`{(1/3)^(-3)-(1/2)^(-3)}-:(1/4)^(-3)` =
(a)`(19)/(64)` (b) `(64)/(19)` (c)`(27)/(16)` (d) `(-19)/(64)`

The value of tan(cos^(-1)(3/5)+tan^(-1)(1/4)) is (a) (19)/8 (b) 8/(19) (c) (19)/(12) (d) 3/4

The value of cotsum_(n=1)^(19)cot^(-1)(1+sum_(p=1)^(n)2p) is equal to (a) (21)/(19) (b) (19)/(21) (c) -(19)/(21) (d) -(21)/(19)

The value of cot sum_(n=1)^(19)(cot^(-1)(1+sum_(p=1)^(n)2p)) is equal to (a) (21)/(19) (b) (19)/(21) (c) -(19)/(21) (d) -(21)/(19)

simplify (i) (1^(3)+2^(3)+3^(3))^(1/2) (ii) (3/5)^(4)(8/5)^(-12)(32/5)^(6) ,(iii) (1/27)^(-2/3) (vi) [((625)^(-1/2)))^(-1/4)]^(2) ,(v) (9^(1/3)xx27^(-1/2))/(3^(1/6)xx3^(-2/3)) (vi) 64^(-1/3)[64^(1/3)-64^(2/3)] (8^(1/3)xx16^(1/3))/(32^(-1/3)

Evaluate each of the following removing radical sign and negative indices wherever they occur (i) (64)^(1/3) (ii) (125)^(-1/3) (iii) (27)^(-2/3) (iv) (64/25)^(-3/2) (v) (-1/2)^(-5) (vi) (1/4)^(-1) (vii) 5^(-2)

Evaluate each of the following : (i){(81)^(1//5)}^(5//2)" "(ii)(3sqrt(64))^(-2)" "(iii)9^(3//2)+3xx4^(0)-((1)/(81))^(-1//2) (vi)sqrt((1)/(9))+(0.01)^(-1//2)-(27)^(4//3)" "(v)((125)/(64))^(2//3)+((256)/(625))^(-1//4)

An ellipse has its centre at (1,-1) and semi major axis =8 and it passes through the point (1,3). The equation of the ellipse is a. ((x+1)^2)/(64)+((y+1)^2)/(16)=1 b. ((x-1)^2)/(64)+((y-1)^2)/(16)=1 c. ((x-1)^2)/(64)+((y+1)^2)/(16)=1 d. ((x+1)^2)/(64)+((y-1)^2)/(16)=1

Simplify : ((8)/(27))^(-1//3)xx((25)/(4))^(1//2)xx((4)/(9))^(0)+((125)/(64))^(1//3)

If 1/3+1/2+1/x=4, then x=? (a) 5/(18) (b) 6/(19) (c) (18)/5 (d) (24)/(11)

If (16)^(2x+3)=(64)^(x+3), then 4^(2x-2)= (a) 64 (b) 256 (c) 32 (d) 512