# Algebraic Expressions Model Questions Set 1 Practice Questions Answers Test With Solutions & More Shortcuts

#### ALGEBRAIC EXPRESSIONS PRACTICE TEST [1 - EXERCISES]

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

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

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

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

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

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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