AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Indicate in each reaction which one is
oxidised or reduced if any:
\( \mathbf{2} N \boldsymbol{a}_{2} \boldsymbol{S}+\mathbf{4} \boldsymbol{H} \boldsymbol{C l}+\boldsymbol{S} \boldsymbol{O}_{3} \rightarrow \mathbf{4} \boldsymbol{N} \boldsymbol{a} \boldsymbol{C l}+ \)
\( 3 S+2 H_{2} O \)
In the above reaction, which one of the following is oxidised?
A \( \cdot N a_{2} S \)
в. \( H C l \)
c. \( N a C l \)
D. None of these
Subject: Physics
A tank is filled with two immiscible
liquids of densities \( 2 \rho \) and \( \rho \) each of height \( h \). Two holes are made to the side wall at \( \frac{h}{2} \) and \( \frac{3 h}{2} \) from upper surface of the liquid, then the ratio of velocity of efflux of the liquids through the holes
A \( \frac{\sqrt{2}}{3} \)
в. \( \frac{\sqrt{3}}{1} \)
c. \( \frac{3}{\sqrt{2}} \)
D. \( \frac{1}{\sqrt{2}} \)
Subject: Maths
If \( (4)^{x+y}=1 \) and \( (4)^{x-y}=4 \) then the
values of \( x \) and \( y \) will be respectively
A \( \cdot \frac{1}{2} \) and \( -\frac{1}{2} \)
B \( \cdot \frac{1}{2} \) and \( \frac{1}{2} \)
c. \( -\frac{1}{2} \) and \( -\frac{1}{2} \)
D. \( -\frac{1}{2} \) and \( \frac{1}{2} \)
Subject: Physics
Two particle \( P \) and \( Q \) are executing
simple harmonic motion with equal amplitude and frequency. At a distance of half the amplitude one of them is moving away from the mean position while the other is observed at a
distance half the amplitude to be
moving towards mean position as
shown in figure. The phase difference between them is:
\( A \cdot \frac{\pi}{2} \)
в. \( \frac{\pi}{3} \)
c. \( \frac{4 \pi}{3} \)
D. \( \frac{\pi}{6} \)
Subject: Physics
In the Boolean algebra : \( \overline{\boldsymbol{A}} . \overline{\boldsymbol{B}}=\ldots \)
\( \mathbf{A} \cdot \overline{A+B} \)
в. \( A . B \)
c. \( \overline{\bar{A}+\bar{B}} \)
D. \( A+B \)
Subject: Physics
An artificial satellite moving in circular orbit around the earth has a total
kinetic + potential ) energy \( \boldsymbol{E}_{0} \). Its
potential energy and kinetic energy respectively are
A \( \cdot 2 E_{0} \) and \( -2 E_{0} \)
B . \( 2 E_{0} \) and \( 3 E_{0} \)
\( \mathbf{c} \cdot 2 E_{0} \) and \( -E_{0} \)
D. \( -2 E_{0} \) and \( -E_{0} \)
Subject: Chemistry
One mole of hydrogen, assumed to be ideal, is adiabatically expanded from
its initial state \( \left(P_{1}, V_{1}, T_{1}\right) \) to the final
state \( \left(P_{2}, V_{2}, T_{2}\right) . \) The decreases in the internal energy of the gas during this process will be given by
A. \( C_{v}\left(T_{1}-T_{2}\right) \)
в. \( C_{p}\left(T_{1}-T_{2}\right) \)
c. \( \frac{C_{P}+C_{V}}{2}\left(T_{1}-T_{2}\right) \)
D. \( \left(C_{p}-C_{v}\right)\left(T_{1}-T_{2}\right) \)
Subject: Physics
The temperature coefficient resistivity of a material is \( 0.0004 / K . \) When the
temperature of the material is
increased by \( 50^{\circ} C, \) its resistivity increases by \( 2 \times 10^{-8} \) ohm - meter
The initial resistivity of the material of the resistance
A . \( 50 \times 10^{-8} \)
B. \( 90 \times 10^{-8} \)
c. \( 100 \times 10^{-8} \)
D. \( 200 \times 10^{-8} \)
Subject: Chemistry
In the process of electroplating, \( \boldsymbol{m} \boldsymbol{g} \) of silver is deposited when 4 ampere of
current flows for 2 minutes. The amount
(in \( g \) ) of silver deposited by 6 ampere of current flowing for 40 seconds will be:
A. \( 4 m \)
в. \( \frac{m}{2} \)
c. \( \frac{4 m}{3} \)
D. \( 3 m \)
Subject: Physics
In a hydraulic lift, used at a service station, the radius of the large and small piston is in the ratio of 20:
1. What weight placed on the small piston will be sufficient to lift a car of mass 1500 kg?
A. \( 3.75 \mathrm{kg} \)
B. 37.5 kg
c. \( 7.5 \mathrm{kg} \)
D. 75 kg
Subject: Maths
The value of \( \sum_{r=1}^{n} \frac{n P_{r}}{r !} \)
\( \mathbf{A} \cdot 2^{n} \)
B . \( 2^{n}-1 \)
\( c \cdot 2^{n-1} \)
D. \( 2^{n+1} \)
Subject: Chemistry
Select correct IUPAC naming of given
compound:
A. 2,3,4,5,6 -pentahydroxyhexanoicacid
B. 2,3,4,5,6 -pentahydroxyhexanol
C. 2,3,4,5,6 -pentahydroxyhexanal
D. 2,3,4,5,7 -pentahydroxyhexanal
Subject: Physics
According to Bernoulli's equation the
expression which remains constant is:
\( ^{\mathbf{A}} \cdot p+\frac{\rho v^{2}}{2} \)
\( ^{\mathbf{B}} P+\frac{\rho v^{2}}{2}-\rho g h \)
\( \mathbf{c} \cdot P+\rho g h \)
\( P+\rho g h+\frac{\rho v^{2}}{2} \)
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{c}{[\boldsymbol{x}] \forall \boldsymbol{x} \geq \mathbf{0}} \\ \mathbf{1}+[\boldsymbol{x}] \forall \boldsymbol{x}<\mathbf{0}\end{array}\right. \)
A. \( f(x) \) is a periodic
B. \( f(x) \) is a many one
c. \( f(x) \) is a one-one
D. None of these
Subject: Physics
The graph represents the motion of a solider during a training exercise. What is the solider's average velocity during
time interval from 10 to 20 seconds.
A. \( 2.0 \mathrm{m} / \mathrm{s} \)
B. \( 2.0 \mathrm{cm} / \mathrm{s} \)
\( c \cdot 0 m / s \)
D. \( 10 \mathrm{cm} / \mathrm{s} \)
E. \( 10 \mathrm{m} / \mathrm{s} \)
Subject: Physics
A cube of side 'a' has a charge \( q \) placed
at each of its eight corneres. The potential at the centre of the cube due
to all the charges is :
A \( \cdot \frac{16 q}{4 \pi \varepsilon_{0} a \sqrt{3}} \)
в. \( \frac{16 q}{4 \pi \varepsilon_{0} a} \)
c. \( \frac{q}{4 \pi \varepsilon_{0} a} \)
D. \( \frac{q}{4 \pi \varepsilon_{0} a \sqrt{3}} \)
Subject: Physics
Let the instantaneous velocity of a rocket just after launching, be given by
the expression \( \boldsymbol{v}=2 \boldsymbol{t}+\boldsymbol{3} \boldsymbol{t}^{2} \) (where \( \boldsymbol{v} \) is
in \( m s^{-1} \) and \( t \) is in seconds). Find out
the distance travelled by the rocket
from \( t=2 s \) to \( t=3 s \)
Subject: Maths
Angles \( Q \) and \( R \) of a \( \Delta P Q R \) are \( 25^{\circ} \) and
\( 65^{\circ} . \) Write which of the following is true:
1. \( \boldsymbol{P Q}^{2}+\boldsymbol{Q} \boldsymbol{R}^{2}=\boldsymbol{R} \boldsymbol{P}^{2} \)
2. \( \boldsymbol{P Q}^{\mathbf{2}}+\boldsymbol{R} \boldsymbol{P}^{2}=\boldsymbol{Q} \boldsymbol{R}^{2} \)
3. \( \boldsymbol{R} \boldsymbol{P}^{2}+\boldsymbol{Q} \boldsymbol{R}^{2}=\boldsymbol{P} \boldsymbol{Q}^{2} \)
Subject: Chemistry
Which of the following pair consists of only network solid?
A. \( \operatorname{si} 0_{2}, \mathrm{CO}_{2} \)
B . Graphite, \( S O_{2} \)
\( \mathrm{c} \cdot P_{4} O_{10}, P_{4} \mathrm{O}_{6} \)
D. Diamond, \( S i O_{2} \)
Subject: Maths
The solution of \( e^{y}\left(1+x^{2}\right) \frac{d y}{d x}=2 x(1+ \)
\( \left.e^{y}\right) \) is:
A \( \cdot \frac{1+e^{y}}{1+x^{2}}=c \)
B \( \cdot e^{y}\left(1+x^{2}\right)=c \)
C \( \cdot\left(1+e^{y}\right)+\left(1+x^{2}\right)=c \)
D. \( \left(e^{y}+1\right) x^{2}=c \)
Subject: Maths
\( I=\int e^{x} \frac{(2+\sin 2 x)}{(1+\cos 2 x)} d x \)
A \( \cdot e^{x} \sin x \)
B. \( e^{x} \cos x \)
\( \mathbf{c} \cdot e^{x} \tan x \)
D. \( e^{x} \cos 2 x \)
Subject: Physics
A tuning fork of frequency \( 480 \mathrm{Hz} \) produces 10 beats/s when sounded with
a vibrating sonometer string. What must have been the frequency of the string if a slight increase in tension produces fewer beats per second than
before?
A. 460 Н
в. 480 н \( z \)
c. 490 н \( z \)
D. 470 нz
Subject: Chemistry
The vapour density of \( N_{2} O_{4} \) and \( N O_{2} \)
mixture at a certain temperature is 30
Calculate the percentage dissociation
of \( N_{2} O_{4} \) at this temperature
\( N_{2} O_{4}(g) \rightleftharpoons 2 N O_{2}(g) \)
A . \( 53.33 \% \)
B. \( 58.56 \% \)
c. \( 62.43 \% \)
D. \( 67.67 \% \)
Subject: Chemistry
The correct statement(s) about surface
properties is (are):
This question has multiple correct options
A. cloud is an emulsion type of colloid in which liquid is dispersed phase and gas is dispersion medium
B. adsorption is accompanied by decrease in enthalpy and decrease in entropy of the system
C. the critical temperatures of ethane and nitrogen are \( 563 K \) and \( 126 K, \) respectively. The adsorption of ethane will be more than that of nitrogen on same amount of activated charcoal at a given temperature
D. brownian motion of colloidal particles does not depend on the size of the particles but depends on viscosity of the solution
Subject: Maths
The middle term in the expansion of
\( \left(\frac{10}{x}+\frac{x}{10}\right)^{10} \)
A . \( ^{10} C_{5} \)
в. \( ^{10} C_{6} \)
c. \( _{10} \mathrm{C}_{5} \frac{1}{x^{10}} \)
D. \( ^{10} C_{5} x^{10} \)
E . \( ^{10} C_{5} 10^{10} \)
Subject: Biology
Assertion
Saline water is not given to patients with hypertension.
Reason
Saline water can cause vomiting and may drop blood pressure suddenly causing cardiac arrest.
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
An aeroplane is rising vertically with acceleration a. Two stones are dropped
from it at an interval of time t. The
distance between them at time \( t^{\prime} \) after
the second stone is dropped will be
A \( \cdot \frac{1}{2} t\left[g t+2 g t^{\prime}+2 a t^{\prime}\right] \)
B \( \cdot \frac{1}{2}(g+a)\left(t+2 t^{\prime}\right) t \)
c. \( \frac{1}{2}(g+a)\left(t-t^{\prime}\right)^{2} \)
D \( \cdot \frac{1}{2}(g+a)\left(t+t^{\prime}\right)^{2} \)
Subject: Chemistry
Which of the following is true in respect of adsorption?
A. \( \Delta G<0 ; \Delta S>0 ; \Delta H<0 \)
B. \( \Delta G<0 ; \Delta S<0 ; \Delta H<0 \)
\( \mathrm{c} \cdot \Delta G>0 ; \Delta S<0 ; \Delta H<0 \)
D. \( \Delta G>0 ; \Delta S>0 ; \Delta H>0 \)
Subject: Biology
A bacterium has a generation time of
50 minutes. A culture containing \( 10^{8} \) cells \( m L \) is incubated for 300 minutes.
What will be the number of cells after
300 minutes?
A \( \cdot 64 \times 10^{3} \) cells
B . \( 64 \times 10^{8} \) cells
c. \( 64 \times 10^{9} \) cells
D. \( 64.4 \times 10^{9} \) cells
Subject: Physics
The fusion of light elements take place at about the temperatures of about
\( \mathbf{A} \cdot 30^{\circ} C \)
B. \( 100^{\circ} \mathrm{C} \)
c. \( 10,000^{\circ} \mathrm{C} \)
D \( .2 \times 10^{0} \mathrm{C} \)
Subject: Physics
The ratio of the radii of the planets \( P_{1} \)
and \( P_{2} \) is \( k_{1} . \) The corresponding ratio of the acceleration due to the gravity on
them is \( k_{2} \). The ratio of the escape velocities from them will be
A \( \cdot k_{1} k_{2} \)
в. \( \sqrt{k_{1} k_{2}} \)
\( \mathbf{c} \cdot \sqrt{\left(k_{1} / k_{2}\right)} \)
D. \( \sqrt{\left(k_{2} / k_{1}\right)} \)
Subject: Physics
An infinitely long straight conductor is uniformly charged with charge density \( \lambda \) per meter. The work done to bring a
charge \( q_{0} \) at perpendicular distance \( b \) to
\( a \) perpendicular distance \( a(a<b) \) from
the conductor is :
A. zero
в. \( \frac{q_{0} \lambda}{2 \pi_{0}} \)
c. \( \frac{q_{0} \lambda}{2 \pi \varepsilon_{0}} \log _{0}\left(\frac{b}{a}\right) \)
D. \( \frac{q_{0} \lambda}{2 \pi \varepsilon_{0}} \log _{0}\left(\frac{a}{b}\right) \)
Subject: Physics
At \( t=0, \) when the magnetic field is
switched on, the conducting rod is
moved to the left at a constant speed of
\( 5 \mathrm{cm} s^{-1} \) by some external means. The
rod moves perpendicular to the rail. At
\( t=2 s, \) induced emf has magnitude
A . \( 0.12 V \)
B. \( 0.08 V \)
c. \( 0.04 V \)
D. \( 0.02 V \)
Subject: Chemistry
A dilute solution of KCl was placed
between two Pt electrodes \( 10.0 \mathrm{cm} \)
a part, cross which a potential
difference of 6.0 volt was applied. \( \boldsymbol{K}^{+} \)
ions move \( x \mathrm{cm} \) in 2 hour at \( 25^{\circ} \mathrm{C} \), then
\( x \) is \( _{-}-------- \) (nearest integer)
lonic conductivity of \( \boldsymbol{K}^{+} \) at infinite dilution is \( 73.52 S c m^{2} m o l^{-1} \) at \( 25^{\circ} C \)
Subject: Physics
A plano-convex lens fits exactly into a plano-concave lens. Their plane surface are parallel to each other. If lenses are
made of different materials of refractive
indices \( \mu_{1} \) and \( \mu_{2} \) and \( R \) is the radius
of curvature of the curved surface of the
lenses, then the focal length of the combination is
A.
\[
\frac{R}{2\left(\mu_{1}+\mu_{2}\right)}
\]
B.
\[
\frac{R}{2\left(\mu_{1}-\mu_{2}\right)}
\]
c. \( \frac{R}{\left(\mu_{1}-\mu_{2}\right)} \)
D. \( \frac{R}{\left(\mu_{2}-\mu_{1}\right)} \)
Subject: Physics
An electron and a proton each travel
with equal speeds around circular
orbits in the same uniform magnetic field as indicated (not to scale) in fig.
The field is into the page on the
diagram. The electron travels .... around
the \( \ldots . \) circle and the proton travels... around the \( \ldots . \) circle
A. clockwise, smaller, counterclockwise, larger
B. counterclockwise, larger, counterclockwise, smaller
c. clockwise, larger, counterclockwise, smaller
D. counterclockwise, larger, clockwise, smaller
Subject: Maths
Find \( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}, \) where \( \boldsymbol{y}=\log \left(\frac{\boldsymbol{x}^{2}}{\boldsymbol{e}^{2}}\right) \)
Subject: Chemistry
Which of the following relations is/are correct for lingmuir adsorption theorem?
(i) \( \frac{x}{m}= \) constant (at high pressure)
(ii) \( \frac{x}{m}= \) constant \( \times P^{1 / n} \) (at intermediate pressure)
(iii) \( \frac{x}{m}= \) constant \( \times P^{n} \) (at low pressure)
A. All the relations are correct
B. All the relations are wrong
c. (i) and (ii) are correct
D. (iii) is correct
Subject: Chemistry
Which of the following represents the poisonous gas which caused the tragedy in Bhopal in \( 1984 ? \)
A. \( C H_{3} C=N=S \)
в. \( C H_{3}-N=C=O \)
c. \( C H_{3}-N=C=S \)
D. \( C H_{3}-O-N=C \)
Subject: Physics
Assertion
The centre of mass of a body may lie where there is no mass
Reason
Centre of mass of a body is a point, where the whole mass of the body is
supposed to be concentrated
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
Subject: Maths
Q Type
elevation of the top \( P \) of the tower \( O P \) at
a point \( A \) on the ground is \( \alpha, \) he then
walks a distance \( A B \) towards the foot \( O \)
of the tower and finds the angle of
elevation as \( \beta, \) he again walks a
distance \( B C \) in the same direction and
observes the angle of elevation now is \( \gamma \)
He notices that \( \boldsymbol{a}+\boldsymbol{\beta}+\boldsymbol{\gamma}= \)
\( 180^{\circ} ; \alpha, \beta, \gamma \) are in A.P. and the distance
of \( C \) from the foot of the tower is half the
distance of \( B \) from the foot \( O \) of the
tower. If the height of tower is \( h \), the distance of \( A \) from the foot \( O \) is \( \frac{5 h}{3 \sqrt{3}} \)
Reason

If the angles of elevation of the top of a
tower at three points on the ground are in A.P. then the distance of the points from the foot of the tower are also in A.P.
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
Subject: Chemistry
Balance the following equation by ion electron method:
\( \boldsymbol{H} \boldsymbol{g} \boldsymbol{S}+\boldsymbol{C l}^{-}+\boldsymbol{H}^{+}+\boldsymbol{N} \boldsymbol{O}_{3}^{-} \rightarrow \)
\( \boldsymbol{H} \boldsymbol{g} \boldsymbol{C l}_{4}^{2-}+\boldsymbol{S}+\boldsymbol{N} \boldsymbol{O}+\boldsymbol{H}_{2} \boldsymbol{O} \)
Subject: Physics
A convex lens of focal length \( \boldsymbol{f} \) is cut
into two halves as shown. Light rays
parallel to the principal axis
are incident on one half of the lens (say
\( \boldsymbol{L}_{1} \) ). This will form an image at :
\( A \cdot f \)
B. \( \frac{f}{2} \)
c. \( 2 f \)
D. \( \frac{f}{4} \)
Subject: Physics
A counter consists of a cylindrical cathode of radius \( 1 c m \) and an anode
wire of radius \( 0.01 c m \) which is placed along the axis of the cathode. A voltage of \( 2.3 k V \) is applied between the
cathode and anode. The electric field on
the anode surface must be:
A \( \cdot 2.3 \times 10^{5} V m^{-1} \)
B. \( 5 \times 10^{6} V m^{-1} \)
\( \mathbf{c} \cdot 4.6 \times 10^{5} \mathrm{Vm}^{-1} \)
D. \( 2.5 \times 10^{6} \mathrm{Vm}^{-1} \)
Subject: Maths
A three-digit code for certain locks uses the digits 0,1,2,3,4,5,6,7,8,9
according to the following constraints. The first digit cannot be 0 or 1 the second digit must be 0 or \( 1, \) and the second and third digits cannot both be
0 in the same code. How many different codes are possible?
A. 144
в. 152
c. 160
D. 168
E. 176
Subject: Maths
If \( A \) is a real skew-symmetric matrix
such that \( A^{2}+I=O, \) then
\( \mathbf{A} \cdot A \) is a square matrix of even order with \( |A|=\pm 1 \)
B. \( A \) is a square matrix of odd order with \( |A|=\pm 1 \)
C \( \cdot A \) can be a square matrix of any order with \( |A|=\pm 1 \)
D. \( A \) is a skew-symmetric matrix of even order with
\( |A|=1 \)
Subject: Physics
Three particles \( A, B \) and \( C \) are situated at the vertices of an equilateral triangle ABC of side d at time \( t=0 . \) Each of the
particles moves with constant speed v. A always has its velocity along \( \mathrm{AB}, \mathrm{B} \) along BC and \( C \) along CA. At what time will the particles meet each other?
A \( \cdot \frac{2 d}{3 v} \)
в. \( \frac{3 d}{2 v} \)
c. \( \frac{4 d}{3 v} \)
D. \( \frac{3 d}{4 v} \)
Subject: Maths
In the figure given, if \( D E \| B C \) and
\( \boldsymbol{A B}=\mathbf{5} \boldsymbol{x}-\mathbf{4}, \boldsymbol{B} \boldsymbol{D}=\mathbf{7} \boldsymbol{x}-\mathbf{5}, \boldsymbol{C} \boldsymbol{E}= \)
\( 5 x-3 \) and \( A D=3 x-2, \) find the value
of \( x \)
4
B.
c. \( \frac{7}{10} \)
" \( \frac{9}{10} \)
Subject: Chemistry
Based on VBT, \( \left[\boldsymbol{F} \boldsymbol{e} \boldsymbol{C l}_{\mathbf{6}}\right]^{3-} \) has \( \boldsymbol{C l}^{-} \) as
weak ligands. Fe is \( s p^{3} d^{2} \) hybridized
(outer orbital complex) having five
unpaired electrons. \( \left[\boldsymbol{F e}(\boldsymbol{C N})_{\boldsymbol{6}}\right]^{3-} \) has
\( C N^{-} \) as strong ligand. Fe is \( d^{2} s p^{3} \) hybridized (inner orbital complex) having only one unpaired electron.
Hence, \( \left[\boldsymbol{F} e C l_{6}\right]^{3-} \) is more paramagnetic
\( \operatorname{than}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{8}}\right]^{\boldsymbol{3}-} \)
If true enter 1 , else enter 0 .
Subject: Physics
1 a.m. \( u \) is equivalent to
\( \mathbf{A} \cdot 931 \mathrm{MeV} \)
В. \( 139 \mathrm{MeV} \)
\( \mathbf{c} .93 \mathrm{MeV} \)
D. \( 39 \mathrm{MeV} \)
Subject: Maths
Examine the following functions for continuity.
(i) \( f(x)=x-5 \)
(ii) \( f(x)=\frac{1}{x-5} \)
\( \boldsymbol{x} \neq \mathbf{5} \)
(iii) \( f(x)=\frac{x^{2}-25}{x+5}, x \neq-5 \)
\( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}-\mathbf{5}| \)
Subject: Physics
When a mass \( m \) is connected
individually to two springs \( S_{1} \) and \( S_{2} \),
the oscillation frequencies are \( \boldsymbol{v}_{1} \) and \( \boldsymbol{v}_{2} \)
If the same mass is attached to the two
springs as shown in figure, the
oscillation frequency would be:
A \( \cdot v_{1}+v_{2} \)
B. \( \sqrt{v_{1}^{2}+v_{2}^{2}} \)
\( \mathbf{c} \cdot\left[\frac{1}{v_{1}}+\frac{1}{v_{2}}\right]^{-1} \)
D. \( \sqrt{v_{1}^{2}-v_{2}^{2}} \)
Subject: Maths
(i) Solve the equation \( \left|\begin{array}{ccc}\boldsymbol{x}-\mathbf{1} & \boldsymbol{2} & \boldsymbol{3} \\ \mathbf{0} & \boldsymbol{x}-\boldsymbol{2} & \boldsymbol{4} \\ \boldsymbol{0} & \boldsymbol{0} & \boldsymbol{x}-\boldsymbol{3}\end{array}\right| \)
(ii) Show that \( \left|\begin{array}{ccc}\mathbf{1} & \boldsymbol{a} & \boldsymbol{b} \boldsymbol{c} \\ \mathbf{1} & \boldsymbol{b} & \boldsymbol{c a} \\ \mathbf{1} & \boldsymbol{c} & \boldsymbol{a b}\end{array}\right|=\left|\begin{array}{ccc}\mathbf{1} & \boldsymbol{a} & \boldsymbol{a}^{2} \\ \mathbf{1} & \boldsymbol{b} & \boldsymbol{b}^{2} \\ \mathbf{1} & \boldsymbol{c} & \boldsymbol{c}^{2}\end{array}\right| \)
Subject: Maths
If \( \frac{\boldsymbol{a}-\boldsymbol{x}}{\boldsymbol{p} \boldsymbol{x}}=\frac{\boldsymbol{a}-\boldsymbol{y}}{\boldsymbol{q} \boldsymbol{y}}=\frac{\boldsymbol{a}-\boldsymbol{z}}{\boldsymbol{r} \boldsymbol{z}} \) and \( \boldsymbol{p}, \boldsymbol{q}, \boldsymbol{r} \)
be in A.P. then \( x, y, z \) are in?
A. A.P
в. G.P.
c. н.P
D. A.G.P.
Subject: Physics
Dimensions of \( \frac{1}{\mu_{o} \epsilon_{o}}, \) where symbols
have their usual meaning, are
A \( \cdot\left[L^{-1} T\right] \)
B . \( \left[L^{-2} T^{2}\right]^{2} \)
c. \( \left[L^{2} T^{-2}\right] \)
D・ \( \left[L T^{-1}\right] \)
Subject: Chemistry
An aqueous solution containing \( \boldsymbol{H} \boldsymbol{g}_{2}^{2+}, \boldsymbol{H} \boldsymbol{g}^{2+}, \boldsymbol{P b}^{2+}, \boldsymbol{F} \boldsymbol{e}^{2+} \) is treated with
dil HCI. The cations that may be
precipitate are This question has multiple correct options
\( \mathbf{A} \cdot H g_{2}^{2+} \)
B. \( H g^{2+} \)
\( \mathrm{c} \cdot P b^{2} \)
D. \( F e^{2} \)
Subject: Physics
The dielectric to be used in a parallelplate capacitor has a dielectric constant of 3.60 and a dielectric
strength of \( 1.60 \times 10^{7} V / \) m. The
capacilnr is to have a capacitance of \( 1.25 \times 10^{-9} F \) and must be able to \( u \)
withstand a maximum potential difference of 5500 V. The minimum area
the plates of the capacitor may have is
equal to \( 135 \times 10^{-x} m^{2} . \) The value of \( x \)
is:
Subject: Maths
Identify the matrix given below:
\( \left[\begin{array}{cccc}1 & 0 & 0 & 0 \\ 0 & 4 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -3\end{array}\right] \)
A. diagonal matrix
B. zero matrix
c. scalar matrix
D. unit matrix
Subject: Physics
\( \ln L_{-} C \) oscillation, maximum charge on
capacitor is \( Q_{0} . \) The current in the
circuit, when \( 50 \% \) energy is electrical
and \( 50 \% \) is magnetic is
A \( \cdot \frac{Q_{0}}{\sqrt{L C}} \)
B. \( \frac{Q_{0}^{2}}{\sqrt{L C}} \)
с. \( \frac{Q_{0}}{2 \sqrt{L C}} \)
D. \( \frac{Q_{0}}{\sqrt{2 L C}} \)
Subject: Physics
Take the potential of the point \( B \) in the
figure, to be zero.
(a) Find the potentials
at the points \( \mathrm{C} \) and \( \mathrm{D} \). (b) If a capacitor is
connected between \( \mathrm{C} \) and \( \mathrm{D} \), What charge
will appear on the capacitor?
Subject: Chemistry
The cyclotrimetaphosphoric acid is:
\( \mathbf{A} \cdot\left(H P O_{3}\right)_{3} \) and contains total 9 bonds
B. \( H_{3} P_{3} O_{6} \) and contains total 12 bonds
C \( \cdot\left(H P O_{3}\right)_{3} \) and contains total 15 bonds.
D. \( H_{3} P_{3} O_{9} \) and contains \( 18 \sigma- \) bonds
Subject: Chemistry
In which of the following pairs is there the greatest difference in the oxidation numbers of the underlined elements?
A. \( \underline{N} O_{2} \) and \( N_{2} O_{4} \)
B. \( P_{2} O_{5} \) and \( P_{4} O_{00} \)
c. \( \underline{N}_{2} \mathrm{O} \) and \( \underline{\mathrm{N}} \mathrm{O} \)
\( \mathrm{D} \cdot \underline{S} \mathrm{O}_{2} \) and \( \underline{S} \mathrm{O}_{3} \)
Subject: Maths
Suppose \( \boldsymbol{U}= \)
\( \{3,4,5,6,7,8,9,10,11,12,13\}, A= \)
\( \{3,4,5,6,9\}, B=\{3,7,9,5\} \) and \( C= \)
\( \{6,8,10,12,7\} . \) Write down the
following set and draw Venn diagram for
\( \boldsymbol{B}^{\prime} \)
Subject: Chemistry
Assertion
STATEMENT-1: 2,2-dimethylpropanal
undergoes cannizzaro reaction with
concentrated \( N \) a \( O H \)
Reason
STATEMENT-2: Cannizzaro reaction is a
disproportionation reaction.
A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-
1
B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1
C. STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True