AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Number of \( \sigma \) and \( \pi \) bonds in \( C_{2} \)
molecule is/are:
\( \mathbf{A} \cdot 1 \sigma \) and \( 1 \pi \)
B. \( 1 \sigma \) and \( 2 \pi \)
c. \( 2 \pi \) only
D. \( 1 \sigma \) and \( 3 \pi \)
Subject: Chemistry
The relative stability of +1 oxidation state of group 13 elements follows the order:
A. \( A l<G a<T l<I n \)
в. \( T l< \)In \( <G a<A l \)
c. \( A l<G a<I n<T l \)
D. \( G a<A l< \)In \( <T l \)
Subject: Maths
Equation of a straight line passing through the point (2,3) and inclined at an angle of \( \tan ^{-1} \frac{1}{2} \) with the line \( y+ \) \( 2 x=5, \) is:
\( \mathbf{A} \cdot y=3 \)
B. \( x=2 \)
c. \( 3 x+4 y-18=0 \)
D. \( 4 x+3 y-17=0 \)
Subject: Chemistry
The value of \( n \) in \( M n O_{4}^{-}+8 H^{+}+ \)
\( \boldsymbol{n} e^{-} \longrightarrow \boldsymbol{M} \boldsymbol{n}^{2+}+\boldsymbol{4} \boldsymbol{H}_{2} \boldsymbol{O} \) is:
A. 5
B. 4
\( c \cdot 2 \)
D.
Subject: Physics
What is the tension in string at \( A \) immediately after the string at \( \mathrm{B} \)
breaks?
A \( \cdot \frac{m g}{5} \)
в. \( \frac{2 m g}{31} \)
c. \( \frac{m g}{37} \)
D. \( \frac{5 m g}{37} \)
Subject: Chemistry
The IUPAC name for the coordination
compound \( \boldsymbol{B} \boldsymbol{a}\left[\boldsymbol{B} \boldsymbol{r} \boldsymbol{F}_{4}\right]_{2} \) is:
A. barium tetrafluorobromate (V)
B. barium tetrafluorobromate (III)
c. barium bis(tetrafluorobromate) (III)
D. none of these
Subject: Chemistry
Arrange the given set of compounds in order of increasing boiling point:
I. 1 -chloropropane
II. Isopropyl chloride
III. 1 -chlorobutane
A. \( I I<I I I<I \)
B. \( I<I I<I I I \)
c. \( I I<I<I I I \)
D. \( I I I<I<I I I \)
Subject: Maths
If \( \boldsymbol{b}>\boldsymbol{a} \) and \( \boldsymbol{I}=\int_{a}^{b} \frac{\boldsymbol{d} \boldsymbol{x}}{\sqrt{(\boldsymbol{x}-\boldsymbol{a})(\boldsymbol{b}-\boldsymbol{x})}} \)
then \( I \) equals
A . \( \pi / 2 \)
в. \( \pi \)
\( \mathrm{c} \cdot 3 \pi / 2 \)
D . 2 \( \pi \)
Subject: Chemistry
In a basic aqueous solution chloromethane undergoes a
substitution reaction in which \( C l^{-} \) is
replaced by \( \boldsymbol{O H}^{-} \) as.
\( \boldsymbol{C H}_{3} \boldsymbol{C l}(\boldsymbol{a q})+\boldsymbol{O H}^{-} \rightleftharpoons \)
\( \boldsymbol{C H}_{3} \boldsymbol{O H}(\boldsymbol{a q})+\boldsymbol{C l}^{-}(\boldsymbol{a q}) \)
The equilibrium constant of above reaction \( \boldsymbol{K}_{c}=\mathbf{1} \times \mathbf{1 0}^{\mathbf{1 5}} . \) If a solution is
prepared by mixing equal volumes of \( 0.1 M C H_{3} C l \) and \( 0.2 M N a O H(100 \% \)
dissociated) then \( \left[O H^{-}\right] \) concentration
at equilibrium in mixture will be
A. \( 0.1 M \)
в. \( 0.5 M \)
\( c .0 .2 M \)
D. \( 0.05 M \)
Subject: Chemistry
\( X e F_{6} \) reacts with quartz forming \( X e O_{3} \)
\[
\mathbf{2} \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{\mathbf{6}}+\boldsymbol{x} \boldsymbol{S} \boldsymbol{i} \boldsymbol{O}_{2} \longrightarrow
\]
What is value of \( x ? \)
Subject: Physics
A body of mass \( 100 g \) moves at the speed of \( 36 k m / h \). The de-Broglie wavelength related to it is of the order
\( \boldsymbol{m} \)
\( \left(h=6.626 \times 10^{-34} J s\right) \)
A \( \cdot 10^{-24} \)
B . \( 10^{-14} \)
c. \( 10^{-34} \)
the \( 4^{-34} 4 \)
D. \( 10^{-44} \)
Subject: Physics
Two ends of an inductor of inductance \( L \)
are connected to two parallel
conducting wires. A rod of length \( l \) and
mass \( m \) is given velocity \( v_{0} \) as shown.
The whole system is placed in
perpendicular magnetic field \( B \). Find the maximum current in the inductor.
\( ^{A} \cdot \frac{m v_{0}}{L} \)
в. \( \sqrt{\frac{m}{L}} v_{0} \)
c. \( \frac{m v_{0}^{2}}{L} \)
D. None of these
Subject: Chemistry
Which of the following set contains oxide in the sequence, basic, amphoteric and acidic respectively?
A. \( S O_{2}, P_{2} O_{5}, C O \)
в. \( B a O, A l_{2} O_{3}, \) SiO \( _{2} \)
c. \( C a O, \operatorname{si} O_{2}, A l_{2} O_{3} \)
D. \( A l_{2} O_{3} . C O_{2}, C O \)
Subject: Chemistry
At \( 100^{\circ} \mathrm{C} \) and 1 atm, if the density of
liquid water is \( 1.0 g \mathrm{cm}^{-3} \) and that of
water vapour is \( 0.0006 g \mathrm{cm}^{-3}, \) then the volume occupied by water molecules in
1 litre of steam at that temperature is:
\( A \cdot 6 c m^{3} \)
B. \( 60 \mathrm{cm}^{3} \)
c. \( 0.6 \mathrm{cm}^{3} \)
D. \( 0.06 \mathrm{cm}^{3} \)
Subject: Physics
What is the non linear \( V-I \) relation in
a pn Junction in forward bias?
A. \( I=I_{s} e^{V / V_{T}} \)
В . \( I=I_{s}\left(e^{V / V_{T}}-1\right) \)
C \( . I=I_{s}\left(1-e^{V / V_{T}}\right) \)
\( D \)
Subject: Physics
A beam of cathode rays is subjected to crossed electric (E) and magnetic fields
(B). The fields are adjusted such that the beam is not deflected. The specific charge of the cathode rays is given by :
\( ^{\mathbf{A}} \cdot \frac{B^{2}}{2 v E^{2}} \)
B. \( \frac{2 v B^{2}}{E^{2}} \)
c. \( \frac{2 v E^{2}}{B^{2}} \)
D. \( \frac{E^{2}}{2 v B^{2}} \)
Subject: Chemistry
Acetic acid was added to a solid \( X \)
taken in a test tube. A colourless and
odourless gas was evolved. The gas was passed through lime water which did not turn milky. However, the gas burnt
with a pop sound. It was concluded
that
A. Solid \( x \) is sodium and the gas evolved is \( C O_{2} \)
B. Solid X is sodium and the gas evolved is \( H_{2} \)
c. solid \( x \) is sodium acetate and the gas evolved is \( C O_{2} \)
D. Solid \( x \) is sodium chloride and the gas evolved is \( H_{2} \)
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:
A. Reversible nature of reaction between \( A g_{2} S \) and NaCN
B. To oxidise \( N a_{2} S \) into \( N a_{2} S O_{4} \)
c. Both (A) and (B)
D. None of the above
Subject: Physics
The angular momentum of a flywheel having a moment of inertia of \( 0.4 k g m^{2} \)
decreases from 30 to \( 20 \mathrm{kg} m^{2} / s \) in a period of 2 second. Find the average torque in \( \mathrm{Nm} \) acting on the flywhee during this period.
Subject: Chemistry
The common formula of Turn bull's blue
and Prussian blue is:
\( \mathbf{A} \cdot F e_{3}\left[F e(C N)_{6}\right]_{2} \)
\( \mathbf{B} \cdot F e_{3}\left[F e(C N)_{6}\right]_{3} \)
c. \( K F e\left[F e(C N)_{6}\right] \)
D. \( K_{4} F e_{2}\left[F e(C N)_{6}\right]_{2} \)
Subject: Physics
A transformer of efficiency \( 90 \% \) has
turns ratio \( 1: 10 . \) If the voltage across
the primary is \( 220 V \) and current in the
primary is \( 0.5 A \), then the current in
secondary is
\( \mathbf{A} \cdot 5.5 A \)
B. \( 5 A \)
\( c \cdot 4 A \)
D. \( 4.5 ~ A \)
Subject: Chemistry
Starch is a mixture of two components, a water soluble component amylose(15\( 20 \% \) and a water insoluble component
amylopectin (80-85\%). The aqueous solution of amylose gives a blue colour with iodine solution due to the
formation of:
A. amylose iodide
B. amylose iodate
c. inclusion complex
D. amylose tetraiodide complex
Subject: Physics
Find the net capacitance between \( A \) and
B in Fig:
\( \mathbf{A} \cdot 5 / 2 \mu F \)
B . \( 2 / 5 \mu F \)
\( \mathbf{c} \cdot 9 / 22 \mu F \)
D. \( 22 / 9 \mu F \)
Subject: Maths
Determine the domain and range of the following relations. \( \boldsymbol{S}=\{(\boldsymbol{a}, \boldsymbol{b}): \boldsymbol{b}=|\boldsymbol{a}-\mathbf{1}|, \boldsymbol{a} \in \boldsymbol{Z} \) and
\( |a| \leq 3\} \)
Subject: Physics
At a place horizontal component of Earth's magnetic field is \( \sqrt{3} \) times the vertical component, then the angle of dip at the given place is :
A \( \cdot 45^{\circ} \)
B. 30 \( ^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 15^{\circ} \)
Subject: Chemistry
\( 2 A \rightarrow \) Product, follows the first order
kinetics. If the half life period of the reaction at \( [\boldsymbol{A}]_{\text {initial}}=\mathbf{0 . 2} \) mole lit\( ^{-1} \) is
20 min. then the value of rate constant
would be:-
\( A \cdot 4 \sec \)
B. 20 sec
c. 4 litmol\( ^{-1} \min ^{-1} \)
D. None of these
Subject: Chemistry
\( \ln S c^{3+}, T i^{2+}, T i^{3+}, V^{2+}, \) increasing
order of spin only magnetic moment is:
A. \( S c^{3+}<T i^{2+}<T i^{3+}<V^{2+} \)
B. \( S c^{3+}<T i^{3+}<T i^{2+}<V^{2+} \)
c. \( T i^{2+}<S c^{3+}<T i^{3+}<V^{2+} \)
D. \( S c^{3+}<T i^{2+}<V^{2+}<T i^{3+} \)
Subject: Chemistry
Alveoli ane the tiny sacks of air in lungs
whose average diameter is \( 5 \times 10^{-5} \mathrm{m} \)
Consider a oxygen molecule \( (5.3 \times \)
\( \mathbf{1 0}^{-\mathbf{2 6}} \mathbf{k g} \) ) trapped within a sec
Calculate uncertainty in velocity of oxygen molecule.
A \( \cdot 1.98 \times 10^{-5} m s^{-1} \)
В . \( 2 \times 10^{-8} \mathrm{ms}^{-1} \)
\( \mathbf{c} \cdot 5 \times 10^{-5} m s^{-} \)
D. \( 3 \times 10^{-8} \mathrm{ms}^{-1} \)
Subject: Physics
Find the electric field at \( z>0.5 d \)
\( \mathbf{A} \cdot E=0 \)
B \( \cdot E=-\frac{\sigma}{\epsilon_{0}} \hat{k} \)
\( \mathbf{c} \cdot E=\frac{\sigma}{\epsilon_{0}} \hat{k} \)
D・ \( E=-\frac{\sigma}{2 \epsilon_{n}} \hat{k} \)
Subject: Maths
\( \ln \Delta A B C, A D \) is drawn such that
\( \Delta A B D \) and \( \Delta A C D \) are equal in area
then, the AD is
A. any segment drawn from A to BC
B. the bisector of \( \angle B A G \)
c. A median of \( \Delta A B C \)
D. None of these
Subject: Maths
\( \sin 12^{\circ} \sin 48^{\circ} \sin 54^{\circ} \) is equal to?
A \( \cdot \frac{1}{8} \)
B. \( \frac{1}{4} \)
\( c \cdot \frac{3}{8} \)
D. \( \frac{7}{8} \)
Subject: Chemistry
Which of the following orders are
Correct?
A. \( A g C l>A g F: \) Covalent character order
B \( \cdot B a O>B a F_{2}: \) Melting point order
\( \mathbf{C} \cdot B e F_{2}>B a F_{2}: \) Solubility order
D. \( L i N O_{3}<R b N O_{3}: \) Thermal stability order
Subject: Maths
The perimeters of two similar triangles
are \( 25 \mathrm{cm} \) and \( 15 \mathrm{cm} \) respectively. If one side of first triangle is \( 9 \mathrm{cm}, \) then the corresponding side of the other triangle is
\( A \cdot 6.2 \mathrm{cm} \)
B. \( 3.4 \mathrm{cm} \)
c. \( 5.4 \mathrm{cm} \)
D. \( 8.4 \mathrm{cm} \)
Subject: Maths
If \( \sin A=\frac{3}{5} \) and \( A \) is not in the first quadrant then find \( \frac{\cos A+\sin 2 A}{\tan A+\sec A} \)
A \( \cdot \frac{16}{25} \)
в. \( \frac{17}{25} \)
c. \( \frac{22}{25} \)
D. \( \frac{19}{25} \)
Subject: Chemistry
Compound \( (X) C_{4} H_{8} O \) decolourises Baeyer's reagent. It undergoes
hydrolysis on reaction with dil. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) and produces (Y) and (Z). Both (Y) and
(z) give positive iodoform test. But, only
(Y) gives positive Tollen's test.Choose
the correct statements.
This question has multiple correct options
\( A \)
\( (Y) \stackrel{a q_{1} N a O H(10 \%) \Delta}_{\longrightarrow} C H_{3}-C H=C H-C H O \)
B. Pyridinium chlorochromate (PCC)
(z)
\( c \)
\( (\mathrm{X}) \frac{\mathrm{B} \mathrm{r}_{2} / \mathrm{CCl}_{4}}{\longrightarrow} \mathrm{CH}_{2}-\mathrm{CH}-\mathrm{O}-\mathrm{CH}_{2}-\mathrm{CH}_{3} \)
\( \mathrm{Br} \quad \mathrm{Br} \)
\( D \)
\[
(X) \frac{(i) O_{3}}{(i j) Z n / H_{2} O}(Y)+\text { other product }
\]
Subject: Physics
According to Bohr's model, if the kinetic
energy of an electron in \( 2^{n d} \) orbit of
\( H e^{+} \) is \( x, \) then what should be the
ionisaion energy of the electron revolving in \( 3^{r d} \) orbit of \( m^{5+} \) ions \( > \)
\( \mathbf{A} \cdot X \)
в. \( 4 x \)
c. \( x / 4 \)
D. \( 2 X \)
Subject: Maths
The value of the determinant
\( \Delta=\left|\begin{array}{lll}\log x & \log y & \log z \\ \log 2 x & \log 2 y & \log 2 z \\ \log 3 x & \log 3 y & \log 3 z\end{array}\right| \)
\( A \cdot 0 \)
\( \mathbf{B} \cdot \log (x y z) \)
\( \mathbf{C} \cdot \log (6 x y z) \)
\( \mathbf{D} \cdot 6 \log (x y z) \)
Subject: Physics
Ramu and Somu are running towards north with \( 3 \mathrm{m} / \mathrm{s} \) and \( 4 \mathrm{m} / \mathrm{s} \). Their friend
Srinu is running towards south with 2 \( \mathrm{m} / \mathrm{s} . \) Then the magnitude of relative velocity of Somu w.r.t Ramu
\( A \cdot 1 \mathrm{m} / \mathrm{s} \)
B. 2 m/s
\( c \cdot 3 m / s \)
D. \( 4 \mathrm{m} / \mathrm{s} \)
Subject: Maths
If \( A, B \) are the feet of the perpendiculars
from (2,4,5) to the \( x \) -axis, \( y \) -axis
respectively, then the distance \( A B \) is
A \( .2 \sqrt{5} \)
B. \( \sqrt{29} \)
c. \( \sqrt{41} \)
D. \( 3 \sqrt{5} \)
Subject: Biology
Which of the following statements is
true about the process shown in the given box?
[Food \( + \) Oxygen \( \rightarrow \) Carbon dioxide \( + \) Water \( +\text { Energy }] \)
A. It is caused by the decay of organic substances.
B. It is an important process in the nitrogen cycle.
C. It is an essential process of aerobic respiration in living organisms.
D. It Is carried out only by green plants and certain type of bacteria.
Subject: Chemistry
Which of the following represents isostructural pairs?
\( \mathbf{A} \cdot\left[N F_{3}, N O_{3}^{-}\right] \) and \( \left[B F_{3}, H_{3} O^{+}\right] \)
B \cdot \( \left[N F_{3}, H N_{3}\right] \) and \( \left[N O_{3}^{-}, B F_{3}\right] \)
\( \mathbf{c} \cdot\left[N F_{3}, H_{3} O^{+}\right] \) and \( \left[N O_{3}^{-}, B F_{3}\right] \)
D・ \( \left[N F_{3}, H_{3} O^{+}\right] \) and \( \left[H N_{3}, B F_{3}\right] \)
Subject: Chemistry
Balance the following equations.
(i) \( \boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{2}+\boldsymbol{H} \boldsymbol{C l} \rightarrow \boldsymbol{K} \boldsymbol{C l}+ \)
\( M n C l_{2}+H_{2} O+C l_{2} \)
(ii) \( \boldsymbol{N} \boldsymbol{H}_{3}+\boldsymbol{O}_{3} \rightarrow \boldsymbol{N} \boldsymbol{O}+\boldsymbol{H}_{2} \boldsymbol{O} \)
Subject: Physics
Q Type your question-
object can affect the shadow formed on
the screen. when she placed the object
at position \( Y \) shadow 1 was formed on
the screen as shown.

When the object was placed at position \( X, \) which of the following would be
observed about the shadow on the
screen?
1. The shadow would be upright.
2. The shadow would be inverted.
3. The shadow would be bigger than
shadow 1.
4. The shadow would be smaller than
shadow 1.
A . 1 and 3 only
B. 2 and 3 only
c. 1 and 4 only
D. 3 and 4 only
Subject: Chemistry
Pick out the isoelectronic structures of
the following
\( \begin{array}{lll}\text { I. } C H^{3+} & \text { II. } \boldsymbol{H}_{3}^{+} & \text {III. } \boldsymbol{N} \boldsymbol{H}_{3}\end{array} \)
A. II, ,II and IV
B. I and II
c. Ill and IV
D. I and III
Subject: Physics
A mass of stainless steel spoon is 0.04
kg and specific heat is \( 0.50 k J / k g \times^{o} C \)
Then calculate the heat which is
required to raise the temperature \( 20^{\circ} C \)
to \( 50^{\circ} \mathrm{C} \) of the spoon.
A. 200 J
B. 400
c. \( 600 \mathrm{J} \)
D. 800
E . 1,000
Subject: Maths
Box-I contains 5 red and 4 white balls
while box-ll contains 4 red and 2 white
balls. A fair die is thrown. If it turns up a
multiple of \( 3, \) a ball is drawn, from boxelse a ball is drawn from box-II. The probability that the ball drawn is white is \( \frac{a}{27} . \) Find \( a \)
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 \( \frac{\boldsymbol{D}}{\mathbf{9 0}}=\frac{\boldsymbol{G}}{\mathbf{1 0 0}}=\frac{\boldsymbol{2} \boldsymbol{C}}{\boldsymbol{\pi}} \) 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:One angle of a triangle is \( \frac{4 x}{3} \)
grades and another is \( 3 x \) degrees, while the third is \( \frac{2 \pi x}{75} \) radians. Then the angles in degrees are -
A \( \cdot 20^{\circ}, 60^{\circ}, 100^{\circ} \)
B . 24 ' , 60 \( ^{\circ}, 96^{\circ} \)
c. \( 36^{\circ}, 60^{\circ}, 84^{\circ} \)
D. \( 20^{\circ}, 40^{\circ}, 120^{\circ} \)
Subject: Maths
The lengths of two sides of a triangle are \( 3 \mathrm{cm} \) and \( 4 \mathrm{cm} . \) Which of the following, can be the length of third side to form a triangle?
A . \( 0.5 \mathrm{cm} \)
B. \( 5 \mathrm{cm} \)
\( c .8 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)
Subject: Chemistry
What are \( X \) and \( Y ? \)
\( \|+N B S \quad \longrightarrow \quad X \frac{(i) M g / \text { ether }}{(i i) C_{2}_{2}:} Y Y \)
A. \( x: 1 \) -bromo cyclohex- 1 -ene \( Y \) : Cyclohex- 1 -enoic acid
B. \( x: 1- \) bromo cyclohex-2-ene Y: Cyclohex-2-enal
c. \( x: 3 \) -bromo cyclohexene \( Y \) : Cyclohex-2-enoic acid
D. None of these
Subject: Physics
Assertion
(A) :When the radius of a
copper wire is doubled, its specific resistance increases
Reason
(R) :Specific resistance is independent of cross-section of
material used
A. Both A \& R are true and R is the correct explanation of \( A \)
B. Both A \& R are true and R is not a correct explanation of
c. A is true but R is false
D. A is false but R is true
Subject: Physics
A glass refractive index 1.5 and radius
\( 10 \mathrm{cm}, \) has a spherical cavity of radius 5
cm concentric with it. A narrow beam of
parallel light is directed into the sphere.Find the final image and its
nature
A . - 25 cm left of \( S_{1} \), virtual
B. 25 cm right of \( S_{4} \), rea
\( \mathbf{c} . \) 15 \( \mathrm{cm} \) left of \( S_{4} \), virtual
D. \( 20 \mathrm{cm} \) right of \( S_{4} \), virtual
Subject: Physics
In a series LCR circuit \( \mathbf{R}=200 \) Omega
and the voltage and the frequency of the main supply is \( 220 \mathrm{V} \) and \( 50 \mathrm{Hz} \)
respectively. On taking out the capacitance from the circuit the
current lags behind the voltage by \( 30^{0} \) On taking out the inductor from the
circuit the current leads the voltage by
\( 30^{0} . \) The power dissipated in the LCR
circuit is
A . \( 305 \mathrm{W} \)
B. \( 210 \mathrm{W} \)
c. ZeroW
D. \( 242 \mathrm{W} \)
Subject: Physics
A luminous object is placed at a distance of \( 30 \mathrm{cm} \) from a convex lens of
focal length \( 20 \mathrm{cm} . \) On the other side of the lens, at what distance from the lens
must a convex mirror of radius of
curvature \( 10 \mathrm{cm} \) be placed in order to have an upright image of the object coincident with it?
\( A . \) 30 \( \mathrm{cm} \)
B. 40 cm
\( c .50 \mathrm{cm} \)
D. \( 12 \mathrm{cm} \)
Subject: Maths
For what value of \( \alpha, \) the system of
equations \( \boldsymbol{\alpha} \boldsymbol{x}+\mathbf{3} \boldsymbol{y}=\boldsymbol{\alpha}-\boldsymbol{3} \)
\( 12 x+\alpha y=\alpha \)
will have no solution
\( \mathbf{A} \cdot \alpha=5 \)
B . \( \alpha=-6 \)
c. \( \alpha=-4 \)
D. \( \alpha=2 \)
Subject: Chemistry
When \( 229 J \) of energy is supplied as
heat as constant pressure to 3 mol
\( \boldsymbol{A} \boldsymbol{r}(\boldsymbol{g}), \) the temperature of the sample is increased by \( 2.55 K . \) Calculate the
molar heat capacity at constant volume
A \( \cdot 40 J K^{-1} m o l^{-1} \)
B. \( 30 J K^{-1} \) mol \( ^{-1} \)
c. \( 21.7 J K^{-1} \) mol \( ^{-1} \)
D. \( 81.7 J K^{-1} \mathrm{mol}^{-1} \)
Subject: Maths
The value of \( \int x^{3} \log x d x \) is
A \( \cdot \frac{1}{16}\left(4 x^{4} \log x-x^{4}+c\right) \)
B \( \cdot \frac{1}{8}\left(x^{4} \log x-4 x^{4}+c\right) \)
c. \( \frac{1}{16}\left(4 x^{4} \log x+x^{4}+c\right) \)
\( \frac{x^{4} \log x}{4}+c \)
Subject: Physics
When a light of wavelength \( 4000 A \) in vacuum travels through the same thickness in diamond and water
separately, the difference in the number of waves is \( 200 . \) Find the thickness, if refractive indices of diamond and water \( \operatorname{are} \frac{5}{2} \) and \( \frac{4}{3} \) respectively.
\( \mathbf{A} \cdot 0.685 m m \)
B. \( 0.0685 \mathrm{mm} \)
\( \mathbf{c} .68 .5 \mathrm{mm} \)
D. \( 6.85 \mathrm{mm} \)
Subject: Physics
The \( (x, y) \) co-ordinates of the corners of
a square plate are \( (\mathbf{0}, \mathbf{0})(\boldsymbol{L}, \mathbf{0})(\boldsymbol{L}, \boldsymbol{L}) \& \)
\( (0, L) . \) The edges of the plate are clamped \& transverse standing waves are set up in it. If \( u(x, y) \) denotes the displacement of the plate at the point \( (x, y) \) at some instant of time, the possible expression(s) for \( u \) is/are : \( (a= \) positive constant) This question has multiple correct options
A \( \cdot a \cos \left(\frac{\pi x}{2 L}\right) \cos \left(\frac{\pi y}{2 L}\right) \)
B. \( a \sin \left(\frac{\pi x}{L}\right) \sin \left(\frac{\pi y}{L}\right) \)
\( ^{\mathbf{c}} \cdot a \sin \left(\frac{\pi x}{L}\right) \sin \left(\frac{2 \pi y}{L}\right) \)
D. \( a \cos \left(\frac{2 \pi x}{L}\right) \sin \left(\frac{\pi y}{L}\right) \)
Subject: Maths
The three solutions of the equation \( \boldsymbol{f}(\boldsymbol{x})=\mathbf{0} \) are \( -\mathbf{2}, \mathbf{0}, \) and \( \mathbf{3} . \) Therefore, the
three solutions of the equation \( f(x- \)
2) \( =\mathbf{0} \) are
Subject: Physics
The potential difference between two parallel plates \( 1 \mathrm{cm} \) apart is \( 100 \mathrm{V} \). The electric field strength between them is :
A. \( 100 V / m \)
в. \( 1000 V / m \)
c. \( 10^{4} V / m \)
D. \( 50 V / m \)
Subject: Chemistry
Assertion: Addition of \( N H_{4} O H \) to
an aqueous solution of \( B a C l_{2} \) in the
presence of excess \( N H_{4} C l \) precipitates
\( \boldsymbol{B} \boldsymbol{a}(\boldsymbol{O} \boldsymbol{H})_{2} \)

Reason: \( \boldsymbol{B a}(\boldsymbol{O H})_{2} \) is soluble in water.
A. Both Assertion and Reason are correct and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion
c. Assertion is correct but Reason is not correct
D. Assertion is not correct but Reason is correct
E. Both Assertion and Reason are not correct
Subject: Chemistry
For the given reaction \( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{S}(\boldsymbol{s}) \longrightarrow \boldsymbol{H}_{2} \boldsymbol{S}(\boldsymbol{g}) ; \boldsymbol{\Delta} \boldsymbol{H}_{\boldsymbol{T}}= \)
\( \mathbf{1 0 0} k J / \) mol and \( \Delta S_{T}= \)
\( 400 J / m o l / K \)
Temperature at which above reaction
occurs reversibly is (Assuming \( \Delta \boldsymbol{H}_{\boldsymbol{T}} \)
and \( \Delta S_{T} \) are independent of
temperature)
\( \mathbf{A} \cdot 200 K \)
B . \( 250 K \)
c. \( 400 K \)
D. None
Subject: Maths
Find the maximum value of \( \left|\begin{array}{ccc}\mathbf{1} & \mathbf{1} & \mathbf{1} \\ \mathbf{1} & \mathbf{1}+\sin \boldsymbol{\theta} & \mathbf{1} \\ \mathbf{1} & \mathbf{1} & \mathbf{1}+\mathbf{c} \mathbf{o} \mathbf{s} \boldsymbol{\theta}\end{array}\right| \)
Subject: Chemistry
For the following reaction: \( \boldsymbol{K}_{\boldsymbol{p}}=\mathbf{1 . 7} \times \)
\( 10^{7} \) at \( 25^{\circ} C \)
\( A g^{+}(a q .)+2 N H_{3}(g) \rightleftharpoons \)
\( \left[\boldsymbol{A} \boldsymbol{g}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2}\right]^{+} \)
what value of \( \Delta G^{o} \) in \( k J ? \)
A. -41.2
B. -17.9
\( \mathrm{c} \cdot+17.9 \)
\( \mathbf{D} .+41.2 \)
Subject: Maths
The smallest value of an angle whose
sine is \( -\frac{\sqrt{\mathbf{3}}}{\mathbf{2}} \) is
\( A \cdot 30^{\circ} \)
B . \( 60^{\circ} \)
\( c \cdot 120^{\circ} \)
D. \( 240^{\circ} \)
Subject: Maths
Evaluate \( : \int_{0}^{1} e^{2-3 x} d x \)
\( \mathbf{A} \cdot e^{2}-e \)
B. \( \frac{1}{3}\left(e^{2}-e\right) \)
c. \( \frac{1}{3}\left(e^{2}-\frac{1}{e}\right) \)
D. \( \frac{1}{2}\left(e^{2}-\frac{1}{e}\right) \)
Subject: Chemistry
Assertion
Cathode rays get deflected towards the positive plate of electric field.
Reason
Cathode rays consist of negatively charged particles known as electrons.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion,
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct.
Subject: Maths
Let \( \boldsymbol{A}=\{1,2,3\} . \) Which of the following
is not an equivalence relation on A?
A \( \cdot\{(1,1),(2,2),(3,3)\} \)
B - \{(1,1),(2,2),(3,3),(1,2),(2,1)\}
C \( \cdot\{(1,1),(2,2),(3,3),(2,3),(3,2)\} \)
D \cdot \{(1,1),(2,1)\}