Let ABC be a triangle. If D(2, 5) and E(5, 9) are the mid-points

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 Multiple Choice QuestionsMultiple Choice Questions

71.

A curve y = memx where m > 0 intersects y-axis at a point P. What is the equation of tangent to the curve at P ?

  • y = mx + m

  • y = mx + 2m

  • y = m2x + 2m

  • y = m2x + m


72.

A curve y = memx where m > 0 intersects y-axis at a point P. How much angle does the tangent at P make with y-axis ?

  • tan-1m2

  • cot-11 + m2

  • sin-1m21 +m4

  • sec-11 + m4


73.

A curve y = memx where m > 0 intersects y-axis at a point P. What is the slope of the curve at the point of intersection P ?

  • m

  • m2

  • 2m

  • 2m2


74.

If 3x 4y 5 = 0 and 3x 4y + 15 = 0 are the equations of a pair of opposite sides of a square, then what is the area of the square ?

  • square units

  • square units

  • 16 square units

  • 25 square units


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75.

What is the obtuse angle between the lines whose slopes are 2 3 and 2 + 3 ?

  • 105°

  • 120°

  • 135°

  • 150°


76.

If the foot of the perpendicular drawn from the point (0, k) to the line 3x – 4y – 5 = 0 is (3, 1), then what is the value of k ?

  • 3

  • 4

  • 5


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77.

Let ABC be a triangle. If D(2, 5) and E(5, 9) are the mid-points of the AB and AC respectively, then what is the length of the side BC ?

  • 8

  • 10

  • 12

  • 14


B.

10

We know that the triangle midpoint theorem, it says that the line segment connecting the mid points of two sides of a triangle is parallel to the third side and is congruent to one half of the third side.

So here DE is parallel to BC and Also DE = 12BCGiven D2, 5 and E5, 9DE = 5 - 23 + 9 - 52 DE = 9 + 16 DE = 5Then,    BC = 2DEBC = 2 ×5 = 10


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78.

If the circumcentre of the triangle formed by the lines x + 2 = 0, y + 2 = 0 and kx + y + 2 = 0 is (1, 1), then what is the value of k ?

  •  - 1

  • - 2

  • 1

  • 2


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79.

The point (1, 1) is one of the vertices of a square. If 3x + 2y = 5 is the equation of one diagonal of the square, then what is the equation of the other diagonal ?

  • 3x 2y = 5

  • 2x 3y = 1

  • 2x 3y = 5

  • 2x + 3y = 1


80.

What is the area of the region enclosed between the curve y2 = 2x and the straight line y = x ? 

  • 12

  • 1

  • 23

  • 2


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