This document provides 30 multiple choice questions for a JEE mathematics exam. It includes instructions that there are 4 marks for each correct answer, a deduction of 1 mark for incorrect answers, and no deduction for unanswered questions. The maximum total marks are 120. The questions cover topics in trigonometry, coordinate geometry, calculus, matrices and other areas of mathematics.

1. JOGLEKAR MATHEMATICS POINT /MPB-19,Mahaveer Nagar-1,KOTA/JEE(Main)/TP-3
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.
01.The number of values of satisfying the equation cot 1 cot for ( 6,3) is;
2
(a) 1 (b) 2 (c) 5 (d) 4
02. From a window h meter high above the ground,ina street,the angles of elevatio

 
        
n and
depression of the top and the foot of another house exactly opposite t o the window in
the same street are and respectively.Then the height of the house onthe opposite
side is :
(a) h(1 tan cot ) (b) h(1 tan cos ) (c) h(1 cot tan ) (
 
        
1 1
0
d) h(1 cot cos )
1 1 14
03. If tan cos tan cos is equal to , then is equal to :
4 2 4 2
2
(a) (b) (c) (d)
2 14 7 7
04. If 11 90 , then tan tan2 tan3 ..............tan10 is equal to :
(a) 0 (b) 1 (c) 1 (d) 2
05.Let R (3,
 
  
    
            
   
     

   3),(5,5),(9,9),(12,12),(5,12),(3,9),(3,12),(3,5) be a relationon setA 3,5,9,12
then R is ;
(a) Reflexive and transitive. (b) Symmetric,transitive but not reflexive.
(c) An equivalence relation. (d) Reflexive,symmetric but no


2 3
t transitive.
1
06. Let 3cos 5cos 7cos ................ then the value of cos is equals to ;
2
(a) 2 5 (b) 2 5 (c) 2 7 (d) 2 7
07. If the mean deviation of numbers 1,(1 d),.......,(1 100d) from their mean is 255,
then a value of d
         
     
 
is :
(a) 10 (b) 20.2 (c) 5.05 (d) 10.1
JMP

2. JOGLEKAR MATHEMATICS POINT /MPB-19,Mahaveer Nagar-1,KOTA/JEE(Main)/TP-3
1 2 3 3 1 2 1 2
2 r r
r 1
08.Let z ,z ,z are three complex number satisfying |z|=1and 4z = 3(z +z ),then|z z |=
2 3 5 2 5
(a) (b) (c) (d)
3 2 3 3
09. Let( , ) are the roots of the equation 12x 5x 1,and thenthe value of ( )
is equals to:
7
(a) (b)
6



      
5 11 1
(c) (d)
6 6 6
10. A 8 digit numbers are formed using the digits 1,1,2,2,2,3,4,4.The number of such
numbers in which the odd digits donot occupy odd places, is:
(a) 160 (b) 120 (c) 60 (d) 48
11. The probability of Virat to become man of the match in first three matchs of india
3 2 1
in T20 world cup 2016 are , and respectively. If virat gets match of the match
7 7 7
in exactly one match,then the probability that he will it in 3rd match, is :
10 10 10 10
(a) (b) (c) (d)
79 79 79 79
12. The sides o
2
f a triangle are 8 and 6 and is angle between them.If these sides varies
such that (0°90°), If c is the length of third side then c varies as :
(a) 2<c< 1 (b) 0<c<10 (c) 2<c< 10 (d) 0< c<14
13. Let AB is focal chord of x 2

 
 x y 2 whose focus is ‘S’. If AS k then BS =
4k k 2k
(a) (b) (c) (d)None of these
4k 1 4k 1 4k 1
14. The area of the triangle inscribed in an ellipse bears the ratio 5:3 to
  
  
the area of
the triangle formed by joining the points on the auxilliary circle corresponding to
the vertices of the first triangle, then the eccentricity of the ellipse is :
5 2 1 3
(a) (b) (c) (d)
3 3 4 5
15. Let im
x 2 y 1 z x 2 y 1 z
age of the line in the plane 2x y z 5 is
1 2 3 a b c
then a b c is equals to :
(a) 10 (b) 7 (c) 11 (d) 12
16. The distance of the origin from the line contained by the planes 2
   
      
 
x 2y z 2 and
x + 2y 2z 4 0, is :
2 3 3 5 2 5
(a) (b) 5 (c) (d)
5 2 3
  
  

3. JOGLEKAR MATHEMATICS POINT /MPB-19,Mahaveer Nagar-1,KOTA/JEE(Main)/TP-3
3 2
17. If the Rolle's theorem holds good for function f(x) 2x bx cx inthe int erval [ 1,1]
1
for the point x ,then the value of 2b c is :
2
(a) 2 (b) 2 (c) 1 (d) 1
18. The minimum area of a triangle formed by any tangent to the ellipse
   
 
 
2 2
A B
3
x y
+ =1 and
16 81
the coordinate axes is :
(a) 12sq. units (b)18sq. units (c) 26sq. units (d) 36sq. units
dx
19. Let =(tan x) C(tan x) k, then A + B + C is equals to :
cos x 2sin2x
16 21 7 27
(a) (b) (c) (d)
5 5 5 10
20. If f(x) [|x|],
 


100
0
thenthe value of f(x) dx is ([.] denotes greatest integer function) :
(a) 4950 (b) 4000 (c) 1000 (d) 4590
21. A curve passes through the point 1, . Let the solpe of the curve at each point (x,y)
6
y y
be sec
x x
 
  



,x 0.Then the equation of the curve is ;
y 1 y 2y 2y 1
(a)sin log x (b)cos ec log x 2 (c)s ec log x 2 (d)cos log x
x 2 x x x 2
22. The area bounded by the curve y n(x), x 0 and the lines y 0, y n(3) and
and x

  
       
                     
   l l
0 is equal :
(a) 3 n(3) 2 (b) 3 (c) 2 (d) 3 n(3) 2
23. In ABC,vertex A is (1,2). If the internal angle bisector of B is 2 x y 10 0 and
the perpendicular bisec tor of AC is y x ,then the equation of BC is ?
(a) 5 x 9 y 15 0. (b)5 x 9 y 11 0. (c)5 x 9

 
    

      
l l
2 50
y 17 0. (d)5 x 9 y 19
24. If B is a 3 3 matrix such that B O, then det. (I B) 50B is ;
(a) 2 (b)1 (c) 3 (d) 50
25. Let k = ab (a b) ab (a b) a b (a b) ab ................. (a > b> 0) are two real
numbers, the value of k is :
(a)
   
     
       
Independent of b. (b) Independent of a.
(c) Independent of both a & b. (d) Dependent on both a & b.

4. JOGLEKAR MATHEMATICS POINT /MPB-19,Mahaveer Nagar-1,KOTA/JEE(Main)/TP-3
1 2
1
2 2 2
2 2 2
2
x 3 y 2 z 1 x 2 y 3 z 2
26. 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 tion of L and the plane x y z 15
then a b c is :
(a) 15 (b) 10 (c) 5 (d) 7
a b c
27. If (a ) (b ) (c )
(a ) (b
     
   
  
 
     
 
2 2 2
2 2
2 2
2
a b c
k a b c ( 0) then k
) (c ) 1 1 1
(a) 4 abc (b) 4 (c) 4 (d) 4 abc
ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ28. If the lines r i j k ( i 2j) and r i j 3k ( j 2k)are int ersec t each other
then the quadratic equation w
2
hose roots are ( , ) is ;
(a) x 2
    
   
     
         
 

 
 
2 2 2
x 2 0 (b)x 2x 2 0 (c) x 2x 2 0 (d) x 2x 2 0
ˆ ˆ ˆ ˆ ˆ29. If a and b are two vectors such that a. a j k if a = i j k , thenthe
vector b is ;
ˆ ˆ ˆ ˆ ˆ ˆ ˆ(a) j k (b) i j k (c) i (d) j
30.Statement 1: The only circle having rad
b 1 and b
     

    
   
 



    


2 2
2 2
ius 10 and a diameter along the line
2x y 5 is x y 6x 2y 0.
Statement 2 : 2 x y 5 is a normal to the circle x y 6x 2y 0.
(a) Statement 1 is false,Statement 2 is true.
(b) Statement 1 is true,Statement 2 is false.
(c) Statement 1 is t
     
      
 
 
 rue,Statement 2 is true,Statement 2 is not a correct exp lanation
for Statement 1
(d) Statement 1 is true,Statement 2 is true. Statement 2 is a correct exp lanation
for Statement 1
 

  
