SPACE FOR ROUGH WORK

PART-A[SINGLE CORRECT CHOICE TYPE]

Q.3 Line L, perpendicular to the line with equation y = 3x – 5, contains the point (1, 4). The x-interceptof L, is(A) 12 (B) 13 (C) 14 (D) 15

Q.4 Locus of the point of intersection of the pair of perpendicular tangents to the circlesx2 + y2 = 1 and x2 + y2 = 7 is the director circle of the circle with radius.

(A) 2 (B) 2 (C) 22 (D) 4

Q.5 LetABC be an equilateral triangle and let D be a point on its circumcircle. If a, b, c denote the distance

of D from the verticesA, B, C respectivelythen the value of the product cbabacacb

equals

(A) 0 (B)8

abc(C)

6

abc3cba 333 (D) None

ANS : B

ANS : B

ANS : A

Q.6 The line x + 3y 2 = 0 bisects the angle between a pair of straight lines of which one has equationx 7y + 5 = 0 . The equation of the other line is :(A) 3x + 3y 1 = 0 (B) x 3y + 2 = 0 (C) 5x + 5y 3 = 0 (D) none ANS : C

Q.5 If variable line 9ax + 4by = 5 (a, b > 0) always passing through (1, 1), then the maximum value

of b2a3 is equal to

(A) 5 (B) 10 (C) 13 (D) 15 ANS : B

[PARAGRAPH TYPE]

Q.7 to Q.9 has four choices (A), (B), (C), (D) out of which ONLY ONE is correct.

Paragraph for question no. 7 to 9Let L1, L2 and L3 be the lengths of tangents drawn from a point P (h, k) to the circles x2 + y2 = 4,x2 + y2 – 4x = 0 and x2 + y2 – 4y = 0 respectively. If L1

4 = L22 L3

2 + 16 then locus of P arethe curves, C1 (straight line) and C2 (circle).

Q.7 Straight line which intersects both the curves C1 and C2 orthogonally, is(A) x + y = 0 (B) x – y – 2 = 0 (C) x + y + 2 = 0 (D) x – y = 0

Q.8 Circumcentre of the triangle formed byC1 and two other lines which are at an angle of 45° with C1 andtangent to the circle C2, is(A) (1, 1) (B) (0, 0) (C) (–1, –1) (D) (2, 2)

Q.9 If S1, S2 and S3 are three circles congruent to C2 and touches both the curves C1 and C2, then the areaof triangle formed by joining centres of the circles S1, S2 and S3, is(A) 2 (B) 4 (C) 8 (D) 16

ANS : D

ANS : B

ANS : C

[PARAGRAPH TYPE]

Q.6 to Q.8 has four choices (A), (B), (C), (D) out of which ONLY ONE is correct.

Paragraph for question nos. 6 to 8Consider the family of circles S = 0 which passes through points A(3, 7) and B(6, 5).A lso, let C : x2 + y2 – 4x – 6y – 3 = 0 be another circle.

Q.6 The member of family of circles S = 0 which cuts chord of maximum length on the given circle C isx2 + y2 + 2gx + 2fy + c = 0, then (2g + c – f ) is equal to(A) 1 (B) 0 (C) –1 (D) –3

Q.7 If the member of family of circles S = 0 whose centre lies on line y = x, cuts intercept of length Lon x-axis, then L is equal to

(A)2

11(B) 11 (C) 9 (D)

2

9

ANS : B

ANS : D

Q.12 If the point P(2a + 1, a – 1) is an interior point of the smaller segment of the circlex2 + y2 – 2x – 4y = 4 made by the chord x + y– 2 = 0, then set of values of a is contained in or equal to

(A)

2

1,0 (B)

2

1,0 (C)

4

3,0 (D)

3

2,

3

1

Q.13 In a triangleABC, if a = 4, b = 8 and C = 60°, then which of the following relations is(are) correct?

[Note: All symbols used have usual meaning in triangleABC.]

(A) The area of triangleABC is 38 . (B) The value of Asin2 = 2.

(C) Inradius of triangleABC is33

34

. (D)ThelengthofinternalanglebisectorofangleCis

3

8.

ANS BC

ANS AB

[MULTIPLE CORRECT CHOICE TYPE]

Q.13 The equation of the line L is 3x + 4y = 12. If a line M whose equation is 3x + 4y + k = 0 is 2 units fromL, then the possible value of k is(A) 2 (B) – 22 (C) – 2 (D) 22

ANS : BC

Q.9 If (1, 2) is the centroid of an equilateral triangle and (– 2, – 2) is one of the vertices, then

(A) inradius of triangle is2

5.

(B) area of triangle is4

225.

(C) equation of side opposite to vertex (– 2, – 2) is 6x + 8y = 47.

(D) area of triangle is34

225.

ANS : ACD

Q.10 Among the lines passing through C (3, 1), BA is farthest from the origin and cuts x-axis and y-axisat A and B respectively, then(A) equation of AB is 4x + y =13 (B) equation of AB is 3x + y = 10

(C) |AB| =3

1010(D) area of AOB equals

3

50, where O is origin

ANS : BCD

Q.7 The slope of the line that bisects the angle formed by the lines l1 and l2 if l1 has a slope of 2 andl2 is a vertical line, can be

(A) 2 + 5 (B) 2 – 5 (C) 1 + 5 (D) 1 – 5 ANS AB

Q.8 If the point (1, 1) lie on the origin side of the straight line l2x + lmy + 1 = 0 R l then the value of m

can be

(A)2

1(B) 1 (C) – 1 (D) – 2 ANS ABC

Q.2 The circles x2 + y2 = 4 and x2 + y2 – 2x – 2y + 1 = 0 intersect at A and B, thenColumn-I Column-II

(A) if ax + 2by = 5 is common chord of given circles, (P)2

7

then

a

bis equal to (Q)

4

3

(B) if is acute angle between given circles then the (R)

value of cos is equal to

(C) length of common tangent of given circles is equal to (S)2

1

(D) diameter of smallest circle which is passing throughA and B is equal to

ANS : A->S, B->Q, C->R, D->P

1

[MATRIX TYPE]

Q.1 has three statements (A, B, C) given in Column-I and four statements (P, Q, R, S) given in Column-II.Anygivenstatement in Column-I canhave correct matching with one or more statement(s)given in Column-II.

Q.1 Column-I Column-II(A) Number of integral values of k for which the lines x + ky = 4 and (P) 0

2x – 3y = 6 intersect in the third quadrant, is

(B) A line with slope 4 and x-intercept – 8 contains the point P which (Q) 2is 40 units above the x-axis. The x-coordinate of point P, is

(C) A line with slope of4

1goes through the point (4, 3). If (– 4, k) is (R) 3

another point on the line, then the value of k is (S) 5

ANS : A->P, B->Q, C->S, D->R

If 2a2 – 7ab – ac + 3b2 – 2bc – c2 = 0 then the family of lines ax + by + c = 0 are either concurrentat the point P(x1, y1) or at the point Q(x2, y2). Find the sum (x1 + y1 + x2 + y2).

(D)

[MATRIX TYPE]

Q.11 Equation of straight line passing through (1, 2) and cuts off equal intercept on coordinate axes can be(A) x + y = 3 (B) 3x – y = 1 (C) x – y +1 = 0 (D) 2x – y = 0

ANS : AD