The odd numbers are divided as follows:
Row $1$: $1, 3$
Row $2$: $5, 7, 9, 11$
Row $3$: $13, 15, 17, 19, 21, 23$
Then the sum of the $n^{th}$ row is:

  • A
    $n^3 + (n-1)^3$
  • B
    $n^3 - (n-1)^3$
  • C
    $2n^3$
  • D
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$\frac{1}{(1 + a)(2 + a)} + \frac{1}{(2 + a)(3 + a)} + \frac{1}{(3 + a)(4 + a)} + \dots + \infty$ का मान क्या है,(जहाँ $a$ एक स्थिरांक है)।

मान लीजिए कि $S$ श्रेणी के पहले $9$ पदों का योग है: $(x+ka) + (x^2+(k+2)a) + (x^3+(k+4)a) + (x^4+(k+6)a) + \dots$ जहाँ $a \neq 0$ और $x \neq 1$ है। यदि $S = \frac{x^{10}-x+45a(x-1)}{x-1}$ है,तो $k$ का मान ज्ञात कीजिए।

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तीन संख्याएँ $G.P.$ में हैं जिनका योग $38$ है और उनका गुणनफल $1728$ है। उनमें से सबसे बड़ी संख्या है

समीकरण $x^2 - 18x + 9 = 0$ के मूलों का $G.M.$ (गुणोत्तर माध्य) क्या है?

यदि $a$ और $b$ के बीच का हरात्मक माध्य (harmonic mean) $H$ है,तो $\frac{H + a}{H - a} + \frac{H + b}{H - b} = $

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