Algebra MCQs for Competitive Examination
Solve the following problems.
Q. 81
If x + (1/x)=1, then the value of (x² + 3x + 1)/(x² + 7x + 1)
(A) 1
(B) 3/7
(C) 1/2
(D) 2
Answer: (C) 1/2
Explanation: N/A
Q. 82
If x=(√5 – √3)/(√5 + √3), y=(√5 + √3)/(√5 – √3); then the value of (x² + xy + y²)/(x² – xy + y²)
(A) 63/61
(B) 67/65
(C) 63/65
(D) 69/67
Answer: (A) 63/61
Explanation: N/A
Q. 83
If x + (1/x) = 1, then the value of 2/(x² – x + 2)
(A) 1
(B) 2/3
(C) 4
(D) 2
Answer: (D) 2
Explanation: N/A
Q. 84
If x = (a – b)/(a + b), y = (b – c)/(b + c), z = (c – a)/c + a), then {(1 – x)(1 – y)(1 – z)}/{(1 + x)(1 + y)(1 + z)} is equal to
(A) 1
(B) 0
(C) 2
(D) 1/2
Answer: (A) 1
Explanation: N/A
Q. 85
For real a, b, c if (a² + b² + c²) = (ab + bc + ca); then the value of (a + c)/b is
(A) 3
(B) 1
(C) 2
(D) 0
Answer: (C) 2
Explanation: N/A
Q. 86
9x² + 25 − 30x can be expressed as the square of
(A) −3x − 5
(B) 3x + 5
(C) 3x − 5
(D) 3×2 − 25
Answer: (C) 3x – 5
Explanation: N/A
Q. 87
If x/3 + 3/x = 1, then the value of x³ is
(A) 0
(B) 1
(C) 27
(D) -27
Answer: (D) – 27
Explanation: N/A
Q. 88
If x + y = 2a, then the value of {a/(x-a)}+{a/(y-a)} is
(A) 0
(B) 1
(C) -1
(D) 2
Answer: (A) 0
Explanation: N/A
Q. 89
If (x + 1)/(x – 1) = a/b, and (1 – y)/(1 + y) = b/a, then the value of {(x – y)/(1 + xy)} is
(A) 2ab/(a² – b²)
(B) (a² – b²)/2ab
(C) (a² + b²)/2ab
(D) (a² – b²)/ab
Answer: (A) 2ab/(a² – b²)
Explanation: N/A
Q. 90
If a/b + b/a = 2, then the value of (a – b) is
(A) 1
(B) 0
(C) -1
(D) 2
Answer: (B) 0
Explanation: N/A
Q. 91
If √y = 4x, then the value of x²/y is
(A) 2
(B) 1/4
(C) 1/16
(D) 4
Answer: (C) 1/16
Explanation: N/A
Q. 92
If x/y = (a + 2)/(a – 2), then the value of (x² – y²)/(x² + y²) is
(A) 4a/(a² + 2)
(B) 2a/(a² + 2)
(C) 2a/(a² + 4)
(D) 4a/(a² + 4)
Answer: (D) 4a/(a² + 4)
Explanation: N/A
Q. 93
If x (x + y + z) = 20, y (x + y + z) = 30, and z (x+ y + z) = 50, then the value of 2 (x + y + z) is
(A) 20
(B) -10
(C) 15
(D) 18
Answer: (A) 20
Explanation: N/A
Q. 94
If x + y = 4, x² + y² = 14 and x > y, then the values of x and y is
(A) 2 + √3, 2 – √3
(B) 2 – √3, √3
(C) 3, 1
(D) 2 + √3, 2√2
Answer: (A) 2 + √3, 2 – √3
Explanation: N/A
Q. 95
If a² + b² + c² = 2(a + b – c) − 3, then the value of a + b+ c is
(A) 2
(B) 1
(C) -2
(D) -1
Answer: (B) 1
Explanation: N/A
Q. 96
If for non-zero x, x² − 4x − 1 = 0, then the value of x² + 1/x² is
(A) 12
(C) 4
(C) 18
(D) 10
Answer: (C) 18
Explanation: N/A
Q. 97
If a + (1/b) = 1, b + (1/c) = 1, then find the value of c + (1/a) is
(A) 0
(B) 1
(C) 2
(D) 1/2
Answer: (B) 1
Explanation: N/A
Q. 98
If (4x – 3) = (3x + 8), then the numerical value of (x + 1)3 is
(A) 1331
(B) 1000
(C) 1728
(D) 729
Answer: (C) 1728
Explanation: N/A
Q. 99
Factorise 24x2 – 54x – 15
(A) 3(2x + 5)(4x – 1)
(B) 3(2x – 5)(4x + 1)
(C) 2(3x – 5)(4x + 1)
(D) 4(2x – 5)(3x + 1)
Answer: (B) 3(2x – 5)(4x + 1)
Explanation: N/A
Q. 100
Which of the following is correct?
(A) (4x – 5y)2 = 16x2 – 20xy + 25y2
(B) (4x – 5y)2 = 16x2 + 40xy – 25y2
(C) (4x – 5y)2 = 16x2 – 40xy + 25y2
(D) (4x – 5y)2 = 16x2 – 20xy – 25y2
Answer: (C) (4x – 5y)2 = 16x2 – 40xy + 25y2
Explanation: N/A