JEE Main Exam Question and answer Paper

JEE MAIN EXAM SET - 1
TOTAL TIME:1.30HR TOTAL MARKS: 100
1. If z1  3  i 3 and z2  3  i , then the complex 13. If an angle  is divided into two parts A and B such that
50 AB  x and tan A : tanB  k :1, then the value of sin x
z  is:
number  1  lies in the quadrant number :
a) k  1 sin b) k k 1
 z2  sin c) sin d) None of these
k 1 k 1 k 1
a) I b) II c) III d) IV
2. Let z and w be two complex numbers such that 14. The maximum value of cos2    x   cos2    x  is:
3  3 
z  1, w  1 and z  iw  z  iw  2. Then z equals :
a)  3 b) 1 c) 3 d) 3
a) 1 or i b) i or –i 2 2 2 2
c) 1 or -1 d) i or -1 15. The number of values of x satisfying the equation
3. The harmonic mean of the roots of the equation : cos x  cos2x  cos3x  sin x  sin2x  sin3x in the
  
5  2 x 2  4  3 x  8  2 3  0 is :  interval  0,2  is:
a) 2 b) 4 c) 6 d) 8 a) 2 b)4 c) 6 d) 8
4. The sum of the series 16. If the sides of a right-angled triangle form an A.P., the sines
13 13  23 13  23  33 of the acute angles are :
   .... upto 16 terms is : a)  1 , 3  b)  3 , 4 
1 13 135 


3 

5 5

a) 246 b)346 c) 446 d) 546
c)  3 1 3 1  d)  5 1 5 1 
5. Let  ,  be the roots of x  x  p  0 and  ,  be the    
2 , ,
 2 2   2 2 
   
roots of x 2  4 x  q  0 . If  ,  ,  , are in G.P., then 17. In a triangle, if a  15  11 and b  17  13 ,then
integral values of p and q respectively are :
a) b  2a b) b  a c) a  2b d) a  b
a) 2, 32 b) 2,3
18. The angle of eelevision of the top of a TV tower from three
c) 6,3 d) 6, 32 points A, B, C in a straight line (in the horizontal plane)
6. In a chess tournament, all participants were to play one through the foot of the tower are  ,2 ,3 respectively. If
game with the another. Two players fell ill after having
played 3 games each. If total number of games played in
AB  a, the height of the tower is :
the tournament is equal to 84, then total number of a) a sin b) a sin2
participants in the beginning was equal to : c) a sin3 d) a sin  
2
a) 10 b) 15 c) 12 d) 14
7. Total number of non-negative integral solutions of 19. On its annual sports day, School awarded 35 medals in
x1  x2  x3  10 is equal to : athletics, 15 Judo and 18 in swimming. If these medals goes
12 10 12 10
to a total of 58 students and only three of them got medals
a) C3 b) C3 c) C2 d) C2 in all the three sports. The number of students who
10 received medals in exactly two of the three sports are:
8. The value of  r. P is : r
r a) 9 b) 4 c) 5 d) 7
r 1 20. Modules of non-zero complex number z satisfying
a)
11
P11 b)
11
P11  1 c)
11
P11  1 d) None of 2
z  z  0 and z  4 zi  z 2 is __________.
these
21. The number of perfect square in the list 11, 111, 1111,
9. A shopkeepers sells three varieties of perfumes and he has 11111, ……… is __________.
a large number of bottles of the same sizes of each variety
22. There are two women participating in a chess tournament
in his stock. There are 5 place in a row in his showcase. The
Every participant played 2 games that the men played
number of different ways of displaying the three varieties of
between themselves exceeded by 66 as compared to the
perfumes in the showcase is :
number of games that the men played with the women. If
a) 6 b) 50 c) 150 d) none of these
the number of participants is n, then the value of n  6 is
10. The number of divisors of the numbers 38808 (excluding 1
_________ .
and the number itself) is :
a) 70 b) 72 c) 71 d) none of these 23. A class has three teachers, Mr P, Ms Q, and Mrs R and six
students A, B, C, D, E, F. Then number of ways in which
11. The value of tan5 is:
they can be seated in a line of 9 chairs,if between any two
tan5   10 tan3   5tan 5tan  10tan3   tan5  teachers there are exactly two students, is k!18  , then the
a b)
5tan   10 tan   1
4 2
1  10tan2   5tan4  value of k is __________.
tan5   10tan3   5tan
c) tan   10 tan   5tan
5 3
24. If Cr 1  36, Cr  84and Cr 1  126, then the value of
n n n
d)
5tan4   10 tan2   1 1  10tan2   5tan4  r
C2 .
3
2 
12.  cos  2k  1  is equal to : a) 1 b)2 c) 3 d) 4
 12 
k 1
x  5 x   6  0, where [.] denote the greatest
2
25. If
a)  1 b) 0 c) 1 d) 3
2 2 2 integer function, then x belongs to -----------------.