The value of `|[-1, 2, 1],[ 3+2sqrt(2), 2+2sqrt(2), 1],[ 3-2sqrt(2), 2-2sqrt(2), 1]|` is equal to a. zero b. `-16sqrt(2)` c. `-8sqrt(2)` d. none of these

If |z| < sqrt(2)-1,t h e n|z^2+2zcosalpha|i s a. less than 1 b. sqrt(2)+1 c. sqrt(2)-1 d. none of these

The value of lim_(x->0)(sqrt(1-cos"x"^2))/(1-cosx) is a. 1/2 b. 2 c. sqrt(2) d. none of these

Prove that (12)/(3 + sqrt5 - 2 sqrt2) = 1 + sqrt5 + sqrt10 - sqrt2

If sqrt2 = 1.414… and sqrt8 = 2.828…. then (sqrt2 + sqrt8)^(2) =

If f^(prime)(x)=1/(-x+sqrt(x^2+1)) and f(0)=(1+sqrt(2))/2 then f(1) is equal to- (a) log"(sqrt(2)+1) (b) 1 (c) 1+sqrt(2) (d) none of these

The value of lim_(xto2) (sqrt(1+sqrt(2+x))-sqrt(3))/(x-2)" is "

cos^(-1)("cos"(2cot^(-1)(sqrt(2)-1))) is equal to (a) sqrt(2)-1 (b) pi/4 (c) (3pi)/4 (d) none of these

A(1/(sqrt(2)),1/(sqrt(2))) is a point on the circle x^2+y^2=1 and B is another point on the circle such that arc length A B=pi/2 units. Then, the coordinates of B can be (a) (1/(sqrt(2)),-1/sqrt(2)) (b) (-1/(sqrt(2)),1/sqrt(2)) (c) (-1/(sqrt(2)),-1/(sqrt(2))) (d) none of these

Factorise : (sqrt(2)-1)x^(2)+2sqrt(2)x+(sqrt(2)+1)

The value of sqrt(2 sqrt(3sqrt(2sqrt(3.......prop)))) is equal to____