Maths MCQs 61 to 90 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.

Who are these MCQs for?

Banking Exams: IBPS, SBI, RBI, Clerk, PO, SO Teaching Eligibility Tests, TET, CTET, State-level exams, Engineering Jobs: Civil & Mechanical Engineering Recruitment, Defence, and more.

Services: Army, Navy, Air Force, Military Police Recruitment: Constable, Sub-Inspector, Railway Exams: RRB NTPC, Group D, ALP, Technician Public Service Exams: MPSC, UPSC, State PSCs, ITI Trades and Technical Exams.

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 3

61. The ratio sinθ / cosθ is equal to:

cotθ tanθ secθ cosecθ

Explanation: This is a fundamental trigonometric identity. tanθ = (opposite/adjacent) = (opposite/hypotenuse) / (adjacent/hypotenuse) = sinθ / cosθ.

62. The area of a segment of a circle is calculated by:

Area of sector - Area of corresponding triangle Area of sector + Area of corresponding triangle (1/2) × length of arc × radius Area of circle - Area of sector

Explanation: A segment is the region bounded by a chord and an arc. Its area is found by taking the area of the corresponding sector and subtracting the area of the isosceles triangle formed by the two radii and the chord.

63. In ΔABC, if M is the midpoint of side BC, then AB² + AC² = ?

2AM² + BM² AM² + 2BM² 2AM² + 2BM² AM² + BM²

Explanation: This is the statement of Apollonius's theorem, which relates the lengths of the sides of a triangle to the length of its median.

64. The product sinθ × cosecθ is equal to:

0 1 -1 tanθ

Explanation: Since cosecθ is the reciprocal of sinθ (i.e., cosecθ = 1/sinθ), their product is always 1.

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

|x| |y| √(x² + y²) x + y

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

66. The slant height (l) of a cone with height (h) and radius (r) is given by:

h² + r² h² - r² √(h² - r²) √(h² + r²)

Explanation: The height, radius, and slant height of a cone form a right-angled triangle with the slant height as the hypotenuse. The formula is derived from the Pythagoras theorem.

67. The number of tangents that can be drawn to a circle at a point on the circle is:

0 1 2 Infinite

Explanation: At any single point on a circle, there is one and only one line that can be drawn tangent to the circle.

68. The value of cos(90° - θ) is:

-cosθ -sinθ sinθ cosθ

Explanation: This is a complementary angle identity. The cosine of an angle is equal to the sine of its complement.

69. The volume of a hemisphere with radius 'r' is:

(4/3)πr³ 3πr² (1/2)πr³ (2/3)πr³

Explanation: The volume of a hemisphere is exactly half the volume of a full sphere. So, V = (1/2) × (4/3)πr³ = (2/3)πr³.

70. If the corresponding angles of two triangles are congruent, the triangles are similar. This is known as the ______ test of similarity.

SSS AAA (or AA) SAS ASA

Explanation: The Angle-Angle-Angle (AAA) similarity test states that if all three corresponding angles of two triangles are equal, then the triangles are similar. Since the third angle is fixed if two are known, this is often shortened to the AA test.

71. The coordinates of any point on the Y-axis are of the form:

(x, x) (x, 0) (0, y) (0, 0)

Explanation: For any point to be on the Y-axis, its horizontal displacement from the origin must be zero. Therefore, its x-coordinate is always 0.

72. An exterior angle of a cyclic quadrilateral is congruent to the ______.

Adjacent interior angle Vertically opposite angle Corresponding angle Interior opposite angle

Explanation: This is a corollary of the cyclic quadrilateral theorem. The exterior angle is congruent to the angle opposite to its adjacent interior angle.

73. The product tanθ × cotθ is equal to:

0 sinθ 1 cosθ

Explanation: Since cotθ is the reciprocal of tanθ (i.e., cotθ = 1/tanθ), their product is always 1.

74. The lateral surface area of a cuboid is:

2h(l + b) 2(lb + bh + hl) lbh 6l²

Explanation: The lateral surface area of a cuboid is the area of its four vertical faces, which is given by the formula 2h(l + b).

75. If secants containing chords AB and CD of a circle intersect outside the circle at point E, then ______.

AE × EC = BE × ED AE × EB = CE × ED AC × BD = AD × BC AE + EB = CE + ED

Explanation: This is the theorem of external division of chords. The product of the lengths of the segments of one secant is equal to the product of the lengths of the segments of the other secant.

76. The measure of an arc corresponding to a major sector is always:

Less than 90° Equal to 180° Greater than 180° Equal to 90°

Explanation: By definition, a major arc is the longer arc connecting two endpoints on a circle. Its measure is always greater than a semicircle (180°).

77. The distance between the points A(2, 3) and B(4, 1) is:

2√2 8 √10 4

Explanation: Using the distance formula: d = √[(4-2)² + (1-3)²] = √[2² + (-2)²] = √[4 + 4] = √8 = 2√2.

78. The value of sin(90° - θ) is:

sinθ -cosθ -sinθ cosθ

Explanation: This is a complementary angle identity. The sine of an angle is equal to the cosine of its complement.

79. If a secant through E intersects a circle at A and B, and a tangent through E touches the circle at T, then ______.

EA × EB = ET EA × EB = ET² EA + EB = ET ET² = EA + EB

Explanation: This is the Tangent-Secant Theorem. The square of the length of the tangent segment from the external point is equal to the product of the lengths of the secant segment and its external part.

80. The volume of a cube with side 'l' is:

6l² 4l² l³ l²

Explanation: The volume of a cube is the length of its side cubed. V = l × l × l = l³.

81. The point of contact of touching circles lies on the line joining their ______.

Centers Circumferences Tangents Chords

Explanation: This is the theorem of touching circles. Whether they touch internally or externally, the centers and the point of contact are collinear.

82. The slope of a vertical line is:

0 1 -1 Not defined

Explanation: A vertical line has an undefined slope because the change in x (the "run") is zero, which would lead to division by zero in the slope formula.

83. The value of cos 60° is:

1/2 √3/2 1/√2 0

Explanation: In a 30°-60°-90° triangle, the side adjacent to the 60° angle is half the hypotenuse. Since cosθ = adjacent/hypotenuse, cos 60° = 1/2.

84. The measure of an inscribed angle is ______ the measure of its intercepted arc.

Equal to Half Double Triple

Explanation: This is the Inscribed Angle Theorem, a fundamental property of circles.

85. If the diagonals of a quadrilateral bisect each other, it must be a:

Parallelogram Kite Trapezium Cyclic quadrilateral

Explanation: A key property of parallelograms (which includes rectangles, rhombuses, and squares) is that their diagonals bisect each other.

86. The section formula for a point dividing a segment in the ratio m:n is used to find its:

Length Slope Coordinates Midpoint

Explanation: The section formula, x = (mx₂ + nx₁)/(m+n) and y = (my₂ + ny₁)/(m+n), is used to find the coordinates of a point that divides a line segment in a specific ratio.

87. The value of tan 90° is:

0 1 -1 Not defined

Explanation: tanθ = sinθ / cosθ. Since cos 90° = 0, tan 90° = sin 90° / 0, which involves division by zero and is therefore not defined.

88. The curved surface area of a frustum of a cone is:

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

Explanation: The formula for the curved surface area of a frustum involves its slant height (l) and the radii of its two circular bases (r₁ and r₂). The correct formula is A = πl(r₁ + r₂).

89. If two lines have slopes m₁ and m₂, and m₁ × m₂ = -1, the lines are:

Parallel Perpendicular Intersecting but not perpendicular The same line

Explanation: A key property in coordinate geometry is that two non-vertical lines are perpendicular if and only if the product of their slopes is -1.

90. Corresponding arcs of congruent chords of a circle are ______.

Unequal Supplementary Congruent Complementary

Explanation: This theorem is the converse of the one in question 60. In the same circle or in congruent circles, if two chords are congruent, then their corresponding minor arcs are congruent.

Previous MCQs

Go back to the previous set

Next MCQs

Proceed to the next set