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If \( y^{2}=a x^{2}+b x+c, \) where \( a, b, c \) are
constants, then \( y^{3} \frac{d^{2} y}{d x^{2}} \) is equal to.
A \( \cdot \frac{-1}{4} \)
в. \( \frac{-1}{6} \)
c. \( \frac{-3}{4} \)
D. \( \frac{-1}{8} \) | 2 | Maths |
The slope of a line is double of the slope
of another line. If the tangent of the angle between them is \( \frac{1}{3} \) find the slopes of the lines. | 2 | Maths |
Find the slope of the line passing
through the points \( A(-2,1) \) and
\( \boldsymbol{B}(\mathbf{0}, \boldsymbol{3}) \) | 2 | Maths |
In the given figure, \( A B C \) is an equilatera
triangle whose side is \( 2 \sqrt{3} \mathrm{cm} . \) A circle
is drawn which passes through the
midpoints \( D, E \) and \( F \) of its sides. The area of the shaded region is:
\( A \)
B \( \cdot \frac{1}{4}(2 \pi-\sqrt{3}) c m^{2} \)
c. \( \frac{1}{4}(\pi-3 \sqrt{3}) c m^{2} \)
D. | 2 | Maths |
A ball dropped from some height covers half of its total height during the last second of its free fall. Find
(a) time of flight
(b) height of its fall
(c) speed wit which it strikes the ground. | 3 | Physics |
What do you call a parallelogram which has equal diagonals?
A. A trapezium
B. A rectangle
c. A rhombus
D. A kite | 2 | Maths |
If \( |z+5| \leq 2 \) then the maximum value of \( |z+3| \) is ( where \( z \) is a complex number)
A. zero
B . 2
\( c \cdot 4 \)
D. 6 | 2 | Maths |
f \( \boldsymbol{A}=\{\mathbf{2}, \mathbf{3}, \mathbf{4}, \mathbf{5}, \mathbf{6}, \mathbf{7}\} \) and \( \boldsymbol{B}= \)
\( \{3,5,7,9,11,13\}, \) then find \( A-B \) and
\( \boldsymbol{B}-\boldsymbol{A} \) | 2 | Maths |
is the heat supplied during change of state of matter.
A. Enthalpy
B. Latent heat
c. Endothermic
D. Exothermic | 3 | Physics |
A substance with more specific heat can absorb a greater amount of heat for a given mass. State whether given statement is True/False
A. True
B. False | 3 | Physics |
Most primitive living vascular plants
are
A. Sphagnum
B. cycads
c. Brown algae
D. Ferns | 0 | Biology |
Which one of the following is employed as Antihistamine?
A. Omeprazole
B. Chloramphenicol
c. Diphenhydramine
D. Norethindrone | 1 | Chemistry |
The three angles of a triangle are in the
ratio \( 1: 2: 1 . \) Find all the angles of the
triangle, classify the triangle in two different ways. | 2 | Maths |
In the figure \( C \) is a right angle DE \( \wedge A B \)
\( A E=6, E B=7 \) and \( B C=5 . \) The area of the
quadrilateral EBCD is
A. 27.5
B . 25
c. 22.5
D. 20 | 2 | Maths |
A table-top measures \( 2 m 25 \mathrm{cm} \) by
1 \( m 50 \mathrm{cm} . \) What is the perimeter of the table-top? | 2 | Maths |
In which year Paul Ehrlich got the Noble Prize for medicine?
A. 1980
B. 1908
\( c \cdot 1907 \)
D. 1478 | 1 | Chemistry |
If \( \boldsymbol{A}=\left[\begin{array}{lll}\mathbf{0} & \mathbf{0} & \mathbf{1} \\ \mathbf{0} & \mathbf{1} & \mathbf{0} \\ \mathbf{1} & \mathbf{0} & \mathbf{0}\end{array}\right], \) then
This question has multiple correct options
A. AdjA is zero matrix
B.
\[
A d j A=\left[\begin{array}{ccc}0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0\end{array}\right]
\]
\( \mathbf{c} \cdot A^{-1}=A \)
D. \( A^{2}=I \) | 2 | Maths |
During which stage of the cell cycle is cell growth and replication of organelles most significant?
A. M phase
B. \( G_{1} \) phase
\( \mathrm{c} \cdot G_{2} \) phase
D. S phase | 0 | Biology |
What are the characteristics of isobars?
A. They have different atomic numbers.
B. They have same electronic configuration.
C. They have same number of neutrons.
D. All of the above | 1 | Chemistry |
The difference of slopes of lines
represent by \( y^{2}-2 x y \sec ^{2} \alpha+ \)
\( \left(3+\tan ^{2} \alpha\right)\left(\tan ^{2} \alpha-1\right) x^{2}=0 \) is
\( A \cdot 3 \)
B. 4
\( c \cdot 0 \)
D. | 2 | Maths |
If \( P, V, T \) represents pressure, volume
and temperature of the gas, the correct representation of Boyle's law is :
A \( \cdot V \propto \frac{1}{P}(\mathrm{P} \text { is constant }) \)
В. \( P V=R T \)
\( ^{\mathrm{c}} \cdot_{V} \propto \frac{1}{P}(\text { at constant } \mathrm{T}) \)
D. \( P V=n R T \) | 1 | Chemistry |
Integrate: \( \frac{\mathbf{3} \boldsymbol{x}-\mathbf{1}}{(\boldsymbol{x}+\mathbf{2})^{2}} \) | 2 | Maths |
The length of a wire of cross-sectional
\( \operatorname{area} 1 \times 10^{-6} m^{2} \) is \( 10 \mathrm{m} . \) The young's
modulus of the material of the wire is
25 G.pa. When the wire is subjected to a tensile force of \( 100 N \), the
elongation produced in \( m m \) is:
A . 0.04
B. 0.4
\( c \cdot 4 \)
D. 40 | 3 | Physics |
Choose the correct answers from the
alternatives given The classification category below the level of family is:
A . class
B. genus
c. phylum
D. species | 0 | Biology |
The study of radioactive substances is
called:
A. Nuclear chemistry
B. Analytical chemistry
c. Radio active chemistry
D. Geo chemistry | 1 | Chemistry |
What relation about elements did
Dobereiner want to establish? | 1 | Chemistry |
If \( \tan \theta=\frac{-4}{3} \) then \( \sin \theta \) is
A \( \cdot \frac{-4}{5} \) but not \( \frac{-4}{3} \)
B. \( \frac{-4}{5} \) or \( \frac{4}{5} \)
c. \( \frac{4}{3} \) but not \( \frac{-4}{5} \)
D. None of thses. | 2 | Maths |
Let \( * \) be a binary operation on \( N \) given by \( a * b=\operatorname{LCM}(a, b) \) for all \( a, b \in N \)
Find \( 5 * 7 \) | 2 | Maths |
Lichen is a pioneer vegetation of
A. Hydrosere
B. Psammosere
c. Lithosere
D. Halosere | 0 | Biology |
Explain the term - 'Hydrocarbons' | 1 | Chemistry |
Magnetic susceptibility \( \chi \) of a paramagnetic material changes with
absolute temperature \( T \) as
A \( \cdot \chi \propto T^{-1} \)
B. \( x= \) constant
c. \( \chi \propto e^{r} \)
D. \( \chi \propto T \) | 3 | Physics |
Which part of the photosynthetic process does not require light and temperature?
A. Hill's reaction
B. Blackman's reaction
c. warburg's reaction
D. Emerson's reaction | 0 | Biology |
A cord is wound around the
circumference of a bicycle wheel
(without tyre) of diameter 1 m. A mass
of \( 2 k g \) is tied to the end of the cord and
it is allowed to fall from rest. The weight
falls \( 2 m \) in \( 4 s \). The axle of the wheel is
horizontal and the wheel rotates with its
plane vertical. The angular acceleration produced is:
\( \left(\operatorname{take} g=10 m s^{-2}\right) \)
A \( \cdot 0.5 \) rads\( ^{-2} \)
B. 1 rads\( ^{-2} \)
c. 2 rads \( ^{-2} \)
D. 4 rads \( ^{-2} \) | 3 | Physics |
Consider the following equation for a
cell
\( \boldsymbol{A}+\boldsymbol{B} \rightleftharpoons \boldsymbol{C}+\boldsymbol{D} \)
\( \boldsymbol{E}^{o}= \)
\( \boldsymbol{X} \boldsymbol{v o l t}, \quad \boldsymbol{K}_{e q}=\boldsymbol{K}_{1} \)
\( \mathbf{2 A}+\mathbf{2 B} \rightleftharpoons \mathbf{2 C}+\mathbf{2 D} ; \quad \boldsymbol{E}^{\boldsymbol{o}}= \)
\( \boldsymbol{y} \) volt, \( \quad \boldsymbol{K}_{e q}=\boldsymbol{k}_{2} \)
A. \( X=y, K_{1}=K_{2} \)
B . \( X=2 y, K_{1}^{2}=K_{2} \)
C . \( X=y, K_{1}^{2}=K_{2} \)
D. \( X^{2}=y, K_{1}^{2}=K_{2} \) | 1 | Chemistry |
The ratio of the mass of \( C-12 \) atom to
that of an atom of element \( X \) (whose
atomicity is four) is \( 1: 9 . \) The molecular mass of element X is :
A \( \cdot 480 \mathrm{gmol}^{-1} \)
в. 432 gmol-\( ^{-1} \)
c. \( 36 g m o l^{-1} \)
D. \( 84 ~ g m o l^{-1} \) | 1 | Chemistry |
A solenoid of inductance \( L \) carrying a certain current is linked with a total
magnetic flux \( \phi \). Now it is connected to a condenser with which it shares half of its initial energy. The total flux now linked with the solenoid is:
\( A \cdot \frac{\phi}{2} \)
в. \( \frac{\phi}{\sqrt{2}} \)
\( c \cdot \frac{\phi}{2 \sqrt{2}} \)
D. | 3 | Physics |
A ring of mass \( m \) and radius r rolls on an inclined plane. A torque is produced in the ring due to
A. mgsin\theta and the radius of the ring
B. the perpendicular distance between the force and the point of contact and the force \( m g \) acting on it
c. the perpendicular distance between the force and the point of contact and the normal force acting on the object
D. the perpendicular distance between the force and the point of contact and the force \( m g \sin \theta \) acting on it | 3 | Physics |
Write the structural formulae for the
compounds that yield the following products on reductive ozonolysis:
penta-3-one + glyoxal + propanal | 1 | Chemistry |
The purpose of soft iron cylinder
between the pole pieces of the horse-
shoe magnet in a moving
coil galvanometer is
A. to increase the magnetic induction in the polar
\( \operatorname{gap} \)
B. to evenly distribute the magnetic lines of force
C. to provide a radial magnetic field
D. to reduce the magnetic flux leakage in the polar
\( \operatorname{gap} \) | 3 | Physics |
Birds produce sound by using:
A. vocal chord
B. larynx
c. glottis
D. syrinx | 3 | Physics |
A transformer with turns ratio \( \frac{N_{1}}{N_{2}}= \) \( \mathbf{5 0} \)
\( \frac{w}{1} \) is connected to a 120 volt \( A C \) supply
If primary and secondary circuit resistance are \( 1.5 k \Omega \) and \( 1 \Omega \)
respectively then find out power out put
A \( .5 .76 \mathrm{w} \)
B. \( 11.4 \mathrm{w} \)
c. \( 2.89 \mathrm{w} \)
D. \( 7.56 \mathrm{w} \) | 3 | Physics |
If a conducting rod of length \( 4 l \) is
rotated about at point \( \boldsymbol{O} \) in a uniform
magnetic field \( B \) directed into the
paper and \( D E=l, E A=3 l \), then which
of the folowing is true?
\[
\begin{array}{rrrrrrrrrr}
\times & \times & \times & \times & \times & \times & \times & \times & \times & \times & \times \\
\times & \times & \times & \times & \times & \times & \times & \times & \times & \times & \times \\
\times & \times & \times & \times & \times & \times & \times & \times & \times & \times & \times \\
\times & \times & \times & \times & \times & \times & \times & \times & \times & \times & \times \\
\times & \times & \times & \times & \multicolumn{1}{c} {\omega_{M}} & \times & \times & \times & \times & \times \\
\multicolumn{1}{c} {\times} & \times & \times & \times E_{\times} & & \times & \times & \times & \times & \times \\
\times & \times & \times & \times & \times & \times & \times & \times & \times & \times & \times \\
\times & \times & \times & \times & \times & \times & \times & \times & \times & \times & \times \\
\times & \times & \times & \times & \times & \times & \times & \times & \times & \times & \times
\end{array}
\]
A.
\[
V_{A}-V_{E}=\frac{9}{2} B \omega l^{2}
\]
B.
\[
V_{E}-V_{A}=\frac{9}{2} B \omega l^{2}
\]
\( \mathbf{c} \)
\[
V_{D}-V_{E}=\frac{B \omega l^{2}}{2}
\]
D. \( V_{A}-V_{E}=4 B \omega l^{2} \) | 3 | Physics |
A thin semicircular conducting ring of
radius \( \mathrm{R} \) is falling with its plane vertical
in a horizontal magnetic field B. At the
position MNQ, the speed of the ring is \( \mathbf{v} \) and the potential difference across the
ring is
A. zero
B \( \cdot \frac{1}{2} B v \pi R^{2} \) and \( \mathrm{M} \) is at higher potential
\( \mathrm{c} . \pi R B v \) and \( \mathrm{Q} \) is at higher potential
D. \( 2 R B v \) and \( Q \) is at higher potential | 3 | Physics |
Assertion
Generally, covalent compounds are gases, liquids or soft solids at room temperature.
Reason
Between covalent compounds Vander
Waals forces of attractions exists
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 |
Which term of the progression
\( 250,240,230 \ldots \ldots \) is the first negative
term? | 2 | Maths |
\( \frac{-8}{11}+\frac{-4}{11}=\frac{p}{11} \)
then
\( \boldsymbol{p}=? \) | 2 | Maths |
\( \int_{0}^{\pi / 2} \frac{\sin x d x}{(\sin x+\cos x)^{2}}= \)
A \( \cdot \sqrt{2} \log (\sqrt{2}+1) \)
B \( \cdot \frac{1}{\sqrt{2}} \log (\sqrt{2}+1) \)
\( \mathbf{c} \cdot 2 \log (\sqrt{2}+1) \)
D \( \frac{1}{2 \sqrt{2}} \log (\sqrt{2}+1) \) | 2 | Maths |
What is the area enclosed by \( |x|+ \) \( |\boldsymbol{y}|=\mathbf{1} ? \)
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D. 4 | 2 | Maths |
If \( 2 \bar{a}-4 \hat{i}-2 \widehat{j}+\widehat{k}=0 \) then find \( \bar{a} \)
\( \mathbf{A} \cdot 2 \bar{j}+\overline{\mathbf{k}} \)
B . \( 2 \hat{i}+\hat{j}-\frac{1}{2} \widehat{k} \)
c. \( 2 \bar{i}+\overline{\mathbf{j}} \)
D. \( 2 \overline{i-j} \) | 2 | Maths |
All living organisms are made up of
A. Blood
B. Cells
c. water
D. All of the above | 0 | Biology |
The value of the equilibrium constant
for the reaction
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{I}_{2}(\boldsymbol{g}) \rightleftharpoons 2 \boldsymbol{H} \boldsymbol{I}(\boldsymbol{g}) \)
at \( 720 \mathrm{K} \) is \( 48 . \) What is the value of the
equilibrium constant for the following
reaction?
\( \frac{1}{2} \boldsymbol{H}_{2}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{I}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{H} \boldsymbol{I}(\boldsymbol{g}) \) | 1 | Chemistry |
Secondary growth occur in which Pteridophyte?
A . Azolla
B. Salvinia
c. Isoetes
D. Selaginella | 0 | Biology |
Which are the sources of phenol?
This question has multiple correct options
A. Cumene
B. Hydrolysis
C. Middle oil of coal tar distillation
D. Reaction of diazonium salt with \( H_{3} P O_{2} \) | 1 | Chemistry |
Write primary and secondary valency of \( \boldsymbol{C o} \operatorname{in}\left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{n}_{\boldsymbol{3}}\right)_{\boldsymbol{6}}\right] \boldsymbol{C l}_{3} ? \) | 1 | Chemistry |
If \( \hat{i}, \hat{j} \) and \( \widehat{k} \) are unit vectors along \( \mathbf{x}, \mathbf{y} \) and z axes respectively. the angle \( \theta \) between the vector \( \hat{\mathbf{i}}+\widehat{\mathbf{j}}+\widehat{\boldsymbol{k}} \) and vector
\( \widehat{\boldsymbol{i}} \)
A \( \cdot \theta=\cos ^{-1}\left(\frac{1}{\sqrt{3}}\right) \)
В \( \cdot \theta=\sin ^{-1}\left(\frac{1}{\sqrt{3}}\right) \)
C \( \cdot \theta=\cos ^{-1}\left(\frac{\sqrt{3}}{2}\right) \)
D. \( \theta=\sin ^{-1}\left(\frac{\sqrt{3}}{2}\right) \) | 3 | Physics |
A bullet of mass \( \mathrm{X}, \) moving with a velocity \( V \), strikes a wooden block of mass \( Z \) and gets embedded. If the block
is free to move, its velocity after impact will be.
A \( \cdot \frac{X}{X+Z} \mathrm{v} \)
в. \( \frac{X+Z}{Z} \vee \)
c. \( \frac{x}{x-Z} V \)
D. \( \frac{X+Z}{X} V \) | 3 | Physics |
What is the basis for classification? | 0 | Biology |
The amount of heat required to raise the temperature of a body by \( 1^{0} \mathrm{C} \) is
called
A . latent heat
B. specific heat
c. thermal capacity
D. none of these | 3 | Physics |
State whether given statement is True or False.
Centre of gravity of a freely suspended body always lies vertically below the point of suspension.
A. True
B. False | 3 | Physics |
Evaluate the given integral: \( \int_{0}^{1} x^{4} d x \) | 2 | Maths |
The water temperature should
preferably be less than \( _{--} \) degree
Celsius.
A . 10
B. 25
c. 15
D. 30 | 1 | Chemistry |
One half of slab of ice is covered with
black cloth and the other half with white
cloth. This is then placed in sunlight. After some time the pieces of cloth are removed. Then
A. ice has melted equally under both the pieces.
B. more ice has melted under white cloth
c. more ice has melted under black cloth.
D. it will depend on the medium in which ice is placed | 3 | Physics |
Find the differential equation of \( \boldsymbol{y}= \)
\( \boldsymbol{a} e^{3 x}+\boldsymbol{b} e^{3 x} \) | 2 | Maths |
A bag contains 6 red balls and 8 green balls. A ball is drawn at random. What
is the probability that the ball is green | 2 | Maths |
If vector \( \vec{a}=4 \hat{i}+5 \hat{j}-3 \hat{k} \) and \( \vec{b}=5 \hat{i}+ \)
\( 3 \hat{j}+8 \hat{k} \) then value of \( \frac{\text { projection of vector b on a }}{\text { projection of vector a on b }} \) is :
A \( \cdot \frac{7}{5} \)
B. \( \frac{2}{7} \)
\( c \cdot \frac{5}{8} \)
D. None of these. | 2 | Maths |
\( \triangle L M N \sim \triangle X Y Z . \ln \triangle L M N, L M= \)
\( 6 \mathrm{cm}, M N=6.8 \mathrm{cm}, L N=7.6 \mathrm{cm} \) and
\( \frac{L M}{X Y}=\frac{4}{5} ; \) Construct \( \triangle X Y Z \) | 2 | Maths |
When a person suffers from a marked
fall in blood pressure, it is helpful to administer the hormone:
A. thyroxine
B. adrenaline
c. insulin
D. parathormone | 0 | Biology |
Which mineral has been
named incorrectly?
A. Bauxite \( : A l_{2} O_{3} \cdot 2 H_{2} O \)
B. Corundum: \( A l_{2} O_{3} \)
C . Cryolite \( : 3 \mathrm{NaF} \cdot \mathrm{AlF}_{3} \)
D. Feldspar: \( B e_{3} A l_{2} S i_{5} O_{18} \) | 1 | Chemistry |
For an electromagnetic radiation,
A. only momentum is quantised
B. only energy is quantised
C. both energy and momentum are quantised
D. neither of them is quantised | 3 | Physics |
A bulb emits light of wavelength \( \lambda= \) \( 4500 A \). The bulb is rated as 150 watt
and \( 8 \% \) of the energy is emitted as light. How many photons are emitted by the bulb per second? | 1 | Chemistry |
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C O O A} \boldsymbol{g}+\boldsymbol{B r}_{2} \stackrel{\boldsymbol{C C l}_{4}}{\longrightarrow} \)
\( \boldsymbol{X} \stackrel{\boldsymbol{a q} \cdot \boldsymbol{K O H}}{\longrightarrow} \boldsymbol{Y} \stackrel{\boldsymbol{r e d} \boldsymbol{P}_{4} / \boldsymbol{B} \boldsymbol{r}_{2}}{\longrightarrow} \boldsymbol{Z} \)
\( Z \) is:
A \( \cdot C H_{3} C H_{2} C H_{2} B r \)
в. \( C H_{3} C H_{2} B r \)
c. \( C H_{3} B r \)
D. \( C H_{3} C H_{2} C H_{3} \) | 1 | Chemistry |
A uniform meter scale can be balanced
at the \( 70.0 \mathrm{cm} \) mark when a mass
\( 0.05 k g \) is hung from the \( 94.0 c m \) mark.
Find the mass of the metre scale :
\( \mathbf{A} \cdot 6 k g \)
в. \( 0.06 \mathrm{kg} \)
c. \( 0.07 \mathrm{kg} \)
D. \( 60 \mathrm{kg} \) | 3 | Physics |
The total number of neutrons in all
isotopes of hydrogen is equal to:
A. 6
B. 2
\( c \cdot 4 \)
D. | 1 | Chemistry |
Methyl phenyl ether can be obtained by reacting:
A. Phenolate ions and methyl iodide
B. Bromobenzene with methoxide ions
c. Methanol and phenol
D. Bromobenzene and methyl iodide | 1 | Chemistry |
A baseball of mass \( 200 \mathrm{g} \) is moving with velocity \( 30 \times 10^{2} \mathrm{cm} / \mathrm{s} \). If we can locate
the baseball with an error equal in
magnitude to the \( \lambda \) of the light used \( \mathbf{5 0 0 0} \boldsymbol{A} \), then the uncertainty in
momentum compared with the total momentum of base ball is:
A \( .1 .75 \times 10^{-29} \)
В. \( 1.34 \times 10^{-29} \)
c. \( 1.89 \times 10^{-29} \)
D. \( 2.03 \times 10^{-29} \) | 1 | Chemistry |
Which of the following rotates the plane of plane polarised light?
A. Compound which is having enantiomeric excess
B. Diastereomers
c. Racemic mixture
D. None | 1 | Chemistry |
Two particles of masses \( m_{1} \) and \( m_{2} \) in
projectile motion have velocities \( \bar{v}_{1} \) and
\( \overline{\boldsymbol{v}}_{2} \) respectively at time \( \boldsymbol{t}=\mathbf{0} . \) They
strike at time \( t_{0} \) and their velocities
become \( \overline{v^{\prime}}_{1} \) and \( \overline{v^{\prime}}_{2} \) at time \( 2 t_{0} \) while
still moving in air. The value of
\( \left|\left(\boldsymbol{m}_{1} \overline{\boldsymbol{v}^{\prime}}_{1}+\boldsymbol{m}_{2} \overline{\boldsymbol{v}^{\prime}}_{2}\right)-\left(\boldsymbol{m}_{1} \overline{\boldsymbol{v}}_{1}+\boldsymbol{m}_{2} \overline{\boldsymbol{v}}_{2}\right)\right| \) is
\( \mathbf{A} \cdot z \) ero
\( \mathbf{B} \cdot\left(m_{1}+m_{2}\right) g t_{0} \)
\( \mathbf{c} \cdot 2\left(m_{1}+m_{2}\right) g t_{0} \)
D \( \cdot \frac{1}{2}\left(m_{1}+m_{2}\right) g t_{0} \) | 3 | Physics |
The ratio of the wavelength for \( 2 \rightarrow 1 \)
transition in \( L i^{+}, H e^{+} \) and \( H \) is :
A .1: 2: 3
B. 1: 4: 9
c. 4: 9: 36
D. 3: 2: 1 | 3 | Physics |
In a given figure,ABCD is a trapezium in
which the parallel sides \( A B \) and \( C D \) are
both perpendicular to BC.If \( \boldsymbol{A B}= \)
\( \mathbf{1 6}, \boldsymbol{A D}=\mathbf{1 7} \) and \( \boldsymbol{C D}=\mathbf{8}, \) then \( \mathbf{B C} \) is
A .15
B. 25
\( c .25 .5 \)
0.39 | 2 | Maths |
The activity of radioactive sample is
measured as 9750 counts per minute at \( t=0 \) and as 975 counts per minute
at \( t=5 \) minutes, the decay constant is
approximately
A . 0.922 per minute
B. 0.270 per minute
c. 0.461 per minute
D. 0.39 per minute | 3 | Physics |
Show that \( f(x)=\frac{-x^{3}}{3}-x^{2}-x+7 \) is
always increasing in \( \mathrm{R} \). | 2 | Maths |
Let the algebraic sum of the perpendicular distance from the points (2,0)(0,2) and (1,1) to a variable straigth line be zero, then the passes through a fixed point whose coordinates
are........ Find the condition on \( a \) and \( b \)
such that the portion of thelineax \( + \)
\( b y-1=0, \) intercepted between the
line axis. | 2 | Maths |
\( \boldsymbol{C}_{4} \boldsymbol{H}_{10}(\boldsymbol{g})+\frac{13}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{4} \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})+ \)
\( \mathbf{5} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) ; \boldsymbol{\Delta} \boldsymbol{H}=-\mathbf{2} \mathbf{8} \mathbf{7} \mathbf{8} \boldsymbol{k} \boldsymbol{J} \)
\( \Delta H \) is the heat of combustion of
butane gas.If true enter 1 else 0
\( A \) | 1 | Chemistry |
If the length of the side of the cube is doubled, then the ratio of the volume of
the new cube and the orignal cube is
A .1: 2
B . 2: 1
c. 4: 1
D. 8: 1 | 2 | Maths |
\( \lim _{x \rightarrow 0} \frac{\sqrt{2}-\sqrt{1+\cos x}}{\sin ^{2} x} \) equals
A \( \cdot \sqrt{2} \)
B. \( \frac{\sqrt{2}}{8} \)
c.
D. none of these | 2 | Maths |
\( \int e^{x}\left(\sec ^{2} x+\tan x\right) d x \) | 2 | Maths |
A liquid is flowing in a horizontal uniform capillary tube under a constant
pressure difference p. The value of pressure for which the rate of flow of the
liquid is doubled when the radius and length both are doubled, is
\( A \cdot \rho \)
в. \( \frac{3 \rho}{4} \)
c. \( \frac{\rho}{2} \)
D. \( \frac{\rho}{4} \) | 3 | Physics |
0
0
\( \widehat{O} \)
\( \widehat{O}_{\operatorname{actg}}^{a k} \)
\( \widehat{O}^{a_{b}} \) | 1 | Chemistry |
There is no resistance in the inductive
circuit. Kirchhoff's voltage law for the
circuit is
A \( \cdot V+L \frac{d i}{d t}=0 \)
B. \( v=L \frac{d i}{d t} \)
\( ^{\mathbf{C}} \cdot V-L^{2} \frac{d i}{d t}=0 \)
D. None of these | 3 | Physics |
If \( \vec{a}=\hat{i}+2 \hat{j}-3 \hat{k}, \vec{b}=2 \hat{i}+\hat{j}-\hat{k} \) and
\( \vec{u} \) is a vector satisfying \( \overrightarrow{\boldsymbol{a}} \times \overrightarrow{\boldsymbol{u}}=\overrightarrow{\boldsymbol{a}} \times \overrightarrow{\boldsymbol{b}} \)
and \( \vec{a} \cdot \vec{u}=0, \) then \( 2|\vec{u}|^{2} \) is equal to
A. 5
B. 4
\( c \cdot 8 \)
D. None of these | 2 | Maths |
Which of the following metal fall under platinum group?
A . Silver
B. Osmium
c. Rhodium
D. Both b and | 1 | Chemistry |
Match the column
\( \begin{array}{lllll}\text { Sr.No } & \text { a } & \text { b } & \text { c } & \\ \text { (i) } & + & + & \text { (1) Commensalism } \\ \text { (ii) } & + & - & \text { (2) Competition } \\ \text { (iii) } & - & - & \text { (3) Parasitism } \\ \text { (iv) } & + & \text { 0 } & \text { (4) mutualism }\end{array} \)
\( A \)
\( (i) 1,(i i) 2,(i i i) 3,(i v) 4 \)
B. \( (i) 2,(i i) 3,(i i i) 1,(i v) \)
C . \( (i) 4,(i i) 3,(i i i) 2,(i v) 1 \)
\( D \)
\( (i) 3,(i i) 2,(i i i) 1,(i v) \) | 1 | Chemistry |
In above shown figure, two speaker, \( \boldsymbol{S}_{1} \)
and \( S_{2} \) are kept at \( 3 \mathrm{m} \) apart. Speakers emit a sound wave of wavelength of \( \mathrm{m} \) Emitted waves are in phase with each other. Compare the amplitude of
resulting wave at point \( P \) and \( Q \) if \( A_{P} \)
and \( A_{Q} \) resulted amplitude at point \( P \) and \( Q \) respectively.
A. \( A_{P}<A_{Q} \)
в. \( A_{P}=A_{Q} \)
c. \( A_{P}>A_{Q} \)
D. \( A_{P}<0, A_{Q}>0 \)
E. \( A_{P} \) and \( A_{Q} \) vary with times, so no comparison can be made | 3 | Physics |
If the temperature of a wire of length
\( 2 m \) area of cross-section \( 1 \mathrm{cm}^{2} \) is
increased from \( 0^{\circ} C \) to \( 80^{\circ} C \) and is not
allowed to increase in length, then force
required for it is \( \left\{\boldsymbol{Y}=\mathbf{1 0}^{\mathbf{1 0}} \boldsymbol{N} / \boldsymbol{m}^{2}, \boldsymbol{\alpha}=\right. \)
\( \left.10^{-6} /^{o} C\right\} \)
A . \( 80 N \)
в. \( 160 N \)
c. \( 400 N \)
D. \( 120 N \) | 3 | Physics |
The Lenz's law gives:
A. direction of induced current
B. magnitude of induced emf
C . magnitude of induced current
D. magnitude and direction of induced current | 3 | Physics |
Find force \( \boldsymbol{F} \) required to keep the system in equilibrium. The dimensions
of the system are \( \boldsymbol{d}=\mathbf{0 . 3 m} \) and \( \boldsymbol{a}= \)
\( 0.2 m . \) Assume the rods to be massless
A . \( 150 \mathrm{N} \)
B. -150 N
c. \( 100 \mathrm{N} \)
D. It cannot be in equilibrium | 3 | Physics |
Which of the following compounds are
formed when \( B C l_{3} \) is treated with
water?
A. \( H_{3} B O_{3} \)
в. \( B_{2} H_{6} \)
\( \mathbf{c} \cdot B_{2} O_{3} \)
D. \( H B O_{2} \) | 1 | Chemistry |
For motion of an object along the \( x \) -axis,
the velocity v depends on the
displacement \( x \) as \( v=3 x^{2}-2 x, \) then
what is the acceleration at \( x=2 m \)
A. \( 48 \mathrm{ms}^{-2} \)
B . \( 80 \mathrm{ms}^{-2} \)
c. \( 18 m s^{-2} \)
D. \( 10 m s^{-2} \) | 3 | Physics |
7 boys and 8 girls have to sit in a row on
15 chairs numbered from 1 to 15 then?
A. Number of ways boys and girls sit alternately is \( 8 ! 7 ! \)
B. Number of ways boys and girls sit alternately is \( 2(8 ! 7 !) \)
C. The number of ways in which first and fifteenth chair are occupied by boys and between any two boys an even number of girls sit is \( ^{9} C_{4} 8 ! 7 ! \)
D. The number of ways in which first and last seat are occupied by boys and between any two boys an even number of girls sit is \( \left(2^{9} C_{4} 8 ! 7 !\right) \) | 2 | Maths |
If \( \sin ^{-1} x+\sin ^{-1} y=\frac{\pi}{2}, \) then \( \frac{d y}{d x} \) is
equal to
A \( \cdot \frac{x}{y} \)
в. \( -\frac{x}{y} \)
c. \( \frac{y}{x} \)
D. \( -\frac{y}{x} \) | 2 | Maths |
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