AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A chain of mass \( \mathrm{m} \) and length Lis over hanging from the edge of a smooth horizontal table such that \( \frac{1}{n} \) of its length is lying on the table. The work done in pulling the chain completely on to the table is
A \( \cdot \frac{m g L}{2 n^{2}} \)
в. \( \frac{m g L(n-1)^{2}}{2 n^{2}} \)
c. \( \frac{m g L(n-1)^{2}}{n^{2}} \)
D. \( \frac{m g L}{n^{2}} \)
Subject: Maths
\( \int_{1}^{2} e^{x}\left(\frac{1}{x}-\frac{1}{x^{2}}\right) d x \) equals to
A \( \cdot e\left(\frac{e}{2}-1\right) \)
B. 1
\( c \cdot e(e-1) \)
D. \( \frac{e}{2} \)
Subject: Physics
The operating magnetic field for accelerating protons in a cyclotron oscillator having frequency of 12 MHz is \( \left(q=1.6 \times 10^{-19} \mathrm{C}, m_{p}=1.67 \times 10^{-27}\right. \)
kg and \( \left.1 \mathrm{MeV}=1.6 \times 10^{-13} \mathrm{J}\right) \)
A . 0.69 न
B . 0.79 न
c. 0.59 न
D. 0.49 \( T \)
Subject: Maths
If \( f(x)=3 x+1, g(x)=x^{3}+2, \) then
\( \frac{\boldsymbol{f}+\boldsymbol{g}}{\boldsymbol{f} \boldsymbol{g}}(\mathbf{0})= \)
A . \( x \)
B. 1
\( c \cdot 3 \)
\( D \cdot \frac{3}{2} \)
Subject: Physics
toppr
Q Type your question
An opaque plate with a triangular
aperture, side \( 1 \mathrm{cm} \), is in contact with
the lens. (see Figs.).

Which one of the following diagrams
best shows to appearance of the patch
of light seen on the screen?
\( \mathbf{A} \)
B.
\( \mathbf{c} \)
D.
Subject: Maths
\( (5 x+2 y+3 z)^{2} \)
\( \mathbf{A} \cdot 25 x^{2}+4 y^{2}+9 z^{2}+20 x y+12 y z+30 z x \)
B \( \cdot 25 x^{2}-4 y^{2}+9 z^{2}+20 x y+12 y z+30 z x \)
\( \mathbf{c} \cdot 25 x^{2}+4 y^{2}-9 z^{2}+20 x y+12 y z+30 z x \)
D. None of these
Subject: Maths
Evaluate:
\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left(\boldsymbol{x}^{100}+\boldsymbol{x}^{99}+\boldsymbol{x}^{98}+\ldots+\boldsymbol{x}^{2}+\boldsymbol{x}+\right. \)
\( \mathbf{1} \)
Subject: Chemistry
Balance the following in basic medium:
\( \boldsymbol{A s O}_{3}^{3+}+\boldsymbol{M n O}_{4}^{-} \rightarrow \boldsymbol{A} \boldsymbol{s} \boldsymbol{O}_{4}^{3-}+\boldsymbol{M n O}_{2} \)
A \( \cdot 3 A s O_{3}^{3+}+2 M n O_{4}^{-}+H_{2} O \rightarrow 3 A s O_{4}^{3-}+2 M n O_{2}+ \)
\( 2 O H^{-} \)
B. \( 3 A s O_{3}^{3+}+2 M n O_{4}^{-}+4 H_{2} O \rightarrow 3 A s O_{4}^{3-}+3 M n O_{2}+ \)
\( 2 O H^{-} \)
\( \mathrm{c} \cdot 3 A s O_{3}^{3+}+4 M n O_{4}^{-}+3 H_{2} O \rightarrow 3 A s O_{4}^{3-}+2 M n O_{2}+ \)
\( 4 O H^{-} \)
D. None of these
Subject: Maths
If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) is defined by \( \boldsymbol{f}(\boldsymbol{x})=\mathbf{3} \boldsymbol{x}- \)
2 then \( (f o f)(x)+2= \)
A \( . f(x) \)
B. \( 2 f(x) \)
c. \( 3 f(x) \)
D. \( -f(x) \)
Subject: Physics
Figure shows a small loop carrying
current \( I . \) The curved portion is an arc of
a circle of radius \( R \) and the straight portion is a chord to the same circle subtending at an angle \( \theta . \) The magnetic
induction at center \( O \) is :
A . zero
B. always inward irrespective of the value of \( \theta \)
c. inward as long as \( \theta \) is less than \( \pi \)
D. always outward irrespective of the value of \( \theta \)
Subject: Maths
If \( A=\{2,4\} \) and \( B=\{3,4,5\}, \) then
\( (\boldsymbol{A} \cap \boldsymbol{B}) \times(\boldsymbol{A} \cup \boldsymbol{B}) \) is
A \( \cdot\{(2,2),(3,4),(4,2),(5,4)\} \)
B - \{(2,3),(4,3),(4,5)\}
c. \{(2,4),(3,4),(4,4),(4,5)\}
D \( \cdot\{(4,2),(4,3),(4,4),(4,5)\} \)
Subject: Maths
In a moderately asymmetrical distribution the distance between mean
\( \& \) median is 'k' times the distance
between mean \( \& \) mode, then 'k' equals
\( \mathbf{A} \cdot \mathbf{3} \)
B. 2
\( c \cdot \frac{2}{3} \)
D. None of these
Subject: Maths
Find the nine rational numbers
between 0 and 1
A. \( 0.1,0.2,0.3, \ldots, 0.9 \)
в. \( 1.1,0.2,10.3, \ldots, 0.9 \)
c. \( 0.1,0.2,0.3, \ldots, 20.9 \)
D. \( 0.1,0.2,10.3, \ldots, 0.9 \)
Subject: Maths
If \( f(x)=\sec (3 x), \) then \( f^{\prime}\left(\frac{3 \pi}{4}\right)= \)
A. \( -3 \sqrt{2} \)
B. \( -\frac{3 \sqrt{2}}{2} \)
\( c \cdot \frac{3}{2} \)
D. \( \frac{3 \sqrt{2}}{2} \)
E. \( 3 \sqrt{2} \)
Subject: Physics
A square of side L meters lies in the \( x-y \) plane in a region, where the magnetic field given by \( \vec{B}=B_{o}(2 \hat{i}+3 \hat{j}+4 \hat{k}) T \)
where \( B_{o} \) is constant. The magnitude of flux passing through the square is :
B. \( 3 B_{o} L^{2} W b \)
\( \mathbf{c} \cdot 4 B_{o} L^{2} W b \)
D. \( \sqrt{29} B_{o} L^{2} W b \)
Subject: Chemistry
A white solid \( X \) on heating gives a white solid Y and an acidic gas Z. Gas Z is
also given out when \( X \) reacts with an acid. The compound Y is also formed if caustic soda is left open in the atmosphere. \( X, Y \) and \( Z \) are :
A \( \cdot X-N a H C O_{3}, Y-N a_{2} C O_{3}, Z-C O_{2} \)
в. \( X-N a_{2} C O_{3}, Y-N a O H, Z-C O_{2} \)
c. \( X-N a H C O_{3}, Y-N a H C O_{3}, Z-C O_{2} \)
D. \( X-N a O H, Y-N a H C O_{3}, Z-C O_{2} \)
Subject: Maths
If the polynomials \( 2 x^{3}+m x^{2}+3 x-5 \)
and \( x^{3}+x^{2}-4 x+m \) leaves the same
remainder when divided by \( x-2, \) then
the value of \( m \) is
A \( \cdot-\frac{3}{13} \)
B. \( -\frac{13}{3} \)
\( c \cdot \frac{3}{13} \)
D. \( \frac{13}{3} \)
Subject: Physics
Assertion
The moon appears purely white during the day but after sunset its colour is
yellowish hue.
Reason
The scattered blue component of white light is mixed with yellow, the colour becomes white.
A. Assertion is True. Reason is also True and is the correct explanation of the Assertion
B. Assertion is True. Reason is also True but is not the correct explanation of Assertion.
c. Assertion is True and Reason is False
D. Assertion is False and Reason is True
Subject: Biology
Which one of the following is the
complementary sequence for the DNA
with \( \mathbf{5}^{\prime} \) -CGTACTA-3' \( ^{\prime} \)
A . \( 5^{\prime} \) '-ТАGТАСG-3
B. 5'-ATCATGA-3
c. \( 5^{\prime} \) -UTCUTGC-3'
D. 3'-GCATGAT-5'
Subject: Physics
Equation of SHM is \( x=10 \sin 10 \pi t . \) Then the time period is, \( x \) is in \( \mathrm{cm} \) and \( \mathrm{t} \) is in
\( \sec \)
\( A \cdot 10 \pi \)
B. 0.2 sec
c. \( 0.1 \mathrm{sec} \)
D. 2 sec
Subject: Physics
A wave represented by \( \boldsymbol{y}= \) \( 100 \sin (a x+b t) \) is reflected from a
dense plane at the origin. If \( 36 \% \) of energy is lost and rest of the energy is reflected, then the equation of the
reflected wave will be
A \( . y=-8.1 \sin (a x-b t) \)
B. \( y=8.1 \sin (a x+b t) \)
c. \( y=-80 \sin (a x-b t) \)
D. \( y=-10 \sin (a x-b t) \)
Subject: Biology
In mammals, the teeth are
(i) Of different types
(ii) Embedded in the cup-like socket of the jaw bones
(iii) Only two sets, present throughout life
These conditions are referred as
A. Heterodont, thecodont and diphyodont
B. Thecodont, heterodont and diphyodont
c. Diphyodont, thecodont and heterodont
D. Heterodont, diphyodont and thecodont
E. Thecodont, diphyodont and heterodont
Subject: Chemistry
\( \mathbf{3 0} \boldsymbol{m} \boldsymbol{L} \) of \( \boldsymbol{C H}_{3} \boldsymbol{O H}\left(\boldsymbol{d}=\mathbf{0 . 8} \boldsymbol{g} / \boldsymbol{c m}^{3}\right) \) is
mixed with \( 60 m L \) of \( C_{2} H_{5} O H(d= \)
\( \left.0.92 g / c m^{3}\right) \) at \( 25^{\circ} C \) to form a solution
of density \( 0.88 g / c m^{3} . \) Select the
correct option. This question has multiple correct options
A. Molarity and molality of resulting solution are 6.33 and 13.59 respectively
B. The mole fraction of solute and molality are 0.385 and 13.59 respectively
c. Molarity and \% change in volume are 13.59 and zero respectively
D. Mole fraction of solvent and molality are 0.615 and 13.59 respectively
Subject: Physics
The speed of a train increases at a
constant rate \( \alpha \) from zero to \( v \) and then
remains constant for an interval and
finally decreases to zero at a constant rate \( \beta . \) The total distance travelled by
the train is \( l . \) The time taken to
complete the journey is \( t . \) Then This question has multiple correct options
A \( \cdot t=\frac{l(\alpha+\beta)}{\alpha \beta} \)
B. \( t=\frac{l}{v}+\frac{v}{2}\left(\frac{1}{\alpha}+\frac{1}{\beta}\right) \)
C \( t \) is minimum when \( v=\sqrt{\frac{2 l \alpha \beta}{(\alpha-\beta)}} \)
D. \( t \) is minimum when \( v=\sqrt{\frac{2 l \alpha \beta}{(\alpha+\beta)}} \)
Subject: Physics
If \( \lambda \) is the wavelength of hydrogen atom
from the transition \( n=3 \) to \( n=1 \), then
what is the wavelength for doubly ionised lithium ion for same transition?
\( A \cdot \frac{\lambda}{3} \)
B. \( 3 \lambda \)
\( c \cdot \frac{\lambda}{9} \)
D. \( 9 \lambda \)
Subject: Chemistry
The standard \( E_{r e d}^{o} \) values of \( A, B \) and \( C \) \( \operatorname{are}+\mathbf{0 . 6 8} \boldsymbol{V},-\mathbf{2 . 5 4} \boldsymbol{V},-\mathbf{0 . 5 0} \boldsymbol{V} \)
respectively. The order of their reducing power is:
A. \( A>B>C \)
в. \( A>C>B \)
c. \( C>B>A \)
D. \( B>C>A \)
Subject: Maths
The values of a \( \& \mathrm{b} \) so that the
polynomial \( \boldsymbol{x}^{\mathbf{3}}-\boldsymbol{a} \boldsymbol{x}^{2}-\mathbf{1 3} \boldsymbol{x}+\boldsymbol{b} \) is
divisible by \( (x-1) \&(x+3) \) are
A. \( a=15, b=3 \)
3
в. \( a=3, b=15 \)
\( \mathbf{c} \cdot a=-3, b=15 \)
D. \( a=3, b=-15 \)
Subject: Physics
A stone is dropped by a person from the top of a tower, which is \( 200 \mathrm{m} \) tall. At
the same time another stone is thrown
upwards, with a velocity of \( 50 m s^{-1} \) by
a person standing at the foot of the
tower. Find the time after which two
stones meet.
A . \( 4 s \)
B. 5 s
\( c .8 s \)
D. 10 s
Subject: Maths
\( \operatorname{Let} \boldsymbol{f}(\boldsymbol{x})=\cos \left[\boldsymbol{\pi}^{2}\right] \boldsymbol{x}+ \)
\( \cos \left[-\pi^{2}\right] x, \) where \( [.] \)
represents greatest integer function
-1 and \( f(-\pi)=? \)
\( A \cdot-1 \)
в.
\( c \cdot 0 \)
D.
Subject: Chemistry
\( \boldsymbol{K}_{\boldsymbol{p}} \) for the reaction \( \boldsymbol{N}_{\mathbf{2}}(\boldsymbol{g})+\mathbf{3} \boldsymbol{H}_{2}(\boldsymbol{g}) \rightleftharpoons \)
\( 2 N H_{3}(g), \) at \( 298 K \) is \( 5.2 \times 10^{-5} . \) What
is the value of \( K_{c} \) at \( 298 K \), for the
reaction \( \frac{1}{2} N_{2}(g)+\frac{3}{2} H_{2}(g) \rightleftharpoons N H_{3}(g) \)
Subject: Chemistry
Which of the following can conduct electricity in the solid state?
A. sucrose, \( C_{12} H_{22} O_{11}(s) \)
B. Graphite, C(s)
C. Sodium hydroxide, NaOH(s)
D. Iron(III) chloride, \( F e C l^{3}(s) \)
E . lodine, \( I_{2}(s) \)
Subject: Physics
For the given circuit, select the correct
alternative(s)
This question has multiple correct options
A. The equivalent capacitance between points \( 1 \& 2 \) is
\( \frac{15 C}{11} \)
B. The equivalent capacitance between points \( 3 \& 6 \) is \( \frac{5 C}{3} \)
C. The equivalent capacitance between points \( 1 \& 3 \) is \( \frac{15 C}{14} \)
D. The equivalent capacitance between points 3 \& 5 is
\( \frac{14 C C}{15} \)
Subject: Physics
A spherical ball of mass \( 20 k g \) is stationary at the top of a hill of height 100 \( m \). It rolls down a smooth surface to
the ground, then climbs up another hill of height \( 30 m \) and finally rolls down to a
horizontal base at a height of \( 20 m \)
above the ground. The velocity attained
by the ball is
\( \mathbf{A} \cdot 40 m / s \)
в. \( 20 \mathrm{m} / \mathrm{s} \)
c. \( 10 m / s \)
D. \( 10 \sqrt{30} \mathrm{m} / \mathrm{s} \)
Subject: Maths
If \( \cos \alpha+\cos \beta+\cos \gamma=0=\sin \alpha+ \)
\( \sin \beta+\sin \gamma \) then \( \cos 2 \alpha+\cos 2 \beta+ \)
\( \cos 2 \gamma \) equals
A. \( 2 \cos (\alpha+\beta+\gamma) \)
B. \( \cos 2(\alpha+\beta+\gamma) \)
\( c \cdot 0 \)
D.
Subject: Physics
The projection of \( \vec{a}=\hat{i}+2 \hat{j}+3 \hat{k} \) on the vector \( \overrightarrow{\boldsymbol{b}}=\hat{\boldsymbol{i}}+2 \hat{\boldsymbol{j}}-\hat{\boldsymbol{k}} \) is :
A. \( \sqrt{\frac{2}{3}} \)
B. \( \sqrt{\frac{3}{2}} \)
c. \( \sqrt{\frac{4}{21}} \)
D. \( \sqrt{\frac{25}{21}} \)
Subject: Physics
The primary and secondary coils of a transformer have 50 and 1500 turns
respectively. If the magnetic flux \( \phi \) linked with the primary coil is given by \( \phi=\phi_{0}+4 t, \) where \( \phi \) is in weber, t is
time in seconds and \( \phi_{0} \) is a constant.
The output voltage across the secondary coil is
A \( .90 V \)
\( V \)
в. \( 6000 V \)
c. \( 220 V \)
D. 30 \( V \)
Subject: Maths
If the lines \( 3 x-4 y+4=0 \) and \( 6 x- \)
\( 8 y-7=0 \) are tangents to a circle,
then find the radius of the circle.
\( A \cdot 3 / 4 \)
в. \( 4 / 3 \)
\( c \cdot 1 / 4 \)
D. \( 7 / 4 \)
Subject: Chemistry
Allyl chloride can be produced by many different methods. The most common
method is chlorination of propene which proceeds via a free-radical substitution
mechanism.
The propenyl radical, \( \boldsymbol{C H}_{2}=\boldsymbol{C H C H}_{2} \)
is formed in the first propagation step
of the reaction.
Write an equation to show the
formation of \( \boldsymbol{C H}_{2}=\boldsymbol{C H C H}_{2}^{\circ} \) in this
propagation step.
Subject: Maths
Find out the modal class for the
following table:
\( \begin{array}{llllll}x & 1- & 3- & 5- & 7- & 9- \\ 3 & 5 & 7 & 9 & 11\end{array} \)
frequency 2
A . \( 1-3 \)
B. \( 3-5 \)
c. \( 5-7 \)
D. \( 7-9 \)
Subject: Physics
When a piece of polythene is rubbed with wool, a charge of \( -2 \times 10^{-7} C \) is
developed on polythene. What mass is transferred to polythene?
\( \mathbf{A} \cdot 5.69 \times 10^{-19} k g \)
B . \( 2.25 \times 10^{-19} k g \)
\( \mathbf{c} \cdot 9.63 \times 10^{-19} k g \)
D. \( 11.38 \times 10^{-19} \mathrm{kg} \)
Subject: Chemistry
For a given exothermic reaction \( \boldsymbol{K}_{\boldsymbol{p}} \) and \( K_{p}^{\prime} \) are the equilibrium constants at
temperature \( T_{1} \) and \( T_{2} \) respectively. Assuming that heat of reaction is constant in temperature range between
183. \( T_{1} \) and \( T_{2} \) it is readily observed
that:
\( \mathbf{A} \cdot K_{p}=K_{p}^{\prime} \)
B . \( K_{p}=1 / K_{p}^{\prime} \)
\( \mathbf{c} \cdot K_{p}>K_{p}^{\prime} \)
D. \( K_{p}<K_{p}^{\prime} \)
Subject: Biology
Correct pathway of water movement in
plant roots is
A. Soil water \( \longrightarrow \) Root hair cell \( \longrightarrow \) Passage cells \( \longrightarrow \) Cortical cells \( \longrightarrow \) Xylem \( \longrightarrow \) Pericycle
B. Soil water \( \longrightarrow \) Root hair cell \( \longrightarrow \) Pericycle \( \longrightarrow \) Cortical cells \( \longrightarrow \) Passage cells \( \longrightarrow \) Xylem
C. Soil water \( \longrightarrow \) Root hair cell \( \longrightarrow \) Cortical cells \( \longrightarrow \) Passage cells \( \longrightarrow \) Pericycle \( \longrightarrow \) Xylem
D. Soil water \( \longrightarrow \) Root hair cell \( \longrightarrow \) Cortical cells \( \longrightarrow \)
Pericycle \( \longrightarrow \) Passage cells \( \longrightarrow \) Xylem
Subject: Physics
The bottom of glass beaker is made of a
thin equiconvex lens having bottom
side silver polished as shown in fig. Now the water is filled in the beaker up to a
height of \( h=4 m . \) The image of point
object floating at middle point of beaker at the surface of water coincides with it.
Find out the value of radius (in \( \mathrm{m} \) ) of
curvature of lens. \( \left(a \boldsymbol{\mu}_{\boldsymbol{g}}=\mathbf{3} / \mathbf{2},_{\boldsymbol{a}} \boldsymbol{\mu}_{\boldsymbol{w}}=\right. \)
\( \mathbf{4} / \mathbf{3}) \)
Subject: Chemistry
The isoelectronic set of ions is:
A \( \cdot N^{3-}, L i^{+}, M g^{2+} \) and \( O^{2-} \)
B. \( L i^{+}, N a^{+}, O^{2-} \) and \( F^{-} \)
c. \( F^{-}, L i^{+}, N a^{+} \) and \( M g^{2} \)
D. \( N^{3},, O^{2-}, F^{-} \) and \( N a^{+} \)
Subject: Maths
The PDF of variable x: number of times
sum 6 appears on in two throw of a pair of dice is
\[
\begin{array}{cc}
\mathbf{0} & \mathbf{1}
\end{array}
\]
\( p(x) \)
then values of \( a, b, c \) are.
A \( \cdot a=\frac{2}{36}, b=\frac{3}{36}, c=\frac{5}{36} \)
В. \( a=\frac{961}{36}, b=\frac{310}{36}, c=\frac{25}{36} \)
\( ^{\mathbf{C}} \cdot_{a}=\frac{961}{1269}, b=\frac{310}{1296}, c=\frac{25}{1296} \)
D. \( a=\frac{91}{36}, b=\frac{30}{36}, c=\frac{25}{36} \)
Subject: Physics
An electric field \( \boldsymbol{E} \) and a magnetic field
\( B \) act over the same region in which an electron enters along the \( x \) -axis. The
combination of \( E \) and \( B \) which
permits the electron to go undeflected
is:
A. \( E \) along \( Y \) -axis and \( B \) along \( Y \) -axis
B. \( E \) along \( Y \) -axis and \( B \) along \( Z \) -axis
c. \( E \) along \( X \) -axis and \( B \) along \( Z \) -axis
D. \( E \) along \( Y \) -axis and \( B \) along \( X \) -axis
Subject: Chemistry
For \( \boldsymbol{Z} \boldsymbol{n}^{2+} / \boldsymbol{Z} \boldsymbol{n}, \boldsymbol{E}^{\boldsymbol{o}}= \)
\( -0.76 V, \) for \( A g^{+} / A g, E^{o}=0.799 V \)
The correct statement is :
A. the reaction \( Z n \) getting reduced \( A g \) getting oxidized is spontaneous
B. \( Z n \) undergoes reduction and \( A g \) is oxidized
C. \( Z n \) undergoes oxidation and \( A g^{+} \) gets reduced
D. no suitable answer
Subject: Maths
An equilateral triangle has area \( A \mathrm{cm}^{2} \) A regular hexagon of maximum area is cut off from the triangle. If the area of
the hexagon is \( 320 \mathrm{cm}^{2} \), then the area \( A \)
is
A \( \cdot 640 \mathrm{cm}^{2} \)
в. \( 480 \mathrm{cm}^{2} \)
\( c \cdot 600 c m^{2} \)
D. \( 400 \mathrm{cm}^{2} \)
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}, \boldsymbol{g}(\boldsymbol{x})=\tan \boldsymbol{x} \) and \( \boldsymbol{h}(\boldsymbol{x})= \)
\( \ln x \)
For \( \boldsymbol{x}=\frac{\sqrt{\boldsymbol{\pi}}}{\mathbf{2}}, \) what is the value of
\( [\boldsymbol{h o}(\boldsymbol{g} \boldsymbol{o} \boldsymbol{f})(\boldsymbol{x})] ? \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot \frac{\pi}{4} \)
D.
Subject: Maths
The p.d.f. of a continuous r.v. x is \( f(x)=\frac{7}{9} x^{2}-2, \quad 0<x<3 \)
\( =\mathbf{0} \)
otherwise
\( \boldsymbol{P}(\boldsymbol{X} \leq-1) \) is?
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( 1 / 2 \)
\( c \cdot 1 / 3 \)
D. \( 1 / 4 \)
Subject: Chemistry
Which the following interaction form nonbonding molecular orbital when zaxis is the bonding axis?
\( \mathbf{A} \cdot d_{y z}+d_{z^{2}} \)
\( \mathbf{B} \cdot d_{y z}+d_{x y} \)
C \( \cdot d_{x^{2}-y^{2}}+d_{x y} \)
D. All form N.B.M.O.
Subject: Chemistry
A conductivity cell has been calibrated
with a \( 0.01 M 1: 1 \) electrolyte solution
(specific conductance \( \kappa=1.25 \times \)
\( 10^{-3} \mathrm{Scm}^{-1} \) ) in the cell and the
measure resistance was \( 800 \Omega \) at \( 25^{\circ} C \)
The cell constant will be:
A \( \cdot 1.02 \mathrm{cm}^{-1} \)
В. \( 0.102 c m^{-1} \)
c. \( 1.00 \mathrm{cm}^{-1} \)
D. \( 0.5 \mathrm{cm}^{-1} \)
Subject: Chemistry
Ratio of frequency of revolution of
electron in second excited state of \( \boldsymbol{H} \boldsymbol{e}^{+} \)
and first excited state of \( \boldsymbol{H} \) is \( \frac{\boldsymbol{2}^{x}}{\mathbf{3}^{y}} . \) Then
the value of \( x+y \) is:
Subject: Physics
Assertion
At depth \( h \) below the water surface
pressure is \( P . \) Then at depth \( 2 h \)
pressure will be \( 2 P . \) (Ignore density variation)
Reason
With depth pressure increases linearly.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Chemistry
A gas is enclosed in a vessel of volume
\( \boldsymbol{V} \) at temperature \( \boldsymbol{T}_{1} \) and pressure \( \boldsymbol{P} \) the vessel is connected to another
vessel of volume \( V / 2 \) by a tube and a stopcock. The second vessel is initially evacuated. If the stopcock is opened, the temperature of the second vessel
becomes \( T_{2} \). The first vessel is
maintained at a temperature of \( T_{1} \)
What is the final pressure \( P_{1} \) in the
apparatus?
A \( \frac{2 P T_{2}}{2 T_{2}+T_{1}} \)
в. \( \frac{2 P T_{2}}{T_{2}+T_{1}} \)
c. \( \frac{P T_{2}}{2 T_{2}+T_{1}} \)
D. \( \frac{2 P T_{2}}{T_{1}+T_{2}} \)
Subject: Maths
Eccentricity of the conic represented by \( \boldsymbol{x}=\frac{\boldsymbol{e}^{\boldsymbol{a}}+\boldsymbol{e}^{-\boldsymbol{a}}}{\mathbf{2} \sqrt{\mathbf{3}}}, \boldsymbol{y}=\frac{\boldsymbol{e}^{\boldsymbol{a}}-\boldsymbol{e}^{-\boldsymbol{a}}}{\mathbf{2}} \) is
Subject: Maths
The direction cosines of the lines
bisecting the internal angle \( \theta \) between the lines whose direction cosines are
\( l_{1}, m_{1}, n_{1} \) and \( l_{2}, m_{2}, n_{2} \) are
\( \mathbf{A} \cdot<l_{1}+l_{2}, m_{1}+m_{2}, n_{1}+n_{2}> \)
B. \( <\frac{l_{1}+l_{2}}{2 \sin \frac{\theta}{2}}, \frac{m_{1}+m_{2}}{2 \sin \frac{\theta}{2}}, \frac{n_{1}+n_{2}}{2 \sin \frac{\theta}{2}}> \)
c. \( <\frac{l_{1}+l_{2}}{2 \cos \frac{\theta}{2}}, \frac{m_{1}+m_{2}}{2 \cos \frac{\theta}{2}}, \frac{n_{1}+n_{2}}{2 \cos \frac{\theta}{2}}> \)
D. none of these
Subject: Physics
If two structures of same cross-
sectional area, but different numerical
apertures \( \mathrm{NA}_{1} \) and \( \boldsymbol{N} \boldsymbol{A}_{2}\left(\boldsymbol{N} \boldsymbol{A}_{2}<\boldsymbol{N} \boldsymbol{A}_{1}\right) \)
are joined longitudinally, the numerical a perture of the combined structure is
A \( \cdot \frac{N A_{1} N A_{2}}{N A_{1}+N_{2}} \)
B. \( N A_{1}+N A_{2} \)
c. \( N A_{1} \)
D. \( N A_{2} \)
Subject: Maths
For two \( 3 \times 3 \) matrices \( A \) and \( B \), let
\( A+B=2 B^{\prime} \) and \( 3 A+2 B=I_{3}, \) where
\( B^{\prime} \) is the transpose of \( B \) and \( I_{3} \) is \( 3 \times 3 \)
identify matrix. Then :
A. \( 5 A+10 B=2 I_{3} \)
В . \( 3 A+6 B=2 I_{3} \)
c. \( 10 A+5 B=3 I_{3} \)
D. \( B+2 A=I_{3} \)
Subject: Maths
If both the mean and the standard
deviation of 50 observations
\( x_{1}, x_{2}, \dots \dots, x_{50} \) are equal to \( 16, \) then the
mean of
\( \left(x_{1}-4\right)^{2},\left(x_{2}-4\right)^{2}, \dots . .\left(x_{50}-4\right)^{2} \) is
A . 525
в. 380
\( c .480 \)
D. 400
Subject: Chemistry
\( C H_{3} C O O H \) is titrated with \( N a O H \)
solution. Which of the following
statement is true?
A. Conductance decreases upto equivalence point, after which it increases.
B. conductance increases upto equivalence point, after which it decreases.
c. conductance first increases (but not rapidly) upto equivalence point and then increases rapidly after equivalence point.
D. None of the above
Subject: Physics
Two identical rods \( A \) and \( B \) are of equal
Iengths and at the same temperature.
The rod \( A \) is placed at smooth surface
but \( \boldsymbol{B} \) is placed at rough surface. If the
temperature of both are raised by the
same amount, then :
A. final length of \( A \) is greater than that of \( B \)
B. final length of both are same
c. final length of \( A \) is lesser than that of \( B \)
D. none of the above
Subject: Maths
If \( \vec{b} \) and \( \vec{c} \) are two non colinear vectors such that \( \vec{a} \|(\vec{b} \vec{c}) \) then prove that \( (\vec{a} \vec{b}) \cdot(\vec{a} \vec{c}) \) is equal to \( |\vec{a}|^{2}(\vec{b} \cdot \vec{c}) \)
Subject: Maths
If \( A=\{1,2,3,4,5,6,7,8\} \) and \( B=\{1,3,5 \)
73, then find \( A-B \) and \( A \cap B \)
\( A \cdot\{3,5\} \) and \{2,4,6\}
B. \{2,4,6) and (1,5\}
c. \{2,4,6,7\} and (1,3,5,6)
D. \{2,4,6,8\} and \{1,3,5,7\}
Subject: Maths
Let \( f(x)= \) \( \left\{\begin{array}{l}1, \quad \text { if } x \text { is a rational number } \\ 0, \quad \text { if } x \text { is an irrational number }\end{array}\right. \)
be a function from \( R \) to \( R \) where \( R \) is
the set of real numbers. Find
(i) \( f\left(\frac{1}{3}\right) \)
(ii) \( f(\sqrt{7}) \)
(iii) \( f(\text { fof })(1.4327) \)
(iv) \( f(\text { fof })(\sqrt{3}) \)
A. 0,0,0,0
0
в. 1,1,1,1
c. 1,0,1,1
D. 0,1,0,1
Subject: Physics
A \( 200 g \) cricket ball is thrown with a
speed of \( 3.0 \times 10^{3} \mathrm{cm} \) sec \( ^{-1} \). What will
be its de Broglie's wavelength? \( \left(h=6.6 \times 10^{-27} g c m^{2} s e c^{-1}\right) \)
\( \mathbf{A} \cdot 1.1 \times 10^{-32} c m \)
B . \( 2.2 \times 10^{-32} \mathrm{cm} \)
C \( .0 .55 \times 10^{-32} \mathrm{cm} \)
D. \( 11.0 \times 10^{-32} \mathrm{cm} \)