Test Session Unit 1 Real Numbers (9th Mathematics)

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📘 Mathematics Test Paper – Class 9th (SNC)

Unit 1: Real Numbers
Time: ______
Total Marks: ______
Obtained Marks: ______

Q1. Choose the correct option. (10×1=10)

Identify the rational number:
(A) 2.236067…
(B) $\sqrt{7}$ 7
(C) 0.6
(D) $π$ π
The number $\sqrt{7}$ 7 is a/an:
(A) Whole number
(B) Rational number
(C) Irrational number
(D) Natural number
$0. \overline{37}$ 0.37 in rational form will be:
(A) $\frac{37}{99}$ 9937
(B) $\frac{37}{100}$ 10037
(C) $\frac{37}{10}$ 1037
(D) 37
If $a < b$ a<b and $\frac{1}{a} > \frac{1}{b}$ a1>b1, then property used is:
(A) Reciprocal property
(B) Division property
(C) Multiplicative property
(D) Reflexive property
Which rational number lies between $\frac{3}{5}$ 53 and $\frac{4}{5}$ 54?
(A) $\frac{7}{10}, \frac{13}{20}$ 107,2013
(B) $\frac{2}{5}, \frac{1}{5}$ 52,51
(C) $\frac{3}{6}, \frac{4}{6}$ 63,64
(D) $\frac{7}{5}, \frac{13}{5}$ 57,513
$- 2 \frac{1}{7}$ −271 on the number line will be represented as:
(A) $\frac{4}{3}$ 34
(B) $\frac{4}{3}$ 34
(C) $\frac{4}{3}$ 34
(D) $\frac{4}{3}$ 34
$\sqrt[3]{81}$ 381 can also be written as:
(A) $81^{2}$ 812
(B) $81^{3}$ 813
(C) $81^{\frac{1}{3}}$ 8131
(D) $81^{\frac{3}{2}}$ 8123
$\sqrt{3} + \sqrt{5}$ 3+5 is:
(A) Whole number
(B) Integer
(C) Rational number
(D) Irrational number
Let $a, b \in R$ a,b∈R, then $a = b$ a=b and $b = a$ b=a is called ______ property:
(A) Reflexive
(B) Symmetric
(C) Transitive
(D) Additive
The product of $(3 + \sqrt{5}) (3 - \sqrt{5})$ (3+5)(3−5) is:
(A) Prime number
(B) Odd number
(C) Irrational number
(D) Rational number

Q2. Write short answers to the following questions. (15×2=30)

[I] Identify the following as a rational or irrational number: $π$ π
[II] Identify the following as a rational or irrational number: $5 + \sqrt{11}$ 5+11
[III] Represent the following number on a number line: $4 \frac{1}{3}$ 431
[IV] Name the property used: $\sqrt{2} + \sqrt{3} = \sqrt{3} + \sqrt{2}$ 2+3=3+2
[V] Name the property used: $16 + 0 = 16$ 16+0=16
[VI] Name the property used: if $a < b$ a<b then $a + c < b + c$ a+c<b+c
[VII] Name the property used: if $a c < b c$ ac<bc and $c < 0$ c<0 then $a > b$ a>b
[VIII] Insert two rational numbers between 3 and 4
[IX] Insert two rational numbers between $\frac{3}{5}$ 53 and $\frac{4}{5}$ 54
[X] If $a = \frac{3}{2}, b = \frac{5}{3}, c = \frac{7}{5}$ a=23,b=35,c=57, verify: $a (b + c) = a b + a c$ a(b+c)=ab+ac
[XI] If $a = \frac{3}{2}, b = \frac{5}{3}, c = \frac{7}{5}$ a=23,b=35,c=57, verify: $(a + b) c = a c + b c$ (a+b)c=ac+bc
[XII] Find two rational numbers between 4 and 5
[XIII] Write the Commutative Property of Multiplication for real numbers
[XIV] Identify the following decimals as rational or irrational:
(i) 0.35
(ii) 0.444…
(iii) 3.5
(iv) 3.367885542…
(v) 1.709975947…
[XV] Define Exponential Form with an example

Q3. Write detailed answers to the following questions. (Answer any 2) (2×5=10)

Simplify: $\frac{54 \times \sqrt[3]{(27)^{2 x}}}{9^{x + 1} + 216 (3^{2 x - 1})}$ 9x+1+216(32x−1)54×3(27)2x
If $a = \frac{2}{3}, b = \frac{3}{2}, c = \frac{5}{3}$ a=32,b=23,c=35, verify the distributive properties over addition.
Simplify: $\frac{5^{n + 3} - 6 \cdot 5^{n + 1}}{9 \times 5^{n} - 4 \times 5^{n}}$ 9×5n−4×5n5n+3−6⋅5n+1