If f (x) = x^3 is defined on the interval [-1, 2], then which of the following is true about it

• A) Its relative minimum value does not exist at the critical point.
• B) Its relative minimum value exists at the critical point.
• C) None of these.
• D) Its absolute minimum value exists at the critical point.

Subdivision of an interval is also called ………. of the interval.

• A) Composition
• B) Evaluation
• C) Partition
• D) Separation

In the indefinite integral of x(y^2) w.r.t ‘y’ , the independent variable is ……..

• A) none of these
• B) y
• C) xy
• D) x

Integral of 3sec(x)tan(x) is NOTE: x^n means ‘x’ to the power ‘n’

• A) 3sec(x)+C
• B) None of these
• C) 3tan(x)+C
• D) (3/2)sec^2(x)+C

If integral of ‘h(x)’ from [-2,4] = -5 and integral of ‘g(x)’ from [-2,4] = -9 ,than integral of (6h(x)-8g(x)) from [-2,4] =……..

• A) 42
• B) 40
• C) 41
• D) 43

The function that uses the previous term to find the next term in the sequence is called a ______ function

• A) bijective
• B) none of these
• C) recursive
• D) onto

Which of the following sets is uncountable?

• A) Set of even integers
• B) Set of prime numbers
• C) Set of real numbers
• D) Set of odd integers

What is recursion in mathematics?

• A) None of these
• B) Solving equations using matrices
• C) Finding derivatives of functions
• D) A function that calls itself

The Cartesian product of two denumerable sets is:

• A) Always finite
• B) Sometimes denumerable
• C) Always denumerable
• D) Some times finite

The set of all possible ordered pairs of natural numbers is:

• A) Countable
• B) Uncountable
• C) non-denumerable
• D) Finite

Which set is NOT an example of a countable set?

• A) Set of natural numbers
• B) Set of integers
• C) Set of rational numbers
• D) Set of real numbers

In a recursive sequence, each term is defined as a function of ___________.

• A) None of these
• B) Only the preceding term
• C) Both the preceding term and the first term
• D) Only the first term

Countable sets include:

• A) Infinite set only
• B) Both finite and denumerable sets
• C) Denumerable sets only
• D) Finite sets only

Which of the following statements about countable sets is FALSE?

• A) Countable sets can be infinite.
• B) Every subset of a countable set is countable.
• C) Countable sets have a cardinality equal to that of the natural numbers.
• D) Countable sets are always finite.

Which of the following sets is countable?

• A) Set of complex numbers
• B) Set of real numbers
• C) Set of rational numbers
• D) Set of irrational numbers

Two sets A = {pencil, copy} and B = {history, maths}are ________ sets.

• A) infinite
• B) equipotent
• C) None of these
• D) equal

If one set in a Cartesian product is uncountable, then the Cartesian product is:

• A) Sometimes denumerable
• B) Always denumerable
• C) Always uncountable
• D) Sometimes uncountable

Which of the following statement holds for a set of rational numbers?

• A) It is uncountable.
• B) It is non-denumerable.
• C) It is denumerable.
• D) It does not contain any denumerable subset.

If a lower bound of A precdes every other lower bound of A, then it is called the infimum of A

• A) Given statement is true.
• B) Given statement is false.
• C)
• D)

Let A be an ordered set. Then A is said to be well-ordered if every subset of A contains a first element.

• A) Given statement is true.
• B) Given statement is false.
• C)
• D)