AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Q Type your question
acceleration due to gravity (g) using a simple pendulum. They use different lengths of the pendulum and/or record time for different number of
oscillations. The observations are
shown in the following table. Least count for length \( =0.1 \mathrm{cm}, \) Least count for
time \( =0.1 s \)
Length of \( \quad \) Number of Student Pendulum \( \quad \) oscillations \( (n) \)
\[
\begin{array}{l}
(\mathrm{cm}) \\
64.0
\end{array}
\]
\[
64.0
\]
\[
20.0
\]
If \( \boldsymbol{E}_{\boldsymbol{I}}, \boldsymbol{E}_{\boldsymbol{I I}}, \boldsymbol{E}_{\boldsymbol{I I I}} \) are the percentage errors
in \( g, \) i.e., \( \left(\frac{\Delta g}{g} \times 100\right) \) for students I, II and
III, respectively, then
A \( \cdot E_{I}=0 \)
B. \( E_{I} \) is minimum
\( \mathbf{c} \cdot E_{I}=E_{I I} \)
D. \( E_{I I} \) is maximum
Subject: Physics
A bullet of mass \( A \) and velocity \( B \) is
fired into a block of wood of mass \( C . \) If
loss of any mass and friction be neglected, the velocity of the system must be
A \( \cdot \frac{A B}{A+C} \)
в. \( \frac{A+C}{B+C} \)
c. \( \frac{A C}{B+C} \)
D. \( \frac{A+B}{A C} \)
Subject: Maths
\( \left|\begin{array}{ccc}\mathbf{1}+\boldsymbol{i} & \mathbf{1}-\boldsymbol{i} & \mathbf{1} \\ \mathbf{1}-\boldsymbol{i} & \boldsymbol{i} & \mathbf{1}+\boldsymbol{i} \\ \boldsymbol{i} & \mathbf{1}+\boldsymbol{i} & \mathbf{1}-\boldsymbol{i}\end{array}\right| \) is a
A. real number
B. irrational number
c. complex member
D. Purely imaginary
Subject: Physics
A river flows \( 3 \mathrm{km} / \mathrm{h} \) and a man is capable of swimming at the rate of
\( 2 k m / h . \) He wishes to cross it such that the displacement parallel to river is minimum. In which direction should he
swim?
\( ^{A} \cdot \sin ^{-1}\left(\frac{2}{3}\right) \)
B. \( \cos ^{-1}\left(\frac{2}{3}\right) \)
\( ^{\mathbf{c}} \cdot \tan ^{-1}\left(\frac{2}{3}\right) \)
D. \( \cot ^{-1}\left(\frac{2}{3}\right) \)
Subject: Maths
Find the expansion of \( (p+2)(p-4)(p+6) \)
A \( \cdot p^{3}+4 p^{2}-20 p-48 \)
в. \( p^{3}-4 p^{2}-20 p-48 \)
c. \( p^{3}+4 p^{2}+20 p-48 \)
D. None of these
Subject: Chemistry
Element Electronegative \begin{tabular}{ccc}
\( P \) & 2.1 \\
\( H \) & 2.2 \\
\( B r \) & 2.8 \\
\hline
\end{tabular} \( B^{r} \) 1
\( O \) 3.5 If What is and
On the basis of the electronegativity values given above, in which of the following are the bonds most polar?
\( \mathbf{A} \cdot P H_{3} \)
B. \( H_{2} O \)
\( \mathbf{c} \cdot H B r \)
D. \( P_{4} \)
E \( . P B r_{3} \)
Subject: Physics
In a typical hydraulic press, a force of \( 20 \mathrm{N} \) is exerted on small piston of area \( 0.050 \mathrm{m} 2 . \) What is force exerted by large piston on load if it has an area of 0.50 m2?
A. 200N
B. 100N
c. 50N
D. 10N
Subject: Maths
A line \( L \) has intercepts \( a \) and \( b \) on the coordinate axes. When the axes are rotated
through an angle, keeping the origin fixed,
the same line \( L \) has intercepts \( p \) and \( q \)
Which of the following options is correct?
A \( \cdot a^{2}+b^{2}=p^{2}+q^{2} \)
B. \( \frac{1}{a^{2}}+\frac{1}{b^{2}}=\frac{1}{p^{2}}+\frac{1}{q^{2}} \)
C. \( a^{2}+p^{2}=b^{2}+q^{2} \)
D. \( \frac{1}{a^{2}}+\frac{1}{p^{2}}=\frac{1}{b^{2}}+\frac{1}{q^{2}} \)
Subject: Physics
In a medium in which, a transverse
progressive wave travelling, the phase difference between the points with a separation of \( 1.25 \mathrm{cm} \) is \( \pi / 4 . \) If the frequency of wave \( 1000 H z \), the velocity
in the medium is :
A \( \cdot 10^{4} m s^{-1} \)
В. \( 125 \mathrm{ms}^{-1} \)
c. \( 100 m s^{-1} \)
D. \( 10 \mathrm{ms}^{-1} \)
Subject: Maths
The orthocentre of the triangle \( A B C \) is \( B \) and the circumstances is \( S(a, b) . \) If \( A \) is the origin, then the coordinates of \( C \)
are:
A. \( (2 a, 2 b) \)
в. \( \quad\left(\frac{a}{2}, \frac{b}{2}\right) \)
c. \( \sqrt{\left(a^{2}+b^{2}, 0\right)} \)
D. None
Subject: Chemistry
Select the correct I.U.P.A.C name for
\( \left[\boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right]\left[\boldsymbol{P t} \boldsymbol{C l}_{4}\right]: \)
(II) tetrachloridoplatinum (II)
A. Tetraamminecopper
B. Tetraamminecopper
(II) tetrachloridoplatinum (IV)
c. Tetraamminecopper(II) tetrachloridoplatinate (II)
D. Tetraamminecuprate(II) tetrachloridoplatinate (II)
Subject: Maths
If \( \boldsymbol{A}=\{1,2,3\} \) and \( B=\{3,8\}, \) then
\( (A \cup B) \times(A \cap B) \) is equal to
A \( \cdot\{(8,3),(8,2),(8,1),(8,8)\} \)
B - \{(1,2),(2,2),(3,3),(8,8)\}
c. \{(3,1),(3,2),(3,3),(3,8)\}
D・ \{(1,3),(2,3),(3,3),(8,3)\}
Subject: Chemistry
The correct relationship between free energy change in a reaction and the corresponding equilibrium constant \( \boldsymbol{K} \) is
\( \mathbf{A} \cdot-\Delta G=R T \ln K \)
B. \( \Delta G^{o}=R T \ln K \)
c. \( \Delta G=-R T \ln K \)
D. \( -\Delta G^{o}=R T \ln K \)
Subject: Physics
Same amount of heat is supplied to two liquids \( A \) and \( B \). The liquid \( A \) shows a greater rise in temperature. What can
you say about the heat capacity of A as compared to that of B?
A. Heat capacity of A is more than that of B
B. Heat capacity of A is less than that of B
c. Heat capacity of A is same as that of B
D. can't say
Subject: Maths
Let \( A \) be a square matrix, all of whose entries are integers. Then, which one of the following is true?
\( \mathbf{A} \cdot \) If \( \operatorname{det}(A)=\pm 1, \) then \( A^{-1} \) need not exist
B . If \( \operatorname{det}(A)=\pm 1 \), then \( A^{-1} \) exists but all its entries ar not necessarily integers
C \( \cdot \) If \( \operatorname{det}(A) \neq\pm 1, \) then \( A^{-1} \) exists and all its entries are non-integers
D. If \( \operatorname{det}(A)=\pm 1 \), then \( A^{-1} \) exists and all its entries are integers
Subject: Chemistry
Select the best combination of reagents
which will bring the above conversion.
\( \mathbf{A} \cdot B r_{2} / F e B r_{3} ; H N O_{3} / H_{2} S O_{4} ; N a O H ; H_{2} / P t \)
B . \( C H_{3} C O C l / A l C l_{3} ; B r_{2} / F e B r_{3} ; N a B H_{4} / C H_{3} O H \)
c. \( C H_{3} C l / A l C l_{3} ; K M n O_{4} ; C H_{3} C l / A l C l_{3} ; N B S / h v \)
\( \operatorname{LiAlH}_{4} / H_{2} O ; N a O H \)
D. \( C H_{3} C l / A l C l_{3} ; H N O_{3} / H_{2} S O_{4} ; N B S / h v / N a O H \)
Subject: Physics
Assertion
Statement-1: In the case of a stationary
wave, a person hear a loud sound at the
pressure nodes as compared to the
antinodes.
and
Reason
Statement-2: In a stationary wave all
the particles of the medium vibrate in
phase.
A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-
B. Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-
c. Statement-1 is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is True.
Subject: Chemistry
Equilibrium constant for the following
equilibrium is given at \( 0^{\circ} \mathrm{C} \)
\( N a_{2} H P O_{4} \cdot 12 H_{2} O(s) \rightleftharpoons \)
\( N a_{2} H P O_{4} \cdot 7 H_{2} O(s)+5 H_{2} O(s) \)
\( \boldsymbol{K}_{\boldsymbol{p}}=\mathbf{3 1 . 2 5} \times \mathbf{1 0}^{-\mathbf{1 3}} \)
The partial pressure of water is:
A \( \cdot \frac{1}{5} \times 10^{-3} \) at
B . \( 0.5 \times 10^{-3} \) atm
c. \( 5 \times 10^{-2} a t m \)
D. \( 5 \times 10^{-3} a \) tm
Subject: Physics
In Fraunhofer diffraction experiment, \( \boldsymbol{L} \)
is the distance between screen and the
obstacle, \( b \) is the size of obstacle and \( A \)
is wavelength of incident light. The general condition for the applicability of Fraunhofer diffraction is
\( ^{\mathrm{A}} \cdot \frac{b^{2}}{L \lambda} \gg 1 \)
B. \( \frac{b^{2}}{L \lambda}=1 \)
c. \( \frac{b^{2}}{L \lambda} \ll 1 \)
D. \( \frac{b^{2}}{L \lambda} \neq 1 \)
Subject: Maths
If \( R \) divides the line segment joining \( P(2, \)
3, 4) and \( Q(4,5,6) \) in the ratio -3: 2 then the value of the parameter which
represents R is
в. \( =(10,9,8) \)
\( \mathbf{c} .=(10,8,9) \)
\( \mathbf{D} .=(9,10,8) \)
Subject: Chemistry
5 moles of \( N H_{4} O H \) and 1 mole of \( \mathrm{HCl} \)
are mixed and diluted to 1 litre. \( p K b \) of
\( N H_{4} O H \) is 4.8. The \( p H \) of the solution
is:
A . 4.8
в. 4.1979
c. 9.8021
D. 9.2
Subject: Chemistry
The solubility product of silver bromide
is \( 5.0 \times 10^{-13} . \) The quantity of
potassium bromide (molar mass is
\( \operatorname{taken} \operatorname{as} 120 \) g \( m o l^{-1} \) ) to be added to 1
liter of \( 0.05 \mathrm{M} \) solution of silver nitrate to
start the precipitate of AgBr is:
A \( .5 .0 \times 10^{-8} \mathrm{g} \)
B . \( 1.2 \times 10^{-10} \mathrm{g} \)
c. \( 1.2 \times 10^{-9} \mathrm{g} \)
D. \( 6.2 \times 10^{-5} \mathrm{g} \)
Subject: Chemistry
Which of the following is true regarding
an \( N e \) atoms with a mass number of 20
and \( O^{2-} \) ion with a mass number of \( 16 ? \)
A. They contain the same number of protons
B. They contain the same number of neutrons
C. They contain the same number of protons plus netrons
D. The are isoelectronic
E. They are isomers
Subject: Physics
Two spheres of radii \( r_{1} \) and \( r_{2}\left(r_{1}>r_{2}\right) \)
is dropped through a tube full of
glycerine. Their terminal velocities \( \boldsymbol{v}_{1} \)
and \( v_{2} \) are calculated in the experiment.
Which of the following is true?
A \( \cdot v_{1}=v_{2} \)
В. \( v_{1}>v_{2} \)
c. \( v_{1}<v_{2} \)
D. \( v_{1} \) and \( v_{2} \) are independent of \( r_{1} \) and \( r_{2} \)
Subject: Maths
\( X \) follows a binomial distribution with
parameters \( \boldsymbol{n}=\boldsymbol{6} \) and \( \boldsymbol{P} . \) If \( \boldsymbol{4} \boldsymbol{P}(\boldsymbol{x}= \)
\( \mathbf{4})=\boldsymbol{P}(\boldsymbol{x}=\mathbf{2}), \) then \( \boldsymbol{P}= \)
A \( \cdot \frac{1}{2} \)
в.
\( c \cdot \frac{1}{6} \)
D.
Subject: Physics
A conductor A is given a charge of amount \( +Q \) and then placed inside a
deep metal can B, without touching it.
Then:
This question has multiple correct options
A. The potential of A does not change when it is place inside B.
B. If \( B \) is earthed, \( +Q \) amount charge flows from it into the earth.
C. If \( B \) is earthed, the potential of \( A \) is reduced
D. Either (B) or (C) is true or both the true only if the outer surface of B is connected to earth and not its inner surface
Subject: Physics
Five charges of magnitudes
\( 24 \mu C,-25 \mu C, 3 \mu C,-7 \mu C \) and \( 28 \mu C \)
are situated along the circumference of
a circle of radius \( 3 \mathrm{cm} \). Then the
potential at the centre of the circle is
A \( .54 \times 10^{7} V \)
В. \( 45 \times 10^{6} V \)
\( \mathbf{c} \cdot 72 \times 10^{6} V \)
\( \mathbf{D} \cdot 69 \times 10^{5} V \)
Subject: Physics
The diameter of a solid disc is \( 0.5 \mathrm{m} \) and
its mass is \( 16 \mathrm{Kg} \). Its angular velocity
increases from zero to 120
rotation/minute in 8 seconds, at what
rate is work done by the torque at the end of 8th second?
A . \( \pi \) Watt \( t \)
B . \( \pi^{2} \) Watt
c. \( \pi^{3} \) Watt
D. \( \pi^{4} \) Watt
Subject: Chemistry
\( \alpha-D-g l u \cos e \) undergoes mutarotation to
\( \alpha-D \) -glucose in aqueous solution. If at
\( 298 \mathrm{K} \) there is \( 60 \% \) conversion,
calculate \( \Delta G^{o} \) of the reaction.
\( \boldsymbol{\alpha}-\boldsymbol{D}-\boldsymbol{G} \boldsymbol{l} \boldsymbol{u} \operatorname{cose} \rightleftharpoons \boldsymbol{\beta}-\boldsymbol{D}-\boldsymbol{G} \boldsymbol{l} \boldsymbol{u} \operatorname{cose} \)
A. 0.525 kJ/mol
B. 1.005 kJ/mol
c. \( 2.45 \mathrm{kJ} / \mathrm{mol} \)
D. None of these
Subject: Maths
Find the position vector of a point \( \boldsymbol{R} \)
which divides the line joining two
points \( P \) and \( Q \) whose position vectors \( \operatorname{are}(2 \vec{a}+\vec{b}) \) and \( (\vec{a}-3 \vec{b}) \) externally in
the ratio \( 1: 2 . \) Also, show that \( P \) is the
mid point of the line segment \( \boldsymbol{R} \boldsymbol{Q} \)
Subject: Physics
When two unknown resistors are
connected in series with a battery, \( 225 W \) power is delivered to the
combination with a total current \( 5 A \). For
the same total current \( 50 W \) is delivered
when the resistors are connected in
parallel. Find the ratio of the two resistances
\( A \cdot 2 \)
B. 5
\( c \cdot 4 \)
D. 10
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})=\mathbf{8} \boldsymbol{x}^{\mathbf{3}} \) and \( \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{x}^{\mathbf{1} / 3} \). Find g o
and \( f \circ g \)
Subject: Chemistry
Which of the following represents
saponification reaction?
\( \mathbf{A} \cdot C H_{3} C O O N a+N a O H \stackrel{C a O}{\longrightarrow} C H_{4}+N a_{2} C O_{3} \)
B \( \cdot C H_{3} C O O H+C_{2} H_{5} O H \frac{H_{2} S O_{4}}{\longrightarrow} C H_{3} C O O C_{2} H_{5}+ \)
\( H_{2} O \)
c. \( 2 C H_{3} C O O H+2 N a \rightarrow 2 C H_{3} C O O N a+H_{2} \)
D. \( C H_{3} C O O C_{2} H_{5}+N a O H \rightarrow C H_{3} C O O N a+C_{2} H_{5} O H \)
Subject: Biology
Match the following.
\begin{tabular}{llll} 
(a) & Protein & (i) & SER \\
(b) & Lipid & (ii) & Golgi body \\
(c) & Glycoprotein & (iii) & Lysosome \\
(d) & Hydrolytic enzyme & (iv) & RER \\
\hline
\end{tabular}
\( A \cdot a-i, b-i i, c-i i i, d-i v \)
B. a-iv, b-ii, c-i, d-iii
c. a-iv, b-i, c-ii, d-iii
D. a-i, b-iii, c-ii, d-iv
Subject: Chemistry
Wurtz reaction of methyl iodide yields an organic compound \( X . \) Which one of
the following reactions also yields \( X ? \)
A \( \cdot C_{2} H_{5} C l+M g \stackrel{\text { Dry ether }}{\longrightarrow} \)
B . \( C_{2} H_{5} C l+L i A l H_{4} \rightarrow \)
c. \( C_{2} H_{5} C l+C_{2} H_{5} O N a \rightarrow \)
D. \( C H C l_{3} \frac{A g \text { powder }}{\wedge} \)
Subject: Biology
Mark the wrong statement
A. Zinc is a cofactor for proteolytic enzyme carboxypeptidase
B. \( K_{m} \) (Michaelis Constant) is numerically equivalent to \( 1 / 2 \mathrm{Vmax} \)
C. Strands of DNA appear like a helical staircase. At each
step of ascent, strand turns \( 36^{\circ} \)
D. Tyrosine, Phenylalanine and Tryptophan are aromatic amino acids
Subject: Chemistry
The diagram shows experiments involving the rusting of iron. The following results were suggested. 1 In tube \( P \), the iron nails rust.
2 In tube \( Q \), the iron nails do not rust.
3 In tube \( R \), the iron nails do not rust.
Which results are correct?
A . 1 and 2 only
B. 1 and 3 only
c. 2 and 3 only
D. 1,2 and 3
Subject: Maths
If \( A \) and \( B \) are events such that
\( \boldsymbol{P}(\boldsymbol{A} \mid \boldsymbol{B})=\boldsymbol{P}(\boldsymbol{B} \mid \boldsymbol{A}), \) then
A \( . A \subset B \) but \( A \neq B \)
в. \( A=B \)
c. \( A \cap B=\Phi \)
D \( \cdot P(A)=P(B) \)
Subject: Physics
Match the Column I with Column II
Column n II
nion Column
I
(Units) (Dimensional formulae)
(A) Pas Pas
\( (p) \)
\( \left[M^{0} L^{2} T^{-2} K^{-1}\right] \)
(B) \( \mathrm{Nm} \mathrm{K}^{-1} \)
\( (q) \)
\( \left[M L T^{-3} K^{-1}\right] \)
\( (C) \)
\( \mathrm{J} \mathrm{kg}^{-1} \mathrm{K} \)
-1
\( (r) \)
\( \left[M L^{-1} T^{-1}\right] \) "
(D) \( \mathrm{W} \mathrm{m}^{-1} \)
\( \mathrm{K}^{-1} \)
(s) \( \left[M L^{2} T^{-2} K^{-1}\right] \)
\( A \cdot A-q, B-p, C-r, D-s \)
B. \( A-p, B-q, C-s, D-r \)
C. \( A-r, B-s, C-p, D-q \)
D. \( A-s, B-r, C-q, D-p \)
Subject: Maths
The two curves \( y=x^{2}-1 \) and \( y= \)
\( 8 x-x^{2}-9 \) at the point (2,3) have
common
A. tangent as \( 4 x-y-5=0 \)
B. tangent as \( x+4 y-14=0 \)
c. normal as \( 4 x+y=11 \)
D. normal as \( x-4 y=10 \)
Subject: Physics
The prefixes \( n a n o(n), m i c r o(\mu) \) and pico \( (p) \) are often used with units.
Which row shows their correct values?
A \( \cdot n=10^{-6}, \mu=10^{-9}, p=10^{-12} \)
B . \( n=10^{-6}, \mu=10^{-12}, p=10^{-9} \)
C \( . n=10^{-9}, \mu=10^{-6}, p=10^{-12} \)
D . \( n=10^{-12}, \mu=10^{-9}, p=10^{-6} \)
Subject: Physics
Comparing the L-C oscillations with the oscillations of a spring block system (force constant of spring \( =k \) and mass
of the block \( =m \) ), the physical quantity
\( m k \) is equal to :
A . \( C L \)
в. \( 1 / C L \)
c. \( C / L \)
D. \( L / C \)
Subject: Maths
\( f(x) \) is cubic polynomial which has local maximum at \( \mathbf{x}=-1 . \) If \( \mathbf{f}(\mathbf{2})= \)
\( \mathbf{1 8}, \mathbf{f}(\mathbf{1})=-\mathbf{1} \) and \( \mathbf{f}(\mathbf{x}) \) has local
minima at \( \mathbf{x}=\mathbf{0}, \) then
This question has multiple correct options
A. the distance between (-1,2) and \( (a, f(a)), \) where \( x=a \) is the point of local minima is \( 2 \sqrt{5} \)
B. f(x) is increasing for \( x \in[1,2 \sqrt{5} \)
\( \mathrm{c} . \mathrm{f}(\mathrm{x}) \) has local minima at \( \mathrm{x}=1 \)
D. the value of \( f(0)=5 \)
Subject: Maths
Points are to be recognised on X-Y plane
to draw graph of equation \( 2 x+3 y=12 \)
So fill the boxes given below and
identify points.
\begin{tabular}{|c|c|c|c|c|}
\hline\( x \) & \( -2 . \) & 3 & 6 & \( \square \) \\
\hline\( y \) & 4 & \( \square \) & \( \square \) & 6 \\
\hline\( (x, y) \) & \( \square \) & \( \square \) & \( \square \) & \\
\hline
\end{tabular}
Subject: Chemistry
If \( \boldsymbol{r}=-\frac{\mathbf{3}}{\mathbf{2}} \frac{\boldsymbol{\Delta}[\boldsymbol{A}]}{\boldsymbol{\Delta} \boldsymbol{t}}=-\mathbf{5} \frac{\boldsymbol{\Delta}[\boldsymbol{B}]}{\boldsymbol{\Delta} \boldsymbol{t}}=+\frac{\boldsymbol{7}}{\boldsymbol{3}} \frac{[\boldsymbol{\Delta} \boldsymbol{C}]}{\Delta \boldsymbol{t}} \)
which of the following is the corresponding stoichiometric equation?
\( ^{\mathbf{A}} \cdot \frac{2}{3} A+\frac{1}{5} B \rightarrow \frac{3}{7} C \)
в. \( \frac{2}{3} A+\frac{5}{2} B \rightarrow \frac{7}{3} C \)
c. \( \frac{3}{2} A+\frac{5}{2} B \rightarrow \frac{7}{3} C \)
D \( \cdot \frac{7}{3} C+\frac{5}{2} B \rightarrow \frac{3}{2} A \)
Subject: Maths
If \( \boldsymbol{D}_{\boldsymbol{r}}=\left|\begin{array}{ccc}\boldsymbol{r} & \boldsymbol{x} & \frac{\boldsymbol{n}(\boldsymbol{n}+\mathbf{1})}{\mathbf{2}} \mid \\ \boldsymbol{2 r}-\boldsymbol{1} & \boldsymbol{y} & \boldsymbol{n}^{2} \\ \boldsymbol{3 r}-\boldsymbol{2} & \boldsymbol{z} & \frac{\boldsymbol{n}(\boldsymbol{3} \boldsymbol{n}-\mathbf{1})}{\mathbf{2}}\end{array}\right|, \) then
\( \sum_{r=1}^{n} D_{r} \) is equal to
A \( \cdot \frac{1}{6} n(n+1)(2 n+1) \)
B. \( \frac{1}{4} n^{2}(n+1)^{2} \)
\( c \cdot 0 \)
D. none of these
Subject: Chemistry
A buffer solution made up of \( B O H \) and
\( B C l \) of total molarity \( 0.29 \mathrm{M} \) has \( p H= \) 9.6 and \( K_{b}=1.8 \times 10^{-5} \)
Concentration of salt and base
respectively is:
A. \( 0.09 \mathrm{M} \) and \( 0.2 \mathrm{M} \)
B. 0.2 M and 0.09 M
c. \( 0.1 \mathrm{M} \) and \( 0.19 \mathrm{M} \)
D. 0.19 M and 0.1 M
Subject: Chemistry
Standard free energies of formation(in
\( k J / m o l \) ) at \( 298 \mathrm{K} \) are -237.2,-394.4
and -8.2 for \( H_{2} O(I), C O_{2}(g) \) and pentane(g) respectively. The value of \( E_{c e l l}^{o} \) for the pentane-oxygen fuel cell is:
A . \( 1.968 \mathrm{v} \)
в. 2.0968 V
c. \( 1.0968 \mathrm{v} \)
D. \( 0.0968 \mathrm{V} \)
Subject: Chemistry
The correct statement among the
following is:
\( \mathbf{A} \cdot\left(S i H_{3}\right)_{3} N \) is pyramidal and more basic than \( \left(C H_{3}\right)_{3} N \)
B. \( \left(\operatorname{Si} H_{3}\right)_{3} N \) is planar and more basic than \( \left(C H_{3}\right)_{3} N \)
C \( \cdot\left(S i H_{3}\right)_{3} N \) is pyramidal and less basic than \( \left(C H_{3}\right)_{3} N \)
D. \( \left(S i H_{3}\right)_{3} N \) is planar and less basic than \( \left(C H_{3}\right)_{3} N \)
Subject: Maths
The factors of \( 63 x^{2}-448 \) is
A. \( 9(7 x+8)(7 x-8) \)
B. \( 7(3 x+8)^{2} \)
c. \( 7(3 x+8)(3 x-8) \)
D. \( 9(7 x-8)^{2} \)
Subject: Chemistry
The compounds \( A \) and \( B \) are mixed in equimolar proportion to form the products, \( \boldsymbol{A}+\boldsymbol{B} \rightleftharpoons \boldsymbol{C}+\boldsymbol{D} . \) At
equilibrium, one-third of \( A \) and \( B \) are
consumed. The equilibrium constant for the reaction is:
A . 0.5
в. 4.0
c. 2.5
D. 0.25
Subject: Maths
Find the square of \( a+2 b+c \)
\( \mathbf{A} \cdot a^{2}+b^{2}+c^{2}+a b+b c+a c \)
B \( \cdot a^{2}+4 b^{2}+c^{2}+4 a b+4 b c+2 a c \)
C \( \cdot a^{3}+4 b^{3}+c^{3}+8 a b+8 b c+8 a c \)
D. \( a^{3}+b^{3}+c^{3}+4 a b+4 b c+2 a c \)
Subject: Physics
The temperature as measured by the
thermometer shown here will be:
A \( \cdot 84^{\circ} \mathrm{C} \)
в. \( 86^{\circ} \mathrm{C} \)
\( \mathrm{c} \cdot 88^{\circ} \mathrm{C} \)
D. \( 90^{\circ} C \)
Subject: Maths
The number of distinct solutions of
\( \sin 5 \theta \cdot \cos 3 \theta=\sin 9 \theta \cdot \cos 7 \theta \) in \( \theta \in \)
\( [\mathbf{0}, \boldsymbol{\pi} / \mathbf{2}] \) is
\( A \cdot 4 \)
B. 5
\( c \cdot 8 \)
D.
Subject: Physics
Uncertainty in position of a 0.25 g particle is \( 10^{-5} \mathrm{m} . \) The uncertainty in its
velocity will be:-
\( \left(h=6.6 \times 10^{-34} J s\right) \)
A. \( 1.2 \times 10^{34} \)
B . \( 2.1 \times 10^{-29} \)
c. \( 1.6 \times 10^{-20} \)
D. \( 1.7 \times 10^{-9} \)
Subject: Physics
Assertion
For practical purposes, the earth is used as a reference at zero potential electrical circuits. and
Reason
The electrical potential of a sphere of radius \( R \) with charge \( Q \) uniformly distributed on the surface is given by
\( \frac{Q}{4 \pi \varepsilon_{0} R} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
Subject: Chemistry
Provide the systematic name of the
compounds shown.
\( \mathbf{A} \cdot 4-b u t y l-2-e t h y l-1- \)methylcycloheptane
B. \( 1-b u t y l-4- \) ethyl \( -3- \) methylcycloheptane
c. \( 2-b u t y l-4- \) ethyl \( -1- \) methylcycloheptane
D. \( 4-b u t y l-1- \) ethyl \( -2- \) methylcycloheptane
Subject: Chemistry
\( \mathbf{2} \boldsymbol{s} \stackrel{I}{\rightarrow} \mathbf{2} \boldsymbol{p} \stackrel{I I}{\rightarrow} \mathbf{3} \boldsymbol{d} \stackrel{I I}{\rightarrow} \mathbf{3} \boldsymbol{p} \stackrel{I V}{\rightarrow} \mathbf{4} \boldsymbol{s} \stackrel{\boldsymbol{V}}{\rightarrow} \mathbf{2} \boldsymbol{p} \)
The electronic transitions show above
are observed when lithium atoms are
sprayed into a hot flame. The various
transitions are numbered for
identification. Which of these
transitions would result in emission of
electromagnetic radiation (light)?
A. I and II only
B. I and III only
c. I and v only
D. III and IV only
E. III and v only
Subject: Chemistry
A golf ball has mass of \( 30 g \) and a speed of \( 50 \mathrm{m} / \mathrm{s} \). If the speed can be
measured within accuracy of \( 1 \% \) then uncertainty in the position is:
A. \( 2.4 \times 10^{-32} \mathrm{m} \)
В. \( 3.5 \times 10^{-33} \mathrm{m} \)
c. \( 3.5 \times 10^{-34} \mathrm{m} \)
D . 2.4 \( \times 10^{-33} \mathrm{m} \)
Subject: Maths
Integrate \( \int\left(x^{3}-1\right)^{\frac{1}{3}} x^{5} d x \)
\( \frac{1}{3}\left(\frac{3}{7}\left(x^{3}-1\right)^{\frac{7}{3}}+\frac{3}{4}\left(x^{3}-1\right)^{\frac{4}{3}}\right) \)
\( \frac{1}{3}\left(\frac{3}{7}\left(x^{3}-1\right)^{\frac{5}{3}}+\frac{3}{4}\left(x^{3}-1\right)^{\frac{4}{3}}\right) \)
\( \frac{1}{3}\left(\frac{3}{7}\left(x^{3}-1\right)^{\frac{7}{3}}-\frac{3}{4}\left(x^{3}-1\right)^{\frac{4}{3}}\right) \)
D. None of these
Subject: Maths
If \( f(x)=\frac{3 x^{2}+a x+a+1}{x^{2}+x-2}, \) then which
of the following can be correct? This question has multiple correct options
A \( \cdot \lim _{x \rightarrow 1} f(x) \) exists \( \Rightarrow a=-2 \)
B. \( \lim _{x \rightarrow-2} f(x) \) exists \( \Rightarrow a=13 \)
\( \mathbf{c} \cdot \lim _{x \rightarrow 1} f(x)=\frac{4}{3} \)
D. \( \lim _{x \rightarrow-2} f(x)=-\frac{1}{3} \)
Subject: Maths
\( \int \sqrt{\frac{\cos x-\cos ^{3} x}{1-\cos ^{3} x}} d x \) is equal to
A \( \cdot \frac{2}{3} \sin ^{-1}\left(\cos ^{3 / 2} x\right)+C \)
B \( \cdot \frac{3}{2} \sin ^{-1}\left(\cos ^{3 / 2} x\right)+C \)
C \( \cdot \frac{2}{3} \cos ^{-1}\left(\cos ^{3 / 2} x\right)+C \)
D. none of these