Question 1: Palette 1/82

AP-EAPCET 2025 MCQ

In $\triangle A B C$, if $C=120^{\circ}, c=\sqrt{19}$ and $b=3$, then $a=$

A

4

B

5

C

2

D

$\sqrt{5}$

Question 2: Palette 2/82

AP-EAPCET 2025 MCQ

In a $\triangle A B C, 2 A+C=300^{\circ}$. If the circumradius of the $\triangle A B C$ is eight times its inradius, then $\sin \frac{C}{2}=$

A

$\frac{1}{2}$

B

$\frac{1}{4}$

C

$\frac{3}{4+\sqrt{3}}$

D

$\frac{1}{\sqrt{2}+1}$

Question 3: Palette 3/82

AP-EAPCET 2025 MCQ

In $\triangle A B C$, if $a=5, b=4$ and $\cos (A-B)=\frac{31}{32}$, then $c=$

A

8

B

$\sqrt{41}$

C

6

D

$\sqrt{24}$

Question 4: Palette 4/82

AP-EAPCET 2025 MCQ

In $\triangle A B C$, if $A, B, C$ are in arithmetic progression, then

$ \sqrt{a^2-a c+c^2} \cdot \cos \left(\frac{A-C}{2}\right)= $

A

$a+c$

B

$\frac{a+c}{2}$

C

$\frac{a+c-b}{2}$

D

$a-c$

Question 5: Palette 5/82

AP-EAPCET 2025 MCQ

If in $\triangle A B C, B=45^{\circ}, a=2(\sqrt{3}+1)$ and area of $\triangle A B C$ is $6+2 \sqrt{3}$ sq. units, then the side $b=$

A

$8-4 \sqrt{3}$

B

$\sqrt{2}(\sqrt{3}+1)$

C

$4 \sqrt{2}$

D

4

Question 6: Palette 6/82

AP-EAPCET 2025 MCQ

In a $\triangle A B C$, if $\sin ^2 B=\sin A$ and $2 \cos ^2 A=3 \cos ^2 B$, then the triangle is

A

acute angled

B

obtuse angled

C

right angled

D

equilateral

Question 7: Palette 7/82

AP-EAPCET 2025 MCQ

In a $\triangle A B C$, if $A=30^{\circ}$ and $\frac{b}{(\sqrt{3}+1)^2+2(\sqrt{2}-1)} =\frac{c}{(\sqrt{3}+1)^2-2(\sqrt{2}-1)}$, then $B$

A

$60^{\circ}$

B

$97.5^{\circ}$

C

$75^{\circ}$

D

$52.5^{\circ}$

Question 8: Palette 8/82

AP-EAPCET 2025 MCQ

In $\triangle A B C$ is the line joining the circumcentre and the incentre is parallel to $B C$, then $\cos B+\cos C=$

A

$1 / 2$

B

$3 / 4$

C

1

D

$3 / 2$

Question 9: Palette 9/82

AP-EAPCET 2025 MCQ

In a $\triangle A B C$, if $r_1: r_2=3: 4$ and $r_2: r_3=2: 3$, then $a:$b:$c$=

A

$2: 3: 4$

B

$3: 4: 5$

C

$4: 5: 6$

D

$5: 6: 7$

Question 10: Palette 10/82

AP-EAPCET 2025 MCQ

In a $\triangle A B C$, if $a, b, c$ are in arithmetic progression and the angle $A$ is twice the angle $C$, then $\cos A: \cos B: \cos C=$

A

$2: 3: 4$

B

$3: 4: 8$

C

$2: 9: 12$

D

$1: 9: 6$

Question 11: Palette 11/82

AP-EAPCET 2025 MCQ

In a $\triangle A B C, A, B$ and $C$ are in arithmetic progression, $r r_3=r_1 r_2$ and $c=10$, then $a^2+b^2+c^2=$

A

128

B

392

C

288

D

200

Question 12: Palette 12/82

AP-EAPCET 2025 MCQ

In a $\triangle A B C, \frac{2\left(r_1+r_3\right)}{a c(1+\cos B)}=$

A

$\frac{\Delta}{b}$

B

$\frac{b}{\Delta}$

C

$\frac{2 \Delta}{2+b+c}$

D

$\frac{a+b+c}{2 \Delta}$

Question 13: Palette 13/82

AP-EAPCET 2025 MCQ

In $\triangle A B C$, if $a=8, b=10, c=12$, then $\frac{r}{R}=$

A

$\frac{8}{15}$

B

$\frac{7}{16}$

C

$\frac{3}{5}$

D

$\frac{5}{8}$

Question 14: Palette 14/82

AP-EAPCET 2025 MCQ

In $\triangle A B C$, if $a=13, b=8, c=7$, then $\cos (B+C)=$

A

$\frac{11}{13}$

B

$\frac{23}{26}$

C

$\frac{3}{4}$

D

$\frac{1}{2}$

Question 15: Palette 15/82

AP-EAPCET 2025 MCQ

In a $\triangle A B C$, if $\left(r_1-r_3\right)\left(r_1-r_2\right)-2 r_2 r_3=0$, then $a^2-b^2=$

A

$c^2+\frac{b^2}{4}$

B

$c^2$

C

$a b c$

D

$\frac{b+a}{c}$

Question 16: Palette 16/82

AP-EAPCET 2025 MCQ

If the median $A D$ of the $\triangle A B C$ is bisected at $E$ and $B E$ meets $A C$ in $E$, then $A F: A C=$

A

$1: 4$

B

$1: 3$

C

$1: 2$

D

$3: 4$

Question 17: Palette 17/82

AP-EAPCET 2025 MCQ

In $\triangle A B C$ if $\cos A \cos B+\sin A \sin B \sin C=1$, then $\sin A+\sin B+\sin C=$

A

$\frac{2+\sqrt{3}}{2}$

B

$1+\sqrt{2}$

C

$\frac{2 \sqrt{3}-1}{2}$

D

$\frac{3+\sqrt{3}}{2}$

Question 18: Palette 18/82

AP-EAPCET 2025 MCQ

In $\triangle A B C$, if $a: b: c=4: 5: 6$, then $\frac{\cos A+3 \cos C}{\cos B}=$

A

1

B

4

C

2

D

3

Question 19: Palette 19/82

AP-EAPCET 2025 MCQ

In $\triangle A B C$, if $a=6, b=8$ and $c=10$, then $\frac{2 r_2 r_3}{r r_1}=$

A

$b+c$

B

$c+a$

C

$a+b$

D

$a+b+c$

Question 20: Palette 20/82

AP-EAPCET 2025 MCQ

If the sides $a, b, c$ of the $\triangle A B C$ are in harmonic progression, then $\operatorname{cosec}^2 A / 2, \operatorname{cosec}^2 B / 2, \operatorname{cosec}^2 C / 2$ are in

A

Arithmetico-geometric progression

B

Arithmetic progression

C

Geometric progression

D

Harmonic progression

Question 21: Palette 21/82

AP-EAPCET 2025 MCQ

In $\triangle A B C$, if $r=3$ and $R=5$, then $\frac{1}{a b}+\frac{1}{b c}+\frac{1}{c a}=$

A

$\frac{1}{30}$

B

$\frac{12}{15}$

C

$\frac{1}{15}$

D

$\frac{5}{36}$

Question 22: Palette 22/82

AP-EAPCET 2025 MCQ

In a $\triangle A B C, A-B=120^{\circ}, R=8 r$, then $\frac{1+\cos C}{1-\cos C}=$

A

16

B

14

C

15

D

10

Question 23: Palette 23/82

AP-EAPCET 2025 MCQ

In $\triangle A B C, \sqrt{\frac{r \cdot r_2}{r_3 r_1}}=$

A

$\left(r_3-r_2\right)\left(r_1-r_2\right)$

B

$r_3+r_1$

C

$\frac{b}{r_3-r_1}$

D

$\frac{b}{r_3+r_1}$

Question 24: Palette 24/82

AP-EAPCET 2025 MCQ

If $A(0,0,0) B(3,4,0)$ and $C(0,12,5)$ are the vertices of a $\triangle A B C$, then the $x$-coordinate of its incentre is

A

$\frac{25}{18+7 \sqrt{2}}$

B

$\frac{25}{26}$

C

$\frac{39}{18+7 \sqrt{2}}$

D

$\frac{39}{26}$

Question 25: Palette 25/82

AP-EAPCET 2025 MCQ

In a $\triangle A B C$, if $\sin \frac{A}{2}=\frac{1}{4} \sqrt{\frac{3}{5}}, a=2, c=5$ and $b$ is an integer, then the area (in sq. units) of $\triangle A B C$ is

A

$\frac{\sqrt{297}}{4}$

B

$\frac{\sqrt{231}}{4}$

C

$\frac{\sqrt{385}}{4}$

D

$\frac{\sqrt{185}}{4}$

Question 26: Palette 26/82

AP-EAPCET 2025 MCQ

In a $\triangle A B C$ if $a+c=5 b$, then $\cot \frac{A}{2} \cot \frac{C}{2}=$

A

2

B

$\frac{1}{2}$

C

$\frac{3}{2}$

D

$\frac{2}{3}$

Question 27: Palette 27/82

AP-EAPCET 2025 MCQ

In a $\triangle A B C$, if $r_1=3, r_2=4, r_3=6$, then $b=$

A

$2 \sqrt{6}$

B

$\frac{5 \sqrt{6}}{3}$

C

$\frac{7 \sqrt{6}}{3}$

D

$3 \sqrt{6}$

Question 28: Palette 28/82

AP-EAPCET 2025 MCQ

In $\triangle A B C$, the sum of the lengths of two sides is $x$ and the product of those lengths is $y$. If $c$ is the length of its third side and $x^2-c^2=y$, then the circumradius of that triangle is

A

$\frac{c}{\sqrt{3}}$

B

$\frac{c}{3}$

C

$\frac{y}{\sqrt{3}}$

D

$\frac{3 y}{2}$

Question 29: Palette 29/82

AP-EAPCET 2025 MCQ

If the area of a $\triangle A B C$ is $4 \sqrt{5}$ sq units. Length of the side $C A$ is 6 units and $\tan \frac{B}{2}=\frac{\sqrt{5}}{4}$, then its smallest side is of length

A

5 units

B

4 units

C

3 units

D

6 units

Question 30: Palette 30/82

AP-EAPCET 2025 MCQ

In a $\triangle A B C$ if $r_1=2 r_2=3 r_3$, then $a: b$ is

A

$3: 5$

B

$5: 3$

C

$4: 5$

D

$5: 4$

Question 31: Palette 31/82

AP-EAPCET 2024 MCQ

In $\triangle A B C, a^2 \sin 2 B+b^2 \sin 2 A$ is equal to

A

$2 a b \cos A$

B

$2 a b \sin A$

C

$2 \mathrm{ab} \sin \mathrm{C}$

D

$2 a b \cos C$

Question 32: Palette 32/82

AP-EAPCET 2024 MCQ

$ \text { In } \triangle A B C, \frac{r_2\left(r_1+r_3\right)}{\sqrt{r_1 r_2+r_2 r_3+r_3 r_1}} \text { is equal to } $

A

a

B

b

C

c

D

s

Question 33: Palette 33/82

AP-EAPCET 2024 MCQ

In $\triangle A B C,\left(r_2+r_3\right) \operatorname{cosec}^2 \frac{A}{2}$ is equal to

A

$4 R$

B

$4 R \cot ^2 \frac{\mathrm{~A}}{2}$

C

$4 R \tan ^2 \frac{A}{2}$

D

$R \tan ^2 \frac{A}{2}$

Question 34: Palette 34/82

AP-EAPCET 2024 MCQ

In a $\triangle A B C$, if $a=13, b=14$ and $c=15$, then $r_1=$

A

$\frac{23}{2}$

B

$\frac{21}{2}$

C

$\frac{25}{2}$

D

$\frac{26}{2}$

Question 35: Palette 35/82

AP-EAPCET 2024 MCQ

In $a \triangle A B C$ if $r: R: r_2=1: 3: 7$, then $\sin (A+C)+\sin B$ is equal to

A

0

B

$\sqrt{3}$

C

1

D

2

Question 36: Palette 36/82

AP-EAPCET 2024 MCQ

In $\triangle A B C,\left(r_1+r_2\right) \operatorname{cosec}^2 \frac{C}{2}$ is equal to

A

$2 R \cot ^2 \frac{C}{2}$

B

$4 R \tan ^2 \frac{C}{2}$

C

$4 R \cot ^2 \frac{C}{2}$

D

$2 R \tan ^2 \frac{C}{2}$

Question 37: Palette 37/82

AP-EAPCET 2024 MCQ

In a $\triangle A B C$, if $A, B$ and $C$ are in arithmetic progression and $\cos A+\cos B+\cos C=\frac{1+\sqrt{2}+\sqrt{3}}{2 \sqrt{2}}$, then $\tan A$ :

A

$\sqrt{3}$

B

$2+\sqrt{3}$

C

1

D

$2-\sqrt{3}$

Question 38: Palette 38/82

AP-EAPCET 2024 MCQ

In $\triangle A B C$, if $b+c: c+a: a+b=7: 8: 9$, then the smaller angle (in radians) of that triangle is

A

$\cos ^{-1}\left(\frac{4}{5}\right)$

B

$\frac{\pi}{3}$

C

$\cos ^{-1}\left(\frac{3}{5}\right)$

D

$\frac{\pi}{4}$

Question 39: Palette 39/82

AP-EAPCET 2024 MCQ

In $\triangle A B C$, if $(a+c)^2=b^2+3 c a$, then $\frac{a+c}{2 R}=$

A

$\frac{\sqrt{3}}{2}$

B

$\sqrt{3} \cos \left(\frac{A-C}{2}\right)$

C

$\cos \left(\frac{A-C}{2}\right)$

D

$\sin \left(\frac{A-C}{2}\right)$

Question 40: Palette 40/82

AP-EAPCET 2024 MCQ

In $\triangle A B C$, if $A, B$ and $C$ are in arithmetic progression $\Delta=\frac{\sqrt{3}}{2}$ and $r_1 r_2=r_2 r$, then $R=$

A

$\sqrt{3}$

B

2

C

1

D

$\sqrt{2}$

Question 41: Palette 41/82

AP-EAPCET 2024 MCQ

If 7 and 8 are the length of two sides of a triangle and $a^{\prime}$ is the length of its smallest side. The angles of the triangle are in AP and ' $a$ ' has two values $a_1$ and $a_2$ satisfying this condition. If $a_1 < a_2$, then $2 a_1+3 a_2=$

A

15

B

21

C

24

D

28

Question 42: Palette 42/82

AP-EAPCET 2024 MCQ

In $\triangle A B C$, if $a=13, b=14$ and $\cos \frac{C}{2}=\frac{3}{\sqrt{13}}$, then $2 r_1=$

A

2 S

B

$\Delta$

C

S

D

$2 \Delta$

Question 43: Palette 43/82

AP-EAPCET 2024 MCQ

In $\triangle A B C$, if $\left(r_2-r_1\right)\left(r_3-r_1\right)=2 r_2 r_3$, then $2(r+R)=$

A

$a+b$

B

$c+a$

C

$2 \sqrt{2} R \cos \left(\frac{C-A}{2}\right)$

D

$2 \sqrt{2} R \cos \left(\frac{B-C}{2}\right)$

Question 44: Palette 44/82

AP-EAPCET 2024 MCQ

In a $\Delta$ if the angles are in the ratio $3: 2: 1$, then the ratio of its sides is

A

$1: 2: 3$

B

$2: \sqrt{3}: 1$

C

$3: \sqrt{2}: 1$

D

$1: \sqrt{3}: 3$

Question 45: Palette 45/82

AP-EAPCET 2024 MCQ

In a $\triangle A B C$, if $B C=5, C A=6$ and $A B=7$, then the length of the median drawn from $B$ onto $A C$ is

A

5

B

$7 \sqrt{5}$

C

$7 \sqrt{2}$

D

$2 \sqrt{7}$

Question 46: Palette 46/82

AP-EAPCET 2024 MCQ

In $\triangle A B C$, if $A B: B C: C A=6: 4: 5$, then $R: r$ is equal to

A

$16: 9$

B

$16: 7$

C

$12: 7$

D

$12: 9$

Question 47: Palette 47/82

AP-EAPCET 2024 MCQ

If $(\alpha, \beta)$ is the orthocentre of the triangle with the vertices $(2,2),(5,1),(4,4)$, then $\alpha+\beta=$

A

6

B

5

C

$\frac{5}{2}$

D

$\frac{7}{2}$

Question 48: Palette 48/82

AP-EAPCET 2024 MCQ

In $\triangle A B C$, if $4 r_1=5 r_2=6 r_3$, then $\sin ^2 \frac{A}{2}+\sin ^2 \frac{B}{2}+\sin ^2 \frac{C}{2}=$

A

$\frac{19}{22}$

B

$\frac{25}{33}$

C

$\frac{74}{99}$

D

$\frac{28}{33}$

Question 49: Palette 49/82

AP-EAPCET 2024 MCQ

In $\triangle A B C, r_1 \cot \frac{A}{2}+r_2 \cot \frac{B}{2}+m_3 \cot \frac{C}{2}=$

A

$3 \Delta$

B

$3 S$

C

$\frac{s}{\Delta}$

D

$\Delta$

Question 50: Palette 50/82

AP-EAPCET 2024 MCQ

In $\triangle A B C, b c-r_2 r_3=$

A

$\pi_1$

B

$\pi_2$

C

$r_1$

D

$a r_1$

Question 51: Palette 51/82

AP-EAPCET 2024 MCQ

If $O(0,0,0), A(3,0,0)$ and $B(0,4,0)$ form a triangle, then the incentre of $\triangle O A B$ is

A

$(0,1,0)$

B

$(0,1,1)$

C

$(1,0,1)$

D

$(1,1,0)$

Question 52: Palette 52/82

AP-EAPCET 2024 MCQ

In $\triangle A B C$, if $r_1=4, r_2=8$ and $r_3=24$, then $a=$

A

0

B

$\frac{16}{\sqrt{5}}$

C

$16 \sqrt{5}$

D

$\sqrt{5}$

Question 53: Palette 53/82

AP-EAPCET 2024 MCQ

Match the items of List I with those of List II (here, $\Delta$ denotes the area of $\triangle A B C$ )

List I		List II
(A)	$ \sum \cot A $	(i)	$ (a+b+c)^2 \frac{1}{4 \Delta} $
(B)	$ \sum \cot \frac{A}{2} $	(ii)	$ \left(a^2+b^2+c^2\right) \frac{1}{4 \Delta} $
(C)	If $\tan A: \tan B: \tan C=1: 2: 3$, then $\sin A: \sin B: \sin C=$	(iii)	$ 8: 6: 5 $
(D)	$ \begin{aligned} &\text { If } \cot \frac{A}{2}: \cot \frac{B}{2}: \cot \frac{C}{2}=3: 7: 9\\ &\text { then } a: b: c= \end{aligned} $	(iv)	$ 12: 5: 13 $
		(v)	$ \sqrt{5}: 2 \sqrt{2}: 3 $
		(vi)	$ 4 \Delta $

$ \text { Then, the correct match is } $

A

A-VI, B-I, C-II, D-III

B

A-II, B-I, C-V, D-III

C

A-II, B-VI, C-V, D-I

D

A-VI, B-II, C-I, D-IV

Question 54: Palette 54/82

AP-EAPCET 2024 MCQ

In a $\triangle A B C$, if $r_1=2 r_2=3 r_3$, then $\sin A: \sin B: \sin C=$

A

$5: 4: 2$

B

$3: 4: 2$

C

$6: 3: 2$

D

$5: 4: 3$

Question 55: Palette 55/82

AP-EAPCET 2024 MCQ

In $\triangle A B C$, if $B=90^{\circ}$, then $2(r+R)=$

A

$a+b$

B

$b+c$

C

$a+c$

D

0

Question 56: Palette 56/82

AP-EAPCET 2024 MCQ

In a $\triangle A B C$, if $(a-b)(s-c)=(b-c)(s-a)$, then $r_1+r_3=$

A

$r_2-r_3$

B

$2 r_2$

C

$3 r_2$

D

$3\left(r_1+r_2\right)$

Question 57: Palette 57/82

AP-EAPCET 2024 MCQ

In $\triangle ABC$, $\cos A + \cos B + \cos C = $

A

$\frac{1 + \sqrt{2}}{R}$

B

$\frac{1}{R}$

C

$\frac{1 + R}{R}$

D

$\frac{1}{\sqrt{R}}$

Question 58: Palette 58/82

AP-EAPCET 2024 MCQ

In a $\triangle A B C$, if $a=26, b=30, \cos c=\frac{63}{65}$, then $c=$

A

2

B

4

C

6

D

8

Question 59: Palette 59/82

AP-EAPCET 2024 MCQ

If $H$ is orthocentre of $\triangle A B C$ and $A H=x ; B H=y$; $C H=z$, then $\frac{a b c}{x y z}=$

A

1

B

$\frac{a+b+c}{x+y+z}$

C

$\frac{a}{x}+\frac{b}{y}+\frac{c}{z}$

D

$\frac{a b+b c+c a}{x y+y z+z x}$

Question 60: Palette 60/82

AP-EAPCET 2022 MCQ

In any $\triangle A B C, \frac{\cos A}{a}+\frac{\cos B}{b}+\frac{\cos C}{c}=$

A

$a^2+b^2+c^2$

B

$\frac{a^2+b^2+c^2}{2 a b c}$

C

$\frac{2 a b c}{a^2+b^2+c^2}$

D

$a+b+c$

Question 61: Palette 61/82

AP-EAPCET 2022 MCQ

In a $\triangle A B C$, if $r_1=36, r_2=18$ and $r_3=12$, then $s=$

A

6

B

8

C

16

D

36

Question 62: Palette 62/82

AP-EAPCET 2022 MCQ

In a $\triangle A B C, a=6, b=5$ and $c=4$, then $\cos 2 A=$

A

$-\frac{31}{32}$

B

$-\frac{15}{16}$

C

$\frac{31}{32}$

D

$\frac{15}{16}$

Question 63: Palette 63/82

AP-EAPCET 2022 MCQ

In a $\triangle A B C,\left(\tan \frac{A}{2} \tan \frac{B}{2} \tan \frac{C}{2}\right)^2 \leq$

A

$\frac{1}{27}$

B

$\frac{1}{18}$

C

$\frac{1}{9}$

D

$\frac{1}{3}$

Question 64: Palette 64/82

AP-EAPCET 2022 MCQ

In a $\triangle A B C, 2(b c \cos A+a c \cos B+a b \cos C)=$

A

$a+b+c$

B

$2(a+b+c)$

C

$a^2+b^2+c^2$

D

$2\left(a^2+b^2+c^2\right)$

Question 65: Palette 65/82

AP-EAPCET 2022 MCQ

In a $\triangle A B C, \frac{a}{b}=2+\sqrt{3}$ and $\angle C=60^{\circ}$. Then, the measure of $\angle A$ is

A

$95^{\circ}$

B

$65^{\circ}$

C

$105^{\circ}$

D

$115^{\circ}$

Question 66: Palette 66/82

AP-EAPCET 2022 MCQ

If $a=2, b=3, c=4$ in a $\triangle A B C$, then $\cos C=$

A

$\frac{1}{4}$

B

$\frac{-1}{4}$

C

$\frac{1}{2}$

D

$\frac{-1}{2}$

Question 67: Palette 67/82

AP-EAPCET 2022 MCQ

In a $\triangle A B C$ $(b+c) \cos A+(c+a) \cos B+(a+b) \cos C=$

A

$2 a b c$

B

$a b c$

C

$a+b+c$

D

$(a+b+c) / 2 a b c$

Question 68: Palette 68/82

AP-EAPCET 2022 MCQ

Suppose $\triangle A B C$ is an isosceles triangle with $\angle C=90^{\circ}, A=(2,3)$ and $B=(4,5)$. Then, the centroid of the triangle is

A

$\left(\frac{13}{8}, \frac{8}{3}\right)$

B

$\left(\frac{11}{3}, \frac{10}{3}\right)$

C

$\left(\frac{10}{3}, \frac{13}{3}\right)$

D

$\left(\frac{10}{3}, \frac{11}{3}\right)$

Question 69: Palette 69/82

AP-EAPCET 2022 MCQ

In a $\triangle A B C$, if $a \neq b, \frac{a \cos A-b \cos B}{a \cos B-b \cos A}+\cos C=$

A

0

B

1

C

2

D

$-$1

Question 70: Palette 70/82

AP-EAPCET 2022 MCQ

If in a $\triangle A B C, a=2, b=3$ and $c=4$, then $\tan (A / 2)=$

A

$\sqrt{\frac{3}{15}}$

B

$\sqrt{\frac{4}{15}}$

C

$\sqrt{\frac{2}{15}}$

D

$\sqrt{\frac{1}{15}}$

Question 71: Palette 71/82

AP-EAPCET 2022 MCQ

If the angles of a $\triangle A B C$ are in the ratio $1: 2: 3$, then the corresponding sides are in the ratio

A

$\sqrt{3}: 2: 1$

B

$1: \sqrt{3}: 2$

C

$\sqrt{3}: 1: 2$

D

$1: 2: \sqrt{3}$

Question 72: Palette 72/82

AP-EAPCET 2022 MCQ

In a $\triangle A B C, r_1 \cot \frac{A}{2}+r_2 \cot \frac{B}{2}+r_3 \cot \frac{C}{2}=$

A

s

B

2s

C

3s

D

s/2

Question 73: Palette 73/82

AP-EAPCET 2021 MCQ

What is the value of $(a-b)^2 \cos ^2 \frac{c}{2}+(a+b)^2 \sin ^2 \frac{c}{2}$ is equal to

A

$c^2$

B

$a^2+b^2$

C

$a^2+b^2+c^2$

D

$a^2-b^2+c^2$

Question 74: Palette 74/82

AP-EAPCET 2021 MCQ

In $\triangle A B C$, suppose the radius of the circle opposite to an angle $A$ is denoted by $r_1$, similarly $r_2 \leftrightarrow$ angle $B, r_3 \leftrightarrow$ angle $C$. If $r_1=2, r_2=3$ and $r_3=6$, then what is $(a, b, c)$ is equal to

A

(3, 4, 5)

B

(3, 5, 4)

C

(5, 4, 3)

D

(5, 3, 4)

Question 75: Palette 75/82

AP-EAPCET 2021 MCQ

If in $\triangle A B C, a \tan A+b \tan B=(a+b). \tan \left(\frac{A+B}{2}\right)$, then which of the following holds?

A

$A=B$

B

$A=2 B$

C

$A=\frac{1}{2} B$

D

$A > B$

Question 76: Palette 76/82

AP-EAPCET 2021 MCQ

In $\triangle A B C$, medians $A D$ and $B E$ are drawn. If $A D=4, \angle D A B=\frac{\pi}{6}$ and $\angle A B E=\frac{\pi}{3}$, then the area of $\triangle A B C$ is

A

$\frac{8}{3}$ sq units

B

$\frac{16}{3} \mathrm{sq}$ units

C

$\frac{32}{3 \sqrt{2}}$ sq units

D

$\frac{64}{3}$ sq units

Question 77: Palette 77/82

AP-EAPCET 2021 MCQ

In a $\triangle A B C, 2 \Delta^2=\frac{a^2 b^2 c^2}{a^2+b^2+c^2}$, then the triangle is

A

equilateral

B

isosceles

C

right angled

D

acute angled triangle

Question 78: Palette 78/82

AP-EAPCET 2021 MCQ

In $\triangle A B C$, suppose the radius of the circle opposite to an angle $A$ is denoted by $r_1$, similarly $r_2 \leftrightarrow$ angle $B, r_3 \leftrightarrow$ angle $C$. If $r_1=2, r_2=3, r_3=6$, what is the value of $r_1+r_2+r_3-r=$ (R - radius of the circum circle).

A

4R

B

3R

C

2R

D

R

Question 79: Palette 79/82

AP-EAPCET 2021 MCQ

In a $\Delta ABC$, if a = 3, b = 4 and $\sin A=\frac{3}{4}$, then $\angle CBA$ is equal to

A

60$\Upsilon$

B

75$\Upsilon$

C

90$\Upsilon$

D

45$\Upsilon$

Question 80: Palette 80/82

AP-EAPCET 2021 MCQ

In $\Delta ABC,A=75\Upsilon$ and $B=45\Upsilon$, then the value of $b+c\sqrt2$ is equal to

A

a

B

3a

C

2a

D

4a

Question 81: Palette 81/82

AP-EAPCET 2021 MCQ

In $\triangle A B C$, suppose the radius of the circle opposite to an $\angle A$ is denoted by $r_1$, similarly $r_2 \leftrightarrow \angle B$ and $r_3 \leftrightarrow \angle C$. If $r$ is the radius of inscribed circle, then, what is the value of $\frac{a b-r_1 r_2}{r_3}$ is equal to

A

$r_1 r_2 r_3$

B

$r$

C

$r_1 r_2 \frac{r_3}{2}$

D

$\frac{r}{2}$

Question 82: Palette 82/82

AP-EAPCET 2021 MCQ

If D, E and F are respectively mid-points of AB, AC and BC in $\Delta ABC$, then BE + AF is equal to

A

DC

B

$\frac{3}{2}$BF

C

$\frac{1}{2}$BF

D

$\frac{1}{2}$DC