Mathematics MCQs - Part 6
151. If the sides of a triangle are a, b, and c, and a² + b² < c², the triangle is ______.
Explanation: This is an extension of the Pythagorean theorem. If the square of the longest side (c) is greater than the sum of the squares of the other two sides, the triangle is obtuse-angled.
152. The point of intersection of the angle bisectors of a triangle is called the ______.
Explanation: The incenter is the center of the circle that can be inscribed within a triangle (the incircle). It is found at the intersection of the angle bisectors.
153. What is the value of cosec 90°?
Explanation: cosecθ is the reciprocal of sinθ. Since sin 90° = 1, cosec 90° = 1/1 = 1.
154. If a line is parallel to the Y-axis, its slope is ______.
Explanation: A line parallel to the Y-axis is a vertical line. For any two points on this line, the change in x (the "run") is zero, leading to division by zero in the slope formula. Thus, the slope is undefined.
155. The area of a circle with radius 'r' is given by the formula:
Explanation: The formula for the area of a circle is A = Ï€r², where r is the radius.
156. The point of intersection of the altitudes of a triangle is called the ______.
Explanation: The orthocenter is the point where the three altitudes of a triangle intersect.
157. If the radius of a circle is 7 cm, what is its circumference?
Explanation: Circumference C = 2Ï€r. Using Ï€ ≈ 22/7, C = 2 × (22/7) × 7 = 44 cm.
158. The value of tan(90° - θ) is:
Explanation: This is a complementary angle identity. The tangent of an angle is equal to the cotangent of its complement.
159. How many common tangents can be drawn to two circles touching internally?
Explanation: Two circles touching internally have only one common tangent, which passes through their point of contact.
160. What is the centroid of a triangle with vertices (-7, 6), (2, -2), and (8, 5)?
Explanation: Using the centroid formula: x = (-7+2+8)/3 = 3/3 = 1. y = (6-2+5)/3 = 9/3 = 3. The coordinates are (1, 3).
161. The value of cos 0° is:
Explanation: For a 0° angle, the adjacent side is equal to the hypotenuse. Since cosθ = adjacent/hypotenuse, cos 0° = hypotenuse/hypotenuse = 1.
162. If the diameter of a sphere is 6 cm, its volume is:
Explanation: If diameter is 6 cm, radius (r) is 3 cm. Volume V = (4/3)Ï€r³ = (4/3)Ï€(3)³ = (4/3)Ï€(27) = 36Ï€ cm³.
163. The SAS test for similarity requires two pairs of corresponding sides to be ______ and the included angles to be congruent.
Explanation: For the Side-Angle-Side (SAS) similarity test, the ratio of the lengths of two pairs of corresponding sides must be equal, and the angles included between these sides must be congruent.
164. The point P(k, 7) divides the segment joining A(8, 9) and B(1, 2) in the ratio 2:5. What is the value of k?
Explanation: First, find the ratio using the y-coordinates: 7 = (m*2 + n*9)/(m+n) => 7m+7n = 2m+9n => 5m=2n => m/n=2/5. Now use this ratio for the x-coordinate: k = (2*1 + 5*8)/(2+5) = (2+40)/7 = 42/7 = 6.
165. The tangent-secant theorem states that the measure of an angle formed by a tangent and a secant from the point of contact is ______ the measure of the intercepted arc.
Explanation: The measure of the angle between a tangent and a secant (chord) drawn through the point of contact is half the measure of the arc intercepted by that angle.
166. In a 45°-45°-90° triangle, the two perpendicular sides are ______.
Explanation: A 45°-45°-90° triangle is an isosceles right-angled triangle, meaning the two sides that form the right angle are equal in length.
167. The value of sec(90° - θ) is:
Explanation: This is a complementary angle identity. The secant of an angle is equal to the cosecant of its complement.
168. The area of a sector with radius 10 cm and arc measure 54° is:
Explanation: Area = (θ/360) × Ï€r² = (54/360) × Ï€(10)² = (3/20) × 100Ï€ = 15Ï€ cm². Using Ï€ ≈ 3.14, the area is 47.1 cm².
169. If two lines are perpendicular and the slope of one is 2, the slope of the other is:
Explanation: For perpendicular lines, the product of their slopes is -1 (m₁ × m₂ = -1). So, 2 × m₂ = -1, which means m₂ = -1/2.
170. The longest chord of a circle is its ______.
Explanation: The diameter is the chord that passes through the center of the circle, and it is the longest possible chord.
171. If sinθ = 7/25, what is cosθ?
Explanation: Using the identity sin²Î¸ + cos²Î¸ = 1, we get (7/25)² + cos²Î¸ = 1. So, 49/625 + cos²Î¸ = 1. This gives cos²Î¸ = 1 - 49/625 = 576/625. Therefore, cosθ = √576/√625 = 24/25.
172. The point P(4, -1) lies in which quadrant?
Explanation: In the Cartesian coordinate system, the fourth quadrant is where the x-coordinate is positive and the y-coordinate is negative.
173. The SSS test for similarity requires all three pairs of corresponding sides to be ______.
Explanation: For the Side-Side-Side (SSS) similarity test, the ratios of the lengths of all three pairs of corresponding sides must be equal.
174. A person is standing 80m from a church. The angle of elevation to the top is 45°. The height of the church is:
Explanation: Let h be the height and d be the distance. tan(45°) = h/d. Since tan(45°) = 1, we have 1 = h/80, which means h = 80 m.
175. The volume of a solid is the measure of the ______ it occupies.
Explanation: Volume is the amount of three-dimensional space occupied by a substance or object.
176. How many common tangents can be drawn to two non-intersecting, non-touching circles?
Explanation: If two circles are separate (one is not inside the other), they have two direct common tangents and two transverse common tangents, for a total of four.
177. If the diagonal of a square is 10√2 cm, its perimeter is:
Explanation: The diagonal of a square with side 's' is s√2. So, s√2 = 10√2, which means the side 's' is 10 cm. The perimeter is 4s = 4 × 10 = 40 cm.
178. The value of cot(90° - θ) is:
Explanation: This is a complementary angle identity. The cotangent of an angle is equal to the tangent of its complement.
179. The centroid divides each median in the ratio ______.
Explanation: The centroid is located 2/3 of the distance from the vertex to the midpoint of the opposite side, thus dividing the median in a 2:1 ratio.
180. If the height of a cylinder is 3 cm and the area of its base is 100 cm², what is its volume?
Explanation: The volume of a cylinder is the area of its base multiplied by its height. V = Base Area × Height = 100 cm² × 3 cm = 300 cm³.
Post a Comment