If p and q are positive real numbers such that p2 + q2 = 1, then

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then the common ratio of this progression equals

  • 1 half left parenthesis 1 minus square root of 5 right parenthesis
  • 1 half square root of 5
  • square root of 5
  • square root of 5
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2. If space sin to the power of negative 1 end exponent space open parentheses straight x over 5 close parentheses space plus space cosec to the power of negative 1 end exponent space open parentheses 5 over 4 close parentheses space equals space straight pi over 2 then the value of x
  • 1

  • 3

  • 4

  • 4

104 Views

3.

In the binomial expansion of (a - b)n, n ≥ 5, the sum of 5th and 6th terms is zero, then
a/b equals

  • 5/n −4

  • 6 /n −5

  • n -5 /6

  • n -5 /6

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4.

The set S: {1, 2, 3, …, 12} is to be partitioned into three sets A, B, C of equal size. Thus, A ∪ B ∪ C = S, A ∩ B = B ∩ C = A ∩ C = φ. The number of ways to partition S is-

  • 12!/3!(4!)3

  • 12!/3!(3!)4

  • 12!/(4!)3

  • 12!/(4!)3

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5.

A body weighing 13 kg is suspended by two strings 5 m and 12 m long, their other ends being fastened to the extremities of a rod 13 m long. If the rod be so held that the body hangs immediately below the middle point. The tensions in the strings are 

  • 12 kg and 13 kg

  • 5 kg and 5 kg

  • 5 kg and 12 kg

  • 5 kg and 12 kg

106 Views

6.

Consider a family of circles which are passing through the point (-1, 1) and are tangent to x-axis. If (h, K) are the co-ordinates of the centre of the circles, then the set of values of k is given by the interva

  • 0 < k < 1/2

  • k ≥ 1/2

  • – 1/2 ≤ k ≤ 1/2

  • – 1/2 ≤ k ≤ 1/2

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7.

The differential equation of all circles passing through the origin and having their centres on the x-axis is

  • straight x squared space equals straight y squared space plus space xy dy over dx
  • straight x squared space equals straight y squared space plus space 3 xy dy over dx
  • straight x squared space equals straight y squared space plus space 2 xy dy over dx
  • straight x squared space equals straight y squared space plus space 2 xy dy over dx
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8.

If p and q are positive real numbers such that p2 + q2 = 1, then the maximum value of (p + q) is

  • 2

  • 1/2

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


D.

fraction numerator 1 over denominator square root of 2 end fraction
Using space straight A. straight M. space greater or equal than space straight G. straight M comma
fraction numerator straight p squared space plus straight q squared over denominator 2 end fraction space greater or equal than pq
rightwards double arrow space pq space less or equal than 1 half
left parenthesis straight p plus straight q right parenthesis squared space equals space straight p squared space plus straight q squared space plus 2 pq
rightwards double arrow space left parenthesis straight p plus straight q right parenthesis squared space equals straight p squared space plus straight q squared space plus 2 pq
rightwards double arrow space straight p plus straight q space less or equal than square root of 2
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9.

A tower stands at the centre of a circular park. A and B are two points on the boundary of the park such that AB (= a) subtends an angle of 60º at the foot of the tower, and the angle of elevation of the top of the tower from A or B is 30º. The height of the tower is

  • 2 straight a divided by square root of 3
  • 2 straight a square root of 3
  • straight a divided by square root of 3
  • straight a divided by square root of 3
167 Views

10.

The sum of the series 20C020C1 + 20C220C3 + …… - ….. + 20C10 is-

  • 20C10

  • 1 half straight C presuperscript 20 subscript 10
  • 0

  • 0

1417 Views

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