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 Multiple Choice QuestionsMultiple Choice Questions

1.

Let C be the circle with centre at(1,1) and radius 1. If T is the circle centred at (0,y) passing through origin and touching the circle externally, then the radius of T is equal to

  • fraction numerator square root of 3 over denominator square root of 2 end fraction
  • fraction numerator square root of 3 over denominator 2 end fraction
  • 1/2

  • 1/2

395 Views

2.

The image of line fraction numerator straight x minus 1 over denominator 3 end fraction space equals space fraction numerator straight y minus 3 over denominator 1 end fraction space equals space fraction numerator straight z minus 4 over denominator negative 5 end fraction in the plane 2x-y+z+3 =0 is the line

  • fraction numerator straight x plus 3 over denominator 3 end fraction space equals space fraction numerator straight y minus 5 over denominator 1 end fraction space equals space fraction numerator straight z minus 2 over denominator negative 5 end fraction
  • fraction numerator straight x plus over denominator negative 3 end fraction space equals space fraction numerator straight y minus 5 over denominator negative 1 end fraction space equals space fraction numerator begin display style straight z plus 2 end style over denominator 5 end fraction
  • fraction numerator straight x minus 3 over denominator 3 end fraction space equals space fraction numerator straight y plus 5 over denominator 1 end fraction space equals space fraction numerator straight z minus 2 over denominator negative 5 end fraction
  • fraction numerator straight x minus 3 over denominator 3 end fraction space equals space fraction numerator straight y plus 5 over denominator 1 end fraction space equals space fraction numerator straight z minus 2 over denominator negative 5 end fraction
382 Views

3.

A bird is sitting on the top of a vertical pole 20m high and its elevation from a point O n the ground is 45o. It flies off horizontally straight away from the point O. After 1s, the elevation of the bird from O is reduced to 30o. Then, the speed (in m/s of the bird is

  • (40 square root of 2 minus end root space 1

  • 40 left parenthesis square root of 3 space space end root space minus space square root of 2 right parenthesis
  • 20 space square root of 2
  • 20 space square root of 2
211 Views

4.

A ray of light along straight x space plus square root of 3 straight y end root space equals space square root of 3 get reflected upon reaching X -axis, the equation of the reflected ray is 

  • straight y equals space straight x plus square root of 3
  • square root of 3 straight y end root space equals space straight x minus square root of 3
  • straight y space equals space square root of 3 straight x end root minus square root of 3
  • straight y space equals space square root of 3 straight x end root minus square root of 3
441 Views

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5.

The number of values of k, for which the system of equations
(k+1) x + 8y = 4k
kx + (k+3)y = 3k -1
has no solution, is 

  • infinite 

  • 1

  • 2

  • 2

269 Views

6.

In a ∆PQR, if 3 sin P + 4 cos Q = 6 and 4 sin Q + 3 cos P = 1, then the angle R is equal to

  • 5π/6

  • π/6

  • π/4

  • π/4

163 Views

7.

An equation of a plane parallel to the plane x – 2y + 2z – 5 = 0 and at a unit distance from the origin is

  • x – 2y + 2z – 3 = 0

  • x – 2y + 2z + 1 = 0

  • x – 2y + 2z – 1 = 0

  • x – 2y + 2z – 1 = 0

457 Views

8.

If the line 2x + y = k passes through the point which divides the line segment joining the points (1, 1) and (2, 4) in the ratio 3 : 2, then k equals

  • 29/5

  • 5

  • 6

  • 6

224 Views

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9.

If the line fraction numerator straight x minus 1 over denominator 2 end fraction space equals space fraction numerator straight y plus 1 over denominator 3 end fraction space equals space fraction numerator straight z minus 1 over denominator 4 end fraction and fraction numerator straight x minus 3 over denominator 1 end fraction space equals fraction numerator straight y minus straight k over denominator 2 end fraction space equals space straight z over 1 intersect, then k is equal to

  • -1

  • 2/9

  • 9/2

  • 9/2

157 Views

10.

Three numbers are chosen at random without replacement from {1, 2, 3, ...... 8}. The probability that their minimum is 3, given that their maximum is 6, is

  • 3/8

  • 1/5

  • 1/4

  • 1/4

206 Views

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