Evaluate without multiplying directly 103 × 107 .

We can write 103 × 107 as ( 100 + 3 ) ( 100 + 7 ) . Using the identity: x + a x + b = x 2 + a + b + a b 100 + 3 100 + 7 = 100 2 + 3 + 7 × 100 + 3 × 7 100 + 3 100 + 7 = 10000 + 1000 + 21 100 + 3 100 + 7 = 11021 Hence, it is the required answer.

Prove that 0 . 87 × 0 . 87 × 0 . 87 + 0 . 13 × 0 . 13 × 0 . 13 0 . 87 × 0 . 87 - 0 . 87 × 0 . 13 + 0 . 13 × 0 . 13 = 1 .

Given: 0 . 87 × 0 . 87 × 0 . 87 + 0 . 13 × 0 . 13 × 0 . 13 0 . 87 × 0 . 87 - 0 . 87 × 0 . 13 + 0 . 13 × 0 . 13 Let us take 0 . 87 = a and 0 . 13 = b Consider the L H S = a × a × a + b × b × b a × a - a × b + b × b = a 3 + b 3 a 2 - a b + b 2 Using the identity, a 3 + b 3 = ( a + b ) a 2 - a b + b 2 We get, = ( a + b ) a 2 - a b + b 2 a 2 - a b + b 2 Since a 2 - a b + b 2 is existing in both numerator and denominator We get, L H S = ( a + b ) Now by replacing the values of a and b in above expression we get, L H S = 0 . 87 + 0 . 13 = 1 = R H S Hence, proved.

E M B I B E

All in One Mathematics>Chapter 13 - Unit Tests (Algebra) {Chapters Covered - 2, 4}>UNIT TEST 2

Brijesh Dwevedi and Jitendra Gupta Solutions for Chapter: Unit Tests (Algebra) {Chapters Covered - 2, 4}, Exercise 2: UNIT TEST 2

Author:Brijesh Dwevedi & Jitendra Gupta

Brijesh Dwevedi Mathematics Solutions for Exercise - Brijesh Dwevedi and Jitendra Gupta Solutions for Chapter: Unit Tests (Algebra) {Chapters Covered - 2, 4}, Exercise 2: UNIT TEST 2

Attempt the practice questions on Chapter 13: Unit Tests (Algebra) {Chapters Covered - 2, 4}, Exercise 2: UNIT TEST 2 with hints and solutions to strengthen your understanding. All in One Mathematics solutions are prepared by Experienced Embibe Experts.

Questions from Brijesh Dwevedi and Jitendra Gupta Solutions for Chapter: Unit Tests (Algebra) {Chapters Covered - 2, 4}, Exercise 2: UNIT TEST 2 with Hints & Solutions

MEDIUM

9th CBSE

IMPORTANT

All in One Mathematics>Chapter 13 - Unit Tests (Algebra) {Chapters Covered - 2, 4}>UNIT TEST 2>Q 4

The integral roots of the polynomial $x^{3} - 6 x^{2} + 11 x - 6$ is

EASY

9th CBSE

IMPORTANT

All in One Mathematics>Chapter 13 - Unit Tests (Algebra) {Chapters Covered - 2, 4}>UNIT TEST 2>Q 5

Evaluate without multiplying directly $103 \times 107$ .

MEDIUM

9th CBSE

IMPORTANT

All in One Mathematics>Chapter 13 - Unit Tests (Algebra) {Chapters Covered - 2, 4}>UNIT TEST 2>Q 8

Write three solutions of the linear equation $x + 2 y = 1$ .

MEDIUM

9th CBSE

IMPORTANT

All in One Mathematics>Chapter 13 - Unit Tests (Algebra) {Chapters Covered - 2, 4}>UNIT TEST 2>Q 9

Prove that $\frac{0.87 \times 0.87 \times 0.87 + 0.13 \times 0.13 \times 0.13}{0.87 \times 0.87 - 0.87 \times 0.13 + 0.13 \times 0.13} = 1$ .

MEDIUM

9th CBSE

IMPORTANT

All in One Mathematics>Chapter 13 - Unit Tests (Algebra) {Chapters Covered - 2, 4}>UNIT TEST 2>Q 11

Simplify the following

$(6 m - n) (36 m^{2} + 6 m n + n^{2}) - (3 m + 2 n)^{3}$ .

EASY

9th CBSE

IMPORTANT

All in One Mathematics>Chapter 13 - Unit Tests (Algebra) {Chapters Covered - 2, 4}>UNIT TEST 2>Q 12

Cost of $1$ pen is $₹ x$ and that of $1$ pencil is $₹ y$ . Cost of $2$ pens and $3$ pencils together is $₹ 18$ . Write a linear equation to represent this information.

MEDIUM

9th CBSE

IMPORTANT

All in One Mathematics>Chapter 13 - Unit Tests (Algebra) {Chapters Covered - 2, 4}>UNIT TEST 2>Q 13

Factorise $2 x^{3} - 5 x^{2} - 19 x + 42$ .

MEDIUM

9th CBSE

IMPORTANT

All in One Mathematics>Chapter 13 - Unit Tests (Algebra) {Chapters Covered - 2, 4}>UNIT TEST 2>Q 14

A part of monthly expenses of a family on milk is fixed which is $₹ 500$ and the remaining varies with the quantity of milk taken extra at the rate of $₹ 20$ per litre. Taking the quantity of milk required extra as $x L$ and the total expenditure on milk is $₹ y$ , write a linear equation for this information.

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