AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Match the following:
A) \( 1.008 \mathrm{g} \)
2
1) 0.1 gram atom 8 gof \( \boldsymbol{H}_{2} \) What is
\( \mathrm{B}) \)
\( C) \)
\( \begin{array}{ll}245 \mathrm{g} \text { of } \mathrm{KClO}_{3} & \text { 2) } 22.4 \mathrm{L} \text { at S.T.P } \\ 71 \mathrm{g} \text { of } \mathrm{Cl}_{2} & \text { 3) } 12.046 \times 10^{23} \\ & \text { 4) } 3.0115 \times 10^{23} \\ \text { 10.8 grams of Ag } & \text { (i) }\end{array} \)
D)
\( A \cdot A-4, B-3, C-2, D-1 \)
B. \( A-2, B-3, C-4, D-1 \)
\( C \cdot A-1, B-2, C-3, D-4 \)
D. \( A-3, B-2, C-4, D-1 \)
Subject: Maths
If \( A \) and \( B \) are mutually exclusive such
that \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 3 5} \) and \( \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 4 5} \)
find
\( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B}) \)
Subject: Chemistry
For the reaction, \( \boldsymbol{P} \boldsymbol{C l} \boldsymbol{l}_{5}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{P} \boldsymbol{C l}_{3}(\boldsymbol{g})+ \)
\( \boldsymbol{C l}_{2}(\boldsymbol{g}) \)
The forward reaction at constant
temperature is favored by:
A. introducing an inert gas at constant volume
B. introducing chlorine gas at constant volume
c. introducing an inert gas at constant pressure
D. none of the above
Subject: Physics
What will be the current flowing through the \( 6 K \Omega \) resistor in the circuit shown
where the breakdown voltage of the
zener is \( 6 \mathrm{V} \) ?
A \( \cdot \frac{2}{3} \mathrm{mA} \)
B. 1mA
c. \( 10 \mathrm{mA} \)
D. \( \frac{3}{2} \mathrm{mA} \)
Subject: Physics
Assertion
(A): Two metallic spheres of
same size, one of copper and other of aluminium heated to the same
temperatures, will cool at the same
rate when they are suspended in the
same enclosure.
Reason (R): The rate of cooling of a body is directly proportional to the excess of
temperature of the body over the surroundings.
A. both \( A \) and \( R \) are true and the \( R \) is correct explanation of the A
B. both A and R are true, but R is not correct explanation of the A
C. A is true, but the R is false.
D. A is false, but the R is true.
Subject: Biology
Which of the following represent correct blood flow pathway in pulmonary circulation?
A. Right ventricle \( \underline{\text {Aorta}} \) Lung \( \underline{\text {Pulmonary } \text {Vein}} \) Left Atrium
B. \( \frac{\text { Pulmonary Vein Left Atrium }}{\text { Pulmonary Vein }} \) Left Atrium
c. Right Ventricle Pulmonary Vein Lung Pulmonary artery Left Atrium
D. \( \frac{\text { Pulmonary Vein }}{\text { Right Atrium }} \) Right Atrium Lung Pulmonary Vein n
Subject: Physics
The radius of a metal sphere at room
temperature \( \boldsymbol{T} \) is \( \boldsymbol{R} \) and the coefficient
of linear expansion is \( \alpha . \) The sphere
heated a little by a temperature \( \triangle T . \) So
that its new temperature is \( \boldsymbol{T}+\triangle \boldsymbol{T} \)
The increase in the volume of the sphere is approximate:
\( \mathbf{A} \cdot 4 \pi R^{3} \alpha \triangle T \)
В \( \cdot 2 \pi R^{3} \alpha \triangle T \)
\( \mathbf{c} \cdot \pi R^{3} \alpha \Delta T \)
D. \( 4 \pi R^{3} \alpha \Delta T / 3 \)
Subject: Chemistry
Which one of the following statements regarding Henry's law is not correct?
A. The value of \( K_{H} \) increases with the function of the nature of the gas
B. Higher the value of \( K_{H} \) at a given pressure, higher is the solubility of the gas in the liquids
C. The partial of the gas in vapour phase is proportional to the mole fraction of the gas in the solution
D. Different gases have different \( K_{H} \) (Henry's law constant) values at the same temperature
Subject: Maths
Find the length of the medians of a \( \triangle A B C \) having vertices at \( \boldsymbol{A}(\mathbf{0},-\mathbf{1}), \boldsymbol{B}(\mathbf{2}, \mathbf{1}) \) and \( \boldsymbol{C}(\mathbf{0}, \mathbf{3}) ? \)
Subject: Chemistry
Statement 1: When a hydrocarbon is
combusted in air, carbon monoxide is
the major product. Statement 2: Air contains much more
nitrogen than oxygen.
A. Both Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1.
B. Both Statement 1 and Statement 2 are correct and Statement 2 is not the correct explanation of Statement 1.
c. Statement 1 is correct but Statement 2 is not correct.
D. Statement 1 is not correct but Statement 2 is correct.
E. Both the Statement 1 and Statement 2 are not correct.
Subject: Maths
Re write each of the following
statements in the form "p if and only if
\( q^{\prime \prime} \)
(i) \( p: \) If you watch television then your mind is free and if your mind is free then you watch television
(ii) \( q: \) For you to get an A grade it is necessary and sufficient that you do all the homework regularly
(iii) \( r: \) If a quadrilateral is equiangular then it is a rectangle and if a quadrilateral is a rectangle then it is equiangular
Subject: Maths
n the given, \( \Delta A B C \) has sides \( A B= \) \( \mathbf{7} . \mathbf{5} \mathrm{cm}, \mathbf{A} \boldsymbol{C}=\mathbf{6 . 5} \mathbf{c m} \) and \( \mathbf{B C}=\mathbf{7} \mathrm{cm} \)
On base \( B C \) a parallelogram \( D B C E \) of
same area as that of \( \Delta A B C \) is
constructed. Find the height \( D F \) of the
parallelogram.
\( 4.7 \mathrm{cm} \)
в. 5 ст
\( c .3 \mathrm{cm} \)
\( 0.2 \mathrm{cm} \)
Subject: Maths
If \( \boldsymbol{x}+\boldsymbol{i} \boldsymbol{y}=\frac{\boldsymbol{3}}{\boldsymbol{2}+\cos \boldsymbol{\theta}+\boldsymbol{i} \sin \boldsymbol{\theta}}, \) then
\( x^{2}+y^{2} \) is equal to
A \( .3 x-4 \)
B. \( 4 x-3 \)
c. \( 4 x+3 \)
D. None of these
Subject: Chemistry
\( \mathbf{5 0} \boldsymbol{m} \boldsymbol{L} \) of \( \mathbf{0 . 1} \boldsymbol{M} \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{O} \boldsymbol{H} \) is added to
\( 75 m L \) of \( 0.1 M N H_{4} C l \) to make a
basic buffer. If \( p K_{a} \) of \( N H_{4}^{+} \) is 9.26
calculate \( \boldsymbol{p} \boldsymbol{H} \)
A .4 .44
B. 7.89
c. 9.56
D. 10.76
Subject: Maths
If \( \bar{a}, \bar{b}, \bar{c} \) are unit vectors satisfying the relation \( \bar{a}+\bar{b}+\sqrt{3} \bar{c}=0, \) then the
angle between \( \bar{a} \) and \( \bar{b} \) is
\( ^{A} \cdot \frac{\pi}{6} \)
в.
\( c \cdot \frac{\pi}{3} \)
D.
Subject: Physics
An electron and a proton are separated by a distance \( r \) so that the potential
energy between them is \( U=k \log r \)
where \( k \) is a constant. The expression for various energy levels of the above said hypothetical atom is:
\( ^{\mathbf{A}} \cdot \frac{k}{2}\left[1+\log \frac{n^{2} h^{2}}{4 \pi^{2} m k}\right] \)
в. \( 2 k\left[2+\log \frac{n^{2} h^{2}}{4 \pi^{2} m k}\right] \)
\( c \cdot k\left[2+\log \frac{n^{2} h^{2}}{4 \pi^{2} m k}\right] \)
D. \( \frac{k}{2}\left[1+\log \frac{n^{2} h^{2}}{2 \pi^{2} m k}\right. \)
Subject: Chemistry
Consider the following statements
(a) The \( p H \) of a mixture containing
\( 400 m L \) of \( 0.1 M H_{2} S O_{4} \) and \( 400 m L \) of
\( 0.1 M N a O H \) will be approximately 1.3
(b) lonic product of water is temperature dependent
(c) A monobasic acid with \( \boldsymbol{K}_{\boldsymbol{a}}=\mathbf{1 0}^{-5} \)
has a \( p H=5 . \) The degree of
dissociation of this acid is \( 50 \% \)
(d) The Le Chatelier's principle is not applicable to common-ion effect.
The correct statement are :
A \( \cdot(a),(b) \) and \( (d) \)
B. (a), (b) and (c)
c. (a) and (b)
D. (b) and (c)
Subject: Physics
A body of mass 400 g slides on a rough horizontal surface. If the frictional force
is \( 3.0 \mathrm{N} \). Find the angle made by the contact force on the body with the vertical.
A \( .37^{\circ} \)
В. \( 53^{\circ} \)
\( c \cdot 63^{0} \)
D. \( 27^{\circ} \)
Subject: Physics
You have learnt that a travelling wave in one dimension is represented by a function \( y=f(x, t) \) where \( x \) and \( t \) must appear in the combination \( x-v t \) or \( x+v \)
t i.e. \( y=f(x \pm v t) . \) Is the converse true
? Examine if the following functions for y can possibly represent a travelling
wave:
(a) \( (x+v t)^{2} \)
(b) \( \log \left[(\boldsymbol{x}+\boldsymbol{v} \boldsymbol{t}) / \boldsymbol{x}_{\boldsymbol{o}}\right] \)
(c) \( 1 /(x+v t) \)
Subject: Chemistry
A system changes from state \( X \) to \( Y \) with a change in internal energy
measuring to \( 25 \mathrm{kJ} \mathrm{mol}^{-1}, \) by a
reversible path and returns from Y to X by an irreversible path, What will be the net change in internal energy?
A. \( 25 \mathrm{kJ} \)
J.
B . >25 kJ
c. \( <25 \mathrm{kJ} \)
D. zero
Subject: Physics
A circular coil of conducting wire has an area \( A \) and number of turns \( N . \) It is lying in a vertical plane in a region where uniform magnetic field B exist with field direction normal to the coil plane. If the coil is rotated about a vertical axis
by an angle \( \pi \) in 0.5 seconds, then the value of the emf induced at the ends of
the coil is
\( A \). 4 NAB
B. \( 4 \pi \) NAB
c. 8 NAB
D. 8 \( \pi \) NAB
Subject: Physics
\( \begin{array}{ll}\text { Column-I } & \text { Column-II } \\ \text { (1) Planet nearest to the sun } & \text { (a) Jupiter } \\ \text { (2) Largest planet } & \text { (b) Saturn } \\ \text { (3) Lightest planet } & \text { (c) Neptune } \\ \text { (4) Farthest planet } & \text { (d) Mercury }\end{array} \)
Subject: Maths
The mean value of the function \( f(x)= \)
\( \frac{2}{e^{x}+1} \) on the interval [0,2] is
A \( \cdot \log \frac{2}{e^{2}+1} \)
B. \( 1+\log \frac{2}{e^{2}+1} \)
c. \( _{2+\log _{e^{2}+1}} \frac{2}{e} \)
D. \( 2+\log \left(e^{2}+1\right) \)
Subject: Maths
The value of \( ^{95} C_{4}+\sum_{j=1}^{5} 100-j C_{3} \) is
\( \mathbf{A} .^{95} C_{5} \)
В. \( ^{100} C_{4} \)
\( \mathrm{c} .^{99} \mathrm{C}_{4} \)
D. \( ^{10} C_{5} \)
Subject: Maths
If \( A \) and \( B \) are square matrices of same order and \( A A^{T}=I \) then \( \left(A^{T} B A\right)^{10} \) is
equal to
A. \( A B^{10} A^{T} \)
B . \( A^{T} B^{10} A \)
c. \( A^{10} B^{10}\left(A^{T}\right)^{10} \)
D. \( 10 A^{T} B A \)
Subject: Maths
The value of
\( \sin ^{-1}\left[\cot \left(\sin ^{-1} \sqrt{\left(\frac{2-\sqrt{3}}{4}\right)}\right)+\cos ^{-1}\right. \)
is
A . 0
в. \( \frac{\pi}{4} \)
\( c \cdot \frac{\pi}{6} \)
D. \( \frac{\pi}{2} \)
Subject: Maths
Martha picked out a pair of shoes she
wanted and brought them to the front of
the store to pay. The cashier told her
that the shoes were on sale for \( 30 \% \) off
the original price. She rang up the sale
price plus \( 5 \% \) sales tax, so Martha
ended up paying \( \$ 58.80 \) for the shoes.
What was the original price for the
shoes?
\( \mathbf{A} \cdot \$ 70 \)
B. \( \$ 75 \)
\( c . \$ 80 \)
D. \( \$ 85 \)
E . \( \$ 90 \)
Subject: Chemistry
Lanthanide are:
A. 14 element in the sixth period (atomic no. \( =90 \) to 103 ) that are filling \( 4 f \) -sublevel
B. 14 element in the seventh period (atomic no. \( =90 \) to
103) that are filling 5f-sublevel
C. 14 element in the sixth period (atomic no. \( =58 \) to 71 ) that are filling \( 4 f \) -sublevel
D. 14 element in the seventh period (atomic no. \( =58 \) to 71 ) that are filling \( 4 f \) -sublevel
Subject: Chemistry
Assertion
Avogadro's law hold's good only under similar conditions of temperature and
pressure.
Reason
Change in temperature or pressure brings about change in volume.
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
The G.M of the numbers \( 3^{1}, 3^{2}, 3^{3}, \ldots, 3^{3 n} \) is
A \( \cdot \frac{n}{2} \)
в. \( \frac{3 n}{2} \)
c. \( \frac{3 n+1}{2} \)
D. \( \frac{n+1}{2} \)
Subject: Physics
A radio transmitting station operating
at a frequency of 120 MHz has two
identical antennas that radiate in
phase. Antenna \( B \) is \( 9 m \) to the right of
antenna \( A . \) Consider point \( P \) at \( a \)
horizontal distance \( x \) to the right of
antenna \( A \) as shown figure. The value of
\( x \) and order for which the constructive
interference will occur at point \( \boldsymbol{P} \) are
This question has multiple correct options
\( \mathbf{A} \cdot x=14.95 m, n=1 \)
B \( . x=5.6 m, n=2 \)
\( \mathbf{c} \cdot x=1.65 m, n=3 \)
D. \( x=0, n=3.6 \)
Subject: Chemistry
Assertion
Nitrogen does not form \( \boldsymbol{N} \boldsymbol{C} \boldsymbol{I}_{\mathbf{5}} \) or \( \boldsymbol{N} \boldsymbol{F}_{\mathbf{5}} \)
but phosphorus can.
Reason
Nitrogen \( \left(1 s^{2} 2 s^{2} 2 p^{3}\right) \) lacks \( 2 d \) -orbitals
in which electrons of 2 s can be excited
to make five orbitals unpaired. Only
three electrons remain unpaired hence
only \( N X_{3} \) is formed. In case of
\( P\left(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{3}\right), 3 s \) electron can be
excited into \( 3 d \) vacant orbitals thus
making five unoaired electrons, thus
\( P X_{5} \) is possible.
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 it rains a dealer in rain coats can earn
Rs.500/- a day. If it is fair he will lose Rs. \( 40 /- \) a day. His mean profit if the probability of a fair day is 0.6 is:
A. Rs. \( 230 /- \)
B. Rs. \( 460 /- \)
c. Rs. \( 176 /- \)
D. Rs. 88/-
Subject: Physics
A solid cylinder of mass, \( m \), and radius,
\( r, \) is rotating at an angular velocity, \( \omega \)
when a non-rotating hoop of equal mass and radius drops onto the cylinder. In terms of its initial angular velocity, \( \omega \)
what is its new angular velocity, \( \omega^{\prime} ? \)
A \( \cdot \omega^{\prime}=\frac{\omega}{3} \)
B. \( \omega^{\prime}=\frac{3 \omega}{4} \)
\( \mathbf{C} \cdot \omega^{\prime}=\omega \)
\( \mathbf{D} \cdot \omega^{\prime}=3 \omega \)
E \( \cdot \omega^{\prime}=\frac{2 \omega}{3} \)
Subject: Chemistry
The IUPAC name of \( \boldsymbol{X} \boldsymbol{e}\left[\boldsymbol{P} \boldsymbol{t} \boldsymbol{F}_{6}\right] \) is :
A. Hexafluoroplatinate(VI)xenon.
B. Xenonhexafluoroplatinate(V).
c. xenonhexafluoroplatinate(VI).
D. Xenoniumhexafluoroplatinum(V)
Subject: Chemistry
The osmotic pressure of equimolar
solutions of \( \mathrm{BaCl}_{2}, \) NaCl and glucose will
be in the order:
A \( . \) glucose \( >N a C l>B a C l_{2} \)
в. \( B a C l_{2}>N a C l> \) glucose
c. \( N a C l>B a C l_{2}>g l u \operatorname{cose} \)
D. \( N a C l>g l u c o s e>B a C l_{2} \)
Subject: Chemistry
Calamine is used to reduce the
irritating effect of ant bite/sting because it reacts with (X) released due
to the bit /sting of ants with (Y) present in calamine. \( (\mathrm{X}) \) and \( (\mathrm{Y}) \) respectively
are:
A. sodium hydrogen carbonate and formic acid
B. formic acid and zinc carbonate
c. acetic acid and common salt
D. hydrochloric acid and zinc oxide
Subject: Chemistry
\( F e(O H)_{3} \) sol can be more easily
coagulated by \( N a_{3} P O_{4} \) in comparison
to \( K C l \) because:
A. mass of \( N a_{3} P O_{4} \) is more than \( K C l \) hence it is more effective than \( K C l \)
B. phosphate ion \( \left(P O^{3-}\right) \) has higher negative charge than \( C l^{-} \) ion hence are more effective for coagulation
c. \( K C l \) is more soluble than \( N a_{3} P O_{4} \) hence less effective
for coagulation
D. \( N a^{+} \) ions are more effective than \( K^{+} \) ions for coagulation
Subject: Physics
The given rod is uniform and has a
mass m. Find the tension in the string.
A \( \cdot \frac{(m g \sin \theta)}{2} \)
B. \( \frac{m g \sin }{2} \)
c. \( \frac{(m g \cos \theta)}{2} \)
D. \( \frac{m g}{2} \)
E . \( m \)
Subject: Physics
A uniform stick of mass \( \mathrm{M} \) is placed in a frictionless well as shown in the figure.
The stick makes an angle \( \theta \) with the
horizontal. Then the force which the
vertical wall exerts on right end of stick
is :
A \( \cdot \frac{M g}{2 \cot \theta} \)
в. \( \frac{M g}{2 \tan \theta} \)
c. \( \frac{M g}{2 \cos \theta} \)
D.
Subject: Physics
When a voltage source that is inducing voltage into a large number of coils is disconnected, and a switch that is in
series with the coils of wire is also
opened, a spark is observed to jump across the switch terminals as the
switch begins to open up. Identify the cause of this spark?
A. Free electrons from the voltage source
B. Free electrons from the coils of wire
c. collapse of the magnetic field in the coils
D. Secondary electron flow from the source
E. Stored voltage in the coils of wire
Subject: Chemistry
The atomic number of chromium is 24
Its electronic configuration in ground
state is \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{1} 3 d^{5} \)
Chromium atom by losing 3 electrons
form \( \mathrm{Cr}^{3+} \) ions. A chromium atom
contains \( 17 \% \) more neutron than the
protons. Now answer the following questions
The number of unpaired electrons in \( \mathrm{Cr} \)
\( 3+ \) ions is :
\( A \cdot 3 \)
B. 6
\( c \cdot 5 \)
D.
Subject: Maths
\( \int_{-a}^{a} \frac{x^{4} d x}{\sqrt{a^{2}-x^{2}}}= \)
A \( \cdot \frac{3 \pi a^{4}}{8} \)
в. \( \frac{\pi a^{4}}{8} \)
c. \( \frac{-\pi a^{4}}{8} \)
D. \( \frac{5 \pi \mathrm{a}^{4}}{8} \)
Subject: Biology
Four phases of cell cycle in sequence
are
A \( \cdot G_{1} \rightarrow S \rightarrow G_{2} \rightarrow M \)
B . \( S \rightarrow G_{1} \rightarrow G_{2} \rightarrow M \)
\( \mathbf{c} \cdot G_{1} \rightarrow G_{2} \rightarrow S \rightarrow M \)
D. \( M \rightarrow G_{1} \rightarrow G_{2} \rightarrow S \).
Subject: Chemistry
Solution \( A, B \) and \( C \) of the same strong electrolyte offered resistance of \( 50 \Omega \) \( 100 \Omega \) and \( 150 \Omega \) in a given conductivity cell. The resistance observed if they are
mixed in a volume proportion which is reciprocal of their resistances and tested in the same conductivity cell would be:
\( \mathbf{A} \cdot 67.3 \Omega \)
B. \( 81.8 \Omega \)
c. \( 100 \Omega \)
D. 300\Omega
Subject: Chemistry
Calculate the weight of \( F e O \) produced
from 6.7 g of \( V O \) and 4.8 g of \( F e_{2} O_{3} \) \( 2 V O+3 F e_{2} O_{3} \rightarrow 6 F e O+V_{2} O_{5} \)
(Given that the atomic weight of \( V \) is 51
amu and of \( F e \) is 56 amu.
A .4 .32
B. 7.755
c. 2.585
D. 0.0718
Subject: Maths
\( \operatorname{Let} f(x)=\left\{\begin{aligned} a x+1, & x<1 \\ 3, & x=1 . \text { The valu } \\ b x^{2}+1, & x>1 \end{aligned}\right. \)
of \( ^{\prime} a^{\prime} \) and \( ^{\prime} b^{\prime} \) for which \( f(x) \) is
continuous at \( x=1 \), is given by
A .2,2
в. 1,2
\( c .3,2 \)
D. \( 1, \)
Subject: Chemistry
\( \boldsymbol{B} \stackrel{\text {Liadlar}}{\longleftrightarrow} \boldsymbol{R}-\boldsymbol{C} \equiv \boldsymbol{C}-\boldsymbol{R} \stackrel{N a / N \boldsymbol{H}_{3}}{\longrightarrow} \boldsymbol{A} \)
What is \( A \) and \( B \) in the given raction repectivley?
Subject: Chemistry
Assertion: Inert gases are monoatomic.
Reason: Inert gases have stable configuration.
A. Both assertion and reason are true and the reason is a
correct explanation of the assertion
B. Both assertion and reason are true but reason is not a
correct explanation of the assertion
C. The assertion is true but reason is false
D. Both the assertion and reason are false
E. The assertion is false but the reason is true
Subject: Physics
If the coefficient of linear expansion is
A, the coefficient of superficial expansion is \( \mathrm{B} \) and the coefficient of cubic expansion is \( \mathrm{C} \), which of the following is false?
A. \( C=3 A \)
В. \( A=B / 2 \)
c. \( B=3 / 2 C \)
\( \mathbf{D} \cdot A=C / 3 \)
Subject: Maths
Three metallic solid cubes whose edges
are \( 1 \mathrm{m}, 2 \mathrm{m}, \) and \( 3 \mathrm{m} \) are melted and
converted into a single cube. Find the edge of the cube so formed?
A. \( 2.2 \mathrm{m} \)
B. 3.0 \( m \)
\( c \cdot 3.3 m \)
D. 3.9 \( m \)
Subject: Maths
\( \int_{0}^{1} \frac{x e^{x}}{(x+1)^{2}} d x= \)
A. \( \frac{e}{2} \)
B. \( \frac{e-1}{2} \)
c. \( \frac{e}{2}-1 \)
D. \( \frac{e-3}{2} \)
Subject: Physics
Light of wavelength \( \lambda \), strikes a photoelectric surface and electrons are ejected with an energy E. If E is to be increased to exactly twice its original
value, the wavelength changes to \( \lambda^{\prime} \)
where
A \( \cdot x^{\prime} \) is less than \( \frac{\lambda}{2} \)
B. \( \lambda^{\prime} \) is greater than \( \frac{\lambda}{2} \)
c. \( \lambda^{\prime} \) is greater than \( \frac{\lambda}{2} \) but less than \( \lambda \)
\( \lambda^{\prime} \lambda^{\prime} \) is exactly equal to \( \frac{\lambda}{2} \)
Subject: Maths
In bridge game of playing cards, 4 players are distributed one card each
by turn so that each player gets 13 cards. Find out the probability of a
specified player getting a black ace and
a king.
This question has multiple correct options
A \( \cdot p=\frac{82251}{978775} \)
В. \( \quad p=\frac{164502}{978775} \)
C \( \quad p=\frac{329004}{978775} \)
D. \( _{p}=\frac{82251}{1957550} \)
Subject: Chemistry
Which of the following statement is/are
true?
This question has multiple correct options
\( \mathbf{A} \cdot C H_{2} C l-C H_{2} C l \) is a gem dihalide.
B. Alkyl iodides develops colour when exposed to light.
C. Halogenation of alkanes proceeds by addition mechanism.
D. Swarts reaction is used to prepare alkyl fluorides.
Subject: Chemistry
Biochemical Oxygen Demand \( (B O D) \) is the amount of oxygen required (in ppm)
A. for the photochemical breakdown of waste present in \( 1 m^{3} \) volume of a water body
B. by bacteria to break-down organic waste in a certain volume of a water sample
c. for sustaining life in a water body.
D. by anaerobic bacteria to break down inorganic waste present in a water body
Subject: Maths
Observe the table and state whether the
income tax is to be paid or not with
reason for the following persons having
taxable income of \( F . Y .2012-13 \) as
given below:
The
tax
is to
be
paidd
or
not \( \begin{array}{ll}\text { Person } & \begin{array}{l}\text { Age } \\ \text { (in } \\ \text { year) }\end{array} & \begin{array}{l}\text { Taxable } \\ \text { income }\end{array} \\ & \text { income }\end{array} \)
\begin{tabular}{lcc} 
Sau. & \multirow{2}{*} {25} & Rs. \\
Shalini & & 1,30,000
\end{tabular}
Shri. Dhiraj \( \quad 32 \quad \begin{array}{l}\text { Rs. } \\ 2,85,000\end{array} \)
Shri
Shashibhai \( \quad 80 \quad \begin{array}{l}\text { Rs. } \\ 2,70,000 \\ \text { stret }\end{array} \) \( \begin{array}{lcc}\mathrm{smt} & & \mathrm{Rs} \\ \text { Minakshi } & & 2,40,000\end{array} \)
Subject: Chemistry
Which of the following pairs constitutes a buffer?
A. \( H N O_{2} \) and \( N a N O_{2} \)
в. \( N a O H \) and \( N a C l \)
c. \( H N O_{3} \) and \( N H_{4} N O_{3} \)
D. \( H C l \) and \( K C l \)
Subject: Physics
One end of a wire \( 2 m \) long and \( 0.2 c m^{2} \)
in cross section is fixed to a ceiling and a load of \( 4.8 k g \) is attached to its free
end. The elongation in the wire in mm is
(if \( y=2.0 \times 10^{11} \mathrm{N} . \mathrm{m}^{-2}, \mathrm{g}=10 \mathrm{ms}^{-2} \) )
A. \( 2.4 \times 10^{-5} \)
B. 2.4
c. 0.024
D. 0.0024
Subject: Chemistry
\( \mathbf{A} \)
\( 2.24 L \) cylinder of oxygen at \( 1 a t m \) and
\( 273 K \) is found to develop a leakage.
When the leakage was plugged the pressure dropped to \( 570 m m \) of Hg. The number of moles of gas that escaped will be:
A. 0.025
B. 0.050
c. 0.075
D. 0.09
Subject: Physics
Two stones \( A \) and \( B \) are projected simultaneously from the top of a \( 100- \)
\( m \) high tower. Stone B is projected
horizontally with speed \( 10 m s^{-1} \). and stone \( A \) is dropped from the tower. Find out the following:
(a) Time of flight of the two stone
(b) Distance between two stones after 3
\( \mathbf{S} \)
(c) Angle of strike with ground
Subject: Physics
A sphere of mass m moving with
constant velocity u, collides with another stationary sphere of same mass. If e is the coefficient of
restitution, the ratio of the final velocities of the first and second sphere
is
A \( \cdot \frac{1+e}{1-e} \)
в. \( \frac{1-e}{1+e} \)
c. \( \frac{e}{1-e} \)
D. \( \frac{1+e}{e} \)