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 x, 2 x + 2, 3 x + 3, … are in G.P., then the fourth term of this sequence is
  • A
    - 27
  • B
    13.75
  • C
    27
  • D
    - 13.5.
    Correct
2
If a, b, c are three positive real numbers then (a+ b) (b +c) (c + a) is not less than
  • A
    ( a + b + c)
  • B
    6 a b c
  • C
    2 ( a + b + c)
  • D
    8 a b c
    Correct
3
In an infinite G.P., each term is equal to the sum of all the terms which follow it. The common ratio of this G.P. is
  • A
    \({1 \over 3}\)
  • B
    none of these
  • C
    \({1 \over 4}\)
  • D
    \({1 \over 2}\)
    Correct
4
Sum of an infinite G.P. is \({5 \over 4}\)times the sum of all the odd terms. The common ratio of the G.P. is
  • A
    \({1 \over 3}\)
  • B
    none of these
  • C
    4
  • D
    \({1 \over 4}\)
    Correct
5
If a, b, c are in G.P., then
  • A
    \({a^2}(b + c) = {c^2}(a + b)\)
  • B
    \(a({b^2} + {a^2}) = c({b^2} + {c^2})\)
  • C
    \(a({b^2} + {c^2}) = c({a^2} + {b^2})\)
    Correct
  • D
    none of these
6
Two positive numbers are in the ratio\(\left( {2 + \sqrt 3 } \right):\left( {2 - \sqrt 3 } \right)\). The ratio of their A.M. to G.M. is :
  • A
    it is 2 : 1
    Correct
  • B
    it is \(\sqrt 3 :1\)
  • C
    none of these
  • D
    it is 2 : 1
7
All the terms of a G.P. are squared. The new series thus formed is
  • A
    H.P.
  • B
    A.P.
  • C
    none of these
  • D
    G.P.
    Correct
8
The least n for which \(1 + 3 + {3^2} + {3^3} + ........... + {3^{n - 1}} > 1000\) is
  • A
    7
    Correct
  • B
    6
  • C
    none of these
  • D
    8
9
The cotangents of \({\pi \over 3},{\pi \over 4}and{\pi \over 6}\) are in
  • A
    H.P.
  • B
    G.P.
    Correct
  • C
    A.P.
  • D
    none of these
10
If one A.M. A and two geometric means B and C be inserted between two numbers, then \({B^3} + {C^3}\) is equal to
  • A
    ABC
  • B
    \({{2\;BC} \over A}\)
  • C
    none of these
  • D
    2 ABC
    Correct
11
In a G.P. the ratio of the sum of first three terms to the sum of first six terms is 125 : 152. The common ratio of the G.P. is
  • A
    none of these
  • B
    \({5 \over 3}\)
  • C
    \({3 \over 5}\)
    Correct
  • D
    3.5
12
In a G.P. (m + n)th and ( m – n)th terms are respectively p and q. Its mth term is
  • A
    \(\sqrt {p\;q} \)
    Correct
  • B
    \({{p\; + q} \over 2}\)
  • C
    non of these
  • D
    p q
13
If a, b, c are in A. P., a , mb , c are in G.P., then a , \({m^2}b\), c are in
  • A
    H.P.
    Correct
  • B
    G.P.
  • C
    A.P.
  • D
    none of these
14
The next term of the sequence \({1 \over 4},{1 \over {36}},{1 \over {144}},\)
  • A
    \({1 \over {576}}\)
  • B
    none of these
  • C
    \({1 \over {1296}}\)
  • D
    \({1 \over {400}}\)
    Correct
15
If the sum of first n natural numbers is one-fifth of the sum of their squares, then n equals
  • A
    6
  • B
    7
    Correct
  • C
    8
  • D
    5