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 : 6
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) $4p^2$ = 16 (ii) $q^2$ – 10q + 25 = 0
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) $4p^2$2 = 16; p = $√4$ = 2
(ii) $q^2 $ – l0q + 25 = 0 ⇒ (q – 5)(q – 5) = 0
or, q = 5 ∴ q > p
Question : 7
Directions :
In each question below one or more equation(s) is /are given. On the basis of these, you have to find out the relationship between p and q. Give answer
- if p = q
- if p > q
- if p < q
- if p ≤ q
- if p ≥ q
I. p ($p^{–1}$) = ($p^{–1}$)
II. $q^2$ = $4q^{–1}$
a) if p ≤ q
b) if p ≥ q
c) if p = q
d) if p < q
e) if p > q
Answer »Answer: (d)
I. $p(p^{– 1}) = p^{–1}$
II. $q^2 = 4(q ^{–1})$
or, p × $1/p=1/p$
∴p = 1
or, $q^3$ = 4
∴q = $(4)^{1/3}$ > 1
Hence, q > p
Question : 8
Directions :
In each of the following questions there are two equations. Solve them and give answer
- if P < Q
- if P > Q
- if P ≤ Q
- if P ≥ Q
- if P = Q
I. $P^2$ + 3P – 4 = 0
II. $3Q^2$ – 10Q + 8 = 0
a) If P ≥ Q
b) If P = Q
c) If P < Q
d) If P ≤ Q
e) If P > Q
Answer »Answer: (c)
I. $P^2$ + 3P – 4 = 0
$P^2$ + 4P – P – 4 = 0
⇒P(P + 4) –1(P + 4) = 0
⇒P = 1, – 4
II. $3Q^2$ – 10Q + 8 = 0
$3Q^2$ – 6Q – 4Q + 8 = 0
3Q (Q – 2) – 4 (Q – 2) = 0
(3Q – 4) (Q – 2) = 0
⇒Q = $4/3$, 2
∴Q > P
Question : 9
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. $a^2$ – 5a + 6 = 0
II. $b^2$ – 3b + 2 = 0
a) if a = b
b) if a > b
c) if a < b
d) if a ≥ b
e) if a ≤ b
Answer »Answer: (d)
For eqn 1, the roots (a) will be 2, ×3. As – 2 – 3 = 6 (ac) and (– 2) + (– 3) = – 5
(b). Similarly, for eqn II, the roots (b) will be 2, 1.
Question : 10
Directions :
In each question below one or more equation(s) is /are given. On the basis of these, you have to find out the relationship between p and q. Give answer
- if p = q
- if p > q
- if p < q
- if p ≤ q
- if p ≥ q
I. 2p (p – 4) = 8 (p + 5)
II. $q^2$ + 12 + 7q
a) if p < q
b) if p ≥ q
c) if p = q
d) if p ≤ q
e) if p > q
Answer »Answer: (e)
I. 2p (p – 4) = 8 (p +5)
or $p^2$ –8p–20 =0
or (p + 2) (p –10) = 0
⇒ p = –2, or + 10
II. $q^2$ + 7q + 12 =0
(q + 3) (q +4) =0
q = –3 or –4
p > q
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Algebraic Expressions Model Questions Set 1 Online Quiz
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