AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Vapour pressures of pure acetone and
chloroform at \( 328 K \) are 741.8 mm \( H g \)
and 632.8 mm \( H g \) respectively. Assuming that they form ideal solution over the entire range of composition,
plot \( \boldsymbol{p}_{\text {total}}, \boldsymbol{p}_{\text {chloroform}}, \) and \( \boldsymbol{p}_{\text {acetone}} \) as a
function of \( x_{\text {acetone}} . \) The experimental
data observed for different
compositions of mixture is:
100x \( x_{\text {acetone }} \) What is and
\( P_{\text {actone}} / m m H g \) 54
\( P_{\text {chloro}} \) of or \( / m m \) \( H g \) 632.8 548.1
Plot this data also on the same graph paper. Indicate whether it has positive
deviation or negative deviation from the
ideal solution.
Subject: Physics
Atmospheric pressure at sea level is approximately equal to
A \( \cdot 10^{5} N / m^{2} \)
В. \( 10^{7} N / m^{2} \)
\( \mathbf{c} \cdot 10^{3} N / m^{2} \)
D. \( 10^{1} N / m^{2} \)
Subject: Maths
\( A \) and \( B \) are two independent events.
The probability that both \( A \) and \( B \) occur is \( 1 / 6 \) and the probability that at least
one of them occurs is \( \frac{2}{3} . \) The probability of the occurrence of \( \boldsymbol{A}=\ldots \ldots \ldots \) if \( \boldsymbol{P}(\boldsymbol{A})= \)
\( 2 P(B) \)
\( A \cdot \frac{2}{9} \)
в. 4
\( c \cdot \frac{5}{9} \)
D. \( \frac{5}{18} \)
Subject: Physics
A sphere of mass \( 40 \mathrm{kg} \) is attracted by a
second sphere of mass \( 15 \mathrm{kg} \), when their
centres are \( 20 \mathrm{cm} \) apart, with a force of
0.1 milligram weight. Calculate the value of gravitational constant.
\( \mathbf{A} \cdot=8.53 \times 10^{-11} N m^{2} k g^{-2} \)
B. \( =6.53 \times 10^{-11} \mathrm{Nm}^{2} \mathrm{kg}^{-2} \)
\( \mathbf{c} .=7.53 \times 10^{-11} \mathrm{Nm}^{2} \mathrm{kg}^{-2} \)
D. \( =9 \times 10^{-11} N m^{2} k g^{-2} \)
Subject: Physics
A resonant A.C. circuit contains a
capacitor of capacitance \( 10^{-6} \mathrm{F} \) and an inductor of \( 10^{-4} \) H. The frequency of oscillations will be :
\( \mathbf{A} \cdot 10^{5} \) Нz
в. 10 Н \( z \)
\( ^{\mathrm{c}} \cdot \frac{10^{5}}{2 \pi} \mathrm{Hz} \)
D. \( \frac{10}{2 \pi} \) нг
Subject: Physics
The peak voltage in the output of a halfwave diode rectifier fed with a
sinusoidal signal without filter is \( 10 \mathrm{V} \) The d.c. component of the output voltage is
A. \( 10 / \sqrt{2} V \)
в. \( 10 / \pi V \)
\( c \cdot 10 v \)
D. \( 20 / \pi V \)
Subject: Maths
The greatest value of \( \boldsymbol{f}(\boldsymbol{x})=(\boldsymbol{x}+ \)
1) \( ^{1 / 3}-(x-1)^{1 / 3} \) on [0,1] is
\( \mathbf{A} \cdot \mathbf{1} \)
B.
\( c \cdot 3 \)
D. \( 1 / 3 \)
Subject: Maths
If \( \boldsymbol{x}+\mathbf{1}<\mathbf{0} \) then \( |\boldsymbol{x}| \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( x+1 \)
\( c .-x \)
D. \( -x-1 \)
\( E \)
Subject: Chemistry
In the reaction, \( X \) is:
\( \mathrm{CH}_{3} \mathrm{C}=\mathrm{C}-\mathrm{CH}_{3} \frac{(\mathrm{i}) X}{(\mathrm{ij}) 2 \mathrm{o} / \mathrm{H}_{2} \mathrm{O}} \rightarrow \mathrm{CH}_{3}-\underset{\mathrm{O}}{\mathrm{I}}-\mathrm{C}_{\mathrm{O}}-\mathrm{CH}_{3} \)
A \( . H N O_{3} \)
в. \( O_{2} \)
\( c \cdot O_{3} \)
D. \( K M n O_{4} \)
Subject: Physics
Electric charges \( \boldsymbol{q}, \boldsymbol{q} \) and \( -\boldsymbol{2} \boldsymbol{q} \) are placed at the corners of an equilateral triangle \( A B C \) of side \( L . \) The magnitude of electric dipole moment of the system is
\( \mathbf{A} \cdot q L \)
в. \( 2 q L \)
c. \( (\sqrt{3}) q L \)
D. \( 4 q L \)
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ccc}x^{\alpha} \cos \left(\frac{1}{x}\right), & \text { if } & x \neq 0 \\ 0 & , \text { if } & x=0\end{array}\right. \)
continuous at \( x=0 \) then
\( \mathbf{A} \cdot \alpha<0 \)
В . \( \alpha>0 \)
c. \( \alpha=0 \)
D. \( \alpha \geq 0 \)
Subject: Chemistry
\( \mathrm{HX} \) is a weak acid \( \left(\boldsymbol{K}_{\boldsymbol{a}}=\mathbf{1 0}^{-\mathbf{5}}\right) . \) It forms
a salt \( \mathrm{NaX}(0.1 \mathrm{M}) \) on reacting with caustic soda. The degree of hydrolysis of NaX is:
A . 0.01 \%
B. 0.0001 \%
c. \( 0.1 \% \)
D. 0.5 \%
Subject: Maths
If \( D_{p}=\left|\begin{array}{ccc}\boldsymbol{p} & \mathbf{1 5} & \mathbf{8} \\ \boldsymbol{p}^{2} & \mathbf{2 5} & \mathbf{9} \\ \boldsymbol{p}^{\mathbf{3}} & \mathbf{4 5} & \mathbf{1 0}\end{array}\right|, \) then \( \operatorname{det}\left(\boldsymbol{D}_{1}+\right. \)
\( D_{2} \) ) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B . 25
\( c .625 \)
D. None of these
Subject: Maths
Find the direction cosines of the vector \( \vec{a}=\hat{i}+\hat{j}-2 \hat{k} \)
\( ^{\mathbf{A}} \cdot\left(\frac{1}{\sqrt{6}}, \frac{1}{\sqrt{6}},-\frac{2}{\sqrt{6}}\right) \)
B \( \cdot\left(\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{6}}, \frac{-2}{\sqrt{6}}\right) \)
\( ^{\mathbf{c}} \cdot\left(\frac{1}{\sqrt{6}}, \frac{1}{\sqrt{6}}, \frac{-2}{\sqrt{3}}\right) \)
D. None of these
Subject: Chemistry
The decreasing basic order of the
following compounds is:
A \( \cdot(i)>(i i)>(i i i)>(i v) \)
B. \( (i v)>(i i i)>(i i)>(i) \)
c. \( (i i)>(i)>(i i i)>(i v) \)
D. \( (i i)>(i)>(i v)>(i i i) \)
Subject: Chemistry
For a reversible equilibrium reaction
\( K_{C}>K_{P} \) at \( 298 K \) and \( \Delta H=+200 \)
\( K J, \) the forward reaction is favoured if:
(i) Pressure is increased
(ii) Temperature is increased
(iii) Temperature is decreased
(iv) Increasing the concnetration of reactants
A . i, i i, iv
B. i, ii
c. ii, iv
D. i, iii, iv
Subject: Physics
A cubical block of side \( 10 \mathrm{cm} \) floats at
the interface of an oil and water as
shown in the figure. The density of oil is
\( 0.6 g c m^{-3} \) and the lower face of ice cube
is \( 2 c m \) below the interface. The
pressure above that of the atmosphere at the lower face of the block is
A. \( 200 P a \)
с. 900 Ра
D. \( 800 P a \)
Subject: Chemistry
\( C-O \) bond lengths designated by
\( \boldsymbol{\alpha}, \boldsymbol{\beta}, \gamma \) and \( \boldsymbol{\delta} \) are in order.
A \( \cdot \alpha=\gamma<\beta=\delta \)
в. \( \alpha<\beta<\gamma=\delta \)
c. \( \alpha<\gamma=\delta<\beta \)
D. All are equal
Subject: Maths
If \( \sin ^{-1} x=\frac{\pi}{5}, \) for some \( x \in(-1,1) \)
then find the value of \( \cos ^{-1} x \)
A. \( -\frac{3 \pi}{10} \)
в. \( \frac{3 \pi}{10} \)
c. \( -\frac{7 \pi}{10} \)
D. \( \frac{7 \pi}{10} \)
Subject: Chemistry
A \( 5 \% \) solution (w/W) of cane sugar
(molar mass \( =342 g \) mol \( ^{-1} \) ) has
freezing point \( 271 K . \) What will be the freezing point of \( 5 \% \) glucose (molar mass \( =18 g \) mol \( ^{-1} \) ) in water if freezing
point of pure water is \( 273.15 K ? \)
\( \mathbf{A} \cdot 273.07 K \)
в. \( 269.07 K \)
c. \( 273.15 K \)
D. \( 260.09 K \)
Subject: Biology
Select the number of incorrect
statements for the process of fermentation.
A. It involves only partial breakdown of
glucose.
\( \mathrm{B} N A D H_{2} \) is oxidized to NAD by reduction of organic compound.
C. No ATP are produced during fermentation as it is extracellular
process in some microbes.
D. There is no ETS and Kreb's cycle.
E. Maximum concentration of alcohol in
alcohol in alcoholic brevarage is \( 100 \% \)
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5
Subject: Chemistry
Assertion
Atom with large atomic radii and low
ionisation potential are more metallic
in nature.
Reason
Atom with large atomic radii and low
ionisation potential have tendency to
loose electron
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
\( N_{2}(g)+3 H_{2}(g) \longrightarrow 2 N H_{3}: \Delta H= \)
\( -92 k J \) is Haber s process for
manufacture of \( N H_{3} . \) What is the heat
of formation of \( \boldsymbol{N} \boldsymbol{H}_{3} ?(\text { in } \mathrm{kJ} / \mathrm{mol}) \)
Subject: Physics
A car is travelling with linear velocity \( \mathbf{v} \) on a circular road of radius R. If its
speed is increasing at the rate of a
\( m / s^{2}, \) then the net acceleration will be
\( ^{\text {A }} \cdot \frac{v^{2}}{R}+a \)
в. \( \frac{v^{2}}{R}-a \)
Subject: Chemistry
A plot of kinetic energy of the emitted electron against frequency of the incident radiation yields a straight line. The slope of the straight line is:
A. \( 0.66 \times 10^{-35} \)
В. \( 0.66 \times 10^{-33} \)
c. \( 0.33 \times 10^{-33} \)
D. \( 3.33 \times 10^{-35} \)
Subject: Maths
What is the sum of two numbers?
I. The bigger of these two numbers is 6 more than the smaller number.
II. \( 40 \% \) of the smaller number is equal to \( 30 \% \) of the bigger number.
III. The ratio between half of the bigger number and one-third of the smaller
number is 2: 1
A. Only II and III are sufficient
B. Only I and II are sufficient
c. I and either II or III is sufficient
D. All, II and III together are sufficient
Subject: Physics
The average thermal energy of a oxygen atom at room temperature \( \left(27^{\circ} C\right) \)
A \( \cdot 4.5 \times 10^{-21} J \)
В. \( 6.2 \times 10^{-21} J \)
c. \( 3.4 \times 10^{-21} J \)
D. \( 1.8 \times 10^{-21} \mathrm{J} \)
Subject: Maths
Expand \( (4 x-3 y)^{3} \)
\( \mathbf{A} \cdot 64 x^{3}-144 x^{2} y+108 x y^{2}-27 y^{3} \)
B. \( 64 x^{3}+144 x^{2} y+108 x y^{2}-27 y^{3} \)
\( \mathbf{c} \cdot 64 x^{3}-144 x^{2} y-108 x y^{2}-27 y^{3} \)
D. None of these
Subject: Maths
From a piece of cardbord, in the shape
of a trapezium \( A B C D, \) and \( A B \| C D \)
and \( \angle B C D=90^{\circ}, \) quarter circle is
removed. Given \( A B=B C=3.5 \mathrm{cm} \) and
\( D E=2 c m . \) Calculate the area of the
remaining piece of the cardboard (Take
to be \( \left.\frac{22}{7}\right) \)
Subject: Maths
If \( y=A \sin 5 x, \) then \( \frac{d^{2} y}{d x^{2}}= \)
\begin{tabular}{l} 
A. \( -25 y \) \\
\hline
\end{tabular}
в. \( 25 y \)
c. \( 5 y \)
D. \( -5 y \)
Subject: Maths
Calculate the median for the following
\[
\begin{array}{lcccc}
\begin{array}{l}
\text { Weight } \\
\text { in kg. }
\end{array} & 20 & 22 & 24 & 27 \\
\begin{array}{l}
\text { No. of } \\
\text { boys }
\end{array} & 8 & 10 & 11 & 9
\end{array}
\]
A . 23
B . 26
c. 23.5
D . 24
Subject: Maths
\( \boldsymbol{P C} \)
\( \mathbf{A} \cdot \overrightarrow{P C}=2 b-a \)
B \( \cdot \overrightarrow{P C}=2 a+b \)
\( \mathbf{c} \cdot \overrightarrow{P C}=2 a-b \)
D. none of these
Subject: Chemistry
The number of molecules present in 2
grams of helium at \( 273^{\circ} \mathrm{C} \) and 1520
mm Hg pressure are:
\( \left[N_{A}=6.02 \times 10^{23}\right] \)
A. \( 3.01 \times 10^{23} \)
B. \( 6.02 \times 10^{23} \)
c. \( 3.01 \times 10^{22} \)
D. \( 6.02 \times 10^{22} \)
Subject: Chemistry
What coefficient is needed for fluorine
to balance the following equation? \( \boldsymbol{L} \boldsymbol{i}+\boldsymbol{F}_{2} \rightarrow \boldsymbol{L} \boldsymbol{i} \boldsymbol{F} \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. 3
Subject: Maths
f a line makes \( \alpha, \beta, \gamma, \delta \) angles with 4
diagonals of a cube, then \( \cos ^{2} \alpha+ \)
\( \cos ^{2} \beta+\cos ^{2} \gamma+\cos ^{2} \delta=? \)
\( \mathbf{A} \cdot \mathbf{1} \)
B.
\( c \cdot \frac{4}{3} \)
D.
Subject: Physics
Twenty four cells each of emf \( 1.5 \mathrm{V} \) and internal resistance 0.5 ohms are to be
connected to a 3 ohm resistance. For
maximum current through this resistance the number of rows and
number of columns that you connect
these cells is?
A. 12 cells in series 2 rows in parallel
B. 8 cells in series 3 rows in parallel
c. 4 cells in series 6 rows in parallel
D. 6 cells in series 4 rows in parallel
Subject: Maths
If \( \mathbf{2} \boldsymbol{A}+\boldsymbol{B}=\left[\begin{array}{cc}\mathbf{1} & \mathbf{-} \mathbf{1} \\ \mathbf{0} & \mathbf{1} \\ \mathbf{1} & \mathbf{-} \mathbf{2}\end{array}\right] \boldsymbol{A}- \)
\( \mathbf{2} \boldsymbol{B}=\left[\begin{array}{cc}\mathbf{0} & \mathbf{1} \\ \mathbf{- 2} & \mathbf{0} \\ \mathbf{1} & \mathbf{- 1}\end{array}\right] \) find \( \boldsymbol{A} \) and \( \boldsymbol{B} \)
Subject: Chemistry
Versene, a chelating agent has chemical formula
\( C_{2} H_{4} N_{2}\left(C_{2} H_{2} O_{2} N a\right)_{4} . \) If each mole of
this compound could bind 1 mole of
\( C a^{2+}, \) then the rating of pure versene
expressed as \( \mathrm{mg} \) of \( \mathrm{CaCO}_{3} \) bound per \( \mathrm{g} \) of chelating agent is:
A. \( 100 \mathrm{mg} \)
в. \( 163 \mathrm{mg} \)
c. \( 200 \mathrm{mg} \)
Subject: Physics
Let \( C \) be the capacitance of a capacitor discharging through a resistor \( \mathrm{R} \).
Suppose \( t_{1} \) is the time taken for the energy stored in the capacitor to
reduced to half its initial value and \( t_{2} \) is the time taken for the charge to reduce to one-fourth its initial value. Then the
ratio \( t_{1} / t_{2} \) will be
\( A \cdot 2 \)
B.
\( c \cdot 1 / 2 \)
D. 1/4
Subject: Chemistry
The standard potential for the reaction, \( \boldsymbol{A} \boldsymbol{g}^{+}(\boldsymbol{a} \boldsymbol{q} \cdot)+\boldsymbol{F} \boldsymbol{e}^{2+}(\boldsymbol{a} \boldsymbol{q} \cdot) \longrightarrow \)
\( \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+}(\boldsymbol{a} \boldsymbol{q} \cdot)+\boldsymbol{A} \boldsymbol{g}(\boldsymbol{s}) \)
is \( 0.028 V . \) What is the standard free
energy change for this reaction?
A. -3.702 kJ \( m o l^{-1} \)
B. -2.702 kJ \( \mathrm{mol}^{-1} \)
c. -5.702 k \( J \) mol \( ^{-1} \)
D. -4.702 kJ \( \mathrm{mol}^{-1} \)
Subject: Physics
A proton moving with a constant velocity passes through a region of space with out change in its velocity. If \( \mathrm{E} \) and \( \mathrm{B} \) represent the electric and magnetic fields respectively, this region
may have
A. \( E=0, B \neq 0 \)
B. \( E \neq 0, B=0 \)
c. \( E \) and \( B \) both parallel \( \$ \$ \)
D. \( E \) and \( B \) inclined at \( 45^{\circ} \) angle
Subject: Physics
A projectile has velocity \( V=(6 \hat{i}+ \) \( 4 \hat{j}) m / s \) at height of \( 1 m \) from horizontal Then angle of projection is
A \( .30^{\circ} \)
B. \( 37^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 60^{\circ} \)
Subject: Physics
A light of wavelength \( \lambda \) is incident on an object of size b. If a screen is at a
distance D from the object. Identify the correct condition for the observation of
different phenomenon:
a) if \( b^{2}=D \lambda \), Fresnel diffraction is
observed
b) if \( b^{2}>>D \lambda \), Fraunhoffer diffraction
is observed
c) if \( b^{2}<<D \lambda \), Fraunhoffer diffraction
is observed
d) if \( b^{2}=D \lambda, \) Fraunhoffer diffraction is
observed
A. a, b and d are true
B. a,c and d are true
\( c \cdot \) a and c are true
D. a and d are true
Subject: Chemistry
Assume that the decomposition of
\( H N O_{3} \) can be represented by the
following equation: \( 4 \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{\boldsymbol{3}}(\boldsymbol{g}) \rightleftharpoons \)
\( 4 N O_{2}(g)+2 H_{2} O(g)+O_{2}(g) \)
The reaction approaches equilibrium at \( 400 \mathrm{K} \) temperature and \( 30 \mathrm{atm} \) pressure. At equilibrium, the partial
pressure of \( H N O_{3} \) is 2 atm.
The value of \( \boldsymbol{K}_{c}\left((\boldsymbol{m o l} / \boldsymbol{L})^{3}\right) \) at \( 400 \mathrm{K} \) is:
(Use \( : \boldsymbol{R}=.08 a t \boldsymbol{m}-\boldsymbol{L} / \boldsymbol{m} \boldsymbol{o l} \boldsymbol{e}-\boldsymbol{K}) \)
Subject: Chemistry
The appropriate reagent for the
transformation:
\( \mathbf{A} \cdot Z n(H g), H C l \)
\( \mathbf{B} \cdot N H_{2} N H_{2}, O H^{-} \)
\( \mathbf{C} \cdot H_{2}, N i \)
\( \mathbf{D} \cdot N a B H_{4} \)
Subject: Chemistry
The freezing point of aqueous solution that contains \( 3 \% \) urea, \( 7.45 \% K C l \) and
\( 9 \% \) of glucose is: \( \left(\operatorname{given} K_{1} \text { of water }=\right. \)
1.86 and assume molarity \( = \) molality
).
A . \( 290 K \)
в. 285.5 К
c. \( 267.42 K \)
D. 250 K
Subject: Chemistry
Assertion
The value of K increases with increase
in temperature in case of endothermic
reaction.
Reason
The increase in temperature shifts the equilibrium in the backward direction in case of exothermic reaction.
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: Chemistry
The standard enthalpy of combustion at
\( 25^{\circ} \mathrm{C} \) of hydrogen, cyclohexene \( \left(C_{6} H_{10}\right) \)
and cyclohexane \( \left(C_{6} H_{12}\right) \) are -241,-3800 and \( -3920 k J / \) mole
respectively. Calculate the heat of hydrogenation of cyclohexene
A. \( -111 k J / \) mole
B . \( -121 k J / \) mole
c. \( -118 k J / \) mole
D. \( -128 k J / \) mole
Subject: Maths
Construct a quadrilateral \( \boldsymbol{P} \boldsymbol{N} \boldsymbol{K} \boldsymbol{J} \)
where \( \mathrm{PN}=7 \mathrm{cm}, \mathrm{NK}=8 \mathrm{cm}, \mathrm{JK}=10 \mathrm{cm} \)
\( P J=5 \mathrm{cm} \) and \( \angle J=75^{\circ} \)
Then, the measure of \( \angle N \) is
A . \( 65^{\circ} \)
B. \( 95^{\circ} \)
\( c \cdot 75^{\circ} \)
D. \( 85^{\circ} \)
Subject: Physics
When a battery connected across a
resistor of \( 16 \Omega, \) voltage across the resistor is \( 12 \mathrm{V} \). When the same battery
is connected across a resistor of \( 10 \Omega \)
voltage across it is 11 V. The internal resistance of the battery (in ohm) is :
A \( \cdot \frac{10}{7} \)
B. \( \frac{20}{7} \)
c. \( \frac{25}{7} \)
D. \( \frac{30}{7} \)
Subject: Chemistry
\( X Y_{2} \) dissociates \( X Y_{2}(g) \rightleftharpoons X Y(g)+ \)
\( Y(g) . \) When the initial pressure of \( X Y_{2} \)
is \( 600 \mathrm{mm} \) Hg, the total equilibrium pressure is \( 800 \mathrm{mm} \) Hg. Calculate \( K \) for the reaction. Assuming that the volume of the system remains unchanged:
A . 50.0
B. 100.0
c. 166.6
D. 400.0
Subject: Chemistry
Uncertainty in position of an electron \( \left.\boldsymbol{m}=\mathbf{9 . 1} \times \mathbf{1 0}^{-\mathbf{2 8}} \boldsymbol{g}\right) \) moving with a
velocity of \( 3 \times 10^{4} \mathrm{cm} / \mathrm{s} \) accurate upto
\( 0.001 \% \) will be :
(Use \( \frac{\boldsymbol{h}}{4 \pi} \) in uncertainty expression
where \( \left.h=6.626 \times 10^{-27} \text {erg } s\right) \)
A \( .5 .79 \mathrm{cm} \)
в. 7.68 ст
c. 1.93 ст
D. 3.84 \( c m \)
Subject: Maths
If two events \( A \) and \( B \) are such that
\( \boldsymbol{P}\left(\boldsymbol{A}^{\prime}\right)=\mathbf{0 . 3}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 4} \) and
\( \boldsymbol{P}\left(\boldsymbol{A} \cap \boldsymbol{B}^{\prime}\right)=\mathbf{0 . 5}, \operatorname{then} \boldsymbol{P}\left(\frac{\boldsymbol{B}}{\boldsymbol{A} \cup \boldsymbol{B}^{\prime}}\right) \)
equala
A \( \cdot \frac{3}{4} \)
B.
\( c \cdot \frac{1}{4} \)
D.
Subject: Physics
A reversible adiabatic path on a P-V diagram for an ideal gas passes
through sate A where \( \boldsymbol{P}=\mathbf{0 . 7} \times \) \( \mathbf{1 0}^{5} \boldsymbol{N} / \boldsymbol{m}^{-2} \) and \( \boldsymbol{v}=\mathbf{0 . 0 0 4 9} \boldsymbol{m}^{3} . \) The
ratio of specific heat of the gas is 1.4 The slope of path at \( A \) is:
A . \( 2.0 \times 10^{7} N m^{-5} \)
B . \( 1.0 \times 10^{7} \mathrm{Nm}^{-5} \)
c. \( -2.0 \times 10^{7} \mathrm{Nm}^{-5} \)
D. \( -1.0 \times 10^{7} \mathrm{Nm}^{-5} \)
Subject: Chemistry
For which of the following compounds, the Lassaigne's test for the detection of
nitrogen will fail?
A. \( H_{2} N-C O-N H_{2} \)
в. \( C_{6} H_{5}-N H-N H_{2} .2 H C l \)
c. \( N H_{2}-N H_{2} .2 H C l \)
D. \( H_{2} N-C O-N H-N H_{2} . H C l \)
Subject: Physics
What is the minimum value of \( F \) needed
so that block begins to move upward on frictionless incline plane as shown
A \( \cdot M g \tan \left(\frac{\theta}{2}\right) \)
B. \( M g \cot \left(\frac{\theta}{2}\right) \)
c. \( \frac{M g \sin \theta}{(1+\sin \theta)} \)
D. \( M g \sin \left(\frac{\theta}{2}\right) \)
Subject: Physics
A wire is stretched through 1 mm by certain load. The extension produced in the wire of same material with double
the length and radius will be
\( \mathbf{A} \cdot 4 m m \)
B. \( 3 m m \)
\( \mathbf{c} \cdot 1 m m \)
D. \( 0.5 m m \)
Subject: Chemistry
The coagulating power of electrolytes
having ions \( N a^{+}, A l^{3+} \) and \( B a^{2+} \) for
arsenic sulphide sol increases in the order:
A \( \cdot N a^{+}<B a^{2+}<A l^{3+} \)
B. \( B a^{2+}<N a^{+}<A l^{3+} \)
c. \( A l^{3+}<N a^{+}<B a^{2+} \)
D. \( A l^{3+}<B a^{2+}<N a^{+} \)
Subject: Chemistry
The EMF of an \( \boldsymbol{H}_{2}-\boldsymbol{O}_{2} \) fuel cell:
\( A \cdot \) is independent of partial pressures of \( H_{2} \) and \( O_{2} \)
B. decreases on increasing \( P_{H_{2}} \) and \( P_{O_{2}} \)
C. increases on increasing \( P_{H_{2}} \) and \( P_{O_{2}} \)
D. varies with the concentration of \( O H^{-} \) ions in the
cathodic and anodic compartments
Subject: Physics
\( S_{1}, S_{2} \) are two coherent sources of
sound located along x-axis separated
by \( 4 \lambda \) where \( \lambda \) is wavelength of sound
emitted by them. Number of maxima
located on the elliptical boundary
around it will be :
\( A \cdot 16 \)
B. 12
\( c \)
\( D \)
Subject: Chemistry
For the reaction, \( 2 N O+C l_{2} \longrightarrow \)
\( 2 N O C l \) at \( 300 K \) following data are
obtained
\( \begin{array}{ll}\underset{\mathrm{No}}{\operatorname{Exp}} & \frac{\text {InitialConcentration}}{[\mathrm{NO}]\left[\mathrm{CI}_{2}\right]}\end{array} \)
1 \( \begin{array}{ll}\text { 0. } 0.010 & \text { 0.010 }\end{array} \)
2 \( \begin{array}{cc}0.010 & 0.020\end{array} \)
3 \( \begin{array}{cc}0.020 & 0.020\end{array} \)
Write rate law for the reaction. What is
the order of the reaction? Also calculate
the specific rate constant.
Subject: Maths
\( \int \frac{\csc ^{2} x-2005}{\cos ^{2005} x} d x \) is equal to
A. \( \frac{\cot x}{(\cos x)^{2005}}+C \)
B. \( \frac{\tan x}{(\cos x)^{2005}}+C \)
c. \( \frac{-\tan x}{(\cos x)^{2005}}+C \)
D. None of these
Subject: Physics
Determine the force acting on a body if the velocity of the body is changed from \( 5 m s^{-1} \) to10 \( m s^{-1} \) in 2 s. The density
and the volume of the object are \( \mathbf{5 0 0 0 k g} \boldsymbol{m}^{-3} \boldsymbol{a n d} \quad \mathbf{0 . 0 0 5} \boldsymbol{m}^{3} \)
\( \mathbf{A} \cdot 100 \mathrm{N} \)
B. 65.5 N
c. \( 32.5 \mathrm{N} \)
D. 62.5 N
Subject: Physics
A jet airplane travelling from east to
west at a speed of \( 500 \mathrm{km} h^{-1} \) eject out gases of combustion at a speed of
\( 1500 k m h^{-1} \) with respect to the jet
plane. What is the velocity of the gases with respect to an observer on the ground?
A. \( 1000 \mathrm{km} h^{-1} \) in the direction west to east.
B. \( 1000 \mathrm{km} h^{-1} \) in the direction east to west.
c. \( 2000 k m h^{-1} \) in the direction west to east.
D. \( 2000 \mathrm{km} h^{-1} \) in the direction east to west.
Subject: Maths
If \( ^{6} C_{n}+2^{6} C_{n+1}+^{6} C_{n+2}>^{8} C_{3} \),then
the quadratic equations whose roots \( \operatorname{are} \alpha, \beta \) and \( \alpha^{n-1}, \beta^{n-1} \) have
A. 2 common root
B. 1 common root
c. no common roots
D. imaginary roots
Subject: Maths
Coefficient of \( \boldsymbol{x}^{r} \) in \( \mathbf{1}+(\mathbf{1}+\boldsymbol{x})+(\mathbf{1}+ \)
\( x)^{2}+\ldots \ldots+(1+x)^{n} \) is
A. \( ^{n+3} C_{r} \)
B. \( ^{n+1} C_{r+1} \)
\( \mathbf{c} \cdot^{n} C_{r} \)
D. \( (n+2) C_{r} \)
Subject: Physics
A particle is dropped from top tower.During its motion its covers \( \frac{\mathbf{9}}{\mathbf{2 5}} \) part of height of tower in last \( 1 . \) then height of tower?
\( \mathbf{A} \cdot 100 m \)
B. \( 125 m \)
c. \( 175 m \)
D. \( 120 m \)
Subject: Chemistry
At a certain temperature 2 moles of
carbonmonoxide and 3 moles of
chlorinw were allowed to reach
equilibrium according to the reaction \( \boldsymbol{C O}_{(g)}+\boldsymbol{C l}_{2} \leftrightharpoons \boldsymbol{C O C l}_{2} \) in a 5 lit vessel.
At equilibrium if one mole of \( C O \) is
present then equilibrium constant for the reaction is
Subject: Physics
If in a wire of Young's modulus \( Y \)
longitudinal strain \( X \) is produced then
the potential energy stored in its unit volume will be :
A. \( 0.5 Y X^{2} \)
2
В. \( 0.5 Y^{2} X \)
c \( .2 Y X^{2} \)
D. \( Y X^{2} \)