JEE Mains · Maths · STD 12 - 5. continuity and differentiation
If \(\mathrm{x}=2 \sin \theta-\sin 2 \theta\) and \(\mathrm{y}=2 \cos \theta-\cos 2 \theta\) ; \(\theta \in[0,2 \pi],\) then \(\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}\) at \(\theta=\pi\) is :
- A \(\frac{3}{2}\)
- B \(-\frac{3}{4}\)
- C \(\frac{3}{4}\)
- D \(\frac{3}{8}\)
Answer & Solution
Correct Answer
(D) \(\frac{3}{8}\)
Step-by-step Solution
Detailed explanation
\(x=2 \sin \theta-\sin 2 \theta\) \(\Rightarrow \frac{d x}{d \theta}=2 \cos \theta-2 \cos 2 \theta=4 \sin \left(\frac{\theta}{2}\right) \sin \left(\frac{3 \theta}{2}\right)\) \(y=2 \cos \theta-\cos 2 \theta\)…
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 the sum of the first \(20\) terms of the series \(\log _{\left(7^{\frac{1}{2}}\right)} x+\log _{\left(7^{\frac{1}{3}}\right)} x+\log _{\left(7^{\frac{1}{4}}\right)} x+\ldots\) is \(460,\) then \(x\) is equal toJEE Mains 2020 Hard
- Let \(R\,= \{(x,y) : x,y \in N\, and\, x^2 -4xy +3y^2\, =0\}\), where \(N\) is the set of all natural numbers. Then the relation \(R\) isJEE Mains 2013 Hard
- In a triangle \(ABC,\) right angled at the vertex \(A,\) if the position vectors of \(A, B\) and \(C\) are respectively \(3\hat i\, + \hat j\, - \hat k,\,\, - \hat i\, + 3\hat j\, + p\hat k\) and \(5\hat i\, + q\hat j\, - 4\hat k,\,\) then the point \((p, q)\) lies on a lineJEE Mains 2016 Hard
- If \(y\, = mx + c\) is the normal at a point on the parabola \(y^2\, = 8x\) whose focal distance is \(8\, units\), then \(\left| c \right|\) is equal toJEE Mains 2017 Hard
- If a tangent to the ellipse \(x^{2}+4 y^{2}=4\) meets the tangents at the extremities of its major axis at \(\mathrm{B}\) and \(\mathrm{C}\), then the circle with \(\mathrm{BC}\) as diameter passes through the point:JEE Mains 2021 Hard
- If the mean and the variance of \(6,4, a, 8, b, 12,10\), 13 are 9 and 9.25 respectively, then \(a+b+a b\) is equal to :JEE Mains 2025 Medium
More PYQs from JEE Mains
- Let \(x _1, x _2 \ldots ., x _{100}\) be in an arithmetic progression, with \(x _1=2\) and their mean equal to \(200\) . If \(y_i=i\left(x_i-i\right), 1 \leq i \leq 100\), then the mean of \(y _1, y _2\), \(y _{100}\) isJEE Mains 2023 Hard
- Suppose \({\tan ^{ - 1}}y = {\tan ^{ - 1}}x + {\tan ^{ - 1}}\left( {\frac{{2x}}{{1 - {x^2}}}} \right)\) , where \(\left| x \right| < \frac{1}{{\sqrt 3 }}\), then one of the value of \( y \) isJEE Mains 2015 Easy
- The square of the distance of the point \(\left(\frac{15}{7}, \frac{32}{7}, 7\right)\) from the line \(\frac{x+1}{3}=\frac{y+3}{5}=\frac{z+5}{7}\) in the direction of the vector \(\hat{i}+4 \hat{j}+7 \hat{k}\) is :JEE Mains 2025 Medium
- A coin is biased so that the head is \(3\) times as likely to occur as tail. This coin is tossed until a head or three tails occur. If \(X\) denotes the number of tosses of the coin, then the mean of \(X\) isJEE Mains 2023 Medium
- Two sets \(A\) and \(B\) are as under: \(A = \{ \left( {a,b} \right) \in R \times R:\left| {a - 5} \right| < 1 \,\,and\,\,\left| {b - 5} \right| < 1\} \); \(B = \left\{ {\left( {a,b} \right) \in R \times R:4{{\left( {a - 6} \right)}^2} + 9{{\left( {b - 5} \right)}^2} \le 36} \right\}\) then : . . . . .JEE Mains 2018 Hard
- If \(\cos \,x\,\frac{{dy}}{{dx}} - y\,\sin \,x = 6x,\,\left( {0 < x < \frac{\pi }{2}} \right)\) and \(y\left( {\frac{\pi }{3}} \right) = 0\), then \(y\left( {\frac{\pi }{6}} \right)\) is equal toJEE Mains 2019 Hard