Algebraic Expressions Model Questions Set 1 Practice Questions Answers Test with Solutions & More Shortcuts
Algebraic Expressions PRACTICE TEST [1 - EXERCISES]
Algebraic Expressions Model Questions Set 1
Question : 11
Directions :
In each of these questions two equations are given. You have to solve these equations and Give answer
- if x < y
- if x > y
- if x =y
- if x ≥ y
- if x ≤ y
I. $x^2$ – 6x = 7
II. $2y^2$ + 13y + 15 = 0
a) if x ≥ y
b) if x ≤ y
c) if x < y
d) if x = y
e) if x > y
Answer »Answer: (e)
I. $x^2$ – 6x = 7
or, $x^2$ – 6x – 7 = 0
or, (x – 7) (x + 1) = 0
or, x = 7, – 1
II. $2y^2$ + 13y + 15 = 0
or, $2y^2$ + 3y + 10y + 15 = 0
or, (2y + 3) (y + 5) = 0 or, y =${-3}/2,$-5
Hence, x > y
Question : 12
Directions :
For the two given equations I and II give answer
- if p is greater than q
- if p is smaller than q
- if p is equal to q
- if p is either equal to or greater than q
- if p is either equal to or smaller than q.
I.$3p^2$ + 15p = –18
II. $q^2$ + 7q + 12 =0
a) if p is either equal to or greater than q
b) if p is either equal to or smaller than q.
c) if p is greater than q
d) if p is equal to q.
e) if p is smaller than q
Answer »Answer: (a)
I. $3p^2$ + 15p + 18 = 0
or,$3p^2$ + 9p + 6p + 18 = 0
or, 3p (p + 3) + 6(p + 3) = 0
or, (3p + 6)( p + 3) = 0
or, p = ${-6}/3,-3$= – 2, – 3
II.$q^2$ + 7q + 12 = 0
or, $q^2$ + 4q + 3q + 12 = 0
or, q(q + 4) + 3(q + 4) = 0
or, (q + 3)(q + 4) = 0
or, q = – 3, –4
Therefore, p ≥ q
Question : 13
Directions :
In each of the following questions two equations I and II are given. You have to solve both the equations and give answer
- if a < b
- if a ≤ b
- if a ≥ b
- if a = b
- if a > b
I. $2a^2$ + 5a + 3 = 0
II. $2b^2$ – 5b + 3 = 0
a) if a = b
b) if a > b
c) if a < b
d) if a ≥ b
e) if a ≤ b
Answer »Answer: (c)
a = –3/2 & –1; b = $3/2$ & 1
Question : 14
Directions :
In each question one or more equation(s) is (are) provided. On the basis of these you have
- if p = q
- if p > q
- if q > p
- if p ≥ q
- if p ≥ q
(i) $4p^2$ – 5p + 1 = 0 (ii) $q^2$ – 2q + 1 = 0
a) if p ≥ q and
b) if q ≥ p
c) if p = q
d) if q > p
e) if p > q
Answer »Answer: (b)
(i) $4p^2$ – 5p + 1 = 0 or, $4p^2$ – 4p – p + i = 0
or, 4p(p – 1) – 1(p – 1) = 0
or, (4p – 1)(p – 1) = 0
or, p = 1 and p = $1/4$
(ii) $q^2$–2q +1 = 0
⇒(q – 1) (q –1) = 0
or, q = 1
∴q ≥ p
Question : 15
Directions :
In each of these questions two equations are given. You have to solve these equations and Give answer
- if x < y
- if x > y
- if x =y
- if x ≥ y
- if x ≤ y
I. $10x^2$ – 7x + 1 = 0
II. $35y^2$ – 12y + 1 = 0
a) if x ≥ y
b) if x ≤ y
c) if x < y
d) if x = y
e) if x > y
Answer »Answer: (a)
I. $10x^2$ – 7x + 1 = 0
or, $10x^2$ – 5x – 2x + 1 = 0
or, (2x – 1) (5x – 1) = 0
or, x = 1/2, 1/5
II. $35y^2$ – 12y + 1= 0
or, $35y^2$ – 7y – 5y + 1 = 0
or, (5y – 1) (7y – 1) = 0
or, y = $1/5 , 1/7$
Hence, x ≥ y
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Algebraic Expressions Model Questions Set 1 Online Quiz
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