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
D.
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
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