**Q 1.(27)**

^{2}

**/**

_{3}

**=x then 3x is equal to**

a) 6 b) 3 c) 27 d)9 e) None

**Q 2. (**

^{27}/_{125 })^{-2/3}= ?a) 625/18 b) 25/9 c) 81/625 e) 9/25

**Q 3. If (64)**

^{2/3}× (256)^{-1/2}= 4^{n }, then n= ?a) 2 b) 4 c) 0 d) 1 e) None

**Q 4.(64)**

^{0.25 }

**× (36)**

^{1.5}

**= ?**

a) None b) 108 c) 48 d) 54 e) 1021

**Q 5.**

^{3√1000000}/_{6√1000000}=(100)^{x}, then x is equal to .a) 4 b) 1/2 c) None of these d) 1/4 e) 2

**Q 6. (-**

^{1}/_{1331})^{-2/3}× √1331 × (^{1}/_{121})^{3/2}a) (

^{1}/

_{11})

^{-1/2}b) (-

^{1}/

_{11})

^{1/3}c) (-

^{1}/

_{11})

^{2/3}d) (-

^{1}/

_{121})

^{2/3}e) 11

^{3}/

_{2}

_{ }

**Q7.(**

^{64}/_{729})^{-1/3}= ?a) -

^{4}/

_{9}b)

^{8}/9 c)

^{8}/27 d) 2

^{1}/

_{4}e) None of these

**Q 8. Simplify [x**

^{2n-1 }+ y^{2n-1}]^{2}[x^{2n-1 }- y^{2n-1}] .a) x

^{2n}+ y

^{2n}b) x

^{2n}c) -y

^{2n}d) x

^{2n}- y

^{2n}e) None of these

**Q 9. Arrange 2**

^{2-1 , 4 0.33 , 60.25}**in ascending order .**

a)1st<2nd<3 b)3rd<2nd<1 c)1st<3rd<2 d)3rd<1st<2 e) None of these

**Q 10. Evaluate (0.04)**

^{-1.5}× (0.125)^{-4/3}- (^{1}/_{121})^{-1/2}a) 1989 b) 22000 c) 2045 d) 2011 e) 2000

^{1}/

_{11}

**Q 11. Express**

^{2}/_{3}√32 as a pure surd .a)√128 b)√128/9 c)√9/128 d) e) None of these

### Solution

**(1)**

**Sol: Option (c)**

(27)

^{2/3}= x ⇒ (3

^{3})

^{2/3}= x ⇒ 3

^{2}= x ⇒ 3x = 2

**(2)**

**Sol: Option (b)**

(

^{27}/

_{125})

^{-2/3}= (

^{125}/

_{27})

^{2/3}=

^{25}/9

**(3)**

**Sol :Option (c)**

(4

^{3})

^{2/3}×(4

^{4})

^{-1/2}= 4

^{n}

4

^{2 }× 4

^{-2 }= 4

^{n}, ⇒4

^{0}⇒ n = 0

**(4)**

**Sol : Option (a)**

(√64

^{2})

^{1/3}=(64)

^{1/3}=(4

^{3})

^{1/3}= 4

**(5)**

**Sol : Option (b)**

^{3√1003}/

_{6√1003 }= (100)

^{x }⇒ 100

^{1}/

_{2}= (100)

^{x}⇒ x =

^{1}/

_{2}

_{ }

**(6)**

**Sol: Option (a)**

Convert each term to the base of 11

(-

^{1}/

_{1331})

^{-2/3}= (-1331)

^{2/3}= (-11)

^{3*2}/

_{3}= (-11)

^{2}= 11

^{2}

√1331 = 11

^{3/2 , (1/121)3/2 = 11-2*3/2 = 11-3 }

**(7)**

**Sol: Option (d)**

^{ (43/93)-1/3 = (4/9)-1 = 9/4 = 21/4 }

**(8)**

Sol : Option (d)

Sol : Option (d)

^{ Given expression = ( a+b ) ( a-b ) = a2 - b2 = [x2n-1 ]2 - [y2n-1]2 = x2n-1×21 - y2n-1×21 = x2n- y2n }

**(9)**

**Sol : Option (c)**

(2

Here, the base and the index both are different .For comparision, either the base should be same or indices of each number should be same. Take LCM of 2,3,4 = 12 and convert each number to same index^{1/2}) , (4^{1/3}) , (6^{1/4})(2

^{1/2}) = (2

^{6})

^{1/12}

**;**(4

^{4})

^{1/12 }

**;**(6

^{3})

^{1/4}

= (64)

^{1/12}= (256)

^{1/12}= (216)

^{1/12}

Clearly,(64)

^{1/12}

**<**(216)

^{1/12}

**<**(256)

^{1/12}⇒2

^{1/2}

**<**6

^{0.25}

**<**4

^{0.33}

^{ }

**(10)**

**Sol : Option (a)**

Given expression = (0.2)

^{-3}×(0.5)^{-4}- 11 = (0.2)^{-3}×(0.5)^{-3}.(0.5)^{-1}-11
= (0.1)

^{-3}×(0.5)^{-1}-11 = 2000-11**(11)****Sol : Option (b)**^{2}/

_{3 }√32 = √(

^{2}/

_{3})

^{2}×32

=√

^{128}/

_{9}a pure surd

Read Simplification notes here

Surds and Indices Formulas

How to Solve Surds and Indices Problems

#### What's trending in BankExamsToday

*Smart Prep Kit for Banking Exams by Ramandeep Singh - Download here*
Sir CHSL tier-2 ka result aa gya kya???

ReplyDeletesir please tell me smart time management for sbi po mains exam ...... and how much attempts are sufficient with good accuracy for general category candidate?

ReplyDeleteSir RBI assistant model ppr second set kb aayega???

ReplyDeletesir plz explain ki pri me bhi sestional cutoff hoga ki nhi

ReplyDeleteDear Sir,

ReplyDeleteWhat are the contents will be there in that combo pack which you offer Rs.500.

Sir, how to order for COD order.

ReplyDeleteThank you.