AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Find the molecular mass of:
(a) \( \boldsymbol{H}_{2} \boldsymbol{S}(\mathbf{b}) \boldsymbol{H} \boldsymbol{C l}(\mathbf{c}) \boldsymbol{N} \boldsymbol{H}_{3} \)
(d) \( C l_{2} \)
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H}(\mathrm{f}) \boldsymbol{C H}_{3} \boldsymbol{C H O} \)
Subject: Physics
An astronaut who weighs 162 pounds on the surface of the earth is orbiting the earth at a height above the surface
of the earth of two earth radii \( (h=2 R \)
where \( R \) is the radius of the earth.
How much does this astronaut weigh while in orbit at this height (With how much force is the earth pulling on him while he is in orbit at this height?)
A. 81 pounds
B. 40.5 pounds
c. 18 pounds
D. 54 pounds
E. 0 pounds (astronaut is weightless
Subject: Physics
A car of mass \( m \) starts moving so that its velocity varies according to the law \( \boldsymbol{v}=\boldsymbol{\beta} \sqrt{\boldsymbol{s}}, \) where \( \boldsymbol{\beta} \) is a constant, and \( \boldsymbol{s} \) is
the distance covered. The total work
performed by all the forces which are acting on the car during the first \( t \) seconds after the beginning of motion is:
\( \mathbf{A} \cdot m \beta^{4} t^{2} / 8 \)
B \( \cdot m \beta^{2} t^{4} / 8 \)
\( \mathbf{c} \cdot m \beta^{4} t^{2} / 4 \)
\( \mathbf{D} \cdot m \beta^{2} t^{4} / 4 \)
Subject: Chemistry
From the following identify the correct
ones.
This question has multiple correct options
A \( \cdot F e_{2} O_{3}+3 C O \rightarrow 2 F e+3 C O_{2} \)
в. \( Z n O+C \rightarrow Z n+C O \)
\( \mathbf{c} \cdot C a_{3}\left(P O_{4}\right)_{2}+C \rightarrow P \)
\( \mathbf{D} \cdot P b O+C \rightarrow P b \)
Subject: Chemistry
When chlorine reacts with cold and
dilute solution of sodium hydroxide, the products obtained are:
A \( \cdot C l^{-}+C l O^{-} \)
в. \( C l^{-}+C l O_{2} \)
c. \( C l^{-}+C l O_{3} \)
D. \( C l^{-}+C l O_{4} \)
Subject: Physics
If the weight of a body on the surface of the moon is \( 100 \mathrm{N} \), what is its mass?
\( \left.=1.6 \mathrm{ms}^{-2}\right) \)
\( A \cdot 160 \mathrm{kg} \)
B. 62.5 kg
\( c \cdot 6.25 \mathrm{kg} \)
D. 625 kg
Subject: Physics
A positively charged sphere suspended with a silk thread is slowly pushed in a
metal bucket. After its insertion the lid
is closed. What will be the electric field
intensity inside when the sphere has touched the bucket?
\( (\sigma \) is the surface charge density of sphere)
A. zero
в. \( \frac{\sigma}{2 \varepsilon_{0}} \)
c. \( \frac{\sigma}{\varepsilon_{0}} \)
D. None of these
Subject: Maths
Solution of \( \left(\frac{\boldsymbol{x}+\boldsymbol{y}-\boldsymbol{a}}{\boldsymbol{x}+\boldsymbol{y}-\boldsymbol{b}}\right)\left(\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right)= \)
\( \left(\frac{\boldsymbol{x}+\boldsymbol{y}+\boldsymbol{a}}{\boldsymbol{x}+\boldsymbol{y}+\boldsymbol{b}}\right) \)
A \( \cdot \log \left[(x+y)^{2}-a b\right]=\frac{2}{b-a}[x-y]+k \)
B \( \cdot \log \left[(x+y)^{2}+a b\right]=\frac{1}{b-a}[x-y]+k \)
c. \( \left(\frac{b-a}{2}\right)\left[\log \left((x+y)^{2}-a b\right)\right]=x+c \)
D.
Subject: Chemistry
Which of the following reactions can be used for the preparation of propane? This question has multiple correct options
\( \mathbf{A} \cdot C H_{3} C H=C H_{2} \underset{2 . C H_{3} C O O H}{1 . B_{2} D_{H}} \)
B. \( C H_{3} C H_{2} C H_{2} C l_{2 . H_{2} O}^{1 . M g / \text { (ther }} \)
C \( \cdot C H_{3} C H_{2} C H_{2} I^{R e d P / H I / 150^{\circ} C} \)
D. \( C H_{3} C H_{2} C H_{2} C O O N a \stackrel{N a O H / C a o}{\Delta} \)
Subject: Physics
An electric bulb of \( 15 \mathrm{V} \) is connected to a
battery of \( 15 \mathrm{V} \) which has negligible resistance. If the resistance offered by
the bulb is \( 5 \Omega \) the power of the bulb is
\( \ldots \) W.
A . 225
B. 75
\( c .30 \)
D. 45
Subject: Physics
Two capacitors of capacitance \( C \) are
connected in series. If one of them is
filled with a substance of dielectric
constant \( K, \) what is the effective
capacitance?
\( ^{A} \cdot \frac{K C}{(1+k)} \)
в. \( C(K+1) \)
c. \( \frac{2 K C}{(1+k)} \)
D. None of these
Subject: Chemistry
Assertion
An orbital cannot have more than two
electrons.
Reason
The two electrons in an orbital create
opposite magnetic field.
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
Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be defined by \( \boldsymbol{f}(\boldsymbol{x})=[\boldsymbol{x}] \)
and \( g(x)=\frac{3-2 x}{4} . \) We can say:
This question has multiple correct options
A. \( f \) is neither one-one nor onto
B. \( g \) is one-one but \( f \) is not one-one
c. \( f \) is one-one and \( g \) is onto
D. neither \( f \) nor \( g \) is onto
Subject: Maths
\( f\left(a_{1}, a_{2}, a_{3}, \dots, a_{n}, \dots a r e \text { in } G P \) then the \right.
determinant \( \Delta= \)
\( \left|\begin{array}{ccc}\log a_{n} & \log a_{n+1} & \log a_{n+2} \\ \log a_{n+3} & \log a_{n+4} & \log a_{n+5} \\ \log a_{n+6} & \log a_{n+7} & \log a_{n+8}\end{array}\right| \) is equal
to
A . 0
B. 1
\( c \cdot 2 \)
D.
Subject: Physics
If a simple harmonic motion is represented by \( \frac{d^{2} x}{d t^{2}}+\alpha x=0, \) its time period is then
A. \( 2 \pi \sqrt{\alpha} \).
. \( \sqrt{\sqrt{\alpha}} \). \( \alpha \).
в. \( 2 \pi \alpha \)
c. \( \frac{2 \pi}{\sqrt{\alpha}} \)
D. \( \frac{2 \pi}{\alpha} \)
Subject: Physics
In an experiment on photoelectric effect, Light of wavelength 800 nm (less than threshold wavelength) is incident
on a cesium plate at the rate of \( 5.0 \mathrm{W} \) The potential of the collector plate is made sufficiently positive with respect on the emitter so that the current
reaches its saturation value. Assuming
that on the average one of every \( 10^{6} \)
photons is able to eject a photoelectron,
find the photo current in the circuit.
Subject: Physics
(i) Two sets \( A \) and \( B \), of three bulbs
each, are glowing in two separate rooms.When one of the bulbs in set A is
fused, the other two bulbs also cease to glow. But in set \( \mathrm{B} \), when one bulb fuses, the other two bulbs continue to glow.
explain why this phenomenon occurs.
(ii) Why do we prefer arrangements of Set B for house circuiting?
Subject: Physics
The charge \( Q \) flowing through a resistance \( \boldsymbol{R} \) varies with time \( t \) as \( \boldsymbol{Q}= \)
\( a t-b t^{2} . \) The total heat produced in \( R \) is
(up to the instant when instantaneous
current is zero)
\( ^{A} \cdot \frac{a^{3} R}{6 b} \)
B. \( \frac{a^{3} R}{3 b} \)
c. \( \frac{a^{3} R}{2 b} \)
D. \( \frac{a^{3} R}{b} \)
Subject: Maths
If \( \overline{O A}=3 \bar{i}+\bar{j}-\bar{k},|\overline{A B}|=2 \sqrt{6} \) and \( A B \)
has the direction ratios 1,-1,2 then
\( |\boldsymbol{O} \boldsymbol{B}|= \)
A . \( \sqrt{35} \)
B. \( \sqrt{41} \)
c. \( \sqrt{26} \)
D. \( \sqrt{55} \)
Subject: Physics
Which of the following statement is
correct?
A. At sunset or sunrise, the suns rays have to pass through a small distance in the atmosphere.
B. At sunset or sunrise the suns rays have to pass through a larger distance in the atmosphere.
C. Rayleigh scattering which is proportional to \( (l / \lambda)^{2} \)
D. Most of the blue and other shorter wavelengths are not removed by scattering.
Subject: Physics
Charge \( Q \), is divided into two parts which are then kept some distance
apart. The force between them will be
maximum if the two parts are having the charge.
\( ^{\text {A }} \cdot \frac{Q}{2} \) each
в. \( \frac{Q}{4} \) and \( \frac{3 Q}{4} \)
c. \( \frac{Q}{3} \) and \( \frac{2 Q}{3} \)
D. \( e \) and \( (Q-e) \), where \( e= \) electronic charge
Subject: Physics
In a calorimeter of water equivalent 20
g, water of mass \( 1.1 \mathrm{kg} \) is taken at \( 288 \mathrm{K} \) temperature \( 373 \mathrm{K} \) is passed through it and temperature of water increases by
\( 6.5^{\circ} \mathrm{C} \) then the mass of steam
condensed is
A. \( 17.5 \mathrm{g} \)
в. \( 11.7 \mathrm{g} \)
c. \( 15.7 \mathrm{g} \)
D. \( 18.2 \mathrm{g} \)
Subject: Maths
The expansion of \( (2 x-3 y)^{2} \) is:
A \( \cdot 2 x^{2}+3 y^{2}+6 x y \)
B. \( 4 x^{2}+9 y^{2}-12 x y \)
c. \( 2 x^{2}+3 y^{2}-6 x y \)
D. \( 4 x^{2}+9 y^{2}+12 x y \)
Subject: Chemistry
Ethers like ROR can be cleaved by concentrated HI but not by HCl because:
A . \( I^{-} \) is a weaker nucleophile than \( C l^{-} \)
B. \( I^{-} \) is stronger nucleophile than \( C l^{-} \)
c. \( S_{N} 1 \) mechanism carried out in this reaction is rapidly in presence of HI
D. None of the above
Subject: Chemistry
Which of the following complex species is not expected to exhibit optical isomerism?
\( \mathbf{A} \cdot\left[\operatorname{Co}(e n)\left(N H_{3}\right)_{2} C l_{2}\right]^{+} \)
B. \( \left[\mathrm{Co}(e n)_{3}\right]^{3+} \)
c. \( \left[\operatorname{Co}(e n)_{2} C l_{2}\right]^{+} \)
D. \( \left[C o\left(N H_{3}\right)_{3} C l_{3}\right] \)
Subject: Chemistry
The name of the process is :
\[
\begin{array}{l}
\mathrm{caCO}_{3} \longrightarrow \mathrm{CaO}+\mathrm{CO}_{2} \\
\mathrm{NH}_{3}+\mathrm{H}_{2} \mathrm{O}+\mathrm{CO}_{2} \stackrel{\longrightarrow}{\longrightarrow} \mathrm{NH}_{4} \mathrm{HCO}_{3} \\
\mathrm{NaCl}+\mathrm{NH}_{4} \mathrm{HCO}_{3} \longrightarrow \mathrm{NH}_{4} \mathrm{Cl}+\mathrm{NaHCO}_{3} \\
2 \mathrm{NH}_{4} \mathrm{Cl}+\mathrm{CaO} \longrightarrow \mathrm{CaC}_{2}+2 \mathrm{NH}_{3}+\mathrm{H}_{2} \mathrm{O}
\end{array}
\]
A. solvay
B. lowing
c. salt cake
D. gossage
Subject: Chemistry
An equilibrium mixture of \( \boldsymbol{P C l}_{5}, \boldsymbol{P C l}_{3} \)
and \( C l_{2} \) at a certain temperature
contains \( 0.5 \times 10^{-3} M P C L_{5} 1.5 \times \)
\( \mathbf{1 0}^{-2} \boldsymbol{M} \boldsymbol{P C L}_{3} \) and \( \boldsymbol{3} \times \mathbf{1 0}^{-\mathbf{2}} \boldsymbol{M} \boldsymbol{C l}_{2} \)
Calculate the equilibrium constant \( \boldsymbol{K}_{c} \)
for the reaction \( \boldsymbol{P} \boldsymbol{C} \boldsymbol{L}_{5}(\boldsymbol{g}) \rightleftharpoons \)
\( \boldsymbol{P C l}_{3}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \)
Subject: Maths
\( \boldsymbol{I}_{\mathrm{n}}=\int_{1}^{\mathrm{e}}(\log \mathrm{x})^{\mathrm{n}} \mathrm{d} \mathbf{x} \) and \( \mathbf{I}_{\mathrm{n}}=\mathbf{A}+\mathbf{B I}_{\mathbf{n}-\mathbf{1}} \)
then \( \mathbf{A}=\dots \dots \dots \dots . . \quad B=\dots . . . . . . . . . . . . . . \)
\( \mathbf{A} \cdot e,-n \)
B. \( 1 / e, n \)
c. \( -e, n \)
D. \( -e \)
Subject: Chemistry
One mole of \( N_{2} H_{4} \) loses 10 moles of
electrons to form a new compound \( \boldsymbol{A} \)
Assuming that all the nitrogen appears in the new compound, what is the oxidation state of nitrogen in \( A \) ? [There is no change in the oxidation state of hydrogen \( ] \)
A \( .+1 \)
B. -3
\( c \cdot+3 \)
D. +5
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{2} & -\mathbf{3} \\ \mathbf{- 4} & \mathbf{1}\end{array}\right], \) then adj \( \left(\mathbf{3} \boldsymbol{A}^{2}+\right. \)
\( 12 A) \) is equal to.
\( \mathbf{A} \cdot\left[\begin{array}{cc}72 & -84 \\ -63 & 51\end{array}\right] \)
В. \( \left[\begin{array}{ll}51 & 63 \\ 84 & 72\end{array}\right] \)
c. \( \left[\begin{array}{ll}51 & 84 \\ 63 & 72\end{array}\right] \)
D. \( \left[\begin{array}{cc}72 & -63 \\ -84 & 51\end{array}\right] \)
Subject: Physics
The correct relation between the size of
the obstacle and wavelength of light in order to observe the diffraction effect is
A \( \cdot a_{/ \lambda}=0 \)
B \( \cdot a_{/ \lambda}=0 \)
\( c \cdot a_{/ \lambda}=\infty \)
\( \mathbf{D} \cdot a_{/ \lambda}=150 \)
Subject: Physics
To convert \( ^{o} \mathrm{F} \) to \( ^{\circ} \mathrm{C} \) formula we use, is
A \( \cdot(F-32) \times \frac{5}{12} \)
B \( \cdot\left(F \times \frac{5}{9}\right)-32 \)
c. \( (F-32) \times \frac{9}{5} \)
D. \( (F-32) \times \frac{5}{9} \)
Subject: Chemistry
The melting point of cadmium bromide
is \( 568^{\circ} \mathrm{C} \). Which of the following
equations best describes what occurs when cadmium bromide is heated to
\( 568^{\circ} C ? \)
A \( \cdot \operatorname{CdBr}(s) \rightarrow \operatorname{CdBr}(l) \)
B . \( \operatorname{CdBr}_{2}(s) \rightarrow \operatorname{CdBr}_{2}(l) \)
c. \( \operatorname{CdBr}_{2}(s) \rightarrow C d(s)+B r_{2}(g) \)
D. \( \operatorname{CdBr}_{2}(s) \rightarrow C d^{2+}(a q)+2 B r^{-}(a q) \)
Subject: Physics
A body is acted on by a force given by \( \boldsymbol{F}=(\mathbf{1 0}+\mathbf{2 t}) \mathrm{N} . \) The impulse received
by the body during the first four seconds is :
A . \( 40 \mathrm{N} \) s
B. 56 N s
c. 72 N s
D. 32 N s
Subject: Chemistry
Study the following graph and mark the incorrect statement following it.
\( \mathbf{T}\left(^{\circ} \mathbf{C}\right) \)
A . At zero volume all lines meet at \( -273.15^{\circ} \mathrm{C} \). This
temperature is known as absolute zero
B. Each line of the volume vs temperature at constant pressure of graph is called isotherm
c. All gases obey charles' law at very low pressure and high temperature
D. Pressure remaining constant, volume of a gas is directly proportional to its absolute temperature
Subject: Physics
The displacement \( x \) of a particle varies
with time according to the relation \( \boldsymbol{x}= \)
\( \frac{a}{b}\left(1-e^{-b t}\right) . \) Which of the following is
not correct? \( (a \text { and } b \) are the positive constants.
A \( \cdot \operatorname{At} t=\frac{1}{b}, \) acceleration of the particle is \( -\frac{a b}{e} \)
B. The velocity and acceleration of the particle at \( t=0 \) are \( a \) and \( -a b, \) respectively.
C. The particle cannot reach a point at a distance \( x^{\prime} \) from its starting position if \( x^{\prime}>a / b \)
D. The particle will come back to its starting point as \( t \rightarrow \infty \)
Subject: Physics
Alida runs her toy car on dry marble
floor, wet marble floor, newspaper and towel spread on the floor. The force of
friction acting on the car on different surfaces in increasing order will be
A. Wet marble floor, dry marble floor, newspaper and towel
B. Newspaper, towel, dry marble floor, wet marble floor
c. Towel, newspaper, dry marble floor, wet marble floor.
D. Wet marble floor, dry marble floor, towel, newspaper
Subject: Chemistry
Which of the following mixture does not obey Daltons law of partial pressures.
A \( \cdot C O_{2} \) and \( O_{2} \) at room temperature
B. \( N H_{3} \) and \( H C l \) at \( 0^{\circ} C \)
C. \( N H_{3} \) and \( H C l \) at room temperature
D. Excess of \( C l_{2} \) and \( N H_{3} \)
Subject: Chemistry
Assertion
On cooling, the brown colour of nitrogen dioxide disappears.
Reason
On cooling, \( N O_{2} \) undergoes
dimerisation resulting in the pairing of
the odd electron in \( N O_{2} \)
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
Which of the following statement is
correct for \( \boldsymbol{C s B r _ { 3 }} \) ?
A. It is a covalent compound
B. It contains \( C s^{3+} \) and \( B r^{-} \) ions
c. It contains \( C s^{+} \) and \( B r_{3}^{-} \) ions
D. It contains \( C s^{+}, B r_{3}^{-} \) and lattice \( B r_{2} \) molecul
Subject: Maths
\( \operatorname{Given} f(x)=\left\{\begin{array}{l}x, 0 \leq x<\frac{1}{2} \\ \frac{1}{2}, x=\frac{1}{2} \\ 1-x, \frac{1}{2}<x \leq 1\end{array} \) and \right.
\( g(x)=\left(x-\frac{1}{2}\right)^{2}, x \epsilon R, \) Then the area
(in sq.units) of the region bounded by the curves \( y=f(x) \) and \( y=g(x) \) between the lines \( 2 x=1 \) and \( 2 x=\sqrt{3} \)
is
\( ^{A} \cdot \frac{1}{3}+\frac{\sqrt{3}}{4} \)
B. \( \frac{1}{2}-\frac{\sqrt{3}}{4} \)
c. \( \frac{1}{2}+\frac{\sqrt{3}}{4} \)
D. \( \frac{\sqrt{3}}{4}-\frac{1}{3} \)
Subject: Chemistry
What volume of \( 0.10 \mathrm{M} \) sodium formate
solution should be added to \( 50 \mathrm{ml} \) of
\( 0.05 \mathrm{M} \) formic acid to produce a buffer
solution of \( p H 4.0 ? \)
\( \left[p K_{a} \text { for formic acid is } 3.80\right] \)
A . \( 3.96 \mathrm{ml} \)
B. 25m
c. \( 39.6 \mathrm{ml} \)
D. \( 100 \mathrm{ml} \)
Subject: Chemistry
\( \boldsymbol{B} \boldsymbol{a} \boldsymbol{S} \boldsymbol{O}_{4}(\boldsymbol{s}) \rightleftharpoons \boldsymbol{B} \boldsymbol{a}^{2+}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{S} \boldsymbol{O}_{4}^{2-}(\boldsymbol{a} \boldsymbol{q}) \)
Whai is \( K_{s p} \) for above reaction?
\( \mathbf{A} \cdot\left[B a^{2+}\right]\left[S O_{4}^{2-}\right] \)
\( ^{\mathbf{B} \cdot} \frac{\left[B a^{2+}\right]\left[S O_{4}^{2-}\right]}{B a S O_{4}} \)
\( ^{\mathrm{c}} \cdot \frac{\left[B a^{2+}\right]\left[S O_{4}^{2-}\right]}{\left[B a S O_{4}\right]} \)
D. None
Subject: Physics
Subtract \( 1.5 \times 10^{3} \) from \( 4.8 \times 10^{4} \) with
due regard to significant figures.
A. \( 4.6 \times 10^{4} \)
B. \( 4.6 \times 10^{5} \)
c. \( 4.6 \times 10^{6} \)
D. \( 5 \times 10^{4} \)
Subject: Physics
If \( h \) is Plancks constant, the
momentum of a photon of wavelength
\( 0.01 A^{\circ} \) is
\( \mathbf{A} \cdot 10^{-2} h \)
B. \( h \)
\( c \cdot 10^{2} \)
D. \( 10^{12} h \)
Subject: Physics
In the given figure pulleys are massless and frictionless and string A are light
and inextensible. A force is applied on pulley A vertically upward. At any time
acceleration of \( 5 \mathrm{kg} \) is \( a_{1} \) (upward) and
\( 10 \mathrm{kg} \) is \( a_{2}(\text { upward }) \) then \( \left(g=10 m / s^{2}\right) \)
A \( \cdot a_{1}=0, a_{2}=0 \) if \( F=100 N \)
B . \( a_{1}=5 m / s^{2}, a_{2}=0 \) if \( F=300 N \)
C \( \cdot a_{1}=15 m / s^{2}, a_{2}=2.5 m / s^{2} \) if \( F=500 N \)
D. All option is correct
Subject: Physics
Starting from an origin, a body oscillates simple harmonically with a period of \( 2 s . \) After what time will its
kinetic energy be \( 75 \% \) of the total
energy?
A . \( 1 / 6 s \)
B. \( 1 / 12 s \)
\( \mathrm{c} \cdot 1 / 3 s \)
D. \( 1 / 4 s \)
Subject: Biology
Study the following statements and select the incorrect ones.
(i) Physical removal of large and small particles through filtration and sedimentation is called primary sewage
treatment.
(ii) Secondary sewage treatment is mainly a mechanical process.
(iii) Activated sludge sediment in a sewage treatment plant is a rich source of aerobic bacteria.
(iv) Biogas, commonly called as gobar
gas, is pure methane.
A . A-(iii), B-(i), C-(iv), D-(ii)
B. A-(i), B-(iii), C-(iv), D-(ii)
c. A-(iii), B-(ii), C-(iv), D-(i)
D. A-(iii), B-(i), C-(ii), D-(iv)
Subject: Chemistry
Calculate the wavelength (in nanometre) associated with a proton moving at \( 1 \times 10^{3} m s e c^{-1} \)
\( \left[\text { mass of proton }=\mathbf{1 . 6 7} \times \mathbf{1 0}^{-\mathbf{2 7}} \mathbf{k g}, \boldsymbol{h}=\right. \)
\( 6.63 \times 10^{-34} J \) sec
\( \mathbf{A} \cdot 0.032 \mathrm{nm} \)
B. \( 0.40 \mathrm{nm} \)
c. \( 2.5 \mathrm{nm} \)
D. \( 14 \mathrm{nm} \)
Subject: Physics
\( \vec{A} \) and \( \vec{B} \) are two vectors \( \operatorname{given} \vec{A}= \) \( 2 \hat{i}+3 \hat{j} \) and \( \vec{B}=\hat{i}+\hat{j} . \) The magnitude of the component \( \vec{A} \) along \( \vec{B} \) is
Subject: Maths
The range of the function \( \boldsymbol{f}(\boldsymbol{x})= \) \( \frac{\sin (\pi[x])}{x^{2}+1} \) (where [.] denotes greatest
integer function) is
\( A \cdot\{0\} \)
в. \( R \)
c. (0,1)
() 5
\( D \cdot(0, \infty) \)
Subject: Chemistry
STATEMENT-1: The order of acidic
character of the given compounds
STATEMENT-2:-I and -R effect of the
group stabilizes the conjugate base decreasing the -ve charge, whereas +1 effect of the group destabilises the conjugate base by intensifying the charge
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
Which of the following does not have \( s-s \) linkage?
\( A \cdot S_{2} O_{8}^{2-} \)
B. \( S_{2} O_{6}^{2-} \)
\( \mathrm{c} \cdot S_{2} O_{5}^{2} \)
D. \( S_{2} O_{3}^{2-} \)
Subject: Physics
Light with an energy flux of \( 20 \mathrm{W} / \mathrm{cm}^{2} \) falls on a non-reflecting surface at normal incidence. If the surface has
an area of \( 30 \mathrm{cm}^{2} \), the total
momentum delivered (for complete
absorption) during 30 minutes is :
A \( .3 .6 \times 10^{-3} \mathrm{kg} \mathrm{m} / \mathrm{s} \)
B. \( 3.3 \times 10^{-8} \mathrm{kg} \mathrm{m} / \mathrm{s} \)
c. \( 10.8 \times 10^{4} \mathrm{kg} \mathrm{m} / \mathrm{s} \)
D. \( 1.08 \times 10^{7} \mathrm{kg} \mathrm{m} / \mathrm{s} \)
Subject: Physics
An object of mass \( 0.2 k g \) executes SHM along the \( x \) -axis with frequency of \( (25 / \pi) \) Hz. At the point \( x=0.04 m \) the
object has \( \mathrm{KE} \mathbf{0 . 5} \boldsymbol{J} \) and PE \( \mathbf{4} \boldsymbol{J} \). The
amplitude of oscillation is
Subject: Chemistry
Molar conductivity \( \left(\lambda_{M}\right) \) and equivalent
conductivity \( \left(\lambda_{e q}\right) \) for an electrolyte
\( A_{x} B_{y} \) at any dilution are related as:
A \( . \lambda_{M}=\lambda_{e q} . \times(x+y) \)
B . \( \lambda_{M}=\lambda_{e q} \). \( \times x \times y \)
c. \( \lambda_{M}=\frac{\lambda_{e q}}{x+y} \)
D. \( \lambda_{M}=\frac{\lambda_{e q}}{x \times y} \)
Subject: Physics
When a plane mirror is placed horizontally on a level ground at a distance of \( 60 \mathrm{m} \) from the front of a
tower, the top of the tower and its image
in the mirror subtend an angle of \( 90^{\circ} \) at the eye. The height of the tower is :
A. \( 30 m \)
в. 60 т
\( \mathrm{c} .90 \mathrm{m} \)
D. \( 120 m \)
Subject: Maths
If \( 2^{x}-2^{y}=2^{x+y} \) then \( \frac{d y}{d x}= \)
\( \mathbf{A} \cdot 2^{y-x} \)
B . \( 2^{y / x} \)
\( \mathbf{c} \cdot-2^{y / x} \)
D. \( 2^{x / y} \)
Subject: Physics
When the load on a wire is increased
from \( 3 k g w t \) to \( 5 k g w t \) the elongation increases from 0.61 \( m m \) to \( 1.02 m m \)
The required work done during the extension of the wire is:
A \( \cdot 16 \times 10^{-3} J \)
В. \( 8 \times 10^{-2} J \)
c. \( 20 \times 10^{-2} J \)
D. \( 11 \times 10^{-3} J \)
Subject: Maths
The Vertex of the parabola \( \boldsymbol{y}^{2}-\mathbf{1 0} \boldsymbol{y}+ \)
\( \boldsymbol{x}+\mathbf{2 2}=\mathbf{0} \) is.
\( A \cdot(3,4) \)
B. (3,5)
\( c \cdot(5,3) \)
D. none of these
Subject: Maths
Let \( M \) and \( N \) be two \( 3 \times 3 \) be two non-
singular skew symmetric matrices
such that \( M N=N M \) further, if \( M \neq \)
\( n^{2} \). If \( P T \) denotes the transpose of \( P \) then
\( M^{2} N^{2}\left(M^{T} N\right)^{-1}(M N)^{-1} T \) is equal to
Subject: Chemistry
The photoelectric effect of Ba consists of emission of electrons from its
ionisation energy on irradiation with light from the ionization energy of \( \boldsymbol{H} e- \) atom is irradiation with light. A photon
with a minimum energy of \( 3.97 \times \)
\( 10^{-19} J \) is necessary to eject electron
from Ba.
(a)What is the frequency of radiation corresponding to this value?
(b) Will a blue light of wavelength
\( 450 n m \) be able to eject at electron from
Ba? (Given \( h=6.626 \times 10^{-27} \) erg \( - \)
\( \boldsymbol{s} \boldsymbol{e} \boldsymbol{c} \)
\( \mathbf{A} \cdot 6 \times 10^{13} H z, \) yes
B. \( 6 \times 10^{13} H z \), no
C \( .5 .99 \times 10^{14} \mathrm{Hz} \), yes
D. \( 3.6 \times 10^{13} \mathrm{Hz} \), no
Subject: Maths
If two events \( A \) and \( B \) such that
\( \boldsymbol{P}\left(\boldsymbol{A}^{c}\right)=\mathbf{0 . 3}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 4} \) and \( \boldsymbol{P}(\boldsymbol{A} \cap \)
\( \left.\left.\boldsymbol{B}^{c}\right)=\mathbf{0 . 5}, \boldsymbol{P}\left[\boldsymbol{B} / \boldsymbol{A} \cup \boldsymbol{B}^{c}\right)\right]=\frac{1}{k}, \) then
value of k is
Subject: Physics
Maximum current that can pass
through galvanometer is \( 0.002 A \) and
resistance of galvonameter is \( \boldsymbol{R}_{\boldsymbol{g}}= \) \( 50 \Omega \) find out shunt resistance to
convert in into ammeter of range \( 0.5 A \)
A . \( 0.5 \Omega \)
B. \( 0.2 \Omega \)
\( c .0 .7 \Omega \)
D. \( 0.9 \Omega \)