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 : 16
Directions :
In each of the following questions, one or two equation(s) is/are given. On their basis you have to determine the relation between x and y and then give answer.
- if x < y
- if x > y
- if x ≤ y
- if x ≥ y
- if x = y
I.$x^2$ + 3x + 2 = 0
II.$2y^2$ = 5y
a) if x ≥ y
b) if x = y
c) if x < y
d) if x ≤ y
e) if x > y
Answer »Answer: (c)
I. $x^2$ + 3x + 2 = 0
or, $x^2$ + 2x + x + 2 = 0
or, (x + 2)(x + 1) = 0
or, x = – 2, – 1
II. $2y^2$ = 5y
or, $2y^2$ – 5y = 0
or, y(2y – 5) = 0
or, y = 0, $5/2$
Hence, y > x
Question : 17
Directions :
In each question below one or more equation(s) is/are provided. On the basis of these, you have to find out relation between p and q.
- if p = q
- if p > q
- if q > p
- if p ≥ q
- if p ≥ q
I. $6q^2+1/2=7/2a$
II. $12p^2$ + 2 = 10p
a) if p ≥ q and
b) if q ≥ p.
c) if p = q,
d) if q > p,
e) if p > q,
Answer »Answer: (a)
I. $6q^2+1/2=7/2q$
or,$12q^2$ - 7q + 1 = 0.
or $(q-{1/4})(q-{1/3})$=0
∴ q = $1/4$ pr $1/3$
II. $12p^2$ + 2 = 10p
or, $6p^2$ – 5p + 1 = 0
or,$(p-{1/3})(p-{1/2})$=0
∴ p=${1/3}$ or $1/2$
Hence, p ≥ q
Question : 18
Directions :
In each question below one or more equation(s) is/are provided. On the basis of these, you have to find out relation between p and q.
- if p = q
- if p > q
- if q > p
- if p ≥ q
- if p ≥ q
I. $2p^2$ + 40 = 18p
II. $q^2$ = 13q – 42
a) if p ≥ q and
b) if q ≥ p.
c) if p = q,
d) if q > p,
e) if p > q,
Answer »Answer: (d)
I. $2p^2$ + 40 = 18p
or, $p^2$ – 9p + 20 = 0
or, (p – 4) (p – 5) = 0
∴ p = 4 or 5
II. $q^2$ = 13q – 42
or, $q^2$ – 13q + 42 = 0
or, (q – 7) (q – 6) = 0
∴ q = 6 or 7
Hence, q > p
Question : 19
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 + 3b = 31
II. 3a = 2b + 1
a) if a = b
b) if a > b
c) if a < b
d) if a ≥ b
e) if a ≤ b
Answer »Answer: (c)
2a + 3b = 31 ... (i)
3a – 2b = 1 ..(ii)
Multiply (i) by 2 and (ii) by 3 and then adding
(i) and (ii), we get a = $65/13$ = 5 . Putting the value of 'a'
in any equation, we get b = 7.
Hence, b > a or a < b.
Question : 20
Directions :
In each of the following questions, one or two equation(s) is/are given. On their basis you have to determine the relation between x and y and then give answer.
- if x < y
- if x > y
- if x ≤ y
- if x ≥ y
- if x = y
I.$ x^2$ – 5x + 6 = 0
II.$y^2$ + y – 6 = 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. $x^2$ – 5x + 6 = 0
or, $x^2$ – 3x – 2x + 6 = 0
or, x(x – 3) – 2(x – 3) = 0
or, (x – 3)(x – 2) = 0
or, x = 2, 3
II. $y^2$ + y – 6 = 0
or, $y^2$ + 3y – 2y – 6 = 0
or, y(y + 3) – 2 (y + 3) = 0
or, (y + 3) (y – 2) = 0
or, y = 2, –3
Hence, x ≥ y
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Algebraic Expressions Model Questions Set 1 Online Quiz
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