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Three numbers \( x, y \) and \( z \) are in
arithmetic progressions. If \( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}= \)
-3 and \( x y z=8, \) then \( x^{2}+y^{2}+z^{2} \) is
equal to
\( A \cdot 0 \)
B. 10
\( c \cdot 21 \)
D. 20
| 2 |
Maths
|
Two billiard balls each of mass \( 0.05 k g \)
moving in opposite directios with speed
\( 6 m s^{-1} \) collide and rebound with the
same speed. What is the impulse imparted to each ball due to the other.
| 3 |
Physics
|
Given, \( C_{\text {graphite }}+O_{2}(g) \rightarrow \)
\( \boldsymbol{C O}_{2}(\boldsymbol{g}) ; \boldsymbol{\Delta}_{r} \boldsymbol{H}^{o}=-\boldsymbol{3} \boldsymbol{9} \boldsymbol{3} . \boldsymbol{5} \boldsymbol{k} \boldsymbol{J} \boldsymbol{m o l}^{-1} \)
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}(l) ; \boldsymbol{\Delta}_{r} \boldsymbol{H}^{o}= \)
\( -285.8 k J m o l^{-1} \)
\( \boldsymbol{C O}_{2}(\boldsymbol{g})+\boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \rightarrow \boldsymbol{C} \boldsymbol{H}_{4}(\boldsymbol{g})+ \)
\( \mathbf{2} \boldsymbol{O}_{\mathbf{2}}(\boldsymbol{g}) ; \boldsymbol{\Delta}^{r} \boldsymbol{H} \mathbf{6} \boldsymbol{o}=+\mathbf{8} \mathbf{9 0 . 3} \boldsymbol{k} \boldsymbol{J} \boldsymbol{m o l}^{-1} \)
Based on the above thermochemical
wquations, the value of Delt\( a_{r} H^{o} \) at
\( 298 K \) for the reaction,
\( \boldsymbol{C}_{(g r a p h i t e)}+\mathbf{2} \boldsymbol{H}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{C} \boldsymbol{H}_{4}(\boldsymbol{g}) \) will be:
A. \( -78.8 k J \) mol \( ^{-1} \)
B. \( +144.0 k J \) mol \( ^{-1} \)
c. \( +74.8 k J \) mol \( ^{-1} \)
D. - 144.0kJ mol \( ^{-1} \)
| 1 |
Chemistry
|
Chiral carbon is:
A. carbon in which all four valencies are satisfied with four different atoms or group of atoms
B. carbon in which at least two of their valency are satisfied with four different atoms or group of atoms
C. carbon in which all four valences satisfied with same
atoms
D. none of these
| 1 |
Chemistry
|
Match the following:
| 1 |
Chemistry
|
Three containers of the same volume
contain three gases. The masses of their
molecules being \( \mathrm{m}_{1}, \mathrm{m}_{2} \) and \( \mathrm{m}_{3} \) and
number of molecules in these containers
is \( \mathrm{N}_{1}, \mathrm{N}_{2} \) and \( \mathrm{N}_{3} \). The pressure in
the containers are \( \mathrm{P}_{1}, \mathrm{P}_{2} \) and \( \mathrm{P}_{3} \)
respectively. All the gases are now mixed up and put in these containers. The
pressure \( \mathrm{P} \) of the mixture is
\( \mathbf{A} \cdot P<\left(P_{1}+P_{2}+P_{3}\right) \)
B. \( P=\frac{P_{1}+P_{2}+P_{3}}{3} \)
\( \mathbf{c} \cdot P=P_{1}+P_{2}+P_{3} \)
D \( \cdot P>\left(P_{1}+P_{2}+P_{3}\right) \)
| 3 |
Physics
|
On which factors from below does
Coulomb's law(i.e. law of electrostatic
attraction and repulsion) depends?
A. Magnitude of charges
B. Distance between charges
c. Both magnitude and distance between charges
D. None of the above
| 3 |
Physics
|
Number of double bond in \( H_{2} N O H \) is:
| 1 |
Chemistry
|
A steel scale is correct at \( 0^{\circ} \mathrm{C} \), the
length of a brass tube measured by it at
\( 40^{\circ} \mathrm{C} \) is \( 5 \mathrm{m} . \) The correct length of the
tube at \( 0^{\circ} \mathrm{C} \) is (Coefficients of linear
expansion of steel and brass are \( 11 \times \) \( \mathbf{1 0}^{-\mathbf{6} /^{\circ} C} \) and \( \mathbf{1 9} \times \mathbf{1 0}^{-\mathbf{6} /^{\circ} \mathbf{C}} \) respectively
A. \( 4.001 \mathrm{m} \)
в. \( 5.001 m \)
\( c .4 .999 m \)
D. \( 4.501 m \)
| 3 |
Physics
|
Calculate maximum number of
electrons in \( _{25} M n \) which have \( n=3, m=0 \)
and \( s==1 / 2 \)
| 1 |
Chemistry
|
The sodium compound which is used for softening hard water:
A. washing soda.
B. bleaching powder.
c. caustic soda
D. lime soda.
| 1 |
Chemistry
|
Why is the ratio of the velocities of light
of wavelengths \( 4000 A \) and \( 8000 A \) in
vacuum \( 1: 1 ? \)
| 3 |
Physics
|
A cylinder of height \( 90 \mathrm{cm} \) and base
diameter \( 8 c m \) is melted and recast into
spheres of diameter \( 12 \mathrm{cm} \). Find the number of spheres.
| 2 |
Maths
|
A uniform metre rule \( A B \) is supported
at its centre of gravity by a knife-edge. A force of \( 4 N \) is applied at a point which
is \( 20 \mathrm{cm} \) from end \( \mathrm{A} \) of the rule.
Calculate the force which must be
applied to end B to restore the
equilibrium of the rod
\( A \cdot 4 N \)
B. 2.4
c. \( 1.2 \mathrm{N} \)
D. 4.8 N
| 3 |
Physics
|
Which of the following is not a Lewis acid?
A. Aluminum chloride
B. Ammonia
c. sulphur trioxide
D. cupric ion
| 1 |
Chemistry
|
Which of the following has the shortest
wavelength?
A. Red light
B. Blue light
c. Gamma rays
D. x rays
E. Radio waves
| 3 |
Physics
|
If \( \theta \) is the angle between the pair of
straight lines \( x^{2}-5 x y+4 y^{2}+3 x- \)
\( 4=0, \) then \( \tan ^{2} \theta \) is equal to
\( A \cdot \frac{9}{16} \)
в. \( \frac{16}{25} \)
c. \( \frac{9}{25} \)
D. \( \frac{21}{25} \)
E \( \cdot \frac{25}{9} \)
| 2 |
Maths
|
Which of the following property is generally not shown by metal?
A . Electrical conduction
B. Sonorous in nature
c. Dullness
D. Ductility
| 1 |
Chemistry
|
Determine the value of \( k \) so that the
following linear equations has no
solution:
\( (3 k+1) x+3 y-2=0 \) and \( \left(k^{2}+\right. \)
1) \( \boldsymbol{x}+(\boldsymbol{k}-\mathbf{2}) \boldsymbol{y}-\mathbf{5}=\mathbf{0} \)
A. \( k=-1 \)
B. \( k=3 \)
c. \( k=-7 \)
D. \( k=8 \)
| 2 |
Maths
|
State whether true or false.
An increase in the base area leads to
the decrease in stability of the object.
A. True
B. False
| 3 |
Physics
|
The solution set of \( f^{\prime}(x)>g^{\prime}(x) \) where
\( f(x)=\left(\frac{1}{2}\right) 5^{2 x+1} \) and \( g(x)=5^{x}+ \)
\( 4 x \log 5 \) is
\( A \cdot(1, \infty) \)
B \( \cdot(0,1) \)
\( c \cdot[2, \infty) \)
D. \( (0, \infty) \)
| 2 |
Maths
|
A wire has a resistance of \( 10 \Omega \). It is
stretched by \( 1 / 10 \) of its original length. Then its resistance will be
A. \( 9 \Omega \)
B. \( 10 \Omega \)
c. \( 11 \Omega \)
D. \( 12.1 \Omega \)
| 3 |
Physics
|
The role of gibberellin is
A. Inhibits lateral buds
B. Stimulates fruit ripening
C. Maintains seed dormancy
D. Stimualtes rapid stem elongation
E. All of the above
| 0 |
Biology
|
Which heat depends on the direction of
current?
A. Joule heat
B. Peltier heat
c. Thompson effect
D. None of these
| 1 |
Chemistry
|
Which of the following is not a measure of central location?
A. Mean
B. Median
c. mode
D. Variance
| 2 |
Maths
|
Two isosceles triangles have equal vertical angles and their areas are in the ratio \( 9: 16 . \) What is the ratio of their
corresponding altitudes?
A .2: 3
B. 3: 2
c. 3: 4
D. 4: 3
| 2 |
Maths
|
If the line joining the points (-1,2,3),(2,-1,4) is perpendicular to the line joining the points \( (x,-2,4),(1,2,3) \) then \( x= \)
\( \mathbf{A} \cdot \mathbf{3} \)
B. 10
\( c \cdot \frac{-3}{10} \)
D. \( \frac{-10}{3} \)
| 2 |
Maths
|
Antichlor is a compound that converts
\( C I_{2} \) into \( _{-}-_{-} ? \)
A. hydrochloride acid
B. kcl
C. nitric acid
D. Nacl
| 1 |
Chemistry
|
How is 1-propoxypropane synthesised from propan-1-ol? Write mechanism of
this reaction.
| 1 |
Chemistry
|
The relation \( R \) define on the set of
natural numbers as \( \{(a, b): a \) differs
from b by \( 3\} \) is given.
A \( \cdot\{(1,4),(2,5),(3,6), \ldots \ldots . .\} \)
в. \( \{(4,1),(5,2),(6,3), \ldots \ldots .\} \)
c. \( \{(1,3),(2,6),(3,9), \ldots \ldots .\} \)
D. None of above
| 2 |
Maths
|
What are the main function of
connective tissue?
| 0 |
Biology
|
A rod of length \( l \) is translating at
velocity \( v \) making an angle \( \theta \) with the
length as shown. If its resistance is \( \boldsymbol{R} \)
then find emf and current in the rod?
| 3 |
Physics
|
The motion described by the string of violin is -
A. oscillatory motion
B. vibratory motion
c. non-periodic motion
D. rectilinear motion
| 3 |
Physics
|
A lake near village suffered heavy mortality of fishes within a few days. Consider the following reasons for this.
(i) Lots of urea and phosphate fertiliser were used in the crops in the vicinity.
(ii) The area was sprayed with DDT by an aircraft.
(iii) The lake turned green and stinky.
(iv) Phytoplankton population in the lake declined initially thereby greatly reducing photosynthesis. Which two of the above were the main
causes of fish mortality in the lake?
A . (i), (ii)
B. (ii), (iii)
\( c . \) (iii), (iv)
D. (i), (iii)
| 0 |
Biology
|
In several fungi and plants the bisexual condition is denoted by
A. Homothallic and monoecious
B. Heterothallic and Monoecious
c. Homothallic and dioecious
D. Heterothallic and dioecious
| 0 |
Biology
|
Which of the following statements are
correct about dissociation?
A. Dissociation generally refers to breaking a compound into smaller pieces, usually reversibly.
B. Dissociation can happen without the formation of charged species
\( c . \) Both \( A \) and \( B \)
D. None of these
| 1 |
Chemistry
|
If the standard deviation of a set of
scores is 1.2 and their mean is \( 10, \) then the coefficient of variation of the scores
is
A . 12
B. 0.12
c. 20
D. 120
| 2 |
Maths
|
Nitrogen oxides released in the
stratosphere cause ozone depletion due
to
A. catalysing conversion of ozone to oxygen
B. Binding ozone
c. Reacting with ozone
D. All of the above
| 0 |
Biology
|
A body is projected up such that its
position vector with time as \( \vec{r}= \)
\( \left\{3 t \hat{i}+\left(4 t-5 t^{2}\right) \hat{j}\right\} m . \) Here, tis in
seconds.
Find the time and \( x- \) coordinate of
particle when its \( y- \) coordinate is zero.
| 3 |
Physics
|
If \( a, b, c \) are in \( A . P ., \alpha, \beta, \gamma \) in H.P., \( \boldsymbol{a} \boldsymbol{\alpha}, \boldsymbol{b} \boldsymbol{\beta}, \boldsymbol{c} \gamma \) in G.P. (with common ratio
not equal to \( 1 . \) ), then prov that \( a: b: c= \) \( \frac{1}{\gamma}: \frac{1}{\beta}: \frac{1}{\alpha} \)
| 2 |
Maths
|
\( \lim _{n \rightarrow \infty} \frac{n(2 n+1)^{2}}{(n+2)\left(n^{2}+3 n-1\right)} \) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B. 2
\( c \cdot 4 \)
\( D \)
| 2 |
Maths
|
If \( h(x)>[2 x-f n(f(x))] f(x) \) and
\( f(x)>0 \) satisfy for \( \forall x>0, \) if \( h(x)= \) \( \int_{0}^{x}(f(t)-t) d t, \) then
A. \( h(x) \) is increasing function
B. \( h(x) \) is decreasing function
\( c \cdot h(1)>1 \)
D. \( h(1)>e-1 \)
| 2 |
Maths
|
In the following redox reaction:
\( \boldsymbol{Z} \boldsymbol{n}(\boldsymbol{s})+\boldsymbol{N} \boldsymbol{O}_{\boldsymbol{3}}^{-}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{H}^{+}(\boldsymbol{a} \boldsymbol{q}) \longrightarrow \)
\( Z n^{2+}(a q)+N H_{4}^{+}(a q) \)
\( Z n(s) \) and \( N O_{3}^{-}(a q) \) respectively are
respectively:
A. oxidant and reductant
B. reductant and oxidant
c. both oxidant
D. both reductant
| 1 |
Chemistry
|
The pH of rain water is \( 7 . \) Is it true or
false?
| 1 |
Chemistry
|
Classify the following polynomial based on their degrees:
\( \boldsymbol{y}^{2}-\boldsymbol{4} \)
| 2 |
Maths
|
Which of the following is NOT a Absolute Temperature Scale?
A. Celsius Scale
B. Rankine Scale
c. Kelvin Scale
D. None of these
| 3 |
Physics
|
Which is the largest open university in India?
A. Indira Gandhi National Open University
B. Dr. B.R. Ambedkar Open University
c. Nalanda Open University
D. Yashwantrao Chavan Maharashtra open University
| 3 |
Physics
|
Let \( \boldsymbol{f}: \boldsymbol{I} \boldsymbol{R} \rightarrow \boldsymbol{I} \boldsymbol{R} \quad \) be defined as
\( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}|+\left|\boldsymbol{x}^{2}-1\right| . \) The total number
of points at which \( f \) attains either a
local maximum or local minimum is
| 2 |
Maths
|
An airplane with wingspan \( 50 m \) is flying horizontally with a speed of
\( 360 k m h r^{-1} \) over a place where the
vertical component of the earth's magnetic field is \( 2 \times 10^{-2} \). The
potential difference between the tips of the wings would be
A. \( 100 V \)
в. \( 1.0 V \)
\( c .0 .2 V \)
D. \( 0.01 V \)
| 3 |
Physics
|
Two positive charges \( \boldsymbol{q}_{1}=\boldsymbol{4} \times \mathbf{1 0}^{-\mathbf{6}} \boldsymbol{C} \)
and \( q_{2}=9 \times 10^{-6} C \) are placed \( 10 \mathrm{cm} \)
a part in air. The position of a third charge to be placed between them, such that there will be no resultant force on it
is:
A \( .6 \mathrm{cm} \) from \( q_{1} \)
B. \( 3 \mathrm{cm} \) from \( q_{1} \)
c. \( 4 \mathrm{cm} \) from \( q_{1} \)
D. \( 7 \mathrm{cm} \) from \( q_{1} \)
| 3 |
Physics
|
Velocity of sound in air is about :
A. \( 330 \mathrm{m} / \mathrm{s} \)
B. \( 460 \mathrm{m} / \mathrm{s} \)
c. \( 380 m / s \)
D. \( 400 \mathrm{m} / \mathrm{s} \)
| 3 |
Physics
|
The \( (x, y, z) \) coordinates of two points \( A \) and \( \mathrm{B} \) are given respectively as (0,4,-2) and \( (-2,8,-4) . \) The displacement vector
from \( A \) to \( B \) is:
A \( \cdot-2 \hat{i}+4 \hat{j}-2 \hat{k} \)
B. \( 2 \hat{i}-4 \hat{j}+2 \hat{k} \)
c. \( 2 \hat{i}+4 \hat{j}-2 \hat{k} \)
D. \( -2 \hat{i}-4 \hat{j}-2 \hat{k} \)
| 3 |
Physics
|
The eccentricity of the conic is \( \frac{l}{r}= \) \( 2+3 \cos \theta+4 \sin \theta \)
\( \mathbf{A} \cdot \mathbf{3} \)
B. 4
\( c .5 \)
D.
| 2 |
Maths
|
Conifer gymnosperm, amongst the following is
A. Gnetum
B. Sequoia
c. cycas
D. Ginko
| 0 |
Biology
|
Conduct an experiment to prepare
nitrogen gas objective :
1.5 :Formation of nitrogen (N \( _{2} \) )
| 1 |
Chemistry
|
in the given figure sides of the angles
are parallel. Find \( \boldsymbol{x} \) and \( \boldsymbol{y} \) if \( \angle \boldsymbol{A}=\mathbf{5 5}^{\circ} \)
| 2 |
Maths
|
Which of the two components of starch
is water soluble?
| 1 |
Chemistry
|
Which one of the following oxy acid of fluorine exists?
\( \mathbf{A} \cdot H O F \)
в. \( H F O_{3} \)
c. \( H F O_{4} \)
D. \( H F O_{2} \)
| 1 |
Chemistry
|
A long elastic spring is stretched by \( 2 \mathrm{cm} \) and its potential energy is \( U \). If the
spring is stretched by \( 10 \mathrm{cm} \), the P.E., will be
A . \( 5 U \)
в. \( 25 U \)
c. \( U / 5 \)
D. \( U / 20 \)
| 3 |
Physics
|
If \( A \) and \( B \) are acute positive angles satisfying the equations \( 3 \sin ^{2} A+ \) \( 2 \sin ^{2} B=1 \) and \( 3 \sin 2 A-2 \sin 2 B= \)
\( 0, \) then \( A+2 B \) is equal to
A \( \cdot \frac{\pi}{4} \)
в.
\( \mathrm{c} \cdot_{3} \frac{\pi}{4} \)
D. \( \frac{2 \pi}{3} \)
| 2 |
Maths
|
Consider a parallel plate capacitor with plates \( 20 \mathrm{cm} \) by \( 20 \mathrm{cm} \) and separated by \( 2 \mathrm{mm} . \) The dielectric constant of the material between the plates is 5.The plates are connected to a voltage source
of \( 500 \mathrm{V} \). The energy density of the field
between the plates will be close to
A \( \cdot 2.65 \mathrm{J} / \mathrm{m}^{3} \)
B . \( 1.95 \mathrm{J} / \mathrm{m}^{3} \)
C. 1.38 J \( / m^{3} \)
D. 0.69 J \( / m^{3} \)
| 3 |
Physics
|
\( Z n \mid Z n^{2+}(a=0.1 M) \| F e^{2+}(a= \)
\( \mathbf{0 . 0 1} \boldsymbol{M}) \mid \boldsymbol{F} e \)
The EMF of the above cell is \( 0.2905 . \) The
equilibrium constant for the cell reaction is:
B . \( 10^{0.32 / 0.0295} \)
D. \( e^{0.32 / 0.0295} \)
| 1 |
Chemistry
|
Explain 'Electric generator' with the help of the following points :
i. Principle of an electric generator.
ii. Function of slip rings.
iii. Any two uses of a generator.
| 3 |
Physics
|
Power of lens is:
A. \( \frac{1}{\text { focal length in centimetre }} \)
B. \( \frac{1}{\text { focal length in metre }} \)
C \( \frac{100}{\text { focal length in kilometre }} \)
D. None
| 3 |
Physics
|
Biological Oxygen Demand (BOD) is a
measure of
A. Industrial wastes poured into water bodies
B. Extent to which water is polluted with organic compounds.
c. Amount of carbon monoxide inseparably combined with haemoglobin
D. Amount of oxygen needed by green plants during night
| 0 |
Biology
|
Evaluate \( \int \frac{\sin \theta}{\sin 3 \theta} d \theta \)
| 2 |
Maths
|
If \( A \) and \( B \) be two events such that
\( \boldsymbol{P}(\boldsymbol{A})=\mathbf{1} / \mathbf{4}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{1} / \mathbf{3} \) and \( \boldsymbol{P}(\boldsymbol{A} \cup \)
\( B)=1 / 2 \) show that \( A \) and \( B \) are
independence events.
| 2 |
Maths
|
If \( \alpha \) and \( \beta \) are the roots of \( a x^{2}+b x+ \)
\( c=0 \) then find the roots of the equation
\( a x^{2}-b x(x-1)+c(x-1)^{2}=0 \)
| 2 |
Maths
|
The ratio of hydraulic stress to the
corresponding strain is known as
A. Compressibility
B. Bulk modulus
c. Young's modulus
D. Rigidity modulus
E. Expansion coefficient
| 3 |
Physics
|
Cr atom is ........... hybridized.
\( \mathbf{A} \cdot s p^{3} d^{2} \) in both complexes
B. \( d^{2} s p^{3} \) in both complexes
\( \mathbf{C} \cdot s p^{3} d^{2} \) in \( A \) and \( d^{2} s p^{3} \) in \( B \)
D. \( d^{2} s p^{3} \) in \( A \) and \( s p^{3} d^{2} \) in \( B \)
| 1 |
Chemistry
|
Which of the following practices adversely effect the environment?
A. Aeration
B. Ploughing
c. weeding
D. None of the above
| 0 |
Biology
|
Find the differential equation of \( y=A \) \( \operatorname{cox}+B \sin x \)
| 2 |
Maths
|
Find the angle between the following pairs of lines:
\( \frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{-3} \) and \( \frac{x+3}{-1}= \)
\( \frac{\boldsymbol{y}-\mathbf{5}}{\mathbf{8}}=\frac{\boldsymbol{z}-\mathbf{1}}{\mathbf{4}} \)
| 2 |
Maths
|
The coordinate of the point dividing internally the line joining the points (4,-2) and (8,6) in the ratio 7: 5 is
A \( .(16,18) \)
в. (18,16)
\( ^{C} \cdot\left(\frac{19}{3}, \frac{8}{3}\right) \)
D. \( \left(\frac{8}{3}, \frac{19}{3}\right) \)
E . (7,3)
| 2 |
Maths
|
Consider the following statements A and B identify the correct statement from the following.
A) The width of the depletion layer in a
p-njjunction diode increases in forward bias.
B) In an intrinsic semiconductor, the
Fermi energy level is exactly in the middle of the forbidden gap.
A. A is true and B is false.
B. Both A and B are false
c. A is false and B is true
D. Both A and B are true
| 3 |
Physics
|
The oxidation state of bismuth in
lithium bismuthate is:
\( A \cdot+5 \)
\( B \cdot+3 \)
\( c \cdot+2 \)
\( D \cdot+4 \)
| 1 |
Chemistry
|
\( \lim _{\mathbf{x} \rightarrow 2}\left(\frac{\sqrt{1-\cos \{2(\mathbf{x}-\mathbf{2})\}}}{\mathbf{x}-\mathbf{2}}\right) \)
A. does not exist
B. equals \( \sqrt{2} \)
c. equals \( -\sqrt{2} \)
D. equals \( \frac{1}{\sqrt{2}} \)
| 2 |
Maths
|
Events \( \boldsymbol{A} \) and \( \boldsymbol{B} \) are such that \( \boldsymbol{P}(\boldsymbol{A})= \) \( \frac{1}{2}, P(B)=\frac{7}{12} \) and
\( P(\text { not } A \text { or } \operatorname{not} B)=\frac{1}{4} . \) State whether
\( A \) and \( B \) are independent?
A. True
B. False
| 2 |
Maths
|
For any two complex numbers \( z_{1}, z_{2} \) we
have \( \left|z_{1}+z_{2}\right|^{2}=\left|z_{1}\right|^{2}+\left|z_{2}\right|^{2}, \) then
A \( \cdot \operatorname{Re}\left(\frac{z_{1}}{z_{2}}\right)=0 \)
в. \( \operatorname{Im}\left(\frac{z_{1}}{z_{2}}\right)=0 \)
c. \( \operatorname{Re}\left(z_{1} z_{2}\right)=0 \)
D・Im \( \left(z_{1} z_{2}\right)=0 \)
| 2 |
Maths
|
Statement : Baking soda or baking powder is different.
Answer whether the above statement is
true or false.
A. True
B. False
| 1 |
Chemistry
|
\( " P O C l_{3}, \) like \( P_{2} O_{5} \) is also used as
dehydrating agent." Answer whether the above statement is
true or false.
If true enter 1 , else enter 0 .
| 1 |
Chemistry
|
Which of the following molecule having resonating electronic configuration?
\( A \cdot S O_{2} \)
в. \( C_{2} H_{6} \)
\( c \cdot C l_{2} \)
D. \( H B r \)
E . \( N a C l \)
| 1 |
Chemistry
|
Evaluate, without using trigonometric
tables:
\( \frac{\sin ^{2} \theta+\sin ^{2}\left(90^{\circ}-\theta\right)}{3\left(\sec ^{2} 61^{\circ}-\cot ^{2} 29^{\circ}\right)} \)
\( \frac{3 \cot ^{2} 30^{\circ} \cdot \sin ^{2} 54^{\circ} \cdot \sec ^{2} 36^{\circ}}{2\left(\csc ^{2} 65^{\circ}-\tan ^{2} 25 o\right)} \)
| 2 |
Maths
|
\( \operatorname{Let} A=\{x, y, z\} \) and \( B=\{1,2\} . \) Find
the number of relations from \( \boldsymbol{A} \) to \( \boldsymbol{B} \)
| 2 |
Maths
|
During photosynthesis
A. Water is reduced and \( C O_{2} \) is oxidized.
B. \( C O_{2} \) is reduced and water is oxidized.
C \( . \) Both \( C O_{2} \) and water get reduced.
D. Both \( C O_{2} \) and water get oxidized.
| 0 |
Biology
|
The source frequency for which a \( 5 \mu \mathrm{F} \)
capacitor has a reactance of \( 1000 \Omega \) is
A \( \cdot \frac{100}{\pi} \) Hz
в. \( \frac{1000}{\pi} \) Н \( z \)
\( c .200 H z \)
D. \( 5000 \mathrm{Hz} \)
| 3 |
Physics
|
Which does not contain cytoplasm?
A. Liver cell
B. Palisade tissue
c. Red blood cell
D. xylem vessel
| 0 |
Biology
|
Three tubes \( A, B \) and \( C \) are connected to a horizontal pipe in which liquid is flowing. The radii of pipe at the joints of \( A, B \) and \( C \) are \( 2 c m, 1 c m \) and \( 2 c m \) respectively. The height of liquid:
\( A \). in A and B is equal
B. in A is maximum
\( c . \) in \( A \) and \( C \) is same
D. is same in all three
| 3 |
Physics
|
What is the mass of one atom of \( C-12 \)
in grams?
\( \mathbf{A} \cdot 1.992 \times 10^{-23} \mathrm{gm} \)
B . \( 1.989 \times 10^{-23} \mathrm{gm} \)
C \( \cdot 1.892 \times 10^{-23} \mathrm{gm} \)
D. \( 1.965 \times 10^{-23} \mathrm{gm} \)
| 3 |
Physics
|
Which of the following is the graph showing stress-strain variation for
elastomers?
(1)
(2)
(3)
(4)
| 3 |
Physics
|
The number of permutations or the letters of the word EXAMINATION taken
4 at a time is
A . 136
в. 2454
\( c .2266 \)
D. None of these
| 2 |
Maths
|
Assertion
Tapeworm, roundworm and pinworm are
endoparasites of human intestine.
Reason
Improperly cooked food is the source of
all intestinal infections.
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.
| 0 |
Biology
|
Two radioactive sample \( A \) and \( B \) have
half \( T_{1} \) and \( T_{2}\left(T_{1}>T_{2}\right) \) respectively. At
\( T=0, \) the activity of a \( B \) was twice the activity of A. Their activity will become equal after a time:
A. \( \frac{T_{1} T_{2}}{T_{1}-T_{2}} \)
в. \( \frac{T_{1}-T_{2}}{2} \)
c. \( \frac{T_{1}+T_{2}}{2} \)
D. \( \frac{T_{1} T_{2}}{12} \)
| 3 |
Physics
|
Now, we construct rectangles with class-limits as bases and respective adjusted frequencies as heights. Draw a histogram for the marks of students given below:
\begin{tabular}{|l|c|c|c|c|c|}
\hline Marks: & \( 0-10 \) & \( 10-30 \) & \( 30-45 \) & \( 45-50 \) & \( 50-60 \) \\
\hline No. of students: & 8 & 32 & 18 & 10 & 6 \\
\hline
\end{tabular}
| 2 |
Maths
|
Reproductive health is related to
A. Physical fitness
B. Emotional compatibility
c. Behavioural inter relationships
D. All of the above
| 0 |
Biology
|
Regular reflection takes place when light is incident on:
A. a rough curved surface
B. a highly polished plane surface
c. either of A and B
D. neither of A and B
| 3 |
Physics
|
The differential equation of the family of parabolas with vertex at (0,-1) and having axis along the \( y \) -axis is:
A \( \cdot y y^{\prime}+2 x y+1=0 \)
В . \( x y^{\prime}+y+1=0 \)
c. \( x y^{\prime}+2 y+2=0 \)
D. \( x y^{\prime}-y-1=0 \)
| 2 |
Maths
|
Radiation coming from transitions \( n= \)
2 to \( n=1 \) of hydrogen atoms falls on
helium ions in \( n=1 \) and \( n=2 \) states.
What are the possible transition of helium ions as they absorb energy from the radiation?
| 3 |
Physics
|
Which of the following changes increases the overall density of the object?
A. A block of iron is formed into a hollow shape
B. A submarine fills its ballast tanks with water
c. A submarine fills its ballast tanks with air
D. A fish increases the amount of gas in its swim bladder
| 1 |
Chemistry
|
Which of the following is not a
monovalent group?
A. Aldehydic
B. Ketonic
c. carboxylic
D. Hydroxy
| 1 |
Chemistry
|
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