AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
A Funtion \( f \) is defined as \( f(x)= \) \( \frac{x^{2}-4 x+3}{x^{2}-1} \) for \( x \neq 1,=2 \) for \( x=1 \) Is
the function continuous at \( x=1 . ? \)
A . True
B. False
Subject: Chemistry
\( \mathrm{CH}_{3} \mathrm{COCl}+\mathrm{H}_{2} \stackrel{(A)}{\longrightarrow}(\mathrm{B}) \)
The given reaction is an example of Rosenmund's reaction. Identify the
product \( \mathbf{B} \)
A. Formaldehyde
B. cloroethane
c. Acetaldehyde
D. Ethanol
Subject: Physics
Given: \( \overrightarrow{\boldsymbol{A}}=\boldsymbol{i}-\mathbf{2} \boldsymbol{j}, \overrightarrow{\boldsymbol{B}}=\mathbf{2} \hat{\mathbf{i}}+ \)
\( \mathbf{3} \hat{\boldsymbol{k}} \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \overrightarrow{\boldsymbol{C}}=\hat{\boldsymbol{i}}+\hat{\boldsymbol{j}} \)
Find component of vector \( \overrightarrow{\boldsymbol{A}}+\overrightarrow{\boldsymbol{B}} \) along:
(i) x-axis
(ii) \( \overrightarrow{\boldsymbol{C}} \)
A \( \cdot 3 ; \frac{1}{\sqrt{2}} \)
в. \( 2 ; \frac{1}{\sqrt{3}} \)
c. \( _{3 ; \frac{1}{\sqrt{3}}} \)
D. \( 2 ; \frac{1}{\sqrt{2}} \)
Subject: Physics
A car covers \( 30 \mathrm{km} \) at a uniform speed
of \( 60 k m h^{-1} \) and the next \( 30 \mathrm{km} \) at a
uniform speed of \( 40 k m h^{-1} \). Find the
total time taken.
A. 30 min
B. 45 min
c. 75 min
D. \( 120 \mathrm{min} \)
Subject: Chemistry
The degree of dissociation \( (\alpha) \) of a weak
electrolyte, \( A_{x} B_{y} \) is related to van't Hoff
factor (i) by the expression:
A \( \cdot \alpha=\frac{i-1}{(x+y-1)} \)
B. \( \alpha=\frac{i-1}{x+y+1} \)
c. \( \alpha=\frac{x+y-1}{i-1} \)
D. \( \alpha=\frac{x+y+1}{i-1} \)
Subject: Chemistry
A cylinder containing an ideal gas
\( \left(0.1 \text { mol of } 1.0 d m^{3}\right) \) is in thermal
equilibrium with a large volume of 0.5 molal aqueous solution of ethylene glycol at its freezing point. If the
stoppers \( S_{1} \) and \( S_{2} \) ( as shown in the
figure) are suddenly withdrawn, the volume of the gas in litres after equilibrium is achieved will be
(Given, \( \boldsymbol{K}_{\boldsymbol{f}}(\boldsymbol{w} \boldsymbol{a} \boldsymbol{t e r})= \)
\( 2.0 K k g m o l^{-1}, R= \)
\( 0.08 d m^{3} \) at \( m \quad K^{-1} m o l^{-1} \)
Subject: Chemistry
The electronic configuration of chlorine
atom is :
A \( \cdot 1 s^{2} 2 s^{2} p^{6} 3 s^{3} p^{5} \)
B \( \cdot 1 s^{2} 2 s^{3} p^{6} 3 s^{3} p^{4} \)
C. \( 1 s^{2} 2 s^{2} p^{6} 3 s^{2} p^{5} \)
D. \( 1 s^{2} 2 s^{2} p^{6} 3 s^{2} p^{6} \)
Subject: Physics
A neutral rubber rod and a neutral piece
of fur have equal amounts of negative and positive charge. When the fur is rubbed against the rod, a transfer of electrons occurs. The transfer of
electrons and mass
transfer respectively takes place from
A. fur to rubber rod; rubber rod to fur
B. fur to rubber rod; fur to rubber rod
c. rubber rod to fur; rubber rod to fur
D. rubber rod to fur; fur to rubber rod
Subject: Physics
A bulbs is connected to a battery of p.d. \( 4 \mathrm{V} \) and internal resistance \( 2.5 \Omega . A \)
stedy current of \( 0.5 \mathrm{A} \)
(i) the total energy supplied by the battery in 10 minutes,
(ii) the resistance of the bulb,and
(iii) the energy displated in the bulb in
10 minutes
Subject: Maths
Find the mean deviation about the
mean for the following data:
\( \begin{array}{ll}\text { Marks obtained } & \text { No. of students } \\ \text { 0-10 } & 5 \\ \text { 10-20 } & 8 \\ \text { 20-30 } & 15 \\ \text { 30-40 } & 16 \\ \text { 40-50 } & 6\end{array} \)
Subject: Physics
A \( 1 \mathrm{kg} \) block is attached by light string
to another block of mass 2 kg. The
string is passed over a pulley of
negligible mass and friction. Calculate the acceleration of the masses?
\( A \cdot 5 m / s^{2} \)
B. \( 6.7 m / s^{2} \)
\( \mathbf{c} \cdot 10 m / s^{2} \)
D. \( 20 m / s^{2} \)
E. \( 30 m / s^{2} \)
Subject: Physics
The top of a water tank is open to air
and its water level is maintained. It is
giving out \( 0.74 m^{3} \) water per minute through a circular opening of \( 2 \mathrm{cm} \) radius in its wall. The depth of the
centre of the opening from the level of
water in the tank is close to :
A. \( 9.6 m \)
в. \( 4.8 \mathrm{m} \)
\( c .2 .9 m \)
D. \( 6.0 m \)
Subject: Chemistry
Assertion: Fluorine exists only in -1
oxidation state.
Reason: Fluorine has \( 2 s^{2} 2 p^{5} \)
configuration
A. If both assertion and reason are true and the reason is a correct explanation of the assertion
B. If both assertion and reason are true but reason is not a correct explanation of the assertion
C. If the assertion is true but reason is false
D. If both the assertion and reason are false
E. If the assertion is false but the reason is true
Subject: Maths
The D.E whose solution is \( y=\left(c_{1} x+\right. \)
\( \left.c_{2}\right) e^{5 x}: \)
A \( \cdot y_{2}+10 y_{1}+24 y=0 \)
B \( \cdot y_{2}-10 y_{1}+25 y=0 \)
c. \( y_{2}-5 y_{1}+25 y=0 \)
D. \( y_{2}-5 y_{1}+10 y=0 \)
Subject: Maths
Let \( z \neq 1 \) be a complex number and let \( \omega=x+i y \neq 0 . \) If \( \frac{\omega-\omega z}{1-z} \) is purely
real, then | \( z \mid \) is equal to :
\( A \cdot|\omega| \)
B . |\omega| \( ^{2} \)
c. \( \frac{1}{|\omega|^{2}} \)
D. \( \frac{1}{|\omega|} \)
\( E \)
Subject: Maths
The denominator of a fraction is greater
than its numerator by \( 7 . \) If 4 is added to both its numerator and denominator,
then it becomes \( \frac{1}{2} . \) Find the fraction.
A \( \cdot \frac{1}{6} \)
B. \( \frac{7}{3} \)
\( c \cdot \frac{3}{10} \)
D. 6 \( \overline{7} \)
Subject: Chemistry
Unsıder the IOIIOwIng melaııurgıcal
processes:
\( (I) \) Heating impure metal with \( C O \) and distilling the resulting volatile carbonyl
(b.p. \( \left.43^{0} \mathrm{C}\right) \) and finally decomposition at
\( 150^{0}-200^{0} C \) to get the pure metal.
\( (I I) \) Heating the sulphide ore in air
until a part is converted to oxide and then further heating in the absence of
air to let the oxide react with
unchanged metal sulphide. \( (I I I) \) Electrolysisof the molten electrolyte containing approximately equal amounts of the metal chloride
and \( N a C l \) to obtain the metal.
The processes used for obtaining magnesium, nickel and copper are
respectively:
\( \mathbf{A} \cdot(I),(I I) \) and \( (I I I) \)
B. \( (I I),(I I I) \) and \( (I) \)
C \( .(I I I),(I) \) and \( (I I) \)
D. \( (I I),(I) \) and \( (I I I) \)
Subject: Chemistry
Lanthanoid contraction is caused due
to:
A. imperfect shielding of outer electrons by \( 4 f \) - electrons from the nuclear charge.
B. appreciable shielding on outer electrons by \( 4 f \) electrons from the nuclear charge.
C . appreciable shielding on outer electrons by \( 5 d \) electrons from nuclear charge.
D. the same effective nuclear charge from Ce to Lu.
Subject: Chemistry
When \( F e C r_{2} O_{4} \) (chromite) is reduced
with \( A l \)
A \( \cdot C r \) and \( F e_{2} O_{3}, \) are formed
B. Fe and \( C r_{2} O_{3} \) are formed
c. \( F e \) and \( C r \) (ferrochrome) are formed
D. \( F e C r O_{4} \). is formed
Subject: Chemistry
Nitrogen reacts with a metal \( M \) to produce a compound \( X . \) This compound \( X \) when dissolved in water forms
pungent gas \( Y \) which can be identified
easily by the formation of white fumes
in the presence of \( \boldsymbol{H} \boldsymbol{C l} \)
Identify \( Y: \)
A. Nitrogen dioxide
B. Ammonia
c. Nitrous oxide
D. Nitric oxide
Subject: Maths
\( 30 \% \) passengers from a train got down at station \( A, 70 \% \) of the remaining got
down at station \( B \). If there are still 1050
passengers in the train, how many passengers were there before stations
\( A, \) provided no one boarded the train at
station \( A \) and \( B ? \)
A . 10,000
B. 5,000
c. 2000
D. 1000
Subject: Chemistry
Assertion
In chemisorption, adsorption keeps on increasing with temperature.
Reason
Heat keeps on providing more and more
activation energy.
A. If both (A) and (R) are true and (R) is the correct explanation of (A).
B. If both (A) and (R) are true, but (R) is not the correct explanation of (A).
c. If (A) is correct, but (R) is incorrect.
D. If (A) and (R) are both incorrect
Subject: Chemistry
Which of the following statements is
not true?
A. The ratio of the mean speed to the \( R M S \) speed is independent of the temperature
B. The square of the mean speed of the molecules is equal to the mean squared speed at certain temperature
C. Mean kinetic energy of the gas molecules at any given temperature is independent of the mean speed
D. The difference between rms speed and mean speed at any temperature for different gases diminishes as larger and larger molar masses are considered
Subject: Physics
A person of mass M kg is standing on a lift. If the lift moves vertically upwards according to given v-t graph then find out the weight of the man at the
following instants : \( \left(\mathrm{g}=10 \mathrm{m} / \mathrm{s}^{2}\right) \)
1) \( t=1 \) second
2) \( t=8 \) seconds
3) \( t=12 \) seconds
Subject: Physics
Area of a parallelogram, whose diagonals are \( 3 \hat{i}+\hat{j}-2 \hat{k} \) and \( \hat{i}-3 \hat{j}+ \) \( 4 \hat{k} \) will be
A . \( 14 u n i t \)
B. \( 5 \sqrt{3} \) unit
c. \( 10 \sqrt{3} \) unit
D. \( 20 \sqrt{3} u \) unit.
Subject: Maths
In the triangle with vertices \( \boldsymbol{A}(\mathbf{1},-\mathbf{1}, \mathbf{2}), \boldsymbol{B}(\mathbf{5},-\mathbf{6}, \mathbf{2}) \) and \( \boldsymbol{C}(\mathbf{1}, \mathbf{3},-\mathbf{1}) \)
find the altitude \( n=|B D| \)
\( A \cdot 5 \)
B. 10
c. \( 5 \sqrt{2} \)
D. \( \frac{10}{\sqrt{2}} \)
Subject: Biology
Assertion
The fungi are widespread in distribution and they even live on or inside other plants and animals.
Reason
Fungi are able to grow anywhere on land, water or on other organisms
because they have a variety of pigments, including chlorophyll, carotenoids, fucoxanthin and
phycoerythrin.
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
Two fixed, equal, positive charges, each of magnitude \( 5 \times 10^{-5} C \) are located at
point \( A \) and \( B \) separated by a distance
\( 6 m . \) An equal and opposite charge moves towards them along the line
COD, the perpendicular bisector of the
line \( A B . \) The moving charge, when it reaches the point \( C \) at a distance of \( 4 m \) from \( O, \) has a kinetic energy of 4
joules. Calculate the distance of the
farthest point \( D \) which the negative
charge will reach before returning
towards \( C \)
Subject: Physics
The equation of an incident wave travelling along +X direction is given by \( \boldsymbol{y}=\boldsymbol{A} \sin (\boldsymbol{2} \boldsymbol{t}-\mathbf{5} \boldsymbol{x}) . \) This wave gets
reflected at a rigid boundary. The equation of the reflected wave is
A \( . y=\operatorname{Asin}(2 t-5 x) \)
B. \( y=\operatorname{Asin}(2 t-5 x+\pi) \)
c. \( y=\operatorname{Asin}(2 t+5 x+\pi) \)
D. \( y=\operatorname{Asin}(2 t-5 x+\pi / 2) \)
Subject: Chemistry
Assertion
Functional groups are specific groups of atoms or bonds within molecules
that are responsible for the characteristic chemical reactions of
those molecules.
Reason
The same functional group will undergo the same or similar chemical
reaction(s) regardless of the size of the molecule.
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 particle of mas \( m \) carrying charge \( q \) is released from restm in a uniform
electric field of intensity \( \boldsymbol{E} \). The kinetic energy acquired by the particle after moving a distance of \( x \) is (neglect gravitational force):
A \( . q E x \)
В \( \cdot q E x^{2} \)
\( \mathbf{c} \cdot q E^{2} x \)
D. \( q^{2} E x \)
Subject: Physics
A motor car is travelling at \( 30 m / s \) on a
circular road of radius \( 500 m \). It is
increaseing in speed at the rate of
\( 2 m / s^{2} . \) Then the acceleration of the car
will be
A \( \cdot 4 m / s^{2} \)
B . \( 3 m / s^{2} \)
c. \( 2.7 m / s^{2} \)
D. \( 8 m / s^{2} \)
Subject: Maths
If \( m \) and \( n \) are order and degree of the
equation \( \left(\frac{d^{2} y}{d x^{2}}\right)^{5}+4 \frac{\left(\frac{d^{2} y}{d x^{2}}\right)}{\left(\frac{d^{3} y}{d x^{3}}\right)}+\left(\frac{d^{3} y}{d x^{3}}\right)=x^{2}- \)
1 then \( (\boldsymbol{m}, \boldsymbol{n})= \)
A \( \cdot(3,3) \)
в. (3,2)
\( c .(3,5) \)
D. (3,1)
Subject: Physics
Which row shows a quantity and an
incorrect unit?
\( \begin{array}{ll}\text { quantity } & \text { unit } \\ \text { A. efficiency } & \text { no unit } \\ \text { B. moment of force } & N m^{-1} \\ \text {C. momentum } & \text { Ns } \\ \text { D. work done } & \text { J }\end{array} \)
Subject: Physics
Figure shows a negatively charged ebonite rod A which is brought near an uncharged metal sphere P touching the other uncharged metal sphere \( Q \). Both
the spheres \( P \) and \( Q \) stand on separate insulating stands. Keeping rod \( A \) in position, sphere \( Q \) is removed by holding the insulating stand of it. State the kind of charge on
spheres \( P \) and \( Q \). Give reason to your
answer.
A. Spheres \( Q \) and \( P \) has positive charge
B. Spheres Q and P has negative charge
c. sphere \( Q \) has negative charge and sphere \( P \) has positive charge
D. spheres \( Q \) and \( P \) has no charge
Subject: Physics
Find the approximate value of induced
current assuming the resistance to the current is confined to the square.
A \( \cdot \frac{B L \omega d t}{\rho} \)
\( ^{\text {В }} \cdot \frac{B L^{2} \omega d t}{\rho} \)
\( ^{\text {c. }} \frac{B L^{2} \omega d}{\rho} \)
\( \frac{B L \omega d^{2}}{\rho} \)
Subject: Physics
In the HCl molecule, the separation between the nuclei of the two atoms is
about \( 1.27 \dot{A}\left(1 \dot{A}=10^{-10} m\right) . \) Find the
approximate location of the CM of the molecule, given that a chlorine atom is about 35.5 times as massive as a
hydrogen atom and nearly all the mass
of an atom is concentrated in its
nucleus.
Subject: Physics
If \( \vec{p}_{2} \) is free to rotate about an axis,
perpendicular to the plane and passing
through \( A, \) the angle between \( \vec{p}_{2} \) and \( \vec{p}_{1} \)
will be :
A \( \cdot \sin ^{-1}\left(\frac{1}{3}\right) \)
\( B \cdot \tan ^{-1}(3) \)
\( \mathbf{c} \cdot \cos ^{-1}\left(\frac{1}{3}\right) \)
\( D \cdot \cot ^{-1}(3) \)
Subject: Chemistry
Isotope per Natural abundance
\[
\begin{array}{ll}
^{1} \boldsymbol{H} & \mathbf{9 9 . 9 8 5} \\
^{2} \boldsymbol{H} & \mathbf{0 . 0 1 5}
\end{array}
\]
The average atomic mass of hydrogen using the following data is
Subject: Physics
The displacement \( x \) of a particle moving in one dimension, under the action of a
constant force is related to time \( t \) by the equation \( t=\sqrt{x}+3 \) where \( x \) is in metre and \( t \) in second. Calculate the
work done by the force in the first \( 6 s \) in Joule
A . 10
B.
\( c .5 \)
D. 2
Subject: Physics
In a circuit a coil of resistance \( 2 \Omega \), then
magnetic flux charges from 2.0 \( W \) b to
10.0 \( W b \) in 0.2 sec. The charge flow in
the coil during this time is:
\( \mathbf{A} \cdot 5.0 C \)
в. \( 4.0 C \)
c. \( 1.0 C \)
D. \( 0.8 C \)
Subject: Physics
A microscope consists of an objective of
focal length \( 1.9 \mathrm{cm} \) and eye piece of
focal length 5 cm. The two lenses are
kept at a distance of \( 10.5 \mathrm{cm} . \) If the
image is to be formed at the least distance of distinct vision, the distance
at which the object is to be placed before the objective is:
(Least distance of distinct vision is 25
\( \mathrm{cm} \)
\( \mathbf{A} \cdot 6.2 \mathrm{cm} \)
B. \( 2.7 \mathrm{cm} \)
c. \( 21.0 \mathrm{cm} \)
D. \( 4.17 \mathrm{cm} \)
Subject: Chemistry
The incorrect IUPAC name is:
\( A \)
в.
2, 3-Dimethylpentane
\( c \)
\( \mathrm{CH}_{3}-\mathrm{C} \equiv \mathrm{CCH}\left(\mathrm{CH}_{3}\right)_{2} \)
4-Methylpent-2-yne
D.
2-Bromo-3-chlorobutane
Subject: Maths
The converse of "If in a triangle \( A B C, A B=A C, \) then \( \angle B=\angle C^{\prime \prime}, \) is
A. If in a triangle \( A B C, \angle B=\angle C \), then \( A B=A C \).
B. If in a triangle \( A B C, A B \neq A C \), then \( \angle B \neq \angle C \).
c. If in a triangle \( A B C, \angle B \neq \angle C \), then \( A B \neq A C \).
D. If in a triangle \( A B C, \angle B \neq \angle C \), then \( A B=A C \).
Subject: Physics
Choose the correct answer from
alternatives given

The mixture of a pure liquid and a
solution in a long vertical column (i.e, horizontal dimensions
A \( -\frac{1}{d}\left(\frac{d u}{d y}\right) \mu \)
B \( \cdot \frac{d}{h}\left(\frac{d u}{d y}\right) \)
c. \( \left(\frac{d u}{d y}\right) \)
" \( -\frac{1}{\mu}\left(\frac{d u}{d y}\right) d \)
Subject: Chemistry
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}(\boldsymbol{O H})- \)
\( \boldsymbol{C H}_{2} \boldsymbol{C H}_{3} \stackrel{[\boldsymbol{O}]}{\rightarrow} \boldsymbol{A} \frac{\boldsymbol{C H}_{3} M \boldsymbol{g}-\boldsymbol{I}}{\boldsymbol{H}_{2} \boldsymbol{O} / \boldsymbol{H}^{+}} \boldsymbol{B} \)
What is \( A \) in the given reaction sequence?
A. \( C H_{3}-C H_{2}-C H_{2}-C O-C H_{3} \)
B. \( C H_{3}-C H_{2}-C O-C H_{2}-C H_{3} \)
c. \( C H_{3}-C H_{2}-O-C H_{2}-C H_{2} C H_{3} \)
D. \( C H_{3}-C H_{2}-C H_{2}-C H_{2}-C H O \)
Subject: Physics
A solid cylinder at rest at the top of an
inclined plane of height \( 2.7 m \) rolls down without slipping. If the same cylinder has to slide down a frictionless inclined
plane and acquire the same velocity as that acquired by the center of mass of
the rolling cylinder at the bottom of the
inclined plane, the height of the inclined plane in meters should be: \( (\boldsymbol{g}= \)
\( \left(0 m / s^{2}\right) \)
A \( .2 .2 m \)
в. \( 1.2 m \)
c. \( 1.6 m \)
D. \( 1.8 m \)
Subject: Physics
A ball is dropped from height hon the ground level. If the coefficient of
restitution is e then the height
upto which the ball will go after \( n^{t h} \)
jump will be-
\( A \cdot \frac{h}{e^{2 n}} \)
B. \( \frac{e^{2 n}}{h} \)
\( \mathbf{c} \cdot h e^{n} \)
D. \( h e^{2 n} \)
Subject: Maths
\( \frac{\boldsymbol{x} \boldsymbol{y}}{\boldsymbol{x}+\boldsymbol{y}}=\frac{\boldsymbol{6}}{\mathbf{5}} \)
\( \frac{x y}{y-x}=6 \)
A. \( x=-2, y=3 \)
в. \( x=3, y=2 \)
c. \( x=2, y=3 \)
D. \( x=-3, y=-2 \)
Subject: Physics
Light with energy flux of 18 w \( / \mathrm{cm}^{2} \) falls
on a non reflecting surface of area 20
\( \mathrm{cm}^{2} \) at normal incidence the
momentum delivered in 30 minutes ise
A \( \cdot 1.2 \times 10^{-6} \mathrm{kgms}^{-1} \)
B . \( 2.16 \times 10^{-3} \mathrm{kgms}^{-1} \)
C. \( 1.8 \times 10^{-3} \mathrm{kgms}^{-1} \)
D. \( 3.2 \times 10^{-3} \mathrm{kgms}^{-1} \)
Subject: Chemistry
At \( 373 \mathrm{K} \), steam and water are in
equilibrium and \( \Delta H=40.98 \mathrm{kJ} \) mol\( ^{-1} \)
What will be \( \Delta S \) fro conversion of
water into steam?
\( \boldsymbol{H}_{2} \boldsymbol{O}_{(l)} \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}_{(g)} \)
A \( \cdot 109.8 \) J \( K^{-1} m o l^{-1} \)
B . 31 J \( K^{-1} \) mol \( ^{-1} \)
c. 21.98 J \( K^{-1} m o l^{-1} \)
D. 326 J \( K^{-1} \) mol \( ^{-1} \)
Subject: Physics
A \( 100 \Omega \) resistor is connected to a
\( 220 V, 50 H z \) AC supply. Find rms value
of current in the circuit and the net
power consumed for a complete cycle.
A. \( 2.20 A, 484 W \)
в. \( 3.20 A, 564 W \)
c. \( 1.60 A, 278 W \)
D. \( 5.80 A, 646 W \)
Subject: Maths
The smallest and the largest values of \( \tan ^{-1}\left(\frac{1-x}{1+x}\right), 0 \leq x \leq 1 \) are
A \( .0, \pi \)
в. \( 0, \frac{\pi}{4} \)
\( c \cdot-\frac{\pi}{4}, \frac{\pi}{4} \)
D. \( \frac{\pi}{4}, \frac{\pi}{2} \)
Subject: Physics
The pressure on a square plate is measured by measuring the force on the plate and the length of the sides of the plate by using the formula \( \boldsymbol{P}= \)
\( \boldsymbol{F} / \boldsymbol{l}^{2} . \) If the maximum errors in the
measurement of force and length are \( 4 \% \) and \( 2 \%, \) respectively, then what is the maximum error in the
measurement of pressure?
Subject: Physics
Which of the following groups of forces could be in equilibrium?
A. \( 3 N, 4 N, 5 N \)
в. \( 4 N, 5 N, 10 N \)
c. \( 30 N, 40 N, 80 N \)
D. \( 1 N, 3 N, 5 N \)
Subject: Chemistry
Assertion
The ability of carbon to form chains gives rise to a homologous series of
compounds.
Reason
Homologous series is a series of
compounds with the same general formula, usually varying by a single
parametersuch as the length of a
carbon chain
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) The magnetic field in a region varies
as shown in figure. Calculate the
average induced emf in a conducting
loop of area \( 10^{-3} m^{2} \) placed
perpendicular to the field in each of the
10 \( m s \) intervals shown
(b) In which interval(s), the emf is not
constant? Neglect the behaviour near
the ends of \( 10 \mathrm{ms} \) intervals.
Subject: Maths
\( \operatorname{Let} A=\left[\begin{array}{lll}1 & 0 & 0 \\ 2 & 1 & 0 \\ 3 & 2 & 1\end{array}\right] . \) If \( u_{1} \) and \( u_{2} \) are
column matrices such that \( \boldsymbol{A} \boldsymbol{u}_{1}=\left[\begin{array}{l}\mathbf{1} \\ \mathbf{0} \\ \mathbf{0}\end{array}\right] \)
and \( A u_{2}=\left[\begin{array}{l}0 \\ 1 \\ 0\end{array}\right] \) then \( u_{1}+u_{2} \) is equal to
\( \mathbf{A} \cdot\left[\begin{array}{c}-1 \\ 1 \\ 0\end{array}\right. \)
B. \( \left[\begin{array}{c}1 \\ -1 \\ -1\end{array}\right. \)
\( \mathbf{c} \cdot\left[\begin{array}{c}-1 \\ -1 \\ 0\end{array}\right. \)
D. \( \left[\begin{array}{c}-1 \\ 1 \\ -1\end{array}\right. \)
Subject: Chemistry
Value of quantum numbers is \( \boldsymbol{n}= \) \( \mathbf{4}, \boldsymbol{I}=\mathbf{1}, \boldsymbol{m}=+\mathbf{1}, \) and \( \boldsymbol{s}=-\frac{\mathbf{1}}{\mathbf{2}} \) find
atomic numbers.
A .22
B. 34
\( c .33 \)
D. 36
Subject: Maths
Let \( A \) be a square matrix of order \( 3 \times 3 \) then \( |\mathbf{5} \boldsymbol{A}|=? \)
A. \( 5|A| \)
в. \( 125|A| \)
c. \( 25|A| \)
D . \( 15|A| \)
Subject: Physics
A uniform stationary sphere starts
rolling down from the upper end of the
surface as shown in the figure, and it
reaches the lower right end. Given, \( \boldsymbol{H}= \)
\( 27 m \) and \( h=20 m . \) The sphere will fall
on the ground level at the following
distance from \( C . \) (Assume horizontal
projection)
\( A \cdot 12 m \)
B. \( 24 m \)
\( c .36 m \)
D. 48 m
Subject: Maths
The area bounded by the curve \( y= \)
\( x^{4}-2 x^{3}+x^{2}+3 \) with \( x \) -axis and
ordinates corresponding to the minima of y is :
\( \mathbf{A} \cdot \mathbf{1} \)
B . \( \frac{91}{30} \)
\( c \cdot \frac{30}{9} \)
D. 4
Subject: Maths
A point \( P \) is outside a circle at a
distance of \( 13 \mathrm{cm} \) from its centre.
secant from \( P \) cuts the circle in \( Q \) and
\( R \) such that \( Q R=7 \mathrm{cm} \) and the
segment \( P Q \) of the secant, exterior to
the circle is \( 9 \mathrm{cm} . \) Therefore, the radius
of circle is
A. 3 cm
в. 4 ст
\( c .5 \mathrm{cm} \)
D. \( 6 \mathrm{cm} \)
Subject: Physics
Three identical bars \( A, B \) and \( C \) are
made of different magnetic materials. When kept in a uniform magnetic field, the field lines around them look as
follows:
Make the correspondence of these bars with their material being diamagnetic
\( (D), \) ferromagnetic \( (\boldsymbol{F}) \) and paramagnetic \( (\boldsymbol{P}) \)
A. \( A \leftrightarrow F, B \leftrightarrow P, C \leftrightarrow D \)
в. \( A \leftrightarrow P, B \leftrightarrow F, C \leftrightarrow D \)
c. \( A \leftrightarrow D, B \leftrightarrow P, C \leftrightarrow F \)
D. \( A \leftrightarrow F, B \leftrightarrow D, C \leftrightarrow P \)