AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Reactions which involve
disproportionation of the oxides of nitrogen :
This question has multiple correct options
A \( \cdot 2 N O_{2}+H_{2} O \longrightarrow H N O_{3}+H N O_{2} \)
в. \( N_{2} O_{4} \rightarrow N O^{+}+N O_{3}^{\text {}} \)
c. \( 3 H N O_{2} \longrightarrow H N O_{3}+2 N O+H_{2} O \)
D. \( 3 N O \longrightarrow N_{2} O+N O_{2} \)
Subject: Chemistry
What is the mass of \( 6.022 \times 10^{23} \)
formula units of \( \left(N H_{4}\right)_{2} S O_{4} ? \)
A. \( 234.11 g \)
в. \( 132.11 g \)
c. \( 210.29 g \)
D. \( 342.14 g \)
Subject: Maths
If the area of the closed figure bounded by the following curves \( \boldsymbol{y}=\boldsymbol{x}^{2}, \boldsymbol{y}=\mathbf{2}- \)
\( \boldsymbol{x}, \boldsymbol{y}=\mathbf{0} \) is k. Find \( 6 \mathbf{k} \)
Subject: Physics
The electron in a hydrogen atom makes
a transition \( n_{1} \rightarrow n_{2} \) whose \( n_{1} \) and \( n_{2} \)
are the principal quantum numbers of the two states. Assume the Bohr model
to be valid. The frequency of orbital
motion of the electron in the initial
state is \( 1 / 27 \) of that in the final state.
The possible value of \( n_{1} \) and \( n_{2} \) are
\( \mathbf{A} \cdot n_{1}=4, n_{2}=2 \)
B \( . n_{1}=3, n_{2}=1 \)
\( \mathbf{c} \cdot n_{1}=8, n_{2}=1 \)
\( \mathbf{D} \cdot n_{1}=6, n_{2}=3 \)
Subject: Physics
What displacement at an angle \( 60^{\circ} \) the \( x \) -axis has an \( x \) -component of \( 5 m ? \hat{i} \) and \( \hat{j} \) are unit vectors in \( x \) and \( y \) directions, respectively.
A . \( 5 i \)
B. \( 5 \hat{i}+5 \hat{j} \)
c. \( 5 \hat{i}+5 \sqrt{3} \hat{j} \)
D. All of the above
Subject: Chemistry
Assertion: The solubility of
\( \boldsymbol{C H}_{3} \) COOAg in water considering
hydrolysis of \( C H_{3} C O O^{-} \) ions would be
greater than that ignoring the hydrolysis. Reason: During hydrolysis, the concentration of acetate ions decrease
as they combine with hydrogen ions to
form acetic acid.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
C. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false
Subject: Maths
\( A B C D \) is a parallelogram with side \( A B=10 \mathrm{cm} . \) Its diagonals \( A C \) and \( B D \)
are of length \( 12 \mathrm{cm} \) and \( 16 \mathrm{cm} \) respectively. Find the area of a
parallelogram \( \boldsymbol{A B C D} \)
Subject: Maths
Let \( \mathrm{R} \) be a relation from \( \mathrm{N} \) to \( \mathrm{N} \) defined
by \( R=\left\{(a, b): a, b \in N \text { and } a=b^{2}\right\} . \) Is
the following statement is true for \( (\boldsymbol{a}, \boldsymbol{a}) \in \boldsymbol{R} \forall \boldsymbol{a} \in \boldsymbol{N} \)
A. True
B. False
Subject: Chemistry
Write the IUPAC names of the given
compounds:
\[
\begin{array}{c}
\mathrm{cl}-\mathrm{CH}_{2}-\mathrm{c}-\mathrm{CH}_{2}-\mathrm{CH}-\mathrm{CH}_{3} \\
\mathrm{O}
\end{array} \mathrm{CH}_{3}
\]
Subject: Physics
A rod AB moves with a uniform velocity
\( v \) in a uniform magnetic field as shown in figure.
\( \begin{array}{llllll}\mathbf{X} & \mathbf{X} & \mathbf{X} & \mathbf{A} & \mathbf{X} & \mathbf{X} & \mathbf{X} \\ \mathbf{X} & \mathbf{X} & \mathbf{X} & \mathbf{n} & \mathbf{X} & \mathbf{X} & \mathbf{X} \\ \mathbf{X} & \mathbf{X} & \mathbf{X} & \mathbf{n} & \mathbf{X} & \mathbf{X} & \mathbf{X} \\ \mathbf{X} & \mathbf{X} & \mathbf{X} & \mathbf{B} & \mathbf{X} & \mathbf{X} & \mathbf{X}\end{array} \)
A. The rod becomes electrically charged
B. The end A becomes positively charged
c. The end B become positively charged
Subject: Maths
Answer the following question in one word or one sentence or as per exact requirement of the question.
If \( \boldsymbol{f}(\mathbf{1})=\mathbf{1}, \boldsymbol{f}^{\prime}(\mathbf{1})=\mathbf{2}, \) then write the
value of \( \lim _{x \rightarrow 1} \frac{\sqrt{\boldsymbol{f}(\boldsymbol{x})}-\mathbf{1}}{\sqrt{\boldsymbol{x}}-\mathbf{1}} \)
Subject: Chemistry
Froth flotation process which is used for
the concentration of sulphide ore:
\( A . \) is based on the difference in wettability of different minerals
B. uses sodium ethyl xanthate, \( C_{2} H_{5} O C S_{2} N a \) as
collector
C. uses NaCN as depresent in the mixture of ZnS and PbS when ZnS forms soluble complex and PbS forms froth
D. All of the above are correct
Subject: Biology
In the following functional human lung studies, identify the total lung capacity.
A) Inspiratory capacity (IC)
B) Functional residual capacity (FRC)
C) Vital capacity (VC)
D) Inspiratory reserve volume (IRV)
E) Residual volume (RV)
F) Expiratory reserve volume (ERV)
G) Tidal volume (TV)
The correct answer is
\( A \cdot(D)+(F) \)
B. \( (A)+(D) \)
\( c \cdot(B)+(C) \)
\( D \cdot(c)+(E) \)
Subject: Maths
The probability distribution function of a random variable \( \boldsymbol{X} \) is given by
\( \boldsymbol{x}_{i}: \quad 0 \quad 1 \quad 2 \)
\[
\begin{array}{lll}
3 c & 4 c & c-1
\end{array}
\]
where \( c>0 . \) Find \( c \)
Subject: Physics
The graph of \( \ln \left(R / R_{O}\right) \) versus \( \ln A \) of nucleus is :
\( \left(R_{0} \text { is a constant } 1.2 \times 10^{-12}, \mathrm{R} \) is \right.
radius and \( A \text { is the atomic number }) \)
A. a straight line
B. a parabola
c. an ellipse
D. a circle
Subject: Maths
Which of the following are in inverse
proportion?
(i) The number of workers on a job and
the time to complete the job.
(ii) The time taken for a journey and the distance travelled in a uniform speed.
(iii) Area of cultivated land and the crop
harvested.
(iv) The time taken for a fixed journey and the speed of the vehicle.
(v) The population of a country and the area of land per person.
Subject: Physics
Consider the situation shown in the
figure. The capacitor A has a charge \( q \) on
it, whereas \( \mathrm{B} \) is uncharged. The charge
appearing on the capacitor \( \mathrm{B} \), after a long time of closing the switch is:
A. zero
B. \( \frac{q}{2} \)
\( c \cdot q \)
D. \( 2 q \)
Subject: Chemistry
toppr
Q Type your question-
magnetic field shows that the atoms
must have magnetic moment. However,
the moment cannot be due to the orbital
angular momentum since \( \varphi=0 . \) Hence
one must assume existence of intrinsic
angular momentum, which as the experiment shows, has only two permitted orientations. Spin of the electron produces angular momentum equal to \( s=\sqrt{s(s+1)} \frac{h}{2 \pi} \)
where \( s=+\frac{1}{2} \)
Total spin of an atom \( =+\frac{n}{2} o r-\frac{n}{2} \)
where \( n \) is the number of unpaired
electron
The Substance which contain species
with unpaired electrons in their orbitals
behave as paramagnetic substances.
The paramagnetism is expressed in terms of magnetic moment. The magnetic moment of an atom \( \boldsymbol{\mu}=\sqrt{\boldsymbol{s}(\boldsymbol{s}+\mathbf{1})} \frac{e h}{2 \pi \boldsymbol{m} c}=\sqrt{\frac{n}{2}\left(\frac{n}{2}+1\right)} \frac{e h}{2 \pi m c} \)
\( s=\frac{n}{2} \)
\( \boldsymbol{\mu}_{s}=\sqrt{\boldsymbol{n}(\boldsymbol{n}+\mathbf{2})} \mathbf{B} . \mathbf{M} \)
n-number of upaired electrons
1.B.M. (Bohr magneton) \( =\frac{e h}{4 \pi m c} \)
f magnetic moment is zero the substance is di-magnetic.
Which of the following ion has highest magnetic moment?
A \( \cdot F e^{2} \)
в. \( M n^{2} \)
\( c \)
D. \( V 3+ \)
Subject: Chemistry
Simultaneous solubility of \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{C} \boldsymbol{N} \boldsymbol{S}(\boldsymbol{a}) \)
and \( A g B r(b) \) in a solution of water will
be
\( \boldsymbol{K}_{s p_{(A g B r)}}=\mathbf{5} \times \mathbf{1 0}^{-13} \) and \( \boldsymbol{K}_{s p_{(A g C N S)}}= \)
\( 10^{-12} \)
A \( \cdot a=4.08 \times 10^{-7} \) mol litre \( ^{-1} ; b=8.16 \times 10^{-7} \) mollitre \( ^{-1} \)
В . \( a=4.08 \times 10^{-7} \) mol litre \( ^{-1} ; b=4.08 \times 10^{-7} \) mollitre \( ^{-1} \)
\( \mathbf{c} \cdot a=8.16 \times 10^{-7} \)mollitre\( ^{-1} ; b=4.08 \times 10^{-7} \)mollitre\( ^{-1} \)
D. None of these
Subject: Chemistry
A \( 10 \% \) solution (by mass) of sucrose in water has a freezing point of \( 269.15 K \)
Calculate the freezing point of \( 10 \% \) glucose in water if the freezing point of
pure water is \( 273.15 K \)
(Given : molar mass of sucrose \( = \)
\( 342 g \) mol \( ^{-} ?, \) Molar mass of glucose \( = \)
\( \left.180 g m o l^{-1}\right) \)
A. 275. 53 K
B. 265. 53 K
c. २७१. 32 \( \mathrm{K} \)
D. 282.43 K
Subject: Physics
A metal wire of mass \( m \) slides without
friction on two rails at distance \( d \) apart.
The track is in a vertical uniform field of
induction \( \vec{B} \). A constant current \( \vec{i} \) flows
along one rail across the wire and back down the other rail the velocity of the wire as a function of time, assuming it to be at rest initially.
A \( \cdot \frac{B i d}{m} \)
в. \( \frac{B i d t}{m} \)
c. \( \frac{m}{\text { Bidt }} \)
D. None of the above
Subject: Physics
When the sun rays are incident at an
angle of \( 60^{0} \) then intensity is \( I . \) What will be the intensity if the sun rays are
incident at \( 30^{\circ} ? \)
A \( \cdot \frac{I}{\sqrt{3}} \)
B. \( \sqrt{3} I \)
c. \( 3 I \)
D. \( \frac{1}{3} \)
Subject: Chemistry
A \( 0.5 ~ M \) Na \( O H \) solution offers a
resistance of 31.6 ohm in a
conductivity cell at room temperature. What shall be the approximate molar conductance of this \( N a O H \) solution if
cell constant of the cell is \( 0.367 \mathrm{cm}^{-1} ? \)
A \( \cdot 234 S \mathrm{cm}^{2} \) mole \( ^{-1} \)
B. \( 23.2 \mathrm{S} \mathrm{cm}^{2} \) mole \( ^{-1} \)
c. \( 4645 S \mathrm{cm}^{2} \) mole \( ^{-1} \)
D. \( 5464 S \mathrm{cm}^{2} \) mole \( ^{-1} \)
Subject: Physics
On observing light from three different stars \( P, Q \) and \( R, \) it was found that
intensity of violet colour is maximum in
the spectrum of \( P, \) the intensity of green colour is maximum in the spectrum of
\( \mathrm{R} \) and the intensity of red colour is maximum in the spectrum of Q. If
\( T_{P}, T_{Q} \) and \( T_{R} \) are the respective absolute temperature of \( P, Q \) and \( R, \) then it can be concluded from the above
observations that
\( \mathbf{A} \cdot T_{P}<T_{R}<T_{Q} \)
В \( \cdot T_{P}<T_{Q}<T_{R} \)
\( \mathbf{c} \cdot T_{P}>T_{Q}>T_{R} \)
\( \mathbf{D} \cdot T_{P}>T_{R}>T_{Q} \)
Subject: Maths
Two adjacent sides of a parallelogram are \( 10 \mathrm{cm} \) and \( 12 \mathrm{cm} . \) If one diagonal of
it is \( 16 \mathrm{cm} \) long; find area of the
parallelogram. Also, find distance between its shorter sides.
A \( \cdot 119.8 \mathrm{cm}^{2} ; 11.98 \mathrm{cm} \)
B . \( 119.9 \mathrm{cm}^{2} ; 11.20 \mathrm{cm} \)
\( \mathrm{c} \cdot 117.6 \mathrm{cm}^{2} ; 10.28 \mathrm{cm} \)
D. \( 120.8 \mathrm{cm}^{2} ; 15.98 \mathrm{cm} \)
Subject: Physics
If the earth is treated as a sphere of
radius \( R \) and mass \( M, \) its angular
momentum about the axis of its
rotation with period \( \boldsymbol{T} \) is
A \( \cdot \frac{4 \pi M R^{2}}{5 T} \)
в. \( \frac{2 \pi M R^{2}}{5 T} \)
\( ^{\mathrm{c}} \cdot \frac{M R^{2} T}{T} \)
D. \( \frac{\pi M R^{3}}{T} \)
Subject: Physics
A large sheet carries uniform surface charge density \( \sigma . \) A rod length \( 2 l \) has a linear charge density \( \lambda \) on one half and \( -\lambda \) on the second half. The rod is hinged at the midpoint 0 and makes and angle \( \theta \) with the normal to the sheet. The
torque experienced by the rod is:
\( A \cdot O \)
B. \( \frac{\sigma \lambda l^{2}}{2 \varepsilon_{0}} \sin \theta \)
\( ^{\text {c. }} \frac{\sigma \lambda l^{2}}{\varepsilon_{0}} \sin \theta \)
D. \( \frac{\sigma \lambda l}{2 \varepsilon_{0}} \)
Subject: Chemistry
The mass of carbon anode consumed
(giving the only carbon dioxide) in the production of \( 270 \mathrm{kg} \) of aluminium
metal from bauxite by the Hall process is:
[Atomic mass : \( A l=27] \)
A. \( 90 \mathrm{kg} \)
в. \( 540 \mathrm{kg} \)
c. \( 180 \mathrm{kg} \)
D. 270 \( k g \)
Subject: Chemistry
Assertion
\( 35 C l \) and \( _{17}^{37} C l \) have the same chemical
\( 17^{7} \)
properties.
Reason
Isotopes have the same number of
protons and electrons and the same
chemical reactions.
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
A circle passes through (0,0) and (1,0) and touches the circle \( x^{2}+y^{2}=9 \)
then the centre of circle is
\( ^{\mathbf{A}} \cdot\left[\frac{3}{2}, \frac{1}{2}\right] \)
В. \( \left[\frac{1}{2}, \frac{3}{2}\right] \)
c. \( \left[\frac{1}{2}, \frac{1}{2}\right] \)
D. \( \left[\frac{1}{2}, \pm \sqrt{2}\right] \)
Subject: Chemistry
The IUPAC name for
\( \left[\boldsymbol{N} \boldsymbol{i}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right]\left[\boldsymbol{N} \boldsymbol{i} \boldsymbol{C l}_{4}\right] \) is :
A. Tetrachloridonickel(II)-tetraamminenickel(II)
B. Tetraamminenickel(II)-tetrachloridonickel(II)
C. Tetraamminenickel(II)-tetrachloronickelate(II)
D. Tetrachloridonickel(II)-tetraamminenickelate(II)
Subject: Chemistry
\( 20 m L \) of \( 0.1 N \) acetic acid is mixed
with \( 10 m L \) of \( 0.1 N \) solution of \( N a O H \)
The \( p H \) of the resulting solution is :
\( \left[\text { Given }: p K_{a} \text { of acetic acid is } 4.74\right] \)
A . 3.74
в. 4.74
\( c .5 .74 \)
D. 6.74
Subject: Physics
It takes 16 min to boil some water in
an electric kettle. Due to some defect it
becomes necessary to remove \( 10 \% \) turns of the heating coil of the kettle. After repairs, how much time will it take
to boil the same mass of water?
A. 17.7 min
B. 14.4 min
c. 20.9 min
D. 13.7 min
Subject: Physics
A man stands at one end of the open
truck which can run on frictionless
horizontal rails. Initially, the man and the truck are at rest. Man now walks to
the other end and stops. Then which of the following is true?
A. The truck moves opposite to direction of motion of the man even after the man ceases to walk
B. The centre of mass of the man and the truck remains at the same point throughout the man's walk
C. The kinetic energy of the man and the truck are exactly equal throughout the man's walk.
D. The truck does not move at all during the man's walk
Subject: Maths
The complete set of values of \( x \)
satisfying equation \( \cot x-\cos x= \)
\( 1-\cot x \cos x \) is
A \( \cdot\left\{x: x=(4 n \pi+1) \frac{\pi}{4}, n \in I\right\} \)
в. \( \left\{x: x=2 n \pi+\frac{\pi}{4}, n \in I\right\} \)
C \( \cdot\{x: x=2 n \pi \pm \pi, n \in I\} \)
D \( \cdot\{x: x=2 n \pi+\pi, n \in I\} \cup\left\{x: x=n \pi+\frac{\pi}{4}, n \in I\right\} \)
Subject: Physics
The distance between the two point
masses \( \boldsymbol{m}_{1} \) and \( \boldsymbol{m}_{2} \) is d. Now, the
distance between them is reduced by two-thirds, Calculate by which factor
new gravitational force would be change?
A. It increases by a factor of 9
B. It increases by a factor of \( \frac{4}{9} \)
c. It increases by a factor of 3
D. It decreases by factor of 9
E. It decreases by a factor of 3
Subject: Physics
A body travels \( 200 \mathrm{cm} \) in the first two
seconds and \( 220 \mathrm{cm} \) in the next 4 seconds with deceleration. The velocity
of the body at the end of the \( 7^{\text {th }} \) second
is
\( A \cdot 20 \mathrm{cm} / \mathrm{s} \)
B. \( 15 \mathrm{cm} / \mathrm{s} \)
c. \( 10 \mathrm{cm} / \mathrm{s} \)
D. \( 0 \mathrm{cm} / \mathrm{s} \)
Subject: Physics
In a common emitter (CE) amplifier having a voltage gain \( G, \) the transistor
used has transconductance 0.03 mho
and current gain \( 25 . \) If the above transistor is replaced with another one with transconductance 0.02 mho and
current gain \( 20, \) the voltage gain will be
A \( \cdot \frac{2}{3} G \)
в. \( 1.5 G \)
c. \( \frac{1}{3} G \)
D. \( \frac{5}{4} G \)
Subject: Maths
If the sides of a parallelogram are \( 2 \hat{i}+ \) \( 4 \hat{j}-5 \hat{k} \) and \( \hat{i}+2 \hat{j}+3 \hat{k}, \) then the unit
vector parallel to one of the diagonals, is
A \( \cdot \frac{1}{7}(3 \hat{i}+6 \hat{j}-2 \hat{k}) \)
B \( \cdot \frac{1}{7}(3 \hat{i}-6 \hat{j}-2 \hat{k}) \)
c \( \cdot \frac{1}{7}(-3 \hat{i}+6 \hat{j}-2 \hat{k}) \)
D \( \cdot \frac{1}{7}(3 \hat{i}+6 \hat{j}+2 \hat{k}) \)
Subject: Chemistry
A monoprotic acid in a \( 0.1 \mathrm{M} \) solution
ionizes to \( 0.001 \% \). Its ionization
constant is:
A \( \cdot 1.0 \times 10^{-3} \)
В. \( 1.0 \times 10^{-6} \)
c. \( 1.0 \times 10^{-8} \)
D. \( 1.0 \times 10^{-1} \)
Subject: Maths
A pack contains 4 blue, 2 red and 3 black pens. If 2 pens are drawn at random from the pack, NOT replaced and then another pen is drawn. What is the probability of drawing 2 blue pens and 1 black pen?
A \( \cdot \frac{2}{9} \)
в. \( \frac{1}{14} \)
c. \( \frac{2}{63} \)
D. \( \frac{2}{14} \)
Subject: Physics
Assertion
Internal energy of a system is an
extensive property.
Reason
The internal energy of a system depends
upon the amount and physical state of
the substance.
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: Biology
Correct sequence of different phases of
growth is
A. Cell division \( \rightarrow \) Cell differentiation \( \rightarrow \) Cell elongation
B. Cell differentiation \( \rightarrow \) Cell division \( \rightarrow \) Cell elongation
C. Cell elongation \( \rightarrow \) Cell division \( \rightarrow \) Cell differentiation
D. Cell division \( \rightarrow \) Cell elongation \( \rightarrow \) Cell differentiation
Subject: Chemistry
A dilute ferrous sulphate solution was
gradually added to the beaker
containing acidified potassium
permanganate solution. The light purple colour of the solution fades and finally disappears. Which of the following is the correct explanation for the observation?
\( \mathbf{A} \cdot K M n O_{4} \) is an oxidising agent, it oxidises \( F e S O_{4} \)
B. \( F e S O_{4} \) acts as an oxidising agent and oxidises \( K M n O_{4} \)
C. The colour disappears due to dilution; no reaction is involved
D. \( K M n O_{4} \) is an unstable compound and decomposes in presence of \( F e S O_{4} \) to a colourless compound
Subject: Maths
The value of \( \int \frac{d x}{\sqrt{8+3 x-x^{2}}} \) is equal to
A \( \cdot \frac{2}{3} \sin ^{-1}\left(\frac{2 x-3}{\sqrt{41}}\right)+C \)
B. \( \frac{3}{2} \sin ^{-1}\left(\frac{2 x-3}{\sqrt{41}}\right)+C \)
c. \( \frac{1}{\sqrt{41}} \sin ^{-1}\left(\frac{2 x-3}{\sqrt{41}}\right)+C \)
D. \( \sin ^{-1}\left(\frac{2 x-3}{\sqrt{41}}\right)+C \)
Subject: Physics
A stone is dropped into water from a bridge \( 44.1 \mathrm{m} \) above the water. Another
stone is thrown vertically downward one second later. Both strike the water
simultaneously, then the initial speed of the second stone is
A \( \cdot 12.25 \mathrm{ms}^{-1} \)
B . \( 14.75 \mathrm{ms}^{-1} \)
c. \( 16.23 m s^{-1} \)
D. \( 17.15 \mathrm{ms}^{-1} \)
Subject: Physics
The image of an object placed on the principal axis of a concave mirror of focal length \( 12 \mathrm{cm} \) is formed at a point which is \( 10 c \) more distance from the
mirror than the object. The magnification of the image is
\( A \cdot 8 / 3 \)
B . 2.
\( c \cdot 2 \)
D. -1.5.
Subject: Physics
When a solid ball of volume \( V \) is falling through a viscous liquid, a viscous force \( F \) acts on it. If another ball of
volume 2 V of the same material
is falling through the same liquid then the viscous force experienced by it will be (when both fall with terminal
velocities).
\( A \cdot 4 F \)
в. \( \frac{F}{2} \)
\( c \cdot 2 F \)
D. \( \frac{F}{4} \)
Subject: Chemistry
The temperature on the Celsius scale is
\( 25^{\circ} C . \) What is the
corresponding temperature on the Fahrenheit scale?
\( \mathbf{A} \cdot 40^{\circ} F \)
В \( \cdot 77^{\circ} \)
\( \mathbf{c} \cdot 50^{\circ} F \)
D. \( 45^{\circ} \) F
Subject: Maths
A fair die is rolled. Consider events \( \boldsymbol{E}= \)
\( \{1,3,5\}, F=\{2,3\} \) and \( G= \)
\{2,3,4,5\} Find
(i) \( \boldsymbol{P}(\boldsymbol{E} \mid \boldsymbol{F}) \) and \( \boldsymbol{P}(\boldsymbol{F} \mid \boldsymbol{E}) \)
(ii) \( \boldsymbol{P}(\boldsymbol{E} \mid \boldsymbol{G}) \) and \( \boldsymbol{P}(\boldsymbol{G} \mid \boldsymbol{E}) \)
(iii) \( P((E \cup F) \mid G) \) and \( P((E \cap F) \mid G) \)
Subject: Maths
Solve for \( \boldsymbol{x} \)
\( \left|\begin{array}{ccc}\boldsymbol{x}-\mathbf{2} & \mathbf{2} \boldsymbol{x}-\mathbf{3} & \mathbf{3} \boldsymbol{x}-\mathbf{4} \\ \boldsymbol{x}-\mathbf{4} & \mathbf{2} \boldsymbol{x}-\mathbf{9} & \mathbf{3} \boldsymbol{x}-\mathbf{1} \mathbf{6} \\ \boldsymbol{x}-\mathbf{8} & \mathbf{2} \boldsymbol{x}-\mathbf{2 7} & \mathbf{3} \boldsymbol{x}-\mathbf{6 4}\end{array}\right|=\mathbf{0} \)
\( A \cdot \frac{7}{4} \)
B. \( \frac{28}{3} \)
\( c \cdot \frac{28}{13} \)
D. \( \frac{14}{0} \)
Subject: Maths
Let \( P(x, y) \) be a moving point in the \( x- \) \( \boldsymbol{y} \) plane such that \( [\boldsymbol{x}] .[\boldsymbol{y}]=2, \) where \( [.] \)
denotes the greatest integer function, then area of the region containing the points \( \boldsymbol{P}(\boldsymbol{x}, \boldsymbol{y}) \) is equal to:
A. 1 sq. units
B. 2 sq. units
c. 4 sq. units
D. None of these
Subject: Maths
Consider the function, \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{l}x\{x\}+1,0 \leq x<1 \\ 2-\{x\}, 1 \leq x \leq 2\end{array} \text { where }\{x\}\right. \)
denotes the fractional part of \( x \). Find
incorrect statements.
A \( \cdot \lim _{x \rightarrow 1} f(x) \) exist
в. \( f(0) \neq f(B) \)
c. \( f(x) \) is continuous in [0,2]
Subject: Physics
The graph gives the magnitude \( B(t) \) of \( a \)
uniform magnetic field that exist throughtout a conducting loop.
perpendicular to the plane of the graph
according to the magnitude of the emf induced in the loop greatest first
A. \( b>(d=\epsilon)<(a=c) \)
В. \( b>(d=\epsilon)>(a=c) \)
c. \( b<d<\epsilon<\epsilon<c \)
D. \( b>(a=c)>(d=\epsilon) \)
Subject: Maths
\( \operatorname{Let} \overline{\boldsymbol{a}}=\mathbf{2} \overline{\boldsymbol{i}}+\overline{\boldsymbol{j}}+\overline{\boldsymbol{k}}, \overline{\boldsymbol{b}}=\overline{\boldsymbol{i}}+\mathbf{2} \overline{\boldsymbol{j}}-\overline{\boldsymbol{k}} \) and
a unit vector \( \bar{c} \) be coplanar. If \( \bar{c} \) is
perpendicular to \( \bar{a} \), then \( \bar{c} \) is
Subject: Physics
The dimensions of \( \frac{v^{2}}{\mu g} \) where \( \mu= \)
coefficient of friction, \( \boldsymbol{v}= \) the velocity
\( g= \) acceleration due to gravity is same
as that of
\( ^{A} \cdot \frac{F}{B q} \)
в. \( \mu F \)
c. \( \frac{F}{m} \)
D. None
Subject: Chemistry
Which of the following is the \( 3^{\circ} \) amine?
A \( \cdot\left(C H_{3}\right)_{3} N \)
в. \( \left(C H_{3}\right)_{2} N H \)
c. \( \left(C H_{3}\right) N H_{2} \)
D. \( N H_{3} \)
Subject: Physics
The level of water in a tank is \( 5 \mathrm{m} \) high.
hole of area of cross section \( 1 \mathrm{cm}^{2} \) is
made at the bottom of the tank. The rate
of leakage of water from the hole in \( \boldsymbol{m}^{3} \boldsymbol{s}^{-1} \) is \( \left(\boldsymbol{g}=10 \mathrm{ms}^{-2}\right) \)
A \( \cdot 10^{-3} \)
B . \( 10^{-4} \)
c. 10
D. \( 10^{-2} \)
Subject: Physics
If \( \left(\frac{0.51 \times 10^{-10}}{4}\right) m, \) is the radius of smallest electron orbit in hydrogen like atom, then this atom is
A. H-atom
в. \( H e^{+} \)
\( \mathrm{c} \cdot L i^{2} \)
\( D \cdot B e^{3} \)