1
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

In a triangle ABC , with usual notations, if $\mathrm{m} \angle \mathrm{A}=45^{\circ}, \mathrm{m} \angle B=75^{\circ}$, then $\mathrm{a}+\mathrm{c} \sqrt{2}$ has the

A
$b$
B
$\frac{b}{2}$
C
$2b$
D
$3b$
2
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If the angles $\mathrm{A}, \mathrm{B}$ and C of a triangle ABC are in the ratio $2: 3: 7$ respectively, then the sides a, b and c are respectively in the ratio

A
$2: \sqrt{2}:(\sqrt{3}+1)$
B
  $\sqrt{2}: 2:(\sqrt{3}+1)$
C
$(\sqrt{3}+1): \sqrt{2}: 2$
D
$2:(\sqrt{3}+1): \sqrt{2}$
3
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
$\frac{-9}{7}$
4
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
$\frac{5 \pi}{6}$
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