If the sum of the slopes of the lines given by x² -2cxy -7y² =0 is four times their product, then c has the value

• -1

• 2

• -2

• -2

The equation of the straight line passing through the point (4, 3) and making intercepts on the co-ordinate axes whose sum is –1 is

If one of the lines given by 6x² -xy +4cy² = 0 is 3x + 4y = 0, then c equals

• 1

• -1

• 3

• 3

The intercept on the line y = x by the circle x2 +y2 -2x = 0 is AB. Equation of the circle on AB as a diameter is

• x² +y² -x-y =0

• x² -y² -x-y =0

• x² +y² +x-y =0

• x² +y² +x-y =0

If the tangent at (1, 7) to the curve x² = y – 6 touches the circle x² + y² + 16x + 12y + c = 0 then the value of c is

• 95

• 195

• 185

• 85

Transforming to parallel axes through a point (p, q), the equation

2x² + 3xy + 4y² + x + 18y + 25 = 0 becomes 2x² + 3xy + 4y² = 1. Then,

• p = - 2, q = 3

• p = 2, q = - 3

• p = 3, q = - 4

• p = - 4, q = 3

The point P(3, 6) is first reflected on the line y =x and then the image point Q is again reflected on the line y = - x to get the image point Q'. Then, the circumcentre of the APQQ' is

• (6, 3)

• (6,- 3)

• (3,- 6)

• (0, 0)

Let d₁ and d₂ be the lengths of the perpendiculars drawn from any point of the line 7x - 9y + 10 = 0 upon the lines 3x + 4y = 5 and 12x +5y = 7, respectively. Then,

• d₁ > d₂

• d₁ = d₂

• d₁ < d₂

• d₁ = 2d₂

The chord of the curve y = x² + 2ax + b, joining the points where $\mathrm{x} = \mathrm{\alpha } \mathrm{and} \mathrm{y} = \mathrm{\beta }$ is parallel to the tangent to the curve at abscissa x is equal to

• $\frac{\mathrm{a} + \mathrm{b}}{2}$

• $\frac{2\mathrm{a} + \mathrm{b}}{2}$

• $\frac{2\mathrm{\alpha } +\mathrm{\beta }}{2}$

• $\frac{\mathrm{\alpha } + \mathrm{\beta }}{2}$

30.

Two particles move in the same straight line starting at the same moment from the same point in the same direction. The first moves with constant velocity u and the second starts from rest with constant acceleration f. Then

• they will be at the greatest distance at the end of time $\frac{\mathrm{u}}{2\mathrm{f}}$ from the start

• they will be at the greatest distance at the end of time $\frac{\mathrm{u}}{\mathrm{f}}$from the start

• their greatest distance is $\frac{{\mathrm{u}}^2}{2\mathrm{f}}$

• their greatest distance is $\frac{{\mathrm{u}}^2}{\mathrm{f}}$