This document contains 30 multiple choice questions related to mathematics for a JEE exam preparation test. It provides instructions that each question is worth 4 marks and 1 mark will be deducted for incorrect answers. The maximum total marks for the test are 120. The questions cover topics in trigonometry, algebra, geometry and calculus.

1. JOGLEKAR MATHEMATICS POINT /MPB-19,Mahaveer Nagar-1,KOTA/JEE(Main)/TP-2
There are 30 questions,Each question is allotted 4 m
t

MPB -19,Mahaveer Nagar -1,Main Road Kota. 8769855992,8387919366
Important Instructions
(JEE(Main))
Mathematics is he King of all Subjects
joglekar MATHEMATICs POINT
arks for correct response.
One Fourth mark will be deducted for incorrect response of each question.
No deduction from the total score will be made if no response is indicated for a question
in the Answ


2009 2009 2008 2007 2006 3 2
2007 2008 2009 20
er Sheet.
The maximum marks are 120.
01. The value of the product
sin cos cos cos cos .....cos cos is ?
2 2 2 2 2 2 2
1 1 1 1
(a) (b) (c) (d)
2 2 2 2

                   
                          
10
02.The total number of solution of tan sin cot cos , [0, 6 ], is ?
2 2
(a) 5 (b) 7 (c) 4 (d) 5
03. Let ten vertical poles standing at equal distances on a straight line, subtand equal
angles at a point O on this line and a
    
           
 ll the poles are on the same side of O.If the
height of longest pole is H and the distance of the foot of the smallest pole from O is
d then the dis tance between two consec utive poles is :
Hcos dsin Hcos dsin Hsin d cos
(a) (b) (c)
9sin 9cos
       
 
1
1 2
Hsin d cos
(d)
9cos 9cos
1 63
04. The value of sin sin is equals to :
4 8
1 1 1 1
(a) (b) (c) (d)
2 42 2 2
05. Let A : 3,8,13,.................503 and A : 6,13,20.................699 are two arithmetic
progressions then th

   
 
  
  
  
  
1 2e number of common terms of A and A are :
(a) 13 (b) 14 (c) 15 (d) 16
z -i
06. The perimeter of the locus represented by arg , where 1 i is :
z+ i 4
3 3 2
(a) (b) (c) (d)
2 32 2
 
    
   
JMP

2. JOGLEKAR MATHEMATICS POINT /MPB-19,Mahaveer Nagar-1,KOTA/JEE(Main)/TP-2
 
161/2 k
07 There are 'n' circles in a plane and the number of radical axes is equals to number
of radical centres then the total number of circles will be :-
(a) 5 (b) 3 (c) 6 (d)7
08.If middle term in the binomial expansion of x x is a
6 5 7 5
lso term independent of x,
then second term in the expansion is :-
(a)120x (b)120x (c)16x (d)16x
3
09. The chance of India winning toss is . If it wins the toss,then its chance of victory
4
4
is otherwise i
5
2
1
t is only .Then chance of India's victory is :
2
1 29 3 3
(a) (b) (c) (d)
5 40 40 5
x 3x + 2 2x 1
10. The total number of real values of 'x' for which 2x 1 4x 3x +1 = 0 is :
7x 2 17x + 6 12x 1
(a)1 (b) 2 (c) 0 (d)
cos cos sin
11.Let A


 

  

2
2 2
1 2
cos cos sin
and B , if AB is a null matrix
cos sin sin cos sin sin
then
(a) n ,n I (b) 2n ,n I (c)(2n 1) ,n I (d) 0
2
12. Let is the area of triangle made by joining mid points of its s.ides and is the
are
     
   
           
   

     
 
1
2
a of same triangle made by centroid and any two vertices,then is equals to :
(a) 3:4 (b) 4:3 (c) 3:2 (d) 2:3
13. The equation of a line passes through (1,2) and which is at a minimum distance from
the point (3,1) is x ky 5 the valu


 
2 2
e of k is ;
(a) 2 (b) 3 (c) 2 (d) 3
14. If x – 7xy – y = 0, x + y = 2,are the sides of a triangle,then distance between the side
x + y = 2 and orthocenter is :
1
(a) 2 (b) 3 (c) 2 (d)
2
15. If e is eccentricity of ellipse whose area is hal
 
f the area of its auxiliary circle then
the value of e is :
1 1 3 2
(a) (b) (c) (d)
2 2 32

3. JOGLEKAR MATHEMATICS POINT /MPB-19,Mahaveer Nagar-1,KOTA/JEE(Main)/TP-2
 
2 2
16. Let a relation R on a set of natural numbers N be definded as (x,y) R such that
x 4xy 3y 0 then relation R is :-
(a) symmetric. (b) transitive. (c) An equivalence. (d) reflexive.
17. The image of a point 7, 1, ,2, in line r 9

  
 

1 2
ˆ ˆ ˆ ˆ ˆ ˆi 5j 5k ( i 3j+5k ) is :
(a) (–9, 5, 2) (b) (9, 5, –2) (c) (9, 5, 2) (d) None
x 3 y 2 z 1 x 2 y 3 z 2
12. If lines whose equations are L : and L : are
2 3 k 3 2 3
coplaner and P(a ,b,c) is the point of int ersec
    
 
     
   
1tion of L and the plane x y z 15
then a b c is :
(a) 15 (b) 10 (c) 5 (d) 7
19. A plane passing through (1,1,1) cuts positive direction of co-ordinate axes at A,B,& C
and if V is the valume of tetrahedron OABC then :
9
(a) V (
2
  
 

9 7 7
b) V (c)V (d) V .
2 2 2
ˆ ˆ ˆ ˆ ˆ ˆ20. Let a = 2i j 2k , b = i 2j 2k are two vectors and a vector c is along angle
bisec tor of a and c on a is 12 then c.b =
(a) 20 (b) 24 (c) 36 (d)
b. If projection of
21. If vector is perpendic
44
a ula
  
   
 
 

  
0
8 8 8
1 2 8
c ,|a| 2,| | 3,| c| 4
c 120 ,then [a c ] is equal to ;
(a) 4 3 (b) 6 3 (c) 12 3 (d) 10 3
22. If f(x) =( C x +1)( C x +1)............
r to b and b and the ang
........
le
( C x +
betwe
1), the
en
b and is b
n f '(0)=
(a) 256 (b) 255 (c) 102
  
  
  
 
 
       
cosx sinx
cosx sinx cosx cos x
2 2
2 2
4 (d)1023
23. The value of (sin x) (cos x cot x log (sin x) ) dx is equals to ;
(a) cosx +c (b) cos +c (c) sinx c (d) log x c
x y
24. If it is possible to draw the tangent to the hyperbola 1 havi
a b

 
 

2
3
2
ng slope 2
and if 'e' is its eccentricity then the range of 'e' is :
(a) 1 e 5 (b ) 5 e 5 (c) 0 e 5 (d) 1 e 5
25. If f(x) is an even function then (x f(x) x f "(x) 2)dx is equals to :
(a) 8 (b) 0 (c) 4 (d) 2


        
 

4. JOGLEKAR MATHEMATICS POINT /MPB-19,Mahaveer Nagar-1,KOTA/JEE(Main)/TP-2
2 2 4 4
2
26. If (x + y )dy = xy dx and y(1)=1, y( )=e and if = k e then k is equals to :
(a) 7 (b) 3 (c) 5 (d) 9
27.Consider the following statements :
(i). The function f(x) x 2cos x is increa sing in the int erval(0, ).
(ii).The function
 
  
2
f(x) In( 1 x x) is decra sing in the int erval( , ).
Which of the above statments is /are correct ?
(a) (i) only (b) (ii) only (c) both(i)and(ii) (d) Neither (i)nor(ii)
28. Let a and b be two unit vectors suchthat a b 3 . If c a 2b 3
    
    
     
 
2
2 2
a b , then
c is equals to:
55 51 43 37
(a) (b) (c) (d)
2 2 2 2
29. Statement 1:Graphof y x x 1 lies above x axis for all real values of x.
Statement 2: Let y ax bx c,a,b,c R if a 0 and b 4ac 0,then y 0 x.
(a)Statement 1 is true,Stateme

    
         



nt 2is true,Statement 2 is acorrect exp lanationfor
Statement 1.
(b)Statement 1 is true,Statement 2 is true,Statement 2 is not a correct exp lanation
for Statement 1.
(c)Statement 1 is true,Statement 2 is false.
(d)Statement
 

  

 

1
1
2
2
1 2
1 is false,Statement 2 is true.
30. Statement-1:- If the perpendicular tangents to circle C meet at P, then the locus
redius of C 1
of P has a circle C , then .
redius of C 2
Statement-2: Circles C and C are co


 ncentric.
(a) Statement 1 is true,Statement 2 is true,Statement 2 is a correct exp lanation
for Statement 1.
(b) Statement 1 is true,Statement 2 is true,Statement 2 is not a correct exp lanation
for Statement 1.
(c) Statement 1 is
  

  

 true,Statement 2 is false.
(d) Statement 1 is false,Statement 2 is true.

 