Class 10 Mathematics – Assertion & Reason Online Quiz (50 Questions)
A. Both A and R are true and R is the correct explanation
B. Both A and R are true but R is not the correct explanation
C. A is true but R is false
D. A is false but R is true
Q1.
Assertion: HCF of two numbers divides their sum.
Reason: HCF divides any linear combination of the numbers.
Q2.
Assertion: A polynomial of degree n has at most n zeroes.
Reason: Graph of polynomial can intersect x-axis at most n times.
Q3.
Assertion: If two lines intersect, system has unique solution.
Reason: Lines intersect at exactly one point.
Q4.
Assertion: Discriminant determines nature of roots.
Reason: Discriminant is b²−4ac.
Q5.
Assertion: Common difference of AP is constant.
Reason: Difference of consecutive terms is same.
Q6.
Assertion: Similar triangles have equal angles.
Reason: Corresponding sides are proportional.
Q7.
Assertion: Distance formula is derived using Pythagoras theorem.
Reason: Coordinates form right-angled triangle.
Q8.
Assertion: sin²θ + cos²θ = 1.
Reason: It is derived using unit circle.
Q9.
Assertion: Trigonometry helps find inaccessible heights.
Reason: Ratios relate angles with sides.
Q10.
Assertion: Tangent is perpendicular to radius at point of contact.
Reason: Angle between radius and tangent is 90°.
Areas related to circles • Surface areas & volumes • Statistics • Probability
(All follow same Assertion–Reason logic and format)
Assertion–Reason Questions (11–50)
Q11.
Assertion: Area of circle depends on square of radius.
Reason: Area = πr².
Q12.
Assertion: Volume of sphere is proportional to cube of radius.
Reason: Volume = 4/3 πr³.
Q13.
Assertion: Mean gives central tendency of data.
Reason: Mean is sum of observations divided by number of observations.
Q14.
Assertion: Probability of impossible event is zero.
Reason: Favorable outcomes are zero.
Q15.
Assertion: Areas of similar triangles are in ratio of squares of sides.
Reason: Corresponding sides are proportional.
Q16.
Assertion: Length of tangent from external point is equal.
Reason: Tangents from same external point are congruent.
Q17.
Assertion: Section formula finds coordinates of a point dividing line segment.
Reason: It is based on ratio of distances.
Q18.
Assertion: tanθ = sinθ / cosθ.
Reason: tanθ is ratio of perpendicular to base.
Q19.
Assertion: Probability of sure event is one.
Reason: Favorable outcomes equal total outcomes.
Q20.
Assertion: Mode represents most frequent observation.
Reason: It is affected by extreme values.
Assertion–Reason Questions (21–50)
Q21.
Assertion: Curved surface area of cylinder depends on height.
Reason: CSA of cylinder = 2πrh.
Q22.
Assertion: Area of triangle is zero if its vertices are collinear.
Reason: Height of triangle becomes zero.
Q23.
Assertion: Quadratic equation may have equal roots.
Reason: Discriminant can be zero.
Q24.
Assertion: nth term of AP depends on common difference.
Reason: aₙ = a + (n−1)d.
Q25.
Assertion: Pythagoras theorem applies only to right-angled triangles.
Reason: Hypotenuse exists only in right triangle.
Q26.
Assertion: Trigonometric ratios are undefined at 90°.
Reason: Base becomes zero.
Q27.
Assertion: Tangent at any point touches circle at one point only.
Reason: Tangent intersects circle at exactly one point.
Q28.
Assertion: Mean is affected by extreme values.
Reason: Mean uses all observations.
Q29.
Assertion: Probability lies between 0 and 1.
Reason: It is ratio of favorable to total outcomes.
Q30.
Assertion: Euclid’s division algorithm finds HCF.
Reason: It repeatedly uses remainder.
Class 10 Mathematics – Assertion & Reason MCQs (31–50)
Choose the correct option:
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
31. Assertion (A): The quadratic equation x² − 5x + 6 = 0 has two equal roots.
Reason (R): The discriminant of the equation is zero.
32. Assertion (A): A pair of linear equations can have infinitely many solutions.
Reason (R): If a₁/a₂ = b₁/b₂ = c₁/c₂, then the system has infinitely many solutions.
33. Assertion (A): The HCF of two consecutive natural numbers is 1.
Reason (R): Consecutive numbers have no common factor other than 1.
34. Assertion (A): The graph of y = x² is symmetric about the y-axis.
Reason (R): The value of y remains same for x and −x.
35. Assertion (A): The value of sin 60° is √3/2.
Reason (R): sin θ = opposite/hypotenuse.
36. Assertion (A): The tangent to a circle is perpendicular to the radius at the point of contact.
Reason (R): The tangent touches the circle at exactly one point.
37. Assertion (A): The sum of interior angles of a triangle is 180°.
Reason (R): A triangle is a three-sided polygon.
38. Assertion (A): A cube has 12 edges.
Reason (R): A cube has 6 square faces.
39. Assertion (A): Mean of first n natural numbers is (n+1)/2.
Reason (R): Sum of first n natural numbers is n(n+1)/2.
40. Assertion (A): Probability of an impossible event is 0.
Reason (R): Probability ranges from 0 to 1.
41. Assertion (A): The value of cos 90° is 0.
Reason (R): Cosine of an angle is adjacent/hypotenuse.
42. Assertion (A): The area of a circle depends on the square of its radius.
Reason (R): Area of a circle = πr².
43. Assertion (A): All circles are similar.
Reason (R): The ratio of radii of any two circles is constant.
44. Assertion (A): The volume of a sphere increases eight times when radius doubles.
Reason (R): Volume of sphere ∝ r³.
45. Assertion (A): The zero of a polynomial is the x-coordinate where graph cuts x-axis.
Reason (R): At x-intercept, y = 0.
46. Assertion (A): Two dice thrown together have 36 outcomes.
Reason (R): Each die has 6 outcomes.
47. Assertion (A): Distance formula is derived from Pythagoras theorem.
Reason (R): Distance between two points forms a right triangle.
48. Assertion (A): If two triangles are similar, their areas are in ratio of squares of sides.
Reason (R): Area ∝ (side)².
49. Assertion (A): A quadratic polynomial has at most two zeroes.
Reason (R): Degree of polynomial determines number of zeroes.
50. Assertion (A): The probability of a sure event is 1.
Reason (R): A sure event always occurs.
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