AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Biology
Assertion
Vertebrate blood can carry larger
volumes of \( \boldsymbol{O}_{2} \% \)
Reason
The presence of respiratory pigment in
blood enables it to carry more \( O_{2} \) than
the same blood could carry without it.
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 200 turn closely wound circular coil of
radius \( 15 \mathrm{cm} \) carries a current of \( 4 \mathrm{A} \)
The magnetic moment of this coil is:
\( \mathbf{A} \cdot 36.5 A m^{2} \)
B . \( 56.5 A m^{2} \)
\( \mathbf{c} \cdot 66.5 A m^{2} \)
D. \( 108 A m^{2} \)
Subject: Chemistry
For the reaction
\( \mathbf{2} \boldsymbol{N} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{N} \boldsymbol{O}(\boldsymbol{g})+\boldsymbol{O}_{2}(\boldsymbol{g}) \)
\( \boldsymbol{K}_{c}=\mathbf{1 . 8} \times \mathbf{1 0}^{-\mathbf{6}} \mathbf{a t} \mathbf{1 8 4}^{\boldsymbol{o}} \boldsymbol{C} \)
\( \boldsymbol{R}=\mathbf{0 . 0 8 3 1 k J} \quad \boldsymbol{K}^{-1} \boldsymbol{m o l}^{-1} \)
when \( K_{p} \) and \( K_{c} \) are compared at
\( 184^{\circ} \mathrm{C} \) it is found that:
\( \mathbf{A} \cdot K_{p} \) is greater than \( K_{c} \)
B. \( K_{p} \) is less than \( K_{c} \)
\( \mathbf{c} \cdot K_{p}=K_{c} \)
D. Whether \( K_{p} \) is greater than, less than or equal to \( K_{c} \) depends upon the total gas pressure
Subject: Chemistry
Which one of the following reactions is
not correct?
\( \mathbf{A} \cdot C H_{3} C H O+\frac{1}{2} O_{2} \stackrel{M n(O A c) 2 / a i r}{\rightarrow} C H_{3} C O O H \)
B. \( C H_{3} C H_{2} O H+O_{2}^{\text {Micodermaceti}} C H_{3} C O O H+H_{2} O \)
c. \( C H_{3} M g B r \underbrace{(1) C O_{2}}_{(2) H_{2} O \oplus} C H_{3} C O O H+M g(O H) B r \)
\( \mathrm{D} \cdot \mathrm{CH}_{3} \mathrm{O} \mathrm{H}+\mathrm{CO}^{\mathrm{Ca} / \Delta_{\rightarrow, \text {prssure}}} \mathrm{CH}_{3} \mathrm{COOH} \)
Subject: Maths
If \( A(x) \) and \( B(x) \) be two polynomials
and \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{A}\left(\boldsymbol{x}^{3}\right)+\boldsymbol{x} \boldsymbol{B}\left(\boldsymbol{x}^{3}\right) . \) If \( \boldsymbol{f}(\boldsymbol{x}) \) is
divisible by \( x^{2}+x+1 \) then show that it
is divisible by \( x-1 \) also.
Subject: Physics
A force \( (2 \hat{i}+\hat{j}-\hat{k}) N \) acts on a body
which is initially at rest. At the end of \( 20 s \) the velocity of the body is \( (4 \hat{i}+ \) \( \mathbf{2} \hat{\boldsymbol{j}}-\mathbf{2} \hat{\boldsymbol{k}}) \boldsymbol{m} \boldsymbol{s}^{-1}, \) then the mass of the
body is:
A. \( 8 \mathrm{kg} \)
B. \( 10 \mathrm{kg} \)
c. \( 5 k g \)
D. \( 4.5 \mathrm{kg} \)
Subject: Chemistry
Atoms of two elements \( P \) and \( Q \) have 5
electrons in \( 2^{n d} \) shell and \( 3^{r d} \) shell
respectively. What will be the atomic
numbers of these elements?
A . 4: 15
B. 5: 15
\( c \cdot 7: 13 \)
D. 7: 15
Subject: Chemistry
When a mixture of conc. \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) and
\( H C l \) is warmed, we get?
A \( \cdot C l_{2}, N O_{2} \) and \( H_{2} O \)
B. \( N O, C l_{2} \) and \( H_{2} O \)
c. \( N O C l, C l_{2} \) and \( N O_{2} \)
D. \( N O C l, C l_{2} \) and \( H_{2} O \)
Subject: Chemistry
For the reaction taking place at certain
temperature \( N H_{2} C O O N H_{4}(s) \rightleftharpoons \)
\( \mathbf{2} N \boldsymbol{H}_{3}(\boldsymbol{g}) \) if equilibrium pressure is \( \mathbf{3} \boldsymbol{X} \)
bar then \( \Delta G^{\circ} \) would be:
A. \( -R T \ln 9-3 R T \ln X \)
B. \( R T \ln 4-3 R T \ln X \)
c. \( -3 R T \ln 4 X \)
D. none of these
Subject: Physics
The period of oscillation of a simple pendulum of length lis given by \( \boldsymbol{T}= \) \( 2 \pi \sqrt{l / g} . \) The length lis about \( 10 \mathrm{cm} \) and
is known to \( 1 \mathrm{mm} \) accuracy. The period of oscillation is about 0.5 s. The time of 100 oscillations has been measured
with a stop watch of 1 s resolution. Find
the percentage error in the determination of \( \mathfrak{g} \)
Subject: Physics
Electric charge is uniformly distributed along a long straight wire of a radius of 1 mm. The Charge per cm length of the wire is Q coulomb. Another cylindrical surface
of radius \( 50 \mathrm{cm} \) and length \( 1 \mathrm{m} \) symmetrically encloses the wire as shown in fig. The total flux passing through the cylindrical surface
is
A \( \cdot \frac{Q}{\epsilon_{0}} \)
в. \( \frac{100 Q}{\epsilon_{0}} \)
c. \( \frac{10 Q}{\pi \epsilon_{0}} \)
D. \( \frac{100 Q}{\pi \epsilon_{0}} \)
Subject: Chemistry
The product formed at anode and
cathode, when dilute \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) is electrolyzed are
A \( . S O_{2}, H \)
в. \( S O_{3}, H_{2} \)
c. \( H_{2} S_{2} O_{8}, H_{2} \)
D. \( O_{2}, H_{2} \)
Subject: Maths
The value of
\( \tan \left(\sin ^{-1}\left(\cos \left(\sin ^{-1} x\right)\right)\right) \tan \left(\cos ^{-1}(\sin \right. \)
where \( \boldsymbol{x} \boldsymbol{\epsilon}(\boldsymbol{0}, \boldsymbol{1}), \) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot-1 \)
D. none of these
Subject: Maths
Identify the cubic polynomial.
A \( \cdot x^{5}+y^{3}-x^{3}+x^{4} \)
В. \( x^{3}+y^{3}-x^{2} \)
c. \( 2 x^{3}+8 y^{3}-9 x^{5} \)
D. \( -7 x^{7}+x^{3} \)
Subject: Chemistry
The EMFs of the following cells are
\( \boldsymbol{C u}\left|\boldsymbol{C u}^{2+}(\mathbf{1} \boldsymbol{M}) \| \boldsymbol{A} \boldsymbol{g}^{+}(\mathbf{1} \boldsymbol{M})\right| \boldsymbol{A} \boldsymbol{g}, \boldsymbol{E}^{o}= \)
\( 0.46 V \)
\( Z n\left|Z n^{2+}(1 M) \| C u^{2+}(1 M)\right| C u, E^{o}= \)
\( 1.10 V \)
The EMF of the cell
\( Z n\left|Z n^{2+}\right|\left|A g^{+}(1 M)\right| A g \) will be:
A . \( 1.56 V \)
B . \( -1.56 V \)
c. \( 0.64 V \)
D. \( 2.02 V \)
Subject: Biology
In pteridophytes, main plant body is a
(i) which is
(ii)
into true roots, stem and leaves.
Fill the blanks in above statement and
select the correct option.
A. (i) - sporophyte, (ii) - differentiated
B. (i) - sporophyte, (ii) - not differentiated
c. (i) - gametophyte,
(ii) - differentiated
D. (i) - gametophyte, (ii) - not differentiated
Subject: Maths
Factorise:
\( 27 a^{2}-75 b^{2} \)
\( \mathbf{A} \cdot(3 a+5 b)(3 a-5 b) \)
B. \( 3(3 a+5 b)(3 a+5 b) \)
\( \mathbf{c} \cdot(3 a+5 b)(a-b) \)
D. \( 3(3 a+5 b)(3 a-5 b) \)
Subject: Physics
A radiation is incident on a metal of
work function \( 2.3 e V . \) The incident
radiation is \( 600 n \) m.lf the total energy of
incident radiation is \( 23 J \), then the
number of photoelectrons is
A. zero
B \( .<10^{4} \)
\( \mathbf{c} .=10^{4} \)
D. \( \infty \)
Subject: Chemistry
Q Type your question
following apparatus was set up. Which
among the following statement(s)
is(are) correct?
(i) Bulb will not glow because electrolyte is not acidic.
(ii) Bulb will glow because NaOH is a strong base and furnishes ions for
conduction.
(iii) Bulb will not glow because circuit
is incomplete.
(iv) Bulb will not glow because it
depends upon the type of electrolytic
solution.
\( A \cdot \) (i) and (iii)
B. (ii) and (iv)
c. (ii) only
D. (iv) only
Subject: Physics
Resistor is coloured as green - orange -
yellow - gold,its resistance will be:
A. \( 53 \times 10^{4} \pm 10 \% \)
В. \( 54 \times 10^{4} \pm 10 \% \)
c. \( 42 \times 10^{4} \pm 10 \% \)
D. \( 53 \times 10^{4} \pm 5 \% \)
Subject: Chemistry
\( \mathbf{5 0} \) mL of \( \mathbf{0 . 1} \boldsymbol{M} \) solution of a salt
reacted with 25 mL of \( 0.1 ~ M \) solution of
sodium sulphite. The half reaction for the oxidation of sulphite ion is,
\( \boldsymbol{S O}_{3}^{2-}(\boldsymbol{a q})+\boldsymbol{H}_{2} \boldsymbol{O}(\ell) \longrightarrow \boldsymbol{S O}_{4}^{2-}(\boldsymbol{a q})+ \)
\( \mathbf{2} \boldsymbol{H}^{+}(\boldsymbol{a} \boldsymbol{q})+\mathbf{2} \boldsymbol{e}^{-} \)
If the oxidation number of metal in the
salt was \( 3, \) what would be the new
oxidation number of metal?
A. 0
B. 1
c. 2
D. 4
Subject: Maths
If the ratio of the areas of the two circles
is \( 25: 16, \) then the ratio of their
circumferences is

This question has multiple correct options
A \( \cdot \frac{625}{500} \)
B. \( \frac{4}{5} \)
\( c \cdot \frac{5}{4} \)
D. \( \frac{500}{625} \)
Subject: Physics
Six equal capacitors each of
capacitance \( C \) are connected as shown
in the figure. The equivalent
capacitance between points \( A \) and \( B \) is :
A \( .1 .5 \mathrm{c} \)
\( B \)
\( c \cdot 2 c \)
D. \( 0.5 \mathrm{c} \)
Subject: Physics
Á is equal to:
\( \mathbf{A} \cdot 0.1 \mathrm{nm} \)
B . \( 10^{-10} \mathrm{cm} \)
\( \mathbf{C} \cdot 10^{-8} m \)
\( \mathbf{D} \cdot 10^{-4} \mu \)
Subject: Physics
An object is placed at a distance of 15 \( \mathrm{cm} \) from a convex lens of focal length 10 \( \mathrm{cm} . \) On the other side of the lens, a convex mirror is placed such that its distance from the lens equals focal length of the lens. The focal length of the convex mirror is
A. 20 cm
B. \( 10 \mathrm{cm} \)
c. \( 15 \mathrm{cm} \)
D. 30 cm
Subject: Maths
Solve: \( \int \frac{1}{1+x^{4}} d x \)
A \( \cdot \frac{1}{4 \sqrt{2}} \log \left(\frac{x^{2}+\sqrt{2} x-1}{x^{2}-\sqrt{2} x+1}\right)+\frac{1}{4 \sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2} x}{1-x^{2}}\right)+C \)
B \( \cdot \frac{1}{\sqrt{2}} \log \left(\frac{x^{2}+\sqrt{2} x+1}{x^{2}-\sqrt{2} x+1}\right)-\frac{1}{2 \sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2} x}{1-x^{2}}\right)+C \)
C \( \frac{1}{2 \sqrt{2}} \tan ^{1} \frac{x^{2}-1}{\sqrt{2} x}+\frac{1}{4 \sqrt{2}} \log \left|\frac{x^{2}+1+\sqrt{2} x}{x^{2}+1-\sqrt{2} x}\right|+c \)
D. \( \frac{1}{2 \sqrt{2}} \log \left(\frac{x^{2}+\sqrt{2} x-1}{x^{2}-\sqrt{2} x+1}\right)-\frac{1}{\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2} x}{1-x^{2}}\right)+C \)
Subject: Physics
Neutron decay in the free space is given
as follows:
\( \mathbf{o} \boldsymbol{n}^{\mathbf{1}} \rightarrow_{\mathbf{1}} \boldsymbol{H}^{\mathbf{1}}+_{-\mathbf{1}} \boldsymbol{e}^{\mathbf{0}}+[\mathbf{j}] \)
Then, the parenthesis represents
A. photon
B. graviton
c. neutrino
D. antineutrino
Subject: Chemistry
Oxidation of which of the following
reagent with manganese dioxide
\( \left(M n O_{2}\right) \) gives chlorine?
A. conc. \( H C l \)
B . Dil. \( H C l \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{SO}_{4} \)
D. \( H N O_{3} \)
Subject: Biology
Read the following features and choose the correct option about anatomy of dicot and monocot stem
(i) Collenchymatous hypodermis.
(ii) Vascular bundles are scattered.
(iii) Eustele.
(iv) Ground tissue is not differentiated.
(v) Pericycle absent
A. Dicot stem i, ii, iii ; Monocot stem iv,
B. Dicot stem i, ii, v; Monocot stem iii, iv
c. Dicot stem iii, v; Monocot stem i, ii, iv
D. Dicot stem i, iii ; Monocot stem ii, iv, \( v \)
Subject: Chemistry
Match the geometry (given in column A) with the complexes (given in column B)
Geometry : A Complex : B
I: Octahedral
\[
\mathrm{P}:\left[N i(C N)_{4}\right]^{2}
\]
\( \| \)
Square planar
\[
\mathrm{Q}: N i(C O)_{4}
\]
III. Tetrahedral \( \mathrm{R}:\left[F e(C N)_{6}\right]^{4-} \)
A. I-P, II-Q, III-R
B. I-R, II-P, III-Q
c. ।-R, ॥-Q, ॥|-P
D. I-Q, II-P, III-R
Subject: Maths
In which of the following situations, the sequence formed will form an A.P?
1) Number of students left in the school
auditorium from the total strength of
1000 students when they leave the
auditorium in batches of 25
2) The amount of money in the account every year when Rs 100 are deposited annually to accumulate at compound
interest at \( 4 \% \) per annum.
Subject: Maths
The number of real solutions of the
equation
\[
\begin{array}{l}
\sin ^{-1}\left(\sum_{i=1}^{\infty} x^{i+1}-x \sum_{i=1}^{\infty}\left(\frac{x}{2}\right)^{i}\right)=\frac{\pi}{2}- \\
\cos ^{-1}\left(\sum_{i=1}^{\infty}\left(-\frac{x}{2}\right)^{i}-\sum_{i=1}^{\infty}(-x)^{i}\right) \text { lying in }
\end{array}
\]
the interval \( \left(-\frac{1}{2}, \frac{1}{2}\right) \) is
Subject: Physics
A copper rod \( 10 \mathrm{cm} \) long rotates 1800
times per minute about an axis passing through one end at a right angle to the rod. A uniform magnetic field of 1 tesla is applied perpendicular to the plane of rotation. The voltage induced between the ends of the rod is
A . \( 0.235 \mathrm{v} \)
B. \( 0.942 \mathrm{V} \)
c. \( 2.35 v \)
D. zero
Subject: Physics
A parallel beam of light is incident on
the system of two convex lenses of focal
lengths \( f_{1}=20 c m \) and \( f_{2}=10 c m \)
What should be the distance between
the two lenses so that rays after
refraction from both the lenses pass
undeviated?
\( \mathbf{A} \cdot 60 \mathrm{cm} \)
B. \( 30 \mathrm{cm} \)
\( \mathrm{c} \cdot 90 \mathrm{cm} \)
D. \( 40 \mathrm{cm} \)
Subject: Chemistry
\( 4 g \) of \( C O_{2} \) and 2.27 litre of \( H_{2} \) at \( S T P \)
(273.15 K and 1 atm pressure) are mixed
in a container. The total number of
molecules present in the container will be:
В. \( 6.022 \times 10^{23} \)
D. \( 12.044 \times 10^{2} \)
Subject: Chemistry
The total pressure or a mixture of
oxygen and hydrogen is 1.0 atm. The mixture is ignited and the water is removed. The remaining gas is pure hydrogen and exerts a pressure of 0.40 when measured at the same values of \( T \)
and \( \mathrm{V} \) as the original mixture. What was
the composition of the original mixture in mole per cent?
A \( \cdot x_{O_{2}}=0.2 ; x_{H_{2}}=0.8 \)
в. \( x_{0}_{0}=0.4 ; x_{H_{2}}=0.6 \)
c. \( x_{o_{2}}=0.6 ; x_{H_{2}}=0.4 \)
D. \( x_{O_{2}}=0.8 ; x_{H_{2}}=0.2 \)
Subject: Maths
The rate at which the population of a city increases at any time is proportional to the population at that time. If there are 1,30,000 people in the city in 1960 and 1,60,000 in \( 1990, \) what approximate population may be anticipated in \( 2020 ? \) \( \left[\log _{e} \frac{16}{13}=0.2070, e^{0.42}=1.52\right] \)
Subject: Maths
If \( A \) is a square matrix of order 5 and
\( \left.9 A^{-1}=4 A^{T} \text { then ladj (adj }(\operatorname{adj} A)\right) \)
(where \( A^{-T} \) and adj \( (A) \) denotes the inverse, transpose and adjoint of matrix A respectively) contains: \( (\log 3= \)
\( \mathbf{0 . 4 7 7}, \log \mathbf{2}=\mathbf{0 . 3 0 3}) \)
A. 56 digits
B. 60 digits
c. 58 digits
D. 53 digits
Subject: Physics
The current drawn by a \( 220 V \) DC series
motor of armature resistance 0.50 and
back emf \( 200 \mathrm{V} \) is
A \( .40 A \)
в. \( 400 A \)
\( \mathbf{c} \cdot 450 A \)
D. \( 500 A \)
Subject: Chemistry
Assertion
lonic compounds are generally hard
solids but brittle in nature.
Reason
Brittleness is because to shift in
alignment of its ions.
Hardness is due to the strong forces of
attraction.
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: Chemistry
Assertion
Iron is found in the free state in nature.
Reason
Iron is highly reactive element.
A. If both Assertion and Reason are correct and Reason is
the correct explanation of Assertion.
B. If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
C. If Assertion is correct but Reason is incorrect.
D. If Assertion is incorrect but Reason is correct.
Subject: Chemistry
(A) Energy emitted in the transition
\( (5 \rightarrow 2) \) is less than that of \( . \) the
transition \( (2 \rightarrow 1) \) in all hydrogen like
atoms.
(R) The energy difference between 1st
and 2 nd shell is greater than that of any two energy levels provided level (1) is not part of those two energy levels.
A. Both (R) and (A) are true and reason is the. correct explanation of assertion
B. Both (R) and (A) are true but reason is not correct explanation of assertion
c. Assertion (A) is true but reason (R) is false
D. Assertion
(A) and reason
(R) both are false
E. Assertion
(A) is false but reason
(R) is true
Subject: Physics
A point object is placed on the principle axis of a convex lens of focal length f at
a distance of \( 2 f \) to the left of it. The
diameter of the lens is d. An eye is placed at a distance of \( 3 f \) to the right of the lens and a distance h below the
optic axis. The maximum value of \( h \) to see the image is?
A. \( d \)
в. \( d / 2 \)
c. \( d / 3 \)
D. \( d / 4 \)
Subject: Chemistry
An inorganic substance liberates oxygen on heating and turns an acidic solution of
\( K I \) brown and reduces acidified \( K M n O_{4} \)
solution. The substance is:
A. \( H g O \)
в. \( H_{2} O_{2} \)
c. \( K n O_{3} \)
D \( \cdot \operatorname{Pb}\left(N O_{3}\right)_{2} \)
Subject: Maths
Find the length of edge of a cube with following surface area
\( 1944 \mathrm{cm}^{2} \)
\( 2646 \mathrm{cm}^{2} \)
A. \( 28 \mathrm{cm} ; 21 \mathrm{cm} \)
в. \( 17 \mathrm{cm} ; 21 \mathrm{cm} \)
\( \mathrm{c} .18 \mathrm{cm} ; 21 \mathrm{cm} \)
D. \( 18 \mathrm{cm} ; 20 \mathrm{cm} \)
Subject: Chemistry
Assertion
The burning of a candle is both a
physical and a chemical change.
Reason
Burning of candle melts the wax and hence physical state of wax has changed from solid to liquid. Again the wax combines with the atmosphere oxygen and changes to carbon dioxide, heat and light.
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: Maths
The vectors \( \overrightarrow{A B}=3 \hat{i}+5 \widehat{j}+4 \widehat{k} \) and
\( A C=5 \hat{i}-5 \hat{j}+2 \widehat{k} \) are the sides of \( a \)
triangle ABC. The length of the median through \( A \) is
Subject: Physics
The sensitivity of a potentiometer can be increased by
a) increasing the series resistance in the primary circuit
b) decreasing the length of the potentiometer wire
c) using a thin and high resistivity wire as a potentiometer wire
d) increasing the length of the wire
A. a and c are correct
B. b and d are correct
\( c . \) b and c are correct
D. a and d are correct
Subject: Chemistry
Choose correct squence for the
following species.
\( \mathbf{A} \cdot F_{2}>C l_{2}>B r_{2}>I_{2}(\text { Reducing power }) \)
B. \( C l_{2}<F_{2}<B r_{2}<I_{2} \) (Reactivity)
\( \mathbf{C} \cdot I_{2}>B r_{2}>F_{2}>C l_{2}(\text { Bond length }) \)
D. \( C l_{2}>B r_{2}>F_{2}>I_{2} \) (Bond dissociation enthalpy)
Subject: Maths
If \( \triangle A B C \sim \triangle D E F B C=4 \mathrm{cm}, \mathrm{EF}=5 \mathrm{cm} \)
and ar \( (\triangle A B C)=80 c m 2 \),the ar
\( (\triangle D E F) \) is
A \( \cdot 120 \mathrm{cm}^{2} \)
B. \( 125 \mathrm{cm}^{2} \)
\( \mathrm{c} \cdot 150 \mathrm{cm}^{2} \)
D. \( 200 \mathrm{cm}^{2} \)
Subject: Physics
Within a spherical charge distribution of charge density \( \rho(r), \) N equipotential
surfaces of potential \( V_{0}, V_{0}+ \)
\( \boldsymbol{\Delta} \boldsymbol{V}, \boldsymbol{V}_{0}+\boldsymbol{2} \boldsymbol{\Delta} \boldsymbol{V}, \ldots . ., \boldsymbol{V}_{0}+ \)
\( N \Delta V(\Delta V>0), \) are drawn and have
increasing radii \( r_{0}, r_{1}, r_{2}, \dots . . r_{N} \)
respectively. If the difference in the radii of the surfaces is constant for all values
of \( V_{0} \) and \( \Delta V \) then :
A \( \cdot \rho(r)= \) constant
B. \( \rho(r) \propto \frac{1}{r^{2}} \)
c. \( \rho(r) \propto \frac{1}{r} \)
D. \( \rho(r) \propto 1 \)
Subject: Physics
A body is executing SHM. If the force
acting on the body is \( 6 \mathrm{N} \) when the displacement is \( 2 \mathrm{cm}, \) then the force acting on the body when the displacement is \( 3 \mathrm{cm} \) in newton is:
A. 6 N
B. 9 N
\( c .4 \mathrm{N} \)
D. \( \sqrt{6} \) N
Subject: Chemistry
For the process \( \boldsymbol{H}_{2} \boldsymbol{O}(l) \rightarrow \)
\( \boldsymbol{H}_{2} \boldsymbol{O}(\mathbf{1} \boldsymbol{b} \boldsymbol{a} \boldsymbol{r}, \boldsymbol{3} \boldsymbol{7} \boldsymbol{3} \boldsymbol{K}), \) the correct set of
thermodynamic parameters is:
A. \( \triangle G=0, \Delta S=+v e \)
B. \( \triangle G=0, \Delta S=-v e \)
c. \( \Delta G=+v e, \Delta S=0 \)
D. \( \triangle G=-v e, \Delta S=+v e \)
Subject: Physics
Two vehicles, each moving with speed \( \mathbf{u} \)
on the same horizontal straight road,
are approaching each other. Wind blows
along the road with velocity w. One of these vehicles blows a whistle of
frequency \( \mathbf{f}_{1} . \) An observer in the other
vehicle hears the frequency of the
whistle to be \( f_{2} . \) The speed of sound in
still air is \( \mathrm{V} \). The correct statement(s) is
\( (\operatorname{are}) \)
This question has multiple correct options
A. If the wind blows from the observer to the source, \( f_{2}> \)
\( f_{1} \)
B. If the wind blows from the source to the observer, \( f_{2}> \)
\( f_{1} \)
C. If the wind blows from observer to the source, \( f_{2}<f_{1} \)
D. If the wind blows from the source to the observer \( f_{2}< \)
\( f_{1} \)
Subject: Maths
The weight of Rahul is \( 5 k g \) more than
Sachin.The weight of Samir is 12 kg less than double the weight of Sachin.lf the total weight of all the three is 93 find the weight of each one of them.
A. Sachin-25 kg, Rahul - 30 kg, Samir 38kg
B. Sachin-25 kg, Rahul -30 kg, Samir 40 kg
c. Sachin- -25 kg, Rahul - 38 kg, Samir -25 kg
D. Sachin- -25 kg, Rahul -38 kg, Samir 38kg
Subject: Maths
If \( D, E, F \) are the mid-points of the sides \( B C, C A \) and \( A B \) respectively of \( \triangle A B C, \) prove that \( B D E F \) is a parallelogram whose area is half to that
of \( \triangle A B C . \) Show that \( a r(\triangle D E F)= \) \( \frac{1}{4} a r(\triangle A B C) \)
Subject: Physics
Figure shows a rectangular conductor PQRS in which the Conductor PQ is free
to move in a uniform magnetic field
perpendicular to the plane of the paper. The filed extends from \( x=0 \) to \( x=b \) and is
zero for \( x>b \). Assume that only the arm
PQ possesses resistance r. when the
\( \operatorname{arm} \) PQ is pulled outward from \( x=0 \) to
\( x=2 b \) and is then moved back to \( x=0 \)
with constant speed \( v, \) Determine the expression for the flux and induced emf
Sketch the variations of these
quantities with distance \( 0 \leq x \leq 2 b \)
Subject: Chemistry
Which of the following represents the
correct order of the acidity in the given
compound?
\( \mathbf{A} \cdot C l C H_{2} C O O H<B r C H_{2} C O O H<C H_{3} C O O H< \)
\( F C H_{2} C O O H \)
B. \( C H_{3} C O O H<B r C H_{2} C O O H<C l C H_{2} C O O H< \)
\( F C H 2 C O O H \)
\( \mathrm{c} \cdot F C H_{2} C O O H<C l C H_{2} C O O H<B r C H_{2} C O O H< \)
\( C H_{3} C O O H \)
D. \( C H_{3} C O O H<F C H_{2} C O O H<C l C H_{2} C O O H< \)
\( B r C H_{2} C O O H \)
Subject: Maths
For \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}+\boldsymbol{x}+\mathbf{1} ; \boldsymbol{x} \in[-1,1], \) the
constant of Meanvalue theorem is
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \frac{1}{2} \)
\( c \cdot-\frac{1}{2} \)
D.
Subject: Chemistry
The hardness of water due to \( H C O_{3}^{\ominus} \) is
122 ppm. Select the correct statement(s).
This question has multiple correct options
A. The hardness of water in terms of \( C a C O_{3} \) is 200 ppm.
B. The hardness of water in terms of \( C a C O_{3} \) is 100 ppm.
C. The hardness of water in terms of \( C a C l_{2} \) is 222 ppm.
D. The hardness of water in terms of \( M g C l_{2} \) is 95 ppm.
Subject: Maths
An equilateral triangle has each of its
sides of length \( 6 \mathrm{cm} . \) If \( \left(x_{1}, y_{1}\right) ;\left(x_{2}, y_{2}\right) \)
\( \&\left(x_{3}, y_{3}\right) \) are its vertices then the value
of determinant (in nearest integer value) \( ,\left|\begin{array}{lll}\boldsymbol{x}_{1} & \boldsymbol{y}_{1} & \mathbf{1} \\ \boldsymbol{x}_{2} & \boldsymbol{y}_{2} & \mathbf{1} \\ \boldsymbol{x}_{3} & \boldsymbol{y}_{3} & \mathbf{1}\end{array}\right| \) is equal to a then
find \( \frac{\boldsymbol{a}}{\mathbf{3 1}} \)
Subject: Maths
Find the slope and \( y \) -intercept of the
line \( 2 x+2 y=-2 \)
A. slope \( =1, \) y-intercept \( =-3 \)
B. slope = -1, y-intercept = -1
c. slope \( =1, y \) -intercept \( =3 \)
D. slope \( =1, y \) -intercept \( =1 \)