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Directions For Questions
In the following questions, two equations numbered I and II are given. You have to solve both the equations and give answer
1. if x > y
2. if x < y
3. if x ≥ y
4. if x ≤ y
5. if x = y or no relation can be established between ‘x’ and ‘y’.
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1. 2x^2 - 11x + 15 = 0
2. 21y^2 - 23y + 6 = 0
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I.2x^2 - 6x - 5x + 15 = 0
or,2x(x - 3) - 5(x - 3) = 0
or, (2x - 5) (x - 3) = 0
x = 3, 5/2
II.21y^2- 14y - 9y + 6 = 0
or,7y(3y - 2) - 3 (3y - 2) = 0
or,(7y - 3)(3y - 2) = 0
y = 3/7, 2/3
x > y
I. 5x^2 - 16x + 11= 0
II. 5y^2 - 3y - 2 = 0
I.5x^2 - 5x - 11x + 11 = 0
or,5x(x - 1) - 11(x - 1) = 0
or,(x - 1) (5x - 11) = 0
x = 1,11/5
II.5y^2- 5y + 2y - 2 = 0
or, 5y (y - 1) + 2(y - 1) = 0
or, (5y + 2)(y - 1) = 0
y = 1, -2/5
x ≥ y
I. x^2 + 11x + 28 = 0
II. 2y^2 + 13y + 20 = 0
I.x^2+ 4x + 7x + 28 = 0
or, x(x + 4) +7(x + 7) = 0
or, (x + 4) (x + 7) = 0
x = - 4, - 7
II.2y^2+ 8y + 5y + 20 = 0
or, 2y(y + 4) + 5(y + 4) = 0
or, (y + 4) (2y + 5) = 0
y = -4,-5/2
x ≤ y
I. 6x^2 + 29x + 35 = 0
II. 3y^2 + 19y + 30 = 0
I.6x^2+ 15x + 14x + 35 = 0
or, 3x(2x + 5) + 7(2x + 5) = 0
or,(3x + 7) (2x + 5) = 0
x=-7/3, -5/2
II.3y^2+ 9y + 10y + 30 = 0
or, 3y(y + 3) +10(y + 3) = 0
or,(3y + 10) (y + 3) = 0
y = -3, -10/3
I. 2x + 5y = 6
II. 5x + 11y = 9
Eqn (I) × 5 - eqn(II) × 2
(10x + 25y = 30) – (10x ± 22y = 18) =
3y = 12
y = 4 and x = -7
y > x
What approximate value should come in place of question mark (?) in the following questions?
184.96% of 4699.658 + 274.93% of 6279.88 – 648 = ?
? = 184.96% of 4699.658 + 274.93% of 6279.88 – 648
= (185/100)×4700 + (275/100) ×6280 – 648
= 185 × 47 + 200 % of 6280 + 75% of 6280 – 648 = 8695 + 12560 + 4710 – 648
?= 8695+17270 – 648 = 25317 = 25320
8789.879 ÷ 375.002 × 24.996 + 6937.004 = ?
? = 8789.879 ÷ 375.002 × 24.996 + 6937.004
= 8790 ÷ 375 × 25 + 6937
= (8970/375) × 25 + 6937 = (8790/15) + 6937 = 586 + 6937 = 7523 = 7525
(17.67)2 + (16.87)3 – (8.947)3 ÷ 103.897 = ?
(17.67)2 + (16.87)3 – (8.947)3 ÷103.897 = ?
Or, ? = (17.7)2 + (16.9)3 – (9)3 ÷ 104
= 313.29 + 4826.809 – 729 ÷ 104
= 313 + 4827 – 7 = 5133 = 5130
5 3/10 × 7 6/7 × 9 ½ = ?
= (53/10) × (55/7) × (19/2)
= 55385/140 = 395 = 400
(2892 ÷12) × 13 = ? % of 2410
241 *13 = (x/100) * 2410
3133 *100 /2410 =x
x= 130
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