AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
\( \boldsymbol{A}=\left[\begin{array}{cc}-\mathbf{3} & -\mathbf{5} \\ -\mathbf{6} & \mathbf{0}\end{array}\right], \boldsymbol{A}-\boldsymbol{B}=\mathbf{2} \boldsymbol{I} . \) Find \( \boldsymbol{B} \)
\( \mathbf{A} \cdot\left[\begin{array}{cc}-5 & -5 \\ -6 & -2\end{array}\right] \)
в. \( \left[\begin{array}{cc}1 & 2 \\ -3 & -6\end{array}\right] \)
с. \( \left[\begin{array}{cc}5 & 5 \\ -3 & -6\end{array}\right] \)
О \( \cdot\left[\begin{array}{ll}1 & 2 \\ 3 & 6\end{array}\right] \)
Subject: Physics
The value of relative magnetic
permeability \( \left(\mu_{r}\right) \) for ferromagnetic materials is
A \( \cdot\left(\mu_{r}=1\right) \)
В \( \cdot\left(\mu_{r}>>1\right) \)
c. \( \left(\mu_{r}<1\right) \)
D. \( \left(\mu_{r}>1\right) \)
Subject: Physics
At room temperature, copper has free electron density of \( 8.4 \times 10^{28} m^{-3} . \) The
electron drift velocity in a copper conductor of cross-sectional area of
\( 10^{-6} m^{2} \) and carrying a current of \( 5.4 A \) will be
A \( \cdot 4 m s^{-1} \)
B. \( 0.4 \mathrm{ms}^{-1} \)
\( \mathrm{c} \cdot 4 \mathrm{cms}^{-1} \)
D. \( 0.4 \mathrm{mms}^{-1} \)
Subject: Maths
\( \left(\frac{2}{5} a b+c\right)\left(\frac{2}{5} a b-c\right) \) is equal to
A \( \cdot \frac{4}{25} a^{2} b^{2}-\frac{4}{5} a b c+c^{2} \)
B \( \cdot \frac{4}{25} a^{2} b^{2}+\frac{4}{5} a b c+c^{2} \)
C \( \frac{4}{25} a^{2} b^{2}-c^{2} \)
D \( \cdot \frac{4}{25} a^{2} b^{2}+c^{2} \)
Subject: Chemistry
Heat of formation of \( \boldsymbol{H}_{2} \boldsymbol{O}(g) \) at \( \boldsymbol{2} \boldsymbol{5}^{0} \boldsymbol{C} \) is
\( -243 \mathrm{KJ} . \Delta U \) for the reaction \( \boldsymbol{H}_{2}(\boldsymbol{g})+ \)
\( \frac{1}{2} O_{2}(g) \rightarrow H_{2} O(g) \) at \( 25^{0} C \) is:
A. 241.8 KJ
B . -241.8 KJ
c. -243 к
D. 243 KJ
Subject: Physics
At a certain place, the angle of dip \( 30^{\circ} \) and the horizontal component of earth's
magnetic field is 0.50 oerested.The earth's total magnetic field (in oerested) is
A. \( \sqrt{3} \)
B.
c. \( \frac{1}{\sqrt{3}} \)
D. \( \frac{1}{2} \)
Subject: Chemistry
Pitch-Blende is the source of some
metals. Find the total No. of such metals
among these:
\( [\boldsymbol{H} \boldsymbol{g}, \boldsymbol{R} \boldsymbol{a}, \boldsymbol{U}, \boldsymbol{T} \boldsymbol{h}, \boldsymbol{Z} \boldsymbol{n}, \boldsymbol{T} \boldsymbol{c}] \)
Subject: Physics
A balloon is rising vertically upwards at a velocity of \( 10 \mathrm{m} / \mathrm{s} \). When it is at a
height of \( 45 m \) from the ground,a parachutist bails out from it. After \( 3 \operatorname{second} s \) he openshis parachute and
decelerates at a constant rate of
\( 5 m / s^{-2} . \) What was the height of the parachutist above the ground when he
opened his parachute?(take \( \boldsymbol{g}= \)
\( \left.\mathbf{1 0 m} / \boldsymbol{s}^{-\mathbf{2}}\right) \)
\( \mathbf{A} \cdot 15 \mathrm{m} \)
B. 30 \( m \)
\( c \cdot 45 m \)
D. \( 60 \mathrm{m} \)
Subject: Maths
\( \operatorname{Let} f(x)=\frac{1}{a x+b} \) then \( f^{\prime \prime}(0)= \)
A \( \cdot \frac{2 a^{3}}{b^{2}} \)
в. \( \frac{2 a^{2}}{b^{3}} \)
c. \( \frac{2 a^{3}}{b^{3}} \)
D. none of these
Subject: Physics
A thin plano-convex lens of focal length
\( f \) is split into two halves. One of the
halves is shifted along the optical axis.
The separation between the object and
image planes is 1.8 m. The
magnification of the image formed by
one of the half lenses is 2

Find the focal length of the lens used.
\( \mathbf{A} \cdot 0.4 m \)
B. \( 0.8 m \)
\( \mathbf{c} .0 .6 m \)
D. \( 2 m \)
Subject: Chemistry
If reaction \( A \) and \( B \) are given with Same temperature and same concentration but rate of \( A \) is double than \( B \). Pre
exponential factor is same for both the reaction then difference in activation
energy \( \boldsymbol{E}_{\boldsymbol{A}}-\boldsymbol{E}_{\boldsymbol{B}} \) is?
\( \mathbf{A} \cdot-R T \ln 2 \)
в. \( R T \ln 2 \)
c. \( 2 R T \)
D. \( \frac{R T}{2} \)
Subject: Maths
Three coins are tossed once. Describe
the following events associated with this random experiment. \( \boldsymbol{A}= \) Getting three heads, \( \boldsymbol{B}= \) Getting
two heads and one tail
\( \boldsymbol{C}= \) Getting three tails, \( \boldsymbol{D}= \) Getting a head on the first coin.
Which events are compound events
Subject: Maths
The cartesian product \( \boldsymbol{A} \times \boldsymbol{A} \) has \( \mathbf{9} \)
elements among which are found
(-1,0) and \( (0,1) . \) Find the set \( A \) and the
remaining elements of \( \boldsymbol{A} \times \boldsymbol{A} \)
Subject: Physics
Three blocks, each of same mass \( m \)
are connected with wire \( W_{1} \) and \( W_{2} \) of
same cross sectional area 'a' and

Young's modulus Y. Neglecting friction,
the strain developed in wire \( W_{2} \) is
A \( \frac{2 m g}{3} \frac{m g}{a Y} \)
в. \( \frac{3}{2} \frac{m g}{a Y} \)
\( c \)
\( D \)
Subject: Physics
A beam of light, consisting of red, green and blue colours, is incident on a right-
angled prism, as shown. the refractive indices of the material of the prism for
the above red, green and blue wavelengths are 1.391 .44 and 1.47
respectively. The prism will :
A. separate part of the red colour from the green and blue colours
B. separate part of the blue colour from the red and green colours
c. separate all the three colours from one another
D. not separate even partially any colour from the other tow colours
Subject: Maths
The rate of change of volume of sphere with respect to its surface area \( S \) is
A. \( \sqrt{\frac{S}{\pi}} \)
в. \( \frac{1}{2} \sqrt{\frac{S}{\pi}} \)
\( ^{c} \cdot \frac{1}{4} \sqrt{\frac{S}{\pi}} \)
D. \( 4 \sqrt{\frac{S}{\pi}} \)
Subject: Chemistry
If \( C u \) reacts with conc. \( H_{2} S O_{4}, \) then
what reactions take place:
A \( . C u \) is oxidised to \( C u^{2} \)
B. \( S O_{4}^{2-} \) is reduced to \( S O_{2} \)
c. Both of the above reactions take place
D. None of the above reaction take place
Subject: Physics
If \( a, b, c \) are the percentage errors in the
measurement of \( \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C} \) then
percentage error in \( \boldsymbol{A B C} \) would be
A \( . a b c \)
B . \( a+b+c \)
c. \( a b+b c+c a \)
D. \( a-b-c \)
Subject: Physics
In a one-dimensional collision between
two particles, their relative velocity is \( \bar{v}_{1} \)
before the collision and \( \bar{v}_{2} \) and the
collision.

This question has multiple correct options
A \( . \overline{v_{1}}=\overline{v_{2}} \) if the collision is elastic.
B. \( \overline{v_{1}}=-\overline{v_{2}} \) if the collision is elastic.
\begin{tabular}{l|l} 
c. \( |\overline{v_{2}}|=\left|v_{1}\right| \) in all cases.
\end{tabular}
D. \( v_{1}=-k \bar{v}_{2} \) in all cases, where \( k \geq 1 \)
Subject: Chemistry
Assertion
The gases \( H e \) and \( H_{2} \) are very different
in their behaviour at any temperature and pressure but their compressibility
factors are nearly the same at the
critical point.
Reason
They have nearly the same critical
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
\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left[(\boldsymbol{x}+\mathbf{1})\left(\boldsymbol{x}^{2}+\mathbf{1}\right)\left(\boldsymbol{x}^{4}+\mathbf{1}\right)\left(\boldsymbol{x}^{\boldsymbol{8}}+\right.\right. \)
1) \( ] \)
\( =\frac{\left(15 x^{p}-16 x^{q}+1\right)}{(x-1)^{2}} \Rightarrow(p, q)= \)
A . (12,11)
B. (15, 14)
\( c \cdot(16,14) \)
D. (16, 15)
Subject: Maths
\( \ln \operatorname{acircle} \) of radius \( 21 \mathrm{cm}, \) an arc
subtends an angle of \( 60^{\circ} \) at the
centre.Find
(i) the length of the arc
\( (i i) \) the area of the sector
(iiii) the area of the minor segment and
\( (i v) \) the area of the major segment.
Subject: Maths
: The area bounded by \( x=2 \cos \theta, y= \)
\( 3 \sin \theta \) is \( 36 \pi \) sq. units.
II: The area bounded by \( x=2 \cos \theta, y= \)
\( 2 \sin \theta \) is \( 4 \pi \) sq.units.
Which of the above statement is
correct?
A. Onlyı
B. Only II
c. Both I and II
D. Neither I nor II.
Subject: Chemistry
Knowing that the chemistry of lanthanoids \( (L n) \) is dominated by its
+3 oxidation state, which of the
following statements is incorrect?
A. The ionic size of \( L n(I I I) \) decrease in general with increasing atomic number
B. \( L n(I I I) \) compounds are generally colourless
c. \( L n(I I I) \) hydroxide are mainly basic in character
D. Because of the large size of the \( L n(I I I) \) ions the bonding in its compound is predominantly ionic in character
Subject: Maths
The Integrating factor of the differential equation \( \left(1-y^{2}\right) \frac{d x}{d y}+y x=a y \) is
A \( \cdot \frac{1}{y^{2}-1} \)
B. \( \frac{1}{\sqrt{y^{2}-1}} \)
c. \( \frac{1}{1-y^{2}} \)
D. \( \frac{1}{\sqrt{1-y^{2}}} \)
Subject: Physics
The electric field just outside the surface of conductor of area \( \boldsymbol{A} \) and
surface charge density \( \sigma \) is given by
A \( \cdot \frac{\sigma}{3 \epsilon_{0}} \)
в. \( \frac{\sigma}{2 \epsilon_{0}} \)
c. \( \frac{\sigma}{\epsilon_{0}} \)
D. \( \frac{2 \sigma}{\epsilon_{0}} \)
Subject: Physics
toppr
Q Type your question
height 1 m above the ground. The
particle is thrown from some point in
such a way that it strikes the ground
(perfectly inelastic) with velocity \( v_{0} \) at
an angle \( 37^{\circ} \) with vertical just below \( O \)
List
(P) Radius of curvature of particle just before striking the ground
(Q) Minimum value of \( v_{0} \) such that at highest point in vertical circle tension in the string \( T=0 \)
(R) Negative of work done by gravity after it strikes the ground to the topmost point in frame moving with constant acceleration on ground is (assume that after collision the particle complete the vertical loop)
(S) Power delivered by the gravity at highest point is (assume that after
\[
\frac{5}{3} \frac{v_{0}^{2}}{g}
\]
collision the particle complete the vertical loop)
A. P- \( 2 ; Q-3 ; R-1 ; S-4 \)
B. P- 3; Q- 2; R- 4; S-1
\( \mathrm{C} \cdot \cdot \mathrm{Q}-1 ; \mathrm{R}-2 ; \mathrm{S}-3 \)
D. P- 2; Q- 3; R-4; S-1
Subject: Physics
A particle moves in a straight path such that its velocity is always 4 times its acceleration. if its velocity at time \( t=0 \) is \( 2 m / s e c, \) its velocity at \( T=2 s e c, \) is
A \( . \sqrt{2 e} m / \) sec
B . \( 2 \sqrt{e} m / \) sec
c. \( \frac{\sqrt{e}}{2} m / \) sec
D. \( \frac{2}{\sqrt{e}} m / \) sec
Subject: Physics
The potential gradients on the
potentiometer wire are \( V_{1} \) and \( V_{2} \) with
an ideal cell and a real cell of same emf
in the primary circuit then
A. \( V_{1}=V_{2} \)
в. \( V_{1}>V_{2} \)
c. \( V_{1}<V_{2} \)
D. \( V_{1} \leq V_{2} \)
Subject: Chemistry
The concentration of acetic acid \( \left(\boldsymbol{K}_{\boldsymbol{a}}=\right. \) \( 1.8 \times 10^{-5} \) ) required to give \( 3.5 \times \)
\( 10^{-4} m o l / L H^{+}, \) is
A. 6.8 mol/L
B. \( 6.8 \times 10^{-3} \) mol \( / \) L
C. \( 1.94 \times 10^{-1} \) mol \( / L \)
D. \( 194 \mathrm{mol} / \mathrm{L} \)
Subject: Chemistry
By which of the following relations, the equilibrium constant varies with
temperature?
\( ^{\mathrm{A}} \cdot \ln K_{2}-\ln K_{1}=\frac{\Delta H^{\circ}}{R} \int_{T_{1}}^{T_{2}} d\left(\frac{1}{T}\right) \)
в. \( \ln K_{2}-\ln K_{1}=-\frac{\Delta H^{o}}{R} \int_{1 T_{1}^{1} T_{1}}^{1 / T_{2}} d\left(\frac{1}{T^{2}}\right) \)
\( ^{\mathrm{c}} \cdot \ln K_{2}-\ln K_{1}=-\frac{\Delta H^{o}}{R} \int_{T_{1}^{T_{1}}}^{T_{2}}\left(\frac{1}{T}\right) \)
D. \( _{\ln K_{2}-\ln K_{1}=-\frac{\Delta H^{o}}{R} \int_{1 / T_{2}}^{1 / T_{1}} d}\left(\frac{1}{T}\right) \)
Subject: Maths
The image of the point (-1,3,4) in the
plane \( \boldsymbol{x}-\mathbf{2} \boldsymbol{y}=\mathbf{0} \) is
A \( \cdot(15,11,4) \)
в. \( \left(\frac{9}{5},-\frac{13}{5}, 4\right) \)
\( c \cdot(8,4,4) \)
D. None of these
Subject: Physics
A current \( l \) is flowing in a straight
conductor of length \( L \). The magnetic
induction at a point on its axis at a
distance \( \frac{L}{4} \) from its centre will be
A . zero
в. \( \frac{\mu_{0} l}{2 \pi L} \)
c. \( \frac{\mu_{0} l}{\sqrt{2} L} \)
D. \( \frac{4 \mu_{0} l}{\sqrt{5} \pi L} \)
Subject: Physics
A series LCR-circuit with \( \boldsymbol{R}=\mathbf{2 0} \boldsymbol{\Omega} \)
\( \boldsymbol{L}=\mathbf{1 . 5} \boldsymbol{H} \) and \( \boldsymbol{C}=\mathbf{3 5} \boldsymbol{\mu} \mathrm{F} \) is connected
to a variable frequency \( 200 V \) ac supply When the frequency of the supply equals the natural frequency of the circuit, the average power transferred to the circuit in one complete cycle is?
\( \mathbf{A} \cdot 200 W \)
в. \( 2000 \mathrm{W} \)
\( c .100 W \)
D. \( 4000 \mathrm{W} \)
Subject: Chemistry
The units of solubility product of silver
chromate \( \left(A g_{2} C r O_{4}\right) \) will be
A \( \cdot m o l^{2} L^{-2} \)
B \( \cdot m o l^{3} L^{-3} \)
\( \mathrm{c} \cdot \operatorname{mol} L^{-1} \)
D. molL"
Subject: Physics
Three containers of the same volume
contain three gases. The masses of their
molecules being \( \mathrm{m}_{1}, \mathrm{m}_{2} \) and \( \mathrm{m}_{3} \) and
number of molecules in these containers
is \( \mathrm{N}_{1}, \mathrm{N}_{2} \) and \( \mathrm{N}_{3} \). The pressure in
the containers are \( \mathrm{P}_{1}, \mathrm{P}_{2} \) and \( \mathrm{P}_{3} \)
respectively. All the gases are now mixed up and put in these containers. The
pressure \( \mathrm{P} \) of the mixture is
\( \mathbf{A} \cdot P<\left(P_{1}+P_{2}+P_{3}\right) \)
B. \( P=\frac{P_{1}+P_{2}+P_{3}}{3} \)
\( \mathbf{c} \cdot P=P_{1}+P_{2}+P_{3} \)
D \( \cdot P>\left(P_{1}+P_{2}+P_{3}\right) \)
Subject: Physics
A man in a balloon rising vertically with an acceleration of \( 4.9 m / s e c^{2} \) releases a ball 2 sec after the balloon is let go from the ground. The greatest height above the ground reaches by the ball is \( (g= \)
\( \mathbf{9 . 8 m} / \boldsymbol{s e c}^{2} \)
A \( .14 .7 m \)
B. \( 19.6 m \)
\( \mathrm{c} .9 .8 \mathrm{m} \)
D. \( 24.5 m \)
Subject: Chemistry
Choose the correct order of reactivity
toward nucleophilic substitution:
\( (\mathbf{I}) \)
\( (\mathbf{I I}) \)
\( (\mathbf{I I I}) \)
\( \mathbf{A} \cdot(1)<(\|)<(\| 1) \)
B. \( (1)<(111)<(11) \)
\( \mathbf{C} \cdot(\| I)<(\|)<(1) \)
D. \( (11)<(111)<(1) \)
Subject: Chemistry
When photons of energy \( 4.25 e V \) strike
the surface of a metal \( A \), the ejected
photo-electrons have maximum kinetic
energy, \( \boldsymbol{T}_{A}(\text { expresses in } \boldsymbol{e} \boldsymbol{V}) \) and de
Broglie wavelength \( \lambda_{A} \). The maximum
kinetic energy of photoelectrons liberated from another metal \( B \) by
photons of energy \( 4.70 e V \) is \( T_{B}=T_{A}- \)
1.50 \( e V \). If the de-Broglie wavelength of
these photo-electrons is \( \lambda_{B}=2 \lambda_{A}, \) then
which is not correct?
A. The work function of \( A \) is \( 2.25 e V \)
B. The work function of \( B \) is \( 1.20 e V \)
\( \mathbf{c} \cdot T_{A}=2.00 e V \)
D. \( T_{B}=0.5 e V \)
Subject: Physics
To a man walking at the rate of \( 3 \mathrm{km} / \mathrm{h} \) the rain appears to fall vertically downwards. When he increases his
speed to \( 6 \mathrm{km} / \mathrm{h} \) it appears to meet him
at an angle of \( 45^{0} \) with vertical. Find the
speed of rain.
Subject: Maths
A regular octagon is formed by cutting congruent isosceles right-angled triangles from the corners of a square. If the square has side-length 1 , the sidelength of the octagon is
A \( \cdot \frac{\sqrt{2}-1}{2} \)
B. \( \sqrt{2}-1 \)
c. \( \frac{\sqrt{5}-1}{4} \)
D. \( \frac{\sqrt{5}-1}{3} \)
Subject: Chemistry
Which of the following are correct statements about white phosphorus
\( \left(P_{4}\right) ? \)
This question has multiple correct options
A. Each P atom has one lone pair of electrons in a
molecules of \( P_{4} \)
B. It has tetrahedral structure with \( 109^{\circ} 28^{\prime} \) bond angle.
C. There are six P-P linkages in a molecule of \( P_{4} \)
D. It undergoes dispropartionation on reaction with alkalies.
Subject: Maths
Assertion(A): \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) defined by
\( f(x)=(x-9)(x-10)(x-11) \) is onto
but not one one
Reason \( (\mathrm{R}): \) If \( \boldsymbol{f}: \boldsymbol{A} \rightarrow \boldsymbol{B} ; \boldsymbol{x}_{1}, \boldsymbol{x}_{2} \in \boldsymbol{A} \) and
\( \boldsymbol{f}\left(\boldsymbol{x}_{1}\right) \neq \boldsymbol{f}\left(\boldsymbol{x}_{2}\right) \Rightarrow \boldsymbol{x}_{1}=\boldsymbol{x}_{2}, \) then \( \boldsymbol{f} \) is
one-one.
A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true but R is not correct explanation of
c. A is true but R is false
D. A is false but R is true
Subject: Maths
Express \( \boldsymbol{f}: \boldsymbol{A} \rightarrow \boldsymbol{N}, \boldsymbol{f}(\boldsymbol{x})=\mathbf{2} \boldsymbol{x} \) where
\( \boldsymbol{A}=\{\boldsymbol{x}: \boldsymbol{x} \in \boldsymbol{N}, \boldsymbol{x} \leq 10\} . \) Determine
range of the function.
Subject: Chemistry
\( P \) is produced by the action of chlorine on dry slaked lime. Q is a non-corrosive base and used for
faster cooking. On heating \( R \) at \( 373 K \), it becomes calcium sulphate hemihydrate. Identify \( P, Q \) and \( R \) respectively:
A \( \cdot C a O C l_{2}, N a H C O_{3}, \) gypsum
в. \( C a O, N a_{2} C O_{3}, C a O C l_{2} \)
\( \mathbf{c} \cdot \operatorname{Ca}(O H)_{2}, \operatorname{NaH} C O_{3}, \operatorname{CaSO}_{4} \)
D. \( \operatorname{CaOCl}_{2}, N a_{2} \mathrm{CO}_{3}, \mathrm{NH}_{4} \mathrm{Cl} \)
Subject: Chemistry
Select correct statements:
Bond order of:
This question has multiple correct options
\( \mathbf{A} \cdot H e_{2} \) is zero
B. \( H e_{2}^{+} \) is 0.5
\( \mathbf{c} \cdot H e_{2}^{2+} \) is 1.0
D. \( B e_{2} \) is zero
Subject: Maths
Evaluate, without using trigonometric
tables:
\( \frac{\sin ^{2} \theta+\sin ^{2}\left(90^{\circ}-\theta\right)}{3\left(\sec ^{2} 61^{\circ}-\cot ^{2} 29^{\circ}\right)} \)
\( \frac{3 \cot ^{2} 30^{\circ} \cdot \sin ^{2} 54^{\circ} \cdot \sec ^{2} 36^{\circ}}{2\left(\csc ^{2} 65^{\circ}-\tan ^{2} 25 o\right)} \)
Subject: Maths
The value of \( \frac{\boldsymbol{f}(\boldsymbol{t})}{\boldsymbol{f}^{\prime}(\boldsymbol{t})} \cdot \frac{\boldsymbol{f}^{\prime \prime}(-\boldsymbol{t})}{\boldsymbol{f}^{\prime}(-\boldsymbol{t})}- \)
\( \frac{f(-t)}{f^{\prime}(-t)} \cdot \frac{f^{\prime \prime}(t)}{f^{\prime}(t)} \forall t \epsilon R \) is equal to
A . -2
B. 2
c. -4
\( D \)
Subject: Physics
Find \( \overrightarrow{\boldsymbol{P}} \cdot \overrightarrow{\boldsymbol{Q}} \)
where \( \overrightarrow{\boldsymbol{P}}=2 \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) and \( \overrightarrow{\boldsymbol{Q}}=\hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}+ \)
\( \boldsymbol{2} \hat{\boldsymbol{k}} \)
Subject: Chemistry
The two half-cell reactions of an
electrochemical cell is given as
\( \boldsymbol{A} \boldsymbol{g}^{+}+\boldsymbol{e}^{-} \longrightarrow \boldsymbol{A} \boldsymbol{g} ; \boldsymbol{E}_{\boldsymbol{A} \boldsymbol{g}^{+} \mid \boldsymbol{A} \boldsymbol{g}}= \)
\( -0.3995 V \)
\( \boldsymbol{F} \boldsymbol{e}^{2+} \longrightarrow \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+}+\boldsymbol{e}^{-} ; \boldsymbol{E}_{\boldsymbol{F} e^{3+} \mid \boldsymbol{F} e^{2+}}= \)
\( -0.7120 V \)
The value of cell EMF will be:
A. \( -0.3125 V \)
B. \( 0.3125 V \)
c. \( 1.114 V \)
D. \( -1.114 V \)
Subject: Maths
If in two triangles \( \Delta A B C \) and \( \Delta P Q R \)
\( A B=Q R, B C=P R \) and \( C A=P Q \)
then :
A. \( \Delta A B C \cong \Delta P Q R \)
в. \( \Delta C B A \cong \Delta P R Q \)
c. \( \Delta B A C \cong \Delta R P Q \)
D. \( \Delta P Q R \cong \Delta B C A \)
Subject: Chemistry
The correct order of decreasing \( \boldsymbol{X}- \) \( O-X \) bond angle is: \( (X=H, F \text { or } C l) \)
A. \( H_{2} O>C l_{2} O>F_{2} O \)
в. \( C l_{2} O>H_{2} O>F_{2} O \)
c. \( F_{2} O>C l_{2} O>H_{2} O \)
D. \( F_{2} O>H_{2} O>C l_{2} O \)
Subject: Physics
STATEMENT-1: At two different points on
the same stream line in streamline flow
velocity of a particle may be different. STATEMENT-2: Pressure and height may be different at two different points on a
streamline.
A. Statement-1 is True, Statement-2 is True; Statementis a correct explanation for Statement-
B. Statement-1 is True, Statement-2 is True; Statementis NOT a correct explanation for Statement-
c. Statement- 1 is True, Statement- 2 is False
D. Statement-1 is False, Statement-2 is True
Subject: Physics
Two bodies of mass \( 10 k g \) and \( 2 k g \) are
moving with velocities \( 2 i-7 j+3 k \) and
\( -10 i+35 j-3 k m / s \) respectively. The
velocity of their \( \mathrm{CM} \) is
A \( .2 i \mathrm{m} / \mathrm{s} \)
B. \( 2 k \) m/s
\( c \cdot(2 i+2 k) m / s \)
D. \( (2 i+2 j+2 k) \mathrm{m} / \mathrm{s} \)
Subject: Maths
Differentiate the following functions
with respect to \( \boldsymbol{x} \) ff \( y=\sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right)+ \)
\( \sec ^{-1}\left(\frac{1+x^{2}}{1-x^{2}}\right), 0<x<1, \) prove that
\( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{\boldsymbol{4}}{\boldsymbol{1}+\boldsymbol{x}^{2}} \)
Subject: Maths
ff \( \boldsymbol{f}:[\mathbf{0}, \boldsymbol{\Pi}] \rightarrow[-\mathbf{1}, \mathbf{1}], \mathbf{f}(\mathbf{x})=\cos \mathbf{x}, \) then
is.
\( A \cdot \) one-one
B. onto
c. one-one onto
D. none of these
Subject: Maths
The coordinates of the point \( P(x, y) \) which divides the line segment joining the points \( \boldsymbol{A}\left(\boldsymbol{x}_{1}, \boldsymbol{y}_{1}\right) \) and \( \boldsymbol{B}\left(\boldsymbol{x}_{2}, \boldsymbol{y}_{2}\right) \)
internally in the ratio \( m_{1}: m_{2} \) are
\( \left(\frac{m_{1} x_{2}-m_{2} x_{1}}{m_{1}+m_{2} 1}, \frac{m_{1} y_{2}-m_{2} y_{1}}{m_{1}+m_{2}}\right) \)
A . True
B. False
c. Ambiguous
D. Data insufficient
Subject: Maths
The mean of the following data is 50 Find the value of a and hence the
frequencies of 30 and 70
\[
\begin{array}{cccccc}
\boldsymbol{X} & \mathbf{1 0} & \mathbf{3 0} & \mathbf{5 0} & \mathbf{7 0} & \mathbf{9 0} \\
\boldsymbol{F} & \mathbf{1 7} & \mathbf{5 a + 3} & \mathbf{3 2} & \mathbf{7 a - 1 1} & \mathbf{1 9}
\end{array}
\]
A .28 and 34
B. 68 and 24
c. 28 and 24
D. None of these
Subject: Physics
A radioactive nucleus can decay by two different processes. The mean value
period for the first process is \( Z_{1} \) and
that for the second process is \( Z_{2} \). The effective mean value period for the two
processes is:
A \( \cdot \frac{Z_{1}+Z_{2}}{2} \)
в. \( Z_{1}+Z_{2} \)
c. \( \sqrt{Z_{1} Z_{2}} \)
D. \( \frac{Z_{1} Z_{2}}{Z_{1}+Z_{2}} \)
Subject: Chemistry
Arrange the following ions in increasing
order of their radius:
\( \mathbf{A} \cdot M n^{+7}<V^{+5}<C a^{+2}<K^{+} C l^{-}<S^{2}<P^{3-} \)
B \( \cdot M n^{+7}<C a^{+2}<V^{+5}<K^{+} C l^{-}<S^{2}<P^{3-} \)
\( \mathbf{c} \cdot M n^{+7}<V^{+5}<C a^{+2}<K^{+} C l^{-}<P^{3-}<S^{2} \)
D. \( V^{+5}<M n^{+7}<C a^{+2}<K^{+} C l^{-}<S^{2}<P^{3-} \)
Subject: Physics
Find the instantaneous axis of rotation
of a rod of length \( l \) when its end \( A \) moves with a velocity \( \overrightarrow{\boldsymbol{v}}_{\boldsymbol{A}}=\boldsymbol{v} \hat{\boldsymbol{i}} \) and the
rod rotates with an angular velocity
\( \omega=-\frac{v}{2 l} \hat{k} \)
Subject: Maths
Determine the value of the constant \( k \)
so that the function
\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{aligned} \frac{\sin 2 x}{\mathbf{5} \boldsymbol{x}}, & \text { if } \boldsymbol{x} \neq \mathbf{0} \\ \boldsymbol{k}, \text { if } \boldsymbol{x} &=\mathbf{0} \end{aligned}\right. \)
continuous at \( \boldsymbol{x}=\mathbf{0} \)
Subject: Physics
The velocity-time graph below
represents the velocity of a toy train as
it moves north and south, with zero
velocity near the middle of the vertical
axis.

During which interval(s) is the toy train
speeding up?
A . A only
B. A and E only
c. \( A, B \) and \( C \) only
D. A and D only
E. \( c \) and D only