Assertion & Reasoning Questions PDF

ASSERTION & REASONING QUESTIONS DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as: (a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). (b)Both...

ASSERTION & REASONING QUESTIONS DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as: (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 but 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 true. 1. Assertion : If angles ‘a ’ and ‘b’ form a linear pair of angles and a = 400, then b = 1500. Reason : Sum of linear pair of angles is always 1800. (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 but 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 true. Ans: We know that the sum of linear pair of angles is always 1800. So, Reason is correct. Now, a + b = 400 + 1500 = 1900 ≠1800 Hence, Assertion is not correct Correct option is (d) Assertion (A) is false but reason (R) is true. 2. Assertion : If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 5 : 4, then the greater of the two angles is 1000. Reason : If a transversal intersects two parallel lines, then the sum of the interior angles on the same side of the transversal is 1800. Ans: We know If a transversal intersects two parallel lines, then the sum of the interior angles on the same side of the transversal is 1800 hat the solution of the line will satisfy the equation of the line. So, Reason is correct. Let the angles be 5x and 4x Since, these two angles are co-interior angles. So, we have 5x + 4x = 1800 ⇒ 9x = 1800 ⇒ x = 200 Hence, greater angle = 5x = 5 x 200 = 1000 So, Assertion is also correct Correct option is (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). 3. Assertion : An angle is 140 more than its complementary angle, then angle is 520. Reason : Two angles are said to be supplementary if their sum of measure of angles is 1800. Ans: We know that two angles are said to be supplementary if their sum of measure of angles is 1800. So, Reason is correct. Let the angle be x. Complement of x = (900 - x) Since, the difference is 140, we have x – (900 – x) = 140 ⇒ 2x = 1040 ⇒ x = 520 So, Assertion is also correct But reason (R) is not the correct explanation of assertion (A). Correct option is (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A). 4. Assertion : Supplement of angle is one fourth of itself. The measure of the angle is 1440. Reason : Two angles are said to be supplementary if their sum of measure of angles is 1800. Ans: We know that two angles are said to be supplementary if their sum of measure of angles is 1800. So, Reason is correct. Let the angle be x. Supplement of x = x So, x + x = 1800 ⇒ x = 1800 ⇒ x = 1440 So, Assertion is also correct Also, reason (R) is the correct explanation of assertion (A). Correct option is (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). 5. Assertion: The value of x from the adjoining figure, if l || m is 150. Reason: If two parallel lines are intersected by a transversal, then each pair of corresponding angles so formed is equal. Ans: We know that If two parallel lines are intersected by a transversal, then each pair of corresponding angles so formed is equal. So, Reason is correct. Also, we know that If a transversal intersects two parallel lines, then the sum of the interior angles on the same side of the transversal is 1800. From figure we have, 1200 – x + 5x = 1800 ⇒ 4x = 1800 – 1200 ⇒ 4x = 600 ⇒ x = 150 So, Assertion is also correct. But reason (R) is not the correct explanation of assertion (A). Correct option is (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A). 6. Assertion : If two internal opposite angles of a triangle are equal and external angle is given to be 1100, then each of the equal internal angle is 550. Reason : A triangle with one of its angle 900, is called a right triangle. Ans: For Assertion: We know that the exterior angle is equal to the sum of its interior opposite angles. So, x + x = 1100. ⇒ 2x = 1100 ⇒ x = 550 So, Assertion is correct Also, we know that a triangle with one of its angle 900, is called a right triangle. So, Reason is also correct. But reason (R) is not the correct explanation of assertion (A). Correct option is (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A). 7. Assertion : Sum of the pair of angles 1200 and 600 is supplementary. Reason : Two angles, the sum of whose measures is 1800, are called supplementary angles. Ans: We know that two angles are said to be supplementary if their sum of measure of angles is 1800. So, Reason is correct. Now, 1200 + 600 = 1800 ⇒ Sum of the pair of angles 1200 and 600 is supplementary. So, Assertion is also correct Also, reason (R) is the correct explanation of assertion (A). Correct option is (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). 8. Assertion : A triangle can have two obtuse angles. Reason : The sum of all the interior angles of a triangle is 1800 (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 but 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 true. Ans: We know that the sum of all the interior angles of a triangle is 1800. So, Reason (R) is true. Since the Sum of two obtuse angles will be more than 1800. So, Assertion (A) is false. Correct option is (d) Assertion (A) is false but reason (R) is true. 9. Assertion: The angles of a triangle are in the ratio 2 : 3 : 4. The largest angle of the triangle is 800. Reason: The sum of all the interior angles of a triangle is 1800 Ans: We know that the sum of all the interior angles of a triangle is 1800. So, Reason (R) is true. Let the angles of a triangle be 2x, 3x and 4x then we have 2x + 3x + 4x = 1800 ⇒ 9x = 1800 ⇒ x = 200. Hence, Largest angle = 4 x 200 = 800. So, Assertion (A) is also true. Also, Reason (R) is a correct explanation of Assertion (A). Correct option is (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). 10. Assertion: In the given figure, AOB is a straight line. If ∠AOC = (3x + 10)° and ∠BOC (4x − 26)°, then ∠BOC = 860 Reason: The sum of angles that are formed on a straight line is equal to 180°. Ans: We know that the sum of angles that are formed on a straight line is equal to 180°. So, Reason is correct We have : ∠AOC+∠BOC=180° [Since AOB is a straight line ] ⇒3x + 10 + 4x − 26 = 180° ⇒7x = 196° ⇒x = 28° ∴∠BOC = [4 × 28 − 26]° ⇒∠BOC=86°. So, Assertion (A) is also true. Correct option is (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). 11. Assertion : The angles of a triangle are in the ration 3 : 5 : 7. The triangle is acute- angled Reason : The sum of angles that are formed on a straight line is equal to 180°. Ans: We know that the sum of angles that are formed on a straight line is equal to 180°. So, Reason is correct Also, the sum of all the interior angles of a triangle is 1800 Let the angles measure (3x)°, (5x)° and (7x)°. Then,3x + 5x + 7x = 180° ⇒15x = 180° ⇒x = 12° Therefore, the angles are 3(12)°=36°, 5(12)°=60° and 7(12)° = 84°. Hence, the triangle is acute-angled. So, Assertion (A) is also true. But reason (R) is not the correct explanation of assertion (A). Correct option is (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A).