Paper II Mathematics
- The area of the triangle formed by the points (2, 2), (5, 5), (6, 7) is equal to (in square units)
(A)
(B) 5
(C) 10
(D)
(E) 14 - If the line px – qy = r intersects the co-ordinates axes at (a, 0) and (0, b), then the value of a + b is equal to
(A)
(B)
(C)
(D)
(E)
- The vertices of a triangle are A(3, 7), B(3, 4) and C(5, 4). The equation of the bisector of the angle ∠ABC is
(A) y = x + 1
(B) y = x – 1
(C) y = 3x – 5
(D) y = x
(E) y = –x - The equation of a straight line which passes through the point (acos3θ, asin3θ) and perpendicular to x secθ + y cosecθ = a is
(A)
= a cosθ
(B) x cosθ – y sinθ = a cos2θ
(C) x cosθ + y sinθ = a cos2θ
(D) x cosθ + y sinθ – a cos2θ = 1
(E) x cosθ – y sinθ + a cos2θ = –1 - The slopes of the lines which make an angle 45° with the line 3x – y = –5 are
(A) 1, –1
(B)
, –1
(C) 1,
(D) 2,
(E) –2, - The equation of one of the lines parallel to 4x + 3y = 5 and at a unit distance from the point (–1, –4) is
(A) 3x + 4y – 3 = 0
(B) 3x + 4y + 3 = 0
(C) 4x – 3y + 3 = 0
(D) 4x – 3y – 3 = 0
(E) 4x – 3y –4 = 0 - The equation of family of circles with centre at (h, k) touching the x – aix is given by
(A) x2 + y2 – 2hx + h2 = 0
(B) x2 + y2 – 2hx – 2ky + h2 = 0
(C) x2 + y2 – 2hx – 2ky – h2 = 0
(D) x2 + y2 – 2hx – 2ky = 0
(E) x2 + y2 + 2hx + 2ky = 0 - If two circles (x + 7)2 + (y – 3)2 = 36 and (x – 5)2 + (y + 2)2 = 49 touch each other externally, then the point of contact is
(A)
(B)
(C)
(D)
(E)
- The equation of the chord of the circle x2 + y2 = 81 which is bisected at the point (–2, 3) is
(A) 3x – y = 13
(B) 3x – 4y = 13
(C) 2x – 3y = 13
(D) 3x – 3y = 13
(E) 2x – 3y = –13 - The distance of the midpoint of line joining two points (4, 0) and (0, 4) from the centre of the circle x2 + y2 = 16 is
(A) √2
(B) 2√2
(C) 3√2
(D) 2√3
(E) √3
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