Let M be the set of all 2 x 2 matrices with entries from the set ofreal number R. Then, the function f : M R defined by f(A) = for ever A M, is
one-one and onto
neither one-one nor onto
one-one but not onto
onto but not one-one
G = is a group under matrix multiplication. Then, which one ofthe following statements in respect of G is ture
is inverse of itself
G is finite group
is not an element of G
is an element of G
If two circles (x - 1)2 + (y - 3)2 = r2 and x2 + y2 - 8x + 2y + 8 = 0 intersect in two distinct points, then
r < 2
8 < r < 10
r = 2
2 < r < 8
D.
2 < r < 8
The given equation ofcircles are
(x - 1)2 + (y - 3)2 = r2 ...(i)
and x2 + y2 - 8x + 2y + 8 = 0
or (x - 4)2 + (y + 1)2 = 32 ...(ii)
Centre and radius of Eq. (i) are C1(1, 3) and r
Centre and radius of Eq. (ii) are C2(4, -1) and 3
For the intersection of 2 circles,
Form Eqs. (iii) and (iv), we get
2 < r < 8
If f(x) = , then at x = 0 the function f is
continuous but not differentiable
differentiable but not continuous
continuous and differentiable
not continuous