C-13-Q141mediumsingle_mcq

For an arithmetic series with $p$ th, $q$ th and $r$ th terms equal to $a, b, c$ respectively, the value of $a(q - r) + b(r - p) + c(p - q)$ is —

a $0$
b $abc$
c $a + b + c$
d $1$

ব্যাখ্যা

For an AP with $n$ th term $t_n = A + (n-1)D$ , substitute $a=A+(p-1)D$ , etc. Expanding $a(q-r)+b(r-p)+c(p-q)$ , the constant- $A$ terms give $A[(q-r)+(r-p)+(p-q)]=0$ and the $D$ terms also cancel completely, so the whole expression is identically $0$ .

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Finite Series — সব প্রশ্ন দেখুন (160টি) →

For an arithmetic series with $p$ th, $q$ th and $r$ th terms equal to $a, b, c$ respectively, the value of $a(q - r) + b(r - p) + c(p - q)$ is —

0

abc

a + b + c

1

For an arithmetic series with pppth, qqqth and rrrth terms equal to a,b,ca, b, ca,b,c respectively, the value of a(q−r)+b(r−p)+c(p−q)a(q - r) + b(r - p) + c(p - q)a(q−r)+b(r−p)+c(p−q) is —

ব্যাখ্যা

এই অধ্যায়ের আরও প্রশ্ন

For an arithmetic series with pppth, qqqth and rrrth terms equal to a,b,ca, b, ca,b,c respectively, the value of a(q−r)+b(r−p)+c(p−q)a(q - r) + b(r - p) + c(p - q)a(q−r)+b(r−p)+c(p−q) is —

ব্যাখ্যা

এই অধ্যায়ের আরও প্রশ্ন

For an arithmetic series with $p$ th, $q$ th and $r$ th terms equal to $a, b, c$ respectively, the value of $a(q - r) + b(r - p) + c(p - q)$ is —

For an arithmetic series with $p$ th, $q$ th and $r$ th terms equal to $a, b, c$ respectively, the value of $a(q - r) + b(r - p) + c(p - q)$ is —