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 thehouse 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 1403. 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.LetR (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.

106. 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

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 1in 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 imx 2 y 1 z x 2 y 1 z

age of the line in the plane 2x y z 5 is1 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

JOGLEKAR MATHEMATICS POINT /MPB-19,Mahaveer Nagar-1,KOTA/JEE(Main)/TP-3

3 217. If the Rolle 's theorem holds good for function f(x) 2x bx cx in the int erval [ 1,1]

1for the po int 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

dx19. 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 ybe 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 2x 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.

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 226. 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 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 2x 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 : 2x 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