If p and q are positive real numbers such that p2 + q2 = 1, then

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161.

If p and q are positive real numbers such that p2 + q2 = 1, then the maximum value of (p + q) is

  • 2

  • 1/2

  • fraction numerator 1 over denominator square root of 2 end fraction
  • fraction numerator 1 over denominator square root of 2 end fraction


D.

fraction numerator 1 over denominator square root of 2 end fraction
Using space straight A. straight M. space greater or equal than space straight G. straight M comma
fraction numerator straight p squared space plus straight q squared over denominator 2 end fraction space greater or equal than pq
rightwards double arrow space pq space less or equal than 1 half
left parenthesis straight p plus straight q right parenthesis squared space equals space straight p squared space plus straight q squared space plus 2 pq
rightwards double arrow space left parenthesis straight p plus straight q right parenthesis squared space equals straight p squared space plus straight q squared space plus 2 pq
rightwards double arrow space straight p plus straight q space less or equal than square root of 2
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162.

The sum of the series fraction numerator 1 over denominator 2 space factorial space end fraction minus fraction numerator 1 over denominator 3 factorial end fraction space plus space fraction numerator 1 over denominator 4 factorial end fraction space..... space upto space infinity

  • e-2

  • e–1

  • e-1/2

  • e-1/2

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163.

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

174 Views

164.

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

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165.

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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166.

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

117 Views

167.

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

322 Views

168.

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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169.

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
114 Views

170.

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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