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.

3 101. 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

6sec 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 3nce 45 ,42 ,39 ,36 .........is

4 2 4

(a) 16th (b) 19th (c) 17th (d) 18th

JMP

JOGLEKAR MATHEMATICSPOINT /MPB-19,Mahaveer Nagar-1,KOTA/JEE(Main)/TP-1

2 -1 -108. 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 15me

2

2 24x

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

1ij 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 po int then the po int 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 and2

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

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

22x

is drawn to ellipse + y =1 such that27

the sum of intercepts on axes made by this tangent is minimum then the value of θ is :

a b c d3 6 4 8

20. If , , be the angles made by a line with x, y and z axes so that

ta2

2 2 22

2 2 2

0 0 0 0

n tan tan3sec then =

1 tan 1 tan 1 tan 2

(a) 18 (b) 15 (c) 30 *(d) 60

x 5 y 7 z 221. A line with direction ratio 2,7, 5 is drawn to intersect the lines

3 1 1

x 3 y 3 z 6and 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 po int ( 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) 48b (b) 24b (c) 48a (d)24a

ˆ ˆ ˆ ˆ ˆ ˆ25.Let PR = 3i + j 2k and SQ= i 3 j 4k determine

diagonals of a parallelogram PQRS

ˆ ˆ ˆ and 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

JOGLEKAR MATHEMATICSPOINT /MPB-19,Mahaveer Nagar-1,KOTA/JEE(Main)/TP-1

2dy x 4x 926. 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

129. 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

22,

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)