TS EAMCET · Maths · Properties of Triangles
In \(\triangle A B C\), the points \(P, Q, R\) divide \(B C, C A, A B\) in the ratio \(3: 4,2: 5,9: 5\), respectively and the point \(D\) divides \(B C\) in the ratio \(2: 3\). If \(\mathbf{A P}+\mathbf{B Q}+\mathbf{C R}=k \mathbf{A D}\), then \((14 k+1):(14 k-1)=\)
- A \(7: 5\)
- B \(4: 3\)
- C \(4: 5\)
- D \(3: 2\)
Answer & Solution
Correct Answer
(D) \(3: 2\)
Step-by-step Solution
Detailed explanation
Here, \(\mathbf{P}=\frac{3 \mathbf{c}+4 \mathbf{b}}{7}, \mathbf{Q}=\frac{5 \mathbf{c}}{7}\) and \(\mathbf{R}=\frac{9 \mathbf{b}}{14}\) Now, \(\mathbf{A P}+\mathbf{B Q}+\mathbf{C R}\)…
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
- Let the line Ldrawn perpendicular to the lines \(2 x-3 y+4=0\) and \(6 x-9 y+7=0\) meet them at \(A\) and \(B\) respectively. If \(\mathrm{P}(1,1)\) is a point on \(\mathrm{L}\), then the ratio in which \(\mathrm{P}\) divides \(\mathrm{AB}\) isTS EAMCET 2022 Easy
- If \(X\) is a Poisson variate such that \(P(X=1)=P(X=2)\), then \(P(X=4)\) is equal toTS EAMCET 2008 Easy
- If \(f(x)=\int \frac{16 x^7+5 x^{10}}{\left(x^3+2+3 x^8\right)^2} d x(x \geq 0)\) and \(f(0)=1\), then the value of \(f(-1)\) isTS EAMCET 2022 Easy
- If \(\int \sqrt{\frac{x}{a^3-x^3}} d x=g(x)+c\), then \(g(x)\) is equal to :TS EAMCET 2006 Hard
- If \(\bar{r} \cdot(2 \bar{i}+3 \bar{j}+4 \bar{k})=5, \bar{r} \cdot(\bar{i}+\bar{j}-\bar{k})=7\) are two planes and \((16,-9,0)\) is a point common to both the planes then the vector equation of the line of intersection of the planes is \(\bar{r}=\)TS EAMCET 2022 Medium
- Let be points on the parabola If and respectively represent the area of and the area of the triangle formed by the tangents at to the above parabola, thenTS EAMCET 2020 Medium
More PYQs from TS EAMCET
- The total number of dative bonds present in all the following and isTS EAMCET 2021 Medium
- The numbers \(\alpha\) and \(\beta\) are such that one of the lines of \(2 x^2+\alpha x y+3 y^2=0\). Coincides with one of the lines of \(2 x^2+\beta x y-3 y^2=0\). If the two lines other than that line are perpendicular, then \(|\alpha+\beta|\) is equal toTS EAMCET 2021 Medium
- \(\sqrt{3} \operatorname{cosec} 20^{\circ}-\sec 20^{\circ}\) is equal toTS EAMCET 2008 Medium
- \((a, b)\) is the point to which the origin has to be shifted by translation of axes so as to remove the first-degree terms from the equation \(2 x^2-3 x y+4 y^2+5 y-6=0\). If the angle by which the axes are to be rotated in positive direction about the origin to remove the \(x y\)-term from the equation \(a x^2+23 a b x y+b y^2=0\) is \(\theta\), then \(\tan 2 \theta=\)TS EAMCET 2024 Medium
- Identify the correct statements about lanthanoids
I. \(\quad \mathrm{Ce}^{4+}\) and \(\mathrm{Tb}^{4+}\) act as oxidising agents
II. \(\quad \mathrm{Eu}^{2+}\) and \(\mathrm{Yb}^{2+}\) act as oxidising agents
III. Mischmetal is an alloy of \(95 \%\) iron and \(5 \%\) lanthanoid metal
IV. \(\quad \mathrm{La}^{3+}\) and \(\mathrm{Ce}^{4+}\) are diamagnetic in natureTS EAMCET 2025 Medium - If the Circumcenter of the triangle formed by the points \(A(a, 3), B(b, 5)\) and \(C(a, b)\) is \((1,1)\), then out of all the possible coordinates of \(\mathrm{C}\) the sum of the absolute values of the distinct coordinates of \(\mathrm{C}\) isTS EAMCET 2023 Easy