A body weighing 13 kg is suspended by two strings 5 m and 12 m l

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


C.

5 kg and 12 kg



straight T subscript 2 space cos space open parentheses straight pi over 2 minus straight theta close parentheses space equals space straight T subscript 1 space cosθ
rightwards double arrow space straight T subscript 1 space cos space straight theta space equals space straight T subscript 2 space sin space straight theta
straight T subscript 1 space sin space straight theta space plus space straight T subscript 2 space cos space straight theta space equals space 13
because space OC space equals space CA space space equals CB
rightwards double arrow space angle space AOC space equals space angle OAC space and space angle COB space equals space angle OBC
therefore space sin space straight theta space equals space sin space straight A space equals space 5 over 13 space and space cos space straight theta space equals 12 over 13
rightwards double arrow space straight T subscript 1 over straight T subscript 2 space equals space 5 over 12 space rightwards double arrow space straight T subscript 1 space equals space 5 over 12 space and space cos space straight theta space equals space 12 over 13
rightwards double arrow space straight T subscript 1 over straight T subscript 2 space equals space 5 over 12 space rightwards double arrow space straight T subscript 1 space equals space 5 over 12 straight T subscript 2
straight T subscript 2 space open parentheses 5 over 12.5 over 13.12 over 13 close parentheses space equals space 13
straight T subscript 2 space open parentheses fraction numerator 169 over denominator 12.13 end fraction close parentheses space equals space 13
straight T subscript 2 space equals space 12 space kgs
rightwards double arrow space straight T subscript 1 space equals space 5 space kgs
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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

169 Views

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
121 Views

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
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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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