09 p.t (straight line + circle) eng

MATHEMATICS /PT # 09 E-1/4
JEE(Main+Advanced)2021
LEADER+ENTHUSIAST COURSE
PRACTICE TEST FOR JEE-ADVANCED # 09 (Straight line + Circle) MATHEMATICS
TIME : 60 MIN. M.M. : 71
SECTION–I(i)
Straight Objective Type (3 Marks each, –1 for wrong answer)
1. Perpendicular distance of point A(a, a2
) from the line x + y + 3 = 0 is 2 2 then total number of possible
value(s) of a if point A lies in 1st
quadrant is :-
(A) 0 (B) 1 (C) 2 (D) infinite
2. Let L1
and L2
are any two lines belonging to family (a + 3b)x + (2a – b)y = (5a + b), where a and b are
parameters. If one bisector of angle between L1
and L2
is 3x – 4y + 5 = 0, then equation of other bisector
is :-
(A) 4x + 3y = 5 (B) 4x + 3y = 10 (C) 4x + 3y = 15 (D) 4x + 3y = 20
3. Number of integral points (g, ƒ) (an integral point is a point both of whose co-ordinates are integers) for
which the area common to the circle x
2
+ y
2
+ 2g
2
x + 2ƒ
2
y + c = 0 & its image in the line x+y+1= 0 is
maximum is -
(A) 1 (B) 2 (C) 3 (D) 4
4. If the family of curves ax2
+ 2hxy + by2
= 0 always passes through (1, 1), then the line ax + by = h always
passes through a fixed point given by :-
(A)
1 1
,
2 2
æ ö
ç ÷
è ø
(B)
1 1
,
2 2
æ ö
- -
ç ÷
è ø
(C) (1, 1) (D) (2, 2)
5. Consider the family of lines (x – y – 6) – l(2x + y + 3) = 0 and (x + 2y – 4) –m(3x – 2y – 4) = 0. If the
lines of these 2 families are at right angle to each other than the locus of their point of intersection is
(A) 2 2
x y 3x 4y 3 0
+ - + - = (B) 2 2
x y 4x 3y 3 0
+ + - - =
(C) 2 2
x y 2x 4y 3 0
+ + - - = (D) 2 2
x y 4x 3y 3 0
+ - + + =
SECTION–I(ii)
Multiple Correct Answer Type (4 Marks each, –1 for wrong answer)
6. If z1, z2, z3 are thevertices of an equilateral triangle with centroid at origin & length of circum radius of
triangle is 1 unit. Then which of the following may be the vertices of an equilateral triangle -
(A) –z1, –z2, –z3 (B) (z1 + |z2|), (z2 + |z3|), (z3 + |z1|)
(C)
2 3 3 1
1 2 (z z ) (z z )
(z z )
, ,
2 2 2
+ +
+
(D)
3
1 2
1 2 3
z
z z
, ,
2 | z | 2| z | 2 | z |
Space for Rough Work
JEE(Main + Advanced) 2021
LEADER + ENTHUSIAST COURSE
NAME : .....................................................................................................................................................

E-2/4 MATHEMATICS /PT # 09
7. Let a family of straight lines is given as ax + by + c = 0, where 2a + 3b + c = 0. Then the line which
belong to the given family & is tangent to the parabola y2
= 4x is/are -
(A) y = x + 1 (B) 3y = 9x + 1 (C) 3y = x + 3 (D) 2y = x + 4
8. Let ƒ (x) = x4 +
3
kx
3
+ 2x2 + kx – k + 1, then which of following is/are correct -
(A) If ƒ (x) is increasing in (0, 2) then k ³ 0 (B) If ƒ (x) is decreasing in (0, 2) then k £ –8
(C) If ƒ (x) is increasing in (–2, 2) then k ³ 8 (D) If ƒ (x) is decreasing in (–2, 2) then k £ –8
SECTION–I(iii)
Linked Comprehension Type (Single Correct Answer Type) (3 Marks each, –1 for wrong answer)
Paragraph for Question 9 to 10
Let Ci(i Î {1,2,3,4}) are four circles of unit radius touching both co-ordinate axes in different quadrants
and each have exactly one common point with the circle C with largest possible radius, then-
9. If a point is selected at random inside the circle C, then the probability that point also lies inside any of
the circle Ci, is-
(A) 3 2 2
- (B) ( )
4 3 2 2
- (C) 2 2 2
- (D) 8 2 11
-
10. Length of latusrectum of hyperbola centered at origin and passing through points of contact of C and Ci
is (given that eccentricity of hyperbola is 3 )-
(A) 2 1
+ (B) ( )
2 2 1
+ (C) ( )
2 2 1
+ (D) ( )
2 2 2 1
+
Consider two circles S1 & S2 given by x4 + y4 + 2x2y2 – 10x2 + 6y2 + 9 = 0.
On the basis of above information answer the following :
11. If (x1,y1) moves on S1 & (x2,y2) moves on S2, then maximum value of (x1 – x2)2 + (y1 – y2)2 is
equal to-
(A) 1 (B) 4 (C) 16 (D) 36
12. Angle between the pair of tangents drawn from (0,0) to S1 is equal to-
(A) 30° (B) 60° (C) 90° (D) 45°
13. Number of circles touching S1 & S2 is equal to-
(A) 2 (B) 4 (C) 6 (D) infinite

MATHEMATICS /PT # 09 E-3/4
Consider a parabola y
2
= 4x. Image of the focus of given parabola in any tangent L of parabola is centre
of a circle C which also touches the line L.
On the basis of above information, answer the following questions :
14. Locus of centre of circle C is -
(A) (x – 1)
2
+ y
2
= 1 (B) x = 0 (C) (x – 2)
2
+ y
2
= 1 (D) x = –1
15. If y = 3x 4 3 3
+ + is tangent of circle C then radius of circle C is -
(A) 3 (B) 2 (C) 3 (D) 4
16. If radius of circle C is equal to latus rectum of given parabola, then slope of common tangent L can be -
(A)
1
17
(B)
1
4
(C)
1
15
(D)
1
13
SECTION–III(i)
Numerical Grid Type (Single digit Ranging from 0 to 9) (4 Marks each, –1 for wrong answer)
1. Let
1
n 2
n
0
I x 1 x dx
= -
ò , then n
n
n 2
I
lim
I
®¥
-
is equal to, (n Î N)
2. A circle having radius N passing through intersection points of circle S : x2 + y2 + 2x – 4y – 4 = 0 &
line L : 2x – 3y = 0 whose centre is at minimum distance from point (–5,8) then the value of
N
31
is
3. Normal at B to the circle x2
+ y2
= 5 intersects it again at C. If a line through C intersecting the circle
At D meet the tangent to it at B at A(3,1) then length of CD is

E-4/4 MATHEMATICS /PT # 09
SECTION–IV
Matrix Match Type (One or More than one option correct)
For each entry in Column-I , +2 If only the bubble(s) corresponding to all the correct matche(es) is
(are) darkened, 0 In none of the bubbles is darkened, –1 In all other cases
1. Column-I Column-II
(A) Number of zeroes at the end of
29
n 5
n!
=
Õ is equal to (P) 30
(B) If the area bounded by the curve y + x
2
y – |x| = 0 (Q) 60
between x = n & x =–n is A(n) then
( )
1
A n A
n
n
n n
æ ö
- ç ÷
è ø
l may be equal to (where n Î N)
(C) If ƒ(x) and g(x) are two functions such that ƒ 2
(x)g(x) = 2 and (R) 80
2 2
3
4ƒ''(x)
g''(x) (g'(x)) (ƒ(x))
(ƒ(x)) 4
l
= - + , then l is a divisor of
(D) If the circles x2 + y2 + 2ax + 2by + c = 0 and (S) 120
x2 + y2 + 2bx + 2ay + c = 0 has exactly one point common,
then the value of
2
(a b)
2c
+
is (T) 1
PRACTICE TEST FOR JEE-ADVANCED # 08 (Function, I.T.F, LCD, MOD) MATHEMATICS
Q. 1 2 3 4 5 6 7 8 9 10
A. B C B C D D D B A,B,C,D B,D
Q. 11 12 13 14 15
A. A,C A,B,C B,C,D A,B,C,D A,B,C,D
Q. 1 2
A. 512 003
Q. 1 2 3
A. 3 3 5
SECTION-I
SECTION-III
SECTION-II

09 p.t (straight line + circle) eng

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09 p.t (straight line + circle) eng