AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Ice at \( -20^{\circ} \mathrm{C} \) is filled upto height \( h= \)
\( 10 \mathrm{cm} \) in a uniform cylindrical vessel
Water at temperature \( \theta^{\circ} C \) is filled in
another identical vessel up to the same
height \( h=10 \mathrm{cm} . \) Now, water from
second vessel is poured into first vessel and it is found that level of upper surface
falls through \( \Delta h=0.5 \mathrm{cm} \) when
thermal equilibrium is reached. Neglecting thermal capacity of vessels, change in density of water due to change in temperature and loss of heat due to radiation, calculate initial
temperature \( \theta \) of water in \( ^{o} C \) Given, Density of water, \( \rho_{w}=1 g \mathrm{cm}^{-3} \)
Density of ice, \( \rho_{i}=0.9 g \mathrm{cm}^{-3} \)
Specific heat of water, \( s_{w}=1 \mathrm{cal} / \mathrm{g}^{\circ} \mathrm{C} \)
Specific heat of ice, \( s_{i}=0.5 \mathrm{cal} / \mathrm{g}^{\circ} \mathrm{C} \)
Specific latent heat of ice, \( L=80 \) cal \( / g \)
Subject: Maths
The population \( p(t) \) a time \( t \) of a certain mouse species satisfies the differential equation \( \frac{\boldsymbol{d} \boldsymbol{p}(\boldsymbol{t})}{\boldsymbol{d} \boldsymbol{t}}=\frac{1}{2} \boldsymbol{p}(\boldsymbol{t})-\boldsymbol{4 5 0} \)
\( \boldsymbol{p}(\boldsymbol{0})=\mathbf{8 5 0}, \) then the time at which the
population becomes zero is:
A \( .2 ~ \ln 18 \)
B. \( \ln 9 \)
c. \( \frac{1}{2} \ln 18 \)
D. \( \ln 18 \)
Subject: Physics
A rod PQ of mass 'm' and length 'I'
rotated about and axis through 'p' as
shown in figure.Find the moment of
inertia about axis of Rotation
A \( \cdot \frac{3 g}{2 L} \)
B. \( \frac{m l^{2}}{3} \)
c. \( \frac{m l^{2}}{3} \cos ^{2} \theta \)
D. \( \frac{m l^{2}}{3}+m l^{2} \)
Subject: Physics
A car moving on a straight path covers a distance of \( 1 k m \) due east in 100 s. What
is the velocity of the car?
\( \mathbf{A} \cdot 10 m s^{-1} \) due east
B . \( 10 m s^{-1} \) due west
c. \( 100 m s^{-1} \) due west
D. \( 100 m s^{-1} \) due east
Subject: Maths
The table below- shows the daily
expenditure on food of 25 households in a locality.
\( \begin{array}{llll}\text { Daily } & \text { 100- } & \text { 150- } & \text { 200- } \\ \text { nenses } & \text { 150 } & \text { 200 } & \text { 250 } \\ \text { (in Rs.) } & \text { 150 } & \text { (i) }\end{array} \) expenses 250 (in Rs.)
No. of households
12
Find the mean daily expenses on food by a suitable method
Subject: Physics
A ray of light travels from air into a perspex block of refractive index 1.5 at
an angle of incidence of \( 45^{0} \). Calculate
the angle of the refraction of the ray at air-to perspex boundary and at perpexto-air boundary
A \( \cdot 28^{0} 7^{\prime} \)
B . \( 25^{0} 87^{\prime} \)
\( \mathbf{c} \cdot 25^{0} \eta^{\prime} \)
D. \( 28^{0} 27^{\prime} \)
Subject: Maths
Let \( h(x) \) be differentiable for all \( x \) and
let \( \boldsymbol{f}(\boldsymbol{x})=\left(\boldsymbol{k} \boldsymbol{x}+\boldsymbol{e}^{\boldsymbol{x}}\right) \boldsymbol{h}(\boldsymbol{x}) \) where \( \boldsymbol{k} \) is
some constant. If \( h(0)=5, h^{\prime}(0)=-2 \)
and \( f^{\prime}(0)=18, \) then the value of \( k \) is equal to
\( A \cdot 3 \)
B. 4
c.
D.
Subject: Maths
If \( \boldsymbol{A}=\{\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}, \boldsymbol{d}\}, \) then a relation \( \boldsymbol{R}= \)
\( \{(a, b),(b, a),(a, a)\} \) on \( A \) is
A. symmetric and transitive only
B. reflexive and transitive only
c. symmetric only
D. transitive only
Subject: Chemistry
Assertion
Standard hydrogen electrode is a half cell having \( 1 M H^{+} \) concentration
bubbled with hydrogen at any pressure
Reason

A hydrogen electrode will always show \( \boldsymbol{E}_{c e l l}=\mathbf{0 . 0 0} \boldsymbol{V} \)
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 simple electric motor has an
armature resistance of \( 1 \Omega \) and runs
from a d.c. source of \( 12 V . \) It draws a
current of \( 2 \mathrm{A} \) when unloaded. When a
certain load is connected to it, its speed reduces by \( 10 \% \) of its initial value. The current drawn by the loaded motor is?
\( A \cdot 3 A \)
B. 6 A
c. 2 A
D. 1A
Subject: Maths
Show that each of the given three
vectors is a unit vector:
\( \frac{1}{7}(2 \bar{i}+3 \bar{j}+6 \bar{k},) \frac{1}{7}(3 \bar{i}+6 \bar{j}+\overline{2} k) \)
\( \frac{1}{7}(6 \bar{i}+2 \bar{j}+3 \bar{k}) \)
Subject: Physics
The Bulk of Ethanol, Mercury and water are given as 0.9,25 and 2.2 respectively in units of \( 10^{8} N m^{-2} \). For a given value
of pressure, the fractional compression in volume is \( \triangle V / V . \) Which of the
following statements about \( \triangle \boldsymbol{V} / \boldsymbol{V} \) for
these three liquids is correct?
A. Mercury > Ethanol > Water
B. Ethanol> Mercury > Water
c. water> Ethanol > Mercury
D. Ethanol> Water> Mercury
Subject: Chemistry
A solution of glucose \( \left(C_{8} H_{12} O_{6}\right) \) is
isotonic with \( 5 g \) of urea
\( \left(N H_{2} C O N H_{2}\right) \) per litre of solution
The concentration of glucose is:
A. \( 48 / L \)
B. 8 g/L
c. 12 g/L
D. \( 15 \mathrm{g} / \mathrm{L} \)
Subject: Physics
toppr IN
Q Type your question
the correct answer in the blanks.
Answer
\( (i)_{6}^{12} C+_{1}^{1} H \longrightarrow_{7}^{13} N \)
\( (i i)_{13}^{27} A l+_{1}^{1} H \longrightarrow_{12}^{24} M g+_{2}^{4} H e \)
\( (i i i)_{92}^{235} U+_{0}^{1} n \longrightarrow_{56}^{140} B a+_{36}^{93} K r+ \)
\( \mathbf{3}_{\mathbf{0}}^{\mathbf{1}} \boldsymbol{n} \)
\( (i v)_{33}^{75} A s+_{1}^{2} H \longrightarrow_{25}^{56} M n+9_{1}^{1} H+ \)
\( 12_{0}^{1} n \)
\( (\boldsymbol{v})_{1}^{2} \boldsymbol{H}+_{1}^{3} \boldsymbol{H} \longrightarrow_{2}^{4} \boldsymbol{H} \boldsymbol{e}+_{0}^{1} \boldsymbol{n} \)
Answers:
A: Projectile capture
B: Spallation
C: Fusion
D: Projectile capture and particle emission
E: Fission
Select the correct answers according to
the given codes.
\( \mathbf{A} \cdot(i)-A,(i i)-D,(i i i)-E,(i v)-B,(v)-C \)
B . \( (i)-D,(i i)-C,(i i i)-A,(i v)-E,(v)-B \)
C \( .(i)-A,(i i)-B,(i i i)-C,(i v)-D,(v)-E \)
D. \( (i)-E,(i i)-D,(i i i)-C,(i v)-B,(v)-A \)
Subject: Maths
\( \mathbf{P}(-1,-1,-1) \) and \( Q(\lambda, \lambda, \lambda) \) are two
points in the space such that \( \boldsymbol{P} \boldsymbol{Q}= \) \( \sqrt{48}, \) then value(s) of \( \lambda \) can be
This question has multiple correct options
A . 3
B. - 5
\( c \cdot 4 \)
D.
Subject: Biology
Although much \( C O_{2} \) is carried in blood,
yet blood does not become acidic,
because
A. \( C O_{2} \) is absorbed by the leukocytes
B. \( C O_{2} \) combines with water to form \( H_{2} C O_{3} \) which is
neutralised by \( N a_{2} C O_{3} \)
c. \( C O_{2} \) transport and blood buffers play an important role in it
D. it is continuously diffused through the tissues and is not allowed to accumulate
Subject: Maths
The range of \( \boldsymbol{f}(\boldsymbol{x})=-\boldsymbol{x}^{3}+\boldsymbol{x}^{2}-\boldsymbol{x}+ \)
\( \cos ^{-1} x \) is:
\( \mathbf{A} \cdot[-1,3+\pi] \)
В. \( [0, \pi-1] \)
c. \( [-1,2+\pi] \)
D. \( [-1, \pi] \)
Subject: Chemistry
Which of the following statements is
not true about the complex ion
\( \left[\boldsymbol{C r} \boldsymbol{C l}\left(\boldsymbol{N} \boldsymbol{O}_{2}\right)(\boldsymbol{e n})_{2}\right]^{+} ? \)
This question has multiple correct options
A. it has two geometrical isomers cis and trans.
B. cis and trans forms are not diastereomers to each other
c. only the cis isomers displays optical activity.
D. it has three optically active isomers: d, land trans forms
Subject: Maths
If \( \frac{\mathbf{3} \boldsymbol{x}^{2}+\mathbf{1 0 x}+\mathbf{1 3}}{(\boldsymbol{x}-\mathbf{1})^{4}}=\frac{\boldsymbol{A}}{(\boldsymbol{x}-\mathbf{1})^{2}}+ \)
\( \frac{B}{(x-1)^{3}}+\frac{C}{(x-1)^{4}} \) then descending
order of \( \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C} \)
A. \( A, B, C \)
в. \( C, B, A \)
c. \( A, C, B \)
D. \( C, A, B \)
Subject: Physics
The positions of a particle moving along a straight line are \( x_{1}=50 \mathrm{m} \) at 10.30
a.m. and \( x_{2}=55 \mathrm{m} \) at 10.35 a.m.
respectively. What is the displacement of the particle between 10.30 a.m. and
10.35 a.m.?
\( A \cdot 2 m \)
B. \( 5 \mathrm{m} \)
\( c \cdot 7 m \)
D. \( 9 \mathrm{m} \)
Subject: Maths
If \( \boldsymbol{A}=\left(\begin{array}{ccc}1 & 2 & 1 \\ -1 & 0 & 3 \\ 2 & -1 & 1\end{array}\right) \) then
characteristic equation is given by
A. \( -\lambda^{3}+2 \lambda^{2}-4 \lambda+18=0 \)
0
B . \( \lambda^{3}+2 \lambda^{2}+4 \lambda+18=0 \)
c. \( 2 \lambda^{3}-\lambda^{2}+6 \lambda-2=0 \)
D. None of these
Subject: Maths
Find the area of the trapezium.
\( \mathbf{A} \cdot 144 \sqrt{3} \mathrm{cm}^{2} \)
B. \( 154 \sqrt{3} \mathrm{cm}^{2} \)
\( \mathbf{C} \cdot 162 \sqrt{3} \mathrm{cm}^{2} \)
D. None of these
Subject: Physics
A force of \( 5 \mathrm{N}, \) making an angle \( \theta \) with
the horizontal, acting on an object displaces it by \( 0.4 \mathrm{m} \) along the horizontal direction. If the object gains kinetic energy of 1 J, the horizontal component of the force is?
A . \( 1.5 \mathrm{N} \)
в. 2.5 N
c. 3.5 N
D. 4.5 N
Subject: Maths
If the distance between a point \( \boldsymbol{P} \) and the point (1,1,1) on the line \( \frac{x-1}{3}= \) \( \frac{\boldsymbol{y}-\mathbf{1}}{\mathbf{4}}=\frac{\boldsymbol{z}-\mathbf{1}}{\mathbf{1 2}} \) is \( \mathbf{1 3}, \) then the
coordinates of \( \boldsymbol{P} \) are
A. (3,4,12)
в. \( \left(\frac{3}{13}, \frac{4}{13}, \frac{12}{13}\right) \)
c. (4,5,13)
D. (40,53,157)
Subject: Maths
Is the line through (-2,3) and (4,1) perpendicular to the line \( \mathbf{3} \boldsymbol{x}=\boldsymbol{y}+\mathbf{1} ? \)
Does the line \( 3 x=y+1 \) bisect the line
joining of (-2,3) and (4,1)\( ? \)
Subject: Chemistry
Consider the following first order competing reactions:
\( \boldsymbol{X} \stackrel{\boldsymbol{k}_{1}}{\rightarrow} \boldsymbol{A}+\boldsymbol{B} \quad \) and \( \quad \boldsymbol{Y} \quad \underline{k}_{2} \quad \boldsymbol{C}+ \)
\( D \)
If \( 50 \% \) of the reaction of \( X \) was
completed when \( 96 \% \) of the reaction of \( Y \) was completed, the ratio of their rate
constants \( \left(k_{2} / k_{1}\right) \) is:
A . 4.0
B. 6.8
c. 3.
D. 4.6
Subject: Maths
State true or false:
In quadrilateral \( A B C D, A D=B C \) and
the diagonals \( A C \) and \( B D \) intersect at
point \( \boldsymbol{O}, \) such that \( \frac{\boldsymbol{O} \boldsymbol{C}}{\boldsymbol{O} \boldsymbol{A}}=\frac{\boldsymbol{O} \boldsymbol{D}}{\boldsymbol{O B}}=\frac{1}{\mathbf{3}}, \) then the quadrilateral
\( A B C D \) is a trapezium.
A. True
B. False
Subject: Physics
A vertical straight conductor carries a current vertically upwards. A point P lies to the east of it at a small distance and
another point \( Q \) lies to the west at the same distance the magnetic field at \( \mathrm{P} \)
is :
A. greater than at \( Q \)
B. same as at \( Q \)
c. less than at \( Q \)
D. greater or less than at Q depending upon the strength of current
Subject: Physics
The amplitude and time period of simple harmonic oscillator are \( a \) and \( T \)
respectively. The time taken by it in
displacing from \( \boldsymbol{x}=\mathbf{0} \) to \( \boldsymbol{x}=\boldsymbol{a} / \mathbf{2} \) will
be
A . \( T \)
в. \( \frac{T}{2} \)
c. \( \frac{T}{4} \)
D. \( \frac{T}{12} \)
Subject: Maths
The area of the region bounded by \( y= \)
\( \boldsymbol{x}^{2}+\mathbf{2}, \boldsymbol{y}=-\boldsymbol{x}, \boldsymbol{x}=\mathbf{0} \) and \( \boldsymbol{x}=\mathbf{1} \) is
A \( \cdot \frac{17}{6} \)
в. \( \frac{17}{3} \)
c. \( \frac{10}{3} \)
D. \( \frac{8}{3} \)
Subject: Physics
A uniform vertical electric field \( \boldsymbol{E} \) is
established in the space between two large parallel plates. A small conducting sphere of mass \( \boldsymbol{m} \) is suspended in the field from a string of
length \( L \). If the sphere is given \( a+q \) charge and the lower plate is charged positively, the period of oscillation of this pendulum is :
\( ^{\mathrm{A}} \cdot 2 \pi \sqrt{\frac{L}{g}} \)
в. \( 2 \pi \sqrt{\frac{L}{g+\frac{q E}{m}}} \)
c. \( _{2 \pi} \sqrt{\frac{L}{g-\frac{q E}{m}}} \)
D. \( 2 \pi \sqrt{\frac{L}{\left(g^{2}+\left(\frac{q E}{m}\right)^{2}\right)^{1 / 2}}} \)
Subject: Chemistry
Assertion
Hydrolysis of sucrose brings about a change in sign of rotation from dextro to laevo.
Reason
Hydrolysis always changes the optical
rotation of a compound.
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
Aqueous solutions of
\( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3}, \boldsymbol{K} \boldsymbol{O} \boldsymbol{H}, \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C O O H}, \) and
\( \boldsymbol{C H}_{3} \boldsymbol{C O O N a} \) of identical
concentrations are provided. The pair(s) of solutions which form a buffer upon
mixing is/ are:
This question has multiple correct options
A. \( H N O_{3} \) and \( C H_{3} \) COOH
в. \( K O H \) and \( C H_{3} C O O N a \)
c. \( H N O_{3} \) and \( C H_{3} C O O N a \)
D. \( C H_{3} C O O H \) and \( C H_{3} C O O N a \)
Subject: Physics
A series RLC circuit is made as shown
in the figure with an \( A C \) source of \( 60 \vee \)
20 Hz. Then
This question has multiple correct options
A. the rms current through the resistor R is 4.2 A
B. the effective potential difference between P and should be \( 42 \mathrm{v} \)
c. the instantaneous current leads the source voltage by 45
D. the instantaneous current lags behind the applied voltage by \( 45^{\circ} \)
Subject: Physics
A body of mass \( 5 \mathrm{kg} \) undergoes a change in speed from 30 to \( 40 \mathrm{m} / \mathrm{s} \). Its
momentum would increase by:
A. \( 50 \mathrm{kgm} / \mathrm{s} \)
B. \( 75 \mathrm{kgm} / \mathrm{s} \)
c. \( 150 \mathrm{kgm} / \mathrm{s} \)
D. \( 350 \mathrm{kgm} / \mathrm{s} \)
Subject: Physics
In the arrangement shown in figure
above, a weight \( A \) possesses mass \( m \), a
pulley \( B \) possesses mass \( M \). Also
known are the moment of inertia \( I \) of
the pulley relative to its axis and the
radii of the pulley \( R \) and \( 2 R \) The mass
of the threads is negligible. If the acceleration of the weight \( \boldsymbol{A} \) after the
system is set free is \( \boldsymbol{w}= \)
find the value of \( b \)
Subject: Chemistry
Resistance and conductivity of a cell containing \( 0.001 \mathrm{M} \) KCl solution at 298
\( \mathrm{K} \) are \( 1500 \Omega \) and \( 1.46 \times 10^{-4} \mathrm{S.cm}^{-1} \)
respectively. What is the cell constant?
\( \mathbf{A} \cdot 0.219 \mathrm{cm}^{-1} \)
B. \( 0.319 \mathrm{cm}^{-1} \)
c. \( 0.419 c m^{-1} \)
D. None of these
Subject: Maths
\( \frac{\sin (\boldsymbol{A}-\boldsymbol{B})}{\cos \boldsymbol{A} \cos \boldsymbol{B}}+\frac{\sin (\boldsymbol{B}-\boldsymbol{C})}{\cos \boldsymbol{B} \cos \boldsymbol{C}}+ \)
\( \frac{\sin (\boldsymbol{C}-\boldsymbol{A})}{\cos \boldsymbol{C} \cos \boldsymbol{A}}=\boldsymbol{0} \)
Subject: Physics
toppr
Q Type your question
time period is proportional to \( \sqrt{\frac{\boldsymbol{m}}{\boldsymbol{k}}}, \) as can be seen easily using dimensional
analysis. However, the motion of a
particle can be periodic even when its
potential energy increases on both
sides of \( x=0 \) in a way different from
\( k x^{2} \) and its total energy is such that the
particle does not escape to infinitely.
Consider a particle of mass m moving
on the x-axis. Its potential energy is
\( \boldsymbol{V}(\boldsymbol{x})=\boldsymbol{\alpha} \boldsymbol{x}^{4}(\boldsymbol{\alpha}>\boldsymbol{0}) \) for \( |\boldsymbol{x}| \) near the
origin and becomes a constant equal to
\( \boldsymbol{V}_{0} \) for \( |\boldsymbol{x}| \geq \boldsymbol{X}_{0}(\text { see figure }) \)
If the total energy of the particle is \( \mathrm{E} \), it
will perform periodic motion only if.
A \( . E<0 \)
в. \( E>0 \)
c. \( V_{0}>E>0 \)
D. \( E>V_{0} \)
Subject: Physics
(i) In Searle's experiment, after every step of loading, one waits for sometime
\( (2 \text { or } 3 \text { min }) \) before taking reading.
(ii) In this duration, the wire becomes free from kinks.
A. Both (i) and (ii) are true and
(ii) is reason for (i)
B. Both (i) and (ii) are true but (ii) is not reason for (i)
c. only (i) is true
D. Only (ii) is true
Subject: Physics
If \( W_{1}, W_{2} \) and \( W_{3} \) represent the work
done in moving a particle from \( \boldsymbol{A} \) to \( \boldsymbol{B} \)
along three different paths 1,2 and 3
respectively (as shown) in a
gravitational field of point mass \( \boldsymbol{m} \)
then find the correct relation between
\( W_{1}, W_{2} \) and \( W_{3} \)
A \( . W_{1}=W_{2}=W_{3} \)
B. \( W_{1}>W_{2}>W_{3} \)
\( \mathbf{c} \cdot W_{1}<W_{2}<W_{3} \)
D. \( W_{2}>W_{1}>W_{3} \)
Subject: Chemistry
Assertion (A): Decrease in free energy
causes spontaneous reaction.

Reason (R): Spontaneous reactions are invariable exothermic reactions.
A. Both Assertion and Reason are true and Reason is the
correct explanation of Assertion.
B. Both Assertion and Reason are true but Reason is not
the correct explanation of Assertion.
C. Assertion is true but Reason is false.
D. Both Assertion and Reason are false.
Subject: Maths
The probabilities of solving a problem
by three students \( A, B \) and \( C \) are \( \frac{1}{2}, \frac{3}{4} \) and \( \frac{1}{4} \) respectively. The probability that the problem will be solved is
\( ^{A} \cdot \frac{3}{32} \)
в. \( \frac{3}{16} \)
c. \( \frac{29}{32} \)
D. None of the above
Subject: Physics
A cube has a side of length \( 1.2 \times 10^{-2} . \) Its volume upto correct significant figures is
A . \( 1.7 \times 10^{-6} m^{3} \)
В . \( 1.73 \times 10^{-6} m^{3} \)
\( \mathbf{c} \cdot 1.78 \times 10^{-6} m^{3} \)
D. \( 1.732 \times 10^{-6} \mathrm{m}^{3} \)
Subject: Maths
\[
\begin{array}{rlr}
\text { If } \boldsymbol{f}(\boldsymbol{x}) & =\frac{\sin 4 \boldsymbol{x}}{\mathbf{5} \boldsymbol{x}}+\boldsymbol{a} & \text { for } \boldsymbol{x}>\mathbf{0} \\
& =\boldsymbol{x}+\mathbf{4}-\boldsymbol{b} & \text { for } \boldsymbol{x}<\mathbf{0} \\
& =\mathbf{1} & \text { for } \boldsymbol{x}=\mathbf{0}
\end{array}
\]
is continuous at \( x=0 . \) Find \( a \& b \)
Subject: Physics
Assertion
The acceleration of an object at a
particular time is the slope of the velocity-time graph at that instant of time.
Reason
For uniform motion acceleration is zero.
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
In YDSE, a white light is formed fringe pattern on the screen. Calculate the path difference of the light waves from the two slits at the center of the first
bright fringe above the central maximum.
A. 0
в. \( \frac{1}{4} \lambda \)
\( c \cdot \frac{1}{2} \lambda \)
D. \( \lambda \)
E \( \cdot \frac{3}{2} \lambda \)
Subject: Chemistry
Given below are two reaction of water
with sodium and carbon dioxide, what is the nature of water in these reaction?
\( (\mathrm{i}) 2 N a+2 H_{2} O \rightarrow 2 N a O H+H_{2} \)
\( (\mathrm{ii}) 6 \mathrm{CO}_{2}+12 \mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{C}_{6} \mathrm{H}_{1} 2_{6}+ \)
\( \mathbf{6} \boldsymbol{H}_{2} \boldsymbol{O}+\mathbf{6} \boldsymbol{O}_{2} \)
A . In (ii) water acts as an oxidising agent and in (i) it acts as a reducing agent
B. In (i) water acts as an oxidising agent and in (ii) it acts as a reducing agent
c. In both (i) and
(ii) hydrogen acts as a reducing agent
D. In both (i) and (ii) hydrogen acts as an oxidizing agent
Subject: Physics
A girl of mass \( 50 \mathrm{kg} \) standing on a rail road car of mass \( 75 \mathrm{kg} \) moving with velocity \( 20 \mathrm{m} / \mathrm{s} \). Now, the girl begins to run with velocity of \( 10 \mathrm{m} / \mathrm{s} \) with respect to the car in the same direction. as that
of the car. Velocity of the car at this instant will be
A. \( 20 \mathrm{m} / \mathrm{s} \)
B. 24 m/s
\( c \cdot 16 m / s \)
D. \( 18 \mathrm{m} / \mathrm{s} \)
Subject: Physics
A particle in SHM is described by the displacement function: \( \boldsymbol{x}(\boldsymbol{t})= \) \( \boldsymbol{A} \cos (\boldsymbol{\omega} \boldsymbol{t}+\boldsymbol{\phi}) . \) If the initial \( (\boldsymbol{t}=\mathbf{0}) \)
position of the particle is \( 1 \mathrm{cm} \) and its initial velocity is \( \omega \mathrm{cm} / \mathrm{sec}, \) what is the
initial phase angle? This question has multiple correct options
A \( \cdot \frac{3 \pi}{4} \)
в. \( \frac{7 \pi}{4} \)
c. \( \frac{7 \pi}{2} \)
D. \( \frac{\pi}{4} \)
Subject: Physics
State the differential equation of linear simple harmonic motion. Hence obtain
the expression for acceleration, velocity and displacement of a particle performing linear simple harmonic motion.

A body cools from \( 80^{\circ} \mathrm{C} \) to \( 70^{\circ} \mathrm{C} \) in 5
minutes and to \( 62^{\circ} C \) in the next 5
minutes. Calculate the temperature of the surroundings.
Subject: Maths
Vector components of the vector with
initial points (2,1) and terminal point (-5,7) are
\( \mathbf{A} \cdot-6 \hat{i}+7 \widehat{j} \)
B. \( -7 \hat{i}+6 \hat{j} \)
c. \( -6 \hat{i}-7 \widehat{j} \)
D. None
Subject: Physics
w."15 ivsiv
circuit is
\( A \)
B.
\[
\left|\begin{array}{lll}
A & B & Y \\
0 & 0 & 1 \\
0 & 1 & 1 \\
1 & 0 & 1 \\
1 & 1 & 1
\end{array}\right|
\]
\( c \)
\( D \)
Subject: Physics
For the given circuit shown in figure, the
potential of the battery is varied from
\( 10 V \) to \( 16 V . \) If by zener diode
breakdown voltage is \( 6 V \), find
maximum current through zener diode.
A. \( 1.5 \mathrm{mA} \)
в. 3.5 тА
\( c .5 m A \)
D. 6.5 m
Subject: Maths
If the difference between the mean and
variance of a binomial distribution for 5 trials is \( \frac{5}{9}, \) then the distribution is
\( ^{A} \cdot\left(\frac{1}{9}+\frac{2}{9}\right)^{5} \)
\( ^{\mathrm{B}}\left(\frac{1}{4}+\frac{3}{4}\right)^{5} \)
\( ^{c}\left(\frac{2}{3}+\frac{1}{3}\right)^{5} \)
\( ^{\mathrm{D}}\left(\frac{3}{4}+\frac{1}{4}\right)^{5} \)
Subject: Maths
Let \( A \) and \( B \) be two sets such that
\( \boldsymbol{n}(\boldsymbol{A})=\mathbf{5} \) and \( \boldsymbol{n}(\boldsymbol{B})=2 . \) If \( \boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}, \boldsymbol{d}, \boldsymbol{e} \)
are distinct and
\( (a, 2),(b, 3),(c, 2),(d, 3),(e, 2) \) are in
\( A \times B, \) find \( A \) and \( B \)
Subject: Chemistry
For \( \boldsymbol{C r}_{2} \boldsymbol{O}_{\mathbf{7}}^{-2}+\mathbf{1 4} \boldsymbol{H}^{+}+\boldsymbol{6} \boldsymbol{e}^{-} \rightarrow \)
\( \mathbf{2} \boldsymbol{C r}^{+\mathbf{3}}+\mathbf{7 H}_{\mathbf{2}} \boldsymbol{O} ; \quad \boldsymbol{E}^{\boldsymbol{o}}=\mathbf{1 . 3 3} \boldsymbol{V} \)
At \( \left[\boldsymbol{C r}_{2} \boldsymbol{O}_{7}^{-2}\right]=\mathbf{4 . 5} \) millimole, \( \left[\boldsymbol{C r}^{+3}\right]= \)
15 millimole, \( \boldsymbol{E} \) is 1.067 V. The pH of the
solution is nearly equal to :
A . 3
B. 4
\( c \cdot 2 \)
D. 5
Subject: Physics
A particle is executing \( S . H . M \) with amplitude \( A \) and has maximum
velocity \( v_{0} . \) Its speed at displacement \( \frac{3 A}{4} \) will be
A \( \cdot \frac{\sqrt{7}}{4} v_{0} \)
в. \( \frac{v_{0}}{\sqrt{2}} \)
c. \( \frac{\sqrt{3}}{2} v_{o} \)
D. \( v_{0} \)
Subject: Maths
If \( A \) and \( B \) are independent events such
that \( \mathbf{0}<\boldsymbol{P}(\boldsymbol{A})<\mathbf{1}, \mathbf{0}<\boldsymbol{P}(\boldsymbol{B})<\mathbf{1} \) then
This question has multiple correct options
A . \( A, B \) are mutually exclusive
B. \( A \) and \( \bar{B} \) are independent
c. \( \bar{A}, \bar{B} \) are independent
D. \( P(A / B)+P(\bar{A} / B)=1 \)
Subject: Maths
Find \( |\vec{a}| \) and \( |\vec{b}|, \) if \( (\vec{a}-\vec{b}) \cdot(\vec{a}+\vec{b})= \)
\( \mathbf{2 7} \) and \( |\overrightarrow{\boldsymbol{a}}|=\mathbf{2}|\overrightarrow{\boldsymbol{b}}| \)