If the direction cosines of a straighat line are k,k,k the (A) `kgt0` (B) `0ltklt1` (C) `k=1` (D) `k=1/sqrt(3) or -1/sqrt(3)`

If the direction cosines of a line are lt k, k, kgt then

If int_0^1 xe^(x^2) dx=k int_0^1 e^(x^2) dx , then (A) kgt1 (B) 0ltklt1 (C) k=1 (D) none of these

If the function f(x)=x^3-9k\ x^2+27 x+30 is increasing on R , then (a) -1lt=k 1 (c) 0

If the area enclosed between the curves y=kx^2 and x=ky^2 , where kgt0 , is 1 square unit. Then k is: (a) 1/sqrt(3) (b) sqrt(3)/2 (c) 2/sqrt(3) (d) sqrt(3)

Four distinct points (k, 2k), (2, 0), (0, 2) and (0,0) lie on a circle for : (A) k = 0 (B) k = 6/5 (C) k = 1 (D) k = -1

If the standard deviation of the numbers -1, 0,1,k is sqrt(5) where k gt 0 , then k is equal to 2 sqrt(l) . The value of l is ________.

If the points (k ,\ 2k),\ (3k ,\ 3k) and (3,\ 1) are collinear, then k (a) 1/3 (b) -1/3 (c) 2/3 (d) -2/3

Let vec a=2 hati+hat j+ hat k , vec b=hat i+2hat j- hatk and a unit vector vec c be coplanar. If vec c is perpendicular to vec a , then vec c is a. 1/(sqrt(2))(-hat j+hat k) b. 1/(sqrt(3))(-hat i-hat j-hat k)"" c. 1/(sqrt(5))(-hat k-2 hat j) d. 1/(sqrt(3))(hat i-hat j- hat k)

The system of linear equations x+y+z=2,2x+y-z=3, 3x+2y+kz=4 has a unique solution if (A) k!=0 (B) -1ltklt1 (C) -2ltklt2 (D) k=0

Find the sum of the series sum_(k=1)^(360)(1/(ksqrt(k+1)+(k+1)sqrt(k)))