1
MHT CET 2024 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\mathrm{A}, \mathrm{B}, \mathrm{C}$ are the angles of a triangle with $\tan \frac{A}{2}=\frac{1}{3}, \tan \frac{B}{2}=\frac{2}{3}$ then the value of $\tan \frac{C}{2}$ is

A
$\frac{-7}{9}$
B
$\frac{7}{9}$
C
$\frac{9}{7}$
D
$\frac{-9}{7}$
2
MHT CET 2024 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The sides of a triangle are $\sin \theta, \cos \theta$ and $\sqrt{1+\sin \theta \cos \theta}$ for some $0<\theta<\frac{\pi}{2}$, then the greatest angle of a triangle is

A
$\frac{\pi}{3}$
B
$\frac{2 \pi}{3}$
C
$\frac{\pi}{6}$
D
$\frac{5 \pi}{6}$
3
MHT CET 2024 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

For the triangle ABC , with usual notations, if the angles $A, B, C$ are in A.P. and $\mathrm{m} \angle \mathrm{A}=30^{\circ}, \mathrm{c}=3$, then the values of a and b are respectively

A
$\frac{\sqrt{3}}{2}, \frac{3}{2}$
B
$\frac{3}{2}, \frac{3 \sqrt{3}}{2}$
C
$\frac{3 \sqrt{3}}{2}, \frac{3}{2}$
D
$\frac{3}{2}, \frac{\sqrt{3}}{2}$
4
MHT CET 2024 4th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $(a+b) \cos C+(b+c) \cos A+(c+a) \cos B=72$ and if $a=18, b=24$, then area of the triangle $A B C$ is

A
144 sq.units
B
216 sq.units
C
256 sq.units
D
296 sq. units
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