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
Directions :
In each of the following questions, one or two equation(s) is/are given. On their basis you have to determine the relation between x and y and then give answer.
- if x < y
- if x > y
- if x ≤ y
- if x ≥ y
- if x = y
I.$y^2$ + 2y – 3 = 0
II.$2x^2$ – 7x + 6 = 0
Answer: (e)
I. $y^2$ + 2y – 3 = 0⇒(y – 1)(y + 3) = 0
or, y = 1, – 3
II. $2x^2$ – 7x + 6 = 0
or, $2x^2$ – 4x – 3x + 6 = 0
or, (2x – 3)(x – 2) = 0
or, x = 2, $3/2$
Hence, x > y
Directions :
For the two given equations I and II, give answer
- if a is greater than b
- if a is smaller than b
- if a is equal to b
- if a is either equal to or greater than b
- if a is either equal to or smaller than b
I. $12a^2$ - 7a + 1 = 0
II. $15b^2$ - 16b + 4 = 0
Answer: (e)
I. $12a^2$ – 7a + 1 = 0
II. $15b^2$ – 16b + 4 = 0
Sum of the two values of a, i.e., $(a_1 , + a_2)$
${-(-7)}/ 12=7/12$
Similarly, Sum of the two values of b,
i.e.,$(b_1+b_2)={-(-16)}/15=16/15$
Since $7/12$ < $16/15$
Therefore, a < b,
Now check the equality of root
${(12×4-15× 1)}^2$= {12×( 16)-15×(- 7)} {(-7) ×4-(-16)×1}
⇒ $33^2$={-87}{-12}
⇒ 1089 = 1044, which is not true.
Therefore, our answer should be a < b.
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) p – 7 = 0 (ii) $3q^2$ – 10q + 7 = 0
Answer: (e)
(i) p – 7 = 0 or, p = 7
(ii) $3q^2$ – 10q + 7 = 0
or,$3q^2$ – 3q – 7q + 7=0
or,3q(q – 1) – 7(q – l) = 0
or, (3q –7) (q –1) or, q = 1 or, $7/3$
∴p > q
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) $5/28×9/8p=15/14×13/16q$
Answer: (e)
$5/{28}×9/8p=15/14×13/16a$
or, ${45p}/224={195q}/224$
or, 3p = 13q
∴ p > q
Directions :
In each of the following questions two equations are given. You have to solve them and Give answer
- if p < q
- if p > q
- if p ≤ q
- if p ≥ q
- if p = q
I. $2p^2$ + 20p + 50 = 0
II. $q^2$ – 25
Answer: (d)
I. $2p^2$ + 20p + 50 = 0
or, $p^2$ + 10p + 25 = 0
or, ${(p + 5)}^2$ = 0
or, p = – 5
II. $q^2$ = 25
or, q = ±5
Hence, p ≤ q
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