1
MHT CET 2023 9th May Evening Shift
+2
-0

Let $$a, b, c$$ be the lengths of sides of triangle $$A B C$$ such that $$\frac{a+b}{7}=\frac{b+c}{8}=\frac{c+a}{9}=k$$. Then $$\frac{(\mathrm{A}(\triangle \mathrm{ABC}))^2}{\mathrm{k}^4}=$$

A
36
B
32
C
38
D
40
2
MHT CET 2023 9th May Evening Shift
+2
-0

In $$\triangle \mathrm{ABC}$$, with usual notations, $$\mathrm{m} \angle \mathrm{C}=\frac{\pi}{2}$$, if $$\tan \left(\frac{A}{2}\right)$$ and $$\tan \left(\frac{B}{2}\right)$$ are the roots of the equation $$a_1 x^2+b_1 x+c_1=0\left(a_1 \neq 0\right)$$, then

A
$$a_1+b_1=c_1$$
B
$$b_1+c_1=a_1$$
C
$$a_1+c_1=b_1$$
D
$$b_1=c_1$$
3
MHT CET 2023 9th May Morning Shift
+2
-0

Two sides of a triangle are $$\sqrt{3}+1$$ and $$\sqrt{3}-1$$ and the included angle is $$60^{\circ}$$, then the difference of the remaining angles is

A
$$30^{\circ}$$
B
$$45^{\circ}$$
C
$$60^{\circ}$$
D
$$90^{\circ}$$
4
MHT CET 2021 21th September Evening Shift
+2
-0

With usual notations, perimeter of a triangle $$A B C$$ is 6 times the arithmetic mean of sine of its angles. If $$\mathrm{a}=1$$, then measure of angle $$\mathrm{A}=$$

A
$$\frac{\pi^{\mathrm{c}}}{3}$$
B
$$\frac{\pi^{\mathrm{c}}}{2}$$
C
$$\frac{\pi^{\mathrm{c}}}{4}$$
D
$$\frac{\pi^{\mathrm{c}}}{6}$$
MHT CET Subjects
Physics
Mechanics
Optics
Electromagnetism
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Calculus
Coordinate Geometry
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