Heat required = mass × latent heat = 50 g × 334 J/g = 16700 J.

The product of the three numbers is equal to LCM * HCF^2. Therefore, 180 * 3^2 = 180 * 9 = 1620.

The product of two numbers is equal to the product of their LCM and HCF. Therefore, 120 * 10 = 1200.

The product of two numbers is equal to the product of their LCM and HCF. Therefore, 60 * 4 = 240.

The product of two numbers is equal to the product of their LCM and GCD. Therefore, 60 * 12 = 720.

The volume of a cube is given by V = a³. If the side length a is doubled, the new volume is (2a)³ = 8a³, which is 8 times the original volume.

Volume of a cube is given by V = a³. If a is doubled, V becomes (2a)³ = 8a³, hence volume increases by 8 times.

Volume V = L³. The maximum error in volume can be calculated using the formula: ΔV = 3L²ΔL. Here, ΔL = 0.1 m, L = 2.0 m, so ΔV = 3(2.0)²(0.1) = 1.2 m³.

Volume = side³ = (2.5 cm)³ = 15.625 cm³. Considering significant figures, it is reported as 16.0 cm³.

Volume = (2.5 cm)³ = 15.625 cm³. The uncertainty in volume can be calculated using the formula for propagation of uncertainty.

Area of square = side². If side is doubled, new area = (2 * side)² = 4 * side², so area quadruples.

Resistance is directly proportional to length; doubling the length doubles the resistance.

Young's modulus is a material property and does not change with the dimensions of the wire.

Resistance (R) is directly proportional to length (L). If length is doubled, resistance also doubles.

If the length is doubled, the area increases by a factor of four (A = length²).

If the length is doubled, the volume increases by a factor of 2^3 = 8, since volume is proportional to the cube of the length.

Increasing the length of the potentiometer wire while keeping the voltage constant will increase the balance point length for the same EMF.

Increasing the length of the potentiometer wire increases the maximum measurable voltage due to a larger potential gradient.

The area of a rhombus can be calculated using the formula (1/2) × d1 × d2 = (1/2) × 10 × 24 = 120 cm².

The distance between the foci is given by 2c, where c = √(a^2 - b^2). Here, c = √(5^2 - 3^2) = √16 = 4, so the distance is 2c = 8.

Perimeter = 2 * (length + width) = 2 * (4 + 6) = 20 cm

A triangle with sides 3 cm, 4 cm, and 5 cm satisfies the Pythagorean theorem (3² + 4² = 5²), thus it is a right triangle.

Using Pythagoras theorem, 7² + 24² = 49 + 576 = 625 = 25², so it is a right triangle.

The maximum length of the third side is less than the sum of the other two sides, so it can be 22 cm.

Torque is directly proportional to the lever arm; if the lever arm is doubled, the torque also doubles.

Setting y = 0 gives 2x = 6, thus x = 3. The point of intersection is (3, 0).

Setting y = 0 gives 2x = 6, thus x = 3. The x-coordinate of the intersection point is 3.

Set y = 0 in the equation: 3x = 12 => x = 4. The point is (4, 0).

Set y = 0 in the equation: 3x = 12 => x = 4.

Setting x = 0 gives 4y = 12, thus y = 3. The point of intersection is (0, 3).