Consider the equationksinx + cos2x = 2k 

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 Multiple Choice QuestionsMultiple Choice Questions

41.

The distance of the point (1, 3) from the line 2x + 3y = 6, measured parallel to the line 4x + y = 4, is

  • 513units

  • 317units

  • 17 units

  • 172units


42.

The equation of a straight line .which cuts off an intercept of 5 units on negative direction of y-axis and makes an angle 120° with positive direction of x-axis is :

  • y + 3x + 5 = 0

  • y - 3x + 5 = 0

  • y + 3x - 5 = 0

  • y - 3x - 5 = 0


43.

The equation of the line passing through the point (2, 3) and the point of intersection of lines 2x - 3y + 7 = 0 and 7x + 4y + 2 = 0 is :

  • 21x + 46y - 180 = 0

  • 21x - 46y + 96 = 0

  • 46x + 21y - 155 = 0

  • 46x - 21y - 29 = 0


44.

A straight line intersects x and y axes at P and Q respectively. If (3, 5) is the middle point of PQ, then what is the area of the triangle OPQ ?

  • 12 square units

  • 15 square units

  • 20 square units

  • 30  square units


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45.

Consider the lines

y = 3x, y = 6x and y = 9

What is the area of the triangle formed by these lines ?

  • 274 square units

  • 272 square units

  • 194 square units

  • 192 square units


46.

Consider the lines

y = 3x, y = 6x and y = 9

The centroid of the triangle is at which one of the following points ?

  • (3, 6)

  • 32, 6

  • (3, 3)

  • 32, 9


47.

Consider the two lines

x + y + 1 = 0 and 3x + 2y + 1 = 0

What is the equation of the line passing through the point of intersection of the given lines and parallel to x -axis ?

  • y + 1 = 0

  • y - 1 = 0

  • y - 2 = 0

  • y + 2 = 0 


48.

Consider the two lines

x + y + 1 = 0 and 3x + 2y + 1 = 0

What is the equation of the line passing through the point of intersection of the given lines and parallel to y-axis

  • x + 1 = 0

  • x - 1 = 0

  • x - 2 = 0

  • x + 2 = 0


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49.

Consider the equation

ksinx + cos2x = 2k - 7

If the equation possesses solution, then what is the minimum value of k ?

  • 1

  • 2

  • 4

  • 6


B.

2

ksinx + cos2x = 2k - 7ksinx +1 - 2sin2x = 2k - 72sin2x - ksinx  2k - 8 = 0sinx = k ±  - k2 - 4 . 2 . 2k - 44           = k ± k - 84 = k2 - 2

For minimum value of ksinx = - 1 = k2 - 2       k = 2


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50.

Consider a parallelogram whose vertices are A(1, 2), B(4, y), C(x, 6) and D(3, 5) taken in order

What is the value of AC2 - BD2 ?

  • 25

  • 30

  • 36

  • 40


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