RD Sharma XII Vol 1 (2020, 2021) - GeniusJnr

Fill in the blanks:

(a). 1 lakh = _________ ten thousand.

(b). 1 million = _________ hundred thousand.

(c). 1 crore = _________ ten lakh.

(d). 1 crore = _________ million.

(e). 1 million = _________ lakh.

Following number line shows the temperature in degree celsius (°C) at different places on a particular day.

(a) Observe this number line and write the temperature of the places marked on it.

(b) What is the temperature difference between the hottest and the coldest places among the above?

(c) What is the temperature difference between Lahulspiti and Srinagar?

(d) Can we say temperature of Srinagar and Shimla taken together is less than the temperature at Shimla? Is it also less than the temperature at Srinagar?

Is zero a rational number? Can you write it in the form, where p and q are integers and q ≠ 0?

Show that any positive odd integer is of the form , or , or , where q is some integer.

Using appropriate properties find:

(i)

(ii)

Which of the following are sets? Justify our answer.

(i) The collection of all months of a year beginning with the letter J.

(ii) The collection of ten most talented writers of India.

(iii) A team of eleven best-cricket batsmen of the world.

(iv) The collection of all boys in your class.

(v) The collection of all natural numbers less than 100.

(vi) A collection of novels written by the writer Munshi Prem Chand.

(vii) The collection of all even integers.

(viii) The collection of questions in this Chapter.

(ix) A collection of most dangerous animals of the world.

Determine whether each of the following relations are reflexive, symmetric and transitive:

(i)Relation R in the set A = {1, 2, 3…13, 14} defined as

R = {(x, y): 3x − y = 0}

(ii) Relation R in the set N of natural numbers defined as

R = {(x, y): y = x + 5 and x < 4}

(iii) Relation R in the set A = {1, 2, 3, 4, 5, 6} as

R = {(x, y): y is divisible by x}

(iv) Relation R in the set Z of all integers defined as

R = {(x, y): x − y is as integer}

(v) Relation R in the set A of human beings in a town at a particular time given by

(a) R = {(x, y): x and y work at the same place}

(b) R = {(x, y): x and y live in the same locality}

(c) R = {(x, y): x is exactly 7 cm taller than y}

(d) R = {(x, y): x is wife of y}

(e) R = {(x, y): x is father of y}

If a and b are two odd positive integers such that a > b, then prove that one of the two numbers $\frac{a+b}{2}\mathrm{and} \frac{a-b}{2}$is odd and the other is even.

Is zero a rational number? Can you write it in the form $\frac{p}{q}$, where p and q are integers and q ≠ 0?

Determine each of the following products:
(i) 12 ☓ 7
(ii) (−15) ☓ 8
(iii) (−25) ☓ (−9)
(iv) 125 ☓ (−8)

What is the difference between a collection and a set? Give reasons to support your answer?