West Bengal: State Level Question Paper (MAT) - 2017-18 | NTSE for Class 10 PDF Download

 Page 1


 
 
 
 
     
        
 
NATIONAL TALENT SEARCH EXAMINATION, 2017-18 
(STATE LEVEL-STAGE1) 
(FOR STUDENTS STUDYING IN CLASS X) 
 MENTAL ABILITY TEST (MAT) 
 
Time: 45 Minutes      Full Marks: 50 
 
 
INSTRUCTIONS TO CANDIDATES 
  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
  
 
 Read the instructions carefully before you start answering the questions. Answers are to be given on a OMR Answer-
Sheet provided. 
 
1. In this Paper you are to answer 50 questions. Each questions carries 1 (one) mark. You are to answer all the questions. 
 
2. Before you proceed to mark in the OMR answer-Sheet, find out the correct answer from the four alternatives (a), (b), (c) 
and (d) against each question in the Question Booklet. Darken the circle with a Black Ball Point Pen, to the 
corresponding correct answer for the item in the OMR Answer-Sheet. 
 
  (Here ‘b’ is the correct answer.) 
 
3. If more than one circle is encoded or darken against a particular answer, it will be treated as a wrong answer. 
 
4. There will be no penalty marks or negative marking for a wrong answer. 
 
5. You are to start recording answers with the ‘start’ instruction from the Officer-in-Charge of your room/hall. 
 
6. You are to write your Name and Roll No. in the space provided with for this purpose on the OMR Answer-Sheet. You 
must encode your Roll No. in OMR Answer Sheet. 
 
7. The OMR Answer-Sheet should be handed over to the Invigilator before leaving the Examination Hall. You may take 
away the used Question Booklet after completion of the examination. 
 
 
 
Enrollment No. :  Batch : 
 
Name :  
 
 
Candidate’s Signature Invigilator’s Signature:   
Page 2


 
 
 
 
     
        
 
NATIONAL TALENT SEARCH EXAMINATION, 2017-18 
(STATE LEVEL-STAGE1) 
(FOR STUDENTS STUDYING IN CLASS X) 
 MENTAL ABILITY TEST (MAT) 
 
Time: 45 Minutes      Full Marks: 50 
 
 
INSTRUCTIONS TO CANDIDATES 
  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
  
 
 Read the instructions carefully before you start answering the questions. Answers are to be given on a OMR Answer-
Sheet provided. 
 
1. In this Paper you are to answer 50 questions. Each questions carries 1 (one) mark. You are to answer all the questions. 
 
2. Before you proceed to mark in the OMR answer-Sheet, find out the correct answer from the four alternatives (a), (b), (c) 
and (d) against each question in the Question Booklet. Darken the circle with a Black Ball Point Pen, to the 
corresponding correct answer for the item in the OMR Answer-Sheet. 
 
  (Here ‘b’ is the correct answer.) 
 
3. If more than one circle is encoded or darken against a particular answer, it will be treated as a wrong answer. 
 
4. There will be no penalty marks or negative marking for a wrong answer. 
 
5. You are to start recording answers with the ‘start’ instruction from the Officer-in-Charge of your room/hall. 
 
6. You are to write your Name and Roll No. in the space provided with for this purpose on the OMR Answer-Sheet. You 
must encode your Roll No. in OMR Answer Sheet. 
 
7. The OMR Answer-Sheet should be handed over to the Invigilator before leaving the Examination Hall. You may take 
away the used Question Booklet after completion of the examination. 
 
 
 
Enrollment No. :  Batch : 
 
Name :  
 
 
Candidate’s Signature Invigilator’s Signature:   
 
        
   
 
 
(Questions 1–10) 
 
DIRECTION: Read the questions carefully and give answer by filling the circle of the letter denoting your 
selected answer on the O.M.R. Answer-Sheet. 
 
1. If the polynomial f(x) = 2x
3
 + mx
2
 + nx – 14 has (x – 1) and (x + 2) as its factors, find the value of 
m
n
 
(a) 27   (b) 
1
3
 
(c) 3   (d) 
1
27
 
2. In how many years the ratio of the principla and its interest at 4% per annum will be 5 : 2? 
(a) 10   (b) 15 
(c) 20   (d) None of the above  
3. 
If 
3 2 3 2
2 3 2 3
a 3ab x 3xy
,
3a b b 3x y y
??
?
??
then 
(a) bx = ay  (b) by = ax 
(c) b
2
y = a
2
x (d) b
2
x = a
2
y 
4. 
The mean of x1 and x2 is M1 and that of x1, x2, x3, x4 is M2 then the medan of ax1, ax2, 
3 4
x x
,
aa
is 
(a) 
12
MM
2
?
 (b) 
2
1
M
aM
a
2
?
 
(c) 
? ?
2
12
1
a 1 M 2M
2a
??
??
??
 (d) 
? ?
2
12
1
2 a 1 M M
2a
??
??
??
 
5. If f(x + 1) = 3x – 9, then what will be the value of f(x
2
 – 1)? 
(a) 3x
2
 – 9  (b) 3x
2
 – 15  
(c) x
2
 – 10  (d) 3x
2
 – 10 
6. The area of the whole surface of a certain cube is equal to the area of the curved surface of a 
certain sphere. The ratio of their volumes is  
(a) :6 ?  (b) :6 ? 
(c) 6: ? (d) 6: ? 
7. If xy ? and x, y are real numbers, and A = x
2
 + y
2
 – xy – x – y + 1, then  
(a) A > 0  (b) A = 0 
(c) A < 0  (d) 0 < A < 1 
8. If sin ? and cos ? are the roots of the equation lx
2
 + mx + n = 0, then  
(a) l
2
 + m
2
 + 2ln = 0 (b) l
2
 – m
2
 + 2ln = 0 
(c) l
2
 – m
2
 – 2ln = 0 (d) l
2
 + m
2
 – 2ln = 0 
9. PQ is the diametre of a semicircle with radius 4cm and PRQ ? is the angle on the semicircle. If QR 
= 27 cm, then length of PR is  
(a) 8 cm  (b) 6 cm 
(c) 5 cm  (d) 2 11 cm 
10. What must be added to x
4
 + 6x
3
 + 19x
2
 + 30x to make it a perfect square? 
(a) 49   (b) 25 
(c)  10   (d) 36 
 
Page 3


 
 
 
 
     
        
 
NATIONAL TALENT SEARCH EXAMINATION, 2017-18 
(STATE LEVEL-STAGE1) 
(FOR STUDENTS STUDYING IN CLASS X) 
 MENTAL ABILITY TEST (MAT) 
 
Time: 45 Minutes      Full Marks: 50 
 
 
INSTRUCTIONS TO CANDIDATES 
  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
  
 
 Read the instructions carefully before you start answering the questions. Answers are to be given on a OMR Answer-
Sheet provided. 
 
1. In this Paper you are to answer 50 questions. Each questions carries 1 (one) mark. You are to answer all the questions. 
 
2. Before you proceed to mark in the OMR answer-Sheet, find out the correct answer from the four alternatives (a), (b), (c) 
and (d) against each question in the Question Booklet. Darken the circle with a Black Ball Point Pen, to the 
corresponding correct answer for the item in the OMR Answer-Sheet. 
 
  (Here ‘b’ is the correct answer.) 
 
3. If more than one circle is encoded or darken against a particular answer, it will be treated as a wrong answer. 
 
4. There will be no penalty marks or negative marking for a wrong answer. 
 
5. You are to start recording answers with the ‘start’ instruction from the Officer-in-Charge of your room/hall. 
 
6. You are to write your Name and Roll No. in the space provided with for this purpose on the OMR Answer-Sheet. You 
must encode your Roll No. in OMR Answer Sheet. 
 
7. The OMR Answer-Sheet should be handed over to the Invigilator before leaving the Examination Hall. You may take 
away the used Question Booklet after completion of the examination. 
 
 
 
Enrollment No. :  Batch : 
 
Name :  
 
 
Candidate’s Signature Invigilator’s Signature:   
 
        
   
 
 
(Questions 1–10) 
 
DIRECTION: Read the questions carefully and give answer by filling the circle of the letter denoting your 
selected answer on the O.M.R. Answer-Sheet. 
 
1. If the polynomial f(x) = 2x
3
 + mx
2
 + nx – 14 has (x – 1) and (x + 2) as its factors, find the value of 
m
n
 
(a) 27   (b) 
1
3
 
(c) 3   (d) 
1
27
 
2. In how many years the ratio of the principla and its interest at 4% per annum will be 5 : 2? 
(a) 10   (b) 15 
(c) 20   (d) None of the above  
3. 
If 
3 2 3 2
2 3 2 3
a 3ab x 3xy
,
3a b b 3x y y
??
?
??
then 
(a) bx = ay  (b) by = ax 
(c) b
2
y = a
2
x (d) b
2
x = a
2
y 
4. 
The mean of x1 and x2 is M1 and that of x1, x2, x3, x4 is M2 then the medan of ax1, ax2, 
3 4
x x
,
aa
is 
(a) 
12
MM
2
?
 (b) 
2
1
M
aM
a
2
?
 
(c) 
? ?
2
12
1
a 1 M 2M
2a
??
??
??
 (d) 
? ?
2
12
1
2 a 1 M M
2a
??
??
??
 
5. If f(x + 1) = 3x – 9, then what will be the value of f(x
2
 – 1)? 
(a) 3x
2
 – 9  (b) 3x
2
 – 15  
(c) x
2
 – 10  (d) 3x
2
 – 10 
6. The area of the whole surface of a certain cube is equal to the area of the curved surface of a 
certain sphere. The ratio of their volumes is  
(a) :6 ?  (b) :6 ? 
(c) 6: ? (d) 6: ? 
7. If xy ? and x, y are real numbers, and A = x
2
 + y
2
 – xy – x – y + 1, then  
(a) A > 0  (b) A = 0 
(c) A < 0  (d) 0 < A < 1 
8. If sin ? and cos ? are the roots of the equation lx
2
 + mx + n = 0, then  
(a) l
2
 + m
2
 + 2ln = 0 (b) l
2
 – m
2
 + 2ln = 0 
(c) l
2
 – m
2
 – 2ln = 0 (d) l
2
 + m
2
 – 2ln = 0 
9. PQ is the diametre of a semicircle with radius 4cm and PRQ ? is the angle on the semicircle. If QR 
= 27 cm, then length of PR is  
(a) 8 cm  (b) 6 cm 
(c) 5 cm  (d) 2 11 cm 
10. What must be added to x
4
 + 6x
3
 + 19x
2
 + 30x to make it a perfect square? 
(a) 49   (b) 25 
(c)  10   (d) 36 
 
 
        
   
(Questions 11––20) 
 
DIRECTION: (In each questions 11 to 20 below, there is a number series with one term missing shown by 
‘?’. The term is given as one of the alternatives among four numbers given below it. Find the term and 
indicate your answer by filling the circle of the corresponding letter of alternatives in the O.M.R. Answer-
Sheet. 
11. 
1
21 ,16,12,9,?
3
 
(a) 7   (b) 6 
(c) 6.75  (d) 5 
12. 21, 34, 55, 89, 144, ? 
(a) 169   (b) 213 
(c) 223   (d) 233 
13. 225, 100, 36, 9, 1, ? 
(a) – 7    (b) – 6 
(c) 0   (d) – 1 
14. 2, 15, 41, 80, ? 
(a) 111   (b) 120 
(c) 121   (d) 132 
15. 462, 420, 380, ?, 306 
(a) 322   (b) 332 
(c) 342   (d) 352 
16. 4, 18, ?, 100, 180, 294 
(a) 32   (b) 36 
(c) 48   (d) 40 
17. (11, 13), ?, (23, 29), (31, 37), (41, 47) 
(a) (13, 17) (b) (19, 21) 
(c) (17, 19)  (d) (13, 18) 
18. 
1 2 4 5
, ,?, ,
39 3 9 3
 
(a) 
3
33
  (b) 
3
3
 
(c) 
1
23
  (d) 
1
3
 
19. 121, 126, 141, 166, 201, ? 
(a) 206   (b) 212 
(c) 230   (d) 246 
20. 0, 6, 24, 60, ?, 210 
(a) 117   (b) 119 
(c) 120   (d) 126 
 
 
(Questions 21––30) 
 
DIRECTION: In each of the questions 21 to 30, there are four items, three of which are alike by some means 
or other while one is out of the class. Find out the odd item and indicate your answer by filling the circle of 
the corresponding letter on the O.M.R. Answer-Sheet. 
 
21. (a) Jagadish Chandra Bose 
(b) Debendra Mohan Bose 
(c) Satyendra Nath Basu 
(d) Prafulla Chandra Roy 
Page 4


 
 
 
 
     
        
 
NATIONAL TALENT SEARCH EXAMINATION, 2017-18 
(STATE LEVEL-STAGE1) 
(FOR STUDENTS STUDYING IN CLASS X) 
 MENTAL ABILITY TEST (MAT) 
 
Time: 45 Minutes      Full Marks: 50 
 
 
INSTRUCTIONS TO CANDIDATES 
  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
  
 
 Read the instructions carefully before you start answering the questions. Answers are to be given on a OMR Answer-
Sheet provided. 
 
1. In this Paper you are to answer 50 questions. Each questions carries 1 (one) mark. You are to answer all the questions. 
 
2. Before you proceed to mark in the OMR answer-Sheet, find out the correct answer from the four alternatives (a), (b), (c) 
and (d) against each question in the Question Booklet. Darken the circle with a Black Ball Point Pen, to the 
corresponding correct answer for the item in the OMR Answer-Sheet. 
 
  (Here ‘b’ is the correct answer.) 
 
3. If more than one circle is encoded or darken against a particular answer, it will be treated as a wrong answer. 
 
4. There will be no penalty marks or negative marking for a wrong answer. 
 
5. You are to start recording answers with the ‘start’ instruction from the Officer-in-Charge of your room/hall. 
 
6. You are to write your Name and Roll No. in the space provided with for this purpose on the OMR Answer-Sheet. You 
must encode your Roll No. in OMR Answer Sheet. 
 
7. The OMR Answer-Sheet should be handed over to the Invigilator before leaving the Examination Hall. You may take 
away the used Question Booklet after completion of the examination. 
 
 
 
Enrollment No. :  Batch : 
 
Name :  
 
 
Candidate’s Signature Invigilator’s Signature:   
 
        
   
 
 
(Questions 1–10) 
 
DIRECTION: Read the questions carefully and give answer by filling the circle of the letter denoting your 
selected answer on the O.M.R. Answer-Sheet. 
 
1. If the polynomial f(x) = 2x
3
 + mx
2
 + nx – 14 has (x – 1) and (x + 2) as its factors, find the value of 
m
n
 
(a) 27   (b) 
1
3
 
(c) 3   (d) 
1
27
 
2. In how many years the ratio of the principla and its interest at 4% per annum will be 5 : 2? 
(a) 10   (b) 15 
(c) 20   (d) None of the above  
3. 
If 
3 2 3 2
2 3 2 3
a 3ab x 3xy
,
3a b b 3x y y
??
?
??
then 
(a) bx = ay  (b) by = ax 
(c) b
2
y = a
2
x (d) b
2
x = a
2
y 
4. 
The mean of x1 and x2 is M1 and that of x1, x2, x3, x4 is M2 then the medan of ax1, ax2, 
3 4
x x
,
aa
is 
(a) 
12
MM
2
?
 (b) 
2
1
M
aM
a
2
?
 
(c) 
? ?
2
12
1
a 1 M 2M
2a
??
??
??
 (d) 
? ?
2
12
1
2 a 1 M M
2a
??
??
??
 
5. If f(x + 1) = 3x – 9, then what will be the value of f(x
2
 – 1)? 
(a) 3x
2
 – 9  (b) 3x
2
 – 15  
(c) x
2
 – 10  (d) 3x
2
 – 10 
6. The area of the whole surface of a certain cube is equal to the area of the curved surface of a 
certain sphere. The ratio of their volumes is  
(a) :6 ?  (b) :6 ? 
(c) 6: ? (d) 6: ? 
7. If xy ? and x, y are real numbers, and A = x
2
 + y
2
 – xy – x – y + 1, then  
(a) A > 0  (b) A = 0 
(c) A < 0  (d) 0 < A < 1 
8. If sin ? and cos ? are the roots of the equation lx
2
 + mx + n = 0, then  
(a) l
2
 + m
2
 + 2ln = 0 (b) l
2
 – m
2
 + 2ln = 0 
(c) l
2
 – m
2
 – 2ln = 0 (d) l
2
 + m
2
 – 2ln = 0 
9. PQ is the diametre of a semicircle with radius 4cm and PRQ ? is the angle on the semicircle. If QR 
= 27 cm, then length of PR is  
(a) 8 cm  (b) 6 cm 
(c) 5 cm  (d) 2 11 cm 
10. What must be added to x
4
 + 6x
3
 + 19x
2
 + 30x to make it a perfect square? 
(a) 49   (b) 25 
(c)  10   (d) 36 
 
 
        
   
(Questions 11––20) 
 
DIRECTION: (In each questions 11 to 20 below, there is a number series with one term missing shown by 
‘?’. The term is given as one of the alternatives among four numbers given below it. Find the term and 
indicate your answer by filling the circle of the corresponding letter of alternatives in the O.M.R. Answer-
Sheet. 
11. 
1
21 ,16,12,9,?
3
 
(a) 7   (b) 6 
(c) 6.75  (d) 5 
12. 21, 34, 55, 89, 144, ? 
(a) 169   (b) 213 
(c) 223   (d) 233 
13. 225, 100, 36, 9, 1, ? 
(a) – 7    (b) – 6 
(c) 0   (d) – 1 
14. 2, 15, 41, 80, ? 
(a) 111   (b) 120 
(c) 121   (d) 132 
15. 462, 420, 380, ?, 306 
(a) 322   (b) 332 
(c) 342   (d) 352 
16. 4, 18, ?, 100, 180, 294 
(a) 32   (b) 36 
(c) 48   (d) 40 
17. (11, 13), ?, (23, 29), (31, 37), (41, 47) 
(a) (13, 17) (b) (19, 21) 
(c) (17, 19)  (d) (13, 18) 
18. 
1 2 4 5
, ,?, ,
39 3 9 3
 
(a) 
3
33
  (b) 
3
3
 
(c) 
1
23
  (d) 
1
3
 
19. 121, 126, 141, 166, 201, ? 
(a) 206   (b) 212 
(c) 230   (d) 246 
20. 0, 6, 24, 60, ?, 210 
(a) 117   (b) 119 
(c) 120   (d) 126 
 
 
(Questions 21––30) 
 
DIRECTION: In each of the questions 21 to 30, there are four items, three of which are alike by some means 
or other while one is out of the class. Find out the odd item and indicate your answer by filling the circle of 
the corresponding letter on the O.M.R. Answer-Sheet. 
 
21. (a) Jagadish Chandra Bose 
(b) Debendra Mohan Bose 
(c) Satyendra Nath Basu 
(d) Prafulla Chandra Roy 
 
        
   
22. (a) Raman Research Institute  
(b) Indian Institute of Science 
(c) Indian institute of Chemical Biology 
(d) International Centre for Theoretical Science 
23. (a) Blade 
(b) Axe 
(c) Scissors 
(d) Needle 
24. (a) India Today 
(b) The Hindu 
(c) The Hindustan Times 
(d) Times of India 
25. (a) Terrence Tao 
(b) Maryam Mirzakhari 
(c) Rene Thom 
(d) Michael Atiyah 
26. (a) Patna 
(b) Kolkata 
(c) Baranasi 
(d) Cuttack 
27. (a) Metre 
(b) Litra 
(c) Nautical mile 
(d) Light year 
28. (a) May Day 
(b) Republic Day 
(c) Gandhi Jayanti Day 
(d) Rabindra Jayanti Day 
29. (a) The Mahabharat 
(b) The Geeta 
(c) The Koran 
(d) The Bible 
30. (a) Atal Behari Bajpaee 
(b) Dr. Manmohan Singh 
(c) Dr. A.P.J.Abdul Kalam 
(d) Morarji Desai 
 
Questions 31––40) 
 
DIRECTION: In each question below there are two words separated by ‘:’ in the upper row. Below that there 
are some words on each side of the symbol ‘:’. Find the relation between two upper words and select one 
word from the right side of ‘:’ below which have the same relation as above. Fill the circle of the letter 
denoting your selected answer on the O.M.R. Answer-Sheet. 
 
31. Prashanta Chandra Mahalanobis : Indian Statistical Institute 
Dr. Mahendralal Sarkar : ? 
(a) Calcutta University (b) Rajabazar Science College 
(c) Indian Association for the Cultivation of Science (d) Indian Institute of Science 
32. Calendar : Dates 
Dictionary : ? 
(A) Sentences  (B) Language    
(C) Words   (D) Books 
 
 
Page 5


 
 
 
 
     
        
 
NATIONAL TALENT SEARCH EXAMINATION, 2017-18 
(STATE LEVEL-STAGE1) 
(FOR STUDENTS STUDYING IN CLASS X) 
 MENTAL ABILITY TEST (MAT) 
 
Time: 45 Minutes      Full Marks: 50 
 
 
INSTRUCTIONS TO CANDIDATES 
  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
  
 
 Read the instructions carefully before you start answering the questions. Answers are to be given on a OMR Answer-
Sheet provided. 
 
1. In this Paper you are to answer 50 questions. Each questions carries 1 (one) mark. You are to answer all the questions. 
 
2. Before you proceed to mark in the OMR answer-Sheet, find out the correct answer from the four alternatives (a), (b), (c) 
and (d) against each question in the Question Booklet. Darken the circle with a Black Ball Point Pen, to the 
corresponding correct answer for the item in the OMR Answer-Sheet. 
 
  (Here ‘b’ is the correct answer.) 
 
3. If more than one circle is encoded or darken against a particular answer, it will be treated as a wrong answer. 
 
4. There will be no penalty marks or negative marking for a wrong answer. 
 
5. You are to start recording answers with the ‘start’ instruction from the Officer-in-Charge of your room/hall. 
 
6. You are to write your Name and Roll No. in the space provided with for this purpose on the OMR Answer-Sheet. You 
must encode your Roll No. in OMR Answer Sheet. 
 
7. The OMR Answer-Sheet should be handed over to the Invigilator before leaving the Examination Hall. You may take 
away the used Question Booklet after completion of the examination. 
 
 
 
Enrollment No. :  Batch : 
 
Name :  
 
 
Candidate’s Signature Invigilator’s Signature:   
 
        
   
 
 
(Questions 1–10) 
 
DIRECTION: Read the questions carefully and give answer by filling the circle of the letter denoting your 
selected answer on the O.M.R. Answer-Sheet. 
 
1. If the polynomial f(x) = 2x
3
 + mx
2
 + nx – 14 has (x – 1) and (x + 2) as its factors, find the value of 
m
n
 
(a) 27   (b) 
1
3
 
(c) 3   (d) 
1
27
 
2. In how many years the ratio of the principla and its interest at 4% per annum will be 5 : 2? 
(a) 10   (b) 15 
(c) 20   (d) None of the above  
3. 
If 
3 2 3 2
2 3 2 3
a 3ab x 3xy
,
3a b b 3x y y
??
?
??
then 
(a) bx = ay  (b) by = ax 
(c) b
2
y = a
2
x (d) b
2
x = a
2
y 
4. 
The mean of x1 and x2 is M1 and that of x1, x2, x3, x4 is M2 then the medan of ax1, ax2, 
3 4
x x
,
aa
is 
(a) 
12
MM
2
?
 (b) 
2
1
M
aM
a
2
?
 
(c) 
? ?
2
12
1
a 1 M 2M
2a
??
??
??
 (d) 
? ?
2
12
1
2 a 1 M M
2a
??
??
??
 
5. If f(x + 1) = 3x – 9, then what will be the value of f(x
2
 – 1)? 
(a) 3x
2
 – 9  (b) 3x
2
 – 15  
(c) x
2
 – 10  (d) 3x
2
 – 10 
6. The area of the whole surface of a certain cube is equal to the area of the curved surface of a 
certain sphere. The ratio of their volumes is  
(a) :6 ?  (b) :6 ? 
(c) 6: ? (d) 6: ? 
7. If xy ? and x, y are real numbers, and A = x
2
 + y
2
 – xy – x – y + 1, then  
(a) A > 0  (b) A = 0 
(c) A < 0  (d) 0 < A < 1 
8. If sin ? and cos ? are the roots of the equation lx
2
 + mx + n = 0, then  
(a) l
2
 + m
2
 + 2ln = 0 (b) l
2
 – m
2
 + 2ln = 0 
(c) l
2
 – m
2
 – 2ln = 0 (d) l
2
 + m
2
 – 2ln = 0 
9. PQ is the diametre of a semicircle with radius 4cm and PRQ ? is the angle on the semicircle. If QR 
= 27 cm, then length of PR is  
(a) 8 cm  (b) 6 cm 
(c) 5 cm  (d) 2 11 cm 
10. What must be added to x
4
 + 6x
3
 + 19x
2
 + 30x to make it a perfect square? 
(a) 49   (b) 25 
(c)  10   (d) 36 
 
 
        
   
(Questions 11––20) 
 
DIRECTION: (In each questions 11 to 20 below, there is a number series with one term missing shown by 
‘?’. The term is given as one of the alternatives among four numbers given below it. Find the term and 
indicate your answer by filling the circle of the corresponding letter of alternatives in the O.M.R. Answer-
Sheet. 
11. 
1
21 ,16,12,9,?
3
 
(a) 7   (b) 6 
(c) 6.75  (d) 5 
12. 21, 34, 55, 89, 144, ? 
(a) 169   (b) 213 
(c) 223   (d) 233 
13. 225, 100, 36, 9, 1, ? 
(a) – 7    (b) – 6 
(c) 0   (d) – 1 
14. 2, 15, 41, 80, ? 
(a) 111   (b) 120 
(c) 121   (d) 132 
15. 462, 420, 380, ?, 306 
(a) 322   (b) 332 
(c) 342   (d) 352 
16. 4, 18, ?, 100, 180, 294 
(a) 32   (b) 36 
(c) 48   (d) 40 
17. (11, 13), ?, (23, 29), (31, 37), (41, 47) 
(a) (13, 17) (b) (19, 21) 
(c) (17, 19)  (d) (13, 18) 
18. 
1 2 4 5
, ,?, ,
39 3 9 3
 
(a) 
3
33
  (b) 
3
3
 
(c) 
1
23
  (d) 
1
3
 
19. 121, 126, 141, 166, 201, ? 
(a) 206   (b) 212 
(c) 230   (d) 246 
20. 0, 6, 24, 60, ?, 210 
(a) 117   (b) 119 
(c) 120   (d) 126 
 
 
(Questions 21––30) 
 
DIRECTION: In each of the questions 21 to 30, there are four items, three of which are alike by some means 
or other while one is out of the class. Find out the odd item and indicate your answer by filling the circle of 
the corresponding letter on the O.M.R. Answer-Sheet. 
 
21. (a) Jagadish Chandra Bose 
(b) Debendra Mohan Bose 
(c) Satyendra Nath Basu 
(d) Prafulla Chandra Roy 
 
        
   
22. (a) Raman Research Institute  
(b) Indian Institute of Science 
(c) Indian institute of Chemical Biology 
(d) International Centre for Theoretical Science 
23. (a) Blade 
(b) Axe 
(c) Scissors 
(d) Needle 
24. (a) India Today 
(b) The Hindu 
(c) The Hindustan Times 
(d) Times of India 
25. (a) Terrence Tao 
(b) Maryam Mirzakhari 
(c) Rene Thom 
(d) Michael Atiyah 
26. (a) Patna 
(b) Kolkata 
(c) Baranasi 
(d) Cuttack 
27. (a) Metre 
(b) Litra 
(c) Nautical mile 
(d) Light year 
28. (a) May Day 
(b) Republic Day 
(c) Gandhi Jayanti Day 
(d) Rabindra Jayanti Day 
29. (a) The Mahabharat 
(b) The Geeta 
(c) The Koran 
(d) The Bible 
30. (a) Atal Behari Bajpaee 
(b) Dr. Manmohan Singh 
(c) Dr. A.P.J.Abdul Kalam 
(d) Morarji Desai 
 
Questions 31––40) 
 
DIRECTION: In each question below there are two words separated by ‘:’ in the upper row. Below that there 
are some words on each side of the symbol ‘:’. Find the relation between two upper words and select one 
word from the right side of ‘:’ below which have the same relation as above. Fill the circle of the letter 
denoting your selected answer on the O.M.R. Answer-Sheet. 
 
31. Prashanta Chandra Mahalanobis : Indian Statistical Institute 
Dr. Mahendralal Sarkar : ? 
(a) Calcutta University (b) Rajabazar Science College 
(c) Indian Association for the Cultivation of Science (d) Indian Institute of Science 
32. Calendar : Dates 
Dictionary : ? 
(A) Sentences  (B) Language    
(C) Words   (D) Books 
 
 
 
        
   
33. 1729 : Rarnanujan 
6174 1 :  ?  
(A) Sir Asutosh Mukhopadhyay  (B) Mahan Maharaj 
(C) S. Chandrasekhar  (D) D. R. Kaprekar  
 
34. 15
th
 August : India  
         ?        : Pakistan 
(A) 21st February (B) 16th December  
(C) 16th August (D) 14th August 
 
35. Coconut: Shell 
Letter : ? 
(A) Letter-box (B) Envelope   
(C) Stamp   (D) Mail 
 
36 Rabishankar : Sitar 
AmjadA1i Khan: ? 
(A) Sitar   (B) Sarod   
(C) Flute  (D) Guiter 
 
37. Prof. Amarthya Sen : Economics  
Prof. Ashoke Sen     :     ? 
(A) Economics (B) Physics   
(C) Chemistry (D) Biology 
 
38. The Ganges : India  
The Nile      :    ? 
(A) Pakistan  (B) China  
(C) Egypt  (D) Nairobi 
 
39. Virat Kohil         :   Cricket 
Pankaj Advani       :       ? 
(A) Basket Ball (B) Billiard   
(C) Snooker (D) Chess 
 
40. Apparel     :  Cloth  
Footwear  :     ? 
(A) Material  (B) Leather    
(D) Cobbler  (D) Shoes 
 
 
(Questions 41––50) 
 
DIRECTION: In each questions 41––50, numbers are placed in figures on the basis of some rules. One 
place in the figure is indicated by the interrogation sign (?). Find out the correct alternative to replace the 
question mark and indicate your answer by filling the circle of the corresponding letter of alternatives in 
the O.M.R. Answer-Sheet.  
 
 
41.