Let $p$ and $q$ be positive integers satisfying $p<q$ and $p+q=k$. What is the smallest value of $k$ that does not determine $p$ and $q$ uniquely?

The total cost of 4 oranges, 6 mangoes and 8 apples is equal to twice the total cost of 1 orange, 2 mangoes and 5 apples. Consider the following statements:

1. The total cost of 3 oranges, 5 mangoes and 9 apples is equal to the total cost of 4 oranges, 6 mangoes and 8 apples.
2. The total cost of one orange and one mango is equal to the cost of one apple.

Which of the statements given above is/are correct?

a + b means a – b; a – b means a x b; a x b means a ÷ b; a ÷ b; means a + b, then what is the value of $10 + 30 – 100 \times 50 \div 25$? (Operations are to be replaced simultaneously)

If P means ‘greater than ( $>$ )’; Q means ‘less than ( $<$ )’; R means ‘not greater than ( $less$ )’; S means ‘not less than ( $geq$ )’ and T means ‘equal to ( $=$ )’, then consider the following statements :

1. If $2x (S) 3y$ and $3x (T) 4z$, then $9y (P) 8z$.
2. If $x (Q) 2y$ and $y (R) z$, then $x (R) z$.

Which of the statements given above is/are correct?

Consider the sequence

A_BCD_BBCDABC_DABC_D

that follows a certain pattern. Which one of the following completes the sequence?

In the expression $5 * 4* 3* 2* 1$, $*$ is chosen from $+$, $-$, $\times$ each at most two times. What is the smallest non-negative value of the expression?