A double-decker bus carry `(u+l)` passengers, `u` in the upper deck and `l` in the lower deck. Find the number of ways in which the `u+l` passengers can be distributed in the two decks, if `r(lt=l)` particular passengers refuse to go in the upper deck and `s(lt=u)` refuse to sit in the lower deck.

Passengers are to travel by a double decked bus which can accommodate 13 in the upper deck and 7 in the lower deck. Find the number of ways that they can be distributed if 5 refuse to sit in the upper deck and 8 refuse to sit in the lower deck.

sintheta+sqrt(3)costheta=6x-x^2-11 ,0lt=4thetapi,x in R , hold for no values of xa n dtheta on ev a l u eof x and two values of theta two values of x and two values of theta two point of values of (x ,theta)

Shows a wire of length l which can slide on a U- shaped rail of negligible resistance. The resistance of the wire is R. The wire is pulled ot the right with a constant speed v. Draw an equivalent circuit diagram representing the induced emf by a battery. Find the current in the wire usingj this diagram.

Let A be an mxxn matrix. If there exists a matrix L of type nxxm such that LA=I_(n) , then L is called left inverse of A. Similarly, if there exists a matrix R of type nxxm such that AR=I_(m) , then R is called right inverse of A. For example, to find right inverse of matrix A=[(1,-1),(1,1),(2,3)] , we take R=[(x,y,x),(u,v,w)] and solve AR=I_(3) , i.e., [(1,-1),(1,1),(2,3)][(x,y,z),(u,v,w)]=[(1,0,0),(0,1,0),(0,0,1)] {:(implies,x-u=1,y-v=0,z-w=0),(,x+u=0,y+v=1,z+w=0),(,2x+3u=0,2y+3v=0,2z+3w=1):} As this system of equations is inconsistent, we say there is no right inverse for matrix A. For which of the following matrices, the number of left inverses is greater than the number of right inverses ?