AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Calculate the change in pH of one litre of buffer solution containing 0.10 mole
each of \( N H_{3} \& N H_{4} C l \) upon addition
of,
(i) 0.02 mole of dissolved gaseous \( H C l \) (ii) 0.02 mole of dissolved \( N a O H \)
Assume no change in solution volume. \( \left(\boldsymbol{K}_{\boldsymbol{b}} \boldsymbol{f} \boldsymbol{o r} \boldsymbol{N} \boldsymbol{H}_{3}=\mathbf{1 . 8} \times \mathbf{1 0}^{-\mathbf{5}}\right) \)
A \( .4 .57,4.92 \)
B. 4.25,4.57
c. 4.83,4.64
D. 3.25,3.9
Subject: Chemistry
In the reaction:
\( \mathbf{2} \boldsymbol{A} \boldsymbol{l}_{(\boldsymbol{6})}+\boldsymbol{6} \boldsymbol{H} \boldsymbol{C l}(\boldsymbol{a q}) \rightarrow \boldsymbol{2} \boldsymbol{A l}^{3+}(\boldsymbol{a q})+ \)
\( 6 C l^{-}(a q)+3 H_{2}(g) \)
A. 6 L \( H C l(a q) \) is consumed for every 3 L \( H 2(g) \) produced
B. 33.6 し \( H_{2}(g) \) is produced regardless of temperature and pressure for every mole \( A l \) that reacts
C. 67.2 L \( H_{2}(g) \) at STP is produced for every mole \( A l \) that reacts
D. \( 11.2 \mathrm{L} H_{2}(g) \) at STP is produced for every mole \( H C l(a q) \) consumed
Subject: Maths
Let \( S_{n}=\sum_{k=1}^{n} \frac{n}{n^{2}+k n+k^{2}} \) and \( T_{n}= \)
\( \sum_{k=0}^{n-1} \frac{n}{n^{2}+k n+k^{2}}, \) for \( n=1,2,3, \dots \)
Then,
This question has multiple correct options
A \( \cdot S_{n}<\frac{\pi}{3 \sqrt{3}} \)
в. \( S_{n}>\frac{\pi}{3 \sqrt{3}} \)
c. \( T_{n}<\frac{\pi}{3 \sqrt{3}} \)
D \( \cdot T_{n}>\frac{\pi}{3 \sqrt{3}} \)
Subject: Chemistry
For the precipitation reaction of \( \boldsymbol{A} \boldsymbol{g}^{+} \) ions with \( N a C l, \) the correct relation is
A. \( \Delta H=0 \)
в. \( \Delta G=0 \)
c. \( \Delta G=-v e \)
\( \mathbf{D} \cdot \Delta G=\Delta H \)
Subject: Maths
Let \( ^{*} \) be a binary operation on the set \( \boldsymbol{Q} \)
of rational numbers as follows:
\( \boldsymbol{a} * \boldsymbol{b}=(\boldsymbol{a}-\boldsymbol{b})^{2} \)
Find which of the binary operations are commutative and which are
associative.
Subject: Chemistry
Barium chloride reacts with sodium
sulphate to form Barium sulphate and
sodium chloride. Then, according to the
law of conservation of mass
A. The total mass of reactants, barium chloride and sodium sulphate taken is greater than the total mass of products, barium sulphate, sodium chloride formed
B. The total mass of reactants, barium chloride and sodium sulphate taken is less than the total mass of products, barium sulphate, sodium chloride formed
C. The total mass of the reactants is equal to the total mass of products
D. None of the above
Subject: Maths
The ends of a diagonal of a square are (2,-3) and \( (-1,1) . \) Another vertex of the square can be
This question has multiple correct options
\( ^{\mathbf{A}} \cdot\left(\frac{-3}{2},-\frac{5}{2}\right) \)
в. \( \left(\frac{5}{2}, \frac{1}{2}\right) \)
\( ^{c} \cdot\left(\frac{1}{2}, \frac{5}{2}\right) \)
D. none of these
Subject: Physics
A bullet of mass \( m \) moving horizontally with a velocity \( v \) strikes a block of wood
of mass \( M \) and gets embedded in the block. The block is suspended from the ceiling by a massless string. The height to which block rises is:
\( A \)
\[
\frac{v^{2}}{2 g}\left(\frac{m}{M+m}\right)^{2}
\]
в.
\[
\frac{v^{2}}{2 g}\left(\frac{M+m}{m}\right)^{2}
\]
\( ^{\mathrm{c} \cdot} \frac{v^{2}}{2 g}\left(\frac{m}{M}\right)^{2} \)
\( D \)
\[
\frac{v^{2}}{2 g}\left(\frac{M}{m}\right)^{2}
\]
Subject: Chemistry
Which reaction represents the oxidising behaviour of \( \boldsymbol{H}_{2} \boldsymbol{S O}_{4} ? \)
A \( \cdot N a C l+H_{2} S O_{4} \rightarrow N a H S O_{4}+H C l \)
в. \( 2 \mathrm{NaOH}+\mathrm{H}_{2} \mathrm{SO}_{4} \rightarrow \mathrm{Na}_{2} \mathrm{SO}_{4}+2 \mathrm{H}_{2} \mathrm{O} \)
\( \mathrm{c} \cdot 2 \mathrm{HI}+\mathrm{H}_{2} \mathrm{SO}_{4} \rightarrow \mathrm{I}_{2}+\mathrm{SO}_{2}+2 \mathrm{H}_{2} \mathrm{O} \)
D. \( 2 P C l_{5}+H_{2} S O_{4} \rightarrow 2 P O C l_{3}+S O_{2} C l_{2}+2 H C l \)
Subject: Chemistry
Write balanced net ionic equation for
the following reactions in acidic
solution.
\[
\begin{array}{l}
\boldsymbol{S}_{4} \boldsymbol{O}_{6}^{2-}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{A l}(\boldsymbol{s}) \rightarrow \boldsymbol{H}_{2} \boldsymbol{S}(\boldsymbol{a} \boldsymbol{q})+ \\
\boldsymbol{A l}^{3+}(\boldsymbol{a} \boldsymbol{q})
\end{array}
\]
\( \mathbf{A} \cdot S_{4} O_{6}^{2-}(a q)+6 A l(s)+20 H^{+} \rightarrow 4 H_{2} S(a q)+ \)
\[
6 A l^{3+}(a q)+6 H_{2} O
\]
\( \mathbf{B} \cdot 2 S_{4} O_{6}^{2-}(a q)+6 A l(s)+20 H^{+} \rightarrow 4 H_{2} S(a q)+ \)
\[
2 A l^{3+}(a q)+6 H_{2} O
\]
\( \mathbf{c} \cdot S_{4} O_{6}^{2-}(a q)+5 A l(s)+20 H^{+} \rightarrow 4 H_{2} S(a q)+ \)
\[
3 A l^{3+}(a q)+6 H_{2} O
\]
D. None of the above
Subject: Chemistry
Compare \( C-O \) bond strength
amongst:
A \( \cdot C O>C O_{2}>C O_{3}^{2} \)
в. \( C O>C O_{3}^{2-}>C O_{2} \)
\( c \cdot C O_{3}^{2-}>C O_{2}>C O \)
D. \( C O<C O_{3}^{2-}<C O_{2} \)
Subject: Physics
A long solenoid is fabricated to closely winding wire of radius \( 0.5 \mathrm{mm} \) over a cylinderical frame, so that the
successive turns nearly touch each other. The magnetic field at the centre of solenoid, if it carries a current of 5 A
is?
\( \mathbf{A} \cdot 2 \pi \times 10^{-2} \mathbf{T} \)
В . \( 2 \pi \times 10^{-3} \mathrm{T} \)
с. \( 2 \pi \times 10^{-4} \mathrm{T} \)
D. \( 2 \pi \times 10^{-5} \mathrm{T} \)
Subject: Physics
Ultrasonic waves are sent in the sea
from a sonar device attached to a ship. These waves take 0.6 s to travel from the
ship to the bottom of the sea and back to the ship in the form of an echo. What is the depth of the sea? (Speed of sound in water \( =1500 \mathrm{m} / \mathrm{s} \) )
A. \( 450 \mathrm{m} \)
B. 900 \( m \)
c. \( 300 \mathrm{m} \)
D. 600
Subject: Chemistry
Which of the following statements
is/are wrong?
This question has multiple correct options
A. Beilstein test is a reliable test for halogens in organic compounds.
B. In Lassaigne's test for N, Prussian blue colour is due to the formation of ferro-ferri cyanide.
C. When \( F e C l_{3} \) solution is added to the Lassaigne's extract, a blue solution is obtained, which indicates the presence of both \( \mathrm{N} \) and \( \mathrm{S} \)
D. Molecular mass of an acid = Equivalent mass \( x \) acidity.
Subject: Physics
A pulse of sound wave travels a distance \( l \) in helium gas in time \( T \) at \( a \)
particular temperature. If at the same temperature a pulse of sound wave is propagated in oxygen gas, it will cover
the same distance \( l \) in time.
A . \( 4.36 T \)
в. \( 0.23 T \)
\( c .3 T \)
D. \( 0.46 T \)
Subject: Chemistry
Which of the following set of species have same hybridisation state but different shapes?
A \( \cdot N O_{2}^{+}, N O_{2}, N O_{2} \)
в. \( C l O_{4}, S F_{4}, X e F_{4} \)
c. \( N H_{4}^{+}, H_{3} O^{+}, O F_{2} \)
D. \( S O_{4}^{2-}, P O_{4}^{3-}, C l O_{4} \)
Subject: Chemistry
If first ionisation energy of hydrogen is
\( \boldsymbol{E}, \) then the ionisation energy of \( \boldsymbol{H} \boldsymbol{e}^{+} \) would be:
A. \( E \)
в. \( 2 E \)
\( c .0 .5 E \)
D. \( 4 E \)
Subject: Physics
If \( x, v \) and a denote the displacement, the velocity and the acceleration of a
particle executing simple harmonic motion of time period \( T, \) then which of the following do not change with time?
A \( \cdot \frac{a T}{v} \)
В . \( a T+2 \pi v \)
c. \( a^{2} T^{2}+4 \pi^{2} v^{2} \)
D. \( a T \)
E . \( v T \)
Subject: Maths
If \( I_{n}=\int_{0}^{\infty} e^{-x} x^{n-1} d x, \) then
\( \int_{0}^{\infty} e^{-\lambda x} x^{n-1} d x \) is equal to?
A \( . \lambda I_{n} \)
B. \( \frac{1}{\lambda} I \)
c. \( \frac{I_{\mathrm{n}}}{\lambda^{\mathrm{n}}} \)
D. \( \lambda^{n} I_{n} \)
Subject: Physics
A block of mass ' \( m^{\prime} \) is placed on floor of a lift which is rough. The coefficient of friction between the block and the floor
is \( \mu . \) When the lift falls freely, the block
is pulled horizontally on the lift floor. The force of friction is:
A . zero
в. \( 2 \mu m g \)
c. \( \frac{1}{2} \mu m g \)
D. \( \mu m g \)
Subject: Chemistry
The formula for calculating \( \bar{M}_{n} \) of a polymer is:
A. \( \frac{\sum N i M i}{\sum N i} \)
в. \( \frac{\sum N i M i}{\sum M i} \)
c. \( \frac{\sum_{N i M i}^{2}}{\sum M i} \)
D. \( \frac{\sum N i M i^{2}}{\sum N N M i} i \)
Subject: Chemistry
Which one of the following is incorrect?
A. The bond order of \( H_{2}, N_{2} \) and \( O_{2} \) follows the order:
\( N_{2}>O_{2}>H_{2} \)
B. In \( C s C I \) lattice, each \( C s \) is surrounded by \( 8 C l^{-} \) ions
C. The ionic nature of \( K C l, M g C l_{2} \) and \( A l C l_{3} \) follows the
order: \( K C l>M g C l_{2}>A l C l_{3} \)
D. The central atoms in \( P F_{3}, C l F_{3} \) and \( X e F_{2} \) have \( s p^{3} d \) hybridisation
Subject: Chemistry
Which one of the following sets form the biodegradable polymer?
A \( \cdot H_{2} N-C H_{2}-C O O H \) and \( H_{2} N-\left(C H_{2}\right)_{5}-C O O H \)
в.
\( \langle\bigcirc\rangle-\mathrm{cH}=\mathrm{cH}_{2} \mathrm{and} \mathrm{CH}_{2}=\mathrm{CH}-\mathrm{CH}=\mathrm{CH}_{2} \)
D. \( C H_{2}=C H-C N \) and \( C H_{2}=C H-C H=C H_{2} \)
Subject: Physics
A uniform rope of length \( 12 \mathrm{m} \) and mass 6 kg hangs vertically from a rigid support. A block of mass 2 kg is attached to the free end of the rope. \( A \)
transverse pulse of wavelength \( 0.06 \mathrm{m} \) is produced at the lower end of the rope.
What is the wavelength of the pulse
when it reaches the top of the rope?
A. \( 0.06 \mathrm{m} \)
B. 0.03
c. \( 0.12 \mathrm{m} \)
D. 0.09 \( m \)
Subject: Chemistry
Which of the following molecules has two lone pairs and bond angle (need not
be all bond angles) \( <109.5^{\circ} ? \)
\( \mathbf{A} \cdot S F_{2} \)
в. \( K r F_{4} \)
\( \mathbf{c} \cdot I O I_{4}^{-} \)
D. All of the above
Subject: Chemistry
\begin{tabular}{ll|l} 
& \( \mathbf{X} \) & \( \mathbf{Y} \) \\
& & \\
Normal & 2,8,7 & \\
Electronic & & 2,8,2 \\
Configuration & Dissolves in & Very low \\
Nature of & water and & solubility in \\
oxide & turns blue & water. \\
& litmus red & Dissolves in \\
& & hydrochloric \\
Tendency for & acid \\
oxidising & Tends to & Tends to act \\
and reducing & oxidise & as a \\
reactions & elements & reducing \\
Electrical and & and & agent \\
thermal & compounds & Good \\
conductivity & Very poor & Electrical \\
& electrical & conductor \\
& conductor & Good \\
& Poor thermal & Thermal \\
& conductivity & conductor \\
Tendency to & & \\
form & No tendency & \\
alloys and & to form & Forms alloys \\
amalgums & alloys &
\end{tabular} Using the information above, complete
the following

Non-metallic elements tend to be electricity
Subject: Maths
The eccentricity of an ellipse is \( \frac{\sqrt{3}}{2}, \) its
length of latus rectum is equal to:
A \( \cdot \frac{1}{2}(\text { Length of major axis }) \)
B. \( \frac{1}{3} \) (Length of major axis)
c. \( \frac{1}{4} \) (Length of major axis)
D. \( \frac{2}{3} \) (Length of major axis)
Subject: Physics
A disc of mass \( m \) and radius \( R \) rolls
down an inclined plane of height \( h \) without slipping. Find out the velocity of the disc when it reaches the bottom
of the incline? The moment of inertia for
a disk is \( (1 / 2) m R^{2} \)
A \( \cdot \sqrt{g h} \)
в. \( \sqrt{\frac{4}{3} g h} \)
c. \( \sqrt{2 g h} \)
D. \( 2 \sqrt{g h} \)
E \( .2 \sqrt{2 g h} \)
Subject: Maths
Find the value of
\[
\tan \left\{\frac{1}{2} \sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right)+\frac{1}{2} \cos ^{-1}\left(\frac{1-}{1+}\right.\right.
\]
if \( \boldsymbol{x}>\boldsymbol{y}>1 \)
Subject: Chemistry
Which is not a disproportionation
reaction?
\( A \)
B.
\[
\begin{array}{ll}
\text { CHO } & \text { CH }_{2} \text { OH } \quad \text { COO }^{-} \\
\text {COOH } & \text { COO }^{-}+\mid
\end{array}
\]
c. \( N a H+H_{2} O \rightarrow N a O H+H_{2} \)
D. All of the above
Subject: Maths
If \( \boldsymbol{A}=\left(\begin{array}{ccc}1 & -1 & 3 & 2 \\ 5 & -4 & 7 & 4 \\ 6 & 0 & 9 & 8\end{array}\right), \) Write down the
elements \( a_{24} \) and \( a_{32} \)
Subject: Physics
Two trains, each \( 50 \mathrm{m} \) long are travelling in opposite direction with velocity 10 \( \mathrm{m} / \mathrm{s} \) and \( 15 \mathrm{m} / \mathrm{s} \) The time of crossing is:
A \( .2 s \)
B. \( 4 s \)
c. \( 2 \sqrt{3} s \)
D. \( 4 \sqrt{3} s \)
Subject: Physics
A bolt of mass \( 0.3 \mathrm{kg} \) falls from the ceilling of an elevator moving down with an uniform speed of \( 7 m / s . \) It hits the floor of the elevator ( length of the elevator \( =3 \mathrm{m} \) ) and does not rebound.
What is the heat produced by impact?
A . 8.82
B . 7.72 J
c. 6.62 J
D. 5.52
Subject: Maths
Solve the given equation for \( y: \) \( \frac{1-9 y}{19-3 y}=\frac{5}{8} \)
A \( -\frac{66}{103} \)
в. \( \frac{38}{73} \)
\( c \cdot-\frac{87}{57} \)
D. None of these
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \max \{1+\sin x, 1,1-\cos x\}, x \in \)
\( [0,2 \pi] \) and \( g(x)= \)
\( \max \{1,|x-1|\}, x \in R, \) then
This question has multiple correct options
A. \( g(f(0))=1 \)
B. \( g(f(1))=1 \)
c. \( f(g(1))=1 \)
D. \( f(g(0))=\sin 1 \)
Subject: Maths
Find the shortest distance between
lines: \( \frac{x-1}{1}=\frac{y-2}{3}=\frac{z-3}{2} \) and
\( \frac{x-4}{2}=\frac{y-5}{3}=\frac{z-6}{1} \)
A . \( \sqrt{6} \)
B. \( \sqrt{5} \)
\( c \cdot \sqrt{3} \)
D. 6
Subject: Physics
A bread gives a boy of mass \( 40 k g \) an
energy of \( 21 k J . \) If the efficiency is \( 28 \% \) then the height can be climbed by him using this energy is
\( \mathbf{A} \cdot 22 \cdot 5 m \)
в. \( 14.7 m \)
\( c .5 m \)
D. \( 10 m \)
Subject: Chemistry
Write order of dipole moment of
following compounds:
\( (\mathrm{i}) \)
(ii)
(iii)
(v)
\( (\mathbf{v i}) \)
A \( .(i i i)>(i i)>(i)>(i v)>(v)>(v i) \)
B. \( (i i i)>(i)>(i i)=(v i)>(i v)>(v) \)
C. \( (i i)>(i)=(i i i)=(i v)>(v)=(v i) \)
D. \( (i i i)>(i)>(i v)>(v)>(i i)>(v i) \)
Subject: Physics
A sphere of brass released in a long liquid column attains a terminal speed
\( \boldsymbol{v}_{0} . \) If the terminal speed attained by sphere of marble of the same radius
and released in the same liquid in \( n v_{0} \) then the value of \( n \) will be (Given : The
specific gravities of brass, marbles and
the liquid are 8.5,2.5 and 0.8 respectively \( ) \)
A \( \cdot \frac{5}{17} \)
в. \( \sqrt{\frac{17}{77}} \)
c. \( \frac{11}{31} \)
D. \( \frac{17}{5} \)
Subject: Maths
If \( a, b, x, y \) be real numbers such that
\( \boldsymbol{a}^{2}+\boldsymbol{b}^{2}=\mathbf{8} \mathbf{1}, \boldsymbol{x}^{2}+\boldsymbol{y}^{2}=\mathbf{1 2} \mathbf{1} \) and \( \boldsymbol{a} \boldsymbol{x}+ \)
\( \boldsymbol{b} \boldsymbol{y}=\mathbf{9} \boldsymbol{9} \), then find the set of all possible
values of \( a y-b x \)
A \( \cdot\left(0, \frac{9}{11}\right] \)
в. \( \left(0, \frac{9}{11}\right) \)
\( c \cdot\{0\} \)
D. \( \left[\frac{9}{11}, \infty\right) \)
Subject: Maths
A pair of straight lines drawn through the origin forms an isosceles right
triangle with the line \( 2 x+3 y=6, \) then
the lines and the area of the triangle thus formed is
\( \mathbf{A} \cdot x-5 y=0 \)
\[
\begin{array}{c}
5 x+y=0 \\
\Delta=\frac{36}{13}
\end{array}
\]
B. \( 3 x-y=0 \)
\[
x+3 y=0
\]
\[
\Delta=\frac{12}{17}
\]
c. \( 5 x-y=0 \)
\[
\begin{array}{c}
x+5 y=0 \\
\Delta=\frac{13}{5}
\end{array}
\]
D. None of these
Subject: Maths
The value of \( \sin ^{-1}(\sin 12)- \)
\( \cos ^{-1}(\cos 12)= \)
\( \mathbf{A} \cdot \mathbf{0} \)
в.
\( c \cdot 8 \pi+24 \)
D. \( 8 \pi-24 \)
Subject: Physics
The electric current in a wire may be
calculated using the equation \( \boldsymbol{I}= \)
Anvq.

Which statement is not correct?
A. \( n \) is the number of charge carriers per unit volume of the wire
B. nA is the number of charge carriers per unit length of the wire
c. q is the charge of each charge carrier
D. v is the velocity of each charge carrier
Subject: Physics
The period of oscillation of a simple pendulum in the experiment is recorded as \( 2.63 s, 2.56 s, 2.42 s, 2.71 s \) and \( 2.80 s \)
respectively. The average absolute error is:
A . \( 0.1 \mathrm{s} \)
B. 0.11s
\( c \cdot 0.01 \)
D. 1.0s
Subject: Maths
n the adjoining figure ABC is a triangle
in which \( \mathrm{D} \) and \( \mathrm{E} \) are the mid points \( \mathrm{AB} \)
and \( A C \) respectively if \( B C=4.6 \mathrm{cm} \) then
\( D E= \)
A. \( 9.2 \mathrm{cm} \)
B. 2.3 \( \mathrm{cm} \)
\( c .5 .0 \mathrm{cm} \)
D. \( 6.4 \mathrm{cm} \)
Subject: Maths
If \( s=\sqrt{t^{2}+1}, \) then \( \frac{d^{2} s}{d t^{2}} \) is equal to
A \( \cdot \frac{1}{s} \)
в. \( \frac{1}{s^{2}} \)
c. \( \frac{1}{s^{3}} \)
D. \( \frac{1}{s^{4}} \)
Subject: Physics
When the object is placed \( 4 \mathrm{cm} \) from the objective of microscope, the final image formed coincides with the object. The final image is at the least distance of distinct vision \( (24 \mathrm{cm}) . \) If the focal
length of eye piece is \( 8 \mathrm{cm} \) then the focal length of objective is
A . \( 3.25 \mathrm{cm} \)
B. \( 2 c m \)
\( \mathrm{c} .3 .9 \mathrm{cm} \)
D. \( 4.2 \mathrm{cm} \)
Subject: Maths
The equation of the normal to the curve
\( x^{4}=4 y \) through the point (2,4) is
A. \( x+8 y=34 \)
B. \( x-8 y+30=0 \)
c. \( 8 x-2 y=0 \)
D. \( 8 x+y=20 \)
Subject: Maths
In a bag there are 6 white and 4 black
balls. Two balls are drawn one after
another without replacement.ff the 1 st ball is known to be white, the probability that the 2 nd ball drawn is also white is
\( A \cdot \frac{2}{9} \)
в. \( \frac{5}{9} \)
\( c \cdot \frac{8}{9} \)
D. \( \frac{8}{13} \)
Subject: Chemistry
In a closed insulated container, a liquid
is stirred, with a paddle to increase the temperature. Which of the following is
true?
A. \( \triangle E=W \neq 0, q=0 \)
В. \( \triangle E=W=q \neq 0 \)
c. \( \triangle E=0, W=q \neq 0 \)
D. \( W=0, \Delta E=q \neq 0 \)
Subject: Maths
\( \mathbf{A}=(\mathbf{1}, \mathbf{1}, \mathbf{4}) \) and \( \mathbf{B}=(\mathbf{5},-\mathbf{3}, \mathbf{4}) \) are two
points. If the points \( P, Q \) are on the line
\( A B \) such that \( A P=P Q=Q B \) then \( P Q= \)
A \( \cdot 2 \sqrt{2} \)
в. 4
c. \( \sqrt{\frac{32}{9}} \)
D. \( \sqrt{2} \)
Subject: Maths
Which number should come in place of
\( \frac{\mathbf{0}}{\mathbf{7}}+\frac{\mathbf{2}}{\mathbf{7}}+\frac{\square}{\mathbf{7}}=\mathbf{1} \frac{\mathbf{3}}{\mathbf{7}} \)
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D. 7
Subject: Chemistry
Consider the following statements:
(a) \( \frac{e}{m} \) ratio of particles of canal rays remains constant
(b) The energy of orbit closest to nucleus is lowest
(c) \( C l^{-} \) has 18 electrons and 18 protons
(d) The maximum number of electrons
in an energy level is equal to \( 2 n^{2} \)

Which of the above statement(s) is/are
correct?
A. Only (b)
B. \( (a),(c) \) and \( (d) \)
\( c \cdot(b) \) and \( (d) \)
D. \( (b),(c) \) and \( (d) \)
Subject: Maths
The domain of \( f(x)=\log (\sin x) \) is
A \( \cdot(-\pi, \pi) \)
В. \( (2 n \pi,(2 n+1) \pi) \) and \( n \in Z \)
с. \( [0,2 \pi] \)
]
D. \( \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \)
Subject: Chemistry
\( 2.8 \times 10^{-2} \mathrm{kg} \) of nitrogen is expanded
isothermally and reversibly at \( 300 K \) from \( 15.15 \times 10^{5} N m^{-2} \) when the work
done is found to be \( -17.33 \mathrm{kJ} \). Find the
final pressure.
Subject: Maths
If \( (2+\sin x) \frac{d y}{d x}+(y+1) \cos x=0 \) and
\( \boldsymbol{y}(\mathbf{0})=\mathbf{1}, \) then \( \boldsymbol{y}\left(\frac{\boldsymbol{\pi}}{\mathbf{2}}\right) \) is equal to:
A \( \cdot \frac{1}{3} \)
в. \( -\frac{2}{3} \)
\( c \cdot-\frac{1}{3} \)
D.
Subject: Chemistry
toppr
Q Type your question
\( N O, N_{2} O_{3}, N_{2} O_{4} \) to \( N_{2} O_{5} \) (O.S of
nitrogen +5 ).
The following points are important regarding the oxides of nitrogen.
(a) All oxides of nitrogen except \( N_{2} O_{5} \) are endothermic because large amount of energy is required to dissociate the stable molecule of oxygen and nitrogen.
(b) The small electronegativity difference between oxygen and nitrogen makes N-O bond easily breakable to give oxygen and hence oxides of nitrogen are said to be better oxidizing
agents
(c) Except \( N_{2} O_{5}, \) all are gases at
ordinary temperature. \( N_{2} O_{3} \) is stable only at a lower temperature \( (253 \mathrm{K}) \)
(d) Except \( N_{2} O \) and \( N O \) which are
neutral oxides, all are acidic oxides that
dissolve in water forming
corresponding oxyacids.
(e) They are also a good example of illustrating the concept of resonance.
The gas which is acidic in nature is
A. \( N O \)
B. \( N_{2} O \)
\( \mathbf{c} \cdot N O_{2} \)
D. Both (A) and (C)
Subject: Maths
If \( \frac{\mathbf{9}^{n} \times \mathbf{3}^{5} \times(\mathbf{2 7})^{\mathbf{3}}}{\mathbf{3} \times(\mathbf{8 1})^{4}}=\mathbf{2 7}, \) then the value
of \( n \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B . 2
\( c \cdot 3 \)
D.
Subject: Chemistry
Replacement of \( C l \) of chlorobenzene to give phenol requires drastic conditions, but \( C l \) of 2,4 -dinitrochlorobenzene is readily replaced. This is because:
A. \( -N O_{2} \) group makes the ring electron rich at ortho and para positions.
B. - NO group withdraws electrons from meta position
C. \( -N O_{2} \) donate electrons at meta position.
D. \( -N O_{2} \) withdraws electrons from ortho and para positions.
Subject: Maths
If \( E_{1} \) and \( E_{2} \) are two events such that \( \boldsymbol{P}\left(\boldsymbol{E}_{1}\right)=\frac{\mathbf{1}}{\mathbf{4}}, \boldsymbol{P}\left(\boldsymbol{E}_{2}\right)=\frac{\mathbf{1}}{\mathbf{2}} ; \boldsymbol{P}\left(\frac{\boldsymbol{E}_{1}}{\boldsymbol{E}_{2}}\right)=\frac{\mathbf{1}}{\mathbf{4}} \)
then choose the correct options.
A. \( E_{1} \) and \( E_{2} \) are mutually exclusive
B. \( E_{1} \& E_{2} \) are dependent
c. \( E_{1} \) and \( E_{2} \) are independent
D. \( E_{1} \) and \( E_{2} \) are exhaustive
Subject: Chemistry
During an electrolysis of conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
perdisulphuric acid \( \left(\boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{8}\right) \) and \( \boldsymbol{O}_{2} \)
form in equimolar amount. The amount
of \( \boldsymbol{H}_{2} \) that will form simultaneously will
be: \( \left(2 H_{2} S O_{4} \rightarrow H_{2} S_{2} O_{8}+2 H^{+}+\right. \)
\( 2 e^{-} \)
A. Thrice that of \( \mathrm{O}_{2} \) in moles
B. Twice that of \( 0_{2} \) in moles
c. Equal to that of \( \mathrm{O}_{2} \) in moles
D. Half of that of \( \mathrm{O}_{2} \) in moles
Subject: Maths
One side of a parallelogram is \( 8 \mathrm{cm} . \) If the corresponding altitude is \( 6 \mathrm{cm}, \) then its area is given by
A \( \cdot 24 \mathrm{cm}^{2} \)
B. \( 36 \mathrm{cm}^{2} \)
c. \( 40 \mathrm{cm}^{2} \)
D. \( 48 \mathrm{cm}^{2} \)
Subject: Physics
The current \( I \) through a rod of a certain metallic oxide is given by \( \boldsymbol{I}=\mathbf{0 . 2} \boldsymbol{V}^{\mathbf{5} / \mathbf{2}} \)
where \( V \) is the potential difference across it. The rod is connected in series
with a resistance to a \( 6 V \) battery of negligible internal resistance. What value should the series resistance have
so that the power dissipated in the rod is twice that dissipated in the resistance?
Subject: Physics
\( \mathbf{A} \mathbf{7} \mathbf{5} \mathbf{0} \boldsymbol{H} \boldsymbol{z}, \mathbf{2 0} \boldsymbol{V} \) source is connected to
a resistance of \( 100 \Omega, \) an inductance of
\( 0.1803 H \) and a capacitance of \( 10 \mu F \)
all in series. The time in which the
resistance (thermal capacity \( \left.=2 J /^{0} C\right) \)
will get heated by \( 10^{0} C \) is
A . 348 s
B. 328 s
c. 248 s
D. 228
Subject: Maths
\( \int \frac{x^{3}}{\sqrt{1+x^{2}}} d x \)
A. \( \quad \sqrt{1+x}-\frac{x}{3}\left(1+x^{2}\right)^{3 / 2}+c \)
B \( \cdot \quad x \sqrt{1+x^{2}}+\frac{2}{3}\left(1+x^{2}\right)^{3 / 2}+c \)
C \( \cdot \frac{x^{2} \sqrt{1+x^{2}}}{3}-\frac{2}{3} \sqrt{1+x^{2}}+c \)
D. \( \quad x^{2} \sqrt{1+x^{2}}-\frac{1}{3}\left(1+x^{2}\right)^{3 / 2}+c \)
Subject: Chemistry
How many \( \sigma \) and \( \pi \) bonds are present in tetracyanoethylene?
A. nine \( \sigma \) and nine \( \pi \)
B. five \( \sigma \) and nine \( \pi \)
c. nine \( \sigma \) and seven \( \pi \)
D. eight \( \sigma \) and eight \( \pi \)