Maths MCQs 451 to 480 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 16

451. The value of cosθ / secθ is equal to:

sin²θ cos²θ 1 tan²θ

Explanation: Since secθ = 1/cosθ, the expression becomes cosθ / (1/cosθ) = cosθ × cosθ = cos²θ.

452. If the volume of a cube is 216 cm³, its side length is:

6 cm 8 cm 12 cm 36 cm

Explanation: Volume = l³. So, l³ = 216. Therefore, l = ³√216 = 6 cm.

453. The distance between the points (a, b) and (a, -b) is:

2a √(4a² + 4b²) 2b 0

Explanation: Using the distance formula: d = √[(a-a)² + (-b-b)²] = √[0² + (-2b)²] = √[4b²] = 2b (assuming b is positive).

454. If two triangles are congruent, the ratio of their corresponding sides is:

1:1 1:2 2:1 1:√2

Explanation: Congruent triangles have corresponding sides of equal length. Therefore, the ratio of their corresponding sides is always 1:1.

455. The value of cos(A) / sin(90°-A) is:

1 0 tanA cotA

Explanation: Since sin(90°-A) = cos(A), the expression becomes cos(A) / cos(A) = 1.

456. The total surface area of a solid hemisphere is 3π cm². Its radius is:

1 cm 2 cm 3 cm 9 cm

Explanation: Total Surface Area = 3πr² = 3π. So, r² = 1, and r = 1 cm.

457. The measure of an arc intercepted by a central angle of 72° is:

36° 72° 144° 288°

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

458. The slope of the line passing through points (c, d) and (c, e) is:

0 1 (e-d) Not defined

Explanation: Using the slope formula: m = (e - d) / (c - c) = (e - d) / 0. Since division by zero is not defined, the slope is undefined. This is a vertical line.

459. The value of tan 60° / cot 30° is:

1 3 1/3 2

Explanation: tan 60° = √3 and cot 30° = √3. Their ratio is √3 / √3 = 1.

460. If the height of a cylinder is 10 cm and its curved surface area is 440 cm², its radius is:

5 cm 10 cm 7 cm 14 cm

Explanation: Curved Surface Area = 2πrh = 440. Using π ≈ 22/7, 2 × (22/7) × r × 10 = 440. So, (440/7)r = 440. This gives r = 7 cm.

461. A 20m ladder leans against a wall, making a 70° angle with the ground. How high up the wall does it reach? (sin 70° ≈ 0.94)

14 m 17 m 18.8 m 20 m

Explanation: The height (h) is the opposite side, and the ladder is the hypotenuse (20m). sin(70°) = h/20. So, 0.94 = h/20. This gives h = 20 × 0.94 = 18.8 m.

462. The point P(x, y) lies in the third quadrant. What are the signs of x and y?

x > 0, y > 0 x < 0, y > 0 x < 0, y < 0 x > 0, y < 0

Explanation: The third quadrant is defined by negative x-coordinates and negative y-coordinates.

463. The value of tan 30° × cot 60° is:

1 3 1/3 2

Explanation: tan 30° = 1/√3 and cot 60° = 1/√3. Their product is (1/√3) × (1/√3) = 1/3.

464. The number of faces of a cuboid is:

4 6 8 12

Explanation: A cuboid is a three-dimensional shape with six rectangular faces.

465. The sum of the angles of a dodecagon (12 sides) is:

1440° 1620° 1800° 1980°

Explanation: The sum of the interior angles of a polygon with n sides is (n-2) × 180°. For a dodecagon, n=12, so the sum is (12-2) × 180° = 10 × 180° = 1800°.

466. If the radius of a cylinder is halved and its height is quadrupled, its curved surface area will:

Remain the same Double Halve Be one-fourth

Explanation: Original CSA = 2πrh. New radius = r/2, new height = 4h. New CSA' = 2π(r/2)(4h) = 4πrh = 2(2πrh) = 2CSA. The area will double.

467. The slope of the line y = 5x - 2 is:

-2 5 -5/2 3

Explanation: The equation is in the slope-intercept form y = mx + c, where 'm' is the slope. In this case, m = 5.

468. The value of (1 + cot²A)sin²A is:

1 0 sin²A cos²A

Explanation: Using the identity 1 + cot²A = cosec²A, the expression becomes cosec²A × sin²A. Since cosec A is the reciprocal of sin A, the product is 1.

469. If the sides of a triangle are 10, 24, and 26, what is its area?

260 120 130 240

Explanation: This is a right-angled triangle (10²+24²=100+576=676=26²). The area is (1/2) × base × height = (1/2) × 10 × 24 = 120.

470. The length of the diagonal of a square with perimeter 32 cm is:

8 cm 16 cm 8√2 cm 16√2 cm

Explanation: Perimeter = 4s = 32 cm, so the side 's' is 8 cm. The diagonal d = s√2 = 8√2 cm.

471. The line y = 0 is another name for the ______.

X-axis Y-axis origin line y = x

Explanation: The X-axis is the set of all points where the y-coordinate is 0. Therefore, its equation is y = 0.

472. The value of sec²θ - tan²θ for θ = 60° is:

1 3 4 2

Explanation: The identity sec²θ - tan²θ = 1 is true for all values of θ where the functions are defined, including 60°.

473. If the volume of a cylinder is 100π cm³ and its radius is 5 cm, its height is:

20 cm 4 cm 5 cm 10 cm

Explanation: Volume = πr²h. So, 100π = π(5)²h = 25πh. Therefore, h = 100π / 25π = 4 cm.

474. The number of vertices of a cuboid is:

4 6 8 12

Explanation: A cuboid has 8 vertices (corners).

475. The sum of the angles of an 11-sided polygon (hendecagon) is:

1440° 1620° 1800° 1980°

Explanation: The sum of the interior angles of a polygon with n sides is (n-2) × 180°. For a hendecagon, n=11, so the sum is (11-2) × 180° = 9 × 180° = 1620°.

476. If the radius of a cylinder is tripled and its height is divided by 9, its volume will:

Remain the same Triple Be one-third Be nine times

Explanation: Original Volume V = πr²h. New radius = 3r, new height = h/9. New Volume V' = π(3r)²(h/9) = π(9r²)(h/9) = πr²h = V. The volume will remain the same.

477. The slope of a line perpendicular to the line x = 3 is:

0 1 -1 Not defined

Explanation: The line x = 3 is a vertical line with an undefined slope. A line perpendicular to a vertical line is a horizontal line, which has a slope of 0.

478. The value of (cosecθ + cotθ)(cosecθ - cotθ) is:

1 0 sin²θ cos²θ

Explanation: This is in the form (a+b)(a-b) = a²-b². So the expression equals cosec²θ - cot²θ, which is one of the Pythagorean identities and is equal to 1.

479. If the sides of a triangle are 6, 7, and 8, what type of triangle is it?

Acute-angled Obtuse-angled Right-angled Equilateral

Explanation: Check using the converse of Pythagoras theorem. 6² + 7² = 36 + 49 = 85. The longest side is 8, and 8² = 64. Since 85 > 64 (a² + b² > c²), the triangle is acute-angled.

480. The length of the diagonal of a rectangle with sides 16 cm and 30 cm is:

46 cm 240 cm 34 cm 30 cm

Explanation: Using the Pythagorean theorem, d² = 16² + 30² = 256 + 900 = 1156. The diagonal d = √1156 = 34 cm. (16, 30, 34 is a scaled version of the 8, 15, 17 triplet).

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