Find the value of `lambda` , a non-zero scalar, if `lambda[1 0 2 3 4 5]+2[1 2 3-1-3 2]=[4 4 10 4 2 14]` .

3.Find the value of (5^0 +4^-1) times 2^2

If lim_(theta->0)((a(1-costheta))/(theta^2)-(bsintheta)/(theta))=1 then the value of 2b-a is -lambda , then the value of lambda is (1) 2 (2) 4 (3) 6 (4) 8

Find the values of lambda ad mu if the points A(-1,4,-2),B(lambda,mu,1) and C(0,2,-1) are collinear.

Let z be a complex number. If the minimum value of |z|^2+|z-3|^2+|z-3i|^2 is lambda , then the value of 6lambda is (1) 23 (2) 42 (3) 72 (4) 84

Find the value of lambda . If the points A(-1,3,2), B(-4,2,-2) and C(5,lambda,10) are collinear.

Find the values of lambda if the following of lines perpendicular : (1-x)/(3) = (7y-14)/(3lambda)=(z+1)/(2) and (7-7x)/(3lambda) = y/1 = (1-z)/(5)

Find the value of lambda so that the following lines are perpendicular to each other. (x-5)/(5lambda+2)=(2-y)/5=(1-z)/(-1), x/1=(2y+1)/(4lambda)=(1-z)/(-3)

Let veca = 2hati+lambda_1 hatj+3hatk , vec(b)=4hati+(3-lambda_2) hatj+6hatk and vec(c)=3hati+6hatj+(lambda_3-1)hatk be three vectors such that vec(b)=2 vec(a) and vec(a) is perpendicular to vec(c) then a possible value of ((lambda)_1,(lambda)_2,(lambda)_3) is: (a) (1,3,1) (b) ((-1/2),4,0) (c) (1,5,1) (d) ((1/2), 4, -2)

If the equation 4x^2-x-1=0 and 3x^2+(lambda+mu)x+lambda-mu=0 have a root common, then the irrational values of lambda and mu are (a) lambda=(-3)/4 b. lambda=0 c. mu=3/4 b. mu=0

The rank of the matrix [(1,2,3),(lambda , 2 , 4),(2,-3,1)] is 3 if :