n a thin spherical fish bowl of radius
\( 10 \mathrm{cm} \) filled with water of refractive
ndex \( \frac{4}{3}, \) there is a fish at a distance of
\( 4 \mathrm{cm} \) there is a small fish at a distance
of \( 4 \mathrm{cm} \) form the center \( C \) as shown. The
mage of the fish appears, when seen
from the point \( D \) would be
\( A \cdot 5.2 \mathrm{cm} \)
в. 4.8 ст
\( c .2 .6 \mathrm{cm} \)
\( 0.7 .4 \mathrm{cm} \)


A rod lies across frictionless rails in a
uniform magnetic field \( \vec{B} \) as shown in
figure. The rid moves to the right with speed \( V . \) In order to make the induced
emf in the circuit to be zero, the
magnitude of the magnetic field should
A. not change
B. increase linearly with time
c. decrease linearly with time
D. decrease nonlinearly with time
E. answer required


Bakelite is a
A. phenol-formaldehyde resin
B. phenol-acetaldehyde resin
C . phenol-propanaldehyde resin
D. resin in alcohol


A uniform circular disc placed on a
rough horizontal surface has initially
velocity \( v_{0} \) and an angular velocity \( \omega_{0} \) as
shown in the figure. The disc comes to
rest after moving some distance in the direction of motion. Then \( \frac{v_{0}}{r \omega_{0}} \) is
A . \( 1 / 2 \)
B.
\( c \cdot 3 / 2 \)
D. 2


The Sl unit of electric flux is
\( \begin{array}{ll}\text { A. } N & C^{-1} m^{2} \\ \end{array} \)
\( \begin{array}{lll}\text { В. } N & C & m^{-2}\end{array} \)
\begin{tabular}{ll}
c. \( N \) & \( C^{-2} m^{2} \) \\
\hline
\end{tabular}
D. \( N \quad C^{-1} m^{-2} \)


A certain radioactive material can
undergo three different types of decay, each with a different decay constant \( \lambda, 2 \lambda \) and \( 3 \lambda . \) Then, the effective decay
constant \( \lambda_{e f f} \) is
\( A \cdot 6 \lambda \)
B. \( 4 \lambda \)
\( c \cdot 2 \lambda \)
D. \( 3 \lambda \)


Calculate \( \left(\frac{\mathbf{3} \boldsymbol{x}}{\boldsymbol{x}+\mathbf{5}}\right) \div\left(\frac{\mathbf{6}}{\mathbf{4} \boldsymbol{x}+\mathbf{2 0}}\right) \)
given that \( \boldsymbol{x} \neq-\mathbf{5} \)
\( \mathbf{A} \cdot 2 x \)
в. \( \frac{x}{2} \)
c. \( \frac{9 x}{2} \)
D. \( 2 x+4 \)


Construct a right-angled triangle whose
base is \( 12 \mathrm{cm} \) and the sum of its
hypotenuse and another side is \( 18 \mathrm{cm} \)


Draw the number line and represent the following rational numbers on it:
\( \frac{3}{4} \)


Which is correct about \( \Delta G ? \)
This question has multiple correct options
\( \mathbf{A} \cdot \Delta G=\Delta H-T \Delta G \)
B. at equilibrium, \( \Delta G^{\ominus}=0 \)
C . at equilibrium \( \Delta G=-R T l o g K \)
\( \mathbf{D} \cdot \Delta G=\Delta G^{\ominus}+R T \log K \)


\( f t_{n}=3 n+5, \) then find A.P.


A uniform rod of mass \( M \) and length \( L \)
is pivoted at one end such that it can
rotate in a vertical plane. There is negligible friction at the pivot. The free end of the rod is held vertically above the pivot and then released. The angular
acceleration of the rod when it makes
an angle \( \theta \) with the vertical is
\( \mathbf{A} \cdot g \sin \theta \)
B.
\( c \)
D. \( 6 q L \sin \theta \)


\( K_{m} \) value of enzyme is substrate
concentration at
A \( \cdot 1 / 4 V_{\max } \)
B. \( 2 V_{\max } \)
c. \( 1 / 2 V_{\max } \)
D. \( 4 V_{\max } \)


What is rectification? With relevant
circuit diagram and waveforms explain
the working of a P-N junction diode as a full-wave rectifier.


The rate of a reaction quadruples when
the temperature changes from 300 to
310K. What is the activation energy of
this reaction?
(Assume activation energy and preexponential factor are independent of temperature ; \( \ln 2=0.693 ; \mathrm{R}=8.314 \)
\( \left.\boldsymbol{m o l}^{-1} \boldsymbol{K}^{-1}\right) \)


Solve the following pair of equations by cross multiplication rule.
\( \frac{x}{a}+\frac{y}{b}=0, \frac{x}{a}-\frac{y}{b}=4 \)
A. \( x=2 a, y=-2 b \)
в. \( x=-3 a, y=-b \)
c. \( x=a, y=2 b \)
D. None of these


For a sustained chain reaction, the reproduction factor should be:
A . zero
B. one
c. two
D. three


An integer is chosen at random from the
first 200 numbers.What is the
probability that the integer chosen is divisible by 6 or 8.


The phosphorus present in an organic compound of mass \( 0.2 \mathrm{g} \) is oxidized to phosphoric acid by heating with fuming nitric acid. The phosphoric acid so obtained is precipitated as
\( M g N H_{4} P O_{4}, \) which on ignition is
converted into \( M g_{2} P_{2} O_{7} \). If the mass of
\( M g_{2} P_{2} O_{7} \) is \( 0.1 \mathrm{g} \), the percentage composition of phosphorus present in the sample of the organic compound is:
A . 12.96
в. 13.96
\( c \cdot 14.96 \)
D. 11.96


In a cathode ray tube, what is the effect on the beam of particles if a hotter filament is used?
A. Rate of electron emission remains unchanged
B. Rate of electron emission decreases
c. Rate of electron emission increases
D. Rate of electron emission increases then decreases


If the function \( f(x)=\frac{a x+b}{(x-1)(x-4)} \)
has a local maxima at \( (2,-1), \) then
A. \( b=1, a=0 \)
В. \( a=1, b=0 \)
c. \( b=-1, a=0 \)
D. \( a=-1, b=0 \)


Which of the following metals are extracted by electrolytic reduction? This question has multiple correct options
A. \( C u \)
в. \( A l \)
\( \mathrm{c} \cdot M g \)
D. \( A g \)


In a biprism experiment, the distance of 20 th bright bandfrom the center of the
interference pattern is \( 8 \mathrm{mm} . \) The distance of 30 th bright band from the center is
A . \( 11.8 \mathrm{mm} \)
B. 12mm
c. \( 14 \mathrm{mm} \)
D. \( 16 \mathrm{mm} \)


Respiratory distress syndrome occur in patients which lack
A . Larynx
B. Dipalmitoy| lecithin
c. surfactant
D. Both b and c


A particle moves along the \( x \) -axis obeying the equation \( \boldsymbol{x}=\boldsymbol{t}(\boldsymbol{t}-\mathbf{1})(\boldsymbol{t}- \)
2), where \( x \) is in meter and \( t \) is in
second
Find the acceleration of the particle when its velocity is zero.


Temporary hardness of water is removed in Clark's process by adding:
A. caustic soda
B. calgon
c. borax
D. lime


Assertion
The images formed by total internal reflections are much brighter than those formed by mirrors or lenses
Reason

There is no loss of intensity in total
internal reflection.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The percentage of s-character of the hybrid orbital of \( C \) involved in the bond
formation of \( >\boldsymbol{C}=\boldsymbol{C}<\mathbf{i s} \)
A . \( 25 \% \)
B. 50\%
c. \( 33.33 \% \)
D. 100\%


If a mirror reverses right and left, why
does not it reverse up and down?


What will be the reduction potential for the following half-cell reaction at \( 298 \mathrm{K} ? \)
(Given: \( \left[\boldsymbol{A} \boldsymbol{g}^{+}\right]=\mathbf{0 . 1} \mathbf{M} \) and \( \boldsymbol{E}_{c e l l}^{o}=+\mathbf{0 . 8 0} \)
\( \mathbf{V}) \)
A . \( 0.741 \mathrm{v} \)
B. \( 0.80 v \)
c. \( -0.80 v \)
D. \( -0.741 \mathrm{V} \)


Why must both the \( f_{0} \) and the \( f_{e} \) of \( a \) compound microscope have short focal length?


Which of the following is called as natural water purifier?
A. Bacteria
B. Algae
c. Protozoa
D. Virus


Find the sum of the following \( \boldsymbol{A P} \) \( \frac{1}{15}, \frac{1}{12}, \frac{1}{10}, \dots ., \) to 11 terms


What is the colour of a solution of
\( \mathbf{A l}_{2}\left(\mathbf{S O}_{4}\right)_{3} \) in water?
A. blue
B. pink
c. green
D. colourless


A body falling freely towards the earth
has
A. uniform speed
B. uniform velocity
c. uniform acceleration
D. none of these


Incident ray is the ray of light striking a surface.
A . True
B. False


Two liquids of densities \( d_{1} \) and \( d_{2} \) are
flowing in identical capillaries under
same pressure difference. If \( t_{1} \) and \( t_{2} \)
are the time taken for the flow of equal quantities of liquids, then the ratio of coefficients of viscosities of liquids
must be
\( \mathbf{A} \cdot \frac{d_{1} d_{2}}{t_{1} t_{2}} \)
B. \( \frac{d_{1} t_{1}}{d_{2} t_{2}} \)
\( \mathbf{c} \cdot \frac{d_{1} t_{2}}{d_{2} t_{1}} \)
D \( \sqrt{\left(\frac{d_{1} t_{1}}{d_{2} t_{2}}\right)} \)


f \( x=2+5 i(\text { where } 1 i=\sqrt{-1}) \) and
\( 2\left(\frac{1}{1 ! 9 !}+\frac{1}{3 ! 7 !}\right)+\frac{1}{5 ! 5 !}=\frac{2^{a}}{b !} \operatorname{then} x^{3}- \)
\( 5 x^{2}+33 x-10= \)
\( \mathbf{A} \cdot a+b \)
в. \( b-a \)
\( \mathbf{c} \cdot a-b \)
D. \( -a-b \)
E \( .(a-b)(a+b) \)


Find the approximate change in the
surface area of a cube of side \( x \) metres
caused by decreasing the side by 1
percent


Define density and relative density.


\( \boldsymbol{A}(\boldsymbol{3}, \boldsymbol{2}, \boldsymbol{0}), \boldsymbol{B}(\boldsymbol{5}, \boldsymbol{3}, \boldsymbol{2}), \boldsymbol{C}(-\boldsymbol{9}, \boldsymbol{6},-\boldsymbol{3}) \) are
three points forming a triangle. If \( \boldsymbol{A} \boldsymbol{D} \)
the bisector of \( \angle B A C \) meets \( B C \) in \( D \)
then coordinates of \( D \) are
\( ^{\mathrm{A}} \cdot\left(-\frac{19}{8}, \frac{57}{16}, \frac{17}{16}\right) \)
В \( \cdot\left(\frac{19}{8},-\frac{57}{16}, \frac{17}{16}\right) \)
\( ^{\mathrm{C}} \cdot\left(\frac{19}{8}, \frac{57}{16}, \frac{17}{16}\right) \)
D. None of these


Light Year is equivalent to how much
metre?
A \( \cdot 9.5 \times 10^{15} \)
B. \( 950 \times 10^{15} \)
c. \( 9.5 \times 10^{19} \)
D. \( 905 \times 10^{15} \)


A tuning fork of frequency \( 480 \mathrm{Hz} \) produces 10 beats/s when sounded with
a vibrating sonometer string. What must have been the frequency of the string if a slight increase in tension produces fewer beats per second than
before?
A. 460 Н
в. 480 н \( z \)
c. 490 н \( z \)
D. 470 нz


\( \lim _{x \rightarrow \infty} \int_{0}^{x / 2} \frac{t^{2}}{x^{2}\left(1+t^{2}\right)} d t \) is equal to
A \( \cdot \frac{1}{4} \)
B.
c. 1
D. None of these


If \( \vec{a}=\hat{i}+\hat{j}+2 \hat{k} \) and \( \vec{b}=3 \hat{i}+2 \hat{j}-\hat{k} \)
find the value of \( (\vec{a}+3 \vec{b}) \cdot(2 \vec{a}-\vec{b}) \)


Nature of shear stress is
A. Positive
B. Negative
C. Positive as well as negative
D. Is always less than 0.5


One of the constituents of the
pancreatic juice, which is released into the duodenum of a man is
A. Trypsin
B. Chymotrypsin
c. Trypsinogen
D. Both B and C


If \( \epsilon_{0} \) and \( \mu_{0} \) are, respectively, the electric
permittivity and magnetic permeability of free space, \( \epsilon \) and \( \mu \) are the corresponding quantities in a medium, the index of refraction of the medium in
terms of the above parameters is
A \( \cdot \sqrt{\frac{\mu \epsilon}{\mu_{0} \epsilon_{0}}} \)
в. \( \sqrt{\frac{\epsilon}{\mu_{0} \epsilon_{0}}} \)
c. \( \sqrt{\frac{2}{\mu_{0} \epsilon_{0}}} \)
D. \( \sqrt{\frac{1}{\mu_{0} \epsilon_{0}}} \)


The correct order regarding the
electronegativity of hybrid orbitals of
carbon is :
\( \mathbf{A} \cdot s p<s p^{2}>s p^{3} \)
В. \( s p<s p^{2}<s p^{3} \)
c. \( s p>s p^{2}<s p^{3} \)
D. \( s p>s p^{2}>s p^{3} \)


\( A X_{4} \) forms square planar type
structure. Distance between A and X
atoms is 4 units, then distance between
two \( X \) atoms in trans position is:


The force exerted by a charged body on another charged or uncharged body is known as force.
A. magnetic
B. electrostatic
c. gravitational
D. friction


\( x^{\prime \prime} \)
for for
for 3 to at?


What is a calorific value of a fuel 2 .
Write any four characteristics of an
idea fuel?


Define the Iymph.


Pyruvic acid \( +C o A+N A D^{+} \frac{M g^{2+}}{X} \rightarrow \)
\( \boldsymbol{Y}+\boldsymbol{C O}_{2}+\boldsymbol{N} \boldsymbol{A} \boldsymbol{D} \boldsymbol{H}+\boldsymbol{H}^{+} \)
In the following reaction, identify \( X \) and Y respectively:
A. Water, Acetyl CoA
B. Acetyl CoA, Pyruvate dehydrogenase
c. Pyruvate dehydrogenase, Acetyl CoA
D. Pyruvate dehydrogenase, Oxalo-acetic acid


If \( a_{r}>0 ; \forall r, n \in N \) and
\( a_{1}, a_{2}, a_{3}, \dots . a_{2 n} \) are in A.P, then \( \frac{\boldsymbol{a}_{\mathbf{1}}+\boldsymbol{a}_{\mathbf{2} n}}{\sqrt{\boldsymbol{a}_{1}}+\sqrt{\boldsymbol{a}_{2}}}+\frac{\boldsymbol{a}_{\mathbf{2}}+\boldsymbol{a}_{\mathbf{2} n-1}}{\sqrt{\boldsymbol{a}_{2}}+\sqrt{\boldsymbol{a}_{3}}}+ \)
\( \frac{\boldsymbol{a}_{\boldsymbol{3}}+\boldsymbol{a}_{\boldsymbol{2} \boldsymbol{n}-\boldsymbol{2}}}{\sqrt{\boldsymbol{a}_{\boldsymbol{3}}}+\sqrt{\boldsymbol{a}_{\boldsymbol{4}}}}+\ldots+\frac{\boldsymbol{a}_{\boldsymbol{n}}+\boldsymbol{a}_{\boldsymbol{n}+1}}{\sqrt{\boldsymbol{a}_{\boldsymbol{n}}}+\sqrt{\boldsymbol{a}_{\boldsymbol{n}+1}}}= \)
\( \mathbf{A} \cdot n-1 \)
в. \( \frac{n\left(a_{1}+a_{2 n}\right)}{\sqrt{a_{1}}+\sqrt{a_{n+1}}} \)
c. \( \frac{n-1}{\sqrt{a_{1}}+\sqrt{a_{n+1}}} \)
D. \( n+1 \)


To find the vector and the Cartesian
equation in symmetric form of line passing through the points, (2,0,-3) and \( (\mathbf{7}, \mathbf{3},-\mathbf{1 0}) \)


Calculate the neutron separation energy from the following data. \( \boldsymbol{m}\left(_{20}^{40} \boldsymbol{C a}\right)=\mathbf{3 9 . 9 6 2 5 9 1} \boldsymbol{u} \)
\( \boldsymbol{m}\left(_{20}^{41} \boldsymbol{C a}\right)=\mathbf{4 0 . 9 6 2 2 7 8} \boldsymbol{u} \)
\( \boldsymbol{m}_{n}=\mathbf{1 . 0 0 8 6 5} \)
\( \mathbf{1} \boldsymbol{u}=\mathbf{9 3 1 . 5} \boldsymbol{M} e \boldsymbol{V} / \boldsymbol{C}^{2} \)
\( \mathbf{A} \cdot 7.57 M e V \)
В. \( 8.36 \mathrm{MeV} \)
c. 9.12 MeV
D. 9.56 MeV


One of the following named reaction is an example of disproportionation reaction. Identify it
A. Birch reduction
B. Aldol condensation
c. Reimer-Tiemann reaction
D. Cannizaro reaction


Calculate the \( \% \) s-character in the lone
pair electron of \( N H_{3}, \) where the
percentage s-character of bond pair is \( 22 \% \) in each \( N-H \) bond
A . \( 60 \% \)
B. 25\%
c. \( 44 \% \)
D. \( 34 \% \)


If \( A \) is non-singular matrix such that
\( (A-2 I)(A-4 I)=0 \) then \( A+ \)
\( \mathbf{8 A}^{-1}= \)
\( A \)
B.
c. \( 3 I \)
D. \( 6 I \)


Neutron is 1842 times heavier than :
A. proton
B. electron
c. both A and B
D. photon


Helium is the lightest gas.
A. True
B. False


Find the value of \( \frac{d y}{d x} \quad \) a \( \theta=\frac{n}{4}, \) if \( x= \)
\( \boldsymbol{a} e^{\theta}(\sin \theta-\cos \theta) \) and \( y=a e^{\theta}(\sin \theta- \)
\( \cos \theta) \)


Assertion
f \( n>1 \) then Statement - 1 :
\( \int_{0}^{\infty} \frac{\boldsymbol{d} \boldsymbol{x}}{\mathbf{1}+\boldsymbol{x}^{n}}=\int_{0}^{1} \frac{\boldsymbol{d} \boldsymbol{x}}{\left(\mathbf{1}-\boldsymbol{x}^{n}\right)^{1 / n}} \)
Reason
Statement
-2: \( \int_{a}^{b} f(x) d x=\int_{a}^{b} f(a+ \)
\( \boldsymbol{b}-\boldsymbol{x}) d \boldsymbol{x} \)
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. Both Assertion and Reason are incorrect


The current in resistance \( \mathrm{R} \) at
resonance in ac circuit is
A . zero
B. minimum but finite
c. maximum but finite
D. infinite


Chloroplast dimorphism is a characteristic feature of
A. Plants with Calvin cycle
B. \( C_{4} \) plants
c. All plants
D. only in algae


Two thin uniform rods \( \boldsymbol{A}(\boldsymbol{M}, \boldsymbol{L}) \) and
\( B(3 M, 3 L) \) are joined as shown. Find
the \( M I \) about an axis passing through
the centre of mass of system of rods and perpendicular to the length.


If \( x=\frac{4}{3} \) is a zeroes of the polynomial
\( p(x)=6 x^{3}-11 x^{2}+k x-20, \) find the
value of \( k \)


A device that converts energy of
combustion of fuels like hydrogen and methane, directly into electrical energy
is known as:
A. dynamo
B. Ni-Cd cell
c. fuel cell
D. electrolytic cell


A double convex lens of focal length \( 30 c m \) is made of glass of R.I. \( 1.6 . \) When it is immersed in a liquid, the focal length is found to be \( 90 \mathrm{cm} \).The R.I. of the liquid is
A . 1.33
в. 1.5
c. 1.4
D. 1.42


Which portion of the heating curve for
water shown above would there be both
liquid and solid water present?
\( A \cdot A-B \)
3. \( B-C \)
\( c \cdot C-D \)
D. \( D-E \)


Which of the following statements is
not true about sucrose?
A. On hydrolysis, it produces glucose and fructose.
B. The glycosidic linkage is present between \( C_{1} \) of \( \alpha \) glucose and \( C_{1} \) of \( \beta \) - fructose.
C. It is also named as invert sugar.
D. It is a non reducing sugar.


Conduction of nerve impulse is
A. Faster in non-myelinated fibres
B. Faster in myelinated fibres
C. No difference in the rate of conduction in myelinated and non-myelinated fibres.
D. None of the above


\( A B C D \) is a trapezium in which \( A B \) is
parallel to \( D C \). If the diagonals
intersect at \( O \), then which one of the
following is correct?
A \( \cdot \frac{O A}{O C}=\frac{O B}{O D} \)
в. \( \frac{A D}{B C}=\frac{A B}{D C} \)
c. \( \frac{O B}{O C}=\frac{B C}{C D} \)
D. \( \frac{O A}{D C}=\frac{D A}{D C} \)


Given;
(i) \( C u^{2+}+2 e^{-} \rightarrow C u, E^{\circ}=0.337 V \)
(ii) \( \boldsymbol{C u}^{2+}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{C u}^{+}, \boldsymbol{E}^{\circ}=\mathbf{0 . 1 5 3} \boldsymbol{V} \)
Electrode potential \( \boldsymbol{E}^{\circ} \) for the reaction,
\( \boldsymbol{C u}^{+}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{C u}, \) will be:
A . \( 0.38 V \)
в. \( 0.52 \mathrm{V} \)
c. \( 0.90 V \)
D. \( 0.30 V \)


For a transistor to work as an amplifier:
A. its emitter junction is in reverse bias and collector junction is in forward bias
B. the transistor must have breakdown region
C. its emitter junction is in forward bias and collector junction is in reverse bias
D. its emitter and collector junction are in forward bias


A gas has
A. one specific heat only
B. two specific heats only
C. many number of specific heats
D. no specific heat


Who among the following first prepared a stable compound of noble gas?
B. Reyleigh
C. Ramsay
D. Rutherford


In the circuit diagram find:
(A) Equivalent resistance
(B) Current shown by the ammeter \( A \)


In Fig. the angle of inclination of the
inclined plane is \( 30^{0} . \) Find the horizonta
velocity \( V_{0} \) so that the particle hits the
inclined plane perpendicularly.
A \( \cdot V_{0}=\sqrt{\frac{2 g H}{5}} \)
B. \( V_{0}=\sqrt{\frac{2 g H}{7}} \)
\( \mathbf{c} \cdot_{V_{0}}=\sqrt{\frac{g H}{5}} \)
D \( \cdot V_{0}=\sqrt{\frac{g H}{7}} \)


Which of the following is the most common fire extinguisher?
A. Foam
в. \( C O_{2} \)
c. water
D. Dry powder


Cells of all living organisms have a nucleus.
A . True
B. False


The dimensional formula for magnetic flux is
\( \mathbf{A} \cdot\left[M L^{2} T^{-2} A^{-1}\right] \)
B \( \cdot\left[M L^{3} T^{-4} A^{-2}\right] \)
c. \( \left[M^{0} L^{-2} T^{-2} A^{-2}\right] \)
D \( \cdot\left[M L^{2} T^{-1} A^{2}\right] \)


Let \( A \) and \( B \) are two matrices of same
order \( 3 \times 3 \) given by \( \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{3} & \boldsymbol{\lambda}+\mathbf{2} \\ \mathbf{2} & \mathbf{4} & \mathbf{6} \\ \mathbf{3} & \mathbf{5} & \mathbf{8}\end{array}\right], \boldsymbol{B}=\left[\begin{array}{ccc}\mathbf{3} & \mathbf{2} & \mathbf{4} \\ \mathbf{3} & \mathbf{2} & \mathbf{5} \\ \mathbf{2} & \mathbf{1} & \mathbf{4}\end{array}\right] \)
If \( A \) is a singular matrix, then \( t r(A+ \)
\( B \) ) is equal to
A .24
в. 11
\( c .22 \)
D. None of these


Find equation of circle which passes through the point (2,3) and touches the line \( 2 x-3 y-13=0 \) at the point
(2,-3)


If \( f(x)=\frac{x^{2}-10 x+25}{x^{2}-7 x+10} \) for \( x \neq 5 \) and \( f \) is
continuous \( a t x=5, \) then \( f(5) \) has the
value equal to-
A .
B. 5
c. 10
D. 25


The relative proportion between the
volume of \( \mathrm{CO}_{2} \) released and \( \mathrm{O}_{2} \) absorbed
in respiration is termed as
A. Respiratory exchange
B. Respiratory quotient
c. Respiratory phase
D. None of the above


In which one of the following intervals
is the function \( f(x)=x^{2}-5 x+6 \)
decreasing?
A \( \cdot x<\frac{5}{2} \)
в. \( x<\frac{2}{5} \)
c. \( _{x>\frac{2}{5}} \)
D. none


The magnetic moment of a divalent ion in aqueous solution with atomic number 25 is:
A. 5.47 В.М
в. 2.9 в.м
c. 6.9 В. .
D. 6.7 в.м


How many kilograms of wet NaOH containing \( 10 \% \) water are required to prepare 60 litre of a \( 0.5 \mathrm{M} \) solution?
A . \( 1.23 \mathrm{kg} \)
B. \( 1.13 \mathrm{kg} \)
c. \( 1.33 \mathrm{kg} \)
D. \( 1.24 \mathrm{kg} \)


Three resistors of \( 10 \Omega, 15 \Omega \) and \( 20 \Omega \)
are connected in series in a circuit. If
the potential drop across the \( 15 \Omega \)
resistor is \( 3 V \), find the current in the
circuit, potential drop across \( 10 \Omega \) and the net emf of the source used in the
circuit. (Draw the circuit diagram)


Two electric dipoles, \( A, B \) with respective dipole moments \( \overrightarrow{\boldsymbol{d}}_{\boldsymbol{A}}= \) \( -4 q a \hat{i} \) and \( \vec{d}_{B}=-2 q a \hat{i} \) placed on the
x-axis with a separation \( R \), as shown in the figure. The distance from \( A \) at which both of
them produce the same potential is
\( A \)
\[
\frac{\sqrt{2} R}{\sqrt{2}+1}
\]
в.
\[
\frac{R}{\sqrt{2}+1}
\]
\( c \)
\[
\frac{\sqrt{2} R}{\sqrt{2}-1}
\]
\( D \)
\[
\frac{R}{\sqrt{2}-1}
\]


The additive used in transparent soaps
is:
A. glycol
B. pyrol
c. methanol
D. glycerol


The average density of the earth in terms of \( g, \) Gand \( R \) is:
A \( \cdot \frac{4 \pi G R}{3 g} \)
в. \( \frac{3 g}{4 \pi G R} \)
c. \( \frac{3 g}{4 \pi G R^{2}} \)
D. \( \frac{4 \pi G R^{2}}{3 g} \)


The conductor \( A D \) moves to the right in
a uniform magnetic field directed into the plane of the paper.
This question has multiple correct options
A. The free electron in \( A D \) will move toward \( A \)
B. Dd will acquire a positive potential with respect to
c. \( A \) current will flow from \( A \) to \( D \) in \( A D \) in closed loop
D. The current in \( A D \) flows from lower to higher potential
E. answer required


in which two infinitely long static line charges of constant positive line charge
density \( \lambda \) are kept parallel to each other.
In their resulting electric field, point
charges \( \boldsymbol{q} \) and \( -\boldsymbol{q} \) are kept in
equilibrium between them. The point
charges are confined to move in the \( x \)
direction only. If they are given a small
displacement about their equilibrium positions, then the correct statement(s) is (are)
A. Both charges execute simple harmonic motion.
B. Both charges will continue moving in the direction of their displacement
c. Charge \( +q \) executes simple harmonic motion while charge \( -q \) continues moving in the direction of its displacement.
D. Charge \( -q \) executes simple harmonic motion while charge \( +q \) continues moving in the direction of its displacement


Assertion
Although \( P F_{5}, P C l_{5} \) and \( P B r_{5} \) are
known, the pentahalide of nitrogen has not been observed.
Reason
Phosphorus has lower electronegativity than nitrogen.
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


Study the bar graph representing the
number of persons in various age
groups in a town shown in Fig.. Observe
the bar graph and answer the following
questions:

What is the age-group of exactly 1200
persons living in the town?


A nuclide \( X \) undergoes \( \alpha \) -decay and
another nuclide undergoes \( \beta \) -decay.
Which of the following statements are
correct?
This question has multiple correct options
A. The \( \beta \) -particles emitted by \( Y \) may have widely different speed
B. The \( \alpha \) -particles emitted by \( X \) may have widely different speed
C. The \( \alpha \) -particles emitted by \( X \) will have almost the same speed
D. The \( \beta \) -particles emitted by \( Y \) will have the same speed


A person standing on a road has to hold
his umbrella at \( 60^{\circ} \) with the vertical to
keep the rain away. He throws the
umbrella and starts running at \( 20 m s^{-1} \)
He find that rain drops are hitting his head vertically. Find the speed of the rain drops with respect to (a) the road
and
(b) the moving person.


Can you think of a triangle in which two
altitudes of the triangle are two of its sides?


Graphite is a good conductor of electricity because:
A. has tetra hedral structure
B. has free electrons
c. is crystalline
D. has free atoms


Umbra and penumbra are seen in:
\( A \). rainbows
B. tides
c. shadows
D. sunlight


Noble gases belongs to group of periodic table.
A. VII A
B. VIII A
c. VIII B
D. VIA


Find the incorrectly matched compounds with the functional group.
A. \( C H_{3} C O O H, \) hydroxy
B. \( C H_{3} O H, \) hydroxy
c. \( C H_{3} C H_{2} N H_{2} \), amine
D. \( C C l_{3} C O O H, \) carboxylic acid
E . \( C_{6} H_{5} C O O H, \) carboxylic acid


The Sl unit of density is:
A \( \cdot g m^{-3} \)
в. \( k g m^{-3} \)
\( \mathrm{c} \cdot g \mathrm{cm}^{-3} \)
D. \( k g c m^{-3} \)


Calorie is defined as the amount of heat
required to raise temperature of \( 1 g \) of water by \( 1^{\circ} \mathrm{C} \) and it is defined under which of the following conditions?
A . From \( 14.5^{\circ} \mathrm{C} \) to \( 15.5^{\circ} \mathrm{C} \) at \( 760 \mathrm{mm} \) of \( \mathrm{Hg} \)
B. From \( 98.5^{\circ} \mathrm{C} \) to \( 99.5^{\circ} \mathrm{C} \) at \( 760 \mathrm{mm} \) of \( \mathrm{Hg} \)
C. From \( 13.5^{\circ} \mathrm{C} \) to \( 14.5^{\circ} \mathrm{C} \) at \( 76 \mathrm{mm} \) of \( \mathrm{Hg} \)
D. From \( 3.5^{\circ} \mathrm{C} \) to \( 4.5^{\circ} \mathrm{C} \) at \( 76 \mathrm{mm} \) of \( \mathrm{Hg} \)


Proton which kinetic energy of \( 1 M e V \)
moves from south to north. It gets an
acceleration of \( 10^{12} m / s^{2} \) by an applied
magnetic field (west to east). The value of magnetic field:
(Rest mass of proton is \( \left.1.6 \times 10^{-27} k g\right) \)
A. \( 0.071 m T \)
B. \( 71 m T \)
\( c .0 .71 m T \)
D. \( 7.1 m T \)


\( \int \frac{e^{x}}{\left(2 e^{x}-3\right)^{2}} d x= \)
A \( \cdot \frac{-1}{2\left(2 e^{x}-3\right)}+c \)
в. \( \frac{1}{2 e^{x}-3}+c \)
c. \( \frac{1}{2\left(2 e^{x}-3\right)^{2}}+c \)
D. \( \frac{1}{\left(2 e^{x}-3\right)^{2}}+c \)


Final major product of this reaction is:
A \( \cdot C H_{3} C_{H_{2}}^{14} C H_{3} \)
В \( \cdot C_{H_{3}}^{14} C H_{2} C H_{3} \)
\( \mathbf{c} \cdot c_{H_{3}} C_{H_{2}-C H O}^{14}-C H O \)
D. \( C_{H_{3}-C H_{2}-C H O}^{14}-C_{3}-C H O \)


What is lateral shift? Establish relation
between focal length and radius of curvature of a mirror.


Assertion
The para-isomers have higher melting point as compared to their ortho and meta-isomers.
Reason
It is due to symmetry of para-isomers that fits in crystal lattice better as
compared to ortho- and meta-isomers.
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


Explain the classification of enzymes.


Assertion
The relative velocity between the bodies
is equal to the sum of the velocities of
two bodies.
Reason
When body moves in opposite directions, the magnitude of the
relative velocity is equal to sum of magnitudes of individual velocities.
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 incorrect but Reason is correct
D. Both Assertion and Reason are incorrect


The following data gives the number (in thousands) of applicants registered with an Employment Exchange during.
\[
1995-2000
\]
year 1995 \( \quad 1996 \quad \) 1997
Number of applicants registered
20
24
in thousands
Construct a bar graph to represent the above data.


Whenever there are two or more chains
with equal number of carbon atoms:
A. the chain that contains double or triple bond is to be selected as the parent chain
B. the chain that has more substituents is selected as
parent chain
c. the chain with less number of substituent is selected
as a parent chain
D. the chain without double bond is selected as parent chain


\( y+x^{2}=\frac{d y}{d x} \) has the solution
A. \( y+x^{2}+2 x+2=c . e^{x} \)
B . \( y+x+2 x^{2}+2=c . e^{x} \)
C \( \cdot y+x+x^{2}+2=c \cdot e^{2 x} \)
D . \( y^{2}+x+x^{2}+2=c . e^{2 x} \)


A ball is dropped from height \( h \) and
another from \( 2 h . \) The ratio of time taken
by the two balls to reach ground is:
A. \( 1: \sqrt{2} \)
2 \( : \sqrt{2} \cdot \sqrt{2} \cdot \sqrt{2} \)
B. \( \sqrt{2}: 1 \)
c. 2: 1
D. 1: 2


What voltage on \( y \) -plate will give such a
deflection
A \( .0 .11 V \)
B. \( 1.1 V \)
\( \mathbf{c} \cdot 11 V \)
D. none


The value of 'a' for which the function \( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{cc}-\boldsymbol{x}^{3}+\cos \boldsymbol{a} & \boldsymbol{0}<\boldsymbol{x}<1 \\ \boldsymbol{x}^{2} & \boldsymbol{x} \geq \mathbf{1}\end{array}\right. \)
has a local minimum at \( x=1 \), is
This question has multiple correct options
A . -1
B. 1
\( c \cdot 0 \)
D. \( -\frac{1}{2} \)


A current of i ampere is flowing in an equilateral triangle of side a. The magnetic induction at the centroid will
be?
A \( \cdot \frac{\mu_{i}}{3 \sqrt{3} \pi a} \)
в. \( \frac{3 \mu_{i}}{2 \pi a} \)
\( ^{\mathrm{c}} \cdot \frac{5 \sqrt{2} \mu_{i}}{3 \pi a} \)
D. \( \frac{9 \mu_{i}}{2 \pi a_{i}} \)


Assertion
To give scientific name to a plant, there
is ICBN.
Reason
It uses articles, photographs and recommendations to name a plant.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of the following is not a drug?
A. Antihistamine
B. Rantadine
c. Aspirin
D. None of the above


The first probable fossil of man was
A. Australopithecus
B. Zinjanthropus
c. Pithecanthropus
D. Plesianthropus


The figure represents a voltage regulator circuit using a Zener diode. The breakdown voltage of the Zener diode is \( 6 V \) and the load resistance is
\( R_{L}=4 k \Omega . \) The series resistance of the
circuit is \( R_{i}=1 k \Omega . \) If the battery
voltage \( V_{B} \) varies from \( 8 V \) to \( 16 V \), what
are the minimum and maximum values
of the current through Zener diode?
A. \( 0.5 \mathrm{mA} ; 6 \mathrm{mA} \)
B. \( 0.5 \mathrm{mA} ; 8.5 \mathrm{mA} \)
c. \( 1.5 m A ; 8.5 m A \)
D. \( 1 \mathrm{mA} ; 8.5 \mathrm{mA} \)


\( 0.3 \mathrm{g} \) of chloroplatinate of an organic diacidic base left 0.09 g of platinum on ignition. The molecular weight (in g/mol) of the organic base is :
A . 120
в. 240
c. 180
D. 60


What will be the mass of a \( 0.500 \mathrm{m} \)
solution of sodium acetate in water
containing \( 0.5 \mathrm{Kg} \) sodium acetate?


A mixture of \( \boldsymbol{H}_{2} \boldsymbol{O} \) and solid \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l} \)
shaken to obtain saturated solution.
The solid is filtered and to \( 100 m L \)
filtrate, \( 100 m L \) of \( 0.03 M N a B r \) is added, will a precipitate formed? \( \boldsymbol{K}_{s p} \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l}=\mathbf{1 0}^{-10}, \boldsymbol{K}_{s p} \boldsymbol{A} \boldsymbol{g} \boldsymbol{B r}=\mathbf{5} \times \)
\( \mathbf{1 0}^{-13} \)


A step up transformer converts \( 100 \mathrm{V} \) at
primary to \( 300 \mathrm{V} \) at secondary. If the primary current is \( 6 A \), then the secondary current is \( A \)
A . 4
B. 8
c. 2
D. 10


Solve:
\( \int e^{x}\left(\tan ^{-1} x+\frac{1}{1+x^{2}}\right) d x \)
A \( \cdot e^{x} \tan ^{-1} x+c \)
B. \( \frac{e^{x}}{1+x^{2}}+c \)
\( \mathbf{c} \cdot e^{x} \tan x+c \)
D. None of these


Fill in the blanks:
The \( \ldots \) tungsten is reduced by coating with barium oxide.
A. Normal function
B. Force function
c. Power function
D. Work function


In a simple microscope, if the final
image is located at \( 25 \mathrm{cm} \) from the eye placed closed to the lens, then
magnifying power is
A \( \cdot \frac{25}{f} \)
в. \( _{1+\frac{25}{f}} \)
c. \( \frac{f}{25} \)
D. \( \frac{25}{f}+ \)


The diagram below shows the path of a light ray in three different materials.
The index of refraction for each material
is shown in the upper right portion of
the material.

Rank the index of refraction values,
greatest first
\( \mathbf{A} \cdot n_{1}, n_{2}, n_{3} \)
В. \( n_{1}, n_{3}, n_{2} \)
\( \mathbf{c} \cdot n_{2}, n_{1}, n_{3} \)
\( \mathbf{D} \cdot n_{2}, n_{3}, n_{1} \)
E \( . n_{3}, n_{1}, n_{2} \)


Assertion
The sum of mole fractions of all the
components of a solution is unity.
Reason
Mole fraction is a temperature
dependent mode of concentration.
Choose the correct option.
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 disease caused due to improper sanitation in public place is
A. Pandemic.
B. Non-communicable.
c. Endemic.
D. None of the above


Name the gas that is produced in the following cases. Action of dilute hydrochloric acid on sodium sulphide.


Match the followings in column I with
column II and choose the correct
combination
\( \begin{array}{llll} & \text { Column I } & & \text { Column II } \\ \text { A } & \text { Xylem vessels } & 1 & \begin{array}{l}\text { Store food } \\ \text { materials }\end{array} \\ \text { B } & \begin{array}{l}\text { Xylem } \\ \text { tracheids }\end{array} & \text { 2 } & \begin{array}{l}\text { Obliterated } \\ \text { lumen }\end{array} \\ \text { D } & \text { Xylem fibre } & \text { 3 } & \begin{array}{l}\text { Perforated } \\ \text { plate }\end{array} \\ \text { D } & \begin{array}{l}\text { Xylem } \\ \text { parenchyma }\end{array} & \text { 4 } & \begin{array}{l}\text { Chisel-like } \\ \text { ends }\end{array}\end{array} \)
A \( \cdot A-4, B-3, C-2, D-1 \)
B. A- 3, B- 2, C-1, D-4
C. \( A-2, B-1, C-4, D-3 \)
D. A-1, B-2, C-3, D-4
E. A- \( 3, \) B- 4, C- 2, D-


While representing \( \frac{2}{3} \) on a number line, between which 2 integers does the point
lie?
A. 1 and 2
B. 0 and 1
\( c \cdot 2 \) and 3
D. 1 and 3


Match the list of noble gas compounds
in column I with their shapes in column
II and mark the appropriate choice.
Column I Column II
(A) \( X e F_{4} \)
(i) Distorted octahedral
(B) \( X e F_{6} \)
(ii) Tetrahedral
(С) \( X e O_{3} \)
(iii) Square planar
(D) \( X e O_{4} \)
(iv) Trigonal pyramidal
\( \mathbf{A} \cdot(A) \rightarrow(i v),(B) \rightarrow(i i i),(C) \rightarrow(i i),(D) \rightarrow(i) \)
B. \( (A) \rightarrow(i),(B) \rightarrow(\text { ii }),(C) \rightarrow(\text { iii), }(D) \rightarrow(i v) \)
C \( \cdot(A) \rightarrow(\text { ii }),(B) \rightarrow(\text { iii }),(C) \rightarrow(i v),(D) \rightarrow(i) \)
\( \mathbf{D} \cdot(A) \rightarrow(\text { iii }),(B) \rightarrow(i),(C) \rightarrow(\text { iv }),(D) \rightarrow(\text { ii }) \)


If
A, B are two independent events, \( P(A)=\frac{3}{4} \) and \( P(B)=\frac{5}{8}, \) then
\( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B})= \)
A \( \cdot \frac{3}{32} \)
в. \( \frac{29}{32} \)
c. \( \frac{15}{32} \)
D. \( \frac{5}{32} \)


The sides of a triangle are given as \( a, 2 a+3 \) and \( 3 a-3 . \) If the perimeter is
\( 60 c m, \) find the number smaller side of the triangle.


Find the inverse of the following matrix
by using elementary row
transformation
\( \left[\begin{array}{ccc}2 & 0 & -1 \\ 5 & 1 & 0 \\ 0 & 1 & 3\end{array}\right] \)


According to J. Chadwick,
is not found in
hydrogen atom.
A. neutron
B. electron
c. proton
D. none of the above


If the nth term of the A.P is \( 6 n-1 \) find
the \( \boldsymbol{S}_{\boldsymbol{n}} \)


A process is said to be reversible if:
A. the system return to their original states
B. the surroundings return to their original states
C. both the system as well as the surroundings return to their original states
D. neither system nor surroundings return to their original states


One side of a parallelogram is \( 8 \mathrm{cm} \) If the corresponding altitude is \( 6 \mathrm{cm} \) then its area is given by
A \( .24 \mathrm{cm}^{2} \)
B. 36 \( c m^{2} \)
\( c \cdot 40 \mathrm{cm}^{2} \)
D. \( 48 \mathrm{cm}^{2} \)


The number of permutations that can be made out of the letters of the word
"MATHEMATICS" When all vowels come
together is:
A \( \cdot \frac{8 ! 4 !}{2 !} \)
в. \( \frac{8 ! 4 !}{(2 !)^{2}} \)
c. \( \frac{7 ! 4 !}{2 !} \)
D. 7!4!


A stone is dropped into a quiet lake and waves move in circles at the sped of 5
cm/sec.

At that instant, when radius of circular
wave is \( 8 \mathrm{cm}, \) how fast is the enclosed area increasing?
\( \mathbf{A} \cdot 8 \pi \mathrm{cm}^{2} / \mathrm{s} \)
B. \( 80 \pi c m^{2} / s \)
c. \( 6 \pi c m^{2} / s \)
D. \( \frac{8}{3} \pi c m^{2} / s \)


A point charge \( +Q \) is placed just
outside an imaginary hemispherical
surface of radius \( R \) as shown in the
figure. Which of the following statements
is/are correct?
This question has multiple correct options
A. The electric flux passing through the curved surface of the hemisphere is \( -\frac{Q}{2_{\varepsilon_{0}}}\left(1-\frac{1}{\sqrt{2}}\right) \)
B. Total flux through the curved and the flat surface is \( \underline{Q} \)
C. The component of the electric field normal to the flat surface is constant over the surface
D. The circumference of the flat surface is an
equipotential


Explain with well labelled diagram different regions of root and also
explain structure of root hair?


The two straight lines \( a_{1} x+b_{2} y+ \)
\( c_{2}=0 \) and \( a_{2} x+b_{2} y+c_{2} z=0 \) will be
parallel to each other, if
A \( \cdot \frac{a_{1}}{b_{1}}=\frac{a_{2}}{b_{2}} \)
В \( \cdot \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}} \)
c. \( a_{1} b_{1}=a_{2} b_{2} \)
D. \( a_{1} a_{2}=b_{1} b_{2} \)


Assertion
Oxidation of one molecule of NADH
gives rise to 3 molecules of ATP and
that of one molecule of \( \boldsymbol{F A D H}_{2} \)
produces 2 molecules of ATP.
Reason

The number of ATP molecules
synthesised depends on the nature of the electron donor.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Assertion
2 is a rational number.
Reason
The square roots of all positive integers
are irrationals.
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


An ideal solenoid of cross-sectional
\( \operatorname{area} 10^{-4} m^{2} \) has 500 turns per metre.
At the centre of this solenoid, another
coil of 100 turns is wrapped closely around it, if the current in the coil
charges from 0 to \( 2 A \) in 3.14 ms, the
emf developed in the second coil is:
\( \mathbf{A} \cdot 1 m V \)
B. \( 2 m V \)
\( \mathbf{c} .3 m V \)
D. \( 4 \mathrm{mV} \)


An example of oxidation-reduction
reaction is:
\( \mathbf{A} \cdot B C l_{3}+C l^{-} \rightarrow B C l_{4} \)
B. \( H C N+H_{2} O \rightarrow H_{3} O^{+}+C N^{-} \)
\( \mathbf{c} \cdot H_{2} O_{2}+2 B r^{-}+2 H^{+} \rightarrow 2 H_{2} O+B r_{2} \)
D. \( 2 N H_{3}(g) \rightarrow N_{2}(g)+3 H_{2}(g) \)


The weight of a satellite on earth is 100
kN. What is the gravitational force on the satellite when it orbits the earth at a
distance of \( 12800 \mathrm{km} \) from the center of
the earth?
A. 11 kilo-newtons
B. 25 kilo-newtons
c. 50 kilo-newtons
D. 100 kilo-newtons
E. 200 kilo-newtons


The decomposition of \( N_{2} O_{5} \) dissolved in carbon tetra chloride occurs followingly
at constant temperature.
\( N_{2} O_{5(s o l u t i o n)} \rightleftharpoons 2 N O_{2(s o l u t i o n)}+ \)
\( \frac{1}{2} O_{2(g)} \)
This reaction is of first order and its
rate constant is \( 5 \times 10^{-4} \mathrm{sec}^{-1} ? \) If
initial concentration of \( N_{2} O_{5} \) is 0.4 mol
litre then
(i) What will be the initial reaction rate?
(ii) What will be the half-life period of
this reaction?
(iii) What time will be taken to
complete \( 75 \% \) reaction?


Two particles are placed at some distance and the magnitude of gravitational force between them is F. If the mass of each of the two particles is doubled, keeping the distance between them unchanged, the new value of gravitational force, in terms of \( F \) between them will be:
A \( \cdot \frac{F}{4} \)
в. \( 4 F \)
c. \( \frac{F}{2} \)
D.


Occurrence of more than one type of leaves is
A. Decussate phyllotaxy
B. Heterophylly
c. Aestivation
D. Anisophylly


What is the shape of each face of a cube?
A. Square
B. Circular
c. Hyperbolic
D. Eliptical


If \( P=\left[\begin{array}{lll}1 & c & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4\end{array}\right] \) is the adjoint of a
\( 3 \times 3 \) matrix \( Q \) and \( \operatorname{det} .(Q)=4, \) then \( c \) is
equal to.
\( \mathbf{A} \cdot \mathbf{0} \)
B. 4
c. 5
D. 11


The king of a province proposes a new law that would give a tax credit to parents who homeschool their children.
\( 10 \% \) of ministers approve of the law. Of these, 7 out of 10 are women. All other ministers are against the law. If there are equal numbers of men and women in his ministry department, then what fraction of male ministers approve of
the ordinance?
A \( \cdot \frac{3}{10} \)
B. \( \frac{3}{47} \)
c. \( \frac{3}{50} \)
D. \( \frac{3}{100} \)


Find the mean of the following
frequency distribution
Height from 200 1000 mean
sea
600
level
No. of
Villages 107 265 143 115


Polarisation of the electron cloud of
cation is less than anion because:
A. p/e ratio is more than one for anion
B. p/e ratio is less than one for cation
C. p/e ratio is more than one for cation by which electrons are relatively loosely held compared to anion
D. p/e ration is more than one for cation while less than one for anion by which electron cloud is relatively loosely held for anion


Incipient heterospory is shown by the pteridophyte
A. Selaginella
B. Dryopteris
c. Lycopodium
D. Equisetum


Number of sigma and pi bonds in \( \mathrm{ClO}_{3}^{-} \)
ion are:
\( \mathbf{A} \cdot 2 \sigma \) and \( 2 \pi \)
B. \( 3 \sigma \) and \( 3 \pi \)
\( \mathbf{c} \cdot 3 \sigma \) and \( 2 \pi \)
D. \( 2 \sigma \) and \( 3 \pi \)


A proton is moving in a uniform magnetic field \( B \) in a circular path of
radius \( a \) in a direction perpendicular to
\( Z \) axis along which field \( B \) exists. Calculate the angular momentum. If the
radius is \( a \) and charge on proton is \( e: \)
A \( \cdot \frac{B e}{a^{2}} \)
B \( \cdot e B^{2} a \)
\( \mathbf{c} \cdot a^{2} e B \)
D. \( a e B \)


Explain the steps involved in translation


Which plant group is exclusively
perennial?
A. Dicots
B. Ferns
c. Gymnosperms
D. Monocots


Velocity' \( V^{\prime} \) of a wave is directly
proportional to modulus of elasticity' \( \boldsymbol{E} \) and density ' \( d \) of a medium. The
expression of ' \( V \) ' using dimensional analysis is:
A \( \cdot V=\frac{E}{\sqrt{d}} \)
B. \( V=\frac{\sqrt{E}}{d} \)
c. \( v=\sqrt{\frac{E}{d}} \)
D. \( V=\sqrt{E D} \)


\( \frac{3+\cot 76^{0} \cot 16^{0}}{\cot 76^{0}+\cot 16^{0}} \) is equal to
This question has multiple correct options
\( A \cdot \tan 16^{0} \)
B \( \cdot \cot 76^{0} \)
\( \mathbf{C} \cdot \tan 46^{\circ} \)
\( \mathbf{D} \cdot \cot 44^{0} \)


In normal ECG, PR and T wave are lies at
A. Above the base line
B. Below the base line
C. partly above and partly below the base line
D. Equal to the base line


On the ellipse, \( 4 x^{2}+9 y^{2}=1, \) the
points at which the tangents are
parallel to the line \( 8 x=9 y \) are
This question has multiple correct options
\( ^{\mathrm{A}} \cdot\left(\frac{2}{5}, \frac{1}{5}\right) \)
B \( \cdot\left(-\frac{2}{5}, \frac{1}{5}\right) \)
\( c \cdot\left(-\frac{2}{5},-\frac{1}{5}\right) \)
D. \( \left(\frac{2}{5},-\frac{1}{5}\right) \)


The I V characteristics of solar cell is
drawn in the fourth quadrant of the
coordinate axes because
A. a solar cell does not draw current but supplies the same to the load
B. a solar cell draws current but supplies no current to the load
c. a solar cell draws voltage and supplies current to the load
D. a solar cell draws current but supplies voltage to the load


Solve the following equation:
\( -8<-(3 x-5)<13 \)


In the given figure, which of the
following is a line of symmetry?
A. Line A
B. Line B
c. Line
D. Line A and Line C


A thermodynamic system is taken from an original state to an intermediate
state by the linear process shown in the
figure. Its volume is then reduced to the
original value from \( \boldsymbol{E} \) to \( \boldsymbol{F} \) by an
isobaric process. Calculate the total
work done by the gas from \( D \) to \( E \) to \( F \)
A .225 J
D. 600


A glass rod rubbed with silk is used to charge a gold leaf electroscope and the leaves are observed to diverge. The electroscope thus charged is exposed to X-rays for a short period. Then:
A. the divergence of leaves will not be affected
B. the leaves will diverge further
c. the leaves will collapse
D. the leaves will melt


An electron of charge \( e \) and mass \( m \) describes a circular path of radius \( r \) when it is projected with a velocity \( v \) perpendicular to a uniform magnetic field, then its frequency is :
\( ^{A} \cdot \frac{1}{2 \pi} \sqrt{\frac{B e}{m}} \)
в. \( \frac{1}{2 \pi} \frac{B e}{m} \)
c. \( \frac{1}{2 \pi} \frac{m}{B e} \)
D. \( \frac{1}{2 \pi} \frac{m e}{2} \)


Hari bought a pen for Rs. 125 and sold it for Rs. 120. The loss is
A . Rs. 245
в. Rs.
c. Rs. 15
D. none


When \( P H_{3} \) absorbed in \( H g C l_{2} \) solution
the corresponding phosphide is
obtained
A. \( H g_{2} P_{3} \)
в. \( H g_{3} P_{2} \)
\( \mathbf{c} \cdot H g_{3}\left(P O_{4}\right)_{2} \)
D. None of these


The hydrides of the first element in
group \( 15-17, \) namely \( N H_{3}, H_{2} O \) and
\( H F, \) respectively show abnormally high
values for melting and boiling points. This is due to:
A. small size of \( N, O \) and \( F \)
B. the ability to form extensive intermolecular \( H \) bonding
c. the ability to form extensive intramolecular \( H \) bonding
D. effective van der Waal's interaction


A bag contains a certain number of
balls, some of which are white; a ball is
drawn and replaced, another is then drawn and replaced; and so on: if is the chance of drawing a white ball in a single trail, find the number of white
balls that is most likely to have been drawn in \( n \) trails.


A triangle is specified by the coordinates of its vertices \( A(3,2,-3), B \)
\( (5,1,-1), \) and \( C(1,-2,1) \). Calculate the coordinates of the vector a which is of the same direction as the vector \( \overrightarrow{A B} \)
and has the same length as the vector \( \boldsymbol{A C} \)


Which one of the following cannot be explained on the basis of Mendel's Law of Dominance?
A. Factor occur in pairs.
B. The discrete unit controlling a particular character is called as factor
c. out of one pair of factor one is dominant, and the other recessive
D. Alleles do not show any blending and both the characters recover as such in \( F_{2} \) generation


Force acting on a particles moving in a
straight line varies with the velocity \( v \) of
the particles as \( \boldsymbol{F}=\boldsymbol{K} \) where \( \boldsymbol{K} \) is a
constant. The work done by this force in time \( t \) is
A \( \cdot \frac{K}{v^{2}} t \)
в. \( 2 K t \)
c. all the above
D. None of these


Identify which of the following quantities remain conserved during an elastic collision?
A. momentum only
B. momentum and potential energy
c. kinetic energy only
D. momentum and kinetic energy
E. momentum end velocity


During a physics lab, a plastic strip was rubbed with cotton and became
positively charged. The correct explanation for why the plastic strip becomes positively charged is that
A. the plastic strip acquired extra protons from the cotton.
B. the plastic strip acquired extra protons during the charging process
c. protons were created as the result of the charging process
D. the plastic strip lost electrons to the cotton during the charging process


The enzymes have a very narrow optima for which of the following factor?
A. Light
B. Temperature
c. pH
D. Humidity


Find the Odd one among : 35,63,105,121 133,210
A . 35
B. 63
\( c \cdot 105 \)
D. 121


Thermal decomposition of higher hydrocarbons into lower hydrocarbons
is called:
\( A \). aromatization
B. cracking
c. reforming
D. isomerization


State, whether the following pairs of
sets are equal or not:
If they are equal then write 1 , else write
\( \mathbf{0} \)
\( A=2,4,6,8 \) and \( B=\{2 n: n \epsilon N \) and
\( \boldsymbol{n}<\mathbf{5}\} \)


Which of the following is NOT a planet of our Solar System?
A . sirius
B. Mercury
c. Saturn
D. Earth


SONAR works on the Principle of :
A. reflection of sound
B. reflections of waves
C. infrasonic waves.
D. all of the above


Four digit numbers are formed using
each of the digits \( 1,2, \ldots \ldots ., 8 \) only once One number from them is picked at random then the probability that the selected number contains unity is
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{8} \)
\( c \cdot \frac{1}{4} \)
D. \( \frac{1}{3} \)


The name of the compound \( \boldsymbol{H} \boldsymbol{C} \equiv \boldsymbol{C}- \)
\( C \equiv C-C \equiv C H \) is hexa-1,3,5-triyne.
A. True
B. False


Which is more reactive nucleophile in
polar protic solvent?
\( \mathbf{A} \cdot \mathbf{F} \)
в. \( \mathrm{Cl} \)
\( c \cdot B r \)
D. I


Electrolysis of water to form hydrogen and oxygen gas is called
A. precipitation
B. oxidation-reduction
c. distillation
D. hydration
E. condensation


The electron in the hydrogen atom is moving with a speed of \( 2.3 \times 10^{6} m / s \) in an orbit of radius 0.53 A. Calculate the
period of revolution of electron. \( (\pi= \) 3.142


Classify the following as motion along a straight line, circular or oscillatory
motion.
(i) Motion of your hands while running.
(ii) Motion of a horse pulling a cart on a straight road.
(iii) Motion of a child in a merry-goround.
(iv) Motion of a child on a see-saw.
(v) Motion of a hammer of an electric
bell.
(vi) Motion of a train on a straight bridge.


While preparing the progress reports of the students, the class teacher found
that \( 70 \% \) of the students passed in
Hindi, \( 80 \% \) passed in English and only \( 65 \% \) passed in both the subjects. Find
out the percentage of students who
failed in both the subjects.
A . \( 15 \% \)
B. 20\%
c. \( 30 \% \)
D. \( 35 \% \)


Name the two groups into which phenomenon of catalysis can be divided. Given an example of each group with the chemical equation involved.


\( X \) has three children in his family. What is the probability that all the three children are boys?
A \( \cdot \frac{1}{8} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{1}{3} \)
D. \( \frac{3}{8} \)


Which is correct in case of Van der
Waals adsorption?
A. High temperature, low pressure
B. High temperature, high pressure
c. Low temperature, low pressure
D. Low temperature, high pressure


A charge \( \boldsymbol{q}(>\mathbf{0}) \) moves towards the
centre of a circular loop of radius \( \boldsymbol{R} \)
along its axis. The magnitude of B along
the periphery of the loop is
A . zero
B. \( \frac{\mu_{0}}{4 \pi} \frac{q v R}{\sqrt{\left(R^{2}+x^{2}\right)^{3}}} \)
c. \( \frac{q v R}{\sqrt{R^{2}+x^{2}}} \)
D. \( \frac{\mu_{0}}{4 \pi} \frac{q v R}{\sqrt{R^{2}+x^{2}}} \)


If \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \frac{\sin 3 x+A \sin 2 x+B \sin x}{x^{5}}, x \neq 0 \)
is continous at \( x=0 \) then
This question has multiple correct options
A. \( A=-4 \)
B. \( B=5 \)
c. \( f(0)=1 \)
D. \( A=-3 \)


Five uniform circular plates, each of
diameter D and mass m are laid out in
a pattern shown. Using the origin
shown, find the y coordinate of the
centre of mass of the fiveplate system.
\( A \cdot 2 D / 5 \)
B. \( 40 / 5 \)
\( c \cdot D / 3 \)
D. D/5


A solid sphere falls with a terminal velocity v in air. If it is allowed to fall in
vacuum,
A. terminal velocity of sphere = v
B. terminal velocity of sphere \( < \) v
c. terminal velocity of sphere \( >v \)
D. sphere never attains terminal velocity


\( A l \) has lower ionization potential than
that of \( M g \) because:
A. \( A l \) atom is bigger than \( M g \) atom
B. \( M g \) atom is bigger than \( A l \) atom
c. all electrons in \( M g \) are paired, but those of \( A l \) are not
D. all belongs to a higher group


Solve \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\boldsymbol{x}+\boldsymbol{y} \)


Which of the following is the isotone of
\( 16^{3^{32}} ? \)
\( \mathbf{A} \cdot_{15} P^{31} \)
В \( \cdot_{7} N^{14} \)
\( \mathbf{c} \cdot_{18} A r^{40} \)
D \( \cdot_{17} C l^{34} \)


If \( f(x)=\frac{4^{x}}{4^{x}+2}, \) then \( f(x)+f(1-x) \)
is equal to.
\( \mathbf{A} \cdot \mathbf{0} \)
B. -
c. 1
D. 4


Milk glands are characteristics of
A. All vertebrates
B. Only mammals
c. only placental mammals
D. Only ruminants


The angle between two vectors \( (2 \hat{i}+ \) \( 3 \hat{j}+\hat{k}) \) and \( (-3 \hat{i}+6 \hat{k}) \) is :-
A \( \cdot 0^{\circ} \)
B . 45
\( c \cdot 60 \)
D. 90


The self inductance of the toroidal
solenoid described in the passage is
\( ^{A} \cdot \frac{\mu_{0} N^{2} h}{2 \pi} \)
B. \( \frac{\mu_{0} N^{2} h}{2 \pi} \log _{e} \frac{b}{a} \)
c. \( \frac{\mu_{0} N h}{2 \pi} \log _{e} \frac{b}{a} \)
D. \( \frac{\mu_{0} N^{2} h}{2 \pi} \log _{e} \frac{a}{b} \)


Find the angle between the two lines
whose direction cosines are given by
equations \( l+m+n=0 \) and \( l^{2}+ \)
\( \boldsymbol{m}^{2}-\boldsymbol{n}^{2}=\mathbf{0} \)
A \( \cdot \frac{\pi}{6} \)
в.
\( c \cdot \frac{\pi}{2} \)
D.


Out of the following functions representing motion of a particle which
represents \( \boldsymbol{S H} \boldsymbol{M} \) ?
(A) \( y=\sin \omega t-\cos \omega t \)
(B) \( y=\sin ^{3} \omega t \)
(C) \( y=5 \cos \left(\frac{3 \pi}{4}-3 \omega t\right) \)
(D) \( \boldsymbol{y}=\mathbf{1}+\boldsymbol{\omega} \boldsymbol{t}+\boldsymbol{\omega}^{2} \boldsymbol{t}^{2} \)
A. Only \( (A) \) and \( (B) \)
B. only \( (A) \)
c. only \( (D) \) does not represent \( S H M \)
D. only \( (A) \) and \( (C) \)


Periscope can not be made with
A. single mirror
B. 2 mirrors
c. 3 mirrors
D. 4 mirrors


\( f(x)=\tan ^{-1}(\sin x+\cos x) \) is an
increasing function in This question has multiple correct options
A \( \cdot\left(0, \frac{\pi}{4}\right) \)
В \( \cdot\left(0, \frac{\pi}{2}\right) \)
c. \( \left(\frac{-\pi}{4}, \frac{\pi}{4}\right) \)
D. None of these


To which plant division does the below
pictorial representation of life cycle belong?
A. Bryophyte
B. Algae
C. Pteridophyte
D. Gymnosperms


Write the mechanism of the given
reaction.


If \( \cos ^{-1} x-\sin ^{-1} x=0, \) then \( x \) is equal
to-
\( ^{\mathrm{A}} \pm \frac{1}{\sqrt{2}} \)
B. 1
\( ^{\mathrm{c}} \pm \frac{1}{\sqrt{3}} \)
D. \( \frac{1}{\sqrt{2}} \)


Example of physical equilibria is:
A. \( H_{2}+I_{2} \rightleftharpoons 2 H I \)
в. \( C a C O_{3} \rightleftharpoons C a O+C O_{2} \)
c. \( H_{2} O(s) \rightleftharpoons H_{2} O(l) \)
D. \( P C l_{5} \rightleftharpoons P C l_{3}+C l_{2} \)


If \( A B C D \) is parallelogram. E is mid-point of \( A B \) and \( C E \) bisects \( \angle B C D, \) then
\( \angle D E C \) is
A \( \cdot 60^{\circ} \)
В. \( 90^{\circ} \)
\( c \cdot 100^{\circ} \)
D. 120


pp 7
Q Type your question
\( \mathbf{A} \)
B.
\( c \)
D.


Cerium shows oxidation state of +4
because:
\( \mathbf{A} \). it resembles alkali metals
B. it has very low I.E.
C. it has tendency to attain noble gas configuration
D. it has tendency to attain \( f^{0} \) configuration


At the highest point of a projectile its velocity i half the initial velocity in magnitude The angle of projection from ground is
A \( .30^{\circ} \)
В . \( 45^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 90^{\circ} \)


Decrease in tropical forests during the
past century was
A . 40\%
B. 50\%
c. \( 60 \% \)
D. 10\%


The laws of reflection are true for
A. the plane mirror only
B. the concave mirror and convex mirror
C. the convex mirror only
D. all reflecting surfaces


Benzoic acid does not undergo FriedelCrafts reaction due to \( - \) - of the
benzene ring by the - - - - - effect of -COOH
group.
A. Activation, electron donating
B. Activation, electron withdrawing
c. Deactivation, electron donating
D. Deactivation, electron withdrawing


The angle between incident ray and
reflected ray is \( 60^{\circ} . \) What is the value of
angle of incidence?
A \( .30^{\circ} \)
B. 60
\( c \cdot 120 \)
D. None of the above


The function \( f: R \rightarrow R \) satisfies
\( \boldsymbol{f}\left(\boldsymbol{x}^{2}\right) \cdot \boldsymbol{f}^{\prime \prime}(\boldsymbol{x})=\boldsymbol{f}^{\prime}(\boldsymbol{x}) \cdot \boldsymbol{f}^{\prime}\left(\boldsymbol{x}^{2}\right) \) for all real \( \boldsymbol{x} \)
Given that \( f(1)=1 \) and compute the
value of \( \boldsymbol{f}^{\prime}(\mathbf{1})+\boldsymbol{f}^{\prime \prime}(\mathbf{1}) \)


The length of the chord of a circle is \( 8 \mathrm{cm} \) and perpendicular distance between centre and the chord is \( 3 \mathrm{cm} \). Then the
radius of the circle is equal to?
A. \( 4 \mathrm{cm} \)
B. \( 5 \mathrm{cm} \)
\( \mathrm{c} \cdot 6 \mathrm{cm} \)
D. \( 8 \mathrm{cm} \)


What role does adsorption play in heterogeneous catalysis?


Papillary muscle is found in
A . Heart
B. Liver
c. Kidney
D. Lung


The middle term in the expansion of \( \left(x+\frac{1}{x}\right)^{10} \)
A \( \cdot \) io \( _{1} \frac{1}{x} \)
в. \( ^{10} C_{5} \)
c. \( ^{10} C_{6} \)
D. \( ^{10} C_{7} x \)


When you ride a cycle, force(s) acting on the cycle is/are
A. muscular force
B. force of friction
c. gravitational force
D. all of the above


If \( A+B=45^{\circ}, \) prove that \( (\cot A- \)
1) \( (\cot B-1)=2 \)


Statement 1: In simple harmonic motion, the velocity is maximum when the acceleration is minimum.

Statement 2: Displacement and velocity of \( S . H . M \) differ in phase by \( \frac{\pi}{2} \)
A. Statement 1 is false, Statement 2 is true
B. Statement 1 is true, Statement 2 is true; Statement 2 is the correct explanation for Statement 1
c. statement 1 is true, statement 2 is true; Statement 2 is not the correct explanation for Statement 1
D. Statement 1 is true, Statement 2 is false


Fill in the blank.
The reflection of sunlight takes place the water droplets to
form a rainbow.
A . outside
B. inside
c. beside
D. below


In the given figure two concentric circle
with centre \( O \) have radii \( 21 c m \) and
\( 42 c m . \) If \( A O B=60 \) Find the area of the
shaded region (Use \( \left.\pi=\frac{22}{7}\right) \)


If \( \sin ^{-1} x+\sin ^{-1} y+\sin ^{-1} z=\frac{3 \pi}{2} \) and
\( \boldsymbol{f}(\mathbf{1})=\mathbf{1}, \boldsymbol{f}(\boldsymbol{p}+\boldsymbol{q})= \)
\( \boldsymbol{f}(\boldsymbol{p}) \cdot \boldsymbol{f}(\boldsymbol{q}) \quad \forall \boldsymbol{p}, \boldsymbol{q} \in \boldsymbol{R} \operatorname{th} \operatorname{en} \boldsymbol{x}^{f(1)}+ \)
\( \boldsymbol{y}^{f(2)}+\boldsymbol{z}^{f(\boldsymbol{3})}-\frac{\boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}}{\boldsymbol{x}^{f(1)}+\boldsymbol{y}^{f(2)}+\boldsymbol{z}^{f(3)}}= \)
\( A \cdot O \)
в.
\( c \cdot 2 \)
\( D \)


At a given instant, there are \( 25 \% \) undecayed radioactive nuclei in a sample. After \( 10 \mathrm{s} \), the number of undecayed nuclei reduces to \( 12.5 \% \) Calculate
(a) mean life of the nuclei and
(b) the time in which the number of
decayed nuclei will further reduce to
\( 6.25 \% \) of the reduced number


f \( p(x)=x^{42}-2 k \) is divided by \( (x+1) \)
the remainder is \( 9, \) what is the value of
k?


Evaluate the integral \( \int_{3}^{5}(2-x) d x \)


The magnitude of pressure measured in
Sl system is greater than that measured in CGS system.
A. True
B. False


If \( \Delta \mathbf{A B C} \sim \)
\( \Delta P Q R \) then find value of \( y+3 \)


What are the products formed when
ammonia is oxidized with copper oxide?
A . \( N_{2} \)
в. \( H_{2} \) С
c. \( C u \)
D. All of the above


0 is a point that lies in the interior of \( \Delta A B C . \) Then \( 2(O A-O B-O C)> \)
Perimeter of \( \Delta A B C \)
A. True
B. False


Which building material is least likely to be rapidly eroded by acid rain?
A. Marble
B. Sand stone
c. Granite
D. lime stone


Fumarase belong to the major class of:
A. oxidoreductases
B. transferases
c. hydrolases
D. ligases


What is Bond formation?
A. always exothermic
B. always endothermic
C. neither exothermic nor endothermic
D. Sometimes exothermic and sometimes endothermic


Three charges \( 2 q,-q \) and \( -q \) are located at the vertices of an equilateral triangle. At the centre of the triangle:
A. the field is zero but potential is non-zero
B. the field is non-zero, but potential is zero
c. both field and potential are zero
D. both field and potential are non-zero


A body travels \( 200 \mathrm{cm} \) in the first two
seconds and \( 220 \mathrm{cm} \) in the next 4 seconds with deceleration. The velocity
of the body at the end of the \( 7^{\text {th }} \) second
is
\( A \cdot 20 \mathrm{cm} / \mathrm{s} \)
B. \( 15 \mathrm{cm} / \mathrm{s} \)
c. \( 10 \mathrm{cm} / \mathrm{s} \)
D. \( 0 \mathrm{cm} / \mathrm{s} \)


The derivative of \( \boldsymbol{y}=(1-\boldsymbol{x})(2- \)
\( x) \ldots(n-x) \) at \( x=1 \) is equal to
A . 0
в. (-1)\( (n-1) ! \)
c. \( n !-1 \)
D \( \cdot(-1)^{n-1}(n-1) ! \)
E \( \cdot(-1)^{n}(n-1) ! \)


The amount of energy released when
one mole of ionic solid is formed by packing of gaseous ion is called:
A. Ionization energy
B. Solvation energy
c. Lattice energy
D. Hydration energy


(a) What are the aims of watershed
management?
(b) Mention the problems caused by the construction of large dams.


The equilibrium constant for the
following reaction at \( 25^{\circ} \mathrm{C} \) is \( 2.9 \times 10^{9} \)
Calculate standard voltage of the cell.
\( \boldsymbol{C l}_{2(\boldsymbol{g})}+\boldsymbol{B r}_{(\boldsymbol{a q})}^{-} \rightleftharpoons \boldsymbol{2} \boldsymbol{C l}_{(\boldsymbol{a q})}^{-} \)
\( \mathbf{A} \cdot 0.18 \mathbf{V} \)
B. \( 0.22 v \)
c. \( 0.26 v \)
D. \( 0.28 \mathrm{v} \)


State whether True or False:
Scalar and Vector, both obey law of
vector algebra.
A. True
B. False


The structure of phenacetin is
\( A \)
B.
\( c \)
\( D \)


\( \frac{x^{2}}{8-a}+\frac{y^{2}}{a-2}=1 \) represents an
ellipse.Then find range of 'a'


A particle executes SHM with a frequency f and its amplitude is A. If the frequency is doubled, the amplitude will be
\( A \cdot A / 2 \)
B. A
c. \( 2 A \)
D. A/4


The number of steps involved in the manufacturing of nitric acid through
Ostwald's process is:
\( A \)
B. 5
\( c \cdot 3 \)
D.


Which of the following experiments have equally likely outcomes? Explain.
(i) A driver attempts to start a car. The car starts or does not start.
(ii) A player attempts to shoot a basketball. She/he shoots or misses the
shot
(iii) \( A \) trial is made to answer a true-
false question. The answer is right or
wrong.
(iv) A baby is born. It is a boy or a girl


The IUPAC name of chloretone is:
A. Trichloroacetone.
B. Trichloronitromethane
C . 1,1,1 -Trichloro-2-methyl-2-propanone.
D. 1,1,1 -Trichloro-2-methyl-2-propanol


A thin straight vertical conductor has
10amp current flows vertically upwards. It is present at a place where \( B_{H}=4 \times 10^{-6} T . \) At which point
magnetic feild will be maximum
A. \( 0.5 m \) on south of conductor
B. \( 0.5 m \) on west of conductor
\( \mathrm{c} .0 .5 \mathrm{m} \) on east of conductor
D. \( 0.5 m \) on north-east of conductor


To make gloves for an electrician, the
material that is most suitable is rubber
Which material has the most similar
properties?
\( \mathbf{A} \cdot M O 1 \)
в. \( M O 2 \)
c. \( M O 3 \)
D. All of these


The focal length of a concave mirror is \( 50 \mathrm{cm} \) where an object is to be placed so that its image is two times magnified, real and inverted:
A. \( 75 \mathrm{cm} \)
B. 72 cm
\( c \cdot 63 \mathrm{cm} \)
D. 50 cm


Ortho-hydrogen and para-hydrogen resembles in which of the following
property?
A. Thermal conductivity
B. Magnetic properties
c. chemical properties
D. Heat capacity


Two monomers in maltose are:
A. \( \alpha-D- \) glucose and \( \alpha-D- \) Fructose
B. \( \alpha-D- \) glucose and \( \alpha-D- \) galactose
C \( . \alpha-D- \) glucose and \( \alpha-D- \) glucose
D. \( \alpha-D- \) glucose and \( \beta-D- \) glucose


Assertion(A): If one arm of a \( U \) -tube
containing a diamagnetic solution is placed in between the poles of a strong magnet with the level in line with the
field, the level of the solution falls Reason(R): Diamagnetic substances are repelled by the magnetic field
A. both \( A, R \) are true and \( R \) is the correct explanation of
B. both A,R are true and R is not correct explanation of A
c. A is true, R is false
D. A is false R is true


In which of the following ionization processes, the bond order has increased and the magnetic behaviour has changed?
\( \mathbf{A} \cdot C_{2} \rightarrow C_{2}^{+} \)
в. \( N O \rightarrow N O^{+} \)
\( \mathbf{c} \cdot O_{2} \rightarrow O_{2}^{+} \)
\( \mathbf{D} \cdot N_{2} \rightarrow N_{2}^{+} \)


A body starts from rest and falls vertically from a height of 19.6 meters. If \( g=9.8 \mathrm{m} / \mathrm{sec} 2 . \) Then, what is the distance
traveled by the body in the last 0.1 second of its motion?


Which one of the following is not a second messenger in hormone action?
A. Sodium
B. сАМР
c. сGмР
D. Calcium


Sum of all components in normalized histogram is equal to
A . 0
B.
c. 100
\( D \)


A plane progressive wave is given by
\( \boldsymbol{y}=2 \cos 6.284(330 t-x) . \) What is
period of the wave?
\( ^{A} \cdot \frac{1}{33^{0}} \)
В. \( 2 \pi \times 330 s \)
c. \( (2 \pi \times 330)^{-1} \) s
D. \( \frac{6.284}{330} \)


Match the following
Physical Quantity Unit in ¿uc is an a it \( \begin{array}{l}\text { a) Magnetic Moment } \\ \text { b) Magnetic Flux Density } \\ \text { c) Intensity of Magnetic Field } & \text { e) } A m p-m \\ \text { d) Pole strength } & \text { g) } N-m^{3} / W b \\ \text { h) Gauss }\end{array} \)
\( A \cdot a-e, b-f, c-g, d-h \)
B. \( a-g, b-h, c-f, d-e \)
\( \mathbf{C} \cdot a-g, b-f, c-h, d-e \)
D. a-e, b-f, c-h, d-g


The highest term in the expansion of \( (2 \sqrt{5}+\sqrt[6]{7})^{6} \) is
A. \( 800 \sqrt{35} \)
55
в. \( 700 \sqrt{35} \)
c. \( 320 \sqrt{5} \)
D. \( 100 \sqrt{7} \)


In a speed-time graph, the area enclosed by the speed-time curve and the time axis gives
A. Velocity
B. Acceleration
c. speed
D. Distance travelled


Paper snippets attracted by a charged
CD is an example of
A. charging by induction
B. charging by conduction
c. charging by ionisation
D. charging by transmission


The moment of inertia of a uniform
semicircular wire of mass \( \mathrm{M} \) and radius
about a line perpendicular to the plane of the wire through the centre is


The weight of a cubic meter of a certain
metal is 480 kg. It is melted and then rolled into a square bar \( 4 m \) long. Now, an exact cube is cut from it. Find the
weight of the cube
A. \( 240 \mathrm{kg} \)
в. \( 80 \mathrm{kg} \)
c. \( 120 \mathrm{kg} \)
D. \( 60 \mathrm{kg} \)


The oxy-acid containing P-O-P bonding
is :
A. Hypo phosphoric acid.
B. Pyro Phosphoric acid.
c. ortho phosphoric acid.
D. Peroxyphosphoric acid


According to theory of significant
figures \( (2.0)^{10} \) is :
A \( \cdot 1024 \)
В. \( 1.024 \times 10^{10} \)
c. \( 1.0 \times 10^{3} \)
D. 1000


Assertion
The proton gradient is broken down due
to the movement of protons across the
membrane channel of the \( F_{0} \) of the
ATPase
Reason
It is the breakdown of proton gradient
that leads to release of energy.
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 and Reason are correct


A body suspended from a spring balance is placed in a satellite. Reading
in balance is \( W_{1} \) when the satellite
moves in an orbit of radius \( R \). Reading
in balance is \( W_{2} \) when the satellite
moves in an or bit of radius \( 2 R \). Then.
A. \( W_{1}=W_{2} \)
в. \( W_{1}>W_{2} \)
\( \mathbf{c} \cdot W_{1}<W_{2} \)
D. \( W_{1}=2 W_{2} \)


The correct expression for Ampere's law
is :
A \( . \int B . d l=\Sigma i \)
в. \( \int B . d l=\frac{1}{\sum i} \)
c. \( \int B . d l=\mu_{0} \sum i \)
' - \( \int B . d l=\frac{\sum i}{\mu_{0}} \)


If \( a, b \) and \( c \) are unit vectors then
\( |a-b|^{2}+|b-c|^{2}+|c-a|^{2} \) does not
exceed
\( \mathbf{A} \cdot \mathbf{4} \)
B. 9
\( c \cdot 8 \)
D. 6


Equivalent weight of the underlined
\( 2 \underline{H}_{3} \boldsymbol{P} \boldsymbol{O}_{2} \longrightarrow \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4}+\boldsymbol{P} \boldsymbol{H}_{3} \)
A . 33
B. 24
\( c \cdot 42 \)
D. 31


\( 0.1 N \) solution of sodium carbonate is
titrated with \( 0.1 N \) solution of sulphuric
acid. The best indicator to be used for
this titration is:
A. phenolphthalein
B. methyl orange
c. litmus
D. starch solution


Two metal strips that constitute a bimetallic strip must necessarily differ in their:
A. length
B. mass
c. coefficient of linear expansion
D. resistivity


The building block of structural organic chemistry is the
A. di valency of carbon atom
B. tetra valency of carbon atom
c. tri valency of carbon atom
D. none of these


The oxidation states of \( S \) atom in
\( S_{4} O_{6}^{2-} \) from left to right respectively are
\( \mathbf{A} \cdot+6,0,0,+6 \)
В. +3,+1,+1,+3
c. +5,0,0,+5
\( \mathbf{D} \cdot+4,+1,+1,+4 \)


Which of the following statements
regarding sulphur dioxide is not true?
\( A \cdot S O_{2} \) is an angular molecule
B. \( S O_{2} \) may be regarded as the resonance hybrid of two canonical structures
\( \mathrm{C} \cdot S \mathrm{O}_{2} \) is an anhydride of sulphuric acid
D. \( S O_{2} \) is an anhydride of sulphurous acid


Which of the following oxides of nitric is anhydride of nitrous acid?
A . \( N O \)
в. \( N_{2} O_{3} \)
\( \mathrm{c} \cdot \mathrm{N}_{2} \mathrm{O}_{4} \)
D. \( N O_{2} \)


Integrate :-
\( \int \log \log x+\frac{1}{(\log x)^{2}} d x \)


What is the code number on plastic
bottle HDPE?


ABCD is a trapezium in which \( \boldsymbol{A B} \| \) \( C D, \) if \( A B=7 \mathrm{cm}, D C=3 \mathrm{cm} \) and if the
area of the trapezium is \( 18 \mathrm{cm}^{2} \), then
the area of \( \triangle B C D \) is
A \( \cdot 5 \frac{2}{5} c m^{2} \)
в. \( 6 \frac{2}{5} \mathrm{cm}^{2} \)
c. \( 7 \frac{2}{5} c m^{2} \)
D. \( 8 \frac{2}{5} c m^{2} \)


Draw lewis structures for the following molecules \( H C O O H . C O_{2}^{2-} \)


For a particular reaction \( \triangle \boldsymbol{H}^{0}= \)
\( -76.6 K J \) and \( \Delta S^{0}=226 J K^{-1} . \) This
reaction is:
A. spontaneous at all temperatures
B. non-spontaneous at all temperatures
C. spontaneous at temperature below \( 66^{\circ} \mathrm{C} \)
D. spontaneous at temperature above \( 66^{\circ} \mathrm{C} \)


\( A \) film projector magnifies a \( 100 \mathrm{cm}^{2} \) film strip on a screen. If the linear
magnification is \( 4, \) the area of the magnified film on the screen is be
\( 1000 \mathrm{cm}^{2} \)
A . True
B. False


The vapour pressure of pure water at
\( 25^{\circ} \mathrm{C} \) is 23.76 torr. The vapour pressure of a solution containing 5.40 g of a nonvolatile substance in 90.0 g water is 23.32 torr. The molecular weight of the solute is:
A. \( 97.24 \mathrm{g} / \mathrm{mol} \)
B. 24.29 g/mol
c. \( 50.44 \mathrm{g} / \mathrm{mol} \)
D. \( 57.24 \mathrm{g} / \mathrm{mol} \)


Assertion
If \( \boldsymbol{H}_{2} \) and \( \boldsymbol{C l}_{2} \) enclosed separately in the
same vessel exert pressures of 100 and \( 200 \mathrm{mm} \) respectively, their mixture in
the same vessel at the same
temperature will exerts a pressure of \( 300 \mathrm{mm} \)
Reason
Dalton's law of partial pressures states that total pressure is the sum of partial
pressures.
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


Assume the temperature of liquid and
surrounding is same, the rate of
melting of ice is maximum at point.
\( A \)
B. 3
\( c \)
D. Both 4 and 5


Fill in the blank
A point source emits sound equally in all direction in a non-absorbing
medium. Two point \( P \) and \( Q \) are at a
distance of \( 9 m \) and \( 25 m \) respectively
from the source. The ratio of the
amplitudes of the waves at \( P \) and \( Q \) is..


At what height \( ^{\prime} h^{\prime} \) from the earth
surface, acceleration due to gravity
becomes half as that of acceleration
due to gravity on the surface of earth. \( [R=\text { Radius of earth }] \)
\( \mathbf{A} \cdot h=R \)
в. \( h=\frac{R}{2} \)
c. \( h=\frac{R}{3} \)
D. \( h=\frac{R}{4} \)


In the fusion reaction \( _{1} H^{2}+_{1} H^{2} \longrightarrow_{2} \)
\( H e^{4}+_{0} n^{1}, \) the masses of deuteron
helium and neutron expresses in amu are 2.05,3.017 and \( 1.009, \) respectively. If
1 \( K g \) of deuterium undergoes complete
fusion, then find the amount of total
energy released
\( \mathbf{1} \boldsymbol{a} \boldsymbol{m} \boldsymbol{u}=\mathbf{9} \mathbf{3} \mathbf{1} . \mathbf{5} \boldsymbol{M} \boldsymbol{e} \boldsymbol{V} / \boldsymbol{c}^{2} \)


Identify the correctly matched structure and its secretion
A. Brunner's gland - Salivary amylase
B. Intestinal mucosa - Insulin
c. Gall bladder - Bile
D. Salivary gland - Lysozyme


If the radian measures of two angles of a triangle are \( \frac{3 \pi}{5}, \frac{4 \pi}{15} . \) Find the radian measure and the degree measure of the third angle.


Carbon dioxide and methane are the
two major components of greenhouse.
A. True
B. False


Explore and answer:
Petrol tankers plying on highways often have metal chains attached to that drag
along the road. Could you say why?


The displacement of a body varies with
the time as \( S=t^{3}+3 t^{2}+2 t-1 . \) If the
velocity at \( t=4 \sec \) is \( 2+12 K m / s \)
then find \( k \)
\( A \cdot 6 \)
B. 3
\( c \cdot 2 \)
D.


Oxygen is considered as the waste
product of
A. Regulation.
B. Respiration.
c. Reproduction.
D. Photosynthesis


A real gas most closely approaches the behaviour of an ideal gas at:
A . 15 atm and \( 200 K \)
B. 1 atm and \( 273 \mathrm{K} \)
c. 0.5 atm and \( 500 K \)
D. 15 atm and \( 500 K \)


Mixture of conc. \( \mathbf{H} \mathbf{N} \mathbf{O}_{3} \) and conc.
\( \mathbf{H}_{2} \mathbf{S} \mathbf{O}_{4} \) is known as :
A. Sulphonating mixture
B. Nitrating mixture
c. Explosion mixture
D. Fusion mixture


The oil used in the froth flotation
method for the purification of ore is:
A. coconut oil
B. olive oil
c. pine oil
D. castor oil


Differentiate: \( e^{\sin ^{-1} x} \)


The evolution of this structure lead to
the human lineage.
A. Bone
B. Cranium
c. Jaws
D. Notochord
E. Vertebrae


Find the principal value of:
\( \sin ^{-1}\left(\frac{\sqrt{\mathbf{3}}+1}{2 \sqrt{2}}\right) \)


The colour of an opaque object is due to the colour it :
A . Reflects
B. Refracts
c. Absorbs
D. Scatters


Which of the following is NOT true
regarding nucleic acid?
This question has multiple correct options
A. Nucleic acids are always genetic material for an organism when found inside a cell
B. Nucleic acids are long chain macromolecules formed by end to end polymerisation of nucleotide monomers
C. Nucleic acids of only one type are available in any organism
D. Nucleic acids show secondary structures


Enzymes provide active sites for holding the substrate molecules through a variety of interactions like:
This question has multiple correct options
A. covalent bonding
B. dipole-dipole interaction
c. ionic bonding
D. hydrogen bonding


Which one of the following is not a thermodynamical co-ordinate?
A. \( V \)
в. \( R \)
\( c . T \)
D. \( P \)


Molecular mass is expressed in :
A. \( k g \)
B. \( g \)
\( c \)
D. \( m g \)


Heat is a
A. form of energy.
B. property of the material.
C. universal constant.
D. theoretical assumption.


A steamer plies between two stations \( \boldsymbol{A} \)
and \( B \) on opposite banks of a river, always following the path \( A B \). The
distance between stations \( A \) and \( B \) is
1200 \( m \). The velocity of the current is \( \sqrt{17} m s^{-1} \) and is constant over the
maim width of the river. The line \( A B \)
makes an angle \( 60^{\circ} \) with the direction
of the flow. The steamer takes 5 min to
cover the distance \( A B \) and back.
a. Find the velocity of steamer with
respect to water.
b In what direction should the steamer
move with respect to line \( \boldsymbol{A B} \) ?


An aircraft, initially stationary on a
runway, takes off with a speed of \( 85 \mathrm{km} \)
\( h^{-1} \) in a distance of no more than 1.20
\( \mathbf{k m} \)
What is the minimum constant
acceleration necessary for the aircraft?
A \( \cdot 0.23 m s^{-2} \)
B. \( 0.46 \mathrm{ms}^{-2} \)
c. \( 3.0 m s^{-2} \)
D. \( 6.0 m s^{-2} \)


Which region is described by the shade in the graph given?
This question has multiple correct options
A \( .2 x+3 y=3 \)
B. \( 2 x+3 y>3 \)
c. \( 2 x+3 y<3 \)
D. None of these


Which of the following molecule will be most polar?
A .1,3,5 trichloro benzene
B. Trans 1,2- dichloro ethene
c. Cls- -1-fluoro propene
D. Trans 1 fluoro propene


Subtract: \( a(b-5) \) from \( b(5-a) \)


The sum of the first 7 terms of an A.P is
63 and the sum of its next 7 terms is
161. Find the 28 th term of this A.P.


A body has a charge of \( -2 \mu C \). If it has
\( 2.5 \times 10^{13} \) protons, then how many
electrons the body has?
A \( \cdot 1.25 \times 10^{13} \)
B. \( 2.5 \times 10^{13} \)
c. \( 3.75 \times 10^{13} \)
D. None of these


Collision diameter is least in case of:
A \( . H_{2} \)
в. \( H e \)
\( c \cdot C O_{2} \)
D. \( N_{2} \)


The rate equation for a reaction, \( \boldsymbol{A} \longrightarrow \)
\( B \) is \( r=k[A]^{0} . \) If the initial
concentration of the reactant is \( a \)
mol.dm \( ^{-3} \), the half-life period of the
reaction is:
A \( \cdot \frac{a}{2 k} \)
в. \( \frac{k}{a} \)
c. \( \frac{a}{k} \)
D. \( \frac{2 a}{k} \)


\( \square A B C D \) is a trapezium in which
\( \boldsymbol{A B} \| \boldsymbol{D C} \) and \( \angle \boldsymbol{A}=\angle \boldsymbol{B}=\mathbf{4 5}^{\boldsymbol{o}} . \) Find \( \angle \boldsymbol{C} \)
and \( \angle D \) of the trapezium.
A \( \cdot 135^{\circ} \) each
B . \( 125^{\circ}, 145^{\circ} \)
c. \( 145^{\circ}, 125^{\circ} \)
D . \( 115^{\circ}, 155^{\circ} \)


If \( A \) and \( B \) are independent events with
\( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 2}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 5 .} \) then find
\( \boldsymbol{P}(\boldsymbol{A} / \boldsymbol{B}) \)


Assertion
The equilibrium (given below) attained in a closed vessel remains unaltered by
the addition of \( C a C O_{3}(s) \) \( \boldsymbol{C a} \boldsymbol{C O}_{3}(\boldsymbol{s}) \rightleftharpoons \boldsymbol{C a O}(\boldsymbol{s})+\boldsymbol{C O}_{2}(\boldsymbol{g}) \uparrow \)
Reason
Heterogenous reaction is unaffected by solid and liquid.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The formal charge on central oxygen
\( \operatorname{atom} \operatorname{in} O_{3} \) molecule is :
A . 0
B. +1
c. -1
D. - 2


What is a voltaic cell?
\( A \cdot A \) cell in which a spontaneous redox reaction produces electricity
B. A cell in which an oxidation reaction produces electricity.
C . A cell that produces voltage.
D. A cell full of volts.
E. Any cell that undergoes a spontaneous reaction.


When the atom Li, Be, B and Na are
arranged in order of increasing atomic radius, what is the correct order?
\( A \cdot B, B e, \) Li, \( N a \)
B. Li, Be, B Na a
c. Ве, Li, В, Na


Sodium sesquicarbonate is
This question has multiple correct options
\( \mathbf{A} \cdot N a_{2} C O_{3} N a H C O_{3} \)
B. a double salt
C . trisodium hydrogen discrabonate
D. water softner


Q Type your question
a convex lens.
Arrange the steps in the proper
sequence.
(a) Place the lens on a V-shaped stand.
(b) Place the object at \( 2 F_{1} \)
(c) Place the object between \( 2 F_{1} \) and \( F_{1} \)
(d) Determine the focal length of the lens by focusing the lens to a distant object like a tree.
(e) Adjust the position of the screen behind the lens to obtain a clear image and study the nature of the image.
(f) Mark the positions of \( F_{1}, 2 F_{1}, F_{2} \)
and \( 2 F_{2} \)
(g) Focus the lens to a distant object like a tree.
(h) Place the object just behind \( 2 F_{1} \)
(i) Place the object at \( \boldsymbol{F}_{1} \)
(j) Place the object between \( F_{1} \) and optic centre of the lens and observe that the image formed is virtual.
\( A \cdot \) a f \( d h \) e \( g \) e b e ce ej
B. b a fhe gec
c. a dfge he bece iej
D. a df ge he cebeje


Actinomorphic flower is found in family
A. Cannaceae
B. Poaceae
C. Papilionaceae
D. Solanaceae


Find out the general form of geometric progression.
A .2,4,8,16
в. 2,-2,2,3,1
c. 0,3,6,9,12
D. 10,20,30,40


In the fusion reaction \( _{1}^{2} \boldsymbol{H} \boldsymbol{e}+_{1}^{2} \boldsymbol{H} \rightarrow_{2}^{3} \)
\( H e+_{0}^{1} n, \) the masses of deuteron, helium, and neutron expressed in amu
are 2.015,3.017 and \( 1.009, \) respectively.
If \( 1 k g \) of deuterium undergoes complete fusion, find the amount of total energy
released. \( \left(1 a m u=931.5 m e V / c^{2}\right) \)
\( \mathbf{A} \cdot \approx 6.02 \times 10^{13} J \)
в. \( \approx 5.6 \times 10^{13} \mathrm{J} \)


Given circuit has \( n \) cells attached to it.
All the cells are identical. When one cell
is reversed, the current decreases to
\( 0.7 A . \) The value of \( n \) is
A . 12
B. 16
\( c \cdot 20 \)
\( D \)


\( \triangle A B C \) and \( \triangle D B C \) are two iosceles
triangle on the same base \( B C \) and
vertices \( A \) and \( D \) are on the same sides
of \( B C . \) If \( A D \) is exerted to intersect \( B C \)
at \( P \), show that
\( \triangle \boldsymbol{A B P} \cong \)
triangleACP


Which process produces alcohol or
lactate?
A. Krebs cycle
B. Glycolysis
C. Electron transport system
D. Fermentation


Identify \( A \) and \( B \) in the given graph and
choose the correct option accordingly.
A. A-Lungs; B-Liver
B. A-Lungs; B-tissue
C. B-tissue :A-Lungs
D. A-kidney: B-Liver


Q Type your
\( A \)
\( c \)
\( D \)


\( \operatorname{Let} a_{i}=i+\frac{1}{t} \) for \( i=1,2, \dots \dots, 20 \) put
\( \boldsymbol{p}=\frac{\mathbf{1}}{\mathbf{2 0}}\left(\boldsymbol{a}_{1}+\boldsymbol{a}_{2}+\ldots \ldots+\boldsymbol{a}_{20}\right) \) and \( \boldsymbol{q}= \)
\( \frac{1}{20}\left(\frac{1}{a_{1}}+\frac{1}{a_{2}}+\ldots . .+\frac{1}{a_{20}}\right) . \) Then
A \( \cdot q \epsilon\left(0, \frac{22-p}{21}\right) \)
В \( \cdot_{q \epsilon}\left(\frac{22-p}{21}, \frac{2(22-p)}{21}\right) \)
c. \( _{q \epsilon}\left(\frac{2(22-p)}{21}, \frac{22-p}{7}\right) \)
D. \( q \epsilon\left(\frac{22-p}{7}, \frac{4(22-p)}{21}\right) \)


Mitochondria are store houses of
A. Glycogen
B. Glucose
c. АтР
D. Fats


Given figure depicts the light
harvesting complex (LHC) of
photosystem I (PSI). Select the correct identification for \( \mathbf{A}, \mathbf{B} \)
C and \( D \)
A. A-molecules; B- Antenna molecule; C- \( P_{680} ; \) D- Primary
\( e^{-} \) acceptor.
B. A-Antenna molecules; B-Core molecule; \( P_{700} ; \) D-
Primary \( e^{-} \) acceptor.
C. A-Antenna molecules; B-Core molecule; \( P_{700} ; \) D-
Plastocyanin
D. A-Core molecules; B- Reaction centre; \( P_{680} ; \) D-
Plastocyanin


Let the universal set U, be a set all
students of your school, A is set of boys. B is the set of girls \( C \) is the set of students participating in sports. Describe the following set in words and represent them by the Venn diagram.
\( \boldsymbol{B} \cap \boldsymbol{C} \)


A straight current carrying conductor is kept along the axis of circular loop carrying current. The force exerted by the straight conductor on the loop is
A. perpendicular to the plane of the loop.
B. in the plane of the loop, away from the center.
C. on the plane of the loop, towards the center.
D. zero.


Evaluate the following:
\( n+1 C_{n} \)


Two moles of helium gas undergo a
cyclic process as shown in Figure.
Assuming the gas to be ideal, calculate
the following quantities in this process
The net work done in Joule


If 1 stands for true and 0 stands for
false, then choose the correct code for
the following statement:
\( H_{2} S O_{4} \) is a weaker acid than \( H C l, \) yet
\( H C l \) is evolved when conc. \( H_{2} S O_{4} \) is
added to \( N a C l \)


The gas phase decomposition of dimethyl ether follows first order kinetics:
\( \boldsymbol{C H}_{3}-\boldsymbol{O}-\boldsymbol{C H}_{3}(\boldsymbol{g}) \rightarrow \boldsymbol{C H}_{4}(\boldsymbol{g})+ \)
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{C} \boldsymbol{O}(\boldsymbol{g}) \)
The reaction is carried out in a constant
volume container at \( 50^{\circ} \mathrm{C} \) and has a
half life of 14.5 minutes. Initially, only
dimethyl ether is present at a pressure of 0.40 atm. What is the total pressure
of the system after 12 minutes? (Assume the ideal gas behaviour.)
A. 0.946 atm
B. 0.785 atm
\( c \cdot 0.777 \) atm
D. 0.749 atm


Find the point on the straight line \( 3 x+ \) \( \boldsymbol{y}+\mathbf{4}=\mathbf{0} \) which is equidistant from the
points (-5,6) and (3,2)


The correct order of boiling point for
primary \( \left(1^{\circ}\right), \) secondary \( \left(2^{\circ}\right) \) and
tertiary \( \left(3^{\circ}\right) \) alcohols is:
A \( \cdot 1^{\circ}>2^{\circ}>3^{\circ} \)
B . \( 3^{\circ}>2^{\circ}>1^{\circ} \)
\( \mathbf{c} \cdot 2^{o}>1^{\circ}>3^{\circ} \)
D . \( 2^{\circ}>3^{\circ}>1^{\text {о }} \)


Correct order of boun angle of the
following is?
A. \( C l O_{2}>O C l_{2}>O F F_{2} \)
в. \( O F_{1}>O C l_{2}>C l_{2} O \)
c. \( O C l_{2}>C l O_{2}>O F_{2} \)
D. \( O C l_{2}>O F_{2}>C l O_{2} \)


Reaction \( =2 O_{3} \rightleftharpoons 3 O_{2} \)
Rate \( =\boldsymbol{K}\left(\boldsymbol{O}_{3}\right)^{2}\left(\boldsymbol{O}_{2}\right)^{-1} \)
Here explain the step of the above rate.


Multinucleate decomposer organism is
A. Physarum
B. Pelomyxa
c. Arcella
D. Dictyoastelium


The area of a rhombus is \( 28 m^{2} . \) If its
perimeter is \( 28 \mathrm{m} \), find its altitude.


\( f(-4)^{-2} \) is \( \frac{1}{m}, \) then the value of \( m \) is


The fuel used to produce electrical energy in the space rocket Saturn \( \mathrm{V} \) used by Neil Armstrong to reach the
moon was:
A. \( C O+O_{2} \)
в. \( F_{2}+O_{2} \)
c. \( C H_{4}+O_{2} \)
D. liquid \( H_{2}+O_{2} \)


Which will have the lowest freezing
point?
A. A 0.01-molar solution of HNO
B. A 0.01-molar solution of \( \mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2} \)
C. A 0.01-molar solution of Cu(NO \( _{3} \) )
D. A 0.01-molar solution of NaNO


Cilia and flagella are absent in life cycle
of
A. Red algae
B. Brown algae
c. Green algae
D. Red algae and blue green algae


Three spraying machines working together can finish painting a house in 60 minutes. How long will it take for 5 machines of the same capacity to do the same job ?(in minutes)


\( \vec{r}=15 t^{2} \hat{t}+\left(20-20 t^{2}\right) \hat{j} \)
Find magnitude of acceleration at \( t=1 \)
sec.
A \( .30 m / s^{2} \)
в. \( 40 \mathrm{m} / \mathrm{s}^{2} \)
c. \( 70 m / s^{2} \)
D. \( 50 m / s^{2} \)


A transformer steps up an AC supply
from \( 220 \mathrm{V} \) to \( 2200 \mathrm{V} \). If the secondary coil of the transformer has 2000
turns,the number of turns in its primary coil will be:
A . 200
B. 100
\( c .50 \)
D. 20


At an extreme point of a function \( \boldsymbol{f}(\boldsymbol{x}) \)
the tangent to the curve is
A. Parallel to the \( x \) -axis
B. Perpendicular to the \( x \) -axis
c. Inclined at an angle \( 45^{\circ} \) to the \( x \) -axis
D. Inclined at an angle \( 60^{\circ} \) to the \( x \) -axis


If one angle of a parallelogram is \( 65^{\circ} \)
What are the other angles?
A \( .50^{\circ}, 120^{\circ}, 50^{\circ} \)
в. \( 115^{\circ}, 65^{\circ} \), \( 115^{\circ} \)
\( \mathbf{c} \cdot 65^{\circ}, 115^{\circ}, 65^{\circ} \)
D. None of the above


The potentiometer wire \( A B \) is \( 100 \mathrm{cm} \) long. The value of \( R \) for which the galvanometer shown no deflection, when \( A C=40 \mathrm{cm} \) shown in figure is
\( A \cdot 13 \Omega \)
В. \( 17 . \)
\( c \cdot 15 \Omega \)
D. 21\Omega


Answer the following questions:
(a) Explain qualitatively on the basis of domain picture the irreversibility in the magnetisation curve of a ferromagnet.
(b) The hysteresis loop of a soft iron piece has a much smaller area than
that of a carbon steel piece. If the material is to go through repeated cycles of magnetisation, which piece will dissipate greater heat energy?
(c) 'A system displaying a hysteresis loop such as a ferromagnet, is a device for storing memory? Explain the meaning of this statement.
(d) What kind of ferromagnetic material is used for coating magnetic tapes in a cassette player, or for building 'memory stores' in a modern computer?
(e) A certain region of space is to be shielded from magnetic fields. Suggest a method.


If \( m-\frac{1}{m}=5, \) then find \( m^{2}+\frac{1}{m^{2}} \)
B. \( \sqrt{27} \)
c. \( 25 \sqrt{29} \)
D. \( 25 \sqrt{27} \)


Differentiate the following w.r.t. \( x: \) \( e^{x}+e^{x^{2}}+\ldots+e^{x^{5}} \)


Study the experimental set up shown
below

Which of the following statements is correct regarding the observations made, after the two visking tubes \( P \) and Q were placed in dilute iodine solution
for 10 minutes?
[Key : Visking tube allows the molecules of iodine to pass through it.
A. Solution in visking tube P turns blue - -black
B. Solution in visking tube Q turns blue - black
c. solution in both the visking tubes \( P \) and \( Q \) turns blue black
D. solution in neither of the visking tubes turns blue black


Find the position of centre of mass of the uniform planner sheet shown in
figure with respect to the origin.


Light is incident normally on a completely absorbing surface with an energy flux of \( 25 W c m^{-2} \). if the surface
has an area of \( 25 \mathrm{cm}^{-2} \), the momentum
transferred to the surface in 40 min
time duration will be :
A \( .5 .0 \times 10^{-3} \mathrm{Ns} \)
s
B . \( 3.5 \times 10^{-6} N s \)
c. \( 1.4 \times 10^{-6} N s \)
D. \( 6.3 \times 10^{-4} N s \)


Q Type your question
\( M_{A}=2 M \) and \( M_{B}=M, \) as indicated
in the figure. The two masses are initially oriented along the Y-axis and connected by a rod of negligible mass of length \( \mathrm{D} \), forming a rigid body. A force of magnitude \( \boldsymbol{F}=|\overrightarrow{\boldsymbol{F}}| \) along the X-axis is
applied to the object at \( \mathrm{B} \) at \( t=0 \) for \( \mathrm{a} \)
short time interval \( \delta t . \) Neglect gravity. The expression for the magnitude of angular velocity of the system after the
collision is:
A \( \cdot \frac{F \delta t}{M D D} \)
в. \( \frac{2 F \delta t}{3 M D} \)
c. \( \frac{F \delta t}{2 M D} \)
D. \( \frac{3 F \delta t}{2 M D} \)


Which one proposes the basic
postulates concerning elements and atoms?
A. Avogadro's number
в. \( P_{1} V_{1}=P_{2} V_{2} \)
c. \( V_{1} T_{2}=V_{2} T_{1} \)
D. Dalton's theory
E. Gay-Lussac's Law


Assertion
An endothermic reaction has a positive \( \Delta H \) value because
Reason
In an endothermic reaction, the total
enthalpy (heat content) of the products
is greater than that of the reactants.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The children are at opposite ends of metal rod. One strikes the end of the rod
with big pebble. Find the ratio of time
taken by the sound waves in air and in the metal to reach it second child. (Speed in rod \( =6420 \mathrm{m} / \mathrm{s} \) ).
A . 221.3
B. 18.55
c. 22.13
D. 185.5


Two particles move in concentric circles
of radii \( r_{1} \) and \( r_{2} \) such that they
maintain a straight line at the center. Find the ratio of their angular velocities.


Define solubility and write the factors which influence the solubility.


A solution contains \( 0.4 M C H_{3} C O O H \)
and \( 0.2 M C H_{3} C O O N a . \) Calculate the
concentration of \( \boldsymbol{H}^{+} \) ions. The
ionisation constant of acetic acid is
\( 1.8 \times 10^{-5} \)


A long thin walled hollow cylinder of radius r is carrying a current I. A very long current carrying straight conductor is passing through the axis of the hollow cylinder, carrying a current
\( i_{0} . \) Find the tension per unit length developed in the hollow cylinder due to the interaction of the straight current
carrying conductor.


Select the oxidant in the given
reactions.
\( \boldsymbol{K} \boldsymbol{I} \boldsymbol{O}_{3}+\boldsymbol{5} \boldsymbol{K} \boldsymbol{I}+\boldsymbol{6} \boldsymbol{H} \boldsymbol{C l} \rightarrow \boldsymbol{3} \boldsymbol{I}_{2}+ \)
\( 6 K C l+3 H_{2} O \)


In the arrangement shown, by what
acceleration the boy must go up so that \( 100 \mathrm{kg} \) block remains stationary on the wedge. The wedge is fixed and friction is
absent everywhere. (takeg \( =\mathbf{1 0 m} / \mathbf{s 2}) \)
\( A \cdot 2 m / s^{2} \)
B \( \cdot 4 m / s^{2} \)
\( \mathrm{c} \cdot 6 \mathrm{m} / \mathrm{s}^{2} \)
\( \mathbf{D} \cdot 8 m / s^{2} \)


A rectangular frame of wire abcd has
dimensions \( 32 \mathrm{cm} \times 8.0 \mathrm{cm} \) and a total
resistance of \( 2.0 \Omega . \) It is pulled out of a
magnetic field \( B=0.020 T \) by applying
a force of \( 3.2 \times 10^{-5} N \) (figure). It is
found that the frame moves with
constant speed. What is constant speed
of the frame?


Find power dissipated in \( 4 \Omega \) resistor:
\( A \cdot 12 w \)
B. 16 \( w \)
\( c \cdot 4 w \)
\( 0.6 \mathrm{w} \)


An infinite long straight wire is bent into a semicircle of radius \( R \), as shown
in the figure. A current \( I \) is sent through the conductor. The magnetic field at the centre of the semicircle is :
A. \( \infty \)
в. 0
c. \( \frac{\mu_{0}}{4 R} I \)
D. \( \frac{\mu_{0} I}{4 \pi R}(\pi+1) \)


Which is the \( 1^{s t} \) organic compound synthesized in lab?
A. Urea
B. Methanol
c. Ammonia
D. Sulphuric Acid


The reason for double helical structure
of DNA is the operation of:
A. electrostatic attractions
B. van der Waals forces
c. dipole - dipole interactions
D. hydrogen bonding


If \( \boldsymbol{\pi}=\mathbf{1 8 0}^{\circ} \) and \( \boldsymbol{A}=\frac{\boldsymbol{\pi}}{\boldsymbol{6}}, \) prove that
\( \frac{(1-\cos A)(1+\cos A)}{(1-\sin A)(1+\sin A)}=\frac{1}{3} \)


What is the electric potential at a distance of \( 9 \mathrm{cm} \) from 3 nC?
\( \mathbf{A} \cdot 270 V \)
в. \( 3 V \)
\( \mathbf{c} .300 V \)
D. 30V


It is proposed to use the nuclear fusion reaction \( _{1} H^{2}+_{1} H^{2} \longrightarrow H e^{4} \) in a
nuclear reactor with an electrical power
rating of \( 200 M W . \) If the energy form
the above reaction is used with 25
percent efficiency in the reactor, how many grams of deuterium fuel will be
needed per day? (The masses of \( _{1} \boldsymbol{H}^{2} \)
and \( _{2} H e^{4} \) are \( 2.0141 a m u \) and 4.0026 amu respectively.)


Retardation means
A . negative acceleration
B. positive acceleration
c. zero acceleration
D. none of these


The point to which the axes are to be translated to eliminate \( x \) and \( y \) terms in
the equation \( 3 x^{2}-4 x y-2 y^{2}-3 x- \)
\( 2 y-1=0 \) is
\( ^{\mathrm{A}} \cdot\left(\frac{5}{2}, 3\right) \)
в. \( \left(-4, \frac{3}{2}\right) \)
c. (-2,3)
D. (2,3)


Na \( C N \) is sometimes added in the froth
floatation process as a depressant when \( Z n S \) and \( P b S \) minerals are
expected because:
A \( \cdot Z n S \) forms soluble complex \( N a_{2}\left[Z n(C N)_{4}\right] \) while \( P b S \)
form froth
B . \( P b(C N)_{2} \) is precipitated while no effect on \( Z n S \) form froth
C . \( P b S \) forms soluble complex \( N a_{2}\left[Z n(P b)_{4}\right] \) while \( Z n S \)
form froth
D. \( N a C N \) is never added in froth floatation process


Explain with examples, why we find animals of certain kind living in particular climatic conditions.


Evaluate the following products without multiplying directly:
\( \mathbf{1 0 4} \times \mathbf{9 6} \)


A reaction has an activation energy of
\( 209 k J . m o l^{-1} . \) The rate increases 10
fold when the temperature is increased
from \( 27^{\circ} \mathrm{C} \) to \( X^{o} C . \) The temperature \( X \) is
closest to.[Gas constant, \( \boldsymbol{R}=\mathbf{8 . 3 1 4} \)
\( \left.\boldsymbol{J} \cdot \boldsymbol{m} \boldsymbol{o} \boldsymbol{l}^{-1} \boldsymbol{K}^{-1}\right] \)
A . 35
B . 40
c. 30
D. 45


The change in momentum of a vehicle weighing 2000 kg when its speed increases from \( 36 \mathrm{km} / \mathrm{h} \) to \( 72 \mathrm{km} / \mathrm{h} \)
uniformly is :
A. \( 15000 \mathrm{kg}, \mathrm{m} / \mathrm{s} \)
B. 4000 kg.m/s
c. \( 20000 \mathrm{kg}, \mathrm{m} / \mathrm{s} \)
D. 7200 kg.m/s


On a hypothetical scale \( A \) the ice point
is \( 42^{\circ} \) and the steam point is \( 182^{\circ} \) For
another scale \( \mathrm{B} \), the ice point is \( -10^{\circ} \)
and steam point in \( 90^{\circ} \) ) If \( \mathrm{B} \) reads \( 60^{\circ} \) the reading of \( A \) is,
\( \mathbf{A} \cdot 160^{\circ} \)
B. \( 140^{\circ} \)
\( c \cdot 120^{\circ} \)
D. \( 110^{\circ} \)


The kind of water is suitable for use is :
A. hard water
B. soft water
c. both A and B
D. none of above


Kyle bought 2 snack boxes. Box A has a measure of 2 in \( \times 3 \) in \( \times 5 \) in. Box B
has a measure of 11 in \( \times 4 \) in \( \times 3 \) in.
Find the surface area of the boxes and
their difference.
A \( \cdot 116 i n^{2} \)
B. \( 201 i n^{2} \)
\( \mathbf{c} \cdot 279 i n^{2} \)
D. \( 198 i n^{2} \)


A card is thrown from a pack of 52 cards
so that each card equally likely to be selected. Then find whether the events
\( A \) and \( B \) independent?
\( A= \) the card drawn is spade, \( B= \) the card drawn in an ace.


The eight term of an \( A . P . \) is half the
second term and eleventh term exceeds
one third of its fourth term by 1. Find its
\( 15^{t h} \) term