Geometrically Rez2 - i = 2, where&n

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 Multiple Choice QuestionsMultiple Choice Questions

21.

The equation of the ellipse whose centre is at origin, major axis is along x-axis with eccentricity, 34 and latus rectum 4 units is :

  • x21024 + 7y264 = 1

  • 49x21024 + 7y264 = 1

  • 7x21024 + 49y264 = 1

  • x21024 + y264 = 1


22.

The equation of the circle which passes through the points (1, 0), (0, - 6) and (3, 4) is :

  • 4x2 + 4y2 + 142x + 47y + 140 = 0

  • 4x2 +4y2 - 142x - 47y + 138 = 0

  • 4x2 +4y2 - 142x + 47y + 138 = 0

  • 4x2 +4y2 + 150x - 49y + 138 = 0


23.

A cylindrical jar without a lid has to be constructed using a given surface area of a metal sheet. If the capacity of the jar is to be maximum, then the diameter of the jar must be k times the height of the jar. The value of k is

  • 1

  • 2

  • 3

  • 4


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24.

Geometrically Rez2 - i = 2, where i =  - 1 and Re is the real part, represents

  • circle

  • ellipse

  • rectangular hyperbola

  • parabola


C.

rectangular hyperbola

Let,  z = x + iyz2 - i = x2 - y2 + 2xyi - i          = x2 - y2 + 2xy - 1iRez2 - i = 2  x2 - y2    = 2

This equation represents rectangular hyperbola


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25.

The following table gives the monthly expenditure of two families :
Expenditure in Rs    
Items Family A Family B
Food 3500 2700
Clothing 500 800
Rent 1500 1000
Education 2000 1800
Miscellaneous 2500 1800

In constructing a pie diagram to the above data, the radii of the circles are to be choosen by which one of the following ratios ?

  • 1 : 1

  • 10 : 9

  • 100 : 91

  • 5 : 4


26.

If a circle of radius b units with centre at (0, b) touches the line y = x - 2, then what is the value of b ?

  • 2 + 2

  • 2 - 2

  • 22

  • 2


27.

Consider the two circles

x - 12 + y - 32 = r2 and x2 + y2 - 8x + 2y + 8 = 0

What is the distance between the centres of the two circles ?

  • 5 units

  • 6 units

  • 8 units

  • 10 units


28.

Consider the two circles

x - 12 + y - 32 = r2 and x2 + y2 - 8x + 2y + 8 = 0

If circles intersect at two distinct. points, then which one of the following is correct ?

  • r = 1

  • 1 < r < 2

  • r = 2

  • 2 < r < 8


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29.

Consider a circle passing through the origin and the points (a, b) and (- b, - a). On which line does the centre of the circle lie ?

  • x + y = 0

  • x - y = 0

  • x + y = a + b

  • x - y = a2 - b2


30.

Consider a circle passing through the origin and the points (a, b) and (- b, - a). What is the sum of the squares of the intercepts cut off by the circle on the axes ?

  • a2 + b2a2 - b22

  • 2a2 + b2a - b2

  • 4a2 + b2a - b2

  • None of the above


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