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

  1. if p = q
  2. if p > q
  3. if q > p
  4. if p ≥ q
  5. 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: (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

  1. if p = q
  2. if p > q
  3. if p < q
  4. if p ≤ q
  5. 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: (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

  1. if P < Q
  2. if P > Q
  3. if P ≤ Q
  4. if P ≥ Q
  5. 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: (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

  1. if a < b
  2. if a ≤ b
  3. if a ≥ b
  4. if a = b
  5. 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: (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

  1. if p = q
  2. if p > q
  3. if p < q
  4. if p ≤ q
  5. 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: (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

IMPORTANT quantitative aptitude EXERCISES

Algebraic Expressions Model Questions Set 1 Online Quiz

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