AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
If \( P=a^{2}-2 a b+b^{2} \) and \( q=4 a b, \) then
\( \boldsymbol{p}+\boldsymbol{q} \boldsymbol{a} \) is:
A \( \cdot(a-b)^{2}+4 a^{2} b \)
B . \( (a-b)^{2}-4 a^{2} b \)
c. \( (a-b)^{2}-4 b a \)
D. \( (a-b)^{2}-4 b^{2} a \)
Subject: Chemistry
Balance the following equation by
oxidation number method.
\( A l+K M n O_{4}+H_{2} S O_{4} \rightarrow \)
\( \boldsymbol{A l}_{2}\left(\boldsymbol{S O}_{4}\right)_{3}+\boldsymbol{K}_{2} \boldsymbol{S} \boldsymbol{O}_{4}+\boldsymbol{M} \boldsymbol{n} \boldsymbol{S} \boldsymbol{O}_{4}+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O} \)
Subject: Maths
Median of the following freq. dist.
\( \boldsymbol{x}_{i} \quad \boldsymbol{3} \quad \boldsymbol{6} \) \( \mathbf{1 2} \) \( \mathbf{1 0} \)
\( f_{i} \quad 3 \quad 4 \quad 2 \) 13
\( A \cdot 7 \)
B. 10
c. 8.5
D. None of these
Subject: Maths
The domain for, \( \boldsymbol{f}(\boldsymbol{x})=\cos ^{-1}[\boldsymbol{x}] \) is
A. \( x \in[-1,2) \)
B . \( x \in[-1,1] \)
c. \( x \in(-1,2) \)
D. \( x \in(-1,1) \)
Subject: Physics
The relation between \( u, v \) (u is the object distance and v is the image distance ) and f for mirror is given by:
A \( \cdot f=\frac{u v}{u-v} \)
B. \( f=\frac{2 u \times v}{u+v} \)
c. \( f=\frac{u \times v}{u+v} \)
D. none of these
Subject: Maths
\( \int x \cdot\left(x^{x}\right)^{x}(2 \log x+1) d x \)
\( \mathbf{A} \cdot x^{\left(x^{x}\right)}+c \)
B. \( \left(x^{x}\right)^{x}+c \)
c. \( x^{x} \cdot \log x+c \)
D. does not exist
Subject: Physics
In a golf tournament, if we designate
the hole as the origin, and the putter
(like a bat) is at \( -5.0 \mathrm{m} \) at time \( 0 \mathrm{s} \), the
velocity-time graph for the golf ball will
be
A. a straight line inclined to the time axis
B. a straight line parallel to the time axis
c. a concave curve
D. a convex curve
Subject: Chemistry
Two moles of \( P C l_{5} \) is heated in a closed
vessel of 2 litre capacity. When the equilibrium is attained, \( 40 \% \) of it has been found to be disssociated. What is
\( \boldsymbol{K}_{c} \) in \( \boldsymbol{m o l} / \boldsymbol{d} \boldsymbol{m}^{3} ? \)
Subject: Maths
Find the direction cosines of vector \( \vec{r} \)
which is equally inclined to \( O X, O Y \)
and \( O Z \). Find total number of such
vectors.
A \( \cdot \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}} ; 6 \)
B. \( \frac{1}{\sqrt{3}}, \pm \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}} ; 8 \)
\( ^{\mathbf{C}} \pm \frac{1}{\sqrt{3}}, \pm \frac{1}{\sqrt{3}}, \pm \frac{1}{\sqrt{3}} ; 8 \)
D. None of these
Subject: Chemistry
The incorrect statement(s) about the
following two compound \( I \) and \( I I \)
is/are:

This question has multiple correct options
A. \( (I I) \) is more acidic than \( (I) \)
B. the resonance effect of phenyl ring with - cooH group is more in \( (I I) \) than in \( (I) \)
C. \( (I I) \) is weaker acid than \( (I) \) because of electron releasing inductive effect of tertiary - butyl group
D. the positive charge of carboxylate anions of \( (I) \) is more delocalized in the benzene ring than the \( (I I) \) compound
Subject: Maths
Evaluate the following definite integrals as limit of sums. \( \int_{0}^{5}(x+1) d x \)
A \( \cdot \frac{15}{2} \)
в. \( \frac{25}{2} \)
c. \( \frac{35}{2} \)
D. \( \frac{45}{2} \)
Subject: Chemistry
A certain reactant \( X O_{3}^{-} \) is getting
converted to \( X_{2} O_{7} \) in solution. The rate
constant of this reaction is measured
by titrating a volume of the solution with a reducing agent which reacts only
with \( X O_{3}^{-} \) and \( X_{2} O_{7} . \) In this process of reduction both the compounds
converted to \( X^{-} . \) At \( t=0, \) the volume of
the reagent consumed is \( 30 \mathrm{mL} \) and at \( \mathrm{t} \)
\( =9.212 \mathrm{min.} \) the volume used up is 36
mL. Find the rate constant(in \( h r^{-1} \) ) of
the conversion of \( \boldsymbol{X} \boldsymbol{O}_{3}^{-} \) to \( \boldsymbol{X}_{2} \boldsymbol{O}_{7} ? \)
Assuming reaction is of 1st order. (Given that \( \ln 10=2.303, \log 2=0.30 \) ).
Subject: Physics
As shown in fig., an object \( O \) is at the
position (-10,2) with respect to the
origin \( P . \) The concave mirror \( M_{1} \) has
radius of curvature \( 30 \mathrm{cm} . \) A plane
mirror \( M_{2} \) is kept at a distance of
\( 40 \mathrm{cm} \) in front of the concave mirror
Subject: Maths
\( \lim _{h \rightarrow 0} \frac{\sqrt{x+h}-\sqrt{x}}{h} \) is equal to
A \( \cdot \sqrt{x} \)
в. \( \frac{1}{2 \sqrt{x}} \)
\( c \cdot 2 \sqrt{x} \)
D. \( \frac{1}{\sqrt{x}} \)
Subject: Maths
The measure of an angle in degrees, grades and radians be \( \mathrm{D}, \mathrm{G} \) and \( \mathrm{C} \)
respectively, then relation between them \( \frac{\boldsymbol{D}}{\mathbf{9 0}}=\frac{\boldsymbol{G}}{\mathbf{1 0 0}}=\frac{\boldsymbol{2 C}}{\boldsymbol{\pi}} \) but \( \mathbf{1}^{\circ}= \)
\( \left(\frac{180}{\pi}\right)^{0} \simeq 57^{\circ}, 17^{\prime}, 44.8^{\prime \prime} \) and sum of
interior angles of a \( n \) -sided regular polygon is \( (2 n-4) \frac{\pi}{2} . \) On the basis of above information, answer the following questions :The number of sides of two
regular polygon are as 5: 4 and the difference between their angles is \( \frac{\pi}{20} \)
then the number of sides in the
polygons respectively are -
A. 25, 20
B. 20, 16
c. 15,12
D. 10,8
Subject: Physics
Two inductance's connected in parallel are equivalent to a single inductance of
\( 1.5 H, \) and when connected in series
are equivalent to a single inductance of
\( 8 H . \) The difference in their inductance
is:-
\( \mathbf{A} \cdot 3 H \)
в. \( 7.5 ~ H \)
c. \( 2 H \)
D. \( 4 H \)
Subject: Physics
Assertion
To move a body uniformly in a circular
path, an external agent has to apply a force.
Reason
To more a body uniformly in a circular path, an external agent has to do work.
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 and Reason is correct
Subject: Maths
Let \( S_{n} \) denote the sum of first \( n \) terms of
an AP and \( 3 S_{n}=S_{2 n} . \) What is \( S_{3 n}: S_{2 n} \)
equal to?
A .2: 1
B. 3: 1
c. 4: 1
D. 5: 1
Subject: Maths
\( \operatorname{Let} \boldsymbol{I}=\int_{\boldsymbol{\pi} / 4}^{\pi / 3} \frac{\sin \boldsymbol{x}}{\boldsymbol{x}} \boldsymbol{d} \boldsymbol{x} . \) Then?
\( ^{\mathrm{A}} \cdot \frac{1}{2} \leq I \leq 1 \)
в. \( 4 \leq I \leq 2 \sqrt{30} \)
\( \frac{\sqrt{3}}{8} \leq I \leq \frac{\sqrt{2}}{6} \)
D. \( 1 \leq I \leq \frac{2 \sqrt{3}}{\sqrt{2}} \)
Subject: Physics
The area of a square is \( 5.29 \mathrm{cm}^{2} \). The
area of 7 such squares taking into account the significant figures is?
\( \mathbf{A} \cdot 37 \mathrm{cm}^{2} \)
в. \( 37.0 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 37.03 \mathrm{cm}^{2} \)
D. \( 37.030 \mathrm{cm}^{2} \)
Subject: Physics
A particle of mass \( m \) is made to move
with uniform speed \( v_{0} \) along the perimeter of a regular hexagon, inscribed in a circle of radius R. The
magnitude of impulse applied at each corner of the hexagon is :
A \( \cdot 2 m v_{0} \sin \frac{\pi}{6} \)
В. \( m v_{0} \sin \frac{\pi}{6} \)
c. \( _{m v_{0} \sin \frac{\pi}{3}} \)
D. \( 2 m v_{0} \sin \frac{\pi}{3} \)
Subject: Physics
A ball is thrown from a height of \( 12.5 m \) from the ground level in the horizontal direction. It falls at a horizontal
distance of \( 200 m . \) The initial velocity of the ball (approximately) is
A. \( 140 \mathrm{m} / \mathrm{s} \)
в. \( 80 \mathrm{m} / \mathrm{s} \)
c. \( 126 m / s \)
D. \( 120 \mathrm{m} / \mathrm{s} \)
Subject: Maths
The differential equation representing
the family of curves \( y=x e^{c x} \) (c is a
constant) is
A \( \cdot \frac{d y}{d x}=\frac{y}{x}\left(1-\log \frac{y}{x}\right) \)
B . \( \frac{d y}{d x}=\frac{y}{x} \log \left(\frac{y}{x}\right)+1 \)
C \( \cdot \frac{d y}{d x}=\frac{y}{x}\left(1+\log \frac{y}{x}\right) \)
D. \( \frac{d y}{d x}+1=\frac{y}{x} \log \frac{y}{x} \)
Subject: Physics
The angles of dip at the poles and the equator respectively are.
A . \( 30^{\circ}, 60^{\circ} \)
B . \( 0^{\circ}, 90^{\circ} \)
c. \( 45^{\circ}, 90^{\circ} \)
D. \( 90^{\circ}, 0^{\circ} \)
Subject: Physics
The effects are produced at a given point in space by two waves described
by the equations \( y_{1}=y_{m} \sin \omega t \) and
\( \boldsymbol{y}_{2}=\boldsymbol{y}_{m} \sin (\omega t+\phi) \) where \( \boldsymbol{y}_{m} \) is the
same for both the waves and \( \phi \) is a
phase angle. Tick the correct statement
among the following
A. the maximum intensity that can be achieved at a point is twice the intensity of either wave and occurs if \( \phi=0 \)
B. the maximum intensity that can be achieved at a point is four times the intensity of either wave and occurs if \( \phi=0 \)
c. the maximum amplitude that can be achieved at the point its twice the amplitude of either wave and occurs at \( \phi=0 \)
D. When the intensity is zero the net amplitude is zero and at this point \( \phi=\pi / 4 \)
Subject: Chemistry
Calculate the pH of a buffer solution
prepared by dissolving 30 g of \( N a_{2} C O_{3} \)
in \( 500 \mathrm{mL} \) of an aqueous solution
containing \( 150 \mathrm{mL} \) of \( 1 \mathrm{M} \) HCl. \( K_{a} \) for:
\( \boldsymbol{H} \boldsymbol{C O}_{3}=\mathbf{5 . 6 3} \times \mathbf{1 0}^{-11}\left[\log \left(\frac{\mathbf{1 3 3}}{\mathbf{1 5 0}}\right)=\right. \)
\( -\mathbf{0 . 0 5} \)
A . 8.25
B. 9.19
c. 10.43
D. 11.56
Subject: Maths
The probability that a student \( x \)
participates in a competition is 0.4
while that for student \( y \) is \( 0.5 . \) The
probability that \( x \) participates in
competition, given that \( y \) also
participates is \( 0.7 . \) Then This question has multiple correct options
A. The probability that both \( x \) and \( y \) participates in that competition simultaneously is 0.35
B. The probability that \( y \) participates in that competition given that \( x \) also participates is \( \frac{7}{8} \)
C. The probability that atleast one of them participates in that competition is 0.55
D. The probability that exactly one of them participates in that competition is 0.20
Subject: Maths
If \( \boldsymbol{R}=\left\{(\boldsymbol{x}, \boldsymbol{y}): \boldsymbol{x}^{2}+\boldsymbol{y}^{2} \leq \mathbf{4} ; \boldsymbol{x}, \boldsymbol{y} \in \mathbb{Z}\right\} \)
a relation on \( \mathbb{Z} \), write the domain of \( \boldsymbol{R} \)
Subject: Chemistry
Vapour pressure of water is \( 360 \mathrm{mm} \mathrm{Hg} \) how much urea should be added to 200
mL water to reduce its vapour pressure by \( 0.5 \% ?(\text { Molecular wt. of urea }=60) \)
A . \( 2.52 g \)
в. 3.33 g
c. \( 3.96 g \)
D. None of these
Subject: Chemistry
The \( I U P A C \) name of \( K_{4}\left[F e(C N)_{6}\right] \) is:
A. potassium hexacyano ferrate \( (I I) \)
B. potassium hexacyanido ferrate \( (I I I) \)
c. tetrapotassium hexacyanido ferrate
D. all of the above
Subject: Maths
If \( \frac{1}{\boldsymbol{q}+\boldsymbol{r}}, \frac{\mathbf{1}}{\boldsymbol{r}+\boldsymbol{p}} \) and \( \frac{\mathbf{1}}{\boldsymbol{p}+\boldsymbol{q}} \) are in AP
then \( p^{2}, q^{2} \) and \( r^{2} \) are in
\( A \cdot A P \)
в. GP
c. нр
D. AGP
Subject: Physics
Obtain the angle between \( \vec{A}+\vec{B} \) and \( \vec{A}-\vec{B} \) if \( \vec{A}=2 \hat{i}+3 \hat{j} \) and \( \vec{B}=\hat{i}-2 \hat{j} \)
\( ^{A} \cdot \cos ^{-1}\left(\frac{4}{\sqrt{65}}\right) \)
в. \( \pi-\cos ^{-1}\left(\frac{4}{\sqrt{65}}\right) \)
\( ^{\mathrm{c}} \cdot \sin ^{-1}\left(\frac{4}{\sqrt{65}}\right) \)
D. \( -\sin ^{-1}\left(\frac{4}{\sqrt{65}}\right) \)
Subject: Physics
The equation of a wave propagating along a stretched string is given by \( \boldsymbol{Y}=\mathbf{4} \sin 2 \boldsymbol{\pi}[(\boldsymbol{t} / \mathbf{0 . 0 2})-(\boldsymbol{x} / \mathbf{1 0 0})] \)
where \( Y \) and \( x \) are in \( \mathrm{cm} \) and \( t \) in
second. Determine direction in which
wave is propagating.
Subject: Physics
For the system shown in figure, the cylinder on the left, at \( L, \) has a mass of \( 600 \mathrm{kg} \) and a cross-sectional area of \( 800 c m^{2} . \) The piston on the right, at \( S \)
has cross-sectional area \( 25 \mathrm{cm}^{2} \) and
negligible weight. If the apparatus is filled with oil \( \left(p=0.78 g / c m^{3}\right) \) what is
the force F required to hold the system in equilibrium?
Subject: Physics
The resistance of a wire of length 100
\( \mathrm{cm} \) and \( 7 \times 10^{-3} \mathrm{cm} \) radius is 6 ohm. Its
specific resistance is
\( \mathbf{A} \cdot 924 \times 10^{-8} \Omega c m \)
В. \( 92.4 \times 10^{-8} \Omega c m \)
c. \( 900 \times 10^{-8} \Omega c m \)
D. \( 224 \times 10^{-8} \Omega c m \)
Subject: Physics
A vessel contains oil (density =
\( 0.8 g / c m^{3} \) ) over mercury (density \( = \) \( \left.13.6 g / c m^{3}\right) . \) A uniform sphere floats with half its volume immersed in
mercury and the other half in oil. The
density of the material of sphere in \( \boldsymbol{g} / \boldsymbol{c m}^{3} \) is
A . 3.3
B. 6.4
c. 7.2
D. 12.8
Subject: Physics
A drawing pin is pushed against a wooden table with a force of \( 10 \mathrm{N} \)
Calculate the pressure exerted by the pin at a point on the table, if area of the
point is \( 0.01 \mathrm{cm}^{2} \)
\( \mathbf{A} \cdot 10^{5} P a \)
B . \( 10^{6} P a \)
\( \mathbf{c} \cdot 10^{7} P a \)
D. \( 10^{8} \mathrm{Pa} \)
Subject: Physics
The work function of metal is in the
range of \( 2 e V \) to \( 5 e V \). Find which of the
following wavelength of light cannot be used for photoelectric effect:
(Consider, Plank constant \( =\mathbf{4} \times \)
\( 10^{-15} e V s, \) velocity of light \( =3 x \)
\( \left.\mathbf{1 0}^{\mathbf{7}} \boldsymbol{m} / \boldsymbol{s}\right) \)
A. 510 nm
B. 650 nm
\( c .400 \mathrm{nm} \)
D. 570 nm
Subject: Maths
State True or False:
Addition of \( a-3 b+3,2 a+5 \)
\( \mathbf{3 c}, \mathbf{6 c}-\mathbf{1 5}+\mathbf{6 b} \) is \( \mathbf{3 a}+\mathbf{3 b}+\mathbf{3 c - 7} \)
A. True
B. False
Subject: Chemistry
The dissociation constants of two acids
\( \boldsymbol{H} \boldsymbol{A}_{1} \) and \( \boldsymbol{H} \boldsymbol{A}_{2} \) are \( \boldsymbol{3} . \boldsymbol{0} \times 10^{-4} \) and
\( 1.8 \times 10^{-5} \) respectively. The relative
strengths of the acids will be:
A .1: 4
в. 4: 1
c. 1: 16
D. 16: 1
Subject: Maths
The minimum value of \( p x+q y \) when
\( \boldsymbol{x} \boldsymbol{y}=\boldsymbol{r}^{2} \) is
A \( .2 r \sqrt{p q} \)
B. \( r \sqrt{p q} \)
c. \( r \sqrt{q / p} \)
D. None of the above
Subject: Chemistry
In the leaching of \( A g_{2} S \) with \( N a C N, \) a
stream of air is also passed. It is because of:

This question has multiple correct options
A . reversible namre of reaction between \( A g_{2} S \) and \( N a C N \)
B. oxidised \( N a_{2} S \) formed into \( N a_{2} S O_{4} \)
c. irreversible namre of reaction between \( A g_{2} S \) and \( ^{N a C N} \)
D. None of the above
Subject: Chemistry
A particle of mass \( M \) at rest decays
into two particles of mass \( m_{1} \) and \( m_{2} \)
having non-zero velocities. The ratio of
the de-Broglie wavelength of the
particles, \( \lambda_{1} / \lambda_{2} \) is:
\( \mathbf{A} \cdot m_{1} / m_{2} \)
в. \( m_{2} / m_{1} \)
\( c .1 .0 \)
D. none of these
Subject: Maths
For what value of \( k \) will \( x^{2}- \)
\( (3 k-1) x+2 k^{2}+2 k=11 \) have equal
roots?
\( \mathbf{A} \cdot 9,-5 \)
В. -9,5
\( c .9,5 \)
D. -9,-5
Subject: Maths
The area of the region bounded by the curve \( y=x^{2} \) and the line \( y=16 \) is
A \( \cdot \frac{128}{3} \) sq.units
в. \( \frac{64}{3} \) sq.units
c. \( \frac{32}{3} \) sq.units
D. \( \frac{256}{3} \) sq.units
Subject: Maths
Assertion
If \( x_{1}>0, i=1,2,3, \dots, 50 \) and \( \sum_{i=1}^{50} x_{i}= \)
\( \mathbf{5 0} \) then minimum value of \( \frac{\mathbf{1}}{\boldsymbol{x}_{\mathbf{1}}}+\frac{\mathbf{1}}{\boldsymbol{x}_{\mathbf{2}}}+ \)
\( +\frac{1}{x_{50}} \) is 50
Reason
\( \boldsymbol{A} \cdot \boldsymbol{M} \geq \boldsymbol{G} \boldsymbol{M} \)
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
Deuterio hydrate of magnesium sulphate contains how many molecules of heavy water?
\( A \cdot 2 D_{2} O \)
B. \( 3 D_{2} \) O
\( \mathrm{c} \cdot 10 \mathrm{D}_{2} \mathrm{O} \)
D. \( 7 D_{2} O \)
Subject: Chemistry
The pH of blood stream is maintained
by a proper balance of \( \boldsymbol{H}_{2} \boldsymbol{C O}_{3} \) and
\( N a H C O_{3} \) concentrations. What
volume of \( 5 M N a H C O_{3} \) solution
should be mixed with a \( 10 m L \) sample
of blood which is \( 2 M \) in \( H_{2} C O_{3} \) in
blood is \( 7.8 \times 10^{-7} ? \)
Subject: Chemistry
Give the IUPAC name of the following compounds:
\( \boldsymbol{O H} \)
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}- \)
\( \boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}- \)
\( \boldsymbol{C H}_{3} \)
\( \boldsymbol{C H}_{2}-\boldsymbol{C H}-\boldsymbol{C H}_{3} \)
Subject: Physics
3 spheres \( A, B \) and \( C \) having radii
\( R, 2 R \) and \( 3 R \) respectively are coated
with carbon black on their surfaces.
The wavelengths corresponding to
maximum intensity are 3000,4000 and
\( \mathbf{5 0 0 0} \) respectively. The power radiated
by them are \( Q_{A}, Q_{B} \) and \( Q_{C} . \) Then
A \( \cdot Q_{A} \) is maximum among all
B. \( Q_{B} \) is maximum among all
c. \( Q_{C} \) is maximum among all
D. \( Q_{A}=Q_{B}=Q_{C} \)
Subject: Maths
If the function \( \mathbf{f}(\boldsymbol{x})= \) \( \frac{\log (1+\boldsymbol{a} \boldsymbol{x})-\log (1-\boldsymbol{b} \boldsymbol{x})}{\boldsymbol{x}} \) for \( \boldsymbol{x} \neq \mathbf{0} \) is
continuous at \( x=0 \) then \( f(0)= \)
A \( . a-b \)
B. \( a+b \)
\( \mathbf{c} \cdot \log a+\log b \)
D. \( \log a-\log b \)
Subject: Chemistry
The \( C a(O H)_{2} \) is \( 4.42 \times 10^{-5} \) at \( 25^{\circ} C \)
with \( 500 m L \) of saturated solution of
\( C a(O H)_{2} \) is mixed with equal volume
of \( 0.4 M \) NaOH. How much \( C a(O H)_{2} \)
in \( m g \) is precipitated?
Subject: Physics
The figure shows a square plate of
uniform mass distribution. \( A A^{\prime} \) and
\( B B^{\prime} \) are the two axes lying in the plane
of the plate and passing through its
centre of mass. It \( I_{0} \) is the moment of
inertia of the plate about \( A A^{\prime} \) then its
moment of inertia. about the \( B B^{\prime} \) axis
is
\( A \cdot I_{b} \)
B \( \cdot I_{6} \cos \theta \)
\( \mathbf{c} \cdot I_{\theta} \cos ^{2} \theta \)
D. None of thes
Subject: Maths
If \( \Delta A B C \cong \Delta D E F, \angle A=47^{\circ}, \angle E= \)
\( 83^{\circ}, \) then the value of \( \angle C \) is:
A \( \cdot 47^{\circ} \)
B. 30
c. 40
\( D \cdot 50^{\circ} \)
Subject: Chemistry
Identify the correct increasing order of the stability of the following alkenes,
I.cis-2-butene;
II.trans-2-butene;
III. isobutene:
A. \( I I<I I I<I \)
в. \( I<I I I<I I \)
c. \( I<I I<I I I \)
D. \( I I I<I I<I \)
Subject: Maths
If \( \boldsymbol{x}^{\boldsymbol{y}}=\boldsymbol{a}^{\boldsymbol{x}}, \) prove that \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{\boldsymbol{x} \log _{e} \boldsymbol{a}-\boldsymbol{y}}{\boldsymbol{x} \log _{e} \boldsymbol{x}} \)
Subject: Chemistry
Consider the dehydrohalogenation of 2 bromo-2-methylhexane with methoxide and tert-butoxide.Which of the following statements is true?
A. Methoxide gives more and t-butoxide gives less Hofmann product
B. Methoxide gives more and t-butoxide gives less Saytzeff product
c. Saytzeff product is the major product in both cases
D. Hofmann product is major in both cases
Subject: Physics
A steel cylindrical rod of length \( l \) and
radius \( r \) is suspended by its end from
the ceiling. Define \( U \) in terms of tensile
\( \operatorname{strain} \frac{\Delta l}{l} \) of the rod
A \( \quad U=\frac{2}{3} \pi r^{2} l E\left(\frac{\Delta l}{l}\right)^{2} \)
в. \( U=\frac{4}{3} \pi r^{3} l E\left(\frac{\Delta l}{l}\right)^{3} \)
\( ^{\mathrm{c}} \cdot u=\frac{2}{4} \pi r^{3} l E\left(\frac{\Delta l}{l}\right)^{2} \)
D. None of these
Subject: Physics
In a semi-conducting material the
mobilities of electrons and holes are \( \mu_{e} \)
and \( \mu_{h} \) respectively. Which of the following is true?
A \( \cdot \mu_{e}>\mu_{h} \)
в. \( \mu_{e}<\mu_{h} \)
c. \( \mu_{e}=\mu_{h} \)
\( \mathbf{D} \cdot \mu_{e}=0 ; \mu_{h}>0 \)
Subject: Maths
Four points \( A(6,3), B(-3,5), C(4,-2) \) and \( D(x, 3 x) \) are given in such a way that \( \frac{A r e a(\Delta D B C)}{A r e a(\Delta A B C)}=\frac{1}{2} \) find \( x \)
This question has multiple correct options
A \( \cdot \frac{11}{8} \)
B. \( \frac{3}{8} \)
\( c \cdot \frac{9}{8} \)
D. None of these
Subject: Maths
Assertion
The points on the curve \( y^{2}=x+\sin x \)
at which tangent is parallel to x-axis lies on a straight line.
Reason Tangent is parallel to \( x \) -axis then \( \frac{d y}{d x}= \)
0 or \( \frac{d x}{d y}=\infty \)
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: Chemistry
Limestone is present in the blast furnace in production of iron in order to
\( (I) \) provide a source of \( C a O \)
\( (I I) \) remove some impurities
\( (\boldsymbol{I I I}) \) supply \( \boldsymbol{C O}_{2} \)
A. \( I, I I, I I I \)
в. \( I, I I \)
c. \( I I, I I I \)
D. I only
Subject: Chemistry
The standard reduction potential data
at \( 25^{\circ} \mathrm{C} \) is given below:
\( \mathbf{E}^{\mathrm{o}}\left(\mathbf{F e}^{\mathbf{3}+}, \mathbf{F e}^{\mathbf{2}+}\right)=+\mathbf{0 . 7 7} \mathbf{V} \)
\( \mathbf{E}^{\mathbf{o}}\left(\mathbf{F e}^{\mathbf{2}+}, \mathbf{F e}\right)=-\mathbf{0 . 4 4} \mathbf{V} \)
\( \mathbf{E}^{\mathrm{o}}\left(\mathbf{C u}^{2+}, \mathbf{C u}\right)=+\mathbf{0 . 3 4} \mathbf{V} \)
\( \mathbf{E}^{\circ}\left(\mathbf{C u}^{+}, \mathbf{C u}\right)=+\mathbf{0 . 5 2 V} \)
\( \mathbf{E}^{\mathrm{o}}\left[\mathbf{O}_{2}(\mathbf{g})+\mathbf{4 H}^{+}+\mathbf{4 e}^{-} \rightarrow \mathbf{2} \mathbf{H}_{\mathbf{2}} \mathbf{0}\right]= \)
\( +1.23 V \)
\( \mathbf{E}^{\circ}\left[\mathbf{O}_{2}(\mathbf{g})+\mathbf{2} \mathbf{H}_{2} \mathbf{O}+\mathbf{4} \mathbf{e}^{-} \rightarrow \mathbf{4 0} \mathbf{H}^{-}\right]= \)
\( +0.40 \mathrm{V} \)
\( \mathbf{E}^{\circ}\left(\mathbf{C r}^{3+}, \mathbf{C r}\right)=-\mathbf{0 . 7 4 V} \)
\( \mathbf{E}^{\mathbf{o}}\left(\mathbf{C r}^{2+}, \mathbf{C r}\right)=-\mathbf{0 . 9 1} \mathbf{V} \)
Match \( \mathrm{E}^{0} \) of the redox pair in List 1 with
the values given in List 2 and select the correct answer using the code given below the lists.
Subject: Chemistry
An ideal mono-atomic gas of given
mass is heated at constant pressure. In this process, the fraction of supplied energy used for the increase of the
internal energy of the gas is
A \( \cdot \frac{3}{8} \)
B. \( \frac{3}{5} \)
\( c \cdot \frac{3}{4} \)
D. \( \frac{2}{5} \)
Subject: Chemistry
Assertion
For a particular reaction, heat of
combustion at constant pressure \( \left(\boldsymbol{q}_{\boldsymbol{P}}\right) \)
is always greater than that at constant
volume \( \left(\boldsymbol{q}_{V}\right) \)
Reason
Combustion reactions are invariably
accomplished by increase in number of
moles.
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