AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
The following reactions take place in the blast furnace in the preparation of impure iron. Identify the reaction pertaining to the formation of the slag.
A \( \cdot F e_{2} O_{3}(s)+3 C O(g) \rightarrow 2 F e(l)+3 C O_{2}(g) \)
B . \( \operatorname{CaCO}_{3}(s) \rightarrow \operatorname{CaO}(s)+\operatorname{CO}_{2}(g) \)
\( \mathbf{c} \cdot \operatorname{CaO}(s)+\operatorname{Si} O_{2}(s) \rightarrow \operatorname{CaSiO}_{3}(s) \)
D \( \cdot 2 C(s)+O_{2}(g) \longrightarrow 2 C O(g) \)
Subject: Maths
The table gives the probability distribution of a random variable \( \boldsymbol{X} \)
\[
\begin{array}{lll}
x & 1 & 2 \\
P(X= & &
\end{array}
\]
\( x) \)
0.2 0.1
\[
\begin{array}{ll}
0.3 & 0.3
\end{array}
\]
(i) Find \( P \)
(ii) Find the mean of \( \boldsymbol{X} \)
(iii) Find the variance of \( \boldsymbol{X} \)
Subject: Physics
Two small loud speakers \( A \) and \( B \) are
driven by the same amplifier as shown in Fig and emit pure sinusoidal waves
in phase. Speaker \( A \) is \( 1 \mathrm{m} \) away as
shown and speaker \( B \) is 2 m away from the amplifier. The microphone is \( 4 \mathrm{m} \)
away from the amplifier in transverse direction as indicated in the Figure. For what frequencies destructive
interference will occur at \( P: \)
A. 500 HZ, 1500 нZ, 2500 Hz,...
B. 500 Нz, 1000 Нz, 1500 Нz,...
c. 1250 Нz, 1750 Нz, 2250 Нz,..
D. 1000 Hz, 2000 Hz
Subject: Chemistry
IUPAC name of this compound \( \boldsymbol{H}_{3} \boldsymbol{C} \quad \boldsymbol{C}_{2} \boldsymbol{H} \)
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2}-\underset{\boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C H}_{2} \boldsymbol{C H}_{3}}{\boldsymbol{C}} \boldsymbol{H}-\boldsymbol{C}_{2} \boldsymbol{H}_{5} \)
Subject: Chemistry
Benzene, ethane and ethylene are just three of a large number of
hydrocarbons-compounds that contain only carbon and hydrogen. By using law of proportions and following data, the mass ratio of carbon in benzene, ethane
and ethylene is a:b:c. Then calculate the value of \( a, b \) and \( c \)
\( A \)
\( a=6, b=2, c=3 a \)
B. \( a=5, b=2, c=1 \)
c. \( a=3, b=2, c=2 \)
D. None of these
Subject: Maths
If a triangle \( P Q R \) has been constructed \( \operatorname{taking} Q R=6 \mathrm{cm}, P Q=3 \mathrm{cm} \) and
\( P R=4 \mathrm{cm}, \) then the correct order of
the angle of triangle is
A. \( \angle P<\angle Q<\angle R \)
в. \( \angle P>\angle Q<\angle R \)
с. \( \angle P>\angle Q>\angle R \)
D. \( \angle P<\angle Q>\angle R \)
Subject: Chemistry
Select the correct statement about:
\( A g F, C a F_{2}, B e F_{2}, M g F_{2} \)
A \( \cdot \) AgF and \( B e F_{2} \) are soluble, and \( C a F_{2} \) and \( M g F_{2} \) are insoluble in water.
B. AgF is soluble, others insoluble
c. \( \mathrm{AgF} \) is insoluble, others are soluble.
D. All are insoluble
Subject: Chemistry
For a 1 st order reaction of the form,
\( A \stackrel{k}{\longrightarrow} B, \) the correct representations
are:
\( \mathbf{I} \)
III
\( \mathbf{A} \cdot I \) and \( I I \)
B. III and \( I V \)
c. \( I \) and \( I V \)
D. II and III
Subject: Maths
\( \int \frac{1}{x \sqrt{1-x^{3}}} d x= \)
\( a \log \left|\frac{\sqrt{1-x^{3}}-1}{\sqrt{1-x^{3}}+1}\right|+b, \) then a is equal
to
A \( \cdot \frac{1}{3} \)
B. \( \frac{2}{3} \)
\( c \cdot \frac{-1}{3} \)
D. \( \frac{-2}{3} \)
Subject: Physics
A force \( \overrightarrow{\boldsymbol{F}}=(\mathbf{5} \hat{\boldsymbol{i}}+\boldsymbol{4} \hat{\boldsymbol{j}}) \boldsymbol{N} \) acts on a body
and produced a displacement \( \overrightarrow{\boldsymbol{S}}= \) \( (6 \hat{i}-5 \hat{j}+3 \hat{k}) m . \) The work done will be
A . \( 10 J \)
в. 20 \( J \)
\( c .30 J \)
D. \( 40 J \)
Subject: Physics
The displacement of a particle from its mean position (in metre) is given by \( \boldsymbol{Y}=\mathbf{0 . 2} \sin (\mathbf{1 0} \boldsymbol{\pi} \boldsymbol{t}+\mathbf{1 . 5} \boldsymbol{\pi}) \cos (\mathbf{1 0} \boldsymbol{\pi} \boldsymbol{t}+ \)
1.5 \( \pi \) ), the motion of the particle is:
A. periodic but not SHM
B. non periodic
c. simple harmonic motion with period 0.1 s
D. simple harmonic motion with period 02.
Subject: Maths
The cost \( C \) of sending a parcel post
package weighing \( P \) gms, \( P \) an integer
is Rs.10 for the first grams and Rs.3 for
each additional grams. The formula for the cost is
A. \( C=10+3 P \)
B. \( C=10 P+3 \)
c. \( C=10+3(P-1) \)
E . \( C=10 P-7 \)
Subject: Maths
Solve the equation
\[
\begin{array}{l}
\frac{(x-b)(x-c)}{(a-b)(a-c)}+\frac{(x-c)(x-a)}{(b-c)(b-a)}+ \\
\frac{(x-a)(x-b)}{(c-a)(c-b)}=1
\end{array}
\]
Subject: Physics
A rod of \( 10 \mathrm{cm} \) length is moving perpendicular to uniform magnetic field of intensity \( 5 \times 10^{-4} W b / m^{2} . \) If the
acceleration of the rod is \( 5 m / s^{2}, \) then the rate of increase of induced emf is
A \( .2 .5 \times 10^{-4} V s^{-1} \)
B . \( 25 \times 10^{-4} V s \)
c. \( 20 \times 10^{-4} V s \)
D. \( 20 \times 10^{-4} V s^{-1} \)
Subject: Physics
The number of gas molecules striking per second per square meter of the top surface of a table placed in a room at
\( 20^{\circ} \mathrm{C} \) and 1 atmospheric pressure is of
the order of \( \left(k_{B}=1.4 \times 10^{-23} J / K, \) and \right.
the average mass of an air molecule is
\( \left.\mathbf{5} \times \mathbf{1 0}^{-\mathbf{2 7}} \mathbf{k g}\right) \)
\( A \cdot 10^{27} \)
B. \( 10^{23} \)
\( c \cdot 10^{25} \)
D. \( 10^{2} \)
Subject: Maths
\( f \int \frac{\cos x-\sin x}{\sqrt{8-\sin 2 x}} d x= \)
\( \sin ^{-1}\left(\frac{\boldsymbol{A}}{\mathbf{4} \mathbf{2 6}}(\sin \boldsymbol{x}+\cos \boldsymbol{x})\right)+\boldsymbol{C} \) then
A is equal to
Subject: Chemistry
In the thermal decomposition of \( N_{2} O \) at
\( 830 \mathrm{K}, \) the time required to decompose half of the reactant was 263 sec at the initial pressure \( 290 \mathrm{mm} . \) It takes 212 sec to decompose half of the reactant if initial pressure was \( 360 \mathrm{mm} \). What is the order of the reaction? Also calculate
\( t_{1 / 2} \) for \( N_{2} O \) decomposition if initial
pressure of \( N_{2} O \) is 1 atm.
A. \( O . R=2 \), Half life \( =100.2 \) sec
B. \( O . R=1 \), Half life \( =10.02 \) sec
c. \( O . R=4 \), Half life \( =1.002 \)sec
D. None of these
Subject: Physics
A solid cylinder of mass \( \mathrm{m} \) is attached
to a horizontal spring with force constant k. The cylinder can roll without slipping along the horizontal plane. (See the accompanying figure.) Show that the center of mass of the cylinder executes simple harmonic motion with a period \( \boldsymbol{T}=\boldsymbol{2} \boldsymbol{\pi} \sqrt{\frac{\boldsymbol{3} \boldsymbol{m}}{\boldsymbol{2} \boldsymbol{k}}}, \) if displaced
from mean position.
Subject: Maths
Two men hit at a target with probabilities \( \frac{1}{2} \) and \( \frac{1}{3} \) respectively. What is the probability that exactly one of them hits the target?
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{1}{6} \)
D. \( \frac{2}{3} \)
Subject: Maths
Let \( \boldsymbol{U} \) be the universal set and \( \boldsymbol{A} \cup \boldsymbol{B} \cup \)
\( C=U . \) Then
\( \{(\boldsymbol{A}-\boldsymbol{B}) \cup(\boldsymbol{B}-\boldsymbol{C}) \cup(\boldsymbol{C}-\boldsymbol{A})\}^{\prime} \) is
equal to
A. \( A \cup B \cup C \)
в. \( A \cup(B \cap C) \)
c. \( A \cap B \cap C \)
D. \( A \cap(B \cup C) \)
Subject: Chemistry
For \( M K_{3} A \) (potassium salt of a
tribasic acid \( \boldsymbol{H}_{3} \boldsymbol{A} \) ) solution:
(Dissociation constants of acid are
\( \left.k_{a_{1}} k_{a_{2}} \& k_{a_{3}} ; h<<1\right) \)
A \( \cdot p H=\frac{1}{2}\left(p K_{w}+p K_{a_{3}}-\log c\right) \)
B・ \( p H=\frac{1}{2}\left(p K_{w}+p K_{a_{2}}+\log c\right) \)
C・ \( p H=\frac{1}{2}\left(p K_{w}+p K_{a_{1}}+\log c\right) \)
D \( \cdot p H=\frac{1}{2}\left(p K_{w}-p K_{a_{3}}-\log c\right) \)
Subject: Chemistry
Which of the following reactions is/are disproportionation reaction(s)?
This question has multiple correct options
A \( \cdot C l_{2}+2 \stackrel{\ominus}{O} H \rightarrow C l^{\ominus}+C l O^{\ominus}+H_{2} O \)
в. \( 2 H C u C l_{2} \rightarrow C u+C u^{2+}+4 C l^{\ominus}+2 H^{\oplus} \)
c. \( _{H C H O}+\stackrel{\ominus}{O H} \longrightarrow C H_{3} O H+H C O O^{\circ} \)
D. \( M g C O_{3} \rightarrow M g O+C O_{2} \)
Subject: Chemistry
The following intramolecular redox
reaction shows a loss and gain of how much electrons?
\( \left(N H_{4}\right)_{2} C r_{2} O_{7} \rightarrow N_{2}+C r_{2} O_{3}+ \)
\( 4 H_{2} O \)
A. Six
B. Seven
c. Eight
D. None of these
Subject: Maths
If \( \vec{A}=-4 \hat{i}+3 \hat{j} \) and \( \vec{B}=2 \hat{i}+5 \hat{j} \) and
\( \vec{C}=\vec{A} \times \vec{B} \) then \( \vec{C} \) makes an angle of :
A \( \cdot 45^{0} \) with \( \mathrm{x} \) -axis
B. \( 180^{\circ} \) with \( Y \) -axis
\( c \cdot 0^{0} \) with \( \mathrm{z} \) -axis
D. \( 180^{\circ} \) with \( z \) -axis
Subject: Physics
mole of a gas with \( \gamma=7 / 5 \) is mixed
with 1 mole of a gas with \( \gamma=5 / 3 \) then
the value of \( \gamma \) for resulting mixture is
A . \( 7 / 5 \)
в. \( 2 / 5 \)
c. \( 24 / 16 \)
D. \( 12 / 7 \)
Subject: Chemistry
In the following sequence of reactions Toluene \( \frac{K M n O_{4}}{\longrightarrow} A \frac{S O C l_{2}}{B G O_{4}} B \frac{H_{2} / P d}{C} C \)
then product \( \boldsymbol{C} \) is:
A \( \cdot C_{6} H_{5} \) СООН
в. \( C_{6} H_{5} C H_{3} \)
\( \mathrm{c} \cdot C_{6} H_{5} C H_{2} O H \)
D. \( C_{6} H_{5} C H O \)
Subject: Physics
When two waves of almost equal
frequency \( n_{1} \) and \( n_{2} \) are produced simultaneously, then the times interval between successive maxima is
A \( \cdot \frac{1}{n_{1}+n_{2}} \)
в. \( \frac{1}{n_{1}}+\frac{1}{n_{2}} \)
c. \( \frac{1}{n_{1}}-\frac{1}{n_{2}} \)
D. \( \frac{1}{n_{1}-n_{2}} \)
Subject: Chemistry
Assertion
\( H_{2} S O_{4} \) in more viscous than water.
Reason
\( \ln H_{2} S O_{4}, S \) has highest oxidation
state.
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
If equal volume of following solutions are mixed, precipitation of \( \boldsymbol{H} \boldsymbol{g}_{2} \boldsymbol{I}_{2}\left(\boldsymbol{K}_{s p}=\mathbf{2 . 5} \times \mathbf{1 0}^{-\mathbf{2 6}}\right) \) will not
occur only with:
A \( \cdot 10^{-4} M H g_{2}^{2+}+10^{-11} M I^{-} \)
B . \( 10^{-5} M \) H \( g_{2}^{2+}+10^{-10} M I^{-} \)
\( \mathbf{c} \cdot 10^{-11} M H g_{2}^{2+}+10^{-7} M I^{-} \)
D. \( 10^{-6} M H g_{2}^{2+}+10^{-9} M I^{-} \)
Subject: Physics
Two copper balls, each weighting \( 10 g \) are kept in air \( 10 \mathrm{cm} \) apart. If one
electron from every \( 10^{6} \) atom is transferred from one ball to the other,
the coulomb force between them is
(atomic weight of copper is 63.5 )
A \( \cdot 2 \times 10^{10} \mathrm{N} \)
B \( .2 \times 10^{4} \mathrm{N} \)
\( \mathbf{c} \cdot 2 \times 10^{8} \mathrm{N} \)
D. \( 2 \times 10^{6} \mathrm{N} \)
Subject: Chemistry
\( 2 K(s)+2 H_{2} O(l) \rightarrow 2 K O H(a q)+ \)
\( \boldsymbol{H}_{2}(\boldsymbol{g}) \)
If 3.0 moles of potassium react with excess water, what volume of hydrogen gas will be produced?
A . \( 1.5 L \)
B. 22.4L
c. \( 67.2 L \)
D. 33.6L
Subject: Chemistry
The major organic product(s) in the reaction given below is/are:
\( \boldsymbol{C H}_{3} \boldsymbol{O C H}\left(\boldsymbol{C H}_{3}\right)_{2}+\boldsymbol{H I} \rightarrow \)
Product\( (s) \)
A \( \cdot I C H_{2} O C H\left(C H_{3}\right)_{2} \)
в. \( C H_{3} O C(I)\left(C H_{3}\right)_{2} \)
c. \( C H_{3} O H+\left(C H_{3}\right)_{2} C H I \)
D. \( C H_{3} I+\left(C H_{3}\right)_{2} C H O H \)
Subject: Physics
Lens \( A \) produces a magnification of -0.8 whereas lens B produces a magnification of \( +0.8 . \) Which one of the following applies to lenses \( A \) and \( B ? \)
A. Both A and B are convex lenses
B. Both A and Bare concave lenses
c. A is a concave lens and B is a convex lens
D. A is a convex lens and B is a concave lens
Subject: Maths
Let \( \mathbf{f}: \boldsymbol{N} \rightarrow \boldsymbol{N}, \) where \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}+ \)
\( (-1)^{x-1}, \) then
A. \( f(x) \) is symmetric about \( x=1 \)
B. \( f(x) \) is symmetric about \( y=x \)
c. \( f(x) \) is not symmetric about \( y=x \)
D. \( f(x) \) is symmetric about \( x=a, a \in N \)
Subject: Physics
against the inner surface of a
larger sphere of radius 6 R. The masses of large and small spheres are \( 4 \mathrm{M} \) and
M respectively. This arrangement is placed on a horizontal table as shown.
There is no friction between any
surfaces of contact. The small sphere is
now released. The coordinates of the
centre of the large sphere when the
smaller sphere reaches the other
extreme position is
A \( \cdot(L-2 R, 0) \)
B. \( (L+2 R, O) \)
c. \( (2 R, 0) \)
D. \( (2 R-L \)
Subject: Maths
A man 1.5 m tall walks away from a
lamp post \( 4.5 ~ m \) high at a rate fo \( 4 k m / h r . \) How fast is the farther end of shadow moving on the pavement?
A. \( 4 \mathrm{km} / \mathrm{hr} \)
B. \( 2 \mathrm{km} / \mathrm{hr} \)
\( \mathrm{c} .6 \mathrm{km} / \mathrm{hr} \)
D. \( 5 \mathrm{km} / \mathrm{hr} \)
Subject: Physics
A charged spherical conductor of radius
a and charge \( q, \) is surrounded by
another charged concentric sphere of
radius \( b(b>a) . \) The potential difference
between conductors is \( V . \) When, the spherical conductor of radius b is
discharged completely, then the potential difference between conductor will be:
A. \( V \)
B. \( \frac{v_{a}}{b} \)
c. \( \frac{q_{1}}{4 \pi \varepsilon_{0} a}-\frac{q_{2}}{4 \pi \varepsilon_{0} b} \)
D. None of the above
Subject: Maths
The order and degree of the differentia equation \( y=\frac{d y}{d x} x+\sqrt{a^{2}\left(\frac{d y}{d x}\right)^{2}+b^{2}} \)
is
\( A \cdot 3,1 \)
в. 1,3
\( c .2,1 \)
D. 1,2
Subject: Chemistry
The de-Broglie wavelength associated with the motion of earth orbiting around the sun at a speed of \( 3 \times 10^{6} \mathrm{m} / \mathrm{s} \) is:
[mass of earth \( \left.6 \times 10^{24} K g\right] \)
A . \( 3.68 \times 10^{-65} \mathrm{m} \)
В . \( 3.68 \times 10^{-56} \mathrm{m} \)
c. \( 4.76 \times 10^{-65} \mathrm{m} \)
D. \( 4.76 \times 10^{-56} m \)
Subject: Chemistry
2.16 grams of \( \mathrm{Cu} \), on reaction with
\( H N O_{3}, \) followed by ignition of the
nitrate, gave 2.7 g of copper oxide. In another experiment 1.15 g of copper oxide, upon reaction with hydrogen, gave 0.92 g of copper. This data illustrate the law of:
A. multiple proportions
B. definite proportions
c. reciprocal proportions
D. conservation of mass
Subject: Chemistry
\( 0.1 M \) formic acid solution is titrated
against \( 0.1 M \) NaOH solution. What
would be the difference in \( p H \) between \( \frac{1}{5} \) and \( \frac{4}{5} \) stages of neutralization of
acid?
A. \( 2 \log 3 / 4 \)
B. 2 \( \log 1 / 5 \)
\( \mathbf{c} \cdot \log 1 / 3 \)
D. \( 2 \log 4 \)
Subject: Chemistry
Calculate the total pressure of a mixture of 8 g of oxygen and 4 g of hydrogen confined in vessel of \( 1 d m^{3} \) at
\( 27^{0} C \)
\( \left(\boldsymbol{R}=\mathbf{0 . 0 8 3} \quad \text { bar } \quad \boldsymbol{d m}^{3} \boldsymbol{k}^{-1} \boldsymbol{m o l}^{-1}\right) \)
Subject: Maths
statement-l: rrom a poınt \( \boldsymbol{r} \) on tne
circle with centre \( \boldsymbol{O} \) the chord \( \boldsymbol{P} \boldsymbol{A}=\mathbf{8} \)
\( \mathrm{cm} \) is drawn. The radius of the circle is
\( 24 \mathrm{cm} . \) Let \( P B \) be drawn parallel to \( O A \)
Suppose \( B O \) extended meet \( P A \)
extended at \( M . \) The length of \( M A \) is 9
\( \mathrm{cm} \)
Reason
Statement-2: \( O A \) is a radius of a circle
with centre at \( O . R \) is a point on \( O A \)
through which a chord \( C D \)
perpendicular to \( \boldsymbol{O} \boldsymbol{A} \) is drawn. Let a chord through A meet the chord \( C D \) at
\( M \) and the circle at \( B \). Also \( O S \) is
perpendicular from \( \boldsymbol{O} \) on chord \( \boldsymbol{A} \boldsymbol{B} \). The radius of the circle is \( 18 \mathrm{cm} . R \) is the mid point of \( \boldsymbol{A O} \) and \( \boldsymbol{A} \boldsymbol{M} / \boldsymbol{M} \boldsymbol{B}=\frac{\mathbf{1}}{\mathbf{2}} \)
The length of \( \boldsymbol{O} \boldsymbol{S} \) is \( \boldsymbol{9} \mathrm{cm} \)
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
Among the following compounds, the one which does NOT produce nitrogen gas upon heating is?
A \( \cdot\left(N H_{4}\right)_{2} C r_{2} O_{7} \)
в. \( \operatorname{NaN}_{3} \)
\( \mathbf{c} \cdot N H_{4} N O_{2} \)
D. \( \left(N H_{4}\right)_{2}\left(C_{2} O_{4}\right) \)
Subject: Physics
A particle of mass \( M \) is moving in a horizontal circle of radius \( R \) with a
uniform speed \( v . \) When it moves from
one point to a diametrically opposite point, its This question has multiple correct options
A. Momentum does not change
B. Momentum changes by 2 \( M v \)
c. Kinetic energy does not change
D. Kinetic energy changes by \( M v^{2} \)
Subject: Chemistry
3 moles of \( \boldsymbol{P} \) and 2 moles of \( \boldsymbol{Q} \) are
mixed, what will be their total vapour pressure in the solution if their partial
vapour pressures are 80 and 60 torr respectively?
A. 80 torr
B. 140 torr
c. 72 torr
D. 70 torr
Subject: Chemistry
The difference between \( \Delta H \) and \( \Delta E \)
(on a molar basis) for the combustion of n-octane (I) at 25C would be :
A. \( -13.6 \mathrm{kJ} \)
The \( -13.6 \mathrm{c} \).
B . - 1.14 k
c. - 11.15 k
D. \( +11.15 \mathrm{kJ} \)
Subject: Chemistry
Egg shell is made up of a chemical. In
which of the two ores this chemical is
present?
A. lime stone: \( C a C O_{3} \), Dolomite \( : C a C O_{3} . M g C O_{3} \)
B. lime stone: \( C a C O_{3} . M g C O_{3} \), Dolomite \( : C a C O_{3} \)
c. lime stone \( : C a_{2} C O_{3} \), Dolomite \( : C a_{2} C O_{3} . M g C O_{3} \)
D. None of these
Subject: Physics
Assertion
A charged particle is moving in a
circular path under the action of
uniform magnetic field as shown in fig.
During motion kinetic energy of
charged particle is constant.
Reason
During the motion, magnetic force
acting on the particle is perpendicular
to instantaneous velocity.
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: Maths
Soluation of D.E. \( \frac{d y}{d x}=\frac{3 x+4 y+3}{12 x+16 y-4} \)
is
A \( \cdot y=4 x+\ln |3 x+4 y|+C \)
B . \( 4 y=x+\ell n|3 x+4 y|+C \)
c. \( y=\ell n|3 x+4 y|+C \)
D・ \( x+y=\ell n|3 x+4 y|+C \)
Subject: Maths
Find the area enclosed between the curves \( \boldsymbol{y}^{2}-\mathbf{2} \boldsymbol{y} e^{s i n^{-1} \boldsymbol{x}}+\boldsymbol{x}^{2}-\mathbf{1}+[\boldsymbol{x}]+ \)
\( e^{2 \sin ^{-1} x}=0 \)
and line \( x=0 \) and \( x=\frac{1}{2} \) is (where [.]
denotes greatest integer function)
A. \( \frac{\sqrt{3}}{4}+\frac{\pi}{6} \)
B. \( \frac{\sqrt{3}}{2}+\frac{\pi}{6} \)
c. \( \frac{\sqrt{3}}{4}-\frac{\pi}{6} \)
D. \( \frac{\sqrt{3}}{2}-\frac{\pi}{6} \)
Subject: Chemistry
The electronegativity difference
between \( N \) and \( F \) is greater than \( N \) and
\( \boldsymbol{H}, \) yet the dipole moment of \( \boldsymbol{N} \boldsymbol{H}_{3}(1.5 \)
D) is greater than that of \( N F_{3}(0.2 D) \)
This is because:
A \( \cdot \) in \( N H_{3} \) as well as \( N F_{3} \), the atomic dipole and bond dipole are in the opposite direction
B. in \( N H_{3} \), the atomic dipole and bond dipole are in the
opposite direction, whereas in \( N F_{3} \) these are in the same direction.
C. in \( N H_{3} \) as well as in \( N F_{3} \) the atomic dipole and bond dipole are in the same direction
D. in \( N H_{3} \) the atomic dipole and bond dipole are in the
same direction, whereas in \( N F_{3} \) these are in the opposite direction.
Subject: Maths
Choose the correct answer from the
alternatives given. Directions for questions 71 to 75: Study the following bar-graph and answer the
questions.

The total units consumption in the year
2013 during these 5 months, in respect
of the same in the previous year has
been
A. decreased by 2.27\%
B. increased by 4.50\%
c. increased by \( 2.27 \% \)
D. increased by 2.22
Subject: Physics
A copper wire of length \( l \) is bent into a
semicircle. It is moved with a velocity \( \boldsymbol{v} \) in a region where magnetic field is uniform and perpendicular to the plane of the wire. If the strength of the field is
\( B \) then emf induced is
\( \mathbf{A} \cdot B l v \)
в. \( \quad B \frac{l}{\pi} v \)
c. \( _{B} \frac{2 l}{\pi} v \)
D. none of these
Subject: Physics
Equal torsional torques act on two rods X and Y having equal length but the
diameter of \( Y \) is twice that wire \( X . \) If \( \theta_{x} \)
and \( \theta_{y} \) are angles of twist,
A \( \cdot \theta_{x}=\frac{1}{2} \theta_{y} \)
в. \( \quad \theta_{x}=\frac{1}{4} \theta_{y} \)
\( \mathbf{c} \cdot_{\theta_{y}}=\frac{\theta_{x}}{8} \)
D. \( _{\theta_{y}}=\frac{1}{16} \theta_{x} \)
Subject: Chemistry
\( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{6} 4 s^{2} \)
The given electronic configuration is
for:
A . Na
B. Fe
c. \( C l^{-} \)
D. Rb
E \( . C a^{+} \)
Subject: Chemistry
The following reaction is known as:
\( \boldsymbol{C}_{6} \boldsymbol{H}_{6}+\boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C l} \frac{A l C l_{3}}{(\boldsymbol{a n h y} .)} \boldsymbol{C}_{6} \boldsymbol{H}_{5} \boldsymbol{C H}_{3}+ \)
\( \boldsymbol{H} \boldsymbol{C l} \)
A. Wurtz-Fittig reaction
B. Friedel-Crafts reaction
c. Rosenmund reaction
D. Sandmeyer reaction
Subject: Chemistry
In an experiment to study the properties of ethanoic acid, a student takes about \( 3 \mathrm{mL} \) of ethanoic acid in a dry test tube He adds an equal amount of distilled water to it and shakes the test tube
well. After some time he is likely to observe that:
A. a colloid is formed in the test tube
B. the ethanoic acid dissolves readily in water
c. the solution becomes light orange
D. water floats over the surface of ethanoic acid
E. a homogenous solution of ethanoic acid and water is formed
Subject: Chemistry
Match the list I with list II.
List I List II
A) \( C l F \)
1) \( s p^{3} d \)
B) \( C l F_{3} \)
2) T- shape
C) \( C l F_{5} \)
3) linear
4) \( s p^{3} d^{2} \)
5) one lone
pair
6)
pentagonal Bi-pyramidal
B. \( A-3 ; B-1,2 ; C-5,6 \)
c. \( A-3 ; \quad B-1,6 ; \quad C-4,5 \)
D. \( A-3 ; B-3,4 ; C-5,6 \)
Subject: Physics
A hydrogen atom emits a photon corresponding to an electron transition from \( n=5 \) to \( n=1 . \) The recoil speed of
hydrogen atom is almost
\( \mathbf{A} \cdot 10^{-4} m s^{-1} \)
B. \( 2 \times 10^{-2} \mathrm{ms}^{-1} \)
c. \( 4 m s^{-1} \)
D. \( 8 \times 10^{2} m s^{-1} \)
Subject: Physics
What will be the magnitude of torque on an electric dipole having dipole moment of \( 4 \times 10^{-9} \mathrm{cm} \) placed in a uniform
electric field of intensity of \( 5 \times \)
\( 10^{4} N C^{-1} \) making an angle \( 180^{\circ} \) with
the field.
A \( \cdot 10^{-4} N-m \)
В. \( 2 \times 10^{-4} N-m \)
\( c .0 \) (zero)
D. \( 10^{-6} N-m \)
Subject: Chemistry
Identify correct statements.
This question has multiple correct options
\( \mathbf{A} \cdot H_{2} S O_{4} \) can be used for drying \( H_{2} S \) gas.
B. \( H_{2} S \) is a better reducing agent than water.
C . Reaction of \( H_{2} S O_{4} \) with \( B a C l_{2} \) shows its oxidising
nature.
D. \( H_{2} S \) can form coloured precipitate's with metal ions.
Subject: Physics
Two parallel wires \( P \) and \( Q \) carry electric currents of \( 10 A \) and \( 2 A \) respectively in mutually opposite directions. The
distance between the wires is \( 10 \mathrm{cm} \). If
the wire \( P \) is of infinite length and wire \( \mathrm{Q} \) is \( 2 m \) long, then the force acting \( \mathrm{Q} \)
will be
\( \mathbf{A} \cdot 4 \times 10^{-5} N \)
B. \( 8 \times 10^{-5} N \)
c. \( 6 \times 10^{-5} N \)
D. \( 14 \times 10^{-5} N \)