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

  

  

  

  

2.12+3.22+4.32+….+(n+1)n2=

  

  

  

  

1.2+2.3+3.4+….n terms

  

  

  

  

2.4+4.7+6.10+….(n-1) terms=

  

  

  

  

(1)+(1+2)+(1+2+3)+…. n brackets=

  

  

  

  

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

  

  

  

  

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+4+13+40+…n terms=

  

  

  

  

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

  

  

  

  

(1)+(2+3)+(4+5+6)+….n brackets=

  

  

  

  

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

  

  

  

  

13+12+1+ 23+22+2+ 33+32+3+…3n terms=

  

  

  

  

2+3+5+6+8+9+…..2n terms=

  

  

  

  

1.4.7+4.7.10+7.10.13+…. n terms

  

  

  

  

13+23+ 33+….+1003=k2, then k=

  

  

  

  

1.3.4+2.4.5+3.5.6+…. n terms

  

  

  

  

1+4+10+19+….(3n2-3n+2)/2=

  

  

  

  

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

  

  

  

  

∑((12+22+32+….+n2)/1+2+3+….+n)=

  

  

  

  

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

  

  

  

  

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

  

  

  

  

12+32+52+…+(2n-1)2=

  

  

  

  

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

  

  

  

  

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

  

  

  

  

102n+1+1 for all n?N is divisible by

  

  

  

  

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

  

  

  

  

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

  

  

  

  

(1)+(2+3+4)+(5+6+7+8+9)+… n brackets=

  

  

  

  

(1/1.3)+(1/3.5)+(1/5.7)+….n terms=

  

  

  

  

1.3+2.32+3.33+4.34+….+n.3n=

  

  

  

  

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