The velocity of a particle increases from u to v in time \( t \) during which it covers a distance s. If the particle has a uniform acceleration, then which one of the following equations does not apply to the motion?


\( 4.00 \mathrm{cm} \) contains air compressed by a piston of mass \( m=13.0 \mathrm{kg} \) which can slide freely in the cylinder. The entire arrangement is immersed in a water
bath whose temperature can be controlled. The system is initially in
equilibrium at temperature \( t=20^{\circ} C \)
The initial height of the piston above the
bottom of the cylinder is \( h_{i}=4.00 \mathrm{cm} \)
The temperature of the water bath is
gradually increased to a final
temperature \( t_{f}=100^{\circ} \mathrm{C} . \) Calculate the
final height \( h_{f} \) of the piston.
\( \mathbf{A} \cdot 25.09 \mathrm{cm} \)
B. \( 5.09 \mathrm{cm} \)
c. \( 15.09 c m \)
D. \( 10.09 \mathrm{cm} \)


The value of a scooter depreciates by 15\% every year. If its present value is Rs. \( 31025, \) what was its value 1 year ago?
2. The price of an article has been reduced by \( 10 \% . \) By how much per cent must the new price be increased to
retain the orignal price?


Pollutant which causes acid rain is
\( A \cdot S O_{2} \)
в. \( C O_{2} \)
\( c \cdot c o \)
D. Hydrocarbons


Let the vectors \( \vec{a} \) and \( \vec{b} \) be such that
\( |\vec{a}|=3 \) and \( |\vec{b}|=\frac{\sqrt{2}}{3}, \) then \( \vec{a} \times \vec{b} \) is a
is
A \( \cdot \frac{\pi}{6} \)
в.
\( c \cdot \frac{\pi}{3} \)
D.


Multiple Correct Answers Type:
Two bodies of masses \( m_{1} \) and \( m_{2} \) are
dropped from heights \( h_{1} \) and \( h_{2} \) respectively. They reach the ground
after time \( t_{1} \) and \( t_{2} \) and strike the
ground with \( v_{1} \) and \( v_{2}, \) respectively.
Choose the correct relations from the
following. This question has multiple correct options
A \( \cdot \frac{t_{1}}{t_{2}}=\sqrt{\frac{h_{1}}{h_{2}}} \)
B. \( \frac{t_{1}}{t_{2}}=\sqrt{\frac{h_{2}}{h_{1}}} \)
c. \( \frac{v_{1}}{v_{2}}=\sqrt{\frac{h_{1}}{h_{2}}} \)
D. \( \frac{v_{1}}{v_{2}}=\frac{h_{2}}{h_{1}} \)


If \( \vec{a}=\hat{i}+\hat{j}+\hat{k} \& \vec{b}=\hat{j}-\hat{k}, \) then the
vector \( \vec{c} \) such that \( \vec{a} . \vec{c}=3 \& \vec{a} \times \vec{c}=\vec{b} \)
is
A \( \cdot \frac{1}{3}(3 \hat{i}-2 \hat{j}+5 \hat{k}) \)
B・\( _{\frac{1}{3}}(5 \hat{i}+2 \hat{j}+2 \hat{k}) \)
c \( \cdot \frac{1}{3}(\hat{i}+2 \hat{j}-5 \hat{k}) \)
D \( \cdot \frac{1}{3}(3 \hat{i}+2 \hat{j}+\hat{k}) \)


If \( \frac{50}{x}+3=13,50 x+3=13, \) then the
value of \( x \) is
\( A \cdot 2 \)
B. 4
c. 5
D.


Which of the following is NOT a
quadratic polynomial?
A \( \cdot p(x)=x^{2}+4 x-16 \)
\( \mathbf{B} \cdot p(y)=y^{2}+8 y-10 \)
\( \mathbf{c} \cdot p(x)=73 x-84 \)
\( \mathbf{D} \cdot p(y)=2 y^{2}-x^{2} \)


Which of the following reactions is/are not correct to get cinnamic acid?
A \( \cdot C_{6} H_{5} C H O \frac{ }{\left(C H_{3} C O\right)_{2} O / C H_{3} C O O N a} \)
B. \( C_{6} H_{5} C H O \frac{1) C H_{2}\left(C O O C_{2} H_{2}\right)_{2}, p y r i \text { dine }}{2 / H_{3} O+, \Delta} \)
c. \( C_{6} H_{5} \) СНО \( \stackrel{\text {СНз} \text {сно} / \text {ОН}}{\text { - }} \)
D. \( C_{6} H_{5} C H O \frac{1) B r C H_{2} C O O C_{2} H_{3} / Z n I \Delta}{2) H_{2} O / H+/ \Delta} \)


Draw a circle with centre \( O \) and radius
\( 4 \mathrm{cm} . \) Take point \( \boldsymbol{A} \) such that \( \boldsymbol{d}(\boldsymbol{O}, \boldsymbol{A})= \)
\( 9 \mathrm{cm} . \) Draw tangents from point \( \boldsymbol{A} \)


The gas which is supposed to be acidic
anhydride :
A \( \cdot N O_{2} \)
в. \( C O \)
\( c \cdot N_{2} O \)
D. \( N O \)


In the figure \( A B=B C, A C=C D \) and
\( \angle A C D=90^{\circ} . \) If the radius of the circle
is "r" units then find the length of the
chord BC.
A \( \cdot r \sqrt{\sqrt{2-1}} \)
B \( \cdot r \sqrt{\sqrt{3-1}} \)
c. \( r \sqrt{2-\sqrt{2}} \)
D. \( r \sqrt{2-\sqrt{3}} \)


IUDs are ideal contraceptives for the females who want to delay pregnancy and/or space children. Justify


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


What are essential and non essential
amino acids?


Let \( ^{\prime} *^{\prime} \) be a binary operation on set \( Q \) of rational number defined as \( a * b=\frac{a b}{5} \)
Write the identity for \( ^{\prime} *^{\prime}, \) if any.


Assertion
Heat of combustion is always negative.
Reason

Heat of combustion is used to calculate
the calorific value of fuels.
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


In somatic cell cycle
A. A short interphase is followed by a long mitotic phase
B. DNA replication takes place in S phase
\( \mathrm{C} \cdot \ln \mathrm{G}_{1} \) phase, DNA content is double the amount of DNA present in the original cell
D. None of these


There is no scum formation when hard
water is being used. The washing
powder can be:
A. \( C_{17} H_{35} \) COONa
B.
\( c . \) both \( A \) and \( B \)
D. none of the above


\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{B r} \) is:
A. bromoderivative of alkanes
B. derivative of bromo alkanes
c. alkyl derivative
D. None of these


\( \int \frac{1}{\sqrt{e^{5 x}, \sqrt[4]{\left(e^{2 x}+e^{-2 x}\right)^{3}}}} d x \)
\( \mathbf{A} \cdot-t^{1 / 4}, \) where \( 1+e^{-4 x}=t \)
B. \( t^{1 / 4}, \) where \( 1+e^{-4 x}=t \)
\( \mathbf{c} \cdot-t^{3 / 4}, \) where \( 1+e^{-4 x}=t \)
\( \mathbf{D} \cdot-t^{1 / 2}, \) where \( 1+e^{-4 x}=t \)


Most antibiotics have no effect on
viruses because
A. They kill all bacteria, which act as host of the virus.
B. Viruses are too small in size for the antibiotics to act
on them
C. Viruses show no metabolism of their own.
D. Viruses produce thick covering and encyst themselves as endospores.


What should a piano tuner do to correct the sound of a string that is flat, that is, it plays at a lower pitch than it should?
A. Tighten the string to make the fundamental frequency higher
B. Tighten the string to make the fundamental frequency lower
c. Loosen the string to make the fundamental frequency higher
D. Loosen the string to make the fundamental frequency lower
E. Find a harmonic closer to the desired pitch


The point on the line \( \frac{\boldsymbol{x}-\mathbf{1}}{\mathbf{1}}=\frac{\boldsymbol{y}+\mathbf{3}}{-\mathbf{2}}= \)
\( \frac{z+5}{-2} \) at a distance of 6 from the point
(1,-3,-5) is
в. (3,-7,-9)
D. (-3,5,3)


\( \frac{1}{2} \tan ^{-1} x=\cos ^{1}\left\{\frac{1+\sqrt{1+x^{2}}}{2 \sqrt{1+x^{2}}}\right\}^{\frac{1}{2}} \)


Which of the following substance acts as stimulator?
A . vitamins
B. enzymes
c. hormones
D. carbohydrates


If the order of the matrix is \( 1 \times 2, \) then it
is a
A. Row matrix
B. Column matrix
c. Square matrix
D. None of these


\( A 16 \mathrm{cm} \) long pencil is placed as shown
in figure. The central point \( C \) is \( 45 \mathrm{cm} \) away from a \( 20 \mathrm{cm} \) focal length lens and \( 15 \mathrm{cm} \) above the optic axis. Find the length of image.
A . \( 14.2 \mathrm{cm} \)
B. \( 12.3 \mathrm{cm} \)
\( c .17 .1 \mathrm{cm} \)
D. \( 4.5 \mathrm{cm} \)


In the clathrates of xenon with water,
the nature of bonding between xenon and water molecule is :
A. Covalent
B. Hydrogen bonding
c. Co-ordinate
D. Dipole-induced dipole interaction


A \( 100 \Omega \) resistor is connected to a
\( 220 V, 50 H z A C \) supply. Find \( r m s \) value
of current in the circuit :
A . \( 1.10 A \)
в. \( 2.20 A \)
c. \( 3.30 A \)
D. \( 4.40 A \)


Evaluate the Given limit: \( \lim _{x \rightarrow \pi}\left(x-\frac{22}{7}\right) \)


Two liquids \( A \) and \( B \) are \( a t 30^{\circ} C \) and
\( 20^{\circ} \mathrm{C} \) respectively. When they are mixed in equal masses, the temperature of the
mixture is found to be \( 26^{\circ} \mathrm{C} \). The ratio of
specific heat is :
\( A \cdot 4: 3 \)
B. 3:4
\( c \cdot 2: 3 \)
D. 3:2


How long will it be before the ball hits the ground? Take \( g=10 m s^{-2} \)


Assertion
Statement 1:The current density \( \bar{J} \) at any point in ohmic resistor is in direction of electric field \( \bar{E} \) at that point.
Reason
Statement \( 2: A \) point charge when released from rest in a region having only electrostatic field always moves along electric lines of force.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Explain the inter-conversion of the three
states of matter in terms of force
attraction and K.E of the molecules.


Uncertainty in position of an electron
\( \left(m a s s=9.1 \times 10^{-28 g}\right) \) moving with a
velocity of \( 3 \times 10^{4} \mathrm{cm} / \mathrm{s} \) accurate upto
\( 0.001 \% \) will be: \( (U \text { se } h / 4 \pi \) in
uncertainty expression where \( h= \) \( \left.6.626 \times 10^{-27} \text {erg }-s\right) \)
A. \( 5.76 \mathrm{cm} \)
B . 7.68 \( \mathrm{cm} \)
\( c .1 .93 \mathrm{cm} \)
D. 3.84 \( \mathrm{cm} \)


How do emulsifying agents stabilise the emulsion?


heat is produced whenever work is done against friction
A. True
B. False


A plank with a uniform sphere placed on it rests on a smooth horizontal plane. The plank is pulled to right by a
constant force F. If the sphere does not slip over the plank, then. This question has multiple correct options
A. Both have same acceleration
B. Acceleration of centre of sphere is less than that of the plank
c. work done by friction acting on the sphere is equal to its total kinetic energy
D. Total kinetic energy of the system is equal to work done by the force \( F \)


Simplify: \( \left(\boldsymbol{x}^{2}-\boldsymbol{x}+\mathbf{1}\right)\left(\mathbf{2} \boldsymbol{x}^{2}+\mathbf{2}\right) \)
A \( \cdot 2 x^{4}-2 x^{3}+4 x^{2}-2 x+2 \)
B . \( 2 x^{4}-2 x^{3}+4 x^{5}-2 x+2 \)
c. \( 2 x^{4}+2 x^{3}+4 x^{2}-2 x+2 \)
D. \( 2 x^{4}-2 x^{3}-2 x+2 \)


The eye of octopus and eye of cat show
different patterns of structure, yet they perform similar function, This is an
example of :
A. Homologous organs that have evolved due to convergent evolution
B. Homologous organs that have evolved due to divergent evolution
C. Analogous organs that have evolved due to convergent evolution
D. Analogous organs that have evolved due to divergent evolution


Sound waves get reflected from:
A. plane surfaces
B. spherical surfaces
\( c . \) hard surfaces
D. all of these


If \( f(x)=\cos ^{-1}\left\{\frac{1-\left(\log _{e} x\right)^{2}}{1+\left(\log _{e} x\right)^{2}}\right\} \), then
\( \boldsymbol{f}^{\prime}(\boldsymbol{e}) \)
A. Does not exist
B.
c.
D. Is equal to 1


A magnetic flux of \( 500 \mu W b \)
passing through a 200 turns coil is
reversed in \( 20 \times 10^{-3} \) seconds. The
average emf per unit area induced in
the coil in \( V / m^{2} \) is
A . 2.5
B. 5.0
\( c .7 .5 \)
D. 10.0


Choose the correct answers from the
alternatives given :
The creation of an RNA molecule from a
section of DNA is known as
A. replication
B. RNA splicing
c. transcription
D. translation


mol of \( N a C l O_{4} \) is to be produced from
the electrolysisi of \( N a C l O_{3} \).FInd the
volume of \( H_{2} \) evolved at STP in the time
during which 12.25 g of \( N a C l_{4} \) are produced.
\( \mathbf{A} \cdot 1 \cdot 12 L \)
B. \( 5.2 L \)
c. \( 2.24 L \)
D. none


Assertion
Fermentation is called zymosis.
Reason
It is based on enzyme complex zymase.
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 perimeter of a rhombus is \( 146 \mathrm{cm} \)
and one of its diagonal is \( 55 \mathrm{cm} . \) Find the other diagonal and the area of the
rhombus.
A. \( 24 \mathrm{cm} 660 \mathrm{sq} . \mathrm{cm} \)
B. \( 24 \mathrm{cm} 330 \) sq. \( \mathrm{cm} \)
c. \( 48 \mathrm{cm} 660 \mathrm{sq} . \mathrm{cm} \)
D. \( 48 \mathrm{cm} 1320 \) sq. \( \mathrm{cm} \)


Which of these describes a way in
which air pollution has been reduced?
A. Raising cattle for food
B. Using fossil fuels
c. Using unleaded gasoline
D. Releasing ozone into the atmosphere
E. Releasing greenhouse gases


A coin is tossed 3 times. The probability of getting head and tail alternately is
A \( \cdot \frac{1}{8} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{1}{4} \)
D.


The direction of current in the smaller
circuit is
A. clockwise
B. anticlockwise
c. always changes with time
D. cannot be calculated
E. answer required


f \( \boldsymbol{A}+\boldsymbol{B}+\boldsymbol{C}=\boldsymbol{\pi}, \) then
\( \left|\begin{array}{ccc}\tan (\boldsymbol{A}+\boldsymbol{B}+\boldsymbol{C}) & \tan \boldsymbol{B} & \tan C \\ \tan (\boldsymbol{A}+\boldsymbol{C}) & \boldsymbol{0} & \tan \boldsymbol{A} \\ \tan (\boldsymbol{A}+\boldsymbol{B}) & -\tan \boldsymbol{A} & \boldsymbol{0}\end{array}\right| \)
equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c . \) tan AtanBtan
D. -2


Find the projection of \( \vec{A}=2 \hat{i}-\hat{j}+ \)
\( \hat{\boldsymbol{k}} \quad \boldsymbol{o} \boldsymbol{n} \quad \overrightarrow{\boldsymbol{B}}=\hat{\boldsymbol{i}}-\boldsymbol{2} \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \)
\( A \cdot \frac{5}{\sqrt{6}} \)
B. \( \frac{7}{10} \)
\( c \cdot \frac{6}{\sqrt{5}} \)
D. \( \$ \$ \) frac \( \{5 \text { ) ( } \mid \text { sqre }\{3\}\} \)


Factorize:
\( 16 a^{4}-9 b^{4} \)


If \( A \) is a square matrix such that \( A^{2}= \)
\( A, \) then \( |A| \) equals
\( \mathbf{A} \cdot 0 \) or 1
B. - 2 or 2
\( c .-3 \) or 3
D. None of these


What number should be added to \( x^{3}- \)
\( 9 x^{2}-2 x+3 \) so that the remainder
may be 5 when divided by \( (x-2) \)


A non conducting rod \( A B \) of length \( \sqrt{3} R \) uniformly distributed charge of linear charge density \( \lambda \) and.a non-conducting ring of uniformly distributed charge \( Q \) are placed as shown in the figure. Point
A is the centre of ring and line \( A B \) is the
axis of the ring, perpendicular to plane of ring. The electrostatic
interaction energy between ring and rod
is
A \( \cdot \frac{Q \lambda}{4 \pi \epsilon_{l}} \ln (2+\sqrt{3}) \)
c. \( \frac{Q \lambda}{4 \pi \epsilon} \ln (2-\sqrt{3}) \)
D・\frac{Q\lambda } \( {2 \pi \epsilon} \ln (2-\sqrt{3}) \)


Define Curie temperature in
magnetism.


A mixture of sulphur and carbon
disulphide is:
A. heterogeneous and shows Tyndall effect
B. homogeneous and shows Tyndall effect
C. heterogeneous and does not show Tyndall effect
D. homogeneous and does not show Tyndall effect


\( f(x)=\frac{4}{\pi} \sin \left(\frac{\pi}{2} x\right)+B \) and
\( \int_{1}^{0} f(x) d x=\frac{4}{\pi} \int \sin \left(\frac{\pi}{2} x\right)+B d x, \) Find
\( \boldsymbol{B} \)


Calculate the volume of gas liberated at the anode at STP during the electrolysis
of a \( C u S O_{4} \) solution by a current of \( 1 A \)
passed for 16 minutes and 5 seconds.
A . \( 224 \mathrm{mL} \)
в. \( 56 \mathrm{mL} \)
\( c \cdot 112 m L \)
D. \( 448 \mathrm{mL} \)


Find if possible, the slope of the line through the points \( (1 / 2,3 / 4) \) and \( (-1 / 3,5 / 4) \)


What is the order of magnitude of one
light year?
\( \mathbf{A} \cdot 10^{15} m \)
B . \( 10^{10} m \)
c. \( 9.2 \times 10^{15} \mathrm{m} \)
D. \( 10^{16} m \)


Four identical capillary tubes \( a, b, c \) and \( d \) are dipped in four beakers containing water with tube 'a' vertically, tube 'b' at
\( 30^{\circ}, \) tube \( ^{\circ} c^{\prime} \) at \( 45^{\circ} \) and tube ' \( d^{\prime} \) at \( 60^{\circ} \) inclination with the vertical. Arrange the lengths of water column in the tubes in descending order
A \( . d, c, b, a \)
в. \( d, a, b, c \)
c. \( a, c, d, b \)
D. \( a, b, c, d \)


If the half-lives of a radioactive element
for \( \alpha \) - decay and \( \beta \) - decay are 4 years and 12 years respectively. What percent would its total activity be of its initial activity after 12 years?
A . 50
B. 25
c. 12.5
D. 6.25


The value of \( \tan 203^{\circ}+\tan 22^{\circ}+ \)
\( \tan 203^{\circ} \tan 22^{\circ} \) is
A . -1
B. 0
c. 1
D. 2


According to the reaction: \( P b(s)+ \)
\( S(s) \rightarrow P b S(s), \) when 20.7 grams of
lead are reacted with 6.4 grams of
Sulfur:
A. there will be an excess of 20.7 grams 04 lead
B. the sulfur will be in excess by 3.2 grams
C. the lead and sulfur will react completely without any excess reactants
D. the sulfur will be the limiting factor in the reaction
E. there will be an excess of 10.35 grams of lead


What is the first stable intermediate
product of photosynthesis?
A. Glucose
B. Formaldehyde
c. Phosphoglyceric acid
D. PGAL


The degree of the polynomial \( 2 x-1 \) is
A. 0
B. \( \frac{1}{2} \)
\( c \cdot-1 \)
D.


Assertion: Two concentric charged
shells are given. The potential difference between the shells depends on
charge of inner shell.
Reason: Potential due to charge of outer
shell remains same at every point
inside the sphere.
A. Both Assertion and Reason are true and the Reason is the correct explanation of the Assertion
B. Both Assertion and Reason are true but the Reason is not the correct explanation of the Assertion
c. Assertion is true statement but Reason is false
D. Both Assertion and Reason are false statements


On over loading of a given circuit a fuse wire will melt.


An electron moving in a electric
potential field \( V_{1} \) enters a higher
electric potential field \( V_{2} \) then the change in kinetic energy of the electron is proportional to


Atomic radius is of the order of \( 10^{-8} \mathrm{cm} \)
and nuclear radius is of the order of
\( 10^{-13} \mathrm{cm} . \) The fraction of atom occupied
by nucleus is:
A \( \cdot 10^{-5} \)
B . \( 10^{5} \)
\( \mathbf{c} \cdot 10^{-15} \)
D. none of these


A charge \( q \) is placed at the corner of a cube of side \( a \). The electric flux passing
through the cube is :
A \( \cdot \frac{q}{a \varepsilon_{0}} \)
в. \( \frac{q}{\varepsilon_{0} a^{2}} \)
c. \( \frac{q}{4 \pi \varepsilon_{0} a^{2}} \)
D. \( \frac{q}{24 \varepsilon_{0}} \)


A particle with total mechanical energy, which is small and negative, is under the influence of a one dimensional
potential \( U(x)=x^{4} / 4-x^{2} / 2 \) Jwhere \( x \)
is in meters. At time \( t=0 \) s, it is at \( x= \)
\( -0.5 \mathrm{m} . \) Then at a later time it can be
found.
A. anywhere on the x axis.
B. between \( x=-1.0 \mathrm{m} \) to \( x=1.0 \mathrm{m} \)
c. between \( x=-1.0 \mathrm{m} \) to \( x=0.0 \mathrm{m} \)
D. between \( x=0.0 \mathrm{m} \) to \( x=1.0 \mathrm{m} \)


Correct order of reducing agent, in \( V^{2+} \)
or \( C o^{2+} \) is:
A \( \cdot V^{2+}=C o^{2+} \)
B. \( V^{2+}<C o^{2+} \)
\( \mathbf{c} \cdot V^{2+}>C o^{2} \)
D. none of these


A newly prepared radioactive nuclide
has a decay constant \( \lambda \) of \( 10^{-6} s^{-1} \)
What is the approximate half-life of the nuclide?
A . 4
B. 1 day
c. 8 week
D. 12 month


If \( z=x+i y \) and \( w=\frac{(1-i z)}{(z-i)}, \) then
\( |\boldsymbol{w}|=1 \) implies that, in the complex
plane
A. \( z \) lies on the imaginary axis
B. \( z \) lies on the real axis
c. \( z \) lies on the unit circle
D. None of these


Carbon dioxide is called a "greenhouse"
gas, because
A. It is involved in photosynthesis
B. It emits light
c. It traps infrared radiations
D. It traps ultraviolet radiations


The large volume of gas can be filled in a small cylinder owing to its high
A. resitivity
B. compressibility
c. pressure
D. boiling point


In a circle with centre \( 0 . \operatorname{seq} \mathrm{PQ}, \) is a
chord such that \( \angle P O Q=70^{\circ} . \) Find the
\( \angle O P Q \)


A flooring tile has the shape of a
parallelogram whose base is \( 24 \mathrm{cm} \) and
the corresponding height is \( 10 \mathrm{cm} . \) How
many such tiles are required to cover a
floor of area \( 1080 m^{2} ? \)
A . 20000
B. 35000
c. 45000
D. 65000


The two extinct lines of the
gymnosperms which are regarded as an ancestral stock from which the modern
gymnosperms might have originated
are?
A. Cordaitales and Bennettitales
B. Cycadales and Coniferales
c. Ginkgoales and Cycadales
D. Gnetales and Coniferales


The \( x \) location and mass of two masses
are given as \( (1 m, 3 k g) \) and \( (-2 m, 2 k g) \)
A third mass weighs \( 1 k g \)
Given that the center of mass of the
system lies at \( x=-1 m, \) what must be
the \( x \) position of the third mass?
A \( . x=-5 m \)
B . \( x=-3 m \)
c. \( x=-2.5 m \)
D. \( x=-2 m \)
E . \( x=2 m \)


Match the Column-I with Column-II for
van der Waals' equation.


There are three elements \( \boldsymbol{E}, \boldsymbol{F}, \boldsymbol{G} \) with
atomic numbers 19,8 and 17
respectively.
Classify the elements as metals and
non-metals.


Which of the following is/are negatively charged sol?
This question has multiple correct options
A. Gold sol
B. Prussian blue dye
c. Haemoglobin
D. starch


What is the valency of magnesium with atomic number \( 12 ? \)
A . 2
B. 4
c. 5
\( D \)


Three metallic solid cubes whose edges
are \( 1 \mathrm{m}, 2 \mathrm{m}, \) and \( 3 \mathrm{m} \) are melted and
converted into a single cube. Find the edge of the cube so formed?
A. \( 2.2 \mathrm{m} \)
B. 3.0 \( m \)
\( c \cdot 3.3 m \)
D. 3.9 \( m \)


A particle is fired with velocity \( u \)
making angle \( \theta \) with the horizontal.
what is the change in velocity when it is at the highest point?
A \( . u \cos \theta \)
B.
c. \( u \sin \theta \)
D. \( (u \cos \theta-u) \)


A straight copper wire is moved in a uniform magnetic field such that it cuts the magnetic lines of force. Then
A. emf will not be induced
B. emf will be induced
c. sometimes emf will be induced and sometimes not
D. nothing can be predicted


The equiconvex lens has focal length \( \boldsymbol{f} \)
If it is cut perpendicular to the principal axis passing through optical centre, then focal length of each half is
A \( \cdot \frac{f}{2} \)
B. \( f \)
\( c \cdot \frac{3 f}{2} \)
D. \( 2 f \)


The optical rotation of the \( \alpha \) form of
pyranose is \( +150.7^{0}, \) that of the \( \beta \) form
is \( +52.8^{0} . \) In solution an equilibrium
mixture of these anomers has an
optical rotation of \( +80.2^{0} . \) The
percentage of the \( \alpha \) - form in equilibrium mixture is:
\( \mathbf{A} \cdot 28 \% \)
B. \( 32 \% \)
\( c .68 \% \)
D. \( 72 \% \)


In a zero order reaction, the time taken
to reduce the concentration of reactant
from \( 50 \% \) to \( 25 \% \) is 30 minutes.What is
the time required to reduce the concentration from 25\% to 12.5\%?


According to 1991 census, the minimum
percent of population increase is in the state
A. Kerala
B. Tamilnadu
c. west Bengal
D. Madhya Pradesh


The tangents at two points, \( P \) and \( Q \), of a conic meet in \( \mathrm{T} \), and \( \mathrm{S} \) is the focus
prove that if the conic be a parabola,
\( \operatorname{then} S T^{2}=S P . S Q \)


Phosphorus forms \( \boldsymbol{P} \boldsymbol{C l}_{5} \) while nitrogen
cannot form \( N C l_{5} . \) Why?


The percentage of copper and oxygen in a sample of Cu0 obtained from different methods were found to be same. This
proves the law of :
A. constant proportion
B. Multiple proportion
c. Reciprocal proportion
D. None of these


In cockroach, the longest podomere is
A. \( \operatorname{coxa} \)
B. Trochanter of Femur
c. Tibia
D. tarsus


Find the focus of the parabola \( \boldsymbol{y}= \)
\( -2(x+4)^{2}-1 \)
\( \mathbf{A} \cdot(-4,-1) \)
в. \( \left(-4, \frac{9}{8}\right) \)
c. (-4,1)
D. \( \left(-4,-\frac{9}{8}\right) \)


Find the degree of the given algebraic
expression \( 2 y^{2} z+10 y z \)
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D. 10


Which of the following element of group IIIA element will show allotropy?
A. boron
B. aluminium
c. gallium
D. indium


Dinitrogen and dihydrogen react with each other to produce ammonia according to the following chemical equation:
\( N_{2}(g)+H_{2}(g) \rightarrow 2 N H_{3}(g) \)
(i) Calculate the mass of ammonia
produced if \( 2.00 \times 10^{2} g \) dinitrogen
react with \( 1.00 \times 10^{3} g \) of dihydrogen
(iii) Will any of the two reactants remain unreacted?
(iii) If yes, which one and what would be its mass?


A student is studying a book placed at the edge of a circular table of radius \( R \)
A point source of light is suspended
directly above the centre of the table.
What should be the height of the lamp
so that maximum illuminance is
produced at the position of the book?
A. \( R \)
в. \( \frac{R}{2} \)
c. \( \frac{R}{\sqrt{2}} \)
D. \( \frac{R}{\sqrt{3}} \)


Answer the following question in one word or one sentence or as per exact requirement of the question.
If \( \boldsymbol{f}(\mathbf{1})=\mathbf{1}, \boldsymbol{f}^{\prime}(\mathbf{1})=\mathbf{2}, \) then write the
value of \( \lim _{x \rightarrow 1} \frac{\sqrt{\boldsymbol{f}(\boldsymbol{x})}-\mathbf{1}}{\sqrt{\boldsymbol{x}}-\mathbf{1}} \)


In the Doberiener's triad, all three
elements have similar:
A. electronic configuration
B. properties
c. number of shells
D. both A and B


By selling 130 cassettes, a man gains an amount equal to the selling price of 5 cassettes. Find the gain percent.


If we drop a cup of water on a plate and
a cup of oil on another plate, water is seen to spread faster along diameter. This is an example related to:
A. fluid friction
B. rolling friction
c. sliding friction
D. static friction


A certain transverse wave is described
by \( \boldsymbol{y}(\boldsymbol{x}, \boldsymbol{t})= \)
\( (6.50 m m) \cos 2 \pi\left(\frac{x}{28.0 c m}-\frac{t}{0.0360}\right. \)
The wave's amplitude is \( 6.50 \times 10^{-x} m \)
Find the value of \( x \)


If \( f(x)=\ln \left(\frac{1+x}{1-x}\right), \) then \( f\left(\frac{2 x}{1+x^{2}}\right) \)
equals.
\( \mathbf{A} \cdot[f(x)]^{2} \)
B. \( f(x)^{3} \)
c. \( 2 f(x) \)
D. \( 3 f(x) \)


One of the following is a growth
retardent
A. Morphactin
B. Zeatin
c. Adenine
D. Ascorbic acid


There is a possibility of melting of polar ice caps and increase in the level of sea
water due to:
A. Depletion of ozone layer
B. Green house effect
c. Acid rain
D. All of the above


\( C u(S)+2 A g^{+}(a q) \rightarrow C u^{2+}(a q)+2 A g(S) \)
In the given reaction, the reduction half
cell reaction is:
A \( \cdot \mathrm{Cu}^{2+}+2 \mathrm{e}^{-} \rightarrow \mathrm{cu} \)
B. \( \operatorname{cu} 2 e^{-} \rightarrow c u^{2} \)
\( \mathrm{c} \cdot \mathrm{Ag}^{+}+\mathrm{e}^{-} \rightarrow \mathrm{Ag} \)
D. \( A g e^{-} \rightarrow A g^{+} \)


The liquids and gases only have cubical expansion. True or false.
A. True
B. False


In a large commercial complex there are four ways to reach the main road. One of the path has loose soil, the second is laid with polished marble, the third is laid with bricks and the fourth
has gravel surface. It is raining heavily and Paheli wishes to reach the main
road. The path on which she is least likely to slip is:
A. loose soil
B. polished marble
c. bricks
D. gravel surface


Which of the following reactions is correct for a given electrochemical cell
\( \operatorname{at} 25^{\circ} C ? \)
\( \boldsymbol{P t}\left|\boldsymbol{B r}_{2}(\boldsymbol{g})\right| \boldsymbol{B r}^{-}(\boldsymbol{a q}) \| \boldsymbol{C l}^{-}(\boldsymbol{a q}) \mid \boldsymbol{C l}_{2}(\boldsymbol{g}) \)
A \( \cdot 2 B r^{-}(a q)+C l_{2}(g) \rightarrow 2 C l^{-}(a q)+B r_{2}(g) \)
B . \( B r_{2}(g)+2 C l^{-}(a q) \rightarrow 2 B r^{-}(a q)+C l_{2}(g) \)
C. \( B r_{2}(g)+C l_{2}(g) \rightarrow 2 B r^{-}(a q)+2 C l^{-}(a q) \)
D \( \cdot 2 B r^{-}(a q)+2 C l^{-}(a q) \rightarrow B r_{2}(g)+C l_{2}(g) \)


Given \( : a x+b y=d \) and \( y=m x+c \)
Find \( x \) in terms of \( b, c, d \) and \( m \)
A \( \cdot x=\frac{d-b c}{a-b m} \)
B. \( x=\frac{d+b c}{a+b m} \)
c. \( _{x}=\frac{d-b c}{a+c m} \)
D. \( x=\frac{d-b c}{a+b m} \)


Nickel shows ferromagnetic property at room temperature. If the temperature is increased beyond Curie temperature,
then it will show the
A. anti ferromagnetism
B. no magnetic property
c. diamagnetism
D. paramagnetism


The value of acceleration due to gravity:
A. is same on equator and poles
B. is least on poles
\( \mathrm{c} \). is least on equator
D. increases from pole to equator


The capacity of a condenser A is \( 10 \mu F \) and it is charged using a battery of \( 100 \mathrm{V} \) The battery is disconnected and the
condenser \( A \) is connected to a condenser
B with common potential as \( 40 \mathrm{V} \). The
capacity of B is:
\( A \cdot 8 \mu F \)
B. \( 15 \mu F \)
\( \mathrm{c} \cdot 2 \mu F \)
D. \( 1 \mu F \)


Consider Newton's formula for the
velocity of sound of a gas depends of
1. Gravitational constant
2. Acceleration due to gravity
3. Pressure
4. Density Which of the given are correct? Choose
the answer from the codes given.
A. 3 and 4
B. 4 only
c. 1 and 2
D. 3 only


Terpinen \( -4-o l \) is one of the active
ingredients in tea tree oil
What is the molecular formula of
terpinen \( -4- \) ol?
A. \( C_{7} H_{11} \) O
в. \( C_{10} \) Нв \( O \)
c. \( C_{10} \) Н \( _{17} \) O
D. \( C_{10} H_{18} O \)


Tubulin binds colchicine and which of
the following, at different binding sites?
A. Vincristin
B. Vinblastin
c. Actin
D. All the above


What are the \( \alpha \) and \( \beta \) particles emitted from \( _{90} T h^{228} \rightarrow_{83} B i^{212} \)
A. Four alpha and one beta
B. Three alpha and seven beta
c. Eight alpha and one beta
D. one alpha and four beta


The most stable allotropic form of sulphur is :
A. rhombic
B. monoclinic
c. plastic
D. colloidal


Draw the electron dot stucture of \( F_{2} \)
(fluroine)


Assertion: A salt dissolved in an organic solvent will be a good electrical
conductor.

Reason: Salts will not dissolve
appreciably in an organic solvent.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false


Time period \( T \) of a simple pendulum of length \( l \) is given by \( T=2 \pi \sqrt{\frac{l}{g}} . \) If the length is increased by \( 2 \% \), then an approximate change in the time period
is
A . \( 2 \% \)
B . \( 1 \% \)
c. \( \frac{1}{2} \% \)
D. None of these


For the three events \( A, B \& C \) probability of exactly one of the events \( A \) or \( B \) occurs \( = \) probability of exactly one of the events \( C \) or \( A \) occurs \( =p \& P \)
(all the three events occur
simultaneously) \( =p^{2}, \) where
A \( \cdot \frac{3 p+2 p^{2}}{2} \)
в. \( \frac{p+3 p^{2}}{4} \)
c. \( \frac{p+3 p^{2}}{2} \)
D. \( \frac{3 p+2 p^{2}}{4} \)


The manganese \( (Z=25) \) has the outer
configuration:
\( A \)
45
\( \uparrow \downarrow \)
B.
45
\( \uparrow \downarrow \) \begin{tabular}{|c|c|c|c|c|}
\hline \multicolumn{2}{|c|} {\( 3 d \)} & \multicolumn{2}{|c|} {} \\
\hline\( \uparrow \) & \( \uparrow \) & \( \uparrow \) & \( \uparrow \) & \( \uparrow \) \\
\hline
\end{tabular}
\( c \)
\begin{tabular}{c}
\( 4 s \) \\
\hline\( \uparrow \downarrow \)
\end{tabular} \begin{tabular}{|c|c|c|c|}
\hline \multicolumn{2}{|c|} {\( \uparrow d \)} & \multicolumn{2}{c|} {} \\
\hline\( \uparrow \downarrow \mid \uparrow \downarrow \) & \( \uparrow \) & & \\
\hline
\end{tabular}
\( D \)
45


If the mass of the planet is \( 10 \% \) less than that of the earth and radius of the
planet is \( 20 \% \) greater than that of the earth the weight of 40 kg person on that planet is
A. \( 10 \mathrm{kg} \) wt
B. 25 kg wt
c. \( 40 \mathrm{kg} \) wt
D. \( 60 \mathrm{kg} \) wt


The IUPAC name of the following compound is "
A. Propane 1,2, 3-tricarbonitrile
B. 3-cyanopetane-1, 5-dinitrile
c. Pentane 1, 3, 5 trinitrile
D. All


If the pressure of \( H_{2} \) gas is increased
from 1atm to 100atm keeping \( \boldsymbol{H}^{+} \) concentration constant at \( 1 M, \) the
change in reduction potential of
hydrogen half cell at \( 25^{\circ} C \) will be:
A. \( 0.059 V \)
\( V \)
B . \( 0.59 V \)
c. \( 0.0295 V \)
D. \( 0.118 V \)


The oxidation state of sulphur in the
anions \( S_{2} O_{4}^{2-}, S_{2} O_{4}^{2-} \) and \( S_{2} O_{6}^{2-} \)
follows the order:
\( \mathbf{A} \cdot S_{2} O_{6}^{2-}-<S_{2} O_{4}^{2-}<S O_{3}^{2} \)
B . \( S_{2} O_{4}^{2-}<S O_{3}^{2-}<S_{2} O_{6}^{2} \)
\( \mathrm{c} \cdot S O_{3}^{2-}<S_{2} O_{4}^{2-}<S_{2} O_{6}^{2} \)
D. \( S_{2} O_{4}^{2-}<S_{2} O_{6}^{2-}-<S O_{3}^{2} \)


In the figure, the velocities are in ground frame and the cylinder is
performing pure rolling on the plank,
velocity of point \( ^{\prime} A^{\prime} \) would be :
\( A \cdot 2 V_{C} \)
В \( \cdot 2 V_{C}+V_{P} \)
\( \mathbf{c} \cdot 2 V_{C}-V_{P} \)
D \( \cdot 2\left(V_{C}-V_{P}\right) \)


Which of the following polymer is condensation as well as cross-linked
polymer?
A. Bakelite
B. Nylon-6.6
c. Nylon-2,, Nylon-6
D. Dacron


A conducting loop carrying a current lis placed in a uniform magnetic field pointing into the plane as shown in Fig.
The loop will have tendency to:
A. Contract
B. Expand
c. Move towards positive x-axis
D. Move towards negative x-axis


You are given prisms made of crown glass and flint glass with a wide variety of angles. Suggest a combination of prisms which will
(a) deviate a pencil of white light without much dispersion,
(b) disperse (and displace) a pencil of white light without much deviation.


When an electron is transferred in
hydrogen atom from \( n=4 \) orbit to \( n=5 \) orbit to which spectral series does this belong?


The simplest way to describe the concentration of solution is :
I) mass by mass
Il) mass by volume
III) volume by pressure
A . ।, ॥
в. ॥, III
\( c \cdot \) ।, ॥
D. I, II, III


Find the
(a) maximum frequency
(b) Minimum wavelength of X-rays produced by \( 30 \mathrm{kV} \) electrons.


If \( \tan ^{-1}(x+1)+\tan ^{-1}(x-1)= \)
\( \tan ^{-1}\left(\frac{8}{31}\right), \) then \( x \) is equal
\( A \cdot \frac{1}{2} \)
B. \( -\frac{1}{2} \)
\( c \cdot \frac{1}{4} \)
D.


\( \sec \theta-\tan \theta=6 \)
Then \( \sec \theta+\tan \theta=? \)


ff \( \vec{a}=2 \hat{i}-\hat{j}+2 \hat{k}, \) then the value of
\( (a \times i)^{2}+(a \times j)^{2}+(a \times k)^{2}= \)
\( A \cdot 2 \)
B. 4
\( c .6 \)
D. 18


Sample space for experiment in which a
dice is rolled is
A . 4
B. 8
c. 12
D. None of these


A gas which bleaches substances by reduction process is:
A. moist \( \mathrm{Cl}_{2} \)
в. \( \mathrm{sO}_{2} \)
\( c \cdot O_{3} \)
D. Dry \( \mathrm{Cl}_{2} \)


In a raceme, the flower arrangement is?
A. Basipetal
B. Centripetal
c. centrifugal
D. Acropetal


When the number of organisms at
successive levels are plotted, they assume the shape of pyramid. This is called as pyramid of
A. Energy
B. Number
c. Biomass
D. Both A and C


Determine all ordered pairs that satisfy \( (x-y)^{2}+x^{2}=25, \) where \( x \) and \( y \) are
integers and \( x \geq 0 . \) Find the number of
different values of \( y \) that occur
A . 3
B. 4
\( c .5 \)
D. 6


The value of the integral \( \int_{-1 / 2}^{1 / 2} \cos x \cdot \log \left(\frac{1+x}{1-x}\right) d x \)
A. 0
B.
\( c \cdot-\frac{1}{2} \)
D.


\( f(a, b, c \text { are in } A . P ., \) prove that the following are also in A.P. \( \boldsymbol{a}^{2}(\boldsymbol{b}+\boldsymbol{c}), \boldsymbol{b}^{2}(\boldsymbol{c}+\boldsymbol{a}), \boldsymbol{c}^{2}(\boldsymbol{a}+\boldsymbol{b}) \) provided
\( \sum a b \neq 0 \)


Which one of the following will happen if
all the dust particles of the earth fly away from the earth's atmosphere?
A. Thinning of earth's atmosphere
B. The speed of sound will decrease
c. The earth will become dark
D. All of the above


The harmonic mean of two numbers is
4. The arithmetic mean \( A \) \& the
geometric mean G satisfy the relation
\( \mathbf{2} \boldsymbol{A}+\boldsymbol{G}^{2}=\mathbf{2} 7 . \) Find the largest of those
numbers?
\( \mathbf{A} \cdot \mathbf{6} \)
B. 4
c. 8
D. 5


The temperature of the sun, if pressure
is \( 1.4 \times 10^{9} \) atm, density is \( 1.4 g c m^{-3} \)
and average molecular weight is \( 2, \) will
be
\( \left[\text {Given } \boldsymbol{R}=\mathbf{8 . 4} \boldsymbol{J} \boldsymbol{m o l}^{-1} \boldsymbol{K}^{-1}\right] \)
A . \( 1.2 \times 10^{7} K \)
В. \( 2.4 \times 10^{7} K \)
c. \( 0.4 \times 10^{7} K \)
D. \( 0.2 \times 10^{7} K \)


The wavelength of an electron:
This question has multiple correct options
A. is equal to that of light
B. remains constant with velocity
C . decreases with an increasing velocity
D. increases with an decreasing velocity


In a ripple tank when one pulse is sent every tenth of a second, the distance between consecutive pulses is \( 30 m m \)
In the same depth of water pulses are produced at half second intervals. What
is the new distance between
consecutive pulses?
A. \( 0.67 m m \)
B. \( 6.0 m m \)
\( \mathrm{c} .150 \mathrm{mm} \)
D. \( 600 \mathrm{mm} \)


Veer spends \( 15 \% \) of this monthly income on house rent and \( 60 \% \) of the
rest on household expenditure. If, he saves \( R s .2210, \) what is his monthly
income?


Represent the following data by histogram and hence compute mode.
Price o
22
24
sugar 18
20
per kg
\[
20
\]
22
24
26
(in Rs.)
Number of f
weeks 4
8
22
A. 21.2 Rs.
B. 22.2 Rs.
c. 23.2 Rs.
D. 24.2 Rs.


What is a hydraulic jack?
A. Device uses force to lift heavy objects
B. Device uses force for pumping water
C. Device uses force to pump air
D. Device use to lower the harder objects


The angle at which the ray is incident on
the second mirror is \( _{--}-? \)
A \( \cdot 10^{\circ} \)
B \( .20^{\circ} \)
\( c \cdot 30 \)
D \( .40^{\circ} \)


Assertion
Time taken for the completion of mitotic phase is \( 5-10 \% \) of the total cell cycle.
Reason
It is the shorter than the interphase.
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 an example of
gaseous solution?
A. Camphor in nitrogen gas
B. Solution of hydrogen in palladium
c. chloroform mixed with nitrogen gas
D. Both (A) and (C)


Which of the following defines the role of producers in any grazing food chain?
A. Feed the herbivores
B. Feed the carnivores
c. clean the atmosphere
D. Capture solar energy


Copper matte contains
\( \mathbf{A} \cdot C u_{2} O, C u_{2} S \)
\( \mathbf{B} \cdot C u_{2} O, F e S \)
\( \mathbf{c} \cdot C u_{2} S, F e S \)
D. \( C u_{2} S, F e O \)


Two equal resistances are connected in the gaps of a meter bridge. If the resistance in the left gap is increased by \( 10 \%, \) the balancing point shift :
A. \( 10 \% \) to right
B. \( 10 \% \) to left
c. \( 9.6 \% \) to right
D. \( 4.8 \% \) to right


What are the compounds represented
by formula \( C_{2} H_{4} C l_{2} ? \)


Match molecules/ions (in Column I)
with their shapes (in Column II).


A pair of dice is thrown 5 times. If getting a doublet is considered as a success, then find the mean and
variance of successes.


Assertion
Many great rivers flow towards the equator. The sediments that they carry
increase the time of rotation of the
earth about its own axis.
Reason
The angular momentum of the earth about its rotation axis is conserved.
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 polynomial \( 4 x^{2}+2 x-2 \) is a
A. Linear polynomial
B. Quadratic polynomial
c. Cubic polynomial
D. constant polynomial


A spherical ball is dropped in a long column of viscous liquid. Which of the
following graphs represent the variation of
i) The gravitational force with time
ii) The viscous force with time
iii) The net force acting on the ball with time
A. \( Q, R, P \)
B. R, Q, P
c. \( P, Q, R \)
D. R, P, Q


Assertion
\( O-O \) bond length in \( H_{2} O_{2} \) is shorter
than that of \( \boldsymbol{O}_{2} \boldsymbol{F}_{2} \)
Reason
\( H_{2} O_{2} \) is a covalent compound.
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


Arrange the following compounds in increasing order of boiling points.
: 3-methyl pentane II: 3chloropentane
III: 3-bromopentane IV: 3,3dichloropentane
A. \( I<I I I<I I<I V \)
в. \( I<I V<I I I<I I \)
c. \( I<I I<I I I<I V \)


Suppose that \( 5 \% \) of men and \( 0.25 \% \) of women have grey hair. A grey haired person is selected at random. What is
the probability of this person being male ? Assume that there are equal number of males and females.


A current flowing in a wire always give rise to a magnetic field.


In the context of accuracy to
measurement and significant figures in expressing results of experiment, which of the following is/are correct?
(1) Out of the measurements \( 50.14 \mathrm{cm} \) and 0.00025 ampere, the first one has greater accuracy.
(2) If one travels \( 478 \mathrm{km} \) by rail and 397
m. by road, the total distance traveled is
\( 478 \mathrm{km} \)
A. Only (1) is correct
B. only (2) is correct
c. Both are correct
D. None of these is correct


Find median:
Wages per \( \mathbf{3 8} \quad \mathbf{4 5} \quad \mathbf{4 8} \quad \mathbf{5 5} \) day
is Cumulative
igure \( \quad 14 \quad 22 \quad 29 \quad 39 \) figure


Equal weights \( C_{2} H_{6} \) and hydrogen are
mixed in an empty container at \( 0^{\circ} \mathrm{C} \)
The fraction of total pressure exerted by hydrogen is-
A . 1: 2
B. 1: 1
c. 1: 16
D. 15: 16


Vapor pressure of pure water at \( 25^{\circ} \mathrm{C} \) is
\( 20.0 \mathrm{mm} \) of \( H g \% . \) And the lowering of
vapor pressure of a sugar solution is
\( 0.070 \mathrm{mm} \) of \( H g . \) What will be the mole
fraction of water?
A . 0.9965
B. 0.0035
c. 0.0024
D. 0.7785


If \( A=[123] \) and \( B=\left[\begin{array}{l}1 \\ 2 \\ 3\end{array}\right], \) then find
\( (A B)^{\prime} \)


Solve the inequalities for real \( x \)
\( 37-(3 x+5) \geq 9 x-8(x-3) \)


Given the reaction between 2 gases
represented by \( A_{2} \) and \( B_{2} \) to give the
compound \( \boldsymbol{A B}_{(\boldsymbol{g})} \)
\( \boldsymbol{A}_{2(g)}+\boldsymbol{B}_{2(g)} \rightleftharpoons \mathbf{2} \boldsymbol{A} \boldsymbol{B}_{(g)} \)
At equilibrium, the concentration
of \( \boldsymbol{A}_{2}=\mathbf{3} . \mathbf{0} \times \mathbf{1 0}^{-\mathbf{3}} \boldsymbol{M} \)
of \( \boldsymbol{B}_{2}=\boldsymbol{4} . \boldsymbol{2} \times \mathbf{1 0}^{-\mathbf{3}} \boldsymbol{M} \)
of \( \boldsymbol{A B}=\mathbf{2 . 8} \times \mathbf{1 0}^{-\mathbf{3}} \boldsymbol{M} \)
If the reaction takes place in a sealed
vessel at \( 527^{\circ} C, \) then the value of \( K_{c} \)
will be:
A . 1.9
B. 0.62
c. 4.5
D. 2.0


Which of the following is a vector quantity
A. Distance
B. Current density
c. Power
D. All


Which of these best describes the
difference between weather and
climate?
A. Weather includes short term changes in the atmosphere while climate includes average temperature, precipitation, sunshine and wind velocity
B. Weather includes temperature and precipitation while climate only includes temperature
C. Weather changes very little while climate changes drastically
D. Weather depends on a particular location while climate is described worldwide
E. Weather includes average temperature and wind velocity while climate includes only precipitation.


Find Stationary points of \( f(x)=\sin x \)
where \( 0<x<2 \pi \)


Which of the one will form aldehyde on reaction with acetylene?
A. Chlorine
B. Hydrogen
c. sulphuric acid
D. Ozone


A disc is rolling without slipping with
angular velocity \( \omega . P \) and \( Q \) are two
points equidistant from the centre \( C \)
The order of magnitude of velocity is:
\( \mathbf{A} \cdot V_{Q}>V_{C}>V_{P} \)
в. \( V_{P}>V_{C}>V_{Q} \)
\( \mathbf{c} \cdot V_{Q}=V_{P}, V_{C}=V_{P} / 2 \)
\( \mathbf{D} \cdot V_{P}<V_{C}>V_{Q} \)


Which of the following is an intensive
property?
A. mass
B. volume
c. length
D. pressure


The tip of seconds' hand of a watch
exhibits uniform circular motion on the
circular dial of the watch
State whether given statement is True/False?
A. True
B. False


Balance the following equation by oxidation number method
¡) \( K_{2} C r_{2} O_{7}+K I+H_{2} S O_{4} \rightarrow \)
\( \boldsymbol{K}_{2} \boldsymbol{S} \boldsymbol{O}_{4}+\boldsymbol{C r}_{2}\left(\boldsymbol{S O}_{4}\right)_{3}+\boldsymbol{I}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \)
ii) \( K M n O_{4}+N a_{2} S O_{3} \rightarrow M n O_{2}+ \)
\( N a_{2} S O_{4}+K O H \)
iii) \( \boldsymbol{C u}+\boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \rightarrow \boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{2}+ \)
\( N O_{2}+H_{2} O \)
iv) \( K M n O_{4}+H_{2} C_{2} O_{4}+H_{2} S O_{4} \rightarrow \)
\( \boldsymbol{K}_{2} \boldsymbol{S} \boldsymbol{O}_{4}+\boldsymbol{M} \boldsymbol{n} \boldsymbol{S} \boldsymbol{O}_{4}+\boldsymbol{C} \boldsymbol{O}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \)


Refer to the given dichotomous key and select the correct option regarding it.
I. \( (a) \) It is a seedless plant - Go to II
(b) It is a plant having seeds - Go to
\|\|
Il. (a) True stem, leaves and roots are absent - \( \mathbb{P} \)
(b) True stem, leaves and roots are present \( -[\boldsymbol{Q} \)
III. (a) Fruit is not formed and seeds are naked \( -\overline{\boldsymbol{R}} \)
(b) Fruits are formed and seeds are protected \( -\overline{\boldsymbol{S}} \)
A. P- Pteridium, Q - Ephedra, R - Lycopodium, S- Acer
B. P- selaginella, Q- Funaria, R - Cycas, S - Fern
c. P- - Marchantia, Q - Pteridium, R - Oryza, S - Thuja
D. P- -Riccia, Q - Azolla, R - Pinus, S - Brassica


When dry \( C l_{2} \) gas is passed over dry
slaked lime, the product obtained is having the formula:
A. \( C a O \)
B. \( C a(O C l)_{2} \)
\( \mathrm{c} \cdot \mathrm{CaOCl} \)
D. \( C a C l_{2} O_{2} \)


coils which lie in a uniform magnetic
field. Plane of the coils is perpendicular
to the magnetic field as shown in figure.
The coil is connected to a current
integrator which measures the total
charge passing through it. The coil is
turned through \( 180^{\circ} \) about the
diameter. The charge passing through the coil is
\( ^{\mathbf{A}} \cdot \frac{N B A}{R} \)
B. \( \frac{\sqrt{3} N B A}{2 R} \)
c. \( \frac{N B A}{\sqrt{2} R} \)
D. \( \frac{2 N B A}{R} \)


Fill up the blank with suitable words
Unit of heat capacity is


What is the structural difference
between glycogen and starch?


Solve:
\( 3 x^{2}-4>x(2 x-3) \)


A train of length \( 100 m \) is moving in a
hilly region. At what speed must it approach a tunnel of length \( 80 m \) so that
a person at rest with respect to the tunnel will see that the entire train is in
the tunnel at one time?
A. \( 1.25 c \)
B. \( 0.8 c \)
c. \( 0.64 c \)
D. \( 0.6 c \)
E \( .0 .36 c \)


Types of histograms includes
A. deviation bar charts
B. paired bar charts
C . grouped charts
D. all of the above


Differentiate from first principles.
(i) \( 3 x \)


A non-conducting sphere has a total charge Q uniformly distributed throughout its volume. the centre of the sphere is at origin and its radius is \( \mathrm{R} \)
let \( U_{1} \) be the electrostatic potential energy in the region inside the sphere and \( U_{2} \) be the electrostatic potential energy in another imaginary spherical shell, having inner radius \( R \) and outer radius infinity, centred at origin. select the correct alternative(s)
\( ^{\mathrm{A}} \cdot U_{1}=\frac{Q^{2}}{8 \pi \varepsilon_{0} R} \)
в. \( U_{2}=\frac{Q^{2}}{8 \pi \varepsilon_{0} R} \)
c. \( U_{1}+U_{2}=\frac{3}{5} \times \frac{Q^{2}}{4 \pi \varepsilon_{0} R} \)
D. \( U_{1}=\frac{3 Q^{2}}{20 \pi \varepsilon_{0} R} \)


A body moves in a straight line along
\( Y- \) axis. Its distance \( y \) (in metre) from
the origin is given by \( y=8 t-3 t^{2}(t \) in
seconds. The average speed in the time interval from \( t=0 \) second to \( t=2 \)
second is
\( \mathbf{A} \cdot 1 \mathbf{m} \mathbf{s}^{-1} \)
в. zero
\( \mathrm{c} \cdot 2 \mathrm{ms}^{-1} \)
D. \( \frac{22}{3} \mathrm{ms}^{-1} \)


Find three numbers which form a
geometric progression, if their product is 64 and the arithmetic mean is \( \frac{14}{3} \)


12 pairs of cranial nerves are present in
A. Reptilia
B. Birds only
c. Mammals only
D. All of the above


Sodium sulphate dissolves in water
with evoluation of heat. Consider a
saturated solution of sodium sulphate. If the temperature is raised, then according to Le-chatelier principal
A. More solid will dissolve
B. Some solid will precipitate out from the solution
c. The solution will become supersaturated
D. Solution concentration will remain unchanged


Select correct statement(s).
A. Helium has the lowest melting point and boiling point
B. Helium can diffuse through rubber, PVC and even glass
C . \( A r, K r \) and \( X e \) form clathrate
D. All of the above


\( y=\frac{2(x-\sin x)^{\frac{3}{2}}}{\sqrt{x}}, \) find \( \frac{d y}{d x} \)
\( \mathbf{A} \cdot \frac{d y}{d x}=y\left\{\frac{3}{2} \cdot \frac{1-\cos x}{x-\sin x}-\frac{1}{2 x}\right\} \)
B. \( \frac{d y}{d x}=y\left\{\frac{3}{4} \cdot \frac{1-\sin x}{x-\cos x}+\frac{1}{2 x}\right\} \)
\( \mathbf{c} \cdot \frac{d y}{d x}=y\left\{\frac{3}{4} \cdot \frac{1-\cos x}{x-\sin x}-\frac{1}{2 x}\right\} \)
D. \( \frac{d y}{d x}=y\left\{\frac{3}{2} \cdot \frac{1-\sin x}{x-\cos x}-\frac{1}{2 x}\right\} \)


reactions.
The products \( (A) \) and \( (B)(B) \) are:
\( A \)
\( B \)
\( \mathbf{N O H} \) and
\( c \)
NOH and
D.
\( \mathbf{N O H} \) and


In fluorescence experiment, which of the light is used?
A . Red
B. Visible
c. uv
D. Infrared


An equiconvex (biconvex) lens has
focus length \( f . \) It is cut into three parts
as shown in the figure. What is the focal length of the cut part I?
A . \( 3 f \)
B. \( \frac{f}{3} \)
\( c \cdot \frac{f}{2} \)
D. \( 2 f \)


If \( \boldsymbol{A}(\cos \boldsymbol{\alpha}, \sin \boldsymbol{\alpha}, \boldsymbol{0}), \boldsymbol{B}(\cos \boldsymbol{\beta}, \sin \beta, \boldsymbol{0}) \)
\( C(\cos \gamma, \sin \gamma, 0) \) are vertices of \( \Delta A B C \)
and let
\[
\begin{array}{l}
\cos \alpha+\cos \beta+\cos \gamma=3 a, \sin \alpha+ \\
\sin \beta+\sin \gamma=3 b, \text { then correct }
\end{array}
\]
matching of the following is:
List:1
\begin{tabular}{ll}
A. Circumcentre & \( 1 .(3 a, 3 b, 0) \) \\
\cline { 0 }
\end{tabular}
B. Centroid
\[
2 .(0,0,0)
\]
c. Ortho centre
\[
3 .(a, b, 0)
\]
A . 432
в. 231
c. 123
D. 234


An experiment can result in only 3 mutually exclusive events \( A, B \) and \( C . \) If
\( \boldsymbol{P}(\boldsymbol{A})=2 \boldsymbol{P}(\boldsymbol{B})=\boldsymbol{3} \boldsymbol{P}(\boldsymbol{C}), \) then \( \boldsymbol{P}(\boldsymbol{A}) \)
equals
A \( \cdot \frac{5}{11} \)
в. \( \frac{9}{11} \)
\( c \cdot \frac{8}{11} \)
D. \( \frac{6}{11} \)


Atomic number of nitrogen is \( 7 . \) The number of protons in Nitrogen atom is equal to
\( A \cdot 14 \)
B. 7
\( c \cdot 2 \)
D. 15


The cost of paving the floor at the rate of
Rs. 18 per \( m^{2} \)
A . Rs. 10239
3. Rs 8839
\( c . \) Rs. 7125
D. Rs. 5040


Parveen wanted to make a temporary shelter for her car, by making box-like structure with tarpoulin that covers all
the four sides and the top of the car (With the front face as a flap which can be rolled up). Assuming that the stitching margins are very small, and therefore negligible, how much tarpaulin would be required to make the shelter of height \( 2.5 m \), with base
dimensions \( 4 m \times 3 m ? \)


In shown diagram, if emf of battery is doubled and resistor kept constant then
what is the new Power dissipated at
resistor?
A \( \cdot \frac{P}{4} \)
в. \( \frac{P}{2} \)
\( c \)
D. 2P
E. 49


In which quadrilateral all sides and
angles are equal?
A. rectangle
B. parallelogram
c. square
D. kite


If \( (x, y) \) is equidistant from \( P(-3,2) \)
and \( Q(2,-3), \) then
A \( .2 x=y \)
в. \( x=-y \)
c. \( x=2 y \)
D. \( x=y \)


Ethyne, on reaction with chlorine
consequently, forms:
A. dichloro methane
B. trichloro ethene
C. dichloro ethane
D. tetrachloro ethane


Consider a rectangular plate of
dimensions \( a \times b \). If the plate is
considered to be made up of four rectangles of dimensions \( \frac{a}{2} \times \frac{b}{2} \) and we
now remove one out of the four
rectangles, find the position where the
centre of mass of the remaining
system will be:


The number of solutions of the equation
\( \left[\sin ^{-1} x\right]=-[x] \) is (where \( \left[^{\star}\right] \) denotes
the greatest integer function)
A .
в.
\( c \cdot 2 \)
D. infinitely many


Percolation tank is a sustainable
development for
A. Soil conservation
B. Solid waste management
c. water conservation
D. None of the above


Which of the following is easily oxidized?
A. \( N i S O_{4} \)
в. \( F e S O_{4} \)
\( \mathrm{c} \cdot \mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3} \)
D. \( S c C l_{3} \)


One advantage of sexual reproduction is that it allows for genetic sameness.
A. True
B. False


Five students, Ankit, Nitin, Deepika, Gunjan and Pooja were given test tubes having solutions with \( \mathrm{pH} 1.2,13.5,10.0 \) 7.4 and 2.2 respectively. The correct
order of decreasing \( \boldsymbol{O} \boldsymbol{H}^{-} \) ion concentration in these solutions is:
A. Ankit>Pooja > Gunjan > Deepika > Nitin
B. Nitin > Gunjan>Ankit>Pooja > Deepika
c. Deepika > Gunjan > Pooja > Nitin > Ankit
D. Nitin > Deepika > Gunjan > Pooja > Ankit


If a point is moving in a line so that its velocity at time \( t \) is proportional to the square of the distance covered, then its
acceleration at time t varies as
A. cube of the distance
B. the distance
c. square of the distance
D. none of these


Eventhough a cinema hall is a place prone to fire hazards, the interiors are mostly made of wood or wood based panels.Why is this so?
A. wood does not catch fire easily
B. Wood is opaque
c. wood can absorb sound
D. Wood is very commonly available


If 2.0 mole each of \( A \) and \( B \) were
allowed to come to equilibrium at \( 300 \mathrm{K} \) for the reaction \( \boldsymbol{A}+\boldsymbol{B} \rightarrow \boldsymbol{C}+\boldsymbol{D} \)
\( \Delta G^{o}=460 \) cal. The equilibrium concentration ratio of \( C \) to \( A \) will be:
\( \mathbf{A} \cdot \mathbf{1} \)
B. \( \frac{1}{2} \)
c. 0.68
D. 0.46


\( \lim _{n \rightarrow \infty} \frac{1^{P}+2^{P}+3^{P}+\ldots .+n^{P}}{n^{P+1}} \) equals-


A moving block having mass \( \mathrm{m} \), collides with another stationary block having mass \( 4 \mathrm{m} \). The lighter block comes to rest after collision. When the initial
velocity of the lighter block is \( v \), then the value of coefficient of restitution (e) will
be:
A . 0.8
B. 0.5
\( c .0 .4 \)
D. 0.25


The number of free electrons per \( 10 \mathrm{mm} \)
ordinary copper wire is about \( 2 \times 10^{21} \)
The average drift speed of the electrons is \( 0.25 \mathrm{mm} \) current flowing is:
A. \( 0.8 \mathrm{A} \)
B. 8 A
\( c .80 \mathrm{A} \)
D. 5 A


A block is kept on a horizontal table.The table is undergoing simple harmonic motion of frequency \( 3 H z \) in a
horizontal plane.The coefficient of static friction between block and the table
surface is \( 0.72 . \) Find the maximum
amplitude (in \( \mathrm{cm} \) ) of the table at which the block does not slip on the surface. ( Take \( \left.g=10 m / s^{2} \text { and } \pi^{2}=10\right) \)


On a plane are two points \( A \) and \( B \) at a
distance of 5 units apart. The number of straight lines in this plane which are at distance of 2 units from \( A \) and 3 units
from \( \mathrm{B} \) are:
A . 1
B. 2
\( c .3 \)
D. 4


The angle between an incident ray and
the mirror is \( 60^{\circ} . \) Then the total angle turned by the ray of light is:
A \( .60^{\circ} \)
B . \( 120^{\circ} \)
\( c \cdot 30^{\circ} \)
D. \( 90^{\circ} \)


If \( \overline{A B}=2 \vec{i}-3 \vec{j}+\vec{k}, \overline{C B}=\vec{i}+\vec{j}+\vec{k} \)
\( C D=4 \vec{i}-7 \vec{j} \) then \( \overline{A D}= \)
A \( .5 \vec{i}+11 \vec{j}-\vec{k} \)
B . \( 5 \vec{i}-11 \vec{j} \)
c. \( 5 \vec{i}+11 \vec{j} \)
D. \( -5 \vec{i}+11 \vec{j} \)


Among the following groups which represents the collection of isoelectronic species?
A \( \cdot N O^{+}, C_{2}^{2-}, O_{2}^{-}, C O \)
в. \( N_{2}, C_{2}^{2-}, C O_{2}^{-}, N O \)
c. \( C O, N O^{+}, C N^{-}, C_{2}^{2} \)
D. \( N O, C N^{-}, N_{2}, O_{2}^{-} \)


A bag contains four tickets numbered
\( 00,01,10,11 . \) Four tickets are chosen at
random with replacement, the probability that the sum of the numbers on the tickets is \( 23, \) is
A \( .3 / 32 \)
в. \( 1 / 64 \)
c. \( 5 / 256 \)
D. \( 7 / 256 \)


Metal spheres, each of radius \( 2 \mathrm{cm}, \) are packed into a rectangular box of internal dimensions \( 16 \mathrm{cm} \times 8 \mathrm{cm} \times 8 \mathrm{cm} \)
When 16 spheres are packed the box is filled with preservative liquid. Find the
volume of this liquid (in \( c m^{3} \) ). Give your
answer to the nearest integer. [Use \( \boldsymbol{\pi}= \)
3.14]


A lightning conductor:
A . conducts light
B. stops lightning
C. protect building from the damaging effects of lightning
D. none of these


The vector \( \vec{c} \) is perpendicular to the vectors \( \overrightarrow{\boldsymbol{a}}=(\mathbf{2},-\mathbf{3}, \mathbf{1}), \overrightarrow{\boldsymbol{b}}=(\mathbf{1},-\mathbf{2}, \mathbf{3}) \)
and satisfies the condition \( \vec{c} .(\hat{i}+2 \hat{j}- \) \( \mathbf{7} \hat{k})=10 . \) Then the vector \( \hat{c}= \)
\( A \cdot(7,5,1) \)
B. (-7,-5,-1)
\( c \cdot(1,1,-1) \)
\( c \)
\( D . \) none


Which of the following is associated with reproduction?
A. Parthenogenesis
B. Fertilization
c. stos
D. All of the above


Lanthanide for which \( +\| \) and \( +\| I \)
oxidation states are common is:
A . \( L a \)
B. \( N d \)
\( c . C e \)
D. \( E u \)


Which of the following reactions will not
have fractional order for \( \boldsymbol{A}_{2} \) or \( \boldsymbol{B}_{2} ? \)
\( \mathbf{A} \cdot A_{2} \rightleftharpoons A+A(\text { fast }) \)
\[
\begin{array}{l}
A+B_{2} \rightleftharpoons A B+B \text { (slow) } \\
A+B \rightleftharpoons A B \text { (fast) }
\end{array}
\]
B \( \cdot A_{2} \rightleftharpoons C \) (slow)
\[
C+B_{2} \rightleftharpoons D \text { (fast) }
\]
\[
D+A_{2} \rightleftharpoons \text { Product }
\]
C. \( B_{2} \rightleftharpoons B+B \) (fast)
\[
\begin{array}{l}
A_{2}+B \rightleftharpoons A B+A \text { (slow) } \\
A B \longrightarrow \text { Products (fast) }
\end{array}
\]
D. None of the above


If \( 2 A+B=\left[\begin{array}{cc}3 & -1 \\ 2 & 4\end{array}\right] \) and \( B= \)
\( \left[\begin{array}{cc}-1 & -5 \\ 0 & 2\end{array}\right], \) then find \( A \)


\( \boldsymbol{f}(\boldsymbol{x})\left\{\begin{array}{l}=\mathbf{2} \boldsymbol{x}^{2}+\frac{2}{x^{2}} \text { for }-\mathbf{2} \leq \boldsymbol{x}<\mathbf{0} \boldsymbol{a} \\ =\mathbf{1} \quad \text { for } \boldsymbol{x}=\mathbf{0}\end{array}\right. \)
Determine the greatest and least values. What is the minimum value of
the function?
A. 0
B. 1
\( c \cdot 4 \)
\( D \)


In order to increase the capacity of
parallel plate condenser one should introduce between the plates, a sheet of
A . mica
B. tin
c. copper
D. stainless steel


A plant having vascular supply, producing spores but lacking seed is a
A. Bryophyte
B. Pteridophyte
c. Gymnosperm
D. Angiosperm


Q Type your question
below. All point charges are of the same
magnitude.

Which table gives the best description
of the electric field at point \( P \) and the
electric potential at point P?
A. Electric Field at \( \mathrm{P} \) - Electric Potential at \( \mathrm{P} \), zero - zero
B. Electric Field at \( P \) - Electric Potential at \( P \), zero -
negative
C. Electric Field at \( P \) - Electric Potential at \( P \), downward
downward
D. Electric Field at \( P \) - Electric Potential at \( P \), downward
negative
E. Electric Field at \( \mathrm{P} \) - Electric Potential at \( \mathrm{P} \), negative -
zero


There are two force vectors, one of \( 5 N \)
and other of \( 12 N . \) At what angle should
the two vectors be added to get the
resultant vector of \( 17 N, 7 N, \) and \( 13 N \)
respectively?


An enantiomerically pure acid is treated with a racemic mixture of an
alcohol having one chiral carbon. The ester formed will be:
A. optically active mixture
B. pure enantiomer
c. meso compound
D. racemic mixture


Fill in the blanks:
In our eyes an image of objects we wish to view is made at the
A . retina
B. pupil
\( c \). iriss
D. cornea


Although sexual reproduction is a long, drawn, energy-intensive complex form
of reproduction, many groups of organisms in kingdom Animalia and Plantae prefer this mode of
reproduction. Give at least 3 reasons for
this.


The light ray which strikes any polished surface at some angle is called:
A . reflected ray
B. incident ray
c. normal ray
D. none of these


Two point charges \( -q \) and \( +q \) are located at points \( (0,0,-a) \) and \( (0,0, a) \) respectively. The electric potential at point \( (0,0, z) \) is :
A \( \cdot \frac{q a}{4 \pi \varepsilon_{0} z^{2}} \)
в. \( \frac{q}{4 \pi \varepsilon_{0} a} \)
c. \( \frac{2 q a}{4 \pi \varepsilon_{0}\left(z^{2}-a^{2}\right)} \)
D. \( \frac{2 q a}{4 \pi \varepsilon_{0}\left(z^{2}+a^{2}\right)} \)


The minimum value of \( 4^{x}+4^{1-x}, x \epsilon R \)
is
\( A \cdot 2 \)
B. 4
\( c \)
D. none of these


When \( 229 J \) of energy is supplied as
heat as constant pressure to 3 mol
\( \boldsymbol{A} \boldsymbol{r}(\boldsymbol{g}), \) the temperature of the sample is increased by \( 2.55 K . \) Calculate the
molar heat capacity at constant volume
A \( \cdot 40 J K^{-1} m o l^{-1} \)
B. \( 30 J K^{-1} \) mol \( ^{-1} \)
c. \( 21.7 J K^{-1} \) mol \( ^{-1} \)
D. \( 81.7 J K^{-1} \mathrm{mol}^{-1} \)


Why does an athlete take run-up before doing longjump?
A. To cheer the crowd
B. She/he likes running
c. To gain momentum
D. To reduce momentum


Which of the following are use of
microwaves?
A. They are used for satellite communication.
B. They are used for analysis of atomic and molecular structure.
C. They are used cooking in microwave ovens.
D. All of the above.


The intensity of the light coming from one of the slits in YDSE is double the
intensity from the other slit. Find the ratio of the maximum intensity to minimum intensity in the interference fringe pattern observed
\( A \cdot 32 \)
B. 34
\( c .36 \)
D. 38


Find the number of ways of selecting 9
balls from 6 red balls, 5 white balls \( \& 5 \)
blue balls. If each selection consists of 3
balls of each color.


An \( A C \) voltage source of variable
angular frequency \( \omega \) and fixed
amplitude \( V_{0} \) is connected in series
with a capacitance \( C \) and an electric bulb of resistance \( \boldsymbol{R} \) (inductance zero)
When \( \omega \) is increased
A. the bulb glows dimmer
B. the bulb glows brighter
C. total impedance of the circuit is unchanged
D. total impedance of the circuit increases


Find the values of \( a \) and \( b \), if the slope of
the tangent to the curve \( \boldsymbol{x} \boldsymbol{y}+\boldsymbol{a} \boldsymbol{x}+ \)
\( b y=2 \) at (1,1) is 2


pH of a \( 0.1 \mathrm{M} \) monobasic acid is found to
be \( 2 . \) Hence, its osmotic pressure at a given temperature T K is :
\( \mathbf{A} \cdot 0.1 \mathrm{RT} \)
B. 0.11RT
c. \( 1.1 \mathrm{RT} \)
D. 0.01RT


The fine structure of hydrogen spectrum can be explained by
A. the presence of neutrons in the nucleus.
B. the finite size of nucleus
c. the orbital angular momentum of electrons.
D. the spin angular momentum of electrons


If \( z=x+i y \) is a complex number such
that \( |z|=\operatorname{Re}(i z)+1, \) then the locus of
\( z \) is
A \( \cdot x^{2}+y^{2}=1 \)
в. \( x^{2}=2 y-1 \)
C \( \cdot y^{2}=2 x-1 \)
D・ \( y^{2}=1-2 x \)
E . \( x^{2}=1-2 y \)


Land mass occupied by forest is about
A . \( 11 \% \)
B. 22\%
c. 31\%
D. 60\%


Identify the wrong statement.
A. Current loop is equivalent to a magnetic dipole
B. Magnetic dipole moment of a planar loop of area \( A \) carrying current \( l \) is \( l^{2} A \)
C. Particles like proton, electron carry an intrinsic magnetic moment
D. The current loop (magnetic moment \( m \) ) placed in a uniform magnetic field, \( B \) experiences a torque \( \tau= \) \( m \times B \)
E. Ampere's circuit law is not independent of Biot Savart's law


\( \mathrm{X}^{\prime} \) is an organic substance obtained from the decomposition of plant or animals wastes which provides lots of humus to the soil. Identify the incorrect statements regarding decomposition.
A. It makes the soil porous
B. It reduces the water holding capacity of the soil
c. it increase the number of friendly microbes
D. It improves the texture of the soil


Which of the following statements
is/are correct?
This question has multiple correct options
A. Extractive metallurgy of iron involves reduction by carbon monoxide and carbon.
B. Extraction of zinc from ore sphalerite involves the roasting and carbon reduction.
C. Tin contain magnetic impurity of \( \mathrm{Fe} \mathrm{Cr} \mathrm{O}_{4} \)
D. Cuprite and argentite are oxide ores.
E. Bauxite is concentrated by leaching process.
F. Electrometallurgy is preferred method for extraction of highly reactive metals.


solve:
\( (i) 6 \frac{1}{4} \div 1 \frac{1}{3} \)
(ii) \( 12 \div 1 \frac{3}{4} \)
\( (\mathrm{iii}) \frac{1}{3} \times 2 \frac{1}{3} \)


Which of the following reactions is possible?
\( A \)
\[
\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{ONa}+\mathrm{PhBr} \rightarrow \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{O}-\mathrm{Ph}
\]
в.
\[
^{\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}-\mathrm{ONa}+\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{Br} \rightarrow}_{\left(\mathrm{CH}_{3}\right)_{3}} \overrightarrow{\mathrm{C}-\mathrm{O}-\mathrm{CH}_{2}-\mathrm{CH}_{3}}
\]
c.
\[
\begin{aligned}
\mathrm{CH}_{3} \mathrm{CH}=\mathrm{CH}-\mathrm{ONa}+\mathrm{CH}_{3} \mathrm{CH}=\mathrm{CH}-\mathrm{Br} \rightarrow \\
\mathrm{CH}_{3} \mathrm{CH}=\mathrm{CH}-\mathrm{O}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}_{3}
\end{aligned}
\]
D.
\[
\begin{array}{l}
\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}-\mathrm{CH}_{2}-\mathrm{ONa}+\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}-\mathrm{CH}_{2} \mathrm{Br} \\
\quad \rightarrow\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}-\mathrm{CH}_{2}-\mathrm{O}-\mathrm{CH}_{2}-\mathrm{C}\left(\mathrm{CH}_{3}\right)_{3}
\end{array}
\]


Write the relation between focal length and radius of curvature of a spherical
mirror?


Below is the distribution of money
collected
by students for flood relief.
Money No. of student
\( 0-10 \)
\( 10-20 \)
\( 20-30 \)
\( 30-40 \)
\( 40-50 \)
find mean of money collected by a student using "Direct Method"


Identity the compound in which
phosphorus exists in the oxidation
state of +1
A. Phosphonic acid \( \left(H_{3} P O_{3}\right) \)
B. Phosphinic acid \( \left(H_{3} P O_{2}\right) \)
C. Pyrophosphorus acid \( \left(H_{4} P_{2} O_{5}\right) \)
D. Orthophosphoric acid \( \left(H_{3} P O_{4}\right) \)


Two nuclei have mass numbers in the
ratio \( 1: 64 . \) What is the ratio of their
nuclear radii ?


The law of multiple proportion was discovered by:
A. John Dalton
B. Richter
c. Joseph Proust
D. A. Lavoisier


If \( \boldsymbol{A}=\left[\begin{array}{cc}\cos \boldsymbol{\alpha} & -\sin \boldsymbol{\alpha} \\ \sin \boldsymbol{\alpha} & \cos \boldsymbol{\alpha}\end{array}\right], \) then \( \boldsymbol{A}+ \)
\( A^{\prime}=I, \) if the value of \( \alpha \) is
A \( \cdot \frac{\pi}{6} \)
в.
\( c \)
D. \( \frac{3 \pi}{2} \)


\( R s .3500 \) is given at \( 7 \% \) p.a rate of interest. Find the interest which will be
received at the end of two years.


For the following arithmetic progression write the first term and common
difference
(i) \( \frac{1}{3}, \frac{5}{3}, \frac{9}{3}, \frac{13}{3}, \dots \)
(ii) \( 0.6,1.7,2.8,3.9, \dots \)


A vessel of volume 4 litres contains a
mixture of 8 gms of \( \mathrm{O}_{2}, 14 \) gms of \( \mathrm{N}_{2} \) and
22 gms of \( \mathrm{CO}_{2} \) at \( 27^{0} \mathrm{C} \). The pressure
exerted by the mixture is
A. 10 atmosphere
B. \( 5 \times 10^{6} \mathrm{N} / \mathrm{m}^{2} \)
C \( .7 .79 \times 10^{5} \mathrm{N} / \mathrm{m}^{2} \)
D. \( 6 \times 10^{5} 5 \mathrm{N} / \mathrm{m}^{2} \)


Which one of the following is correct for blooming of short day plants?
A. The long dark period is not critical.
B. It is affected by interruption of long dark period by brief exposure of light
C. It is not affected by interruption of long dark period by brief exposure of light
D. It is affected if the continuous light period is interrupted


A ball of mass \( \frac{1}{10} \mathrm{kg} \) is thrown against a wall. It strikes the wall normally with a velocity of \( 30 m s^{-1} \) and rebounds from
there with a velocity \( 20 m s^{-1} \). The
impulse of the force exerted by the ball on the wall is
A. 0.5Ns
B. 50Ns
\( c \cdot 5 N s \)
D. 1Ns


As we go up the layer of the atmosphere,
the pressure
A. increases
B. decreases
c. remains same
D. none of these


If \( \boldsymbol{A}=\{\mathbf{1}, \mathbf{2}, \mathbf{3}\}, \boldsymbol{B}=\{\mathbf{3}, \boldsymbol{4}\} \) and \( \boldsymbol{C}= \)
\( \{1,3,5\}, \) then \( A \times(B-C)= \)
A \( \cdot(A \times B)-(A \times C) \)
в. \( (A \times B)+(A \times C) \)
c. \( (A \times B)-(B \times C) \)
D. \( (A \times B)-(C \times A) \)


Find the variance and standard
deviation of the following scores:
68,72,80,84,92,100


In \( \triangle A B C \) the mid points of the sides
\( A B, B C \) and \( C A \) are respectively
\( (l, 0,0),(0, m, 0) \) and \( (0,0, n) . \) Then
\( \frac{A B^{2}+B C^{2}+C A^{2}}{l^{2}+m^{2}+n^{2}} \) is equal to
\( A \cdot 2 \)
B. 4
c. 8
D. 16


An antiseptic is used when one needs to
remove microbes from:
A. foods, prior to canning
B. food preparation areas
c. skin, prior to injection
D. toilet surface


Estuaries are considered as nutrient
trap due to the mixing of
A. River and sea water
B. Pond and lake
c. A and B
D. None of the above


If the magnetic moment of the coil is \( 36 \times 10^{-X} A m^{2} . \) Find \( X ? \)


Physical and chemical conditions of soil are studied under ..... factors.
A. Biotic
B. Climatic
c. Edaphic
D. Topographic


Estimate the difference in energy between I and II Bohr Orbit for a
hydrogen atom. At what minimum at no a transition from \( n=2 \) to \( n=1 \) energy level would result in the emission of X-rays with \( \lambda=3.0 x 10^{8} \) m? Which hydrogen
like species does this at no correspond
to


The resistance of the bulb filament is
\( 100 \Omega \) at a temperature of \( 100^{\circ} \mathrm{C} \). If its temperature co-efficient of resistance
be 0.005 per \( ^{\circ} C, \) its resistance will
become \( 200 \Omega \) at a temperature
\( \mathbf{A} \cdot 300^{\circ} \mathrm{C} \)
B . \( 400^{\circ} \mathrm{C} \)
c. \( 500^{\circ} \mathrm{C} \)
D. \( 200^{\circ} \mathrm{C} \)


\( \lim _{n \rightarrow \infty} \frac{\sqrt{x^{2}+1}-\sqrt[3]{x^{3}+1}}{\sqrt[4]{x^{4}+1}-\sqrt[5]{x^{4}+1}} \) equals
\( \mathbf{A} \cdot \mathbf{1} \)
B.
\( c .-1 \)
D. none of these


Prove that \( y=a e^{-2 x}+b e^{x} \) is the
solution of differential equation \( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}+ \)
\( \frac{d y}{d x}-2 y=0 \)


If 'OLYMPIAD' is the unit of a new
physical quantity. How many times more then 1 Mega OLYMPIAD when compered to ten milli OLYMPIAD?


When a cross is made between a tall
plant with yellow seeds (Tt Yy) and a tall plant with green seeds (Tt yy), what is true regarding the proportions of phenotypes of the offsprings in \( F 1 \) generation? Proportion of Tall and Green Proportion of Dwarf and Green
A \( \cdot \frac{3}{8} \frac{1}{8} \)
в. \( \frac{2}{8} \frac{1}{8} \)
c. \( \frac{1}{8} \frac{3}{8} \)
D. \( \frac{2}{8} \frac{2}{8} \)


Calculate the molarity of a solution
containing \( 5 g \) of NaOH dissolved in the
product of a \( \boldsymbol{H}_{2}-\boldsymbol{O}_{2} \) fuel cell operated
at \( 1 A \) current for 595.1 hours.
(Assume \( 1 F=96500 \mathrm{C} / \mathrm{mol} \) of
electrons and molecular weight of NaOH as \( 40 \mathrm{g} \) mol \( ^{-1} \) )
A . 0.05 M
B. 0.025 м
\( c .0 .1 \mathrm{m} \)
D. 0.075 м
E. 1 M


Among the following pairs, the one containing examples of metalloid elements in the periodic table is:
\( \mathbf{A} \cdot N a \) and \( K \)
B. \( F \) and \( C l \)
c. \( C u \) and \( A g \)
D. \( B \) and \( S i \)


Prove that:
\( 2 \sin ^{2} \frac{3 \pi}{4}+2 \cos ^{2} \frac{\pi}{4}+2 \sec ^{2} \frac{\pi}{3}=10 \)


The probability distribution function of a random variable \( \boldsymbol{X} \) is given by
: 0 1.2
\( \boldsymbol{x}_{i} \)
\[
10 c \quad 5 c-1
\]
\( 3 c \)
where \( c>0 . \) Find \( c \)


The sum of 7 consecutive the positive integers is equal to the sum of the next five consecutive integers. What is the largest among the 12 numbers?
A .24
B . 23
\( c \cdot 22 \)
D. 21


A chain lies on a rough horizontal table. It starts sliding when one-fourth of its length hangs over the edge of the table. The coefficient of static friction
between the chain and the surface of
the table is:
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{1}{4} \)
D. 1 \( \overline{5} \)


The perpendicular distance from the
point (3,1,1) on the plane passing through the point (1,2,3) and containing the line, \( \vec{r}=\hat{i}+\hat{j}+ \) \( \lambda(2 \hat{i}+\hat{j}+4 \hat{k}), \) is:
\( ^{A} \cdot \frac{1}{\sqrt{11}} \)
в. \( \frac{4}{\sqrt{41}} \)
\( c .0 \)
D. \( \frac{3}{\sqrt{11}} \)


If \( f(x-y), f(x) . f(y) \) and \( f(x+y) \) are
in AP for all \( x, y \) and \( f(0) \neq 0, \) then This question has multiple correct options
A \( . f(2)=f(-2) \)
B. \( f(3)+f(-3)=0 \)
c. \( f^{\prime}(2)+f^{\prime}(-2)=0 \)
D \( \cdot f^{\prime}(3)=f^{\prime}(-3) \)


Complete the following equation:
\( N a_{2} O_{2}+2 H_{2} O \rightarrow(\underline{W})+H_{2} O_{2} \)
\( 2 K O_{2}+2 H_{2} O \rightarrow(\underline{X})+(\underline{Y})+O_{2} \)
\( N a_{2} O+C O_{2} \rightarrow(Z) \)
A. \( W-4 N a, X-K_{2} O, Y-H_{2} O, Z-N a_{2} O_{2} \)
B. \( W-4 N a, X-K_{2} O, Y-H_{2} O_{2}, Z-N a_{2} C O_{3} \)
c. \( W-4 \) NaOH \( , X-2 \)КОН \( , Y-H_{2} \) О \( , Z- \) Na\( _{a} \) О \( _{3} \).
D. \( W-2 N a O H, X-2 K O H, Y-H_{2} O_{2}, Z-N a_{2} C O_{3} \)


Which equation represents the time to complete \( 90 \% \) of first order reaction?
A \( \cdot \frac{k}{2.303} \log \frac{4}{3} \)
в. \( \frac{2.303}{k} \log _{\frac{3}{4}} \)
c. \( \frac{2.303}{k} \)
D. \( \frac{2.303}{k} \log 3 \)


Find the sum of \( n \) terms.Also find the
sum to infinite terms:
\( 1+\frac{1}{1+2}+\frac{1}{1+2+3}+\dots \)


Anxiety and eating spicy food together in an otherwise normal human, may
lead to
A. Diarrhoea and vomiting
B. Hepatitis
c. Indigestion
D. Jaundice


A hydrogen-like atom(atomic number
Z) is in a higher excited state of quantum number n. This excited atom can make a transition to the first state
by successively emitting two photons of energies \( 10.20 \mathrm{eV} \) and \( 17.00 \mathrm{eV} \)
Alternatively, the atom from the same excited state can make a transition to
the energy 4.24 eV and 5.95 eV. If the
excited level for second transition is
3.The value of atomic number(z)
is
\( A \cdot 2 \)
B. 4
\( c \cdot 6 \)
D. 3


In the reaction:
\( 2 F e C l_{2}+C l_{2} \rightarrow 2 F e C l_{3} \)
Chlorine may be regarded as:
A. an oxidising agent
B. a reducing agent
c. a catalyst
D. providing an inert medium


From the following find out groups of isotopes, isobars and isotones:
\( _{8}^{16} \boldsymbol{O}_{, 19}^{39} \boldsymbol{K}_{, 6}^{14} \boldsymbol{C}_{, 92}^{239} \boldsymbol{U}_{, 7}^{14} \boldsymbol{N}_{, 20}^{40} \boldsymbol{C} \boldsymbol{a}_{, 92}^{238} \boldsymbol{U}_{, 32}^{77} \boldsymbol{G} \)


A man moves in \( x-y \) plane along the
path along the path shown. At what point is his average velocity vector in the same direction as his
instantaneous velocity vector. The man
starts from point \( \boldsymbol{P} \)
\( A \cdot A \)
в. \( B \)
\( c . C \)
D. \( D \)


Assertion
Mass of moving photon varies inversely as the wavelength.
Reason
Energy of the particle \( = \) Mass \( \times \) (speed
of light) \( ^{2} \)
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. If Assertion is incorrect but Reason is correct


If saturated vapours are compressed slowly (temperature remains constant) to half the initial volume, their pressure
will:
A. become four times
B. become double
c. remain unchanged
D. become half


In a certain town, \( 40 \% \) of the people have
brown hair, \( 25 \% \) have brown eyes and 15 \( \% \) have both brown hair and brown eyes.
If a person selected at random from the town has brown hair, the probability that he also has brown eyes is
A . \( 1 / 5 \)
B. 3/8
\( c \cdot 1 / 3 \)
D. \( 2 / 3 \)


Two cells having emf's of \( 10 V \) and \( 8 V \)
and internal resistance of \( 1 \Omega \) (each) are
connected as shown with an external
resistance of \( 8 \Omega \). Find the current
flowing through the circuit.


The end product 'W' in the following
sequence of reactions is :
\( A \)
\( P h-C H_{2}-C H_{2}-O-C H-P h \)
B. \( P h-C H-O-C H-P h \)
c. \( P h-C H_{2}-O-C H_{2}-C H_{2}-P h \)
\( D \)


What are the number of significant
figures in the measurement \( 0.0040 \times \)
\( 10^{-15} m ? \)
\( A \)
B. 2
\( c \cdot 4 \)
D. 5


The decreasing value of bond angles
from \( N H_{3}\left(106^{\circ}\right) \) to \( S b H_{3}\left(101^{\circ}\right) \) down
group-15 of the periodic table is due to:
A. decreasing p-orbital character in sp \( ^{3} \)
B. decreasing electronegativity
c. increasing bp-bp repulsion
D. none of the above


Construct a tangent to a circle of the
line segment is \( 5 \mathrm{cm} \)


Given that \( T \) stands for time period and stands for the length of simple pendulum. If \( g \) is the acceleration due to gravity, then which of the following
statements about the relation \( \boldsymbol{T}^{2}= \)
\( (l / g) \) is correct?
A. It is correct both dimensionally as well as numerically y
B. It is neither dimensionally correct nor numerically.
c. It is dimensionally correct but not numerically.
D. It is numerically correct but not dimensionally.


Find the area bounded by curves
\( \left\{(x, y): y \geq x^{2} \text { and } y=|x|\right\} \)


In which group are mushrooms, toadstools, puff balls and bracket fungi
placed?
A. Sporomycetes
B. zygomycetess
c. Ascomycetes
D. Basidiomycetes


Three forces \( \overrightarrow{\boldsymbol{A}}=\{\hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}\}, \overrightarrow{\boldsymbol{B}}= \)
\( \{2 \hat{i}-\hat{j}-3 \hat{k}\} \) and \( \vec{C} \) acting on a body
To keep it in the equilibrium, the value of \( \vec{C} \) is:
\( \mathbf{A} \cdot-\{3 \hat{i}-2 \hat{k}\} \)
B . \( -\{2 \hat{i}-3 \hat{k}\} \)
c. \( 3 \hat{i}+4 \hat{j} \)
D. \( 2 \hat{i}-3 \hat{k} \)


Construct a quadrilateral \( P Q R S \) in
which \( P Q=3.8 \mathrm{cm}, Q R=3.4 \mathrm{cm} \)
\( \boldsymbol{R} \boldsymbol{S}=\mathbf{4 . 5} \mathrm{cm}, \boldsymbol{S} \boldsymbol{P}=\mathbf{5} \mathrm{cm} \) and \( \angle \boldsymbol{Q}= \)
\( 80^{\circ} . \) State which of these is the last
step.
A. From \( Q \), set \( Q R=3.4 \mathrm{cm} \)
B. With \( P \) as center and radius equal to \( 5 \mathrm{cm} \), draw an arc
c. Join \( P S \) and \( R S \)
D. Make \( \angle P Q X=80^{\circ} \)


The total number of \( 9- \) digit numbers of different digits is
A. \( 10(9 !) \)
в. \( 8(9 !) \)
c. \( 9(9 !) \)
D. none of these


In the figure, given below, CE is the
perpendicular to \( A B, \angle A C E= \)
\( 20^{\circ} \) and \( \angle A B D=50^{\circ} . \) Find the
measure of \( \angle B D A \)
A \( \cdot 36^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 56^{\circ} \)
D. none of the above


If the line \( 3 x-4 y-8=0 \) divides the
circumference of the circle with centre
(2,-3) in the ratio \( 1: 2 . \) Then, the radius of the circle is
A.
B. 2
\( c \cdot 3 \)
D. 4


\( I E_{1} \) value of \( M g \) is more than that of
Na while its \( I E_{2} \) value is less. Explain?


Physical adsorption is high at high temperature while chemical adsorption is high at low temperature
A. True
B. False


Among the isomers of \( C_{6} H_{1} 4, \) which
will give maximum number of mono-
chloro-derivatives ?
A. 2, 3-dimethyl butane
B. 2-methylpentane
c. 3-methylpentane
D. Hexane


Match the statements in Column I with
those in Column II. One or more
matching is possible.


is the characteristic of
colour
A. Wavelength
B. Frequency
c. speed
D. None of the above


Two resistances 6 and 12 ohms are
connected in parallel to a battery of 10 volts. The current in amperes in 12 ohm
resistor is
A . \( 5 / 6 \)
B. 6/5
\( c \cdot 4 / 3 \)
D. 3/4


If \( \boldsymbol{f}(\boldsymbol{x})=\sum_{\boldsymbol{r}=\mathbf{0}}^{\boldsymbol{n}} \boldsymbol{a}_{\boldsymbol{r}} \boldsymbol{x}^{\boldsymbol{r}} \)
for
\( \boldsymbol{a}_{\boldsymbol{r}} \boldsymbol{\epsilon} \boldsymbol{R} ; \boldsymbol{r} \boldsymbol{\epsilon} \boldsymbol{N} ; \boldsymbol{n} \geq \mathbf{3} \)
If \( \boldsymbol{f}(\boldsymbol{x}) \neq \mathbf{0} \) for \( \boldsymbol{x} \boldsymbol{\epsilon}(\boldsymbol{\alpha}, \boldsymbol{\beta}) \)
Then, if \( (\boldsymbol{\alpha}<\boldsymbol{t}<\boldsymbol{\beta}) \)
This question has multiple correct options
A. \( f(x) \) is continuous and Differentiable over \( (\alpha, \beta) \) atleast
B. \( (x-\alpha)(x-\beta) f(x) \) is continuous and Differentiable over \( (\alpha, \beta) \) atleast
C \( .(x-\alpha)(x-\beta) f(x) \) is continuous, but Not
differentiable over \( (\alpha, \beta) \)
\( \frac{f^{\prime}(t)}{f(t)}=\frac{1}{\alpha-t}+\frac{1}{\beta-t}, \) for atleast one \( ^{\prime} t^{\prime} \) in \( (\alpha, \beta) \)


How much length of a very wire is required to obtain a solenoid of length \( I_{0} \) and inductance \( L: \)
A \( \cdot \sqrt{\frac{2 \pi L l}{\mu_{0}}} \)
в. \( \sqrt{\frac{4 \pi L l}{\mu_{0}^{2}}} \)
c. \( \sqrt{\frac{4 \pi L l}{\mu_{0}}} \)
D. \( \sqrt{\frac{8 \pi L l}{\mu_{0}}} \)


At \( 500 \mathrm{K}, \) equilibrium constant, \( \boldsymbol{K}_{c} \) for
the following reaction is 5
\( \frac{1}{2} \boldsymbol{H}_{2(g)}+\frac{1}{2} \boldsymbol{I}_{2(g)} \rightleftharpoons \boldsymbol{H} \boldsymbol{I}_{(g)} \)
What would be the equilibrium
constant \( \boldsymbol{K}_{c} \) for the reaction:
\( \mathbf{2} \boldsymbol{H} \boldsymbol{I}_{(g)} \rightleftharpoons \boldsymbol{H}_{2(g)}+\boldsymbol{I}_{2(g)} ? \)
A .0 .04
B. 0.4
\( c \cdot 25 \)
D. 2.


A Pelton wheel develops \( 1750 k W \) under
a head of 100 metres while running at 200 r.p.m. and discharging 2500 litres of water per second. The unit power of the wheel is
A. \( 1.75 K V \)
В. \( 0.25 K v \)
c. \( 0.75 K v \)
D. \( 1 K v \)


Find the value of \( k \) for which the
following system of equations has no solution:
\( \boldsymbol{x}+\mathbf{2} \boldsymbol{y}=\mathbf{0} \)
\( 2 x+k y=5 \)


Arrange the following ions in order of increasing strength as a reducing agent, and account for the trend:
A \( \cdot C r^{2+}<C r_{2} O_{7}^{2-}<C r^{3+} \)
B. \( C r^{2+}<C r^{3+}<C r_{2} O_{7}^{2} \)
c. \( C r_{2} O_{7}^{2-}<C r^{3+}<C r^{2} \)
D. \( C r_{2} O_{7}^{2-}<C r^{2+}<C r^{3+} \)


Let \( f(x) \) be a non-constant twice differentiable function defined on
\( (-\infty, \infty) \) such that \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{f}(\mathbf{1}-\boldsymbol{x}) \)
and \( f^{\prime}\left(\frac{1}{4}\right)=0 . \) Then
This question has multiple correct options
A \( \cdot f^{\prime}(x) \) vanishes at least twice on [0,1]
B \( ^{\prime} f^{\prime}\left(\frac{1}{2}\right)=0 \)
\( ^{\mathrm{c}} \int_{-1 / 2}^{1 / 2} f\left(x+\frac{1}{2}\right) \sin x d x=0 \)
D \( \cdot \int_{0}^{1 / 2} f(t) e^{\sin \pi t} d t=\int_{1 / 2}^{1} f(1-t) e^{\sin \pi t} d t \)


Which of these half-reactions
represents an oxidation?
I. \( \boldsymbol{S} \boldsymbol{n}^{\boldsymbol{4}+} \rightarrow \boldsymbol{S} \boldsymbol{n}^{2+} \)
II. \( M n O_{4}^{-} \rightarrow M n^{2+} \)
III. \( \boldsymbol{C l}_{2} \rightarrow \boldsymbol{C l O}_{\mathbf{3}}^{-} \)
A. I only
B. II only
c. III only
D. I and II only
E. II and III only


Match the pairs correctly.


The element which forms oxides in all
the oxidation states from +1 to +5
is
A.
B. P
c. As
D. sb


If \( C_{r} \) denotes the binomial coefficient
\( ^{n} C_{r} \) then \( (-1) C_{0}^{2}+2 C_{1}^{2}+5 C_{2}^{2}+ \)
\( \ldots(3 n-1) C_{n}^{2}= \)
A \( \cdot(3 n-2)^{2 n} C_{n} \)
\( ^{\text {В }} \cdot\left(\frac{3 n-2}{2}\right)^{2 n} C_{n} \)
c. \( (5+3 n)^{2 n} C_{n} \)
D \( \cdot\left(\frac{3 n-5}{2}\right)^{2 n} C_{n+1} \)


In vulcanization of rubber:
A. sulphur reacts to form a new compound
B. sulphur cross-links are introduced
C. sulphur forms a very thin protective layer over rubber
D. all statements are correct


Which of the following is not a limitation of hydel energy?
A. Hydel power stations are pollution free.
B. A vast reservoir is needed
c. It leads to a loss of wildlife habitat.
D. It can be harnessed at only a few places


Write the name and structure of an
alcohol with four carbon atoms in its
molecule.


Write the following rational numbers in
ascending order:
\( \frac{-3}{7}, \frac{-3}{2}, \frac{-3}{4} \)


Which of the following pair of elements follows Newland's law of octave?
A. \( N e, A r \)
в. \( C, N \)
c. \( N a, K \)
D. \( P, S \)


How many person can be
accommodated in hall of length \( 16 \mathrm{m} \)
breadth \( 12.5 \mathrm{m} \) and height 4.5
assuming that \( 3.6 m^{3} \) of air is required
for each person?


Identify which of the following best
describe the Mutual inductance?
A. the ability of a current carrying conductor to induce a voltage in another conductor through a mutual magnetic field.
B. the ability of current carrying conductor to produce a changing magnetic field.
C. the ability of a conductor to induce a magnetic field in another current carrying conductor
D. the ability of a current carrying conductor to induce a current in another conductor through a mutual magnetic field.
E. the ability of a magnetic field to induce a voltage in a current carrying conductor.


Dimensions of ohm are same as:
\( A \cdot \frac{h}{e} \)
в. \( \frac{h^{2}}{e} \)
\( c \cdot \frac{h}{e^{2}} \)
D. \( \frac{h^{2}}{e^{2}} \)


For every positive integer \( n, \frac{n^{7}}{7}+\frac{n^{5}}{5}+ \) \( \frac{2 n^{3}}{3}-\frac{n}{105} \) is
A. an integer
B. a rational number
c. a negative real number
D. an odd integer


Fish vertebrates are
A. Ostractodermi
B. Placodermi
C . Cyclostomates
D. Choanochthyes


Standard atmospheric pressure is equivalent to pressure given by
A. 76 cm of mercury
B. 7.6 cm of mercury
c. \( 760 \mathrm{cm} \) of mercury
D. none of these


Concentrated nitric acid is converted to
sulphuric acid by the reaction with:
A. Sulphur dioxide
B. conc.sulphuric acid
c. sulphur
D. Sulphur trioxide


Draw \( \angle A B C \) of measure \( 110^{\circ} \) and
bisect it.


A light ray is incident on a glass slab it is partially reflected and partially transmitted. Then the reflected ray is
A. completely polarised and highly intense.
B. partially polarised and poorly intense
c. partially polarised and highly intense
D. completely polarised and poorly intense.


For any two complex numbers \( z_{1} \) and \( z_{2} \) with \( \left|z_{1}\right| \neq\left|z_{2}\right|,\left|\sqrt{2} z_{1}+i \sqrt{3} \overline{z_{2}}\right|^{2}+ \)
\( \left|\sqrt{3} \overline{z_{1}}+i \sqrt{2} z_{2}\right|^{2} \) is
A \( \cdot \) less than \( 5\left(\left|z_{1}\right|^{2}+\left|z_{2}\right|^{2}\right) \)
B. greater than \( 10 \mid z_{1} z_{2} \)
C . equal to \( 2\left|z_{1}\right|^{2}+3\left|z_{2}\right|^{2} \)
D. zero


Glycine \( N H_{2} C H_{2} C O O H \) behaves:
A. As a Bronsted acid
B. As a Bronsted base
c. Both as an acid nor as a base
D. Neither as an acid nor as a base


A 100 feet long classroom maintains
seating row after every 10 feet and has doors on both front and back sides. A
laughing gas \( \left(N_{2} O\right) \) cylinder and a tear gas (methane) cylinder were opened simultaneously at the front and the back door respectively. Assuming both the gases were present at the same temperature and pressure and the cylinder has similar valve dimensions. If the student of \( n^{t h} \) row, from the front,
simultaneously weeps and laughs, the value of \( n \) is
A. 5
B. 4
\( c \cdot 6 \)
D.


Which ranks the following atoms \( (L i, N a, K, R b) \) from the smallest to
largest atomic radius?
A. \( L i<N a<K<R b \)
в. \( R b<K<N a<L i \)
c. \( K<N a<L i<R b \)
D. \( N a<L i<R b<K \)


The degree of hydrolysis of
\( C H_{3} C O O N H_{4} \) is independent of its
concentration in solution.
If true write 1 , else write 0


Find the angle measure of 4 radians.
A \( \cdot 114.591^{\circ} \)
В. \( 141.372^{\circ} \)
c. \( 229.183^{\circ} \)
D . \( 282.743^{\circ} \)
E \( .458 .366^{\circ} \)


Figure shows the shape of a part of a
long string in which transverse waves
are produced. Which pair of particles
are in phase?
\( A \). A and
3. D and G
\( c . \) В and \( E \)
D. c and


Construct a triangle \( P Q R \) in which \( \boldsymbol{P Q}=\mathbf{5 . 4 c m}, \boldsymbol{Q} \boldsymbol{R}=\mathbf{5 . 5 c m} \) and
\( \angle P Q R=55^{\circ} \)


In a hand at whist find the chance that a
specified player holds both the king and queen of trumps.

Note:Whist is a game of cards in which a standard pack of 52 cards is used.The game is played in pairs.In each round, a suit is randomly selected as 'Trump' which gets a preference over other suits for that particular round.


Find the slope of the line joining the
points (-5,0) and (0,-7)


since the beginning of \( 1990, \) the number of squirrels in a certain wooded area has tripled during every 3-year period of time. If there were 5,400 squirrels in the wooded area at the beginning of \( 1999, \) how many squirrels were in the wooded area at the
beginning of \( 1990 ? \)
A . 50
B. 100
\( c \cdot 200 \)
D. 300


The average, \( S-F \) bond energy in \( S F_{6} \)
if the \( \Delta H_{f}^{\circ} \) value are -1100,+275 and
\( +80 k J / m o l \) respectively for \( S F_{6}(g) \)
\( S(g) \) and \( F(g) \) is
A. \( 390.1 k J / \) mol
в. \( 103.9 k J / \) mol
c. \( 903.1 k J / \) mol
D. \( 309.1 k J / \) mol


For any substance, why does the
temperature remain constant during the change of state?


Show that \( \triangle A B C \) is an isosceles
triangle, if the determinant \( \mid \begin{array}{ccc}\mathbf{1} & \mathbf{1} \\ \mathbf{1}+\cos \boldsymbol{A} & \mathbf{1}+\cos \boldsymbol{B} & \mathbf{1} \\ \cos ^{2} \boldsymbol{A}+\cos \boldsymbol{A} & \cos ^{2} \boldsymbol{B}+\cos \boldsymbol{B} & \mathbf{c o s}^{2}\end{array} \)
\( \mathbf{D} \)


Draw the structure of the isomer of
compound B?


The adjoining figure shows an \( \boldsymbol{A C} \)
circuit with resistance \( \boldsymbol{R} \), inductance \( \boldsymbol{L} \)
and source voltage \( V_{s} . \) Then
A. the source voltage \( V_{s}=72.8 \mathrm{V} \)
B. the phase angle between current and source voltage is \( \tan ^{-1}(7 / 2) \)
c. Both \( (a) \) and
( \( b \) ) are correct.
D. Both \( (a) \) and
\( (b) \) are wrong.


Petroleum is a renewable fossil fuel
A. True
B. False


Which one of the following class of phylum mollusca is correctly matched with its general characteristics? Gastropoda - larvae are bilaterally symmetrical; but in adult, the twisting
of viscera makes them lose this
symmetry. some, like land snail and slug (a shell-less form), live on land. Bivalvia - They are sedentary filter feeders.
Cephalopoda - They are at the apex of invertebrate evolution in terms of
learned behaviour they exhibit. The eyes
are image forming, same what similar
to ours.
Pelecypoda - They have sensory tentacles and their foot is reduced into
a tongue - shaped structure which helps them to burrow into sea floor.


Consider the following statements:
(a) \( \frac{e}{m} \) ratio of particles of canal rays remains constant
(b) The energy of orbit closest to nucleus is lowest
(c) \( C l^{-} \) has 18 electrons and 18 protons
(d) The maximum number of electrons
in an energy level is equal to \( 2 n^{2} \)

Which of the above statement(s) is/are
correct?
A. Only (b)
B. \( (a),(c) \) and \( (d) \)
\( c \cdot(b) \) and \( (d) \)
D. \( (b),(c) \) and \( (d) \)


Using remainder theorem, find the
remainder when \( 2 x^{3}-3 x^{2}+4 x-5 \) is
divided by \( \boldsymbol{x}+\mathbf{3} \)
\( \mathbf{A} \cdot 204 \)
B . -136
\( c .-98 \)
D. 42


A bullet of mass \( 20 g \) and moving with a
velocity of \( 200 m / s \) strikes a heap of
sand and comes to rest after
penetrating \( 3 c m \) inside it. The force exerted by the sand on the bullet will be:
\( \mathbf{A} \cdot 11.2 \times 10^{8} d y n e \)
B . \( 15.7 \times 10^{8} \) dyne
c. \( 13.3 \times 10^{8} \) dyne
D. \( 18.6 \times 10^{8} \) dyne


Congestion of the lungs is one of the main symptoms in
A. Hypotension
B. Coronary artery disease
C. Angina
D. Heart failure
E. Atherosclerosis


Solve the differential equation \( \left(x^{2}+\right. \)
\( \left.\boldsymbol{y}^{2}\right) \boldsymbol{d} \boldsymbol{x}-\boldsymbol{2} \boldsymbol{x} \boldsymbol{y} \boldsymbol{d} \boldsymbol{y}=\mathbf{0} \)


is the amount of air
in a respiratory cycle.
A. Air capacity
B. Respiration capacity
c. Lung volume
D. None of the above


During hydrogenation of oil, the catalyst commonly used is:
A. \( P d \) on \( C u C l_{2} \)
в. \( F e \)
c. \( N i \)
D. \( U_{2}+O_{2} \)


Choose the correct answer from the four
alternatives given in the brackets:
Number of periods in modern periodic table is
(7,17,8,18)


\( l=\lim _{x \rightarrow \alpha} \frac{f(x)}{x(x-\alpha)(x-2)} \) is
A . positive
B. negative
\( c \cdot 0 \)
D. sign of \( l \) depends upon \( \alpha \pi \)


Isobutyraldehyde on oxidation gives:
A. 2-Methylpropanoic acid
B. 2-Methylpropanone
c. Propanoic acid
D. 2-Methyl butanoic acid


Two wires of the same material and
same mass are stretched by the same
force. Their length are in the ratio 2: 3
Their elongations are in the ratio
A .3: 2
B. 2: 3
c. 4: 9
D. 9: 4


A light ray is incident perpendicularly to
one face of a \( 90^{\circ} \) prism and is totally
internally reflected at the glass-air
interface. If the angle of reflection is \( 45^{\circ} \)
we conclude that the refractive index \( n \)
A \( \cdot n>\frac{1}{\sqrt{2}} \)
В . \( n>\sqrt{2} \)
c. \( _{n<\frac{1}{\sqrt{2}}} \)
D. \( n<\sqrt{2} \)


The diatomaceous earth is used for
insulating boilers and steam pipes, because
A. The diatomaceous earth is very cheap.
B. It is a good conductor of heat
c. It is a bad conductor of heat.
D. It is composed of calcium carbonate.


The binomial system of naming a species was first devised by
A . Aristotle
B. Hugo de Vries
c. carolus Linnaeus
D. Bentham and Hooker


A wedge of mass \( M=2 \mathrm{kg} \) is placed
over a rough horizontal surface having
coefficient of friction \( \mu, \) a block of mass
\( m=1 \mathrm{kg} \) is placed over this wedge as
shown in figure. If coefficient of friction
between wedge and block is \( \mu_{1}=0.8 \)
then the minimum value of \( \mu \) so that
wedge does not slip over a horizontal
surface, is
\( A .0 .8 \)
в. 0.75
\( c .0 .5 \)
D. zero


\( f\left(\mu_{1}=1.58 \text { and } \mu_{2}=1.53, \text { what is } \theta ?\right. \)


A moving coil galvanometer A has 100
turns and resistance \( 10 \Omega \). Another
galvanometer B has 50 turns and resistance 5\Omega. The other quantities are same in both the cases. Then the
voltage sensitivity of
A. A is greater than that of
B. B is greater than that of
c. A and B is Same
D. cannot be compared


Lower carboxylic acid are soluble in
water due to:
A. low molecular weight
B. hydrogen bonding
c. dissociation into ions
D. easy hydrolysis


Alkaline earth (group 2 or IIA elements) differ from group 12 (or IIB) elements in the electronic configuration of their:
A. Anitipenultimate shell
B. Innermost shell
c. Outermost shell
D. Penultimate shel


\( \boldsymbol{A E} \)
A \( \cdot \overrightarrow{A E}=\frac{1}{2}(\bar{a}+\bar{b}) \)
B \( \cdot \overrightarrow{A E}=\frac{1}{2}(\bar{a}-\bar{b}) \)
C \( \cdot \overrightarrow{A E}=\frac{1}{2}(\bar{b}-\bar{a}) \)
D. none of these


Latent heat of vapourisation of a liquid
at \( 500 K \) and 1 atm pressure is 10 \( k c a l / \) mol. What is the change in internal energy when 3 moles of the liquid is vapourised at the same
temperature
A . \( 27 k c a l \)
B. \( 7 k c a l \)
c. \( 33 k c a l \)
D. \( 25 k c a l \)


Assertion
Carbon shows tetravalency in all hydrocarbons.
Reason
Carbon shares its four valence electrons
with other atoms and forms four single covalent bonds to get nearest noble gas
formation.
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 mineral contains two metals?
A. Carnallite
B. Dolomite
c. Asbestos
D. All of the above


Endosperm of flowering plants develops
from
A. Haploid nucleus
B. Diploid nucleus
c. Triploid nucleus
D. Tetraploid nucleus
E. Polyploid nucleus


Length of a wire at room temperature is \( 4.55 m, \) when the temperature increase
upto \( 100^{\circ} \mathrm{C} \) then its length becomes
4.57 \( m \). The coefficient of linear
expansion \( (\alpha) \) of the given wire is
A. \( 5.021 \times 10^{-5} K^{-1} \)
B. \( 6.021 \times 10^{-5} K^{-1} \)
c. \( 7.021 \times 10^{-5} K^{-1} \)
D. \( 8.021 \times 10^{-5} K^{-1} \)


Mg is an important component of which biomolecule occurring extensively in living world?
A. Hemoglobin
B. Chlorophyll
c. Florigen
D. ATP


The earth is considered as a short
magnet with its centre coinciding with the geometric centre of earth. The angle of dip \( \phi \) related to the magnetic latitude
\( \alpha \lambda \) as
\( ^{\mathbf{A}} \cdot \tan \phi=\frac{1}{2 \tan \alpha} \)
B. \( \tan \lambda=\tan \phi \)
c. \( \tan \lambda=2 \tan \phi \)
D. \( \tan \phi=2 \tan \lambda \)


What is PHBV ? How is it useful to man?


If resistance of wire at \( 50^{\circ} \mathrm{C} \) is \( 5 \mathrm{R} \Omega \) and
\( 100^{\circ} \mathrm{C} \) is \( 6 \mathrm{R} \Omega, \) find resistance of \( 0^{\circ} \mathrm{C} \)


Which one of the following statements
is true?
\( \mathbf{A} \cdot \operatorname{If} \lim _{x \rightarrow c} f(x) \cdot g(x) \) and \( \lim _{x \rightarrow c} f(x) \) exist, then \( \lim _{x \rightarrow c} g(x) \) exists.
\( \mathbf{B} \cdot \operatorname{If} \lim _{x \rightarrow c} f(x) \cdot g(x) \) exists, then \( \lim _{x \rightarrow c} f(x) \) and \( \lim _{x \rightarrow c} g(x) \) exist.
C. \( \operatorname{If} \lim _{x \rightarrow c} f(x)+g(x) \) and \( \lim _{x \rightarrow c} f(x) \) exist, then \( \lim _{x \rightarrow c} g(x) \) also
exists.
\( \mathbf{D} \cdot \operatorname{If} \lim _{x \rightarrow c} f(x)+g(x) \) exists, then \( \lim _{x \rightarrow c} f(x) \) and \( \lim _{x \rightarrow c} g(x) \) also
exist.


There are six friends of Saurav. In how
many ways he can invite one or more friends to take dinner?


How many grams of NaCl will be required to make a \( 100 . \) milliliters of \( 2 \mathrm{M} \)
solution?
A . 5.85
в. 11.7
c. 29.2
D. 58.5
E .117