Eamcet - Maths - Mathematical Induction Test

Test Instructions :

1. The Test is 1hr duration.
2. The Test Paper consists of 30 questions. The maximum marks are 30.
3. All the questions are multiple choice question type with three options for each question.
4. Out of the three options given for each question, only one option is the correct answer.
5. Each question is allotted 1 mark for each correct response.
6. 0.25 will be deducted for incorrect response of each question.
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102n+1+1 for all n?N is divisible by

  

  

  

  

If 23+43+63+….+(2n)3=kn2(n+1)2, then k=

  

  

  

  

1+4+13+40+…n terms=

  

  

  

  

13+12+1+ 23+22+2+ 33+32+3+…3n terms=

  

  

  

  

1.3+2.32+3.33+4.34+….+n.3n=

  

  

  

  

1.2+2.3+3.4+….n terms

  

  

  

  

The area bounded by y = 3x and y = x2 is (in sq units)

  

  

  

  

13+23+ 33+….+1003=k2, then k=

  

  

  

  

(1/1.3)+(1/3.5)+(1/5.7)+….n terms=

  

  

  

  

(12/3)+(12+22/5)+(12+22+32/7)+… n terms

  

  

  

  

If nεN then 3.52n+1+23n+1 is divisible by

  

  

  

  

1.3.4+2.4.5+3.5.6+…. n terms

  

  

  

  

Sum of n brackets of (1)+(1/3+1/32)+(1/33+1/34+1/35)+…. Is

  

  

  

  

∑((12+22+32+….+n2)/1+2+3+….+n)=

  

  

  

  

1.4.7+4.7.10+7.10.13+…. n terms

  

  

  

  

12+32+52+…+(2n-1)2=

  

  

  

  

(1)+(2+3+4)+(5+6+7+8+9)+… n brackets=

  

  

  

  

(1)+(2+3)+(4+5+6)+….n brackets=

  

  

  

  

(13/1)+(13+23/1+3)+(13+23+33/1+3+5)+….. n terms

  

  

  

  

1.22+2.32+3/42+….n(n+1)2/12.2+22.3+32.4+…n2(n+1)=

  

  

  

  

If nεN then 10n+3.4n+2+5 is divisible by

  

  

  

  

2.4+4.7+6.10+….(n-1) terms=

  

  

  

  

(14/1.3)+(24/3.5)+(34/5.7)+….+n4/(2n+1)(2n-1)=

  

  

  

  

The equation of lines passing through the intersection of  lines x-2y+5=0 and 3x+2y+7=0 and perpendicular to x-y=0 is

  

  

  

  

The sum of the first n terms of the series 12+2.22+32+2.42+52+2.62+…. Is n(n+1)2/2 when n is even. When n is odd the sum is

  

  

  

  

(1)+(1+2)+(1+2+3)+…. n brackets=

  

  

  

  

2+3+5+6+8+9+…..2n terms=

  

  

  

  

2.12+3.22+4.32+….+(n+1)n2=

  

  

  

  

The value of the sum in the n th bracket of (1)+(2+3)+(4+5+6+7)+(8+9+10+15)+… is

  

  

  

  

1+4+10+19+….(3n2-3n+2)/2=

  

  

  

  

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