Geometry & Mensuration
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Q121.In a triangle puzzle, the first triangle has outer keys 5,3,4 with inner 19. The second has 7,5,6. What is the inner key?
Correct Answer: A
The pattern multiplies the side keys and adds the base: (7 * 5) + 6 = 35 + 6 = 41.
Q122.If a triangle has a length (base) of 5 units and width (height) of 4 units, what is its area?
Correct Answer: D
Area of a triangle = (1/2) × base × height = (1/2) × 5 × 4 = 10 square units.
Q123.How many squares are there in a figure with 4 concentric squares where the two innermost squares form a 3×3 grid using two perpendicular lines?
Correct Answer: C
Concentric squares count: The 3×3 grid yields 9 (1×1) + 4 (2×2) + 1 (3×3) = 14 squares. Adding the remaining 2 outer concentric square outlines yields 14 + 2 = 16 squares.
Q124.What is the height of a triangle if its base is 8 cm and its area is 16 cm²?
Correct Answer: D
Area = (1/2) × base × height → 16 = (1/2) × 8 × height → 16 = 4 × height → Height = 4 cm.
Q125.If a rectangle has a length of 9 units and a width of 4 units, what is its area?
Correct Answer: B
Area of a rectangle = Length × Width = 9 × 4 = 36 square units.
Q126.A square region has an area of 2304 sq. m. Find its perimeter?
Correct Answer: D
Side of square = sqrt(2304) = 48 m. Perimeter = 4 * side = 4 * 48 = 192 m.
Q127.If P(2, 1) and Q(8, 1) are two of the vertices of a rectangle, which of the following could not be another vertex?
Correct Answer: D
Rectangle vertices must have x-coordinates 2 or 8, and y-coordinates matching the opposite sides. (-2, 8) has x = -2, which does not match either of the possible vertical side lines (x = 2 or x = 8).
Q128.The volume of a cylinder is to be calculated using the formula V = πr²L. If the radius (r) is 3 cm and the length (L) is 10 cm, what is the volume?
Correct Answer: A
V = π × r² × L = π × 3² × 10 = π × 9 × 10 = 90π cm³.
Q129.The volume of a cone is 245π cm³ and its radius is 7 cm. Find its height?
Correct Answer: A
Volume of a cone = (1/3)πr²h. Substituting the known values: 245π = (1/3)π × 7² × h => 245 = (49/3)h => h = (245 × 3) / 49 = 5 × 3 = 15 cm.
Q130.A room is 16 feet in length, 15 feet in width, and 12 feet in height. What is the maximum distance possible in feet along a straight line between any two points in the room?
Correct Answer: C
The maximum distance is the 3D space diagonal: d = √(l² + w² + h²) = √(16² + 15² + 12²) = √(256 + 225 + 144) = √625 = 25 feet.
Q131.In a right triangle with angles of 90° and 30°, what is the third angle?
Correct Answer: B
The sum of angles in a triangle is always 180°. Third angle = 180° - 90° - 30° = 60°.
Q132.At what angle is the projectile range maximum?
Correct Answer: D
Neglecting air resistance, the maximum horizontal range of a projectile is achieved at a launch angle of 45°.
Q133.Find the distance between the points (1, 2) and (4, 6).
Correct Answer: B
By the distance formula: d = sqrt((4 - 1)^2 + (6 - 2)^2) = sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5.
Q134.If the sum of two angles is 90°, then the angles are called? (Complementary)
Correct Answer: C
Two angles are complementary if their sum is exactly 90 degrees, and supplementary if their sum is exactly 180 degrees.
Q135.If radius of a circle bisects a chord, it will be ____ to the chord?
Correct Answer: B
A standard theorem in circle geometry states that a line drawn from the center of a circle (the radius) that bisects a chord is perpendicular to that chord.
Q136.Median term relates with?
Correct Answer: C
In geometry, a median of a triangle is a line segment connecting a vertex to the midpoint of the opposite side.
Q137.Circumference of a circle is 154 cm. Find the radius:
Correct Answer: A
Circumference = 2 * pi * r = 154. Using pi ≈ 22/7: 2 * (22/7) * r = 154 => 44/7 * r = 154 => r = (154 * 7) / 44 = 24.5 cm. (Note: The website lists 11 cm as the official key, which is a common typo, but the actual mathematical calculation yields 24.5 cm).
Q138.What is the ratio of the circumference of a circle to its radius?
Correct Answer: A
Circumference = 2 * pi * r. Radius = r. Ratio of Circumference to Radius = 2 * pi * r / r = 2 * pi (or 2π:1).
Q139.What is sinθ equal to in a right-angled triangle?
Correct Answer: B
In a right-angled triangle, sinθ is the ratio of perpendicular to hypotenuse: p/h.
Q140.Find the surface area of a cube when its side length is 3 cm.
Correct Answer: C
Surface area of a cube = 6 × (side)² = 6 × 3² = 6 × 9 = 54 cm².