If the coefficients of rth, (r+ 1)th and (r + 2)th terms in the

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 Multiple Choice QuestionsMultiple Choice Questions

21.

Let a1, a2, a3, … be terms of an A.P. If fraction numerator straight a subscript 1 space plus straight a subscript 2 space plus......... straight a subscript straight p over denominator straight a subscript 1 space plus straight a subscript 2 space plus.......... straight a subscript straight q end fraction space equals space straight p squared over straight q squared comma space straight p not equal to straight q comma space then space straight a subscript 6 over straight a subscript 21 equals

  • 41/11

  • 7/2

  • 2/7

  • 2/7

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22.

If the coefficients of rth, (r+ 1)th and (r + 2)th terms in the binomial expansion of (1 + y)m are in A.P., then m and r satisfy the equation

  • m2 – m(4r – 1) + 4r2 – 2 = 0

  • m2 – m(4r+1) + 4r2 + 2 = 0

  • m2 – m(4r + 1) + 4r2 – 2 = 0

  • m2 – m(4r + 1) + 4r2 – 2 = 0


C.

m2 – m(4r + 1) + 4r2 – 2 = 0

Given space to the power of straight m straight C subscript straight r minus 1 end subscript space comma space to the power of straight m straight C subscript straight r space plus straight C presuperscript straight m subscript straight r plus 1 end subscript space are space in space straight A. straight P.
2 to the power of space straight m end exponent straight C subscript 2 space equals space fraction numerator blank to the power of straight m straight C subscript straight r minus 1 end subscript over denominator straight C presuperscript straight m subscript straight r end fraction space plus fraction numerator straight C presuperscript straight m subscript straight r plus 1 end subscript over denominator straight C presuperscript straight m subscript straight r end fraction
space equals space fraction numerator straight r over denominator straight m minus straight r plus 1 end fraction space plus fraction numerator straight m minus straight r over denominator straight r plus 1 end fraction
rightwards double arrow space straight m squared minus straight m space left parenthesis 4 straight r plus 1 right parenthesis space plus 4 straight r squared space minus 2 space equals space 0 space
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23.

If the letters of word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word SACHIN appears at serial number

  • 601

  • 600

  • 602

  • 602

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24.

If straight x space equals space sum from straight n equals space 0 to infinity of straight a to the power of straight n comma space straight y space equals space sum from straight n equals 0 to infinity of straight b to the power of straight n comma space sum from straight n equals 0 to infinity of straight c to the power of straight n where a, b, c are in A.P. and |a| < 1, |b|<1, |c|< 1, then x, y, z are in

  • G.P.

  • A.P.

  • Arithmetic − Geometric Progression

  • Arithmetic − Geometric Progression

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25.

If in a triangle ABC, the altitudes from the vertices A, B, C on opposite sides are in H.P., then sin A, sin B, sin C are in

  • G.P.

  • A.P.

  • Arithmetic − Geometric Progression

  • Arithmetic − Geometric Progression

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26.

If non-zero numbers a, b, c are in H.P., then the straight line straight x over straight a space plus straight y over straight b space plus 1 over straight c space equals space 0 always passes through a fixed point. That point is

  • (-1, 2)

  • (-1, -2)

  • (1, -2)

  • (1, -2)

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27.

The sum of the series space 1 plus space fraction numerator 1 over denominator 4.2 factorial end fraction space plus fraction numerator 1 over denominator 16.4 space factorial end fraction space plus fraction numerator 1 over denominator 64.6 space factorial end fraction plus........ space ad space inf. space is

  • fraction numerator straight e minus 1 over denominator square root of 2 end fraction
  • fraction numerator straight e plus 1 over denominator square root of 2 end fraction
  • fraction numerator straight e minus 1 over denominator 2 square root of 2 end fraction
  • fraction numerator straight e minus 1 over denominator 2 square root of 2 end fraction
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28.

If a1, a2, a3 , ....,an , .... are in G.P., then the value of the determinant open square brackets table row cell log space straight a subscript straight n end cell cell log subscript straight n plus 1 end subscript end cell cell log subscript straight n plus 2 end subscript end cell row cell log space straight a subscript straight n plus 3 end subscript end cell cell log space straight a subscript straight n plus 4 end subscript end cell cell log space straight a subscript straight n plus 5 end subscript end cell row cell log space straight a subscript straight n plus 6 end subscript end cell cell log space straight a subscript straight n plus 7 end subscript end cell cell log space straight a subscript straight n plus 8 end subscript end cell end table close square brackets is

  • 0

  • -2

  • 1

  • 1

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29.

Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation

  • x2 + 18x +16 = 0

  • x2-18x-16 = 0

  • x2+18x-16 =0

  • x2+18x-16 =0

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30.

Let T be the rth term of an A.P. whose first term is a and the common difference is d. If for r some positive integers m, n, m ≠ n, Tm = 1/n  and Tn = 1/m, then a-b equals

  • 0

  • 1

  • 1/mn

  • 1/mn

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