JEE Mains Mock tests

MATHS
SECTION-1(SINGLE ANSWER TYPE QUESTIONS)
1. There were two women participating in a chess tournament. Every participant played
two games with the other participants. the number of games that the men played
between themselves proved to exceed by 66 the number of games that the men
played with the women. The number of participants is
a) 6 b) 11 c) 13 d) 10
2. Given 5 different green, 4 different blue, and 3 different red dice. The number of
combinations of dice that can be choosen by taking atleast one green and one blue
die is
a) 3680 b) 3690 c) 3700 d)) 3720
3. The number of ways in which 13 gold coins can be distributed among three persons
such that each one gets at least two gold coins is
a) 36 b) 24 c) 12 d) 6
4. A quesion paper consisting of 10 questions is divided into 3 parts with 5,3,2
quesions. A candidate is to answer 6 quesions without neglecting any part. The
number of ways in which he can make up his choice is
a) 175 b) 200 c) 225 d) 150
5. There are 15 trees in a row. 4 trees are to be cut down. The number of ways that no
two of the cut down trees are consecutive is
a) 11C4 b) 12 C4 c) 15 C4 d) 14 C4
6. The number of ways in which four letters can be selected from the letters of the
word "MATHEMATICS" is
a) 133 b) 146 c) 136 d) 73
7. A is a set containing n elements. A subset P of A is chosen.The set A is recon-
structed by replacing the elements of P. A subset Q of A is again chosen. The
number of ways of choosing P and Q so that P  Q contains exactly two elements
is
a) 9.n C2 b) 3 n  n C 2 c) 2·n Cn d) n C2 3n2
8. If N denotes set of all positive integers and if f : N  N is defined by f (n)  the
sum of positive divisors of n . then f  2k .3 where ' k ' is a positive integer is

a) 2k 1  1 b) 2  2 k 1  1 c) 3  2k 1  1 d) 4  2 k 1  1

TRIVIDYAA JUNIOR COLLEGE 2

, 9. A train going from Vijayawada to Hyderabad stops at nine intermediate stations. Six
persons enter the train during the journey with six different tickets of the same class.
The no. of different tickets they may have
a) 11 C6 b) 45 C6 c) 9 C6 d) 10 C6
10. 10 persons are seated at round table. The number of ways of selecting 3 persons out
of them if no two persons are adjacent to each other is
a) 50 b) 62 c) 56 d) 57
 logx 2 - 7logx + 9 dx =
11.  
x  log x   9log x   c x  log x   9log x  18  c
2 2
a)   b)  

x  log x   9log x  18  c x  log x   7 log x  9   c
2 2
c)   d)  

 3 
 x + x +1 dx =
12.  e 
x


 1+ x  
2 3/2 



x ex x
a) ex c b) e .
x
c c) ex  c d)
1 x 2
1 x 2
1  x2 e x 1  x2  c

sin -1x - cos-1x
13.  sin -1x + cos-1x dx =
4
a) x sin 1 x  1  x 2   x  c b) log sin 1 x  cos 1 x   c
  
4 4
c) x sin 1 x  1  x 2   c d) x sin 1 x  1  x 2   c
     

 x - x + 2
3

 e x +1 dx =
x
14.
  2 2



xe x  x  1 e x  c x 2e x x 2e x
a) c b) c) c d) c
x2  1 x2  1 x 1 x2  1

log 1- x 
15.  x2
dx =

 1    1
a) 1  x  log 1  x   log x   c b) 1  x  log 1  x   log x  c
    

1  1 
c)  x  1 log 1  x   log x  c d)  x  1 log 1  x   log x  c
   



TRIVIDYAA JUNIOR COLLEGE 3