AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
If linear magnification for a spherical mirror is \( \frac{3}{2}, \) then we may write: (symbols have their usual meanings)
A \( \cdot f=\frac{u}{2} \)
B. \( f=\frac{3 u}{2} \)
\( c \cdot f=\frac{3 u}{5} \)
D. None of these
Subject: Chemistry
Assertion
According to Mendeleev's periodic law;
The properties of elements are the
periodic a function of their atomic
numbers.
Reason
Mendeleev's periodic law could explain
the phenomenon of anomalous pairs.
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
The most contributing tautomeric enol
form of \( M e C O C H_{2} C O_{2} E t \) is :
A \( \cdot H_{2} C=C(O H) C H_{2} C O_{2} E t \)
в. \( \operatorname{Me} C(O H)=C H C O_{2} E t \)
c. \( \operatorname{MeCOCH}=C(O H) \) OEt
D. \( H_{2} C=C(O H) C H=C(O H) E t \)
Subject: Chemistry
\( H_{2} \) reacts much faster with \( C l_{2} \) then \( D_{2} \)
because:
A. rate of diffusion of \( H_{2} \) is greater than \( D_{2} \)
B. \( H_{2} \) has lower energy of activation than \( D_{2} \)
C. both (A) and (B) are correct
D. none of the above is correct
Subject: Maths
The shape of the top surface of a table is
trapezium. Find its area if its parallel
sides are 1 m and \( 1.2 m \) and the
perpendicular distance between them
is \( 0.8 m \)
A \( \cdot 0.88 m^{2} \)
B \( .0 .8 m^{2} \)
\( \mathbf{c} \cdot 8.8 m^{2} \)
D. \( 0.88 \mathrm{cm}^{2} \)
Subject: Physics
A coil is used in a circuit in which an
A.C. of frequency \( 50 \mathrm{Hz} \) is flowing. The self-inductance of the coil, in order to
produce an impedance of \( 100 \Omega, \) will be
\( H \)
A . \( \pi \)
B.
c. \( \pi^{2} \)
D. \( \frac{1}{\pi^{2}} \)
Subject: Physics
An infinite number of charges each equal to \( ^{\prime} q^{\prime} \) are placed along the \( X \) -axis at \( x=1 \)
\( x=2, x=4, x=8 \) The potential at the
point \( x=0 \) due to this set of charges is :
\( ^{A} \cdot \frac{Q}{4 \pi \epsilon_{0}} \)
в. \( \frac{2 Q}{4 \pi \epsilon_{0}} \)
с. \( \frac{3 Q}{4 \pi \epsilon_{0}} \)
D. \( \frac{Q}{\pi \epsilon_{0}} \)
Subject: Biology
Select the wrong statement
A. Presence of chromogenic substrate gives blue colour colonies if the plasmid in the bacteria does not have an insert
B. Retroviruses in animals have the ability to transform normal cells into cancerous cellsın microinjection, cells are bombarded with high velocity microparticles of gold or tungsten coated with DNA
C. since DNA is a hydrophilic molecule it cannot pass through cell membranes
D. DNA is a negatively charged molecule
Subject: Maths
Evaluate
\( 8 \sqrt{3} \operatorname{cosec}^{2} 30^{\circ} \sin 60^{\circ} \cos 60^{\circ} \cos ^{2} 45^{\circ} \)
A \( \cdot 2 \sqrt{3} \)
B. \( 4 \sqrt{3} \)
\( c \cdot 8 \sqrt{3} \)
D. \( 12 \sqrt{3} \)
Subject: Chemistry
The ratio of number of exchange pairs
present in \( d^{9} \) and magnetic moment of Cr in B.M. is:-
\( A \cdot \frac{2}{\sqrt{3}} \)
B. \( \frac{2 \sqrt{3}}{3} \)
c. \( \frac{2 \sqrt{3}}{4} \)
D. \( \frac{16}{\sqrt{35}} \)
Subject: Maths
Find the value of \( x, y \) and \( z \) in the figure.
\( \mathbf{A} \cdot x=60^{\circ}, y=120^{\circ}, z=60^{\circ} \)
B \( \cdot x=60^{\circ}, y=60^{\circ}, z=120^{\circ} \)
\( \mathbf{C} \cdot x=120^{\circ}, y=60^{\circ}, z=60^{\circ} \)
D \( \cdot x=70^{\circ}, y=100^{\circ}, z=70^{\circ} \)
Subject: Chemistry
Concentration of \( \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{C l} \) and \( \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{O} \boldsymbol{H} \)
in a buffer solution are in the ratio of
\( 1: 10, \mathrm{Kb} \) for \( N H_{4} O H \) is \( 10^{-10} . \) The pH of
the buffer is:
(BHU, 1994)
A .4
B. 5
\( c \cdot 9 \)
D. 1
Subject: Physics
There are two radioactive substances \( A \)
and
B. Decay constant of B is two times that of A. Initially, both have equal number of nuclei. After 'n' half-lives of A,
rates of disintegration of both are equal
The value of \( ^{\prime} \boldsymbol{n}^{\prime} \) is
A . 1
B . 2
\( c \cdot 4 \)
D. all of these
Subject: Chemistry
\( a \) moles of \( P C l_{5} \) are heated in a closed
container to equilibrate \( \boldsymbol{P} \boldsymbol{C l}_{5(\boldsymbol{g})} \rightleftharpoons \)
\( \boldsymbol{P C l}_{5(g)}+\boldsymbol{C l}_{2(g)} \) at a pressure of \( \boldsymbol{P} \) atm.
If \( x \) moles of \( P C l_{5} \) dissociate at
equilibrium, then:
A \( \cdot \frac{x}{a}=\frac{K_{P}}{K_{P}+P} \)
\( ^{\mathbf{B}} \cdot \frac{x}{a}=\left(\frac{K_{P}+P}{K_{P}}\right)^{1 / 2} \)
\( \stackrel{x}{a}=\left(\frac{K_{P}}{P}\right)^{1 / 2} \)
\( \stackrel{x}{a}=\left(\frac{K_{P}}{K_{P}+P}\right)^{1 / 2} \)
Subject: Physics
Assertion: The product of magnetic susceptibility and absolute temperature for a paramagnetic substance is constant.
Reason: Susceptibility is positive but
very small for paramagnetic substance
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: Physics
Two bodies \( A \) and \( B \) at temperatures
\( 327^{\circ} \mathrm{C} \) and \( 277^{\circ} \mathrm{C} \) are kept in vacuum
chamber at \( 27^{\circ} \mathrm{C} \). Then ratio of their
rates of loss of heat in a given time interval is nearly.
\( A \cdot 2: \)
B. 1: 2
\( c \cdot 1: 4 \)
D. 4: 1
Subject: Maths
Find the area of the shaded region in
given Fig.where arcs drawn with
centres \( A, B, C \) and \( D \) intersect in pairs
at mid-points \( P, Q, R \) and \( S \) of the sides
\( A B, B C, C D \) and \( D A, \) respectively of a
square \( A B C D(\text { Use } \pi=3.14) \)
\( \mathbf{A} \cdot 30.96 \mathrm{cm}^{2} \)
B. \( 90.96 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 120.96 \mathrm{cm}^{2} \)
D. \( 180.96 \mathrm{cm}^{2} \)
Subject: Physics
In AC circuit having only capacitor, the
current
A \( \cdot \) Leads the voltage by \( \frac{\pi}{2} \) in phase
B \cdot Lags behind the voltage by \( \frac{\pi}{2} \) in phase
C. Leads the voltage by \( \pi \) in phase
D. Lags behind the voltage by \( \pi \) in phase
Subject: Maths
\( \int \sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right) d x \) is equal to
A \( \cdot 2\left(x \tan ^{-1} x+\ln \left|\cos \left(\tan ^{-1} x\right)\right|\right)+C \)
B・ \( 2\left[\left(x \tan ^{-1} x\right)^{2}+\ln \left|\sec \left(\tan ^{-1} x\right)\right|\right]+c \)
c. \( 2\left[\left(x \tan ^{-1} x\right)^{2}-\ln \left|\cos \left(\tan ^{-1} x\right)\right|\right]+c \)
D. None of these
Subject: Chemistry
In aqueous solution, \( \left[\boldsymbol{C o}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right]^{2+}(\boldsymbol{X}) \)
reacts with molecular oxygen in the
presence of excess liquor \( N H_{3} \) to give
a new complex \( Y \). The number of
unpaired electrons in \( X \) and \( Y \) are,
respectively.
A . 3,1
в. 3,0
c. 3,3
D. 7,0
Subject: Chemistry
If a \( 0.1 \mathrm{M} \) solution of \( \mathrm{HCN} \) is \( 0.01 \% \)
ionised, the ionisation constant for
\( \boldsymbol{H} \boldsymbol{C} \boldsymbol{N} \) is:
A \( \cdot 10^{-9} \)
B. \( 10^{-7} \)
\( c \cdot 10^{-5} \)
D. \( 10^{-3} \)
Subject: Biology
Active transport involves the transport of molecules across a cell membrane.
In order to establish and maintain a
concentration gradient, which of the following condition is suitable?
A. Free energy is used to drive molecules back-and-forth across the transmembrane protein
B. Free energy is used to drive molecules and across a transmembrane protein against the concentration gradient.
c. No free energy is required
D. There must be an equal quantity of molecules on both sides of the membrane
Subject: Maths
A bag A contains 4 green and 6 red balls. Another bag B contains 3 green and 4 red balls. If one ball is drawn from
each bag, find the probability that both are green.
\( A \cdot 13 / 70 \)
B. \( 1 / 4 \)
\( c \cdot 6 / 35 \)
D. 8/35
Subject: Physics
Two identical straight wires are stretched so as to produce 6 beats per second when vibrating simultaneously. On changing the tension slightly in one of them, the beat frequency remains
unchanged. Denoting by \( \mathrm{T}_{1} \) and \( \mathrm{T}_{2}, \) the higher and the lower initial tension in
the strings, then it could be said that
while making the above changes in tension:
This question has multiple correct options
\( \mathbf{A} \cdot \mathbf{T}_{2} \) was decreased
B. \( \mathrm{T}_{2} \) was increased
\( \mathrm{c} \cdot \mathrm{T}_{1} \) was decreased
D. \( T_{1} \) was increased
Subject: Physics
A fiat circular coil, carrying a current,
has a magnetic moment \( \mu \)
This question has multiple correct options
A. \( \mu \) has only magnitude; it does not have direction
B. the direction of \( \mu \) is along the normal to the plane of the coil
C. the direction of \( \mu \) depends on the direction of the current flow
D. the direction of \( \mu \) does not change if the current in the coil is reversed
Subject: Chemistry
Which of the following statements are
correct about Nylon - 6, 6 ?
This question has multiple correct options
A. Nylon fibers have higher tensile strength than teylene fibres.
B. Nylon fibers have lower tensile strength than terylene fibres.
C. In nylon, there is strong intermolecular H-bonding, while in terylene there is weak dipole-dipole interaction.
D. In nylon, there is weak dipole-dipole interaction, while in terylene there is strong intermolecular H-bonding.
Subject: Physics
Consider a two-input AND gate of figure
below. Out of the four entries for the
Truth Table given here, the correct ones
are
\( -1-1 \) \begin{tabular}{|c|c|c|c|}
\hline \multirow{2}{*} {1} & A & B & C \\
\cline { 2 - 5 } & 0 & 1 & 0 \\
\cline { 2 - 4 } & 1 & 0 & 0 \\
\cline { 2 - 4 } 3 & 1 & 1 & 1 \\
\hline \multirow{2}{*} {4} & 0 & 0 & 1 \\
\hline
\end{tabular}
\( \mathbf{A} \cdot \) Al
B. 1 and 2 only
C. 1,2 and 3 only
D. 1,3 and 4 only
Subject: Chemistry
A piece of zinc may be distinguished from a piece of magnesium by:
(1) determining which conducts electricity
(2) determining which releases \( H_{2} \) gas from a 1-molar hydrochloric acid solution
(3) measuring the density of each
A. If 1,2 and 3 are correct
B. If only 1 and 2 are correct
c. If only 2 and 3 are correct
D. If only 1 is correct
E. If only 3 is correct
Subject: Chemistry
The most reactive towards \( S_{N} 1 \) is:
A \( \cdot P h C H_{2} C l \)
в. \( P h C l \)
\( \mathbf{c} \cdot \operatorname{Ph} C H C l\left(C H_{3}\right) \)
D. \( p-N O_{2} C_{6} H_{4} C H_{2} C l \)
Subject: Maths
The volume of metal in a hollow sphere
is constant.If the inner radius is
increasing at the rate of \( 1 \mathrm{cm} / \mathrm{sec} \), then the rate of increase of the outer radius
when the radii are \( 4 c m \) and \( 8 c m \)
respectively is.
A. \( 0.75 \mathrm{cm} / \mathrm{sec} \)
B. \( 0.25 \mathrm{cm} / \mathrm{sec} \)
\( \mathrm{c} \cdot 1 \mathrm{cm} / \mathrm{sec} \)
D. \( 0.50 \mathrm{cm} / \mathrm{sec} \)
Subject: Physics
A circuit has a section \( \mathrm{ABC} \) as shown in
figure. If the potentials at points \( A, B \)
and \( \mathrm{C} \) are \( V_{1}, V_{2} \) and \( V_{3} \) respectively.
The potential at point 0 is?
A \( \cdot V_{1}+V_{2}+V_{3} \)
\( ^{\mathbf{B}} \cdot\left[\frac{V_{1}}{R_{1}}+\frac{V_{2}}{R_{2}}+\frac{V_{3}}{R_{3}}\right]\left[\frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}}\right]^{-1} \)
c. zero
\( ^{\mathrm{D}} \cdot\left[\frac{V_{1}}{R_{1}}+\frac{V_{2}}{R_{2}}+\frac{V_{3}}{R_{3}}\right]\left(R_{1}+R_{2}+R_{3}\right) \)
Subject: Chemistry
Define non-metallic character.
\( A . \) An atom is said to be a non-metal if it loses one or
more electrons when supplied with energy
B. An atom is said to be a non-metal if it loses only one electron when supplied with energy
C. An atom is said to be a non-metal if it gains one or more electrons when supplied with energy
D. An atom is said to be a non-metal if it gains only one electron when supplied with energy
Subject: Physics
In the decay process:
\( \boldsymbol{A} \stackrel{-\boldsymbol{\alpha}}{\longrightarrow} \boldsymbol{B} \stackrel{-\boldsymbol{\beta}}{\longrightarrow} \boldsymbol{C} \stackrel{-\boldsymbol{\beta}}{\longrightarrow} \boldsymbol{D} \)
This question has multiple correct options
\( \mathbf{A} \cdot A \) and \( B \) are isodiapheres
B. \( A \) and \( D \) are isotopes
C. \( B, C \) and \( D \) are isobars
D. \( A \) and \( C \) are isotones
Subject: Maths
In the adjoining figure, \( D \) and \( E \) are
respectively the midpoints of sides \( A B \) and \( A C \) of \( \triangle A B C . \) If \( P Q \| B C \) and
\( C D P \) and \( B E Q \) are straight lines then prove that \( \boldsymbol{a} \boldsymbol{r}(\triangle \boldsymbol{A} \boldsymbol{B} \boldsymbol{Q})=\boldsymbol{a} \boldsymbol{r}(\triangle \boldsymbol{A} \boldsymbol{C} \boldsymbol{P}) \)
Subject: Maths
The value of \( k \) when the distance
between the points \( (3, k) \) and (4,1) is \( \sqrt{10} \) is
A . \( 30 r 4 \)
B. \( -4 o r-2 \)
c. \( -4 o r 2 \)
D. \( 4 o r-2 \)
Subject: Chemistry
The element having electronic configuration \( [\boldsymbol{K} \boldsymbol{r}] \boldsymbol{4} \boldsymbol{d}^{10} \boldsymbol{4} \boldsymbol{f}^{14} \boldsymbol{5} \boldsymbol{s}^{2} \boldsymbol{5} \boldsymbol{p}^{6} \boldsymbol{5} \boldsymbol{d}^{1} \boldsymbol{6} \boldsymbol{s}^{2} \) belongs to
A. s-block
B. p-block
c. d-block
D. f-block
Subject: Physics
A potential difference across the terminals of a battery is \( 50 V \) when \( 11 A \)
current is drawn and \( 60 V, \) when \( 1 A \)
current is drawn. The emf and the
internal resistance of the battery are
A. \( 62 V, 2 \Omega \)
в. \( 63 V, 1 \Omega \)
\( \mathrm{c} \cdot 61 V, 1 \Omega \)
D. \( 64 V, 2 \Omega \)
Subject: Maths
The simplified form of \( i^{n}+i^{n+1}+ \)
\( \boldsymbol{i}^{\boldsymbol{n}+\boldsymbol{2}}+\boldsymbol{i}^{\boldsymbol{n}+\boldsymbol{3}} \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot-1 \)
D.
Subject: Maths
Solve for \( \boldsymbol{x}, \boldsymbol{y} \)
\( (a+2 b) x+(2 a-b) y=2,(a- \)
2b) \( x+(2 a+b) y=3 \)
A. \( x=(5 b-2 a), y=10 a b \)
в. \( x=\frac{5 b-2 a}{10 a b}, y=\frac{a+10 b}{10 a b} \)
c. \( x=\frac{5 b-2 a}{10 a b}, y=\frac{5 a+10 b}{10 a b} \)
D. \( x=\frac{5 b+2 a}{10 a b}, y=\frac{a+10 b}{10 a b} \)
Subject: Physics
When a body is in SHM, match the
statements in Column A with that in
Column B
Column A
Column B
a) Velocity is maximum
e) At half of the amplitude
b) Kinetic energy is At the mean position \( 3 / 4 \) th of total energy
c) Potential energy is
g) At extreme position \( 3 / 4 \) th of total energy
d) Acceleration is
h) \( \mathrm{At} \sqrt{3} / 2 \) times amplitude maximum
A. a-f, b-e, c-h, d-g
B. a-e, b-f, c-g, d-h
c. a-g, b-h, c-e, d-f
D. a-h, b-e, c-f, d-e
Subject: Maths
If \( x \epsilon N, \) then range of function \( f(x)= \) \( \frac{16-x}{20-3 x} C_{x-1} \) is
A. [1,15]
В \( \cdot_{14} C_{4}, \frac{^{10} C_{5}}{2} \)
c. \( ^{11} C_{4} \)
\( \mathbf{D} \cdot[5,15 \)
Subject: Physics
Assertion
When current through a bulb decreases by \( 0.5 \%, \) the glow of bulb decreases by
\( 1 \% \)
Reason
Glow (Power) which is directly proportional to square of current.
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 incorrect
Subject: Physics
A man of mass \( \mathrm{m} \) is applying a
horizontal force to slide a box of mass
\( \mathrm{m}^{\prime} \) on a rough horizontal surface. It is known that the man does not slide. The
coefficient of friction between the shoes
of the man and the floor is \( \mu \) and
between the box and the floor is \( \mu^{\prime} . \) In
which of the following cases it is certainly not possible to slide the box?
Subject: Physics
A ball of radius R carries a positive charge whose volume charge density depends only on the distance r from the ball's centre as: \( \rho=\rho_{0}\left(1-\frac{r}{R}\right) \) where
\( \rho_{0} \) is constant. Assume \( \epsilon \) as the
permittivity of the ball.
Then the magnitude of the electric field as a function of the distance r outside
the ball is given by :
A. \( \quad E=\frac{\rho_{0} R^{3}}{8 \epsilon r^{2}} \)
в. \( \quad E=\frac{\rho_{0} R^{3}}{12 r r^{2}} \)
c. \( _{E=\frac{\rho_{0} R^{3}}{16 \epsilon^{2}}} \)
D. \( \quad E=\frac{\rho_{0} R^{3}}{24 r^{2}} \)
Subject: Chemistry
Tritium, \( T \) (an isotope of \( H \) ) combines with fluorine to form weak acid TF,
which ionizes to give Tritium is radioactive and is \( \alpha \beta- \)emitter.
freshly prepared aqueous solution of TF has pT (an equivalent of pH) of 1.5 and freezes at \( -0.372^{\circ} \mathrm{C} . \) If \( 600 \mathrm{ml} \) of
freshly prepared solution were allowed to stand for 24.8 years. Calculate (i) ionization constant of TF. (ii)Number
of lbeta-particles emitted?(Given \( \boldsymbol{K}_{f} \) forwater \( =\mathbf{1 . 8 6 k g m o l} \boldsymbol{K}^{-1}, \boldsymbol{t}_{1 / 2} \) for
tritium \( =12.4 y \) ears
A \( \cdot(i) K_{a}=7.3 \times 10^{-3}(i i) 4.55 \times 10^{22} \)
B . (i)K \( _{a}=7.3 \times 10^{-5}(i i) 4.55 \times 10^{24} \)
C . \( (i) K_{a}=14.3 \times 10^{-3}(i i) 9.1 \times 10^{22} \)
D . (i) \( K_{a}=14.3 \times 10^{-5}(i i) 9.1 \times 10^{24} \)
Subject: Physics
Two trains, each of length \( 100 \mathrm{m} \) moving in opposite directions along parallel lines, meet each other with speeds of \( 50 \mathrm{kmh}^{-1} \) and \( 40 \mathrm{kmh}^{-1} \). If
their accelerations are \( 30 \mathrm{cms}^{-2} \) and
\( 20 \mathrm{cms}^{-2}, \) respectively, find the time they will take to pass each other
Subject: Physics
When a lens is inserted between an
object and a screen which are at a fixed distance apart, the size of the image in either \( 6 \mathrm{cm} \) and \( 2 / 3 \mathrm{cm} \). The size of the
object in cm is then
\( A \cdot 9 \)
B. 4
\( c \cdot 3 \)
D.
Subject: Physics
If \( \bar{A} \) and \( \bar{B} \) two different physical quantities, Which of the following mathematical operations is/are valid.
A. \( \bar{A}+\bar{B} \)
в. \( \overline{A . \bar{B}} \)
c. \( \bar{A} \times \bar{B} \)
D. Both and (b) and (c)
Subject: Maths
The value of
\( \lim _{n \rightarrow \infty}\left[\frac{\sqrt{\boldsymbol{n}+\mathbf{1}}+\sqrt{\boldsymbol{n}+\mathbf{2}}+\ldots+\sqrt{\boldsymbol{n}+\boldsymbol{r}}}{\boldsymbol{n} \sqrt{\boldsymbol{n}}}\right. \)
is
A \( \cdot \frac{2(2 \sqrt{2}-1)}{3} \)
B. \( \frac{(2 \sqrt{2}-1)}{3} \)
c. \( \frac{(2 \sqrt{2}+1)}{3} \)
D. \( \frac{(\sqrt{2}+1)}{3} \)
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}-\boldsymbol{x}^{2}+\boldsymbol{x}+\mathbf{1} \) and
\( \boldsymbol{g}(\boldsymbol{x})= \)
\( \left\{\begin{array}{l}\max \{f(t)\}, \quad 0 \leq t \leq x \quad 0 \leq x \leq 1 \\ 3-x, \quad 1<x \leq 2\end{array}\right. \)
Then in the interval \( [0,2], g(x) \) is
This question has multiple correct options
A. Continuous for all \( x \)
B. Differentiable for all \( x \)
c. Discontinuous at \( x=1 \)
D. Not differentiable at \( x=1 \)
Subject: Physics
If the light moving in a straight line bends by a small but fixed angle, it may
be a case of
(i) reflection
(ii) refraction
(iiii) diffraction
\( (i v) \) dispersion
A. only ( \( i \) ) and ( \( (i) \)
B. (ii) and (iii)
C . \( (i),(i i) \) and \( (i v) \)
D. only \( (i v) \)
Subject: Physics
Which of the following is the lens
maker's formula
\( \mathbf{A} \cdot 1 / f=(n-1)\left(1 / R_{1}+1 / R_{2}\right) \)
B . \( 1 / f=(n+1)\left(1 / R_{1}-1 / R_{2}\right) \)
\( \mathbf{c} \cdot 1 / f=(n-1)\left(1 / R_{1}-1 / R_{2}\right) \)
D. \( 1 / f=(n+1)\left(1 / R_{1}+1 / R_{2}\right) \)
Subject: Maths
\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left[\sin ^{-1}\left(\frac{\sqrt{\mathbf{1}+\boldsymbol{x}}+\sqrt{\mathbf{1}-\boldsymbol{x}}}{\mathbf{2}}\right)\right] \mathbf{w} \cdot \mathbf{r} \)
to \( x \) equals
A \( \cdot \frac{1}{2 \sqrt{1-x^{2}}} \)
в. \( \frac{-2}{\sqrt{1-x^{2}}} \)
c. \( \frac{-1}{2 \sqrt{1-x^{2}}} \)
D. None of these
Subject: Physics
Select correct options.
This question has multiple correct options
A. In hitting or kicking a ball we decrease the time of contact so that large force acts on the ball producing greater acceleration.
B. In catching a ball by drawing hands backwards, increases the time of contact and so, lesser force acts on hands and hands are saved from getting hurt.
C. An athlete is advised to come to stop slowly after finishing a fast race. So that time of stop increases and hence force experienced by him decreases.
D. None of these
Subject: Physics
A ball of radius \( R \) and with bulk
modulus of elasticity \( K \) is kept in a liquid inside a cylindrical container. It is pressed by putting a mass \( \mathrm{m} \) on a massless piston of cross-sectional area
A, then the fractional decrease in the
radius of ball will be
A \( \cdot \frac{M g}{3 K R} \)
в. \( \frac{M g}{3 K A} \)
c. \( \frac{M g}{K A} \)
D. \( \frac{M g K}{3 A R} \)
Subject: Physics
Two particles \( A \) and \( B \) each of mass \( m \)
are attached by a light inextensible string of length \( 2 l . \) The whole system
lies on a smooth horizontal table with \( \boldsymbol{B} \)
initially at a distance \( l \) from \( A \). The
particle at end \( B \) is projected across the table with speed \( u=4 \sqrt{3} m / s \)
perpendicular to \( A B \). Find velocity of
ball \( A \) just after the jerk?
Subject: Physics
The coordinates of a moving particle at time \( t \) are given by \( x=c t^{2} \) and \( y=b t^{2} \)
The speed of the particle is given by
A \( \cdot 2 t(c+b) \)
B . \( 2 t \sqrt{\left(c^{2}-b^{2}\right)} \)
c. \( t \sqrt{\left(c^{2}+b^{2}\right)} \)
D. \( 2 t \sqrt{\left(c^{2}+b^{2}\right)} \)
Subject: Physics
Assertion
A convex lens of glass \( (\mu=1.5) \) behave as a diverging lens when immersed in carbon disulphide of higher refractive index \( (\mu=1.65) \)
Reason
A diverging lens is thinner in the middle
and thicker at the edges.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Physics
A parallel plate condenser with a dielectric of dielectric constant \( \boldsymbol{K} \)
between the plates has a capacity \( C \) and is charged to a potential \( V \) volt. The dielectric slab is slowly removed from between the plates and then reinserted. The net work done by the system in this process is :
A . zero
в. \( \frac{1}{2}\left[(K-1) C V^{2}\right. \)
c. \( \frac{C V^{2}(K-1)}{K} \)
D. \( (K-1) C V^{2} \)
Subject: Physics
Which one of the following statements
does hold good when two balls of
masses \( m_{1} \) and \( m_{2} \) undergo elastic
collision?
A. When \( m_{1}<m_{2} \) and \( m_{2} \) at rest, there will be maximum
B. When \( m_{1}>m_{2} \) and \( m_{2} \) at rest, after collision the ball of mass \( m_{2} \) moves with four times the velocity of \( m_{1} \)
c. When \( m_{1}=m_{2} \) and \( m_{2} \) at rest, there will be maximum
transfer of K.E
D. When collision is oblique and \( m_{2} \) at rest with \( m_{1}=m_{2} \) after collision the ball moves in opposite direction
Subject: Physics
Consider the following statements:
(a) No net force acts on a rain drop
falling vertically with a constant speed.
(b) If net force acting on the body is
zero, momentum of the body remains
constant.
(c) Particle of different masses falls
with different acceleration on earth.
(d) It is easier to start motion in a
heavier body than a lighter body. Which of the above statements are
correct?
\( A \cdot(b) \) and \( (c) \)
B. (a) and (b)
c. \( (a),(b) \) and \( (d) \)
D. All of the above
Subject: Physics
A loop of area \( 1 \mathrm{m}^{2} \) is placed in a magnetic
field \( B=2 T, \) such that plane of the loop
is parallel to the magnetic field. If the loop is rotated by 180 , the amount of net charger passing through any point of loop, if its resistance is \( 10 \Omega \) is then
A. \( 0.4 \mathrm{c} \)
B. \( 0.2 \mathrm{c} \)
c. \( 0.8 \mathrm{c} \)
D. o c