AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Choose the incorrect statement about
effective nuclear charge.
A. \( Z_{e f f}=Z-\sigma(\sigma \text { is Slater's screening constant }) \)
B. \( Z_{\text {eff}} \) increases as we move across the period
C. \( Z_{\text {eff}} \) decreases from top to bottom in a group
D. \( Z_{\text {eff}} \) is constant or almost constant for f-block elements
Subject: Chemistry
In a gaseous mixture, if an alkane
\( \left(C_{x} H_{2 x+2}\right) \) and an alkene \( \left(C_{y} H_{2 y}\right) \) are taken in 2: 1 mole ratio, the average
molecular weight of the mixture is
observed to be \( 20 . \) If the same alkane
and alkene are taken in 1: 2 mole ratio,
the average molecular weight of the mixture is observed to be \( 24 . \) Then, the
value of \( x \) and \( y \) are respectively:
A . 2,1
в. 1,2
\( c \cdot 2,3 \)
D. 3.2
Subject: Maths
Discuss the continuity of the function
\( \boldsymbol{f}(\boldsymbol{x})= \)
\[
\left\{\frac{\log (2+x)-\log (2-x)}{\tan x}, \quad \text { for } x \neq 0\right.
\]
at the point \( \boldsymbol{x}=\mathbf{0} \)
Subject: Chemistry
What is the type of reaction?
\( \boldsymbol{C H}_{2}-\boldsymbol{C H}-\boldsymbol{C H}_{3}+\boldsymbol{H B r} \rightarrow \)
\( \boldsymbol{C H}_{3} \boldsymbol{C H B r} \boldsymbol{C H}_{3} \)
A. Nucleophilic addition
B. Electrophilic substitution
c. Electrophilic addition
D. Free radial addition
Subject: Chemistry
The relative formula mass, \( M_{r}, \) of
calcium carbonate, \( C a C O_{3}, \) is 100
What is the mass of carbon present in \( 100 g \) of calcium carbonate?
A \( .12 g \)
B. \( 36 g \)
c. \( 40 g \)
D. \( 60 g \)
Subject: Maths
Find the median for the following data
given below:
\( \begin{array}{lllll}\text { Class } & 0- & 2- & 4- & 6 \\ \text { interval } & 2 & 4 & 6 & 8\end{array} \)
Frequencies 3. 2 3
A . 5.3
в. 5.4
c. 5.1
D. 5.6
Subject: Biology
Which of the following statements is/are incorrect about lymph?
(i)Lymph is colourful as it has haemoglobin but no RBC.
(ii)lt contains specialised Iymphocytes which are responsible for immunity of the body.
(iii)Lymph is an important carrier for nutrients and hormones.
(iv)Fats are absorbed through lymph in
the lacteals present in the intestinal villi.
A. i only
B. iii and iv
c. ii and iii
D. iv only
Subject: Chemistry
The vapour density of undecomposed
\( N_{2} O_{4} \) is \( 46 . \) When heated, vapour density decreases to 24.5 due to its
dissociation to \( N O_{2} . \) The percentage
dissociation of \( N_{2} O_{4} \) at the final
temperature is:
\( \mathbf{A} \cdot 88 \)
B. 60
c. 40
D. 70
Subject: Maths
In adjoining figure \( A B \) is a chord of a
circle and \( \angle A D B=45^{\circ}, \angle A C B \) will be:
A \( .45^{\circ} \)
B \( \cdot 60^{\circ} \)
\( c \cdot 90^{\circ} \)
D. \( 135^{\circ} \)
Subject: Physics
A force of 50 dynes is acted on a body of mass \( 5 g \) which is at rest for an interval
of 3 seconds, then impulse is \( (\text { in } N s) \)
A. \( 1.5 \times 10^{-3} \)
B. \( 1.5 \times 10^{-2} \)
c. \( 2.5 \times 10^{-} 3 \)
D. \( 1.5 \times 10^{3} \)
Subject: Maths
fthe matrix \( \boldsymbol{A}=\left[\begin{array}{lll}2 & 0 & 0 \\ 0 & 2 & 0 \\ 2 & 0 & 2\end{array}\right], \) then
\( \boldsymbol{A}^{n}=\left[\begin{array}{lll}\boldsymbol{a} & \boldsymbol{0} & \boldsymbol{0} \\ \boldsymbol{0} & \boldsymbol{a} & \boldsymbol{0} \\ \boldsymbol{b} & \boldsymbol{0} & \boldsymbol{a}\end{array}\right] . \boldsymbol{n} \in \boldsymbol{N} \) where
A \( \cdot a=2 n, b=2^{n} \)
B . \( a=2^{n}, b=2 n \)
c. \( a=2^{n}, b=n 2^{n-1} \)
D. \( a=2^{n}, b=n 2^{n} \)
Subject: Chemistry
To which of the following mixtures Dalton's law is not applicable?
This question has multiple correct options
A \( \cdot C O_{2} \) and \( \operatorname{co~at~room~temperature~} \)
B. Ammonia and hydrogen chloride at room temperature
\( \mathrm{c} \cdot N H_{3} \) and steam at room temperature
D. He and \( H_{2} \)
Subject: Physics
A particle executes S.H.M with a period of 6 seconds. If the maximum speed is \( 3.14 \mathrm{cm} / \mathrm{sec}, \) then what is its amplitude?
A. \( 3 \mathrm{cm} \)
B. \( 5 \mathrm{cm} \)
\( c \cdot 6 \mathrm{cm} \)
D. \( 9 \mathrm{cm} \)
Subject: Maths
A body travels a distance \( s \) in \( t \) seconds.
It starts from rest and ends at rest. In
the first part of the journey, it move with
constant acceleration \( f \) and in the
seconds part with constant retardation
\( r . \) The value of \( t \) given by
\( ^{\mathrm{A}} \cdot_{2 s}\left(\frac{1}{f}+\frac{1}{r}\right) \)
в. \( \frac{2 s}{\frac{1}{f}+\frac{1}{r}} \)
c. \( \sqrt{2 s(f+r)} \)
D. \( \sqrt{2 s\left(\frac{1}{f+r}\right)} \)
Subject: Physics
In an experiment of verification of
Ohm's law, following observations are obtained:
Potential difference 0.5
\( \begin{array}{lll}\text { 1.0 } & \text { 1.5 } & \text { 2.0 }\end{array} \) \( v \) (in volt')
Current
in 0.2
\( 0.4 \quad 0.6 \)
ampere
From observation table the resistance
in circuit is
A. \( 2.5 \Omega \)
в. \( 2 \Omega \)
\( c .5 \Omega \)
D. \( 3 \Omega \)
Subject: Physics
Two particles of equal mass go around
a circle of radius \( R \) under the action of
their mutual gravitational attraction.The speed of each particle is
\( ^{\mathbf{A}} \cdot_{v}=\frac{1}{2 R} \sqrt{\left(\frac{1}{G m}\right)} \)
в. \( v=\sqrt{\left(\frac{G m}{2 R}\right)} \)
\( ^{\mathrm{c}} v=\sqrt{\left(\frac{G m}{R}\right)} \)
D. \( v=\sqrt{\left(\frac{4 G m}{R}\right)} \)
Subject: Chemistry
The correct order of increasing number of alpha particles passing undeflected through the foils of \( A u, A g, C u \) and \( A l \)
of 1000 atoms thickness each in a
simulated alpha particle scattering experiment of Rutherford would be:
A. \( A u<A g<C u<A l \)
в. \( A l<C u<A g<A u \)
c. \( A u<C u<A l<A g \)
D. \( A g<C u<A l<A u \)
Subject: Maths
The set of values of ' \( x^{\prime} \) for which the
formula \( 2 \sin ^{-1} x=\sin ^{-1}(2 x \sqrt{1-x^{2}}) \)
is true, is
A. (-1,0)
B. [0,1]
c. \( \left[-\frac{\sqrt{3}}{2}, \frac{\sqrt{3}}{2}\right] \)
D. \( \left[-\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right] \)
Subject: Maths
Given planes are \( \boldsymbol{P}_{1}: \boldsymbol{c} \boldsymbol{y}+\boldsymbol{b} \boldsymbol{z}=\boldsymbol{x} \quad \boldsymbol{P}_{2}: \boldsymbol{a} \boldsymbol{z}+\boldsymbol{c} \boldsymbol{x}=\boldsymbol{y} \quad \boldsymbol{P}_{3} \)
\( P_{1}, P_{2} \) and \( P_{3} \) pass through one line, if
A \( \cdot a^{2}+b^{2}+c^{2}=a b+b c+c a \)
B . \( a^{2}+b^{2}+c^{2}+2 a b c=1 \)
\( \mathbf{c} \cdot a^{2}+b^{2}+c^{2}=1 \)
D. \( a^{2}+b^{2}+c^{2}+2 a b+2 b c+2 c a+2 a b c=1 \)
Subject: Maths
A ball is drawn at random from box \( \boldsymbol{I} \)
and transferred to box \( I I \). If the
probability of drawing a red ball from box \( I, \) after this transfer, is \( \frac{1}{3}, \) then the correct option(s) with the possible
values of \( n_{1} \) and \( n_{2} \) is (are)
This question has multiple correct options
A \( \cdot n_{1}=4 \) and \( n_{2}=6 \)
B . \( n_{1}=2 \) and \( n_{2}=3 \)
c. \( n_{1}=10 \) and \( n_{2}=20 \)
D. \( n_{1}=3 \) and \( n_{2}=6 \)
Subject: Chemistry
The decomposition of a substance
follows first order kinetics. If its
concentration is reduced to \( 1 / 8 \) of its
initial value in 12 minutes, the rate
constant of the decomposition system is ?
\( ^{\text {A }} \cdot\left(\frac{2.303}{12} \log \frac{1}{8}\right) \) min. \( ^{-1} \)
B. \( \left(\frac{2.303}{12} \log 8\right) \) min. \( ^{-1} \)
c. \( \left(\frac{0.693}{12}\right) \) min. \( ^{-1} \)
D. \( \left(\frac{1}{12} \log 8\right) \) min. \( ^{-1} \)
Subject: Physics
Assertion
During storms, communication may be disrupted, and electrical discharges may be seen between sharp points on signalling equipment that is
inadequately earthed.
Reason
Atmospheric electricity often has an effect on electrical communications.
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
For the configuration of media of
permitivities \( \varepsilon_{o}, \varepsilon \) and \( \varepsilon_{o} \) between
parallel plates each of area \( A \), as show
in figure, the equivalent capacitance is
\( \mathbf{A} \cdot \varepsilon_{0} A / d \)
В \( \cdot \varepsilon_{0} \varepsilon A / d \)
C. \( \frac{\varepsilon_{0} \varepsilon A}{d\left(\varepsilon+\varepsilon_{0}\right)} \)
D. \( \frac{\varepsilon_{0} \varepsilon A}{\left(2 \varepsilon+\varepsilon_{0}\right)} \)
Subject: Chemistry
The EMF of the cell :
\( \boldsymbol{P t}, \boldsymbol{H}_{2}(\boldsymbol{1} \boldsymbol{a} \boldsymbol{t m})\left|\boldsymbol{H}^{\oplus}(\boldsymbol{a} \boldsymbol{q}) \| \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l}\right| \boldsymbol{A} \boldsymbol{g} \) is
0.27 and \( 0.26 \mathrm{V} \) at \( 25^{\circ} \mathrm{C} \) and \( 35^{\circ} \mathrm{C} \)
respectively. The posituve value of heat of the reaction occurring inside the cell
\( \operatorname{at} 25^{\circ} C\left(i n k J K^{-1}\right) \) is: \( ( \) write your
answer to nearest integer)
Subject: Physics
Assertion
Kepler's second law can be understood by conservation of angular momentum principle.
Reason
Kepler's second law is related with areal
velocity which can further be proved to
be based on conservation of angular
momentum as \( (\boldsymbol{d A} / \boldsymbol{d t})=\left(\boldsymbol{r}^{2} \boldsymbol{\omega}\right) / 2 \)
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
Assertion: A quick collision between two bodies is more violent than a slow
collision; even when the initial and final velocities are identical.
Reason: The momentum is greater in first case
A. If both assertion and reason are true but the reason is the correct explanation of assertion.
B. If both assertion and reason are true but the reason is not the correct explanation of assertion
c. If assertion is true but reason is false
D. If both the assertion and reason are false.
E . If reason is true but assertion is false
Subject: Physics
A particle moves along the parabolic
path \( y=a x^{2} \) in such a way that the \( y- \)
component of the velocity remains constant, say \( c . \) The \( x \) and \( y \) coordinates
are in meters. Then acceleration of the
particle at \( \boldsymbol{x}=\mathbf{1} \boldsymbol{m} \) is:
\( \mathbf{A} \cdot a c \hat{k} \)
B \( \cdot 2 a c^{2} \hat{j} \)
c. \( -\frac{c^{2}}{4 a^{2}} \)
D. \( -\frac{c}{2 a} \hat{i} \)
Subject: Maths
Assertion
STATEMENT-1: If \( f(x) \) is continuous on
\( [a, b], \) then there exists a point \( c \in(a, b) \)
such that \( \int_{a}^{b} f(x) d x=f(c)(b-a) \)
Reason
STATEMENT-2: For \( a<b \), if \( m \) and \( M \) are,
respectively, the smallest and greatest
values of \( \boldsymbol{f}(\boldsymbol{x}) \) on \( [\boldsymbol{a}, \boldsymbol{b}] \)
\( \operatorname{then} m(b-a) \leq \int_{a}^{b} f(x) d x \leq(b- \)
\( \boldsymbol{a}) \boldsymbol{M} \)
A. STATEMENT-1 is True, STATEMENT-2 is True STATEMENT-2 is a correct explanation for STATEMENT-
1
B. STATEMENT-1 is True, STATEMENT-2 is True STATEMENT-2 is NOT a correct explanation for STATEMENT-1.
C . STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True
Subject: Physics
The dimensional formula for magnetic flux is
A \( \cdot\left[M L^{2} T^{-2} A^{-1}\right] \)
B \( \cdot\left[M L^{3} T^{-2} A^{-2}\right] \)
c. \( \left[M^{0} L^{-2} T^{-2} A^{-2}\right] \)
D・ \( \left[M L^{2} T^{-1} A^{2}\right] \)
Subject: Physics
The inductor in a LC oscillation has a
maximum potential difference of \( 16 \mathrm{V} \)
and maximum energy of \( 640 \mu \) J. Find
the value of capacitor in \( \mu \) F in LC circuit.
A. \( F=5 \mu F \)
В. \( F=6 \mu F \)
c. \( F=7 \mu F \)
D. \( F=8 \mu F \)
Subject: Chemistry
Assertion: Receptor proteins show
selectivity for one chemical messenger
Over the other

Reason: Chemical messenger binds to the receptor site and inhibits is natural
function
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. Both Assertion and Reason are incorrect
D. Assertion is correct but Reason is incorrect
E. Assertion is incorrect but Reason is correct
F. Answer required
Subject: Physics
Figure shows a piece of semiconductor pure one) \( \mathrm{S} \) in series with a variable
resistors \( \mathrm{R} \) and a source of constant
voltage \( V . S \) is heated and the current is
kept constant by adjustment of R. Which of the following factors will decrease during the precess?
1. The drift velocity of the conduction electrons in S.
2. The DC resistors of \( S \)
3. The number of conduction electrons
in S.
A. Only 1
B. 1 and 2
c. \( 1,2, \) and 3
D. only
Subject: Physics
A Centigrade and Fahrenheit thermometers are dipped in boiling water. The water temperature is lowered until the Fahrenhit thermometer
registers \( 140 . \) The fall in temperature as registered by centigrade thermometer
is
\( A \cdot 30 \)
B . 40
\( c \cdot 60 \)
D. \( 80^{\circ} \)
Subject: Biology
and
D in the given figure and match the
correct names from the list (i - viii)
given below.
(i) Reissner's membrane
(ii) Basilar membrane
(iii) Tectorial membrane
(iv) Organ of Corti
(v) Hair cells
(vi) Ototlith organ
(vii) Scala media
(viii) Scala vestibuli
A. \( A-(\text { ii) }, B-(v), C- \) (iii), D - (i)
B. A - (vii), B - (iv), C - (ii), D - (iii)
C. \( A-(v \text { ii }), B-(i v), C-(i), D-(i i) \)
D. \( A-(v \text { ii }), B-(v i), C-(i), D- \) (iii)
Subject: Chemistry
The solubility curve of \( \boldsymbol{K} \boldsymbol{N} \boldsymbol{O}_{3} \) in water is shown below.

The amount of \( K N O_{3} \) that dissolves in
\( 50 g \) of water at 40 is closest to:
A . 100 g
B. 150 g
c. \( 200 g \)
D. \( 50 g \)
Subject: Physics
\( M_{1} \) and \( M_{2} \) are plane mirrors and kept
parallel to each other. At point 0 , there
will be a maxima for wavelength \( \lambda \). Light
from a monochromatic source \( \boldsymbol{S} \) of
wavelength \( \lambda \) is not reaching directly on
the screen. Then, \( \lambda \) is:
\( ^{A} \cdot \frac{3 d^{2}}{D} \)
B. \( \frac{3 d^{2}}{\text { on }} \) \( 2 D \)
\( c \cdot \underline{d^{2}} \)
\( \bar{D} \)
D. \( 2 d^{d} \)
Subject: Maths
The domain of \( \mathbf{f}(\mathbf{x})=\frac{\mathbf{3}}{\mathbf{4}-\mathbf{x}^{2}}+ \)
\( \log _{10}\left(x^{3}-x\right) \) is
A \( .(1,2) \)
B. (-1,0)\( \cup(1,2) \)
c. (1,2)\( \cup(2, \infty) \)
D. (-1,0)\( \cup(1,2) \cup(2, \infty) \)
Subject: Physics
Q Type your question-
\( T_{A}=300 \mathrm{K} . \) At time \( t=0 \) the
temperature of \( X \) is \( T_{0}=400 K . \) It cools
according to Newton's law of cooling. At
time \( t_{1}, \) its temperature is found to be
\( 350 \mathrm{K} \)
At this time \( \left(t_{1}\right), \) the body \( X \) is connected to a large body Y at atmospheric temperature \( \boldsymbol{T}_{\boldsymbol{A}}, \) through a conducting rod of length L, cross-
sectional area \( A \) and thermal
conductivity K. The heat capacity of Y is so large that any variation in its temperature may be neglected. The cross-sectional area \( A \) of the connecting rod is small compared to the surface area of \( X . \) Find the temperature of \( X \) at
time \( t=3 t_{1} \)
A. \( \quad \frac{2 K A}{I} \) ti
\[
T=\left[12.5 e^{\frac{C L}{1}}+900\right] K
\]
B. \( \left.\quad \frac{2 K A}{C^{t_{1}}}+300\right] K \)
\( T=\left[12.5 e^{C L}\right. \)
c. \( \left.\quad \frac{2 K A}{l^{t_{1}}}+600\right] K \)
\( T=\left[12.5 e^{C L}\right. \)
D. \( \quad T=\left[12.5 e^{\frac{2 K A}{C L} t_{1}}+700\right] K \)
Subject: Physics
A coil of moving coil galvanometer
twists through \( 90^{\circ} \) when a current of one microampere is passed through it.lf the area of the coil is \( 10^{-4} m^{2} \) and it has
100 turns, calculate the magnetic field of the magnet of the galvanometer.Given \( k=10^{-8} N- \)
\( \boldsymbol{m} / \) degree
Subject: Chemistry
Statement 1: Conc \( \mathbf{H}_{2} \mathbf{S} \mathbf{O}_{4} \) is a low
volatility and viscos nature acid. Statement2: It is due to Hydrogen
bonding.
A. Statement 1 and 2 are correct and 2 is correct explanation of 1
B. Statement 1 and 2 are correct and 2 is not correct explanation of 1
c. statement 1 is correct and 2 is not correct
D. Statement 1 is not correct and 2 is correct.
Subject: Physics
A \( 120 m \) long train is moving in a
direction with speed \( 20 m / s . A \) train \( B \) moving with \( 30 m / s \) in the opposite direction and \( 130 \mathrm{m} \) long crosses the
first train in a time of :
\( \mathbf{A} \cdot 5 s \)
в. \( 36 s \)
\( c .38 s \)
D. None of these
Subject: Physics
What is the effect of temperature on the
resistance of a metal? The resistance of
a platinum resistances thermometer at
\( 0^{\circ} \mathrm{C} \) temperature is \( 3.0 \Omega \) and at \( 100^{\circ} \mathrm{C} \) it
is \( 3.75 \Omega . \) Its resistance at an unknown
temperature is \( 3.15 \Omega \). Find the value of
the unknown temperature
Subject: Physics
Identify which of the following equations represents alpha decay in a nuclear fission reaction?
\( \begin{array}{ll}\text { A } \cdot & \frac{2}{1} H+_{1}^{2} H \rightarrow \quad_{1}^{3} H+_{1}^{1} H+\text { energy } \\ & \text { y } H\end{array} \)
B \( \cdot \frac{226}{88} R a \rightarrow \quad \frac{222}{86} R n+_{2}^{4} H e \)
\( \begin{array}{ll}\text { C. }_{83}^{209} B i \rightarrow & \frac{209}{84} P o+_{-1}^{0} e \\ & e\end{array} \)
D \( \cdot \frac{235}{92} U+_{0}^{1} n \rightarrow \quad \frac{140}{54} X e+_{38}^{94} S r+_{2}^{1} n \)
E \( \cdot \frac{4}{2} \mathrm{He}+_{13}^{27} \mathrm{Al} \rightarrow \quad_{15}^{30} \mathrm{P}+_{0}^{1} n \)
Subject: Physics
Electrons at rest are accelerated by a
potential of \( \boldsymbol{V} \) volt. These electrons enter the region of space having a uniform, perpendicular magnetic induction field \( B \). The radius of the path
of the electrons inside the magnetic field is:
A \( .1 / B \sqrt{m V / e} \)
B. \( \frac{\sqrt{2 m V / e}}{B} \)
c. \( m V / q B \)
D. \( 1 / B \sqrt{V / e} \)
Subject: Maths
Let \( \cos ^{-1}\left(4 x^{3}-3 x\right)=a+b \cos ^{-1} x \)
\( x \epsilon\left[-\frac{1}{2},-1\right) \) then the value of \( a+b \pi \) is
A \( .2 \pi \)
в. \( 3 \pi \)
\( c \)
D. \( -2 \pi \)
Subject: Chemistry
Assertion: pH of water increases with an
increase in temperature
Reason: \( K_{W} \) of water increases with
increase in temperature
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
E. Both Assertion and Reason are incorrect
Subject: Chemistry
When a substance A reacts with water, it
produces a combustible gas \( \mathrm{B} \) and a solution of substance \( C \) in water. D reacts
with this solution of \( \mathrm{C} \) and produces the
same gas B on warming. D can also
produce gas \( \mathrm{B} \) on reaction with dilute
\( H_{2} S O_{4} . \) A imparts a deep golden yellow colour to smokeless flame. \( A, B, C \) and \( D \)
respectively are:
\( \mathbf{A} \cdot N a, H_{2}, N a O H, Z n \)
B . \( K, H_{2}, K O H, A l \)
\( \mathbf{c} \cdot_{C a}, H_{2}, C a(O H)_{2}, S n \)
D \( \cdot \operatorname{caC}_{2}, C_{2} H_{2}, C a(O H)_{2}, F e \)
Subject: Maths
A data consists of \( n \) observation:
\( \boldsymbol{x}_{1}, \boldsymbol{x}_{2}, \ldots \ldots . ., \boldsymbol{x}_{n} . \) If \( \sum_{i=1}^{n}\left(\boldsymbol{x}_{i}+\mathbf{1}\right)^{2}=\mathbf{9} \boldsymbol{n} \)
and \( \sum_{i=1}^{n}\left(x_{i}-1\right)^{2}=5 n, \) then the standard deviation of this data is:
A . 5
B. \( \sqrt{5} \)
c. \( \sqrt{7} \)
\( D \)
Subject: Maths
In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then the
common ratio of this progression equals
A \( \cdot \frac{1}{2}(1-\sqrt{5}) \)
B \( \cdot \frac{1}{2} \sqrt{5} \)
c. \( \frac{1}{5} \sqrt{2} \)
D. \( \frac{1}{2}(\sqrt{5}-1) \)
Subject: Physics
The largest and the shortest distance of
the earth from the sun is \( r_{1} \) and \( r_{2} \). Its
distance from the sun when it is at
perpendicular to the major axis of the orbit drawn from the sun:
\( \mathbf{A} \cdot\left(r_{1}+r_{2}\right) / 4 \)
B . \( \left(r_{1}+r_{2}\right) /\left(r_{1}-r_{2}\right) \)
\( \mathbf{c} \cdot 2 r_{1} r_{2} /\left(r_{1}+r_{2}\right) \)
D. \( \left(r_{1}+r_{2}\right) / 3 \)
Subject: Chemistry
Q Type your question
IOr \( 1.00 \times 10 \). \( \kappa g \) or oxygen gas at two
different temperatures.
(a) What does the dotted plot signify?
(b) Which is true \( : T_{1}>T_{2} \) or \( T_{1}<T_{2} ? \)
(c) What is the value of PV / T where the
curves meet on the y-axis?
(d) If we obtained similar plots for
\( 1.00 \times 10^{-3} k g \) of hydrogen, would we
get the same value of PV/T at the point
where the curves meet on the y-axis? If
not, what mass of hydrogen yields the
same value of PV/T (for low pressure
high temperature region of the plot)?
(Molecular mass of \( \boldsymbol{H}_{2}=\mathbf{2 . 0 2} \boldsymbol{u}, \) of
\( O_{2}=32.0 u, R=8.31 J m o l^{-1} K^{-1} . \)
Subject: Chemistry
The pH of blood stream is maintained
by a proper balance of \( \boldsymbol{H}_{2} \boldsymbol{C O}_{3} \) and
\( N a H C O_{3} \) concentration. What volume
of \( 5 M N a H C O_{3} \) solution should be
mixed with a \( 10 \mathrm{mL} \) sample of blood
which is \( 2 M \) in \( H_{2} C O_{3} \) in order to
maintain its pH?
\( \mathbf{A} \cdot 40 \mathrm{mL} \)
B . \( 38 \mathrm{mL} \)
c. \( 50 \mathrm{mL} \)
D. \( 78 \mathrm{mL} \)
Subject: Physics
The work done in bringing a unit positive charge from infinite distance to a point at distance \( x \) from a positive charge \( Q \) is \( W \). Then the potential \( \phi \) at that point is:
A. \( \frac{W Q}{x} \)
B. \( W \)
c. \( \frac{W}{x} \)
D. \( W Q \)
Subject: Maths
\( \mathbf{a}=\left|\begin{array}{lll}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{c} & \boldsymbol{a} & \boldsymbol{b} \\ \boldsymbol{b} & \boldsymbol{c} & \boldsymbol{a}\end{array}\right|, \) then the value of
\( \left|\begin{array}{ccc}a^{2}-b c & b^{2}-c a & c^{2}-a b \\ c^{2}-a b & a^{2}-b c & b^{2}-c a \\ b^{2}-c a & c^{2}-a b & a^{2}-b c\end{array}\right| \)
\( A \cdot \Delta^{2} \)
B \( .2 \Delta^{2} \)
\( c \cdot \Delta^{3} \)
D. none of these
Subject: Physics
One \( k g \) of a diatomic gas is at a
pressure of \( 8 \times 10^{4} \mathrm{N} / \mathrm{m}^{2} . \) The density
of the \( \operatorname{gas} \) is \( 4 \mathrm{kg} / \mathrm{m}^{3} . \) What is the energy of the gas due to its thermal
motion?
A. \( 3 \times 10^{4} \mathrm{J} \)
B . \( 5 \times 10^{4} \mathrm{J} \)
c \( \cdot 6 \times 10^{4} \mathrm{J} \)
D. \( 7 \times 10^{4} \mathrm{J} \)
Subject: Maths
Let \( A=\{0,1,2,3,4\}, B=\{1,-2,3,4,5,6\} \)
and \( C=\{2,4,6,7\} \)
(i) Show that \( \boldsymbol{A} \cup(\boldsymbol{B} \cap \boldsymbol{C})=(\boldsymbol{A} \cup \)
\( \boldsymbol{B}) \cap(\boldsymbol{A} \cup \boldsymbol{C}) \)
(ii) Verify this relation using Venn diagram.
Subject: Physics
Two rings each of mass ' \( m^{\prime} \) and radius
\( r^{\prime} \) are placed such that their centres
are at a common point and their planes
are normal to each other. The moment of
inertia of the system about an axis passing through the centre and perpendicular to plane of one of ring is:
A \( \cdot 2 m r^{2} \)
B. \( m r^{2} \)
c. \( \frac{1}{2} m r^{2} \)
D. \( \frac{3}{2} m r^{2} \)
Subject: Physics
A cricket ball of mass \( 150 g \) moving with a speed of \( 126 k m / h \) hits at the
middle of the bat, held firmly at its position by the batsman. The ball moves straight back to the bowler after hitting the bat. Assuming that collision between ball and bat is completely elastic and the two remain in constant
for \( 0.001 s, \) the force that the batsman
had to apply to hold the bat firmly at its place would be:
A . \( 10.5 N \)
B. \( 21 N \)
c. \( 1.05 \times 10^{4} N \)
D. \( 2.1 \times 10^{4} N \)