Assertion-Reason MCQs for Sub-Topics of Topic 4: Geometry

Question 1. Assertion (A): A point in geometry has no size.

Reason (R): A point represents a specific location in space.

(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.

Question 2. Assertion (A): A line extends infinitely in both directions.

Reason (R): A line has no thickness or breadth.

(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.

Question 3. Assertion (A): Two distinct points in a plane uniquely determine a line segment.

Reason (R): A line segment is a part of a line with two endpoints.

(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.

Question 4. Assertion (A): A plane is a 2-dimensional geometric element.

Reason (R): A plane can be visualized as a flat surface extending without end.

(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.

Question 5. Assertion (A): Parallel lines in a plane never intersect.

Reason (R): Parallel lines maintain a constant distance from each other.

(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.

Question 6. Assertion (A): A ray has only one endpoint.

Reason (R): A ray extends infinitely in one direction from its endpoint.

(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.

Question 1. Assertion (A): A ruler is a common tool for measuring the length of a line segment.

Reason (R): Length is the measure of the distance between the two endpoints of a line segment.

(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.

Question 2. Assertion (A): A protractor is used to measure angles.

Reason (R): Angles are typically measured in degrees.

(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.

Question 3. Assertion (A): The vertex of an angle is the point where the two rays forming the angle meet.

Reason (R): The two rays forming an angle are called its arms.

(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.

Question 4. Assertion (A): The measure of an angle depends on the length of its arms.

Reason (R): The measure of an angle depends on the opening between the two rays.

(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.

Question 5. Assertion (A): A point P is in the interior of $\angle \text{ABC}$ if P lies between the rays BA and BC.

Reason (R): The interior of an angle is a region in the 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.

Question 6. Assertion (A): Comparing two line segments means comparing their lengths.

Reason (R): Length is a numerical value associated with a line segment.

(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.

Question 1. Assertion (A): A right angle measures exactly $90^\circ$.

Reason (R): A right angle is half the measure of a straight angle.

(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.

Question 2. Assertion (A): Perpendicular lines intersect at a right angle.

Reason (R): The symbol '$\perp$' denotes perpendicularity.

(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.

Question 3. Assertion (A): A perpendicular bisector of a line segment is perpendicular to the segment and passes through its midpoint.

Reason (R): The perpendicular bisector contains all points equidistant from the segment's endpoints.

(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.

Question 4. Assertion (A): A reflex angle is always greater than $180^\circ$.

Reason (R): A complete angle is $360^\circ$.

(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.

Question 5. Assertion (A): The angle formed by the hands of a clock at 3:00 PM is an acute angle.

Reason (R): An acute angle is an angle whose measure is less than $90^\circ$ (but greater than $0^\circ$).

(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.

Question 6. Assertion (A): If line $l$ is perpendicular to line $m$, and line $p$ is perpendicular to line $m$, then line $l$ is parallel to line $p$.

Reason (R): Two lines perpendicular to the same line are parallel to each other.

(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.

Question 1. Assertion (A): If the sum of two angles is $90^\circ$, they are complementary.

Reason (R): Complementary angles always form a right angle when placed adjacent.

(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.

Question 2. Assertion (A): A linear pair of angles is always supplementary.

Reason (R): The non-common arms of angles in a linear pair form a straight line.

(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.

Question 3. Assertion (A): Vertically opposite angles are always equal.

Reason (R): They are formed by two intersecting lines.

(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.

Question 4. Assertion (A): If two angles form a linear pair and one angle is $70^\circ$, the other angle is $110^\circ$.

Reason (R): Angles in a linear pair are supplementary, so their sum is $180^\circ$.

(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.

Question 5. Assertion (A): Two acute angles can be supplementary.

Reason (R): The sum of two acute angles is always less than $180^\circ$.

(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.

Question 6. Assertion (A): If two lines intersect such that a pair of adjacent angles are equal, then each of these angles is $90^\circ$.

Reason (R): Adjacent angles formed by intersecting lines form linear pairs, and a linear pair is supplementary.

(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.

Question 1. Assertion (A): A transversal intersects two lines at distinct points.

Reason (R): A transversal creates eight angles when it intersects two lines.

(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.

Question 2. Assertion (A): If a transversal intersects two parallel lines, then corresponding angles are equal.

Reason (R): This is a fundamental property of parallel lines intersected by a transversal.

(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.

Question 3. Assertion (A): If a transversal intersects two lines such that a pair of alternate interior angles are equal, then the two lines are parallel.

Reason (R): This is the converse of the property of alternate interior angles when lines are parallel.

(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.

Question 4. Assertion (A): If a transversal intersects two lines such that the sum of interior angles on the same side is $180^\circ$, then the lines are parallel.

Reason (R): Interior angles on the same side of the transversal are consecutive interior angles.

(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.

Question 5. Assertion (A): If two lines are parallel, then any transversal will create equal alternate exterior angles.

Reason (R): Alternate exterior angles are located on opposite sides of the transversal and outside the parallel lines.

(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.

Question 6. Assertion (A): If line $l$ is parallel to line $m$, and line $m$ is parallel to line $n$, then line $l$ is parallel to line $n$.

Reason (R): This property is a consequence of Euclid's Fifth Postulate (or Playfair's Axiom).

(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.

Question 1. Assertion (A): Euclidean geometry is a deductive system of mathematics.

Reason (R): It is built upon a set of assumed true statements and logical deductions.

(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.

Question 2. Assertion (A): In Euclidean geometry, "Point," "Line," and "Plane" are undefined terms.

Reason (R): Definitions in Euclidean geometry are based on these undefined terms.

(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.

Question 3. Assertion (A): Axioms (Common Notions) are statements specific to geometry that are assumed true.

Reason (R): Postulates are statements assumed true that are generally applicable in mathematics.

(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.

Question 4. Assertion (A): A theorem is a statement that is proven to be true.

Reason (R): Proofs are based on definitions, axioms, postulates, and previously proven theorems.

(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.

Question 5. Assertion (A): The sum of angles in any Euclidean triangle is $180^\circ$.

Reason (R): This theorem is equivalent to Euclid's Fifth Postulate.

(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.

Question 6. Assertion (A): Through a point not on a given line, there exists exactly one line parallel to the given line.

Reason (R): This statement is known as Playfair's Axiom and is equivalent to Euclid's Fifth Postulate.

(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.

Question 1. Assertion (A): A polygon is a simple closed curve made up of only line segments.

Reason (R): The line segments forming a polygon are called its sides.

(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.

Question 2. Assertion (A): A triangle is a polygon with the minimum number of sides.

Reason (R): A triangle has 3 sides.

(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.

Question 3. Assertion (A): The sum of the interior angles of any convex quadrilateral is $360^\circ$.

Reason (R): Any convex quadrilateral can be divided into two triangles by a diagonal, and the sum of angles in a triangle is $180^\circ$.

(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.

Question 4. Assertion (A): A regular polygon is always both equilateral and equiangular.

Reason (R): A square is an example of a regular polygon.

(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.

Question 5. Assertion (A): A concave polygon has at least one interior angle greater than $180^\circ$.

Reason (R): In a concave polygon, at least one diagonal lies partly or entirely outside the polygon.

(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.

Question 6. Assertion (A): The sum of the exterior angles of any convex polygon is $360^\circ$.

Reason (R): This sum is independent of the number of sides of the polygon.

(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.

Question 1. Assertion (A): A triangle is formed by three non-collinear points joined by line segments.

Reason (R): Three collinear points would lie on a straight line and cannot form a closed figure.

(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.

Question 2. Assertion (A): An isosceles triangle has two equal sides.

Reason (R): In an isosceles triangle, the angles opposite the equal sides are also equal.

(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.

Question 3. Assertion (A): An obtuse-angled triangle can have two obtuse angles.

Reason (R): The sum of two obtuse angles is always greater than $180^\circ$, which is the sum of all angles in a triangle.

(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.

Question 4. Assertion (A): A triangle can be both isosceles and right-angled.

Reason (R): An isosceles right-angled triangle has angles $45^\circ, 45^\circ, 90^\circ$.

(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.

Question 5. Assertion (A): All equilateral triangles are acute-angled.

Reason (R): Each angle in an equilateral triangle measures $60^\circ$, which is less than $90^\circ$.

(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.

Question 6. Assertion (A): A scalene triangle has all sides of different lengths.

Reason (R): In a scalene triangle, all three angles are also of different measures.

(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.

Question 1. Assertion (A): The sum of the interior angles of any triangle is always $180^\circ$.

Reason (R): This property holds true for all triangles in Euclidean geometry, regardless of their type or size.

(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.

Question 2. Assertion (A): The exterior angle of a triangle at a vertex is equal to the sum of the two opposite interior angles.

Reason (R): This is a direct consequence of the Angle Sum Property and the property of a linear pair.

(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.

Question 3. Assertion (A): In $\triangle$ABC, if AB = AC, then $\angle B = \angle C$.

Reason (R): This is the statement of the Isosceles Triangle Theorem.

(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.

Question 4. Assertion (A): The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Reason (R): This is known as the Triangle Inequality Theorem.

(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.

Question 5. Assertion (A): In any triangle, the angle opposite the longest side is the largest angle.

Reason (R): This is a property relating side lengths and angle measures in a triangle.

(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.

Question 6. Assertion (A): A triangle can be formed with side lengths 5 cm, 5 cm, and 10 cm.

Reason (R): The sum of any two sides of a triangle must be greater than the third side.

(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.

Question 1. Assertion (A): The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Reason (R): This theorem is applicable only to right-angled triangles.

(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.

Question 2. Assertion (A): A triangle with side lengths 3 cm, 4 cm, and 5 cm is a right-angled triangle.

Reason (R): $3^2 + 4^2 = 9 + 16 = 25$, and $5^2 = 25$. Since $3^2 + 4^2 = 5^2$, the converse of the Pythagorean theorem states it is a right triangle.

(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.

Question 3. Assertion (A): The hypotenuse is always the longest side in a right-angled triangle.

Reason (R): According to the Pythagorean theorem, the square of the hypotenuse equals the sum of the squares of the other two sides, implying the hypotenuse value must be largest.

(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.

Question 4. Assertion (A): A triangle with side lengths 7, 8, 10 is an acute-angled triangle.

Reason (R): $7^2 + 8^2 = 49 + 64 = 113$. Since $113 > 10^2 (100)$, the angle opposite the side 10 is acute.

(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.

Question 5. Assertion (A): Finding the distance between two points (x1, y1) and (x2, y2) in a coordinate plane is an application of the Pythagorean theorem.

Reason (R): The distance formula $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ is derived from the Pythagorean theorem applied to a right triangle.

(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.

Question 6. Assertion (A): A triangle with sides 5, 12, 13 is a Pythagorean triplet.

Reason (R): $5^2 + 12^2 = 25 + 144 = 169 = 13^2$, satisfying the Pythagorean relationship.

(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.

Question 1. Assertion (A): Two geometric figures are congruent if they have exactly the same shape and size.

Reason (R): Congruent figures can be superimposed on each other by rigid transformations (translation, rotation, reflection).

(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.

Question 2. Assertion (A): Two line segments are congruent if their lengths are equal.

Reason (R): Length is the measure that determines the size of a line segment.

(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.

Question 3. Assertion (A): The SSS criterion is a valid test for triangle congruence.

Reason (R): If all three sides of one triangle are equal to the corresponding three sides of another triangle, the triangles are congruent.

(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.

Question 4. Assertion (A): The AAA congruence criterion can be used to prove that two triangles are congruent.

Reason (R): Triangles with all three corresponding angles equal are similar, not necessarily congruent.

(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.

Question 5. Assertion (A): If $\triangle \text{ABC} \cong \triangle \text{XYZ}$, then corresponding parts like sides and angles are equal.

Reason (R): This property is formally stated as CPCTC (Corresponding Parts of Congruent Triangles are Congruent).

(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.

Question 6. Assertion (A): The RHS criterion is used for proving congruence in any triangle.

Reason (R): The RHS criterion is specifically for right-angled triangles, requiring the hypotenuse and one side to be equal.

(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.

Question 1. Assertion (A): Two figures are similar if they have the same shape but possibly different sizes.

Reason (R): For similar figures, corresponding angles are equal and corresponding sides are proportional.

(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.

Question 2. Assertion (A): The AA similarity criterion states that if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

Reason (R): If two pairs of angles are equal, the third pair must also be equal due to the angle sum property of a triangle.

(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.

Question 3. Assertion (A): The Basic Proportionality Theorem (BPT) is also known as Thales Theorem.

Reason (R): The BPT states that a line parallel to one side of a triangle intersecting the other two sides divides the two sides proportionally.

(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.

Question 4. Assertion (A): If a line divides two sides of a triangle in the same ratio, then the line is parallel to the third side.

Reason (R): This is the converse of the Basic Proportionality Theorem.

(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.

Question 5. Assertion (A): All congruent triangles are similar.

Reason (R): Congruent triangles have equal corresponding angles and corresponding sides are proportional with a ratio of 1:1.

(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.

Question 6. Assertion (A): All squares are similar.

Reason (R): All squares have four $90^\circ$ angles and their sides are always in proportion to each other.

(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.

Question 1. Assertion (A): If two triangles are similar, the ratio of their areas is equal to the square of the ratio of their corresponding sides.

Reason (R): This theorem relates the scaling factor of lengths to the scaling factor of areas in similar figures.

(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.

Question 2. Assertion (A): If the ratio of corresponding sides of two similar triangles is 3:5, the ratio of their areas is 9:25.

Reason (R): The area is a 2-dimensional measurement, so the ratio scales with the square of the linear dimensions.

(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.

Question 3. Assertion (A): In a right-angled triangle, the altitude drawn from the right angle to the hypotenuse divides the original triangle into two similar triangles.

Reason (R): These two smaller triangles are also similar to the original triangle.

(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.

Question 4. Assertion (A): Similarity of triangles is used in calculating the height of tall structures based on shadow lengths.

Reason (R): The sun's rays can be considered parallel, creating similar triangles formed by the objects and their shadows.

(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.

Question 5. Assertion (A): If the areas of two similar triangles are equal, then the triangles are congruent.

Reason (R): If the ratio of areas is 1:1, the ratio of corresponding sides is also 1:1, which is the condition for congruence.

(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.

Question 6. Assertion (A): If the ratio of areas of two similar triangles is $a:b$, then the ratio of their corresponding altitudes is $\sqrt{a}:\sqrt{b}$.

Reason (R): The ratio of corresponding linear measures in similar triangles is the square root of the ratio of their areas.

(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.

Question 1. Assertion (A): The sum of the interior angles of any convex quadrilateral is $360^\circ$.

Reason (R): A quadrilateral can be divided into two triangles by a diagonal.

(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.

Question 2. Assertion (A): A parallelogram has opposite sides parallel and equal.

Reason (R): In a parallelogram, opposite angles are equal and adjacent angles are supplementary.

(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.

Question 3. Assertion (A): A rhombus is a parallelogram with all sides equal.

Reason (R): The diagonals of a rhombus are perpendicular bisectors of each other.

(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.

Question 4. Assertion (A): A square is a special type of rectangle.

Reason (R): A square is a rectangle with all four sides equal.

(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.

Question 5. Assertion (A): If the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram.

Reason (R): This property is a defining characteristic and criterion for a parallelogram.

(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.

Question 6. Assertion (A): A trapezium has exactly one pair of parallel sides.

Reason (R): An isosceles trapezium has non-parallel sides equal in length.

(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.

Question 1. Assertion (A): The line segment joining the midpoints of two sides of a triangle is parallel to the third side.

Reason (R): This is the first part of the Mid-Point Theorem.

(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.

Question 2. Assertion (A): In $\triangle$ABC, if D and E are midpoints of AB and AC, then DE = $\frac{1}{2}$ BC.

Reason (R): The Mid-Point Theorem states that the segment joining the midpoints is half the length of the third side.

(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.

Question 3. Assertion (A): The converse of the Mid-Point Theorem is used to prove that a line is parallel to a side of a triangle.

Reason (R): The converse states that a line through the midpoint of one side, parallel to another side, bisects the third side.

(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.

Question 4. Assertion (A): The figure formed by joining the midpoints of the sides of any quadrilateral is always a parallelogram.

Reason (R): Applying the Mid-Point Theorem to the triangles formed by the diagonals shows that opposite sides of the midpoint figure are parallel to the diagonals.

(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.

Question 5. Assertion (A): In $\triangle$ABC, if D, E, F are midpoints of sides, the area of $\triangle$DEF is one-fourth the area of $\triangle$ABC.

Reason (R): $\triangle$DEF is similar to $\triangle$ABC with a similarity ratio of 1:2, and the ratio of areas is the square of the similarity ratio.

(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.

Question 6. Assertion (A): If the figure formed by joining the midpoints of a quadrilateral is a rhombus, then the diagonals of the original quadrilateral are perpendicular.

Reason (R): In the midpoint figure, the sides are parallel to the diagonals of the original quadrilateral, and the diagonals of a rhombus are perpendicular.

(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.

Question 1. Assertion (A): Area is the measure of the region enclosed by the boundary of a plane figure.

Reason (R): Area is always measured in square units, such as $\text{cm}^2$ or $\text{m}^2$.

(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.

Question 2. Assertion (A): If two figures are congruent, then they are equal in area.

Reason (R): Congruent figures have the same shape and size, so they cover the same amount of plane surface.

(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.

Question 3. Assertion (A): Parallelograms on the same base and between the same parallels have equal area.

Reason (R): The area of a parallelogram is given by the product of its base and height, and the height is constant between the same parallels.

(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.

Question 4. Assertion (A): A triangle and a parallelogram on the same base and between the same parallels have equal area.

Reason (R): The area of such a triangle is half the area of the parallelogram.

(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.

Question 5. Assertion (A): A median of a triangle divides it into two triangles of equal area.

Reason (R): The two triangles have equal bases (halves of the original side) and the same altitude from the opposite vertex.

(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.

Question 6. Assertion (A): If two triangles have the same area and the same base, they lie between the same parallels.

Reason (R): If the base and area are the same, the height must be the same, and points at a constant distance from a line lie on a parallel line.

(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.

Question 1. Assertion (A): A circle is the set of all points in a plane that are equidistant from a fixed point.

Reason (R): The fixed point is called the centre, and the fixed distance is called the radius.

(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.

Question 2. Assertion (A): The diameter of a circle is the longest chord.

Reason (R): The diameter passes through the centre of the circle, which is the farthest point from any point on the circumference among points on a chord.

(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.

Question 3. Assertion (A): The circumference of a circle is the perimeter of the circle.

Reason (R): The formula for the circumference of a circle with radius $r$ is $2\pi r$.

(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.

Question 4. Assertion (A): A sector of a circle is the region bounded by a chord and its corresponding arc.

Reason (R): A segment of a circle is the region bounded by two radii and an arc.

(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.

Question 5. Assertion (A): Two circles are congruent if they have the same radius.

Reason (R): Congruent figures have the same size and shape, and the radius determines both for a circle.

(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.

Question 6. Assertion (A): All circles are similar.

Reason (R): Any circle can be scaled (resized) to match any other circle while preserving its shape.

(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.

Question 1. Assertion (A): The angle subtended by a chord at the centre of a circle is twice the angle subtended by the same chord at any point on the remaining part of the circle.

Reason (R): This is a fundamental theorem in circle geometry.

(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.

Question 2. Assertion (A): Equal chords of a circle subtend equal angles at the centre.

Reason (R): This is because the triangles formed by the chords and radii to the endpoints are congruent by SSS criterion.

(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.

Question 3. Assertion (A): The perpendicular from the centre of a circle to a chord bisects the chord.

Reason (R): This property can be proven using congruent right triangles formed by the radii, the perpendicular, and the halves of the chord.

(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.

Question 4. Assertion (A): Angles in the same segment of a circle are equal.

Reason (R): These angles are subtended by the same arc at points on the circumference in that segment.

(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.

Question 5. Assertion (A): The angle in a semicircle is always a right angle.

Reason (R): The diameter subtends a straight angle ($180^\circ$) at the centre, and the angle at the circumference is half the angle at the centre.

(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.

Question 6. Assertion (A): Chords that are equidistant from the centre of a circle are equal in length.

Reason (R): This is the converse of the property that equal chords are equidistant from the centre.

(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.

Question 1. Assertion (A): A cyclic quadrilateral is one whose all four vertices lie on a circle.

Reason (R): The circle passing through the vertices is called the circumscribed circle.

(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.

Question 2. Assertion (A): In a cyclic quadrilateral, the sum of opposite angles is $180^\circ$.

Reason (R): Opposite angles of a cyclic quadrilateral are supplementary.

(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.

Question 3. Assertion (A): A quadrilateral is cyclic if and only if the sum of one pair of opposite angles is $180^\circ$.

Reason (R): If one pair of opposite angles is supplementary, the other pair must also be supplementary because the total sum of interior angles is $360^\circ$.

(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.

Question 4. Assertion (A): The exterior angle of a cyclic quadrilateral at a vertex is equal to the interior opposite angle.

Reason (R): The exterior angle and its adjacent interior angle form a linear pair, summing to $180^\circ$, and the adjacent interior angle is supplementary to the opposite interior angle.

(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.

Question 5. Assertion (A): All rectangles are cyclic quadrilaterals.

Reason (R): The opposite angles of a rectangle are all $90^\circ$, and $90^\circ + 90^\circ = 180^\circ$, which is the condition for a quadrilateral to be cyclic.

(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.

Question 6. Assertion (A): All rhombuses are cyclic quadrilaterals.

Reason (R): A rhombus has opposite angles equal, but they are not always supplementary unless the rhombus is a square.

(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.

Question 1. Assertion (A): A tangent line intersects a circle at exactly one point.

Reason (R): This single point is called the point of contact.

(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.

Question 2. Assertion (A): The radius drawn to the point of contact of a tangent is perpendicular to the tangent.

Reason (R): The shortest distance from the centre to the tangent line is along the radius at the point of contact.

(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.

Question 3. Assertion (A): From a point inside a circle, exactly one tangent can be drawn to the circle.

Reason (R): Any line passing through a point inside the circle must intersect the circle at two distinct points.

(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.

Question 4. Assertion (A): The lengths of the two tangents drawn from an external point to a circle are equal.

Reason (R): This can be proven by showing the triangles formed by the external point, points of contact, and the centre are congruent using the RHS criterion.

(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.

Question 5. Assertion (A): Two parallel tangents can be drawn to a circle.

Reason (R): The line segment joining the points of contact of two parallel tangents is a diameter of the circle.

(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.

Question 6. Assertion (A): A secant intersects a circle at two points.

Reason (R): The segment of the secant inside the circle is called a chord.

(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.

Question 1. Assertion (A): A figure has line symmetry if it can be folded along a line such that the two halves match exactly.

Reason (R): This line is called the axis of symmetry.

(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.

Question 2. Assertion (A): A square has exactly 4 lines of symmetry.

Reason (R): A square is a regular quadrilateral, and a regular n-sided polygon has n lines of symmetry.

(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.

Question 3. Assertion (A): A circle has infinite lines of symmetry.

Reason (R): Any line passing through the centre of a circle is an axis of symmetry.

(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.

Question 4. Assertion (A): Reflection is a rigid transformation.

Reason (R): A rigid transformation preserves the distance between any two points, and reflection does this.

(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.

Question 5. Assertion (A): The letter A has horizontal line symmetry.

Reason (R): When reflected across the horizontal line through its middle, the top and bottom parts do not coincide exactly.

(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.

Question 6. Assertion (A): A parallelogram that is not a rhombus or a rectangle has no line symmetry.

Reason (R): Its only symmetry is rotational symmetry of order 2 about the intersection of its diagonals.

(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.

Question 1. Assertion (A): A figure has rotational symmetry if it coincides with its original position after a rotation less than $360^\circ$ about a fixed point.

Reason (R): The fixed point is called the centre of rotation.

(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.

Question 2. Assertion (A): The order of rotational symmetry is the number of times a figure fits onto itself during a $360^\circ$ rotation.

Reason (R): The angle of rotational symmetry is $360^\circ$ divided by the order of rotational symmetry.

(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.

Question 3. Assertion (A): A square has rotational symmetry of order 4.

Reason (R): Its angle of rotational symmetry is $90^\circ$.

(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.

Question 4. Assertion (A): A rectangle (that is not a square) has rotational symmetry of order 2.

Reason (R): It coincides with its original position after a rotation of $180^\circ$ about the intersection of its diagonals.

(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.

Question 5. Assertion (A): A circle has infinite rotational symmetry.

Reason (R): Any angle of rotation about its centre maps the circle onto itself.

(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.

Question 6. Assertion (A): A scalene triangle has no rotational symmetry other than the $360^\circ$ rotation.

Reason (R): Its order of rotational symmetry is 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.

Question 1. Assertion (A): 3-dimensional shapes have length, breadth, and height (or depth).

Reason (R): 2-dimensional shapes have only length and breadth.

(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.

Question 2. Assertion (A): A cube is a 3D shape with 6 square faces.

Reason (R): The intersection of two faces of a cube is an edge, and the intersection of edges is a vertex.

(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.

Question 3. Assertion (A): A cylinder is a polyhedron.

Reason (R): A cylinder has curved surfaces, and polyhedra are bounded by plane faces.

(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.

Question 4. Assertion (A): A sphere has no edges or vertices.

Reason (R): A sphere is bounded by a single curved surface, unlike polyhedra which have edges and vertices formed by intersecting plane faces.

(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.

Question 5. Assertion (A): A square pyramid has 5 faces, 8 edges, and 5 vertices.

Reason (R): A square pyramid has a square base and four triangular side faces meeting at an apex.

(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.

Question 6. Assertion (A): The faces of a cuboid are all squares.

Reason (R): A cuboid is a rectangular prism.

(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.

Question 1. Assertion (A): Oblique and isometric sketches are ways to represent 3D shapes on a 2D surface.

Reason (R): They provide a visual representation of the solid's form.

(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.

Question 2. Assertion (A): A cross-section is the 2D shape obtained by slicing a 3D solid with a plane.

Reason (R): Cross-sections help in understanding the internal structure of a solid.

(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.

Question 3. Assertion (A): If you slice a sphere with any plane, the cross-section is always a circle.

Reason (R): All points on the surface of a sphere are equidistant from its centre.

(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.

Question 4. Assertion (A): The Front View, Side View, and Top View of a solid are examples of orthographic projections.

Reason (R): Orthographic projections show the shape from different perpendicular directions, with projection lines parallel to each other.

(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.

Question 5. Assertion (A): In an oblique sketch, the front face is drawn in its true shape and size.

Reason (R): Lines showing depth in an oblique sketch are typically drawn at an angle to the front face, and their lengths may be foreshortened.

(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.

Question 6. Assertion (A): The top view of a square pyramid is a square with diagonals drawn from the centre.

Reason (R): The base is a square, and the apex is usually located directly above the centre of the square base, projecting onto the centre point in the top view.

(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.

Question 1. Assertion (A): A polyhedron is a solid bounded by plane polygonal faces.

Reason (R): Solids like cylinders and cones are also polyhedra.

(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.

Question 2. Assertion (A): A convex polyhedron has the property that for any face, the rest of the polyhedron lies entirely on one side of the plane of that face.

Reason (R): Cubes, prisms, and pyramids are examples of convex polyhedra.

(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.

Question 3. Assertion (A): Euler's formula for convex polyhedra is V - E + F = 2.

Reason (R): V represents vertices, E represents edges, and F represents faces.

(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.

Question 4. Assertion (A): A cube has 8 vertices, 12 edges, and 6 faces. It satisfies Euler's formula.

Reason (R): $8 - 12 + 6 = 2$, which is equal to 2.

(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.

Question 5. Assertion (A): A square pyramid is a regular polyhedron (Platonic solid).

Reason (R): A regular polyhedron must have faces that are congruent regular polygons, and the same number of faces must meet at each vertex.

(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.

Question 6. Assertion (A): There are exactly 5 Platonic solids.

Reason (R): These 5 solids are the only convex polyhedra whose faces are congruent regular polygons and where the same number of faces meet at each vertex.

(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.