The correct answer is Option 3 i.e. Both Conclusion II and III are true.

The least possible Venn Diagram is drawn below:

Conclusions:

I. Some Red is Yellow - False (This is possible but not definite, as no direct relationship between the two is given).

II. Some White is not Black - True (This is true, as Only a few White is Black is given which means Some White are Black and Some White are not Black).

III. All Yellow can be Black - True (Some Black is Yellow is given, so All Yellow can be Black is possible).

Hence, the correct answer is Both Conclusion II and III are true.

The correct answer is option 3 i.e. 10

Logic: (2nd number)³ × 5 = 1st number 

625 : 5 → 5³ × 5 = 625

2560 : 8 → 8³ × 5 = 2560

Similarly,

5000 : ? → 10³ × 5 = 5000

The correct answer is option 4 i.e. L, X, V, X, V, Z, C, Z, X, C.

The sequence is – L, Z, X, C, V 

Given sequence: _ Z _ C _ L Z _ C _ L _ X _ V L _ _ _ V

Option 1: L, X, V, V, X, C, C, X, Z, Z

L Z X C V / L Z V C X / L C X C V / L X Z Z V

Option 2: L, X, C, X, V, C, Z, C, Z, C

L Z X C C / L Z X C V / L C X Z V / L C Z CV

Option 3: X, Z, L, X, V, Z, C, C, C, L

X Z Z C L L Z X C V L Z X C V L C C L V

Option 4: L, X, V, X, V, Z, C, Z, X, C

L Z X C V / L Z X C V / L Z X C V / L Z X C V

Option 4 forms a particular pattern.

Hence, L, X, V, X, V, Z, C, Z, X, C is the correct answer.

The correct answer is option 1 i.e. 29

Given equation: 75 × 15 + 10 ÷ 17 - 2 = ?

After replacing the signs, we get

(75 ÷ 15) - 10 + (17 × 2)

= 5 - 10 + 34

= 39 - 10

= 29

Hence, the correct answer is 29.

The correct answer is option 1 i.e. 29 - 6 × 2 ÷ 4 + 3 = 38

29 - 6 × 2 ÷ 4 + 3 = 38

On interchanging + and -, 4 and 2

⇒ 29 + 6 × (4 ÷ 2) - 3 = 38

⇒ 29 + (6 × 2) - 3 = 38

⇒ (29 + 12) - 3 = 38

⇒ 41 - 3 = 38

⇒ 38 = 38

So, no need to solve this further.

Hence, the correct answer is 29 - 6 × 2 ÷ 4 + 3 = 38.

The correct answer is option 1 i.e. 9 + 6 × 4 + 2 - 3 = 20

9 + 6 × 4 + 2 - 3 = 20

On interchanging 6 and 2

⇒ 9 + (2 × 4) + 6 - 3 = 20 

⇒ (9 + 8 + 6) - 3 = 20 

⇒ 23 - 3 = 20 

⇒ 20 = 20

So, no need to solve this further.

Hence, the correct answer is 9 + 6 × 4 + 2 - 3 = 20.

The correct answer is Option 3 i.e. D

Clearly, D faces Q.

Hence, the correct answer is D.

The correct answer is Option 1 i.e. I

C is the only immediate neighbour of F and both are facing the same direction.

E is third from the left end facing the direction opposite G who is an immediate neighbour of C.

(This means that F is sitting at the right end of the row.)

I and G are immediate to the right of each other.

B is second to the left of D who is second to the left of I.

(This means that I and G are facing North and South respectively.)

D is an immediate neighbour of both E and H and all of them are facing the same direction.

A is facing north and there are more people to his right than to the left of F. (This means that F and C are facing South.)

Immediate neighbours of E are facing the opposite direction. (This means that B is facing South.)

Hence, the correct answer is I.

The correct answer is option 4 i.e. OFSWPVT

The logic used here is:

PENALTY : QFOBMUZ

P + 1 = Q, E + 1 = F, N + 1 = O, A + 1 = B, L + 1 = M, T + 1 = U, Y + 1 = Z

OFFENSE : PGGFOTF

O + 1 = P, F + 1 = G, F + 1 = G, E + 1 = F, N + 1 = O, S + 1 = T, E + 1 = F

Similarly,

NERVOUS : ?

N + 1 = O, E + 1 = F, R + 1 = S, V + 1 = W, O + 1 = P, U + 1 = V, S + 1 = T

The correct answer is option 1 i.e. Wednesday.

31st January, 2007 = (2006 years + Number of days from 1.1.2007 to 31.1.2007)

Odd days in 1600 years = 0; Odd days in 400 years = 0

6 years = (1 leap years + 5 ordinary years) = (1 x 2 + 5 x 1) = 7 days → 0 odd days

Jan 31 = 31 days

Therefore, 31 days = (4 weeks + 3 day) → 3 odd days

Total number of odd days = (0 + 0 + 0 + 3) = 3 → 3 odd days

Thus, the day is Wednesday.