MHT CET · Maths · Vector Algebra

In the above figure, P divides AC in the ratio 3:4 and Q divides BC in the ratio \(4: 3\). Then \(M\) divides \(A Q\) in the ratio
- A 15:14
- B 29:13
- C 21:16
- D 28:9
Answer & Solution
Correct Answer
(C) 21:16
Step-by-step Solution
Detailed explanation
Apply Menelaus' Theorem to \( \triangle ACQ \) with transversal \( BPM \). \( \frac{AP}{PC} \cdot \frac{CB}{BQ} \cdot \frac{QM}{MA} = 1 \)
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 equation of the normal to the curve \(3 x^2-y^2=8\), which is parallel to the line \(x+3 y=10\), isMHT CET 2023 Easy
- The value of \(\int_{0}^{\infty} \frac{x}{(1+x)\left(x^{2}+1\right)} d x\) isMHT CET 2012 Medium
- Water is being poured at the rate of \(36 \mathrm{~m}^3 / \mathrm{min}\). into a cylindrical vessel, whose circular base is of radius \(3 \mathrm{~m}\). then the water level in the cylinder is rising at the rate ofMHT CET 2021 Easy
- The scalar product of the vector \(\hat{i}+\hat{j}+\hat{k}\) with a unit vector along the sum of the vectors \(2 \hat{i}+4 \hat{j}-5 \hat{k}\) and \(\lambda \hat{i}+2 \hat{j}+3 \hat{k}\) is equal to 1 , then value of \(\lambda\) isMHT CET 2023 Easy
- If \(\lim _{x \rightarrow 1} \frac{x^2-\mathrm{a} x+\mathrm{b}}{x-1}=7\), then \(\mathrm{a}+\mathrm{b}\) is equal toMHT CET 2024 Medium
- Angle between the tangents to the circle \(x^2+y^2=25 x^2\) from the point \((1,7)\) isMHT CET 2022 Medium
More PYQs from MHT CET
- For \(\mathrm{X} \sim \mathrm{B}(\mathrm{n}, \mathrm{p})\), if \(\mathrm{p}=0.6, \mathrm{E}(\mathrm{X})=6\), then \(\operatorname{Var}(\mathrm{X})=\)MHT CET 2021 Easy
- Let \(\mathrm{f}: \mathbb{R}-\{2\} \rightarrow \mathbb{R}-\{1\}\) defined by \(\mathrm{f}(x)=\frac{x-3}{x-2}\) and \(\mathrm{g}: \mathbb{R} \rightarrow \mathbb{R}\) defined by \(\mathrm{g}(x)=3 \mathrm{x}-2\), then sum of all values of \(x\) for which \(\mathrm{f}^{-1}(x)+\mathrm{g}^{-1}(x)=\frac{19}{6}\) isMHT CET 2025 Medium
- \(\lim _{x \rightarrow \infty}\left(\frac{x+8}{x+1}\right)^{x+5}=\ldots\)MHT CET 2025 Medium
- The relation between magnetic moment ' \(\mathrm{M}\) ' of revolving electron and principal quantum number ' \(n\) ' isMHT CET 2021 Easy
- The potential energy of the orbital electron in the ground state of hydrogen atoms is \(-\mathrm{E}\). What is the kinetic energy?MHT CET 2022 Medium
- A weak base is \(1.42 \%\) dissociated in its \(0.05 \mathrm{M}\) solution. Calculate its dissociation constant.MHT CET 2023 Medium