Find the angle subtended by the double ordinate of length 2a of the parabola y² = ax at its vertex.

The equation to the pairs of opposite sides of a parallelogram are x² - 5x + 6 = 0 and y² - 6y + 5. Find the equations its diagonals.

A common tangent to 9x² - 16y² = 144 and x² + y² = 9 is

• $\mathrm{y} = \frac{3}{\sqrt{7}}\mathrm{x} + \frac{15}{\sqrt{7}}$

• $\mathrm{y} = 3\sqrt{\frac{2}{7}}\mathrm{x} + \frac{15}{\sqrt{7}}$

• $\mathrm{y} = 2\sqrt{\frac{3}{7}}\mathrm{x} + 15\sqrt{7}$

• None of these

The locus of a point P which moves such that 2PA = 3PB, where A(0, 0) and B(4,- 3) are points, is

• 5x² - 5y² - 72x + 54y + 225 = 0

• 5x² + 5y² - 72x + 54y + 225 = 0

• 5x² + 5y² + 72x - 54y + 225 = 0

• 5x² + 5y² - 72x - 54y - 225 = 0

The points P is equidistant from A(1, 3), B (- 3, 5) and C(5, - 1), then PA is equal to

• 5

• $5\sqrt{5}$

• 25

• $5\sqrt{10}$

The equation of the plane through the intersection of the planes x + y + z = 1 and 2x + 3y - z + 4 = 0 and parallel to X-axis, is

• y - 3z + 6 = 0

• 3y - z + 6 = 0

• y + 3z + 6 = 0

• 3y - 2z + 6 = 0

If the direction cosines of two lines are connected by the equations l + m + n = 0, l² + m² - n² = 0, then the angle between the lines is

• $\frac{\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{6}$

• $\frac{\mathrm{\pi }}{2}$

• $\frac{\mathrm{\pi }}{3}$

The equation of the plane which contains the origin and the line of intersection of the planes r · a = d₁ and r · b = d₂, is

• r . (d₁a + d₂b) = 0

• r . (d₂a - d₁b) = 0

• r . (d₂a + d₁b) = 0

• r . (d₁a - d₂b) = 0

If from a point P(a, b, c) perpendiculars PA and PB are drawn to YZ and ZX - planes, then the equation of the plane OAB is

• bcx + cay + abz = 0

• bcx + cay - abz = 0

• - bcx + cay + abz = 0

• bcx - cay + abz = 0

If (2, 7, 3) is one end of a diameter of the sphere x² + y² + z² - 6x - 12y - 2z + 20 = 0, then the coordinates of the other end of the diameter are

• (- 2, 5, - 1)

• (4, 5, 1)

• (2, - 5, 1)

• (4, 5. - 1)