CBSE Class 9 Mathematics Number System VBQs

Question. If 2^{x – 3} ·3^{2x – 8} = 36, then the value of x is ______.
(A) 2
(B) 5
(C) 3
(D) 1
Answer : B

Question. The rationalising factor of 5√a²b³c⁴ is _____.
(A) 5√a³b²c
(B) 4√a³b²c
(C) 3√a³b²c
(D) √a³b²c
Answer : A

Question. Rational number -18/5 lies between consecutive integers ______.
(A) –2 and –3
(B) –3 and –4
(C) –4 and –5
(D) –5 and –6
Answer : B

Question. If x = (7+4√3), then (x + 1/x) = ______.
(A) 8 3
(B) 14
(C) 49
(D) 48
Answer : B

Question. 7√3/(√10+√3) - 2√5(√6/√5) - 3√2/(15+3√2) = ______.
(A) 1
(B) 2
(C) 1/2
(D) 3
Answer : A

Question. The denominator of

(A) a²
(B) b²
(C) a² – b²
(D) 4a² – 2b²/b²
Answer : B

Question. Which of the following numbers has the terminating decimal representation?
(A) 5/12
(B) 8/35
(C) 7/24
(D) 13/80
Answer : D

Question. The value of 1/3 of 15²⁷ is ______.
(A) 5²⁷
(B) 15⁹
(C) 5 × 15²⁶
(D) 5 × 3⁹
Answer : C

Question. If x = 2 − √3 , then the value of x² + 1/x² and x² - 1/x² respectively, are ______.
(A) 14, 8√3
(B) −14, − 8√3
(C) 14, − 8√3
(D) −14, 8√3
Answer : C

Question. An irrational number between 1/7 and 2/7 is _____.
(A) 1/2 (1/7 + 2/7)
(B) (1/7 x 2/7)
(C) √1/7 x 2/7 
(D) None of these
Answer : C

Question. If

then N equals ______.
(A) 1
(B) 2√2 -1
(C) √5/2
(D) 2/√√5 +1
Answer : A

Question. Express the mixed recurring decimal 4.32 in the form p/q.
(A) 389/90
(B) 329/90
(C) 29/90
(D) 233/990
Answer : A

Question. The ascending order of the surds ³√2, ⁶√3, ⁹√4 is ______.
(A) ⁹√4, ⁶√3, ³√2
(B) ⁹√4, ³√2, ⁶√3
(C) ³√2, ⁶√3, ⁹√4
(D) ⁶√3, ⁹√4, ³√2
Answer : A

Question. The greater number among √17 − √12 and √11 −√ 6 is ______.
(A) √17 − √12
(B) √11 − √6
(C) Both are equal
(D) Can’t be compared
Answer : B

Question. The value of x, if 5^{x – 3} · 3^2x – 8 = 225 is ______.
(A) 3
(B) 4
(C) 2
(D) 5
Answer : D

Question. Fill in the blanks.
(i) The decimal form of an irrational number is neither P nor Q .
(ii) There are R rational numbers between any two consecutive integers.
(iii) Every rational number is S .

Answer : B

Question. Read the statements carefully.
Statement-1 : Every point on the number line represent a unique real number.
Statement-2 : Irrational numbers cannot be represented on a number line. Which of the following options hold?
(A) Both Statement-1 and Statement-2 are true.
(B) Statement-1 is true but Statement-2 is false.
(C) Statement-1 is false but Statement-2 is true.
(D) Both Statement-1 and Statement-2 are false.
Answer : B

Question. Match the following.

(A) (a)→(i); (b)→(ii); (c)→(iii); (d)→(iv)
(B) (a)→(iii); (b)→(iv); (c)→(i); (d)→(ii)
(C) (a)→(i); (b)→(iv); (c)→(ii); (d)→(iii)
(D) (a)→(iii); (b)→(iv); (c)→(ii); (d)→(i)
Answer : D

Question. If x and y are positive real numbers, then which of the following is CORRECT?
(A) x > y ⇒ –x > –y
(B) x > y ⇒ –x < –y
(C) x > y ⇒ 1/x > 1/y
(D) x > y ⇒ 1/x < -1/y
Answer : B

Question. If x = 1− √2 , then find the value of (x − 1/x)
(A) 2
(B) 3
(C) 4
(D) 5
Answer : C

Question. The value of

is ______.
(A) 0
(B) 1
(C) 2
(D) 4
Answer : C

Question. If (√3−1)/(√3+1) = (a−b√3), find the values of a and b.
(A) a = 1, b = 2
(B) a = 2, b = 1
(C) a = 2, b = 3
(D) a = 3, b = 2
Answer : B

Question. Which of the following statements is INCORRECT ?
(A) Every integer is a rational number.
(B) Every natural number is an integer.
(C) Every natural number is a real number.
(D) Every real number is a rational number.
Answer : D

Question. The number x = 1.242424....... can be expressed in the form x p/q = , where p and q are positive integers having no common factors. Then p + q equals ______.
(A) 72
(B) 74
(C) 41
(D) 53
Answer : B

Question. Which of the following statements is INCORRECT?
(A) If ‘a’ is a rational number and ‘b’ is irrational, then a + b is irrational.
(B) The product of a non-zero rational number with an irrational number is always irrational.
(C) Addition of any two irrational numbers can be rational.
(D) Division of any two integers is an integer.
Answer : D