The area bounded by y = xelxl and lines lxl = 1, y = 0 is,
4 sq units
6 sq units
1 sq unit
2 sq unit
The differential equation of the rectangular hyperbola, where axes are the asymptotes of the hyperbola, is
xdy + ydx = c
The length of longer diagonal of the parallelogram constructed on 5a + 2b and a - 3b, if it is given that and the angle between a and b is , is
15
If a, b, c are three non-coplanar vectors and p, q, rare reciprocal vectors, then (la + mb + nc) · (lp + mq + nr) is equal to
l + m + n
l3 + m3 + n3
l2 + m2 + n2
None of these
C.
l2 + m2 + n2
p, q and r are reciprocal vectors of a, b and c respectively.
p . r = 1, p . b = 0 = p . c
q . a = 0, q . b = 1, q . c = 0
r . a = 0, r . b = 0, r . c = 1
(la + mb + nc) . (lp + mq + nr) = l2 + m2 + n2
If the integers m and n are chosen at random from 1 to 100, then the probability that a number of the form 7n + 7m is divisible by 5, equals to
Let X denote the sum of the numbers obtained when two fair dice are rolled. The variance and standard deviation of X are