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UIIC ASSISTANT RECRUITMENT Numerical Ability Study Material

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Quadratic Equations

Thevalue of (x+y+z)3 - (y+z-x)3 -(Z+x-y)3-(x+y-z)3 is

a) 0
b) 12xyz
c) 24xyz
d) 36xyz

✔Answer

✔Solution

Correct Answer Is : 24xyz

Solution Is :

If a =b²/ b-a ,then the value of a³ + b³ is

a) 0
b) 1
c) 2
d) 6 ab

✔Answer

✔Solution

Correct Answer Is : 0

Solution Is :

If xy+yz +zx=0 ,then (1/x² + yz + 1/y² -zx +1/ z²- xy) (x ,y, z is not equal to 0) is equal to

a) 1
b) X+y+z
c) 0
d) 3

✔Answer

✔Solution

Correct Answer Is : 0

Solution Is :

Theequation cos2 θ =(x+y)²/4xy is only possible when

a) X>y
b) X=y
c) X d) X=-y

✔Answer

✔Solution

Correct Answer Is : X=y

Solution Is :

If x + y + z = 15, xy + yz + zx = 75, then x + 4y + z / 3z is equal to

a) 1
b) 0
c) 2
d) -1

✔Answer

✔Solution

Correct Answer Is : 2

Solution Is :

(a + b - 2c)³ + (b + c - 2a)³ + (c + a - 2b) ³ is equal to

a) (a+b-2c)(b+c-2a)(c+a-2b)
b) 2(a+b+2c)(b+c-2a)(c+a+-2b)
c) 3(a+b-2c)(b+c-2a)(c+a-2b)
d) 0

✔Answer

✔Solution

Correct Answer Is : 0

Solution Is :

Let 3√a = 3√26 + 3√7 + 3√63 . Then ,

a) A > 729
b) A = 729
c) A< 729 but a > 216
d) A < 216

✔Answer

✔Solution

Correct Answer Is : A< 729 but a > 216

Solution Is : 3√a = 3√26 + 3√7 + 3√63 , 3√a = 3√27 + 3√8 + 3√64
3√a = 3 + 2 + 4 ---> 3√a = 9
Accrding to question the digits are 26 , 7 , 63
But according to cube values we use digits as 27 , 8 , 64
thewrefore a < 93 or a < 729

If x + y + z = 13 and x² + y² + z² = 69 , then the value of xy + z(x+y) is

a) 50
b) 60
c) 70
d) 40

✔Answer

✔Solution

Correct Answer Is : 50

Solution Is :

If 3 sinθ + 5 cosθ = 5 , then 5sinθ - 3 cosθ is equal to

a) 1
b) +/- 2
c) +/- 3
d) +/- 5

✔Answer

✔Solution

Correct Answer Is : +/- 3

Solution Is :

If (x-2) is a factor of x² +3Qx - 3Q then the value of Q is

a) 2
b) -2
c) 1
d) -1

✔Answer

✔Solution

Correct Answer Is : -1

Solution Is :

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UIIC ASSISTANT RECRUITMENT Numerical Ability Study Material

Quadratic Equations

Thevalue of (x+y+z)3 - (y+z-x)3 -(Z+x-y)3-(x+y-z)3 is

Correct Answer Is : 24xyz

Solution Is :

If a =b2/ b-a ,then the value of a3 + b3 is

Correct Answer Is : 0

Solution Is :

If xy+yz +zx=0 ,then (1/x2 + yz + 1/y2 -zx +1/ z2- xy) (x ,y, z is not equal to 0) is equal to

Correct Answer Is : 0

Solution Is :

Theequation cos2 θ =(x+y)2/4xy is only possible when

Correct Answer Is : X=y

Solution Is :

If x + y + z = 15, xy + yz + zx = 75, then x + 4y + z / 3z is equal to

Correct Answer Is : 2

Solution Is :

(a + b - 2c)3 + (b + c - 2a)3 + (c + a - 2b) 3 is equal to

Correct Answer Is : 0

Solution Is :

Let 3√a = 3√26 + 3√7 + 3√63 . Then ,

Correct Answer Is : A< 729 but a > 216

Solution Is : 3√a = 3√26 + 3√7 + 3√63 , 3√a = 3√27 + 3√8 + 3√64 3√a = 3 + 2 + 4 ---> 3√a = 9 Accrding to question the digits are 26 , 7 , 63 But according to cube values we use digits as 27 , 8 , 64 thewrefore a < 93 or a < 729

If x + y + z = 13 and x2 + y2 + z2 = 69 , then the value of xy + z(x+y) is

Correct Answer Is : 50

Solution Is :

If 3 sinθ + 5 cosθ = 5 , then 5sinθ - 3 cosθ is equal to

Correct Answer Is : +/- 3

Solution Is :

If (x-2) is a factor of x2 +3Qx - 3Q then the value of Q is

Correct Answer Is : -1

Solution Is :

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If a =b²/ b-a ,then the value of a³ + b³ is

If xy+yz +zx=0 ,then (1/x² + yz + 1/y² -zx +1/ z²- xy) (x ,y, z is not equal to 0) is equal to

Theequation cos2 θ =(x+y)²/4xy is only possible when

(a + b - 2c)³ + (b + c - 2a)³ + (c + a - 2b) ³ is equal to

Solution Is : 3√a = 3√26 + 3√7 + 3√63 , 3√a = 3√27 + 3√8 + 3√64
3√a = 3 + 2 + 4 ---> 3√a = 9
Accrding to question the digits are 26 , 7 , 63
But according to cube values we use digits as 27 , 8 , 64
thewrefore a < 93 or a < 729

If x + y + z = 13 and x² + y² + z² = 69 , then the value of xy + z(x+y) is

If (x-2) is a factor of x² +3Qx - 3Q then the value of Q is