Exercise 5A
Q1 Ex-5A Class 7 SChand New Learning Composite mathematics Solution
Question 1
Which of the following algebraic expression are polynomials?
(a) 5–7x
(b) y3+16y2–11
(c) $2y^2–xy +\frac{5}{y}–3$
(d) $2 –\frac{9}{x}$
(e) 8 – 3x + 4x2 – 6x3
(f) 19
(g) 17z
(h) $x + \frac{1}{3}x – 2$
Sol :
(a),(b),(e),(f),(g),(h) are polynomials
Question 2
State the numerical coefficient and degree of each monomial
(a) 45
Sol :
Degree 0, as there is no variables , no coefficient
(b) $\frac{4x^2}{y}$
Sol : is not a monomial as the variable y is in the denominator
(c) $42x^{\frac{-1}{4}}$
Sol : is not a monomial as the as the exponent is not a whole number
(d) 9b
Sol :
Coefficient : 3
Degree : 3
(e) 8pq
Sol :
Coefficient : 8
Degree : 2
(f) -12m2n
Sol :
Coefficient : -12
Degree : 3
(g)$\frac{5}{t^2}$
Sol : is not a monomial as the power of t is t-2 which is not a whole number
(h) xy2
Sol :
Coefficient : 1
Degree : 3
(i) -7d3
Sol :
Coefficient : -7
Degree : 3
(j) -25x2y
Sol :
Coefficient : -25
Degree : 3
Question 3
Select the like terms in each polynomial, if any.
(a) 7x – 3x + 8
Sol :
The like terms are 7x, 3x
(b) a + b + 2a – c
Sol :
The like terms are a , 2a
(c) a + 3b – c + 5b
Sol :
The like terms are 3b, 5b
(d) 2xy – 5xz + 4yz – yz
Sol :
The like terms are 4yz, -yz
(e) mn2 + m2n2 – 2mn2 + 6m2n2
Sol :
The like terms are mn2,-2mn2 and m2n2,6m2n2
(f) 2ab2 – 7a2b + 9a2b2 + 8a2b
Sol :
The like terms are -7a2b, 8a2b
(g) 8(r + s) – 3(r + s) + 5(r – s)
Sol :
The like terms are 8r, -3r, 5r and 8s, -3s, -5s
Question 4
State the degree of each polynomial
(a) 7 + 3y + y2
Sol :
∴Degree=2
(b) 9p3 + 16q2
Sol :
∴Degree=3
(c) 8a2b + ab2 – 5ab + 2
Sol :
∴Degree=3
(d) 3x3 + 15 + x – 2x2
Sol :
∴Degree=3
(e) 0.5x2y + 0.25xy2 + 6x2 + 0.75
Sol :
∴Degree=3
Question 5
Determine whether the given polynomials are monomials, binomials, trinomials or none of these. Then, state the degree and coefficient of the polynomials.
(a) 5c2d
Sol : is monomial of degree 3 , coefficient 5
(b) 12x2 + d
Sol : is binomial of degree 2 , coefficient 12 and 1
(c) 15m2 – 2p + 5
Sol : is trinomial of degree 2 , coefficient 15 and -2
(d) 8x – 5y2 + 11x3
Sol : is trinomial of degree 3, coefficient -5 and 11
(e) 12ab – 8a2b
Sol : is binomial of degree 3, coefficient 12 and -8
(f) -7a3 + 5a2b – ab2 + 10b3
Sol :Name of them; Polynomial of degree 3, coefficients are -7,5,-1,10
Question 6
Arrange the given polynomials in order of decreasing degree in x.
(a) 4x + x2 – 8
Sol : x2+4x-8
(b) 8x2 – 3x – 12 + 6x3
Sol : 6x3+8x2-3x-12
(c) x2y – 3y3 + 4x3 – 2xy2
Sol : 4x3+x2y-2xy2-3y3
(d) 2x2y – 8xy3 + x3 – y3 + 3xy
Sol : x3+2x2y+3xy-8xy3-y3
Question 7
Write each polynomial in standard form.
(a) 17 – 3x2 + x + 8x3
Sol :
8x3-3x2+x+17
(b) 20y3 – 13y – 3y2 + 1
Sol :
20y3-3y2-13y+1
Question 8
Evaluate, If a -= 2, b = 1 and c = 10.
(a) c3
Sol : (10)3
=1000
(b) (2b)2
Sol :
=(2×1)2
=4(c) (c + b)2
Sol :
=(10+1)2
=(11)2
=121
(d) (a – 3)2
Sol :
=(2-3)2
=(-1)2
=1
(e) (-3c)3
Sol :
=(-3×10)3
=(-30)5
=-27000
(f) $\frac{3a^3}{b}$
Sol :
$=\frac{3\times 2^3}{1}$
=3×8=24
(g) 9(a2 – b2)
Sol :
=9(22–12)
=9(4-1)
=9×3=27
(h) 3b(a3 – c)
Sol :
=(3×1)(23–10)
=3(8-10)
=3×(-2)
=-6
(i) (a3 + b2 + c)2
Sol :
=23+12+(10)2
=8+1+100=109
(j) (-a-b+c)2
Sol :
=(-2-1+10)2
=72
=49
Question 9
Write the algebraic expression for the following situations.
(a) Rita’a age is 4 less than 4 times her daughter’s age x.
Sol :
Rita's daughter's age x
∴Rita's age=(4x-4)
(b) The perimeter of an isosceles triangle whose equal sides are of length p cm each and unequal side is q cm.
Sol :
∴The expression is (100a+10b+c)
(c)
Sol :
∴The perimeter of an isosceles triangle=(2p+q)
(d) The speed of a bus is z m/s. Write its speed in km/h.
Sol :
The speed of a bus is $\frac{18}{5}z$ km
(e) A pair of shoes cost Rs. x. The cost of a dress is Rs. 200 more than 5 times the cost of the shoes.
Sol :
A pair of shoes cost ₹x
∴The cost of dress=₹(5x+200)
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