NTT Data Algebra Quiz -1

Let’s add the two equations as coordinates x and y satisfy the two equations of the two

intersecting lines.

x + 5y = 9

+

- x – 3y = -19

2y = - 10

y = - 5

by substituting y by - 5 in one of the equations to find x.

x + 5(-5) = 9

x = 25 + 9

= 34

The point of intersection will be

(34 , -5)

 

Let the four numbers be

X, x + 3, x + 6, x + 9

Add the first and fourth value and you get

2x + 9 = 27

X = 9

The second largest value is

X +3=12

The third largest value is

X +6 =15

sum of the second largest and  third largest number in the series = 12 + 15 = 27

If x > 0, then

| x | = x

3b - a < 0

Therefore 0 < a - 3b

=>  |a - 3b| = a - 3b

So the equation is false

Or

Since LHS is positive and RHS is negative therefore the equation is false

Substituting b = 6 in the given equation

y^{2} - 6 y = -9

By solving it we get,

y^{2} - 6 y + 9 = 0

(y - 3 )^{2} = 0

By solving it we get two same solutions: y = 3 and y = 3

According to the given equation,

 

= y+ 1/y = 7

 

=>  y-7 = -(1/y)

 

Now,

 

(y - 7)^{81} + 1/ y^{81} (Substitute \: the\:  value\:  of \: y - 7)<br /> <br /> = (- 1/y)^{81} + (1/ y)^{81}<br /> <br /> = - ( 1/y)^{81} + (1/ y)^{81}

= 0

x^{2} + y^{2} = 30            - - - - (i)

xy = 17              - - - - (ii)

Multiplying the equation (ii) by 2 and adding to Equation (i), we get,

x^{2} + y^{2} + 2xy = 30 + 34

( x + y )^{2}= 64

Hence, x + y = +8, -8

| x + y | = 8

According to the given information in the question,

 

We know that (x+y)^{2}=x^{2}+y^{2} + 2xy

(19)^{2}= 163 + 2xy

361 = 163 + 2xy

198 = 2xy

99 = xy

5 xy = 5* 99

= 495

a^{3} + b^{3} + c^{3}– 3abc = (a + b+ c) ( a^{2} + b^{2} + c^{2}− ab − bc – ca )

But (a + b + c) = 0

Hence, a^{3} + b^{3} + c^{3}– 3abc = 0

a^{3} + b^{3} + c^{3}= 3abc

54 + a^{3} + b^{3} + c^{3}

= 54 + 3abc

The formula for the sum of natural no's is

N*(1+ N) / 2

 

As given n = last number that is 25

Sum = 17/2 (1+17)

= 153

Let the number be y.

=> y – 7y/9 = 178

=> (9y- 7y)/9 = 178

=> 2y/9 = 178

=> 2y = 178*9

Y = 801