Electronics and Communication Engineering (EC) 2016 GATE Paper (Set B) with solution | GATE, ISRO & IES/ESE Previous Year Solved Papers - Mechanical Engineering PDF Download

 Page 1


		: 	2 	: 	 		Gate 2016 – ECE 	– 	Set	2 															
Q.1 – Q.5 Carry one mark each 
01. Based on the given statements, select the appropriate option with respect to grammar a
 statements. 
(i) The height of Mr. X is 6 feet. (ii) The height of Mr. Y is 5 feet 
(A) Mr. X is longer than Mr. Y 
(B) Mr. X  is more elongated than Mr. Y 
(C) Mr. X is taller than Mr. Y 
(D) Mr. X is lengthier than Mr. Y   
01. Ans: (C)
Sol:  In degrees of comparison Mr. X is taller than Mr. Y is apt. 
Positive degree – tall
Comparative degree  – taller
Superlative degree – tallest
02. The students _____ the teachers on teachers   day for twenty years of dedicated teaching.
(A) facilitated  (B) felicitated    (C) fantasized (D) facilitated 
02. Ans: (B)
Sol: Felicitate means honour. 
03. After India’s cricket world cup victory in 1985, Shrotria who was playing both tennis and cricket
till then, decided to concentrate only on cricket. And the  rest is history.
What does the underlined phrase mean  in this context?
(A) history will rest in peace  (B) rest is recorded in history books
(C) rest is well known   (D) rest in archaic
03. Ans: (C)
Sol: ‘rest is history’ is an idiomatic expression which means ‘rest is well known 
04. Given (9 inches)
1/2
 = (0.25 yards)
1/2
, which one of the following statements is TRUE?
(A) 3 inches = 0.5 yards   (B) 9 inches = 1.5 yards
(C) 9 inches = 0.25 yards  (D) 81 inches = 0.0625 yards
04. Ans: (C)
Sol: Given (9 inches)
1/2
 = (0.25 yards)
1/2
 
              9 inches = 0.25 yards 
05. S, M, E and F  are working in shifts in a term to finish a project. M works with twice the efficiency
of other but for half as many days as E worked. S and M have 6 hour shifts in a day, whereas E
and F have 12 hours shifts. What is the ratio of contribution of M to contribution of E in the
project?
(A) 1:1        (B) 1:2   (C) 1:4      (D) 2:1
05. Ans: (B)
Sol: M efficiency = 2 [ efficiency of S,E, and F] 
Contribution of M in the project = x days × 6 hrs ×2 
Contribution of E in the project = 2x days × 12 hrs ×1 
Contribution of M : Contribution of E 
x × 6 × 2 : 2x × 12 × 1 
 1 : 2 
Page 2


		: 	2 	: 	 		Gate 2016 – ECE 	– 	Set	2 															
Q.1 – Q.5 Carry one mark each 
01. Based on the given statements, select the appropriate option with respect to grammar a
 statements. 
(i) The height of Mr. X is 6 feet. (ii) The height of Mr. Y is 5 feet 
(A) Mr. X is longer than Mr. Y 
(B) Mr. X  is more elongated than Mr. Y 
(C) Mr. X is taller than Mr. Y 
(D) Mr. X is lengthier than Mr. Y   
01. Ans: (C)
Sol:  In degrees of comparison Mr. X is taller than Mr. Y is apt. 
Positive degree – tall
Comparative degree  – taller
Superlative degree – tallest
02. The students _____ the teachers on teachers   day for twenty years of dedicated teaching.
(A) facilitated  (B) felicitated    (C) fantasized (D) facilitated 
02. Ans: (B)
Sol: Felicitate means honour. 
03. After India’s cricket world cup victory in 1985, Shrotria who was playing both tennis and cricket
till then, decided to concentrate only on cricket. And the  rest is history.
What does the underlined phrase mean  in this context?
(A) history will rest in peace  (B) rest is recorded in history books
(C) rest is well known   (D) rest in archaic
03. Ans: (C)
Sol: ‘rest is history’ is an idiomatic expression which means ‘rest is well known 
04. Given (9 inches)
1/2
 = (0.25 yards)
1/2
, which one of the following statements is TRUE?
(A) 3 inches = 0.5 yards   (B) 9 inches = 1.5 yards
(C) 9 inches = 0.25 yards  (D) 81 inches = 0.0625 yards
04. Ans: (C)
Sol: Given (9 inches)
1/2
 = (0.25 yards)
1/2
 
              9 inches = 0.25 yards 
05. S, M, E and F  are working in shifts in a term to finish a project. M works with twice the efficiency
of other but for half as many days as E worked. S and M have 6 hour shifts in a day, whereas E
and F have 12 hours shifts. What is the ratio of contribution of M to contribution of E in the
project?
(A) 1:1        (B) 1:2   (C) 1:4      (D) 2:1
05. Ans: (B)
Sol: M efficiency = 2 [ efficiency of S,E, and F] 
Contribution of M in the project = x days × 6 hrs ×2 
Contribution of E in the project = 2x days × 12 hrs ×1 
Contribution of M : Contribution of E 
x × 6 × 2 : 2x × 12 × 1 
 1 : 2 
		: 	3 	: 	 	Questions & Solutions 	
Q.6 – Q.10 Carry two marks each 
06. The Venn diagram shows the preference of the student population for leisure activities.
From the data given, the number of students who like to read books or play sports is __________. 
(A) 44 (B) 51 
(C) 79 (D) 108 
06. Ans: (D)
Sol: Read books = n(R) = 12 + 44 + 7 + 13  
     = 76 
Play sports = n(s) = 44 + 7 + 17 +15  
  = 83 
n (R ?? S) = 44 + 7  
   = 51 
n (R ? S) = n (R) + n (S) – n (R ? S) 
  = 76 + 83 – 51 
  = 108 
07. Social science disciplines were in existence in an amorphous form until the colonial period when
they were institutionalized. In varying degrees, they were intended to further the colonial interest.
In the time of globalization and the economic rise of postcolonical countries like India,
conventional ways of knowledge production have become obsolete.
Which of the following can be logically inferred from the above statements?
(i) Social science disciplines have become obsolete.
(ii) Social science disciplines had a pre-colonial origin
(iii) Social science disciplines always promote colonialism
(iv) Social science must maintain disciplinary boundaries
(A) (ii) only     (B) (i) and (iii) only
(C) (ii) and (iv) only    (D) (iii) and (iv) only
07. Ans: (A)
Sol: Until the colonial period means pre-colonial origin. Other options can’t be inferred. 
Read  
books 
Watch Tv
13
12
7
17
44
15
19
Play sports
Page 3


		: 	2 	: 	 		Gate 2016 – ECE 	– 	Set	2 															
Q.1 – Q.5 Carry one mark each 
01. Based on the given statements, select the appropriate option with respect to grammar a
 statements. 
(i) The height of Mr. X is 6 feet. (ii) The height of Mr. Y is 5 feet 
(A) Mr. X is longer than Mr. Y 
(B) Mr. X  is more elongated than Mr. Y 
(C) Mr. X is taller than Mr. Y 
(D) Mr. X is lengthier than Mr. Y   
01. Ans: (C)
Sol:  In degrees of comparison Mr. X is taller than Mr. Y is apt. 
Positive degree – tall
Comparative degree  – taller
Superlative degree – tallest
02. The students _____ the teachers on teachers   day for twenty years of dedicated teaching.
(A) facilitated  (B) felicitated    (C) fantasized (D) facilitated 
02. Ans: (B)
Sol: Felicitate means honour. 
03. After India’s cricket world cup victory in 1985, Shrotria who was playing both tennis and cricket
till then, decided to concentrate only on cricket. And the  rest is history.
What does the underlined phrase mean  in this context?
(A) history will rest in peace  (B) rest is recorded in history books
(C) rest is well known   (D) rest in archaic
03. Ans: (C)
Sol: ‘rest is history’ is an idiomatic expression which means ‘rest is well known 
04. Given (9 inches)
1/2
 = (0.25 yards)
1/2
, which one of the following statements is TRUE?
(A) 3 inches = 0.5 yards   (B) 9 inches = 1.5 yards
(C) 9 inches = 0.25 yards  (D) 81 inches = 0.0625 yards
04. Ans: (C)
Sol: Given (9 inches)
1/2
 = (0.25 yards)
1/2
 
              9 inches = 0.25 yards 
05. S, M, E and F  are working in shifts in a term to finish a project. M works with twice the efficiency
of other but for half as many days as E worked. S and M have 6 hour shifts in a day, whereas E
and F have 12 hours shifts. What is the ratio of contribution of M to contribution of E in the
project?
(A) 1:1        (B) 1:2   (C) 1:4      (D) 2:1
05. Ans: (B)
Sol: M efficiency = 2 [ efficiency of S,E, and F] 
Contribution of M in the project = x days × 6 hrs ×2 
Contribution of E in the project = 2x days × 12 hrs ×1 
Contribution of M : Contribution of E 
x × 6 × 2 : 2x × 12 × 1 
 1 : 2 
		: 	3 	: 	 	Questions & Solutions 	
Q.6 – Q.10 Carry two marks each 
06. The Venn diagram shows the preference of the student population for leisure activities.
From the data given, the number of students who like to read books or play sports is __________. 
(A) 44 (B) 51 
(C) 79 (D) 108 
06. Ans: (D)
Sol: Read books = n(R) = 12 + 44 + 7 + 13  
     = 76 
Play sports = n(s) = 44 + 7 + 17 +15  
  = 83 
n (R ?? S) = 44 + 7  
   = 51 
n (R ? S) = n (R) + n (S) – n (R ? S) 
  = 76 + 83 – 51 
  = 108 
07. Social science disciplines were in existence in an amorphous form until the colonial period when
they were institutionalized. In varying degrees, they were intended to further the colonial interest.
In the time of globalization and the economic rise of postcolonical countries like India,
conventional ways of knowledge production have become obsolete.
Which of the following can be logically inferred from the above statements?
(i) Social science disciplines have become obsolete.
(ii) Social science disciplines had a pre-colonial origin
(iii) Social science disciplines always promote colonialism
(iv) Social science must maintain disciplinary boundaries
(A) (ii) only     (B) (i) and (iii) only
(C) (ii) and (iv) only    (D) (iii) and (iv) only
07. Ans: (A)
Sol: Until the colonial period means pre-colonial origin. Other options can’t be inferred. 
Read  
books 
Watch Tv
13
12
7
17
44
15
19
Play sports
		: 	5 	: 	 	Questions & Solutions 	
08. Two and a quarter hours back, when seen in a mirror, the reflection of a wall clock without
number markings seemed to show 1:30. What is the actual current time shown by the clock?
(A) 8:15   (B) 11:15   (C) 12:15   (D) 12:45
08. Ans: (D)
Sol: Time back = 
4
1
2 = 2 hrs 15 min
Clock time (C.T) + Mirror Time (M.T) = 12 
    ? 
   1.30 
? The actual time shown by the clock = 10.30 + 2.15 = 12.45 
09. M and N start from the same location. M travels 10 km East and then 10 km North-East. N travels
5 km South and then 4 km South-East. What is  the shortest distance (in km) between M and N at
the end of their travel?
(A) 18.60   (B) 22.50 (C) 20.61   (D) 25.00 
09. Ans: (C)
Sol: From the given data, the following diagram is possible 
4
DE
45 cos
o
?
DE = cos45
o
× 4  
    = 2.828 km 
4
EN
45 sin
o
?
EN = sin 45
o
 × 4 = 2.828 km 
         60 
? C.T = 12.00 
   1.30 
   10.30 
10 km 
5 km 
5 km 
E 
N 
4 km 
B
M
10 km
45 ? D 
A 
C 
Page 4


		: 	2 	: 	 		Gate 2016 – ECE 	– 	Set	2 															
Q.1 – Q.5 Carry one mark each 
01. Based on the given statements, select the appropriate option with respect to grammar a
 statements. 
(i) The height of Mr. X is 6 feet. (ii) The height of Mr. Y is 5 feet 
(A) Mr. X is longer than Mr. Y 
(B) Mr. X  is more elongated than Mr. Y 
(C) Mr. X is taller than Mr. Y 
(D) Mr. X is lengthier than Mr. Y   
01. Ans: (C)
Sol:  In degrees of comparison Mr. X is taller than Mr. Y is apt. 
Positive degree – tall
Comparative degree  – taller
Superlative degree – tallest
02. The students _____ the teachers on teachers   day for twenty years of dedicated teaching.
(A) facilitated  (B) felicitated    (C) fantasized (D) facilitated 
02. Ans: (B)
Sol: Felicitate means honour. 
03. After India’s cricket world cup victory in 1985, Shrotria who was playing both tennis and cricket
till then, decided to concentrate only on cricket. And the  rest is history.
What does the underlined phrase mean  in this context?
(A) history will rest in peace  (B) rest is recorded in history books
(C) rest is well known   (D) rest in archaic
03. Ans: (C)
Sol: ‘rest is history’ is an idiomatic expression which means ‘rest is well known 
04. Given (9 inches)
1/2
 = (0.25 yards)
1/2
, which one of the following statements is TRUE?
(A) 3 inches = 0.5 yards   (B) 9 inches = 1.5 yards
(C) 9 inches = 0.25 yards  (D) 81 inches = 0.0625 yards
04. Ans: (C)
Sol: Given (9 inches)
1/2
 = (0.25 yards)
1/2
 
              9 inches = 0.25 yards 
05. S, M, E and F  are working in shifts in a term to finish a project. M works with twice the efficiency
of other but for half as many days as E worked. S and M have 6 hour shifts in a day, whereas E
and F have 12 hours shifts. What is the ratio of contribution of M to contribution of E in the
project?
(A) 1:1        (B) 1:2   (C) 1:4      (D) 2:1
05. Ans: (B)
Sol: M efficiency = 2 [ efficiency of S,E, and F] 
Contribution of M in the project = x days × 6 hrs ×2 
Contribution of E in the project = 2x days × 12 hrs ×1 
Contribution of M : Contribution of E 
x × 6 × 2 : 2x × 12 × 1 
 1 : 2 
		: 	3 	: 	 	Questions & Solutions 	
Q.6 – Q.10 Carry two marks each 
06. The Venn diagram shows the preference of the student population for leisure activities.
From the data given, the number of students who like to read books or play sports is __________. 
(A) 44 (B) 51 
(C) 79 (D) 108 
06. Ans: (D)
Sol: Read books = n(R) = 12 + 44 + 7 + 13  
     = 76 
Play sports = n(s) = 44 + 7 + 17 +15  
  = 83 
n (R ?? S) = 44 + 7  
   = 51 
n (R ? S) = n (R) + n (S) – n (R ? S) 
  = 76 + 83 – 51 
  = 108 
07. Social science disciplines were in existence in an amorphous form until the colonial period when
they were institutionalized. In varying degrees, they were intended to further the colonial interest.
In the time of globalization and the economic rise of postcolonical countries like India,
conventional ways of knowledge production have become obsolete.
Which of the following can be logically inferred from the above statements?
(i) Social science disciplines have become obsolete.
(ii) Social science disciplines had a pre-colonial origin
(iii) Social science disciplines always promote colonialism
(iv) Social science must maintain disciplinary boundaries
(A) (ii) only     (B) (i) and (iii) only
(C) (ii) and (iv) only    (D) (iii) and (iv) only
07. Ans: (A)
Sol: Until the colonial period means pre-colonial origin. Other options can’t be inferred. 
Read  
books 
Watch Tv
13
12
7
17
44
15
19
Play sports
		: 	5 	: 	 	Questions & Solutions 	
08. Two and a quarter hours back, when seen in a mirror, the reflection of a wall clock without
number markings seemed to show 1:30. What is the actual current time shown by the clock?
(A) 8:15   (B) 11:15   (C) 12:15   (D) 12:45
08. Ans: (D)
Sol: Time back = 
4
1
2 = 2 hrs 15 min
Clock time (C.T) + Mirror Time (M.T) = 12 
    ? 
   1.30 
? The actual time shown by the clock = 10.30 + 2.15 = 12.45 
09. M and N start from the same location. M travels 10 km East and then 10 km North-East. N travels
5 km South and then 4 km South-East. What is  the shortest distance (in km) between M and N at
the end of their travel?
(A) 18.60   (B) 22.50 (C) 20.61   (D) 25.00 
09. Ans: (C)
Sol: From the given data, the following diagram is possible 
4
DE
45 cos
o
?
DE = cos45
o
× 4  
    = 2.828 km 
4
EN
45 sin
o
?
EN = sin 45
o
 × 4 = 2.828 km 
         60 
? C.T = 12.00 
   1.30 
   10.30 
10 km 
5 km 
5 km 
E 
N 
4 km 
B
M
10 km
45 ? D 
A 
C 
		: 	6 	: 	 		Gate 2016 – ECE 	– 	Set	2 															
 sin 45
o
 = 
4
EN
EN = sin 45
o
 × 4 = 2.828 km 
CN = NE + CE = 2.828 + 5   
    = 7.828 km 
CB = AB – AC = 10 – 2.828  
    = 7.171 km 
 (NB)
2
 = (NC)
2
 + (BC)
2
 
       = (7.828)
2
 + (7.171)
2
 
? NB = ?? ? ?
2 2
171 . 7 828 . 7 ? = 10.616 km 
? NM = NB + BN = 10.616 + 10  = 20.61 km 
10. A wire of length 340 mm is to be cut into two parts. One of the parts is to be made into a square
and the other into a rectangle where sides are in the ratio of 1:2. What is the length of the side of
the square (in mm) such that the combined area of the square and the rectangle is a MINIMUM?
(A) 30 (B) 40          (C) 120 (D) 180 
10. Ans: (B)
Sol:  Length of the wire = 340 m 
Perimeter of rectangle = 
?
?
?
?
?
?
?
3
x 2
3
x
2 
= 2x 
Perimeter of square = 340 – 2x 
Side of square     
4
x 2 340 ?
?
Total area = Area of square + Area of rectangle 
  
3
x 2
3
x
4
x 2 340
2
? ?
?
?
?
?
?
? ?
? 
9
x 2
4
x 2 340
2
2
?
?
?
?
?
?
? ?
?
Combined area of square + rectangle = minimum 
 f ?(x) = 0 
??
2
2
x
9
2
4
x 2 340
x f ?
?
?
?
?
?
? ?
?
?? 0
4
x 2 340
x
9
4
x f
2
?
?
? ? ? 
x 
x 
3
x 2
3
x
Square Rectangle
Page 5


		: 	2 	: 	 		Gate 2016 – ECE 	– 	Set	2 															
Q.1 – Q.5 Carry one mark each 
01. Based on the given statements, select the appropriate option with respect to grammar a
 statements. 
(i) The height of Mr. X is 6 feet. (ii) The height of Mr. Y is 5 feet 
(A) Mr. X is longer than Mr. Y 
(B) Mr. X  is more elongated than Mr. Y 
(C) Mr. X is taller than Mr. Y 
(D) Mr. X is lengthier than Mr. Y   
01. Ans: (C)
Sol:  In degrees of comparison Mr. X is taller than Mr. Y is apt. 
Positive degree – tall
Comparative degree  – taller
Superlative degree – tallest
02. The students _____ the teachers on teachers   day for twenty years of dedicated teaching.
(A) facilitated  (B) felicitated    (C) fantasized (D) facilitated 
02. Ans: (B)
Sol: Felicitate means honour. 
03. After India’s cricket world cup victory in 1985, Shrotria who was playing both tennis and cricket
till then, decided to concentrate only on cricket. And the  rest is history.
What does the underlined phrase mean  in this context?
(A) history will rest in peace  (B) rest is recorded in history books
(C) rest is well known   (D) rest in archaic
03. Ans: (C)
Sol: ‘rest is history’ is an idiomatic expression which means ‘rest is well known 
04. Given (9 inches)
1/2
 = (0.25 yards)
1/2
, which one of the following statements is TRUE?
(A) 3 inches = 0.5 yards   (B) 9 inches = 1.5 yards
(C) 9 inches = 0.25 yards  (D) 81 inches = 0.0625 yards
04. Ans: (C)
Sol: Given (9 inches)
1/2
 = (0.25 yards)
1/2
 
              9 inches = 0.25 yards 
05. S, M, E and F  are working in shifts in a term to finish a project. M works with twice the efficiency
of other but for half as many days as E worked. S and M have 6 hour shifts in a day, whereas E
and F have 12 hours shifts. What is the ratio of contribution of M to contribution of E in the
project?
(A) 1:1        (B) 1:2   (C) 1:4      (D) 2:1
05. Ans: (B)
Sol: M efficiency = 2 [ efficiency of S,E, and F] 
Contribution of M in the project = x days × 6 hrs ×2 
Contribution of E in the project = 2x days × 12 hrs ×1 
Contribution of M : Contribution of E 
x × 6 × 2 : 2x × 12 × 1 
 1 : 2 
		: 	3 	: 	 	Questions & Solutions 	
Q.6 – Q.10 Carry two marks each 
06. The Venn diagram shows the preference of the student population for leisure activities.
From the data given, the number of students who like to read books or play sports is __________. 
(A) 44 (B) 51 
(C) 79 (D) 108 
06. Ans: (D)
Sol: Read books = n(R) = 12 + 44 + 7 + 13  
     = 76 
Play sports = n(s) = 44 + 7 + 17 +15  
  = 83 
n (R ?? S) = 44 + 7  
   = 51 
n (R ? S) = n (R) + n (S) – n (R ? S) 
  = 76 + 83 – 51 
  = 108 
07. Social science disciplines were in existence in an amorphous form until the colonial period when
they were institutionalized. In varying degrees, they were intended to further the colonial interest.
In the time of globalization and the economic rise of postcolonical countries like India,
conventional ways of knowledge production have become obsolete.
Which of the following can be logically inferred from the above statements?
(i) Social science disciplines have become obsolete.
(ii) Social science disciplines had a pre-colonial origin
(iii) Social science disciplines always promote colonialism
(iv) Social science must maintain disciplinary boundaries
(A) (ii) only     (B) (i) and (iii) only
(C) (ii) and (iv) only    (D) (iii) and (iv) only
07. Ans: (A)
Sol: Until the colonial period means pre-colonial origin. Other options can’t be inferred. 
Read  
books 
Watch Tv
13
12
7
17
44
15
19
Play sports
		: 	5 	: 	 	Questions & Solutions 	
08. Two and a quarter hours back, when seen in a mirror, the reflection of a wall clock without
number markings seemed to show 1:30. What is the actual current time shown by the clock?
(A) 8:15   (B) 11:15   (C) 12:15   (D) 12:45
08. Ans: (D)
Sol: Time back = 
4
1
2 = 2 hrs 15 min
Clock time (C.T) + Mirror Time (M.T) = 12 
    ? 
   1.30 
? The actual time shown by the clock = 10.30 + 2.15 = 12.45 
09. M and N start from the same location. M travels 10 km East and then 10 km North-East. N travels
5 km South and then 4 km South-East. What is  the shortest distance (in km) between M and N at
the end of their travel?
(A) 18.60   (B) 22.50 (C) 20.61   (D) 25.00 
09. Ans: (C)
Sol: From the given data, the following diagram is possible 
4
DE
45 cos
o
?
DE = cos45
o
× 4  
    = 2.828 km 
4
EN
45 sin
o
?
EN = sin 45
o
 × 4 = 2.828 km 
         60 
? C.T = 12.00 
   1.30 
   10.30 
10 km 
5 km 
5 km 
E 
N 
4 km 
B
M
10 km
45 ? D 
A 
C 
		: 	6 	: 	 		Gate 2016 – ECE 	– 	Set	2 															
 sin 45
o
 = 
4
EN
EN = sin 45
o
 × 4 = 2.828 km 
CN = NE + CE = 2.828 + 5   
    = 7.828 km 
CB = AB – AC = 10 – 2.828  
    = 7.171 km 
 (NB)
2
 = (NC)
2
 + (BC)
2
 
       = (7.828)
2
 + (7.171)
2
 
? NB = ?? ? ?
2 2
171 . 7 828 . 7 ? = 10.616 km 
? NM = NB + BN = 10.616 + 10  = 20.61 km 
10. A wire of length 340 mm is to be cut into two parts. One of the parts is to be made into a square
and the other into a rectangle where sides are in the ratio of 1:2. What is the length of the side of
the square (in mm) such that the combined area of the square and the rectangle is a MINIMUM?
(A) 30 (B) 40          (C) 120 (D) 180 
10. Ans: (B)
Sol:  Length of the wire = 340 m 
Perimeter of rectangle = 
?
?
?
?
?
?
?
3
x 2
3
x
2 
= 2x 
Perimeter of square = 340 – 2x 
Side of square     
4
x 2 340 ?
?
Total area = Area of square + Area of rectangle 
  
3
x 2
3
x
4
x 2 340
2
? ?
?
?
?
?
?
? ?
? 
9
x 2
4
x 2 340
2
2
?
?
?
?
?
?
? ?
?
Combined area of square + rectangle = minimum 
 f ?(x) = 0 
??
2
2
x
9
2
4
x 2 340
x f ?
?
?
?
?
?
? ?
?
?? 0
4
x 2 340
x
9
4
x f
2
?
?
? ? ? 
x 
x 
3
x 2
3
x
Square Rectangle
		: 	7 	: 	 	Questions & Solutions 	
?? x 2 340
4
1
x
9
4
2
? ?
 = x = 90 
Side of square = mm 40
4
x 2 340
?
?
Another method: 
Elimination procedure from alternatives option [C] and [D] are not possible because area may be 
maximum. 
Option (A) 
Side of the square = x = 30 mm 
Perimeter of the square = 30 + 30 + 30 + 30 = 120 mm 
? Perimeter of the rectangle = 340 – 120 = 220 mm 
2x + 2  × 2x = 220 
  x = 37 
 2x =  37 ×2 = 74 
Area of square = x
2
 = (30)
2
 = 900 
Area of rectangle = x × 2x = 37 × 74 = 2738 
Total area = 900 + 2738 = 3638 mm
2
 
Option (B) 
Side of the square = x = 40 mm 
Perimeter of the square = 340 – 160 = 180 mm 
2x + 2 × 2x = 180 mm 
6x = 180 mm 
  x = 30 mm 
Area of the square = 40 × 40 = 1600 mm
2
 
Area of the rectangle = 30 × 2  × 30 = 1800 mm
2
 
? Total area = 1600 + 1800 = 3400 mm
2
 
? 3400 mm
2
 < 3638 mm
2
 
Option B is correct. 
Q.1 – Q.25 Carry one mark each. 
01. The value of x for which the matrix A =
?
?
?
?
?
?
?
?
?
?
? ? ? ? x 9 4 6
13 7 9
4 2 3
has zero as an eigen value is ________ 
01. Ans: x = 1
Sol: For eigen value of A is to be zero, det (A) = 0 
 3 {( ?63 + 7x ) + 52} ?2{ ( ?81 + 9x)+78} + 4 { ?36 + 42} = 0 
? x = 1