TS EAMCET · Maths · Basic of Mathematics
For all positive integers \(k\), if the greatest divisor of \(25^k+12 k-1\) is \(d\), then \(4 \sqrt{d}=\)
- A 36
- B 8
- C 20
- D 24
Answer & Solution
Correct Answer
(D) 24
Step-by-step Solution
Detailed explanation
We have, \(25^k+12 k-1\), for all positive integer \(k\). when \(k=1,25^1+12(1)-1=36\) when \(k=2,25^2+12(2)-1\) \(=625+24-1=648\) HCF of 36 and 648 is 36. So, greatest divisor is 36 . \(\therefore d=36\) Now, \(4 \sqrt{d}=4 \sqrt{36}=4 \times 6=24\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Let be unit vectors such that ThenTS EAMCET 2021 Medium
- If \(f(x)=(2 x-1)(3 x+2)(4 x-3)\) is a real valued function defined on \(\left[\frac{1}{2}, \frac{3}{4}\right]\), then the value(s) of ' \(c\) ' as defined in the statement of Rolle's theoremTS EAMCET 2024 Hard
- If \(R\) is the set of all real numbers and \(f: R-\{2\} \rightarrow R\) is defined by \(f(x)=\frac{2+x}{2-x}\) for \(x \in R-\{2\}\)TS EAMCET 2014 Medium
- If a point \(P\) moves such that its distances from the point \(A(1,1)\) and the line \(x+y+2=0\) are equal, then the locus of \(P\) isTS EAMCET 2005 Medium
- \(\lim _{x \rightarrow 8} \frac{\sqrt{1+\sqrt{1+x}}-2}{x-8}\) is equal toTS EAMCET 2011 Medium
- If the sum of two of the roots of \(x^3+p x^2-q x+r=0\) is zero, then \(p q\) is equal toTS EAMCET 2003 Easy
More PYQs from TS EAMCET
- If \(y=f(\cosh x)\) and \(f^{\prime}(x)=\log \left(x+\sqrt{x^2-1}\right)\) then \(\frac{d^2 y}{d x^2}=\)TS EAMCET 2025 Medium
- Assertion : If and are respectively the orthocentre and circumcentre of a triangle, then is its centroid. Reason : Centroid of the triangle divides the line segment joining the orthocentre and the circumcentre in the ratio . Which one of the following is true?TS EAMCET 2018 Easy
- The average atmospheric residence time is lowest for which of the given the greenhouse gas?TS EAMCET 2020 Easy
- If \(\frac{3 \pi}{4} < x < \frac{7 \pi}{4}\) then \(\int\left(2^x-\sqrt{1+\sin 2 x}+\frac{1}{x^2}-\frac{1}{x}\right) d x=\)TS EAMCET 2022 Medium
- The length of a metal rod is 20 cm and its area of cross-section is \(4 \mathrm{~cm}^2\). If one end of the rod is kept at a temperature of \(100^{\circ} \mathrm{C}\) and the other end is kept in ice at \(0{ }^{\circ} \mathrm{C}\), then the mass of the ice melted in 7 minutes is
(Thermal conductivity of the metal \(=90 \mathrm{Wm}^{-1} \mathrm{~K}^{-1}\) and latent heat of fusion of ice \(=336 \times 10^3 \mathrm{~J} \mathrm{~kg}^{-1}\) )TS EAMCET 2025 Medium - By shifting the origin to the point \((2,3)\) and then rotating the coordinate axes through an angle \(\theta\) in the counter clockwise direction, if the equation \(3 x^2+2 x y+3 y^2-18 x-22 y+50=0\) is transformed to \(4 X^2+2 Y^2-1=0\), then the angle \(\theta=\)TS EAMCET 2020 Hard