Mathematics MCQs - Part 17
481. The value of tanθ / cot(90°-θ) is:
Explanation: Since cot(90°-θ) = tanθ, the expression becomes tanθ / tanθ = 1.
482. If the volume of a sphere is 4851 cm³, what is its radius? (Use π ≈ 22/7)
Explanation: V = (4/3)πr³ => 4851 = (4/3)(22/7)r³ => r³ = (4851 × 3 × 7) / (4 × 22) = 1157.625. So, r = ³√1157.625 = 10.5 cm.
483. The distance between the points (x, y) and (0, 0) is:
Explanation: This is a direct application of the distance formula where one point is the origin.
484. All circles are ______.
Explanation: All circles have the same shape, but not necessarily the same size. Therefore, all circles are similar to each other.
485. The value of cos²17° - sin²73° is:
Explanation: Since 73° = 90° - 17°, sin(73°) = sin(90°-17°) = cos(17°). The expression becomes cos²17° - cos²17° = 0.
486. The area of a circle is 314 cm². Its radius is approximately:
Explanation: Area A = πr² = 314. Using π ≈ 3.14, we have 3.14r² = 314. So, r² = 100, and r = 10 cm.
487. A quadrilateral ABCD is drawn to circumscribe a circle. Then AB + CD is equal to:
Explanation: This is Pitot's theorem, which states that for a tangential quadrilateral (a quadrilateral that circumscribes a circle), the sums of opposite sides are equal. So, AB + CD = AD + BC.
488. The slope of the line passing through points (0, 4) and (0, -3) is:
Explanation: The line passes through two points with the same x-coordinate (0), which means it is a vertical line (the Y-axis). The slope of a vertical line is undefined.
489. The value of sin 30° / cos 60° is:
Explanation: sin 30° = 1/2 and cos 60° = 1/2. Their ratio is (1/2) / (1/2) = 1.
490. If the height of a cylinder is equal to its radius, its volume is:
Explanation: Volume V = πr²h. If h = r, then V = πr²(r) = πr³.
491. A tree casts a shadow 15m long when the angle of elevation of the sun is 60°. The height of the tree is:
Explanation: The shadow is the adjacent side (15m). Let h be the height (opposite side). tan(60°) = h/15. So, √3 = h/15, which gives h = 15√3 m.
492. The point P(x, y) lies in the fourth quadrant. What are the signs of x and y?
Explanation: The fourth quadrant is defined by positive x-coordinates and negative y-coordinates.
493. The value of tan 45° × cot 45° is:
Explanation: Since cotθ is the reciprocal of tanθ, their product is always 1.
494. The number of edges of a cube is:
Explanation: A cube has 12 edges (the line segments where the faces meet).
495. The sum of the angles of a 20-sided polygon (icosagon) is:
Explanation: The sum of the interior angles of a polygon with n sides is (n-2) × 180°. For an icosagon, n=20, so the sum is (20-2) × 180° = 18 × 180° = 3240°.
496. If the radius of a cone is tripled and its height is divided by 3, its volume will:
Explanation: Original Volume V = (1/3)πr²h. New radius = 3r, new height = h/3. New Volume V' = (1/3)π(3r)²(h/3) = (1/3)π(9r²)(h/3) = 3 × [(1/3)πr²h] = 3V. The volume will triple.
497. The slope of a line perpendicular to the line y = -3x + 1 is:
Explanation: The slope of the given line is -3. The slope of a perpendicular line is the negative reciprocal. So, m_perp = -1/(-3) = 1/3.
498. The value of sin A / cos A is:
Explanation: This is the definition of the tangent function in terms of sine and cosine.
499. If the sides of a triangle are 2, 2, and 3, what type of triangle is it?
Explanation: Since two sides are equal, it is isosceles. Check for angle type: 2² + 2² = 4 + 4 = 8. The longest side is 3, and 3² = 9. Since 8 < 9 (a² + b² < c²), the triangle is obtuse-angled.
500. The length of the diagonal of a rectangle with sides 20 cm and 21 cm is:
Explanation: Using the Pythagorean theorem, d² = 20² + 21² = 400 + 441 = 841. The diagonal d = √841 = 29 cm. (20, 21, 29 is a Pythagorean triplet).
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