A) 2675.5 B) 2642.5 C) 2733.5 D) 2879.5
2. 16x4+ 36x2y 2 + 81y4 = 21; 4x2 + 9y2 − 6xy = 7. Find the value of 72xy
A) − 36 B) − 24 C) 48 D) 76
Sol: 16x4 + 36x2y2 + 81y4 = 21,
4x2 + 9y2 − 6xy = 7
a 4 + b4 + a2b2 = (a2 + b2 + ab)(a2 + b2 − ab)
(2x)4 + (3y)4+ (2x)2 × (3y)2 = [(2x)2 + (3y)2 − (2x)(3y)] [(2x)2 + (3y)2 + (2x)(3y)]
Ans: B
3. (4x − 7)3+ (3x − 5)3 + (5x + 6)3 = 3(4x − 7)(3x − 5)(5x + 6). Then what is the value of 4x + 5?
A) 8 B) 15 C) 7 D) 10
8. If a = 12; b = 20; c = 26; then find the value of (a)3 + (b)3 + (c)3 − 3abc ?
A) 8984 B) 8784 C) 8584 D) 8564]
Sol: a =12; b = 20; c = 26
a3 + b3+ c3 − 3abc
= (a + b + c)(a2 + b2 + c2 − ab − bc − ca)
9. If 2a = 5b = 4c and a + b + c = 57 ; Find the value of (a)2+ (b)2 + (c)2
A) 1145 B) 1358 C) 1481 D) 1269
Sol: 2a = 5b = 4c
a : b : c = 20 : 8 :10
10 : 4 : 5
10x + 4x + 5x = 57 19x = 57 ⇒ x = 3
a = 10x = 30
b = 4x = 12
c = 5x = 15
a2 + b2 + c2 = 900 + 144 + 225 = 1269
Ans: D
10. 64 + 27x3 + 144x + qx3 = (4 + 3x)3 then the value of q + 11 is.....
A) 163 B) 144 C) 125 D) 108
Sol: (a + b)3 = a3 + b3 + 3a2b + 3ab2
(4 + 3x)3 = 64 + 27x3 + 3(16)(3x) + 3(4)(9x2 ) (4 + 3x)3
= 64 + 27x3 + 144x + 108x2 64 + 27x3 + 144x + qx2q = 108
Ans: D
12. If 245x + 555y = 1600; 555x + 245y = 480, find the value of x + y
A) 2.1 B) 1.75 C) 2.6 D) 3.5
