AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
The gravitational force of attraction between two bodies at a certain
distance is \( 10 \mathrm{N} \). If the distance
between them is doubled, the force of
attraction:
A. decreases by \( 50 \% \)
B. decreases by \( 75 \% \)
C. increases by \( 50 \% \)
D. increases by \( 75 \% \)
Subject: Physics
toppr
Q Type your question
totally reflected internally and is "trapped" within the rod even if it is curved, provided the curvature is not
too great. the rod. is something referred to as a light pipe. A bundle of fine fiber will behave in the same way and has the
advantage of being flexible. The study of the properties of such a bundle is an active field of research known as fiber
optics. A bundle may consist of thousand of individual fibers, each of the order of
0.002 to \( 0.01 \mathrm{mm} \) in diameter. If the fiber
can be assembled in the bundle so that
the relative positions of the ends are the same at both ends, the bundle can transmit an image as shown in Fig.(b) Bundles several km in length have been
made. Device using fiber optics are finding a wide range of applications in medical science. The interior of lungs
and other passage in the human body can be viewed by insertion of a fiber bundle that can be enclosed in a
hypodermic needle for the study of
tissues and blood vessels far beneath
the skin. Despite the enormous technical difficulties of manufacturing fiber-optic components, such system promise to become an extremely important class of optical systems.
(1) what are the losses in fiber optic?
this question has multiple correct options
A. Brillouin zone and Raman scattering
B. polarisation
c. evanscent field
D. diffraction
Subject: Chemistry
Which choice or choices demonstrate
amphoterism?
\( . H C l+H_{2} O \rightarrow H_{3} O^{+}+C l^{-} \) and
\( \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{N}_{3} \rightarrow \boldsymbol{O} \boldsymbol{H}^{-}+\boldsymbol{N} \boldsymbol{H}_{4}^{-} \)
ii. \( \boldsymbol{H} \boldsymbol{S}^{-}+\boldsymbol{H} \boldsymbol{C l} \rightarrow \boldsymbol{C l}^{-}+\boldsymbol{H}_{2} \boldsymbol{S} \) and
\( \boldsymbol{H} \boldsymbol{S}^{-}+\boldsymbol{N} \boldsymbol{H}_{3} \rightarrow \boldsymbol{N} \boldsymbol{H}_{4}^{+}+\boldsymbol{S}^{2-} \)
iii. \( \boldsymbol{H C l}+\boldsymbol{N a O H} \rightarrow \boldsymbol{N a C l}+\boldsymbol{H}_{2} \boldsymbol{O} \)
and \( N a C l+H_{2} O \rightarrow H C l+N a O H \)
A . i only
B. ii only
c. iii only
D. i and ii only
E. i and iii only
Subject: Physics
\( \chi_{1} \) and \( \chi_{2} \) are susceptibility of \( a \)
paramagnetic material at
temperatures \( T_{1} K \) and \( T_{2} K \)
respectively, then
A \( \cdot x_{1}=x_{2} \)
в. \( \chi_{1} T_{1}=\chi_{2} T_{2} \)
c. \( \chi_{1} T_{2}=\chi_{2} T_{1} \)
D \cdot \( \chi_{1} \sqrt{T_{1}}=\chi_{2} \sqrt{T_{2}} \)
Subject: Physics
Assertion
The center of mass of a body may lie where there is no mass.
Reason
Centre of mass of a body is a point, where the whole mass of the body is
supposed to be concentrated.
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
Escape velocity at surface of earth is
11.2Km/s. Escape valocity from a planet whose mass is the same as that of earth and radius \( 1 / 4 \) that of earth, is?
A \( .2 .8 \mathrm{km} / \mathrm{s} \)
B. \( 15.6 \mathrm{km} / \mathrm{s} \)
c. \( 22.4 \mathrm{km} / \mathrm{s} \)
D. \( 44.8 \mathrm{km} / \mathrm{s} \)
Subject: Physics
Given a body has a heat capacity of
1.6 \( c a l /^{o} C . \) What is the amount of heat
required to raise its temperature by
\( \mathbf{1 0}^{\circ} \boldsymbol{C} ? \)
\( \mathbf{A} \cdot 16 \mathrm{cal} \)
B. 1.6 call
\( c .8 \) са\( a l \)
D. 4 call \( l \)
Subject: Physics
A capacitor of capacitance \( C \) is charged
to a potential difference \( V \) from a cell and then disconnected from it. A charge
\( +Q \) is now given to its positive plate. The potential difference across the capacitor is now
A. \( V \)
B. \( V+\frac{Q}{C} \)
c. \( _{V}+\frac{Q}{2 C} \)
D. \( V-\frac{Q}{C}, \) if \( Q<C V \)
Subject: Physics
Two wave of wavelength \( 1.00 \mathrm{m} \) and 1.01
\( \mathrm{m} \) produce 10 beats in \( 3 \mathrm{s} \) in a gas. The speed of sound in the gas will be
A \( .316 .6 m s^{-1} \)
B. \( 336.6 m s^{-1} \)
\( \mathbf{c} \cdot 356.6 m s^{-1} \)
D. \( 396.6 m s^{-1} \)
Subject: Chemistry
Chlorine does not show hydrogen bonding in its compounds while nitrogen shows hydrogen bonding in its compounds. Identify the correct reason
A. Chlorine is not as highly electronegative as nitrogen
B. Chlorine has vacant d-orbitals while nitrogen has no vacant'd' sub shell
c. \( H-C l \) bond is stronger than \( N-H \) bond
D. chlorine has larger size than nitrogen
Subject: Physics
Two capacitors of plate area \( A \) are joined as shown in the figure. Their central rigid part is movable. The capacity of the combination will be:
A \( \cdot \frac{\epsilon_{0} A}{a-b} \)
в. \( \frac{\epsilon_{0} A}{a+b} \)
c. \( \frac{2 \in_{0} A}{a+b} \)
D. \( \frac{a-b}{\epsilon_{0} a} \)
Subject: Physics
The free end of a thread wound on a
bobbin is passed round a nail \( \boldsymbol{A} \)
hammered into the wall. The thread is
pulled at a constant velocity. Assuming
pure rolling of bobbin, find the velocity
\( v_{0} \) of a center of theybobbin at heh
center at he instant when the thread
forms an angle \( \alpha \) with the vertical.
A \( \cdot \frac{v R}{R \sin \alpha-r} \)
в. \( \frac{v R}{\text { R } \sin \alpha+r} \)
c. \( \frac{2 v R}{\text { Rsind }+r} \)
D. \( \frac{v}{\text { Rsin } \alpha+r} \)
Subject: Maths
The position vectors of \( \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C}, \boldsymbol{D} \) are
\( \bar{a}, \bar{b}, \bar{c}, \bar{d} \) respectively and \( |\bar{a}-\overline{\boldsymbol{d}}|= \)
\( |\bar{b}-\bar{d}|=|\bar{c}-\bar{d}|, \) then for the triangle
\( A B C, D \) is
A. Ortho centre
B. Centroid
c. circumcentre
D. Incentre
Subject: Physics
In LCR series circuit, an alternating emf
\( e \) and current \( i \) are given by the
equations \( e=100 \sin (100 t) \) volt
\[
\boldsymbol{i}=\mathbf{1 0 0} \sin \left(\mathbf{1 0 0 t}+\frac{\boldsymbol{\pi}}{\mathbf{3}}\right) \boldsymbol{m} \boldsymbol{A}
\]
The average power dissipated in the circuit will be
\( \mathbf{A} \cdot 100 W \)
в. \( 10 W \)
\( \mathrm{c} \cdot 5 \mathrm{W} \)
D. \( 2.5 W \)
Subject: Maths
Evaluate \( \mathbf{7}+\mathbf{7 7}+\mathbf{7 7 7}+\ldots \ldots \ldots \ldots . . \) upto
\( n \) terms.
A \( \cdot \frac{7}{81}\left[10^{n+1}-9 n\right] \)
B. \( \frac{7}{81}\left[10^{n+1}-9 n-10\right] \)
c. \( \frac{7}{81}\left[10^{n}-9 n-10\right] \)
D. \( \frac{7}{81}\left[10^{n+1}-n-10\right] \)
Subject: Physics
A parallel plate capacitor is to be designed with a voltage rating \( 1 \mathrm{kV} \) using a material of dielectric constant
3 and dielectric strength about \( \mathbf{1 0}^{\mathbf{7}} \boldsymbol{V} \boldsymbol{m}^{-1} . \) (Dielectric strength is the
maximum electric field a material can
tolerate without breakdown, i.e., without
starting to conduct electricity through partial ionisation.) For safety, we should like the field never to exceed, say \( 10 \% \) of the dielectric strength.What minimum area of the plates is required to have a capacitance of 50 pF ?
Subject: Chemistry
The molar conductances of HCl, NaCl and
\( C H_{3} C O O N a \) are \( 426,12691 \Omega^{-1} c m^{2} m o l^{-1} \)
respectively. The molar conductances of
\( C H_{3} C O O H \) is :
A \( \cdot 561 \Omega^{-1} \mathrm{cm}^{2} \mathrm{mol}^{-1} \)
B. \( 391 \Omega^{-1} c m^{2} \) mol \( ^{-1} \)
c. \( 261 \Omega^{-1} c m^{2} m o l^{-1} \)
D. \( 612 \Omega^{-1} c m^{2} m o l^{-1} \)
Subject: Physics
A body of mass \( m \) is raised from the
surface of the earth to a height \( n R\left(R^{-}\right. \)
radius of earth). Magnitude of the change in the gravitational potential energy of the body is \( \left(g^{-}\right. \) acceleration due to gravity on the surface of earth)
A \( \cdot\left(\frac{n}{n+1}\right) m g R \)
\( ^{\mathbf{B}} \cdot\left(\frac{n-1}{n}\right) m g R \)
c. \( \frac{m g R}{n} \)
D. \( \frac{m g R}{(n-1)} \)
Subject: Physics
The surface of some material is
radiated in turn by waves of \( \lambda=3.5 \times \) \( 10^{-7} \) and \( \lambda=5.4 \times 10^{-7} m \) respectively
The ratio of the stopping potential in the two cases in \( 2: 1 . \) The work function of
the metal is:
A . \( 1.05 e V \)
B. \( 1.5 e V \)
c. \( 2.05 e V \)
D. \( 2.5 e V \)
Subject: Chemistry
Two glass bulbs of internal volume 0.5 and \( 0.2 L \) respectively are connected by a narrow tube of negligible volume. The
pressure of air in the vessel is \( 75 \mathrm{cm} \) at
\( 17^{\circ} \mathrm{C} . \) The smaller bulb is immersed in
melting ice and the larger bulb in boiling water. Calculate final pressure in the bulbs neglecting the expansion of glass.
Subject: Physics
thickness and refractive index \( n_{1}=1.4 \)
is coated on the convex spherical
surface of radius \( R \) at one end of a long
solid glass cylinder of refractive index
\( \boldsymbol{n}_{2}=1.5, \) as shown in the figure. Rays of
light parallel to the axis of the cylinder
traversing through the film from air to
glass get focused at distance \( f_{1} \) from
the film, while rays of light traversing from glass to air get focused at
distance \( f_{2} \) from the film. Then
This question has multiple correct options
\( \mathbf{A} \cdot\left|f_{1}\right|=3 R \)
B . \( \left|f_{1}\right|=2.8 R \)
\( \mathbf{c} \cdot\left|f_{2}\right|=2 R \)
D \cdot \( \left|f_{2}\right|=1.4 R \)
Subject: Chemistry
The \( K_{s p} \) of \( C a(O H)_{2} \) is \( 4.42 \times 10^{-5} \) at
\( 25^{\circ} \mathrm{C} . \mathrm{A} 500 \mathrm{m} L \) of saturated solution of
\( \boldsymbol{C} \boldsymbol{a}(\boldsymbol{O} \boldsymbol{H})_{2} \) is mixed with equal volume
of \( 0.4 M \) NaOH. How much \( C a(O H)_{2} \)
in \( m g \) is precipitated?
A. \( 659.2 \mathrm{mg} \)
в. \( 759.2 \mathrm{mg} \)
c. \( 578.2 \mathrm{mg} \)
D. \( 785.2 \mathrm{mg} \)
Subject: Chemistry
\( \boldsymbol{p} \boldsymbol{K}_{a} \) of acetic acid is \( \mathbf{4 . 7}, \) which implies
that?
A. pH of 1N acetic acid is 4.74
B. At pH 4.74 , the dissociation of acetic acid is maximum
c. At pH 4.74 half of acetic acid molecules are dissociated in the solution
D. At pH 4.74 , the dissociation of acetic acid is minimumm
Subject: Chemistry
\( ;(b)-(v) \) (d) \( - \) (iii) \( ;(e)- \) (i)
\( A \cdot(a)-(i i) \)
; (c) - (iv)
\( (n) \)
\( (\mathrm{i}) \) (b) \( -(v) ;(c)-(\text { iii) } ;(d)-(i v) ;(e)-(i) \)
(b) \( -(i v) ;(c)-(v) ;(d)-(i i i) ;(e)-(i i) \) :
-1
i)
(iii) \( (b)-(v) \) \( (c)- \) in (d) \( :(e)-(i) \)
\( D \cdot(a) \)
- (ii) :
Subject: Physics
The phase space diagram for simple
Momentum harmonic motion is a circle
centered at the origin. In the figure, the
two circles represent the same oscillator but for different initia
conditions, and \( E_{1} \) and \( E_{2} \) are the total
mechanical energies respectively. Then:
\( \mathbf{A} \cdot E_{1}=\sqrt{2} E_{2} \)
\( \mathbf{B} \cdot E_{1}=2 E_{2} \)
\( \mathbf{c} \cdot E_{1}=4 E_{2} \)
\( \mathbf{D} \cdot E_{1}=16 E_{2} \)
Subject: Physics
A student wrote the relation for one
unified atomic mass unit (u) as \( 1 u= \)
\( 931.5 M e V . \) What is the correct
relation?
A. \( 1 u \times c=931.5 \) MeV
В . \( 1 u \times c^{2}=931.5 \mathrm{MeV} \)
c. \( \frac{1 u}{c^{2}}=931.5 \mathrm{MeV} \)
D. \( (1 u)^{2} \times c=931.5 \mathrm{MeV} \)
Subject: Chemistry
Which of the statements given below is
incorrect?
A. \( O N F \) is isoelectronic with \( O_{2} N^{-} \)
B. \( O F_{2} \) is an oxide of fluorine
c. \( C l_{2} O_{7} \) is an anhydride of perchloric acid
\( \mathrm{D} \cdot O_{3} \) molecule is bent
Subject: Maths
If \( n>1, x>-1, x \neq 0, \) then the
statement \( (1+x)^{n}>1+n x \) is true for
\( \mathbf{A} \cdot n \epsilon N \)
в. \( \forall n>1 \)
c. \( x>-1 \) and \( x \neq 0 \)
D. None of these
Subject: Maths
Consider the following three
statements:
\( P: 5 \) is a prime number
\( Q: 7 \) is a factor of 192
\( \mathrm{R}: \) L.C.M. of 5 and 7 is 35
Then the truth value of which one of
thefollowing statements is true?
A \( \cdot(P \wedge Q) \vee(\sim R) \)
в. \( (\sim P) \wedge(\sim Q \wedge R) \)
c. \( (\sim P) \vee(Q \wedge R) \)
D. \( P \vee(\sim Q \wedge R) \)
Subject: Biology
toppr
Q Type your question
\( 0.1 \mathrm{M} \) starch solution. Dialysis bags
model the selective permeability of cell
membranes and allow very small
molecules, ions and water to pass
through according to the surrounding
concentration gradient.

Starch is too large a molecule to pass
through the dialysis membrane. The
student massed the bags every 5
minutes to monitor the amount of mass
gained or lost by each bag over the
course of 30 minutes. The percent
change in mass for each bag was
calculated and the data were plotted in
the graph:
Which line on the graph would the
student have obtained with the data
from the bag containing a \( 0.1 \mathrm{M} \) starch
solution?
\( A \cdot A \)
B. B
\( c \cdot c \)
\( D \)
Subject: Physics
The formula for the resistance of a fluid
is:
\( ^{\mathrm{A}} \cdot_{R}=\frac{\pi r^{4}}{8 \eta l} \)
в. \( _{R}=\frac{8 \eta l}{\pi r^{2}} \)
c. \( _{R}=\frac{8 \eta l}{\pi r^{3}} \)
D. \( _{R}=\frac{8 \eta l}{\pi r^{4}} \)
Subject: Physics
A double star system consists of two stars \( A \) and \( B \) which have time periods
\( T_{A} \) and \( T_{B} . \) Radius \( R_{A} \) and \( R_{B} \) and
\( \operatorname{mass} M_{A} \) and \( M_{B}, \) choose the correct
answer,
A \( \cdot\left(T_{A} / T_{B}\right)^{2}=\left(R_{A} / R_{B}\right)^{3} \)
B. If \( T_{A}>T_{B} \) then \( R_{A}>R_{B} \)
\( \mathbf{c} \cdot T_{A}=T_{B} \)
D. \( T_{A}>T_{B} \) then \( M_{A}>M_{B} \)
Subject: Maths
The given figure shows a parallelogram
\( A B C D \) with area \( 324 s q . c m . P \) is a
point in \( A B \) such that \( A P: P B=1: 2 \)
Find:the ratio \( O P: O D \)
4: 3
в. 2:
\( c \cdot 1: 4 \)
D. 4: 3
Subject: Physics
A disc of mass \( M \) is attached to a
horizontal massless spring of force
constant \( K \) so that it can roll without
slipping along a horizontal surface. If the disc is pushed a little towards right and then released, its center of
mass executes SHM with a period of
A \( \cdot 2 \pi \sqrt{\frac{M}{K}} \)
В. \( 2 \pi \sqrt{\frac{3 M}{K}} \)
с. \( _{2 \pi} \sqrt{\frac{M}{2 K}} \)
D. \( 2 \pi \sqrt{\frac{3 M}{2 K}} \)
Subject: Physics
rotating in the horizontal plane with
constant angular speed \( \omega, \) as shown in
the figure. At time \( t=0, \) a small insect
starts from \( O \) and moves with constant
speed \( v \) with respect to the rod towards
the other end. It reaches the end of the
rod at \( t=T \) and stops. The angular
speed of the system remains \( \omega \)
throughout. The magnitude of the torque \( |\vec{\tau}| \) on the system about \( \boldsymbol{O}, \) as a function of time is best represented by
which plot?
\( A \cdot A \)
B. B
\( c \cdot c \)
D.
Subject: Maths
If \( \cot ^{-1} x+\cot ^{-1} y+\cot ^{-1} z=\frac{\pi}{2} \) then
\( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z} \) equals
A \( . x y z \)
в. \( x y+y z+z x \)
\( \mathrm{c} \cdot 2 x y z \)
D. None of these
Subject: Chemistry
Which element has:
(a) two shells, both of which are completely filled with electrons?
(b) the electronic configuration \( 2,8,2 ? \)
(c) a total of three shells, with four
electrons in its valence shell?
(d) a total of two shells, with three
electrons in its valence shell?
(e) twice as many electrons in its second shell as in its first shell?
Subject: Physics
A point particle of mass \( 0.1 \mathrm{kg} \) is executing SHM with amplitude of 0.1m.When the particle passes through the mean position, its K.E is \( 8 \times 10^{-3} J . \) Obtain the equation of
motion of this particle if the initial
phase of oscillation is \( 45^{\circ} \)
\( \mathbf{A} \cdot y=0.2 \sin (4 t+\pi / 2) \)
B \cdot \( y=0.1 \sin (4 t+\pi / 4) \)
C \( \cdot y=0.2 \sin (4 t+\pi / 4) \)
D. None of these
Subject: Maths
f \( \boldsymbol{f}: \boldsymbol{x} \rightarrow \boldsymbol{p}+\boldsymbol{q} \boldsymbol{x}, \boldsymbol{f}^{-1}(\boldsymbol{9})=(-1) \) and
\( \boldsymbol{f}(\mathbf{3})=(-11) . \) find the value of \( \boldsymbol{p} \) and \( \boldsymbol{q} \)
Subject: Physics
Biomass based energy can be obtained
from:
This question has multiple correct options
A. direct burning of wood, agricultural residue etc.
B. biomass may be converted in to some other form of fuel which can release energy.
C. bacterial decomposition of organic matters like cow dung, agricultural wastes, human excreta etc. in presence of water in absence of air, a mixture of
\( C H_{4}, C O_{2}, H_{2}, H_{2} S \) etc.
D. burning of industrial waste.
Subject: Physics
Two source of sound placed closed to each other, are emitting progressive
wave given by \( y_{1}=4 \sin 600 \pi t \) and
\( \boldsymbol{y}_{2}=\mathbf{5} \sin \mathbf{6 0} \mathbf{8} \boldsymbol{\pi} \boldsymbol{t} . \) An observed located
near these two sources will hear:
A. 8 beats per second with intensity ratio 81: 1 between waxing and waning
B. 4 beats per second with intensity ratio 81: 1 between waxing and waning
c. 4 beats per second with intensity ratio 25: 16 between waxing and waning
D. 8 beats per second with intensity ratio 25 : 16 between waxing and waning
Subject: Maths
If \( \boldsymbol{f}(1)=\mathbf{1} \) and \( \boldsymbol{f}(\boldsymbol{x}+\mathbf{1})=\boldsymbol{2} \boldsymbol{f}(\boldsymbol{x})+\mathbf{1} \)
for \( \boldsymbol{x} \geq 1, \) then find the range of \( \boldsymbol{f}(\boldsymbol{x}) \)
A. \( R \)
B. A series like \( 1,3,5,7,9, \ldots \)
C. A series like \( 1,3,7,15, \ldots \)
D. \( R-\{1,3,7,15, \ldots\} \)
Subject: Chemistry
The expression relating mole fraction of
solute \( \left(\chi_{2}\right) \) and molarity \( (\mathrm{M}) \) of the
solution is (where dis the density of the
solution in \( g L^{-1} \) and \( M w_{1} \) and \( M w_{2} \)
are the molar masses of solvent and
solute, respectively
A \( \cdot x_{2}=\frac{M \times M w_{1}}{M\left(M w_{1}-M w_{2}\right)+1000 d} \)
B. \( x_{2}=\frac{M \times M w_{1}}{M\left(M w_{1}-M w_{2}\right)+d} \)
c. \( _{x_{2}}=\frac{M \times M w_{1}}{M\left(M w_{1}-M w_{2}\right)-1000 d} \)
D. \( _{x_{2}}=\frac{M \times M w_{1}}{M\left(M w_{1}-M w_{2}\right)-d} \)
Subject: Maths
A piggy bank contains a hundred 50 paise coins, fifty Rs. 1 coins, twenty Rs. 2 coins and ten Rs. 5 coins. If it is
equally likely that one of the coins will fall out when the bank is turned upside down, find the probability that the coin which fell
(i) will be a 50 paise win
(ii) will be of
value more than Rs. 1
(iiii) will be of
value less than Rs. 5 (iv) will be Rs. 1 or
Rs. 2 coin
Subject: Physics
The wire used in the arrangement shown in the figure has a resistance of \( r \Omega \) per metre. The equivalent resistance
between points \( A \) and \( B \) is:
\( ^{A} \cdot\left(\frac{6}{11}\right)^{r} \)
в. \( \frac{2 \pi r}{(\pi+1)} \)
c. \( \frac{6 \pi r}{(16+3 \pi)} \)
D. \( \frac{3 \pi r}{(10+3 \pi)} \)
Subject: Physics
The equation of a wave disturbance is given as:
\( y=0.02 \sin \left(\frac{\pi}{2}+50 \pi t\right) \cos (10 \pi x) \)
where \( x \) and \( y \) are in metres and \( t \) is in
seconds.
Choose the correct statement(s):
This question has multiple correct options
A. the wavelength of wave is \( 0.2 m \)
B. displacement node occurs at \( x=0.15 \mathrm{m} \)
c. displacement antinode occurs at \( x=0.3 \mathrm{m} \)
D. the speed of constituent waves is \( 0.2 \mathrm{m} / \mathrm{s} \)
Subject: Biology
Match the columns:
\( \mathbf{A} \)
\( 1-b, 2-e, 3-a, 4-c, 5-d \)
B. \( 1-b, 2-c, 3-d, 4-e, 5-a \)
\( C \cdot 1-a, 2-e, 3-b, 4-d, 5-c \)
D. \( 1-e, 2-d, 3-c, 4-b, 5-a \)
\( \mathrm{E} \cdot 1-\mathrm{c}, 2-\mathrm{b}, 3-\mathrm{a}, 4-\mathrm{e}, \mathrm{S}-\mathrm{d} \)
Subject: Maths
t is known that an urn containing altogether 10 balls was filled in the following manner: A coin was tossed 10 times, and according as it showed heads or tails, one white or on black ball was put into the urn. Balls are drawn
from this urn one at a time, 10 times in
succession (with replacements) and every one turns out to be white. The
chance that the urn contains nothing but white balls is \( \frac{1}{2^{k}} . \) Find the value of \( k \)
Subject: Maths
Solve the following:
n \( \Delta M N P, \angle M N P= \)
\( 90^{\circ}, \operatorname{seg} N Q \perp \operatorname{seg} M P . \) If \( M Q= \)
\( \mathbf{9}, \boldsymbol{Q} \boldsymbol{P}=\mathbf{4}, \) then find \( \boldsymbol{N} \boldsymbol{Q} \)
Subject: Physics
Find the work requires to compress adiabatically \( 1 g \) of air initially at \( N T P \) to half its volume. Density of air at \( N T P=0.001129 g c m^{-3} \) and \( \frac{C_{p}}{C_{v}}=1.4 \)
A . \( 62.64 J \)
в. \( 32.64 J \)
c. \( -32.64 J \)
D. \( -62.64 J \)
Subject: Maths
\( \int_{1}^{4} \frac{\mathbf{x} \mathbf{d x}}{\sqrt{\mathbf{2 + 4 x}}}= \)
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{\sqrt{2}} \)
\( c \cdot \frac{3}{2} \)
D. \( \frac{3}{\sqrt{2}} \)
Subject: Physics
A neutron moving with a certain kinetic energy collides head on with an atom of mass number A. The fractional kinetic
energy retained by it is
A \( \frac{A-1}{A+1} \)
\( ^{\mathrm{B}}\left(\frac{A+1}{A-1}\right)^{2} \)
c. \( \frac{A+1}{A-1} \)
\( ^{D \cdot}\left(\frac{A-1}{A+1}\right)^{2} \)
Subject: Physics
The work done in rearranging a system of 3 identical particles of mass 1kg on a right angled triangle to an equilateral triangle is (length of the side in both the configuration is \( 1 \mathrm{m} \) )
A. \( W=G(1+1 \sqrt{2}) \)
в. \( W=G(1-1 \sqrt{(} 2)) \)
c. \( W=G(1-2 \sqrt{(} 2)) \)
D. \( W=G(1+2 \sqrt{(} 2)) \)
Subject: Physics
Consider two points 1 and 2 in a region outside a charged sphere. Two points are not vary far away from the sphere. If \( \boldsymbol{E} \) and \( \boldsymbol{V} \) represent the electric field vector and the electric potential, which of the following is not possible?
A \( \cdot\left|\vec{E}_{1}\right|=\left|\vec{E}_{2}\right|, V_{1}=V_{2} \)
в. \( \left|\vec{E}_{1}\right| \neq\left|\vec{E}_{2}\right|, V_{1} \neq V_{2} \)
c \( \cdot\left|\vec{E}_{1}\right| \neq\left|\vec{E}_{2}\right|, V_{1}=V_{2} \)
D . \( \left|\vec{E}_{1}\right|=\left|\vec{E}_{2}\right|, V_{1} \neq V_{2} \)
Subject: Physics
A ball is thrown vertically upwards. It
has a speed of \( 10 m s^{-1}, \) when it has
reached on half of its maximum height. How high does the ball rise? (Take \( g= \)
\( \left.10 m s^{-2}\right) \)
A . \( 10 \mathrm{m} \)
B. \( 5 \mathrm{m} \)
\( c \cdot 15 m \)
D. 20 \( m \)
Subject: Chemistry
\( 50 \mathrm{g} \) of \( \mathrm{CaCO}_{3} \) is allowed to react with 70 g of \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \). Calculate :
(i) amount of \( \boldsymbol{C} \boldsymbol{a}_{\boldsymbol{3}}\left(\boldsymbol{P} \boldsymbol{O}_{4}\right)_{2} \) formed
(ii) amount of unreacted reagent
Subject: Chemistry
A group of students took an old shoe
box and covered it with a black paper
from all sides. They fixed a source of light (a torch) at one end of the box by making a hole in it and made another
hole on the other side to view the light They placed a milk sample contained in a beaker/tumbler in the box as shown
in the Fig.2.4. They were amazed to see that milk taken in the tumbler was
illuminated. They tried the same activity by taking a salt solution but found that light simply passed through it?

Same results were not observed with a
salt solution. Explain.
Subject: Physics
\( 420 J \) of energy supplied to \( 10 g m \) of water will raise its temperature by
\( \mathbf{A} \cdot 1^{\circ} C \)
в. \( 4.2^{\circ} \mathrm{C} \)
\( \mathrm{c} \cdot 10^{\circ} \mathrm{C} \)
D. \( 42^{\circ} \mathrm{C} \)
Subject: Maths
Based on the given figure, which of the
following statements is true?
A. \( \angle 5 \) and \( \angle 7 \) are supplementary angles.
B \( . \angle 7=55^{\circ} \)
C. \( \angle 8 \) and \( \angle 1 \) are corresponding angles.
D. \( \angle 4 \) and \( \angle 5 \) are alternate angles.