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
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
A.
Let l = 7n + 7m, then we observe that 71, 72, 73 and 74 ends in 7, 9, 3 and 1, respectively. Thus, tends in 7, 9, 3 or 1 according as i is of the form 4K + 1, 4K + 2, 4K - 1 or 4K, respectively.
If S is the sample space, then n(S) = (100)2. 7m + 7n is divisible by 5, if
(i) m is of the form 4K + 1 and n is of the form 4K - 1 or
(ii) m is of the form 4K + 2 and n is of the form 4K or
(iii) m is of the form 4K - 1 and n is of the form 4K + 1 or
(iv) m is of the form 4K and n is of the form 4K + 1.
Thus, number of favourable ordered pairs (m, n) = .
Hence, required probability =
Let X denote the sum of the numbers obtained when two fair dice are rolled. The variance and standard deviation of X are