Question 3

A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?

Answer

Number of revolutions made by the wheel in 1 minute = 360

∴Number of revolutions made by the wheel in 1 second =360/60 = 6

In one complete revolution, the wheel turns an angle of 2π radian.

Hence, in 6 complete revolutions, it will turn an angle of 6 × 2π radian, i.e.,

12 π radian

Thus, in one second, the wheel turns an angle of 12π radian.

- Q:-
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

- Q:-
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.

- Q:- Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.
- Q:-
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.

- Q:-
How many terms of G.P. 3, 3

^{2}, 3^{3}, … are needed to give the sum 120? - Q:-
Find the sum of all numbers between 200 and 400 which are divisible by 7.

- Q:- Write the following sets in roster form:

(i) A = {x: x is an integer and - 3 < x < 7}.

(ii) B = {x: x is a natural number less than 6}.

(iii) C = {x: x is a two-digit natural number such that the sum of its digits is 8}

(iv) D = {x: x is a prime number which is divisor of 60}.

(v) E = The set of all letters in the word TRIGONOMETRY.

(vi) F = The set of all letters in the word BETTER. - Q:-
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.

- Q:-
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.

- Q:-
The 4th term of a G.P. is square of its second term, and the first term is –3. Determine its 7th term.

- Q:- Write the following sets in roster form:

(i) A = {x: x is an integer and - 3 < x < 7}.

(ii) B = {x: x is a natural number less than 6}.

(iii) C = {x: x is a two-digit natural number such that the sum of its digits is 8}

(iv) D = {x: x is a prime number which is divisor of 60}.

(v) E = The set of all letters in the word TRIGONOMETRY.

(vi) F = The set of all letters in the word BETTER. - Q:-
A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of terms occupying odd places, then find its common ratio.

- Q:-
If

*f*is a function satisfying f(x +y) = f(x) f(y) for all x,y N such that f(1) = 3and , find the value of

*n*. - Q:-
The sum of some terms of G.P. is 315 whose first term and the common ratio are 5 and 2, respectively. Find the last term and the number of terms.

- Q:-
If is the A.M. between

*a*and*b*, then find the value of*n*. - Q:-
Between 1 and 31,

*m*numbers have been inserted in such a way that the resulting sequence is an A.P. and the ratio of 7th and (*m*– 1)thnumbers is 5:9. Find the value of*m*. - Q:-
The sum of three numbers in G.P. is 56. If we subtract 1, 7, 21 from these numbers in that order, we obtain an arithmetic progression. Find the numbers.

- Q:-
Find the sum to

*n*terms of the series 3 × 8 + 6 × 11 + 9 × 14 +… - Q:- Find the sum to n terms of the A.P., whose kth term is 5k + 1.
- Q:-
Find the sum to

*n*terms of the series 1^{2}+ (1^{2}+ 2^{2}) + (1^{2}+ 2^{2}+ 3^{2}) + …

Rishabh
2020-09-07 16:47:46

Thanks sir

Hamdha
2019-12-13 06:42:09

Thanks....

Alwin
2019-08-11 20:41:24

Thanks to give the correct simple answer for this solution

krishna maheshwari
2019-08-09 22:07:06

Helpful solution

Tulika parija
2019-08-08 20:24:44

Thanks

Ram Rahim
2019-07-28 22:06:32

Thanks again sir

Tgfds
2019-07-27 17:30:24

Thanks a lot...ððððððð

Surbhi kariyar
2019-07-08 22:09:17

Thanks for help

Surbhi kariyar
2019-07-08 22:08:50

Thanks for help

Shaliha
2019-07-06 14:14:45

Thanks sir

- NCERT Chapter