The mapping f: N N given by f(n) = 1 + n2, n N where N is the set of natural numbers, is
one - to - one and onto
onto but not one - to - one
one - to - one but not onto
neither one - to - one nor onto
If N is a set of natural numbers, then under binary operation a · b = a + b, (N, ·) is
quasi-group
semi-group
monoid
group
The relation R defined on set A = by is
{(- 2, 2), (- 1, 1), (0, 0), (1, 1), (2, 2)}
{(- 2, - 2), (- 2, 2), (-1, 1), (0, 0), (1, - 2), (1, 2), (2, - 1), (2, - 2)}
{(0, 0), (1, 1), (2, 2)}
None of the above
The roots of (x - a)(x - a - 1) + (x - a - 1)(x - a - 2) + (x - a)(x - a - 2) = 0, are always
equal
imaginary
real and distinct
rational and equal
Let f(x) = x2 + ax + b, where a, b R. If f(x) = 0 has all its roots imaginary, then the roots of f(x) + f'(x) + f''(x) = 0 are
real and distinct
imaginary
real and distinct
rational and equal
If f(x) = 2x4 - 13x2 + ax + b is divisible by x2 - 3x + 2, then (a, b) is equal to
(- 9, - 2)
(6, 4)
(9, 2)
(2, 9)
C.
(9, 2)
Given, f(x) = 2x4 - 13x2 + ax + b = 0 is divisible by (x- 2)(x - 1).
On solving Eqs. (i) and (ii), we get
a = 9, b = 2