A line is drawn through the point (1, 2) to meet the coordinate axes at P and Q such that it forms a triangle OPQ, where O is the origin. If the area of the triangle OPQ is least, then the slope of the line PQ is

• -1/4

• -4

• -2

• -2

Three distinct points A, B and C are given in the 2 – dimensional coordinate plane such that the ratio of the distance of any one of them from the point (1, 0) to the distance from the point ( - 1, 0) is equal to 1/3 . Then the circumcentre of the triangle ABC is at the point

• (0,0)

• (5/4, 0)

• (5/2, 0)

• (5/2, 0)

The point diametrically opposite to the point P (1, 0) on the circle x²+ y² + 2x + 4y − 3 = 0 is 

• (-3,4)

• (-4,3)

• (-3,-4)

• (-3,-4)

The perpendicular bisector of the line segment joining P (1, 4) and Q (k, 3) has y−intercept − 4. Then a possible value of k is

• 1

• 2

• -2

• -2

If |z + 4| ≤ 3, then the maximum value of |z + 1| is

• 4

• 10

• 6

• 6

A body falling from rest under gravity passes a certain point P. It was at a distance of 400 m from P, 4s prior to passing through P. If g = 10 m/s² , then the height above the point P from where the body began to fall is

• 720 m

• 900 m

• 320 m

• 320 m

A straight line through the point A(3, 4) is such that its intercept between the axes is bisected at A. Its equation is

• x + y = 7

• 3x − 4y + 7 = 0

• 4x + 3y = 24

• 4x + 3y = 24

18.

The two lines x = ay + b, z = cy + d; and x = a′y + b′, z = c′y + d′ are perpendicular to each other if

• aa′ + cc′ = −1

• aa′ + cc′ = 1

• 
• 

The system of equations 
αx + y + z = α - 1, 
x + αy + z = α - 1, 
x + y + αz = α - 1 

has no solution, if α is

• -2

• either-2 or 1

• not -2

• not -2

Two points A and B move from rest along a straight line with constant acceleration f and f′ respectively. If A takes m sec. more than B and describes ‘n’ units more than B in acquiring the same speed then

• (f - f′)m2 = ff′n

• (f + f′)m² = ff′n

• 1/2(f - f′)m = ff′n²

• 1/2(f - f′)m = ff′n²