AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Q Type your question
\( \left.\begin{array}{lll}\mathbf{0} & \mathbf{0} & \mathbf{1}\end{array}\right], \mathbf{i} \mathbf{z}- \)
\( \left[\begin{array}{lll}\mathbf{1} & \mathbf{0} & \mathbf{0} \\ \mathbf{0} & \mathbf{0} & \mathbf{1} \\ \mathbf{0} & \mathbf{1} & \mathbf{0}\end{array}\right], \boldsymbol{P}_{\mathbf{3}}=\left[\begin{array}{lll}\mathbf{0} & \mathbf{1} & \mathbf{0} \\ \mathbf{1} & \mathbf{1} & \mathbf{0} \\ \mathbf{0} & \mathbf{0} & \mathbf{1}\end{array}\right] \)
\( \boldsymbol{P}_{4}=\left[\begin{array}{ccc}0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 1\end{array}\right], P_{5}= \)
\( \left[\begin{array}{lll}0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0\end{array}\right], P_{6}=\left[\begin{array}{lll}0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{array}\right], \) and
\( \boldsymbol{X}=\sum_{\boldsymbol{k}=1}^{6} \boldsymbol{P}_{\boldsymbol{K}}\left[\begin{array}{lll}2 & 1 & 3 \\ 1 & 0 & 2 \\ 3 & 2 & 1\end{array}\right] \boldsymbol{P}_{K}^{T} \)
Where \( P_{K}^{T} \) denotes the transpose of
matrix \( P_{k} \). Then which of the following
option is / are correct?
This question has multiple correct options
A. \( X \) is symmetric matrix
B. The sum of the diagonal entries of \( X \) is 18
c.
If \( X\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right]=\alpha\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right] \) then \( \alpha=30 \)
D. \( X-30 I \) is an invertible matrix
Subject: Maths
\( \lim _{\boldsymbol{x} \rightarrow \mathbf{5}}\left(\frac{\sqrt{1-\cos (2 \boldsymbol{x}-\mathbf{1 0})}}{\sin (\boldsymbol{x}-\mathbf{5})}\right) \)
\( A \cdot-\sqrt{2} \)
B. \( \sqrt{2} \)
c. does not exist
D. none of these
Subject: Chemistry
The outer shell electronic configuration
of \( \operatorname{Gd}(Z=64) \) is:
A \( \cdot 4 f 5 d^{1} 6 s^{2} \)
B \( \cdot 4 f^{8} 6 s^{2} \)
c. \( 4 f^{9} 9 s^{\text {। }} \)
D. \( 4 f^{7} 5 d^{1}^{6} s^{2} \)
Subject: Physics
A particle of mass \( m \) moving in \( x \) direction with speed \( 2 v \) is hit by another
particle of mass \( 2 m \) moving in the \( y \) direction with speed \( v \). If the collisioni is
perfectly inelastic, the percentage of the energy retained by the colliding particles after the collision is close to
A . \( 56 \% \)
B. 80\%
c. \( 35 \% \)
D. 44\%
Subject: Physics
Assertion
The coil in the resistance boxes are
made by doubling the wire.
Reason
Thick wire is required in resistance box.
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 triangle with vertices \( \boldsymbol{A}(\mathbf{0}, \mathbf{0}), \boldsymbol{B}(\mathbf{5}, \mathbf{7}) \) and \( \boldsymbol{C}(\mathbf{9}, \mathbf{5}) \)
B. \( \sqrt{74}+\sqrt{106} \)
c. \( \sqrt{74}+\sqrt{20}+\sqrt{106} \)
D. None of the above
Subject: Chemistry
5 mole of oxygen are heated at constant
volume from \( 10^{\circ} \mathrm{C} \) to \( 20^{\circ} \mathrm{C} \). What will be
the change in the internal energy of gas? The molar heat of oxygen at
constant pressure, \( C_{P}=7.03 \mathrm{cal} \)
\( m o l^{-1} d e g^{-1} \) and \( R= \)
\( 8.31 J \) mol\( ^{-1} d e g^{-1} \)
Subject: Chemistry
Sulphuryl chloride \( \left(\boldsymbol{S} \boldsymbol{O}_{2} \boldsymbol{C l}_{2}\right) \) reacts
with white phosphorus \( \left(P_{4}\right) \) to give:
A. \( P C l_{5}, S O_{2} \)
в. \( O P C l_{3}, S O C l_{2} \)
c. \( P C l_{5}, S O_{2}, S_{2} C l_{2} \)
D. \( O P C l_{3}, S O_{2}, S_{2} C l_{2} \)
Subject: Maths
If the fourth term in the expansion of
\( \left(\sqrt{\frac{1}{x \log x+1}}+x \frac{1}{12}\right)^{6} \) is equal to
200 and \( x>1, \) then \( x \) is
A . 10
B. \( 10^{-4} \)
\( c \cdot 1 \)
D. -4
Subject: Maths
The area of the region bounded by \( x= \)
\( \mathbf{0}, \boldsymbol{y}=\mathbf{0}, \boldsymbol{x}=\mathbf{2}, \boldsymbol{y}=\mathbf{2}, \boldsymbol{y} \leq \boldsymbol{e}^{\boldsymbol{x}} \) and
\( \boldsymbol{y} \geq \ln \boldsymbol{x}, \) is
\( \mathbf{A} \cdot 6-4 \ln 2 \)
B. 4 \ellп \( 2-2 \)
\( c \cdot 2 \ln 2 \)
D. \( 6-2 \) \ellп 2
Subject: Physics
A uniform rod of mass \( m \) and length \( l \)
hinged at its end is released from rest when it is in the horizontal position. The normal reaction at the hinged when the rod becomes vertical is
A \( \cdot \frac{m g}{4} \)
B. 5 \( \frac{-m g}{2} \)
c. \( \frac{m g}{6} \)
\( \stackrel{\mathrm{D}}{-}_{2}^{7} m g \)
Subject: Chemistry
\( N H_{3} \quad P H_{3} \)
The bond angle in \( N H_{3} \) is larger than, in \( P H_{3} \) because the \( P-H \) bonds are
longer and the lower electronegativity of P permits electron-density to be displaced towards hydrogen to a greater
extent than in the case of \( N H_{3} \). Both of these effects diminish the repulsion
due to bond-pairs.
If true enter 1 , else enter 0 .
Subject: Physics
A steel ball of mass 'm' falls in a viscous
liquid with a terminal velocity \( 4 m s^{-1} .1 \)
another steel ball of mass \( 8 \mathrm{m} \) falls
through the same liquid then its terminal velocity is
\( \mathbf{A} \cdot 4 m s^{-1} \)
B. \( 8 m s^{-1} \)
\( \mathrm{c} \cdot 16 \mathrm{ms}^{-1} \)
D. \( 2 m s^{-1} \)
Subject: Biology
Assertion
Stomata are generally open in light and
close in dark
Reason
Transpiration is enhanced by heating
effect of light
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Maths
The domain of the function \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \log _{10} \log _{10}\left(1+x^{3}\right) \) is
A. \( (-1,+\infty) \)
(i) \( (-1,-\infty) \)
B. \( (0,+\infty) \)
\( c \cdot[0,+\infty) \)
D. (-1,0)
Subject: Physics
A particle moves along a circle of a fixed
radius with a variable centripetal
acceleration \( a_{n}=k t^{n}, \) where \( k \) is a
constant and \( t \) is time. If slope of \( \boldsymbol{P}-\boldsymbol{t} \)
graph on log-log scale is \( 2, \) then value of
\( n \) is
(Here, \( P \) is instantaneous power)
A . 1
B. 2
\( c .-1 \)
D. 3
Subject: Chemistry
\( \boldsymbol{E}^{0}\left(\boldsymbol{N} \boldsymbol{i}^{2+} / \boldsymbol{N} \boldsymbol{i}\right)= \)
\( -0.25 v o l t, E^{0}\left(A u^{3+} / A u\right)=1.50 v o l t \)
The standard emf of the voltaic cell.
\( \boldsymbol{N} \boldsymbol{i}_{(s)}\left|\boldsymbol{N} \boldsymbol{i}_{(a q)}^{2+}(\mathbf{1} . \boldsymbol{0} \boldsymbol{M}) \| \boldsymbol{A} \boldsymbol{u}_{(a q)}^{3+}(\mathbf{1} . \boldsymbol{0} \boldsymbol{M})\right| \boldsymbol{A} \boldsymbol{u}_{(s)} \)
is:
A. 1.25 volt
B . - 1.75 volt
c. 1.75 volt
D. 4.0 volt
Subject: Maths
Find the value of \( x \) and \( y \) using cross multiplication method:
\( \boldsymbol{x}+\boldsymbol{y}=\mathbf{0} \) and \( \boldsymbol{x}-\boldsymbol{y}=\mathbf{2} \)
\( A \cdot(1,1) \)
B . (-1,1)
\( c \cdot(1,-1) \)
D. (-1,-1)
Subject: Physics
A charge \( q \) is placed at 0 in the cavity in a spherical uncharged conductor, Point S is outside the conductor. If q is
displaced from 0 towards \( S \) (still
remaining within the cavity)
A . electric field at S will increase
B. electric field at S will decrease
c. electric field at \( S \) will first increase and then decreas
D. electric field at S will not change
Subject: Physics
A solid metal cube of edge length \( 2 \mathrm{cm} \)
is moving in a positive \( y \) direction at a constant speed of \( 6 m / s . \) There is a
uniform magnetic field of \( 0.1 T \) in the
positive \( z- \) direction. The potential
difference between the two faces of the
cube perpendicular to the \( x- \) axis, is:
\( \mathbf{A} \cdot 6 m V \)
B. \( 1 \mathrm{mV} \)
c. \( 12 \mathrm{mV} \)
D. \( 2 m V \)
Subject: Physics
A transformer is used to light a 140 watt, 24 volt lamp from \( 240 V \) AC mains.
The current in the main cable is 0.7
amp. The efficiency of the transformer
is
A . \( 48 \% \)
B . \( 63.8 \% \)
c. \( 83.3 \% \)
D. 90\%
Subject: Maths
Find the slope of the line passing through the following pairs:
\( (-1,2 \sqrt{3}) \) and \( (-2, \sqrt{3}) \)
A. \( \sqrt{3} \)
B. \( 3 \sqrt{3} \)
c. \( \frac{1}{\sqrt{3}} \)
D. \( \frac{\sqrt{3}}{3} \)
Subject: Physics
The mass of earth is 80 times that of
moon. Their diameters are \( 12800 K m \)
and \( 3200 K m \) respectively. The value
of g on moon will be if its
value on earth is \( 980 \mathrm{cm} / \mathrm{s}^{2} \)
A \( \cdot 98 \mathrm{cm} / \mathrm{s}^{2} \)
В \( \cdot 196 \mathrm{cm} / \mathrm{s}^{2} \)
c. \( 100 \mathrm{cm} / \mathrm{s}^{2} \)
D. \( 294 \mathrm{cm} / \mathrm{s}^{2} \)
Subject: Physics
When the sun is directly overhead, the surface of the earth receives \( 1.4 \times \)
\( 10^{3} W m^{-2} \) of sunlight. Assume that the
light is monochromatic with average wavelength \( 500 n m \) and that no light is
absorbed in between the sun and the
earth's surface. The distance between
the sun and the earth is \( 1.5 \times 10^{11} m \) (a)
Calculate the number of photons falling per second on each square metre of
earth's surface directly below the sun
(b) How many photons are there in each cubic metre near the earth's surface at
any instant?
(c) How many photons does the sun emit per second?
Subject: Physics
Gases like
and \( ------ \) are generated in a biogas
plant.
A. Methane \( \left(C H_{4}\right),\left(C O_{2}\right), \) Hydrogen \( \left(H_{2}\right) \) and \( H_{2} S \)
B. Sulphuric acid, \( \left(C O_{2}\right) \), Hydrogen \( \left(H_{2}\right) \) and \( H_{2} S \)
C. Methane \( \left(C H_{4}\right), \) Oxygen, Hydrogen \( \left(H_{2}\right) \) and \( H_{2} S \)
D. methane \( \left(C H_{4}\right), C O_{2}, \) Sulphuric acid and \( H_{2} S \)
Subject: Maths
If the difference between the
circumference and radius of a circle is
\( 37 \mathrm{cm}, \) then the area of the circle is
A \( \cdot 111 c m^{2} \)
В. \( 148 \mathrm{cm}^{2} \)
\( \mathrm{c} \cdot 259 \mathrm{cm}^{2} \)
D. \( 154 \mathrm{cm}^{2} \)
Subject: Physics
A tennis ball has a mass of 57 g and a diameter of \( 7 \mathrm{cm} . \) Find the moment of
inertia about its diameter. Assume the
ball is a thin spherical shell:
A . \( 4.65 \times 10^{-5} \)
В. \( 9.65 \times 10^{-5} \)
c. \( 4.65 \times 10^{-3} \)
D. \( 9.65 \times 10^{-3} \)
Subject: Chemistry
The correct stability order for \( N_{2} \) and its given ions is:
A \( \cdot N_{2}>N_{2}^{+}>N_{2}^{-}>N_{2}^{2-} \)
B . \( N_{2}^{-}>N_{2}^{+}>N_{2}>N_{2}^{2} \)
C \( \cdot N_{2}^{+}>N_{2}^{-}>N_{2}>N_{2}^{2-} \)
D. \( N_{2}>N_{2}^{+}=N_{2}^{-}>N_{2}^{2} \)
Subject: Maths
If \( x^{y}+y^{x}=a^{b} \) then show that \( \frac{d y}{d x}= \) \( -\left[\frac{\boldsymbol{y} \boldsymbol{x}^{\boldsymbol{y}-\mathbf{1}}+\boldsymbol{y}^{\boldsymbol{x}} \log \boldsymbol{y}}{\boldsymbol{x}^{\boldsymbol{y}} \log \boldsymbol{x}+\boldsymbol{x} \boldsymbol{y}^{\boldsymbol{x}-1}}\right] \)
Subject: Maths
If \( g(X)=\frac{x}{[X]} \) for \( X>2 \) then \( \lim _{x \rightarrow 2^{+}} \)
\( \frac{\boldsymbol{g}(\boldsymbol{X})-\boldsymbol{g}(\boldsymbol{2})}{\boldsymbol{X}-\boldsymbol{2}}= \)
A . -
B.
c. \( \frac{1}{2} \)
D.
Subject: Maths
AP and BQ are the bisectors of two
alternate interior angles formed by the
intersection of a transversal t with
parallel lines \( l \) and \( m . \) If \( \angle P A B= \)
\( \boldsymbol{x} \angle \boldsymbol{Q} \boldsymbol{B} \boldsymbol{A} . \) Find \( \boldsymbol{x} \)
Subject: Biology
Assertion
In a terrestrial ecosystem, detritus food chain is a major conduit for energy flow.
Reason

Solar energy is direct source of energy
supply in detritus food 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: Biology
In PS I, the reaction centre Chl a has absorption maxima at whereas in PS II, the reaction centre Chl
a has absorption maxima at
A. \( 700 \mathrm{nm}, 680 \mathrm{nm} \)
B. \( 680 \mathrm{nm}, \) 700nm
c. \( 400 \mathrm{nm}, 500 \mathrm{nm} \)
D. 700 \( \mathrm{nm}, 800 \mathrm{nm} \)
Subject: Maths
If the angle between the lines joining the end points of minor axis of an ellipse with its foci is \( \frac{\pi}{2}, \) then the eccentricity of the ellipse is
A \( \cdot \frac{1}{2} \)
в. \( \frac{1}{\sqrt{2}} \)
c. \( \frac{\sqrt{3}}{2} \)
D. \( \frac{1}{2 \sqrt{2}} \)
Subject: Physics
The plot of velocity vs time of a moving
particle is given above. How do the acceleration and
displacement of the particle at point \( \boldsymbol{B} \) compare to the acceleration and
displacement of the particle at point \( A ? \)
A. Acceleration is less, displacement is less
B. Acceleration is less, displacement is the same
C. Acceleration is less, displacement is greater
D. Acceleration is greater, displacement is less
E. Acceleration is greater, displacement is greater
Subject: Maths
Which of the following statements is
true?
A \( \cdot \frac{-5}{8} \) lies to the left of 0 on the number line
B. \( \frac{3}{7} \) lies to the right of 0 on the number line.
C the rational numbers \( \frac{1}{3} \) and \( \frac{-7}{3} \) are on opposite sides of 0 on the number line
D. All the above
Subject: Physics
500 g of water at \( 100^{\circ} C \) is mixed with \( 300 \mathrm{g} \) at \( 30^{\circ} \mathrm{C} \). Find the temperature of the mixture. Specific heat of water \( = \) \( 4.2 J g^{-1} o C^{-1} \)
A \( .73 .8^{\circ} \mathrm{C} \)
B. \( 53.8^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 40^{\circ} \mathrm{C} \)
D. \( 60^{\circ} \mathrm{C} \)
Subject: Maths
If \( A \) is a \( 2 \times 3 \) matrix and \( B \) is \( 3 \times 2 \)
matrix then the order of \( (A B)^{T} \) is equal
to the order of
\( \mathbf{A} \cdot A B \)
в. \( A^{T} B^{T} \)
\( c . \) ВА
D. All of these
Subject: Chemistry
In compound \( A, 1.0 \) g nitrogen combines with 0.57 g oxygen. In compound \( \mathrm{B}, 2.0 \mathrm{g} \) nitrogen unite with 2.24 g oxygen and in compound \( C, 3.0 \) g nitrogen combine with \( 5.11 \mathrm{g} \) oxygen. These results obey
the law of:
A. multiple proportions
B. constant proportions
C. reciprocal proportions
D. none of these
Subject: Chemistry
What is correct order of rate of nitration
of the following compounds?
\( \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{5}} \boldsymbol{N} \boldsymbol{R}_{\boldsymbol{3}} \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{5}} \boldsymbol{N} \boldsymbol{M} \boldsymbol{e}_{\boldsymbol{2}} \)
\( \boldsymbol{F} \)
\( A \cdot G>A>B>C>D>E>F \)
B. \( G>B>C>D>A>F \)
\( \mathrm{c} \cdot \mathrm{G}>\mathrm{A}>\mathrm{B}=\mathrm{C}=\mathrm{D}>\mathrm{E}>\mathrm{F} \)
D. \( G>A>B>C=D>E>F \)
Subject: Maths
The Sum of three numbers in AP is 75
and product of extremities is \( 609 . \) The numbrs and AM of 1st two numbers is
\( \mathbf{A} \cdot\{21,25,29\}, \) АМ \( =23 \)
B. \( \{13,17,21\}, \) АМ \( =22 \)
c. \( \{21,25,29\}, \) АМ \( =25 \)
D. \( \{21,22,29\}, \) АМ \( =23 \)
Subject: Chemistry
\( C_{2} D_{2} \stackrel{?}{\longrightarrow} C_{2} D_{2} H_{2}(\text { trans }) \)
Give the best reagent for this conversion.
A . \( L i /(a q .) N H_{3} \)
в. \( H_{2} / P d \)
c. \( H_{2} / N i \)
D. None of these
Subject: Physics
Two concentric shells have radii R and
2R, charges \( \boldsymbol{q}_{A} \) and \( \boldsymbol{q}_{B} \) and potentials \( 2 \mathbf{V} \)
and (3/2)V respectively. Now shell B is earthed and let charges on them
become \( \boldsymbol{q}_{A}^{\prime} \) and \( \boldsymbol{q}_{B}^{\prime} . \) Then
This question has multiple correct options
B \( \cdot\left|q_{A}^{\prime}\right| / q_{B}^{\prime} \mid=1 \)
c. Potential of A after earthing becomes (3/2)V
D. Potential difference between A and B after earthing becomes V/2
Subject: Physics
When 5 V potential difference is applied across a wire of length \( 0.1 \mathrm{m} \), the drift speed of electrons is \( 2.5 \times 10^{-4} \)
\( \mathrm{m} / \mathrm{s} . \) If the electron density in the wire is \( 8 \times 10^{28} m^{-3}, \) calculate the resistivity of
the material of the wire.
Subject: Physics
A body is dropped form the top of a tower. It falls through 40 m during the last two seconds of its fall.The height of
tower in \( \mathrm{m} \) is \( \left(\boldsymbol{g}=\mathbf{1 0 m} \boldsymbol{s}^{-2}\right) \)
\( A \cdot 45 \mathrm{m} \)
B. 50 \( m \)
c. \( 60 \mathrm{m} \)
D. 80 \( m \)
Subject: Physics
toppr
Q Type your question
secondary coil, current through the primary coil and input power are given.
(a) Let the given data be taken as \( \frac{N_{1}}{N_{2}} \)
(turn-ratio), \( i_{1}, \) (input current) and \( P \)
(input power).
(b) Substitute the given values of \( \frac{N_{1}}{N_{2}} \)
and \( i_{1}, \) in the above formula and get the
value of \( i_{2} \)
(c) Write the relation between turn-ratio
and the currents as \( \frac{N_{1}}{N_{2}}=\frac{i_{2}}{i_{1}}, \) where \( i_{2} \) is the current in the secondary coil.
(d) Write the relation between input
power and output power in terms of
\( V_{1}, i_{1}, V_{2}, i_{2} \) i.e. \( V_{1} i_{1}=V_{2} i_{2}=P, \) where
\( V_{1} \) and \( V_{2} \) are the voltage in the primary and secondary coils respectively.
(e) Substitute the values of \( i_{2} \) and \( P \) in
the above relation to get the value of \( V_{2} \)
A \( . \) abdce
B. bcade
c. acbde
D. \( d b c a e \)
Subject: Biology
Refer to the given figure and select the
correct option.
A. (A) - Stipe, (B) - Holdfast, (C) - Frond
B. (A) - Frond, (B) - Stipe, (C) - Holdfast
C. (A) - Holdfast, (B) - Frond, (C) - Stipe
D. (A) - stipe, (B) - Frond, (C) - Holdfast
Subject: Physics
A large number of liquid drops, each of radius \( r, \) coalesce to form a single drop
of radius R. The energy released in the process is converted into the kinetic
energy of the big drop so formed. The
speed of the big drop is : \( (T= \) surface tension, \( \rho=\text { density of liquid }) \)
\( ^{\mathbf{c}} \cdot \sqrt{\frac{4 T}{\rho}\left(\frac{1}{r}-\frac{1}{R}\right)} \)
\( \sqrt[n]{\frac{6 T}{\rho}\left(\frac{1}{r}-\frac{1}{R}\right)} \)
Subject: Chemistry
The value of Planck's constant is
\( 6.63 \times 10^{34} \mathrm{Js} . \) The speed of light is \( 3 \times \)
\( 10^{17} \mathrm{nm} s^{1} . \) Which value is closest to the
wavelength in nanometer of a quantum
of light with a frequency of \( 6 \times 10^{15} s^{1} ? \)
A . 10
B. 25
\( c .50 \)
D. 75
Subject: Physics
The internal resistance of a primary cell
is 4 ohm. It generates a current of 0.2 ampere in an external resistance of 2
ohm. The rate at which chemical energy
is consumed in providing the current is
A \( .0 .42 \mathrm{J} / \mathrm{s} \)
B. 0.24 J/
\( c \cdot 5 J / s \)
\( D \cdot 1 J / s \)
Subject: Chemistry
Highest oxidation State of manganese in fluorides is \( +4\left(M n F_{4}\right) \) but highest
oxidation state in oxides is \( +7\left(M n_{2} O_{7}\right) \) because:
A. fluorine is more electronegative than oxygen
B. fluorine does not possess d-orbitals
c. fluorine stabilises lower oxidation state
D. in covalent compounds, fluorine can form single bond only while oxygen forms double bond
Subject: Maths
The two lines \( \boldsymbol{x}=\boldsymbol{m} \boldsymbol{y}+\boldsymbol{n}, \boldsymbol{z}=\boldsymbol{p} \boldsymbol{y}+\boldsymbol{q} \)
and \( \boldsymbol{x}=\boldsymbol{m}^{\prime} \boldsymbol{y}+\boldsymbol{n}^{\prime}, \boldsymbol{z}=\boldsymbol{p}^{\prime} \boldsymbol{y}+\boldsymbol{q}^{\prime} \) are
perpendicular to each other, if
\( \mathbf{A} \cdot m m^{\prime}+p p^{\prime}=1 \)
В \( \cdot \frac{m}{m^{\prime}}+\frac{p}{p^{\prime}}=-1 \)
c. \( \frac{m}{m^{\prime}}+\frac{p}{p^{\prime}}=1 \)
D. \( m m^{\prime}+p p^{\prime}=-1 \)
Subject: Physics
If the racing cars move on a circular road of radius \( 100 \mathrm{m}, \) with a speed of \( 30 \mathrm{m} / \mathrm{s}, \) with an angle of banking equal to 15 degrees, what will be the coefficient of friction for safe driving
A . \( 0 . \)
B. 0.3
\( c \cdot 0.5 \)
D. 0.8
Subject: Physics
If in a plano-convex lens, the radius of curvature of the convex surface is \( 10 \mathrm{cm} \)
and the focal length of the lens is \( 30 \mathrm{cm} \) then the refractive index of the material
fo lens will be
A . 1.5
B. 1.66
c. 1.33
D. 3
Subject: Maths
Find the solution of \( (x+y-1) d y= \)
\( (\boldsymbol{x}+\boldsymbol{y}) \boldsymbol{d} \boldsymbol{x} \)
\( \mathbf{A} \cdot 2(y-x)-\log (2 x-2 y-1)=k \)
B \( \cdot 2(y+x)-\log (2 x+2 y-1)=k \)
\( \mathbf{c} \cdot 2(y-x)-\log (x+2 y-1)=k \)
D \( \cdot 2(y-x)-\log (2 x+2 y-1)=k \)
Subject: Physics
A string of length \( 20 \mathrm{cm} \) and linear
mass density \( 0.4 g / c m \) is fixed at both ends and is kept under a tension of
16 \( N . \) A wave pulse is produced at \( t=0 \)
near an end as shown in figure which travels towards the other end. The string have the shape shown in the figure \( \operatorname{again} \operatorname{in} 2 \times 10^{-x} \) sec. Find \( x \)
\( A \)
B.
\( c \)
D.
Subject: Maths
If \( \boldsymbol{x}+\mathbf{4}=\mathbf{8}, \) then \( \boldsymbol{x}=\mathbf{4}, \) Inverse of the
statement is-
A. If \( x+4=8 \), then \( x \neq 4 \)
B. If \( x+4 \neq 8 \), then \( x \neq 4 \)
c. If \( x+4 \neq 8 \), then \( x=4 \)
D. none of the above
Subject: Physics
I torr is equal to the pressure exerted by
A. \( 1 \mathrm{mm} \) of a mercury column
B. \( \frac{1}{10} \mathrm{mm} \) of a mercury column
C. \( 10 \mathrm{mm} \) of a mercury column
D \( \cdot \frac{1}{5} \mathrm{mm} \) of a mercury column
Subject: Physics
Three objects, A:(a solid sphere), B: (a thin circular disk) and \( \mathrm{C} \) : \( (\mathrm{a} \) circular
ring \( ), \) each have the same mass \( \mathrm{M} \) and radius R. They all spin with the same angular speed \( \omega \) about their own
symmetry axes. The amounts of work
(W) required to bring them to rest, would satisfy the relation.
A \( \cdot W_{B}>W_{A}>W_{C} \)
в. \( W_{C}>W_{B}>W_{A} \)
c. \( w_{A}>W_{C}>W_{B} \)
D. \( W_{A}>W_{B}>W_{C} \)
Subject: Physics
A p-n photodiode is manufactured from
a semiconductor with gap of \( 3.1 \mathrm{eV} \) Which of the following wavelengths can be detected by it?
\( A \cdot 4000 \hat{A} \)
в. 3900 ,
\( c \cdot 4200 \hat{A} \)
D. Both (1) \& (2)
Subject: Maths
Calculate the number of patients in the hospital using step deviation method.
\begin{tabular}{|l|l|l|l|l|}
\hline Rooms & 20 & 30 & 40 & 50 \\
\hline Nübbrof patients & 7 & 14 & 21 & 28 \\
\hline
\end{tabular}
A . 30
в. 40
c. 50
D. 60
Subject: Physics
The density of mercury is \( 13.6 g m / c c \) Convert it into S.I. units:
A \( \cdot 13.6 \times 10^{3} k g / m^{3} \)
B. \( 13.6 \times 10^{2} k g / m^{3} \)
c. \( 13.6 \times 10^{4} k g / m^{3} \)
D. \( 13.6 \times 10^{5} \mathrm{kg} / \mathrm{m}^{3} \)
Subject: Chemistry
The \( p H \) of pure water at \( 25^{\circ} C \) and \( 60^{\circ} C \)
are 7 and 6.5 respectively. HCl gas is
passed through water at \( 25^{\circ} \mathrm{C} \) till the resulting 1 litre solution aquires a \( p H \)
of
3. Now \( 4 \times 10^{-3} \) mole of \( N a C N \) are
added into this solution. Also a fresh
\( 0.1 M H C N \) solution has \( p H 5.1936 \)
Now in the one part of solution obtained after addition of \( N a C N \), one millimole
of \( N a O H \) are added and in the second
part of this solution 0.5 miili mole of
\( H C l \) are added.

The volume of \( H C l \) passed through the
solution at \( 25^{\circ} C \) and 1 atm is :
A. \( 24.46 \mathrm{mL} \)
в. \( 2.446 \mathrm{mL} \)
c. \( 244.6 \mathrm{mL} \)
D. \( 0.2446 \mathrm{mL} \)
Subject: Chemistry
Compound (A) is:
\( \mathbf{A} \)
\[
C H_{3}-\underset{_{C H_{3}}^{\mid}}{C}^{\text {сснз }}-C H_{2} C H_{2} B r
\]
В. \( C H_{3}-\begin{array}{c}C H-C H-C H_{2} B r \\ _{I H_{3}}^{\mid}\end{array} \)
D.
\[
C H_{3}-\underbrace{C}_{C H_{3}}^{\text {СС }}-C_{\text {। }} H-C H_{3}
\]
Subject: Chemistry
The IUPAC name for the complex
compound \( \boldsymbol{L} \boldsymbol{i}\left[\boldsymbol{A l} \boldsymbol{H}_{4}\right] \) is:
A. Lithium aluminium hydride
B. Hydride aluminium lithium (III)
C. Lithium tetrahydridoaluminate (III)
D. Llithium tetrahydridoaluminate (I)