Number Operations and Properties

First term $=5$

Common difference d = (10 - 28) / (11 + 1) = -18 / 12 = -1.5. The 6th A.M. is a + 6d = 28 + 6(-1.5) = 28 - 9 = 19.

Since $25$ is the arithmetic mean of $X$ and $46$, 

As there are $ 3 $ negative numbers, which is an odd number, the product will be negative.

So, $ -5 \times -12 \times 2\times -3 = - 360 $

$4 \times (-3)\times (-2)\times 6\times (-5)$
$=24\times -30$
$=-720$

Given, $

\dfrac { (-60)\times (-72) }{ 36\times (-15) } $

As there are $ 2 $ negative numbers in the numerator and $ 1 $ in the

denominator, the answer will be negative.

Cancelling out the common factors and simplifying we get

$ \dfrac { (-60)\times (-72) }{ 36\times (-15) }=-4\times 2  = - 8 $

As there are $ 4 $ negative numbers, which is an even number, the product

will be positive.





So, $ -5 \times -2 \times -2\times -3 = 60 $

$ (-5)\times 8 = - 40 $

$ 3\times (-2) = -6 $

Hence, $ ((-5)\times 8 ) \times (3\times (-2)) = -40 \times -6 = 240 $

$(-54)\times (64)\div (-27)\times (-128)$
$=-3456 \div 3456$
$=-1$

$96\times (-25) \div (-75)\times (-16)$
$=-2400\div 1200$
$=-2$

$-112 \times (-1) = +112$

$(132)\div (-12)=\frac{132}{-12}$
                             $=\frac{12\times11}{-12}$
                             $=-1\times11$
                             $=-11$
Option D is correct.

There are $3$ negative signs . So, the resultant of $3$ multiplications would be negative.