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Questions(204)
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Find the number which, when added to the terms of the ratio 11:23 makes it equal to the ratio 4:7
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How many numbers between 1 and 200 are exactly divisible by exactly two of 3,9 and 27?
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Factorise $x^4+1+x^2$
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$x^2+\dfrac{1}{4x^2}=17$, find the value of $x-\dfrac{1}{2x}$
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If the ratio of the sum of the first 6 terms of a geometric progression to the sum of first 3 terms is 9, what is the common ratio?
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The length of the shadow of a tower standing on a level ground is found to be $2x$ meters longer when the sun's altitude is 30° than when it was 45°. Prove that height of the tower is $\left(\sqrt{3}+1\right)x$ m.
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If $4x^2-12x+k$ is a perfect square, find the numerical value of $k$
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If $x+\dfrac{1}{x}=m$, then show that $x^3+\dfrac{1}{x^3}=m(m^2-3)$
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If $a^2-4a-1=0$ find the value of $a^2+\dfrac{1}{a^2}+3a-\dfrac{3}{a}$
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If $x-\dfrac{1}{x}=\sqrt{2}$, show that $x^2+\dfrac{1}{x^2}=4$
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