This document contains a 30 question mathematics practice test with multiple choice answers for JEE Main exam preparation. Each question is allotted 4 marks for a correct response and there is a 1 mark deduction for an incorrect response. The maximum total marks are 120. The questions cover topics in trigonometry, coordinate geometry, calculus, and vectors. Instructions provide details on the marking scheme and conditions for the exam.

1. JOGLEKAR MATHEMATICSPOINT /MPB-19,Mahaveer Nagar-1,KOTA/JEE(Main)/TP-1
There are 30 questions,Each question is allotted 4 mar
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
ks 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 Answer


2
Sheet.
The maximum marks are 120.
3 1
01. If cos cos and sin sin and is the arithmatic mean of and then
2 2
the value of sin2 cos 2 is equals to :
7 4 3 8
(a) (b) (c) (d)
5 5 5 5
02.The number of solutions of the equation tan x

          
   
6
sec x +1 = 0 in (0,13) is :-
(a)4 (b) 6 (c) 0 (d) 13
03. Let AB is a vertical pole resting at the end A on the level ground.P is a point on the
level ground such that AP = 3AB. If C is the mid point of AB and CB

   
   
–1 2 –1
subtends an
angle at P, then the value of tan is :-
18 3
(a) (b) (c) 6 (d) 3
19 19
04. Let 1 sin cos x sin cos x ....................... 2 then x is equals to :
3 1 1
(a) (b) (c) (d) 1
2 2 2
05.Let A : sin( ) tan( ) and B : cos( ) 1 be
 
    
         two sets,then;
(a) A B and B A (b) A B (c) A B (d) B A
06. Let z be a complex number such that 5z 3z 8 2i, then arg(z) is
3 5
(a)2n + ; n I (b)2n + ; n I (c)2n + ; n I (d)2n + ;n I
4 2 4 4
07. The first negative term of the seque
      
   
   
       
1 1 3
nce 45 ,42 ,39 ,36 .........is
4 2 4
(a) 16th (b) 19th (c) 17th (d) 18th
JMP

2. JOGLEKAR MATHEMATICSPOINT /MPB-19,Mahaveer Nagar-1,KOTA/JEE(Main)/TP-1
2 -1 -1
08. If and are the roots of x + 5x 49 = 0 then the value of cot(cot + cot ) is :
(a)12 (b) 8 (c) 20 (d) 10
09. The number of ways of selecting 15 teams from 15 me
    
2
2 2
4x
y 10 2y
n and 15 women,such that
each team consists of a man and a women, is :
(a) 1120 (b) 1240 (c) 1880 (d) 1960
10. If in the expansion of (1 ) the co-efficient of T and T be equal, then the
eccentricity of the conic on which (

 
0 0
x,y) will lie is-
5 7 3 1
(a) (b) (c) (d)
2 2 2 2
11. If 0 < < and the system of equations (sin ) x + y + z =0, x +(cos )y +z =0 and
(sin )x +(cos )y +z = 0 has non-trivial solution then is equals to :
(a) 60 (b) 30 (c)
   
  
0 0
1
ij ij 22 2
90 (d) 45
i j, if i j.
12. If A a where a then A is equals to :
i 2j, if i j
0 3 0 3 0 3 0 31 1 1 1
(a) (b) (c) (d)
3 1 3 1 3 1 3 19 9 9 9
13. An unbaised dice is tossed until a number greater than 4 appear


 
      
       
               
s.What is the
probability that an even number of tosses is needed ?
2 1 3 4
(a) (b) (c) (d)
5 5 5 5
14. If in a ABC, verte A is (1,2) and int ernal angle bisec tors of B and C are y x
and y x then the perimeter of incircle of this triangle is :
(a) 10 (b) 2
   
 
1 (c)15 (d) 12
15. If the three distinct lines x 2ay a 0, x 3by b 0 and x 4ay a 0 are meet
at a common point then the point P(a,b) lies on a :
(a) circle (b) hyperbola (c) straight line (d) parabola
16.The area of the region above the x axis bou
        

 
nded by the curve y tan x,0 x and
2
the tangent to the curve at x is:
2
1 1 1 1 1 1
(a) log 2 (b) log 2 (c) 1 log 2 (d) (1 log 2)
2 2 2 2 2 2

  


   
         

3. JOGLEKAR MATHEMATICSPOINT /MPB-19,Mahaveer Nagar-1,KOTA/JEE(Main)/TP-1
2 2 2
1
2 2 2 2 2 2
2 3 1 2 3
17. If the chord of contact of tangents from a point on the circle x y r to circle
x y r touches the circle x y r then r ,r , r are in:
(a) A.P. (b) H.P. (c) G.P.
 
   
2
(d) A.G.P
18.If the focus of parabola ( y ) 4( x ) always lies between the line x y 1 0
and x y 3, then
(a)( ) (0 2) (b)( ) ( 2, 1) (c)( ) (2,4) (d)( ) (4,13)
19. The tangent at (3 3 cosθ,sinθ) where θ 0,
2
       
 
                 
 
 
       
2
2x
is drawn to ellipse + y =1 such that
27
the sum of intercepts on axes made by this tangent is minimum then the value of θ is :
a b c d
3 6 4 8
20. If , , be the angles made by a line with x, y and z axes so that
ta
2

   
  
2 2 2
2
2 2 2
0 0 0 0
n tan tan
3sec then =
1 tan 1 tan 1 tan 2
(a) 18 (b) 15 (c) 30 *(d) 60
x 5 y 7 z 2
21. A line with direction ratio 2,7, 5 is drawn to intersect the lines
3 1 1
x 3 y 3 z 6
and at P and Q respectively,then
3 2 4
    
          
  
  

  
 

2 2
length of PQ is :
(a) 78 (b) 77 (c) 54 (d) 74
22. Let Q be the foot of perpendicular drawn from origin to the plane 4x 3y z 13 0
and R be a point ( 1,1, 6) on the plane then length QR is :
7 19 3
(a) 3 (b) 14 (c) (d)
2 2 2
ˆ ˆ23.The value of |a × i| +|a × j| +
   
 
  2
2 2 2 2
ˆ|a ×k| is equals to :
(a)|a| (b) 2|a| (c) 3|a| (d) 4|a|
24. If a 2 and b 3 and a b , then (a (a (a (a b )))) is equal to :
ˆ ˆ ˆ ˆ(a) 48 b (b) 24b (c) 48a (d)24a
ˆ ˆ ˆ ˆ ˆ ˆ25.Let PR = 3i + j 2k and SQ= i 3j 4k determine
       
 
  

   
       
 
diagonals of a parallelogram PQRS
ˆ ˆ ˆand PT = i +2j 3k be another vector. Then the volume of the parallelepiped whose
coterminus edges are the vectors PT PQ PS is :
(a) 5 (b) 20 (c) 10 (d) 30


  

4. JOGLEKAR MATHEMATICSPOINT /MPB-19,Mahaveer Nagar-1,KOTA/JEE(Main)/TP-1
2
dy x 4x 9
26. If y(x) is the solution of the differential equation ,x 2 and y(0) 0,
dx (x 2)
then y( 4) is equals to:
(a) 0 (b) 1 (c) 1 (d) 2
27. Let a function g(x) be the inverse of an invertible function f(x) and f(x) is differen
 
   



3 3
3 3
tiable
for all real x, then g"(f(x)) equals to :
f "(x) f '(x)f "(x) (f '(x)) (f '(x)) f '(x)f "(x) f "(x)
(a) (b) (c) (d)
f '(x) f '(x)(f '(x)) (f '(x))
28. A function y = f(x),(xy 0) is defined parametrically as x = co
 

   2 2
2
3
3 5
s and y = sin , R .
x
and if at a point P(x, y) function has a vertical tangent, then is equal to -
y(x y)
1 1
(a) 4 (b) 2 (c) (d)
2 2
1
29. If dx cot x tan x c, then :
sin x cos x
2 2 2
(a) 2, (b) 2, (c) 2, (d)
3 3 3
   

    
                

7 3
2
7 4
2
2,
3
30. The value of tan x dx is equals to :
(a) 2log(2) (b)log(2 2) (c)log(2) (d)log(2 2)


  
