AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
The correct order of lattice energy is:
\( \mathbf{A} \cdot L i F>C a F_{2}>M g O \)
B. \( M g O>C a F_{2}> \) LiF
\( \mathbf{c} \cdot C a F_{2}>M g O>L i F \)
D. \( C a F_{2}>L i F>M g O \)
Subject: Maths
If \( \tan \alpha=2, \) then the value of
\( \frac{\sin \alpha}{\sin ^{3} \alpha+\cos ^{3} \alpha} \) is
\( A \cdot \frac{2}{9} \)
в. \( \frac{5}{9} \)
c. \( \frac{10}{9} \)
D. \( \frac{5.5}{9} \)
Subject: Chemistry
\( \boldsymbol{B r} \boldsymbol{O}_{3}^{-}(\boldsymbol{a q})+\mathbf{5 B r}_{(a q)}^{-}+\boldsymbol{6 H}^{+} \rightarrow \)
\( \mathbf{3} \boldsymbol{B r}_{2}(\mathbf{1})+\mathbf{3} \boldsymbol{H}_{2} \boldsymbol{O}_{(1)} \).The rate of
apprearance of bromine \( \left(B r_{2}\right) \) is related
to rate of disappearance of bromide ions as following:
A \( \cdot \frac{d\left(B r_{2}\right)}{d t}=-\frac{5}{3} \frac{d\left(B r^{-}\right)}{d t} \)
B. \( \frac{d\left(B r_{2}\right)}{d t}=\frac{5}{3} \frac{d\left(B r^{-}\right)}{d t} \)
C \( \cdot \frac{d\left(B r_{2}\right)}{d t}=\frac{3}{5} \frac{d(B r)}{d t} \)
D. \( \frac{d\left(B r_{2}\right)}{d t}=-\frac{3}{5} \frac{d\left(B r^{-}\right)}{d t} \)
Subject: Maths
\( A B C \) is a triangle in which \( A B= \)
\( A C=4 \mathrm{cm} \) and \( \angle A=90^{\circ} . \) Calculate
the length of perpendicular from \( \boldsymbol{A} \) to \( \boldsymbol{B C} \)
A. \( 2.83 \mathrm{cm} \)
B. \( 1.414 \mathrm{cm} \)
\( c .2 .6 \mathrm{cm} \)
D. 2.20 cm
Subject: Physics
The M.I. of a disc about an axis passing through its centre and perpendicular to plane is \( \frac{1}{2} M R^{2}, \) then its M.I. about a tangent parallel to its diameter is
\( ^{\mathbf{A}} \cdot \frac{1}{2} M R^{2} \)
в. \( \frac{4}{5} M R^{2} \)
c. \( \frac{5}{4} M R^{2} \)
D. \( \frac{3}{4} M R^{2} \)
Subject: Maths
By selling pens at 4 for \( R s .10 \), a shopkeeper makes a profit of \( 20 \% \) on the cost price. If he sells them at \( R s . x \)
per dozen, he loses \( 10 \% \) on the cost
price. Calculate \( \boldsymbol{x} \)
A. \( R s .18 .50 \)
B. \( R s .22 .50 \)
c. \( R s .20 \)
D. \( R s .18 .75 \)
Subject: Physics
In a potentiometer using two cells in series gives a balance length of \( 600 \mathrm{cm} \) When the same cells are connected
opposing each other then balance length is \( 100 \mathrm{cm} \). The ratio of
emf of larger to smaller cell is:
A .7: 5
в. 5: 7
\( c \cdot 6: 1 \)
D. 1: 6
Subject: Chemistry
The energy required to break one mole
of hydrogen-hydrogen bonds in \( H_{2} \) is \( 436 k J . \) What is the longest wavelength
of light required to break a single hydrogen-hydrogen bond?
A \( .68 .5 \mathrm{nm} \)
в. 137 пт
\( c .274 n m \)
D. 548 пт
Subject: Physics
A block of mass \( 2 k g \) is placed on the floor. The coefficient of static friction is
0.4. Force of \( 2.8 N \) is applied on the
block. The force of friction between the
block and the floor is (Taken \( g= \)
\( \left.10 m / s^{2}\right) \)
\( A \cdot 2.8 \mathrm{N} \)
B. 8 N
c. 2.0 N
D. zero
Subject: Chemistry
A solution contains \( 20 \% \) solute by
weight at \( 60^{\circ} \) C. When cooled to \( 30^{\circ} \mathrm{C} \)
the solution contains \( 10 \% \) solute by weight. When 45 g solution is cooled from \( 60^{\circ} \mathrm{C} \) to \( 30^{\circ} \mathrm{C} \), the mass of solute
deposited is :
A. \( 4.5 \mathrm{g} \)
B. 48
\( c \cdot 5 g \)
D. \( 4.75 \mathrm{g} \)
Subject: Maths
Inverse circular functions,Principal values of \( \sin ^{-1} x, \cos ^{-1} x, \tan ^{-1} x \)
\[
\tan ^{-1} x+\tan ^{-1} y=\tan ^{-1} \frac{x+y}{1-x y}
\]
\( x y<1 \)
\( \boldsymbol{\pi}+\boldsymbol{\operatorname { t a n }}^{-1} \frac{\boldsymbol{x}+\boldsymbol{y}}{1-\boldsymbol{x} \boldsymbol{y}}, \quad \boldsymbol{x} \boldsymbol{y}>1 \)
(a) If \( \tan ^{-1} \frac{\sqrt{1+x^{2}}-\sqrt{1-x^{2}}}{\sqrt{\left(1+x^{2}\right)}+\sqrt{\left(1+x^{2}\right)}}= \)
\( \alpha . \) then prove that \( x^{2}=\sin 2 \alpha \)
(b) If \( \frac{\operatorname{mtan}(\alpha-\theta)}{\cos ^{2} \theta}=\frac{n \tan \theta}{\cos ^{2}(\alpha-\theta)} \)
then prove that \( \boldsymbol{\theta}= \) \( \frac{1}{2}\left[\alpha-\tan ^{-1}\left(\frac{n-m}{n+m} \tan \alpha\right)\right] \)
(c) \( \cos ^{-1} \frac{\cos \alpha+\cos \beta}{1+\cos \alpha \cos \beta}= \)
\( 2 \tan ^{-1}\left(\tan \frac{\alpha}{2} \tan \frac{\beta}{2}\right) \)
Subject: Chemistry
Consider the following statements and arrange in the order of true/false as given in the codes.
\( S_{1}: \) Sodium amalgam reacts with hot water and produces sodium hydroxide and hydrogen gas.
\( S_{2}: \) Sodium is more reactive than
potassium.
\( S_{3}: \) Alkaline earth metals dissolve in liquid ammonia to give deep blue-black solutions which are conducting.
\( S_{4}: \) Alkaline earth metal salts have
more number of water molecules as
compared to those of alkali metal salts.
A. TTFF
в. тFा
c. FTT
D. TFFT
Subject: Maths
\( \int \frac{e^{x}-1}{e^{x}+1} d x \)
A \( \cdot \log \left(e^{x}+1\right)-\log e^{x} \)
B \( \cdot 2 \log \left(e^{x}-1\right)-\log e^{x} \)
C \( \cdot 2 \log \left(e^{x}+1\right)-\log e^{x} \)
D \( \cdot 2 \log \left(e^{x}+1\right)+\log e^{x} \)
Subject: Physics
A stone is thrown with an initial speed
of \( 4.9 \mathrm{m} s^{-1} \) from a bridge in the vertically upward direction. It falls down in water after 2 s. The height of the bridge is :
A . 24.7 \( \mathrm{m} \)
B. 19.8 \( m \)
c. \( 9.8 \mathrm{m} \)
D. 4.9 \( m \)
Subject: Physics
\( \mathrm{R} \) is a radius of a planet and \( \rho \) is its
density. The escape velocity on its surface will be
A \( \cdot R^{2} \sqrt{4 \pi G \rho / 3} \)
в. \( R \sqrt{4 \pi G \rho / 3} \)
c. \( R^{2} \sqrt{8 \pi G \rho / 3} \)
D. \( R \sqrt{8 \pi G \rho / 3} \)
Subject: Chemistry
product in each of the following
reactions:
(i) \( C H_{3} C H_{2} C H_{2} C l+N a I \frac{\text { acetone }}{h e a t} \)
(ii) \( \left(C H_{3}\right)_{3} C B r+K O H \frac{e \text {thanol}}{\text {heat}} \)
(iii) \( C H_{3} C H(B r) C H_{2} C H_{3}+ \)
\( N a O H \stackrel{w a t e r}{\longrightarrow} \)
(iv) \( \left(C H_{3}\right)_{3} C B r+K O H \frac{\text {ethanol}}{\text {heat}} \)
(v) \( C_{6} H_{5} O N a+C_{2} H_{5} C l \longrightarrow \)
\( (\mathrm{vi}) C H_{3} C H_{2} C H_{2} O H+S O C l_{2} \longrightarrow \)
(vii) \( C H_{3} C H_{2} C H=C H_{2}+ \)
\( \boldsymbol{H} \boldsymbol{B} \boldsymbol{r} \stackrel{\text {peroxide}}{\longrightarrow} \)
\( \left(\text { viii) } \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C H}=\boldsymbol{C}\left(\boldsymbol{C H}_{3}\right)_{2}+\right. \)
\( \boldsymbol{H} \boldsymbol{B} \boldsymbol{r} \longrightarrow \)
Subject: Biology
Juxta-glomerular apparatus is made up
of
A. Juxta-glomerular cell, macula densa and lacis cell
B. Juxta-glomerular cell, Purkinjee cell and chief cell
C. Juxta-glomerular cell, lacis cell and myoepithelial cell
D. Juxta-glomerular cell, macula densa and argentaffin cell
Subject: Physics
A force of \( \left(4 x^{2}+3 x\right) N \) acts on a
particle which displaces it from \( \boldsymbol{x}= \)
\( 2 m \) to \( x=3 m . \) Te work done by the force
is:
A . \( 32.8 \mathrm{J} \)
B. \( 3.281 J \)
c. \( 0.328 J \)
D. zero
Subject: Biology
Read the statements 1 and 2 . Choose the
correct option:
Statement 1: RNAi take place in all prokaryotic and eukaryotic organisms as a method ofcellular defence.

Statement 2: RNA interference is a pre-
translational process.
A. Both statements are correct
B. Statement I correct, statement 2 incorrect
c. Both statements are incorrect
D. Statement-1 incorrect, statement 2 correct.
Subject: Maths
A symmetrical form of the line of intersection of the planes \( \boldsymbol{x}=\boldsymbol{a} \boldsymbol{y}+\boldsymbol{b} \)
and \( \boldsymbol{z}=\boldsymbol{c} \boldsymbol{y}+\boldsymbol{d} \) is :
A. \( \frac{x-b}{a}=\frac{y-1}{1}=\frac{z-d}{c} \)
\( ^{\text {В }} \cdot \frac{x-b-a}{a}=\frac{y-1}{1}=\frac{z-d-c}{c} \)
c. \( \frac{x-a}{b}=\frac{y-0}{1}=\frac{z-c}{d} \)
D. \( \frac{x-b-a}{b}=\frac{y-1}{0}=\frac{z-d-c}{d} \)
Subject: Chemistry
An aqueous solution of a gas \( (\boldsymbol{X}) \) shows the following reactions.
(i) It turns red litmus blue.
(ii) When added in excess to a \( C u S O_{4} \)
solution, a deep blue colour is obtained.
(iii) On addition of \( F e C l_{3} \) solution, a
brown precipitate soluble in dilute
\( H N O_{3} \) is obtained
Then the gas \( (\boldsymbol{X}) \) will be :
\( A \cdot S O_{2} \)
в. \( N H_{3} \)
\( c \cdot N O_{2} \)
D. \( N_{2} \) O
Subject: Maths
The range of the function, \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left(1+\sec ^{-1} x\right)\left(1+\cos ^{-1} x\right) \) is
\( A \cdot(-\infty, \infty) \)
В \( \cdot(-\infty, 0] \cup[4, \infty) \)
\( ^{c} \cdot\left\{0,(1+\pi)^{2}\right\} \)
D. \( \left[1,(1+\pi)^{2}\right] \)
Subject: Chemistry
Which one of the following sets of ions represents a collection of isoelectronics
species?
A. \( K^{+}, C l^{-}, C a^{2+} \)
B. \( B a^{2+}, S r^{2+}, K^{+}, C a^{2+} \)
c. \( N^{3}-, O^{2-}, C a^{2+}, S^{2} \)
D. \( L i^{+}, N a^{+}, M g^{2+}, C a^{2+} \)
Subject: Physics
The coefficient of apparent volume expansion of a liquid in a copper vessel is \( C \) and in a silver vessel is \( S \). The
coefficient of volume expansion of
copper is \( \gamma_{c} . \) What is the coefficient of linear expansion of silver?
A \( \cdot \frac{\left(C+\gamma_{c}+S\right)}{3} \)
в. \( \frac{\left(C-\gamma_{c}+S\right)}{3} \)
c. \( \frac{\left(C+\gamma_{c}-S\right)}{3} \)
D. \( \frac{\left(C-\gamma_{c}-S\right)}{3} \)
Subject: Physics
A conducting wire in the shape of \( Y \)
with each side of length \( l \) is moving in a uniform magnetic field B, with a uniform speed v as shown in the figure.
The induced emf at the two ends \( X \) and
Y of the wire will be
A. zero
в. 2Blv
\( c . \) 2Blv \( \sin (\theta / 2) \)
D. 2Blv \( \cos (\theta / 2) \)
Subject: Maths
Value of \( \left|\begin{array}{lll}\sin \alpha & \cos \alpha & \sin \alpha+\cos \beta \\ \sin \beta & \cos \alpha & \sin \beta+\cos \beta \\ \sin \gamma & \cos \alpha & \sin \gamma+\cos \beta\end{array}\right| \) is
\( A \cdot \sin \alpha+\sin \beta+\sin \gamma \)
B. \( \cos \alpha+\cos \beta+\cos \gamma \)
\( \mathbf{c} \cdot \sin \alpha-\sin (\alpha+\beta)-\cos \alpha+\cos (\gamma+\beta) \)
\( D \)
Subject: Maths
\( \boldsymbol{X} \) has three children in his family. Probability of atleast two girls in the family is....
A \( \cdot \frac{1}{8} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{1}{4} \)
D. \( \frac{3}{4} \)
Subject: Physics
Q Type your question
following statements:
It will be easier to compress this
rubber then expand it
II. Rubber does not return to its
original length after it is stretched
III. The rubber band will get heated if it
is stretched and released.

Which of these can be deduced from the
graph?
A. III only
B. II and III
c. \( I \) and \( I I I \)
D. I only
Subject: Maths
If \( a^{2}+10 b^{2}+5 c^{2}+6 a b+2 b c-16 c+ \)
\( \mathbf{1 6}=\mathbf{0} \) then the possible value of \( \boldsymbol{a}- \)
\( b+c= \)
A . 5
B. -3
\( c \cdot-2 \)
D. 10
Subject: Maths
If \( S \) is any point in the interior of \( \Delta P Q R \) prove that \( (\boldsymbol{S} \boldsymbol{Q}+\boldsymbol{S} \boldsymbol{R})<(\boldsymbol{P} \boldsymbol{Q}+\boldsymbol{P} \boldsymbol{R}) \)
Subject: Biology
Assertion
"Fungi imperfect does not show
alternation of generation.
Reason
The diploid phase is present in only
zygote.
A. If both the assertion and the reason are true and the
reason
is a correct explanation of the assertion
B. If both the assertion and reason are true but the reason is
not a correct explanation of the assertion
C. If the assertion is true but the reason is false
D. If both the assertion and reason are false
Subject: Chemistry
Which of the following complex ions absorbs the light of minimum wavelength?
\( ^{\mathrm{A}} \cdot\left[C o\left(H_{2} O\right)_{6}\right]^{3+} \)
B \( \cdot\left[\mathrm{CoF}_{6}\right]^{3-} \)
\( \mathbf{c} \cdot\left[\operatorname{Co}(C N)_{6}\right]^{3-} \)
D \( \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{6}\right]^{3+} \)
Subject: Chemistry
Acidity of diprotic acids in aqueous
solutions increases in the order
A. \( H_{2} S<H_{2} S e<H_{2} T e \)
в. \( H_{2} S e<H_{2} S<H_{2} T e \)
c. \( H_{2} T e<H_{2} S<H_{2} S e \)
D. \( H_{2} S e<H_{2} T e<H_{2} S \)
Subject: Physics
Two long straight cylindrical conductors
with resistivities \( \rho_{1} \) and \( \rho_{2} \) respectively
are joined together as shown in figure. If current I flows through the conductors, the magnitude of the total free charge at the interface of the two conductors is
A . zero
в. \( \frac{\left(\rho_{1}-\rho_{2}\right) I \varepsilon_{0}}{2} \)
\( \mathbf{c} \cdot \varepsilon_{0} I\left|\rho_{1}-\rho\right| \)
\( \mathbf{D} \cdot \varepsilon_{0} I\left|\rho_{1}+\rho\right| \)
Subject: Physics
A student has obtained an image of a
well-illuminated distant object on
a screen to determine the focal length,
\( F_{1} \) of the given spherical mirror. The teacher then gave him another
mirror of focal length, \( F_{2} \) and asked
him to obtain a focused image of the
same object on the same screen. The student found that in order to focus
the same object using the second mirror, he has to move the
mirror away from the screen. From this observation it may be concluded that both the spherical mirrors given to the student were (select the correct
option)
A. Concave and \( F_{1}<F_{2} \)
B. Concave and \( F_{1}>F_{2} \)
C. Convex and \( F_{1}<F_{2} \)
D. Convex and \( F_{1}>F_{2} \)
Subject: Chemistry
At equimolar concentrations of \( \boldsymbol{F} \boldsymbol{e}^{2+} \)
and \( F e^{3+}, \) what must \( \left[A g^{+}\right] \) be so that
the voltage of the galvanic cell made
from the \( \left(A g^{+} \mid A g\right) \) and \( \left(F e^{3+} \mid F e^{2+}\right) \) electrodes equals zero? \( \boldsymbol{F} \boldsymbol{e}^{2+}+\boldsymbol{A} \boldsymbol{g}^{+} \rightleftharpoons \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+}+\boldsymbol{A} \boldsymbol{g} \)
\( \boldsymbol{E}_{A \boldsymbol{g}^{o} \mid \boldsymbol{A} \boldsymbol{g}}^{o}=\boldsymbol{0 . 7 9 9 1} ; \boldsymbol{E}_{\boldsymbol{F e}^{3+} \mid \boldsymbol{F} e^{2-}}=\mathbf{0 . 7 7 1} \)
A .0 .34
B. 0.44
c. 0.47
D. 0.61
Subject: Physics
Assuming the speed of sound in air equal to \( 340 m s^{-1} \) and in water equal to
\( 1360 m s^{-1}, \) find the time taken to trave
a distance \( 1700 \mathrm{m} \) by sound in water
A . \( 0.8 s \)
B. \( 1 s \)
c. \( 1.5 s \)
D. \( 1.25 s \)
Subject: Physics
A particle is executing SHM of amplitude \( A, \) about the mean position \( x=0 . \) Which of the following is a
possible phase difference between the positions of the particle at \( x=+\frac{A}{2} \) and \( \boldsymbol{x}=-\frac{\boldsymbol{A}}{\sqrt{\mathbf{2}}} \)
This question has multiple correct options
A . 75
B . \( 165^{\circ} \)
\( \mathbf{c} \cdot 135^{\circ} \)
D. 195
Subject: Physics
The diagram shows a sphere of radius
\( \boldsymbol{R} \) that carries a charge \( \boldsymbol{Q} \) uniformly
distributed throughout its volume. \( A \)
Gaussian sphere of radius \( a \) is
imagined that is concentric to the
charged sphere.
If \( a<R, \) what is the charge enclosed in
the Gaussian surface?
\( ^{\mathbf{A}} \cdot Q_{e n c}=Q \frac{a^{4}}{R^{4}} \)
\( ^{\mathbf{B}} \cdot Q_{e n c}=Q \frac{a}{R} \)
\( ^{\mathbf{C}} Q_{e n c}=Q \frac{a^{2}}{R^{2}} \)
\( ^{\mathrm{D}} Q_{e n c}=Q \frac{a^{3}}{R^{3}} \)
\( ^{\mathrm{E}} \cdot Q_{e n c}=Q \frac{a^{5}}{R^{5}} \)
Subject: Physics
A closed circuit consists of a resistor \( \boldsymbol{R} \) inductor of inductance \( L \) and a source
of emf \( \boldsymbol{E} \) are connected in series. If the
inductance of the coil is abruptly
decreased to \( L / 4 \) (by removing its magnetic core), the new current immediately after this moment is :
(before decreasing the inductance the circuit is in steady state)
A. Zero
B. \( \frac{E}{R} \)
\( c \cdot 4 \frac{E}{R} \)
D. \( \frac{E}{4 B} \)
Subject: Maths
If \( \bar{a}, \bar{b}, \bar{c} \) are three non-coplanar, non-
zero vectors and \( \bar{r} \) is any vector then \( \bar{r} \) can be represented as \( \boldsymbol{x} \overline{\boldsymbol{a}}+\boldsymbol{y} \overline{\boldsymbol{b}}+\boldsymbol{z} \overline{\boldsymbol{c}} \)
A. always
B. never
c. is one and only one way
D. None of these
Subject: Chemistry
Density of oxygen gas at 1 atm pressure is \( 0.01429 g / c c \) at a given temperature.
The \( r m s \) velocity of oxygen is:
A. \( 4.612 \times 10^{4} \mathrm{cm} / \mathrm{s} \)
B. \( 1.45 \times 10^{4} \mathrm{cm} / \mathrm{s} \)
c. \( 4.612 \times 10^{3} \mathrm{cm} / \mathrm{s} \)
D. \( 1.35 \times 10^{4} \mathrm{cm} / \mathrm{s} \)
Subject: Physics
A point object is placed at the centre of
a glass sphere of radius \( 6 \mathrm{cm} \) and
refractive index \( 1.5 . \) The distance of
virtual image from the surface is:
A. \( 6 \mathrm{cm} \)
в. 4 ст
c. \( 12 \mathrm{cm} \)
D. 9 ст
Subject: Physics
A long straight cable of lenght \( l \) is
placed symmetrically along z - axis has radius \( a(<<l) \). The cable consists of a
thin wire and a coaxial conducting tube
An alternating current \( \boldsymbol{I}(\boldsymbol{t})= \)
\( I_{0} \sin (2 \pi v t) \) flows down the central thin
wire and return along the coaxial conducting tube. The induced electric field at a distance s from the wire inside
the cable is \( \boldsymbol{E}(\boldsymbol{s}, \boldsymbol{t})= \)
\( \mu_{o} I_{o} v \cos (2 \pi v t) \ln \left(\frac{s}{a}\right) \hat{k} . \) The
displacement current density inside the cable is
A \( \cdot \frac{2 \pi}{\lambda^{2}} I_{0} \ln \left(\frac{a}{s}\right) \sin (2 \pi v t) \hat{k} \)
в. \( \frac{I}{\lambda^{2}} I_{0} \) ln \( \left(\frac{a}{s}\right) \sin (2 \pi v t) \hat{k} \)
c. \( \frac{\pi}{\lambda^{2}} I_{0} \ln \left(\frac{a}{s}\right) \sin (2 \pi v t) \hat{k} \)
D. Zero
Subject: Maths
The domain of \( \boldsymbol{f}(\boldsymbol{x})=\cot \frac{\boldsymbol{x}}{\mathbf{3}} \) is
\( A \cdot(-\infty, \infty) \)
B . \( R-\{n \pi: n \in Z\} \)
c. \( R-\{3 n \pi: n \in Z\} \)
D. \( (0, \infty) \)
Subject: Physics
slit separation dis \( 0.3 \mathrm{mm} \) and the
screen distance D is 1 m. A paralle
beam of light of wavelength 600 nm is
incident on the slits at angle \( \alpha \) as
shown in figure. On the screen, the point O is equidistant from the slits and
distance PO is \( 11.0 \mathrm{mm} \). Which of the
following statement (s) is/are correct?
A. For \( \alpha=0 \), there will be constructive interference at
point P.
B. For \( \alpha=\frac{0.36}{\pi} \) degree, there will be destructive
interference at point P.
C \( \cdot_{\text {Fro } \alpha}=\frac{0.36}{\pi} \) degree, there will be destructive
interference at point 0
D. Fringe spacing depends
Subject: Chemistry
Which of the following is a redox
reaction?
\( \mathbf{A} \cdot 2 C r O_{4}^{2-}+2 H^{+} \rightarrow C r_{2} O_{7}^{2-}+H_{2} O \)
В \( \cdot \quad C u S O_{4}+4 N H_{3} \rightarrow\left[C u\left(N H_{3}\right)_{4}\right] S O_{4} \)
\( \mathbf{c} \cdot N a_{2} S_{2} O_{3}+I_{2} \rightarrow N a_{2} S_{4} O_{6}+N a I \)
D. \( C r_{2} O_{7}^{2-}+2 O H^{-} \rightarrow 2 C r O_{4}^{2-}+H_{2} O \)
Subject: Maths
Evaluate: \( \left(3 n^{2}-2 n+5 n^{4}+3\right)(-6) \)
A. \( -30 n^{4}+18 n^{2}-12 n-18 \)
B. \( -30 n^{4}-18 n^{2}-12 n-18 \)
c. \( 30 n^{4}-18 n^{2}-12 n-18 \)
D. \( 30 n^{4}+18 n^{2}-12 n-18 \)
Subject: Chemistry
Assume that impure copper contains only \( F e, A u \) and \( A g \) as impurities. After
passage of 140 ampere for 482.5 sec
the mass of anode decreased by 22.260 \( g \) and the cathode increased in mass by 22.011 g. Calculate the percentage of iron and percentage of copper originally present
A. \( F e=3 \% C u=93 \% \)
в. \( F e=2.5 \% C u=89 \% \)
c. \( F e=3.5 \% C u=93 \% \)
D. None of these
Subject: Physics
The electric field due to the electric
potential \( V=\left(2 x^{2}-4 x\right) \) is
\( \mathbf{A} \cdot(4 x+4) \hat{i} \)
B. \( (4 x-4) \hat{i} \)
c. \( (-4 x+4) \hat{i} \)
D. \( (-4 x-4) \hat{i} \)
Subject: Maths
Let
\( [x] \) denotes the greatest integer less than or equal to \( x \). Then, the value of \( \alpha \)
for which the function \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ll}\frac{\sin \left[-\boldsymbol{x}^{2}\right]}{\left[-\boldsymbol{x}^{2}\right]} & \boldsymbol{x} \neq \mathbf{0} \\ \boldsymbol{\alpha} & \boldsymbol{x}=\mathbf{0}\end{array} \) is continuous at \right.
\( \boldsymbol{x}=\mathbf{0}, \) is
\( \mathbf{A} \cdot \alpha=0 \)
B. \( \alpha=\sin (-1) \)
c. \( \alpha=\sin (1) \)
\( \mathbf{D} \cdot \alpha=1 \)
Subject: Maths
The price of an article rises by \( 25 \% \) every odd year and falls by \( 20 \% \) next year. Which of the following statement is correct about the price exactly after
10 years?
A. Price would have risen by \( 50 \% \)
B. The price would have fallen by \( 20 \% \)
c. The price would remain as it is
D. The price would have risen by \( 25 \% \)
Subject: Physics
An object and its real image are located at distances \( 25 \mathrm{cm} \) and \( 40 \mathrm{cm} \)
respectively from the two principal focii of a convex lens. The linear
magnification of the image is near to
A . +1.3
в. -1.3
\( c .+1.8 \)
D. -1.8.8. -1.8
Subject: Physics
Two equal charges \( A \) and \( B \) each of \( 1 / 3 \times 10^{-6} C \) are placed \( 200 \mathrm{cm} \) apart
in air. A particle carrying a charge of \( -1 / 3 \times 10^{-6} C \) is projected along the
perpendicular bisector from the point 0 midway between \( A \) and \( B \) with a kinetic
energy of \( 10^{-3} J . \) Before the particle
starts to return it will cover a distance
A. \( 1 m \)
B. \( \sqrt{2} \mathrm{m} \)
c. \( \sqrt{3} \mathrm{m} \)
D. \( 1 / \sqrt{3} \mathrm{m} \)
Subject: Physics
Assertion
A sphere, a cube and thin circular plate
of the same mass are made of the same
material. If all of them are heated to the
same high temperature the rate of
cooling is maximum for the plate and minimum for the sphere.
Reason
The rate of loss of heat by radiation is proportional to the surface area.
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: Maths
Let \( S_{1}, S_{2}, S_{3}, \dots \) be squares such that
for each \( n \geq 1 ; \) the length of a side of \( S_{n} \)
equals the length of a diagonal of \( S_{n+1} \)
If the length of a side of \( S_{1} \) is \( 10 \mathrm{cm} \) then for which of the following values of
\( n \) is the area of \( S_{n} \) less than 1 sq.cm? This question has multiple correct options
\( A \cdot 7 \)
B. 8
c. 9
D. 10
Subject: Maths
Using properties of determinants, prove
the following
\[
\mid \begin{array}{ccc}
1+a^{2}-b^{2} & 2 a b & -2 b \\
2 a b & 1-a^{2}+b^{2} & 2 a \\
2 b & -2 a & 1-a^{2}-b^{2}
\end{array}
\]
\( \left(1+a^{2}+b^{2}\right)^{3} \)
Subject: Maths
Evaluate \( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B}), \) if \( \boldsymbol{2} \boldsymbol{P}(\boldsymbol{A})= \)
\( \boldsymbol{P}(\boldsymbol{B})=\frac{\mathbf{5}}{13} \) and \( \boldsymbol{P}(\boldsymbol{A} \mid \boldsymbol{B})=\frac{2}{\mathbf{5}} \)
Subject: Maths
The four angles of a quadrilateral are equal. Draw this quadrilateral in your notebook. Find each of them.
A. \( 60^{\circ}, 120^{\circ}, 30^{\circ}, 150^{\circ} \)
\( ^{\circ} \)
B. \( 60^{\circ}, 120^{\circ}, 60^{\circ}, 120^{\circ} \)
\( \mathbf{c} \cdot 90^{\circ}, 90^{\circ}, 90^{\circ}, 90^{\circ} \)
D. \( 60^{\circ}, 60^{\circ}, 120^{\circ}, 120^{\circ} \)
Subject: Chemistry
Calculate the current (in mA) required to deposit \( 0.195 g \) of platinum metal in
5.0 hours from a solution of \( \left[\boldsymbol{P t} C l_{6}\right]^{2-} \) (Atomic weight: \( \boldsymbol{C r}=\mathbf{5 2 . 0} \) )
A . 310
B. 31
c. 21.44
D. 5.36
Subject: Maths
Evaluate the following limits. \( \lim _{x \rightarrow 3} \frac{x^{2}-4 x+3}{x^{2}-2 x-3} \)
A \( \cdot \frac{1}{2} \)
B. \( \frac{2}{3} \)
\( c \cdot \frac{1}{3} \)
D.
Subject: Chemistry
With boiling water or steam, diethylether results in the formation of:
A \( \cdot\left(C_{2} H_{5}\right)_{2} S O_{4} \)
в. \( C_{2} H_{5} O H \)
c. \( C H_{2}=C H_{2} \)
D. \( C_{2} H_{5} O H+C_{2} H_{5} S O_{4} \)
Subject: Chemistry
The increasing order of specific charge of electron (e), proton (p), alpha partial
\( \alpha \) ) and neutron (n) is:
A. e, p, n, \( \alpha \)
B. n, p, e, \( \alpha \)
\( c \cdot n, \alpha, p, e \)
D. \( n, \) p, \( \alpha \), e