Question 2

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

Answer

Let the three numbers in A.P. be *a* – *d*, *a*, and *a* + *d*.

According to the given information,

(*a* – *d*) + (*a*) + (*a* + *d*) = 24 … (1)

⇒ 3*a* = 24

∴ *a* = 8

(*a* – *d*) *a* (*a* + *d*) = 440 … (2)

⇒ (8 – *d*) (8) (8 + *d*) = 440

⇒ (8 – *d*) (8 + *d*) = 55

⇒ 64 – *d*2 = 55

⇒ *d*2 = 64 – 55 = 9

⇒ *d *= ± 3

Therefore, when *d* = 3, the numbers are 5, 8, and 11 and when *d* = –3, the numbers are 11, 8, and 5.

Thus, the three numbers are 5, 8, and 11.

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

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

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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.

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- 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:-
Name the octants in which the following points lie:

(1, 2, 3), (4, –2, 3), (4, –2, –5), (4, 2, –5), (–4, 2, –5), (–4, 2, 5), (–3, –1, 6), (2, –4, –7)

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

- Q:- If the sum of n terms of an A.P. is (pn + qn
^{2}), where p and q are constants, find the common difference - Q:-
The ratio of the sums of

*m*and*n*terms of an A.P. is*m*2:*n*2. Show that the ratio of*m*th and*n*th term is (2*m*– 1): (2*n*– 1). - Q:-
Find the sum to

*n*terms of the series whose*n*th term is given by*n*(*n*+ 1) (*n*+ 4). - Q:-
Given a G.P. with

*a*= 729 and 7th term 64, determine S_{7}. - Q:-
Find the sum of all numbers between 200 and 400 which are divisible by 7.

- Q:-
Find the sum to

*n*terms of the series 3 × 8 + 6 × 11 + 9 × 14 +… - Q:-
A die is thrown. Describe the following events:

(i) A: a number less than 7 (ii) B: a number greater than 7 (iii) C: a multiple of 3

(iv) D: a number less than 4 (v) E: an even number greater than 4 (vi) F: a number not less than 3

Also find A ∪ B, A ∩ B, B ∪ C, E ∩ F, D ∩ E, A – C, D – E, E ∩ F’, F’

- Q:-
If A.M. and G.M. of roots of a quadratic equation are 8 and 5, respectively, then obtain the quadratic equation.

Asif
2019-12-15 20:19:13

Thnx

Asif
2019-12-15 20:18:38

Thnx

Deekshitha
2019-09-04 18:24:24

Thank you it for solving the problem and helped me

Deekshitha
2019-09-04 18:24:01

Thank you it for solving the problem and helped me

KICCHA balaji
2019-03-12 23:10:08

Tq bro Usefullll

Nikhil
2019-03-04 14:58:14

Thanx

QAMAR
2016-11-17 12:23:41

HOW CAN WE TAKE NUMBER I MEAN ON WHICH BASES

Mabel
2016-01-17 00:57:58

I luv dis.. Its easier and explanatory. Thanks!

- NCERT Chapter