–31 = 7 × (–5) + 4 –31 mod 7 = 4

Find –31 mod 7

In what ratio must rice at ₹ 69 per kg be mixed with rice ₹ 100 per kg so that the mixture be worth ₹ 80 per kg?

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Find the differential equation of the family of lines passing through the origin.

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What is the relationship between arrival time, burst time, completion time and waiting time?

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Write the number of all possible matrices of order $2 \times 2$ with each entry 1,2 or 3 .

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Check whether $(l+m+n)$ is a factor of the determinant $\left|\begin{array}{ccc}l+m & m+n & n+l \\ n & l & m \\ 2 & 2 & 2\end{array}\right|$ or not. Give reason.

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A container contains $70 /$ of orange squash. The squash being too concentrated $7 /$ of squash was taken out from this container and replaced by water. This process was repeated thrice to reduce the concentration of squash. How much quantity of orange squash is left in the container?

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Find $7^6(\bmod 3)$.

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Find the compound interest on ₹ 7000 at $6 \%$ p.a for 18 months compounded quarterly. [Use $(1.015)^{6}=1.093$ ]

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Find the order and degree (if defined) of the differential equation. $\frac{d^2 y}{d x^2}+x\left(\frac{d y}{d x}\right)^2=2 x^2 \log \left(\frac{d^2 y}{d x^2}\right)$

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For the following probability distribution:

$X$	$1$	$2$	$3$	$4$
$P(X)$	$1/10$	$1/5$	$3/10$	$2/5$

Find $E\left(X^2\right).$

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Numbers and Quantification — Applied Maths STD 12 Science — Question

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