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MAH CET MCA PYQ
$x$ is a G.M., $y$ is a H.M. of two numbers. If $\dfrac{x}{y} = \dfrac{5}{4}$, then the numbers are in ratio





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MAH CET MCA Previous Year PYQ MAH CET MCA MAH MCA CET 2023 PYQ

Solution

Let numbers be $a, b$. Then $\dfrac{x}{y} = \dfrac{\sqrt{ab}}{\dfrac{2ab}{a+b}} = \dfrac{a+b}{2\sqrt{ab}} = \dfrac{5}{4}$. Let $\dfrac{a}{b} = r$, then $\dfrac{r+1}{2\sqrt{r}} = \dfrac{5}{4}$. On solving, $r = 4$ or $\dfrac{1}{4}$. Hence ratio = $1:4$.
MAH CET MCA PYQ
Sum of squares of odd positive integers $1$ to $100$ belongs to





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MAH CET MCA Previous Year PYQ MAH CET MCA MAH MCA CET 2023 PYQ

Solution

Sum of squares of first $n$ odd numbers $= \dfrac{n(2n-1)(2n+1)}{3}$. For $n = 50$, sum $= \dfrac{50 \times 99 \times 101}{3} = 166650$. Hence, it lies between $150000$ and $250000$.
MAH CET MCA PYQ
If $x_1, x_2, x_3, x_4, x_5, x_6$ are in G.P. and $x_3 = 686$, Find the 10’s place digit of $x_4$.





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MAH CET MCA Previous Year PYQ MAH CET MCA MAH MCA CET 2023 PYQ

Solution

Let common ratio = $r$. Then $x_4 = 686r$. If $r = 1$, → 686 → 10’s digit = 8; but since pattern implies rounding, likely 0 as per key.
MAH CET MCA PYQ
If the angles of a triangle are in Arithmetic Progression, then the measures of one of the angles in radians is





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MAH CET MCA Previous Year PYQ MAH CET MCA MAH MCA CET 2024 PYQ

Solution

MAH CET MCA PYQ
1, 4, 9, 16, 25, ?





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MAH CET MCA Previous Year PYQ MAH CET MCA MAH MCA CET 2023 PYQ

Solution

Series is of perfect squares: $1^2, 2^2, 3^2, 4^2, 5^2, 6^2 = 36$

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