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# Simplification Questions

Home > Quantitative Aptitude > Simplification > General Questions
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Choose the correct option.

What is the value of 77!*(77!-2*54!)^3/(77!+54!)^3+54!*(2*77!-54!)^3/(77!+54!)^3

A77! - 54!

B77! + 54!

C77!^2 - 54!^2

D77!

Explanation:

take 77!=a
and 54!=b
now the given expression will look like
(a(a-2b)^3 )/(a+b)^3 + (b(2a-b)^3 )/(a+b)^3

( a (a^3 - 6a^2 b + 12ab^2 - 8b^3) + b (8a^3 - 12a^2 b + 6ab^2 - b^3) ) / (a+b)^3
(a^4 - 6a^3 b + 12 a^2 b^2 - 8ab^3 + 8a^3 b - 12a^2 b^2 + 6ab^3 - b^4) / (a+b)^3
(a^4 + 2a^3 b - 2ab^3 - b^4) / (a+b)^3
( a^4 - b^4 + 2ab(a^2 - b^2) ) / (a+b)^3
( (a^2 + b^2)(a^2 - b^2) + 2ab(a^2 - b^2) ) / (a+b)^3
( (a^2 - b^2) (a^2 + b^2 + 2ab) ) / (a+b)^3
( (a^2 - b^2)(a+b)^2 ) / (a+b)^3
( (a+b)(a-b) (a+b)^2 ) / (a+b)^3
( (a+b)^3 (a-b) ) / (a+b)^3
a-b
i.e 77! - 54!

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g[0]=1,g[1]=-1,g[n]=2*g[n-1]-3*g[n-2]
Then calculate g[4]= ?

A2

B1

C3

D0

Explanation:

From the given function g[n] =2*g [n-1]-3*g [n-2]
put values of n as first 2 then 3, then 4 and you will get the answer. G[2] = 2*g[1]-3*g[0]=-2-3 =-5 , G[3]=2*g[2]-3*g[1] =2*(-5)-3*(-1)=-7, G [4] =2*g[3]-3*g[2]=2*(-7)-3*(-5) =1

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In the polynomial f(x) =2*x^4 - 49*x^2+54, what is the product of the roots, and what is the roots (Note that x^n denotes the x raised to the power n, or x multiplied by itself n times)?

A27, 0

B49, 27

C49/2, 54

D54, 2

Explanation:

sum of roots= -(coeff of x^3/coeff of x^4)= -b/a = -0/2=0
product of roots=(-1)^n*(coeff of constant term/coeff of x^4)= e/a = 54/2 =27

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If (x-4)/7 + (7-2x)/6 = (8-x)/2 , then x= ?

A9

B7

C11

D2

Explanation:

(x-4)/7 + (7-2x)/6 = (8-x)/2
(6x-24+49-14x)/42 = (8-x)/2
=> 50-16x = 336-42x
=> 26x = 286
=> x = 11

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What should come in place of both question marks?
2.5/? = ?/1.6

A2.5*1.6

B4

C2

D0.09

ENone of these

Explanation:

Solution: 2.5/? = ?/1.6

2.5/x = x/1.6  =>  x^2= 4 therefore x=2

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Choose the correct option.

?/sqrt(0.0036) = 600

A36000

B36

C360

D3600

ENone of these

Explanation:

Solution:

x /sqrt(0.0036) = 600

x= 600* 0.06=36

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Choose the correct option.

? * 1.5 * 1.4 = 2.1

A1

B10

C0.14

D100

ENone of these

Explanation:

Solution:

x*1.5*1.4= 2.1

x=2.1/(1.5*1.4)= 1

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If a+b+c =0 ,
Then find the value of the expression (a^2+b^2+c^2)/(a^2-bc)= ?

A1

B2

C5

DCannot be determined.

Explanation:

Let's assume a=1, b=-1 & c = 0, these value will satisfy the a+b+c=0

so (a^2+b^2+c^2)/(a^2-bc) = (1+1+0)/(1-(-1)*0) = 2

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If a^x= b , b^y= c and c^z = a , then what is the value of x*y*z ?

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B3

C2

DCannot be determined

Explanation:

((((a)^x)^y)^z)=a
so.(a)^xyz=a
so xyz=1

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In this question A^B means A raised to the power B. If f(x) = ax^4 - bx^2 + x + 5 and f(-3) = 2, then f(3) =

A1

B-2

C3

D8

Explanation:

Putting the value of x= -3 in equation ax^4 - bx^2 + x + 5=2 we get 81a=9b

Now putting the values of x=3 again in equation

ax^4 - bx^2 + x + 5

81a-9b + 3 + 5

9b-9b + 3 + 5=8  therefore the answer is 8.

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