JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
The solutions of the equation \(\left|\begin{array}{ccc}1+\sin ^{2} x & \sin ^{2} x & \sin ^{2} x \\ \cos ^{2} x & 1+\cos ^{2} x & \cos ^{2} x \\ 4 \sin 2 x & 4 \sin 2 x & 1+4 \sin 2 x\end{array}\right|=0,(0< x< \pi), \operatorname{are}\)
- A \(\frac{\pi}{12}, \frac{\pi}{6}\)
- B \(\frac{\pi}{6}, \frac{5 \pi}{6}\)
- C \(\frac{5 \pi}{12}, \frac{7 \pi}{12}\)
- D \(\frac{7 \pi}{12}, \frac{11 \pi}{12}\)
Answer & Solution
Correct Answer
(D) \(\frac{7 \pi}{12}, \frac{11 \pi}{12}\)
Step-by-step Solution
Detailed explanation
\(\left|\begin{array}{ccc}1+\sin ^{2} x & \sin ^{2} x & \sin ^{2} x \\ \cos ^{2} x & 1+\cos ^{2} x & \cos ^{2} x \\ 4 \sin 2 x & 4 \sin 2 x & 1+4 \sin 2 x\end{array}\right|=0\) use \(R _{1} \rightarrow R _{1}+ R _{2}+ R _{3}\)…
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
- If \(\alpha ,\beta \in C\) are distinct roots, of the equatin \({x^2} - x + 1 = 0\) ,then \({\alpha ^{101}} + {\beta ^{107}}\) is equal to :JEE Mains 2018 Medium
- Let \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) be three points on the parabola \(y^2=6 x\) and let the line segment \(A B\) meet the line \(L\) through \(\mathrm{C}\) parallel to the \(\mathrm{x}\)-axis at the point \(\mathrm{D}\). Let \(\mathrm{M}\) and \(\mathrm{N}\) respectively be the feet of the perpendiculars from \(\mathrm{A}\) and \(\mathrm{B}\) on \(\mathrm{L}\). Then \(\left(\frac{\mathrm{AM} \cdot \mathrm{BN}}{\mathrm{CD}}\right)^2\) is equal to ...........JEE Mains 2024 Hard
- The sum \(\sum\limits_{r = 1}^{10} {\left( {{r^2} + 1} \right)} \times \left( {r!} \right)\) is equal toJEE Mains 2016 Hard
- The smallest natural number \(n,\) such that the coefficient of \(x\) in the expansion of \({\left( {{x^2}\, + \,\frac{1}{{{x^3}}}} \right)^n}\) is \(^n{C_{23}}\) isJEE Mains 2019 Hard
- Let the solution curve \(y=f(x)\) of the differential equation \(\frac{d y}{d x}+\frac{x y}{x^{2}-1}=\frac{x^{4}+2 x}{\sqrt{1-x^{2}}}, x \in(-1,1)\) pass through the origin. Then \(\int_{-\frac{\sqrt{3}}{2}}^{\frac{\sqrt{3}}{2}} f ( x ) dx\) is equal toJEE Mains 2022 Hard
- Let the line \(\frac{x}{1}=\frac{6-y}{2}=\frac{z+8}{5}\) intersect the lines \(\frac{x-5}{4}=\frac{y-7}{3}=\frac{z+2}{1}\) and \(\frac{x+3}{6}=\frac{3-y}{3}=\frac{z-6}{1}\) at the points \(A\) and \(B\) respectively. Then the distance of the mid-point of the line segment \(A B\) from the plane \(2 x-2 y+z=14\) isJEE Mains 2023 Hard
More PYQs from JEE Mains
- Let \(A\) and \(B\) be two invertible matrices of order \(3 \times 3\). If det \((ABA^T) = 8\) and \(det\,(AB^{-1}) = 8\), then \(det\, (BA^{-1} B^T)\) is equal toJEE Mains 2019 Hard
- The number of five digit numbers, greater than \(40000\) and divisible by \(5\), which can be formed using the digits \(0,1,3,5,7\) and \(9\) without repetition, is equal toJEE Mains 2023 Hard
- The value of \(4+\frac{1}{5+\frac{1}{4+\frac{1}{5+\frac{1}{4+\ldots \ldots \infty}}}}\) isJEE Mains 2021 Medium
- Let \(S=\mathbf{N} \cup\{0\}\). Define a relation \(R\) from \(S\) to \(\mathbf{R}\) by :
\(\mathrm{R}=\left\{(x, y): \log _{\mathrm{e}} y=x \log _{\mathrm{e}}\left(\frac{2}{5}\right), x \in \mathrm{~S}, y \in \mathbf{R}\right\}\)
Then, the sum of all the elements in the range of \(R\) is equal to :JEE Mains 2025 Medium - The area of the region : \(R =\left\{( x , y ): 5 x ^{2} \leq y \leq 2 x ^{2}+9\right\}\) is ........ \(square\, units\)JEE Mains 2021 Hard
- The angle of elevation of the top of a vertical tower from a point \(A\), due east of it is \(45^o\) . The angle of elevation of the top of the same tower from a point \(B\). due south of \(A\) is \(30^o\). If the distance between \(A\) and \(B\) is \(54\sqrt 2 \,m\), then the height of the tower (in metres), isJEE Mains 2016 Hard