MHT CET · Maths · Straight Lines
If the points \(A(5, k), B(-3,1)\) and \(C(-7,-2)\) are collinear, then \(\mathrm{k}=\)
- A \(7\)
- B \(\frac{-1}{7}\)
- C \(\frac{1}{7}\)
- D \(-7\)
Answer & Solution
Correct Answer
(A) \(7\)
Step-by-step Solution
Detailed explanation
Slope of \(A B=\) Slope of \(B C\)
\(\frac{1-k}{-3-5}=\frac{-2-1}{-7+3} \Rightarrow \frac{1-k}{-8}=\frac{-3}{-4}\)
\(\frac{1-k}{2}=-3 \Rightarrow k=7\)
\(\frac{1-k}{-3-5}=\frac{-2-1}{-7+3} \Rightarrow \frac{1-k}{-8}=\frac{-3}{-4}\)
\(\frac{1-k}{2}=-3 \Rightarrow k=7\)
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 set of all points, where the derivative of the functions \(\mathrm{f}(x)=\frac{x}{1+|x|}\) exists, isMHT CET 2023 Medium
- If \(g(x)=\int_0^x \cos ^4 t \mathrm{~d} t\), then \(g(x+\pi)\) equalsMHT CET 2022 Hard
- If the function \(f(x)=2 x^{3}-9 a x^{2}+12 a^{2} x+1\) attains its maximum and minimum at \(p\) and \(q\) respectively such that \(p^{2}=q\), then \(a\) equalsMHT CET 2007 Medium
- \(\int\left(\frac{\tan \left(\frac{1}{x}\right)}{x}\right)^2 \mathrm{~d} x=\)MHT CET 2023 Easy
- If \(\bar{a}=2 \hat{i}+3 \hat{j}+2 \hat{k}, \bar{b}=2 \hat{i}+\hat{j}-\hat{k}\) and \(\bar{c}=3 \hat{i}-\hat{j} \quad\) are such that \(\bar{a}+\lambda \bar{b}\) is perpendicular to \(\bar{c}\), then the value of \(\lambda\) isMHT CET 2023 Easy
- The value of \(m\), such that \(\frac{x-4}{1}=\frac{y-2}{1}=\frac{z-m}{2}\) lies in the plane \(2 x-4 y+z=7\), isMHT CET 2024 Easy
More PYQs from MHT CET
- Out of the following which law obeys the law of conservation of energy?MHT CET 2025 Easy
- The minimum value of \(f(x)=a^{2} \cos ^{2} x+b^{2} \sin ^{2} x\) if \(a^{2}>b^{2}\), isMHT CET 2020 Medium
- Which from following molecules exhibits highest acidic nature?MHT CET 2023 Easy
- The area of the region bounded by the curve \(y=\log x, x\) -axis and the lines
\(x=1, x=e\) isMHT CET 2020 Medium - The objective function of L.L.P defined over the convex set attains its optimum value atMHT CET 2022 Easy
- It is observed that of the cases related to child labour reported to the police station are solved. If new cases are reported, then the probability that atleast of them will be solved is ________MHT CET 2019 Medium