SSC CGL Algebra Practice Test 8
15 SSC CGL algebra questions on cubic identities, reciprocal expressions, and simultaneous equations.
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SSC CGL Algebra Practice Test 8
15 SSC CGL algebra questions on cubic identities, reciprocal expressions, and simultaneous equations.
Preview all 14 questions in SSC CGL Algebra Practice Test 8 (no login required)
- Reciprocal
1. 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.
- Cubic Identity
2. 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.
- Linear Equation
3. If x/3 + 5 = 8, find x.
- A. 6
- B. 8
- C. 9 (Correct)
- D. 12
Explanation: x/3=3 → x=9.
- Quadratic
4. Which value of x satisfies x² − 7x + 12 = 0?
- A. x=3 or x=4 (Correct)
- B. x=2 or x=6
- C. x=1 or x=12
- D. x=3 or x=5
Explanation: (x−3)(x−4)=0.
- Identity
5. If a+b=6 and ab=8, find a²+b².
- A. 18
- B. 20 (Correct)
- C. 22
- D. 24
Explanation: a²+b²=(a+b)²−2ab=36−16=20.
- Linear Equation
6. Ages of two brothers differ by 5 years. Sum of their ages is 29. Younger brother's age:
- A. 10
- B. 11
- C. 12 (Correct)
- D. 13
Explanation: x+(x+5)=29 → x=12.
- Polynomial
7. If p(x)=x³−3x²+4x−12, find p(3).
- A. 0 (Correct)
- B. 3
- C. 6
- D. 9
Explanation: 27−27+12−12=0.
- Identity
8. Value of (a+b)² + (a−b)² =
- A. 2a²+2b² (Correct)
- B. 4ab
- C. 2a²−2b²
- D. a²+b²
Explanation: (a+b)²+(a−b)²=a²+2ab+b²+a²−2ab+b²=2a²+2b².
- Quadratic
9. Product of roots of 3x²−5x+2=0 is:
- A. 2/3 (Correct)
- B. 3/2
- C. 5/3
- D. 5/2
Explanation: Product = c/a = 2/3.
- Reciprocal
10. If x + y = 10 and xy = 21, find 1/x + 1/y.
- A. 10/21 (Correct)
- B. 21/10
- C. 1/2
- D. 2/3
Explanation: 1/x+1/y=(x+y)/xy=10/21.
- Linear Equation
11. A two-digit number is thrice the sum of its digits. Its units digit is 5 more than its tens digit. The number is:
- A. 24
- B. 27 (Correct)
- C. 36
- D. 48
Explanation: Let the tens digit be t, so the units digit is t + 5. Then the number is 11t + 5 and the digit sum is 2t + 5. So 11t + 5 = 3(2t + 5), giving t = 2. The number is 27.
- Polynomial
12. If x+2 is a factor of x²+5x+k, find k.
- A. 4
- B. 5
- C. 6 (Correct)
- D. 7
Explanation: x=−2: 4−10+k=0 → k=6.
- Identity
13. If a/b + b/a = 1, then a³+b³ = ?
- A. 0 (Correct)
- B. 1
- C. −1
- D. 2
Explanation: a/b+b/a=1 → a²+b²=ab. a³+b³=(a+b)(a²−ab+b²)=(a+b)(ab−ab)=0.
- Linear Equation
14. If 4(x+1) = 3(x+4), find x.
- A. 6
- B. 7
- C. 8 (Correct)
- D. 9
Explanation: 4x+4=3x+12 → x=8.