
B. 5
c. 8
D. 6


Photo-electric cell is not used in:
A . television
B. photography
C. reproduction of sound in cinema
D. automatic switching of street lightening circuits


Which of the following equations indicates the oxidizing property of
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} ? \)
A. \( H_{2} S O_{4} \rightarrow S O_{3}+H_{2} O \)
B. \( H_{2} S O_{4} \rightarrow H_{2} S O_{3}+H_{2} O \)
c. \( H_{2} S O_{4} \rightarrow S O_{2}+H_{2} O+[O] \)
D. \( H_{2} S O_{4} \rightarrow S O_{3}+2[H] \)


Among sodium phosphate, sodium sulphate and sodium chloride the solubility in water decreases as:
A. sulphate > phosphate > chloride
B. chloride > sulphate > phosphate
c. chloride > phosphate > sulphate
D. phosphate \( > \) chloride \( > \) sulphate


Beryllium and aluminium exhibit many properties which are similar. But, the two elements differ in:
A. maximum covalency in compounds
B. forming polymeric hydrides
c. forming covalent halides
D. exhibiting amphoteric nature in their oxides


Read the following questions for \( \mathrm{N}, \mathrm{P}, \mathrm{C} \) Si elements.
(i) Element which has least atomic radii
(ii) Element which has maximum
ionization energy
(iii) Element which has least electron
affinity
(iv) Element which has Maximum
electronegativity Select the correct code of elements for
given questions respectively.
A. P N P N
B. N N N N
c. \( \mathrm{N} \) N P N
D. \( C C C C \)


The radius of each coil of a Helmholtz
galvanometer is \( 0.1 m \) and number of
turns in each is \( 25 . \) When a current is
passed in it then the deflection of
magnetic needle observed as \( 45^{\circ} . \) If the
horizontal component of earth's magnetic field is \( 0.314 \times 10^{-4} T \) then
the value of current will be
\( \mathbf{A} \cdot 0.14 A \)
B. \( 0.28 A \)
c. \( 0.42 A \)
D. \( 0.07 A \)


Distinguish between linearly polarised and unpolarised light.


Name the body structure concerned with the given functional activity:
Transports oxygen to the body cells


Show diagrammatically the behaviour
of magnetic field lines in the presence of
(i) paramagnetic and
(ii) diamagnetic substances. How does one explain this distinguishing feature?


Solve the equation:
\( 6 x=12 \)


What does the area of an 'velocity-time graph of a uniformly accelerating body
represent?


The spectrum of a molecule is so detailed that a molecule can be
identified by its spectrum.
A. Only if it is small
B. Only by test-tube analysis
c. with great difficulty
D. Easily, like a fingerprint


The average velocity of an ideal gas
molecule at \( 27^{\circ} \mathrm{C} \) is \( 0.3 m s^{-1} . \) The
average velocity at \( 927^{\circ} \mathrm{C} \) will
be
Write numerical value (upto 2 digit only) after decimal point only as for 0.19 write \( 19) \)


If \( \boldsymbol{y}=\cos \left(\boldsymbol{m} \sin ^{-1} \boldsymbol{x}\right), \) the value of \( (\boldsymbol{1}- \)
\( \left.x^{2}\right) y^{\prime \prime}-x y^{\prime} \) is
A. \( -m^{2} y \)
в. \( \frac{y}{m^{2}} \)
c. \( m^{2} y \)
D. \( \frac{m^{2}}{y} \)


Assertion
A solid sphere placed in the fluid under high pressure is compressed uniformly on all sides.
Reason
The volume of solid sphere will decrease
with change of its geometrical shape.
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


Expand \( (x+1)^{3} \) using an identity


Of the following transitions in the hydrogen atom, the one which gives an absorption line of maximum wavelength is:
A \( n=1 \) to \( n=2 \)
2
в. \( n=3 \) to \( n=8 \)
c. \( n=2 \) to \( n=1 \)
D. \( n=8 \) to \( n=3 \)


Noradrenaline is one of the example of :
A. anti-depressant
B. anti-Histamine
c. neurotransmitter
D. antacid


In a fermentation tank, molasses
solution is mixed with yeast enzymes. After three days alcohol was observed.
The speed of the reaction in this case is
A. slow
B. medium
\( c . \) fast
D. very fast


A uniform rod of length \( L \) and mass \( 2 M \)
rests over two supports \( A \) and \( B . A \)
particle having mass, \( M \) is placed at the right end. Determine the reactions
at supports \( \boldsymbol{A} \) and \( \boldsymbol{B} \)


A horizontal pipe of non-uniform crosssection allows water to flow through it with a velocity \( 1 \mathrm{ms}^{-1} \) when pressure is 50kPa at a point. If the velocity of flow has to be \( 2 \mathrm{ms}^{-1} \) at some other piont,the pressure at that point should
be:
A. 50 kPa
B. 100kPa
c. \( 48.5 \mathrm{kPa} \)
D. 24.25 kPa


Solve \( :\left(\frac{2 n}{2 n-1}\right)^{p}=\left(\frac{1}{1-\left(\frac{p}{2 n}\right)}\right)^{p} \)


How can photoelectric effect be used to produce electricity


A small block of mass \( m \) is lying at a
rest at point \( \boldsymbol{P} \) of wedge having a
smooth semicircular track of radius \( \boldsymbol{R} \)
The maximum value of horizontal
acceleration \( a_{0} \) of wedge so that mass
can just reach the point \( Q ? \)
A \( . g / 2 \)
B. \( \sqrt{g} \)
\( c \)
D. not possible


The coordinates of the point which is
equidistant from the three vertices of the \( \Delta A O B \) as shown in the given
figure
\( \mathbf{A} \cdot(x, y) \)
B . \( (y, x) \)
c. \( \frac{x}{2}, \frac{y}{2} \)
D. \( \frac{y}{2}, \frac{x}{2} \)


Give balanced equation for reaction in
which \( N H_{3} \) is oxidized by a gas which
is not oxygen.
A. \( 8 N H_{3}+3 C l_{2} \rightarrow 6 N H_{4} C l+2 N_{2} \)
B . \( 4 N H_{3}+3 C l_{2} \rightarrow 3 N H_{4} C l+N_{2} \)
\( \mathrm{c} \cdot 8 N H_{3}+3 C l_{2} \rightarrow 6 N H_{4} C l+N_{2} \)
D. None of these


The value of \( \left(^{7} C_{0}+^{7} C_{1}\right)+ \)
\( \left(^{7} C_{1}+^{7} C_{2}\right)+\ldots+\left(^{7} C_{6}+^{7} C_{7}\right) \) is
\( \mathbf{A} \cdot 2^{8}-2 \)
B . \( 2^{8}-1 \)
\( \mathbf{c} \cdot 2^{8}+1 \)
D. \( 2^{8} \)


The altitudes of triangle are 12,15 and 20 units. The largest angle in the triangle is:
A \( .75^{\circ} \)
B. \( 90^{\circ} \)
\( c \cdot 120^{\circ} \)
D. \( 135^{\circ} \)


Mixture of iodine in carbon tetrachroide
is :
A. heterogenous and shows tyndall effect
B. homogenous and shows tyndall effect
C. heterogenous and doesnot show tyndall effect
D. homogenous and doesnot show tyndall effect


Give reasons for the following observation:
The smell of hot sizzing food several metres away, but to get the smell from
cold food you have to go close.


Lightning is caused due to discharge of
oppositely charged clouds. Give reason.


Power dissipated in the circuit shown in the figure 30 watt. The value of R is
A . \( 5 \Omega \)
B. \( 15 \Omega \)
\( c \cdot 10 \Omega \)
D. 20 \( \Omega \)


The \( 0_{2} \) in the exhaled air is
A. About 8\%
B. About 10\%
c. About 15\%
D. About 20\%


In Funaria, archegonia attracts antherozoids by
A. Sucrose / Sugar
B. Malic acid
c. Maleic acid
D. Citric acid


The volume of oil contained in a certain
hydraulic press is \( 0.2 m^{3} . \) The
compressibility of oil is \( 20 \times 10^{-6} \) per
atmosphere. The decrease in volume of the oil when subjected to 200
atmospheres is (1 atmosphere \( = \)
\( \left.1.02 \times 10^{5} N / m^{2}\right) \)
A \( \cdot 4 \times 10^{-4} m^{3} \)
B. \( 8 \times 10^{-4} m^{3} \)
c. \( 16 \times 10^{-4} m^{3} \)
D. \( 2 \times 10^{-4} m^{3} \)


As per the diagram a point charge \( +q \) is placed at the origin 0. work done in
taking another point charge - \( \mathrm{Q} \) from the point \( A[\text { coordinates }(0, a)] \) to another point \( \mathrm{B}[\text { coordinates }(\mathrm{a}, 0)] \) along the
straight line \( A B \) is:
A. zero
B. \( \left(\frac{q Q}{4 \pi \varepsilon_{0}} \frac{I}{a^{2}}\right) \sqrt{2} a \)
c. \( \left(\frac{-q Q}{4 \pi \varepsilon_{0}} \frac{I}{a^{2}}\right) \sqrt{2} a \)
D. \( \left(\frac{q Q}{4 \pi \varepsilon_{0}}-\frac{I}{a^{2}}\right)\left(\frac{a}{\sqrt{2}}\right) \)


Two objects \( A \) and \( B \) when placed in front of a concave mirror of focal length
\( 7.5 \mathrm{cm}, \) give images of equal size. If \( \mathrm{A} \) is three times the size of \( B \) and is placed \( 30 \mathrm{cm} \) from the mirror, what is the distance of B from the mirror?
\( \mathbf{A} \cdot 10 \mathrm{cm} \)
в. \( 12.5 \mathrm{cm} \)
\( \mathbf{c} \cdot 15 c m \)
D. \( 17.5 \mathrm{cm} \)


In electrolytic refining, which of the following is used as an electrolyte?
A. Impure metal
B. Pure metal
c. Metal salt
D. None of the above


a) Redraw the above diagram.
b) This diagram represents
c) Label the parts of the diagram
d) Mention the working principle of the
device denoted by this diagram.


Fill in the blank.
Dynamic Fluid Friction is the
sliding friction of solids.
A. higher than
B. lower than
c. same as
D. higher than or equal to