Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

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31. If space left parenthesis top enclose straight a space straight x space top enclose straight b right parenthesis space straight x space top enclose straight c space equals space top enclose straight a space straight x space left parenthesis top enclose straight b space straight x space top enclose straight c right parenthesis comma space where space top enclose straight a comma space top enclose straight b space and space top enclose straight c space are any three vectors such that top enclose straight a. top enclose straight b space not equal to 0 space top enclose straight b. top enclose straight c space not equal to 0 comma space then space straight a with bar on top space and space straight c with bar on top space are
  • inclined at an angle of π/3 between them

  • inclined at an angle of π/6 between them

  • perpendicular

  • perpendicular


D.

perpendicular

left parenthesis top enclose straight a space straight x space top enclose straight b right parenthesis space straight x top enclose straight c space equals space top enclose straight a space straight x space left parenthesis top enclose straight b space straight x top enclose straight c right parenthesis comma space top enclose straight a. top enclose straight b space not equal to 0 comma space straight b with rightwards arrow on top. straight c with rightwards arrow on top space not equal to 0
rightwards double arrow space left parenthesis top enclose straight a. top enclose straight c right parenthesis. top enclose straight b space minus left parenthesis top enclose straight b. top enclose straight c right parenthesis top enclose straight a space equals space left parenthesis top enclose straight a. top enclose straight c right parenthesis top enclose straight b space minus left parenthesis top enclose straight a. top enclose straight b right parenthesis top enclose straight c
left parenthesis top enclose straight a. top enclose straight b right parenthesis top enclose straight c space equals left parenthesis top enclose straight b. top enclose straight c right parenthesis top enclose straight a
top enclose straight a space vertical line vertical line top enclose straight c
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32.

A particle has two velocities of equal magnitude inclined to each other at an angle θ. If one of them is halved, the angle between the other and the original resultant velocity is bisected by the new resultant. Then θ is

  • 90°

  • 120°

  • 45°

  • 45°

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33.

At a telephone enquiry system, the number of phone cells regarding relevant enquiry follow Poisson distribution with an average of 5 phone calls during 10-minute time intervals. The probability that there is at the most one phone call during a 10-minute time period is

  • 6/5

  • 5/6

  • 6/55

  • 6/55

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34. integral subscript 0 superscript straight pi space xf space left parenthesis sin space straight x space right parenthesis space dx is equal to
  • straight pi integral subscript 0 superscript straight pi space straight f left parenthesis cos space straight x right parenthesis space dx
  • straight pi integral subscript 0 superscript straight pi space straight f left parenthesis sin space straight x right parenthesis space dx
  • straight pi over 2 integral subscript 0 superscript straight pi space straight f left parenthesis cos space straight x right parenthesis space dx
  • straight pi over 2 integral subscript 0 superscript straight pi space straight f left parenthesis cos space straight x right parenthesis space dx
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35.

The values of a, for which the points A, B, C with position vectors 2 straight i with hat on top minus straight j with hat on top plus straight k with hat on top comma space straight i with hat on top minus 3 straight j with hat on top minus 5 straight k with hat on top space and space straight a straight i with hat on top minus 3 straight j with hat on top plus straight k with hat on toprespectively are the vertices of a right-angled triangle with C =π/2  are

  • 2 and 1

  • −2 and −1

  • −2 and 1

  • −2 and 1

102 Views

36. integral subscript negative 3 straight pi divided by 2 end subscript superscript negative straight pi divided by 2 end superscript open square brackets open parentheses straight x plus straight pi close parentheses cubed plus space cos space left parenthesis straight x space plus 3 straight pi right parenthesis close square brackets dx space is space equal space to
  • straight pi to the power of 4 over 32
  • straight pi to the power of 4 over 32 space plus space pi over 2
  • pi over 2
  • pi over 2
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37.

If x is real, the maximum value of fraction numerator 3 straight x squared space plus 9 straight x space plus 17 over denominator 3 straight x squared space plus 9 straight x space plus 7 end fraction space is

  • 1/4

  • 41

  • 1

  • 1

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38.

The function straight f left parenthesis straight x right parenthesis space equals straight x over 2 space plus 2 over straight x has a local minimum at

  • x = 2

  • x = −2

  • x = 0

  • x = 0

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39.

Angle between the tangents to the curve y = x2 − 5x + 6 at the points (2, 0) and (3, 0) is

  • π/2

  • π/4

  • π/6

  • π/6

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40.

The image of the point (−1, 3, 4) in the plane x − 2y = 0 is

  • open parentheses 9 over 5 comma negative 13 over 5 comma space 4 close parentheses
  • open parentheses fraction numerator negative 17 over denominator 3 end fraction comma fraction numerator negative 19 over denominator 3 end fraction comma 1 close parentheses
  • (15, 11, 4)

  • (15, 11, 4)

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