If the centroid of a triangle formed by (7, x), (y, - 6) and (9,

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 Multiple Choice QuestionsMultiple Choice Questions

21.

What is the equation of straight line passing through the point of intersection of the lines x2 +y3 = 1  and x3 + y2 = 1, and parallel to the line 4x + 5y -  6 = 0 ?

  • 20x + 25 - 54 = 0

  • 25x + 20y - 54 = 0

  • 4x + 5y - 54 = 0

  • 4x + 5y - 45 = 0


22.

Coordinates of the points O, P, Q and R are respectively (0, 0, 0), (4, 6, 2m), (2, 0, 2n) and (2, 4, 6). Let L, M, N and K be points on the sides OR, OP, PQ and QR respectively such that LMNK is a parallelogram whose two adjacent sides LK and LM are each of length 2.What are the values of m anon respectively ?

  • 6, 2

  • 1, 3

  • 3, 1

  • None of the above


23.

Consider the following statements :

Statement I : If the line segment joining the points P(m, n) and Q(r, s) subtends an angle a at the origin then

cosα = ms - nrm2 + n2r2 +s2Statements II : In any triangle ABC, it is true that a2 = b2 + c2 - 2bccosA

Which one of the following is correct in respect of the above two statements?

  • Both Statement I and Statement II are true and Statement II is the correct explanation of Statement I

  • Both Statement I and Statement II are true, but Statement II is not the correct explanation of Statement I

  • Statement I is true, but Statement II is false

  • Statement I is false, but Statement II is true


24.

Let the slope of the cureve y = cos-1sinx be tanθ.Then the value of θ in the interval 0, π is

  • π6

  • 3π4

  • π4

  • π2


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25.

From the top of a lighthouse, 100 m high, the angle of depression of a boat is tan-1512. What is the distance between the boat and the lighthouse ?

  • 120m

  • 180m

  • 240m

  • 360m


26.

If a vertex of a triangle is (1, 1) and the midpoints of two sides of the triangle through this vertex are ( - 1, 2) and (3, 2), then the centroid of the triangle is

  •  - 13, 73

  •  - 1, 73

  • 13, 73

  • 1, 73


27.

What is the ratio in which the point C - 27, - 207 divides the line joining the  points A( - 2, - 2) and B(2, - 4) ?

  • 1 : 3

  • 3 : 4

  • 1 : 2

  • 2 : 3


28.

What is the equation of the straight line parallel to 2x + 3y + 1 = 0 and passes through the point( - 1, 2) ?

  • 2x + 3y - 4 = 0

  • 2x + 3y - 5 = 0

  • x + y - 1 = 0 

  • 3x - 2y + 7 = 0 


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29.

What is the acute angle between the pair of straight lines 2x + 3y = 1 and 3x + 2y = 2 ?

  • tan-1126

  • tan-112

  • tan-13

  • tan-113


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30.

If the centroid of a triangle formed by (7, x), (y, - 6) and (9, 10) is (6, 3), then the values of x and y are respectively

  • 5, 2

  • 2, 5

  • 1, 0

  • 0, 0


B.

2, 5

Centroid of the triangle= x1 +x2 +x33, y1 + y2 +y33= 7 + y + 93 = 6, x - 6 + 103 = 3= y = 2, x = 5Hence, centroid of the triangle = 2, 5


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