AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Assertion
Moment of inertia is always constant.
Reason

Angular moment is conserved that is
why moment of inertia is constant.
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: Maths
In the parallelogram ABCD the angles \( A \) and \( C \) are obtuse Points \( X \) and \( Y \) are
taken on the diagonal BD such that the angles \( \mathrm{XAD} \) and \( \mathrm{YCB} \) are right angles. And hence, \( \boldsymbol{X} \boldsymbol{A}=\boldsymbol{Y} \boldsymbol{C} \)
If the above statement is true then
mention answer as 1 , else mention 0 if
false
Subject: Physics
A ball is thrown vertically upwards with speed \( 10 \mathrm{m} / \mathrm{s} \) and it comes back at
initial point with same speed. At what point during flight is the ball's acceleration greatest?
A. The answer cannot be determined from this information
B. The acceleration remains constant throughout the flight
c. Just after lunch
D. Just5 before landing
E. At the highest point of the flight
Subject: Chemistry
The passage of electricity in the Daniell cell when \( Z n \) and \( C u \) electrodes are
connected is from:
A. \( C u \) to \( Z n \) in the cell
B. \( C u \) to \( Z n \) outside the cell
c. \( Z n \) to \( C u \) outside the cell
D. \( Z n \) to \( C u \) in the cell
Subject: Physics
Two points \( A \) and \( B \) are located at distance of \( 100 \mathrm{cm} \) from on electric
dipole. A is sn axial point while B is in perpendicular bisector. The electric field intensity at \( A \) is \( \vec{E} \). Then the intensity at B will be
\( A \cdot \vec{E} \)
в. \( 2 \vec{E} \)
\( c \cdot-\vec{E} \)
D. \( -\frac{\vec{E}}{2} \)
Subject: Chemistry
Calculate the wavelength of radiation emitted producing a line in Lyman series, when an electron falls from fourth stationary state in hydrogen \( \operatorname{atom}\left(\boldsymbol{R}_{\boldsymbol{H}}=\mathbf{1 . 1} \times \mathbf{1 0}^{\mathbf{7}} \boldsymbol{m}^{-\mathbf{1}}\right) . \) If the
answer is \( x \times 10^{-8} \mathrm{m} \), then find the
value of \( x \)
Subject: Physics
A certain transverse wave is described
by \( \boldsymbol{y}(\boldsymbol{x}, \boldsymbol{t})= \)
\( (6.50 m m) \cos 2 \pi\left(\frac{x}{28.0 c m}-\frac{t}{0.0360}\right. \)
The wave's amplitude is \( 6.50 \times 10^{-x} m \)
Find the value of \( x \)
Subject: Physics
A tap supplies water at \( 22^{0} \) C.A man
takes 1 litre per minute at \( 37^{0} \) from the
geyser. If the mains supply is \( 210 \mathrm{V} \), then the current flowing in the geyser is :
A. 7.5A
B. 2.5A
c. \( 5.0 A \)
D. 10A
Subject: Physics
Two walls of thickness \( d_{1} \) and \( d_{2} \)
thermal conductivities \( K_{1} \) and \( K_{2} \) are
in contact. In the steady state if the temperatures at the outer surfaces are
\( T_{1} \) and \( T_{2}, \) the temperature at
the common wall will be
A. \( \frac{K_{1} T_{1}+K_{2} T_{2}}{d_{1}+d_{2}} \)
в. \( \frac{K_{1} T_{1} d_{2}+K_{2} T_{2} d_{1}}{K_{1} d_{2}+K_{2} d_{1}} \)
c. \( \frac{\left(K_{1} d_{1}+K_{d} d_{2}\right) T_{1} T_{2}}{T_{1}+T_{2}} \)
D. \( \frac{K_{1} d_{1} T_{1}+K_{2} d_{2} T_{2}}{K_{1} d_{1}+K_{2} d_{2}} \)
Subject: Chemistry
Which of the following statements are
correct?
This question has multiple correct options
\( A \cdot A \) plot of \( \log K_{P} \) vs. \( 1 / T \) is linear.
B. A plot of log [X] vs. time is linear for I order reaction \( X \rightarrow P \)
C. A plot of log P vs. 1/T is linear at constant volume.
D. A plot of P vs. 1/V is linear at constant temperature.
Subject: Maths
The ratio of fifth term from the
beginning to the fifth term from the end in the expansion of \( \left(\sqrt[4]{2}+\frac{1}{\sqrt[4]{3}}\right)^{n} \) is
\( \sqrt{6}: 1 . \) If \( n=\frac{20}{\lambda}, \) find the value of \( \lambda \)
Subject: Chemistry
A Mixture of nitrogen and oxygen has a density of \( 1.00 g / 1 \) and the average
molecular weight \( \left(M_{a y}\right) \) of \( 31.2 g \) at
\( 27^{\circ} C \) and \( 600 \mathrm{mm} \) Hg per mole pressure
What is the mole fraction of nitrogen? (Assume ideal gas behavior)
A . 0.8
B. 0.6
\( c .0 .4 \)
D. 0.2
Subject: Physics
The motion of a planet around sun in an
elliptical orbit is shown in the following
figure. Sun is situated on one focus. The
shaded areas are equal. If the planet
takes time \( t_{1} \) and \( t_{2} \) in moving from \( A \) to
B and from \( C \) to D respectively then
\( \mathbf{A} \cdot t_{1}>t_{2} \)
B . \( t_{1}<t_{2} \)
c. \( t_{1}=t_{2} \)
D. information incomplete
Subject: Maths
The straight lines \( A B \) and \( C D \) intersect
at \( E . \) If \( E F \) and \( E G \) are bisectors of
\( \angle D E A \) and \( \angle A E C \)
respectively and if \( \angle A E F=x \) and
\( \angle A E G=y, \) then
A \( \cdot x+y>90^{\circ} \)
В . \( x+y<90^{\circ} \)
c. \( x+y=90^{\circ} \)
D. \( x+y=180^{\circ} \)
Subject: Chemistry
If equal concentrations are mixed (of products \( \& \text { reactants }) \) then will the reaction proceed to the right or left?
\[
H_{2} \operatorname{sO}_{4}(\text { aq })+N H_{3}(\text { aq }) \mapsto N H_{4}^{+}(\text {aq })+H \mathrm{SO}_{4}^{-}(\text {аๆ })
\]
Subject: Maths
\( \sinh ^{-1}\left(\frac{x}{4}\right) d x \) is equal to
A \( \cdot x \sinh ^{-1}\left(\frac{x}{4}\right)-\sqrt{x^{2}+16}+c \)
B. \( x \sinh ^{-1}\left(\frac{x}{4}\right)+\sqrt{x^{2}+16}+c \)
c. \( x \sinh ^{-1}\left(\frac{x}{4}\right)-\frac{1}{2} \sqrt{x^{2}+16}+c \)
D \( x \sinh ^{-1}\left(\frac{x}{2}\right)-x \sqrt{x^{2}+16}+c \)
Subject: Maths
If \( \bar{a}, \bar{b} \) and \( \bar{c} \) are non-zero non collinear vectors and \( \theta(\neq 0, \pi) \) is the angle between \( \bar{b} \) and \( \bar{c} \) if \( (\bar{a} \times \bar{b}) \times \bar{c}=\frac{1}{2}|\bar{b}| \bar{c} \mid \bar{a} \)
then \( \sin \theta= \)
A \( \cdot \sqrt{\frac{2}{3}} \)
B. \( \frac{\sqrt{3}}{2} \)
\( c \cdot \frac{4 \sqrt{2}}{3} \)
D. \( \frac{2 \sqrt{2}}{3} \)
Subject: Maths
For given A.P. \( -\frac{1}{2},-\frac{3}{2}, \frac{1}{2},-\frac{3}{2}, . . \) find the
common difference.
A . -1
B. \( -\frac{1}{2} \)
\( c \cdot \frac{3}{2} \)
\( D \)
Subject: Chemistry
pH of the buffer containing \( 0.6 g \) of
acetic acid and \( 8.2 g \) of sodium acetate
in 1 litre of water is: \( \left(p K_{a} \) of acetic acid \right.
\( =4.5) \)
A . 7.5
в. 4.5
c. 5.5
D. 6.5
Subject: Chemistry
A solution is prepaired by mixing \( 8.5 g \)
of \( C H_{2} C l_{2} \) and \( 11.95 g \) of \( C H C l_{3} \). If
vapour pressure of \( \boldsymbol{C H}_{2} \boldsymbol{C l}_{2} \) and
\( C H C l_{3} \) at \( 4298 K \) are 415 and
\( 200 m m H g \) respectively, the mole
fraction of \( \boldsymbol{C H C l}_{3} \) in vapour form is :
(molar mass of \( \left.\boldsymbol{C l}=\mathbf{3 5 . 5} \boldsymbol{g} \boldsymbol{m o l}^{-1}\right) \)
\( \mathbf{A} \cdot 0.162 \)
B. 0.675
c. 0.325
D. 0.486
Subject: Physics
The magnifications produced by a convex lens for two different positions of
an object are \( m_{1} \) and \( m_{2} \) respectively
\( \left(m_{1}>m_{2}\right) . \) If \( d \) is the distance of
separation between the two positions of the object then the focal length of the lens is
A. \( \sqrt{m_{1} m_{2}} \)
в. \( \frac{d}{\sqrt{m_{1}-m_{2}}} \)
c. \( \frac{d m_{1} m_{2}}{m_{1}-m_{2}} \)
D. \( \frac{d}{m_{1}-m_{2}} \)
Subject: Maths
If \( \alpha, \beta \) are the roots of the equation
\( \left(\tan ^{-1}(x / 5)\right)^{2}+(\sqrt{3}- \)
1) \( \tan ^{-1}(x / 5)-\sqrt{3}=0,|\alpha|>|\beta| \) then
This question has multiple correct options
A \( \cdot \alpha+\beta=-5 \pi / 12 \)
в. \( |\alpha-\beta|=35 \pi / 12 \)
\( \mathbf{c} \cdot \alpha \beta=-25 \pi^{2} / 12 \)
D. \( 3 \alpha+4 \beta=0 \)
Subject: Physics
A uniform magnetic field of induction \( \mathrm{B} \)
is confined to a cylindrical region of
radius R. The magnetic field is
increasing at a constant rate of \( \frac{d B}{d t} T s^{-1} . \) An electron of charge \( e \) placed at the point \( P \) on the periphery of the field experiences an acceleration
A \( \cdot \frac{1}{2} \frac{e R}{m} \frac{d B}{d t} \) toward left
B. \( \frac{1}{2} \frac{e R}{m} \frac{d B}{d t} \) toward right
c. \( \frac{e R}{m} \frac{d B}{d t} \) toward left
D. zero
Subject: Chemistry
A reaction in equilibrium is represented by the following equation:
\( \mathbf{2 A}(s)+\mathbf{3 B}(\boldsymbol{g}) \rightleftharpoons \mathbf{3} \boldsymbol{C}(\boldsymbol{g})+\boldsymbol{D}(\boldsymbol{g})+\boldsymbol{O}_{2} \)
if the pressure on the system is reduced to half of its original value then
A. The amounts of \( C \) and \( D \) increases
B. The amounts of \( C \) and \( D \) decreases
c. The amounts of \( B \) and \( D \) decreases
D. All the amounts remain constant
Subject: Physics
To ensure almost 100 per cent
transmittivity, photographic lenses are often coated with a thin layer of dielectric material. The refractive index
of this material is intermediated between that of air and glass (which makes the optical element of the lens)
A typically used dielectric film is \( M g F_{2} \) \( (n=1.38) . \) What should the thickness of the film be so that at the center of the
visible spectrum \( (5500 A) \) there is maximum transmission.
A \( \cdot 5000 \) a
в. 2000 А
c. 1000 a
D. 3000 ,
Subject: Physics
Value(s) of \( \mathrm{m} \) for which system remains at rest (pulleys and strings are ideal)
\( \left[\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right] \)
This question has multiple correct options
\( A \cdot 1 k g \)
B. \( 2 k g \)
\( c .18 k g \)
D. \( 20 k g \)
Subject: Physics
Q Type your question
speed \( v \) in such a way that \( K \) always
moves directly towards \( L, L \) directly
moves towards \( M, M \) directly towards
\( N \) and \( N \) directly towards \( K . \) The four
persons will meet at time \( t= \)
\( ^{A} \cdot \underline{4 d} \)
\( v \)
в. \( \frac{3 d}{v} \)
c. \( \frac{2 d}{v} \)
\( D \cdot d \)
Subject: Maths
The ratio of the measure of the angles in
a rhombus is \( 2: 7 . \) What is the measure
of the four angles?
В. \( 40^{\circ}, 140^{\circ}, 40^{\circ}, 140^{\circ} \)
C \( \cdot 65^{\circ}, 115^{\circ}, 65^{\circ}, 115^{\circ} \)
D. None of the above
Subject: Chemistry
For the reaction, \( \boldsymbol{A}_{2}+\boldsymbol{B}+\boldsymbol{C} \rightarrow \boldsymbol{A} \boldsymbol{C}+ \)
\( A B, \) it is found that tripling the
concentration of \( A_{2} \) triples the rate,
doubling the concentration of C doubles the rate and doubling the concentration of B has no effect.
(a) What is the rate law?
(b) Why the change in concentration of
B has no effect?
Subject: Chemistry
\( Y \) and \( Z \) are, respectively:
A \( \cdot N_{2} O_{5} \) and \( H P O_{3} \)
B. \( N_{2} O_{4} \) and \( H P O_{3} \)
c. \( N_{2} O_{4} \) and \( H_{3} P O_{3} \)
D. \( N_{2} O_{3} \) and \( H_{3} P O_{4} \)
Subject: Physics
A radioactive element has rate of
disintegration 10,000 disintegrations per minute at a particular instant. After four minutes it becomes 2500
disintegrations per minute. The decay constant per minute is
A \( \cdot 0.2 \log _{e}^{2} \)
B . \( 0.5 \log _{e}^{2} \)
c. \( 0.6 \log _{e}^{2} \)
D. \( 0.8 \log _{e}^{2} \)
Subject: Chemistry
\( \boldsymbol{C}_{6} \boldsymbol{H}_{5} \boldsymbol{N} \boldsymbol{H}_{2} \frac{\boldsymbol{0}-\boldsymbol{5}^{0} \boldsymbol{C}}{N a N \boldsymbol{O}_{2}+\boldsymbol{H} C l}(\boldsymbol{A}) \frac{\boldsymbol{K} \boldsymbol{C} \boldsymbol{N}}{\boldsymbol{C u}_{2}(\boldsymbol{C H})_{2}} \)
\( (B) \stackrel{H^{+} / H_{2} O}{\longrightarrow}(C) \)
The product (C) is:
A. \( C_{6} H_{5} C H_{2} N H_{2} \)
в. \( C_{6} H_{5} \)СООН
\( \mathbf{c} \cdot C_{6} H_{5} C O \)
D. All of the above
Subject: Physics
The change in the gravitational
potential energy when a body of mass \( m \)
is raised to a height \( n R \) above the
surface of the earth is (here \( R \) is the
radius of the earth)
A \( \cdot\left(\frac{n}{n+1}\right) m g R \)
B \( \cdot\left(\frac{n}{n-1}\right) m g R \)
c. \( n m g R \)
D. \( \frac{m g R}{n} \)
Subject: Chemistry
(A) 1 faraday \( =96,500 \) coulomb. It is a charge of 1 mole electrons.
(R) 1 faraday charge liberates one gram equivalent of substance at an electrode.
A. Both (R) and (A) are true and reason is the. correct explanation of assertion
B. Both (R) and (A) are true but reason is not correct explanation of assertion
c. Assertion
(A) is true but reason
(R) is false
D. Assertion
(A) and reason
(R) both are false
E. Assertion (A) is false but reason (R) is true
Subject: Chemistry
Assertion
Benzaldehyde does not undergoes aldol condensation
Reason
Benzaldehyde does not contain acidic \( \alpha \)
-Hydrogen
A. Statement- -I is True, Statement-II is True ; Statement-I is a correct explanation for Statement-
is NOT a correct explanation for Statement-
c. statement-l is True, Statement-II is False
D. Statement-lis False, Statement-II is True
Subject: Chemistry
Which one of the following is a correct
set?
A \( \cdot H_{2} O, s p^{3}, \) angular
B. \( H_{2} O, s p^{2} \), linear
c. \( N H_{4}^{+}, d s p^{2} \), square planar
D. \( C H_{4}, d s p^{2} \), tetrahedral
Subject: Physics
The magnitude of a magnetic field at
the centre of a circular coil of radius \( R \)
having \( N \) turns and carrying a current
can be doubled by changing
\( \mathbf{A} \cdot I \) to \( 2 I \) and \( N \) keeping \( R \) unchanged
B. \( N \) to \( \frac{N}{2} \) and keeping \( I \) and \( R \) unchanged
C . \( N \) to \( 2 N \) and \( R \) keeping \( 2 R \) keeping/unchanged
D. \( R \) to \( 2 R \) and \( l \) to \( 2 I \) keeping \( N \) unchanged
E . \( I \) to \( 2 I \) and keeping \( N \) and \( R \) unchanged
Subject: Maths
The constraints
\( -\boldsymbol{x}_{1}+\boldsymbol{x}_{2} \leq 1 \)
\( -\boldsymbol{x}_{1}+\mathbf{3} \boldsymbol{x}_{2} \leq \mathbf{9} \)
\( \boldsymbol{x}_{1}, \boldsymbol{x}_{2} \geq \mathbf{0} \) defines on
A. Bounded feasible space
B. Unbounded feasible space
C. Both bounded and unbounded feasible
D. None of the above
Subject: Maths
If \( \Delta=\left|\begin{array}{lll}\mathbf{5} & \mathbf{3} & \mathbf{8} \\ \mathbf{2} & \mathbf{0} & \mathbf{1} \\ \mathbf{1} & \mathbf{2} & \mathbf{3}\end{array}\right|, \) white the cofactor of
the element \( a_{32} \)
Subject: Chemistry
Assertion
Galvanic cell convert chemical energy into electrical energy.
Reason
Redox reactions are those in which
oxidation takes place at anode and reduction at cathode.
A. If both Assertion and Reason are correct and Reason is the correct explanation of assertion
B. If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion
C. If Assertion is correct but Reason is incorrect
D. If Assertion is incorrect but Reason is correct
Subject: Physics
The fundamental frequency of vibration of \( 1 \mathrm{cm} \) long string is \( 256 \mathrm{Hz} \). If the length of the string is reduced to \( \frac{1}{4} c m \) keeping the tension unaltered, the new fundamental frequency will be
A \( .256 \mathrm{Hz} \)
в. 512 Нг
c. \( 1024 \mathrm{Hz} \)
D. \( 2048 \mathrm{Hz} \)
Subject: Maths
The coordinates of a point on the line
\( \boldsymbol{x}+\boldsymbol{y}+\mathbf{3}=\mathbf{0} \) whose distance from
\( x+2 y+2=0 \) is \( \sqrt{5} \) is equal to
в. (-9,6)
c. (-9,-6)
(年 (-9,-6),(-6)
D. none of these
Subject: Physics
A conductor of non uniform cross
section is connected across a potentia
difference \( V \) as shown in the figure,

Choose the correct option regarding the
conductor
This question has multiple correct options
A. current at \( B \) is same as that of \( A \)
B. current density near at the end A inside the conductor is more than the current density near the end B inside the conductor
C. resistance of thickness dx near the end B is less than
the resistance near the end
D. electric field near the end \( A \) is more than at \( B \)
Subject: Maths
Find the derivative of the following fuctions (it is to be understood that
\( a, b, c, d, p, q, r \) and \( s \) are fixed non-zero
constants and \( \boldsymbol{m} \text { and } \boldsymbol{n} \text { are integers }) \) \( \frac{x}{\sin ^{2} x} \)
Subject: Chemistry
For \( \boldsymbol{H} \) -like atoms:
\[
\boldsymbol{E}_{\boldsymbol{n}}=-\frac{\boldsymbol{Z}^{2} \boldsymbol{R} \boldsymbol{h}}{\boldsymbol{n}^{2}} ; \boldsymbol{u}_{\boldsymbol{n}}=\frac{\boldsymbol{u}_{1} \boldsymbol{Z}}{\boldsymbol{n}} \text { and }
\]
\( r_{n}=\frac{r_{1} \times n^{2}}{Z} ; \) where \( R h \) is Rydberg.
What is the potential energy of electron
\( \operatorname{in} 2^{n d} \) orbit of \( H \) -atom?
\( A \cdot-\frac{R h}{2} \)
B. \( -2 R h \)
c. \( -4 R h \)
D. - Rh
Subject: Maths
Calculate the mean of the following data, using direct method:
\( \begin{array}{lllll}\text { Class } & \begin{array}{l}25- \\ 35\end{array} & \begin{array}{l}35- \\ 45\end{array} & \begin{array}{l}45- \\ 55\end{array} & \begin{array}{l}55- \\ 65\end{array}\end{array} \)
10
8
Frequency 6
Subject: Chemistry
Assertion
\( A \beta \) keto acid is decarboxylated to a ketone on simple heating, even in absence of sodalime catalyst.
Reason
A resonance stabilized carbonion is
formed
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 reaction \( A \rightarrow B \) follows first-order
kinetics. The time taken for 0.8 mol of \( A \)
to produce 0.6 mol of \( \mathrm{B} \) is 1 hr. What is the time taken for the conversion of 0.9
mol of \( A \) to produce 0.675 mol of B?
\( A \cdot 1 h r \)
B. 0.5 hr
c. \( 0.25 \mathrm{hr} \)
\( D \cdot 2 h r \)
Subject: Physics
Displacement of a particle is given by the expression \( x=3 t^{2}+7 t-9, \) where
\( x \) is in meter and \( t \) is in second. What is
acceleration?
\( \mathbf{A} \cdot 1 m / s^{2} \)
B . \( 3 m / s^{2} \)
\( \mathbf{c} \cdot 6 m / s^{2} \)
D. \( 9 m / s^{2} \)
Subject: Chemistry
Four metals \( Z n, F e, C u \) and \( A l \) are
taken and added to the following solutions one by one. The results obtained are tabulated below
Metal \( \quad Z n S O_{4}(a q) \quad F e S O_{4}(a q) \) Displaced \( Z n \) \( \mathrm{Fe} \quad \) No reaction \( \begin{array}{ll}C u & \text { No reaction }\end{array} \quad \) No reaction \( A l \) Displaced \( \quad \) Displaced
From the above data, the decreasing
order of reactivity of metals is
A. \( A l>C u>F e>Z n \)
в. \( A l>Z n>F e>C u \)
c. \( A l>Z n>C u>F e \)
D. \( A l>F e>C u>Z n \)
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{cc}\cos \boldsymbol{\alpha} & -\sin \boldsymbol{\alpha} \\ \sin \boldsymbol{\alpha} & \cos \boldsymbol{\alpha}\end{array}\right], \) then \( \boldsymbol{A}+ \)
\( A^{\prime}=I, \) if the value of \( \alpha \) is
A \( \cdot \frac{\pi}{6} \)
в.
\( c \)
D. \( \frac{3 \pi}{2} \)
Subject: Maths
Add the following expressions: \( 3 x+ \) \( y-8 \) and \( y+4-7 x \)
A. \( 4 x+2 y-4 \)
в. \( -4 x+2 y-4 \)
c. \( -4 x+3 y-4 \)
D. \( 4 x+3 y+4 \)
Subject: Physics
List
List II
A) Constant
I) At highest point speed and varying \( \quad \) of body velocity \( \quad \) projected vertically up
B) Zero
II) Uniform displacement and \( \quad \) circular motion finite distance
III) At any
C) Zero velocity \( \quad \) intermediate point of and finite acceleration \( \quad \) freely falling body
D) Non-zero
IV) Body on reaching point of velocity and nonzero acceleration
The correct match is:
\( A \cdot A-|V, B-| I, C-|I|, D-1 \)
B. \( A-11, B-1 V, C-1, D-11 \)
\( \mathbf{C} \cdot A-\|I, B-I, C-I V, D-\| \)
D. \( A-1, B-111, C-11, D-1 V \)
Subject: Physics
A chain of length \( L \) and mass \( m \) is placed upon a smooth surface. The length of BA is \( (\boldsymbol{L}-\boldsymbol{b}) \). Calculate the
velocity of the chain when its end
reaches B.
B. \( 2 \sqrt{\frac{g \sin \theta}{L}}\left(L^{2}-b^{2}\right) \)
c. \( \sqrt{\frac{g \sin \theta}{L}\left(L^{2}-b^{2}\right)} \)
D. \( \sqrt{\frac{g \sin \theta}{2 L}}\left(L^{2}-b^{2}\right) \)
Subject: Maths
The distance between the points
\( (0,0),\left(x_{1}, y_{1}\right) \) is
units
A \( \cdot \sqrt{x_{1}^{2}+y_{1}^{2}} \)
в. \( \sqrt{x_{1}+y_{1}} \)
\( \mathbf{c} \cdot \sqrt{x_{1}^{2}+y_{1}} \)
\( \mathbf{D} \cdot \sqrt{x_{1}+y_{1}^{2}} \)
Subject: Physics
The distance of \( n^{t h} \) bright band on the
screen from the central bright band on either sides of central bright band is
A \( \cdot x_{n}=\frac{n \lambda D}{d} \)
B・ \( _{x_{n}}=(2 n-1) \frac{\lambda D}{d} \)
c. \( _{x_{n}}=\frac{n \lambda d}{D} \)
D. \( x_{n}=(2 n-1) \frac{\lambda D}{2 d} \)
Subject: Physics
A flat plate moves normally towards a discharging jet of water at the rate of \( \mathbf{3} \boldsymbol{m} / \boldsymbol{s} . \) The jet discharges the water at
the rate of \( 0.1 m^{3} / s \) and at the speed of
\( 18 m / s . \) The force exerted on the plate
due to the jet is:
в. 2100 N
c. \( 2450 N \)
D. \( 1560 N \)
Subject: Chemistry
The degree of dissociation of \( N_{2} O_{4} \) into
\( N O_{2} \) at 1.5 atmosphere and \( 40^{\circ} C \) is
0.25. Calculate its \( K_{p} \) at \( 40^{\circ} \mathrm{C} \). Also report degree of dissociation at 10 atmospheric pressure at same
temperature:
A. \( K_{P}=0.2, \alpha \simeq 0.2 \)
B . \( K_{P}=0.4, \alpha \simeq 0.1 \)
c. \( K_{P}=0.8, \alpha \simeq 0.4 \)
D. None of these
Subject: Chemistry
What is the molarity of \( H C l \) in a solution prepared by dissolving \( 5.5 \mathrm{g} \) \( H C l \) in 200 g ethanol if the density of the solution is 0.79 g/ mL?
A . 0.58 M
B. 0.21
c. 0.93 M
D. 1.7 м
Subject: Physics
A charge of +2 nC is separated from a charge of \( -2 \mathrm{nC} \) by \( 1.5 \mathrm{cm} \) forming an electric dipole. What torque acts on the
dipole moment vector makes an angle
of \( 30^{0} \) in the clockwise sense with the
field of magnitude \( 5000 \mathrm{N} / \mathrm{C} ? \)
Subject: Biology
The given schematic diagram depicts heterodont teeth and its thecodont
arrangement. Find the correct labelling
for \( A-D \) fom the options given below.
A. A - Incisor, B- Canine, C - Premolar
D- Molar
B. A - Molar, B - Premolar, C -Canine, D-Incisor
C. A- Incisors, B-Premolar, C-Canine, D- Molar
D. A - Molar, B- Premolar, C-Incisor, D- Canine
Subject: Chemistry
Assertion
Atoms can neither be created nor
destroyed.
Reason
Under similar condition of temperature
and pressure, equal volume of gases
does not contain equal number of
atoms.
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: Biology
Study the figure which shows the effect
of light on the rate of photosynthesis
based on the graph, answer the following question:
What does \( C \) represent on the curve?
A. It represents that at higher light intensity there is no further increase in photosynthesis and other factors become limiting.
B. It represents that at lower light intensity there is no further increase in photosynthesis and other factors become limiting.
c. Maximum light intensity which can affect the rate of photosynthesis
D. None of the above
Subject: Maths
If \( \boldsymbol{A}=\left[\boldsymbol{a}_{i j}\right] \) is a scalar matrix of order
\( \boldsymbol{n} \times \boldsymbol{n} \) such that \( \boldsymbol{a}_{\boldsymbol{i} i}=\boldsymbol{k} \) for all \( \boldsymbol{i}, \) then
trace of \( \boldsymbol{A} \) is equal to
\( \mathbf{A} \cdot n k \)
\( \mathbf{B} \cdot n+k \)
c. \( \frac{n}{k} \)
D. None of these
Subject: Physics
The phase difference between the two
simple harmonic oscillations, \( \boldsymbol{y}_{1}= \) \( \frac{1}{2} \sin \omega t+\left(\frac{\sqrt{3}}{2}\right) \cos \omega t \) and \( y_{2}= \)
\( \sin \omega t+\cos \omega t \) is
A \( \cdot \frac{\pi}{6} \)
B. \( -\frac{\pi}{6} \)
c. \( \frac{\pi}{12} \)
D. \( \frac{7 \pi}{12} \)