Take a two-digit number ab and reverse its digits. If the difference between ab and the new number is cd, then by which number is cd divisible?

The total number of 6-digit numbers that can be made using digits 1, 2, 3, 4, if all the digits should appear in the number at least once is:

A) 1560

B) 840

C) 1080

D) 480

Choose the correct statements: S1: All the numbers divisible by 10 are also divisible by 5. S2: A number divisible by 3 is also divisible by 6. S3: A number is divisible by 7, if the last two digits are divisible by 7. S4: If a number divides the product of two numbers exactly then it must exactly divide the numbers separately. S5: If a number exactly divides two numbers separately, and after division, if its difference is taken then this difference will also be exactly divisible by that number.

A palindrome is a positive integer which is unchanged if you reverse the order of its digits. If all palindromes are written in increasing order, how many possible prime values can the difference between successive palindromes take?

A. 1

B. 2

C. 3

D. none of the above

One mole of an ideal gas $(γ=1.4)$ at $500 \mathrm{~K}$ is filled in an adiabatic cylinder with a piston which is free to move against atmospheric pressure as shown. If a nonconducting fan is inserted into the gas space and rotated vigorously, so that the gas expands slowly until its volume doubles. If the work done by the fan is $7x \mathrm{~kJ}$, then the value of $x$ is. Write up to two digits after the decimal point. (Take $\mathrm{R}=8 \mathrm{~J/mol}• \mathrm{K}$ and neglect the heat capacity of the cylinder, piston, and fan.)

Take a political map of India (with State outlines) and mark:

(a) two states where Congress was not in power at some point during 1952-67.

(b) two states where the Congress remained in power through this period.