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.
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.
Mathematics MCQs - Part 14
391. The value of secθ / tanθ is equal to:
Explanation: secθ = 1/cosθ and tanθ = sinθ/cosθ. The expression becomes (1/cosθ) / (sinθ/cosθ) = (1/cosθ) × (cosθ/sinθ) = 1/sinθ = cosecθ.
392. If the surface area of a sphere is 324π cm², its radius is:
Explanation: Surface Area A = 4πr² = 324π. So, r² = 324/4 = 81. Therefore, r = √81 = 9 cm.
393. The distance between the points (a, -b) and (-a, -b) is:
Explanation: Using the distance formula: d = √[(-a-a)² + (-b-(-b))²] = √[(-2a)² + 0²] = √[4a²] = 2a (assuming a is positive).
394. If ΔABC ~ ΔPQR and Area(ΔABC)/Area(ΔPQR) = 16/25, then AB/PQ = ?
Explanation: The ratio of the areas of two similar triangles is the square of the ratio of their corresponding sides. So, (AB/PQ)² = 16/25. Taking the square root gives AB/PQ = 4/5.
395. The value of (sinθ)(cotθ) + (cosθ)(tanθ) is:
Explanation: (sinθ)(cosθ/sinθ) + (cosθ)(sinθ/cosθ) = cosθ + sinθ.
396. The area of a circle is 100π cm². Its circumference is:
Explanation: Area A = πr² = 100π. So, r² = 100, and r = 10 cm. Circumference C = 2πr = 2π(10) = 20π cm.
397. In a circle, if a chord is equal to the radius, the angle subtended by the chord at the center is:
Explanation: The chord and the two radii to its endpoints form a triangle. Since all three sides are equal to the radius, it is an equilateral triangle, and all its angles are 60°.
398. The slope of the line passing through points (0, 0) and (3, 6) is:
Explanation: Using the slope formula: m = (6 - 0) / (3 - 0) = 6 / 3 = 2.
399. The value of (1 + tanθ)(1 - tanθ) is:
Explanation: This is in the form (a+b)(a-b) = a²-b². So the expression equals 1² - tan²θ = 1 - tan²θ.
400. If the height of an equilateral triangle is 5√3 cm, its area is:
Explanation: Height h = (√3/2)s. So, 5√3 = (√3/2)s. This gives s/2 = 5, so the side 's' is 10 cm. Area = (√3/4)s² = (√3/4)(10)² = (√3/4) × 100 = 25√3 cm².
401. A person is at the top of a 100m lighthouse and sees a ship at an angle of depression of 30°. The distance of the ship from the lighthouse is:
Explanation: The angle of elevation from the ship is also 30°. Let d be the distance. tan(30°) = height/distance = 100/d. So, 1/√3 = 100/d. This gives d = 100√3 m.
402. The point P(3, -3) lies in which quadrant?
Explanation: The fourth quadrant is where the x-coordinate is positive and the y-coordinate is negative.
403. The value of sin 30° × cosec 30° is:
Explanation: Since cosecθ is the reciprocal of sinθ, their product is always 1, regardless of the angle.
404. The number of perpendicular bisectors in a triangle is:
Explanation: A perpendicular bisector is a line that is perpendicular to a side and passes through its midpoint. Since a triangle has three sides, it has three perpendicular bisectors.
405. The sum of the angles of a nonagon (9 sides) is:
Explanation: The sum of the interior angles of a polygon with n sides is (n-2) × 180°. For a nonagon, n=9, so the sum is (9-2) × 180° = 7 × 180° = 1260°.
406. If the radius of a cone is doubled and its height is also doubled, its curved surface area will increase by a factor of:
Explanation: Original CSA = πrl = πr√(h²+r²). New r' = 2r, h' = 2h. New slant height l' = √((2h)²+(2r)²) = √(4h² + 4r²) = 2√(h²+r²) = 2l. New CSA' = π(2r)(2l) = 4(πrl) = 4CSA. The area increases by a factor of 4.
407. The slope of the line x = -2 is:
Explanation: The line x = -2 is a vertical line. Vertical lines have an undefined slope.
408. The value of (1 + tan²45°)(1 - sin²45°) is:
Explanation: tan 45° = 1, so 1 + tan²45° = 1 + 1 = 2. sin 45° = 1/√2, so 1 - sin²45° = 1 - (1/√2)² = 1 - 1/2 = 1/2. The expression is 2 × (1/2) = 1.
409. If the sides of a triangle are 9, 12, and 15, what is the length of the altitude to the longest side?
Explanation: This is a right-angled triangle (9²+12²=81+144=225=15²). The area is (1/2)×9×12 = 54. The longest side (hypotenuse) is 15. Area = (1/2)×base×height = (1/2)×15×h. So, 54 = 7.5h. h = 54/7.5 = 7.2.
410. The length of an arc of a circle with radius 6 cm and arc measure 90° is:
Explanation: Arc Length = (θ/360) × 2πr = (90/360) × 2π(6) = (1/4) × 12π = 3π cm.
411. The line y = x makes an angle of ______ with the positive X-axis.
Explanation: The slope of the line y = x is 1. The angle of inclination θ is given by tan(θ) = slope. tan(θ) = 1, so θ = 45°.
412. The value of tan²θ / sec²θ is:
Explanation: tan²θ = sin²θ/cos²θ and sec²θ = 1/cos²θ. The expression becomes (sin²θ/cos²θ) / (1/cos²θ) = sin²θ.
413. If the volume of a cube is 64 cm³, its side length is:
Explanation: Volume = l³ = 64 cm³, so the side 'l' is ³√64 = 4 cm.
414. The number of perpendiculars that can be drawn to a line from a point not on it is:
Explanation: From a point outside a line, there is exactly one line that can be drawn perpendicular to the given line. This represents the shortest distance from the point to the line.
415. The sum of the angles of a dodecagon (12 sides) is:
Explanation: The sum of the interior angles of a polygon with n sides is (n-2) × 180°. For a dodecagon, n=12, so the sum is (12-2) × 180° = 10 × 180° = 1800°.
416. If the radius of a cylinder is doubled and its height is also doubled, its volume will increase by a factor of:
Explanation: Original Volume V = πr²h. New radius = 2r, new height = 2h. New Volume V' = π(2r)²(2h) = π(4r²)(2h) = 8(πr²h) = 8V.
417. The midpoint of the segment joining (22, 20) and (0, 16) is:
Explanation: Using the midpoint formula: x = (22+0)/2 = 11. y = (20+16)/2 = 36/2 = 18. The coordinates are (11, 18).
418. The value of cot²θ / cosec²θ is:
Explanation: cot²θ = cos²θ/sin²θ and cosec²θ = 1/sin²θ. The expression becomes (cos²θ/sin²θ) / (1/sin²θ) = cos²θ.
419. If the sides of a triangle are 5, 6, and 7, what type of triangle is it?
Explanation: Check using the converse of Pythagoras theorem. 5² + 6² = 25 + 36 = 61. The longest side is 7, and 7² = 49. Since 61 > 49 (a² + b² > c²), the triangle is acute-angled.
420. The length of the diagonal of a square with area 50 cm² is:
Explanation: Area = s² = 50, so the side 's' is √50 = 5√2 cm. The diagonal d = s√2 = (5√2)√2 = 5 × 2 = 10 cm.
إرسال تعليق