Maths MCQs 361 to 390 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 13

361. The value of cotθ × sinθ is equal to:

sinθ tanθ cosθ 1

Explanation: Since cotθ = cosθ/sinθ, the expression becomes (cosθ/sinθ) × sinθ. The sinθ terms cancel out, leaving cosθ.

362. If the volume of a sphere is 288π cm³, its radius is:

6 cm 8 cm 12 cm 9 cm

Explanation: Volume V = (4/3)πr³. So, 288π = (4/3)πr³. Dividing by π gives 288 = (4/3)r³. Multiplying by 3/4 gives 216 = r³. Therefore, r = ³√216 = 6 cm.

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

2b √(4a² + 4b²) 2a 0

Explanation: Using the distance formula: d = √[(-a-a)² + (b-b)²] = √[(-2a)² + 0²] = √[4a²] = 2a (assuming a is positive).

364. If ΔABC ~ ΔDEF and Area(ΔABC)/Area(ΔDEF) = 9/4, then BC/EF = ?

9/4 3/2 81/16 2/3

Explanation: The ratio of the areas of two similar triangles is the square of the ratio of their corresponding sides. So, (BC/EF)² = 9/4. Taking the square root gives BC/EF = 3/2.

365. The value of sin(45°) + cos(45°) is:

1 1/√2 2 √2

Explanation: sin 45° = 1/√2 and cos 45° = 1/√2. Their sum is 1/√2 + 1/√2 = 2/√2 = √2.

366. The circumference of a circle is 22π cm. Its area is:

22π cm² 484π cm² 121π cm² 11π cm²

Explanation: Circumference C = 2πr = 22π. So, r = 11 cm. Area A = πr² = π(11)² = 121π cm².

367. The measure of an angle in a segment smaller than a semicircle is always ______.

Acute Obtuse Right Straight

Explanation: An angle in a minor segment intercepts a major arc (greater than 180°). The inscribed angle is half the arc's measure, so it will be greater than 90°, making it obtuse.

368. The slope of a line is -1. What is its angle of inclination?

45° 90° 120° 135°

Explanation: The slope m = tan(θ). We need to find θ for which tan(θ) = -1. This occurs at 135°.

369. The value of (1 + cosθ)(1 - cosθ) is:

sin²θ cos²θ 1 2

Explanation: This is in the form (a+b)(a-b) = a²-b². So the expression equals 1 - cos²θ. From the identity sin²θ + cos²θ = 1, we know this is equal to sin²θ.

370. If the height of an equilateral triangle is 3√3 cm, its perimeter is:

9 cm 12 cm 18 cm 27 cm

Explanation: Height h = (√3/2)s. So, 3√3 = (√3/2)s. This gives s/2 = 3, so the side 's' is 6 cm. The perimeter is 3s = 3 × 6 = 18 cm.

371. A ladder 5.8m long is placed with its top reaching a window 4m high. How far is the base of the ladder from the wall?

1.8 m 4.2 m 9.8 m 3.2 m

Explanation: Let the distance be d. By Pythagoras theorem, d² + 4² = 5.8². d² + 16 = 33.64. d² = 17.64. d = √17.64 = 4.2 m.

372. The point P(0, 0) is known as the ______.

X-intercept Y-intercept Origin Midpoint

Explanation: The point (0, 0) where the X and Y axes intersect is called the origin of the Cartesian coordinate system.

373. The value of tan 45° + cot 45° is:

1 2 0 √2

Explanation: tan 45° = 1 and cot 45° = 1. Their sum is 1 + 1 = 2.

374. The number of angle bisectors in a triangle is:

1 2 3 4

Explanation: An angle bisector divides an angle into two equal angles. Since a triangle has three angles, it has three angle bisectors.

375. The sum of the angles of a heptagon is:

720° 900° 1080° 1260°

Explanation: The sum of the interior angles of a polygon with n sides is (n-2) × 180°. For a heptagon, n=7, so the sum is (7-2) × 180° = 5 × 180° = 900°.

376. If the radius of a cylinder is halved and its height is quadrupled, its volume will:

Remain the same Double Halve Be one-fourth

Explanation: Original Volume V = πr²h. New radius = r/2, new height = 4h. New Volume V' = π(r/2)²(4h) = π(r²/4)(4h) = πr²h = V. The volume will remain the same.

377. The slope of the line passing through (5, -2) and (7, 3) is:

2/5 -5/2 -2/5 5/2

Explanation: Using the slope formula: m = (3 - (-2)) / (7 - 5) = 5 / 2.

378. The value of cosec²θ(1 - cos²θ) is:

1 0 sin²θ cos²θ

Explanation: Since 1 - cos²θ = sin²θ, the expression becomes cosec²θ × sin²θ. As cosecθ is the reciprocal of sinθ, the product is 1.

379. If the sides of a triangle are 2, 3, and 4, what type of triangle is it?

Acute-angled Obtuse-angled Right-angled Isosceles

Explanation: Check using the converse of Pythagoras theorem. 2² + 3² = 4 + 9 = 13. The longest side is 4, and 4² = 16. Since 13 < 16 (a² + b² < c²), the triangle is obtuse-angled.

380. The length of the diagonal of a square with perimeter 20 cm is:

5 cm 10 cm 5√2 cm 10√2 cm

Explanation: Perimeter = 4s = 20 cm, so the side 's' is 5 cm. The diagonal d = s√2 = 5√2 cm.

381. 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.

382. The value of cosec²θ - cot²θ for θ = 60° is:

1 1/3 4/3 2/3

Explanation: The identity cosec²θ - cot²θ = 1 is true for all values of θ where the functions are defined, including 60°.

383. If the volume of a cube is 1000 cm³, its total surface area is:

100 cm² 400 cm² 600 cm² 1000 cm²

Explanation: Volume = l³ = 1000 cm³, so the side 'l' is ³√1000 = 10 cm. Total Surface Area = 6l² = 6 × (10²) = 6 × 100 = 600 cm².

384. In a circle, if two chords are equal, they are ______ from the center.

at different distances parallel equidistant perpendicular

Explanation: This is a property of circles. Chords that are congruent (equal in length) are always the same distance from the center.

385. The slope of a line that rises from left to right is:

Positive Negative Zero Undefined

Explanation: A positive slope indicates that the line goes upwards as you move from left to right on the coordinate plane.

386. If the radius of a sphere is doubled, its surface area becomes:

Double the original Four times the original Eight times the original Half the original

Explanation: Original Surface Area A = 4πr². New radius = 2r. New Area A' = 4π(2r)² = 4π(4r²) = 16πr² = 4A. The area becomes four times the original.

387. The value of tan²30° is:

1/3 1 3 1/9

Explanation: tan 30° = 1/√3. Therefore, tan²30° = (1/√3)² = 1/3.

388. The sum of all angles around a point is:

90° 180° 270° 360°

Explanation: A full rotation around a central point completes a circle, which measures 360 degrees.

389. If the points (2, 5), (3, 3), and (5, k) are collinear, what is the value of k?

1 -1 2 -2

Explanation: For the points to be collinear, the slope between any two pairs must be the same. The slope between (2, 5) and (3, 3) is (3-5)/(3-2) = -2. The slope between (3, 3) and (5, k) is (k-3)/(5-3) = (k-3)/2. Setting them equal: -2 = (k-3)/2. So, -4 = k-3, and k = -1.

390. The length of the diagonal of a rectangle with sides 7 cm and 24 cm is:

31 cm 25 cm 17 cm 26 cm

Explanation: Using the Pythagorean theorem, d² = 7² + 24² = 49 + 576 = 625. The diagonal d = √625 = 25 cm. (7, 24, 25 is a Pythagorean triplet).

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