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Seven different coins are to be divided
amongst three persons. If no two of the persons receive the same number of
coins but each receives at least one
coin \( \& \) none is left over, then the
number of ways in which the division
may be made is
| 2 |
Maths
|
Match the scientists and their
contribution given in the columns.
Scientists \( \quad \) Contribution
A. Pasteur
p. Beer and butter milk are products of fermentation by yeast
B. Hansen \( \quad \) q. Diastase
C. Payen and \( \quad \) r. Purified rennet
Perso
D. \( \quad \) s. Streptomycin Waksman
\( A \cdot A-p, B-q, C-r, D-s \)
B. A - p, B - r, C - q, D - s
C. \( A-p, B-s, C-r, D-q \)
D. \( A-s, B-r, C-q, D-p \)
| 0 |
Biology
|
Let \( R \) be the equivalence relation in the
\( \operatorname{set} A=0,1,2,3,4,5 \) given by \( R= \)
\( (a, b): 2 \) divides \( (a-b) . \) Write the
equivalence class [0].
| 2 |
Maths
|
The \( V-I \) graph for a conductor at
temperature \( T_{1} \) and \( T_{2} \) are shown in fig.
\( \left(T_{2}-T_{1}\right) \) is proportional to
A \( . \cos 2 \theta \)
B. \( \sin 2 \theta \)
c. \( \cot 2 \theta \)
D. \( \operatorname{Tan} 2 \theta \)
| 3 |
Physics
|
Which of the following makes water a very essential element for growth of plant?
A. Turgidity of cells helps in extension growth
B. Water provides the medium for enzymatic activities
c. Cell enlargement
D. All of the above
| 0 |
Biology
|
Figure shows a parallel beam of monochromatic light incident on a convex spherical surface, radius of
curvature \( \boldsymbol{R}=\mathbf{3} \mathbf{0} \mathrm{cm}, \) which separates
glass(refractive index \( =1.6 \) ) from air.
Find the position of the image formed due to refraction of light at this single
spherical surface
| 3 |
Physics
|
A fair coin is tossed 100 times. The
probability of getting tails an odd number of times is
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{4} \)
c. \( \frac{1}{8} \)
D. \( \frac{3}{8} \)
| 2 |
Maths
|
An \( s p^{3} \) hybrid orbital contains:
A . \( 1 / 4 \) s-character
B. 1/2 s-character
c. \( 2 / 3 \) s-character
D. 3/4 s-character
| 1 |
Chemistry
|
Four identical cubes are joined end to
end to form a cuboid. If the total surface
area of the resulting cuboid is \( 648 \mathrm{cm}^{2} \)
find the length of edge of each cube. Also, find the ratio between the surface area of resulting cuboid and the surface
area of a cube.
A. \( 9 \mathrm{cm} \) and 3: 1
B. 2 cm and 3: 1
c. \( 6 \mathrm{cm} \) and 3: 1
D. \( 3 \mathrm{cm} \) and 3: 1
| 2 |
Maths
|
The moles of \( B a\left(N O_{3}\right)_{2} \) which on
dissolving in 12 moles of water lowers the vapour pressure of water to \( 80 \% \) are
| 1 |
Chemistry
|
Gelatin is often used as an ingredient in
the manufacture of ice-cream. The
reason for this is :
A. to prevent the formation of a colloid.
B. to stabilize the colloid and prevent crystal growth.
c. to cause the mixture to solidify
D. to improve the flavour.
| 1 |
Chemistry
|
The tarnishing of silver ornaments in the atmosphere is due to the formation
of:
\( \mathbf{A} \cdot A g_{2} O, A g_{2} S \)
B. \( A g N O_{3}, A g_{2} S \)
c. \( A g O H, A g_{2} C O_{3} \)
D. \( A g \)
| 1 |
Chemistry
|
Sulfuric acid is produced from sulfur, oxygen and water via
A. oiling process
B. contact process
c. vitroling process
D. none of the above
| 1 |
Chemistry
|
Assertion
Electric filed of a dipole can't be found using only Gauss law. (i.e. without using superposition principle)
Reason
Gauss law is valid only for symmetrical charge distribution
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
| 3 |
Physics
|
If \( a, b, c \) are in A.P., then \( \frac{1}{\sqrt{b}+\sqrt{c}}, \frac{1}{\sqrt{c}+\sqrt{a}}, \frac{1}{\sqrt{a}+\sqrt{b}} \) are in
A. \( A . P \)
в. G.Р.
c. \( H . P \)
D. None of these
| 2 |
Maths
|
What will happen if one kidney is removed from the body of a human
being?
A. Death due to poisoning
B. Uremia and death
c. Stoppage of urination
D. The person will survive
| 0 |
Biology
|
When a rubber-band is stretched by a
distance \( x, \) it exerts a restoring force of
magnitude \( F=a x+b x^{2} \) where \( a \) and \( b \)
are constants. The work done in stretching the unstretched rubber band
by \( \boldsymbol{L} \) is
\( ^{\mathbf{A}} \cdot \frac{a L^{2}}{2}+\frac{b L^{3}}{3} \)
B \( \cdot \frac{1}{2}\left(\frac{a L^{2}}{2}+\frac{b L^{3}}{3}\right) \)
\( \mathbf{c} \cdot a L^{2}+b L^{3} \)
D \( \cdot \frac{1}{2}\left(a L^{2}+b L^{3}\right) \)
| 3 |
Physics
|
Solve:
\( 8 l^{3}-36 l^{2} m+54 l m^{2}-27 m^{3} \)
| 2 |
Maths
|
\( C_{6} H_{6} \frac{H N O_{3}}{H_{2} S O_{4}} A \frac{B r_{2}}{F e B r_{3}} B, \) Find the final
product B.
| 1 |
Chemistry
|
An organic compound has \( C \) and \( H \) percentage in the ratio 6: 1 by mass
and \( \mathrm{C} \) and 0 percentage in the ratio 3: 4
by mass. The compound is:
A. \( H C H O \)
в. \( C H_{3} O H \)
c. \( C H_{3} C H_{2} \) ОН
D. \( (C O O H)_{2} \)
| 1 |
Chemistry
|
Sodium carbonate is used to:
A. preserve pickles, fish
B. baking industry
c. manufacture borax
D. all of above
| 1 |
Chemistry
|
What will be the length of eukaryotic
DNA segment having 10 pairs of nucleotides?
| 0 |
Biology
|
If \( \frac{\mathbf{x}^{4}+\mathbf{2 4 x}^{2}+\mathbf{2 8}}{\left(\mathbf{x}^{\mathbf{2}}+\mathbf{1}\right)^{\mathbf{3}}} \)
\( =\frac{\mathbf{A} \mathbf{x}+\mathbf{B}}{\mathbf{x}^{2}+\mathbf{1}}+\frac{\mathbf{C} \mathbf{x}+\mathbf{D}}{\left(\mathbf{x}^{2}+\mathbf{1}\right)^{2}}+\frac{\mathbf{E} \mathbf{x}+\mathbf{F}}{\left(\mathbf{x}^{2}+\mathbf{1}\right)^{3}} \)
then \( \boldsymbol{A}= \)
\( A \)
B. -
c.
\( D \)
| 2 |
Maths
|
The ends of a diagonal of a square are (2,-3) and \( (-1,1) . \) Another vertex of the square can be
This question has multiple correct options
\( ^{\mathbf{A}} \cdot\left(\frac{-3}{2},-\frac{5}{2}\right) \)
в. \( \left(\frac{5}{2}, \frac{1}{2}\right) \)
\( ^{c} \cdot\left(\frac{1}{2}, \frac{5}{2}\right) \)
D. none of these
| 2 |
Maths
|
Find \( x, \) if the angles of a triangle have
measures \( \left(x+40^{0}\right),\left(2 x+20^{0}\right) \) and \( 3 x \)
also state which type of triangle is this.
A . \( x=60^{\circ} \) and Equilateral triangle
B. \( x=20^{\circ} \) and Scalene triangle
C . \( x=20^{\circ} \) and Equilateral triangle
D. \( x=40^{\circ} \) and Scalene triangle
| 2 |
Maths
|
A small metal ball of mass 'm' is
dropped in a liquid contained in a vessel, attains a terminal velocity 'v'. If a metal ball of same metarial but of mass
\( 8 \mathrm{m}^{\prime} \) is dropped in same liquid, then the terminal velocity will be:
A. \( V \)
B. \( 2 V \)
\( c .4 V \)
D. \( 8 V \)
| 3 |
Physics
|
\( \boldsymbol{x}+\mathbf{1} \leq \mathbf{7}, \) where \( \boldsymbol{x} \in \boldsymbol{N} \)
A \( \cdot\{1,2,3,4,5,6,7\} \)
в. \{1,2,3,4,5,6\}
c. Data insufficient
D. None of these
| 2 |
Maths
|
Which of the following statement best
describe torque?
A. is the vector product of force and lever arm length.
B. is a scalar and has no direction associated with it
C. is always equal to force.
D. is always greater for shorter lever arms.
E. must always equal zero
| 3 |
Physics
|
For a given value of the degree of dissociation \( (\alpha), \) which of the following
have correct van't Hoff factor?
This question has multiple correct options
A. \( N a C l ; i=2+\alpha \)
в. \( C a\left(N O_{3}\right)_{2} ; i=1+2 \alpha \)
c. \( K_{4}\left[\left(F e(C N)_{6}\right] ; i=1+4 \alpha\right. \)
D. \( \left(N H_{4}\right)_{3} P O_{4} ; i=3+\alpha \)
| 1 |
Chemistry
|
A car moving on a straight road covers
the one third of the total distance with
\( 20 \mathrm{Km} / \mathrm{h} \) and the rest with \( 60 \mathrm{Km} / \mathrm{h} \)
.The average speed is
| 3 |
Physics
|
A vessel has \( 6 g \) of hydrogen at pressure \( P \) and temperature \( 500 K . A \) small hole is made in it so that hydrogen leaks out. How much hydrogen leaks out if the final pressure is \( \boldsymbol{P} / 2 \) and temperature falls to \( 300 \mathrm{K} ? \)
\( A \cdot 28 \)
B. 3g
\( c \cdot 4 g \)
D. 18
| 3 |
Physics
|
Derivation of second equation of motion
is:
\( \mathbf{A} \cdot d \theta=w d 2 t \)
B \( . d \theta=w d t \)
\( \mathbf{c} \cdot d \theta=w d 3 t \)
\( \mathbf{D} \cdot d \theta=w d t^{2} \)
| 3 |
Physics
|
Write the differences between static
electricity and electric current.
| 3 |
Physics
|
What does the mass number of an atom
represent?
A. Only the number of protons
B. The number of protons and neutrons
c. The number of protons and electrons
D. Only the number of neutrons
| 1 |
Chemistry
|
The molar mass of \( N_{2} O \) as well as \( C O_{2} \)
is \( 44 g m o l^{-1} . A t 25^{o} C \) and 1 atm
pressure, \( 1 \mathrm{L} N_{2} \mathrm{O} \) contains \( \mathrm{n} \) molecules
of gas. The number of \( C O_{2} \) molecules in
2 L under same conditions will be:
\( A \)
B. \( 2 n \)
\( c \cdot \frac{n}{2} \)
\( D \cdot \frac{n}{n} \)
| 1 |
Chemistry
|
\( I_{2} \) produced, when ozone reacts with
moist \( K I \), is used to convert \( C_{2} H_{5} O H \)
to \( C I_{3} C H O . \) The number of moles of
ozone required to convert 1 mol of
\( C_{2} H_{5} O H \) into \( C I_{3} C H O \) is :
A . 1
B . 2
\( c \cdot 4 \)
D. 3
| 1 |
Chemistry
|
Arrange following according to boiling point
\( \boldsymbol{C}_{4} \boldsymbol{H}_{10}, \boldsymbol{C}_{3} \boldsymbol{H}_{8}, \boldsymbol{C}_{5} \boldsymbol{H}_{12} \)
| 1 |
Chemistry
|
The velocity \( v \) versus \( t \) graph of a body in
a straight line is as shown in Fig. The
displacement of the body in five
seconds is
\( A \cdot 2 m \)
B. \( 3 m \)
\( c .4 m \)
D. 5 m
| 3 |
Physics
|
Wisdom tooth appears in a human being, when age is between
A. 4 to 8 years
B. 10 to 14 years
\( c . \) 17 to 30 years
D. 30 to 40 years
| 0 |
Biology
|
How do plants change their shape?
A. By photosynthesis
B. By changing amount of water
C. By using minerals from the soil
D. All of the above
| 0 |
Biology
|
A distinct monocot character shown by the flowers of Liliaceae is
A. Hypogynous flowers
B. Actinomorphic flowers
c. Trimerous flowers
D. Bisexual flowers
| 0 |
Biology
|
Obturator foramen is found in
A. Frog's pelvic girdlel
B. Frog's pectoral girdle
c. Rabbit's pelvic girdle
D. Rabbit's pectoral girdle
| 0 |
Biology
|
Match the column I with II and column I
and mark the appropriate choice.
Column I
İ
Uncertainty of an
(i)
(A) \( \quad \) object
(B) Bohr's radius of an
(ii) \( \frac{h}{4 \pi m} \) orbit
Angular
(C) momentum of an
(iii) \( \frac{h}{m v} \) electron
(D) de Broglie
(iv) \( n \cdot \frac{h}{2 \pi} \) wavelength
A \( \cdot(A) \rightarrow(i i i),(B) \rightarrow(i v),(C) \rightarrow(i),(D) \rightarrow(i i) \)
в. \( (A) \rightarrow(i i),(B) \rightarrow(i),(C) \rightarrow(i v),(D) \rightarrow(i i i) \)
C. \( (A) \rightarrow(i v),(B) \rightarrow(i i i),(C) \rightarrow(i),(D) \rightarrow(i i) \)
D. \( (A) \rightarrow(i),(B) \rightarrow(i i),(C) \rightarrow(i v),(D) \rightarrow(i i i) \)
| 1 |
Chemistry
|
The equivalent inductance of two inductor is \( 2.4 m H \) when connected in
parallel and \( 10 m H \) when connected in
series. The difference between two
inductance is (neglecting mutual induction between coils)
\( \mathbf{A} \cdot 3 m H \)
в. \( 2 m H \)
\( \mathrm{c} .4 \mathrm{mH} \)
D. \( 16 m H \)
| 3 |
Physics
|
Assertion
\( \mid \mathfrak{f}^{6} \boldsymbol{C}_{\boldsymbol{n}}+\boldsymbol{2} \cdot^{\boldsymbol{6}} \boldsymbol{C}_{\boldsymbol{n}+1}+^{\boldsymbol{6}} \boldsymbol{C}_{\boldsymbol{n}+\boldsymbol{2}}>^{\boldsymbol{8}} \boldsymbol{C}_{\boldsymbol{3}} \) then
the quadratic equations whose roots \( \operatorname{are} \alpha, \beta \) and \( \alpha^{n-1}, \beta^{n-1} \) (for least value
of
n) have two common roots.
Reason
Equation \( a x^{2}+b c+c=0 \) and \( a^{1} x^{2}+ \)
\( b^{1} x+c^{1}=0 \) have two roots common
\( \operatorname{then}\left(b c^{1}-b^{1} c\right)\left(a b^{1}-a^{1} b\right)=\left(c a^{1}-\right. \)
\( \left.\boldsymbol{c}^{1} \boldsymbol{a}\right)^{2} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
| 2 |
Maths
|
Effective nuclear charge \( \left(Z^{*}\right) \) can be
calculated by using the formula:
\( \mathbf{A} \cdot Z^{*}=Z-S \)
B . \( Z^{*}=Z+S \)
c. \( Z^{*}=S-Z \)
D. \( Z=Z^{*}-S \)
| 1 |
Chemistry
|
Find the order of the differential
equation:
\( \log \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}=\left(\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right)^{3}+\boldsymbol{x} \)
| 2 |
Maths
|
Find the first term and the difference of
an arithmetic progression if the sum of its first five even terms is equal to 15
and the sum of the first three terms is
equal to (3)
| 2 |
Maths
|
Vitamin \( C \) is an organic acid known as:
A. ascorbic acid
B. citrus acid
c. glycolic acid
D. acetic acid
| 1 |
Chemistry
|
Assertion
Two particles moving in the same direction do not lose all their energy in a completely inelastic collision
Reason
Principle of conservation of momentum holds true for all kinds of collision
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
| 3 |
Physics
|
andiscilicia du
consists of two identical uniform solid
cylinders, each of mass \( m, \) on which two
light threads are wound symmetrically.
The friction in the axle of the upper
cylinder is assumed to be absent. If the
tension of each thread in the process of motion is \( \boldsymbol{T}=\frac{\boldsymbol{m} \boldsymbol{g}}{\boldsymbol{x}}, \) then the value of \( \boldsymbol{x} \)
is :
A . 10
B. 20
c. 15
\( D \)
| 3 |
Physics
|
Choose the correct statement
B. \( \alpha: \beta: \gamma:: 2: 3: 1 \)
c. \( \alpha: \beta: \gamma:: 3: 1: 1 \)
D. \( \alpha: \beta: \gamma:: 1: 2: 3 \)
| 3 |
Physics
|
A student uses a magnetic compass to
perform a laboratory experiment in the Northern Hemisphere. She then carries the same magnetic compass with her to the Southern Hemisphere, taking care not to damage the compass in any way. When she reaches her destination at the equivalent latitude and longitude in the Southern Hemisphere, she prepares to perform the same laboratory experiment. The student looks at the compass before performing the experiment to see if the compass needle has changed. How has the compass changed?
A. The compass needle points \( 90^{\circ} \) to the left of the expected direction
B. The compass needle points \( 90^{\circ} \) to the right of the expected direction
c. The compass needle slowly rotates in a counter clockwise direction
D. The compass needle slowly rotates in a clockwis tion
as been no he co
| 3 |
Physics
|
The ionisation potential of isotopes of
an element will be:
A. same
B. different
c. dependent on atomic masses
D. dependent on the number of neutrons present in the nucleus
| 1 |
Chemistry
|
Evaluate \( \sqrt{11 \sqrt{11 \sqrt{11 \sqrt{11 \dots \dots \infty}}}} \)
| 2 |
Maths
|
For each given solid, identify the top view, front view and side view.
| 2 |
Maths
|
Which of the following will best give
resorcinol (1,3-dihydroxy benzene)?
\( A \)
B.
\( c \)
\( D \)
| 1 |
Chemistry
|
In the following reaction Phenol\( \stackrel{Z n d u s t}{\rightarrow} X \frac{C H_{3} C l}{a n h . A l c l_{3}} \)
\( \boldsymbol{Y}^{\boldsymbol{a l k} \cdot \boldsymbol{K} \underline{M n} \boldsymbol{O}_{4} / \triangle} \boldsymbol{Z} \)
The product \( Z \) is:
A. toulene
B. benzaldehyde
c. benzoic acid
D. benzene
| 1 |
Chemistry
|
Assertion
In order to reduce sliding friction, lubricants are used.
Reason Lubrication changes the conditions of rubbing, replacing the sliding friction by rolling friction, there by reducing the force of friction.
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
| 3 |
Physics
|
Find the principle value of
\( \operatorname{cosec}^{-1}(-\sqrt{2}) \)
| 2 |
Maths
|
In Kolbe's reaction with phenol as the
reactant, the number of \( O \) atoms in the
final product is:
| 1 |
Chemistry
|
The increasing order of reactivity among group 1 element is \( L i<N a< \)
\( R b<C s, \) whereas that among group 17
element is \( F>C I>B r>I . \) Explain?
| 1 |
Chemistry
|
Emulsion can be destroyed by:
This question has multiple correct options
\( A \). the addition of emulsifier which tends to form another
emulsion
B. electrophoresis with high potential
C. freezing
D. all
| 1 |
Chemistry
|
Derive relationship between H and U.
| 1 |
Chemistry
|
The process of introducing impurities in small quantities into an intrinsic semiconductor is called Doping.
A. True
B. False
| 3 |
Physics
|
Area of \( \Delta A B C \) is
A. 45 squares units
B. 55 squares units
c. 65 squares units
D. none of these
| 2 |
Maths
|
Which property of water is used by plants for taking minerals from the soil?
I) Water can form aqueous solutions.
Il) Water can dissolve a wide variety of
substances
\( A \)
B. I
\( c \cdot 1,1 \)
D. none of the above
| 1 |
Chemistry
|
A simple harmonic motion has an amplitude \( A \) and time period \( T . \) Find the time required by it to travel directly from \( \boldsymbol{x}=\boldsymbol{A} \) to \( \boldsymbol{x}=\boldsymbol{A} / \mathbf{2} \)
| 3 |
Physics
|
Prove the following by using the principle of mathematical induction for
all \( \boldsymbol{n} \in \boldsymbol{N} \)
\( \mathbf{1}+\mathbf{3}+\mathbf{3}^{2}+\ldots+\mathbf{3}^{n-1}=\frac{\left(\mathbf{3}^{n}-\mathbf{1}\right)}{\mathbf{2}} \)
| 2 |
Maths
|
If the function \( u=f(x) \) is continuous at
the point \( x=a \) and the
function \( y=g(u) \) is continuous at the
point \( u=f(a), \) then the
composite function \( \boldsymbol{y}=(\boldsymbol{g} \boldsymbol{o} \boldsymbol{f})(\boldsymbol{x})= \)
\( g(f(x)) \) is
A. continuous at the point \( x=f(a) \)
B. continuous at the point \( x=a \)
c. discontinuous at the point \( x=a \)
D. continuous at the point \( x=g(a) \)
| 2 |
Maths
|
Specify the co-ordination geometry
around and hybridization of \( N \) and \( B \)
\( \operatorname{atom} \operatorname{in} \mathbf{a} 1: 1 \) complex of \( B F_{3} \) and
\( \boldsymbol{N} \boldsymbol{H}_{3}: \)
\( \mathbf{A} \cdot N: \) tetrahedral, \( s p^{3} ; B: \) tetrahedral, \( s p^{3} \)
B. \( N: \) pyramidal, \( s p^{3} ; B \) : pyramidal, \( s p^{3} \)
C \( . N: \) pyramidal, \( s p^{3} ; B: \) planar, \( s p^{3} \)
D. \( N: \) pyramidal, \( s p^{3} ; B: \) tetrahedral, \( s p^{3} \)
| 1 |
Chemistry
|
The van der Waal's parameters for
\( \operatorname{gases} A, B, C \) and \( D \) are:
\begin{tabular}{lll}
Gas & \( a \) \( \left(l i t r e^{2} a t m / m o l^{2}\right) \) & \( b(l i t r e / m o l \) ) \\
\( A \) & 4.0 & 0.027 \\
\( B \) & 8.0 & 0.030 \\
\( C \) & 6.0 & 0.032 \\
\( D \) & 12.0 & 0.027 \\
\hline
\end{tabular} Which one of these gases has the
highest critical temperature?
\( \mathbf{A} \cdot A \)
\( \mathbf{B} \cdot B \)
\( c \cdot C \)
D. \( D \)
| 1 |
Chemistry
|
The mass of particle executing S.H.M is gm.lf its periodic time is \( \pi \) seconds,
the value of force constant is:-
A. 4 dynes/cm
B. \( 4 \mathrm{N} / \mathrm{cm} \)
\( c \cdot 4 N / m \)
D. 4 dynes/m
| 3 |
Physics
|
Two molecules indicated below are
capable to intramolecular H-bonding. Which is likely to form more stable
hydrogen bonds?
\( A \)
B. II
C. Both are equally capable
D. Cannot be predicted
| 1 |
Chemistry
|
The third term from the end in the
expansion of \( \left(\frac{4 x}{3 y}-\frac{3 y}{2 x}\right)^{9} \) is
A \( \cdot \) s \( _{C_{7}} \frac{3^{5}}{2} \frac{y^{5}}{x^{5}} \)
В. \( -_{-9} \sigma_{7} \frac{3^{5}}{2^{3}} \frac{y^{5}}{x^{5}} \)
c. \( _{9} C_{7} \frac{3^{5}}{2^{3}} \frac{y^{5}}{x^{3}} \)
D. none of these
| 2 |
Maths
|
In the above figure, 0 is the centre of the
circle. The angle \( C B D \) is equal to
\( A \cdot 25 \)
B. 50
\( c \cdot 40^{\circ} \)
D. 130
| 2 |
Maths
|
If the roots of a quadratic expression
\( a x^{2}+b x+c \) are complex, then
A \( \cdot b^{2}<4 a c \)
В. \( b^{2}>4 a c \)
c. \( b^{2}=4 a c \)
\( \mathbf{D} \cdot a=0 \)
| 2 |
Maths
|
During glycolysis, the compounds PGAL and DHAP are formed from fructose 1,6
diphosphate by
A . Cleavage.
B. Isomerisation.
c. Phosphorylation.
D. Condensation
| 0 |
Biology
|
In a process 701 J of heat is absorbed by a system and 394 J of work is done by system. What is the change in internal energy for the process?
| 1 |
Chemistry
|
Explain the following terms giving one
example for each:
(i) Micelles
(ii) Aerosol
| 1 |
Chemistry
|
What are emulsions? What are their
different types? Give examples of each
type
| 1 |
Chemistry
|
In a trapezium. ABCD, \( \angle A D C=110^{\circ} \)
Find \( \angle \boldsymbol{A} \)
A \( .50^{\circ} \)
B. \( 60^{\circ} \)
\( c .70^{\circ} \)
D. \( 80^{\circ} \)
| 2 |
Maths
|
If \( \frac{(x+1)^{2}}{x^{3}+x}=\frac{A}{x}+\frac{B x+C}{x^{2}+1}, \) then
\( \sin ^{-1} A+\tan ^{-1} B+\sec ^{-1} C= \)
A \( \cdot \frac{\pi}{2} \)
B.
\( c \cdot c \)
D. \( \frac{5 \pi}{6} \)
| 2 |
Maths
|
Three point charges \( +\boldsymbol{q},+\mathbf{2} \boldsymbol{q} \) and \( -\mathbf{4 q} \)
where \( \boldsymbol{q}=\mathbf{0 . 1} \boldsymbol{\mu} \boldsymbol{C}, \) are placed at the
vertices of an equilateral triangle of
side \( 10 \mathrm{cm} \) as shown in figure. The potential energy of the system is
A \( \cdot 3 \times 10^{-3} J \)
В. \( -3 \times 10^{-3} J \)
\( \mathbf{c} \cdot 9 \times 10^{-3} J \)
\( \mathbf{D} \cdot-9 \times 10^{-3} \mathbf{J} \)
| 3 |
Physics
|
Which of the following statements concerning Lanthanide elements is false?
A. All Lanthanides are highly dense metals
B. Most characteristic oxidation state of Lanthanide elements is +3
C. The ionic radii of trivalent Lanthanides steadily increase with increase in the atomic number
D. Lanthanoids are separated from one another by ion exchange methods
| 1 |
Chemistry
|
Draw the graph of the linear equations
\( 4 x-3 y+4=0 \) and \( 4 x+3 y-20=0 \)
Find the area bounded by these lines and x-axis.
| 2 |
Maths
|
All x satisfying the inequality
\( \left(\cot ^{-1} x\right)^{2}-7\left(\cot ^{-1} x\right)+10>0, \) lie in
the interval:-
A \( \cdot(-\infty, \cot 5) \cup(\cot 4, \cot 2) \)
B. (cot \( 5, \) cot 4 ) \( \$ \$ \)
c. \( (\cot 2, \infty) \)
D. \( (-\infty, \cot 2) \cup(\cot 5, \infty) \)
| 2 |
Maths
|
If the following ion is coloured enter 1
else enter 0
\( N i^{2+} \)
| 1 |
Chemistry
|
Select the correct order of lattice
energy.
This question has multiple correct options
\( \mathbf{A} \cdot L i F<L i B r<L i I \)
B. \( L i C l>L i B r>L i I \)
C \( . L i C l>N a C l>K C l \)
D. \( B e C O_{3}<M g C O_{3}<S r C O_{3}<B a C O_{3} \)
| 1 |
Chemistry
|
A block of wood mass \( 5 k g \) is placed on a
plane making an angle \( 30^{\circ} \) with the horizontal. If the coefficient of friction
between the surface of contact of the
body and the plane is \( 0.5 . \) What force is required to keep the body sliding down with uniform velocity?
A. \( 1.6 N \)
B. \( 4.8 N \)
\( c \cdot 6.4 N \)
D. \( 3.35 N \)
| 3 |
Physics
|
In the vulcanization of rubber:
A. sulphur reacts to form a new compound
B. sulphur cross-links are introduced
c. sulphur forms a very thin protective layer over rubber
D. All of the above
| 1 |
Chemistry
|
There are n identical capacitors, which are connected in parallel to a potential
difference \( V . \) These capacitors are then reconnected, in series. The potential difference between the extreme ends is:
A . zero
в. \( n V \)
c. \( (n-1) V \)
D. none of the above
| 3 |
Physics
|
A circular loop of radius \( 2 \mathrm{cm} \), is placed in a time varying magnetic field with rate of \( 2 T / \)sec. Then induced electric
field in this loop will be:
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( 0.002 \mathrm{V} / \mathrm{m} \)
c. \( 0.01 V / m \)
D. \( 2 V / m \)
| 3 |
Physics
|
Use Lagrange's Mean Value Theorem to
determine a point on the curve \( y= \) \( \sqrt{x-2} \) at the tangent is parallel to the
chord joining the points (2,0) and (3,1)
| 2 |
Maths
|
Most abundant bacteria are
| 0 |
Biology
|
The geometry of \( N i(C O)_{4} \) and
\( N i\left(P P h_{3}\right)_{2} C l_{2} \) are:
A. both square planar
B. tetrahedral and square planar, respectively
c. both tetrahedral
D. square planar and tetrahedral, respectively
| 1 |
Chemistry
|
With the usual notations, check if the
following equation \( S_{t}=u+\frac{1}{2} a(2 t-1) \)
is dimensionally correct or not.
| 3 |
Physics
|
Let \( p, q \in\{1,2,3,4\} . \) The number of
equation of the form \( p x^{2}+q x+1=0 \)
having real roots, is
A . 15
B. 9
c. 8
D. 7
| 2 |
Maths
|
Evaluating the following:
\( (1+2 \sqrt{x})^{5}+(1-2 \sqrt{x})^{5} \)
A \( \cdot 2\left(1+40 x^{2}+80 x\right) \)
B. \( 2\left(1-40 x+81 x^{2}\right) \)
c. \( 2\left(1+40 x+80 x^{2}\right) \)
D. None of these
| 2 |
Maths
|
In the third period of the periodic table,the element having smallest size is :
A. \( N a \)
в. \( A r \)
c. \( C l \)
D. \( s i \)
| 1 |
Chemistry
|
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