AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Given figure shows measuring cylinder \( \left(\text { in } c m^{3}\right) \) before and after the immersion
of an irregular solid object. The volume
of the object is
A \( \cdot \) 82 \( c m^{3} \)
B. \( 12 \mathrm{cm}^{3} \)
c. \( 30 \mathrm{cm}^{3} \)
\( \mathrm{D} \cdot 18 \mathrm{cm}^{3} \)
Subject: Maths
\( \sin x+i \cos 2 x \) and \( \cos x-i \sin 2 x \) are
conjugate to each other for
A . \( x=n \pi \)
B. \( x=\left(n+\frac{1}{2}\right) \frac{\pi}{2} \)
c. \( x=0 \)
D. No value of \( x \)
Subject: Chemistry
For a first order reaction \( t_{0.75} \) is
138.6 sec. Its specific rate constant is
\( \left(\operatorname{in} s^{-1}\right) \)
A \( \cdot 10^{-2} \)
- \( ^{-2} \)
B . \( 10^{-6} \)
\( \mathrm{c} \cdot 10^{-4} \)
D. \( 10^{-5} \)
Subject: Physics
The disc of radius \( r \) is confined to roll
without slipping at \( A \) and \( B \). If the plates have the velocities shown, then
This question has multiple correct options
A. angular velocity of the disc is \( 2 V / r \)
B. linear velocity, \( V_{0}=V \)
c. angular velocity of the disc is \( 3 V / 2 r \)
D. none of these
Subject: Chemistry
The activation energy for a hypothetical
reaction, \( \boldsymbol{A} \longrightarrow \) Product, is
\( 12.49 k c a l / \) mol. If the temperature is
raised from \( 295 ~ K \) to \( 305 K \), the rate of reaction increases by:
A . \( 60 \% \)
B. \( 100 \% \)
c. \( 50 \% \)
D. 20\%
Subject: Chemistry
In representative elements the
ionization energy values generally
decrease smoothly down the group. But
in boron group the values show an
erratic trend. This is mainly due to:
A. increase in metallic nature down the group
B. inert pair effect in the heavier elements of the group
c. d-block contraction and lanthanide contraction affecting the values of later elements due to poor shielding by d and f electrons
D. the different type of packing in their crystalline structure
Subject: Physics
A concaved lens has focal length of 15 cms. At what distance should the object
from the lens is placed so that it forms an erect and virtual image at \( 10 \mathrm{cm} \) from the lens?
\( \mathbf{A} \cdot 30 \mathrm{cm} \)
B. \( 15 \mathrm{cm} \)
\( c .60 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)
Subject: Chemistry
Hydrogen reacts with a metal(A) to give an ionic hydride(B). The metal (A) gives a brick red color with bunsen flame. The
hydride formed is commonly known by its trade name. The compound (B) on
treating with water gives back \( \mathrm{H}_{2} \) and
(C). Identify the metal \( A \)
\( A \cdot K \)
B. Na a
c. мg
D. ca
Subject: Maths
If \( \mathbf{S} \) and \( \mathbf{S}^{\prime} \) are the foci and \( \mathbf{B} \) is an
endpoint of the minor axis of an ellipse. If \( \angle S B S^{\prime}=120^{\circ} \) then its eccentricity
is:
A \( \cdot \frac{\sqrt{5}}{2} \)
B. \( \frac{\sqrt{3}}{2} \)
c. \( \frac{1}{\sqrt{2}} \)
D. \( \frac{1}{\sqrt{3}} \)
Subject: Maths
A lamp post stands on a horizontal plane. From a point situated at a distance \( 150 \mathrm{m} \) from its foot, the angle
of elevation of the top is \( 30^{\circ} . \) What is the
height of the lamp post?
A . \( 50 m \)
в. \( 50 \sqrt{3} m \)
c. \( \frac{50}{\sqrt{3}} m \)
D. \( 100 m \)
Subject: Chemistry
Two zinc rods are placed in contact with
dil. \( H N O_{3} \) and conc. \( H N O_{3} \) in two
separate containers A and B. The characteristics of gases evolved in the containers are respectively:
A. The gas in container A turns \( K_{2} C r_{2} O_{7} \) green and the gas in container B turns lead acetate black.
B. A \( \rightarrow \) Pungent smelling gas, B \( \rightarrow \) colourless, odourless gass
\( \mathrm{c} \cdot \mathrm{A} \rightarrow \operatorname{Inflammable} \operatorname{gas}, \mathrm{B} \rightarrow \operatorname{Turns} K_{2} \mathrm{Cr}_{2} \mathrm{O}_{7} \) green
D. \( A \rightarrow \) Can react with \( O_{2} \) explosively, \( B \rightarrow \) No reaction with \( O_{2} \) at all.
Subject: Physics
Dimensional methods provide three major advantages in verification, derivation and changing the system of units. Any empirical formula that is derived based on this method has to be
verified and proportionality constants
found by experimental means. The presence or absence of certain factors -
non dimensional constants or variables
cannot be identified by this method. So every dimensionally correct relation
cannot be taken as perfectly correct. The energy of an SHM is dependent on mass \( m \), frequency \( f \), and amplitude \( A \) of oscillation. The relation is
\( \mathbf{A} \cdot M f / A^{2} \)
B. \( M f A^{-2} \)
\( \mathbf{c} \cdot M f^{2} A^{-2} \)
\( \mathbf{D} \cdot M f^{2} A^{2} \)
Subject: Physics
Match List I with List II
List-I
a) Dalton's Law
e) \( P V= \)
constant \( (T=\text { constant }) \)
b) Charle's Law-I
\( f) P / T= \)
constant \( (\mathrm{V}=\text { constant }) \)
c) Charle's Law-II
\( g) \vee / T= \)
constant \( (\mathrm{P}=\text { constant }) \)
d) Boyle's Law
h) \( P=P_{1}+ \)
\( P_{2}+\ldots \ldots P_{\infty} \)
A \( \cdot a-f, b-h, c-g, d-e \)
B. a-g, b-h,c-e, d-f.
c. a-f, b-e,c-g,d-h.
D. a-h, b-g,c-f,d-e.
Subject: Physics
Assertion
In the three cases shown in the figure,
force exerted by liquid on three vessels
is the same.
Reason
Pressure at the bottom in each case is
same.
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
Two particles of equal mass \( m \) go around in a circle of radius \( R \) under the action of
their mutual gravitational attraction. The
speed of each particle is \( v \). Find value of \( v \)
\( ^{\mathrm{A}} \cdot_{v}=\frac{1}{2 R} \sqrt{\left(\frac{1}{G m}\right)} \)
в. \( v=\sqrt{\left(\frac{G m}{2 R}\right)} \)
c. \( v=\frac{1}{2} \sqrt{\left(\frac{G m}{R}\right)} \)
D. \( v=\sqrt{\left(\frac{4 G m}{R}\right)} \)
Subject: Physics
When a man is standing, rain drops appear to him falling at \( 60^{\circ} \) from the
horizontal from his front side. When he
is travelling at \( 5 k m / h \) on a horizontal
road they appear to him falling at \( 30^{\circ} \) from the horizontal from his front side.
The actual speed of the rain is \( ( \) in
\( \boldsymbol{k m} / \boldsymbol{h}) \)
A . 3
B. 4
c. 5
D. 6
Subject: Maths
The length \( x \) of an rectangle is
decreasing at the rate \( 2 \mathrm{cm} / \) sec and width y is increasing at the rate of
\( 2 c m / \)sec. When \( x=12 c m \) and \( y= \)
\( 12 c m, \) the rate of change of the area of
the rectangle is \( k c m^{2} / s e c, \) then \( k-9 \) is
Subject: Maths
\( \frac{x^{2}}{\left(x^{2}+1\right)\left(x^{2}+4\right)}=\frac{A}{x^{2}+1}+ \)
\( \frac{B}{x^{2}+4} \Rightarrow A+B= \)
A.
B.
\( c \cdot 2 \)
D. 3
Subject: Chemistry
Assertion
Tetravalency of carbon leading to formation of single, double and triple bonds.
Reason
The electronic configuration of carbon is \( 1 s^{2} 2 s^{2} 2 p^{2} . \) Carbon has 4 valence electrons and by sharing 4 electrons. It will have a stable configuration. It has all the valence electrons unpaired in the excited state.
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 body initially at \( 80^{\circ} \mathrm{C} \) cools to \( 64^{\circ} \mathrm{C} \) in
\( 5 \min \) and \( \operatorname{to} 52^{\circ} C \) in 10 min. The
temperature of the surrounding is
\( A \cdot 26^{\circ} C \)
B. \( 16^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 36^{\circ} C \)
D. \( 40^{\circ} \mathrm{C} \)
Subject: Maths
If \( \cos \alpha, \cos \beta \) and \( \cos \gamma \) are direction
cosines of a vector, then they satisfy which of the following? Prove it.
A \( \cdot \cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} \gamma=0 \)
B . \( \cos ^{2} \alpha+\cos ^{2} \beta=\cos ^{2} \gamma \)
c. \( \cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} \gamma=-1 \)
D. \( \cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} \gamma=1 \)
Subject: Physics
In a potentiometer experiment, it is found that no current passes through the galvanometer when the terminals of
the cell are connected across \( 52 \mathrm{cm} \) of
the potentiometer wire. If the cell is shunted by a resistance of \( 5 \Omega, \) a balance is found when the cell is
connected across \( 40 \mathrm{cm} \) of the wire. Find
the internal resistance of the cell.
A . \( 1.5 \Omega \)
B . 2\Omega
\( c .2 .5 \Omega \)
D. 12
Subject: Physics
A liquid takes 5 min. to cool from \( 80^{\circ} \mathrm{C} \)
to \( 50^{\circ} \mathrm{C} \). How much time does it take to
cool from \( 60^{\circ} \mathrm{C} \) to \( 30^{\circ} \mathrm{C} \) ? Temperature of
surroundings is \( 20^{\circ} \mathrm{C} \)
A. 2 mins
B. 3 mins
c. 5.5 mins
D. None of these
Subject: Maths
The compouned interest, calculate
yearly, on a certain sum of money for the second year is Rs.1,089 and for the third year it is Rs. \( 1,197.90 . \) Calculate the rate of interest and the sum of money
\( A \cdot 11 \%, \) Rs. 800
B. 12\%, Rs. 400
c. 13\%, Rs. 700
D. None of these
Subject: Maths
Solve the following system of equations \( \frac{\mathbf{6}}{\boldsymbol{x}+\boldsymbol{y}}=\frac{\mathbf{7}}{\boldsymbol{x}-\boldsymbol{y}}+\mathbf{3}, \frac{\mathbf{1}}{\mathbf{2}(\boldsymbol{x}+\boldsymbol{y})}= \)
\( \frac{1}{3(x-y)} \) where \( x+y \neq 0 \) and \( x \)
\( \boldsymbol{y} \neq \mathbf{0} \)
Subject: Chemistry
The group of molecules having identical
shape is:
\( \mathbf{A} \cdot B F_{3}, P C l_{3}, X e O_{3} \)
B. \( S F_{4}, X e F_{4}, C C I_{4} \)
\( \mathbf{c} \cdot P C l_{5}, I F_{5}, X e O_{2} F_{2} \)
D. \( C I F_{3}, X e O F_{2}, X e F_{3}^{+} \)
Subject: Physics
Unpolarized light falls first on polarizer
\( (P) \) and then on analyzer \( (A) . \) If the
intensity of the transmitted light from the analyser is \( \frac{1}{8} \) th of the incident unpolarized light. What will be the angle between optic axes of \( \boldsymbol{P} \) and \( \boldsymbol{A} \) ?
A \( \cdot 45^{\circ} \)
B. \( 30^{\circ} \)
c. zero
D. \( 60^{\circ} \)
Subject: Physics
Assertion
Threshold wavelength of certain metal
is \( \lambda_{0} . \) Light of wavelength slightly less
than \( \lambda_{0} \) is incident on the plate. It is
found that after some time the
emission of electrons stops
Reason
The ejected electrons experience force
of attraction due to development of
positive.
A. Assertion is incorrect but Reason is correct
B. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect and Reason is correct explanation for Assertion.
Subject: Maths
If \( A \) is a non zero square matrix of order
\( \boldsymbol{n} \) with \( \operatorname{det}(\boldsymbol{I}+\boldsymbol{A}) \neq \mathbf{0}, \) and \( \boldsymbol{A}^{3}=\mathbf{0} \)
where \( I, O \) are unit and null matrices of
order \( n \times n \) respectively, then
\( (\boldsymbol{I}+\boldsymbol{A})^{-1}= \)
A \( \cdot I-A+A^{2} \)
B . \( I+A+A^{2} \)
c. \( I+A^{2} \)
\( \mathbf{D} \cdot I+A \)
Subject: Maths
If \( P \) is a point inside the scalene
triangle \( A B C \) such that \( \Delta A P B \)
\( \Delta B P C \) and \( \Delta C P A \) have the same
area, then \( P \) must be:
A. In centre of \( \Delta A B C \)
B. Circum centre of \( \Delta A B C \)
c. Centroid of \( \Delta A B C \)
D. Ortho centre of \( \Delta A B C \)
Subject: Chemistry
If LPG cylinder contains a mixture of butane and isobutane, then the amount
of oxygen that would be required for combustion of 1 kg of it will be:
A. \( 1.8 \mathrm{kg} \)
в. \( 2.7 \mathrm{kg} \)
c. \( 4.5 \mathrm{kg} \)
D. \( 3.58 \mathrm{kg} \)
Subject: Maths
Find the value of the polynomial \( y^{3}- \)
\( 5 y-2 y^{2}+3 \) when, \( y=-b \)
A. \( -b^{3}-2 b^{2}+5 b+3 \)
3
В. \( b^{2}-2 b^{3}+b+1 \)
C. \( -b^{3}-2 b^{2}-b+3 \)
D. \( b^{3}-2 b^{2}+b-3 \)
Subject: Chemistry
If the lowest energy X-rays have \( \lambda= \)
\( 3.055 \times 10^{-8} m, \) estimate the
minimum difference in energy between
two Bohr's orbits such that an
electronic transition would correspond
to the emission of an X-ray. Assuming that the electrons in other shells exert
no influence, at what \( Z(\text { minimum }) \) would a transition from a second energy
level to the first result in the emission
of an X-ray?
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
D. 4
Subject: Physics
Q Type your question
status when the applied force is
removed. They are termed as elastic. Those of which not regaining are called
plastic. There may be delay in the regaining in some materials. They are said to have got elastic aftereffect,
since they have gone beyond the elastic limit. Repeated application and removal of force break at any point time and so are avoided.
The stress strain graph for two materials \( A \) and \( B \) is shown in the
following figure:
If the intensity of \( A \) and \( B \) is \( E_{A} \) and \( E_{B} \) respectively, then
В. \( E_{A}>E_{B} \)
c. \( E_{A}<E_{B} \)
D. \( E_{A}<<E_{B} \)
Subject: Maths
The solution of \( \frac{d y}{d x}+1=e^{x+y} \) is:
A \( \cdot e^{-(x+y)}+x+c=0 \)
B \( \cdot e^{-(x+y)}-x+c=0 \)
c. \( e^{x+y}+x+c=0 \)
D. \( e^{x+y}-x+c=0 \)
Subject: Chemistry
Assertion
Statement-1: The order of \( \pi \) bond
formation tendency is \( \boldsymbol{S} \boldsymbol{i}-\boldsymbol{O}<\boldsymbol{P}- \)
\( \boldsymbol{O}<\boldsymbol{S}-\boldsymbol{O}<\boldsymbol{C l}-\boldsymbol{O} \)
Reason
On moving from left to right along a period, the effective nuclear charge generally increases and consequently
the energy of the \( 3 d \) -orbital decreases from \( \boldsymbol{S} \boldsymbol{i}, \rightarrow \boldsymbol{P} \rightarrow \boldsymbol{S} \rightarrow \boldsymbol{C l} \)
A. Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-
B. Statement-1 is true, statement-2 is true and statement-2 is not the correct explanation for statement-1
c. statement- lis true, statement-2 is false
D. Statement-1 is false, statement-2 is true
Subject: Maths
Given a parallelogram \( \boldsymbol{A B C D} \). If \( |\overrightarrow{A B}|=a,|\overrightarrow{A D}|=b \&|\overrightarrow{A C}|=c, \) then
\( \overrightarrow{D B} \cdot \overrightarrow{A B} \) has the value
\( ^{\text {A } \cdot} \frac{3 a^{2}+b^{2}-c^{2}}{2} \)
B. \( \frac{a^{2}+3 b^{2}-c^{2}}{2} \)
c. \( \frac{a^{2}+b^{2}-3 c^{2}}{2} \)
D. None
Subject: Physics
A particle moves along +x-axis with initial velocity \( 5 \mathrm{m} / \mathrm{s} \). If acceleration (a)
varies with time (t) as shown in a-tt
graph, then the velocity of the particle
just after 4 second is
A \( .2 .5 m / s \)
B. \( 10 \mathrm{m} / \mathrm{s} \)
c. \( -1.25 m / s \)
D. \( -5 m / s \)
Subject: Chemistry
\( 2.2016 \mathrm{g} \) of acetaldehyde produced 13.9
kcal of heat on combustion in \( \boldsymbol{O}_{2} \)
Calculate the heat of combustion of
\( C H_{3} C O O H \) will be:
A. 279 kcal
B. 972 kcal
c. २७.९ kcal
D. 2.79 kcal
Subject: Chemistry
Write down the four quantum number
for \( 8 t h \) electron of oxygen atom?
A \( \cdot n=2, l=1, m=+2 \) or \( -2, s=+\frac{1}{2} \) or \( -\frac{1}{2} \)
B. \( n=2, l=1, m=+1 \) or \( -1, s=+\frac{1}{2} \) or \( -\frac{1}{2} \)
c. \( n=2, l=1, m=0, s=+\frac{1}{2} \) or \( -\frac{1}{2} \)
D. \( n=2, l=0, m=0, s=+\frac{1}{2} \) or \( -\frac{1}{2} \)
Subject: Chemistry
A light of wavelength \( 1218 \mathrm{A}^{\circ} \) is emitted when the electron of a hydrogen atom
drops from fifth to third quantum level. Find the wavelength of the photon emitted when electron falls fro third to
ground level?
A \( .1025 A^{0} \)
B . 2050 \( A^{0} \)
c. \( 1320 A^{\circ} \)
D. 2460 \( A^{0} \)
Subject: Chemistry
According to valence bond theory, the
predicted bond angle for \( \boldsymbol{H}_{2} \boldsymbol{O} \) is:
A \( \cdot 90^{\circ} \)
B. \( 109^{\circ} 28 \)
\( \mathbf{c} \cdot 107^{\circ} 18 \)
D. \( 104^{\circ} 28 \)
Subject: Maths
If the equation \( 2 x^{2}-6 x+p=0 \) has
real and different roots, then the values
of \( p \) are given by
\( ^{A} \cdot_{p}<\frac{9}{2} \)
в. \( \quad p \leq \frac{9}{2} \)
c. \( _{p>\frac{9}{2}} \)
\( \mathrm{D} \cdot_{p} \geq \frac{9}{2} \)
Subject: Physics
A wire fixed at the upper end stretches by length \( l \) by applying a force \( F \). The work done in stretching is:
\( ^{A} \cdot \frac{F}{2 l} \)
в. \( F l \)
c. \( \frac{2 F}{l} \)
D. \( \frac{F l}{2} \)
Subject: Physics
A body of mass \( m \) and radius \( r \) is
released from rest along a smooth inclined plane of angle of inclination \( \boldsymbol{\theta} \) The angular momentum of the body about the instantaneous point of
contact after a time \( t \) from the instant
of release is equal to
A. mgrt cos \( \theta \)
B. \( m g r t \sin \theta \)
c. \( (3 / 2) \) mgrt sin \( \theta \)
D. None of the above
Subject: Maths
If the points whose position vectors are \( \mathbf{2} \overline{\mathbf{i}}+\overline{\boldsymbol{j}}+\overline{\boldsymbol{k}}, \mathbf{6} \overline{\mathbf{i}}-\overline{\boldsymbol{j}}+\mathbf{2} \overline{\mathbf{k}} \) and \( \mathbf{1 4} \overline{\mathbf{i}}-\mathbf{5} \overline{\mathbf{j}}+ \)
\( p \bar{k} \) are collinear then the value of \( \mathbf{p} \) is
\( A \cdot 2 \)
B. 4
\( c \cdot 6 \)
D. 8
Subject: Physics
A copper wire of cross sectional area
\( 3 m m^{2} \) carrying a current of \( 4 A \) has \( 10^{29} \) free electrons \( / m^{3} . \) If this wire is
now placed in a field of induction \( 0.15 T \) perpendicular to wire. The force on each electron is :
A . \( 20 \times 10^{-25} \mathrm{N} \)
В. \( 37.5 \times 10^{-25} N \)
\( \begin{array}{ll}\text { С } & 10 \times 10^{-25} N\end{array} \)
D. \( 41.7 \times 10^{-25} N \)
Subject: Maths
The coefficient of \( 1 / x \) in the expansion of
\( (1+x)^{n}(1+1 / x)^{n} \) is
A. \( \frac{n !}{(n-1) !(n+1) !} \)
B. \( \frac{2 n !}{(n-1) !(n+1) !} \)
c. \( \frac{2 n !}{(2 n-1) !(2 n+1) !} \)
D. none of these
Subject: Chemistry
Which of the following compound may be optical active?
A \( \cdot C o(e n)_{2} C I_{2} \)
В・ \( \left[R h C I B r N H_{3} P H_{3}\right] \)
\( \mathbf{c} \cdot C u(e n)_{2} C I_{2} \)
D. All of these
Subject: Chemistry
\( \boldsymbol{C C l}_{4}+\mathbf{2}(\boldsymbol{H}) \stackrel{\boldsymbol{F} e / \text {Steam}}{\longrightarrow} \boldsymbol{A}+\boldsymbol{H C l} \)
\( \boldsymbol{C H}_{3}-\boldsymbol{C} \equiv \boldsymbol{C H}+\boldsymbol{H}_{2} \boldsymbol{O} \frac{40 \% \boldsymbol{H}_{2} \boldsymbol{S O}_{4}}{1 \% \boldsymbol{H g S O}_{4} / \boldsymbol{6 0}^{\circ} \boldsymbol{C}} \)
\( \boldsymbol{B} \)
The organic compound formed when \( \boldsymbol{A} \)
and \( B \) reacts together is
and it is used as
A. chloropicrin, insecticide
B. chloretone, wargas
c. chloretone, hypnotic
D. chloropicrin, hypnotic
Subject: Chemistry
Relative decrease in vapor pressure is 0.4 for a solution containing 1 mole AB in 3 mol \( H_{2} O \), therefore \( A B \) is ionised at the
extent(percentage) of:
\( \mathbf{A} \cdot 60 \% \)
B. \( 50 \% \)
\( c \cdot 100 \% \)
D. \( 40 \% \)
Subject: Biology
Which of the following statements are
true?
(a) Proteins are the heteropolymer of \( \alpha \)
amino acid.
(b) Sugar found in nucleic acid, is in the
form of \( \beta \) -form.
(c) Nucleic acids show acidic nature.
(d) 5-methyl uracil binds with first carbon atom of ribose sugar.
(e) Collagen is most abundant protein in plant world.
\( A \cdot a, b, e \)
B. \( a, b, d \)
\( c \cdot b, c, d, e \)
D. a, b, c
Subject: Physics
Trajectory of two particles projected
from origin with speed \( v_{1} \) and \( v_{2} \) and
angles \( \theta_{1} \) and \( \theta_{2} \) with positive \( x \) - axis
respectively as shown in the figure
given that \( g=-10 m / s^{2}(j) . \) Choose the
correct option related to diagram:
This question has multiple correct options
\( \mathbf{A} \cdot v_{1}-v_{2}=2 v_{1} \)
B . \( \theta_{2}-\theta_{1}=2 \theta_{1} \)
\( \mathbf{c} \cdot 3\left(v_{1}-v_{2}\right)=0 \)
D. \( 3\left(\theta_{1}-\theta_{2}\right)=-\theta_{1} \)
Subject: Physics
Which of the following is/are correct?
This question has multiple correct options
A. If centre of mass of three particles is at rest and it is known that two of them are moving along different lines, then the third particle must be moving.
B. If centre of mass remains at rest, then net work done
by the forces acting on the system must be zero.
C. If centre of mass remains at rest, then the net external force must be zero.
D. If speed of centre of mass is changing, then there must be some net work being done on the system from outside.
Subject: Chemistry
Following Reaction \( N H_{4}^{+}(a q)+C N^{-}(a q) \rightleftharpoons \)
\( \boldsymbol{H} \boldsymbol{C N}(\boldsymbol{a q})+\boldsymbol{N H}_{3}(\boldsymbol{a q}) \)
proceeds in:
A. forward direction
B. backward direction
C. in both sides equally
D. can't be predicted
Subject: Maths
Solve \( \int \frac{x e^{x}}{(x+1)^{2}} d x \)
A \( \cdot \frac{e^{x}}{x+1}+C \)
в. \( \frac{x}{(x+1)^{2}}+C \)
c. \( e^{x}(x+1)+C \)
D. \( x(x+1)^{2}+C \)
Subject: Maths
Consider the following statements:
When two straight lines intersect,
(i) adjacent angles are complementary
(ii) adjacent angles are supplementary
(iii) opposite angles are equal
(iv) opposite angles are
supplementary
\( A \cdot \) (i) and (iii)
B. (ii) and (iii)
c. (i) and (iv)
D. (ii) and (iv)
Subject: Physics
In the given figure, the radius of
curvature of a curved surface for both
the piano-convex and plano-concave
lens is \( 10 \mathrm{cm} \) and refractive index for
both is \( 1.5 . \) The location of the final
image after all the refractions through
lenses is:
\( \mathbf{A} \cdot 15 \mathrm{cm} \)
B. \( 20 \mathrm{cm} \)
\( \mathbf{c} \cdot 25 c m \)
D. \( 40 \mathrm{cm} \)
Subject: Maths
Evaluate \( 1.6+2.9+3.12+\ldots+ \)
\( \mathbf{n}(\mathbf{3 n}+\mathbf{3})= \)
A \( \cdot n(n+1)(n+2) \)
B. \( (n+1)(n+2)(n+3) \)
c. \( (n+2)(n+3)(n+4) \)
D. \( (n-1) n(n+1) \)
Subject: Chemistry
A precipitate of \( A g C l \) is formed when
equal volumes of the following are \( \operatorname{mixed}\left[\boldsymbol{K}_{s p} f o r \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l}=\mathbf{1 0}^{-\mathbf{1 0}}\right] \)
A \( \cdot 10^{-4} M A g N O_{3} \) and \( 10^{-7} M H C l \)
B. \( 10^{-5} M A g N O_{3} \) and \( 10^{-6} M H C l \)
c. \( 10^{-5} M A g N O_{3} \) and \( 10^{-4} M H C l \)
D. \( 10^{-6} M A g N O_{3} \) and \( 10^{-6} M H C l \)
Subject: Physics
An electron having mass ' \( m \) ' charge ' \( q^{\prime} \) and \( K . E . K \) enters a uniform magnetic
field - ' \( B \) ' perpendicularly. Then its frequency of rotation.
A \( \cdot \frac{q B}{\pi m} \)
в. \( \frac{q B}{2 \pi m} \)
с. \( \frac{q B E}{2 \pi m} \)
D. \( \frac{q B}{2 \pi} \)
Subject: Maths
The parabola \( y^{2}=4 x \) and \( x^{2}=4 y \)
divide the square region bounded by the \( \operatorname{lines} x=4, y=4 \) and the coordinate
axes. If \( S_{1}, S_{2} \) and \( S_{3} \) are respectively
the areas of these parts numbered from
top-to-bottom, then \( S_{1}: S_{2}: S_{3} \) is
A. 1: 1: 1
B. 2: 1: 2
c. 1: 2: 3
D. 1: 2: 1
Subject: Physics
The e.m.f of a cell is \( 2.0 \mathrm{V} \) and the
internal resistance is \( 0.1 \Omega \). It is
connected with a resistance of \( 3.9 \Omega \)
Then potential difference across the cell is :-
\( \mathbf{A} \cdot 0.20 V \)
B. \( 1.90 V \)
c. \( 1.95 V \)
D. \( 2.00 V \)
Subject: Chemistry
Assertion: \( P H_{3} \) is more basic than
\( N H_{3} \)
Reason: EN of N is more than that of P
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true and Reason is not the correct explanation of Assertion
c. The Assertion is true and Reason is false
D. Assertion is false but Reason is true
Subject: Maths
In a factory machine \( \boldsymbol{A} \) produce \( \mathbf{3 0 \%} \) of the total output, machine \( B \) produced
\( 25 \% \) and the machine \( C \) produced the remaining output. If defective items produced by machine \( A, B \) and \( C \) are \( 1 \%, 1.2 \%, 2 \% \) respectively. Three machine working together produced
10000 item in a day. An item is drawn at random from a day's output and found to be defective.
Find the probability that it was produced by machine \( \boldsymbol{B} \) ?