AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Solve \( \tan \theta+\tan 2 \theta+ \)
\( \sqrt{3} \tan \theta \tan 2 \theta=\sqrt{3} \)
A. \( \theta=\frac{n \pi}{3}+\frac{\pi}{3}, n \in Z \)
в. \( \theta=\frac{n \pi}{3}+\frac{\pi}{6}, n \epsilon Z \)
c. \( \theta=\frac{n \pi}{3}+\frac{\pi}{12}, n \in Z \)
D. \( \theta=\frac{n \pi}{3}+\frac{\pi}{9}, n \in Z \)
Subject: Maths
If \( z_{1} \) and \( z_{2} \) be complex numbers such that \( z_{1}+i(\overline{z_{2}})=0 \) and \( \arg \left(\overline{z_{1}} z_{2}\right)=\frac{\pi}{3} \)
Then, \( \arg (\overline{z_{1}}) \) is equal to
A \( \cdot \frac{\pi}{3} \)
B. \( \pi \)
c.
D. \( \frac{5 \pi}{12} \)
E \( \cdot \frac{5 \pi}{6} \)
Subject: Physics
Water is flowing in streamline motion through a horizontal tube. The pressure at a point in the tube is \( \boldsymbol{P} \) where the velocity of flow is \( v . \) At another point,
where the pressure is \( P / 2 \), the velocity
of flow is:
[Density of water \( =\rho \)
A \( \cdot \sqrt{v^{2}+\frac{P}{\rho}} \)
B. \( \sqrt{v^{2}-\frac{P}{\rho}} \)
c. \( \sqrt{v^{2}+\frac{2 P}{\rho}} \)
D. \( \sqrt{v^{2}-\frac{2 P}{\rho}} \)
Subject: Physics
A hockey player receives a corner shot
at a speed of \( 15 \mathrm{m} / \mathrm{s} \) at angle \( 30^{\circ} \) with \( \mathrm{y} \)
axis and then shoots the ball along \( x \)
axis with the speed \( 30 \mathrm{m} / \mathrm{s} \). If the mass
of the ball is 150 g and it remains in contact with the hockey stick for 0.01 s, the force exerted on the ball along \( x \)
axis is :
\( A \cdot 281 \mathrm{N} \)
B. 187.5
c. \( 562.5 \mathrm{N} \)
\( D .3 \)
Subject: Physics
The moment of inertia of a circular disc
of radius \( 2 m \) and mass \( 1 k g \) about an
axis passing through its centre of mass
and perpendicular to plane is \( 2 k g-m^{2} \)
Its moment of inertia about an axis
parallel to this axis and passing through its edge in \( k g-m^{2} \) is
A . 10
B. 8
\( c \cdot 6 \)
D. 4
Subject: Chemistry
Calculate the difference between heat of
combustion of carbon monoxide gas at
constant pressure and at constant
volume at \( 27^{\circ} \mathrm{C} ?\left(\mathrm{R}=2 \text { cal. } K^{-1} \mathrm{mol}^{-1}\right. \)
\( \mathbf{A} \cdot 54 \mathrm{cal} \)
B. 600 call
c. -300 cal
D. 27 cal
Subject: Physics
An iron ball of mass \( \boldsymbol{m}=\mathbf{5 0} \boldsymbol{g} \) falls from
a height of \( h_{1}=5 m \) and rises upto
\( h_{2}=2 m \) after colliding with the
horizontal surface. If the time of the
glass half is \( \Delta t=0.02 s, \) find the
average contact force exerted on the ball by the horizontal surface.
Subject: Maths
A regular polygon with 4 sides has area:
\( \mathbf{A} \cdot \) length \( \times \) breadth
B. (side) \( ^{2} \)
C. \( \frac{\sqrt{3}}{4}(\text { side })^{2} \)
D \( \cdot \frac{1}{2}(\text { sum of two parallel sides }) \)
Subject: Physics
Assertion
An object from a greater height reaches a steady terminal velocity.
Reason
The viscous forces on a body depends upon its velocity. The greater the velocity the greater is the viscous force.
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: Physics
Assertion
Two thin blankets put together are warmer than a single blanket of double the thickness.
Reason
Air gets trapped between two blanket which is a bad conductor of heat.
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: Physics
Calculate the electrostatic potential
energy of an electron-proton system of hydrogen atom. In the first Bohr orbit of hydrogen atom, the radius of the orbit is \( 5.3 \times 10^{-11} m \)
A. \( -4.35 \times 10^{-18} \mathrm{J} \)
В. \( -2.175 \times 10^{-18} \mathrm{J} \)
c. \( -4.35 \times 10^{-19} J \)
D. \( -2.175 \times 10^{-19} \mathrm{J} \)
Subject: Maths
If the roots of the equation \( x^{2}-15- \)
\( \boldsymbol{m}(\mathbf{2} \boldsymbol{x}-\mathbf{8})=\mathbf{0} \) are equal, then \( \boldsymbol{m}= \)
A. 3,-5
в. 3,5
c. -3,5
D. -3,-5
Subject: Chemistry
Amount of zinc deposited when \( 3.01 \times \)
\( 10^{20} \) electrons pass through \( Z n S O_{4} \)
solution is:
A . \( 16.35 g \)
B . \( 16.375 \times 10^{-3} g \)
c. \( 32.7 \times 10^{-3} g \)
D. 32.7g
Subject: Physics
The topmost and bottom most
velocities of a disc are \( v_{1} \) and \( v_{2} \) in the
same direction. The radius is R. What is
the angular velocity of the disc
A \( \cdot \frac{\left(v_{1}-v_{2}\right)}{R} \)
в. \( \frac{\left(v_{1}-v_{2}\right)}{2 R} \)
c. \( \frac{\left(v_{1}+v_{2}\right)}{2 R} \)
D. \( _{\text {a }} \frac{\left(v_{1}+v_{2}\right)}{R} \)
Subject: Chemistry
Match the items in column-I with those
in column - II
\begin{tabular}{lllll} 
& Column I & & Column II \\
& & & \\
1. & Electric Fuse & A & Chemical Effect \\
\hline 2. & Relay & B & Electric Discharge \\
3. & CFL & C & Magnetic effect \\
4. & Button Cell & D & Heating Effect
\end{tabular} Which of the following shows the correct
matching?
\( A \cdot 1-C, 2-B, 3-A, 4-D \)
B. \( 1-B, 2-A, 3-C, 4-D \)
c. \( 1- \) D, \( 2-c, 3-B, 4-A \)
D. \( 1- \) D, \( 2-B, 3-C, 4-A \)
Subject: Physics
A parallel plate capacitor has two square plates with equal and opposite charges. The surface charge densities
on the plate are \( +\sigma \) and \( -\sigma \)
respectively. In the region between the plates the magnitude of electric field is:
A \( \cdot \frac{\sigma}{2 \varepsilon_{0}} \)
в. \( \frac{\sigma}{\varepsilon_{0}} \)
\( c \cdot 0 \)
D. none of these
Subject: Chemistry
In a fuel cell \( H_{2} \) and \( O_{2} \) react to produce
electricity. In the process \( H_{2} \) gas is
oxidised at the anode and \( O_{2} \) is reduced
at the cathode. If 67.2 litre of \( H_{2} \) at
NTP reacts in 15 minute, what is the
average current produced? If the entire current is used for electro-deposition of \( C u \) from \( C u^{2+}, \) how many \( g \) of \( C u \) are deposited?
Subject: Physics
A cell of emf \( E \) is connected across a
resistance \( R \). The potential difference
across the terminals of the cell is \( V \)
What is the internal resistance of the
cell?
A \( \cdot E-\frac{V}{R} \)
в. \( \frac{E-V}{V} \)
c. \( \frac{E-V}{R} \times V \)
D. \( \frac{E-V}{V} \times R \)
Subject: Physics
Calculate the neutrons ratio for the
isotopes \( \boldsymbol{O}^{\mathbf{1 6}} \) and \( \boldsymbol{O}^{\mathbf{1 8}} \)
This question has multiple correct options
\( A \cdot 8: 10 \)
B. 4: 5
\( c \cdot 9: 8 \)
\( D \cdot 1: 1 \)
Subject: Chemistry
\( 5 \mathrm{g} \) of a polymer of molar mass \( 50 k g m o l^{-1} \) is dissolved in \( 1 d m^{3} \)
solution. The height of solution \( (m m) \) that will represent its osmotic pressure if density of solution at
equilibrium is \( 0.96 \mathrm{kg} \mathrm{dm}^{-3} \) is (divide
answer by 5 and write nearest integer value).
Subject: Physics
The magnitude of electric force on \( 2 \mu c \)
change placed at the centre \( O \) of two
equilateral triangle each of side \( 10 \mathrm{cm} \)
as shown in figure is \( P \). If charge
\( A, B, C, D, E \& F \) are
\( 2 \mu c, 2 \mu c, 2 \mu c,-2 \mu c,-2 \mu c,-2 \mu c \)
respectively, then \( \boldsymbol{P} \) is:
A . \( 21.6 N \)
B. \( 64.8 N \)
\( c \)
D. \( 43.2 N \)
Subject: Physics
A car starts from rest and is uniformly
accelerated to a speed of \( 30 \mathrm{m} / \mathrm{s} \) in \( 6 \mathrm{s} \)
What is the distance travelled by the
car?
\( A \cdot 5 \) n
B. 30
\( c \cdot 90 \)
D. \( 180 \mathrm{m} \)
Subject: Physics
The water equivalent of a copper
calorimeter is 4.5 g. If specific heat of
copper is \( 0.09 c a l / g /^{0} C, \) then \( \left(L_{f}=\right. \)
\( 80 c a l / g m \)
This question has multiple correct options
A. Mass of the calorimeter is \( 0.5 \mathrm{kg} \)
B. Thermal capacity of the calorimeter is \( 4.5 \mathrm{cal}^{0} / \mathrm{C} \)
C. The heat required to raise the temperature of the calorimeter by \( 8^{0} C \) will be 36 cal.
D. Heat required to melt \( 15 \mathrm{gm} \) of ice at \( 0^{\circ} \mathrm{C} \) Placed in the calorimeter will be 1200 cal
Subject: Physics
A horizontal circular loop carries a
current that looks clockwise when
viewed from above. It is placed by an equivalent magnetic dipole consisting
of a south pole \( S \) and a north pole \( N \)
This question has multiple correct options
A. The line \( S N \) should be along a diameter of the loop.
B. The line \( S N \) should be perpendicular to the plane of the loop.
C. The south pole should be below the loop.
D. The north pole should be below the loop.
Subject: Maths
and \( m \) are two parallel lines
intersected by another pair of paralle
lines \( p \) and \( q . \) Then
A. \( \triangle A B C \cong \triangle C D A \)
B. \( \triangle A B C \cong \triangle A D C \)
c. \( \triangle A B C \cong \triangle D C A \)
\( \triangle A B C \cong \triangle C A D \)
Subject: Maths
One diagonal of a square is the portion of \( \frac{x}{97}+\frac{y}{79}=1 \) intercepted between
the axes. \( \boldsymbol{p}_{1}, \boldsymbol{p}_{2} \) are the lengths of the perpendiculars from the vertices of the other diagonal on the axis of \( y \) then \( p_{1}^{2}+p_{2}^{2} \) is equal to
Subject: Physics
Water flows through two identical tubes
\( A \) and \( B . A \) volume \( V_{0} \) of water passes
through the tube \( A \) and \( 2 V_{0} \) through \( B \)
in a given time. Which of the following may be correct?
This question has multiple correct options
A. Flow in both the tubes are steady
B. Flow in both the tubes are turbulent
c. Flow is steady in \( A \) but turbulent in \( B \)
D. Flow is steady in \( B \) but turbulent in \( A \)
Subject: Chemistry
Fill in the blanks.
\begin{tabular}{llll} 
S.No. & Molecular formula & Common name & IUPA nam \\
\hline \( 1 . \) & \( \mathrm{CH}_{3} \mathrm{COOH} \) & \( \ldots \) & Ethan acid \\
\hline \( 2 . \) & \( \mathrm{HCHO} \) & Formaldehyde & \( \ldots \) \\
\hline
\end{tabular}
Subject: Maths
\[
\begin{array}{lllll}
X=x & -2 & -1 & 0 & 1 \\
P(X= & 0.1 & K & 0.2 & 2 K
\end{array}
\]
\( x) \)
is the probability distribution of random variable \( X \). Find the value of \( K \)
and variance of \( \boldsymbol{X} \)
Subject: Maths
A and \( \mathrm{B} \) are the centres of two circles
that just touch each other at \( P \) If \( A \) is
\( (4,1), B \) is (2,2) and the radii of the
circles are 2 and 3 respectively then \( P \)
has coordinates
\( A \cdot(4,3) \)
B. (3,3)
\( c \cdot(16 / 5,7 / 5) \)
D. \( (4 / 5,4 / 5) \)
Subject: Physics
A circular coil of radius \( R \) carries an
electric current. The magnetic field due to the coil at a point on the axis of the coil located at a distance \( r \) from the
centre of the coil, such that \( r>>R \)
varies as
A. \( 1 / r \)
B . \( 1 / r^{3 / 2} \)
c. \( 1 / r^{2} \)
D. \( 1 / r^{3} \)
Subject: Maths
ff \( \boldsymbol{f}: \boldsymbol{R}-\{\mathbf{0}\} \rightarrow \boldsymbol{R} \) is defined by
\( f(x)=x^{3}-\frac{1}{x^{3}} \) then show that \( f(x)+ \)
\( \boldsymbol{f}\left(\frac{1}{x}\right)=\mathbf{0} \)
Subject: Biology
The nucleus of a diploid organism
contains 3 ng of DNA in \( G_{1} \) phase. Which
one of the following statements describes the state of the cell at the end
of S phase?
A. The nucleus divides into two, and each nucleus contains 3 ng of DNA.
B. The nucleus does not divide, and it contains 3 ng of DNA.
c. The nucleus divides into two, and each nucleus contains \( 1.5 \mathrm{ng} \) of DNA
D. The nucleus does not divide, and it contains 6 ng of DNA.
Subject: Physics
Which statement defines force?
A. When a force acts on a body that is free to move, the force is the product of the mass of the body and its acceleration
B. When a force acts on a body that is free to move, the force is the rate of change of momentum of the body
C. When a force acts on a body that is free to move, the force is the work done by the force divided by the distance moved by the body
D. When a force acts on a lever and causes a moment, the force is the moment divided by the perpendicular distance of the force from the pivot
Subject: Maths
What is the general solution of the
differential equation \( x^{2} d y+y^{2} d x=0 ? \)
A. \( x+y=c \) where \( c \) is the constant of integration
B. \( x y=c \) where \( c \) is the constant of integration
c. \( c(x+y)=x y \) where \( c \) is the constant of integration
D. None of the above
Subject: Chemistry
For \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3} \) and \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4}, \) the correct
choice is
A \( \cdot H_{3} P O_{3} \) is dibasic and reducing agent
B. \( H_{3} P O_{3} \) is dibasic and non-reducing agent
\( \mathrm{c} \cdot H_{3} P O_{4} \) is tribasic and reducing agent
D. \( H_{3} P O_{3} \) is tribasic and non-reducing agent
Subject: Maths
Let \( A B C D \) be a parallelogram and let \( L \) and \( \mathrm{M} \) be the midpoints of the sides \( B C \) and \( C D \) respectively. Then \( \overrightarrow{A L}+ \) \( \boldsymbol{A} \overrightarrow{\boldsymbol{M}}= \)
\( A \cdot \overrightarrow{A C} \)
В \( \cdot \frac{2}{3} \overrightarrow{A C} \)
c. \( \frac{3}{2} \overrightarrow{A C} \)
D. \( 2 A C \)
Subject: Maths
If 400 dollars is deposited in a bank account for 4 years at \( 8 \% \) per annum. Compare interest using simple interest formula and compound interest formula

This question has multiple correct options
A . \( \mathrm{Cl}=144.195 \)
B. \( \mathrm{S} 1=200 \)
c. \( \mathrm{c} 1>\mathrm{s} \)
D. SI <C
Subject: Chemistry
Assertion
If \( \boldsymbol{\lambda}_{N a^{+}}^{\circ} \) and \( \boldsymbol{\lambda}_{C l^{-}}^{\circ} \) are molar limiting
conductivity of sodium and chloride ions respectively, then the limiting
molar conductivity for sodium chloride
is given by the equation: \( \wedge_{N a C l}^{\circ}= \) \( \boldsymbol{\lambda}_{N a^{+}}^{\circ}+\boldsymbol{\lambda}_{C l^{-}}^{\circ} \)
Reason
This is according to Kohlrausch law of independent migration of ions.
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
A sum of Rs. 1550 was lent partly at \( 5 \% \) and partly at \( 8 \% \) p.a. simple interest. The total interest received after 3 years
was Rs. 300. The ratio of the money lent
at \( 5 \% \) to that of lent at \( 8 \% \) is
A . 5: 8
B. 8: 5
c. 16: 15
D. 31: 6
Subject: Chemistry
\( X e F_{6} \) on partial hydrolysis with water
produces a compound \( X \). The same
compound \( X \) is formed when \( X e F_{6} \)
reacts with silica. The compound \( \boldsymbol{X} \) is:
A. \( X e F_{2} \)
в. \( X e F_{4} \)
\( \mathrm{c} \cdot_{X e O_{3}} \)
D. \( X e O F_{4} \)
Subject: Maths
In the given figure, \( \boldsymbol{T} \boldsymbol{T}^{\prime} \) is the tangent
line. Which one of the following
relationship is true?
\( \mathbf{A} \cdot x+y=2 z \)
B . \( x+y=z \)
c. \( z-3 x=y \)
D. \( z-2 x=y \)
Subject: Chemistry
The position of both, an electron and a range of helium atom is known within
1.0 \( n m . \) Further the momentum of the
electron is known within a range of \( \mathbf{5 . 0} \times \mathbf{1 0}^{-\mathbf{2 6}} \mathbf{k g} \mathbf{m s}^{-1} . \) The minimum
uncertainty in the measurement of the
momentum of the helium atom is:
A. \( 50 \mathrm{kg} \mathrm{ms}^{-1} \)
B. \( 80 \mathrm{kg} \mathrm{ms}^{-1} \)
c. \( 80 \times 10^{-26} \) kg \( m s^{-1} \)
D. \( 5 \times 10^{-26} \mathrm{kg} \mathrm{ms}^{-1} \)
Subject: Physics
A step-up transformer operates on a \( 230 \mathrm{V} \) line and a load current of \( 2 \mathrm{A} \). The ratio of primary and secondary
windings is \( 1: 25 . \) Then the current in
the primary is?
A . 25 A
B. 50 A
c. 15 A
D. 12.5 A
Subject: Physics
For Bragg's diffraction by a crystal to occur, then which of the following is
correct for the X-ray of wavelength \( \lambda \)
and interatomic distance d:
A . \lambda is greater than \( 2 d \)
B. \lambdaequals \( 2 d \)
c. \( \lambda \) is smaller than or equal to \( 2 d \)
D. \lambda is smaller than \( 2 d \)
Subject: Maths
\( \operatorname{lf}\left|\begin{array}{lll}\boldsymbol{x}_{1} & \boldsymbol{y}_{1} & \mathbf{1} \\ \boldsymbol{x}_{2} & \boldsymbol{y}_{2} & \mathbf{1} \\ \boldsymbol{x}_{3} & \boldsymbol{y}_{3} & \mathbf{1}\end{array}\right|=\left|\begin{array}{lll}\boldsymbol{a}_{1} & \boldsymbol{b}_{1} & \mathbf{1} \\ \boldsymbol{a}_{2} & \boldsymbol{b}_{2} & \mathbf{1} \\ \boldsymbol{a}_{3} & \boldsymbol{b}_{3} & \mathbf{1}\end{array}\right| \) then the
two triangles with vertices \( \left(x_{1}, y_{1}\right),\left(x_{2}, y_{2}\right),\left(x_{3}, y_{3}\right) \) and
\( \left(a_{1}, b_{1}\right),\left(a_{2}, b_{2}\right),\left(a_{3}, b_{3}\right) \) are
A . equal in area
B. similar
c. congruent
D. none of these
Subject: Chemistry
On mixing, heptane and octane form an ideal solution. At \( 373 \mathrm{K} \), the vapour pressure of the two liquid components (heptane and octane) are \( 105 \mathrm{kPa} \) and
45 kPa respectively. Vapour pressure of the solution obtained by mixing 25 g of heptane and 35 g of octane will be :
(molar mass of heptane \( =100 \) g \( m o l^{-2} \) and of octane \( =114 \) g \( m o l^{-1} \)
A \( .96 .2 k P a \)
в. \( 144.5 k P a \)
c. \( 72 k P a \)
D. \( 36.1 k P a \)
Subject: Chemistry
The pH of a solution of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) is 6.0
Some chloride gas is bubbled into this solution. Which of the following is correct?
A. The pH of the resultant solution is less than 6.0 and \( 0 x \)
B. The pH of the resultant solution is less than 8.0
c. \( C l O_{2} \) will be formed in the resultant solution
D. None of these
Subject: Chemistry
Formation of polyethylene from calcium carbide takes place is follows:
\( \boldsymbol{C a C}_{2}+\mathbf{2 H _ { 2 }} \boldsymbol{O} \rightarrow \boldsymbol{C a}(\boldsymbol{O H})_{2}+\boldsymbol{C}_{2} \boldsymbol{H}_{2} \)
\( \boldsymbol{C}_{2} \boldsymbol{H}_{2}+\boldsymbol{H}_{2} \rightarrow \boldsymbol{C}_{2} \boldsymbol{H}_{4} \)
\( \boldsymbol{n} \boldsymbol{C}_{2} \boldsymbol{H}_{4} \rightarrow+\boldsymbol{C} \boldsymbol{H}_{2}-\boldsymbol{C} \boldsymbol{H}_{2}+\boldsymbol{n} \)
The amount of polyethylene obtained from \( 64.0 \mathrm{kg} \) of \( \mathrm{CaC}_{2} \) is:
\( A \cdot 27 \mathrm{kg} \)
в. \( 24 \mathrm{kg} \)
c. \( 22 \mathrm{kg} \)
D. \( 28 \mathrm{kg} \)
Subject: Chemistry
Which two orbitals are located along the
axis, not between the axis?
\( \mathbf{A} \cdot d_{x^{2}-y^{2}}, d_{z^{2}} \)
B . \( d_{x y}, p_{z} \)
\( \mathbf{c} \cdot d_{y z}, p_{x} \)
D \( \cdot p_{x}, d_{x^{2}-y^{2}} \)
Subject: Chemistry
Reaction \( \boldsymbol{A}+\boldsymbol{B} \longrightarrow \boldsymbol{C}+\boldsymbol{D} \) follow's
following rate law rate \( =\boldsymbol{k}=[\boldsymbol{A}]^{\frac{1}{2}}[\boldsymbol{B}]^{\frac{1}{2}} \)
Starting with initial conc. of one mole of
\( A \) and \( B \) each, what is the time taken for
amount of A of become 0.25 mole. Given
\( k=2.31 \times 10^{-3} s e c^{-1} . \) (in sec). (Answer
in the form of \( 100 x \) )
Subject: Maths
Sum of the series \( 4+6+9+13+ \)
\( 18+\ldots \) to \( n \) terms be \( = \)
\( \frac{\boldsymbol{n}}{\boldsymbol{k}}\left(\boldsymbol{n}^{2}+\boldsymbol{3} \boldsymbol{n}+\boldsymbol{m}\right) \cdot \) Find \( \boldsymbol{m}-\boldsymbol{k} ? \)
Subject: Physics
toppr OG
Q Type your question_
is \( 50^{\circ} \mathrm{C} \) and \( 15 \Omega \) respectively The rate of
change of resistance \( R \) with temperature \( \frac{1}{2} \Omega /^{\circ} C \) and rate of decrease of temperature of \( R \) is \( \frac{(e n 3)}{100} \)
times the temperature difference from
surrounding Assume the resistance \( R \)
loses heat only in accordance with
newton's law of cooling If key k is closed
at \( t=0 \) then choose the incorrect option
A. The value of R for which power dissipation in it is maximum is \( 5 \Omega \)
B. Temperature of R when power dissipation in it is maximum is \( 30^{\circ} \mathrm{C} \)
C. Time after which power dissipation in it is maximum is 100 sec
D. Current throughout 10 v battery when power dissipation in \( R \) is maximum is 2.5 A
Subject: Physics
The cubical container ABCDEFGH which
is completely filled with an ideal (nonviscous and incompressible) fluid,
moves in a gravity free space with a acceleration of \( \boldsymbol{a}=\boldsymbol{a}_{0}(\hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}) \)
where \( a_{0} \) is a positive constant. Then,
the pressure will be minimum at point:
\( A \)
B.
\( c \)
2
Subject: Chemistry
Assertion
A rate of reaction of most of the
reactions doubles, when temperature
increased from \( 298 K \) to \( 308 K \)
Reason

The activation energy of reaction
decreases with increase in
temperature.
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 equation to the sides \( A B, B C, C A \)
of a \( \triangle \operatorname{are} \boldsymbol{x}+\boldsymbol{y}=\mathbf{1} ; \mathbf{4} \boldsymbol{x}-\boldsymbol{y}+\mathbf{4}= \) and
\( 2 x+3 y=6 . \) Circle are drawn on
\( A B, B C, C A \) as diameter. The point of
concurrence of the common chord is
A. centroid of the triangle
B. orthocenter
c. circumcenter
D. incenter
Subject: Chemistry
A gas absorbs \( 250 J \) of heat and
expands from 1 litre to 10 litre at constant temperature against external
pressure of 0.5 atm. The values of \( q, w \) and \( \triangle \boldsymbol{U} \) will be respectively:
A. \( -250 J, 455 J, 710 J \)
\( J \)
В. \( 250 J,-455 J,-205 J \)
c. \( -250 J,-455 J,-205 J \)
D. \( -250 J, 455 J, 205 J \)
Subject: Physics
E. Negative temperature
A. Hole \( \quad \) coefficient of resistance
B. Copper
F. Energy vacancy
G. Positive temperature coefficient
C. Doping \( \quad \) of resistance
H. Addition of impurity to increase
D. \( \quad \) the conductivity Germanium
Charges are holes and electrons
Match the above lists:
\( A \cdot A-H, I B-E C-F D-G \)
B. A-E B-F,I C-G D-H
C \( . \) A-F B-G C-H D-E,
D. A-G,I B-H C-E D-F
Subject: Chemistry
1 mole of \( H_{2}, 2 \) moles of \( I_{2} \) and 3 moles
of \( H I \) were taken in a 1 litre flask. The
equilibrium constant of the reaction \( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{I}_{2}(\boldsymbol{g}) \rightleftharpoons 2 \boldsymbol{H} \boldsymbol{I}(\boldsymbol{g}) \) is 50 at
\( 330^{\circ} \mathrm{C} . \) The concentration of \( \mathrm{HI} \) at
equilibrium is (moles.lit \( ^{-1} \) ):
A . 0.3
в. 1.3
c. 4.4
D. 2.
Subject: Maths
Identify the rational numbers represented by \( \mathrm{B}, \mathrm{C} \) and \( \mathrm{D} \) if \( \mathrm{AB}=\mathrm{CD}=\mathrm{DE} \)
as drawn on the number line.
\[
\begin{array}{|c|c|c|}
\hline E D & C & A \\
\hline-2 & 0 & 2 \\
\hline
\end{array}
\]
A. 0,-1,-2
в.
\[
\frac{-1}{2},-1, \frac{-3}{2}
\]
c.
\[
\frac{1}{2}, 1, \frac{3}{2}
\]
D.
\[
\frac{-1}{4},-1, \frac{-5}{2}
\]
Subject: Chemistry
Assertion
Fluorine is most electronegative
element.
Reason
Fluorine can form only ionic bond.
A. Both Assertion and Reason are true and Reason is the
correct explanation for Assertion
B. Both Assertion and Reason are true but Reason is not
the correct explanation for Assertion
C. Assertion is true statement but Reason is false
D. Both Assertion and Reason are false statement.
Subject: Maths
If \( f(x) \) is a polynomial satisfying
\( \boldsymbol{f}(\boldsymbol{x}) \boldsymbol{f}\left(\frac{1}{x}\right)=\boldsymbol{f}(\boldsymbol{x})+\boldsymbol{f}\left(\frac{1}{x}\right), \operatorname{and} \boldsymbol{f}(\boldsymbol{3})=\mathbf{8} \mathbf{2} \)
then \( \int \frac{f(x)}{x^{2}+1} d x= \)
A \( \cdot x^{3}-x+2 \tan ^{-1} x+c \)
B. \( \frac{1}{3} x^{3}-x+\tan ^{-1} x+c \)
c. \( \frac{x^{3}}{3}-x+2 \tan ^{-1} x+c \)
D. \( \frac{1}{3} x^{3}+x+2 \tan ^{-1} x+c \)