AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Biology
Match the columns of size with soil
particles
\begin{tabular}{lll|l} 
& Column 1 (size) & \multicolumn{2}{c} { Column 2 (soil particle) } \\
a. & 0.2- 2.00 \( \mathrm{mm} \) & (i) & Silt \\
b. & Less than 0.002 \( \mathrm{mm} \) & (ii) & Clay \\
c. & 0.02 - 0.2 \( \mathrm{mm} \) & (iii) & Coarse sand particles \\
d. & \( 0.02-0.02 \) \( \mathrm{mm} \) & (iv) & Fine sand particles
\end{tabular}
B. a- iii, b- ii, c- iv, d-i
c. a- ii, b- iii, c- iv, d-i
D. None of the above
Subject: Chemistry
The number of \( C l^{-} \) and \( C a^{2+} \) ions in
\( 222 g \) of \( C a C l_{2} \) is:
A \( \cdot 4 N_{A}, 2 N_{A} \)
в. \( 2 N_{A}, 4 N_{A} \)
C \( .1 N_{A}, 2 N_{A} \)
D. \( 2 N_{A}, 1 N_{A} \)
Subject: Chemistry
Calculate the useful work of the
reaction \( \boldsymbol{A} \boldsymbol{g}(\boldsymbol{s})+\mathbf{1} / \mathbf{2} \boldsymbol{C l}_{2}(\boldsymbol{g}) \rightarrow \)
\( A g C l(s) \)
\( \operatorname{Given} \boldsymbol{E}_{c_{2} / C l^{-}}^{0}=+\mathbf{1 . 3 6} \boldsymbol{V} \)
\( \boldsymbol{E}_{A \boldsymbol{g}|A \boldsymbol{g} C l| C l^{-}}^{0}=\mathbf{0 . 2 2} \boldsymbol{V} \) if \( \boldsymbol{P}_{C l_{2}}=\mathbf{1} \boldsymbol{a} \boldsymbol{t m} \)
and \( \boldsymbol{T}=\mathbf{2} \mathbf{9} \mathbf{8} \boldsymbol{K} \)
A. 110 kJ/mol
B. 220 kJ/mol
c. 55 kJ/mol
D. 1000 kJ/mol
Subject: Maths
\( \mathbf{f} \mathbf{A}=\left[\begin{array}{cc}\boldsymbol{a} & \boldsymbol{b} \\ -\boldsymbol{b} & \boldsymbol{a}\end{array}\right] \boldsymbol{B}=\left[\begin{array}{cc}\boldsymbol{c} & \boldsymbol{d} \\ -\boldsymbol{d} & \boldsymbol{c}\end{array}\right] \) show
that \( A \) product \( B \) commute
i. e. \( A B=B A \) also verify that \( |\boldsymbol{A B}|=|\boldsymbol{A}| \cdot|\boldsymbol{B}| \)
Subject: Maths
The following table gives the daily wages of workers in a factory. Compute the standard deviation and the
coefficient of variation of the wages of
the workers.
\( \begin{array}{lllll}\begin{array}{l}\text { Wages } \\ \text { (Rs) }\end{array} & \begin{array}{l}\text { 125- } \\ \text { 175 }\end{array} & \begin{array}{l}\text { 175- } \\ \text { 225 }\end{array} & \begin{array}{l}\text { 225- } \\ \text { 275 }\end{array} & \begin{array}{l}\text { 275- } \\ \text { 325 }\end{array}\end{array} \)
of
workers
?
Subject: Physics
Three bodies of the same material and
having masses \( \mathrm{m}, \mathrm{m} \) and \( 3 \mathrm{m} \) are at
temperatures \( 45^{\circ} \mathrm{C}, 50^{\circ} \mathrm{C} \) and \( 60^{\circ} \mathrm{C} \)
respectively. If the bodies are brought in thermal contact, the final temperature
will be.
A \( \cdot 45^{\circ} \mathrm{C} \)
В. \( 54^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 52^{\circ} C \)
D. \( 48^{\circ} \mathrm{C} \)
Subject: Maths
Sum of the fractions \( \frac{\mathbf{7}}{\mathbf{1 2}}, \frac{\mathbf{1 2}}{\mathbf{1 2}}, \frac{\mathbf{8}}{\mathbf{1 2}} \) is
equal to
A \( \cdot \frac{26}{12} \)
в. \( \frac{19}{12} \)
c. \( \frac{27}{12} \)
D. \( \frac{23}{12} \)
Subject: Physics
If a simple harmonic motion is represent by \( \frac{d^{2} x}{d t^{2}}+a x=0, \) its time period is
A \( \cdot \frac{2 \pi}{\alpha} \)
в. \( \frac{2 \pi}{\sqrt{\alpha}} \)
\( c \cdot 2 \pi \alpha \)
D. \( 2 \pi \sqrt{\alpha} \)
Subject: Physics
Some liquid is filled in a cylindrical
vessel of radius \( R \) Let \( F_{1} \) be the force
applied by the liquid on the bottom of the cylinder. Now the same liquid is poured into a vessel of uniform square
cross-section of side \( \boldsymbol{R} \). Let \( \boldsymbol{F}_{2} \) be the
force applied by the liquid on the bottom of this new vessel. (Neglect atmosphere pressure). Then
\( \mathbf{A} \cdot F_{1}=\pi F_{2} \)
B. \( F_{1}=\frac{F_{2}}{\pi} \)
\( \mathbf{C} \cdot F_{1}=\sqrt{\pi F_{2}} \)
\( \mathbf{D} \cdot F_{1}=F_{2} \)
Subject: Chemistry
Decomposition of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) is a first order
reaction. A 16 volume solution of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \)
of half life 30 min is present at start. When will the solution become one
volume?
A. After 120 min
B. After 90 min
c. After 60 min
D. After 150 min
Subject: Chemistry
In the redox reaction: \( \boldsymbol{x} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}+ \)
\( \boldsymbol{y} \boldsymbol{P} \boldsymbol{b} \boldsymbol{O}_{2}+\boldsymbol{z} \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \rightarrow \boldsymbol{H} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4}+ \)
\( \boldsymbol{P b}\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \)
A. \( x=2, y=5, z=10 \)
в. \( x=2, y=7, z=8 \)
c. \( x=2, y=5, z=8 \)
D. \( x=2, y=5, z=5 \)
Subject: Physics
A cube has sides of length \( L=0.2 \mathrm{m} \). It is placed with one corner at the origin as shown in figure.The electric field is uniform and given by \( \overrightarrow{\boldsymbol{E}}= \) \( (2.5 N / C) \dot{I}-(4.2 N / C) j . \) Find the
electric flux through the entire cube.
Subject: Maths
The differential equation for the family of curves \( x^{2}+y^{2}-2 a y=0, \) where \( a \) is
an arbitrary constant is
A \( \cdot 2\left(x^{2}-y^{2}\right) y^{\prime}=x y \)
B \( \cdot 2\left(x^{2}+y^{2}\right) y^{\prime}=x y \)
c. \( \left(x^{2}-y^{2}\right) y^{\prime}=2 x y \)
D. \( \left(x^{2}+y^{2}\right) y^{\prime}=2 x y \)
Subject: Physics
With what velocity should a ball be
thrown vertically upward with so that it reaches a height of \( 40 m \)
\( \mathbf{A} \cdot 7 m s^{-1} \)
B. \( 14 \mathrm{ms}^{-1} \)
\( \mathrm{c} \cdot 21 \mathrm{ms}^{-1} \)
D. \( 28 m s^{-1} \)
Subject: Physics
A homogeneous rod \( X Y \) of length \( L \) and
mass \( M \) is pivoted at the centre \( C \)
such that it can rotate freely in the vertical plane. Initially, the rod is in the horizontal position. A blob of wax of
same mass \( M \) as that of the rod falls
vertically with the speed \( V \) and sticks
to the rod midway between points \( C \)
and \( Y . \) If the rod rotates with angular
speed \( \omega \) what will be angular speed in
terms of \( \boldsymbol{V} \) and \( \boldsymbol{L} \) ?
Subject: Physics
Two identical loops \( P \) and \( Q \) each of
radius \( 5 \mathrm{cm} \) are lying in perpendicular
planes such that they have a common centre as shown in the figure. Find the magnitude and direction of the net magnetic field at the common centre of
the two coils, if they carry currents
equal to \( 3 A \) and \( 4 A \) respectively.
Subject: Physics
Two nichrome wires \( A \) and \( B \), each of
length \( 5 \mathrm{cm} \) and of radius \( 1 \mathrm{cm} \) and
\( 3 \mathrm{cm} \) respectively are connected to each
other in series. If a current of \( 5 A \) flows
through the combination of wires, the ratio of potential difference across wire \( A \) to that across wire \( B \) will be
A .1: 3
B. 3: 1
c. 9: 1
D. 1: 9
Subject: Physics
Voltage \( V \) and current i in AC circuit is given by \( \mathrm{V}=\mathbf{5 0} \sin (\mathbf{5 0} t) \) volt
\( \mathrm{i}=50 \sin \left(50 t+\frac{\pi}{3}\right) m A . \) The power
dissipated in circuit is:
\( \mathbf{A} \cdot 5.0 W \)
B . \( 2.5 W \)
c. \( 1.25 W \)
D. zero
Subject: Physics
A rocket of initial mass 6000 kg ejects
mass at a constant rate of \( 16 k g / s \) with
constant relative speed of \( 11 k m / s \) What is the acceleration of the rocket a
minute after the blast? (Neglect gravity)
\( \mathbf{A} \cdot 28.7 \mathrm{m} / \mathrm{s}^{2} \)
B . \( 34.9 \mathrm{m} / \mathrm{s}^{2} \)
c. \( 39.4 \mathrm{m} / \mathrm{s}^{2} \)
D. \( 27.8 \mathrm{m} / \mathrm{s}^{2} \)
Subject: Chemistry
The mass of ice (in dag to the nearest
integer) that will separate out on cooling a solution containing 50 g ethylene glycol in 200 g water to \( -9.3^{\circ} \mathrm{C}\left(\mathrm{K}_{f} \text { for water }=\right. \)
\( \left.1.86 K m o l^{-1} k g\right) \) is
Subject: Maths
The number of real roots of the
equation \( (x-1)^{2}+(x-2)^{2}+(x- \)
\( \mathbf{3})^{2}=\mathbf{0} \) is :
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D. None of these
Subject: Biology
Match the animals listed below with
their nature of blood. Choose the answer
which gives the correct combination of
alphabets of the two columns.
Animals \( \quad \) Nature of blood
A. Man
(p) Plasma and cells are colourless
B.
(q) Plasms is colourless and Earthworm nucleated
\( \mathrm{C} \)
(r) Plasma is colourless and cockroach enucleated RBC
(s) Plasma is red and nucleated,
D. Frog \( \quad \) colourless RBC
(t) Plasma and RBC have haemoglobin
\( A \cdot A-p, B-s, C-q, D-r \)
B. A-t, B- r, C- p, D-s
C. \( A-r, B-s, C-p, D-q \)
D. \( A-s, B-t, C-r, D-q \)
Subject: Chemistry
Name the following compound according to the IUPAC system or nomenclature:
\( \boldsymbol{C H}_{3} \boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right) \boldsymbol{C H}_{2} \boldsymbol{C}\left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C O C H}_{3} \)
Subject: Chemistry
If the ionic product of \( M(O H)_{2} \) is \( 5 \times \) \( 10^{-10}, \) then the molar solubility of
\( M(O H)_{2} \) in \( 0.1 M N a O H \) is:
A \( .5 \times 10^{-12} \mathrm{M} \)
В. \( 5 \times 10^{-8} \) М
c. \( 5 \times 10^{-10} M \)
D. \( 5 \times 10^{-9} M \)
E \( .5 \times 10^{-16} M \)
Subject: Maths
If value of \( x \) which satisfy \( \sin ^{-1} x \leq \) \( \cos ^{-1} x \) is \( x \epsilon\left[a, \frac{b}{\sqrt{c}}\right] \)
Find the value of \( a+b+c \)
A.
B.
\( c \cdot 2 \)
D.
Subject: Physics
Free \( ^{238} \boldsymbol{U} \) nuclei kept in a train emit
alpha particles.When the train is stationary and a uranium nucleus decays, a passenger measures that the separation between the alpha particles
and the recoiling nucleus becomes \( x, \) in
\( t \) time after the decay. If a decay takes
places, when the train is moving at a
uniform speed \( v, \) the distance between the alpha particle and the recoiling nucleus at a time \( t \) after the decay, as
measured by the passenger will be
A \( . x+v t \)
B. \( x-v t \)
\( c \)
D. depends on the directions of the train
Subject: Physics
The area of cross-sections of three
metals roads of equal length and made
of same materials are \( A_{1}, A_{2} \) and \( A_{3} \)
respectively. when heated through the same change in temperature their
linear expansions are found to be \( \boldsymbol{I}_{1}, \boldsymbol{I}_{2} \)
and \( I_{3} \) respectively which among the following is the correct relation between
\( \boldsymbol{I}_{1}, \boldsymbol{I}_{2} \) and \( \boldsymbol{I}_{3} ? \)
\( \mathbf{A} \cdot I_{1}=I_{2}=I_{3} \)
\( \mathbf{B} \cdot I_{1}>I_{2}>I_{3} \)
\( \mathbf{c} \cdot I_{1}<I_{2}<I_{3} \)
\( \mathbf{D} \cdot I_{1}=I_{2}<I_{3} \)
Subject: Physics
Door hinge is about \( 1.5 \mathrm{m} \) away from handle, and a boy applies a force of \( 4 \mathrm{N} \) moment of force will be
A. \( 5.5 \mathrm{N} \) m
B. 2.66 N m
\( c \cdot 6 N m \)
D. 2.5 N m
Subject: Physics
Taking the mass of a proton to be \( 1.67 \times 10^{-27} \mathrm{kg}, \) the order of magnitude
of the number of protons in 1 g is \( 5.88 \times \) \( \mathbf{1 0}^{(\mathbf{2 0}+\boldsymbol{x})} \). What is \( \boldsymbol{x} \)
Subject: Maths
Find the area of a parallelogram having base \( 4 \mathrm{cm} \) and height \( 2 \mathrm{cm} \)
A. 6 sq. \( \mathrm{cm} \)
B. 8 sq. \( \mathrm{cm} \)
c. 10 sq. \( \mathrm{cm} \)
D. 12 sq. \( \mathrm{cm} \)
Subject: Chemistry
A microscope using suitable photons is employed to locate an electron in an atom within a distance of 0.1 A. What is
the uncertainty involved in the measurement of its velocity? \( (h=6.626 \)
\( \times 10^{-34} \mathrm{Js}, \) mass of electron \( =9.1 \)
\( \times 10^{-31} \mathrm{kg} \)
Subject: Physics
In a nuclear reactor the number of \( U^{235} \)
nuclei undergoing fissions per second
is \( 4 \times 10^{20} . \) If the energy released per
fission is \( 250 M e V \), the total energy
released in 10 hours is
\( \left(1 e V=1.6 \times 10^{-19} J\right) \)
A \( .576 \times 10^{6} J \)
В. \( 576 \times 10^{12} J \)
c. \( 576 \times 10^{15} J \)
D. \( 576 \times 10^{18} J \)
Subject: Chemistry
When \( I^{-} \) is oxidized by \( M n O_{4}^{-} \) in
alkaline medium, \( I^{-} \) is converted into
\( A \cdot I O_{3}^{-} \)
в. \( I_{2} \)
\( \mathbf{c} \cdot I O_{4}^{-3} \)
D. IO
Subject: Chemistry
A system can be taken from the initial
state \( p_{1}, V_{1} \) to final state \( p_{2}, V_{2} \) by two
different methods. Let \( \Delta Q \) and \( \Delta W \)
represent the heat given to the system and the work done by the system. Which of the following must be the same in both the methods.?
\( A \cdot \Delta Q \)
в. \( \Delta W \)
c. \( \Delta Q+\Delta W \)
D. \( \Delta Q-\Delta W \)
Subject: Physics
State an expression for \( \boldsymbol{K} . \boldsymbol{E} \) (kinetic energy) and \( P . E \) (potential energy) at
displacement ' \( x^{\prime} \) for a particle
performing linear \( \boldsymbol{S} . \boldsymbol{H} . \boldsymbol{M} . \) Represent
them graphically. Find the displacement at which \( K . E \) is equal to \( \boldsymbol{P} . \boldsymbol{E} \)
Subject: Maths
Using the properties of determinant and without expanding, prove that:
\( \left|\begin{array}{ccc}\boldsymbol{x} & \boldsymbol{a} & \boldsymbol{x}+\boldsymbol{a} \\ \boldsymbol{y} & \boldsymbol{b} & \boldsymbol{y}+\boldsymbol{b} \\ \boldsymbol{z} & \boldsymbol{c} & \boldsymbol{z}+\boldsymbol{c}\end{array}\right|=\mathbf{0} \)
Subject: Physics
The electric potential at any point
inside the first shell is:
\( \mathbf{A} \cdot 18 \times 10^{4} V \)
B. \( 9 \times 10^{4} V \)
c. \( 4.5 \times 10^{4} V \)
D . \( 1.8 \times 10^{4} V \)
Subject: Maths
Assertion
If \( A, B, C \) are acute positive angles then \( \frac{(\sin A+\sin B)(\sin B+\sin C)(\sin C+s)}{\sin A \sin B \sin C} \)
8
Reason
\( \boldsymbol{A M} \geq \boldsymbol{G} \boldsymbol{M} \)
A. Statement-1 is false, statement-2 is true
B. Statement-1 is true, statement-2 is true,statement-2 is correct explanation for statement-
c. statement-1 is true, statement-2 is true,statement-2 is not a correct explanation for statement-
D. Statement-1 is true, statement-2 is false
Subject: Biology
A dwarf pea plant was treated with gibberellic acid (GA), it grew as tall as the homozygous tall pea plant. If this GA-treated plant is now crossed with a pure tall pea plant then the phenotypic ratio in the next generation is likely to be
A. All dwarf.
B. 50\% dwarf, 50\% tall.
c. 75\% tall, 25\% dwarf
D. All tall
Subject: Chemistry
The partial pressure of \( N_{2}, O_{2} \) and \( C O_{2} \)
in a vessel are \( 38 \mathrm{cm} \) of \( \mathrm{Hg}, 190 \) torr and
0.5 atm, respectively. The total pressure
of the mixture at the same temperature is?
A. 0.96 atm
B . 1.02 atm
c. 1.64 atm
D. 1.25 atm
Subject: Maths
Let \( \boldsymbol{f}:[\mathbf{0}, \mathbf{1}] \rightarrow \boldsymbol{R} \) be a continuous
function then the maximum value of \( \int_{0}^{1} f(x) \cdot x^{2} d x-\int_{0}^{1} x \cdot(f(x))^{2} d x \) for all
such function(s) is
\( A \cdot \frac{1}{8} \)
B. \( \frac{1}{20} \)
c. \( \frac{1}{12} \)
D. \( \frac{1}{16} \)
Subject: Physics
Statement -1: NAND and NOR gates are called digital building blocks. Statement-2: The repeated use of NAND (or NOR) gates can produce all the basis or complicated gates.
A. Statement-1 is false, Statement-2 is true
B. Statement 1-is true, Statement - 2 is true and Statement- -2 is correct explanation of Statement-1
c. Statement 1 -is true, Statement - 2 is true and statement- - 2 is not correct explanation of statement- -
D. Statement 1-is true, Statement-2 is false
Subject: Chemistry
The heat of combustion of methane is
\( -880 \mathrm{kJ} \mathrm{mol}^{-1} . \) If \( 3.2 \mathrm{g} \) of methane is
burnt
\( A \cdot 88 k J \)
B. 264 kJ
c. 176 kJ
D. 440 kJ
Subject: Biology
Study the four statements, a-d, given
below and select the two correct ones
out of them.
(a) Definition of biological species was
given by Ernst Mayr.
(b) Photoperiod does not affect reproduction in plants.
(c) Binomial nomenclature system was
given by R.H. Whittaker.
(d) In unicellular organisms
reproduction is synonymous with growth.
\( A \cdot \) a and \( b \)
B. b and c
c. \( c \) and \( d \)
D. a and d
Subject: Physics
The initial velocity of a particle is \( u(\mathrm{at} \)
\( t=0 \) ) and the acceleration a is given by
\( \alpha t^{3 / 2} . \) Which of the following relations is valid?
A \( \cdot v=u+\alpha t^{3 / 2} \)
B. \( v=u+\frac{3 \alpha t^{3}}{2} \)
c. \( v=u+\frac{2}{5} \alpha t^{5 / 2} \)
D. \( v=u+\alpha t^{5 / 2} \)
Subject: Physics
An average emf of \( 32 V \) is induced in a
coil in which the current drops from
\( 10 A \) to \( 2 A \) in \( 0.1 s . \) The inductance of the
coil is:
A \( .0 .32 H \)
в. \( 0.4 H \)
\( c .4 H \)
D. \( 0.04 H \)
Subject: Biology
Select the correct option:
Match column I with column II and
select the correct option from the codes given below.
Column I Column I I I I nnn
(A) Vermicomposting
(i) Ectonephric
(B) Phayngeal nephridia
(ii) Locomotion
(C) Integumentary
(iii) Earthworm nephridia
(D) Setae
(iv) Enteronephric
(v) Store
(E) Spermathecae \( \quad \) spermatozoa
A \( \cdot A-(\text { iii) } ; B-(i v) ; C-(i) ; D-(\text { ii }) ; E-(v) \)
B. \( A-(v) ; B-(i) ; C-(i v) ; D-(\text { ii }) ; E-(\text { iii }) \)
c. \( A- \) (iii); \( B- \) (ii); \( C-(\text { iv } v) ; D-(i) ; E-(v) \)
D. A- (iii); B- (v); C- (i); D- (iv): E- (ii)
Subject: Physics
A car traveling at a constant speed of \( 30 m / s \) passes a highway patrol car, which is at rest. The police officer
accelerates at a constant rate of \( 3 m / s^{2} \)
and maintains this rate of acceleration
until he pulls next to the speeding car. Assume that the police car starts to
move at the moment the speeder passes the police car. What is the time required for the police officer to catch
the speeder?
\( \mathbf{A} \cdot 20 s \)
B. \( 30 s \)
c. \( 40 s \)
D. \( 50 s \)
Subject: Physics
Equal volumes of two immiscible
liquids of densities \( \rho \) and \( 2 \rho \) are filled in
a vessel as shown figure. Two small
holes are punches at depth \( h / 2 \) and
\( 3 h / 2 \) from the surface of lighter liquid.
If \( v_{1} \) and \( v_{2} \) are the velocities of a flux at
these two holes then \( v_{1} / v_{2} \) is :
A \( \cdot \frac{1}{2 \sqrt{2}} \)
в. \( \overline{2} \)
\( c \cdot \frac{1}{4} \)
D. \( \frac{1}{\sqrt{2}} \)
Subject: Chemistry
In the preparation of \( \boldsymbol{C H} \boldsymbol{C l}_{3} \) from
ethanol and moist bleaching powder, the latter provides:
A \( \cdot C H_{3} C H O \)
в. \( H C l \)
\( \mathbf{c} \cdot \) Both \( C H_{3} C H O \) and \( H C l \)
D. Calcium formate
Subject: Chemistry
Assertion
Nitric oxide is paramagnetic while \( N_{2} O \)
is diamagnetic.
Reason
Nitrogen exhibits variable valency in
\( N O \) and \( N_{2} O \)
A. Both assertion and reason are CORRECT and reason is
the CORRECT explanation of the assertion.
B. Both assertion and reason are CORRECT, but reason is NOT THE CORRECT explanation of the assertion.
C. Assertion is CORRECT, but reason is INCORRECT.
D. Assertion is INCORRECT, but reason is CORRECT.
Subject: Physics
The circuit shown in figure was set up
to determine the emf of a thermocell. As
Pis moved away from \( X \) to \( Y \), the
galvanometer deflection is always in
the same direction but decrease
continuously until Y is reached. In order
to obtain a balance point between \( X \)
and \( Y, \) it is necessary to
A. decreases R
B. increases R
c. reverse the terminals of E
D. interchange the hot and cold iunctions
Subject: Maths
Let \( R \) be the set of all real numbers. If
\( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be a function such that
\( |\boldsymbol{f}(\boldsymbol{x})-\boldsymbol{f}(\boldsymbol{y})|^{2} \leq|\boldsymbol{x}-\boldsymbol{y}|^{3}, \forall \boldsymbol{x}, \boldsymbol{y} \varepsilon \boldsymbol{R}, \) then
\( f^{\prime}(x) \) is equal to
A. \( f(x) \)
B. 1
\( c \cdot 0 \)
D. \( x^{2} \)
\( E \)
Subject: Chemistry
How many of the following can be oxidising agent?
\( \boldsymbol{H}_{2} \boldsymbol{S}, \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}, \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{3}, \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{3} \)
Subject: Maths
Choose the correct answer from the
alternatives given:

Directions for questions 71 to 75: The
graph shows the production of wheat in different years of a particular State
The year in which the production
reached maximum is
\( \mathbf{A} \cdot 1995 \)
B. 1997
\( \mathbf{c} .1999 \)
D. 2000
Subject: Chemistry
In the manufacture of \( A l, A l_{2} O_{3} \) is
dissolved in \( N a_{3} A l F_{6} \) at \( 300 K \) and
electrolysed between \( A l \) and carbon electrodes following the net reaction,
\( \mathbf{2} \boldsymbol{A} \boldsymbol{l}_{2} \boldsymbol{O}_{3}(\boldsymbol{s} \boldsymbol{o l u t i o n})+\boldsymbol{3} \boldsymbol{C} \rightarrow \boldsymbol{4} \boldsymbol{A l}(l)+ \)
\( \mathbf{3} \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g}) \)
The minimum voltage required between the electrodes if the Gibbs energy
change for the above reaction is -1370 \( k J m o l^{-1} \) is \( _{-1} \) (write nearest
integer)
Subject: Chemistry
The IUPAC name of this compound is:
\( \boldsymbol{C H}_{3} \quad \boldsymbol{O} \)
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}-\stackrel{\|}{\boldsymbol{C}}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2} \boldsymbol{O H} \)
A. 1 -Hydroxy- 4 -methyl-3-pentanone
B. 2-Methyl-5-hydroxy-3-pentanone
c. 4-Methyl-3-oxo-1-pentanol
D. Hexan-1-one-3-o
Subject: Biology
Milk caesin- - - -Y- - -> Paracaesin- - - -M- - ->
Calcium paracaesinate (curding of milk). In the above equation 'Y' and 'M' indicates
A. Rennin and \( C a^{++} \) respectively
B. \( C a^{++} \) and Renin respectively
C. Renin and HCl, \( C a^{++} \) respectively
D. Renin and \( C a^{++} \) respectively
Subject: Biology
Which of the following strategy is not a
correct approach to reduce global warming?
A. Reducing the green house gas emission by limiting the use of fossil fuels.
B. Increase the vegetation cover, particularly the forest for photosynthetic utilization of \( C O_{2} \)
C. Minimizing the use of nitrogen fertilizers in agriculture for reducing \( N_{2} \) O emission.
D. Increasing the use of air conditioners, refrigeration unit and production of plastic foams and propellants in aerosal spray cans.
E. Developing substitutes for chlorofluorocarbons.
Subject: Maths
Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) and \( \boldsymbol{g}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be
continuous functions, then the value of \( \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}(f(x)+f(-x))(g(x)-g(-x)) d x \)
is equal to
\( A \)
B.
\( c \cdot 1 \)
D. none of these
Subject: Physics
Match the physical quantities given in Column I with suitable dimensions
expressed in Column II.
II Column I \( \quad \) Column
a) Angular momentum
1) \( M^{-1} L^{3} T^{-2} \)
b) Torque
2) \( M L T^{-2} \)
c) Gravitational constant
3) \( M L^{2} T^{-2} \)
d) Tension
4) \( M L^{2} T^{-1} \)
A. a-1, b-3, c-4, d-2
B. a-1, b-4, c-3 d-2
c. \( a-4, b-3, c-1, d-2 \)
D. a-1, b-2, c-4, d-3
Subject: Maths
Show that the points \( \boldsymbol{O}(\mathbf{0}, \mathbf{0}), \boldsymbol{A}(\mathbf{2},-\mathbf{3}, \mathbf{3}), \boldsymbol{B}(-\mathbf{2}, \mathbf{3},-\mathbf{3}) \) are
collinear. Find the ratio in which each point divides the segment joining the other two.
Subject: Physics
The area of two holes \( A \) and \( B \) are \( 2 a \) and
\( a \) respectively. The holes are at height
\( \frac{\boldsymbol{H}}{\mathbf{3}} \) and \( \frac{\boldsymbol{2} \boldsymbol{H}}{\mathbf{3}} \) from the surface of water.
Find the correct option(s)
This question has multiple correct options
A. the velocity of efflux at hole \( B \) is 2 times the velocity of efflux at hole \( A \)
B. the velocity of efflux at hole \( B \) is \( \sqrt{2} \) time the velocity of efflux at hole
C. the discharge is same through both the holes
D. the discharge through hole A is \( \sqrt{2} \) time the discharge through hole
Subject: Maths
If \( l(\bar{b} \times \bar{c})+m(\bar{c} \times \bar{a})+n(\bar{a} \times \bar{b})=0 \)
And at least one of \( l, \boldsymbol{m}, \boldsymbol{n} \) is not zero then the vectors \( \bar{a}, \bar{b}, \bar{c} \) are
A. Parallel
B. Coplanar
c. Mutually perpendicular
D. None of these