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Question 1011 Mark

The sum of the multiplication table of natural number ‘n’ is given by 55 × n. Find the sum of:
Table of 7

Answer

Given, the sum of multiplication table of n natural numbers = 55 × n
Sum of table of 7 = 55 × 7 = 385 [put n = 7]

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Question 1021 Mark

The sum of the multiplication table of natural number ‘n’ is given by 55 × n. Find the sum of:
Table of 19

Answer

Given, the sum of multiplication table of n natural numbers = 55 × n
Sum of table of 19 = 55 × 19 = 1045 [put n = 19]

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Question 1031 Mark

The sum of the multiplication table of natural number ‘n’ is given by 55 × n. Find the sum of:
Table of 10

Answer

Given, the sum of multiplication table of n natural numbers = 55 × n
Sum of table of 10 = 55 × 10 = 550 [put n = 10]

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Question 1041 Mark

Subtracting a term from a given expression is the same as adding its additive inverse to the given expression.

Answer

True.
Solution:
Because additive inverse is the negation of a number or expression.

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Question 1051 Mark

Subtract 9a² - 15a + 3 from unity.

Answer

In order to find solution, we will subtract 9a²- 15a + 3 from unity, i.e. 1. Required ‘expression is
1 - (9a²- 15a + 3)
= 1 - 9a² + 15a -3
= -9a²+ 15a - 2

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Question 1061 Mark

$\frac{7}{8-\text{x}}$

Answer

Quotient on dividing seven by the difference of eight and x(x < 8).

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Question 1071 Mark

$17\Big(\frac{16}{\text{w}}\Big)$

Answer

Seventeen times quotient of sixteen divided by w.

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Question 1081 Mark

Find the values of the following polynomials at a = -2 and b = 3:
$\frac{\text{a}^2-\text{b}^2}{3}$

Answer

Given a = -2 and b = 3
So,
putting a = -2 and b = 3in the given expressions
we get:
$\frac{\text{a}^2-\text{b}^2}{3}=\frac{(-2)^2-(3)^2}{3}=\frac{4-9}{3}=\frac{-5}{3}$

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Question 1091 Mark

Find the values of the following polynomials at a = -2 and b = 3:
$\frac{\text{a}^2+\text{b}^2}{3}$

Answer

Given a = -2 and b = 3
So, putting a = -2 and b = 3in the given expressions we get.
$\frac{\text{a}^2+\text{b}^2}{3}=\frac{(-2)^2+(3)^2}{3}=\frac{4+9}{3}=\frac{13}{3}$

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Question 1101 Mark

Find the values of the following polynomials at a = -2 and b = 3:

$\frac{\text{a}}{\text{b}}+\frac{\text{b}}{\text{a}}$

Answer

Given a = -2 and b = 3
So,
putting a = -2 and b = 3in the given expressions
we get:
$\frac{\text{a}}{\text{b}}+\frac{\text{b}}{\text{a}}=\frac{(-2)}{3}+\frac{3}{(-2)}$
$=\frac{-2}{3}-\frac{3}{2}=\frac{-4-9}{6}=\frac{-13}{6}$
[$\because\ $LCM of 2 and 3 is 6]

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Question 1111 Mark

Find the values of the following polynomials at a = -2 and b = 3:
a³ - 3a²b + 3ab² - b³

Answer

Given a = -2 and b = 3
So, putting a = -2 and b = 3in the given expressions we get.
a³ - 3a²b + 3ab² - b³
= (-2)³ - 3(-2)² - (3) + 3(-2) (3)² - (3)³
= -8 - 36 - 54 - 27 = -125

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Question 1121 Mark

Find the values of the following polynomials at a = -2 and b = 3:
a³ + 3a²b + 3ab² + b³

Answer

Given a = -2 and b = 3
So, putting a = -2 and b = 3in the given expressions we get.
a³ + 3a²b + 3ab² + b³
= (-2)³ + 3(-2)² (3) + 3(-2) (3)² + (3)³
= -8 - 36 - 54 - 27
= 1

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Question 1131 Mark

Find the values of the following polynomials at a = -2 and b = 3:
a²- 2ab + b²

Answer

Given a = -2 and b = 3
So, butting a = -2 and b = 3in the given expressions we get.
a² - 2ab + b²
= (-2)² - 2(-2) (3) + (3)²
= 4 + 12 + 9
= 25

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Question 1141 Mark

Find the values of the following polynomials at a = -2 and b = 3:
a² + b²- ab - b² - a²

Answer

Given a = -2 and b = 3
So,
putting a = -2 and b = 3in the given expressions we get.
a² + b² - ab - b² - a²
= (-2)² + (3)² - (-2) (3) - (3)² - (-2)²
= 4 + 9 + 6 - 9 - 4
= 6

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Question 1151 Mark

Find the values of the following polynomials at a = -2 and b = 3:
a² + 2ab + b²

Answer

Given a = -2 and b = 3
So, butting a = -2 and b = 3in the given expressions we get.
a² + 2ab + b²
= (-2)² + 2(-2) (3) + (3)²
= 4 - 12 + 9
= 1

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Question 1161 Mark

Find the values of following polynomials at m = 1, n = -1 and p = 2:
m³ + n³ + p³

Answer

Given, m = 1, n = -1 and p = 2
So,
putting m = 1, n = -1 and p = 2 in the given expressions
we get:
m³+ n³+ p³
=(1)³ + (-1)³ + (2)³
=1 - 1 + 8
= 8

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Question 1171 Mark

Find the values of following polynomials at m = 1, n = -1 and p = 2:
m³ + n³ + p³ - 3mnp

Answer

Given, m = 1, n = -1 and p = 2
So,
putting m = 1, n = -1 and p = 2 in the given expressions
we get:
m³ + n³ + p³ - 3mnp
= (1)³ + (-1)³ + (2)³ - 3(1) (-1) (2)
= 1 - 1 + 8 + 6
= 14

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Question 1181 Mark

Find the values of following polynomials at m = 1, n = -1 and p = 2:
m² + n² + p²

Answer

Given, m = 1, n = -1 and p = 2
So,
putting m = 1, n = -1 and p = 2 in the given expressions
we get:
m²+ n²+ P²
= (1)² + (-1)² + (2)²
= 1 + 1 + 4
= 6

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Question 1191 Mark

Find the values of following polynomials at m = 1, n = -1 and p = 2:
m²n² + n²p² + p²m²

Answer

Given, m = 1, n = -1 and p = 2
So,
putting m = 1, n = -1 and p = 2 in the given expressions
we get:
m²n² + n²p² + p²m²
= (1)²× (-1)² + (-1)² × (2)² + (2)² × (1)²
= 1 + 4 + 4
= 9

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Question 1201 Mark

Find the values of following polynomials at m = 1, n = -1 and p = 2:
m + n + p

Answer

Given, m = 1, n = -1 and p = 2
So,
putting m = 1, n = -1 and p = 2 in the given expressions
we get:
m + n + p
= 1 - 1 + 2
= 2

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Question 1211 Mark

Find the values of following polynomials at m = 1, n = -1 and p = 2:
mn + np + pm

Answer

Given, m = 1, n = -1 and p = 2
So,
putting m = 1, n = -1 and p = 2 in the given expressions
we get:
mn + np + pm
= (1) (-1) + (-1) (2) + (2) (1)
=1 - 2 + 2
= -1

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Question 1221 Mark

Express the following properties with variables x, y and z:
Distributive property of multiplication over addition.

Answer

We know that,
Distributive property of multiplication over
addition, a × (b + c)
= a × b + a × c
$\therefore\ $Required expression is x × (y + z)
= x × y + x × z

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Question 1231 Mark

Express the following properties with variables x, y and z:
Commutative property of multiplication.

Answer

We know that,
Commutative property of multiplication, axb
= bxa
$\therefore $Required expression is x × y
= y × x

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Question 1241 Mark

Express the following properties with variables x, y and z:
Commutative property of addition.

Answer

We know that,
Commutative property of addition, a + b
= b + c
$\therefore $ Required expression is x + y
= y + x

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Question 1251 Mark

Express the following properties with variables x, y and z:
Associative property of multiplication.

Answer

We know that,
Associative property of multiplication, a × (b × c)
= (a × b) × c
$\therefore \ $Required expression is x × (y × z)
= (x × y) × z

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Question 1261 Mark

Express the following properties with variables x, y and z:
Associative property of addition.

Answer

We know that,
Associative property of addition, a + (b + c)
= (a + b) + c
$\therefore $Required expression is x + (y + z)
= (x + y) + z

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Question 1271 Mark

Critical Thinking Write two different algebraic expressions for the word phrase $\Big(\frac{1}{4}\Big)$ of the sum of x and 7.

Answer

First expression $=\frac{1}{4}(\text{x} +7)$
As we know, the addition is commutative.
So, it can also be written as $\frac{1}{4}(7+\text{x})$

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Question 1281 Mark

A wire is (7x - 3) metres long. A length of (3x - 4) metres is cut for use. Now, answer the following questions:
How much wire is left?

Answer

Given, length of wire = (7x - 3)m
And wire cut for use has length = (3x - 4)m
Left wire = (7x - 3) - (3x - 4)
= 7x - 3 - 3x + 4
= 7x - 3x - 3 + 4
= (4x + 1)m.

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Question 1291 Mark

8(m + 5)

Answer

Eight times the sum of m and 5.

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Question 1301 Mark

4b - 3

Answer

Three subtracted from four times b.

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Question 1311 Mark

3x + 23x² + 6y² + 2x + y² + ____________ = 5x + 7y².

Answer

3x + 23x² + 6y² + 2x + y² + M = 5x + 7y².
Solution:
Let (3x + 23x² + 6y²+ 2x + y²) + M = 5x + 7y²
⇒ M = (5x + 7y²) - (3x + 23x² + 6y²+ 2x + y²)
⇒ M = 5x + 7y²- 3x - 23x²– 6y² - 2x - y²
⇒ M = 5x - 3x - 2x + 7y²- 6y²- y2 - 23x²
M = 0 + 0 - 23x² = -23x²
[with - ve sign, + ve sign in the bracket will change on opening it]

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1 Marks Question - Page 3 - MATHS STD 7 Questions - Vidyadip

MATHS 1 Marks Question

1 Marks Question