Multiple Choice QuestionsLet R be the real line. Consider the following subsets of the plane R × R.
S = {(x, y) : y = x + 1 and 0 < x < 2}, T = {(x, y) : x − y is an integer}. Which one of the following is true?
neither S nor T is an equivalence relation on R
both S and T are equivalence relations on R
S is an equivalence relation on R but T is not
S is an equivalence relation on R but T is not
Let f(x) = 
Then which one of the following is true?
f is neither differentiable at x = 0 nor at x = 1
f is differentiable at x = 0 and at x = 1
f is differentiable at x = 0 but not at x = 1
f is differentiable at x = 0 but not at x = 1
The largest interval lying in 
for which the function 
is defined, is
[0, π]
[-π/4, π/2)
[-π/4, π/2)
Let f : R → R be a function defined by f(x) = Min {x + 1, |x| + 1}. Then which of the following is true ?
f(x) ≥ 1 for all x ∈ R
f(x) is not differentiable at x = 1
f(x) is differentiable everywhere
f(x) is differentiable everywhere
The number of values of x in the interval [0, 3π] satisfying the equation 2sin2 x + 5sinx − 3 = 0 is
4
6
1
1
The set of points where x f(x) = x /1+|x| is differentiable is
(−∞, 0) ∪ (0, ∞)
(−∞, −1) ∪ (−1, ∞)
(−∞, ∞)
(−∞, ∞)
Let R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on the set A = {3, 6, 9, 12} be a relation on the set A = {3, 6, 9, 12}. The relation is
reflexive and transitive only
reflexive only
an equivalence relation
an equivalence relation
Let f : (-1, 1) → B, be a function defined by 
then f is both one-one and onto when B is the interval
[0, π/2)
A function is matched below against an interval where it is supposed to be increasing. Which of the following pairs is incorrectly matched?
| Interval | Function |
| (-∞, ∞) | x3 – 3x2 + 3x + 3 |
| Interval | Function |
| [2, ∞) | 2x3 – 3x2 – 12x + 6 |
| Interval | Function |
| (-∞, 1/3] | 3x2 – 2x + 1 |
| Interval | Function |
| (-∞, 1/3] | 3x2 – 2x + 1 |
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