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- Question
- If a + b + c = 14 and a 2 + b 2 + c 2 = 96, then (ab + bc + ca) =?
Options- A. 51
- B. 55
- C. 50
- D. 65
- Correct Answer
- 50
ExplanationWe know that,
(a + b + c)2 = (a2 + b2 + c2) + 2(ab + bc + ca )
? 196 = 96 + 2(ab + bc + ca)
? 2(ab + bc + ca) = 196 - 96 = 100
? (ab + bc + ca) = 100/2 = 50 - 1. If a + b + c = 0, then the value of [(a + b)/c + (b + c)/a + (c + a)/b] x [a/(b + c) + b/(c + a) + c/(a + b)] is?
Options- A. 9
- B. 0
- C. 8
- D. -3 Discuss
- 2. If a, b and c are non-zero, a + 1/b = 1 and b + 1/c = 1, then the value of abc is?
Options- A. -3
- B. 1
- C. -1
- D. 3 Discuss
- 3. If a 2 + 1 = a, then the value of a 12 + a 6 + 1 is?
Options- A. 2
- B. 3
- C. -3
- D. 1 Discuss
- 4. If a 2 + b 2 = 234 and ab = 108, find the value of a + b / a - b .?
Options- A. 10
- B. 8
- C. 5
- D. 4 Discuss
- 5. ? 132 + 28 / 4 - (3)3 + 107 = (?) 2
Options- A. 2
- B. 16
- C. 256
- D. 4 Discuss
- 6. [5 - [3/4 + {2 1/ 2 - (1/2 + 1/6 - 1/7)}]] / 2 =?
Options- A. 123/168
- B. 223/168
- C. 323/168
- D. 423/168 Discuss
- 7. [0.5 x 0.5 x 0.5 + 0.2 x 0.2 x 0.2 + 0.3 x 0.3 x 0.3 - 3 x 0.5 x 0.3 x 0.2 ] / [0.5 x 0.5 + 0.2 x 0.2 + 0.3 x 0.3 - 0.5 x 0.2 - 0.2 x 0.3- 0.5 x 0.3] =?
Options- A. 1
- B. 0.6
- C. 0.4
- D. 0.03 Discuss
- 8. Solve [(999 + 588) 2 - (999 - 588) 2] / (999 x 588)
Options- A. 8
- B. 3
- C. 2
- D. 4 Discuss
- 9. Solve [(238 + 131) 2 + (238 - 131) 2] / (238 x 238 + 131 x 131)
Options- A. 4
- B. 2
- C. 8
- D. 9 Discuss
- 10. If ? 2 = 1.4142, then the value of 7 / (4 + ? 2) is?
Options- A. 3.5858
- B. 4.4142
- C. 1.2929
- D. 1.5858 Discuss
Simplification problems
Search Results
Correct Answer: 9
Explanation:
Since, a + b + c = 0
Then, a + b = -c ....(i)
a + c = -b .........(ii)
b + c = -a ....(iii)
Now, [(a + b)/c + (b + c)/a + (c + a)/b] x [a/(b + c) + b/(c + a) + c/(a + b)]
Now, putting the value of a + b , b + c and c + a from Eqs. (i), (ii) and (iii) , we get
[(-c)/c + (-a)/a + (-b)/b] x [a/-a + b/-b + c/-c]
[(-1) + (-1) + (-1)] [(-1) + (-1) + (-1)]
= (-3) x (-3) = 9
Correct Answer: -1
Explanation:
? a + 1/b = 1
ab + 1 = b ...(i)
Also, b + 1/c = 1
? b = 1 - 1/c ...(ii)
From Eqs. (i) and (ii), we get
ab + a = 1 - 1/c
? ab = -1/c
? abc = -1
Correct Answer: 3
Explanation:
a2 + 1 = a
? a + 1/a = 1
On squaring both sides, we get
a2 + 1/a2 + 2 = 1
On cubing both sides, we get
(a2 + 1/a2)3 = (-1)3
? a6 + 1/a6 + 3a2 x 1/a2 (a2 + 1/a2) = -1
? a6 + 1/a6 + 3 x (-1) = -1
Now, a6 + 1/a6 + 1 = 3
As, a12 + a6 + 1 can be written as a6 + 1/a6 + 1
? a12 + a6 + 1 = 3
Correct Answer: 5
Explanation:
We know that, (a + b)2 = a2 + b2 + 2ab
= 234 + 2 x 108 = 450
(a - b)2 = a2 + b2 - 2ab
= 234 - 2 x 108 = 18
? (a + b)2/(a - b)2 = 450/18 = 25
? [(a + b)/(a - b)]2 = 25
? (a + b)/(a - b) = ?25 = 5
Correct Answer: 4
Explanation:
(?)2 = ?132 + 28 / 4 - (3)3 + 107
= ?169 + 7 - 27 + 107
= ?256
= ?16
= 4
Correct Answer: 123/168
Explanation:
? = [5 -[3/4 + {21/2 - (1/2 + 1/6 - 1/7)}]]/2
= [5 - [3/4 + {5/2 -(1/2 + 7 - 6/42)}]]/2
= [5 - [3/4 + {5/2 - (1/2 + 1/42)}]]/2
= [5 - [3/4 + {5/2 - (21 + 1 /42)}]]/2
= [5 - [3/4 + {5/2 - 22/42}]]/2
= [5 - [3/4 + {105 - 22/42}]]/2
= [5 - [3/4 + 83/42]] / 2
= [5 - [63 + 166/84]]/2
= (191/84)/2
=191/168 = 123/168
Correct Answer: 1
Explanation:
Given expression
[a3 + b3 + c3 - 3abc] / [a2 + b2 + c2 - ab - bc - ca]
= a + b + c
= 0.5 + 0.2 + 0.3
where, a = 0.5, b = 0.2, c = 0.3
Correct Answer: 4
Explanation:
Given expression
= [(a + b )2 - (a - b )2] / ab
= 4ab/ab
= 4
where, a = 999, b = 588
Correct Answer: 2
Explanation:
Given expression
= [(a + b)2 + (a - b)2] / [a2 + b2]
= 2(a2 + b2) / (a2 + b2)
= 2
where, a = 238, b = 131
Correct Answer: 1.2929
Explanation:
?7 / (4 + ?2) = [7 / (4 + ?2)] x [(4 - ?2 ) / (4 - ?2]
= 7(4 - ?2) / (16 - 2)
[? (a + b)(a - b) = a2 - b2]
= 7(4 - ?2 )/14
= (4 - ?2)/2
= (4 - 1.4142)/2
= 2.5858/2 = 1.2929
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