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 : 1

Directions :
For the two given equations I and II give answer

  1. if p is greater than q
  2. if p is smaller than q
  3. if p is equal to q
  4. if p is either equal to or greater than q
  5. if p is either equal to or smaller than q.

I. p = $√4/√9$
II. $9q^2$ – 12q + 4 =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: (d)

I. p = $√4/√9$=$2/3$

II. $9q^2$ – 12q + 4 = 0

or, $9q^2$ – 6q – 6q + 4 = 0

or, 3q(3q – 2) – 2(3q – 2) = 0

or, (3q – 2)(3q – 2) = 0

or, q = $2/3$

Therefore, p = q

Question : 2

Directions:
In each question, one/two equations are provided. On the basis of these you have to find out the relation between p and q.

  1. if p = q
  2. if p > q
  3. if q > p
  4. if p ≥ q, and
  5. if q ≥ p

I. $q^2$ + q = 2
II. $p^2$ + 7p +10 = 0

a) if p ≥ q, and

b) if q ≥ p

c) if p = q

d) if q > p

e) if p > q

Answer: (b)

I. $q^2$ + q = 2

or, $q^2$ + q – 2 = 0

II. $p^2$ + 7p + 10 = 0

or, $p^2$ + 5p + 2p + 10 = 0

or, (q + 2) (q – 1) = 0

or, (q + 5)(p + 2) = 0

∴ q = – 2 or 1

∴p = – 5 or – 2

Hence, q ≥ p

Question : 3

Directions :
For the two given equations I and II, give answer

  1. if a is greater than b
  2. if a is smaller than b
  3. if a is equal to b
  4. if a is either equal to or greater than b
  5. if a is either equal to or smaller than b

I. 3a + 2b = 14
II. a + 4b – 13 = 0

a) if a is either equal to or greater than b

b) if a is either equal to or smaller than b

c) if a is greater than b

d) if a is equal to b

e) if a is smaller than b

Answer: (c)

I. 3a + 2b = 14

II. a + 4b = 13

Subtract equation I from equation II after multiplying II by 3.

We get 3a + 12b – 3a – 2b = 39 – 14

⇒10b = 25

⇒b = 2.5

Put value of b in equation II. We set a + 4 × 2.5 = 13.

Therefore, a = 3. Thus, a > b

Question : 4

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. $2p^2$ = 23p – 63
II. 2q ($q^{– 8}$) = $q^{–36}$

a) if p ≤ q

b) if p ≥ q

c) if p = q

d) if p < q

e) if p > q

Answer: (e)

I. $2p^2$ = 23p – 63

or, $2p^2$ – 23p + 63 = 0

II. 2q ($q ^{–8}$) = $q^{ –36}$

or, (2p – 9) (p – 7) = 0

or, $q^{ –7} × q^{36} = 1/2$

∴p = $9/2$ or 7

or, $q^{29} = 1/2$

∴q = $(1/2)^{1/29}$

Hence, p > q

Question : 5

Directions :
For the two given equations I and II, give answer

  1. if a is greater than b
  2. if a is smaller than b
  3. if a is equal to b
  4. if a is either equal to or greater than b
  5. if a is either equal to or smaller than b

I. $√2304$ a
II. $b^2$ = 2304

a) if a is either equal to or greater than b

b) if a is either equal to or smaller than b

c) if a is greater than b

d) if a is equal to b

e) if a is smaller than b

Answer: (d)

From I :

If $√{2304}$= a

then a = ± 48

(Do not consider – 48 as value of a)

Again,

From II :

If $b^2$ = 2304 then b = ± 48

Hence a = b

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Algebraic Expressions Model Questions Set 1 Online Quiz

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