This page offers a step-by-step solution to the specific question **NCERT Class 11th Mathematics - Mathematical Reasoning | which of the following sentences are statements g Answer ** from NCERT Class 11th Mathematics, Chapter Mathematical Reasoning.

Question 1

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.

Answer

(i) This sentence is incorrect because the maximum number of days in a month is 31. Hence, it is a statement.

(ii) This sentence is subjective in the sense that for some people, mathematics can be easy and for some others, it can be difficult. Hence, it is not a statement.

(iii) The sum of 5 and 7 is 12, which is greater than 10. Therefore, this sentence is always correct. Hence, it is a statement.

(iv) This sentence is sometimes correct and sometimes incorrect. For example, the square of 2 is an even number. However, the square of 3 is an odd number. Hence, it is not a statement.

(v) This sentence is sometimes correct and sometimes incorrect. For example, squares and rhombus have sides of equal lengths. However, trapezium and rectangles have sides of unequal lengths. Hence, it is not a statement.

(vi) It is an order. Therefore, it is not a statement.

(vii) The product of (–1) and 8 is (–8). Therefore, the given sentence is incorrect. Hence, it is a statement.

(viii) This sentence is correct and hence, it is a statement.

(ix) The day that is being referred to is not evident from the sentence. Hence, it is not a statement.

(x) All real numbers can be written as *a* × 1 + 0 × *i*. Therefore, the given sentence is always correct. Hence, it is a statement.

- 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:- Write the first five terms of the sequences whose nth term is a
_{n}=n(n+2) - 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:-
Find the sum to

*n*terms of the series 1^{2}+ (1^{2}+ 2^{2}) + (1^{2}+ 2^{2}+ 3^{2}) + … - 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:-
Given a G.P. with

*a*= 729 and 7th term 64, determine S_{7}. - 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:- Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.
- Q:-
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.

- 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:-
The sum of two numbers is 6 times their geometric mean, show that numbers are in the ratio

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

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