Assertion (A) & Reason (B) MCQ

MCQ 11 Mark

Assertion (A): A right triangle can have $8 cm, 15 cm$ and 17 cm as the lengths of its sides.
Reason $( R )$ : In a right triangle, the hypotenuse is the longest side.

A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
✓
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
C
Assertion (A) is true but Reason (R) is false.
D
Assertion (A) is false but Reason (R) is truе.

Answer

Correct option: B.

Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).

(b): We have, $8^2+15^2=64+225=289=17^2$.
Thus, $(8,15,17)$ is a Pythagorean triplet.
Clearly, $8 cm, 15 cm$ and 17 cm can be the lengths of the sides of a right triangle (by Pythagoras' theorem).
$\therefore A$ is true.
R is also true but R is not the correct explanation of A .

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MCQ 21 Mark

Assertion (A): If two sides of a triangle are 3 cm and 4 cm long then the length (say $x cm$ ) of its third side is such that $0<x<7$.
Reason $( R )$ : The sum of any two sides of a triangle is greater than the third side.

A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
C
Assertion (A) is true but Reason (R) is false.
✓
Assertion (A) is false but Reason (R) is truе.

Answer

Correct option: D.

Assertion (A) is false but Reason (R) is truе.

(d): By triangle inequality, the sum of any two sides of a triangle is greater than the third side.
$
\therefore x<3+4, \text { i.e., } x<7
$
Also, we know that the difference of any two sides of a triangle is less than the third side.
$
\therefore 4-3<x, \text { i.e., } 1<x
$
So we have, $1<x<7$.
$\therefore A$ is false.
R is clearly true (by triangle inequality).

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MCQ 31 Mark

Assertion (A): The sum of the exterior angles of a triangle is twice the sum of the interior angles.
Reason (R): An exterior angle of a triangle is always obtuse.

A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
✓
Assertion (A) is true but Reason (R) is false.
D
Assertion (A) is false but Reason (R) is truе.

Answer

Correct option: C.

Assertion (A) is true but Reason (R) is false.

(c): The sum of the exterior angles of a triangle is always $360^{\circ}$ which is twice the sum of the interior angles, i.e., $180^{\circ}$.
$\therefore A$ is true.
Consider a triangle having the measures of its angles as $20^{\circ}, 30^{\circ}$ and $130^{\circ}$. Clearly, the measures of one of its exterior angles is $20^{\circ}+30^{\circ}=50^{\circ}$, which is acute.
$\therefore R$ is false.

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MCQ 41 Mark

Assertion (A): In a right triangle, there always exists an angle which is equal to the sum of the other two angles.
Reason (R): There exists an isosceles triangle which is also a right triangle.

A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
✓
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
C
Assertion (A) is true but Reason (R) is false.
D
Assertion (A) is false but Reason (R) is truе.

Answer

Correct option: B.

Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).

(b): In every right triangle, one of the angles measures $90^{\circ}$ and the sum of the other two angles is also $90^{\circ}$. So, the sum of the other two angles is always equal to the first angle.
$\therefore A$ is true.
An isosceles triangle can also be a right triangle if its angles measure $90^{\circ}, 45^{\circ}$ and $45^{\circ}$ respectively.
$\therefore R$ is also true but R is not the correct explanation of A.

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MCQ 51 Mark

Assertion (A): A triangle can have more than one right angle.
Reason (R): Sum of the angles of a triangle is $180^{\circ}$.

A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
C
Assertion (A) is true but Reason (R) is false.
✓
Assertion (A) is false but Reason (R) is truе.

Answer

Correct option: D.

Assertion (A) is false but Reason (R) is truе.

(d): If a triangle has more than one right angle (say two right angles), the sum of the measures of its angles will be more than $180^{\circ}$, which is not possible since the sum of the angles of any triangle is always $180^{\circ}$.
So, a triangle cannot have more than one right angle.
$\therefore A$ is false but R is true.

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MCQ 61 Mark

Assertion (A): An isosceles triangle can be an obtuse triangle.
Reason (R): An obtuse triangle has only one obtuse angle.

✓
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
C
Assertion (A) is true but Reason (R) is false.
D
Assertion (A) is false but Reason (R) is truе.

Answer

Correct option: A.

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(a): Consider a triangle, the measures of whose angles are $120^{\circ}, 30^{\circ}$ and $30^{\circ}$. Such a triangle is both obtuse and isosceles.
$\therefore A$ is true.
R is also true (by the definition of obtuse triangle) and R is the correct explanation of A .

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MATHS Assertion (A) & Reason (B) MCQ

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