AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Two plates (area \( =5 \) ) charged to \( +q_{1} \)
and \( +q_{2}\left(q_{2}<q_{1}\right) \) are brought closer to
form a capacitor of capacitance \( C \). The potential difference across the plates is
A \( \cdot \frac{q_{1}-q_{2}}{2 C} \)
в. \( \frac{q_{1}-q_{2}}{C} \)
c. \( \frac{q_{1}-q_{2}}{4 C} \)
D. \( \frac{2\left(q_{1}-q_{2}\right)}{C} \)
Subject: Physics
Consider a spherical shell of radius \( \boldsymbol{R} \) at
temperature \( T . \) The black body radiation inside it can be considered as
an ideal gas of photons with internal energy per unit volume \( u=\frac{U}{V} \propto T^{4} \) and pressure \( \boldsymbol{P}=\frac{1}{\mathbf{3}}\left(\frac{\boldsymbol{U}}{\boldsymbol{V}}\right) . \) If the shell
now undergoes an adiabatic expansion the relation between \( T \) and \( R \) is :
A \( \cdot T \propto e^{-R} \)
В . \( T \propto e^{-3 R} \)
\( c \cdot T \propto \frac{1}{R} \)
D. \( T \propto \frac{1}{R^{3}} \)
Subject: Physics
The average value of acceleration due to gravity on the surface of the earth is
equal to:
A. \( 9.8 \mathrm{ms}^{-2} \)
B. \( 9.8 \mathrm{ms}^{-1} \)
c. \( 19.6 \mathrm{ms}^{-2} \)
D. \( 9.8 s^{-2} \)
Subject: Physics
Find the inductance \( L \) of a solenoid of
length I whose windings are made of material of density D and resistivity \( \rho \) The winding resistance is \( \mathrm{R} \) :
A \( \cdot \frac{\mu_{0}}{4 \pi l} \cdot \frac{R_{m}}{\rho D} \)
в. \( \frac{\mu_{0}}{4 \pi R} \cdot \frac{l_{m}}{\rho D} \)
c. \( \frac{\mu_{0}}{4 \pi l} \cdot \frac{R^{2} m}{\rho D} \)
D. \( \frac{\mu_{0}}{2 \pi R} \cdot \frac{l_{m}}{\rho D} \)
Subject: Maths
If \( f(x)=x^{3} \) and \( g(x)=\sin 2 x, \) then
A \( \cdot g[f(1)]=1 \)
B. \( f(g(\pi / 12)=1 / 8 \)
c. \( g f(2)=\sin 2 \)
D. none of these
Subject: Chemistry
toppr
Q Type your question-
molecules reacts with \( H_{2} O \) to form
\( N H_{4} O H \) molecules. \( N H_{4} O H \) again
dissociates into \( N H_{4}^{+} \) and \( O H^{-} \) ions.
In solution therefore, we have \( \boldsymbol{N} \boldsymbol{H}_{3} \)
molecules, \( N H_{4} O H \) molecules and
\( N H_{4}^{+} \) ions and the following equilibrium exist:
\( N H_{3}(g) \rightleftharpoons N H_{3}(l)+H_{2} O(l) \rightleftharpoons \)
\( N H_{4} O H(a q) \rightleftharpoons N H_{4}^{+}(a q)+ \)
\( \boldsymbol{O} \boldsymbol{H}^{-}(\boldsymbol{a} \boldsymbol{q}) \)
Let, \( c_{1}(\text { mol } / L) \) of \( N H_{3} \) pass in liquid
state which on dissolution in water
forms \( c_{2}(m o l / L) \) of \( N H_{4} O H . \) The
solution contains \( c_{3}(m o l / L) \) of \( N H_{4}^{+} \) ions.
Concentration of undissociated
ammonium hydroxide is
\( \mathbf{A} \cdot c_{1}+c_{2} \)
в. \( c_{2}-c_{3} \)
\( \mathbf{c} \cdot c_{1}+c_{3} \)
D. \( c_{1}-c_{2} \)
Subject: Chemistry
The formula of exhausted permutit
is
A. \( C a A l_{2}, S i_{2} O_{8} . x H_{2} O \)
B. \( N a A l_{2}, S i_{2} O_{8} . x H_{2} O \)
\( \mathrm{c} \cdot \mathrm{CaB}_{2} \mathrm{Si}_{2} \mathrm{O}_{8} \cdot x \mathrm{H}_{2} \mathrm{O} \)
D. \( K_{2} A l_{2}, S i_{2} O_{8} . . x H_{2} O \)
Subject: Maths
The sum of \( 2 n \) terms of a geometric
progression whose first term is ' \( a^{\prime} \) and
common ratio \( ^{\prime} r^{\prime} \) is equal to the sum of
\( n \) terms of a geometric progression
whose first term is 'b' and common ' \( r^{2} \) '
then \( b \) is equal to
A. The sum of the first two terms of the first series
B. The sum of the first and last terms of the first series.
c. The sum of the last two terms of the first series
D. None of these
Subject: Maths
The dot product of a vector with vectors \( \hat{\mathbf{i}}+\hat{\mathbf{j}}-\mathbf{3} \hat{\mathbf{k}}, \hat{\mathbf{i}}+\mathbf{3} \hat{\mathbf{j}}-\mathbf{2} \hat{\mathbf{k}}, \mathbf{2} \hat{\mathbf{i}}+\hat{\mathbf{j}}+\mathbf{4} k \) are
0,5 and 8 respectively. Find the vector
Subject: Physics
A closely wound flat circular coil of 25
turns of wire has diameter of \( 5 \mathrm{cm} \)
which carries current of 4 amperes, the flux density at the centre of a coil will be
A \( \cdot 1.256 \times 10^{-3} \) tesla
В. \( 1.679 \times 10^{-5} \) tesla
c. \( 1.512 \times 10^{-5} \) telsa
D. \( 2.28 \times 10^{-4} \) telsa
Subject: Biology
Vascularisation in plants occurs
through.
A. Differentiation of procambium followed by primary phloem and then primary xylem
B. Differentiation of procambium followed by development of xylem and phloem
C. Simultaneous differentiation of procambium, xylem and phloem
D. Differentiation of procambium is immediately followed by development of secondary xylem and secondary phloem
Subject: Chemistry
The products obtained at cathode and anode on electrolysis of aqueous sodium succinate are :
A. anode: ethene \( +C O_{2} \), cathode : \( H_{2} \)
B. anode: ethyne \( +C O_{2} \), cathode : \( H_{2} \)
c. anode : ethyne + \( H_{2} \), cathode : Na
D. anode: ethyne \( +C O_{2} \), cathode : Na
Subject: Physics
The potentiometer wire of length has
\( 100 \mathrm{cm} \) has a resistance of \( 10 \Omega \).It is
connected in series with a resistance of
\( 5 \Omega \) and an acceleration of emf \( 3 V \)
having magnitude resistance. A source A source of \( 1.2 \mathrm{V} \) is balanced against
ength I' Of the potential wire. Find the
value of L.
Subject: Biology
The correct floral formula of chilli is
\( A \)
\[
\oplus \bigoplus_{2+2} C_{4} A_{2+4} C_{(2)}
\]
B. \( B r . \%, K_{4} C_{4} \) Аа \( G_{1} \)
\( c \)
\[
\bigoplus \bigoplus_{(5)} A_{(5)} G_{(2)}
\]
\( D \)
\[
\bigoplus \bigoplus_{3+3} A_{3+3} G_{(3)}
\]
Subject: Chemistry
Statement 1:
In a zero order reaction, if the
concentration of the reactant is
doubled, the half-life period is also
doubled.
Statement 2:
For a zero-order reaction, the rate of the
reaction is independent of initial
concentration.
A. Statement 1 is True, statement 2 is True, statement 2 is a correct explanation of statement 1.
B. Statement 1 is True, statement 2 is True, statement 2 is not a correct explanation of statement 1
c. Statement 1 is true, Statement 2 is False
D. Statement 1 is False, Statement 2 is True.
Subject: Maths
Assertion Derivative of \( (\boldsymbol{p} \boldsymbol{x}+\boldsymbol{q})\left(\frac{\boldsymbol{r}}{\boldsymbol{x}}+\boldsymbol{s}\right) \) is \( \boldsymbol{p s}+ \)
\( \frac{\boldsymbol{q} \boldsymbol{r}}{\boldsymbol{x}^{2}} \)
Reason
\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}(\boldsymbol{u} \boldsymbol{v})=\boldsymbol{u}^{\prime} \boldsymbol{v}+\boldsymbol{u} \boldsymbol{v}^{\prime} \)
where \( u \) and \( v \) are two distinct
functions.
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
If a vector \( \bar{A}=2 \bar{i}+2 \bar{j}+3 \bar{k} \) and \( \bar{B}= \)
\( \mathbf{3} \overline{\mathbf{i}}+\mathbf{6} \overline{\mathbf{j}}+n \bar{k}, \) are perpendicular to each
other, then the value of 'n' is:
A . 4
B. 12
\( c \cdot 6 \)
D. - -
Subject: Maths
\( O \) is the center of the circle. \( O P=12 \)
\( \mathrm{cm}, \) and \( \boldsymbol{O B}=\mathbf{1 3} \mathrm{cm} . \) Find \( \boldsymbol{A B} \)
A. \( 8 \mathrm{cm} \)
B. \( 10 \mathrm{cm} \)
\( \mathrm{c} \cdot 12 \mathrm{cm} \)
D. \( 13 \mathrm{cm} \)
Subject: Maths
Find the values of \( k, \) if the points \( \boldsymbol{A}(\boldsymbol{k}+ \) 1, \( 2 k \) ), \( B(3 k, 2 k+3) \) and \( C(5 k+1,5 k) \)
are collinear.
This question has multiple correct options
A .
B. \( \frac{1}{2} \)
\( c \cdot 2 \)
D. 2.
Subject: Chemistry
An organic compound on analysis gave \( C=54.2 \%, H=9.2 \% \) by mass. Its
empirical formula is :
A. \( C H O_{2} \)
в. \( C H_{2} \) О
\( \mathrm{c} \cdot C_{2} H_{8} \mathrm{O} \)
D. \( C_{2} H_{4} O \)
Subject: Chemistry
(i) \( B a C_{2}+N_{2} \stackrel{\Delta}{\rightarrow}(B) \)
(ii) \( \boldsymbol{C a C}_{2}+\boldsymbol{N}_{2} \stackrel{\boldsymbol{\Delta}}{\rightarrow}(\boldsymbol{A}) \)
Identify \( (\boldsymbol{A}) \) and \( (\boldsymbol{B}) \)
A \( \cdot A: C a(N=C=N) ; \) В \( : B a(C \equiv N) \)
B. \( A: C a(N=C=N) ; \) В \( : B a_{2}(C \equiv N)_{4} \)
c. \( A: C a(N=C=N)_{2} ; \) в: \( B a(C \equiv N)_{2} \)
D. \( A: C a(N=C=N)_{2} ; \) B: \( B a_{2}(C \equiv N)_{4} \)
Subject: Maths
In an election, candidate \( A \) got \( 75 \% \) of
the total valid votes. If \( 15 \% \) of the total
votes were declared invalid and the
total numbers of votes is 560000 , find
the number of valid vote polled in favour of candidate.
A . 357000
B. 365796
c. 375000
D. 500000
Subject: Physics
A 50 V d.c power supply is used to charge a battery of eight lead
accumulators, each of emf \( 2 \mathrm{V} \) and
internal resistance \( 1 / 8 \Omega \). The charging current also runs a motor connected in
series with the battery. The resistance of the motor is \( 5 \Omega \) and the steady current supply is 4 A. The chemical power stored in the battery is
\( A \cdot 64 \mathrm{W} \)
B. 96 \( w \)
\( c \cdot 16 w \)
D. 50 w
Subject: Maths
The contrapositive of \( \sim \boldsymbol{p} \rightarrow(\boldsymbol{q} \rightarrow \sim \boldsymbol{r}) \)
is
\( \mathbf{A} \cdot(q \wedge r) \rightarrow p \)
в. \( (q \rightarrow r) \rightarrow p \)
c. \( (q \vee r) \rightarrow p \)
D. None of these
Subject: Maths
If \( 2\left[\begin{array}{ll}3 & 4 \\ 5 & x\end{array}\right]+\left[\begin{array}{ll}1 & y \\ 0 & 1\end{array}\right]=\left[\begin{array}{cc}7 & 0 \\ 10 & 5\end{array}\right], \) find
\( (x-y) \)
Subject: Physics
Two waves of wavelengths \( 2 \mathrm{m} \) and 2.02 m respectively moving with the same velocity superpose to produce 2 beats
/s. The velocity of the wave is:
A. \( 400 \mathrm{m} / \mathrm{s} \)
B. 402 m/s
c. \( 404 \mathrm{m} / \mathrm{s} \)
D. \( 406 \mathrm{m} / \mathrm{s} \)
Subject: Physics
An infinitely long cylinder of radius
\( \mathrm{R}=2 \mathrm{cm} \) carries a uniform charge density
\( =18 \mu \mathrm{C} / \mathrm{m} 3 \)
Calculate the electric field at distance
\( r=1 \mathrm{cm} \)
from the axis of the cylinder.
A. The magnitude of electric field intensity at the \( x x \) axis of charged body is \( \left(\frac{p r^{2}}{2 \epsilon_{0} d}\right) \)
B. The magnitude of electric field intensity at the \( x x \) axis of charged body is zero.
C. The magnitude of electric field intensity at the yy axis of charged body is \( \left(\frac{p d^{2}}{2 \epsilon_{0}}\right) \)
D. The magnitude of electric field intensity at the \( x x \) any point in the cavity is \( \frac{p^{2}}{2 \epsilon_{0}} d \)
Subject: Chemistry
An element A (atomic weight \( =12 \) ) and
B (atomic weight \( =35.5 \) ) combines to
form a compound X. If 4 mol of B
combines with 1 mol of \( A \) to give 1 mol
of X. The weight of 1 mol of \( X \) would be :
A. \( 47.5 \mathrm{g} \)
B. 74.0 g
c. \( 154.0 \mathrm{g} \)
D. 148.8 g
Subject: Physics
A body initially at rest and sliding along
a frictionless track from a height \( h \) (as
shown in the figure) just completes as
vertical of diameter \( \boldsymbol{A B}=\boldsymbol{D} \). The
height \( h \) is equal to:
A \( \cdot \frac{3}{2} D \)
в. \( D \)
c. \( \frac{5}{4} D \)
D. \( \frac{7}{5} L \)
Subject: Maths
The general solution of the equation \( \sin ^{100} x-\cos ^{100} x=1 \) is
A \( \cdot 2 n \pi+\frac{\pi}{3}, n \epsilon I \)
В \( \cdot n \pi+\frac{\pi}{2}, n \epsilon I \)
c. \( n \pi+\frac{\pi}{4}, n \epsilon I \)
D. \( 2 n \pi-\frac{\pi}{3}, n \epsilon I \)
Subject: Chemistry
Pseudo first-order rate for the reaction,
\( A+B \longrightarrow P, \) when studied in \( 0.1 M \) of
\( B \) is given by \( -\frac{\boldsymbol{d}[\boldsymbol{A}]}{\boldsymbol{d} \boldsymbol{t}}=\boldsymbol{k}[\boldsymbol{A}] \) where
\( k=1.85 \times 10^{4} \mathrm{sec}^{-1} \). Calculate the
value of second order rate constant.
Subject: Maths
\( \left|\begin{array}{ccc}\boldsymbol{a}+\boldsymbol{b} & \boldsymbol{a}+\mathbf{2} \boldsymbol{b} & \boldsymbol{a}+\boldsymbol{3} \boldsymbol{b} \\ \boldsymbol{a}+\mathbf{2} \boldsymbol{b} & \boldsymbol{a}+\boldsymbol{3} \boldsymbol{b} & \boldsymbol{a}+\boldsymbol{4} \boldsymbol{b} \\ \boldsymbol{a}+\boldsymbol{4} \boldsymbol{b} & \boldsymbol{a}+\boldsymbol{5} \boldsymbol{b} & \boldsymbol{a}+\boldsymbol{6} \boldsymbol{b}\end{array}\right|= \)
A \( \cdot a^{2}+b^{2}+c^{2}-3 a b \)
B. \( 3 a b c \)
\( c \cdot 3 a+5 b \)
\( D \)
Subject: Physics
A potential difference of \( V \) volts is
applied on an \( \alpha \) -particle at rest in order
to get sufficient velocity so that when it is projected from infinity towards \( \boldsymbol{A} \boldsymbol{u} \)
foil, it can reach closest upto \( x \) meters
from \( A u \) nucleus. If instead of an \( \alpha \)
particle, a proton is used in the above experiment and is accelerated from rest by the same potential difference, then
the closest distance from the \( \boldsymbol{A} \boldsymbol{u} \)
nucleus upto which it can reach is \( y \)
meters. The ratio \( x: y \) is
A . 2: 1
B. 3:2
\( c \cdot 1: 1 \)
D. 2:3
Subject: Physics
Which nuclide is formed as a result of
this fission reaction?
\( _{92}^{235} U+_{0}^{1} n \rightarrow 3_{0}^{1} n+_{56}^{139} B a+ \)
A \( \cdot \frac{96}{33} \mathrm{Br} \)
B. 96
36
c. 彎 \( R b \)
\( b \)
E \( \cdot \frac{90}{33} \mathrm{Sr} \)
Subject: Maths
The sign of the quadratic polynomial
\( a x^{2}+b x+c \) is always positive, if?
\( \mathbf{A} \cdot \) a is positive and \( b^{2}-4 a c \leq 0 \)
B. a is positive and \( b^{2}-4 a \geq 0 \)
\( \mathrm{C} \cdot \) a can be any real number and \( b^{2}-4 a c \leq 0 \)
D. a can be any real number and \( b^{2}-4 a c \geq 0 \)
Subject: Chemistry
Assertion
carbon tetraiodide \( \left(C I_{4}\right) \) is a solid
whereas carbon tetrafluoride \( \left(C F_{4}\right) \) is a
gas.
Reason
This is due to the London dispersion to
dipole-dipole interaction because of the increased polarity.
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
A man is 24 years older than his son. 12 years ago, he was five times as old as
his son. Find the present ages of both.
A. Present age of father is 44 years and Present age of son is 20 years
B. Present age of father is 42 years and Present age of son is 18 years
c. Present age of father is 60 years and Present age of son is 36 years
D. Present age of father is 48 years and Present age of son is 24 years
Subject: Maths
Solve the following pairs of equations.
\( \mathbf{3} \boldsymbol{x}+\mathbf{2} \boldsymbol{y}=\mathbf{4} ; \mathbf{9} \boldsymbol{x}+\mathbf{6} \boldsymbol{y}-\mathbf{1 2}=\mathbf{0} \)
A. Many solution
B. No solution
c. Unique solution
D. None of these
Subject: Maths
If \( \boldsymbol{x}>1, \) then the value of \( 2 \tan ^{-1} x+\sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right) \) is
\( ^{A} \cdot \frac{2 \pi}{4} \)
в.
\( c \)
D. \( \frac{3 \pi}{2} \)
Subject: Chemistry
The vapour pressure of a mixture of two
volatile liquids is expressed as \( \boldsymbol{P}_{\boldsymbol{m}}= \)
\( 6.0+1.5 X_{B}, \) where, \( X_{B} \) is mole
fraction of \( \boldsymbol{B} \) is a mixture. The vapour
pressure of \( \boldsymbol{A} \) at the same temperature is:
Subject: Maths
Check the continuity of \( f \) given by
\[
f(x)=\left\{\begin{array}{ccc}
4-x^{2} & \text { if } & x \leq 0 \\
x-5 & \text { if } & 0<x \leq 1 \\
4 x^{2}-9 & \text { if } & 1<x<2 \\
3 x+4 & \text { if } & x \geq 2
\end{array}\right.
\]
the points 0,1 and 2
Subject: Maths
\( \left|\begin{array}{ccc}\mathbf{8} & \mathbf{- 5} & \mathbf{1} \\ \mathbf{5} & \boldsymbol{x} & \mathbf{3} \\ \mathbf{6} & \mathbf{3} & \mathbf{1}\end{array}\right|=\mathbf{2} \) then what is the
value of \( x \) ?
A . 44
B. 55
c. 61
D. 84
Subject: Chemistry
An excited hydrogen atom emits a photon of wavelength \( \lambda \) in returning to
the ground state. If \( R \) is the Rydberg
constant, then the quantum number \( n \)
of the excited state will be:
\( A \cdot \sqrt{\lambda R} \)
B. \( \sqrt{\lambda R-1} \)
c. \( \sqrt{\frac{\lambda R}{\lambda R-1}} \)
D. \( \sqrt{\lambda R(\lambda R-1)} \)
Subject: Physics
Figure as shown a rod \( P Q \) of length
\( 20.0 \mathrm{cm} \) and mass \( 200 \mathrm{g} \) suspended through a fixed point \( O \) by two threads
of length \( 20.0 \mathrm{cm} \) each. A magnetic field
of strength \( 0.500 T \) exists in the vicinity
of the wire \( P Q \) as shown in the figure.
The wires connecting with \( P Q \) with the battery are loose and exert no force on
\( P Q \)
(a) Find the tension in the threads when
the switch \( S \) is open.(b) A current of
\( 2.0 A \) is established when the switch \( S \)
is closed. Find the tension in the thread.
Subject: Physics
For capacitors in the series combination, the total capacitance \( C \) is
given by
\( ^{\mathbf{A}} \cdot_{C}=\left(\frac{1}{C_{1}}+\frac{1}{C_{2}}+\ldots \ldots\right) \)
в. \( C=C_{1}+C_{2}+\ldots \)
\( ^{\mathbf{c}} \cdot \frac{1}{\bar{C}}=\left(\frac{1}{C_{1}}+\frac{1}{C_{2}}+\ldots . .\right) \)
\( \stackrel{\mathrm{D}}{\mathrm{C}}=C_{1}+C_{2}+\ldots \)
Subject: Maths
The differential equation, whose solution is \( \boldsymbol{y}=\boldsymbol{a} \cos (\log \boldsymbol{x})+ \)
\( \boldsymbol{b} \sin (\log \boldsymbol{x}), \) is:
A \( \cdot x^{2} y_{2}-x y_{1}+y=0 \)
В. \( x^{2} y_{2}+x y_{1}-y=0 \)
c. \( x^{2} y_{2}+x y_{1}+y=0 \)
D. \( x^{2} y_{2}-x y_{1}-y=0 \)
Subject: Physics
A mass of \( 200 g m \) has initial velocity \( V_{i}=2 \hat{i}+3 \hat{j} \) and final velocity \( -2 \hat{i}-3 \hat{j} \)
Find magnitude of change in
momentum.
A \( \cdot|\Delta \vec{p}|=3.84 \)
В . \( |\Delta \vec{p}|=3.04 \)
c. \( |\Delta \vec{p}|=1.44 \)
D . \( |\Delta \vec{p}|=2.04 \)
Subject: Maths
The area bounded by the curves \( |\boldsymbol{x}|+ \) \( |y| \geq 1 \) and \( x^{2}+y^{2} \leq 1 \) is
A. 2 sq unit
B. \( \pi \) sq unit
c. \( (\pi-2) \) sq unit
D. None of these
Subject: Chemistry
Among the metals \( F e ; Z n ; P b ; A g \) and
\( P t, \) which do not give a metal nitrate on
treatment with concentrated \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) ?
A . Fe and \( P t \)
B. Fe and \( Z n \)
\( \mathrm{c} \cdot F e, A g \) and \( P t \)
D. \( P b, A g \) and \( P t \)
Subject: Maths
For the three events \( A, B \& C \) probability of exactly one of the events \( A \) or \( B \) occurs \( = \) probability of exactly one of the events \( C \) or \( A \) occurs \( =p \& P \)
(all the three events occur
simultaneously) \( =p^{2}, \) where
A \( \cdot \frac{3 p+2 p^{2}}{2} \)
в. \( \frac{p+3 p^{2}}{4} \)
c. \( \frac{p+3 p^{2}}{2} \)
D. \( \frac{3 p+2 p^{2}}{4} \)
Subject: Physics
The length of the rod is \( 150 \mathrm{cm} \) at \( 25^{\circ} \mathrm{C} \)
Find its length when it is heated \( 150^{\circ} \mathrm{C} \)
\( \left(\alpha \operatorname{steel}=2.2 \times 10^{-5} /^{o} C\right) \)
Subject: Maths
Delegates from 9 countries include
countries \( A, B, C, D \) are to be seated in a
row. The number of possible seating arrangements, when the delegates of the countries \( A \) and \( B \) are to be seated
next to each other and the delegates of the countries \( C \) and \( D \) are not to be
seated next to each other is :
A . 10080
B. 5040
c. 3360
D. 60480
Subject: Biology
Assertion
The enlarged \( Q \) and \( R \) waves indicate myocardial infraction.
Reason
Any deviation in the normal recording of ECG indicates possible abnormality or disease.
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
If \( P(x, y, z) \) is a point on the line segment joining \( \boldsymbol{A}(\mathbf{2}, \mathbf{2}, \mathbf{4}) \) and
\( B(3,5,6) \) such that projection of \( \overrightarrow{O P} \) on axes are \( \frac{13}{5}, \frac{19}{5}, \frac{26}{5} \) respectively, then \( P \) divide AB in the ratio
A .3: 2
B. 2: 3
c. 1: 2
D. 1: 3
Subject: Maths
If the vertex \( =(2,0) \) and the
extremities of the latus rectum are
(3,2) and \( (3,-2), \) then the equation of the parabola is
A \( \cdot y^{2}=2 x-4 \)
B . \( x^{2}=4 y-8 \)
c. \( y^{2}=4 x-8 \)
D. None
Subject: Maths
By applying \( S A S \) congruence rule, you
want to establish that \( \triangle \boldsymbol{P} \boldsymbol{Q} \boldsymbol{R} \equiv \)
\( \triangle F E D . \) It is given that \( P Q=F E \) and
\( R P=D E . \) What additional information
is needed to establish the congruence?
Subject: Physics
In a potentiometer experiment of a cell of emf \( 1.25 \mathrm{V} \) gives balancing length of \( 30 \mathrm{cm} . \) If the cell is replaced by another cell, balancing length is found to be 40
cm. What is the emf of second cell?
\( \mathbf{A} \cdot \simeq 1.57 V \)
\( \mathbf{B} \cdot \simeq 1.67 V \)
\( \mathbf{c} . \simeq 1.47 V \)
\( \mathbf{D} \cdot \simeq 1.37 V \)
Subject: Maths
A particle moves along the x-axis obeying the equation \( \boldsymbol{x}=\boldsymbol{t}(\boldsymbol{t}-\mathbf{1})(\boldsymbol{t}- \)
2), where \( x \) is in meter and \( t \) is in
second. Find the initial velocity of the particle \( (\boldsymbol{m} / \boldsymbol{s}) \)
Subject: Physics
An engine of a train moving with uniform acceleration passes an electric pole with velocity u and the last compartment with velocity v. The middle part of the train passes past the same pole with a velocity of
A \( \cdot \frac{u+v}{2} \)
в. \( \frac{u^{2}+v^{2}}{2} \)
c. \( \sqrt{\frac{u^{2}+v^{2}}{2}} \)
D. \( \sqrt{\frac{u^{2}-v^{2}}{2}} \)
Subject: Physics
\( \ln \operatorname{an} A C \) Generator, if the number of
turns for the armature coil is doubled
keeping all other specifications to be the same, which of the following applies to the voltage generated
A. Peak Voltage will remain the same but the rms value of Voltage generated double
B. Peak Voltage will double but the rms value of Voltage generated will remain the same
c. Both the peak Voltage and the rms value of Voltage generated will double.
D. Both the peak Voltage and the rms value of Voltage generated will reduce to half the original value
Subject: Chemistry
The presence of carbon in an organic
compound is detected by heating it
with :
A. sodium metal to convert it to \( N a C N \)
B. \( C a O \) to convert it into \( C O \) which burns with a blue flame
c. \( C u O \) to convert it into \( C O_{2} \) which turns lime water milky
D. \( C u \) wire to give a bluish-green flame
Subject: Chemistry
Three reactions involving \( \mathbf{H}_{2} \mathbf{P} \mathbf{O}_{4}^{-} \) are given below:
(i) \( \mathbf{H}_{3} \mathbf{P} \mathbf{O}_{4}+\mathbf{H}_{2} \mathbf{O} \rightarrow \mathbf{H}_{3} \mathbf{O}^{+}+\mathbf{H}_{2} \mathbf{P} \mathbf{O}_{4}^{-} \)
(ii) \( \mathbf{H}_{2} \mathbf{P} \mathbf{O}_{4}^{-}+\mathbf{H}_{2} \mathbf{O} \rightarrow \mathbf{H} \mathbf{P} \mathbf{O}_{4}^{2-}+\mathbf{H}_{3} \mathbf{O}^{+} \)
(iii) \( \mathbf{H}_{2} \mathbf{P O}_{4}^{-}+\mathbf{O H}^{-} \rightarrow \mathbf{H}_{3} \mathbf{P} \mathbf{O}_{4}+\mathbf{O}^{2-} \)
In which of the above reactions, does
\( H_{2} P O_{4}^{-} \) act as an acid?
A . (ii) only
B. (i) and (ii)
\( c . \) (iii) only
D. (i) and (iii)
Subject: Chemistry
Acidified solution of \( K_{2} C r_{2} O_{7} \) on
treatment with \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) yields:
A. \( C r O_{3}+H_{2} O+O_{2} \)
в. \( C r_{2} O_{2}+H_{2} O+O_{2} \)
\( \mathrm{c} \cdot \mathrm{Cr} \mathrm{O}_{5}+\mathrm{H}_{2} \mathrm{O}+\mathrm{K}_{2} \mathrm{SO}_{4} \)
D. \( H_{2} C r_{2} O_{7}+H_{2} O+O_{2} \)
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. Assertion is incorrect but Reason is correct