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- Question
- If x + 1/x = 3, then x5 + 1/x5 is equal to?
Options- A. 123
- B. 83
- C. 92
- D. 112
- Correct Answer
- 123
Explanationx + 1/x = 3 ........................ (i)
On squaring both side, we will get
(x + 1/x)2 = (3)2
Use the Square algebra formula (a + b)2 = a2 + 2ab + b2
? x2 + 1/x2 + 2 = 9
? x2 + 1/x2 = 7 ..................(ii)
Again squaring both sides, we will get
(x2 + 1/x2)2 = (7)2
Use the Square algebra formula (a + b)2 = a2 + 2ab + b2
? x4 + 1/4 + 2 = 49
? x4 + 1/x4 = 47 .....................(iii)
On cubing the equation (i) both side, we will get
(x + 1/x)3 = (3)3
Use the cube algebra formula (a + b)3 = a3 + 3a2b + 3ab2 + b3
? x3+ 1/x3 + 3(x + 1/x) = 27
? x3 + 1/x3 + 9 = 27 [? (x + 1/x) = 3]
? x3 + 1/x3 = 18 ...................(iv)
On multiplying Eqs. (i) and (iii) , we get
? (x4 + 1/x4) (x + 1/x) = 47 x 3
? x5 + 1/x5 + x3 + 1/x3 = 141
? x5 + 1/x5 + 18 = 141 [from Eq. (iv)]
? x5 + 1/x5 = 123 - 1.
The roots of x + 4 + x - 4 = 10 are : x - 4 x + 4 3
Options- A. ± 4
- B. ± 6
- C. ± 8
- D. 2 ± ?3 Discuss
- 2. 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
- 3. The sum of the squares of 2 natural consecutive odd numbers is 394. The sum of the numbers is :
Options- A. 24
- B. 32
- C. 40
- D. 28 Discuss
- 4. (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
- 5. Find the greatest possible length which can be used to measure 4m 3cm, 4m 34cm and 4m 65cm exactly.
Options- A. 31 cm
- B. 29 cm
- C. 28 cm
- D. 32 cm Discuss
- 6. Divide 16 into 2 parts such the twice the square of the larger part exceeds the square of the smaller part by 164.
Options- A. 10, 6
- B. 8, 8
- C. 12, 4
- D. None of these Discuss
- 7. ?. 4x + 7y = 209
?. 12x ? 14y = ? 38
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
- 8. 54 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780. The bigger part is :
Options- A. 24
- B. 34
- C. 30
- D. 32 Discuss
- 9. One says "Give me a hundred friend ! I shall then become twice as rich as you ". The other replies, "If you give me ten, I shall be six times as rich as you." Find the amount of their capitals.
Options- A. ? 40, ? 170
- B. ? 60, ? 180
- C. ? 80, ? 200
- D. Cannot be determined Discuss
- 10. The respective ratio between the speeds of a car, a train and a bus is 5 : 9 : 4. The average speed of the car, the bus and the train is 72 Km/h together. What is the average speed of the car and the train together?
Options- A. 82 km/h
- B. 78 km/h
- C. 84 km/h
- D. Cannot be determined Discuss
More questions
Correct Answer: ± 8
Explanation:
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: 28
Explanation:
Let, the two natural consecutive odd numbers be n and (n + 2)
Now, according to the question,
? n2 + ( n + 2 )2 = 394
? n2 + n2 + 4 + 4n = 394
? 2n2 + 4n - 390= 0
? n2 + 2n - 195 = 0
? n2 + 15n - 13n - 195 = 0
? n( n + 15 ) - 13( n + 15 ) = 0
? ( n + 15 ) ( n - 13 ) = 0
? n = 13 and n ? - 15
? The two natural consecutive odd numbers be 13 and (13 + 2) = 15 .
? the sum of the numbers = 13 + 15 = 28
Quicker Approach:
By mental operation, 132 + 152 = 169 + 225 = 394
? Required sum = 13 + 15 = 28
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: 31 cm
Explanation:
Required measure = HCF of 403, 434 and 465
= 31 cm
Correct Answer: 10, 6
Explanation:
Let the smaller part be x. Then the larger part = 16 ? x.
According to question , we have
2( larger part )2 - ( smaller part )2 = 164
Now , 2( 16 - x )2 - x2 = 164
? 2( 256 + x2 - 32x ) - x2 = 164
? x2 - 64x + 348 = 0
? x2 - 6x - 58x + 348 = 0
? x(x - 6) - 58(x - 6) = 0
? (x - 6) (x - 58)
x = 6 or x = 58
But m = 58 is not possible, since sum of the two parts is 16
? smaller part ( x ) = 6,
? other part = 16 - x = 16 - 6 = 10.
Hence , required answer will be option A .
Correct Answer:
Explanation:
According to question ,we can say that
?. 4x + 7y = 209 ...............( 1 )
?. 12x ? 14y = ? 38 .................... ( 2 )
Multiplying (1) by (2):
8x + 14y = 418 ................(3)
Adding (2) and (3):
20x = 380 ? x = 19
Substituting the value of x in (1), we get
76 + 7y = 209
? 7y = 133 ? y = 19
From above equations it is clear that x = y is correct answer .
Correct Answer: 34
Explanation:
Let us assume the two parts be y and (54 - y).
Then, According to question
10(54 - y) + 22y = 780
? 540 - 10y + 22y = 780
? 12y = 780 -540
? 12y = 240
? y = 20.
? Bigger part = (54 - y) = (54 - 20) = 34
Correct Answer: ? 40, ? 170
Explanation:
Let the capital of one is x and that of another is y .
According to the question.
x + 100 = 2(y - 100)
x + 100 = 2y - 200
or x - 2y = -300 ...(i)
Again, according to the question
y + 10 = 6(x - 10)
? y + 10 = 6x - 10
? 6x - y = 70 ..(ii)
On multiplying Eq. (ii) by 2 and subtracting from Eq. (i) , we get
x - 2y = -300
12x - 2y = 140
----------------
-11x = -440
? x = 40
On putting the value of x in Eq. (i) , we get
40 - 2y = -300
? 2y = 340
? y = 170
So, their capital are ? 40 and ? 170.
Correct Answer: 84 km/h
Explanation:
Total speed of car, bus and train = 72 × 3 = 216 Km
Speed of car and train = ( 5 + 9 ) x 216 / ( 5 + 9 + 4 ) = 168 Km
Average = 168 / 2 = 84 Km
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