AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
A flask contains a mixture of isohexane
and 3-methylphentane. One of the
liquids boils at \( 63^{\circ} \mathrm{C} \) while the other
boils at \( 60^{\circ} \mathrm{C} \). What is the best way to
separate the two liquids and which one will be distilled out first?
A. fractional distillation, 3-methylpentane
B. simple distillation, isohexane
c. fractional distillation, isohexane
D. simple distillation, 3-methylpentane
Subject: Chemistry
Which of the following is true about the reaction \( \boldsymbol{F} \boldsymbol{e}+\boldsymbol{S} \rightarrow \boldsymbol{F} \boldsymbol{e} \boldsymbol{S} ? \)
This question has multiple correct options
A \( \cdot F e+2 e^{-} \rightarrow F e^{2+} \)
B. \( F e \rightarrow F e^{2+}+2 e^{-} \)
C \( \cdot F e^{2+} \rightarrow F e+2 e^{-} \)
D. \( S \rightarrow S^{2-}+2 e^{-} \)
E \( . S+2 e^{-} \rightarrow S \)
Subject: Maths
A shelf contains 15 books, of which 4
are single volume and the others are 8
and 3 volumes respectively. In how
many ways can these books be arranged on the shelf so that order of
the volumes of same work is
maintained ?
A . \( 4 ! \)
в. \( 8 ! \)
\( c .3 ! \)
D. 4!:8:3!3!
Subject: Maths
If
\( [x] \) denotes the integral part of \( x, \) then domain of the function
\( \boldsymbol{f}(\boldsymbol{x})=\frac{\sqrt{3-x}}{(x-1)(x-2)(x-3)}+\sin ^{-1}\left[\frac{3 x-2}{2}\right] \) is
A . [0,2]
в. \( [0,2)-\{1\} \)
C \( .(-\infty, 3)-\{1,2\} \)
D. None of these
Subject: Physics
A piece of thread folded 6 times is placed along a \( 15 \mathrm{cm} \) long measuring scale as shown in the figure. The length of the thread is between
A. \( 0.15-0.50 \mathrm{m} \)
B. \( 0.50 \mathrm{m}-1.0 \mathrm{m} \)
c. \( 1.0 \mathrm{m}-1.5 \mathrm{m} \)
D. \( 1.5 \mathrm{m}-2.0 \mathrm{m} \)
Subject: Chemistry
\( \Delta H \) and \( \Delta S \) for the reaction,
\( \boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{O}(\boldsymbol{s}) \longrightarrow \boldsymbol{2} \boldsymbol{A} \boldsymbol{g}(\boldsymbol{s})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \)
are \( 30.56 k J m o l^{-1} \) and
\( 66.0 J K^{-1} \) mol \( ^{-1} \) respectively. Calculate the temperature at which free energy change for the reaction will be zero.
Predict whether the forward reaction
will be forward above or below this
temperature.
Subject: Chemistry
An electric heater supplies heat to a
system at a rate of 120 W. If system
performs work at a rate of \( 80 \mathrm{J} s^{-1} \), the
rate of increase in internal energy is :
A. 30 J \( s^{-1} \)
B. 40 J \( s^{-1} \)
c. 50 \jmath \( s^{-1} \)
D. 60 J \( s^{-1} \)
Subject: Physics
A stone thrown into still water, creates a
circular wave pattern moving radially outwards. If \( r \) is the distance measured
from the centre of the pattern. the amplitude of the wave aries as
A \( \cdot r^{-1 / 2} \)
B . \( r^{-1} \)
\( c \cdot r^{-2} \)
D. \( r^{-3 / 2} \)
Subject: Chemistry
In the leaching of \( A g_{2} S \) with \( \mathrm{NaCN} \)
a stream of air is also passed. Which of the following is the correct explanation for this step?
A. Reversible nature of reaction between \( A g_{2} S \) and \( ^{N a C N} \)
B. To oxidize \( N a_{2} S \) formed into \( N a_{2} S O_{4} \) and sulphur
c. both (1) and (2)
D. both are not suitable
Subject: Chemistry
The enolic form of acetone contains:
A. \( 9 \sigma \) -bonds, \( 1 \pi \) -bond and 2 lone pairs
B. \( 8 \sigma \) -bonds, \( 2 \pi \) -bond and 2 lone pairs
C. \( 10 \sigma \) -bonds, \( 2 \pi \) -bond and 1 lone pairs
D. \( 10 \sigma \) -bonds, \( 1 \pi \) -bond and 2 lone pairs
Subject: Physics
If the masses of deuterium and that of
helium are 2.0140 amu and 4.0026
amu, respectively and that \( 22.4 \mathrm{MeV} \) energy is liberated in the reaction
\( _{6}^{3} L i+_{1}^{2} H \rightarrow_{2}^{4} H+_{2}^{4} H e, \) has the mass
of \( _{3}^{6} L i \) is
A . 6.015 amu
B. 6.068 amu
c. 5.980 amu
D. 6.00 amu
Subject: Biology
Find the sequence of binding of the
following amino acyl-tRNA complexes during translation of an mRNA transcribed by a DNA segment having the base sequence 3'TACATGGGTCCG5'. Choose the answer showing the correct order of alphabets.
A. P, Q, s,
в. Q, Р, s,
c. Р, \( Q, \) R,
D. Q, P, R,
Subject: Maths
Find \( (f . g)(2) \) when \( f(x)=x-1 \) and
\( \boldsymbol{g}(\boldsymbol{x})=-\mathbf{5} \boldsymbol{x}^{2}+\mathbf{1 4} \boldsymbol{x}+\mathbf{7} \)
A . 45
B. -39
c. 39
D. 15
Subject: Physics
An ideal fluid flown through a pipe of circular cross-section made of two
sections with diameters 25 an and 3.75
\( \mathrm{cm} . \) The ratio of the velocities in the two
pipes is
A .9: 4
B. 3:2
c. \( \sqrt{3}: \sqrt{2} \)
D. \( \sqrt{2}: \sqrt{3} \)
Subject: Chemistry
\( P b\left(I O_{3}\right)_{2} \) is a springly soluble salt
\( \left(K_{s p}=2.6 \times 10^{-13}\right) . \) To \( 35 \mathrm{mL} \) of \( 0.15 \mathrm{M} \)
\( P b\left(N O_{3}\right)_{2} \) solution, \( 15 \mathrm{mL} \) of \( 0.8 \mathrm{M} \)
\( K I O_{3} \) solution is added, and a
precipitate of \( \boldsymbol{P b}\left(\boldsymbol{I} \boldsymbol{O}_{3}\right)_{2} \) is formed
What will be the molarity of \( I O_{3}^{\Theta} \) ions in the solution after completion of the
reaction?
A. 0.152
B. 0.081
c. 0.4
D. 0.03
Subject: Chemistry
The correct order of acidity is:
\( \mathbf{A} \cdot C H F_{3}>C H C l_{3}>C H B r_{3}>C H I_{3} \)
B \( \cdot C H I_{3}>C H B r_{3}>C H C l_{3}>C H F_{3} \)
\( \mathbf{c} \cdot C H C l_{3}>C H F_{3}>C H B r_{3}>C H I_{3} \)
D. \( C H I_{3}>C H B r_{3}>C H F_{3}>C H C l_{3} \)
Subject: Chemistry
Assertion:
\( \mathbf{P}_{4} \) is more reactive than \( \mathbf{N}_{2} \)
Reason:
\( \mathbf{P}-\mathbf{P} \) bonds are relatively weaker than
\( \mathbf{N}-\mathbf{N} \)
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: Physics
A compound microscope has an objective of focal length \( 1 \mathrm{cm} \) and an
eyepiece of \( 4 \mathrm{cm} . \) If the tube length is 20 \( \mathrm{cm} . \) Then the magnification of the compound microscope is : (final image is at D
A . 145
B. 14.5
\( c \cdot 1.45 \)
D. None of these
Subject: Biology
medium that contains excess glucose.
The graph below shows glucose
utilisation under different growth
conditions. \( (A),(B), \) and \( (C) \) in the graph
indicates.
A. A- Anaerobic respiration
B- Introduction of \( O_{2} \) to culture medium
C- Aerobic respiration
B. A- Aerobic respiration
B-Introduction of \( C O_{2} \) to culture medium
C- Anaerobic respiration
C. A- Aerobic respiration
B- Supply of organic triphosphate
C- Aerobic respiration
D. A- Aerobic respiration
B- - Introduction of CO to culture medium
C- Anaerobic respiration
Subject: Maths
Area of parallelogram \( A B C D=60 c m^{2} \)
then find the area of parallelogram
ABEF
\( A \cdot 30 \mathrm{cm}^{2} \)
B. \( 60 \mathrm{cm}^{2} \)
\( c \cdot 40 c m^{2} \)
None of the above
Subject: Physics
A flow of \( 10^{6} \) electrons per second in a
conducting wire constitutes a flow of
current
A . \( 1.6 \times 10^{-15} A \)
В. \( 1.6 \times 10^{-11} \) А
c. \( 1.6 \times 10^{-12} A \)
D. \( 1.6 \times 10^{-19} A \)
E . \( 1.6 \times 10^{-13} A \)
Subject: Chemistry
The increasing order of the rate of
oxidation with \( H I O_{4} \) of the following is:
\( (\Pi) \)
(III)
\( (\mathrm{IV}) \)
A. \( |V<\|\mid<\|<1 \)
B. \( |<||<|||<\mid V \)
C. \( |V<\|\mid=\|<1 \)
D. \( \mid<\|=\|<I V \)
Subject: Physics
In steel, the Young's modulus and the strain at the breaking point are \( 2 \times \) \( 10^{11} N / m^{2} \) and 0.15 respectively. The
stress at the breaking point for steel is therefore:
A \( \cdot 1.33 \times 10^{11} \mathrm{Nm}^{-2} \)
В. \( 1.33 \times 10^{12} \mathrm{Nm}^{-2} \)
c. \( 7.5 \times 10^{-13} \mathrm{Nm}^{-2} \)
D. \( 3 \times 10^{10} \mathrm{Nm}^{-2} \)
Subject: Physics
\( 10^{-3} W \) of \( 5000 A \) light is directed on a
photoelectric cell. If the current in the cell is \( 0.16 \mu A \), the percentage of incident photons which produce photoelectrons, is
A . \( 40 \% \)
B . 0.04\%
c. 20\%
D. 10\%
Subject: Physics
A solid sphere starts rolling down on an inclined plane from a vertical height
\( 3.5 m . \) The velocity of centre of mass of sphere on reaching the bottom of inclined plane is :
A \( .2 .45 \mathrm{ms}^{-1} \)
в. \( 4.9 \mathrm{ms}^{-1} \)
\( \mathbf{c} \cdot 7 m s^{-1} \)
D. \( 9.8 m s^{-1} \)
Subject: Physics
If \( \overrightarrow{\boldsymbol{A}}=\mathbf{3} \hat{\boldsymbol{i}}-\mathbf{2} \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{B}}=\hat{\boldsymbol{i}}-\boldsymbol{3} \hat{\boldsymbol{j}}+ \)
5 \( \hat{k} a n d \vec{C}=2 \hat{i}+\hat{j}-4 \hat{k} \) form a right
angled triangle then out of the following which one is satisfied?
A \( \cdot \vec{A}=\vec{B}+\vec{C} \)and \( A^{2}=B^{2}+C^{2} \)
B . \( \vec{A}=\vec{B}+\vec{C} \)and\( B^{2}=A^{2}+C^{2} \)
c. \( \vec{B}=\vec{A}+\vec{C} a n d B^{2}=A^{2}+C^{2} \)
D. \( \vec{B}=\vec{A}+\vec{C} a n d A^{2}=B^{2}+C^{2} \)
Subject: Maths
ABCD is a parallelogram. The sides AB
and \( A D \) are produced to \( E \) and \( F \) respectively, such that \( A B=B E \) and \( A D= \)
DF.
Hence \( \Delta B E C \cong \Delta D C F \)
State whether the above statement is
true or false.
A. True
B. False
Subject: Chemistry
Calculate approximate \( p H \) of the resultant solution formed by titration of
\( 25 m L \) of \( 0.4 M N a_{2} C O_{3} \) with \( 50 m L \)
of \( 0.025 M H C l \)
[Given that: \( p K_{a_{1}}=6.4 \) and \( p K_{a_{2}}= \)
10.3 for \( H_{2} C O_{3} \)
A .5 .92
B. 11.14
\( c .6 .4 \)
D. 5.88
Subject: Maths
If \( \boldsymbol{a}=\boldsymbol{e}^{\boldsymbol{i} \boldsymbol{\alpha}}, \boldsymbol{b}=\boldsymbol{e}^{\boldsymbol{i} \boldsymbol{\beta}}, \boldsymbol{c}=\boldsymbol{e}^{\boldsymbol{i} \gamma} \) and \( \cos \boldsymbol{\alpha}+ \)
\( \cos \beta+\cos \gamma=0=\sin \alpha+\sin \beta+ \)
\( \sin \gamma, \) then prove the following
\( \sum \cos 2 \alpha=0=\sum \sin 2 \alpha \)
Subject: Maths
The values of \( A \) and \( B \) represented on
the number line are
\begin{tabular}{cccccccccc}
\hline & & & & & & & & & \\
\( \frac{-6}{1} \) & \( \frac{-5}{1} \) & \( \frac{-4}{1} \) & \( \frac{-3}{\mathrm{A}} \) & \( \frac{-2}{1} \) & \( \frac{-1}{1} \) & \( \frac{0}{1} \) & \( \frac{1}{\mathrm{B}} \) & \( \frac{2}{1} \) & \( \frac{3}{1} \)
\end{tabular}
A . 1,1
B. -1,1
\( c \cdot 1,-1 \)
D. -1,-1
Subject: Chemistry
The IUPAC name of the Wilkinson's
catalyst
\( \left[\boldsymbol{R h C l}\left(\boldsymbol{P P h}_{3}\right)_{3}\right] \) is:
A. Chlorotris (triphenylphosphine) rhodium (I)
B. Chlorotris (triphenylphosphine) rhodium (IV)
C. Chlorotris (triphenylphosphine) rhodium (0)
D. Chlorotris (triphenylphosphine) rhodium (VI)
Subject: Physics
The half life for \( \alpha \) -decay of uranium \( 92 U^{228} \) is \( 4.47 \times 10^{8} y r . \) If a rock
contains \( 60 \% \) of original \( _{92} U^{228} \) atoms, then its age is \( [\operatorname{take} \log 6=0.778, \log 2=0.3] \)
A \( \cdot 1.2 \times 10^{7} y r \)
B. \( 3.3 \times 10^{8} y r \)
c. \( 4.2 \times 10^{9} y r \)
D. \( 6.5 \times 10^{9} y r \)
Subject: Physics
A light source is placed \( 100 \mathrm{cm} \) away from a screen. A converging lens placed at a certain position between the source and the screen focuses the image of the source on the screen. The lens is moved
a distance of \( 40 \mathrm{cm} \) and it is found that
it again focuses the image of the source on the screen. The focal length of the lens is :
\( A \cdot 21 \mathrm{cm} \)
B. 30 cm
c. \( 40 \mathrm{cm} \)
D. \( 67 \mathrm{cm} \)
Subject: Maths
f the line \( x \cos \alpha+y \sin \alpha=p \)
represents the common chord \( A P Q B \) of
the circles \( x^{2}+y^{2}=a^{2} \) and \( x^{2}+y^{2}= \)
\( b^{2}(a>b) \) as shown in the figure, then
\( A P \) is equal to
A \( \cdot \sqrt{a^{2}+p^{2}}+\sqrt{b^{2}+p^{2}} \)
B. \( \sqrt{a^{2}-p^{2}}+\sqrt{b^{2}-p^{2}}^{2} \)
c. \( \sqrt{a^{2}-p^{2}}-\sqrt{b^{2}-p^{2}} \)
D. \( \sqrt{a^{2}+p^{2}}-\sqrt{b^{2}+p^{2}}^{2} \)
Subject: Physics
Charge \( 5 \mu C,-2 \mu C, 3 \mu C \) and \( -9 \mu C \)
are placed on a square ABCD of side 1 cm. The net electric potential at the centre is:
A. \( -27 K V \)
В. \( -27 \sqrt{2} \times 10^{5} V \)
\( \mathrm{c} .-9 \mathrm{KV} \)
D. \( 0 V \)
Subject: Physics
What is the minimum coefficient of
friction for a solid sphere to roll without slipping on an incined plane of
inclination \( \boldsymbol{\theta} \) ?
A \( \cdot \frac{2}{7} \tan \theta \)
B \( \cdot \frac{1}{3} g \tan \theta \)
c. \( \frac{1}{2} \tan \theta \)
D. \( \frac{2}{5} \tan \theta \)
Subject: Maths
\( \frac{1}{3} x-\frac{1}{6} y=4 \)
\( 6 x-a y=8 \)
In the system of equations above, \( a \) is a
constant. If the system has no solution,
what is the value of \( \boldsymbol{a} \)
A \( \cdot \frac{1}{3} \)
B.
\( c .3 \)
D.
Subject: Physics
A capacitor of capacitance \( 10, \mathrm{f} \) is charged to a potential of \( 100 \mathrm{V} \) Now connecting it in parallel with an uncharged capacitor, the resultant potential difference becomes 40 volt.The capacitance of this capacitor is
A \( .2 .5, \mathrm{F} \)
в. \( 5, \) F
\( c .10, F \)
D. \( 15, \) F
Subject: Maths
A piece of wire \( 22 \mathrm{cm} \) long is bent into the form of an arc of a circle subtending an angle of \( 60^{\circ} \) at its center. Find the radius of the circle \( \left[\boldsymbol{U s e} \boldsymbol{\pi}=\frac{\mathbf{2 2}}{\mathbf{7}}\right] \)
Subject: Chemistry
The formation of \( \boldsymbol{P} \boldsymbol{H}_{\mathbf{4}}^{+} \) is difficult
compared to \( N H_{4}^{+} \) because :
A. lone pair of phosphorus is optically inertt
B. lone pair of phosphorus resides in almost pure \( p \) orbital
C. lone pair of phosphorous resides at \( s p^{3} \) orbital
D. lone pair of phosphorus resides in almost pure s orbital
Subject: Chemistry
According to the Bohr model of the atom, which electron transition will emit the lowest energy photon?
A \( n=2 \) to \( n=5 \)
5
B . \( n=3 \) to \( n=2 \)
c. \( n=3 \) to \( n=4 \)
D. \( n=6 \) to \( n=2 \)
2
Subject: Maths
In a cuboid,of 3 sides are \( 4 a^{2} b^{2}, 6 a^{2} b^{2} \) and \( 6 a \), then the volume of the cuboid
is
A \( \cdot 144 a^{5} b^{4} \)
B. \( 144 a^{3} b^{2} \)
c. \( 144 a^{2} b^{3} \)
D. \( 12 a^{2} b^{2} \)
Subject: Maths
\( A B C D \) is parallelogram. \( L \) and \( M \) are points on \( A B \) and \( D C \) respectively such that \( A L=C M . \) The diagonal \( B D \)
intersects \( L M \) at point \( O . \) If \( A B= \) \( 14 c m, A D=9 c m \) and \( L O=5 c m, \) find
the length of \( M O \)
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{a}, \boldsymbol{b})= \)
\( \int_{a}^{b}\left(x^{2}-4 x+3\right) d x,(b>a) \) then
A \( \cdot f(a, 3) \) is least when \( a=1 \)
B . \( f(4, b) \) is an increasing function \( \forall b \geq 4 \)
C \( \cdot f(0, b) \) is least for \( b=2 \)
\( \mathrm{D} \cdot \min \{f(a, b)\}=-\frac{4}{3} \forall a, b \in R \)
Subject: Chemistry
If the equilibrium constants of the
reacrions \( 2 A \rightarrow B \) and \( B \rightarrow 2 A \) are \( K_{1} \)
and \( K_{2} \) respectively, than:
A \( . K_{2}=2 K_{2} \)
в. \( _{K_{1}=} \frac{1}{K_{2}} \)
C \( . K_{2}=\left(K_{1}\right)^{2} \)
D. \( _{K_{2}}=\frac{1}{K_{2}^{2}} \)
Subject: Maths
Find the value of \( k \) for which the
equation \( \boldsymbol{x}^{2}+\boldsymbol{k}(\boldsymbol{2} \boldsymbol{x}+\boldsymbol{k}-\mathbf{1})+\boldsymbol{2}=\mathbf{0} \)
has real and equal roots.
Subject: Maths
Assertion
In rolling a dice, the probability of getting number 8 is zero.
Reason

Its an impossible event.
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
toppr LoGın
Q Type your question
and was caught. Which reading helped
the teacher to arrive at the conclusion
that he cheated?
\( \begin{array}{lll}\text { S. No. } & \text { Value of rheostat } & \text { Null point } \\ \text { 1. } & R_{1} & \text { 50 cm } \\ \text { 2. } & R_{2} & \text { 60 cm } \\ \text { 3. } & R_{3} & \text { 70cm } \\ \text { 4. } & R_{4} & \text { 80 cm }\end{array} \)
This question has multiple correct options
A.
B. 2
\( c \cdot 3 \)
\( D \)
Subject: Maths
The position vector of a particle at time \( t^{\prime} \) is given by \( \vec{r}=t^{2} \hat{t}+t^{3} \hat{j} \). The velocity
makes an angle \( \theta \) with positive \( x \) -axis. Find the of \( \frac{\boldsymbol{d} \boldsymbol{\theta}}{\boldsymbol{d} \boldsymbol{t}} \) at \( \boldsymbol{t}=\frac{\sqrt{\mathbf{2}}}{\mathbf{3}} \)
Subject: Maths
The sum of nn is equal to
A \( \cdot \frac{1}{4} n(n+1)(n+2) \)
B. \( \frac{1}{4} n(n+1)(n+2)(n+3) \)
c \( \cdot \frac{1}{2} n(n+1)(n+2)(n+3) \)
D. None of these
Subject: Physics
With a monochromatic light, the fringe-
width obtained in a Young's double slit
experiment is \( 0.133 \mathrm{cm} . \) The whole setup is immersed in water of refractive index 1.33 , then the new fringe-width is
A. \( 0.133 \mathrm{cm} \)
B. 0.1 \( \mathrm{cm} \)
c. \( 1.33 \times 1.33 \mathrm{cm} \)
D. \( \frac{1.33}{2} \mathrm{cm} \)
Subject: Physics
A uniform metal disc of radius R is
taken and out of it a disc of diametere \( \mathrm{R} \)
is out off from the end. The centre of
mass of the remaining part will be
\( ^{A} \cdot \frac{R}{4} \) from the centre
B. \( \frac{R}{3} \) from the centre
\( ^{\mathrm{C}} \cdot \frac{R}{5} \) from the centre
D. \( \frac{R}{6} \) from the centre
Subject: Maths
For \( \boldsymbol{x} \in \boldsymbol{R}, \boldsymbol{f}(\boldsymbol{x})=|\log 2-\sin \boldsymbol{x}| \) and
\( \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{f}(\boldsymbol{f}(\boldsymbol{x})), \) then:
A. g is not differential at \( X=0 \)
B \( \cdot g^{\prime}(0)=\cos (\log 2) \)
C・ \( g^{\prime}(0)=-\cos (\log 2) \)
D. g is differentiable at \( x=0 \) and \( g^{\prime}(0)=-\sin (\log 2) \)
Subject: Maths
If the relation \( \boldsymbol{R}: \boldsymbol{A} \rightarrow \boldsymbol{B} \) where \( \boldsymbol{A}= \)
\( \{1,2,3,4\}, B=\{1,3,5\} \) is defined by
\( \boldsymbol{R}=\{(\boldsymbol{x}, \boldsymbol{y}): \boldsymbol{x}<\boldsymbol{y}, \boldsymbol{x} \in \boldsymbol{A}, \boldsymbol{y} \in \boldsymbol{B}\} \) then
find \( R \) and \( R^{-1} \)
Subject: Maths
Solve the following equations:
\( \boldsymbol{x} \boldsymbol{y}+\boldsymbol{x}+\boldsymbol{y}=\boldsymbol{2} \boldsymbol{3} \)
\( \boldsymbol{x} \boldsymbol{z}+\boldsymbol{x}+\boldsymbol{z}=\boldsymbol{4} \mathbf{1} \)
\( \boldsymbol{y} \boldsymbol{z}+\boldsymbol{y}+\boldsymbol{z}=\mathbf{2 7} \)
A. \( x=4,-2 ; y=2 ; 6 ; z=6,-5 \)
в. \( x=2,-4 ; y=2,4 ; z=2,-6 \)
c. \( x=5,-7 ; y=3,-5 ; z=6,-8 \)
D. \( x=3,4 ; y=2,-5 ; z=2,-7 \)
Subject: Physics
At some planet 'g' is \( 1.96 m / s^{2} . \) If it is safe to jump from a height of \( 2 m \) on
earth, then what should be
corresponding safe height for jumping on that planet
A. \( 5 m \)
в. \( 2 m \)
\( c .10 m \)
D. 20m
Subject: Maths
If \( R \) is relation from a finite \( \operatorname{set} A \)
having \( m \) elements to a finite set \( B \)
having \( n \) elements, then the number of relations from \( \boldsymbol{A} \) to \( \boldsymbol{B} \) is
\( A \cdot 2^{m} \)
B . \( 2^{m n}-1 \)
\( c \cdot 2 m n \)
D. \( m^{n} \)
Subject: Chemistry
Which of the following statement is true about the complex \( \left[\boldsymbol{C r} \boldsymbol{C l}_{3}(\boldsymbol{O H})_{2}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)\right]^{2-} \) ion?
This question has multiple correct options
A. It has three geometrical isomers.
B. Only one space isomers is optically active and remaining are inactive
c. There are total four space isomers.
D. The magnetic moment of complex ion is 3.89 BM.
Subject: Physics
When an equiconvex lens \( \left(\mu_{\text {lens}}=\mathbf{1 . 5}\right) \)
is placed over a plane mirror as shown,
then object needle and its image coincide at \( 15 \mathrm{cm} . \) When a liquid of
refractive index \( \mu \) is filled in the gap
between mirror and lens, the object
needle and its image coincide at \( 40 \mathrm{cm} \)
Find the refractive index \( \mu \) of the liquid.
\( A \cdot 8 \)
5
B. 5 8
\( c \cdot \frac{13}{8} \)
D. \( \frac{5}{13} \)
E \( \cdot \frac{13}{5} \)
Subject: Physics
As shown in the figure, a charge \( +2 C \) is situated at the origin 0 and another charge \( +5 C \) is on the \( x \) -axis at the point
A. The later charge from the point \( A \) is then brought to a point \( \mathrm{B} \) on the \( \mathrm{y} \) -axis. The work done is :
\( \left(\operatorname{given} \frac{1}{4 \pi \epsilon_{0}}=9 \times 10^{9} N m^{2} C^{-2}\right) \)
A \( \cdot 45 \times 10^{9} J \)
В \( \cdot 90 \times 10^{9} J \)
c. zero
D. \( -45 \times 10^{9} J \)
Subject: Maths
\( \sim[\boldsymbol{p} \wedge(\sim \boldsymbol{q})]= \)
\( \mathbf{A} \cdot \sim p \wedge \sim q \)
в. \( \sim p \vee \sim q \)
\( \mathbf{c} . \sim p \wedge q \)
\( \mathrm{D} \cdot \sim p \vee q \)
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{ccc}2 & 4 & -1 \\ -1 & 0 & 2\end{array}\right], B=\left[\begin{array}{cc}3 & 4 \\ -1 & 2 \\ 2 & 1\end{array}\right] \)
find \( (A B)^{T} \)
Subject: Physics
Consider the following statements \( A \) and \( \mathrm{B} \) and identify the correct choice
A) For a given value of angle of incidence, the angle of deviation produced by a prism increases with increasing of refractive index of the prism
B) Angle of deviation produced by a thin prism is independent of angle of incidence
A. A is true and B is false
B. A is false and B is true
c. A and B are true
D. A and B are false
Subject: Maths
The condition that the roots of the
equation \( l x^{2}+m x+n=0 \) may be in
the ratio 3: 4 is
A \( \cdot 14 n^{2}=49 m l \)
B . \( m^{2}=9 n l \)
\( \mathbf{c} \cdot 12 m^{2}=49 n l \)
\( \mathbf{D} \cdot 4 l^{2}=49 m l \)
Subject: Maths
Evaluate \( \left(\frac{7}{8} x+\frac{4}{5} y\right)^{2} \)
A. \( \frac{49}{64} x^{2}+\frac{6}{25} y^{2}+\frac{7}{5} x y \)
B \( \cdot \frac{18}{77} x^{2}+\frac{16}{5} y^{2}+\frac{1}{5} x y \)
c. \( \frac{13}{22} x^{2}+\frac{16}{25} y^{2}+\frac{1}{5} x y \)
D. \( \frac{49}{64} x^{2}+\frac{16}{25} y^{2}+\frac{7}{5} x y \)
Subject: Maths
The line L given by \( \frac{x}{5}+\frac{y}{b}=1 \) passes
through the point \( (13,32) . \) The line \( \mathrm{K} \) is parallel to L and has the equation \( \frac{x}{e}+ \) \( \frac{y}{3}=1 . \) Then the distance between L and
K is
A. \( \frac{23}{\sqrt{15}} \)
в. \( \sqrt{17} \)
c. \( \frac{17}{\sqrt{15}} \)
D. \( \frac{23}{\sqrt{17}} \)
Subject: Physics
A ball is dropped downwards, after 1 sec another ball is dropped downwards from the same point. What is the distance between them after 3 sec? (Take \( g= \)
\( \left.10 m s^{-2}\right) \)
A \( .20 m \)
B. \( 25 m \)
\( c .50 m \)
D. \( 9.8 m \)
Subject: Maths
Below is given frequency distribution of
I.Q. (Intelligent Quotient) of 80
candidates.
\[
70
\]
80
\[
90 \quad 100
\]
I.Q. \( \begin{array}{lll}\text { 80 } & \text { 90 } & \text { 100 }\end{array} \)
No. o 16
20
Candidates
Find median I.Q. of candidates
A. 100.5
B. 98.5
c. 94.5
D. None of these
Subject: Chemistry
One gas bleaches the color of the
flowers by reduction while the other by oxidation. The gases are:
A. co and \( C O_{2} \)
B. \( H_{2} S \) and \( B r_{2} \)
\( \mathrm{c} \cdot \mathrm{SO}_{2} \) and \( \mathrm{Cl}_{2} \)
D. \( N H_{3} \) and \( S O_{3} \)
Subject: Maths
The mean deviation of a frequency dist. is equal to
A. \( \frac{\Sigma d_{i}}{\Sigma f_{i}} \)
в. \( \frac{\Sigma\left|d_{i}\right|}{\Sigma f_{i}} \)
c. \( \frac{\Sigma f_{i} d_{i}}{\Sigma f_{i}} \)
D. \( \frac{\Sigma f_{i} \mid d_{i}}{\Sigma f_{i}} \)
Subject: Chemistry
The decomposition of \( N_{2} O_{5} \) dissolved in carbon tetra chloride occurs followingly
at constant temperature.
\( N_{2} O_{5(s o l u t i o n)} \rightleftharpoons 2 N O_{2(s o l u t i o n)}+ \)
\( \frac{1}{2} O_{2(g)} \)
This reaction is of first order and its
rate constant is \( 5 \times 10^{-4} \mathrm{sec}^{-1} ? \) If
initial concentration of \( N_{2} O_{5} \) is 0.4 mol
litre then
(i) What will be the initial reaction rate?
(ii) What will be the half-life period of
this reaction?
(iii) What time will be taken to
complete \( 75 \% \) reaction?