KCET · Maths · Binomial Theorem
The digit in the unit place of the number \(2009 !+3^{7886}\) is
- A 7
- B 3
- C 1
- D 9
Answer & Solution
Correct Answer
(D) 9
Step-by-step Solution
Detailed explanation
The digit in the unit place of (2009)! is 0 . Now, \(3^{1}=3, \quad 3^{2}=9, \quad 3^{3}=27, \quad 3^{4}=81\), \(3^{5}=243\)
\[
\therefore \quad 3^{7886}=\left(3^{4}\right)^{1971} 3^{2}
\]
The digit in the unit place of \(3^{7886}\) is 9 .
\(\therefore\) The digit in the unit place of (2009)! \(+3^{7886}\) is \(9 .\)
\[
\therefore \quad 3^{7886}=\left(3^{4}\right)^{1971} 3^{2}
\]
The digit in the unit place of \(3^{7886}\) is 9 .
\(\therefore\) The digit in the unit place of (2009)! \(+3^{7886}\) is \(9 .\)
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
- The inverse of the matrix \( \left[\begin{array}{rrr}2 & 5 & 0 \\ 0 & 1 & 1 \\ -1 & 0 & 3\end{array}\right] \) isKCET 2019 Easy
- \( \int_{0}^{\frac{\pi}{2}} \frac{\sin ^{1000} x d x}{\sin ^{1000} x+\cos ^{1000} x} \) is equal toKCET 2016 Easy
- Area bounded by \( y=x^{3}, y=8 \) and \( x=0 \) isKCET 2015 Easy
- The equation of the curve passing through the point \( (1,1) \) such that the slope of the tangent at
any point \( (x, y) \) is equal to the product of its co-ordinates isKCET 2019 Medium - If \( x^{m} y^{n}=(x+y)^{m+n} \) then \( \frac{d y}{d x} \) is equal toKCET 2016 Hard
- Let \(f, g: R \rightarrow R\) be two functions defined as
\(f(x)=|x|+x\)
and
\(g(x)=|x|-x \forall x \in R\).
Then \((f \circ g)(x)\) for \(x < 0\) isKCET 2018 Easy
More PYQs from KCET
- The mass of a non-volatile solute of molar mass \(40 \mathrm{~g} \mathrm{~mol} \mathrm{~m}^{-1}\) that should be dissolved in \(114 \mathrm{~g} \mathrm{of}\) octane to lower its vapour pressure by \(20 \%\) isKCET 2012 Medium
- In a polysaccharide, number of monosaccharides are linked byKCET 2016 Easy
- The amino acid which is not optically active isKCET 2007 Medium
- The activation energy of a chemical reaction can be determined by,KCET 2016 Medium
- \( 50 \mathrm{~cm}^{3} \) of \( 0.04 \mathrm{M} \mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7} \) in acidic medium oxidizes a sample of \( \mathrm{H}_{2} \mathrm{~S} \) gas to sulphur.
Volume of \( 0.03 \mathrm{M} \mathrm{KMnO}_{4} \) required to oxidize the same amount of \( \mathrm{H}_{2} \mathrm{~S} \) gas to sulphur, in
acidic medium isKCET 2014 Easy - Stalk of the stamen isKCET 2022 Easy