8/10/2019 JEE Main Maths Practice Paper

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PRACTICE PAPER FOR JEE MAIN

1. 49n + 16n 1 is divisible by(a) 3

(b) 29

(c) 19

(d) 64 [ Ans. d]

2. The equation of the circle passing through (1,1) and the points of inter-section of x2 +y2 + 13x 3y = 0 and 2x2 + 2y2 + 4x 7y 25 = 0is

(a) 4x2 + 4y2

30x

10y= 25

(b) 4x2 + 4y2 + 30x 13y 25 = 0(c) 4x2 + 4y2 17x 10y+ 25 = 0(d) none of these

3. If z1 and z2 are two non zero complex numbers such that|z1 +z2| =|z1| + |z2| then arg(z1) -arg(z2) is equal to

(a)(b)

2

(c) 2

(d) 0 [ Ans. d ]

4. An equilateral triangle is inscribed in the parabolay2 = 4ax, such thatone vertex of this triangle coincides with the vertex of the parabola.Sidelength of this triangle is

(a) 4a

3

(b) 6a

3

(c) 2a

3

(d) 8a

3 [ Ans. d]

5. The normal at (a,2a) meet the curve again at (at2, 2at) then the value oft equals

(a) 1

(b) 2

(c) 3

(d) -3 [ Ans. d ]

6. If the distance between the foci and distance between the two directricesof the hyperbola x

2

a2 y2

b2= 1 are in the ration 3 : 2 then find the ratio b:a

(a) 1 :

2

(b) 1 :

3

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8/10/2019 JEE Main Maths Practice Paper

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(c) 2 :

3

(d) 1 : 5 [ Ans. a ]7. The value of limx0

1

2(1cos2x)

x

(a) 1

(b) -1

(c) 0

(d) none of these

8. The number of ways in which a mixed double game can be arrangedamongst 9 married couples if no husband and wife play in the same gameis

(a) 756

(b) 1512

(c) 3024

(d) none of these

9. If a,b,c,d are rational and are in G.P then the roots of the equation :(a c)2x2 + (b c)2x+ (b d)2 (a d)2 = 0 are necessarily :

(a) imaginary

(b) irrational

(c) rational

(d) real and equal

10. If the roots of the equationax2 + bx + c= 0 be , then the roots of theequationcx2 +bx+a = 0 is

(a),(b) , 1

(c) 1, 1

(d) none of these [ Ans. c]

11. The point on the axis of x, whose perpendicular disntance from the straightline x

a+ y

b= 1 is a , are

(a) ba

(a

a2 +b2, 0)

(b) (ab (ba2 +b2), 0)(c) a

b(a+b, 0)

(d) ab

(aa2 +b2, 0) [ Ans. b ]12. The set of all x in (, ) satisfying|4sinx 1| < 5 is given by

(a) ( 10 , 710 )(b) ( 10 ,

710 )

(c) ( 10 , 310 )(d) (

7, 310

) [ Ans. c ]

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