CTET Maths - Algebra
- Option : D
- Explanation : 210 - 1 => 1024 - 1 = 1023
which is divisible by 3
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- Option : A
- Explanation : Given, A/B= 2/3 , B/C = 4/5 , C/D = 5/8 A/D = A/B × B/C × C/D = 2/3 × 4/5 × 5/8 = 1/3
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- Option : D
- Explanation : Let the addition of two sums be x . First sum = 48 ∴ 8/ (8+13) × x = 48 ⇒ (8/21) x = 48 ⇒ x = 126 INR
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4. The correct ascending order of magnitude, if the ratios 1 : 2 , 2 : 5 and 3: 4 is
- Option : A
- Explanation : Given, ratios are 1/2, 2/5 and 3/4. ∴ LCM(2,5, 4) = 20 ⇒ 1/2 = 1/2 × 10/10 = 10/20, 2/5 = 2/5 × 4/4 = 8/20 and 3/4 = 3/4 × 5/5 = 15/20. Clearly, 8/20<10/20<15/20 =2/5<1/2<3/4. so, 2:5<1:2<3:4
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5. If a/b = b/c = c/d, then (b3 + c3 + d3 ) / (a3 + b3 + c3 ) will be equal to
- Option : D
- Explanation : Let a/b = b/c = c/d =k.
⇒ a=bk=ck2=dk3, b=dk2 and c=dk.
(b3 + c3 + d3 ) / (a3 + b3 + c3 ) = [(dk2)3 + (dk)3 + d3 ]/ [(dk3)3 + (dk2)3 + (dk)3 ]
=d3 [ K6 + K3 +1] / d3 [K9 + K6 + K3 ]
=[ K6 + K3 +1]/K3 [ K6 + K3 +1]
=1/K3 =1/a/d =d/a
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