If `2 (3)/(4) - (5)/(8) + (-5)/(12) + 1 (1)/(6) = k,` then find k.

If cosA=(3)/(4) and k sin ((A)/(2))sin((5A)/(2))=(11)/(8) . Find k.

if the lines (x - 1)/(-3) = ( y - 2)/(2k) = ( z -3)/(2) and (x -1) /(3k) = ( y - 5)/(1) = (z - 6 ) /(-5) are at night angle , then find the value of k .

If the rank of the matrix [[4,2,1-x],[5,k,1],[6,3,1+x]] is 2 then .k= (5)/(2) ,x= (1)/(5) k= (5)/(2) , x!=(1)/(5) k= 1/5 , x= 5/2 none of these

Find the angle between the following pairs of lines : (i) vec(r) = 3 hat(i) + 2 hat(j) - 4 hat(k) + lambda (hat(i) + 2 hat(j) + 2 hat(k) ) . vec(r) = 5 hat(j) - 2 hat(k) + mu ( 3 hat(i) + 2 hat(j) + 6 hat(k)) (ii) vec(r) = 3 hat(i) + hat(j) - 2 hat(k) + lambda (hat(i) - hat(j) - 2 hat(k) ) . vec(r) =(2 hat(i) - hat(j) - 56 hat(k)) + mu ( 3 hat(i) - 5 hat(j) - 4 hat(k)) (iii) (x-2)/(2) = (y - 1)/(5) = (z + 3)/(-3) and (x + 2)/(-1) = (y - 4)/(8) = (z - 5)/(4) (iv) (x - 4)/(3) = (y + 1)/(4) = (z - 6)/(5) and (x-5)/(1) = (2y +5)/(-2) = (z - 3)/(1) (v) (5 -x)/(3) = (y + 3)/(-4) , z = 7 and x = (1-y)/(2) = (z - 6)/(2) (vi) (x + 3)/(3) = (y - 1)/(5) = (z + 3)/(4) and (x + 1)/(1) = (y - 4)/(1) = (z-5)/(2) .

If the lines (x-1)/(-3)=(y-2)/(2k)=(z-3)/(-2) and (x-1)/(3k)=(y-5)/(1)=(z-6)/(-5) are at right angle,then find the value of k

If A=[(2, 3),(5,-2)] be such that A^(-1)=k\ A , then find the value of k .

If (3)/(4!)+(4)/(5!)+(5)/(6!)+....+50term=(1)/(3!)-(1)/((k-3)!) ,then sum of coefficients in the expansion (1+2x_(1)+3x_(2)+....+100x_(100))^(k) is:

If the lines (x-1)/(-3)=(y-2)/(2k)=(z-3)/(2)(x-1)/(3k)=(y-1)/(1)=(z-6)/(-5) are perpendicular,find the value of k.

If x=4^(log_(2)(sqrt(9^(k-1)+7))) and y=(1)/(32^(log_(2)(3^(k-1)+1)^((1)/(5)))) and xy=4 then find sum of the squares of the real values of k