Evaluate , where M and l are constants.

Find the value of , where G,M and m are constants.

A square loop of side 'l' each side having uniform linear charge density 'lambda' is placed in 'xy' lane as shown in the figure There exists a non uniform electric field vec(E)=a/l(x+l)hat(i) where a and l are constants and x is the position of the point from origin along x-axis. Find the resultant electric force on the loop (in Newtons) if l=10 cm lambda=20 muC//m and a=5 xx 10^(5) N//C .

FInd the derivative by first principle ax+b where a and b are constants

Evaluate int^t _0 A sin omega dt where A and omega are constants.

Show that the sequence defined by a_(n) = m + (2n - 1) d, where m and d are constants , is an A.P. Find its common difference .

If (x+a) is a factor of both the quadratic polynomials x^(2) + px+ q and x^(2) + lx + m , where p,q,l and m are constants, then which one of the following is correct?

Find the derivative of 3sinx+2sinalpha , where 'alpha' is a constant.

A particle moves along an arc of a circle of radius R according to the law l=a sin omegat , where l is the displacement from the initial position measured along the arc, and a and omega are constants. Assuming R=1.00m , a=0.80m , and omega=2.00rad//s , find: (a) the magnitude of the total acceleration of the particle at the points l=0 and l=+-a , (b) the minimum value of the total acceleration w_(min) and the corresponding displacement l_m .

If lx + my + n = 0 , where l, m, n are variables, is the equation of a variable line and l, m, n are connected by the relation al+bm+cn=0 where a, b, c are constants. Show that the line passes through a fixed point.