AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
f \( \boldsymbol{\alpha}, \boldsymbol{\beta} \neq \mathbf{0}, \) and \( \boldsymbol{f}(\boldsymbol{n})=\boldsymbol{\alpha}^{n}+\boldsymbol{\beta}^{n} \) and
\( \left|\begin{array}{ccc}\mathbf{3} & \mathbf{1}+\boldsymbol{f}(\mathbf{1}) & \mathbf{1}+\boldsymbol{f}(\mathbf{2}) \\ \mathbf{1}+\boldsymbol{f}(\mathbf{1}) & \mathbf{1}+\boldsymbol{f}(\mathbf{2}) & \mathbf{1}+\boldsymbol{f}(\mathbf{3}) \\ \mathbf{1}+\boldsymbol{f}(\mathbf{2}) & \mathbf{1}+\boldsymbol{f}(\mathbf{3}) & \mathbf{1}+\boldsymbol{f}(\mathbf{4})\end{array}\right|= \)
\( \boldsymbol{K}(\mathbf{1}-\boldsymbol{\alpha})^{2}(\mathbf{1}-\boldsymbol{\beta})^{2}(\boldsymbol{\alpha}-\boldsymbol{\beta})^{2}, \) then \( \mathrm{K} \) is
equal to?
\( A \)
B.
\( c \cdot \alpha \beta \)
D. \( \frac{1}{\alpha} \)
Subject: Physics
Electric field strength due to a point charge of \( 5 \mu C \) at a distance of \( 80 \mathrm{cm} \) front he charge is
A \( \cdot 8 \times 10^{4} N / C \)
в. \( 7 \times 10^{4} \mathrm{N} / \mathrm{C} \)
C \( .5 .55 \times 10^{4} N / C \)
D. \( 4 \times 10^{4} N / C \)
Subject: Physics
Two small spheres each carrying a charge \( q \) are placed \( r \) metre apart. If one of the spheres is taken around the other
one in a circular path, the work done will
be equal to :
A. force between them \( x \) r
B. force between them \( \times 2 \pi r \)
c. force between them / r \( \pi \) r
D. zero
Subject: Biology
Read the following table and answer the
following questions.
sı. Structure Location
No.
1
Tricuspid Right auriculoriculo-
lar aperture valve
2
Guard cells \( \quad \) Epidermis of leaves
3. Glomerulus Nephron
4. Alveoli
5
Acrosome Above the head of a
sperm
Name the part performing Excretion.
Subject: Physics
Assertion
In meter bridge experiment, a high resistance is always connected in
series with a galvanometer.
Reason
As resistance increases current
through the circuit increases.
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
Identify the incorrect statement among
the following.
A. Lanthanide contraction is the accumulation of
successive shrinkages.
B. As a result of lanthanoid contraction, the properties of 4d series of the transition elements have no
similarities with the \( 5 \mathrm{d} \) series of elements.
C. Sheilding power of 4f electrons is quite weak.
D. There is a decrease in the radii of the atoms or ions as one proceeds from La to Lu.
Subject: Chemistry
The quantity of electricity required to deposit 1.15 g of sodium from molten \( \mathrm{NaCl}(\mathrm{Na}=23, \mathrm{Cl}=35.5) \) is :
\( A \cdot 1 F \)
в. 0.5 F
c. \( 0.05 \mathrm{F} \)
D. 1.5 F
Subject: Chemistry
Calculate simultaneous solubility of AgCNS and AgBr in a solution of water.
[Ksp of \( A g B r=5 \times 10^{-13} \) and Ksp of
\( \left.A g C N S=1 \times 10^{-12}\right] \)
A \( \cdot 8.1610^{-7} M, 4.0810^{-7} M \)
B . \( 5.78 \times 10^{-8} M, 0.037 M \)
C. \( 0.04 M, 6.25 \times 10^{-8} M \)
D. \( 1.58 \times 10^{-3} M, 1.26 \times 10^{-5} M \)
Subject: Maths
Let \( T_{r} \) be the \( r^{t h} \) term of an A.P for \( r= \)
\( 1,2,3, \dots \) if for some positive integers \( \boldsymbol{m}, \boldsymbol{n}, \) we have \( \boldsymbol{T}_{\boldsymbol{m}}=\frac{\mathbf{1}}{\boldsymbol{n}} \) and \( \boldsymbol{T}_{\boldsymbol{n}}=\frac{\mathbf{1}}{\boldsymbol{m}} \)
then \( T_{m n} \) equals
A \( \cdot \frac{1}{m n} \)
B. \( \frac{1}{m}+\frac{1}{n} \)
c. 1
D.
Subject: Maths
Consider two events \( A, B \) of an
zperiment satisfying \( \boldsymbol{P}(\boldsymbol{A} \cup \overline{\boldsymbol{B}})=\frac{\mathbf{3}}{\boldsymbol{4}} \boldsymbol{\&} \)
\( P(B)=\frac{1}{2}, \) then \( P\left(\frac{A}{B}\right) \) is equal to
A \( \cdot \frac{1}{3} \)
B. \( \frac{1}{4} \)
\( c \cdot \frac{1}{2} \)
D.
Subject: Chemistry
Which of the following statements
is/are true?
This question has multiple correct options
\( \mathbf{A} \cdot C H_{3}-C H_{2}-C H_{2}-I \) will react more readily than
\( \left(C H_{3}\right)_{2} C H I \) for \( S_{N} 2 \) reactions
B. \( C H_{3}-C H_{2}-C H_{2}-C l \) will react more readily than
\( C H_{3}-C H_{2}-C H_{2}-B r \) for \( S_{N} 2 \) reaction
\( \mathbf{c} \cdot C H_{3}-C H_{2}-C H_{2}-B r \) will react more readily than
\( \left(C H_{3}\right)_{3} C-C H_{2}-B r \) for \( S_{N} 2 \) reactions
D. \( C H_{3}-O-C_{6} H_{4}-C H_{2} B r \) will react more readily
than \( N O_{2}-C_{6} H_{5}-C H_{2}-B r \) for \( S_{N} 2 \) reaction
Subject: Chemistry
At \( 80^{0} \mathrm{C}, \) the vapour pressure of pure liquid \( A \) is \( 250 m m \) of \( H g \) and that of pure liquid B is \( 1000 \mathrm{mm} \) of Hg. If a
solution of \( A \) and \( B \) boils at \( 80^{\circ} \mathrm{C} \) and 1
atm pressure, the amount of A in the
mixture is : \( (1 a t m=760 m m H g) \)
A . 50 mole percent
B. 52 mole percent
c. 32 mole percent
D. 48 mole percent
Subject: Chemistry
The reaction \( : \boldsymbol{C a} \boldsymbol{C O}_{3}(\boldsymbol{g}) \rightleftharpoons \)
\( \boldsymbol{C a O}(s)+\boldsymbol{C O}_{2}(\boldsymbol{g}), \) would proceed to
completion if the reaction vessel is
connected to bottle containing \( K O H \)
solution or carried out in open vessel. If true enter \( 1, \) if false enter 0
Subject: Maths
The domain of the function \( f(x)=^{24-x} \)
\( \boldsymbol{C}_{3 x-1}+^{40-6 x} \boldsymbol{C}_{8 x-10} \) is
A \( \cdot\{2,3\} \)
3 \( \} \)
в. \{1,2,3\}
D. None of these
Subject: Maths
Let \( f(x) \) be a function satisfying \( f(x+ \) \( \boldsymbol{y})=\mathbf{f}(\mathbf{x}) \mathbf{f}(\mathbf{y}) \) for all \( \boldsymbol{x}, \boldsymbol{y} \in \mathbf{R} \) and
\( \mathbf{f}(\mathbf{x})=\mathbf{1}+\mathbf{x} \mathbf{g}(\mathbf{x}), \) where \( \lim _{x \rightarrow 0} \mathbf{g}(\mathbf{x})=\mathbf{1} \)
then \( f^{\prime}(x) \) is equal to
A. \( x g(x) \)
в. \( \mathrm{g}^{\prime}(\mathrm{x}) \)
c. \( f(x) \)
D.
Subject: Biology
Observe the reflex arc pathway shown in
the flow the chart given below. Which of
the following is represented by \( X \) and \( Y ? \)
\begin{tabular}{|l|l|}
\hline \multicolumn{2}{|l|} {\multirow{2}{*} { Hot plate \( \rightarrow \) Receptors }\text { Hot plate } \rightarrow \text { Receptors }} \\
\cline { 2 - 3 } & \\
\hline Response & Effectors \\
\hline
\end{tabular}
A. \( x \) - Brain, Y - Sensory neuron
B. X - Spinal cord, Y - Motor neuron
c. \( x \) - Brain, \( Y \) - Motor neuron
D. \( x \) - sensory neuron, Y - spinal cord
Subject: Chemistry
Assertion
The magnetic moment of \( M g \) -atom is
more than \( K \) -atom as the former has
two electrons in outermost shell.
Reason
The magnetic moment of \( N \) -atom is
more than magnetic moment of \( O \) -atom
and former has more number of
unpaired electrons.
A. Assertion is correct but Reason is wrong.
B. Assertion is wrong but Reason is correct.
c. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
D. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
Subject: Chemistry
Assertion
\( H_{2} O_{2} \) and \( N_{2} H_{4} \) have oxidising as well
as reducing nature
Reason
Both have equivalent mass of 8
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 plates of a parallel plate capacitor
are charged with surface densities \( \sigma_{1} \)
and \( \sigma_{2}\left(\sigma_{1}=\sigma \text { and } \sigma_{2}=-\sigma\right) \)
respectively and placed horizontally. The electric field at points :
This question has multiple correct options
A. inside the region between the plates will be zeroro
B. above the upper plate and below the lower plate will be zero
c. everywhere in space will be zero
D. inside the region between the plates will be uniform and non zero (neglecting other effects)
Subject: Physics
A film of water is formed between two
straight parallel wires of length \( 10 \mathrm{cm} \)
each separated by \( 0.5 \mathrm{cm} \). If their separation is increased by \( 1 m m \) while still maintaining their parallelism how much work will have to be done of
water (Surface tension of water \( = \)
\( \left.7.2 \times 10^{-2} N / m\right) \)
A \( \cdot 7.22 \times 10^{-6} \mathrm{J} \)
В. \( 1.44 \times 10^{-5} \mathrm{J} \)
c. \( 2.88 \times 10^{-5} \mathrm{J} \)
D. \( 5.76 \times 10^{-5} J \)
Subject: Maths
The vector \( \boldsymbol{\alpha} \hat{\boldsymbol{i}}+\boldsymbol{2} \hat{\boldsymbol{j}}+\boldsymbol{\beta} \hat{\boldsymbol{k}} \) lies in the
plane of vectors \( \vec{b}=\hat{i}+\hat{j} \) and \( \vec{c}=\hat{j}+\hat{k} \) and bisects the angle between \( \vec{b} \) and \( \vec{c} \) Which one of the following gives
possible values of \( \boldsymbol{\alpha} \) and \( \boldsymbol{\beta} \)
A. \( \alpha=2, \beta=2 \)
2
в. \( \alpha=1, \beta=2 \)
c. \( \alpha=2, \beta=1 \)
D. \( \alpha=1, \beta=1 \)
Subject: Chemistry
A mixture of ethanol and propanol has
vapor pressure \( 279 \mathrm{mm} \) of \( \mathrm{Hg} \) at \( 300 \mathrm{K} \) The mol fraction of ethanol in the
solution is 0.6 and vapour pressure of pure propanol is \( 210 \mathrm{mm} \) of Hg. Vapour pressure of pure ethanol will be:
\( \mathbf{A} \cdot 336.6 \mathrm{mm} \)
B . \( 325 \mathrm{mm} \)
c. \( 375 \mathrm{mm} \)
D. \( 415 \mathrm{mm} \)
Subject: Biology
Assertion
Coordination is the process through which two or more organs interact and complement the functions of one
another
Reason
In our body the neural system and the endocrine system jointly coordinate all the activities of the organs
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
\( \int \frac{\left(e^{2 x}-1\right)}{e^{2 x}+1} d x \)
\( \mathbf{A} \cdot \log \left(e^{x}+e^{-x}\right)+C \)
B \( \cdot \log \left(e^{x}-e^{-x}\right)+C \)
\( \mathbf{c} \cdot \log \left(e^{2 x}+e^{-2 x}\right)+C \)
D. \( \log \left(e^{2 x}-e^{-2 x}\right)+C \)
Subject: Chemistry
An ideal gas is expanded irreversible against 10 bar pressure from 20 litre to 30 litre. Calculate ' \( q^{\prime} \) if process is
isoenthalpic.
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( +100 J \)
\( c \cdot-100 J \)
D. \( +10 k J \)
Subject: Maths
If \( \vec{b}=3 \hat{i}+4 \hat{j} \) and \( \vec{a}=\hat{i}-\hat{j} \) the vector
having the same magnitude as that of \( \vec{b} \) and parallel to \( \vec{a} \) is
A \( \cdot \frac{5}{\sqrt{2}}(\hat{i}-\hat{j}) \)
B. \( \frac{5}{\sqrt{2}}(\hat{i}+\hat{j}) \)
\( \mathbf{c} \cdot 5(\hat{i}+\hat{j}) \)
D. \( 5(\hat{i}-\hat{j}) \)
Subject: Maths
Choose the correct answer from the
alternative given. Area of triangle formed by straight lines
\( \boldsymbol{x}-\boldsymbol{y}=\mathbf{0}, \boldsymbol{x}+\boldsymbol{y}=\mathbf{0} \) and \( \mathbf{2} \boldsymbol{x}=\mathbf{5} \) is
A . 25
в. \( \frac{25}{2} \)
c. \( \frac{25}{4} \)
D. None of these
Subject: Chemistry
A button cell used in watches functions
as following:
\( \boldsymbol{Z n}(s)+\boldsymbol{A g}_{2} \boldsymbol{O}(s)+\boldsymbol{H}_{2} \boldsymbol{O}(l) \rightleftharpoons \)
\( 2 A g(s)+Z n^{2+}(a q)+2 O H^{-}(a q) \)
f half cell potentials are: \( Z n^{2+}(a q)+ \)
\( 2 e \rightarrow Z n(s) ; E^{0}=-0.76 V \)
\( A g_{2} O(s)+H_{2} O(l) 2 e \rightarrow 2 A g(s)+ \)
\( \mathbf{2} \boldsymbol{O} \boldsymbol{H}^{-}(\boldsymbol{a} \boldsymbol{q}), \boldsymbol{E}^{0}=\mathbf{0} . \boldsymbol{3} \mathbf{4} \boldsymbol{V} \)
The cell potential will be:
A . \( 1.10 V \)
B. \( 0.42 V \)
c. \( 0.84 V \)
D. \( 1.34 V \)
Subject: Maths
A quadratic equation whose roots are
\( \operatorname{cosec}^{2} \theta \) and \( \sec ^{2} \theta \operatorname{can} b e \)
A. \( x^{2}-5 x+2=0 \)
B . \( x^{2}-2 \sin 2 \theta x+6 \sin \theta=0 \)
c. \( x^{2}-4 \operatorname{cosec} 2 \theta x+4 \operatorname{cosec} 2 \theta=0 \)
D. none of these
Subject: Maths
Express the following as improper fractions:
\( \mathbf{7} \frac{\mathbf{3}}{\mathbf{4}} \)
\( \mathbf{5} \frac{\mathbf{6}}{\mathbf{7}} \)
\( 2 \frac{5}{6} \)
\( 10 \frac{3}{5} \)
Subject: Physics
An object is placed \( 20 \mathrm{cm} \) to the left of a convex lens of focal length \( 10 \mathrm{cm} \). If a concave mirror of focal length \( 5 \mathrm{cm} \) is placed \( 30 \mathrm{cm} \) to the right of the lens, find the magnification.
A . 1.5
B. 1
c. 2
D. 2.5
Subject: Maths
If \( \boldsymbol{P}=(\mathbf{0}, \mathbf{0}, \mathbf{0}), \boldsymbol{Q}=(\mathbf{3}, \mathbf{6}, \mathbf{9}) \) and \( \boldsymbol{R} \) is a
point of trisection of \( \boldsymbol{P Q}, \) then \( \boldsymbol{R}_{\boldsymbol{y}}= \)
\( A \cdot \frac{4}{3} \)
B . 2
\( c .3 \)
D.
Subject: Physics
During the phase change, when water
freezes, its converted to ice in which
molecules is in more structured order.
Why doesn't this contradict the Second
Law of Thermodynamics?
A. Because the density of the water is decreasing
B. Because the water is gaining entropy as it goes from liquid to solid state
C. Because the water's internal energy is decreasing
D. Because the surroundings are losing entropy
E. Because the surroundings are gaining entropy
Subject: Chemistry
Amino acids usually exist in the form of zwitter ions. This means that they
consist of:

This question has multiple correct options
A. the basic \( N H_{2} \) group and acidic \( C O O H \) group
B. the basic group and the acidic \( C O O^{-} \) group
c. basic group and acidic group
D. no acidic or basic group as such
Subject: Chemistry
A gas mixture 3.67 L in volume contain
\( C_{2} H_{4} \) and \( C H_{4} \) is proportion of 2: 1 by
moles and is at \( 25^{\circ} \mathrm{C} \) and 1 atm. If the
\( \boldsymbol{\Delta} \boldsymbol{H}_{C}^{\circ}\left(\boldsymbol{C}_{2} \boldsymbol{H}_{4}\right) \) and \( \boldsymbol{\Delta} \boldsymbol{H}_{C}^{\circ}\left(\boldsymbol{C} \boldsymbol{H}_{4}\right) \) are
-1400 and \( -900 \mathrm{kJ} / \mathrm{mol} \) find heat evolved
on burning this mixture
A. \( 20.91 \mathrm{kJ} \)
J.
B. 50.88 kJ
c. 185 k
D. 160 k
Subject: Physics
If \( \vec{A}=2 \hat{i}+3 \hat{j}+8 \hat{k} \) is perpendicular to \( \vec{B}=4 \hat{j}-4 \hat{i}+\alpha \hat{k}, \) then the value of ' \( \alpha^{\prime} \)
is
A .
B.
c. -1
D. \( \frac{1}{-2} \)
Subject: Chemistry
The electrons identified by quantum
numbers \( n \) and \( l, \) are as follows:
I. \( \boldsymbol{n}=\mathbf{4}, \boldsymbol{l}=\mathbf{1} \)
Il. \( \boldsymbol{n}=\mathbf{4}, \boldsymbol{l}=\mathbf{0} \)
III. \( \boldsymbol{n}=\mathbf{3}, \boldsymbol{l}=\mathbf{2} \)
IV. \( n=3, l=1 \)
If we arrange them in order of increasing energy, i.e. from lowest to highest, the correct order is:
A. \( I V<I I<I I I<I \)
B. \( I I<I V<I<I I \)
c. \( I<I I I<I I<I V \)
D. III \( <I<I V<I I \)
Subject: Physics
One Newton is the force which produces an acceleration of -
A \( \cdot 1 m \cdot s^{-2} \) on a body of mass \( 1 \mathrm{gm} \)
B. \( 1 \mathrm{cm} . s^{-2} \) on a body of mass \( 1 \mathrm{kg} \)
c. \( 1 \mathrm{cm} . \mathrm{s}^{-2} \) on a body of mass \( 1 \mathrm{gm} \)
D. \( 1 m . s^{-2} \) on a body of mass \( 1 \mathrm{kg} \)
Subject: Chemistry
Consider the cell:
\( \boldsymbol{Z} \boldsymbol{n} \mid \boldsymbol{Z} \boldsymbol{n}^{2+}(\boldsymbol{a q})(\boldsymbol{1} . \boldsymbol{0} \boldsymbol{M}) \| \boldsymbol{C u}^{2+}(\boldsymbol{a q}) \)
The standard reduction potential are \( 0.350 \mathrm{V} \) for \( \boldsymbol{C u}^{2+}(\boldsymbol{a q})+\boldsymbol{2} \boldsymbol{e}^{-} \rightarrow \boldsymbol{C u} \)
and \( -0.763 \mathrm{V} \) for \( \mathrm{Zn}^{2+}(a q)+2 e^{-} \rightarrow \)
\( Z n \)
The EMF (in V) of the cell is (write your answer as nearest integer):
Subject: Physics
Value(s) of m for which the system
remains at rest (pulleys and strings are
ideal) is/are: \( \left(\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right) \)
This question has multiple correct options
\( A \cdot 1 \mathrm{kg} \)
B. 2 kg
c. \( 18 \mathrm{kg} \)
D. 20 kg
Subject: Maths
Show that each of the three given vectors is a unit vectors. also Show that
they are mutually \( \perp \) to each other \( \vec{a}=\frac{1}{7}(2 \hat{i}+3 \hat{j}+6 \hat{k}) \)
\( \vec{b}=\frac{1}{7}(3 \hat{i}-6 \hat{j}+2 \hat{k}) \)
\( \overrightarrow{\boldsymbol{c}}=\frac{1}{7}(6 \hat{i}+2 \hat{j}-3 \hat{k}) \)
Subject: Maths
The volume of a sphere is \( 300.5 \mathrm{cm}^{3} \)
Find its surface area.
A . \( 21.3146 \mathrm{cm} \)
в. \( 216.3146 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 216.3146 \mathrm{mm}^{2} \)
D. \( 216.3146 \mathrm{m}^{2} \)
Subject: Chemistry
The gases evolved in the decomposition of lead nitrate are:
A. \( N_{2} O_{3}, N O \)
в. \( N O_{2}, O_{2} \)
\( \mathrm{c} \cdot \mathrm{N}_{2} \mathrm{O}_{3}, \mathrm{O}_{2} \)
D. \( N_{2} O, O_{2} \)
Subject: Physics
An observer on the sea shore observes
54 waves reaching the coast per minute. If the wavelength is \( 10 m \), the
velocity is
A \( .9 \mathrm{ms}^{-1} \)
В. \( 54 m s^{-1} \)
c. \( 18 \mathrm{ms}^{-1} \)
D. \( 36 m s^{-1} \)
Subject: Maths
Diagonals \( A C \) and \( B D \) of a trapezium
\( A B C D \) with \( A B \| D C \) intersect each
other at the point \( 0, \frac{O A}{O C}=? \)
A \( \cdot \frac{B D}{O B} \)
в. \( \frac{B O}{O D} \)
c. \( \frac{A O}{O B} \)
D. \( \frac{c o}{O D} \)
Subject: Chemistry
Which of the following reactions will not
produce any hydrogen gas?
A. Reaction between \( F e \) and dil. \( H C l \)
B. Reaction between \( Z n \) and conc. \( H_{2} S O_{4} \)
C. Reaction between \( Z n \) and \( N a O H \)
D. Electrolysis of \( N a C l \) in Nelson's cell.
Subject: Physics
A rod \( 0.5 \mathrm{m} \) long has two masses each
of 20 gram stuck at its ends. If the
masses are treated as point masses and if the mass of the rod is neglected, then the moment of inertia of the
system about a transverse axis passing
through the centre is
A \( \cdot 1.25 \times 10^{-3} \mathrm{kg}-\mathrm{m}^{2} \)
B . \( 2.5 \times 10^{-3} \mathrm{kg}-\mathrm{m}^{2} \)
C \( \cdot 4 \times 10^{-3} \mathrm{kg}-\mathrm{m}^{2} \)
D. \( 5 \times 10^{-3} \mathrm{kg}-\mathrm{m}^{2} \)
Subject: Chemistry
A body drinks \( 500 \mathrm{mL} \) of \( 9 \% \) glucose solution. The number of glucose molecules he has consumed is :
[Molecular weight of glucose \( =180] \)
A \( \cdot 0.5 \times 10^{23} \)
B . \( 1.0 \times 10^{23} \)
c. \( 1.5 \times 10^{23} \)
D. \( 2.0 \times 10^{23} \)
Subject: Physics
For \( a=0, \) the value of \( d( \) maximum
value of \( \rho \) as shown in the figure) is
\( ^{A} \cdot \frac{3 Z e}{4 \pi R^{3}} \)
в. \( \frac{3 Z}{\pi R^{3}} \)
c. \( \frac{4 Z e}{3 \pi R^{3}} \)
D. \( \frac{Z e}{3 \pi R^{3}} \)
Subject: Chemistry
Select the correct statement(s):
This question has multiple correct options
\( \mathbf{A} \cdot P b I_{4}, F e I_{3} \) do not exist while \( P b C l_{4}, F e C l_{3} \) exist.
B \( \cdot P b C l_{4}, F e C l_{3} \) do not exist while \( P b I_{4}, F e I_{3} \) exist.
\( \mathrm{C} \cdot \mathrm{CO}_{2} \) is gaseous while \( \mathrm{SiO}_{2} \) is solid.
D. \( C O_{2} \) is solid while \( S i O_{2} \) is gaseous.
Subject: Maths
Let \( p: A \) triangle is equilateral, \( q: A \) triangle is equiangular then inverse of
\( \boldsymbol{q} \rightarrow \boldsymbol{p} \) is
A. If a triangle is not equilateral then it is not equiangular
B. If a triangle is not equiangular then it is not equilateral
C. If a triangle is equiangular then it is not equilateral
D. If a triangle is equiangular then it is equilateral
Subject: Chemistry
1.0 \( g \) of a weak monobasic acid \( (H A) \) when dissolved in \( 150 \mathrm{mL} \) water, lowers
the freezing point by \( 0.186^{\circ} \mathrm{C} \). Also \( 1.0 \mathrm{g} \) of the same acid required 125 mL of a 0.10N Nate solution for complete neutralisation. Determine dissociation
constant \( \left(k_{a}\right) \) of the weak acid. \( k_{f} \) of
water is \( 1.86 \mathrm{K} \mathrm{kg} \) mol \( ^{-1} \)
A \( \cdot 4.16 \times 10^{-3} \)
B . \( 2.38 \times 10^{-6} \)
c. \( 6.43 \times 10^{-3} \)
D. \( 3.78 \times 10^{-6} \)
Subject: Maths
Find the values of \( x, y \) and \( z \) if \( \left[\begin{array}{lll}\boldsymbol{x} & \mathbf{5} & \mathbf{4} \\ \mathbf{5} & \mathbf{9} & \mathbf{1}\end{array}\right]=\left[\begin{array}{lll}\mathbf{3} & \mathbf{5} & \boldsymbol{z} \\ \mathbf{5} & \boldsymbol{y} & \mathbf{1}\end{array}\right] \)
Subject: Maths
The velocity vector of a sphere after it hits a vertical wall which is parallel to \( \hat{j} \) is \( (-\hat{\mathbf{i}}+\mathbf{3} \hat{\mathbf{j}}) \) on a smooth horizontal
surface. The coefficient of restitution
between ball and wall is (1/2). Find the
velocity vector of sphere immediately before collision:
\( \mathbf{A} \cdot \hat{i}+3 \hat{j} \)
В. \( -2 \hat{i}+3 \hat{j} \)
c. \( -\hat{i}+3 \hat{j} \)
D. \( 2 \hat{i}+3 \hat{j} \)
Subject: Physics
An electric current is passed through a circuit containing two wires of the same material, connected in parallel. If the lengths and radii of the wires are in the ratio of \( \frac{4}{3} \) and \( \frac{2}{3}, \) then the ratio of the currents passing through the wire will be:
\( A \cdot 3 \)
B. \( 1 / 3 \)
\( c \cdot 8 / 9 \)
D.
Subject: Maths
Given \( M=(0,1,2) \) and \( N=(1,2,3) \)
Find \( (\boldsymbol{N}-\boldsymbol{M}) \times(\boldsymbol{N} \cap \boldsymbol{M}) \)
\( A \cdot\{(3,1),(3,2)) \)
B. \{(3,-1),(3,-2)
c. \{(-3,-1),(-3,2)\}
\( \mathbf{D} \cdot\{(3,-1),(-3,-2)\} \)
Subject: Chemistry
Methylene blue is adsorbed on
activated charcoal at \( 25^{\circ} \mathrm{C} \) from its
aqueous solution. For this process,
select the correct statement.
A. The adsorption requires activation at \( 25^{\circ} \mathrm{C} \)
B. The adsorption is accompanied by a decrease in enthalpy
c. The adsorption increases with increase of temperature
D. The adsorption is irreversible
Subject: Physics
Two particles of masses \( m_{1} \) and \( m_{2} \) in
projectile motion have velocities \( \bar{v}_{1} \) and
\( \overline{\boldsymbol{v}}_{2} \) respectively at time \( \boldsymbol{t}=\mathbf{0} . \) They
strike at time \( t_{0} \) and their velocities
become \( \overline{v^{\prime}}_{1} \) and \( \overline{v^{\prime}}_{2} \) at time \( 2 t_{0} \) while
still moving in air. The value of
\( \left|\left(\boldsymbol{m}_{1} \overline{\boldsymbol{v}^{\prime}}_{1}+\boldsymbol{m}_{2} \overline{\boldsymbol{v}^{\prime}}_{2}\right)-\left(\boldsymbol{m}_{1} \overline{\boldsymbol{v}}_{1}+\boldsymbol{m}_{2} \overline{\boldsymbol{v}}_{2}\right)\right| \) is
\( \mathbf{A} \cdot z \) ero
\( \mathbf{B} \cdot\left(m_{1}+m_{2}\right) g t_{0} \)
\( \mathbf{c} \cdot 2\left(m_{1}+m_{2}\right) g t_{0} \)
D \( \cdot \frac{1}{2}\left(m_{1}+m_{2}\right) g t_{0} \)
Subject: Physics
A step-down transformer has primary voltage \( 1100 V . \) The ratio of turns of
primary to secondary coil is \( 5: 1 . \) If the
primary current is \( 10 A \) then what is the secondary voltage and secondary current assuming the transformer to be an ideal transformer?
\( \mathbf{A} \cdot 220 V, 50 A \)
в. \( 220 V, 5 A \)
c. \( 22 V, 50 A \)
D. \( 22 V, 5 A \)
Subject: Maths
\( * \) is said to be commutative in \( \boldsymbol{A} \) for all
\( \boldsymbol{a}, \boldsymbol{b} \in \boldsymbol{A} \)
A \( . a+b=b+a \)
B. \( a * b=b * a \)
c. \( a-b=b-a \)
\( a \)
D. \( a * b \neq b * a \)
Subject: Physics
A cannon fires successively two shells
with velocity \( v_{0}=250 m / s ; \) the first at
the angle \( \theta_{1}=60^{\circ} \) and the second at
the angle \( \theta_{2}=45^{\circ} \) to the horizontal, the
azimuth being the same. Neglecting the air drag, the time interval(in seconds) between firings leading to the collision of the shells is \( (10+x) \). Find the value of
x. (Take \( g=10 m / s^{2} \) and round-off your
answer to the nearest integer.)
Subject: Physics
A wire of length \( 50 \mathrm{cm} \) has a mass of 20
gm. It its radius is halved by stretching, its new mass per unit length will be
A. \( 0.4 \mathrm{g} \mathrm{cm}^{-1} \)
B. 0.2 \( \mathrm{kg} \mathrm{m}^{-1} \)
c. \( 0.1 \mathrm{g} \mathrm{cm}^{-1} \)
D. \( 0.2 \mathrm{g} \mathrm{cm}^{-1} \)