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SSC CGL Algebra Verified Practice Test 5

15 structurally validated Algebra questions with unique options, mapped answers and explanations.

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SSC CGL Practice Session

SSC CGL Algebra Verified Practice Test 5

15 structurally validated Algebra questions with unique options, mapped answers and explanations.

Questions
15
Marking
+2 correct, -0.5 wrong
Format
15-question practice session
Preview all 15 questions in SSC CGL Algebra Verified Practice Test 5 (no login required)
  1. Linear Equation

    1. Solve: 3x+7=25.

    • A. x=5
    • B. x=6 (Correct)
    • C. x=7
    • D. x=8

    Explanation: 3x=18 → x=6.

  2. Quadratic

    2. Roots of x²−5x+6=0 are:

    • A. 2 and 3 (Correct)
    • B. 1 and 6
    • C. 3 and 4
    • D. 2 and 4

    Explanation: Factors: (x−2)(x−3)=0.

  3. Identity

    3. If a−b=3 and a+b=7, then a²−b²=

    • A. 18
    • B. 21 (Correct)
    • C. 24
    • D. 28

    Explanation: a²−b²=(a+b)(a−b)=7×3=21.

  4. Substitution

    4. If x=2 and y=−1, value of x³−y³:

    • A. 7
    • B. 9 (Correct)
    • C. 10
    • D. 12

    Explanation: x³−y³=8−(−1)=9.

  5. Linear Equation

    5. If 2x+3y=12 and x−y=1, find x.

    • A. 2
    • B. 3 (Correct)
    • C. 4
    • D. 5

    Explanation: From second: x=y+1. Substituting: 2(y+1)+3y=12 → 5y=10 → y=2, x=3.

  6. Polynomial

    6. If x+1/x=3, find x²+1/x².

    • A. 5
    • B. 6
    • C. 7 (Correct)
    • D. 9

    Explanation: (x+1/x)²=x²+2+1/x². So x²+1/x²=9−2=7.

  7. Identity

    7. Value of (a+b)³−(a−b)³ in simplified form:

    • A. 2b³
    • B. 2a³
    • C. 6a²b+2b³ (Correct)
    • D. 6ab²+2b³

    Explanation: Expand both cubes: (a+b)^3 - (a-b)^3 = a^3+3a^2b+3ab^2+b^3 - (a^3-3a^2b+3ab^2-b^3) = 6a^2b + 2b^3.

  8. Linear Equation

    8. If 5x−3=2x+9, find x.

    • A. 3
    • B. 4 (Correct)
    • C. 5
    • D. 6

    Explanation: 3x=12 → x=4.

  9. Substitution

    9. If x=√5+√3 and y=√5−√3, find xy.

    • A. 2 (Correct)
    • B. 4
    • C. 6
    • D. 8

    Explanation: xy=(√5+√3)(√5−√3)=5−3=2.

  10. Quadratic

    10. For equation 2x²−7x+3=0, sum of roots is:

    • A. 3/2
    • B. 5/2
    • C. 7/2 (Correct)
    • D. 9/2

    Explanation: Sum = 7/2 (from −b/a = 7/2).

  11. Identity

    11. If x²+y²=17 and xy=4, find x+y.

    • A. 4
    • B. 5 (Correct)
    • C. 6
    • D. 7

    Explanation: (x+y)²=x²+y²+2xy=17+8=25. x+y=5.

  12. Linear Equation

    12. In a fraction, numerator is 3 less than denominator. If both are increased by 2, fraction becomes 4/5. Original fraction is:

    • A. 7/10
    • B. 8/11
    • C. 9/12
    • D. 10/13 (Correct)

    Explanation: Let denominator be d, so numerator is d - 3. Then (d - 1)/(d + 2) = 4/5. Solving gives d = 13, so the original fraction is 10/13.

  13. Polynomial

    13. Factor of x²−16 is:

    • A. (x−4)(x+4) (Correct)
    • B. (x−8)(x+2)
    • C. (x−2)(x+8)
    • D. (x+4)²

    Explanation: Difference of squares: a²−b²=(a−b)(a+b).

  14. Reciprocal

    14. If x + 1/x = 4, find x² + 1/x².

    • A. 12
    • B. 14 (Correct)
    • C. 16
    • D. 18

    Explanation: (x+1/x)²=x²+2+1/x²=16. So x²+1/x²=14.

  15. Cubic Identity

    15. If x+y+z=0, find x³+y³+z³.

    • A. 0
    • B. 3xyz (Correct)
    • C. xyz
    • D. 3(x+y+z)

    Explanation: When x+y+z=0, x³+y³+z³=3xyz.