AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Assertion
STATEMENT-1: If the mass of the
colliding particles remains constant, then the linear velocity of the individual particles change during collision along common normal direction.
Reason
STATEMENT-2: A pair of equal and
opposite impulses act along common normal direction.
A. Both statements 1 and 2 are true and statement 2 is the correct explanation of statement 1
B. Both statements 1 and 2 are true but statement 2 is not correct explanation of statement 1
c. Statement 1 is true but statement 2 is false
D. Statement-1 is False, Statement-2 is True
Subject: Physics
A compass needle whose magnetic
moment is \( 60 A m^{2} \) pointing
geographical north at a certain place where the horizontal component of
earth's magnetic field is \( 40 \times \)
\( 10^{-6} W b m^{-2} \) experiences a torque of
\( 1.2 \times 10^{-3} N m . \) The declination of the
place is
\( \mathbf{A} \cdot 20^{0} \)
B. \( 45^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 30^{\circ} \)
Subject: Maths
If \( y=\frac{x+c}{1+x^{2}}, \) then the value of \( x y \)
where \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\mathbf{0} \) is
A \( \cdot \frac{1}{2} \)
B. \( \frac{3}{4} \)
\( c \cdot \frac{5}{4} \)
D. None of these
Subject: Physics
There are two thin wire rings, each of radius R, whose axes coincide. The charges on the rings are \( \mathrm{q} \) and q.Evaluate the potential difference between the centers of the rings separates by a distance a.
A \( \cdot \frac{q}{\pi \varepsilon_{0}}\left[\frac{1}{R}+\frac{1}{\sqrt{R^{2}+a^{2}}}\right] \)
B \( \cdot \frac{q}{2 \pi \varepsilon}\left[\frac{1}{R}+\frac{1}{\sqrt{R^{2}+a^{2}}}\right] \)
c. \( \frac{q}{2 \pi \varepsilon_{0}}\left[\frac{1}{R}-\frac{1}{\sqrt{R^{2}+a^{2}}}\right] \)
D. \( \frac{2 q}{\pi \varepsilon_{0}}\left[\frac{1}{R}-\frac{1}{\sqrt{R^{2}+a^{2}}}\right] \)
Subject: Chemistry
Consider the following compounds, The correct order towards electrophilic substitution reaction is :
\( A \cdot(\text { iv })>(\text { iii })>(\text { ii })>(i) \)
B. (i)> (ii) > (iii) > (iv)
\( c \cdot(\text { iv })>(\text { iii })>(i)>(\text { ii }) \)
D. (iii) > (iv) > (i) > (ii)
Subject: Maths
Let \( \boldsymbol{A}=\{1,2\}, \boldsymbol{B}=\{1,2,3,4\}, C= \)
\{5,6\} and \( D=\{5,6,7,8\} \) Verify that
(i) \( \boldsymbol{A} \times(\boldsymbol{B} \cap \boldsymbol{C})=(\boldsymbol{A} \times \boldsymbol{B}) \cap(\boldsymbol{A} \times \boldsymbol{C}) \)
(ii) \( A \times C \) is a subset of \( B \times D \)
Subject: Chemistry
At a certain temperature, \( \boldsymbol{K}_{\boldsymbol{C}} \) for
\( \boldsymbol{S O}_{2}(\boldsymbol{g})+\boldsymbol{N} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{S} \boldsymbol{O}_{3}(\boldsymbol{g})+\boldsymbol{N} \boldsymbol{O}(\boldsymbol{g}) \)
is \( 16 . \) If we take one mole of each of all
the four gases in one litre container, what would be the equilibrium
concentration of \( N O \) and \( N O_{2} ? \)
\( N O_{2}=10 M \)
B. \( N O=2 M \)
\( N O_{2}=2.4 M \)
\( N O_{2}=1.2 M \)
D. \( N O=1.6 M \)
\( N O_{2}=0.4 M \)
Subject: Physics
A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube
is then rotated in a horizontal plane about one of its ends with a uniform
angular velocity \( \omega . \) The force exerted by the liquid at the other ends is:-
A \( \cdot \frac{M L \omega^{2}}{2} \)
B. \( \frac{M L^{2} \omega}{2} \)
c. \( M L \omega^{2} \)
D. \( \frac{M L^{2} \omega^{2}}{2} \)
Subject: Chemistry
\( 10 m l \) of hydrocarbon requires \( 55 m l \) of oxygen for complete combustion
producing \( 40 m l \) of \( C O_{2} . \) The formula of the hydrocarbon is :
A \( \cdot C_{4} H_{6} \)
в. \( C_{5} H_{10} \)
\( \mathbf{c} \cdot C_{4} H_{8} \)
D. \( C_{4} H_{10} \)
Subject: Chemistry
Which of the following is not optically
active?
\( \mathbf{A} \cdot\left[\operatorname{Co}(e n)_{3}\right]^{3+} \)
B . \( \left[C r(o x)_{3}\right]^{3} \)
c. \( \operatorname{cis}-\left[\operatorname{CoCl}_{2}(e n)_{2}\right] \)
D. \( \operatorname{trans}-\left[\operatorname{CoCl}_{2}(e n)_{2}\right]^{+} \)
Subject: Chemistry
The IUPAC name of the complex
\( \left[\boldsymbol{C r} \boldsymbol{C l}_{2}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{4}\right] \boldsymbol{N} \boldsymbol{O}_{3} \) is :
A. Dichlorotetraaquachromium(III) nitrate
B. Tetraaquadichlorochromium(III) nitrate
c. chromiumtetraaquadichloro nitrate
D. Dichlorotetraaquadnromium nitrate
Subject: Chemistry
What will be the abnormal molecular
\( \operatorname{mass} \) of \( \mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right] . \) If in a aqueous
solution it is \( 40 \% \) dissociated? (Given, normal molecular weight of
\( \left.\mathbf{K}_{3}\left[\mathbf{F e}(\mathbf{C N})_{6}\right] \text { is } 329\right) \)
A . 149.54
B. 723.8
c. 82.25
D. 329.0
Subject: Maths
Area lying in the first quadrant and bounded by the circle \( x^{2}+y^{2}=4 \) and
the line \( \boldsymbol{x}=\boldsymbol{y} \sqrt{\mathbf{3}} \) is:
A . \( \pi \)
в. \( \frac{\pi}{2} \)
c. \( \frac{\pi}{3} \)
D. None of these
Subject: Physics
Consider the following statements about electroplating:
I. Electroplating is the coating of metal objects with a thin layer of a different
metal.
II. Electroplating makes objects look more attractive and protects them from corrosion and rusting.
III. Electroplating forms and envelops around the object to protect them from magnetism. Which of the above statements is true?
A. Only statement I
c. Statements land II
D. Statements II and III
E. All of the above statements
Subject: Physics
A police van moving on a highway with a speed of \( 30 \mathrm{km} h^{-1} \) fires a bullet at a
thief's car speeding away in the same
direction with a speed of \( 192 \mathrm{km} h^{-1} . \) If
the muzzle speed of the bullet is 150
\( \mathrm{m} s^{-1}, \) with what speed does the bullet
hit the thief's car?
\( \mathbf{A} \cdot 95 \mathrm{m} \mathrm{s}^{-1} \)
B . \( 105 \mathrm{m} s^{-1} \)
C. \( 115 \mathrm{m} s^{-1} \)
D. \( 125 \mathrm{m} s^{-1} \)
Subject: Physics
A body starts from rest with an
acceleration \( a_{1} . \) After two seconds
another body \( B \) starts from rest with an
acceleration \( a_{2} \). If they travel equal
distances in fifth second after the
starts of \( A, \) the ratio \( a_{1}: a_{2} \) will be
equal to:
A .9: 5
B. 5: 7
\( \mathrm{c} .5: 9 \)
D. 7: 9
Subject: Physics
The elongation produced in a copper wire of length \( 2 \mathrm{m} \) and diameter \( 3 \mathrm{mm} \) when a force of \( 30 \mathrm{N} \) is applied is \( [\mathrm{Y}= \) \( \left.1 \times 10^{11} \mathrm{N} \cdot \mathrm{m}^{-2}\right] \)
A. \( 8.5 m m \)
B. \( 0.85 \mathrm{mm} \)
c. \( 0.085 m m \)
D. \( 85 m m \)
Subject: Chemistry
Complete the following statements by selecting the correct alternative from
the choices given:

The geometry of \( X e F_{6} \) molecule and
the hybridization of \( X e \) atom in the
molecule is:
A. Distorted octahedral and \( s p^{3} d^{3} \)
B. Square planar and \( s p^{3} d^{2} \)
C. Pyramidal and \( s p^{3} \)
D. Octahedral and \( s p^{3} d^{3} \)
Subject: Physics
What is the value of \( (\overrightarrow{\boldsymbol{A}}+\overrightarrow{\boldsymbol{B}}) \cdot(\overrightarrow{\boldsymbol{A}} \times \overrightarrow{\boldsymbol{B}}) ? \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( A^{2}-B^{2} \)
c. \( A^{2}+B^{2}+2 A B \)
D. None of these
Subject: Physics
The electric field associated with an
e.m. wave in vacuum is given by \( \overrightarrow{\boldsymbol{E}}= \) \( 40 \cos \left(k z-6 \times 10^{8} t\right) \hat{i}, \) where \( E, z \) and \( t \)
in volt\( / \boldsymbol{m}, \) meter and seconds
respectively. The value of wave vector \( k \)
is
\( A \cdot 6 m^{-1} \)
B. \( 3 m^{-1} \)
\( \mathbf{c} \cdot 2 m^{-1} \)
D. \( 0.5 m^{-1} \)
Subject: Physics
Length of a wire is increased by \( 1 \mathrm{mm} \) on the application of a given load. If same load is applied to another wire of same material but of length and radius twice that of the first then increase in its
length will be
\( \mathbf{A} \cdot 2 m m \)
в. \( \frac{1}{2} m m \)
\( \mathrm{c} .4 \mathrm{mm} \)
D. \( \frac{1}{4} m m \)
Subject: Physics
Find the electric field in the region
labelled 3
\( A \cdot 0 \)
B \( \cdot k_{e} \frac{q}{r^{2}} \)
\( c \cdot 2 k_{e} \frac{q}{r^{2}} \)
\( \mathrm{D} \cdot 3 k_{e} \frac{q}{r^{2}} \)
Subject: Maths
Given: \( \boldsymbol{x}, \boldsymbol{y} \) and \( \boldsymbol{z} \) are integers and
\( \mathbf{3}^{x+5}=\mathbf{2 7}^{y+1}, \) then \( \boldsymbol{x} \) is even
A. True
B. False
Subject: Physics
Assertion
STATEMENT-1: The current density \( \overrightarrow{\boldsymbol{J}} \) at any point in ohmic resistor is in direction of electric field \( \overrightarrow{\boldsymbol{E}} \) at that point.
Reason
STATEMENT-2:A point charge when released from rest in a region having only electrostatic field always moves along electric lines of force.
A. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-
B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-
c. Statement-1 is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is True
Subject: Chemistry
Consider the following statements in respect of lanthanoids.
1. The basic strength of hydroxides of
lanthanoids increases from \( \mathrm{La}(O H)_{3} \) to
\( \boldsymbol{L} \boldsymbol{u}(\boldsymbol{O} \boldsymbol{H})_{4} \)
2. The lanthanoid ions \( \boldsymbol{L} \boldsymbol{u}^{3+}, \boldsymbol{Y} \boldsymbol{b} \boldsymbol{6} \boldsymbol{2}+, \boldsymbol{C} \boldsymbol{e}^{4+} \) are diamagnetic.
Which of the statement(s) given above is are correct?
A. Only 1
B. Only 2
c. Both 1 and 2
D. Neither 1 nor 2
Subject: Chemistry
Vapour pressure of water at certain
temperature is \( 155 \mathrm{mm} \) Hg and that of the another solvent 'X' is 'p' mm Hg. Molecular weight of 'X' is 128. An
aqueous solution of 'X'(64\% by wt) has
a vapour pressure of \( 145 \mathrm{mm} \) Hg. What is 'p'?
Subject: Biology
Read the following about pollution and
identify the correct matching combinations.
\( \begin{array}{lll}\text { List I } & \text { List II } & \text { List III } \\ \text { (A) Chernobyl } & \begin{array}{l}\text { Accidental } \\ \text { leakage }\end{array} & \begin{array}{l}\text { Radioactive } \\ \text { wastes }\end{array} \\ \begin{array}{l}\text { (B) Elnino } \\ \text { effect }\end{array} & \begin{array}{l}\text { Global } \\ \text { warming }\end{array} & \begin{array}{l}\text { Causing } \\ \text { climatic } \\ \text { change }\end{array} \\ \begin{array}{l}\text { (C) } \\ \text { Chlorofloro } \\ \text { carbons }\end{array} & \begin{array}{l}\text { Ozone } \\ \text { degradation }\end{array} & \begin{array}{l}\text { Fluorine } \\ \text { atoms } \\ \text { released }\end{array} \\ \begin{array}{l}\text { (D)Snow } \\ \text { blindness }\end{array} & \begin{array}{l}\text { UV-B } \\ \text { Radiation }\end{array} & \begin{array}{l}\text { Inflammation } \\ \text { of cornea }\end{array}\end{array} \)
\( A \cdot A, C \)
B. A, D
\( c \cdot A, B, D \)
D. B.
Subject: Chemistry
Which of the following combination of
reagents can bring the
shown transformation?
\( \mathbf{A} \cdot C H_{3} O N a, M g / \)ether\( , C O_{2}, H_{2} O / H^{+} \)
в. \( C H_{3} \) ONa, \( K C N / D M S O, H_{2} O / H_{2} S O_{4}, \) heat
\( \mathbf{c} \cdot M g / \)ether\( , C O_{2}, H_{2} O / H^{+}, C H_{3} O N a \)
D. \( N a O H, M g / \)ether\( , C O_{2}, H_{2} O / H^{+}, C H_{3} I \)
Subject: Maths
State the following statement is True or
False
The area (in sq. units) of the triangle formed by the points with polar coordinates (1,0)\( \left(2, \frac{\pi}{3}\right) \) and \( \left(3, \frac{2 \pi}{3}\right) \)
is \( \frac{5 \sqrt{3}}{4} \)
A. True
B. False
Subject: Physics
A block of mass \( m=0.1 \mathrm{kg} \) is released
from a height of \( 4 \mathrm{m} \) on a curved smooth
surface. On the horizontal surface, path
AB is smooth and path BC offers
coefficient of friction \( \mu=0.1 . \) If the
impact of block with the vertical wall at \( \mathrm{C} \) be perfectly elastic, the total distance covered by the block on the horizontal
surface before coming to rest will be :
\( \left.\operatorname{take} g=10 m / s^{2}\right) \)
A \( .29 m \)
в. \( 49 m \)
\( \mathbf{c} .59 m \)
\( \mathbf{D} \cdot 109 m \)
Subject: Maths
Binomial expansion of \( \left(\boldsymbol{x}^{k}+\frac{\mathbf{1}}{\mathbf{2}^{\mathbf{2 k}}}\right)^{\mathbf{3 n}} \)
where \( n \) is a positive integer, always contains a term which is independent of
\( \mathbf{A} \cdot x^{2} \)
B. \( x \)
\( \mathbf{c} \cdot x^{3} \)
D. none of the above
Subject: Physics
Three capacitors connected in series
have an effective capacitance of \( 4 \mu F \). If one of the capacitance is removed, the net capacitance of the capacitor increases to \( 6 \mu F . \) The removed
capacitor has a capacitance of
\( \mathbf{A} \cdot 2 \mu F \)
в. \( 4 \mu F \)
\( \mathbf{c} \cdot 10 \mu F \)
D. \( 12 \mu F \)
E \( .24 \mu F \)
Subject: Physics
A body initially at rest travels a
distance \( 100 \mathrm{m} \) in \( 5 \mathrm{s} \) with a constant
acceleration. Find the acceleration.
A \( \cdot 20 m s^{-2} \)
B. \( 4 m s^{-2} \)
\( \mathbf{c} \cdot 8 m s^{-2} \)
D. \( 10 m s^{-2} \)
Subject: Physics
Find out the correct relation for the
dependance of change in acceleration due to gravity on the angle at the latitude due to rotation of earth?
A \( . d g \propto \cos \phi \)
B. \( d g \propto \cos ^{2} \phi \)
c. \( d g \propto \cos ^{3 / 2} \phi \)
D. \( d g \propto \frac{1}{\cos \phi} \)
Subject: Chemistry
IUPAC name of \( \beta \) - Chloro- \( \alpha \) - methyl
butyric acid:
A. 3 -Chloro-2 methyl-butanoic acid
B. 2-chloro-3-methyl Butanoic acid
C. 2 -chloro-3- methyl-Butan-4-acid
D. 3-chloro-isopentanoic acid
Subject: Physics
The orbital radius of moon around the
earth is \( 3.8 \times 10^{8} \) meter and its time
period is 27.3 days. The centripetal acceleration of moon will be
A. \( -2.4 \times 10^{-3} \mathrm{m} / \mathrm{s}^{2} \)
B. \( 11.2 m / s^{2} \)
c. \( 2.7 \times 10^{-3} \mathrm{m} / \mathrm{s}^{2} \)
D. \( 9.8 m / s^{2} \)
Subject: Chemistry
\( \boldsymbol{C d}(s)\left|\boldsymbol{C d C l}_{2}(\mathbf{0 . 1 0} \boldsymbol{M})\right| \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l}(\boldsymbol{s}) \mid \boldsymbol{A} \boldsymbol{g}(s \)
The EMF of the above cell is 0.6315 V at
\( 0^{\circ} \mathrm{C} \) and \( 0.6753 \mathrm{V} \) at \( 25^{\circ} \mathrm{C} \). The \( \Delta H \) of
reaction in \( \mathrm{kJ} \) at \( 25^{\circ} \mathrm{C} \) is:
A . - 176
B. - 234.7
c. 123.5
D . - 167.6
Subject: Physics
The binding energy per nucleon of \( _{20}^{40} C a \)
is
\( \left(_{20}^{40} C a=39.962589 \mathrm{amu}, m_{p}=1.007825\right. \)
amu; \( m_{n}=1.008665 a m u \) and \( 1 a m u \) is equivalent to \( 931.5 M e V) \)
\( \mathbf{A} .6 .55 M e V \)
в. \( 7.55 \mathrm{MeV} \)
c. \( 8.55 \mathrm{MeV} \)
D. \( 9.55 \mathrm{MeV} \)
Subject: Physics
Two concentric coils each of radius
equal to \( 2 \pi \mathrm{cm} \) are placed at right
angles to each other. 3 ampere and 4 ampere are the currents flowing in each coil respectively. The magnetic
induction in \( w e b e r / m^{2} \) at the centre of
the coils will be
\( \left(\mu_{0}=4 \pi \times 10^{-7} w b / A . m\right) \)
A \( \cdot 10^{-5} \)
B . \( 12 \times 10^{-5} \)
C \( .7 \times 10^{-5} \)
D. \( 5 \times 10^{-5} \)
Subject: Chemistry
\( \log \frac{K_{p}}{K_{c}}+\log R T=0 \) is true relationship
for the following reaction:
A \( . P C l_{5} \rightleftharpoons P C l_{3}+C l_{2} \)
в. \( 2 S O_{2}+O_{2} \rightleftharpoons 2 S O_{3} \)
c. \( N_{2}+3 H_{2} \rightleftharpoons 2 N H_{3} \)
D. \( (b) \) and \( (c) \) both
Subject: Maths
The function \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) defined by
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{4}^{\boldsymbol{x}}+\boldsymbol{4}^{|\boldsymbol{x}|} \) is
A. One-one and into
B. Many-one and into
c. one-one and onto
D. Many-one and onto
Subject: Biology
After forceful inspiration, the amount of air that can be breathed out by maximum forced expiration is equal to
A. Inspiratory Reserve Volume (IRV) + Expiratory Reserve Volume (ERV) + Tidal Volume (TV) + Residual Volume \( (R V) \)
B. IRV + RV + ERV
C. \( \operatorname{IRV}+\mathrm{TV}+\mathrm{ERV} \)
D. TV + RV + ERV
Subject: Chemistry
Assertion
Graphite cannot be converted into
diamond.
Reason
Graphite is conducting in nature.
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
For a black body at a temperature of
\( 727^{\circ} \mathrm{C}, \) Its radiated power is 60 watt
and temperature of the surrounding is
\( 227^{\circ} \mathrm{C} \) If the temperature of the black
body is changed to \( 1227^{\circ} \mathrm{C} \), Then its radiating power will be
\( \mathbf{A} \cdot 304 W \)
B. 320 W
c. \( 240 W \)
D. \( 120 W \)
Subject: Physics
A piano-convex lens (refractive index \( \mu_{1} \)
fits exactly into a piano-concave lens (refractive index \( \mu_{2} \) ). Their plane surfaces are parallel to each other. R is the radius of curvature of the curved
surface of the lenses, then focal length of the combination is:
A. \( \frac{R}{\mu_{1}-\mu_{2}} \)
в. \( \frac{2 R}{\mu_{2}-\mu_{1}} \)
c. \( \frac{R}{2\left(\mu_{1}-\mu_{2}\right)} \)
D. none of these
Subject: Chemistry
The outer electronic configuration of transitional elements is:
A \( \cdot(n-1) s^{2} n d^{1-2} \)
B \( \cdot(n+1) s^{2} n d^{1-5} \)
C \( \cdot(n-1) s^{2} n p^{6}(n-1) d^{1-10} n s^{1,2} \)
D \( \cdot n s^{2}(n-1) d^{1-10} \)
Subject: Chemistry
Complete the following reactions:
(i) \( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{M}_{m} \boldsymbol{O}_{o}(\boldsymbol{s}) \stackrel{\boldsymbol{\Delta}}{\rightarrow} \)
(ii) \( \boldsymbol{C O}(\boldsymbol{g})+\boldsymbol{H}_{2}(\boldsymbol{g}) \frac{\boldsymbol{\Delta}}{\text {catalyst}} \)
(iii) \( C_{3} H_{8}(g)+3 H_{2} O(g) \frac{\Delta}{\text { catalyst }} \)
\( (\mathrm{iv}) C_{3} H_{8}(g)+3 H_{2} O(g) \frac{\Delta}{\text {catalyst}} \)
Subject: Physics
\( n \) moles of an ideal gas undergoes a
process \( A \rightarrow B \) as shown in the figure.
Maximum temperature of the gas
during the process is:
A \( \cdot \frac{3 P_{o} V_{o}}{2 n R} \)
B. \( \frac{9 P_{o} V_{o}}{4 n R} \)
c. \( \frac{9 P_{o} V_{o}}{2 n R} \)
D. \( \frac{9 P_{o} V_{o}}{n R} \)
Subject: Maths
Evaluate: \( \int e^{x} \sin \left(e^{x}\right) d x \)
A \( \cdot \cos e^{x}+C \)
B. - \( \cos e^{x}+C \)
c. \( \left(\cos e^{x}\right)^{-1}+C \)
\( \mathbf{D} \cdot \sin e^{x}+C \)
Subject: Physics
Two free charges \( q \) and \( 4 q \) are placed at a distance d apart. A third charge \( Q \) is placed between them at a distance \( x \) from charges q such that the system is in equilibrium.Then
\( A \cdot Q=\frac{4 q}{9} \)
B . \( Q=\frac{7 q}{9} \)
c. \( Q=-\frac{3 q}{9} \)
D \( \cdot Q=-\frac{2 q}{9} \)
Subject: Physics
toppr
\( Q \)
meters. Arter this the bus travels at a
constant speed for 15 seconds. Then the driver notices a red light 18 meters ahead and applies brakes with
acceleration \( a_{b} . \) Assume that the bus
decelerates at a constant rate and
comes to a stop sometime later just at the light.
1. What was the initial acceleration of
the bus?
2. What was the velocity of the bus after
5 seconds?
3. Calculate \( a_{b} \)
4. How long did does the bus brake?
b) Two athletes Usha and Shiney are playing athletic games. Usha is running at a constant velocity towards Shiney who is stationary. When Usha is 12 meters away from Shiney, Shiney starts to accelerate at a constant rate of
\( 1.5 m s^{-2} \)
1. What is the minimum velocity with which Usha needs to run in order to just catch up with Shiney?
2. How long does Usha take to catch up with Shiney?
Subject: Maths
Let the vector \( \vec{a}, \vec{b}, \vec{c} \) and \( \vec{d} \) be such \( \operatorname{that}(\overrightarrow{\boldsymbol{a}} \times \overrightarrow{\boldsymbol{b}}) \times(\overrightarrow{\boldsymbol{c}} \times \overrightarrow{\boldsymbol{d}})=\mathbf{0} \cdot \operatorname{Let} \boldsymbol{P}_{1} \)
and \( P_{2} \) be planes determined by the pairs of vectors \( \vec{a}, \vec{b} \) and \( \vec{c}, \vec{d} \)
respectively then the angle between \( P_{1} \)
and \( P_{2} \) is
A. 0
в. \( \frac{\pi}{4} \)
c. \( \frac{\pi}{3} \)
D. \( \frac{\pi}{2} \)
Subject: Maths
The value of \( 2^{n}\{1.3 .5 \ldots \ldots .(2 n- \)
\( \mathbf{3})(\mathbf{2 n - 1})\} \) is
A \( \cdot \frac{(2 n) !}{n !} \)
B. \( \frac{(2 n) !}{2^{n}} \)
c. \( \frac{n !}{(2 n !) !} \)
D. None of these
Subject: Physics
Q Type your question
\( \left(\sigma_{1}>\sigma_{2}\right) \) are placed near each other
separated by distance 'd. A small
change ' \( q \) ' is placed in between two
plates such that there is no effect on charge distribution on plates. Now this
charge is moved at an angle of \( 45^{\circ} \) with the horizontal towards plate having
charge density \( \sigma_{2} \) by distance ' \( a^{\prime}(a< \) \( <\boldsymbol{d}) . \) Find the work done by electric
field in the process.
A \( \cdot \frac{q a\left(\sigma_{1}-\sigma_{2}\right)}{5 \sqrt{2} \epsilon_{0}} \)
B. \( \frac{q a\left(\sigma_{1}-\sigma_{2}\right)}{2 \sqrt{2} \epsilon_{0}} \)
c. \( \frac{q a\left(\sigma_{1}-\sigma_{2}\right)}{3 \sqrt{2} \epsilon_{0}} \)
D. \( \frac{q a\left(\sigma_{1}-\sigma_{2}\right)}{4 \sqrt{2} \epsilon_{0}} \)
Subject: Chemistry
Which one of the following pairs of
compounds are functional isomers?
\( \mathbf{A} \cdot C H_{3} C H_{2} C H_{2} O H, C H_{3} C H(O H) C H_{3} \)
B \( \cdot C H_{3} C H_{2} C H_{2} C H_{2} O H,\left(C H_{3}\right)_{2} C H C H_{2} O H \)
\( \mathbf{c} \cdot C H_{3} C H_{2} C H_{2} O H, C H_{3} C H_{2} C H_{2} C l \)
D. \( C H_{3} C H_{2} C H_{2} O H, C H_{3}-O-C H_{2} C H_{3} \)
Subject: Maths
\( O \) is the centre of the circle. \( A B \) and
\( C D \) are two chords of the circle. \( O M \perp \)
\( A B \) and \( O N \perp C D . \) If \( O M=O N=3 \)
\( \operatorname{cmand} A M=B M=4.5 \mathrm{cm}, \) then \( C D \)
is equal to
\( A \cdot 8 \mathrm{cm} \)
B. 9 cm
\( c .10 \mathrm{cm} \)
D. None of these
Subject: Physics
The relationship between A.C voltage and time in Sl unit is \( V= \)
\( 120 \sin (100 \pi T) \cos (100 \pi t) \) volt value
of peak voltage and frequency will be :
A. 120 volt and 100 \( \mathrm{Hz} \)
B . \( \frac{120}{\sqrt{2}} \) volt and \( 100 \mathrm{Hz} \)
c. 60 volt and 200 Hz
D. 60 volt and 100 нz
Subject: Physics
The velocity ' \( V \) ' of a particle varies with distance ' \( x \) ' and time 't' as \( \boldsymbol{V}= \)
\( \boldsymbol{A} \sin (\boldsymbol{B} \boldsymbol{x}) \cos (\boldsymbol{C} \boldsymbol{t}) \) when \( \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C} \) are
constants, then \( \frac{\boldsymbol{A} \boldsymbol{B}}{\boldsymbol{C}} \) will have the dimensions of:
A. velocity
B. acceleration
c. pressure
D. strain
Subject: Physics
A ray of light passes through an equilateral prism (refractive index 1.5 ) such that angle of incidence is equal to angle of emergence and the latter is equal to \( 3 / 4^{t h} \) of the angle of prism. The angle of deviation is
A .60
B. \( 30^{\circ} \)
c. 45
D. \( 120^{\circ} \)
Subject: Maths
\( \left|\begin{array}{ccc}-\mathbf{2} \boldsymbol{a} & \boldsymbol{a}+\boldsymbol{b} & \boldsymbol{a}+\boldsymbol{c} \\ \boldsymbol{b}+\boldsymbol{a} & -\boldsymbol{2 b} & \boldsymbol{b}+\boldsymbol{c} \\ \boldsymbol{c}+\boldsymbol{a} & \boldsymbol{c}+\boldsymbol{b} & -\boldsymbol{2 c}\end{array}\right|=\boldsymbol{4}(\boldsymbol{b}+\boldsymbol{c})(\boldsymbol{c}+ \)
\( \boldsymbol{a})(\boldsymbol{a}+\boldsymbol{b}) \)
Subject: Physics
Refraction index of water is \( 4 / 3 \)
Calculate speed of light in water.
A \( \cdot 3 \times 10^{8} m / s \)
В. \( 62 m / s \)
C \( .2 .25 \times 10^{8} \mathrm{m} / \mathrm{s} \)
D. 1.25
Subject: Chemistry
According to Charles' law.
This question has multiple correct options
A \( \cdot V \propto \frac{1}{T} \)
\( ^{\mathbf{B}} \cdot\left(\frac{d V}{d T}\right)_{P}=K \)
\( ^{\mathbf{C}} \cdot\left(\frac{d T}{d V}\right)_{P}=K \)
\( ^{\mathrm{D}}\left(\frac{1}{T}-\frac{V}{T^{2}}\right)_{P}=0 \)