Puzzles [With Answers]

Puzzle 1: What time should the last watch show?

Answer: 3:36

Explanation: On each watch, the time shown contains two digits that are the same.

Puzzle 2: Where should the missing hand point to?

Answer: To the 8

Explanation: Start with the top clock face and move clockwise around the others. The sum of the numbers pointed to by the 2 hands follows the sequence 5, 10, 15, 20.

Puzzle 3: Which letter replaces the question mark?

Answer: O

Explanation: In each segment of the diagram are a pair of letters, one of which is the same distance from the start of the alphabet as the other is from the end.

Puzzle 4: Which letter replaces the question mark?

Answer: K

Explanation: The numerical values of the letters in opposite segments of the circle always add up to 17.

Puzzle 5: Which letter replaces the question mark?

Answer: N

Explanation: The sum of the numerical value of the letters around each star is always 55.

Types of colloidal solution

1. Depending on dispersion medium and dispersed phase:

Dispersion medium	Dispersed phase	Type of colloid
Solid	Solid	Solid sol Ex: gem stones, glasses
	Liquid	Gel Ex: cheese, butter, gelatin
	Gas	Solid foam Ex: pumice stone
Liquid	Solid	Sol Ex: paints, ink, blood
	Liquid	Emulsion Ex: milk, mayonnaise, hand cream
	Gas	Foam Ex: whipped cream, shaving cream
Gas	Solid	Solid aerosol Ex: smoke, ice cloud, atmospheric particulate matter
	Liquid	Liquid aerosol Ex: fog, hair sprays, mist, cloud
	Gas	None All gases are miscible and thus do not form colloids
Examples:

2. Based on nature of interaction between dispersed phase and dispersion medium:

a. Lyophobic

b. Lyophilic

a. Lyophobic:

⇒ Liquid-hating

⇒ Colloidal solutions in which dispersed phase has very little affinity for the dispersion medium.

⇒ Form precipitates on adding small amounts of electrolytes

⇒ These are less stable and irreversible in nature.

⇒ These are also called suspensoids.

b. Lyophilic:

⇒ Liquid loving

⇒ Dispersed phase has great affinity for dispersion medium.

⇒ These are stable and reversible in nature. These are also called emulsoids. 

⇒ The colloidal solutions are also named according to the dispersion phase or medium used.

Dispersion Medium	Name of Colloidal Solutions
Water	Hydrosols
Alcohol	Alcosols
Benzene	Benzosols
Air	Aerosols

Puzzles

Puzzle 1: What time should the last watch show?

Puzzle 2: Where should the missing hand point to?

Puzzle 3: Which letter replaces the question mark?

Puzzle 4: Which letter replaces the question mark?

Puzzle 5: Which letter replaces the question mark?

Inductor in series and parallel

We shall first consider an ideal voltage source applied to the series combination of N inductors.

Applying KVL to the original circuit,

V_s = V₁ + V₂ + … + V_n

But for the equivalent circuit we have,

And thus the equivalent inductance is

L_eq = (L₁ + L₂ + … + L_N)

i_s = i₁ + i₂ + … + i_n

We know that

Brain Teaser 9 [With Answers]

Puzzle 1: Fill in the blanks with a word which makes two different words if you read from both sides:

Tim's father has kept his ______ in the ______ for scoring good marks in math.

Answer: Reward and Drawer.

Puzzle 2: There are 17 pigeons sitting in a row on a wall. A boy shoots the fifth pigeon. How many pigeons remain?

Answer: None.

Explanation: They all fly away at the sound of the gunshot.

Puzzle 3: What is the largest number you can get using only 2 digits?

Answer: 387420489 (i.e. 99)

Puzzle 4: Complete the sequence:

Z   O   T   T   F   F   S   S   __

Answer: E

Explanation: The sequence is Zero, One, Two, Three, Four, Five, Six, Seven, Eight.

Puzzle 5: Using four 7s and one 1 make 100. You can use (), /, X, +, -

Answer: 177 - 77 = 100.

Equation of Normal

Normal: The normal at any point P of the centre is the line which passes through P and is perpendicular to the tangent at P.

Equation of Normal:

i. The equation of the normal at p(x₁, y₁) of the circle

⇒ S = 0

⇒ x² + y² + 2gx + 2fy + c = 0 is (x - x₁) (y₁ + f) - (y - y₁) (x₁ + g) = 0

ii. The equation of the normal to the circle x² + y² = r² at p(x₁, y₁) is xy₁ - yx₁ = 0.

iii. The line lx + my + n = 0 is a normal to the circle x² + y² + 2gx + 2fy + c = 0 if and only if gl + mf = n.

Brain Teaser 9

Puzzle 1: Fill in the blanks with a word which makes two different words if you read from both sides:

Tim's father has kept his ______ in the ______ for scoring good marks in math.

Puzzle 2: There are 17 pigeons sitting in a row on a wall. A boy shoots the fifth pigeon. How many pigeons remain?

Puzzle 3: What is the largest number you can get using only 2 digits?

Puzzle 4: Complete the sequence:

Z   O   T   T   F   F   S   S   __

Puzzle 5: Using four 7s and one 1 make 100. You can use (), /, X, +, -.

Adsorption II

Adsorption isotherms: Plot of the amount of gas adsorbed on the surface of the adsorbent and pressure at constant temperature.

a. Freundlich adsorption isotherm:

 (n > 1) … 1

x = mass of the gas adsorbed

m = mass of the adsorbent

P = pressure

k, n = constants. Depend on the nature of the adsorbent and the gas.

Taking logarithm of eqn 1 → 

The plot of log(x/m) and log P is a straight line. If the plot is not a straight line then Freundlich isotherm is not valid. The slope of the straight line is 1/n and the y intercept is equal to k.

If 1/n = 0, then x/m is constant and doesn’t depend on pressure

If 1/n = 1, then x/m α P

b. Langmuir adsorption isotherm:

Postulates:

⇒ Gases undergoing adsorption behave ideally

⇒ The surface containing the adsorbing sites is perfectly flat plane with no corrugations (assume the surface is homogeneous).

⇒ The adsorbing gas adsorbs into an immobile state.

⇒ All sites are equivalent.

⇒ Each site can hold at most one molecule of gas (mono-layer coverage only).

⇒ There are no interactions between adsorbate molecules on adjacent sites.

⇒ Dynamic equilibrium exists between adsorbed gaseous molecules and the free gaseous molecules.

Where A(g) is unabsorbed gaseous molecule, B(s) is unoccupied metal surface and AB is Adsorbed gaseous molecule. He gave the following relation:

, k_ad = adsorption rate constant, k_d = description rate constant

K’ = kK

The plot of  and P is a straight line, whose slope is (K/K’) and y intercept is (1/K’)

 

When pressure is very high, then 1 + KP = KP

Thus, at high pressures the degree of adsorption approaches a limiting value.

When pressure is low then 1 + KP = 1

The degree of adsorption is directly proportional to pressure.

Adsorption from solution phase:

⇒ The adsorption decreases with increase in temperature.

⇒ Adsorption increases with increase in surface area.

⇒ The extent of adsorption depends on concentration of solute in solution.

⇒ The extent of adsorption depends on nature of adsorbent and adsorb ate.

The Freundlich equation is modified as 

C - Equilibrium concentration

Positive adsorption: The concentration of adsorbate is more on the surface of adsorbent than in the bulk of the solution

Negative adsorption: The concentration of adsorbate is more in the bulk of the solution than in the surface of the adsorbent.

Riddles 8 [With Answers]

Puzzle 1: Imagine you’re in a room that is filling with water. There are no windows or doors. How do you get out?

Answer: Stop imagining.

Puzzle 2: The more you take, the more you leave behind. What are they?

Answer: Footprints.

Puzzle 3: What two keys can’t open any door?

Answer: A monkey and a donkey.

Puzzle 4: What invention lets you look right through a wall?

Answer: A window.