Simplification for IBPS PO test 6-Solved questions with detailed explanations for SSC, IBPS PO, SBI PO, RRB, RBI, CSE, CGL, CHSL, CDA, CSE, UPSC

6)

What will come in place of question mark (?) in the following questions

${}^{3}{\sqrt{1331}} =?$

[OBC (PO), 2009]

A)
27
B)
21
C)
17
D)
9
E)
None of these

Answer: Option E

Explanation

$\begin{array}{l} Here, \\ = {}^{3}{\sqrt{1331}} \\ = {}^{3}{\sqrt{11 \times 11 \times 11}} \\ {= (11}^{3})^{1/3} {= 11}^{3 \times \frac{1}{3}} \\ = 11 \end{array}$

Hence, Option E is correct.

Discussion

7)

$8^{1 .1} \times 4^{2 .7} \times 2^{3 .3} = 2^{?}$

[Indian Bank (PO), 2009]

A)
7.1
B)
14
C)
0.5
D)
9
E)
None of these

Answer: Option E

Explanation

$\begin{array}{l} Here, \\ \Rightarrow (2^{3})^{1.1} \times (2^{2})^{2.7} \times 2^{3 .3} = 2^{?} \\ \Rightarrow 2^{3 \times 1 .1} \times 2^{2 \times 2 .7} \times 2^{3 .3} = 2^{?} \\ \Rightarrow 2^{3 .3 + 5 .4 + 3 .3} = 2^{?} \\ \Rightarrow 2^{12} = 2^{?} \\ \Rightarrow ? = 12 \end{array}$

Hence, Option E is correct.

Discussion

8)

${If 289 = 17}^{x \frac{1}{5}}, then x = ?$

[OBC (PO), 2009]

A)
16
B)
83
C)
32
D)
$\frac{2}{5}$
E)
None of these

Answer: Option E

Explanation

$\begin{array}{l} Here, \\ \Rightarrow 17^{x \frac{1}{5}} = 289 \\ \Rightarrow 17^{x + \frac{1}{5}} = {(17)}^{2} [∵ 289 = 17^{2}] \\ \Rightarrow x + \frac{1}{5} = 2 \\ \Rightarrow x = 2 - \frac{1}{5} = \frac{9}{5} \end{array}$

Hence, Option E is correct.

Discussion

9)

$348 \div 29 \times {15 + 156 = (?)}^{3} +120$

[OBC (PO), 2009]

A)
12
B)
6
C)
36
D)
9
E)
None of these

Answer: Option B

Explanation

$\begin{array}{l} Here, \\ \Rightarrow 348 \div 29 \times {15 + 156 = (?)}^{3} +120 \\ Applying the BODMAS rule, we get \\ \Rightarrow 12 \times {15 + 156 = (?)}^{3} +120 \\ \Rightarrow 336 - {120 = (?)}^{3} \\ \Rightarrow {(?)}^{3} = 216 \\ \Rightarrow ? = {\sqrt{216}}_{3} = 6 \end{array}$

Hence, Option B is correct.

Discussion

10)

$(4 \times {4)}^{3} \div (512 \div {8)}^{4} \times (32 \times {8)}^{4} = (2 \times {2)}^{?+4}$

[Corporation Bank (PO), 2009]

A)
8
B)
12
C)
6
D)
14
E)
None of these

Answer: Option C

Explanation

$\begin{array}{l} Here \\ \Rightarrow (4 \times {4)}^{3} \div ((512 \div {8)}^{4} \times (32 \times {8)}^{4}) =(2 \times {2)}^{?}^{+4} \\ \Rightarrow {(16)}^{3} \div {(64)}^{4} \times {(256)}^{4} {= (4)}^{?}^{+4} \\ \Rightarrow {(4)}^{2 \times 3} \div {(4^{4})}^{4} \times {(4^{5})}^{4} {= (4)}^{?}^{+4} \\ \Rightarrow {4^{6}}^{-16} {+20 = (4)}^{?}^{+4} \\ \Rightarrow ?+4=10 \\ \Rightarrow ?=6 \end{array}$

Hence, Option C is correct.

Discussion

Simplification-Test 6 (Based on Surds and Indices/Percentages)

Answer: Option E

Answer: Option E

Answer: Option E

Answer: Option B

Answer: Option C