(iii) `(2-sqrt(2)) (2+sqrt(2))`

Simplify : (5+sqrt(5))(5-sqrt(5)) (ii) (3+2sqrt(2))(3-2sqrt(2))

Simplify: (5+sqrt(5))(5-sqrt(5))( ii) (3+2sqrt(2))(3-2sqrt(2))

If (0,1),(1,1) and (1,0) be the middle points of the sides of a triangle,its incentre is (2+sqrt(2),2+sqrt(2))( b) [2+sqrt(2),-(2+sqrt(2))](2-sqrt(2),2-sqrt(2)) (d) [2-sqrt(2),(2+sqrt(2))]

Examine,whether the following numbers are rational or irrational: (2-sqrt(2))(2+sqrt(2)) (ii) (sqrt(2)+sqrt(3))^(2)

If P and Q are two points on the circle x^2 + y^2 - 4x + 6y-3=0 which are farthest and nearest respectively from the point (7, 2) then. (A) P-=(2-2sqrt(2), -3-2sqrt(2)) (B) Q-= (2+2sqrt(2), -3 + 2 sqrt(2)) (C) P-= (2+2sqrt(2), -3 + 2 sqrt(2)) (D) Q-= (2-2sqrt(2), -3 + 2 sqrt(2))

Evaluate : (i) 1 + 2 + 4 + … to 10 terms " " (ii) sqrt(2) - 2 + 2 sqrt(2) - …+ 64 sqrt(2)

If 0 < x < pi/2 , intsqrt(1+secx)dx=2sin^(-1)(asin^(-1)(x/b))+C , where C is arbitrary constant, then ordered pair (a , b) is (1,sqrt(2)) (2) (sqrt(2),1) (sqrt(2),2) (4) (2,sqrt(2))

int_0^(sqrt(2)) [x^2] dx is equal to (A) 2-sqrt(2) (B) 2+sqrt(2) (C) sqrt(2)-1 (D) sqrt(2)-2

The value of int_(0)^(sqrt(2))[x^(2)]dx ,where [.] is the greatest integer function (A) 2-sqrt(2) (B) 2+sqrt(2) (C) sqrt(2)-1 (D) sqrt(2)-2