CAT (QA) PYQs

The number of integers $x$ such that $0.25 < 2^x < 200$, and $2^x + 2$ is perfectly divisible by either $3$ or $4$, is

In a six-digit number, the sixth, that is, the rightmost, digit is the sum of the first three digits, the fifth digit is the sum of first two digits, the third digit is equal to the first digit, the second digit is twice the first digit and the fourth digit is the sum of fifth and sixth digits. Then, the largest possible value of the fourth digit is

For a $4$-digit number, the sum of its digits in the thousands, hundreds and tens places is $14$, the sum of its digits in the hundreds, tens and units places is $15$, and the tens place digit is $4$ more than the units place digit. Then the highest possible $4$-digit number satisfying the above conditions is