AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
In a new set of units, unit of mass is 10
kg, unit of length is \( 1 \mathrm{km} \) and unit of time is 1 minute. The value of 1 joule in this new hypothetical system is
A \( \cdot 3.6 \times 10^{-4} \) new units
B. \( 6 \times 10^{7} \) new units
c. \( 10^{11} \) new units
D. \( 1.67 \times 104 \) new units
Subject: Biology
The excretory system of human beings includes a pair of ............, a pair of \( \ldots . . . . . . . \) a and a ............ which helps in the filtration of blood.
A. Kidneys, ureters, urinary bladder, urethra
B. Urethra, ureters, urinary bladder, kidneys
C. Kidneys, urethra, ureters, urinary bladder
D. Kidneys, urinary bladder, ureters, urethra
Subject: Maths
\( f\left(a_{1}, a_{2}, \dots a_{n} \) be an A.P.of tive terms, \right. then \( \sum_{k=1}^{n} a_{k} \geq n \sqrt{a_{1}^{2}+(n-1) d a_{1}} \)
where dis common difference of A.P. If
you think this is true write 1 otherwise
write 0 ?
Subject: Chemistry
\( \boldsymbol{K}_{2} \boldsymbol{C r}_{2} \boldsymbol{O}_{7}+\boldsymbol{H} \boldsymbol{C l} \rightarrow \boldsymbol{C r} \boldsymbol{C l}_{3}+\boldsymbol{H}_{2} \boldsymbol{O}+ \)
\( \boldsymbol{C l}_{2}+\boldsymbol{K} \boldsymbol{C l} \)
Balance in basic medium by ionelectron identity spectator ion.
Subject: Chemistry
The equilibrium constant \( \boldsymbol{K}_{\boldsymbol{p}} \) for the reaction \( \boldsymbol{A}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{B}(\boldsymbol{g})+\boldsymbol{C}(\boldsymbol{g}) \) is 1 at
\( 27^{\circ} \mathrm{C} \) and 4 at \( 47^{\circ} \mathrm{C} . \) Calculate enthalpy
change for: \( \boldsymbol{B}(\boldsymbol{g})+\boldsymbol{C}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{A}(\boldsymbol{g}) \)
(Given \( \boldsymbol{R}=\mathbf{2} \) cal / mol. \( \boldsymbol{K} \) ).
A \( .-13.31 \mathrm{kcal} / \mathrm{mol} \)
B. \( 13.31 \mathrm{kcal} / \mathrm{mol} \)
c. \( -19.2 \mathrm{kcal} / \mathrm{mol} \)
D. \( 55.63 \mathrm{kcal} / \mathrm{mol} \)
Subject: Chemistry
Calculate the given expression in the Kelvin scale
\( \frac{\left(24^{3}-21^{3}-3 \times(24)^{2}(21)+3 \times 24 \times\right.}{27} \)
where all numbers are in Celsius scale.
A. 300 к
B. 274 к
c. 282 к
D. 273 к
Subject: Maths
A container shaped like a right circular
cylinder having diameter \( 12 \mathrm{cm} \) and height \( 15 \mathrm{cm} \) is full of ice cream. The ice cream is to be filled into cones of height \( 12 \mathrm{cm} \) and diameter \( 6 \mathrm{cm}, \) having a hemispherical shape on the top. Find
the number of such cones which can be
filled with ice cream.
Subject: Physics
A particle of mass \( m \) is made to move
with uniform speed \( v_{0} \) along the
perimeter of a regular hexagon, inscribed in a circle of radius \( \boldsymbol{R} \). The
magnitude of impulse applied at each corner of the hexagon is:
\( \mathbf{A} \cdot 2 m v_{0} \sin \pi / 6 \)
в. \( m v_{0} \sin \pi / 6 \)
c. \( m v_{0} \sin \pi / 3 \)
D. \( 2 m v_{0} \sin \pi / 3 \)
Subject: Chemistry
Which of the following order is correct for the decreasing reactivity of ring
monobromination of the following
compounds?
A \( I>I I>I I I>I V \)
\( V \)
B. \( I I>I I I>I V>I \)
c. \( I>I I I>I I>I V \)
D. \( I I I>I>I I>I V \)
Subject: Maths
If \( \vec{a}=3 \hat{i}-6 \hat{i}-\hat{k}, \vec{b}=-1 \hat{i}+4 \hat{i}- \)
\( \mathbf{3} \hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{c}}=\mathbf{3} \hat{\boldsymbol{i}}-\mathbf{4} \hat{\boldsymbol{i}}-\mathbf{1 2} \hat{\boldsymbol{k}}, \) then the length
of projection of \( \vec{a} \times \vec{b} \) on \( \bar{c} \) is
A \( \cdot \frac{250}{13} \)
B. \( 5 \sqrt{2} \)
c. \( \frac{250}{\sqrt{13}} \)
D. 14
Subject: Physics
Which of the following relations is
correct?
A \( \cdot \) Distance \( =\frac{\text {Speed}}{\text {Timed} e e d \text { ed }} \)
B. Distance \( =\frac{\text { Trime }}{\text { speed }} \)
c. Distance = Speed \( \times \) Time
D. Distance = \( \frac{1}{\text { 5peedss } \times \text { ss Time }} \)
Subject: Chemistry
When a small quantity of \( \boldsymbol{F e C l} \) la solution is added to the fresh
precipitate of \( \boldsymbol{F e}(\boldsymbol{O H})_{3}, \) a colloidal sol is obtained. The process through which this sol is formed is known as:
A. exchange of solvent
B. chemical double decomposition
c. peptization
D. electrophoresis
Subject: Physics
A elevator car whose floor to distance is
\( 2.7 \mathrm{m} \) starts ascending with a constant
acceleration of \( 1.2 m / s^{2}, 2 s \) after a bolt is begin to fall from the ceiling of the car. The free fall time of the bolt is \( (g= \)
\( \left.9.8 m / s^{e}\right) ? \)
A \( \cdot \sqrt{\frac{2.7}{9.8}} s \)
в. \( \sqrt{\frac{5.4}{9.8}} s \)
c. \( \sqrt{\frac{5.4}{8.6}} s \)
D. \( \sqrt{\frac{5.4}{11}} \)
Subject: Physics
In Millikan's oil drop experiment, an oil drop is held stationary by a potential deference of \( 400 \mathrm{V} \). If another drop of double the radius, but carrying the same charge, is to be held stationary, the potential difference required will be
A . \( 800 \mathrm{v} \)
B. 1600
c. 3200
D. 400
Subject: Chemistry
Surface area covered by each molecule
of \( \boldsymbol{N} \boldsymbol{H}_{3} \) is :
A \( \cdot 7.065 \times 10^{-20} m^{2} \)
B . 2.8 \( \times 10^{-20} \mathrm{m}^{2} \)
D. 2.8 \( \times 10^{-19} \mathrm{m}^{2} \)
Subject: Physics
\( A 1^{\circ} C \) rise in temperature is observed in a conductor by passing a certain current. If the current is doubled, then
the rise in temperature is approximately
\( \mathbf{A} \cdot 2.5^{\circ} \mathrm{C} \)
B . \( 4^{\circ} \mathrm{C} \)
\( \mathrm{c} \cdot 2^{\circ} \mathrm{C} \)
D. \( 1^{\circ} \mathrm{C} \)
Subject: Chemistry
EDTA is used for the estimation of:
\( A \cdot N a^{+} \) and \( K^{+} \) ions
B. CI' and Br" ions
\( c \cdot c u 2^{2+} \) and \( A g^{+} \) ions
D. \( \mathrm{Ca}^{2+} \) and \( \mathrm{Mg}^{2+} \) ions
Subject: Maths
Prove that the Greatest Integer Function \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \operatorname{given} \) by \( \boldsymbol{f}(\boldsymbol{x})=[\boldsymbol{x}], \) is
neither one-one nor onto, where \( [\boldsymbol{x}] \)
denotes the greatest integer less that or
equal to \( x \)
Subject: Chemistry
At \( 1200^{\circ} C, \) the following equilibrium is established between chlorine atoms \&
molecule.
\( \boldsymbol{C l}_{2}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{C l}(\boldsymbol{g}) \)
The composition of the equilibrium mixture may be determined by measuring the rate of effusion of the mixture through a pinhole. It is found
that at \( 1200^{\circ} \) Cand 1 atm pressure the
mixture effuses 1.16 times as fast as
krypton effuses under the same condition.
Calculate the equilibrium constant \( \boldsymbol{K}_{c} \)
A \( .3 .1 \times 10^{5} \)
В . \( 6.3 \times 10^{4} \)
c. \( 12.6 \times 10^{5} \)
D. None of these
Subject: Maths
A certain radioactive material is known
to decay at a rate proportional to the amount present. If after one hour it is
observed that 10 percent of the material has decayed, find the half-life (period of time it takes for the amount of material
to decrease by half) of the material (in hrs.)
A . 6.58
B. 8.58
c. 10.58
D . 12.58
Subject: Maths
A dice is thrown \( 2 n+1 \) times, \( n \epsilon N \)
The probability that faces with even numbers show odd number of times is
A \( \cdot \frac{2 n+1}{4 n+3} \)
B. less than \( \frac{1}{2} \)
c. greater than \( \frac{1}{2} \)
D. none of these
Subject: Physics
U-r graph of a particle performance SHM is as shown in figure. What
conclusion cannot be drawn from the
graph?
A. Mean position of the particle is at \( r=2 \mathrm{m} \)
B. Potential energy of the particle at mean position is 10 .
C. Amplitude of oscillation is \( 1 \mathrm{m} \)
D. None of these
Subject: Maths
If \( A \) and \( B \) are independent events with
\( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 2}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 5 .} \) then find
\( \boldsymbol{P}(\boldsymbol{A} / \boldsymbol{B}) \)
Subject: Physics
The velocity of a particle moving with
constant acceleration at an instant \( t_{0} \) is
\( 10 m / s . \) After 5 seconds of that instant
the velocity of the particle is \( 20 m / s \)
The velocity at 3 second before \( t_{0} \) is:
A. \( 8 \mathrm{m} / \mathrm{s} \)
B. \( 6 m / s \)
c. \( 4 m / s \)
D. \( 7 \mathrm{m} / \mathrm{s} \)
Subject: Physics
Two waves of amplitudes \( A_{0} \) and \( x A_{0} \)
pass through a region.If \( x>1, \) what is the difference in the maximum and
minimum resultant amplitude is :
A \( \cdot(x+1) A_{0} \)
в. \( (x-1) A_{0} \)
c. \( 2 x A_{0} \)
D. \( 2 A_{0} \)
Subject: Chemistry
The half reaction which correctly represents the change that takes place
in the reaction between \( H_{2} O_{2} \) and
alkaline potassium ferricyanide is?
A \( \cdot H_{2} O_{2}+2 H^{+}+2 e^{-} \rightarrow 2 H_{2} O \)
в. \( H_{2} O_{2} \rightarrow 2 H^{-}+O_{2}+2 e^{-} \)
c. \( H_{2} O_{2} \rightarrow 2 H^{-}+O_{2}+2 H_{2} O+2 e^{-} \)
D. \( H_{2} O_{2}+2 e^{-} \rightarrow 2 O H \)
Subject: Chemistry
1.8 g hydrogen atoms are excited to radiations. The study of spectra indicates that \( 27 \% \) of the atoms are in
3rd energy level and \( 15 \% \) of atoms in 2 nd
energy level and the rest in the ground
state. If I.P. of \( \mathrm{H} \) is \( 21.7 \times 10^{-12} \) erg. The
number of atoms present in III \& II energy level and total energy evolved
when all the atoms return to ground
state respectively are:
A . \( 292.68 \times 10^{21} \) atoms \( , 162.60 \times 10^{21} \) atoms and \( 823 k J \)
B . \( 292.68 \times 10^{34} \) atoms \( , 162.60 \times 10^{43} \) atoms and \( 990 k J \)
c. \( 292.68 \times 10^{36} \) atoms \( , 162.60 \times 10^{28} \) atoms and \( 594.1 k J \)
D . \( 292.68 \times 10^{28} \) atoms \( , 162.60 \times 10^{36} \) atoms and \( 594.1 k J \)
Subject: Maths
The Coefficient of \( x^{53} \) in
\( \sum_{m=0}^{100} C_{m}^{100}(x-3)^{100-m} 2^{m} \) is
\( \mathbf{A} \cdot=-^{100} C_{53} \)
B \( .=-^{101} C_{53} \)
\( \mathbf{C} .=^{101} C_{47} \)
\( \mathbf{D} .=-^{100} C_{47} \)
Subject: Chemistry
Which of the following will act as cathode when connected to standard
hydrogen electrode which has \( \boldsymbol{E}^{0} \) value
given as zero?
¡) \( Z n / Z n+2, E^{0}=-0.76 V \)
ii) \( \boldsymbol{C u}^{+2} / \boldsymbol{C u}, \boldsymbol{E}^{0}=+\mathbf{0 . 3 4} \boldsymbol{V} \)
iii) \( \boldsymbol{A l} / \boldsymbol{A l}^{+3}, \boldsymbol{E}^{0}=-\mathbf{1 . 6 6} \boldsymbol{V} \)
iv \( \mathbf{H} \boldsymbol{g}^{\mathbf{2}+} / \boldsymbol{H} \boldsymbol{g}, \boldsymbol{E}^{\mathbf{0}}=+\mathbf{0 . 8 8 5} \boldsymbol{V} \)
A . i and i i
B. ii and iv
c. i and iii
D. i,ii,iii and iv
Subject: Biology
Which of these steps in Krebs cycle
indicates substrate level
phosphorylation?
A. Conversion of succinic acid to \( \alpha \) -ketoglutaric acid
B. Conversion of succinic acid to malic acid
c. conversion of succinyl CoA to succinic acid
D. Conversion of malic acid to oxaloacetic acid
E. conversion of citric acid to \( \alpha \) -ketoglutaric acid
Subject: Maths
Solution of \( \boldsymbol{y}^{2} \boldsymbol{d} \boldsymbol{x}+\left(\boldsymbol{x}^{2}-\boldsymbol{x} \boldsymbol{y}+\boldsymbol{y}^{2}\right) \boldsymbol{d} \boldsymbol{y}= \)
\( \mathbf{0} \)
A \( \cdot \tan ^{-1}\left(\frac{x}{y}\right)+\log y+c=0 \)
B \( \cdot 2 \tan ^{-1}\left(\frac{x}{y}\right)+\log y+c=0 \)
\( \mathbf{c} \cdot \log y(y+\sqrt{x^{2}+y^{2}})+\log y+c=0 \)
D \cdot \( \log y(y-\sqrt{x^{2}+y^{2}})+\log y+c=0 \)
Subject: Chemistry
Assertion
\( F r C l O_{4}, F r_{2} P t C l_{6} \) are low solubility
compounds of \( \boldsymbol{F r} \)
Reason
\( \boldsymbol{F r} \boldsymbol{C l O}_{4}, \boldsymbol{F r}_{2} \boldsymbol{P t C l}_{6} \) have larger alkali
metal ion.
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 perimeter of a quadrant of a circle of radius \( \frac{7}{2} \mathrm{cm} \) is:
\( \mathbf{A} \cdot 3.5 \mathrm{cm} \)
B. \( 5.5 \mathrm{cm} \)
c. \( 7.5 \mathrm{cm} \)
D. \( 12.5 \mathrm{cm} \)
Subject: Chemistry
IUPAC name of \( \left[\boldsymbol{F e}\left(\boldsymbol{O}_{2}\right)(\boldsymbol{C} \boldsymbol{N})_{4} \boldsymbol{C l}\right]^{4-} \) is :
A. chlorotetracyano dioxoferrate (II) ion
B. Chlorotetracyano peroxoferrate (II) ion
c. chlorotetracyano superoxoferrate (II) ion
D. Tetracyanochloro superoxoferrate (II) ion
Subject: Physics
A potential barrier of \( 0.5 \mathrm{V} \) exists
across a p-njjunction. If the width of depletion layer is \( 10^{-6} m \), then intensity
of electric field in this region will be
A \( .1 \times 10^{6} V / m \)
в. \( 5 \times 10^{5} \mathrm{V} / \mathrm{m} \)
c. \( 4 \times 10^{4} V / m \)
D. \( 2 \times 10^{6} \mathrm{V} / \mathrm{m} \)
Subject: Maths
Find the inverse of the statement," If
\( \triangle A B C \) is equilateral, then it is
isosceles".
\( \mathbf{A} \cdot \) If \( \triangle A B C \) is isosceles, then it is equilateral
B. If \( \triangle A B C \) is not equilateral, then it is isosceles.
C. If \( \triangle A B C \) is not equilateral, then it is not isosceles.
D. If \( \triangle A B C \) is not isosceles, then it is not equilateral.
Subject: Chemistry
Which one of the following arrangements of molecules is correct on the basis of their dipole moments?
A. \( B F_{3}>N F_{3}>N H_{3} \)
B. \( N F_{3}>B F_{3}>N H_{3} \)
c. \( N H_{3}>B F_{3}>N F_{3} \)
D. \( N H_{3}>N F_{3}>B F_{3} \)
Subject: Chemistry
Terpinen \( -4-o l \) is one of the active
ingredients in tea tree oil
What is the molecular formula of
terpinen \( -4- \) ol?
A. \( C_{7} H_{11} \) O
в. \( C_{10} \) Нв \( O \)
c. \( C_{10} \) Н \( _{17} \) O
D. \( C_{10} H_{18} O \)
Subject: Maths
If \( \boldsymbol{A}^{\prime}=\left[\begin{array}{cc}-2 & 3 \\ 1 & 2\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{cc}-1 & 0 \\ 1 & 2\end{array}\right] \)
then find \( (\boldsymbol{A}+\mathbf{2} \boldsymbol{B})^{\prime} \)
Subject: Physics
Force acting on a particle moving in a straight line varies with the velocities of
the particle as \( \boldsymbol{F}=\boldsymbol{K} . \boldsymbol{V} . \) Where \( \boldsymbol{K} \) is
constant. The work done by this force in time \( t \) is
A . \( K V t \)
B. \( K^{2} V^{2} t^{2} \)
c. \( K^{2} V t \)
D. \( K V^{2} t \)
Subject: Physics
When two liquid of same volume but
different densities \( \rho_{1} \) and \( \rho_{2} \) are mixed
together, then the density of the mixture is
A \( \cdot \frac{p_{1}+p_{2}}{2} \)
B . \( p_{1}+p_{2} \)
c. \( \frac{2 p_{1} p_{2}}{p_{1}+p_{2}} \)
D. \( 2 p_{1}+2 p_{2} \)
Subject: Physics
Figure shows two conducting
thin concentric shells of radii \( r \) and \( 3 r \)
The outer shell carries charge \( q \) and the
inner shell is neutral. The amount of
charge that flows from the inner shell to
the earth after the key K is closed is
equal to \( (1 / n)^{t h} \) of the charge on the
outer shell. What is the value of n?
Subject: Physics
At the bottom of a lake where the
temperature is \( \$ \$\{7\} \wedge\{0\} \backslash, \mathrm{C} \$ \$ \) the pressure is 2.8 atmosphere. An air bubble of radius \( 1 \mathrm{cm} \) at the bottom rises to
the surface. Where the temperature is \( \$ \$\{27\} \wedge\{0\} \backslash, \) C\$ \( \$ . \) The radius of the air
bubble at the surface is
A \( \cdot 3^{1 / 3} \)
B. \( 4^{1 / 3} \)
\( \mathbf{c} \cdot 5^{1 / 3} \)
D. \( 6^{1 / 3} \)
Subject: Chemistry
A cylinder is filled with a gaseous mixture containing equal masses of
\( C O \) and \( N_{2} . \) The ratio of their partial
pressure is:
\( \mathbf{A} \cdot P_{N_{2}}=P_{C O} \)
B . \( P_{C O}=0.875 P_{N_{2}} \)
c. \( P_{C O}=2 P_{N_{2}} \)
D. \( P_{C O}=\frac{1}{2} P_{N_{2}} \)
Subject: Maths
There are \( n \) persons sitting in a row. Two of them are selected at random. The
probability that the two selected
persons are not together, is
A \( \cdot \frac{2}{n} \)
в. \( _{1-} \frac{2}{n} \)
c. \( \frac{n(n-1)}{(n+1)(n+2)} \)
D. None of these
Subject: Physics
toppr
Q Type your question
'8
center of the sphere according to the equation \( =C r . \) The diagram also shows
the cross-section of a Gaussian sphere
of radius \( a \) that is concentric with the
charged sphere

Which of the following expresses the
charge enclosed in the Gaussian
sphere?
\( ^{\mathrm{A}} \cdot \frac{2}{3}^{\pi} C a^{3} \)
в \( \cdot \frac{4}{3} \pi C a^{4} \)
c \( \cdot \frac{1}{4} \pi C a^{4} \)
D \( \cdot \pi C a^{4} \)
E \( \frac{4}{15} \pi C a \)
Subject: Chemistry
Among \( \boldsymbol{V}(\boldsymbol{Z}=\mathbf{2 3}), \boldsymbol{C r}(\boldsymbol{Z}=\mathbf{2 4}) \)
\( M n(Z=25) \) and \( F e(Z=26), \) which
will have the highest magnetic
moment?
A. \( V \)
в. \( C r \)
\( c . M n \)
D. \( F e \)
Subject: Physics
The acceleration due to gravity at a depth of \( 1600 k m \) inside the earth is
\( \mathbf{A} \cdot 6.65 \mathrm{ms}^{-2} \)
B. \( 7.35 \mathrm{ms}^{-2} \)
c. \( 8.65 \mathrm{ms}^{-2} \)
D. \( 4.35 \mathrm{ms}^{-2} \)
Subject: Physics
A current carrying ring is placed in a magnetic field. The direction of the field
is perpendicular to the plane of the ring. Which of the following correct for this? This question has multiple correct options
A. There is no net force on the ring
B. The ring will tend to expand
c. The ring will tend to contract
(b) or
D. Either
(c) depending on the directions of the current in the ring and the magnetic field
Subject: Chemistry
For an ideal binary solution \( (A) \) and \( (B) \)
\( \boldsymbol{y}_{A} \) is the mole fraction of \( \boldsymbol{A} \) in vapor
phase. Which of the following plot should be linear?
A \( \cdot P_{\text {total }} \) vs \( y_{A} \)
B. \( P_{\text {total }} \) vs \( y_{B} \)
\( ^{c} \frac{1}{P_{\text {total}}} \) vs \( y_{A} \)
D. \( \frac{1}{P_{\text {total }}} \) vs \( y_{B}+y_{A} \)
Subject: Physics
A substance of mass \( M \) requires a
power input of \( \boldsymbol{P} \) watts to ramain in the
molten state at its melting point. When the power source is turned off, the
sample completely solidifies in time \( t \)
sec. The specific latent heat of fusion of the substance is:
A \( . P t \)
в. \( \frac{P t}{M} \)
c. \( P t M \)
D. \( \frac{P M}{t} \)
Subject: Physics
Assertion
In an ideal thermodynamically reversible process, the energy from work performed by or on the system would be maximized, and that from heat would
be minimized.
Reason
A reversible process is a process whose direction can be "reversed" by inducing infinitesimal changes to some property of the system via its surroundings, while not increasing entropy.
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
Equivalent mass of \( K M n O_{4} \) is equal to
one-fifth of its molecular mass when it
acts as an oxidisng agent in acidic medium.
Reason
Oxidation number of \( M n \) in \( K M n O_{4} \) is
+7
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: Maths
\begin{tabular}{lccccc} 
Size & \( \boldsymbol{6} \) & \( \boldsymbol{7} \) & \( \boldsymbol{8} \) & \( \boldsymbol{9} \) & \( \boldsymbol{1 0} \) \\
No. of Shoes & 4 & 5 & 1 & 2 & 1 \\
\hline
\end{tabular} Find the mode
\( \mathbf{A} \cdot \mathbf{7} \)
\( B . \quad 8 \)
\( \mathbf{C} \cdot \mathbf{6} \)
D. 10
Subject: Physics
A car is traveling at a high speed when it banks into a sharp left turn. Which of the following statements best describes the reason a passenger in the vehicle is pressed outwards against the
right side of the vehicle?
A. The centrifugal force of the circular turn pushes them outwards
B. The centripetal force of the circular turn pushes them outwards
C. The passenger's inertia maintains their velocity through the circular path since objects in motion tend to stay in motion
D. The force of friction between the seat and the passenger does not generates sufficient force
E. The force exerted by the door on the passenger does not exert sufficient force
Subject: Physics
A petite young woman of \( 50 k g \) distributes her weight equally over her high-heeled shoes. Each heel has an area of \( 0.75 \mathrm{cm}^{2} . \) Find the pressure
exerted by each heel? Take \( g=10 m / s^{2} \)
A \( .6 .66 \times 10^{6} P a \)
B . \( 3.33 \times 10^{6} P a \)
c. \( 1.67 \times 10^{6} P a \)
D. \( 4.44 \times 10^{6} \mathrm{Pa} \)
Subject: Maths
Construct \( \Delta P Q R \) such that, \( m \angle P= \)
\( \mathbf{8 0}^{o}, \boldsymbol{m} \angle \boldsymbol{Q}=\mathbf{7} 0^{o}, l(\boldsymbol{Q} \boldsymbol{R})=\mathbf{5 . 7} \boldsymbol{c m} \)
Subject: Physics
Persons A and B are standing on the opposite sides of a \( 3.5 \mathrm{m} \) wide water
stream which they wish to cross. Each one of them has a rigid wooden plank
whose mass can be neglected. However,
each plank is only slightly longer than 3
m. So they decide to arrange them
together as shown in the figure
schematically. With B(mass 17kg) standing, the maximum mass of \( A, \) who can walk over the plank is close to.
A . \( 17 \mathrm{kg} \)
B. \( 65 \mathrm{kg} \)
\( c .80 \mathrm{kg} \)
D. \( 105 \mathrm{kg} \)
Subject: Chemistry
If \( \boldsymbol{K}_{s p} \) for \( \boldsymbol{H} \boldsymbol{g} \boldsymbol{S} \boldsymbol{O}_{4} \) is \( \boldsymbol{6} . \boldsymbol{4} \times 10^{-5}, \) then
solubility of this substance in mole per
\( \boldsymbol{m}^{3} \) is
A \( .8 \times 10^{3} \)
В. \( 6.4 \times 10^{3} \)
c. \( 8 \times 10^{6} \)
D. none of these
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}|, \) then
\( \mathbf{A} \cdot f^{\prime}(0)=0 \)
B. \( f(x) \) has a maximum at \( x=0 \)
\( \mathbf{c} \cdot f(x) \) has a minimum at \( x=0 \)
D. \( f(x) \) has no maximum and not minimum
Subject: Maths
Let \( \boldsymbol{f}:[\mathbf{2}, \mathbf{7}] \rightarrow[\mathbf{0}, \infty] \) be a continuous
and differentiable function. Then, the
value of \( (\boldsymbol{f}(\mathbf{7})- \)
\( f(2)) \frac{(f(7))^{2}+(f(2))^{2}+f(2) \cdot f(7)}{3}, \) is
(where \( c \epsilon(2,7)) \)
\( \mathbf{A} \cdot 3 f^{2}(c) f^{\prime}(c) \)
B. \( 5 f^{2}(c) . f(c) \)
c. \( 5 f^{2}(c) \cdot f^{\prime}(c) \)
D. none of these
Subject: Chemistry
A flask containing 0.5 atm pressure of
\( A_{2}(g), \) some solid \( A B \) added into flask which undergoes dissociation according to :
\[
\boldsymbol{2} \boldsymbol{A} \boldsymbol{B}(\boldsymbol{s}) \rightleftharpoons \boldsymbol{A}_{2}(\boldsymbol{g})+\boldsymbol{B}_{2}(\boldsymbol{g})
\]
\( \boldsymbol{K}_{\boldsymbol{p}}=\mathbf{0 . 0 6} \boldsymbol{a t m}^{2} . \) The total pressure (in
atm) at equilibrium is :
A . 0.70
B. 0.6
c. 0.10
D. none of these
Subject: Physics
A plank with a uniform sphere placed on it rests on a smooth horizontal plane. The plank is pulled to right by a
constant force F. If the sphere does not slip over the plank, then. This question has multiple correct options
A. Both have same acceleration
B. Acceleration of centre of sphere is less than that of the plank
c. work done by friction acting on the sphere is equal to its total kinetic energy
D. Total kinetic energy of the system is equal to work done by the force \( F \)