Maths MCQs 31 to 60 questions

 

 This comprehensive Mathematics MCQ collection is designed to meet the needs of candidates preparing for a wide range of competitive examinations and job recruitment tests. It includes carefully selected multiple-choice questions with detailed solutions, covering all essential mathematical concepts required for various sectors and exams.

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Key Features:

MCQs with solutions for effective practice and revision. Covers Arithmetic, Algebra, Geometry, Trigonometry, Mensuration, Statistics, Probability, and Advanced Mathematics. Questions are organized by topic for systematic learning and review. Includes previous year exam patterns and model questions. Helpful for both technical and non-technical posts. Improves speed, accuracy, and problem-solving skills essential for competitive exams.

Why these MCQs?

Mathematics is a core subject in almost every competitive exam. We offers

comprehensive coverage, clear concepts, and enough practice questions to ensure success across various job sectors.

Mathematics MCQs - Part 2

31. The ratio of areas of two triangles with equal bases is equal to the ratio of their corresponding ______.

Bases Heights Perimeters Medians

Explanation: Property: The ratio of the areas of two triangles with equal bases is equal to the ratio of their corresponding heights. A(Δ1)/A(Δ2) = h₁/h₂.

32. In a 30°-60°-90° triangle, the side opposite the 60° angle is ______ times the hypotenuse.

1/2 1/√2 √3/2 1

Explanation: This is a property of 30°-60°-90° triangles. The side opposite the 60° angle is √3/2 times the length of the hypotenuse.

33. If two circles touch internally, the distance between their centers is equal to the ______.

Sum of their radii Difference of their radii Product of their radii Half the sum of their radii

Explanation: For two circles touching internally, the distance between their centers is the difference between the radius of the larger circle and the radius of the smaller circle (R - r).

34. What is the distance of the point P(3, 4) from the origin (0, 0)?

3 4 5 7

Explanation: Using the distance formula, d = √[(3-0)² + (4-0)²] = √[3² + 4²] = √[9 + 16] = √25 = 5. This is also a classic 3-4-5 Pythagorean triplet.

35. The identity 1 + cot²θ = ?

sec²θ cosec²θ tan²θ sin²θ

Explanation: This is one of the three Pythagorean trigonometric identities. It's derived by dividing the identity sin²θ + cos²θ = 1 by sin²θ.

36. The volume of a cuboid with length l, breadth b, and height h is:

2(lb + bh + hl) 2h(l + b) l + b + h lbh

Explanation: The volume of a cuboid is the product of its three dimensions: length, breadth, and height. V = l × b × h.

37. Angles inscribed in the same arc are ______.

Supplementary Complementary Congruent Unequal

Explanation: This is a corollary of the inscribed angle theorem. All angles that are inscribed in the same arc intercept that arc, and therefore have the same measure, making them congruent.

38. What is the slope of a line with an inclination of 60°?

1 √3 1/√3 0

Explanation: The slope (m) of a line is equal to the tangent of its angle of inclination (θ). So, m = tan(60°) = √3.

39. The area of a sector of a circle with radius r and arc length l is given by:

(1/2)lr lr 2lr (1/3)lr

Explanation: The area of a sector can be calculated using the formula A = (1/2) × (length of arc) × (radius).

40. If ΔABC ~ ΔPQR and AB/PQ = 7/5, then which triangle is bigger?

ΔABC ΔPQR Both are equal Cannot be decided

Explanation: The ratio of corresponding sides AB to PQ is 7/5, which is greater than 1. This means the sides of ΔABC are longer than the corresponding sides of ΔPQR, making ΔABC the bigger triangle.

41. The point of concurrence of the medians of a triangle is called the:

Incenter Circumcenter Centroid Orthocenter

Explanation: The centroid is the point where the three medians of a triangle intersect. It divides each median in a 2:1 ratio.

42. What is the value of cos 90°?

1 0 1/2 Not defined

Explanation: For a 90° angle in a right triangle, the adjacent side has a length of 0. Since cosθ = adjacent/hypotenuse, cos 90° = 0/hypotenuse = 0.

43. The curved surface area of a cone is given by the formula:

πr²h 2πrh πrl (1/3)πr²h

Explanation: The curved surface area of a cone depends on its radius (r) and slant height (l). The formula is A = πrl.

44. A tangent at any point of a circle is ______ to the radius at the point of contact.

Perpendicular Parallel Equal Secant

Explanation: This is the tangent-radius theorem, which states that the radius drawn to the point of tangency is always perpendicular to the tangent line.

45. If a pair of opposite angles of a quadrilateral is supplementary, the quadrilateral is ______.

A parallelogram A rhombus A rectangle Cyclic

Explanation: This is the converse of the cyclic quadrilateral theorem. If the opposite angles of a quadrilateral sum to 180°, then its vertices lie on a single circle, making it a cyclic quadrilateral.

46. The total surface area of a solid hemisphere with radius 'r' is:

2πr² 3πr² 4πr² (2/3)πr³

Explanation: The total surface area of a solid hemisphere is the sum of its curved surface area (2πr²) and the area of its circular base (πr²), which equals 3πr².

47. If the slope of two lines are m₁ and m₂, and the lines are parallel, then:

m₁ = m₂ m₁ × m₂ = -1 m₁ = -m₂ m₁ + m₂ = 0

Explanation: Parallel lines have the same inclination with the x-axis, and therefore, they have equal slopes.

48. What is the value of sin 30°?

√3/2 1/√2 1/2 1

Explanation: In a 30°-60°-90° triangle, the side opposite the 30° angle is half the hypotenuse. Since sinθ = opposite/hypotenuse, sin 30° = 1/2.

49. The bisector of an angle of a triangle divides the side opposite to the angle in the ratio of the ______.

Remaining sides Altitudes Medians Angles

Explanation: This is the Angle Bisector Theorem, which states that the angle bisector of a triangle divides the opposite side into two segments that are proportional to the other two sides of the triangle.

50. The measure of a complete circle is:

90° 180° 270° 360°

Explanation: A complete revolution around a circle covers an angle of 360 degrees.

51. The distance of a point P(x, y) from the Y-axis is:

|x| |y| x² y²

Explanation: The distance of any point from the Y-axis is the absolute value of its x-coordinate.

52. Tangent segments drawn from an external point to a circle are ______.

Parallel Perpendicular Congruent Different lengths

Explanation: This is the Tangent Segment Theorem, which states that if two tangent segments are drawn to a circle from the same external point, they are equal in length (congruent).

53. The angle of depression is the angle formed by the line of vision with the horizontal when the point being viewed is:

Above the horizontal level Below the horizontal level At the horizontal level To the left of the observer

Explanation: The angle of depression is used when an observer looks down at an object from a higher position.

54. The volume of a frustum of a cone is given by:

(1/3)πh(r₁² + r₂²) πl(r₁ + r₂) (1/3)πh(r₁ + r₂ + r₁r₂) (1/3)πh(r₁² + r₂² + r₁r₂)

Explanation: The formula for the volume of a frustum involves the height (h) and the radii of its two circular bases (r₁ and r₂). The correct formula is V = (1/3)πh(r₁² + r₂² + r₁r₂).

55. The number of circles that can be drawn through three non-collinear points is:

Zero One Two Infinite

Explanation: There is one and only one unique circle that passes through any three given non-collinear points.

56. If a line divides any two sides of a triangle in the same ratio, then the line is ______ to the third side.

Parallel Perpendicular Equal Not related

Explanation: This is the statement of the Converse of the Basic Proportionality Theorem.

57. The total surface area of a cylinder is:

2πrh πr²h 2πr(r + h) 2πr²

Explanation: The total surface area of a cylinder is the sum of its curved surface area (2πrh) and the area of its two circular bases (2πr²). The combined formula is 2πr(r + h).

58. The measure of a semicircle arc is:

90° 180° 270° 360°

Explanation: A semicircle is exactly half of a full circle, so its measure is half of 360°, which is 180°.

59. The slope of a line is also known as:

tan of its inclination sin of its inclination cos of its inclination its length

Explanation: The slope of a line is defined as the tangent of the angle it makes with the positive direction of the X-axis. m = tan(θ).

60. Chords corresponding to congruent arcs of a circle are ______.

Parallel Perpendicular Congruent Unequal

Explanation: This theorem states that in the same circle or in congruent circles, if two arcs are congruent, then their corresponding chords are equal in length (congruent).

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