AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
The construction of \( \triangle A B C \) in which
\( A B=6 \mathrm{cm}, \angle A=30^{\circ}, \) is not possible
when \( \boldsymbol{A C}+\boldsymbol{B C}= \)
\( \mathbf{A} \cdot 6.3 \mathrm{cm} \)
B. \( 7.2 \mathrm{cm} \)
\( c .5 .6 \mathrm{cm} \)
D. \( 6.9 \mathrm{cm} \)
Subject: Physics
An aluminium block of \( 2 \mathrm{m} \) mass and an
iron block of \( \mathrm{m} \) mass,each absorbs the
same amount of heat, and both blocks
remain solid. If the specific heat of aluminium is twice the specific heat of iron, then find out the correct
statement?
A. The increase in temperature of the aluminum block is twice the increase in temperature of the iron block
B. The increase in temperature of the aluminum block is four times the increase in temperature of the iron block
c. The increase in temperature of the aluminum block is the same as increase in temperature of the iron block
D. The increase in temperature of the iron block is twice the increase in temperature of the aluminum block
E. The increase in temperature of the iron block is four
block
Subject: Chemistry
An organic compound of molecular
formula \( C_{4} H_{10} O \) does not react with
sodium. In excess of \( \boldsymbol{H} \boldsymbol{I} \), it gives only
one type of alkyl iodide. The compound
is:
A. ethoxy ethane
B. 2-methoxy propan
c. 1-methoxy propane
D. 1-butanol
Subject: Maths
If \( I_{n}=\int_{0}^{\pi / 4} \tan ^{n} x d x \) then \( \lim _{n \rightarrow \infty} n\left(I_{n}+\right. \)
\( \left.\boldsymbol{I}_{n-2}\right)= \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. 1/2
\( c \cdot \infty \)
D.
Subject: Physics
Choose the correct option
This question has multiple correct options
A. Temperature of a water kept inside a beaker is measured when the laboratory thermometer is held inside the water
B. Temperature of a water kept inside a beaker is measured when the laboratory thermometer is removed from the water
C. Temperature of our body is measured when the clinical thermometer is kept inside the mouth
D. Temperature of our body is measured when the clinical thermometer is removed from the mouth
Subject: Maths
A rectangular solid has a square base,
with each side of the base measuring 4
meters. If the volume of the solid is 112
cubic meters, what is the surface area
of the solid?
A. \( \$ 1,500 \)
B. \( \$ 1,700 \)
\( c . \$ 2,200 \)
D. \( \$ 3,000 \)
Subject: Chemistry
The conductivity of saturated solution
of \( A g C l \) is found to be \( 1.86 \times \) \( 10^{-6} \) ohm \( ^{-1} c m^{-1} \) and that of water is
\( 6 \times 10^{-8} o h m^{-1} c m^{-1} . \) If \( \lambda^{0} A g C l \) is 138
\( o h m^{-1} c m^{2} e q^{-1} \) the solubility product
of \( A g C l \) is:
A \( \cdot 1.3 \times 10^{-5} \)
В. \( 1.69 \times 10^{-10} \)
C \( .2 \times 10^{-10} \)
D. \( 2.7 \times 10^{-10} \)
Subject: Chemistry
Which of the following are pseudo
unimolecular reactions?
This question has multiple correct options
\( \mathbf{A} \cdot C H_{3} C O O C_{2} H_{5}+H O H \stackrel{H^{+}}{\longrightarrow} C H_{3} C O O H+ \)
\( C_{2} H_{5} O H \)
B \( \cdot C H_{3} C O O C_{2} H_{5}+H O H \stackrel{O H^{-}}{\longrightarrow} C H_{3} C O O H+ \)
\( C_{2} H_{5} O H \)
\( ^{\mathbf{C}} \cdot C_{12} H_{22} O_{11}+H O H \frac{H^{+}}{\rightarrow} \begin{aligned} C_{6} H_{12} O_{6}_{+} C_{6} H_{12} O_{6} & \\ & g l u c o s e \quad \text { fructose } \end{aligned} \)
D \( \cdot S O_{2} C l_{2}(g) \longrightarrow S O_{2}(g)+C l_{2}(g) \)
Subject: Biology
In which one of the following steps of citric acid cycle, FAD is reduced to \( \$ \$ \mathrm{FADH}_{-} 2 \$ \$ \)
A. Pyruvate Acetyl CoA
B. Succinic acid Malic acid
c. Malic acid Oxalosuccinic acid
D. Citric acid-Ketoglutaric acid
E. -Ketoglutasic Succinic acid
Subject: Chemistry
The average, \( S-F \) bond energy in \( S F_{6} \)
if the \( \Delta H_{f}^{\circ} \) value are -1100,+275 and
\( +80 k J / m o l \) respectively for \( S F_{6}(g) \)
\( S(g) \) and \( F(g) \) is
A. \( 390.1 k J / \) mol
в. \( 103.9 k J / \) mol
c. \( 903.1 k J / \) mol
D. \( 309.1 k J / \) mol
Subject: Physics
A horizontal overhead power line carries a current of \( 90 \mathrm{A} \) in east to west
direction. Magnitude of magnetic field due to the current \( 1.5 \mathrm{m} \) below the line is
A . 1.27
в. \( 1.2 \times 10^{-10} T \)
c. \( 0 T \)
D. \( 1.2 \times 10^{-5} T \)
Subject: Chemistry
Select the correct I.U.P.A.C. name for
\( \left[\boldsymbol{P t} \boldsymbol{C l}_{2}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right]\left[\boldsymbol{P t} \boldsymbol{C l}_{4}\right] \)
A. Tetraamminedichloridoplatinate(IV) tetrachloridoplatinate(II)
B. Tetraamminedichloridoplatinate(II) tetrachloridoplatinate(IV)
c. Tetraamminedichloridoplatinum(IV) tetrachloridoplatinate(II)
D. All are correct
Subject: Physics
A voltmeter of 998 ohm resistance is
connected to a cell of emf 2 volt, having internal resistance of 2 ohms The
error in measuring emf will b
A \( \cdot 4 \times 10^{-1} \mathrm{V} \)
B. \( 2 \times 10^{-3} \mathrm{V} \)
c. \( 4 \times 10^{-3} \mathrm{V} \)
D. \( 2 \times 10^{-1} \mathrm{V} \)
Subject: Physics
A uniformly charged ring of radius \( R \) is
rotated about its axis with constant
linear speed \( v \) of each of it's particles.
The ratio of electric field to magnetic
field at a point \( \boldsymbol{P} \) on the axis of the ring
at a distant \( x=R \) from the centre of
the ring is :
\( (c \text { is speed of light }) \)
A \( \frac{c^{2}}{v} \)
в. \( \frac{v^{2}}{c} \)
c. \( \frac{c}{v} \)
\( D \cdot \underline{v} \)
Subject: Chemistry
\( 25.0 \mathrm{mL} \) of \( 1.0 \mathrm{M} \mathrm{HCl} \) is combined with
\( 35.0 \mathrm{mL} \) of \( 0.5 \mathrm{M} \) NaOH. The initial
temperature of the solutions is \( 25^{\circ} C \) the density of the solution is \( 1.0 \mathrm{g} / \mathrm{mL} \) the specific heat capacity of the
solution is \( 4.184 \mathrm{J} / \mathrm{g}^{\circ} \mathrm{C} \), the reaction is
completed in an insulated coffee cup,
and the standard enthalpy of reaction
for \( \boldsymbol{H}_{(\boldsymbol{a q})}^{+}+\boldsymbol{O H}_{(\boldsymbol{a q})}^{-} \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}_{(1)} \) is - 56
kJ/mol. What is the final temperature of the solution?
\( \mathbf{A} \cdot 28.9^{\circ} C \)
B. \( 30.1^{\circ} \mathrm{C} \)
c. \( 32.8^{\circ} \mathrm{C} \)
D. none of the above
Subject: Physics
The moment of inertia and rotational
kinetic energy of a fly wheel are \( 20 k g-m^{2} \) and 1000 joule
respectively. Its angular frequency per minute would be
A. \( \frac{600}{\pi} \)
B. \( \frac{25}{\pi^{2}} \)
c. \( \frac{5}{\pi} \)
D. \( \frac{300}{\pi} \)
Subject: Chemistry
The equilibrium of the reaction
\( N_{2}(g)+3 H_{2}(g) \Leftrightarrow 2 N H_{3}(g) \) will shift
to the product side when
A. Concentration of \( N_{2} \) is increased
B. Concentration of \( N_{2} \) is decreased
c. concentration of \( N H_{3} \) is increased
D. concentration of \( H_{2} \) is decreased
Subject: Maths
The point \( P \) on the parabola \( y^{2}=4 a x \)
for which IPR PQI is maximum, where R \( (-a, 0), Q(0, a), \) is
A \( \cdot(a, 2 a) \)
в. \( (a,-2 a) \)
c. \( (4 a, 4 a) \)
D. \( (4 a,-4 a) \)
Subject: Physics
A satellite moves in a circular orbit
around the earth at height \( \boldsymbol{R} / 2 \) from
earth's surface where \( R_{e} \) is the radius
of the earth. Calculate its period of
revolution. Given \( \boldsymbol{R}_{e}=\mathbf{6 . 3 8} \times \mathbf{1 0}^{\mathbf{6}} \mathbf{m} \)
Subject: Chemistry
With in each set, select the compound which is more reactive to nucleophilic addition at carbonyl carbon.
\( (I) C H_{3} C O C H_{2} C H_{2} B r \) or \( C H_{3} C O C \)
\( (\boldsymbol{I I}) \boldsymbol{C H}_{3} \boldsymbol{C H O} \) or \( \boldsymbol{C H}_{3} \boldsymbol{C O C H}_{3} \)
\( (I I I) C H_{3} C O C H_{3} \) or \( C H_{3} C O C F_{3} \)
\( (I V) P h C H O \) or \( C H_{3} C H O \)
Subject: Chemistry
Which of the following are peroxoacids
of sulphur?
\( \mathbf{A} \cdot H_{2} S O_{5} \) and \( H_{2} S_{2} O_{8} \)
\( \mathbf{B} \cdot H_{2} S O_{5} \) and \( H_{2} S_{2} O_{7} \)
\( \mathbf{c} \cdot H_{2} S_{2} O_{7} \) and \( H_{2} S_{2} O_{8} \)
D. \( H_{2} S_{2} O_{6} \) and \( H_{2} S O_{5} \)
Subject: Physics
Three bodies \( A, B \) and \( C \) are in thermal
equilibrium. The temperature of \( B \) is
\( 45^{\circ} \mathrm{C}, \) then the temperature of \( C \) is
A \( \cdot 45^{\circ} \mathrm{C} \)
в. \( 50^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 40^{\circ} C \)
D. Any temperature
Subject: Chemistry
\( \boldsymbol{C}\left(\boldsymbol{C H}_{3}\right)_{2}=\boldsymbol{C}\left(\boldsymbol{C H}_{3}\right)_{2} \frac{C l_{2}}{\boldsymbol{H}_{2} \boldsymbol{O}} \boldsymbol{A} \stackrel{\boldsymbol{O H}^{-}}{\boldsymbol{\beta}} \boldsymbol{B} \)
The compound \( B \) is:
\( A \)
в. \( \left(C H_{3}\right)_{2} C-C\left(C H_{3}\right) \)
он \( C l \)
\( \mathrm{c} \cdot\left(C H_{3}\right)_{2} C-C\left(C H_{3}\right)_{2} \)
\( _{O H O H} \)
D. none of the above
Subject: Chemistry
Water is boiled under a pressure of 1.0atm. When an electric current of
\( 0.50 A \) from a \( 12 V \) supply is passed for 300 second through a resistance in thermal contact with it, it is found that
\( 0.789 g \) of water is vapourized. The molar internal energy change at boiling point (373.15K) is
A. \( =37.9 k J m o l^{-1} \)
В. \( =27.5 k J \) mol \( ^{-1} \)
\( \mathbf{c} .=47.5 k J m o l^{-1} \)
\( \mathbf{D} \cdot=17.5 k J m o l^{-1} \)
Subject: Chemistry
Compare relative stability of the
following resonating structure.
(ii)
(iii)
\( \mathbf{A} \cdot(i)>(i i)>(i i i) \)
\( \mathbf{B} \cdot(i i)>(i)>(i i i) \)
\( \mathbf{c} \cdot(i)>(i i i)>(i i) \)
\( \mathbf{D} \cdot(i i)>(i i i)>(i) \)
Subject: Maths
If \( \vec{a}, \vec{b}, \vec{c} \) are unit vectors such that \( \vec{a} \cdot \vec{b}=0=\vec{a} \cdot \vec{c} \) and the angle between \( \vec{b} \)
and \( \vec{c} \) is \( \pi / 3, \) then the value to \( |\vec{a} \times \vec{b}-\vec{a} \times \vec{c}| \) is \( ? \)
A. \( 1 / 2 \)
B.
\( c \cdot 2 \)
D. 3
Subject: Maths
If \( A=5 \) units, \( B=6 \) units and \( |\vec{A} \times \vec{B}|= \) 15 units, then the angle between \( \vec{A} \) and \( \vec{B} \)
is:
This question has multiple correct options
\( A \cdot 30^{\circ} \)
B. \( 60^{\circ} \)
c. \( 90^{\circ} \)
D. \( 150^{\circ} \)
Subject: Maths
If \( \boldsymbol{A}=\{\boldsymbol{x}: \boldsymbol{x} \boldsymbol{\epsilon} \boldsymbol{W}, \boldsymbol{3} \leq \boldsymbol{x}<\mathbf{6}\}, \boldsymbol{B}= \)
\( \{\mathbf{3}, \boldsymbol{5}, \boldsymbol{7}\} \) and \( \boldsymbol{C}=\{\mathbf{2}, \boldsymbol{4}\} \)
find \( : \boldsymbol{n}(\boldsymbol{A}-\boldsymbol{B}) \)
Subject: Physics
A tension in wire is \( 40 \mathrm{N} \) and \( 10 \mathrm{m} \) of wire
has a mass of \( 0.01 \mathrm{kg} \). The speed of transverse waves in \( \mathrm{m} / \mathrm{s} \) in the wire is :
A . 200
B. 80
\( c .300 \)
D. 180
Subject: Chemistry
Assertion
The calculated value of dipole moment
of \( L i I=11.5 D \) in the gaseous state is
more than its experimental value
\( (3.25 D) \)
Reason
In \( L i I \) the electron charge cloud of \( I^{-} \)
ion is polarized by \( L i^{+} \) ion; hence the
flow of electric charge occurs from \( \boldsymbol{I}^{-} \) to
\( \boldsymbol{L} \boldsymbol{i}^{+} \) ion.
Read the above assertion and reason
and choose the correct option regarding
¡t.
A. Assertion is true, Reason is true and Reason is correct explanation for Assertion
B. Assertion is true, Reason is true and Reason is NOT the correct explanation for Assertion
c. Assertion is true, Reason is false
D. Assertion is false, Reason is true
Subject: Maths
Assertion
For any two events \( A \) and \( B \) \( \boldsymbol{P}(\overline{\boldsymbol{A}} \cap \boldsymbol{B})=\boldsymbol{P}(\boldsymbol{B})-\boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B}) \)
Reason
\( A \cap B \) and \( \bar{A} \cap B \) are mutually
exclusive events.
A. Both Assertion \& Reason are individually true \& Reason is correct explanation of Assertion
B. Both Assertion \& Reason are individually true but Reason is not the , correct (proper) explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
Subject: Chemistry
The four quantum numbers of the
valence electron of potassium are:
\( \mathbf{A} \cdot 4,0,1,+\frac{1}{2} \)
B. \( 4,1,0,+\frac{1}{2} \)
\( \mathbf{c} \cdot 4,0,0,+\frac{1}{2} \)
D. \( 4,1,1,+\frac{1}{2} \)
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x}) \) be a differentiable function in
\( [2,7] . \) If \( f(2)=3 \) and \( f^{\prime}(x) \leq 5 \) for all \( x \)
in \( (2,7), \) then the maximum possible
value of \( f(x) \) at \( x=7 \) is
\( A \cdot 7 \)
B. 15
c. 28
D. 14
Subject: Chemistry
Assertion
All \( C-C-C \) bonds angles in
Isobutene \( \left(\boldsymbol{C H}_{3}-\underset{\mid}{\boldsymbol{C}}=\boldsymbol{C H}_{2}\right) \) are
\( \boldsymbol{C H}_{3} \)
different.
Reason
\( C H_{3}( \) Methyl group) show steric crowding.
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
Differentiate \( \sin \boldsymbol{h}^{-1}\left(\frac{\boldsymbol{x}}{\mathbf{3}}\right) \) with respect
to
\( x \). Find out the solution of the
integration \( \int \frac{1}{\left(x^{2}+9\right)} d x \) Further find
out the value of the integral
\( \int \frac{1}{\left(x^{2}+49\right)} d x ? \)
Subject: Maths
Compute \( \left[\begin{array}{cc}\cos ^{2} x & \sin ^{2} x \\ \sin ^{2} x & \cos ^{2} x\end{array}\right]+ \)
\( \left[\begin{array}{cc}\sin ^{2} x & \cos ^{2} x \\ \cos ^{2} x & \sin ^{2} x\end{array}\right] \)
Subject: Physics
\( P-V \) diagram of an ideal gas for a
process \( A B C \) is as shown in the figure. If the total heat absorbed or released by
the gas during the process \( A B C \) is
\( \operatorname{given} \operatorname{by} \boldsymbol{H}=-\boldsymbol{x} \boldsymbol{P}_{0} \boldsymbol{V}_{0}, \) what is the
value of \( x \) ?
Subject: Maths
Mean of the first \( n \) terms of the A.P.
\( \boldsymbol{a},(\boldsymbol{a}+\boldsymbol{d}),(\boldsymbol{a}+\boldsymbol{2} \boldsymbol{d}), \ldots \ldots . . \) is
A \( \cdot a+\frac{n d}{2} \)
в. \( a+\frac{(n-1) d}{2} \)
c. \( a+(n-1) d \)
D. \( a+n d \)
Subject: Chemistry
Which of following molecules is not linear?
\( \mathbf{A} \cdot \mathbf{O}=\mathbf{C}=\mathbf{C}=\mathbf{C}=\mathbf{0} \)
B. \( \mathrm{H}_{2} \mathrm{C}=\mathrm{C}=\mathrm{O} \)
c. \( \mathrm{HC} \equiv \mathrm{C}-\mathrm{C} \equiv \mathrm{CH} \)
D. \( \mathrm{HC} \equiv \mathrm{CH} \)
Subject: Chemistry
Which of the following has least polar
\( C-X \) bond?
A. \( H_{3} C-C H=C H_{2}-C l \)
в. \( H O-C H=C H_{2}-C l \)
c. \( O_{2} N-C H=C H_{2}-C l \)
D. \( H S-C H=C H_{2}-C l \)
Subject: Maths
Show that the relative \( R \) in the \( \operatorname{set} A= \)
\{1,2,3,4,5\} given by \( R= \)
\( \{(a, b):|a-b| \text { is even }\}, \) is an
equivalence relation. Show that all the
elements of \{1,3,5\} are related to each
other and all the elements of \{2,4\} are
related to each other. But no element of
\{1,3,5\} is related to any element of
\{2,4\}
Subject: Chemistry
For \( Z n^{2+} / Z n, E^{\circ}=-0.76 V, \) for
\( \boldsymbol{A} \boldsymbol{g}^{+} / \boldsymbol{A} \boldsymbol{g}, \boldsymbol{E}^{\circ}=\mathbf{0 . 7 9 9} \boldsymbol{V} . \) The correct
statement is:
A. the reaction Zn getting reduced Ag getting oxidized is spontaneous
B. Zn undergoes reduction and Ag is oxidized
C. zn undergoes oxidation Ag gets reduced
D. No suitable answer
Subject: Physics
A particle of mass \( \mathrm{M} \) is situated at the
centre of spherical shell of same mass and radius a. The gravitational potential at a point situated at a/2 distance from the centre will be
A. \( -\frac{3 G M}{a} \)
В. \( -\frac{2 G M}{a} \)
c. \( -\frac{G M}{a} \)
D. \( -\frac{4 G M}{a} \)
Subject: Chemistry
What hybrid orbitals are employed by carbon atoms 1,2 nad \( 3, \) respectively, as labeled in the compound shown? 0
\( \boldsymbol{H}_{3} \boldsymbol{C}-\underset{2}{\boldsymbol{C}}-\underset{3}{\boldsymbol{1}} \equiv \boldsymbol{N} \)
\( \mathbf{A} \cdot s p^{3}, \mathbf{s p}, \mathbf{s p} \)
B \( \cdot s p^{2}, s p^{2}, \) sp
\( \mathbf{c} \cdot s p^{3}, s p^{2}, \mathbf{s p} \)
D. \( s p^{3}, s p^{2}, s p^{2} \)
Subject: Maths
Find the mean deviation about median
for the following data.
\begin{tabular}{lllll}
\multirow{2}{*} {\( \boldsymbol{C I} \)} & \( \mathbf{2 0}- \) & \( \mathbf{3 0 -} \) & \( \mathbf{4 0 -} \) & \( \mathbf{5 0 -} \) \\
\( \mathbf{3 0} \) & \( \mathbf{4 0} \) & \( \mathbf{5 0} \) & \( \mathbf{6 0} \)
\end{tabular}
18
Subject: Chemistry
A mixture of three proteins \( (\boldsymbol{A}) \) \( (\text { pepsin }),(B) \) (haemoglobin) and \( (C) \)
(lysozyme) was separated by
eletrophoresis method at \( \boldsymbol{p} \boldsymbol{H}=\mathbf{7} \). The
\( \boldsymbol{p} \boldsymbol{H} \) at isoelectric point \( (\boldsymbol{p} \boldsymbol{I}) \) of the
proteins are \( \boldsymbol{p} \boldsymbol{I} \) of \( (\boldsymbol{A}),(\boldsymbol{B}) \) and \( (\boldsymbol{C}) \)
which are 1.1,6.7 and 11.0 respectively.
Which of the statement are correct?
This question has multiple correct options
A. Pepsin \( (A) \) will migrate to the cathode
B. Lysozyme \( (C) \) will migrate to the anode
C. Haemoglobin will not migrate
D. At \( p H=7,(A) \) and \( (C) \) would precipitate out while \( (B) \) would remain in the solution.
Subject: Maths
When the polynomial \( a^{3}+2 a^{2}- \)
\( 5 a x-7 \) is divided by \( a+1, \) the
remainder is \( R_{1} . \) If \( R_{1}=14 \), find the
value of \( \boldsymbol{x} \)
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D.
Subject: Chemistry
Which one of the following is wrongly matched?
A \( \cdot\left[C u\left(N H_{3}\right)_{4}\right]^{2+} \) - Square planar
B . \( \left[N i(C O)_{4}\right] \) - Neutral ligand
c. \( \left[F e(C N)_{6}^{3-}\right]-s p^{3} d^{2} \)
D. \( \operatorname{Co}(e n)_{3}^{3+} \) - Follows EAN rule
Subject: Chemistry
In a mixture of concentrated \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
and \( H N O_{3} \) intermediate formed is:
A \( \cdot H_{2} S O_{4}^{+} \)
B. \( S O_{4}^{2-} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{N} \mathrm{O}_{3}^{-} \)
D. \( H_{2} N O_{3}^{+} \)
Subject: Chemistry
If the \( \Delta G \) of a cell reaction, \( A g C l+ \)
\( e^{-} \rightarrow A g+C l^{-} \) is \( -21.20 \mathrm{kJ}, \) the
standard emf of cell is
A . \( 0.239 \mathrm{v} \)
B. \( 0.220 v \)
c. \( -0.320 v \)
D. - 0.110v
Subject: Maths
Compute Mean deviation about median for the following Frequency distribution.
Variable(
\( x \)
\( \mathbf{1 0} \)
\( \mathbf{1 5} \quad \mathbf{2 0} \quad \mathbf{2 5} \)
Frequency
\[
f)
\]
A . 10.5
в. 10.1
c. 13.2
D. 12.1
Subject: Physics
A car is travelling along a circular curve that has a radius of \( 50 m \). If its speed is \( 16 m / s \) and is increasing uniformly at
\( 8 m / s^{2} . \) Determine the magnitude of its
acceleration at this instant.
A \( .5 .5 \mathrm{m} / \mathrm{s}^{2} \)
B. \( 7.5 \mathrm{m} / \mathrm{s}^{2} \)
c. \( 9.5 \mathrm{m} / \mathrm{s}^{2} \)
D. \( 12.5 \mathrm{m} / \mathrm{s}^{2} \)
Subject: Physics
In a Wheatstone's bridge, there resistances \( P, Q \) and \( R \) connected in the three arms and the fourth arm is
formed by two resistances \( S_{1} \) and \( S_{2} \) connected in parallel. The condition for bridge to be balanced will be :
\( ^{\text {A } \cdot \frac{P}{Q}}=\frac{R}{S_{1}+S_{2}} \)
в. \( \frac{P}{Q}=\frac{2 R}{S_{1}+S_{2}} \)
c. \( \frac{P}{Q}=\frac{R\left(S_{1}+S_{2}\right)}{S_{1} S_{2}} \)
D. \( \frac{P}{Q}=\frac{R\left(S_{1}+S_{2}\right)}{2 S_{1} S_{2}} \)
Subject: Chemistry
\( S-S \) bond is present in :
A \( \cdot \alpha-\left(S O_{3}\right)_{n} \)
B \( \cdot \gamma-\left(S_{3} O_{9}\right) \)
c. \( H_{2} S_{2} O_{3} \)
D. \( H_{2} S_{2} O_{8} \)
Subject: Physics
A body falls through a distance 'h' in a
certain time on the earth. Then if the
same body is related on another planet having mass and radius twice as that of the earth, the distance through which it falls in the same time is:
\( A \cdot \frac{h}{2} \)
в. \( 2 h \)
\( c \cdot h \)
D. \( 4 h \)
Subject: Chemistry
When heating \( P C l_{5}, \) it decompose
\( P C l_{3} \) and \( C l_{2} \) in form of gas. The vapour density of gas mixture is 70.2 and 57.9
at \( 200^{\circ} \mathrm{C} \) and \( 250^{\circ} \mathrm{C} \). The degree of
dissociation of \( P C l_{5} \) at \( 200^{\circ} C \) at \( 250^{\circ} C \)
is:
A . \( 48.50 \% \) and \( 80 \% \)
B. 60\% and 70\%
c. \( 70 \% \) and \( 80 \% \)
D. 80\% and 90\%
Subject: Physics
The diagram shows three capacitor with
their capacitances with breakdown
voltages.what should be the maximum
value of external emf of source such
that no capacitor breaks down:-
\( A \cdot \frac{33}{2} v o l t \)
B . \( \frac{11}{3} \) volt
\( c \cdot \frac{13}{3} v o l t \)
D. \( \frac{11}{2} \) volt
Subject: Maths
For \( \boldsymbol{n} \in \boldsymbol{N}, \boldsymbol{x}^{n+1}+(\boldsymbol{x}+\mathbf{1})^{2 n-1} \) is
divisible by
\( A \)
B. \( x+1 \)
c. \( x^{2}+x+1 \)
D. \( x^{2}-x+1 \)
Subject: Physics
The potential energy of 1 kg particle free to move along the X-axis is given by \( \boldsymbol{U}=\left(\frac{\boldsymbol{x}^{4}}{\boldsymbol{4}}-\frac{\boldsymbol{x}^{2}}{\mathbf{2}}\right) \boldsymbol{J} \)
The total mechanical energy of the particle is 2 J. Then Maximum speed of the particle is :
A \( \cdot \frac{3}{\sqrt{2}} \)
B. \( \frac{1}{\sqrt{2}} \)
\( c \cdot \sqrt{2} \)
D. 2
Subject: Maths
The sum of \( n \) terms of the series \( 1+ \)
\( (\mathbf{1}+\boldsymbol{a})+\left(\mathbf{1}+\boldsymbol{a}+\boldsymbol{a}^{2}\right)+(\mathbf{1}+\boldsymbol{a}+ \)
\( \left.\boldsymbol{a}^{2}+\boldsymbol{a}^{3}\right)+\ldots . \) is
A \( \cdot \frac{n}{1+a}-\frac{1-a^{n}}{(1-a)^{2}} \)
в. \( \frac{n}{1-a}+\frac{a\left(1-a^{n}\right)}{(1-a)^{2}} \)
c. \( \frac{n}{1-a}+\frac{a\left(1+a^{n}\right)}{(1-a)^{2}} \)
D. none of the above
Subject: Physics
A circular platform is mounted on a
vertical frictionless axle. Its radius is
\( r=2 m \) and its moment inertia is \( I= \)
\( 200 k g m^{2} . \) It is initially at rest. A \( 70 k g \)
man stands on the edge of the platform
and begins to walk along the edge at
speed \( v_{0}=10 m s^{-1} \) relative to the
ground. The angular velocity of the
platform is
A \( .1 .2 \mathrm{rad} \mathrm{s}^{-1} \)
B. 0.4 rad \( s^{-1} \)
c. 2.0 rad \( s^{-1} \)
D. 7.0 rad \( s^{-1} \)
Subject: Physics
Mass per unit of a semicircular disc of
total mass m radius R varies linearly
with radial distance from the point 0 (base centre). Find the height of centre of mass from 0
A \( \cdot \frac{2 R}{\pi} \)
в. \( \frac{3 R}{2 \pi} \)
c. \( \frac{4 R}{3 \pi} \)
D. \( \frac{3 R}{8} \)
Subject: Physics
Two
friends \( A \) and \( B \) are standing a distance \( x \) apart in an open field and wind is blowing from \( A \) to \( B \). A beats a drum and
B hears the sound \( t_{1} \) time
after he sees the event. A and B
interchange their positions and the experiment is repeated. This time B hears the drum
\( t_{2} \) time after he sees
the event. Calculate the velocity of sound in still air v and the velocity of
wind
u. Neglect the time light takes in travelling between the friends.
A \( \cdot \frac{1}{2}\left(\frac{1}{t_{1}}+\frac{1}{t_{2}}\right), \frac{x}{2}\left(\frac{1}{t_{1}}-\frac{1}{t_{2}}\right) \)
B. \( \frac{x}{2}\left(\frac{1}{t_{1}}+\frac{1}{t_{2}}\right), \frac{x}{2}\left(\frac{1}{t_{1}}-\frac{1}{t_{2}}\right) \)
\( ^{\mathbf{c}} \cdot \frac{x}{2}\left(\frac{1}{t_{1}}+\frac{1}{t_{2}}\right), \frac{3 x}{2}\left(\frac{1}{t_{1}}-\frac{1}{t_{2}}\right) \)
D. \( \frac{3 x}{2}\left(\frac{1}{t_{1}}+\frac{1}{t_{2}}\right), \frac{x}{2}\left(\frac{1}{t_{1}}-\frac{1}{t_{2}}\right) \)
Subject: Maths
If \( \left|\begin{array}{lll}\boldsymbol{a} & \boldsymbol{a}^{2} & \mathbf{1}+\boldsymbol{a}^{3} \\ \boldsymbol{b} & \boldsymbol{b}^{2} & \mathbf{1}+\boldsymbol{b}^{3} \\ \boldsymbol{c} & \boldsymbol{c}^{2} & \boldsymbol{1}+\boldsymbol{c}^{3}\end{array}\right|=\mathbf{0} \) and vectors
\( \left(1, a, a^{2}\right),\left(1, b, b^{2}\right) \) and \( \left(1, c, c^{2}\right) \) are non
coplanar then \( a b c \) equals
A . -1
B. 1
\( c \cdot 0 \)
D.