AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Which of the following are Lewis acid-
base reactions:
This question has multiple correct options
A \( \cdot C u C l_{2}+4 H_{2} O \longrightarrow\left[C u\left(H_{2} O\right)_{4}\right]^{2+}+2 C l^{-} \)
в. \( _{K I+4 S O_{2}(s) \rightarrow K^{+}\left[\left(S O_{4}\right)_{4} I^{-}\right]} \)
\( \mathbf{c} \cdot B F^{3}+N H_{3} \longrightarrow\left[H_{3} N \cdot B F_{3}\right] \)
D. \( S O_{3}^{2-}+O \longrightarrow S O_{4}^{2} \)
Subject: Physics
Two cells of ends \( E_{1} \) and \( E_{2}\left(E_{1}>E_{2}\right) \)
are connected as shown In figure. When a potentiometer is connected between \( A \) and \( B \), the balancing length of the potentiometer wire is \( 300 \mathrm{cm} . \) On connecting the same potentiometer between \( A \) and \( C, \) the balancing length is \( 100 \mathrm{cm} . \) The ratio I is \( \frac{E_{1}}{E_{2}} \) is
A . 3: 1
B. 1: 3
\( c \cdot 2: 3 \)
D. 3: 2
Subject: Chemistry
All members of group 14 when heated n in oxygen form oxides. Which of the following is the correct trend of oxides?
A. Dioxides \( C O_{2}, \operatorname{Si} O_{2} \) and \( G e O_{2} \) are acidic while \( S n O_{2} \) and \( P b O_{2} \) are amphoteric.
B. \( \mathrm{c} 0, \) Ge0, SnO and PbO are amphoteric.
c. Monoxides react with haemoglobin to form toxic compounds.
D. All oxides burn with blue flame
Subject: Physics
A block of mass \( m \) is moving with a
constant acceleration \( a \) on a rough
horizontal plane. If the coefficient of friction between the block and ground is
\( \mu, \) the power delivered by the external
agent in a time interval \( t \) from the
beginning is equal to:
A \( \cdot m a^{2} t \)
в. \( \mu \) mgat
\( \mathbf{c} \cdot \mu m(a+\mu g) g t \)
D. \( m(a+\mu g) a t \)
Subject: Maths
If \( a=3, b=4, c=5 \) each one of \( \vec{a}, \vec{b} \)
and \( \vec{c} \) is perpendicular to the sum of the remaining then \( |\overrightarrow{\boldsymbol{a}}+\overrightarrow{\boldsymbol{b}}+\overrightarrow{\boldsymbol{c}}| \)
A \( \cdot \frac{5}{\sqrt{2}} \)
B. \( \frac{2}{\sqrt{5}} \)
\( c \cdot 5 \sqrt{2} \)
D. \( \sqrt{5} \)
Subject: Physics
Two cells of same emf E but different
internal resistances \( r_{1} \) and \( r_{2} \) are
connected in series with an external
resistance \( R \). The potential drop across
the first cell is found to be zero.
The external resistance \( \boldsymbol{R} \) is
A \( \cdot r_{1}+r_{2} \)
В. \( r_{1}-r_{2} \)
c. \( r_{2}-r_{1} \)
D. \( r_{1} r_{2} \)
Subject: Chemistry
Statement \( -1: P b O_{2} \) is an oxidising agent and reduced to Pbo.

Statement - 2 : Stability of Pb (II) > Pb
(IV) on account of inert pair effect.
A. Statement - - lis True, Statement - 2 is True; Statement 2 is a correct explanation for Stetement- -
B. Statement - 1 is True. Statement - 2 is True; Statement 2 is NOT a correct explanation for Statement-
c. Statement - - lis True, Statement - 2 is False
D. Statement-lis False, Statement- - 2 is True
Subject: Maths
OPQR is a square. \( M, N \) are the midpoints of the sides \( P Q \) and \( Q R \)
respectively. If the ratio of the areas of
the square and the \( \triangle O M N \) is \( \lambda: 6 \) then \( \frac{\lambda}{4} \) is equal to
A .2
B. 4
c. 8
D. 16
Subject: Physics
A particle executes simple harmonic motion along a straight line with mean position at \( x=0 \) and period of \( 20 s \) and amplitude of \( 5 \mathrm{cm} . \) The shortest time taken by the particle to go from \( \boldsymbol{x}=\mathbf{4 c m} \) to \( \boldsymbol{x}=-\mathbf{3 c m} \) is
A . \( 4 s \)
B. 7 s
\( c .5 s \)
D. \( 6 s \)
Subject: Chemistry
\( \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C} \boldsymbol{H}_{2}-\underset{\boldsymbol{O}}{\|}-\boldsymbol{C} \boldsymbol{H}_{3} \frac{N a N \boldsymbol{O}_{2}}{\boldsymbol{H} C l} \)
Major product of this reaction is:
\( \mathbf{A} . \)
\( C H_{3} C H-C_{1} H-C-C H_{3} \)
\( N O \)
B.
\[
C H_{3}-C H_{2}-C-C H=N-O H
\]
\( c \)
\( C H_{3}-\underset{N-O H}{C}-\stackrel{0}{N}-C H_{3} \)
D. \( C H_{3}-C H_{2}-\underset{N-O H}{\|}-C H_{3} \)
Subject: Physics
The momentum of a body of mass 0.5 kg dropped from a certain height (h),
when reaches the ground is \( 10 \mathrm{N} \) s. The value h is \( _{---} \) m. \( \left(g=10 m s^{-2}\right) \)
A . 20
B . 40
c. 10
D. 80
Subject: Physics
Assertion
The earth's magnetic field is due to iron present in its core.
Reason
At a high temperature magnet losses its magnetic property or magnetism.
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
A hollow double concave lens is made of
very thin transparent material. It can be
filled with air or either of two liquid \( L_{1} \)
or \( L_{2} \) having refractive indices \( \mu_{1} \) and
\( \mu_{2} \) respectively \( \left(\mu_{2}>\mu_{1}>1\right) . \) The lens
will diverge a parallel beam of light if it is filled
This question has multiple correct options
A. \( L_{1} \) and immersed in \( L_{2} \)
B. \( L_{2} \) and immersed in water
c. water and immersed in \( L_{2} \)
D. Air and immersed in either water or \( L_{1} \) or \( L_{2} \)
Subject: Chemistry
The volume vs. temperature graph of
mole of an ideal gas is given below.
The pressure of the gas (in atm) at
\( X, Y \) and \( Z, \) respectively, are:
A. 0.328,0.820,0.820
0
B. 3.28,8.20,3.28
c. 0.238,0.280,0.280
D. 32.8,0.280,82.0
Subject: Chemistry
In the first order reaction, \( \boldsymbol{A}(\boldsymbol{g}) \rightarrow \)
\( B(g)+C(g), \) at constant volume and
temperature, the initial pressure of \( \boldsymbol{A} \) is
\( 11200 P a \) and the total pressure at the
end of 16 minutes is 14667 Pa.

Calculate the half life period of reaction.
Subject: Maths
If \( \int \sin ^{-1} x \cos ^{-1} x d x= \)
\( \boldsymbol{f}^{-1}(\boldsymbol{x})\left[\frac{\boldsymbol{\pi}}{2} \boldsymbol{x}-\boldsymbol{x} \boldsymbol{f}^{-1}(\boldsymbol{x})-\boldsymbol{2} \sqrt{1-\boldsymbol{x}^{2}}\right] \frac{\boldsymbol{\pi}}{\boldsymbol{2}} \)
\( 2 x+C, \) then
A \( \cdot f(x)=\sin x \)
B . \( f(x)=\cos x \)
c. \( f(x)=\tan x \)
D. None of these
Subject: Maths
Assertion If \( n>1 \) then \( \int_{0}^{\infty} \frac{d x}{1+x^{n}}= \)
\( \int_{0}^{1} \frac{d x}{\left(1-x^{n}\right)^{1 / n}} \)
Reason \( \int_{a}^{b} f(x) d x=\int_{a}^{b} f(a+b-x) d x \)
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
Assertion
The equation \( x^{2}+2 \lambda x y+y^{2}-2 x- \)
\( 2 y+2=0 \) represent an ellipse if \( \lambda \in \)
(-1,1)
Reason
The general equation of second degree \( \operatorname{given} \operatorname{by} a x^{2}+2 h x y+b y^{2}+2 g x+ \)
\( 2 f y+c=0 \) represent an ellipse if
\( a b c+2 f g h-a f^{2}-b g^{2}-c h^{2} \neq 0 \& \)
\( h^{2}<a b \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Physics
In a metre bridge, the gaps are closed by two resistances \( \mathrm{P} \) and \( \mathrm{Q} \) and the
balance point is obtained at \( 40 \mathrm{cm} \)
When \( Q \) is shunted by a resistance of 10
\( \Omega, \) the balance point shifts to \( 50 \mathrm{cm}, \) The
values of \( P \) and \( Q \) arc
A \( \cdot \frac{10}{3} \Omega, 5 \Omega \)
B. \( 20 \Omega, \) 30\Omega
c. \( 10 \Omega, \) 15\Omega
D. \( 5 \Omega, \frac{15}{2} \Omega \)
Subject: Biology
Which of the following statements is correct about reflex arc?
(i). Reflex arcs are efficient quick
responses.
(ii). Reflex arcs are evolved for functioning in the absence of true thought processes.
(iii). A reflex arc is a neural pathway that controls reflex action.
A \( . \) (i), (ii) and (iii)
B. Only (i)
c. only (ii)
D. Only (i) and (ii)
Subject: Physics
A satellite orbiting the Earth at \( 400 \mathrm{km} \) above the surface of the Earth has a \( 2 m \)
long antenna oriented perpendicular to
the Earth's surface. At the equator the Earth's magnetic field is \( 8 \times 10^{-5} T \) and
is horizontal. Assuming the orbit to the circular, find emf induced across the
ends of the antenna.(Given radius of
\( \left.\operatorname{earth} R_{e}=6400 K m\right) \)
A. \( 1.3 V \)
В. \( 1.2 V \)
c. \( 1.0 V \)
D. \( 0.12 V \)
Subject: Maths
Evaluate :
\( \frac{\mathbf{5 0 x y z}(\boldsymbol{x}+\boldsymbol{y})(\boldsymbol{y}+\boldsymbol{z})(\boldsymbol{z}+\boldsymbol{x})}{\mathbf{1 0 0 x y}(\boldsymbol{x}+\boldsymbol{y})(\boldsymbol{y}+\boldsymbol{z})} \)
A \( \cdot \frac{1}{2} \)
В. \( \frac{z(z+x)}{2} \)
c. \( \frac{z+x}{2} \)
D \( \cdot z(z+x) \)
Subject: Chemistry
An ideal solution has two components
\( A \) and \( B . A \) is more volatile than \( B \), i.e.
\( \boldsymbol{P}_{A}^{\circ}>\boldsymbol{P}_{B}^{\circ} \) and also \( \boldsymbol{P}_{A}^{\circ}>\boldsymbol{P}_{\text {total}} . \) If \( \boldsymbol{X}_{\boldsymbol{A}} \)
and \( Y_{A} \) are mole fractions of
components \( A \) in liquid and vapour
phases, then :
A. \( X_{A}=Y_{A} \)
в. \( X_{A}>Y_{A} \)
c. \( X_{A}<Y_{A} \)
D. Data insufficient
Subject: Physics
A \( 100 W / 200 V \) bulb and an inductor are connected in series to a
\( 220 V / 50 H z \) supply. Find the power
consumed by the bulb.
\( \mathbf{A} \cdot 100 W \)
в. \( 92 W \)
\( \mathrm{c} .84 \mathrm{W} \)
D. \( 74 W \)
Subject: Maths
If \( a^{x}=b^{y}=c^{z} \) and \( b^{2}=a c, \) then show
that \( \boldsymbol{y}=\frac{\boldsymbol{2} \boldsymbol{z} \boldsymbol{x}}{\boldsymbol{z}+\boldsymbol{x}} \)
Subject: Chemistry
\( \left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{C O C H}_{3} \) and \( \boldsymbol{C H}_{3} \boldsymbol{O C}_{2} \boldsymbol{H}_{5} \) are
treated with hydroiodic acid.The fragments obtained after reactions are respectively:
A \( \cdot\left(C H_{3}\right)_{3} C I+C H_{3} O H ; C H_{3} I+C_{2} H_{5} O H \)
B. \( \left(C H_{3}\right)_{3} C I+C H_{3} O H ; C H_{3} O H+C_{2} H_{5} I \)
c. \( \left(C H_{3}\right)_{3} C O H+C H_{3} I ; C H_{3} O H+C_{2} H_{5} I \)
D. \( C H_{3} I+\left(C H_{3}\right)_{3} C O H ; C H_{3} I+C_{2} H_{5} O H \)
Subject: Maths
If the median of the distribution
(arranged in ascending order) \( 1,3,5,7,9, x, 15,17, \) is \( 8, \) what is the
value of \( x ? \)
A . 11
B. 13
c. \( 9<x<15 \)
D. \( 9 \leq x \leq 15 \)
5
Subject: Maths
The area enclosed between the curves
\( x^{2}=y \) and \( y^{2}=x \) is equal to
This question has multiple correct options
A \( \cdot \frac{1}{3} \cdot \) sq.unit
B \( \cdot 2 \int_{0}^{1}\left(x-x^{2}\right) d x \)
C \cdot area of the region \( \left\{(x, y): x^{2} \leq y \leq|x|\right\} \)
D. none of the above
Subject: Physics
The dimensional formula of arial
velocity is
\( \mathbf{A} \cdot\left[M^{0} L^{-2} T^{1}\right] \)
B . \( \left[M^{0} L^{-2} T^{-1}\right] \)
C . \( \left[M^{0} L^{2} T^{-1}\right] \)
\( \mathbf{D} \cdot\left[M^{0} L^{2} T^{1}\right] \)
Subject: Maths
If \( f(x)=\frac{\log (1+a x)-\log (1-b x)}{x} \) for
\( \boldsymbol{x} \neq \mathbf{0} \) and \( \boldsymbol{f}(\mathbf{0})=\boldsymbol{k} \) and \( \boldsymbol{f}(\boldsymbol{x}) \) is
continuous at \( x=0, \) then \( k \) is equal to:
A \( \cdot a+b \)
в. \( a-b \)
\( c \)
D.
Subject: Chemistry
IUPAC name of \( \boldsymbol{N} \boldsymbol{a}_{3}\left[\boldsymbol{C o}(\boldsymbol{O} \boldsymbol{N} \boldsymbol{O})_{6}\right] \) is:
A. Sodium cobaltinitrite
B. Sodium hexanitritocobaltate (III)
c. Sodium hexanitrocobalt (III)
D. Sodium hexanitritocobaltate (II)
Subject: Physics
A boy of mass \( 40 \mathrm{kg} \) is climbing a vertical pole at a constant speed. If the coefficient of friction between his
palms and the pole is 0.8 and \( g=10 m s^{-2} \) the horizontal force that he is applying on the pole is:
A. 300 N
B. 400 N
c. \( 500 \mathrm{N} \)
D. 600 N
Subject: Chemistry
If the values of \( \wedge_{\infty} \) of \( \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{C l}, \boldsymbol{N} \boldsymbol{a} \boldsymbol{O H} \)
and \( N a C l \) are 130,217 and
109 ohm \( ^{-1} \cdot c m^{2} \cdot e q u i v^{-1} \)
respectively, the \( \wedge_{\infty} \) of \( N H_{4} O H \) in
\( o h m^{-1} \cdot c m^{2} \cdot e q u i v^{-1} \) is:
A .238
в. 198
c. 22
D. 456
Subject: Chemistry
The commonly used pain reliever, aspirin, has the molecular formula
\( C_{9} H_{8} O_{4} . \) If a sample of aspirin contains
\( 0.968 g \) of carbon, what is the mass of hydrogen in the sample?
A \( .0 .717 g \)
в. \( 0.0717 g \)
c. \( 8.000 g \)
D. \( 0.645 g \)
Subject: Maths
The function \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) defined by
\( f(x)=(x-1)(x-2)(x-3) \) is.
A. One-one but not onto
B. Onto but not one-one
c. Both one-one and onto
D. Neither one nor onto
Subject: Chemistry
\( \boldsymbol{C a}+\boldsymbol{C}_{2} \rightarrow \boldsymbol{C a} \boldsymbol{C}_{2} \stackrel{N_{2}}{\longrightarrow} \boldsymbol{A} \)
Compound \( (A) \) is used as a / an :
A. fertilizer
B. dehydrating agent
c. oxidising agent
D. reducing agent
Subject: Maths
For an ellipse, \( A \) and \( B \) are the ends of major axis and minor axis respectively. Area of \( \Delta O A B \) is 16 sq.units and \( e= \) \( \frac{\sqrt{3}}{2}, \) then equation of the ellipse is:
\( \stackrel{\text { A }}{-} \frac{x^{2}}{32}+\frac{y^{2}}{8}=1 \)
в. \( \frac{x^{2}}{16}+\frac{y^{2}}{64}=1 \)
c. \( \frac{x^{2}}{64}+\frac{y^{2}}{8}=1 \)
D. \( \frac{x^{2}}{64}+\frac{y^{2}}{16}=1 \)
Subject: Chemistry
\( 3.2 \mathrm{g} \) sulphur combines with \( 3.2 \mathrm{g} \) of oxygen to form a compound in one set of conditions. In another set of conditions,
\( 0.8 \mathrm{g} \) of sulphur combines with \( 1.2 \mathrm{g} \) of oxygen to form another compound. State the law illustrated by these
chemical combinations.
A. Law of constant composition
B. Law of reciprocal proportion
c. Law of multiple proportion
D. None of the above
Subject: Maths
Examine whether \( \boldsymbol{A}=\{\boldsymbol{x}: \boldsymbol{x} \) is a
positive integer divisible by \( 3\} \) is a subset of \( B=\{x: x \text { is a multiple of } 5 \)
\( \boldsymbol{x} \in \boldsymbol{N}\} \)
Subject: Maths
If \( \boldsymbol{x} \in \boldsymbol{R}, \) find the minimum value of the
expression \( 3^{x}+3^{1-x} \)
\begin{tabular}{l} 
A \( 3 \sqrt{2} \) \\
\hline
\end{tabular}
B. \( 2 \sqrt{3} \)
\( c \cdot 3 \sqrt{3} \)
D. none of these
Subject: Physics
The resistance of a bulb filament is 100
\( \Omega \) at a temperature of \( 100^{0} \mathrm{C} \). If its temperature coefficient of resistance be 0.005 per \( ^{0} \mathrm{C} \), its resistance will become \( 200 \Omega \) at a temperature of :
A \( \cdot 300^{0} \mathrm{C} \)
B. \( 400^{\circ} \mathrm{C} \)
\( c \cdot 500^{0} c \)
D. 200^
Subject: Chemistry
Polarity of a bond depends on the difference in the electronegativity of the bonded atoms. The higher the difference in the electronegativity, the higher will be the polarity of the bond.

The boiling point of \( I C l \) is about \( 40^{\circ} C \)
higher than \( B r_{2} \). This might be because
A. \( I-C l \) bond is stronger than \( B r-B r \) bond
B. I.E. of \( I<I . E \) of \( B r \)
c. \( I-C l \) is polar whereas \( B r_{2} \) is non-polar
D. the size of \( I>B r \)
Subject: Physics
A straight conductor carrying a current is split into identical semicircular
turns of radius \( r \) as shown in the figure.
The magnetic induction at the center \( C \)
of the circular loop is:
A \( \cdot \frac{\mu_{0}}{4 r_{n}} \)
в. \( \frac{\mu_{0} i}{8 r} \)
c. \( \frac{\mu_{0}}{2 r} \)
D. zero
Subject: Maths
I. If the curve \( y=x^{2}+b x+c \) touches
the straight line \( y=x \) at the point
(1,1) then \( b \) and \( c \) are given by 1,1
Il. If the line \( \boldsymbol{P x}+\boldsymbol{m} \boldsymbol{y}+\boldsymbol{n}=\boldsymbol{0} \) is a
normal to the curve \( x y=1, \) then \( P> \)
\( \mathbf{0}, \boldsymbol{m}<\mathbf{0} \)
Which of the above statements is
correct
A. onlyı
B. only II
c. both I and II
D. Neither I nor II
Subject: Maths
The distance of the point \( 3 \hat{i}+5 \hat{k} \) from the line parallel to the vector \( 6 \hat{i}+\hat{j}- \) \( 2 \hat{k} \) and passing through the point \( 8 \hat{i}+ \) \( \mathbf{3} \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) is
A . 1
B . 2
\( c .3 \)
D.
Subject: Physics
In a meter bridge, a standard resistor of \( \mathrm{R} \) ohm is connected in the left gap and two wires \( A \) and \( B \) are connected one
after the other in the right gap. The balancing length measured from the left is \( 50 \mathrm{cm} \) for either of them. If the two wires are connected is series and put in
the right gap, the balancing length measured from the left would be (in cm)
A . 25
в. 33.3
\( c .66 .7 \)
D. 75
Subject: Physics
Assertion
A dipole \( P \) applies a force \( F \) on dipole \( Q \) and dipole \( Q \) applies a force \( F \) on dipole
\( \boldsymbol{P} \)
Reason
Action and reaction are equal and opposite.
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
The van't Hoff's factor for \( 0.1 \mathrm{M} \)
\( B a\left(N O_{3}\right)_{2} \) solution is \( 2.74 . \) The degree of dissociation is:
A . \( 91.3 \% \)
B. 87\%
c. \( 100 \% \)
D. 74\%
Subject: Chemistry
Write the IUPAC name of the complex
\( \left[\boldsymbol{A} \boldsymbol{g}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2}\right]\left[\boldsymbol{A} \boldsymbol{g}(\boldsymbol{C} \boldsymbol{N})_{2}\right] \)
Subject: Chemistry
The osmotic pressure of a solute is 600 \( \mathrm{mm} \) at \( 300 \mathrm{K} \). The solution is diluted
and the temperature is raised to \( 400 \mathrm{K} \)
and the solution shows an osmotic
pressure of \( 200 \mathrm{mm} \). The solution was
diluted to \( x \) times. \( x \) is :
Subject: Physics
An electric cell of emf \( E \) is connected
across a copper wire of diameter \( \boldsymbol{d} \) and
length \( l . \) The drift velocity of electrons in
the wire is \( v_{d} . \) If the length of the wire is
changed to \( 2 l \), the new drift velocity of electrons in the copper wire will be:
\( \mathbf{A} \cdot v_{d} \)
в. \( 2 v_{d} \)
c. \( v_{d} / 2 \)
D. \( v_{d} / 4 \)
Subject: Physics
Three solid spheres each of mass \( P \) and
radius \( Q \) are arranged as shown in
figure. The moment inertia of the
arrangement about \( Y Y^{\prime} \) axis will be
\( ^{A} \cdot \frac{7}{2} P Q^{2} \)
B. \( \frac{2}{7} P Q^{2} \)
c. \( \frac{2}{5} P Q^{2} \)
D. \( \frac{5}{2} P Q \)
Subject: Maths
\( \operatorname{Let} f(x)=\frac{a x+b}{x+1}, l i m_{x \rightarrow 0} f(x)=2 \)
and \( \lim _{x \rightarrow \infty} f(x)=1 \) then \( f(-2)= \)
A . 1
B . 2
c. -1
D.
Subject: Physics
A string oscillates according to the
equation \( \boldsymbol{y}^{\prime}= \)
\( (0.50 c m) \sin \left[\left(\frac{\pi}{3} c m^{-1}\right) x\right] \cos \left[\left(40 \pi s^{-1}\right)\right. \)
What is the speed of the two waves(identical except for direction of travel) whose superposition gives this oscillation?
Subject: Chemistry
Equilibrium constant, \( K_{c} \) for the
reaction, \( N_{2(g)}+3 H_{2(g)} \rightleftharpoons 2 N H_{3(g)} ; \) at
\( 500 K \) is \( 0.061 l i t r e^{2} m o l e^{-2} . A t \)
particular time, the analysis shows that composition of the reaction mixture is 3.00 mol litre\( ^{-1}, N^{2}, 2.00 \) mol litre\( ^{-1} \boldsymbol{I} \)
and 0.500 mol litre \( ^{-1} N H_{3} \). Is the
reaction at equilibrium? If not, in which
direction does the reaction tend to
proceed to reach equilibrium?
Subject: Physics
The masses \( 4 m \) and \( m \) are connected
by a light string passing over a frictionless pulley fixed at inclined
plane of inclination \( 45^{\circ} \) as shown in
figure. The coefficient of friction
between \( 4 m \) and inclined plane is \( \frac{1}{\sqrt{2}} \)
When two blocks are released, then
This question has multiple correct options
A. the tension in the string is mg
B. the frictional force on the block of \( 4 \mathrm{m} \) will be \( 2 \mathrm{mg} \)
c. the block of \( \mathrm{m} \) will move in upward direction
D. the frictional force on block of mass \( 4 \mathrm{m} \) has magnitude \( (2 \sqrt{2}-1) \mathrm{mg} \)
Subject: Chemistry
Calculate the value of molar gas
constant, \( ^{\prime} \boldsymbol{R}^{\prime} \) in (i) \( \boldsymbol{c} \boldsymbol{c} \boldsymbol{a} \boldsymbol{t} \boldsymbol{m} \boldsymbol{K}^{-1} \boldsymbol{m} \boldsymbol{o} \boldsymbol{l}^{-1} \)
(ii) \( \operatorname{tor} r c c K^{-1} m o l^{-1}(\text {iii }) \)
kPalitre \( \boldsymbol{K}^{-1} \boldsymbol{m o l}^{-1} \)
Subject: Maths
Point \( D \) has coordinates as (3,4,5)
Find the coordinates of point \( G \)
\( \mathbf{A} \cdot(0,3,5) \)
B. (3,0,4)
\( \mathbf{C} \cdot(3,5,4) \)
\( \mathbf{D} \cdot(3,0,5) \)
Subject: Maths
If \( f(x)=x^{11}+x^{9}-x^{7}+x^{3}+ \)
1 and \( f\left(\sin ^{-1}(\sin 8)\right)=\alpha, \alpha \) is a
constant, the \( \left.f \tan ^{-1}(\tan 8)\right) \) is equal
to
Note : consider 8 in radians.
\( A \)
B. \( \alpha-2 \)
c. \( \alpha+2 \)
D. \( 2-\alpha \)
Subject: Chemistry
When chlorine is passed over dry slaked
lime at room temperature, the main reaction product is:
A \( \cdot C a\left(C l O_{2}\right)_{2} \)
в. \( C a C l_{2} \)
c. \( C a O C l \)
D. \( \operatorname{Ca}\left(O C l_{2}\right)_{2} \)
Subject: Physics
Consider a jet traveling at \( 1000 \mathrm{km} / \mathrm{hr} \). If the jet shoots a laser in the same
direction it is traveling, how fast will the laser be traveling relative to the jet?
A. \( 300,000 \mathrm{km} / \mathrm{sec} \)
B. 1000 km/hr minus 300,000 km/sec
c. \( 300,000 \mathrm{km} / \mathrm{sec} \) plus \( 1000 \mathrm{km} / \mathrm{hr} \)
D. cannot determine with information available
E. \( 300,000 \mathrm{km} / \mathrm{sec} \) minus \( 1000 \mathrm{km} / \mathrm{hr} \)
Subject: Maths
The two adjacent sides of a parallelogram are \( 5 \mathrm{cm} \) and \( 4 \mathrm{cm} \) respectively and if the respective diagonal is \( 7 \mathrm{cm}, \) then find the area of the parallelogram?
\( A \cdot 8 \sqrt{6} \)
B. \( 6 \sqrt{6} \)
c. \( 4 \sqrt{6} \)
D. \( 8 \sqrt{3} \)
Subject: Biology
Which row in the table shows the
correct percentage of oxygen in atmospheric and exhalend air?
\begin{tabular}{lll} 
& Atmospheric air \( / \% \) & Exhaled air \( / \% \) \\
\( \mathrm{A} \) & 78 & 21 \\
\( \mathrm{B} \) & 21 & 16 \\
\( \mathrm{c} \) & 16 & 4 \\
\( \mathrm{D} \) & 4 & 0.04 \\
\hline
\end{tabular}
Subject: Maths
If for \( \boldsymbol{x} \in\left(\mathbf{0}, \frac{\mathbf{1}}{\mathbf{4}}\right), \) the derivative
\( \tan ^{-1}\left(\frac{6 x \sqrt{x}}{1-9 x^{3}}\right) \) is \( \sqrt{x} . g(x), \) then \( g(x) \)
equals:
A \( \cdot \frac{3}{1+9 x^{3}} \)
в. \( \frac{9}{1+9 x^{3}} \)
c. \( \frac{3 x \sqrt{x}}{1-9 x^{3}} \)
D. \( \frac{3 x}{1-9 x^{3}} \)
Subject: Physics
When a person stands on a weighing balance, working on the principle of Hooke's law, it shows a reading of \( 60 \mathrm{kg} \)
after a long time and the spring gets compressed by \( 2.5 \mathrm{cm} . \) If the person jumps on the balance from a height of \( \mathbf{1 0} c \boldsymbol{m}, \) the maximum reading of the balance will be
A. \( 60 \mathrm{kg} \)
в. \( 120 \mathrm{kg} \)
c. \( 180 \mathrm{kg} \)
D. 240 kg
Subject: Maths
The latus rectum of a parabola whose focal chord is \( P S Q \) such that \( S P=3 \)
and \( S Q=2, \) is given by
A \( \cdot \frac{24}{5} \)
в. \( \frac{12}{5} \)
\( c \cdot \frac{6}{5} \)
D. \( \frac{48}{5} \)
Subject: Maths
Prove that:
\( \boldsymbol{a}_{n^{2}+1}=\left(\boldsymbol{n}^{2}+\mathbf{1}^{2}\right)-\left(\boldsymbol{n}^{2}+\mathbf{1}\right)+\mathbf{1}= \)
\( \left(n^{2}+n+1\right)\left(n^{2}-n+1\right)= \)
\( \mathbf{A} \cdot a_{n-1} a_{n} \)
В \( \cdot a_{n+1} a_{n} \)
\( \mathbf{c} \cdot a_{n+1} a_{n-1} \)
D. \( a_{n+2} a_{n} \)