AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Certain perfect gas is found to obey
\( P V^{3 / 2}= \)constant during an adiabatic
process. If such a gas at initial temperature \( T \) is adiabatically compressed to half the initial volume,
its final temperature will be
A \( \cdot \sqrt{2} T \)
в. 27
c. \( 2 \sqrt{2} T \)
D. 47
Subject: Physics
A circular conductor is made of a
uniform wire of resistance \( 2 \times \)
\( 10^{-3} \) ohm / meter and the diameter of
this circular conductor is 2 meter. Then
the resistance measured between the
ends of the diameter is (in ohms):
A \( \cdot \pi \times 10^{-3} \)
В. \( 2 \pi \times 10^{-3} \)
c. \( 4 \pi \times 10^{-3} \)
D. \( 4 \times 10^{-3} \)
Subject: Physics
The figure shows three concentric metallic spherical shells. The outermost
shell has charged \( q_{2}, \) the innermost
shell has charged \( q_{1} \), and the middle shell is undercharged. The charge
appearing on the inner surface of the outermost shell is
A \( \cdot(a) q_{1}+q \)
\[
q
\]
B. \( (b) \frac{q}{2} \)
\( c \cdot(c)-q \)
\( D \cdot(d) \) Zero
Subject: Chemistry
Minimum amount of \( A g_{2} C O_{3}(s) \) required to produce sufficient oxygen
for the compelete combusion of \( C_{2} H_{2} \)
which produces \( 11.2 l t r \) of \( C O_{2} \) at S.T.P after combusion is : \( [\mathrm{Ag}=108] \)
\( \boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{C} \boldsymbol{O}_{3}(\boldsymbol{s}) \rightarrow \boldsymbol{2} \boldsymbol{A} \boldsymbol{g}(\boldsymbol{s})+\boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})+ \)
\( \mathbf{1} / \mathbf{2} \mathbf{o}_{\mathbf{2}}(\boldsymbol{g}) \)
\( \boldsymbol{C}_{2} \boldsymbol{H}_{2}+\mathbf{5} / \mathbf{2} \boldsymbol{O}_{2} \rightarrow \boldsymbol{2} \boldsymbol{C} \boldsymbol{O}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \)
A \( .276 g \)
в. \( 345 g \)
\( c .690 g \)
D. \( 1380 g \)
Subject: Physics
Correct form of gravitational law is:
A \( \cdot \vec{F}=-\frac{G m_{1} m_{2}}{r^{2}} \)
В \( \cdot \vec{F}=-\frac{G m_{2} m_{1}}{r^{2}} \)
c. \( \vec{F}=-\frac{G m_{1} m_{2}}{r^{2}} \hat{r} \)
D・ \( \vec{F}=-\frac{G m_{1} m_{2}}{r^{3}} \vec{r} \)
Subject: Maths
The difference between the greatest and
the least values of the function \( f(x)= \) \( \int_{0}^{x}\left(a t^{2}+1+\cos t\right) d t, a>0, x \in[2,3] \)
is:
A \( \cdot \frac{19}{3} a+1+\sin 3-\sin 2 \)
в. \( \frac{18}{3} a+1+2 \sin 3 \)
c. \( \frac{18}{3} a-1+2 \sin 3 \)
D. none of these
Subject: Physics
A germanium specimen is doped with aluminum. The concentration of
acceptor atoms is \( 10^{21} \) atoms \( / m^{3} \). Given that the intrinsic concentration of
electron-hole pairs is \( 10^{19} / m^{3}, \) the concentration of electrons in
the specimen is
A \( \cdot 10^{17} / m^{3} \)
В. \( 10^{15} 5 m^{3} \)
c. \( 10^{4} / m^{3} \)
D. \( 10^{3} / m^{3} \)
Subject: Physics
If \( \boldsymbol{d}=\mathbf{0 . 5 m m}, \boldsymbol{\lambda}=\mathbf{5 0 0 0} \boldsymbol{A} \) and \( \boldsymbol{D}= \)
100 \( c m \), find the value of \( n \) for the
closest second bright ring.
\( A \cdot 888 \)
В. 83
\( c .914 \)
D. 998
Subject: Maths
n right triangle \( A B C, \overline{D E} \)
\( B C, C D=1.5, \) and \( B E=2.0 \)
The sine of angle \( \theta \) is equal to
\( \mathbf{A} \cdot \mathbf{1} \)
2
B. 3 4
\( c \cdot \frac{\sqrt{2}}{2} \)
\( \frac{\sqrt{3}}{2} \)
E . 3
\( F \)
Subject: Maths
\( \boldsymbol{D}(\mathbf{2}, \mathbf{1}, \mathbf{0}), \boldsymbol{E}(\mathbf{2}, \mathbf{0}, \mathbf{0}), \boldsymbol{F}(\mathbf{0}, \mathbf{1}, \boldsymbol{0}) \) are mid
point of the sides \( B C, C A, A B \) of \( \Delta \)
\( A B C \) respectively, The the centroid of \( \Delta \)
\( A B C \) is
A \( \cdot\left(\frac{1}{3}, \frac{1}{3}, \frac{1}{3}\right) \)
B. \( \left(\frac{4}{3}, \frac{2}{3}, 0\right) \)
\( ^{c} \cdot\left(-\frac{1}{3}, \frac{1}{3}, \frac{1}{3}\right) \)
D. \( \left(\frac{2}{3}, \frac{1}{3}, \frac{1}{3}\right) \)
Subject: Maths
Repeated application of integration by parts gives us the reduction formula, if the integrand is dependent on a natural
number \( n \)
If \( \int \frac{\cos ^{m} x}{\sin ^{n} x} d x=\frac{\cos ^{m-1} x}{(m-n) \sin ^{n-1} x}+ \)
\( A \int \frac{\cos ^{m-2} x}{\sin ^{n} x} d x+C, \) then \( A \) is equal
to
A \( \cdot \frac{m}{m+n} \)
в. \( \frac{m-1}{m+n} \)
c. \( \frac{m}{m+n-1} \)
D. \( \frac{m-1}{m-n} \)
Subject: Physics
In the fig the bar is uniform and
weighting \( 500 N \). How large must \( W \) be
f \( T_{1} \) and \( T_{2} \) are to equal?
\( A \cdot 500 N \)
3. \( 300 N \)
\( c .750 N \)
D. \( 1500 N \)
Subject: Chemistry
\( \mathbf{n}\left[\boldsymbol{A} \boldsymbol{g}\left(\boldsymbol{C} \boldsymbol{N}_{2}\right)\right]^{-}, \) the number of \( \boldsymbol{\pi} \) bonds
is :
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 6
Subject: Physics
If mass \( \mathrm{M} \) is split into two parts, \( \mathrm{m} \) and \( (M-m) \) which are then separated by a
certain distance. What ratio of \( \mathrm{m} / \mathrm{M} \)
maximizes the gravitational force between the two parts.
A . \( 1 / 3 \)
B. \( 1 / 2 \)
c. \( 1 / 4 \)
D. \( 1 / 5 \)
Subject: Physics
The phenomenon of nuclear fission can be carried out both in a controlled and
in an uncontrolled way. Out of the following, the correct statements vis-
avis these phenomena are
This question has multiple correct options
A. the fission energy released per reaction is much more than conventional nuclear reactions and one of the products of the reaction is that very particle which initiates the reaction
B. it is the "surface to volume" ratio of the sample of nuclear fuel used which determines whether or not the reaction would sustain itself as a "chain reaction"
c. the "control rods" in a nuclear reactor must be made of material that absorbs neutrons effectively
D. the energy released per fission as well as energy released per unit mass of the fuel in nuclear fission are both greater than the corresponding quantities for nuclear fusion
Subject: Physics
The elongation of a steel wire stretched
by a force is 'e'. If a wire of the same material of double the length and half the diameter is subjected to double the force, its elongation will be
A. \( 16 e \)
B . \( 4 e \)
c. \( \left(\frac{1}{4}\right) e \)
D. \( \left(\frac{1}{16}\right) \)
Subject: Chemistry
Assertion
STATEMENT-1: m-Chlorobenzoicacid is a
stronger acid than p-chlorobenzoic acid
Reason

STATEMENT-1: In m-chlorobenzoicacid,
both - I effect and +M effect of \( C l \)
operate, but in p-isomer only +M effect
of \( C l \) operates.
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-1
c. stateMENT-1 is True, stateMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True
Subject: Physics
When an a.c. source of e.m.f. \( \boldsymbol{E}= \)
\( E_{0} \sin 100 t \) is connected across a
circuit, it is observed that voltage leads the current by a phase angle \( \frac{\pi}{4} . \) If the circuit consists possible only R-L, R-C or L-C in series the two elements could be.
B. \( R=10 \Omega, C=1000 \mu F \)
c. \( R=100 \Omega, C=1000 \mu F \)
D. \( R=10 \Omega, L=100 m H \)
Subject: Physics
A string is stretched between fixed points separated by \( 75.0 \mathrm{cm} \). It is observed to have resonant frequencies
of \( 420 H z \) and \( 315 H z . \) There are no
other resonant frequencies between these two. Then, the lowest resonant
frequency for this string is
\( \mathbf{A} \cdot 105 H z \)
в. \( 1.05 \mathrm{Hz} \)
\( \mathrm{c} .1050 \mathrm{Hz} \)
D. \( 10.5 \mathrm{Hz} \)
Subject: Maths
\( \mathrm{f}\left|\begin{array}{ccc}\boldsymbol{x}^{2}+\boldsymbol{x} & \boldsymbol{x}+\mathbf{1} & \boldsymbol{x}-\mathbf{2} \\ \mathbf{2} \boldsymbol{x}^{2}+\mathbf{3} \boldsymbol{x}-\mathbf{1} & \mathbf{3} \boldsymbol{x} & \mathbf{3} \boldsymbol{x}-\mathbf{3} \\ \boldsymbol{x}^{\mathbf{2}}+\mathbf{2} \boldsymbol{x}+\mathbf{3} & \mathbf{2} \boldsymbol{x}-\mathbf{1} & \mathbf{2} \boldsymbol{x}-\mathbf{1}\end{array}\right|= \)
\( A x-12, \) then the value of \( A \) is
\( A \cdot 12 \)
в. 24
\( c .-12 \)
\( D .-24 \)
Subject: Maths
(i) Find the real values of \( x \) and \( y \) for
which \( z_{1}=9 y^{2}-4-10 i x \) is complex
conjugate of each other.
(ii) Find the value of \( x^{4}-x^{3}+x^{2}+ \)
\( 3 x-5 \) if \( x=2+3 i \)
Subject: Physics
An ideal gas goes from state \( A \) to state
B via three different processes as
indicated in the P-V diagram. If
\( Q_{1}, Q_{2}, Q_{3} \) indicate the heat absorbed
by the gas along the three processes
and \( \Delta U_{1}, \Delta U_{2}, \Delta U_{3} \) indicate the
change in internal energy along the
three processes respectively, then,
\( \mathbf{A} \cdot Q_{3}>Q_{2}>Q_{1} \) and \( \Delta U_{1}=\Delta U_{2}=\Delta U_{3} \)
B \( \cdot Q_{1}=Q_{2}=Q_{3} \) and \( \Delta U_{1}=\Delta U_{2}=\Delta U_{3} \)
\( \mathbf{c} \cdot Q_{1}>Q_{2}>Q_{3} \) and \( \Delta U_{1}=\Delta U_{2}=\Delta U_{3} \)
D \( \cdot Q_{3}>Q_{2}>Q_{1} \) and \( \Delta U_{1}>\Delta U_{2}>\Delta U_{3} \)
Subject: Physics
A plane electromagnetic wave propagating in \( x(-) \) direction as a wave function (in Sl units) is given as
\( \mathbf{\Phi}(x, t)=10^{3} \sin \pi\left(3 \times 10^{6} x-9 x\right. \)
\( \mathbf{1 0}^{\mathbf{1 4}} \boldsymbol{t} \)
The speed of the wave is
A. \( 3 \times 10^{6} \) m / \( s \)
В. \( 3 \times 10^{7} \mathrm{m} / \mathrm{s} \)
\( \mathrm{c} \cdot 3 \times 10^{8} \mathrm{m} / \mathrm{s} \)
D. \( 9 \times 10^{14} \mathrm{m} / \mathrm{s} \)
Subject: Physics
A block of \( 1 k g \) is stopped against a wall
by applying a force \( F \) perpendicular to
the wall. If \( \mu=0.2 \) then minimum value
of \( \boldsymbol{F} \) will be :
\( \begin{array}{ll}\text { A } & \text { N }\end{array} \)
в. \( 49 N \)
\( \mathbf{c} .98 N \)
D. \( 490 N \)
Subject: Maths
The D.E of the family of prabolas of which has a latus retum and whose
axes are parallel to \( x- \) axis
A \( \cdot y_{1}^{3}+2 a y_{2}=0 \)
B . \( y_{1}^{3}+a y_{2}=0 \)
c. \( y_{1}^{3}+4 a y_{2}=0 \)
D. \( y_{1}^{3}+3 a y_{2}=0 \)
Subject: Chemistry
An electron is allowed to move freely in
a closed cubic box of length of side 10 cm. The uncertainty in its velocity will be:
A . \( 3.35 \times 10^{-4} \mathrm{msec}^{-1} \)
B. \( 5.8 \times 10^{-4} \mathrm{m} \mathrm{sec}^{-1} \)
c. \( 4 \times 10^{-5} \mathrm{msec}^{-1} \)
D. \( 4 \times 10^{-6} \mathrm{msec}^{-1} \)
Subject: Maths
Consider the ten numbers
\( \boldsymbol{a r}, \boldsymbol{a r}^{2}, \boldsymbol{a r} \boldsymbol{3}, \ldots \ldots \ldots \boldsymbol{a} \boldsymbol{r}^{10} \)
If their sum is 18 and the sum of their
reciprocal is 6 then the product of these ten numbers, is
A \( \cdot 3^{5} \)
B . \( 3^{8} \)
\( c \cdot 3^{1} 0 \)
D. \( 3^{1} 5 \)
Subject: Chemistry
The optical rotation of the \( \alpha \) form of
pyranose is \( +150.7^{0}, \) that of the \( \beta \) form
is \( +52.8^{0} . \) In solution an equilibrium
mixture of these anomers has an
optical rotation of \( +80.2^{0} . \) The
percentage of the \( \alpha \) - form in equilibrium mixture is:
\( \mathbf{A} \cdot 28 \% \)
B. \( 32 \% \)
\( c .68 \% \)
D. \( 72 \% \)
Subject: Maths
What are the value of \( c \) for which Rolle's
theorem for the function \( f(x)=x^{3}- \)
\( 3 x^{2}+2 x \) in the interval [0,2] is
verified?
A \( . c=\pm 1 \)
B. \( _{c=1 \pm \frac{1}{\sqrt{3}}} \)
c. \( c=\pm 2 \)
D. None of these
Subject: Physics
When a \( 15 V \) dc source was applied across a choke coild then a current of 5
Amp flows in it. If the same coil is
connected to a \( 15 V, 50 \) rad/s ac source
a current of \( 3 A m p \) flows in the circuit
and its resonance frequency if a \( 2500 \mu f \) capacitor is connected in series with the coil.
Subject: Chemistry
The correct increasing order of the acidic strength of acids, butyric acid (I),
\( 2- \) chlorobutyric acid \( (\|), 3 \) chlorobutyric acid (III) and 2, 2dichlorobutyric acid (IV) is :
\( A \cdot|<||<|||<\mid V \)
B. III <II IV <1
c. \( |<|||<||<\mid V \)
D. \|\|\( <1<\|<\mathbb{V} \)
E. IV \( <\|1<\|<1 \)
Subject: Chemistry
\( \left[\boldsymbol{F} e^{I I}\left(\boldsymbol{O}_{2}\right)(\boldsymbol{C} \boldsymbol{N})_{4} \boldsymbol{C l}\right]^{4-} \) is named as:
A. chlorotetracyanodioxoferrate (II) ion
B. chlorotetracyanoperoxoferrrate (II) ion
c. chlorotetracyanosuperoxoferrate (II) ion
D. none of the above
Subject: Maths
If a line makes angles \( \boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\gamma} \) with
positive axes, then the range of \( \sin \alpha \sin \beta+\sin \beta \sin \gamma+\sin \gamma \sin \alpha \) is
\( ^{\mathrm{A}} \cdot\left(\frac{-1}{2}, 1\right) \)
в. \( \left(\frac{1}{2}, 2\right) \)
c. (-1,2)
D. (-1,2]
Subject: Physics
A short bar magnet allowed to fall along the axis of horizontal metallic ring.
Starting from rest, the distance falls by the magnet in one second may be:
A . \( 4.0 \mathrm{m} \)
B. \( 5.0 \mathrm{m} \)
c. \( 6.0 m \)
D. \( 7.0 m \)
Subject: Maths
If \( x^{3}+y^{3}=3 a x y, \) then \( \frac{d y}{d x} \) is
A \( \cdot \frac{a y-y^{2}}{x^{2}-a x} \)
В. \( \frac{a y-x^{2}}{y^{2}-a x} \)
c. \( \frac{b y-x^{2}}{y^{2}-b x} \)
D. None of these
Subject: Physics
A uniform bar of mass \( M \) and length \( L \)
is horizontally suspended from the ceiling by two vertical cables as shown
in the above figure. Cable \( A \) is
connected \( 1 / 4 t h \) distance from the left
end of the bar. Cable \( B \) is attached at
the far right end of the bar. What is the
tension in cable \( A \) ?
A. \( 1 / 4 M g \)
B. \( 1 / 3 v M g \)
\( \mathbf{c} \cdot 2 / 3 M g \)
D. \( 3 / 4 M g \)
Subject: Physics
Observe the given figure and identify
the correct statements.
(i) Poles 1,3 and 5 are unlike poles
(ii) Poles 2,4 and 6 are like poles
(iii) Pole 1 will attract pole 3 and 5
(iv) Pole 4 will be attracted by pole 1
\begin{tabular}{|l|l|l|}
\hline 1 & 2 & 3 & 4 & 5 \\
\hline Magnet & Magnet & Magnet
\end{tabular}
A. Only (i) and (iii)
B. Only (ii) and (iv)
c. Only (i) and (ii)
D. Only (iii) and (iv)
Subject: Physics
What is the focal length of double
concave lens kept in air with two
spherical surface of radii \( \boldsymbol{R}_{1}=\mathbf{3 0} \boldsymbol{c m} \)
and \( R_{2}=60 \mathrm{cm} . \) Take refractive index
of lens as \( \mu=1.5 \)
Subject: Chemistry
Relative lowering of vapour pressure is maximum for:
A. \( 0.1 \mathrm{m} \) urea
B. 0.1m Nacı
\( \mathbf{c} \cdot 0.1 m \quad M g C I_{2} \)
D. \( 0.1 m \quad A I_{2}\left(S O_{4}\right)_{3} \)
Subject: Physics
A plane wave of wavelength \( 6250 A \) is
incident normally on a slit of width \( 2 x \)
\( 10^{-2} \mathrm{cm} . \) The width of the principal
maximum on a screen distant \( 50 \mathrm{cm} \)
will be
A. 312.5 \( \times 10^{-3} \mathrm{cm} \)
В. 32.5 \( \times 10^{-3} \mathrm{m} \)
c. \( 312.5 \times 10^{-3} \mathrm{m} \)
D. 312 m
Subject: Chemistry
Conjugate acid of a weak base is always stronger. What will be the decreasing order of basic strength of the following conjugate bases?
\( \boldsymbol{O H}^{-}, \boldsymbol{R O}^{-}, \boldsymbol{C H}_{3} \boldsymbol{C O O}^{-}, \boldsymbol{C l}^{-} \)
Subject: Chemistry
Identify 'A' and 'B' in the following reaction and rewrite the complete
reaction.
\[
\boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{B r}+\boldsymbol{A g C N} \stackrel{\boldsymbol{\Delta}}{\rightarrow}
\]
\( \frac{\boldsymbol{N} \boldsymbol{a}}{\boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O} \boldsymbol{H}} \)
Explain Hoffmann bromamide degradation reaction.
Subject: Physics
The pressure on a square plate is measured by measuring the force on the plate and the length of the sides of
the plate. If the maximum errors in the
measurement of force and length are respectively \( 4 \% \) and \( 2 \% \), then the maximum error in the measurement of
pressure is?
A . \( 1 \% \)
B. 2\%
\( c .6 \% \)
D. \( 8 \% \)
Subject: Physics
Q Type your question
Nưe:
points at infinite distance from the
spheres)? The diagram shows two spheres, charged uniformly as indicated. All
regions are along a line connecting the centers of the objects.

Region \( A \) is anywhere to the left of the 5.0 Coulomb charge. Region B is to the right of the 5.0 Coulomb charge and closer to the 5.0 Coulomb charge than to the 3.0 Coulomb charge. Region \( C \) is to
the right of the 5.0 Coulomb charge but closer to the 3.0 Coulomb charge than to the 5.0 Coulomb charge. Region D is anywhere to the right of the 3.0 Coulomb charge.
\( A \cdot A \)
B. B
\( c \cdot c \)
D.
E. There is no region where the electric potential could possibly be zero
Subject: Maths
The equations of two planes are \( P_{1} \)
\( 2 x-y+z=2, \) and \( P_{2}: x+2 y-z= \)
3. The equation of the plane which
passes through the point (-1,3,2) and is perpendicular to each of the planes
\( P_{1} \) and \( P_{2} \) is
A \( \cdot x+3 y-5 z+2=0 \)
B. \( x+3 y+5 z-18=0 \)
c. \( x-3 y-5 z+20=0 \)
D. \( x-3 y+5 z=0 \)
Subject: Physics
The binding energy of an electron in the
ground state of \( \boldsymbol{H} \boldsymbol{e} \) atom is \( \boldsymbol{E}_{\mathbf{0}}= \)
24.6e \( V \). The energy required to remove
both the electrons from the atom is
A . \( 24.6 e V \)
в. \( 79.0 e V \)
c. \( 54.4 e V \)
D. None of these
Subject: Maths
\( \int_{0}^{\infty} \boldsymbol{f}\left(\boldsymbol{x}+\frac{\mathbf{1}}{\boldsymbol{x}}\right) \cdot \frac{\ln \boldsymbol{x}}{\boldsymbol{x}} \boldsymbol{d} \boldsymbol{x} \)
A. Is equal to zero
B. Is equal to one
\( ^{\mathrm{c}} \). \( _{\text {Is equal to }} \frac{1}{2} \)
D. can not be evaluated
Subject: Maths
Let \( n \) be an odd integer greater than 1
and let \( c_{1}, c_{2}, \cdots, c_{n} \) be integers. For
each permutation \( \boldsymbol{a}=\left(\boldsymbol{a}_{1}, \boldsymbol{a}_{2}, \cdots, \boldsymbol{a}_{n}\right) \)
of \( (1,2, \cdots, n) \) define \( S(a)=\sum_{i=1}^{n} c_{i} a_{i} \)
Prove that there exist permutations
\( a \neq b \) of \( \{1,2, \cdots, n\} \) such that \( n ! \) is a
divisor of \( \mathrm{S}(\mathrm{a})-\mathrm{S}(\mathrm{b}) \)
A \( \cdot \frac{1}{2} n !(n !-1) \equiv \frac{1}{2}(n+1) ! \sum_{i=1}^{n} c_{i}(\bmod n !) . \) Because \( n>1 \)
is odd, the right-hand side is congruent to 0 mod \( n ! \) while the lefthand side is not, a contradiction
B \( \cdot \frac{1}{2} n !(n !+1) \equiv \frac{1}{2}(n+1) ! \sum_{i=1}^{n} c_{0}(\text { modn! }) . \) Because \( n>1 \)
is odd, the right-hand side is congruent to 0 mod \( n ! \) while the lefthand side is not, a contradiction.
c. \( \frac{1}{2} n !(n !-1) \equiv \frac{1}{2}(n-1) ! \sum_{i=1}^{n} c_{0}(\text { modn! }) . \) Because \( n> \)
is odd, the right-hand side is congruent to 0 mod \( n ! \) while the lefthand side is not, a contradiction.
D. None of the above
Subject: Chemistry
Percentage of unoccupied volume in case of simple cubic arrangement and body cenred arrangement of metals is
given by respectively.
A \( .52 \% \) \& \( 60 \% \)
B. \( 52 \% \& 26 \% \)
c. \( 48 \% \) \& \( 32 \% \)
D. \( 48 \% \) \& \( 26 \% \)
Subject: Physics
A point moves with uniform
acceleration and \( v_{1}, v_{2}, v_{3} \) denote the
average velocities in three successive
intervals of time \( t_{1}, t_{2}, t_{3} . \) Then, the
relation \( \frac{\boldsymbol{v}_{1}-\boldsymbol{v}_{2}}{\boldsymbol{v}_{2}-\boldsymbol{v}_{3}} \) is
A \( \frac{t_{1}-t_{2}}{t_{2}+t_{3}} \)
B. \( \frac{t_{1}+t_{2}}{t_{2}+t_{3}} \)
c. \( \frac{t_{1}-t_{2}}{t_{1}+t_{3}} \)
\( \mathbf{D} \cdot \frac{t_{1}-t_{2}}{t_{2}-t_{3}} \)
Subject: Maths
If \( z \) is unimodular complex number then \( \mathbf{z}=\left(\frac{\mathbf{1}+\mathbf{i} a}{\mathbf{1}-\mathbf{i} \mathbf{a}}\right)^{\mathbf{4}} \) has
A. 2 real 2 imaginary roots
B. 4 real roots
c. 4 imaginary roots
D. 3 real and imaginary roots
Subject: Physics
A bar magnet has coercivity \( 4 \times \)
\( 10^{3} A m^{-1} . \) It is desired to demagnetize
it by inserting it inside a solenoid \( 12 \mathrm{cm} \) long and has 60 turns. The current that
should be sent through the solenoid is:
\( A \cdot 8 A \)
в. \( 10 A \)
\( c .12 A \)
D. \( 14 A \)
Subject: Maths
A examination consists of 8 questions in each of which one of the 5
alternatives is the correct one. On
the assumption that a candidate who has done no preparatory work chooses for each question any one of the five alternatives with equal probability, the probability that he gets more than one correct answer is equal to five alternatives with equal probability,the probability that he gets more than one correct answer is equal to
A \( \cdot(0.8)^{8} \)
B. \( 3(0.8)^{8} \)
c. \( 1-(0.8)^{8} \)
D. \( 1-3(0.8)^{8} \)
Subject: Maths
\( \left.\begin{array}{l}\text { Find } \boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}, \boldsymbol{d} \text { if }\left[\begin{array}{cc}\boldsymbol{d}+\mathbf{1} & \mathbf{1 0}+\boldsymbol{a} \\ \mathbf{3} \boldsymbol{b}-\mathbf{2} & \boldsymbol{a}-\mathbf{4}\end{array}\right]= \\ \mathbf{2} \quad \mathbf{2} \boldsymbol{a}+\mathbf{1} \\ \boldsymbol{b}-\mathbf{5} \quad \boldsymbol{4} \boldsymbol{c}\end{array}\right] \)
Subject: Physics
A ray of light incident normally on the
horizontal face of the slab and just fail
to emerge from the diagonal face of the
prism. If prism angle is \( 30^{\circ} \) then
refractive index of the prism can be
\( A \cdot \sqrt{2} \)
B. \( \sqrt{3} \)
c. slightly greater than 2
D. slightly less than 2
Subject: Maths
Discuss the continuity of
\[
\boldsymbol{f}(\boldsymbol{x})=
\]
\( \left\{\begin{array}{l}\frac{\sin 2 x}{\sqrt{1-\cos 2 x}} \text { for } 0<x \leq \pi / 2 \\ \frac{\cos }{\pi-2 x} \quad \text { for } \frac{\pi}{2}<x<\pi\end{array} \) at \right.
\( \boldsymbol{x}=\boldsymbol{\pi} / 2 \)
Subject: Maths
The solution of differential equation \( \left(x^{2}+y^{2}\right) d y=x y d x \) is \( y=y(x) . \) If
\( \boldsymbol{y}(\mathbf{1})=\mathbf{1} \) and \( \boldsymbol{y}\left(\boldsymbol{x}_{0}\right)=\boldsymbol{e}, \) then \( \boldsymbol{x}_{0} \) is:
A \( \cdot \sqrt{2\left(\mathrm{e}^{2}-1\right)} \)
B . \( \sqrt{2\left(\mathrm{e}^{2}+1\right)} \)
\( c \cdot \sqrt{3} e \)
D. \( \sqrt{\frac{e^{2}+1}{2}} \)
Subject: Physics
The average velocity of a body moving
with uniform acceleration after
travelling a distance of \( 3.06 m \) is \( \mathbf{0 . 3 4} \boldsymbol{m} / \boldsymbol{s} . \) The change in velocity of the body is \( 0.18 m / s . \) During this time, its acceleration is
A \( \cdot 0.01 \mathrm{m} / \mathrm{s}^{2} \)
B. \( 0.02 \mathrm{m} / \mathrm{s}^{2} \)
c. \( 0.03 \mathrm{m} / \mathrm{s}^{2} \)
D. \( 0.04 \mathrm{m} / \mathrm{s}^{2} \)
Subject: Maths
The co-ordinates of the vertices of
ロPQRS are
\( P(-1,2), Q(-4,-2), R(-4,-3) \) and
\( \boldsymbol{S}(-1,-\mathbf{5}) \) respectively. Draw \( \square \boldsymbol{P} Q \boldsymbol{R} \boldsymbol{S} \)
and state it is which type of
quadrilateral.
Subject: Maths
An experiment can result in only 3 mutually exclusive events \( A, B \) and \( C \)
If \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{2} \boldsymbol{P}(\boldsymbol{B})=\mathbf{3} \boldsymbol{P}(\boldsymbol{C}), \) then
\( \boldsymbol{P}(\boldsymbol{A})= \)
\( A \cdot \frac{6}{11} \)
B. \( \frac{5}{11} \)
\( c \cdot \frac{9}{11} \)
D. None
Subject: Physics
An object swinging on the end of a string forms a simple pendulum. Some students (and some texts) often cite the
simple pendulum's motion as an example of SHM. That is not quite accurate because the motion is really
A. approximately SHM only for small amplitudes
B. exactly SHM only for amplitudes that are smaller than a certain value
c. approximately SHM for all amplitudes.
D. None of the above
Subject: Chemistry
How is electrical conductance of a
conductor related with length and area of cross section of the conductor?
\( \mathbf{A} \cdot G=l \cdot a \cdot k^{-1} \)
B . \( G=k . l . a^{-1} \)
c. \( G=k . a . l^{-1} \)
D. \( G=k . l^{-1} . a^{-1} \)
Subject: Maths
If \( A+B+C=180^{\circ}, \) then the value of
\( (\cot B+\cot C)(\cot C+ \)
\( \cot A)(\cot A+\cot B) \) will be
\( \mathbf{A} \cdot \sec A \sec B \sec C \)
B. \( \csc A \csc B \csc C \)
\( \mathbf{c} \cdot \tan A \tan B \tan C \)
D.
Subject: Chemistry
Elements \( P \) and \( Q \) react to form a
compound \( P_{x} Q_{y} . \) R and P react to form
\( \boldsymbol{R}_{\boldsymbol{y}} \boldsymbol{P}_{\boldsymbol{z}} \)
If \( P_{x} Q_{y} \) is a binary acid with \( x=2 y \) then the acid is:
A. sulphuric acid
B. hydrochloric acid
c. chloric acid
D. hydrogen sulphide