AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
cosine of an angle between the vectors \( \vec{a}+\vec{b} \) and \( \vec{a}-\vec{b} \) if \( |\vec{a}|=2,|\vec{b}|=1 \) and \( \vec{a} \)
\( \wedge \vec{b}=60^{\circ} \) is?
A \( \cdot \sqrt{\frac{3}{7}} \)
B. \( \frac{9}{\sqrt{21}} \)
c. \( \frac{3}{\sqrt{7}} \)
D. None
Subject: Physics
A wire of length ' \( l^{\prime} \) and radius ' \( r^{\prime} \) is
clamped rigidly at one end. When the other end of the wire is pulled by a force
\( F^{\prime}, \) its length increases by \( ^{\prime} x^{\prime} . \) Another wire of same material of length '2l
and radius \( ^{\prime} 2 r^{\prime} \) is pulled by a force \( ^{\prime} 2 F^{\prime} \) the increase in its length will be :
\( A \)
B. \( 2 x \)
c. \( x / 2 \)
D. \( 4 x \)
Subject: Physics
Consider a uniformly charged sphere that has a total charge of \( Q \) that has a
radius of \( R \). What is the electrostatic
potential difference, \( \Delta V \), between the
centre of the sphere and the surface of
the sphere?
A \( \cdot \frac{4 k_{e} q}{R} \)
в. \( \frac{2 k_{e} q}{R} \)
c. \( \frac{k_{e} q}{R} \)
D. \( \frac{k_{e q}}{2 R_{q}} \)
Subject: Chemistry
Show that for reaction \( A B(g) \rightleftharpoons A(g)+ \) \( \mathrm{B}(\mathrm{g}), \) the total pressure at which \( \mathrm{AB} \) is \( 50 \% \) dissociated is numerically equal to
three times of \( \boldsymbol{K}_{\boldsymbol{p}} \)
Subject: Maths
Let \( f \) be differentiable for all \( x \). If \( f(1)= \)
-2 and \( f^{\prime}(x) \geq 2 \) for \( x \in[1,6], \) then
\( \mathbf{A} \cdot \mathbf{f}(6) \geq 8 \)
B. \( f(6)<8 \)
\( \mathrm{c} \cdot \mathrm{f}(6)<5 \)
D. \( f(6)=5 \)
Subject: Physics
A thermometer reads \( 0^{\circ} \mathrm{C} \) as \( 10^{\circ} \mathrm{C} \) and
\( 100^{\circ} \mathrm{C} \) as \( 90^{\circ} \mathrm{C} \) then
Find the correct temperature if the
thermometer reads \( 20^{\circ} \mathrm{C} \)
A \( \cdot 20^{\circ} \mathrm{C} \)
B . \( 12.5^{\circ} \mathrm{C} \)
\( \mathrm{c} \cdot 25^{\circ} \mathrm{C} \)
D. \( 30^{\circ} \mathrm{C} \)
Subject: Physics
A line formly changed eonducting sphere of \( 24 m \) diameter has a surface
change density of \( 80.0 \mu c / m^{2} \)
(i) Find the charge on the sphere
(ii) What is the total electric flux learning the surface of the sphere?
A \( \cdot 1.447 \times 10^{-3} c, 1.63 \times 10^{8} \frac{N m^{2}}{C} \)
В. \( _{2.447} \times 10^{-3} c, 1.63 \times 10^{8} \frac{N m^{2}}{C} \)
c. \( _{1.447} \times 10^{-3} c, 2.63 \times 10^{8} \frac{N m^{2}}{C} \)
D. \( 41.447 \times 10^{-3} c, 1.63 \times 10^{8} \frac{N m^{2}}{C} \)
Subject: Maths
\( A B C \) and \( B D E \) are two equilateral
triangles such that \( D \) is the midpoint of
\( B C . \) Ratio of the areas of triangles \( A B C \)
and \( B D E \) is
A .2: 1
B. 1: 2
\( c \cdot 4: 1 \)
D. 1: 4
Subject: Chemistry
One of the steps involved in the depletion of ozone in the stratosphere by nitric acid ( \( N O \) ) may be represented
as:
\[
\begin{array}{c}
\boldsymbol{N O}(\boldsymbol{g})+\boldsymbol{O}_{3}(\boldsymbol{g}) \longrightarrow \boldsymbol{N} \boldsymbol{O}_{2}(\boldsymbol{g})+ \\
\boldsymbol{O}_{2}(\boldsymbol{g})
\end{array}
\]
The oxidation number of \( N \) changes
from +2 to +4
If true enter 1 , else enter 0
Subject: Chemistry
Which of the following statements is incorrect?
A \( \cdot O_{3} \) is used as disinfectant.
B. \( N O_{2} \) is oxidised to \( N_{2} O_{5} \) by \( O_{3} \)
C. \( O_{3}^{-} \) is paramagnetic in nature
D. Dry iodine reacts with ozone and form \( I_{2} O_{5} \)
Subject: Chemistry
The decomposition of hydrocarbon follows the equation, \( k=(4.5 x \)
\( \left.\mathbf{1 0}^{11} \boldsymbol{s}^{-1}\right) e^{-\mathbf{2 8 0 0 0 K} / \boldsymbol{T}} \)
Calculate \( \boldsymbol{E}_{\boldsymbol{a}} \)
Subject: Chemistry
The solubility product of iron (III) hydroxide is \( 1.6 \times 10^{-39} . \) If \( X \) is the
solubility of iron(III) hydroxide, then which one of the following expressions
can be used to calculate \( X ? \)
\( \mathbf{A} \cdot K_{s p}=X^{4} \)
B. \( K_{s p}=9 X^{4} \)
C \( . K_{s p}=27 X^{3} \)
D. \( K_{s p}=27 X^{4} \)
Subject: Maths
If \( \boldsymbol{x}=\boldsymbol{a}(\boldsymbol{k} \sin \boldsymbol{t}+\sin \boldsymbol{k} \boldsymbol{t}), \boldsymbol{y}= \)
\( a(k \cos t+\cos k t), \) then find \( \frac{d^{2} y}{d x^{2}} \) in
terms of t.
A \( \cdot \frac{k+1}{4 a k} \frac{1}{\cos ^{3} \frac{k+1}{2} t \cos \frac{k+1}{2} t} \)
в. \( \frac{k+1}{4 a k} \frac{1}{\cos ^{3} \frac{k-1}{2} t \cos \frac{k+1}{2} t} \)
c. \( \frac{k+1}{4 a k} \frac{1}{\cos ^{3} \frac{k+1}{2} t \cos \frac{k-1}{2} t} \)
D. \( -\frac{k+1}{4 a k} \frac{1}{\cos ^{3} \frac{k+1}{2} t \cos \frac{k-1}{2} t} \)
Subject: Physics
possible reversible processes performed on a monatomic ideal gas
Process \( A \) is isobaris (constant
pressure). Pressure \( B \) is isothermal
(constant temperature). Process \( C \) is
adiabatic. Process \( D \) is isochoric
(constant volume). For which
process(es) does the temperature of the gas decreases
A. Process A only
B. Process C only
c. only process \( C \) and \( D \)
D. Only process \( B, C \) and
Subject: Physics
A train is travelling at a speed of \( 108 k m / h . \) Brakes are applied so as to
produce a uniform retardation of \( 1 m / s^{2} . \) Find how far the train will go before it is brought to rest:
\( \mathbf{A} .800 m \)
B. \( 450 m \)
c. \( 1000 m \)
D. \( 1050 m \)
Subject: Physics
If a boat can travel with a speed of \( v \) in
still water, which of the following trips will take the least amount of time?
A. travelling a distance of \( 2 d \) in still water.
B. travelling a distance of \( 2 d \) across (perpendicular to) the current w.r.t. in a stream
C. travelling a distance \( d \) downstream and returning a distance \( d \) upstream
D. travelling a distance \( d \) upstream and returning a distance \( d \) downstream
Subject: Physics
A man can swim in still water with a
velocity 5 m/s. He wants to reach at
directly opposite point on the other bank of a river which is flowing at a rate of \( 4 m / s . \) River is 15 m wide and the man can run with twice the velocity
as compared with velocity of swimmer
with respect to river. If he swims
perpendicular to river flow and then run along the bank. Time, in seconds, taken by him to reach the opposite point is
A. 4.0
B. 4.2
\( c .5 .4 \)
D. 3.6
Subject: Maths
\( \frac{C_{1}}{C_{0}}+2 \cdot \frac{C_{2}}{C_{1}}+3 \cdot \frac{C_{3}}{C_{2}}+\dots+n \cdot \frac{C_{n}}{C_{n-1}}= \)
A. \( \frac{n(n+1)}{2} \)
в. \( \frac{n(n-1)}{2} \)
c. \( \frac{(n-1)(n+1)}{2} \)
D. \( \frac{n(n+2)}{2} \)
Subject: Physics
The speed of a wave of time period \( T \)
and propagation constant \( \boldsymbol{K} \) is
\( ^{\text {A }} \cdot \frac{2 \pi}{T K} \)
в. \( \frac{T K}{2 \pi} \)
c. \( \frac{1}{T K} \)
D. \( \frac{T}{K} \)
Subject: Maths
\( \int_{-5}^{5} \log \left(\frac{130-x^{3}}{130+x^{3}}\right) d x \) is equal to
\( \mathbf{A} \cdot \log \frac{57}{5} \)
B. \( 2 \int_{-5}^{5} \log \left(\frac{130-x^{3}}{130+x^{3}}\right) d x \)
c. 0
D. -
Subject: Physics
An electric cell of e.m.f. E is connected
across a copper wire of diameter d and length I. The drift velocity of electrons in
the wire is \( v_{d} \). If the length of the wire is changed to 21, the new drift velocity of electrons in the copper wire will be
\( \mathbf{A} \cdot v_{d} \)
в. \( 2 v_{d} \)
c. \( v_{d} / 2 \)
D. \( v_{d} / 4 \)
Subject: Physics
Two equal charges ' \( q \) ' of opposite sign are separated by a small distance '2a'. The electric intensity ' \( E \) ' at a point on the perpendicular bisector of the line joining the two charges at a very large distance
\( ^{\prime} r^{\prime} \) from the line is :
A \( \cdot \frac{1}{4 \pi \varepsilon_{0}} \frac{q a}{r^{2}} \)
В. \( \frac{1}{4 \pi \varepsilon_{0}} \frac{2 q a}{r^{3}} \)
c. \( \frac{1}{4 \pi \varepsilon_{0}} \frac{2 q a}{r^{2}} \)
D. \( \frac{1}{4 \pi \varepsilon_{0}} \frac{q a}{r^{3}} \)
Subject: Maths
If \( A, B \) are acute angles, \( \sin A= \) \( \frac{4}{5}, \tan B=\frac{5}{12} \) then \( \sin (A+B)= \)
A \( \cdot \frac{36}{65} \)
в. \( \frac{65}{56} \)
c. \( \frac{65}{63} \)
D. \( \frac{63}{65} \)
Subject: Physics
Consider a classroom of dimensions
\( (5 \times 10 \times 3) m^{3} \) at temperature \( 20^{\circ} C \)
and pressure 1 atm. There are 50 people in the room, each losing energy at the average of 150 watts. Assuming that the walls, ceiling, floor, and furniture are perfectly insulated and none of them is absorbing heat. How much time will be needed for raising the temperature of air in the room to the
body temperature \( \left(37^{\circ} C\right) ?\left[\text { For air } C_{p}=\right. \) \( \frac{7}{2} R \) and neglect the loss of air to the outside as the temperature rises
A .422 sec
в. \( 411.3 \mathrm{sec} \)
c. \( 421.1 \mathrm{sec} \)
D. \( 413.1 \mathrm{sec} \)
Subject: Physics
A cell develops the same power across
two resistance \( \boldsymbol{R}_{1} \) and \( \boldsymbol{R}_{2} \) seprarately.The internal resistance of the cell is :
A \( \cdot R_{1}+R_{2} \)
в. \( \frac{R_{1}+R_{2}}{2} \)
c. \( \sqrt{R_{1} R_{2}} \)
D. \( \frac{\sqrt{R_{1} R_{2}}}{2} \)
Subject: Chemistry
Which of the following pair have almost
similar size
A \( \cdot T i_{22} \) and \( Z r_{4} \)
B. \( N b_{41} \) and \( T a_{73} \)
C \( \cdot Y_{39} \) and \( L a_{57} \)
D. \( C a_{20} \) and \( I r_{r} \)
Subject: Physics
A wheel rotating at an angular speed of
\( 20 \mathrm{rad} s^{-1}, \) is brought to rest by a constant torque in 4s.If the M.l is 0.2 kg \( m^{2}, \) the work done in first \( 2 s \) is:
\begin{tabular}{l} 
A \( .50 \mathrm{J} \) \\
\hline
\end{tabular}
в. \( 30 J \)
\( c .20 J \)
D. 10 J
Subject: Maths
Is the function \( f \) defined by
\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{l}\boldsymbol{x}, \boldsymbol{i} \boldsymbol{f} \boldsymbol{x} \leq 1 \\ \boldsymbol{5}, \boldsymbol{i f} \boldsymbol{x}>1\end{array}\right. \)
continuous at \( \boldsymbol{x}=\mathbf{0} ? \) At \( \boldsymbol{x}=\mathbf{1} \) ? At \( \boldsymbol{x}= \)
\( \mathbf{2} ? \)
Subject: Physics
A particle of mass \( M \) is moving in a
horizontal circle of radius \( \boldsymbol{R} \) with
uniform speed \( V . \) When it moves from one point to a diametrically opposite point, its
A
B. momentum does not change
c. momentum changes by \( 2 M V \)
D. kinetic energy changes by \( M V^{2} \)
Subject: Chemistry
The correct representation of \( \boldsymbol{C u} \boldsymbol{S O}_{4} \)
\( \mathbf{5} \boldsymbol{H}_{2} \boldsymbol{O} \) is:
\( \mathbf{A} \cdot\left[C u\left(H_{2} O\right)_{5}\right] S O_{4} \)
B \( \cdot\left[C u\left(H_{2} O\right)_{3} S O_{4}\right] \cdot 2 H_{2} O \)
c. \( \left[C u S O_{4} \cdot H_{2} O\right] \cdot 4 H_{2} O \)
D. \( \left[C u\left(H_{2} O\right)_{4}\right] S O_{4} \cdot H_{2} O \)
Subject: Physics
A beam of ultraviolet radiation having wavelength between \( 100 n m \) and
\( 200 n m \) is incident on a sample of atomic hydrogen gas. Assuming that the atoms are in ground state, which wavelengths will have low intensity in the transmitted beam?
A . \( 104 n m \)
в. \( 103 n m \)
c. \( 105 n m \)
D. 100 nm
Subject: Chemistry
The ore chromite is:
A \( \cdot F e C r_{2} O_{4} \)
в. \( \operatorname{CoCr}_{2} \mathrm{O}_{3} \)
\( \mathbf{c} \cdot \operatorname{Cr} F e_{2} O_{4} \)
D. \( F e C r_{2} O_{3} \)
Subject: Physics
Statement-1: When two conducting wires of different resistivity having same cross section area are joined in
series, the electric field in them would
be equal when they carry current

Statement-2: When wires are in series
they carry equal current
A. Statement-1 is true and Statement-2 is correct explanation for Statement- -
B. Statement-1 is true and Statement-2 is NOT the correct explanation for Statement-
c. Statement-1 is true, Statement-2 is false
D. Statement-1 is false, Statement-2 is true
Subject: Physics
Neglecting the mass of the thread, find the time dependence of the
instantaneous power developed by the
gravitational force :
\( ^{\mathbf{A}} \cdot P=\frac{2}{3} m g^{2} t \)
B. \( P=\frac{3}{2} m g^{2} t \)
\( ^{\mathbf{C}} P=2 \frac{2}{3} m g^{2} t \)
D. \( P=2 \frac{3}{2} m g^{2} t \)
Subject: Physics
A racing car is travelling along a track
at a constant speed of \( 60 m s^{-1} . \) A
television cameraman is recording the event from a distance of \( 30 m \) directly away from the track as shown in the
figure. In order to keep the car under view at the situation shown in the
figure, find the angular speed at which
the camera should be rotated?
A \( \cdot \operatorname{lrads}^{-} \)
B. \( \frac{1}{2} \) rads \( ^{-1} \)
\( c \cdot 2 r a d s^{-1} \)
\( D \)
Subject: Chemistry
Which of the following order of acidic strength is correct?
A. \( H C l O>H C l O_{2}>H C l O_{3}>H C l O_{4} \)
в. \( H C l O_{4}>H C l O_{2}>H C l O_{3}>H C l O \)
с. \( H C l O_{2}>H C l O>H C l O_{4}>H C l O_{3} \)
D. \( H C l O_{4}>H C l O_{3}>H C l O_{2}>H C l O \)
Subject: Maths
If the median of the observation \( \frac{x}{5}, x, \frac{x}{4}, \frac{x}{2} \) and \( \frac{x}{3} \) is \( 8, \) then \( x= \)
\( \boldsymbol{x}>0 \)
\( A \cdot 2 \)
B. 4
c. 24
D. 16
Subject: Physics
When the object is at distance \( u_{1} \) and
\( u_{2} \) from a lens, a real image and virtual
image are formed respectively having the same magnification. The focal length of the lens is :
A \( . u_{1}-u_{2} \)
в. \( \frac{u_{1}-u_{2}}{2} \)
c. \( \frac{u_{1}+u_{2}}{2} \)
D. \( u_{1}+u_{2} \)
Subject: Physics
A body at rest starts from a point at a distance \( r(>R) \) from the center of the
earth. If \( \mathrm{M} \) and \( \mathrm{R} \) stand for the mass and
the radius of earth respectively, then the speed of the body when it reaches the Earth surface is
\( ^{\mathrm{A}} \cdot \sqrt{\frac{2 G M}{R}} \)
в. \( \sqrt{\frac{2 G M}{R-r}} \)
c. \( \sqrt{\frac{2 G M(r-R)}{R r}} \)
D. zero
Subject: Physics
Two particles of masses \( m_{1} \) and \( m_{2} \) are moving velocities \( \vec{V}_{1} \) and \( \vec{V}_{2} \) Momentum
of the particle of mass \( m_{1} \) with respect to center of mass is
A. zero
B. \( \frac{m_{1} m_{2}}{m_{1}+m_{2}}\left(\vec{V}_{1}-\vec{V}_{2}\right) \)
c. \( \frac{m_{2}}{m_{1}+m_{2}}\left(\vec{V}_{1}-\vec{V}_{2}\right) \)
D. None of these
Subject: Chemistry
An organic compound contains \( C, H \) and \( O . \) If \( C(\%): H(\%)=6: 1, \) what is the
simplest formula of the compound given that one mole of the compound contains half as much oxygen as would
be required to burn all the \( C \) and \( H \)
atoms in it to \( C O_{2} \) and \( H_{2} O ? \)
\( \mathbf{A} \cdot C H_{2} O \)
в. \( C_{2} H_{4} O_{3} \)
\( \mathbf{c} \cdot C_{3} H_{6} \)
D. \( C_{3} H_{6} O_{2} \)
Subject: Maths
\( \operatorname{Resolve} \frac{x^{4}-x^{2}+1}{x^{2}\left(x^{2}+1\right)^{2}} \) into partial
fractions.
A \( \cdot-\frac{2}{x^{2}}+\frac{1}{\left(x^{2}+1\right)^{2}} \)
B. \( -\frac{1}{x^{2}}+\frac{3}{\left(x^{2}+1\right)^{2}} \)
c. \( \frac{1}{x^{2}}-\frac{5}{\left(x^{2}+1\right)^{2}} \)
D. \( \frac{1}{x^{2}}-\frac{3}{\left(x^{2}+1\right)^{2}} \)
Subject: Chemistry
Name the following compound according to the IUPAC system or
nomenclature.
\( \boldsymbol{p}-\boldsymbol{O} \boldsymbol{H} \boldsymbol{C} \boldsymbol{C}_{6} \boldsymbol{H}_{4} \boldsymbol{C} \boldsymbol{H} \boldsymbol{O} \)
Subject: Maths
The value of \( \frac{1}{\cos 290^{\circ}}+\frac{1}{\sqrt{3} \sin 250^{\circ}} \) is?
\( A \cdot \frac{2 \sqrt{3}}{3} \)
B. \( \frac{4 \sqrt{3}}{3} \)
\( c \cdot \sqrt{3} \)
D. None
Subject: Physics
If \( \boldsymbol{v}_{s}, \boldsymbol{v}_{\boldsymbol{x}} \) and \( \boldsymbol{v}_{m} \) are the velocities of soft
gamma rays, X-rays and Microwaves respectively in vacuum, then
A. \( v_{s}<v_{x}<v_{m} \)
В . \( v_{s}=v_{x}=v_{m} \)
c. \( v_{s}>v_{x}>v_{m} \)
D. \( v_{x}<v_{s}<v_{m} \)
Subject: Chemistry
Select redox reaction from the following
A \( . Z n+C u S O_{4} \rightarrow Z n S O_{4}+C u \)
в. \( C a O+2 H C l \rightarrow C a C l_{2}+H_{2} O \)
c. \( N a O H+2 H C l \rightarrow N a C l_{2}+H_{2} O \)
D. \( C a C O_{3} \rightarrow C a O+C O_{2} \)
Subject: Chemistry
The pH of pure water at \( 25^{\circ} \mathrm{C} \) and \( 35^{\circ} \mathrm{C} \)
are 7 and 6 respectively. The heat of
formation of \( \boldsymbol{H}^{+} \) and \( \boldsymbol{O H}^{-} \) ions in
\( k c a l m o l^{-1} \) is :
A . -84.5
B. +84.5
c. +184.5
D. -184.5
Subject: Maths
Let \( \bar{\alpha}, \bar{\beta}, \bar{\gamma} \) be three vectors such that
\( \overline{\boldsymbol{\alpha}} \cdot(\overline{\boldsymbol{\beta}}+\bar{\gamma})+\overline{\boldsymbol{\beta}} \cdot(\bar{\gamma}+\overline{\boldsymbol{\alpha}})+\bar{\gamma} \)
\( (\bar{\alpha}+\bar{\beta})=\mathbf{0} \) and \( |\overline{\boldsymbol{\alpha}}|=\sqrt{\mathbf{3}},|\bar{\beta}|=\mathbf{2} \) and
\( |\bar{\gamma}|=\mathbf{3} \) then \( |\overline{\boldsymbol{\alpha}}+\overline{\boldsymbol{\beta}}+\bar{\gamma}| \) is
A \( . \sqrt{17} \)
B. 4
\( c .5 \)
D. \( \sqrt{15} \)
Subject: Physics
The radius of a hypothetical nucleus (atomic number \( =\mathbf{7} 9 \) ) is about \( \mathbf{7} \times \)
\( 10^{-15} \mathrm{m} . \) Assuming that charge
distribution is uniform, the electric
field at distance of \( 3.5 \times 10^{-15} \) of the
nucleus is :
A \( \cdot 3 \times 10^{20} \)
В. \( 1.7 \times 10^{21} \)
c. \( 3.5 \times 10^{20} \)
D. \( 3.5 \times 10^{21} \)
Subject: Chemistry
\( A B, A_{2}, \) and \( B_{2} \) are diatomic molecules. If the bond enthalpies of
\( A_{2}, A B, \) and \( B_{2} \) are in the ratio 2: 2: 1
and ethalpy of formation \( A B \) from \( A_{2} \)
and \( B_{2} \) is \( -100 k J \) mol \( ^{-1} . \) What is the
bond energy of \( \boldsymbol{A}_{2} ? \)
В. \( 100 k J \) mol\( ^{-1} \)
c. \( 300 k J \) mol\( ^{-1} \)
D. \( 400 \mathrm{kJ} \mathrm{mol}^{-1} \)
Subject: Chemistry
According to Bohr's atomic theory, which of the following relations is/are incorrect?
This question has multiple correct options
A . kinetic energy of electron \( \propto \frac{z^{2}}{n^{2}} \)
B. The product of velocity of electron and the principal quantum number \( \propto z^{2} \)
C. Frequency of revolution of the electron in an orbit \( \alpha \) \( \frac{z^{2}}{n^{3}} \)
D. coulombic force of attraction on the electron \( \propto \frac{z^{2}}{n^{4}} \)
Subject: Maths
The centre of the circle given by \( \mathbf{r} \cdot(\mathbf{i}+ \)
\( 2 \mathbf{j}+2 \mathbf{k})=15 \) and \( |\mathbf{r}-(\mathbf{j}+2 \mathbf{k})|=\mathbf{4} \)
A \( .(0,1,2) \)
в. (1,3,4)
c. (-1,3,4)
D. None of these
Subject: Maths
The value of \( \sin 105^{0} \) is
A \( \cdot \frac{\sqrt{3}-1}{2 \sqrt{2}-1} \)
B. \( \frac{\sqrt{3}-1}{\sqrt{2}-1} \)
c. \( \frac{\sqrt{3}+1}{2 \sqrt{2}} \)
D. \( \frac{\sqrt{3}+1}{\sqrt{2}} \)
Subject: Chemistry
Consider the following reaction. \( o^{16} \)
\( \boldsymbol{C H}_{3}-\stackrel{\|}{\boldsymbol{C}}-\boldsymbol{O}^{18}-\boldsymbol{C}_{2} \boldsymbol{H}_{5}+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O}^{16} \frac{\boldsymbol{H} \boldsymbol{e} \boldsymbol{a} \boldsymbol{t}}{\boldsymbol{H}^{+}} \)
The products formed in the reaction are:
\( A \)
\( C H_{3}-\stackrel{\vartheta^{16}}{C}-O^{16} H \) and \( C_{2} H_{5} O^{18} H \)
В.
\[
C H_{3}-C^{\mid 6}-O^{18} H \text { and } C_{2} H_{5} O^{16} H
\]
\( c \)
\( C H_{3}-\stackrel{\vartheta^{16}}{C}-O^{16} H \) and \( C_{2} H_{5} O^{16} H \)
D. \( C H_{3}-\stackrel{\vartheta_{1}^{\prime 8}}{C}-O^{18} H \) and \( C_{2} H_{5} O^{18} H \)
Subject: Physics
The rectangular surface of area \( 8 \mathrm{cm} \times \)
\( 4 c m \) of a block body at a temperature of
\( 127^{\circ} C \) emits energy at the rate of \( E \) per
second. If the length and breath of the surface are each reduced to half of the
initial value and the temperature is
raised to \( 327^{\circ} \mathrm{C} \), the rate of emission of
energy will become
\( ^{\mathbf{A}} \cdot \frac{3}{8}^{E} \)
B \( \cdot \frac{81}{16} E \)
c. \( \frac{9}{16} E \)
D. \( \frac{81}{64} \)
Subject: Chemistry
The equivalent conductance at infinite
dilution of \( B a C l_{2}, H_{2} S O_{4} \) and \( H C l \)
aqueous solutions are \( x_{1}, x_{2} \) and \( x_{3} \)
respectively. The equivalent
conductance of \( B a S O_{4} \) solution is:
A. \( x_{1}+x_{2}-x_{3} \)
В. \( x_{1}-x_{2}-x_{3} \)
c. \( x_{1}+x_{2}-2 x_{3} \)
D. \( x_{1}-2 x_{2}-x_{3} \)
Subject: Physics
Calculate the change in the
gravitational potential energy of the
skier between \( A \) and \( B \) :
A \( \cdot 1.8 \times 10^{4} J \)
B . \( 3.6 \times 10^{2} J \)
c. \( 3.6 \times 10^{4} J \)
D \( .1 .8 \times 10^{2} J \)
Subject: Chemistry
Choose the correct answer among the alternatives given :
2-Chloro-2methylpropane on reaction
with alc. \( K O H \) gives \( X \) as the product \( x \) is \( ? \)
A. but-2-ene
B. 2-methylbut-1-ene
c. 2-methylprop-1-ene
D. 2-methylbutan-2-01
Subject: Physics
When we express the velocity of light,
\( \mathbf{3 0}, \mathbf{0 0}, \mathbf{0 0}, \mathbf{0 0 0} / \mathbf{m s}^{-1}, \) in standard form
up to three significant figures, it's value
is:
A \( \cdot 3 \times 10^{8} \mathrm{ms}^{-1} \)
B . \( 3.00 \times 10^{8} \mathrm{ms}^{-1} \)
c. \( 3 \times 10^{10} \mathrm{cms}^{-1} \)
D. \( 3 \times 10^{6} \mathrm{ms}^{-1} \)
Subject: Biology
Assertion
Specialization of cells is advantageous
for
the organism
Reason
It increase the operational efficiency of
an
organism
A. If both the assertion and the reson are true and the
reason
is correct explanation of the assertion.
B. If both the assertion and the reson are true but the
reason
is not correct explanation of the assertion.
C. If the assertion is true but the reason is false
D. If both the assertion and reason are false
Subject: Chemistry
Assertion
A reaction which is spontaneous and accompanied by decrease of
randomness must be exothermic.
Reason
All exothermic reactions are
accompanied by decrease of
randomness.
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
Select the correct option, among \( \boldsymbol{S} \boldsymbol{c}(\boldsymbol{I} \boldsymbol{I} \boldsymbol{I}), \boldsymbol{T} \boldsymbol{i}(\boldsymbol{I} \boldsymbol{V}), \boldsymbol{P} \boldsymbol{d}(\boldsymbol{I} \boldsymbol{I}) \) and \( \boldsymbol{C} \boldsymbol{u}(\boldsymbol{I} \boldsymbol{I}) \)
ions.
A. All are paramagnetic
c. \( S c(I I I), T i(I V) \) are paramagnetic and \( P d(I I I), C u(I I) \) are diamagnetic
D. \( S c(I I I), T i(I V) \) are diamagnetic and \( P d(I I), C u(I I) \) are paramagnetic
Subject: Chemistry
Rate constant K varies with
temperature by equation
\[
\log K\left(m i n^{-1}\right)=\log 5-
\]
\( \frac{2000}{R T \quad X \quad 2.303} \) we can conclude that?
A. Pre-exponential factor A is \( 10^{5} \)
B . \( E_{a} \) IS \( 2000 \mathrm{K} \) cal
C. \( E_{a} \) is \( 9.12 \mathrm{K} \) cal
D. The pre-exponential factor A is 5
Subject: Chemistry
The weight of an atom of Uranium is 238 amu. Its actual weight is
8
A. \( 1.43 \times 10^{26} \)
B. \( 3.82 \times 10^{-22} \)
c. \( 6.99 \times 10^{-23} \)
D. \( 1.53 \times 10^{-22} \)
Subject: Chemistry
The energy of the electron in the second
and third Bohr orbits of the hydrogen atom is \( -5.42 \times 10^{-12} \) erg and \( -2.41 \times 10 \)
-12 erg, respectively. The wave length of the emitted radiation when the electron
drops from third to second orbit will be :
\( A \cdot 6.6 \times 10^{3} \)
B. \( 6.6 \times 10^{-3} \)
c. \( 13.2 \times 10^{3} \)
D. 13.2 \( \times 10^{-3} \)
Subject: Chemistry
The reaction \( \boldsymbol{A}(s) \rightarrow 2 B(g)+C(g) \) is
first order. The pressure after 20 min. and after a very long time are \( 150 \mathrm{mm} \) Hg and 225 mm Hg. The value of rate
constant and pressure after 40 min are?
A. 0.05 In 1.5 min \( ^{-1}, 200 \) mm men
B. 0.5 In 2 min \( ^{-1}, 300 \) mm
c. 0.05 In 3 min\( ^{-1} \), 300 mm
D. \( 0.05 \operatorname{In} 3 \) min\( ^{-1}, 200 \mathrm{mm} \)
Subject: Physics
Two positive charges \( q \) and \( q \) are placed at
the diagonally opposite corners of a square and two negative charges \( -q \) and
\( -q \) are placed at the other two corners of the square. Then at the centre of the square the resultant electric intensity and the net electric potential Vare
A. \( E \neq 0, V=0 \)
в. \( E=0, V=0 \)
c. \( E=0, V \neq 0 \)
D. \( E \neq 0, V \neq 0 \)