AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A solid sphere of radius \( \boldsymbol{R} \) has a charge
\( +2 Q . \) A hollow spherical shell of radius
\( 3 R \) placed concentric with the first
sphere has net charge \( -Q . \) If the inner
sphere is earthed, what will be the
charge on it?
A \( \cdot \frac{2 Q}{3} \)
B. \( \frac{-6}{3} \)
c. \( \frac{Q}{3} \)
D. \( \frac{-2 Q}{3} \)
Subject: Maths
Let \( \boldsymbol{f}: \mathbb{R} \rightarrow \mathbb{R} \) be a differentiable function such that \( \boldsymbol{f}(\mathbf{0})=\mathbf{0}, \boldsymbol{f}\left(\frac{\boldsymbol{\pi}}{\mathbf{2}}\right)=\mathbf{3} \)
and \( \boldsymbol{f}^{\prime}(\mathbf{0})=\mathbf{1 .} \) If \( \boldsymbol{g}(\boldsymbol{x})= \)
\( \int_{x}^{\frac{\pi}{2}}\left[f^{\prime}(t) \operatorname{cosec} t-\cot t \operatorname{cosec} t f(t)\right] d t \) for
\( \boldsymbol{x} \in\left(\mathbf{0}, \frac{\boldsymbol{\pi}}{\mathbf{2}}\right], \) then \( \lim _{\boldsymbol{x} \rightarrow 0} \boldsymbol{g}(\boldsymbol{x})= \)
Subject: Chemistry
Account for the following:
(i) Primary amines \( \left(\boldsymbol{R}-\boldsymbol{N} \boldsymbol{H}_{2}\right) \) have
higher boiling point than tertiary
\( \operatorname{amines}\left(\boldsymbol{R}_{3} \boldsymbol{N}\right) \)
(ii) Aniline does not undergo Friedel-
Crafts reaction.
(iii) \( \left(C H_{3}\right)_{2} N H \) is more basic than
\( \left(C H_{3}\right)_{3} N \) in an aqueous solution
Subject: Physics
Which of the following combination should be selected for better turning of an L.C.R circuit used for
communication?
A. \( R=25 \Omega, L=1 \cdot 5 H, C=45 \mu F \)
в. \( R=25 \Omega, L=1 \cdot 5 H, C=35 \mu F \)
c. \( R=25 \Omega, L=2 \cdot 5 H, C=45 \mu F \)
Subject: Chemistry
Which of the following complexes is used to be as an anticancer agent?
A \( \cdot \) mer \( -\left[\operatorname{Co}\left(N H_{3}\right)_{3} C l\right] \)
B. \( \operatorname{cis}-\left[P t C l_{2} N H_{3}\right)_{2} \)
c. \( \operatorname{cis}-K_{2}\left[P t C l_{2} B r_{2}\right] \)
D. \( N a_{2} \) Co \( C l_{4} \)
Subject: Physics
A constant force \( F \) acts on a particle of
mass \( 1 \mathrm{kg} \) moving with a velocity \( v, \) for
one second. The distance moved in that
time is :
A . 0
в. \( \frac{F}{2} \)
c. \( 2 F \)
D. \( \frac{v}{2} \)
E \( \cdot v+\frac{F}{2} \)
Subject: Physics
Two blocks \( A \) and \( B \) of masses \( M_{A} \) and
\( M_{B} \) respectively, are located \( 1.0 m \) apart on a horizontal surface. The
coefficient of static friction \( \mu_{s} \) between
the block and the surface is \( 0.50 . \) Block
\( A \) is secured to the surface and cannot
move, what is the minimum mass of
Block \( A \) that provides enough gravitational attraction to move Block
B? The universal gravitation constant is \( 6.67 \times 10^{-11} N m^{2} / k g^{2} .(g= \)
\( 9.8 m s^{-2} \)
A \( \cdot 7.5 \times 10^{9} k g \)
в. \( 7.3 \times 10^{16} k g \)
c. \( 14.7 \times 10^{11} k g \)
D. The problem cannot be solved without knowing the mass of Block \( B \)
Subject: Physics
115410
monochromatic point source emitting
light of wavelength \( \lambda=500 \) nm. A thin
lens of circular shape of focal length \( 0.10 m \) is cut into two identical halves
\( L_{1} \) and \( L_{2} \) by a plane passing through a
diameter. The two halves are placed
symmetrically about the central axis
SO with a gap of 0.5 mm. The distance
along the axis from \( S \) to \( L_{1} \) and \( L_{2} \) is
\( 0.15 m, \) while that from \( L_{1} \) and \( L_{2} \) to \( O \)
is 1.30 m. The screen at \( O \) is normal to
\( \boldsymbol{S O} \)
If the third intensity maximum occurs
at point \( A \) on the screen, find distance
OA in mm.
Subject: Maths
100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows:
Number \( \begin{array}{ccc}\mathbf{1 -} & \mathbf{4}- & \mathbf{7 -} \\ \mathbf{4} & \mathbf{7} & \mathbf{1 0}\end{array} \) of letters
Number
of
30
surnames
Determine the median number of
letters in the surnames. Find the mean
number of letters in the surnames?
Also, find the modal size of the
surnames.
Subject: Maths
A man starts from \( O \) moves 500 m turns
by \( 60^{\circ} \) and moves \( 500 m \) again turns by
\( 60^{\circ} \) and moves \( 500 m \) and so on. Find
the displacement after
\( (i) 5 \) th turn \( ,(i i) \) 3rd turn.
A . \( -500 m, 1000 m \)
в. \( 500 m, 500 \sqrt{3} m \)
c. \( 1000 m, 500 \sqrt{3} m \)
D. none of these
Subject: Physics
Match the columns
\begin{tabular}{ll|l|l} 
& A & B \\
a. & green plastic covering & 1. & live wire \\
\hline b. & black plastic covering & 2. & neutral wire \\
c. & red plastic covering & 3. & earth wire
\end{tabular}
A. a-2, b-3, c-1
B. \( a-1, b-2, c-3 \)
c. \( a-3, b-1, c-2 \)
D. \( a-3, b-2, c-1 \)
Subject: Physics
A particle of mass \( 2 \times 10^{-5} k g \) moves
horizontally between two horizontal plates of a charged parallel plate capacitor between which there is an electric field of \( 200 N C^{-1} \) acting upward. A magnetic induction of \( 2.0 T \) is applied at right angles to the electric field in a direction normal to both \( \vec{B} \) and
\( \vec{v} \). If \( g \) is \( 9.8 m s^{-2} \) and the charge on the
particle is \( 10^{-6} C, \) then find the velocity of charge particle so that it continues to move horizontally
\( \mathbf{A} \cdot 2 m s^{-1} \)
B. 20 \( m s^{-1} \)
c. \( 0.2 m s^{-1} \)
D. \( 100 \mathrm{ms}^{-1} \)
Subject: Physics
Two points charges placed at a distance
\( r, \) in the air experience a certain force then the distance at which they will experience the same force in the
medium off dielectric constant K is
A. \( K r \)
в. \( \frac{r}{K} \)
c. \( \frac{r}{\sqrt{K}} \)
D. \( r \sqrt{K} \)
Subject: Chemistry
\( \boldsymbol{C a C O}_{3} \rightarrow \boldsymbol{C a O}+\boldsymbol{C O}_{2} \)
\( \boldsymbol{E}+\boldsymbol{C O}_{2} \rightarrow \boldsymbol{F} \)
\( N a C l+F \rightarrow A+N a H C O_{3} \)
The other compound formed with sodium bicarbonate is:
A. \( C a C l_{2} \)
в. \( N H_{4} C l \)
c. \( N H_{4} O H \)
D. none of these
Subject: Physics
Two monatomic ideal gases 1 and 2 of
molecular masses \( m_{1} \) and \( m_{2} \)
respectively are enclosed in separate containers kept at the same temperature. The ratio of the speed of sound in gas 1 to gas 2 is given by
A. \( \frac{m_{1}}{m_{2}} \)
B. \( \sqrt{\frac{m_{1}}{m_{2}}} \)
c. \( \frac{m_{2}}{m_{1}} \)
D. \( \sqrt{\frac{m_{2}}{m_{1}}} \)
Subject: Physics
The value of \( C_{v} \) for 1 mol of polyatomic
gas is \( (\mathrm{F}= \) number of degrees of freedom) :
A \( \cdot \frac{f R}{2 T} \)
в. \( \frac{f R}{2} \)
c. \( \frac{f R T}{2} \)
D. \( 2 f R T \)
Subject: Maths
A biased coin with probability \( P,(0<p< \)
1) of heads is tossed until a head
appear for the first time. If the
probability that the number of tosses
required is even is \( \frac{2}{5} \) then \( P= \)
\( A \cdot \frac{2}{5} \)
B.
\( c \cdot \frac{1}{3} \)
\( D \cdot \frac{3}{5} \)
Subject: Chemistry
For a real gas (mol. mass \( =30 \) ) if
density at critical point is \( 0.40 \mathrm{g} . \mathrm{cm}^{3} \) and its \( T_{c}=\frac{2 \times 10^{5}}{821} K, \) then calcium
Vander Waal's constant \( a \) (in atm
\( \left.\boldsymbol{L}^{2} \boldsymbol{m} \boldsymbol{o l}^{-2}\right) \)
Subject: Chemistry
Among the following groupings, which represents the collection of isoelectronic species?
A \( \cdot C O, N O^{+}, C N^{-}, C_{2}^{2} \)
B. \( N_{2}, C_{2}^{2-}, C O, N O \)
c. \( N O, C N, N_{2}, O_{2}^{-} \)
D. \( N O^{+}, C_{2}^{2-}, O_{2}^{-}, C O \)
Subject: Maths
If \( p \) is the length of the perpendicular from the origin to the line \( \frac{x}{a}+\frac{y}{b}=1 \)
then which of the following is true?
A \( \cdot \frac{1}{a^{2}}+\frac{1}{b^{2}}+\frac{1}{p^{2}}=0 \)
B . \( a^{2}+b^{2}-p^{2}=0 \)
c. \( \frac{1}{a^{2}}-\frac{1}{b^{2}}=\frac{1}{p^{2}} \)
D. \( \frac{1}{a^{2}}+\frac{1}{b^{2}}-\frac{1}{p^{2}}=0 \)
Subject: Physics
Two points \( A \) and \( B \) are situated at
distance \( x \) and \( 2 x \) respectively from the
nearer pole of a magnet 2cm long. The
ratio of magnetic field at \( A \) and \( B \) is?
A. 4: 1 exactly
B. 4 : 1 approximately
c. 8: 1 exactly
D. 8: 1 approximately
Subject: Biology
Find the correct order of life process in
plants.
A. Pollination \( \rightarrow \) Fertilisation \( \rightarrow \) Plant \( \rightarrow \) Embryo
B. Plant \( \rightarrow \) Embryo \( \rightarrow \) Fertilisation \( \rightarrow \) Pollination
c. Pollination \( \rightarrow \) Fertilisation \( \rightarrow \) Embryo \( \rightarrow \) Plant
D. Embryo \( \rightarrow \) Pollination \( \rightarrow \) Fertilisation \( \rightarrow \) Plant
Subject: Physics
Electric potential due to a point charge \( q \) at a distance \( r \) from is given by
A \( \cdot V=\frac{q}{4 \pi \epsilon_{0}} \)
B. \( V=\frac{q}{4 \pi \epsilon_{0} r^{2}} \)
\( \mathbf{c} \cdot v=\frac{q}{4 \pi \epsilon_{0} r} \)
D. \( v=\frac{q^{2}}{4 \pi \epsilon_{6} r} \)
Subject: Maths
Two chords \( A B \) and \( C D \) of lengths \( 5 \mathrm{cm} \)
and \( 11 \mathrm{cm} \) respectively of a circle are parallel to each other and are on opposite sides of its centre. If the distance between \( A B \) and \( C D \) is \( 6 \mathrm{cm} \)
find the radius of the circle.
Subject: Maths
\( \int_{0}^{\pi} \frac{\boldsymbol{d} \boldsymbol{x}}{\boldsymbol{3}+\boldsymbol{2} \sin \boldsymbol{x}+\cos \boldsymbol{x}}= \)
A . \( \pi / 3 \)
B . \( \pi / 4 \)
c. \( \pi / 6 \)
D . \( \pi / 2 \)
Subject: Physics
A dip needle lies initially in the magnetic meridian when it shows an angle of dip \( \theta \) at a place. The dip circle
is rotated through an angle \( x \) in the
horizontal plane and then it shows an angle of \( \operatorname{dip} \theta \) '. Then \( \frac{\tan \theta^{\prime}}{\tan \theta} \) is
A \( \cdot \frac{1}{\cos x} \)
B. \( \frac{1}{\sin x} \)
c. \( \frac{1}{\tan x} \)
D. \( \cos x \)
Subject: Chemistry
Find out the wavelength of the next line in the series having lines of spectrum of \( \boldsymbol{H} \) -atom of wavelengths \( \mathbf{6 5 6 5} \boldsymbol{\boldsymbol { A }}, \mathbf{4 8 6 3} \boldsymbol{\boldsymbol { A }} \)
\( 4342 A \) and \( 4103 \dot{A} \)
Subject: Physics
In series \( L-C-R \) circuit voltage drop
across resistance is \( 8 V, \) across
inductor is \( 6 V \) and across capacitor is
\( \mathbf{1 2} V \). Then
A. Voltage of the source will be leading in the circuit
B. Voltage drop across each element will be less than the applied voltage.
c. Power factor of the circuit will be \( 3 / 4 \)
D. None of the above
Subject: Maths
If \( \boldsymbol{y}=(\mathbf{1}+\boldsymbol{x})\left(\mathbf{1}+\boldsymbol{x}^{\mathbf{2}}\right)\left(\mathbf{1}+\boldsymbol{x}^{\mathbf{4}}\right) \dots \mathbf{.} \)
\( \left.x^{2^{n}}\right), \) then \( \left(\frac{d y}{d x}\right)_{x=0}= \)
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( \frac{1}{2} \)
\( c \cdot 1 \)
\( D \)
Subject: Maths
The area bounded by the curve \( \boldsymbol{y}=\boldsymbol{e}^{\boldsymbol{x}} \)
and the lines \( \boldsymbol{y}=|\boldsymbol{x}-\mathbf{1}|, \boldsymbol{x}=\mathbf{2} \) is
given by
\( \mathbf{A} \cdot e^{2}+1 \)
B \( \cdot e^{2}-1 \)
c. \( e^{2}-2 \)
D. \( e-2 \)
Subject: Physics
Estimate the mean free path of a
cosmic ray proton in the atmosphere at sea level. Given \( \sigma=10^{-26} \mathrm{cm}^{2} \)
\( \mathbf{A} \cdot 10^{4} c m \)
B. \( 10^{-4} \mathrm{cm} \)
\( \mathbf{c} \cdot 10^{6} c m \)
D. \( 10^{-6} \mathrm{cm} \)
Subject: Chemistry
The ionic conductances of \( A l^{3+} \) and
\( \boldsymbol{S} \boldsymbol{O}_{3}^{2-} \) ions at infinite dilution are \( \boldsymbol{x} \) and \( y \) oh \( m^{-1} c m^{2} m o l^{-1} \) respectively. If
Kohlrausch's law is valid, then molar
conductance of aluminium sulphate at infinite dilution will
be
A \( .3 x+2 y \)
в. \( 3 y+2 x \)
\( c \cdot 2 x+2 y \)
D. \( 3 x+3 y \)
Subject: Chemistry
On passing 0.01 Faraday of elctricity through a solution of aluminum chloride, the weight of Aluminium metal (at.wt. \( =\mathbf{2 7} \) ) deposited on
cathode is:
\( \mathbf{A} \cdot 0.9 g m \)
В. \( 0.09 g m \)
c. \( 2.7 g m \)
D. \( 0.27 g m \)
Subject: Physics
Assertion
Newton's third law of motion is
applicable only when bodies are in
motion.
Reason
Newton's third law applies to all types of
forces. e.g. gravitational, electric or
magnetic force etc.
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: Chemistry
The dissociation constant of \( N H_{4} O H \)
can be given as
\( ^{\mathbf{A}} \cdot_{K_{b}}=\frac{\left(c_{3}\right)^{2}}{\left(c_{2}-c_{3}\right)} \)
B. \( \quad K_{b}=\frac{\left(c_{3}\right)^{2}}{c_{2}} \)
\( ^{\mathbf{c}} \cdot_{K_{b}}=\frac{c_{3}}{\left(c_{2}-c_{3}\right)} \)
D. \( _{K_{b}}=\frac{c_{3}}{\left(c_{1}-c_{2}\right)} \)
Subject: Physics
A car moves on a horizontal track of
radius \( r, \) the speed increasing constantly at rate \( \frac{\boldsymbol{d} \boldsymbol{v}}{\boldsymbol{d} \boldsymbol{t}}=\boldsymbol{a} . \) The
coefficient of friction between road and
tyre is \( \mu . \) Find the speed at which the car
will skid.
A \( \cdot\left[\left(\mu^{2} g^{2}+a^{2}\right) r^{2}\right]^{1 / 4} \)
B . \( \sqrt{\mu g r} \)
\( ^{\mathrm{C}} \cdot\left[\left(\mu^{2} g^{2}-a^{2}\right) r^{2}\right]^{1 / 4} \)
D. \( \sqrt{a r} \)
Subject: Physics
The angular frequency of the damped oscillator is given by \( \omega=\sqrt{\left(\frac{k}{m}-\frac{r^{2}}{4 m^{2}}\right)} \) where \( k \) is the
spring constant, \( m \) is the mass of the oscillator and \( r \) is the damping constant. If the ratio \( \frac{r^{2}}{m k} \) is \( 80 \%, \) the change in time period compared to the undamped oscillator is approximately
as follows:
A. increases by 8\%
B. decreases by 8\%
C. increases by \( 1 \% \)
D. decreases by 1\%
Subject: Chemistry
Identify the products (which can be in the form of ions \( ) \) in the following:
(a) \( \boldsymbol{K} \boldsymbol{F}+\boldsymbol{I} \boldsymbol{F}_{5} \rightarrow \)
(b) \( \boldsymbol{C s} \boldsymbol{F}+\boldsymbol{I} \boldsymbol{F}_{5} \rightarrow \)
(c) \( K C l+I C l \rightarrow \)
\( (d) C s I_{3} \triangle \)
\( (e) R b\left[I C l_{2}\right]_{\rightarrow} \)
\( (f) K[B r I C l]_{\rightarrow} \)
\( (g) I_{2}+I C l+A l C l_{3} \triangle \)
Subject: Chemistry
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{B r} \stackrel{\boldsymbol{a q} \boldsymbol{K O H}}{\rightarrow} \boldsymbol{A} \stackrel{\boldsymbol{K M n O}_{4} / \boldsymbol{H}^{+}}{\rightarrow} \)
\( \boldsymbol{B} \frac{N \boldsymbol{H}_{3}}{\Delta} \boldsymbol{C} \frac{\boldsymbol{B} \boldsymbol{r}_{2}}{a l k a l i} \boldsymbol{D} \)
D is:
A \( \cdot C H_{3} B r \)
в. \( C H_{3} C O N H_{2} \)
c. \( C H_{3} N H_{2} \)
D. \( C H_{2} B r_{2} \)
Subject: Chemistry
The molecular shapes of \( S F_{4}, C F_{4} \) and
\( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{4} \)
A. differ with 1,0 and 2 lone pairs of electrons on the central atom, respectively.
B. differ with 0,1 and 2 lone pairs of electrons on the central atom, respectively.
c. are same with 1,1 and 1 lone pair of electrons on the central atom, respectively.
D. are same with 2,0 and 1 lone pair of electrons on the central atom, respectively.
Subject: Physics
An artificial satellite moving in a
circular orbit around the earth has a
total (kinetic \( + \) potential ) energy \( \frac{\boldsymbol{E}_{0}}{\boldsymbol{4}} \)
Its potential energy is
A \( \cdot \frac{E_{0}}{4} \)
в. \( \frac{E_{0}}{2} \)
c. \( \frac{E_{0}}{8} \)
D. \( E_{0} \)
Subject: Maths
If the 20 th and 21 st terms in the
expansion of \( (1+x)^{40} \) are equal, then
the value of \( x \) is
A \( \cdot \frac{20}{21} \)
в. \( \frac{21}{20} \)
c. 25
D. \( \frac{1}{25} \)
Subject: Physics
A rectangular coil \( A B C D \) is rotated
anticlockwise with a uniform angular velocity about the axis shown in figure.
The axis of rotation of the coil as well as
the magnetic field \( B \) is horizontal. The
induced emf in the coil would be
minimum when the plane of the coil
A. is horizontal
B. makes and angle \( 45^{\circ} \) with direction of magnetic field
\( \mathrm{c} \). is at right angle to the magnetic field
D. makes and angle of \( 30^{\circ} \) with the magnetic field
E. answer required
Subject: Maths
If \( f(x-y), f(x) . f(y) \) and \( f(x+y) \) are
in AP for all \( x, y \) and \( f(0) \neq 0, \) then This question has multiple correct options
A \( . f(2)=f(-2) \)
B. \( f(3)+f(-3)=0 \)
c. \( f^{\prime}(2)+f^{\prime}(-2)=0 \)
D \( \cdot f^{\prime}(3)=f^{\prime}(-3) \)
Subject: Chemistry
The ionization constant and degree of
dissociation of water at \( 25^{\circ} \mathrm{C} \), is:
A \( \cdot 1.8 \times 10^{-9}, 1.8 \times 10^{-16} \)
B . \( 1.8 \times 10^{-16}, 1.8 \times 10^{-9} \)
c. \( 1.8 \times 10^{-12}, 1.8 \times 10^{-14} \)
D. \( 1.8 \times 10^{-14}, 1.8 \times 10^{-12} \)
Subject: Physics
A transverse wave passes through a string with the equation \( \boldsymbol{y}= \)
\( 10 \sin \pi(0.02 x-2 t) \) where \( x \) is in
metres and \( t \) in seconds. The maximum
velocity of the particle in wave motion is
A \( \cdot 63 m s^{-1} \)
B. \( 78 \mathrm{ms}^{-1} \)
c. \( 100 m s^{-1} \)
D. \( 121 \mathrm{ms}^{-1} \)
Subject: Maths
Construct a quadrilateral \( P Q R S \) in
which \( P Q=3.8 \mathrm{cm}, Q R=3.4 \mathrm{cm} \)
\( \boldsymbol{R} \boldsymbol{S}=\mathbf{4 . 5} \mathrm{cm}, \boldsymbol{S} \boldsymbol{P}=\mathbf{5} \mathrm{cm} \) and \( \angle \boldsymbol{Q}= \)
\( 80^{\circ} . \) State which of these is the last
step.
A. From \( Q \), set \( Q R=3.4 \mathrm{cm} \)
B. With \( P \) as center and radius equal to \( 5 \mathrm{cm} \), draw an arc
c. Join \( P S \) and \( R S \)
D. Make \( \angle P Q X=80^{\circ} \)
Subject: Physics
Two particles having position vectors \( \overrightarrow{\boldsymbol{r}}=(\mathbf{3} \overrightarrow{\boldsymbol{i}}+\mathbf{5} \boldsymbol{j}) \boldsymbol{m} \) and \( \overrightarrow{\boldsymbol{r}}_{2}=(-\mathbf{5} \boldsymbol{i}+\boldsymbol{3} \boldsymbol{j}) \boldsymbol{m} \)
are moving with velocities \( \overrightarrow{\boldsymbol{V}}_{1}=(\mathbf{4} \hat{\mathbf{i}}- \)
\( 4 \hat{j}) m s^{-1} \) and \( \vec{V}_{2}=(a \hat{i}-3 \hat{j}) m s^{-1} . \) If
they collide after 2 seconds, the value
of \( a \) is
\( A \cdot-2 \)
B . -4
\( c \cdot-6 \)
\( D .-8 \)
Subject: Chemistry
A solution of 1.25 g of \( \mathrm{P} \) in 50 g of water lowers freezing point by 0.3. Molar mass of 'Pis 94. \( \boldsymbol{K}_{f(\text {water})}=\mathbf{1 . 8 6} \mathrm{K} \mathrm{kg} \mathrm{mol}^{-1} \)
The degree of association of P in water is:
A . \( 60 \% \)
B. 75\%
c. \( 80 \% \)
D. 65\%
Subject: Maths
If the \( z x \) -plane divides the line segment joining (1,-1,5) and (2,3,4) in the ratio \( p: 1, \) then \( p+1= \)
A \( \cdot \frac{1}{3} \)
B. 1: 3
\( c \cdot \frac{3}{4} \)
D. \( \frac{4}{3} \)
Subject: Physics
A simple harmonic oscillator is of mass \( 0.100 \mathrm{kg} . \) It is oscillating with a frequency of \( \frac{5}{\pi} \mathrm{Hz} \). If its amplitude of
vibration is \( 5 \mathrm{cm}, \) the force acting on the particle at its extreme position is
A. 2 N
B. 1.5 N
\( c \cdot 1 \mathrm{N} \)
D. 0.5 N
Subject: Maths
OABC is a tetrahedron express the vectors \( \overrightarrow{B C}, \overrightarrow{C A}, \) and \( \overrightarrow{A B} \) in terms of the vectors \( \overrightarrow{\boldsymbol{O A}}, \overrightarrow{\boldsymbol{O B}} \) and \( \overrightarrow{\boldsymbol{O C}} \)
A \( \cdot \overrightarrow{B C}=\overrightarrow{O C}+\overrightarrow{O B} \quad ; \overrightarrow{C A}=\overrightarrow{O A}+\overrightarrow{O C} \quad ; \overrightarrow{A B}=\overrightarrow{O B}+ \)
\( \overrightarrow{O A} \)
в . \( \overrightarrow{B C}=\overrightarrow{O C}-\overrightarrow{O B} \quad ; \overrightarrow{C A}=\overrightarrow{O A}-\overrightarrow{O C} \quad ; \overrightarrow{A B}=\overrightarrow{O B} \)
\( \overrightarrow{O A} \)
c. \( \overrightarrow{B C}=\overrightarrow{O C}-\overrightarrow{B O} \quad ; \overrightarrow{C A}=\overrightarrow{O A}-\overrightarrow{C O} \quad ; \overrightarrow{A B}=\overrightarrow{O B} \)
\( \overrightarrow{A O} \)
D. none of these
Subject: Chemistry
Assertion
Agriculture output increased several
times after introduction of DDT.
Reason
DDT was the first insecticide used on a
wide scale.
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: Maths
Find \( |\overrightarrow{\boldsymbol{b}}|, \) if \( (\overrightarrow{\boldsymbol{a}}+\overrightarrow{\boldsymbol{b}}) \cdot(\overrightarrow{\boldsymbol{a}}-\overrightarrow{\boldsymbol{b}})=8 \) and
\( |\overrightarrow{\boldsymbol{a}}|=\mathbf{8}|\overrightarrow{\boldsymbol{b}}| \)
Subject: Physics
A ball of mass 'm' moves normal to a
wall with a velocity 'u' and rebounds
with a velocity 'v'. The change in momentum of the ball is (surface of the
wall is smooth):
A. \( m(u+v) \) towards the wall
B. \( m(u-v) \) towards the wall
c. \( m(u+v) \) away from the wall
D. \( m(u-v) \) away from the wall
Subject: Physics
The distance from the surface of the
earth at which above and below the
surface acceleration due to gravity is
same will be
\( ^{\mathrm{A}} \cdot_{h}=\frac{\sqrt{5}-1}{2} R \)
B. \( h=\frac{\sqrt{3}-1}{2} R \)
c. \( h=\frac{\sqrt{3}-1}{3} R \)
D. None of these
Subject: Physics
An air bubble rises from the bottom to
the surface of lake and it is found that
its diameter is doubled. If the height of water barometer is \( 11 \mathrm{m} \), the depth of the lake in meters is
A. \( 70 \mathrm{m} \)
B. 77m
\( c .7 .7 \mathrm{m} \)
D. 78m
Subject: Chemistry
The vapour pressure of the solution of
two liquids \( A\left(P^{\circ}=80 m m\right) \) and
\( B\left(p^{\circ}=120 m m\right) \) is found to be
\( 100 m m \) when \( x_{A}=0.4 . \) The result
shows that:
A. Solution exhibits ideal behaviour
B. Solution shows positive deviations
c. Solution shows negative deviations
D. Solution will show positive deviations for lower concentration and negative deviations for higher concentrations
Subject: Maths
Find the middle term in the expansion
of \( \left(1-2 x+x^{2}\right)^{n} \)
A \( \cdot \frac{(2 n) !}{(n !)^{2}}(-1)^{n} x^{n} \)
B. \( \frac{(2 n) !}{(n !)}(-1)^{n} x^{2} n \)
c. \( \frac{(2 n) !}{(n !)^{2}} x^{n} \)
D. None of these
Subject: Physics
A ball has the dimensions \( 10 m \times \)
\( 12 m \times 14 m . A \) fly starting at one corner
ends up of a diametrically opposite corner. What is the magnitude of its displacement.
A . \( 17 \mathrm{m} \)
B. 26 m
c. \( 36 \mathrm{m} \)
D. 21
Subject: Chemistry
Composition of azurite mineral is:
A. \( C u C O_{3} . C u O \)
в. \( C u\left(H C O_{3}\right)_{2} . C u(O H)_{2} \)
\( \mathbf{c} \cdot 2 C u C O_{3} \cdot C u(O H) \)
D. \( C u C O_{3} .2 C u(O H) \)
Subject: Physics
Match the following:
\( \begin{array}{ll}\text { List- I } & \text { List - II } \\ \text { a) Resistivity } & \text { e) volt } \\ \text { b) Conductivity } & \text { f) siemen } \\ \text { c) emf } & \text { g) ohm-metre } \\ \text { d) conductance } & \text { h) mho / metre }\end{array} \)
\( A \cdot a-e, b-f, c-g, d-h \)
B. \( a-f, b-e, c-g, d-h \)
\( c \cdot a-g, b-h, c-e, d-f \)
\( D \cdot a-h, b-g, c-e, d-f \)
Subject: Chemistry
Assertion
The placement of isotopes in Mendeleev's periodic table overcome in the modern periodic table.
Reason
In modern periodic table, the elements have been allotted places based on their atomic numbers
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: Maths
If the roots of the equation \( x^{2}-8 x+ \)
\( a^{2}-6 a=0 \) are real, then the value of \( a \)
will be
A \( .-2<a<8 \)
в. \( -2 \leq a \leq 8 \)
\( \mathbf{c} \cdot 2<a<8 \)
D. \( 2 \leq a \leq 8 \)