The value of `pi` upto 50 decimal places is given below:
`3.14159265358979323846264338327950288419716939937510`
(i) Make a frequency distribution of the digits from 0 to 9 after the decimal point.
(ii) What are the least and most frequently occurring digits ?

How many 6 digit numbers can be formed from the digits 0,1,3,5,7,9 which are divisible by (i) 10, (ii) 5.

The distance (in km) of 40 engineers from their residence to their place of work were found as follows : {:(5,3,10,20,25,11,13,7,12,31),(19,10,12,17,18,11,32,17,16,2),(7,9,7,8,3,5,12,15,18,3),(12,14,2,9,6,15,15,7,6,12):} Construct a grouped frequency distribution table with class size for the data given above taking the first interval as 0-5 (5 not included). What main features do you observe from this tabular representation ?

(i) Define universal indicator. For what purpose it is used? (ii) Two solutions A and B have pH values of 3.0 and 9.5 respectively. Which of these will turn litmus solution from blue to red and which will turn phenolphthalein from colourless to pink? (iii) What is a neutral substance. WHat colour will you get when you add a few drops of universal you get when you add a few drops of universal indicator of a test tube containing distilled water?

If 4-digit numbers greater than 5,000 are randomly formed from the digits 0,1, 3, 5, and 7, what is the probability of forming a number divided by 5 when, (i) the digits are repeated? (ii) the repeition of digits is not allowed?

Suppose U denotes the number of digits in the number (60)^(100) and M denotes the number of cyphers after decimal, before a significant figure comes in (8)^(-296) . If the fraction U/M is expressed as rational number in the lowest term as p//q (given log_(10)2=0.301 and log_(10)3=0.477 ) . The equation whose roots are p and q, is

Suppose U denotes the number of digits in the number (60)^(100) and M denotes the number of cyphers after decimal, before a significant figure comes in (8)^(-296) . If the fraction U/M is expressed as rational number in the lowest term as p//q (given log_(10)2=0.301 and log_(10)3=0.477 ) . The value of p is

Suppose U denotes the number of digits in the number (60)^(100) and M denotes the number of cyphers after decimal, before a significant figure comes in (8)^(-296) . If the fraction U/M is expressed as rational number in the lowest term as p//q (given log_(10)2=0.301 and log_(10)3=0.477 ) . The value of q is

Among the points given below some of the poitns lie on X-axis. Identify them (i) (0,5) (ii) (0,0) (iii) (3,0) (iv) (-5,0) (v) (-2,-3) (vi) (-6,0) (viii) (0,a) (ix) (b,0)