Maths MCQs 331 to 360 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 12

331. The value of cotθ / cosecθ is equal to:

sinθ tanθ cosθ secθ

Explanation: cotθ = cosθ/sinθ and cosecθ = 1/sinθ. The expression becomes (cosθ/sinθ) / (1/sinθ) = (cosθ/sinθ) × (sinθ/1) = cosθ.

332. If the surface area of a sphere is 16π cm², its volume is:

32π/3 cm³ 16π cm³ 64π cm³ 8π cm³

Explanation: Surface Area A = 4πr² = 16π. So, r² = 4, and r = 2 cm. Volume V = (4/3)πr³ = (4/3)π(2)³ = (4/3)π(8) = 32π/3 cm³.

333. The distance of the point P(a, b) from the origin is:

a + b a² + b² |a| + |b| √(a² + b²)

Explanation: Using the distance formula from the origin (0, 0): d = √[(a-0)² + (b-0)²] = √(a² + b²).

334. If ΔPQR ~ ΔXYZ and PQ/XY = 2/3, then Area(ΔPQR)/Area(ΔXYZ) = ?

2/3 3/2 4/9 9/4

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

335. The value of tan²θ - sec²θ is:

1 0 -1 2

Explanation: From the identity 1 + tan²θ = sec²θ, if we subtract sec²θ and 1 from both sides, we get tan²θ - sec²θ = -1.

336. The area of a circle is 49π cm². Its circumference is:

7π cm 14π cm 21π cm 49π cm

Explanation: Area = πr² = 49π. So, r² = 49, and r = 7 cm. Circumference C = 2πr = 2π(7) = 14π cm.

337. The measure of an arc of a semicircle is:

90° 120° 180° 360°

Explanation: A semicircle is half of a full circle. Therefore, its arc measure is 360°/2 = 180°.

338. The slope of the line passing through points (a, b) and (-a, -b) is:

1 a/b b/a -1

Explanation: Using the slope formula: m = (-b - b) / (-a - a) = -2b / -2a = b/a.

339. The value of sin 30° + cos 60° is:

√3/2 1 1/2 √3

Explanation: sin 30° = 1/2 and cos 60° = 1/2. Their sum is 1/2 + 1/2 = 1.

340. If the height of an equilateral triangle is √3 cm, its side length is:

1 cm 2 cm 3 cm 4 cm

Explanation: The height of an equilateral triangle with side 's' is (√3/2)s. So, (√3/2)s = √3. This gives s/2 = 1, so the side 's' is 2 cm.

341. A boy is standing 48m from a building. He observes the top at a 30° angle of elevation. The height of the building is:

48 m 24 m 16√3 m 48√3 m

Explanation: Let h be the height. tan(30°) = h/48. So, 1/√3 = h/48. This gives h = 48/√3 = (48√3)/3 = 16√3 m.

342. The point P(x, y) is equidistant from A(7, 1) and B(3, 5). Which equation must be true?

y = x - 2 y = 2x + 1 x = y - 2 y = -x + 6

Explanation: Set the squared distances equal: (x-7)² + (y-1)² = (x-3)² + (y-5)². Expanding gives x²-14x+49+y²-2y+1 = x²-6x+9+y²-10y+25. Simplifying gives -14x-2y+50 = -6x-10y+34. Rearranging gives 8y = 8x - 16, so y = x - 2.

343. The value of sec 0° + tan 45° is:

1 2 0 Not defined

Explanation: sec 0° = 1 and tan 45° = 1. Their sum is 1 + 1 = 2.

344. A segment formed by a diameter of a circle is called a ______ segment.

Minor Semicircular Major Central

Explanation: A diameter divides a circle into two equal halves, each of which is called a semicircle. The region bounded by the diameter and the semicircle arc is a semicircular segment.

345. The sum of the angles of an octagon is:

720° 900° 1260° 1080°

Explanation: The sum of the interior angles of a polygon with n sides is (n-2) × 180°. For an octagon, n=8, so the sum is (8-2) × 180° = 6 × 180° = 1080°.

346. If the radius of a cone is doubled and its height is also doubled, its volume will increase by a factor of:

2 4 8 16

Explanation: Original Volume V = (1/3)πr²h. New radius = 2r, new height = 2h. New Volume V' = (1/3)π(2r)²(2h) = (1/3)π(4r²)(2h) = 8 × [(1/3)πr²h] = 8V.

347. The slope of the line passing through (2, 4) and (3, 6) is:

2 1/2 -2 -1/2

Explanation: Using the slope formula: m = (6 - 4) / (3 - 2) = 2 / 1 = 2.

348. The value of sin²(2x) + cos²(2x) is:

1 2 4 sin²x

Explanation: The identity sin²θ + cos²θ = 1 holds true for any angle θ, including the angle 2x.

349. If the sides of a triangle are 4, 5, and 6, what type of triangle is it?

Acute-angled Obtuse-angled Right-angled Scalene

Explanation: Check using the converse of Pythagoras theorem. 4² + 5² = 16 + 25 = 41. The longest side is 6, and 6² = 36. Since 41 > 36 (a² + b² > c²), the triangle is acute-angled. Since all sides are different, it is also scalene, but acute-angled is the more specific classification based on angles.

350. The length of the diagonal of a rectangle with sides 8 cm and 15 cm is:

23 cm 7 cm 17 cm 120 cm

Explanation: Using the Pythagorean theorem, d² = 8² + 15² = 64 + 225 = 289. The diagonal d = √289 = 17 cm. (8, 15, 17 is a Pythagorean triplet).

351. The line x = 0 is another name for the ______.

X-axis Y-axis origin line y = x

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

352. The value of sec²θ - tan²θ for θ = 30° is:

1 1/3 4/3 2/3

Explanation: The identity sec²θ - tan²θ = 1 is true for all values of θ where the functions are defined, including 30°.

353. If the volume of a cylinder is 900 cm³ and its height is 9 cm, the area of its base is:

10 cm² 100 cm² 8100 cm² 300 cm²

Explanation: Volume = Base Area × Height. So, 900 = Base Area × 9. Therefore, Base Area = 900 / 9 = 100 cm².

354. The number of medians in a triangle is:

1 2 3 4

Explanation: A median connects a vertex to the midpoint of the opposite side. Since a triangle has three vertices, it has three medians.

355. The sum of the angles of a decagon is:

1080° 1260° 1440° 1800°

Explanation: The sum of the interior angles of a polygon with n sides is (n-2) × 180°. For a decagon, n=10, so the sum is (10-2) × 180° = 8 × 180° = 1440°.

356. If the radius of a cone is doubled and its height is halved, its curved surface area will:

Remain the same Double Halve Change by a factor of √(r²+h²/4)

Explanation: Original CSA = πrl = πr√(h²+r²). New r' = 2r, h' = h/2. New slant height l' = √((h/2)²+(2r)²) = √(h²/4 + 4r²). New CSA' = π(2r)√(h²/4 + 4r²). The change is complex and not a simple factor like double or half.

357. The slope of the line y = mx + c represents its:

Steepness Y-intercept X-intercept Length

Explanation: The slope 'm' in the equation y = mx + c is a measure of the line's steepness or gradient.

358. The value of (secθ + tanθ)(secθ - tanθ) is:

1 0 sin²θ cos²θ

Explanation: This is in the form (a+b)(a-b) = a²-b². So the expression equals sec²θ - tan²θ, which is one of the Pythagorean identities and is equal to 1.

359. If the sides of a triangle are 7, 8, and 10, what type of triangle is it?

Acute-angled Obtuse-angled Right-angled Equilateral

Explanation: Check using the converse of Pythagoras theorem. 7² + 8² = 49 + 64 = 113. The longest side is 10, and 10² = 100. Since 113 > 100 (a² + b² > c²), the triangle is acute-angled.

360. The length of the diagonal of a cube with side 6 cm is:

6√2 cm 12 cm 6√3 cm 18 cm

Explanation: The diagonal of a cube with side 's' is given by the formula d = s√3. Therefore, the diagonal is 6√3 cm.

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