AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
\( \left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C H}-\boldsymbol{C}- \)
\( \boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right)_{2} \frac{\left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C H} \boldsymbol{M} \boldsymbol{g} \boldsymbol{B r}}{\boldsymbol{H}_{3} \boldsymbol{O}^{+}}[\boldsymbol{N}]+[\boldsymbol{O}] \)
\( \overbrace{H_{2} O}^{\left(C H_{3}\right)_{2} C H-L i}[\mathrm{M}] \)
Then [M] is:
\( \mathbf{A} \cdot[\mathrm{M}] \) is \( C H_{3}-C H=C H_{2} \) while \( [\mathrm{N}] \) and \( [\mathrm{O}] \) are
\( \left[\left(C H_{3}\right)_{2} C H\right]_{3} \) СОН апа \( C H_{3}-C H=C H_{2} \)
B . \( [M] \) is \( \left(C H_{3}\right)_{2} C H-C H-C H\left(C H_{3}\right)_{2} \) while \( [N] \) and
\( [O] \operatorname{are}\left(C H_{3}\right)_{2} C H O H \) and \( C H_{3}-C H=C H_{2} \)
c. \( [M] \) is \( \left(C H_{3}\right)_{2} C H-_{\text {। }}^{C H}-C H\left(C H_{3}\right)_{2} \) while \( [N] \) and
\( [O] \operatorname{are}\left(\left(C H_{3}\right)_{2} C H\right)_{3} C-O H \) and \( C H_{3}-C H=C H_{2} \)
D - \( [M] \) is \( \left[\left(C H_{3}\right)_{2} C H\right]_{3} C-O H \) while \( [N] \) and \( [O] \) are
\( -S H \)
\( \left(C H_{3}\right)_{2} C H-C H-C H\left(C H_{3}\right)_{2} \) and \( C H_{3} \)
\( _{O H} \)
\( C H_{2} \)
Subject: Chemistry
\( 2 C H_{3} C O C H_{3}+6 C a O C l_{2} \rightarrow \)
\( \boldsymbol{C a}\left(\boldsymbol{C H}_{3} \boldsymbol{C O O}_{2}\right)_{2}+\boldsymbol{2 C H} \boldsymbol{C l}_{3}+ \)
\( \mathbf{3} C a C l_{2}+2 C a(O H)_{2} \)
If the yield of chloroform obtainable from acetone and bleaching powder is
\( 58 \% \). The weight of acetone required for
producing \( 47.8 \mathrm{g} \) of chloroform is :
A . 40
в. 20
\( c \cdot 4 \)
D. 10
Subject: Physics
A alatnermıc piscon alvıaes aalapatıc
cylinder of volume \( V_{0} \) into two equal
parts as shown in the figure.Both the parts contain ideal monoatomic gases.
The initial pressure and temperature of
gas in left compartment are \( P_{0} \) and \( T_{0} \)
while that in right compartment are
\( 2 P_{0} \) and \( 2 T_{0} . \) Initially the piston is kept
fixed and the system is allowed to
acquire a state of thermal equilibrium. The pressure in left compartment after
thermal equilibrium is achieved is:
\( A \cdot P_{o} \)
B. \( \frac{3}{2} P \)
\( c \cdot \frac{4}{3} P \)
D. None
Subject: Physics
Calculate the work done in stretching steel wire of length \( 2 \mathrm{m} \) and of cross sectional area \( 0.0225 m m^{2}, \) when a
load of \( 100 \mathrm{N} \) is applied slowly to its free end. (Young's modulus of steel = 20 x
\( \mathbf{1 0}^{\mathbf{1 0}} \mathbf{N} / \boldsymbol{m}^{\mathbf{2}} \mathbf{)} \)
Subject: Physics
Mirror formula can also be written as:
A \( \cdot \frac{1}{2 v}+\frac{1}{2 u}=\frac{1}{2 f} \)
B. \( \frac{1}{v}+\frac{1}{u}=\frac{2}{R} \)
c. \( \frac{1}{v}+\frac{2}{u}=\frac{1}{f} \)
D. \( \frac{1}{2 v}+\frac{4}{u}=\frac{3}{R} \)
Subject: Biology
Which the following commercial application of phytohormones are correct?
A. Auxins are extensively used in agriculture to promote flowering in pineapples
B. Ethephon is used for promoting female flower in cucumbers, thereby increase the yield
C. Abscisic acid is of great use in the ripening the fruits like mango, orange, pineapple etc.
D. Cytokinins are used for keeping freshness in leafy and green vegetables.
\( A \cdot a, b \) and \( c \)
B. b, cand d
\( c \cdot a, \) cand d
D. a band d
Subject: Chemistry
The carbon atoms in \( C_{2}(C N)_{4} \) are:
\( \mathbf{A} \cdot s p \) hybridized
B \( \cdot s p^{2} \) hybridized
C \( . s p \) and \( s p^{2} \) hybridized
D. \( s p, s p^{2} \) and \( s p^{3} \) hybridized
Subject: Maths
If \( \boldsymbol{I}_{n}=\int_{0}^{\frac{\pi}{4}} \tan ^{n} x d x \)
then \( \frac{1}{I_{2}+I_{4}}, \frac{1}{I_{3}+I_{5}}, \frac{1}{I_{4}+I_{6}} \) are in?
A . \( A . P \)
в. \( H . P \)
c. \( G . P \)
D. None of these
Subject: Maths
Evaluate
\( \int_{0}^{\sqrt{3}} \frac{1}{1+x^{2}} \cdot \sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right) d x \)
A \( \cdot \frac{5}{72} \pi^{2} \)
в. \( \frac{13}{144} \pi^{2} \)
c. \( \frac{7}{72} \pi^{\text {? }} \)
D. \( \frac{1}{12} \pi^{2} \)
Subject: Maths
A line touches a circle of radius \( 4 \mathrm{cm} \)
Another line is drawn which is tangent
to the circle. If the two lines are parallel then distance between them is
A \( .4 \mathrm{cm} \)
в. 6 ст
\( c .7 c m \)
D. \( 8 \mathrm{cm} \)
Subject: Physics
The decrease in potential energy between top position \( A \) and bottom position B is,
\( =\boldsymbol{m} \boldsymbol{g} \boldsymbol{r}-(-\boldsymbol{m} \boldsymbol{g} \boldsymbol{r})=\boldsymbol{2 m} \boldsymbol{g} \boldsymbol{r} \quad \ldots \)
This must be equal to the increase in kinetic energy, when particle move from \( A \) to \( B \)
i.e. \( \frac{1}{2} \boldsymbol{m} \boldsymbol{v}_{2}^{2}-\frac{1}{2} \boldsymbol{m} \boldsymbol{v}_{1}^{2} \)
Subject: Chemistry
Assertion
Boron always forms covalent bond.
Reason
The small size of \( B^{3+} \) favours
formations of covalent bond.
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
The observed dipole moment of \( H C l \) is 1.3 \( D \). If the bond length of \( H C l \) is \( 1.3 \dot{A} \)
then percentage ionic character of \( \boldsymbol{H}- \)
\( C l \) bond is nearly :
(Charge on electron \( =4.8 \times 10^{-10} \) esu)
A . \( 50 \% \)
B . \( 40 \% \)
\( c .30 \% \)
D. \( 17 \% \)
Subject: Maths
The value of \( \int \frac{d^{2}}{d x^{2}}\left(\tan ^{-1} x\right) d x \) is equal
to
A \( \cdot \frac{1}{1+x^{2}}+c \)
B. \( \tan ^{-1} x+c \)
c. \( x \tan -\frac{1}{2} \log \left(1+x^{2}\right)+C \)
D. \( \frac{1+x^{2}}{2}+c \)
Subject: Maths
Consider \( \mathbf{f}(\mathbf{x})=\left\{\begin{array}{l}\frac{x^{2}}{|x|}, \mathbf{x} \neq 0 \\ \mathbf{0}, \mathbf{x}=0\end{array}\right. \)
Then find the continuity of the function
\( f(x) \)
\( \mathbf{A} \cdot f(\mathrm{x}) \) is discontinuous every where
B. \( f(x) \) is continuous only at \( x=0 \)
C \( . f(x) \) is discontinuous everywhere except at \( x=0 \)
D. \( f(x) \) is continuous everywhere
Subject: Maths
Find a relationship between \( x \) and \( y \) so that the distance between the points
\( (x, y) \) and (-2,4) is equal to 5
A \( \cdot x^{2}+y^{2}+4 x-8 y-4=0 \)
B . \( x^{2}+y^{2}+4 x-8 y-5=0 \)
c. \( x^{2}+y^{2}+4 x-8 y-6=0 \)
D. \( x^{2}+y^{2}+4 x-8 y-53=0 \)
Subject: Physics
Light of wavelength \( 6000 \mathrm{nm} \) falls on a
p-njunction photodiode. This photodiode is fabricated from a semiconductor with a band gap of 2.8
eV. Then, which of the following statement is true?
A. This wavelength is not detected by the photodode
B. This wavelength is detected by the photodiode
c. Light is reflected back completely
D. None of the above
Subject: Physics
State expression for acceleration due to gravity at depth 'd' and altitude 'h' Hence show that ratio is equal to \( \frac{\boldsymbol{R}-\boldsymbol{d}}{\boldsymbol{R}-\mathbf{2} \boldsymbol{h}}, \) assuming that \( \boldsymbol{h}<\mathbf{R}, \) where \( \mathbf{R} \)
is radius of the earth.
Subject: Chemistry
Acid catalysed hydrolysis of the cyclic
acetal gives:
A. ethanal and 2 -chlorocyclohexanol
B. ethanol and 2 -chlorocyclohexanol
C. 1,2 -ethanediol and 2 -chlorocychlohexanone
D. 1,2 -ethanediol and 2 -chlorocyclohexanol
Subject: Maths
Let \( \alpha \) and \( \beta \) be the distinct roots of
\( a x^{2}+b x+c=0, \) then
\( \lim _{x \rightarrow \alpha} \frac{1-\cos \left(a x^{2}+b x+c\right)}{(x-\alpha)^{2}} \) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B \( \cdot \frac{1}{2} a^{2}(\alpha-\beta)^{2} \)
c. \( \frac{1}{2}(\alpha-\beta)^{2} \)
D. \( -\frac{1}{2} a^{2}(\alpha-\beta)^{2} \)
Subject: Maths
The middle term in the expansion of \( \left(\frac{a}{x}+b x\right)^{12} \)
A \( \cdot 924 a^{6} b^{6} \)
B. \( 924 a^{6} b^{5} \)
\( \mathbf{c} \cdot 924 a^{5} b^{5} \)
D. \( 924 a^{5} b^{6} \)
Subject: Maths
Inverse circular functions,Principal
values of \( \sin ^{-1} x, \cos ^{-1} x, \tan ^{-1} x \)
\[
\tan ^{-1} x+\tan ^{-1} y=\tan ^{-1} \frac{x+y}{1-x y}
\]
\( \boldsymbol{x} \boldsymbol{y}<\mathbf{1} \)
\[
\boldsymbol{\pi}+\tan ^{-1} \frac{\boldsymbol{x}+\boldsymbol{y}}{\mathbf{1}-\boldsymbol{x} \boldsymbol{y}}, \quad \boldsymbol{x} \boldsymbol{y}>1
\]
(a) \( \tan ^{-1} \frac{1}{2}+\tan ^{-1} \frac{1}{3}=\frac{\pi}{4} \)
\( (b) \tan ^{-1} \frac{1}{2}+\tan ^{-1} \frac{1}{5}+\tan ^{-1} \frac{1}{8}=\frac{\pi}{4} \)
\( (c) \tan ^{-1} \frac{3}{4}+\tan ^{-1} \frac{3}{5}-\tan ^{-1} \frac{8}{19}=\frac{\pi}{4} \)
Subject: Physics
A copper ball of density \( p_{c} \) and diameter
d is immersed in oil of density \( p_{o} . \) What
charge should be present on the ball, so that it could be suspended in the oil, if a homogeneous electric field E is applied vertically upward?
\( ^{\mathrm{A}} \cdot_{\mathrm{Q}}=\frac{\pi d^{2}\left(p_{c}-p_{0}\right) g}{6 E} \)
в. \( \quad Q=\frac{\pi d^{3}\left(p_{c}-p_{0}\right) g}{6 E} \)
c. \( _{Q}=\frac{\pi d^{3}\left(p_{c}-p_{0}\right) g}{E} \)
D. \( _{Q}=\frac{\pi d^{2}\left(p_{c}-p_{0}\right) g}{2 E} \)
Subject: Physics
Rays of light from Sun falls on a
biconvex lens of focal length \( f \) and the
circular image of Sun of radius \( r \) is formed on the focal plane of the lens. Then
A. Area of image is \( \pi r^{2} \) and area is directly proportional of \( f \)
B. Area of image is \( \pi r^{2} \) and area is directly proportional to \( t^{2} \)
c. Intensity of image increases if \( f \) is increased
D. If lower half of the lens is covered with black paper, area will become half
Subject: Maths
Find \( \frac{d y}{d x}, \) when
\( \boldsymbol{x}=\boldsymbol{a}(\mathbf{1}-\cos \boldsymbol{\theta}) \) and \( \boldsymbol{y}=\boldsymbol{a}(\boldsymbol{\theta}+\sin \boldsymbol{\theta}) \)
\( \operatorname{at} \theta=\frac{\pi}{2} \)
Subject: Physics
\( P \) and \( Q \) are two elements which form
\( P_{2} Q_{3} \) and \( P Q_{2} . \) If 0.15 mole of \( P_{2} Q_{3} \)
weight \( 15.9 \mathrm{g} \) and 0.15 mole of \( P Q_{2} \) weight 9.3 g. what are atomic weights of
\( P \) and \( Q ? \)
\( A \cdot 18 \) and 26
B. 26 and 26
c. 26 and 18
D. 18 and 18
Subject: Physics
The compass needle of the airplane shows that it is heading due North and
speedometer indicates a velocity
\( 240 k m h^{-1} . \) Wind is blowing \( 100 k m h^{-1} \)
due east. Find the velocity of airplane
with respect to earth.
A \( \cdot 260 m s^{-1}, 23^{\circ} \) East of North
B. \( 260 \mathrm{ms}^{-1}, 23^{\circ} \) West of North
\( \mathbf{c} \cdot 260 m s^{-1}, 32^{\circ} \) East of North
D. none of these
Subject: Chemistry
\( \boldsymbol{A} \rightleftharpoons \mathbf{2} \boldsymbol{B}, \boldsymbol{K}_{\boldsymbol{p}} \) and \( \boldsymbol{C} \rightleftharpoons \boldsymbol{D}+\boldsymbol{E}, \boldsymbol{K}_{\boldsymbol{p}^{*}}^{\prime} \) If
degrees of dissociation of \( A \) and \( C \) are
same and \( K_{p}=2 K_{p}^{\prime}, \) then the ratio of total pressure \( \frac{\boldsymbol{p}}{\boldsymbol{p}^{\prime}} \) is:
A. \( 1 / 2 \)
B. \( 1 / 3 \)
c. \( 1 / 4 \)
D. 2
Subject: Maths
\( \operatorname{Let} f(x)=\left\{\begin{array}{cc}-1, & -2 \leq x<0 \\ x^{2}-1, & 0<x \leq 2\end{array} \) and \right.
\( \boldsymbol{g}(\boldsymbol{x})=|\boldsymbol{f}(\boldsymbol{x})|+\boldsymbol{f}|\boldsymbol{x}| \) then the number
of points which \( g(x) \) is non
differentiable, is
A. at most one point
B. 2
c. exactly one point
D. infinite
Subject: Physics
Two painters are working from a wooden board \( 5 \mathrm{m} \) long suspended from the top of a building by two ropes attached to the ends of the plank. Either rope can withstand a maximum tension of 1040
N. Painter A of mass \( 80 \mathrm{kg} \) is working at
a distance of \( 1 \mathrm{m} \) from one end. Painter
B of mass \( 60 \mathrm{kg} \) is working at a
distance of \( x \) m from the centre of mass
of the board on the other side. Take
mass of the board as \( 20 \mathrm{kg} \) and \( g= \)
\( 10 m s^{-2} . \) The range of \( x \) so that both the
painters can work safely is :
A \( \cdot \frac{1}{3}<x<\frac{11}{6} \)
в. \( 0<x<\frac{11}{6} \)
c. \( _{0<x}<\frac{10}{3} \)
D. \( \frac{1}{3}<x<2 \)
Subject: Chemistry
State whether the given statement is true or false:
\( \boldsymbol{H} \boldsymbol{g}_{2} \boldsymbol{C l}_{2} \) is precipitated if \( \left[\boldsymbol{H} \boldsymbol{g}_{2}^{2+}\right]\left[\boldsymbol{C l}^{-}\right]^{2} \)
is greater than \( \boldsymbol{K}_{\boldsymbol{s p}}\left(\boldsymbol{H} \boldsymbol{g}_{2} \boldsymbol{C l}_{2}\right) \)
Subject: Physics
Two blocks of masses \( 2 k g \) and \( 1 k g \)
respectively are tied to the ends of a
strings which passes over a light
frictionless pulley. The masses are held
at rest at the same horizontal level and
then released. The distance traversed by
centre of mass in 2 seconds is: \( (g= \)
\( \left.10 m / s^{2}\right) \)
A \( .1 .42 m \)
B. \( 2.22 m \)
c. \( 3.12 m \)
D. \( 3.33 m \)
Subject: Chemistry
The products formed when heavy water
is reacted with magnesium nitride, is/are
A \( \cdot N H_{3} M g(O H)_{2} \)
В \( \cdot \operatorname{NH}_{3} M g(O D)_{2} \)
\( \mathbf{c} \cdot_{N D_{3}} M g(O H)_{2} \)
D. \( _{N D_{3} M g}(O D)_{2} \)
Subject: Maths
In the given figure, if area of \( \triangle A D E \) is
\( 60 \mathrm{cm}^{2} ; \) state, giving reason, the area of
\( \triangle A B E \)
A \( \cdot 60 \mathrm{cm}^{2} \)
В. \( 120 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 160 \mathrm{cm}^{2} \)
D. \( 210 \mathrm{cm}^{2} \)
Subject: Physics
The equivalent capacitance between
points \( \mathrm{M} \) and \( \mathrm{N} \) is :
A . Infinity
в. \( c_{1}+\frac{C_{2}}{C_{1}} \)
\( c_{C_{2}+\frac{C_{2}}{C_{1}}} \)
D. \( \frac{C_{1} C_{2}}{C_{1}+C_{2}} \)
Subject: Chemistry
\( 32 g \) of oxygen and \( 3 g \) of hydrogen are mixed and kept in a vessel at 760 mm
pressure and \( 0^{\circ} \mathrm{C} \). The total volume occupied by the mixture will be nearly:
A . 22.4 litre
B. 11.2 litre
c. 44.8 litre
D. 56 litre
Subject: Physics
A block of mass \( 5 \mathrm{kg} \) rests on a rough horizontal surface. It is found that a
force of \( 10 \mathrm{N} \) is required to make the block just move. However, once the motion begins, a force of only \( 8 \mathrm{N} \) is enough to maintain the motion. Find the
coefficients of kinetic and static
friction between the block and the
horizontal surface.
\( \sqrt{38}-7 \)
Subject: Physics
A man fired a bullet against a wall and hears an echo after 2 s. He walks 80 m
towards the wall and fired bullet, such that he hears echo after 1 s. Find the
distance from wall to the second fired
place
A . \( 140 \mathrm{m} \)
B. 150 \( m \)
\( c .80 \mathrm{m} \)
D. 170 \( m \)
Subject: Physics
One \( k g \) of water, at \( 20^{\circ} C \), is heated in an
electric kettle whose heating element has a mean (temperature averaged) resistance of \( 20 \Omega \). The rms voltage in the mains is \( 200 \mathrm{V} \). Ignoring heat loss from the kettle. time taken for water to
evaporate folly. is close to:
[Specific heat of water \( =4200 J / k g^{o} C \)
, Latent heat of water \( =\mathbf{2 2 6 0} \boldsymbol{k} \boldsymbol{J} / \boldsymbol{k g}] \)
A. 3 minutes
B. 22 minutes
c. 10 minutes
D. 16 minutes
Subject: Chemistry
Which of the following represents the chemical equation involved in the
preparation of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) from barium
peroxide?
A \( \cdot B a O_{2} \cdot 8 H_{2} O+H_{2} S O_{4} \rightarrow B a S O_{4}+H_{2} O_{2}+8 H_{2} O \)
в. \( C H_{3} C H O H C H_{3} \rightarrow C H_{3} C O O C H_{3}+H_{2} O_{2} \)
\( \mathbf{c} \cdot B a O_{2}+C O_{2}+H_{2} O \rightarrow B a C O_{3}+H_{2} O_{2} \)
D. \( B a_{3}\left(P O_{4}\right)_{2}+3 H_{2} S O_{4} \rightarrow 3 B a S O_{4}+2 H_{3} P O_{4} \)
Subject: Physics
Four plates of same area of cross-
section are joined as shown in figure. The distance between each plate is d.
The equivalent capacity between \( A \) and
B will be
A \( \cdot \frac{2 \epsilon_{0} A}{d} \)
B. \( \frac{\epsilon_{0} A}{d} \)
с. \( \frac{3 \epsilon_{0} A}{d} \)
D. \( \frac{3 \epsilon_{0} A}{2 d} \)
Subject: Maths
A rhombus has sides of length \( 1 \mathrm{cm} \) and the area \( \frac{1}{2} c m^{2} \). Find the angle between the two adjacent sides of the rhombus.
\( \mathbf{A} \cdot 60^{\circ} \)
B . 75
\( c \cdot 45 \)
D. \( 30^{\circ} \)
Subject: Physics
The circuit shown given contains two
ideal diodes, each with a forward
resistance of \( 50 \Omega \). If the battery voltage
is \( 6 \mathrm{V} \), the current through the \( 100 \Omega \) resistance (in Amperes) is?
A .0 .027
В. 0.020
\( c .0 .030 \)
D. 0.036
Subject: Physics
A toy car with charge \( q \) moves on a frictionless horizontal plane surface under the influence of a uniform electric field \( \vec{E} \). Due to the force \( \boldsymbol{q} \overrightarrow{\boldsymbol{E}} \), its
velocity increases from 0 to 6 m/s in
one second duration. At that instant the
direction of the field is reversed. The car
continues to move for two more seconds
under the influence of this field. The
average velocity and the average speed
of the toy car between 0 to 3 seconds
are respectively
A \( .2 \mathrm{m} / \mathrm{s}, 4 \mathrm{m} / \mathrm{s} \)
B. \( 1 \mathrm{m} / \mathrm{s}, 3.5 \mathrm{m} / \mathrm{s} \)
c. \( 1 \mathrm{m} / \mathrm{s}, 3 \mathrm{m} / \mathrm{s} \)
D. \( 1.5 \mathrm{m} / \mathrm{s}, 3 \mathrm{m} / \mathrm{s} \)
Subject: Maths
Evaluate: \( \lim _{x \rightarrow \infty} \frac{\sin ^{4} x-\sin ^{2} x+1}{\cos ^{4} x-\cos ^{2} x+1} \) is
equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B.
c. \( \frac{1}{2} \)
D.
Subject: Chemistry
The equilibrium constant for the redox change
\( \left[2 A g\left(N H_{3}\right)_{2}^{+}+C_{6} H_{12} O_{6}+H_{2} O \rightarrow\right. \)
\( \boldsymbol{C}_{6} \boldsymbol{H}_{12} \boldsymbol{O}_{7}+\boldsymbol{2} \boldsymbol{A} \boldsymbol{g}(\boldsymbol{s})+\boldsymbol{C}_{6} \boldsymbol{H}_{12} \boldsymbol{O}_{2}+ \)
\( \left.\mathbf{2} \boldsymbol{H}^{+}\right] \) is:
\( \mathbf{A} \cdot 5.15 \times 10^{9} \)
В. \( 4,2 \times 10^{5} \)
c. \( 1.72 \times 10^{-11} \)
Subject: Physics
Fig shown below represents an area
\( A=0.5 m^{2} \) situated in a uniform
magnetic field \( B=2.0 w e b e r / m^{2} \) and
making an angle of \( 60^{\circ} \) with respect to
magnetic field. The value of the
magnetic flux through the area would be equal to:
A. 2.0 weber
B. \( \sqrt{3} \)weber
c. \( \sqrt{3} / 2 \) weber
D. 0.5 weber
Subject: Chemistry
Two bars of same length and same cross -sectional area but of different
thermal conductivities \( K_{1} \) and \( K_{2} \) are
joined end to end as shown in the figure One end of the compound bar is at
temperature \( T_{1} \) and the opposite end at
temperature \( T_{2}\left(w h e r e T_{1}>T_{2}\right) \)
The temperature of the junction is
\( \mathbf{A} \)
\[
\frac{K_{1} T_{1}+K_{2} T_{2}}{K_{1}+K_{2}}
\]
B.
\[
\frac{K_{1} T_{2}+K_{2} T_{1}}{K_{1}+K_{2}}
\]
c. \( \frac{K_{1}\left(T_{1}+T_{2}\right)}{K_{2}} \)
D.
\[
\frac{K_{2}\left(T_{1}+T_{2}\right)}{K_{1}}
\]
Subject: Physics
A square frame of side \( 10 \mathrm{cm} \) and a long straight wire carrying current \( 1 A \) are in
the plane of the paper. Starting from close to the wire, the frame moves
towards right with a constant speed of \( 10 m / s \) (see figure). The e.m.f.
induced at the time the left arm of the
frame is at \( x=10 \mathrm{cm} \) from the wire is:
A. \( 2 \mu V \)
B. \( 1 \mu V \)
c. \( 0.75 \mu V \)
D. \( 0.5 \mu V \)
Subject: Maths
The number of continuous functions on
R which satisfy \( (f(x))^{2}=x^{2} \) for all \( x \in \)
\( \boldsymbol{R} \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c \cdot 4 \)
D. 8
Subject: Physics
A copper ball of mass \( 100 g m \) is at a
temperature \( T . \) It is dropped in a copper
calorimeter of mass \( 100 g m \), filled with
\( 170 g m \) of water at room temperature. Subsequently the temperature of the system is found to \( 6475^{\circ} . T \) is given by
then (Given: room temperature \( =\mathbf{3 0}^{\circ} \boldsymbol{C} \)
specific heat of copper \( = \) \( \mathbf{0 . 1} c \mathbf{a l} / \mathbf{g m}^{o} \boldsymbol{C} \)
A. \( 825^{\circ} \mathrm{C} \)
в. \( 800^{\circ} \mathrm{C} \)
c. \( 885^{\circ} \mathrm{C} \)
D. \( 1250^{\circ} \mathrm{C} \)
Subject: Physics
\( A C B \) is right-angled prism with other
angles as \( 60^{\circ} \) and \( 30^{\circ} . \) Refractive index
of the prism is \( 1.5 . A B \) has thin layer of
liquid on it as shown. Light falls
normally on the face \( A C . \) For total
internal reflections, maximum
refractive index of the liquid is
\( \mathbf{A} \cdot 1.4 \)
B. 1.3
c. 1.2
D. 1.6
Subject: Physics
f maximum energy is stored in
capacitor at \( t=0 \) then find the time
after which current in the circuit will be
maximum.
\[
\mathrm{L}=25 \mathrm{mH}
\]
A. \( \frac{\pi}{2} m s \)
в. \( \frac{\pi}{4} m s \)
\( c . \pi m s \)
D. \( 2 m \)
Subject: Maths
The modal class of the given frequency distribution is
\( \begin{array}{llll}\text { Marks } & \mathbf{1 0}- & \mathbf{2 0}- & \mathbf{3 0}- \\ \text { Obtained } & \mathbf{2 0} & \mathbf{3 0} & \mathbf{4 0}\end{array} \)
7 35 Cumulative
Frequency 27
A . \( 10-20 \)
в. \( 30-40 \)
\( c \cdot 20-30 \)
D. \( 40-50 \)
Subject: Maths
When the base of a triangle is increased by \( 10 \% \) and the altitude to this base is
decreased by \( 10 \% \), the change in area is
A . \( 1 \% \) increase
B. \( \frac{1}{2} \% \) increase
\( c .0 \% \)
D. \( 1 \% \) decrease
Subject: Chemistry
In Allene \( \left(C_{3} H_{4}\right), \) the type(s) of
hybridization of the carbon atoms is \( (\operatorname{are}) ? \)
A. \( s p \) and \( s p^{3} \)
B. \( s p \) and \( s p^{2} \)
C . only \( s p^{2} \)
D. \( s p^{2} \) and \( s p^{3} \)
Subject: Maths
Find the value of \( x \) if \( \sin (\arcsin x)= \)
\( \frac{\sqrt{2}}{4} \)
A \( \cdot \frac{\sqrt{2}}{4} \)
B. \( \frac{\sqrt{7}}{7} \)
c. \( \frac{\sqrt{2}}{2} \)
D. \( \frac{2 \sqrt{2}}{3} \)
Subject: Maths
If \( x^{2}-2 x^{2} y^{2}+5 x+y-5=0 \) and
\( \boldsymbol{y}(1)=1, \) then
This question has multiple correct options
A \( \cdot y^{\prime}(1)=1 \)
в. \( y^{\prime \prime}(1)=-\frac{4}{3} \)
c. \( \quad y^{\prime \prime}(1)=-\frac{22}{3} \)
D. \( y^{\prime}(1)=\frac{2}{3} \)
Subject: Physics
What is the refractive index of material
of a plano-convex lens, if the radius of curvature of the convex surface is \( 10 \mathrm{cm} \) and focal length of the lens is \( 30 \mathrm{cm} ? \)
A \( \cdot \frac{6}{5} \)
B. \( \frac{7}{4} \)
\( c \cdot \frac{2}{3} \)
D. \( \frac{4}{3} \)
Subject: Physics
A train of length 200 m travelling at 30 \( m s^{-1} \) overtakes another train of length
\( 300 \mathrm{m} \) travelling at \( 20 \mathrm{ms}^{-1} \). The time
taken by the first train to pass the second is
A . 30 sec
B. 40 sec
c. \( 50 \mathrm{sec} \)
D. 60 sec
Subject: Maths
State True or False.
\( \mathbf{2} a^{2}+2 b^{2}+2 c^{2}-2 a b-2 b c-2 c a= \)
\( \left[(a-b)^{2}+(b-c)^{2}+(c-a)^{2}\right] \)
A. True
B. False
Subject: Physics
Sunlight of intensity \( 1.3 k W m^{-2} \) is
incident normally on a thin convex lens of focal length \( 20 \mathrm{cm} \). Ignore the energy loss of light due to the lens and assume
that the lens aperture size is much smaller than its focal length. The
average intensity of light, in \( k W m^{-2}, \) at
a distance \( 22 c m \) from the lens on the
other side is
Subject: Chemistry
A definite amount of gaseous
hydrocarbon was burnt with just
sufficient amount of \( O_{2} \). The volume of all reactants was \( 600 \mathrm{ml} \), after the explosion the volume of products
\( \left[\boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g}) \text { and } \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g})\right] \) was found to be
700 ml under the similar conditions.
The molecular formula of the compound
is :
A. \( C_{3} H_{8} \)
в. \( C_{3} H_{6} \)
c. \( c_{3} H_{4} \)
D. \( C_{4} H_{10} \)
Subject: Chemistry
The IUPAC name of the structure is:
A. 5 -Amino-3-bromo-5-methyl-6-nitroundec-3-en-2-ol
B. 9-Amino-3-bromo-7-methyl-4-nitroundec-2-en-2-ol
C. 10 -Amino-8-bromo-7-methyl-6-nitroundec-4-en-2-ol
D. 2-Amino-6-bromo-5-methyl-4-nitroundec-2-en-2-ol