MHT CET · Maths · Properties of Triangles
In a triangle ABC , with usual notations, the sides \(a, \mathrm{~b}, \mathrm{c}\) are such that they are roots of the equation \(x^3-11 x^2+38 x-40=0\) then
\(\frac{\cos A}{a}+\frac{\cos B}{b}+\frac{\cos C}{c}=\)
- A \(\frac{9}{16}\)
- B \(\frac{3}{4}\)
- C 1
- D \(\frac{5}{16}\)
Answer & Solution
Correct Answer
(A) \(\frac{9}{16}\)
Step-by-step Solution
Detailed explanation
\(a+b+c = 11\) \(ab+bc+ca = 38\)
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 unit vector which is orthogonal to the vector \(5 \hat{i}+2 \hat{j}+6 \hat{k}\) and is coplanar with the vectors \(2 \hat{i}+\hat{j}+\hat{k}\) and \(\hat{i}-\hat{j}+\hat{k}\) isMHT CET 2024 Medium
- The angle between the lines whose direction cosines are \(\frac{-\sqrt{3}}{4}, \frac{1}{4}, \frac{-\sqrt{3}}{2}\) and \(\frac{-\sqrt{3}}{4}, \frac{1}{4}, \frac{\sqrt{3}}{2}\) isMHT CET 2025 Easy
- Let \(\overline{\mathrm{a}}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-2 \hat{\mathrm{k}}\) and \(\overline{\mathrm{b}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}\). If \(\overline{\mathrm{c}}\) is a vector such that \(\overline{\mathrm{a}} \cdot \overline{\mathrm{c}}=|\overline{\mathrm{c}}|,|\overline{\mathrm{c}}-\overline{\mathrm{a}}|=2 \sqrt{2}\) and the angle between \((\overline{\mathrm{a}} \times \overline{\mathrm{b}})\) and \(\overline{\mathrm{c}}\) is \(30^{\circ}\), then the value of \(|(\bar{a} \times \bar{b}) \times \bar{c}|\) is equal toMHT CET 2024 Medium
- \(\lim _{x \rightarrow 0} \frac{\sin \left(\pi \cos ^2 x\right)}{x^2}\) is equal toMHT CET 2024 Easy
- The entries in the last column of the truth table for \(\sim(\mathrm{p} \wedge \mathrm{q})\) areMHT CET 2020 Easy
- The area bounded by the parabola \(y^{2}=16 x\) and its latus - rectum in the first quadrant isMHT CET 2020 Medium
More PYQs from MHT CET
- If the area of the parallelogram with \(\bar{a}\) and \(\bar{b}\) as two adjacent sides is 16 sq. units, then the area of the parallelogram having \(3 \bar{a}+2 \bar{b}\) and \(\overline{\mathrm{a}}+3 \overline{\mathrm{b}}\) as two adjacent sides (in sq. units) isMHT CET 2023 Easy
- Three isolated metal spheres A, B, C have radius R, 2R, 3R respectively, and the same charge, \(Q . U_A, U_B\) and \(U_C\) be the energy density just outside the surface of the spheres. The relation between \(\mathrm{U}_{\mathrm{A},} \mathrm{U}_{\mathrm{B}}\) and \(\mathrm{U}_{\mathrm{C}}\) isMHT CET 2022 Easy
- Given below are two statements with respect to amniocentesis
Statement I: Amniocentesis is a process in which amniotic fluid containing foetal cells is collected using a hollow needle inserted into the uterus.
Statement II: X-ray imaging is used to determine the position of the foetus in the uterus.
In light of above statements, select the correct answer from the options given below.MHT CET 2024 Hard - Identify the formula of potassium trioxalato aluminate (III)MHT CET 2020 Easy
- Aldol condensation product of acetone on dehydration givesMHT CET 2011 Medium
- A wave travelling along uniform string represented by \(Y=A \sin (\omega t-k x)\) is superimposed on another wave travelling along the same string represented by \(Y=A \sin (\omega t+k x)\). The resultant isMHT CET 2022 Medium