AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
In the figure, \( O \) is the centre of a circle
such that diameter \( A B=13 \mathrm{cm} \) and
\( A C=12 \mathrm{cm} . B C \) is joined. Find the
area of the shaded region. (Take \( \pi= \)
\( \mathbf{3 . 1 4}) \)
Subject: Biology
Which of the following is a correct sequence of layers in typical monocot root (from outer surface to inside)?
A. Pericycle, cortex, endodermis, epiblema
B. Epiblema, endodermis, cortex, pericycle
c. Epiblema, cortex, endodermis, pericycle
D. Epiblema, pericycle, cortex, endodermis
Subject: Maths
The value of \( 2 x^{4}+5 x^{3}+7 x^{2}-x+41 \)
when \( \boldsymbol{x}=-\boldsymbol{2}-\sqrt{\mathbf{3} \boldsymbol{i}} \) is:
A . -
B. 4
\( c \cdot-6 \)
D. 6
Subject: Chemistry
Arrange the following in the increasing order of basicity:
\( \boldsymbol{C H}_{3} \boldsymbol{N} \boldsymbol{H}_{2},\left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{N} \boldsymbol{H},\left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{N} \)
Subject: Maths
If \( I=\int(\sqrt{\frac{a+x}{a-x}}+\sqrt{\frac{a-x}{a+x}}) d x, \) then
equals
\( \mathbf{A} \cdot 2 \sin ^{-1}\left(\frac{x}{a}\right)+C \)
B. \( 2 a \sin ^{-1}\left(\frac{x}{a}\right)+C \)
\( c \cdot 2 \cos ^{-1}\left(\frac{x}{a}\right)+C \)
D \( \cdot 2 a \cos ^{-1}\left(\frac{x}{a}\right)+C \)
Subject: Physics
Hysteresis loops for two magnetic
materials \( A \) and \( B \) are given below:
These materials are used to make
magnets for electric generators, transformer core and electromagnet
core. Then it is proper to use:
A. A for electric generators and transformers
B. A for electromagnets and B for electric generators
c. A for transformer and B for electric generators
D. B for electromagnets and transformers
Subject: Physics
The displacement-time equation of a
straight line motion is \( \boldsymbol{x}=\mathbf{4} \boldsymbol{t}-\mathbf{5} \boldsymbol{t}^{2}+ \)
\( 3 t^{3}-4 t^{4} . \) The velocity at \( t=2 \sec \) is
A. - -86 units
B. +26 units
c. -12 units
D. +16 units
Subject: Maths
If \( 5 f(x)+3 f\left(\frac{1}{x}\right)=x+2 \) and \( y= \)
\( \boldsymbol{x} \boldsymbol{f}(\boldsymbol{x}) \)
\( \operatorname{then} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{n}} \) at \( \boldsymbol{x}=\mathbf{1} \)
A . 14
в. \( \frac{7}{8} \)
c. 1
D.
Subject: Maths
Solve \( \boldsymbol{x}+\mathbf{2}+\boldsymbol{y}+\mathbf{3}+ \)
\( \sqrt{(x+2)(y+3)}=39 \)
\( (x+2)^{2}+(y+3)^{2}+(x+2)(y+ \)
3)\( =741 \)
Subject: Physics
Consider an "L"-shaped object where the vertical leg extends from the origin to
(0,5) and the horizontal segment
extends from the origin to (3,0)
Assume that the object has uniform
linear density throughout. Where is the location of the center of
\( \operatorname{mass}(\boldsymbol{C o} \boldsymbol{M}) ? \)
A \( \cdot(1.5,1.5) \)
B . (1.5,2.5)
\( \mathbf{c} \cdot(2.5,2.5) \)
D. The center of mass for an "L" is undefined because there is no single point on the object where it can be supported, such that it will not rotate
E. None of these
Subject: Chemistry
\( \Delta G^{o} \) at \( 25^{\circ} C \) for the reaction
\( \frac{1}{2} N_{2}(g)+\frac{3}{2} H_{2} \rightleftharpoons N H_{3}(g) \) is
\( -16.5 k J \) mol \( ^{-1} . \) Hence
thermodynamic equilibrium constant is:
A . 1.08
B. \( 7.80 \times 10^{2} \)
C \( .4 .57 \times 10^{6} \)
D. \( 7.98 \times 10^{34} \)
Subject: Chemistry
\( k_{p} \) for a reaction at \( 25^{0} C \) in 10 atm. Then
\( K_{c} \) for the reaction at \( 40^{0} C \) will be:
(Given \( : \Delta H=-8 k J \) and antilog
\( (0.067)=0.1167) \)
A \( \cdot 4.33 \times 10^{-1} M \)
В. \( 3.33 \times 10^{-2} M \)
\( \mathrm{c} \cdot 3.33 \times 10^{-1} \mathrm{M} \)
D. None of these
Subject: Physics
Two metallic spheres \( A \) and \( B \) are made of same material and have got an identical surface finish. The mass of
sphere \( \mathbf{A} \) is four times that of \( \mathbf{B} . \) Both
the spheres are heated to the same
temperature and placed in a room having a lower temperature but thermally insulated from each other.
A. The ratio of heat loss of A to that of B is \( 2^{4 / 3} \)
B. The ratio of heat loss of A to that of B is \( 2^{2 / 3} \)
C. The ratio of the initial rate of cooling of A to that of B is \( 2^{2 / 3} \)
D. The ratio of the initial rate of cooling of \( A \) to that of \( B \) is \( 2^{-1 / 3} \)
Subject: Physics
Potentiometer wire Pq of length Im is
connected to a standard cell \( \boldsymbol{E}_{1} \) Another
cell of E2 of emf1.02v/s connected as
shown in the circuit diagram with a
resistance 'r' and with a switch 's'. With
the switch \( \mathrm{S} \) open, null position is
obtained at a distance of \( 51 \mathrm{cm} \) from
p,Calculate
A. Potential gradient of the wire.
B. emf of the cell
C. When switch S is closed, will null point moves towards p or \( Q ? \)
D. insufficient data
Subject: Physics
If the distance between the centres of
earth and moon is \( \mathrm{D} \) and mass of earth
is 81 times that of moon. At what
distance from the centre of earth
gravitational field will be zero:
A \( \cdot \frac{D}{2} \)
в. \( \frac{3 D}{2} \)
c. \( \frac{4 D}{5} \)
D. \( \frac{D}{10} \)
Subject: Physics
The variation of magnitude field \( (B) \)
due to circular coil as the distance \( \boldsymbol{X} \)
varies is shown in the graph.
Which of the following is false?
A. Point \( A \) and \( A^{\prime} \) are known as point of zero curvature.
B. \( B \) varies linearly with \( X \) at point \( A \) and \( A^{\prime} \)
\( \frac{d B}{d t}=0 \) at point \( A \) and \( A^{\prime} \)
\( \frac{d^{2} B}{d t^{2}}=0 \) at point \( A \) and \( A^{\prime} \)
Subject: Maths
A force \( \overrightarrow{\boldsymbol{F}}=\mathbf{3} \hat{\mathbf{i}}+\mathbf{4} \hat{\mathbf{j}}-\mathbf{3} \hat{\boldsymbol{k}} \) is applied at
the point \( P, \) whose position vector is \( \vec{r}=2 \hat{i}-2 \hat{j}-3 \hat{k} . \) What is the
magnitude of the moment of the force about the origin?
A . 23 units
B. 19 units
c. 18 units
D. 21 units
Subject: Maths
Consider the following equation, \( \frac{d y}{d x}+ \) \( \boldsymbol{P}(\boldsymbol{x}) \boldsymbol{y}=\boldsymbol{Q}(\boldsymbol{x}) \)
(i) If two particular solutions of given equation \( u(x) \) and \( v(x) \) are known, find the general solution of the same equation in terms of \( u(x) \) and \( v(x) \)
(ii) If \( \alpha \) and \( \beta \) are constants such that
the linear combinations \( \boldsymbol{\alpha} \cdot \boldsymbol{u}(\boldsymbol{x})+\boldsymbol{\beta} \)
\( v(x) \) is a solution of the given equation,
find the relation between \( \alpha \) and \( \beta \)
(iii) If \( \boldsymbol{w}(\boldsymbol{x}) \) is the third particular
solution different from \( u(x) \) and \( v(x) \) then find the ratio \( \frac{\boldsymbol{v}(\boldsymbol{x})-\boldsymbol{u}(\boldsymbol{x})}{\boldsymbol{w}(\boldsymbol{x})-\boldsymbol{u}(\boldsymbol{x})} \)
Subject: Chemistry
The empirical formula of a compound of
molecular mass 120 is \( C H_{2} O . \) The
molecular formula of the compound is:
\( \mathbf{A} \cdot C_{2} H_{2} O_{2} \)
B \( \cdot C_{4} H_{8} O_{4} \)
c. \( C_{3} H_{6} O_{9} \)
D. none of the above
Subject: Chemistry
\( D- \) Glucose and \( D- \) fructose both form
the same osazone. Which statements
are correct about the above reaction?
This question has multiple correct options
A. Glucose and fructose are epimers
B. Glucose and fructose are anomers
c. The configurations of the \( O H \) group at \( C-3 \) and \( C \) -
4 in glucose and fructose are same
D. The configurations of the \( O H \) group at \( C-4 \) and \( C \) 5 in glucose and fructose are same
Subject: Biology
(A) Used extensively in agriculture and horticulture practice
(B) rapid cell division
(C) Initiate rooting in stem cutting
(D) Speed up malting process
(E) Promotes female flower in cucumbers
(F) Dormancy in seeds/buds. How many function from above perform by the Auxin in plants.
A. Three
в. Two
\( c . \) Five
D. Four
Subject: Maths
In a square \( A B C D, \angle A B D=3 x= \)
\( \angle A D B, \) then \( \angle B D C ? \)
\( \mathbf{A} \cdot 6 x^{\circ} \)
B. \( (90-6 x)^{\text {d }} \)
\( \mathbf{c} \cdot 45^{\circ} \)
D. None
Subject: Maths
What are the coordinates of the center
of this circle?
\( \boldsymbol{x}^{2}+(\boldsymbol{y}+\mathbf{7})^{2}=\mathbf{1 1} \)
\( A \cdot(7,7) \)
B. (0,7)
c. (-7,-7)
D. (0,-7)
Subject: Maths
Which of the following is a geometric series?
A \( \cdot 2,4,6,8, \dots \dots \)
B \( \cdot 1 / 2,1,2,4 \ldots \ldots \)
c. \( 1 / 4,1 / 6,1 / 8,1 / 10, \ldots \ldots \)
D・ \( 3,9,18,36, \ldots \)
Subject: Chemistry
For an electrolyte solution of \( \mathbf{0 . 0 5} \boldsymbol{M} \) the conductivity has been found to be
\( 0.0110 \mathrm{S} \mathrm{cm}^{-1} . \) The molar conductivity
is:
A. \( 0.055 \mathrm{Scm}^{2} \mathrm{mol}^{-1} \)
B. \( 550 \mathrm{Scm}^{2} \mathrm{mol}^{-1} \)
c. \( 0.22 \mathrm{Scm}^{2} \mathrm{mol}^{-1} \)
D. \( 220 \mathrm{Scm}^{2} \mathrm{mol}^{-1} \)
Subject: Physics
It is observed that for a ratio \( \frac{\boldsymbol{m}_{1}}{\boldsymbol{m}_{2}}= \)
\( \left(3-x^{2}+x\right), \) maximum transfer of
momentum takes places from body 1 to body \( 2 . \) Then This question has multiple correct options
A \( . x=1 \)
B. \( x=2 \)
\( c \cdot x=3 \)
D. x = -
Subject: Chemistry
Q Type your question
Determine the time it would take to
plate \( 10.0 g A g \) with a current of \( 0.452 A \)
A \( .2 .5 h r \)
B. \( 3.5 h r \)
c. \( 4.5 h r \)
\( 0.5 .5 h \)
Subject: Maths
Solve the following:
\( \frac{4}{5}\left(x+\frac{5}{6}\right)+\frac{2}{3}\left(x-\frac{1}{4}\right)=1 \frac{1}{9} \)
A \( \cdot \frac{9}{14} \)
в. \( \frac{5}{12} \)
\( c \cdot \frac{3}{11} \)
D. \( \frac{7}{11} \)
Subject: Physics
Which of the following is wrong
statement?
A \( \cdot D=\frac{1}{f} \) where \( f \) is focal length and \( D \) is optical power of lens.
B. Power is in diopter when \( f \) is in meters.
C. Power is in diopter and does not depend upon the system of unit used to measure \( f \)
D. \( D \) is positive for convergent lens and \( D \) is negative for divergent lens.
Subject: Physics
Which of the following are not correct?
This question has multiple correct options
A. The escape velocity for the Moon is \( 6 k m s^{-1} \)
B. The escape velocity from the surface of Moon is \( v \). The orbital velocity for a satellite to orbit very close to the surface of Moon is \( v / 2 \)
C. When an earth satellite is moved from one stable orbit to a further stable orbit, the gravitational potential energy increases
D. The orbital velocity of a satellite revolving in a circular path close to the planet is independent of the density of the planet.
Subject: Physics
An unnumbered wall clock shows time
\( 04: 25: 37, \) where ist term represents
hours, 2nd represents minutes and the last term represents seconds. What time will its image in a plane mirror show
\( \mathbf{A} \cdot 08: 35: 23 \)
B. \( 0 .: 35: 23 \)
c. 07: 35: 23
D. none of these
Subject: Physics
The drift velocity of the electron in a
copper wire of length \( 2 \mathrm{m} \) under the application of a potential difference of
\( 200 \mathrm{V} \) is \( 0.5 \mathrm{ms}^{-1} \).Their mobility is (in
\( \left.m^{-2} V^{-1} s^{-1}\right) \)
\( \mathbf{A} \cdot 5 \times 10^{-3} \)
B. \( 2.5 \times 10^{-2} \)
c. \( 5 \times 10^{2} \)
D. \( 10^{-3} \)
Subject: Chemistry
In this diol:
\( \mathbf{A} \cdot O H^{-} \) at \( C_{2} \) is more basic than that of at \( C_{5} \)
B. \( O H^{-} \) at \( C_{2} \) is more acidic than at \( C_{5} \)
C. both have same basicity
D. both have same acidic strength
Subject: Chemistry
The first order rate constant for the
decomposition of ethyl iodide by the
reaction \( C_{2} H_{5} I_{(g)} \rightarrow C_{2} H_{5(g)}+H I_{(g)} \)
at \( 600 K \) is \( 1.60 \times 10^{-5} S^{-1} \) Its energy of
activation is \( 209 \mathrm{kJ} / \mathrm{mol} \). Calculate the
rate constant of the reaction at \( 700 \mathrm{K} \)
Subject: Physics
In a very long solenoid of radius \( \boldsymbol{R} \), if
the magnetic field changes at the rate of \( d B / d t . A B=B C . \) The induced emf
for the triangular circuit \( A B C \) shown in
figure is :
\( ^{A} \cdot_{R^{2}}\left(\frac{d B}{d t}\right) \)
в. \( _{4 R^{2}}\left(\frac{d B}{d t}\right. \)
\( ^{\mathrm{C}} \cdot \frac{1}{2} R^{2}\left(\frac{d B}{d t}\right) \)
D. \( 2 R^{2}\left(\frac{d B}{d t}\right. \)
Subject: Chemistry
Statement-1: Micelles are formed by surfactant molecules above the critical
micellar concentration \( (\boldsymbol{C} \boldsymbol{M} \boldsymbol{C}) \)
Statement-2: The conductivity of a solution having surfactant molecules
decreases sharply at the CMC.
A. Statement-1 is True, Statement-2 is True; Statementis a correct explanation for Statement-
B. Statement-1 is True, Statement-2 is True; Statementis NOT a correct explanation for Statement-1
c. Statement-1 is True, Statement-2 is False.
D. Statement- is False, Statement-2 is True
Subject: Chemistry
Assertion
Nitrogen and oxygen are the main
components in the atmosphere but do not react to form oxides of nitrogen
Reason

The reaction between nitrogen and
oxygen requires high temperature
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
Subject: Physics
Consider a sinusoidal travelling wave shown in figure. The wave velocity is \( +40 c m / s . \) The velocity of a particle at
point \( P \) at the instant shown is \( -126 \times \)
\( 10^{-x} m / s . \) Find \( x \)
4
B. 2
\( c \cdot 4 \)
\( D \)
Subject: Physics
The light of wavelength \( 6328 A^{\circ} \) is incident on a slit of width 0.2 mm
perpendicularly, the angular fringe width will be:
A \( \cdot 0.36^{\circ} \)
B. \( 0.18^{\circ} \)
\( c \cdot 0.72^{\circ} \)
D. \( 0.09^{\circ} \)
Subject: Maths
Which one of the following is not true?
\( \mathbf{A} \cdot A \backslash B=A \cap B^{\prime} \)
в. \( A \backslash B=A \cap B \)
C \( . A \backslash B=(A \cup B) \cap B^{\prime} \)
D. \( A \backslash B=(A \cup B) \backslash B \)
Subject: Maths
If \( A B \perp B C, \) then the value of \( \lambda \) equal
where \( \boldsymbol{A}(\mathbf{2 k}, \mathbf{2}, \mathbf{3}), \boldsymbol{B}(\boldsymbol{k}, \mathbf{1}, \mathbf{5}), \boldsymbol{C}(\boldsymbol{3}+ \)
\( k, 2,1) \)
\( \mathbf{A} \cdot \mathbf{3} \)
B.
\( c .-3 \)
D. \( -\frac{1}{3} \)
Subject: Physics
A charge \( Q \) is placed at the corner of a cube. The electric flux through all the faces of the cube is
\( \mathbf{A} \cdot Q / \varepsilon_{0} \)
в. \( Q / 6 \varepsilon_{0} \)
c. \( Q / 8 \varepsilon_{0} \)
D. \( Q / 3 \varepsilon_{0} \)
Subject: Maths
If \( \alpha \) and \( \beta \) are complex conjugates to each other and \( \boldsymbol{\alpha}=-\sqrt{\mathbf{2}}+\boldsymbol{i} \) then find
\( \boldsymbol{\alpha}^{2}+\boldsymbol{\beta}^{2}-\boldsymbol{\alpha} \boldsymbol{\beta} \)
Subject: Physics
A thin convex lens made of glass of \( \mu= \) 1.5 has refracting surfaces of radii of curvature \( 10 \mathrm{cm} \) each. The left space of lens contains air and the right space is filled with water of refractive index \( \frac{4}{3} \cdot A \) parallel beam of light is incident on it. The position of the image is :
\( \mathbf{A} \cdot 16 \mathrm{cm} \)
B. \( 20 \mathrm{cm} \)
\( c \cdot 24 c m \)
D. \( 10 \mathrm{cm} \)
Subject: Maths
Construct a triangle similar to a given \( \triangle A B C \) such that each of its sides is
\( (5 / 7)^{t h} \) of the corresponding sides of \( \triangle A B C . \) It is given that \( A B= \)
\( \mathbf{5} c \boldsymbol{m}, \boldsymbol{B} \boldsymbol{C}=\mathbf{7} \boldsymbol{c m} \) and \( \angle \boldsymbol{A} \boldsymbol{B} \boldsymbol{C}=\mathbf{5 0}^{\circ} \)
Subject: Chemistry
Assertion
Silver may be prepared by using silver
coins; in this process, coins are treated
with \( H N O_{3} \) and then treated with \( H C l \)
to get \( A g C l, \) but directly coins are not
treated with \( \boldsymbol{H} \boldsymbol{C l} \)
Reason
HCl is not a good oxidizing agent.
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
Subject: Physics
The distance covered by a particle in \( t \)
second is given by \( \boldsymbol{x}=\mathbf{3}+\mathbf{8} \boldsymbol{t}-\mathbf{4} \boldsymbol{t}^{2} \)
After \( 1 s \) its velocity will be
A. 0 unit \( / \) s
B. 3unit/
c. \( 4 u n i t / s \)
D. \( 7 u n i t / s \)
Subject: Chemistry
At \( 25^{\circ} \mathrm{C} \), the molar conductances at
infinite dilution for the strong
electrolytes \( N a O H, N a C l \) and \( B a C l_{2} \)
\( \operatorname{are} 248 \times 10^{-4}, 126 \times 10^{-4} \) and \( 280 \times \)
\( 10^{-4} S m^{2} m o l^{-1} \) respectively.
\( \wedge_{m}^{\circ} B a(O H)_{2} \) in \( S m^{2} m o l^{-1} \) is :
A. \( 52.4 \times 10^{-4} \)
В. \( 524 \times 10^{-4} \)
c. \( 402 \times 10^{-4} \)
\( \mathbf{D} \cdot 262 \times 10^{-4} \)
Subject: Chemistry
Which of the following is a monounsaturated hydrocarbon, i.e. the compound that contains one carbon -
carbon double bond?
A \( \cdot C_{3} H_{6} \)
в. \( C_{2} H_{2} \)
\( \mathbf{c} \cdot C_{6} H_{6} \)
D. \( C_{5} H_{8} \)
Subject: Maths
Find the greatest value of \( x y z \) for
positive value of \( x, y, z \) subject to the
condition \( \boldsymbol{x} \boldsymbol{y}+\boldsymbol{y} \boldsymbol{z}+\boldsymbol{z} \boldsymbol{x}=\mathbf{1 2} \)
Subject: Physics
A small sphere of mass \( \boldsymbol{m}=\mathbf{1} \boldsymbol{k} \boldsymbol{g} \) is
moving with a velocity \( (4 \hat{i}-\hat{j}) m / s . \) It
hits fixed smooth wall and rebounds with velocity \( (\hat{\mathbf{i}}+\mathbf{3} \hat{\mathbf{j}}) \boldsymbol{m} / \boldsymbol{s} . \) The
coefficient of restitution between the
sphere and the wall is \( n / 16 . \) Find the
value of \( n \)
Subject: Physics
A cubical ball is taken to a depth of \( 200 \mathrm{m} \) in a sea. The decrease in volume
observed to be \( 0.1 \% \). The bulk modulus of
the ball is \( \left(10=m s^{-2}\right) \)
\( \begin{array}{ll}\text { A. } 2 \times 10^{7} & \text { Pa } \\ a\end{array} \)
В. \( 2 \times 10^{6} \) Ра
C \( .2 .1 \times 10^{9} \) Pa
D. \( 1.2 \times 10^{9} \) Pa
Subject: Chemistry
The pressure \( v / s \) volume graph of an
ideal gas is given in different thermodynamics process which of the
following option in relevant order:
(Isochoric, isobaric, isothermal, adiabatic)
A \( \cdot d, \) a, b,
B. a, d, c,
\( c \cdot a, c, d, b \)
D. a, b, c,
Subject: Physics
Block \( A \) has a weight of \( 300 N \) and
block \( B \) has a weight of \( 50 N . \) The coefficient of kinetic friction between
the incline and block \( \boldsymbol{A} \) is \( \boldsymbol{\mu}_{\boldsymbol{k}}=\mathbf{0 . 2} \)
Determine the speed of block \( \boldsymbol{A} \) after it
moves \( 1 \mathrm{m} \) down the plane, starting
from rest. Neglect the mass of the cord
and pulleys. (Take \( g=10 m / s^{2} \) )
A. \( 1.12 m / s \)
в. \( 1.2 m / s \)
c. \( 1.32 m / s \)
D. \( 1.4 m / s \)
Subject: Chemistry
Balance the following equation:
\( \boldsymbol{H} \boldsymbol{g}_{2}(\boldsymbol{C} \boldsymbol{N})_{2}+\boldsymbol{C} \boldsymbol{e}^{4+} \rightarrow \boldsymbol{C} \boldsymbol{O}_{3}^{-}+\boldsymbol{N} \boldsymbol{O}_{3}^{-}+ \)
\( \boldsymbol{H} \boldsymbol{g}(\boldsymbol{O} \boldsymbol{H})_{2}+\boldsymbol{C} \boldsymbol{e}^{\boldsymbol{3}+} \)
Subject: Physics
The length of an iron wire is \( L \) and area
of cross-section is \( A \). The increase in
length is \( l \) on applying the force \( F \) on its two ends. Which of the statement is
correct?
A. Increase in length is inversely proportional to its length
B. Increase in length is proportional to area of crosssection
C. Increase in length is inversely proportional to area of cross-section
D. Increase in length is proportional to Young's modulus
Subject: Chemistry
When \( P H_{3} \) absorbed in \( H g C l_{2} \) solution
the corresponding phosphide is
obtained
A. \( H g_{2} P_{3} \)
в. \( H g_{3} P_{2} \)
\( \mathbf{c} \cdot H g_{3}\left(P O_{4}\right)_{2} \)
D. None of these
Subject: Physics
A circular coil expands radially in a
region of magnetic field and no electromotive force is produced in the coil. This is because
A. the magnetic field is constant
B. the magnetic field is in the same plane as the circular coil and it may or may not vary
c. the magnetic field has a perpendicular (to the plane of the coil) component whose magnitude is decreasing suitably
\( D . \) both \( (b) \) and \( (c) \)
Subject: Maths
The sum of the series \( 1+\frac{\log _{e} x}{1 !}+ \)
\( \frac{\left(\log _{e} x\right)^{2}}{2 !}+\dots \dots . . \) is
A . \( x \)
B . \( x^{2} \)
c. \( x^{3} \)
D. none of these
Subject: Chemistry
At \( 300 K, 36 g \) of glucose present per
litre in its solution has an osmotic
pressure of 4.98 bar. If the osmotic
pressure of solution is 1.52 bar at the
same temperature, what would be its concentration?
A \( \cdot 11 g L^{-1} \)
в. \( 22 g L^{-1} \)
c. \( 36 g L^{-1} \)
D. \( 42 g L^{-1} \)
Subject: Physics
Two locomotives approach each other on the parallel tracks. Each has speed of \( 95 k m / h \) with respect to the ground. If they are initially \( 8.5 k m \) apart, how long will it be before they reach each other? (in hours)
\( \mathbf{A} \cdot 0.045 \)
B. 0.065
c. 0.025
D. 0.078
Subject: Maths
Assertion
Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be a function such that
\( f(x)=x^{3}+x^{2}+3 x+\sin x . \) Then, \( f \) is
one-one.
Reason
\( f(x) \) is decreasing function
A. Assertion and Reason are correct and the reason is the correct explanation for the assertion
B. Assertion and Reason are correct and the reason is Not the correct explanation for the assertion.
c. Assertion is correct while the Reason is incorrect
D. Assertion is incorrect while the Reason is correct
Subject: Physics
A resistor \( R, \) an inductor \( L \) and
capacitor \( C \) are connected in series to
an oscillator of frequency \( n \). If the
resonant frequency is \( n_{r}, \) then the current lags behind voltage, when
\( \mathbf{A} \cdot n=0 \)
в. \( n<n_{r} \)
c \( \cdot n=n_{r} \)
\( \mathbf{D} \cdot n>n_{r} \)
Subject: Physics
A vehicle is running with a velocity of \( 5 m / s . \) If the momentum of the vehicle
is \( 5000 \mathrm{kg} \mathrm{m} / \mathrm{s}, \) What is its mass?
A. \( 1 \mathrm{kg} \)
в. \( 100 \mathrm{kg} \)
c. \( 1000 k g \)
D. \( 1.1 \mathrm{kg} \)
Subject: Biology
Match column I with column II and
select the correct option from the codes
given below.
Column I
A. Suicide bag of the \( \quad \) column \( \| \) cell
1. Mitochondria
B. Powerhouse of the
2. Ribosome cell
3. Lysosome
C. Protein factory of the
4. Endoplasmic cell \( \quad \) reticulum
D. Kitchen of the cell
E. Circulatory system of
5. Chloroplast
the cell
A. A- \( 3, \) B- \( 1, \) C- \( 2, \) D- \( 5, \) E- 4
B. A- 3, B-1, C- 5, D-2, E-4
c. \( A-3, B-2, C-1, D-5, E-4 \)
D. A-1,B-3,C-2,D-5,E-4
Subject: Biology
What does the following sequence represent?
Blue-Green Algae \( \rightarrow \) Crustose Lichens
\( \rightarrow \) Foliose Lichens \( \rightarrow \) Mosses \( \rightarrow \) Shrubs
\( \rightarrow \) Dicotyledonous trees
A. A food pyramid
B. Ecological succession
c. Genetic drift
D. Phylogenetic trend
Subject: Maths
Orthocentre of an equilateral triangle
\( A B C \) is the origin O. If \( A=\bar{a}, B= \) \( \boldsymbol{b}, \boldsymbol{C}=\overline{\boldsymbol{c}} \) then \( \overline{\boldsymbol{A} \boldsymbol{B}}+\mathbf{2} \overline{\boldsymbol{B} \boldsymbol{C}}+\boldsymbol{3} \overline{\boldsymbol{C} \boldsymbol{A}}= \)
A . \( 3 \bar{c} \bar{c} \bar{c} \)
B. \( 3 \bar{a} \bar{a} \bar{a} \) a
\( c \cdot 0 \)
\( D .3 \bar{b} \bar{b} \)
Subject: Maths
If \( \int \sqrt{\boldsymbol{x}}\left(1-\boldsymbol{x}^{3}\right)^{-1 / 2} \boldsymbol{d} \boldsymbol{x}=\frac{\boldsymbol{2}}{\boldsymbol{3}} \boldsymbol{g}(\boldsymbol{f}(\boldsymbol{x}))+\boldsymbol{c} \)
then
A \( \cdot f(x)=\sqrt{x}, g(x)=\sin ^{-1} x \)
B . \( f(x)=x^{3 / 2}, g(x)=\sin ^{-1} x \)
C \( \cdot f(x)=x^{2 / 3}, g(x)=\cos ^{-1} x \)
D. \( f(x)=\sqrt{x}, g(x)=\cos ^{-1} x \)