AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A ray of light is incident at an angle \( i \) on
a glass slab of refractive index \( \mu \). The
angle between reflected and refracted
light is \( 90^{\circ} . \) Then, the relationship
between i and \( \mu \) is :
A \( \cdot i=\tan ^{-1}\left(\frac{1}{\mu}\right) \)
В. \( \tan i=\mu \)
\( \mathrm{c} \cdot \sin i=\mu \)
D. \( \cos i=\mu \)
Subject: Physics
If the wave equation is \( y= \)
\( 0.08 \sin \frac{2 \pi}{\lambda}(150 t-x) s . \) Then velocity of
the wave will be
A. 150 units
B. \( 150 \sqrt{2} \) units
c. 300 units
D. \( 300 \sqrt{2} \) units
Subject: Physics
A small object of linear dimension \( x \) lies on the axis of an optical mirror of local length \( f \) at a distance \( a \) from mirror
The linear dimension of image:
\( ^{A} \cdot_{x}\left(\frac{f}{f-a}\right)^{2} \)
B. \( x\left(\frac{f}{f-a}\right) \)
c. \( x\left(\frac{f}{a-f}\right)^{1 / 2} \)
D. \( x\left(\frac{a-f}{f}\right)^{1 / 2} \)
Subject: Maths
The value of \( p \) for which the function
\[
\left\{\begin{array}{ccc}
\boldsymbol{f}(\boldsymbol{x})= & & \\
& \left(\boldsymbol{4}^{\boldsymbol{x}}-\mathbf{1}\right)^{\mathbf{3}} & \\
\hline \multirow{2}{*} {\sin \frac{\boldsymbol{x}}{\boldsymbol{p}} \log \left(1+\frac{\boldsymbol{x}^{2}}{\mathbf{3}}\right)} & ; & \boldsymbol{x} \neq \mathbf{0} \\
& \mathbf{1 2}(\log \mathbf{4})^{\mathbf{3}} & ; \boldsymbol{x}=\mathbf{0}
\end{array}\right.
\]
continuous at \( \boldsymbol{x}=\mathbf{0}, \) is
A . 4
B. 2
\( c .3 \)
\( D \)
Subject: Physics
The displacement of a charge \( Q \) in the electric field \( \boldsymbol{E}=\boldsymbol{e}_{1} \hat{\boldsymbol{i}}+\boldsymbol{e}_{2} \hat{\boldsymbol{j}}+\boldsymbol{e}_{3} \hat{\boldsymbol{k}} \) is
\( \hat{\boldsymbol{r}}=\boldsymbol{a} \hat{\mathbf{1}}+\boldsymbol{b} \hat{\boldsymbol{j}} . \) The work done is-
A \( Q\left(a e_{1}+b e_{2}\right) \)
() \( a\left(a_{1}+b_{2}\right)+b_{2}+b_{2} \)
в. \( Q \sqrt{\left(a e_{1}\right)^{2}+\left(b e_{2}\right)^{2}} \)
c. \( Q\left(e_{1}+e_{2}\right) \sqrt{a^{2}+b} \)
D. \( Q(\sqrt{e_{1}^{2}+e_{2}^{2}})(a+b) \)
Subject: Maths
On the ellipse, \( 4 x^{2}+9 y^{2}=1, \) the
points at which the tangents are
parallel to the line \( 8 x=9 y \) are
This question has multiple correct options
\( ^{\mathrm{A}} \cdot\left(\frac{2}{5}, \frac{1}{5}\right) \)
B \( \cdot\left(-\frac{2}{5}, \frac{1}{5}\right) \)
\( c \cdot\left(-\frac{2}{5},-\frac{1}{5}\right) \)
D. \( \left(\frac{2}{5},-\frac{1}{5}\right) \)
Subject: Maths
What is the geometric mean of the
sequence \( 1,2,4,8, \dots \dots 2^{n} ? \)
\( \mathbf{A} \cdot 2^{n / 2} \)
B. \( 2^{(n+1) / 2} \)
c. \( 2^{(n+1)}-1 \)
D. \( 2^{(n-1)} \)
Subject: Maths
If \( \boldsymbol{A}=\{\boldsymbol{a}, \boldsymbol{b}\}, \boldsymbol{B}=\{1,2,3\}, \) find \( \mathbf{B} \times \mathbf{A} \)
A. \( B \times A=\{(1, a),(2, a),(3, a),(1, b)(2, b),(3, b)\} \)
B. \( B \times A=\{(2, a),(3, a),(1, b)(2, b),(3, b)\} \)
C. \( B \times A=\{(1, a),(2, a),(3, a),(1, b)(2, b)\} \)
D. None of these
Subject: Physics
of length \( L \) and resistance \( 9 r \) is joined
to the cell \( D \) of emf \( \varepsilon \) and internal
resistance \( r . \) The cell \( C^{\prime} s \) emf is \( \varepsilon / 2 \) and
its internal resistance is \( 2 r \). The
galvanomater \( G \) will show no deflection
when the length \( A J \) is
' \( \frac{4 L}{9} \)
\( 3 \cdot \frac{5 L}{9} \)
c. \( \frac{7 L}{18} \)
D. \( \frac{11}{18} \)
Subject: Chemistry
The de-Broglie wavelength of a tennis
ball of mass \( 60 g \) moving with a velocity of \( 10 \mathrm{m} / \mathrm{s} \) is approximately (planck's
constant, \( \boldsymbol{h}=\mathbf{6 . 6 3} \times \mathbf{1 0}^{-\mathbf{3 4}} \boldsymbol{J}-\boldsymbol{s} \)
A \( \cdot 10^{-33} m \)
В. \( 10^{-31} \) m
c. \( 10^{-16} m \)
D. \( 10^{-25} \mathrm{m} \)
Subject: Maths
\( \mathbf{f} \boldsymbol{y}=\tan ^{-1}\left[\frac{\sqrt{\mathbf{1}+\boldsymbol{x}^{2}}-\mathbf{1}}{\boldsymbol{x}}\right], \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} ? \)
Subject: Chemistry
Identify Z in the given reaction. \( \mathrm{CH} \equiv \mathrm{CH} \frac{\mathrm{H}_{2} \mathrm{SO}_{4}+\mathrm{HgSO}_{4}+60^{0} \mathrm{C}}{\longrightarrow} \boldsymbol{Z} \)
A \( \cdot C_{2} H_{5} I \)
в. \( C_{2} H_{5} O H \)
с. \( C H I_{3} \)
D. \( C H_{3} C H O \)
Subject: Chemistry
In the given reaction,
\( \boldsymbol{C H}_{3}-\underset{C H_{3}}{C}=\boldsymbol{C H}-\boldsymbol{O}-\boldsymbol{C H}_{3}+ \)
\( \boldsymbol{C H}_{3}-\boldsymbol{O}-\boldsymbol{H}(\boldsymbol{e} \boldsymbol{x} \boldsymbol{c} \boldsymbol{e} \boldsymbol{s} \boldsymbol{s}) \frac{\boldsymbol{H} \boldsymbol{C I}}{d r \boldsymbol{y}} \)
\( \boldsymbol{X}(M \boldsymbol{a} \boldsymbol{j} \boldsymbol{o} \boldsymbol{r}) \)
Then \( X \) will be:
\( ^{\mathbf{A}} \cdot_{C H_{3}-} \stackrel{_{C H_{3}}^{O C H_{3}}}{C}-C H_{2}-O C H_{3} \)
B.
(2)
\( \mathrm{c} \cdot_{C H_{3}-C_{C H_{3}}^{I}-C H_{2}-\ddot{O}-C H_{3}} \)
\( ^{\mathrm{D}} \mathrm{CH}_{3}-\underset{_{C H_{3}}^{\mathrm{H}}}{C H}-C_{H}^{\text {сл }}-\ddot{O}-C H_{3} \)
Subject: Chemistry
The vapour pressure of \( 2.1 \% \) of an aqueous solution of a non-electrolyte at
\( 373 K \) is \( 755 \mathrm{mm} \). Calculate the molar
mass of solution \( \left(M_{2}\right) \)
A . \( 46.1 \mathrm{gm} / \mathrm{mol} \) le
B. \( 57.456 \mathrm{gm} / \mathrm{mole} \)
c. \( 10 \mathrm{gm} / \mathrm{mole} \)
D. \( 87.12 \mathrm{gm} / \mathrm{mole} \)
Subject: Physics
A curved road of \( 50 m \) in radius is
banked to correct angle for a given speed. If the speed is to be doubled keeping the same banking angle, the radius of curvature of the road should
be changed to
A. 200 \( \mathrm{m} \)
B. 100 \( m \)
\( c \cdot 50 m \)
D. None of the above
Subject: Maths
In the following letter sequence, some of the letters are missing. These are given in order as one of the alternatives below
Choose the correct alternative.
\( \boldsymbol{\alpha} \boldsymbol{\beta}_{-} \boldsymbol{\alpha} \boldsymbol{\alpha}_{-} \boldsymbol{\beta} \boldsymbol{\beta} \boldsymbol{\beta}_{-} \boldsymbol{\alpha} \boldsymbol{\alpha} \boldsymbol{\alpha} \boldsymbol{a}_{-} \boldsymbol{\beta} \boldsymbol{\beta} \boldsymbol{\beta} \ldots \)
\( \mathbf{A} \cdot \alpha \beta \beta \alpha \)
B. \( \beta \alpha \beta \alpha \)
\( \mathrm{c} \cdot \alpha \alpha \alpha \beta \)
\( \mathbf{D} \cdot \alpha \beta \alpha \beta \)
Subject: Maths
The area of the region bounded by the curve \( y=2 x-x^{2} \) and the line \( y=x \) is
square units.
A \( \cdot \frac{1}{6} \)
в. \( \frac{1}{2} \)
\( c \cdot \frac{1}{3} \)
D. \( \frac{7}{6} \)
Subject: Maths
A resistance of \( 100 \Omega \) and inductance \( L \)
henry are connected in series with a
battery of 20 volts.The current at any instant, if the relation between is \( \boldsymbol{L}, \boldsymbol{R}, \boldsymbol{E} \) is \( \boldsymbol{L} \frac{\boldsymbol{d} \boldsymbol{i}}{\boldsymbol{d} \boldsymbol{t}}+\boldsymbol{R} \boldsymbol{i}=\boldsymbol{E} \) is given by?
A \( . i=0.6\left(-e^{-200 t}\right) \)
В \( \cdot i=0.4\left(-e^{-200 t}\right) \)
c. \( \quad i=0.2\left(1-e^{\frac{-100}{L} t}\right) \)
D . \( i=0.8\left(-e^{-200 t}\right) \)
Subject: Chemistry
Permanent hardness is due to \( C l^{\ominus} \) and
\( \boldsymbol{S O}_{4}^{2-} \) of \( \boldsymbol{M} \boldsymbol{g}^{2+} \) and \( \boldsymbol{C} \boldsymbol{a}^{2+} \) and is
removed by adding \( N a_{2} C O_{3} \)
\( \boldsymbol{C a} \boldsymbol{S O}_{4}+\boldsymbol{N a}_{2} \boldsymbol{C O}_{3} \rightarrow \boldsymbol{C a} \boldsymbol{C O}_{3}+ \)
\( N a_{2} S O_{4} \)
\( \boldsymbol{C a C l}_{2}+\boldsymbol{N a}_{2} \boldsymbol{C O}_{3} \rightarrow \boldsymbol{C a C O}_{3}+ \)
\( 2 N a C l \)
Which of the following statements is/are correct?
This question has multiple correct options
\( A \cdot \) If hardness is 100 ppm \( C a C O_{3} \), the amount of \( N a_{2} C O_{3} \) required to soften 10 L of hard water is 1.06 g.
B. If hardness is 100 ppm \( C a C O_{3} \), the amount of \( N a_{2} C O_{3} \) required to soften 10 L of hard water is 10.6 g.
C. If hardness is 420 ppm \( M g C O_{3} \), the amount of \( N a_{2} C O_{3} \) required to soften 10 L of hard water is \( 53.0 \mathrm{g} \)
D. If hardness is 420 ppm \( M g C O_{3} \), the amount of \( N a_{2} C O_{3} \) required to soften 10 L of hard water is \( 5.3 \mathrm{g} \)
Subject: Physics
A water film is formed on a glass-block. A light ray is incident on water film from air at an angle of \( 60^{\circ} \) with the normal. The angle of incidence on glass slab is \( \left(\mu_{g}=1.5, \mu_{w}=\frac{4}{3}\right) \)
A \( \cdot \sin ^{-1}\left(\frac{3 \sqrt{3}}{8}\right) \)
в. \( \sin ^{-1}\left(\frac{1}{\sqrt{3}}\right) \)
c. \( \sin ^{-1}\left(\frac{4 \sqrt{3}}{9}\right) \)
D. \( \sin ^{-1}\left(\frac{9 \sqrt{3}}{16}\right) \)
Subject: Physics
An element undergoes reaction as shown:
\( X+2 e-, \) energy released \( = \)
\( 30.87 e V / \) atom. If the energy released,
is used to dissociate 4 g of \( \boldsymbol{H}_{2} \)
molecules, equally into \( \boldsymbol{H}^{+} \) and \( \boldsymbol{H}^{*} \)
where \( \boldsymbol{H}^{*} \) is excited state of \( \mathrm{H} \) atoms,
where the electrons travels in in orbit
whose circumference equal to four times it's de Broglie's wavelength.
Determine the least moles of \( X \) that
would be required:

Given: I.E. of \( \mathrm{H}=13.6 \mathrm{eV} / \) atom, bond
energy of \( \boldsymbol{H}_{2}=\mathbf{4 . 5 2 6 e V} / \) molecule
A . 1
B. 2
\( c .3 \)
D. 4
Subject: Maths
A chord of a circle is \( 12 \mathrm{cm} \) in length and its distance from the centre is 8 cm. The length of the chord of the same
circle which is at a distance of \( 6 \mathrm{cm} \)
from the centre is
\( A .30 \mathrm{cm} \)
B. \( 24 \mathrm{cm} \)
\( c .16 \mathrm{cm} \)
D. \( 18 \mathrm{cm} \)
Subject: Physics
A npn transistor is connected in
common emitter configuration in a given amplifier. A load resistance of \( 800 \Omega \) is connected in the collector
circuit and the voltage drop across it is
\( 0.8 V . \) If the current amplification factor
is 0.96 and the input resistance of the circuit is \( 192 \Omega \), the voltage gain and the power gain of the amplifier will respectively be
A .4,3.84
в. 3.69,3.84
\( c \cdot 4,4 \)
D. 4.3 .69
Subject: Chemistry
How many gram of \( K M n O_{4} \) is
contained in 4 litre of \( 0.05 N \) solution.
The \( K M n O_{4} \) is to used as an oxidant in
acid medium \( \left(M_{W}=158\right): \)
A. \( 1.58 g \)
B. \( 15.8 g \)
c. \( 6.32 g \)
D. \( 31.6 g \)
Subject: Chemistry
\( K_{a} \) for \( H C N \) is \( 5 \times 10^{-10} \) at \( 25^{\circ} C . \) For
maintaining a constant \( p H=9 \), the volume of \( 5 M K C N \) solution required
to be added to \( 10 \mathrm{ml} \) of \( 2 M H C N \)
solution is:
\( \left[\text { Given } \log _{10} 5=0.69: \) antilog \right.
\( (-0.3010)=0.5] \)
A. \( 4 m l \)
B. 2 ml
c. \( 7.95 \mathrm{ml} \)
D. \( 9.3 \mathrm{ml} \)
Subject: Chemistry
Which of the following molecules
possess same shape as \( \boldsymbol{H}_{3} \boldsymbol{O}^{+} \) ? This question has multiple correct options
\( \mathbf{A} \cdot N H_{4}^{+} \)
в. \( N H_{3} \)
\( \mathrm{c} . P H_{3} \)
D. \( C H_{4} \)
Subject: Physics
The car \( A \) of mass \( 1500 k g \) travelling at
\( 40 m / s \) collides with another car \( ^{\prime} B^{\prime} \) of
mass \( 1250 k g \) travelling at \( 25 m / s \) in the same direction. After collision the
velocity of car ' \( A^{\prime} \) becomes \( 30 m / s \)
calculate the velocity of car \( ^{\prime} B^{\prime} \) after the
collision.
Subject: Chemistry
The equilibrium constants for the
reactions are:
\[
\begin{array}{l}
\boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \stackrel{\boldsymbol{K}_{1}}{\rightleftharpoons} \boldsymbol{H}^{+}+\boldsymbol{H}_{2} \boldsymbol{P} \boldsymbol{O}_{4}^{-} ; \boldsymbol{K}_{\mathbf{1}} \\
\boldsymbol{H}_{2} \boldsymbol{P} \boldsymbol{O}_{4}^{-} \frac{\boldsymbol{K}_{2}}{\rightleftharpoons} \boldsymbol{H}^{+}+\boldsymbol{H} \boldsymbol{P} \boldsymbol{O}_{4}^{2-} ; \boldsymbol{K}_{2} \\
\boldsymbol{H} \boldsymbol{P} \boldsymbol{O}_{4}^{2-} \stackrel{\boldsymbol{K}_{3}}{\rightleftharpoons} \boldsymbol{H}^{+}+\boldsymbol{P} \boldsymbol{O}_{4}^{3-} ; \boldsymbol{K}_{3}
\end{array}
\]
The equilibrium constant for
\[
\boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \rightleftharpoons \mathbf{3} \boldsymbol{H}^{+}+\boldsymbol{P} \boldsymbol{O}_{4}^{3-} \text { will be: }
\]
\( A \)
\[
\frac{K_{1}}{K_{2} \times K_{3}}
\]
В. \( K_{1} \times K_{2} \times K_{3} \)
\( c \)
\[
\frac{K_{2}}{K_{1} \times K_{3}}
\]
D. \( K_{1}+K_{2}+K_{3} \)
Subject: Chemistry
When \( S O_{2} \) is passed through acidified
\( K_{2} C r_{2} O_{7} \) solution :
A. the solution turned blue
B. the solution is decolourised
\( \mathrm{c} \cdot \mathrm{SO}_{2} \) is reduced
D. green \( \mathrm{Cr}_{2}\left(\mathrm{SO}_{4}\right)_{3} \) is formed
Subject: Physics
Two blocks of masses \( 10 \mathrm{kg} \) and \( 4 \mathrm{kg} \) and are connected by a spring of negligible mass and placed on a
frictionless horizontal surface. An
impulse gives a velocity of \( 14 \mathrm{m} / \mathrm{s} \) to the heavier block in the direction of the
lighter block. The velocity of the centre of mass is
Subject: Maths
The area bounded by \( y=f(x), x-a x i s \)
and the line \( y=1, \) where \( f(x)=1+ \) \( \frac{1}{x} \int_{1}^{x} f(t) d t \) is
A \( \cdot 2(e+1) \)
B \( \cdot\left(1-\frac{1}{e}\right) \)
c. \( 2(e-1) \)
D. None of these
Subject: Maths
Determine the order and degree(if defined) of the following differentia
equation. \( \left(\frac{\boldsymbol{d} \boldsymbol{s}}{\boldsymbol{d} \boldsymbol{t}}\right)^{\boldsymbol{4}}+\boldsymbol{3} \boldsymbol{s} \frac{\boldsymbol{d}^{2} \boldsymbol{s}}{\boldsymbol{d} \boldsymbol{t}^{2}}=\mathbf{0} \)
Subject: Maths
Which of the following is true for a
plane?
This question has multiple correct options
A. A locus is called a plane if the line joining any two arbitrary points on the locus is also a part of the locus.
B. Value of \( y \) in a \( z x \) plane is non-zero.
C. Value of \( z \) in a \( x y \) plane is zero.
D. None of the above
Subject: Maths
At point \( x=1, \) the function \( f(x)= \) \( \left\{\begin{array}{ll}x^{3}-1 ; & 1<x<\infty \\ x-1 ; & -\infty<x \leq 1\end{array}\right. \)
A. continuous and differentiable
B. continuous but not differentiable
c. discontinuous and differentiable
D. discontinuous and not differentiable
Subject: Chemistry
Among the following, the strongest base
is:
A \( \cdot C_{6} H_{5} N H_{2} \)
в. \( p-N O_{2} C_{6} H_{4} N H_{2} \)
\( \mathbf{c} \cdot m-N O_{2} C_{6} H_{4} N H_{2} \)
D. \( C_{6} H_{5} C H_{2} N H_{2} \)
Subject: Chemistry
What is(are) true regarding free radical
iodination of the alkane?
This question has multiple correct options
A. It occur very rapidly because of very small value of bond energy of \( I_{2} \)
B. Direct iodination of alkane with \( I_{2} \) in presence of light is impractical
c. lodination of alkane can be achieved successfully using an oxidizing agent catalyst
D. Presence of some \( H C I \) active the free radical
iodination
Subject: Physics
A student says that he had applied a force \( F=k \sqrt{x} \) on a particle moved in simple harmonic motion. He refuses to
tell whether \( k \) is a constant or not.
Assume that he has worked only with
positive \( x \) and no other force acted on
the particle.
A . As \( x \) increases \( k \) increases
B. AS \( x \) increases \( k \) decreases
C. As \( x \) increases \( k \) remains constant
D. The motion cannot be simple harmonic.
Subject: Physics
A rod of mass \( M \) and length \( L \) is hinged
at its one end and carries a particle of
mass \( m \) at its lower end. A spring of
force constant \( k_{1} \) is installed at
distance \( a \) from the hinge and another
of force constant, \( k_{2} \) at a distance \( b \) as
shown in the figure. The whole
arrangement rests on a smooth
horizontal table top. Find the frequency
of vibration
Subject: Maths
Rational numbers on the number line
represented by \( \boldsymbol{A}, \boldsymbol{E} \) and \( \boldsymbol{H} \)
\( \operatorname{are} \boldsymbol{A}=\frac{\mathbf{1}}{\mathbf{1 0}}, \boldsymbol{E}=\frac{\mathbf{5}}{\mathbf{1 0}}, \boldsymbol{H}=\frac{\mathbf{8}}{\mathbf{1 0}} . \) Are the
values correct?
A. Yes
B. No
c. cannot be determined
D. None
Subject: Chemistry
At \( 300 \mathrm{K} \) and 1 atmospheric pressure, 10
mL of a hydrocarbon required 55 mL of
\( O_{2} \) for complete combustion and \( 40 \mathrm{mL} \)
of \( C O_{2} \) is formed. The formula of the
hydrocarbon is:
A \( \cdot C_{4} H_{8} \)
в. \( C_{4} H_{7} \) С \( l \)
\( \mathbf{c} \cdot C_{4} H_{10} \)
D. \( C_{4} H_{6} \)
Subject: Chemistry
A sigma bond may be formed by the
overlap of 2 atomic orbitals of atoms \( \boldsymbol{A} \)
and \( B \). If the bond is formed along the
\( x- \) axis, which of the following overlaps
is acceptable?
\( \mathbf{A} \cdot s \) orbital of \( A \) and \( p_{z} \) orbital of \( B \)
B. \( p_{x} \) orbital of \( A \) and \( p_{y} \) orbital of \( B \)
C . \( p_{z} \) orbital of \( A \) and \( p_{x} \) orbital of \( B \)
D. \( p_{x} \) orbital of \( A \) and \( s \) orbital of \( B \)
Subject: Physics
A block of weight \( 100 \mathrm{N} \) is suspended by copper and steel wires of same cross
sectional area \( 0.5 \mathrm{cm}^{2} \) and, length \( \sqrt{3} m \)
and \( 1 m, \) respectively. Their other ends
are fixed on a ceiling as shown in figure. The angles subtended by copper and
steel wires with ceiling are \( 30^{\circ} \) and \( 60^{\circ} \) respectively. If elongation in copper wire
is \( \left(\Delta l_{C}\right) \) and elongation in steel wire is
\( \left(\Delta l_{S}\right), \) then the ratio \( \frac{\Delta l_{C}}{\Delta l_{S}} \) is
(Young's modulus for copper and steel
\( \operatorname{are} 1 \times 10^{11} N / m^{2} \) and \( 2 \times 10^{11} N / m^{2} \)
respectively)
Subject: Maths
BD is one of the diagonals of a quadrilateral ABCD.AM and CN are the perpendiculars from \( A \) and \( C \) respectively, on BD. Show that \( \boldsymbol{a r}(\boldsymbol{q u a d} . \boldsymbol{A B C D})=\frac{1}{2} \boldsymbol{B D} \cdot(\boldsymbol{A M}+ \)
\( \boldsymbol{C} \boldsymbol{N}) \)
Subject: Maths
\( \boldsymbol{n} \stackrel{L}{\rightarrow} \infty\left[\frac{1}{\boldsymbol{n}}+\frac{\boldsymbol{n}^{2}}{(\boldsymbol{n}+1)^{3}}+\frac{\boldsymbol{n}^{2}}{(\boldsymbol{n}+2)^{3}}+\right. \)
\( \left.\ldots+\frac{\mathbf{1}}{\mathbf{8 n}}\right]= \)
A. 2/5
B. 3/5
\( c \cdot 3 / 8 \)
D. \( 11 / 7 \)
Subject: Maths
The circumference and area of a circle
of diameter \( 91 \mathrm{cm} \) are, respectively
A \( \cdot 367 \mathrm{cm}, 4986.5 \mathrm{cm}^{2} \)
B . \( 442 \mathrm{cm}, 6166.5 \mathrm{cm}^{2} \)
\( \mathbf{c} .286 \mathrm{cm}, 6506.5 \mathrm{cm}^{2} \)
D. \( 456 \mathrm{cm}, 5466.5 \mathrm{cm}^{2} \)
Subject: Physics
A ball falls from a height of \( 5 m \) and strikes the floor of the lift,which is
moving upwards with a velocity of
1 \( m / s \) what is the velocity of rebound of the ball? Assume the collision to be
elastic.
\( \mathbf{A} \cdot 12 m / s \)
в. \( 9 m / s \)
\( \mathrm{c} \cdot 6 \mathrm{m} / \mathrm{s} \)
D. \( 3 m / s \)
Subject: Physics
A prism \( (\mu=1.5) \) has the refracting
angle of \( 60^{\circ} . \) The deviation of a monochromatic ray incident normally on its one surface will be \( \left(\sin 48^{\circ} 36^{\prime}=\right. \) \( \mathbf{0 . 7 5}) \)
\( \mathbf{A} \cdot 36^{\circ} 72 \)
B . \( 20^{\circ} 30^{\prime} \)
\( c \cdot 18^{\circ} \)
D. \( 22^{\circ} 1^{\prime} \)
Subject: Biology
Assertion
Presence of connective tissue inside the
brain is essential for conduction of
nerve impulse
Reason
Connective tissue hold together the
nerve cells of brain
A. If both the assertion and the reson are true and the reason is correct explanation of the assertion.
B. If both the assertion and the reson are true but the reason is not correct explanation of the assertion
c. If the assertion is true but the reason is false
D. If both the assertion and reason are false
Subject: Physics
\( \ln \) a series \( L-C-R \) circuit, current in
the circuit is \( 11 A \) when the applied voltage is \( 220 V . \) Voltage across the
capacitor is \( 200 V . \) If value of resistor
\( 20 \Omega, \) then the voltage across the unknown inductor is
A. zero
в. \( 200 \mathrm{V} \)
\( c .20 V \)
D. None of these
Subject: Chemistry
Consider the following statements:
(a) All hydrocarbons show phenomena of isomerism.
(b) The members of a homologous series have similar chemical and
physical properties.
(c) Cyclic hydrocarbons are saturated or unsaturated organic compounds that contain ring of carbon atoms.
(d) Synthetic detergents are sodium or potassium salts of long chain carboxylic acids. Which of the above statement(s) is/are
correct?
A. only (c)
B. only (d)
\( c \cdot(a),(b) \) and \( (c) \)
D. \( (a),(c) \) and \( (d) \)
Subject: Physics
If there were only one type of charge in
the universe, then
\( \mathbf{A} \cdot \oint_{s} \vec{E} \cdot d \vec{s} \neq 0 \) on any surface
B \( \cdot \oint_{s} \vec{E} \cdot d \vec{s}=0 \) if the charge is outside the surface
C \( \cdot \oint_{s} \vec{E} \cdot d \vec{s}=\frac{q}{\varepsilon_{0}} \) if charges of magnitude \( q \) were inside the surface
D. both (b) and (c) are correct
Subject: Physics
for two materials \( P \) and \( Q \), a student by
mistake puts strain on the y-axis and
stress on the \( x \) -axis as shown in the
figure. Then the correct statement(s) is
(are)
This question has multiple correct options
A. P has more tensile strength than \( Q \)
B. P is more ductile than \( Q \)
\( c . \) P is more brittle than \( Q \)
Deng's modulus of than that of
Subject: Biology
Which of the following are represented by \( P, Q, R \) and \( S \) in the given figure?
\begin{tabular}{|c|c|c|c|}
\hline \( \mathbf{P} \) & \( \mathbf{Q} \) & \( \mathbf{R} \) & \( \mathbf{S} \) \\
\hline & & & \\
& & & \\
& & & \\
& & & \\
& & & \\
\hline
\end{tabular}
A. \( P \) - Diatoms, \( Q \) - Chlamydomonas, R - Spirogyra, \( S \) Volvox
B. P- -Volvox, Q - Chlamydomonas
R - Spirogyra, S Diatoms
c. P- -Volvox, Q - Diatoms, R - Spirogyra, SChlamydomonas
D. P- -Volvox, Q - Chlamydomonas
R - Spirogyra, S Euglena
Subject: Chemistry
A mixture of \( C S_{2} \) vapour and nitrogen monoxide, \( N O \), gives a vivid blue flame
when ignited. A yellow solid is left afterwards. Write the equation.
A \( \cdot 2 N O(g)+C S_{2} \rightarrow \underset{\text {yellowssild}}{2 S(s)}+N_{2}(g)+C O_{2}(g) \)
B. \( 2 N O(g)+C S_{2} \rightarrow \underset{\text { yellowsoild }}{2 S(s)}+N_{2} O(g)+C O(g) \)
c. \( 2 N O(g)+C S_{2} \rightarrow \underset{\text { yellowsoid }}{2 S O(s)}+N_{2}(g)+C O(g) \)
D. \( 2 N O(g)+C S_{2} \rightarrow \underset{\text { yellowsoild }}{2 S(s)}+N_{2} O_{2}(g)+C(g) \)
Subject: Maths
Let \( \mathbf{f}: \mathbf{R} \rightarrow \mathbf{R} \) be any function. Define
\( \mathbf{g}: \mathbf{R} \rightarrow \mathbf{R} \) by \( \boldsymbol{g}(\boldsymbol{x})=|\boldsymbol{f}(\boldsymbol{x})| \) for all \( \boldsymbol{x} \)
Then \( g \) is
A. \( g \) may be bounded even if \( f \) is unbounded
B. one-one if fis one
c. continuous if \( f \) is continuous
D. differentiable if f is differentiable
Subject: Physics
The time dependence of the position of a particle of mass \( m=2 \) is given by \( \vec{r}(t)=2 t \hat{i}-3 t^{2} \hat{j} . \) Its angular
momentum, with respect to the origin at time \( t=2 \) is :
\( \mathbf{A} \cdot 36 \hat{k} \)
B . \( -34(\hat{k}-\hat{i}) \)
c. \( 48(\hat{i}+\hat{j}) \)
D. \( -48 \hat{k} \)
Subject: Maths
The equation, \( \left[\begin{array}{ccc}\mathbf{1} & \boldsymbol{x} & \boldsymbol{y}\end{array}\right]\left[\begin{array}{ccc}\mathbf{1} & \boldsymbol{3} & \mathbf{1} \\ \mathbf{0} & \boldsymbol{2} & -\mathbf{1} \\ \mathbf{0} & \mathbf{0} & \mathbf{1}\end{array}\right]\left[\begin{array}{l}\mathbf{1} \\ \boldsymbol{x} \\ \boldsymbol{y}\end{array}\right]=[\mathbf{0}] \) has
for
(i) \( y=0 \)
(p) rational
roots
(ii) \( y=-1 \)
(q) irrational
roots
(r) integral roots
A \( . \) (i) \( (p) \) (ii) \( (r) \)
B. (i) (q) (ii) (p)
\( c \cdot(i)(p)(\text { ii) }(q) \)
D. (i) (r) (ii) (p)