Assertion Reasoning Quiz

Question 1 of 7

Assertion (A): The distance between points \(P(1, 2, 3)\) and \(Q(1, 2, 7)\) is \(4\text{ units}\).
Reason (R): The distance between any two distinct points in 3D Euclidean space is always a positive real number.

A Both (A) and (R) are true and (R) is the correct explanation of (A). B Both (A) and (R) are true but (R) is NOT the correct explanation of (A). C (A) is true but (R) is false. D (A) is false but (R) is true.

Select one option. Answers are shown after the test.

Question 2 of 7

Assertion (A): The points \(A(1, 2, 3)\), \(B(2, 3, 1)\), and \(C(3, 1, 2)\) are vertices of an equilateral triangle.
Reason (R): All three side lengths \(AB\), \(BC\), and \(CA\) are equal to \(\sqrt{6}\text{ units}\).

A Both (A) and (R) are true and (R) is the correct explanation of (A). B Both (A) and (R) are true but (R) is NOT the correct explanation of (A). C (A) is true but (R) is false. D (A) is false but (R) is true.

Select one option. Answers are shown after the test.

Question 3 of 7

Assertion (A): If a point \(P(a, b, c)\) lies in Octant V, then \(a > 0\), \(b > 0\), and \(c < 0\).
Reason (R): Octant V consists of all points in space where the \(x\) and \(y\) coordinates are positive while the \(z\) coordinate is negative.

A Both (A) and (R) are true and (R) is the correct explanation of (A). B Both (A) and (R) are true but (R) is NOT the correct explanation of (A). C (A) is true but (R) is false. D (A) is false but (R) is true.

Select one option. Answers are shown after the test.

Question 4 of 7

Assertion (A): The locus of a point moving in space such that its distance from the \(XY\)-plane is \(4\text{ units}\) consists of two parallel planes \(z = 4\) and \(z = -4\).
Reason (R): The perpendicular distance of any point \((x, y, z)\) from the \(XY\)-plane is \(|z|\).

A Both (A) and (R) are true and (R) is the correct explanation of (A). B Both (A) and (R) are true but (R) is NOT the correct explanation of (A). C (A) is true but (R) is false. D (A) is false but (R) is true.

Select one option. Answers are shown after the test.

Question 5 of 7

Assertion (A): The perpendicular distance of the point \(P(4, -3, 7)\) from the \(ZX\)-plane is \(3\text{ units}\).
Reason (R): The perpendicular distance of any point \(P(x, y, z)\) from the \(XY\)-plane is \(|z|\).

A Both (A) and (R) are true and (R) is the correct explanation of (A). B Both (A) and (R) are true but (R) is NOT the correct explanation of (A). C (A) is true but (R) is false. D (A) is false but (R) is true.

Select one option. Answers are shown after the test.

Question 6 of 7

Assertion (A): If the centroid of the triangle with vertices \((a, 1, 2)\), \((1, b, 3)\), and \((2, 3, c)\) is at the origin \((0,0,0)\), then \(a + b + c = -9\).
Reason (R): If the origin is the centroid of a triangle, the sum of \(x\)-coordinates, \(y\)-coordinates, and \(z\)-coordinates of its vertices must each separately equal \(0\).

A Both (A) and (R) are true and (R) is the correct explanation of (A). B Both (A) and (R) are true but (R) is NOT the correct explanation of (A). C (A) is true but (R) is false. D (A) is false but (R) is true.

Select one option. Answers are shown after the test.

Question 7 of 7

Assertion (A): The point \(P(3, 4, 5)\) and point \(Q(-3, -4, -5)\) are symmetric with respect to the origin.
Reason (R): The distance of \(P(3, 4, 5)\) from the origin is equal to the distance of \(Q(-3, -4, -5)\) from the origin.

A Both (A) and (R) are true and (R) is the correct explanation of (A). B Both (A) and (R) are true but (R) is NOT the correct explanation of (A). C (A) is true but (R) is false. D (A) is false but (R) is true.

Select one option. Answers are shown after the test.

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