AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
The electric potential between a proton and an electron is given by \( \boldsymbol{V}= \) \( \mathbf{V}_{0} \ln \frac{\mathbf{r}}{\mathbf{r}_{0}}, \) where \( \mathbf{r}_{0} \) is a constant
Assuming Bohr's model to be
applicable, write variation of \( \mathbf{r}_{\mathbf{n}} \) with
\( \mathbf{n}, \mathbf{n} \) being the principal quantum number?
\( A \cdot r_{n} \propto n \)
в . \( \mathrm{r}_{\mathrm{n}} \propto 1 / \mathrm{n} \)
\( c \cdot r_{n} \propto n^{2} \)
D. \( \mathrm{r}_{\mathrm{n}} \propto 1 / \mathrm{n}^{2} \)
Subject: Chemistry
\( A \) and \( B \) are two different chemical
species undergoing 1st order decomposition with half lives equal to 5 \( \sec \) and 7.5 sec respectively. If the initial concentration of \( A \) and \( B \) are in
the ratio \( 3: 2 . \) Calculate \( \frac{C_{A_{1}}}{C_{B_{1}}} \) after three
half lives of \( A \). Report your answer after
multiplying it with 100
Subject: Chemistry
Chloro compound of vanadium has only
spin magnetic moment of \( 1.73 B M \) This vanadium chloride has the
formula:
[Atomic number of \( \boldsymbol{V}=\mathbf{2 3}] \)
A \( \cdot V C l_{2} \)
в. \( V C l_{4} \)
c. \( V C l_{3} \)
D. \( V C l_{5} \)
Subject: Physics
A charge \( q \) is placed at the centre of the open end of cylindrical vessel. The flux of electric field through the surface of
the vessel is
A . 0
в. \( \frac{q}{\epsilon_{0}} \)
c. \( \frac{q}{2 \epsilon_{0}} \)
D. \( \frac{2 q}{\epsilon_{0}} \)
Subject: Maths
Let \( \boldsymbol{A}=\{\mathbf{1}, \mathbf{2}\} \) and \( \boldsymbol{B}=\{\mathbf{2}, \mathbf{3}, \mathbf{4}\}, \) then
\( \boldsymbol{A} \times \boldsymbol{A}=\{(\mathbf{1}, \mathbf{1}),(\mathbf{1}, \mathbf{2}),(\mathbf{2}, \mathbf{1}),(\mathbf{2}, \mathbf{2})\} . \) If
true enter \( 1, \) or else enter 0
Subject: Maths
n given figure \( A B C D \) is a
quadrilateral in which \( P, Q, R \) and \( S \) are
mid-points of the sides. \( A B, B C, C D \)
and \( D A . A C \) is a diagonal. Show that:
(i) \( \boldsymbol{S R} \| \boldsymbol{A C} \) and \( \boldsymbol{S R}=\frac{\mathbf{1}}{\mathbf{2}} \boldsymbol{A C} \)
(ii) \( \boldsymbol{P Q}=\boldsymbol{S} \boldsymbol{R} \)
(iii) \( P Q R S \) is a parallelogram
Subject: Maths
The function \( f(x)=\frac{x}{1+x \tan x} \) has
a point of minimum in the interval \( \left(0, \frac{\pi}{2}\right) \)
Bne point of maximum in the interval \( \left(0, \frac{\pi}{2}\right) \)
C. No point of maximum, no point of minimum in the interval \( \left(0, \frac{\pi}{2}\right) \)
Two points of maxima in the interval \( \left(0, \frac{\pi}{2}\right) \)
Subject: Physics
Two 220 volt, 100 watt bulbs are connected first in series and then in
parallel. Each time the combination is connected to a 220 volt a.c.supply line. The power drawn by the combination in each case respectively will be
A. 50 watt, 100 watt
B. 100 watt, 50 watt
c. 200 watt, \( , 150 \) watt
D. 50 watt, 200 watt
Subject: Maths
A factory has 500 workers, 15 percent of whom are women. If 50 additional
workers are to be hired and all of the
present workers remain, how many of the additional workers must be women
in order to raise the percent of women employees to 20 percent?
\( \mathbf{A} \cdot \mathbf{3} \)
B. 10
c. 25
D. 30
E. 35
Subject: Physics
A ball is moving uniformly in a circular path of radius \( 1 m \) with a time period of
1.5 \( s \). If the ball is suddenly stopped at
\( t=8.3 s, \) the magnitude of the
displacement of the ball with respect to
its position at \( t=0 s \) is closest to:
\( \mathbf{A} \cdot 1 m \)
в. 33 т
\( c .3 m \)
D. \( 2 m \)
Subject: Physics
If the dielectric constant and dielectric
strength be denoted by \( K \) and \( X \) respectively, then a material, suitable for use as a dielectric in a capacitors,
must have :
A. high \( K \) and high \( X \)
B. high \( K \) and low \( X \)
c. low \( K \) and high \( X \)
D. low \( K \) and low \( X \)
Subject: Physics
When a solid ball of volume \( V \) is
dropped into a viscous liquid, then a viscous force \( F \) acts on it. If another ball
of volume \( 2 V \) of the same material is
dropped in the same liquid then the viscous force experienced by it will be
\( \mathbf{A} \cdot 2 n F \)
в. \( \frac{n F}{2} \)
\( c .2 F \)
D. \( \frac{F}{2} \)
Subject: Physics
ABC represents the principal cross-
section of an equilateral prism made
with a transparent material. If PQRS
indicates the path of a light ray, find the refractive index of the material.
A \( \cdot \frac{1}{\sqrt{2}} \)
B. \( \frac{2}{\sqrt{3}} \)
\( c \cdot \sqrt{2} \)
D. \( \frac{\sqrt{3}}{2} \)
Subject: Physics
A plane electromagnetic wave in a non magnetic dielectric medium is given by \( \overline{\boldsymbol{E}}=\overline{\boldsymbol{E}}_{0}\left(\mathbf{4} \times \mathbf{1 0}^{-\mathbf{7}} \times-\mathbf{5 0} \boldsymbol{t}\right) \) with
distance being in meter and time in seconds. The dielectric constant of the
medium is:
A . 2.4
в. 5.8
\( c \cdot 8.2 \)
D. 4.8
Subject: Physics
Two identical equiconcex lenses made of glass of refractive index \( 1.5, \) placd in contact has power P. When a liquid of refractive index \( \mu \) is filled in the gap between the lenses, the power becomes \( \boldsymbol{P} \)
\( \overline{\mathbf{3}} \)
\( i f \mu=\frac{x}{3} . \) Find the value of \( x \)
Subject: Chemistry
Assertion
Dipole moment of bromobenzene is same as chloro benzene.
Reason
Dipole moment of \( C l-C \) bond is
greater than \( B r-C \) bond.
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
The integral \( \int_{\pi / 12}^{\pi / 4} \frac{8 \cos 2 x}{(\tan x+\cot x)^{3}} d x \)
equals:
A \( \cdot \frac{15}{128} \)
в. \( \frac{15}{64} \)
c. \( \frac{13}{32} \)
D. \( \frac{13}{256} \)
Subject: Physics
The electric potential at a point in free space due to a charge \( Q \) coulomb is \( Q \times 10^{11} V . \) The electric field at that
point is
A \( \cdot 4 \pi \varepsilon_{0} Q \times 10^{22} V / m \)
B . \( 127 \pi \varepsilon_{0} Q \times 10^{20} V / m \)
C. \( 4 \pi \varepsilon_{0} Q \times 10^{20} V / m \)
D . \( 12 \pi \varepsilon_{0} Q \times 10^{22} \mathrm{V} / \mathrm{m} \)
Subject: Maths
Solution of \( \sin ^{-1}\left[\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right]=\boldsymbol{x}+\boldsymbol{y} \) is:
A \( \cdot 1+\tan \left(\frac{x+y}{2}\right)=-\frac{2}{x+c} \)
B. \( 1+\cos \left(\frac{x+y}{2}\right)=-\frac{2}{x+c} \)
c. \( 1+\sec \left(\frac{x+y}{2}\right)=-\frac{2}{x+c} \)
D. \( 1+\cos \left(\frac{x+y}{2}\right)=\frac{2}{x+c} \)
Subject: Chemistry
The uncertainty in the position of an electron \( \left(\text { mass }=\mathbf{9 . 1} \times \mathbf{1 0}^{-\mathbf{2 8}} \mathbf{g}\right) \)
moving with a velocity of \( 3.0 \times \) \( 10^{4} c m^{-1} \) accurate up to \( 0.011 \%, \) will
be:
A . \( 1.92 \mathrm{cm} \)
B. 7.68 ст
c. \( 0.175 \mathrm{cm} \)
D. \( 3.84 \mathrm{cm} \)
Subject: Chemistry
Consider the reactions:
\( \boldsymbol{C}(s)+\mathbf{2} \boldsymbol{H}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{C} \boldsymbol{H}_{4}(\boldsymbol{g}) ; \boldsymbol{\Delta} \boldsymbol{H}= \)
\( -\boldsymbol{X} \boldsymbol{k} c a l \)
\( \boldsymbol{C}(\boldsymbol{g})+\boldsymbol{4} \boldsymbol{H}(\boldsymbol{g}) \longrightarrow \boldsymbol{C} \boldsymbol{H}_{4}(\boldsymbol{g}) ; \boldsymbol{\Delta} \boldsymbol{H}= \)
\( -\boldsymbol{X}_{1} \boldsymbol{k} c a l \)
\( \boldsymbol{C H}_{4}(\boldsymbol{g}) \longrightarrow \boldsymbol{C H}_{3}(\boldsymbol{g})+\boldsymbol{H}(\boldsymbol{g}) ; \boldsymbol{\Delta} \boldsymbol{H}= \)
\( +\boldsymbol{Y} \boldsymbol{k} c a l \)
The average bond energy of \( C-H \) bond
is
A \( \cdot \frac{X}{4} k c a l m o l^{-1} \)
B. \( Y \) kcal mol-
c. \( \frac{X_{1}}{4} k c a l m o l^{-} \)
D. \( X_{1} \) kcal mol\( ^{-1} \)
Subject: Maths
If \( A \) and \( B \) are two events then
This question has multiple correct options
\( \mathbf{A} \cdot P(A \cap B) \geq P(A)+P(B)-1 \)
B \( . P(A \cap B) \geq P(A)+P(B) \)
\( \mathbf{c} \cdot P(A \cap B)=P(A)+P(B)-P(A \cup B) \)
\( \mathbf{D} \cdot P(A \cap B)=P(A) \cdot P(B) \)
Subject: Biology
If the systolic pressure is \( 120 \mathrm{mm} \mathrm{Hg} \) and diastolic pressure is \( 80 \mathrm{mm} \) Hg, the pulse pressure is
B. \( 120+80=200 \mathrm{mm} \mathrm{Hg} \)
c. \( 120-80=40 \mathrm{mm} \) Hg
\( \mathbf{D} \cdot \frac{120}{80}=1.5 \mathrm{mm} \mathrm{Hg} \)
Subject: Physics
\( \operatorname{In} \operatorname{an} \operatorname{SHM} x=\operatorname{asin} \omega t, \) the minimum
0.5 second what is the minimum time
A . \( 0.3 \mathrm{s} \)
B. \( 0.4 \mathrm{s} \)
\( c \cdot 0.2 s \)
D. \( 0.1 \mathrm{s} \)
Subject: Physics
At a given instant, there are \( 25 \% \) undecayed radioactive nuclei in a sample. After \( 10 \mathrm{s} \), the number of undecayed nuclei reduces to \( 12.5 \% \) Calculate
(a) mean life of the nuclei and
(b) the time in which the number of
decayed nuclei will further reduce to
\( 6.25 \% \) of the reduced number
Subject: Chemistry
The rate of the reaction:
\( \boldsymbol{C H}_{3} \boldsymbol{C O O C}_{2} \boldsymbol{H}_{5}+\boldsymbol{N a O H} \rightarrow \)
\( \boldsymbol{C H}_{3} \boldsymbol{C O O N a}+\boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O H} \)
is given by the equation,
rate\( =\boldsymbol{k}\left[\boldsymbol{C H}_{3} \boldsymbol{C O O C}_{2} \boldsymbol{H}_{5}\right][\boldsymbol{N a O H}] \)
If concentration is expressed in \( m o l / L \)
the units of \( k \) are:
A \( \cdot m o l^{-2} L^{2} s^{-1} \)
B . \( \operatorname{molL}^{2} s^{-1} \)
c. \( L m o l^{-1} s^{-1} \)
D. \( s^{-1} \)
Subject: Maths
If \( f(g(a))=0 \) where \( g(x)=\frac{x}{4}+2 \) and
\( \boldsymbol{f}(\boldsymbol{x})=\left|\boldsymbol{x}^{2}-\boldsymbol{3}\right|, \) find the possible value
of \( \boldsymbol{a} \)
This question has multiple correct options
A. \( -8+4 \sqrt{3} \)
(
B . \( -(8+4 \sqrt{3}) \)
\( c \cdot 6 \)
D. 18
Subject: Chemistry
Consider the following statements
regarding halides of \( \boldsymbol{S} \)
(i) \( S F_{4} \) and \( S C l_{4} \) act as Lewis acid only.
(ii) \( S F_{4} \) and \( S C l_{4} \) act as Lewis base
only.
(iii) \( S F_{4} \) and \( S C l_{4} \) act both as Lewis acid and Lewis base.
The correct option is:
A. both (ii) a (iii) are correct
B. both (i) a (ii) are correct
c. only (iii) is correct
D. all are correct
Subject: Physics
A solenoid of length \( 50 \mathrm{cm}, \) having 100 turns carries a current of 2.5 A. The
magnetic field at one end of the solenoid is:
A. 3.14 \( \times 10^{4} \) न
B. 6.28 \( \times 10^{4} \) Т
c. \( 1.57 \times 10^{4} \) न
D. 9.42 \( \times 10^{4} \) न
Subject: Maths
The value of \( b \) such that scalar product of the vector \( (\hat{i}+\hat{j}+\hat{k}) \) with the unit vector parallel to the sum of the vectors \( (2 \hat{i}+4 \hat{j}-5 \hat{k}) \) and \( (b \hat{i}+2 \hat{j}+3 \hat{k}) \) is 1
is
A . -2
B. -
\( c .0 \)
D.
Subject: Maths
If the altitude of an equilateral triangle is \( \sqrt{6}, \) then the area is:
\begin{tabular}{l} 
A \( 2 \sqrt{2} \) \\
\hline
\end{tabular}
B. \( 2 \sqrt{3} \)
\( c \cdot 3 \sqrt{3} \)
D. \( 6 \sqrt{2} \)
E. 12
Subject: Physics
Q Type your question
red. Similarly if you look through a price of blue-tinted glass. Everything will be
seen in shades of blue.
Consider the following statements
I. The tinting process makes the glass absorb the corresponding colour, i.e. red tinted glass strongly absorbs red light, making ever thing appear red.
II. The tinting process makes the glass absorb all colours except the corresponding colour, i.e., red -tinted glass will strongly absorb blue and green, but not red
III. If you stack the red and blue-tinted pieces of glass and look through them, everything will look quite dark.
Which of these statements is/are true?
A . I and ॥
B. I and III
c. ॥ and III
D. Only I
Subject: Physics
A particle of mass \( 2 \mathrm{kg} \) moving with a velocity of \( 3 \mathrm{m} / \mathrm{s} \) is acted upon by a force which changes its direction of
motion by an angle of \( 90^{\circ} \) without changing its speed. What is the magnitude of impulse experienced by the particle?
\( A \cdot 6 N \)
B. 2 N s
c. \( 3 \sqrt{2} \) N s
D. \( 6 \sqrt{2} \) N s
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})= \)
\( (x-4)(x-5)(x-6)(x-7) \) then
A \( \cdot f^{\prime}(x)=0 \) has four roots
B. three roots of \( f^{\prime}(x)=0 \) lie in (4,5)\( \cup(5,6) \cup(6,7) \)
C. the equation \( f^{\prime}(x)=0 \) has only one root
D. three roots of \( f^{\prime}(x)=0 \) lie in (3,4)\( \cup(4,5) \cup(5,6) \)
Subject: Maths
\( \boldsymbol{A}=\{\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}\} \) and \( \boldsymbol{B}=\{\mathbf{5}, \mathbf{7}, \boldsymbol{9}\} . \) The
relation from \( B \) to \( A \) is
This question has multiple correct options
A \( \cdot\{(a, 5),(a, 7),(b, 7),(c, 9)\} \)
B . \{(5,7),(9,9),(7,5)\}
c. \( \{(5, a),(5, b),(5, c)\} \)
D \cdot \( \{(5, b),(7, c),(7, a),(9, b)\} \)
Subject: Chemistry
Assertion
Energy can be transferred between gaseous molecules during collisions
but \( u_{\mathrm{rms}} \) remains constant.
Reason
The average kinetic energy of gaseous
molecules remains constant as long as
the temperature is constant and
therefore, \( u_{\mathrm{rms}} \) remains unchanged during the collision.
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
A wave of frequency 500 Hz has a phase velocity of \( 360 \mathrm{m} / \mathrm{s} \). The phase difference between the two displacements at a certain point in a time interval of \( 10^{-3} \) seconds will be
how much?
A \( \cdot \frac{\pi}{2} \) radian
B. \( \pi \) radian
c. \( \frac{\pi}{4} \) radian
D. \( \frac{\pi}{8} \) radian
Subject: Maths
If \( \sqrt{\frac{\boldsymbol{v}}{\boldsymbol{\mu}}}+\sqrt{\frac{\boldsymbol{\mu}}{\boldsymbol{v}}}=\mathbf{6}, \) then \( \frac{\boldsymbol{d} \boldsymbol{v}}{\boldsymbol{d} \boldsymbol{\mu}}= \)
A. \( \frac{17 \mu-v}{\mu-17 v} \)
в. \( \frac{\mu-17 v}{17 \mu-v} \)
c. \( \frac{17 \mu+v}{\mu-17 v} \)
D. \( \frac{\mu+17 v}{17 \mu-v} \)
Subject: Chemistry
At what \( \left[O H^{-}\right] \) does the following half-
reaction have a potential of \( 0 V \) when other species are at 1 M?
\( N O_{3}^{-}+H_{2} O+2 e^{-} \rightarrow N O_{2}^{-}+ \)
\( \mathbf{2 O H}^{-}, \boldsymbol{E}_{c e l l}^{\circ}=\mathbf{0 . 0 1} \boldsymbol{V} \)
Subject: Chemistry
A radioactive element has atomic
number' \( Z \) and mass number'A'. Select
the correct statements among the
following.
This question has multiple correct options
A. Both ' \( A \) ' and ' \( Z \) ' decrease in \( \alpha \) -decay
B. Both 'A' and ' \( Z \) ' remain unchanged in \( \gamma \) -decay
C . 'A' remains unchanged and' \( Z \) ' decreases by one; the
process is called \( \beta^{+} \) (positron) decay or \( K \) -electron capture
D. Both 'A' and 'Z' increase in the nuclear isomerism
Subject: Physics
Choose the correct answer from the
alternatives given

A parallel plate capacitor with plate
area \( A \) and separation between the
plates \( d \) is charged by a constant current \( I . \) Consider a plane surface of area \( \frac{\boldsymbol{A}}{\mathbf{2}} \) parallel to the plate and drawn between the plates. The displacement current through the area is :
\( A \)
в. \( \frac{I}{2} \)
c. \( \frac{I}{4} \)
D. \( \frac{I}{8} \)
Subject: Physics
A wire of length \( 1 m \) and mass \( 20 g \) is stretched with a force of \( 800 N \). The
frequencies of the first two overtones
are
A. \( 200 H z, 300 H z \)
в. \( 300 H z, 200 H z \)
c. \( 100 H z, 400 H z \)
D. \( 400 H z, 100 H z \)
Subject: Maths
\( 2 \tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\left(\frac{1}{7}\right) \) is equal to
A. \( \frac{\pi}{6} \)
в. \( \frac{\pi}{4} \)
\( c \cdot \frac{\pi}{3} \)
\( D \cdot \frac{\pi}{2} \)
Subject: Maths
Using remainder theorem, find the
remainder when \( 2 x^{3}-3 x^{2}+4 x-5 \) is
divided by \( \boldsymbol{x}+\mathbf{3} \)
\( \mathbf{A} \cdot 204 \)
B . -136
\( c .-98 \)
D. 42
Subject: Chemistry
Calculate the e.m.f. (in \( V \) ) of the cell:
\( \boldsymbol{P t}\left|\boldsymbol{H}_{2}(\boldsymbol{g})\right| \boldsymbol{B O H}(\boldsymbol{a q}) \| \boldsymbol{H} \boldsymbol{A}(\boldsymbol{a q})\left|\boldsymbol{H}_{2}(\boldsymbol{g})\right| \boldsymbol{P} \)
Given: \( \boldsymbol{K}_{\boldsymbol{a}}(\boldsymbol{H} \boldsymbol{A})=\mathbf{1 0}^{-\mathbf{7}}, \boldsymbol{K}_{\boldsymbol{b}}(\boldsymbol{B O H})= \)
\( 10^{-5} \)
A . \( 0.43 \mathrm{V} \)
B . \( 0.36 V \)
c. \( 0.93 V \)
D. None of these
Subject: Maths
If \( y=\cos ^{-1}(\sqrt{x}), \) then find \( \frac{d y}{d x} \) using
first principle.
A \( \cdot-\frac{1}{\sqrt{1-x}} \)
в. \( \frac{1}{\sqrt{1-x}} \)
c. \( -\frac{1}{2 \sqrt{x} \sqrt{1-x}} \)
D. \( \frac{1}{2 \sqrt{x} \sqrt{1-x}} \)
Subject: Physics
In the nuclear reaction, \( 92 U^{238} \rightarrow 82 \)
\( P b^{208}, \) the number of \( \alpha \) and \( \beta \) particles
emitted are:
\( \mathbf{A} \cdot 7 \alpha, 5 \beta \)
B. \( 6 \alpha, 4 \beta \)
c. \( 4 \alpha, 3 \beta \)
D. \( 8 \alpha, 6 \beta \)
Subject: Chemistry
For the reaction, \( \boldsymbol{A}(\boldsymbol{g})+\boldsymbol{B}(\boldsymbol{g}) \rightarrow \)
\( C(g)+D(g) \)
\( \Delta H^{0} \) and \( \Delta S^{0} \) are,respectively \( -29.8 k J m o l^{-1} \) and \( -0.100 k J K^{-1} \)
\( \operatorname{mol}-1 \) at \( 298 \mathrm{K} \)
The equilibrium constant for the
reaction at \( 298 K \) is :
Subject: Chemistry
Two liquids \( A \) and \( B \) form a non ideal
solution which obey the equation:
\( \boldsymbol{P}_{\boldsymbol{T}}+\boldsymbol{P}_{\boldsymbol{A}}^{\boldsymbol{o}}+\boldsymbol{3}\left(\boldsymbol{P}_{\boldsymbol{B}}^{\boldsymbol{o}}-\boldsymbol{P}_{\boldsymbol{A}}^{\boldsymbol{o}}\right) \boldsymbol{X}_{\boldsymbol{B}}+\boldsymbol{2}\left(\boldsymbol{P}_{\boldsymbol{A}}^{\boldsymbol{o}}-\right. \)
\( \left.P_{B}^{o}\right) X_{B}^{2} \)
When an equimolar mixture of \( A \) and \( B \) is distilled, find the composition (by mole) when this mixture will have a
single boiling point.
\( \left(P_{B}^{o}>P_{A}^{o}\right) \) where \( P_{A}^{o} \) and \( P_{B}^{o} \) are vapour
pressure of pure \( A \) and \( B \) respectively
and \( X_{B}= \) is the mole fraction of \( B \) in
the liquid phase.
A. 3:
B. 2:3
c. 1: 2
D. 1: 3
Subject: Maths
\( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{l}a \tan ^{-1}\left(\frac{1}{x-4}\right) \text { if } 0 \leq x<4 \\ b \tan ^{-1}\left(\frac{2}{x-4}\right) \text { if } 4<x<6 \\ \sin ^{-1}(7-x)+a \frac{\pi}{4} \quad \text { if } \sin ^{-1}(7-2)\end{array}\right. \)
and \( f(4)=\pi / 2 \) is continuous on (0,8)
then
A . (1,1)
B. (1,-1)
c. (-1,1)
D. (-1,-1)
Subject: Maths
The value of \( \left|\begin{array}{ccc}\boldsymbol{a}-\boldsymbol{b}-\boldsymbol{c} & \boldsymbol{2} \boldsymbol{a} & \boldsymbol{2} \boldsymbol{a} \\ \boldsymbol{2} \boldsymbol{b} & \boldsymbol{b}-\boldsymbol{c}-\boldsymbol{a} & \boldsymbol{2} \boldsymbol{b} \\ \boldsymbol{2} \boldsymbol{c} & \boldsymbol{2} \boldsymbol{c} & \boldsymbol{c}-\boldsymbol{a}-\boldsymbol{b}\end{array}\right| \) will
n \( \mathbf{2 C} \)
A \( \cdot(a+b+c)^{2} \)
B \( \cdot(a+b+c)^{3} \)
c. \( (a-b-c)^{2} \)
D \( \cdot(a+b-c)^{2} \)
Subject: Chemistry
The standard e.m.f. of the cell involving
the reaction, \( 2 A g^{+}(a q)+H_{2}(g) \rightarrow \)
\( 2 A g(s)+2 H^{+}(a q), \) is \( 0.80 \mathrm{V} . \) The
standard oxidation potential of \( \mathrm{Ag} \) electrode is:
A . \( 0.80 V \)
в. \( -0.80 V \)
c. \( 0.40 V \)
D. \( 0.20 V \)
Subject: Physics
The input to the digital circuit are as
shown below. The output Y is:
\( \mathbf{A} \cdot A+B+\bar{C} \)
B . \( (A+B) \bar{C} \)
c. \( \bar{A}+\bar{B}+\bar{C} \)
\( \mathbf{D} \cdot \bar{A}+\bar{B}+C \)
Subject: Physics
An inset crawls up a hemispherical
surface very slowly. The coefficient of friction between the insect and the
surface is \( 1 / 3 . \) If the line joining the
center of the hemispherical surface to
the insect makes an angle \( \alpha \) with the
vertical, the maximum possible value of
\( \alpha \) is given by
\( \mathbf{A} \cdot \cot \alpha=3 \)
\( \mathbf{B} \cdot \tan \alpha=3 \)
\( \mathbf{c} \cdot \sec \alpha=3 \)
D. \( \operatorname{cosec} \alpha=3 \)
Subject: Chemistry
Which of the following statements
about anhydrous aluminium chloride is
correct?
A. It conducts electricity in aqueous solutions
B. It exists as dimer both in the vapour state below \( 350^{\circ} \mathrm{C} \)
and in non-polar solvents
C. It is prepared by heating \( A l_{2} O_{3} \) in a stream of sulphur
chloride \( \left(S_{2} C l_{2}\right) \) vapour and chlorine
D. All of these
Subject: Chemistry
Balanced reaction \( : 2 \mathrm{MnO}_{4}^{-}+\mathrm{I}^{-}+\mathrm{H}_{2} \mathrm{O} \)
\( \rightarrow 2 \mathrm{MnO}_{2}+2 \mathrm{OH}^{-}+\mathrm{IO}_{3}^{-1} \)
If true enter 1 else 0
\( A \)
Subject: Maths
Thecost of 3 televisions and \( 2 V . C . R . s \) is
Rs. 35,000 . The shop-keeper wants profit
of \( R s .1,000 . \) per television and \( R s .500 \)
per \( V . C . R . \) He can sell 2 televisions and
\( 1 V . C . R \) and he gets the total revenue as
Rs. 21,500 . Find the cost and the selling
price of a television and a \( V . C . R \)
Subject: Chemistry
In the reaction of phenol with \( \boldsymbol{C} \boldsymbol{H} \boldsymbol{C l}_{3} \)
and aqueous \( N a O H, \) the electrophile attacking the ring is:
A. \( C H C l_{3} \)
в. \( C H C l_{2} \)
\( \mathbf{c} \cdot: C C l_{2} \)
D. \( C O C l_{2} \)
Subject: Chemistry
A tester is used to check the conduction
of electricity through two liquids, labelled \( A \) and \( B \). It is found that the
bulb of the tester glows brightly for liquid A while it glows very dim for liquid B. You would conclude that:
A. liquid \( A \) is a better conductor than liquid \( B \)
B. liquid \( B \) is a better conductor than liquid \( A \)
c. both liquids are equally conducting
D. conducting properties of liquid cannot be compared in this manner.
Subject: Chemistry
Assertion: The Nernst equation gives concentration dependence of EMF of the
cell.
Reason: In a Daniell cell current flows
from cathode to anode.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false
Subject: Physics
Mark the correct statement(s):
A. The magnitude of the velocity of particle is equal to its speed
B. The magnitude of average velocity in an interval is equal to its average speed in that interval.
C. It is possible to have a situation in which the speed of a particle is always zero but the average speed is not
zero.
D. It is possible to have a situation in which the speed of the particle is never zero but the average speed in an interval is zero.
Subject: Chemistry
A vessel of 250 litre was filled with 0.01
mole of \( S b_{2} S_{3} \) and 0.01 mole of \( H_{2} \) to
attain the equilibrium at \( 440^{\circ} \mathrm{C} \) as :
\[
\begin{array}{r}
\boldsymbol{S b}_{2} \boldsymbol{S}_{3}(\boldsymbol{s})+\mathbf{3} \boldsymbol{H}_{2}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{S} \boldsymbol{b}(\boldsymbol{s})+ \\
\mathbf{3} \boldsymbol{H}_{2} \boldsymbol{S}(\boldsymbol{g})
\end{array}
\]
After equilibrium, the \( H_{2} S \) formed was analysed by dissolved it in water and treating with excess of \( P b^{2+} \) to give
1.19g of \( P b S \) as precipitate. What is the
value of \( \boldsymbol{K}_{c} \) at \( \mathbf{4 4 0}^{\circ} \boldsymbol{C} \)
A .
B. 2
\( c \cdot 4 \)
D.
Subject: Maths
If the system of linear equations
\( 2 x+2 a y+a z=0 \)
\( 2 x+3 b y+b z=0 \)
\( 2 x+4 c y+c z=0 \)
where \( a, b, c \epsilon R \) are non-zero and
distinct; has a non-zero solution, then:
A \( \cdot \frac{1}{a}, \frac{1}{b}, \frac{1}{c} \) are in A.P
B . \( a+b+c=0 \)
c. \( a, b, c \) are in A.P
\( \mathbf{D} \cdot a, b, c \) are in G.P