JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(S\) be the set of all values of \(\theta \in[-\pi, \pi]\) for which the system of linear equations \(x+y+\sqrt{3} z=0\) \(-x+(\tan \theta) y+\sqrt{7} z=0\) \(x+y+(\tan \theta) z=0\) has non-trivial solution. Then \(\frac{120}{\pi} \sum_{\theta \in s} \theta\) is equal to
- A \(40\)
- B \(10\)
- C \(20\)
- D \(30\)
Answer & Solution
Correct Answer
(C) \(20\)
Step-by-step Solution
Detailed explanation
For non trivial solutions \(D =0\) \(\left|\begin{array}{ccc}1 & 1 & \sqrt{3} \\-1 & \tan \theta & \sqrt{7} \\1 & 1 & \tan \theta\end{array}\right|=0\) \(\tan ^2 \theta-(\sqrt{3}-1)-\sqrt{3}=0\) \(\tan \theta=\sqrt{3},-1\)…
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
- A ray of light along \(x + \sqrt 3 y = \sqrt 3 \) gets reflected upon reaching \(x- \) axis , the equation of the reflected ray isJEE Mains 2013 Hard
- If the line \(\frac{{x - 3}}{2} = \frac{{y + 2}}{{ - 1}} = \frac{{z + 4}}{3}\) lies in the plane \(lx + my - z = 9\) then \({l^2} + {m^2} = \;.\;.\;.\;.\;.\;\)JEE Mains 2016 Medium
- The letters of the word "UDAYPUR" are written in all possible ways with or without meaning and these words are arranged as in a dictionary. The rank of the word "UDAYPUR" is:JEE Mains 2026 Hard
- The locus of the mid-points of the perpendiculars drawn from points on the line, \(\mathrm{x}=2 \mathrm{y}\) to the line \(\mathrm{x}=\mathrm{y}\) isJEE Mains 2020 Hard
- If \(f(x)=x^3-x^2 f^{\prime}(1)+x f^{\prime \prime}(2)-f^{\prime \prime \prime}(3), x \in R\), thenJEE Mains 2023 Hard
- At present, a firm is manufacturing \(2000\) items. It is estimated that the rate of change of production \(P\) w.r.t. additional number of workers \(x\) is given by \(\frac{{dp}}{{dx}} = 100 - 12\sqrt x \) . If the firm employs \(25 \) more workers, then the new level of production of itmes isJEE Mains 2013 Hard
More PYQs from JEE Mains
- Let \(f: R-\{0\} \rightarrow R\) be a function such that \(f(x)-6 f\left(\frac{1}{x}\right)=\frac{35}{3 x}-\frac{5}{2}\).
If the \(\lim _{x \rightarrow 0}\left(\frac{1}{\alpha x}+f(x)\right)=\beta ; \alpha, \beta \in R\), then \(\alpha+2 \beta\) is equal toJEE Mains 2025 Easy - Let the foci of hyperbola coincide with the foci of the ellipse \( \frac{x^{2}}{36}+\frac{y^{2}}{16}=1. \) If the eccentricity of the hyperbola is 5, then the length of its latus rectum is:JEE Mains 2026 Medium
- Two parabolas have the same focus \((4,3)\) and their directrices are the \(x\)-axis and the \(y\)-axis, respectively. If these parabolas intersects at the points \(A\) and \(B\), then \((A B)^2\) is equal to :JEE Mains 2025 Medium
- The sum of all the solutions of the equation \((8)^{2 x}-16 \cdot(8)^x+48=0\) is :JEE Mains 2024 Hard
- The area (in \(sq. \,units\)) of the region, given by the set \(\left\{(x, y) \in R \times R \mid x \geq 0,2 x^{2} \leq y \leq 4-2 x\right\}\) is:JEE Mains 2021 Hard
- Let \(f : R \to R\) be a function such that \(f(2 - x)\, = f(2 + x)\) and \(f(4 -x)\, = f(4 + x)\), for all \(x \in R\) and \(\int\limits_0^2 {f\left( x \right)\,dx = 5} \) . Then the value of \(\int\limits_{10}^{50} {f\left( x \right)\,\,dx} \) isJEE Mains 2015 Hard