CUET Mathematics Previous Year Paper 2024 | Mathematics CUET Preparation - Commerce PDF Download

 Page 1


A 
Test Booklet No.  Test Booklet Code 
 
 
                                       (Do not open this Test Booklet until you are asked to do so) 
Time Allowed : 60 minutes  Maximum Marks : 200 
Total Questions : 
15+35+35 
Number of questions to be answered : 15+25 
Kindly read the Instructions given on this Page and Back Page carefully before attempting this Question Paper.
 
Important Instructions for the Candidates : 
1. This Question Paper contains two sections i.e. Section A and Section B (B1 and B2).  
 Section A has 15 questions covering both i.e. Mathematics and Applied Mathematics which is compulsory for all 
candidates. 
 Section B1 has 35 questions (Q. No. 16 to 50) from Mathematics out of which 25 questions need to be attempted. 
 Section B2 has 35 questions (Q. No. 51 to 85) purely from Applied Mathematics out of which 25 questions need to 
be attempted. 
 If a candidate answers more than 25 questions from Section B1/B2, the first 25 answered questions will be considered 
for evaluation. 
2. When you are given the OMR Answer Sheet, fill in your particulars on it carefully with blue/black ball point pen only. 
3. Use only Blue/Black Ball Point Pen for marking responses. Kindly select Mathematics (Q. No. 16 to 50) OR Applied 
Mathematics (Q. No. 51 to 85) very carefully for marking responses on the OMR Answer Sheet.   
4.  The CODE for this Test Booklet is A. Make sure that the CODE printed on the OMR Answer Sheet is the same as that 
on this Test Booklet. Also ensure that your Test Booklet No. and OMR Answer Sheet No. are exactly the same. In case 
of discrepancy, the candidate should immediately report the matter to the Invigilator for replacement of both the Test 
Booklet and the OMR Answer Sheet. No claim in this regard will be entertained after five minutes from the start of the 
examination. 
5. Before attempting the question paper kindly check that this Test Booklet has total 28 pages and OMR Answer Sheet 
consists of one sheet. At the start of the examination within first five minutes, candidates are advised to ensure that all 
pages of Test Booklet and OMR Answer Sheet are properly printed and they are not damaged in any manner. 
6. Each question has four options. Out of these four options choose the MOST APPROPRIATE OPTION and 
darken/blacken the corresponding circle on the OMR Answer Sheet with a Blue/Black Ball Point Pen.  
7. Five (5) marks will be given for each correct answer. One (1) mark will be deducted for each incorrect answer. If more 
than one circle is found darkened/blackened for a question, then it will be considered as an incorrect answer. 
Unanswered questions will be given no mark.                                        
P.T.O. 
 
Name of the Candidate (in Capital Letters) : ___________________________________________________________________ 
  
 Application Number (in figures) : ______________________________________________________________________________ 
  
 Roll Number (in figures) : ___________________________________________________________________________________  
  
 Centre of Examination (in Capital Letters) : ___________________________________________________________________ 
  
 Candidate’s Signature : ____________________________ Invigilator’s Signature : ___________________________________ 
  
 Facsimile signature stamp of Centre Superintendent : __________________________________________________________ 
 Subject :  Mathematics/Applied Mathematics 
 Code : 319 E 
 Medium : English 
Page 2


A 
Test Booklet No.  Test Booklet Code 
 
 
                                       (Do not open this Test Booklet until you are asked to do so) 
Time Allowed : 60 minutes  Maximum Marks : 200 
Total Questions : 
15+35+35 
Number of questions to be answered : 15+25 
Kindly read the Instructions given on this Page and Back Page carefully before attempting this Question Paper.
 
Important Instructions for the Candidates : 
1. This Question Paper contains two sections i.e. Section A and Section B (B1 and B2).  
 Section A has 15 questions covering both i.e. Mathematics and Applied Mathematics which is compulsory for all 
candidates. 
 Section B1 has 35 questions (Q. No. 16 to 50) from Mathematics out of which 25 questions need to be attempted. 
 Section B2 has 35 questions (Q. No. 51 to 85) purely from Applied Mathematics out of which 25 questions need to 
be attempted. 
 If a candidate answers more than 25 questions from Section B1/B2, the first 25 answered questions will be considered 
for evaluation. 
2. When you are given the OMR Answer Sheet, fill in your particulars on it carefully with blue/black ball point pen only. 
3. Use only Blue/Black Ball Point Pen for marking responses. Kindly select Mathematics (Q. No. 16 to 50) OR Applied 
Mathematics (Q. No. 51 to 85) very carefully for marking responses on the OMR Answer Sheet.   
4.  The CODE for this Test Booklet is A. Make sure that the CODE printed on the OMR Answer Sheet is the same as that 
on this Test Booklet. Also ensure that your Test Booklet No. and OMR Answer Sheet No. are exactly the same. In case 
of discrepancy, the candidate should immediately report the matter to the Invigilator for replacement of both the Test 
Booklet and the OMR Answer Sheet. No claim in this regard will be entertained after five minutes from the start of the 
examination. 
5. Before attempting the question paper kindly check that this Test Booklet has total 28 pages and OMR Answer Sheet 
consists of one sheet. At the start of the examination within first five minutes, candidates are advised to ensure that all 
pages of Test Booklet and OMR Answer Sheet are properly printed and they are not damaged in any manner. 
6. Each question has four options. Out of these four options choose the MOST APPROPRIATE OPTION and 
darken/blacken the corresponding circle on the OMR Answer Sheet with a Blue/Black Ball Point Pen.  
7. Five (5) marks will be given for each correct answer. One (1) mark will be deducted for each incorrect answer. If more 
than one circle is found darkened/blackened for a question, then it will be considered as an incorrect answer. 
Unanswered questions will be given no mark.                                        
P.T.O. 
 
Name of the Candidate (in Capital Letters) : ___________________________________________________________________ 
  
 Application Number (in figures) : ______________________________________________________________________________ 
  
 Roll Number (in figures) : ___________________________________________________________________________________  
  
 Centre of Examination (in Capital Letters) : ___________________________________________________________________ 
  
 Candidate’s Signature : ____________________________ Invigilator’s Signature : ___________________________________ 
  
 Facsimile signature stamp of Centre Superintendent : __________________________________________________________ 
 Subject :  Mathematics/Applied Mathematics 
 Code : 319 E 
 Medium : English 
319 E/A ( 2 )  
   
SPACE FOR ROUGH WORK  
Section A (Compulsory) 
1.  The corner points of the feasible region determined by   
 x + y ? 8,  2x + y ? 8,  x ? 0,  y ? 0 
 are A(0, 8), B(4, 0) and C(8, 0). If the objective function Z = ax + by has its maximum value on the line 
segment AB, then the relation between a and b is : 
(1) 8a + 4 = b   (2) a = 2b  
(3) b = 2a   (4) 8b + 4 = a 
2.  If  t = e
2x
  and  y = log
e 
t
2
,  then 
2
2
dy
dx
 is : 
(1) 0    (2) 4t  
(3) 
2t
4e
t
   (4) 
2t
2
e ( 4 t – 1 )
t
 
3. An objective function  Z = ax + by  is maximum at points (8, 2) and (4, 6). If a ? 0 and b ? 0 and ab = 25,  
then the maximum value of the function is equal to : 
(1) 60    (2) 50  
(3) 40    (4) 80 
4. The area of the region bounded by the lines  x + 2y =12, x = 2,  x = 6  and  x-axis is : 
(1) 34 sq units  
(2) 20 sq units  
(3) 24 sq units  
(4) 16 sq units 
5.  A die is rolled thrice. What is the probability of getting a number greater than 4 in the first and the 
second throw of dice and a number less than 4 in the third throw ? 
(1) 
1
3
  (2) 
1
6
 (3) 
1
9
 (4) 
1
18
 
Page 3


A 
Test Booklet No.  Test Booklet Code 
 
 
                                       (Do not open this Test Booklet until you are asked to do so) 
Time Allowed : 60 minutes  Maximum Marks : 200 
Total Questions : 
15+35+35 
Number of questions to be answered : 15+25 
Kindly read the Instructions given on this Page and Back Page carefully before attempting this Question Paper.
 
Important Instructions for the Candidates : 
1. This Question Paper contains two sections i.e. Section A and Section B (B1 and B2).  
 Section A has 15 questions covering both i.e. Mathematics and Applied Mathematics which is compulsory for all 
candidates. 
 Section B1 has 35 questions (Q. No. 16 to 50) from Mathematics out of which 25 questions need to be attempted. 
 Section B2 has 35 questions (Q. No. 51 to 85) purely from Applied Mathematics out of which 25 questions need to 
be attempted. 
 If a candidate answers more than 25 questions from Section B1/B2, the first 25 answered questions will be considered 
for evaluation. 
2. When you are given the OMR Answer Sheet, fill in your particulars on it carefully with blue/black ball point pen only. 
3. Use only Blue/Black Ball Point Pen for marking responses. Kindly select Mathematics (Q. No. 16 to 50) OR Applied 
Mathematics (Q. No. 51 to 85) very carefully for marking responses on the OMR Answer Sheet.   
4.  The CODE for this Test Booklet is A. Make sure that the CODE printed on the OMR Answer Sheet is the same as that 
on this Test Booklet. Also ensure that your Test Booklet No. and OMR Answer Sheet No. are exactly the same. In case 
of discrepancy, the candidate should immediately report the matter to the Invigilator for replacement of both the Test 
Booklet and the OMR Answer Sheet. No claim in this regard will be entertained after five minutes from the start of the 
examination. 
5. Before attempting the question paper kindly check that this Test Booklet has total 28 pages and OMR Answer Sheet 
consists of one sheet. At the start of the examination within first five minutes, candidates are advised to ensure that all 
pages of Test Booklet and OMR Answer Sheet are properly printed and they are not damaged in any manner. 
6. Each question has four options. Out of these four options choose the MOST APPROPRIATE OPTION and 
darken/blacken the corresponding circle on the OMR Answer Sheet with a Blue/Black Ball Point Pen.  
7. Five (5) marks will be given for each correct answer. One (1) mark will be deducted for each incorrect answer. If more 
than one circle is found darkened/blackened for a question, then it will be considered as an incorrect answer. 
Unanswered questions will be given no mark.                                        
P.T.O. 
 
Name of the Candidate (in Capital Letters) : ___________________________________________________________________ 
  
 Application Number (in figures) : ______________________________________________________________________________ 
  
 Roll Number (in figures) : ___________________________________________________________________________________  
  
 Centre of Examination (in Capital Letters) : ___________________________________________________________________ 
  
 Candidate’s Signature : ____________________________ Invigilator’s Signature : ___________________________________ 
  
 Facsimile signature stamp of Centre Superintendent : __________________________________________________________ 
 Subject :  Mathematics/Applied Mathematics 
 Code : 319 E 
 Medium : English 
319 E/A ( 2 )  
   
SPACE FOR ROUGH WORK  
Section A (Compulsory) 
1.  The corner points of the feasible region determined by   
 x + y ? 8,  2x + y ? 8,  x ? 0,  y ? 0 
 are A(0, 8), B(4, 0) and C(8, 0). If the objective function Z = ax + by has its maximum value on the line 
segment AB, then the relation between a and b is : 
(1) 8a + 4 = b   (2) a = 2b  
(3) b = 2a   (4) 8b + 4 = a 
2.  If  t = e
2x
  and  y = log
e 
t
2
,  then 
2
2
dy
dx
 is : 
(1) 0    (2) 4t  
(3) 
2t
4e
t
   (4) 
2t
2
e ( 4 t – 1 )
t
 
3. An objective function  Z = ax + by  is maximum at points (8, 2) and (4, 6). If a ? 0 and b ? 0 and ab = 25,  
then the maximum value of the function is equal to : 
(1) 60    (2) 50  
(3) 40    (4) 80 
4. The area of the region bounded by the lines  x + 2y =12, x = 2,  x = 6  and  x-axis is : 
(1) 34 sq units  
(2) 20 sq units  
(3) 24 sq units  
(4) 16 sq units 
5.  A die is rolled thrice. What is the probability of getting a number greater than 4 in the first and the 
second throw of dice and a number less than 4 in the third throw ? 
(1) 
1
3
  (2) 
1
6
 (3) 
1
9
 (4) 
1
18
 
319 E/A ( 3 )  
 
SPACE FOR ROUGH WORK  
6.  
n1
x – x
?
?
?
 dx =  
(1) 
n
e
n
x – 1
log C
n
x
?
?   (2) 
n
e
n
x1
log C
x – 1
?
? 
(3) 
n
e
n
x1
log C
n
x
? ?
?  (4) 
n
e
n
x
log C
x – 1
? ? 
7.  The value of 
? ?
1
2
2
2
0
a – b x
dx
a bx ?
?
 is : 
(1) 
a – b
ab ?
   (2) 
1
a – b
  
(3) 
ab
2
?
   (4) 
1
ab ?
 
8.  The second order derivative of which of the following functions is 5
x
 ? 
(1) 5
x
 log
e
 5   (2) 5
x
 (log
e
 5)
2  
(3) 
x
e
5
log 5
   (4) 
x
2
e
5
(log 5)
 
9.  The degree of the differential equation 
3/2
2 2
2
dy d y
1 – k
dx
dx
??
??
?
?? ??
??
??
??
 is : 
(1) 1    (2) 2  
(3) 3    (4) 
3
2
 
Page 4


A 
Test Booklet No.  Test Booklet Code 
 
 
                                       (Do not open this Test Booklet until you are asked to do so) 
Time Allowed : 60 minutes  Maximum Marks : 200 
Total Questions : 
15+35+35 
Number of questions to be answered : 15+25 
Kindly read the Instructions given on this Page and Back Page carefully before attempting this Question Paper.
 
Important Instructions for the Candidates : 
1. This Question Paper contains two sections i.e. Section A and Section B (B1 and B2).  
 Section A has 15 questions covering both i.e. Mathematics and Applied Mathematics which is compulsory for all 
candidates. 
 Section B1 has 35 questions (Q. No. 16 to 50) from Mathematics out of which 25 questions need to be attempted. 
 Section B2 has 35 questions (Q. No. 51 to 85) purely from Applied Mathematics out of which 25 questions need to 
be attempted. 
 If a candidate answers more than 25 questions from Section B1/B2, the first 25 answered questions will be considered 
for evaluation. 
2. When you are given the OMR Answer Sheet, fill in your particulars on it carefully with blue/black ball point pen only. 
3. Use only Blue/Black Ball Point Pen for marking responses. Kindly select Mathematics (Q. No. 16 to 50) OR Applied 
Mathematics (Q. No. 51 to 85) very carefully for marking responses on the OMR Answer Sheet.   
4.  The CODE for this Test Booklet is A. Make sure that the CODE printed on the OMR Answer Sheet is the same as that 
on this Test Booklet. Also ensure that your Test Booklet No. and OMR Answer Sheet No. are exactly the same. In case 
of discrepancy, the candidate should immediately report the matter to the Invigilator for replacement of both the Test 
Booklet and the OMR Answer Sheet. No claim in this regard will be entertained after five minutes from the start of the 
examination. 
5. Before attempting the question paper kindly check that this Test Booklet has total 28 pages and OMR Answer Sheet 
consists of one sheet. At the start of the examination within first five minutes, candidates are advised to ensure that all 
pages of Test Booklet and OMR Answer Sheet are properly printed and they are not damaged in any manner. 
6. Each question has four options. Out of these four options choose the MOST APPROPRIATE OPTION and 
darken/blacken the corresponding circle on the OMR Answer Sheet with a Blue/Black Ball Point Pen.  
7. Five (5) marks will be given for each correct answer. One (1) mark will be deducted for each incorrect answer. If more 
than one circle is found darkened/blackened for a question, then it will be considered as an incorrect answer. 
Unanswered questions will be given no mark.                                        
P.T.O. 
 
Name of the Candidate (in Capital Letters) : ___________________________________________________________________ 
  
 Application Number (in figures) : ______________________________________________________________________________ 
  
 Roll Number (in figures) : ___________________________________________________________________________________  
  
 Centre of Examination (in Capital Letters) : ___________________________________________________________________ 
  
 Candidate’s Signature : ____________________________ Invigilator’s Signature : ___________________________________ 
  
 Facsimile signature stamp of Centre Superintendent : __________________________________________________________ 
 Subject :  Mathematics/Applied Mathematics 
 Code : 319 E 
 Medium : English 
319 E/A ( 2 )  
   
SPACE FOR ROUGH WORK  
Section A (Compulsory) 
1.  The corner points of the feasible region determined by   
 x + y ? 8,  2x + y ? 8,  x ? 0,  y ? 0 
 are A(0, 8), B(4, 0) and C(8, 0). If the objective function Z = ax + by has its maximum value on the line 
segment AB, then the relation between a and b is : 
(1) 8a + 4 = b   (2) a = 2b  
(3) b = 2a   (4) 8b + 4 = a 
2.  If  t = e
2x
  and  y = log
e 
t
2
,  then 
2
2
dy
dx
 is : 
(1) 0    (2) 4t  
(3) 
2t
4e
t
   (4) 
2t
2
e ( 4 t – 1 )
t
 
3. An objective function  Z = ax + by  is maximum at points (8, 2) and (4, 6). If a ? 0 and b ? 0 and ab = 25,  
then the maximum value of the function is equal to : 
(1) 60    (2) 50  
(3) 40    (4) 80 
4. The area of the region bounded by the lines  x + 2y =12, x = 2,  x = 6  and  x-axis is : 
(1) 34 sq units  
(2) 20 sq units  
(3) 24 sq units  
(4) 16 sq units 
5.  A die is rolled thrice. What is the probability of getting a number greater than 4 in the first and the 
second throw of dice and a number less than 4 in the third throw ? 
(1) 
1
3
  (2) 
1
6
 (3) 
1
9
 (4) 
1
18
 
319 E/A ( 3 )  
 
SPACE FOR ROUGH WORK  
6.  
n1
x – x
?
?
?
 dx =  
(1) 
n
e
n
x – 1
log C
n
x
?
?   (2) 
n
e
n
x1
log C
x – 1
?
? 
(3) 
n
e
n
x1
log C
n
x
? ?
?  (4) 
n
e
n
x
log C
x – 1
? ? 
7.  The value of 
? ?
1
2
2
2
0
a – b x
dx
a bx ?
?
 is : 
(1) 
a – b
ab ?
   (2) 
1
a – b
  
(3) 
ab
2
?
   (4) 
1
ab ?
 
8.  The second order derivative of which of the following functions is 5
x
 ? 
(1) 5
x
 log
e
 5   (2) 5
x
 (log
e
 5)
2  
(3) 
x
e
5
log 5
   (4) 
x
2
e
5
(log 5)
 
9.  The degree of the differential equation 
3/2
2 2
2
dy d y
1 – k
dx
dx
??
??
?
?? ??
??
??
??
 is : 
(1) 1    (2) 2  
(3) 3    (4) 
3
2
 
319 E/A ( 4 )  
   
SPACE FOR ROUGH WORK  
10. If A and B are symmetric matrices of the same order, then AB – BA is a : 
(1) symmetric matrix   (2) zero matrix 
(3) skew symmetric matrix  (4) identity matrix 
11. If A is a square matrix of order 4 and |A|= 4, then |2A| will be : 
(1) 8  (2) 64 (3) 16 (4) 4 
12. If [A]
3 ?2
 [B]
x ?y
 = [C]
3 ?1
,
 
then : 
(1) x = 1, y = 3 (2) x = 2, y = 1 (3) x = 3, y = 3 (4) x = 3, y = 1 
13. If a function  f(x) = x
2
 + bx + 1  is increasing in the interval [1, 2], then the least value of b is : 
(1) 5  (2) 0 (3) – 2 (4) – 4 
14. Two dice are thrown simultaneously. If X denotes the number of fours, then the expectation of X will be : 
(1) 
5
9
  (2) 
1
3
 (3) 
4
7
 (4) 
3
8
 
15. For the function f(x) = 2x
3
 – 9x
2
 + 12x – 5, x ? [0, 3], match List-I with List-II : 
 
 List-I 
 
 List-II 
 (A)  Absolute maximum value  (I)  3 
 (B)  Absolute minimum value  (II)  0 
 (C)  Point of maxima  (III)  – 5 
 (D)  Point of minima  (IV)  4 
Choose the correct answer from the options given below : 
(1) (A) - (IV), (B) - (II), (C) - (I), (D) - (III)  (2) (A) - (II), (B) - (III), (C) - (I), (D) - (IV) 
(3) (A) - (IV), (B) - (III), (C) - (II), (D) - (I) (4)  (A) - (IV), (B) - (III), (C) - (I), (D) - (II) 
Page 5


A 
Test Booklet No.  Test Booklet Code 
 
 
                                       (Do not open this Test Booklet until you are asked to do so) 
Time Allowed : 60 minutes  Maximum Marks : 200 
Total Questions : 
15+35+35 
Number of questions to be answered : 15+25 
Kindly read the Instructions given on this Page and Back Page carefully before attempting this Question Paper.
 
Important Instructions for the Candidates : 
1. This Question Paper contains two sections i.e. Section A and Section B (B1 and B2).  
 Section A has 15 questions covering both i.e. Mathematics and Applied Mathematics which is compulsory for all 
candidates. 
 Section B1 has 35 questions (Q. No. 16 to 50) from Mathematics out of which 25 questions need to be attempted. 
 Section B2 has 35 questions (Q. No. 51 to 85) purely from Applied Mathematics out of which 25 questions need to 
be attempted. 
 If a candidate answers more than 25 questions from Section B1/B2, the first 25 answered questions will be considered 
for evaluation. 
2. When you are given the OMR Answer Sheet, fill in your particulars on it carefully with blue/black ball point pen only. 
3. Use only Blue/Black Ball Point Pen for marking responses. Kindly select Mathematics (Q. No. 16 to 50) OR Applied 
Mathematics (Q. No. 51 to 85) very carefully for marking responses on the OMR Answer Sheet.   
4.  The CODE for this Test Booklet is A. Make sure that the CODE printed on the OMR Answer Sheet is the same as that 
on this Test Booklet. Also ensure that your Test Booklet No. and OMR Answer Sheet No. are exactly the same. In case 
of discrepancy, the candidate should immediately report the matter to the Invigilator for replacement of both the Test 
Booklet and the OMR Answer Sheet. No claim in this regard will be entertained after five minutes from the start of the 
examination. 
5. Before attempting the question paper kindly check that this Test Booklet has total 28 pages and OMR Answer Sheet 
consists of one sheet. At the start of the examination within first five minutes, candidates are advised to ensure that all 
pages of Test Booklet and OMR Answer Sheet are properly printed and they are not damaged in any manner. 
6. Each question has four options. Out of these four options choose the MOST APPROPRIATE OPTION and 
darken/blacken the corresponding circle on the OMR Answer Sheet with a Blue/Black Ball Point Pen.  
7. Five (5) marks will be given for each correct answer. One (1) mark will be deducted for each incorrect answer. If more 
than one circle is found darkened/blackened for a question, then it will be considered as an incorrect answer. 
Unanswered questions will be given no mark.                                        
P.T.O. 
 
Name of the Candidate (in Capital Letters) : ___________________________________________________________________ 
  
 Application Number (in figures) : ______________________________________________________________________________ 
  
 Roll Number (in figures) : ___________________________________________________________________________________  
  
 Centre of Examination (in Capital Letters) : ___________________________________________________________________ 
  
 Candidate’s Signature : ____________________________ Invigilator’s Signature : ___________________________________ 
  
 Facsimile signature stamp of Centre Superintendent : __________________________________________________________ 
 Subject :  Mathematics/Applied Mathematics 
 Code : 319 E 
 Medium : English 
319 E/A ( 2 )  
   
SPACE FOR ROUGH WORK  
Section A (Compulsory) 
1.  The corner points of the feasible region determined by   
 x + y ? 8,  2x + y ? 8,  x ? 0,  y ? 0 
 are A(0, 8), B(4, 0) and C(8, 0). If the objective function Z = ax + by has its maximum value on the line 
segment AB, then the relation between a and b is : 
(1) 8a + 4 = b   (2) a = 2b  
(3) b = 2a   (4) 8b + 4 = a 
2.  If  t = e
2x
  and  y = log
e 
t
2
,  then 
2
2
dy
dx
 is : 
(1) 0    (2) 4t  
(3) 
2t
4e
t
   (4) 
2t
2
e ( 4 t – 1 )
t
 
3. An objective function  Z = ax + by  is maximum at points (8, 2) and (4, 6). If a ? 0 and b ? 0 and ab = 25,  
then the maximum value of the function is equal to : 
(1) 60    (2) 50  
(3) 40    (4) 80 
4. The area of the region bounded by the lines  x + 2y =12, x = 2,  x = 6  and  x-axis is : 
(1) 34 sq units  
(2) 20 sq units  
(3) 24 sq units  
(4) 16 sq units 
5.  A die is rolled thrice. What is the probability of getting a number greater than 4 in the first and the 
second throw of dice and a number less than 4 in the third throw ? 
(1) 
1
3
  (2) 
1
6
 (3) 
1
9
 (4) 
1
18
 
319 E/A ( 3 )  
 
SPACE FOR ROUGH WORK  
6.  
n1
x – x
?
?
?
 dx =  
(1) 
n
e
n
x – 1
log C
n
x
?
?   (2) 
n
e
n
x1
log C
x – 1
?
? 
(3) 
n
e
n
x1
log C
n
x
? ?
?  (4) 
n
e
n
x
log C
x – 1
? ? 
7.  The value of 
? ?
1
2
2
2
0
a – b x
dx
a bx ?
?
 is : 
(1) 
a – b
ab ?
   (2) 
1
a – b
  
(3) 
ab
2
?
   (4) 
1
ab ?
 
8.  The second order derivative of which of the following functions is 5
x
 ? 
(1) 5
x
 log
e
 5   (2) 5
x
 (log
e
 5)
2  
(3) 
x
e
5
log 5
   (4) 
x
2
e
5
(log 5)
 
9.  The degree of the differential equation 
3/2
2 2
2
dy d y
1 – k
dx
dx
??
??
?
?? ??
??
??
??
 is : 
(1) 1    (2) 2  
(3) 3    (4) 
3
2
 
319 E/A ( 4 )  
   
SPACE FOR ROUGH WORK  
10. If A and B are symmetric matrices of the same order, then AB – BA is a : 
(1) symmetric matrix   (2) zero matrix 
(3) skew symmetric matrix  (4) identity matrix 
11. If A is a square matrix of order 4 and |A|= 4, then |2A| will be : 
(1) 8  (2) 64 (3) 16 (4) 4 
12. If [A]
3 ?2
 [B]
x ?y
 = [C]
3 ?1
,
 
then : 
(1) x = 1, y = 3 (2) x = 2, y = 1 (3) x = 3, y = 3 (4) x = 3, y = 1 
13. If a function  f(x) = x
2
 + bx + 1  is increasing in the interval [1, 2], then the least value of b is : 
(1) 5  (2) 0 (3) – 2 (4) – 4 
14. Two dice are thrown simultaneously. If X denotes the number of fours, then the expectation of X will be : 
(1) 
5
9
  (2) 
1
3
 (3) 
4
7
 (4) 
3
8
 
15. For the function f(x) = 2x
3
 – 9x
2
 + 12x – 5, x ? [0, 3], match List-I with List-II : 
 
 List-I 
 
 List-II 
 (A)  Absolute maximum value  (I)  3 
 (B)  Absolute minimum value  (II)  0 
 (C)  Point of maxima  (III)  – 5 
 (D)  Point of minima  (IV)  4 
Choose the correct answer from the options given below : 
(1) (A) - (IV), (B) - (II), (C) - (I), (D) - (III)  (2) (A) - (II), (B) - (III), (C) - (I), (D) - (IV) 
(3) (A) - (IV), (B) - (III), (C) - (II), (D) - (I) (4)  (A) - (IV), (B) - (III), (C) - (I), (D) - (II) 
319 E/A ( 5 )  
 
SPACE FOR ROUGH WORK  
Section B1 (Mathematics) 
16.  The rate of change (in cm
2
/s) of the total surface area of a hemisphere with respect to radius   
r at r = 
3
331 . 1 cm is : 
(1) 66 ?  (2) 6.6 ? (3) 3.3 ? (4) 4.4 ? 
17.  The area of the region bounded by the lines 
x
7 3a
 + 
b
y
 = 4, x = 0 and y = 0 is : 
(1) 56 3ab (2) 56a (3) ab/2 (4) 3ab 
18.  If A is a square matrix and I is an identity matrix such that A
2
 = A, then A(I – 2A)
3
 + 2A
3 
is equal to : 
(1) I + A (2) I + 2A (3) I – A (4) A 
19. The value of the integral 
e
e
2x
log 3
2x
log 2
e – 1
dx
e1 ?
?
 is : 
(1) log
e
 3
   
(2) log
e
 4
  
–  log
e
 3 
(3) log
e
 9
  
–  log
e
 4
   
(4) log
e
 3
  
–  log
e
 2 
20.  If 
?
a , 
?
b and 
?
c are three vectors such that 
?
a + 
?
b + 
?
c = 
?
0 , where 
?
a and 
?
b are unit vectors and 
|
?
c | = 2, then the angle between the vectors 
?
b and 
?
c is :  
(1) 60
o    
(2) 90
o  
(3) 120
o    
(4) 180
o 
21.  Let [x] denote the greatest integer function. Then match List-I with List-II : 
 List-I  List-II 
(A) |x – 1| + |x – 2| (I) is differentiable everywhere except at x = 0 
(B) x – |x| (II) is continuous everywhere 
(C) x – [x] (III) is not differentiable at x = 1 
(D) x |x| (IV) is differentiable at x = 1 
Choose the correct answer from the options given below : 
(1) (A) - (I), (B) - (II), (C) - (III), (D) - (IV) 
(2) (A) - (I), (B) - (III), (C) - (II), (D) - (IV) 
(3) (A) - (II), (B) - (I), (C) - (III), (D) - (IV) 
(4) (A) - (II), (B) - (IV), (C) - (III), (D) - (I)