Median = 80 (middle value when arranged: 60, 70, 80, 90, 100).

Perimeter = a + b + c = 7 + 24 + 25 = 56 cm.

A triangle with sides in the ratio 3:4:5 is a right triangle, as it satisfies the Pythagorean theorem.

When the slit width is equal to the wavelength, a wide central maximum is observed due to significant diffraction.

Halving the slit width increases the angular width of the central maximum, making it double.

If the slit width is halved, the width of the central maximum doubles, as it is inversely proportional to the slit width.

Ksp = [Ag+][Cl-] = s^2, thus s = sqrt(1.77 x 10^-10) = 1.77 x 10^-5 M.

Frequency f = v/λ = 300 m/s / 3 m = 100 Hz.

Centripetal acceleration a_c = v²/r. If v is doubled, a_c increases by a factor of 4.

Speed of light in medium = c/n = (3 x 10^8 m/s) / 1.5 = 2 x 10^8 m/s.

A standard deviation of 0 indicates that all values in the data set are the same.

Variance = (Standard Deviation)^2 = 3^2 = 9.

Variance = (Standard Deviation)² = 4² = 16.

Variance is the square of the standard deviation. Variance = 5² = 25.

Stress = Young's modulus × Strain = 150 GPa × 0.01 = 150 MPa.

According to Hooke's Law, if stress is doubled, strain also doubles for elastic materials.

n(n + 1)/2 = 55, solving gives n = 10.

Using the formula S_n = a(1 - r^n) / (1 - r), we have 81 = 3(1 - r^n) / (1 - r). Solving gives r = 3.

When r = 1, S_n = a(1 - 1^n)/(1 - 1) is indeterminate, but the sum of n terms is na.

The 4th term a_4 = S_4 - S_3 = (3(4^2) + 2(4)) - (3(3^2) + 2(3)) = (48 + 8) - (27 + 6) = 56 - 33 = 23.

The 5th term can be found using a_n = S_n - S_(n-1). Calculate S_5 and S_4, then find a_5 = S_5 - S_4 = (5(5^2) + 3(5)) - (5(4^2) + 3(4)) = 38.

The sum of the roots is given by -b/a = 3. Here, -(-3)/1 = 3, so p can be any value.

Increasing the supply voltage does not affect the balance condition; it remains dependent on the resistance ratios.

Force = Surface Tension × Length = 0.072 N/m × 0.5 m = 0.036 N.

According to Newton's law of cooling, the rate of heat transfer increases with an increase in temperature difference.

Maximum possible temperature = Measured value + Error = 30 + 0.5 = 30.5°C

For most conductors, resistivity increases with temperature due to increased atomic vibrations.

According to Charles's Law, at constant pressure, the volume of a gas is directly proportional to its temperature.

According to Gay-Lussac's Law, if the temperature of a gas is increased while keeping the volume constant, the pressure will also increase proportionally, thus it doubles.

The RMS speed is proportional to the square root of the temperature. If the temperature is doubled, the RMS speed increases by a factor of sqrt(2).