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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
Which of the following is true
A. If $a\cos A=b\cos B$, then the triangle is isosceles or right angled.
B. If in a triangle $ABC$, $\cos A\cos B+\sin A\sin B\sin C=1$, then the triangle is isosceles right angled.
C. If the ex-radii $r_1,r_2,r_3$ of $\triangle ABC$ are in H.P., then its sides are not in A.P.
Choose the correct answer from the options given below:
Solution
A:
$a\cos A=b\cos B \Rightarrow \cos A\cos A=\cos B\cos B$
This holds when $A=B$ (isosceles) or one angle is $90^\circ$
✔ True
B:
Maximum value of $\cos A\cos B+\sin A\sin B\sin C$ is $1$
This occurs when $A=B=45^\circ,\ C=90^\circ$
✔ True
C:
If ex-radii are in H.P., sides cannot be in A.P.
✔ True
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