AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Choose the wrong statement of the following:
A. The peak voltage across the inductor can be less than the peak voltage of the source in an LCR circuit
B. In a circuit containing and a capacitor and an ac source the current is zero at the instant source voltage is maximum
C. When an AC source is connected to a capacitor, then the rms current in the circuit gets increased if a dielectric slab is inserted into the capacitor
D. In a pure inductive circuit emf will be in phase with the current
Subject: Physics
A \( 4 \mathrm{cm} \) tall object is placed on the
principal axis of a convex lens. The distance of the object from the optical
centre of the lens is \( 12 \mathrm{cm} \) and its sharp image is formed at a distance of \( 24 \mathrm{cm} \) from it on a screen on the other side of
the lens. If the object is now moved a
little away from the lens, in which way (towards the lens or away from the lens) will he have to move the screen to get a
sharp image of the object on it again? How will the magnification of the image be affected?
Subject: Physics
A small hollow sphere, which has a small hole in it, is immersed in water to
a depth of \( 0.5 \mathrm{m} \) before any drop
penetrates into it. If surface tension for water is \( 0.073 \mathrm{N} / \mathrm{m} \), the radius of the
hole is :
[Assume pressure inside the sphere to be atmospheric pressure]
\( A .0 .06 \mathrm{mm} \)
B. \( 0.03 \mathrm{mm} \)
c. \( 0.09 \mathrm{mm} \)
D. 0.15 mm.
Subject: Maths
The population of a town at percent is \( 80000 . \) If the annual rate of increase is
\( 4 \% \), find the population after 4 years (use the formula: \( \boldsymbol{A}=\boldsymbol{p}\left(1+\frac{\boldsymbol{r}}{\mathbf{1 0 0}}\right)^{\boldsymbol{n}} \)
where \( p \) is the original population)
Subject: Physics
Assertion
A piece of paper wrapped tightly around a wooden rod gets charred quickly when
held over a flame compared to a piece of
paper wrapped around a brass rod.
Reason
Thermal conductivity of wood is smaller than the conductivity of brass
A. Assertion is false and Reason is True
B. Reason is false and assertion is True.
C. Both Assertion and Reason are True and reason correctly explains assertion
D. Both Assertion and Reason are True but assertion does not correctly explain reason
Subject: Chemistry
Assertion
\( \boldsymbol{C H}_{3} \boldsymbol{N} \boldsymbol{H}_{3}^{+}-\boldsymbol{C H}_{3} \boldsymbol{N H}_{2} \) is a conjugate
acid base pair.
Reason
\( \boldsymbol{H}_{3} \boldsymbol{O}^{+}, \boldsymbol{O} \boldsymbol{H}^{-} \) is a conjugate acid base
pair.
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
For an ideal binary liquid solution with
\( P_{A}^{\circ}>P_{B}^{\circ}, \) which relation between \( X_{A} \)
(mole fraction of \( A \) in liquid phase) and
\( Y_{A}(\text { mole fraction of } A \text { in vapour phase }) \)
is correct?
\( \mathbf{A} \cdot Y_{A}<Y_{B} \)
В . \( X_{A}>X_{B} \)
c. \( \frac{Y_{A}}{Y_{B}}>\frac{X_{A}}{X_{B}} \)
D. \( \frac{T_{A}}{Y_{B}}<\frac{X_{A}}{X_{B}} \)
Subject: Maths
The value of \( k \) for which the function
\( f(x)=\frac{\left(e^{x}-1\right)^{4}}{\sin \left(\frac{x^{2}}{k^{2}}\right) \log \left\{1+\left(\frac{x^{2}}{2}\right)\right\}}, x \neq \)
\( \mathbf{0} ; \boldsymbol{f}(\mathbf{0})=\mathbf{8} \) may be continuous function
is
This question has multiple correct options
\( A \)
B. -
\( c \cdot 2 \)
\( D \cdot-2 \)
Subject: Maths
The non-zero vectors \( \bar{a}, \bar{b} \) and \( \bar{c} \) are related \( \bar{a}=8 \bar{b} \) and \( \bar{c}=-7 \bar{b} . \) Then the
angle between \( \bar{a} \) and \( \bar{c} \)
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( \pi / 4 \)
c. \( \pi / 2 \)
D. \( \pi \)
Subject: Maths
Prove that the angle between the straight lines joining the origin to the intersection of the straight line \( y= \)
\( 3 x+2 \) with the curve \( x^{2}+2 x y+ \)
\( 3 y^{2}+4 x+8 y-11=0 \) is \( \tan ^{-1} \frac{2 \sqrt{2}}{3} \)
Subject: Maths
If \( x_{1}, x_{2}, x_{3}, x_{4} \) are in G.P then its
common ratio is,
\( ^{\mathbf{A}} \cdot\left(\frac{a r}{c p}\right)^{\frac{1}{4}} \)
\( ^{\mathrm{B}}\left(\frac{c r}{a p}\right)^{\frac{1}{3}} \)
\( ^{c} \cdot\left(\frac{c r}{a p}\right)^{\frac{1}{2}} \)
\( ^{\mathrm{D}}\left(\frac{a p}{b q}\right)^{\frac{1}{2}} \)
Subject: Maths
Show that \( \left|\begin{array}{ccc}\mathbf{1} & \mathbf{1} & \mathbf{1} \\ \boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{a}^{2} & \boldsymbol{b}^{2} & \boldsymbol{c}^{2}\end{array}\right|=(\boldsymbol{a}-\boldsymbol{b})(\boldsymbol{b}- \)
\( c)(c-a) \)
Subject: Maths
Assertion
If a line makes angles \( \boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\gamma} \) with
\( O X, O Y, O Z \) respectively, then \( \sin ^{2} \alpha+\sin ^{2} \beta+\sin ^{2} \gamma=2 \)
Reason
If \( l=\cos \alpha, m=\cos \beta, n=\cos \gamma, \) are
direction cosines of a line, then \( l^{2}+ \)
\( \boldsymbol{m}^{2}+\boldsymbol{n}^{2}=\mathbf{1} \)
A. Both Assertion \& Reason are individually true \& Reason is correct explanation of Assertion
B. Both Assertion \& Reason are individually true but Reason is not the ,correct (proper) explanation of Assertion
C. Assertion is true but Reason is false
D. Assertion is false but Reason is true
Subject: Physics
If the total charge stored in the LC
circuit is \( Q_{0}, \) then for \( t \geq 0 \)
A \( \cdot \) the charge on the capacitor is \( \mathrm{Q}=\mathrm{Q}_{0} \cos \left(\frac{\pi}{2}+\frac{\mathrm{t}}{\sqrt{\mathrm{LC}}}\right) \)
B. the charge on the capacitor is \( \mathrm{Q}=\mathrm{Q}_{0} \cos \left(\frac{\pi}{2}-\frac{\mathrm{t}}{\sqrt{\mathrm{LC}}}\right) \)
c. the charge on the capacitor is \( Q=-L C \frac{d^{2} Q}{d t^{2}} \)
D. the charge on the capacitor is \( \mathrm{Q}=-\frac{1 \mathrm{d}^{2} \mathrm{Q}}{\sqrt{\mathrm{LC}} \mathrm{d}^{2}} \)
Subject: Physics
A body of mass \( 1 k g \) is made to trave with a uniform acceleration of
\( 30 \mathrm{cm} / \mathrm{s}^{2} \) over a distance of \( 2 \mathrm{m} \), the work done is:
\( \mathbf{A} \cdot 6 J \)
в. \( 60 J \)
\( c .0 .6 . J \)
D. 0.3 .5
Subject: Chemistry
The number of mole of \( A g I \) which may
be dissolved in 1.0 litre of \( 1.0 M C N^{-} \)
solution whose
\( \boldsymbol{K}_{s p} \) for \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{I} \) and \( \boldsymbol{K}_{c} \) for \( \boldsymbol{A} \boldsymbol{g}(\boldsymbol{C} \boldsymbol{N})_{2}^{-} \) are
\( 1.2 \times 10^{-17} \) and \( 7.1 \times 10^{19} M^{-2} \)
respectively.
A. \( 0.40 \mathrm{mol} \)
B. \( 0.45 \mathrm{mol} \)
c. 0.50 mol
D. None of these
Subject: Chemistry
\( \boldsymbol{C r}_{2} \boldsymbol{O}_{\mathbf{7}}^{2-} \stackrel{\boldsymbol{p H}=\boldsymbol{x}}{\boldsymbol{\longrightarrow} \boldsymbol{r} \boldsymbol{O}_{4}^{2-} \stackrel{\boldsymbol{p H}=\boldsymbol{y}}{\boldsymbol{U}} \boldsymbol{C}_{\mathbf{2}} \boldsymbol{O}_{\boldsymbol{7}}^{2-}} \)
pH values \( x \) and \( y \) can be:
A. 4 and 5
B. 4 and 8
\( c \cdot 8 \) and 4
D. 8 and 9
Subject: Physics
(A). The reverberation time is
dependent on the shape of the enclosure, position of the sources and observer.
(B) The unit of absorption coefficient in
S.I. system in metric is sabine
A. both (A) and (B) are true
B. both (A) and (B) are false
c. (A) is true but (B) is false
D. (A) is false but (B) is true
Subject: Chemistry
Latent heat of vapourisation of a liquid
at \( 500 K \) and 1 atm pressure is 10 \( k c a l / \) mol. What is the change in internal energy when 3 moles of the liquid is vapourised at the same
temperature
A . \( 27 k c a l \)
B. \( 7 k c a l \)
c. \( 33 k c a l \)
D. \( 25 k c a l \)
Subject: Chemistry
Which of the following statements is
not correct about order of a reaction?
A. The order of a reaction can be a fractional number
B. Order of a reaction is experimentally determined quantity
C. The order of a reaction is always equal to the sum of the stoichiometric coefficients of reactants in the
balanced chemical equation for a reaction
D. The order of a reaction is the sum of the powers of molar concentration of the reactants in the rate law expression
Subject: Chemistry
An electron in \( 2^{n d} \) orbit gains energy
and goes to \( 4^{t h} \) orbit. What are the
differences in angular momentums experienced by the electron due to the transition?
A \( \cdot \frac{2 h}{\pi} \)
в. \( \frac{h}{2 \pi} \)
\( c \cdot \frac{h}{\pi} \)
D. \( \frac{3 h}{4 \pi} \)
Subject: Chemistry
Which of the following statement are
correct?
This question has multiple correct options
A. Orthophosphoric acid is used as a stabilizer for \( H_{2} O_{2} \)
B. Orthophosphoric acid is used for making phosphorus and phosphates.
C. Orthophosphoric acid is used preparation of \( H B r \) in the laboratory.
D. Orthophosphoric acid is a tribasic acid.
Subject: Chemistry
A metal was irradiated by light of frequency \( 3.2 \times 10^{15} s^{-1} . \) The
photoelectron produced had its \( \mathrm{KE}, 2 \) times the KE of the photoelectron which was produced when the same metal was irradiated with a light of frequency \( 2.0 \times 10^{15} s^{-1} . \) What is the ionization
energy of metal?
Subject: Chemistry
\( 100 m l 0.1 M H_{2} O_{2} \) is mixed with
\( 400 m l 0.5 M H_{2} O_{2} . \) The volume of
\( 0.1 M K M n O_{4}(\text { acidic }) \) required to
react with \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) mixture is :
A. \( 840 \mathrm{ml} \)
B. 420 m1
\( c .630 \mathrm{ml} \)
D. None of these
Subject: Chemistry
In which of the following arrangements, the sequence is not strictly according to the property written against it?
A \( \cdot \mathrm{CO}_{2}>\mathrm{SiO}_{2}<\mathrm{SnO}_{2}<\mathrm{PbO}_{2}: \) increasing oxidizing
power
B. HF < HCl < HBr < HI: increasing acid strength
C. \( \mathrm{NH}_{3}<\mathrm{PH}_{3}<\mathrm{A} s \mathrm{H}_{3}<\mathrm{SbH}_{3} \) : increasing basic
strength
D. \( \mathrm{B}<\mathrm{C}<\mathrm{O}<\mathrm{N}: \) increasing first ionization enthalpy
Subject: Physics
The terminal velocity \( V \) of a spherical
ball of lead of radius \( R \) falling through a
viscous liquid varies with \( \boldsymbol{R} \) such that:
A \( \cdot \frac{V}{R}= \) constant
B. \( V R= \) constant
c. \( V= \) constant
D. \( \frac{V}{R^{2}}= \) constant
Subject: Maths
A design is made on a rectangular tile
of dimensions \( 50 \mathrm{cm} 70 \mathrm{cm} \) as shown in
Fig. \( 12.7 . \) The design shows 8 triangles,
each of sides \( 26 \mathrm{cm}, 17 \mathrm{cm} \) and \( 25 \mathrm{cm} \) os
cut out. Find the total area of the design
in \( c m^{2} \)
Subject: Physics
Screen S is illuminated by two point
sources \( A \) and \( B \). Another source
C sends a parallel beam of light towards
point \( P \) on the screen. Line \( A P \) is normal
to the screen and the lines \( A P, B P \)
and \( \mathrm{CP} \) are 6,3 and \( 3 \mathrm{m} \) respectively. The
radiant powers of sources A and B are 45 and \( 90 \mathrm{W} \) respectively. The beam
from \( C \) is of intensity \( 0.4 ~ W / m^{2} . \) The total incident intensity at \( \mathrm{P} \) is
Subject: Chemistry
In which of the following reactions does
hydrogen act as an oxidising agent:
\( \mathbf{A} \cdot H_{2}+F_{2} \longrightarrow \)
B. \( H_{2}+S i C I_{2} \longrightarrow \)
\( \mathbf{c} \cdot N a_{2}+H_{2} \longrightarrow \)
\( \mathbf{D} \cdot C u O+H_{2} \longrightarrow \)
Subject: Physics
The potential across a 25.0 microfarad capacitor is \( 5.0 \mathrm{V} \). What is the charge on the capacitor?
A. 0.20 microcoulombs
B. 5.0 microcoulombs
c. 125 microcoulombs
D. 30.0 microcoulombs
E. we cannot determine the charge on the capacitor with the given information.
Subject: Chemistry
Few pairs of molecule are given below. Which bond of the molecule of the pair
is more polar?
(i) \( \quad H_{3} C-H, H_{3} C-B r \)
(ii) \( \quad H_{3} C-N H_{2}, H_{3} C-O H \)
(iii) \( \boldsymbol{H}_{3} \boldsymbol{C}-\boldsymbol{O} \boldsymbol{H}, \boldsymbol{H}_{3} \boldsymbol{C}-\boldsymbol{S} \boldsymbol{H} \)
(iv) \( \boldsymbol{H}_{3} \boldsymbol{C}-\boldsymbol{C l}, \boldsymbol{H}_{3} \boldsymbol{C}-\boldsymbol{B r} \)
A. \( C-B r, C-N, C-O, C-B r \)
в. \( C-B r, C-O, C-O, C-C l \)
c. \( C-B r, C-N, C-S, C-C l \)
D. \( C-B r, C-O, C-S, C-B r \)
Subject: Chemistry
In the following sequence the product \( D \) \( \mathrm{is}: C H \equiv C H \frac{H B r}{\longrightarrow} A \quad \stackrel{H B r}{\longrightarrow} \)
\( \boldsymbol{B} \quad \stackrel{a l c . K O H}{\longrightarrow} \boldsymbol{C} \stackrel{N a N H_{2}}{\longrightarrow} \quad \boldsymbol{D} \)
A. ethanol
B. ethane
c. ethyne
D. ethanal
Subject: Physics
An experiment's diary reads as follows; "a charged particle is projected in a magnetic field of \( (7.0 \hat{i}-3.0 \hat{j}) \times \)
\( 10^{-3} T . \) The acceleration of the particles
is found to be \( (x \hat{i}+7.0 \hat{j}) \times 10^{-6} m / s^{2} \)
Find the value of \( x \)
Subject: Chemistry
Assertion
For the reaction, \( N a_{2} C O_{3}+H C l \rightarrow \)
\( N a C l+N a H C O_{3}, \) the suitable
indicator is phenolphthalein.
Reason
Phenolphthalein provides its colour in
acidic medium.
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: Physics
Which of the following statements are incorrect?
(i) Average velocity is path length divided by time interval.
(ii) In general, speed is greater than the magnitude of the velocity.
(iii) A particle moving in a given direction with a non-zero velocity can have zero speed.
(iv) The magnitude of average velocity is the average speed.
A. (ii) and (iii)
B. (ii) and (iv)
c. (i), (iii) and (iv)
D. All four
Subject: Chemistry
On treatment of \( 100 \mathrm{mL} \) of \( 0.1 \mathrm{M} \) solution
of \( C o C l_{3} .6 H_{2} O \) with excess
\( A g N O_{3}, 1.2 \times 10^{22} \) ions are
precipitated. The complex is :
A \( \cdot\left[C o\left(H_{2} O\right)_{4} C l_{2}\right] C l .2 H_{2} O \)
в. \( \left[C o\left(H_{2} O\right)_{3} C l_{3}\right] .3 H_{2} O \)
\( \mathbf{c} \cdot\left[\operatorname{Co}\left(H_{2} O\right)_{6}\right] C l_{3} \)
D. \( \left[\operatorname{Co}\left(H_{2} O\right)_{5} C l\right] C l_{2} . H_{2} O \)
Subject: Chemistry
Which one of the following reactions is not a redox reaction?
A \( \cdot I_{2}+2 F e^{2+} \rightarrow 2 I^{-}+2 F e^{3+} \)
в. \( H C l+N a O H \rightarrow N a C l+H_{2} O \)
c. \( 2 M g+O_{2} \rightarrow 2 M g O \)
D. \( Z n+C u^{2+} \rightarrow Z n^{2+}+C u \)
Subject: Chemistry
For the reaction \( 4 N H_{3}+5 O_{2} \rightarrow \)
\( 4 N O+6 H_{2} O, \) the rate disappearance
of ammonia is \( 3.6 \times 10^{-3} \) mol \( L^{-1} s^{-1} \)
What is the rate of formation of water?
Subject: Chemistry
Dipole moment \( \propto \) diff.in \( e^{-} \) unity is
\( \boldsymbol{H} \boldsymbol{F}>\boldsymbol{H} \boldsymbol{C l}>\boldsymbol{H} \boldsymbol{B r}>\boldsymbol{H} \boldsymbol{I} \)
A. True
B. False
Subject: Physics
A compound microscope consists of an objective of focal length \( 2 \mathrm{cm} \) and an eye piece of focal length \( 5 \mathrm{cm} \). When an object is kept \( 2.4 \mathrm{cm} \) from the objective, final image formed is virtual and \( 25 \mathrm{cm} \) from the eye piece. Determine magnifying power of this compound microscope in this set up i.e., in normal
use.
Subject: Physics
A block of mass \( M \) is hanging over a
smooth and light pulley through a light string. The other end of the string is pulled by a constant force \( \boldsymbol{F} \). The kinetic energy of the block increases by \( 40 J \) in
1 \( s . \) The tension in the string is:
A. \( F \)
в. \( M g \)
c. \( F+M g \)
D. \( F-M g \)
Subject: Chemistry
Select the correct statement
for electrolysis of \( A l_{2} O_{3} \) by Hall-Heroult
process.
A . Cryolite \( N a_{3}\left[A l F_{6}\right] \) lowers the melting point of \( A l_{2} O_{3} \) and increases its electrical conductivity.
B. Al is obtained at cathode and probably \( C O_{2} \) at anode.
C. Both of the above statements are correct.
D. None of the above statements are correct.
Subject: Chemistry
A tube of uniform cross-sectional area
\( 1 c m^{2} \) is closed at one end with the
semipermeable membrane. a solution of 5 g glucose per 100 mL is placed inside the tube and is dipped in pure
water at \( 27^{\circ} \mathrm{C} \). When equilibrium is established the height developed in a vertical column in cm is \( 1000 x \). (Assume the density of final glucose solution \( 18 / \mathrm{mL} \)
Find the value of \( X \)
Subject: Chemistry
Which of the following is/are derived by Hisenberg in his uncertainty principle?
A \( \cdot \Delta p \times \Delta x=\frac{h}{4 \pi} \)
B . \( \triangle v \times \triangle x=\frac{h}{4 \pi m} \)
C \( \cdot \triangle E \times \Delta t=\frac{h}{4 \pi} \)
D. \( \Delta p \times \Delta E=\frac{h}{4 \pi} \)
Subject: Chemistry
Which of the following is an example of liquid dishwashing detergent?
A \( \cdot C H_{3}\left(C H_{2}\right)_{10}-C H_{2} O S O_{3}^{-} N a^{+} \)
в.
\( c \)
\( ^{\mathrm{D} \cdot}\left[\begin{array}{cc}C H_{3} & \\ C H_{3}\left(C H_{2}\right)_{15}-N & N \\ C H_{3} & C H_{3}\end{array}\right]^{+} B r \)
Subject: Physics
A man standing on a trolley pushes another identical trolley (both trolleys are at rest on a rough surface), so that
they are set in motion and stop after some time. If the ratio of mass of first
trolley with man to mass of second trolley is \( 3, \) then find the ratio of the stopping distances of the second trolley to that of the first trolley. (Assume coefficient of friction to be the same for
both the trolleys)
Subject: Maths
Mark the correct alternative of the
following.

If the measures of the angles of a triangle are \( (2 x-5)^{o},\left(3 x-\frac{1}{2}\right) \) and \( \left(30-\frac{x}{2}\right), \) then \( x=? \)
A \( \cdot \frac{311}{9} \)
в. \( \frac{309}{11} \)
c. \( \frac{310}{9} \)
D. \( \frac{301}{9} \)
Subject: Physics
A group of N cells whose emf varies
directly with the internal resistance as
per the equation \( \boldsymbol{E}_{N}=\mathbf{1 . 5 r}_{N} \) are
connected as shown in the figure. The current I in the circuit is :-
A . 5.1 A
B. 0.51 A
\( c \cdot 1.5 \mathrm{A} \)
D. 0.15 A
Subject: Physics
Assertion
The number of significant figures depends on the least count of measuring instrument.
Reason
Significant figures define the accuracy of measuring instrument.
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
Find the second term and \( n \) th term of
an AP whose 6 th term is 12 and 8 th
term is 22
A \( \cdot a_{2}=-9, a_{n}=3 n-43 \)
в. \( a_{2}=7, a_{n}=3 n-52 \)
c. \( a_{2}=-8, a_{n}=5 n-18 \)
D \( \cdot a_{2}=-9, a_{n}=5 n-38 \)
Subject: Physics
The co-ordinates of a moving particle at a time \( t, \) are given by \( \boldsymbol{x}= \)
\( 5 \sin 10 t, y=5 \cos 10 t . \) The speed of
the particle is
\( \mathbf{A} \cdot 25 \)
B. 50
c. 10
D. \( 50 \sqrt{2} \)
Subject: Physics
A body of mass \( 0.2 \mathrm{kg} \) falls from a height of \( 10 \mathrm{m} \) to a height of \( 6 \mathrm{m} \) above the ground. Find the loss in potential energy taking place in the body. \( [\boldsymbol{g}= \)
\( \left.10 m s^{-2}\right] \)
Subject: Physics
A spherical rigid ball is released from rest and starts rolling down an inclined
plane from height \( h=7 m \), as shown in
the figure, It hits a block at rest on the horizontal plane (assume elastic collision). If the mass of the both the
ball and the block is \( m \) and the ball is
rolling without sliding, then the speed of the after collision is close to :
\( A \cdot 6 m / s \)
в. \( 8 m / s \)
c. \( 10 m / s \)
D. \( 12 m / s \)
Subject: Maths
Find the perpendicular distance from
\( \boldsymbol{A}(\mathbf{1}, \mathbf{0}, \mathbf{3}) \) to the line \( \overrightarrow{\boldsymbol{r}}=(\mathbf{4}, \mathbf{7}, \mathbf{1})+ \)
\( k(1,2,-2), k \in R . \) Also find the foot of
the perpendicular.
Subject: Physics
Exercise:
[ A transverse harmonic wave on a
string is described by \( \boldsymbol{y}(\boldsymbol{x}, \boldsymbol{t})=\mathbf{3} . \mathbf{0} \sin (\mathbf{3 6} \boldsymbol{t}+\mathbf{0 . 0 1 8} \boldsymbol{x}+\boldsymbol{\pi} / \mathbf{4}) \)
where \( x \) and \( y \) are in \( c m \) and \( t \) in s. The
positive direction of \( x \) is from left to right. For the wave described in the above
Exercise, plot the displacement \( (y) \)
versus
(t) graphs for \( x=0,2 \) and \( 4 \mathrm{cm} \) What are the shapes of these of these
graphs? In which aspects does the oscillatory motion in travelling wave differ from one point to another:
amplitude, frequency or phase?
Subject: Maths
The domain of \( \boldsymbol{f}(\boldsymbol{x})=\sqrt{\log \left(\frac{\mathbf{5} \boldsymbol{x}-\boldsymbol{x}^{2}}{\mathbf{6}}\right)} \)
is
A. \( 2 \leq x \leq 3 \)
в. \( 3 \leq x \leq 4 \)
c. \( -3 \leq x \leq-2 \)
D. \( 1 \leq x \leq 3 \)
Subject: Chemistry
Compared to other acids like
\( \boldsymbol{H} \boldsymbol{C l}, \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3}, \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) is highly syrupy
and viscous in nature. Identify the
correct reason.
A \( \cdot H_{2} S O_{4} \) is highly concentrated
B. \( H_{2} S O_{4} \) is a stronger acid than \( H C l, H N O_{3} \)
C. \( H_{2} S O_{4} \) is associated by more number of hydrogen bonds
D. Both (A) and (B)
Subject: Chemistry
\( 50 \mathrm{ml} \) of \( 0.2 \mathrm{M} \) solution of a compound
with empirical formula \( \boldsymbol{C o C l}_{3} \cdot \boldsymbol{4} \boldsymbol{N} \boldsymbol{H}_{3} \)
on treatment with excess of
\( A g N O_{3}(a q) \) yields 1.435 g of \( A g C l \)
(white ppt).
Ammonia is not removed by treatment
with concentrated \( \boldsymbol{H}_{2} \boldsymbol{S} \mathbf{0}_{\mathbf{4}} \)
The formula of the compound is:
\( \mathbf{A} \cdot \operatorname{Co}\left(N H_{3}\right)_{4} C l_{3} \)
B. \( \left[\operatorname{Co}\left(N H_{3}\right)_{4} C l_{2}\right] C l \)
\( \mathbf{c} \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{4} C l_{3}\right. \)
D. \( \left[\operatorname{CoCl}_{3}\left(N H_{3}\right)\right] N H_{3} \)
Subject: Chemistry
In a reaction, 4 moles of electrons are
transferred to 1 mole of \( H N O_{3} \) when acted as an oxidant. The possible reduction product is:
A \( \cdot 1 / 2 \) mole of \( N_{2} \)
B. \( 1 / 2 \) mole of \( N_{2} O \)
c. 1 mole of \( N O_{2} \)
D. 1 mole of \( N H_{3} \)
Subject: Physics
A system is taken from state \( A \) to state
B along two different paths 1 and 2 . The work done on the system along these
two paths are \( W_{1} \) and \( W_{2} \) respectively. The heat absorbed by the system along
these two paths are \( Q_{1} \) and \( Q_{2} \) respectively. The internal energies at \( A \)
and \( \mathrm{B} \) are \( U_{A} \) and \( U_{B} \) respectively. Then,
\( \mathbf{A} \cdot W_{1}=W_{2}=U_{B}-U_{A} \)
в. \( Q_{1}=Q_{2}=U_{A}-U_{B} \)
c. \( Q_{1}+W_{1}=Q_{2}+W_{2}=U_{A}+U_{B} \)
D. \( Q_{1}+\left(-W_{1}\right)=Q_{2}+\left(W_{2}\right)=U_{B}-U_{A} \)
Subject: Maths
\( \operatorname{Let} P \equiv(a, b), Q \equiv(c, d) \) and \( 0<a<b< \)
\( \mathbf{c}<\mathrm{d} \boldsymbol{L} \equiv(\boldsymbol{a}, \mathbf{0}), \boldsymbol{M} \equiv(\boldsymbol{c}, \mathbf{0}), \mathbf{R} \) lies on \( \mathbf{x} \)
axis such that PR + RQ is minimum
then \( R \) divides \( L M \)
A. internally in the ratio a :
B. internally in the ratio b:
c. internally in the ratio b: \( d \)
D. internally in the ratio c : d