1
###
Let f(x) = min{2x^2, 52 − 5x}, where x is any positive real number

Let f(x) = min{2x^{2}, 52 − 5x}, where x is any positive real number. Then the maximum possible value of f(x) is

2
###
If f(x + 2) = f(x) + f(x + 1) for all positive integers x

If f(x + 2) = f(x) + f(x + 1) for all positive integers x, and f(11) = 91, f(15) = 617, then f(10) equals

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3
###
The domain of sin-1[log3(x/3)] is

The domain of sin^{-1}[log_{3}(x/3)] is

- [-9, -1]
- [-9, 1]
- [-1,9]
- [1, 9]

4
###
Let W denote the words in the English dictionary

Let W denote the words in the English dictionary. Define the relation R by:

R = {(x, y) ε W × W | the words x and y have at least one letter in common}. Then R is

- reflexive, symmetric and not transitive
- reflexive, symmetric and transitive
- not reflexive, symmetric and transitive
- reflexive, not symmetric and transitive

5
###
A function is matched below against an interval

A function is matched below against an interval where it is supposed to be increasing. Which of the following pairs is incorrectly matched?

- (-∞,1/3] ; 3x
^{2}- 2x + 1 - [2,∞) ; 2x
^{3}- 3x^{2}-12x + 6 - (-∞,∞) ; x
^{3}- 3x^{2}+ 3x + 3 - (-∞,-4] ; x
^{3}+ 6x^{2}+ 6

6
###
The domain of the function f(x) = 1/√(|x| - x) is

The domain of the function f(x) = 1/√(|x| - x) is

- (0,∞)
- (-∞,0)
- (-∞,∞)
- (-∞,∞) - {0}

7
###
The function f(x) = log (x + √(x^2 +1)), is

The function f(x) = log (x + √(x^{2} +1)) is

- an even function
- an odd function
- neither an even nor an odd function
- a periodic function

8
###
Let R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation

Let R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation on the set A = {1, 2, 3, 4}. The relation R is

- not symmetric
- transitive
- reflexive
- a function

9
###
If a ϵ R and the equation -3(x - [x])^2 + 2(x - [x]) + a^2 = 0 has no integral solution

If a ϵ R and the equation -3(x - [x])^{2} + 2(x - [x]) + a^{2} = 0 (where [x] denotes the greatest integer ≤ x) has no integral solution, then all possible values of a lie in the interval

- (-1, 0) U (0, 1)
- (-2, -1)
- (1, 2)
- (-∞, -2) U (2, ∞)

10
###
For real x, let f(x) = x^3 + 5x + 1, then

For real x, let f(x) = x^{3} + 5x + 1, then

- f is one-one and onto R
- f is onto R but not one-one
- f is neither one-one nor onto R
- f is one-one but not onto R

11
###
A function f from the set of natural numbers to integers

A function f from the set of natural numbers to integers defined by

f(n) = (n-1)/2, when n is odd

f(n) = -n/2, when n is even

- one-one and onto both
- one-one and but not onto
- neither one-one nor onto
- onto but not one-one

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In a class test, the sum of Arun’s marks in Hindi and English is 30
When they work alone, B needs 25% more time to finish a job than A does
Humans and robots can both perform a job but at different efficiencies
The distance from A to B is 60 km. Partha and Narayan start from A