C-11-Q091mediumsingle_mcq

If $a, b, c, d$ are continued proportional, then $(a^2+b^2+c^2)(b^2+c^2+d^2)$ equals—

a $(ab + bc + cd)^2$
b $(abcd)^2$
c $(a+b+c+d)^2$
d $a^2 + d^2$

ব্যাখ্যা

With $\frac{a}{b}=\frac{b}{c}=\frac{c}{d}$ , the products $ab,\,bc,\,cd$ behave like a geometric chain so that the cross terms align perfectly. The expression is therefore the perfect square $(ab+bc+cd)^2$ .

এই অধ্যায়ের আরও প্রশ্ন

C-11-Q092Given , the value of is—
C-11-Q093If , then
C-11-Q094The solutions of Example 5, where , include—
C-11-Q095The condition in Example 5 ensures—
C-11-Q096By componendo-dividendo on , the next simplified form is—
C-11-Q097If , then equals—
C-11-Q098If , with positive, equals—
C-11-Q099If , then equals—
C-11-Q100The compound ratio of and is—
C-11-Q101Two ratios and can be combined into the continued ratio—

Algebraic Ratio and Proportion — সব প্রশ্ন দেখুন (180টি) →

If $a, b, c, d$ are continued proportional, then $(a^2+b^2+c^2)(b^2+c^2+d^2)$ equals—

(ab + bc + cd)^2

(abcd)^2

(a+b+c+d)^2

a^2 + d^2

If a,b,c,da, b, c, da,b,c,d are continued proportional, then (a2+b2+c2)(b2+c2+d2)(a^2+b^2+c^2)(b^2+c^2+d^2)(a2+b2+c2)(b2+c2+d2) equals—

ব্যাখ্যা

এই অধ্যায়ের আরও প্রশ্ন

If a,b,c,da, b, c, da,b,c,d are continued proportional, then (a2+b2+c2)(b2+c2+d2)(a^2+b^2+c^2)(b^2+c^2+d^2)(a2+b2+c2)(b2+c2+d2) equals—

ব্যাখ্যা

এই অধ্যায়ের আরও প্রশ্ন

If $a, b, c, d$ are continued proportional, then $(a^2+b^2+c^2)(b^2+c^2+d^2)$ equals—

If $a, b, c, d$ are continued proportional, then $(a^2+b^2+c^2)(b^2+c^2+d^2)$ equals—