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Identify a possible graph for function \( \boldsymbol{f} \)
given by
\( \boldsymbol{f}(\boldsymbol{x})=-\sqrt{(\boldsymbol{x}-\mathbf{1})}-\mathbf{1} \)
A. graph a
B. graph b
c. graph c
D. graph d
| 2 |
Maths
|
\( \int_{0}^{\pi / 2} \frac{\sin ^{6} x}{\cos ^{6} x+\sin ^{6} x} d x \) is equal to
A . 0
в. \( \pi \)
c. \( \frac{\pi}{4} \)
D . \( 2 \pi \)
| 2 |
Maths
|
Two resistances are connected in two
gaps of a metre bridge. The balance point is \( 20 \mathrm{cm} \) from the zero end. \( A \)
resistance of \( 15 \Omega \) is connected in series with the smaller of the two. The null
point shifts to \( 40 \mathrm{cm} . \) The value of the smaller resistance in ohms is.
A . 3
B. 6
c. 9
D. 12
| 3 |
Physics
|
Evaluate: \( \lim _{\boldsymbol{\pi}} \frac{\boldsymbol{c o t}^{3} \boldsymbol{x}-\boldsymbol{t a n} \boldsymbol{x}}{\cos (\boldsymbol{x}+\boldsymbol{\pi} / \mathbf{4})} \)
\( \boldsymbol{x} \rightarrow \boldsymbol{\boldsymbol { 4 }} \)
\( A \)
B. \( 8 \sqrt{2} \)
\( c \cdot 4 \)
D. \( 4 \sqrt{2} \)
| 2 |
Maths
|
In zone-refining method, the molten
zone:
A. consists of impurities only
B. contains more impurity than the original metal
c. contains the purified metal only
D. moves to either side
| 1 |
Chemistry
|
The figure shows a bar magnet coil.
Consider four situations.
(I) Moving the magnet away from the
coil.
(II) Moving the coil towards the magnet.
(III) Rotating the coil about the vertical
diameter
(IV) Rotating the coil about its axis.
An emf in the coil will be generated for the following situations.
\( A \cdot(1) \) and (11) only
B. (I), (II) and (IV) only
C. (I), (II) and (III) only
D. (I), (II), (III) and (IV) only
| 3 |
Physics
|
An open end manometer consists of
0.75 moles of \( X_{g} \) taken in a container of
volume 24.63 lit at \( 300 K . \) The level of
mercury in the open tube is found to be \( 14 \mathrm{cm} \) lower. The height difference when manometer is heated to \( 450 K \) will be:
A . \( 14.5 \mathrm{cm} \)
B. \( 21 \mathrm{cm} \)
\( \mathbf{c} \cdot 13 c m \)
D. \( 17 \mathrm{cm} \)
| 1 |
Chemistry
|
For a reaction \( \boldsymbol{A} \stackrel{\boldsymbol{K}_{1}}{\longrightarrow} \boldsymbol{B} \stackrel{\boldsymbol{K}_{2}}{\longrightarrow} \boldsymbol{C} . \) If the
reaction are of \( 1^{s t} \) order then \( \frac{\boldsymbol{d}[\boldsymbol{B}]}{\boldsymbol{d} \boldsymbol{t}} \) is
equal to:
A . \( -k[B] \)
B. \( +k_{1}[A] \)
\( \mathbf{c} \cdot k_{1}[A]-k_{2}[B] \)
D. \( k_{1}[A]+k_{2}[B] \)
| 1 |
Chemistry
|
Curved portion of Henle's loop is lined by
A. Columnar epithelium
B. Cuboidal epithelium
c. Squamous epithelium
D. cinated epithelium
| 0 |
Biology
|
Show that each of the three given vectors is a unit vectors. also Show that
they are mutually \( \perp \) to each other \( \vec{a}=\frac{1}{7}(2 \hat{i}+3 \hat{j}+6 \hat{k}) \)
\( \vec{b}=\frac{1}{7}(3 \hat{i}-6 \hat{j}+2 \hat{k}) \)
\( \overrightarrow{\boldsymbol{c}}=\frac{1}{7}(6 \hat{i}+2 \hat{j}-3 \hat{k}) \)
| 2 |
Maths
|
Which one of the following statements
is incorrect about soaps?
A. Soaps are biodegradable
B. Soaps are sodium salts of higher fatty acids
C. Soaps are prepared from natural oils and fats
D. Soaps can be used in acidic solutions
| 1 |
Chemistry
|
Van't Hoff factor for \( \boldsymbol{T} \boldsymbol{H}\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{4} \) in an
aqueous solution is :
| 1 |
Chemistry
|
The strength of sigma bonds formed by axial overlap of \( s \) - orp-orbitals of 2 nd
shell of participating atoms decreases
as:
| 1 |
Chemistry
|
Factorise the following: \( 2 a^{3}-54 b^{3} \)
\( \mathbf{A} \cdot 2(a b+3 b)\left(a^{2}+3 b+9 a b^{2}\right) \)
B \( \cdot 2(a+2 b)\left(a^{3}+3 a b-9 b^{3}\right) \)
C \( \cdot(a-3 b)\left(a^{2}+3 b+9 a b^{2}\right) \)
D \( \cdot 2(a-3 b)\left(a^{2}+3 a b+9 b^{2}\right) \)
| 2 |
Maths
|
A plank of mass \( m_{1} \) with a bar of mass
\( m_{2} \) placed on it lies on a smooth
horizontal plane. A horizontal force growing with time \( t \) as \( \boldsymbol{F}=\boldsymbol{a t}(\boldsymbol{a} \) is
constant) is applied to the bar. Find how
the accelerations of the plank \( w_{1} \) and of
the bar \( w_{2} \) depend on \( t, \) if the
coefficient of friction between the plank and the bar is equal to \( k \)
| 3 |
Physics
|
If \( \left(x^{2}+y^{2}\right)^{2}=x y, \) find \( \frac{d y}{d x} \)
| 2 |
Maths
|
Figure shows two large cylindrical
shells having uniform linear charge
densities \( +a \lambda \) and \( -\lambda . \) Radius of inner
cylinder as 'a' and that o outer cylinder
is 'b'. A charged particle of mass m,
charge q revolves in a circle of radius
r.Then its speed 'v' is : (Neglect gravity and assume the radii of both the
cylinders to be very small in
comparision to their length)
A \( \cdot \sqrt{\frac{\lambda q}{2 \pi \epsilon_{0} m}} \)
B. \( \sqrt{\frac{2 \lambda q}{\pi \epsilon_{0} m}} \)
c. \( \sqrt{\frac{\lambda q}{\pi \epsilon_{0} m}} \)
D. \( \sqrt{\frac{\lambda q}{4 \pi \epsilon_{0} m}} \)
| 3 |
Physics
|
Predict the direction of the reaction
from the comparison of \( Q_{c}, K_{c} . \) Mark the
incorrect statement.
A \( \cdot \) If \( Q_{c}<K_{c} \), reaction goes from left to right.
B. If \( Q_{c}=K_{c} \), reaction goes from right to left
\( \mathrm{c} \cdot \) If \( Q_{c}>K_{c} \), net reaction goes from right to left
D. If \( Q_{c}=K_{c} \), reactants and products are at equilibrium.
| 1 |
Chemistry
|
Mention two limitations of Ohm's law.
| 3 |
Physics
|
The split of white light into its constituent colours, by a triangular prism, is known as:
A. scattering
B. dispersion
c. refraction
D. deviation
| 3 |
Physics
|
In resonance tube experiment, the velocity of sound is given by \( \boldsymbol{v}= \)
\( 2 f_{0}\left(l_{1}-l_{1}\right) . \) We found \( l_{1}=25.0 c m \) and
\( l_{2}=75.0 c m . \) If there is no error in
frequency, what will be the maximum
permissible error in the speed of sound? \( \left(\text {Take} f_{0}=\mathbf{3 2 5 H z}\right) \)
| 3 |
Physics
|
Let \( A \) and \( B \) be two events such that \( P(\overline{A \cup B})=\frac{1}{6}, P(A \cap B)=\frac{1}{4} \) and
\( P(\bar{A})=\frac{1}{4}, \) then events \( A \) and \( B \) are
A. equally likely, but not independent
B. equally likely and mutually exclusive
c. mutually exclusive and independent
D. independent but not equally likely
| 2 |
Maths
|
Drugs that bind to the receptor sites and inhibit its natural function, are
called:
A. antipyretics
B. analgesics
c. agonist
D. antagonist
| 1 |
Chemistry
|
Solve
\( \int \frac{\cos (x+a)}{\cos (x-a)} d x \)
| 2 |
Maths
|
Assertion
The points on the curve \( y^{2}=x+\sin x \)
at which tangent is parallel to x-axis lies on a straight line.
Reason Tangent is parallel to \( x \) -axis then \( \frac{d y}{d x}= \)
0 or \( \frac{d x}{d y}=\infty \)
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
|
A beam of light converges towards a point \( 0, \) behind a convex mirror of focal length \( 20 \mathrm{cm} . \) Find the magnification
and nature of the image when point 0 is \( 30 \mathrm{cm} \) behind the mirror.
A. 2 (virtual, inverted)
B. 3 (real, inverted)
c. 3, (virtual, enlarged)
D. +1 (real, enlarged)
| 3 |
Physics
|
Name the following compound according to the IUPAC system or nomenclature:
\( \boldsymbol{C H}_{3} \boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right) \boldsymbol{C H}_{2} \boldsymbol{C}\left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C O C H}_{3} \)
| 1 |
Chemistry
|
What is coagulation? Explain.
| 1 |
Chemistry
|
Which of the following correctly represents symbol for chlorine in Berzelius system?
A.
в. с
\( c . \) мп
D.
| 1 |
Chemistry
|
The number of ways of choosing 10 balls from infinitely many white, red , blue and green balls is:
\( A \cdot 70 \)
B. 84
\( c \cdot 286 \)
D. 86
| 2 |
Maths
|
A fricionless wire \( A B \) is fixed on
sphere of radius R. A very small particle slips on the wire. The journey from \( A \) to \( B \) is performed in time
A .2 Rg \( \cos \theta \)
B. \( 2 \sqrt{R g} \cos \theta \)
\( c \cdot 2 \sqrt{\frac{R}{g}} \)
\( 0.2 \sqrt{\frac{9}{2}} \)
| 3 |
Physics
|
Substract \( x^{2} \) from \( x^{2}+y^{2}-3 y \)
| 2 |
Maths
|
The velocity of the body at any instant is
A \( \cdot \frac{M+2 N t^{4}}{4} \)
B. 2N
c. \( \frac{M+2 N}{4} \)
D. \( 2 N t^{3} \)
| 3 |
Physics
|
Electromagnetic waves travel only
through.
\( \mathbf{A} \). material medium
B. vacuum
C. oscillating electric and magnetic fields
D. oscillating electric and magnetic fields whose directions are perpendicular to each other
| 3 |
Physics
|
Is the point (0,3) lie on the graph of the
linear equation \( 3 x+4 y=12 ? \)
| 2 |
Maths
|
The standard enthalpies of n-pentane, isopentane and neopentane are -35.0,-37.0 and \( -40.0 K \) cal / mole
respectively. The most stable isomer of
pentane in terms of energy is
A. n-pentane
B. isopentane
c. neopentane
D. n-pentane and isopentane
| 1 |
Chemistry
|
The number of neutrons accompanying the formation of 139
54 \( \mathrm{Xe} \) and 94
38 \( \mathrm{Sr} \) from
the absorption of a slow neutron by 235 92 followed by nuclear fission is:
\( A \cdot O \)
B. 2
\( c \)
D. 3
| 3 |
Physics
|
Which of the following is not a carbonate mineral?
A. siderite
B. Calamine
c. limestone
D. Fluorospar
| 1 |
Chemistry
|
The standard electrode potential \( \left(E^{\circ}\right) \)
for Daniel cell is \( +1.1 \mathrm{V} \). Calculate \( \Delta G^{\circ} \)
for the reaction.
\( \boldsymbol{Z} \boldsymbol{n}(\boldsymbol{s})+\boldsymbol{C} \boldsymbol{u}_{(a q)}^{2+} \rightarrow \boldsymbol{Z} \boldsymbol{n}_{(a q)}^{2+}+\boldsymbol{C u}(\boldsymbol{s}) \)
\( (1 F=96500 C / m o l) \)
| 1 |
Chemistry
|
A ball is projected upwards from a height h above the surface of the earth with velocity v.The time at which the ball trikes the ground is This question has multiple correct options
A \( \cdot \frac{v}{g}+\frac{2 h g}{\sqrt{2}} \)
в. \( \frac{v}{g}[1-\sqrt{1+\frac{2 h}{g}}] \)
c. \( \frac{v}{g}[1+\sqrt{1+\frac{2 g h}{v^{2}}}] \)
D. \( \frac{v}{g}[1+\sqrt{v^{2}+\frac{2 g}{h}}] \)
| 3 |
Physics
|
A positive test charge is released from rest in a uniform electric field. Which of
the following best describes its initial
motion?
A. It will move with constant velocity along an equipotential line
B. It will move with constant acceleration along an equipotential line
c. It will move with constant acceleration along an electric field line
D. It will move with constant velocity along an electric field line
| 3 |
Physics
|
From 2011 to \( 2016, \) find the difference
between the total number of people who
preferred to play Basketball and Badminton (in millions)?
(Preferences of people in playing different games over the years.
A . 525
В. 275
\( c .730 \)
D. 250
| 2 |
Maths
|
All meteors reach the surface of the
Earth. This statement is
A. True
B. False
| 3 |
Physics
|
A restaurant owner has a few bottles of
soft drink in his restaurant. But, unfortunately, these are not labelled. He
has to serve the drinks on the
demand of customers. One customer
wants acidic drink, another wants basic
and the third wants neutral drink. How
will the restaurant owner decide which
drink is to be served to whom?
| 1 |
Chemistry
|
Chemical agent that has important role in flowering is
A. Fluorocarbon
B. GA \( _{3} \)
c. Florigen
D. Auxins
| 0 |
Biology
|
Construct a \( 2 \times 2 \) matrix \( A=\left[a_{i j}\right] \)
| 2 |
Maths
|
The mean score of 1000 students for an
examination is 34 and \( S . D . \) is 16
(i) How many candidates can be
expected to obtain marks between 30
and 60 assuming the normality of the distribution and
(ii) determine the limit of the marks of
the central \( 70 \% \) of the candidates:
\( \{\boldsymbol{P}[\mathbf{0}<\boldsymbol{z}<\mathbf{0 . 2 5}]=\mathbf{0 . 0 9 8 7} \boldsymbol{P}[\mathbf{0}<\boldsymbol{z}<\mathbf{1} \)
| 2 |
Maths
|
Q туре your question
3.
\( c \)
D.
| 1 |
Chemistry
|
Explain the effects of pressure on the following equilibria.
\( \boldsymbol{L}(\boldsymbol{g})+\boldsymbol{M}_{(\boldsymbol{g})} \rightleftharpoons \boldsymbol{N}_{(\boldsymbol{g})}+\boldsymbol{O}_{(g)} \)
| 1 |
Chemistry
|
If \( \frac{x+3 i}{2+i y}=1-i, \) then the value of
\( (5 x-7 y)^{2} \) is
A . 1
B. 0
\( c \cdot 2 \)
D.
| 2 |
Maths
|
In the following diagram, the Potential
difference across \( 6 V \) cell is:
\( \mathbf{A} \cdot 6 V \)
\( \mathbf{B} \). \( 5.6 V \)
\( \mathbf{c} .8 .2 V \)
D. \( 8.4 V \)
| 3 |
Physics
|
You have two solutions, \( A \) and \( B \). The
\( p H \) of solution \( A \) is 6 and \( p H \) of
solution \( B \) is \( 8 . \) Which solution has
more hydrogen ion concentration? Which of this acidic and which one is
basic?
A. A \( p H \) value less then 7 indicates an acidic solution, while greater than 7 indicates a basic solution. Therefore, the solution with \( p H=6 \) is acidic and has more hydrogen ion concentration than the solution of \( p H=8 \) which is basic.
B. A \( p H \) value less then 7 indicates an basic solution, while greater than 7 indicates a acidic solution. Therefore, the solution with \( p H=8 \) is acidic and has more hydrogen ion concentration than the solution of \( p H=6 \) which is basic
C. A \( p H \) value less then 7 indicates an acidic solution, while greater than 7 indicates a basic solution. Therefore, the solution with \( p H=8 \) is acidic and has
more hydrogen ion concentration than the solution of \( p H=6 \) which is basic.
D. None of the above
| 1 |
Chemistry
|
By what factor the velocity of an electron in a Bohr's orbit for a hydrogen atom will change, if the principal quantum number is doubled:
A. velocity is doubled
B. velocity is halved
C . velocity is reduced to \( \frac{1}{3} \)
D. velocity remains unchanged
| 1 |
Chemistry
|
\( \dots \)
the function \( Z \) of \( X \) and \( Y \) represented by
given figure is :
\( A \)
\begin{tabular}{|c|c|c|}
\hline\( X \) & \( Y \) & \( Z \) \\
\hline 0 & 0 & 0 \\
0 & 1 & 0 \\
1 & 0 & 1 \\
1 & 1 & 1 \\
\hline
\end{tabular}
B. \begin{tabular}{|c|c|c|}
\hline\( X \) & \( Y \) & \( Z \) \\
\hline 0 & 0 & 1 \\
0 & 1 & 1 \\
1 & 0 & 0 \\
1 & 1 & 0 \\
\hline
\end{tabular}
\( c \)
\begin{tabular}{|c|c|c|}
\hline\( X \) & \( Y \) & \( Z \) \\
\hline 0 & 0 & 1 \\
0 & 1 & 0 \\
1 & 0 & 1 \\
1 & 1 & 0 \\
\hline
\end{tabular}
D. None of these
| 3 |
Physics
|
The most basic oxide among
\( M n O, M n_{2} O_{3}, M n O_{2} \) and \( M n_{2} O_{7} \) is :
\( \mathbf{A} \cdot M n O \)
в. \( M n O_{2} \)
\( \mathrm{c} \cdot M n_{2} O_{3} \)
D. \( M n_{2} O_{7} \)
| 1 |
Chemistry
|
The tube in simple barometer is filled with mercury.
A. Half
B. Three-fourth
c. completely
D. Two-third
| 3 |
Physics
|
Which of the following is an example of a disproportionation reaction?
A. \( C a C O_{3} \rightarrow C a O+C O_{2} \)
в. \( 2 H C u C l_{2} \rightarrow C u+C u^{2+}+4 C l^{-}+2 H^{+} \)
c. \( P C l_{5} \rightarrow P C l_{3}+C l_{2} \)
D. \( 2 H_{2} S+S O_{2} \rightarrow 2 H_{2} O+3 S \)
| 1 |
Chemistry
|
Which property of DNA double helix led Watson and Crick to hypothesise semiconservative mode of DNA replication? Explain.
| 0 |
Biology
|
In which of the following option, covalent bond is having maximum \( s \% \) character?
A. \( S-H \) bond in \( H_{2} S \)
B. \( P-H \) bond in \( P H_{3} \)
c. \( N-H \) bond in \( N H_{3} \)
D. All have equal \( s \% \) character
| 1 |
Chemistry
|
\( i f \angle A=\angle B=45^{\circ} \) verify that \( , \sin \)
\( (A+B)=\sin A \cos B+\cos A \sin B \)
| 2 |
Maths
|
The properties of medicine is/are:
This question has multiple correct options
A. it cures the diseases
B. it does not causes addiction
C . it has negligible toxicity
D. none of the above
| 1 |
Chemistry
|
If \( \sin ^{-1} x=y, \) then
A. \( 0 \leq y \leq \pi \)
B. \( -\frac{\pi}{2} \leq y \leq \frac{\pi}{2} \)
c. \( 0<y<\pi \)
D. \( -\frac{\pi}{2}<y<\frac{\pi}{2} \)
| 2 |
Maths
|
During denaturation of proteins which structure is destroyed?
A. secondaary
B. primary
c. tertiary
D. secondary and tertiary
| 1 |
Chemistry
|
Which of the following statements is true?The entropy of the universe:
A. increases and tends towards maximum value
B. decreases and tends to be zero
c. remains constant
D. decreases and increases with a periodic rate
| 1 |
Chemistry
|
What are the major change significant at the stage of adolescents?
| 0 |
Biology
|
A common device which can supply
small electric current continuously for a sufficient time
| 3 |
Physics
|
Find the number of sides of a regular
polygon if each exterior angle
measures: \( 45^{\circ} \)
| 2 |
Maths
|
The compound \( \left[\boldsymbol{P t} \boldsymbol{C l}_{2}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2}\right] \) can
form:
A. geometrical isomers.
B. coordination isomers.
c. linkage isomers.
D. optical isomers.
| 1 |
Chemistry
|
In the Leibigs method, if \( w \) is the mass of compound taken and \( x \) is the amount
of \( C O_{2} \) formed then
\( \mathbf{A} \cdot \% C=\frac{12 \times x}{16 \times w} \)
B . \% \( C=\frac{12}{44} \times \frac{w}{x} \times 100 \)
C \( \cdot \) \% \( C=\frac{12}{44} \times \frac{x}{w} \times 100 \)
D・\% \( C=\frac{12}{44} \times \frac{x}{w} \)
| 1 |
Chemistry
|
Solve \( \int \boldsymbol{a}^{\boldsymbol{m} \boldsymbol{x}} \boldsymbol{b}^{\boldsymbol{n} \boldsymbol{x}} \boldsymbol{d} \boldsymbol{x} \)
| 2 |
Maths
|
If in the expansion of \( \left(\frac{1}{x}+x \tan x\right)^{5}, \) the ratio of \( 4^{t h} \) term to the \( 2^{n d} \) term is \( \frac{2}{27} \pi^{4} \) then the value of \( x \) can be
A \( \cdot \frac{-\pi}{6} \)
в. \( \frac{-\pi}{3} \)
c.
D. \( \frac{\pi}{12} \)
| 2 |
Maths
|
toppr
Q Type your question
heat with the liquid. The bubble
contains n moles of gas. The
temperature of the gas when the
bubbles is at the bottom is \( T_{0}, \) the
height of the liquid is \( \mathrm{H} \) and the
atmospheric pressure is \( P_{0} \) (neglect
surface tension). When the gas bubble
is at height \( y \) from the bottom, its
temperature is:
A \( \cdot \quad T_{0}\left(\frac{P_{0}+\rho_{1} g H}{P_{0}+\rho_{1} g y}\right)^{\frac{2}{5}} \)
\( ^{\mathbf{B}} T_{0}\left(\frac{P_{0}+\rho_{1} g(H-y)}{P_{0}+\rho_{1} g H}\right)^{\frac{2}{3}} \)
c.
\[
T_{0}\left(\frac{P_{0}+\rho_{1} g H}{P_{0}+\rho_{1} g y}\right) \overline{5}
\]
\( P_{0}\left(\frac{P_{0}+\rho_{1} g(H-y)}{P_{0}+\rho_{1} g y}\right)^{\frac{3}{5}} \)
| 3 |
Physics
|
A Shell following a parabolic path explodes somewhere in its flight. The centre of mass of fragments will continue to move in
A. vertical direction
B. any direction
c. horizontal direction
D. same parabolic path
| 3 |
Physics
|
Derivative of which function is \( \boldsymbol{f}^{\prime}(\boldsymbol{x})= \)
\( x \sin x ? \)
This question has multiple correct options
A. \( x \sin x+\cos x \)
B. \( x \cos x+\sin x \)
c. \( x \sin \left(\frac{\pi}{2}-x\right)+\cos \left(\frac{\pi}{2}-x\right) \)
D. \( x \cos \left(\frac{\pi}{2}-x\right)+\sin \left(\frac{\pi}{2}-x\right) \)
| 2 |
Maths
|
The oxide of an element whose
electronic configuration \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{1} \)
is:
A. Neutral
B. Atmospharic
c. Basic
D. Acidic
| 1 |
Chemistry
|
Let \( \boldsymbol{f}:\{\boldsymbol{x}, \boldsymbol{y}, \boldsymbol{z}\} \rightarrow\{1,2,3\} \) be a one-one
mapping such that only one of the following three statements and remaining two are false : \( \boldsymbol{f}(\boldsymbol{x}) \neq \) \( \mathbf{2}, \boldsymbol{f}(\boldsymbol{y})=\mathbf{2}, \boldsymbol{f}(\boldsymbol{z}) \neq 1, \) then
A \( . f(x)>f(y)>f(z) \)
в. \( f(x)<f(y)<f(z) \)
c. \( f(y)<f(y)<f(z) \)
D. \( f(y)<f(z)<f(x) \)
| 2 |
Maths
|
Construct a \( \triangle A B C \) in which \( A C= \)
\( \mathbf{5} c m, \) and \( \angle B A C=60^{\circ} \) and \( A B- \)
\( B C=1.2 \mathrm{cm} \)
| 2 |
Maths
|
(a) Obtain an expression for the mutual
inductance between a long straight
wire and a square loop of side a as
shown in Fig.
(b) Now assume that the straight wire
carries a current of \( 50 \mathrm{A} \) and the loop is moved to the right with a constant velocity, \( v=10 \mathrm{m} / \mathrm{s} \). Calculate the induced emf in the loop at the instant
when \( x=0.2 \mathrm{m} . \) Take \( a=0.1 \mathrm{m} \) and
assume that the loop has a large
resistance.
| 3 |
Physics
|
\( A B C D \) is a square of length \( a, a \in \)
\( N, a>1 . \) Let \( L_{1}, L_{2}, L_{3} \dots \dots, \) be point on
BC such that \( \boldsymbol{B} \boldsymbol{L}_{1}=\boldsymbol{L}_{1} \boldsymbol{L}_{2}=\boldsymbol{L}_{2} \boldsymbol{L}_{3}= \)
\( \ldots=1 \) and \( M_{1}, M_{2}, M_{3} \ldots \ldots \ldots \) be points
on CD such that \( \boldsymbol{C} \boldsymbol{M}_{\mathbf{1}}=\boldsymbol{M}_{\mathbf{1}} \boldsymbol{M}_{\mathbf{2}}= \)
\( =1 . \) Then \( \sum_{n=1}^{a-1}\left(A L_{2}^{2}+L_{n} M_{n}^{2}\right) \) is
equal to
A \( \cdot \frac{1}{2} a(a-1)^{2} \)
B.
\[
\frac{1}{2}(a-1)(2 a-1)(4 a-1)
\]
c.
\[
\frac{1}{2} a(a-1)(4 a-1)
\]
D. None of these
| 2 |
Maths
|
The volume of a largest sphere that can be cut from cylindrical log of wood of
base radius \( 1 m \) and height \( 4 m \) is:
A \( \cdot \frac{8}{3} \pi m^{3} \)
в. \( \frac{10}{3} \pi m^{3} \)
c. \( \frac{16}{3} \pi m^{3} \)
D. \( \frac{4}{3} \pi m^{3} \)
| 2 |
Maths
|
In the bandgap between valence band and conduction band in a material is
\( \mathbf{5} . \mathbf{0} e \boldsymbol{V}, \) then the material is
A. semiconductor
B. good conductor
c. superconductor
D. insulator
| 3 |
Physics
|
\( \lim _{x \rightarrow a} \frac{x^{7}-a^{7}}{x-a} \)
| 2 |
Maths
|
Which scientist synthesised 1st organic compound in lab?
A. Friedrich Wohler
B. Antoine Lavoisier
c. Robert Boyle
D. Willard Gibbs
| 1 |
Chemistry
|
Assertion
\( \left(H_{2}+O_{2}\right) \) fuel cell gives a constant
voltage throughtout its life.
Reason In this fuel cell, \( H_{2} \) reacts with \( \stackrel{\ominus}{O H} \) ions, yet the over all \( [\stackrel{\ominus}{O} \boldsymbol{H}] \) does not change.
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
| 1 |
Chemistry
|
A graph and the system of inequalities are shown above. Which region of the
graph could represent the solution for
the system of in equations?
\( \boldsymbol{y}>\boldsymbol{x} \)
\( \mathbf{3} \boldsymbol{y} \leq-\mathbf{4} \boldsymbol{x}+\mathbf{6} \)
\( A \cdot A \)
в. \( B \)
\( c . c \)
D. \( D \)
| 2 |
Maths
|
Which of the following is(are) the merit(s) of Mendeleev's periodic table?
A. Could also predict the properties of these unknown elements
B. Grouping of chemically dissimilar elements.
c. Position given to isotopes.
D. Presence of anomalous pairs
| 1 |
Chemistry
|
For what value of \( a \), the function
\[
\boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{ll}
\frac{1-\cos 4 x}{\boldsymbol{x}^{2}}, & \boldsymbol{i f} \quad \boldsymbol{x}<0 \\
\boldsymbol{a}, \quad \boldsymbol{i f x}=\mathbf{0} & \\
\frac{\sqrt{\boldsymbol{x}}}{\sqrt{\mathbf{1 6 + \sqrt { \boldsymbol { x } }}-\boldsymbol{4}}}, & \boldsymbol{i f} \boldsymbol{x}>0
\end{array}\right.
\]
continuous at \( \boldsymbol{x}=\mathbf{0} \)
| 2 |
Maths
|
The most abundant organic compound in the world is:
A . cellulose
B. alkaloids
c. methane
D. chlorophyll
| 1 |
Chemistry
|
In a parallel plate capacitor, the region between the plates is filled by a delectric slab. The capacitor is connected to a cell and the slab is taken
out.
A. Some charge is drawn from the cell
B. Some charge is returned to the cell
c. The potential difference across the capacitor is reduced
D. No work is done by an external agent in taking the slab out
| 3 |
Physics
|
Select the incorrect order(s) among
the following:
This question has multiple correct options
\( \mathbf{A} \cdot C l O^{-}<B r O^{-}<I O^{-} \) - disproportionation
B \( \cdot C l O_{4}^{-}<B r O_{4}^{-}<l O_{4}^{-} \) - oxidising power
c. \( H C l O<H C l O_{2}<H C l O_{3}<H C l O_{4} \) - acid strength
D. \( H O C l>H O I>H O B r \) -acid strength
| 1 |
Chemistry
|
The result of the operation \( 2.5 \times 1.25 \) should be which of the following on the basis of significant figures?
A . 3.125
B. 3.13
c. 3.
D. 31.25
| 1 |
Chemistry
|
Calculate \( \gamma\left(\text { ratio of } C_{p} \text { and } C_{v}\right) \) for triatomic linear gas at high
temperature. Assume that the
contribution of the vibrational degree of freedom is \( 75 \% ? \)
A. 1.222
B. 1.121
c. 1.18
D. 1.33
| 3 |
Physics
|
Assertion
If the bodies in question have spatial extent (rather than being theoretical point masses), then the gravitational force between them is calculated by summing the contributions of the notional point masses which constitute the bodies.
Reason
Every point mass attracts every single other point mass by a force pointing along the line intersecting both points.
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
|
If \( A=\left|\begin{array}{ll}2 & 3 \\ 6 & 9\end{array}\right| \) then \( |A|= \)
A .
B. 1
\( c \cdot 2 \)
D.
| 2 |
Maths
|
A positively charged particle in a uniform magnetic field moves in a circular path in the clockwise direction,
parallel to the plane of the page. In what direction do the magnetic field lines point?
A. Out of the page
B. Into the page
c. To the left
D. To the right
E. In a clockwise pattern parallel to the plane of the page
| 3 |
Physics
|
The length of the perpendicular from the
vertex \( D \) on the opposite face is
A \( \cdot \frac{14}{\sqrt{6}} \)
в. \( \frac{2}{\sqrt{6}} \)
c. \( \frac{3}{\sqrt{6}} \)
D. none of these
| 2 |
Maths
|
Evaluate the following:
\( \sin ^{-1}(\sin 5) \)
| 2 |
Maths
|
Which of the following pigments is present in brown algae?
A. Anthocyanin
B. Fucoxanthin
c. Phycobilins
D. Biliverdin
| 0 |
Biology
|
Himanshu borrowed \( \boldsymbol{R} \boldsymbol{s} \mathbf{1 2}, \mathbf{0 0 0} \) at
\( 15 \frac{1}{2} \% \) rate of simple interest for certain years. At the end of the period, he paid a total sum of \( \boldsymbol{R} \boldsymbol{s} \boldsymbol{2} \boldsymbol{0}, \boldsymbol{3} \boldsymbol{7} \boldsymbol{0} . \) Find the period.
| 2 |
Maths
|
Which of the following is an EAN of iron in potassium ferricyanide?
A . 28
B. 36
c. 35
D. 39
| 1 |
Chemistry
|
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