If there is an error of K % is measuring the edge of a cube, then the per cent error in estimating its volume is
k
3k
None of these
The equation of the tangent to the curve y = be- x/a at the point where it crosses the Y-axis, is
ax + by = 1
ax - by = 1
Which of the following function is not differentiable at x = 1 ?
f(x) =
f(x) =
f(x) =
None of the above
If the direction cosines of two lines are connected by the equations l + m + n = 0, l2 + m2 - n2 = 0, then the angle between the lines is
The equation of the plane which contains the origin and the line of intersection of the planes r · a = d1 and r · b = d2, is
r . (d1a + d2b) = 0
r . (d2a - d1b) = 0
r . (d2a + d1b) = 0
r . (d1a - d2b) = 0
If from a point P(a, b, c) perpendiculars PA and PB are drawn to YZ and ZX - planes, then the equation of the plane OAB is
bcx + cay + abz = 0
bcx + cay - abz = 0
- bcx + cay + abz = 0
bcx - cay + abz = 0
The order of the differential equation whose general solution is given by
y = (C1 + C2)sin(x + C3) - C4ex + C5, is
2
3
4
5
B.
3
We have, y = (C1 + C2)sin(x + C3) - C4ex + C5
y = C6sin(x + C3) - C4eC5 . ex
where, C6 = C1 + C2
y = C6sin(x + C3) - C7ex
where, C4eC5 = C7
Clearly, the above relation contains three arbitrary constants. So, the order of the given differential equation is 3.
If d = a x b + b x c + c x a is a non-zero vector and = 0, then
a, b and c are coplanar
None of the above
Let u, v and w be such that = 1, = 2 and = 3. If the projection of v along u is equal to that of w along u and vectors v and w are perpendicular to each other, then equals
2
14