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Clathrates are
A. Inert gases
B. Inert gases + organic or inorganic compounds
C. Halogen + carbon black
D. Halogen + transition elements
| 1 |
Chemistry
|
A bar of iron is \( 10 \mathrm{cm} \) at \( 20^{\circ} \mathrm{C} \). At \( 19^{\circ} \mathrm{C} \) it
will be \( \left(\alpha_{F e}=11 \times 10^{-6} /^{o} C\right) \)
A. \( 11 x 10^{-6} \mathrm{cm} \) longer
B. \( 11 x 10^{-6} \) cm shorter
\( \mathrm{c} \cdot 11 x 10^{-5} \mathrm{cm} \) shorter
D. \( 11 x 10^{-5} \mathrm{cm} \) longer
| 3 |
Physics
|
The magnitude of force experienced by
the arc \( M N \) is
A. zero
B. \( \frac{\mu_{0} V I_{0}}{\pi R b} \)
C \( \frac{\mu_{0} V I_{0}}{2 \pi R b} \)
D. none of these
| 3 |
Physics
|
If \( f(x)=(\cos x+i \sin x)(\cos 3 x+ \)
\( i \sin 3 x) \ldots(\cos (2 n-1) x+i \sin (2 n- \)
1) \( x \), then \( f^{\prime \prime}(x)= \)
\( \mathbf{A} \cdot n^{2} f(x) \)
B . \( -n^{4} f(x) \)
\( \mathbf{c} \cdot-n^{2} f(x) \)
D. \( n^{4} f(x) \)
| 2 |
Maths
|
The total mechanical energy E
possessed by a body of mass 'm', moving with a velocity 'v' at a height 'h' is given by \( : E=\frac{1}{2} m v^{2}+m g h . \) Make
\( \mathrm{m}^{\prime} \) the subject of formula.
A \( \cdot m=\frac{2 E}{v^{2}+g h} \)
B. \( m=\frac{2 E}{v^{2}+2 g h} \)
c. \( _{m}=\frac{3 E}{v^{2}+2 g h} \)
D. \( _{m}=\frac{E}{v^{2}+2 g h} \)
| 3 |
Physics
|
If \( \theta \) be the angle between the lines
whose direction cosines's are given by \( \mathbf{3} l+\boldsymbol{m}+\mathbf{5} \boldsymbol{n}=\mathbf{0}, \boldsymbol{6} \boldsymbol{m} \boldsymbol{n}-\boldsymbol{2} \boldsymbol{n} l+\mathbf{5} \boldsymbol{l} \boldsymbol{m}= \)
0. Find value of \( 6 \cos \theta \)
| 2 |
Maths
|
Atoms in a \( P_{4} \) molecule of white phosphorus are arranged regularly in which of the following way?
A. At the corners of a cube
B. At the corners of an octahedron
c. At the corners of a tetrahedron
D. At the centre and corners of a tetrahedron
| 1 |
Chemistry
|
A car accelerates on a horizontal road
due to the force exerted by
A. The engine of the car
B. The driver of the car
c. The car on earth
D. The road on the car
| 3 |
Physics
|
Prove that the line segment joining the
mid points of the sides of a triangle form four triangles, each of which is similar to the original triangle.
| 2 |
Maths
|
In the expression \( y=a \sin (\omega t+\theta), y \)
is displacement and \( t \) is the time. Write
the dimensions of \( \omega \)
\( \mathbf{A} \cdot\left[M^{0} L T^{0}\right] \)
В \( \cdot\left[M^{0} L^{0} T^{0}\right] \)
C . \( \left[M^{0} L^{0} T^{-1}\right. \)
\( \mathbf{D} \cdot\left[M^{1} L^{0} T^{0}\right] \)
| 3 |
Physics
|
The displacement \( x \) of a particle in
motion is given in terms of time by \( x(x- \)
4) \( =1-5 \cos \omega t \)
A. The particle executes SHM
B. The particle executes oscillatory motion which is not SHM
C. motion of the particle is neither oscillator; nor simple harmonic
D. The particle is not acted upon by a force when it is at \( x \) \( =4 \)
| 3 |
Physics
|
The tones that are separated by three octaves have a frequency ratio of
A . 3: 1
B. 6: 1
c. 8: 1
D. 16: 1
| 3 |
Physics
|
The IUPAC name of given compound is:
A. 2,2 -dimethylbutanal
B. 2,3 -dimethylbutnal
C. 2,3 -dimethylbutanol
D. 2,3 -dimethylbutanal
| 1 |
Chemistry
|
What is the order of rotational
symmetry about the marked point?
| 2 |
Maths
|
Photosynthesis is absent in
A. Photic layer
B. Aphotic layer
c. Benthic layer
D. Pelagic layer
| 0 |
Biology
|
Which does not represent correct
method?
\( \mathbf{A} \cdot T i C l_{4}+2 M g \stackrel{\Delta}{\longrightarrow} T i+2 M g C l_{2}: K \) roll process
B. \( N i(C O)_{4} \stackrel{\Delta}{\longrightarrow} N i+4 C O: \) Mond's process
\( \mathbf{c} \cdot P b I_{2} \stackrel{\Delta}{\longrightarrow} P b+I_{2}: \) Van arkel process
D. \( Z r I_{4} \stackrel{\Delta}{\longrightarrow} Z r+2 l_{2}: \) Van arkel process
| 1 |
Chemistry
|
The pH of 0.05 M aqueous solution of
diethyl amine is 12. calculate its \( K_{b} \)
A. \( 2 \times 10^{-3} \)
В. \( 2.5 \times 10^{-4} \)
c. \( 2.5 \times 10^{-3} \)
D. \( 2 \times 10^{-4} \)
| 1 |
Chemistry
|
Assertion: A resistance is connected to
an ac source. Now a capacitor is included in the series circuit. The
average power absorbed by the resistance will remain same.
Reason: By including a capacitor or an inductor in the circuit average power
across resistor does not change.
A. A and R both are true and R is correct explanation of
B. A and R both are true but R is not the correct explanation of
c. A is true R is false
D. A is false and R is true
| 3 |
Physics
|
The stage of meiosis at which sperm
cell precursor contain two sister chromatids.
A. Anaphase!
B. Metaphase II
c. Prophase I
D. Anaphase II
E. Telophase II
| 0 |
Biology
|
\( \operatorname{Let} \boldsymbol{S}=\{(\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}) \in \boldsymbol{N} \times \boldsymbol{N} \times \boldsymbol{N}: \boldsymbol{a}+ \)
\( \boldsymbol{b}+\boldsymbol{c}=\mathbf{2 1}, \boldsymbol{a} \leq \boldsymbol{b} \leq \boldsymbol{c}\} \) and \( \boldsymbol{T}= \)
\( \{(a, b, c) \in N \times N \times N: \)
\( a, b, c a r e i n A P\}, \) where \( N \) is the set of
all natural numbers. Then, the number
of elements in the set \( S \cap T \) is
\( A \cdot 6 \)
B. 7
c. 13
D. 14
| 2 |
Maths
|
The correct IUPAC name of \( M n_{3}(C O)_{12} \)
is:
A. mangesedodecylcarbonyl(0)
B. dodecacarbonylmanganate(0)
c. dodecacarbonylmanganic(II)
D. dodecacarbonyltrimanganese(0)
| 1 |
Chemistry
|
A square metal wire loop of side \( 10 \mathrm{cm} \)
and of resistance \( 2 \Omega \) moves with
constant velocity in the presence of a uniform magnetic field of induction \( 4 \mathrm{T} \)
perpendicular and into the plane of the loop. The loop is connected to a network
of resistance as shown in the Figure. If
the loop should have a steady current of \( 2 \mathrm{mA} \), the speed of the loop must be (in \( \left.\mathrm{cm} \mathrm{s}^{-1}\right): \)
4
B.
\( c \)
)
| 3 |
Physics
|
Using Binomial theorem, evaluate \( (\mathbf{9 9})^{5} \)
| 2 |
Maths
|
Solve \( : \sin ^{-1}\left(\frac{2 \pi}{4}\right) \)
| 2 |
Maths
|
Which reaction conditions would be
best for the synthesis of isobutyl sec-
butyl ether \( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right)-\boldsymbol{O} \)
\( \boldsymbol{C H}_{2} \boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right)_{2} ? \)
A \( \cdot\left(C H_{3}\right)_{2} C H C H_{2} O H+H_{2} S O_{4}+ \) heat
B . \( C H_{3} C H_{2} C H\left(C H_{3}\right) O H+H_{2} S O_{4}+ \) heat
c. \( C H_{3} C H_{2} C H\left(C H_{3}\right) O N a+\left(C H_{3}\right)_{2} C H C H_{2} B r \)
D. \( \left(C H_{3}\right)_{2} C H C H_{2} O N a+C H_{3} C H_{2} C H\left(C H_{3}\right) B r \)
| 1 |
Chemistry
|
A radioactive sample of \( U^{238} \) decay to \( P b \)
through a process for which half life is
\( 4.5 \times 10^{9} \) years. The ratio of number of
nuclei of \( P b \) to \( U^{238} \) after a time of \( 1.5 \times \)
\( 10^{9} \) years.
(Given \( 21 / 3=1.26) \)
A . 0.12
B. 0.26
\( c \cdot 1.2 \)
D. 0.37
| 1 |
Chemistry
|
Metals generally form:
A. basic oxides
B. acidic oxides
c. neutral oxides
D. none
| 1 |
Chemistry
|
Represent the cell in which the following
reaction takes place \( M g(s)+ \)
\( \mathbf{2} \boldsymbol{A} \boldsymbol{g}^{+}(\mathbf{0 . 0 0 0 1} \boldsymbol{M}) \rightarrow \)
\( M g^{2+}(0.130 M)+2 A g(s) \)
Calculate its \( E_{(c e l l)} \) if \( E_{(c e l l)}^{o}=3.17 V \)
| 1 |
Chemistry
|
\( \triangle P Q R \) is an isosceles triangle with
\( P Q=P R, Q P \) is produced to \( S \) and \( P T \)
bisects the extension angle \( 2 x^{\circ} . \) Prove
that \( \angle Q=x^{o} \) and hence prove that
\( \boldsymbol{P T} \| \boldsymbol{Q} \boldsymbol{R} \)
| 2 |
Maths
|
Find mean deviation from the mean for
the given data
\( \mathbf{8} \quad \mathbf{1 0} \quad \mathbf{1 2} \quad \mathbf{1 4} \) Item
Frequency \( \quad 10 \quad 5 \quad 11 \)
A .2 .12
в. 3.04
c. 10.45
D. 5.76
| 2 |
Maths
|
State True or False.
Electrolysis of molten \( K C l \) gives \( \mathrm{Cl}_{2} \) at
cathode.
A. True
B. False
| 1 |
Chemistry
|
What is the work of progesterone which is present in oral contraceptive pills?
A. To inhibit ovulation
B. To check oogenesis
c. To check entry of sperms in to cervix and to make them inactive
D. To check sexual behaviour
| 0 |
Biology
|
60 percent people in a group of 10 people, have brown eyes. Two people are to be selected at random from the
group. What is the probability that neither person selected will have brown
eyes?
A . 0.13
B. 0.18
c. 0.25
D. 0.36
| 2 |
Maths
|
Show that \( f(x)= \) \( \left\{\begin{array}{ll}\frac{\cos a x-\cos b x}{x^{2}}, & \text { if } x \neq 0 \\ \frac{1}{2}\left(b^{2}-a^{2}\right), & \text { if } x=0\end{array}\right. \)
where \( a \) and \( b \) are real constants, is
continuous at \( \boldsymbol{x}=\mathbf{0} \)
| 2 |
Maths
|
If \( \cos (A-B)=\frac{3}{5} \& \tan A \tan B=2 \)
then
This question has multiple correct options
A \( \cdot \cos A \cos B=\frac{1}{5} \)
B. \( \sin A \sin B=-\frac{2}{5} \)
\( c \cdot \cos (A+B)=-\frac{1}{5} \)
D. \( \sin A \sin B=\frac{2}{5} \)
| 2 |
Maths
|
Branchless angiosperm trees are called
as
A. Excurrent
B. caudex
c. shrub
D. Deliquscent
| 0 |
Biology
|
Factorial of negative numbers is always
greater than 1
A. True
B. False
c. Either
D. Neither
| 2 |
Maths
|
Keystone species deserve protection
because these
A. Are capable of surviving in harsh environmental conditions
B. Indicates presence of certain minerals in the soil
C. Have become rare due to the over-exploitation
D. Play an important role in supporting other species
| 0 |
Biology
|
Name five objects which can be made
from wood.
| 1 |
Chemistry
|
Assertion
Hemichordata are connecting link between Chordata and non-Chordata.
Reason In vertebrates the origin of coelom is schizocoelic formed by splitting of mesoderm, whereas all invertebrates except echinoderms are enterocoelic.
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
|
\( \underbrace{y} \)
| 1 |
Chemistry
|
Two bodies of mass \( 10 \mathrm{kg} \) and \( 2 \mathrm{kg} \) are moving with velocities \( 2 \hat{i}-7 \hat{j}+ \) \( 3 \hat{k} m s^{-1} \) and \( -10 \hat{i}+35 \hat{j}-3 \hat{k} m s^{-1} \)
respectively. The velocity of their centre of mass is:
A . 2 ims \( ^{-1} \)
B. \( 2 \hat{k} m s^{-1} \)
\( \mathbf{c} \cdot(2 \hat{j}+2 \hat{k}) m s^{-1} \)
D. \( (2 \hat{j}+2 \hat{k}+\hat{k}) m s^{-1} \)
| 3 |
Physics
|
Which of the following relation is
incorrect?
A \( . \Delta S=\Delta H+T \Delta G \)
B . \( \Delta S=\frac{\Delta H-\Delta G}{T} \)
c. \( -\Delta G=-W_{\text {non exp}} \)
D. \( W_{P V}=-P \Delta V \)
| 1 |
Chemistry
|
For an A.P., find \( S_{7} \) if \( a=5 \) and \( d=4 \)
| 2 |
Maths
|
The following reaction happens in which
test?
\( \boldsymbol{N} \boldsymbol{a}_{2} \boldsymbol{S}+\boldsymbol{N} \boldsymbol{a}_{2}\left[\boldsymbol{F} e(\boldsymbol{C} \boldsymbol{N})_{5} \boldsymbol{N} \boldsymbol{O}\right] \longrightarrow \)
\( N a_{4}\left[F e(C N)_{5} N O S\right] \)
A. Sodium sulphide test
B. Sodium nitroprusside test
c. Both \( A \) and \( B \)
D. None of the above
| 1 |
Chemistry
|
Find the angular fringe width in Young's double slits experiments with a bluegreen light of wavelength 6000 A. The separation between the slits is \( 3.0 x \)
\( 10^{-3} m \)
| 3 |
Physics
|
What do you think would be the observation if the \( \alpha \) -particle
scattering experiment is carried out
using a foil of a metal other than gold?
A. \( \alpha \) particles would deflect by the foil by large angles
B. Most of the fast moving \( \alpha \) particles would not pass straight through the metal foil
c. There would be no change in the observation
D. All particles would appear rebound
| 1 |
Chemistry
|
Two circular coils \( X \) and \( Y \)
having radii \( \mathrm{R} \) and \( \mathrm{R} / 2 \) respectively are placed in horizontal plane with their centres coinciding with each other. Coil X has current I flowing through it in the clockwise sense. What must be the
current in the coil \( Y \) to make the total
magnetic field at the centre of two coils zero?
| 3 |
Physics
|
Write the sum of geometrical isomers \( \operatorname{in}\left[\mathrm{Pt}\left(\mathrm{H}_{2} \mathrm{N}-\mathrm{CH}\left(\mathrm{CH}_{3}\right)-\mathrm{COO}^{-}\right)_{2}\right] \) complex
and stereoisomers of \( \left[\mathrm{Pt}(\mathrm{gly})_{3}\right]^{+} \) complex.
| 1 |
Chemistry
|
Express \( (1-i)-(1+i 6) \) as \( a+i b \)
| 2 |
Maths
|
Find the species which is not perfectly planar.
A \( \cdot \dot{C} H_{3} \)
B . \( \dot{C} H F_{2} \)
\( \mathbf{c} \cdot: C H_{2} \)
D. \( \dot{N} O_{2} \)
| 1 |
Chemistry
|
Predict the \( \beta \) -elimination product(s) formed when each chloroalkane is
treated with sodium ethoxide in
ethanol. If two or more products might be formed, predict which is the major
product.
| 1 |
Chemistry
|
Assertion
In acidic medium, \( Z n^{2+} \) is not
precipitated by \( S^{2-} \) ions.
Reason
Common ion effect reduces the
concentration of \( S^{2-} \) ions to the
minimum level.
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
|
Monthly expenditures on milk in 100 familes of a housing
\( \begin{array}{llll}\text { Monthly } & 0- & 175- & 350- \\ \begin{array}{l}\text { expenditure } \\ \text { (in Rs) }\end{array} & \begin{array}{l}\mathbf{1 7 5} \\ \mathbf{3 5 0}\end{array} & \mathbf{5 2 5}\end{array} \)
Number of
10
14
familes
Find the mean, mode and median for this distribution
| 2 |
Maths
|
In Amoeba, cell membrane help in engulfing the food during the process called as endocytosis
| 0 |
Biology
|
A minute spherical air bubble is rising slowly through a column of mercury contained in a deep jar. If the radius of the bubble at a depth of \( 100 \mathrm{cm} \) is 0.1
\( \mathrm{mm}, \) calculate its depth where its radius is \( 0.126 \mathrm{mm} \) given that the surface tension of mercury is 567 dyne/cm. Assume that the atmospheric pressure is \( 76 \mathrm{cm} \) of mercury
A \( \cdot h_{2}=9.48 \mathrm{cm} \)
В . \( h_{2}=18.48 \mathrm{cm} \)
\( \mathbf{c} \cdot h_{2}=9.48 \mathrm{m} \)
D. \( h_{2}=19.48 \mathrm{cm} \)
| 3 |
Physics
|
Which of the following quantities is zero, when a uniform object is being supported at its center of gravity?
A . Mass
B. Weight
c. Force
D. Moment
| 3 |
Physics
|
An edge of a variable cube is increasing at the rate of \( 5 \mathrm{cm} / \mathrm{s} \). How fast is the
volume of the cube increasing when the
edge is \( 10 \mathrm{cm} \) long?
| 2 |
Maths
|
Find \( \frac{\sqrt[3]{\mathbf{7 2 9}}+\sqrt[3]{\mathbf{3 4 3}}}{\sqrt[3]{\mathbf{5 1 2}}} \)
| 2 |
Maths
|
DNA strands are anti-parallel because
of
A. H-bonds
B. Phosphate diester bonds
c. Disulphide bonds
D. Peptide bonds
| 0 |
Biology
|
Which one among the following has an octet of valence electrons?
A. Cation
B. Inert Gas
c. crystal
D. Anion
E . Element
| 1 |
Chemistry
|
If \( \mathbf{2} \boldsymbol{A}+\boldsymbol{B}=\left[\begin{array}{cc}\mathbf{1} & \mathbf{-} \mathbf{1} \\ \mathbf{0} & \mathbf{1} \\ \mathbf{1} & \mathbf{-} \mathbf{2}\end{array}\right] \boldsymbol{A}- \)
\( \mathbf{2} \boldsymbol{B}=\left[\begin{array}{cc}\mathbf{0} & \mathbf{1} \\ \mathbf{- 2} & \mathbf{0} \\ \mathbf{1} & \mathbf{- 1}\end{array}\right] \) find \( \boldsymbol{A} \) and \( \boldsymbol{B} \)
| 2 |
Maths
|
A bicycle wheel starts at rest and has a
constant angular acceleration \( \alpha . A \mathrm{t} \) time
\( t, \) it has roated through an angle \( \theta \) and
has an angular velocity \( \omega \).What are \( \omega \) and \( \alpha \) in term of \( \theta \) and \( t \)
| 3 |
Physics
|
Non-Lanthanoid element is:
A . La
B . Lu
\( c \cdot P r \)
D. Pm
| 1 |
Chemistry
|
A wave of length \( 2 m \) is superposed on
its reflected wave to form a stationary wave. A node is located at \( x=3 m \) The
next node will be located at \( x= \)
A. \( 4 m \)
B. \( 3.75 m \)
\( c .3 .50 m \)
D. \( 3.25 m \)
| 3 |
Physics
|
Asexual reproduction is mostly seen in which type of organism?
A . Unicellular
B. Bicellular
c. Multicellular
D. Both A and B
| 0 |
Biology
|
How many electrons flow through a wire,
when 1 A current passes for a millisecond?
| 3 |
Physics
|
Multiple Correct Answers Type Which of the following pairs have the
same dimensions?
This question has multiple correct options
A. \( h / e \) and magnetic flux
B. \( h / e \) and electric flux
C . Electric flux and \( a / \epsilon_{6} \)
D. Electric flux and \( \mu_{0} I \)
| 3 |
Physics
|
In which of the following mixtures, the London dispersion force is acting as major intermolecular force of attraction?
A. Sodium chloride and water
B. Cyclohexane and carbon tetrachloride
c. water and ethyl alcohol
D. Benzene and acetone
| 1 |
Chemistry
|
Which of the following is a geminal dihalide?
A. Ethylene dibromide
B. Propylidene chloride
c. Isopropyl bromide
D. None of the above
| 1 |
Chemistry
|
Percolation tank is constructed to
impound
A. Runoff water
B. Water vapour
c. Purified water
D. None of the above
| 0 |
Biology
|
Their common speed \( \mathbf{v} \) will be
\( \mathbf{A} \cdot \frac{q}{4} \sqrt{\frac{1}{m R \pi \varepsilon_{0}}} \)
\( \mathbf{B} \cdot q \sqrt{\frac{m R \pi \varepsilon_{0}}{4}} \)
\( \mathbf{c} \cdot 4 q \sqrt{m R \pi \varepsilon_{0}} \)
D. \( \frac{4 q}{\sqrt{m R \pi \varepsilon_{0}}} \)
| 3 |
Physics
|
In which of the following pairs, both of them are common greenhouse gases?
A. Oxygen, water vapour
B. Methane, carbondioxide
c. ozone, sulphurdioxide
D. Nitric oxide, chlorofluoro carbons
| 1 |
Chemistry
|
In Myasthenia gravis, acetylcholine
A. Receptors on motor end plate are reduced
B. Secretion from nerve terminal is reduced
C. Esterase activity is inhibited
D. Secretion from nerve terminals is enhanced
| 0 |
Biology
|
Find the complement of the following angle.
\( 45^{\circ} \)
| 2 |
Maths
|
Which term of the sequence 4,9,14,19
..., is \( 124 ? \)
A . 25
B. 30
c. 15
D. 35
| 2 |
Maths
|
Which of the following are isoelectronic and isostructural?
A \( \cdot N O_{3}^{-}, \mathrm{CO}_{3}^{2} \)
B. \( S O_{3}, N O_{3}^{-} \)
\( \mathrm{c} \cdot \mathrm{CO}_{3}^{-}, \mathrm{CO}_{3}^{2} \)
D. \( \mathrm{CO}_{3}^{2-}, \mathrm{SO}_{3} \)
| 1 |
Chemistry
|
Two long thin charged rods with charge density \( \lambda \) each are placed parallel to each other at a distance d apart. The
force per unit length exerted on one rod by the other will bewhere \( \left(\boldsymbol{K}=\frac{\mathbf{1}}{\mathbf{4} \boldsymbol{\pi} \varepsilon_{0}}\right) \)
A \( \cdot \frac{K 2 \lambda}{d} \)
в. \( \frac{K 2 \lambda^{2}}{d} \)
c. \( \frac{K 2 \lambda}{d^{2}} \)
D. \( \frac{K 2 \lambda^{2}}{d^{2}} \)
| 3 |
Physics
|
The function \( f(x)=\left\{\begin{array}{cc}\frac{e^{1 / x}-1}{e^{1 / x}+1} & x \neq 0 \\ 0, & x=0\end{array}\right. \)
is
A. continuous at \( x=0 \)
B. discontinuous at \( x=0 \)
c. discontinuous at \( x=0 \) but can be made continuous at
\( x=0 \)
D. None of these
| 2 |
Maths
|
If two events \( A \) and \( B \) are such that
\( \boldsymbol{P}(\overline{\boldsymbol{A}})=\mathbf{0 . 3}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 5} \) and
\( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})=\mathbf{0 . 3}, \) then \( \boldsymbol{P}\left(\frac{\boldsymbol{B}}{\boldsymbol{A} \cup \overline{\boldsymbol{B}}}\right) \) is
equal to
A \( \cdot \frac{5}{8} \)
B. \( \frac{7}{8} \)
\( c \cdot \frac{3}{8} \)
D.
| 2 |
Maths
|
Which rule explains the electronic configuration of chromium is \( [\mathrm{Ar}] \) \( 3 d^{5} 4 s^{1} \) instead of \( [A r] 3 d^{4} 4 s^{2} ? \)
A. Pauli's exclusion principle
B. Aufbau Principle
c. Hund's rule
D. Heisenberg principle
| 1 |
Chemistry
|
Which of the following is the consequence of man's interference with
nature?
A. Increase in natural resources
B. Biological imbalance
c. Increase in the ozone layer
D. All of the above
| 0 |
Biology
|
Generally solubility of gases in liquids is decreases as increasing temperature. Give reason
| 1 |
Chemistry
|
Evaluate \( : 125 \sqrt[3]{a^{6}}-\sqrt[3]{125 a^{6}} \)
| 2 |
Maths
|
Which of the following is false regarding an isotope?
A. Same atomic number
B. Different number of neutrons
c. Same mass number
D. Same number of the electrons
E. Same number of protons
| 1 |
Chemistry
|
Express in centimetres.
\( \mathbf{1 5 . 0 8 m} \)
| 2 |
Maths
|
RQ of sprouting potato is
\( A \)
B. >
\( c \cdot c \)
D. zero
| 0 |
Biology
|
Assertion
If in a \( \triangle A B C, \) a line \( D E \| B C \)
intersects \( A B \) in \( D \) and \( A C \) in \( E, \) then \( \frac{A B}{A D}=\frac{A C}{A E} \)
Reason
If a line is drawn parallel to one side of a triangle intersecting the other two sides, then the other two sides are
divided in the same ratio.
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
| 2 |
Maths
|
In the given figure you find two
triangles. Indicate whether the triangles
are similar. Give reasons in support of
your answer.
| 2 |
Maths
|
The racemic mixture of Alanine
\( \left(\begin{array}{c}\mathbf{C H}_{3} \mathbf{C} \mathbf{H}-\mathbf{C} \mathbf{O} \mathbf{O} \mathbf{H} \\ \mathbf{N} \mathbf{H}_{2}\end{array}\right) \) can be resolved
by using:
(a) \( (+)-2-B u t a n o \)
(b) (I) - 2-Chlorobutanoic acid
\( (c)(\pm)-2-B u t a n o \)
(d) (dl mix)-2-Chlorobutanoic acid
\( A \cdot a \) and \( b \) only
B. a and conly
C. \( b \) and \( d \) only
D. a and donly
| 1 |
Chemistry
|
Find the probability of successes in
toss of a die, where a success is defined
as
(i) Number greater than 4
(ii) Six appears on die
| 2 |
Maths
|
The incentre of the triangle formed by the points \( \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}, \boldsymbol{4} \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}, \) and
\( 4 \hat{i}+5 \hat{j}+\hat{k} \) is
A \( \cdot \frac{\hat{i}+\hat{j}+\hat{k}}{3} \)
B. \( \hat{i}+2 \hat{j}+3 \hat{k} \)
c. \( 3 \hat{i}+2 \hat{j}+\hat{k} \)
D. \( \hat{i}+\hat{j}+\hat{k} \)
| 2 |
Maths
|
Assertion: AgCl will not dissolve in a concentrated solution.
Reason: The chloride ions from NaCl
suppress the solubility of AgCl.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false
| 1 |
Chemistry
|
For a chemical reaction, \( \boldsymbol{A} \longrightarrow \boldsymbol{E} \), it is
found that rate of reaction is doubled
when the concentration of \( A \) is
increased four times. The order of the
reaction is:
A . 1
B. 2
c. \( 1 / 2 \)
D. 0
| 1 |
Chemistry
|
If \( \lim _{x \rightarrow-a} \frac{x^{7}+a^{7}}{x+a}=7 \)
then the value of a is
This question has multiple correct options
\( A \cdot 1 \)
B. -
c. 7
D. none of these
| 2 |
Maths
|
Which of the following has highest boiling point?
A. 1-chloropentane
B. 2-chloropentane
c. 3 -chloropentane
D. All have equal boiling point
| 1 |
Chemistry
|
The scientists who study ecosystems
are called
A. Ecologists
B. Economists
c. Engineers
D. Environmentalists
| 0 |
Biology
|
Two strings \( A \) and \( B \) with \( \mu=2 k g / m \)
and \( \mu=8 k g / m \) respectively are joined
in series and kept on a horizontal table with both the ends fixed. The tension in
the string is \( 200 \mathrm{N} \). If a pulse of amplitude \( 1 \mathrm{cm} \) travels in \( \mathrm{A} \) towards the junction, then find the amplitude of reflected and transmitted pulse.
A \( . A_{r}=2 A_{T}=7 \)
в. \( _{A_{r}}=\frac{-1}{3} A_{T}=\frac{2}{3} \)
c. \( A_{r}=8 A_{T}=9 \)
D. \( A_{r}=3 A_{t}=4 \)
| 3 |
Physics
|
If the system is not in free fall, which of
the following statements are true about
hydrostatic pressure?
This question has multiple correct options
A. In a liquid, point at different depths can never be at the
same pressure.
B. In a liquid, points at different depths may be at the
same pressure.
C. In different liquids, points at different depths can be at the same pressure.
D. In different liquids, points at the same depth can never be at same pressure.
| 3 |
Physics
|
The number of nine digit numbers that can be formed with different digits is
A. 9.8
B. \( 8.9 ! \)
c. \( 9.9 ! \)
D. 10
| 2 |
Maths
|
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