RD Sharma Chapter 1 : Number System Multiple Choice Questions (MCQs) Solutions
Which of the following is true about x = 0.3 bar ? (a) x is a rational number, because x can be expressed in the form p/q by solving the equation 10x = 3 + x. (b) x is a rational number because x can be expressed in the form p/q by solving the equation 10x = 3 – x. (c) x is an irrational number because x can be expressed in the form p/q by solving the equation 10x = 3 + x. (d) x is an irrational number because x can be expressed in the form p/q by solving the equation 10x = 3 – x. Watch Solution
If the some of the following numbers between 7 and 11 are written in the form m/6, then integer values of m lie between (a) 42 and 60 (b) 42 and 66 (c) 42 and 77 (d) 48 and 60 Watch Solution
Which of the following statements is/ are correct ? (i) Every integer is a rational number (ii) Every rational number is an integer (iii) A real number is either rational or irrational number (iv) Every whole number is a natural number. (a) (ii) (b) (iii) (c) (i) and (iii) (d) all of these Watch Solution
The decimal expansion of a rational number is (a) terminating or non-terminating non-repeating (b) terminating or non-terminating repeating (c) terminating and repeating (d) none of these Watch Solution
A number is an irrational if and only if its decimal representation is (a) non-terminating (b) non-terminating and repeating (c) non-terminating and non-repeating (d) terminating Watch Solution
Which of the following is an irrational number ? (a) 0.13 (b) 0.1315 (c) 0.1315 (d) 0.301323100523 … Watch Solution
The value of 0.4 bar in the form p/q, where p and q are integers and q ≠ 0, is (a) 4/9 (b) 2/5 (c) 1/5 (d) 4/5 Watch Solution
The simplest form of 1.6 bar is (a) 8/5 (b) 5/3 (c) 833/500 (d) 7/6 Watch Solution
Which of the following is a rational number? (a) π (b) √5 (c) 0.101001000100001 … (d) 0.835835835 … Watch Solution
How many digits are there in the repeating block of digits in the decimal expansion of 17/7 ? (a) 16 (b) 6 (c) 26 (d) 7 Watch Solution
The decimal expansion that a rational number cannot have is (a) 0.25 (b) 0.2528 (c) 0.2528 (d) 0.5030030003… Watch Solution
Which of the following statements is true? (a) π and 22/7 are both rationals (b) π and 22/7 are both irrationals (c) π is rational and 22/7 is irrational (d) π is irrational and 22/7 is rational Watch Solution
Which of the following numbers is irrational? (a) √4/9 (b) √1250/√8 (c) √8 (d) √24/√6 Watch Solution
Which of the following is a rational number? (a) √3 + 1 (b) π (c) 2√3 (d) 0 Watch Solution
A rational number between -3 and 3 is (a) 0 (b) -4.3 (c) -3.4 (d) 1.101100110001 … Watch Solution
Which of the following is an irrational number? (a) 3.14 (b) 3.141414 … (c) 3.1444444… (d) 3.14114111411114 … Watch Solution
The product of a non-zero rational number with an irrational number is (a) irrational number (b) rational number (c) whole number (d) natural number Watch Solution
The sum of 0.2 bar and 0.5 bar is (a) 7/10 (b) 7/9 (c) 7/99 (d) 3/10 Watch Solution
The sum of 0.2 bar and 0.5 bar is (a) 7/10 (b) 7/9 (c) 7/99 (d) 3/10 Watch Solution
The value of 0.2 × 0.5 bar is (a) 1 (b) 10/9 (c) 10/81 (d) 10/99 Watch Solution
There is a number x sum that x^2 is irrational but x^4 is rational. Then x can be (a) √5 (b) √2 (c) 3√2 (d) 4√5 Watch Solution
Which one of the following is a correct statement? (a) Decimal expansion of a rational number is terminating (b) Decimal expansion of a rational number is non-terminating (c) Decimal expansion of an irrational number is terminating (d) Decimal expansion of an irrational number is non-terminating and non-repeating Watch Solution
Which one of the following statements is true? (a) The sum of two irrational numbers is always an irrational number (b) The sum of two irrational numbers is always a rational number (c) The sum of two irrational numbers may be a rational number or an irrational number (d) The sum of two irrational numbers is always an integer Watch Solution
Which of the following is a correct statement? (a) Sum of two irrational numbers is always irrational (b) Sum of a rational and irrational number is always an irrational number (c) Square of an irrational number is always a rational number (d) Sum of two rational numbers can never be an integer Watch Solution
Which of the following statements is true? (a) Product of two irrational numbers is always irrational (b) Product of a non-zero rational and an irrational number is always irrational (c) Sum of two irrational numbers can never be irrational (d) Sum of an integer and a rational number can never be an integer Watch Solution
Which of the following is irrational? (a) √4/9 (b) 4/5 (c) √7 (d) √81Watch Solution
Which of the following is irrational ? (a) 0.14 (b) 0.1416 (c) 0.1416 (d) 0.1014001400014.. Watch Solution
Which of the following is rational ? (a) √3 (b) π (c) 4/0 (d) 0/4 Watch Solution
The number 0.318564318564318564 ……… is : (a) a natural number (b) an integer (c) a rational number (d) an irrational number Watch Solution
If n is a natural number, then √n is (a) always a natural number (b) always a rational number (c) always an irrational number (d) sometimes a natural number and sometimes an irrational number Watch Solution
Which of the following numbers can be represented as non-terminating repeating decimals ? (a) 39/24 (b) 3/16 (c) 3/11 (d) 137/25 Watch Solution
Every point on number line represents (a) a unique real number (b) a natural number (c) a rational number (d) an irrational number Watch Solution
Which of the following is irrational ? (a) 0.15 (b) 0.01516 (c) 0.1516 (d) 0.5015001500015.. Watch Solution
The number 1.27 bar in the form p/q, where p and q are integers and q ≠ 0, is (a) 14/9 (b) 14/11 (c) 14/13 (d) 14/15 Watch Solution
The number 0.3 bar in the form p/q, where p and q are integers and q ≠ 0, is (a) 33/100 (b) 3/10 (c) 1/3 (d) 3/100 Watch Solution
0.32 bar when expressed in the form p/q (p,q are integers q ≠ 0), is (a) 8/25 (b) 29/90 (c) 32/99 (d) 32/199 Watch Solution
23.43 bar when expressed in the form p/q (p,q are integers q ≠ 0), is (a) 2320/99 (b) 2343/100 (c) 2343/999 (d) 2320/199 Watch Solution
0.01 bar when expressed in the form p/q (p, q are integers, q ≠ 0), is (a) 1/1000 (b) 1/100 (c) 1/1999 (d) 1/999 Watch Solution
The value of 0.23 bar + 0.22 bar is (a) 0.45 (b) 0.43 (c) 0.54 (d) 0.45 Watch Solution
An irrational number between 2 and 2.5 is (a) √11 (b) √5 (c) √22.5 (d) √12.5 Watch Solution
The number of consecutive zeroes in 2^3 × 3^4 × 5^4 × 7, is (a) 3 (b) 2 (c) 4 (d) 5 Watch Solution
The smallest rational number by which 1/3 should be multiplied so that its decimal expansion terminates after one place of decimal, is (a) 1/10 (b) 3/10 (c) 3 (d) 30 Watch Solution
Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer. Mark the correct choice. (a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1. (b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1. (c) Statement-1 is true, Statement-2 is false. (d) Statement-1 is false, Statement-2 is true. Statement-1 (Assertion): √2 is an irrational number. Statement-2 (Reason): The decimal expansion of √2 is non-terminating non-recurring. Watch Solution
Statement-1 (Assertion): The sum of any two irrational numbers is an irrational number. Statement-2 (Reason): There are two irrational numbers whose sum is a rational number. Watch Solution
Statement-1 (Assertion): The product of any two irrational numbers is an irrational number. Statement-2 (Reason): There are two irrational numbers whose product is not an irrational number. Watch Solution
Statement-1 (Assertion): √3 is an irrational number. Statement-2 (Reason): The square root of a positive integer which is not a perfect square is an irrational number. Watch Solution
Statement-1 (Assertion): √2 is an irrational number. Statement-2 (Reason): The sum of a rational number and an irrational number is an irrational number. Watch Solution
Statement-1 (Assertion): There are two rational numbers whose sum and product both are rationals. Statement-2 (Reason): There are numbers which cannot be written in the form p/q, q≠0 , p, q both are integers. Watch Solution
Statement-1 (Assertion): The decimal representation of 3/8 is terminating. Statement-2 (Reason): If the denominator of a rational number is of the form 2^m x 2^n where m, n are non-negative integers, then its representation is terminating. Watch Solution
