enEnglishguગુજરાતી
JEE Mains · Maths · STD 11 - 3. trignometrical ratios,functions and identities
Consider the following two statement. Statement \(p\) : The value of \(sin\,120^o\) can be divided by taking \(\theta\, = 240^o\) in the equation \(2\,\sin \frac{\theta }{2} = \sqrt {1 + \sin \theta } - \sqrt {1 - \sin \theta } \) Statement \(q\) : The angles \(A, B, C\) and \(D\) of any quadrilateral \(ABCD\) satisfy the equation \(\cos \left( {\frac{1}{2}\left( {A + C} \right)} \right) + \cos \left( {\frac{1}{2}\left( {B + D} \right)} \right) = 0\) Then the truth values of \(p\) and \(q\) are respectively.
- A \(F, T\)
- B \(T, T\)
- C \(F, F\)
- D \(T, F\)
Answer & Solution
Correct Answer
(A) \(F, T\)
Step-by-step Solution
Detailed explanation
For statement \(p\): \(\sin {120^ \circ } = \frac{{\sqrt 3 }}{2}\) \( \Rightarrow 2\sin {120^ \circ } = \sqrt 3 \) \( = \sqrt {1 + \sin {{240}^o}} - \sqrt {1 - \sin {{240}^o}} \) \( = \sqrt {\frac{{1 - \sqrt 3 }}{2}} - \sqrt {\frac{{1 + \sqrt 3 }}{2}} \ne \sqrt 3 \) For…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Let \(A=\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right]\) and \(B=\left[\begin{array}{ccc}9^{2} & -10^{2} & 11^{2} \\ 12^{2} & 13^{2} & -14^{2} \\ -15^{2} & 16^{2} & 17^{2}\end{array}\right]\), then the value of \(A ^{\prime} BA\) is.JEE Mains 2022 Medium
- If the \(10^{\text {th }}\) term of an A.P. is \(\frac{1}{20}\) and its \(20^{\text {th }}\) term is \(\frac{1}{10},\) then the sum of its first \(200\) terms isJEE Mains 2020 Medium
- Let the determinant of a square matrix \(A\) of order \(m\) be \(m-n\), where \(m\) and \(n\) satisfy \(4 m+n=22\) and \(17 m +4 n =93\). If \(\operatorname{det}(n \operatorname{adj}(\operatorname{adj}( mA )))=\) \(3^{ a } 5^{ b } 6^{ c }\). then \(a + b + c\) is equal to:JEE Mains 2023 Hard
- A data consists of \(n\) observations \({x_1},{x_2},......,{x_n}.\) If \(\sum\limits_{i - 1}^n {{{({x_i} + 1)}^2}} = 9n\) and \(\sum\limits_{i - 1}^n {{{({x_i} - 1)}^2}} = 5n,\) then the standard deviation of this data isJEE Mains 2019 Hard
- Let \([\mathrm{t}]\) denote the greatest integer \(\leq \mathrm{t}\). Then the value of \(8 \cdot \int \limits_{-\frac{1}{2}}^{1}([2 x]+|x|) \,d x\) is .... .JEE Mains 2021 Hard
- For \(x \in R -\{0,1\},\) \({f_1}\left( x \right) = \frac{1}{x},{f_2}\left( x \right) = 1 - x\) and \(f_{3}(x)=\frac{1}{1-x}\) be three given functions. If a function, \(J ( x )\) satisfies \(\left( {{f_2}oJo{f_1}} \right)\left( x \right)= f _{3}( x )\) then \(J ( x )\) is equal toJEE Mains 2019 Hard
More PYQs from JEE Mains
- Let \(R_{1}\) and \(R_{2}\) be relations on the set \(\{1,2, \ldots, 50\}\) such that \(R _{1}=\left\{\left( p , p ^{ n }\right)\right.\) : \(p\) is a prime and \(n \geq 0\) is an integer \(\}\) and \(R _{2}=\left\{\left( p , p ^{ n }\right)\right.\) : \(p\) is a prime and \(n =0\) or \(1\}\). Then, the number of elements in \(R _{1}- R _{2}\) is........JEE Mains 2022 Hard
- Let the three sides of a triangle \(A B C\) be given by the vectors \(2 \hat{i}-\hat{j}+\hat{k}, \quad \hat{i}-3 \hat{j}-5 \hat{k}\) and \(3 \hat{i}-4 \hat{j}-4 \hat{k}\). Let \(G\) be the centroid of the triangle \(A B C\). Then \(6\left(|\overrightarrow{\mathrm{AG}}|^2+|\overrightarrow{\mathrm{BG}}|^2+|\overrightarrow{\mathrm{CG}}|^2\right)\) is equal to ________JEE Mains 2025 Medium
- If \(\alpha x+\beta y=109\) is the equation of the chord of the ellipse \(\frac{x^2}{9}+\frac{y^2}{4}=1\), whose mid point is \(\left(\frac{5}{2}, \frac{1}{2}\right)\), then \(\alpha+\beta\) is equal to :JEE Mains 2025 Medium
- Let \(\left\{a_{n}\right\}_{n=0}^{\infty}\) be a sequence such that \(a _{0}= a _{1}=0\) and \(a _{ n +2}=2 a _{ n +1}- a _{ n }+1\) for all \(n \geq 0\). Then, \(\sum\limits_{ n =2}^{\infty} \frac{ a _{ n }}{7^{ n }}\) is equal toJEE Mains 2022 Hard
- Let \(\alpha, \beta\) be the roots of the equation \(x^{2}-\sqrt{2} x+\sqrt{6}=0\) and \(\frac{1}{\alpha^{2}}+1, \frac{1}{\beta^{2}}+1\) be the roots of the equation \(x^{2}+a x+b=0\). Then the roots of the equation \(x ^{2}-( a + b -2) x +( a + b +2)\) \(=0\) are\(...\)JEE Mains 2022 Hard
- The term independent of \(x\) in the expression of \(\left(1-x^{2}+3 x^{3}\right)\left(\frac{5}{2} x^{3}-\frac{1}{5 x^{2}}\right)^{11}, x \neq 0\) isJEE Mains 2022 Hard