JEE Mains · Maths · STD 11 - 12. limits
\(\mathop {\lim }\limits_{x \to 0} \,\frac{{{{\sin }^2}\,x}}{{\sqrt 2 - \sqrt {1 + \cos \,x} }}\) equals
- A \(\sqrt 2 \)
- B \(4\sqrt 2 \)
- C \(4\)
- D \(2\sqrt 2 \)
Answer & Solution
Correct Answer
(B) \(4\sqrt 2 \)
Step-by-step Solution
Detailed explanation
\(\mathop {\lim }\limits_{x \to 0} \frac{{\left( {\frac{{{{\sin }^2}x}}{{{x^2}}}} \right)\left( {\sqrt 2 + \sqrt {1 + \cos x} } \right)}}{{\left( {\frac{{1 - \cos x}}{{{x^2}}}} \right)}}\)…
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
- Let \([ t ]\) denote the greatest integer \(\leq t\). If for some \(\lambda \in R -\{0,1\}, \lim \limits_{x \rightarrow 0}\left|\frac{1-x+|x|}{\lambda-x+[x]}\right|=L,\) then \(L\) is equal toJEE Mains 2020 Hard
- The number of the real roots of the equation \((x+1)^{2}+|x-5|=\frac{27}{4}\) is ....... .JEE Mains 2021 Medium
- Let \(\vec{a}=2 \hat{i}+\hat{j}-2 \hat{k}\) and \(\vec{b}=\hat{i}+\hat{j} .\) If \(\vec{c}\) is a vector such that \(\vec{a} \cdot \vec{c}=|\vec{c}|,|\vec{c}-\vec{a}|=2 \sqrt{2}\) and the angle between \((\vec{a} \times \vec{b})\) and \(\vec{c}\) is \(\frac{\pi}{6}\), then the value of \(|(\vec{a} \times \vec{b}) \times \vec{c}|\) is:JEE Mains 2021 Hard
- Let \(A=\left[\begin{array}{cc}i & -i \\ -i & i\end{array}\right], i=\sqrt{-1}\).Then, the system of linear equations \(A^{8}\left[\begin{array}{l}x \\ y\end{array}\right]=\left[\begin{array}{c}8 \\ 64\end{array}\right]\) has :JEE Mains 2021 Hard
- If the probability that the random variable X takes the value \(x\) is given by \(P(X=x)=k(x+1) 3^{-x}\), \(\mathrm{x}=0,1,2,3 \ldots \ldots\), where k is a constant, then \(\mathrm{P}(\mathrm{X} \geq 3)\) is equal toJEE Mains 2025 Medium
- Let the parabola \(y = x^2 + px + q\) passing through the point \((1, -1)\) be such that the distance between its vertex and the \(x\)-axis is minimum. Then the value of \(p^2 + q^2\) is:JEE Mains 2026 Medium
More PYQs from JEE Mains
- Let \(\vec{a}\) and \(\vec{b}\) be two vectors such that \(|\vec{a}|=1,|\vec{b}|=4\) and \(\vec{a} \cdot \vec{b}=2\). If \(\vec{c}=(2 \vec{a} \times \vec{b})-3 \vec{b}\) and the angle between \(\vec{b}\) and \(\vec{c}\) is \(\alpha\), then \(192 \sin ^2 \alpha\) is equal toJEE Mains 2024 Medium
- Let \(y=y(x)\) be the solution of the differential equation \(\left(x^2+4\right)^2 d y+\left(2 x^3 y+8 x y-2\right) d x=0 \text {. If } y(0)=0 \text {, }\) then \(y(2)\) is equal toJEE Mains 2024 Hard
- The integer \('k'\), for which the inequality \(x^{2}-2(3 k-1) x+8 k^{2}-7>0\) is valid for every \(x\) in \(R ,\) isJEE Mains 2021 Medium
- The number of \(4\) letter words (with or without meaning) that can be formed from the eleven letters of the word \('EXAMINATION'\) isJEE Mains 2020 Hard
- The equation \(y = \sin \,x\,\sin \,\left( {x + 2} \right) - {\sin ^2}\,\left( {x + 1} \right)\) represents a straight line lying inJEE Mains 2019 Hard
- Let \(f(x)\) and \(g(x)\) be twice differentiable functions satisfying \(f''(x) = g''(x)\) for all \(x \in \mathbf{R}\), \(f'(1) = 2g'(1) = 4\) and \(g(2) = 3f(2) = 9\). Then \(f(25) - g(25)\) is equal to :JEE Mains 2026 Medium