Question 6

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

Answer

The two-digit numbers, which when divided by 4, yield 1 as remainder, are

13, 17, … 97.

This series forms an A.P. with first term 13 and common difference 4.

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

It is known that the *n*th term of an A.P. is given by, *a**n* = *a* + (*n* –1) *d*

∴97 = 13 + (*n* –1) (4)

⇒ 4 (*n* –1) = 84

⇒ *n* – 1 = 21

⇒ *n* = 22

Sum of *n* terms of an A.P. is given by,

Thus, the required sum is 1210.

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

- Q:- In an A.P., if pth term is \begin{align} \frac{1}{q} \; and \;qth\; term \; is\; \frac{1}{p}\end{align} , prove that the sum of first pq terms is \begin{align} \frac{1}{2}(pq+1) \; where \; p ≠ q \end{align}
- Q:-
The sum of first three terms of a G.P. is and their product is 1. Find the common ratio and the terms.

- Q:-
A point is in the XZ-plane. What can you say about its

*y*-coordinate? - Q:-
A man starts repaying a loan as first installment of Rs. 100. If he increases the installment by Rs 5 every month, what amount he will pay in the 30th installment?

- Q:-
If the p

^{th}, q^{th}and r^{th}terms of a G.P. are*a, b*and*c*, respectively. Prove that a^{q-r}b^{r-p}c^{p-q}=1 - 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 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?

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

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

*a*and*b*, then find the value of*n*. - Q:-
Find the sum to

*n*terms of the series 5^{2}+ 6^{2}+ 7^{2}+ ... + 20^{2}

Siddhant Saxena
2019-09-19 19:39:28

Thanks

Shivangi Mishra
2019-09-14 11:43:16

kindly try to change the background theme.

Yashraj
2019-09-06 22:21:24

Excellent

Sr
2019-07-20 16:40:28

Excellent

Preetam
2016-10-14 01:28:02

Thanks

- NCERT Chapter