What is released when \( B_{2} H_{6} \) reacts
with oxygen?
A. Hydrogen gas
в. \( B_{2} O_{3} \)
c. no reaction
D. \( B O_{2} \)


If \( \boldsymbol{A}= \)
\( \frac{1}{\pi}\left[\begin{array}{cc}\sin ^{-1}(\pi x) & \tan ^{-1}\left(\frac{\pi}{\pi}\right) \\ \sin ^{-1}\left(\frac{x}{\pi}\right) & \cot ^{-1}(\pi x)\end{array}\right], B= \)
\( \frac{1}{\pi}\left[\begin{array}{cc}-\cos ^{-1}(\pi x) & \tan ^{-1}\left(\frac{x}{\pi}\right) \\ \sin ^{-1}\left(\frac{x}{\pi}\right) & -\tan ^{-1}(\pi x)\end{array}\right], \) then
\( A-B \) is equal to
\( A \)
B.
\( c .2 \)
\( D \cdot \underline{1} \)


A plant which manufactures its own
food is
A. Autotrophic
B. Symbiotic
c. Heterotrophic
D. Saprophyticç


A shipment of 8 similar microcomputers to a retail outlet
contains 3 that are defective. If aschool
makes a random purchase of 2 of these computers, find the probability distribution for the number of
defectives? Also, find its mean and
standard deviation.


The probability of a sure event is


A rubber ball dropped from a certain height is an example of
A. Uniform acceleration
B. Uniform retardation
C. Uniform speed
D. Non of these


Pollination by bat is called
A. Ornithophily
B. Chiropterophily
c. Malacophily
D. Anemophily


\( H_{2} S \) gas passed in all the following test
tube so that precipitation abserve so
which is correct match:
\( \boldsymbol{C u}, \boldsymbol{S b} \boldsymbol{Z n}, \boldsymbol{C d}, \boldsymbol{P d}, \boldsymbol{S n}, \boldsymbol{N i} \)
A . \( C d- \) Black
в. \( S b \) - orange
c. \( N i- \)yellow
D. \( Z n- \) Brown


The Binding energy per nucleon of \( _{3}^{7} L i \)
and \( _{2}^{4} H e \) nucleon are \( 5.60 M e V \) and
7.06 \( M e V \), respectively. In the nuclear
reaction \( _{3}^{7} L i+_{1}^{1} H \rightarrow_{2}^{4} H e+_{2}^{4} H e+Q \)
the value of energy \( Q \) released is
A. \( 19.6 \mathrm{MeV} \)
в. \( -2.4 \mathrm{MeV} \)
c. \( 8.4 \mathrm{MeV} \)
D. \( 17.3 \mathrm{MeV} \)


Fruit drop is prevented by spraying
A. Auxin
B. Ethylene
c. Gibberellins
D. cytokinins


The depletion region in a semiconductor diode is formed at the
Junction.
A. True
B. False


Three men \( A, B, C \) of mass \( 40 \mathrm{kg}, 50 \mathrm{kg} \) and \( 60 \mathrm{kg} \) are standing on a plank of mass \( 90 \mathrm{kg} \) which is kept on a smooth
horizontal plane B sits in the middle of
the plane \( B \) sits in the middle of the plane \( A \) and \( C \) sit 2 meters away from opposite sides. If \( A \) and \( C \) exchange there positions then mass B will shift


toppr
Q
5
particle with respect to time tis correctly shown in.
\( V \)


The correct order of heat of
hydrogenation of given molecule is :
\( A \cdot d>c>a>b \)
B. \( d>c>b>a \)
C. \( b>a>c>d \)
\( D \cdot d>a>c>b \)


The self induction of a coil having 400 turns is \( 10 \mathrm{mH} \). The magnetic flux through the cross section of the coil corresponding to current \( 2 \mathrm{mA} \) is :
A \( \cdot 2 \times 10^{-5} \mathrm{Wb} \)
В. \( 8 \times 10^{-3} \mathrm{Wb} \)
c. \( 4.3 \times 10^{-5} \mathrm{Wb} \)
D. \( 4.8 \times 10^{-3} \mathrm{Wb} \)


A girl standing in front of a vertical plane mirror, is able to see herself only upto her knees. She can see the lower
part of her legs, if :
A. she moves towards the mirror
B. she moves away from the mirror
c. she bends down
D. she stands on a stool


A body of mass \( m \) slides down a smooth inclined plane having an inclination of
\( 45^{\circ} \) with the horizontal. It takes 4 sec to
reach the bottom. If the body is placed on a similar plane having coefficient of friction \( 0.5 . \) What is the time taken for it
to reach bottom?
A \( .4 \sqrt{2} s e c \)
B. 4 sec
\( \mathrm{c} \cdot 3 \sqrt{2} \mathrm{sec} \)
D. \( 2 s e c \)


In a transformer, there are 10000 turns
in the primary coil and 25000 turns in the secondary coil.An AC EMF \( e= \)
\( 50 \sin \pi t \) is applied across primary coil
,find the peak EMF across the secondary coil in ideal conditions


Prime factors of 140 are :
A. \( 2 \times 2 \times 7 \)
В. \( 2 \times 2 \times 5 \)
c. \( 2 \times 2 \times 5 \times 7 \)
D. \( 2 \times 2 \times 5 \times 7 \times 3 \)


Identify the reaction that does not take place in a blast furnace.
A. \( C a C O_{3} \rightarrow C a O+C O_{2} \)
в. \( C a O+S i O_{2} \rightarrow C a S i O_{3} \)
\( \mathbf{c} \cdot 2 F e_{2} O_{3}+3 C \rightarrow 4 F e+3 C O_{2} \)
D. \( C O_{2}+C \rightarrow 2 C O \)


The atomicity of noble gases is:
A. diatomic
B. monoatomic
c. triatomic
D. tetraatomic


If you have a solution in equilibrium
containing \( C l^{-} \) ions and you added
NaCl to the solution, what is going to
happen?
A. The reaction will shift to the left to compensate for the increased concentration of \( C l^{-} \) ions
B. The reaction will become unbalanced and stay unbalanced
C. Le Chatelier's principle says that nothing will happen
D. More \( N a^{+} \) ions will be made so that concentrations of
\( N a^{+} \) and \( C l^{-} \) even out
E . Equilibrium will be restored


A conducting rod of length \( \boldsymbol{L}=\mathbf{0 . 1 m} \) is
moving with a uniform speed \( \boldsymbol{v}= \)
\( 0.2 m / s \) on conducting rails in a
magnetic field \( B=0.5 T \) as shown. On
one side, the end of the rails is
connected to a capacitor of capacitance \( C=20 \mu F . \) Then the charges on the
capacitor plates are :
A \( \cdot q_{A}=0=q_{B} \)
B \( \cdot q_{A}=+20 \mu C \) and \( q_{B}=-20 \mu C \)
\( \mathbf{c} \cdot q_{A}=+0.2 \mu C \) and \( q_{B}=-0.2 \mu C \)
\( \mathbf{D} \cdot q_{A}=-0.2 \mu C \) and \( q_{B}=-0.2 \mu C \)


Which of the following will have highest nucleophilicity?
\( \mathbf{A} \cdot \boldsymbol{\theta} \)
\( C l \)
B. \( \theta \) \( F \)
\( c . \theta \)
\( C H_{3} \)
D. \( \theta \) \( O H \)


The structure of \( \boldsymbol{S} \boldsymbol{i} \boldsymbol{O}_{2} \) ?
A. trigonal
B. linear
c. tetrahedral
D. angular


Differentiate the following functions
with respect to \( \boldsymbol{x} \)
\[
\mathbf{f} \boldsymbol{y}=\cot ^{-1}\left\{\frac{\sqrt{\mathbf{1}+\sin \boldsymbol{x}}+\sqrt{\mathbf{1}-\sin \boldsymbol{x}}}{\sqrt{\mathbf{1}+\sin \boldsymbol{x}}-\sqrt{\mathbf{1}-\sin \boldsymbol{x}}}\right\}
\]
\( 0<x<\frac{\pi}{2}, \) show that \( \frac{d y}{d x} \) is
independent of \( \boldsymbol{x} \)


Mark the incorrect option.
A. Ampere's law states that flux \( B \) through any closed
surface is \( \mu_{0} \) times the current passing through the area bounded by closed sourface
B. Gauss's law for magnetic field in magnetostatics serves the same purpose as Gauss's law for electric for electric field in electrostatics
C. Gauss's law for magnetic field states that the flux of \( B \) through any closed surface is always zero, whether or not there are currents within the surface
D. All the above


List two factors on which resistance of a
conductor depends.


Newton's law of motion were stated by
the scientist named as Charles-
Augustin
A. True
B. False


The aperture diameter of a telescope is
5 \( m \). The separation between the moon and the earth is \( 4 \times 10^{5} \mathrm{km} . \) With light of wavelength of \( 5500 A \), the minimum separation between objects on the surface of moon, so that they are just
resolved, is close to?
A. \( 60 \mathrm{m} \)
в. 20
c. 600 m
D. 200 m


\( \boldsymbol{C r}_{2} \boldsymbol{O}_{\mathbf{7}}^{2-} \stackrel{\boldsymbol{p H}=\boldsymbol{x}}{\boldsymbol{\longrightarrow} \boldsymbol{r} \boldsymbol{O}_{4}^{2-} \stackrel{\boldsymbol{p H}=\boldsymbol{y}}{\boldsymbol{U}} \boldsymbol{C}_{\mathbf{2}} \boldsymbol{O}_{\boldsymbol{7}}^{2-}} \)
pH values \( x \) and \( y \) can be:
A. 4 and 5
B. 4 and 8
\( c \cdot 8 \) and 4
D. 8 and 9


A metal wire of length L is loaded and an
elongation of \( \Delta L \) is produced. If the area of cross section of the wire is \( A \) then the change in volume of the wire, when elongated is. Take Poisson's ratio
as 0.25
A \( \cdot \Delta V=(\Delta L)^{2} A / L \)
B . \( \Delta V=(\Delta L)^{2} A / 4 L \)
c. \( \Delta V=(\Delta L)^{2} A / 2 L \)
D. \( \Delta V=(\Delta L)^{2} A / 3 L \)


Which of the following is /are type of reflection?
A. Regular reflection
B. Irregular reflection
c. Diffused reflection
D. All of the above


List I and List II contains four entries
each. Entries of List I are to be
matched some entries of List II. One or
more than one entries of List I may have
the match with the same entry of List II


Assertion
Concentrated and not dilute \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
behaves as a dehydrating agent.
Reason
Concentrated sulphuric acid behaves
as a strong dehydrating agent as the hydration reaction is highly exothermic. It has strong affinity for water removing water molecules from other compounds
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 bullet loses \( \frac{1}{20} \) of its velocity after
penetrating a plank. How many planks are required to stop the bullet?
\( \mathbf{A} \cdot \mathbf{9} \)
B. 11
\( c \cdot 7 \)
D.


Natural processes are:
A. reversible.
B. irreversible.
C. isothermal.
D. adiabatic.


If positive numbers \( x, y, z \) are in \( A . P \) then the minimum value of \( \frac{\boldsymbol{x}+\boldsymbol{y}}{\mathbf{2} \boldsymbol{y}-\boldsymbol{x}}+ \)
\( \frac{y+z}{2 y-z} \) is equal to


Due to an increase of \( 30 \% \) in the price of
eggs, 3 eggs less are available for Rs. 7.80. Find the increased price per
dozen?
A . Rs. 8.64
B. Rs. 8.88
\( c \cdot \) Rs. 9.36
D. Rs. 10.40


Which one of the following metal ion is coloured?
A \( \cdot T i^{2} \)
в. \( C u^{+} \)
c. \( V^{4+} \)
D. \( Z n^{2+} \)


A 2.00 g. of sample containing \( N a_{2} C O_{3} \) and \( N a H C O_{3} \) loses 0.248 g when
heated to \( 300^{\circ} \mathrm{C} \), the temperature at
which \( N a H C O_{3} \) decomposes.Find \%
composition of \( N a_{2} C O_{3} \) in the mixture
\( ? \)


If the energy \( (\boldsymbol{E}), \) velocity \( (\boldsymbol{v}) \) and force
\( (F) \) be taken as fundamental
quantities, then the dimensions of
mass will be
A. \( F v^{-2} \)
B. \( F v^{-1} \)
\( \mathbf{c} \cdot E v^{-2} \)
D. \( E v^{2} \)


Energy dependent absorption of water against osmotic gradient is
A. Active absorption
B. Passive absorption
c. Imbibition
D. Bulk absorption


A vessel contains air at a temperature
of \( 15^{0} C \) and \( 60 \% \) R.H. What will be the
R.H if it is heated to \( 20^{0} C ? \) (S.V.P at
\( 15^{0} C \) is \( 12.67 \& \) at \( 20^{0} C \) is \( 17.36 \mathrm{mm} \) of
Hg respectively)
A . 262\%
B . 26.2\%
c. \( 44.5 \% \)
D. 46.2\%


A natural number \( x \) is chosen at
random from the first 120 natural
numbers and it is observed to
be divisible by 8 , then the probability that it is not divisible by 6 is
\( A \cdot \frac{1}{3} \)
B.
\( c \cdot \frac{3}{4} \)
D. \( \frac{2}{3} \)


The frequency of alternating current in
India is
A. 50 cylces/s
B. 100 cylces/s
c. 150 cylces/s
D. 200 cylces/s


For absorption and emission spectra of atoms which one of the following particle changes energy levels?
A. Alpha
B. Electron
c. Neutron
D. Photon
E. Proton


\( \mathbf{f} \mathbf{\Delta}=\left|\begin{array}{ccc}\mathbf{1} & \mathbf{5} & \mathbf{6} \\ \mathbf{0} & \mathbf{1} & \mathbf{7} \\ \mathbf{0} & \mathbf{0} & \mathbf{1}\end{array}\right| \) and \( \Delta^{\prime}=\left|\begin{array}{ccc}\mathbf{1} & \mathbf{0} & \mathbf{1} \\ \mathbf{3} & \mathbf{0} & \mathbf{3} \\ \mathbf{4} & \mathbf{6} & \mathbf{1 0 0}\end{array}\right| \)
then
A \( \cdot \Delta^{2}-3 \Delta^{\prime}=0 \)
B. \( \left(\Delta+\Delta^{\prime}\right)^{2}-3\left(\Delta+\Delta^{\prime}\right)+2=0 \)
c. \( \left(\Delta+\Delta^{\prime}\right)^{2}+3\left(\Delta+\Delta^{\prime}\right)+5=0 \)
D. \( \Delta+3 \Delta^{\prime}+1=0 \)


n Fig. \( P Q R \) is an equilateral
triangle. Arcs have been drawn with
radii \( 14 \mathrm{cm} \) each and with centres \( \boldsymbol{P}, \boldsymbol{Q} \)
and \( R \). The area of the shaded region is
A \( \cdot 102.6 \mathrm{cm}^{2} \)
B \( .206 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 308 \mathrm{cm}^{2} \)
D. \( 345 \mathrm{cm}^{2} \)


The ratio of the radii of gyration of the disc about its axis and about a tangent perpendicular to its plane will be:
A \( \cdot \frac{1}{\sqrt{3}} \)
в. \( \sqrt{\frac{3}{2}} \)
c. \( \frac{1}{\sqrt{2}} \)
D. \( \sqrt{\frac{5}{3}} \)


Find the points of intersection of the
line \( x-y+2=0 \) and the circle \( 2 x^{2}+ \)
\( 2 y^{2}-29 x-19 y+56=0 . \) Also
determine the length of the chord intercepted.


The overall formation constant for the
reaction of 6 mole of \( C N^{-} \) with cobalt
(II) is \( 1 \times 10^{19} . \) Given that
\( \boldsymbol{C o}(\boldsymbol{C N})_{\boldsymbol{6}}^{\boldsymbol{3}-}+\boldsymbol{e} \rightarrow \boldsymbol{C o}(\boldsymbol{C N})_{\boldsymbol{6}}^{\boldsymbol{4}-} ; \boldsymbol{E}_{\boldsymbol{R} \boldsymbol{P}}^{\boldsymbol{o}}= \)
\( -0.83 V \)
\( \boldsymbol{C o}^{3+}+\boldsymbol{e} \rightarrow \boldsymbol{C o}^{2+} ; \boldsymbol{E}_{R P}^{o}=\mathbf{1 . 8 2} \boldsymbol{V} \)
If the formation constant for the
reaction of 6 mole of \( C N^{-} \) with cobalt
(III) is \( x \times 10^{63} \) then \( 100 x \)
is


If \( y \) and \( z \) are the functions of \( x \) and if \( \boldsymbol{y}^{2}+\boldsymbol{z}^{2}=\boldsymbol{\lambda}^{2}, \) then \( \boldsymbol{y} \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left(\frac{\boldsymbol{y}}{\boldsymbol{\lambda}}\right)+ \)
\( \frac{d}{d x}\left(\frac{z^{2}}{\lambda}\right) \) is equal to
A \( \cdot \frac{z}{\lambda} \frac{d z}{d x} \)
B. \( \frac{z}{\lambda} \frac{d x}{d z} \)
c. \( \frac{\lambda}{z} \frac{d z}{d x} \)
D. None of these


Do electromagnetic waves carry energy
and momentum?


A man spinning in free space changes the shape of his body, eg. by spreading his arms or curling up. By doing this, he can change his :
This question has multiple correct options
A. moment of inertia
B. angular momentum
c. angular velocity
D. rotational kinetic energy


nace
resistance \( 2 \Omega \) is connected with two
resistors \( A \) and \( B \) of resistance \( 4 \Omega \) and
\( 6 \Omega \) respectivelyjoined in series. Find:
(i) Current in the circuit.
(ii) The terminal voltage of the cell.
(iii) The potential difference across \( 6 \Omega \)
Resistor.
(iv) Electrical energy spent per minute
in \( 4 \Omega \) Resistor.


Why does \( H e \) exist whereas \( H e_{2} \) does
not?


As the carbon chain increases in
aldehyde and ketone compounds, solubility in water:
A . decreases
B. increases
c. may increase
D. may decrease


Photorespiration takes place only in
A. Lysosomes of plant cell
B. Yellow parts of the plant
c. Mitochondria of plant cell
D. None of the above


Which has maximum ionisation
potential?
A. \( N \)
в. \( O \)
\( c \cdot O^{+} \)
D. \( N a \)


Fill in the blank.
If \( 100 \mathrm{mL} \) of \( S O_{2} \) solution requires 50 \( \mathrm{mL} \) of \( 0.01 \mathrm{M} C r_{2} O_{7}^{2-} \) in acidic
medium, then \( S O_{2} \) solution is
\[
\mathbf{1 0}^{-\mathbf{3}} \mathbf{M}
\]


Find the initial velocity of projection of a ball thrown vertically up if the distance moved by it in \( 3^{r d} \) second is twice the
distance covered by it in 5th second. (Take \( \left.g=10 \mathrm{m} s^{-2}\right) \)
A. \( 85 \mathrm{m} s^{-1} \)
B. 75 \( \mathrm{m} s^{-1} \)
c. \( 65 \mathrm{m} s^{-1} \)
D. \( 95 \mathrm{m} s^{-1} \)


Due to air a falling body faces a resistive force proportional to square of velocity \( v, \) consequently its effective
downward acceleration is reduced and
is given by \( a=g-k v^{2} \) where \( k= \)
\( 0.002 m^{-1} . \) The terminal velocity of the
falling body is \( (\operatorname{in} \mathrm{m} / \mathrm{s}) \)
A . 60
B. 70
c. 80
D. 90


The sum of the squares of deviations of
a set of values is minimum when taken
about
A . \( A M \)
в. \( G M \)
с. \( H M \)
D. median


These questions consist of two statements each, printed as assertion and reason. While answering these questions you are required to choose anyone of the following five responses.
Assertion: Ozone is powerful oxidising
agent in comparison to \( \boldsymbol{O}_{\mathbf{2}} \)

Reason: Ozone is diamagnetic but \( \boldsymbol{O}_{2} \)
is paramagnetic.
A. If both assertion and reason are true and the reason is correct explanation of the assertion
B. If both assertion and reason are true but reason is not correct explanation of the assertion
c. If the assertion is true but reason is false
D. If both the assertion and reason are false
E. If the assertion is false but the reason is true


The space between cornea and eye lens is filled with a liquid known as:
A. aqueous humour
B. vitreous humour
c. corneal fluid
D. none of these


At perihelion, the gravitational potential energy of Pluto in its orbit has
A. its maximum value
B. its mimimum value
c. the same value as at every other point in the orbitt
D. value which depends on sense of rotation


Camphor can be separated using:
A. distillation
B. sublimation
C. fractional distillation
D. centrifugation


Insoluble impurities from solution during crystallization are removed by :
A. drying
B. filtration
c. heating
D. cooling


In higher plants, continuity of
cytoplasm from one cell to its neighboring cells is established through the
A. Apoplast
B. Chloroplast
c. Leucoplast
D. symplast


Which is formed when
\( K_{2} C r_{2} O_{7}, C a C l_{2}, \) and conc. \( H_{2} S O_{4} \) are
heated?
\( \mathbf{A} \cdot C r_{2}\left(S O_{4}\right) \)
в. \( C r C l_{3} \)
\( \mathrm{c} \cdot \mathrm{Cr} \mathrm{O}_{2} \mathrm{Cl}_{2} \)
D. \( K_{2} C r O_{4} \)


Which of the following segments has photoreceptors in cockroach?
A. Head
B. Abdomen
c. Thorax
D. None of the above


Silk, honey and lac are.
A. Secretory products of animalss
B. Secretory products of plants.
c. Synthetic chemicals
D. Both A and C


What will the course of action if a
person goes through a kidney failure


Which of the following has more inertia
\( ? \)
A rubber ball or a stone of the same size


The three vertices of a parallelogram taken in order are (-1,0),(3,1) and (2,2) respectively.Find the coordinates of the fourth vertex


An example of an equipotential surface
in earth is
A. A line passing through the centre of the earth connecting two points along the diameter
B. A plane that passes through the circular section of the hemisphere of the earth
C. A spherical surface at a distance of 1km from the surface of the earth with its centre at centre of earth
D. A plane on the surface of the earth, which is a tangent to the earth


The uses of ammonia is/are:
A. manufacture of Explosives
B. manufacture of Plastics and Raisins
\( \mathrm{C} \). it is a main source of hydrogen
D. all of the above


Match the geometry (given in column A) with the complexes (given in column B)
Geometry : A Complex : B
I: Octahedral
\[
\mathrm{P}:\left[N i(C N)_{4}\right]^{2}
\]
\( \| \)
Square planar
\[
\mathrm{Q}: N i(C O)_{4}
\]
III. Tetrahedral \( \mathrm{R}:\left[F e(C N)_{6}\right]^{4-} \)
A. I-P, II-Q, III-R
B. I-R, II-P, III-Q
c. ।-R, ॥-Q, ॥|-P
D. I-Q, II-P, III-R


The north poles of pole strengths \( \mathrm{m}, 9 \mathrm{m} \) are kept apart by a certain distance. Find the distance of full point from
larger pole.
A \( \cdot \frac{3 d}{4} \)
в. \( \frac{3 d}{8} \)
c. \( \frac{3 d}{16} \)
D. \( \frac{3 d}{2} \)


\( \lim _{x \rightarrow 0} \frac{\sin \left(\pi \cos ^{2} x\right)}{x^{2}}= \)


The continuity of water column in xylem is maintained due to
A. Evaporation of water
B. Cohesive property of water
c. Pressure of air bubbles in water
D. Small size of xylem vessels


Resistivity of pure metal is:
A. less than alloys
B. more than alloys
c. equal to alloys
D. unpredictable


The prefix zepto stands for:
[Note : unit in \( \mathrm{m}] \)
A \( \cdot 10^{9} \)
B. \( 10^{-12} \)
\( \mathbf{c} \cdot 10^{-15} \)
D. \( 10^{-21} \)


If \( S_{0}, S_{1}, S_{2} \) and \( S_{3} \) are the solubilities
in water of \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l} \)
\( \mathbf{0 . 0 1} \boldsymbol{M} \boldsymbol{C a C l}_{2}, \mathbf{0 . 0 1} \boldsymbol{M} \boldsymbol{N a C l} \) and
\( \mathbf{0 . 5} \boldsymbol{M} \boldsymbol{A} \boldsymbol{g} \boldsymbol{N} \boldsymbol{O}_{3} \) solutions, respectively
then which of the following is true?
A \( . S_{0}>S_{2}>S_{1}>S_{3} \)
B. \( S_{0}=S_{2}=S_{1}>S_{3} \)
c. \( S_{3}>S_{1}>S_{2}>S_{0} \)
D. none of these


The equation \( y=4 \sin \pi\left[200 t-\left(\frac{x}{25}\right)\right] \)
represents a transverse wave that
travels in a stretched wire, where \( \boldsymbol{x}, \boldsymbol{y} \)
are in \( c m \) and \( t \) in second.
Its wavelength and velocity are
A \( \cdot 0.5 m, 25 m s^{-1} \)
B . \( 0.5 m, 50 m s^{-1} \)
c. \( 1 m, 50 m s^{-1} \)
D. \( 1 m, 25 m s^{-1} \)


Find the radius of the circle whose
circumference is \( 44 \mathrm{cm} .(\pi=22 / 7) \)


Cadmium rods are used as moderators
in a nuclear reactor
A. True
B. False


If radius of circle is \( 5 \mathrm{cm} \) and distance
from centre to the point of intersection of 2 tangents in \( 13 \mathrm{cm} . \) Find length of
tangent.
A . \( 11 \mathrm{cm} \)
B. \( 10 \mathrm{cm} \)
c. \( 12 \mathrm{cm} \)
D. \( 13 \mathrm{cm} \)


Boric acid is polymeric due to
A. its acidic nature
B. presence of H-bonds
C. its monobasic nature
D. its geometry


\( x-t \) equation of a particle in SHM is,
\( \boldsymbol{x}=\mathbf{4}+\mathbf{6} \sin \boldsymbol{\pi} \boldsymbol{t} \)
Match the following tables corresponding to time taken in moving from:


At \( t=0, \) a force \( F=k t \) is applied on a
block making an angle \( \alpha \) with the horizontal. Assume surfaces to be
smooth. Find the velocity of the body at the time of breaking off the plane:
\( ^{A} \cdot \frac{m g \cos \alpha}{2 k \sin \alpha} \)
B. \( \frac{m^{2} g^{2} \cos \alpha}{2 k \sin ^{2} \alpha} \)
c. \( \frac{m g^{2} \cos \alpha}{2 k \sin ^{2} \alpha} \)
D. \( \frac{m g^{2} \cos \alpha}{2 k \sin \alpha} \)


Let \( \vec{F} \) be the force acting on a particle having position vector \( \vec{r} \) and \( \vec{\tau} \) be the torque of this force about the origin then:
\( \mathbf{A} \cdot \vec{r} \cdot \vec{\Gamma}=0 \) and \( \vec{F} \cdot \vec{\Gamma} \neq 0 \)
B . \( \vec{r} . \vec{\Gamma} \neq 0 \) and \( \vec{F} . \vec{\Gamma}=0 \)
c. \( \vec{r} . \vec{\Gamma} \neq 0 \) and \( \vec{F} \cdot \vec{\Gamma} \neq 0 \)
D. \( \vec{r} . \vec{\Gamma}=0 \) and \( \vec{F} \cdot \vec{\Gamma}=0 \)


State the laws of refraction.


Chlorine is prepared in the laboratory by the reaction between:
A. \( Z n \) and \( H C l \)
в. \( M n O_{2} \) and \( H C l \)
c. \( C a C O_{3} \) and \( H C l \)
D \( \cdot P b\left(N O_{3}\right)_{2} \) and \( H C l \)


Assertion
\( \int_{-\pi / 4}^{\pi / 4} x^{3} \sin ^{4} x d x \neq 0 \)
Reason
\( \int_{-a}^{a} f(x) d x=0 \) if \( f(-x)=-f(x) \)
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


The eccentricity of the ellipse \( 12 x^{2}+ \) \( 7 y^{2}=84 \) is equal to:
A \( \frac{\sqrt{5}}{7} \)
B. \( \sqrt{\frac{5}{7}} \)
c. \( \frac{\sqrt{5}}{12} \)
D.
E. \( \frac{7}{12} \)


Atoms may be regarded as comprising of protons, neutrons and electrons. If the
mass attributed to a neutron were
halved and that attributed to the
electron were doubled, the atomic mass
of \( \frac{12}{6} \mathrm{C} \) would:
A. remain approximately the same
B. be approximately doubled
c. be approximately halved
D. be reduced approximately by 25\%


What is the momentum of an object of
mass \( m, \) moving with a velocity \( v ? \)
A \( \cdot(m v)^{2} \)
a) \( ^{\infty} \)
B. \( m v^{2} \)
c. \( 1 / 2 m v^{2} \)
D. \( m v \)


Consider the railway platform which is in square shape having side length \( 2 k m . \) Then area of the platform is 4
A . \( m \)
в. \( k m \)
\( \mathrm{c} \cdot k m^{2} \)
D. \( m^{2} \)


Three charges, each \( +q \), are placed at
the corners of an isosceles triangle
\( A B C \) of sides \( B C \) and \( A C, 2 a . D \) and \( E \)
are the mid points of \( B C \) and \( C A \). The
work done in taking a charge \( Q \) from \( D \)
to \( \boldsymbol{E} \) is :
A \( \cdot \frac{e q Q}{8 \pi \epsilon_{0} a} \)
в. \( \frac{q Q}{4 \pi \epsilon_{0} a} \)
c. zero
D. \( \frac{3 q Q}{4 \pi \epsilon_{n} a} \)


toppr
Q Type your question
solution?
\( A \)
3
\( c \)
\( D \)


Focal length of a lens is \( 50 \mathrm{cm} \). Its power would be:
A. 50 dioptres
B. 2 dioptres
c. 20 dioptres
D. None of these


\( \left(14 x^{2} y z-28 x^{2} y^{2} z^{3}+32 y^{2} z^{2}\right) \div \)
\( (-4 x y) \)
A. \( \frac{7}{2} y z+7 x y z^{2}+8 x y z \)
B. \( -\frac{7}{2} x z+7 x y z^{3}-\frac{8 y z^{2}}{x} \)
c. \( -\frac{7}{2} x z-7 x y z^{3}+\frac{8 y z^{2}}{x} \)
D. \( \frac{7}{2} x z-7 x y z^{2}-\frac{8 y z^{2}}{x} \)


Only one subject
A . 0.72
B. 0.36
c. 0.48
D. 0.24


Which of the following is a locomotory organ in a snail?
A. Outer snail
B. Muscular foot
c. Muscular rings
D. All of the above


Length of exposed portion of top of box is equal to
\( \mathbf{A} \cdot 2 m \)
в. \( 3 m \)
c. \( 4 m \)
D. \( 2.5 m \)


If the rate of reaction is equal to the rate constant, the order of the reaction is:
A. 0
B.
\( c \cdot 2 \)
\( D \)


The side of an equilateral triangle is \( 20 \sqrt{3} \mathrm{cm} . \) The numerical value of the
radius of the circle circumscribing the triangle is:
\( \mathbf{A} \cdot 20 \mathrm{cm} \)
в. \( 20 \sqrt{3} \mathrm{cm} \)
c. \( 20 \pi c m \)
D. \( \frac{20}{\pi} \)


is the first and the only state in India, which has made roof top rain
water harvesting structure and is compulsory to all the houses across the
state
A. Tamil Nadu
B. Andhra Pradesh
c. Maharashtra
D. Madhya Pradesh


Two identical rods each of moment of
inertia \( ^{\prime} I^{\prime} \) about a normal axis through
centre are arranged in the from of a cross. The \( M . I . \) of the system about an
axis through centre and perpendicular
to the plane of system is:
A . \( 2 I \)
B. \( I \)
c. 2.5
D. \( 6 I \)


Acetyl salicylic acid (aspirin) ionises in
water as: \( \boldsymbol{H} \boldsymbol{C}_{9} \boldsymbol{H}_{7} \boldsymbol{O}_{4}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \)
\( \boldsymbol{H}_{3} \boldsymbol{O}^{+}+\boldsymbol{C}_{9} \boldsymbol{H}_{7} \boldsymbol{O}_{4}^{-} ;\left(\boldsymbol{K}_{a}=\boldsymbol{2} . \boldsymbol{7} \boldsymbol{5} \times \mathbf{1} \boldsymbol{0}^{-\boldsymbol{9}}\right) \)
If two tablets of aspirin each of 0.32 g is dissolved in water to produce \( 250 \mathrm{mL} \) solution, calculate \( [\stackrel{\ominus}{\boldsymbol{O}} \boldsymbol{H}] \)
A \( \cdot 1.61 \times 10^{-9} M \)
В. \( 1.61 \times 10^{-7} \) М
c. \( 1.61 \times 10^{-3} M \)
D. \( 1.61 \times 10^{-5} M \)


Find the square root of the following
decimal fraction:
\( \mathbf{0 . 0 6 2 5} \)


A newly discovered element \( X \) is placed
in group \( I A \) of the periodic table since it forms :
A. an oxide which is acidic
B. a volatile chloride having a formula \( X C l \)
c. an ionic chloride having the formula \( X C l \)
D. an insoluble \( X S O_{4} \)


The \( \boldsymbol{K}_{s p}\left(\mathbf{2 5}^{o} \boldsymbol{C}\right) \) of sparingly salt
\[
\boldsymbol{X} \boldsymbol{Y}_{2}(\boldsymbol{s}) \text { is } \boldsymbol{3} . \mathbf{5 6} \times \mathbf{1 0}^{-5}\left(\boldsymbol{m o l} \quad \boldsymbol{L}^{-1}\right)^{3}
\]
and at \( 30^{\circ} \mathrm{C} \),the vapour pressure of its saturated solution in water is \( 31.78 \mathrm{mm} \)
of Hg.Calculate the enthalpy change of the reaction.( write your answer to
nearest integer)
\[
\boldsymbol{X} \boldsymbol{Y}_{2}(\boldsymbol{s}) \rightleftharpoons \boldsymbol{X}^{2+}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{2} \boldsymbol{Y}^{\ominus}(\boldsymbol{a} \boldsymbol{q})
\]
Given : Vapour pressure of pure water \( =31.82 \mathrm{mm} \) of \( \mathrm{Hg} \)


Which of the following statement is
false regarding isotopes?
A. They are atoms of same element having same number of protons and electrons but different number of neutrons.
B. Isotopes of an element have similar chemical perperties but different physical properties.
C. All the isotopes of an element have same number of valence electrons
D. The three isotopes of hydrogen (Protium, Deuterium and Tritium) contains one, two and three neutrons respectively.


The lens used to correct long sightedness or hypermetropla.
A. Convex lens
B. Concave lens
c. simple lens
D. Cylindrical lens


Which of the following is used in the hydrogenation of vegetable oils?
A \( \cdot C l_{2} \)
в. \( N_{2} \)
\( c \cdot O_{2} \)
D. \( H_{2} \)


State whether the given statement is
true or false:

Interhalogen compounds are strong reducing agents.
A. True
B. False


If \( 2 \vec{a} \cdot \vec{b}=|\vec{a}||\vec{b}| \) then the angle between \( \vec{a} \) and \( \vec{b} \) is
A \( .30^{\circ} \)
в. \( 0^{\circ} \)
\( c \cdot 90^{\circ} \)
D. \( 60^{\circ} \)


\( 10^{-4} m^{2} \) and a resistance of \( 2 \Omega \) (figure)
The larger circular loop is fixed and has
a radius of \( 0.1 m . \) Both the loops are
concentric and coplanar. The smaller
loop is rotated with an angular velocity
end \( s^{-1} \) about its diameter. The
magnetic flux with the smaller loop is
A \( \cdot 2 \pi \times 10^{-6} W b \)
В \( \cdot \pi \times 10^{-9} W b \)
C \( \cdot \pi \times 10^{-9} \cos \omega t W b \)
D. zer


By what least number 4320 be multiplied to become a perfect cube?
A . 10
B. 30
c. 20
D. 50


Which one of the following compounds,
on transamination, DOES NOT result in
one of the genetically-coded 20 amino
acids?
\( A \)
B.
\( c \)
\( D \)


Find the area of the segment \( \boldsymbol{A Y B} \)
show in the figure, if radius of the circle
is \( 21 c m \) and \( \angle A O B=120^{\circ} \) (Use \( n= \)
\( \frac{22}{7} \)


If an LC circuit has \( C=1 \mu F \)
\( \& \boldsymbol{L}= \)
0.25 henry. neglecting any resistance in the circuit, what is the frequency of oscillation?


Assertion
\( \mathrm{f} \sin ^{-1} x+\sin ^{-1} y+\sin ^{-1} z=\frac{3 \pi}{2}, \) then
\( \frac{3 \sum_{r=1}^{2008}\left(x^{r}+y^{r}\right)}{2 \sum_{r=1}^{2008}\left(x^{r} y^{r}\right)}=3 \)
Reason
\( \sin ^{-1} x+\sin ^{-1} y+\sin ^{-1} z=\frac{3 \pi}{2} \) is
possible only if \( \boldsymbol{x}=\boldsymbol{y}=\boldsymbol{z}=\mathbf{1} \)
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 false but Reason is true


The extraction of metals from their ores
and then refining them for use is known
as
A. metallurgy
B. extacting
c. metal technology
D. none of these


What are magnetic field lines? How is the direction of magnetic field at a
point in a magnetic field determined using field lines?


Isoelectronic structural molecules are:
This question has multiple correct options
\( \mathbf{A} \cdot C H_{3}^{+} \)
B. \( H_{3}^{+} O \)
\( \mathbf{c} \cdot N H_{3} \)
D. \( C H_{3}^{-} \)


Two circles with centres \( A \) and \( B \) of
radii \( 3 \mathrm{cm} \) and \( 4 \mathrm{cm}, \) respectively
intersect at two points \( C \) and \( D \) such that \( A C \) and \( B C \) are tangents to the
two circles. Find the 10 times length of
the common chord \( C D \)
A .48
B. 58
\( c \cdot 56 \)
D. 54


A substance 'P' does not have a fixed,
volume. It occupies the total space of the container and it can be compressed. What is 'P' likely to be?
A. Solid
B. Liquid
c. Gas
D. All of these


The term meristem was coined by
A. Hanstein
B. Nageli
c. Schmidt
D. Esau


The reactivity of the metals
\( A l, C a, M g \) and \( N a \) follows the order.
A. \( N a>C a>M g>A l \)
в. \( N a>M g>C a>A l \)
c. \( A l>M g>C a>N a \)
D. \( M g>N a>C a>A l \)


The radius vector drawn from the sun to
a planet sweeps out areas
in equal time.
A. equal
B. unequal
c. greater
D. less


The reflecting surface of a plane mirror is vertical. A particle is a project in a vertical plane also perpendicular to the mirror the initial speed of the particle
is \( 10 \mathrm{m} / \mathrm{s} \) and the angle of project \( 60^{\circ} \)
from the normal of the mirror. the point of projection is at a distance \( 5 \mathrm{m} \) from particle moves towards the mirror.just before the particle touches the mirror.
the velocity of approving of the particle
and the image is:
A. \( 12 \mathrm{m} / \mathrm{s} \)
B. \( 5 \mathrm{m} / \mathrm{s} \)
c. \( 10 \mathrm{m} / \mathrm{s} \)
D. \( 5 \sqrt{5} \) m/s


the fundamental period, if any, of the
functions:
\( \sin (x / 3) \) is \( k \pi, \) then \( k \) is


A charge \( Q \) is distributed over two concentric hollow spheres of radii \( r \) and
\( R(R>r) \) such that their surface
densities are equal. The charge on smaller and bigger shells are:
A. \( \frac{Q r^{2}}{r^{2}+R^{2}} \) and \( \frac{Q R^{2}}{r^{2}+R^{2}}, \) respectively
в. \( Q\left(1+\frac{r^{2}}{R^{2}}\right) \) and \( Q\left(1+\frac{R^{2}}{r^{2}}\right) \), respectivel
\( ^{\mathrm{c}} Q\left(1-\frac{r^{2}}{R^{2}}\right) \) and \( Q\left(1-\frac{R^{2}}{r^{2}}\right) \), respectivel
D. \( \frac{Q R^{2}}{r^{2}+R^{2}} \) and \( \frac{Q r^{2}}{r^{2}+R^{2}}, \) respectively


Solutions of alkali metals in liquid
ammonia at \( -33^{\circ} \mathrm{C} \) conduct electricity
without chemical reaction at the
electrodes. Hence, conductivity should :
A. increase as temperature is lowered
B. decrease as temperature is lowered
c. remain constant on changing the temperature
D. there is always interaction of alkali metal with liquid ammonia


Q Type your question
the shape of track is defined by equation \( y=\frac{x^{2}}{a} \) where \( a \) is a constant.
A ring of mass \( m \) which can slide freely
on wire track, is placed at the position
\( (a, a) . \) The track is rotated
with constant angular speed \( \omega \) such
that there is no relative slipping
between the ring and the track then \( \omega \) is
equal to
A. \( \sqrt{\frac{2 g}{a}} \)
B. \( \sqrt{\frac{g}{a}} \)
c. \( \sqrt{\frac{g}{2 a}} \)
D. None of these


Annual rings are formed basically due
to
A. Marked seasonal variations
B. Different development of xylem and phloem
c. Uniform climate conditions
D. Different kinds of phloem


For what angle \( \theta \) does the induced emf
have the largest amplitude?


Isotopes that are used in nuclear imaging include:
A. fluorine-18
B. iodine-123
c. nitrogen-13
D. All of the above


The resistance of platinum wire is 2.4
ohms at \( 0^{\circ} \mathrm{C} \) and 3.4 ohms at \( 100^{\circ} \mathrm{C} \). If
the resistance at \( t^{\circ} C \) is 4 ohms then the
temperature \( t \) is equal to
A \( \cdot 160^{\circ} \mathrm{C} \)
В. \( 140^{\circ} \mathrm{C} \)
c. \( 180^{\circ} \mathrm{C} \)
D. \( 120^{\circ} \mathrm{C} \)


From the given examples which one is not considered as vegetable fibre?
A. cotton
B. Jute
c. Nylon
D. silk


If \( 0 \leq x \leq \pi, \) the interval in which the
function \( f(x)=\frac{\tan x}{\sin x} \) is defined is:
A. \( 0 \leq x \leq \pi \)
В. \( 0<x<\pi \)
c. \( 0<x<\frac{\pi}{2} \)
D \( \cdot \frac{\pi}{2}<x \leq \pi \)
E \( \cdot 0<x<\frac{\pi}{2} \) and \( \frac{\pi}{2}<x<\pi \)


Oral administration of small doses of
which of the following hormonal drugs are popular contraceptive methods used by the females?
A. Progesterone
B. Progesterone and estrogen
c. Lactogen
D. Both A and B


Which of the following physical quantities has the same units as that of impulse?
A. Momentum
B. Force
c. Torque
D. couple


A ray of monochromatic light is incident on one refracting face of a prism of
angle \( 75^{\circ} . \) It passes through the prism and is incident on the other face at the
critical angle. If the refractive index of the material of the prism is \( \sqrt{2} \), the angle of incidence on the first face of
the prism is:
A . \( 30^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 0^{\circ} \)


A die is thrown. Write the sample space.
If \( A \) is the event that the number is less
than four, write the event \( \boldsymbol{A} \) using set
notation.


COM of a semicular here


Two parallel plate capacitor of capacitances \( C \) and \( 2 C \) are connected in parallel and charged to a potential difference V. If the battery
is disconnected and the space between the plate of the capacitor of capacince \( C \) is completely filled with a material of dielectric constant \( K, \) then the potential difference across the capacitor will be
come
A. \( 3 V(K+2) \)
B. \( \frac{(K+2)}{3 V} \)
c. \( \frac{3 V}{(K+2)} \)
D. \( \frac{3(K+2)}{V} \)


Gases begin to conduct electricity at
low pressure because:
A. at low pressure gases turn to plasma
B. colliding electrons can acquire higher kinetic energy due to increased mean free path leading to ionisation of atoms
C . atoms break up into electrons and protons
D. the electrons in atoms can move freely at low pressure


Which of the following sets is of coinage metals?
A. \( C u, A g, A u \)
в. \( Z n, \)Сд\( , \)Н \( g \)
c. \( A u, A g, Z n \)
D. \( L i, N a, K \)


The work done to pull them (the
molecules apart if they are at \( R_{0}, \) is:
A. \( U_{0} \)
в. \( 2 U_{0} \)
c. \( -2 U_{0} \)
D. none


Prove the following by using principle of mathematical induction for all \( \boldsymbol{n} \in \boldsymbol{N} \)
\( \mathbf{1} . \mathbf{3}+\mathbf{3 . 5}+\mathbf{5 . 7}+\ldots \ldots .+(\mathbf{2 n}- \)
\( \mathbf{1})(\mathbf{2 n}+\mathbf{1})=\frac{\boldsymbol{n}\left(\mathbf{4} \boldsymbol{n}^{2}+\mathbf{6} \boldsymbol{n}-\mathbf{1}\right)}{\mathbf{3}} \)


Which of the following is not the basic postulate(s) of Dalton's atomic theory?
A. Atoms are neither created nor destroyed in a chemical reaction
B. In a compound, the relative number and kinds of atom are constant
c. Atoms of all elements are alike, including their masses
D. Each element is composed of extremely small particles called atoms


Freon used as refrigerant is:
A. \( C F_{2}=C F_{2} \)
в. \( C H_{2} F_{2} \)
c. \( C C l_{2} F_{2} \)
D. \( C F_{4} \)


If in an A.C., L-C series circuit \( \boldsymbol{X}_{c}>\boldsymbol{X}_{\boldsymbol{L}} \)
Hence potential
A. Lags behind the current by \( \pi / 2 \)
B. Leads the current by \( \pi \) in phase
c. Leads the current by \( \pi / 2 \) in phase
D. Lags behind the current by \( \pi \) in phase


Which of the following practices will not
come under green chemistry?
A. If possible, making use of soap made of vegetable oils instead of using synthetic detergents.
B. Using \( H_{2} O_{2} \) for bleaching purpose instead of using chlorine based bleaching agents.
C. Using bicycle for travelling small distances instead of using petrol/diesel based vehicles.
D. Using plastic cans for neatly storing substances.


During dispersion through prism, red light travels fastest and violet travels
slowest of all the seven colours. As a
result:
A. red bends the least and violet bends the most
B. red bends the most and violet bends the least
C. both red and violet bend the least of all colours
D. both red and violet bend the most of all colours


A body of mass \( 1 \mathrm{kg} \) falls freely form a height of \( 100 \mathrm{m}, \) on a platform of mass 3 kg which is mounted on a spering having spering constant \( \mathrm{k}=1.25 \) \( \times 10^{6} N / m . \) The body sticks to the platform and the spring's maximum compression is found to be \( x \). Given that
\( \mathrm{g}=10 \mathrm{m} \mathrm{s}^{-2}, \) the value of \( \mathrm{x} \) will be close
to :
A. \( 4 \mathrm{cm} \)
B. \( 8 \mathrm{cm} \)
\( c \cdot 80 \mathrm{cm} \)
D. 40 cm


Methyl orange is used as an indicator. It shows colour changes in acid, base and
neutral substance. Tabulate your
results as follows:
Inference interence \( \begin{array}{ll}\text { Indicator } & \text { Colour Change } \\ & \text { No change } \\ \text { Methyl Orange } & \cdots \\ & \text { Yellow }\end{array} \) Acid


A ball is thrown vertically upwards with
a velocity \( u \). What is the maximum
height to which it will rise before falling back?
A \( \cdot u^{2} / 2 g \)
в. \( g / u \)
\( \mathrm{c} \cdot 2 g / u \)
D. \( u / 2 g \)


The reaction: \( 3 C l O^{-} \rightarrow C l O_{3}^{-}+2 C l^{-} \)
is an example of
A. Oxidation reaction
B. Reduction reaction
c. Disproportionation reaction
D. Decomposition reaction


The longest rod that can be placed flat on the bottom of a box is \( 45 \mathrm{cm} \). The box
is \( 8 \mathrm{cm} \) longer than it is wide. Find the
length and breadth of the box.


The band spectrum is caused by:
A . molecules
B. atoms
c. any substance in solid state
D. any substance in liquid state


For gaseous reaction, the unit of the
rate of reaction is:
\( A \cdot L a t m \sec ^{-1} \)
B. atm mol sec \( ^{-1} \)
\( \mathbf{c} \cdot \operatorname{atm} \sec ^{-1} \)
D. mol sec


Which of the assumptions of the kinetic-molecular theory best explains the observations that a gas can be
compressed?
A. Gas molecules move at random with no attractive forces between them
B. The velocity of gas molecules is proportional to their kelvin temperature
c. The amount of space occupied by a gas is much greater than the space occupied by the actual gas molecules
D. In collisions with the walls of the container or with other molecules, energy is conservedd


Write the reaction involved in extraction
of copper from its ore by the process of electrolytic refining.


Find the harmonic conjugate of the
point \( R(5,1) \) with respect to points
\( \boldsymbol{P}(\mathbf{2}, \mathbf{1 0}) \) and \( \boldsymbol{Q}(\boldsymbol{6},-\mathbf{2}) \)


A rod is made of uniform material and
has non-uniform cross-section. It is
fixed at both ends as shown and heated
at the mid-section. Which of the
following statements are not correct?
his question has multiple correct options
A. Force of compression in the rod will be maximum at mid-section
B. Compressive stress in the rod will be maximum at left end
c. since the rod is fixed at both the ends, its length will remain unchanged. Hence, no strain will be induced in it.
D. None of above


The value of \( (-32) \div(-4) \) is equal to
\( A \cdot+8 \)
B. -18
\( c \cdot+18 \)
D. - 8


The solution of differential equation
\( \boldsymbol{x}^{2} \boldsymbol{y}^{2} \boldsymbol{d} \boldsymbol{y}=\left(1-\boldsymbol{x} \boldsymbol{y}^{3}\right) d \boldsymbol{x} \) is
A \( \cdot x^{3} y^{3}=x^{2}+C \)
B. \( 2 x^{3} y^{3}=3 x^{2}+C \)
c. \( x^{3} y^{3}=x^{2}+x+C \)
D. \( x^{3} y^{3}=3 x^{2}+C \)


Raghav, Ajay and Nita were given three test tubes \( K, L \) and \( M \) respectively containing unknown substances They observed the following properties about their solutions
Substance Property
The components can be separated by filtration
Particles scatter the light
Particles size is \( 10^{-9} \) to \( 10^{-7} \mathrm{m} \)
On the basis of the above properties identify the solutions \( K, L \) and \( M \)
respectively
A. Ferrous sulphate solution, tonic, paints
B. Calcium carbonate solution, paints, milk
c. Muddy water, milk, calcium carbonate solution
D. Paints, ferrous sulphate solution, calcium carbonate solution


If \( \left(a b^{-1}\right)^{2 x-1}=\left(b a^{-1}\right)^{x-2}, \) then what is
the value of \( x ? \)
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D.


What is a lunar month?
A. month having 29 days
B. a lunar month is the time between two identical syzgies (new moons or full moons)
C. Moon's orbital period in a non-rotating frame of reference
D. average time for the Moon to pass twice through the same equinox point of the sky


A particle is thrown vertically with a velocity of \( 50 m / s . \) What will be its
velocity at the highest point of the journey? How high would the particle rise? What time would it take to reach
the highest point \( ?\left(g=10 m / s^{2}\right) \)


Observations of a data are
\( \mathbf{1 6}, \mathbf{7 2}, \mathbf{0}, \mathbf{5 5}, \mathbf{6 5}, \mathbf{5 5}, \mathbf{1 0}, \) and \( \mathbf{4 1} \)
Chaitanya calculated the mode and median without taking the zero into consideration. Did Chaitanya do the right thing?


if the percentage of air pollution from different sources are given in the table.
With the help of this, answer the following questions:
Sources of air \( \quad \) Industry \( \quad \) Transportation pollution
Percentage \( \quad 52 \% \) 27\%
a) Which are the two sources to be
monitored more to control air pollution?
(b) Mention the preventive measure for each one of these two sources to control
air pollution?


In the shown figure the magnitude of
acceleration of centre of mass of the
system is \( \left(\boldsymbol{g}=\mathbf{1 0 m} \boldsymbol{s}^{-\mathbf{2}}\right) \)
A \( \cdot 4 m s^{-2} \)
B. \( 10 \mathrm{ms}^{-2} \)
c. \( 2 \sqrt{2} \mathrm{ms}^{-2} \)
\( D \cdot 5 m s^{-2} \)


Prove: If a chord of circle \( x^{2}+y^{2}=8 \)
makes equal intercepts of length 'a' on the coordinate axes then \( |a|<4 \)


Which of the following does not belong to the group formed by the others?
A. Iron
B. Tin
c. Glass
D. stee


the angle of reflection of the ray from
mirror PQ


A body of mass Mkg is on the top point of a smooth hemisphere of radius \( 5 \mathrm{m} \). It is released to slide down the surface of
hemisphere it leaves the surface when its velocity is \( 5 m s^{-1} \) At this instant the
angle made by the radius vector of the body with the vertical is \( \left(g=10 m s^{-2}\right) \)
A \( \cdot \cos ^{-1}\left(\frac{3}{4}\right) \)
B . \( 45^{\circ} \)
\( c \cdot 60 \)
D. \( 90^{\circ} \)


Unpolarised light is passed through a
polaroid \( P_{1} \).When this polarised beam
passes through another polaroid \( P_{2} \) and
if the pass axis of \( P_{2} \) makes angle \( \theta \)
with the pass axis of \( P_{1} \). then write the
intensity when \( \theta \) varies from 0 to \( 2 \pi \)


Which of the following book most impressed the opinion of taxonomists?
A. Enquiry into plants
B. Origin of life
c. Genera plantarum
D. origin of species


Industries like Mathura Oil Refinery
produce pollutants like:
A. sulphur dioxide
B. nitrogen dioxide
c. both a and \( b \)
D. hydrochloric acid


Two angles of one triangle are \( 85^{\circ} \) and \( 65^{\circ} \)
is equal to angles of the other. Are they similar? Prove it.


Differentiate between ATP and
AlDS based on their abbreviations.


If \( \vec{a}=i+j+k, \vec{b}=4 i+3 j+4 k, \vec{c}=i+\alpha i+ \)
\( \beta \mathrm{k} \) are linearly dependent and \( |c|=\sqrt{3} \)
then
B. \( \alpha=2, \beta=1 \)
c. \( \alpha=3, \beta=1 \)
D. \( \alpha=4, \beta=1 \)


The sum of first 20 terms of \( \boldsymbol{A P} \) :
\( \mathbf{8}, \mathbf{3},-\mathbf{2}, \dots . . \) is:
\( \mathbf{A} \cdot-790 \)
B. -970
\( \mathbf{c} .-979 \)
D. -779


If \( A \) is a square matrix of order 3 and \( |A|=4 \) find the value of \( |2 A| \)


A boy throws a ball straight up in in the air from a \( 100 m \) tall building and the ball travels \( 20 m \) upwards before it starts falling down and comes to rest when it reaches the ground. What are the magnitudes of displacement and distance of the ball?
A. \( 100 m, 140 m \)
n
в. \( 120 m, 120 m \)
\( \mathrm{c} .140 \mathrm{m}, 120 \mathrm{m} \)
D. 240 \( m, 120 m \)


A technique used to determine the concentration of odour compounds in a
sample is known as:
A. Stripping
B. Chlorination
c. Flushing
D. Settling


Obtain the expression of the electric field due to an infinitely long linear
charged wire along the perpendicular distance from the wire.


The distance between two stations is
\( 240 \mathrm{km} . \) A train takes 4 hours to cover
this distance. Calculate the speed of the
train.


Which of the following is reactions is an example of autoreduction?
A \( \cdot F e_{3} O_{4}+4 C O \rightarrow 3 F e+4 C O_{2} \)
в. \( C u O+C \rightarrow 2 C u+C O \)
c. \( C u_{\left(a_{a}\right)}^{2+}+F e_{(s)} \rightarrow C u_{(s)}+F e_{\left(a_{9}\right)+}^{(2)} \)
D. \( C u_{2} O+\frac{1}{2} C u_{2} S \rightarrow 2 C u+\frac{1}{2} S O_{2} \)


In a semiconductor, which of the
following statement is correct?
A. At \( 0 K \), Si is a super conductor.
B. In a p-type semiconductor the acceptor level lies near the conduction band.
C. Each donor atom contributes one hole.
D. \( p-n \) junction is electrically neutral


If \( A \) is the set of even natural numbers
less than 8 and \( B \) is the set of prime
numbers less than \( 7, \) then the number
of relations from \( A \) to \( B \) is
A \( \cdot 2^{9} \)
B \( \cdot 9^{2} \)
\( c \cdot 3^{2} \)
D. \( 2^{9}-1 \)


Which of the following are the demerits
of Mendeleev periodic table?
This question has multiple correct options
A. No proper position for hydrogen is given.
B. Grouping of chemically dissimilar elements.
C. Position given to isotopes.
D. Presence of anomalous pairs.


Octahedral complex of \( \mathrm{Ni}(\|) \) must be :
A. inner orbital
B. outer orbital
C. inner or outer orbital depending upon the strong or weak field ligand
D. none of these


Sulphur sol contains:
A. discrete sulphur atoms
B. discrete sulphur molecules
C. water dispersed in solid sulphur
D. large aggregates of sulphur molecules


\( \lim _{x \rightarrow 0} \frac{\sin \left(x^{g}\right)}{x}(g=g r a d) \)
A \( \cdot \frac{\pi}{180} \)
в. \( \frac{\pi}{90} \)
c. \( \frac{\pi}{100} \)
D. \( \frac{\pi}{200} \)


A metal wire upon excess stress moves
to a region of permanent set. Before yielding to the fracture stress, it undergoes an extension equal to twice its length in its plastic region. The nature of the metal is
A . Brittle
B. Ductile
c. Perfectly elastic
D. Perfectly plastic


\( \lim _{n \rightarrow \infty} n\left[\frac{1}{(n+1)(n+2)}+\frac{1}{(n+2)(n+}\right. \)
is equal to
\( ^{A} \cdot \log \left(\frac{3}{2}\right) \)
в. \( \log \left(\frac{5}{2}\right) \)
c. \( \log \left(\frac{1}{2}\right) \)
D. \( \log \left(\frac{7}{4}\right) \)


\( \frac{n}{L} \)


The IUPAC name of dimethyl sec.butylamine is:
A. 2-amino-3-methyl butane
B. 2(N-methyl amino) butane
c. N,N-dimethyl-butan-2-amine
D. 2-(N,N-dimethyl amino) propane


Compared to other animals, the ability of speech has developed more in humans. Mainly development of which organ is responsible for this?
A. Mouth
B. Heart
c. Tongue
D. Brain


Infrared radiation was discovered in
1800 by :
A. William Wallaston
B. William Herschel
c. wilhelm Roentgen
D. Thomas Young


The number of electrons present in the outer most shell of the halogens are:
A . 4
B. 0
\( c \cdot 7 \)
\( D \)


The reaction(s) which (do) not occur in
the reduction zone in the extraction of
iron from haematite ore is (are):-
This question has multiple correct options
A. \( F e_{2} O_{3}+C O \rightarrow 2 F e O+C O_{2} \)
в. \( F e O+C O \rightarrow F e+C O_{2} \)
\( \mathbf{c} \cdot F e_{2} O_{3}+3 C \rightarrow 2 F e+3 C O \)
D. \( C a O+S i O_{2} \rightarrow C a S i O_{3} \)


Give scientific reasons. Roots of plants grow away from light.


A car is moving with a speed of \( 30 m / s \)
on a circular path on a radius \( 500 m \). It
is increasing at the rate of \( 2 m / s e c^{2} \) What is the acceleration of the car?
\( \mathbf{A} \cdot 9.8 m / s e c^{2} \)
B. \( 2.7 m / s e c^{2} \)
c. \( 2.4 m / s e c^{2} \)
D. \( 1.8 m / s e c^{2} \)


The mean salary paid per week to 1000 employees of an establishment was found to be Rs. \( 900 . \) Later on, it was
discovered that the salaries of two
employees were wrongly recorded as Rs.
\( \mathbf{7 5 0} \) and Rs. \( \mathbf{3 6 5} \) instead of Rs. \( \mathbf{5 7 0} \) and
Rs. \( 635 . \) Find the corrected mean salary.
A . 900.90
B. 1,115
c. 1,225
D. 900.09


Equations of a stationary and a travelling waves are as follows, \( \boldsymbol{y}_{1}= \)
\( a \sin k x \cos \omega t \) and \( y_{2}=a \sin (\omega t-k x) \)
The phase difference between two points \( x_{1}=\frac{\pi}{3 k} \) and \( x_{2}=\frac{3 \pi}{2 k} \) are \( \phi_{1} \) and
\( \phi_{2} \) respectively for two waves. The ratio \( \frac{\phi_{1}}{\phi_{2}} \) is
A.
в. \( 5 / 6 \)
\( c .3 / 4 \)
D. 6/7


Solve \( \sin (50+\theta)-\cos (40-\theta)+ \)
\( \tan 1 \tan 10 \)
\( \tan 20 \tan 70 \tan 80 \tan 89=1 \)


Solvents used to dry clean clothes are
usually \( C_{2} C l_{4} . \) A substitute has been discovered which is environmental
friendly is an application of
A. Green revolution
B. Green chemistry
c. waste management
D. Revolution resource recovery


If \( \mathbf{p}_{1}, \mathbf{p}_{2}, \mathbf{p}_{3} \) are the principal values of following trigonometric equations \( \sin \theta=-\frac{1}{\sqrt{2}} \)
2) \( \cos \theta=-\frac{\sqrt{3}}{2} \)
3) \( \tan \theta=\sqrt{3}-2 \)
A. \( p_{1}<p_{2}<p_{3} \)
в. \( p_{1}<p_{3}<p_{2} \)
c. \( p_{3}<p_{1}<p_{2} \)
D . \( p_{2}<p_{3}<p_{1} \)


\( \int_{1}^{e^{37}} \frac{\pi \sin \left(\pi \log _{e} x\right)}{x} d x \) is equal to
A . 2
B. -
c. \( 2 / \pi \)
D. \( 2 \pi \)


An electromagnets magnetic field can be rapidly manipulated over a wide
range by controlling the amount of electric current supplied to the electromagnet. State whether the above statement is
true or not?
A. True
B. False


A farmer treats the soil of his field with
lime when the soil has:
A. acidic nature
B. basic nature
c. neutral nature
D. None of the above


A pair of dice is thrown 4 times, then the
probability of getting doublets at least twice is
A \( \cdot \frac{19}{44} \)
в. \( \frac{21}{44} \)
\( c \cdot \frac{31}{44} \)
D. \( \frac{39}{44} \)


Give examples of natural causes of deforestation.
A. Forest fires
B. Drought
c. Both A and B
D. None of the above


Determine the relations in \( x, y \) and \( z \) if
\( 1, \log _{y} x, \log _{z} y,-15 \log _{x} z \) are in A.P.


\( H_{2} O \) has a higher boiling point than
HF because:
A. \( H_{2} O \) is more polar than \( H F \)
B. \( H_{2} O \) can form more hydrogen bonds
C. \( H_{2} O \) has a higher molecular weight
D. \( H_{2} O \) has more atoms
E. \( H_{2} O \) does not have a higher boiling point that \( H F \)


Mendel was born in
A. Australia
B. Heizendorf
C . Maravia
D. Brunn


The area of cross-section of the two
\( \operatorname{arms} \) of a hydraulic press are \( 1 \mathrm{cm}^{2} \) and
\( 10 \mathrm{cm}^{2} \) respectively(fig.). A force of \( 5 \mathrm{N} \) is applied on the water in the thinner
arm. What force should be applied
on the water in the thicker arm so that
the water may remain in equilibrium?
\( A \cdot 50 N \)
B. 60 N
c. 70 n
D. 80N


Let \( f(x)=a x^{5}+b x^{3}+c \sin x+d \tan ^{3} x- \)
1
f \( f(-\alpha)=-5, \) then \( f(\alpha) \) equals


Which of the following halides is the
most stable?
A. \( C C l_{4} \)
в. \( C B r_{4} \)
c. \( C F_{4} \)
D. \( C l_{4} \)


Tritium contains
A .4
B. 3
\( c \cdot 2 \)
D.


One of the following is not a common disorder associated with digestive
system.
A. Tetanus
B. Diarrhoea
c. Jaundice
D. Dysentery


Give appropriate Re reasons for each of
the following:Addition of chlorine to potassium iodide solution gives it a brown colour but excess of chlorine makes it colourless


The equilibrium constants of the reactions,
\[
\begin{array}{l}
\boldsymbol{S O}_{2}+\frac{1}{2} \boldsymbol{O}_{2} \rightleftharpoons \boldsymbol{S O}_{2} \\
\boldsymbol{2} \boldsymbol{S} \boldsymbol{O}_{2}+\boldsymbol{O}_{2} \rightleftharpoons \boldsymbol{2} \boldsymbol{S} \boldsymbol{O}_{3}
\end{array}
\]
and \( K_{1} \) and \( K_{2} \) respectively. The
relationship between \( K_{1} \) and \( K_{2} \) is :
This question has multiple correct options
A \( \cdot K_{1}=K_{2} \)
B . \( K_{2}=K_{1}^{2} \)
c. \( K_{1}=\sqrt{K_{2}} \)
D. \( K_{2}=\sqrt{K_{1}} \)


\( \boldsymbol{n} \stackrel{\boldsymbol{L} t}{\rightarrow} \infty \sum_{r=0}^{\boldsymbol{n}-1} \frac{1}{\sqrt{\boldsymbol{n}^{2}-\boldsymbol{r}^{2}}} \)
\( A \)
B . \( \pi / 2 \)
c. \( \pi / 3 \)
D . \( \pi / 6 \)


If a vector \( \vec{A}=3 \hat{i}-7 \) jbk \( a n d \vec{B}=2 \hat{j}- \)
\( 3 \hat{k} \) are perpendicular find to each other find value \( =\mathbf{b} \)


If \( f(x)=\frac{2 x+3}{3 x-2} \)
Prove that fof is an identity function


All of the following statements are
regarding sieve tube elements that are
true except
A. Their end walls have perforated sieve plates which become impregnated with lignin at maturity.
B. They possess a peripheral cytoplasm as well as a large vacuole.
C. Distinct proteinaceous inclusions, the P-proteins are seen evenly distributed throughout the lumen.
D. Long, slender, tube-like structures arranged in longitudinal series.
E. They are devoid of nucleus at maturity.


Mark the correct statement:
A. Frictional force also exist when there is no motion.
B. Frictional force only exist when there is motion between two objects.
C. Frictional force is nothing but the weight of the body
D. None


According to the property of A.P. If each term of a given A.P \( (1,2,3, \ldots) \) is divided by a non-zero constant \( t, \) then the resulting sequence will be
A. \( _{\text {A.P }}\left(\frac{1}{t^{\prime}}, \frac{2}{t^{\prime}}, \frac{3}{t} \ldots\right), \) with common difference \( \frac{1}{t} \)
B. G.P \( \left(\frac{1}{t}, \frac{2}{t}, \frac{3}{t} \ldots\right) \), with common difference \( \frac{1}{t} \)
C. \( _{\text {H.P }}\left(\frac{1}{t}, \frac{2}{t}, \frac{3}{t} \cdots\right) \), with common difference \( \frac{1}{t} \)
D. A.P \( (t, 2 t, 3 t \ldots), \) with common difference \( t \)


Solve and find the value of \( x \)
\( \mathbf{2}^{\boldsymbol{x}-\mathbf{5}}=\mathbf{2 5 6} \)


Why does the police used dogs for
detective work?
A. Because they have sharp eyesight
B. Because they can hear ultrasonic waves
C. Because they can identify objects by smell
D. All of these


\( \Delta A M T \sim \Delta A H E . \ln \Delta A M T, A M= \)
\( 6.3 \mathrm{cm}, \angle M A T=120^{\circ}, A T=4.9 \mathrm{cm} \)
and \( \frac{M A}{H A}=\frac{7}{5} . \) Construct both the
triangles.


Point \( ^{\prime} A^{\prime} \) moves uniformly with speed
\( v_{1}(=20 m / \text {sec}) \) so that vector \( \vec{v}_{1} \) is
continuously 'aimed' at point ' \( B^{\prime} \) which in turn moves rectilinearly and uniformly with velocity \( v_{2}(=10 m / s e c) \)
along the path \( P \rightarrow Q \) as shown in the
figure. If the time (in sec)when the
points \( A \) and \( B \) converge is \( \frac{3 k}{7} . \) Then
find the value of \( k ? \)


\( \sum_{r=0}^{m} n+r C_{n}= \)
A. \( ^{n+m+1} C_{n+1} \)
В. \( ^{n+m+2} C_{n} \)
\( \mathbf{c} \cdot n+m+3 C_{n+1} \)
D. none of these


In which process under metabolism energy is liberated because of
respiration?
A. Catabolism
B. Anabolism
c. Excretion
D. Digestion


Expand:
\( \left|\begin{array}{lll}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{c} & \boldsymbol{a} & \boldsymbol{b} \\ \boldsymbol{b} & \boldsymbol{c} & \boldsymbol{a}\end{array}\right| \)


Which of the following is not correct regarding the properties of ionic compounds?
A. lonic compounds have high melting and boiling points
B. Their reaction velocity in aqueous medium is very high
c. lonic compounds in their molten and aqueous solutions do not conduct electricity
D. They are highly soluble in polar solvents


Aldehydes and ketones with or more carbon atoms are either
sparingly soluble or insoluble in water
A. 5
B. 6
\( c \cdot 7 \)
D. 8


Statement 1: One mole of NaCl contains
2 moles of ions.
Statement 2: NaCl is a stable salt at
room temperature.
A. Both Statement 1 and Statement 2 are correct and
Statement 2 is the correct explanation of Statement 1
B. Both Statement 1 and Statement 2 are correct and
Statement 2 is not the correct explanation of Statement 1.
c. Statement 1 is correct but Statement 2 is not correct.
D. Statement 1 is not correct but Statement 2 is correct.
E. Both the Statement 1 and Statement 2 are not correct


The force required to double the length of a steel wire of area of cross-section
\( 5 \times 10^{-5} m^{2}(\text { in } N) \) is :
\( \left(Y=20 \times 10^{10} P a\right) \)
A . \( 10^{7} \)
B . \( 10^{6} \)
\( \mathrm{c} \cdot 10^{-7} \)
D. \( 10^{5} \)


are connected on the top by a capacitor
C. A sliding conductor AB of length L
slides with its ends in contact with the
bars. The arrangement is placed in a uniform horizontal magnetic field
directed normal to the plane of the
figure. The conductor is released from
rest. The displacement \( (x) \) in meter of
the conductor at time \( t=2 \) sec is:
\( \left(\text { Given } \boldsymbol{m}=\mathbf{1 0 0} \boldsymbol{g} \boldsymbol{m}, \boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}, \boldsymbol{B}=\right. \)
100Tesla, \( \boldsymbol{L}=\mathbf{1} \boldsymbol{m}, \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \boldsymbol{C}=\mathbf{1 0} \boldsymbol{\mu} \boldsymbol{F}) \)
A . 10
B. 14
\( c \cdot 7 \)
\( D \)


The two cells are connected in series, in
a potentiometer experiment, in such a
way so as to support each other and to
oppose each other. The balancing lengths in two conditions are obtained as \( 150 \mathrm{cm} \) and \( 50 \mathrm{cm} \) respectively. The ratio of emf's of two cells will be
A . 1: 2
B. 2:
c. 1: 4
D. 4:


Construct a quadrilateral \( \boldsymbol{A B N V} \) where \( \boldsymbol{A} \boldsymbol{V}=\mathbf{7} \boldsymbol{c m}, \boldsymbol{B} \boldsymbol{A}=\mathbf{8} \boldsymbol{c m}, \boldsymbol{B} \boldsymbol{N}= \)
\( \mathbf{1 0} c \boldsymbol{m}, \boldsymbol{N} \boldsymbol{V}=\mathbf{5} \boldsymbol{c m} \) and \( \boldsymbol{B} \boldsymbol{V}=\mathbf{1 1} \boldsymbol{c m} \)
Then, the perimeter of \( \Delta B N V \) is
\( \mathbf{A} \cdot 26 \mathrm{cm} \)
B. \( 24 \mathrm{cm} \)
c. \( 28 \mathrm{cm} \)
D. \( 22 \mathrm{cm} \)


Let \( A \) be a square matrix. Which of the
following is/are not skew-symmetric matrix/ces?
A . \( A-A^{T} \)
B. \( A^{T}-A \)
c. \( A A^{T}-A^{T} A \)
D. \( A+A^{T} \), when A is skew-symmetric


Equations of preparation of alcohol from sugar are given:
\( C_{12} H_{22} O_{11}+H_{2} O \stackrel{\text {Invertase}}{\longrightarrow} \)
\( C_{6} H_{12} O_{6}+C_{6} H_{12} O_{6} \)
\( A \)
\( \boldsymbol{C}_{6} \boldsymbol{H}_{12} \boldsymbol{O}_{6} \stackrel{z \text { ymase}}{\longrightarrow} \mathbf{2} \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O} \boldsymbol{H}+\mathbf{2} \boldsymbol{C} \boldsymbol{O}_{2} \)
(a) Write the names of the Compounds
\( A \) and \( B \)
(b) The alcohol obtained here is known
as
(c) How can this alcohol be converted into reflected spirit?
(d) How can power alcohol be prepared?


Find \( \boldsymbol{\theta}, \) if \( \boldsymbol{0} \leq \boldsymbol{\theta} \leq \mathbf{9 0}^{\boldsymbol{o}} \)
\( \sqrt{\boldsymbol{3}} \tan \boldsymbol{\theta}=\mathbf{1} \)


In the following given systems of equations determine whether the system has a unique solution, no solution or infinitely many solutions. In case there is a unique solution, find it
\( 2 x+y=5 \)
\( 4 x+2 y=10 \)


The area bounded by the parabola \( \boldsymbol{x}= \)
\( y^{2} \) and the line \( y=x-6 \) is
A \( \cdot \frac{125}{3} \) sq. units
B. \( \frac{125}{6} \) sq. units
c. \( \frac{125}{4} \) sq. units
D. \( \frac{115}{3} \) sq. units


The total number of lone pair of
electrons in \( N_{2} O_{3} \) is:


A closed surface S is constructed
around a conducting wire connected to
a battery and switch (Fig) As the switch
is closed, the free electrons in the wire
start moving along the wire. In any time
interval, the number of electrons
entering the closed surface \( S \) is equal to
the number of electrons leaving it. After
closing the switch, the flux of the
electric field through the closed surface
will :
This question has multiple correct options
A. increase
B. decrease
C. remain unchanged
D. be zero


Which one of the following pairs of
compounds are functional isomers?
\( \mathbf{A} \cdot C H_{3} C H_{2} C H_{2} O H, C H_{3} C H(O H) C H_{3} \)
B \( \cdot C H_{3} C H_{2} C H_{2} C H_{2} O H,\left(C H_{3}\right)_{2} C H C H_{2} O H \)
\( \mathbf{c} \cdot C H_{3} C H_{2} C H_{2} O H, C H_{3} C H_{2} C H_{2} C l \)
D. \( C H_{3} C H_{2} C H_{2} O H, C H_{3}-O-C H_{2} C H_{3} \)


A two-digit number is 3 more than six times the sum of its digits. If 18 is added to the number obtained by
interchanged by interchanging the digits, we get the original number. Find
the number
A . 25
B. 45
c. 75
D. None of these


Four terms are in \( A . P . \) If sum of
numbers is 50 and largest number is four times the smaller one, then find the
terms.


Number of bivalents, chromatid tetrads,
DNA strands, telomeres present in pachytene phase of meiocyte of maize is
A .20,20,80,80
в. 20, 20, 40, 80
\( c \cdot 10,10,40,80 \)
D. 10, 20, 40, 40


The dimensional formula for
permittivity of free space \( \left(\epsilon_{0}\right) \) in the equation \( \boldsymbol{F}=\frac{\mathbf{1}}{\mathbf{4} \boldsymbol{\pi} \boldsymbol{\epsilon}_{0}} \frac{\boldsymbol{q}_{1} \boldsymbol{q}_{2}}{\boldsymbol{r}^{2}} \) where
symbols have their usual meaning is
\( \mathbf{A} \cdot\left[M^{1} L^{3} A^{-2} T^{-4}\right. \)
B \( \cdot\left[M^{-1} L^{-3} T^{4} A^{2}\right] \)
C \( \cdot\left[M^{-1} L^{-3} A^{-2} T^{-4}\right] \)
D・ \( \left[M^{1} L^{3} A^{2} T^{-4}\right] \)


Earthquakes are caused mostly due to:
A. Iandslide
B. flood
C. tsunami
D. movement of Earth's plates


The number of moles of \( C O_{2} \) that can be
dissolved in a liter of water increases
when the
(1) pressure of the \( C O_{2} \) is increased
(2) temperature of the water is increased
(3) liquid is stirred
A. If 1,2 and 3 are correct
B. If only 1 and 2 are correct
c. If only 2 and 3 are correct
D. If only 1 is correct
E. If only 3 is correct


Let \( \mathbb{Z} \) be the set of integers and \( \boldsymbol{f}: \mathbb{Z} \rightarrow \)
\( \mathbb{Z} \) be defined as \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}, \boldsymbol{x} \in \mathbb{Z} \)
then function is
A. bijection
B. injection
c. surjection
D. none of these


atoms of the same element may also possess different atomic weights.
A. isotopes
B. isotones
c. isobars
D. isomers


Name major excretory products. How are these products eliminated from, the body?


A solid body rotates about a stationary axis according to the law
\( \varphi=a t-b t^{3}, \) where \( a=6.0 \mathrm{rad} / \mathrm{s} \) and
\( \boldsymbol{b}=\mathbf{2} . \mathbf{0} \boldsymbol{r} \boldsymbol{a} \boldsymbol{d} / \boldsymbol{s}^{\mathbf{3}} \)
Find the mean values of the angular velocity and angular acceleration averaged over the time interval between
\( t=0 \) and the complete stop. The sum of
their magnitudes is x. Find the value of
\( \mathbf{x} \)


Why did Mendeleev's leave some gaps in his periodic table of elements?


A rain drop of radius 0.3 mm has a
terminal velocity in air \( 1 \mathrm{m} / \mathrm{s} \). The viscosity of air is \( 18 \times 10^{-5} \) poise. The
viscous force on it is
A \( \cdot 101.73 \times 10^{-4} d y n e \)
B . \( 101.73 \times 10^{-5} \) dyne
c. \( 16.95 \times 10^{-5} \) dyne
D. \( 16.95 \times 10^{-4} \) dyne


If \( (2 \cos x+\sin x)=1, \) then sum of all
possible value of \( (7 \cos x+6 \sin x) \)
is


Why was the basis of classification of
elements changed from the atomic
mass to the atomic number?


Given are \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{2}, \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3}, \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \) and
\( \boldsymbol{H}_{4} \boldsymbol{P}_{2} \boldsymbol{O}_{7} \)
Which of the above oxoacids results
into two series of salts?
A \( . H_{3} P O_{2} \)
в. \( H_{3} P O_{3} \)
\( \mathrm{c} . H_{3} P O_{4} \)
D. \( H_{4} P_{2} O_{7} \)


If \( A_{1} \) is the area bounded by \( y= \)
\( \cos x, y=\sin x \& x=0 \) and \( A_{2} \) the
area bounded by \( \boldsymbol{y}=\cos \boldsymbol{x}, \boldsymbol{y}= \)
\( \sin x, y=0 \) in \( \left(0, \frac{\pi}{2}\right) \) then \( \frac{A_{1}}{A_{2}} \) equals to:
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{\sqrt{2}} \)
c.
D. None of these


Soda bottles are made of thick glass so that they can withstand an increase in:
A. pressure during summer
B. temperature during summer
c. viscosity
D. potential energy


A large open top container of negligible mass and uniform cross sectional area
\( A \) has a small hole of cross sectional
area \( ^{\prime} a^{\prime} \) in its side wall near the bottom.
The container is kept over a smooth horizontal floor and contains a liquid of
density' \( \rho^{\prime} \) and mass \( ^{\prime} m^{\prime} . \) Assuming
that the liquid starts flowing through the hole the acceleration of the
container will be:
\( ^{A} \cdot \frac{2 a g}{A} \)
в. \( \frac{a g}{A} \)
c. \( \frac{2 A g}{a} \)
D. \( \frac{A g}{a} \)


The normal force of an object of mass 5 kg , measured by a force metre is seen to be 50 N. Determine the acceleration
due to gravity in \( \mathrm{cm} / \mathrm{s}^{2} \)
A. 1000
B. 100
c. 0.01
D. \( 0 . \)


\( 0.1 M \) formic acid solution is titrated
against \( 0.1 M \) NaOH solution. What
would be the difference in \( p H \) between \( \frac{1}{5} \) and \( \frac{4}{5} \) stages of neutralization of
acid?
A. \( 2 \log 3 / 4 \)
B. 2 \( \log 1 / 5 \)
\( \mathbf{c} \cdot \log 1 / 3 \)
D. \( 2 \log 4 \)


A solid cylinder of mass 20 kg rotates about its axis with angular speed 100 rad \( s^{-1} \). The radius of the cylinder is \( 0.25 \mathrm{m} . \) What is the kinetic energy
associated with the rotation of the
cylinder? What is the magnitude of angular momentum of the cylinder about its axis?


The wave function of a pulse is given by \( y=\frac{5}{(4 x+6 t)^{2}} \) where \( x \) and \( y \) are in
meter and \( t \) is in second, then
determine the wave velocity of the
pulse.
A. \( 2 m / s \)
в. \( 1 \mathrm{m} / \mathrm{s} \)
c. \( -1.5 m / s \)
D. \( 2.5 \mathrm{m} / \mathrm{s} \)


\( \left(-\frac{1}{2}+\frac{\sqrt{3}}{2} i\right)^{1000} \) is equal to
\( \frac{1-\sqrt{3} i}{2} \)
B. \( \frac{1+\sqrt{3} i}{2} \)
c. \( \frac{-1+\sqrt{3} i}{2} \)
D. \( \frac{-1-\sqrt{3} i}{2} \)


The distance between the straight lines
\( \mathbf{y}=\mathbf{m} \mathbf{x}+\mathbf{c}_{1}, \mathbf{y}=\mathbf{m} \mathbf{x}+\mathbf{c}_{2} \) is \( \left|\mathbf{c}_{1}-\mathbf{c}_{2}\right| \)
then \( \mathbf{m}= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. 3


An astronaut in a space station orbits
above the Earth.

In the space station, the acceleration
due to gravity is \( 7.5 m / s^{2} \) On Earth, the acceleration due to gravity
is \( 10 m / s^{2} \)
Which statement about the astronauts
mass and weight in the space station is
correct?
A. Mass of astronaut - Same as on the Earth, weight of astronaut - less than on the Earth
B. Mass of astronaut - Same as on the Earth, weight of astronaut - greater than on the Earth
c. Mass of astronaut - lower than as on the Earth, weight of astronaut - less than on the Earth
D. Mass of astronaut - lower than as on the Earth, weight of astronaut - greater than on the Earth


State whether the given statement is true or false.
\( X^{2+}+2 e^{-} \rightarrow X \) is an example of
oxidation.
A. True
B. False


In an ideal solution of non-volatile
solute \( \mathrm{B} \) in solvent \( \mathrm{A} \) in 2: 5 molar ratio
has vapour pressure \( 250 \mathrm{mm} \). If another solution in ratio 3: 4 prepared then vapour pressure above this solution is:
\( A \cdot 200 \mathrm{mm} \)
B. 250 mm
c. 350 \( \mathrm{mm} \)
D. \( 400 \mathrm{mm} \)


Two coils connected in parallel having
resistances \( 300 \Omega \) and \( 200 \Omega a t 20^{0} C \)
and temperature coefficient of resistivity \( 0.001 K^{-1} \) and \( 0.006 K^{-1} \)
respectively.The effective temperature coefficient of the combination is
A. \( 0.007 K^{-1} \)
B . \( 0.004 K^{-1} \)
D. \( 0.003 K^{-1} \)


A 3.4 g sample of \( \mathrm{H}_{2} \mathrm{O}_{2} \) solution containing \( x \% \mathrm{H}_{2} \mathrm{O}_{2} \) by mass requires \( \mathrm{x} \)
\( \mathrm{ml} \) of a \( \mathrm{KMnO}_{4} \) solution for complete oxidation under acidic condition. The
molarity of \( \mathrm{KMnO}_{4} \) solution is :
\( A \)
B. 0.5
\( c \cdot 0.4 \)
D. 0.2


Two coaxial coils are very close to each
other and their mutual inductance is
\( 5 m H . \) If a current 50 sin500t is passed
in one of the coils then the peak value of induced emf in the secondary coil will
be
A . \( 5000 V \)
B. \( 500 V \)
\( \mathbf{c} \cdot 150 V \)
D. \( 125 V \)


State whether the following expressions are polynomials in one variable or not. Give reasons for your answer. \( \sqrt[3]{t}+2 t \)


On moving away from the nucleus, the successive permitted orbits are further a part in the distance, but closer in
energy'. Justify this statement.


The area of two holes \( A \) and \( B \) are \( 2 a \) and
\( a \) respectively. The holes are at height
\( \frac{\boldsymbol{H}}{\mathbf{3}} \) and \( \frac{\boldsymbol{2} \boldsymbol{H}}{\mathbf{3}} \) from the surface of water.
Find the correct option(s)
This question has multiple correct options
A. the velocity of efflux at hole \( B \) is 2 times the velocity of efflux at hole \( A \)
B. the velocity of efflux at hole \( B \) is \( \sqrt{2} \) time the velocity of efflux at hole
C. the discharge is same through both the holes
D. the discharge through hole A is \( \sqrt{2} \) time the discharge through hole


Two sources of equal emf are connected
to an external resistance R. The internal
resistance of the two sources are \( \boldsymbol{R}_{1} \)
\( \operatorname{and} R_{2}\left(R_{1}>R_{2}\right) . \) If the potential
difference across the source having
internal resistance \( \boldsymbol{R}_{2} \) is zero, then:
A. \( R=R_{2}-R_{1} \)
в. \( \quad R=\frac{R_{2}\left(R_{2}+R_{1}\right)}{R_{2}-R_{1}} \)
\( c \cdot R=\frac{R_{2} R_{1}}{R_{2}-R_{1}} \)
D. \( R=\frac{R_{2} R_{1}}{R_{1}-R_{2}} \)


The distance between two parallel wires carrying current of \( 1 A \) is 1 m. The force per unit length between the conductors
is
A \( \cdot 2 \times 10^{7} N m^{-1} \)
В. \( 2 \times 10^{-7} \mathrm{Nm}^{-1} \)
c. \( 4 \times 10^{7} N m^{-1} \)
D. \( 4 \times 10^{-7} \mathrm{Nm}^{-1} \)


A star is 1.45 parsec light years away. How much parallax would this star show when viewed from two locations of
the earth six months apart in its orbit
around the sun?
A .2 Parsec
B. 0.725 Parsec
c. 1.45 Parsec
D. 2.9 Parsec


If \( \boldsymbol{x}=\mathbf{3} \) and \( \boldsymbol{y}=-\mathbf{2}, \) the value of \( \boldsymbol{x}^{\boldsymbol{x}}+ \)
\( \boldsymbol{y}^{\boldsymbol{y}} ? \)
A . 27
B. 9
c. 8
D. none of the above


Hydrogen differs from elements of \( \mathrm{V} \|-\mathbf{A} \)
group as:
A. it can gain one electron
B. it has one electron in its valence shell
C. its electronic configuration is different from other elements
D. both \( B \) and \( C \)


A wire of cross-sectional area \( 4 \times 10^{-4} m^{2} \)
modulus of elasticity \( 2 \times 10^{11} N / m^{2} \)
and length \( 1 m \), is stretched between two
vertical rigid poles. A mass of \( 1 \mathrm{kg} \) is suspended at its center. If the angle it makes with the horizontal is \( \frac{1}{2} \times 10^{-x} \) rad. Find \( x \)


State how bats can locate objects in the
dark.


A lawyer who is currently earning \( \$ \) 42,380 annually receives a \( 6.5 \% \) raise. What is his new annual salary?
A. \( \$ 45,122.70 \)
B. \$ 48,134.80
c. \( \$ 45,134.70 \)
D. \$ 45,162.90


Calculate y (ratio of \( C_{p} \) and \( C_{v} \) ) for triatomic linear gas at high temperature. Assume that the
contribution of the vibrational degree of freedom is \( 75 \% \)
A . 1.29
B. 1.121
c. 1.18
D. 1.33


Plants having little or no secondary growth are
A. Conifers
B. Grasses
c. cycads
D. Deciduous angiosperms


How many grams of \( C O_{2} \) are produced by the complete reaction of 100 g \( \mathrm{CaCO}_{3} \) with excess \( \boldsymbol{H C l} \) ?
A .22 g
в. 44 g
c. 79 g
D. \( 110 \mathrm{g} \)
E . 132 g


Of the following which change will shift the reaction towards the product?
\( \boldsymbol{I}_{2}(\boldsymbol{g}) \rightleftharpoons 2 \boldsymbol{I}(\boldsymbol{g}), \triangle \boldsymbol{H}_{r}^{0}(\mathbf{2 9 8} \boldsymbol{K})= \)
\( +150 k J \)
This question has multiple correct options
A. Increase in concentration of \( I \)
B. Decrease in concentration of \( I_{2} \)
c. Increase in temperature
D. Increase in total pressure


The figure shows the cross section of
six identical spheres. The spheres, touching each other, are placed on a horizontal plane. The volume of each sphere is \( \frac{32 \pi}{3} c m^{3} . \) Calculate the length of \( \boldsymbol{P Q}, \) in \( \boldsymbol{c m} \)
A . 18
B. 24
c. 36
D. 58


Find the surface area of the wooden box
which is in the shape of a cube, if the edge of the box is \( 27 \mathrm{cm} \)


Find how many terms of G.P. \( \frac{2}{9}-\frac{1}{3}+\frac{1}{2} \ldots \) must be added to get the
sum equal to \( \frac{55}{72} ? \)


Enzyme encolase catalyses the
conversion of 2 PGA to phosphoenol pyruvic acid in presence of which is the
cofactor.
\( \mathbf{A} \cdot M n^{+} \)
B. \( F e^{++} \)
c. \( M g^{++} \)
D. \( Z n^{+} \)


Hydrogen peroxide does not act as:
A . a reducing agent
B. an oxidising agent
C . a dehydrating agent
D. a bleaching agent


For the reaction \( F_{2} \rightleftharpoons 2 F, \) Calculate the
degree of dissociation of fluorine at 4
\( \operatorname{atm} \) and \( 1000 k, \) when \( K_{p}=1.4 \times 10^{-2} \)
\( \operatorname{atm} \)


The fundamental particle(s) not present in the nucleus of hydrogen atom is :
A . electron
B. proton
c. neutron
D. all of the above


A radioactive sample decays by two different processes. Half-life of first
process is \( t_{1}, \) and for second process is
\( t_{2} . \) Then, the effective half-life is
A \( \cdot t_{1}-t_{2} \)
в. \( t_{1}+t_{2} \)
c. \( \frac{t_{1}, t_{2}}{t_{1}+t_{2}} \)
D. \( \frac{t_{1}^{2}+\frac{2}{2}}{t_{1}-t_{2}} \)


The anhydrous calcium sulphate is called :
A. gypsum
B. anhydrite
c. plaster of Paris
D. lime


\( x \sqrt{1+y}+y \sqrt{1+x}=0, \) then \( \frac{d y}{d x} \) equal
to
\( \mathbf{A} \cdot 1+x \)
В. \( (1-x)^{-2} \)
C. \( -(1+x)^{-1} \)
D. \( -(1+x)^{-2} \)


Name the famous scientist who
described eight centres of the world showing maximum diversity in plants.
A. Borloug
B. Vavilov
c. Swaminathan
D. columbus


Secretion of estrogen is controlled by
A . HCG
B. Progesterone
c. LH
D. FSH


There are two sections \( A \) and \( B \) of a
class consisting of 36 and 44 students respectively. If the average weight of section \( \boldsymbol{A} \) is \( \mathbf{4 0} \) kg and that of section \( \boldsymbol{B} \)
is \( 35 \mathrm{kg} \), find the average weight of the
whole class?


Convert the following to percents:
\( \frac{12}{16} \)


The amplitude of a damped oscillator decreases to 0.9times its original magnitude in 5 s. In another 10 s it will
decrease to \( \alpha \) times its original
magnitude, where \( \alpha \) equals
A. 0.7
B. 0.81
c. 0.729
D. 0.6


Which of the following statement is/are true about mycoplasmas?
A. They can survive without oxygen.
B. They are resistant to penicillin.
c. They are smallest, cell wall less prokaryote
D. All of the above.


How accurate is one-dimensional
model?
A. Less accurate
B. Quite accurate
c. cannot say
D. None


Solve
\( 12 x^{2}-27=0 \)


A man is know to speak the truth 3 out
of 4 times. He throws a die and reports
that it is a six. the probability that it is actually a six is
A \( \cdot \frac{3}{8} \)
B. \( \frac{1}{5} \)
\( c \cdot \frac{3}{4} \)
D. None of these


Pick out the bad conductor of
electricity from the following:
A. copper
B. steel
c. impure water
D. air


Light enters an isosceles right
triangular prism at normal incidence
through face \( A B \) and undergoes
total internal reflection at face \( \mathrm{BC} \) as
shown below.

The minimum value of the refractive
index of the prism is close to
A \( \cdot 1.10 \)
B . 1.55
c. 1.42
D. 1.72


A steel wire of length \( 1 \mathrm{m} \) has cross sectional area \( 1 \mathrm{cm}^{2} \). If young's modulus
of steel is \( 10^{11} N / m^{2}, \) then force required to increase the length of wire by \( 1 \mathrm{mm} \) will be :
\( \mathbf{A} \cdot 10^{11} N \)
В. \( 10^{7} N \)
\( \mathbf{c} \cdot 10^{4} N \)
D. \( 10^{2} N \)


Read the following statements regarding euglenoids and select the incorrect ones.
(i) These are mostly freshwater organisms found in stagnant water.
(ii) Their body is covered by a protein rich layer called pellicle which makes their body flexible.
(iii) They are photosynthetic in the presence of sunlight but become heterotrophs in the absence of sunlight.
(iv) They usually possess two flagella, one long and one short.
(v) Euglenoids are multicellular ciliate protists.
A \( \cdot \) (i) and (v)
B. (iv) and (v)
c. (iii) only
D. (v) only


Oleum on hydrolysis gives sulphuric
acid.


An urn contains one black ball and one
green ball. A second urn contains one
white and one green ball. One ball is
drawn at random from each urn.Find the
probability of getting at least one green ball.
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{2}{3} \)
D.


Two moles of an ideal monoatomic gas
is heated from \( 27^{\circ} C \) to \( 627^{\circ} C \)
reversibly and isochorically. The entropy of gas:
A. increases by \( 2 R \ln 3 \)
B. increases by \( 3 R \ln 3 \)
c. decreases by \( 2 R \ln 3 \)
D. decreases by \( 3 R \ln 3 \)


Smilax belongs to
A. Liliaceae
B. Solanaceae
c. Leguminosae
D. Cruciferae


\( \mathrm{Na}^{\oplus} \) and Ne are \( _{-1-} \ldots_{-} \) to each
other.
A. isotopes
B. isoelectronic
\( c . \) isobars
D. allotropic


Electronic energy is negative because:
A. electron has negative charge
B. energy is zero near the nucleus and decreases as the distance from nucleus increases
C. energy is zero at infinite distance from the nucleus and decreases as the electron comes towards nucleus
D. these are interelectronic repulsions


Butyne on oxidation with hot alkaline
\( K M n O_{4} \) gives:
\( \mathbf{A} \cdot C H_{3} C H_{2} C H_{2} C O O H \)
в. \( C H_{3} C H_{2} C O O H \)
\( \mathrm{c} \cdot \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COOH}+\mathrm{CO}_{2}+\mathrm{H}_{2} \mathrm{O} \)
D. \( C H_{2} C H_{2} C O O H+H C O O H \)


The rate equation for the reaction \( \boldsymbol{A}+ \)
\( 2 B \rightarrow \) Products is given as rate\( = \)
\( \boldsymbol{K}[\boldsymbol{A}][\boldsymbol{B}]^{2} . \) If the volume of the vessel is
decreased to half of the initial volume,
then the reaction rate bears the
following relation to the original rate as:
A. \( 1 / 2 \) times
B. 2 times
c. 4 times
D. 8 times


Solve:
\( 2 \tan ^{-1} \frac{3}{4}-\tan ^{-1} \frac{17}{31} \)


Cell body is known as
A. Axon
B. Cyton
c. Neuron
D. None of he above


Parallel rays (in air) are incident on a
transparent sphere along its one diameter. After refraction, these rays converge at the other end of this
diameter. The refractive index for the
material of sphere is
\( A \)
B. 1.5
\( c \cdot 1.6 \)
\( D \cdot 2 \)


A particle is projected from ground with velocity \( 40 \sqrt{2} m / s a t 45^{\circ} . \) Find the displacement of the particle after 2 s.
\( \left(g=10 m / s^{2}\right) \)


If \( \boldsymbol{f}(\boldsymbol{x})=\cos (\log \boldsymbol{x}), \) then
\( f\left(\frac{1}{x}\right) f\left(\frac{1}{y}\right)- \)
\( \frac{1}{2}\left\{f\left(\frac{x}{y}\right)+f(x y)\right\}= \)
\( A \cdot \log x \)
B. \( \cos (\log x) \)
\( c \cdot \sin (\log x) \)
D.


Which of the following gases is regarded as an atmospheric pollutant?
\( A \cdot O_{2} \)
в. \( O_{3} \)
\( c \cdot s O_{2} \)
D. \( N_{2} \)


If \( A \Delta B=A \cup B, \) then which of the
following can be correct?
A \( . A=B \)
в. \( A \cap B=\phi \)
\( \mathbf{c} \cdot A \Delta B=\phi \)
D. \( A \Delta B=A \sim B \)


In which of the following ketonic group is absent?
A. Guanine
B. Thymine
c. Adenine
D. Uracil


inflated with both helium and nitrogen
gas. Between the two gases, the balloon
can be inflated up to 8 liters in volume.
The density of helium is 0.20 grams per
liter, and the density of nitrogen is 1.30 grams per liter. The balloon must be
filled so that the volumetric average
density of the balloon is lower than that
of air, which has a density of 1.20 grams per liter. Which of the following system of inequalities best describes
how the balloon will be filled, if \( x \)
represents the number of liters of
helium and \( y \) represents the number of
liters of nitrogen?
A \( \cdot\left\{\begin{array}{l}x+y>8 \\ 20 x+130 y>120\end{array}\right. \)
B. \( \left\{\begin{array}{l}x+y=8 \\ \frac{0.2 x+1.30 y}{2}<1.20\end{array}\right. \)
c. \( \left\{\begin{array}{l}x+y \leq 8 \\ 0.20\left(\frac{x}{x+y}\right)+1.30\left(\frac{y}{x+y}\right)<1.20\end{array}\right. \)
D \( \cdot\left\{\begin{array}{l}x+y \leq 8 \\ 0.20 x+1.30 y<1.20\end{array}\right. \)


\( 40 \% \) of a mixture of 0.2 mole of \( N_{2} \) and
0.6 mole of \( H_{2} \) react to give \( N H_{3} \)
according to the equation, \( N_{2}(g)+ \)
\( \mathbf{3} \boldsymbol{H}_{\mathbf{2}}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{N} \boldsymbol{H}_{\mathbf{3}}(\boldsymbol{g}) \) at constant
temperature and pressure. Then the
ratio of the final volume to the initial
volume of gases are:
A . 4: 5
B. 5: 4
c. 7: 10
D. 8: 5


What is the mode from the following
table \( ? \)
\( \begin{array}{ll}\text { Marks obtained } & \text { Frequency } \\ & \\ 3 & 7 \\ 1 & 11 \\ 23 & 15 \\ 33 & 8 \\ 43 & 3\end{array} \)
\( \mathbf{A} \cdot 13 \)
B. 43
c. 33
D. 23


Two metal spheres of radius \( r \) are kept
in contact. If \( ^{\prime} d^{\prime} \) is the density of each sphere material, the gravitational force between them is proportional to
\( \mathbf{A} \cdot d^{2} r^{6} \)
B. \( d^{2} r^{4} \)
c. \( \frac{d^{2}}{r^{4}} \)
D. \( \frac{r^{4}}{d^{2}} \)


An electron beam can undergo
diffraction by crystals. Through what potential should a beam of electrons be
accelerated so that its wavelength becomes equal to 1.54 A?
A. 13.6 volt
B . 1.54 volt
c. 1 volt
D. 63.44 volt


Which of the following is incorrect
statement?
\( \mathbf{A} \cdot P b F_{4} \) is covalent in nature
B. \( S i C l_{4} \) is easily hydrolysed
\( \mathbf{c} \cdot \operatorname{Ge} X_{4}(X=F, C l, B r, I) \) is more stable than \( G e X_{2} \)
D. \( S n F_{4} \) is ionic in nature


Express \( \boldsymbol{R}= \)
\( (x, y), y=3 x, x \in(1,2,3) \) and \( y \in(3,6 \)
as a set of ordered pair.


If the coefficients of \( a^{m} \) and \( a^{n} \) in the
expansion of \( (1+a)^{m+n} \) are \( \alpha \) and \( \beta \) then which one of the following is correct?
A \( \cdot \alpha=2 \beta \)
в. \( \alpha=\beta \)
c. \( 2 \alpha=\beta \)


An inset crawls up a hemispherical
surface very slowly. The coefficient of friction between the insect and the
surface is \( 1 / 3 . \) If the line joining the
center of the hemispherical surface to
the insect makes an angle \( \alpha \) with the
vertical, the maximum possible value of
\( \alpha \) is given by
\( \mathbf{A} \cdot \cot \alpha=3 \)
\( \mathbf{B} \cdot \tan \alpha=3 \)
\( \mathbf{c} \cdot \sec \alpha=3 \)
D. \( \operatorname{cosec} \alpha=3 \)


Which is the correct order for different
forces?
\( \mathbf{A} \cdot E_{D} \) (Dipole - induced dipole interaction) \( >E_{x} \) (Dipole
induced dipole interaction) \( >E_{L} \) (London force)
B. \( E_{K} \) (Dipole \( _{-} \) dipole interaction) \( >E_{D} \) (Dipole - induce
dipole interaction) \( >E_{L} \) (London force)
C . \( E_{D} \) (Dipole - induced dipole interaction) \( >E_{L} \) (London
force) \( E_{K} \) (Dipole - Dipole interaction)
D. All forces are equally strong.


\( \frac{x}{\sqrt{x+4}}, x>0 \)


Prove: \( 1+2+3+4+5 \cdot . .+n= \)
\( \frac{n(n+1)}{2} \)


If the equilibrium constant for the
reaction \( 2 A B \leftrightharpoons A_{2}+B_{2} \) is \( 36, \) then
what is the equilibrium constant for \( A B \leftrightharpoons \frac{1}{2} A_{2}+\frac{1}{2} B_{2} ? \)
\( A \cdot 2 \)
B. 6
\( c . \) 36
D. 72


Assertion
\( H_{3} P O_{2} \) can act as strong reducing agent and gives disproportionation reaction on heating.
Reason
Due to presence of one \( -O H \) group and
\( \boldsymbol{P}-\boldsymbol{H} \) group, \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{2} \) is a monobasic
bronsted acid.
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


Solve: \( \boldsymbol{y} \boldsymbol{d} \boldsymbol{x}+\left(\boldsymbol{x}-\boldsymbol{y}^{2}\right) \boldsymbol{d} \boldsymbol{y}=\mathbf{0} \)


Elements in the same group have equal
valency. Comment on it.


A ball is projected upwards. As it rises, there is increase in its:
A. Momentum
B. Retardation
c. Kinetic energy
D. Potential energy


The second, the first, and the third term
of an arithmetic progression, whose common difference is nonzero, form a geometric progression in that order.
Find its common ratio.


How many of the fuel gases have \( C O \)
and \( H_{2} \) both as combustible gases?
\( A \cdot 2 \)
B. 3
\( c \cdot 1 \)
D. 4


If \( \frac{\pi}{4}<\alpha<\frac{\pi}{2}, \) value of
\( \int_{-\pi / 2}^{\pi / 2} \frac{\sin 2 x}{\sqrt{1+\sin 2 \alpha \sin x}} \) is
A \( \cdot-\frac{4}{3} \tan \alpha \sec \alpha \)
B. \( -\frac{4}{3} \cot \alpha \operatorname{cosec} \alpha \)
c. \( -\frac{4}{3} \tan \alpha \operatorname{cosec} \alpha \)
D. \( -\frac{4}{3} \cot \alpha \sec \alpha \)


An element which posses luster and are good conductor of electricity are:
A. metalloid
B. non-metal
c. metal
D. alloys


Simplify
\( 12-\left(x+x^{2}\right)\left(8-x-x^{2}\right) \)


Multiply the given matrix:
\( \left[\begin{array}{cc}\boldsymbol{a} & \boldsymbol{b} \\ -\boldsymbol{b} & \boldsymbol{a}\end{array}\right]\left[\begin{array}{cc}\boldsymbol{a} & -\boldsymbol{b} \\ \boldsymbol{b} & \boldsymbol{a}\end{array}\right] \)


Convert into factors \( a^{2}+4 a+4-b^{2} \)


A red flower when viewed through blue light appears:
A . red
B. blue
c. black
D. violet


If \( \boldsymbol{A}=\left[\begin{array}{ccc}1 & -2 & 3 \\ -4 & 2 & 5\end{array}\right] \) and \( B= \)
\( \left[\begin{array}{cc}1 & 3 \\ -1 & 0 \\ 2 & 4\end{array}\right], \) then show that \( (A B)^{\prime}= \)
\( \boldsymbol{B}^{\prime} \boldsymbol{A}^{\prime} \)


Among the following, the alkene on ozonolysis giving rise to only one aldehyde as the product, is:
A. \( 1- \) butene
B. Prop - 1 - ene
c. \( 2- \) butene
D. \( 2- \) methyl \( - \) prop \( -1- \) ene


The decomposition of a substance
follows first order kinetics. If its
concentration is reduced to \( 1 / 8 \) of its
initial value in 12 minutes, the rate
constant of the decomposition system is ?
\( ^{\text {A }} \cdot\left(\frac{2.303}{12} \log \frac{1}{8}\right) \) min. \( ^{-1} \)
B. \( \left(\frac{2.303}{12} \log 8\right) \) min. \( ^{-1} \)
c. \( \left(\frac{0.693}{12}\right) \) min. \( ^{-1} \)
D. \( \left(\frac{1}{12} \log 8\right) \) min. \( ^{-1} \)


Applying \( \boldsymbol{C}_{1} \rightarrow \boldsymbol{C}_{1}-^{8} \boldsymbol{C}_{3}, \) we
getWithout expanding the determinant, prove that \( \left|\begin{array}{ccc}\mathbf{4 1} & \mathbf{1} & \mathbf{5} \\ \mathbf{7 9} & \mathbf{7} & \mathbf{9} \\ \mathbf{2 9} & \mathbf{5} & \mathbf{3}\end{array}\right|=\mathbf{0} \)


What conditions are required for
rusting to take place?
A. Water only
B. Oxygen only
c. water and oxygen
D. water and carbon dioxide


The correct representation of \( \boldsymbol{C u} \boldsymbol{S O}_{4} \)
\( \mathbf{5} \boldsymbol{H}_{2} \boldsymbol{O} \) is:
\( \mathbf{A} \cdot\left[C u\left(H_{2} O\right)_{5}\right] S O_{4} \)
B \( \cdot\left[C u\left(H_{2} O\right)_{3} S O_{4}\right] \cdot 2 H_{2} O \)
c. \( \left[C u S O_{4} \cdot H_{2} O\right] \cdot 4 H_{2} O \)
D. \( \left[C u\left(H_{2} O\right)_{4}\right] S O_{4} \cdot H_{2} O \)


A student was given \( \mathrm{Mg}, \mathrm{Zn}, \mathrm{Fe} \) and \( \mathrm{Cu} \) metals. He puts each of them in dil.HC contained in different test tubes.

Identify which of them will not displace
\( \boldsymbol{H}_{2} \) from dil. HCl?


The mean and standard deviation of a
random variable \( x \) is given by 5 and 3
respectively. The standard deviation of
\( 2-3 x \) is
A . -7
B. 81
\( c .34 \)
D. 9


nucleophilic addition reaction?
\( A \)
B.
\( c \)
D.


The vapour pressure of a deliquescent
substance is:
A. equal to the atmospheric pressure
B. equal to that of the water vapour in air
C . greater than that of the water vapour in air
D. less than that of the water vapour in air


Which one is classified as a
condensation polymer?
A. Dacron
B. Neoprene
c. Teflon
D. None of these


The incorrect statements among the
following are:
This question has multiple correct options
A. \( N C l_{5} \) does not exist while \( P C l_{5} \) does
B. Pb prefers to form tetravalent compounds
C. The three \( C-O \) bond are not equal in the carbonate
ion
D. Both \( O_{2}^{+} \) and \( N O \) are paramagnetic


The circuit given represents which of
\( \log i c \) operations
A. AND
B. NOT
\( c . \) ов
D. NOR


Runoff of excess fertiliser from farm
fields into nearby waterways can result in
A. Ozone depletion
B. Air pollution
c. Biomagnification
D. Acidification
E. Eutrophication


When concentrated nitric acid is heated
with \( P_{2} O_{5} ; \) it forms?
A \( . H_{3} P O_{4} \)
в. \( N O_{2} \)
c. \( N_{2} O_{5} \)
D. \( N O \)


A ball is dropped from a satellite revolving around the earth at height of 120km. The ball will
A. Continue to move with same speed along a straight line tangentially to the satellite at that time
B. Continue to move with same speed along the original orbit of satellite
c. Fall down to earth gradually
D. Go far away in space


Current passing through a coil of resistance R decreases uniformly as shown in the figure. If total amount of
charge q is passing through the coil
during a time interval \( t_{0} \) then what will
be the total amount of heat generated through it?
A \( \cdot \frac{3}{4} \frac{q^{2} R}{t_{0}} \)
в. \( \frac{4}{3} \frac{q^{2} R}{t_{0}} \)
c. \( \frac{q^{2}}{t_{R}} \)
D. \( \frac{q^{2} R^{2}}{t^{2}} \)


How soon will the frame come to the
orientation shown in figure (b) after
collision?
\( ^{A} \cdot \frac{\pi l}{4 v} \)
B. \( \frac{7 \pi l}{8 v} \)
c. \( \frac{\pi l}{v} \)
D. \( \frac{7 \pi l}{4 v} \)


The smallest number by which 5400 must be multiplied so that it becomes a perfect cube is:
\( \mathbf{A} \cdot 12 \)
B . 10
\( c .5 \)
D. 3


Distillation works when liquids have:
A. same melting points
B. different melting points
c. different boiling points
D. both \( B \) and \( C \)


State Huygen's principle, Using this principle draw a diagram to show how a plane wave front incident at the interface of the two media gets
refracted when it propagates from a rarer to a denser medium.Hence verify
Snell's law of refraction


A coconut fruit hanging high in a palm tree has .......... owing to its location.
A. Free energy
B. Kinetic energy
c. Activation energy
D. Potential energy


Assertion
The solubility of a substance changes
with temperature.
Reason
Heat is required to break the bonds
holding molecules together so solubility is dependent on temperature.in dissolution, energy, in the form of heat, is required to break the bonds joining
the molecules in the solid together.
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


\begin{tabular}{|ccc}
if \( \boldsymbol{f}(\boldsymbol{x})= \) & \\
\( \mathbf{1} \) & \( \boldsymbol{x} \) & \( \boldsymbol{x}+ \) \\
\( \boldsymbol{2} \boldsymbol{x} \) & \( \boldsymbol{x}(\boldsymbol{x}-\mathbf{1}) \) & \( (\boldsymbol{x}+ \) \\
\( \boldsymbol{3} \boldsymbol{x}(\boldsymbol{x}-\mathbf{1}) \) & \( \boldsymbol{x}(\boldsymbol{x}-\mathbf{1})(\boldsymbol{x}-\mathbf{2}) \) & \( (\boldsymbol{x}+\mathbf{1}) \boldsymbol{x} \)
\end{tabular}
then \( f(100) \) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B. 1
\( c .100 \)
D. -


In A.C generator increasing no. of turns
in coil :
A. decreases the EMF
B. EMF remains same
c. increases the EMF
D. EMF becomes zero


Assertion
An alternating current does not show
any magnetic effect.
Reason
Alternating current does not vary with time
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


Wires \( A \) and \( B \) are made from the same
material. Wire A has length 12m and weight 50 g, while wire \( B \) is 18 m long and weighs 40 g. Then the ratio \( \left(R_{A} / R_{8}\right) \) of their resistances will be
\( A \cdot 16 / 45 \)
B. 415
\( c \cdot 8 / 15 \)
D. 419


Which of the following is better nucleophile?
A. \( H_{2} O \)
B. \( H O^{-} \)
\( \mathbf{c} \cdot C_{2} H_{5} O^{-} \)
D. \( C H_{3} C O O^{-} \)


Lower aldehyde and ketones attributed to the formation of \( _{--}-_{-}- \) bonding with water molecules.
A. Sigma bonding
B. pii bonding
c. covalent bonding
D. Hydrogen bonding


A current of \( 3.14 A \) flows in an infinitely long wire with cross section in the form of a semicircular ring of radius \( 5 \mathrm{cm} \) The magnitude of magnetic induction on its axis is :
A . \( 8.0 \times 10^{-6} T \)
В. \( 1.6 \times 10^{-5} T \)
c. \( 2.0 \times 10^{-5} T \)
D. \( 4.0 \times 10^{-6} T \)


Evaluate
\( \int \frac{d x}{(2 x-7) \sqrt{(x-3)(x-4)}} \)


The volume of oxygen at \( S T P \) required
to burn \( 2.4 g \) of carbon completely is:
\( \mathbf{A} \cdot 1.12 L \)
B. \( 8.96 L \)
c. \( 2.24 L \)
D. 4.48L


If \( f(x)=\frac{\tan x}{\sqrt{1+\tan ^{2} x}}, \lim _{x \rightarrow(\pi / 2)^{-}} f(x)= \)
\( \boldsymbol{a} \) and \( \lim _{\boldsymbol{x} \rightarrow(\boldsymbol{\pi} / \mathbf{2})^{+}} \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{b} \) then
\( \mathbf{A} \cdot a=b \)
B . \( a=1+b \)
\( \mathbf{c} \cdot a+b=0 \)
D. \( a+b=2 \)


left of a thin convex lens of focal length
\( 30 \mathrm{cm} . \) A convex spherical mirror of
radius of curvature \( 100 \mathrm{cm} \) is placed to
the right of the lens at a distance of
\( 50 \mathrm{cm} . \) The mirror is titled such that the
axis of the mirror is at a angle \( \boldsymbol{\theta}=\mathbf{3 0}^{\circ} \)
to the axis of the lens, as shown in the
figure.

If the origin of the coordinate system is
taken to be at the centre of the lens, the
coordinates \( (\text { in } c m) \) of the point \( (x, y) \)
at which the image is formed are:
\( \mathbf{A} \cdot(125 / 3,25 / \sqrt{3}) \)
B \( \cdot(50-25 \sqrt{3}, 25) \)
c. (0,0)
D. \( (25,25 \sqrt{3}) \)


In a recent survey, \( 40 \% \) houses contained two or more people. Of those houses containing only one person, \( 25 \% \) were having only a male What is the percentage of all houses, which contain exactly one female and no males?
A . 15
B. 45
c. 75
D. Can't be determined


Given the reaction: \( N_{2}(g)+3 H_{2}(g) \rightleftharpoons \)
\( 2 N H_{3}(g)+22 k c a l \)
When 6 moles of \( N H_{3} \) are consumed to
produce nitrogen gas and hydrogen gas, determine the value of \( \Delta H \) for the
reverse reaction?
\( \mathbf{A} \cdot+22 k c a l \)
B . +66 kcal
c. -22 kcal
D. - 66 kcal
E . +33 kcal


If \( \boldsymbol{L} \boldsymbol{M} \| \boldsymbol{Q} \boldsymbol{R}, \frac{\boldsymbol{P} \boldsymbol{L}}{\boldsymbol{L} \boldsymbol{Q}}=\frac{\boldsymbol{3}}{\mathbf{5}}, \boldsymbol{P} \boldsymbol{R}=\mathbf{5 . 6} \boldsymbol{c m} \)
then \( P M \) is
A \( .2 .4 \mathrm{cm} \)
B. 2.3 ст
\( c .2 .1 \mathrm{cm} \)
D. 2.2 cm