MHT CET · Maths · Differential Equations
Bismath has half life of 5 days. If sample originally has a mass of \(800 \mathrm{mg}\). then the mass remaining after 30 days will be
- A \(10 \mathrm{mg} .\)
- B \(10.5 \mathrm{mg} .\)
- C \(12 \mathrm{mg} .\)
- D \(12.5 \mathrm{mg} .\)
Answer & Solution
Correct Answer
(D) \(12.5 \mathrm{mg} .\)
Step-by-step Solution
Detailed explanation
Original mass \(=800 \mathrm{mg}\).
Half life \(=5\) days.
We have to calculate remaining mass after 30 days. Understand that \(30 \div 5=6\).
\(\begin{aligned} \therefore \text { Mass remaining } &=\left(\frac{1}{2}\right)^{6} \times 800 \\ &=\frac{800}{64}=\frac{100}{8}=12.5 \end{aligned}\)
Half life \(=5\) days.
We have to calculate remaining mass after 30 days. Understand that \(30 \div 5=6\).
\(\begin{aligned} \therefore \text { Mass remaining } &=\left(\frac{1}{2}\right)^{6} \times 800 \\ &=\frac{800}{64}=\frac{100}{8}=12.5 \end{aligned}\)
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 \(\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}, g: \mathrm{R} \rightarrow \mathrm{R}\) defined by \(f(x)=x^{2}-3 x+4\) and \(g(x)=2 x+1\), then the
value of \(x\) for which \(f(x)=f \circ g)(x)\) isMHT CET 2020 Easy - The derivative of \(\sin ^{-1}\left(\frac{\sqrt{1+x}+\sqrt{1-x}}{2}\right)\) w.r.t. \(\cos ^{-1} x\) isMHT CET 2020 Medium
- If \(D_{30}\) is the set of all divisors of \(30, x, y \in D_{30}\), we define \(x+y=\operatorname{LCM}(x, y), x \cdot y=\operatorname{GCD}(x, y)\),
\(x^{\prime}=\frac{30}{x}\) and \(f(x, y, z)=(x+y) \cdot\left(y^{\prime}+z\right)\), then
\(f(2,5,15)\) is equal toMHT CET 2009 Hard - The number of positive integral solutions of \(\tan ^{-1} x+\cos ^{-1}\left(\frac{y}{\sqrt{1+y^2}}\right)=\sin ^{-1}\left(\frac{3}{\sqrt{10}}\right)\) areMHT CET 2025 Medium
- The value of \(\sin ^{-1}\left(-\frac{1}{\sqrt{2}}\right)+\cos ^{-1}\left(-\frac{1}{2}\right)-\cot ^{-1}\left(-\frac{1}{\sqrt{3}}\right)+\tan ^{-1}(+\sqrt{3})\)MHT CET 2025 Medium
- The product of the perpendicular distances from \((2,-1)\) to the pair of lines \(2 x^2-5 x y+2 y^2=0\) isMHT CET 2021 Medium
More PYQs from MHT CET
- If \(f(x)=2 x^{2}+b x+c, f(0)=3\) and \(f(2)=1\), then \((f o f)(1)=\)MHT CET 2020 Easy
- If the lines \(x^2-4 x y+y^2=0\) and \(x+y=10\) contain the sides of an equilateral triangle, then the area of equilateral triangle isMHT CET 2022 Medium
- Which of the following compounds has high lattice enthalpy?MHT CET 2025 Medium
- Which from following represents the Freundlich's empirical equation for adsorption of gas on solid (for \(\mathrm{n}>1\))MHT CET 2025 Easy
- A body is projected vertically upwards from earth's surface. If velocity of projection is \(\left(\frac{1}{3}\right)^{\text {rd }}\) of escape velocity, then the height upto which a body rises is
\((\mathrm{R}=\) radius of earth \()\)MHT CET 2020 Medium - When tension 'T' is applied to a sonometer wire of length \(\ell^{\prime}\), it vibrates with the fundamental frequency 'n'. Keeping the experimental setup same, when the tension is increased by 8 newton, the fundamental frequency becomes three times the earlier fundamental frequency (n). The initial tension applied to the wire in newton, wasMHT CET 2020 Medium