Which of the following is a Baudhāyana triple generated using the idea where is an odd square?
  • (60, 11, 61)
  • (8, 15, 17)
  • (21, 28, 35)
  • (14, 48, 50)
Does the odd-number method yield non-primitive Baudhāyana triples?
  • No, it yields primitive triples
  • Yes, it yields non-primitive triples
  • Only when n is even
  • Only when n is a square
Which primitive Baudhāyana triple cannot be obtained through the odd-number method where one smaller sidelength is one less than the hypotenuse?
  • (8, 15, 17)
  • (3, 4, 5)
  • (5, 12, 13)
  • (11, 60, 61)
In Bhāskarāchārya’s Līlāvatī problem: a lotus tip is 1 unit above the water; when a gentle breeze sways it, the tip touches the water 3 units away from its original position. Assuming the stem is perpendicular to the water surface, what is the depth of the lake (the length of the stem inside the water)?
  • 3 units
  • 4 units
  • 5 units
  • 6 units
Find the side length of a rhombus whose diagonals measure 24 units and 70 units.
  • 25 units
  • 37 units
  • 38 units
  • 46 units
Is the hypotenuse the longest side of a right triangle? Choose the correct explanation.
  • Yes; it is opposite the right angle and, by , its length exceeds either leg.
  • Yes; but only in isosceles right triangles because the legs are equal.
  • No; the hypotenuse can be shorter than one leg when the legs are very unequal.
  • No; the longest side is always the leg opposite the largest acute angle.
Every Baudhayana triple is either a primitive triple or a scaled version of a primitive triple. Determine whether this statement is true or false.
  • True
  • False
Which collection lists five rectangles whose side lengths and diagonals are all integers? Each triplet (a, b, c) denotes sides a, b and diagonal c.
  • (3, 4, 5), (5, 12, 13), (6, 8, 10), (7, 24, 25), (9, 12, 15)
  • (2, 3, 4), (3, 6, 7), (4, 5, 7), (5, 5, 7), (6, 7, 9)
  • (1, 2, 2), (2, 2, 3), (4, 6, 8), (6, 6, 11), (8, 9, 13)
  • (4, 4, 8), (6, 8, 12), (7, 7, 10), (8, 10, 13), (9, 9, 14)
A square has area equal to the difference of the areas of squares with side lengths 5 units and 7 units. What is the side length of this square?
  • 2√6 units
  • 4√6 units
  • √12 units
  • √48 units
Using the dots of a grid as vertices, can you create a square with area 2 square units? Select the correct answer.
  • Yes
  • No
Using the dots of a grid as vertices, can you create a square with area 3 square units? Select the correct answer.
  • Yes
  • No
Using the dots of a grid as vertices, can you create a square with area 4 square units? Select the correct answer.
  • Yes
  • No
Using the dots of a grid as vertices, can you create a square with area 5 square units? Select the correct answer.
  • Yes
  • No
Suppose the grid of lattice points extends indefinitely. Which description correctly characterizes all possible integer-valued areas of squares that can be formed using grid points as vertices?
  • Exactly the integers that can be expressed as for some integers m and n.
  • Only perfect squares, because sides must align with the grid.
  • All even integers, because odd areas cannot occur on a grid.
  • All integers greater than or equal to 2.
Find the area of an equilateral triangle with side length 6 units.
  • 9√3 square units
  • 18 square units
  • 12√3 square units
  • 27 square units
There are three closed boxes—one containing only red balls, the second only blue balls and the third only green balls. The boxes are labelled RED, BLUE and GREEN such that no box has the correct label. You may open only one box. Which strategy guarantees determining the correct label of each box?
  • Open any one box and draw a single ball; the color you draw is that box’s true label, and the remaining two labels are fixed by elimination because every initial label was wrong.
  • Open the box labelled RED and BLUE together and compare; the one with more balls is RED.
  • Open the box labelled GREEN and move its label to the box labelled RED; then swap the remaining two.
  • Do not open any box; just permute the labels at random until none match their original labels.
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