Question 4

Find the sum of all numbers between 200 and 400 which are divisible by 7.

Answer

The numbers lying between 200 and 400, which are divisible by 7, are

203, 210, 217, … 399

∴First term, *a* = 203

Last term, *l* = 399

Common difference, *d* = 7

Let the number of terms of the A.P. be *n*.

∴ *a*_{n} = 399 = *a* + (*n* –1) *d*

⇒ 399 = 203 + (*n* –1) 7

⇒ 7 (*n* –1) = 196

⇒ *n* –1 = 28

⇒ *n* = 29

Thus, the required sum is 8729.

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

- 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:- 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:-
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.

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

^{2}, 3^{3}, … are needed to give the sum 120? - Q:-
Find the sum to

*n*terms of the series 1^{2}+ (1^{2}+ 2^{2}) + (1^{2}+ 2^{2}+ 3^{2}) + … - Q:-
The base of an equilateral triangle with side 2a lies along the y-axis such that the mid-point of the base is at the origin. Find vertices of the triangle.

- 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:-
Find the sum to

*n*terms of the series whose*n*th terms is given by (2*n*– 1)^{2} - Q:-
A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?

- Q:-
Three coins are tossed. Describe

(i) Two events which are mutually exclusive.

(ii) Three events which are mutually exclusive and exhaustive.

(iii) Two events, which are not mutually exclusive.

(iv) Two events which are mutually exclusive but not exhaustive.

(v) Three events which are mutually exclusive but not exhaustive.

Harsh
2019-08-22 21:32:16

Good

saranya
2019-02-18 18:52:33

ummma thank you

Neelam
2019-01-07 13:03:24

But how I know that first no. Is 203

David N Maikundu
2018-11-09 16:44:45

thank you great elucidation

David N Maikundu
2018-11-09 16:32:27

wonderfull explanation

Shilpa
2018-09-20 12:53:07

Thank you for your help

DHARMAPADA KARUA
2018-06-03 11:06:42

Good solution.

Puru
2017-10-10 21:25:27

Thanks for the explanation

shethra krishna
2016-11-16 07:34:16

it was a wonderful explanation

karthik
2016-10-12 14:20:48

Good explanation

- NCERT Chapter