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Through the process of photosynthesis plants absorb from the
atmosphere and release into it.
A. Carbon dioxide, oxygen
B. Exhaustible
c. Non-renewable
D. Natural
| 0 |
Biology
|
The vapour pressure of two miscible liquids \( A \) and \( B \) are 300 and 500 mm of
Hg respectively. In a flask, 10 moles of \( A \)
is mixed with 12 moles of \( B \). However,
as soon as \( B \) is added, \( A \) starts
polymerizing into a completely insoluble solid. After 100 minutes,
0.525 moles of a non-volatile solute is
dissolved which arrests the polymerization completely. The final vapour pressure of the solution is 400 mm of Hg. Assume negligible volume
change on mixing, polymerization and ideal behaviour for the final solution.
If a number of moles of \( \boldsymbol{A} \) polymerized
in 100 minutes are expressed as \( x, \) then
a value of \( 10 x \) is:
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D. 4
| 1 |
Chemistry
|
Evaluate the following:
\( \left|\begin{array}{ccc}1 & a & b c \\ 1 & b & c a \\ 1 & c & a b\end{array}\right| \)
| 2 |
Maths
|
A uniform rod of mass \( M \) and length \( L \) hinged at centre is rotating in
horizontal plane with angular speed \( \omega_{0} \)
Now two objects each of mass \( m \) are kept on rod near the hinge on both sides. They starts sliding towards ends.
Find \( \omega \) of rod finally.
A \( \frac{M \omega_{0}}{6 M+m} \)
в. \( \frac{M \omega_{0}}{M+6 m} \)
c. \( \frac{6 M \omega_{0}}{M+m} \)
D. \( \frac{M \omega_{0}}{M+2 m} \)
| 3 |
Physics
|
A particle is moving in a straight line with initial velocity and uniform
acceleration \( a \). If the sum of the
distance travelled in \( t^{t h} \) and \( (t+1)^{t h} \)
seconds is \( 100 \mathrm{cm}, \) then its velocity
after \( t \) seconds, in \( \mathrm{cm} / \mathrm{s}, \) is
A . 80
B. 50
c. 20
D. 30
| 3 |
Physics
|
In figure given below, find the value of
resistance \( X \) for which points \( A \) and \( B \) are at the same potential:
| 3 |
Physics
|
If the mass ratio of non-reacting gases
\( O_{2} \) and \( N_{2} \) in a vessel is \( 2: 7, \) then the
ratio of their molecules will be:
A \( \cdot 1: 2 \)
B. 3:5
c. 2: 7
D. 1: 4
| 1 |
Chemistry
|
A candle is placed \( 20 \mathrm{cm} \) from the surface of a convex mirror and a plane mirror is also placed so that the virtual images in the two mirrors coincide. If the plane mirror is \( 12 \mathrm{cm} \) away from the object, what is the focal length of the convex mirror?
\( \mathbf{A} \cdot 20 \mathrm{cm} \)
B. \( 15 \mathrm{cm} \)
\( \mathbf{c} \cdot 10 \mathrm{cm} \)
D. \( 5 \mathrm{cm} \)
| 3 |
Physics
|
Earthworm has no special sense organs, still they are sensitive to
A. Light and sound
B. touch and sound
c. Touch, taste and light
D. Touch, taste, light and vibrating
| 0 |
Biology
|
The area of the shaded region in the diagram below where the given triangle is isoceles with vertices of base lying on
axis of the radius perpendicular to the diameters of the two small semicircles,
is
в. \( 16(\pi-1) \)
c. \( 32(\pi-1) \)
D. \( 32(\pi+1) \)
| 2 |
Maths
|
The oil used as frothing agent in froth floatation process is?
| 1 |
Chemistry
|
In how many different orders can five boys stand on a line?
A . 40
B. 50
\( c \cdot 80 \)
D. 120
| 2 |
Maths
|
In the figure shown in thin parallel beam of light is incident on a plane
mirror \( \boldsymbol{m}_{1} \) at small angle \( ^{\prime} \boldsymbol{\theta}^{\prime} \boldsymbol{m}_{2} \) is a
concave mirror of focal length ' \( f^{\prime} \). After
three successive reflections of this
beam the \( x \) and \( y \) coordinates of the
image is:
A \( . x=f-d, y=f \theta \)
B. \( x=f+d, y=f \)
c. \( x=f-d, y=-f \theta \)
D. \( x=d-f, y=-f \theta \)
| 3 |
Physics
|
Consider the situation shown in the
figure . The tension in the string connecting the 1.0 kg blocks.
| 3 |
Physics
|
An electrical heater and a capacitor are joined in series across a \( 220 V, 50 H z \)
\( A C \) supply. The
potential difference across the heater is
\( 90 V . \) The potential difference across the
capacitor will be about
\( \mathbf{A} \cdot 200 V \)
B. \( 130 V \)
\( \mathrm{c} \cdot 110 \mathrm{V} \)
D. \( 90 V \)
| 3 |
Physics
|
\( N H_{4} C l, N H_{4} N O_{3} \) and \( \left(N H_{4}\right)_{2} C O_{3} \)
gives \( N H_{3} \) gas on heating.
A. True
B. False
| 1 |
Chemistry
|
Rapid water absorption takes place by :
A. Osmosis
B. Active absorption
c. Both \( A \& B \)
D. None of this
| 0 |
Biology
|
A student writes the equation of an angular \( \mathrm{SHM} \) as \( \boldsymbol{\pi} / \mathbf{3}=\boldsymbol{\pi} / \mathbf{6} \sin (\boldsymbol{\omega} \boldsymbol{t}) . \) Is
this correct?
A. This equation is correct as it is of the form \( \theta= \) \( \phi \sin (\omega t) \)
B. This equation is incorrect as instantaneous angular displacement is more than the angular amplitude
C. This equation is incorrect as the equation lacks a phase factor
D. This equation is correct since the SHM has a sin factor in it
| 3 |
Physics
|
Identify the correct option amongst the following:
An \( \alpha \) particle is :
A. a hydrogen molecule
B. a helium nucleus
c. an electron
D. a proton
| 1 |
Chemistry
|
In plant nutrition elements are classified as major or minor depending
on
A. Their availability in the soil.
B. Their relative production in the ash obtained after burning the plants.
c. Their relative amounts required by the plants.
D. Their relative importance in plant growth
| 0 |
Biology
|
In a single slit diffraction experiment,
the width of the slit is made half the
original width
A. the width of the central maxima becomes double
B. the width of the central maxima becomes half
c. the width of the central maxima becomes one fourth
D. the width of the central maxima becomes four times
| 3 |
Physics
|
Without expanding, show that the value
of the following determinant is zero:
\( \left|\begin{array}{ccc}\mathbf{0} & \boldsymbol{x} & \boldsymbol{y} \\ -\boldsymbol{x} & \boldsymbol{0} & \boldsymbol{z} \\ -\boldsymbol{y} & -\boldsymbol{z} & \boldsymbol{0}\end{array}\right| \)
| 2 |
Maths
|
Non-metals combine with oxygen to
form usually:
A. basic oxides
B. neutral oxides
c. acidic oxides
D. amphoteric oxides
| 1 |
Chemistry
|
When a bullet is fired from a gun
a) Kinetic Energy of bullet is more than
that of gun
b) acceleration of bullet is more than
that of gun
c) momentum of bullet is more that of
gun
d) velocity of bullet is more than that of
gun
A. only a \( \& \) b are true
B. only b \& c are true
\( \mathrm{c} \cdot \mathrm{a}, \mathrm{b} \& \mathrm{d} \) are true
D. a, b, c \& d are true
| 3 |
Physics
|
Assertion : Current is passed through a metallic wire, heating it red. When cold water is poured on half of it, the rest
becomes more hot.
Reason: Resistance decreases due to
the decrease in temperature and then
current through wire increases.
A. Both (A) and (R) are true and (R) is the correct explanation of A
B. Both (A) and (R) are true but (R) is not the correct explanation of A
c. (A) is true but (R) is false
D. (A) is false but (R) is true
| 3 |
Physics
|
\( \mathrm{g}_{2} U^{235} \) nucleus absorbs a neutron and disintegrates into \( _{54} X e^{139},_{38} S r^{94} \) and
X. What will be the product \( X ? \)
A. 2 neutrons
B. 3 neutrons
c. \( \alpha \) -particle
D. \( \beta \) -particle
| 3 |
Physics
|
When the intermolecular distance
decreases due to compressive force,
there is :
A. zero resultant force between molecules
B. Repulsive force between molecules
c. Attractive force between molecules
D. No force between molecules
| 3 |
Physics
|
Atomslions needed in very small
amounts function mainly as ............. of enzymatic reactions.
| 0 |
Biology
|
Which name is associated with the
chemical substances produced in endocrine ductless glands?
A. Vitamins
B. Antigens
c. Bile acids
D. Hormones
| 1 |
Chemistry
|
Atomic weight of boron is 10.81 and it
has two isotopes \( _{5} B^{10} \) and \( _{5} B^{11} . \) Then
ratio of \( _{5} B^{10}:_{5} B^{11} \) in nature would be
A . 19: 81
B. 10: 11
c. 15: 16
D. 81: 19
| 3 |
Physics
|
Which of the following radiations has the least wavelength?
A. \( \gamma \) -rays
B. \( \beta \) -rays
c. \( \alpha \) -rays
D. X-rays
| 3 |
Physics
|
If \( x \) and \( y \) vary inversely as each other, and \( x=10 \) when \( y=6 . \) Find \( y \) when
\( \boldsymbol{x}=\mathbf{1 5} \)
A . 2
B. 4
c. 8
D.
| 2 |
Maths
|
If the escape speed of a projectile on Earth's surface is \( 11.2 k m s^{-1} \) and \( a \)
body is projected out with thrice this speed, then determine the speed of the body far away from the Earth:
A \( .56 .63 k m s^{-1} \)
B. \( 33 k m s^{-1} \)
\( \mathbf{c} \cdot 39 k m s^{-1} \)
D. \( 31.7 k m s^{-1} \)
| 3 |
Physics
|
Assertion
Permanent hardness of water can be
removed by using washing soda
Reason
Washing soda reacts with soluble calcium and magnesium chlorides and sulphates in hard water to form
insoluble carbonates
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
| 1 |
Chemistry
|
For \( \frac{\boldsymbol{x}^{\mathbf{3}}+\mathbf{2} \boldsymbol{x}+\mathbf{1}}{\mathbf{5}}-\frac{\mathbf{7}}{\mathbf{2}} \boldsymbol{x}^{2}-\boldsymbol{x}^{\mathbf{6}}, \) write
i) the degree of the polynomial
ii) the coefficient of \( x^{3} \)
iii) the coefficient of \( x^{6} \)
iv) the constant term
| 2 |
Maths
|
In what ways lithium shows similarities to magnesium in its chemical behaviour?
| 1 |
Chemistry
|
Find an expression for \( \boldsymbol{y} \) given \( \frac{d y}{d x}=7 x^{5} \)
| 2 |
Maths
|
Q Type your question
volume. This is strictly true only if there are no external influences. A gas
column under gravity, for example, does not have uniform density (and
pressure). As you might expect, its density decreases with height. The precise dependence is given by the socalled law of atmospheres
\( \boldsymbol{n}_{2}=\boldsymbol{n}_{1} \exp \left[-\boldsymbol{m} \boldsymbol{g}\left(\boldsymbol{h}_{2}-\boldsymbol{h}_{1}\right) / \boldsymbol{k}_{B} \boldsymbol{T}\right] \)
where \( n_{2}, n_{1} \) refer to number density at
heights \( h_{2} \) and \( h_{1} \) respectively. Use this
relation to derive the equation for sedimentation equilibrium of a suspension in a liquid column:
\( \boldsymbol{n}_{2}=\boldsymbol{n}_{1} \exp \left[-\boldsymbol{m} \boldsymbol{g} \boldsymbol{N}_{\boldsymbol{A}}\left(\boldsymbol{\rho}-\boldsymbol{\rho}^{\prime}\right)\left(\boldsymbol{h}_{2}-\right.\right. \)
\( \left.\left.\boldsymbol{h}_{1}\right) /(\boldsymbol{\rho} \boldsymbol{R} \boldsymbol{T})\right] \)
where \( \rho \) is the density of the suspended
particle and \( \rho^{\prime} \) that of surrounding
medium. \( \left[\mathrm{N}_{A} \) is Avogadro's number, and \right. \( \mathrm{R} \) the universal gas constant. [Hint : Use Archimedes principle to find
the apparent weight of the suspended particle.]
| 3 |
Physics
|
Galileos law of odd numbers:
"The distances traversed, during equal intervals of time, by a body falling from rest, stand to one another in the same
ratio as the odd numbers beginning with unity [namely,1 : 3 : 5 : 7..]". Prove
it
| 3 |
Physics
|
Define the term 'electrical conductivity of a metallic wire. Write its S.I. unit.
| 3 |
Physics
|
The dual nature of radiation was
proposed by :
A. De Broglie
B. Heisenberg
c. JJ Thomson
D. Einstein
| 1 |
Chemistry
|
Which pressure is NOT standard
pressure?
A. 760 torr
B. 1 atm
c. \( 101.325 k P a \)
D. \( 70 \mathrm{mm} \mathrm{Hg} \)
| 1 |
Chemistry
|
The addition of two numbers \( 6.75 \times 10^{3} \)
\( \mathrm{cm} \) and \( 4.52 \times 10^{2} \mathrm{cm} \) with regard to
significant figures is:
A \( \cdot 7.20 \times 10^{3} \mathrm{cm} \)
В. \( 7.20 \times 10^{3} \mathrm{mm} \)
c. \( 7.20 \times 10^{4} \mathrm{cm} \)
D. None of these
| 3 |
Physics
|
Choose the correct statement from the
following?
This question has multiple correct options
A. Pressure is same at all points in the horizontal plane
B. A liquid seeks its own level
C. The lateral pressure exerted by a liquid decreases with the increase in depth of the liquid
D. The upper surface of a stationary liquid is always horizontal
| 3 |
Physics
|
The differential equation which
represents the family of curves \( \mathbf{y}= \)
\( \mathbf{c}_{1} \mathbf{e}^{\mathbf{c}_{2} \mathbf{x}} \) where \( \mathbf{c}_{1} \) and \( \mathbf{c}_{2} \) are arbitrary
constants, is:
A \( \cdot y^{\prime}=y^{2} \)
B. \( \mathrm{y}^{\prime \prime}=\mathrm{y}^{\prime} \mathrm{y} \)
\( \mathbf{C} \cdot \mathbf{y y}^{\prime \prime}=\mathbf{y}^{\prime} \)
D・yy" = (y') 2
| 2 |
Maths
|
The acceleration due to gravity at a depth of \( 1600 k m \) inside the earth is
\( \mathbf{A} \cdot 6.65 \mathrm{ms}^{-2} \)
B. \( 7.35 \mathrm{ms}^{-2} \)
c. \( 8.65 \mathrm{ms}^{-2} \)
D. \( 4.35 \mathrm{ms}^{-2} \)
| 3 |
Physics
|
Explain the different types of adaptations in plants with suitable examples.
| 0 |
Biology
|
Which one is not a co-factor?
A. Coenzyme
B. Apoenzyme
c. Prosthetic group
D. Metal ion
| 0 |
Biology
|
A series LCR circuit with \( \mathrm{R}=22 \Omega, \mathrm{L}=1.5 \)
\( \mathrm{H} \) and \( \mathrm{C}=40 \mu \mathrm{F} \) is connected to a variable frequency \( 220 \mathrm{V} \) ac supply.
When the frequency of the supply equals the natural frequency of the circuit, what is the average power transferred to the circuit in one
complete cycle?
A. 2000
B. 2200 W
c. 2400 \( w \)
D. 2500 W
| 3 |
Physics
|
\( P Q, Q R \) and \( R S \) are three consecutive
sides of a regular polygon. If \( <Q P R= \)
\( 20^{\circ} \) find the number of side in the
polygon.
| 2 |
Maths
|
Functional unit of kidney is
A. Neuron
B. Nephorn
c. Glomerulous
D. Bowman's capsule
| 0 |
Biology
|
Describe an experiment to demonstrate the thermal expansion in a gas.
| 3 |
Physics
|
Equal lengths of magnesium ribbons are taken in two test-tubes \( X \) and \( Y \)
Hydrochloric acid is added to test-tube
\( X \) and acetic acid is added to test-tube
\( \boldsymbol{Y} \)
In which test-tube, the reaction will be
more vigorous ? Why?
| 1 |
Chemistry
|
Assertion
Boiling point of \( H F \) is lesser than
water
Reason
Hydrogen bonding in water is weaker
than \( \boldsymbol{H} \boldsymbol{F} \)
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
| 1 |
Chemistry
|
After \( n p \) -orbitals are filled, the next orbital filled will be:
A \( \cdot(n+1) s \)
B \( \cdot(n+2) p \)
\( \mathbf{c} \cdot(n+1) d \)
D. \( (n+2) s \)
| 1 |
Chemistry
|
A ball strikes a horizontal floor at
\( 45^{\circ} .25 \% \) of its kinetic energy is lost
collision. Find the coefficient of
restitution
A .
в. \( \frac{1}{\sqrt{2}} \)
c. \( \frac{1}{\sqrt{4}} \)
D.
| 3 |
Physics
|
Radio active carbon \( C^{14} \) in a wood
sample, decays with a half life of 5700 years. The fraction of the radio active
carbon \( C^{14}, \) that remains after a decay
period of 17,100 years is :
A. \( 1 / 4 \)
B. 3/4
\( c \cdot 1 / 8 \)
D. \( 7 / 8 \)
| 3 |
Physics
|
Each of the urns contains 4 white and 6
blackballs. The \( (n+1) \) th urn contains 5
white and 5black balls. One of the \( (n+1) \)
urns is chosen atrandom and two balls
are drawn from it withoutreplacement and both the balls turn out to beblack.
Then the probability that the \( (n+1) \) th urn was chosen to draw the balls is \( 1 / 16 \) the value of \( n \) is
A . 10
в. 11
c. 12
D. 13
| 2 |
Maths
|
At the molecular level what can be said
about Heat energy?
A. Heat energy is equal to total mechanical energy of all its molecules
B. Heat energy is equal to total potential energy of all its molecules
C. Heat energy is equal to total kinetic energy of all its molecules
D. Heat energy is equal to total heat energy of all its molecules
| 3 |
Physics
|
Describe the factors that effects the
season.
| 0 |
Biology
|
What is the minimum energy required
to lunch a satellite of mass \( m \) from the
surface of a planet of mass \( M \) and radius \( R \) In a circular orbit at an
altitude of \( 2 R ? \)
A \( \cdot \frac{2 G m M}{3 R} \)
в. \( \frac{G m M}{2 R} \)
c. \( \frac{G m M}{3 R} \)
D. \( \frac{5 G m M}{6 R} \)
| 3 |
Physics
|
For a pair production, the minimum
frequency of the gamma ray must be:
A \( \cdot 2.5 \times 10^{14} \mathrm{Hz} \)
B. \( 2.5 \times 10^{20} \mathrm{Hz} \)
C \( \cdot 2.5 \times 10^{28} \mathrm{Hz} \)
D. \( 2.5 \times 10^{34} \mathrm{Hz} \)
| 3 |
Physics
|
Q Type your question
consisting or two semıcircles eacn of
radius \( r \) is placed in such a way that
the centre \( C \) of the conducting wire is at
a distance \( 2 r \) from the end of
the wire.The rod AB moves with velocity
of \( 5 m s^{-1} \) along the direction of the
current flow as shown in the figure. If
the line joining the ends of the rod
makes an angle \( 30^{\circ} \) with the wire then,
This question has multiple correct options
A. the emf induced between the ends of the rod is
\( \ln 4) \mu V \)
B. the end \( A \) is at higher potential than end \( B \).
C. the end \( A \) is at lower potential than end \( B \)
D. the emf induced between the ends of the rod is \( \ln 3) \mu V \)
| 3 |
Physics
|
Given \( \boldsymbol{A}=\{\mathbf{5}, \mathbf{6}, \mathbf{7}\} \) and \( \boldsymbol{B}=\{\mathbf{3}, \mathbf{4}\} \)
Form all possible ordered pairs and write the total number of ordered pairs formed. So that the first component is from \( \mathrm{B} \) and second is from \( \mathrm{A} \)
Find the total number of such pairs.
| 2 |
Maths
|
of green plants are called factories
of food production.
A. Mitochondria
B. Chloroplasts
c. Endoplasmic reticulum
D. Nucleus
| 0 |
Biology
|
According to law of conservation of
energy, heat energy is transformed into which two types of energy?
A. Kinetic and potential energy
B. Mechanical and potential energy
c. Kinetic and thermal energy
D. Nuclear and potential energy
| 3 |
Physics
|
What is the correct sequence of the
following in a heart attack?
1. Narrowing of the inner orifice of the vessel
2. 'Plaque' from fibrous tissue and high cholesterol
3. Inadequate supply of blood and
oxygen
4. Clots of blood carried Into the
coronary arteries
A .2,3,1,4
B. 2, 4, 1, 3
\( c \cdot 1,2,3,4 \)
D. 4,2,1,3
| 0 |
Biology
|
Mamta knitted a circular pattern and
then she put a handle around it and
used it as a hand fan. Find the area of
the design she has made, if outer circle
radius is \( 17.5 \mathrm{mm} \) and inner circle
radius is \( 7.5 \mathrm{mm} .\left[\boldsymbol{U} \boldsymbol{s e} \boldsymbol{\pi}=\frac{22}{7}\right] \)
| 2 |
Maths
|
The foci of the ellipse \( 4 x^{2}+9 y^{2}=1 \) are
\( ^{\mathbf{A}} \cdot\left(\pm \frac{\sqrt{3}}{2}, 0\right) \)
B. \( \left(\pm \frac{\sqrt{5}}{2}, 0\right) \)
\( ^{\mathbf{c}} \cdot\left(\pm \frac{\sqrt{5}}{3}, 0\right) \)
D \( \cdot\left(\pm \frac{\sqrt{5}}{6}, 0\right) \)
E \( \cdot\left(\pm \frac{\sqrt{5}}{4}, 0\right) \)
| 2 |
Maths
|
ff \( \boldsymbol{A}=\left[\begin{array}{cc}\cos \boldsymbol{x} & \sin \boldsymbol{x} \\ -\sin \boldsymbol{x} & \cos \boldsymbol{x}\end{array}\right], \) then find \( \boldsymbol{x} \)
satisfying \( \mathbf{0}<\boldsymbol{x}<\frac{\boldsymbol{\pi}}{\mathbf{2}} \) when \( \boldsymbol{A}+\boldsymbol{A}^{\boldsymbol{T}}=\boldsymbol{I} \)
| 2 |
Maths
|
Which is more hazardous to human
health?
A. Pyrethrum
B. DDT
c. Rotenone
D. Humulin
| 1 |
Chemistry
|
In the case of plane mirror. from the
mirror distance of the image \( = \) distance of the
A. Second image
B. object
c. both
D. none
| 3 |
Physics
|
Which of the following compounds gives
acetone \( \left(C H_{3}\right)_{2} C=o \) as one of the
product of its ozonolysis?
\( A \)
B.
\( c \)
\( D \)
| 1 |
Chemistry
|
How many factors of 1080 a
A .32
B. 36
c. 8
D. 25
| 2 |
Maths
|
In the depletion layer of p-njunction diode, these are presents.
A. Only holes
B. Only electrons
c. Electrons and holes both
D. Neither electron nor hole
| 3 |
Physics
|
Find the variance of first 10 multiples of
3
\( \mathbf{A} \cdot 72.65 \)
B. 74.05
c. 74.25
D. 73.85
| 2 |
Maths
|
The approximate concentration of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) in perhydrol is :
A. 30 gm/litre
B. \( 300 \mathrm{gm} / \mathrm{ml} \)
c. \( 10 \mathrm{gm} / \) /litre
D. 300 gm/litre
| 1 |
Chemistry
|
Kinetic energy of the liquid per unit mass is
\( \mathbf{A} \cdot \frac{1}{2} m v^{2} \)
B \( \cdot \frac{1}{2} v^{2} \)
C \( \cdot \frac{1}{2} m^{2} v \)
D. \( m v^{2} \)
| 3 |
Physics
|
If the function \( \boldsymbol{f}(\boldsymbol{x})=\log \left(\frac{1+\boldsymbol{x}}{1-\boldsymbol{x}}\right) \)
then the value of \( f\left(\frac{2 x}{1+x^{2}}\right) \) is equal to
A \( . f(x) \)
B. \( 2 f(x) \)
c. \( 3 f(x) \)
D. \( 4 f(x) \)
| 2 |
Maths
|
Heat evolved in the reaction \( \boldsymbol{H}_{2}+ \)
\( C l_{2} \rightarrow 2 H C l \) is \( 182 k J \)
(Bond energies \( \boldsymbol{H}-\boldsymbol{H}= \)
\( 430 k J / m o l e, C l-C l-242 k J / m o l e) \)
The \( H-C l \) bond energy is:
A. \( 763 k J / \) mole
в. \( 427 k J / \) mole
c. \( 336 k J / \) mole
D. \( 154 k J / \) mole
| 1 |
Chemistry
|
A man is standing on a boat in still water. If he walks towards the shore the
boat will:
A. move away from the shore
B. remain stationary.
c. move towards the shore
D. sink
| 3 |
Physics
|
What should be lengths of steel and copper rod, so that the length of steel rod is \( 5 \mathrm{cm} \) longer than the copper rod
at all temperature? ( \( \alpha \) for copper \( = \) \( 1.7 \times 10^{-5} \circ C^{-1} \) and \( \alpha \) for steel \( = \)
\( \left.1.1 \times 10^{-5}^{\circ} C^{-1}\right) \)
| 3 |
Physics
|
The magnitude of scalar product of two
vectors is 8 and of vector product is \( 8 \sqrt{3} . \) The angle between them is This question has multiple correct options
A. 30
B. \( 60^{\circ} \)
\( c .120 \)
D. 150
| 3 |
Physics
|
How does the proper inflation of tyre
save fuel?
A. Normal reaction decreases.
B. Normal reaction increases
c. Sliding contact with the road decreases.
D. Sliding contact with the road increases
| 3 |
Physics
|
The snakes are included under
A. Saprophytes
B. Primary consumers
c. Second trophic level
D. None of the above
| 0 |
Biology
|
The oxidation number of sulphur in the
sulphur molecule \( \left(S_{8}\right) \) is :
| 1 |
Chemistry
|
A person climbs up a stopped escalator
in \( 60 s . \) If standing on the same escalator but escalator running with constant velocity, he takes 40 s. How much time is taken by the person to walk up in the moving escalator?
A. \( 37 s \)
в. 27 s
\( c \cdot 24 s \)
D. \( 45 s \)
| 3 |
Physics
|
An organic compound undergoes firstorder decomposition. The time taken for its decomposition to \( 1 / 8 \) and \( 1 / 10 \) of its
initial concentration are \( t_{1 / 8} \) and \( t_{1 / 10} \) respectively. The value of \( \frac{\left[t_{1 / 8]}\right.}{\left[t_{1 / 10}\right]} \times 10 \) is \( ? \)
\( \left(\operatorname{take} \log _{10} 2=0.3\right) \)
| 1 |
Chemistry
|
The thickness of cathode increases in :
A . electrorefining of copper
B. electroplating of copper
c. anodizing of copper
D. none of the above
| 1 |
Chemistry
|
Construct the bisector of an angle \( 75^{\circ} \)
| 2 |
Maths
|
What type of isomerism is exhibited by? \( \boldsymbol{O} \)
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2}-\stackrel{\|}{\boldsymbol{C}}-\boldsymbol{O}-\boldsymbol{C H}_{2} \boldsymbol{C H}_{3} \)
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2}-\stackrel{\|}{\boldsymbol{C}}-\boldsymbol{O}-\boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{C H}_{3} \)
| 1 |
Chemistry
|
Which of the following is steam volatile?
A. Phenol
B. o-Nitrophenol
c. m-Nitrophenol
D. p-Nitrophenol
| 1 |
Chemistry
|
Which one of the following is the best material for making connecting wires?
A. Nichrome
B. Constantan
c. copper
D. Tungsten
| 3 |
Physics
|
One gram of radium is reduced by \( 2 m g \)
in 5 years by \( \alpha \) - decay. The half life of radium is:
\( \left(\log _{10} 998=2.9991\right) \)
A. 1520.4 years
B. 1671.7 years
c. 1617.5 years
D. 1732.86 years
| 3 |
Physics
|
The \( p H \) of \( 0.001 M C H_{3} C O O H \) is:
\( A \cdot 3 \)
B. 1
c. \( 3-7 \)
D.
| 1 |
Chemistry
|
The mass of a spaceship is 1000 kg. It is to be launched from the earths
surface out into free space. The value of \( g \) and \( R(\text { radius of earth) are } 10 m / s \)
and \( 6400 \mathrm{km} \) respectively. The required energy for this work will be:
A \( \cdot 6.4 \times 10^{11} J \)
\( J \)
В. \( 6.4 \times 10^{8} J \)
c. \( 6.4 \times 10^{9} J \)
D. \( 6.4 \times 10^{10} J \)
| 3 |
Physics
|
Evaluate \( \int e^{x}\left(\log (x)+\frac{1}{x^{2}}\right) d x \)
A. \( e^{x}\left(\log x+\frac{1}{x^{2}}\right) \)
B. \( \quad e^{x}\left(\log x+\frac{1}{x}\right) \)
c. \( \quad e^{x}\left(\log x-\frac{1}{x^{2}}\right) \)
D. \( \quad e^{x}\left(\log x-\frac{1}{x}\right) \)
| 2 |
Maths
|
Find the \( 10^{t h} \) term from end for the A.P.
\( \mathbf{3 . 6 . 9 . 1 2} \ldots \ldots .300 \)
| 2 |
Maths
|
In a dsDNA number of phosphodiester
bonds are 3250 , then find the number of
base pairs.
A. 1625
B. 1626
c. 3252
D. 3250
| 0 |
Biology
|
Let \( E_{1}(r), E_{2}(r) \) and \( E_{3}(r) \) be the
respective electric fields at a distance from a point charge \( Q, \) an infinitely long wire with constant linear charge density \( \lambda, \) and an infinite plane with uniform
surface charge density \( \sigma . \) If \( \mathrm{E}_{1}\left(r_{0}\right)= \)
\( E_{2}\left(r_{0}\right)=E_{3}\left(r_{0}\right) \) at a given distance \( r_{0} \)
then :
A \( \cdot Q=4 \sigma \pi r_{0}^{2} \)
B . \( r_{0}=\frac{\lambda}{2 \pi \sigma} \)
c. \( E_{1}\left(r_{0} / 2\right)=2 E_{2}\left(r_{0} / 2\right) \)
D. \( E_{2}\left(r_{0} / 2\right)=4 E_{3}\left(r_{0} / 2\right) \)
| 3 |
Physics
|
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