This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Here are the solutions to the questions: 1. The quadrilateral whose diagonals bisect the vertex through which they pass is In a square, the diagonals bisect the angles at the vertices (each angle is 90 degrees, and the diagonal divides it into two 45-degree angles). Answer: b) Square* 2. The figure that is not a parallelogram is A parallelogram is a quadrilateral with two pairs of parallel sides. A square is a parallelogram. A rhombus is a parallelogram. A trapezium (or trapezoid) has only one pair of parallel sides, so it is not a parallelogram. Answer: b) Trapezium* 3. The length of the longest rod that can fit in a cuboidal box of dimensions a × b × c is The longest rod that can fit in a cuboidal box is its space diagonal. The formula for the space diagonal of a cuboid with dimensions a, b, c is sqrt(a^2+b^2+c^2). Answer:* b) sqrt(a^2+b^2+c^2) 4. Three cubes of edges x cm, 4 cm and 5 cm are melted and shaped into a large cube of edge 6 cm. Then the value of x is Step 1: Calculate the volumes of the given cubes. Volume of cube 1 = x^3 cm^3 Volume of cube 2 = (4 cm)^3 = 64 cm^3 Volume of cube 3 = (5 cm)^3 = 125 cm^3 Volume of the large cube = (6 cm)^3 = 216 cm^3 Step 2: Apply the principle of conservation of volume. The sum of the volumes of the small cubes equals the volume of the large cube. x^3 + 64 + 125 = 216 x^3 + 189 = 216 Step 3: Solve for x.