(iii) `sqrt-3sqrt-6`=

Which of the following are AP's ? If they form an AP, find the common difference d and write three more terms. (i) 2, 4, 8, 16, . . . (ii) 2,5/2,3,7/2,. . . (iii) -1.2 ,- 3.2 ,- 5.2 ,- 7.2 ,... (iv) -10 ,-6,-2,2.... (v) 3,3+sqrt2,3+2sqrt2,3+3sqrt2,..." " (vi) 0.2,0.22,0.222,0.2222,..." " (vii) 0,-4,-8,-12,..." " (viii) -(1)/(2),-(1)/(2),-(1)/(2),-(1)/(2),..." " (ix) 1,3,9,27,..." " (x) a,2a,3a,4a,..." " (xi) a,a^(2),a^(3),a^(4),..." " (xii) sqrt2,sqrt8,sqrt18,sqrt32,..." " (xiii) sqrt3,sqrt6,sqrt9,sqrt12,..." " (xiv) 1^(2),3^(2),5^(2),7^(2),..." " (xv) 1^(2),5^(2),7^(2),73,...

Rationalies the denominator and simplify: (i) (1+sqrt(2))/(3-2sqrt(2)) (ii) (2sqrt(6)-\ sqrt(5))/(3sqrt(5)-\ 2sqrt(6))

Which of the following are A.P.'s ? If they form an A.P., find the common difference 'd' and write three more terms : (i) -10, -6, -2, 2, ..... " " (ii) 3, 3+sqrt(2), 3+2sqrt(2), 3+3sqrt(2), ... (iii) 0, -4, -8, -12, .... " " (iv) a, 2a, 3a, 4a, ..... (v) sqrt(3), sqrt(6), sqrt(9), sqrt(12), .....

Ratonalise the denominator in each of the following and hence evalute by taking sqrt2=1.414, sqrt3=1.732 and sqrt(5)= 2.236 upto three places of decimal. (i)4/sqrt3 , (ii) 6/sqrt6 , (iii)(sqrt10-sqrt5)/2 (iv)sqrt2/(2+sqrt2) ,(v) 1/(sqrt3+sqrt2)

Let k be a real number such that the inequality sqrt(x-3) +sqrt(6 -x) ge k has a solution then the maximum value of k is sqrt3 (2) sqrt6 -sqrt3 (3) sqrt6 (4) sqrt6 +sqrt3

Prove that tan 7 (1^(@))/(2) = sqrt2 - sqrt3 -sqrt4 + sqrt6 = (sqrt3 - sqrt2) (sqrt2 -1).

Let f(x ,y)=x y^2 if xa n dy satisfy x^2+y^2=9 then the minimum value of f(x ,y) is 0 (2) -3sqrt(3) -6sqrt(3) (4) -3sqrt(6)

The director circle of a hyperbola is x^(2) + y^(2) - 4y =0 . One end of the major axis is (2,0) then a focus is (a) (sqrt(3),2-sqrt(3)) (b) (-sqrt(3),2+sqrt(3)) (c) (sqrt(6),2-sqrt(6)) (d) (-sqrt(6),2+sqrt(6))

The value of sin(sin^-1 (1/2)+ cos ^-1 (1/3)) is equal to (A) ((sqrt(3)+sqrt(8))/6) (B) ((1+2sqrt(6))/6) (C) - ((1+2sqrt(6))/6) (D) 0

If sqrt(2)=1.414,sqrt(3)=1.732 , find the value of the following : (i)(sqrt(2)+1)/(sqrt(2)-1)" "(ii)(sqrt(3)-1)/(sqrt(3)+1)" "(iii)(2+sqrt(6))/(sqrt(2))