# JEE Main & Advanced Mathematics Trigonometric Equations Question Bank

### done Critical Thinking

• A) $n\pi +\frac{\pi }{8}$

B) $\frac{n\pi }{2}+\frac{\pi }{8}$

C) ${{(-1)}^{n}}\frac{n\pi }{2}+\frac{\pi }{8}$

D) $2n\pi +{{\cos }^{-1}}\frac{3}{2}$

• A) $2n\pi \pm \frac{\pi }{4}$

B) $n\pi \pm \frac{\pi }{4}$

C) $n\pi +{{(-1)}^{n}}\frac{\pi }{4}$

D) None of these

• A) $\frac{n\pi }{4}$

B) $\frac{n\pi }{2}$

C) $\frac{n\pi }{8}$

D) None of these

• A) $\frac{\pi }{6}$

B) $\frac{5\pi }{6}$

C) $\frac{7\pi }{6}$

D) $-\frac{\pi }{6}$

• A) $x=n\pi +{{\cos }^{-1}}\left( \frac{c}{\sqrt{{{a}^{2}}+{{b}^{2}}}} \right)$

B) $x=2n\pi -{{\tan }^{-1}}\left( \frac{b}{a} \right)$

C) $x=2n\pi -{{\tan }^{-1}}\left( \frac{b}{a} \right)\pm {{\cos }^{-1}}\left( \frac{c}{\sqrt{{{a}^{2}}+{{b}^{2}}}} \right)$

D) $x=2n\pi +{{\tan }^{-1}}\left( \frac{b}{a} \right)\pm {{\cos }^{-1}}\left( \frac{c}{\sqrt{{{a}^{2}}+{{b}^{2}}}} \right)$

• A) $(2n+1)\frac{\pi }{4}$

B) $(2n+1)\frac{\pi }{10}$

C) $n\pi +\frac{\pi }{2}$or $\frac{n\pi }{5}+\frac{\pi }{10}$

D) None of these

• A) $\frac{n\pi }{3}$

B) $n\pi +\frac{\pi }{3}$

C) $2n\pi \pm \frac{\pi }{3}$

D) None of these

• A) $(2n+1)\frac{\pi }{4}$

B) $\frac{4}{(2n+1)\pi }$

C) $4\pi (2n+1)$

D) None of these

• A) $\left\{ \frac{\pi }{3},\,\frac{2\pi }{3} \right\}$

B) $\left\{ \frac{\pi }{3},\,\pi \right\}$

C) $\left\{ \frac{2\pi }{3},\frac{4\pi }{3} \right\}$

D) $\left\{ \frac{2\pi }{3},\frac{5\pi }{3} \right\}$

• A) $x=\frac{\pi }{6}$

B) $x=\frac{\pi }{3}$

C) $x=\frac{\pi }{3}$or $\frac{\pi }{6}$

D) $x=\frac{\pi }{3}$or $\frac{2\pi }{3}$

• A) $\frac{\pi }{p+q}$

B) $\frac{2\pi }{p+q}$

C) $\frac{\pi }{2(p+q)}$

D) $\frac{1}{p+q}$

• A) 1

B) 2

C) Infinite

D) None of these

• A) 2

B) 4

C) 6

D) $\infty$

• A) $8abc\le (a+b)(b+c)(c+a)$

B) $3abc\le {{a}^{3}}+{{b}^{3}}+{{c}^{3}}$

C) $6abc\le bc(b+c)+ca(c+a)+ab(a+b)$

D) $abc\le (a+b-c)(b+c-a)(c+a-b)$

• A) ${{a}^{2}}-{{b}^{2}}$

B) ${{b}^{2}}-{{c}^{2}}$

C) ${{c}^{2}}-{{a}^{2}}$

D) ${{a}^{2}}+{{b}^{2}}+{{c}^{2}}$

• A) $n=({{n}^{2}}+1)\tan \alpha$

B) $n=(2{{n}^{2}}-1)\tan \alpha$

C) ${{n}^{2}}=(2{{n}^{2}}+1)\tan \alpha$

D) $n=(2{{n}^{2}}+1)\tan \alpha$

• A) $s$

B) $\frac{s}{abc}$

C) $\frac{{{s}^{2}}}{abc}$

D) $\frac{{{s}^{3}}}{abc}$

• A) ${{a}^{2}}+{{b}^{2}}={{c}^{2}}$

B) ${{b}^{2}}+{{c}^{2}}={{a}^{2}}$

C) ${{c}^{2}}+{{a}^{2}}={{b}^{2}}$

D) $b-c=c-a$

• A) $a,\ b,\ c$are in A.P.

B) $\cos A,\ \cos B,\ \cos C$are in A.P.

C) $\sin A,\ \sin B,\ \sin C$are in A.P.

D) (a) and (c) both

• A) $\frac{\pi }{2}$

B) $\frac{\pi }{3}$

C) $\frac{\pi }{4}$

D) $\frac{\pi }{6}$

• A) 1 : 2

B) 2 : 1

C) 2 : 3

D) 1: 1

• A) $a+b$

B) $a-b$

C) $\frac{b}{a}$

D) $\frac{a}{b}$

• A) Right angled

B) Obtuse angled

C) Equilateral

D) Isosceles

• A) $\frac{\pi }{2}$

B) $\frac{\pi }{3}$

C) $\frac{\pi }{4}$

D) $\frac{\pi }{6}$

• A) $5-\sqrt{6}$only

B) $5+\sqrt{6}$only

C) $5-\sqrt{6}$or $5+\sqrt{6}$

D) Neither$5-\sqrt{6}$nor $5+\sqrt{6}$

• A) 0

B) 1

C) b

D) 2b

• A) $a,\ b,\ c$are in A.P.

B) ${{a}^{2}},\ {{b}^{2}},\ {{c}^{2}}$are in A.P.

C) ${{a}^{2}},\ {{b}^{2}},\ {{c}^{2}}$are in G. P.

D) None of these

• A) $\frac{69}{48}$

B) $\frac{96}{48}$

C) $\frac{48}{69}$

D) None of these

• A) $xy$

B) $xy\sqrt{3}$

C) $3xy$

D) $2xy$

• A) ${{105}^{o}}$

B) ${{120}^{o}}$

C) ${{135}^{o}}$

D) None

• A) 1

B) 2

C) $\sqrt{3}$

D) $\sqrt{2}$

• A) Right angled

B) Equilateral

C) Acute angled

D) Obtuse angled

• A) $a+b$

B) $b+c$

C) $c+a$

D) $a+b+c$

• A) $\frac{a+b}{a-b}$

B) $\frac{a-b}{a+b}$

C) $\sqrt{ab}$

D) ${{(ab)}^{1/3}}$

• A) 50 m

B) 25 m

C) 40 m

D) None of these

• A) $\frac{h\tan (\alpha -\beta )}{\tan (\alpha -\beta )-\tan \alpha }$

B) $\frac{h\cot (\alpha -\beta )}{\cot (\alpha -\beta )-\cot \alpha }$

C) $\frac{\cot (\alpha -\beta )}{\cot (\alpha -\beta )-\cot \alpha }$

D) None of these

• A) 100

B) 50

C) $50(\sqrt{3}+1)$

D) $50(\sqrt{3}-1)$

• A) $100\sqrt{3}$

B) $\frac{200\sqrt{3}}{3}$

C) $\frac{100\sqrt{3}}{3}$

D) $200\sqrt{3}$

• A) $\frac{150}{\sqrt{3}}metres$

B) $100\sqrt{3}metres$

C) $150metres$

D) $100metres$

• A) 2

B) 3

C) 4

D) 5