MHT CET 2026 15th April Morning Shift | Properties of Triangles Question 19 | Mathematics

In $\triangle ABC$ with usual notations, if $1 + \tan\left(\dfrac{A}{2}\right)\tan\left(\dfrac{B}{2}\right) = \dfrac{k}{s}$ (where $s$ is the semi-perimeter), then the value of $k$ is...

$2$

$a + b - c$

$a + b$

$s - c$

MHT CET 2025 5th May Evening Shift

MCQ (Single Correct Answer)

-0

With usual notation, in a triangle ABC $\frac{b+c}{11}=\frac{c+a}{12}=\frac{a+b}{13}$, then the value of $\cos B$ is equal to

$\frac{17}{35}$

$\frac{17}{70}$

$\frac{19}{35}$

$\frac{19}{70}$

MHT CET 2025 5th May Evening Shift

MCQ (Single Correct Answer)

-0

In a triangle $A B C$, with usual notations, the sides $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are such that they are roots of the equation $x^3-11 x^2+38 x-40=0$ then $\frac{\cos \mathrm{A}}{\mathrm{a}}+\frac{\cos \mathrm{B}}{\mathrm{b}}+\frac{\cos \mathrm{C}}{\mathrm{c}}=$

$\frac{9}{16}$

$\frac{3}{4}$

$\frac{5}{16}$

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