CBSE Class 9 Maths Number Systems MCQs Set 03

Question: Multiplicative inverse of ‘O’ is

Question. Which of the following is true?
(a) Every whole number is a natural number
(b) Every integer is a rational number
(c) Every rational number is an integer
(d) Every integer is a whole number

Question. Out of the following, the irrational number is 

Question. To rationalize the denominator of 1/√a+b , we multiply this by
(a) 1/√a+b
(b) 1/√a-b
(c) √a+b/√a+b
(d) √a-b/√a-b

Question. For Positive real numbers a and b, which is not true?
(a) √ab = √a √b
(b) (a+√b)(a-√b) =a2 - b2
(c) √a/b = √a/√b
(d) (√a+√b)(√a-√b) = a+b

Question. The number of rational numbers between √3 and √5 is
(a) One
(b) 3
(c) none
(d) infinitely many

Question. If we add two irrational numbers, the resulting number
(a) is always an irrational number
(b) is always a rational number
(c) may be a rational or an irrational number
(d) always an integer

Question. The rationalizing factor of 7-2√3 is
(a) 7-2√3 
(b) 7+2√3 
(c) 5+2√ 3
(d) 4+2√ 3

Question.

Question. The value of √n for which n be a rational number is
(a) 2
(b) 4
(c) 3
(d) 5

Question. 3√12/6√27 equals
(a) 1/2 
(b) √2 
(c) √3
(d) 1/3

Question. (3+√3) (3-√2) equals
(a) 9 -5 √2 - √6
(b) 9 -√6
(c) 3+√2
(d) 9-3√2 + 3√3 - √6

Question. The arrangement of √2 , √5 , √3 in ascending order is
(a) √2,√3,√5
(b) √2,√5,√3
(c) √5,√3,√2
(d) √3,√2,√5

Question. If √10 = 3.162 , then the value of 1/√10 is
(a) 0.3162
(b) 3.162
(c) 31.62
(d) 316.2

Question. If (3/4)⁶ x (16/9)⁵ = (4/3)^x+2 , then the value of x is
(a) 2
(b) 4
(c) -2
(d) 6

Question. If m and n are two natural numbers and mⁿ = 32, then n^mn is
(a) 5²
(b) 5³
(c) 5¹⁰
(d) 5¹²

Question. (3+√3)(3-√2) equals
(a) 9-5 √2-√6
(b) 9-√6
 (c) 3+√2
(d) 9-3√2+3√3-√6

Question. The arrangement of √2, √5, √3 in ascending order is
(a) √2, √3, √5
(b) √2, √5, √3
(c) √5, √3, √2
(d) √3, √2, √5

Question. If m and n are two natural numbers and mⁿ = 32, then n^mn is
(a) 5²
(b) 5³
(c) 5¹⁰
(d) 5¹²

Exponents and Radicals

1.. An equation which has an unknown quantity as an exponent is called an exponential equation.
e.g., (i) 5^x = 625
(ii) 3^x–5 = 1

2. a^1/n is called then nth root of ‘a’ and may be written as n√a

3. n√a is called a radical of index ‘n’ and ‘a’ is called the radicand.

4. Law of exponents:
If ‘a’ and ‘b’ are any rational numbers different from zero and if x, y are any rational numbers, then
(i) a^x × ay = a^x+y
(ii) a^x ÷ ay = a^x–y
(iii) (a^x)^y = a^xy
(iv) (ab)^x = a^x × b^x
(v) (a/b)^x = a^x/b^x
(vi) a° = 1

5. Radicals of index 2 are know as square root radicals. e.g., √3, 7√5, √39,....etc.

6. A radical consisting of the product of an irrational and a rational is called a mixed radical. e.g., 5√7, 23√11,......etc.

7. A radical that contains no rational factor is called a pure radical e.g., √143, √20, √45,.....etc.

8. An expression of the from a + √b, where ‘a’ and ‘b’ are rational and non-zero is called a bionomial surd. e.g., 3 + √5, 2 – √3, 9 + √11,......., etc.
Note: The surd (a – √b) is called the conjugate surd of a + √b.

9. A square root radical is in simplest form if
(i) there is no fraction in the radicand.
(ii) no perfect square is a factor of the radicand and
(iii) there is no radical on the denominator e.g., √75 = 5√3

Question. 7/√10 + √3 =
(A) (√10 + √3)2
(B) 7(√10 - √3)
(C) √10 - √3
(D) none

Answer : C

Question. The value of 4√3 -4/√3+1 - 2-√3/2+√3/ is
(A) 0
(B) 1
(C) 8√3
(D) 15

Answer : B

Question. If x^y = y^x, then (x/y)^x/y is equal to
(A) x^{x /y}
(B) x ^{x/y 1}
(C) x ^y/x
(D) x ^{y/x 1}

Answer : B

Question. If x/y = 6/5 then x2+y2/x2 - y2 is
(A) 36/25
(B) 25/36
(C) 61/11
(D) 11/61

Answer : C

Question. (64)-2/3 x (1/4)-3 equals to
(A) 4
(B) 1/4
(C) 1
(D) 16

Answer : A

Question. The value of (5)^0.25 x (12.5)^0.25/(256)^0.10 x (253)^0.15 is
(A) √5/2
(B) 5/4
(C) 25/2
(D) 25/16

Answer : B

Question. The value of (67.542)² - (32.458)²/75.458 40.374 is
(A) 1
(B) 10
(C) 100
(D) none

Answer : C

Question. Which of the following values are equals?
I. 1⁴ II. 4⁰ III. 0⁴ IV. 4¹
(A) I and II 
(B) II and III
(C) I and III 
(D) I and IV

Answer : A

Question. The sum of the powers of the prime factors in 108 × 192 is
(A) 5 
(B) 7
(C) 8 
(D) 12

Answer : D

Question. The value of √1³ + 2³ + 3³ is
(A) 5 
(B) 6
(C) 7
(D) 8

Answer : B