Simplification for IBPS clerk test 5-Solved questions with detailed explanations for SSC, IBPS PO, SBI PO, RRB, RBI, CSE, CGL, CHSL, CDA, CSE, UPSC

11)

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

${(4)}^{?} = 1024$

[Bank of Baroda (PO), 2008]

A)
1
B)
2
C)
4
D)
3
E)
None of these

Answer: Option E

Explanation

$\begin{array}{l} Here, \\ \Rightarrow {(4)}^{?} = 1024 \\ \Rightarrow {(4)}^{4} {= 2}^{10} \\ [1024=2 \times 2 \times 2 . ... 10 times] \\ Now, {(2^{2})}^{?} {= 2}^{10} \\ \Rightarrow 2^{2x?} {=2}^{10} [∵ 2^{2 \times ?} = 2^{2 \times ?}] \\ \Rightarrow 2 \times ? = 10 \Rightarrow ? = 5 \end{array}$

Hence, Option E is correct.

Discussion

12)

${{(45)}^{3} {+ (65)}^{2}} \div ? = 1907$

[Andhra Bank (PO), 2008]

A)
80
B)
70
C)
60
D)
50
E)
None of these

Answer: Option D

Explanation

$\begin{array}{l} Here, \\ \Rightarrow {{(45)}^{3} {+ (65)}^{2}} \div ? = 1907 \\ \Rightarrow {91125 + 4225} \div ? = 1907 \\ \Rightarrow ? = \frac{95350}{1907} = 50 \end{array}$

Hence, Option D is correct.

Discussion

13)

${[(144)}^{2} \div 48 \times 18] + 36 = \sqrt{?}$

[SBI (PO), 2008]

A)
23328
B)
36
C)
216
D)
46656
E)
None of these

Answer: Option D

Explanation

$\begin{array}{l} Here, \\ \Rightarrow [\frac{144 X 144}{48} \times 18] \div 36= \sqrt{?} \\ \Rightarrow [144 \times 3 \times 18] \div 36 = \sqrt{?} \\ \Rightarrow ? = 7776 \div {36 = (216)}^{2} = 46656 \end{array}$

Hence, Option D is correct.

Discussion

14)

$\sqrt{5^{2} \times 14 - 6 \times {7+ (4)}^{?}} = 18$

[UK GBO, 2007]

A)
1
B)
3
C)
4
D)
5
E)
None of these

Answer: Option D

Explanation

$\begin{array}{l} Here, \\ \Rightarrow \sqrt{25 \times 14 - 6 \times {7+(4)}^{?}} = 18 \\ \Rightarrow \sqrt{350 - {42 + (4)}^{?}} = 18. \\ On taking squares both sides, we get \\ \Rightarrow 350 - {42 + (4)}^{?} = 324 \\ \Rightarrow {(4)}^{?} = 16 \Rightarrow {(4)}^{?} {= (4)}^{2} \Rightarrow ? = 2 \end{array}$

Hence, Option D is correct.

Discussion

15)

$\sqrt{24^{4}} + 224 = ? \times 20^{2}$

[UK GBO, 2007]

A)
20
B)
4
C)
2
D)
16
E)
None of these

Answer: Option B

Explanation

$\begin{array}{l} Here, \\ \Rightarrow {(24^{4})}^{\frac{1}{2}} + 224 = ? \times {(20)}^{2} \\ \Rightarrow {(24)}^{4 \times \frac{1}{2}} + 224 = ? \times {(20)}^{2} \\ \Rightarrow 576 + 224 = (?) \times 400 \\ \Rightarrow ?= \frac{800}{400} =2 \end{array}$

Hence, Option B is correct.

Discussion

Simplification-Test 5 (Based on Square roots and Cube roots/Surds and Indices)

Answer: Option E

Answer: Option D

Answer: Option D

Answer: Option D

Answer: Option B