AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A new temperature scale uses \( X \) as a
unit of temperature, where the
numerical value of the temperature \( t_{x} \)
in this scale is related to the absolute
temperature \( T \) by \( t_{x}=3 T+300 . \) If the
specific heat of a material using this
unit is \( 1400 \mathrm{Jkg}^{-1} \mathrm{X}^{-1} \) its specificne in
the S.I. system of units is
A. \( 4200 \mathrm{Jkg}^{-1} \mathrm{K}^{-1} \)
B. \( 1400 \mathrm{J} \mathrm{kg}^{-1} \mathrm{K}^{-1} \)
\( \mathbf{C} \cdot 466.7 \mathrm{J} \mathrm{kg}^{-1} \mathrm{K}^{-1} \)
D. impossible to determine from the information provided
Subject: Chemistry
Identify the hybridisation of underline \( \operatorname{atom} \operatorname{in} \boldsymbol{H}_{3} \boldsymbol{O}^{+} \)
\( \mathbf{A} \cdot s p \)
B . \( s p^{2} \)
\( c \cdot s p^{3} \)
D. \( d^{2} s p^{3} \)
Subject: Chemistry
Select the correct I.U.P.A.C. name for the
following complex:
This question has multiple correct options
A. di bromidoplatinum(II)bis- - \( \mu \) -(dimethylthioether)
dibromidoplatinum(II)
B. bisf \( \mu \) (dimethylthioether)dibromidoplatinum(II))
C. bis- \( \mu \) -dimethylthioethertetrabromidodiplatinum(II)
D. bis-f.L-dimethylthioethertetrabromidodiplatinate(II)
Subject: Chemistry
Trans-1,2-dideuterocyclopropane
\( (\boldsymbol{A}) \)
undergoes a first-order decomposition. The observed rate constant at a certain
temperature measured in terms of
disappearance of ' \( \boldsymbol{A} \) ' has \( 1.52 \times \) \( 10^{-4} s e c^{-1} . \) Analysis of products showed
that the reaction followed two parallel paths, one leading to dideuteropropane
\( (B) \) and the other to cis- 1,2
dideuterocyclopropane \( (C) .(B) \) was
found to constitute \( 11.2 \% \) of the
reaction product, independently of the extent of reaction. What is the order of
reaction for each path and what is the
value of the rate constant for the
formation of each of the products?
Subject: Physics
A broadcasting station transmits waves
of frequency \( 71 \times 10^{4} H z \) with a speed
of \( 3 \times 10^{8} m / s . \) The wavelength of the
wave is :
A \( .418 .8 m \)
в. \( 324.6 m \)
c. \( 208.4 m \)
D. \( 422.5 \mathrm{m} \)
Subject: Chemistry
The correct sequences of reagents for
the following conversation will be:
A \( \cdot C H_{3} M g B r, H^{+} / C H_{3} O H,\left[A g\left(N H_{3}\right)_{2}\right]^{+} O H \)
B. \( C H_{3} M g B r,\left[A g\left(N H_{3}\right)_{2}\right]^{+} O H^{-}, H^{+} / C H_{3} O H \)
c. \( \left[A g\left(N H_{3}\right)_{2}\right]^{+} O H^{-}, C H_{3} M g B r, H^{+} / C H_{3} O H \)
\( \mathrm{D} \cdot\left[A g\left(N H_{3}\right)_{2}\right]^{+} O H^{-}, H^{+} / C H_{3} O H, C H_{3} M g B r \)
Subject: Physics
The equation of motion for an oscillating particle is given by
\( \boldsymbol{x}=\boldsymbol{3} \sin (\boldsymbol{4} \boldsymbol{\pi} \boldsymbol{t})+\boldsymbol{4} \cos (\boldsymbol{4} \boldsymbol{\pi} \boldsymbol{t}), \) where \( \boldsymbol{x} \) is
in mm and t is in second
This question has multiple correct options
A. The motion is simple harmonic
B. The period of oscillation is 0.5 s
c. The amplitude of oscillation is \( 5 \mathrm{mm} \)
D. The particle starts its motion from the equilibrium
Subject: Physics
The distance between two points
differing in phase by \( 60^{\circ} \) on a wave
having a wave velocity \( 360 m / s \) and frequency \( 500 H z \) is
A . \( 0.72 \mathrm{m} \)
B. \( 0.18 m \)
c. \( 0.12 m \)
D. 0.36 m
Subject: Physics
Figure shows three concentric thin
spherical shells \( A, B, \) and \( C \) of radii \( R \)
\( 2 R, \) and \( 3 R \) respectively. The shell B is
earthed and \( A \) and \( C \) are given charges
and \( 2 q \) respectively. If the charge on
surfaces \( 1,2,3, \) and 4 are \( q_{1}, q_{2}, q_{3}, \) and
\( q_{4} \) respectively, then match the
following columns :
Subject: Physics
A parallel plate capacitor has a uniform electric field \( E \) in the space between the
plates. If the distance between the plates is \( d \) and area of each plate is \( A \)
the energy stored in the capacitor is :
A \( \cdot E^{2} A d / \varepsilon_{0} \)
в. \( \frac{1}{2} \varepsilon_{0} E^{2} A d \)
\( \mathbf{c} \cdot \varepsilon_{0} E A d \)
D \( \cdot \frac{1}{2} \varepsilon_{0} E^{2} \)
Subject: Chemistry
For a first order reaction \( \boldsymbol{A} \rightarrow \mathbf{2} \boldsymbol{B}+\boldsymbol{C} \)
It was found that at the end of 10
minutes from the start,the total optical
rotation of the system was \( 60^{0} \) and when the reaction is complete.lt was
\( 180^{0} . \) The \( \mathrm{B} \) and \( \mathrm{C} \) are only optically active and initially only A was taken.
i) What is the rate constant of the above
reaction (in hour)?
ii) At what time (in minute) from the
start, total optical rotation will be \( 90^{0} \) Take \( \log 2=0.3, \log 3=0.48, \log 7=0.85, \) in 10
\( =2.3 \)
Subject: Chemistry
Atoms present in a molecule of heavy
water are:
A. \( _{1} H^{1},_{8} O^{16} \)
B . \( _{1} H^{2},_{8} O^{18} \)
c. \( _{1} H^{2},_{8} O^{16} \)
D. \( _{1} H^{1},_{8} O^{18} \)
Subject: Chemistry
Internal energy of \( n_{1} \) moles of hydrogen at temperature \( T \) is equal to the internal
energy of \( n_{2} \) moles of helium at
temperature 2T. Then the ratio \( n_{1} / n_{2} \) is:
A
B. \( \frac{2}{3} \)
\( c \cdot \frac{6}{5} \)
D. \( \frac{3}{7} \)
Subject: Chemistry
The molarity of \( M g^{2+} \) ions in a
saturated solution of \( M g_{3}\left(P O_{4}\right)_{2} \)
whose solubility product is \( 1.08 \times \)
\( \mathbf{1 0}^{-13} \boldsymbol{M}^{\mathbf{5}} \) is
A . \( 1.0 \times 10^{-3} M \)
В. \( 2.0 \times 10^{-3} M \)
c. \( 3.0 \times 10^{-3} M \)
D. \( 4.0 \times 10^{-3} M \)
Subject: Maths
If \( \boldsymbol{a}=\boldsymbol{i}+\boldsymbol{j}+\boldsymbol{k}, \boldsymbol{b}=\boldsymbol{i}+\boldsymbol{3} \boldsymbol{j}+\mathbf{5} \boldsymbol{k} \) and
\( c=7 i+9 j+11 k, \) then the area
of Parallelogram having diagonals \( a+b \) and \( b+c \) is.
A. \( 4 \sqrt{6} \) sq. units
B . \( \frac{1}{2} \sqrt{21} \) sq. units
c. \( \frac{\sqrt{6}}{2} \) sq.units
D. \( \sqrt{6} \) sq. units
Subject: Maths
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{6} \boldsymbol{x}+\mathbf{5} \) find \( \boldsymbol{f}(-\mathbf{1}) \)
\( A \cdot-1 \)
B.
\( c \cdot c \)
D. None of these
Subject: Maths
Let \( A \) be the set of all points in a plane
and let 0 be the origin. Show that the relation \( \boldsymbol{R}=\{(\boldsymbol{P}, \boldsymbol{Q}): \boldsymbol{P}, \boldsymbol{Q} \in \boldsymbol{A} \) and
\( \boldsymbol{O P}=\boldsymbol{O Q}\} \) is an equivalence relation.
Subject: Chemistry
Calculate the work done injoules when
3 moles of an ideal gas at \( 27^{\circ} C \) expands isothermally and reversibly from 10 atm to 1 atm \( (1 a t m=1.013 x \)
\( 10^{5} N m^{-2} \) ). What will be the work done
if the expansion is against the constant
pressure of 1 atm?
Subject: Physics
\( 28 g \) of \( N_{2} \) gas is contained in a flask at
a pressure 10 atm and at a
temperature of \( 57^{0} C . \) It is found that
due to leakage in the flask, the pressure is reduced to half and the temperature
reduced to \( 27^{0} \) C.The quantity of \( N_{2} \) gas
that leaked out is:
\( \mathbf{A} \cdot \frac{11}{20} \mathrm{g} \)
B. \( \frac{80}{11} \) g
c. \( \frac{5}{63} \) g
D. \( \frac{63}{5} g \)
Subject: Chemistry
For an ideal solution containing a nonvolatile solute, which of the followig expressions represents the vapour
pressure of the solution? \( \left(x_{1} \rightarrow\right. \) mole fraction of solvent
A \( . p=x_{2} p_{2} \)
В . \( p=x_{1} p_{2}^{*} \)
c. \( p=x_{1} p_{1}^{*} \)
D. \( p_{1}^{*}-p=x_{2} \)
Subject: Physics
A second lens is now placed adjacent to
the first in contact with it. The new lens
is concave, with a focal length \( \boldsymbol{f}=-\mathbf{3} \boldsymbol{f} \)
In which region does the focus of the
two lens system lie? Treat the lenses as
thin.
\( A \)
B.
\( c \cdot c \)
\( D \)
Subject: Chemistry
What type of glycoside linkage is the following?
A \( \cdot \alpha\left(1 \rightarrow 4^{\prime}\right) \)
В \( \cdot \beta\left(1 \rightarrow 4^{\prime}\right) \)
c. \( \alpha\left(1 \rightarrow 6^{\prime}\right) \)
D. \( \beta\left(1 \rightarrow 6^{\prime}\right) \)
Subject: Maths
If the global maximum value of \( \boldsymbol{f}(\boldsymbol{x})= \)
\( -x^{2}+a x-a^{2}-2 a-2 \) for \( x \epsilon[0,1] \) be
-5', then 'a' can take the value
This question has multiple correct options
\( ^{\mathrm{A}} \cdot \frac{-4+2 \sqrt{13}}{3} \)
B. \( \frac{-4-2 \sqrt{13}}{3} \)
c. 1
D. - 3
Subject: Physics
A point moves such that its displacement as a function of time is given by \( x^{3}=t^{3}+1 . \) Its acceleration as
a function of time \( t \) will be:
A \( \cdot \frac{2}{x^{5}} \)
B. \( \frac{2 t}{x^{3}} \)
\( c \cdot \frac{2 t}{x^{4}} \)
D. \( \frac{2 t^{2}}{x^{5}} \)
Subject: Maths
\( \ln \Delta L M N, \angle L=60^{\circ}, \angle M=50^{\circ} . \) If
\( \Delta L M N \sim \Delta P Q R, \) then the value of
\( \angle R \) is
A \( \cdot 40^{\circ} \)
B. 30
\( c \cdot 70 \)
D. \( 110^{\circ} \)
Subject: Maths
If the function \( \boldsymbol{f}(\boldsymbol{x})=\log \left(\frac{1+\boldsymbol{x}}{1-\boldsymbol{x}}\right) \)
then the value of \( f\left(\frac{2 x}{1+x^{2}}\right) \) is equal to
A \( . f(x) \)
B. \( 2 f(x) \)
c. \( 3 f(x) \)
D. \( 4 f(x) \)
Subject: Maths
Length of the chord joining the points
\( P(\alpha) \) and \( Q(\beta) \) on the circle \( x^{2}+y^{2}= \)
\( a^{2} \) is
A \( \cdot \cos \left(\frac{\alpha-\beta}{2}\right) \)
в. \( 2 a \sin \left(\frac{\alpha-\beta}{2}\right) \)
c. \( 2 a \tan \left(\frac{\alpha-\beta}{2}\right) \)
D. \( 2 a \csc \left(\frac{\alpha-\beta}{2}\right) \)
Subject: Chemistry
Which of the following acids is
produced by treating \( \boldsymbol{K} \boldsymbol{N} \boldsymbol{O}_{3} \) with
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) under suitable experimental
conditions?
A. \( H N O_{2} \)
в. \( H_{2} S O_{3} \)
c. \( H N O_{3} \)
D. \( H_{2} S_{2} O_{7} \)
Subject: Maths
Assertion
\( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}| \cdot \sin \boldsymbol{x} \) is differentiable at
\( \boldsymbol{x}=\mathbf{0} \)
Reason
If \( f(x) \) is not differentiable and \( g(x) \) is differentiable at \( x=a \), then \( f(x) \cdot g(x) \)
will be differentiable at \( \boldsymbol{x}=\boldsymbol{a} \)
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
When a cylinder is spinned and placed
somewhere on surface of a rough inclined planes as shown then after
release.
A. The cylinder may continue to accelerate down and never be in pure rolling
B. The cylinder may accelerate up for some time then retard and come down in pure rolling
C. The cylinder may accelerate down continuously and pure rolling will start after some time
D. Friction will act on cylinder in upward direction initially and later it will be downward direction
Subject: Chemistry
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{O H} \stackrel{^{\prime} \boldsymbol{X}^{\prime}}{\longrightarrow} \boldsymbol{C H}_{2}=\boldsymbol{C H}_{2} \)
'X' may be:
This question has multiple correct options
A . conc. \( H_{2} S O_{4} / 170^{0} C \)
B . \( A l_{2} O_{3} / 350^{0} C \)
c. conc. \( H_{2} S O_{4} / 140^{\circ} C \)
D. conc. \( H_{2} S O_{4} / 110^{0} C \)
Subject: Physics
The work done in turning a magnet of
magnetic moment \( M \) by an angle of \( 90^{\circ} \)
from the meridian is \( n \) times the
corresponding work done to turn it
through an angle of \( 60^{\circ} . \) Where \( n \) is
given by
A \( \cdot 1 / 2 \)
B. 2
c. \( 1 / 4 \)
D.
Subject: Maths
If \( \vec{a} \) and \( \vec{b} \) are two non-zero and non collinear vectors, then \( \vec{a}+\vec{b} \) and \( \vec{a}-\vec{b} \)
are
A. linearly dependent vectors
B. linearly independent vectors
c. linearly dependent and independent vectors
D. none of the above
Subject: Chemistry
Hydrogen chloride and \( S O_{2} \) are the side products in the reaction of ethanol with thionyl chloride. Which of the following is the main product in this reaction?
A. \( C_{2} H_{5} O C_{2} H_{5} \)
B. \( C_{2} H_{6} \)
c. \( C H_{3} C l \)
D \( \cdot C_{2} H_{5} C l \)
Subject: Maths
What is the eccentricity of the conic \( 4 x^{2}+9 y^{2}=144 \)
A \( \frac{\sqrt{5}}{3} \)
в. \( \frac{\sqrt{5}}{6} \)
c. \( \frac{3}{\sqrt{5}} \)
D. \( \frac{2}{3} \)
Subject: Physics
Speed of sound in air is \( 350 m s^{-1} \)
fundamental frequency of an open
organ pipe of \( 50 \mathrm{cm} \) length will be
\( \mathbf{A} \cdot 175 H z \)
в. \( 350 H z \)
c. \( 700 H z \)
D. \( 500 H z \)
Subject: Chemistry
When conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) is electrolysed with high current using Pt electrodes, the product obtained at anode is:
\( A \cdot S O_{2} \)
в. \( S O_{3} \)
\( c \cdot O_{2} \)
D. \( H_{2} S O_{4} \)
Subject: Maths
Degree of \( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}+\left(\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right)^{3}+\mathbf{3} \boldsymbol{y}=\boldsymbol{x}^{2} \) is
\( \mathbf{A} \cdot \mathbf{4} \)
B. 2
\( c .3 \)
D.
Subject: Maths
\( A=\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right], B=\left[\begin{array}{ll}-1 & -1 \\ -1 & -1\end{array}\right], C=\left[\begin{array}{ll}x & y \\ z & r\end{array}\right] \)
If \( \boldsymbol{A}+\mathbf{3} \boldsymbol{B}=\boldsymbol{C}, \) then \( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}+\boldsymbol{r} \) is
\( A \)
B. - 2
\( c .-1 \)
\( D \)
Subject: Physics
Three resistances \( 2 \Omega, 4 \Omega, 5 \Omega \) are combines in series and this
combination is connected to a battery
of \( 12 \mathrm{V} \) emf and negligible internal resistance. The potential drop across these resistances are.
A . (5.45,4.36,2.18) V
B. (2.18,5.45,4.36) \( \mathrm{v} \)
c. (4.36,2.18,5.45) v
D. (2.18,4.36,5.45)\( \vee \)
Subject: Physics
A fighter plane of length \( 20 \mathrm{m}, \) wing span (distance from tip of one wing to the tip of the other wing) of \( 15 \mathrm{m} \) and height \( 5 \mathrm{m} \) is flying towards east over Delhi. Its speed is \( 240 m s^{-1} \). The earth's
magnetic field over Delhi is \( 5 \times 10^{-5} \mathrm{T} \)
with the declination angle \( \sim 0^{\circ} \) and dip
of \( \theta \) such that \( \sin \theta=\frac{2}{3} . \) If the voltage
developed is \( V_{B} \) between the lower and
upper side of the plane and \( V_{W} \) between
the tips of the wings then \( V_{B} \) and \( V_{W} \)
are close to
A \( \cdot V_{B}=40 m V ; V_{W}=135 \mathrm{mV} \) with left side of pilot at
higher voltage
B . \( V_{B}=45 \mathrm{mV} ; V_{W}=120 \mathrm{mV} \) with right side of pilot at
higher voltage
C. \( V_{B}=40 \mathrm{mV} ; V_{W}=135 \mathrm{mV} \) with right side of pilot at high voltage
D. \( V_{B}=45 \mathrm{mV} ; V_{W}=120 \mathrm{mV} \) with left side of pilot at
higher voltage
Subject: Chemistry
State whether given statement is true or false:
Given reaction is for preparing \( \boldsymbol{S} \boldsymbol{O}_{2} \)
such that the oxidation state of
sulphur is not effected.
\( \boldsymbol{S}+\boldsymbol{O}_{2} \longrightarrow \boldsymbol{S} \boldsymbol{O}_{2} \)
A. True
B. False
Subject: Maths
Integrate:
\( \int \frac{x^{4}}{x^{2}+1} d x= \)
A \( \cdot \frac{x^{3}}{3}-x+\tan ^{-1} x+c \)
B. \( \frac{x^{5}}{5}+\tan ^{-1} x+c \)
C \( \cdot 4 x^{3}+\tan ^{-1} x+c \)
D \( \frac{x^{4}}{4}-x+\tan ^{-1} x+c \)
Subject: Physics
A thin film with index of refraction 1.33
coats a glass lens with index of
refraction \( 1.50 . \) Which of the following
choices is the smallest film thickness
that will not reflect light with
wavelength \( 640 n m ? \)
A . \( 160 n m \)
B. \( 240 n m \)
\( c .360 n m \)
D. \( 480 n m \)
Subject: Physics
A block of mass \( 10 \mathrm{kg} \) is pulled by a constant horizontal force of \( 19 \mathrm{N} \) and it
is displaced by \( 15 \mathrm{m} \) across the floor. Calculate the work done.
A . 1.3
в. 30 J
c. 285 J
D. 5586 J
E. 1
Subject: Chemistry
What is the molecular formula of
pyrogallol?
\( \mathbf{A} \cdot C_{6} H_{4}(O H) \)
в. \( C_{6} H_{5}(O H)_{3} \)
c. \( C_{6} H_{3}(O H)_{3} \)
D. \( C_{6} H_{5} O H \)
Subject: Maths
f \( x=\{a, b, c, d\} \) and \( y=\{b, d, g, f\} \)
find \( \boldsymbol{x}-\boldsymbol{y} \) and \( \boldsymbol{y}-\boldsymbol{x} \)
Draw the appropriate venn diagram for
\( \boldsymbol{A}^{\prime} \cap \boldsymbol{B}^{\prime} \)
Subject: Maths
The point of intersection of the lines \( \overrightarrow{\boldsymbol{r}}=(-\overrightarrow{\boldsymbol{i}}+\mathbf{2} \overrightarrow{\boldsymbol{j}}+\boldsymbol{3} \overrightarrow{\boldsymbol{k}})+\boldsymbol{t}(-\boldsymbol{2} \overrightarrow{\boldsymbol{i}}+\overrightarrow{\boldsymbol{j}}+\overrightarrow{\boldsymbol{k}}) \)
and \( \vec{r}=(2 \vec{i}+3 \vec{j}+5 \vec{k})+s(\vec{i}+2 \vec{j}+ \)
\( \mathbf{3} \overrightarrow{\boldsymbol{k}}) \) is:
A \( .(1,1,2) \)
в. (2,1,1)
c. (1,1,1)
D. (1,2,1)
Subject: Physics
The equivalent resistance \( R \) of three
resistors \( R_{1}, R_{2} \) and \( R_{3} \) joined in
parallel is
A \( \cdot R=R_{1}+R_{2}+R_{3} \)
B . \( R=1 / R_{1}+1 / R_{2}+1 / R_{3} \)
\( ^{\mathbf{C}} \cdot_{R}=\frac{R_{1} R_{2} R_{3}}{R_{1} R_{2}+R_{2} R_{3}+R_{3} R_{1}} \)
D. \( R=1 /\left(R_{1}+R_{2}+R_{3}\right) \)
Subject: Physics
surface under the influence of a force \( \boldsymbol{P} \)
of the same magnitude in all the three
cases.
CoOefficient of friction is the same
between each block and the ground.
What possible relation holds between the magnitude of normal
reaction and friction forces? (Assume
that the block do not overturn about
edge.) Here, \( \boldsymbol{f}_{A}, \boldsymbol{f}_{B} \) and \( \boldsymbol{f}_{C} \) are frictional
forces and \( N_{A}, N_{B} \) and \( N_{C} \) are
reactions.

This question has multiple correct options
\( \mathbf{A} \cdot N_{A}>N_{C}>N_{B} \)
B . \( f_{A}>f_{C}>f_{B} \)
\( \mathbf{c} \cdot f_{C}>f_{A}=f_{B} \)
D. \( N_{C}>N_{A}=N_{B} \)
Subject: Maths
A line passes through the point (6,-7,-1) and \( (2,-3,1) . \) if the angle \( \alpha \) which the line makes with the positive
direction of \( x \) -axis is acute, the
direction cosines of the line are,
A \( .2 / 3,-2 / 3,-1 / 3 \)
в. \( 2 / 3,2 / 3,-1 / 3 \)
c. \( 2 / 3,-2 / 3,1 / 3 \)
D. \( 2 / 3,2 / 3,1 / 3 \)
Subject: Physics
The potential energy of a particle of mass \( 5 k g \) moving in the \( x \) -y plane is given by the equation, \( U=-7 x+24 y \)
Joule. Here \( x \) and \( y \) are in the meter at
\( \boldsymbol{t}=\mathbf{0}, \) the particle is at the origin and moving with velocity \( (2 i+3 j) m / s . \) The
magnitude of the acceleration of the particle is:
A \( .3 m / s^{2} \)
в. \( 5 m / s^{2} \)
c. \( 31 m / s^{2} \)
D. \( 15 m / s^{2} \)
Subject: Maths
\( A \) point \( C \) with position vector \( \frac{3 a+4 b-5 c}{3} \)
(where \( a, b \) and \( c \) are non co-planar
vectors) divides the line joining \( A \) and \( B \) in the ratio \( 2: 1 . \) If the position vector
of \( A \) is \( a-2 b+3 c, \) then the position
vector of \( \boldsymbol{B} \) is
A \( .2 a+3 b-4 c \)
B . \( 2 a-3 b+4 c \)
c. \( 2 a+3 b+4 c \)
D. \( a+3 b-4 c \)
Subject: Maths
The line joining two points \( A(2,0), B(3,1) \) is rotated about \( A \) in anti-clockwise direction through an
angle of \( 15^{\circ} . \) The equation of the line in the now position, is
A \( \cdot \sqrt{3} x-y-2 \sqrt{3}=0 \)
B. \( x-3 \sqrt{y}-2=0 \)
c. \( \sqrt{3} x+y-2 \sqrt{3}=0 \)
D. \( x+\sqrt{3} y-2=0 \)
Subject: Chemistry
In a reaction, a substance undergoes decomposition which is catalyzed in the presence of finely divided nickel. If there
are enough sites on the surface of catalysts so that 20 molecules of
substance react per second, the rate of reaction for a \( 1.0 \mathrm{M} \) solution is:
A \( .3 .34 \times 10^{-23} \) mol \( L^{-1} s^{-1} \)
B . 3.14 \( \times 10^{-23} \) mol \( L^{-1} s^{-1} \)
c. \( 3.68 \times 10^{-23} \) mol \( L^{-1} s^{-1} \)
D. None of these
Subject: Chemistry
What is the empirical formula for a compound containing \( 25.9 \% \mathrm{N} \) and \( 74.1 \% \)
O?
\( A \cdot N_{2} O_{5} \)
В. \( N_{2} O_{3} \)
\( c \cdot N O_{2} \)
D. \( N O \)
E. \( N_{2} \) O
Subject: Physics
Binding energy per nucleon of \( _{1} H^{2} \) and
\( _{2} H e^{4} \) are \( 1.1 M e V \) and \( 7.0 M e V \)
respectively. Energy released in the process \( _{1} H^{2}+_{1} H^{2} \longrightarrow_{2} H e^{4} \) is
A. \( 20.8 \mathrm{MeV} \)
в. \( 16.6 \mathrm{MeV} \)
c. \( 25.2 \mathrm{MeV} \)
D. \( 23.6 \mathrm{MeV} \)
Subject: Chemistry
Predict respectively' \( X^{\prime} \) and \( ^{\prime} Y^{\prime} \) in the
following reactions \( \boldsymbol{A r}-\boldsymbol{N} \boldsymbol{H}_{2} \stackrel{\boldsymbol{X}}{\longrightarrow} \boldsymbol{A} \boldsymbol{r}-\dot{\boldsymbol{N}} \equiv \)
\( N . C l^{-} \quad^{Y} \quad A r-C l \)
A. \( N a N O_{3} \& C l_{2} \)
в. \( N a N O_{3}-H C l \& H C l \)
c. \( N a N O_{2}-H C l \& C u / H C l \)
D. \( N a N O_{2}-H C l \& N a N H_{2} \)
Subject: Physics
A \( 10 \mathrm{V} \) battery with internal resistance 1
\( \Omega \) and a \( 15 V \) battery with internal
resistance \( 0.6 \Omega \) are connected in
parallel to a voltmeter. The reading in
the voltmeter will be close to
\( A, 11.9 \mathrm{V} \)
в. 13.1
c. \( 24.5 \mathrm{v} \)
D. \( 12.5 \mathrm{v} \)
Subject: Maths
Two measurements of a cylinder are varying in such a way that the volume is kept constant. If the rates of change of the radius \( (r) \) and height \( (h) \) are equal in magnitude but opposite in sign, then
A \( . r=2 h \)
B . \( h=2 r \)
c. \( h=r \)
D. \( h=4 r \)
Subject: Maths
The value of \( \int \frac{\cos \sqrt{x}}{\sqrt{x}} d x \) is
\( A \cdot 2 \cos \sqrt{x}+C \)
B. \( \sqrt{\frac{\cos x}{x}}+C \)
\( c \cdot \sin \sqrt{x}+C \)
D. \( 2 \sin \sqrt{x}+C \)
Subject: Biology
Assertion
Algal blooms occur in nutrient poor
water.
Reason
Algal blooms make water unfit for
human consumption but cause enormous growth of fish.
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
An electric dipole moment \( \vec{p}=(2.0 \hat{i}+ \) \( \mathbf{3} .0 \hat{\boldsymbol{j}}) \mu C . \mathrm{m} \) is placed in a uniform
electric field \( \overrightarrow{\boldsymbol{E}}=(\boldsymbol{3} \cdot \boldsymbol{0} \hat{\boldsymbol{i}}+\boldsymbol{2} \cdot \boldsymbol{0} \widehat{\boldsymbol{k}}) \times \)
\( \mathbf{1 0}^{\mathbf{5}} \mathbf{N} \boldsymbol{C}^{-\mathbf{1}} \)
This question has multiple correct options
A. The torque that \( \vec{E} \) exerts on \( \vec{p} \) is \( (0.6 \vec{i}-0.4 \vec{j}- \) \( 0.9 \vec{k}) N m \)
B. The potential energy of the dipole is \( -0.6 J \)
C. The potential energy of the dipole is \( 0.6 J \).
D. If the dipole is rotated in the electric field, the maximum potential energy of the dipole is \( 1.3 J \)
Subject: Physics
The magnetic flans associated with a metal ring varies with time all. to \( \phi= \) \( \mathbf{3}\left(\boldsymbol{a} \boldsymbol{t}^{3}-\boldsymbol{b} \boldsymbol{t}^{2}\right) \boldsymbol{T} \boldsymbol{m}^{2}, \boldsymbol{a}=\boldsymbol{2} \boldsymbol{s} \boldsymbol{e} \boldsymbol{c}^{-3}, \boldsymbol{b}= \)
\( 6 \sec ^{-2} . \) If the resistance of the ring is
\( 24 \Omega, \) the current induced in the ring
during the time \( t=2 \sec \) is
A. \( 2 a m p \)
в. \( 4 a m p \)
c. \( 6 a m p \)
D. zero
Subject: Maths
If \( A \) is a square matrix of order \( n \times n \)
then adj(adj A) is equal to
\( \mathbf{A} \cdot|A|^{n} A \)
B \( \cdot|A|^{n-1} A \)
\( \mathbf{c} \cdot|A|^{n-2} A \)
D \( \cdot|A|^{n-3} A \)
Subject: Maths
If sum of \( n \) terms of an A.P.is given by
\( \boldsymbol{S}_{n}=\boldsymbol{a}+\boldsymbol{b} \boldsymbol{n}+\boldsymbol{c} \boldsymbol{n}^{2} \) where \( \mathbf{a}, \mathbf{b}, \mathbf{c} \) are
independent of \( n, \) then This question has multiple correct options
\( \mathbf{A} \cdot a=0 \)
B. Common difference of A.P. must be 2b.
c. Common difference of A.P. must be 2 c
D. All above