Part A: Mathematics Exam Paper PDF

## PART-A: MATHEMATICS ### SECTION-I ### Multiple Choice Questions: 1. Let C:x² + y² = 4; C':x² + y²-4λx+9=0 be two circles. If the set of all values of λ so that the circles C and C' intersect at two distinct points, is R-[a,b], then the point (8a+12,16b-20) lies on the curve: a) x²+2y² +5x+6y...

## PART-A: MATHEMATICS ### SECTION-I ### Multiple Choice Questions: 1. Let C:x² + y² = 4; C':x² + y²-4λx+9=0 be two circles. If the set of all values of λ so that the circles C and C' intersect at two distinct points, is R-[a,b], then the point (8a+12,16b-20) lies on the curve: a) x²+2y² +5x+6y = 3 b) 5x² - y = -11 c) x²-4y² = 7 d) 6x² + y² = 42 2. Let the circles C₁:(x−a)²+(y-β)² = r² and C₂:(x-8)² + (y-15/2)² = r² touch each other externally at the point (6, 6). If the point (6, 6) divides the line segment joining the centres of the circles C₁ and C₂ internally in the ratio 2:1, then (a+β)+4(r²+r²)= a) 125 b) 130 c) 110 d) 145 3. The straight line x + 2y = 1 meets the coordinate axes at A and B. A circle is drawn through A, B and the origin. Then the sum of perpendicular distances from A and B on the tangent to the circle at the origin is: a) √5/2 b) 2√5 c) √5/4 d) 4√5 4. Let the centre of a circle C be (a,β) and its radius r < 8. Let 3x+4y=24 and 3x-4y = 32 be two tangents and 4x+3y = 1 be a normal to C. Then (a-β+r) is equal to a) 7 b) 5 c) 6 d) 9 5. The points of intersection of the line ax + by = 0, (a≠b) and the circle x² + y²-2x = 0 are A(a,0) and B(1,β). The image of the circle with AB as a diameter in the line x+y+2=0 is a) x² + y² +5x+5y + 12 = 0 b) x² + y² +3x+5y+8=0 c) x² + y² +3x+3y+4=0 d) x² + y²-5x-5y+12=0