(iv) `1/sqrt3+sqrt3/3`

sqrt3 xx sqrt3

1/(sqrt3 + sqrt2) + 1/(sqrt3 -sqrt2)=

If A equiv (2, 3, 4), B equiv (3, 4, 5). The direction cosine of a line are (1/sqrt(3), 1/sqrt(3), 1/sqrt(3)) Now integral value of the projection of AB on the given line is _______.

From point P(4,0) tangents PA and PB are drawn to the circle S: x^2+y^2=4 . If point Q lies on the circle, then maximum area of triangleQAB is- (1) 2sqrt3 (2) 3sqrt3 (3) 4sqrt3 A) 9

Find the eccetricity of hyperbola through (4,2) whose centre is (0,0) length of transverse axis is 4 and transverse axis along x-axis. (1) 2 (2) sqrt(3) (3) sqrt(3)/2 (4) 2/sqrt(3)

If n-1C_r=(k^2-3)^nC_(r+1), then (a) (-oo,-2] (b) [2,oo) (c) [-sqrt3, sqrt3] (d) (sqrt3,2]

A plane passing through three points (-lamda^2, 1, 1) (1, -lamda^2, 1),(1, 1, -lamda^2) also passes through (-1,-1,1) then set consisting all the real value of lamda is (A) {-sqrt3,sqrt3} (B) {3,-3} (C) {-1,1} (D) {sqrt3, -sqrt3}

(iii) (sqrt 5+ sqrt 3)/(sqrt5-sqrt3)+(sqrt5-sqrt3)/(sqrt5+sqrt3) =?

If the volume of parallelopiped formed by the vectors hati+lamdahatj+hatk,hatj+lamdahatk and lamdahati+hatk is minimum then lamda is equal to (1) -(1)/(sqrt(3)) (2) (1)/(sqrt(3)) (3) sqrt(3) (4) -sqrt(3)

Simplify: 2/(sqrt(5)+\ sqrt(3))+1/(sqrt(3)+\ sqrt(2))-3/(sqrt(5)+\ sqrt(2))