The value  of  from Mathematics JEE Year 2005 Free Solved Pre

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

11.

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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12.

The value  of straight C presuperscript 50 subscript 4 space plus sum from straight r space equals 1 to 6 of straight C presuperscript 56 minus straight r end presuperscript subscript 3 space is

  • straight C presuperscript 55 subscript 4
  • straight C presuperscript 55 subscript 3
  • straight C presuperscript 56 subscript 3
  • straight C presuperscript 56 subscript 3


D.

straight C presuperscript 56 subscript 3
straight C presuperscript 50 subscript 4 space plus sum from straight r equals space 1 to 6 of space to the power of 56 minus straight r end exponent straight C subscript 3
rightwards double arrow to the power of 50 straight C subscript 4 space plus left square bracket to the power of 55 straight C subscript 3 space plus to the power of 54 straight C subscript 3 plus to the power of 53 straight C subscript 3 plus to the power of 52 straight C subscript 3 plus to the power of 50 straight C subscript 3 right square bracket
space equals left parenthesis to the power of 50 straight C subscript 4 space plus to the power of 50 straight C subscript 3 right parenthesis space plus space to the power of 51 straight C subscript 3 plus to the power of 52 straight C subscript 3 plus to the power of 53 straight C subscript 3 plus to the power of 54 straight C subscript 3 plus to the power of 55 straight C subscript 3
rightwards double arrow left parenthesis to the power of 51 straight C subscript 4 plus space to the power of 51 straight C subscript 3 right parenthesis plus space to the power of 52 straight C subscript 3 space plus to the power of 53 straight C subscript 3 space plus space to the power of 54 straight C subscript 3 space plus space to the power of 55 straight C subscript 3
rightwards double arrow space to the power of 55 straight C subscript 4 space plus space to the power of 55 straight C subscript 3 space equals space to the power of 56 straight C subscript 4
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13.

If A = open square brackets table row 1 0 row 1 1 end table close square brackets and I = open square brackets table row 1 0 row 0 1 end table close square brackets , then which one of the following holds for all n ≥ 1, by the principle of mathematical induction

  • An = nA – (n – 1)I

  • An = 2n-1A – (n – 1)I

  • An = nA + (n – 1)I

  • An = nA + (n – 1)I

131 Views

14.

If the coefficient of x7  open square brackets ax squared space plus open parentheses 1 over bx close parentheses close square brackets to the power of 11in equals the coefficient of x-7 inopen square brackets ax squared space minus open parentheses 1 over bx close parentheses close square brackets to the power of 11then a and b satisfy the relation

  • a – b = 1

  • a + b = 1

  • a/b =1

  • a/b =1

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15.

If z1 and z2 are two non-zero complex numbers such that |z1 + z2| = |z1| + |z2| then argz1 – argz2 is equal to

  • π/2

  • 0

  • 0

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16. If space straight omega space equals space fraction numerator straight z over denominator straight z minus begin display style 1 third end style straight i space end fraction space and space vertical line straight omega vertical line space equals 1 comma space then space straight z space lies space on
  • an ellipse

  • a circle

  • a straight line

  • a straight line

208 Views

17.

Let α and β be the distinct roots of ax2 + bx + c = 0, then limit as straight x rightwards arrow straight alpha of space fraction numerator 1 minus cos space left parenthesis ax squared plus bx plus space straight c right parenthesis over denominator left parenthesis straight x minus straight alpha right parenthesis squared end fraction space is equal to

  • straight a squared over 2 left parenthesis straight alpha minus straight beta right parenthesis squared
  • 0

  • negative straight a squared over 2 left parenthesis straight alpha minus straight beta right parenthesis squared
  • negative straight a squared over 2 left parenthesis straight alpha minus straight beta right parenthesis squared
100 Views

18.

If x is so small that x3 and higher powers of x may be neglected, then fraction numerator left parenthesis 1 plus straight x right parenthesis to the power of 3 divided by 2 end exponent space minus open parentheses 1 plus begin display style 1 half end style straight x close parentheses cubed over denominator left parenthesis 1 minus straight x right parenthesis to the power of 1 divided by 2 end exponent end fraction spacemay be approximated as

  • 1 minus 3 over 8 straight x squared
  • 3 x 6 plus 3 over 8 straight x squared
  • negative 3 over 8 straight x squared
  • negative 3 over 8 straight x squared
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19.

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

20.

In a triangle, ABC, let ∠C = π/2 . If r is the in radius and R is the circumradius of the triangle ABC, then 2 (r + R) equals

  • b + c

  • a+b

  • a + b + c

  • a + b + c

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