10 Question MCQ (including Assertion)

If the ordered pairs \((x + 1, y - 2)\) and \((3, 1)\) are equal, what are the values of \(x\) and \(y\)?

Let \(P = \{a, b, c\}\) and \(Q = \phi\) (the null set). Which of the following is true for the Cartesian product \(P \times Q\)?

A monitoring system reports the absolute deviation from \(20\) using \[ f(x)=|x-20|,\qquad 16\le x\le25. \] What is the range of \(f\)?

Six customers must each receive exactly one coupon type from \(4\) available types. How many different assignment functions are possible?

Assertion (A): The domain of the real-valued function \(f(x) = \sqrt{16 - x^2}\) is \([-4, 4]\).

Reason (R): For a square root function \(\sqrt{g(x)}\) to yield real values, the expression inside the root must be non-negative (\(g(x) \ge 0\)).

Assertion (A): The mapping shown below represents a function from the set of students to the set of lockers.
Reason (R): Every student has exactly one locker as image, although two different students may have the same locker as image.

If \(f:\mathbb R\to\mathbb R\) is defined by \(f(x)=-5\) for every \(x\in\mathbb R\), then the range of \(f\) is

If \(A=\{1,2\}\) and \(B=\{3,4\}\), how many subsets does \(A\times B\) have?

Assertion (A): For any two non-empty sets \(A\) and \(B\), the Cartesian product \(A \times B\) is generally not equal to \(B \times A\).

Reason (R): The ordered pair \((a, b)\) is not equal to \((b, a)\) unless \(a = b\).