Maths MCQs 271 to 300 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 10

271. The value of (1 + tan²θ)(1 - sin²θ) is:

0 1 2 sin²θ

Explanation: Using identities, 1 + tan²θ = sec²θ and 1 - sin²θ = cos²θ. The expression becomes sec²θ × cos²θ. Since secθ = 1/cosθ, the product is (1/cos²θ) × cos²θ = 1.

272. If the radius of a circle is 15 cm and the area of a sector is 30 cm², what is the length of the arc of the sector?

2 cm 4 cm 5 cm 6 cm

Explanation: The area of a sector is given by A = (1/2)lr, where l is the arc length and r is the radius. So, 30 = (1/2) × l × 15. This gives 60 = 15l, and l = 4 cm.

273. The point P(5, 0) lies on ______.

the X-axis the Y-axis the origin the second quadrant

Explanation: Since the y-coordinate is 0, the point lies on the X-axis.

274. If ΔABC ~ ΔLMN and ∠B = 40°, then ∠M = ?

20° 40° 80° 140°

Explanation: In similar triangles, corresponding angles are congruent (equal). Since B and M are corresponding vertices, ∠M = ∠B = 40°.

275. The value of cot 0° is:

0 1 -1 Not defined

Explanation: cotθ = cosθ / sinθ. Since sin 0° = 0, the expression for cot 0° involves division by zero, making it undefined.

276. If the volume of a sphere is 36π cm³, its radius is:

6 cm 3 cm 9 cm 4 cm

Explanation: Volume V = (4/3)πr³. So, 36π = (4/3)πr³. Dividing by π gives 36 = (4/3)r³. Multiplying by 3/4 gives 27 = r³. Therefore, r = ³√27 = 3 cm.

277. The measure of an angle in a major segment is always ______.

Acute Obtuse Right Straight

Explanation: An angle in a major segment intercepts a minor arc (which is less than 180°). The measure of the inscribed angle is half the arc, so it will be less than 90°, making it an acute angle.

278. The slope of the line passing through points (-2, -3) and (-6, -8) is:

4/5 -5/4 5/4 -4/5

Explanation: Using the slope formula: m = (-8 - (-3)) / (-6 - (-2)) = (-8 + 3) / (-6 + 2) = -5 / -4 = 5/4.

279. The value of sec 45° is:

1/√2 √2 1 2

Explanation: secθ is the reciprocal of cosθ. Since cos 45° = 1/√2, sec 45° = 1 / (1/√2) = √2.

280. If the area of a circle is 154 cm², its radius is:

7 cm 14 cm 22 cm 49 cm

Explanation: Area = πr² = 154. Using π ≈ 22/7, (22/7)r² = 154. So, r² = 154 × (7/22) = 7 × 7 = 49. Therefore, r = 7 cm.

281. A kite is flying at a height of 60m. The string makes a 60° angle with the ground. The length of the string is:

60 m 120 m 40√3 m 60√3 m

Explanation: The height is the opposite side (60m), and the string is the hypotenuse (L). sin(60°) = opposite/hypotenuse = 60/L. So, √3/2 = 60/L. L = 120/√3 = (120√3)/3 = 40√3 m.

282. The point P(1, 2) lies in which quadrant?

First Second Third Fourth

Explanation: The first quadrant is where both the x-coordinate and the y-coordinate are positive.

283. The value of sin 90° is:

0 1 1/2 Not defined

Explanation: For a 90° angle, the opposite side is equal to the hypotenuse. Since sinθ = opposite/hypotenuse, sin 90° = hypotenuse/hypotenuse = 1.

284. If two circles intersect at two distinct points, the line joining their centers is the ______ of the common chord.

Perpendicular bisector Parallel line Angle bisector Tangent

Explanation: This is a property of intersecting circles. The line connecting the centers of two intersecting circles is always the perpendicular bisector of their common chord.

285. The sum of the measures of the angles of a hexagon is:

360° 540° 720° 1080°

Explanation: The sum of the interior angles of a polygon with n sides is given by the formula (n-2) × 180°. For a hexagon, n=6, so the sum is (6-2) × 180° = 4 × 180° = 720°.

286. If the radius of a cylinder is doubled and its height remains the same, its volume increases by a factor of:

2 4 8 16

Explanation: Original Volume V = πr²h. New radius = 2r. New Volume V' = π(2r)²h = π(4r²)h = 4(πr²h) = 4V. The volume increases by a factor of 4.

287. The slope of the line y = -x is:

1 0 -1 Not defined

Explanation: The equation is in the form y = mx + c. Here, m = -1.

288. The value of (sinθ + cosθ)² - 2sinθcosθ is:

1 0 2 -1

Explanation: Expanding (sinθ + cosθ)² gives sin²θ + 2sinθcosθ + cos²θ. Subtracting 2sinθcosθ leaves sin²θ + cos²θ, which is equal to 1.

289. If the sides of a triangle are 5, 12, 13, its area is:

60 30 65 78

Explanation: Since 5² + 12² = 25 + 144 = 169 = 13², this is a right-angled triangle. The area is (1/2) × base × height = (1/2) × 5 × 12 = 30.

290. The length of an arc of a circle with radius 7 cm and arc measure 30° is:

11/3 cm 22/3 cm 11 cm 22 cm

Explanation: Arc Length = (θ/360) × 2πr = (30/360) × 2 × (22/7) × 7 = (1/12) × 44 = 44/12 = 11/3 cm.

291. The line y = -3 is a line parallel to the ______.

X-axis Y-axis line y = x line y = -x

Explanation: The equation y = k (where k is a constant) always represents a horizontal line, which is parallel to the X-axis.

292. The value of sec 90° is:

0 1 -1 Not defined

Explanation: secθ = 1/cosθ. Since cos 90° = 0, the expression for sec 90° involves division by zero, making it undefined.

293. If the total surface area of a cube is 24 cm², its volume is:

4 cm³ 8 cm³ 16 cm³ 64 cm³

Explanation: Total Surface Area = 6l² = 24 cm², so l² = 4, and the side 'l' is 2 cm. The volume is l³ = 2³ = 8 cm³.

294. In a circle, if two chords are unequal, the larger chord is ______ the center.

nearer to farther from equidistant from at the same distance as

Explanation: A property of circles states that of two unequal chords, the one that is longer is closer to the center of the circle.

295. The slope of a line with an angle of inclination of 0° is:

0 1 -1 Not defined

Explanation: A line with a 0° inclination is a horizontal line. The slope m = tan(0°) = 0.

296. If the radius of a sphere is halved, its volume decreases by a factor of:

2 4 8 16

Explanation: Original Volume V = (4/3)πr³. New radius = r/2. New Volume V' = (4/3)π(r/2)³ = (4/3)π(r³/8) = (1/8) × [(4/3)πr³] = V/8. The volume becomes 1/8 of the original.

297. The value of tan²60° is:

1/3 1 3 9

Explanation: tan 60° = √3. Therefore, tan²60° = (√3)² = 3.

298. The measure of an angle in a minor segment is always ______.

Acute Obtuse Right Straight

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

299. If the points A, B, and C are collinear, what is the area of ΔABC?

0 1 Cannot be determined Infinite

Explanation: If three points are collinear, they lie on the same straight line and cannot form a triangle. The area of such a "degenerate" triangle is zero.

300. The total surface area of a cylinder with radius 5 cm and height 40 cm is:

400π cm² 425π cm² 450π cm² 200π cm²

Explanation: Total Surface Area = 2πr(r + h) = 2π(5)(5 + 40) = 10π(45) = 450π cm².

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