AP EAMCET · Maths · Binomial Theorem
For any natural number \(n,\left(15 \times 5^{2 n}\right)+\left(2 \times 2^{3 n}\right)\) is divisible by
- A 7
- B 11
- C 13
- D 17
Answer & Solution
Correct Answer
(D) 17
Step-by-step Solution
Detailed explanation
We have, \(\left(15 \times 5^{2 n t}\right)+\left(2 \times 2^{3 n t}\right)\) For \[ \begin{aligned} & \text { For } \begin{aligned} n & =1, \\ \text { we get } 15 \times 5^2+2 \times 2^3 & =15 \times 25+2 \times 8 \\ & =375+16=391 \end{aligned} \end{aligned} \] which is…
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
- [.] represents greatest integer function. Let \(g(x)=1+x-[x]\) and \(f(x)=\left\{\begin{array}{cl}-3, & x < 0 \\ 0, & x=0, \text { then } \\ 5, & x>0\end{array}\right.\) \(f(g(x))\) isAP EAMCET 2021 Medium
- The ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(b>a)\) and the parabola \(y^2=4 a x\) cut at right angles. If \(e\) is the eccentricity of the ellipse, then \(2 e^2=\)AP EAMCET 2019 Easy
- The solution of \((x+y+1) \frac{d y}{d x}=1\) isAP EAMCET 2007 Easy
- If \(x^2+p x+1\) is a factor of \(a x^3+b x+c\), thenAP EAMCET 2021 Easy
- In \(\triangle \mathrm{ABC}\), if the midpoints of the sides \(\mathrm{AB}, \mathrm{BC}\) and \(\mathrm{CA}\) are respectively \((l, 0,0),(0, \mathrm{~m}, 0)\) and \((0,0, \mathrm{n})\), then \(\frac{\mathrm{AB}^2+\mathrm{BC}^2+\mathrm{CA}^2}{l^2+\mathrm{m}^2+\mathrm{n}^2}=\)AP EAMCET 2023 Medium
- A point on the plane passing through the points \((\sqrt{2}, 1,4)\) , \((0,-1,0)\) and \((0,0,1)\) isAP EAMCET 2023 Easy
More PYQs from AP EAMCET
- Which of the following options is correct for the object having a straight-line motion represented by the following graph?
AP EAMCET 2020 Medium - Calculate the amount of hydrogen gas required in order to produce \(100 \mathrm{~g}\) of ammonia by the reaction of \(\mathrm{N}_2(g)\) and \(\mathrm{H}_2(g)\) gases.AP EAMCET 2021 Easy
- Polymers that can be softened on heating and hardened on cooling are calledAP EAMCET 2024 Easy
- The heat liberated when \(1.89 \mathrm{~g}\) of benzoic acid is burnt in a bomb calorimeter at \(25^{\circ} \mathrm{C}\) increases the temperature of \(18.94 \mathrm{~kg}\) of water by \(0.632^{\circ} \mathrm{C}\). If the specific heat of water at \(25^{\circ} \mathrm{C}\) is \(0.998 \mathrm{cal} /\left(\mathrm{g}^{\circ} \mathrm{C}\right)\), then find the heat of combustion of benzoic acid.AP EAMCET 2021 Medium
- If \(\sqrt{x-x y}+\sqrt{y-x y}=1\), then \(\frac{d y}{d x}=\)AP EAMCET 2025 Medium
- \(\lim _{n \rightarrow-\infty} \frac{\left[6^2+12^2+18^2+\ldots .+(6 n)^2\right]^2}{[5+10+15+\ldots .+5 n]\left[2^3+4^3+6^3+\ldots .+8 n^3\right]}=\)AP EAMCET 2018 Medium