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# Simplification Questions

Home > Quantitative Aptitude > Simplification > General Questions
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91 / 106

Choose the correct option.

if x-y+z=19,y+z=20,x-z=3
Find the value of x+4y-5z

A13

B-14

C-13

DNone of these

Explanation:

x-y+z=19 ------ (1)
y+z=20 -------- (2)
x-z=3 -----------(3)
Now substract eq 4 and eq 1
=> z=12.

By, Using z = 12 in eq 2
=> y=8
By, Using z=12 in eq 3
=> x=15

By, Putting values of x, y and z in
x+4y-5z = 15+32-60 = -13

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92 / 106

Choose the correct option.

Consider the following two curves in the X-Y plane.
y = x^3 + x^2 + 5
y = x^2 + x + 5
Which of the following statements is true for -2 < x < 2?

AThe two curves do not intersect.

BThe two curves intersect thrice.

CThe two curves intersect twice.

DThe two curves intersect once.

ENone of the above

Explanation:

Here x^3 + x^2 + 5 = x^2 + x + 5
=> x^3 - x = 0
Factor: x(x^2 - 1) = 0
Factor: x(x+1)(x-1) = 0
x= -1, 0, 1
Three points of intersection.

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Choose the correct option.

Find the remainder when ( X^3 + 4 X^2 + 6X - 2 ) is divided (X+5)

A-57

B57

C34

DNone of these

Explanation:

X+5) X^3 + 4 X^2 + 6 X -2 ( - X^2 + X -11
-X^3 - 5 X^2
..................................
- X^2 + 6 X
+ X^2 + 5 X
........................................
+ 11 X -2
- 11 X - 55
...........................................
- 57

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Choose the correct option.

What will be the minimum value of X in $$X^{3}-7X^{2}+11X-5$$. So we get a positive number.

A4

B5

C8

DNone of these

Explanation:

If we substitute 4 in the given equation then it becomes
(4)^3-(7*(4)^2)+(11*4)-5=-9
then substitute 5 in the equation
(5)^3-(7*(5)^2)+(11*5)-5=0
then substitute 8 in the equation
(8)^3-(7*(8)^2)+(11*8)-5=147 which is a positive integer.

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Choose the correct option.

Let f(x) = x^2 and g(x) = 2^x for all real x. Then the value of f(f(g(x)) + g(f(x)) ) at x = 1 is

A16

B18

C36

D40

Explanation:

Here is no explanation for this answer

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Choose the correct option.

How man Y different pairs(a,b) of positive integers are there such that a<=b and 1/a+1/b = 1/9?

A4

B7

C3

D1

Explanation:

Here is no explanation for this answer

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Choose the correct option.

f(x) = (5x+2)/(3x-5) and g(x) = x^2 - 2x - 1, then the value of g(f(f(3))) is.

A2

B1/3

C6

D2/3

Explanation:

Here is no explanation for this answer

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Choose the correct option.

if f1(x) = x^2 + 11x + n and f2(x) = x, then the largest positive integer n for which equation f1(x) = f2(x) has two distinct real root is

A23

B24

C22

D43

Explanation:

Here is no explanation for this answer

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Choose the correct option.

For how many integers n, will the inequality (n-5)(n-10)-3(n-2) <=0 be satisfied?

A11

B10

C13

DNone of these

Explanation:

Here is no explanation for this answer

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Choose the correct option.

If f(ab) = f(a)f(b) for all positive integers a and b, then the largest possible value of f(1) is

A3

B1

C4

D5

Explanation:

Here is no explanation for this answer

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