Explanation : 

The given series is: _b_a_ba_b_abab_aab

The pattern being followed in the above series is: abb, then aab. Again abb, and then aab, and so on.
The blanks have been highlighted below:
a b b / a a b / a b b / a ab / ab b / aab

Explanation : 

Three points P,Q and R on straight line

CASE – 1
Assuming PQ = 3x, QR = 5x and PR = PQ + QR, we get
PQ : PR = 3x : (3x + 5x)
⇒ PQ : PR = 3 : 8

CASE – 2
Assuming PQ = 3x, QR = 5x and PR = QR – PQ, we get
PQ : PR = 3x : (5x – 3x)
⇒ PQ : PR = 3 : 2

So, we have n = 2 possible values.

Explanation : 

X & Y Age Relationship Analysis

Given:
– X’s present age = 42 years
– At Y’s birth, X was twice Y’s current age
– Let Y’s present age = y

Step 1: Initial Equation
– 42 – y = 2y (X’s age at Y’s birth = 2 × Y’s current age)
– 42 = 3y
– Therefore, y = 14 (Y’s current age)

Step 2: Testing Statement 1 (8 years ago)
– X’s age: 42 – 8 = 34
– Y’s age: 14 – 8 = 6
– Check: 34 ≠ 5 × 6 (30)
– Result: Statement 1 is false

Step 3: Testing Statement 2 (14 years later)
– X’s age: 42 + 14 = 56
– Y’s age: 14 + 14 = 28
– Check: 56 = 2 × 28
– Result: Statement 2 is true

Answer: Only Statement 2 is correct.

Explanation : 

Joseph visits the club on every 5th day

– Joseph visits every 5th day
– Harsh visits every 24th day
– Sumit visits every 9th day
– They first meet on a Sunday

Solution Method:
1. Find LCM of visit intervals (5, 24, 9)
– LCM = 360 days

2. Calculate odd days
– 360 ÷ 7 = 51 weeks + 3 days
– Extra days after complete weeks = 3

3. Count days from Sunday
– Starting day: Sunday
– Add 3 days
– Final day: Wednesday

Answer: (b) Wednesday

Explanation : 

Relations between radios, mobiles, computers, and watches

Given statements:
1. Some radios are mobiles
2. All mobiles are computers
3. Some computers are watches

Analysis of conclusions:

Conclusion I: “Some radios are watches”
– We can only say some radios are computers
– We can’t establish a definite connection between radios and watches
– Not valid

Conclusion II: “Some mobiles are watches”
– All mobiles are computers
– But only some computers are watches
– No definite connection between mobiles and watches
– Not valid

Answer: (d) Neither Conclusion-I nor Conclusion-II follows

Explanation : 

In a class 60 of students are from india

Given:
– Total students = 100
– Indian students = 60%
– Foreign students = 40
– Total girls = 50%
– Indian girls = 30% of 60 = 18

Step-by-step solution:
1. Foreign girls = Total girls – Indian girls
= 50 – 18 = 32

2. Foreign boys = Total foreign – Foreign girls
= 40 – 32 = 8

3. Percentage of boys among foreign students
= (8/40) × 100 = 20%

Answer: (d) 20%

Explanation : 

A woman runs 12km

Initial position: (0,0)
Movements:
1. North 12 km → (0,12)
2. South 6 km → (0,6)
3. East 8 km → (8,6)

Final position: (8,6)

Direction calculation of women:

– Angle = tan⁻¹(6/8)
– Angle = tan⁻¹(0.75)
– Angle = 36.87°

Since:
– tan 45° = 1
– 6/8 = 0.75 < 1
– Therefore, angle is less than 45°

Explanation : 

A bank employee drives 10 km south

Starting point: (0,0) – House

Movement sequence:
1. South 10 km → (0, -10)
2. Left turn, East 20 km → (20, -10)
3. Left turn, North 40 km → (20, 30)
4. Right turn, East 5 km → (25, 30)
5. Right turn, South 30 km → (25, 0) – Bank

Shortest distance calculation:
– Using Pythagorean theorem
– Distance = √[(x₂-x₁)² + (y₂-y₁)²]
– Distance = √[(25-0)² + (0-0)²]
– Distance = √(625 + 0)
– Distance = √625
– Distance = 25 km

Therefore, the shortest distance between her house and bank is 25 kilometers.

Explanation : 

Mirror images of consonants of the english alphabet

To determine the number of consonant letters in the English alphabet whose mirror images do not resemble their original shapes, follow these steps:

1. Identify the Consonants:

The English alphabet consists of 26 letters. The vowels are A, E, I, O, and U. Sometimes Y is considered a vowel, but typically it’s treated as a consonant in such contexts.
Consonants: B, C, D, F, G, H, J, K, L, M, N, P, Q, R, S, T, V, W, X, Y, Z
Total Consonants: 21

2. Determine Symmetrical Letters:

A letter is considered symmetrical if its mirror image is identical to the original. For capital letters, the following consonants are symmetrical:

– Symmetrical Consonants: H, M, T, V, W, X, Y
Total Symmetrical Consonants: 7

3. Calculate Non-Symmetrical Consonants:

Subtract the number of symmetrical consonants from the total number of consonants to find the number of non-symmetrical consonants.

Non-Symmetrical Consonants: 21 (total) – 7 (symmetrical) = 14
Answer: (b) 14

Explanation :

Conclusions from Cat, Almirah, Chair Statement

Given Statements:
1. Some cats are almirahs
2. Some almirahs are chairs
3. All chairs are tables

Let’s analyze each conclusion:

Conclusion I: “Some almirahs are tables”

– Some almirahs are chairs (given)
– All chairs are tables (given)
– Therefore, those almirahs that are chairs must also be tables
– This makes Conclusion I logically valid

Conclusion II: “Some cats may not be chairs”

– Some cats are almirahs (given)
– Some almirahs are chairs (given)
– We don’t know if ALL cats are almirahs
– We don’t know if ALL almirahs are chairs
– Therefore, it’s possible that some cats may not be chairs
– This makes Conclusion II logically valid

Answer: Both conclusions I and II logically follow from the given statements.