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.

Explanation : 

A person X from place a & other Y from B

Given information:
– Total distance between A and B = 15 km
– Person X’s speed = constant 1.5 km/hr
– Person Y’s speed increases by 0.25 km/hr every hour:
Hour 1: 1.0 km/hr
Hour 2: 1.25 km/hr
Hour 3: 1.5 km/hr
Hour 4: 1.75 km/hr
Hour 5: 2.0 km/hr

Step 1: Calculate X’s distance in 5 hours
– X’s distance = Speed × Time
– X’s distance = 1.5 × 5 = 7.5 km

Step 2: Calculate Y’s total distance in 5 hours
– Hour 1: 1.0 km
– Hour 2: 1.25 km
– Hour 3: 1.5 km
– Hour 4: 1.75 km
– Hour 5: 2.0 km
Total = 7.5 km

Step 3: Verify statements
1. They take 5 hours to meet
– Total distance covered = X’s distance + Y’s distance
– 7.5 + 7.5 = 15 km (complete distance)
– Therefore, they meet in 5 hours (True)

2. They meet midway
– Both cover 7.5 km each
– 7.5 km is exactly half of 15 km
– Therefore, they meet midway (True)

Answer: Option (c) Both statements 1 and 2 are correct.

Explanation : 

8 4 6 15 x 236.25

Let us solve this step by step:

Sequence I:
Let us start with 8:
8 × 0.5 → 4
4 × 1.5 → 6
6 × 2.5 → 15
15 × 3.5 → 52.5
52.5 × 4.5 → 236.25

Sequence II:
Let us start with 5:
5 × 0.5 → 2.5 (A)
2.5 × 1.5 → 3.75 (B)
3.75 × 2.5 → 9.375 (C)

Let us observe the pattern:
The multipliers increase by 1 each time:
0.5, 1.5, 2.5, 3.5, 4.5

Explanation : 

7b 10a 3c

Row 1 : 10 – 7 = 3
Row 2 : 9 – 3 = 3
Row 3 = 13 – 10 = 3, B was missing in row 3

Explanation : 

Given sequence: 2, 7, 22, 67, 202, X, 1822

Pattern: Each number is generated by multiplying the previous number by 3 and adding 1.

Let’s verify each step:
2 → 7: 2 × 3 + 1 = 7
7 → 22: 7 × 3 + 1 = 22
22 → 67: 22 × 3 + 1 = 67
67 → 202: 67 × 3 + 1 = 202
202 → X: 202 × 3 + 1 = 607
607 → 1822: 607 × 3 + 1 = 1822

Answer: X = 607

Explanation :

Replacing the incorrect term by correct term

Let’s solve this sequence problem step by step:

1. Original sequence:
3, 2, 7, 4, 13, 10, 21, 18, 31, 28, 43, 40

2. Analysis of odd-positioned numbers (1st, 3rd, 5th…):
3, 7, 13, 21, 31, 43
Differences: 4, 6, 8, 10, 12
Pattern: Each difference increases by 2

3. Analysis of even-positioned numbers (2nd, 4th, 6th…):
2, 4, 10, 18, 28, 40
Differences: 2, 6, 8, 10, 12
Problem: First difference is 2, breaking the pattern

4. Correction needed:
Starting from 3 (first number)
For consistent pattern, next number should create difference of 4
Therefore, second number should be 0 (not 2)
Because: 3 → 0 gives difference of 3
And: 0 → 4 gives difference of 4

5. After correction:
Odd terms differences: 4, 6, 8, 10, 12
Even terms differences: 4, 6, 8, 10, 12

Answer: (a) 0 is correct.

The sequence becomes perfect when 2 is replaced with 0, making both odd and even terms follow same pattern of differences increasing by 2.

Explanation : 

Seven Book P, Q, R, S, T, U & V Arrangement

From the given information, we know that R, Q and T have blue covers and other books have red covers. We also know that only S and U are new books and the rest are old. Finally, we know that P, R and S are law reports; the rest are Gazetteers.

Based on this information, we can conclude that Q and T are old Gazetteers with blue covers. This is because they both have blue covers (as stated in the first sentence), they are both old (since only S and U are new), and they are both Gazetteers (since P, R and S are law reports).

Explanation : 

Arrangement of English Alphabet

The English alphabet is: ABCD EFGH IJKL MNOP QRST UVWX YZ

As per the question, the letters are arranged as follows:

DCBA HGFE LKJI PONM TSRQ XWVU ZY

The 13th letter in this arrangement is P.

The 4th letter to its right is T.