algebraic expressions Model Questions & Answers, Practice Test for ssc cgl tier 1 2023

ssc cgl tier 1 2023 SYLLABUS WISE SUBJECTS MCQs

Number System

Ratio Proportion & Partnership

Averages

Percentages

Profit & Loss

Time & Work

Time & Distance

Simple Interest & Compound Interest

Mensuration: Area & Volumes

Algebraic Expressions

Linear Equations

Squareroots & Cuberoots

Click To More Exercise For Algebraic Expressions
Question :6

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.$ 4P^2$ – 8P + 3 = 0
II. $2Q^2$ – 13Q + 15 = 0

Answer: (d)

I. $4P^2$ – 8P + 3 = 0

$4P^2$ – 2P – 6P + 3 = 0

2P (2P – 1) – 3 (2P – 1) = 0

(2P – 3) (2P – 1) = 0

⇒P = 1/2, 3/2

II. $2Q^2$ – 13Q + 15 = 0

$2Q^2$ – 10Q – 3Q + 15 = 0

2Q(Q – 5) – 3(Q – 5) = 0

⇒ (2Q – 3) (Q – 5) = 0

⇒ Q = $3/2$ , 5

∴Q ≥ P

Question :7

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. $a^2$ – 7a + 12 = 0
II. $b^2$ – 9b + 20 = 0

Answer: (b)

I. $a^2$ – 7a + 12 = 0

Here, $F_1$ = – 4 and $F_2$ = – 3

Now, values of a=${-(-4)}/1=4$

and ${-12}/{-4}=3$

II. $b^2$ – 9b + 20 = 0

Here $F_1$ = – 5 and $F_2$ = – 4

Now, values of a = ${-(-5)}/1=5$ and ${-20}/{-5}=4$

Thus b ≥ a.

Question :8

Directions :
In each of the following questions two equations are given. You have to 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. $12p^2$ – 7p = – 1
II. $6q^2$ – 7q + 2 = 0

Answer: (c)

I. $12p^2$ – 7p = – 1

or, $12p^2$ – 7p + 1 = 0

or, (3p – 1) (4p – 1) = 0

or, p = $1/4 or 1/3$

II. $6q^2$ – 7q + 2 = 0

or, (3q – 2) (2q – 1) = 0

or, q = $1/2 or 2/3$

Hence, q > p

Question :9

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. $20P^2$ + 31P + 12 = 0
II.$21Q^2$ + 23Q + 6 = 0

Answer: (e)

I. $20P^2$ + 31P + 12 = 0

$20P^2$ + 16P + 15P + 12 = 0

5P(4P + 3) + 4 (4P + 3) = 0

∴P = ${–4}/5, {–3}/4$

II. $21Q^2$ + 23 Q + 6 = 0

$21Q^2$ + 14Q + 9Q + 6 = 0

7Q(3Q + 2) + 3 (3Q + 2) = 0

(7Q + 3) (3Q + 2) = 0

⇒ Q = ${-3}/7, {–2}/3$

∴ Q > P

Question :10

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. $4a^2$ = 1
II. $4b^2$ – 12b + 5 = 0

Answer: (e)

a = ±1/2; b = 1/2, 5/2

Click To More Exercise For Algebraic Expressions
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