[SINGLE [SINGLE CORREC CORRECT T CHOICE CHOICE TYPE] TYPE]
Q.6
Q.5
The line x + 3y 2 = 0 bise bisect ctss the the angl anglee betw betwee een n a pair pair of stra straig ight ht line liness of whic which h one one has has equa equati tion on x 7y + 5 = 0 . The equation of the other lin line is : ANS : C (A) (A) 3x + 3y 1 = 0 (B) x 3y + 2 = 0 (C) 5x + 5y 3 = 0 (D) non none If variab variable le line line 9ax + 4by 4by = 5 (a, b > 0) 0) alway alwayss passi passing ng thro through ugh (1, 1), then then the the maximu maximum m value value of 3 a (A)
5
2 b is is equal qual to
(B) 10
(C)
(D) 15
13
ANS : B
Q.3 Q.3
Line ine L, perp perpen endi diccular ular to the the line line with with equa equati tion on y = 3x – 5, cont contai ains ns the the poin pointt (1, (1, 4). 4). The The x-in x-inte terc rcep eptt of L, L, is (A) 12 (B) 13 (C) 14 (D) 15 ANS : B
Q.4 Q.4
Locu Locuss of the point point of interse intersect ction ion of the pair pair of perp perpend endic icula ularr tangen tangents ts to the the circle circless 2 2 2 2 x + y = 1 a n d x + y = 7 is the the dire direct ctor or circ circle le of the the circ circle le with with radi radius us.. (A)
Q.5
2
(B) 2
(C ) 2 2
(D) 4 (D
ANS : B
LetABC etABC bean equi equila late tera rall tria triang ngle le and and let let D be a poin pointt on its its circ ircumci umcirc rcle le.. If a, b, c deno denote te the the dist distaance nce of D from from the the vert vertic icesA, esA, B,C B, C resp respec ecti tive velythe lythen n the the valu valuee ofth of thee prod produc uctt b c a c a b a b c equals (A) 0
(B)
abc 8
(C)
a 3 b 3 c3 3abc
SPACE SPACE FOR ROUGH WORK
6
(D) None
ANS : A
[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 9 Let L1, L 2 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 L14 = L22 L32 + 16 then locus of P are the curves, C 1 (straight line) and C2 (circle).
Q.7
Straight line which intersects both the curves C1 andC2 orthogonally, is (A) x + y = 0 (B) x – y – 2 = 0 (C) x + y + 2 = 0 (D) x – y = 0
Q.8
Circumcentreof the triangle formed byC1 and two other lines which are at an angle of 45° with C1 and tangent to the circle C2, is ANS : B (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 area of triangle formed by joining centres of the circles S1, S2 and S3, is (A) 2 (B) 4 (C) 8 (D) 16 ANS : C
ANS : D
[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 8 Consider the family of circles S = 0 which passes through points A(3, 7) and B(6, 5). A lso, let C : x 2 + 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 is x2 + y2 + 2gx + 2fy + c = 0, then (2g + c – f ) is equal to ANS : D (A) 1 (B) 0 (C) –1 (D) –3
Q.7
If the member of familyof circles S = 0 whose centrelies on line y = x, cuts intercept of length L on x-axis, then L is equal to (A)
11 2
(B) 11
(C) 9
(D)
9 2
ANS : B
[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 unitsfrom L, 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 is (B) area of triangle is
5
.
2
225
. 4 (C) equation of side opposite to vertex (– 2, – 2) is 6x + 8y= 47. (D) area of triangle is
Q.10
225 4 3
ANS : ACD
.
Among the lines passing through C (3, 1), BA is farthest from the origin and cuts x-axis and y-axis at A and B respectively, then (A) equation of AB is 4x + y =13 (B) equation of AB is 3x + y = 10
ANS : BCD
10 10
(C) |AB| = Q.12
3
50 3
, where O is origin
If the point P(2a + 1, a – 1) is an interior point of the smaller segment of the circle x2 + y2 – 2x – 4y = 4 made by the chord x + y – 2 = 0, then set of values of a is contained in or equal to
1 2
(A) 0,
Q.13
(D) area of AOB equals
(B) 0,
1
3 4
2
1 2 (D) , 3 3
(C) 0,
ANS BC
In a triangleABC, if a = 4, b = 8 and C = 60°, then which of the following relations is(are) correct? [Note: All symbolsused have usual meaning in triangleABC.]
sin 2 A = 2.
(A) The area of triangleABC is 8 3 .
(C) Inradius of triangleABC is
Q.7
3 3
.
5
(B) 2 – 5
(C) 1 +
5
1 2
(B) 1
(C) – 1
l 2 if l 1 has
(D) 1 – 5
If thepoint (1,1) lieon the origin side of the straight line l 2x + l m y + 1 = 0 can be (A)
ANS AB
(D) Thelength ofinternalanglebisector ofangleC is
The slope of the line that bisects the angle formed by the lines l 1 and l 2 is a vertical line, can be (A) 2 +
Q.8
4 3
(B) The value of
8 3
a slope of 2 and ANS AB
l R then the value of
(D) – 2
.
m
ANS ABC
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
[MATRIX TYPE] The circles x2 + y2 = 4 and x2 + y2 – 2x – 2y + 1 = 0 intersect at A and B, then
Q.2
Column-I
(A)
(B)
Column-II
if ax + 2by = 5 is common chord of given circles,
(P)
b then is equal to a
(Q)
if isacute angle between given circles then the
(R)
7 2 3 4
1
value of cos is equal to (C)
length of common tangent of given circles is equal to
(D)
diameter of smallest circle which ispassing through A and B is equal to
(S)
1 2
ANS : A->S, B->Q, C->R, D->P
[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. Any givenstatement in Column-I can have correct matching with one or more statement(s) given in Column-II.
Q.1
(D)
Column-I
Column-II
(A)
Number of integral values of k for which the lines x + ky = 4 and 2x – 3y= 6 intersect in the third quadrant, is
(P)
0
(B)
A line with slope 4 and x-intercept – 8 contains the point P which is 40 units above the x-axis. The x-coordinate of point P, is
(Q)
2
(C)
A line with slope of
(R)
3
(S)
5
1
goes through the point (4, 3). If (– 4, k) is 4 another point on the line, then the value of k is
If 2a2 – 7ab – ac + 3b2 – 2bc – c2 = 0 then the family of lines ax + by + c = 0 are either concurrent at the point P(x1, y1) or at the point Q(x2, y2). Find the sum (x1 + y1 + x2 + y2). ANS : A->P, B->Q, C->S, D->R
