AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
\( N \) similar slabs of cubical shape of
edge \( b \) are lying on the ground. Density
of material of the slab is \( \rho . \) Work done to
arrange them one over the other is :
(Given acceleration due to gravity \( =g) \)
A \( \cdot\left(N^{2}-1\right) b^{3} \rho g \)
в. \( (N-1) b^{4} \rho g \)
c. \( \frac{1}{2}\left(N^{2}-N\right) b^{4} \rho g \)
D. \( \left(N^{2}-N\right) b^{4} \rho g \)
Subject: Chemistry
A complex cation is formed by Pt(in some oxidation state) with ligands (in
proper number so that coordination
number of Pt becomes six)
Which of the following can be its correct IUPAC name:
A. Diammineethylenediaminedithiocyanato-s platinum(II)
B. Diammineethylenediaminedithiocyanato-Splatinate(IV) ion
c. Diammineethylenediaminedithiocyanato-Splatinum(IV) ion
D. Diamminebis (ethylenediamine) dithiocyanato-Splatinum(IV) ion
Subject: Physics
A moving coil galvanometer has 48 turns and area of coil is \( 4 \times 10^{-2} m^{2} . \) If
the magnetic field is \( 0.2 T, \) then to increase the current sensitivity by \( 25 \% \) without changing area (A) and field (B) the number of turns should become:
A . 24
B. 36
\( c \cdot 60 \)
\( D \cdot 54 \)
Subject: Chemistry
In the hydrolysis of organic chloride in
the presence of a large excess of water,
\( \boldsymbol{R C l}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{R O H}+\boldsymbol{H} \boldsymbol{C l} \)
A. Molecularity and order of reaction both are 2
B. Molecularity is 2 but order of reaction is 1
c. Molecularity is 1 but order of reaction is also 1
D. Molecularity is 1 and order of reaction is also 1
Subject: Maths
\( \lim _{x \rightarrow 1}\left(\frac{1+x}{2+x}\right)^{\frac{(1-\sqrt{x})}{(1-x)}}= \)
\( \mathbf{A} \cdot \mathbf{1} \)
в. \( \ln 2 \)
\( c \cdot \sqrt{\frac{2}{3}} \)
D. Does not exist
Subject: Physics
The breakdown electric intensity for air is
\( 3 \times 10^{6} \mathrm{V} / \mathrm{m} . \) The maximum charge that
can be held by a sphere of radius \( 1 \mathrm{mm} \) is
A \( .0 .33 C \)
в. 0.33 пС
\( c .3 .3 C \)
D. \( 3.3 \mu C \)
Subject: Physics
A uniform wire of resistance \( 1 \Omega m^{-1} \) is
bent into a circle of radius 1 m. The
same wire is connected across a
diameter \( A B \) as shown in the figure.
The effective resistance between \( A \) and
\( \boldsymbol{B} \) is:
\( A \)
B. \( \frac{2 \pi}{\pi+2} \Omega \)
c. \( \frac{\pi+4}{2 \pi} \Omega \)
D. \( \frac{2 \pi}{\pi+4} \Omega \)
Subject: Physics
The gravitational field intensity at a point \( 10,000 \mathrm{km} \) from the centre of the
earth is \( 4.8 N k g^{-1} . \) The gravitational
potential at the point is
A \( .-4.8 \times 10^{7} J k g^{-1} \)
B . \( -2.4 \times 10^{7} \mathrm{Jkg}^{-1} \)
C \( .4 .8 \times 10^{6} \mathrm{Jkg}^{-1} \)
D. \( 3.6 \times 10^{6} \mathrm{Jkg}^{-1} \)
Subject: Maths
Suppose \( A \) is any \( 3 \times 3 \) non-singular
matrix and \( (\boldsymbol{A}-\mathbf{3} \boldsymbol{I})(\boldsymbol{A}-\mathbf{5} \boldsymbol{I})=\boldsymbol{O} \)
where \( \boldsymbol{I}=\boldsymbol{I}_{3} \) and \( \boldsymbol{O}=\boldsymbol{O}_{3}, \) If \( \boldsymbol{\alpha} \boldsymbol{A}+ \)
\( \beta A^{-1}=4 I, \) then \( \alpha+\beta \) is equal to
A . 8
B. 7
c. 13
D. 12
Subject: Physics
Four identical mirrors are made to
stand vertically to form a square arrangement as shown in a top view. A ray starts from the midpoint M of mirror Ad and after two reflections reaches
cornor D. Then, angle \( \theta \) must be
A \( \cdot \tan ^{-1}(0.75) \)
B \( \cdot \cot ^{-1}(0.75) \)
c. \( \sin ^{-1}(0.75) \)
D \cdot \( \cos ^{-1}(0.75) \)
Subject: Chemistry
Name the following halides according to IUPAC system and classify them
as alkyl, allyl, benzyl (primary, secondary, tertiary), vinyl or aryl
halides:
i) \( \left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C H C H}(\boldsymbol{C l}) \boldsymbol{C H}_{3} \)
ii) \( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right) \boldsymbol{C H}\left(\boldsymbol{C}_{2} \boldsymbol{H}_{5}\right) \boldsymbol{C l} \)
iii) \( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C}\left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C H}_{2} \boldsymbol{I} \)
iv) \( \left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{C C H}_{2} \boldsymbol{C H}(\boldsymbol{B r}) \boldsymbol{C}_{6} \boldsymbol{H}_{5} \)
v) \( \boldsymbol{C H}_{3} \boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right) \boldsymbol{C H}(\boldsymbol{B r}) \boldsymbol{C H}_{3} \)
vi) \( \boldsymbol{C H}_{3} \boldsymbol{C}\left(\boldsymbol{C}_{2} \boldsymbol{H}_{5}\right)_{2} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{B r} \)
vii) \( \boldsymbol{C H}_{3} \boldsymbol{C}(\boldsymbol{C l})\left(\boldsymbol{C}_{2} \boldsymbol{H}_{5}\right) \boldsymbol{C H}_{2} \boldsymbol{C H}_{3} \)
viii) \( \boldsymbol{C H}_{3} \boldsymbol{C H}= \)
\( \boldsymbol{C}(\boldsymbol{C l}) \boldsymbol{C H}_{2} \boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right)_{2} \)
ix) \( \boldsymbol{C H}_{3} \boldsymbol{C H}=\boldsymbol{C H C}(\boldsymbol{B r})\left(\boldsymbol{C H}_{3}\right)_{2} \)
\( \mathbf{x} \) ) \( \boldsymbol{p}-\boldsymbol{C l} \boldsymbol{C}_{6} \boldsymbol{H}_{4} \boldsymbol{C H}_{2} \boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right)_{2} \)
xi) \( \boldsymbol{m}-\boldsymbol{C l} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C}_{6} \boldsymbol{H}_{4} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C}\left(\boldsymbol{C} \boldsymbol{H}_{3}\right)_{3} \)
xii) \( o-B r- \)
\( \boldsymbol{C} \quad \mathscr{C H}\left(\boldsymbol{C H}_{3}\right) \boldsymbol{C H}_{2} \boldsymbol{C H}_{3} \)
Subject: Maths
What is the volume in cubic
centimetres of a 0.6 L bottle of
shampoo?
A \( .6000 \mathrm{cm}^{3} \)
B. \( 60 \mathrm{cm}^{3} \)
\( c \cdot 400 c m^{3} \)
D. \( 600 \mathrm{cm}^{3} \)
Subject: Chemistry
Assertion
Wrought iron is more malleable and
ductile than steel.
Reason
It contains slightly less percentage of
carbon.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect and Reason is correct
Subject: Physics
Assuming that \( m \ll M, \) find at what
distance \( x \) from the upper end of the rod
the bullet must strike for the
momentum of the system "bullet-rod" to remain constant during the impact.
A \( \cdot x \approx \frac{1}{3} l \)
в. \( x \approx \frac{4}{3} l \)
c. \( _{x} \approx \frac{4}{5} l \)
D. \( _{x} \approx \frac{2}{3} l \)
Subject: Maths
The value of \( \cos ^{2} 30^{0}-\cos ^{2} 60^{0}- \)
\( \cos 60^{0} \) is
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( \frac{1}{2} \)
\( c \cdot \frac{3}{4} \)
D.
Subject: Maths
Use the principle of mathematical induction to prove that \( \boldsymbol{a}+(\boldsymbol{a}+\boldsymbol{d})+ \)
\( (\boldsymbol{a}+\mathbf{2 d})+\ldots .+[\boldsymbol{a}+(\boldsymbol{n}-\mathbf{1}) \boldsymbol{d}]= \)
\( \boldsymbol{n} / 2[2 \boldsymbol{a}+(\boldsymbol{n}-1) \boldsymbol{d}] \)
Subject: Chemistry
4- pentenoic acid when treated with \( I_{2} \)
and \( N a H C O_{3} \) gives:
A. 4,5 -diiodopentanoic acid
B. 5 - idomethyl - dihydrofuran -2-one
c. 5-iodo tetrahydropyran-2-one
D. 4-pentenolyiodide
Subject: Maths
In a circle of radius \( 25 \mathrm{cm} \) two parallel chords of the length \( 14 \mathrm{cm} \) and \( 48 \mathrm{cm} \) respectively, are drawn on the same
side of the centre. The distance between
them is
A . \( 14 \mathrm{cm} \)
B. \( 24 \mathrm{cm} \)
\( c \cdot 17 \mathrm{cm} \)
D. \( 31 \mathrm{cm} \)
Subject: Physics
If a charge on the body is 1 nC, then how many electrons are present on the body?
A \( \cdot 1.6 \times 10^{19} \)
B . \( 6.25 \times 10^{9} \)
c. \( 6.25 \times 10^{27} \)
D. \( 6.25 \times 10^{28} \)
Subject: Maths
\( \triangle L M N \sim \triangle X Y Z . \ln \triangle L M N, L M= \)
\( 6 \mathrm{cm}, M N=6.8 \mathrm{cm}, L N=7.6 \mathrm{cm} \) and
\( \frac{L M}{X Y}=\frac{4}{5} ; \) Construct \( \triangle X Y Z \)
Subject: Physics
A letter \( A \) is constructed of a uniform
wire of resistance \( 1 \Omega / c m . \) The sides of
the letter are \( 20 \mathrm{cm} \) and the cross piece
in the middle is \( 10 \mathrm{cm} \) long.The resistance between the ends of the legs will be:
A . \( 32.4 \Omega \)
B. \( 28.7 \Omega \)
c. \( 26.7 \Omega \)
D. \( 24.7 \Omega \)
Subject: Physics
Q Type your question-
She placed a lighted candle on one end
of a laboratory table, a screen on its other end and the lens in between the
two as shown in the figure. She
adjusted the positions of the three to
obtain a sharp image of the candle
flame on the screen.
Shoe now removes the candle flame and
obtains the image of a distant lamp on
an electric pole. She would be able to
get a sharp image of the lamp on the
screen by moving
A. the screen towards of the lens or the lens towards the screen
B. the screen towards of the lens or the lens away from the screen
c. the screen away from the lens or the lens towards the screen
D. neither the screen
Subject: Physics
A charged particle moving with constant velocity passes through a region of space without any change in its velocity. If \( \mathrm{E} \) and \( \mathrm{B} \) represent electric and magnetic fields in that region respectively,what is the \( \mathrm{E} \) and \( \mathrm{B} \) in this space?
A \( . E=0 \) and \( B=0 \)
B. \( E=0 \) and \( B \neq 0 \)
c. \( E \neq 0 \) and \( B=0 \)
D. \( E \neq 0 \) and \( B \neq 0 \)
Subject: Maths
The number of solid spheres, each of diametres \( 6 \mathrm{cm}, \) that could be moulded to form a solid metal cylinder of height \( 45 \mathrm{cm} \) and diameter \( 4 \mathrm{cm} \) is
\( A \cdot 3 \)
B. 4
\( c .5 \)
\( D \)
Subject: Maths
The value of \( \int(x-1) e^{-x} d x \) is equal to
This question has multiple correct options
\( \mathbf{A} \cdot-x e^{x}+C \)
B . \( x e^{x}+C \)
c. \( -x e^{-x}+C \)
D. \( x e^{-x}+C \)
Subject: Maths
Find the domain of the function \( \boldsymbol{f}(\boldsymbol{x})=\frac{\mathbf{1}}{\sqrt{|\boldsymbol{x}|-\boldsymbol{x}}} \)
A. \( [0, \infty) \)
(n)
в. \( (-\infty, 0) \)
\( c \cdot[1, \infty) \)
D. \( (-\infty, 0 \)
Subject: Physics
One surface of a lens is convex and the
other is concave. If the radii of
curvatures are \( \boldsymbol{R}_{1} \) and \( \boldsymbol{R}_{2}, \) then the lens
Will be convex, if :
A. \( R_{1}<R_{2} \)
в. \( R_{1}>R_{2} \)
c. \( R_{1}=R_{2} \)
D. None of these
Subject: Physics
Two concentric coils of 10 turns each
are placed in the same plane. Their radii are \( 20 \mathrm{cm} \) and \( 40 \mathrm{cm} \) and carry \( 0.2 \mathrm{A} \) and 0.3 A current respectively in opposite directions. The magnetic induction (in tesla) at the centre is :
A \( \cdot \frac{3}{4} \mu_{0} \)
в. \( \frac{5}{4} \mu_{0} \)
c. \( \frac{7}{4} \mu_{0} \)
D. \( \frac{9}{4} \mu_{0} \)
Subject: Chemistry
Bhawna took a pale green substance \( \boldsymbol{A} \) in a test tube and heated it over the
flame of a burner. A brown coloured
residue \( \boldsymbol{B} \) was formed along with the evolution of two gases with buring smell of sulphur. Identify \( \boldsymbol{A} \) and \( \boldsymbol{B} \)
Write the chemical reaction involved.
Subject: Chemistry
Assertion
Molecular formula shows the exact
number of different types of atoms
present in a molecule of a compound.
Reason
Molecular formula can be obtained
directly from empirical formula which represents the simplest whole number ratio of various atoms present in a
compound.
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: Physics
A battery has six cells in series and each cell has an electromagnetic force \( 1.5 V \) and internal resistance \( 1 \Omega . \) If
an external load of resistance \( 24 \Omega \) is
connected to it. The potential drop across the load is
A. \( 7.2 V \)
B. \( 0.3 V \)
c. \( 6.8 V \)
D. \( 0.4 V \)
Subject: Chemistry
Which of the following statement is
incorrect?
\( \mathbf{A} \cdot S O_{2}, \mathrm{CO}, \mathrm{Pb} \) and \( \mathrm{Hg} \) are pollutants
B. Methyl isocyanate and oil spills from ships are contaminants
C . Sea water is receptor for \( C O_{2} \)
D. Microorganisms is sink for dead animals and plants
Subject: Physics
Water stored in a tank flows out through
a hole of radius \( 1 \mathrm{mm} \) at a depth \( 10 \mathrm{m} \)
below the surface of water.The rate of
flow of water in \( m^{3} / s \) will be
A \( .4 .4 \times 10^{-5} \)
B. \( 4.4 \times 10^{-4} \)
c. \( 4.4 \times 10^{-3} \)
D. \( 4.4 \times 10^{-2} \)
Subject: Physics
A particle performing SHM with a frequency of \( 5 \mathrm{Hz} \) and amplitude \( 2 \mathrm{cm} \) is initially in the positive extreme position. The equation for its displacement is
A. \( x=0.02 \sin 10 \pi t \mathrm{m} \)
B. \( x=0.02 \sin 5 \pi t \mathrm{m} \)
c. \( x=0.02 \cos 10 \pi t \mathrm{m} \)
D. \( x=0.02 \cos 5 \pi t \mathrm{m} \)
Subject: Maths
Find the value of
\( (b-c)(c-a)(a-b)+ \)
\( (b-\omega c)(c-\omega a)(a-\omega b)+ \)
\( \left(b-\omega^{2} c\right)\left(c-\omega^{2} a\right)\left(a-\omega^{2} b\right) \)
Subject: Physics
A bomb of mass 3.0 kg explodes in air
into two pieces of masses \( 2.0 \mathrm{kg} \) and 1.0 kg. The smaller mass goes at a speed of \( 80 \mathrm{m} / \mathrm{s} \). The total energy imparted to the two fragments is:
A. \( 1.07 \mathrm{kJ} \)
J
B . 2.14 k
c. \( 2.4 \mathrm{kJ} \)
D. \( 4.8 \mathrm{kJ} \)
Subject: Physics
A solenoid of inductance \( L \) and length \( l \)
and mass \( m, \) whose windings are made
of material of density \( D \) and resistivity
is \( \rho, \) (the winding resistance is \( \boldsymbol{R} \) ). Find out the inductance in terms of others.
A \( \cdot \frac{\mu_{0}}{4 \pi l} \frac{R m}{\rho D} \)
В. \( \frac{\mu_{0}}{4 \pi R} \frac{l m}{\rho D} \)
c. \( \frac{\mu_{0}}{4 \pi l} \frac{R^{2} m}{\rho D} \)
D. \( \frac{\mu_{0}}{2 \pi R} \frac{l m}{\rho D} \)
Subject: Physics
Assertion
When a pulse on string reflects from free end, the resultant pulse is formed
in such a way that slope of string at free end is zero.
Reason
Zero resultant slope ensures that there
is no force component perpendicular to string.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
Subject: Physics
Find the component of \( \vec{r} \) in the direction of \( \vec{a}: \)
A \( \cdot \frac{(\vec{r} \cdot \vec{a}) \vec{a}}{a^{2}} \)
B. \( \frac{(\vec{r} \cdot \vec{a}) \vec{a}}{a} \)
c. \( \frac{(\vec{r} \times \vec{a}) \vec{a}}{a^{2}} \)
D. None of above
Subject: Chemistry
The conductivity of N/50 solution of KC
in a cell at \( 25^{\circ} \mathrm{C} \) is \( 0.002765 \mathrm{Scm}^{-1} . \) If
the resistance of a cell containing this
solution is 400 ohm, cell constant will
be:
A \( .1 .106 \mathrm{cm}^{-1} \)
В. \( 3.101 \mathrm{cm}^{-1} \)
D. None of these
Subject: Chemistry
An organic compound having molecular mass 60 is found to contain \( C=20 \% \)
\( \boldsymbol{H}=\mathbf{6 . 6 7 \%} \) and \( \boldsymbol{N}=\mathbf{4 6 . 6 7} \%, \) while rest
is oxygen. On heating, it gives \( \boldsymbol{N} \boldsymbol{H}_{3} \) along with a solid residue. The solid residue gives violet colour with alkaline
copper sulphate solution. The compound is:
A \( \cdot C H_{3} N C O \)
в. \( C H_{3} C O N H_{2} \)
c. \( \left(N H_{2}\right)_{2} C O \)
D. \( C H_{3} C H_{2} C O N H_{2} \)
Subject: Maths
The odds that a book will be reviewed
favourably by three independent critics are 5 to 2,4 to 3 and 3 to 4 respectively; what is the probability that of three reviews a majority will be favourable?
A \( \cdot p=\frac{149}{343} \)
В. \( p=\frac{209}{343} \)
c. \( _{p}=\frac{129}{3 \frac{13}{33}} \)
D. \( _{p}=\frac{185}{343} \)
Subject: Biology
Choose the right from the following.
(i) In light, hormone auxin, helps the cells to grow longer in plants.
(ii) Plant hormone gibberellins help in growth of a stem.
(iii) Cytokinin inhibits cell division.
(iv) Abscisic acid promotes growth in plants.
A . (I) and (iii) are correct
B. (ii) and (iv) are correct.
c. (i) and (ii) are correct.
D. (i) and (iv) are correct.
Subject: Chemistry
The name of the compound
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5} \boldsymbol{N} \boldsymbol{O}_{2}\right] \boldsymbol{C l}_{2} \) will be?
A. pentaamminonitrocobalt(II) chloride
B. pentaamminenitrochloridecobaltate(III)
c. pentaamminenitrocobalt(III) chloride
D. pentanitrosoamminechlorocobaltate(III)
Subject: Physics
A conducting disc of radius R is rotating with angular velocity \( \omega . \) Mass of electron is and charged e. If electrons are the
current carries in a conductor, the
potential difference between the center and the edge of the disc is:
\( ^{A} \cdot \frac{m \omega^{2} R^{2}}{e} \)
B. \( \frac{m \omega^{2} R^{2}}{4 e} \)
c. \( \frac{m \omega^{2} R^{2}}{3 e} \)
D. \( \frac{m \omega^{2} R^{2}}{2 e} \)
Subject: Maths
Solve for \( x \) and \( y \) by using method of
substitution:
\( \mathbf{0 . 2 x + 0 . 3 y}=\mathbf{1 . 3 ; 0 . 4 x + 0 . 5 y}=\mathbf{2 . 3} \)
A. -2,-3
B. 2,-3
c. 2,3
D . -2,3
Subject: Physics
\( \chi_{1} \) and \( \chi_{2} \) are susceptibilities of \( a \)
diamagnetic substance at
temperatures \( T_{1} K \) and \( T_{2} K \)
respectively, then,
A \( \cdot \chi_{1} T_{1}=\chi_{2} T_{2} \)
B . \( x_{1}=x_{2} \)
c. \( \chi_{1} \sqrt{T_{1}}=\chi_{2} \sqrt{T_{2}} \)
D. \( \chi_{1} T_{2}=\chi_{2} T_{1} \)
Subject: Physics
Two rods \( A \) and \( B \) of the same material
and length have radii \( r_{1} \) and \( r_{2} \)
respectively. When they are rigidly fixed at one end twisted by the same torque applied at the other end, the ratio \( \left[\begin{array}{lllllll}\text {the} & \text {angle} & \text {of} & \text {twist} & \text {at} & \text {the} & \text {er} \\ \hline \text {the} & \text {angle} & \text {of} & \text {twist} & \text {at} & \text {the} & \text {er}\end{array}\right. \)
equals to:
A \( \cdot \frac{r_{1}^{2}}{r_{2}^{2}} \)
B \( \cdot \frac{r_{1}^{3}}{r_{2}^{3}} \)
\( c \cdot \frac{r_{2}^{4}}{r_{1}^{4}} \)
D \( \cdot \frac{r_{1}^{4}}{r_{2}^{4}} \)
Subject: Maths
The plane \( \boldsymbol{x}-\mathbf{2} \boldsymbol{y}+\boldsymbol{z}-\boldsymbol{6}=\mathbf{0} \) and the
line \( \frac{x}{1}=\frac{y}{2}=\frac{z}{3} \) are related as
A. Parallel to the plane
B. At right angle to the plane
c. Lies in the plane
D. Meets the plane obliquely
Subject: Physics
Two glass prisms \( P_{1} \) and \( P_{2} \) are to be combined together to produce dispersion without deviation. The
angles of the prisms \( P_{1} \) and \( P_{2} \) are
selected as \( 4^{\circ} \) and \( 3^{\circ} \) respectively. If the refractive index of prism \( P_{1} \) is 1.54 , then
that of \( P_{2} \) will be
A . 1.48
B. 1.58
\( c \cdot 1.62 \)
D. 1.72
Subject: Physics
Find the amplitude response \( \left|\frac{V_{2}}{V_{1}}\right| \) for
the ciircuit shown in figure. Determine
the half-power frequency.
A \( \cdot \frac{1}{B C} \)
B. \( \frac{2}{R C} \)
\( c \cdot \frac{4}{R C} \)
D.
Subject: Physics
If \( \delta_{1} \) and \( \delta_{2} \) are the angles of dip observed in two vertical planes at right angles to each other and \( \delta \) is the true
value of dip then :
A \( \cdot \tan ^{2} \delta=\tan ^{2} \delta_{1}+\tan ^{2} \delta_{2} \)
B . \( \cot ^{2} \delta=\cot ^{2} \delta_{1}+\cot ^{2} \delta_{2} \)
\( ^{\mathrm{C}} \tan ^{2} \delta=\frac{\tan ^{2} \delta_{1}+\tan ^{2} \delta_{2}}{\tan ^{2} \delta_{1} \tan ^{2} \delta_{2}} \)
D. \( \cot ^{2} \delta=1+\cot ^{2} \delta_{1} \cos ^{2} \delta_{2} \)
Subject: Physics
A boat moving perpendicular to the bank with a velocity of \( 7.2 \mathrm{km} / \mathrm{h} \). The
current carries it \( 150 \mathrm{m} \) downstream,
find the velocity of the current.(The
width of the river is \( 0.5 \mathrm{km} \) )
A \( \cdot 0.4 m s^{-1} \)
В. \( 1.2 m s^{-1} \)
c. \( 0.5 m s^{-1} \)
D. \( 0.6 m s^{-1} \)
Subject: Maths
If \( (2 \bar{i}+4 \bar{j}+2 \bar{k}) \times(2 \bar{i}-x \bar{j}+5 \bar{k})= \)
\( 16 \bar{i}-6 \bar{j}+2 x \bar{k}, \) then the value of \( x \) is
\( A \cdot 2 \)
B. -2
\( c . \)
D. 3
Subject: Maths
Chord \( A B \) of the circle \( x^{2}+y^{2}=100 \)
passes through the point (7,1) and
subtends an angle of \( 60^{\circ} \) at the
circumference of the circle. If \( m_{1} \) and
\( m_{2} \) are the slopes of two such chords
then the value of \( m_{1} m_{2} \) is
A . -1
B.
c. \( 7 / 12 \)
D. -
Subject: Maths
If \( \left(\sin ^{-1} x\right)^{2}+\left(\sin ^{-1} y\right)^{2}+\left(\sin ^{-1} z\right)^{2}= \)
\( \frac{3 \pi^{2}}{4}, \) then find the minimum value of
\( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z} \)
Subject: Chemistry
\( A \)
\( 0.1(\mathrm{M}) \) solution of an acid HA of density \( 1.01 \mathrm{gm} / \mathrm{ml} \) is taken in a beaker. The molec ular mass of HA is \( 300 \mathrm{g} / \mathrm{mol} \) The freezing point of solution is
\( 0.2087^{\circ} \mathrm{C} . \) For \( \mathrm{H}_{2} \mathrm{O}, \quad K_{f}=1.86 \mathrm{K} / \mathrm{m} \)
What is the degree of dissociation of HA i
n its \( 0.1(\mathrm{M}) \) aqueous solution (in percentage) ?
A . \( 10 \% \)
B. 20\%
c. \( 25 \% \)
D. \( 55.56 \% \)
Subject: Physics
The radius of an atom is of the order of:
A \( \cdot 10^{-12} \mathrm{cm} \)
B . \( 10^{-14} \mathrm{cm} \)
\( c \cdot 10^{-10} \mathrm{cm} \)
\( D \cdot 10^{-8} \mathrm{cm} \)
Subject: Physics
Observe the given situation and answer the following questions. Rahul and Ravi are playing in a ground. They start
running from the same point \( x \) simultaneously in the ground and reach point \( Y \) at the same time by following paths marked 1 and 2 respectively, as shown in the figure.
Which of the following is correct
statement for the given situation?
A. Rahul covers a longer distance with a lower speed
B. Rahul covers a longer distance with a higher speed
C. Rahul and Ravi both cover different distances with same speed.
D. Ravi covers a shorter distance with higher speed
Subject: Physics
Dimension of capacitance is?
A \( \cdot M^{-1} L^{-2} A^{2} T^{4} \)
B. \( M L^{2} A^{-2} T^{-4} \)
c. \( M L A^{-1} T^{4} \)
D. \( M^{-1} L^{-1} A^{2} T^{2} \)
Subject: Physics
Two particles of mass \( m \), constrained to move along the circumference of a smooth circular hoop of equal mass \( m \)
are initially located at opposite ends of
a diameter and given equal velocities \( v_{0} \)
shown in the figure. The entire
arrangement is located in gravity free space. Their velocityjust before collision is?
\( A \)
в. \( \frac{\sqrt{3}}{2} v_{0} \)
c. \( \frac{2}{\sqrt{3}} v \)
D. \( \frac{\sqrt{7}}{3} v_{0} \)
Subject: Physics
The number of vectors of unit length perpendicular to vectors \( \overline{\boldsymbol{a}}=(\mathbf{1}, \mathbf{1}, \mathbf{0}) \& \)
\( \bar{b}=(0,1,1) \) is:
\( A \)
B. 2
\( c \cdot 3 \)
D. \( \infty \)
Subject: Biology
Assertion
In humans, the gamete contributed by the male determines whether the child
produced will be male or female.
Reason

Sex in humans is a polygenic trait
depending upon a cumulative effect of
some genes on X-chromosome and
some on \( Y \) - chromosome.
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
The balanced equation in basic
medium is :
\( \boldsymbol{C l O}_{2}+\boldsymbol{S b O}_{2}^{-} \rightarrow \boldsymbol{C l O}_{2}^{-}+\boldsymbol{S b}(\boldsymbol{O H})_{6}^{-} \)
A \( \cdot 2 C l O_{2}+S b O_{2}^{-}+2 O H^{-}+2 H_{2} O \rightarrow 2 C l O_{2}^{-}+ \)
\( S b(O H)_{6} \)
B . \( 2 C l O_{2}+5 S b O_{2}^{-}+2 O H^{-}+3 H_{2} O \rightarrow 2 C l O_{2}^{-}+ \)
\( 2 S b(O H)_{6} \)
\( \mathrm{c} \cdot 2 \mathrm{ClO}_{2}+\mathrm{SbO}_{2}^{-}+3 \mathrm{OH}^{-}+4 \mathrm{H}_{2} \mathrm{O} \rightarrow 2 \mathrm{ClO}_{2}^{-}+ \)
\( 3 S b(O H)_{6} \)
D. None of these