This page offers a step-by-step solution to the specific question **NCERT Class 11th Mathematics - Sequence and Series | find the sum of odd integers from 1 to 2001 Answer ** from NCERT Class 11th Mathematics, Chapter Sequence and Series.

Question 1

## Find the sum of odd integers from 1 to 2001.

Answer

The odd integers from 1 to 2001 are 1, 3, 5, …1999, 2001.

This sequence forms an A.P.

Here, first term, a = 1

Common difference, d = 2

Here,

\begin{align} a + (n - 1)d = 2001 \end{align}

\begin{align} => 1 + (n - 1)(2) = 2001 \end{align}

\begin{align} => 2n -2 = 2000 \end{align}

\begin{align} => n = 1001 \end{align}

\begin{align} S_n = \frac {n}{2}\left[2a + (n -1)d\right]\end{align}

\begin{align} \therefore S_n = \frac {1001}{2}\left[2 × 1 + (1001 -1)×2\right]\end{align}

\begin{align} = \frac {1001}{2}\left[2 + 1000×2\right]\end{align}

\begin{align} = \frac {1001}{2} × 2002\end{align}

\begin{align} =1001 × 1001 \end{align}

\begin{align} = 1002001 \end{align}

Thus, the sum of odd numbers from 1 to 2001 is 1002001.

- 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:-
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:-
The difference between any two consecutive interior angles of a polygon is 5°. If the smallest angle is 120°, find the number of the sides of the polygon.

- Q:-
Solve 24x < 100, when

(i) x is a natural number. (ii) x is an integer. - Q:-
Draw a quadrilateral in the Cartesian plane, whose vertices are (– 4, 5), (0, 7), (5, – 5) and (– 4, –2). Also, find its area.

- Q:-
A point is on the

*x*-axis. What are its*y*-coordinates and*z*-coordinates? - 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:-
Find the equation of the circle with centre (0, 2) and radius 2

- Q:-
Describe the sample space for the indicated experiment: A coin is tossed three times.

- Q:-
Which of the following sentences are statements? Give reasons for your answer.

(i) There are 35 days in a month.

(ii) Mathematics is difficult.

(iii) The sum of 5 and 7 is greater than 10.

(iv) The square of a number is an even number.

(v) The sides of a quadrilateral have equal length.

(vi) Answer this question.

(vii) The product of (–1) and 8 is 8.

(viii) The sum of all interior angles of a triangle is 180°.

(ix) Today is a windy day.

(x) All real numbers are complex numbers.

- Q:-
If the set A has 3 elements and the set B = {3, 4, 5}, then find the number of elements in (A×B).

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

*y*-coordinate?

- Q:-
Describe the sample space for the indicated experiment: A coin is tossed and a die is thrown.

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

*y*-coordinate? - Q:-
Which of the following sentences are statements? Give reasons for your answer.

(i) There are 35 days in a month.

(ii) Mathematics is difficult.

(iii) The sum of 5 and 7 is greater than 10.

(iv) The square of a number is an even number.

(v) The sides of a quadrilateral have equal length.

(vi) Answer this question.

(vii) The product of (–1) and 8 is 8.

(viii) The sum of all interior angles of a triangle is 180°.

(ix) Today is a windy day.

(x) All real numbers are complex numbers.

- 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:-
How many 5–digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67 and no digit appears more than once?

- 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 coin is tossed. If it shows a tail, we draw a ball from a box which contains 2 red and 3 black balls. If it shows head, we throw a die. Find the sample space for this experiment.

- Q:-
A die is thrown repeatedly until a six comes up. What is the sample space for this experiment?

- Q:-
A box contains 1 red and 3 identical white balls. Two balls are drawn at random in succession without replacement. Write the sample space for this experiment.

- Q:-
Three coins are tossed once. Let A denote the event ‘three heads show”, B denote the event “two heads and one tail show”. C denote the event “three tails show” and D denote the event ‘a head shows on the first coin”. Which events are

(i) mutually exclusive? (ii) simple? (iii) compound?

Ravi Kiran
2017-02-24 21:06:58

WRONG AF!

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