is
continuous but not differentiable at x = 1
differentiable at x = 1
neither continuous nor differentiable at x = 1
continuous everywhere
Find C of Lagrange's mean value theorem for the function f(x) = 3x2 + 5x + 7 in the interval [1, 3].
2
The length of the perpendicular from the point (1 2, 3) on the line is
3 units
4 units
5 units
7 units
The equation of the plane passing through the intersection ofthe planes 2x - 3y + z - 4 = 0 and x - y + z + 1 = 0 and perpendicular to the plane x + 2y - 3z + 6 = 0 is
x - 5y + 3z - 23 = 0
x - 5y - 3z - 23 = 0
x + 5y - 3z + 23 = 0
x - 5y + 3z + 23 = 0
The points with position vectors 60i + 3j, 40i - 8 j and ai - 52j are collinear, if
a = - 40
a = 40
a = - 20
a = 20
A.
a = - 40
Given that the points with position vectors 60i + 3j, 40i - 8j and ai - 52j are collinear, then there exist three scalars 1, x and y such that
1 + x + y = 0 ...(i)
and (60i + 3j) . 1 + (40i - 8j) . x + (ai - 52j) . y = 0
(60 + 40x + ay)i + (3 - 8x - 52y)j = 0
= 0i + 0j
Comparing both sides, we get
60 + 40x + ay = 0 ...(i)
and 3 - 8x - 52y = 0 ...(iii)
Solving Eqs. (i) and (iii), we get
Then, from Eq. (ii),