If a1, a2, … , an are in H.P., then the expression a1a2 + a2a3 + … + an−1an is equal to
n(a1 − an)
(n − 1) (a1 − an)
na1an
na1an
The number of values of x in the interval [0, 3π] satisfying the equation 2sin2 x + 5sinx − 3 = 0 is
4
6
1
1
If A and B are square matrices of size n × n such that A2 − B2 = (A − B) (A + B), then which of the following will be always true?
A = B
AB = BA
either of A or B is a zero matrix
either of A or B is a zero matrix
Let a , b ∈ N. Then
there cannot exist any B such that AB = BA
there exist more than one but finite number of B’s such that AB = BA
there exists exactly one B such that AB = BA
there exists exactly one B such that AB = BA
The set of points where x f(x) = x /1+|x| is differentiable is
(−∞, 0) ∪ (0, ∞)
(−∞, −1) ∪ (−1, ∞)
(−∞, ∞)
(−∞, ∞)
The differential equation whose solution is Ax2 + By2 = 1, where A and B are arbitrary constants is of
second order and second degree
first order and second degree
first order and first degree
first order and first degree
D.
first order and first degree
ABC is a triangle, right angled at A. The resultant of the forces acting along respectively is the force along where D is the foot of the perpendicular from A onto BC. The magnitude of the resultant is