AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
The acid strength of active methylene group in given compounds decreases
as:
(a) \( \boldsymbol{C H}_{3} \boldsymbol{C O C H}_{2} \boldsymbol{C O O C}_{2} \boldsymbol{H}_{5} \)
(b) \( C H_{3} C O C H_{2} C O C H_{3} \)
(c) \( C_{2} H_{5} O O C C H_{2} C O O C_{2} H_{5} \)
\( \mathbf{A} \cdot a>b>c \)
В . \( c>a>b \)
\( \mathbf{c} \cdot a>c>b \)
D. \( b>a>c \)
Subject: Chemistry
In the \( \ln \boldsymbol{K} \boldsymbol{v} \boldsymbol{s} \cdot \frac{\boldsymbol{1}}{\boldsymbol{T}} \) plot of chemical
process having \( \Delta S^{\circ}>0 \) and \( \Delta H^{\circ}<0 \)
the slope is proportional to (where Kis equilibrium constant)
A . \( -\left|\Delta H^{\circ}\right| \)
в . \( \left|\Delta H^{\circ}\right| \)
\( \mathrm{c} \cdot-\Delta S^{\circ} \)
D. \( \Delta G^{\circ} \)
Subject: Maths
Show graphically that each one of the following systems of equations has infinitely many solutions:
\( \boldsymbol{x}-2 \boldsymbol{y}+11=\mathbf{0} \)
\( \mathbf{3} \boldsymbol{x}-\mathbf{6} \boldsymbol{y}+\mathbf{3 3}=\mathbf{0} \)
Subject: Chemistry
Which one is correct for stability order of given diatomic molecules?
A. \( H_{2}>B_{2}>L i_{2} \)
В. \( H_{2}>L i_{2}>B_{2} \)
\( \mathbf{c} \cdot B_{2}>L i_{2}>H_{2} \)
D. \( L i_{2}>B_{2}>H_{2} \)
Subject: Physics
Assertion
When a vessel is heated,the heat is transferred from base to another
part,bringing the vessel to uniform temperature.This process is cannot be reversed.
Reason
If the process is reversed it will violate the second law of thermodynamics as the part of the vessel will not get cooler spontaneously and warm up at the
base.
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
Identify the correct sequence of increasing number of \( \pi \) -bonds in the structures of the following molecules:
(I) \( \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{6}(\|) \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{3}(\|) \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{5} \)
A . ।, ॥।, ॥।
B. II, III,
c. ॥, ।, ॥।
D. I, III, II
Subject: Physics
A particle goes from \( A \) to \( B \) with a speed
of \( 40 \mathrm{km} / \mathrm{h} \) and \( \mathrm{B} \) to \( \mathrm{C} \) with a speed of 60
\( \mathrm{km} / \mathrm{h} . \) If \( \mathrm{AB}=6 \mathrm{BC}, \) then the average
speed in \( \mathrm{km} / \mathrm{h} \) between \( \mathrm{A} \) and \( \mathrm{C} \) is
(40+x). The value of x is:
Subject: Physics
A thin bar of mass 'M' and length 'L' is
free to rotate about a fixed horizontal
axis through a point at its end.The bar is brought to a horizontal position and then released. The angular velocity when it reaches the lowest point is:
A. directly proportional to its length and inversely proportional to its mass
B. independent of mass and inversely proportional to the square root of its length
c. dependent only upon the acceleration due to gravity
D. directly proportional to its length and inversely proportional to the acceleration due to gravity.
Subject: Physics
Two particles are executing simple harmonic motion of the same
amplitude \( A \) and frequency \( \omega \) along the \( \boldsymbol{x}-\boldsymbol{a} \boldsymbol{x} \boldsymbol{i} \boldsymbol{s} . \) Their mean position is
separated by distance \( \boldsymbol{X}_{\mathbf{0}}\left(\boldsymbol{X}_{\mathbf{0}}>\boldsymbol{A}\right) . \) If
the maximum separation
between them is \( \left(X_{0}+A\right), \) the phase
difference between their motion is :-
A \( \cdot \frac{\pi}{4} \)
в. \( \frac{\pi}{6} \)
c. \( \frac{\pi}{2} \)
D. \( \frac{\pi}{3} \)
Subject: Physics
A system goes from \( A \) to \( B \) via two
processes I and II as shown in the figure
If \( \Delta U_{1} \) and \( \Delta U_{2} \) are the changes in
internal energies in the processes land II respectively, the
A \( \cdot \Delta U_{1}=\Delta U_{2} \)
B. relation between \( \Delta U_{1} \) and \( \Delta U_{2} \) cannot be determined
c. \( \Delta U_{2}>\Delta U_{1} \)
D. \( \Delta U_{2}<\Delta U_{1} \)
Subject: Physics
In the Searle's method to determine the
Young's modulus of a wire, a steel wire of length \( 156 c m \) and diameter
\( 0.054 \mathrm{cm} \) is taken as experimental wire the average increase in length for 1.5 \( k g w t \) is found to be \( 0.050 c m \). then
the Ypung's modulus of the wire is
A \( .3 .002 \times 10^{11} N / m^{2} \)
В. \( 1.002 \times 10^{11} N / m^{2} \)
c. \( 2.002 \times 10^{11} N / m^{2} \)
D. \( 2.5 \times 10^{11} N / m^{2} \)
Subject: Chemistry
Which of the following statements is
correct about the given Daniell cell?
Solution containing Solution containing salt of Zinc \( \quad \) salt of Copper
A. This cell converts the electrical energy liberated during the redox reaction to chemical energy
B. This cell has an electrical potential greater than \( 1.1 \mathrm{v} \) when concentration of \( Z n^{2+} \) and \( C u^{2+} \) ions by unity (1 \( \left.\operatorname{mol} d m^{-3}\right) \)
c. In this cell, zinc is acting as anode and copper is acting as cathode
D. Redox reaction occurring in this cell is \( C u_{(s)}+ \) \( Z n_{(a q)}^{2+} \rightarrow C u_{(a q)}^{2+}+Z n_{(s)} \)
Subject: Chemistry
\( H_{2} S \) gas passed in all the following test
tube so that precipitation abserve so
which is correct match:
\( \boldsymbol{C u}, \boldsymbol{S b} \boldsymbol{Z n}, \boldsymbol{C d}, \boldsymbol{P d}, \boldsymbol{S n}, \boldsymbol{N i} \)
A . \( C d- \) Black
в. \( S b \) - orange
c. \( N i- \)yellow
D. \( Z n- \) Brown
Subject: Chemistry
A Null di culsianc vulume Is didacıled
to a manometer tube open at other end
as shown in the figure. The manometer
is filled with a liquid of density \( (1 / 3)^{r d} \)
that of mercury. Initially \( h \) was \( 228 \mathrm{cm} \)
Through a small hole in the bulb, gas
leaked. Assuming the pressure decreases as \( \frac{\boldsymbol{d P}}{\boldsymbol{d t}}=-\boldsymbol{k} \boldsymbol{P} \) and the value
of \( h \) is \( 114 \mathrm{cm} \) after 14 min. What is the
value of \( k\left(\text { in hour }^{-1}\right) ?(\ln (4 / 3)=0.28 \)
and density of \( \boldsymbol{H} \boldsymbol{g}=\mathbf{1 3 . 6} \boldsymbol{g} / \boldsymbol{m} \boldsymbol{L} \) )
\( A \cdot 0.6 \)
B. 1.2
c. 2.4
D. none of the above
Subject: Chemistry
The pair of amphoteric hydroxides is:
A \( \cdot \operatorname{Be}(O H)_{2} \) and \( Z n(O H)_{2} \)
B \( \cdot \operatorname{Al}(O H)_{3} \) and \( L i O H \)
c. \( _{B}(O H)_{3} \) and \( B e(O H)_{2} \)
D. \( B e(O H)_{2} \) and \( M g(O H) \)
Subject: Chemistry
\( 2 S O_{2}+O_{2} \rightleftharpoons 2 S O_{3} \) starting with 2
mol of \( S O_{2} \) and 1 mol of \( O_{2} \) in 1 litre
flask, mixture required 0.4 mol of
\( M n O_{4}^{-} \) in acid medium. Hence \( K_{c} \) is:
\( \mathbf{A} \cdot 80 \)
B. 2
\( c \cdot ! 6 \)
D. 2.6
Subject: Physics
At the corners of an equilateral triangle
of side a \( (1 \text { metre }), \) three point charges
are placed (each of \( 0.1 C \) ). If this
system is supplied energy at the rate of
1 kw, then calculate the time required
to move one of the mid-point of the line
joining the other two.
A . \( 50 h \)
B. \( 60 h \)
\( \mathbf{c} \cdot 48 h \)
\( \mathbf{D} \cdot 54 h \)
Subject: Chemistry
What is the solubility of \( \boldsymbol{A I}(\boldsymbol{O} \boldsymbol{H})_{3}\left(\boldsymbol{K}_{s p}=1 \times 10^{-33}\right) \) in a
buffer solution \( \boldsymbol{p} \boldsymbol{H}=\mathbf{4} ? \)
В \( \cdot 10^{-6} M \)
c. \( 1 \times 10^{-4} M \)
D. \( 0.25 \times 0^{-8} M \)
Subject: Physics
The electric field of a plane polarized electromagnetic Wave in free space at time \( t=0 \) i given by an expression \( \overrightarrow{\boldsymbol{E}}(\boldsymbol{x}, \boldsymbol{y})=10 \hat{j} \cos [(\boldsymbol{6} \boldsymbol{x}+\boldsymbol{8} \boldsymbol{z})] \)
The magenetic field \( \vec{B}(x, z, t) \) is given by ; (c is the velocity of light will be:
A \( \cdot \frac{1}{c}(4 \hat{k}+8 \hat{i}) \cos [(2 x-8 z+20 c t)] \)
B \( \cdot \frac{1}{c}(6 \hat{k}-8 \hat{i}) \cos [(6 x+8 z-10 c t)] \)
c. \( \frac{1}{c}(5 \hat{k}+8 \hat{i}) \cos [(6 x+8 z-80 c t) \)
D \( \cdot \frac{1}{c}(4 \hat{k}-8 \hat{i}) \cos [(6 x+8 z+70 c t)] \)
Subject: Chemistry
The rate law of gaseous reaction:
\( \boldsymbol{A}_{(g)}+\boldsymbol{B}(\boldsymbol{g}) \rightarrow \) product is given by
\( \boldsymbol{K}[\boldsymbol{A}]^{2}[\boldsymbol{B}] . \) If the \( ^{\prime} \mathbf{V}^{\prime} \) of one reaction
vessel is suddenly doubled, which of the following will happen?
A. The rate \( w . r . t^{\prime} A^{\prime} \) will decrease Two times.
B. The rate \( w . r . t^{\prime} A^{\prime} \) will decrease Four times.
c. The rate \( w . r . t^{\prime} B^{\prime} \) will decrease Two times
D. The overall rate will decrease Eight Times of the original Value.
Subject: Chemistry
In transforming 0.01 mole of \( P b S \) to
\( P b S O_{4}, \) the volume of 10 volume \( H_{2} O_{2} \)
required will be:
A. \( 11.2 \mathrm{mL} \)
B. \( 22.4 \mathrm{mL} \)
c. \( 33.6 m L \)
D. \( 44.8 \mathrm{mL} \)
Subject: Chemistry
The value of Planck's constant
is
\( \mathbf{A} \cdot 6.627 \times 10^{-34} \)joulesec.
B. \( 6.083 \times 10^{-34} \) joulesec.
c. \( 6.627 \times 10^{-27} \) joulesec.
D. \( 6.627 \times 10^{-30} \) joulesec.
Subject: Physics
by two statements, Statement 1 and
Statement \( 2 . \) Of the given four
alternatives after the statements,
choose the one that best describes
the statements.
A thin air film is formed by putting the
convex surface of a plane convex lens
over a plane glass plate. With monochromatic light, this film gives an
interference pattern due to light reflected from the top (convex) surface and the bottom (glass plate) surface of the film.

Statement 1: When light reflects from the air-glass plate interface, the reflected wave suffers a phase change
of \( \pi \)
Statement 2: The center of the
interference pattern is dark.
A. Statement 1 is True, Statement 2 is False
B. Statement 1 is True, Statement 2 is True; Statement 2 is a correct explanation for Statement 1
c. Statement 1 is True, Statement 2 is True; Statement 2 is not the correct explanation for Statement 1.
D. Statement 1 is False, Statement 2 is True.
Subject: Physics
A long circular tube of length \( 10 m \) and
radius \( 0.3 \mathrm{m} \) carries a current I along its curved surface as shown. A wire-loop of resistance 0.0005 ohm and of radius 0.1
\( \mathrm{m} \) is placed inside the tube with its axis coinciding with the axis of the tube. The
current varies as \( \boldsymbol{I}=\boldsymbol{I}_{0} \cos (\boldsymbol{3} \boldsymbol{0} \boldsymbol{0} \boldsymbol{t}) \)
where \( I_{0} \) is constant. If the magnetic
moment of the loop is \( N \mu_{0} I_{0} \sin (300 t) \)
then 'N' is
Subject: Maths
In the figure given, 0 is the center of the
circle. If \( \angle O B C=37^{\circ}, \) the \( \angle B A C \) is
equal to
A \( \cdot 74^{\circ} \)
B . \( 106^{\circ} \)
\( c \cdot 53^{\circ} \)
D. 37
Subject: Chemistry
Assertion
In the following reaction,
\( \boldsymbol{S O}_{2}+\boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{S} \longrightarrow \boldsymbol{3} \boldsymbol{S}+\boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O} \)
1 mole \( S O_{2} \) and 1 mole \( H_{2} S \) forms 3
moles sulphur.
Reason
1 mole \( S O_{2} \) and 2 mole \( H_{2} S \) form 3
moles sulphur and 2 moles \( H_{2} O \)
A. Both Assertion and Reason are are true and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation for Assertion
C. Assertion is true but Reason is false
D. Assertion is false but Reason is true
Subject: Maths
\( A \) vertical tower stands on a declivity
which isinclined at \( 15^{0} \) to the horizon.
From the foot of the tower a man
ascends the declivity for80 feet and then finds that the tower subtends an
angle of \( 30^{0} . \) The height of the tower is
A \( \cdot 20(\sqrt{6}-\sqrt{2}) f t \)
B . \( 40(\sqrt{6}-\sqrt{2}) f t \)
c. \( 40(\sqrt{6}+\sqrt{2}) f t \)
D. \( 40 \mathrm{ft} \)
Subject: Maths
Determine whether the argument used to check the validity of the following statement is correct.
\( p: \) If \( x^{2} \) is irrational, then \( x \) is rational
The statement is true because the
number \( x^{2}=\pi^{2} \) is irrational, therefore
\( x=\pi \) irrational.
A. True
B. False
Subject: Physics
A body projected from the bottom of a smooth inclined plane with a velocity \( 9.8 m / \)sec. The angle of inclination of
the plane is \( 30^{\circ} . \) If it comes to rest after
reaching the top of the plane, then the time of ascent is
A. 2 sec
B. 1 sec
\( c .0 .5 \mathrm{sec} \)
D. 1.5 sec
Subject: Chemistry
Burning of coal is represented as
\( \boldsymbol{C}(\boldsymbol{s})+\boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g}) \cdot \) The rate of
this reaction is increased by:
A. Decreasing in the concentration of oxygen
B. Powdering the lumps of coal
c. Decreasing the temperature of coal
D. Providing inert atmosphere
Subject: Maths
If the hypotenuse of a right angled triangle is \( 41 \mathrm{cm} \) and the area of the
triangle is 180 sq \( c m \), then the
difference between the lengths of the triangle must be
\( \mathbf{A} \cdot 22 \mathrm{cm} \)
B. \( 25 \mathrm{cm} \)
\( c \cdot 27 \mathrm{cm} \)
D. \( 31 \mathrm{cm} \)
Subject: Physics
Monatomic, diatomic and polyatomic
ideal gases each undergo slow adiabatic expansions from the same initial volume and same initial
pressure to the same final volume. The
magnitude of the work done by the
environment on the gas is
A. the greatest for polyatomic gas
B. the greatest for monatomic gas
c. the greatest for diatomic gas
D. the question is irrelevant, there is no meaning of slow adiabatic expansion
Subject: Chemistry
In which of the following reactions, products are not correctly matched in:
A \( \cdot R M g X+C O_{2} \frac{(i) C O_{2}}{(i) H \oplus} \) Carboxylic acio
B . \( R M g X+C_{2} H_{5} O H \rightarrow \) Alkane
c. \( R M g X+C H_{3} C H_{2} C l \rightarrow \) Alkene
D.
\[
\operatorname{RMgX}+\text { cl } \widehat{\operatorname{lth} e r}
\]
Subject: Chemistry
The standard Gibbs energy change at \( 300 K \) for the reaction \( 2 A \leftrightharpoons B+C \) is
\( 2494.2 J . \) At a given time, the composition of the reaction mixture is \( [A]=\frac{1}{2},[B]=2 \) and \( [C]=\frac{1}{2} . \) The reaction
proceeds in the \( :[R= \) \( \mathbf{8 . 3 1 4 J} / \mathbf{K} / \mathbf{m o l}, e=\mathbf{2 . 7 1 8} \)
A . forward direction because \( Q>K_{e} \)
B. reverse direction because \( Q>K_{e} \)
C. forward direction because \( Q<K_{e} \)
D. reverse direction because \( Q<K_{e} \)
Subject: Chemistry
Phenolphthalein indicator is colourless in an acid and turns pink in an alkaline solution. When an aqueous
solution of potassium iodide is electrolysed with phenolphthale in indicator, what colours appear at the
electrodes?
Cathode: \( 2 H_{2} O_{(l)}+2 e^{-} \rightarrow H_{(g)}+ \)
\( 2 O H^{-}(a q) \)
Anode: \( 2 I_{(a q)}^{-} \rightarrow I_{2(s)}+2 e^{-} \)
A. Brown at the cathode and pink at the anode
B. Red at the cathode and pink at the anode
c. Brown at the anode and colourless at the cathode
D. Pink at the cathode and brown at the anode
Subject: Maths
In a trapezium whose parallel sides measure \( 24 \mathrm{cm} \) and \( 15 \mathrm{cm} \) and the
distance between them is \( 10 \mathrm{cm} . \) Find
the area of trapezium.
A \( \cdot 215 \mathrm{cm}^{2} \)
В. \( 205 \mathrm{cm}^{2} \)
\( c \cdot 195 \mathrm{cm}^{2} \)
D. \( 295 \mathrm{cm}^{2} \)
Subject: Maths
Solve the following equations by substitution method.
\( \mathbf{5} \boldsymbol{x}+\mathbf{3} \boldsymbol{y}=\mathbf{2} \mathbf{1} ; \mathbf{2} \boldsymbol{x}-\boldsymbol{y}=\mathbf{4} \)
A. \( x=3, y=2 \)
в. \( x=-3, y=2 \)
c. \( x=3, y=-2 \)
D. None of these
Subject: Physics
What is the basic difference between a
real image and a virtual image?
A. Real image are the image that can be obtained on a screen whereas virtual image cannot be obtained on the screen
B. Virtual image can be obtained on a screen while real images cannot be obtained on a screen
C. Virtual images are formed only in refraction not in reflection while real image can be formed in both
D. Virtual images are formed only in reflection while real image are also only found in refraction
Subject: Physics
The equation of a standing wave produced on a string fixed at both ends is
\( \boldsymbol{y}=\mathbf{0 . 4} \sin [\mathbf{0 . 3 1 4 x}] \cos [\mathbf{6 0 0} \boldsymbol{\pi} \boldsymbol{t}] \) where \( \boldsymbol{x} \)
and \( y \) are in \( c m \) and \( t \) in seconds. The
smallest possible length of the string is
\( \mathbf{A} \cdot 10 \mathrm{cm} \)
B. \( 20 \mathrm{cm} \)
\( \mathbf{c} .30 \mathrm{cm} \)
D. \( 40 \mathrm{cm} \)
Subject: Maths
A vertical line \( l \) passes through the point \( (2,3) . \) A horizontal line \( m \) passes
through the point \( (-1,6) . \) Where do lines \( l \) and \( m \) intersect?
\( \mathbf{A} \cdot(0,5) \)
в. (2,6)
c. (6,2)
D. (-1,3)
E \( .(3,-1) \)
Subject: Physics
The magnetic field of the earth can be modelled by that of a point dipole placed at the centre of the earth. The
dipole axis makes an angle of \( 11.3^{\circ} \)
with the axis of the earth. At Mumbai,
declination is nearly zero. Then,
A. The declination varies between \( 11.3^{\circ} \mathrm{W} \) to \( 11.3^{\circ} \mathrm{E} \)
B. The least declination is \( 0^{\circ} \)
C. The plane defined by dipole axis and the earth axis passes through Greenwich
D. Declination averaged over the earth must be always negative
Subject: Maths
If the error committed in measuring the radius of the circle is \( 0.05 \% \), then the
corresponding error in calculating the area is:
\( \mathbf{A} \cdot 0.05 \% \)
B. \( 0.025 \% \)
c. \( 0.25 \% \)
D. \( 0.1 \% \)
Subject: Physics
Let PQR is a right angled prism with
other angles as \( 60^{\circ} \) and \( 30^{\circ} . \) PQ has a
thin layer of liquid and light falls normally on the face PR as shown in
figure. If the refractive index of prism is
1.5, then for total internal reflection,
maximum refractive index of liquid will
be
A . 1.2
B. 1.3
\( c .1 .4 \)
D. 1.5
Subject: Physics
Three rings each of mass \( m \) and radius
are so placed that they touch each
other. The radius or gyration of the
system about the axis as shown in the
figure is:
A \( \cdot \sqrt{\frac{6}{5}} \)
B. \( \sqrt{\frac{5}{6}} \)
c. \( \sqrt{\frac{6}{7}} \)
D. \( \sqrt{\frac{7}{6}} \)
Subject: Physics
A "moving sidewalk" in a busy airport terminal moves \( 1 m / s \) and is \( 200 m \)
long. A passenger steps onto one end and walks, in the same direction as the
sidewalk is moving, at a rate of \( 2.0 \mathrm{m} / \mathrm{s} \) relative to the moving sidewalk. How much time does it take the passenger
to reach the opposite end of the walkway? (in seconds)
A . 66.7
B. 67.3
c. 63
D. 66
Subject: Physics
The intensity of magnetic induction field at the centre of a single turn circular coil of radius \( 5 \mathrm{cm} \) carrying of
0.9 A current is:
A . \( 36 \pi \times 10^{-7} \mathrm{T} \)
В . \( 9 \pi \times 10^{-7} T \)
\( \mathbf{c} \cdot 36 \pi \times 10^{-6} T \)
D. \( 9 \pi \times 10^{-6} T \)
Subject: Maths
The number of \( \boldsymbol{A} \) in \( \boldsymbol{T}_{\boldsymbol{p}} \) such that \( \boldsymbol{A} \) is either symmetric or skew-symmetric or both, and det \( (A) \) divisible by \( p, \) is
A \( \cdot(p-1)^{2} \)
в. \( 2(p-1) \)
c. \( (p-1)^{2}+1 \)
D. \( 2 p-1 \)
Subject: Physics
Two different coils have self inductance
\( \boldsymbol{L}_{1}=\mathbf{8} \boldsymbol{m} \boldsymbol{H} \) and \( \boldsymbol{L}_{2}=\boldsymbol{2 m} \boldsymbol{H} . \) The
currents in both are increasing at the
same constant rate. At a certain instant
of time, the power given to the two coils
is the same. At this moment the
current, the induced voltage and energy
stored in the first coil are \( i_{1}, V_{1} \) and \( U_{1} \)
respectively. The corresponding values
in the second coil are \( i_{2}, V_{2} \) and \( U_{2} \) respectively. Then the values of \( \frac{i_{1}}{i_{2}}, \frac{V_{1}}{V_{2}} \) and \( \frac{\boldsymbol{U}_{1}}{\boldsymbol{U}_{2}} \) are respectively:
A \( \cdot \frac{1}{4}, 4, \frac{1}{4} \)
в. \( 4, \frac{1}{4}, \frac{1}{4} \)
c. \( \frac{1}{4}, \frac{1}{4}, 4 \)
D. \( _{4,4, \frac{1}{4}} \)
Subject: Maths
Find the direction angles of vector \( -8 \hat{i}+3 \hat{j}+2 \hat{k} \)
A \( \cdot 156^{\circ}, 70^{\circ}, 77^{\circ} \)
В. \( 155^{\circ}, 72^{\circ}, 80^{\circ} \)
c. \( 145^{\circ}, 83^{\circ}, 74^{\circ} \)
D. \( 150^{\circ}, 76^{\circ}, 83^{\circ} \)
Subject: Maths
The number of permutation of the letters of the word \( H I N D U S T A N \)
such that neither the pattern \( ^{\prime} \boldsymbol{H} \boldsymbol{I} \boldsymbol{N}^{\prime} \)
nor \( ^{\prime} D U S^{\prime} \) nor \( ^{\prime} T A N^{\prime} \) appears, are :
A . 166674
B. 169194
c. 166680
D. 181434
Subject: Physics
A soap film of thickness \( t \) is surrounded
by air and is illuminated at near normal
incidence by monochromatic light with wavelength \( \lambda \) in the film. With respect
to the wavelength of the monochromatic light in the film, what film thickness will produce maximum constructive interference?
A \( \cdot \frac{1}{4} \lambda \)
B. \( \frac{1}{2} \lambda \)
c. \( 1 \lambda \)
D. \( 2 \lambda \)
Subject: Maths
If \( \boldsymbol{A}=\{1,2,3\} \) and \( \boldsymbol{B}=\{4,5,6\} \) then
which of the following sets are relation from \( \boldsymbol{A} \) to \( \boldsymbol{B} \)
(i) \( R_{1}=\{(4,2)(2,6)(5,1)(2,4)\} \)
(ii) \( \boldsymbol{R}_{2}=\{(1,4)(1,5)(3,6)(2,6)(3,4)\} \)
(iii) \( R_{3}=\{(1,5)(2,4)(3,6)\} \)
(iv) \( \boldsymbol{R}_{4}=\{(\mathbf{1}, \mathbf{4})(\mathbf{1}, \mathbf{5})(\mathbf{1}, \mathbf{6})\} \)
A. \( R_{1}, R_{2}, R_{3} \)
в. \( R_{1}, R_{3}, R_{4} \)
\( \mathbf{c} \cdot R_{2}, R_{3}, R_{4} \)
D. \( R_{1}, R_{2}, R_{3}, R_{4} \)
Subject: Maths
If \( \boldsymbol{y}=4 \boldsymbol{x}^{4}+\boldsymbol{2} \boldsymbol{x}^{3}+\frac{\mathbf{5}}{\boldsymbol{x}}+\boldsymbol{9}, \) then find
\( \boldsymbol{d} \boldsymbol{y} / \boldsymbol{d} \boldsymbol{x} \)
Subject: Physics
At a place, the angle of dip is \( 30^{0} . \) If the horizontal component of earth's field is
\( B_{H}, \) then the net field intensity at the place will be :
A \( \cdot \frac{B_{H}}{2} \)
в. \( \frac{2 B_{H}}{\sqrt{3}} \)
c. \( B_{H} \sqrt{2} \)
D. \( B_{H} \sqrt{3} \)
Subject: Maths
Given below are Matching type questions, with two columns(each
having some items) each.Each item of column \( I \) has to be matched with the
items of column \( I I \), by enclosing the
correct match.
Note:An item of column \( I \) can be
matched with more than one items of
columnII.All the items of column \( I I \)
have to be matched. The equation of conics represented by the general equation of second degree \( \boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{2 h x} \boldsymbol{y}+\boldsymbol{b} \boldsymbol{y}^{2}+\boldsymbol{2} \boldsymbol{g} \boldsymbol{x}+\boldsymbol{2} \boldsymbol{f} \boldsymbol{y}+\boldsymbol{c}= \)
0
and the discriminant of above equation is represented by \( \triangle, \) where \( \triangle=a b c+ \) \( 2 f g h-a f^{2}-b g^{2}-c h^{2} \) or \( \left(\begin{array}{lll}a & h & g \\ h & b & f \\ g & f & c\end{array}\right) \)
Now, match the entries from the
following two columns
Subject: Physics
A steel ring of radius \( r \) and cross
sectional area \( A \) is fitted onto a wooden
disc of radius \( R(R>r) . \) If the Young's
modulus of steel is \( Y \), then the force
with which the steel ring is expanded is
A. \( A Y(R / r) \)
в. \( A Y(R-r) / r \)
c. \( (Y / A)[(R-r) / r] \)
D. \( Y r / A R \)
Subject: Chemistry
The pressure of moist gas at a given temperature is \( 10 \mathrm{mm} \) Hg at volume \( V \)
Aqueous tension at this temperature is \( 3 \mathrm{mm} \) Hg point the final pressure of gas at the same temperature if the volume is reduced to \( 1 / 3 \) original volume is:
A. 30mm Hg
B. 27mm Hg
c. \( 24 \mathrm{mm} \) ну
D. \( 21 \mathrm{mm} \) Hg