Answers posted by priyanka.clay6

0 votes

The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is 20 cm, the length of the open organ pipe is :

answered Feb 26, 2020

Fundamental frequency of open pipe $= 3^{rd}$ harmonic of closed organ pipe $\qquad \large\frac{V}{2...

0 votes

At what temperature will the rms speed of oxygen molecules become just sufficient for escapig from the Earth's atmosphere ?
(Given :
Mass of oxygen molecule (m) = $2.76 \times 10^{-25} kg$
Boltzmann's constant $(K_B) = 1.38 \times 10^{-23} JK^{-1}$ )

answered Feb 26, 2020

$V_{rms} = \sqrt{\large\frac{3K_B T}{m_{O_2}}}$Escape velocity $= 11200\;m/s$$\qquad \qquad \;\;\; ...

0 votes

The effciency of an ideal heat engine workong between the freezing point and boiling point of water, is

answered Feb 26, 2020

Efficiency of ideal heat engine $\qquad \eta = (\large 1 - \frac{T_2}{T_1})\qquad \qquad $ $T_2; \te...

0 votes

If $0 \leq x \leq 2\pi$, then the number of real values of $x$, which satisfy the equation $\cos x+\cos 2x+\cos 3x+\cos 4x=0$, is :

answered Feb 20, 2020

Given $\cos x + \cos 2x + \cos3x+ \cos 4x = 0$$(\cos x + \cos 4x) + (\cos 2x+\cos 3x) = 0$$\implies...

0 votes

Let two fair six-faced dice $A$ and $B$ be thrown simultaneously. If $E_1$ is the event that die $A$ shows up four, $E_2$ is the event that die $B$ shows up two and $E_3$ is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true ?

answered Feb 20, 2020

$P(E_1) = \frac{1}{6} , \;\; P(E_2) = \frac{1}{6}, \;\; P(E_3) = \frac{1}{2}$$P(E_1 \cap E_2) = \fra...

0 votes

If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true ?

answered Feb 20, 2020

$S.D = \sqrt{\large\frac{\sum d^2}{N} -(\frac{\sum d}{N})^2}$$\implies \large\frac{4+9+a^2 +121}{4} ...

0 votes

Let $\overrightarrow{a}, \; \overrightarrow{b}$ and $\overrightarrow{c}$ be three unit vectors such that $ \overrightarrow{a} \times (\overrightarrow{b} \times \overrightarrow{c} ) = \frac{\sqrt 3}{2} (\overrightarrow{b} + \overrightarrow{c})$. If $\overrightarrow{b}$ is not parallel to $\overrightarrow{c}$, then the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is :

answered Feb 20, 2020

$\overrightarrow{a} \times (\overrightarrow{b} \times \overrightarrow{c}) =\frac{ \sqrt{3}}{2} (\ove...

0 votes

If the line, $\frac{x-3}{2} = \frac{y+2}{-1} = \frac{z+4}{3}$ lies in the plane, $lx + my - z =9$, then $l^2 + m^2$ is equal to

answered Feb 20, 2020

The point on the line is $P=(3,-2,-4)$$P$ lies on the $lx+my-z=9$$\implies 3l-2m +4=9$$\implies 3l -...

0 votes

The distance of the point $(1, −5, 9)$ from the plane $x−y+z=5$ measured along the line $x=y=z$ is :

answered Feb 20, 2020

Let $Q$ be $(1, -5,9)$Hence $\large\frac{x-0}{1} =\frac{y-0}{1}=\frac{z-0}{1}$Equation of line is $\...

0 votes

The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal to half of the distance between its foci, is :

answered Feb 20, 2020

Length of the latus rectum is $\large\frac{2b^2}{a}=8$$\implies b^2=4a$$\qquad\;\; 2b = \frac{1}{2}(...

0 votes

Let P be the point on the parabola, $y^2=8x$ which is at a minimum distance from the centre C of the circle, $x^2+(y+6)^2=1$. Then the equation of the circle, passing through C and having its centre at P is :

answered Feb 19, 2020

https://clay6.com/mpaimg/1821_a.jpg Normal at $P(at^2, 2at)$ is $y+tx= 2at+at^3$Given it passes $(0,...

0 votes

If one of the diameters of the circle, given by the equation, $x^2+y^2−4x+6y−12=0$, is a chord of a circle S, whose centre is at (−3, 2), then the radius of S is :

answered Feb 18, 2020

Given :$\qquad x^2+y^2-4x+6y-12=0$centre $(2,-3)$radius $\sqrt{2^2+(-3)^2+12}=5$Distance between two...

0 votes

The centres of those circles which touch the circle, $x^2+y^2−8x−8y−4=0$, externally and also touch the x-axis, lie on :

answered Feb 18, 2020

$x^2 + y^2 -8x -8y -4 = 0$Hence the coordinates of the centre of the circle is $(4,4)$$\therefore $ ...

0 votes

Two sides of a rhombus are along the lines, $x−y+1=0$ and $7x−y−5=0$. If its diagonals intersect at $(−1, −2)$, then which one of the following is a vertex of this rhombus ?

answered Feb 18, 2020

https://clay6.com/mpaimg/1820_a.jpgLet us find the coordinates of $A,$by solving $x-y = -1$ and $7x ...

0 votes

If a curve $y = f(x)$ passes through the point $(1, -1)$ and satifies the differential equation, $y(1+xy) dx = x ;dy$, then $f(-\frac{1}{2})$ is equal to :

answered Feb 18, 2020

Given : $y (1+xy)dx = x \;dy$$\implies {\large\frac{y}{x}} (1+xy)= \large\frac{dy}{dx}$This is a hom...

0 votes

A spring of force constant k is cut into lengths of ratio 1 : 2 : 3. They are connected in series and the new force constant is k'. Then they are connected in parallel and force constant is k''. Then k' : k'' is :

answered Feb 16, 2020

Let total length be $6 \ell$ and force constant $k$Cut in the ratio $1:2:3$$k_1$ Force constant of l...

0 votes

The diagrams below show regions of equipotentials.

A positive charge is moved from A to B in each diagram.

answered Feb 16, 2020

Work done $= q[V_B - V_A]$It is Independent of path.$\therefore $ Work done is same in all cases.

0 votes

The x and y coordinates of the particle at any time are $x = 5t – 2t^2$ and $y = 10 t$ respectively, where x and y are in meters and t in seconds. The acceleration of the particle at t = 2s is :

answered Feb 16, 2020

$x = 5t-2t^2$ and $y = 10t$Velocity $V_x={\large\frac{dx}{dt}}=5-4t$ and$\qquad\qquad V_y={\large\f...

0 votes

The de-Broglie wavelength of a neutron in thermal equilibrium with heavy water at a temperature T (Kelvin) and mass m, is :

answered Feb 16, 2020

Kinetic energy of heavy water at temperature $T$ is $KE = K = \frac{3}{2}k T$de Broglie wavelength o...

0 votes

Young's double slit experiment is first performed in air and then in a medium other than air. It is found that $8^{th}$ bright fringe in the medium lies where $5^{th}$ dark fringe lies in air. The refractive index of the medium is nearly :

answered Feb 16, 2020

In YDSE${\large y_{_{dark}}}\;n^{th} = \large\frac{(2n-1) \lambda D}{2}=\frac{9 \lambda D}{2}$${\lar...

0 votes

A U tube with both ends open to the atmosphere, is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a distance of 10 mm above the water level on the other side. Meanwhile the water rises by 65 mm from its original level (see diagram). The density of the oil is :

answered Feb 16, 2020

Pressure at point $B =P_A +\rho_{\text{due to oil column}}$$\qquad \qquad \qquad \qquad= P_A +\rho_{...

0 votes

In an electromagnetic wave in free space the root mean square value of the electric field is $E_{rms} = 6\; V/m$. The peak value of the magnetic field is :

answered Feb 16, 2020

For electromagnetic wave$c = \large\frac{E_{peak}}{B_{peak}}$$E_{peak} = \sqrt{2} \; E_{rms} = \sqrt...

0 votes

A spherical black body with a radius of 12 cm radiates 450 watt power at 500 K. If the radius were halved and the temperature doubled, the power radiated in watt would be :

answered Feb 16, 2020

Power radiated from black body$\;\;P = \sigma A e T ^4 \qquad [A = 4 \pi R^2]$$\therefore P \propto ...

0 votes

Which of the following statements are correct ?
(a) Centre of mass of a body always coincides with the centre of gravity of the body.
(b) Centre of mass of a body is the point at which the total gravitational torque on the body is zero.
(c) A couple on a body produce both translational and rotational motion in a body
(d) Mechanical advantage greater than one means that small effort can be used to lift a large load.

answered Feb 16, 2020

Centre of mass of body is the point at which total gravitational torque is zero.Mechanical advantage...

0 votes

Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities $\omega_1$ and $\omega_2$. They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is :

answered Feb 16, 2020

Angular momentum of $1^{st}$ disc $=I \omega_1$Angular momentum of $2^{nd}$ disc $=I \omega_2$$\ther...

0 votes

Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time $t_1$. On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time $t_2$. The time taken by her to walk up on the moving escalator will be :

answered Feb 16, 2020

When preeti walks up a moving esculator Total velocity $V_t = V_{esc}+V_{walk}$$\large\frac{d}{t} = ...

0 votes

Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are $K_1$ and $K_2$. The thermal conductivity of the composite rod will be

answered Feb 16, 2020

When two rod are welded together the effective conductivity in parallel combination is $\qquad K_{eq...

0 votes

Figure shows a circuit that contains three identical resistors with resistance R = 9.0 $\Omega$ each, two identical inductors with inductance L = 2.0 mH each, and an ideal battery with emf $\varepsilon$ = 18 V. The current 'I' through the battery just after the switch closed is,â€¦â€¦..

answered Feb 16, 2020

Jut after the switch is closed, capacitor will be short circuited and inductor will be in the open c...

0 votes

The bulk modulus of a sperical object is 'B'. If it is subjected to uniform pressure 'p', the fractional decrease in radius is :

answered Feb 16, 2020

Bulk modulus $B = \large\frac{P}{\Delta V/V}$$\qquad{ \large\frac{\Delta V}{V} = \frac{P}{B}} \qquad...

0 votes

If $\theta_1$ and $\theta_2$ be the apparent angles of dip observed in two vertical planes at right angles to each other, then the true angle of dip $\theta$ is given by :

answered Feb 16, 2020

Relation between real dip and apparent dip$\tan \theta' = \large\frac{\tan \theta}{\cos \alpha}$$\ta...

0 votes

Two blocks A and B of masses 3m and m respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in figure. The magnitudes of acceleration of A and B immediately after the string is cut, are respectively :

answered Feb 16, 2020

For block Bhttps://clay6.com/mpaimg/1799_a.jpg $mg = ma$$\;\;g = a_1$For block $A$https://clay6.com/...

0 votes

The two nearest harmonics of a tube closed at one end and open at other end are 220 Hz and 260 Hz. What is the fundamental frequency of the system ?

answered Feb 16, 2020

Fundamental frequency of closed pipe $= \large\frac{V}{4L}$Two nearest harmonic $n \frac{V}{4L} = 2...

0 votes

The ratio of wavelengths of the last line of Balmer series and the last line of Lyman series is :

answered Feb 15, 2020

Last line of Lyman series $\large\frac{1}{\lambda_1} = R (\frac{1}{1^2} - \frac{1}{\infty^2}]$$\lamb...

0 votes

A thin prism having refracting angle $10^o$ is made of glass of refractive index $1.42$. This prism is combined with another thin prism of glass of refractive index $1.7$. This combination produces dispersion without deviation. The refracting angle of second prism should be :

answered Feb 15, 2020

Condition for dispersion without deviation $\large\frac{A'}{A} =\large\frac{(\mu -1)}{(\mu'-1)}$$\la...

0 votes

A physical quantity of the dimensions of length that can be formed out of c, G and $\frac{e^2}{4 \pi \epsilon_0}$ is [ c is velocity of light, G is universal constant of gravitation and e is charge] ;

answered Feb 15, 2020

$M^o L^1 T^o Q^o = C^x G^y (\large\frac{e^2}{4 \pi \in_o })^z$$\qquad \qquad = (M^oL T^{-1})^2 \beg...

0 votes

One end of string of length l is connected to a particle of mass 'm' and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in circle with speed 'v' the net force on the particle (directed towards center) will be (T represents the tension in the string)

answered Feb 15, 2020

When string of length $\ell$ is connected to mass $m$ and moves in a horizontal circle the net forc...

0 votes

A beam of light from a source L is incident normally in a plane mirror fixed at a certain distance x from the source. The beam is reflected back as a spot on a scale placed just above the source L. When the mirror is rotated through a small angle $\theta$, the spot of the light is found to move through a distance y on the scale. The angle $\theta$ is given by-

answered Feb 15, 2020

When mirror turn through an angle $\theta$, the reflected ray turns through an angle equal to $2 \t...

0 votes

The resistance of a wire is 'R' ohm. If it is melted and stretched to 'n' times its original length, its new resistance will be

answered Feb 15, 2020

Resistance $=\large\frac{\rho \ell}{A}=\frac{\rho \ell}{\pi r^2}$when melted volume remains constant...

0 votes

An arrangement of three parallel straight wires placed perpendicular to plane of paper carrying same current 'I' along the same direction is shown in Fig. Magnitude of force per unit length on the middle wire 'B' is given by :

answered Feb 15, 2020

Force due to wire $A$ on wire $B = F_{BA} = \large\frac{\mu_o I I}{2\pi d}$Force due to wire $C$ on ...

0 votes

Suppose the charge of a proton and an electron differ slightly. One of them is $– e$, the other is $(e + \Delta e)$. If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance d (much greater than atomic size) apart is zero, then $\Delta e$ is of the order of [Given mass of hydrogen $mh = 1.67 \times 10^{–27} kg$]

answered Feb 15, 2020

Electrostatic force = Gravitational force$\qquad \large\frac{K q_1q_2}{r^2} =\frac{Gm_1m_2}{r^2} $$\...

0 votes

The photoelectric threshold wavelength of silver is $3250 \times 10^{–10} m$. The velocity of the electron ejected from a silver surface by ultraviolet light of wavelength $2536 \times 10^{–10} m$ is :
(Given $h = 4.14 \times 10^{-15} \; eVs$ and $ c = 3 \times 10^8 \; ms^{-1}$ )

answered Feb 15, 2020

By photoelectric equation$KE = hc [\large\frac{1}{\lambda} - \frac{1}{\lambda_o}]$$\qquad = \frac{1}...

0 votes

A carnot engine having an efficiency of $\frac{1}{10}$ as heat engine, is used as a refrigerator. If the work done on the system is 10 J, the amount of energy absorbed from the reservoir at lower temperature is :

answered Feb 15, 2020

Efficiency of carhot engine when used as a refrigerator ${\eta = \large\frac{W}{Q}} \qquad [W- \text...

0 votes

A particle executes linear simple harmonic motion with an amplitude of 3 cm. When the particle is at 2 cm from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period in seconds is :

answered Feb 15, 2020

For Simple Harmonic motion $SHM$Velocity $= w \sqrt{a^2 - x^2} \qquad \qquad [a-amplitude]$accelerat...

0 votes

The acceleration due to gravity at a height 1 km above the earth is the same as at a depth d below the surface of earth. Then

answered Feb 15, 2020

Acceleration due to gravity at a height $h$$\qquad g'=g(1-\frac{2h}{R})$Acceleration due to gravity ...

0 votes

A capacitor is charged by a battery. The battery is removed and another identical uncharged capacitor is connected in parallel. The total electrostatic energy of resulting system :

answered Feb 15, 2020

Initially when the capacitor is charged energy of the system =12CV2" role="presentation" style="posi...

0 votes

A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N ?

answered Feb 15, 2020

$\tau = I \alpha \qquad [\text{For cylinder $I = MR^2$}]$$\tau F = I \alpha$$0.4 \times 30 = MR^2 \a...

0 votes

A long solenoid of diameter 0.1 m has $2 \times 10^4$ turns per meter. At the centre of the solenoid, a coil of 100 turns and radius 0.01 m is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to 0 A from 4 A in 0.05 s. If the resistance of the coil is $10 \pi^2 \Omega$, the total charge flowing through the coil during this time is :

answered Feb 15, 2020

Emf $E = -\frac{d \phi}{dt}$$\qquad I R = -\frac{d \phi}{dt}$$\qquad \frac{dq }{dt} = -\frac{d \phi}...

0 votes

Which one of the following represents forward bias diode ?

answered Feb 15, 2020

Forward biased diode is represented byhttps://clay6.com/mpaimg/1797_a.jpg

0 votes

A gas mixture consists of 2 moles of $O_2$ and 4 moles of Ar at temperature T. Neglecting all vibrational modes, the total internal energy of the system is :

answered Feb 15, 2020

Internal energy of oxygen $U_{O_2} = \mu C_V T = 2 \times \frac{5}{2} R T $$\qquad \qquad \qquad = ...

0 votes

Two astronauts are floating in gravitational free space after having lost contact with their spaceship. The two will :

answered Feb 15, 2020

The two astronauts move towards each other due to matual gravitational force.

Ask Questions, Get Answers