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Practice Test 7
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SSC CGL Algebra Practice Test 7

15 fresh SSC CGL algebra questions on identities, equations, polynomials, and substitution.

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SSC CGL Practice Session

SSC CGL Algebra Practice Test 7

15 fresh SSC CGL algebra questions on identities, equations, polynomials, and substitution.

Questions
15
Marking
+2 correct, -0.5 wrong
Format
15-question ad-supported session
Preview all 15 questions in SSC CGL Algebra Practice Test 7 (no login required)
  1. Identity

    1. If x+y=5 and xy=6, then x²+y² is:

    • A. 11
    • B. 12
    • C. 13 (Correct)
    • D. 14

    Explanation: x²+y²=(x+y)²−2xy=25−12=13.

  2. Linear Equation

    2. Solve: 3x+7=25.

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

    Explanation: 3x=18 → x=6.

  3. Quadratic

    3. 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.

  4. Identity

    4. 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.

  5. Substitution

    5. 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.

  6. Linear Equation

    6. 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.

  7. Polynomial

    7. 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.

  8. Identity

    8. 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.

  9. Linear Equation

    9. If 5x−3=2x+9, find x.

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

    Explanation: 3x=12 → x=4.

  10. Substitution

    10. 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.

  11. Polynomial

    11. If x=3, value of x³−9x+1:

    • A. −1
    • B. 0
    • C. 1 (Correct)
    • D. 2

    Explanation: 27−27+1=1.

  12. Quadratic

    12. 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).

  13. Identity

    13. 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.

  14. Linear Equation

    14. 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.

  15. Polynomial

    15. 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).