Maths MCQs 1 to 30 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.

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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 1

1. If a line parallel to a side of a triangle intersects the remaining sides in two distinct points, then the line divides the sides in the ______ proportion.

Different Inverse Same Cannot be determined

Explanation: This is the statement of the Basic Proportionality Theorem. When a line is drawn parallel to one side of a triangle intersecting the other two sides, it divides the two sides proportionally (in the same ratio).

2. In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the remaining two sides. This theorem is known as:

Apollonius Theorem Pythagoras Theorem Angle Bisector Theorem Basic Proportionality Theorem

Explanation: The relationship PR² = PQ² + QR² in a right-angled triangle PQR (right-angled at Q) is famously known as the Pythagoras Theorem.

3. How many tangents can be drawn to a circle from a point outside the circle?

One Two Infinite Zero

Explanation: From any single point in the exterior of a circle, exactly two tangents can be drawn to the circle. These tangent segments are equal in length.

4. The distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula:

√[(x₂-x₁)² + (y₂-y₁)²] √[(x₂+x₁)² + (y₂+y₁)²] (x₂-x₁) + (y₂-y₁) |x₂-x₁| + |y₂-y₁|

Explanation: This is the distance formula, derived from the Pythagoras theorem, used to find the distance between any two points in a Cartesian plane.

5. What is the value of sin²θ + cos²θ?

0 -1 1 2

Explanation: This is a fundamental trigonometric identity derived from the Pythagoras theorem. For any angle θ, the sum of the square of its sine and the square of its cosine is always 1.

6. The volume of a cone is given by the formula:

πr²h 2πrh πrl (1/3)πr²h

Explanation: The volume of a cone is one-third of the volume of a cylinder with the same base radius (r) and height (h). Hence, the formula is V = (1/3)πr²h.

7. If two triangles are similar, the ratio of their areas is equal to the ratio of the:

Sum of their corresponding sides Squares of their corresponding sides Cubes of their corresponding sides Perimeters

Explanation: According to the theorem of areas of similar triangles, the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.

8. Which of the following is a Pythagorean triplet?

(2, 3, 4) (4, 5, 6) (5, 12, 13) (1, 2, 3)

Explanation: A Pythagorean triplet consists of three positive integers a, b, and c, such that a² + b² = c². Here, 5² + 12² = 25 + 144 = 169, which is equal to 13².

9. The measure of an angle inscribed in a semicircle is:

45° 90° 180° 360°

Explanation: An angle inscribed in a semicircle always intercepts a 180° arc. According to the inscribed angle theorem, the measure of the angle is half the measure of its intercepted arc, which is 180°/2 = 90°.

10. The coordinates of the midpoint of a line segment joining points (x₁, y₁) and (x₂, y₂) are:

((x₁-x₂)/2, (y₁-y₂)/2) (x₁+x₂, y₁+y₂) ((x₁+y₁)/2, (x₂+y₂)/2) ((x₁+x₂)/2, (y₁+y₂)/2)

Explanation: The midpoint formula finds the average of the x-coordinates and the average of the y-coordinates of the endpoints.

11. What is the value of tan 45°?

0 1 √3 Not defined

Explanation: In a 45°-45°-90° triangle, the lengths of the opposite and adjacent sides to the 45° angle are equal. Since tanθ = opposite/adjacent, tan 45° = 1.

12. The total surface area of a cube with side 'l' is:

l³ 4l² 6l² 2(l+l)

Explanation: A cube has 6 identical square faces. The area of one face is l². Therefore, the total surface area is 6 times the area of one face, which is 6l².

13. Opposite angles of a cyclic quadrilateral are:

Supplementary Complementary Equal Unequal

Explanation: According to the theorem of cyclic quadrilaterals, the sum of opposite angles is always 180°. Angles that sum to 180° are called supplementary.

14. The slope of a line parallel to the X-axis is:

1 -1 0 Not defined

Explanation: A line parallel to the X-axis has no change in its y-coordinate (y₂ - y₁ = 0). Since slope = (y₂ - y₁)/(x₂ - x₁), the slope is 0.

15. The reciprocal of the sine ratio is called:

Secant (sec) Cosecant (cosec) Cotangent (cot) Cosine (cos)

Explanation: The cosecant ratio is defined as the reciprocal of the sine ratio. cosec θ = 1/sin θ.

16. The surface area of a sphere with radius 'r' is:

πr² 2πr² 4πr² (4/3)πr³

Explanation: The formula for the surface area of a sphere is A = 4πr². The formula (4/3)πr³ is for the volume of a sphere.

17. In a 30°-60°-90° triangle, the side opposite the 30° angle is:

Half of the hypotenuse Equal to the hypotenuse √3 times the hypotenuse Half of the side opposite 60°

Explanation: This is a key property of 30°-60°-90° triangles. The side opposite the 30° angle is the shortest side and is exactly half the length of the hypotenuse.

18. A line that intersects a circle in two distinct points is called a:

Tangent Secant Chord Radius

Explanation: A secant is a line that passes through two points on a circle. A chord is a line segment whose endpoints are on the circle. A tangent touches the circle at exactly one point.

19. The formula to find the coordinates of the centroid of a triangle with vertices (x₁, y₁), (x₂, y₂), and (x₃, y₃) is:

((x₁+x₂)/2, (y₁+y₂)/2) ((x₁+x₂+x₃)/2, (y₁+y₂+y₃)/2) (x₁+x₂+x₃, y₁+y₂+y₃) ((x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3)

Explanation: The centroid is the "center of mass" of a triangle. Its coordinates are the average of the coordinates of the three vertices.

20. The identity 1 + tan²θ = ?

sin²θ cosec²θ sec²θ cot²θ

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

21. The length of an arc of a sector with angle θ and radius r is given by:

(θ/360) × 2πr (θ/360) × πr² (θ/180) × πr θr

Explanation: The length of an arc is a fraction of the total circumference (2πr). The fraction is determined by the ratio of the sector's central angle (θ) to the total angle in a circle (360°).

22. In a 45°-45°-90° triangle, if the hypotenuse is 10√2 cm, what is the length of the other two sides?

5 cm 5√2 cm 10 cm 10√3 cm

Explanation: In a 45°-45°-90° triangle, the perpendicular sides are equal and are 1/√2 times the hypotenuse. So, side = (1/√2) × 10√2 = 10 cm.

23. If two circles touch each other externally, the distance between their centers is equal to the:

Sum of their radii Difference of their radii Product of their radii Ratio of their radii

Explanation: For two circles touching externally, the point of contact lies on the line segment joining their centers. Therefore, the distance between the centers is r₁ + r₂.

24. The slope of a line passing through points (x₁, y₁) and (x₂, y₂) is given by:

(x₂ - x₁) / (y₂ - y₁) (x₁ + x₂) / (y₁ + y₂) (y₂ + y₁) / (x₂ + x₁) (y₂ - y₁) / (x₂ - x₁)

Explanation: The slope (m) of a line is the ratio of the change in the y-coordinate (rise) to the change in the x-coordinate (run). The formula is m = (y₂ - y₁) / (x₂ - x₁).

25. The angle of elevation 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 same horizontal level Behind the observer

Explanation: The angle of elevation is used when an observer looks up at an object. The angle of depression is used when looking down.

26. The volume of a sphere is given by the formula:

4πr² (4/3)πr³ 2πr² πr³

Explanation: The formula for the volume of a sphere with radius 'r' is V = (4/3)πr³.

27. In a right-angled triangle, the perpendicular segment to the hypotenuse from the opposite vertex is the ______ of the segments into which the hypotenuse is divided.

Arithmetic mean Harmonic mean Algebraic mean Geometric mean

Explanation: This is the theorem of geometric mean. If an altitude is drawn to the hypotenuse of a right triangle, its length is the geometric mean of the two segments it divides the hypotenuse into.

28. The measure of a central angle of a circle is equal to the measure of its:

Corresponding minor arc Corresponding major arc Inscribed angle Diameter

Explanation: By definition, the measure of a minor arc is equal to the measure of its corresponding central angle.

29. The slope of the Y-axis is:

0 1 -1 Not defined

Explanation: For any two points on the Y-axis, the change in the x-coordinate (run) is 0. Since division by zero is not defined, the slope of the Y-axis cannot be determined.

30. The curved surface area of a cylinder with radius 'r' and height 'h' is:

πr²h 2πr(r+h) 2πrh πr²

Explanation: The curved surface area (or lateral surface area) of a cylinder is the area of its rectangular side if unrolled. The formula is A = 2πrh.

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