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- Question
- If 2p + 3q = 17 and 2p + 2 - 3q + 1 = 5, then, find the value of p and q?
Options- A. -2 , 3
- B. 2, -3
- C. 3, 2
- D. 2, 3
- Correct Answer
- 3, 2
ExplanationApply the law of Fractional Exponents and Laws of Exponents
(am) x (an) = am + n
a-m = 1/am
p0 = 1
and if pX = pY then X will be equal to Y. means X = Y;
(am)n = am x n
(am) x (an) = am + n
am ÷ an = am ? n
Or
am/an = am ? n
Given equation is
2p + 3q = 17 ----------------(i)
2p + 2 - 3q + 1 = 5
? 2p x 22 - 3q x 3 = 5
? 2p x 4 - 3q x 3 = 5
? 4 x 2p - 3 x 3q = 5---------------(ii)
On multiplying Eq. (i) by 3 and adding it, with Eq. (ii), we get
3 x 2p + 3 x 3q = 51
4 x 2p - 3 x 3q = 5
_____________________________
7 x 2p = 56
? 7 x 2p = 7 x 8
? 2p = 8
? 2p = 23
? p = 3
On substituting the value of p in Eq. (i) . we get
23 + 3q = 17
? 8 + 3q = 17
? 3q = 17 - 8
? 3q = 9
? 3q = 32
? q = 2 - 1. L?M is surd of order ........, where M is a rational number; L is a positive integer and L?M is irrational.
Options- A. L
- B. M
- C. 2
- D. 4 Discuss
- 2. If 289 = 17x/5 , then x =?
Options- A. 16
- B. 8
- C. 10
- D. 2/5 Discuss
- 3. Solve the below equation.
173.5 x 177.3 ÷ 174.2 = 17?
Options- A. 8.4
- B. 8
- C. 6.6
- D. 6.4 Discuss
- 4. ( x2/3)- 3/4 is equivalent to :
Options- A. 1 x
- B. 1 ?x
- C. 1 x2
- D. 1 x- 2 Discuss
- 5. Third power of 4 is equivalent to :
Options- A. 64
- B. 81
- C. 12
- D. 49 Discuss
- 6. ( 42 x 229 ) ÷ ( 9261)1/3 =?
Options- A. 448
- B. 452
- C. 456
- D. 458 Discuss
- 7. 812.5 x 94.5 ÷ 34.8 = 9?
Options- A. 7.1
- B. 9.4
- C. 4.7
- D. 4.5 Discuss
- 8. ?5 + ?x = 3, then the value of x is?
Options- A. 64
- B. 125
- C. 9
- D. 27 Discuss
- 9. If ( 5 + 2?3 ) / ( 7 + 4?3 ) = a + b?3, then the value of a and b is?
Options- A. a = 11, b = -6
- B. a = 6, b = 11
- C. a = -11, b = 6
- D. a = -11, b = -6 Discuss
- 10. The expression [(?2)?2]?2 gives
Options- A. a natural number
- B. a integer and not a natural number
- C. a rational number but not an integer.
- D. a real number but not a rational number Discuss
Surds and Indices problems
Search Results
Correct Answer: L
Explanation:
L?3 = M1/L = Surd of Lth order.
Correct Answer: 10
Explanation:
Given that , 289 = 17x/5
Use the formula if ax = a y then x = y will be true.
? 171/2 = 17x/5
? x /5 = 1/2
? x = 10 .
Correct Answer: 6.6
Explanation:
173.5 x 177.3 ÷ 174.2 = 17?
Apply the Laws of Exponents ::
(am) x (an) = am+n
Fractional Exponents ::
am÷ a n=am?n
? 173.5 + 7.3 - 4.2 = 17?
? 176.6 = 17?
? ? = 6.6
Correct Answer: 1 ?x
Explanation:
Correct Answer: 64
Explanation:
Third power of 4 = 43 = 4 × 4 × 4 = 64
Correct Answer: 458
Explanation:
Given that, (42 x 229) ÷ (9261)1/3 = ?
As we know that (9621)1/3 = (21 x 21 x 21)1/3 = 213x1/3
? 42 x 229 ÷ (213 x )1/3 = ?
? 42 x 229 ÷ 21 = ?
? 42 x 229 x 1/ 21 = ?
? 2 x 229 = ?
? ? = 2 x 229
? ? = 458
Correct Answer: 7.1
Explanation:
812.5 X 94.5 ÷ 34.8 = 9?
? 812.5 x 94.5 ÷ 34.8 = 9?
Apply the law of Fractional Exponents and Laws of Exponents
(am)n = am x n ----------------1
(am) x (an) = am + n-------------2
am ÷ an = am ? n----------------3
and if pX = pY then X will be equal to Y. means X = Y;----------------4
Apply Law 1
? (92)2.5 x 94.5 ÷ 32 x 2.4 = 9?
? 95 x 94.5 ÷ 92.4 = 9?
Apply law 2 and 3,
? 9(5 + 4.5 - 2.4) = 9?
? 9? = 97.1
Apply the Law 4
? ? = 7.1
Correct Answer: 64
Explanation:
?5 + ?x = 3
Apply the law of Algebra Law.
Square both side of equation.
(?5 + ?x)2 = 32
? 5 + ?x = 9
? ?x = 9 - 5
? ?x = 4
Now cube the both side of equation,
? ( ?x ) 3 = 43
? x = (4)3
? x = 64
Correct Answer: a = 11, b = -6
Explanation:
Given equation is,
( 5 + 2?3 ) / (7 + 4?3 )
Now Multiply and divide by ( 7 - 4?3 ) in above given equation.
By Rationalization, we will get,
[ ( 5 + 2?3 ) / ( 7 + 4?3 ) ] x [ ( 7 - 4?3 ) / ( 7 - 4?3 ) ]
[ ( 5 + 2?3 ) x ( 7 - 4?3 ) ] / [ ( 7 + 4?3 ) x ( 7 - 4?3 ) ]
Apply the formula and multiplication rule of algebra,
( P + Q ) x (R - S ) = P x R - P x S + Q x R - Q x S .................(1)
( a + b ) x ( a - b) = a2 - b2.......................................................(2)
= ( 5 x 7 - 5 x 4?3 + 7 x 2?3 - 2?3 x 4?3 )/ ( 72 - (4?3)2 )
= 35 - 20?3 + 14?3 - 8 x 3 / ( 49 - 16 x 3 )
= ( 35 - 24 - 6?3 )/(49 - 48 )
= 11 - 6?3
? ( 5 + 2?3 ) /( 7 + 4?3 ) = a + b?3
? a + b?3 = 11 - 6?3
on equating the above equation and we get,
or a = 11 and b = - 6
Correct Answer: a real number but not a rational number
Explanation:
Given expression = [(?2)?2]?2
= (?2)(2)?2/2
= (?2)(2)1/?2
= (2)1/2 x 21/?2
= 2(2/21/?2)
= (2)(2)(1/?2 - 1)
which denotes a real number but not a rational number .
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