`(3)/(sqrt(8))/(2)/(sqrt(11))`

The direction cosines of a line passing through the points P(-2,4,-5) and Q(1,2,3) and is so directed that it makes an acute angle alpha with the positive direction of x-axis, are 3/(sqrt(77)),(-2)/(sqrt(77)),(-8)/(sqrt(77)) 2. 3/(sqrt(77)),(-2)/(sqrt(77)),8/(sqrt(77)) 3. 3/(sqrt(77)),2/(sqrt(77)),(-8)/(sqrt(77)) 4. 3/(sqrt(77)),2/(sqrt(77)),8/(sqrt(77)) 5. -3/(sqrt(77)),2/(sqrt(77)),8/(sqrt(77))

Find the 8th term of the G.P. sqrt(3),(1)/(sqrt(3)),(1)/(3sqrt(3)), ....

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

Rationalise the denominator in each of the following: (i) 2/(sqrt(7)) (ii) 2/(3sqrt(3)) (iii) (2sqrt(7))/(sqrt(11))

Rationalise the denominator in each of the following : i) 2/7 (ii) 2/(3sqrt(3)) (iii) (2sqrt(7))/(sqrt(11))

(sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2))-(sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2))+(1)/(sqrt(2)+1)-(1)/(sqrt(2)-1)

The value of lim_(xto2) (((x^(3)-4x)/(x^(3)-8))^(-1)-((x+sqrt(2x))/(x-2)-(sqrt(2))/(sqrt(x)-sqrt(2)))^(-1))" is "

(3+sqrt(2))(2-sqrt(3))(3-sqrt(2))(2+sqrt(3))

Sum of 1/(sqrt(2)+sqrt(5))+1/(sqrt(5)+sqrt(8))+1/(sqrt(8)+sqrt(11))+1/(sqrt(11)+sqrt(14))+..to n terms= (A) n/(sqrt(3n+2)-sqrt(2)) (B) 1/3 (sqrt(2)-sqrt(3n+2) (C) n/(sqrt(3n+2)+sqrt(2)) (D) none of these

Find the values of a and b in each of the following : (a)(5+2sqrt3)/(7+4sqrt(3))=a-6sqrt(3)" "(b)(3-sqrt(5))/(3+2sqrt(5))=asqrt(5)-(19)/(11) (c )(sqrt(2)+sqrt(3))/(3sqrt2-2sqrt(3))=2-bsqrt(6)" "(d)(7+sqrt(5))/(7-sqrt(5))-(7-sqrt(5))/(7+sqrt(5))=a+(7)/(11)sqrt(5b)