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1
TS EAMCET 2020 (Online) 11th September Morning Shift
MCQ (Single Correct Answer)
+1
-0

The perimeter of a $\triangle A B C$ is 6 times the arithmetic mean of the sine of its angles. If its side $B C$ is of unit length, then $\angle A=$

A

$\pi / 6$

B

$\pi / 3$

C

$\pi / 2$

D

$\pi$

2
TS EAMCET 2020 (Online) 11th September Morning Shift
MCQ (Single Correct Answer)
+1
-0

In a $\triangle A B C$, with usual notation, if $r=r_1-r_2-r_3$, then $2 R=$

A

$a$

B

$b+c$

C

C

D

$c+a$

3
TS EAMCET 2020 (Online) 11th September Morning Shift
MCQ (Single Correct Answer)
+1
-0

In a $\triangle A B C$, let $a, b, c, s, r, R, I, S, r_1, r_2, r_3$ stand for their usual meaning. Then Match the items of List-I with those of the items of List-II.

List-I List-II
A. tan ⁡ 
<mi>A</mi>

<mn>2</mn>
= 
<mi>r</mi>

<mrow>

  <mi>s</mi>

  <mo>−</mo>

  <mi>a</mi>

</mrow>
tan ⁡ 
<mi>A</mi>

<mn>2</mn>
= 
<mi>r</mi>

<mrow>

  <mi>s</mi>

  <mo>−</mo>

  <mi>a</mi>

</mrow>
tan((A)/(2))=(r)/(s-a)		 I. ( A l ) 
<mo data-mjx-texclass="OPEN">(</mo>

<mfrac>

  <msqrt>

    <mo stretchy="false">(</mo>

    <mi>s</mi>

    <mo>−</mo>

    <mi>b</mi>

    <mo stretchy="false">)</mo>

    <mo stretchy="false">(</mo>

    <mi>s</mi>

    <mo>−</mo>

    <mi>c</mi>

    <mo stretchy="false">)</mo>

  </msqrt>

  <mrow>

    <mi>b</mi>

    <mi>c</mi>

  </mrow>

</mfrac>

<mo data-mjx-texclass="CLOSE">)</mo>
( A l ) 
<mrow>

  <mfrac>

    <msqrt>

      <mo stretchy="false">(</mo>

      <mi>s</mi>

      <mo>−</mo>

      <mi>b</mi>

      <mo stretchy="false">)</mo>

      <mo stretchy="false">(</mo>

      <mi>s</mi>

      <mo>−</mo>

      <mi>c</mi>

      <mo stretchy="false">)</mo>

    </msqrt>

    <mrow>

      <mi>b</mi>

      <mi>c</mi>

    </mrow>

  </mfrac>  

</mrow>
(Al)((sqrt((s-b)(s-c)))/(bc))
B. r r r II. 
<mi>R</mi>

<mn>2</mn>

<mi>R</mi>

<mn>2</mn>
R^(2)
C. ( S I 
<mo stretchy="false">)</mo>

<mn>2</mn>
+ 2 R r ( S I 
<mo stretchy="false">)</mo>

<mn>2</mn>
+ 2 R r (SI)^(2)+2Rr		 III. ( 4 R + r + 
<mn>2</mn>

<mtext> </mtext>

<mi mathvariant="normal">s</mi>
) ( 4 R + r − 
<mn>2</mn>

<mtext> </mtext>

<mi mathvariant="normal">s</mi>
) ( 4 R + r + 
<mn>2</mn>

<mtext></mtext>

<mi mathvariant="normal">s</mi>
) ( 4 R + r − 
<mn>2</mn>

<mtext></mtext>

<mi mathvariant="normal">s</mi>
) (4R+r+sqrt2s)(4R+r-sqrt2s)
D. 
<mi>r</mi>

<mn>1</mn>

<mn>2</mn>
+ 
<mi>r</mi>

<mn>2</mn>

<mn>2</mn>
+ 
<mi>r</mi>

<mn>3</mn>

<mn>2</mn>

<mrow>

  <mi>r</mi>

</mrow>

<mn>1</mn>

<mn>2</mn>
+ 
<mrow>

  <mi>r</mi>

</mrow>

<mn>2</mn>

<mn>2</mn>
+ 
<mrow>

  <mi>r</mi>

</mrow>

<mn>3</mn>

<mn>2</mn>
r_(1)^(2)+r_(2)^(2)+r_(3)^(2)		 IV. Rr 
<mo>/</mo>

<mi mathvariant="normal">S</mi>
Rr 
<mo>/</mo>

<mi mathvariant="normal">S</mi>
Rr//S
V. 
<mrow>

  <mo stretchy="false">(</mo>

  <mi>s</mi>

  <mo>−</mo>

  <mi>b</mi>

  <mo stretchy="false">)</mo>

  <mo stretchy="false">(</mo>

  <mi>s</mi>

  <mo>−</mo>

  <mi>c</mi>

  <mo stretchy="false">)</mo>

</mrow>

<mi mathvariant="normal">Δ</mi>

<mrow>

  <mo stretchy="false">(</mo>

  <mi>s</mi>

  <mo>−</mo>

  <mi>b</mi>

  <mo stretchy="false">)</mo>

  <mo stretchy="false">(</mo>

  <mi>s</mi>

  <mo>−</mo>

  <mi>c</mi>

  <mo stretchy="false">)</mo>

</mrow>

<mi mathvariant="normal">Δ</mi>
((s-b)(s-c))/(Delta)

$$ \text { The correct match is } $$

A
A B C D
I V IV III
B
A B C D
V I II III
C
A B C D
V I IV III
D
A B C D
I IV III II
4
TS EAMCET 2020 (Online) 10th September Evening Shift
MCQ (Single Correct Answer)
+1
-0

In a $\triangle A B C,\left(b^2-c^2\right) \cot A+\left(c^2-a^2\right) \cot B=$

A

0

B

$2 R^2[\sin 2 A-\sin 2 B]$

C

$\left(b^2-a^2\right) \cot (A+B)$

D

$2 R^2[\tan 2 A-\tan 2 B]$

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