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Defence NDA / CDS

NDA & CDS MCQ questions — Mathematics, English, GK, Reasoning for defence exams.

1,216 Q 4 Subjects 12th / Graduate
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Difficulty: All Easy Medium Hard 1161–1170 of 1,216
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Q.1161 Medium Reasoning Ability
Mirror image of SMART?
A TRAMS
B TRAMS reversed
C SMART same
D None
Correct Answer:  B. TRAMS reversed
EXPLANATION

This question asks what the mirror image of the word "SMART" would look like when reflected horizontally.

Step 1: Understand mirror image reflection

When a word is reflected in a mirror, each letter is reversed and the order of letters is also reversed (reading right to left instead of left to right).

\[\text{SMART} \rightarrow \text{mirror reflection} \rightarrow \text{TRAMS (reversed)}\]
Step 2: Reverse the letter sequence

Original word: S-M-A-R-T

When mirrored horizontally, the sequence becomes right-to-left: T-R-A-M-S

\[\text{Original: S-M-A-R-T} \rightarrow \text{Reversed: T-R-A-M-S}\]
Step 3: Account for individual letter orientations

Each letter in the mirror image would also be horizontally flipped (S becomes reversed S, M becomes reversed M, etc.), so the complete mirror image is "TRAMS reversed" (meaning TRAMS with each letter flipped).

\[\text{Mirror Image} = \text{TRAMS with each letter horizontally flipped}\]

The mirror image of SMART is TRAMS reversed (each letter is flipped and the sequence is reversed).

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Q.1162 Hard Reasoning Ability
5 cats catch 5 rats in 5 min. Cats needed for 100 rats in 100 min?
A 5
B 10
C 100
D 50
Correct Answer:  A. 5
EXPLANATION

This question tests understanding of work rates and proportional reasoning with multiple workers and time periods.

Step 1: Find the rate per cat

If 5 cats catch 5 rats in 5 minutes, each cat catches rats at a constant rate.

\[\text{Rate per cat} = \frac{5 \text{ rats}}{5 \text{ cats} \times 5 \text{ min}} = \frac{1}{5} \text{ rats per cat per minute}\]
Step 2: Calculate total rat-catching capacity needed

To catch 100 rats in 100 minutes, we need the total work capacity.

\[\text{Total capacity needed} = \frac{100 \text{ rats}}{100 \text{ min}} = 1 \text{ rat per minute}\]
Step 3: Determine number of cats required

Since each cat catches \(\frac{1}{5}\) rats per minute, we need enough cats to produce 1 rat caught per minute.

\[\text{Number of cats} = \frac{1 \text{ rat/min}}{\frac{1}{5} \text{ rats/cat/min}} = 1 \times 5 = 5 \text{ cats}\]

**The same 5 cats are needed to catch

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Q.1163 Hard Reasoning Ability
Clock shows 3:15. Angle between hands?
A
B 7.5°
C 15°
D 22.5°
Correct Answer:  B. 7.5°
EXPLANATION

This question asks us to find the angle between the hour and minute hands on an analog clock displaying 3:15.

Step 1: Calculate the minute hand position

The minute hand moves 360° in 60 minutes, so it moves 6° per minute.

\[\text{Minute hand angle} = 15 \times 6 = 90°\]
Step 2: Calculate the hour hand position

The hour hand moves 360° in 12 hours (720 minutes), so it moves 0.5° per minute. At 3:15, it has moved from 12 o'clock.

\[\text{Hour hand angle} = (3 \times 30) + (15 \times 0.5) = 90 + 7.5 = 97.5°\]
Step 3: Find the angle between both hands

The angle between the hands is the absolute difference between their positions.

\[\text{Angle between hands} = |97.5 - 90| = 7.5°\]

The angle between the hour and minute hands at 3:15 is 7.5°.

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Q.1164 Medium Reasoning Ability
P walks 5km North, 3km East, 5km South. Distance from start?
A 3 km
B 5 km
C 8 km
D 13 km
Correct Answer:  A. 3 km
EXPLANATION

This question tests the ability to track position changes on a coordinate system and calculate the straight-line distance from the starting point.

Step 1: Set up a coordinate system

Let P start at the origin point (0, 0), with North as positive Y-axis and East as positive X-axis.

\[\text{Starting position} = (0, 0)\]
Step 2: Track position after each movement

After walking 5 km North, then 3 km East, then 5 km South, the vertical movements cancel out and only the eastward movement remains.

\[\text{Final position} = (0 + 3, 5 - 5) = (3, 0)\]
Step 3: Calculate distance from starting point

Use the distance formula to find the straight-line distance between the starting point (0, 0) and final position (3, 0).

\[\text{Distance} = \sqrt{(3-0)^2 + (0-0)^2} = \sqrt{9} = 3 \text{ km}\]

The distance from the starting point is 3 km.

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Q.1165 Easy Reasoning Ability
A is 2 yrs older than B who is twice C's age. C=10, A=?
A 20
B 22
C 24
D 18
Correct Answer:  B. 22
EXPLANATION

This question involves finding A's age using the given relationships between the ages of three people.

Step 1: Find B's age

We know C = 10 and B is twice C's age.

\[B = 2 \times C = 2 \times 10 = 20 \text{ years}\]
Step 2: Find A's age

We know A is 2 years older than B.

\[A = B + 2 = 20 + 2 = 22 \text{ years}\]
Step 3: Verify the relationships

Check: C = 10, B = 2 × 10 = 20, A = 20 + 2 = 22 ✓

\[\text{All conditions satisfied: B is twice C's age and A is 2 years older than B}\]

A's age is 22 years, making the correct answer B) 22.

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Q.1166 Medium Reasoning Ability
Next letter: A, C, F, J, O, __?
A T
B U
C V
D W
Correct Answer:  B. U
EXPLANATION

This question tests your ability to identify the pattern in a sequence of letters.

Step 1: Identify the position of each letter in the alphabet

Convert each letter to its numerical position where A=1, B=2, C=3, and so on.

\[A=1, C=3, F=6, J=10, O=15, ?\]
Step 2: Find the pattern in the differences

Calculate the difference between consecutive numbers in the sequence.

\[\text{Differences: } 3-1=2, \quad 6-3=3, \quad 10-6=4, \quad 15-10=5\]
Step 3: Apply the pattern to find the next letter

The differences increase by 1 each time (2, 3, 4, 5...), so the next difference should be 6.

\[15 + 6 = 21, \quad \text{and the 21st letter is } U\]

The next letter in the sequence is U, making the correct answer (B).

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Q.1167 Medium Reasoning Ability
Statement: Some pens are books. All books are tables. Conclusion: Some pens are tables.
A True
B False
C Uncertain
D Cannot say
Correct Answer:  A. True
EXPLANATION

This question tests logical deduction using set theory and Venn diagrams to determine if a conclusion necessarily follows from given statements.

Step 1: Identify the sets and relationships

We have three sets: Pens, Books, and Tables. The first statement "Some pens are books" means there is an intersection between the Pens set and Books set.

\[\text{Pens} \cap \text{Books} \neq \emptyset\]
Step 2: Apply the second statement

The statement "All books are tables" means every element in the Books set is also in the Tables set, so Books is a subset of Tables.

\[\text{Books} \subseteq \text{Tables}\]
Step 3: Deduce the conclusion

Since some pens are books (Step 1) AND all books are tables (Step 2), any pen that is a book must also be a table. Therefore, some pens must be tables.

\[\text{If } x \in (\text{Pens} \cap \text{Books}) \text{ and } \text{Books} \subseteq \text{Tables, then } x \in \text{Tables}\]

**The conclusion "Some pens are tables" is logically True because any pen belonging to the Books set must also belong to the Tables set, given that all books

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Q.1168 Hard Reasoning Ability
Squares in a 3×3 grid?
A 9
B 14
C 16
D 12
Correct Answer:  B. 14
EXPLANATION

This question asks you to count all possible squares of different sizes that can be formed in a 3×3 grid.

Step 1: Count 1×1 squares

In a 3×3 grid, the smallest squares are individual cells.

\[1 \times 1 \text{ squares} = 3 \times 3 = 9\]
Step 2: Count 2×2 squares

Larger squares formed by combining four cells in a 2×2 pattern can fit in multiple positions.

\[2 \times 2 \text{ squares} = 2 \times 2 = 4\]
Step 3: Count 3×3 squares and find total

The largest possible square is the entire grid itself.

\[3 \times 3 \text{ squares} = 1 \times 1 = 1\]

Total squares = 1×1 squares + 2×2 squares + 3×3 squares

\[\text{Total} = 9 + 4 + 1 = 14\]

The total number of squares in a 3×3 grid is 14.

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Q.1169 Medium Reasoning Ability
All roses are flowers. Some flowers fade. Therefore?
A All roses fade
B Some roses may fade
C No roses fade
D Roses never fade
Correct Answer:  B. Some roses may fade
EXPLANATION

This question tests logical reasoning through categorical statements and syllogisms.

Step 1: Identify the Given Statements

We have two premises: (1) All roses are flowers, and (2) Some flowers fade.

\[\text{Roses} \subset \text{Flowers} \quad \text{and} \quad \text{Some Flowers} \rightarrow \text{Fade}\]
Step 2: Determine What We Can Conclude About Roses

Since only "some" flowers fade (not all), we cannot conclude that all roses fade. However, roses ARE flowers, so roses could potentially be part of the group that fades.

\[\text{Roses} \subset \text{Flowers} \quad \text{and} \quad \text{Some Flowers fade} \Rightarrow \text{Some roses MAY fade}\]
Step 3: Eliminate Incorrect Options

- (A) "All roses fade" — Too strong; we only know some flowers fade, not all

- (C) "No roses fade" — Contradicts the fact that some flowers fade

- (D) "Roses never fade" — Same as (C); impossible to conclude

\[\text{Only (B) acknowledges the possibility without making an absolute claim}\]

**The correct answer is (B) Some roses may fade, because while

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Q.1170 Medium Reasoning Ability
If BOOK=CPPL, DOOR=?
A EPPS
B EQPS
C EQOR
D FQPS
Correct Answer:  A. EPPS
EXPLANATION

This question tests pattern recognition by finding the cipher rule that transforms letters in a word.

Step 1: Analyze the given transformation BOOK=CPPL

Each letter shifts by a consistent number of positions in the alphabet.

\[B \to C \text{ (shift +1)}, \quad O \to P \text{ (shift +1)}, \quad O \to P \text{ (shift +1)}, \quad K \to L \text{ (shift +1)}\]
Step 2: Apply the same rule to DOOR

Each letter in DOOR shifts forward by 1 position in the alphabet.

\[D \to E, \quad O \to P, \quad O \to P, \quad R \to S\]
Step 3: Write the transformed word

Combining all shifted letters in sequence.

\[\text{DOOR} = \text{EPPS}\]

The answer is (A) EPPS, as each letter in DOOR shifts forward by exactly one position in the alphabet.

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