Assertion Reasoning Quiz

Question 1 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.

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Question 2 of 7

Assertion (A): The point \((-2, 3, -4)\) lies in Octant VI.
Reason (R): The point \((2, -3, 4)\) lies in Octant IV.

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.

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Question 3 of 7

Assertion (A): The reflection of the point \(P(2, -3, 5)\) across the \(XY\)-plane is \((-2, 3, 5)\).
Reason (R): When a point is reflected in the \(XY\)-plane, its \(z\)-coordinate changes sign while its \(x\) and \(y\) coordinates remain unchanged.

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.

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Question 4 of 7

Assertion (A): The volume of the tetrahedron formed by origin \(O(0,0,0)\) and intercepts \(A(3,0,0)\), \(B(0,4,0)\), \(C(0,0,5)\) on the axes is \(10\text{ cubic units}\).
Reason (R): The volume of a tetrahedron with mutually perpendicular edges of lengths \(a, b, c\) meeting at a vertex is given by \(V = \frac{1}{6}abc\).

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.

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Question 5 of 7

Assertion (A): The centroid of a triangle with vertices \((1,2,3)\), \((2,3,1)\), and \((3,1,2)\) is \((3,3,3)\).
Reason (R): The centroid of a triangle divides each of its medians in the ratio \(2:1\).

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.

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Question 6 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.

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Question 7 of 7

Assertion (A): If a point \(P(x, y, z)\) lies on the \(z\)-axis, then \(x = 0\) and \(y = 0\).
Reason (R): Points on the \(z\)-axis have zero perpendicular distance from both the \(YZ\)-plane and \(ZX\)-plane.

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.

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Assertion Reasoning Quiz