1
MHT CET 2026 19th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
In $\triangle ABC$, with usual notations, if the sides $a$, $b$ and $c$ are in the ratio $18 : 17 : 7$, then $\cot\dfrac{A}{2} : \cot\dfrac{B}{2} : \cot\dfrac{C}{2} =$
A
$4 : 3 : 14$
B
$14 : 4 : 3$
C
$3 : 4 : 14$
D
$4 : 14 : 3$
2
MHT CET 2025 5th May Evening Shift
MCQ (Single Correct Answer)
+2
-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

A

$\frac{17}{35}$

B

$\frac{17}{70}$

C

$\frac{19}{35}$

D

$\frac{19}{70}$

3
MHT CET 2025 5th May Evening Shift
MCQ (Single Correct Answer)
+2
-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 $\frac{\cos \mathrm{A}}{\mathrm{a}}+\frac{\cos \mathrm{B}}{\mathrm{b}}+\frac{\cos \mathrm{C}}{\mathrm{c}}=$

A
$\frac{9}{16}$
B
$\frac{3}{4}$
C
1
D
$\frac{5}{16}$
4
MHT CET 2025 26th April Evening Shift
MCQ (Single Correct Answer)
+2
-0

In a triangle $A B C$ with usual notations if $\angle A=30^{\circ}$, then the value of $\left(1+\frac{a}{c}+\frac{b}{c}\right)\left(1+\frac{c}{b}-\frac{a}{b}\right)=$

A

$\sqrt{3}-2$

B

$2+\sqrt{5}$

C

$\sqrt{3}+2$

D

$2-\sqrt{5}$

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