AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Assertion
For stabilization of an emulsion, a third component called emulsifying agent is usually added.
Reason
Emulsions of oil in water are unstable
and sometimes they separate into two layers on standing.
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: Chemistry
Which of the following complex is useful in the dehydrogenation of alkanes?
\( \mathbf{A} \cdot\left[\left(P h_{3} P\right) R h C l\right. \)
B. \( \left[\left(P h_{3} P\right)_{3} R h_{2} C l\right. \)
\( \mathbf{c} \cdot\left[\left(P h_{3} P\right)_{3} R h C l\right] \)
D. \( \left[\left(P h_{3} P\right)_{3} R h C l_{2}\right] \)
Subject: Physics
A parallel plate capacitor with circular plates of radius \( R \) is being charged as shown. At the instant shown, the
displacement current in the region between the plates enclosed between \( \frac{R}{2} \) and \( R \) is given by
A \( \cdot \frac{3}{4} \)
в. \( \frac{1}{4} \)
\( c \cdot 3 i \)
D. \( \frac{4}{3} i \)
Subject: Physics
If a lens of focal length, \( f, \) made of glass of refractive index \( \frac{5}{3} \) is placed in a liquid of refractive index, \( 4 \frac{5}{3}, \) then the focal length of the lens becomes
\( A \cdot f \)
в. \( 2 f \)
c. \( 4 f \)
D. \( -4 f \)
Subject: Maths
Based on equations reducible to linear
equations Solve for \( x \) and \( y: \frac{2}{x-1}+\frac{y-2}{4}= \) \( 2 ; \frac{3}{2(x-1)}+\frac{2(y-2)}{5}=\frac{47}{20} \)
A \( . x=3, y=6 \)
в. \( x=1, y=5 \)
c. \( x=2, y=-7 \)
D. \( x=5, y=-9 \)
Subject: Chemistry
The correct order of equivalent
conductance at infinite dilution of
\( L i C l, N a C l \) and \( K C l \) is :
A. \( L i C l>N a C l>K C l \)
в. \( K C l>N a C l>L i C l \)
c. \( N a C l>K C l>L i C l \)
D. \( L i C l>K C l>N a C l \)
Subject: Maths
The coordinate of any point, which lies
in \( \boldsymbol{x} \boldsymbol{y} \) plane, is
\( \mathbf{A} \cdot(x, 0, y) \)
в. \( (x, x, 0) \)
c. \( (x, 0, x) \)
D. \( (y, 0, x) \)
Subject: Maths
In a infinite G.P., the sum of first three
terms is \( 70 . \) If the extreme terms are multiplied by 4 and the middle term is multiplied by \( 5, \) the resulting terms form an A.p. then the sum to infinite
terms of G.p.
A . 120
B. -40
\( c \cdot 160 \)
D. 80
Subject: Maths
\( \sec h^{-1}\left(\frac{1}{5}\right)= \)
\( \mathbf{A} \cdot \log (\sqrt{24}+5) \)
\( \mathbf{B} \cdot \log 5+\sqrt{27} \)
\( \mathbf{C} \cdot \log 26+\sqrt{5} \)
D. \( \log 27+\sqrt{5} \)
Subject: Physics
Consider two identical charges placed at a distance \( 2 \mathrm{d} \) apart as shown in the
figure. The equilibrium of a positive test
charge placed at point 0 midway
between them may be:

This question has multiple correct options
A. Neutral
B. Stable for displacement along the X-axis
C. Stable for displacement along the \( y \) -axis
D. Unstable for displacement along the x-axis
Subject: Chemistry
Gibbs-Helmholtz equation relates the free energy change to the enthalpy and entropy changes of the process as \( (\Delta G)_{P T}=\Delta H-T \Delta S \)
The magnitude of \( \Delta H \) does not change
much with the change in temperature
but the entropy factor \( \boldsymbol{T} \boldsymbol{\Delta} \boldsymbol{S} \) changes
appreciably.
Thus, spontaneity of a process depends
very much on temperature.
For the reaction at \( 25^{\circ} C, X_{2} O_{4}(l) \longrightarrow \)
\( 2 X O_{2} \)
\( \Delta H=2.0 K c a l \) and \( \Delta S=20 c a l K^{-1} \)
the reaction would be:
A. spontaneous
B. at equilibrium
C. unpredictable
D. non-spontaneous
Subject: Maths
\( \ln \triangle A B C, P, Q \) and \( R \) are the midpoints of the sides \( A B, B C \) and \( C A \)
respectively. If \( D \) is any point
(i) then express \( D A+D B+D C \)
interms of \( D P, D Q \) and \( D R \)
(ii) if \( \boldsymbol{P A}+\boldsymbol{Q B}+\boldsymbol{R C}=\boldsymbol{a}, \) then find \( \boldsymbol{a} \)
Subject: Physics
A thin lens of focal length \( f \) and its aperture has a diameter d. It forms an image of intensity I. Now the central part of the aperture upto diameter (d/2)
is blocked by an opaque paper. The focal length and image intensity would change to
A \( \cdot \) f/2, \( 1 / 2 \)
B. f, \( 1 / 4 \)
c. \( 3 f / 4,1 / 2 \)
D. f, 31/4
Subject: Physics
The velocity of sound in air is \( 330 \mathrm{m} / \mathrm{s} \) The r.m.s velocity of air molecules \( (\gamma= \)
1.4) is approximately equal to
A. \( 400 \mathrm{m} / \mathrm{s} \)
B. 471.4 m/s
c. \( 231 \mathrm{m} / \mathrm{s} \)
D. \( 462 \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
A small amount of solution containing \( ^{24} \mathrm{Na} \) radio nuclide with activity \( \boldsymbol{A}= \) \( 2 \times 10^{3} \) dps was administered into
blood of a patient in hospital. After 5 hour, a sample of the blood drawn out from the patient showed an activity of 16 dpm per cc. \( t_{1 / 2} \) for \( ^{24} \mathrm{Na}=15 \) hr. The
activity of blood sample drawn after a further time of 5 hr is :
A. 0.2118 dpm per \( m L \)
B. 0.4232 dps per \( m L \)
c. 0.4232 dpm per \( m L \)
D. 0.2118 dps per \( m L \)
Subject: Physics
Which of the following is the most
accurate instrument?
A. A scale whose least count is \( 0.1 \mathrm{cm} \)
B. A vernier caliper in which 10 vernier divisions coincide with 9 main scale divisions whose main scale is millimetre scale.
C. A microscope in which 50 vernier divisions coincide with 49 main scale divisions whose main scale is millimetre scale.
D. A microscope in which 50 vernier divisions coincide with 49 main scale divisions and in the main scale
there are 20 divisions in \( 1 \mathrm{cm} \)
Subject: Chemistry
Correct wrong statements if found any from those given below:
(a) When difference in electronegativity increases, the possibility of covalent bonding increases.
(b) Electronegativity increases while moving from left to right along a period.
(c) lonic bond is present in \( \boldsymbol{H} \boldsymbol{C l} \) molecule.
(d) Partial ionic bond is also there in
polar molecule
Subject: Physics
A plane wave \( \boldsymbol{y}=\boldsymbol{a} \sin (\boldsymbol{\omega} \boldsymbol{t}-\boldsymbol{k} \boldsymbol{x}) \)
propagates through a stretched string. The particle velocity versus \( x \) graph at \( \boldsymbol{t}=\mathbf{0} \) is :
\( A \)
\( B \)
\( c \)
\( D \)
Subject: Physics
The magnetic force per unit length on a wire carrying a current of \( 10 \mathrm{A} \) and
making an angle of \( 45^{0} \) with the direction of a uniform magnetic field of \( 0.20 \mathrm{T} \) is
A \( \cdot 2 \sqrt{2} N m^{-1} \)
B. \( \frac{2}{\sqrt{2}} N m^{-1} \)
\( ^{c} \cdot \frac{\sqrt{2}}{2} N m^{-1} \)
D. \( 4 \sqrt{2} N m^{-1} \)
Subject: Physics
If the acceleration due to gravity on the surface of the earth is \( 9.8 ~ m / s^{2}, \) what
will be the acceleration due to gravity
on the surface of a planet whose mass and radius both are two times the
corresponding quantities for the earth
\( ? \)
A. \( 4.9 \mathrm{m} / \mathrm{s}^{2} \)
B. \( 9.8 \mathrm{m} / \mathrm{s}^{2} \)
C \( \cdot 19.8 \mathrm{m} / \mathrm{s}^{2} \)
D. None of the above
Subject: Physics
Assertion
Maximum air flow due to convection
does not occur at the north pole but it
occurs at \( \mathbf{3 0}^{\circ} \) N.
Reason
There is maximum temperature
difference between equator and \( 30^{\circ} \mathrm{N} \)
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: Chemistry
Assertion
\( H_{2} O_{2} \) under goes dispropontionation on heating.
Reason
It gives \( H_{2} O \) and \( O_{2} \) on heating.
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
\( A, B \) and \( C \) are the three forces each of
magnitude \( 4 N \) acting in the plane of
paper as shown in Fig. The point \( O \) lies
in the same plane. Which force has the
greatest moment about \( O \) ?
A . \( A \)
в. \( B \)
\( c . c \)
D. all of the above
Subject: Biology
Match the column:
List I list II \( \quad \) List III A) BOD \( \quad \) i) Supernatant
as effluent \( \begin{array}{ll}\text { B) } & \text { ii) Measure of } \\ \text { FLOCS } & \text { Organic Matter }\end{array} \) All \( \| \textrm{ } \)
\( \mathrm{sol} \) SOlids
\( \mathrm{n} \) te carbon \( \begin{array}{l}\text { C) } \\ \text { Primary } \\ \text { sludge }\end{array} \mid \begin{array}{l}\text { iii) Masses of } \\ \text { bacteria } \\ \text { associated with } \\ \text { fungus }\end{array} \) has more
\( \mathbf{A} \cdot A-i i, I V B-i i i, I C-i,\|D-i v,\| I \)
B. A-ii, I B-i, III C-iv, II D-iii, IV
C \( . A \) -i, IV B-iii, II C-iv, I D-ii, III
D. A-ii, III B-ii, IV C-iii, I D-i, II
Subject: Physics
The freezing point on a thermometer is
marked as \( 20^{\circ} \) and the boiling point as
\( 150^{\circ} . A \) temperature of \( \left(60^{\circ} C\right) \) on this thermometer will be read as:
A \( \cdot 40^{\circ} \)
B . \( 65^{\circ} \)
\( \mathrm{c} \cdot 98^{\circ} \)
D. None of these
Subject: Chemistry
If benzoic acid (mol. mass = 122) is associated into double molecules when
dissolved in benzene and the osmotic
pressure of a solution of 5 g of benzoic acid in \( 100 \mathrm{mL} \) benzene is 5.73 atm at
\( 10^{\circ} \mathrm{C}, \) what is the percentage
association of benzoic acid?
\( \mathbf{A} \cdot 60 \% \)
B. \( 70 \% \)
\( c .80 \% \)
D. \( 85 \% \)
Subject: Maths
\( \operatorname{Let} \int_{0}^{x}\left(\frac{b t \cos 4 t-a \sin 4 t}{t^{2}}\right) d t= \)
\( \frac{a \sin 4 x}{x} \) then \( a \) and \( b \) are given by
A \( \cdot a=\frac{1}{4}, b=1 \)
В. \( a=2, b=2 \)
c. \( a=-1, b=4 \)
D. \( a=2, b=4 \)
Subject: Chemistry
Standard free energies of formation (in kJ/mol) at \( 298 \mathrm{K} \) are -237.2,-394.4 and
-8.2 for \( \boldsymbol{H}_{2} \boldsymbol{O}(l), \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g}) \) and pentane \( (g) \)
respectively The value of \( E_{c e l l}^{0} \) for the pentane-oxygen fuel cell is:
A \( .1 .0968 \mathrm{V} \)
в. \( 0.0968 V \)
c. \( 1.968 V \)
D. \( 2.0968 V \)
Subject: Maths
A \( 13 f t . \) ladder is leaning against a wall when its base starts to slide away At the instant when the base is 12 ft. away from the wall, the base is moving away from the wall at the rate of 5 ft/sec. The
rate at which the angle \( \theta \) between the ladder and the ground is changing is
A \( \cdot-\frac{12}{13} r a d / \sec \)
B. - 1 rad\( / \)sec.
c. \( -\frac{13}{12} r a d / s e c \)
D. \( -\frac{10}{13} \) rad/sec
Subject: Physics
The radius of earth is about \( 6400 \mathrm{km} \)
and that of mars is \( 3200 \mathrm{km} \). Thus
mars of the earth is about 10 times
mass of mars. An object weighs \( 200 \mathrm{N} \) on the surface of earth. Then its weight on the surface of mars will be
A. 80 N
B. 40 N
\( c \cdot 20 N \)
\( D \cdot 8 N \)
Subject: Biology
The condition of erythroblastosis
foetalis occurs only when
A. The husband is \( R h^{+} \) and wife is \( R h^{-} \)
B. The husband is \( R h^{-} \) and wife is \( R h^{+} \)
C. The mother is \( R h^{+} \) and the foetus is \( R h^{-} \)
D. The mother is \( R h^{-} \) and the foetus is \( R h^{+} \)
Subject: Physics
What is the value of \( R_{4}(\text { in ohm }) \) in figure (a) and (b) ?
(a) \( -4 w w-w w w w w w=-w w w \)
\( 20 \Omega+3.5 \Omega+4.92=\quad R_{42} \)
(b)
A. 28.4,0.58
B. 0.58, 28
c. 7.1,1.85
D. 6.15,1.80
Subject: Chemistry
Which of the following examples does not represent disproportionation?
A \( \cdot M n O_{2}+4 H C l \rightarrow M n C l_{2}+C l_{2}+2 H_{2} O \)
в. \( 2 H_{2} O_{2} \rightarrow 2 H_{2} O+O_{2} \)
c. \( 4 K C l O_{3} \rightarrow 3 K C l O_{4}+K C l \)
D. \( 3 C l_{2}+6 N a O H \longrightarrow 5 N a C l+N a C l O_{3}+3 H_{2} O \)
Subject: Maths
The figure obtained by joining the midpoints of the adjacent sides of a rectangle of sides \( 8 \mathrm{cm} \) and \( 6 \mathrm{cm} \) is
A . a rectangle of area \( 24 \mathrm{cm}^{2} \)
B. a square of area \( 25 \mathrm{cm}^{2} \)
c. a rhombus of area \( 24 \mathrm{cm}^{2} \)
D. a trapezium of area \( 12 \mathrm{cm}^{2} \)
Subject: Physics
The displacement of a particle varies
with time according to the relation \( y= \)
asin\omegat \( + \)bcos\omegat.
A. The motion is oscillatory but not SHM.
B. The motion is SHM with amplitude a + b.
c. The motion is SHM with amplitude \( a^{2}+b^{2} \)
D. The motion is SHM with amplitude \( \sqrt{a^{2}+b^{2}} \)
Subject: Physics
The time period of the variation of potential energy of a particle executing \( \boldsymbol{S H} \boldsymbol{M} \) with period \( \boldsymbol{T} \) is
\( \mathbf{A} \cdot T / 4 \)
в. \( T \)
c. \( 2 T \)
D. \( T / 2 \)
E . \( T / 3 \)
Subject: Physics
A laser used to weld detached retinas
emits light with a wavelength of \( 652 n m \) in pulses that are of 20 ms duration. The average power during each pulse is \( 0.6 W . \) Find the energy in each pulse in
\( e V \) and in a single photon
A \( .7 .5 \times 10^{15} e V, 1.9 e V \)
В. \( 7.5 \times 10^{15} e V, 1.19 e V \)
c. \( 7.5 \times 10^{16} e V, 0.19 e V \)
D. \( 7.5 \times 10^{16} e V, 1.9 e V \)
Subject: Maths
A new flag is to be designed with six vertical strips using some or all of the colour yellow, green, blue and red. Then,
the number of ways this can be done such that no two adjacent strips have
the same colour is?
A. \( 12 \times 81 \)
B . \( 16 \times 192 \)
c. \( 20 \times 125 \)
D. \( 24 \times 216 \)
Subject: Maths
If \( \pi<\alpha<2 \pi \) then
\( \frac{1}{\sin \alpha-\sqrt{\cot ^{2} \alpha-\cos ^{2} \alpha}}= \)
\( A \cdot \sin \alpha \)
B. - \( \sin \alpha \)
c. \( \frac{1}{\sin \alpha} \)
\( D \)
Subject: Chemistry
Which of the following compounds are
involved in the formation of sulfur
trioxide?

This question has multiple correct options
A \( \cdot H_{2} S_{2} O_{5} \)
в. \( N a H S O_{4} \)
c. \( N a_{2} S_{2} O_{7} \)
D. \( H_{2} S_{2} O_{7} \)
Subject: Physics
A body is projected horizontally from a certain height, (h) then time of descent
is
\( ^{\mathrm{A}} t_{d}=\sqrt{\frac{2 h}{g}} \)
в. \( _{t_{d}}=\sqrt{\frac{h}{g}} \)
\( \mathbf{c} \cdot t_{d}=\sqrt{h g} \)
D. \( t_{d}=\sqrt{h+g} \)
Subject: Maths
In fig two circular flower bds have been
shown on two sides of a lawn \( A B C D \) of
side \( 56 \mathrm{m} \). If the centre of each circular
flower bed is the point of intersection \( \boldsymbol{O} \)
of the diagonals of the square lawn, find
the sum of the areas of the lawn and
flower beds
\( \mathbf{A} \cdot 4032 m^{2} \)
B . \( 4428 \mathrm{m}^{2} \)
\( \mathbf{c} \cdot 4628 m^{2} \)
D. None of these
Subject: Maths
In throwing of a die, let \( A \) be the event
'an odd humber turns up', \( B \) be the
event 'a number divisible by 3 turns up' and \( C \) be the event 'a number \( \leq 4 \) turns
up', Then find the probability that exactly two of \( A, B \) and \( C \) occur.
A \( \cdot \frac{2}{3} \)
B. \( \frac{1}{6} \)
\( c \cdot \frac{1}{3} \)
D.
Subject: Maths
Three positive real numbers \( l, \boldsymbol{m}, \boldsymbol{n} \) are in A.P. with product taken all at a time
is \( 4, \) then the minimum value of \( m \) is
\( \mathbf{A} \cdot 4^{1 / 3} \)
B. 3
\( c \cdot 2 \)
D. \( 1 / 2 \)
Subject: Chemistry
The hybridization of atomic orbitals
of nitrogen in \( N O_{2}^{+}, N O_{2}^{-} \) and \( N H_{4}^{+} \) is:
A \( \cdot s p^{2}, s p^{3} \) and \( s p^{2} \) respectively
B. \( s p, s p^{2} \) and \( s p^{3} \) respectively
C. \( s p^{2}, s p \) and \( s p^{3} \) respectively
D. \( s p^{2}, s p^{3} \) and \( s p \) respectively
Subject: Chemistry
Let \( x \) be the energy needed to raise the
temperature of 5 moles of \( N_{2} \) held at
constant pressure by one degree. Let \( y \) be the energy needed to raise temperature of 5 moles of \( C 0 \) by one degree with constant pressure. Then ratio \( x: y \) is -
A . 5: 7
B. 1:
\( c \cdot 7: 5 \)
D. 7: 9
E. 7: 2
Subject: Physics
Take, bulk modulus of water \( \boldsymbol{B}= \)
\( \mathbf{2 1 0 0} \boldsymbol{M P a} \)
What increase in pressure is required to decrease the volume of 200 litres of
water by 0.004 percent?
A \( .210 k P a \)
в. \( 840 \mathrm{kPa} \)
c. \( 8400 k P a \)
D. \( 84 k P a \)
Subject: Maths
AB is a line segment \( C \) and \( D \) are points on opposite sides of \( A B \) such that each
of them is equidistant from the point \( \mathbf{A} \)
and \( \mathrm{B} \) as in the figure. The line \( \mathrm{CD} \) is
perpendicular bisector of \( \mathrm{AB} \)
A. True
B. False
Subject: Maths
\( \frac{7}{8} \times\left(\frac{17}{13}+\frac{14}{13}\right)=\left(\frac{7}{8} \times \frac{14}{13}\right)+ \)
\( \left(\frac{7}{8} \times \frac{17}{13}\right) \)
If true then enter 1 and if false then
enter 0
Subject: Maths
Find the mass of 200 steel spherical ball bearings, each of which has radius \( 0.7 \mathrm{cm}, \) given that the density of steel is \( 7.95 g / c m^{3} .(\text { Mass }=\text { Volume } \times \text { Density }) \)
A . \( 2.29 \mathrm{Kg} \)
в. \( 2.9 \mathrm{Kg} \)
\( \mathrm{c} .3 .29 \mathrm{Kg} \)
D. None of these
Subject: Chemistry
The reaction, \( \boldsymbol{A}(\boldsymbol{g})+\mathbf{2} \boldsymbol{B}(\boldsymbol{g}) \rightarrow \boldsymbol{C}(\boldsymbol{g})+ \)
\( D(g), \) is an elementary process. In an
experiment involving this reaction, the initial partial pressures of \( A \) and \( B \) are
\( \boldsymbol{P}_{\boldsymbol{A}}=\mathbf{0 . 6 0} \) atm and \( \boldsymbol{P}_{\boldsymbol{B}}=\mathbf{0 . 8 0} \) atm
respectively. When \( P_{C}=0.20 \) atm, the rate of the reaction relative to the initial
rate is:
A \( \cdot 1 / 6 \)
B. 1/12
\( c \cdot 1 / 36 \)
D. 1/18
Subject: Physics
Assertion: Diamagnetism is universal, it is present in all materials.

Reason: Field due to induced magnetic
moment is opposite to the magnetising
field
A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true and reason is not the correct explanation of assertion
c. If assertion is true but reason is false.
D. If both assertion and reason are false
Subject: Chemistry
Consider following reaction in equilibrium with equilibrium concentration \( 0.01 \mathrm{M} \) of every species
(।) \( \boldsymbol{P} \boldsymbol{C l}_{5}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{P} \boldsymbol{C l}_{3}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \)
(II) \( 2 H I(g) \rightleftharpoons H_{2}(g)+I_{2}(g) \)
(III) \( N_{2}(g)+3 H_{2}(g) \rightleftharpoons 2 N H_{3}(g) \)
Extend of the reaction taking place is:
A. \( I>I I>I I I \)
в. \( I<I I<I I I \)
c. \( I I<I I I<I \)
D. III \( <I<I I \)
Subject: Physics
Mark out the correct statement(s)
This question has multiple correct options
A. in alpha decay, the energy released is shared between alpha particle and daughter nucleus in the form of kinetic energy and share of alpha particle is more than that of the daughter nucleus
B. in beta decay, the energy released is in the form of kinetic energy of beta particles
C. in beta minus decay, the energy released is shared between electron and antineutrino
D. in gamma decay, the energy released is in the form of energy carried by photons termed as gamma rays
Subject: Maths
Arrangement of the following areas between the curves is descending order:
\( \mathbf{A}: \boldsymbol{y}^{2}=\mathbf{4} \boldsymbol{x}, \boldsymbol{x}^{2}=\mathbf{4} \boldsymbol{y} \)
\( \mathbf{B} \cdot \boldsymbol{y}=\boldsymbol{x}, \boldsymbol{y}=\boldsymbol{x}^{3} \)
\( \mathbf{C} \cdot \boldsymbol{y}^{2}=\mathbf{8} \boldsymbol{x}, \boldsymbol{y}=\mathbf{2} \boldsymbol{x} \)
\( \mathbf{D} \cdot \boldsymbol{y}=\sqrt{\boldsymbol{x}}, \boldsymbol{y}=\boldsymbol{x}^{2} \)
\( A \cdot A, B, C, D \)
B. A,C,B,D
c. \( \mathrm{D}, \mathrm{B}, \mathrm{C}, \mathrm{A} \)
D. D,C,B,A
Subject: Maths
Let \( \boldsymbol{x} \in \boldsymbol{R} \) and let
\( \boldsymbol{P}=\left[\begin{array}{lll}1 & 1 & 1 \\ 0 & 2 & 2 \\ 0 & 0 & 3\end{array}\right], Q=\left[\begin{array}{lll}2 & x & x \\ 0 & 4 & 0 \\ x & x & 6\end{array}\right] \) and
\( \boldsymbol{R}=\boldsymbol{P Q P}^{-1} \)
Then which of the following is are
correct

This question has multiple correct options
A. there exists a real number x such that \( P Q=Q P \)
B.
det \( R=\operatorname{det}\left[\begin{array}{lll}2 & x & x \\ 0 & 4 & 0 \\ x & x & 5\end{array}\right]+8 \) for all \( x \in R \)
C. For \( x=1 \) there exists a unit vector \( \alpha \hat{i}+\beta \hat{j}+\gamma \hat{k} \) for
which are \( R\left[\begin{array}{l}\alpha \\ \beta \\ \gamma\end{array}\right]=\left[\begin{array}{l}0 \\ 0 \\ 0\end{array}\right] \)
D. \( \quad \) For \( x=0 \) if \( R\left[\begin{array}{l}1 \\ a \\ b\end{array}\right]=6\left[\begin{array}{l}1 \\ a \\ b\end{array}\right] \) then \( a+b= \)
Subject: Physics
A ray of light incident on a \( 60^{\circ} \) angled prism of refractive index \( \sqrt{2} \) suffers
minimum deviation. The angle of incidence is :
A \( \cdot 70^{\circ} \)
B . \( 0^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 60^{\circ} \)
Subject: Chemistry
The density of water is maximum at:
A \( \cdot 40^{\circ} \mathrm{C} \)
B . \( 4^{\circ} \mathrm{C} \)
\( \mathrm{c} \cdot 14^{\circ} \mathrm{C} \)
D \( \cdot 24^{\circ} C \)
Subject: Biology
Select in incorrect statement:
a) alimentary canal begins with an anterior cavity called buccal cavity.
b) tooth is embedded in a socket of
mandible bone only
c) human shows strict diphyodont type of dentition.
d) oesophagus and the trachea open into the phatynx
\( A \cdot a, b, c \& d \)
B. a, b \&
\( c \cdot a, c \& d \)
D. \( a, b \& d \)
Subject: Maths
Show that \( \triangle A B C, \) where
\( \boldsymbol{A}(-\mathbf{2}, \mathbf{0}), \boldsymbol{B}(\mathbf{2}, \mathbf{0}), \boldsymbol{C}(\mathbf{0}, \mathbf{2}) \) and \( \triangle \boldsymbol{P} \boldsymbol{Q} \boldsymbol{R} \)
where \( \boldsymbol{P}(-\mathbf{4}, \mathbf{0}), \boldsymbol{Q}(\mathbf{4}, \mathbf{0}), \boldsymbol{R}(\mathbf{0}, \mathbf{4}) \) are
similar.
Subject: Maths
A tank initially holds 10 lit. of fresh
water. \( A t t=0, \) a brine solution containing \( \frac{1}{2} \) kg of salt per lit. is poured into tank at a rate 1 lit/min while the
well-stirred mixture leaves the tank at
the same rate. Find the amount of salt
in a tank at a particular time
A \( \cdot-5 e^{-t}+5 \)
B. \( 5 e^{-t}+5 \)
\( \mathbf{c} \cdot 5 e^{-t}-5 \)
D. \( -5 e-5 \)
Subject: Maths
If the number of terms in the expansion
\( (2 x+y)^{n}-(2 x-y)^{n} \) is \( 8, \) then the
value of \( n \text { is } \ldots \ldots . . . . \text { (where } n \text { is odd }) \)
A . 17
B. 19
c. 15
D. 13
Subject: Chemistry
The magnetic moment order is correctly
given in:
\( \mathbf{A} \cdot F e^{2+}<F e^{3+}<M n^{4+}<C r^{3+} \)
B \( \cdot C r^{3+}=M n^{4+}<F e^{2+}<F e^{3+} \)
\( \mathbf{c} \cdot C r^{3+}=M n^{4+}<F e^{3+}<F e^{2+} \)
D \( \cdot F e^{2+}<C r^{3+}<F e^{3+}<M n^{4+} \)
Subject: Maths
Let y be an implicit function of \( \mathbf{x} \) defined by \( \mathbf{x}^{2 \mathbf{x}}-\mathbf{2} \mathbf{x}^{\mathbf{x}} \cot \boldsymbol{y}-\mathbf{1}=\mathbf{0} \)
Then \( y^{\prime}(1) \) equals
A . -1
B.
\( c \cdot \log 2 \)
D. \( -\log 2 \)
Subject: Physics
Find the initial velocity of projection of a ball thrown vertically up if the distance moved by it in \( 3^{r d} \) second is twice the
distance covered by it in 5th second. (Take \( \left.g=10 \mathrm{m} s^{-2}\right) \)
A. \( 85 \mathrm{m} s^{-1} \)
B. 75 \( \mathrm{m} s^{-1} \)
c. \( 65 \mathrm{m} s^{-1} \)
D. \( 95 \mathrm{m} s^{-1} \)