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A point particle of mass m moves along the uniformly rough track PQR as shown in the figure. The coefficient of friction, between the particle and the rough track equals µ. The particle is released from rest, from point P and it comes to rest at a point R. The energies lost by the ball, over the parts PQ and QR of the track, are equal to each other and no energy is lost when particle changes direction from PQ to QR. the values of the coefficient of friction µ and the distance x (=QR), are respectively close to

A) 0.2 and 6.5 m

B) 0.2 and 3.5 m

C) 0.29 and 3.5m

D) 0.29 and 6.5 m

A satellite is revolving in a circular orbit at a height h from the Earth's surface (radius of earth R, h<<R). The minimum I lease in its orbital velocity required so that the satellite could escape from the earth's gravitational field, is close to (neglect the effect of the atmosphere.)

A) $\sqrt{2gR}$

B) $\sqrt{gR}$

C) $\sqrt{gR}/2$

D) $\sqrt{gR}(\sqrt{2}-1)$

A particle performs simple harmonic motion with amplitude A. Its speed is trebled at the instant that it is at a distance

$\frac{2}{3}$ A from the equilibrium position. The new amplitude of the motion is

A) $\frac{A}{3}\sqrt{41}$

B) 3A

C) $A\sqrt{3}$

D) $\frac{7}{3}A$

A uniform string of length 20m is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the support is (Take , g=10 ms^-2)

A) $2\pi\sqrt{2}s$

B) 2 s

C) $2\sqrt{2}s$

D) $\sqrt{2}s$

The region between two concentric spheres of radii a and b, respectively (see the figure), has volume charge density

$\rho =\frac{A}{r}$ where A is a constant and r is distance from the center. At the centre of the spheres is a point charge Q. The value of A, such that the electric field in the region between the sphere will be constant is

A) $\frac{Q}{2\pi a^{2}}$

B) $\frac{Q}{2\pi (b^{2} -a^{2})}$

C) $\frac{2Q}{\pi (a^{2} -b^{2})}$

D) $\frac{2Q}{\pi a^{2} }$

A screw gauge with a pitch of 0.5 mm and a circular scale with 50 divisions is used to measure the thickness of a thin sheet of Aluminium. Before starting the measurement. it is found that when the two jaws of the screw gauge are brought in contact, the 45th division coincides with the main scale line and that the zero of the main scale is barely visible. What is the thickness of the sheet, if the main scale reading is 0.5mm and the 25th division coincides with the main scale line?

A) 0.75mm

B) 0.80mm

C) 0.70 mm

D) 0.50mm

A pipe open at both ensa has a fundamental frequency f in air. The pipe is dipped vertically in the water, so that half of it is in water, The fundamental frequency of the air column is now

A) $\frac{f}{2}$

B) $\frac{3f}{4}$

C) $2f$

D) $f$

If the 2nd, 5 th and 9th terms of a non-constant AP are in GP., then the common ratio of this GP is

A) $\frac{8}{5}$

B) $\frac{4}{3}$

C) 1

D) $\frac{7}{4}$

A wire of length 2 units is cut into two parts which are bent respectively to form a square of side =x units and a circle of radius =r units. If the sum of the areas of the square and the circle so formed is minimum, then

A) $2x=(\pi+4)r$

B) $(4-\pi)x+4)=\pi r$

C) x=2r

D) 2x=r

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

A) (-3,-9)

B) (-3,-8)

C) $(\frac{1}{3},-\frac{8}{3})$

D) $(-\frac{10}{3},-\frac{7}{3})$

The heats of combustion of carbon and carbon monoxide are - 393.5 and - 283.5 kJ mol^-1, respectively. The heat of formation (in kI) of carbon monoxide per mole is

A) 676.5

B) -676.5

C) -110.5

D) 110.5

The pair have the same magnetic moment is[ at no. Cr=24, Mn=25, Fe=26 and Co=27]

A) $[Cr(H_2O)_6]^{2+}$ and $[Fe(H_2O)_6]^{2+}$

B) $[Mn(H_2O)_6]^{2+}$ and $[Cr(H_2O)_6]^{2+}$

C) $[CoCl_4]^{2-}$ and $[Fe(H_2O)_6]^{2+}$

D) $[Cr(H_2O)_6]^{2+}$ and $[CoCl_4]^{2-}$

The absolute configuration of

A) (2S,3R)

B) (2S,3S)

C) (2R,3R)

D) (2R,3S)

Which one of the following ores is best concentrated by froth floatation method

A) Siderite

B) Galena

C) Malachite

D) Magnetite

Which of the following atoms has the highest first ionization energy?

A) Na

B) K

C) Sc

D) Rb

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