This document provides information about a mathematics test from Joglekar Mathematics Point in Kota, India. It includes 30 questions for the JEE Main exam with instructions. Each question is worth 4 marks for a correct response and there is a 1 mark deduction for an incorrect response. The maximum total marks for the test are 120. The document then lists the 30 questions and possible multiple choice answers for each.

1. JOGLEKAR MATHEMATICS POINT /MPB-19,Mahaveer Nagar-1,KOTA/JEE(Main)/TP-5
There are 30 questions,Each question is allotted 4 m
t

MPB -19,Mahaveer Nagar -1,Main Road Kota. 8769855992,8387919366
(JEE(Main))
Important Instructions
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.
x x x x x
01.The value of sin cos cos cos cos is equal to :
16 2 4 8 16
sin x sin x sin x
(a) (b) (c) (d) 8cos x
4 8 16
02. Total number of integral values of n so that sinx(sinx +cosx) = n has a soluti


100 100
1 2 3 n 2n 2n 1
n 1 n 1
on
(a) 1 (b) 2 (c) 0 (d)3
03.Let a ,a ,a ,..,a are positive terms of a G. P. such that a and a
and , then the common ratio of this G. P. is :
(a) (b) (c) (d)
04. If the argument of ( z 2) (z 1) is eq

 
   
  
   
   
 
 

9
th
1/3
( 3 i)(i 3 1)
ual to argument of then the locus
(1 i)
of z is a circle with centre at (a,b), where a +b is equal to
(a) 2 (b) 4 (c) 1 (d) 6
3
05. If 7 term from beginning in the binomial expansion 3 ln x ,x 0
84
 

 
   
2
3 2
1 1
1
is 729,
then the product of possible values of x is :-
(a) e (b) e (c) 1 (d) 2e
06. A relation R is defined on the set R of real numbers as follows : (x,y) R x = x y,
then relation R is-
(a) symmetric. (b) tr
 
2
ansitive. (c) reflexive. (d) Bothreflexive & transitive
c
07. If , are the roots of x 4x 0 , c 0 such that 1 2 3 ,then the
4
number of int eger value of c is :
(a) 12 (b) 3 (c) 11 (d) 9
          
JMP

2. JOGLEKAR MATHEMATICS POINT /MPB-19,Mahaveer Nagar-1,KOTA/JEE(Main)/TP-5
 
 
2 22
2 2
2 2
(x 2) 5x 2x3x
08. Let A= 1 ,B =[a b c] and C= 5x 2x (x 2) a,b, c,x R be three given
6x 2x (x 2) 5x
matrices and Tr(AB) = Tr(C) x R, where Tr(A) denotes trace of A. then (a +b+c)=
(a) 5 (b) 7 (c)
  
  
   
       
 
 
2 (d) 4
x y
09.Through the point P , , where 0 the straight line 1 is drawn so as
a b
to form with coordinate axes a triangle of area . if ab > 0, then least value of is :
1
(a) (b) 2 (c) 4 (d)
2
10. If
     
 
   
2 2
a variable line y = kx + 2h is tangent to an ellipse 2x + 3y = 6, then locus of P(h, k)
is a conic whose eccentricity equals to :-
7 7 7
(a) (b) (c) 1 (d)
2 3 3
11. In ABC if A (2,3,5),B ( 1,3,2) and C ( ,5, ). If the m       edian through A is equally
inclined to the axes then:
(a) 5 (b) 5, 7 (c) 7, 10 (d) 0, 0
x 2 y 3 z 4 x 2 y 3 z 4
12. Consider the lines and The distance of the
1 2 5 1 2 5
point (1,1,1) from the plane passing throug
               
     
   
 
2
h the point ( 1, 2, 1)and whose normal
is perpendicular to both the lines is
3 3 3 2 2 3
(a) (b) (c) (d)
26 2 3
13. A chord is drawn through focus of the parabola y 6x such that its dis tance from
5
the vertex of the parabola is ,the
2
  

n its slope can be ?
3 5 2 2
(a) (b) (c) (d)
2 2 3 5
14. In a triangle ABC, right angled at the vertex A, if the position vectors of A, B and C are
ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ3 i + j k , i +3j+pk, 5i +qj 4k respectively then the point (p,q) lies o   n a line :
(a) parallel to y-axis. (b)making an acute angle with the positive direction of x -axis.
(c) parallel to x-axis. (d)making an obtuse angle with the position direction of x-axis.
ˆ ˆIf lines r ( j15. i 

       ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ+k) (1 p)i 3j 2k =0 & r (3i j 5 k) (3 p)i 4j 8 k =0 are
coplanar then p is equal to
3 4 1 2
(a) (b) (c) (d)
4 3 3 3
          
 

3. JOGLEKAR MATHEMATICS POINT /MPB-19,Mahaveer Nagar-1,KOTA/JEE(Main)/TP-5
x
1
16. If the volume of the parallelopiped with coterminal edges i+a j+k , j+a k , a i +k
is minimum, then a =
1 1
(a) 3 (b) (c) (d) 3
33
log t 1
17. Let f(x) dt, x 0 then the value of f(x) f is equals to :
1 t x
(a) log x
      
 
     
2 2 2
1 2 4 2 12
2
2
(log x) log(x) (log x)
(b) (c) (d)
2 4 4
dx 1
18. Let sin (k sin x) c then (1 +k )(1 + k )(1 + k + k ) is equal to :
k1 tan x
(a) 1005 (b) 2012 (c) 2011 (d) 2010
19. The area of the region described by A={ (x,y)|y x 5x+

 

 

4,x+y 1, y 0 } is :
7 13 17 19
(a) sq.units (b) sq.units (c) sq.units (d) sq.units
2 2 2 2
20. An ellipse is inscribed in a circle and a point within the circle is chosen at random.
If the probability that this point lies o
 
2
2
utside the ellipse is then the eccentricity
3
of the ellipse is :
2 2 2 1 2
(a) (b) (c) (d)
3 3 3 3
21. The equation of the curve passing through (3,4)& satisfying the differential equation,
dy dy
y (x y) x
dx dx
 
     
2 2 2 2
0 can be :
(a) x y+1=0 (b) x + y =25 (c) x +y 5x -10 = 0 (d) x + y 7 = 0
22. The dimensions of a rectangle are continuously changing. The width increases at rate
of 3 inch/sec. while the length decreas
  
2 2 2 2
es at rate of 2 inch/sec. At one instant if the
each side of rectangle is 20 inch, then the rate of change of area after 3 seconds is :
(a) 32 inch /sec (b) 32 inch /sec (c) 16 inch /sec (d) 16 inch /sec
23. If f(
 
2 2 2 2
x) sin(sin x) and f "(x) tan x f '(x) g(x) 0 then g(x) is :
*(a)cos x sin(sin x) (b) cos x cos(sin x) (c) sin x cos(cos x) (d)sin x sin(cos x)
24. Let f(x) is an odd function defined on R such that f(1) 2,f(3) 5 and f( 5) 1.
f
then the value of
   
    
(f(f( 3))) f(f(0))
is :
3f(1) 2f(3) f(5)
2 2 2 2
(a) (b) (c) (d)
3 5 5 3
 

 
 

4. JOGLEKAR MATHEMATICS POINT /MPB-19,Mahaveer Nagar-1,KOTA/JEE(Main)/TP-5
2 2 2 2 2 2 2 2
25. Let P (a,b) is a point inthe first quadrant.If the two circles which passes through P
and touch both the coordinates axes cut at right angles,then :
(a) a 6ab b 0 (b) a 2ab b 0 (c) a 4ab b 0 (d) a 8ab b 0
26. Let LL ' be the latu

           
2 2
2 2
x y
s rectum through the focus of the hyperbola 1 and A ' be
a b
the farther vertex . If A 'LL ' is equilatral,then the eccentricity of the hyperbola is:
( consider axes are the hyperbola are coordinate axes )
( 3 1) ( 3 1
(a) 3 (b) 3 1 (c) (d)
2
 

 

1 2 1 2 3 k
1 1 2 3 k 2
)
3
27. Two straight lines L and L are intersects at a point A,points P ,P ,P ............P .are
taken on L and points Q ,Q ,Q ............Q are taken on L ,if point A is not used
then total number of triangles that be made using these p
2 2 2 2
oints as vertices is ;
(a) k(k 1) (b)k(k 1) (c) k (k 1) (d) k (k 1)
28. Let A(3, 4),B(1,2) are two points and let P(2k 1,2k 1) be a var iable point such
that PA PB is the minimum, then the value of k is :
7 7
(a) (b) 0 (c) (d)1
9 8
29. State
   
  
 
2 2
2
2 2
32 2
2 2
d y d x
ment-1: - Let f :[0, ) [0, ) be defined by y = f(x) = x ,then =1
dx dy
d y d x dy
Statement-2 : - = .
dxdx dy
(a) Statement 1 is true,Statement 2is true,Statement 2 is acorrect exp lanationfor
Stat
   
         
 
   
  
2
ement 1.
(b) Statement 1 is true,Statement 2is true,Statement 2 is not a correct exp lanation
for Statement 1
(c) Statement 1 is true,Statement 2is false
(d) Statement 1 is false,Statement 2 is true
x
30. Statement 1: Hyperbola

  

 
 

2
2 2
y
1 0 is known as a central curve.
a b
Statement 2: Every chord passing through its centre gets bisec ted.
(a) Statement 1 is true,Statement 2is true,Statement 2 is acorrect exp lanationfor
Statement 1.
(b) Statement 1 is true,S
  

  

 tatement 2is true,Statement 2 is not a correct exp lanation
for Statement 1
(c) Statement 1 is true,Statement 2is false
(d) Statement 1 is false,Statement 2 is true
 

 
 