If the point (x, y, - 3), (2, 0, - 1) and (4, 2, 3) lie

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 Multiple Choice QuestionsMultiple Choice Questions

61.

What is the equation of the straight line which passethrough the point of intersection of the straight linex + 2y=5 and 3x + 7y = 17 and is perpendicular tthe straight line 3x + 4= 1?

  • 4x + 3y + 2 = 0

  • 4x - y + 2 = 0

  • 4x - 3y - 2 = 0

  • 4x - 3y + 2 = 0


62.

If (a, b) is at unit distance from the lin8x + 6y + 1 0, then which of the following conditionare correct ?

1. 3a - 4b - 4 = 0

2. 8a + 6b + 11 = 0

3. 8a + 6b - 9 = 0

Select the correct answer using the code given below : 

  • 1 and 2 only

  • 2 and 3 only

  • 1 and 3 only

  • 1, 2 and 3


63.

A straight line cuts off an intercept of 2 units on thpositive direction of x-axis and passes through thpoint 3, 5). What is the foot of the perpendiculadrawn from the point (3, 3) on this line

  • (1, 3)

  • (2, 0)

  • (0, 2)

  • (1, 1)


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64.

If the point (x, y, 3), (2, 0, 1) and (4, 2, 3) lie on a straight line, then what are the values of x and y respectively ?

  • 1, - 1

  • - 1, 1

  • 0, 2

  • 3, 4


A.

1, - 1

We have points (x, y, - 3), (2, 0, - 2) and (4, 2, 3)

For points lying in a straight line it satisfy collinearity.

For collinear, slopes are equal 

ABm = BCm = CAm  i.e. y1 - y2x1 - x2 = y2 - y3x2 - x3Then, y - 0x - 2 = 0 - 22 - 4yx - 2 = 1  y = x - 2  x - y = 2 ... iThere is 2nd condition for collinearity is x1y1z1x2y2z2x3y3z3 = 0Then, xy- 320 - 1423 = 0x0 + 2 - y6 + 4 - 34 - 0 = 02x - 10y - 12 = 0                                 ... iiSolving eq i and ii4y = - 4  y = - 1Put value of y in eq (i)x -  - 1 = 2  x = 1Hence x and y are (1, - 1) respectively


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65.

An equilateral triangle has one vertex at (1, 1) and another vertex at  - 3, 3. The third vertex may lie on

  •  - 2, 2

  • 2, - 2

  • (1, 1)

  • (1, - 1)


66.

What is the distance between the points P(m.cos2α, m.sin2α) and Q(m.cos2β, m.sin2β) ?

  • 2msinα - β

  • 2mcosα - β

  • 2msin2α - 2β

  • msin2α - 2β


67.

What is the angle between the lines xcos(α) + ysin(α) = α and xsin(β) – ycos(β) = α ?

  • β - α

  • π + β - α

  • π + 2β + 2α2

  • π - 2β + 2α2


68.

The equation ax + by + c = 0 represents a straight line

  • for all real numbers a, b and c

  • only when a ≠ 0

  • only when b ≠ 0

  • only when at least one of a and b is non-zero


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69.

A ladder 9 m long reaches a point 9 m below the top of a vertical flag staff. From the foot of the ladder, the elevation of the flag staff is 60o. What is the height of the flag staff ?

  • 9m

  • 10.5m

  • 13.5m

  • 15m


70.

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

  • 23 Square units

  • 43 Square units

  • 13 Square units

  • 1 Square units


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