Sequences And Series CBSE Questions & Answers

Sequences And Series

This is Mathematics Class 11 Sequences and Series CBSE Questions & Answers. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
If a, b, c, d , e are in G. P., then \({e \over c}\) equals
  • A
    \({b \over a}\)
  • B
    \({d \over c}\)
  • C
    \({c \over b}\)
  • D
    \({d \over b}\)
    Correct
2
The product of first n odd terms of a G.P. whose middle term is m is
  • A
    mn
  • B
    \({m^n}\)
    Correct
  • C
    \({n^m}\)
  • D
    none of these
3
The fourth term of a G. P. is 2, then product of first 7 terms is
  • A
    32
  • B
    64
  • C
    \({1 \over {27}}\)
  • D
    128
    Correct
4
If three positive numbers a, b, c are in G. P. then log a, log b, log c are in
  • A
    A.G.P.
  • B
    A.P.
    Correct
  • C
    H.P.
  • D
    G.P.
5
The nth term of the sequence 5 + 55 + 555 + …. Is
  • A
    \({5 \over 9}({10^n} - 1)\)
    Correct
  • B
    none of these
  • C
    \(5 \times {10^{n - 1}}\)
  • D
    \(5 \times {11^{n - 1}}\)
6
The sum of first three terms of a G.P. is to the sum of next three terms is 125 : 27. The common ratio of the G.P. is
  • A
    none of these
  • B
    \({5 \over 3}\)
  • C
    \({3 \over 5}\)
    Correct
  • D
    \({1 \over 2}\)
7
Sum of an infinitely many terms of a G.P. is 3 times the sum of even terms. The common ratio of the G.P. is
  • A
    2
  • B
    none of these
  • C
    \({1 \over 2}\)
    Correct
  • D
    \({3 \over 2}\)
8
If \({{{a^n} + {b^n}} \over {{a^{n - 1}} + {b^{n - 1}}}}\) be the geometric mean between two distinct positive reals a and b then the value of n is
  • A
    0
  • B
    \({1 \over 2}\)
    Correct
  • C
    1
  • D
    -\({1 \over 2}\)
9
\(If{{a + b\;x} \over {a - b\;x}} = {{b + c\;x} \over {b - c\;x}} = {{c + dx} \over {c - dx}},x \ne 0,\)then a, b, c, d are in
  • A
    G.P.
    Correct
  • B
    H.P.
  • C
    none of these
  • D
    A.P.
10
The A.M. between two positive numbers a and b is twice the G.M. between them. The ratio of the numbers is
  • A
    \((2 + \sqrt 3 ):\left( {2 - \sqrt 3 } \right)\)
    Correct
  • B
    \((2 + 3):\left( {\sqrt 2 - 3} \right)\)
  • C
    \((\sqrt 3 + 1):\left( {\sqrt 3 - 1} \right)\)
  • D
    none of these
11
If A, G, H denote respectively the A.M., G.M. and H.M. between two unequal positive numbers, then
  • A
    \({G^2} = HA\)
    Correct
  • B
    \({A^2} = GH\)
  • C
    \(A = {G^2}H\)
  • D
    A = GH
12
The arithmetic, harmonic and geometric means between two +ve numbers are \({{144} \over {15}},15\) and 12 but not necessarily in this order, then the H.M. G.M. and A.M. respectively are
  • A
    \(12,\;15,\,\,{{144} \over {15}}\)
  • B
    \(15,\;12,\;{{144} \over {15}}\)
  • C
    \({{144} \over {15}},12,15\)
    Correct
  • D
    \(12,\;\,{{144} \over {15}},15\)
13
The sum of first eight terms of a G.P. is 82 times the sum of first four terms. The common ratio of the G.P. is
  • A
    4
  • B
    2
  • C
    3
  • D
    5
    Correct
14
The sum of first 10 terms of a G.P. is equal to 244 times the sum of its first five terms. Then the common ratio is
  • A
    5
  • B
    7
  • C
    4
  • D
    3
    Correct
15
The product of terms equidistant from the beginning and end in a G.P. (finite) is equal to
  • A
    first term
  • B
    last term
  • C
    product of the first and last terms
    Correct
  • D
    none of these