20 Powerful SSC CGL Basic Algebraic Identities Mcqs

Practice SSC CGL Basic Algebraic Identities MCQs with 20 latest questions, detailed solutions, shortcut tricks, and exam-oriented explanations based on the latest SSC CGL pattern.

SSC CGL Basic Algebraic Identities MCQs

1. If x +1/x = 5, then the value of x² +1/x² is.

A) 21  B) 23

C) 25  D) 27

Correct Answer: B) 23

Explanation:

(x +1/x)² = 5²

⟹ x² + 2 (x)(1/x) + 1/x² = 25

⟹  x² +  2 + 1/x² = 25

⟹  x² + 1/x² = 25 – 2 = 23

2. If a – b = 8 and ab=9, then find (a²+b²).

A) 70  B) 78

C) 82  D) 86

Correct Answer: C) 82

Explanation:

a – b = 8

(a – b)² = 8²

a² – 2ab + b² = 64

a² – 2(9) + b² = 64

a² – 18 + b² = 64

a² + b² = 64 + 18

a² + b² = 82

3. Evaluate: 99²

A) 9800  B) 9801

C) 9901  D) 9810

Correct Answer: B) 9801

Explanation:

99² = (100 –1)²

=10000 –200+1

=9801

4. Find 103²

A) 10509  B) 10609

C) 10809  D) 10909

Correct Answer: B) 10609

Explanation:

103² = (100 + 3)²

=10000 + 600 + 9

=10609

SSC CGL Basic Algebraic Identities MCQs

5. If x – y = 4, x + y = 10, then find xy.

A) 18  B) 20

C) 21  D) 24

Correct Answer: C) 21

Explanation:

We know that (x + y)² – (x – y)² = 4xy

⟹ 100–16 = 4xy

84 = 4xy[

⟹ xy=21

6. The value of 48 × 52 is

A) 2496  B) 2500

C) 2490  D) 2484

Correct Answer: A) 2496

Explanation:

48 × 52 = (50 – 2)(50 + 2)

=2500 – 4

=2496

7. If a+1/a=4 then find a³+1/a³

A) 52  B) 56

C) 60  D) 64

Correct Answer: A) 52

Explanation:

We know that a³ + b³ = (a + b)(a² – ab + b²)

a²+1/a² = (a + 1/a)² – 2

=16 – 2=14

Now

a³+1/a³ = (a + 1/a)(a² – a(1/a) + (1/a)²)

a³+1/a³ = 4(a² – 1 + 1/a²)

a³+1/a³ = 4(a² + 1/a² – 1)

a³+1/a³ = 4(14 – 1)

a³+1/a³ = 4(13) = 52

8. Evaluate 101² – 99²

A) 200  B) 400

C) 600  D) 800

Correct Answer: B) 400

Explanation:

We know that a² – b² = (a + b) (a – b)

101² – 99² = (101 + 99) (101 – 99)

101² – 99² = (200) (2) = 400

9. If a + b=12, ab=20, the value of a²+b² is

A) 96  B) 100

C) 104  D) 108

Correct Answer: C) 104

Explanation:

a² + b² = (a + b)² – 2ab

=144 –  40=104

SSC CGL Basic Algebraic Identities MCQs

10. The value of (2x+3)² is

A) (4x² + 9)               B) (4x²+12x + 9)

C) (2x²+12x + 9)       D) (4x²+6x + 9)

Correct Answer: B

Explanation:

We know that (a + b)²=a² + 2ab + b²

(2x+3)² = (2x)² + 2(2x)(3) + (3)²

(2x+3)² = 4x² + 12x + 9

11. Evaluate 999²

A) 998001  B) 999001

C) 997001  D) 998999

Correct Answer: A

Explanation:

(1000 –1)² =1000000 – 2000+1

=998001

12. If x +1/x = 6 , then find x²+1/x²

A) 30  B) 32

C) 34  D) 36

Correct Answer: C

Explanation:

x²+1/x² = (x + 1/x)² – 2

= 36 – 2 = 34

13. Evaluate 75²

A) 5525  B) 5625

C) 5725  D) 5825

Correct Answer: B

Explanation[

(70 + 5)² = 4900 + 700 + 25

=5625

14. Simplify (a + b)² – (a – b)²

A) 2ab              B) 4ab

C) a² + b²       D) 2(a + b)

Correct Answer: B

Explanation:

(a + b)² – (a – b)² = 4ab

SSC CGL Basic Algebraic Identities MCQs

15. Evaluate 198 × 202

A) 39996  B) 40000

C) 39992  D) 39990

Correct Answer: A

Explanation:

198 × 202 = (200 – 2) (200 + 2)

= 40000 – 4

=39996

16. If a + b=7, a² + b²=29, then the value of ab is

A) 8  B) 9

C) 10  D) 11

Correct Answer: C

Explanation:

a + b=7

(a + b)² =7²

a² + b² + 2ab = 49

29+2ab = 49

2ab=20

ab=10

SSC CGL Basic Algebraic Identities MCQs

17. Expand (x – 5)²

A) (x² –10x + 25)        B) (x²+10x + 25)

C) (x² – 25)                 D) (x² – 5x + 25)

Correct Answer: A

Explanation:[

(a – b)² = a² – 2ab + b²

(x – 5)² = x² – 2x(5) + (5)²

= x² – 10x + 25

18. Evaluate 49 × 51

A) 2499  B) 2501

C) 2498  D) 2500

Correct Answer: A

Explanation:

49 × 51  = (50 – 1)(50 + 1)

=2500 – 1

=2499

19. If x – 1/x = 2,  find x² + 1/x²

A)  4    B)   5

C)   6    D)   7

Correct Answer:   C) 6

  Explanation:

   x – 1/x = 2

   (x – 1/x)² = 2²

   x² – 2x(1/x) + (1/x)² = 4

   x² – 2 + 1/x² = 4

   x² + 1/x² = 6

20. If x + 1/x = 2, find  x³ + 1/x³.

A)  1    B)   2

C)   3    D)   4

Correct Answer:     B) 2

  Explanation:

We know that a³ + b³ = (a + b)(a² – ab + b²)

x²+1/x² = (x + 1/x)² – 2

=4 – 2= 2

Now

x³+1/x³ = (x + 1/x)(x² – x(1/x) + (1/x)²)

x³+1/x³ = 2(x² – 1 + 1/x²)

x³+1/x³ = 2(x² + 1/x² – 1)

x³+1/x³ = 2(2 – 1)

x³+1/x³ = 2(1) = 2

SSC CGL Basic Algebraic Identities MCQs

SSC CGL Basic Algebraic Identities MCQs

SSC CGL Quantitative Aptitude Topics

• Number System
• Decimals
• Fractions
• Percentages
• Ratio & proportion
• Square roots
• Averages
• Interest (simple & compound)
• Profit & loss
• Discount
• Partnerships
• Mixture & Alligation
• Time & speed & distance
• Time & work.
• Advanced math includes basic algebraic identities
• Elementary surds
• Graphs of linear equations
• Triangles
• Circles
• Regular polygons, right prisms, cones, cylinders, spheres
• Trigonometry.

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