Answers posted by priyanka.clay6

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The distance, from the origin of the normal to the curve, $x = 2 \cos t + 2 t \sin t,\; y = 2\sin t - 2t \cos t$ at $ t = \frac{\pi}{4}$, is:

answered Apr 1, 2020

Given : $x = 2 \cos t + 2 t \sin t,\; y = 2\sin t - 2t \cos t$ at $ t = \frac{\pi}{4}$${\large\frac{...

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$\displaystyle{\lim_{x \to 0} \frac{e^{x^2}-\cos x}{\sin^2x}}$ is equal to :

answered Apr 1, 2020

$\displaystyle{\lim_{x \to 0} \frac{e^{x^2}-\cos x}{\sin^2x}}$ we know $\displaystyle\lim_{x \to 0} ...

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The value of $\displaystyle\sum_{r=16}^{30} (r+2)(r-3)$ is equal to :

answered Apr 1, 2020

Given :$\displaystyle\sum_{r=16}^{30} (r^2 -r-6) \;\;\;= \displaystyle\sum_{r=1}^{30}(r^2-r-6)- \di...

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If $A = \begin{bmatrix} 0 & -1 \\ 1& 0 \end{bmatrix}$, then which one of the following statement is not correct ?

answered Mar 31, 2020

$A^2=\begin{bmatrix} 0& -1 \\ 1&0 \end{bmatrix} \begin{bmatrix} 0 &-1 \\ 1& 0\end{b...

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The least value of the product $xyz$ for which the determinant $\begin{vmatrix} x& 1& 1 \\ 1 & y & 1 \\ 1 & 1 & z \end{vmatrix}$ is non negative, is:

answered Mar 31, 2020

Given : $\begin{vmatrix} x& 1& 1 \\ 1 & y & 1 \\ 1 & 1 & z \end{vmatrix} \ge...

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If $2 + 3i$ is one of the roots of the equation $2x^3 - 9x^2 + kx - 13 = 0, \; k \in R$, then the real root of this equation :

answered Mar 31, 2020

Since $2+3i$ is one of the roots, $\qquad 2-3i$ is the other root, Let the $3^{rd}$ root be...

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The largest value of $r$ for which the region represented by the set $\{ \omega \in C | \omega - 4 - i | \leq r \}$ is contained in the region represented by the set $\{z \in C / |z-1| \leq |z+i| \}$, is equal to :

answered Mar 31, 2020

Given : $|w - 4 - i| \leq r$$\implies $ The centre of the circle is $(4,1)$ and radius is $r$$\qquad...

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If the coefficients of the three successive terms in the binomial expansion of $(1+x)^n$ are in the ratio $1 : 7 : 42$, then the first of these terms in the expansion is :

answered Mar 31, 2020

$nC_{r-1} \;\; : \;nC_r \;\; :\; nC_{r+1}$ is$\;\;1 \qquad : \;\; 7 \qquad : \; 42$(ie)$\large\frac{...

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Let the sum of the first three terms of an A.P. be 39 and the sum of its last four terms be 178. If the first term of this A.P. is 10, then the median of the A.P. is :

answered Mar 31, 2020

Sum of first three terms is $10 + 10 +d +10 + 2d = 39$$\qquad \qquad \qquad \qquad \implies 30 + 3d ...

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The number of ways of selecting 15 teams from 15 men and 15 women, such that each team consists of a man and a woman, is :

answered Mar 31, 2020

No. of men = 15No. of women = 15Total selection of one men and one women out of 15 men and 15 women ...

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In a certain town, 25% of the families own a phone and 15% own a car ; 65% families own neither a phone nor a car and 2,000 families own both a car and a phone. Consider the following three statements :
(a) 5% families own both a car and a phone.
(b) 35% families own either a car or a phone.
(c) 40,000 families live in the town.
Then :

answered Mar 31, 2020

https://clay6.com/mpaimg/1838_a.jpg$65 \% +(25-x) \% + x\%+ (15-x)\% = 100$$\implies 105\% - x =100\...

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A particle moving with velocity $\overrightarrow {\rm{V}}$ is acted by three forces shown by the vector triangle PQR. The velocity of the particle will :

answered Mar 23, 2020

Since all the forces forms a closed loop in same order net force is zero.$\qquad F_{net} = 0$$\impli...

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In a double slit experiment, when light of wavelength 400 nm was used, the angular width of the first minima formed on a screen placed 1m away, was found to be 0.2°. What will be the angular width of the first minima, if the entire experimental apparatus is immersed in water$(\mu _{water} = \frac{4}{3})$

answered Mar 23, 2020

Angular fringe with $\theta_{air } = \large\frac{\beta}{D}$Angular fringe with in water $\theta_{wat...

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The work done to raise a mass m from the surface of the earth to a height h, which is equal to the radius of the earth, is

answered Mar 23, 2020

Initial potential energy at earth surface $\qquad U_i = \large\frac{-GMm}{R}$Final potential energy ...

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Ionized hydrogen atoms and a-particles with same momenta enters perpendicular to a constant magnetic field B. The ratio of their radii of their paths $rH:r\alpha$ will be

answered Mar 23, 2020

Radius of hydrogen $\qquad r_{_H} = \large\frac{P}{eB}$Radius of $\alpha$ particle$\qquad r_{\alpha}...

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Two point charges A and B, having charges +Q andQ respectively, are placed at certain distance apart and force acting between them is F. If 25% charge of A is transferred to B, then force between the charges becomes :

answered Mar 23, 2020

$F = k \large\frac{Q_1Q_2}{r^2}$$\;\;\; = \large\frac{k Q^2}{r^2}$$Q_1 = Q_2 =Q$when $25\%$ of charg...

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A small hole of area of cross-section $2 mm^2$ is present near the bottom of a fully filled open tank of height 2m. Taking g = $10\frac{ m}{s^2}$, the rate of flow of water through the open hole would be nearly :

answered Mar 23, 2020

Rate of water flow $= A \times V$$A - Area$$V = \text{velocity of efflux}$$R = 2 \times 10^{-6}\;m^2...

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When an object is shot from the bottom of a long smooth inclined plane kept at an angle 60° with horizontal, it can travel a distance $x_1$ along the plane. But when the inclination is decreased to 30° and the same object the shot with the same velocity, it can travel $x-2$ distance. Then $x_1 : x_2$ will be

answered Mar 22, 2020

https://clay6.com/mpaimg/1837_a.jpgusing $v^2 = u^2 -2as;\;\;\;v=0$$\therefore \;\; 2as = u^2$$\qqua...

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An electron is accelerated through a potential difference of 10,000 V. Its de Broglie wavelength is, (nearly):$(m_c=9\times10^{-31}kg)$

answered Mar 22, 2020

For electron accelerated through a potential $V$ the wave length $\lambda ={ \large\frac{12.27}{\sqr...

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$\alpha-particle$ consists of :

answered Mar 22, 2020

$\alpha $ particle consists of two proton and two neutrons, it is doubly ionised $He$ atom.

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In the circuits shown below, the readings of the voltmeters and the ammeters will be:

answered Mar 22, 2020

$v_1 = i_1 \times R ={ \large\frac{10}{10} }\times 10 = 10\;V$$v_2 = i_2 \times R ={ \large\frac{10}...

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A parallel plate capacitor of capacitance $20\mu F$ is being charged by a voltage source whose potential is changing at the rate of $3\frac{ V}{s}$. The conduction current through the connecting wires, and the displacement current through the plates of the capacitor, would be, respectively :

answered Mar 22, 2020

$c = 20 \times 10^{-6} F$Rate of change of potential $={\large\frac{dv}{dt}}= 3\;v/s$$q=cv$${\large\...

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Which of the following acts as a circuit protection device?

answered Mar 22, 2020

Fuse wire has low melting point, when excess current flows, heat produced, melts it.

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For a p-type semiconductor which of the following statements is true?

answered Mar 22, 2020

In p-type semi conductors holes are majority carriers and trivalent atoms are the dopants.

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In total internal reflection when the angle of incidence is equal to the critical angle for the pair of media in contact, what will be angle

answered Mar 22, 2020

In total internal reflection, if angle of incidence is critical angle, the angle of refraction is $9...

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Two parallel infinite line charges with linear charge densities$\lambda +\frac{C}{m} \;and \;-\lambda \frac{C}{m}$ are placed at a distance of 2R in free space. What is the electric field midway between two line charges?

answered Mar 21, 2020

Electric field mid way between two line charge of charge density $+\lambda$ and $-\lambda$ is $E = \...

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answered Mar 21, 2020

For air lens$\large\frac{1}{F_1} =\frac{1}{f} +\frac{1}{f} $$\qquad = \large\frac{2}{f}$For glycerin...

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Two particles A and B are moving in uniform circular motion in concentric circles of radius rA and rB with speed uA and uB respectively. The time period of roation is the same. The ratio of angular speed of A to that of B will be :

answered Mar 21, 2020

Since the time periods are same,$T = T_1 = T_2$$T = \large\frac{2 \pi}{w}$Angular velocity $w_A={\l...

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A cylindrical conductor of radius R is carrying a constant current. The plot of the magnitude of the magnetic field, B with the distance d, from the centre of the conductor, is correctly represented by the figure

answered Mar 21, 2020

Magnetic field inside the conductor $B = \large\frac{\mu_o i}{2 \pi R^3}d$$B \propto d\;\;\;\implies...

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Pick the wrong answer in the context with rainbow.

answered Mar 21, 2020

Rainbow cannot be observed when the observer is facing the sun.

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A force $F = 20 + 10y$ acts on a particle in y-direction where F is in newton and y in meter. Work done by this force to move the particle from $y = 0$ to $y = 1;m$ is :

answered Mar 21, 2020

Work done = $\displaystyle \int_{y_i}^{y_f} F\;dy; \qquad y_i = 0 \qquad y_f = 1\;m$$\qquad W = \di...

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At a point A on the earth's surface the angle of dip, $\delta = +25^{\circ}$. At a point B on the earth's surface the angle of dip, $\delta =-25^{\circ}$. We can interpret that.

answered Mar 21, 2020

Angle of dip is zero at equator and positive at northern hemisphere. Southern hemisphere dip is cons...

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answered Mar 21, 2020

https://clay6.com/mpaimg/1835_a.jpg$R_{eq}= R/3 + R/3$$\qquad =\large \frac{2R}{3}$Power = $P_1 =\la...

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In which of the following devices, the eddy current effect is not used ?

answered Mar 21, 2020

Electric heater uses the principle of Joule's heating effect. It does not use the principle of eddy ...

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A hollow metal sphere of radius R is uniformly charged. The electric field due to the sphere at a distance r from the centre :

answered Mar 21, 2020

Electric field inside a shell is zero$\therefore $ for $r < R; \; E = 0$For $r > R$ as $r$ i...

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The radius of circle the period of revolution initial position and sense of revolution are indicated in the fig

y-projection of the radius vector of rotating particle P is:

answered Mar 21, 2020

$T=4s$$w=\frac{2 \pi}{T}=\frac{2\pi}{4}$$\;\;=\frac{\pi}{2}\;rad/s$$a = 3$Since it has a maximum dis...

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A solid cylinder of mass 2 kg and radius 4 cm is rotating about its axis at the rate of 3 rpm. The torque required to stop after $2\pi$ revolutions is :

answered Mar 21, 2020

Work done = change in rotational K.E$\qquad \qquad = \frac{1}{2} I (w_f^2 - w_i^2)$$\qquad \;\;\thet...

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Which colour of the light has the longest wavelength ?

answered Mar 21, 2020

Red has the longest wavelength among the given options.

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A body weighs 200 N on the surface of the earth.How much will it weigh half way down to the centre of the earth ?

answered Mar 21, 2020

Acceleration due to gravity at depth of$g' = g(1-\frac{d}{R})$ and $d = \frac{R}{2}$$mg' = mg(1-\fra...

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In an experiment, the percentage of error occurred in the measurment of physical quantities A, B, C and D are 1%, 2%, 3% and 4% respectively. Then the maximum percentage of error in the measurement X, where $X=\frac{A^2B^\frac{1}{2}}{C^\frac{1}{3}D^3}$, will be

answered Mar 21, 2020

$\large x = \frac{A^x B^{1/2}}{C^{1/3}D^3}$Error Percentage $\Delta x \% = 2 \times \%\; \text{of A}...

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A disc of radius 2m and mass 100 kg rolls on a horizontal floor.Its center of mass has speed of $20\frac{cm}{s}$.How much work is needed to stop it?

answered Mar 21, 2020

Worth required $= K_{final} - K_{initial }$$\qquad \;\; K_{initial}=0$$\qquad \;\; K_{final }=\frac{...

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When a block of mass M is suspended by a long wire of length L, the length of the wire become (L+l).The elastic potential energy stored in the extended wire is

answered Mar 6, 2020

The extension in the wire $= \ell$Energy store $= \frac{1}{2}k \ell^2$But $k = \large\frac{mg}{\ell}...

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The unit of thermal conductivity is

answered Mar 6, 2020

Unit of Thermal conductivity $\qquad K =\large\frac{Q}{A \;t \Delta T}$$\qquad \;\;\; = W m^{-1}K^{-...

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A copper rod of 88 cm and an aluminum rod of unknown length have their increase in length independent of increase in temperature. The length of aluminum rod is : ($\propto Cu=1.7\times10^{-5}K^{-1}and \propto Al=2.2\times 10^{-5}K^{-1}$)

answered Mar 6, 2020

Since the aluminum rod and copper rod have increase in length, independent of temperature.$\qquad \q...

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A soap bubble, having radius of 1 mm, is blown from a detergent solution having a surface tension of $2.5 \times 10^{-2}$ $\frac{ N}{m}$. The pressure inside the bubble equals at a point $Z_0$ below the free surface of water in a container. Taking $g = 10 \frac{m}{s^2} $ density of water $= 103\frac{ kg}{m^3}$, the value of $Z_0$ is :-

answered Mar 6, 2020

Excess pressure inside a soap bubble$\qquad P = \large\frac{4T}{R}$Gauge pressure $= \rho g Z_0 $$P_...

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Average velocity of a particle executing SHM in one complete vibration is :

answered Mar 6, 2020

Total displacement in one complete oscillation is zero.$\therefore \text{Average velocity} = \large...

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A 800 turn coil of effective area $0.05 m^2$ is kept perpendicular to a magnetic field $5\times 10^{5}$ T. When the plane of the coil is rotated by 90° around any of its coplanar axis in 0.1 s, the emf induced in the coil will be :

answered Mar 6, 2020

Change in magnetic flux$\phi = NBA (\cos 90^{\circ} - \cos 0^{\circ})$$\;\;\; = -NBA$$\;\;\; = -800 ...

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The displacement of a particle executing simple harmonic motion is given by $y = A0 + Asin{\omega}{t}+ Bcos\omega{t}$. Then the amplitude of its oscillation is given by :

answered Mar 6, 2020

$y = A_o+A \sin wt + B \cos w t$Define $y' = y-A_o \qquad $ [shifting origin]$\qquad \qquad = A \sin...

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A mass m is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when:

answered Mar 6, 2020

Tension is maximum at lowest point $\qquad T = mg + \frac{mu^2}{\ell}$So chance of breaking is maxim...

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The speed of a swimmer in still water is $20\frac{ m}{s}$. The speed of river water is $10 \frac{m}{s}$ and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes w.r.t. north is given by :

answered Mar 6, 2020

$V_m=20\;m/s$$V_R=10\;m/s$https://clay6.com/mpaimg/1833_a.jpg $\sin \theta = \large\frac{|\overright...

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