Selina Solutions Concise Mathematics Class 6 Chapter 18 Fundamental Concepts Exercise 18(B) has detailed answers to the concepts explained under this exercise. The solved examples before each exercise, help students evaluate the type of problems that would appear in the final examination. Students can clear their doubts, without any delay, using solutions PDF, designed by subject matter experts. Those who aim to cross check their answers, can refer to Selina Solutions Concise Mathematics Class 6 Chapter 18 Fundamental Concepts Exercise 18(B) PDF, from the links which are provided, with a free download option.

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Exercise 18(B)

**1. Separate the constants and the variables from each of the following:**

**6, 4y, -3x, 5 / 4, (4 / 5)xy, az, 7p, 0, 9x / y, 3 / 4x, – xz / 3y**

**Solution:**

6, 5 / 4and 0 are the constants

4y, -3x, (4 / 5)xy, az, 7p, 9x / y, 3 / 4x and â€“ xz / 3y are the variables

**2. Group the like terms together:**

**(i) 4x, -3y, -x, (2 / 3)x, (4 / 5)y and y.**

**(ii) (2 / 3) xy, -4yx, 2yz, (-2 / 3)yz, zy / 3 and yx.**

**(iii) â€“ab ^{2}, b^{2}a^{2}, 7b^{2}a, -3a^{2}b^{2} and 2ab^{2}**

**(iv) 5ax, -5by, by / 7, 7xa and 2ax / 3**

**Solution:**

(i) 4x, -3y, -x, (2 / 3)x, (4 / 5)y and y.

Here, the like term are as follows

4x, -x, (2 / 3)x and -3y, (4 / 5)y, y

(ii) (2 / 3) xy, -4yx, 2yz, (-2 / 3)yz, zy / 3 and yx.

Here, the like terms are as follows

(2 / 3) xy, -4yx, yx and 2yz, (-2 / 3)yz, zy / 3

(iii) â€“ab^{2}, b^{2}a^{2}, 7b^{2}a, -3a^{2}b^{2} and 2ab^{2}

Here, the like terms are as follows

-ab^{2}, 7b^{2}a, 2ab^{2} and b^{2}a^{2}, -3a^{2}b^{2}

(iv) 5ax, -5by, by / 7, 7xa and 2ax / 3

Here, the like terms are as follows

5ax, 7xa, 2ax / 3 and â€“ 5by, by / 7

**3.State whether true or false:**

**(i) 16 is a constant and y is a variable but 16y is variable**

**(ii) 5x has two terms 5 and x**

**(iii) The expression 5 + x has two terms 5 and x**

**(iv) The expression 2x ^{2} + x is a trinomial**

**(v) ax ^{2} + bx + c is a trinomial**

**(vi) 8 Ã— ab is a binomial**

**(vii) 8 + ab is a binomial**

**(viii) x ^{3} â€“ 5xy + 6x + 7 is a polynomial**

**(ix) x ^{3} â€“ 5xy + 6x + 7 is a multinomial**

**(x) The coefficient of x in 5x is 5x**

**(xi) The coefficient of ab in â€“ab is -1**

**(xii) The coefficient of y in -3xy is -3**

**Solution:**

(i) 16 is a constant and y is a variable but 16y is variable

The given statement is **true**

(ii) 5x has two terms 5 and x

The given statement is **false**

(iii) The expression 5 + x has two terms 5 and x

The given statement is **true**

(iv) The expression 2x^{2} + x is a trinomial

The given statement is **false**

(v) ax^{2} + bx + c is a trinomial

The given statement is **true**

(vi) 8 Ã— ab is a binomial

The given statement is **false**

(vii) 8 + ab is a binomial

The given statement is **true**

(viii) x^{3} â€“ 5xy + 6x + 7 is a polynomial

The given statement is **true**

(ix) x^{3} â€“ 5xy + 6x + 7 is a multinomial

The given statement is **true**

(x) The coefficient of x in 5x is 5x

The given statement is **false**

(xi) The coefficient of ab in â€“ab is -1

The given statement is **true**

(xii) The coefficient of y in -3xy is -3

The given statement is **false**

**4. State the number of terms in each of the following expressions:**

**(i) 2a â€“ b**

**(ii) 3 Ã— x + a / 2**

**(iii) 3x â€“ x / p**

**(iv) a Ã· x Ã— b + c**

**(v) 3x Ã· 2 + y + 4**

**(vi) xy Ã· 2**

**(vii) x + y Ã· a**

**(viii) 2x + y + 8 Ã· y**

**(ix) 2 Ã— a + 3 Ã· b + 4**

**Solution:**

(i) 2a â€“ b

The number of terms in given expression is two

(ii) 3 Ã— x + a / 2

The number of terms in given expression is two

(iii) 3x â€“ x / p

The number of terms in given expression is two

(iv) a Ã· x Ã— b + c

The number of terms in given expression is two

(v) 3x Ã· 2 + y + 4

The number of terms in given expression is three

(vi) xy Ã· 2

The number of terms in given expression is one

(vii) x + y Ã· a

The number of terms in given expression is two

(viii) 2x + y + 8 Ã· y

The number of terms in given expression is three

(ix) 2 Ã— a + 3 Ã· b + 4

The number of terms in given expression is three

**5. State whether true or false:**

**(i) xy and â€“yx are like terms.**

**(ii) x ^{2}y and â€“y^{2}x are like terms.**

**(iii) a and â€“a are like terms.**

**(iv) â€“ba and 2ab are unlike terms.**

**(v) 5 and 5x are like terms.**

**(vi) 3xy and 4xyz are unlike terms.**

**Solution:**

(i) xy and â€“yx are like terms

Yes, xy and â€“yx are like terms. Hence, the given statement is **true**

(ii) x^{2}y and â€“y^{2}x are like terms

No, x^{2}y and â€“y^{2}x are not like terms. Hence, the given statement is **false**

(iii) a and â€“a are like terms.

Yes, a and â€“a are like terms. Hence, the given statement is **true**

(iv) â€“ba and 2ab are unlike terms.

No, â€“ba and 2ab are like terms. Hence, the given statement is **false**

(v) 5 and 5x are like terms.

No, 5 and 5x are not like terms. Hence, the given statement is **false**

(vi) 3xy and 4xyz are unlike terms.

Yes, 3xy and 4xyz are unlike terms. Hence, the given statement is **true**

**6. For each expression, given below, state whether it is a monomial, or a binomial or a trinomial.**

**(i) xy **

**(ii) xy + x**

**(iii) 2x Ã· y**

**(iv) â€“a**

**(v) ax ^{2} â€“ x + 5**

**(vi) -3bc + d**

**(vii) 1 + x + y**

**(viii) 1 + x Ã· y**

**(ix) x + xy â€“ y ^{2}**

**Solution:**

(i) xy

Here xy has one term

Therefore, xy is a **monomial**

(ii) xy + x

Here xy + x has two terms

Therefore, xy + x is a **binomial**

(iii) 2x Ã· y

Here 2x Ã· y has one term

Therefore, 2x Ã· y is **monomial**

(iv) â€“a

Here â€“a has one term

Therefore, â€“a is a **monomial**

(v) ax^{2} â€“ x + 5

Here ax^{2} â€“ x + 5 has three terms

Therefore, ax^{2} â€“ x + 5 is a **trinomial**

(vi) -3bc + d

Here -3bc + d has two terms

Therefore, -3bc + d is a **binomial**

(vii) 1 + x + y

Here 1 + x + y has three terms

Therefore, 1 + x + y is a **trinomial**

(viii) 1 + x Ã· y

Here 1 + x Ã· y has two terms

Therefore, 1 + x Ã· y is a **binomial**

(ix) x + xy â€“ y^{2}

Here x + xy â€“ y^{2} has three terms

Therefore, x + xy â€“ y^{2} is a **trinomial**

**7. Write down the coefficient of x in the following monomial:**

**(i) x**

**(ii) â€“x**

**(iii) -3x**

**(iv) -5ax**

**(v) 3 / 2 xy**

**(vi) ax / y**

**Solution:**

(i) x

The coefficient of x in the given monomial x is 1

(ii) â€“ x

The coefficient of x in the given monomial â€“x is -1

(iii) -3x

The coefficient of x in the given monomial -3x is -3

(iv) -5ax

The coefficient of x in the given monomial -5ax is -5a

(v) 3 / 2 xy

The coefficient of x in the given monomial is (3 / 2)y

(vi) ax / y

The coefficient of x in the given monomial is (a / y)

**8. Write the coefficient of:**

**(i) x in -3xy ^{2}**

**(ii) x in â€“ax**

**(iii) y in â€“y**

**(iv) y in (2 / a)y**

**(v) xy in -2xyz**

**(vi) ax in â€“axy ^{2}**

**(vii) x ^{2}y in -3ax^{2}y**

**(viii) xy ^{2} in 5axy^{2}**

**Solution:**

(i) x in -3xy^{2}

– 3y^{2} is the coefficient of x in -3xy^{2}

(ii) x in â€“ax

– a is the coefficient of x in â€“ax

(iii) y in â€“y

-1 is the coefficient of y in â€“y

(iv) y in (2 / a)y

(2 / a) is the coefficient of y in (2 / a)y

(v) xy in -2xyz

– 2z is the coefficient of xy in -2xyz

(vi) ax in â€“axy^{2}

– y^{2} is the coefficient of ax in â€“axy^{2}

(vii) x^{2}y in -3ax^{2}y

– 3a is the coefficient of x^{2}y in -3ax^{2}y

(viii) xy^{2} in 5axy^{2}

5a is the coefficient of xy^{2} in 5axy^{2}

**9. State the numeral coefficient of the following monomials:**

**(i) 5xy **

**(ii) abc**

**(iii) 5pqr**

**(iv) -2x / y**

**(v) (2 / 3) xy ^{2}**

**(vi) -15xy / 2z**

**(vii) -7x Ã· y**

**(viii) -3x Ã· (2y)**

**Solution:**

(i) 5xy

The numeral coefficient of the given monomial is 5

(ii) abc

The numeral coefficient of the given monomial is 1

(iii) 5pqr

The numeral coefficient of the given monomial is 5

(iv) -2x / y

The numeral coefficient of the given monomial is -2

(v) (2 / 3) xy^{2}

The numeral coefficient of the given monomial is (2 / 3)

(vi) -15xy / 2z

The numeral coefficient of the given monomial is (-15 / 2)

(vii) -7x Ã· y

The numeral coefficient of the given monomial is -7 Ã· 1 = -7

(viii) -3x Ã· (2y)

The numeral coefficient of the given monomial is -3 Ã· 2 i.e. (-3 / 2)

**10. Write the degree of each of the following polynomials:**

**(i) x + x ^{2}**

**(ii) 5x ^{2} â€“ 7x + 2**

**(iii) x ^{3} â€“ x^{8} + x^{10}**

**(iv) 1 â€“ 100x ^{20}**

**(v) 4 + 4x â€“ 4x ^{3}**

**(vi) 8x ^{2}y â€“ 3y^{2} + x^{2}y^{5}**

**(vii) 8z ^{3} â€“ 8y^{2}z^{3} + 7yz^{5}**

**(viii) 4y ^{2} â€“ 3x^{3} + y^{2}x^{7}**

**Solution:**

(i) x + x^{2}

The degree of the polynomial is the greatest of sums of degree of two or more variables of the given polynomial

Therefore, the degree of the given polynomial x + x^{2} is 2

(ii) 5x^{2} â€“ 7x + 2

The degree of the polynomial is the greatest of sums of degree of two or more variables of the given polynomial

Therefore, the degree of the given polynomial 5x^{2} â€“ 7x + 2 is 2

(iii) x^{3} â€“ x^{8} + x^{10}

The degree of the polynomial is the greatest of sums of degree of two or more variables of the given polynomial

Therefore, the degree of the given polynomial x^{3} â€“ x^{8} + x^{10} is 10

(iv) 1 â€“ 100x^{20 }

Therefore, the degree of the given polynomial 1 â€“ 100x^{20 }is 20

(v) 4 + 4x â€“ 4x^{3}

Therefore, the degree of the given polynomial 4 + 4x â€“ 4x^{3} is 3

(vi) 8x^{2}y â€“ 3y^{2} + x^{2}y^{5}

Therefore, the degree of the given polynomial 8x^{2}y â€“ 3y^{2} + x^{2}y^{5} is 7

(vii) 8z^{3} â€“ 8y^{2}z^{3} + 7yz^{5}

Therefore, the degree of the given polynomial 8z^{3} â€“ 8y^{2}z^{3} + 7yz^{5} is 6

(viii) 4y^{2} â€“ 3x^{3} + y^{2}x^{7}

Therefore, the degree of the given polynomial 4y^{2} â€“ 3x^{3} + y^{2}x^{7} is 9