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 x01.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

305. If 7 term from beginning in the binomial expansion 3 ln x ,x 0

84

2

3 21 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

c07. 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

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 y09.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 412. 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

5the 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 +3 j+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 3 j 2k =0 & r (3i j 5k) (3 p)i 4 j 8k =0 are

coplanar then p is equal to

3 4 1 2(a) (b) (c) (d)

4 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 117. 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 118. 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

2utside 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 dyy (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.

fthen 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

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 po int in the 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 ys 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

o ints 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 po ints and let P(2k 1,2k 1) be a var iable po int such

that PA PB is themin imum, then the value of k is :

7 7(a) (b) 0 (c) (d)1

9 8

29. State

2 22

2 2

32 2

2 2

d y d xment -1 : - Let f : [0, ) [0, ) be defined by y = f(x) = x ,then =1

dx dy

d y d x dyStatement -2 : - = .

dxdx dy

(a) Statement 1 is true,Statement 2is true,Statement 2 is acorrect exp lanation for

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

x30. Statement 1: Hyperbola

2

2 2

y1 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 lanation for

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