AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
The temperature of equal masses of three different liquids \( A, B \) and \( C \) are
\( 12^{\circ} \mathrm{C}, 19^{\circ} \mathrm{C} \) and \( 28^{\circ} \mathrm{C} \) respectively. The
temperature when \( A \) and \( B \) are mixed is
\( 16^{\circ} \mathrm{C} \) and when \( \mathrm{B} \) and \( \mathrm{C} \) are mixed it is
\( 23^{\circ} \mathrm{C} . \) What should be the temperature
when \( A \) and \( C \) are mixed?
A \( \cdot 20.25^{\circ} \mathrm{C} \)
В. \( 15.87^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 25^{\circ} C \)
D. \( 30^{\circ} \mathrm{C} \)
Subject: Physics
A capillary tube is dipped in water vertically.Water rises to a height of 10mm. The tube is now tilted and makes
an angle \( 60^{\circ} \) with vertical.Now water
rises to a height of:
\( A \cdot 10 \mathrm{mm} \)
B. \( 5 \mathrm{mm} \)
c. \( 20 \mathrm{mm} \)
D. 40 mm
Subject: Physics
The moment of inertia of a circular disc
about an axis passing through the circumference perpendicular to the plane of the disc is
\( \mathbf{A} \cdot M R^{2} \)
B. \( \frac{3}{2} M R^{2} \)
c. \( \frac{M R^{2}}{2} \)
D. \( \frac{5}{4} M R^{2} \)
Subject: Physics
Assertion
Time-dependent magnetic field generates electric field
Reason
Direction of electric field generated
from time variable magnetic field does
obey Lenz's law.
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: Maths
If \( \boldsymbol{x}=\sqrt{\frac{1-\boldsymbol{t}^{2}}{1+\boldsymbol{t}^{2}}} \) and \( \boldsymbol{y}= \)
\( \frac{\sqrt{1+t^{2}}-\sqrt{1-t^{2}}}{\sqrt{1+t^{2}}+\sqrt{1-t^{2}}}, \) then the value of
\( \frac{d^{2} y}{d x^{2}} \) at \( t=0 \) is given by
A \( \cdot \frac{-1}{2} \)
B. \( \frac{1}{2} \)
c. \( \frac{-1}{4} \)
D. \( \frac{1}{4} \)
Subject: Physics
A cold Object \( A \) is placed on top of a hot object \( \mathrm{B} \) in a closed system. Identify which of the following is the best description of what occurs in the
system?
I. Both \( A \) and \( B \) eventually reach the
same temperature.
Il. Gravity stops heat from moving up into A.
III. Heat flows from A to B
A. I only
B. II only
C. I and III only
D. II and III only
E . ।, II, and III
Subject: Physics
Three concentric spherical shells have radii \( a, b \) and \( c(a<b<c) \) and have
surface charge densities \( +\boldsymbol{\sigma},-\boldsymbol{\sigma},+\boldsymbol{\sigma} \)
respectively. If \( V_{A}, V_{B} \) and \( V_{C} \) denote the potentials of three shells, then for \( c=a+b, \) we have
A. \( V_{C}=V_{B}=V_{A} \)
B. \( V_{C}=V_{B} \neq V_{A} \)
c. \( V_{C} \neq V_{B}=V_{A} \)
D. \( V_{C} \neq V_{B} \neq V_{A} \)
Subject: Chemistry
Read the table and answer the question
below:
\( \begin{array}{llllll}\text { Elements } & \boldsymbol{A} & \boldsymbol{B} & \boldsymbol{C} & \boldsymbol{D} & \boldsymbol{E} \\ \begin{array}{l}\text { MASS } \\ \text { NO. }\end{array} & 1 & 7 & 14 & 40 & 40 \\ \begin{array}{l}\text { Atomic } \\ \text { No. }\end{array} & 1 & 3 & 7 & 18 & 20\end{array} \)
Subject: Maths
Find the value of \( k \) for which \( f(x)= \) \( \left\{\begin{array}{l}\frac{1-\cos 4 x}{8 x^{2}}, \text { when } x \neq 0 \\ k, \quad \text { when } x=0\end{array}\right. \)
continuous at \( \boldsymbol{x}=\mathbf{0} \)
Subject: Maths
\( \operatorname{Let} A=\left[\begin{array}{lll}1 & 0 & 0 \\ 1 & 1 & 0 \\ 1 & 1 & 1\end{array}\right] \) and \( B=A^{10} \)
Then the sum of elements of the first
column of \( \boldsymbol{B} \) is
Subject: Chemistry
The molar heat capacities of lodine vapour and solid are 7.8 and 14 cal/mol respective enthalpy of
sublimation of iodine is 6096 cal \( / \) mol
\( \operatorname{at} 200^{\circ} C, \) then what is \( \Delta H \) the value at
\( 250^{\circ} \mathrm{C} \) in cal/mol.
A . 5360
в. 4740
\( c .6406 \)
D. none of these
Subject: Chemistry
Which of the following is a redox
reaction?
\( \mathbf{A} \cdot N a C l+K N O_{3} \rightarrow N a N O_{3}+K C l \)
B \( \cdot C a C_{2} O_{4}+2 H C l \rightarrow C a C l_{2}+H_{2} C_{2} O_{4} \)
\( \mathbf{c} \cdot M g(O H)_{2}+2 N H_{4} C l \rightarrow M g C l_{2}+2 N H_{4} O H \)
\( \mathbf{D} \cdot Z n+2 A g C N \rightarrow 2 A g+Z n(C N)_{2} \)
Subject: Chemistry
In aqueous solution, amino acids
mostly exist as:
A. \( H_{2} N-C H(R)-C O O H \)
в. \( H_{2} N-C H(R)-C O O \)
c. \( H_{3} N^{+}-C H(R)-C O O H \)
D. \( H_{3} N^{+} C H(R)-C O O^{-} \)
Subject: Chemistry
A certain mass of gas is expanded from \( (1 \mathrm{L} .10 \mathrm{atm}) \) to \( (4 \mathrm{L} .5 \mathrm{atm}) \) against a
constant external pressure of 1 atm. If
initial temperature of gas is \( 300 \mathrm{K} \) and
the heat capacity of process is \( 50 \mathrm{J} /^{\circ} \mathrm{C} \)
Then the enthalpy change during the process is: \( (-1 \mathrm{L} \text { atm } 100 \mathrm{J}) \)
A \( . \Delta H=15 \mathrm{kJ} \)
в. \( \Delta H=15.7 \mathrm{k} \)
c. \( \Delta H=14.4 \mathrm{kJ} \)
D. \( \Delta H=14.7 \mathrm{kJ} \)
Subject: Physics
Motion of bodies \( A \) and \( B \) is depicted by the \( x \) -t graph. Now consider the following statements (a), (b), (c) and (d) and select the incorrect option.
(a) A has uniform motion
(b) \( \mathrm{B} \) has less velocity than A initially
(e) B crosses A at a displacement X
(d) A comes to rest at a displacement \( x \)
\( A \cdot \) Only \( (a) \)
B. (b) and (c)
\( c \cdot(b),(c) \) and \( (d) \)
D. All of them
Subject: Physics
Assertion
If the angles of the base of the prism are
equal, then in the position of minimum deviation, the refracted ray will pass parallel to the base of prism.
Reason
In the case of minimum deviation, the
angle of incidence is equal to the angle
of emergence.
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: Physics
The drift velocity of electrons in a
conducting wire is of the order of
\( 1 m m / s, \) yet the bulb glows very quickly after the switch is put on because
A. the random speed of electrons is very high of the order of \( 10^{-6} \mathrm{m} / \mathrm{s} \)
B. the electrons transfer their energy very quickly through collision.
c. electric field is set up in the wire very quickly, producing a current through each cross section almost intantaneously
D. All the above
Subject: Physics
A bullet of mass \( 20 \mathrm{g} \) travelling horizontally with a speed of \( 500 \mathrm{m} / \mathrm{s} \)
passes through a wooden block of mass
10.0kg initially at rest on a surface. The bullet emerges with a speed of \( 100 \mathrm{m} / \mathrm{s} \)
and the block slides \( 20 \mathrm{cm} \) on the
surface before coming to rest, the coefficient of friction between the block
and the surface. \( \left(\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right) \)
A . 0.16
B. 0.8
c. 0.32
D. 0.24
Subject: Maths
Vectors \( \vec{A}, \vec{B} \) and \( \vec{C} \) are such that \( \vec{A} \) \( \vec{B}=0 . \) Then the vector parallel to \( \vec{A} \) is
A. \( \vec{B} \) and \( \vec{C} \)
в. \( \vec{A} \times \vec{B} \)
c. \( \vec{B}+\vec{C} \)
D. \( \vec{B} \times \vec{C} \)
Subject: Chemistry
Statement I : An indicator will allow to
determine whether a solution is acidic
or basic.
Statement II : Indicator will change
colors in solutions with different pH.
A. Statement I is True, Statement II is True and statement I is correct explanation of statements
B. Statement lis True, Statement II is True and statement II is NOT correct explanation of statements
c. Statement lis True, Statement II is False
D. Statement I is False, Statement II is True
E. Statement lis False, Statement II is False
Subject: Chemistry
Determine the change in oxidation
number of sulphur in \( H_{2} S \) and \( S O_{2} \) respectively in the following reaction.
\( 2 H_{2} S+S O_{2} \rightarrow 2 H_{2} O+3 S \)
A .0,+2
в. +2,-4
c. -2,+2
\( \mathbf{D} \cdot+4,0 \)
Subject: Chemistry
When potassium ferrocyanide crystals
are heated with conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}, \) the gas
evolved is:
\( A \cdot S O_{2} \)
B. \( N H_{3} \)
\( c \cdot C O_{2} \)
D. \( C O \)
Subject: Maths
\( \boldsymbol{x}=\sin \boldsymbol{t} \quad \boldsymbol{y}=\cos \boldsymbol{m} \boldsymbol{t} \)
Prove \( :\left(\boldsymbol{1}-\boldsymbol{x}^{2}\right) \boldsymbol{y}_{n+2}-(\boldsymbol{2} \boldsymbol{n}+\boldsymbol{1}) \boldsymbol{y}_{n+1}- \)
\( \left(\boldsymbol{n}^{2}-\boldsymbol{m}^{2}\right) \boldsymbol{y}_{n}=\boldsymbol{0} \)
Subject: Maths
Tne probability that Krishna will be alive
10 years is \( \frac{7}{15} \) and that Hari will be alive
is \( \frac{7}{10} . \) The probability that both Krishna
and Hari will be dead is -
A \( \cdot \frac{21}{150} \)
B. \( \frac{24}{150} \)
\( \mathbf{c} \cdot \frac{49}{150} \)
D. \( \frac{56}{150} \)
Subject: Physics
For a parallel beam of monochromatic light of wavelength \( ^{\prime} \lambda^{\prime}, \) diffraction is produced by a single slit whose width 'a is of the order of the wavelength of the light. If 'D' is the distance of the screen
from the slit, the width of the central
maxima will be
\( ^{\text {A }} \cdot \frac{D a}{\lambda} \)
B. \( \frac{2 D a}{\lambda} \)
c. \( \frac{2 D \lambda}{a} \)
D. \( \frac{D \lambda}{a} \)
Subject: Maths
Construct a \( \triangle A B C, \) when \( B C= \)
\( \mathbf{6 . 2} c \boldsymbol{m}, \boldsymbol{C A}=\mathbf{9 . 0} \boldsymbol{c m} \) and \( \angle \boldsymbol{B}=\mathbf{9 0}^{\circ} \)
Subject: Chemistry
Benzoic acid undergoes dimerization in benzene solution. The Van't Hoff factor \( i \)
is related to the degree of assoication \( \alpha \)
of the acid as :
B. \( i=1+(\alpha / 3) \)
c. \( i=1-(\alpha / 2) \)
D. \( i=1+(\alpha / 2) \)
Subject: Chemistry
Three isotopes of oxygen, each containing 8,9,10 neutrons respectively has the \( \% \) of one isotope (containing 8 neutrons) \( 90 \% . \) The abundance of other
isotopes is :
(The atomic weight of oxygen is 16.12 )
A . 7\%, 3\%
B. 5\%, 5\%
c. 8\%, २\%
D. none of these
Subject: Maths
The angle between the lines \( 2 x+ \)
\( 11 y-7=0 \)
and \( x+3 y+5=0 \) is equal to
A \( \cdot \tan ^{-1}\left(\frac{17}{31}\right) \)
B. \( \tan ^{-1}\left(\frac{11}{35}\right) \)
\( ^{\mathbf{c}} \cdot \tan ^{-1}\left(\frac{1}{7}\right) \)
D \( \cdot \tan ^{-1}\left(\frac{33}{35}\right) \)
E \( \cdot \tan ^{-1}\left(\frac{7}{33}\right) \)
Subject: Chemistry
Which one of the following has a potential more than zero?
A \( \cdot P t, \frac{1}{2} H_{2}(\operatorname{latm}) \mid H C l(1 M) \)
в. \( P t_{2} \frac{1}{2} H_{2}(1 a t m) \mid H C l(2 M) \)
c. \( \quad P t, \frac{1}{2} H_{2}(1 a t m) \mid H C l(0.1 M) \)
D \( \cdot \operatorname{Pt}, \frac{1}{2} H_{2}(1 \text { at } m) \mid H C l(0.5 M) \)
Subject: Physics
A person connects four \( \frac{1}{4} \Omega \) cells in
series but one cell has its terminal
reversed. The external resistance is \( 1 \Omega \)
If each cell has an emf of \( 1.5 \mathrm{V} \), the
current flowing is
A \( \cdot \frac{4}{3} A \)
B . \( \frac{3}{4} A \)
\( c \cdot 1.5 \mathrm{A} \)
D. zero
Subject: Physics
What is meant by power of a lens?
Define its SI unit.

You have two lenses \( A \) and \( B \) of focal lengths \( +10 \mathrm{cm} \) and \( -10 \mathrm{cm}, \) respectively. State the nature and power of each lens. Which of the two lenses will form a
virtual and magnified image of an object placed \( 8 \mathrm{cm} \) from the lens? Draw
a ray diagram to justify your answer.
Subject: Physics
Suppose refractive index \( \mu \) is given as \( \boldsymbol{\mu}=\boldsymbol{A}+\frac{\boldsymbol{B}}{\boldsymbol{\lambda}^{2}} \)
where \( A \) and \( B \) are constants and \( \lambda \) is
wavelength, then dimensions of B are
same as that of
A. Wavelength
B. volume
c. Pressure
D. Area
Subject: Chemistry
\( \Delta U^{\circ} \) of combustion of methane is \( -X \)
\( k J \) mol \( ^{-1} \). The value of \( \Delta H^{o} \) is:
\( A \cdot=\Delta U^{o} \)
В \( \cdot>\Delta U^{\circ} \)
\( \mathrm{c} \cdot<\Delta U^{\circ} \)
\( \mathrm{D} \cdot=0 \)
Subject: Physics
A point mass starts moving in a straight line with constant acceleration
"a". At a time \( t \) after the beginning of
motion, the acceleration changes sign,
without change in magnitude.
Determine the time \( t_{0} \) from the
beginning of the motion in which the
point mass returns to the initial
position.
\( \mathbf{A} \cdot(2+\sqrt{3}) t \)
B \( \cdot(2+\sqrt{2}) t \)
\( \mathbf{c} \cdot(3+\sqrt{2}) t \)
D. \( (12+\sqrt{2}) t \)
Subject: Physics
For an \( L C R \) series circuit with an A.C.
source of angular frequency \( \omega, \) which statement is correct?
A \cdot circuit will be capacitive if \( \omega>\frac{1}{\sqrt{L C}} \)
B. circuit will be capacitive if \( \omega=\frac{1}{\sqrt{L C}} \)
c. Power factor of circuit will be unity if capacitive reactance equals inductive reactance
D. current will be leading voltage if \( \omega>\frac{1}{\sqrt{L C}} \)
Subject: Chemistry
What is the maximum precision with which the momentum of an electron
can be known if the uncertainty in the position of electron is \( \pm \mathbf{0 . 0 0 1} \boldsymbol{A} \) ? Will there be any problem in describing the momentum if it has a value of \( \frac{\boldsymbol{h}}{\mathbf{2} \boldsymbol{\pi} \boldsymbol{a}_{\mathbf{0}}} \)
where \( a_{0} \) is Bohr's radius of first orbit,
i.e., 0.529 A?
Subject: Physics
Two soap bubbles \( A \) and \( B \) are kept in a
closed chamber where the air is
maintained at pressure \( 8 N / m^{2} . \) The radii of bubble \( A \) and \( B \) are 2 cm and
\( 4 \mathrm{cm}, \) respectively. Surface tension of the soap water used to make bubbles is \( 0.04 N / m . \) Find the ratio \( n B / n A \) where \( n A \) and \( n B \) are the number of
moles of air in bubbles \( A \) and \( B \)
respectively. (Neglect the effect of gravity).
Subject: Maths
A shop-keeper increases the price of
commodity by \( \boldsymbol{x} \% \). Some time later, he
reduces the new price by \( y \% \) and
notices that the price is now the same as it was originally. The value of \( \frac{1}{y}-\frac{1}{x} \)
İS
A \( \cdot-\frac{1}{100} \)
B. 0
c. \( \frac{1}{100} \)
D. not uniquely determinable
Subject: Chemistry
The reaction \( \left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{C}-\boldsymbol{B r} \rightarrow \)
\( \left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{C}^{+}+\boldsymbol{B r}^{-} \) is an example of:
A. homolytic fission
B. heterolytic fission
c. cracking
D. all of the above
Subject: Maths
Find \( k \) if \( P Q \| \) RS and
\( \boldsymbol{P}(\mathbf{2}, \boldsymbol{4}) \boldsymbol{Q}(\boldsymbol{3}, \boldsymbol{6}), \boldsymbol{R}(\boldsymbol{3}, \boldsymbol{1}), \boldsymbol{S}(\boldsymbol{5}, \boldsymbol{k}) \)
Subject: Chemistry
A series of reactions starting from allyl
chloride is shown.
In reaction \( 2, \) the organic product of reaction 1 is mixed with concentrated
\( H_{2} S O_{4} \) and an organic acid, and then
heated under reflux.
State the role of the concentrated
\( H_{2} S O_{4} \). Identify the organic acid used.
role of the concentrated \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
identity of the organic acid
Subject: Chemistry
Two isotopes of an elements \( Q \) are \( Q^{97} \)
(23.4\% abundance) and \( Q^{94} \) (76.6\%
abundance). \( Q^{97} \) is 8.082 times heavier
\( \operatorname{than} C^{12} \) and \( Q^{94} \) is 7.833 times
heavier than is \( C^{12} \). What is the average
atomic weight of the elements \( Q ? \)
A .94 .702
B. 78.913
c. 96.298
D. 94.695
Subject: Chemistry
The correct order of increasing ionic character is:
A. \( B e C l_{2}<M g C l_{2}<C a C l_{2}<B a C l_{2} \)
в. \( B e C l_{2}<C a C l_{2}<M g C l_{2}<B a C l_{2} \)
c. \( B a C l_{2}<C a C l_{2}<M g C l_{2}<B e C l_{2} \)
D. \( M g C l_{2}<C a C l_{2}<B e C l_{2}<B a C l_{2} \)
Subject: Chemistry
Which is the best description of the
behaviour of bromine in the reaction
given below?
\( \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{B} \boldsymbol{r}_{2} \rightarrow \boldsymbol{H} \boldsymbol{O} \boldsymbol{B} \boldsymbol{r}+\boldsymbol{H} \boldsymbol{B} \boldsymbol{r} \)
A. Proton acceptor only
B. Both oxidised and reduced
c. oxidised only
D. Reduced only
Subject: Chemistry
The bond dissociation energies of the following \( \boldsymbol{C H}_{3}-\boldsymbol{H} \boldsymbol{C H}_{3} \boldsymbol{C H}_{2}-\boldsymbol{H} ; \boldsymbol{C H}_{2}=\boldsymbol{C H} \)
vary in the order of:
\( A \cdot|>||>|||>\mid V \)
B. IV>|||> || > |
c. \( |V>|>||>|| \mid \)
Subject: Chemistry
\( \mathbf{A} \)
\( 3 \mathrm{M} \)
3L solution of NaOH is mixed with
another \( 3 \mathrm{M} \) 5L solution of \( \mathrm{NaOH} \). How
much should the mixture be diluted so
that the final molarity of the solution becomes 1M?
Subject: Maths
What should be taken away from \( 3 x^{2}- \) \( 4 y^{2}+5 x y+20 \) to \( \operatorname{get}-x^{2}-y^{2}+ \)
\( 6 x y+20 \)
A \( \cdot x^{2}-y^{2}-x y \)
в. \( x^{3}-3 y^{2}-x y \)
c. \( x^{2}-y^{3}-x y \)
D. \( 4 x^{2}-3 y^{2}-x y \)
Subject: Chemistry
\( 25 g \) of an unknown hydrocarbon upon
burning produces \( 88 g \) of \( C O_{2} \) and \( 9 g \) of
\( H_{2} O . \) This unknown hydrocarbon
contains.
A. \( 20 g \) of carbon and \( 5 g \) of hydrogen
B. \( 24 g \) of carbon and \( 1 g \) of hydrogen
c. \( 18 g \) of carbon and \( 7 g \) of hydrogen
D. \( 22 g \) of carbon and \( 3 g \) of hydrogen
Subject: Maths
Prove that, \( \left(^{2 n} C_{1}\right)^{2}+2 \cdot\left(^{2 n} C_{1}\right)^{2}+ \)
3. \( \left(^{2 n} C_{3}\right)^{2}+\ldots .+2 n .\left(^{2 n} C_{2 n}\right)^{2}= \)
\( \frac{(4 n-1) !}{\{(2 n-1) !\}^{2}} \)
Subject: Maths
Solve the following pair of equations:
\( \frac{\mathbf{9}}{\boldsymbol{x}}-\frac{\mathbf{4}}{\boldsymbol{y}}=\mathbf{8}, \frac{\mathbf{1 3}}{\boldsymbol{x}}+\frac{\mathbf{7}}{\boldsymbol{y}}=\mathbf{1 0 1} \)
A \( \cdot x=\frac{2}{3} ; y=\frac{4}{3} \)
B. \( x=\frac{1}{4} ; y=\frac{1}{7} \)
c. \( x=\frac{5}{4} ; y=\frac{2}{5} \)
D. \( x=\frac{3}{2} ; y=\frac{6}{5} \)
Subject: Maths
The value of \( \frac{\mathbf{3 6}}{\boldsymbol{\pi}} \int_{\boldsymbol{\pi} / \boldsymbol{6}}^{\boldsymbol{\pi} / \boldsymbol{3}} \frac{\boldsymbol{d} \boldsymbol{x}}{\boldsymbol{1}+\sqrt{\cot \boldsymbol{x}}} \) is
Subject: Chemistry
Which of the following statement is not
correct?
\( \mathbf{A} \cdot L a(O H)_{3} \) is less basic than \( L u(O H)_{3} \)
B. In lanthanide series ionic radius of \( L n^{3+} \) ion
decreases.
C. La is actually an element of transition series rather lanthanide.
D. Atomic radius of Zr and Hf are same because of lanthanide contraction.
Subject: Maths
The average of \( 1 \frac{1}{6}, 2 \frac{1}{3}, 6 \frac{2}{3} \) and \( 8 \frac{5}{6} \) is
A \( \cdot 6 \frac{3}{4} \)
в. \( _{5} \frac{3}{4} \)
c. \( _{4} \frac{3}{4} \)
D. \( _{3} \frac{3}{4} \)
Subject: Chemistry
Substances used in two different
projects done by the members of a science club are given in the table.
Project - 1

Project - 2
Ethanoic acid
Ethanol
concentrated sulphuric acid
water
(a) In which project (Project 1 or Project
2) a compound with pleasant fruity smell is formed?
(b) How will you distinguish between distilled water and hard water by using the precipitate formed in Project 2 ?
Subject: Physics
The captain of a plane wishes to proceed due west. The cruising speed of the plane is \( 245 m / s \) relative to the air.
A weather report indicates that a
\( 38 m / s \) wind is blowing from the south to the north. In what direction, measured to due west, should the pilot
head the plane relative to the air? (in
degrees)
\( A \cdot 8 \)
B. 9
\( c .6 \)
D. 5
Subject: Physics
A Zener diode, having breakdown
voltage equal to \( 15 V \) is used in a
voltage regulator circuit shown in
figure. The current through the diode is
\( A \cdot 10 m A \)
B. \( 15 m A \)
\( c \cdot 20 m A \)
\( \mathbf{D} \cdot 5 m A \)
Subject: Maths
If in \( N \times N, R \) is a relation defined by
the formula \( (x, y) R(p, q) \) if and only if
\( \boldsymbol{x}+\boldsymbol{q}=\boldsymbol{y}+\boldsymbol{p}, \) show that \( \mathrm{R} \) is an
equivalence relation
Subject: Chemistry
Which of the following statements are
correct?
A. A meso compound has chiral centres but exhibits no optical activity
B. A racemic mixture is optically inactive because of two equal and opposite rotation of same isomers of the molecules in the mixture.
C. A meso compound has molecules which are superimpossible on their mirror images even though they contain chiral centres
D. a meso compound is optically inactive because the rotation caused by any molecule is cancelled by equal and opposite rotation caused by another molecules that is the mirror image of the first.
Subject: Maths
Let \( x=2 \) be a root of \( y=4 x^{2}-14 x+ \)
\( \boldsymbol{q}=\mathbf{0} . \) Then \( \boldsymbol{y} \) is equal to
A \( \cdot(x-2)(4 x-6) \)
В. \( (x-2)(4 x+6) \)
c. \( (x-2)(-4 x-6) \)
D. \( (x-2)(-4 x+6) \)
Subject: Maths
The value of
\( \sin ^{-1}\left(\cot \left(\sin ^{-1} \sqrt{\frac{2-\sqrt{3}}{4}}+\cos ^{-1} \frac{\sqrt{2}}{2}\right)\right. \)
is
A . 0
B. \( \frac{\pi}{2} \)
\( c \cdot \frac{\pi}{3} \)
D. none of these
Subject: Physics
In a p-n-p transistor, working as a common base amplifier, current gain is 0.96 and emitter current is \( 7.2 \mathrm{mA} \). The
base current is
\( A \cdot 0.20 \mathrm{mA} \)
B. 0.36 mA
c. \( 0.29 \mathrm{mA} \)
D. \( 0.45 \mathrm{mA} \)
Subject: Maths
Simplify \( \tan ^{-1}\left(\frac{6 x}{1-8 x^{2}}\right) \)
\( A \cdot \tan ^{-1} 2 x+\tan ^{-1} 4 x \)
B. \( \tan ^{-1} 2 x-\tan ^{-1} 4 x \)
c. \( -\tan ^{-1} 2 x-\tan ^{-1} 4 x \)
D. \( 2 \tan ^{-1} 2 x-\tan ^{-1} 4 x \)
Subject: Physics
In the circuit shown, a \( 30 \mathrm{V} \) d.c source
gives a current \( 2.0 \mathrm{A} \) as recorded in the
ammeter \( A \) and \( 30 V \) a.c. source of
frequency \( 100 \mathrm{Hz} \) gives a current \( 1.2 \mathrm{A} \)
The inductive reactance is
\( A \cdot \) 10ohm
B. 20 ohm
\( \mathbf{c} \cdot 5 \sqrt{34} \) ohm
D. 40 ohm
Subject: Maths
The ratio in which the plane \( \vec{r} .(\hat{i}-2 \hat{j}+ \) \( \mathbf{3} \hat{k})=17 \) divides the line joining the points \( (-2 \hat{i}+4 \hat{j}+7 \hat{k}) \) and \( (3 \hat{i}-5 \hat{j}+ \)
\( \mathbf{8} \hat{\boldsymbol{k}}) \) is
A .1: 5
B. 1: 10
\( c .3: 5 \)
D. 3: 10
Subject: Physics
A ball of mass \( m \) is fired vertically upwards from the surface of the earth
with velocity \( n \nu_{e}, \) where \( \nu_{e} \) is the
escape velocity and \( n>1 . \) To what height will the ball rise? Neglecting air resistance, take radius of the earth as
\( \boldsymbol{R} \)
A \( \cdot \frac{R}{n^{2}} \)
в. \( \frac{R}{\left(1-n^{2}\right)} \)
c. \( \frac{R n^{2}}{\left(1-n^{2}\right)} \)
D. \( R n^{2} \)
Subject: Chemistry
\( \mathbf{A} \)
0.1 M solution of a monobasic acid
has a specific resistance of 'r' ohm-cm. Its molar conductivity is:
A \( \cdot \frac{10}{r} \)
в. \( 10 r \)
c. \( \frac{10^{4}}{r} \)
D. \( \frac{10^{4}}{2 r} \)
Subject: Physics
The wind appears to blow from north to
a man moving in the north-east
direction. When he doubles his velocity,
the wind appears to move in the
direction cot \( ^{-1} \)
(2) east of north. If the
actual magnitude of velocity of the wind
is \( V=\frac{1}{\sqrt{x}} \times \) magnitude of velocity of
man and direction along east. Find \( x \)
Subject: Maths
\( \int \sqrt{\frac{\cos x-\cos ^{3} x}{1-\cos ^{3} x}} \cdot d x \) is equal to
A \( \cdot \frac{2}{3} \sin ^{-1}\left(\cos ^{3 / 2} x\right)+C \)
B. \( \frac{3}{2} \sin ^{-1}\left(\cos ^{3 / 2} x\right)+C \)
C \( \cdot \frac{2}{3} \cos ^{-1}\left(\cos ^{3 / 2} x\right)+C \)
D. none of these
Subject: Physics
A stationary man observes that the rain
strikes him at an angle of \( 60^{\circ} \) to the horizontal. When he begins to move with
the velocity of \( 25 m / s \) then the drops
appear to strike him at an angle \( 30^{\circ} \)
from horizontal. The velocity of the rain drops is :
\( \mathbf{A} \cdot 25 m / s \)
B. \( 50 \mathrm{m} / \mathrm{s} \)
c. \( 12.5 m / s \)
D. \( 25 \sqrt{2} \)