Puzzle Test Questions in English

(C) To determine the hill stations,we analyze the given constraints:
$1$. $A$ is not a hill station.
$2$. $B$ and $E$ are not historical places.
$3$. $D$ is not an industrial city.
$4$. $A$ and $D$ are not historical cities.
$5$. $A$ and $B$ are not alike.
Based on the logical deduction of city characteristics (Hill Station,Historical,Industrial),and given that $A$ is not a hill station,we evaluate the options. By process of elimination and mapping the constraints,$B$ and $D$ are identified as the cities that satisfy the criteria for being hill stations.

(A) To solve this,we analyze the constraints given for the six cities $A, B, C, D, E, F$ regarding their characteristics: Hill Station $(H)$,Industrial Centre $(I)$,and Historical Place $(S)$.
$1$. $A$ is not a hill station $(A
eq H)$.
$2$. $B$ and $E$ are not historical places $(B
eq S, E
eq S)$.
$3$. $D$ is not an industrial city $(D
eq I)$.
$4$. $A$ and $D$ are not historical cities $(A
eq S, D
eq S)$.
$5$. $A$ and $B$ are not alike.
Based on the logical deduction of the attributes,city $E$ satisfies the condition of being a hill station and an industrial centre while not being a historical place.

(D) Let us classify the cities based on the given conditions:
$1$. $A$ is not a hill station. $A$ is not a historical city.
$2$. $B$ and $E$ are not historical places.
$3$. $D$ is not an industrial city. $D$ is not a historical city.
$4$. $A$ and $B$ are not alike.
By analyzing the constraints:
- $A$ is not historical and not a hill station,so $A$ must be an industrial city.
- Since $A$ and $B$ are not alike,and $A$ is industrial,$B$ cannot be industrial. $B$ is also not historical. Therefore,$B$ must be a hill station.
- $D$ is not historical and not industrial,so $D$ must be a hill station.
- Thus,$B$ and $D$ are both hill stations,meaning they are neither historical places nor industrial centres.

(A-D) Mode of Transport: $R$ travels by Car,$Q$ by Aeroplane,$S$ by Boat,and $T$ by Train. Now,only $P$ remains. So,$P$ travels by Bus.
$(B)$ Place of Travel: $R$ goes to Bangalore,$Q$ to Calcutta. Now,bus transport is not available for Delhi or Chennai. So,$P$ who travels by Bus goes to Hyderabad. $S$ travels by boat and hence,by $(ii)$,did not go to Delhi. So,$S$ goes to Chennai. Now,only $T$ remains. So,$T$ goes to Delhi.

Person	Place - Mode
$P$	Hyderabad - Bus
$Q$	Calcutta - Aeroplane
$R$	Bangalore - Car
$S$	Chennai - Boat
$T$	Delhi - Train

Based on the analysis,all given options $(P-Bus, Q-Aeroplane, R-Car, S-Boat)$ are correct. The question asks for the incorrect combination. Since the provided options are all correct,none of them is the answer. However,based on the logic,$T-Train$ is correct,and any other combination for $T$ would be incorrect.

(C) Modes of Transport: $R$ travels by Car,$Q$ by Aeroplane,$S$ by Boat,and $T$ by Train. Since only $P$ remains,$P$ must travel by Bus.
$(B)$ Places of Travel: $R$ goes to Bangalore,$Q$ to Calcutta. Since bus transport is not available for Delhi or Chennai,$P$ (who travels by Bus) must go to Hyderabad. $S$ travels by boat and,according to $(ii)$,did not go to Delhi. Therefore,$S$ must go to Chennai. Finally,$T$ goes to Delhi.

Friend	Place and Mode
$P$	Hyderabad $-$ Bus
$Q$	Calcutta $-$ Aeroplane
$R$	Bangalore $-$ Car
$S$	Chennai $-$ Boat
$T$	Delhi $-$ Train

Clearly,the correct combination for $S$ is Chennai $-$ Boat.

(A) Mode of Transport: $R$ travels by Car,$Q$ by Aeroplane,$S$ by Boat,and $T$ by Train. Since only $P$ remains,$P$ must travel by Bus.
$(B)$ Place of Travel: $R$ goes to Bangalore,$Q$ goes to Calcutta. Since bus transport is not available for Delhi or Chennai,$P$ (who travels by Bus) must go to Hyderabad. $S$ travels by boat and,according to $(ii)$,did not go to Delhi. Therefore,$S$ goes to Chennai. Finally,$T$ goes to Delhi.

Person	Place $-$ Mode
$P$	Hyderabad $-$ Bus
$Q$	Calcutta $-$ Aeroplane
$R$	Bangalore $-$ Car
$S$	Chennai $-$ Boat
$T$	Delhi $-$ Train

Clearly,the incorrect combination is Delhi $-$ Bus.

(B) Mode of Transport: $R$ travels by Car,$Q$ by Aeroplane,$S$ by Boat,and $T$ by Train. Now,only $P$ remains. So,$P$ travels by Bus.
$(B)$ Place of Travel: $R$ goes to Bangalore,$Q$ to Calcutta. Now,bus transport is not available for Delhi or Chennai. So,$P$ (who travels by Bus) must go to Hyderabad. $S$ travels by boat and,according to $(ii)$,did not go to Delhi. Since $R, Q,$ and $P$ are already assigned,$S$ must go to Chennai. Now,only $T$ remains. So,$T$ goes to Delhi.

Person	Place and Mode
$P$	Hyderabad,Bus
$Q$	Calcutta,Aeroplane
$R$	Bangalore,Car
$S$	Chennai,Boat
$T$	Delhi,Train

Clearly,$T$ travelled to Delhi by Train.

(C) Mode of Transport: $R$ travels by Car,$Q$ by Aeroplane,$S$ by Boat,and $T$ by Train. Now,only $P$ remains. So,$P$ travels by Bus.
$(B)$ Place of Travel: $R$ goes to Bangalore,$Q$ to Calcutta. Now,bus transport is not available for Delhi or Chennai. So,$P$ who travels by Bus goes to Hyderabad. $S$ travels by boat and hence,by $(ii)$,did not go to Delhi. So,$S$ goes to Chennai. Now,only $T$ remains. So,$T$ goes to Delhi.

Person	Place $\&$ Mode
$P$	Hyderabad,Bus
$Q$	Calcutta,Aeroplane
$R$	Bangalore,Car
$S$	Chennai,Boat
$T$	Delhi,Train

Clearly,$T$ travelled to Delhi.

(B) Let us analyze the subjects taught by each teacher based on the given information:

Teacher	Subjects Taught
$A$	Hindi,English,Mathematics
$B$	Hindi,English,Geography,History,French
$C$	English,Geography
$D$	Mathematics,Hindi
$E$	History,French

From the table,we can count the number of subjects taught by each teacher:
- $A$: $3$ subjects
- $B$: $5$ subjects
- $C$: $2$ subjects
- $D$: $2$ subjects
- $E$: $2$ subjects
Thus,teacher $B$ teaches the maximum number of subjects,which is $5$.

(D) Let us analyze the subjects taught by each teacher based on the given information:

Teacher	Subjects Taught
$A$	Hindi,English,Mathematics
$B$	Hindi,English,Geography,History,French
$C$	English,Geography
$D$	Mathematics,Hindi
$E$	History,French

From the analysis:
$1$. Teacher $B$ teaches both Hindi and Geography.
$2$. No other teacher teaches both these subjects.
$3$. The question asks for a pair teaching both subjects. However,based on the data,only $B$ teaches both. Reviewing the options,if we look for a pair where one teaches Hindi and the other teaches Geography,or a combination,we must re-evaluate. Since the question asks for a pair teaching both,and only $B$ does,there might be an error in the question's premise. Given the options,let's check if any pair covers both subjects collectively. $B$ teaches both,so any pair containing $B$ covers both. Among the options,$D$ and $B$ ($D$ teaches Hindi,$B$ teaches Geography) is the most logical fit for a pair covering both subjects.

(B) Let us analyze the teaching assignments for each teacher:

Teacher	Subjects Taught
$A$	Hindi,English,Mathematics
$B$	Hindi,English,Geography,History,French
$C$	English,Geography
$D$	Mathematics,Hindi
$E$	History,French

Now,count the number of teachers for each subject:
- Hindi: $A, B, D$ ($3$ teachers)
- English: $A, B, C$ ($3$ teachers)
- Geography: $B, C$ ($2$ teachers)
- Mathematics: $A, D$ ($2$ teachers)
- History: $B, E$ ($2$ teachers)
- French: $B, E$ ($2$ teachers)
Since Hindi and English are taught by $3$ teachers each,and the question asks for a subject taught by more than two teachers,Hindi is the correct option.

(C) Based on the provided information,we can map the subjects taught by each teacher:

Teacher	Subjects Taught
$A$	Hindi,English,Mathematics
$B$	Hindi,English,Geography,History,French
$C$	English,Geography
$D$	Mathematics,Hindi
$E$	History,French

Now,we identify the common subjects taught by $D, B,$ and $A$:
- Teacher $A$ teaches: Hindi,English,Mathematics
- Teacher $B$ teaches: Hindi,English,Geography,History,French
- Teacher $D$ teaches: Mathematics,Hindi
The subject common to all three ($A, B,$ and $D$) is Hindi.

(D) Let us analyze the subjects taught by each teacher based on the provided information:
$1$. $A$ teaches: Hindi,English,Mathematics ($3$ subjects).
$2$. $B$ teaches: Hindi,English,Geography,History,French ($5$ subjects).
$3$. $C$ teaches: English,Geography ($2$ subjects).
$4$. $D$ teaches: Mathematics,Hindi ($2$ subjects).
$5$. $E$ teaches: History,French ($2$ subjects).
Summary of subjects taught:
- $A$: $3$ subjects
- $B$: $5$ subjects
- $C$: $2$ subjects
- $D$: $2$ subjects
- $E$: $2$ subjects
Since every teacher is teaching at least $2$ subjects,there is no teacher who teaches less than $2$ subjects.

(C) To solve this,we can create a table to track the subjects each person is good at:

Name	Dramatics	Computer Science	Physics	History	Mathematics
Madhu	Yes	Yes	Yes	No	No
Shobha	Yes	Yes	No	Yes	No
Anjali	No	Yes	Yes	Yes	No
Poonam	Yes	No	Yes	Yes	No
Nisha	No	No	Yes	Yes	Yes

From the table,we can see that Shobha is good in Computer Science,History,and Dramatics.

(C) To solve this,we can create a table to track the subjects each person is good at:

Name	Dramatics,Computer Science,Physics,History,Mathematics
Madhu	Dramatics,Computer Science,Physics
Shobha	Dramatics,Computer Science,History
Anjali	Computer Science,Physics,History
Poonam	Physics,History,Dramatics
Nisha	Physics,History,Mathematics

From the table,we can see that Madhu is good in Physics,Dramatics,and Computer Science.

(A) We can represent the information in a table as follows:

Name	Dramatics	Computer Science	Physics	History	Mathematics
Madhu	Yes	Yes	Yes	No	No
Shobha	Yes	Yes	No	Yes	No
Anjali	No	Yes	Yes	Yes	Yes
Poonam	Yes	No	Yes	Yes	No
Nisha	No	No	Yes	Yes	Yes

From the table,we can see that Poonam is good in Physics,History,and Dramatics.

(D) To solve this,we create a table to track the subjects each person is good at:

Name	Dramatics	Computer Sc.	Physics	History	Mathematics
Madhu	Yes	Yes	Yes	No	No
Shobha	Yes	Yes	No	Yes	No
Anjali	No	Yes	Yes	Yes	Yes
Poonam	Yes	No	Yes	Yes	No
Nisha	No	No	Yes	Yes	Yes

From the table,we can see that Anjali is good in Computer Science,Physics,History,and Mathematics. Therefore,the correct answer is Anjali.

(C) We can represent the information in a table to determine who is good in Physics,History,and Mathematics but not in Computer Science.

Name	Dramatics	Computer Science	Physics	History	Mathematics
Madhu	Yes	Yes	Yes	No	No
Shobha	Yes	Yes	No	Yes	No
Anjali	No	Yes	Yes	Yes	Yes
Poonam	Yes	No	Yes	Yes	No
Nisha	No	No	Yes	Yes	Yes

From the table,we can see that Nisha is good in Physics,History,and Mathematics,but she is not good in Computer Science.

(D) Let the four colours be $C_1, C_2, C_3, C_4$. We know Sachin wears red. Since all four wear different colours,the remaining three people (Ravi,Ajay,Sohan) must wear the remaining three colours.
Given:
$1$. Ravi is not wearing white.
$2$. Ajay is not wearing blue.
$3$. Sachin wears red.
Since we do not know the specific set of four colours being used,we cannot uniquely determine Sohan's colour based on the given constraints. Therefore,the information is insufficient.

(C) We can represent the given information in a table as follows:

Name	Intelligent	Hard-working	Honest	Ambitious
Kailash	Yes	Yes	No	Yes
Govind	Yes	No	No	Yes
Harinder	Yes	No	Yes	No
Rajesh	No	Yes	Yes	No
Jitendra	No	Yes	Yes	Yes

From the table,we check the criteria for each person:
- Kailash: Hard-working (Yes),Ambitious (Yes)
- Govind: Hard-working (No),Ambitious (Yes)
- Harinder: Hard-working (No),Ambitious (No)
- Rajesh: Hard-working (Yes),Ambitious (No)
- Jitendra: Hard-working (Yes),Ambitious (Yes)
Therefore,Harinder is neither hard-working nor ambitious.

(B) We can represent the given information in a table as follows:

Person	Intelligent	Hard-working	Honest	Ambitious
Kailash	Yes	Yes	No	Yes
Govind	Yes	No	No	Yes
Harinder	Yes	No	Yes	No
Rajesh	No	Yes	Yes	No
Jitendra	No	Yes	Yes	Yes

We are looking for a person who is:
$1$. Not honest
$2$. Not hard-working
$3$. Ambitious
From the table:
- Kailash: Hard-working (Does not fit)
- Govind: Not honest,not hard-working,and is ambitious (Fits the criteria)
- Harinder: Not hard-working,but not ambitious (Does not fit)
- Rajesh: Hard-working (Does not fit)
- Jitendra: Hard-working (Does not fit)
Therefore,Govind is the correct answer.

(B) $1$. $Sushma$ and $Vimla$ are friends. $Prem$'s girlfriend is friendly with $Sushma$. Since $Sushma$ and $Vimla$ are friends,$Prem$'s girlfriend must be $Vimla$.
$2$. $Ved$'s girlfriend does not like $Sushma$ and $Vimla$. This leaves $Kusum$ or $Poonam$. Since $Kusum$ does not care for $Ved$,$Ved$'s girlfriend must be $Poonam$.
$3$. $Sushma$ does not like $Raj$. Therefore,$Raj$'s girlfriend cannot be $Sushma$. Since $Vimla$ and $Poonam$ are already paired with $Prem$ and $Ved$ respectively,$Raj$'s girlfriend must be $Kusum$.
$4$. By elimination,$Ashok$'s girlfriend is $Sushma$.
Thus,$Raj$'s girlfriend is $Kusum$.

(D) $Sushma$ and $Vimla$ are friends,and $Prem$'s girlfriend is friendly with $Sushma$. This implies that $Prem$'s girlfriend is $Vimla$.
$Ved$'s girlfriend does not like $Sushma$ and $Vimla$. Therefore,she is either $Kusum$ or $Poonam$. Since $Kusum$ does not care for $Ved$,$Ved$'s girlfriend must be $Poonam$.
$Sushma$ does not like $Raj$. Therefore,$Raj$'s girlfriend is $Kusum$.
By elimination,$Ashok$'s girlfriend is $Sushma$.
Thus,$Sushma$ is friendly with $Ashok$.

(B) Let the pairs be (Boy,Girl).
Sushma and Vimla are friends. Prem's girlfriend is friendly with Sushma,so Prem's girlfriend is Vimla.
Ved's girlfriend does not like Sushma and Vimla,so she must be either Kusum or Poonam. Since Kusum does not care for Ved,Ved's girlfriend is Poonam.
Sushma does not like Raj (Rfy),so Raj's girlfriend is Kusum.
Finally,Ashok's girlfriend is Sushma.
Therefore,Poonam's boyfriend is Ved.

(A) $1$. Sushma and Vimla are friends. Prem's girlfriend is friendly with Sushma,which implies Prem's girlfriend is Vimla.
$2$. Ved's girlfriend does not like Sushma and Vimla. This means she is either Kusum or Poonam.
$3$. Since Kusum does not care for Ved,Ved's girlfriend must be Poonam.
$4$. Sushma does not like Raj,so Raj's girlfriend is Kusum.
$5$. By elimination,Ashok's girlfriend is Sushma.
$6$. Therefore,Ved's girlfriend,Poonam,is the one who does not like Sushma and Vimla.

(C) Let us calculate the number of losses for each country:
$1$. Australia: Lost to India ($2$ times).
$2$. India: Lost to West Indies ($2$ times).
$3$. West Indies: Lost to Australia ($2$ times).
$4$. New Zealand: Lost to India ($2$ times) and West Indies ($2$ times),totaling $4$ losses.
Therefore,New Zealand has lost the most number of times.

(B) We can represent the given information in a table as follows:

Student	House	Height	Glasses
$A$	Nehru	Short	Yes
$B$	Nehru	Short	No
$C$	Gandhi	Short	Yes
$D$	Gandhi	Tall	Yes
$E$	Gandhi	Short	No
$F$	Gandhi	Tall	No

From the table,we identify the students who are short and not wearing glasses:
$1$. Student $B$ is short and does not wear glasses.
$2$. Student $E$ is short and does not wear glasses.
Therefore,the correct answer is $B$ and $E$. However,looking at the options provided,there seems to be a discrepancy. Re-evaluating the logic: $B$ and $E$ are the only ones who are short and not wearing glasses. Since $B$ and $E$ is not an option,we check the constraints again. If $F$ is tall,then $B$ and $E$ are the only short students without glasses. Given the options,$B$ and $F$ $(C)$ or $E$ and $F$ $(D)$ are provided. Based on standard logic,$B$ and $E$ is the correct pair.

(B) We can organize the information in a table to determine the characteristics of each student:

Student	House	Height	Glasses
$A$	Nehru	Short	Yes
$B$	Nehru	Short	No
$C$	Gandhi	Short	Yes
$D$	Gandhi	Tall	Yes
$E$	Gandhi	Short	No
$F$	Gandhi	Tall	No

From the table,we need to find a student who is in Gandhi House,is short,and does not wear glasses.
$1$. Students in Gandhi House are $C, D, E, F$.
$2$. Among these,the short students are $C$ and $E$.
$3$. Among $C$ and $E$,$C$ wears glasses,while $E$ does not.
Therefore,$E$ is the student who is short,belongs to Gandhi House,and does not wear glasses.

(D) To solve this,we can categorize the students based on the given information:
$1$. House: $A, B$ (Nehru House); $C, D, E, F$ (Gandhi House).
$2$. Height: $D, F$ (Tall); $A, B, C, E$ (Short).
$3$. Glasses: $A, C, D$ (Wearing glasses); $B, E, F$ (Not wearing glasses).
We are looking for a student who meets three criteria: Gandhi House,Tall,and No glasses.
- Gandhi House students: $C, D, E, F$.
- Among these,the tall students are: $D, F$.
- Among $D$ and $F$,the one who is not wearing glasses is $F$.
Thus,$F$ is the tall student of Gandhi House who is not wearing glasses.

(B) To find the tall girl from Bangalore,we analyze the given information:
$1$. Students: $A, B, C, D, E, F$.
$2$. Location: $A, B$ are from Delhi; $C, D, E, F$ are from Bangalore.
$3$. Height: $D, F$ are tall; $A, B, C, E$ are short.
$4$. Gender: $A, C, D$ are girls; $B, E, F$ are boys.
We need a student who is: $(i)$ From Bangalore,(ii) Tall,and (iii) $A$ girl.
- From Bangalore: $C, D, E, F$.
- Tall: $D, F$.
- Girls: $A, C, D$.
Comparing these sets:
- Intersection of (Bangalore) and (Tall) is ${D, F}$.
- Intersection of ${D, F}$ and (Girls) is ${D}$.
Therefore,$D$ is the tall girl from Bangalore.

(D) To solve this,we categorize each volume based on the given criteria:
$1$. Covers: Green $(B, C, E, F)$,Yellow $(A, D)$
$2$. Age: New $(A, B, D)$,Old $(C, E, F)$
$3$. Type: Law Reports $(A, B, C)$,Medical Extracts $(D, E, F)$
Let's analyze the properties for each volume:
- $A$: Yellow,New,Law Report
- $B$: Green,New,Law Report
- $C$: Green,Old,Law Report
- $D$: Yellow,New,Medical Extract
- $E$: Green,Old,Medical Extract
- $F$: Green,Old,Medical Extract
We are looking for volumes that are: $(1)$ Old,$(2)$ Medical Extracts,and $(3)$ Green covers.
From the analysis,$E$ and $F$ satisfy all three conditions.

(A) Let $C$ denote Compulsory and $O$ denote Optional.
$1$. $F$'s compulsory subject is Mathematics. $F$ also has Physics as a subject,so Physics is $F$'s optional subject.
$2$. $E$ and $F$ have Physics as a subject. Since $F$ has Physics as optional,$E$ must have Physics as a compulsory subject.
$3$. $C$ and $E$ have Mathematics as an optional subject.
$4$. $A$ and $D$ have History and English as their subjects. $D$'s optional is History,so $D$'s compulsory is English. $A$'s subjects are the reverse of $D$'s,so $A$'s compulsory is History and optional is English.
$5$. History is a compulsory subject for three teachers. We know $A$ has it as compulsory. Since $D$ is the only female teacher (English compulsory),and $B$ and $C$ are the remaining candidates,History must be the compulsory subject for $B$ and $C$.
$6$. Chemistry is an optional subject for only one teacher. Since all other slots are filled,$B$ must have Chemistry as an optional subject.
Thus,$C$'s compulsory subject is History.

(D) Let $C$ denote Compulsory and $O$ denote Optional.

Subject	$A$	$B$	$C$	$D$	$E$	$F$
History	$C$	$C$	$C$	$O$	-	-
Physics	-	-	-	-	$C$	$O$
Mathematics	-	-	$O$	-	$O$	$C$
English	$O$	-	-	$C$	-	-
Chemistry	-	$O$	-	-	-	-

$1$. $F$'s compulsory subject is Mathematics. Since $F$ also teaches Physics,Physics must be $F$'s optional subject.
$2$. $E$ has Physics as one of his subjects. Since Mathematics is $E$'s optional subject,Physics must be $E$'s compulsory subject.
$3$. $A$ and $D$ have History and English. $D$'s optional is History,so $D$'s compulsory is English.
$4$. $A$'s subjects are the reverse of $D$'s,so $A$'s compulsory is History and optional is English.
$5$. History is a compulsory subject for three people. We know $A$ has it as compulsory. Since $B$ and $C$ are the only ones left for the third compulsory slot,and Chemistry is the optional subject of only one person $(B)$,we deduce the table above.
$6$. The problem states the only female teacher has English as her compulsory subject. Looking at the table,$D$ has English as her compulsory subject.
Therefore,$D$ is the female member.

(D) Let $C$ denote Compulsory and $O$ denote Optional.

Subject	$A$	$B$	$C$	$D$	$E$	$F$
History	$C$	$C$	$C$	$O$	-	-
Physics	-	-	-	-	$C$	$O$
Mathematics	-	-	$O$	-	$O$	$C$
English	$O$	-	-	$C$	-	-
Chemistry	-	$O$	-	-	-	-

$1$. $F$ has Mathematics as compulsory and Physics as optional.
$2$. $E$ has Physics as compulsory and Mathematics as optional.
$3$. $A$ has History as compulsory and English as optional.
$4$. $D$ has English as compulsory and History as optional.
$5$. $B$ has History as compulsory and Chemistry as optional.
$6$. $C$ has History as compulsory and Mathematics as optional.
Comparing the subject distribution of $F$ (Compulsory: Mathematics,Optional: Physics) with others,no one matches this configuration. Therefore,the answer is 'None of these'.

(C) Let $C$ denote Compulsory and $O$ denote Optional.
$1$. $F$ has Physics and Mathematics. Since Mathematics is $F$'s compulsory subject,Physics is $F$'s optional subject.
$2$. $E$ has Physics as one subject. Since Mathematics is $E$'s optional subject,Physics must be $E$'s compulsory subject.
$3$. $A$ and $D$ have History and English. $D$'s optional is History,so $D$'s compulsory is English. $A$'s subjects are the reverse of $D$'s,so $A$'s compulsory is History and optional is English.
$4$. History is a compulsory subject for three people. We know $A$ has it as compulsory. Since $D$ is the only female teacher and has English as compulsory,and $B$ and $C$ are the remaining candidates for History as a compulsory subject,we assign History as compulsory to $A, B,$ and $C$.
$5$. Chemistry is an optional subject for only one person,which must be $B$.
Summary Table:

Teacher	Compulsory	Optional
$A$	History	English
$B$	History	Chemistry
$C$	History	Mathematics
$D$	English	History
$E$	Physics	Mathematics
$F$	Mathematics	Physics

Comparing the subjects,$E$ has Physics and Mathematics,which is the same combination as $F$.

(D) Let '$C$' denote a compulsory subject and '$O$' denote an optional subject.

Subject	$A$	$B$	$C$	$D$	$E$	$F$
History	$C$	$C$	$C$	$O$	-	-
Physics	-	-	-	-	$C$	$O$
Mathematics	-	-	$O$	-	$O$	$C$
English	$O$	-	-	$C$	-	-
Chemistry	-	$O$	-	-	-	-

$1$. $F$'s compulsory subject is Mathematics. $F$ has Physics as one of the subjects,so Physics is an optional subject for $F$.
$2$. $E$ has Physics as one of the subjects. Since $F$'s optional is Physics,$E$ must have Physics as a compulsory subject.
$3$. $A$ and $D$ have History and English. $D$'s optional is History,so $D$'s compulsory is English. $A$'s subjects are the reverse of $D$'s,so $A$'s compulsory is History and optional is English.
$4$. Chemistry is an optional subject for only one person,which must be $B$.
$5$. History is a compulsory subject for three teachers. Since $A$ has it as compulsory,and $D$ has it as optional,the other two must be $B$ and $C$.
$6$. Thus,$A, B,$ and $C$ have History as their compulsory subject.

(B) $(i)$ Analysis of choices: Jayant likes Chocolates (given). Tanmay likes Bengali sweets (given). Namita does not like Dry fruits or Ice cream. Since Chocolates and Bengali sweets are taken,Namita must like Pastries. Asha does not like Ice cream. Since Chocolates,Bengali sweets,and Pastries are taken,Asha must like Dry fruits. Finally,Kamal likes Ice cream.
$(ii)$ Analysis of birth months: The one who likes Pastries (Namita) is born in the middle month,i.e.,March. Tanmay is born in the month immediately after Namita,i.e.,April. Jayant's birthday is in February.

Member	Choice
Jayant	Chocolates
Kamal	Ice cream
Namita	Pastries
Asha	Dry fruits
Tanmay	Bengali sweets

Therefore,the choice of Asha is Dry fruits.

(D) $(i)$ Analysis of items: Jayant likes Chocolates (given). Tanmay likes Bengali sweets. Namita does not like Dry fruits or Ice cream. Since Chocolates and Bengali sweets are taken,Namita must like Pastries. Asha does not like Ice cream,so she likes Dry fruits. Finally,Kamal likes Ice cream.
$(ii)$ Analysis of months: The one who likes Pastries (Namita) is born in the middle month,which is March. Tanmay is born in the month immediately after Namita,i.e.,April. Jayant's birthday is in February.

Name	Item	Month
Jayant	Chocolates	February
Kamal	Ice cream	January/May
Namita	Pastries	March
Asha	Dry fruits	January/May
Tanmay	Bengali sweets	April

The correct combination for Jayant is February $-$ Chocolates. Since this is not among the options,the correct choice is $D$.

(A) $(i)$ Analysis of choices: Jayant likes Chocolates (given). Tanmay likes Bengali sweets (given). Namita does not like Dry fruits or Ice cream. Since Chocolates and Bengali sweets are taken,Namita must like Pastries.
$(ii)$ Asha does not like Ice cream. Since Chocolates,Bengali sweets,and Pastries are taken,Asha must like Dry fruits.
$(iii)$ Consequently,Kamal must like Ice cream.
$(iv)$ Birth month analysis: The one who likes Pastries (Namita) is born in the middle month (March). Tanmay is born in the month immediately after Namita (April). Jayant's birthday is in February.

Name	Choice
Jayant	Chocolates
Kamal	Ice cream
Namita	Pastries
Asha	Dry fruits
Tanmay	Bengali sweets

Therefore,the choice of Kamal is Ice cream.

(C) $(i)$ Choice: Jayant likes Chocolates; Tanmay likes Bengali sweets. Namita does not like Dry fruits or Ice cream. So,Namita likes Pastries. Asha does not like Ice cream. So,she is fond of Dry fruits. Finally,Kamal likes Ice cream.
$(ii)$ Date of Birth: The one who likes Pastries,i.e.,Namita,is born in the middle of the months given,i.e.,in March. Tanmay is born in the month after Namita,i.e.,in April. Jayant's birthday is in February.

$Name$	$Choice$	$Date \text{ of } birth$
Jayant	Chocolates	February
Kamal	Ice cream	January or May
Namita	Pastries	March
Asha	Dry fruits	January or May
Tanmay	Bengali sweets	April

Kamal was born in January or May.

(A) $(i)$ $T$ stays as a $PG$; $S$ stays in a hostel. $U$ stays in a hostel and $Q$ stays at home. Since $R$ does not stay as a $PG$,and the $PG$ spots are taken by $T$ and one other person,$P$ must be the other $PG$. Thus,$R$ stays at home.
$(ii)$ $S$ studies Physics,$R$ studies Philosophy,and $T$ studies Mathematics. Since $P$ stays as a $PG$,and students studying Statistics and History do not stay as $PG$,$P$ must study English.

Student	Place of stay and Subject
$P$	$PG$,English
$Q$	Home,Statistics/History
$R$	Home,Philosophy
$S$	Hostel,Physics
$T$	$PG$,Mathematics
$U$	Hostel,Statistics/History

Therefore,$P$ studies English.

(A) $(i)$ $T$ stays as a $PG$; $S$ stays in a hostel. $U$ stays in a hostel and $Q$ stays at home. Since $R$ does not stay as a $PG$,$P$ must stay as a $PG$. Consequently,$R$ stays at home.
$(ii)$ $S$ studies Physics; $R$ studies Philosophy and $T$ studies Mathematics. Since $P$ stays as a $PG$,$P$ cannot study Statistics or History (as per rule $(iv)$). Thus,$P$ studies English.

Student	Place of stay	Subject
$P$	$PG$	English
$Q$	Home	Statistics/History
$R$	Home	Philosophy
$S$	Hostel	Physics
$T$	$PG$	Mathematics
$U$	Hostel	History/Statistics

Clearly,the incorrect combination is English $-$ Hostel.

(B) $(i)$ $T$ stays as a $PG$; $S$ stays in a hostel. $U$ stays in a hostel and $Q$ stays at home. Now,$R$ does not stay as a $PG$. So,$P$ must stay as a $PG$. Clearly,$R$ stays at home.
$(ii)$ $S$ studies Physics; $R$ studies Philosophy and $T$ studies Mathematics. Now,$P$ who stays as a $PG$ does not study Statistics or History. So,$P$ studies English.

Student	Place of stay	Subject
$P$	$PG$	English
$Q$	Home	Statistics or History
$R$	Home	Philosophy
$S$	Hostel	Physics
$T$	$PG$	Mathematics
$U$	Hostel	Statistics or History

From the table,$S$ stays in a hostel and $R$ stays at home. Thus,the pair $(S, R)$ satisfies the condition.

(C) $(i)$ From the given information: $T$ stays as $PG$; $S$ and $U$ stay in a hostel; $Q$ stays at home. Since $R$ does not stay as a $PG$,$R$ must stay at home. Consequently,$P$ must stay as a $PG$.
$(ii)$ Subjects assigned: $S$ studies Physics,$R$ studies Philosophy,and $T$ studies Mathematics. The students studying Statistics and History do not stay as $PG$. Since $P$ stays as a $PG$,$P$ cannot study Statistics or History. Thus,$P$ studies English.
$(iii)$ The remaining subjects are Statistics and History,which must be studied by $Q$ and $U$. Since $Q$ stays at home and $U$ stays in a hostel,and there are no further constraints to distinguish between them,$Q$ studies either History or Statistics.

Student	Place of stay and Subject
$P$	$PG$,English
$Q$	Home,History or Statistics
$R$	Home,Philosophy
$S$	Hostel,Physics
$T$	$PG$,Mathematics
$U$	Hostel,History or Statistics

(B) $(i)$ $T$ stays as a $PG$; $S$ stays in a hostel. $U$ stays in a hostel and $Q$ stays at home. Now,$R$ does not stay as a $PG$. So,$P$ must stay as a $PG$. Clearly,$R$ stays at home.
$(ii)$ $S$ studies Physics; $R$ studies Philosophy and $T$ studies Mathematics. Now,$P$ who stays as a $PG$ does not study Statistics or History. So,$P$ studies English.

Student	Place of stay
$P$	$PG$
$Q$	Home
$R$	Home
$S$	Hostel
$T$	$PG$
$U$	Hostel

Thus,$Q$ and $R$ stay at home.

(C) $(I)$ Kunal stays close to the school. So,the other three $-$ Rohit,Ashish,and John stay far from the school.
$(II)$ Rohit,Kunal,and Ashish do not study in class $VI$. So,John studies in class $VI$. Rohit and Kunal are not good at all subjects,and John is in class $VI$. Therefore,Ashish is good at all subjects and studies in class $V$. Clearly,Rohit and Kunal study in class $IV$.
$(III)$ Rohit is good at Mathematics. Kunal is weak in Mathematics. Ashish is good at all the subjects. Clearly,John is weak in all the subjects.

Name	Stay	Class	Good at	Weak in
Rohit	Far	$IV$	Mathematics	Hindi,Science,Social Science
Kunal	Close	$IV$	Hindi,Science,Social Science	Mathematics
Ashish	Far	$V$	All subjects	-
John	Far	$VI$	-	All subjects

Ashish is good at all the subjects.

(D) $(I)$ Kunal stays close to the school. So,the other three $-$ Rohit,Ashish,and John stay far from the school.
$(II)$ Rohit,Kunal,and Ashish do not study in class $VI$. So,John studies in class $VI$. Since Rohit and Kunal are not good at all subjects and John is in class $VI$,Ashish must be the one who is good at all subjects and studies in class $V$. Consequently,Rohit and Kunal study in class $IV$.
$(III)$ Rohit is good at Mathematics. Kunal is weak in Mathematics. Ashish is good at all the subjects. Clearly,John is weak in all the subjects.

Name	Stay	Class	Good at	Weak in
Rohit	Far	$IV$	Mathematics	Hindi,Science,Social Science
Kunal	Close	$IV$	Hindi,Science,Social Science	Mathematics
Ashish	Far	$V$	All subjects	None
John	Far	$VI$	None	All subjects

Therefore,John is the boy who is weak in all the subjects.

(B) $(I)$ Kunal stays close to the school. So,the other three (Rohit,Ashish,and John) stay far from the school.
$(II)$ Rohit,Kunal,and Ashish do not study in class $VI$. Therefore,John studies in class $VI$. Since the one who is good at all subjects studies in class $V$,and Rohit,Kunal,and John are not that person,Ashish must be good at all subjects and studies in class $V$. Rohit and Kunal study in class $IV$.
$(III)$ Rohit is good at Mathematics only. Kunal is weak in Mathematics only. Ashish is good at all subjects. John is weak in all subjects.

Name	Stay	Class	Good at	Weak in
Rohit	Far	$IV$	Mathematics	Hindi,Science,Social Science
Kunal	Close	$IV$	Hindi,Science,Social Science	Mathematics
Ashish	Far	$V$	All subjects	None
John	Far	$VI$	None	All subjects

Thus,Kunal and Ashish are good at Hindi.

(A) $(I)$ Kunal stays close to the school. So,the other three $-$ Rohit,Ashish,and John stay far from the school.
$(II)$ Rohit,Kunal,and Ashish do not study in class $VI$. So,John studies in class $VI$. Since the one who is good at all subjects studies in class $V$,and Rohit,Kunal,and John are accounted for (Rohit and Kunal in class $IV$,John in class $VI$),Ashish must be the one who is good at all subjects and studies in class $V$.
$(III)$ Rohit is good at Mathematics. Kunal is weak in Mathematics. Ashish is good at all subjects (including Mathematics). John is weak in all subjects. Therefore,Rohit and Ashish are good at Mathematics.

Student	Stay	Class	Good at	Weak in
Rohit	Far	$IV$	Mathematics	Others
Kunal	Close	$IV$	Others	Mathematics
Ashish	Far	$V$	All subjects	None
John	Far	$VI$	None	All subjects

(D) $(I)$ Kunal stays close to the school. So,the other three—Rohit,Ashish,and John—stay far from the school.
$(II)$ Rohit,Kunal,and Ashish do not study in class $VI$. Therefore,John studies in class $VI$. Rohit and Kunal are not good at all subjects,and John is in class $VI$. Thus,Ashish is good at all subjects and studies in class $V$. Consequently,Rohit and Kunal study in class $IV$.
$(III)$ Rohit is good at Mathematics. Kunal is weak in Mathematics. Ashish is good at all the subjects. Clearly,John is weak in all the subjects.

Name	Stay	Class	Good at	Weak in
Rohit	Far	$IV$	Mathematics	Hindi,Science,Social Science
Kunal	Close	$IV$	Hindi,Science,Social Science	Mathematics
Ashish	Far	$V$	All subjects	None
John	Far	$VI$	None	All subjects

Other than Rohit and Ashish (the boy good at all subjects),John stays far from the school.