SSC Exams - Quantitative Aptitude

Algebra, Trigonometry, Geometry & Mensuration question bank (Advanced Mathematics)

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Q1.

Algebra: If $x + \frac{1}{x} = 3$ in 'Algebra: Basic Algebraic Identities ($(a+b)^3, a^3+b^3+c^3-3abc$) and Linear Equations', then what is the value of $x^3 + \frac{1}{x^3}$?

(A)

$18$ ($3^3 - 3(3) = 27 - 9$) (Algebra: Basic Algebraic Identities ($(a+b)^3, a^3+b^3+c^3-3abc$) and Linear Equations)

(B)

$27$

(C)

$36$

(D)

$24$

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Q2.

Mensuration 3D: A solid metallic cone of radius 6 cm and height 24 cm is melted and recast into small spheres of radius 2 cm in 'Algebra: Basic Algebraic Identities ($(a+b)^3, a^3+b^3+c^3-3abc$) and Linear Equations'. Number of spheres is:

(A)

36 ($\frac{\frac{1}{3}\pi r_1^2 h}{\frac{4}{3}\pi r_2^3} = \frac{36 \times 24}{4 \times 8}$) (Algebra: Basic Algebraic Identities ($(a+b)^3, a^3+b^3+c^3-3abc$) and Linear Equations)

(B)

(C)

(D)

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