AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{3} & \mathbf{4} \\ \mathbf{5} & \mathbf{6} \\ \mathbf{7} & \mathbf{8}\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{lll}\mathbf{3} & \mathbf{5} & \mathbf{7} \\ \mathbf{4} & \mathbf{6} & \mathbf{8}\end{array}\right] \)
then which one of the following is
correct?
\( A \cdot B \) is the inverse of \( A \)
B. \( B \) is the adjoint of \( A \)
c. \( B \) is the transpose of \( A \)
D. None of the above
Subject: Physics
Two radio active elements \( X \) and \( Y \) have
half lives of 50 minutes and 100
minutes respectively. Samples of \( X \) and initially contain equal number of atoms. After 200 minutes, the ratio
of number of atoms of X unchanged to that of Y is
A .4
B . 2
c. \( 1 / 2 \)
D. \( 1 / 4 \)
Subject: Maths
Find the value of \( x \) in \( \left[\begin{array}{cc}2 x-y & 5 \\ 3 & y\end{array}\right]= \)
\( \left[\begin{array}{cc}\mathbf{6} & \mathbf{5} \\ \mathbf{3} & -\mathbf{2}\end{array}\right] \)
Subject: Maths
Let \( C(\theta)=\sum_{n=0}^{\infty} \frac{\cos (n \theta)}{n !} \)
Which of the following statements is
FALSE?
B. \( C(0) . C(\pi)>2 \)
c. \( C(\theta)>0 \) for all \( \theta \in R \)
D. \( C(\theta) \neq 0 \) for all \( \theta \in R \)
Subject: Chemistry
Select the correct option.
\( \mathbf{A} \cdot \Delta H_{f}[H(g)] \) is equal to \( \Delta H_{\text {atomisation}} \) of \( H_{2}(g) \)
B. \( \Delta H_{B E}[(H-H)] \) is equal to \( \Delta H_{f} \) of \( H(g) \)
\( \mathbf{C} \cdot \Delta H_{B E}[(H-H)] \) is equal to \( \Delta H_{\text {atomisation}} \) of \( H_{2}(g) \)
D. \( \Delta H_{\text {combustion}}\left[H_{2}(g)\right] \) is equal to \( \Delta H_{f} \) of \( \left[H_{2}(g)\right] \)
Subject: Physics
A charge \( +\mathrm{Q} \) is located in space at the
point \( (\boldsymbol{x}=\mathbf{1} \boldsymbol{m}, \boldsymbol{y}=\mathbf{1 0 m}, \boldsymbol{z}=\mathbf{5} \boldsymbol{m}) \)
What is the total electric flux that
passes through the yz-plane?
A \( \cdot \frac{Q}{\varepsilon_{0}} \)
в. \( \frac{Q}{3 \varepsilon_{0}} \)
c. \( \frac{Q}{6 \varepsilon_{0}} \)
D \( \cdot \frac{Q}{2 \varepsilon_{0}} \)
Subject: Chemistry
After electrolysis of NaCl solution with
inert electrodes for a certain period of
time, \( 600 \mathrm{mL} \) of the solution was left. Which was found to be \( 1 \mathrm{N} \) in \( \mathrm{NaOH} \) During the same time, 31.75 g \( \mathrm{Cu} \) deposited in the copper voltameter in series with the electrolytic cell. Calculate the percentage yield of NaOH obtained.
A. \( n=60 \% \)
a
B . \( n=50 \% \)
c. \( n=70 \% \)
D. None of these
Subject: Physics
Two identical thin rings each of radius
\( \boldsymbol{R} \) metre are kept on the same axis at a
distance of \( \boldsymbol{R} \) metre apart. If the
charges on them are \( 10 C \) and \( 5 C \)
respectively. Calculate the work done in
moving charge \( q \) coulomb from the
centre of one ring to that of another
A \( \cdot \frac{5 q}{4 \pi \varepsilon_{0} R}\left[1-\frac{1}{\sqrt{2}}\right] J \)
В. \( \frac{5 q}{4 \pi \varepsilon_{0} R}\left[\frac{\sqrt{2}-1}{2}\right] J \)
\( ^{\mathbf{C}} \cdot \frac{15 q}{4 \pi \varepsilon_{0} R}\left[\frac{\sqrt{2}-1}{\sqrt{2}}\right] J \)
\( ^{\mathrm{D}} \frac{10 q}{4 \pi \varepsilon_{0} R}\left[\frac{\sqrt{2}-1}{\sqrt{2}}\right] J \)
Subject: Physics
A ray of light is incident on a medium
with angle of incidence i and refracted
into a second medium with angle of
refraction \( r . \) The graph of \( \sin (i) \vee s \) \( \sin (r) \) is as shown in the figure. Then
the velocity of light in the first medium
is \( \ldots \ldots . . . . . . . . . \) times the velocity of light in
the second medium.
\( A \cdot \sqrt{3} \)
B. \( 1 / \sqrt{3} \)
c. \( \sqrt{3} / 2 \)
D. \( 2 / \sqrt{3} \)
Subject: Physics
In a series LCR circuit with an AC
source, \( \boldsymbol{R}=\mathbf{3 0 0} \boldsymbol{\Omega}, \boldsymbol{C}=\mathbf{2 0} \boldsymbol{\mu} \boldsymbol{F}, \boldsymbol{L}= \)
10 henry \( \epsilon_{\text {max }}=50 V \) and \( v= \)
\( \mathbf{5 0} / \boldsymbol{\pi} \boldsymbol{H z} . \) Find
(a) the \( r m s \) current in the circuit.
(b) the \( r m s \) potential differences
across the capacitor, the resistor and the inductor, Note that the sum of the
rms potential difference across the
three elements is greater than the \( r m s \) voltage of the source.
Subject: Physics
An insulating sphere with radius a has
a uniform charge density \( \rho . \) The sphere
is not centered at the origin but at \( r=b \)
Find the electric field at any point inside sphere is \( \boldsymbol{E}=\frac{\boldsymbol{\rho}(\boldsymbol{x}-\boldsymbol{b})}{\boldsymbol{n} \varepsilon_{0}} . \) what is
the value of \( n \)
Subject: Physics
A body of mass \( 6 \mathrm{kg} \) is under a force of 6 N which causes displacement in it given by \( S=\frac{t^{2}}{4} \) at where 't' is time. The
work done by the force in 2 s is:
A . 12
B. 9 J
c. 6 J
D. 3 J
Subject: Biology
Select the correct option:
Four different steps that occur during meiosis are given in the following list.
(i) Complete separation of chromatids
(ii) Pairing of homologous chromosomes
(iii) Lining up of paired chromosomes on equator
(iv) Crossing over between chromatids Select the correct sequential arrangement of the steps.
A \( . \) (ii), (iii), (iv), (i)
B. (iii), (ii), (iv), (i)
\( c \cdot(\text { ii) }, \) (iv), (iii), (i)
D. (iii), (i), (ii), (iv)
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})=\sin ^{-1} \boldsymbol{x}+\cos ^{-1} \boldsymbol{x}, \) then \( \frac{\boldsymbol{\pi}}{2} \) is
equal to This question has multiple correct options
A \( \cdot f\left(-\frac{1}{2}\right) \)
B . \( f\left(k^{2}-2 k+3\right), k \in R \)
c. \( f\left(\frac{1}{1+k^{2}}\right), k \in R \)
D. \( f(-2) \)
Subject: Maths
For any two events \( A \) and \( B \) in a sample
space:
This question has multiple correct options
\( ^{\mathbf{A}} \cdot p(A \mid B) \geq \frac{P(A)+P(B)-1}{P(B)}, P(B) \neq 0, \) is always true
B \( . P(A \cap \bar{B})=P(A)-P(A \cap B) \), does not hold
C \( . P(A \cup B)=1-P(\bar{A}) P(\bar{B}) \), if \( A \) and \( B \) are independent
D \( . P(A \cup B)=1-P(\bar{A}) P(\bar{B}) \), if \( A \) and \( B \) are disjoint
Subject: Physics
In a step-down transform the turn ratio is 1: 2 and output power is \( 2.2 k W \). if
output current is \( 10 A \) then the value of
input voltage and input current:
A. \( 100 V, 20 A \)
в. \( 110 V, 10 A \)
c. \( 440 V, 5 A \)
D. \( 440 V, 20 A \)
Subject: Physics
A beam of light \( A O \) is incidents on a glass slab \( (\mu=1.54) \) in a direction as
shown, in the Fig. The reflected ray \( O B \)
is passed through a Nicol prism. On rotating the Nicol prism we observe the
A. the intensity is reduced to zero and remains zero
B. the intensity reduces somewhat and rise again
c. there is no change in intensity
D. the intensity is gradually to reduces to zero and then again it increases
Subject: Maths
Let \( \hat{a}, \hat{b}, \hat{c} \) be unit vectors such that \( \hat{a}+ \) \( \hat{\boldsymbol{b}}+\hat{\boldsymbol{c}}=\hat{\mathbf{0}} \) and \( \mathbf{x}, y, \mathbf{z} \) be distinct integers
then minimum value of \( |\boldsymbol{x} \hat{\boldsymbol{a}}+\boldsymbol{y} \hat{\boldsymbol{b}}+\boldsymbol{z} \hat{\boldsymbol{c}}| \)
is
\( A \cdot 2 \)
B. \( \sqrt{2} \)
\( c \cdot \sqrt{3} \)
D.
Subject: Chemistry
\( 500 m L \) of \( 0.2 M \) aqueous solution of
acetic acid is mixed with \( 500 m L \) of
\( 0.2 M H C l \) at \( 25^{\circ} C \)
(a) Calculate the degree of dissociation of acetic acid in the resulting solution and pH of the solution.
(b) If \( 6 g \) of \( N a O H \) is added to the above solution, determine final pH. Assume there is no change in volume on mixing. \( K_{a} \) for acetic acid is \( 1.75 \times 10^{-5} M L^{-1} \)
Subject: Chemistry
According to Henry's law, the partial
pressure of \( \operatorname{gas}\left(\mathrm{P}_{\text {gas}}\right) \) is directly
proportional to mole fraction of gas in
dissolved state, i.e., \( \boldsymbol{P}_{\text {gas}}=\boldsymbol{K}_{\boldsymbol{H}} \cdot \boldsymbol{X}_{\boldsymbol{g a s}} \)
where \( K_{H} \) is Henry's constant. Now, choose the correct option(s). This question has multiple correct options
\( \mathbf{A} \cdot K_{H} \) is characteristic constant for a given gas-solvent system.
B. Higher is the value of \( K_{H} \), lower is the solubility of gas for a given partial pressure of gas.
\( \mathbf{C} \cdot K_{H} \) is temperature dependent
D. \( K_{H} \) increases with temperature.
Subject: Physics
Two isotopes \( P \) and \( Q \) of atomic weight 10 and \( 20, \) respectively are mixed in equal amount by weight. After 20 days their weight ratio is found to be 1: 4 Isotope \( P \) has a half-life of 10 days. The half-life of isotope \( Q \) is
A . zero
B. 5 days
c. 20 days
D. infinite
Subject: Chemistry
The osmotic pressure of \( 0.1 \mathrm{M} \) aqueous
solution of \( M g C l_{2} \) at \( 300 \mathrm{K} \) is \( 4.92 \mathrm{atm} \)
What will be the percentage ionization of the salt?
A . \( 49 \% \)
B. \( 29 \% \)
\( c .39 \% \)
D. \( 69 \% \)
Subject: Chemistry
Two closed vessel \( A \) and \( B \) of equal
volume of \( 8.21 L \) are connected by a
narrow tube of negligible volume with open valve. The left hand side container
id found to contain 3 mole \( C O_{2} \) and
2 mole of \( H e \) at \( 400 K . \) What is the
partial pressure of \( H e \) in vessel \( B \) at
\( \mathbf{5 0 0 K ?} \)
A. 2.4 atm
B. 8 atm
c. 12 atm
D. None of these
Subject: Physics
At a particular position the velocity of a particle in SHM with amplitude a is \( \frac{\sqrt{3}}{2} \) that at its mean position. In this position, its displacement is:
A \( \cdot \frac{a}{2} \)
в. \( \sqrt{3} \frac{a}{2} \frac{a}{2} \)
\( c \cdot a \sqrt{2} \)
D. \( \sqrt{2 a} \)
Subject: Maths
For which sequence below can we use
the formula for the general term of a geometric sequence?
A. \( 1,3,5,7,9, \ldots \)
.
в. \( 2,4,6,8,10 \ldots \)
c. \( 4,8,16,32,64 \dots \)
D. 1,-1,3,-2,4
Subject: Maths
\( \tan \left[2 \tan ^{-1} \frac{1}{5}-\frac{\pi}{4}\right]=? \)
\( A \cdot \frac{7}{17} \)
в. \( \frac{-7}{17} \)
\( c \cdot \frac{7}{12} \)
D. \( \frac{-7}{12} \)
Subject: Chemistry
Phenol \( \frac{(i) N a O H}{(i i) C O_{2} / 140^{\circ} C} A \frac{H^{+} / H_{2} O}{\longrightarrow} \)
\( \boldsymbol{B} \frac{\boldsymbol{A} \boldsymbol{l}_{2} \boldsymbol{O}_{3}}{\boldsymbol{C H}_{3} \operatorname{COOH}, \boldsymbol{\Delta}} \boldsymbol{C} \)
In this reaction, the end product \( C \) is:
A. salicylaldehyde
B. salicylic acid
c. phenyl acetate
D. aspirin
Subject: Maths
A sprinter runs 6 meters in the first second of a certain race and increase
her speed by \( 25 \mathrm{cm} / \mathrm{sec} \). in each succeeding second. (This means that she goes \( 6 \mathrm{m} 25 \mathrm{cm} \). the second second, \( 6 \mathrm{m} 50 \mathrm{cm} . \) the third second, and so on.)
How far does she go during the eight second?
A. \( 8.75 \mathrm{m} \)
B. 7.75 m
\( c .8 .25 \mathrm{m} \)
D. 9.25 m
Subject: Maths
Multiplication of 3 with the matrix \( \left[\begin{array}{lll}\mathbf{4} & \mathbf{1} & \mathbf{1}\end{array}\right] \) gives
\( \mathbf{A} \cdot\left[\begin{array}{lll}12 & 3 & 3\end{array}\right] \)
B \cdot \( \left[\begin{array}{lll}12 & 1 & 1\end{array}\right] \)
\( \mathbf{c} \cdot\left[\begin{array}{lll}4 & 3 & 1\end{array}\right] \)
D. \( \left[\begin{array}{lll}4 & 1 & 3\end{array}\right] \)
Subject: Maths
The numerator of a fraction is 5 less
than its denominator. If 3 is added to
the numerator and denominator both, the fraction becomes \( \frac{4}{5} . \) Find the original fraction.
A \( \cdot \frac{1}{22} \)
в. \( \frac{17}{22} \)
c. \( \frac{17}{2} \)
D. \( \frac{7}{22} \)
Subject: Chemistry
The equilibrium constant for the
reaction: \( 2 S O_{2(g)}+O_{2(g)} \rightleftharpoons 2 S O_{3(g)} \) is
5. If the equilibrium constant mixture
contains equal moles of \( S O_{3} \) and \( S O_{2} \)
the equilibrium partial pressure of \( \boldsymbol{O}_{2} \) gas is:
A. 0.2 atm
B. 2 atm
c. 0.02 atm
D. 0.04 atm
Subject: Maths
Equations of the two straight lines
passing through the point (3,2) and
making an angle of \( 45^{\circ} \) with the line
\( x-2 y=3, \) are
A. \( 3 x+y-7=0 \) and \( x+3 y+9=0 \)
B. \( 3 x-y-7=0 \) and \( x+3 y-9=0 \)
C \( . x+3 y-7=0 \) and \( x+3 y-9=0 \)
D. none of these
Subject: Physics
A stone is thrown vertically upward with
an initial velocity \( V_{0} . \) The distance
traveled in time \( 4 v_{0} / 3 g \) is
\( ^{A} \cdot \frac{2 v_{0}^{2}}{g} \)
в. \( \frac{v_{0}^{2}}{2 g g g} \)
\( ^{\mathrm{c}} \cdot \frac{4 v_{0}^{2}}{9 g} \)
D. \( \frac{5 v_{0}^{2}}{9 g} \)
Subject: Maths
Prove that \( \left(x^{2}+y^{2}\right)^{4}=\left(x^{4}-6 x^{2} y^{2}+\right. \)
\( \left.y^{4}\right)^{2}+\left(4 x^{3} y-4 x y^{3}\right)^{2} \)
Subject: Physics
Assertion
Force experienced by moving charge
will be maximum if direction of velocity of charge is parallel to applied magnetic field.
Reason
Force on moving charge is independent of direction of applied magnetic field.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Chemistry
\( S(s)+O_{2}(g) \rightarrow S O_{2}(g) ; \quad \Delta H=-296.1 k J \)
\( 2 S O_{3}(g) \rightarrow 2 S O_{2}(g)+O_{2}(g) ; \quad \Delta H= \)
\( 198.2 k J \)
How to find the \( \Delta H \) for \( 2 S(s)+3 O_{2}(g) \rightarrow \)
\( 2 S O_{3}(g) ? \)
\( \mathbf{A} \cdot-395.8 k J \)
B. \( 395.8 k J \)
c. \( 295.8 k J \)
D. \( -790.4 k J \)
Subject: Chemistry
Nitro chloroform is prepared by the
action of \( \boldsymbol{C H C l}_{3} \) and
A. hot aq. \( K N O_{3} \)
B. hot aq. solution of \( N a N O_{2} \)
c. hot conc. \( H N O_{3} \)
D. hot dil. \( H C l+a q . N a N O_{2} \) solution
Subject: Chemistry
For which one of the following reactions
will \( \boldsymbol{K}_{\boldsymbol{C}}=\boldsymbol{K}_{\boldsymbol{P}} \)
A \( \cdot C O(g)+2 H_{2}(g) \rightleftharpoons C H_{3} O H(g) \)
в. \( Z n O(s)+C O(g) \rightleftharpoons Z n(s)+C O_{2}(g) \)
\( \mathrm{c} \cdot 2 \mathrm{O}_{3}(g) \rightleftharpoons 3 \mathrm{O}_{2}(g) \)
D. \( \operatorname{COCl}_{2}(g) \rightleftharpoons \operatorname{CO}(g)+C l_{2}(g) \)
Subject: Biology
Assertion
Asexual reproduction involves formation of clones of an organism.
Reason
Clones are morphologically and genetically similar individuals.
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 copper wire having a resistance of 0.01 ohm in each metre is used to wind
a 400 turn solenoid of radius \( 1.0 \mathrm{cm} \)
and length \( 20 \mathrm{cm} . \) Find the emf of a battery which when connected across the solenoid will cause a magnetic field
of \( 1.0 \times 10^{-2} \) T near the centre of the
solenoid.
Subject: Maths
The value of integral \( \int_{0}^{\pi} \frac{x^{2} \sin x}{(2 x-\pi)\left(1+\cos ^{2} x\right)} d x \) is equal to
\( ^{A} \cdot \frac{\pi^{2}}{4} \)
в. \( \frac{\pi^{2}}{2} \)
c. \( \frac{\pi^{2}}{6} \)
D. none of these
Subject: Physics
A heavy plank is moving with horizontal
acceleration \( a=2 m / s^{2} . \) A hollow
cylinder of mass \( \boldsymbol{m}=\mathbf{3} k \boldsymbol{g} \) and
radius \( =25 \mathrm{cm} \) is on the upper surface
of the plank and moves without slipping. Find the angular acceleration (about the axis in \( r a d / s^{2} \) ) of the hollow
cylinder?
Subject: Physics
(a) Deduce the expression for the
potential energy of a system of two
charges \( q_{1} \) and \( q_{2} \) located \( \overrightarrow{r_{1}} \) and \( \overrightarrow{r_{2}} \)
respectively, in an external electric
field.
(b) Three point charges, \( +Q+2 Q \) and
\( 3 Q \) are placed at the vertices of an equilateral triangle ABC of side I. If these charges are displaced to the mid-
point \( A_{1}, B_{1} \) and \( C_{1}, \) respectively, find
the amount of the work done in shifting
the charges to the new locations.
Subject: Physics
A block performs simple harmonic
motion with equilibrium point \( \boldsymbol{x}=\mathbf{0} \)
Graph of acceleration of the block as a
function of time is shown. Which of the
following statement is correct about the
block?
A. Displacement from equilibrium is maximum at \( t=4 s \)
B. Speed is maximum at \( t=4 s \)
C. Speed is maximum at \( t=2 s \)
D. Speed is maximum at \( t=3 s \)
Subject: Physics
A car travels a distance \( 100 \mathrm{m} \) with a constant acceleration and average
velocity of \( 20 m s^{-1} . \) The final velocity
acquired by the car is \( 25 m s^{-1} \). Find the
acceleration of the car.
A \( \cdot 1 m s^{-2} \)
B. \( 2 m s^{-2} \)
\( \mathbf{c} \cdot 0 m s^{-2} \)
D. \( 4 m s^{-2} \)
Subject: Maths
The sum of the fractions \( \frac{1}{2}+\frac{1}{6}+\frac{1}{12}+ \) \( \frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+ \)
\( \frac{1}{110}+\frac{1}{132} \) is
\( A \cdot \frac{7}{8} \)
в. \( \frac{11}{12} \)
\( c \cdot \frac{15}{16} \)
D. \( \frac{17}{18} \)
Subject: Chemistry
Label the given diagram showing lead
storage battery
\( \mathbf{A} \cdot p-P b, q-P b O_{2}, r-5 M H_{2} S O_{4} \)
B. p- \( P b O_{2}, q-P b, \) r- conc. \( H_{2} S O_{4} \)
c. \( p-P b_{3} O_{4}, q-P b O_{2}, r-50 \% H_{2} S O_{4} \)
D. \( p-P b O_{2}, q-P b, r- \) dil. \( 38 \% H_{2} S O_{4} \)
Subject: Chemistry
If the elevation in boiling point of a solution of non-volatile, non-electrolytic and non-associating solute in a solvent \( \left(K_{b}=x K k g m o l^{-1}\right) \) is \( y K, \) then the depression in freezing point of solution of same concentration would be:
\( \left[\boldsymbol{K}_{f} \text { of the solvent }=\boldsymbol{z} \boldsymbol{K} \boldsymbol{k} \boldsymbol{g} \boldsymbol{m o l}^{-1}\right] \)
A \( \cdot \frac{2 x z}{y} \)
в. \( \frac{y z}{x} \)
c. \( \frac{x z}{y} \)
D. \( \frac{y z}{2 x} \)
E \( \cdot \frac{x z}{2 y} \)
Subject: Physics
Four charges \( +\boldsymbol{Q},-\boldsymbol{Q},+\boldsymbol{Q} \) and \( -\boldsymbol{Q} \) are
situated at the corners of a square; in a
sequence then at the centre of the
square:
A. \( E=0, V=0 \)
в. \( E=0, V \neq 0 \)
c. \( E \neq 0, V=0 \)
D. \( E \neq 0, V \neq 0 \)
Subject: Maths
A line makes angle \( \theta_{1}, \theta_{2}, \theta_{3}, \theta_{4} \) with the
diagonals of the cube. Show that \( \cos ^{2} \theta_{1}+\cos ^{2} \theta_{2}+\cos ^{2} \theta_{3}+\cos ^{2} \theta_{4}= \)
\( \frac{4}{3} ? \)
Subject: Biology
Refer to the given figure of human
urinary system and select the option
that correctly identifies the labelled
parts \( A \) to \( E \)
A. Superior vena cava Inferior vena cava Dorsal aorta Urethra Pelvis
B. Inferior vena cava Superior vena cava Dorsal aorta Urinary bladder Cortex
c. Ureter Inferior vena cava Dorsal aorta Urinary bladder Pelvis
D. Dorsal aorta Inferior vena cava Superior vena cava Urinary bladder Cortex
Subject: Physics
N lamps each of resistance \( r, \) are fed by a machine of resistance R. If light
emitted by any lamp is proportional to
the square of the heat produced, prove that the most efficient way of arranging
them is to place them in parallel arcs,
each containing n lamps, where n is the
integer nearest to.
\( ^{\mathbf{A}} \cdot\left(\frac{r}{N R}\right)^{3 / 2} \)
\( ^{\mathbf{B}} \cdot\left(\frac{N R}{r}\right)^{1 / 2} \)
\( \mathbf{C} \cdot(N R r)^{3 / 2} \)
D. \( (N R r)^{1 / 2} \)
Subject: Chemistry
\( K M n O_{4} \) spot can be bleached by:
A. \( H_{2} O_{2} / H^{+} \)
в. \( S O_{2} / H^{+} \)
\( \mathrm{c} \cdot \mathrm{C}_{2} \mathrm{O}_{4}^{2-} / \mathrm{H}^{+} \)
D. all of these
Subject: Physics
A heating element has a resistance of
\( 100 \Omega \) at room temperature. When it is
connected to a supply of \( 220 V, a \) steady current of \( 2 A \) passes in it and
temperature is \( 500^{\circ} \mathrm{C} \) more than room
temperature. What is the temperature
coefficient of resistance of the heating element?
A. \( 1 \times 10^{-4} \cdot C^{-1} \)
-
B. \( 5 \times 10^{-4} \circ C^{-1} \)
D. \( 0.5 \times 10^{-4} \cdot C^{-1} \)
Subject: Chemistry
In a sample of ethyl ethanoate
\( \left(C H_{3} C O O C_{2} H_{5}\right), \) the two oxygen
atoms have the same number of
electrons but different number of
neutrons. Which of the following is the correct reason for it?
A. One of the oxygen atoms has gained electrons
B. One of the oxygen atoms has gained two neutrons
c. The two oxygen atoms are isotopes
D. The two oxygen atoms are isobars
Subject: Maths
Let \( A=\{4,6,8,10\} \) and \( B= \)
\{3,4,5,6,7\} and \( f: A \rightarrow B \) be defined
by \( f(x)=\frac{1}{2} x+1, \) then represent \( f \) by:
(i) An arrow diagram
(ii) A set of
ordered pairs (iii) \( A \) table
Subject: Physics
The circuit diagram shows that resistors \( 2 \Omega, 4 \Omega \) and \( R \Omega \) connected to
a battery of e.m.f. 2 V and
internal resistance \( 3 \Omega \). A main
current of 0.25 A flows through the
circuit. The p.d. across the internal
resistance of the cell is :
A . \( 0.75 \mathrm{v} \)
B. 2
\( c \cdot 0.5 v \)
0.11
Subject: Physics
A particle hanging from a spring
stretches it by \( 1 \mathrm{cm} \) at earth's surface.
Radius of earth is \( 6400 k m . \) At a place
\( 800 k m \) above the earths surface, the same particle will stretch the spring by
A \( .0 .79 \mathrm{cm} \)
B. \( 1.2 \mathrm{cm} \)
\( c .4 c m \)
D. \( 17 \mathrm{cm} \)
Subject: Maths
A bag contain 8 red, 3 white and 9 blue
balls. If three balls are drawn at random,
determine the probability that all the three balls are blue balls
A \( \cdot \frac{7}{93} \)
в. \( \frac{6}{92} \)
c. \( \frac{7}{95} \)
D. \( \frac{8}{95} \)
Subject: Chemistry
Because of lanthanoid contraction, which of the following pairs of elements have nearly the same atomic radii?
A. \( z r(40) \) and \( H f(72) \)
B. \( \operatorname{Zr}(40) \) and \( \operatorname{Ta}(73) \)
c. \( \operatorname{Ti}(22) \) and \( z r(40) \)
D. \( z r(40) \) and \( N b(41) \)
Subject: Physics
A vessel of \( 125 \mathrm{cc} \) contains \( _{1}^{3} \mathrm{H}\left(t_{1 / 2}=\right. \) 12.3 \( y \) ) at \( 500 \mathrm{kPa} \) and \( 300 \mathrm{K} \). Find the
activity of the gas
A. \( 0.754 \mathrm{Ci} \)
в. 7.24 Сг
c. \( 72.4 \mathrm{Ci} \)
D. 724 С\( i \)
Subject: Physics
The moon's radius is \( \frac{1}{4} \) that of the earth and its mass is \( \frac{1}{80} \) times that of the earth. If \( g \) represents the acceleration due to gravity on the surface of the earth, that on the surface of the moon
is
A. \( \frac{g}{4} \)
в. \( \frac{g}{5} \)
c. \( \frac{g}{6} \)
D. \( \frac{g}{8} \)
Subject: Maths
If \( a \) and \( b \) are the non-zero distinct roots
of \( x^{2}+a x+b=0, \) then the least value
of \( x^{2}+a x+b \) is
A \( \cdot \frac{3}{2} \)
B. 9
c. \( -\frac{9}{4} \)
D.
Subject: Physics
A planet of mass \( m \) is in an elliptical
orbit about the sun \( \left(\boldsymbol{m}<<\boldsymbol{M}_{\text {sun }}\right) \) with
an orbital period. If \( A \) be the area of orbit, then its angular momentum would be:
\( ^{\mathrm{A}} \cdot \frac{2 m A}{T} \)
в. \( m A T \)
c. \( \frac{m A}{2 T} \)
D. \( 2 \mathrm{mAT} \)
Subject: Maths
If \( \boldsymbol{\alpha} \boldsymbol{\epsilon}\left(\boldsymbol{0}, \frac{\boldsymbol{\pi}}{2}\right), \) then the expression
\( \sqrt{x^{2}+x}+\frac{\tan ^{2} x}{\sqrt{x^{2}+x}} \) is always greater
than or equal to
\( A \cdot 2 \tan \alpha \)
B. 2
\( c . \)
\( D \cdot \sec ^{2} \alpha \)
Subject: Biology
Arrange the following step in correct sequence found during the mechanism of lipid insoluble hormone (epinephrine) function or action.
A. Second messenger formation
B. Binding to the surface receptor
C. Glycogenolysis
D. Adenylate cyclase activation
\( A \cdot C, A, D \) and \( B \)
B. B, D, A and C
\( c . D, B, c \) and \( A \)
D. None of the above
Subject: Physics
If the values of \( L, C \) and \( R \) in a series
\( \boldsymbol{L}-\boldsymbol{C}-\boldsymbol{R} \) circuit are \( 10 \mathrm{mH}, 100 \mu \boldsymbol{F} \)
and \( 100 \Omega \) respectively then the value of resonant frequency will be
\( ^{\mathbf{A}} \cdot \frac{10^{3}}{2 \pi} H z \)
в. \( 2 \times 10^{3} H z \)
c. \( _{2 \times \frac{10^{3}}{p i}} H z \)
D. \( 10^{3} H z \)