11.
(243)n/5 x 32n + 1 = ?
9n x 3n – 1
A. 1 B. 2
C. 9 D. 3n
Answer & Explanation
Answer: Option C
Explanation:
Given Expression
= (243)(n/5) x 32n + 1
9n x 3n – 1
= (35)(n/5) x 32n + 1
(32)n x 3n – 1
= (35 x (n/5) x 32n + 1)
(32n x 3n – 1)
= 3n x 32n + 1
32n x 3n – 1
= 3(n + 2n + 1)
3(2n + n – 1)
=
33n + 1
33n – 1
= 3(3n + 1 – 3n + 1) = 32 = 9.
12.
1 + 1 = ?
1 + a(n – m) 1 + a(m – n)
A. 0 B.
1
2
C. 1 D. am + n
Answer & Explanation
Answer: Option C
Explanation:
1 + 1 =
1 + 1
1 + an
am
1 + am
an
1 + a(n – m) 1 + a(m – n)
= am + an
(am + an) (am + an)
= (am + an)
(am + an)
= 1.
13.
If m and n are whole numbers such that mn = 121, the value of (m – 1)n + 1 is:
A. 1 B. 10
C. 121 D. 1000
Answer & Explanation
Answer: Option D
Explanation:
We know that 112 = 121.
Putting m = 11 and n = 2, we get:
(m – 1)n + 1 = (11 – 1)(2 + 1) = 103 = 1000.
14.
xb (b + c – a) . xc (c + a – b) . xa (a + b – c) = ?
xc xa xb
A. xabc B. 1
C. xab + bc + ca D. xa + b + c
Answer & Explanation
Answer: Option B
Explanation:
Given Exp.
= x(b – c)(b + c – a) . x(c – a)(c + a – b) . x(a – b)(a + b – c)
= x(b – c)(b + c) – a(b – c) . x(c – a)(c + a) – b(c – a)
. x(a – b)(a + b) – c(a – b)
= x(b2 – c2 + c2 – a2 + a2 – b2) . x-a(b – c) – b(c – a) – c(a – b)
= (x0 x x0)
= (1 x 1) = 1.
15.
If x = 3 + 22, then the value of x – 1 is:
x
A. 1 B. 2
C. 22 D. 33
Answer & Explanation
Answer: Option B
Explanation:
x – 1 2 = x + 1 – 2
x x
= (3 + 22) + 1 – 2
(3 + 22)
= (3 + 22) + 1 x (3 – 22) – 2
(3 + 22) (3 – 22)
= (3 + 22) + (3 – 22) – 2
= 4.
x – 1 = 2.
x