Eamcet - Maths - Mathematical Induction

1.3+2.32+3.33+4.34+….+n.3n=

A.  (2n-1)3n+1+3/4

B.  (2n+1)3n+1+3/4 

C.  (2n+1)3n+1-3/4

D.  (2n-1)3n+1-3/4

View Answer  

Correct Answer :

(2n-1)3n+1+3/4



Explanation :
No Explanation available for this question

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

A.  10

B.  5

C.  4.5

D.  9

View Answer  

Correct Answer :

4.5



Explanation :
No Explanation available for this question

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

A.  (3n-1)3/2.4n-1

B.  (3n-1)/2.3 (n-1)(n+2)/2

C.  (3n+1)/3.7n-1

D.  none

View Answer  

Correct Answer :

(3n-1)/2.3 (n-1)(n+2)/2



Explanation :
No Explanation available for this question

1.3.4+2.4.5+3.5.6+…. n terms

A.  n(n+1)(n+2)/6

B.  n(n+1)(3n2+23n+46)/12

C.  n(27n3+90n2+45n-50)/4

D.  n(n+1)(2n+1)/6

View Answer  

Correct Answer :

n(n+1)(3n2+23n+46)/12



Explanation :
No Explanation available for this question

(1)+(2+3)+(4+5+6)+….n brackets=

A.  n(n+1)(n2+n+2)/8

B.  n(n+1)(n2-n+2)/8

C.  n(n-1)(n2+n+2)/8

D.  n(n-1)(n2-n+2)/8

View Answer  

Correct Answer :

n(n+1)(n2+n+2)/8



Explanation :
No Explanation available for this question

1.2+2.3+3.4+….n terms

A.  n(n+1)(n+5)/3

B.  n(n+1)(n+2)/3

C.  n(4n2+6n-1)/3

D.  n(n+1)(n+2)

View Answer  

Correct Answer :

n(n+1)(n+2)/3



Explanation :
No Explanation available for this question

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

A.  3n+5/3n+1

B.  3n+1/3n+5

C.  (3n+1)(3n+5)

D.  none

View Answer  

Correct Answer :

3n+5/3n+1



Explanation :
No Explanation available for this question

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

A.  2n(2n+2n-1-1)

B.  2n-1(2n+2n-1-1)

C.  2n-2(2n+2n-1-1)

D.  none

View Answer  

Correct Answer :

2n-2(2n+2n-1-1)



Explanation :
No Explanation available for this question

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

A.  3

B.  8

C.  9

D.  11

View Answer  

Correct Answer :

9



Explanation :
No Explanation available for this question

(1)+(2+3+4)+(5+6+7+8+9)+… n brackets=

A.  n(n+1)(n+2)/6

B.  n2(n2+1)/2

C.  n(n+1)(n+2)

D.  n(n+1)(2n+1)/6

View Answer  

Correct Answer :

n2(n2+1)/2



Explanation :
No Explanation available for this question

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

A.  n(n+1)(n+2)/6n

B.  n(n+1)(n2+n+1)/6(2n+1)

C.  n(n+2)(n+3)2

D.  none

View Answer  

Correct Answer :

n(n+1)(n2+n+1)/6(2n+1)



Explanation :
No Explanation available for this question

13+12+1+ 23+22+2+ 33+32+3+…3n terms=

A.  n(n+1)2

B.  n2(n-1)

C.  n(n+1)(3n2+7n+8)/12

D.  none

View Answer  

Correct Answer :

n(n+1)(3n2+7n+8)/12



Explanation :
No Explanation available for this question

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

A.  1/2

B.  1

C.  3/2

D.  2

View Answer  

Correct Answer :

2



Explanation :
No Explanation available for this question

1+4+10+19+….(3n2-3n+2)/2=

A.  n(n+1)(2n+1)/6

B.  n2(n+1)2/4

C.  n(n+1)(n+2)/6

D.  n(n2+1)/2

View Answer  

Correct Answer :

n(n2+1)/2



Explanation :
No Explanation available for this question

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

A.  x + y = 0

B.  x + y = 2

C.  x + y + 2=0

D.  x + y +1=0

View Answer  

Correct Answer :

x + y + 2=0



Explanation :
No Explanation available for this question

(1)+(1+2)+(1+2+3)+…. n brackets=

A.  n(n+1)(n+2)/6

B.  n(n+1)(3n2+23n+46)/12

C.  n(27n3+90n2+45n-50)/4

D.  n(n+1)(2n+1)/6

View Answer  

Correct Answer :

n(n+1)(n+2)/6



Explanation :
No Explanation available for this question

2+3+5+6+8+9+…..2n terms=

A.  3n2+2n

B.  4n2+2n

C.  4n2

D.  none

View Answer  

Correct Answer :

3n2+2n



Explanation :
No Explanation available for this question

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

A.  3n(n+1)/2

B.  [n(n+1)/2]2

C.  n(n+1)2/4

D.  n2(n+1)/2

View Answer  

Correct Answer :

n2(n+1)/2



Explanation :
No Explanation available for this question

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

A.  24

B.  64

C.  17

D.  676

View Answer  

Correct Answer :

17



Explanation :
No Explanation available for this question

13+23+ 33+….+1003=k2, then k=

A.  10100

B.  5000

C.  5050

D.  1010

View Answer  

Correct Answer :

5050



Explanation :
No Explanation available for this question

1.4.7+4.7.10+7.10.13+…. n terms

A.  n(n+1)(n+2)/6

B.  n(n+1)(3n2+23n+46)/12

C.  n(27n3+90n2+45n-50)/4

D.  n(n+1)(2n+1)/6

View Answer  

Correct Answer :

n(27n3+90n2+45n-50)/4



Explanation :
No Explanation available for this question

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

A.  n(n+1)(n+2)/18

B.  n(n+1)(n+2)/6

C.  n(n+1)(n+2)/3

D.  2n(n+1)(n+2)/3

View Answer  

Correct Answer :

n(n+1)(n+2)/18



Explanation :
No Explanation available for this question

(1/1.3)+(1/3.5)+(1/5.7)+….n terms=

A.  1/n+1

B.  n/n+1

C.  n/2n+1

D.  n/3n+1

View Answer  

Correct Answer :

n/2n+1



Explanation :
No Explanation available for this question

12+32+52+…+(2n-1)2=

A.  n(2n-1)(2n+1)/3

B.  n(2n+1)(2n+1)/3

C.  (2n-1)(2n-1)/3

D.  none

View Answer  

Correct Answer :

n(2n-1)(2n+1)/3



Explanation :
No Explanation available for this question

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

A.  n(2n2+9n+13)/24

B.  n(2n3+9n+13)/18

C.  n(n2+9n+13)/24

D.  n(n2+9n+13)/8

View Answer  

Correct Answer :

n(2n2+9n+13)/24



Explanation :
No Explanation available for this question

2.4+4.7+6.10+….(n-1) terms=

A.  2n3-2n2

B.  (n3+3n2+1)/6

C.  2n3+2n

D.  none

View Answer  

Correct Answer :

2n3-2n2



Explanation :
No Explanation available for this question

∑((12+22+32+….+n2)/1+2+3+….+n)=

A.  (n2+2n)/3

B.  n2-2n/6

C.  n2+11/12n

D.  none

View Answer  

Correct Answer :

(n2+2n)/3



Explanation :
No Explanation available for this question

1+4+13+40+…n terms=

A.  3n+1-2n/2n

B.  (3n+1-2n-3)/4

C.  3n-1+3n/9

D.  (3n+1+2n2)/8

View Answer  

Correct Answer :

(3n+1-2n-3)/4



Explanation :
No Explanation available for this question

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

A.  2

B.  3

C.  7

D.  11

View Answer  

Correct Answer :

11



Explanation :
No Explanation available for this question

2.12+3.22+4.32+….+(n+1)n2=

A.  n(n+1)(n+2)(3n+5)/12

B.  n(n+1)(n+2)(n+3)/4

C.  2n(n+1)(n+2)(n+3)

D.  n(n+1)(n+2)(3n+1)/12

View Answer  

Correct Answer :

n(n+1)(n+2)(3n+1)/12



Explanation :
No Explanation available for this question