An AP has the property that the sum of first ten terms is half th

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

If the complex numbers z1, z2, z3 and z4 denote the vertices of a square taken in order. If z1 = 3 + 4i and z3 = 5 + 6i, then the other two vertices z2 and z4 are respectively

  • 5 + 4i, 5 + 6i

  • 5 + 4i, 3 + 6i

  • 5 + 6i, 3 + 5i

  • 3 + 6i, 5 + 3i


2.

The 100th term of the sequence 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, ... , is

  • 12

  • 13

  • 14

  • 15


3.

Let Sn denotes the sum of first n terms of an AP.If S4 = - 34, S5 = - 60 and S6 = - 93, then the common difference and the first term of the AP are respectively

  • - 7, 2

  • 7, - 4

  • 7, - 2

  • - 7, - 2


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4.

An AP has the property that the sum of first ten terms is half the sum of next ten terms. If the second term is 13, then the common difference is

  • 3

  • 2

  • 5

  • 4


B.

2

Let a and d be the first term and common difference, respectively.

Given, T2 = 13  a + d = 13        ...(i)

According to the question,

a1 +a2  ... + a10 = 12a11 + a12 + a20 2a1 +a2 + ... + a10 = a11 + a12 + a20 3a1 +a2 + ... + a10 = a1 +a2 + ... + a20add  a1 + a2 + ... + a10 on both sides 3 × 1022a + 9d = 2022a + 19d 6a + 27d = 4a + 38d 2a = 11d                     ...iiFrom Eqs. (i) and (ii), we get11d2 + d = 13  d = 2


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5.

If 8!13! + 54! = Pr9, then the value of r is

  • 4

  • 5

  • 3

  • 2


6.

The domain of the function f(x) = log2x +3x2 + 3x +2 is

  • R - {- 1, - 2}

  • R - {- 1, - 2, 0}

  • (- 3, - 1) ∪ (- 1, )

  • (- 3, ) - {- 1, - 2}


7.

If * is defined by a * b = a - b2 and is defined by a b = a2 + b, where a and b are integers, then (3 4) * 5 is equal to

  • 164

  • 38

  • - 12

  • - 28


8.

If cos-11 - x21 + x2 + cos-11 - y21 + y2 = π2, where xy < 1, then

  • x - y - xy = 1

  • x - y + xy = 1

  • x + y - xy = 1

  • x + y + xy = 1


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9.

If tan3tan-115, - π4 is equal to

  • - 1346

  • - 1146

  • - 746

  • - 946


10.

If tan-1- x + cos-1- 12 = π2, then the value of x is

  • 3

  • - 13

  • 13

  • - 3


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