Correct Answer: addddb

Solution : Given:
_ cb _ ca _ bacb _ ca _ bac_ d

To fill the series we have to divide the series→_ cb _ / ca _ b / acb _ / ca _ b / ac_ d
Let's check each option –
First option: badddb; bcba / cadb / acbd / cadb / acbd (No repeated pattern has been found.)
Second option: bbbddd; bcbb / cabb / acbd / cadb / acdd (No repeated pattern has been found.)
Third option: addddb; acbd / cadb / acbd / cadb / acbd (acbd and cadb are repeated alternatively.)
Fourth option: addbbb; acbd / cadb / acbb / cabb / acbd (No repeated pattern has been found.)

So, the series becomes→acbdcadbacbdcadbacbd. Hence, the third option is correct.

Correct Answer: ddaacc

Solution : Given: 
a _ ca _ c _ dc _ d _ ad _

To fill the series we have to divide the series – a _ c / a _ c / _ dc / _ d _ / ad _
Let's check each option –
First option: ddacdc; adc / adc / adc / cdd / adc (No repeated pattern has been found.)
Second option: daadca; adc / aac / adc / ddc / ada (No repeated pattern has been found.)
Third option: dadaac; adc / aac / ddc / ada / adc (No repeated pattern has been found.)
Fourth option: ddaacc; adc / adc / adc / adc / adc (adc is repeated in the series.)

So, the series becomes→adcadcadcadcadc. Hence, the fourth option is correct.

Correct Answer: cacc

Solution : Given:–
a _ ca _ ca _ caa _

Let's check the given options –

First option: caca
The series becomes accaacaccaaa
There is no pattern in the above series.

Second option: cacc
The series becomes accaacaccaac
The pattern in the series becomes accaac / accaac

Third option: caac
The series becomes accaacaacaac
There is no pattern in the above series.

Fourth option: ccca
The series becomes accaccaccaaa
There is no pattern in the above series.

Hence, second option is correct.

Correct Answer: a c a c a b

Solution : Given -

a _ b _ ca _ b _ c _ a _ cc

Let's check the options.

option first: a c b c a b

The series becomes aabccabbccaabcc

There is no pattern in the above series.

option second: a b a b c a

The series becomes aabbcaabbccaacc

There is no pattern in the above series.

option third: a c a c a b

The series becomes aabccaabccaabcc

The pattern in the series becomes aabcc/aabcc/aabcc.

option fourth: a b a b a c

The series becomes aabbcaabbcaaccc

There is no pattern in the above series.

Hence, third option is correct.

Correct Answer: Ca(HCO₃)₂

Solution : The correct option is Ca(HCO₃)_2.

The presence of bicarbonates of calcium and magnesium causes water to become temporarily hard, but the presence of soluble chlorides and sulphates of calcium and magnesium causes permanent hardness. Calcium bicarbonate, also called calcium hydrogen carbonate, has the chemical formula Ca(HCO₃)₂. 

Correct Answer: 19

Solution : Given,
a + b + c = 19 and ab + bc + ca = 120
We know,
a³ + b³ + c³ – 3abc = (a + b + c) [(a + b + c)² – 3(ab + bc + ca)]
= 19[19² – 3 × 120]
= 19[361 – 360]
= 19 × 1
= 19
Hence, the correct answer is 19.