Tuesday, August 17, 2021

Sequence And Series : Mathematics

 


Q.1. The sum to n terms of the series

left parenthesis n squared minus 1 squared right parenthesis plus 2 left parenthesis n squared minus 2 squared right parenthesis plus 3 left parenthesis n squared minus 3 squared right parenthesis plus... i s 

A right parenthesis space n squared over 4 left parenthesis n squared minus 1 right parenthesis
B right parenthesis space n over 4 left parenthesis n plus 1 right parenthesis squared C right parenthesis space 0
D right parenthesis space 2 n left parenthesis n squared minus 1 right parenthesis 

ANS- A


Q.2. The sum up to (2n+1) terms of the series

a squared minus left parenthesis a plus b right parenthesis plus left parenthesis a plus 2 d right parenthesis squared minus left parenthesis a plus 3 d right parenthesis squared plus....... comma i s 

A right parenthesis space a squared plus 3 n d squared
B right parenthesis space a squared plus n a d plus n left parenthesis n minus 1 right parenthesis space d squared
C right parenthesis space a squared plus 3 n a d space plus n left parenthesis n minus 1 right parenthesis space d squared
D right parenthesis space a squared plus 2 n a d plus n left parenthesis space 2 n plus 1 right parenthesis space d squared

ANS- D


Q.3. If a,b,c are in H.P ., then the value of 

open parentheses 1 over b plus 1 over c minus 1 over a close parentheses open parentheses 1 over c plus 1 over a minus 1 over b close parentheses space comma space i s 

A right parenthesis space fraction numerator 2 over denominator b c end fraction minus 1 over b squared
B right parenthesis space 1 fourth open parentheses 3 over c squared plus fraction numerator 2 over denominator c a end fraction minus 1 over a squared close parentheses
C right parenthesis space 3 over b squared minus fraction numerator 2 over denominator a b end fraction
D right parenthesis space a l l space o f space t h e s e 

ANS- D


Q.4. In an arithmetic sequence a subscript 1 comma a subscript 2 comma space a subscript 3 comma.... comma a subscript n comma
increment equals open vertical bar table row cell a subscript m end cell cell a subscript n end cell cell a subscript p end cell row m n p row 1 1 1 end table close vertical bar space e q u a l s 

A)1

B) -1

C)0

D) mnp

ANS- C


Q.5. I f x to the power of 18 equals y to the power of 21 equals z to the power of 28 comma space t h e n space 3 comma 3 space log subscript y space x space comma space 3 space log subscript z space y space comma 7 space log subscript x z space a r e space i n space  

A) A.P

B) G.P.

C) H.P.

D) none of these


Q.6. For a sequence , if d subscript 1 equals 2 space a n d space fraction numerator a subscript n plus 1 over denominator a subscript n end fraction equals 1 third comma space T h e n space comma sum from r equals 1 to 20 of space a subscript r space i s 

A right parenthesis space space 20 over 2 left curly bracket 4 plus 19 plus 3 right curly bracket
B right parenthesis space 3 open parentheses 1 minus 1 over 30 to the power of 20 close parentheses
C right parenthesis space 2 left parenthesis 1 minus 3 to the power of 20 right parenthesis
D right parenthesis space n o n e space o f space t h e s e space 

ANS- B


Q.7. If a,b,c,d are in H.P., then ab+bc+cd is equal to 

A) 3 ad

B) (a+b) (c+d)

C) 3 ac

D) none of these 


Q.8. If a,b,c are in H.P., then the value of fraction numerator b plus a over denominator b minus a end fraction plus fraction numerator b plus c over denominator b minus c end fraction comma space i s space 

A) 1

B) 2

C) 3

D) 0


Q.9. If a,b,c  are in H.P., then 

A right parenthesis space fraction numerator a minus b over denominator b minus c end fraction equals a over c
B right parenthesis space fraction numerator b minus c over denominator c minus a end fraction equals b over a
C right parenthesis fraction numerator c minus a over denominator a minus b end fraction equals c over b
D right parenthesis space fraction numerator a minus b over denominator b minus c end fraction equals c over a 

ANS- A


Q.10. If S subscript 1 comma S subscript 2 comma end subscript S subscript 3 are the sum of n,2n,3n terms respectively of an A.P., then S subscript 3 divided by left parenthesis S subscript 2 minus S subscript 1 right parenthesis equals 

A) 1

B) 2

C) 3

D) 4





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