MHT CET · Maths · Straight Lines
The slope of the line through the origin which makes an angle of \(30^{\circ}\) with the positive direction of \(\mathrm{Y}\)-axis measured anticlockwise is
- A \(\frac{-2}{\sqrt{3}}\)
- B \(-\sqrt{3}\)
- C \(\frac{\sqrt{3}}{2}\)
- D \(\frac{-1}{\sqrt{3}}\)
Answer & Solution
Correct Answer
(B) \(-\sqrt{3}\)
Step-by-step Solution
Detailed explanation
Refer figure
Angle made by line \(\mathrm{L}\) with positive direction of \(\mathrm{X}\) axis is \(\left(90^{\circ}+30^{\circ}\right)\) i.e. \(120^{\circ}\).
\(\therefore\) Slope of line \(\mathrm{L}=\tan \left(120^{\circ}\right)=\tan \left(\pi-60^{\circ}\right)=-\tan 60^{\circ}=-\sqrt{3}\)
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 \(x=\sin \theta, y=\sin ^3 \theta\), then \(\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}\) at \(\theta=\frac{\pi}{2}\) isMHT CET 2024 Easy
- Let \(\overline{\mathrm{a}}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-2 \hat{\mathrm{k}}\) and \(\overline{\mathrm{b}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}\). Let \(\overline{\mathrm{c}}\) be a vector such that \(|\bar{c}-\bar{a}|=3\) and \(|(\overline{\mathrm{a}} \times \overline{\mathrm{b}}) \times \overline{\mathrm{c}}|=3\) and the angle between \(\overline{\mathrm{c}}\) and \(\overline{\mathrm{a}} \times \overline{\mathrm{b}}\) is \(30^{\circ}\), then \(\overline{\mathrm{a}} \cdot \overline{\mathrm{c}}\) is equal toMHT CET 2024 Hard
- If p : switch \(\mathrm{s}_1\) is closed, q : switch \(\mathrm{s}_2\) is closed then correct interpretation from the following circuit is
MHT CET 2025 Easy - Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Let X denote the random variable of number of jacks obtained in the two drawn cards. Then \(\mathrm{P}(\mathrm{X}=1)+\mathrm{P}(\mathrm{X}=2)\) equalsMHT CET 2024 Hard
- If the volume of the parallelopiped is \(158 \mathrm{cu}\). units whose coterminus edges are given by the vectors \(\bar{a}=(\hat{i}+\hat{j}+n \hat{k}), \bar{b}=2 \hat{i}+4 \hat{j}-n \hat{k}\) and \(\bar{c}=\hat{i}+n \hat{j}+3 \hat{k}\), where \(n \geq 0\), then the value of \(n\) isMHT CET 2023 Medium
- The value of \(\lim _{x \rightarrow 0} \frac{15^{x}-5^{x}-3^{x}+1}{1-\cos 2 x}\) isMHT CET 2010 Medium
More PYQs from MHT CET
- If \(\overline{\mathrm{a}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}\) and \(\bar{b}=\hat{i} \times(\bar{a} \times \hat{i})+\hat{j} \times(\bar{a} \times \hat{j})+\hat{k} \times(\bar{a} \times \hat{k})\) then \(|\vec{b}|\) isMHT CET 2024 Medium
- If \(x^{3}+y^{3}-3 a x y=0\), then \(\frac{d y}{d x}\) equalsMHT CET 2008 Medium
- A parallel plate capacitor has plate area ' \(\mathrm{A}\) ' and separation between plates is 'd'. It is charged to a potential difference of \(V_0\) volt. The charging battery is then disconnected and plates are pulled apart three times the initial distance. The work done to increase the distance between the plates is \(\left(\varepsilon_0=\right.\) permittivity of free space \()\)MHT CET 2023 Medium
- Which among the following phenols does NOT correctly match with their IUPAC names?MHT CET 2023 Easy
- \(22 \mathrm{~g}\) of carbon dioxide at \(27^{\circ} \mathrm{C}\) is mixed in closed container with \(16 \mathrm{~g}\) of oxygen at \(37^{\circ} \mathrm{C}\). If both gases are considered as ideal gases, then the temperature of the mixture is nearlyMHT CET 2022 Hard
- Identify the product ' \(B\) ' in the following reaction.MHT CET 2024 Medium