What are the binary representations of the following decimal numbers?
18, 27, 42

In how many ways can the letters of MAHABHARAT be arranged so that
i) B and T are never together
ii) M, A, T, H occurs at first four places.

The annual income of Sohan (excluding HRA is Rs. 2,10,000. He contributes Rs. 4000 per month in his provident fund account and pays on annual insurance Premimum of Rs. 22000. Calculate the income tax including surcharge sohan has to pay in the last month of the year if his earlier deductions as income tax for the first 11 month were at the rate of Rs. 1800 per month. (2) Assuming the following while calculating income tax

a) Standard deduction: 1/3rd of the total annual income subject to a maximum of Rs. 20,000 (Rs. 25000 in case the annual income is less then Rupees one lakh).

b) Rates of income tax

  Slab                                              Income tax
i)       upto 50,000                                   No tax
ii)     From Rs. 50,001 to Rs. 60,000     10% of the amount exceeding Rs. 50,000
 
iii)    From Rs. 60,001 to Rs.            Rs. 1000+20% of the amount exceeding
Rs. 60,000
150,000
 

 
iv)     From Rs. 150,001 & onwards        Rs. 19,000+30% of the amount exceeding
                                          Rs. 150,000
 

c)    Rebate in tax       20% of the total savings subject to a
                                                                                                                                     maximum of Rs. 12,000

d) Surcharge                        10% of the total tax payable (after rebate)

i) 25.034                                 ii) 25.304

iii) 25.64                                  iv) 25.0034

Perform the following steps listed below and check whether the answer is a multiple of 9?
Step-1 Choose a number between 100 and 1000
Step-2 Interchange its first and last digits to make another number
Step-3 Subtract the small number from the largest number
Step-4 Repeat step-2 for the number obtained in step-3
Step-5 Now add the numbers obtained in step-3 and step-4.
Try with some other starting number between 100 and 1000 and check whether the answer is a again a multiple of 9.

Using the result C(n, r) + C(n, r -1) = C(n +1, r), computeC(8,5) +C(8,4) .

If the length and width of a tape are 2m and 28cm respectively, then they are in the ratio of
1) 100 : 16                             2) 7 : 50
3) 50 : 7                                 4) 1 : 8