AP EAMCET · Maths · Binomial Theorem
Let \(n=1 !+4 !+7 !+\ldots+400 !\). Then ten's digit of \(n\) is
- A 1
- B 6
- C 2
- D 7
Answer & Solution
Correct Answer
(B) 6
Step-by-step Solution
Detailed explanation
Given, \(n=1 !+4 !+7 !+\ldots+400 !\) \(1 !=1,4 !=24,7 !=5040,10 !=3628800\) and further the terms has last two digits \(=00\) So, \(1 !+4 !+7 !+\ldots+400 !=\ldots \ldots 65\) Here ten digit is 6 . Hence, 6 is the answer.
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
- If \(f:[0,3] \rightarrow[0,3]\) is defined by \(f(x)\) \(=\left\{\begin{array}{ll}1+x, & 0 \leq x \leq 2 \\ 3-x, & 2 < x \leq 3\end{array}\right.\), then fof isAP EAMCET 2018 Medium
- For a set of observations, if the coefficient of variation is 25 and mean is 44 , then the variance isAP EAMCET 2024 Medium
- The equations of the latusrectum of the ellipse \(9 x^2+4 y^2-18 x-8 y-23=0\) areAP EAMCET 2018 Medium
- The length of the latus rectum of the parabola \(169\left\{(x-1)^2+(y-3)^2\right\}=(5 x-12 y+17)^2\) isAP EAMCET 2020 Easy
- If \(m_1, m_2, m_3\) and \(m_4\) are respectively the magnitudes of the vectors
\(\overrightarrow{\mathbf{a}}_1=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, \quad \overrightarrow{\mathbf{a}}_2=3 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}-4 \hat{\mathbf{k}}\),
\(\overrightarrow{\mathbf{a}}_3=\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}} \quad\) and \(\quad \overrightarrow{\mathbf{a}}_4=-\hat{\mathbf{i}}+3 \hat{\mathbf{j}}+\hat{\mathbf{k}}\),
then the correct order of \(m_1, m_2, m_3\) and \(m_4\) isAP EAMCET 2009 Easy - The arithmetic means of the following discrete data \(12,14,20,23,25,32\) is given byAP EAMCET 2021 Easy
More PYQs from AP EAMCET
- Identify the correct statements from the following.
(I) \(\mathrm{SnCl}_2\) is ionic, but \(\mathrm{SnCl}_4\) is covalent in nature.
(II) All linear diatomic molecules have zero dipole moment.
(III) Both \(\mathrm{NO}\) and \(\mathrm{O}_2\) are paramagnetic.AP EAMCET 2022 Easy - \(\lim _{x \rightarrow 0} \frac{\left(1+\frac{x}{2}\right)^{5 / 7}-1}{x}=\)AP EAMCET 2020 Easy
- Identify the statements which are not correct from the following:
a) In the structure of ice each oxygen atom is surrounded by 4 other ' \(\mathrm{O}\) ' atoms
b) Temporary hardness of water is due to dissolved \(\mathrm{NaHCO}_3\)
c) In the reaction of acidified \(\mathrm{KMnO}_4\) and \(\mathrm{H}_2 \mathrm{O}_2, \mathrm{H}_2 \mathrm{O}_2\) acts as oxidising agent
d) \(3 \mathrm{gL}^{-1} \mathrm{H}_2 \mathrm{O}_2\) is equal in strength to 100 volume \(\mathrm{H}_2 \mathrm{O}_2\)AP EAMCET 2017 Easy - Let \(\mathbf{u}, \mathbf{v}\) and \(\mathbf{w}\) be three vectors such that \(\mathbf{u}+\mathbf{v}+\mathbf{w}=0,|\mathbf{u}|=3,|\mathbf{v}|=5\) and \(|\mathbf{w}|=7\). Then the angle between \(\mathbf{u}\) and \(\mathbf{v}\) isAP EAMCET 2020 Easy
- If the direction cosines \(l, m, n\) of two lines are satisfying the relations \(l+m+n=0\), \(l m=0\), then the angle between those two lines isAP EAMCET 2017 Medium
- If the quadratic equation \(4^{\sec ^2 \alpha} \cdot x^2+2 x+\left(\beta^2-\beta+\frac{1}{2}\right)=0\) has real roots, then the value of \(\cos ^2 \alpha+\cos ^{-1} \beta\) isAP EAMCET 2018 Medium