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Four identical balls A,B, C and D are placed in a line on frictionless horizontal surface. A and D are moed with the same speed u towards the middle as shown. Assuming elastic collisions, find the final velocities.

The force experienced by a pole of strength 100 Am at a distance of 0.2 m from a short magnet of length 5 cm and pole strength of 200 Am on its axial line will be

Assertion : The line l is parallel to the plane P. Reason: The normal of the plane P is perpendicular to the line l. (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

Assertion: Straighat lines l_1 and l_2 are perpendicular to each other. Reason: aa\'+bb\'+cc\'=sintheta (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

Assertion:The centre of the sphere which passes through the point (a,0,0),(0,b,0), (0,0,c) and (0,0,0) si (a/2,0,0) Reason: Points on a sphere are equidistant from its centre. (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

The equation of a straighat line through the point (a,b,c) and parallel to x-axis is (x-a)/1(y-b)/0=(z-c)/0 , Reason: The direction ratiof of the y-axis are ,0, 1, 0gt (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

Assertion: The straighat line x/1=y/2=z/3 is parallel to the plane x-2y+z-6=0 Reason: The normal of the plane is perpendicular to the line. (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

Assertion: The point A(1,0,7) is the mirror image of the point b(1,6,3) in the line x/1=(y-1)/2=(z-2)/3 Reason: The line x/1=(y-1)/2=(z-2)/3 bisects the segment joining A(1,0,7) and B(1,6,3). (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not the correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

A positive charge +Q is fixed at a poibt A. Another positively charged particle of mass m and charge +q is projected from a point B with velocity u as shown in (Fig. 3.103). Point B is at a large distance from A and at distance d from the line A C. The initial velocity is parallel to the line A C. The point C is at a very large distance from A. Find the minimum distance (in meter) of +q from +Q during the motion. Take Q q = 4 pi epsilon_0 m u^2 d and d (sqrt(2) - 1) m . .

Supose directioncoisnes of two lines are given by u l+vm+wn=0 and al^2+bm^2+cn^2=0 where u,v,w,a,b,c are arbitrary constnts and l,m,n are directioncosines of the lines. For u=v=w=1 directionc isines of both lines satisfy the relation. (A) (b+c)(n/l)^2+2b(n/l)+(a+b)=0 (B) (c+a)(l/m)^2+2c(l/m)+(b+c)=0 (C) (a+b)(m/n)^2+2a(m/n)+(c+a)=0 (D) all of the above