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# SNAP Quadratic Equation Questions PDF [Most Important]

The Quadratic Equations is an important topic in the Quant section of the SNAP Exam. You can also download this Free Quadratic Equations Questions for SNAP PDF with detailed answers by Cracku. These questions will help you practice and solve the Quadratic Equations questions in the SNAP exam. Utilize this PDF practice set, which is one of the best sources for practicing.

Question 1:Â Four of the following five parts numbered A,B,C,D,E are in the following equation are exactly equal.Which of the part is not equal to the other four.The number of that part is the answer

a)Â $xy^{2}-x^{2}y+2x^{2}y^{2}$

b)Â $xy^{2}(1-2x)+x^{2}y(2y-1)$

c)Â $xy^{2}(1+2x)-x^{2}y(2y+1)$

d)Â $xy[y(1+x)-x(1+y)]$

e)Â $xy[(x+y)^{2}+y(1-y)-x(1+x)-2xy]$

Solution:

(A) :Â $xy^{2}-x^{2}y+2x^{2}y^{2}$

= $xy(y-x+2xy)$

(B) :Â $xy^{2}(1-2x)+x^{2}y(2y-1)$

= $(xy^2-2x^2y^2)+(2x^2y^2-x^2y)$

= $xy^2-x^y = xy(y-x)$

(C) :Â $xy^{2}(1-2x)+x^{2}y(2y-1)$

= $(xy^2-2x^2y^2)+(2x^2y^2-x^2y)$

= $xy^2-x^y = xy(y-x)$

(D) :Â $xy[y(1+x)-x(1+y)]$

= $xy(y+xy-x-xy) = xy(y-x)$

(E) :Â $xy[(x+y)^{2}+y(1-y)-x(1+x)-2xy]$

= $xy[(x^2+y^2+2xy)+(y-y^2)+(-x-x^2)-2xy]$

= $xy(y-x)$

=> Ans – (A)

Question 2:Â If 2x+y= 15, Â 2y+z= 25 Â  and Â  2z+x =26 ,what is value of z?

a)Â 4

b)Â 7

c)Â 9

d)Â 12

e)Â None of these

Solution:

Equation (i) : $2x+y=15$

Equation (ii) : $2y+z=25$

Equation (iii) : $2z+x=26$

Adding the three equations, => $3x+3y+3z=15+25+26$

=> $3(x+y+z)=66$

=> $x+y+z=\frac{66}{3}=22$ ————(iv)

Subtracting equation (i) from (iv), => $(z)+(x-2x)+(y-y)=(22-15)$

=> $z-x=7$ ————-(v)

Adding equations (v) and (iii), => $3z=26+7=33$

=> $z=\frac{33}{3}=11$

=> Ans – (E)

Instructions

In the following questions two equations numbered I and II are given. You have to solve both the equations and
Give answer a: if x > y
Give answer b: if x â‰¥ y
Give answer c: if x < y
Give answer d: if x â‰¤ y
Give answer e: if x = y or the relationship cannot be established.

Question 3:Â I.Â  $2x^{2}+21x+10=0$
II.Â $3y^{2}+13y+14=0$

a)Â if x > y

b)Â if x â‰¥ y

c)Â if x < y

d)Â if x â‰¤ y

e)Â if x = y or the relationship cannot be established.

Solution:

I.$2x^{2} + 21x + 10 = 0$

=> $2x^2 + x + 20x + 10 = 0$

=> $x (2x + 1) + 10 (2x + 1) = 0$

=> $(x + 10) (2x + 1) = 0$

=> $x = -10 , \frac{-1}{2}$

II.$3y^{2} + 13y + 14 = 0$

=> $3y^2 + 6y + 7y + 14 = 0$

=> $3y (y + 2) + 7 (y + 2) = 0$

=> $(y + 2) (3y + 7) = 0$

=> $y = -2 , \frac{-7}{3}$

$\therefore$Â No relation can be established.

Question 4:Â I.Â  $3x^{2}+10x+8=0$
II.Â $3y^{2}+7y+4=0$

a)Â if x > y

b)Â if x â‰¥ y

c)Â if x < y

d)Â if x â‰¤ y

e)Â if x = y or the relationship cannot be established.

Solution:

I.$3x^{2} + 10x + 8 = 0$

=> $3x^2 + 6x + 4x + 8 = 0$

=> $3x (x + 2) + 4 (x + 2) = 0$

=> $(x + 2) (3x + 4) = 0$

=> $x = -2 , \frac{-4}{3}$

II.$3y^{2} + 7y + 4 = 0$

=> $3y^2 + 3y + 4y + 4 = 0$

=> $3y (y + 1) + 4 (y + 1) = 0$

=> $(y + 1) (3y + 4) = 0$

=> $y = -1 , \frac{-4}{3}$

$\therefore x \leq y$

Question 5:Â I.Â  $2x^{2}-11x+12=0$
II.Â $2y^{2}-19y+44=0$

a)Â if x > y

b)Â if x â‰¥ y

c)Â if x < y

d)Â if x â‰¤ y

e)Â if x = y or the relationship cannot be established.

Solution:

I.$2x^{2} – 11x + 12 = 0$

=> $2x^2 – 8x – 3x + 12 = 0$

=> $2x (x – 4) – 3 (x – 4) = 0$

=> $(x – 4) (2x – 3) = 0$

=> $x = 4 , \frac{3}{2}$

II.$2y^{2} – 19y + 44 = 0$

=> $2y^2 – 8y – 11y + 44 = 0$

=> $2y (y – 4) – 11 (y – 4) = 0$

=> $(y – 4) (2y – 11) = 0$

=> $y = 4 , \frac{11}{2}$

$\therefore x \leq y$

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Question 6:Â I.Â  $5x^{2}+29x+20=0$
II.Â $25y^{2}+25y+6=0$

a)Â if x > y

b)Â if x â‰¥ y

c)Â if x < y

d)Â if x â‰¤ y

e)Â if x = y or the relationship cannot be established.

Solution:

I.$5x^{2} + 29x + 20 = 0$

=> $5x^2 + 25x + 4x + 20 = 0$

=> $5x (x + 5) + 4 (x + 5) = 0$

=> $(x + 5) (5x + 4) = 0$

=> $x = -5 , \frac{-4}{5}$

II.$25y^{2} + 25y + 6 = 0$

=> $25y^2 + 10y + 15y + 6 = 0$

=> $5y (5y + 2) + 3 (5y + 2) = 0$

=> $(5y + 3) (5y + 2) = 0$

=> $y = \frac{-3}{5} , \frac{-2}{5}$

Therefore $x < y$

Question 7:Â I.Â  $x^{2}-3x-88=0$
II.Â $y^{2}+8y-48=0$

a)Â if x > y

b)Â if x â‰¥ y

c)Â if x < y

d)Â if x â‰¤ y

e)Â if x = y or the relationship cannot be established.

Solution:

I.$x^{2} – 3x – 88 = 0$

=> $x^2 + 8x – 11x – 88 = 0$

=> $x (x + 8) – 11 (x + 8) = 0$

=> $(x + 8) (x – 11) = 0$

=> $x = -8 , 11$

II.$y^{2} + 8y – 48 = 0$

=> $y^2 + 12y – 4y – 48 = 0$

=> $y (y + 12) – 4 (y + 12) = 0$

=> $(y + 12) (y – 4) = 0$

=> $y = -12 , 4$

$\therefore$Â No relation can be established.

Question 8:Â I.Â $x^{2}+3x-28=0$
II.Â $y^{2} -y-20=0$

a)Â x > y

b)Â x â‰¥ y

c)Â x < y

d)Â x â‰¤ y

e)Â x = y or the relation cannot be established.

Solution:

I.$x^{2} + 3x – 28 = 0$

=> $x^2 + 7x – 4x – 28 = 0$

=> $x (x + 7) – 4 (x + 7) = 0$

=> $(x – 4) (x + 7) = 0$

=> $x = 4 , -7$

II.$y^{2} – y – 20 = 0$

=> $y^2 – 5y + 4y – 20 = 0$

=> $y (y – 5) + 4 (y – 5) = 0$

=> $(y + 4) (y – 5) = 0$

=> $y = -4 , 5$

$\therefore$ No relation can be established.

Question 9:Â I.Â $6x^{2}+29x+35=0$
II.Â $3y^{2} +11y+10=0$

a)Â x > y

b)Â x â‰¥ y

c)Â x < y

d)Â x â‰¤ y

e)Â x = y or the relation cannot be established.

Solution:

I.$6x^{2} + 29x + 35 = 0$

=> $6x^2 + 15x + 14x + 35 = 0$

=> $3x (2x + 5) + 7 (2x + 5) = 0$

=> $(2x + 5) (3x + 7) = 0$

=> $x = \frac{-7}{3} , \frac{-5}{2}$

II.$3y^{2} + 11y + 10 = 0$

=> $3y^2 + 6y + 5y + 10 = 0$

=> $3y (y + 2) + 5 (y + 2) = 0$

=> $(y + 2) (3y + 5) = 0$

=> $y = -2 , \frac{-5}{3}$

Hence $x < y$

Question 10:Â Â I.Â $2x^{2}+18x+40=0$
II.Â $2y^{2} +15y+27=0$

a)Â x > y

b)Â x â‰¥ y

c)Â x < y

d)Â x â‰¤ y

e)Â x = y or the relation cannot be established.

Solution:

I.$2x^{2} + 18x + 40 = 0$

=> $2x^2 + 8x + 10x + 40 = 0$

=> $2x (x + 4) + 10 (x + 4) = 0$

=> $(x + 4) (2x + 10) = 0$

=> $x = -4 , -5$

II.$2y^{2} + 15y + 27 = 0$

=> $2y^2 + 6y + 9y + 27 = 0$

=> $2y (y + 3) + 9 (y + 3) = 0$

=> $(y + 3) (2y + 9) = 0$

=> $y = -3 , \frac{-9}{2}$

$\therefore$ No relation can be established.

Instructions

In each of these questions two equations numbered I and II are given. You have to solve both the equations and â€“
Give answer a: if x < y
Give answer b: if x â‰¤ y
Give answer c: if x > y
Give answer d: if x â‰¥ y
Give answer e: if x = y or the relationship cannot be established.

Question 11:Â I.$x^{2}+12x+32=0$
II.Â $y^{2} +17y+72=0$

a)Â if x < y

b)Â if x â‰¤ y

c)Â if x > y

d)Â if x â‰¥ y

e)Â if x = y or the relationship cannot be established.

Solution:

I.$x^{2} + 12x + 32 = 0$

=> $x^2 + 8x + 4x + 32 = 0$

=> $x (x + 8) + 4 (x + 8) = 0$

=> $(x + 8) (x + 4) = 0$

=> $x = -8 , -4$

II.$y^{2} + 17y + 72 = 0$

=> $y^2 + 9y + 8y + 72 = 0$

=> $y (y + 9) + 8 (y + 9) = 0$

=> $(y + 9) (y + 8) = 0$

=> $y = -9 , -8$

$\therefore x \geq y$

Question 12:Â I.Â $x^{2}-22x+120=0$
II.Â $y^{2} -26y+168=0$

a)Â if x < y

b)Â if x â‰¤ y

c)Â if x > y

d)Â if x â‰¥ y

e)Â if x = y or the relationship cannot be established.

Solution:

I.$x^{2} – 22x + 120 = 0$

=> $x^2 – 10x – 12x + 120 = 0$

=> $x (x – 10) – 12 (x – 10) = 0$

=> $(x – 10) (x – 12) = 0$

=> $x = 10 , 12$

II.$y^{2} – 26y + 168 = 0$

=> $y^2 – 12y – 14y + 168 = 0$

=> $y (y – 12) – 14 (y – 12) = 0$

=> $(y – 12) (y – 14) = 0$

=> $y = 12 , 14$

$\therefore x \leq y$

Question 13:Â I.Â $x^{2}+7x+12=0$
II.Â $y^{2} +6y+8=0$

a)Â if x < y

b)Â if x â‰¤ y

c)Â if x > y

d)Â if x â‰¥ y

e)Â if x = y or the relationship cannot be established.

Solution:

I.$x^{2} + 7x + 12 = 0$

=> $x^2 + 3x + 4x + 12 = 0$

=> $x (x + 3) + 4 (x + 3) = 0$

=> $(x + 3) (x + 4) = 0$

=> $x = -3 , -4$

II.$y^{2} + 6y + 8 = 0$

=> $y^2 + 4y + 2y + 8 = 0$

=> $y (y + 4) + 2 (y + 4) = 0$

=> $(y + 4) (y + 2) = 0$

=> $y = -4 , -2$

Because $-2 > -4$ and $-3 > -4$

Therefore, no relation can be established.

Question 14:Â I.Â  Â $x^{2}-15x+56=0$
II.Â $y^{2} -23y+132=0$

a)Â if x < y

b)Â if x â‰¤ y

c)Â if x > y

d)Â if x â‰¥ y

e)Â if x = y or the relationship cannot be established.

Solution:

I.$x^{2} – 15x + 56 = 0$

=> $x^2 – 8x – 7x + 56 = 0$

=> $x (x – 8) – 7 (x – 8) = 0$

=> $(x – 8) (x – 7) = 0$

=> $x = 8 , 7$

II.$y^{2} – 23y + 132 = 0$

=> $y^2 – 11y – 12y + 132 = 0$

=> $y (y – 11) – 12 (y – 11) = 0$

=> $(y – 11) (y – 12) = 0$

=> $y = 11 , 12$

$\therefore x < y$

Question 15:Â I.Â  $x^{2}+13x+42=0$
II.Â $y^{2} +19y+90=0$

a)Â if x < y

b)Â if x â‰¤ y

c)Â if x > y

d)Â if x â‰¥ y

e)Â if x = y or the relationship cannot be established.

Solution:

I.$x^{2} + 13x + 42 = 0$

=> $x^2 + 7x + 6x + 42 = 0$

=> $x (x + 7) + 6 (x + 7) = 0$

=> $(x + 7) (x + 6) = 0$

=> $x = -7 , -6$

II.$y^{2} + 19y + 90 = 0$

=> $y^2 + 9y + 10y + 90 = 0$

=> $y (y + 9) + 10 (y + 9) = 0$

=> $(y + 9) (y + 10) = 0$

=> $y = -9 , -10$

$\therefore x > y$

Question 16:Â Â I.Â  Â Â $2x^{2}+15x+28=0$
II.Â  Â Â $4y^{2} +18y+14=0$

a)Â x > y

b)Â x â‰¥ y

c)Â x < y

d)Â x â‰¤ y

e)Â x = y or the relation cannot be established.

Solution:

I.$2x^{2} + 15x + 28 = 0$

=> $2x^2 + 8x + 7x + 28 = 0$

=> $2x (x + 4) + 7 (x + 4) = 0$

=> $(x + 4) (2x + 7) = 0$

=> $x = -4 , \frac{-7}{2}$

II.$4y^{2} + 18y + 14 = 0$

=> $4y^2 + 4y + 14y + 14 = 0$

=> $4y (y + 1) + 14 (y +1) = 0$

=> $(y + 1) (4y + 14) = 0$

=> $y = -1 , \frac{-7}{2}$

$\therefore x \leq y$

Question 17:Â I.Â  $2x^{2}-19x+45 =0$
II.Â $6y^{2}-48y+90=0Â$

a)Â x > y

b)Â x â‰¥ y

c)Â x < y

d)Â x â‰¤ y

e)Â x = y or the relation cannot be established.

Solution:

I.$2x^{2} – 19x + 45 = 0$

=> $2x^2 – 10x – 9x + 45 = 0$

=> $2x (x – 5) – 9 (x – 5) = 0$

=> $(x – 5) (2x – 9) = 0$

=> $x = 5 , \frac{9}{2}$

II.$6y^{2} – 48y + 90 = 0$

=> $y^2 – 8y + 15 = 0$

=> $y^2 – 3y – 5y + 15 = 0$

=> $y (y – 3) – 5 (y – 3) = 0$

=> $(y – 3) (y – 5) = 0$

=> $y = 3 , 5$

Hence no relation can be established.

Instructions

In the following questions two equations numbered I and II are given. You have to solve both equations and

a. x Ëƒ y
b. x â‰¥ y
c. x Ë‚ y
d. x â‰¤ y
e. x = y or the relationship cannot be established

Question 18:Â I. x = $\sqrt {3136}$
II.${y^2}$ = 3136

a)Â x Ëƒ y

b)Â x â‰¥ y

c)Â x Ë‚ y

d)Â x â‰¤ y

e)Â x = y or the relationship cannot be established

Solution:

I. $x = \sqrt {3136}$

=> $x = 56$

II.${y^2} = 3136$

=> $y = \sqrt{3136} = \pm 56$

$\therefore x \geq y$

Question 19:Â I. ${x^2}$ + 8x + 15 = 0
II. ${y^2}$ + 11y + 30 = 0

a)Â x Ëƒ y

b)Â x â‰¥ y

c)Â x Ë‚ y

d)Â x â‰¤ y

e)Â x = y or the relationship cannot be established

Solution:

I.$x^{2} + 8x + 15 = 0$

=> $x^2 + 5x + 3x + 15 = 0$

=> $x (x + 5) + 3 (x + 5) = 0$

=> $(x + 5) (x + 3) = 0$

=> $x = -5 , -3$

II.$y^{2} + 11y + 30 = 0$

=> $y^2 + 5y + 6y + 30 = 0$

=> $y (y + 5) + 6 (y + 5) = 0$

=> $(y + 6) (y + 5) = 0$

=> $y = -6 , -5$

$\therefore x \geq y$

Question 20:Â I.2x – 3y = – 3.5
II. 3x + 2y = – 6.5

a)Â x Ëƒ y

b)Â x â‰¥ y

c)Â x Ë‚ y

d)Â x â‰¤ y

e)Â x = y or the relationship cannot be established

Solution:

I : $2x – 3y = -3.5$

II : $3x + 2y = -6.5$

Multiplying eqn(I) by 2 and eqn(II) by 3, and then adding both equations, we getÂ :

=> $(4x + 9x) + (-6y + 6y) = (-7 -19.5)$

=> $13x = -26.5$

=> $x = \frac{-26.5}{13} \approx -2$

=> $y = \frac{3x + 6.5}{2} = 0.25$

Hence $x < y$

Question 21:Â I. ${x^2}$ + 28x + 192 = 0
II. ${y^2}$ + 16y + 48 = 0

a)Â x Ëƒ y

b)Â x â‰¥ y

c)Â x Ë‚ y

d)Â x â‰¤ y

e)Â x = y or the relationship cannot be established

Solution:

I.$x^{2} + 28x + 192 = 0$

=> $x^2 + 16x + 12x + 192 = 0$

=> $x (x + 16) + 12 (x + 16) = 0$

=> $(x + 16) (x + 12) = 0$

=> $x = -16 , -12$

II.$y^{2} + 16y + 48 = 0$

=> $y^2 + 12y + 4y + 48 = 0$

=> $y (y + 12) + 4 (y + 12) = 0$

=> $(y + 12) (y + 4) = 0$

=> $y = -12 , -4$

$\therefore x \leq y$

Question 22:Â I. ${x^2}$ – 7x + 10 = 0
II. ${y^2}$ + 11y + 10 = 0

a)Â x Ëƒ y

b)Â x â‰¥ y

c)Â x Ë‚ y

d)Â x â‰¤ y

e)Â x = y or the relationship cannot be established

Solution:

I.$x^{2} – 7x + 10 = 0$

=> $x^2 – 5x – 2x + 10 = 0$

=> $x (x – 5) – 2 (x – 5) = 0$

=> $(x – 5) (x – 2) = 0$

=> $x = 5 , 2$

II.$y^{2} + 11y + 10 = 0$

=> $y^2 + 10y + y + 10 = 0$

=> $y (y + 10) + 1 (y + 10) = 0$

=> $(y + 10) (y + 1) = 0$

=> $y = -10 , -1$

$\therefore x > y$