Mathematical and Logical Reasoning — NCERT Solutions

Given Statements:

• Some ants are parrots. (partial overlap: ants ∩ parrots ≠ ∅)
• All parrots are apples. (parrots ⊂ apples)

Analysis of Conclusion (1): "All the apples are parrots."
Statement II says all parrots are apples, i.e., parrots ⊂ apples. The converse (all apples are parrots) does not necessarily follow. ✗ Conclusion (1) does not follow.

Analysis of Conclusion (2): "Some ants are apples."
Since some ants are parrots (Statement I) and all parrots are apples (Statement II), those ants that are parrots must also be apples. Therefore, some ants are apples. ✓ Conclusion (2) follows.

Answer: (B) — Only conclusion (2) follows.

Given: CAMEL → DBNFM

Finding the pattern:
$$C \xrightarrow{+1} D, \quad A \xrightarrow{+1} B, \quad M \xrightarrow{+1} N, \quad E \xrightarrow{+1} F, \quad L \xrightarrow{+1} M$$

Each letter is replaced by the next letter in the alphabet (shifted by +1).

Applying the same rule to ROOM:
$$R \xrightarrow{+1} S, \quad O \xrightarrow{+1} P, \quad O \xrightarrow{+1} P, \quad M \xrightarrow{+1} N$$

So ROOM is coded as SPPN.

Answer: (b) SPPN

Given:

• BLEPIN = 9 8 7 4 1 6
• MATPIN = 1 2 3 4 1 6

Decoding individual letters:
$$B=9,\ L=8,\ E=7,\ P=4,\ I=1,\ N=6$$
$$M=1,\ A=2,\ T=3,\ P=4,\ I=1,\ N=6$$

So: $T=3,\ A=2,\ B=9,\ L=8,\ E=7$

TABLE = $3\ 2\ 9\ 8\ 7$ = 32987

Answer: (a) 32987

Given codes:

• 'hi mi si' = 'Air is life'
• 'si ni zi' = 'Balloon of Air'
• 'ci zi mi' = 'Life of PI'

Step 1: Find the code for 'Air'.
Comparing statement 1 and statement 2: common word is 'Air' and common code is 'si'. So si = Air.

Step 2: Find the code for 'life'.
Comparing statement 1 and statement 3: common word is 'life' and common code is 'mi'. So mi = life.

Step 3: From statement 1 (hi mi si = Air is life), with si = Air and mi = life, the remaining word 'is' = hi.

Step 4: Find the code for 'of'.
Comparing statement 2 and statement 3: common word is 'of' and common code is 'zi'. So zi = of.

Step 5: From statement 2 (si ni zi = Balloon of Air), with si = Air and zi = of, the remaining word 'Balloon' = ni.

Step 6: From statement 3 (ci zi mi = Life of PI), with zi = of and mi = life, the remaining word 'PI' = ci.

Answer: (c) ci

Given codes:

• 321 = 'Glass of Tea'
• 426 = 'Tea is Brown'
• 796 = 'Trunks are Brown'

Step 1: Find the code for 'Tea'.
Comparing statement 1 and statement 2: common word is 'Tea' and common digit is 2 (wait — let us check carefully).

• Statement 1 digits: 3, 2, 1
• Statement 2 digits: 4, 2, 6

Common digit: 2 → common word: 'Tea'. So 2 = Tea.

Step 2: Find the code for 'Brown'.
Comparing statement 2 and statement 3: common word is 'Brown' and common digit:

• Statement 2 digits: 4, 2, 6
• Statement 3 digits: 7, 9, 6

Common digit: 6 → common word: 'Brown'. So 6 = Brown.

Step 3: From statement 2 (426 = Tea is Brown), with 2 = Tea and 6 = Brown, the remaining digit for 'is' = 4.

Answer: (c) 4

Given: The man says, "The lady in the picture is my nephew's maternal grandmother."

Step 1: The man's nephew is the son of the man's sister (since the sister has no other sister, the nephew must be the sister's son).

Step 2: The nephew's maternal grandmother is the mother of the nephew's mother, i.e., the mother of the man's sister.

Step 3: The mother of the man's sister is also the mother of the man (they share the same family).

Step 4: Therefore, the lady in the picture is the mother of the man's sister.

Answer: (c) Mother

Given information:

• Meenakshi is Kirti's sister → Meenakshi and Kirti are siblings.
• Kaavya is Kirti's mother → Kaavya is also Meenakshi's mother.
• Dipesh is Kaavya's father → Dipesh is the grandfather of Kirti and Meenakshi.
• Esha is Dipesh's mother (additional info, not needed here).

Relationship chain:
$$\text{Dipesh} \xrightarrow{\text{father of}} \text{Kaavya} \xrightarrow{\text{mother of}} \text{Meenakshi}$$

So Dipesh is Meenakshi's maternal grandfather, and Meenakshi is Dipesh's granddaughter.

Answer: (d) Granddaughter

Given operations:

• $+$ : P+Q → P is the brother of Q
• $-$ : R−S → R is the father of S
• $/$ : S/T → S is the sister of T
• $\times$ : T×U → T is the mother of U

We need to find the expression that means "O is the mother of N."

Checking option (d): $M+L/O \times N$

• $M+L$: M is the brother of L
• $L/O$: L is the sister of O → O and L are sisters
• $O \times N$: O is the mother of N ✓

This directly gives us O is the mother of N.

Let us verify the other options do not give this:

• Option (a): $L+M/N-O$ → L is brother of M; M is sister of N; N is father of O. This gives N as father of O, not O as mother of N. ✗
• Option (b): $L-M \times O/P$ → L is father of M; M is mother of O; O is sister of P. Does not give O as mother of N. ✗
• Option (c): $N/M \times L/O$ → N is sister of M; M is mother of L; L is sister of O. Does not give O as mother of N. ✗

Answer: (d) $M+L/O \times N$

Given options: Insurance, Provident Fund, Salary, Shares.

Analysis:

• Insurance: a form of financial security/investment.
• Provident Fund: a form of savings/investment for the future.
• Salary: income earned from employment (not an investment or saving instrument).
• Shares: a form of investment.

Insurance, Provident Fund, and Shares are all forms of investment or financial security instruments. Salary is the odd one out as it is earned income, not an investment.

Answer: (c) Salary

Given numbers: 3, 5, 11, 14, 17, 21.

Analysis:

• 3 → odd number
• 5 → odd number
• 11 → odd number
• 14 → even number
• 17 → odd number
• 21 → odd number

All numbers except 14 are odd numbers. 14 is the only even number in the list.

Answer: (c) 14

Note: The actual figures (a, b, c, d) cannot be seen from the OCR. However, based on the official answer key provided in the textbook, the answer is option (c).

General approach for such questions: Examine each figure for a common property (e.g., number of sides, shading pattern, symmetry, rotation). The figure that does not share the common property of the other three is the odd one out.

Answer: (c) — as per the official solution provided in the textbook.