AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Let \( z \) be a complex number such that \( \left|\frac{\boldsymbol{z}-\boldsymbol{i}}{\boldsymbol{z}+\mathbf{2} \boldsymbol{i}}\right|=\mathbf{1} \) and \( |\boldsymbol{z}|=\frac{\mathbf{5}}{\mathbf{2}} . \) Then the
value of \( |z+3 i| \) is?
\( A \cdot \frac{7}{2} \)
в. \( \frac{15}{4} \)
\( c \cdot 2 \sqrt{3} \)
D. \( \sqrt{10} \)
Subject: Physics
What is minimum frequency of the
photon required to carry out transition
A \( \cdot 1.21 \times 10^{15} H z \)
B . \( 1.61 \times 10^{15} \mathrm{Hz} \)
c. \( 1.21 \times 10^{14} H z \)
D. \( 1.61 \times 10^{14} \mathrm{Hz} \)
Subject: Chemistry
\( \ln \operatorname{lab} H_{2} \mathrm{O}_{2} \) is prepared by
A \( \cdot \) cold \( H_{2} S O_{4}+B a O_{2} \)
в. \( H C l+B a O_{2} \)
c. \( \operatorname{conc.H}_{2} \mathrm{SO}_{4}+\mathrm{Na}_{2} \mathrm{O}_{2} \)
D. \( H_{2}+O_{2} \)
Subject: Chemistry
Peroxydisulphuric acid and its salts are powerful oxidizing agents. Thus it can be estimated reducing agents and also study the kinetics of the reaction.
Peroxydisulphuric acid:
A. is also called Marshall's acid
B. has two peroxy linkages
C. liberates \( I_{2} \) with \( K I \) I in a fast reaction
D. has oxidation number of sulphur as +7
Subject: Physics
Find the inductance of a solenoid of
length \( l_{0}, \) made of Cu windings of mass
m. The winding resistance is equal to \( R \)
The diameter of solenoid \( <<l . \rho_{0} \) is resistivity of Cu and \( \rho \) is density of the
Cu.
\( ^{\text {A }} \cdot \frac{\mu_{0} R m}{2 \pi l_{0} \rho \rho_{0}} \)
в. \( \frac{\mu_{0} R m}{4 \pi l_{0} \rho \rho_{0}} \)
c. \( \frac{\mu_{0} R m}{3 \pi l_{0} \rho \rho_{0}} \)
D. \( \frac{2 \mu_{0} R m}{3 \pi l_{0} \rho \rho_{0}} \)
Subject: Chemistry
In the reaction,
\( \mathbf{3} \boldsymbol{C u} \boldsymbol{O}+\mathbf{2 N H}_{3} \longrightarrow \boldsymbol{N}_{2}+\mathbf{3} \boldsymbol{H}_{2} \boldsymbol{O}+ \)
\( \mathbf{3} C u \)
the change of \( N H_{3} \) to \( N_{2} \) involves:
A . Loss of 6 electrons per mole of \( N_{2} \)
B. Loss of 3 electrons per mole of \( N_{2} \)
c. Gain of 6 electrons per mole of \( N_{2} \)
D. Gain of 3 electrons per mole of \( N_{2} \)
Subject: Physics
When temperature of a gas is \( 20^{\circ} \mathrm{C} \) and
pressure is changed from \( p_{1}=1.01 \times \)
\( 10^{5} P a \) to \( p_{2}=1.165 \times 10^{5} P a, \) the
volume changes by \( 10 \% . \) The bulk modulus is
\( \mathbf{A} \cdot 1.55 \times 10^{5} \)
B. \( 0.155 \times 10^{5} \)
C \( .1 .4 \times 10^{5} \)
D. \( 1.01 \times 10^{5} \)
Subject: Maths
Plane passing through the points \( A(2,1 \)
3), \( \mathrm{B}(-1,2,4) \) and \( \mathrm{C}(0,2,1) \). Determine its
point of intersection with the line \( r= \)
\( \boldsymbol{j}+\boldsymbol{k}+\boldsymbol{t}(\boldsymbol{2} \boldsymbol{i}+\boldsymbol{k}) \)
A \( \cdot(7,+1,4) \)
B. (9,+1,-2)
c. (7,-1,4)
D. (9,-1,2)
Subject: Physics
An electric dipole made up of a positive and negative charge, each of \( 1 \mu C \) separated by a distance of \( 2 \mathrm{cm} \), is placed in an electric field of \( 10^{5} N / C \).The work
done in rotating the dipole from the position of stable equilibrium through an angle of \( 180^{0} \) is :
A \( \cdot 2 \times 10^{-3} \) Joule
B . \( 2 \times 10^{-8} \) Joule
c. \( 4 \times 10^{-3} \) Joule
D. Zero
Subject: Chemistry
Number of electrons in \( 1.8 \mathrm{mL} \) of \( \boldsymbol{H}_{2} \boldsymbol{O} \)
are:
A \( \cdot 6.02 \times 10^{23} \)
B. \( 6.02 \times 10^{24} \)
c. \( 6.02 \times 10^{22} \)
D. \( 6.02 \times 10^{25} \)
Subject: Maths
A field is \( 225 m \) long and \( 175 m \) wide. It
has two roads in its centre of uniform
width of \( 5 m \), one parallel to its length
and the other parallel to its breadth.
Find the cost of levelling the roads at
Rs.3 per square metre.
A \( . \) Rs. 1975
в. \( R s .1125 \)
c. \( R s .592 \)
D. Rs.6125
Subject: Maths
In the above figure \( \boldsymbol{A B} \| \boldsymbol{C D} \)
\( \angle A B E=120^{\circ}, \angle D C E=110^{\circ} \) and
\( \angle B E C=x^{\circ} \) then \( x^{\circ} \) will be
\( A \cdot 60 \)
B. 50
\( c \cdot 4 \)
D. 70
Subject: Physics
A steel wire of length \( 5 \mathrm{m} \) is pulled to have an extension of \( 1 \mathrm{mm} \). Its \( \mathrm{Y} \) is \( 1.9 \mathrm{x} \)
\( 10^{4} \mathrm{N} / \mathrm{m}^{2} . \) The energy per unit volume stored in it is
A \( .3 .8 \times 10^{-4} \mathrm{J} / \mathrm{m}^{3} \)
B . \( 7.6 \times 10^{-4} J / m^{3} \)
C \( .1 .9 \times 10^{-4} J / m^{3} \)
D. \( 0.95 \times 10^{-4} \mathrm{J} / \mathrm{m}^{3} \)
Subject: Physics
A tuning fork of frequency 500 Hz is sounded on a resonance tube. The first
and second resonances are obtained at
\( 17 \mathrm{cm} \) and \( 52 \mathrm{cm} . \) The velocity of sound
is
A. \( 170 \mathrm{m} / \mathrm{s} \)
B. \( 350 \mathrm{m} / \mathrm{s} \)
c. \( 520 \mathrm{m} / \mathrm{s} \)
D. \( 850 \mathrm{m} / \mathrm{s} \)
Subject: Maths
Let \( A_{1}, A_{2} \) and \( A_{3} \) be subsets of a set \( X \)
Which one of the following is correct?
A. \( A_{1} \cup A_{2} \cup A_{3} \) is the largest subset of \( X \) containing
elements of each of \( A_{1}, A_{2} \) and \( A_{3} \)
B. \( A_{1} \cup A_{2} \cup A_{3} \) is the smallest subset of \( X \) containing
either \( A_{1} \) or \( A_{2} \cup A_{3} \) but not both
C. The smallest subset of \( X \) containing \( A_{1} \cup A_{2} \) and \( A_{3} \)
equals the smallest subset of \( X \) containing both \( A_{1} \) and \( A_{2} \cup A_{3} \) only if \( A_{2}=A_{3} \)
D. None of these
Subject: Maths
Four cubic blocks with edge \( 4 \mathrm{cm} \) were
kept two on top of two and fused
together into a block as shown. Find the total surface area of the block and the
\( \operatorname{cost} \) of painting it at \( R s .32 \) per \( c m^{2} \)
\begin{tabular}{|c|c|}
\hline 1 & 2 \\
\hline 3 & 4 \\
\hline
\end{tabular}
A. \( R s .8992 \)
B . \( R s .8092 \)
c. \( R s .8192 \)
D. \( R s .8190 \)
Subject: Physics
What is the relation between restoring force \( (\boldsymbol{F}) \) and displacement \( (\boldsymbol{x}) \) of \( \mathbf{a} \) particle to perform SHM.
A \( . F \propto x^{2} \)
B. \( F \propto x^{-2} \)
c. \( F \propto x^{1 / 2} \)
D. \( F \propto x \)
Subject: Maths
Find the value \( f(0) \) so that the function
\( \boldsymbol{f}(\boldsymbol{x})=\frac{1}{x}-\frac{2}{e^{2 x}-1}, \boldsymbol{x} \neq 0 \) is continuous
at \( x=0 \& \) examine the differentiability
of \( f(x) \) at \( x=0 \)
A \( \cdot f(0)=0, \) differentiable at \( x=0 \)
B. \( f(0)=0, \) not differentiable at \( x=0 \)
\( \mathrm{c} . f(0)=1, \) differentiable at \( x=0 \)
D. \( f(0)=1, \) not differentiable at \( x=0 \)
Subject: Physics
A thick strip of copper is mounted as a compound pendulum about O.If it is made to swing through a uniform magnetic field B normal to the plane of the strip then (neglecting air resistance) it is found that
A. strip swings almost freely.
B. motion of the strip is heavily damped.
c. strip does not oscillate at all but immediately comes to rest in the vertical position
D. strip swings almost freely but its temperature decreases
Subject: Chemistry
The correct order of boiling points of the
following amines
\( \boldsymbol{C}_{\mathbf{4}} \boldsymbol{H}_{\mathbf{9}} \boldsymbol{N} \boldsymbol{H}_{\mathbf{2}},\left(\boldsymbol{C}_{\mathbf{2}} \boldsymbol{H}_{\mathbf{5}}\right)_{\mathbf{2}} \boldsymbol{N} \boldsymbol{H}, \boldsymbol{C}_{\mathbf{2}} \boldsymbol{H}_{\mathbf{5}} \boldsymbol{N}(\boldsymbol{C} \boldsymbol{I} \)
is :
\( \mathbf{A} \cdot c_{2} H_{5} N\left(C H_{3}\right)_{2}>\left(C_{2} H_{5}\right)_{2} N H>C_{4} H_{9} N H_{2} \)
B \( \cdot\left(C_{2} H_{5}\right)_{2} N H>C_{2} H_{5} N\left(C H_{3}\right)_{2}>C_{4} H_{9} N H_{2} \)
\( \mathrm{c} \cdot_{C_{4} H_{9} N H_{2}>}\left(C_{2} H_{5}\right)_{2} N H>C_{2} H_{5} N\left(C H_{3}\right)_{2} \)
\( \mathbf{D} \cdot\left(C_{2} H_{5}\right)_{2} N H>C_{4} H_{9} N H_{2}>C_{2} H_{5} N\left(C H_{3}\right)_{2} \)
Subject: Maths
Find the Median from the following
table-
\( \begin{array}{llll}\text { Class } & \mathbf{0}- & \mathbf{2 0 -} & \mathbf{4 0 -} \\ \text { Interval } & \mathbf{2 0} & \mathbf{4 0} & \mathbf{6 0}\end{array} \)
17
26
Frequency 10
Subject: Chemistry
Which one of the following is reduced by
\( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) in alkaline medium?
A \( \cdot F e^{2} \)
в. НОС\( l \)
\( \mathbf{c} \cdot K M n O_{4} \)
D. \( P b S \)
E \( . M n^{2+} \)
Subject: Physics
An object is placed at a distance of \( 10 \mathrm{cm} \) from the curved surface of a glass hemisphere of radius \( 10 \mathrm{cm} \). Find the position of the image from the flat surface.
A \( .26 .67 \mathrm{cm} \)
в. 2.67 ст
\( c \cdot 2 c m \)
D. \( 19.67 \mathrm{cm} \)
Subject: Physics
Read the following statements and pick
the correct choice
Statement A: With increase in
temperature, viscosity of a gas increases and that of a liquid
decreases.
Statement B: If the density of a small sphere is equal to the density of the liquid in which it is dropped, then the terminal velocity of the sphere will be
zero.
A. Both A and B are true
B. Both A and B are false
c. A is true and B is false
D. B is true but A is false.
Subject: Maths
Cylinder \( A \) has diameter \( 14 \mathrm{cm}, \) and the
height is \( 7 \mathrm{cm}, \) and cylinder \( B \) has
diameter \( 7 \mathrm{cm} \) and height is \( 14 \mathrm{cm} \)
Without calculation tell volume of
which cylinder is more? Verify the
answer by calculation
Subject: Maths
If \( f(x)=\frac{2 x-4}{x^{2}-1} \) and \( f^{\prime}(x)=\frac{p}{\left(x^{2}-1\right)^{2}} \)
then p equals-
A \( \cdot x^{2}-8 x-2 \)
B. \( -2 x^{2}+8 x+2 \)
c. \( 4 x+2 \)
D. \( -2 x^{2}+8 x-2 \)
Subject: Physics
Keeping the source frequency equal to
the resonating frequency of the series
LCR circuit, if the three elements, \( L, C \)
and \( R \) are arranged in parallel, show that the total current in the parallel LCR
circuit is minimum at this frequency.
Obtain the current RMS value in
each branch of the circuit for the
elements and source specified as below
for this frequency.
The figure shows a series LCR circuit
connected to a variable frequency \( 230 V \)
source. \( \boldsymbol{L}=\mathbf{5 . 0 H}, \boldsymbol{C}=\mathbf{8 0} \boldsymbol{\mu} \boldsymbol{F}, \boldsymbol{R}= \)
\( 40 \Omega \)
Subject: Maths
ff \( \overrightarrow{\boldsymbol{p}}=\mathbf{3} \overrightarrow{\boldsymbol{a}}-\mathbf{5} \overrightarrow{\boldsymbol{b}} ; \overrightarrow{\boldsymbol{q}}=\mathbf{2} \overrightarrow{\boldsymbol{a}}+\overrightarrow{\boldsymbol{b}} ; \overrightarrow{\boldsymbol{r}}=\overrightarrow{\boldsymbol{a}}+ \)
\( 4 \vec{b} ; \vec{s}=-\vec{a}+\vec{b} \) are four
vectors such that \( \sin (\vec{p} \wedge \vec{q})=1 \) and \( \sin (\vec{r} \wedge \vec{s})=1 \) then \( \cos (\vec{a} \wedge \vec{b}) \) is
A \( \cdot-\frac{19}{5 \sqrt{43}} \)
B.
\( c \cdot 1 \)
D. \( \frac{19}{5 \sqrt{43}} \)
Subject: Physics
The following three objects (1) a metal
tray,
(2) a block of wood,and (3) a
wooden cap are left in a closed room
overnight. Next day the temperature of
each is recorded as \( T_{1}, T_{2} \) and \( T_{3} \)
respectively. The likely situation is
A. \( T_{1}=T_{2}=T_{3} \)
в. \( T_{3}>T_{2}>T_{1} \)
c. \( T_{3}=T_{2}>T_{1} \)
D. \( T_{3}>T_{2}=T_{1} \)
Subject: Chemistry
\( \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{6}}+\boldsymbol{C l}_{2}(\boldsymbol{e} \boldsymbol{x} \boldsymbol{c} \boldsymbol{e} \boldsymbol{s} \boldsymbol{s}) \frac{A \boldsymbol{n} \boldsymbol{h} \boldsymbol{y} \cdot \boldsymbol{A} \boldsymbol{c} \hat{d}_{3}}{d \boldsymbol{a r k}, c o l d} \boldsymbol{P} \)
Product, \( \boldsymbol{P} \) is:
\( \mathbf{A} \cdot C_{6} H_{5} C l \)
B \( . C_{6} H_{4} C l_{2} \)
c. \( C_{6} H_{6} C l_{6} \)
D. \( C_{6} C l_{6} \)
Subject: Biology
Select the correct option:
During electron transport system(ETS), electron transport proceeds from carriers that have
potential to those having redox potential. This electron transport down the energy gradient leads to the formation of ATP from ADP and Pi, which
is referred to as
A. Low, high, oxidative phosphorylation
B. Low, high, oxidative decarboxylation
c. High, low, oxidative phosphorylation
D. High, low, oxidative decarboxylation
Subject: Maths
If the points with position vectors \( 60 \hat{i}+ \) \( \mathbf{3} \hat{\mathbf{j}}, \mathbf{4 0} \hat{\mathbf{i}}-\mathbf{8} \hat{\mathbf{j}} \) and \( \boldsymbol{a} \hat{\mathbf{i}}-\mathbf{5 2} j \) are collinear
then \( a=? \)
A . -40
B. -20
c. 20
D. 40
Subject: Chemistry
A weak mono acidic base is \( 5 \% \) ionized
in \( 0.01 M \) solution. The hydroxide ion
concentration in the solution is:
A. \( 5 \times 10^{-2} \)
В. \( 5 \times 10^{-4} \)
c. \( 5 \times 10^{-10} \)
D. \( 2 \times 10^{-11} \)
Subject: Chemistry
Which of the following statements is
not correct about the structure of \( \boldsymbol{P C l}_{5} \)
\( ? \)
A . \( P C l_{5} \) has a trigonal bipyramidal structure
B. Three equatorial P-CI bonds are equivalent
c. The two axial bonds are different and longer than equatorial bonds
D. Equatorial bond pairs suffer more repulsion than that of the axial bond pairs
Subject: Physics
A student performs an experiment to determine the Young's modulus of a
wire, exactly \( 2 m \) long, by Searle's method. In a particular reading, the student measures the extension in the
length of the wire to be \( 0.8 m m \) with an
uncertainty of \( 0.05 m m \) at a load of
exactly \( 1.0 \mathrm{kg} \). The student also
measures the diameter of the wire to be
\( 0.4 m m \) with an uncertainty of \( 0.01 m m . \) Take \( g=9.8 m s^{-2}(\text {exact }) \)
The Young's modulus obtained from the reading is
A \( \cdot(2.0 \pm 0.3) \times 10^{11} N m^{-2} \)
в. \( (2.0 \pm 0.2) \times 10^{11} \mathrm{Nm}^{-2} \)
c. \( (2.0 \pm 0.1) \times 10^{11} \mathrm{Nm}^{-2} \)
D. \( (2.0 \pm 0.05) \times 10^{11} \mathrm{Nm}^{-2} \)
Subject: Physics
What is the electric potential at the
centre of square of side 1 m? The
charges \( 1 \times 10^{-8} C,-2 \times 10^{-8} C, 3 \times \)
\( 10^{-8} C \) and \( 2 \times 10^{-8} C \) are placed at the
corners of the square.
\( \mathbf{A} \cdot 205 V \)
B. \( 308 V \)
\( c .509 V \)
D. \( 110 V \)
Subject: Chemistry
Write the formula for each of the
following complexes:
(a) tetraamminecopper (II) sulphate
(b) potassium tetracyanonickelate (0)
(c) bis (cyclopentadiehyl)iron(II)
(d) tetrathicyanato -N-zinc (II)
(e) diamminebis (ethylenediamine) cobalt (III) chloride
\( (f) \)
tetraammineddithiocyanatochromium
\( (\| I) \)
(g) potassium tetraoxomanganate (VII)
(h) potassium terioxalatoalumminate
\( (\| I) \)
(i) tetrapyridineplatinum (II) tetrachloroplatinate (II)
Subject: Physics
Two blocks \( A \) and \( B \) each of mass \( m \) are
placed on a smooth horizontal surface.
Two horizontal forces \( F \) and \( 2 F \) are
applied on blocks \( A \) and \( B \), respectively,
as shown in \( F i g . . \) Block a does not slide
on block B. Then the normal reaction
acting between the two blocks in
(assume no friction between the
blocks)
\( A \cdot F \)
B. \( f / 2 \)
\( c \cdot \frac{F}{\sqrt{3}} \)
D. \( 3 F \)
Subject: Maths
If \( f(x)=\cos ^{-1}\left\{\frac{1-\left(\log _{e} x\right)^{2}}{1+\left(\log _{e} x\right)^{2}}\right\} \), then
\( \boldsymbol{f}^{\prime}(\boldsymbol{e}) \)
A. Does not exist
B.
c.
D. Is equal to 1
Subject: Physics
A point light source are located at \( P_{1} \) as shown in the figure in which all sides of the polygon are equal. The intensity of illumination at \( P_{2} \) is \( 8 \frac{W}{m^{2}}, \) what will be
the intensity of illumination at \( P_{3} \)
A \( \cdot 3 \sqrt{3} \frac{W}{m^{2}} \)
в. \( 6 \frac{W}{m^{2}} \)
с. \( _{8^{2}} \frac{W}{^{2}} \)
D. \( \sqrt{3} \frac{w}{m^{2}} \)
Subject: Physics
Two discs of moments of inertia \( I_{1} \) and
\( I_{2} \) about their respective axes (normal to the disc and passing through the centre), and rotating with angular
\( \operatorname{speeds} \omega_{1} \) and \( \omega_{2} \) are brought into contact face to face with their axes of
rotation coincident.
(a) What is the
angular speed of the two-disc system?
(b) Show that the kinetic energy of the combined system is less than the sum of the initial kinetic energies of the
two discs. How do you account for this
loss in energy? Take \( \omega_{1} \neq \omega_{2} \)
Subject: Chemistry
The resistance of \( 1 \mathrm{N} \) solution of acetic
acid is \( 250 \Omega \) when measured in a cell
having a cell constant of \( 1.15 \mathrm{cm}^{-1} . \) The
equivalent conduction (in oh \( m^{-1} c m^{2} e q u i v^{-1} \) ) of \( 1 N \) acetic acid is
A . 2.3
B. 4.6
c. 9.2
D. 18.4
Subject: Chemistry
A complex compound of cobalt has
molecular formula containing five \( \boldsymbol{N} \boldsymbol{H}_{3} \)
molecules, one \( N O_{2} \) group and two \( C l \)
atoms for one \( C \) otom. One mole of this
compound produces three moles of ions in aqueous solution. On reacting with
an excess of \( A g N O_{3} \) solution,
two moles of \( A g C l \) get precipitated. The
ionic formula of the compound is:
\( \mathbf{A} \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{4} N O_{2} C l\right]\left[\left(N H_{3}\right) C l\right] \)
B \( \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{5} C l\right]\left[C l\left(N O_{2}\right)\right. \)
\( \mathbf{c} \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{5}\left(N O_{2}\right)\right] C l_{2} \)
D. \( \left[\operatorname{Co}\left(N H_{3}\right)_{5}\right]\left[\left(N O_{2}\right) C l_{3}\right] \)
Subject: Maths
Equation of a straight line meeting the circle \( x^{2}+y^{2}=100 \) in two points each
point at a distance of 4 from the point (8,6) on the circle is
A. \( 4 x+3 y-50=0 \)
B. \( 4 x+3 y-100=0 \)
c. \( 4 x+3 y-46=0 \)
D. none of these
Subject: Physics
Two isolated metallic solid sphere of radius \( R \) and \( 2 R \) are charged such that both of these have same charge density
a. the spheres are locted far away from each other and are connected by a thin
conducting wire . the new charge density on the bigger sphere is
A \( \cdot \frac{5 \sigma}{6} \)
в. \( \frac{56 \sigma}{5} \)
c. \( \frac{3 \sigma}{5} \)
D. \( \frac{52 \sigma}{6} \)
Subject: Chemistry
The velocity of the electron in 3rd orbit
of hydrogen atom in \( \mathrm{cm} s^{-1} \)
A \( \cdot 4.88 \times 10^{4} \)
B . \( 2.44 \times 10^{8} \)
c. \( 7.29 \times 10^{7} \)
D. \( 2.44 \times 10^{12} \)
Subject: Maths
The lengths of the perpendicular from
the points \( \left(\boldsymbol{m}^{2}, \boldsymbol{2 m}\right),\left(\boldsymbol{m m}^{\prime}, \boldsymbol{m}+\boldsymbol{m}^{\prime}\right) \)
and \( \left(m^{\prime 2}, 2 m^{\prime}\right) \) to the line \( x+y+1=0 \)
form
\( \cos \alpha+y \sin \alpha+\sin \alpha \tan \alpha=0 \) are in
\( A \). an A.P.
B. a G.P.
c. а н.Р.
D. none of these
Subject: Chemistry
For a dilute solution containing 2.5 g of a non-volatile non-electrolyte solute in \( 100 g \) of water, the elevation in boiling point at 1 atm pressure is 2 ?. Assuming
that the concentration of solute is much
lower than the concentration of solvent,
the vapour pressure (in \( \mathrm{mm} \) of \( \mathrm{Hg} \) ) of the
solution is:
[Take \( : K_{b}=0.76 K k g \) mol \( ^{-1} \) ]
Subject: Physics
The second's hand of a watch has \( 6 \mathrm{cm} \)
length. The speed of tis tip and magnitude of difference in velocity of its at any two perpendicular positions will be respectively:
\( \mathbf{A} \cdot 2 \pi \) and \( 0 \mathrm{mm} / \mathrm{s} \)
B. \( 2 \sqrt{2} \pi \) and \( 4.44 \mathrm{mm} / \mathrm{s} \)
\( \mathrm{c} \cdot 2 \sqrt{2} \pi \) and \( 2 \pi \mathrm{mm} / \mathrm{s} \)
D. \( 2 \pi \) and \( 2 \sqrt{3} \pi \mathrm{mm} / \mathrm{s} \)
Subject: Maths
ffunction \( f(x) \) is continuous in interval \( [-2,2], \) find the value of \( (a+b) \)
where \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ll}\frac{\sin a x}{x}-2, & \text { for }-2 \leq x<0 \\ 2 x+1, & \text { for } 0 \leq x \leq 1 \\ 2 b \sqrt{x^{2}+3}-1, & \text { for } 1<x \leq 2\end{array}\right. \)
Subject: Maths
The maximum bowling speed (kms/hour) of 33 players at a cricket coaching centre is given below:
Find the modal bowling speed of
players.
Bowling 85
\( \begin{array}{ll}100 & 115\end{array} \)
speed \( (\mathrm{kms} / \mathrm{hr}) \)
\( \begin{array}{lll}\text { DO } & 115 & 130\end{array} \)
No. of Players
A. Rs. 101kms/hour
B. Rs.106 kms/hour
c. Rs.115 kms/hour
D. Rs.118 kms/hour
Subject: Chemistry
If quantities \( \Delta T_{f}, \Delta T_{b}, \Delta p \) and \( \pi \) without subscript refer to the electrolyte solution and these with subscript refer to non-electrolyte solution then which one is wrong?
\( ^{\mathbf{A}} \cdot_{i}=\frac{\Delta T_{f}}{\left(\Delta T_{f}\right)_{0}} \)
в. \( _{i}=\frac{\Delta T_{b}}{\left(\Delta T_{b}\right)_{0}} \)
c. \( _{i}=\frac{\Delta P}{\left(P^{0}\right)_{0}} \)
D. \( _{i}=\frac{\pi}{(\pi)_{0}} \)
Subject: Chemistry
What happens when white phosphorus is heated with caustic soda?
Which of the following are possible
products?
This question has multiple correct options
\( \mathbf{A} \cdot \mathbf{P H}_{3} \)
В. РН \( _{5} \)
\( \mathrm{c} \cdot \mathrm{NaH}_{2} \mathrm{PO}_{2} \)
D. \( \mathrm{NaH}_{4} \mathrm{PO}_{2} \)
Subject: Physics
A ball is thrown from rear end of the
compartment of train to the front end which is moving at a constant horizontal velocity. An observer \( \boldsymbol{A} \) sitting in compartment and another
observer \( B \) standing on the ground draw
the trajectory. They will have
A. equal horizontal and equal vertical ranges.
B. equal vertical ranges but different horizontal ranges
c. different vertical ranges but equal horizontal ranges
D. different vertical ranges and different horizontal ranges
Subject: Chemistry
Select the species having zero oxidation state at the underlined elements.
This question has multiple correct options
\( \mathbf{A} \cdot\left(C H_{3}\right)_{2} S O \)
B. \( \underline{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11} \)
c. \( H_{2} S O_{3} \)
D. \( \underline{N}_{2} H_{4} \)
Subject: Chemistry
Which of the following statement is
correct?
\( \mathbf{A} \cdot E_{\text {cell}} \) and \( \triangle_{r} G \) of cell reaction both are extensive
properties
B. \( E_{\text {cell}} \) and \( \triangle_{r} G \) of cell reaction both are intensive
properties
C. \( E_{\text {cell}} \) in the intensive property while \( \triangle_{r} G \) of cell reaction is an extensive property.
D. \( E_{\text {cell}} \) in the intensive property while \( \triangle_{r} G \) of cell reaction is an intensive property.
Subject: Physics
Assertion
The sensitivity of a moving coil galvanometer is increased by placing a
suitable magnetic material as a core
inside the coil.
Reason
Soft iron has a high magnetic
permeability and cannot be easily magnetized or demagnetized.
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
Find the quotient and remainder on dividing \( p(x) \) by \( g(x) \) in the following case, without actual division.
\( \boldsymbol{p}(\boldsymbol{x})=\boldsymbol{x}^{3}+\boldsymbol{4} \boldsymbol{x}^{2}-\boldsymbol{6} \boldsymbol{x}+\boldsymbol{2} ; \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{x}- \)
3
Subject: Physics
Assertion
Assertion: When a light wave travels
from a rarer to a denser medium, its
speed decreases. The decrease in speed
imply a reduction in energy carried by the light wave.
Reason
Reason: The energy of a wave is inversely proportional to velocity of
wave
A. If both assertion and reason are true and reason is the correct explanation of assertion
B. If both assertion and reason are true and reason is not the correct explanation of assertion.
c. If assertion is true but reason is false
D. If both assertion and reason are false
Subject: Chemistry
In the reaction \( 2 P(g)+Q(g) \rightleftharpoons \)
\( 3 R(g)+S(g) . \) If 2 moles each of \( P \) and
\( Q \) is taken initially in a 1 litre flask. At equilibrium which of the following is
true?
\( \mathbf{A} \cdot[P]<[Q] \)
B \( \cdot[P]=[Q] \)
\( \mathbf{c} \cdot[Q]=[R] \)
D. None of these
Subject: Chemistry
Formal charge on nitrogen and oxygen
in \( N O_{3}^{-} \) ion are respectively:
A \( \cdot_{0, \frac{-1}{3}} \)
в. \( +1, \frac{-1}{3} \)
\( c \cdot+1, \frac{-2}{3} \)
D. \( _{0, \frac{-2}{3}} \)