JKSSB Reasoning MCQs

Explanation

The correct option is: Both (A) and (R) are true, but (R) is NOT the correct explanation of (A)

Explanation

The correct option is: Both (A) and (R) are true, but (R) is NOT the correct explanation of (A)

Explanation

True

Explanation

Step 1: Calculate the total distance to be covered

When two trains cross each other completely, the total distance they need to cover is equal to the sum of their individual lengths.

• Length of Train 1 ($L_1$) = $120 \text{ m}$

• Length of Train 2 ($L_2$) = $180 \text{ m}$

  $$\text{Total Distance} = L_1 + L_2 = 120 + 180 = 300 \text{ m}$$

Step 2: Calculate the relative speed

Since the two trains are moving in opposite directions, their speeds are added up to find the relative speed.

• Speed of Train 1 = $54 \text{ km/h}$

• Speed of Train 2 = $72 \text{ km/h}$

  $$\text{Relative Speed} = 54 + 72 = 126 \text{ km/h}$$

Step 3: Convert the relative speed into metres per second (m/s)

Since the distance is in metres, we need the speed to be in $\text{m/s}$. To convert $\text{km/h}$ to $\text{m/s}$, multiply by $\frac{5}{18}$:

$$\text{Relative Speed in m/s} = 126 \times \frac{5}{18}$$

$$\text{Relative Speed in m/s} = 7 \times 5 = 35 \text{ m/s}$$

Step 4: Calculate the time taken

Using the time, speed, and distance formula:

$$\text{Time} = \frac{\text{Total Distance}}{\text{Relative Speed}}$$

$$\text{Time} = \frac{300}{35} = \frac{60}{7} \text{ seconds}$$

$$\text{Time} \approx 8.57 \text{ seconds} \text{ (or } 8\frac{4}{7} \text{ seconds)}$$

The two trains will take $8.57$ seconds (or $\frac{60}{7}$ seconds) to completely cross each other.

Explanation

Since the distance remains constant, speed and time are inversely proportional to each other ($\text{Speed} \propto \frac{1}{\text{Time}}$).

1. Find the Speed Ratio:

   An increase of $25\%$ means if the original speed was $100\%$, the new speed is $125\%$.

   $$\text{Ratio of Speed (Original : New)} = 100 : 125 = 4 : 5$$

2. Find the Time Ratio:

   Since time is inversely proportional to speed, we flip the ratio:

   $$\text{Ratio of Time (Original : New)} = 5 : 4$$

3. Calculate the Original Time:

   The difference between the original time and the new time in the ratio is $5 - 4 = 1 \text{ unit}$.

   According to the question, this $1 \text{ unit}$ difference is equal to $1 \text{ hour}$.

   $$\text{Original Time} = 5 \text{ units} = 5 \times 1 \text{ hour} = \mathbf{5 \text{ hours}}$$

Explanation

1. Substitute the values into the formula:

   $$\text{Average Speed} = \frac{2 \times 50 \times 40}{50 + 40}$$

2. Simplify the numerator and denominator:

   $$\text{Average Speed} = \frac{4000}{90}$$

3. Calculate the final value:

   $$\text{Average Speed} = \frac{400}{9} \approx 44.44 \text{ km/h}$$

The average speed for the whole journey is $44.44 \text{ km/h}$ (or $44\frac{4}{9} \text{ km/h}$).

Explanation

True

Explanation

The correct option is that Both I and II are possible causes for the sharp increase in online education platforms.

Here is the breakdown of why both statements act as immediate and valid causes:

• Cause I (Affordable internet availability): This provides the necessary technological infrastructure. Without cheap and widespread internet access, the general public would not be able to stream lectures or access digital course materials, meaning platforms could not grow on a large scale.

• Cause II (Increased demand for flexible learning): This provides the market demand. Working professionals, students in remote areas, and individuals looking to upskill require learning options that fit their own schedules, driving the growth of these platforms.

Explanation

• "My mother-in-law": This refers to the mother of Raj's wife.

• "The only son of my mother-in-law": The only son of Raj's mother-in-law would be his wife's brother (Raj's brother-in-law).

• "She is the wife of [this only son]": The wife of Raj's brother-in-law is Raj's sister-in-law (specifically, his wife's brother's wife).

Explanation

1. $P - Q$ * According to "$A - B$", this means $P$ is the brother of $Q$.

   • (So, $P$ is male and they belong to the same generation).

2. $Q \times R$ * According to "$A \times B$", this means $Q$ is the father of $R$.

   • (So, $Q$ is male and belongs to the generation above $R$).

3. $R + S$ * According to "$A + B$", this means $R$ is the mother of $S$.

   • (So, $R$ is female and belongs to the generation above $S$).

Putting It All Together (Family Tree Analysis):

• $P$ and $Q$ are brothers.

• $Q$ has a child named $R$ (specifically, $R$ is $Q$'s daughter because $R$ is the mother of $S$).

• Since $P$ is the brother of $R$'s father ($Q$), $P$ is the paternal uncle of $R$.

• $R$ has a child named $S$, making $Q$ the grandfather and $P$ the paternal grand-uncle of $S$.

Conclusion:

The expression $P - Q \times R + S$ establishes the following primary relationships:

• $P$ is the paternal uncle of $R$ (Father's brother).

• $P$ is the paternal grand-uncle of $S$.

• $R$ is the niece of $P$.

Explanation

1. Initial Direction: South

2. First Turn: $90^\circ$ Clockwise ($+90^\circ$)

3. Second Turn: $180^\circ$ Anticlockwise ($-180^\circ$)

4. Third Turn: $270^\circ$ Clockwise ($+270^\circ$)

Calculate Net Turn:

$$\text{Net Turn} = 90^\circ - 180^\circ + 270^\circ$$

$$\text{Net Turn} = -90^\circ + 270^\circ = +180^\circ \text{ (Clockwise)}$$

Determining the Final Direction:

A net turn of $180^\circ$ (whether clockwise or anticlockwise) means the man will face the exact opposite direction of his starting point.

• Since he started facing South, turning $180^\circ$ will make him face North.

Explanation

1. Starting Point ($A$): Let's assume Ravi starts at the origin $(0,0)$.

2. First Move: He walks $15\text{ m}$ East. He is now $15\text{ m}$ east of the starting point.

3. Second Move: He turns and walks $12\text{ m}$ North. He is now $15\text{ m}$ east and $12\text{ m}$ north of the starting point.

4. Third Move: He turns and walks $15\text{ m}$ West. Since he walked $15\text{ m}$ east earlier and now walks $15\text{ m}$ back west, he is now directly aligned vertically with his starting point ($0\text{ m}$ east/west), but still $12\text{ m}$ North.

5. Final Move: He walks $5\text{ m}$ South. Moving south reduces his northward distance: $12\text{ m} - 5\text{ m} = 7\text{ m}$.

Conclusion:

Ravi ends up exactly $7\text{ m}$ North of his original starting point.

Explanation

If we look at the positions of the letters in the standard English alphabet, we can see that each letter is paired with its exact opposite letter from the end of the alphabet (meaning the sum of their positions equals 27):

• D (4th from start) $\rightarrow$ W (4th from end)

• O (15th from start) $\rightarrow$ L (15th from end)

• G (7th from start) $\rightarrow$ T (7th from end)

Now, we apply the exact same "opposite letter" rule to CAT:

• C (3rd from start) $\rightarrow$ X (3rd from end)

• A (1st from start) $\rightarrow$ Z (1st from end)

• T (20th from start) $\rightarrow$ G (20th from end)

The code for CAT is XZG.

Explanation

To find how SCIENCE is coded, let's analyze the relationship between the letters of the word COMPUTER and its code FRPSXWHU.

Let's look at the position of each letter in the standard English alphabet ($A=1, B=2, \dots Z=26$):

• C (+3) $\rightarrow$ F

• O (+3) $\rightarrow$ R

• M (+3) $\rightarrow$ P

• P (+3) $\rightarrow$ S

• U (+3) $\rightarrow$ X

• T (+3) $\rightarrow$ W

• E (+3) $\rightarrow$ H

• R (+3) $\rightarrow$ U

The rule is simple: Each letter is shifted forward by 3 positions.

Now, applying the exact same pattern ($+3$) to the word SCIENCE:

• S (+3) $\rightarrow$ V

• C (+3) $\rightarrow$ F

• I (+3) $\rightarrow$ L

• E (+3) $\rightarrow$ H

• N (+3) $\rightarrow$ Q

• C (+3) $\rightarrow$ F

• E (+3) $\rightarrow$ H

The code for SCIENCE is VFLHQFH.

Explanation

Pattern 1: Odd Positions (1st, 3rd, 5th, 7th letters)

• 1st letter: A (1)

• 3rd letter: B (2) — (Moved $+1$)

• 5th letter: D (4) — (Moved $+2$)

• 7th letter: ? — Following the $+1, +2, +3$ pattern, the next step should be $+3$.

  • $4 + 3 = 7$

  • The 7th letter of the alphabet is G.

Pattern 2: Even Positions (2nd, 4th, 6th letters)

• 2nd letter: C (3)

• 4th letter: E (5) — (Moved $+2$)

• 6th letter: H (8) — (Moved $+3$)

  (The even series follows a $+2, +3, +4$ progression).

Since we need the next term (the 7th letter), we follow Pattern 1. Adding 3 positions to D gives us G.

The next letter in the series is G.

Explanation

First Letter Pattern:

The first letters move forward sequentially through the alphabet:

• A $\rightarrow$ B $\rightarrow$ C $\rightarrow$ D $\rightarrow$ ?

• The next letter in this sequence is E.

Second Letter Pattern:

The second letters move backward sequentially from the end of the alphabet:

• Z $\rightarrow$ Y $\rightarrow$ X $\rightarrow$ W $\rightarrow$ ?

• The next letter going backward from W is V.

Explanation

Alphabet Positions:

• Z = 26

• X = 24 (Moved backward by 2 positions: $26 - 2 = 24$)

• U = 21 (Moved backward by 3 positions: $24 - 3 = 21$)

• Q = 17 (Moved backward by 4 positions: $21 - 4 = 17$)

• L = 12 (Moved backward by 5 positions: $17 - 5 = 12$)

Finding the next letter:

The pattern of backward steps is increasing by one each time: $-2, -3, -4, -5$.

Following this logic, the next step must be to move backward by 6 positions from L:

• $12 - 6 = 6$

The 6th letter of the alphabet is F.

The next letter in the series is F.

Explanation

To complete the number series, we can look at the differences between the consecutive numbers:

• $3 - 1 = 2$

• $6 - 3 = 3$

• $10 - 6 = 4$

• $15 - 10 = 5$

The number added to each term increases by $1$ each time ($+2, +3, +4, +5$). Following this pattern, the next number should be obtained by adding $6$:

• $15 + 6 = \mathbf{2 1}$

Explanation

Pattern 1: Increasing differences (Consecutive odd numbers)

If you find the difference between consecutive numbers:

• $8 - 3 = 5$

• $15 - 8 = 7$

• $24 - 15 = 9$

• $35 - 24 = 11$

The differences are consecutive odd numbers: $5, 7, 9, 11$. Following this pattern, the next difference should be $13$.

• $35 + 13 = \mathbf{48}$

Pattern 2: Perfect squares minus 1 ($n^2 - 1$)

Each number in the series can be expressed as one less than a perfect square:

• $2^2 - 1 = 4 - 1 = 3$

• $3^2 - 1 = 9 - 1 = 8$

• $4^2 - 1 = 16 - 1 = 15$

• $5^2 - 1 = 25 - 1 = 24$

• $6^2 - 1 = 36 - 1 = 35$

Following this rule, the next term will be based on $7^2$:

• $7^2 - 1 = 49 - 1 = \mathbf{48}$

Explanation

Pattern 1: Multiply by 2 and add 1

• $5 \times 2 + 1 = 11$

• $11 \times 2 + 1 = 23$

• $23 \times 2 + 1 = 47$

• $47 \times 2 + 1 = 95$

Following this rule, the next number is:

• $95 \times 2 + 1 = 190 + 1 = \mathbf{191}$

Pattern 2: Doubling the difference

Alternatively, if you look at the differences between the numbers:

• $11 - 5 = 6$

• $23 - 11 = 12$ (which is $6 \times 2$)

• $47 - 23 = 24$ (which is $12 \times 2$)

• $95 - 47 = 48$ (which is $24 \times 2$)

The difference doubles each time. Therefore, the next difference should be $48 \times 2 = 96$.

• $95 + 96 = \mathbf{191}$

The next number in the series is 191.

Explanation

• Conclusion I follows: Since "Some books are fiction" and "All fictional books are popular," the books that fall into the "fiction" category are automatically "popular." Therefore, it is logically certain that some books are popular.

• Conclusion II does not follow: The statement says all fiction is popular, but it does not say that only fiction is popular. There could be many other popular things (like movies or sports) that are not fiction. In logic, you cannot reverse an "All A are B" statement to mean "All B are A."

Explanation

• Conclusion I follows: Import duty is a tax added to the price of foreign goods. Reducing this tax lowers the cost for importers, which usually leads to a decrease in the market price for consumers. Therefore, prices may fall.

• Conclusion II does not follow: A reduction in import duty increases competition, but it is an extreme and illogical leap to assume domestic production will stop entirely. Domestic companies may adjust prices or improve efficiency, but they do not simply cease to exist because of a policy change.

Explanation

• Speed Ratio: Since Ram reduces his speed to $4/5$ of the actual speed, the ratio of his Actual Speed to New Speed is $5 : 4$.

• Time Ratio: Speed and time are inversely proportional ($Time \propto 1/Speed$). Therefore, the ratio of his Actual Time to New Time is $4 : 5$.

• Identify the Difference: The difference in the time ratio is $5 - 4 = \mathbf{1 \text{ unit}}$.

• Relate to Real Time: We are told he is $15 \text{ minutes}$ late, so this $1 \text{ unit}$ difference is equal to $15 \text{ minutes}$.

  • $1 \text{ unit} = 15 \text{ minutes}$

• Find Actual Time: The actual time corresponds to 4 units in our ratio.

  • $\text{Actual Time} = 4 \text{ units} \times 15 \text{ minutes} = \mathbf{60 \text{ minutes}}$

Explanation

1. Analyze the given strings:

   • $P \geq Q > R$

   • $R \leq S < T$

   • $P > T$

2. Evaluate Option D ($T > R$):

   • From the second string, we have $R \leq S < T$.

   • Since $S$ is greater than or equal to $R$, and $T$ is strictly greater than $S$, it follows that $T$ must be strictly greater than $R$.

   • This relationship is direct and independent of $P$ or $Q$.

Why the other options are incorrect:

• A) $P = S$: We know $P > T$ and $T > S$, which implies $P > S$. Therefore, $P$ cannot equal $S$.

• B) $S < Q$: Both $Q$ and $S$ are greater than $R$, but there is no direct link to compare $Q$ and $S$ to each other.

• C) $Q > T$: $Q$ is greater than $R$, and $T$ is greater than $R$, but we cannot establish a definitive relationship between $Q$ and $T$ with the information provided.

Explanation

1. "My father's only son": Since the speaker is a man, his father's only son is himself.

2. "My father's only son's wife": This refers to the man's wife.

3. "The daughter of... my wife": The daughter of the man's wife is the man's daughter.

Final Answer: The girl is the man's Daughter.

Explanation

To find the final direction, we calculate the net rotation by treating clockwise (CW) as negative and anticlockwise (ACW) as positive (or vice versa):

1. Initial Direction: East

2. Clockwise Turn: $-135^\circ$

3. Anticlockwise Turn: $+90^\circ$

4. Net Result: $-135^\circ + 90^\circ = \mathbf{-45^\circ}$ (or $45^\circ$ Clockwise)

Conclusion

Starting from East and turning $45^\circ$ Clockwise puts the man between East and South.

Final Direction: South-East

Explanation

Applying the Rules to MONDAY

Step 1: Reverse the word

• MONDAY $\rightarrow$ YADNOM

Step 2: Replace the vowels with their position numbers

• Y (Consonant) $\rightarrow$ Y

• A (Vowel) $\rightarrow$ 1

• D (Consonant) $\rightarrow$ D

• N (Consonant) $\rightarrow$ N

• O (Vowel) $\rightarrow$ 15

• M (Consonant) $\rightarrow$ M

Final Result

The code for MONDAY is Y1DN15M.

Explanation

• Map the positions:

  Convert each letter to its numerical position in the alphabet ($A=1, B=2, \dots$):

  • A = 1

  • D = 4

  • I = 9

  • P = 16

  • Y = 25

• Identify the pattern:

  The numbers represent the sequence of perfect squares:

  • $1^2 = 1$

  • $2^2 = 4$

  • $3^2 = 9$

  • $4^2 = 16$

  • $5^2 = 25$

• Find the next term:

  The next square is $6^2 = \mathbf{36}$.

• Map the number back to a letter:

  Since the alphabet has only 26 letters, subtract 26 to find the position in the next cycle:

  $$36 - 26 = 10$$

  The 10th letter of the alphabet is J.

Explanation

Convert letters to positions:

C = 3, E = 5, K = 11, Q = 17, W = 23

Pattern:
+2, +6, +6, +6

So next = 23+6=29

Since alphabet has 26 letters:
29−26=3→ C

Explanation

Step 1: Calculate the first differences

Subtract each term from the one following it:

• $9 - 1 = 8$

• $35 - 9 = 26$

• $99 - 35 = 64$

• $225 - 99 = 126$

First differences: 8, 26, 64, 126

Step 2: Calculate the second differences

Subtract the first differences:

• $26 - 8 = 18$

• $64 - 26 = 38$

• $126 - 64 = 62$

Second differences: 18, 38, 62

Step 3: Calculate the third differences

Subtract the second differences:

• $38 - 18 = 20$

• $62 - 38 = 24$

Third differences: 20, 24

Step 4: Calculate the fourth difference

Subtract the third differences:

• $24 - 20 = 4$

Fourth difference: 4

Step 5: Extend the sequence

Assuming the fourth difference is constant (4), we can work our way back up to find the next term:

1. Next third difference: $24 + 4 = 28$

2. Next second difference: $62 + 28 = 90$

3. Next first difference: $126 + 90 = 216$

4. Next term in the sequence: $225 + 216 = \mathbf{441}$