Which one set of letters when sequentially placed at the gaps in the given letter series shall complete it?
a __ ca __ c __ dc __ d __ ad __

As per given question, the letter series is following the below pattern.
r t x y s x y z
After using the pattern the complete letter series will be as below.
r t x y s x y z/ r t x y sx y z

As per given question, the letter series is following the below pattern.
a b c
After using the pattern the complete letter series will be as below.
a b c/ c b a/ a b c/ c b a

The given letter series in below pattern.
ab a d n a
After completing the pattern, we will get complete letter series.
ab a d n a/ a b a d na/ a badna/ a badna

The pattern of given letter series is :-
a a b b
Using the same pattern, we will get complete letter series.
a a b b /a a b b/a a b b/ a a b b

The given letter series in below pattern.
a b c a b
Using the same pattern, we will get complete letter series.
a b c a b/ b c a b c/ c a b c a/ a b

The given letter series in below pattern.
pp q q/qp p p
After completing the pattern, we will get complete letter series.
pp q q /qp p p/ qq q p/qq p q /qq p q

16 x 2 ÷ 25 + 7 - 4
After replacing the sign according to the given question
16 ÷ 2 + 25 - 7 x 4
Apply the rule BODMAS
B - Brackets first
O - Orders (i.e. Powers and Square Roots, etc.)
DM - Division and Multiplication (left-to-right)
AS - Addition and Subtraction (left-to-right)
             = 16 ÷ 2 + 25 - 7 x 4
             = 8 + 25 - 28
             = 25 - 20
             = 5

Try all option one by one;
From option ( b )
49 - 7 + 3 ÷ 5 x 8 = 24
Change the sign, as per the question,
49 ÷ 7 x 3 - 5 + 8 = 24
Apply the BODMAS rule
B - Brackets first
O - Orders (i.e. Powers and Square Roots, etc.)
DM - Division and Multiplication (left-to-right)
AS - Addition and Subtraction (left-to-right)
Now Applying the BODMAS rule one by one.
49 ÷ 7 x 3 - 5 + 8 = 24
After Division
7 x 3 - 5 + 8 = 24
After Multiplication
21 - 5 + 8 = 24
After Addition
29 - 5 = 24
After subtraction
24 = 24

Try all option one by one;
From option (d),
6 * 4 * 12 * 12
Change the sign, as per the question,
6 x 4 - 12 = 12
Apply the BODMAS rule
After Multiplication
24 - 12 = 12
After Substraction
?     &nbsp12 = 12

Using the proper symbols in ( c ), we get
5 x 2 ÷ 2 < 10 -4 + 8
After Replacing the Sign Apply the BODMAS Rule.
?      &nbsp5 x 1 < 18 - 4
?      &nbsp5 < 14
which is true .