Which term of the following sequences:
(a) The given sequence is
Here, a = 2 and r =
Let the nth term of the given sequence be 128.
Thus, the 13th term of the given sequence is 128.
(b) The given sequence is
Here, a=
Let the nth term of the given sequence be 729.
Thus, the 12th term of the given sequence is 729.
(c) The given sequence is
Here,
a=
Let the nth term of the given sequence be .
Thus, the 9th term of the given sequence is .
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.
A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?
The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.
How many terms of G.P. 3, 32, 33, … are needed to give the sum 120?
Find the sum of all numbers between 200 and 400 which are divisible by 7.
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.
How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that
(i) repetition of the digits is allowed?
(ii) repetition of the digits is not allowed?
Find the derivative of 99x at x = l00.
Find the sum of all numbers between 200 and 400 which are divisible by 7.
If A and G be A.M. and G.M., respectively between two positive numbers, prove that the numbers are .
How many terms of G.P. 3, 32, 33, … are needed to give the sum 120?
Find the sum to n terms of the series 1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + …
Find the sum to n terms of the series
A die is rolled. Let E be the event “die shows 4” and F be the event “die shows even number”. Are E and F mutually exclusive?
The 5th, 8th and 11th terms of a G.P. are p, q and s, respectively. Show that q2 = ps.
A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?