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- Question
- x 2 - 8x + 15 = 0 ; y 2 - 3y + 2 = 0
Options- A. If x > y
- B. If x ? y
- C. If x < y
- D. If x ? y
- Correct Answer
- If x > y
Explanationx2 - 8x + 15 = 0
? x2 - 5x - 3x + 15 = 0
? x(x - 5) -3(x - 5) = 0
? (x - 5) (x - 3) = 0
? x = 5, 3
and y2 - 3y + 2 = 0
? y2 - 2y - y + 2 = 0
? y(y - 2) -1(y - 2) = 0
? (y -2) (y - 1) = 0
? y = 2, 1
? x > y - 1. x 2 - 32 = 112; y - ? 169 = 0
Options- A. If x > y
- B. If x ? y
- C. If x < y
- D. If x ? y Discuss
- 2. x 2 - 16 = 0 y 2 - 9y + 20 = 0
Options- A. if x > y
- B. if x ? y
- C. if x < y
- D. if x ? y Discuss
- 3. x - ? 121 = 0
y 2 - 121 = 0
Options- A. If x > y
- B. If x ? y
- C. If x < y
- D. If x ? y Discuss
- 4. 225x 2 - 4 = 0; ? 225y + 2 = 0
Options- A. If x > y
- B. If x ? y
- C. If x < y
- D. If x ? y Discuss
- 5. x 2 + x - 20 = 0
y 2 - y - 30 = 0
Options- A. If x > y
- B. If x ? y
- C. If x < y
- D. If x ? y Discuss
- 6. x 2 - x - 12 = 0; y 2 + 5y + 6 = 0
Options- A. If x > y
- B. If x ? y
- C. If x < y
- D. If x ? y Discuss
- 7. 3x 2 + 8x + 4 = 0; 4y 2 - 19y + 12 = 0
Options- A. If x > y
- B. If x ? y
- C. If x < y
- D. If x ? y Discuss
- 8. x 2 - 365 = 364; y - ? 324 = ? 81
Options- A. If x > y
- B. If x ? y
- C. If x < y
- D. If x ? y Discuss
- 9. (4/? x) + (7/? x) = ? x;
y 2 - (11) 5/2/? y = 0
Options- A. if x > y
- B. if x ? y
- C. if x < y
- D. if x ? y Discuss
- 10. Mr. Arjun is on tour and he has ? 360 for his expenses. If he exceeds his tour by 4 days, he must cut down his daily expenses by ? 3. For how many days is Mr. Arjun out on tour?
Options- A. 40
- B. 20
- C. 60
- D. 15 Discuss
Quadratic Equation problems
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Correct Answer:
Explanation:
x2 - 32 = 112
? x2 = 112 + 32 ? x2 = 144
? x = ± 12
and y - ?169 = 0
? y = ?169
? y = ± 13
? Relation cannot be established.
Correct Answer: if x ? y
Explanation:
x2 - 16 = 0
? x2 = 16 ? x = ?16 = ± 4
and y2 - 9y + 20 = 0
y2 - 4y - 5y + 20 = 0
? y(y - 4) - 5(y - 4) = 0
? y = 5, 4
? y ? x or x ? y
Correct Answer:
Explanation:
x - ?121 = 0
? x = ?121 ? x = ± 11
and y2 - 121 = 0 ? y2 = 121
? y = ?121 = ± 11
? x = y
Correct Answer:
Explanation:
225x2 - 4 = 0;
? 225x2 = 4 ? x2 = 4/225
? x = ?4/225 = ± 2/15, i.e., 2/15 and -2/15
and ?225y + 2 = 0 or ?225y = -2
On squaring both sides, we get
(?225y)2 = (-2)2
? 225y = 4
? y = 4/225
So, relation cannot be established because 4/225 lies between 2/15 and -2/15.
Correct Answer: If x ? y
Explanation:
x2 + x - 20 = 0
[by factorisation method]
? x2 + 5x - 4x - 20 = 0
? x(x + 5) - 4(x + 5) = 0
(x + 5) (x - 4) = 0
? x = -5 or 4
and y2 - y - 30 = 0
? y2 - 6y + 5y - 30 = 0
? y(y - 6) + 5(y - 6) = 0
? (y - 6) (y + 5) = 0
? y = 6 or - 5
Hence, y ? x or x ? y
Correct Answer: If x ? y
Explanation:
x2 - x - 12 = 0
? x2 - 4x + 3x - 12 = 0
? x(x - 4) + 3 (x - 4) = 0
? (x - 4) (x + 3) = 0
? x = - 3, 4
and y2 + 5y + 6 = 0
? y2 + 3y + 2y + 6 = 0
? y(y + 3) + 2(y + 3) = 0
? (y + 3) (y + 2) = 0
? y = - 3, - 2
? x ? y
[? x = - 3 and y = - 3, so x = y and x = 4 and y = - 2, hence x > y]
Correct Answer: If x < y
Explanation:
3x2 + 8x + 4 = 0
? 3x2 + 6x + 2x + 4 = 0
? 3x(x + 2) + 2(x + 2) = 0
? (x + 2) (3x + 2) = 0
? x = - 2, - 2/3
and 4y2 - 19y + 12 = 0
? 4y2 - 16y - 3y + 12 = 0
? 4y(y - 4) -3(y - 4) = 0
? (y - 4) (4y - 3) = 0
? y = 4, 3/4
Hence, y > x or x < y
Correct Answer: If x ? y
Explanation:
x2 - 365 = 364
? x2 = 364 + 365
? x = ?729 = ± 27
and y - ?324 = ?81 ? y - 18 = 9
? y = 27
So, y ? x or x ? y because y = 27 and x = 27 and - 27.
Correct Answer:
Explanation:
4/?x + 7/?x = ?x;
? 11/?x = ?x
? x = 11
and y2 - (11)5/2/?y = 0
? y2 = (11)5/2/(y)1/2
? y2 x y1/2 = (11)5/2
? (y)5/2 = (11)5/2
? y = 11
? x = y
Correct Answer: 20
Explanation:
Let Mr . Arjun is on tour for N days.
Then, according to the question,
Difference in expenses per day for original and extended tour = 3
360/N - 360/(N + 4) = 3
? 1/N - 1/(N + 4) = 3/360 = 1/120
? [N + 4 - N] / [ N x (N + 4)] = 1/120
? N(N + 4) = 4 x 120 = 480
? N2 + 4N - 480 = 0
? N2 + 24 - 20x - 480 = 0
? N(N + 24) - 20(N + 24) = 0
? (N + 24) (N - 20) = 0
? N = 20
(we ignore -ve value of x, that is, -24 because days cannot be negative)
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