The end error of a meter bridge can be generated due to which of the following causes/(s)
A. Generation of heat due to the flow of current in the wirce may change the length of the wire
B. Due to the change of the weather, the length of the meter bridge wire may change its length.
c. The meter bridge wire is mounted over the wooden plary some metal screw or some metal
D. The thickness of the wire may be non uniform.


Three bricks each of length \( L \) and mass
\( M \) are arranged as shown from the wall.
The distance of the centre of mass of
the system from the wall is?
A \( \frac{11}{12} L \)
в. \( \frac{7}{8} L \)
c. \( \frac{1}{12} L \)
D. \( \frac{15}{1} L \)


When phosphorus reacts with caustic
soda, the products are \( P H_{3} \) and
\( N a H_{2} P O_{2} . \) This reaction is an example
of.
A. Oxidation
B. Reduction
c. Disproportionation
D. None of these


Tell whether the following is certain to happen, impossible can happen but not certain.
You are older today than yesterday.


Show that the equilibrium is unstable.


A body falls freely from rest. If at an instant, the velocity acquired is numerically equal to the displacement, then the velocity acquired is:
A. \( 9.8 \mathrm{m} / \mathrm{s} \)
B. \( 19.6 \mathrm{m} / \mathrm{s} \)
c. \( 29.4 \mathrm{m} / \mathrm{s} \)
D. \( 39.2 \mathrm{m} / \mathrm{s} \)


From an external point, \( K \) tangents can be drawn to a circle, then \( \mathrm{K} \) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B.
c. 1
\( D \cdot \alpha \)


Green leaf like one internode long stem branches/phylloclades are called
A. Phylloclades
B. Phyllodes
c. Bulbils
D. Cladodes


Very short answer type. Mention the most significant function/role of rennin


\( M^{3+} \) has electronic configuration as
\( [A r] 3 d^{10}, \) hence it lies in:
A. \( s \) -block
B. p-block
c. \( d \) -block
D. \( f \) -block


The volume of cylinder if the base area
is \( 20 c m^{2} \) and height is \( 5 c m \)


Companion cells are closely associated
with
A. Sieve elements
B. Vessel elements
c. Trichomes
D. Guard cells


Explain with an example how the concentration of the reactants affects
the rate of a chemical reaction.


Evaluate \( \lim _{x \rightarrow \pi / 2} \frac{\cos x}{\pi-2 x} \)


Among the following compounds which will react with acetone to give a product containing \( >\boldsymbol{C}=\boldsymbol{N}-? \)
A. \( C_{6} H_{5} N H C O C l \)
в. \( \left(C H_{3}\right)_{2} N-C H_{3} \)
c. \( C_{6} H_{5} N H N H_{2} \)
D. \( C_{6} H_{5} N H C_{6} H_{5} \)


A large steel wheel is to be fitted on to a
shaft of the same material. At \( 27^{\circ} C \) the
outer diameter of the shaft is \( 8.70 \mathrm{cm} \)
and the diameter of the central hole in
the wheel is \( 8.69 \mathrm{cm} . \) The shaft is cooled
using 'dry ice'. At what temperature of the shaft does the wheel slip on the shaft? Assume coefficient of linear
expansion of the steel to the constant over the required temperature range:
\( \boldsymbol{\alpha}_{\text {steel}}=\mathbf{1 . 2 0} \times \mathbf{1 0}^{-\mathbf{5}} \mathbf{K}^{-\mathbf{1}} \)


The circle and the square have the
same center and the same area. If the
circle has radius \( 1, \) the length of \( A B \) is
A \( .4-7 \)
B . \( 4-2 \sqrt{\pi} \)
\( c \cdot 2-\sqrt{\pi} \)
D. \( \sqrt{4-\pi} \)


Distinction between speed and velocity
is :
A. speed is vector while velocity is scalar
B. speed is scalar while velocity is vector
C. speed and velocity are scalars.
D. speed and velocity are vectors.


Number of value of \( \boldsymbol{x} \in[\mathbf{0}, \mathbf{4} \boldsymbol{\pi}] \) and
satisfying \( \sqrt{2} \sec x+\tan x=1 \) is?


Differentiate between
radially symmetrical and bilaterally symmetrical organisms.


Which is \( 2^{n d} \) step?
\( a \)
\( (b) \)
\( e \cdot(c) \)
).


The attached figure shows a planet
revolving a star. It was recorded that the
planet takes 50 days to travel from \( T \) to
U. Which other two observations could
be 50 days apart?
A. \( \mathrm{V} \) and \( \mathrm{W} \)
B. Wand Y
c. \( x \) and \( Y \)
D. \( x \) and \( z \)
E. \( Y \) and


Evaluate the following integral:
\( \int_{0}^{3}\left(2 x^{2}+3 x+5\right) d x \)


Relative stabilities of the following
structures of \( \boldsymbol{C} \boldsymbol{H}_{2}=\boldsymbol{C} \boldsymbol{H}-\boldsymbol{C} \boldsymbol{H} \boldsymbol{O} \) are
in this decreasing order:
\( A \cdot\|>1>\| \)
c. \( \|\mid>\|>1 \)
D. |>॥|| > ||


What do you understand by the static or
frictional electricity?
A. Discarging of two bodies on rubbing them together is called static or frictional electricity.
B. Charging of two bodies on rubbing them together is called static or frictional electricity.
C. Electricity which is static is called static or frictional electricity.
D. Electricity on high friction bodies is called static or frictional electricity.


Iron is rendered passive in:
A. aquaregia
B. conc. H_so
c. con. HNO \( _{3} \)
D. conc. HCI


Find the slope of the straight line passing through the points (3,-2) and (-1,4)


The enthalpy and entropy change for a chemical reaction are \( -2.5 \times 10^{3} \mathrm{cal} \)
and 7.4 cal \( K^{-1} \) respectively. Predict
the nature of reaction at \( 298 \mathrm{K} \)


A circle with area \( A_{1} \) is contained in the
interior of a larger circle with area \( \boldsymbol{A}_{\mathbf{1}}+ \)
\( A_{2} . \) If the radius of the larger circle is 3
and \( A_{1}, A_{2}, A_{1}+A_{2} \) are in A.P., what is
the radius of the smaller circle?
A \( \cdot \frac{\sqrt{3}}{2} \)
B. \( \frac{2}{\sqrt{3}} \)
\( c \cdot \sqrt{3} \)
D. \( \frac{3}{2} \)


The binding energy per nucleon for the
parent nucleus is \( \mathrm{E}_{1} \) and that for the
daughter nuclei is \( \mathrm{E}_{2} \). Then
A \( \cdot \mathrm{E}_{2}=2 \mathrm{E}_{1} \)
в. \( \mathrm{E}_{1}>\mathrm{E}_{2} \)
c. \( \mathrm{E}_{2}>\mathrm{E}_{1} \)
D. \( \mathrm{E}_{1}=2 \mathrm{E}_{2} \)


The power of plane mirror is
\( \mathbf{A} \cdot \mathbf{0} \)
B . \( \infty \)
\( c .2 D \)
D. \( 4 D \)


\( M g^{2+} \) and \( C l^{-} \) are required during
transfer of electron from
A \( \cdot O H^{-} \) to \( C h l \) orophyll \( -a_{683} \)
B. \( O H^{-} \) to \( P_{700} \)
c. \( F D \) to \( F R S \)
D. Cytochrome \( -b \) to cytochrome \( -f \)


What is common about Trypanosoma,
Noctiluca, Monocystis and Giardia?
A. These are all parasites
B. These are all unicellular protists
c. They have flagella
D. They produce spores


Which of the following properties generally decreases along a period?
A. Ionisation energy
B. Electron affinity
c. Metallic character
D. valency


Phenanthrene is a fused polycyclic compound containing benzene rings.
A. two
B. three
c. four
D. five


If the centre \( O \) of circle is the
intersection of \( x- \) axis and line \( y= \) \( \frac{4}{3} x+4, \) and the point (3,8) lies on
circle, then the equation of circle will be
A \( \cdot x^{2}+y^{2}=25 \)
B - \( (x+3)^{2}+y^{2}=25 \)
c. \( (x+3)^{2}+y^{2}=100 \)
D. \( (x+3)^{2}+(y-8)^{2}=100 \)


The chances of defective screws in three
boxes \( A, B \) and \( C \) are \( \frac{1}{5}, \frac{1}{6}, \frac{1}{7} \) respectively. A box is selected at
random and a screw drawn from it at
random, is found to be defective.

The probability that it came from the
box'A' is
A \( \cdot \frac{16}{29} \)
B. \( \frac{1}{15} \)
c. \( \frac{27}{59} \)
D. \( \frac{42}{107} \)


How many terms of the \( \mathrm{AP} 27,24,21, \ldots \)
should be taken so that their sum is 0


The diagram summarises the pathway of glucose break down.
Hexose
Triose phosphate
\( 6 \mathrm{C} \) compound
\[
\mathrm{H}_{2} \mathrm{O}+\mathrm{CO}_{2}
\]


State whether the statement is True or
False.
\( (4+5 x)(4-5 x) \) is equal to \( 16-25 x^{2} \)
A. True
B. False


How many \( S-O-S \) linkages are
there in dithionous acid?


Q Type your question_
statement regarding this -
A. When agricultural fields are sprayed with DDT, it is carried by runoff water into nearby aquatic bodies
B. River water may have a very low concentration of DDT,
but the concentration of DDT, which is still suitable for
consumption by human beings
C. Increased concentration of DDT in birds affects
calcium metabolism due to which egg shells become thin and break before maturity
D. None of these


Determine the current through zener
diode for the circuit shown in figure is:
(Given: zener diode break down voltage
\( \left.V_{z}=5.6 V\right) \)
\( \mathbf{A} \cdot 7 m A \)
В. \( 17 m A \)
c. \( 10 m A \)
D. \( 15 \mathrm{mA} \)


Which of the following is incorrect about polysaccharides?
I. These are amorphous solids.
II. These are sparingly soluble in water.
III. These are sugars
A . Only III
B. Il and II
c. I and III
D. All of the above


Find the derivative of \( f(x) \) from the first
principle. \( \sin x \div \cos x \)


State and explain work energy principle. Mention any three examples for it.


Large intestine in man mainly carries
out
A. Absorption of water
B. Assimilation
c. Digestion of fats
D. Digestion of carbohydrates


Consider the following statements:
1. \( 1^{\circ} \) in radian measure is less than
0.02 radians.
2. 1 radian in degree measure is
greater than \( 45^{\circ} \)

Which of the above statements
is/are correct?
A. 1 only
B. 2 only
c. Both 1 and 2
D. Neither 1 nor 2


When \( 20 g F e_{2} O \) is reacted with \( 50 g \) of
\( \boldsymbol{H} \boldsymbol{C l}, \boldsymbol{F e} \boldsymbol{C l}_{3} \) and \( \boldsymbol{H}_{2} \boldsymbol{O} \) are formed. The
amount of unreacted \( \boldsymbol{H} \boldsymbol{C l} \) is \( (\boldsymbol{F e}=\mathbf{5 6}) \)
A. \( 27.375 g \)
в. \( 22.625 g \)
c. \( 30 g \)
D. \( 4.75 g \)


Which of the following types of water is not in its free state?
A . River water
B. Well water
c. Distilled water
D. Rain water


Does pure water conduct electricity?
A. Yes
B. No
c. Sometimes
D. None of above


The percentage of gold present in 20 carat gold is
A . 100
B. 73.86
c. 50
D. 83.33


Name the mode of reproduction that ensures the creation of new variants.


Find the common difference in the
following pattern:
(a) 4,7,10,13
(b) 5,9,13,17,21,25


Differentiate \( \sin ^{2} x \) w. \( r . \) t. \( e^{\cos x} \)


Calculate resonant frequency and \( Q \)
factor of a series L-C-R circuit
containing a pure inductor of inductance \( 3 \mathrm{H} \), Capacitor of
capacitance \( 27 \mu F \) and resistor of resistance \( 7.4 \Omega \)


Given, matrix \( \boldsymbol{A}=\left[\begin{array}{l}\mathbf{3} \\ \mathbf{2}\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{l}-\mathbf{2} \\ -\mathbf{1}\end{array}\right] \)
find the matrix \( X \) such that \( X-A=B \)
\( A \cdot\left[\begin{array}{l}0 \\ 0\end{array}\right] \)
в. \( \left[\begin{array}{l}1 \\ 1\end{array}\right] \)
\( c \cdot\left[\begin{array}{l}4 \\ 0\end{array}\right] \)
D. \( \left[\begin{array}{l}1 \\ -1\end{array}\right. \)


Which of the following is a medicine?
A. Arsphenamine
B. Heroin
c. Morphine
D. codeine


Two points charges \( 4 \mu C \) and \( -2 \mu C \) are separated by a distance of \( 1 \mathrm{m} \) in air. \( \mathrm{At} \) what point in between the charges and on the line joining the charges, is the electric potential zero?
A. In the middle of the two charges
B. \( 1 / 3 m \) from \( 4 \mu C \)
c. \( 1 / 3 m \) from \( -2 \mu C \)
D. Nowhere the potential is zero


n the figure, \( P Q=R S \) and \( \angle O R S= \)
\( 48^{\circ} \) Find \( \angle O P Q \) and \( \angle R O S \)


The radius of hollow metallic sphere is \( r \) If the potential difference between its surface and a at a distance \( 3 r \) from its
centre is v then the electric field
intensity at a distance of \( 3 r \) its centre is:
A. v/2r
B. \( \vee / 3 \) r
c. \( \vee / 4 r \)
D. V/6


Which one of the following muscles is responsible for moving and shaking the skin?
A. Arrector pilli
B. Collagen fibres
c. Panniculus carnosus
D. sphincter muscles


A metallic cylinder of diameter \( 5 \mathrm{cm} \) and height \( 3 \frac{1}{3} \mathrm{cm} \). is melted cast into a sphere. What is its diameter.


Which era is considered as the age of
reptiles?


If \( \boldsymbol{x}^{\mathbf{3}}-\boldsymbol{a} \boldsymbol{x}^{\mathbf{2}}+\boldsymbol{b} \boldsymbol{x}- \)
\( \boldsymbol{6} \) is exactly divisible by \( \boldsymbol{x}^{2}- \)
\( \mathbf{5 x + 6 . t h e n} \frac{a}{b} \) is
A. an integer
B. an irrational number
\( c \cdot \frac{6}{11} \)
D.


Most of the fossils occur in the rocks as
A. Matamorphic
B. Igneous
c. sedimentary
D. All of the above


Match the following.
A. Homeostasis
1) Insulin
B. Emergency hormone
2) Structure
of insulin
C. Metabolism
3) Adrenaline
D. Peptide hormones
4) Thyroxine
E. Pancreatic islets
5)
Maintenance of constant internal
environment
F. Sanger
6) Affect
the properties of Plasma membrane
\( A \cdot A-1 ; B-5 ; C-3 ; D-4 ; E-6 ; F-2 \)
B. \( A-2 ; B-4 ; C-3 ; D-1 ; E-6 ; F-2 \)
\( \mathrm{C} \cdot \mathrm{A}-3 ; \mathrm{B}-5 ; \mathrm{C}-3 ; \mathrm{D}-4 ; \mathrm{E}-6 ; \mathrm{F}-1 \)
D. \( A-5 ; B-3 ; C-4 ; D-1,6 ; E-1 ; F-2 \)


An electric bulb of resistance \( 480 \Omega \) is
connected to \( 220 V . \) Find electric energy
consumed in \( 10 s \)
A . \( 1000 J \)
в. \( 9600 J \)
c. 1008.35
D. \( 1118.7 J \)


Neutron was discovered by:
A. J.J. Thomson
B. Chadwick
c. Rutherford
D. Priestley


How many vocal cords does a person have?
\( A \cdot 3 \)
B.
\( c \cdot 2 \)
\( D \)


\( y=\left(\frac{2^{x+1}}{1+4^{x}}\right) \) Find \( \frac{d y}{d x} \)


Evaluate the following:
\( \int \frac{1}{\sqrt{x^{2}+4 x+29}} d x \)


Determine the horizontal component of
the earth's magnetic field at the
location.


toppr
Q Type your question
\( N a, M g, A l \) and \( S i \) plotted
against their first ionisation energies?
\( A \)
B.
\( c \)
\( D \)


What do you mean by power of accommodation of an eye?


Assertion
When two long parallel wires, hanging freely are connected in series to a battery, they come closer to each other.
Reason
Wires carrying current in opposite direction repel each other.
A. Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
B. Both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Identify which of the following quantities is a scalar quantity?
A. displacement
B. mass
c. resultant
D. equilibrant
\( E \cdot 101 \mathrm{m} / \mathrm{s} \) at \( 30^{\circ} \) north of east


The solubility of a solute with increase
of temperature when the dissolution is attended by absorption of heat:
A . decreases
B. remains same
c. may increase or decrease
D. increases


Natural length of a massless spring (of spring constant \( k \) ) is \( x \). It is slowly stretched by applying an external force. What is the work done in slowly stretching it from length \( 3 x \) to \( 4 x ? \)
A \( .1 .5 k x^{2} \)
B. \( 2.5 k x^{2} \)
c. \( 3.5 k x^{2} \)
D. \( 4.5 \mathrm{kx}^{2} \)


In how many ways we can select 5 cards
from a deck of 52 cards, if each selection must include atleast one king


For the reaction
\( \mathbf{2} \boldsymbol{A}+\boldsymbol{B} \rightleftharpoons \mathbf{3} \boldsymbol{C} \) at \( \mathbf{2} \mathbf{9 8} \boldsymbol{K}, \boldsymbol{K}_{\boldsymbol{c}}=\mathbf{4 9} \)
A \( 3 L \) vessel contains 2,1 and 3 moles of
\( A, B \) and \( C \) respectively. The reaction at
the same temperature:
A. must proceed in forward direction
B. must proceed in backward direction
c. must be in equilibrium
D. cannot be predicted


Why does the sky appears dark instead
of blue to astronauts?


The two particle \( A \) and \( B \) have de Broglie wavelengths 1 nm and 5 nm respectively. If mass of \( A \) is 4 times that of mass of \( B \)
the ratio of KE of \( A \) and \( B \) would be:
A . 5:
B. 25: 4
\( c \cdot 20: 1 \)
D. 5: 4


Some substances and their uses are
given in the table. Match them suitably.
Substance
Antacids Pesticide
Benedict's solution \( \quad \) To test glucose
Thermosetting \( \quad \) To give blue colour to Plastics
cobalt toxide
Tobacco extract \( \quad \) To reduce acidity


\( 5^{t h} \) term from the end in the expansion
of \( \left(\frac{x^{2}}{2}-\frac{2}{x^{2}}\right)^{12} \) is
B . \( 7920 x^{4} \)
c. \( 7920 x^{-4} \)
D. \( -7920 x^{4} \)


The oxidation state of Fe in browns ring
complex \( \left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5} \mathrm{NO}^{+}\right] \mathrm{SO}_{4} \) is:
\( A \cdot+1 \)
\( B \cdot+2 \)
\( c \cdot+3 \)
\( D \cdot+4 \)


A potentiometer wire has length \( 4 \mathrm{m} \) and resistance \( 8 \Omega . \) The resistance that
must be connected in series with the
wire and an accumulator of e.m.f \( 2 \mathrm{V}, \) so as to get a potential gradient \( 1 \mathrm{mV} \) per \( \mathrm{cm} \) on the wire is
A . \( 44 \Omega \)
B. \( 48 \Omega \)
\( c .32 \Omega \)
D. \( 40 \Omega \)


A lake with an inflow of domestic
sewage rich in organic waste may result in:
A. Drying of the lake very soon due to algal bloom.
B. An increased production of fish due to lot of nutrients
c. Death of fish due to lack of oxygen.
D. Increased population of aquatic food web organisms.


Edaphology is connected with
A. Plant and biosphere
B. Soil and living microorganisms
C. Animals and ecosystem
D. Soil and biosphere


Which statements is true in case of
catalyst?
This question has multiple correct options
A. The catalyst is unchanged chemically at the end of a reaction.
B. The catalyst accelerated the reaction.
C. In a reversible reaction, the catalyst alters the equilibrium position.
D. A small amount of catalyst is often sufficient to bring about a large change in reaction.


Draw a line segment of 6cm and divide it in the ratio 3: 2


Select the correct sequence of light entering the different parts of human
eye
A. Cornea, lens, iris, pupil, retina
B. Pupil, cornea, iris, lens, retina
c. cornea, pupil, iris, lens, retina
D. Cornea, iris, pupil, , lens, retina


A current of 1 A through a coil of inductance of \( 200 \mathrm{mH} \) is increasing at
a rate of \( 0.5 \mathrm{A} s^{-1} \). The energy stored in
the inductor per second is then
A. 0.5 J \( s^{-1} \)
B. 5.0 Js \( ^{-1} \)
c. \( 0.1 \mathrm{Js}^{-1} \)
D. 2.0 Js \( ^{-1} \)


What is the enthalpy of vaporisation of
liquid water in \( k J \) mol \( ^{-1} \) if:
\( (\mathrm{i}) \boldsymbol{H}_{2}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{H}_{2} \boldsymbol{O}(l)+ \)
\( 285.77 k J m o l^{-1} \)
\( (\text { ii }) \boldsymbol{H}_{2}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{v})+ \)
\( 241.84 k J \) mol \( ^{-1} \)
\( \mathbf{A} \cdot+43.93 \)
B . -43.93
c. +527.61
D. -527.61


A medicine-capsule is in the shape of a cylinder of diameter \( 0.5 \mathrm{cm} \) with two hemispheres stuck to each of its ends. The length of entire capsule is \( 2 \mathrm{cm} . \) The capacity of the capsule is
A \( \cdot 0.36 c m^{3} \)
в. \( 0.35 \mathrm{cm}^{3} \)
\( \mathrm{c} \cdot 0.34 \mathrm{cm}^{3} \)
D. \( 0.33 c m^{3} \)


Consider the following equilibrium
\( A g C l \downarrow+2 N H_{3} \rightleftharpoons\left[A g\left(N H_{3}\right)_{2}\right]^{+}+ \)
\( \boldsymbol{C l}^{-} . \) White precipitate of of \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l} \)
appears on which of the following?
A \( \cdot N H_{3} \)
B. Aqueous NaCl
c. Aqueous \( H N O_{3} \)
D. Aqueous \( N H_{4} C l \)


Velocity versus time graph of a ball of mass \( 50 \mathrm{g} \) rolling on a concrete floor is shown in the figure. Calculate the acceleration
A . \( -10 m s^{-2} \)
B . \( -20 m s^{-2} \)
c. \( -30 m s^{-2} \)
D. \( -40 m s^{-2} \)


Find the value of \( x^{3}+7 x^{2}-x+16 \)
when \( \boldsymbol{x}=\mathbf{1}+\mathbf{2} \boldsymbol{i} \)
\( \mathbf{A} \cdot-11+24 i \)
B . \( -17+24 i \)
c. \( -17-24 i \)
D. \( -1+24 i \)


An electric field \( \overrightarrow{\boldsymbol{E}}=\mathbf{4} \boldsymbol{x} \hat{\boldsymbol{i}}-\left(\boldsymbol{y}^{2}+\right. \)
1) \( \hat{j} N / C \) passes through the box shown
in figure. The flux of the electric field
through surfaces \( A B C D \) and \( B C G F \)
are marked as \( \phi_{I} \) and \( \phi_{I I} \) respectively.
The difference between \( \left(\phi_{I}-\phi_{I I}\right) \) is \( ( \) in
\( \left.N m^{2} / C\right) \)


In which of the following the bond angle
is maximum:
A \( . H_{2} O \)
в. \( H_{2} \).
\( c \cdot S O_{2} \)
D. \( S O_{3} \)


What is the order of reactivity of hydrogen atoms attached to the carbon atom in an alkane for free radical
substitution?
\( \mathbf{A} \cdot 3^{\circ}>1^{\circ}>2^{\circ} \)
В . \( 2^{\circ}>1^{\circ}>3^{\circ} \)
c. \( 3^{\circ}>2^{\circ}>1^{\text {о }} \)
D. \( 1^{\circ}>2^{\circ}>3^{\circ} \)


When propyne is treated with dilute sulphuric acid in presence of mercury
(II) sulphate, the major product is:
A. acetone
B. propene
c. propanol
D. propanal


op
Q Type your question
direction. The number of turns is \( n \) and
the cross sectional area of the coil is \( A \)
When the coil turns through \( 180^{\circ} \) about
its diameter, the charge flowing through the coil is \( Q \). The total
resistance of the circuit is \( R \). What is
the magnitude of the magnetic
induction?
\( ^{A} \cdot \frac{Q R}{n A} \)
в. \( \frac{2 Q R}{n A} \)
c. \( \frac{Q n}{2 R A} \)
D. \( \frac{Q R}{2 n A} \)


The resistance of \( \frac{1}{10} \mathrm{M} \) solution is \( 2.5 \times \) \( 10^{3} \) ohm. What is the molar conductivity
of solution? (cell constant= \( 1.25 \mathrm{cm}^{-1} \) )
A. 3.5 ohm \( ^{-1} c m^{2} \) mol \( ^{-} \)
B. 5.0 ohm \( ^{-1} c m^{2} \) mol \( ^{-} \)
c. 2.5 ohm\( ^{-1} \mathrm{cm}^{2} \) mol \( ^{-1} \)
D. 2.0 ohm \( ^{-1} \mathrm{cm}^{2} \) mol-


Complete the following, so as to make a
true statement:

The number of pairs of opposite angles of a quadrilateral is


In the extraction of copper, the smelt
formed in the blast furnace contains:
A. \( C u_{2} S+ \) little \( F e S \)
в. \( C u_{2} S+ \) little \( F e O \)
c. \( C u_{2} O+ \) little \( F e S \)
D. \( C u_{2} O+ \) little \( F e O \)


Evaluate: \( \lim _{n \rightarrow \infty} \frac{1+3+5+\ldots . n t e r m s}{2+4+6+\ldots n t e r m s} \)
\( A \cdot 2 \)
в.
\( c \cdot 3 \)
D.


What is the value of inductance \( L \) for
which the current flowing is maximum in a series LCR circuit with \( C=10 \mu F \)
and \( \omega=1000 s^{-1} ? \)
A. \( 100 m H \)
в. \( 1 m H \)
c. Cannot be calculated unless \( R \) is known
D. \( 10 m H \)


Give reasons why copper is used to make hot water tanks and not steel (an
alloy of iron).


If \( E_{F e^{2+} / F e}^{+} \) is \( x_{1}, E_{F e^{3+} / F e}^{+} \) is \( x_{2} \) then
what will be \( \boldsymbol{E}_{\boldsymbol{F} e^{+} / \boldsymbol{F} e^{2+}}^{\boldsymbol{?}} \)


Calculalte R,when \( \boldsymbol{R}= \) \( \sqrt{A^{2}+B^{2}+2 A B \cos \theta} \) given that, \( A=6 \)
\( \mathrm{m}, \mathrm{B}=8 \mathrm{m} \) and angle is \( 60^{0} \)


A closed bulb capacity 200ml
containing \( \boldsymbol{C H}_{4}, \boldsymbol{H}_{2} \) and He at \( 300 \mathrm{K} \)
The ratio of partial pressure of \( \boldsymbol{C} \boldsymbol{H}_{4}, \boldsymbol{H}_{2} \) and He, respectively is 2:3:5. Calculate
the ratio of their weights present in the container.
A. 2: 4: 6
B . 16: 8: 100
\( c \cdot 16: 3: 10 \)
D. 4:9:25


BOD is measure of.
A. Industrial waste being poured in water body
B. Extent of pollution with organic compounds
C. \( \mathrm{CO} \) combined with haemoglobin
D. \( O_{2} \) required by green plants during night


Two charge are brought near then:
A. The P.E. of system of charge increases
B. The P.E. of system of charge decreases
C. The P.E. of system of charge may increases
D. The P.E. of system of charge remain constant


The intensity of radiation emitted by to \( \operatorname{star} A A \) and \( B \) are in the ratio of 16: 1
The wavelength corresponding to their peak emission of radiation will be the ratio of :
A .2: 1
B . 4: 1
c. 1: 2
D. 16: 1


For hydrogen-oxygen fuel cell, the cell reaction is:
\( \mathbf{2} \boldsymbol{H}_{\mathbf{2}}(\boldsymbol{g})+\boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \)
If \( \Delta G_{f}^{o}\left(H_{2} O\right)=-237.2 k J m o l^{-1}, \) then
emf of this cell is:
A . \( +2.46 V \)
в. \( -2.46 V \)
c. \( +1.23 V \)
D. \( -1.23 V \)


Identify the wrong combination.
A. Dryopteris - Rhizome
B. Cycas - Coralloid roots
c. Volvox - Colonial form
D. Marchantia - Pseudo elaters


The line joining two points \( A(2,0) \) and
\( B(3,1) \) ir rotated about \( A \) about in the anticlock wise direction through an
angle of \( 15^{\circ} . \) The equation of the line in the new position is:
A \( . x-\sqrt{3} y-2=0 \)
В. \( x-2 y-2=0 \)
c. \( \sqrt{3} x-y-2 \sqrt{3}=0 \)
D. \( \sqrt{2} x-y-2 \sqrt{2}=0 \)


A force \( \overrightarrow{\boldsymbol{F}}=(\mathbf{5} \hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}} 2 \hat{\boldsymbol{k}}) \boldsymbol{N} \quad \) is
applied over a partivle which displaces it from its origin to the point \( \vec{r}= \) \( (2 \hat{i}-\hat{j}) m . \) The work done on the particle in joules is then
A . -7
B. +7
\( c \cdot+10 \)
D. +13


A trust fund has Rs. 30,000 that must
be invested in two different type of bounds the fist bond pays \( 5 \% \) interest
per year and the second bond pays \( 7 \% \) interest per yer using matrix multiplication determine how to divide Rs.30,000 among the two type of bound if the trust fund must obtain an annual
total interest of
a)Rs.1800


A pure germanium crystal at absolute zero is:
A. An insulator.
B. A good conductor.
c. A semiconductor
D. None of the above


Assertion
The solubility of ammonium chloride increases with increase in temperature
Reason In case of substances whose solubility increases with increase in temperature is due to the dissolution process being endothermic.
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 function of urea being produced as an excretory material in mammals and
sharks is that
A. It raises the pH level of the blood
B. It sends signals from cells that produce it to other organs
c. It provides energy to some cells and tissues
D. It prevents ammonia from building up in the body
E. It eliminates water from the bloodstream


DNA replication occurs in which of the following stages?
A. \( G_{0} \) and \( G_{1} \)
B. \( G_{2} \) stage
c. s stage
D. Mitotic phase


In the reaction
\[
\left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{C}-\boldsymbol{O}-\boldsymbol{C H}_{2} \boldsymbol{C H}_{3}+
\]
\[
\begin{array}{c}
\boldsymbol{H I} \\
(\mathbf{1 m o l e})
\end{array}
\]
the product(s) formed is(are):
\( A \)
\[
\left(C H_{3}\right)_{3} C-O H \text { and } C H_{3} C H_{2} I
\]
в.
\[
\left(C H_{3}\right)_{3} C-I \text { and } C H_{3} C H_{2} O H
\]
c. \( \left(C H_{3}\right)_{3} C-I \) and \( C H_{3} C H_{2} I \)
D.
\[
\begin{array}{ccc}
C- & O^{+} & -C H_{2} C H_{3} I
\end{array}
\]
\[
\left(C H_{3}\right)_{3}
\]


The solution of the differential equation
\( x d x+y d y=0 \) is \( f(x, y)=c \) passes
through (1,1) then value of \( c \) is :
\( A \cdot-2 \)
B. 2
\( c .-1 \)
D.


Which of the following reactions will not
yield phenol?
\( A \)
B.
\( c \)
D.


Net Capacitance of three identical in
series is \( 1 \mu F \). What will be their net
capacitance, if connected in parallel?
Find the ratio of energy stored in the two configurations, if they are both connected to the same source.


The characteristic not associated with
Planck's theory is:
A. radiations are associated with energy
B. the magnitude of energy associated with a quantum is proportional to frequency
C. radiation energy is neither emitted nor absorbed continuously
D. radiation energy is neither emitted nor absorbed discontinuously


\( N_{2}(g)+3 H_{2}(g) \rightleftharpoons 2 N H_{3}(g) \)
For the reaction initially the mole was 1
3 of \( N_{2} \) and \( H_{2} . \) At equilibrium \( 50 \% \) of each has reacted. If the equilibrium pressure is \( p, \) the partial pressure of
\( N H_{3} \) at equilibrium is :
A \( \cdot \frac{p}{3} \)
в. \( \frac{p}{4} \)
c. \( \frac{p}{6} \)
D. \( \frac{p}{8} \)


The correct statement(s) about the
compound is/are:
This question has multiple correct options
A. The total number of meso compounds possible for \( x \) are 2
B. R,R-cis stereo isomer of \( X \) is enantiomer of \( S \), S-cis stereo isomer of the same compound.
c. If the stereo chemistry about the double bond in \( x \) is trans, the number of enantiomers possible for \( x \) is 4
D. If the stereo chemistry about the double bond in \( x \) is cis, the number of enantiomers possible for \( x \) is 2


A decimolar solution of potassium ferrocyanide is \( 50 \% \) dissociated at 300
K. Calculate the osmotic pressure of the
solution.


What are magnetic field lines with the properties give direction of magnetic field for a point and an electric dipole


Find out relation between \( \boldsymbol{I}_{1} \) and \( \boldsymbol{I}_{2} \)
Where \( I_{1} \) and \( I_{2} \) moment of inertia of a
rigid body mass \( m \) about an axis as
shown in the figure.


The idealized P-V diagram above shows
a complete cycle through compression
and expansion of a gas. The questions below relate to the processes within the
cycle.
Which letter shows isothermal
compression?
\( A \)
B. B
\( c \cdot c \)
\( D . \) D
\( E \)


Find the slope of the line joining the
points \( (2 a, 3 b) \) and \( (a,-b) \)


The conductivity of a saturated solution of \( B a S O_{4} \) is \( 3.06 \times 10^{-6} \) ohm \( ^{-1} c m^{-1} \)
and its molar conductance is \( 1.53 o h m^{-1} c m^{-1} m o l^{-1} \) the \( K_{s p} \) of
\( B a S O_{4} \) will be ?
A \( \cdot 4 \times 10^{-12} \)
В. \( 2.5 \times 10^{-9} \)
c. \( 2.5 \times 10^{-13} \)
D. \( 4 \times 10^{-6} \)


Assertion
Equivalent mass of \( K M n O_{4} \) is equal to
one-fifth of its molecular mass when it
acts as an oxidisng agent in acidic medium.
Reason
Oxidation number of \( M n \) in \( K M n O_{4} \) is
+7
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


An open knife edge of mass \( M \) is
dropped from a height \( h \) on a wooden
floor. If the blade penetrates distance in to the wood, the average resistance offered by the wood to the blade is
A. \( M g \)
в. \( M g\left(1+\frac{h}{s}\right) \)
c. \( \operatorname{Mg}\left(\frac{1-h}{s}\right) \)
D. \( M g\left(\frac{1+h}{s}\right)^{ } \)


The image formed by a plane mirror is :
A. at the same distance behind the mirror as the object is in front of it
B. Iaterally inverted
c. of the same size as that of the object
D. all of the above


Match the items in column I and
column II and choose the correct option.
II Column Lid
Biomagnificatror
Eutrophication \begin{tabular}{lll|l|l}
& \multicolumn{2}{l} { Column I } & \multicolumn{2}{l} { Colu } \\
& & & \\
A. & UV & (i) & Bion \\
B. & Biodegradable & (ii) & Eutro \\
C. & DDT & (iii) & Snow \\
D. & Phosphates & (iv) & BOD \\
\hline
\end{tabular} Snow blindness
\( A \)
A-(ii),B-(i), C-(iv), D-(iii)
в. \( A-(\| I), B-(i i), C-(i v), D-(i) \)
\( c \)
A-(iii), B-(iv), C-(i), D-(ii)
B-(i), C-(iv),
D. A-(iii) D-(ii)


a) How are work, force and distance
related.
b) Find the work done by a pulley when
it lifts a block which is 5 m off the
ground with a \( 10 \mathrm{N} \) force.


During one Krebs cycle, number of \( C O_{2} \) molecules released are
\( A \)
B. 2
\( c \cdot 3 \)
D. 4


A dextrorotatory compound:
A. must have a dextrorotatory enantiomer
B. may have a dextrorotatory enantiomer
C. must have a laevorotatory enantiomer
D. may have a laevorotatory enantiomer


Which of the following statements are
correct?
This question has multiple correct options
\( \mathbf{A} \cdot O_{2}^{+} \) has higher bond energy than \( O_{2} \)
B. Bond length of \( O_{2} \) is \( 0.121 n m \) and bond length of \( O_{2}^{-} \) is \( 0.112 n m \)
C. The hybrid orbitals of \( C \) in \( C O \) can be shown by \( (s p)^{2}(s p)^{0}\left(p_{x}\right)^{1}\left(p_{y}\right)^{1} \)
D. Bond dissociation energy of \( C l_{2} \) is greater than \( F_{2} \)


Find the greatest and the least values of the following functions. \( f(x)=\sin x+\cos 2 x \) on the interval
\( [\mathbf{0}, \boldsymbol{\pi}] \)


\( \mathrm{ff}=\left[\begin{array}{ccc}\boldsymbol{a} & \mathbf{0} & \mathbf{0} \\ {[\mathbf{0 . 3 e m}] \mathbf{0}} & \boldsymbol{a} & \mathbf{0} \\ {[\mathbf{0 . 3 e m}] \mathbf{0}} & \mathbf{0} & \boldsymbol{a}\end{array}\right], \) then the value
of |A| |Adj. A|
A \( \cdot a^{3} \)
в. \( a^{6} \)
\( c \cdot a^{9} \)
\( \mathbf{D} \cdot a^{2} \)


Two concentric shells have radii R and
2R charges \( \boldsymbol{q}_{A} \) and \( \boldsymbol{q}_{B} \) and potentials \( 2 \mathbf{V} \) and (3/2) V respectively. Now shell B is earthed and let charges on
them become \( \boldsymbol{q}_{A}^{\prime} \) and \( \boldsymbol{q}_{B} \) '. Then :
This question has multiple correct options
A \( \cdot q A / q B=1 / 2 \)
B \( \cdot q A^{\prime} / q B^{\prime}=1 \)
c. potential of A after earthing becomes (3/2)
D. potential difference between A and B after earthing becomes V/2


Transform \( 2 x-3 y+5=0 \) to the
parallel axes through the point (2,-3)


The bob of a pendulum of mass \( \mathrm{m} \) and length I and a charge of q is in the rest position in a uniform horizontal electric field of E. The tension in the string of the
pendulum is :
A . \( m g \)
в. \( q E \)
c. \( \left[(m g)^{2}+(q E)^{2}\right]^{1 / 2} \)
D \( \cdot\left[(m g)^{2}+(q E)^{2}\right]^{1 / 4} \)


Nucleic acids are found in which of the
following?
A. Nucleus
B. Cytoplasm
c. Both nucleus and cytoplasm
D. Nucleus and ribosomes


(i) Give two examples of macromolecules that are chosen as
drug targets.
(ii) What are antiseptic? Give an example.
(iii) Why is use of aspartame limited to cold foods and soft drinks?


The atomic mass of an element is 133
and number of neutrons is \( 41.8 \% \) more
than number of protons. Find the number of unpaired electrons.


Working of electric bells is an example
of
A. Mechanical effect of electric current
B. Heating effect of electric current
c. Magnetic effect of electric current
D. None of these


Two current-carrying parallel conductors are shown in the figure. The
magnitude and nature of force acting between them per unit length will be :
A \( \cdot 8 \times 10^{-8} N / m, \) attractive
B. \( 3.2 \times 10^{-5} N / m \), repulsive
c. \( 3.2 \times 10^{-5} N / m \), attractive
D. \( 8 \times 10^{-8} N / m \), repulsive


Find the correct order of life process in
plants.
A. Pollination \( \rightarrow \) Fertilisation \( \rightarrow \) Plant \( \rightarrow \) Embryo
B. Plant \( \rightarrow \) Embryo \( \rightarrow \) Fertilisation \( \rightarrow \) Pollination
c. Pollination \( \rightarrow \) Fertilisation \( \rightarrow \) Embryo \( \rightarrow \) Plant
D. Embryo \( \rightarrow \) Pollination \( \rightarrow \) Fertilisation \( \rightarrow \) Plant


Make \( r \) the subject of formula.
A \( \cdot_{r}=\sqrt{\frac{\pi R^{2} l+V}{\pi l}} \)
в. \( r=\sqrt{\frac{\pi R^{2} l-V}{\pi l}} \)
c. \( _{r}=\sqrt{\frac{\pi R^{2} l+V}{2 \pi l}} \)
D. none of the above


Ampere-second stands for the unit of
A. Power
B. Charge
c. e.m.f.
D. Energy


Social forestry is
A. Planting of different kinds of trees in the same area
B. Greening of hills with the efforts of common men
C. Raising trees on common village lands and other vacant areas of fodder, minor timber and fire wood
D. None of the above


\( \gamma \) -globulins are synthesized inside
A. Liver
B. Kidney
\( c . \) Bone
D. Thyroid


\( \ln L i^{++}, \) electron in first Bohr orbit is
excited to a level by a radiation of wavelength \( \lambda \). when the ion gets
deexcited to the ground state in all possible ways (including intermediate emissions), a total of six spectral lines are observed. What is the value of \( \lambda \) ?
(Given \( : \boldsymbol{h}=\mathbf{6 . 6 3} \times \mathbf{1 0}^{\mathbf{3 4} \mathbf{J}} \mathbf{s} ; \quad \mathbf{l}, \mathbf{c}=\mathbf{3} \)
ltimes \( 10^{\wedge} 8 \mathrm{ms}^{\wedge}\{-13 \$ \$) \)
\( \mathbf{A} \cdot 9.4 n m \)
в. \( 12.3 n m \)
\( c .10 .8 n m \)
D. \( 11.4 n m \)


Find the values of \( k \) so that the function
\( f \) is continuous at the indicated point:
\[
\boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{ll}
\boldsymbol{k} \boldsymbol{x}^{2}, & \text { if } \boldsymbol{x} \leq \boldsymbol{\pi} \\
\cos \boldsymbol{x}, & \text { if } \boldsymbol{x}>\pi
\end{array}\right.
\]
at \( \boldsymbol{x}=\boldsymbol{\pi} \)


Which of the following helps in differentiation of cells of immune
system?
A. cortisol
B. Thyroxine
c. Thymosin
D. steroid


The resistance of the meter bridge \( A B \)
is given figure is 4 \Omega. With a cell of emf
\( \varepsilon=0.5 V \) and rheostat resistance
\( R h=2 \Omega \) the null point is obtained at
some point \( J . \) When the cell is replaced
by another one of emf \( \varepsilon=\varepsilon_{2} \) the same
null point \( J \) is found for \( R_{h}=6 \Omega \). The
emf \( \varepsilon \) is
A \( .0 .6 ~ V \)
B. \( 0.5 V \)
c. \( 0.3 V \)
D. \( 0.4 V \)


When \( I^{-} \) is oxidized by \( M n O_{4}^{-} \) in
alkaline medium, \( I^{-} \) is converted into
\( A \cdot I O_{3}^{-} \)
в. \( I_{2} \)
\( \mathbf{c} \cdot I O_{4}^{-3} \)
D. IO


Why are non-metals not ductile?
A. They are hard
B. They are soft
C. They are brittle
D. All of above


The voltage induced across a certain
coil is \( 200 m V . A 120 \Omega \) resistor is
connected to the coil terminals. The
induced current is
A \( .1 .7 m A \)
в. \( 16 m A \)
c. \( 12 m A \)
D. \( 120 m A \)


Which of the following are correct about
Langmuir adsorption isotherm at a very
high pressure?
This question has multiple correct options
A. It is valid for chemisorption.
B. \( \frac{x}{m}=\frac{a}{b} \)
\( ^{\mathbf{C}} \cdot \ln \frac{x}{m}=\frac{\Delta S^{\circ}}{R}-\frac{\Delta H^{\circ}}{R T} \)
D. At very high pressure, rate of adsorption \( > \) rate of desorption.


Factorize \( 16 x^{6}-8 x^{3} y^{3}+y^{6} ? \)
A \( \cdot\left(4 x^{3}-y^{3}\right)^{2} \)
B. \( \left(4 x^{3}+y^{3}\right)^{2} \)
\( \mathbf{c} \cdot(4 x+y)^{6} \)
D. \( \left(16 x^{2}+y\right)^{2} \)


A negligibly small current is passed through a wire of length \( 15 \mathrm{m} \) and uniform cross-section \( 6.0 \times 10^{-7} m^{2} \)
and its resistance is measured to be
5.0\Omega. What is the resistivity of the material at the temperature of the experiment?


Complete the following reactions
\( (i) C r_{2} O_{7}^{2-}+3 S O_{2}+2 H^{+} \rightarrow \)
\( 2 C r^{3+}+_{---}-+H_{2} O \)
\( (i i) 2 M n O_{4}^{-}+5 S O_{3}^{2-}+6 H^{+} \rightarrow \)
\( 2 M N^{2+}+_{---}-3 H_{2} O \)
\( (i i i) C r_{2} O_{7}^{2-}+6 F e^{2+}+14 H^{+} \rightarrow \)
\( 2 C r^{3+}_{---}-7 H_{2} O \)
A \( \cdot 3 S O_{4}^{2-}, S O_{2}^{2-}, F e^{3+} \)
B \( \cdot 3 S O_{4}^{2-}, 5 S O_{4}^{2-}, 6 F e^{3+} \)
\( \mathrm{c} \cdot 3 \mathrm{SO}_{4}^{2-}, \mathrm{SO}_{2}, \mathrm{K}^{+} \)
D. \( S, S O_{2}, F e^{3+} \)


f \( \sum_{r=1}^{n} t_{r}=\frac{1}{12} n(n+1)(n+2), \) then the
value of \( \sum_{r=1}^{n} \frac{1}{t_{r}} \) is
A \( \cdot \frac{2 n}{n+1} \)
в. \( \frac{n}{(n+1)} \)
c. \( \frac{4 n}{n+1} \)
D. \( \frac{3 n}{n+1} \)


Find \( \boldsymbol{A}^{\boldsymbol{T}}: \)
\( \boldsymbol{A}=\left[\begin{array}{lll}\mathbf{4} & \mathbf{3} & \mathbf{- 1} \\ \mathbf{6} & \mathbf{8} & \mathbf{- 3} \\ \mathbf{4} & \mathbf{1} & \mathbf{3}\end{array}\right] \)


Consider a film of thickness \( L \) as shown
in four different cases below. Notice the
observation of film with perpendicularly falling light. Mark the correct statement(s). (Take \( L=1.5 \lambda) \)
This question has multiple correct options
A. For (1) and (2), the reflection at film interfaces causes zero phase difference for two reflected rays
B. For 92 ) and (3), the reflection at film interfaces causes phase difference of \( \pi \) for two reflected rays
C. For (1) , the film will appear dark, if it is observed through reflected rays from film interfaces
D. For
(3), the film will appear dark, if it is observed through reflected rays from film interfaces


Point where whole weight of body acts vertically is called
A. center of mass
B. mid point
c. center of gravity
D. none of above


The \( \left[\boldsymbol{H}_{3} \boldsymbol{O}^{+}\right] \) in a solution having \( \left[\boldsymbol{O H}^{-}\right]=\mathbf{5} \times \mathbf{1 0}^{-\mathbf{3}} \boldsymbol{M} \) is:
A \( \cdot 2 \times 10^{-3} \)
B. \( 2 \times 10^{-12} \)
c. \( 5 \times 10^{-3} \)
D. none of these


Transpiration is best defined as
A. loss of water from the plant
B. loss of water as vapour from the plant
C . evaporation of water from the surface of leaves
D. None of the above


Suppose in the previous problem, the
child stays at rest on the platform and one of his friend throws a ball of mass
\( m_{1} \) towards him with a velocity of \( v \)
from a direction tangential to the platform and the child on the platform catches the ball. Find the angular
velocity of the platform after he catches the ball.


Which is true for the far sightedness or hypermetorpia from the following?
A. Eyelense does not become thin as per requirement
B. Distant object cannot be seen clearly
c. Nearby object cannot be seen clearly
D. Defect can be corrected by using concave lens


Two complex numbers are represented by ordered pairs \( z_{1}:(6,4) \& z_{2}:(4,-5) \)
which of the following is imaginary
part of \( z_{1}+z_{2} ? \)
A . -1
B. -6
c. 10
D. None of these


Simplify \( 3 \times(-1) \)
\( A \cdot 3 \)
B. -
c. 1
D. 2


The reciprocal of a negative rational
number is
A. negative
B. positive
c. cannot be determined
D. none


Fill in the blanks:
Force comes into action when
A. objects interact.
B. objects do not interact
c. object move
D. None of these


If \( \boldsymbol{y}=(\mathbf{1}+\boldsymbol{x})\left(\mathbf{1}+\boldsymbol{x}^{\mathbf{2}}\right)\left(\mathbf{1}+\boldsymbol{x}^{\mathbf{4}}\right) \dots \mathbf{.} \)
\( \left.x^{2^{n}}\right), \) then \( \left(\frac{d y}{d x}\right)_{x=0}= \)
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( \frac{1}{2} \)
\( c \cdot 1 \)
\( D \)


Which of the following will have the most negative electron gain enthalphy and which the least negative?
\( A \cdot F, C \)
в. С।,
c. \( \mathrm{Cl} \),
D. CL,


The birth control pills are which kind of drug?
A. analgesics
B. tranquilizers
c. sulphapyridine
D. antifertility


Find the coordinates of the focus,
equation of the directrix and the latus rectum of
\( \boldsymbol{x}^{2}=-2 \boldsymbol{y} \)


Time required to deposit one millimole of aluminium metal by the passage of
9.65 amperes through aqueous solution of aluminium ion is :
A . \( 30 s \)
в. \( 10 s \)
c. \( 30,000 s \)
D. \( 10,000 s \)


If the \( n^{t h} \) term of an A.P. is \( a_{n}=3+2 n \)
then the common difference \( d \) is
A .2
B. 3
\( c \cdot 4 \)
D. 5


A current passes through a wire of non-
uniform crosssection. Which of the
following quantities are independent of the cross-section?
This question has multiple correct options
A. The charge crossing in a given time interval
B. Drift speed
c. Current density
D. Free-electron density


\( Z n+H_{2} S O_{4}(d i l) \rightarrow Z n S O_{4}+H_{2} \uparrow \)
Above reaction is:
A. decomposition reaction
B. displacement reaction
c. combination reaction
D. synthesis reaction


Which of the following is the source of
\( \boldsymbol{S} \boldsymbol{O}_{\boldsymbol{x}} \) pollution?
A) Volcanoes
B) Fossil fuel
C) Thermal power plant
\( A \cdot A \& B \)
B. B \& \( c \)
\( c \cdot c \& A \)
D. \( A, B \& C \)


Identify which of the following wave has the longest frequency?
A. Red light
B. Blue light
c. Gamma rays
D. x rays
E. Radio waves


In the given figure, a circle with centre \( O \) is given in which a diameter \( A B \)
bisects the chord \( C D \) at a point \( E \) such
that \( C E=E D=8 c m \) and \( E B=4 c m \)
Find the radius of the circle.


Consider 3 identical charges of charge
q placed at the vertices of an equilatera triangle, as shown in the figure. What is the force on one of the charges due to
the others?
\( ^{\mathbf{A}} \cdot \frac{1}{4 \pi \epsilon_{0}} \frac{q^{2}}{l^{2}} \)
B. \( \frac{\sqrt{2}}{4 \pi \epsilon_{0}} \frac{q^{2}}{l^{2}} \)
C. \( \frac{\sqrt{3}}{4 \pi \epsilon_{0}} \frac{q^{2}}{l^{2}} \)
D \( \cdot \frac{2 \sqrt{3}}{4 \pi \epsilon_{0}} \frac{q^{2}}{l^{2}} \)


The equation of the progressive wave is \( \boldsymbol{y}=\boldsymbol{a} \sin 2 \pi\left(\boldsymbol{n} \boldsymbol{t}-\frac{\boldsymbol{x}}{\mathbf{5}}\right) . \) The ratio of
maximum particle velocity to wave velocity is
A \( \cdot \frac{\pi a}{5} \)
в. \( \frac{2 \pi a}{5} \)
c. \( \frac{3 \pi a}{5} \)
D. \( \frac{4 \pi a}{5} \)


Fuming nitric acid is:
A . conc. \( H N O_{3}+N O_{2} \)
B. conc. \( H N O_{3}+N O_{3} \)
c. conc. \( H N O_{3}+N 2 O_{3} \)
D. conc. \( H N O_{3}+N O \)


What will be the wave velocity, if the radar gives 54 waves per min and
wavelength of the given wave is \( 10 \mathrm{m} ? \)
\( A \cdot 4 \mathrm{m} \mathrm{s}^{-1} \)
B. \( 6 \mathrm{m} \mathrm{s}^{-1} \)
\( c \cdot 9 m s^{-1} \)
\( D \cdot 5 \mathrm{m} \mathrm{s}^{-1} \)


Calculate the number of grams of
magnesium chloride that could be obtained from 17.0 g of \( H C l \) when \( H C I \)
is reacted with an excess of
magnesium oxide.


If \( y=x \sin y, \) then prove that \( \frac{d y}{d x}= \) \( \frac{\boldsymbol{y}}{\boldsymbol{x}(1-\boldsymbol{x} \cos \boldsymbol{y})} \)


In set of 4 number the first three
number are in \( G P \) and the last three are
in \( A P \) with common different is 6
If first number is same as the fourth
number. Find the numbers


Consider the following two statements \( A \) and \( B \) and identify the correct answer.
A) When the length of a wire is doubled, the Young's modulus of the wire is also doubled
B) For elastic bodies Poisson's ratio is \( + \)
Ve and for inelastic bodies Poissons
ratio is -Ve
A. Both A \& B are true
B. A is true but B is false
c. \( A \) is true but \( B \) is true
D. Both A \& B are false


If \( A \) is a symmetric matrix then \( A^{T}= \)
A. \( A \)
в. \( |A| \)
c. 0
D. diagonal matrix


Estimate the maximum possible
temperature of a Bunsen burnur flame.


How many types of prism are possible
\( A \)
B. 2
\( c \cdot 3 \)
D. \( \infty \)


The vapour pressure of pure liquid is 70
Torr at \( 27^{\circ} \mathrm{C} \). The vapour pressure of a
solution of this liquid and another liquid (mole fraction 0.2) is 84 Torr at
\( 27^{\circ} \mathrm{C} . \) The vapour pressure of pure
liquid \( B \) at \( 27^{\circ} C \) is?
A. 140 Torr
B. 280 Torr
c. 160 Torr
D. 200 Torr


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


dentify the major product in the
following reaction.


A man is walking from east to west on a level rough surface. The force of friction
on the man is directed:
A. from west to east
B. from east to west
c. along the north
D. along the west


In the modern periodic table, magnesium is surrounded by elements with atomic number 4,11,13 and 20 Identify the elements. Which of these have chemical properties resembling magnesium?


The atomic radius of \( A g \) is closed to :
A. \( C u \)
в. \( H g \)
c. \( N i \)
D. \( A u \)


Animals return water to the
environment by
(i) Perspiring
(ii) Drinking
(iii) Urinating
(iv) Breathing
A. (i), (iii) and (iv)
B. (i) and (ii)
c. (i) and (iii)
D. (iii) and (iv)


Solve: \( 4 \cos ^{2} x+6 \sin ^{2} x=5 \)
A \( \cdot x=n \pi+\frac{\pi}{2} \)
B. \( x=n \pi-\frac{\pi}{3} \)
c. \( x=n \pi \pm \frac{\pi}{4} \)
D. None of these


The correct decreasing order of following alkyl halides according to the rate of \( \beta \) - elimination reaction with
alcoholic KOH will be:
\( (\mathrm{i}) C H_{3}-\underset{C H_{3}}{C}^{H}-C H_{2} B r \)
(ii) \( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{B r} \)
(iii) \( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{B r} \)
\( A \cdot(\text { i) }>(\text { ii) }>(\text { iii }) \)
B. (iii) > (ii) > (i)
c. (ii)> (iii) > (i)
D. (i) > (iii) > (ii)


Find the equation of the circle passing through the points (0,-1) and (2,0) and whose centre lies on the line \( 3 x+ \)
\( \boldsymbol{y}=\mathbf{5} \)


\( \ln \operatorname{areaction} 2 H I \rightarrow H_{2}+I_{2}, \) the
concentration of \( H I \) decreases from
0.5 mol \( L^{-1} \) to 0.4 mol \( L^{-1} \) in 10
minutes.What is the rate of reaction
during this interval?
A \( .5 \times 10^{-3} \mathrm{M} \min ^{-1} \)
B . \( 2.5 \times 10^{-3} \mathrm{M} \) min\( ^{-1} \)
c. \( 5 \times 10^{-2} M \) min \( ^{-1} \)
D. 2.5 \( \times 10^{-2} \mathrm{M} \) min\( ^{-1} \)


\( \mathrm{K}_{m} \) is related to
A. Morphology
B. ABO blood group
c. ES complex
D. chromatography


Q Type your question
the surface of Mars it is \( 4.0 m s^{-2} . A 60 \)
kg passenger goes from the Earth to the
Mars in a spaceship moving with a constant velocity. Neglect all other
objects in the sky. Which part of figure
best represents the weight (net gravitational force) of the passenger as
a function of time.??
\( A \)
B. B
\( c \cdot c \)
\( D \)


Find the mean number of heads in three
tosses of a fair coin.


In producing chlorine through electrolysis 100 watt power at 125 V is being consumed. How much chlorine
per minute is liberated?

Electrochemical Equivalent of chlorine is \( 0.367 \times 10^{-6} \) kg/coulomb:
A. \( 21.3 \mathrm{mg} \)
в. \( 17.6 \mathrm{mg} \)
c. \( 24.3 \mathrm{mg} \)
D. \( 13.6 \mathrm{mg} \)


If relative decrease in \( \mathrm{V} . \mathrm{P} \) is 0.4 for \( \mathrm{a} \)
solution containing 1 mol \( N a C l \) in 3
mol of \( \mathrm{H}_{2} \mathrm{O} \). Calculate \( \% \) ionization of
NaCl.
A . 100
B. 95
c. 90
D. 85


Hyperventilation is
A. Extra deep breathing
B. Rapid breathing
C . Rapid shallow breathing
D. Rapid deep breathing


f \( y=\cos 2 x \cos 3 x, \) then \( y_{n} \) is equal to
Where, \( y_{n} \) denotes the \( n^{t h} \) derivative of
\( \boldsymbol{y} \)
A \( \cdot 6^{n} \cos \left(2 x+\frac{n \pi}{2}\right) \cos \left(3 x+\frac{n \pi}{2}\right) \)
B. \( \frac{1}{2}\left[5^{\text {n }} \cos \left(\frac{\text { n } \pi}{2}+5 x\right)+\cos \left(\frac{\text { n } \pi}{2}+x\right)\right] \)
c. \( \frac{1}{2}\left[5^{\mathrm{n}} \sin \left(5 x+\frac{\mathrm{n} \pi}{2}\right)+\sin \left(x+\frac{\pi}{2}\right)\right] \)
D.


The addition compounds which lose their identity in solution are called:
A. normal salts
B. double salts
c. complex compounds
D. co-ordination compounds


An object drop from a with a constant
acceleration of \( 10 m / s^{2} . \) Find its speed
2 sec after it was dropped.


Find the variance of numbers obtained
on thrown an unbiased die.


Solve
\( \boldsymbol{x}+\boldsymbol{y}=\mathbf{3} \)
\( \boldsymbol{x}-\boldsymbol{y}=\mathbf{1} \)


A vector \( \vec{A} \) has magnitude of 3 units and it points towards east while another vector \( \vec{B} \) has magnitude of 4 units and it points towards north.The ratio between \( \vec{A} \cdot \vec{B} \) and \( |\vec{A} \times \vec{B}| \) is:
A . 1:
B. 1:
c. 0: 12
D. 12:0


A boy wants to buy new shoes. To find
out his correct shoe size the
of his feet should
be measured
A. Length
B. Thickness
c. Area
D. volume


The \( 4^{t h} \) and \( 10^{t h} \) terms of an AP are 13
and 25 respectively. Find the first term
and the common difference of the AP.
Also, find its \( 17^{t h} \) term.


The slope and y-intercept of the following line are respectively
\( 4 x-y=0 \)
A. slope \( =m=4 \) and \( y- \) intercept \( =0 \)
B. slope \( =m=-4 \quad \) and \( \quad y- \) intercept \( =0 \)
C \( . \) slope \( =m=1 / 4 \) and \( y- \) intercept \( =0 \)
D. slope \( =m=0 \) and \( y- \) intercept \( =1 / 4 \)


If \( \boldsymbol{y}=\tan ^{-1}\left(\frac{1+\boldsymbol{x}^{2}}{1-\boldsymbol{x}^{2}}\right) \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=? \)
A. \( \frac{2 x}{\left(1+x^{4}\right)} \)
B. \( \frac{-2}{\left(1+x^{4}\right)} \)
c. \( \frac{x}{\left(1+x^{4}\right)} \)
D. none of these


Polyphosphates are used as water softening agents because they:
A. form soluble complexes with anionic species
B. precipitate anionic species
C. form soluble complexes with cationic species
D. precipitate cationic species


In the manufacture of acetic acid from
aerial oxidation of acetaldehyde, the catalyst used is :
A . acidified \( K_{2} C r_{2} O_{7} \)
в. \( \left(C H_{3} C O O\right)_{2} M n \)
\( \mathrm{c} \cdot \mathrm{HgSO}_{4} \)
D. \( N i \)


The oscillations about a systems equilibrium position that occur in the absence of an external excitation are
This question has multiple correct options
A. free vibrations
B. damped vibrations
c. natural vibrations
D. None of these


Arrange the following in increasing
order of their acidic strength.
\( \mathbf{A} \cdot I I I<I<I V<I I \)
В . \( I I<I<I V<I I I \)
\( \mathbf{c} \cdot I<I I I<I V<I I \)
D . \( I I<I I I<I<I V \)


Match the column:


\( 20 \mathrm{ml} \) of \( H_{2} O_{2} \) after acidification with
\( \operatorname{dil} H_{2} S O_{4} . \) required \( 30 \mathrm{ml} \) of \( \mathrm{N} / 2 \)
\( K M n O_{4} \) for complete oxidation
Calculate the \( \% \) of \( H_{2} O_{2} \) in g/lit.
A . 10.75 g/lit
B. 11.75 g/lit
c. \( 12.75 \mathrm{g} / \) lit
D. 13.75 g/lit


Find the maximum and minimum
distances between the bars during the subsequent motion of the system, if the
masses of the bars are equal to \( m_{1} \) and
\( m_{2}, \) and the force \( F \) is applied to the bar
of mass \( \boldsymbol{m}_{2} \)


Copper and Germanium are cooled from
room temperature to \( 100 K . \) Then the
resistance of
A. Germanium decreases, Copper increases
B. Germanium decreases, Copper decreases
c. Germanium increases, Copper decreases
D. Germanium increases, Copper increases


Statement I : Ammonia has a trigonal pyramidal molecular geometry. Statement II : Ammonia has a
tetrahedral electron pair geometry with the three atoms bonded to the central
atom
A. true, true, correct explanation
B. true, true, not correct explanation
c. true, false
\( \mathbf{D} \cdot \) false, true


Calculate the distance between the
points (-3,6,7) and (2,-1,4) in \( 3 D \)
space.
A . 4.36
в. 5.92
c. 7.91
D. 9.11
E . 22.25


A field is \( 225 m \) long and \( 175 m \) wide. It
has two roads in its centre of uniform
width of \( 5 m \), one parallel to its length
and the other parallel to its breadth.
Find the cost of levelling the roads at
Rs.3 per square metre.
A \( . \) Rs. 1975
в. \( R s .1125 \)
c. \( R s .592 \)
D. Rs.6125


Which of the following is not optically
active?
\( \mathbf{A} \cdot\left[\operatorname{Co}(e n)_{3}\right]^{3+} \)
B . \( \left[C r(o x)_{3}\right]^{3} \)
c. \( \operatorname{cis}-\left[\operatorname{CoCl}_{2}(e n)_{2}\right] \)
D. \( \operatorname{trans}-\left[\operatorname{CoCl}_{2}(e n)_{2}\right]^{+} \)


If the first term of a GP is 729 and \( 7^{t h} \)
term is \( 64, \) then the sum of its first
seven terms is
A . 2187
в. 2059
\( c .1458 \)
D. 2123
E . 1995


A physical balance has its arms of
length \( 60 \mathrm{cm} \) and \( 40 \mathrm{cm} . \) What weight kept on pan of longer arm will balance an object of weight \( 100 g f \) kept on other pan?
A. \( 33.33 g f \)
\( f \)
в. \( 66.67 g f \)
\( c .50 g f \)
D. \( 16.67 g f \)


Verify Lagrange's mean value theorem for the following function on the indicated interval. In each case find a
point \( ^{\prime} c^{\prime} \) in the indicated interval as
stated by the Lagrange's mean value theorem:
\( \boldsymbol{f}(\boldsymbol{x})=\sin \boldsymbol{x}-\sin 2 \boldsymbol{x}-\boldsymbol{x} \) on \( [\mathbf{0}, \boldsymbol{\pi}] \)


As the temperature of a conductor
increases, its resistivity and
conductivity change. The ratio of resistivity to conductivity
A. increases
B. decreases
c. remains constant
D. may increase or decrease depending on the actual temperature


\( \cos \left[\pi^{2}\right] \theta-\sin [e] \theta=? \)


Find the value of \( \mathrm{m} \) and \( \mathrm{n} \) using cross multiplication method:
\( 3 m+n=15 \) and \( m+2 n=10 \)
\( A \cdot(4,3) \)
B. (-4,3)
\( c \cdot(-4,-3) \)
D. (4,-3)


Based on above isomers answer the
following. Which isomers on dehydration with
conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) give alkene which is capable to show geometrical isomerism?
\( A \cdot g, h, f \)
B. b, d, a
\( c \cdot a, b, c \)
\( D \)
of these


Choose the incorrect statement:
A. Flemings right-hand rule is a simple rule to know the direction of induced current
B. The right-hand thumb rule is used to find the direction of magnetic fields due to current carrying conductors
C. The difference between the direct and alternating currents is that the direct current always flows in one direction, whereas the alternating current reverses its direction periodically
D. In India the AC changes direction after every \( \frac{1}{50} \) second


From three men and two women,
environment committee of two person to be formed.

Condition for event \( \boldsymbol{A} \) : There must be at
least one woman member.
Condition for event \( B: \) One man, one
woman committee to be formed.
Condition for event \( C \) : There should not
be a woman member.


n the figure, an ideal gas changes its
state from state \( A \) to state \( C \) by two
paths \( A B C \) and \( A C \)

The internal energy of gas of \( A \) is \( 30 J \)
and the amount of heat supplied to
change its state to \( C \) through path \( A C \)
is \( 210 J . \) Calculate the internal energy
of gas at \( C \)


In an average soil, the percentage of organic matter is about
A . 20
B. 30
\( c \cdot 45 \)
D.


Name two chemicals used to disinfect
water


The velocity of a particle moving along a straight line increases according to
the linear law \( v=v_{0}+k x, \) where \( k \) is a
constant. Then
This question has multiple correct options
A. the acceleration of the particle is \( k\left(v_{0}+k x\right) \)
B the particle takes a time \( \frac{1}{k} \log _{e}\left(\frac{v_{1}}{v_{0}}\right) \) to attain a velocity \( v_{1} \)
c. velocity varies linearly with displacement with slope of velocity displacement curve equal to \( k \).
D. the acceleration of the particle is zero.


Statement 1: In simple harmonic motion, the motion is to and fro and
periodic.

Statement 2: Velocity of the particle
\( (v)=\omega \sqrt{k^{2}-x^{2}} \) (where \( x \) is the
displacement).
A. Statement 1 is false, Statement 2 is true
B. Statement 1 is true, Statement 2 is true; Statement 2 is the correct explanation for Statement 1
c. statement 1 is true, Statement 2 is true; Statement 2 is not the correct explanation for Statement
D. Statement 1 is true, Statement 2 is false


In mammals, the teeth are
(i) Of different types
(ii) Embedded in the cup-like socket of the jaw bones
(iii) Only two sets, present throughout life
These conditions are referred as
A. Heterodont, thecodont and diphyodont
B. Thecodont, heterodont and diphyodont
c. Diphyodont, thecodont and heterodont
D. Heterodont, diphyodont and thecodont
E. Thecodont, diphyodont and heterodont


The given figure shows the plant for the
formation of an important compound \( \mathbf{X} \)
Identify \( X \)
A. Washing soda
B. Common salt
c. Baking powder
D. Bleaching powder


The vertical component of earth's magnetic field is zero at
A. magnetic equator
B. magnetic poles
c. geographical poles
D. everywhere


A value of \( C \) for which the conclusion of
Mean Value Theorem holds for the
function \( f(x)=\log _{e} x \) on the interval
[1,3] is
\( \mathbf{A} \cdot 2 \log _{3} e \)
B. \( \frac{1}{2} \log _{3} e \)
\( \mathbf{c} \cdot \log _{3} e \)
D. \( 2 \log _{e} 3 \)


Match the Column-I and Column-II:


The speed-time graph for a car is shown in Fig.
(a) Find how far does the car travel in
the first 4 seconds. Shade the area on
the graph that represents the distance travelled by the car during the period.
(b) Which part of the graph represents
uniform motion of the car?


Can you remove the shell of an unboiled egg without boiling, keeping the egg's thin membrane intact? If yes, explain.


If energy( \( E \) ), velocity \( (V) \) and force \( (F) \) be taken as fundamental quantity, then what are the dimension of mass?
A \( . E V^{2} \)
B. \( E V^{-2} \)
\( \mathbf{c} \cdot F V^{-1} \)
D. \( F V^{-2} \)


In an alkaline solution, the following equilibrium exists.
\( S^{2-}+S \leftrightharpoons S_{2}^{2-}, K_{1}=12 \)
\( \boldsymbol{S}_{2}^{2-}+\boldsymbol{S} \leftrightharpoons \boldsymbol{S}_{3}^{2-}, \boldsymbol{K}_{2}=\mathbf{1 1} \)
What is the equilibrium constant for the given equilibrium?
\( S_{3}^{2-} \leftrightharpoons S^{2-}+2 S \)
A \( \cdot 23 \)
в. 132
\( c \cdot 1 / 132 \)
D. \( 1 / 32 \)


What is the type of reaction?
\( \boldsymbol{C H}_{2}-\boldsymbol{C H}-\boldsymbol{C H}_{3}+\boldsymbol{H B r} \rightarrow \)
\( \boldsymbol{C H}_{3} \boldsymbol{C H B r} \boldsymbol{C H}_{3} \)
A. Nucleophilic addition
B. Electrophilic substitution
c. Electrophilic addition
D. Free radial addition


The \( 100^{t h} \) element is named in honor of
A. Einstein
B. Bohr
c. Fermi
D. Curie


A point at a distance of \( \sqrt{6} \) from the origin which lies on the straight line \( \frac{x-1}{1}=\frac{y-2}{2}=\frac{z+1}{3} \) will be
\( \mathbf{A} \cdot(1,-1,2) \)
В. (1,2,-1)
C \( \cdot\left(\frac{5}{7}, \frac{10}{7}, \frac{-13}{7}\right) \)
D. \( \left(\frac{5}{7}, \frac{2}{7}, \frac{-6}{7}\right) \)


Find the missing number:
\( (+6) \times-----(-42) \)


The value of \( \int \frac{x^{2}+1}{x^{4}-x^{2}+1} d x \) is
A \( \cdot \tan ^{-1}\left(2 x^{2}-1\right)+C \)
B. \( \tan ^{-1}\left(\frac{x^{2}-1}{x}\right)+C \)
\( ^{\mathrm{c}} \cdot \sin ^{-1}\left(x-\frac{1}{x}\right)+C \)
D. \( \tan ^{-1} x^{2}+C \)


The total intensity of the earth's magnetic field at equator is 5 units. What is its value at the poles?
A . 5
B. 4
\( c .3 \)
D. 2


The intercept on the line \( y=x \) by the
\( \operatorname{circle} x^{2}+y^{2}-2 x=0 \) is \( A B \)
Equation of the circle with \( A B \) as a
diameter is
A \( \cdot x^{2}+y^{2}+x+y=0 \)
B . \( x^{2}+y^{2}-x-y=0 \)
c. \( x^{2}+y^{2}+x-y=0 \)
D. None of these


What is the main function of lightning conductor?
A. To capture lightning stroke and conduct discharge current safely to the ground
B. To capture lightning stroke and conduct discharge current safely to the cloud
C. To capture lightning stroke and conduct discharge current safely to the building
D. None


The velocity of a particle moving in straight line depends on its position \( x \)
w.r.t. to fixed origin according to the relation \( 16 x^{2}+4 v^{2}=9 . \) The
acceleration of particle when it is at
\( x=2 m \) is:
A \( .-2 m / s^{2} \)
B. \( -8 m / s^{2} \)
c. \( -6 m / s^{2} \)
D. Not defined


Find the value of \( \cos \left(\sec ^{-1} x+\right. \)
\( \left.\operatorname{cosec}^{-1} x\right),|x| \geq 1 \)


Which of the two tautomers is more
stable?
\( A \)
\( B \)
c. \( I=I I \)
D. None of these


Choose the correct answers from the
alternatives given The prokaryotic genetic system contains:
A. either DNA or histones
B. DNA but no histones
c. neither DNA nor histones
D. DNA and histones


Paramagnetism of oxygen is explained on the basis of which of the following electronic configuration?
A \( \cdot\left(2 \pi^{*} p y\right)^{1}\left(2 \pi^{*} p z\right)^{1} \)
B . \( \left(2 \pi^{*} p x\right)^{1}\left(2 \pi^{*} p y\right)^{1} \)
C \( \cdot(2 \sigma p x)^{1}(2 \pi p y)^{1} \)
D. \( (2 \sigma p y)^{1}(2 \pi p y)^{1} \)


In Boolean algebra \( \boldsymbol{A} . \boldsymbol{B}=\boldsymbol{Y} \) implies
that:
A. product of \( A \) and \( B \) is \( Y \)
B. \( Y \) exists when \( A \) exists or \( B \) exists
c. \( Y \) exists when both \( A \) and \( B \) exist but not when only \( A \) or \( B \) exists
D. \( Y \) exists when \( A \) or \( B \) exists but not both \( A \) and \( B \) exist


In a geometric progression with common ratio 'q', the sum of the first 109 terms exceeds the sum of the first
100 terms by \( 12 . \) If the sum of the first nine terms of the progression is \( \frac{\boldsymbol{\lambda}}{\boldsymbol{q}^{100}} \) then the value of \( \lambda \) equals to
A . 10
B. 14
c. 12
D. 22


The number of \( U^{238} \) nuclei in a rock
sample is equal to the number of \( \mathrm{Pb}^{206} \)
atoms. The half-life of \( \mathrm{U}^{238} \) is \( 4.5 \times 10^{9} \)
years.The age of the rock is
A \( \cdot 4.5 \times 10^{9} y \)
B. \( 9 \times 10^{9} y \)
C. \( 13.5 \times 10^{9} y \)
D. \( 18 \times 10^{9} y \)


A dynamo
A. Creates mechanical energy
B. Creates electrical energy
C. Converts electrical energy into mechanical energy
D. Converts mechanical energy into electrical energy


If \( 72 K \) is a perfect cube, find the value
of \( \boldsymbol{K} \)
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D.


A particle moves in the \( x-y \) plane under the action of a force \( \vec{F} \) such that the value of its linear momentum \( (\vec{P}) \) at
anytime \( t \) is \( P_{x}=2 \cos t, P_{y}=2 \sin t \)
The angle \( \theta \) between \( \vec{F} \) and \( \vec{P} \) at a
given time \( t \) will be
\( \mathbf{A} \cdot \theta=0^{\circ} \)
B . \( \theta=30 \)
c. \( \theta=90 \)
D. \( \theta=180^{\circ} \)


State whether True or False:
Hysteresis is the number of lines of force per unit area in a magnetic field.
A. True
B. False


If \( \boldsymbol{A}=\left(\begin{array}{ccc}1 & 2 & 1 \\ -1 & 0 & 3 \\ 2 & -1 & 1\end{array}\right) \) then
characteristic equation is given by
A. \( -\lambda^{3}+2 \lambda^{2}-4 \lambda+18=0 \)
0
B . \( \lambda^{3}+2 \lambda^{2}+4 \lambda+18=0 \)
c. \( 2 \lambda^{3}-\lambda^{2}+6 \lambda-2=0 \)
D. None of these


Identify the constituent radiations of electromagnetic spectrum which
(a) is obsorbed by ozone layer in the atmosphere
(b) i produced by bombarding a metal target by high speed electrons
(c) is used in satellite communication
(d) has wavelength range between 400 nm to \( 700 \mathrm{nm} \)


Which of the following non-metals belongs to the halogen family?
A. Flourine
B. Chlorine
c. Bromine
D. All of the above


A uniform ladder of length \( 5 m \) is placed
against the wall as shown in the figure.
If coefficient of friction \( \mu \) is the same for
both the walls, what is the minimum
value of \( \mu \) for it not to slip?
A \( \cdot \mu=\frac{1}{2} \)
B. \( \mu=\frac{1}{4} \)
\( c \cdot_{\mu}=\frac{1}{3} \)
D. \( \mu=\frac{1}{5} \)


Methanol is a:
A. yellow coloured liquid
B. brown coloured liquid
C . colourless liquid
D. blue coloured liquid


Which element is not present in chlorophyll?
A. carbon
B. Calcium
c. Magnesium
D. Hydrogen


Catenation is defined as:
A. formation of double bond between carbon atoms.
B. linking of carbon atoms with of atoms other elements.
C . indefinite linking of carbon atoms
D. the formation of four covalent bonds by a carbon
atom.


End product of fermentation of sugars is
A. Water and carbon dioxide
B. Alcohol and carbon dioxide
c. Carbon dioxide
D. Alcohol


When a horse pulls a cart, the force that helps the horse to move forward is the force exerted by
A. the cart on the horse
B. the ground on the horse
c. the ground on the carttt
D. the horse on the ground


The order of \( [x, y, z]\left[\begin{array}{lll}a & h & g \\ h & b & f \\ g & f & c\end{array}\right]\left[\begin{array}{l}x \\ y \\ z\end{array}\right] \) is
\( A \cdot 3 \times 1 \)
B. \( 1 \times 1 \)
c. \( 1 \times 3 \)
D. \( 3 \times 3 \)


The n-side of the depletion layer of a p-n junction.
A. Always has same width as of the p-side
B. Has no bound charges
c. Is negatively charged
D. Is positively chargedd


If the equation \( a x^{2}+2 b x+c=0 \) has
real roots, \( a, b, c \) being real numbers
and if \( m \) and \( n \) are real number such
that \( m^{2}>n>0 \) then show that the
equation \( a x^{2}+2 m b x+n c=0 \) has
real roots.


The interparticle forces between linear chains in Nylon - 6,6
are
A. hydrogen bonds
B. covalent bonds
c. ionic bonds
D. coordinate bonds


If \( \boldsymbol{y}=\log _{e}\left(\frac{\boldsymbol{x}^{2}}{e^{2}}\right), \) then \( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}} \) equals
\( A \cdot-\frac{1}{x} \)
B. \( -\frac{1}{x^{2}} \)
c. \( \frac{2}{x^{2}} \)
D. \( -\frac{2}{x^{2}} \)


\( \$ \$ \operatorname{lint}|,| \operatorname{left}\left[x \sin ^{\wedge}\{-1\} x \mid, \text { lleft } \mid\{1\right. \)
\( \left|\operatorname{sqrt}\left\{\left(1|,-|, \mathbf{x}^{\wedge} 2\right\}|,| r i g h t \mid\right\} \wedge\{-1\}\right| \)
|right \( ] \wedge \mid, \$ \$ d x \)


The metal oxide which cannot be
reduced to metal by carbon is
A \( . Z n O \)
в. \( F e_{2} O_{3} \)
\( c . P b O \)
D. \( A l_{2} O_{3} \)


Which of the following property is not a thermodynamic property of the system?
A. pressure
B. temperature
c. specific volume
D. heat


Differentiate with respect to \( x \) :
\( \frac{3 x^{2} \sin x}{\sqrt{7-x^{2}}} \)


An artificial satellite in the presence of frictional forces will move into an orbit
closer to the earth and may have increased kinetic energy. Explain this.


Which of the following compound cannot be thermally decomposed even
at high temperature?
A. \( C s H C O_{3} \)
в. \( R b_{2} C O_{3} \)
\( \mathrm{c} \cdot L i_{2} \mathrm{CO}_{3} \)
D. \( \left(N H_{4}\right)_{2} C O_{3} \)


Find the equation of all lines having slope 2 and being tangent to the curve \( \boldsymbol{y}+\frac{\mathbf{2}}{\boldsymbol{x}-\mathbf{3}}=\mathbf{0} \)


Which of the following processes produces a decrease of the entropy of the system?
A. Dissolving sodium chloride in water
B. Sublimation of naphthalene
c. Dissolving oxygen in water
D. All of these


The real part of \( \left(\frac{1+i}{3-i}\right)^{2}= \)
\( \mathbf{A} \cdot \mathbf{1} \)
B . 16
\( c \cdot 16 \omega^{2} \)
D. \( \frac{-3}{25} \)


When potassium chloride and lead \( (I I) \) nitrate react in an aqueous solution, which of the following terms will be present in the balanced molecular
equation?
A \( \cdot P b C l_{s} \)
B \( \cdot P b_{2} C l_{(s)} \)
\( \mathbf{c} \cdot K N O_{3(a q)} \)
D. \( 2 K N O_{3(a q)} \)
E \( \cdot 2 K C l_{2(s)} \)


The radius of hydrogen atom, when it is in its second excited state, becomes:
A . half
B. double
c. four times
D. nine times


Which of the following is an antifreeze?
A. water
B. ether
c. ethyl alcohol
D. aniline


Assertion
\( N H_{3} \) and \( C H_{3}^{-} \) both have pyramidal shape.
Reason
\( \mathrm{N} \) in \( N H_{3} \) and \( \mathrm{C} \) in \( C H_{3}^{-} \) both have \( s p^{3} \) hybridisation with one lone pair of electron on each.
A. Assertion is true, Reason is true and Reason is correct explanation for Assertion.
B. Assertion is true, Reason is true and Reason is NOT the correct explanation for Assertion.
c. Assertion is true, Reason is false.
D. Assertion is false, Reason is true


When sodium hydroxide solution is added to a freshly prepared solution of ferrous sulphate, a green precipitate of ferrous hydroxide is formed which on standing turns brown because:
A. ferric salts are unstable
B. the mixture becomes dirty
c. ferrous hydroxide becomes ferric oxide
D. green ferrous hydroxide oxidises to brown ferric hydroxide


Renewable sources of energy
are produced in nature:
A. biennial
B. annually
c. continuously
D. quarterly


Distance of the center of mass of a solid
uniform cone from its vertex is \( z_{0} . \) If the
radius of its base is \( R \) and its height is
\( h \) then \( z_{0} \) is equal to:
A \( \cdot \frac{h^{2}}{4 R} \)
в. \( \frac{3 h}{4} \)
\( c \cdot \frac{5 h}{8} \)
D. \( \frac{3 h^{2}}{8 R} \)


When hydrogen sulphide gas is passed through a blue solution of copper sulphate, a black precipitate of copper sulphide is obtained and the sulphuric acid so formed remains in the solution.
The reaction is an example of:
A. a combination reaction
B. a displacement reaction
c. a decomposition reaction
D. a double displacement reaction


Find the radian measures
corresponding to \( 5^{0} 37^{\prime} 0^{\prime \prime} \)


Nodal planes of \( \pi \) bonds in benzene are
located in:
A. molecular plane
B. one in a molecular plane and two in a plane perpendicular to the molecular plane which contains C one in the molecular plane and two in the plane perpendicular to the molecular plane which contains Cone in the molecular plane and two in plane perpendicular to molecular plane which contains \( \mathrm{C} \mathrm{C} \sigma \) bonds
C. one in molecular plane and two in plane perpendicular to molecular plane which contain \( \mathrm{C} \mathrm{C} \sigma \) bond and \( \mathrm{C}-\mathrm{H} \) \( \sigma \) bond.
D. perpendicular to molecular plane which bisect benzene ring in two equal half


If \( f(x) \) is a polynomial satisfying
\( \boldsymbol{f}(\boldsymbol{x}) \boldsymbol{f}\left(\frac{1}{x}\right)=\boldsymbol{f}(\boldsymbol{x})+\boldsymbol{f}\left(\frac{1}{x}\right), \operatorname{and} \boldsymbol{f}(\boldsymbol{3})=\mathbf{8} \mathbf{2} \)
then \( \int \frac{f(x)}{x^{2}+1} d x= \)
A \( \cdot x^{3}-x+2 \tan ^{-1} x+c \)
B. \( \frac{1}{3} x^{3}-x+\tan ^{-1} x+c \)
c. \( \frac{x^{3}}{3}-x+2 \tan ^{-1} x+c \)
D. \( \frac{1}{3} x^{3}+x+2 \tan ^{-1} x+c \)


Na \( C l \) and \( C a C l_{2} \) are added to fused
\( M g C l_{2} \) in the electrolysis of \( M g C l_{2} \) so
that
A. melting point is decreased and conductivity is increased
B. melting point is increased and conductivity is decreased
c. melting point and conductivity both are decreased
D. melting point and conductivity both are increased


In an AC generator, maximum number
of lines of force pass though the coil when the angle between the plane of coil and lines of force is :
A \( \cdot 0^{\circ} \)
B. 60
\( c \cdot 30 \)
D. \( 90^{\circ} \)


Condensed solid produced during sublimation is:
A. crystals
B. sublimate
c. residue
D. insoluble


The wavelength of light visible to eye is of the order of
\( \mathbf{A} \cdot 10^{-4} m \)
B. \( 10^{-8} \mathrm{m} \)
\( \mathbf{c} \cdot 10^{-10} m \)
D. \( 10^{-7} m \)


A condenser is charged and then battery is removed. A dielectric plate is put
between the plates of condenser, then correct statement is
A. Q is constant, v and U decrease
B. Q is constant, V increases U decreases
c. Q increases, v decreases U increases
D. \( Q, v \) and \( U \) increase


Histone proteins are associated with
A. DNA
B. mRNA
c. rRNA
D. snRNA
E. tRNA


When two coins are tossed and a
cubical dice is rolled, then the total
outcomes for the compound event is
A . 48
B. 52
\( c .36 \)
D. 24


Two positive charges \( q \) and \( q \) are placed at
the diagonally opposite corners of a square and two negative charges \( -q \) and
\( -q \) are placed at the other two corners of the square. Then at the centre of the square the resultant electric intensity and the net electric potential Vare
A. \( E \neq 0, V=0 \)
в. \( E=0, V=0 \)
c. \( E=0, V \neq 0 \)
D. \( E \neq 0, V \neq 0 \)


Lead pipes are readily corroded by:
A. water
B. acetic acid
c. conc. \( H_{2} S O_{4} \)
D. dil. \( H_{2} S O_{4} \)


\( \boldsymbol{C}_{3} \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{H}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{C}_{2} \boldsymbol{H}_{6}(\boldsymbol{g})+ \)
\( \boldsymbol{C} \boldsymbol{H}_{4}(\boldsymbol{g}) \triangle \boldsymbol{H}^{0}=? \)
\( \begin{array}{ll}C_{2} \boldsymbol{H}_{6} & \boldsymbol{H}_{2}(\boldsymbol{g}) \\ (g)\end{array} \quad \boldsymbol{C H}_{4}(\boldsymbol{g}) \quad \) graphit
-1560.1 \( \quad \) -225.0 \( \quad-090.0 \quad \) -393.5
\( \triangle H^{0} \)combustion\( \left(K J m o l^{-1}\right. \)


The median and mode of a frequency
distribution are 525 and 500 then mean
of same frequency distribution is-
A . 75
в. 107.5
c . 527.5
D. 537.5


Match the Column-I with Column-II.


In unilocular ovary the ovules develop on the inner wall of ovary. Placentation
can be
A . Basal
B. Axile
c. Parietal
D. Free central


Concentration of which of the following ore is carried out by froth floatation process?
A. Bauxite
B. Chalcocite
c. Haematite
D. Calamine


Amphetamine \( \left(C_{3} H_{13} N\right) \) is a weak
base with \( p K_{b} \) of \( 4.2 . \) Calculate the \( p H \) of a solution containing an amphetamine concentration of \( 220 m g / L \)
A . 3.49
B. 5.21
c. 10.5
D. 13.7


Which is a characteristic of a catalyst?
A. It changes the equilibrium point
B. It initiates the reaction
c. It alters the rate of reaction
D. It increases the average kinetic energy of the molecul


Assertion
Gravitational potential is maximum at infinity.
Reason
Gravitational potential is the amount of
work done to shift a unit mass from
infinity to a given point in gravitational attraction force field.
A. STATEMENT-1 is True, STATEMENT-2 is True
STATEMENT-2 is a correct explanation for STATEMENT1
B. STATEMENT-1 is True, STATEMENT-2 is True STATEMENT-2 is NOT a correct explanation for STATEMENT-1
C. STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True


The rate of change of area of a circle with respect to its radius at \( r=2 \mathrm{cm} \) is
A .4
в. \( 2 \pi \)
\( c \cdot 2 \)
D. \( 4 \pi \)


Three small interlocking bones: the hammer, the anvil, and the stirrup transmit the vibrations of the eardrum
to the inner ear.
A. True
B. False
c. Ambiguous
D. Data insufficient


If \( \int_{1}^{2} e^{x^{2}} d x=a, \) then \( \int_{e}^{e^{4}} \sqrt{\ln x} d x \) is
equal to
A \( \cdot 2 e^{4}-2 e-a \)
B \( \cdot 2 e^{4}-e-a \)
\( \mathbf{c} \cdot 2 e^{4}-e-2 a \)
D. \( e^{4}-e-a \)


For a given material, the Young's modulus is 2.4 times that of the
modulus of rigidity. Its Poisson's ratio is
A . 2.4
B. 1.2
\( c .0 .4 \)
D. 0.2


\( (-46)+(+15)= \)
A. +31
B. 31
\( c \cdot-31 \)
D. none of these


A particle executes \( S H M \) with time period \( T \) and amplitude \( A \), The maximum possible average velocity in time \( T / 4 \) is
A \( \cdot \frac{2 A}{T} \)
в. \( \frac{4 A}{T} \)
c. \( \frac{8 A}{T} \)
D. \( \frac{4 \sqrt{2 A}}{T} \)


Which property of starch is used as indicator in iodometric titration?
A. Absorption
B. Adsorption
c. solubility
D. Polarity


Find the median value from the given
table by drawing the curve of the values.
\begin{tabular}{|l|l|}
\hline Weight (in kg) & No of students \\
\hline Less than 38 & 0 \\
\hline Less than 40 & 3 \\
\hline Less than 42 & 5 \\
\hline Less than 44 & 9 \\
\hline Less than 46 & 14 \\
\hline Less than 48 & 28 \\
\hline Less than 50 & 32 \\
\hline Less than 52 & 35 \\
\hline
\end{tabular}
A . 18.5
B. 16.5
c. 17.5
D. 21.5


Select the option which correctly fills up the blanks, in the following
statement-
(i) Destruction of embryo or foetus in the uterus is called
(ii) Government of India legalised MTP in the year
(iii) Natural family planning method is also called
(iv) is a method in which the
male partner withdraws his penis from vagina just before ejaculation.
(v) \( ----- \) is a copper releasing and is a hormone releasing intra uterine devices.
A . (i) foeticide
(ii) 1961
(iii) rhythm method, (iv) safety period, (v) Multiload 375, LNG-20
B. (i) foeticide
(ii) 1971
(iii) rhythm method, (iv) coitus interruptus
(v) Multiload 375, LNG-20
c. (i) foeticide,
(ii) 1965
(iii) rhythm method, (iv) coitus interruptus,
(v) Multiload 375, CuT
D (ii) matricide
(ii) 1982
(iii) contraception method, (iv) interruptus, (v) Multiload 375, LNG-20


If the surface area of a sphere is
\( 154 c m^{2}, \) find its radius


A circular loop of radius \( r \) is placed at
the centre of current carrying
conducting square loop of side \( a . \) If both
loops are coplanar and \( a>>r, \) then the
mutual inductance between the loops
will be:
A \( \frac{\mu_{0} r^{2}}{2 \sqrt{2}(a)} \)
B. \( \frac{\mu_{0} r^{2}}{4 a} \)
c. \( \frac{2 \sqrt{2} \mu_{0} r^{2}}{\pi a} \)
D. \( \frac{\mu_{0} r^{2}}{4 \sqrt{2} a} \)


The number of real roots of the equation
\( \mathbf{5}+\left|\mathbf{2}^{x}-\mathbf{1}\right|=\mathbf{2}^{x}\left(\mathbf{2}^{x}-\mathbf{2}\right) \) is:
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
\( D \)


What is Werner's Theory


Whcih of the following characteristics are related to group to which plant Marsilea belongs?(i) Plant body is not
differentiated into roots, stem and leaves.(ii) They have specialised tissue for the conduction of water and other
substances.(iii) They are predominanty aquatic in nature.(iv) They have naked embryos called spores.(v) They are called amphibians of plant kingdom.
A. (ii) and (iv) only
B. (iii), (iv) and (v)
\( c . \) (ii), (iii) and (iv)
D. (i), (iv) and (v)


The key elements that determine
differences in environmental conditions
of different habitats include
A. Temperature
B. Light
c. Soil
D. All of these


Find a continuous function \( f, \) where
\( \left(x^{4}-4 x^{2}\right) \leq f(x) \leq\left(2 x^{2}-x^{3}\right) \) such
that the area bounded by \( \boldsymbol{y}=\boldsymbol{f}(\boldsymbol{x}), \boldsymbol{y}= \)
\( x^{4}-4 x^{2}, y \) -axis, and the line \( x=t \)
where \( (0 \leq t \leq 2) \) is \( k \) times the area
bounded by \( \boldsymbol{y}=\boldsymbol{f}(\boldsymbol{x}), \boldsymbol{y}=\mathbf{2} \boldsymbol{x}^{2}-\boldsymbol{x}^{3}, \mathbf{y} \)
axis, and line \( \boldsymbol{x}=\boldsymbol{t} \text { (where } \mathbf{0} \leq \boldsymbol{t} \leq \mathbf{2}) \)


If \( 3 x+7 \leq 1, \) where \( x \in Z, \) then find
values of \( x \)
A \( \cdot\{2,2\} \)
в. \( \{-2,-3,-4, \ldots\} \)
c. \( \{-2,-1,0,1, \ldots\} \)
D. None of these


Electromagnetic induction is the:
A. charging of a body with a positive charge
B. production of current by relative motion between a magnet and a coil
C. rotation of the coil of an electric motor
D. generation of magnetic field due to a current carrying solenoid


Derive Lens Maker's formula for a
convex lens.


Give any two applications of Faraday's law of Induction in daily life.


In a reaction mechanism consisting of elementary reaction steps where the relative rate of each is given, which of the following is most likely to be the rate-determining step?
A. A step labeled fast
B. A step labeled moderate
C. A step labeled slow
D. It is not possible to tell which step is rate determining from this information


The vertical section of a road over a
canal bridge in the direction of its length is in the form of circle of radius \( 8.9 m . \) Then the greatest speed at which the car can cross this bridge without losing contact with the road at its
highest point, the centre of gravity of the car being at a height \( h=1.1 m \)
from the ground (Take \( \left.g=10 m / s e c^{2}\right) \)
A. \( 5 \mathrm{m} / \mathrm{sec} \)
в. \( 10 \mathrm{m} / \mathrm{sec} \)
c. \( 15 \mathrm{m} / \mathrm{sec} \)
D. \( 20 \mathrm{m} / \mathrm{sec} \)


DNA differs from RNA in having
A. Uracil
B. Thymine
C. Adenine
D. Guanine


A gas in an airtight container is heated
from \( 25^{\circ} \mathrm{C} \) to \( 90^{\circ} \mathrm{C} \). The density of gas will
A. increase slightly
B. increase considerably
c. remain the same
D. decrease slightly


What is the sum of the mole fractions of
all the components in a three
component system?
\( A \)
B. 2
\( c \cdot 3 \)
\( D \cdot 1 / 3 \)


One hundred identical coins, each with
probability \( p, \) of showing up heads are tossed. If \( 0<p<1 \) and the probability
of heads showing on 50 coins is equal to that of the heads showing in 51 coins, then the value of \( p \) is
A \( \cdot \frac{1}{2} \)
в. \( \frac{49}{101} \)
c. \( \frac{50}{101} \)
D. \( \frac{51}{101} \)


Long answer type questions
If a collection of invertebrates are
presented to you what criteria would you use to classify them?


Four persons \( A, B, C \) and \( D \) at the corners
of an square of side \( X \) move at a
constant speed \( V . \) Each person
maintains a direction towards the
person at the next corner. The time, the persons take to meet each other is
A \( \cdot \frac{2 X}{3 V} \)
в. \( \frac{2 X}{V} \)
\( c \cdot \frac{X}{V} \)
D. \( \frac{3 X}{4 V} \)


n Fig \( 6.23, \) if \( A B \| C D, \angle A P Q=50^{\circ} \)
and \( \angle P R B=127^{\circ}, \) find \( a \) and \( y \)


Three successive measurement in an
experiment gave value 10.9,11.4042 and 11.42 the correct way of reporting the average value is:


The junction area is kept much larger in
a solar cell
A. for solar radiation to be incident because we are
interested in more power.
B. for solar radiation to be incident because we are interested in less power
C. for solar radiation to be properly reflected from the junction.
D. None of these.


Consider the function
\( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ll}a x-2 & \text { for }-2<x<-1 \\ -1 & \text { for }-1 \leq x \leq 1 \\ a+2(x-1)^{2} & \text { for } \quad 1<x<2\end{array}\right. \)
What is the value of a for which \( f(x) \) is
continuous at \( x=-1 \) and \( x=1 ? \)
\( A \cdot-1 \)
B.
\( c \cdot 0 \)
\( D \)


The characteristics of a ideal fuel are:
A. it should release more energy
B. it should be safe
c. it should be easily transportable
D. all of the above


Resultant of two vectors \( \vec{A} \) and \( \vec{B} \) is of magnitude P. If \( \vec{B} \) is reversed, then resultant is of magnitude Q. What is the
value of \( P^{2}+Q^{2} ? \)
\( A \cdot 2\left(A^{2}+B^{2}\right) \)
B. \( 2\left(A^{2}-B^{2}\right) \)
c. \( A^{2}-B^{2} \)
D. \( A^{2}+B^{2} \)


Why do jewellery makers electroplate gold or silver on metals?
A. To protect it from corrosion.
B. To prevent spoilage of jewellery
c. To make it shine.
D. To reduce cost.


The mass of electron is \( 9.11 \times 10^{-31} \)
Kg Planck constant is \( 6.626 \times 10^{-34} \mathrm{Js} \)
the uncertainty involved in the measurement of velocity within a
distance of \( 0.1 A^{\circ} \) is:
A \( \cdot 5.79 \times 10^{6} m / s \)
B . \( 5.79 \times 10^{7} \mathrm{m} / \mathrm{s} \)
\( \mathbf{c} \cdot 5.79 \times 10^{8} \mathrm{m} / \mathrm{s} \)
D. \( 5.79 \times 10^{5} \mathrm{m} / \mathrm{s} \)


Total normal electric field =
\( \mathbf{A} \cdot \epsilon_{0} \vec{E} \cdot \overrightarrow{d S} \)
в. \( \vec{E} \cdot \overrightarrow{d S} \)
\( \mathbf{c} \cdot \epsilon_{0} \vec{E} \)
D. \( \epsilon_{0} \overline{d S} \)


In \( N O_{3}^{-} \) ion, the number of bond pairs
and lone pairs of electrons on nitrogen
atom are:
A .2,2
в. 3,1
c. 1,3
D. 4,0


In which type of inheritance the results are affected by reciprocal cross?
A. Nuclear
c. Blending
D. All of the above


The degree of dissociation of an
electrolyte does not depend on:
A. nature of electrolyte
B. catalytic action
c. dilution
D. temperature


After rotating by \( 60^{\circ} \) about a centre, a figure looks exactly the same as at its original position. At what other angle will this happen for the figure?
\( \mathbf{A} \cdot 120^{\circ} \)
B. 100
\( c \cdot 150 \)
D. \( 90^{\circ} \)


Q Type your question
wall. The shearing strength of steel is
\( 345 M N / m^{2} . \) The dimensions \( A B=5 \)
\( \mathrm{cm}, \mathrm{BC}=\mathrm{BE}=2 \mathrm{cm} . \) The maximum
load that can be put on the face ABCD
is:(neglect bending of the rod)
\( \left(g=10 m / s^{2}\right) \)
A. 3450 kgf
B. 1380 kgf
c. \( 13800 \mathrm{kgf} \)
D. 345 kgf
E. None of these


Let a light of wavelength \( \lambda \) and intensity
\( \boldsymbol{I}^{\prime} \) strikes a metal surface to emit \( \boldsymbol{x} \)
electrons per second. Average energy of each electron is ' \( y^{\prime} \) unit. What will
happen to ' \( x \) ' and ' \( y \) ' when
(a) \( \lambda \) is halved
(b) intensity \( I \) is doubled?


Life expectancy is defined by the formula \( \frac{2 S B}{G}, \) where \( S= \) shoe size \( \boldsymbol{B}= \) average monthly electric bill in dollars, and \( G=\mathrm{GMAT} \) score. If Melvin's
GMAT score is twice his monthly electric bill, an his life expectancy is 50 what is his shoe size?
A . 40
B. 50
c. 60
D. 80


Find the 12 th term from the end of the
following arithmetic progression.
\( 3,8,13, ., 253 \)


Using Euclid's division of lemma, find
H.C.F. of 15 and 575


As the water is released through control valves, \( _{--}-_{-} \) of water changed to
A. Rotational energy, potential energy
B. Kinetic energy, potential energy
c. Potential energy, rotational energy
D. Rotational energy, thermal energy


Find the values of \( x, \) if \( \left|\begin{array}{cc}\mathbf{2 x} & \mathbf{5} \\ \mathbf{8} & \boldsymbol{x}\end{array}\right|=\left|\begin{array}{ll}\mathbf{6} & \mathbf{5} \\ \mathbf{8} & \mathbf{3}\end{array}\right| \)


A car traveling at a constant speed of \( 30 m / s \) passes a highway patrol car, which is at rest. The police officer
accelerates at a constant rate of \( 3 m / s^{2} \)
and maintains this rate of acceleration
until he pulls next to the speeding car. Assume that the police car starts to
move at the moment the speeder passes the police car. What is the time required for the police officer to catch
the speeder?
\( \mathbf{A} \cdot 20 s \)
B. \( 30 s \)
c. \( 40 s \)
D. \( 50 s \)


Stability constants of \( \left[\boldsymbol{C d}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right]^{2-} \) and
\( \left[N i(C N)_{4}\right]^{2-} \) are \( 1.28 \times 10^{17} \) and \( 1.0 \times \)
\( 10^{31} \) respectively. Which is more stable?
\( \mathbf{A} \cdot\left[N i(C N)_{4}\right]^{2} \)
B . \( \left[C d(C N)_{6}\right]^{2} \)
c. Both are equally stable
D. None of the above


Define an atomic orbital.


Which of the follwoing Hydrocarbon is
used as a fuel?
A. \( C O_{2} \)
B. \( C_{4} H_{10} \)
\( \mathbf{c} \cdot C H_{3} O H \)
D. \( C H_{3} \) СООН


A hydrocarbon \( A(V . D .=36) \) forms only one monochloro substitution product. A
will be:
A. iso-pentane
B. neo-pentane
c. cyclohexane
D. methyl-cyclohexane


An insect is sitting in front of a plane
mirror at a distance 1 m from it.
(a) Where is the image of the insect
formed?
(b) What is the distance between the
insect and its image?
\( \mathbf{A} \cdot(a) 2 m \) behind the mirror \( (b) 1 m \)
B. \( (a) 2 m \) infront of the mirror
\( (b) 1 m \)
C \( .(a) 1 m \) infront of the mirror
\( (b) 2 m \)
D. \( (a) 1 m \) behind the mirror
\( (b) 2 m \)


What are Comets?


Assertion: The magnetic field lines of the earth resemble that of a magnetic
dipole located at the centre of the earth. Reason: The axis of the dipole coincide with the axis of rotation of the earth.
A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true and reason is not the correct explanation of assertion.
c. If assertion is true but reason is false
D. If both assertion and reason are false


What we have learnt about heating
effect of electric current. In studied
about magnets and magnetic lines of force


In winter season, a mild spark is often
seen when a man touches somebody
else's skin.Why?
A. Due to lack of humidity and rubbing with clothes, charge accumulate on human body which is discharged via sparking
B. Due to cold, electrostatic charge on body finds a lower resistance path to the skin of other's body
C. The static charge on sweaters worn by the two persons is different, hence discharge through sparking occurs
D. Similar to the lightning, extremely high potential exists on both the bodies and hence they discharge through sparking


Snow is falling vertically at a constant speed of \( 8.0 \mathrm{m} / \mathrm{s} . \) At what angle from the
vertical do the snowflakes appear to be
falling as viewed by the driver of a car travelling on a straight, level road with a speed of \( 50 \mathrm{km} / \mathrm{h} \) ?


Which among the following is not an anomalous pair in Mendeleev's periodic
table?
A . Co, Ni
в. Te,
c. Ar, \( k \)
D. Sc, Ga


If the volume density of the elastic deformation energy in fresh water at the depth of \( h=1000 m \) is \( x K J / m^{3}, \) find the value of \( \frac{x}{5} . \) (rounded off to nearest integer)


A water sample has ppm level concentration of following anions \( \boldsymbol{F}^{-}=\mathbf{1 0} ; \boldsymbol{S} \boldsymbol{O}_{4}^{2-}=\mathbf{1 0 0} ; \boldsymbol{N} \boldsymbol{O}_{3}^{-}=\mathbf{5 0} \)
The anion/anions that make/makes the
water sample unsuitable for drinking is/are:
A. both \( S O_{4}^{2-} \) and \( N O_{3} \)
B . only \( F^{-} \)
C . only \( S O_{4}^{2} \)
D. only \( N O_{3}^{-} \)


Which of the following is the use of superconductor?
A. They are used in powerful electromagnets
B. They are used in microwaves
c. They are used in MRI
D. All of the above


One gas bleaches the colour of the
flowers by reduction, while the other by oxidation. The gases are:
A. \( N H_{3} \) and \( S O_{3} \)
B. CO and Cu
\( \mathrm{c} \cdot \mathrm{SO}_{2} \) and \( \mathrm{Cl}_{2} \)
D. \( H_{2} S \) and \( M n C l_{2} \)


Let \( N \) denote the set of all natural
numbers and \( R \) be the relation on \( N \times \)
\( N \) defined by \( (a, b) R(c, d), \) if \( a d(b+ \)
\( c)=b c(a+d), \) then show that \( R \) is an
equivalence relation.


Which features adapt polar bears to live in extremely cold climate?
A. A white fur, fat below skin, keen sense of smell
B. Thin skin, large eyes, a white fur
c. A long tail, strong claws, white large paws
D. White body, paws of swimming, gills for respiration


In the Carius method, the sealed Carius
tube containing organic compound, fuming nitric acid and silver nitrate is
heated at \( 300^{0} C \) for six hours in the
estimation of halogens.
A. True
B. False


\( \operatorname{Given} \boldsymbol{F}(\boldsymbol{x})=\left[\begin{array}{ccc}\cos \boldsymbol{x} & -\sin \boldsymbol{x} & \mathbf{0} \\ \sin \boldsymbol{x} & \cos \boldsymbol{x} & \boldsymbol{0} \\ \boldsymbol{0} & \boldsymbol{0} & \boldsymbol{1}\end{array}\right] \)
\( \boldsymbol{x} \in \boldsymbol{R} \) Then prove \( \boldsymbol{y}, \boldsymbol{F}(\boldsymbol{x}+\boldsymbol{y})= \)
\( \boldsymbol{F}(\boldsymbol{x}) \boldsymbol{F}(\boldsymbol{y}) \)


Which of the following are failures of
Bohr's Atomic model
A. Bohr model could not explain those atoms which have more than one electron like lithium, helium. This model was applicable only for those atoms which have one electron
B. Bohr theory explained only spherical orbits. There was no explanation for elliptical orbits
c. Bohr's atomic model propose that the electron revolve round then nucleus
D. Both A and B


Identify the series \( \frac{1}{3}, \frac{5}{3}, \frac{9}{3}, \frac{13}{3}, \)


A ring type flywheel of mass \( 100 k g \) and
diameter \( 2 m \) is rotating at the rate of \( \frac{5}{11} r e v / s . \) Then
A. the moment of inertia of the wheel is 100 kgm \( ^{-2} \).
B. the kinetic energy of rotation of the flywheel is \( 5 x \) \( 10^{3} J \)
C. the angular momentum associated with the flywheel is \( 10^{3} J s \)
D. the flywheel, if subjected to a retarding torque of \( 250 N m, \) will come to rest in \( 4 s \)


For the equilibrium, \( \Delta G=-R T l n K \)
If true enter 1 else 0
A .


Assertion
Hydrogen bomb is more powerful than
atomic bomb.
Reason
In hydrogen bomb, reaction is initiated.
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 one of the following pairs of structure distinguishes a nerve cell from other types of cell?
A. Flagellum and medullary sheath
B. Nucleus and mitochondria
c. Perikaryon and dendrites
D. vacuoles and fibres


A uniform thin rod of length \( l \) is
standing on a smooth horizontal
surface. A slight disturbance causes
the lower end to slip to the smooth
surface and the rod starts falling. Based
on this information mark the correct
option.
A. The center of mass will move along a straight line.
B. The path followed by the end of the rod which is in contact with the ground is circular
C. the path followed by the end of the rod (which is not in contact with the ground) is circular
D. The angular velocity of the rod when it is about to hit about to hit the ground is \( \sqrt{\frac{3 g}{2 l}} \)


A boat at anchor is rocked by a wave whose crests are 100 m apart and
whose velocity is \( 25 m s^{-1} \).how often does the crest reach the boat?
A . \( 2500 s \)
B. \( 1500 s \)
c. \( 4.0 s \)
D. \( 0.25 s \)


Mathematical Induction is the principle
containing the set
\( A \cdot R \)
B.
\( c \cdot Q \)
\( D \)


Derive an expression for electric
potential at a point due to an electric dipole. Discuss the special cases.


Which of the following is always true?
\( \mathbf{A} \cdot \sim(p \rightarrow q) \equiv \sim p \wedge q \)
В . \( (p \vee q) \equiv \sim p \vee \sim q \)
c. \( \sim(p \Rightarrow q) \equiv(p \wedge \sim q) \)
D. \( (p \wedge q) \equiv \sim p \wedge \sim q \)


Why sun appears red during sunrise \( \& \)
sunset?


The COD values of three water samples
\( A, B \) and \( C \) are 60 ppm, 990 ppm and 120 ppm respectively. The most polluted water sample is:
\( A \cdot A \)
B. B
\( c \cdot c \)
D. All are equally polluted


Population of a town increased by 1200 persons in a year and then this new population decreased by \( 11 \% \) during the next year. If the town now has 32 persons less than it had before the increase, then the original population of the town is:
\( A \cdot 9968 \)
B. 10000
c. 11232
D. 12000


Solve for \( x \) and \( y: 6 x+3 y=6 x y \) and
\( 2 x+4 y=5 x y \)


If \( 6,6^{2}, 6^{3}, 6^{4} \cdots 6^{n} \) be n observation
then the quantity \( (\sqrt{6})^{n+1} \) is called
A . G.M
в. Н.М
c. А.М
D. None of these


Light travels with a speed of \( 3 \times 10^{8} \) \( \{m s\} \wedge\{-1\} . \) The distance travelled by light in 1 femto second is:
A. \( 0.03 \mathrm{mm} \)
B. \( 0.003 m m \)
\( \mathbf{c} .3 m m \)
D. \( 0.0003 \mathrm{mm} \)


Which term of the G.P. \( 2,8,32, \ldots \) is
\( 131072 ? \)


The major product of mononitration
reaction has incoming \( -N O_{2} \) group at
position


The first term of an infinite geometric
progression is \( x \) and its sum is 5 . then
A. \( x<-10 \)
B. \( 0<x<10 \)
c. \( -10<x<10 \)
D. \( x>10 \)


Five equal point charges with \( Q= \)
\( 10 n C \) are located at \( x=2,4,5,10 \) and
\( 20 m . \) If \( \varepsilon_{0}=\frac{10^{-9}}{36 \pi} F / m, \) then the
potential at the origin \( (x=0) \) is?
A . \( 9.9 v \)
B. \( 11.1 \mathrm{v} \)
c. \( 90 v \)
D. \( 99 v \)
E. 111


What was the requirement for introducing atomic orbital concept?


Show that the vector is parallel to a vector \( \vec{A}=\hat{i}-\hat{j}+2 \hat{k} \) is parallel to a vector \( \vec{B}=3 \hat{i}-3 \hat{j}+6 \hat{k} \)
A \( \cdot \frac{1}{3} \) times the magnitude of \( \vec{B} \)
B. \( \frac{1}{4} \) times the magnitude of \( \vec{B} \).
C \( \cdot \frac{1}{2} \) times the magnitude of \( \vec{B} \)
D. None of these


Electrostatic precipitators are extensively employed to control
A. Water pollution
B. Air pollution
c. Radioactive pollution
D. None of the above


Which of the following is incorrect?
A. \( M g \) burns in air releasing dazzling light rich in \( U V \)
rays
B. \( C a C l_{2} \cdot 6 H_{2} O \) when mixed with ice gives freezing
mixture
c. \( M g \) cannot form complexes
D. \( B e \) can form complexes due to its very small size


A balloon weighting \( 50 K g \) is filled with
\( 685 k g \) of helium at 1 at \( m \) pressure and
\( 25^{\circ} \mathrm{C} . \) What will be its pay load if it
displaced \( 5108 k g \) of air?
A \( .4373 k g \)
в. \( 4423 k g \)
c. \( 5793 k g \)
D. None of these