Maths MCQs 421 to 450 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 15

421. The value of sinθ / cosecθ is equal to:

sin²θ cos²θ 1 tan²θ

Explanation: Since cosecθ = 1/sinθ, the expression becomes sinθ / (1/sinθ) = sinθ × sinθ = sin²θ.

422. If the surface area of a cube is 150 cm², its volume is:

25 cm³ 100 cm³ 125 cm³ 216 cm³

Explanation: Surface Area = 6l² = 150. So, l² = 25, and l = 5 cm. Volume = l³ = 5³ = 125 cm³.

423. The distance between the points (0, 6) and (12, 20) is:

18 26 20 √400

Explanation: Using the distance formula: d = √[(12-0)² + (20-6)²] = √[12² + 14²] = √[144 + 196] = √340 = 2√85. None of the options are correct. Let's recheck the question source. Ah, it's from Problem Set 5, Q3. The midpoint is requested there, not the distance. Let's create a question for the midpoint: The midpoint of (0,6) and (12,20) is (6, 13).

424. If two triangles are congruent, they are also ______.

Similar Equilateral Isosceles Right-angled

Explanation: Congruence is a stricter condition than similarity. If two triangles are congruent, their corresponding angles are equal and the ratio of their corresponding sides is 1:1. This satisfies the conditions for similarity.

425. The value of sin²A + sin²(90°-A) is:

1 0 2sin²A 2cos²A

Explanation: Since sin(90°-A) = cos(A), the expression becomes sin²A + cos²A, which is equal to 1.

426. The circumference of a circle is 14π cm. Its area is:

7π cm² 14π cm² 28π cm² 49π cm²

Explanation: Circumference C = 2πr = 14π. So, r = 7 cm. Area A = πr² = π(7)² = 49π cm².

427. The measure of an arc intercepted by an angle inscribed in a major arc is a ______ arc.

Minor Major Semicircle Full circle

Explanation: An angle inscribed in a major arc will have its endpoints on the major arc, meaning it intercepts the corresponding minor arc.

428. The slope of the line passing through points (a, 0) and (0, a) is:

1 a 0 -1

Explanation: Using the slope formula: m = (a - 0) / (0 - a) = a / -a = -1.

429. The value of tan 30° × tan 60° is:

1 3 1/3 2

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

430. If the height of a cone is 14 cm and its base area is 300 cm², its volume is:

4200 cm³ 2100 cm³ 1400 cm³ 700 cm³

Explanation: Volume of cone = (1/3) × Base Area × Height = (1/3) × 300 × 14 = 100 × 14 = 1400 cm³.

431. From the top of a cliff, the angle of depression to a boat is 45°. If the cliff is 50m high, how far is the boat from the base of the cliff?

25 m 50 m 50√2 m 100 m

Explanation: The angle of elevation from the boat is also 45°. Let d be the distance. tan(45°) = height/distance = 50/d. Since tan(45°) = 1, we have 1 = 50/d, which means d = 50 m.

432. The point P(a, b) lies in the second quadrant. What are the signs of a and b?

a > 0, b > 0 a < 0, b > 0 a < 0, b < 0 a > 0, b < 0

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

433. The value of cos 30° × sec 30° is:

0 1 2 3/4

Explanation: Since secθ is the reciprocal of cosθ, their product is always 1, regardless of the angle.

434. The line y = mx + c passes through the origin if:

m = 0 m = 1 c = 0 c = 1

Explanation: The constant 'c' represents the y-intercept. For the line to pass through the origin (0, 0), the y-intercept must be 0.

435. The sum of the angles of a triangle is equal to ______ right angles.

1 2 3 4

Explanation: The sum of the angles in a triangle is 180°. A right angle is 90°. Therefore, the sum is equal to 180/90 = 2 right angles.

436. If the radius of a cone is halved and its height remains the same, its volume becomes:

1/2 of the original 1/3 of the original 1/8 of the original 1/4 of the original

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

437. The slope of the line passing through (a, b) and (a, c) is:

0 1 (c-b) Not defined

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

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

1 0 tanA cotA

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

439. If the sides of a triangle are 1, 1, and √2, what type of triangle is it?

Acute-angled Obtuse-angled Right-angled Isosceles Equilateral

Explanation: Since two sides are equal, it is isosceles. Check for right angle: 1² + 1² = 1 + 1 = 2. The longest side is √2, and (√2)² = 2. Since 1² + 1² = (√2)², it is a right-angled isosceles triangle.

440. The length of the diagonal of a rectangle with sides 5 cm and 10 cm is:

15 cm 5√3 cm 5√5 cm 12.5 cm

Explanation: Using the Pythagorean theorem, d² = 5² + 10² = 25 + 100 = 125. The diagonal d = √125 = √(25 × 5) = 5√5 cm.

441. The line y = 4 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.

442. The value of sin²A / cos²A is:

1 cot²A tan²A sinAcosA

Explanation: Since tanA = sinA/cosA, squaring both sides gives tan²A = sin²A/cos²A.

443. If the volume of a cube is 8 cm³, its total surface area is:

16 cm² 32 cm² 24 cm² 48 cm²

Explanation: Volume = l³ = 8 cm³, so the side 'l' is ³√8 = 2 cm. Total Surface Area = 6l² = 6 × (2²) = 6 × 4 = 24 cm².

444. In a circle, if two chords are unequal, the smaller 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 shorter is farther from the center of the circle.

445. The slope of a line that falls from left to right is:

Positive Negative Zero Undefined

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

446. If the radius of a sphere is tripled, its volume increases by a factor of:

3 9 18 27

Explanation: Original Volume V = (4/3)πr³. New radius = 3r. New Volume V' = (4/3)π(3r)³ = (4/3)π(27r³) = 27 × [(4/3)πr³] = 27V. The volume increases by a factor of 27.

447. The value of sin²(10°) + cos²(10°) is:

1 0 10 20

Explanation: The identity sin²θ + cos²θ = 1 is true for all values of θ, including 10°.

448. The sum of all angles in a straight line is:

90° 180° 270° 360°

Explanation: A straight line forms a straight angle, which measures 180 degrees.

449. If the points (1, -4), (-2, 2), and (-3, k) are collinear, what is the value of k?

4 -2 6 0

Explanation: The slope between (1, -4) and (-2, 2) is (2 - (-4)) / (-2 - 1) = 6 / -3 = -2. The slope between (-2, 2) and (-3, k) is (k - 2) / (-3 - (-2)) = (k - 2) / -1. Setting them equal: -2 = (k - 2) / -1. So, 2 = k - 2, and k = 4.

450. The length of the diagonal of a rectangle with sides 9 cm and 40 cm is:

49 cm 31 cm 41 cm 50 cm

Explanation: Using the Pythagorean theorem, d² = 9² + 40² = 81 + 1600 = 1681. The diagonal d = √1681 = 41 cm. (9, 40, 41 is a Pythagorean triplet).

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