For some calculations, we want an algorithm that accepts only positive integers up to 100. Accept_1to100_Algo INPUT Number IF (0 <= Number) AND (Number <= 100) ACCEPT Else REJECT a) On what values will this algorithm fail? b) Can you improve the algorithm?

To go from town A to town B, a plane must fly about 1780 km at an angle of 30° west of north. How far north of A is B?

A) 1542 km B) 1452 km C) 1254 km D) 11 km

In a class, 20% of students are below 14 years of age. Out of the remaining students, 10% are of the age 14-15 years and the ratio of students who are between 15-16 years of age to students above 16 years of age is 3:2. If the number of students who are above 16 years is 72, what is the total number of students in the class?

A. 200

B. 250

C. 300

D. 400

10 moles of a mixture of hydrogen and oxygen gases at a pressure of 1 atm at constant volume and temperature react to form 3.6 g of liquid water. The pressure of the resulting mixture will be closest to:

A) 1.07 atm

B) 0.97 atm

C) 1.02 atm

D) 0.92 atm

Estimate the mean free path and collision frequency of a nitrogen molecule in a cylinder containing nitrogen at $2.0 \mathrm{~atm}$ and temperature $17^{\circ} \mathrm{C}$. Take the radius of a nitrogen molecule to be roughly 1.0 Ã…. Compare the collision time with the time the molecule moves freely between two successive collisions (Molecular mass of $\left.\mathrm{N}_{2}=28.0 \mathrm{u}\right)$.

As a charged particle '$q$' moving with a velocity $\vec{v}$ enters a uniform magnetic field $\vec{B}$, it experiences a force $\vec{F} = q(\vec{v} \times \vec{B})$. For $\theta = 0^{\circ}$ or $180^{\circ}$ (with $\theta$ being the angle between $\vec{v}$ and $\vec{B}$), the force experienced is zero and the particle passes undeflected. For $\theta = 90^{\circ}$, the particle moves along a circular arc, and the magnetic force ($qvB$) provides the necessary centripetal force $\left(\frac{mv^{2}}{r}\right)$. For other values of $\theta$ (where $\theta \neq 0^{\circ}, 180^{\circ}, 90^{\circ}$), the charged particle moves along a helical path, which is the resultant motion of simultaneous circular and translational motions.

Suppose a particle that carries a charge of magnitude $q$ and has a mass $4 \times 10^{-15} , \text{kg}$ is moving in a region containing a uniform magnetic field $\vec{B} = -0.4 \hat{k} , \text{T}$. At some instant, the velocity of the particle is $\vec{v} = (8 \hat{i} - 6 \hat{j} + 4 \hat{k}) \times 10^{6} , \text{ms}^{-1}$ and the force acting on it has a magnitude $1.6 , \text{N}$.

The angular frequency of rotation of the particle, also called the cyclotron frequency, is:

A. $25 , \text{Hz}$
B. $35 , \text{Hz}$
C. $15 , \text{Hz}$
D. $45 , \text{Hz}$