A frame is formed by the uniform rods having constant linear mass density. ACB part of frame is semicircular of radius R and AB is a straight rod . Center of mass of the system from center O of AB is at a distance
(A) `frac {piR} {pi+1}`
(B) `frac {(pi+1)R} {pi}`
(C) `frac {(pi+2)R} {pi}`
(D) `frac {2R} {pi+2}`

sin^-1 (sin frac {2pi}3 )

The rate of change of the area of a circle with respect to its radius r at r = 6 cm is (A) 10pi (B) 12pi (C) 8pi (D) 11pi

The moment of inertia of a uniform semicircular wire of mass m and radius r, about an axis passing through its centre of mass and perpendicular to its plane is mr^(2)(-(k)/(pi^(2))) . Find the value of k.

The centre of mass shifts by a distance S, when a square of side frac{R}{2} is cut from a uniform disc of radius R as shown in figure. The value of S is

If tan^-1 x=y then : (a) -1lt y lt 1 (b) frac(-pi)(2)le y le frac(pi)(2) (c) frac(-pi)(2)lt y lt frac(pi)(2) (d) y in {frac(-pi)(2),frac(pi)(2)}

The area of the curved surface of a cone of radius 2r and slant height l/2 is a) pirl b) 2pirl c) 1/2 pir l d) pi(r+l)r

1.The inverse of cosine function is defined in the intervals (A) [ -pi , 0 ] (B) [ -pi/2,0 ] (C) [ 0,pi/2 ] (D) [ pi/2 , pi ]

A sphere is placed inside a right circular cylinder so as to touch the top, base and lateral surface of the cylinder. If the radius of the sphere is r , then the volume of the cylinder is 4pi\ r^3 (b) 8/3pi\ r^3 (c) 2pi\ r^3 (d) 8pi\ r^3

A conducting sphere A of radius a , with charge Q , is placed concentrically inside a conducting shell B of radius b . B is earthed. C is the common center of A and B . Study the following statements. (i) The potential at a distance r from C , where a le r le b, is (1)/(4 pi epsilon_0)(q/( r)) (ii) The potential difference between A and B is (1)/(4 pi epsilon_0) Q ((1)/( r) - (1)/B) (iii) The potential at a distance r from C , where a le r le b, is (1)/(4 pi epsilon_0) Q ((1)/r - (1)/B) Which of the following statements are correct ? .

The distance of a point on the ellipse (x^2)/6+(y^2)/2=1 from the center is 2. Then the eccentric angle of the point is pi/4 (b) (3pi)/4 (c) (5pi)/6 (d) pi/6