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

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 Multiple Choice QuestionsMultiple Choice Questions

11.

A particle starts moving from rest from a fixed point in a fixed direction. The distance s from the fixed point at a time t is given by s = t2 + at - b + 17, where a and b are real numbers. If the particle comes to rest after 5 s at a distance of s = 25 units from the fixed point, then values of a and b are, respectively

  • 10, - 33

  • - 10, - 33

  • - 8, 33

  • - 10, 33


12.

If a, band c are in AP, then the straight line ax + 2by + c = 0 will always pass through a fixed point whose coordinates are

  • (1, - 1)

  • (- 1, 1)

  • (1, - 2)

  • (- 2, 1)


13.

The number of diagonals in a regular polygon of 100 sides is

  • 4950

  • 4850

  • 4750

  • 4650


14.

Let p, q and r be the altitudes of a triangle with area S and perimeter 2 t. Then, the value of 1p + 1q + 1r is

  • St

  • tS

  • S2t

  • 2St


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15.

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


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16.

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


A.

5x + y - 11 = 0

Since, the points A(1, 6), B(3,- 4) and C(x, y) are collinear.

 1613- 41xy1 = 0 1(- 4 - y) - 6(3 - x) +1(3y + 4x) = 0                                     10x + 2y - 22 = 0                                         5x + y - 11 = 0


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17.

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

  • 5

  • 6

  • 8

  • 10


18.

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

  • 2

  • - 1

  • 12

  • 1


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19.

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

  • 1p +1q = 1

  • 1p +1q = 2

  • 1p +1q = 3

  • 1p +3q = 1


20.

The equation y = ± 3x, y = 1 are the sides

  • an equilateral triangle

  • a right angled triangle

  • a isosceles triangle

  • an obtuse angled triangle


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