Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET201923 Apr 2019Morning ShiftMathematicsSequences and SeriesActual

If (2 4^ 2 k+1 +3^ 3 k+1 =11 t ) and (2 4^ 2 k+3 +3^ 3 k+4 =11 ) ( (p t+3^q ) ), where (k, t Z⁺ ), then ((p, q)= )

Options

  1. A((16,3 k+1) )
  2. B((16,3 k+4) )
  3. C((32,3 k+1) )
  4. D((32,3 k+4) )

Correct answer

A. ((16,3 k+1) )

Step-by-step solution

By verification method, if (k=0 ) Then, (2 4^1+3^1=11 t ) ( 8+3=11 t t=1 ) Now, from the second given relation on putting the values of ((k, t)=(0,1) ), we get ( aligned 2 (64)+81 & =11 (p+3^q ) 128+81 & =11 (p+3^4 ) 11 (p+3^q ) & =209 p+3^q=19 aligned ) Now, from the option (p ) must be 16 and (q=1 ) (=(3 k+1)_ k=0 . ) Hence, option (a) is correct.

Practice Sequences and Series on Quantrex Academy →

More from Sequences and Series

Every term of a geometric progression is positive , and every term is the sum of the two preceding terms. Then the common ratio of the geometric progression is: 2026If k is the arithmetic mean of two given quantities and p, q are the geometric means between the same two quantities, then p^3 + q^3 is: 2026Let ' a ' and ' b ' be two numbers where a < b . The geometric mean of these numbers exceeds the smaller number by 12 and the arithmetic mean is smaller than the larger number by 2 2026The product of three numbers in geometric progression is 8 and the sum of the product of the numbers taken in pairs is 14. Find the numbers. 2026Let a₁, a₂, a₃, be a geometric progression of positive integers such that a₁ = 3 and a_ n+2 - 2a_n = a_ n+1 for all positive integers n . What is the value of a₁ + a₂ + a₃ + a₄ + a 2026The angles of a triangle are in A.P and the greatest angle is double the least angle, then sine of the third angle is 2026If we insert two numbers between 2 and 4 so that the resulting sequence is in G.P, then the inserted numbers in the order are 2026If S _ n =1^3+2^3+ . .+ n ^3 and T _ n =1+2+ . .+ n , then 2025 Full Sequences and Series list All AP EAMCET PYQs