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If x1/4 + x-1/4 = 2, then what is the value of x81 + (1/x81 )?

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If a(a + b + c) = 45, b(a + b + c) = 75 and c(a + b + c) = 105, then what is the value of (a2 + b2 + c2 )?

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If x2 + (1/x2 ) = 1, then what is the value of x48 + x42 + x36 + x30 + x24 + x18 + x12 + x6 + 1?

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In the given figure, PQRS is a trapezium in which PM||SN, NR=9cm,PS=12cm,QM=NR and NR=SN.What is the area (in cm2 )of trapezium?

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In the given figure , PQR is an equilateral triangle and PS is the angle bisector $\angle$ P. What is the value of RT:RQ?

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Two chords of length 20 cm and 24 cm are drawn perpendicular to each other in a circle of radius is 15 cm. What is the distance between the Points of intersection of these chords (in cm) from the center of the circle?

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In the given figure,QRTS is a cyclic quadrilateral.If PT=5 cm,SQ=4cm and $/angle $ PQR=63º, then what is the value (in cm)of TR?

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What is the simplified value of sin2 (90 – θ) – [{sin(90 – θ)sin θ}/tan θ]?

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What is the simplified value of $ \left[ \dfrac{cos^{2}\theta}{1+sin\theta}-\dfrac{sin^{2}\theta}{1+cos\theta}\right]^{2}?$

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If 5 sec θ – 3 tan θ = 5, then what is the value of 5 tan θ – 3 sec θ?

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The table below shows the distribution of number of people living in 8 different countries and the per capita income of each of the countries.The total population of these countries taken together is 200 crores.
Per captia income=total GDP of country/population of the country

What is the difference (in crores) in population of the most and the least populated country?

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