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Which gas is more soluble in water, \( \boldsymbol{O}_{2} \)
or \( N_{2} ? \)
| 1 |
Chemistry
|
Calculate the scalar product of the following vectors. Find the vector c being given that it is perpendicular to the vectors \( \boldsymbol{a}= \)
\( \{2,3,-1\}, b=\{1,-2,3\} \) and
satisfies the condition
\( \boldsymbol{c} \cdot\{\boldsymbol{2} \boldsymbol{i}-\boldsymbol{j}+\boldsymbol{k}\}=-\boldsymbol{6} \)
| 2 |
Maths
|
If a mole of hydrogen molecule is heated to a high temoerature then which of the following reactions take place?
A \( \cdot H_{2}(g)+436 k J m o l^{-1} \rightarrow H(g)+H(g) \)
B . \( 2 H 2(g)+820 k J m o l^{-1} \rightarrow 2 H_{2}(g) \)
C \( \cdot H_{2}(g)+H_{2}(g)+436 k J m o l^{-1} \rightarrow H_{(a q)}^{+}+H_{(a q)}^{-} \)
D. \( H_{2}(g)+200 k J m o l^{-1} \rightarrow H_{(g)}+H_{(g)} \)
| 1 |
Chemistry
|
If \( A B C D \) is a parallelogram with two adjacent angles \( A \) and \( B \) equal to each other, then the parallelogram is?
A. Rhombus
B. Trapezium
c. Rectangle
D. None of These
| 2 |
Maths
|
Which of the following are examples of celestial objects?
A. Asteroids
B. Moons
c. Planets
D. All of above
| 3 |
Physics
|
Which of the following species are having peroxy linkages? This question has multiple correct options
\( \mathbf{A} \cdot B r O_{4}^{-} \)
в. \( S_{2} O_{8}^{2} \)
\( \mathrm{c} \cdot P_{2} \mathrm{O}_{8}^{4} \)
D. \( P O_{5}^{3} \)
| 1 |
Chemistry
|
Five resistance are connected as shown
in figure. If total current flowing is \( 0.5 A \)
then the potential difference \( \boldsymbol{V}_{\boldsymbol{A}}-\boldsymbol{A}_{\boldsymbol{B}} \)
is:
\( A \cdot 8 V \)
в. \( 6 V \)
\( c \cdot 2 V \)
D. \( 4 V \)
| 3 |
Physics
|
The statements regarding ozone
i) It oxidises \( C l_{2} \) to \( H C l \)
ii) It oxidises \( P b S \) to \( P b S O_{4} \)
iii) It oxidises \( \boldsymbol{K}_{4}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}\right] \) to
\( \boldsymbol{K}_{3}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}\right] \)
The correct combination is:
A. All are correct
B. (ii) and (iii) are correct
c. only (ii) is correct
D. Only (iii) is correct
| 1 |
Chemistry
|
Ileum is
A. First part of the small intestine
B. Middle part of the small intestine
C. Last part of the small intestine
D. Not a part of the small intestine
| 0 |
Biology
|
Which carbon is the most
electronegative?
A \( \cdot s p^{3}- \) hybridized carbon
B. \( s p \) - hybridized carbon
c. \( s p^{2}- \) hybridized carbon
D. Always same irrespective of its hybrid state
| 1 |
Chemistry
|
A prism of \( \boldsymbol{R} . \boldsymbol{I} .=1.5 \) is immersed in
water of \( \boldsymbol{R} . \boldsymbol{I} .=\mathbf{4} / \mathbf{3} \) as shown in the
figure. For the total internal reflection
the correct choice is:
A \( \cdot \sin \theta<\frac{8}{9} \)
B. \( \sin \theta>\frac{8}{9} \)
\( \mathrm{c} \cdot \sin \theta=\frac{8}{9} \)
D. \( \sin \theta \leq \frac{8}{9} \)
| 3 |
Physics
|
In Young's double-slit experiment, the angular width of a fringe formed on
a distant screen is \( 1^{\circ} . \) The slit
separation is \( 0.01 \mathrm{mm} . \) The wavelength of the light is
A. \( 0.174 \mathrm{nm} \)
в. 0.174 А
c. \( 0.174 \mu m \)
D. \( 0.174 \times 10^{-4} \mathrm{m} \)
| 3 |
Physics
|
\( \int_{0}^{1} x e^{x} d x= \)
\( A \cdot 1 \)
B. 2
\( c .3 \)
D.
| 2 |
Maths
|
Which fat soluble vitamin in necessary for blood clotting?
\( A \cdot A \)
B.
\( c \cdot E \)
D.
| 0 |
Biology
|
State and prove Addition theorem on
probability.
| 2 |
Maths
|
A solution has a \( p H \) of \( 7 . \) Explain how
would you:
Increase its \( p H \)
Decrease its \( p H \)
| 1 |
Chemistry
|
The radii of curvature of the surfaces of
a double convex lens are \( 20 \mathrm{cm} \) and 40
\( \mathrm{cm} \) respectively, and its focal length is \( 20 \mathrm{cm} . \) What is the refractive index of
the material of the lens.?
A \( \cdot \frac{5}{2} \)
B. \( \frac{4}{3} \)
\( c \cdot \frac{5}{3} \)
D. \( \frac{4}{5} \)
| 3 |
Physics
|
Each interior angle of a regular polygon is double of its exterior angle. Find the number of sides in the polygon.
| 2 |
Maths
|
There are \( n \) persons sitting in a row. Two of them are selected at random. The
probability that the two selected
persons are not together, is
A \( \cdot \frac{2}{n} \)
в. \( _{1-} \frac{2}{n} \)
c. \( \frac{n(n-1)}{(n+1)(n+2)} \)
D. None of these
| 2 |
Maths
|
Veena and Rani are on the moon, Veena
calls out her friend, but Rani does not hear Veena's call even though she is near. Discuss.
| 3 |
Physics
|
The interior angles of a polygon are in arithmetic progression. The smallest angle is \( 120^{\circ} \) and the common
difference is \( 5 . \) Find the number of sides
of the polygon.
| 2 |
Maths
|
Simplify:
\( \left(\frac{2 i}{1+i}\right)^{2} \)
| 2 |
Maths
|
The hybridisation involved in
\( \left[\boldsymbol{C o}\left(\boldsymbol{C}_{2} \boldsymbol{O}_{4}\right)_{3}\right]^{3-} \) is \( ? \)
A \( \cdot s p^{3} d^{2} \)
B. \( s p^{3} d^{3} \)
c. \( d s p^{3} \)
D. \( d^{2} s p^{3} \)
| 1 |
Chemistry
|
Concept of stationary orbit was introduced by :
A. Bohr
B. Rutherford
c. Sommerfeld
D. Thomson
| 1 |
Chemistry
|
Which of the following is not correctly
matched?
\( \begin{array}{clc}\text { Complex ion } & \text { CFSE } \\ \text { a } & {\left[\operatorname{Co}\left(N H_{3}\right)_{6}\right]^{3+}} & 24 D q \\ \text { b } & {\left[\operatorname{Cr}\left(N H_{3}\right)_{6}\right]^{3+}} & 12 D q \\ \text { c } & {\left[F e F_{6}\right]^{3-}} & 4 D q \\ \text { d } & {\left[F e(C N)_{6}\right]^{3-}} & 20 D q\end{array} \)
| 1 |
Chemistry
|
The equilibrium constant \( K \) for the
reaction \( : 2 H I(g) \rightleftharpoons H_{2}(g)+I_{2}(g) \) at
room temperature is 2.85 and that at \( 698 K \) is \( 1.4 \times ! 0^{-2} . \) This implies that
the forward reaction is:
A. exothermic
B. endothermic
c. slow
D. unpredictable
| 1 |
Chemistry
|
A fungal spore
A. Contains an embryonic organism
B. Germinates directly into an organism
C. Is always windblown
D. Both
(b) and (c)
| 0 |
Biology
|
Zinc can be coated on iron to produce galvanized iron but the reverse is not possible. It is because:
A. zinc has lower negative electrode potential than iron
B. zinc has higher negative electrode potential than iron
c. zinc is lighter than iron
D. zinc has lower melting point than iron
| 1 |
Chemistry
|
Assertion(A): The minimum value
of \( 16 \cot x+9 \tan x \) is 3
Reason (R): For two positve real
numbers a and b, \( \boldsymbol{A} . \boldsymbol{M} \geq \boldsymbol{G} . \boldsymbol{M} \)
This question has multiple correct options
A. Both A and R are true and \( R \) is the correct explanation of A
B. Both A and R are true and R is not the correct explanation of
\( \mathrm{c} . \) A is true and \( \mathrm{R} \) is false
D. A is false and R is true
| 2 |
Maths
|
A long straight cable of lenght \( l \) is
placed symmetrically along z - axis has radius \( a(<<l) \). The cable consists of a
thin wire and a coaxial conducting tube
An alternating current \( \boldsymbol{I}(\boldsymbol{t})= \)
\( I_{0} \sin (2 \pi v t) \) flows down the central thin
wire and return along the coaxial conducting tube. The induced electric field at a distance s from the wire inside
the cable is \( \boldsymbol{E}(\boldsymbol{s}, \boldsymbol{t})= \)
\( \mu_{o} I_{o} v \cos (2 \pi v t) \ln \left(\frac{s}{a}\right) \hat{k} . \) The
displacement current density inside the cable is
A \( \cdot \frac{2 \pi}{\lambda^{2}} I_{0} \ln \left(\frac{a}{s}\right) \sin (2 \pi v t) \hat{k} \)
в. \( \frac{I}{\lambda^{2}} I_{0} \) ln \( \left(\frac{a}{s}\right) \sin (2 \pi v t) \hat{k} \)
c. \( \frac{\pi}{\lambda^{2}} I_{0} \ln \left(\frac{a}{s}\right) \sin (2 \pi v t) \hat{k} \)
D. Zero
| 3 |
Physics
|
If the perimeter is half of the area of the
circle numerically then find the radius of the circle.
| 2 |
Maths
|
A retailer buys a cooler for Rs 1200 and overhead expenses on it are Rs \( 40 . \) If he sells the cooler for Rs 1550 , determine
his profit (in percent).
| 2 |
Maths
|
Silkworm larva spins silk from
A. Inside to outside
B. Outside to inside
c. Random fashion
D. Anterior to posterior side
| 1 |
Chemistry
|
\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left[\cos ^{2}\left(\tan ^{-1}\left(\sin \left(\cot ^{-1} x\right)\right)\right)\right]= \)
A. \( \frac{2}{\left(x^{2}+2\right)^{2}} \)
B. \( \frac{2 x}{\left(x^{2}+2\right)^{2}} \)
c. \( \frac{\left(x^{2}+1\right)}{\left(x^{2}+2\right)} \)
D. \( \frac{-2 x}{\left(x^{2}-1\right)^{2}} \)
| 2 |
Maths
|
f the following function is continuous at \( x=\frac{\pi}{2}, \) then find \( a \) and \( b \) \( f(x)=\left\{\begin{array}{l}\frac{1-\sin ^{2} x}{3 \cos ^{2} x}, \text { if } x<\frac{\pi}{2} \\ a, \text { if } x=\frac{\pi}{2} \\ \frac{b(1-\sin x)}{(\pi-2 x)^{2}}, \text { if } x>\frac{\pi}{2}\end{array}\right. \)
| 2 |
Maths
|
When the temperature of an iron sphere
of mass \( 1 k g \) falls from \( 30^{\circ} C \) to \( 25^{\circ} C \)
then 550 cal of heat is released. The
heat capacity of the iron sphere will be
in \( \left.\operatorname{cal}^{\circ} C^{-1}\right) \)
A . 440
в. 330
\( c \cdot 220 \)
D. 110
| 3 |
Physics
|
Choose the correct statements -
This question has multiple correct options
\( \mathbf{A} \cdot C_{2} H_{6}+O_{2} \rightarrow C O_{2}+H_{2} O \) is an unbalanced
combustion reaction.
B. \( 2 H_{2} O_{2} \rightarrow 2 H_{2} O+O_{2} \) is a balanced combustion
reaction.
C \( . A+B C \rightarrow A C+B \) represents a single replacement
reactions.
D. \( H N O_{3}+C a(O H)_{2} \rightarrow C a\left(N O_{3}\right)_{2}+2 H_{2} O \) is an
unbalanced neutralization reaction.
| 1 |
Chemistry
|
One mole of a monoatomic gas is mixed with 3 mole of a diatomic gas. The
molar heat capacity at constant volume of mixture (in cal) is :
A . 4.5
B. 2
\( c \cdot 4 \)
D.
| 3 |
Physics
|
The solution of the differential equation,
\( \boldsymbol{e}^{\boldsymbol{x}}(\boldsymbol{x}+\mathbf{1}) \boldsymbol{d} \boldsymbol{x}+\left(\boldsymbol{y} \boldsymbol{e}^{\boldsymbol{y}}+\boldsymbol{x} \boldsymbol{e}^{\boldsymbol{x}}\right) \boldsymbol{d} \boldsymbol{y}=\mathbf{0} \)
with initial condition \( f(0)=0, \) is-
A \( \cdot x e^{x}+2 y^{2} e^{y}=0 \)
В \( \cdot 2 x e^{x}+y^{2} e^{y}=0 \)
C. \( x e^{x}-2 y^{2} e^{y}=0 \)
D. \( 2 x e^{x}-y^{2} e^{y}=0 \)
| 2 |
Maths
|
Three cations \( A, B, C \) are allowed to
react with ammonium hydroxide solution. \( A \) and \( B \) produce a dirty green
precipitate and a reddish brown precipitate respectively, both of which do not dissolve on further addition of
\( N H_{4} O H . C \) gives pale blue colour precipitate with less amount of ammonium hydroxide and on further
addition of \( N H_{4} O H, \) precipitate becomes soluble and deep blue colour
solution is formed:
A \( \cdot F e^{+2}, F e^{+3}, C u^{+2} \)
B. \( F e^{+3}, F e^{+2}, C u^{+2} \)
c. \( C u^{+2}, F e^{+2}, F e^{+3} \)
D. \( C u^{+2}, F e^{+3}, F e^{+2} \)
| 1 |
Chemistry
|
What is the volume of water consumed
during acid hydrolysis of \( 1.368 K g \) of
sucrose?
(Given - molar masses of sucrose \( =\mathbf{3 4 2} \)
water \( =18, \) density of water \( =1 g / c m^{3} \)
В. \( 0.720 d m^{3} \)
c. \( 0.18 d m^{3} \)
D. \( 0.018 d m^{3} \)
| 1 |
Chemistry
|
When a substance is dissolved in a
solvent, the vapour pressure of solvent decrease. It brings This question has multiple correct options
A. a decrcase in boilings point of solution
B. an increase in boiling point of the solution
c. a decrease in freezing point of the solution
D. an increase in freezeing point of the solution
| 1 |
Chemistry
|
A compass needle free to turn in a horizontal plane is placed at the centre of circular coil of 30 turns and radius 12
\( \mathrm{cm} . \) The coil is in a vertical plane
making an angle of \( 45^{\circ} \) with the magnetic meridian. When the current in the coil is 0.35 A, the needle points west
to east.
(a) Determine the horizontal component of the earth's magnetic field at the location.
(b) The current in the coil is reversed, and the coil is rotated about its vertical
axis by an angle of \( 90^{\circ} \) in the anticlockwise sense looking from above. Predict the direction of the
needle. Take the magnetic declination at the places to be zero.
| 3 |
Physics
|
Which is the correct sequence of cranial
capacities according to increasing
manner?
A. Australopithecus - Homo erectus - Cro magnon man Neanderthal man
B. Homo erectus Ramapithecus Homo habilis Neanderthal man
C. Australopithecus - Homo habilis - Homo erectus Neanderthal man
D. Cro-Magnon man- Dryopithecus - Heidelberg man Neanderthal man
| 0 |
Biology
|
The equation of the hyperbola whose foci are \( (\mathbf{6}, \mathbf{5}),(-\mathbf{4}, \mathbf{5}) \) and eccentricity \( \mathbf{5} / \mathbf{4} \) is?
A \( \cdot \frac{(x-1)^{2}}{16}-\frac{(y-5)^{2}}{9}=1 \)
В. \( \frac{x^{2}}{16}-\frac{y^{2}}{9}=1 \)
c. \( \frac{(x-1)^{2}}{16}-\frac{(y-5)^{2}}{9}=-1 \)
D. \( \frac{(x-1)^{2}}{4}-\frac{(y-5)^{2}}{9}=1 \)
| 2 |
Maths
|
For a solution of an electrolyte at a
particular concentration and temperature, which of the following is not the function of cell constant?
1) specific conductance
2) molar conductance
3) equivalent conductance
4) conductance
A \( \cdot 1,2 \)
B. 1,2,3
c. 2,3,4
D. 1,4
| 1 |
Chemistry
|
Which if the following is used in making smoke bombs?
A. Sulphur
B. Phosphorus
c. Hydrogen
D. carbon
| 1 |
Chemistry
|
\( \lim _{x \rightarrow 1} \frac{\sqrt{3+x}-\sqrt{5-x}}{x^{2}-1} \)
| 2 |
Maths
|
Define following:
Position vector
| 3 |
Physics
|
When a bar of iron \( 50.0 \mathrm{cm} \) long at \( 15^{\circ} \mathrm{C} \) is heated in a furnace, it becomes
\( 50.4 \mathrm{cm} . \) If the coefficient of linear
expansion of iron is \( 1.1 \times 10^{-5} C^{o-1} \)
find the temperature of furnace.
| 3 |
Physics
|
A liquid takes 5 minutes to cool from 80
\( ^{o} \mathrm{C} \) to \( 50^{\circ} \mathrm{C} \). How much time will it take
to cool from \( 60^{\circ} \mathrm{C} \) to \( 30^{\circ} \mathrm{C} ? \)
(Temperature of the surrounding \( \left.=20^{\circ} \mathrm{C}\right) \)
A. 10 minutes
B. 15 minutes
c. 5 minutes
D. 7.5 minutes
| 3 |
Physics
|
The area of the smaller part of the circle \( x^{2}+y^{2}=a^{2}, \) cut off by the line \( x=\frac{a}{\sqrt{2}} \)
is given by:
\( ^{\text {A }} \cdot \frac{a^{2}}{2}\left(\frac{\pi}{2}+1\right) \)
в. \( \frac{a^{2}}{2}\left(\frac{\pi}{2}-1\right) \)
c. \( a^{2}\left(\frac{\pi}{2}-1\right) \)
D. None of these
| 2 |
Maths
|
An object falls from rest with an
acceleration \( g \). The uncertainty in the value of the time is \( \pm 6 \% \) and the
uncertainty in the value of \( g \) is \( \pm 4 \% \). The
best estimate for the uncertainty of the position of the of the object is:-
\( \mathbf{A} \cdot \pm 16 \% \)
B . \( \pm 10 \% \)
\( c . \pm 5 \% \)
D. \( \pm 8 \% \)
| 3 |
Physics
|
The time required to produce \( 2 \mathrm{F} \) of electricity with a current of 2.5 amperes is:
A. 21.44
B. 1200 min
c. 50000 s
D. 1.5 \( h \)
| 1 |
Chemistry
|
Evaluate :
\( \int \frac{x+1}{x^{2}+3 x+12} d x \)
| 2 |
Maths
|
Explain the reason for the fusion of an organic compound with metallic sodium for testing nitrogen. sulphur, and halogens.
| 1 |
Chemistry
|
When two nonmetals react, what do
they form?
A. A covalent bond
B. An ionic bond
c. A synthesis reaction
D. A decomposition reaction
E. A hybrid bond
| 1 |
Chemistry
|
If \( a^{2}+10 b^{2}+5 c^{2}+6 a b+2 b c-16 c+ \)
\( \mathbf{1 6}=\mathbf{0} \) then the possible value of \( \boldsymbol{a}- \)
\( b+c= \)
A . 5
B. -3
\( c \cdot-2 \)
D. 10
| 2 |
Maths
|
The diagram in Fig. shows a three-pin
socket marked as 1,2 and \( 3 . \) To which wire is the fuse connected?
4
\( c \)
D. 1 and 3
| 3 |
Physics
|
Base surface area of a cylinder is 20
\( c m^{2} \) and its height is \( 10 \mathrm{cm} . \) Find the
volume of the cylinder.
| 2 |
Maths
|
In eukaryotic cell cycle, cell fusion
experiments show that
A. When an S phase cell is fused with a G_phase cell, \( G_{1} \)
phase cell is stimulated to synthesize DNA
B. When an S phase cell is fused with a Ga phase cell, DNA
synthesis is induced in \( \mathrm{G}_{2} \) phase cell
C. When a Gi phase cell is fused with a Ga phase cell, DNA
synthesis is induced in both \( \mathrm{G}_{1} \) and \( \mathrm{G}_{2} \) phase cells
D. When a Gi phase cell is fused with an M phase
cell both \( \mathrm{G}_{1} \) and \( \mathrm{M} \) phase cells are stimulated to synthesise DNA
| 0 |
Biology
|
Study of effect of potassium bisulphate as food preservative under various conditions (temperature, concentration,
time etc.)
| 1 |
Chemistry
|
Which of the following was not proposed by Thomson?
A. The negative and positive charges are equal in magnitude
B. The electrons revolve around the nucleus in circular paths
C. The electrons are embedded in a positive sphere
D. Atoms are electrically neutral
| 1 |
Chemistry
|
A rectangular tank is \( 80 m \) long and \( 25 m \) broad. Water flows into it through
a pipe whose cross-section is \( 25 \mathrm{cm}^{2}, \) at
the rate of \( 16 k m \) per hour. How much
the level of the water rises in the tank in
45 minutes?
| 2 |
Maths
|
During extraction of \( N a C l \), sodium is deposited at :
A. anode
B. cathode
c. Depends on \( N a C l \)
D. No deposition takes place
| 1 |
Chemistry
|
Integrate w.r.t \( \times \frac{3 x}{1+2 x^{4}} \)
A \( \cdot \frac{3}{\sqrt{2}} \tan ^{-1} \sqrt{2} x^{2}+c \)
B. \( \frac{3}{2 \sqrt{2}} \tan ^{-1} \sqrt{2} x^{2}+c \)
\( \frac{3}{2 \sqrt{2}} \tan ^{-1} 2 x^{2}+c \)
D \( \cdot \frac{3}{\sqrt{2}} \tan ^{-1} x^{2}+c \)
| 2 |
Maths
|
The process of separation of cream from milk is called:
A. emilsification
B. demulsification
c. electro-osmosis
D. peptization
| 1 |
Chemistry
|
The measure of an angle in degrees,
grades and radians be \( \mathrm{D}, \mathrm{G} \) and \( \mathrm{C} \)
respectively, then relation between them \( \frac{\boldsymbol{D}}{\mathbf{9 0}}=\frac{\boldsymbol{G}}{\mathbf{1 0 0}}=\frac{\boldsymbol{2 C}}{\boldsymbol{\pi}} \) but \( \mathbf{1}^{\circ}= \)
\( \left(\frac{180}{\pi}\right)^{0} \simeq 57^{\circ}, 17^{\prime}, 44.8^{\prime \prime} \) and sum of
interior angles of a \( n \) -sided regular polygon is \( (2 n-4) \frac{\pi}{2} . \) On the basis of above information, answer the following
questions :The angles between the hour hand and minute hand of a clock at half
past three is -
\( A \cdot \frac{\pi}{3} \)
B. \( \frac{\pi}{4} \)
c. \( \frac{5 \pi}{12} \)
D. \( \frac{7 \pi}{12} \)
| 2 |
Maths
|
Which of the following does not react
with cold water?
A . \( S i C \)
в. АIN
c. \( C a C_{2} \)
D. \( A l_{4} C_{3} \)
| 1 |
Chemistry
|
A magnified, inverted image is located
a distance of \( 32.0 \mathrm{cm} \) from a concave
mirror with a focal length of \( 12.0 \mathrm{cm} \) Determine the object distance and tell whether the image is real or virtual.
| 3 |
Physics
|
If \( A \) is a singular matrix, then \( A(\operatorname{adj} A) \)
is a
A. scalar matrix
B. zero matrix
c. identity matrix
D. orthogonal matrix
| 2 |
Maths
|
The most abundant metal in the earth's
crust is :
A . Silver
B. Aluminium
c. Calcium
D. Gold
| 1 |
Chemistry
|
Define peptide linkage.
| 1 |
Chemistry
|
A cricket ball of mass \( 500 \mathrm{g} \) is moving with speed of \( 36 k m h^{-1} . \) It is reflected
back with the same speed. What is the
impulse applied on it?
A. \( 20 \mathrm{Kg} \mathrm{m} / \mathrm{s} \)
B. \( 10 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
c. \( 5 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
D. none of the above
| 3 |
Physics
|
If \( f(x)=(x-[x]) \sin \frac{1}{x}, \) then at \( x=0 \)
| 2 |
Maths
|
In the equation of \( \boldsymbol{A C}, \boldsymbol{I}=\boldsymbol{I}_{0} \sin (\boldsymbol{\omega} \boldsymbol{t}) \)
the current amplitude and frequency will respectively be
A \( \cdot I_{0}, \frac{\omega}{2 \pi} \)
В. \( \frac{I_{0}}{2}, \frac{\omega}{2 \pi} \)
\( c \cdot I_{r m s}, \frac{\omega}{2 \pi} \)
D. \( I_{0}, \omega \)
| 3 |
Physics
|
Chromatography is used to separate:
A . molecules
B. atoms
C. solution
D. mixtures
| 1 |
Chemistry
|
Which one of the following is the unit vector perpendicular to both \( \overrightarrow{\boldsymbol{a}}=-\hat{\mathbf{i}}+ \) \( \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) and \( \overrightarrow{\boldsymbol{b}}=\hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} ? \)
A \( \cdot \frac{\hat{i}+\hat{j}}{\sqrt{2}} \)
в. \( \hat{k} \)
\( c \cdot \frac{\hat{j}+\hat{k}}{\sqrt{2}} \)
D. \( \frac{\hat{i}-\hat{\jmath}}{\sqrt{2}} \)
| 2 |
Maths
|
A body of mass 2 kg moving with velocity of \( 6 \mathrm{m} / \mathrm{s} \) strike another body of same mass at rest and sticks to it. The
amount of heat evolved during collision is:
A . 18 J
B. 36 J
c. 9 J
D. 3
| 3 |
Physics
|
Write the structure of 2-hydroxybenzoic acid.
| 1 |
Chemistry
|
Fibres with tapering ends and spindle shape are seen in case of
A . Striated muscle
B. Cardiac muscle
c. skeletal muscle
D. Smooth muscle
| 0 |
Biology
|
If \( \lambda \) is the wavelength of hydrogen atom
from the transition \( n=3 \) to \( n=1 \), then
what is the wavelength for doubly ionised lithium ion for same transition?
\( A \cdot \frac{\lambda}{3} \)
B. \( 3 \lambda \)
\( c \cdot \frac{\lambda}{9} \)
D. \( 9 \lambda \)
| 3 |
Physics
|
In parallelogram \( A B C D, A B=10 \mathrm{cm}, A D= \)
\( 24 \mathrm{cm} \) and \( \mathrm{BD}=26 \mathrm{cm}, \) find the area
of parallelogram(in \( \mathrm{cm}^{2} \) )
| 2 |
Maths
|
The nuclear material without nuclear
membrane is observed in
A. Bacteria and green algae
B. Cyanobacteria and red algae
c. Bacteria and cyanobacteria
D. Mycoplasma and green algae
| 0 |
Biology
|
Silicon has 4 electrons in its outer most
orbit. In forming the bond:
A. it gains electrons
B. it loses electrons
c. it shares electrons
D. none of the above
| 1 |
Chemistry
|
A charged body is brought near an uncharged gold leaf electroscope. What will be your observation if the body is charged?
A. leaves will diverge
B. leaves will converge
c. leaves will remain unaffected
D. none
| 3 |
Physics
|
If \( S_{n}=2+0.4 n, \) find initial velocity
and acceleration
A . 2.2 units, 0.4 units
B. 2.1 units, 0.3 units
c. 1.2 units, 0.4 units
D. 2.2 units, 0.3 units
| 3 |
Physics
|
(a) State Joule's law of heating. Name two gases which are filled in electric bulbs and explain why these gases are filled in electric bulbs.
(b) An electric iron consumes energy at
a rate of \( 840 \mathrm{W} \), when heating is at the maximum rate. The voltage of electric
source is \( 220 \mathrm{V} \). Calculate the value of
current and the resistance
| 3 |
Physics
|
The solution of the D.E \( y y_{1}= \)
\( \left[\frac{\boldsymbol{y}^{2}}{\boldsymbol{x}^{2}}+\frac{\boldsymbol{f}\left(\boldsymbol{y}^{2} / \boldsymbol{x}^{2}\right)}{\boldsymbol{f}^{\prime}\left(\boldsymbol{y}^{2} / \boldsymbol{x}^{2}\right)}\right] \) is:
\( ^{A} \cdot f\left(\frac{y^{2}}{x^{2}}\right)=c x^{2} \)
B. \( x^{2} f\left(\frac{y^{2}}{x^{2}}\right)=c^{2} y^{2} \)
C \( \cdot x^{2} f\left(y^{2} / x^{2}\right)=c \)
D. \( f\left(\frac{y^{2}}{x^{2}}\right)=c y / x \)
| 2 |
Maths
|
Which statements is/ are correct?
This question has multiple correct options
A. When \( F e C l_{3} \) is added to excess of hot water, a
positively charged colloidal solution form
B. Amount of electrolyte required to cause coagulation is higher for lyophobic than Iyophillic colloids
C. High pressure is favaourable for physical as well as chemical adsorption
D. Physical and chemical adsorption both decrease entropy of universe
| 1 |
Chemistry
|
If the vertices of a \( \Delta A B C \) are \( A= \)
\( (1,-1,-3), B=(2,1,-2) \) and \( C= \)
(-5,2,-6) then the length of the
internal bisector of angle \( \boldsymbol{A} \) is
A \( \cdot \frac{3 \sqrt{10}}{2} \)
в. \( \frac{3 \sqrt{10}}{5} \)
c. \( \frac{3 \sqrt{10}}{7} \)
D. \( \frac{3 \sqrt{10}}{4} \)
| 2 |
Maths
|
When 1 coulomb of charge flows through a conductor in 1 sec, then the current passing through the conductor is?
A. \( 1 \mathrm{Hp} \)
B. 1A
c. \( 1 \mathrm{C} \)
\( D \cdot 1 P \)
| 3 |
Physics
|
Sum the series to \( n \) terms
\( \frac{1}{2.4 .6}+\frac{1}{4.6 .8}+\frac{1}{6.8 .10}+\dots \)
| 2 |
Maths
|
\( 2 g \) of \( N a O H \) are dissolved in water to
make 1 litre solution. What is pH of
solution?
| 1 |
Chemistry
|
Find the real values of \( x \) and \( y, \) if
\( (x+i y)(2-3 i)=4+i \)
| 2 |
Maths
|
In above shown figure, fringe pattern is produced by a monochromatic light passing through two narrow slit. If the fringe width is \( 2 \mathrm{cm} \) then, which of the following changes would increase the distance between the bands?
A. Moving the slits closer together
B. Making the light source brighter
c. Moving the slits closer to the screen
D. Increasing the frequency of the light
E. shortening the wavelength of the light
| 3 |
Physics
|
Draw the graph of the following linear
equation
\( -\boldsymbol{x}+\boldsymbol{y}=\boldsymbol{6} \)
| 2 |
Maths
|
A point charge \( +\boldsymbol{q} \& \) mass \( 100 g \boldsymbol{m} \)
experiences a force of \( 100 N \) at a point
at a distance \( 20 \mathrm{cm} \) from a long infinite uniformly charged wire. If it is released its speed is \( 20 \sqrt{\ln x} \) m/ \( s \) when
it is at a distance \( 40 \mathrm{cm} \) from wire. Find
\( \boldsymbol{x} \)
| 3 |
Physics
|
A uniform current is flowing along the length of an infinite, straight, thin, hollow cylinder of radius 'R'. The magnetic field 'B' produced at a perpendicular distance 'd' from the axis
of the cylinder is plotted in a graph Which of the following figures looks like the plot?
\( A \)
в.
\( c \)
D.
| 3 |
Physics
|
Aquatic ancestry of bryophytes is evidenced by
A. Theirgreen colour
B. Algae like protonema
C. Many aquatic bryophytes
D. Flagellated male gametes
| 0 |
Biology
|
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