Maths MCQs 241 to 270 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 9

241. The value of sec²θ - tan²θ is:

1 0 -1 2

Explanation: This is a rearrangement of the identity 1 + tan²θ = sec²θ. Subtracting tan²θ from both sides gives 1 = sec²θ - tan²θ.

242. If the radius of a circle is 14 cm, what is the area of a sector with a central angle of 60°?

154/3 cm² 308/3 cm² 308/3 cm² 154 cm²

Explanation: Area of sector = (θ/360) × πr² = (60/360) × (22/7) × 14² = (1/6) × (22/7) × 196 = (1/6) × 22 × 28 = 616/6 = 308/3 cm².

243. The point P(-1, -1) lies in which quadrant?

First Second Third Fourth

Explanation: The third quadrant is where both the x-coordinate and the y-coordinate are negative.

244. If two triangles are similar, their corresponding angles are ______.

Congruent Proportional Unequal Supplementary

Explanation: The definition of similar triangles is that their corresponding angles are equal (congruent) and their corresponding sides are in proportion.

245. The value of cot 60° is:

√3 1/√3 1 0

Explanation: cotθ is the reciprocal of tanθ. Since tan 60° = √3, cot 60° = 1/√3.

246. The surface area of a cuboid is given by the formula:

2(lb + bh + hl) 2h(l + b) lbh l + b + h

Explanation: The total surface area of a cuboid is the sum of the areas of its six rectangular faces. The formula is 2(lb + bh + hl).

247. The perpendicular from the center of a circle to a chord ______ the chord.

bisects trisects is parallel to is longer than

Explanation: This is a fundamental property of circles. A line drawn from the center perpendicular to a chord will always divide the chord into two equal parts.

248. The distance between points R(0, -3) and S(0, 5/2) is:

5/2 1/2 11/2 -1/2

Explanation: Since both points are on the Y-axis, the distance is the absolute difference of their y-coordinates: |5/2 - (-3)| = |2.5 + 3| = 5.5 = 11/2.

249. The value of cosec(90° - θ) is:

cosecθ secθ -cosecθ -secθ

Explanation: This is a complementary angle identity. The cosecant of an angle is equal to the secant of its complement.

250. If the area of a square is 144 cm², its perimeter is:

12 cm 24 cm 36 cm 48 cm

Explanation: Area = s² = 144 cm², so the side 's' is √144 = 12 cm. The perimeter is 4s = 4 × 12 = 48 cm.

251. A storm broke a tree. The treetop rested 20 m from the base, making a 60° angle with the horizontal. What was the height of the broken part?

20 m 20√3 m 60 m 40 m

Explanation: This forms a right-angled triangle. The broken part is the hypotenuse (h). The distance from the base is the adjacent side (20m). cos(60°) = adjacent/hypotenuse = 20/h. So, 1/2 = 20/h, which gives h = 40 m.

252. The point P(-4, 4) lies in which quadrant?

First Second Third Fourth

Explanation: The second quadrant is where the x-coordinate is negative and the y-coordinate is positive.

253. The value of cot 90° is:

0 1 -1 Not defined

Explanation: cotθ = cosθ / sinθ. Since cos 90° = 0 and sin 90° = 1, cot 90° = 0 / 1 = 0.

254. Circles that lie in the same plane are called ______ circles.

Congruent Coplanar Concentric Collinear

Explanation: Objects that lie on the same plane are called coplanar. This is a condition for many geometric theorems involving circles.

255. The sum of the angles in a triangle is:

180° 360° 90° 270°

Explanation: The Angle Sum Property of a triangle states that the sum of the measures of the interior angles of a triangle is always 180°.

256. If the radius of a cone is halved and its height is doubled, its volume will:

Remain the same Double Halve Be one-fourth

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

257. The slope of the line y = 3x + 5 is:

3 5 -3/5 8

Explanation: The equation is in the slope-intercept form y = mx + c, where 'm' is the slope. In this case, m = 3.

258. The value of cosec²θ - 1 is:

sin²θ cos²θ tan²θ cot²θ

Explanation: This is from the identity 1 + cot²θ = cosec²θ. Subtracting 1 from both sides gives cot²θ = cosec²θ - 1.

259. If the diagonal of a cube is 5√3 cm, its volume is:

25 cm³ 75 cm³ 125 cm³ 150 cm³

Explanation: The diagonal of a cube with side 'l' is l√3. So, l√3 = 5√3, which means the side 'l' is 5 cm. The volume is l³ = 5³ = 125 cm³.

260. If two chords are equidistant from the center of a circle, they are ______.

Parallel Perpendicular Equal in length Unequal in length

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

261. The slope of the line y = 7 is:

0 1 7 Not defined

Explanation: The line y = 7 is a horizontal line. All horizontal lines have a slope of 0.

262. The value of sin²θ + cos²θ for θ = 45° is:

1/2 1 2 0

Explanation: The identity sin²θ + cos²θ = 1 is true for any angle θ, including 45°.

263. If the volume of a cube is 27 cm³, its total surface area is:

27 cm² 36 cm² 54 cm² 81 cm²

Explanation: Volume = l³ = 27 cm³, so the side 'l' is ³√27 = 3 cm. Total Surface Area = 6l² = 6 × (3²) = 6 × 9 = 54 cm².

264. Two concentric circles have radii 5 cm and 3 cm. The length of the chord of the larger circle which touches the smaller circle is:

4 cm 6 cm 10 cm 8 cm

Explanation: This forms a right-angled triangle where the hypotenuse is the radius of the larger circle (5 cm), one leg is the radius of the smaller circle (3 cm), and the other leg is half the chord length (x). So, x² + 3² = 5². x² + 9 = 25, x² = 16, and x = 4 cm. The full chord length is 2x = 8 cm.

265. The line x = -4 is a line parallel to the ______.

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

Explanation: The equation x = k (where k is a constant) always represents a vertical line, which is parallel to the Y-axis.

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

Remain the same Double Halve Be one-fourth

Explanation: Original CSA = 2πrh. New radius = r/2, new height = 2h. New CSA' = 2π(r/2)(2h) = 2πrh = CSA. The curved surface area will remain the same.

267. The value of tanθ is not defined for θ = ______.

0° 90° 45° 180°

Explanation: tanθ = sinθ / cosθ. Since cos 90° = 0, the expression for tan 90° involves division by zero, making it undefined.

268. The perpendicular bisector of a chord of a circle passes through the ______.

Center Circumference Tangent point Major arc

Explanation: This is a key property of circles used in constructions. The perpendicular bisector of any chord will always pass through the center of the circle.

269. If the slope of a line is 1, its angle of inclination is:

30° 45° 60° 90°

Explanation: Since slope m = tan(θ), we need to find the angle θ for which tan(θ) = 1. This angle is 45°.

270. The length of the diagonal of a rectangle with sides 12 cm and 35 cm is:

47 cm 23 cm 37 cm 30 cm

Explanation: Using the Pythagorean theorem, d² = 12² + 35² = 144 + 1225 = 1369. The diagonal d = √1369 = 37 cm. (12, 35, 37 is a Pythagorean triplet).

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