The sum of first 20  terms of the sequence 0.7,0.77,0.777......

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of A × B having 3 or more elements is

  • 256

  • 220

  • 219

  • 219

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2.

The real number k for which the equation, 2x3 +3x +k = 0 has two distinct real roots in [0,1]

  • lies between 1 and 2

  • lies between 2 and 3

  • lies between -1 and 0

  • lies between -1 and 0

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3.

The sum of first 20  terms of the sequence 0.7,0.77,0.777...... is

  • 7 over 81 space left parenthesis 179 minus 10 to the power of negative 20 end exponent right parenthesis
  • 7 over 9 left parenthesis 99 minus 10 to the power of negative 20 end exponent right parenthesis
  • 7 over 81 left parenthesis 179 plus 10 to the power of negative 20 end exponent right parenthesis
  • 7 over 81 left parenthesis 179 plus 10 to the power of negative 20 end exponent right parenthesis


C.

7 over 81 left parenthesis 179 plus 10 to the power of negative 20 end exponent right parenthesis

Let S = 0.7 + 0.77 +0.777 + .... upto 20 terms

7 over 10 plus 77 over 10 squared plus 777 over 10 cubed plus..... space upto space 20 space terms
space equals space open square brackets 1 over 10 space plus 11 over 10 squared plus 111 over 10 cubed plus........ plus space upto space 20 space terms close square brackets
equals space 7 over 9 open square brackets 9 over 10 plus 99 over 100 plus 999 over 1000 plus..... plus space upto space 20 space terms close square brackets
space equals 7 over 9 open square brackets open parentheses 1 minus 1 over 10 close parentheses plus open parentheses 1 minus 1 over 10 squared close parentheses plus open parentheses 1 minus 1 over 10 cubed close parentheses plus space..... upto space 20 space terms close square brackets

7 over 9 open square brackets left parenthesis 1 plus 1 plus..... upto space 20 space terms right parenthesis minus open parentheses 1 over 10 plus fraction numerator begin display style 1 end style over denominator begin display style 10 squared end style end fraction plus fraction numerator begin display style 1 end style over denominator begin display style 10 cubed end style end fraction plus.... upto space 20 space terms close parentheses close square brackets
space equals space 7 over 9 space open square brackets 20 minus fraction numerator begin display style 1 over 10 open curly brackets 1 minus open parentheses 1 over 10 close parentheses to the power of 20 close curly brackets end style over denominator 1 minus begin display style 1 over 10 end style end fraction close square brackets
space equals space 7 over 9 open square brackets 20 minus 1 over 9 open curly brackets 1 minus open parentheses 1 over 10 close parentheses to the power of 20 close curly brackets close square brackets space equals space 7 over 9 open square brackets 179 over 9 plus 1 over 9 open parentheses 1 over 10 close parentheses to the power of 20 close square brackets
equals space 7 over 181 space open square brackets 179 plus left parenthesis 10 right parenthesis to the power of negative 20 end exponent close square brackets

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4.

A ray of light along straight x space plus square root of 3 straight y end root space equals space square root of 3 get reflected upon reaching X -axis, the equation of the reflected ray is 

  • straight y equals space straight x plus square root of 3
  • square root of 3 straight y end root space equals space straight x minus square root of 3
  • straight y space equals space square root of 3 straight x end root minus square root of 3
  • straight y space equals space square root of 3 straight x end root minus square root of 3
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5.

The number of values of k, for which the system of equations
(k+1) x + 8y = 4k
kx + (k+3)y = 3k -1
has no solution, is 

  • infinite 

  • 1

  • 2

  • 2

269 Views

6.

If the equations x2 + 2x + 3 = 0 and ax2 + bx + c = 0, a, b, c ∈ R, have a common root, then a : b : c is

  • 1:2:3

  • 3:2:1

  • 1:3:2

  • 1:3:2

177 Views

7.

The circle passing through (1,-2) and touching the axis of x at (3,0) also passes through the point

  • (-5,2)

  • (2,-5)

  • (5,-2)

  • (5,-2)

181 Views

8.

If x, y, z are in A.P. and tan−1 x, tan−1 y and tan−1 z are also in A.P., then

  • x= y= z

  • 2x =3y = 6z

  • 6x = 3y= 2z

  • 6x = 3y= 2z

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9.

Consider :
Statement − I : (p ∧ ~ q) ∧ (~ p ∧ q) is a fallacy.
Statement − II : (p → q) ↔ (~ q → ~ p) is a tautology.

  • Statement -I is True; Statement -II is True; Statement-II is a correct explanation for Statement-I 

  • Statement - I is True; Statement -II is true; Statement-II is not a correct explanation for Statement-I

  • Statement -I is True; Statement -II is False.

  • Statement -I is True; Statement -II is False.

289 Views

10. limit as straight x space rightwards arrow 0 of fraction numerator left parenthesis 1 minus cos space 2 straight x right parenthesis left parenthesis 3 plus cos space straight x right parenthesis over denominator straight x space tan space 4 straight x end fraction space is space equal space to space
  • -1/4

  • 1/2

  • 1

  • 1

188 Views

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