This document provides 30 mathematics questions with multiple choice answers for a JEE Main exam practice test. It includes instructions that there are 120 total marks, each question is worth 4 marks, and a 1/4 mark deduction for incorrect answers. The questions cover a range of mathematics topics including trigonometry, coordinate geometry, algebra, calculus, and probability.

1. JOGLEKAR MATHEMATICS POINT /MPB-19,Mahaveer Nagar-1,KOTA/JEE(Main)/TP-4
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


er Sheet.
The maximum marks are 120.
3 1 cos 1 cos
01. If , then the value of is :
2 1 cos 1 cos
2 2 1 1
(a) (b) (c) (d)
sin sin sin sin
x x
02. The sum of the solutions in x (0,4 ) of equation 7sin sin
3 3

    
    
   
 
   
    
      
2
4 4
1 1
2 2 2 2
x
sin 1 is :
3
(a) 6 (b)2 (c) 4 (d) 8
03. The dis tance of the point( 9,0) from director circle of the parabola y 16(x 3) is:
(a) 0 (b) 3 (c) 2 (d) 1
x y 1
04. If sin x sin y then the value of is equals to :
2 x x y y
(a) 3 (b)
 
  
    
   
  
  
 
 
 
2 (c)8 (d) 1
log 2 log 4 log 8 log16
05. The sum of the infinite series + + + +.................. , is :
3 9 27 81
log 2 3log 2 5 log 2
(a) log 8 (b) (c) (d)
2 4 2
06. A point P( , ), , I is selected at random from inside of t

     he triangle formed by
x + y =10 and both co-ordinate axes. If , are odd integers, then probability that
both and are prime numbers is :-
3 1 7 5
(a) (b) (c) (d)
10 3 10 18
07. A stair - case of length rests against a
 
 
l vertical wall and a floor of a room. Let P be
a point on the stair - case, nearer to its end on the wall, that divides its length in
the ratio 1: 2. If the stair - case begins to slide on the floor, then the locus of P is :
3 1
(a) an ellipse of eccentricity . (b) an ellipse of eccentricity .
2 2
3 1
(c) a circle of radius . (d) a circle of radius .
2 2
JMP

2. JOGLEKAR MATHEMATICS POINT /MPB-19,Mahaveer Nagar-1,KOTA/JEE(Main)/TP-4
6 6 6 6
3 3 3 3
1/5 1/3 100
08. Given six line segments of lengths 2, 3, 4, 5, 6, 7 units, the number of triangles that
canbe formed by these lines is ?
(a) C 7 (b) C 6 (c) C 5 (d) C 4
09. In the expansion of (3 7 ) ,the number
   

1 2 3 4 5
2
3 2 1
2
4 3 2
2
5 4 3
3 4 4 3
of irrational terms is ?
(a) 62 (b) 94 (c) 78 (d) 82
10. If a ,a ,a ,a ,a are consec utive terms of an A.P. with comman difference 'd' then
a a a
the value of the det er minant a a a in terms of d is :
a a a
(a) d (b) 2d (c) d (d) 2d
11. If a r r
1 2 2008
2 2
r r 1
matrix M is definded as M ,r 1, 2, 3, ......., then the value of the
r 1 r
det (M ) det (M ) ................... det (M ) is:
(a) 2007 (b) 2008 (c) (2008) (d) (2007)
12. The number of real values of for whic
 
   
  

2 2
h the area of the triangle formed by the points
A( 2,1) , B(1,3) and C(3 , 2 3) as a vertices is 8 sq. units is :
(a) 0 (b) 1 (c) 2 (d) infinitely
13. Let x + y 4x 2y 11 be a circle. A pair of tangents drawn fr
   
  
2
om the point P(4,5)
with a pair of radii forms a quadrilateral, then the area of this quadrilateral is :
(a) 4 (b) 7 (c) 6 (d) 5
14. The straight line x y k touches the parabola y x x ,thenk is equals to;
(a) 1 (b) 1 (c) 2 (d) 2
5
-
1
   

2
[a +b 2c b c a +2c ] =m[a b c ] then the value of m is :
1 1 2 3
If plane containing point (1,4, 2) intersects axes at points A,B & C such that centroid
of
. Let
(a) (b) (c) (d)
16
ABC is (1, , ) then volume of tetra
.
 


  
        
hedron OABC is (O being origin)
9 27
9 18
2 2
17.The shortest dis tance between the lines 2x y z 1,3x y 2z 2 and x y z is :
(a) (b) (c) (d)
1 3 3
(a ) (b ) 2 (c ) (d )
22 2
       

3. JOGLEKAR MATHEMATICS POINT /MPB-19,Mahaveer Nagar-1,KOTA/JEE(Main)/TP-4
18. Let a,b,c are three unit vectors,no two of which are collinear, a 2b is collinear
with c and b 3c is collinear with a then magnitude of (a 2b 8c) is :
1 2 3
1
19. The area of region e
(a) 4 (b)
nclosed
(
by curves y x ,
c)
x e, y
)
x
(d

  
  
   
     
and positive x axis is :
1 3 5
(a) square units (b) 1 square units (c) square units (d) square units
2 2 2
20.The volume of a parallelopiped whose concurrent edges are given by vectors a,b& c
is 2 cu. units, then the volume of a parallelopiped w

 
x 0
hose concurrent edges are given
by vectors 2(a +c),(b c) and 3(a +b ) is :
(a) 12cu. units. (b) 24cu. units. (c) 36cu. units. (d) 6cu. units.
f (x) f (4 x) f (7 x) f (10 x) ........upto n terms
21.Let f(0) 0 and f '(0) 1 and lim
n(1 x

   
 

    

2 3
2
2
1
2
2 2 2 2
x x x
590
x )
then n is equal to
(a) 120 (b) 20 (c) 90 (d) 60
1 1 x
22. Let f(x)=cos thenf '(x)
2 1 x
1 1 1 1
(a) (b) (c) (d)
1 x 2(1 x ) 1 x 2(1 x )
23. The equation of tangent at x = 1 of the curve y f(x)= e +e +e +..

 
  
 
 
  
  

   

n
x
2
.......+e , n N
is y p = 45e(x + q), then the value of n is:
(a) 9 (b)6 (c)4 (d)1
24. An open box is made by cutting out 4 square from 4 corners of a square tin sheet
of area 36 m and then folding up the flaps. The max imum volume of box is ?


3 3 3 3
233
2
In7 2
2 2
In5
(a) 25 m (b) 16m (c) 10m (d) 12m
2 2 x 3
25. If dx f (x) C,then f '(1) is equal to :
2 x 4(2 x)
1
(a) 3 (b) (c) 4 (d) 4
3
x cos x dx
26. The integral is equals to :
cos(ln35 x ) cosx
1 5 1 5 1 1 7
(a) In (b) In (c) In (d) In
4 7 2 7 4 5 2 5
 
   

 




4. JOGLEKAR MATHEMATICS POINT /MPB-19,Mahaveer Nagar-1,KOTA/JEE(Main)/TP-4
1 2
1 1
27. A line L has a slope of 2 and passes through the point P(r, 3). A second line L ,
is perpendicular to L , intersects L at A(a,b) and passes through B(6,r),then the
value of 'a' is equal to :
(a) r (b) 2r /5 (
 
 1
1 1 1
1 1 1
2 tan y
tan y tan y 2tan y
tan y 1 2tan y tan y
c) 2r 3 (d) 5r /2
dy
28.The solution of the differential equation (1 y ) x e 0, is :
dx
(a)(x 2) ke (b) 2xe e k
(c)x e tan y k (d) x e e k
29. Statement-1 :- The equation of A

  
  


   
   
   
2 2
2 2x y
uxiliary circle of ellipse 1 is x y 25.
25 16
Statement-2 :- If two mutually perpendicular tangents are drawn to an ellipse then
locus of their point of intersection is a circle which is known as
   
auxiliary circle of the ellipse.
(a) Statement 1 is true,Statement 2is true,Statement 2 is acorrect exp lanationfor
Statement 1.
(b) Statement 1 is true,Statement 2is true,Statement 2 is not a correct exp lanation
for Stateme
  

  
nt 1
(c) Statement 1 is true,Statement 2 is false.
(d) Statement 1 is false,Statement 2 is true.

 
 