Algebra MCQs for Competitive Examination
Solve the following problems.
Q. 21
If x + y = 7 and xy = 10, then the value of (1/x³) + (1/y³) is
(A) 0.543
(B) 0.131
(C) 0.133
(D) 0.453
Answer: (C) 0.133
Explanation: N/A
Q. 22
If 8x² + y² – 12x – 4xy + 9 =0, then the value of (14x – 5y) is
(A) 6
(B) 5
(C) 9
(D) 3
Answer: (A) 6
Explanation: N/A
Q. 23
If x + y + z = 19, xyz = 216 and xy + yz + zx = 114, then the value of √(x³+y³+z³+xyz)
(A) 32
(B) 30
(C) 28
(D) 35
Answer: (D) 35
Explanation: N/A
Q. 24
If a² + 4b² + 49c² + 18 = 2(2b + 28c – a), then the value of (3a + 2b + 7c) is
(A) 0
(B) 1
(C) 2
(D) 3
Answer: (D) 3
Explanation: N/A
Q. 25
If a + b + c = 5, a² + b² + c² = 27, and a³ + b³ + c³= 125, then the value of 4abc is
(A) -20
(B) -15
(C) 15
(D) 20
Answer: (A) -20
Explanation: N/A
Q. 26
If a³ + b³= 110 and a + b = 5, then (a + b)²– 3ab is equal to
(A) 52
(B) 32
(C) 42
(D) 22
Answer: (D) 22
Explanation: N/A
Q. 27
If a + b + c = 5, and a² + b²+ c² = 33, then what is the value of a³ + b³ + c³ – 3abc?
(A) 195
(B) 180
(C) 192
(D) 185
Answer: (D) 185
Explanation: N/A
Q. 28
If x² + 1 = 3x, then the value of (x4+x-2 )/(x2+5x+1) is
(A) 7/2
(B) 9/4
(C) 5/2
(D) 3/2
Answer: (B) 9/4
Explanation: N/A
Q. 29
x + (1/x) = 7, then x³ + (1/x)³ is
(A) 300
(B) 322
(C) 364
(D) 343
Answer: (B) 322
Explanation: N/A
Q. 30
If 8(a + b)³ + (a – b)³ = (3a + b) (Aa²+ Bab + Cb²), then what is the value of (A +B – C)?
(A) 2
(B) 4
(C) 10
(D) 11
Answer: (A) 2
Explanation: N/A
Q. 31
If (x – 7)³ + (x – 8)³ + (x + 6)³ = 3(x – 7) (x – 8) (x + 6), then what is the value of x?
(A) 6
(B) 8
(C) 10
(D) 3
Answer: (D) 3
Explanation: N/A
Q. 32
If a²+ b² = 88 and ab = 6, (a > 0, b >0) then what is the value of (a³ + b³) ?
(A) 980
(B) 1180
(C) 820
(D) 1000
Answer: (C) 820
Explanation: N/A
Q. 33
x4+ x-4 = 2207, (x > 0) then the value of x+x-1 is
(A) 19
(B) 7
(C) 11
(D) 9
Answer: (B) 7
Explanation: N/A
Q. 34
If a² + b² = 135 and ab = 7, (a > 0, b > 0) then the value of (a³– b³) is
(A) 1562
(B) 1600
(C) 1680
(D) 1350
Answer: (A) 1562
Explanation: N/A
Q. 35
If x = 2 – √3 then the value of x³– x-3 is
(A) 30√2
(B) -30√3
(C) -30√2
(D) 30√3
Answer: (C) -30√2
Explanation: N/A
Q. 36
If (3x + 1)³ + (x – 3)³ + (4 – 2x)³ + 6 (3x + 1) (x – 3) (x – 2) = 0, then x is equal to
(A) 1
(B) -1
(C) 1/2
(D) -1/2
Answer: (B) -1
Explanation: N/A
Q. 37
If a + b – c = 12 and a2 + b2 + c2 = 110, then which among the following relations is true?
(A) ab + bc + ca = 34,
(B) ab + bc – ca = 17,
(C) ab – bc + ca = 17,
(D) ab – bc – ca = 17
Answer: (D) ab – bc – ca = 17
Explanation: N/A
Q. 38
a1/3 + b1/3 + c1/3 = 0, then (a + b + c)6 is equal to
(A) 81 a2b2c2
(B) 729 abc
(C) 729 a2b2c2
(D) 81 abc
Answer: (C) 729 a2b2c2
Explanation: N/A
Q. 39
If a + 1/a = 3, the the value of (a6 + 1/a6) is equal to
(A) 319
(B) 780
(C) 730
(D) 322
Answer: (D) 322
Explanation: N/A
Q. 40
The value of the expression 1/4 {(a + 1/a)² – (a – 1/a)²} is
(A) 1
(B) 4
(C) 1/4
(D) 1/2
Answer: (A) 1
Explanation: N/A