AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
The difference between the wave
number of \( 1^{s t} \) line of Balmer series and
last line of paschen series for \( L i^{2+} \) ion
is :
A \( \cdot \frac{R}{36} \)
в. \( \frac{5 R}{36} \)
c. \( 4 R \)
D. \( \frac{R}{4} \)
Subject: Chemistry
The reactivity of the metals
\( A l, C a, M g \) and \( N a \) follows the order.
A. \( N a>C a>M g>A l \)
в. \( N a>M g>C a>A l \)
c. \( A l>M g>C a>N a \)
D. \( M g>N a>C a>A l \)
Subject: Physics
At two different places, the angles of dip
are respectively \( 30^{\circ} \) and \( 45^{\circ} . \) At these
two places the ratio of horizontal component of earth's magnetic field is:
A. \( \sqrt{3}: \sqrt{2} \)
B. \( 1: \sqrt{2} \)
c. 1: 2
D. \( 1: \sqrt{3} \)
Subject: Physics
The equivalent capacitance of three
capacitors of capacitance \( C_{1}, C_{2} \) and \( C_{3} \)
connected in parallel is 12 units and the
product \( C_{1} C_{2} C_{3}=48 . \) When the
capacitors \( C_{1} \) and \( C_{2} \) are connected in
parallel the equivalent capacitance is 6
units. Then the capacitance are:
\( \mathbf{A} \cdot 1.5,2.5,8 \)
B. 2,3,7
\( \mathbf{c} \cdot 4,2,6 \)
D. 1,5,6
Subject: Maths
Let \( \boldsymbol{R}=\{(\boldsymbol{a}, \boldsymbol{b}): \boldsymbol{a}, \boldsymbol{b} \in \boldsymbol{N} \text { and } \boldsymbol{a}+\boldsymbol{3} \boldsymbol{b}= \)
12 \( \} . \) Find the domain and range of R.
Subject: Physics
A particle of mass 'm' and charge 'Q' is acceleration in cyclotron. if magnetic field is 'B' and radius cyclotron is \( r \) then the kinetic energy of particle.
A \( \cdot \frac{Q B r}{2 m} \)
\( ^{\text {в. }} \frac{Q^{2} B^{2} r}{2 m} \)
c. \( \frac{Q^{2} B^{2} r^{2}}{2 m} \)
D. \( \frac{Q^{2} B^{2} r^{2}}{m} \)
Subject: Physics
A thin conducting strip of width \( h= \) \( 2.0 \mathrm{cm} \) is tightly wound in the shape of
a very long coil with cross-section radius \( R=2.5 \mathrm{cm} \) to make a single-
layer straight solenoid. A direct current \( \boldsymbol{I}=\mathbf{5 . 0} \boldsymbol{A} \) flows through the strip. Find
the magnetic induction inside and
outside the solenoid as a function of the
distance \( r \) from its axis.
Subject: Maths
If the tangent at any point of an ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \) makes an angle \( \alpha \) with
the major axis and an angle \( \beta \) with the
focal radius of the point of contact then show that the eccentricity'e' of the ellipse is given by the absolute value of \( \frac{\cos \beta}{\cos \alpha} \)
Subject: Chemistry
Assertion
Boiling point of \( H F \) is lesser than
water
Reason
Hydrogen bonding in water is weaker
than \( \boldsymbol{H} \boldsymbol{F} \)
A. Assertion is true, Reason is true and Reason is correct explanation for Assertion
B. Assertion is true, Reason is true and Reason is not the correct explanation for Assertion
C. Assertion is true, Reason is false
D. Assertion is false, Reason is true
Subject: Biology
The correct labels from A to E are
A. \( A \) - Spathe bract, \( B \) - Female flowers, \( C \) - Male flowers, Neuter flowers, E - Appendage
B. A- Appendage, B - Female flowers, C - Male flowers, D Neuter flowers, E -Spathe bract
C. A - Appendage, B - Male flowers, C - Female flowers, D Neuter flowers, E -Spathe bract
D. A - Appendage, B - Male flowers, C - Neuter flowers, D Female flowers, E - Spathe bract
Subject: Chemistry
\( C(\text { diamond }) \rightarrow C(\text { graphite }), \Delta S_{300}= \)
\( \mathbf{1 0} \) cal \( \boldsymbol{m o l}^{-1} \)
\( \boldsymbol{C}(\text { diamond })+\boldsymbol{O}_{2} \rightarrow \boldsymbol{C} \boldsymbol{O}_{2} ; \boldsymbol{\Delta} \boldsymbol{H}=-\mathbf{9 1} \)
kcal \( m o l^{-1} \) at \( 300 K \)
\( \boldsymbol{C}(\text { graphite })+\boldsymbol{O}_{2} \rightarrow \boldsymbol{C} \boldsymbol{O}_{2} ; \boldsymbol{\Delta} \boldsymbol{H}=\boldsymbol{x} \) at
\( \mathbf{3 0 0 K} \)
\( x \) is:
A. -81 kcal
B. 101 kcal
c. -94 kcal
D. 88 kcal
Subject: Chemistry
If enthalpies of formation for
\( C_{2} H_{4}(g), C O_{2}(g) \) and \( H_{2} O(I) \) at \( 25^{0} C \)
and 1 atm pressure are \( 52 ;-394 \) and \( -286 k J / m o l \) respectively, then
enthalpy of combustion of \( C_{2} H_{4}(g) \) will
be?
Subject: Maths
Evaluate \( \frac{(\boldsymbol{x}+\boldsymbol{\alpha})(\boldsymbol{x}+\boldsymbol{\beta})}{(\boldsymbol{\alpha}-\gamma)(\boldsymbol{\beta}-\boldsymbol{\gamma})}+ \)
\( \frac{(\boldsymbol{x}+\boldsymbol{\beta})(\boldsymbol{x}+\boldsymbol{\gamma})}{(\boldsymbol{\beta}-\boldsymbol{\alpha})(\boldsymbol{\gamma}-\boldsymbol{\alpha})}+\frac{(\boldsymbol{x}+\boldsymbol{\alpha})(\boldsymbol{x}+\boldsymbol{\gamma})}{(\boldsymbol{\gamma}-\boldsymbol{\beta})(\boldsymbol{\alpha}-\boldsymbol{\beta})}=? \)
Subject: Physics
Two balls are moving on the same smooth horizontal plane. Their velocity components along one edge of the square plane are \( 10 \sqrt{3} m / s \) and \( 20 m / s \) respectively. Their velocity components along a perpendicular edge are \( 30 m / s \) and \( 20 m / s \) respectively Find the angle between their directions of motion.
A . 15
в. \( 30^{\circ} \)
\( c \cdot 60 \)
D. 45
Subject: Chemistry
\( K_{P} \) for reaction \( A+B \rightleftharpoons C+D \) is 1.34
\( \operatorname{at} 60^{\circ} \mathrm{C} \) and 6.64 at \( 100^{\circ} \mathrm{C} . \) Determine
the free energy change of this reaction at each temperature and \( \Delta H^{o} \) for the reaction over this range of
temperature?
A. 405J/mol ; 5872 J/mol and 41.3 kJ/mol
B. 810 J/mol ; 5870 J/mol and 41.3 kJ/mol
c. \( 405 J / \mathrm{mol} \); \( 5 \mathrm{J} / \mathrm{mol} \) and \( 20.56 \mathrm{kJ} / \mathrm{mol} \)
D. 810 J/mol; 29362 J/mol and 20.56 kJ/mo
Subject: Chemistry
Freshly precipitated \( A l \) and \( M g \) hydroxides are stirred vigorously in a buffer solution containing \( 0.25 M \) of \( N H_{4} C l \) and \( 0.05 M \) of \( N H_{4} O H .\left[A l^{3+}\right] \)
and \( \left[M g^{2+}\right] \) in solution are:
Given:
\( \boldsymbol{K}_{b} \) for \( \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{O} \boldsymbol{H}=\mathbf{1} . \boldsymbol{8} \times \mathbf{1 0}^{-\mathbf{5}} \)
\( \boldsymbol{K}_{s p_{A(O H)_{3}}}=\boldsymbol{6} \times \mathbf{1 0}^{-\mathbf{3 2}} \)
\( \boldsymbol{K}_{s p_{M g(O H)_{2}}}=\mathbf{8 . 9} \times \mathbf{1 0}^{-12} \)
A. \( 0.656 M \)
A
в. 0.686 М
\( c .0 .698 M \)
D. none of these
Subject: Maths
If \( \boldsymbol{A}=(-2,3,4), B=(1,2,3) \) are two
points and \( P \) is the point of intersection
of \( A B \) and \( z x \) -plane, then \( P_{x}+P_{y}+ \)
\( \boldsymbol{P}_{z}= \)
\( \mathbf{A} \cdot \mathbf{6} \)
B. -8
c. 8
D.
Subject: Physics
If the equation \( y_{1}=A \sin \omega t \) and \( y_{2}= \) \( \frac{\boldsymbol{A}}{\mathbf{2}} \sin \omega \boldsymbol{t}+\frac{\boldsymbol{A}}{\mathbf{2}} \cos \omega \boldsymbol{t} \) represent SHM
then the ratio of the amplitudes of the two motions is
A . 0.5
B. \( \sqrt{2} \)
c. 1
D. 2
Subject: Chemistry
For the reaction: \( \mathbf{3} \boldsymbol{A}+\boldsymbol{B} \rightarrow \boldsymbol{C}+\boldsymbol{D} \)
mechanism is Step \( 1: \boldsymbol{A}+\boldsymbol{B} \stackrel{\boldsymbol{k}_{1}}{\longrightarrow} \boldsymbol{E} \)
Step \( 2: E+2 A \stackrel{k_{2}}{\longrightarrow} C+D \)
What is the total order of reaction
considering steady state approximation?
Subject: Chemistry
For the reaction equilibrium \( 2 N O B r_{(g)} \leftrightharpoons 2 N O_{(g)}+B r_{2(g)}, \) if
\( P_{B r_{2}}=\frac{P}{9} \) at equilibrium and \( P \) is the initial total pressure, then the ratio \( \frac{\boldsymbol{K}_{\boldsymbol{P}}}{\boldsymbol{P}} \)
is equal to :
A \( \cdot \frac{1}{9} \)
в. \( \frac{4}{441} \)
c. \( \frac{1}{27} \)
D. \( \frac{1}{3} \)
Subject: Physics
When a car of mass \( 1200 \mathrm{kg} \) is moving
with a velocity of \( 15 \mathrm{ms}^{-1} \) on a rough horizontal road. Its engine is switched off. How far does the car travel before it
comes to rest if the coefficient of
kinetic friction between the road and
tyres of the car is \( 0.5 ?\left(g=10 m s^{-2}\right) \)
\( \mathbf{A} \cdot 6.2 m \)
в. 20 \( m \)
c. \( 22.5 m \)
D. 30
Subject: Maths
The order of the matrix \( \left[\begin{array}{c}-1 \\ 3 \\ 4\end{array}\right] \) is :
\( \mathbf{A} \cdot 1 \times 3 \)
B. \( 3 \times 1 \)
c. \( 1 \times 1 \)
D. \( 3 \times 3 \)
Subject: Maths
If the latus rectum of an ellipse \( \boldsymbol{x}^{2} \tan ^{2} \varphi+\boldsymbol{y}^{2} \sec ^{2} \varphi=1 \) is \( 1 / 2 \) then \( \varphi \)
is
\( \mathbf{A} \cdot \pi / 2 \)
в. \( \pi / 6 \)
c. \( \pi / 3 \)
D. \( 5 \pi / 12 \)
Subject: Chemistry
Assertion: The solubility product of hydroxide of \( F e^{2+} \) is higher than that of
\( \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+} \)
Reason: The lattice energy of \( \boldsymbol{F e}(\boldsymbol{O} \boldsymbol{H})_{2} \)
is lower than that of \( F e(O H)_{3} \)
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false
Subject: Maths
If \( \vec{a}, \vec{b}, \vec{c}, \vec{d} \) are the position vectors of the points \( A, B, C, D \) respectively such that \( 3 \vec{a}+5 \vec{b}-3 \vec{c}-5 \vec{d}=0 \) then \( A B \)
intersects \( C D \) in the ratio
A .2: 3
B. 3: 2
c. 3: 5
D. 5: 3
Subject: Physics
Two particles move on a circular path (one just inside and the other just
outside) with angular velocities \( \omega \) and
\( 5 \omega \) starting from the same point. Then:
This question has multiple correct options
A \cdot they cross each other at regular intervals of time \( \frac{\pi}{2 \omega} \) when their angular velocities are directed opposite to each other
B. they cross each other at points on the path subtending an angle of \( 60^{\circ} \) at the centre if their angular velocities are directed opposite to each other
C . they cross at intervals of time \( \frac{\pi}{3 \omega} \) if their angular velocities are directed opposite to each other
D. they cross each other at points on the path subtending \( 90^{\circ} \) at the centre if their angular velocities are similar to each other
Subject: Maths
The vertices \( A \) and \( B \) of a triangle \( A B C \)
\( \operatorname{are}(2,1) \) and (3,-2) respectively. If the third vertex \( C \) lies on the locus \( y=x+ \)
9 and the centroid of \( \triangle A B C \) lies on \( Y \)
axis, then find the area.
Subject: Maths
If \( \boldsymbol{A}=\left|\begin{array}{lll}\boldsymbol{a} & \boldsymbol{0} & \boldsymbol{0} \\ \boldsymbol{0} & \boldsymbol{a} & \boldsymbol{0} \\ \boldsymbol{0} & \boldsymbol{0} & \boldsymbol{a}\end{array}\right|, \) then the value of
\( |\boldsymbol{A}||\boldsymbol{a} \boldsymbol{d} \boldsymbol{j}(\boldsymbol{A})| \) is
A \( \cdot a^{3} \)
в. \( a^{6} \)
\( c \cdot a^{9} \)
D. \( a^{2} \)
Subject: Chemistry
Which of the following reactions occurs
at cathode during charging of storage
battery?
\( \mathbf{A} \cdot P b^{2+}+2 e^{-} \rightarrow P b \)
B \( \cdot P b \rightarrow P b^{2+}+2 e^{-} \)
\( \mathbf{c} \cdot P b^{2+}+S O_{4}^{2-} \rightarrow P b S O_{4} \)
D \( \cdot P b S O_{4}+2 H_{2} O \rightarrow P b O_{2}+4 H^{+}+S O_{2}^{2-}+2 e^{-} \)
Subject: Maths
A vertical tree stands on a hill side that
makes an angle \( \alpha \) with the horizontal From a point directly up the hill from the tree, the angle of elevation of three top
is
\( \beta . \) From a point \( \mathrm{m} \mathrm{cm}, \) further up the
hill, the angle of depression of the tree top is \( \gamma \). If the tree is \( \mathrm{H} \mathrm{cm} \). tall, express
\( \mathrm{H} \) in terms of \( \boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\gamma} \)
Subject: Physics
Two boats \( A \) and \( B \) having same speed relative to river are moving ina river Boat A moves normal to the river
current as observed by an observer moving with velocity of river current.Boat B moves normal to the river
as observed by the observer on the ground.
A. To a ground observer boat B moves faster than A
B. To a ground observer boat A moves faster than B
c. To the given moving observer boat B moves faster than A
D. To the given moving observer boat A moves faster than B
Subject: Chemistry
The following data were obtained during the first order thermal decomposition of
\( S O_{2} C l_{2} \) at constant volume
\[
\boldsymbol{S} \boldsymbol{O}_{2} \boldsymbol{C l}_{2(\boldsymbol{g})} \rightarrow \boldsymbol{S} \boldsymbol{O}_{2(\boldsymbol{g})}+\boldsymbol{C l}_{2(\boldsymbol{g})}
\]
Expt Time / \( S^{-1} \quad \) Total pressure/ atm
0.5
\( 0 . \)
when the total pressure is 0.65 atm then the rate constant of reaction is
if \( a=p i, \) and \( a-x=2 p i-P t \)
A. 2.0 \( \times 10^{-3} \mathrm{S}^{-1} \)
в. 2.12 \( \times 10^{-3} S^{-1} \)
c. \( 2.23 \times 10^{-3} S^{-1} \)
D. 2.34 \( \times 10^{-3} S^{-1} \)
Subject: Chemistry
A substance 'A decomposes in solution following the first order kinetics. Flask contains I L of 1 M solution of A and flask
II contains \( 100 \mathrm{mL} \) of \( 0.6 \mathrm{M} \) solution
After \( 8 \mathrm{hr} \), the concentration, of \( \mathrm{A} \) in flask I becomes 0.25 M. What will be the
time for concentration of \( A \) in flask II to
become 0.3 M?
A. \( 0.4 \mathrm{hr} \)
B. 2.4 hr
c. \( 4.0 \mathrm{hr} \)
D. Unpredictable as rate constant is not given
Subject: Chemistry
The mechanism of the reaction:
\( 2 N O+O_{2} \longrightarrow 2 N O_{2} \) is,
\( N O+N O \overbrace{K_{-1}}^{k_{1}} N_{2} O_{2}(f a s t) \)
\( N_{2} O_{2}+O_{2} \stackrel{k_{2}}{\longrightarrow} 2 N O_{2}(s l o w) \)
The rate constant of the reaction is :
A \( \cdot k_{2} \)
B. \( k_{2} k_{1}\left(k_{-1}\right) \)
\( c \cdot k_{2} k \)
D. \( k_{2}\left(\frac{k_{1}}{k_{1}}\right) \)
Subject: Physics
Two point dipoles \( p \hat{k} \) and \( \frac{p}{2} \hat{k} \) are located at (0,0,0) and \( (1 \mathrm{m}, 0,2 \mathrm{m}) \). Find
the field at the point (1,0,0)
\( ^{A} \cdot \frac{9 p}{32 \pi \varepsilon_{0}} \hat{k} \)
в. \( \frac{-7 p}{32 \pi \varepsilon_{0}} \)
c. \( \frac{7 p}{32 \pi \varepsilon_{0}} \)
D. none of these
Subject: Chemistry
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{C H C l}_{2}+ \)
\( N a N H_{2} / N H_{3} \rightarrow \)
How many \( s p \) hybridized carbon atoms are present in the product.
Subject: Chemistry
In the following reaction
\[
\begin{array}{c}
\boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{2}+\boldsymbol{B} \boldsymbol{r} \boldsymbol{O}_{3}^{-}+\boldsymbol{H}_{2} \boldsymbol{O} \longrightarrow \boldsymbol{X} \boldsymbol{e}+ \\
\boldsymbol{B r} \boldsymbol{O}_{4}^{-}+\mathbf{2} \boldsymbol{H} \boldsymbol{F}
\end{array}
\]
equivalent mass of \( B r O_{3}^{-}= \)
molar mass
Subject: Maths
Solve the equation:cos \( ^{-1}\left(\frac{x^{2}-1}{x^{2}+1}\right)+ \)
\( \sin ^{-1}\left(\frac{2 x}{x^{2}+1}\right)+\tan ^{-1}\left(\frac{2 x}{x^{2}-1}\right)= \)
3
A \( \cdot \frac{1}{\sqrt{3}} \)
B. \( \cot 20^{\circ} \)
\( c \cdot \frac{-1}{\sqrt{3}} \)
D. \( \tan 20 \)
Subject: Maths
The angle between the vectors \( \overrightarrow{\boldsymbol{a}}=\hat{\boldsymbol{i}}+ \) \( \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) and \( \overrightarrow{\boldsymbol{b}}=\hat{\boldsymbol{i}}+\boldsymbol{2} \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) is?
A \( \cdot \tan ^{-1} \frac{1}{2 \sqrt{2}} \)
в. \( \tan ^{-1} \frac{1}{3} \)
\( ^{\mathbf{c}} \cdot \tan ^{-1}\left(\frac{1}{2}\right) \)
D. \( 90^{\circ} \)
Subject: Physics
501
\( (G e) \) and other of silicon \( (S i) \) are
connected as shown in figure to a
battery of emf 12 v and a load
resistance \( 10 k \) \Omega. The germanium
diode conducts at \( 0.3 \mathrm{V} \) and silicon
diode at \( 0.7 \mathrm{V} \). When a current flows in
the circuit, then the potential of
terminal \( Y \) will be:
\( \mathbf{A} \cdot 12 V \)
B. \( 11 V \)
c. \( 11.3 V \)
D. \( 11.7 V \)
Subject: Physics
Give the essential conditions (any two)
for the source to be Coherent.
(b) In
Young's double slit experiment, using
monochromatic light of wavelength \( \lambda \)
the intensity of light at a point on the screen where path difference is I, is \( 2 K \) units. Find out the intensity of light at a point where path difference is \( \lambda / 6 \)
Subject: Physics
Assertion
Snow is better insulator than ice.
Reason
Snow contain air packet and air is good
insulator of heat.
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: Physics
Q Type your question
two parts are tield together by a ring made of a metal strip of cross-sectional area \( \mathrm{S} \) and length L. L is slightly less
than \( 2 \pi R \). To fit the ring on the wheel, it
is heated so that its temperature rises
by \( \Delta T \) and it just steps over the wheel
As it cools down to surrounding
temperature, it presses the semicircular parts together. If the coefficient of linear expansion of the
metal is \( \alpha \) and its Young's modulus is
U, the force that one part of the wheel
applies on the other part is?
\( \mathbf{A} \cdot S Y \alpha \Delta T \)
в. \( \pi S Y \alpha \Delta T \)
\( \mathbf{c} \cdot 2 S Y \alpha \Delta T \)
Subject: Physics
A proton of mass \( m \) and charge \( q \) is
moving in a plane with kinetic energy \( \boldsymbol{E} \) If there exists a uniform magnetic field
\( B, \) perpendicular to the plane of the motion the portion will move in a circular path of radius
A \( \cdot \frac{2 E m}{q B} \)
в. \( \frac{\sqrt{2 E m}}{q B} \)
c. \( \frac{\sqrt{E m}}{2 q B} \)
D. \( \sqrt{\frac{2 E q}{m B}} \)
Subject: Maths
Which of the following are not equivalence relations on I?
\( A \). a \( R b \) if \( a+b \) is an even integer
B. a R b if \( a-b \) is an even integer
\( \mathbf{c} \cdot \) a \( \mathrm{R} \mathrm{b} \) if \( a<b \)
D. a R b if \( a=b \)
Subject: Maths
\( \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \sin ^{2} x \cdot \cos ^{3} x d x \) is equal to
A. \( \frac{4 \pi}{30} \)
B. \( \frac{4}{15} \)
c. \( \frac{\pi}{30} \)
D. \( \frac{1}{15} \)
Subject: Biology
Fill in the blanks.
\( \boldsymbol{C}_{6} \boldsymbol{H}_{12} \boldsymbol{O}_{6} \rightarrow \ldots \ldots \ldots+2 \boldsymbol{C} \boldsymbol{O}_{2}+\boldsymbol{2} \boldsymbol{A} \boldsymbol{T} \boldsymbol{P} \)
Subject: Maths
The function \( f(x)=\sin x-k x-c \)
where \( k \) and \( c \) are constants, decreases
always when
\( \mathbf{A} \cdot k>1 \)
в. \( k \geq 1 \)
c. \( k<1 \)
D. \( k \leq 1 \)
E . \( k<-1 \)
Subject: Chemistry
An atom has \( x \) energy level, then total
number lines in its spectrum are?
A \( .1+2+3 \ldots .(x+1) \)
B. \( 1+2+3 \ldots\left(x^{2}\right) \)
c. \( 1+2+3 \ldots .(x-1) \)
D. \( (x+1)(x+2)(x+4) \)
Subject: Chemistry
Which of the following statements is/are correct about the ionic product of
water?
This question has multiple correct options
A \( . \) K (equilibrium constant of water) \( <\mathrm{K}_{w} \)
\( \mathbf{B} \cdot \mathrm{pK}>\mathrm{pK}_{w} \)
C \( \left.. \text { At } 100^{\circ} \mathrm{C} \mathrm{Kw}=7.5 \times 10^{-14} \text {(moles } / \text {lit}\right)^{2} \)
D. Ionic product of water at \( 25^{0} \mathrm{Cis} 10^{-14} \)
Subject: Physics
The optical path of a monochromatic light is the same if it goes through 2.00 \( \mathrm{cm} \) of glass or \( \mathrm{x} \mathrm{cm} \) of ruby. If the refractive index of glass is 1.510 and that of ruby is 1.760 find the value of \( x \)
is
\( \mathbf{A} \cdot 1.716 \)
B. 1.525
c. 2.716
D. 2.525
Subject: Physics
The dimension of coefficient of viscosity
\( \eta \) is :
\( \mathbf{A} \cdot\left[M L^{-1} T^{-1}\right] \)
\( \mathbf{B} \cdot\left[M L T^{-2}\right] \)
\( \mathbf{c} \cdot\left[M L T^{-1}\right] \)
D. \( \left[M L^{2} T^{-2}\right] \)
Subject: Physics
Assertion
Voltmeter is much better than a
potentiometer for measuring emf of cell
Reason

A potentiometer draws no current while measuring emf of a cell.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
Subject: Chemistry
Which of the hydrated species may
exist?
\( \mathrm{I}: \boldsymbol{H}_{5} \boldsymbol{O}_{2}^{+} \)
\( \|: \boldsymbol{H}_{3} \boldsymbol{O}^{+} \)
\( \|: \boldsymbol{H}_{5} \boldsymbol{O}_{2} \)
\( \mathbf{I V}: \boldsymbol{H}_{\mathbf{7}} \boldsymbol{O}_{\mathbf{3}}^{+} \)
A. Il only
B. 1 and I
c. I, Il and IV
D. I. II. III and IV
Subject: Physics
A beam of protons with a velocity \( 4 \times \) \( 10^{5} m s^{-1} \) enters a uniform magnetic
field of \( 0.3 \mathrm{T} \) at an angle of \( 60^{\circ} \) to the
magnetic field. Find the pitch of the helix (which is the distance travelled by a proton in the beam parallel to the magnetic field during one period of the rotation). Mass of the proton \( =1.67 \times \)
\( \mathbf{1 0}^{-2 \mathbf{7}} \mathbf{k g} \)
\( A \cdot 2.3 \mathrm{cm} \)
B. 5.35 \( \mathrm{cm} \)
\( c \cdot 4.35 \mathrm{cm} \)
D. 6.35 \( \mathrm{cm} \)
Subject: Physics
If a rubber ball is taken at the depth of \( 200 \mathrm{m} \) in a pool its volume decreases by
\( 0.1 \% \) If the density of the water is \( 1 \times \) \( 10^{3} k g / m^{3} \) and \( g=10 m / s^{2} \) then the
volume elasticity in \( N / m^{2} \) will be
A \( \cdot 10^{8} \)
в. \( 2 \times 10^{8} \)
\( c \cdot 10^{9} \)
D. \( 2 \times 10^{9} \)
Subject: Physics
topp
rype vourquestion
above. If a student plots graphs of the
square of maximum charge \( \left(Q_{\operatorname{Max}}^{2}\right) \) on the capacitor with time (t) for two
different values \( L_{1} \) and \( L_{2}\left(L_{1}>L_{2}\right) \) of
then which of the following represents
this graph correctly? (plots schematic and not drawn to scale
Subject: Physics
Assertion
In the siphon shown in figure, pressure
at \( P \) is equal to atmospheric pressure.
Reason

Pressure at \( Q \) is atmospheric pressure
and points \( \mathrm{P} \) and \( \mathrm{Q} \) are at same levels.
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: Physics
A tank of large base area is filled with
water up to a height of 5 m. A hole of
\( 2 \mathrm{cm}^{2} \) cross section section in the
bottom allows the water to drain out in
continuous streams. For this situation,
mark out the correct statement(s) (take
\[
\left.\boldsymbol{\rho}_{\boldsymbol{w} \boldsymbol{a} \boldsymbol{t} e r}=\mathbf{1 0 0 0} \boldsymbol{k} \boldsymbol{g} /^{2}, \boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} / \boldsymbol{s}^{2}\right)
\]
This question has multiple correct options
A. The cross sectional area of the emerging stream of water decreases as it falls down
B. The cross sectional area of the emerging stream of water increases as it falls down
C. At a distance of \( 5 \mathrm{m} \) below the bottom of the tank, the
cross-sectional area of the stream is \( 1.414 \mathrm{cm}^{2} \)
D. At a distance of \( 5 m \) below the bottom of the tank, the cross-sectional area of the stream is \( 2.86 \mathrm{cm}^{2} \)
Subject: Chemistry
The correct IUPAC name of the following compound is
\( \left[\boldsymbol{C r}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5}(\boldsymbol{N} \boldsymbol{C S})\right]\left[\boldsymbol{Z n C l}_{4}\right] \)
A. pentaammine isothiocyanato chromium(III) tetrachlorozincate(II)
B. pentammine isothiocyanate zinc chloridechromate(III)
c. pentaammine isothiocyanato chromate(II)
D. isothiocyanato pentaammine chromium(II) zinc chloride(IV).
Subject: Physics
The focal length of a concave mirror is and the distance from the object to the principal focus is p. The ratio of the size of the real image to the size of the object is:
A. \( -\frac{f}{p} \)
в.
\[
\left(\frac{f}{p}\right)^{2}
\]
\( c \)
\[
\left(\frac{f}{p}\right)^{\frac{1}{2}}
\]
D. \( -\frac{p}{f} \)
E . \( -f p \)