Maths MCQs 121 to 150 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 5

121. The ratio cosθ / sinθ is equal to:

cotθ tanθ secθ cosecθ

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

122. A circle is a locus of points equidistant from a fixed point called the ______.

Radius Circumference Center Diameter

Explanation: The definition of a circle is the set of all points in a plane that are at a given distance (the radius) from a given point (the center).

123. If the sides of a triangle are a, b, and c, and a² + b² > c², the triangle is ______.

Obtuse-angled Acute-angled Right-angled Equilateral

Explanation: This is an extension of the Pythagorean theorem. If the square of the longest side (c) is less than the sum of the squares of the other two sides, the triangle is acute-angled.

124. The product cosθ × secθ is equal to:

0 1 -1 tanθ

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

125. The points of trisection of a segment joining A(-14, -10) and B(6, -2) are found. What are the coordinates of the point closer to A?

(-4, -6) (1, -4) (-22/3, -22/3) (-9, -8)

Explanation: The point closer to A divides the segment in the ratio 1:2. Using the section formula: x = (1*6 + 2*(-14))/(1+2) = (6-28)/3 = -22/3. y = (1*(-2) + 2*(-10))/(1+2) = (-2-20)/3 = -22/3.

126. The ratio of the circumference of a circle to its diameter is a constant known as ______.

Alpha (α) Pi (π) Theta (θ) Gamma (γ)

Explanation: The definition of Pi (π) is the ratio of a circle's circumference to its diameter. C/d = π.

127. In ΔABC, ray BD bisects ∠ABC. If AB/BC = AD/DC, this property is known as the ______.

Angle Bisector Theorem Converse of Angle Bisector Theorem Pythagoras Theorem Apollonius Theorem

Explanation: The Angle Bisector Theorem states that the bisector of an angle of a triangle divides the opposite side in the ratio of the remaining sides.

128. What is the value of cot 45°?

0 1 √3 Not defined

Explanation: cotθ is the reciprocal of tanθ. Since tan 45° = 1, cot 45° = 1/1 = 1.

129. The point of intersection of the perpendicular bisectors of the sides of a triangle is called the ______.

Centroid Circumcenter Incenter Orthocenter

Explanation: The circumcenter is the center of the circle that passes through all three vertices of the triangle (the circumcircle). It is found at the intersection of the perpendicular bisectors of the sides.

130. If the sides of a triangle are 7 cm, 24 cm, and 25 cm, is it a right-angled triangle?

Yes No Cannot be determined

Explanation: We check using the converse of the Pythagoras theorem. 7² + 24² = 49 + 576 = 625. And 25² = 625. Since the condition is met, it is a right-angled triangle.

131. The measure of a major arc is 360° minus the measure of its corresponding ______.

Major arc Semicircle Minor arc Central angle

Explanation: A major arc and its corresponding minor arc together make up a full circle (360°). Therefore, Measure of major arc = 360° - Measure of minor arc.

132. The slope of a line that is not vertical is the ratio of the vertical change (rise) to the horizontal change (______).

run fall jump slide

Explanation: The slope of a line is commonly defined as "rise over run", which represents the change in y-coordinates divided by the change in x-coordinates.

133. The value of cosec 30° is:

1/2 √2 2 2/√3

Explanation: cosecθ is the reciprocal of sinθ. Since sin 30° = 1/2, cosec 30° = 1 / (1/2) = 2.

134. The number of circles that can be drawn through one point is:

0 1 2 Infinite

Explanation: An infinite number of circles can be drawn passing through a single given point, each with a different center and radius.

135. If the sides of a triangle are 8, 15, and 17, what type of triangle is it?

Acute-angled Obtuse-angled Right-angled Equilateral

Explanation: Check using the converse of Pythagoras theorem. 8² + 15² = 64 + 225 = 289. And 17² = 289. Since 8² + 15² = 17², it is a right-angled triangle.

136. The ratio of the circumference to the radius of a circle is:

π 2π π/2 4π

Explanation: Circumference C = 2πr. The ratio C/r = (2πr)/r = 2π.

137. What are the coordinates of the midpoint of the segment joining P(-2, -5) and Q(4, 3)?

(1, -1) (2, -2) (3, -1) (1, 1)

Explanation: Using the midpoint formula: x = (-2+4)/2 = 2/2 = 1. y = (-5+3)/2 = -2/2 = -1. The coordinates are (1, -1).

138. The value of sin 60° is:

1/2 √3/2 1/√2 1

Explanation: In a 30°-60°-90° triangle, the side opposite the 60° angle is √3/2 times the hypotenuse. Since sinθ = opposite/hypotenuse, sin 60° = √3/2.

139. If two circles intersect, and each passes through the center of the other, what is the relationship between their radii and the distance between their centers?

radius = distance between centers radius = 2 × distance between centers radius = (1/2) × distance between centers radius = distance²

Explanation: If circle 1 passes through the center of circle 2, the distance between their centers must be equal to the radius of circle 2. If circle 2 also passes through the center of circle 1, the distance must also equal the radius of circle 1. Therefore, both radii are equal to the distance between the centers.

140. The lateral surface area of a cube with side 4 cm is:

16 cm² 96 cm² 64 cm² 24 cm²

Explanation: The lateral surface area of a cube is 4l². For l = 4 cm, the area is 4 × (4²) = 4 × 16 = 64 cm².

141. The number of circles that can be drawn through two distinct points is:

0 1 2 Infinite

Explanation: An infinite number of circles can be drawn passing through two distinct points. Their centers will all lie on the perpendicular bisector of the segment connecting the two points.

142. The slope of a horizontal line is:

0 1 -1 Not defined

Explanation: A horizontal line has no change in its y-coordinate (the "rise" is 0). Therefore, its slope is 0.

143. The value of tan 30° is:

√3 1 1/√3 0

Explanation: In a 30°-60°-90° triangle, the side opposite 30° is 1, the side adjacent is √3, and the hypotenuse is 2 (in ratio). tanθ = opposite/adjacent, so tan 30° = 1/√3.

144. If all vertices of a quadrilateral lie on the same circle, it is called a ______ quadrilateral.

Tangential Cyclic Inscribed Regular

Explanation: A quadrilateral whose vertices all lie on a single circle is defined as a cyclic quadrilateral.

145. The sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its ______.

sides altitudes angles vertices

Explanation: This is a property of parallelograms derived from Apollonius's theorem. For parallelogram ABCD, AC² + BD² = AB² + BC² + CD² + DA².

146. If the radius of a sphere is 3 cm, its volume is:

9π cm³ 18π cm³ 36π cm³ 12π cm³

Explanation: Volume V = (4/3)πr³. For r = 3, V = (4/3)π(3)³ = (4/3)π(27) = 4π × 9 = 36π cm³.

147. The point P(-2, 3) lies in which quadrant?

First Second Third Fourth

Explanation: In the Cartesian coordinate system, the second quadrant is where the x-coordinate is negative and the y-coordinate is positive.

148. The value of sin²60° + cos²60° is:

1 2 1/2 3/4

Explanation: The fundamental trigonometric identity sin²θ + cos²θ = 1 holds true for any angle θ, including 60°.

149. If the diagonals of a rectangle are 10 cm and one side is 6 cm, what is the length of the other side?

4 cm 16 cm 8 cm √64 cm

Explanation: The diagonal and two adjacent sides of a rectangle form a right-angled triangle. By Pythagoras theorem, 6² + b² = 10². So, 36 + b² = 100, which gives b² = 64, and b = 8 cm.

150. The point where a tangent touches a circle is called the ______.

Point of intersection Point of contact Origin Center

Explanation: The single point where a tangent line touches a circle is known as the point of contact or point of tangency.

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