Quadratic Equation Questions For IBPS RRB Clerk

Download Top-20 IBPS RRB Clerk Quadratic Equation Questions PDF. Quadratic Equation questions based on asked questions in previous year exam papers very important for the IBPS RRB Assistant exam

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Instructions

In each of these questions, two equations are given. You have to solve these equations and find out the values of x and y and give answer

Question 1: I: $x^2-2x-323=0$
II: $y^2-40y+399=0$

a) x is greater than y

b) x is less than y

c) x is greater than or equal to y

d) x is less than or equal to y

e) x is equal to y (or) The relationship between x and y cannot be established

Question 2: I: $\sqrt{x-14}+\sqrt{1444}=\sqrt{2116}$
II: $\dfrac{\sqrt{y}}{\sqrt{3}{y}}=64^\frac{1}{18}$

a) x is greater than y

b) x is less than y

c) x is greater than or equal to y

d) x is less than or equal to y

e) x is equal to y (or) The relationship between x and y cannot be established

Question 3: I: $x^2-170x+7221=0$
II: $3y^2+170y+2407=0$

a) x is greater than y

b) x is less than y

c) x is greater than or equal to y

d) x is less than or equal to y

e) x is equal to y (or) The relationship between x and y cannot be established

Question 4: I: $x^2+12\sqrt{11}+143=0$
II: $y^2-22\sqrt{3}y+360=0$

a) x is greater than y

b) x is less than y

c) x is greater than or equal to y

d) x is less than or equal to y

e) x is equal to y (or) The relationship between x and y cannot be established.

Question 5: I: $x^3-128=1727872$
II: $\sqrt{3}{y^2} = \dfrac{\sqrt{2}{y^3}}{121^\frac{5}{6}}$

a) x is greater than y

b) x is less than y

c) x is greater than or equal to y

d) x is less than or equal to y

e) x is equal to y (or) The relationship between x and y cannot be established.

Instructions

In each of these questions, two equations are given. You have to solve these equations and find out the values of x and y and give answer

Question 6: I: $x^2-x-812=0$
II: $y^2+y-1332=0$

a) x is greater than y

b) x is less than y

c) x is greater than or equal to y

d) x is less than or equal to y

e) x is equal to y (or) The relationship between x and y cannot be established.

Question 7: I: $x^2+0.25x-60=0$
II: $y^2-0.33y-8=0$

a) x is greater than y

b) x is less than y

c) x is greater than or equal to y

d) x is less than or equal to y

e) x is equal to y (or) The relationship between x and y cannot be established.

Question 8: I: $\sqrt{x+14}+\sqrt{841} = \sqrt{1369}$
II: $y^2+0.5y-60=0$

a) x is greater than y

b) x is less than y

c) x is greater than or equal to y

d) x is less than or equal to y

e) x is equal to y (or) The relationship between x and y cannot be established.

Question 9: I: $x^2-16\sqrt{5}x+300=0$
II: $y^2-31\sqrt{5}y+750=0$

a) x is greater than y

b) x is less than y

c) x is greater than or equal to y

d) x is less than or equal to y

e) x is equal to y (or) The relationship between x and y cannot be established.

Question 10: I: $6\sqrt{x}+\dfrac{5}{\sqrt{x}} = \sqrt{x}$
II: $\dfrac{2^\frac{5}{9}}{\sqrt[3]{y}} = y^\frac{2}{9}$

a) x is greater than y

b) x is less than y

c) x is greater than or equal to y

d) x is less than or equal to y

e) x is equal to y (or) The relationship between x and y cannot be established.

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Instructions

In each of these questions, two equations are given. You have to solve these equations and find out the values of x and y and give answer

Question 11: I: $x^2+15\sqrt{3}x-378=0$
II: $y^2-6\sqrt{2}y-224=0$

a) x is greater than y

b) x is less than y

c) x is greater than or equal to y

d) x is less than or equal to y

e) x is equal to y (or) The relationship between x and y cannot be established.

Question 12: I: $\dfrac{19}{\sqrt{x}}+\dfrac{18}{\sqrt{x}}=\sqrt{x}$
II: $\dfrac{1369}{\sqrt{y^{-1}}} = y^\frac{5}{2}$

a) x is greater than y

b) x is less than y

c) x is greater than or equal to y

d) x is less than or equal to y

e) x is equal to y (or) The relationship between x and y cannot be established.

Question 13: I: $3x^2-76x+481=0$
II: $y^2+6y-187=0$

a) x is greater than y

b) x is less than y

c) x is greater than or equal to y

d) x is less than or equal to y

e) x is equal to y (or) The relationship between x and y cannot be established.

Question 14: I: $x^2+3x-270=0$
II: $y^2+4y-285=0$

a) x is greater than y

b) x is less than y

c) x is greater than or equal to y

d) x is less than or equal to y

e) x is equal to y (or) The relationship between x and y cannot be established.

Question 15: I: $x = \sqrt{9604}$
II: $y^2 = 7569$

a) x is greater than y

b) x is less than y

c) x is greater than or equal to y

d) x is less than or equal to y

e) x is equal to y (or) The relationship between x and y cannot be established.

Instructions

In each of these questions, two equations are given. You have to solve these equations and find out the values of x and y and give answer

Question 16: I: $3x^2+5x-68=0$
II: $y^2-33y+272=0$

a) x is greater than y

b) x is less than y

c) x is greater than or equal to y

d) x is less than or equal to y

e) x is equal to y (or) The relationship between x and y cannot be established.

Question 17: I: $x^2+6x-1147=0$
II: $y^2-6x-667=0$

a) x is greater than y

b) x is less than y

c) x is greater than or equal to y

d) x is less than or equal to y

e) x is equal to y (or) The relationship between x and y cannot be established.

Question 18: I: $x^2=13456$
II: $y=\sqrt{15129}$

a) x is greater than y

b) x is less than y

c) x is greater than or equal to y

d) x is less than or equal to y

e) x is equal to y (or) The relationship between x and y cannot be established.

Question 19: I: $2x^2-3x-629=0$
II: $y^2-4y-252=0$

a) x is greater than y

b) x is less than y

c) x is greater than or equal to y

d) x is less than or equal to y

e) x is equal to y (or) The relationship between x and y cannot be established.

Question 20: I: $x^2+x-306 = 0$
II: $y^2+5y-696=0$

a) x is greater than y

b) x is less than y

c) x is greater than or equal to y

d) x is less than or equal to y

e) x is equal to y (or) The relationship between x and y cannot be established.

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Answers & Solutions:

1) Answer (D)

I: $x^2-2x-323=0$
$x^2-19x+17x-323=0$
$x(x-19)+17(x-19)=0$
$(x-19)(x+17)=0$
$x=19$ or $x=-17$

II: $y^2-40y+399=0$
$y^2-19y-21y+399=0$
$y(y-19)-21(y-19)=0$
$(y-19)(y-21)=0$
$y=19$ or $y=21$

Comparing x and y,
$19 = 19$
$19 < 21$
$-17 < 19$
$-17 < 21$
Therefore, x is less than or equal to y.

2) Answer (A)

I: $\sqrt{x-14}+\sqrt{1444}=\sqrt{2116}$
$\sqrt{x-14}+38=46$
$\sqrt{x-14}=8$
$x-14=64$
$x=78$

II: $\dfrac{\sqrt{y}}{\sqrt{3}{y}}=64^\frac{1}{18}$

$\dfrac{y^\frac{1}{2}}{y^\frac{1}{3}} = (64^\frac{1}{3})^\frac{1}{6}$

$y^\frac{1}{6} = 4^\frac{1}{6}$
$y=4$

Comparing x and y,
$78>4$
Therefore,x is greater than y.

3) Answer (A)

I: $x^2-170x+7221=0$
$x^2-87x-83x+7221=0$
$x(x-87)-83(x-87)=0$
$(x-87)(x-83)=0$
$x=87$ or $x=83$

II: $3y^2+170y+2407=0$
$3y^2+87y+83y+2407=0$
$3y(y+29)+83(y+29)=0$
$(y+29)(3y+83)=0$
$y=-29$ or $y=-\dfrac{83}{3}$

Comparing x and y
$87>-29$
$87>-\dfrac{83}{3}$
$83>-29$
$83>-\dfrac{83}{3}$
Therefore, x is greater than y.

4) Answer (B)

I: $x^2+12\sqrt{11}+143=0$
$x^2+13\sqrt{11}x+\sqrt{11}x+143=0$
$x(x+13\sqrt{11})+\sqrt{11}(x+13\sqrt{11})=0$
$(x+13\sqrt{11})(x+\sqrt{11})=0$
$x=-13\sqrt{11}$ or $x=-\sqrt{11}$
The approximate value of $\sqrt{11} = 3$
Then, $x=-39$ or $x=-3$

II: $y^2-22\sqrt{3}y+360=0$
$y^2-20\sqrt{3}y-12\sqrt{3}y+360=0$
$y(y-20\sqrt{3})-12\sqrt{3}(y-20\sqrt{3})=0$
$(y-20\sqrt{3})(y-12\sqrt{3})=0$
$y=20\sqrt{3}$ or $y=12\sqrt{3}$
The approximate value of $\sqrt{3}=1$
Then, $x=20$ or $x=12$

Comparing x and y,
Both the x values are negative and both the y values are positive.
Therefore, x is less than y.

5) Answer (B)

I: $x^3-128=1727872$
$x^3 = 1728000$
$x=120$

II: $\sqrt{3}{y^2} = \dfrac{\sqrt{2}{y^3}}{121^\frac{5}{6}}$

$y^\frac{2}{3} = \dfrac{y^\frac{3}{2}}{121^\frac{5}{5}}$

$y^{\frac{3}{2}-\frac{2}{3}} = 121^\frac{5}{6}$
$y^\frac{5}{6}=121^\frac{5}{6}$
$y = 121$

Comparing x and y,
$120 < 121$.
Therefore, x is less than y.

6) Answer (E)

I: $x^2-x-812=0$
$x^2-29x+28x-812=0$
$x(x-29)+28(x-29)=0$
$(x-29)(x+28)=0$
$x=29$ or $x=-28$

II: $y^2+y-1332=0$
$y^2+37y-36y-1332=0$
$y(y+37)-36(y+37)=0$
$(y+37)(y-36)=0$
$y=-37$ or $y=36$

Comparing x and y,
$29>-37$
$29<36$
$-28>-37$
$-29<36$

Therefore, The relationship between x and y cannot be established.

7) Answer (E)

I: $x^2+0.25x-60=0$
$x^2+\dfrac{x}{4}-60=0$

$4x^2+x-240=0$
$4x^2+16x-15x-240=0$
$4x(x+16)-15(x+16)=0$
$(x+16)(4x-15)=0$
$x=-16$ or $x=\dfrac{15}{4}$

II: $y^2-0.33y-8=0$
$y^2-\dfrac{y}{3}-8=0$

$3y^2-y-24=0$
$3y^2-9y+8y-24=0$
$3y(y-3)+8(y-3)=0$
$(y-3)(3y+8)=0$
$y=3$ or $y=\dfrac{-8}{3}$

Comparing x and y
$-16<3$
$-16$\dfrac{15}{4}>3$

$\dfrac{15}{4}>\dfrac{-8}{3}$

Therefore, The relationship between x and y cannot be established.

8) Answer (A)

I: $\sqrt{x+14}+\sqrt{841} = \sqrt{1369}$
$\sqrt{x+14}+29=37$
$\sqrt{x+14}=8$
$x+14=64$
$x=40$

II: $y^2+0.5y-60=0$
$2y^2+y-120=0$
$2y^2+16y-15y-120=0$
$2y(y+8)-15(y+8)=0$
$(y+8)(2y-15)=0$
$y=-8$ or $y=\dfrac{15}{2}=7.5$

Comparing x and y
$40 > -8$
$40 > 7.5$
Therefore, x is greater than y.

9) Answer (E)

I: $x^2-16\sqrt{5}x+300=0$
$x^2-10\sqrt{5}x-6\sqrt{5}x+300=0$
$x(x-10\sqrt{5})-6\sqrt{5}(x-10\sqrt{5})=0$
$(x-10\sqrt{5})(x-6\sqrt{5})=0$
$x=10\sqrt{5}$ or $x=6\sqrt{5}$

II: $y^2-31\sqrt{5}y+750=0$
$y^2-25\sqrt{5}y-6\sqrt{5}y+750=0$
$y(y-25\sqrt{5})-6\sqrt{5}(y-25\sqrt{5})=0$
$(y-25\sqrt{5})(y-6\sqrt{5})=0$
$y=25\sqrt{5}$ or $y=6\sqrt{5}$

Comparing x and y,
$10\sqrt{5} < 25\sqrt{5}$
$10\sqrt{5} > 6\sqrt{5}$
$6\sqrt{5} < 25\sqrt{5}$
$6\sqrt{5}=6\sqrt{5}$

Therefore, The relationship between x and y cannot be determined.

10) Answer (B)

I: $6\sqrt{x}+\dfrac{5}{\sqrt{x}} = \sqrt{x}$

$\dfrac{6x+5}{\sqrt{x}} = \sqrt{x}$

$6x+5=x$
$5x=-5$
$x=-1$

II: $\dfrac{2^\frac{5}{9}}{\sqrt[3]{y}} = y^\frac{2}{9}$

$2^\frac{5}{9} = y^\frac{2}{9} \times y^\frac{1}{3}$
$2^\frac{5}{9} = y^\frac{5}{9}$
$y=2$

By comparing x and y,
$-1<2$

Therefore, x is less than y.

11) Answer (E)

I: $x^2+15\sqrt{3}x-378=0$
$x^2+21\sqrt{3}x-6\sqrt{3}x-378=0$
$x(x+21\sqrt{3})-6\sqrt{3}(x+21\sqrt{3})=0$
$(x+21\sqrt{3})(x-6\sqrt{3})=0$
$x=-21\sqrt{3}$ or $x=6\sqrt{3}$
Approximate value of $\sqrt{3}=2$.
Then, $x = -21\times2 = -42$ or $x = 6\times2 = 12$

II: $y^2-6\sqrt{2}y-224=0$
$y^2-14\sqrt{2}y+8\sqrt{2}y-224=0$
$y(y-14\sqrt{2})+8\sqrt{2}(y-14\sqrt{2})=0$
$(y-14\sqrt{2})(y+8\sqrt{2})=0$
$y=14\sqrt{2}$ or $y=-8\sqrt{2}$
Approximate value of $\sqrt{2} = 1$
Then, $y = 14$ or $y = -8$

By comparing x and y,
$-42 < 14$
$-42 < -8$
$12 < 14$
$12 > -8$

Therefore, The relationship between x and y cannot be determined.

12) Answer (C)

I: $\dfrac{19}{\sqrt{x}}+\dfrac{18}{\sqrt{x}}=\sqrt{x}$

$\dfrac{19+18}{\sqrt{x}} = \sqrt{x}$

$x=37$

II: $\dfrac{1369}{\sqrt{y^{-1}}} = y^\frac{5}{2}$

$\dfrac{1369}{y^\frac{-1}{2}} = y^\frac{5}{2}$

$y^\frac{5-1}{2} = 1369$
$y^2 = 1369$
$y = -37$ or $y = +37$

By comparing x and y,
$37 > -37$
$37 = 37$
Therefore, x is greater than or equal to y.

13) Answer (A)

I: $3x^2-76x+481=0$
$3x^2-39x-37x+481=0$
$3x(x-13)-37(x-13)=0$
$(x-13)(3x-37)=0$
$x=13$ or $x=\dfrac{37}{3}$

II: $y^2+6y-187=0$
$y^2+17y-11y-187=0$
$y(y+17)-11(y+17)=0$
$(y+17)(y-11)=0$
$y=-17$ or $y=11$
By comparing x and y,
$13>-17$
$13>11$
$\dfrac{37}{3}>-17$
$\dfrac{37}{3}>11$
Therefore, x is greater than y.

14) Answer (E)

I: $x^2+3x-270=0$
$x^2+18x-15x-270=0$
$x(x+18)-15(x+18)=0$
$(x-15)(x+18)=0$
$x=15$ or $x=-18$

II: $y^2+4y-285=0$
$y^2+19y-15y-285=0$
$y(y+19)-15(y+19)=0$
$(y-15)(y+19)=0$
$y=15$ or $y=-19$

By comparing x and y,
$15=15$
$15>-19$
$-18<15$
$-18>-19$
Therefore, The relationship between x and y cannot be established.

15) Answer (A)

I: $x = \sqrt{9604}$
$x = 98$
II: $y^2 = 7569$
$y = \pm 87$
$y = -87$ or $y=87$

By comparing x and y,
$98 > -87$
$98 > 87$
Therefore, x is greater than y.

16) Answer (B)

I: $3x^2+5x-68=0$
$3x^2-12x+17x-68=0$
$3x(x-4)+17(x-4)=0$
$(x-4)(3x+17)=0$
$x=4$ or $x=\dfrac{-17}{3}$

II: $y^2-33y+272=0$
$y^2-16y-17y+272=0$
$y(y-16)-17(y-16)=0$
$(y-16)(y-17)=0$
$y=16$ or $y=17$

By comparing x and y values,
$4 < 16$
$4 <17$
$\dfrac{-17}{3}<16$
$\dfrac{-17}{3}<17$
Therefore, x is less than y.

17) Answer (E)

I: $x^2+6x-1147=0$
$x^2+37x-31x-1147=0$
$x(x+37)-31(x+37)=0$
$(x+37)(x-31)=0$
$x=-37$ or $x=31$

II: $y^2-6x-667=0$
$y^2-29y+23y-667=0$
$y(y-29)+23(y-29)=0$
$(y-29)(y+23)=0$
$y=29$ or $y=-23$

By comparing x and y,
$-37 < 29$
$-37 < -23$
$31 > 29$
$31 > -23$
Therefore, The relationship between x and y cannot be established.

18) Answer (B)

I: $x^2 = 13456$
$x = \pm 116$
$x = -116$ or $x=116$

II: $y = \sqrt{15129}$
$y = 123$

By comparing x and y values,
$-116 < 123$
$116 < 123$
Therefore, x is less than y.

19) Answer (E)

I: $2x^2-3x-629=0$
$2x^2+34x-37x-629=0$
$2x(x+17)-37(x+17)=0$
$(x+17)(2x-37)=0$
$x=-17$ or $x=\dfrac{37}{2}$

II: $y^2-4y-252=0$
$y^2-18y+14y-252=0$
$y(y-18)+14(y-18)=0$
$(y-18)(y+14)=0$
$y=18$ or $y=-14$

By comparing x and y values,
$-17 < 18$
$-17 < -14$
$\dfrac{37}{2}>18$

$\dfrac{37}{2}>-14$

Therefore, The relationship between x and y cannot be determined.

20) Answer (E)

I: $x^2+x-306 = 0$
$x^2+18x-17x-306=0$
$x(x+18)-17(x+18)=0$
$(x+18)(x-17)=0$
$x=-18$ or $x=17$

II: $y^2+5y-696=0$
$y^2+29y-24y-696=0$
$y(y+29)-24(y+29)=0$
$(y+29)(y-24)=0$
$y = -29$ or $y = 24$

By comparing x and y values,
-18 > -29
18 < 24
17 > -29
17 < 24
Therefore, The relationship between x and y cannot be established.

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