SSC Exams - Quantitative Aptitude

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

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Q1.

Trigonometry: If $\tan \theta + \cot \theta = 2$ ($0^\circ < \theta < 90^\circ$) in 'Algebra: Basic Algebraic Identities ($(a+b)^3, a^3+b^3+c^3-3abc$) and Linear Equations', then $\tan^7 \theta + \cot^7 \theta$ is:

(A)

$2$ (Since $\theta = 45^\circ \implies \tan 45^\circ = 1$) (Algebra: Basic Algebraic Identities ($(a+b)^3, a^3+b^3+c^3-3abc$) and Linear Equations)

(B)

$1$

(C)

$4$

(D)

$2^7$

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Q2.

Geometry (Circles & Tangents): In 'Algebra: Basic Algebraic Identities ($(a+b)^3, a^3+b^3+c^3-3abc$) and Linear Equations', if tangents $PA$ and $PB$ from point $P$ to a circle with centre $O$ are inclined at $80^\circ$, then $\angle POA$ is:

(A)

$50^\circ$ ($\angle APB = 80^\circ \implies \angle AOB = 100^\circ$; $\angle POA = \frac{100^\circ}{2} = 50^\circ$) (Algebra: Basic Algebraic Identities ($(a+b)^3, a^3+b^3+c^3-3abc$) and Linear Equations)

(B)

$60^\circ$

(C)

$70^\circ$

(D)

$80^\circ$

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