141.

Let P and Q be the points on the parabola y² = 4x so that the line segment PQ subtends right angle at the vertex. If PQ intersects the axis of the parabola at R, then the distance of the vertex from R is

• 1

• 2

• 4

• 6

If the three points A(1, 6), B(3,- 4) and C(x, y) are collinear, then the equation satisfying by x and y is

• 5x + y - 11 = 0

• 5x + 13y + 5 = 0

• 5x - 13y + 5 = 0

• 13x - 5y + 5 = 0

The number of diagonals in a polygon is 20. The number of sides of the polygon is

• 5

• 6

• 8

• 10

In a right-angled triangle, the sides are a, b and c with c as hypotenuse and c - b $\ne$ 1, c + b $\ne$ 1. Then the value of (log_{c + b}(a) + log_{c - b}(a))/ (2log_{c + b}(a) x log_{c - b}(a)) will be

• 2

• - 1

• $\frac{1}{2}$

• 1

If the three points (3q, 0), (0, 3p) and (1, 1) are collinear, then which one is true?

• $\frac{1}{\mathrm{p}} +\hspace{0.17em}\frac{1}{\mathrm{q}} = 1$

• $\frac{1}{\mathrm{p}} +\hspace{0.17em}\frac{1}{\mathrm{q}} = 2$

• $\frac{1}{\mathrm{p}} +\hspace{0.17em}\frac{1}{\mathrm{q}} = 3$

• $\frac{1}{\mathrm{p}} +\hspace{0.17em}\frac{3}{\mathrm{q}} = 1$

The equation $\mathrm{y} = \pm \sqrt{3}\mathrm{x}$, y = 1 are the sides

• an equilateral triangle

• a right angled triangle

• a isosceles triangle

• an obtuse angled triangle

If C is a point on the line segment joining A(- 3, 4) and B(2, 1) such that AC = 2BC, then the coordinate of C is

• $\left(\frac{1}{3}, 2\right)$

• $\left(2, \frac{1}{3}\right)$

• (2, 7)

• (7, 2)

A train moving with constant acceleration takes t seconds to pass a certain fixed point and the front and back end of the train pass the fixed point with velocities u and v respectively. Show that the length of the train is  $\frac{1}{2}\left(\mathrm{u} + \mathrm{v}\right)\mathrm{t}$.

One possible condition for the three points (a, b), (b, a) and (a², - b²) to be collinear is

• a - b = 2

• a + b = 2

• a = 1 + b

• a = 1 - b

The coordinates of the foot of perpendicular from (a, 0) on the line y = mx + $\frac{\mathrm{a}}{\mathrm{m}}$ are

• $\left(0, \frac{\mathrm{a}}{\mathrm{m}}\right)$

• $\left(0, - \frac{\mathrm{a}}{\mathrm{m}}\right)$

• $\left(\frac{\mathrm{a}}{\mathrm{m}}, 0\right)$

• $\left(- \frac{\mathrm{a}}{\mathrm{m}}, 0\right)$