AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
When a nucleus with atomic number \( Z \)
and mass number \( A \) undergoes a
radioactive decay process
This question has multiple correct options
A. both \( Z \) and \( A \) will decrease, if the process is \( \alpha^{-} \) decay
B. \( Z \) will decrease but \( A \) will not change, if the process is \( \beta+ \) decay
C \( . Z \) will increase but \( A \) will not change, if the process is \( \beta- \) decay
D. \( Z \) and \( A \) will remain unchanged, if the process is \( \gamma \) decay
Subject: Maths
Let \( 0<\alpha<\frac{\pi}{2} \) be a fixed angle. If \( P= \)
\( (\cos \theta, \sin \theta) \) and \( Q=(\cos (\alpha- \)
\( \boldsymbol{\theta}), \sin (\boldsymbol{\alpha}-\boldsymbol{\theta})) \) then \( \boldsymbol{Q} \) is obtained from
\( P \) by
A. clockwise rotation around the origin through an angle
B. anticlockwise rotation around the origin through an angle \( \alpha \)
c. reflection in the line through origin with slope \( \tan \alpha \)
D. reflection in the line through the origin with slope \( \tan (\alpha / 2) \)
Subject: Physics
The figure shows a bar magnet coil.
Consider four situations.
(I) Moving the magnet away from the
coil.
(II) Moving the coil towards the magnet.
(III) Rotating the coil about the vertical
diameter
(IV) Rotating the coil about its axis.
An emf in the coil will be generated for the following situations.
\( A \cdot(1) \) and (11) only
B. (I), (II) and (IV) only
C. (I), (II) and (III) only
D. (I), (II), (III) and (IV) only
Subject: Physics
An air conditioner is rated
\( 240 V, 1.5 k W . \) The air conditioner is
switched on 8 hrs each day. What is
electrical energy consumed in 30 days?
\( \mathbf{A} \cdot 2.88 k W h \)
в. \( 360 k W h \)
c. \( 120 k W h \)
D. \( 240 k W h \)
Subject: Physics
For a given gas, which of the following relationships is correct at a given temp?
\( \mathbf{A} \cdot u_{r m s}>u_{a v}>u_{m p} \)
B . \( u_{r m s}<u_{a v}<u_{m p} \)
c. \( u_{r m s}>u_{a v}<u_{m p} \)
D. \( u_{r m s}<u_{a v}>u_{m p} \)
Subject: Chemistry
Which is the correct expression in the
formation of \( \mathrm{NaCl} \) ?
\( \mathbf{A} \cdot \Delta H_{f}=\Delta H_{s u b}+E_{i}+0.5 E_{b o n d} \) dissociation \( +E_{e a}+ \)
\( U_{\text {lattice enthalpy}} \)
\( \mathbf{B} \cdot \Delta H_{f}=\Delta H_{s u b}-E_{i}+0.5 E_{b o n d} d i s s o c i a t i o n+E_{E A}+ \)
\( U_{\text {lattice enthalpy}} \)
\( \mathbf{C} \cdot \Delta H_{f}=\Delta H_{s u b}+E_{i}-0.5 E_{b o n d} d i s s o c i a t i o n+E_{E A}+ \)
\( U_{\text {lattice enthalpy}} \)
\( \mathbf{D} \cdot \Delta H_{f}=\Delta H_{s u b}+E_{i}+0.5 E_{b o n d} d i s s o c i a t i o n+E_{E A}- \)
\( U_{\text {lattice enthalpy}} \)
Subject: Maths
The intercept on the line \( y=x \) by the
\( \operatorname{circle} x^{2}+y^{2}-2 x=0 \) is \( A B \)
Equation of the circle with \( A B \) as a
diameter is
A \( \cdot x^{2}+y^{2}+x+y=0 \)
B . \( x^{2}+y^{2}-x-y=0 \)
c. \( x^{2}+y^{2}+x-y=0 \)
D. None of these
Subject: Chemistry
Valence electrons in the element \( A \) are 3
and that in element \( B \) are \( 6 . \) Most
probable compound formed from \( A \) and
\( B \) is:
A \( . A_{2} B \)
в. \( A B_{2} \)
\( \mathbf{c} \cdot A_{6} B_{3} \)
D. \( A_{2} B_{3} \)
Subject: Chemistry
Consider the graph Identify correct option:
A \( \cdot \Delta U_{a}=\Delta_{b}, Q_{b}>Q_{a} \)
В . \( \Delta_{a}>\Delta U_{b}, Q_{a}=Q_{b} \)
C \( \cdot \Delta U_{a}=\Delta U_{b}, Q_{a}<Q_{b} \)
D. \( \Delta U_{a}=\Delta U_{b}, Q_{a}=Q_{b} \)
Subject: Chemistry
Which gas sample contains the fewest molecules?
A \( \cdot 1.00 d m^{3} \) of carbon dioxide at \( 27^{\circ} C \) and \( 2.0 k P a \)
B. \( 1.00 d m^{3} \) of hydrogen at \( 100^{\circ} \mathrm{C} \) and \( 2.0 \mathrm{kPa} \)
C \( \cdot 1.00 d m^{3} \) of nitrogen at \( 300^{\circ} \mathrm{C} \) and \( 4.0 k P a \)
D. \( 1.00 d m^{3} \) of oxygen at \( 250^{\circ} \mathrm{C} \) and \( 3.0 \mathrm{kPa} \)
Subject: Maths
\[
\begin{array}{rlr}
\text { If } \boldsymbol{f}(\boldsymbol{x}) & =\frac{\boldsymbol{x}^{2}-\mathbf{9}}{\boldsymbol{x}-\mathbf{3}}+\boldsymbol{\alpha}, \text { for } \boldsymbol{x}>\mathbf{3} \\
& =\mathbf{5}, & \text { for } \boldsymbol{x}=\mathbf{3} \\
& =\mathbf{2} \boldsymbol{x}^{2}+\mathbf{3} \boldsymbol{x}+\boldsymbol{\beta}, & \text { for } \boldsymbol{x}<\mathbf{3}
\end{array}
\]
is continuous at \( x=3, \) find \( \alpha \) and \( \beta \)
Subject: Maths
If \( y^{2}=4 a x, \) then \( \frac{\left(1+y_{1}^{2}\right)^{3 / 2}}{y_{2}} \) at \( x=a \)
is
A. \( -4 \sqrt{2} a \)
an \( a \sqrt{2} \) an \( \sqrt{2} \)
B. \( 4 \sqrt{2} a \)
\( c \cdot \frac{4 \sqrt{2}}{a} \)
D. \( -4 a \)
Subject: Physics
An \( L-C \) circuit consists of an
inductor of \( L=0.0900 H \) and a
capacitor of \( C=4 \times 10^{-4} F . \) The initial
charge on the capacitor is \( 5.00 \mu C \) and the initial current in the inductor is
zero. When the current in the inductor
has half its maximum value, what is
the energy stored in the inductor?
A \( .7 .8 \times 10^{-9} J \)
B . \( 9.8 \times 10^{7} J \)
c. \( 7.8 \times 10^{7} J \)
D. \( 9.8 \times 10^{-7} J \)
Subject: Chemistry
Assertion
Statement \( -1: P C l_{3} \) on hydrolysis
\( \operatorname{gives} H_{3} P O_{3} \)
Reason
Statement \( -2: H_{3} P O_{3} \) exists in two
tautomeric forms:
A. Statement - 1 is true, Statement - 2 is true and Statement - 2 is correct explanation for Statement -
1
B. Statement -1 is true, Statement - 2 is true and Statement - 2 is NOT the correct explanation for Statement - 1
c. statement -1 is true, statement -2 is false
D. Statement - 1 is false, Statement - 2 is true
Subject: Maths
\( \operatorname{Let} F(x)=f(x) g(x) h(x) \) for all real \( x \)
where \( f(x), g(x) \) and \( h(x) \) are differentiable functions. At some point
\( \boldsymbol{x}_{0}, \boldsymbol{F}^{\prime}\left(\boldsymbol{x}_{0}\right)=\mathbf{2 1} \boldsymbol{F}\left(\boldsymbol{x}_{0}\right), \boldsymbol{f}^{\prime}\left(\boldsymbol{x}_{0}\right)= \)
\( 4 f\left(x_{0}\right), g^{\prime}\left(x_{0}\right)=-7 g\left(x_{0}\right) \) and
\( \boldsymbol{h}^{\prime}\left(\boldsymbol{x}_{0}\right)=\boldsymbol{k h}\left(\boldsymbol{x}_{0}\right) . \) Then \( \boldsymbol{k} \) is equal to
Subject: Maths
Length of the latus rectum of the parabola \( 25\left[(x-2)^{2}+(y-3)^{2}\right]= \)
\( (3 x-4 y+7)^{2} \) is :
\( A \cdot 4 \)
B. 2
\( c \cdot 1 / 5 \)
D. 2/5
Subject: Physics
Two moles of an ideal gas at \( 300 K \) were cooled at constant volume so that
the pressure is reduced to half the
initial value. Then as a result of heating at constant pressure, the gas expands till it attains the original temperature
Find the total heat absorbed by the gas, if \( R \) is the gas constant.
A. \( 150 R \) \( J \)
в. \( 300 R \) Л
c. \( 75 R J \)
D. \( 100 R J \)
Subject: Physics
The wavelength of a spectral line
coming from a star is changed by the motion of the star from 6000 A to 6001
A. What is the velocity of the star with respect to earth? (The velocity of light is \( 3 \times 10^{8} \mathrm{m} / \mathrm{sec} \)
A \( \cdot 5 \times 10^{4} \mathrm{m} / \mathrm{sec} \) receding
B. \( 5 \times 10^{4} \mathrm{m} / \mathrm{sec} \) approaching
c. \( 3 \times 10^{4} \mathrm{m} / \) sec receding
D. 3 \( \times 10^{4} \mathrm{m} / \) sec approaching
Subject: Physics
The resistance of the bulb filament is
\( 100 \Omega \) at a temperature of \( 100^{\circ} \mathrm{C} \). If its temperature co-efficient of resistance
be 0.005 per \( ^{\circ} C, \) its resistance will
become \( 200 \Omega \) at a temperature
\( \mathbf{A} \cdot 300^{\circ} \mathrm{C} \)
B . \( 400^{\circ} \mathrm{C} \)
c. \( 500^{\circ} \mathrm{C} \)
D. \( 200^{\circ} \mathrm{C} \)
Subject: Chemistry
A student mixes \( 10.0 m L \) of
\( 0.10 M A g N O_{3} \) with excess copper metal. The reaction should produce 0.107 gram of silver; however, the student obtains a mass of 150 grams of silver. Plausible explanations for this yield \( >100 \% \) might include :
I. the student did not subtract the mass of the filter paper before recording
results.
II. the student did not thoroughly dry the sample before massing.
III. the copper metal did not react
completely.
A . I only
B. II only
c. I and II only
D. I and III only
E. I, II, and III
Subject: Chemistry
Two liquids \( A \) and \( B \) form an ideal solution at temperature T. When the
total vapour pressure above the solution is 400 torr, the mole fraction of
\( A \) in the vapour phase is 0.40 and in the liquid phase \( 0.75 . \) What are the vapour
pressure of pure \( A \) and pure \( B \) at
temperature T?
Subject: Physics
A boy of mass \( M \) stands on a platform
of radius \( R \) capable to rotate freely
about its axis. The moment of inertia of
the platform is \( I . \) The system is at rest.
The friend of the boy throws a ball of mass \( m \) with a velocity \( v \) horizontally. The boy on the platform catches it. Find the angular velocity of the system in the
process.
A \( \cdot \frac{m v R}{(M+m) R^{2}} \)
в. \( \frac{m v}{I+M R^{2}} \)
c. \( \frac{m v R}{I+m R^{2}} \)
D. \( \frac{m v R}{I+(M+m) R^{2}} \)
Subject: Physics
If \( 5 \% \) of the energy supplied to a bulb is radiated as visible light, the number of visible quanta emitted per second by a
100W bullb, assuming the wavelength
of visible light to be \( 5.6 \times 10^{-5} \mathrm{cm}, \) is
A. \( 1.4 \times 10^{19} \)
B . \( 1.4 \times 10^{20} \)
\( \mathrm{c} \cdot 2 \times 10^{19} \)
D. \( 2 \times 10^{20} \)
Subject: Physics
The position \( x \) of a particle varies with time \( (t) \) as \( x=a t^{2}-b t^{3} . \) The
acceleration of the particle will be equal
to zero, at time
A \( \cdot \frac{2 a}{3 b} \)
B. \( \frac{a}{b} \)
c. \( \frac{a}{3 b} \)
D. \( \frac{2 a}{b} \)
Subject: Physics
Electron accelerated by potential \( V \) are
diffracted from a crystal. If \( \boldsymbol{d}=\mathbf{1} \boldsymbol{A} \) and
\( \boldsymbol{i}=\mathbf{3 0}^{\circ} . \boldsymbol{V} \) should be about \( \boldsymbol{h}=\mathbf{6 . 6} \times \)
\( \mathbf{1 0}^{-\mathbf{2 4}} \mathbf{J s m}_{e}=\mathbf{9 . 1} \times \mathbf{1 0}^{-\mathbf{3 3} \mathbf{k g} . \boldsymbol{e}}= \)
\( \mathbf{1} . \mathbf{6} \times \mathbf{1 0}^{-\mathbf{1 9}} \mathbf{C} \)
A . \( 2000 V \)
в. \( 50 V \)
\( \mathbf{c} .500 V \)
D. \( 1000 V \)
Subject: Maths
The value of \( \sec ^{-1}\left(\sec \frac{8 \pi}{5}\right) \) is
A \( \cdot \frac{2 \pi}{5} \)
в. \( \frac{3 \pi}{5} \)
\( c \cdot \frac{8 \pi}{5} \)
D. none of these
Subject: Maths
If \( 2 x=t+\sqrt{t^{2}+4} \) and \( 3 y=t- \)
\( \sqrt{t^{2}+4} \) then the value of \( y \) when \( x=\frac{2}{3} \)
is
A . -2
B. 1
\( c \cdot-1 \)
D.
Subject: Chemistry
\( A t 817^{\circ} C, K_{p} \) is 10 atm for the reaction
between pure \( C O_{2} \) and excess hot graphite to form \( 2 \mathrm{CO}(\mathrm{g}) \) Then at what total pressure will the gas
mixture analyze \( 6 \%, C O_{2} \) by volume?
A \( \cdot P_{\text {Total }}=0.34 a t m \)
B. \( P_{\text {Total}}=0.68 a t m \)
C \( . P_{\text {Total}}=1.3 a t m \)
D. None of these
Subject: Maths
Add:
(i) \( 3 m n,-5 m n, 8 m n,-4 m n \)
(ii) \( \boldsymbol{t}-\mathbf{8} \boldsymbol{t} \boldsymbol{z}, \boldsymbol{3} \boldsymbol{t} \boldsymbol{z}, \boldsymbol{-} \boldsymbol{z}, \boldsymbol{z}-\boldsymbol{t} \)
\( (\text { iii) }-7 m n,+5,12 m n+2,9 m n- \)
\( \mathbf{8}, \mathbf{2 m n},-\mathbf{3} \)
\( (i v) a+b-3, b-a+3, a-b+3 \)
(v) \( 14 x+10 y-12 x y-13,18-7 x \)
\( \mathbf{1 0} \boldsymbol{y}+\mathbf{8} \boldsymbol{x} \boldsymbol{y}, \boldsymbol{4} \boldsymbol{x} \boldsymbol{y} \)
\( (v i) 5 m-7 n, 3 n-4 m+2,2 m- \)
\( 3 m n-5 \)
\( (v i i) 4 x^{2} y,-3 x y^{2},-5 x y^{2}, 5 x^{2} y \)
Subject: Maths
The principal argument of
\( \sqrt{2}\left[\cos \frac{5 \pi}{3}+i \sin \frac{5 \pi}{3}\right] \) is
A \( \cdot \frac{5 \pi}{3} \)
B. \( \frac{\pi}{3} \)
\( c \cdot-\frac{\pi}{3} \)
D. \( -\frac{\pi}{2} \)
Subject: Maths
If \( x \) is real, then find the solution of
\( \sqrt{x+1}+\sqrt{x-1}=1 \)
A \( \cdot \frac{5}{4} \)
B. \( \frac{4}{5} \)
\( c \cdot \frac{3}{5} \)
D. No such \( x \) exists
Subject: Maths
Which of the following statements is/are correct for \( 0<\theta<\frac{\pi}{2} ? \)
This question has multiple correct options
A \( \cdot(\cos \theta)^{1 / 2} \leq \cos \frac{\theta}{2} \)
B. \( (\cos \theta)^{3 / 4} \geq \cos \frac{3 \theta}{4} \)
c. \( \cos \frac{5 \theta}{6} \geq(\cos \theta)^{5 / 6} \)
D. \( \cos \frac{7 \theta}{8} \geq(\cos \theta)^{7 / 8} \)
Subject: Physics
How soon will the frame come to the
orientation shown in figure (b) after
collision?
\( ^{A} \cdot \frac{\pi l}{4 v} \)
B. \( \frac{7 \pi l}{8 v} \)
c. \( \frac{\pi l}{v} \)
D. \( \frac{7 \pi l}{4 v} \)
Subject: Physics
If a body loses half of its initial velocity on permenenting \( 2 \mathrm{cm} \) in a wooden block, them how much it penetrate
more before its velocity reduces to one fourth of its initial velocity [Assume retaradation of body in uniform \( ] \)
A. \( 2 \mathrm{cm} \)
B. \( 1 \mathrm{cm} \)
\( c \cdot 0.5 \mathrm{cm} \)
D. \( 4 \mathrm{cm} \)
Subject: Chemistry
If \( c \) is the concentration of \( n \) moles of a
gas at pressure \( P \) and temperature \( T \)
then for the ideal gas reaction. the rate of reaction can be given by :
A \( \cdot-\frac{d[A]}{d t} \)
B. \( -\frac{1}{R T} \frac{d P}{d t} \)
c. \( -\frac{1}{\nu} \frac{d n}{d t} \)
D. either of these
Subject: Maths
Given that \( \prod_{n=1}^{n} \cos \frac{x}{2^{n}}=\frac{\sin x}{2^{n} \sin \left(\frac{x}{2^{n}}\right)} \)
and \( \boldsymbol{f}(\boldsymbol{x})= \)
\[
\left\{\begin{array}{c}
\lim _{n \rightarrow \infty} \sum_{n=1}^{n} \frac{1}{2^{n}} \tan \left(\frac{x}{2^{n}}\right), \quad x \in(0, \\
\frac{2}{\pi}
\end{array}\right.
\]
Then which one of the following is true?
A. \( f(x) \) has non-removable discontinuity of finite type at
\[
x=\frac{\pi}{2}
\]
B.
\( f(x) \) has removable discontinuity at \( x=\frac{\pi}{2} \)
C \( \quad f(x) \) is continuous at \( x=\frac{\pi}{2} \)
D. \( f(x) \) has non-removable discontinuity of infinite type at \( x=\frac{\pi}{2} \)
Subject: Maths
Equation of tangent at that point of the curve \( \boldsymbol{y}=\mathbf{1}-\boldsymbol{e}^{\frac{x}{2}}, \) where it meets \( \mathbf{y} \) -axis
\( \mathbf{A} \cdot x+2 y=0 \)
в. \( 2 x+y=0 \)
c. \( x-y=2 \)
D. None of these
Subject: Maths
The angle of elevation of the top of a
tower from a point \( 20 m \) away from its
base is \( 60^{\circ} . \) The height of the tower is-
\( A \cdot 2 \sqrt{3} m \)
В. \( -20 \sqrt{3} \mathrm{m} \)
c. \( \sqrt{3} m \)
D. \( 20 \sqrt{3} \) m
Subject: Maths
Let \( \left|\begin{array}{lll}\boldsymbol{x} & \boldsymbol{2} & \boldsymbol{x} \\ \boldsymbol{x}^{2} & \boldsymbol{x} & \boldsymbol{6} \\ \boldsymbol{x} & \boldsymbol{x} & \boldsymbol{6}\end{array}\right|=\boldsymbol{a} \boldsymbol{x}^{4}+\boldsymbol{b} \boldsymbol{x}^{3}+\boldsymbol{c} \boldsymbol{x}^{2}+ \)
\( d x+e, \) then the value of \( 5 a+4 b+3 c+ \)
\( 2 d+e \) is
equal to
A.
B. 16
\( c .-16 \)
D. - -
Subject: Maths
Following is the distribution function
\( (x) \) of a discrete \( r . v . x \)
\( F(x) \) \begin{tabular}{l}
0.2 \\
\hline
\end{tabular} 0.37 \( \begin{array}{ll}\text { 0.48 } & \text { 0.62 }\end{array} \)
(i) Find the probability distribution of \( x \)
(ii) Find \( P(x \leq 3),(2<x<5) \)
Subject: Physics
The magnitude of the magnetic field at the centre of the tightly wound 150 turn coil of radius \( 12 \mathrm{cm} \) carrying a current of
\( 2 \mathrm{A} \) is:
A . 18 G
B. 19.7 G
c. \( 15.7 \mathrm{G} \)
D. 17.7 G
Subject: Chemistry
Buna \( -N, \) a synthetic rubber is
copolymer of:
\( \mathbf{A} \cdot H_{2} C=C H-C H=C H_{2} \) and \( H_{5} C_{6}-C H=C H_{2} \)
B \( \cdot H_{2} C=C H-C N \) and \( H_{2} C=C H-C H=C H_{2} \)
\( \mathbf{C} \)
\( H_{2} C=C H-C=C H_{2} \) and \( H_{2} C=C H-C H=C H_{2} \)
D. \( H_{2} C=C N-C N \) and \( H_{2} C=C H-C=C H_{2} \)
Subject: Maths
The area of the smaller part of the circle \( x^{2}+y^{2}=a^{2}, \) cut off by the line \( x=\frac{a}{\sqrt{2}} \)
is given by:
\( ^{\text {A }} \cdot \frac{a^{2}}{2}\left(\frac{\pi}{2}+1\right) \)
в. \( \frac{a^{2}}{2}\left(\frac{\pi}{2}-1\right) \)
c. \( a^{2}\left(\frac{\pi}{2}-1\right) \)
D. None of these
Subject: Chemistry
Why does \( H^{+} \) ion always get
associated with other atoms or
molecules?
A. Ionisation enthalpy of hydrogen resembles that of alkali metals.
B. Its reactivity is similar to halogens
C. It resembles both alkali metals and halogens
D. Loss of an electron from hydrogen atom results in a nucleus of very small size as compared to other atoms or ions. Due to small size it cannot exist free
Subject: Chemistry
Extraction of silver is achieved by initia complexation of the ore (Argentite) with \( X \) followed by reduction with \( Y . X \) and
\( \boldsymbol{Y}, \) respectively, are:
A . \( C N^{-} \) and \( Z n \)
B. \( C N^{-} \) and \( C u \)
c. \( C l^{-} \) and \( Z n \)
D. \( B r^{-} \) and \( Z n \)
Subject: Maths
\( f \sin ^{-1}\left(x-\frac{x^{2}}{2}+\frac{x^{3}}{4}-\dots \dots \dots \infty\right)+ \)
\( \cos ^{-1}\left(x^{2}-\frac{x^{4}}{2}+\frac{x^{6}}{4}-\dots \dots \dots \infty\right)=\frac{\pi}{2} \)
and \( 0<x<\sqrt{2} \) then \( x= \)
\( A \cdot \frac{1}{2} \)
B.
\( c \cdot-\frac{1}{2} \)
D. - -
Subject: Maths
Evaluate: \( \lim _{x \rightarrow 2}\left\{\frac{1}{x-2}-\frac{4}{x^{2}-4}\right\} \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. 4
\( c \cdot \frac{1}{4} \)
D. \( -\frac{1}{4} \)
Subject: Maths
If \( \boldsymbol{A}=\{\boldsymbol{m}, \boldsymbol{a}, \boldsymbol{t}, \boldsymbol{h}, \boldsymbol{e}, \boldsymbol{m}, \boldsymbol{a}, \boldsymbol{t}, \boldsymbol{i}, \boldsymbol{c}, \boldsymbol{s}\}, \boldsymbol{B}= \)
\( \{a, m, t, h, e, i, c, s\}, \) then:
A \( . A=B \)
в. \( A \neq B \)
c. \( A \subset B \)
D. \( B \subset A \)
Subject: Physics
1 unified atomic mass unit (1 \( u \) ) is equal
to the
A \( \cdot 1.66 \times 10^{-25} \mathrm{kg} \)
B . \( 1.66 \times 10^{-27} \mathrm{kg} \)
C \( .1 .66 \times 10^{-29} \mathrm{kg} \)
D. \( 1.66 \times 10^{-31} \mathrm{kg} \)
Subject: Physics
For a given voltage \( V \), if resistance is
changed from \( R \) to \( \left(\frac{R}{n}\right), \) power
consumed changes from \( P \) to:
\( A \cdot n P \)
B. \( \frac{p}{n} \)
\( c \cdot n^{2} p \)
D. \( \frac{P}{n^{2}} \)
Subject: Physics
A wheel is rotating with an angular speed 20 rad \( / \) s. It is stopped to rest by applying constant torque in \( 4 s \). If the moment of inertia of the wheel about is
axis is \( 0.20 k g / m^{2}, \) then the work done
by the torque in two seconds will be :
A . \( 10 J \)
B. \( 20 J \)
c. \( 30 J \)
D. \( 40 J \)
Subject: Chemistry
Balance the following reaction.
\( \boldsymbol{C r}_{2} \boldsymbol{O}_{7}^{2-}+\boldsymbol{C}_{2} \boldsymbol{H}_{4} \boldsymbol{O}+\boldsymbol{H}^{+} \rightarrow \)
\( \boldsymbol{C}_{2} \boldsymbol{H}_{4} \boldsymbol{O}_{2}+\boldsymbol{C} \boldsymbol{r}^{3+} \)
A \( \cdot C r_{2} O_{7}^{2-}+3 C_{2} H_{4} O+8 H^{+} \rightarrow 3 C_{2} H_{4} O_{2}+2 C r^{3+}+ \)
\( 4 H_{2} O \)
B . \( C r_{2} O_{7}^{2-}+C_{2} H_{4} O+8 H^{+} \rightarrow 3 C_{2} H_{4} O_{2}+5 C r^{3+}+H_{2} O \)
C. \( C r_{2} O_{7}^{2-}+4 C_{2} H_{4} O+4 H^{+} \rightarrow C_{2} H_{4} O_{2}+2 C r^{3+}+ \)
\( 4 H_{2} O \)
D. None of these
Subject: Maths
Assertion
Set of any four vectors is always linearly dependent
Reason
If a subset of \( n \) vectors is \( L . D, \) then set
of those \( n \) vectors is linearly dependent
\( \boldsymbol{L} \cdot \boldsymbol{D} \)
A. Both Assertion \& Reason are individually true \& Reason is correct explanation of Assertion
B. Both Assertion \& Reason are individually true but Reason is not the , correct (proper) explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
Subject: Chemistry
The van't Hoff factor for \( 0.1 M \) barium
nitrate is \( 2.74 . \) The percentage of dissociation of barium nitrate is:
A . \( 91.3 \% \)
B. \( 87 \% \)
c. \( 100 \% \)
D. \( 74 \% \)
Subject: Chemistry
\( a c \)
Chlorobenzene
Reaction \( \rightarrow \) Salicylaldehyde. \( X \) and \( Y \)
reactions are respectively:
A. Fries rearrangement and Kolbe-Schmidt
B. Cumene and Reimer-Tiemann
c. Dow and Reimer-Tiemann
D. Dow and Friedal-Craft
Subject: Maths
If 0 is the origin and \( A \) is the point \( (a, b, c), \) then the equation of the plane through \( A \) and at right angles to \( O A \) is
A. \( a(x-a)-b(y-b)-c(z-c)=0 \)
В. \( a(x+a)+b(y+b)+c(z+c)=0 \)
c. \( a(x-a)+b(y-b)+c(z-c)=0 \)
D. None of the above
Subject: Physics
Select correct alternative :
Statement -1: An electric dipole can not
produce zero electric field at a point which is situated at finite distance
from the dipole. Statement -2: Mass of a moving photon is proportional to \( \lambda^{-1} \). Statement -3: Equation of continuity for fluid is based on conservation of
volume.
A. FFF
в. тт
c. тFF
D. गा
Subject: Physics
If the lens is slivered at one side what
will be the new focal length (Given
refractive index of lens \( =n \) and focal
length \( =\boldsymbol{f} \) )?
A \( \cdot f^{\prime}=\frac{f}{2} \)
B. \( f^{\prime}=\frac{f(n)}{4} \)
\( ^{\mathbf{C}} f^{\prime}=\frac{f(n-1)}{2 n-1} \)
D. \( f^{\prime}=\frac{f(n+1)}{(2 n-1)} \)
Subject: Physics
The number of free electrons per \( 10 \mathrm{mm} \)
ordinary copper wire is about \( 2 \times 10^{21} \)
The average drift speed of the electrons is \( 0.25 \mathrm{mm} \) current flowing is:
A. \( 0.8 \mathrm{A} \)
B. 8 A
\( c .80 \mathrm{A} \)
D. 5 A
Subject: Chemistry
The boiling point of \( D_{2} O \) is greater than
\( H_{2} O . \) It is because:
A \( . D_{2} O \) has lower \( K_{w} \) value
B. \( D_{2} O \) has a lower dielectric constant
\( \mathrm{c} \cdot D_{2} O \) is a associated liquid
D. the molecular weight of \( D_{2} O \) is greater than \( H_{2} O \)
Subject: Maths
The domain of \( f(x)=\tan 2 x \) is
\( A \cdot(-\infty, \infty) \)
B . \( R-\left\{(2 n+1) \frac{\pi}{4}, n \in Z\right\} \)
c. \( R-\left\{(n+1) \frac{\pi}{4}, n \in Z\right\} \)
D. \( R-\{n \pi, n \in Z\} \)
Subject: Maths
If \( \sin x+i \cos 2 x, \cos x-i \sin 2 x \) are
conjugate to each other, then \( \mathbf{x}= \)
\( \mathbf{A} \cdot n \pi \)
B. \( (n+1) \frac{\pi}{2} \)
\( c \cdot \phi \)
D. \( (n+1) \pi \)
Subject: Chemistry
Which of the following is sec-butyl alcohol?
A. \( C H_{3} C H_{2} C H_{2} C H_{2} O H \)
в. \( C H_{3} C H(O H) C H_{2} C H_{3} \)
c. \( \left(C H_{3}\right)_{2} C H C H_{2} O H \)
D. \( \left(C H_{3}\right)_{3} C C H_{2} O H \)
Subject: Maths
The area of the region
\( \left\{(x, y): x y \leq 8,1 \leq y \leq x^{2}\right\} \) is
\( \mathbf{A} \cdot 16 \log _{6} 2-6 \)
в. \( 8 \log _{6} 2-\frac{7}{3} \)
\( \mathrm{c} \cdot_{16 \log _{6} 2-\frac{14}{3}} \)
D. \( 8 \log _{6} 2-\frac{14}{3} \)
Subject: Chemistry
At 373 K,a gaseous reaction \( \boldsymbol{A} \rightarrow 2 \boldsymbol{B}+ \)
\( C \) is found to be of first order.Starting
with pure \( A \), the total pressure at the end of 10 min was 176 mm of Hg and after a
long time when A was completely dissociated,it was 270 mm of Hg.The pressure of \( A \) at the end of 10 minutes
was:
A. \( 94 \mathrm{mm} \) of \( \mathrm{Hg} \)
B. 47 mm of Hg
c. \( 43 \mathrm{mm} \) of \( \mathrm{Hg} \)
D. \( 90 \mathrm{mm} \) of \( \mathrm{Hg} \)
Subject: Biology
Passage of air through the respiratory tract during inspiration is
A. Nostril - Nasal cavity - Larynx - Pharynx - Bronchi Trachea - Bronchioles - Alveoli
B. Nostril - Nasal cavity - Pharynx - Larynx - Trachea Bronchi -Bronchioles - Alveoli
C. Nostril - Nasal cavity - Larynx - Pharynx - Trachea Bronchi -Bronchioles - Alveoli
D. Nostril - Nasal cavity - Bronchioles - Bronchi - Larynx Pharynx - Trachea - Alveoli
Subject: Maths
Simplify and express with positive zponents \( \left[\left(\frac{\mathbf{9}}{\mathbf{1 1}}\right)^{-\mathbf{3}} \times\left(\frac{\mathbf{9}}{\mathbf{1 1}}\right)^{-\mathbf{7}}\right] \div \)
\( \left(\frac{9}{11}\right)^{-3} \)
Subject: Maths
\( \sum_{n=0}^{\infty}(-1)^{n} \frac{x^{2 n+1}}{2 n+1} \) is equal to
\( (-1<x<1) \)
A \( \cdot \tan ^{-1} x-x+c \)
B \( \cdot \log (1+x) \)
c. \( \frac{1}{1-x}+\frac{1}{1+x} \)
\( \mathbf{D} \cdot \sin ^{-1} x \)
Subject: Maths
Find the mean of the following frequency distribution:
\( \begin{array}{llll}\text { Class } & \text { 0- } & \text { 6- } & \text { 1 } \\ \text { interval: } & \text { 6 } & \text { 12 } & \text { 1 }\end{array} \) \( 12- \)
18
3
24
Frequency: \( \quad 7 \) 10