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JOGLEKAR MATHEMATICS POINT /MPB-19,Mahaveer Nagar-1,KOTA/JEE(Main)/TP-2

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

2009 2009 2008 2007 2006 3 2

2007 2008 2009 20

er Sheet.

The maximum marks are 120.

01. The value of the product

sin cos cos cos cos .....cos cos is ?2 2 2 2 2 2 2

1 1 1 1(a) (b) (c) (d)

2 2 2 2

10

02.The total number of solution of tan sin cot cos , [0, 6 ], is ?2 2

(a) 5 (b) 7 (c) 4 (d) 5

03. Let ten vertical poles standing at equal distances on a straight line, subtand equal

angles at a po int O on this line and a

ll the poles are on the same side of O.If the

height of longest pole is H and the distance of the foot of the smallest pole from O is

d then the dis tance between two consec utive poles is :

Hcos dsin Hcos dsin Hsin dcos(a) (b) (c)

9sin 9cos

1

1 2

Hsin dcos(d)

9cos 9cos

1 6304. The value of sin sin is equals to :

4 8

1 1 1 1(a) (b) (c) (d)

2 42 2 2

05. Let A : 3,8,13,.................503 and A : 6,13,20.................699 are two arithmetic

progressions then th

1 2e number of common terms of A and A are :

(a) 13 (b) 14 (c) 15 (d) 16

z -i06. The perimeter of the locus represented by arg , where 1 i is :

z+ i 4

3 3 2(a) (b) (c) (d)

2 32 2

JMP


16

1/2 k

07 There are 'n ' circles in a plane and the number of radical axes is equals to number

of radical centres then the total number of circles will be :-

(a) 5 (b) 3 (c) 6 (d)7

08.If middle term in the binomial expansion of x x is a

6 5 7 5

lso term independent of x,

then second term in the expansion is :-

(a)120x (b)120x (c)16x (d)16x

309. The chance of India winning toss is . If it wins the toss,then its chance of victory

4

4is otherwise i

5

2

1t is only .Then chance of India's victory is :

2

1 29 3 3(a) (b) (c) (d)

5 40 40 5

x 3x +2 2x 1

10. The total number of real values of 'x' for which 2x 1 4x 3x +1 = 0 is :

7x 2 17x +6 12x 1

(a) 1 (b) 2 (c) 0 (d)

cos cos sin11.Let A

2

2 2

1 2

cos cos sinand B , if AB is a null matrix

cos sin sin cos sin sin

then

(a) n ,n I (b) 2n ,n I (c)(2n 1) ,n I (d) 02

12. Let is the area of triangle made by joining mid points of its s.ides and is the

are

1

2

a of same triangle made by centroid and any two vertices,then is equals to :

(a) 3:4 (b) 4:3 (c) 3:2 (d) 2:3

13. The equation of a line passes through (1,2) and which is at a minimum distance from

the po int (3,1) is x ky 5 the valu

2 2

e of k is ;

(a) 2 (b) 3 (c) 2 (d) 3

14. If x – 7xy – y = 0, x + y = 2,are the sides of a triangle,then distance between the side

x + y = 2 and orthocenter is :

1(a) 2 (b) 3 (c) 2 (d)

2

15. If e is eccentricity of ellipse whose area is hal

f the area of its auxiliary circle then

the value of e is :

1 1 3 2(a) (b) (c) (d)

2 2 32


2 2

16. Let a relation R on a set of natural numbers N be definded as (x,y) R such that

x 4xy 3y 0 then relation R is :-

(a) symmetric. (b) transitive. (c) An equivalence. (d) reflexive.

17. The image of a point 7, 1, ,2, in line r 9

1 2

ˆ ˆ ˆ ˆ ˆ ˆi 5 j 5k ( i 3 j+5k ) is :

(a) (–9, 5, 2) (b) (9, 5, –2) (c) (9, 5, 2) (d) None

x 3 y 2 z 1 x 2 y 3 z 212. If lines whose equations are L : and L : are

2 3 k 3 2 3

coplaner and P(a ,b,c) is the po int of int ersec

1tion of L and the plane x y z 15

then a b c is :

(a) 15 (b) 10 (c) 5 (d) 7

19. A plane passing through (1,1,1) cuts positive direction of co-ordinate axes at A,B,& C

and if V is the valume of tetrahedron OABC then :

9(a) V (

2

9 7 7

b) V (c)V (d) V .2 2 2

ˆ ˆ ˆ ˆ ˆ ˆ20. Let a = 2i j 2k , b = i 2j 2k are two vectors and a vector c is along angle

bisec tor of a and c on a is 12 then c.b =

(a) 20 (b) 24 (c) 36 (d)

b. If projection of

21. If vector is perpendic

44

a ula

0

8 8 81 2 8

c ,|a| 2,| | 3,|c| 4

c 120 ,then [a c ] is equal to ;

(a) 4 3 (b) 6 3 (c) 12 3 (d) 10 3

22. If f(x) =( C x +1)( C x +1)............

r to b and b and the ang

........

le

( C x +

betwe

1), the

en

b and is b

n f '(0)=

(a) 256 (b) 255 (c) 102

cosx sinx

cosx sinx cosx cos x

2 2

2 2

4 (d)1023

23. The value of (sin x) (cos x cot x log (sin x) ) dx is equals to ;

(a) cosx +c (b) cos +c (c) sinx c (d) log x c

x y24. If it is possible to draw the tangent to the hyperbola 1 havi

a b

2

3

2

ng slope 2

and if 'e ' is its eccentricity then the range of 'e ' is :

(a) 1 e 5 (b ) 5 e 5 (c) 0 e 5 (d) 1 e 5

25. If f(x) is an even function then (x f(x) x f "(x) 2)dx is equals to :

(a) 8 (b) 0 (c) 4 (d) 2


2 2 4 4

2

26. If (x + y )dy = xy dx and y(1)=1, y( )=e and if = k e then k is equals to :

(a) 7 (b) 3 (c) 5 (d) 9

27.Consider the following statements :

(i). The function f(x) x 2cos x is increa sing in the int erval (0, ).

(ii).The function

2f(x) In( 1 x x) is decra sing in the int erval ( , ).

Which of the above statments is/are correct ?

(a) (i) only (b) (ii) only (c) both(i)and(ii) (d) Neither (i)nor (ii)

28. Let a and b be two unit vectors suchthat a b 3 . If c a 2b 3

2

2 2

a b , then

c is equals to:

55 51 43 37(a) (b) (c) (d)

2 2 2 2

29. Statement 1:Graphof y x x 1 lies above x axis for all real valuesof x.

Statement 2: Let y ax bx c,a,b,c R if a 0 and b 4ac 0,then y 0 x.

(a)Statement 1 is true,Stateme

nt 2is true,Statement 2 is acorrect exp lanation for

Statement 1.

(b)Statement 1 is true,Statement 2 is true,Statement 2 is not a correct exp lanation

for Statement 1.

(c)Statement 1 is true,Statement 2 is false.

(d)Statement

1

12

2

1 2

1 is false,Statement 2 is true.

30. Statement -1:- If the perpendicular tangents to circle C meet at P, then the locus

redius of C 1 of P has a circle C , then .

redius of C 2

Statement-2: Circles C and C are co

ncentric.

(a) Statement 1 is true,Statement 2 is true,Statement 2 is a correct exp lanation

for Statement 1.

(b) Statement 1 is true,Statement 2 is true,Statement 2 is not a correct exp lanation

for Statement 1.

(c) Statement 1 is

true,Statement 2 is false.

(d) Statement 1 is false,Statement 2 is true.

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