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.
Mathematics MCQs - Part 4
91. The ratio of areas of two triangles with equal height is 2:3. If the base of the smaller triangle is 6 cm, what is the base of the bigger triangle?
Explanation: For triangles with equal height, the ratio of their areas is equal to the ratio of their bases. So, A₁/A₂ = b₁/b₂. This gives 2/3 = 6/b₂. Solving for b₂, we get 2b₂ = 18, so b₂ = 9 cm.
92. In a right-angled triangle, if an altitude is drawn to the hypotenuse, the two triangles formed are similar to ______.
Explanation: This is the theorem of similarity in right-angled triangles. The altitude to the hypotenuse creates three similar triangles: the original one and the two smaller ones.
93. A line perpendicular to a radius at its endpoint on the circle is a ______ to the circle.
Explanation: This is the converse of the tangent-radius theorem. It provides a method for constructing a tangent to a circle.
94. What is the slope of the line passing through the points (2, 3) and (4, 7)?
Explanation: Using the slope formula, m = (y₂ - y₁) / (x₂ - x₁) = (7 - 3) / (4 - 2) = 4 / 2 = 2.
95. The value of sec 60° is:
Explanation: secθ is the reciprocal of cosθ. Since cos 60° = 1/2, sec 60° = 1 / (1/2) = 2.
96. The total surface area of a cone with radius 'r' and slant height 'l' is:
Explanation: The total surface area of a cone is the sum of its curved surface area (Ï€rl) and the area of its circular base (Ï€r²). The combined formula is Ï€r(r + l).
97. If three parallel lines are intersected by a transversal, the intercepts made on the transversal are ______.
Explanation: This is the property of three parallel lines and their transversals. The ratio of the intercepts made on one transversal is equal to the ratio of the corresponding intercepts made on any other transversal.
98. The points A(1, 2), B(1, 6), and C(1 + 2√3, 4) are vertices of a(n) ______ triangle.
Explanation: By calculating the distances AB, BC, and AC using the distance formula, you will find that all three sides have a length of 4 units, making the triangle equilateral.
99. How many common tangents can be drawn to two circles touching externally?
Explanation: Two circles touching externally have two direct common tangents and one transverse common tangent that passes through the point of contact, for a total of three common tangents.
100. The coordinates of any point on the X-axis are of the form:
Explanation: For any point to be on the X-axis, its vertical displacement from the origin must be zero. Therefore, its y-coordinate is always 0.
101. What is the value of sin 0°?
Explanation: For a 0° angle, the opposite side has a length of 0. Since sinθ = opposite/hypotenuse, sin 0° = 0/hypotenuse = 0.
102. The volume of a cylinder is given by the formula:
Explanation: The volume of a cylinder is the area of its circular base (Ï€r²) multiplied by its height (h). V = Ï€r²h.
103. In ΔPQR, if PS/SQ = PT/TR, then ______.
Explanation: This is the Converse of the Basic Proportionality Theorem. If a line divides two sides of a triangle proportionally, then it is parallel to the third side.
104. The distance of point (-3, 4) from the origin is:
Explanation: Using the distance formula: d = √[(-3-0)² + (4-0)²] = √[(-3)² + 4²] = √[9 + 16] = √25 = 5.
105. The angle between a tangent and a secant drawn from the point of contact is ______ the measure of its intercepted arc.
Explanation: This is the Tangent-Secant Theorem. The measure of the angle formed by a tangent and a secant through the point of contact is half the measure of the intercepted arc.
106. The coordinates of the origin in a Cartesian plane are:
Explanation: The origin is the point where the X-axis and Y-axis intersect, and its coordinates are (0, 0).
107. The product tanθ × tan(90° - θ) is equal to:
Explanation: Since tan(90° - θ) = cotθ, and cotθ is the reciprocal of tanθ, the product is tanθ × (1/tanθ) = 1.
108. The curved surface area of a hemisphere with radius 'r' is:
Explanation: The curved surface area of a hemisphere is half the surface area of a full sphere. So, A = (1/2) × 4Ï€r² = 2Ï€r².
109. The ratio of intercepts made by three parallel lines on one transversal is equal to the ratio of ______.
Explanation: This is the property of three parallel lines and their transversals. AB/BC = DE/EF for any two transversals.
110. In a right-angled triangle, if one side is half the hypotenuse, the angle opposite to that side is:
Explanation: This is the converse of the 30°-60°-90° theorem. If the side opposite an angle is half the hypotenuse, that angle must be 30°.
111. If two chords of a circle intersect inside the circle, then the product of the lengths of the segments of one chord is ______ the product of the lengths of the segments of the other chord.
Explanation: This is the theorem of internal division of chords. If chords AB and CD intersect at E, then AE × EB = CE × ED.
112. If the slope of a line is √3, what is its angle of inclination?
Explanation: Since slope m = tan(θ), we need to find the angle θ for which tan(θ) = √3. This angle is 60°.
113. The value of cos 45° is:
Explanation: In a 45°-45°-90° triangle, if the equal sides are 1, the hypotenuse is √2. Since cosθ = adjacent/hypotenuse, cos 45° = 1/√2.
114. The perimeter of a sector of a circle with radius 'r' and arc length 'l' is:
Explanation: The perimeter of a sector is the sum of the lengths of its two radii and its arc length. Perimeter = r + r + l = 2r + l.
115. If ΔABC ~ ΔDEF, A(ΔABC)/A(ΔDEF) = 1/2, and AB = 4, find DE.
Explanation: The ratio of areas of similar triangles is the square of the ratio of their corresponding sides. So, 1/2 = (AB/DE)² = (4/DE)². This gives DE² = 16 × 2 = 32. Therefore, DE = √32 = 4√2.
116. A circle touches all sides of a parallelogram. The parallelogram must be a ______.
Explanation: If a circle can be inscribed in a parallelogram, it means the sums of opposite sides are equal. In a parallelogram, opposite sides are already equal, so this implies all four sides are equal, which defines a rhombus.
117. The two points of trisection divide a line segment in the ratios ______.
Explanation: The two points that divide a segment into three equal parts are called points of trisection. The first point divides the segment in a 1:2 ratio, and the second point divides it in a 2:1 ratio.
118. The value of secθ in terms of cosθ is:
Explanation: The secant ratio is defined as the reciprocal of the cosine ratio. secθ = 1/cosθ.
119. In the formula for the lateral surface area of a cube, 4l², what does 'l' represent?
Explanation: The lateral surface area is the area of the four side faces. Since each face is a square with area l², the total lateral area is 4l², where 'l' is the length of a side (or edge) of the cube.
120. The number of circles that can pass through 3 collinear points is:
Explanation: A circle is defined by three non-collinear points. If the points are collinear (all lie on the same straight line), it is impossible to draw a circle that passes through all three.
Post a Comment