WBJEE · Maths · Limits
\(\lim _{x \rightarrow 0} \frac{\sin \left(\pi \sin ^2 x\right)}{x^2}=\)
- A \(\pi^2\)
- B \(3 \pi\)
- C \(2 \pi\)
- D \(\pi\)
Answer & Solution
Correct Answer
(D) \(\pi\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text {Hints : }=\operatorname{Lt}_{x \rightarrow 0} \frac{\sin \left(\pi \sin ^2 x\right)}{x^2}=\pi_{x \rightarrow 0} \frac{\sin ^2 x}{x^2}=\pi \\ & =\pi \end{aligned}\)
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 isWBJEE 2021 Easy
- Let \(\rho\) be a relation defined on \(N\), the set of natural numbers, as \(\rho=\{(x, y) \in N \times N: 2 x+y=41\} .\) ThenWBJEE 2018 Easy
- Let \(\mathrm{I}(\mathrm{n})=\mathrm{n}^{\mathrm{n}}, \mathrm{J}(\mathrm{n})=1.3 .5 \ldots . .(2 \mathrm{n}-1)\) for all \((\mathrm{n}>1), \mathrm{n} \in \mathrm{N}\), thenWBJEE 2020 Easy
- The number of solutions of the equation \(x+y+z=10\) where \(x, y\) and \(z\) are positive integersWBJEE 2013 Easy
- If \(\mathrm{f}: \mathrm{S} \rightarrow \mathbb{R}\) where \(S\) is the set of all non-singular matrices of order 2 over \(\mathbb{R}\) and \(f\left[\left(\begin{array}{ll}a & b \\ c & d\end{array}\right)\right]=a d-b c\), thenWBJEE 2020 Easy
- \(\int_{0}^{100} e^{x-[x]} d x\) is equal toWBJEE 2017 Medium
More PYQs from WBJEE
- The reactive species in chlorine bleach isWBJEE 2019 Easy
- Let \([x]\) denotes the greatest integer less than or equal to \(x\). Then, the value of \(\alpha\) for which the function \(f(x)=\left\{\begin{array}{c}\frac{\sin \left[-x^{2}\right]}{\left[-x^{2}\right]}, x \neq 0 \\ \alpha, \quad x=0\end{array}\right.\) is continuous at \(x=0,\) isWBJEE 2015 Easy
- The ratio of the diameter of the sun to the distance between the earth and the sun is approximately \(0.009 .\) The approximate diameter of the image of the sun formed by a concave spherical mirror of radius of curvature \(0.4 \mathrm{m}\) isWBJEE 2017 Medium
- If \((2+i)\) and \((\sqrt{5}-2 i)\) are the roots of the equation \(\left(x^{2}+a x+b\right)\left(x^{2}+c x+d\right)=0\) where \(a, b, c\) and \(d\) are real constants, then product of all the roots of the equation isWBJEE 2015 Easy
- A biased coin with probability \(p(0 \lt p \lt 1)\) of getting head is tossed until a head appears for the first time. If the probability that the number of tosses required is even is \(\frac{2}{5}\), then \(p=\)WBJEE 2024 Medium
- Domain of \(y=\sqrt{\log _{10} \frac{3 x-x^2}{2}}\) isWBJEE 2022 Easy