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 11
301. The value of tanθ × cosθ is equal to:
Explanation: Since tanθ = sinθ/cosθ, the expression becomes (sinθ/cosθ) × cosθ. The cosθ terms cancel out, leaving sinθ.
302. If the radius of a sphere is 2 cm, its surface area is:
Explanation: Surface Area A = 4πr². For r = 2, A = 4π(2)² = 4π(4) = 16π cm².
303. The point P(0, 5) lies on ______.
Explanation: Since the x-coordinate is 0, the point lies on the Y-axis.
304. If two triangles are similar, their corresponding sides are ______.
Explanation: The definition of similar triangles is that their corresponding angles are equal and their corresponding sides are in proportion.
305. The value of sin 60° / cos 30° is:
Explanation: Since sin 60° = √3/2 and cos 30° = √3/2, the ratio is (√3/2) / (√3/2) = 1. Alternatively, using the identity sin(θ) = cos(90°-θ), sin 60° = cos 30°.
306. The area of a regular hexagon with side 'a' is:
Explanation: A regular hexagon is composed of 6 equilateral triangles. The area of one equilateral triangle with side 'a' is (√3/4)a². Therefore, the area of the hexagon is 6 times that amount.
307. In a circle, the angle subtended by an arc at the center is ______ the angle subtended by it at any point on the remaining part of the circle.
Explanation: This is another way of stating the inscribed angle theorem. The central angle is always twice the measure of any inscribed angle that intercepts the same arc.
308. What is the slope of the line passing through points (2, 5) and (3, 3)?
Explanation: Using the slope formula: m = (3 - 5) / (3 - 2) = -2 / 1 = -2.
309. The value of sin²θ + cos²θ + tan²θ is equal to:
Explanation: We know sin²θ + cos²θ = 1. So the expression becomes 1 + tan²θ. From another identity, we know 1 + tan²θ = sec²θ.
310. If the perimeter of a circle is 88 cm, its area is:
Explanation: Perimeter (Circumference) C = 2πr = 88. Using π ≈ 22/7, 2 × (22/7) × r = 88. So, (44/7)r = 88, which gives r = 14 cm. Area = πr² = (22/7) × 14² = (22/7) × 196 = 22 × 28 = 616 cm².
311. From the top of a 10m high building, the angle of elevation to the top of a second building is 60°. The buildings are 12m apart. What is the height of the second building?
Explanation: This forms a right triangle where the adjacent side is the distance between buildings (12m). The opposite side (h) is the height of the second building above the first. tan(60°) = h/12. So, √3 = h/12, and h = 12√3 m. The total height is 10 + 12√3 m.
312. The point P(-2, 0) lies on ______.
Explanation: Since the y-coordinate is 0, the point lies on the X-axis. Specifically, it is on the negative part of the X-axis.
313. The value of tan 0° is:
Explanation: tanθ = sinθ / cosθ. Since sin 0° = 0 and cos 0° = 1, tan 0° = 0 / 1 = 0.
314. The number of altitudes in a triangle is:
Explanation: An altitude is a perpendicular line segment from a vertex to the opposite side. Since a triangle has three vertices, it has three altitudes.
315. The sum of the lengths of the diagonals of a rhombus is ______ the sum of the lengths of its sides.
Explanation: For any convex quadrilateral, the sum of the lengths of the diagonals is less than the perimeter. This holds true for a rhombus.
316. If the radius of a cone is halved and its height is also halved, its volume will become:
Explanation: Original Volume V = (1/3)πr²h. New radius = r/2, new height = h/2. New Volume V' = (1/3)π(r/2)²(h/2) = (1/3)π(r²/4)(h/2) = (1/8) × [(1/3)πr²h] = V/8.
317. The slope of the line passing through (1, -1) and (-5, 3) is:
Explanation: Using the slope formula: m = (3 - (-1)) / (-5 - 1) = 4 / -6 = -2/3.
318. The value of sin(A+B) is NOT generally equal to:
Explanation: Trigonometric functions do not distribute over addition. The correct sum identity is sin(A+B) = sinAcosB + cosAsinB. Therefore, sin(A+B) is not equal to sinA + sinB.
319. If the sides of a triangle are 6, 8, and 10, what is the length of the median to the longest side?
Explanation: The sides 6, 8, 10 form a right-angled triangle (since 6²+8²=10²). The longest side (10) is the hypotenuse. The median to the hypotenuse of a right-angled triangle is always half the length of the hypotenuse. So, the median length is 10/2 = 5.
320. The length of a tangent segment from a point 12.5 cm from the center of a circle is 12 cm. What is the radius of the circle?
Explanation: The radius, tangent segment, and line from the center to the point form a right-angled triangle. Let r be the radius. r² + 12² = 12.5². r² + 144 = 156.25. r² = 12.25. r = √12.25 = 3.5 cm.
321. The slope of a line perpendicular to the line y = 2x - 3 is:
Explanation: The slope of the given line is 2. The slope of a perpendicular line is the negative reciprocal. So, m_perp = -1/2.
322. The value of sec²θ(1 - sin²θ) is:
Explanation: Since 1 - sin²θ = cos²θ, the expression becomes sec²θ × cos²θ. As secθ is the reciprocal of cosθ, the product is 1.
323. If the volume of a cylinder is 300 cm³ and the area of its base is 100 cm², its height is:
Explanation: Volume = Base Area × Height. So, 300 = 100 × Height. Therefore, Height = 300 / 100 = 3 cm.
324. A line can intersect a circle at most at ______ point(s).
Explanation: A line can miss the circle (0 points), be tangent to it (1 point), or be a secant (2 points). The maximum number of intersection points is two.
325. The sum of the angles of a pentagon is:
Explanation: The sum of the interior angles of a polygon with n sides is (n-2) × 180°. For a pentagon, n=5, so the sum is (5-2) × 180° = 3 × 180° = 540°.
326. If the radius of a sphere is halved, its surface area becomes:
Explanation: Original Surface Area A = 4πr². New radius = r/2. New Area A' = 4π(r/2)² = 4π(r²/4) = πr² = A/4. The area becomes one-fourth of the original.
327. The line segment joining the vertices of a triangle to the midpoints of their opposite sides are called ______.
Explanation: This is the definition of a median of a triangle.
328. The value of (1 + cot²θ)(1 - cos²θ) is:
Explanation: Using identities, 1 + cot²θ = cosec²θ and 1 - cos²θ = sin²θ. The expression becomes cosec²θ × sin²θ. Since cosecθ = 1/sinθ, the product is (1/sin²θ) × sin²θ = 1.
329. If the sides of a triangle are 3, 4, and 6, what type of triangle is it?
Explanation: Check using the converse of Pythagoras theorem. 3² + 4² = 9 + 16 = 25. The longest side is 6, and 6² = 36. Since 25 < 36 (a² + b² < c²), the triangle is obtuse-angled.
330. The length of the diagonal of a square with side 5 cm is:
Explanation: The diagonal of a square with side 's' is given by the formula d = s√2. Therefore, the diagonal is 5√2 cm.
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