AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A wheel is rotating at 1800 rpm about its own axis. When the power is switched oft it comes to rest in 2 min.
Then, the angular retardation in rad \( s^{-1} \)
is
\( \mathbf{A} \cdot 2 \pi \)
в. \( \pi \)
c. \( \pi / 2 \)
D . \( \pi / 4 \)
E . \( \pi / 6 \)
Subject: Maths
\( \int_{1}^{2} \frac{\mathbf{d x}}{\sqrt{1+\mathbf{x}^{2}}}= \)
\( ^{\mathbf{A}} \cdot \log _{\mathbf{e}}\left(\frac{2+\sqrt{5}}{\sqrt{2}+1}\right) \)
в. \( \log _{e}\left(\frac{\sqrt{2}+1}{2+\sqrt{5}}\right) \)
\( ^{\mathrm{c}} \cdot \log _{\mathrm{e}}\left(\frac{2-\sqrt{5}}{\sqrt{2}-1}\right) \)
D.
Subject: Physics
The equation of a simple harmonic
wave is given by \( \boldsymbol{y}= \)
\( 6 \sin 2 \pi(2 t-0.1 x), \) where \( x \) and \( y \) are
in \( m m \) and \( t \) is in seconds. The phase
difference between two particles \( 2 m m \)
apart at any instant is
A \( \cdot 18^{\circ} \)
В. \( 36^{\circ} \)
\( c \cdot 54^{\circ} \)
D. \( 72^{\circ} \)
Subject: Maths
state \( \quad \) Minimum Wage per Hour
daho \( \$ 7.25 \)
Montana
\[
\$ 7.90
\]
Orego \( \$ 9.10 \)
Wahington \( \quad \$ 9.32 \)
The table above shows the 2014 minim
wages for several states that share a
border. Assuming an average workweek of between 35 and 40 hours, which
inequality represents how much more a worker who earns minimum wages can
earn per week in Oregon than in Idaho?
A \( . x \geq 1.85 \)
в. \( 7.25 \leq x \leq 9.10 \)
c. \( 64.75 \leq x \leq 74 \)
D. \( 253.75 \leq x \leq 364 \)
Subject: Maths
For every pair of continuous functions
\( \boldsymbol{f}, \boldsymbol{g}:[\mathbf{0}, \mathbf{1}] \rightarrow \boldsymbol{R} \) such that max
\( \{\boldsymbol{f}(\boldsymbol{x}): \boldsymbol{x} \in[\mathbf{0}, \mathbf{1}]\}= \)
\( \max \{g(x): x \in[0,1]\}, \) the correct
statement (s) is (are)
A \( \cdot(f(c))^{2}+3 f(c)=(g(c))^{2}+3 g(c) \) for some \( c \in[0,1] \)
B \( \cdot(f(c))^{2}+f(c)=(g(c))^{2}+3 g(c) \) for some \( c \in[0,1] \)
\( (f(c))^{2}+3 f(c)=(g(c))^{2}+g(c) \) for some \( c \in[0,1] \)
D \( \cdot(f(c))^{2}=(g(c))^{2} \) for some \( c \in[0,1] \)
Subject: Physics
Assertion
When the radius of a copper wire is doubled, its specific resistance is increased.
Reason
Specific resistance is independent of cross-section of material used.
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
\( p H \) of a \( 0.1 \mathrm{M} \) monobasic acid is
measured to be \( 2 . \) Its osmotic pressure
at a given temperature of \( \boldsymbol{T} \) Kis:
A . 0.1 RT
в. 0.11 RТ
c. \( 1.1 \mathrm{RT} \)
D. 0.01 RT
Subject: Chemistry
Choose the correct statement from the
following:
This question has multiple correct options
A \( . \) He gas diffuses \( \sqrt{2} \) times more than \( O_{2} \)
B. \( O_{2} \) gas diffuses 2 times more than \( S O_{2} \)
\( \mathrm{C} \cdot \mathrm{CH}_{4} \) gas diffuse \( \sqrt{2} \) times more than \( \mathrm{O}_{2} \)
D. \( H_{2} \) difusses \( \sqrt{2} \) times more than \( H e \) gas
Subject: Chemistry
Which of the following is/are example(s) of induced radioactivity
reaction?
Select correct statement(s)
A. Photon or particle is ionised and collected by the positive electrode in a Geiger counter
B. A scintillation counter contains a phosphor, a substance that emits a flash of light when struck by a photon or particle.
c. Both of the above
D. None of the aobve
Subject: Biology
Which of the following sequences
correctly portrays the flow of electrons
during photosynthesis?
\( \mathbf{A} \cdot H_{2} O \rightarrow \mathrm{NADPH} \rightarrow \) Calvin cycle
B. NADPH \( \rightarrow \) chlorophyll \( \rightarrow \) Calvin cycle
\( \mathrm{C} \cdot H_{2} \mathrm{O} \rightarrow \) photosystem-I \( \rightarrow \) photosystem-I
D. NADPH \( \rightarrow \) electron transport chain \( \rightarrow O_{2} \)
Subject: Maths
Integrate the following functions with espect to \( x: \int \frac{d x}{4 x+5} \)
This question has multiple correct options
A \( \cdot \frac{1}{4} \ln (4 x+5)+c \)
B. \( \frac{1}{4} \ln (4 x+5)-c \)
\( ^{\mathbf{c}} \cdot \frac{-1}{4} \ln (4 x+5)-c \)
D. \( 4 \ln (4 x-5)-c \)
Subject: Physics
The mean distance between the atoms
of iron is \( 3 \times 10^{-10} m \) and interatomic
force constant for iron is \( \mathbf{7} N \boldsymbol{m}^{-1} \). The
Young's modulus of electricity for iron
is
A \( .2 .33 \times 10^{5} \mathrm{Nm}^{-2} \)
в. \( 23.3 \times 10^{10} \mathrm{Nm}^{-2} \)
c. \( 2.33 \times 10^{9} \mathrm{Nm}^{-2} \)
D. \( 2.33 \times 10^{10} \mathrm{Nm}^{-2} \)
Subject: Chemistry
Consider the given statements:
I. Maltose is also known as malt sugar.
II. Sucrose is also known as cane sugar.
III. Lactose is also known as grape
sugar.
IV. Starch is also known as amylum.
The correct statement(s) is/are:
\( A \cdot \) ।, ॥ and IV
B. I, II and III
c. ॥, ॥ा and IV
D. All
Subject: Chemistry
The IUPAC name is:
\[
\begin{array}{l}
C H=C H \\
C H O N H_{2}
\end{array}
\]
A. 1- Amino prop - 2 - enal
B. 3-Amino prop - 2 - enal
c. \( 1- \) Amino -2 - formyl ethane
D. 3 - Amino -1 -oxo prop - 2 - ene
Subject: Physics
Tuning fork \( C \) of frequency 305 Hz gives 5 beats/sec with tuning fork D when sounded together. When prongs of D are filled a little they produce 3 beats/s. The frequency of tuning fork D before filling is:
A . 310 \( \mathrm{Hz} \)
в. зоо нz
c. 295 н
D. 315 нz
Subject: Physics
Express \( q \) as a function of time.
A \( \cdot 10^{4} \cos \left(6.28 \times 10^{3} t\right) \)
B \( \cdot 10^{-4} \cos \left(9.28 \times 10^{3} t\right) \)
\( \mathbf{c} \cdot 10^{-4} \cos \left(6.28 \times 10^{3} t\right) \)
D \( \cdot 10^{-4} \cos \left(6.28 \times 10^{-3} t\right) \)
Subject: Maths
The radius of a solid sphere is 'r' cm. It is bisected, then the total surface area of the two pieces obtained is
\( \mathbf{A} \cdot 8 \pi r^{2} c m^{2} \)
B . \( 4 \pi r^{2} c m^{2} \)
c. \( 5 \pi r^{2} c m^{2} \)
D. \( 6 \pi r^{2} c m^{2} \)
Subject: Chemistry
The formula of meta phosphoric acid is :
A. \( \mathrm{H}_{2} \mathrm{PO}_{3} \)
в. \( \mathrm{H}_{3} \mathrm{PO}_{3} \)
\( \mathrm{c} \cdot \mathrm{HPO}_{3} \)
D. \( \mathrm{H}_{4} \mathrm{P}_{2} \mathrm{O}_{7} \)
Subject: Chemistry
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C O N H}_{2} \frac{\boldsymbol{B r}_{2}}{N a O \boldsymbol{H}} \boldsymbol{A} \)
Aqueous solution of \( \boldsymbol{A} \)
A. Turns blue litmus to red
B. Turns red litmus to blue
c. Does not affect the litmus
D. Decolourise the litmus
Subject: Chemistry
Identify the term/substance in each of
the following:
(i) The tendency of an atom to attract
electrons to itself when combined in a
compound.
(ii) The method used to separate ore
from gangue by preferential wetting.
(iii) The catalyst used in the conversion of ethyne to ethane
(iv) The type of reactions alkenes
undergo.
(v) The electrons present in the
outermost shell of an atom.
Subject: Chemistry
Among \( K O_{2}, A l O_{2}^{-}, B a O_{2} \) and \( N O_{2}^{+} \)
unpaired electron is present in:
A. \( K O_{2} \) only
B. \( N O_{2}^{+} \) and \( B a O_{2} \)
c. \( K O_{2} \) and \( A l O_{2}^{-} \)
D. \( B a O_{2} \) only
Subject: Physics
Plates of a parallel plate capacitor \( \mathbf{C} \)
have charges \( \mathrm{CV} \) and \( 3 \mathrm{CV} \) on its plates.
If switch is closed at t=0. Then initial
rate at which heat energy is produced in resistance R is:
\( A \cdot \frac{V^{2}}{R} \)
B. \( \frac{4 V^{2}}{R} \)
c. \( \frac{9 V^{2}}{R} \)
D. \( \frac{16 V^{2}}{R} \)
Subject: Chemistry
When \( M n O_{2} \) is fused with KOH in the
presence of air, a coloured compound is formed, the product and its colour is :
A \( \cdot K_{2} M n O_{4}, \) dark green
B. \( K M n O_{4} \), purple
c. \( M n_{2} O_{3} \), brown
D. \( M n_{3} O_{4} \), black.
Subject: Maths
paragraph, find the resultant vectors \( \boldsymbol{A} \)
and \( B \) in figure.
\( |\vec{R}|=13.54 m s^{-1}, \tan \beta=\frac{3}{13.196} \) with respect to \( 8 m s^{-1} \)
vector
3 \( |\vec{R}|=15.54 m s^{-1}, \tan \beta=\frac{3}{13.196} \) with respect to \( 8 m s^{-1} \)
vector
\( ^{\mathrm{C}}|\vec{R}|=15.54 m s^{-1}, \tan \beta=\frac{3}{13.196} \) with respect to \( 9 m s^{-1} \)
vector
\( |\vec{R}|=13.54 m s^{-1}, \tan \beta=\frac{3}{13.196} \) with respect to \( 9 m s^{-} \)
vector
Subject: Chemistry
Assertion
Glucose does not gives \( 2,4-D N P \)
test.
Reason
Glucose exists in cyclic hemiacetal form
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
Two \( n \times n \) square matrices \( A \) and \( B \) are
said to be similar if there exists a non-
singular matrix \( \boldsymbol{P} \) such that
\( \boldsymbol{P}^{-1} \boldsymbol{A} \boldsymbol{P}=\boldsymbol{B} \)
If \( A \) and \( B \) are two non-singular
matrices, then
\( \mathbf{A} \cdot A \) is similar to \( B \)
B. \( A B \) is similar to \( B A \)
C. \( A B \) is similarto \( A^{-1} B \)
D. none of these
Subject: Chemistry
According to Aufbau principle, the correct order of energy of \( 3 d, 4 s \) and \( 4 p \) orbitals is :
A. \( 4 p<3 d<4 s \)
в. \( 4 s<4 p<3 d \)
c. \( 4 s<3 d<4 p \)
D. \( 3 d<4 s<4 p \)
Subject: Physics
Estimate the change in the density of
water in ocean at a depth of \( 400 \mathrm{m} \)
below the surface. The density of water
at the surface \( =1030 \mathrm{kg} m^{-3} \) and the
bulk modulus of water \( =2 \times 10^{9} \mathrm{N} m^{-2} \)
Subject: Maths
Let \( \vec{a}, \vec{b}, \vec{c} \) be the vectors of length 3,4 5 respectively. Let \( \vec{a} \) be perpendicular to \( \vec{b}+\vec{c}, \vec{b} \) to \( \vec{c}+\vec{a} \) and \( \vec{c} \) to \( \vec{a}+\vec{b} \)
Then \( |\vec{a}+\vec{b}+\vec{c}| \) is equal to
A \( \cdot 2 \sqrt{5} \)
B. \( 2 \sqrt{2} \)
с. \( 10 \sqrt{5} \)
।
D. \( 5 \sqrt{2} \)
Subject: Physics
Two trains each of length \( 100 m \) moving parallel towards each other at speed \( \mathbf{7} 2 k \boldsymbol{m} / \boldsymbol{h} \) and \( \boldsymbol{3} \boldsymbol{6} \boldsymbol{k} \boldsymbol{m} / \boldsymbol{h} \) respectively. In
how much time will they cross each
other?
\( \mathbf{A} \cdot 4.5 S \)
B. \( 6.67 s \)
\( c .3 .5 s \)
D. \( 7.25 s \)
Subject: Physics
When a big drop of water is formed from
\( n \) small drops of water, the energy loss
is \( 3 E, \) where \( E \) is the energy of the bigger drop. If \( R \) is the radius of the
bigger drop and \( r \) is the radius of the
smaller drop, then number of smaller drops \( (n) \) is:
A \( \cdot \frac{4 R}{r^{2}} \)
в. \( \frac{4 R}{r} \)
c. \( \frac{2 R^{2}}{r} \)
D. \( \frac{4 R^{2}}{r^{2}} \)
Subject: Physics
Assertion
An astronaut inside a massive
spaceship orbiting around the earth will experience a finite but smal
gravitational force.
Reason
The centripetal force necessary to keep the spaceship in orbit around the earth is provided to keep the spaceship in orbit.
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
What is the maximum concentration of
equimolar solutions of ferrous sulphate and sodium sulphide so that when mixed in equal volumes, there is no precipitation of iron sulphide?(For iron sulphide, \( \boldsymbol{K}_{s p}=\mathbf{6 . 3} \times \mathbf{1 0}^{-\mathbf{1 8}} \) ).
Subject: Chemistry
\( \boldsymbol{A l}+\boldsymbol{N} \boldsymbol{O}_{\mathbf{2}}^{-} \rightarrow \boldsymbol{A l}(\boldsymbol{O} \boldsymbol{H})_{4}^{-}+\boldsymbol{N} \boldsymbol{H}_{3} \)
The oxidizing agent for this reaction
is
A . \( A l \)
в. \( N \)
\( c \cdot O \)
D. both \( A \) and \( B \)
Subject: Physics
A uniform field of induction \( B \) is
changing in magnitude at a constant rate \( d B / d t . \) You are given a mass \( m \) of copper which is to be drawn into a wire
of radius \( r \) and formed into a circular
loop of radius \( R \). Show that the induced current in the loop does not depend on the size of the wire of the loop.

Assuming \( B \) perpendicular the loop
prove that the induced current \( i= \) \( \frac{m}{4 \pi \rho \delta} \frac{d B}{d t} \) where \( \rho, \) is the resistivity and
\( d \) is the density of copper
Subject: Physics
An emf of 100 millivolts is induced in a
coil when the current in another nearby coil becomes \( 10 A \) from zero to 0.1 sec
The corfficient of mutual induction
between the two coils will be
\( \mathbf{A} \cdot 1 m H \)
в. \( 10 \mathrm{mH} \)
c. \( 100 \mathrm{mH} \)
D. \( 1000 m H \)
Subject: Physics
Two sound waves each of amplitude \( a \) and of frequencies \( 500 H z \) and \( 512 H z \)
superpose. Then the resultant of the amplitude of the resultant wave at \( t= \) \( \frac{5}{48} s \) is
A . 0
в. \( \frac{a}{\sqrt{2}} \)
\( c \cdot a \sqrt{2} \)
D. \( 2 a \)
Subject: Maths
The value of \( \mathbf{f}(\mathbf{0}) \) such \( \mathbf{f}(\mathbf{x})= \)
\( \frac{1-\cos ^{2} x+\sin ^{2} x}{\sqrt{x^{2}+1}-1}(x \neq 0) \) is
continuous at \( \mathbf{x}=\mathbf{0} \) is
Subject: Physics
Two cars \( c_{1}, \) and \( c_{2} \) moving in the same
direction on a straight single lane road
with velocities \( \boldsymbol{v}_{1}=12 m s^{-1} \) and \( \boldsymbol{v}_{2}= \)
\( 10 m s^{-1}, \) respectively. When the
separation between the two was \( d=200 \)
\( \mathrm{m}, \mathrm{c}_{2} \) started accelerating to avoid
collision. What is the minimum
acceleration of car \( c_{2} \) so that they do not
collide?
Subject: Maths
\( \frac{2 x}{3}-\frac{x-1}{6}+\frac{7 x-1}{4}=2 \frac{1}{6} \)
Hence, find the value of \( x \) and \( a \), if \( \frac{1}{a}+ \)
\( \mathbf{5} \boldsymbol{x}=\mathbf{8} \)
A \( x=2 \) and \( a=\frac{1}{2} \)
B. \( x=3 \) and \( a=\frac{1}{4} \)
c. \( _{x}=4 \) and \( a=\frac{1}{5} \)
D. \( x=1 \) and \( a=\frac{1}{3} \)
Subject: Maths
A random survey of the number of
children of various age group playing in
a park was found as follows:

Draw a histogram to represent the data
above
\begin{tabular}{|c|c|}
\hline Age (in years) & Number of children \\
\hline \( 1-2 \) & 5 \\
\( 2-3 \) & 3 \\
\( 3-5 \) & 6 \\
\( 5-7 \) & 12 \\
\( 7-10 \) & 9 \\
\( 10-15 \) & 10 \\
\( 15-17 \) & 4 \\
\hline
\end{tabular}
Subject: Chemistry
The correct stability order of the following resonance structure is:
(।) \( \mathbf{H}_{2} \overline{\mathbf{C}}-\dot{\mathbf{N}} \equiv \mathbf{N} \)
\( (\mathrm{II}) \mathbf{H}_{2} \mathbf{C}=\stackrel{+}{\mathbf{N}}=\overline{\mathbf{N}} \)
\( (\| I) \mathbf{H}_{2} \stackrel{+}{C}-N=\bar{N} \)
\( (\mid V) \mathbf{H}_{2} \overline{\mathbf{C}}-\mathbf{N}=\dot{\mathbf{N}} \)
\( A \cdot(1)>(11)>(1)>(111) \)
B. (I) > (III) > (II) > (IV)
\( c \cdot(11)>(1)>(111)>(1 v) \)
\( D \cdot(\| I)>(I)>(I V)>(I I) \)
Subject: Chemistry
For an ideal solution of two components
A and B, which of the following is true?
\( \mathbf{A} \cdot \Delta H_{m i x i n g}<0(z e r o) \)
B. \( \Delta H_{\text {mixing}}>0(z \text {ero}) \)
C. \( A \) - \( B \) interaction is stronger than \( A-A \) and \( B-B \) interactions
D. \( A-A, B-B \) and \( A-B \) interactions are identical
Subject: Chemistry
\( \boldsymbol{K}_{a} \) for \( \boldsymbol{H}_{2} \boldsymbol{O} ;\left(\boldsymbol{K}_{\boldsymbol{w}}=\mathbf{1 0}^{-14}\right) \) is \( \mathbf{1 . 8} \times \)
\( 10^{-x} \)
Then find the value of \( x \). (Moar conc. of
pure water is 55.55 )
Subject: Physics
A certain region of a soap bubble
reflects red light of vacuum wavelength
\( \boldsymbol{\lambda}=\mathbf{6 5 0 n m} . \) The minimum thickness
that this region of soap bubble could
have is \( 13 \times 10^{-x} \) m. Find \( x \)
(The index of refraction of the soap film
is \( 1.25) \)
Subject: Physics
A bar magnet is moved along the axis of a copper ring placed far away from the magnet. Looking from the side of the magnet, an anti-clockwise current is
found to be induced in the ring. Which
of the following may be true? This question has multiple correct options
A. The south pole faces the ring and the magnet moves towards it
B. The north pole faces the ring and the magnet moves towards it.
c. The south pole faces the ring and the magnet moves away from it.
D. The north pole faces the ring and the magnet moves away from it.
Subject: Maths
The ratio in which the joint of
(2,1,5),(3,4,3) is divided by the plane \( 2 x+2 y-2 z-1=0 \)
\( \mathbf{A} \cdot 5: 12 \)
B. 12: 5
\( c .5: 7 \)
D. 7: 5
Subject: Chemistry
Which of the following compounds will not give ammonia on heating?
\( \mathbf{A} \cdot\left(N H_{4}\right)_{2} S O_{4} \)
B. \( \left(N H_{4}\right)_{2} C O_{3} \)
c. \( N H_{4} N O_{2} \)
D. \( N H_{4} C l \)
Subject: Maths
Divide the following polynomial \( p(x) p(x) \) by the polynomial \( S(x) 5(x) \)
\( \boldsymbol{P}(\boldsymbol{x})=\frac{2}{3} \boldsymbol{x}^{2}+\mathbf{5} \boldsymbol{x}+\boldsymbol{6}, \boldsymbol{S}(\boldsymbol{x})=\boldsymbol{x}+\boldsymbol{6} \)
Subject: Chemistry
How many of the following statements
are correct?
This question has multiple correct options
A. In crystalline compounds of group- 2 , number of molecules of water of crystallization generally decreases as the ions become larger.
B. As the electropositive character of alkali metals increase down the group, the stabilities of their carbonates and hydrogen carbonates increases.
C. The oxide and hydroxide of beryllium are amphoteric in nature
D. \( B e C l_{2} \) has a chain structure in vapour phase and in solid state tends to form a chloro-bridged dimer
E. Alkaline earth metal nitrates on heating decompose \( \operatorname{giving~both} N O_{2} \) and \( O_{2} \)
F. The crystal structures of \( N a H C O_{3} \) and \( K H C O_{3} \), both show hydrogen bonding.
Subject: Physics
A scientist wants to raise the
temperature of \( 0.1 \mathrm{Kg} \) sample of glass
from \( -45^{0} C \) to \( 15^{0} C . \) How much heat
energy is required to raise the temperature? (SHC of glass
\( \left.\boldsymbol{8} \boldsymbol{J} / \boldsymbol{K} \boldsymbol{g} /^{o} \boldsymbol{C}\right) \)
Subject: Physics
A transistor has \( \beta=40 . \) A change in
base current of \( 100 \mu \) A, produces
change in collector current
A. \( 40 \times 100 m A \)
в. \( (100-40) m A \)
c. \( (100+40) m A \)
D. \( 100 / 40 m A \)
Subject: Maths
\( n(\geq 5) \) persons are sitting in a row. Three of these are selected at random,
the probability that no two of the
selected persons are together is This question has multiple correct options
\( ^{\mathbf{A}} \cdot \frac{n-3}{^{n} P_{2}} P_{2} \)
в. \( \frac{n-3}{^{n} C_{2}} \)
c. \( \frac{(n-3)(n-4)}{n(n-1)} \)
D. \( \frac{n-3}{n P_{2}} \)
Subject: Chemistry
If 0.5 mole of silver salt is taken and the
weight of residue obtained is 216 g. \( (\mathrm{Ag} \) \( =108 \mathrm{g} / \mathrm{mol} \) ).Than which the following
is correct?
\[
\begin{array}{c}
C_{2} H_{3} \\
(C \quad H-C O O H)_{3}+ \\
C_{2} H_{3} \\
A g N O_{3}(E x c e s s) \longrightarrow S i l v e r s a l t \longrightarrow \\
A g(m e t a l)
\end{array}
\]
\( \mathbf{A} \cdot n=4 \)
B \( . n=2 \)
C. M.wt. of silver salt is 718 g/mol
D. M.wt. of silver salt is \( 388 \mathrm{g} / \mathrm{mol} \)
Subject: Maths
A tank contains \( 40 l \) of solution
containing \( 2 g \) of substance per liter.
Salt water containing \( 3 g \) of this
substance per liter runs in at the rate of \( 4 l / m i n \) and the well-stirred mixture
runs out at the same rate. Find the
amount of substance in the tank after
15minutes (in grams).
A. 110.075
в. 121.075
c. 111.075
D. 211.075
Subject: Maths
Range of \( \boldsymbol{y}=\log _{\frac{3}{4}}(\boldsymbol{f}(\boldsymbol{x})) \)
\( A \cdot(-\infty, 1] \)
в. \( \left[\frac{3}{4}, \infty\right) \)
\( c \cdot(-\infty, \infty) \)
D. \( R \)
Subject: Maths
If \( f(x)=x^{\frac{1}{x}} \) then \( f^{\prime \prime}(e) \) is equal to
B \( \cdot e^{1 / e} \)
\( \mathbf{c} \cdot e^{1 /(e-2)} \)
D. \( \left.-e^{((1 / e)-3}\right) \)
Subject: Physics
The motion of a particle executing SHM is given by \( \boldsymbol{x}=\mathbf{0 . 0 1} \sin 100 \pi(\boldsymbol{t}+\mathbf{0 . 0 5}) \)
where \( x \) is in metre and \( t \) in second. The
time period of motion(in second) is:
A . 0.01
B. 0.02
c. \( 0 . \)
D. 0.2
Subject: Maths
\( \boldsymbol{A}=(\mathbf{2}, \mathbf{4}, \mathbf{5}) \) and \( \boldsymbol{B}=(\mathbf{3}, \mathbf{5},-\mathbf{4}) \) are two
points. If the \( X Y \) -plane, \( Y Z \) -plane divide \( A B \) in the ratio \( a: b \) and \( p: q \)
respectively, then \( \frac{a}{b}+\frac{p}{q}= \)
A \( \cdot \frac{23}{12} \)
B. \( \frac{-7}{12} \)
c. \( \frac{7}{12} \)
D. \( \frac{-22}{15} \)
Subject: Physics
A hollow cylinder has mass \( M \) outside
radius \( R_{2} \) and inside radius \( R_{1} \).Its
moments of inertia about an axis
parallel to its symmetry axis and tangent to the outer surface in equal to:
\( ^{\mathrm{A}} \cdot \frac{M}{2}\left(R_{2}^{2}+R_{1}^{2}\right) \)
B. \( \frac{M}{2}\left(R_{2}^{2}-R_{1}^{2}\right) \)
c. \( \frac{M}{4}\left(R_{2}+R_{1}\right)^{2} \)
D. \( \frac{M}{2}\left(3 R_{2}^{2}+R_{1}^{2}\right) \)
Subject: Chemistry
In a 500 ml flask, the degree of
dissociation of \( \boldsymbol{P C l}_{5} \) at equilibrium is
\( 40 \% \) and the initial amount is 5 moles.
The value of equilibrium constant in
mol.lit \( ^{-1} \) for the decomposition of
\( \boldsymbol{P C l}_{5} \) is :
A . 2.33
B . 2.66
\( c .5 .32 \)
D. 4.66
Subject: Physics
One calorie is defined as the heat
required to raise the temperature of 1
\( \mathrm{gm} \) of water by \( 1^{\circ} \mathrm{C} \) in a certain interval
of temperature and at certain pressure. The temperature interval and pressure is?
A \( \cdot 13.5^{\circ} \mathrm{C} \) to \( 14.5^{\circ} \mathrm{C} \& 76 \mathrm{mm} \) of \( \mathrm{Hg} \)
B . \( 6.5^{\circ} \mathrm{C} \) to \( 7.5^{\circ} \mathrm{C} \& 76 \mathrm{mm} \) of \( \mathrm{Hg} \)
C. \( 14.5^{\circ} \mathrm{C} \) to \( 15.5^{\circ} \mathrm{C} \& 760 \mathrm{mm} \) of \( \mathrm{Hg} \)
D. \( 98.5^{\circ} \mathrm{C} \) to \( 99.5^{\circ} \mathrm{C} \& 760 \mathrm{mm} \) of \( \mathrm{Hg} \)
Subject: Chemistry
\( \mathbf{A} \)
0.1 molar solution of \( N a C l \) is found
to be isotonic with \( 1 \% \) urea solution.
Calculate
(a) Van't Hoff factor
(b)Degree of dissociation of sodium
chloride.

Assume density of \( 1 \% \) urea equal to
\( 1 g c m^{-3} \)
\( \begin{array}{ll}\text { A. }(a) & 1.667, \text { (b) } 0.667\end{array} \)
В. (а) \( 1.82, \) (b) 0.69
Subject: Maths
A seven digit number is formed by using 0,1,2,3,4,8,9 without repetition. Then the probability that it is divisible by 4 is
A \( \cdot \frac{53 \times 4 !}{5 \times 6 !} ! \)
в. \( \frac{53}{180} \)
c. \( \frac{53}{6 \times 6 !} \)
D. None of these
Subject: Physics
A ray incident at a point at an angle of
incidence of \( 60^{\circ} \) enters a glass sphere of \( R . l . n=\sqrt{3} \) and is reflected and
refracted at the further surface of the
sphere. The angel between the reflected
and refracted rays at this surface is
\( \begin{array}{l}\text { A } .50^{\circ} \\ ^{\circ}\end{array}^{\circ}^{5^{\circ}} \)
В. \( 60^{\circ} \)
\( c \cdot 90^{\circ} \)
D. \( 40^{\circ} \)
Subject: Physics
Dimension of \( \epsilon_{0} \) are
\( \mathbf{A} \cdot\left[M^{0} L^{0} T^{0} A^{0}\right] \)
в. \( \left[M^{0} L^{-3} T^{3} A^{3}\right. \)
\( \mathbf{c} \cdot\left[M^{-1} L^{-3} T^{3} A^{1}\right] \)
\( \mathbf{D} \cdot\left[M^{-1} L^{-3} T^{4} A^{2}\right] \)
Subject: Physics
Assertion
The mass of a body cannot be
considered to be concentrated at the
centre of mass of the body for the
purpose of computing its moment of inertia.
Reason
Then the moment of inertia of every
body about an axis passing through its centre of mass would be zero.
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