JEE Mains · Maths · STD 11 - 12. limits
If \(\lim _{x \rightarrow 0} \frac{\cos (2 x)+a \cos (4 x)-b}{x^4}\) is finite, then \((a+b)\) is equal to :
- A \(\frac{1}{2}\)
- B \(0\)
- C \(\frac{3}{4}\)
- D \(-1\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\(\lim _{x \rightarrow 0} \frac{\cos 2 x+a \cos 4 x-b}{x^4}=\) finite…
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 \(X\) be a random variable such that the probability function of a distribution is given by \(P(X=\) 0) \(=\frac{1}{2}, \mathrm{P}(\mathrm{X}=\mathrm{j})=\frac{1}{3^{j}}(\mathrm{j}=1,2,3, \ldots, \infty)\). Then the mean of the distribution and \(\mathrm{P}(\mathrm{X}\) is positive and even) respectively are:JEE Mains 2021 Medium
- Let the ellipse \(E: \frac{x^{2}}{144}+\frac{y^{2}}{169}=1\) and the hyperbola \(H:\frac{x^{2}}{16}-\frac{y^{2}}{\lambda^{2}}=-1\) have the same foci. If e and L respectively denote the eccentricity and the length of the latus rectum of H, then the value of \(24(e+L)\) is:JEE Mains 2026 Hard
- If the variance of the terms in an increasing \(A.P.\), \(b _{1}, b _{2}, b _{3}, \ldots b _{11}\) is \(90,\) then the common difference of this \(A.P.\) isJEE Mains 2020 Medium
- Let \(\vec a = 2\hat i + \hat j - 2\hat k\) and \(\vec b = \hat i + \hat j\) . Let \(\vec c\) be vector such that \(\left| {\vec c - \vec a} \right| = 3,\;\left| {\left( {\vec a \times \vec b} \right) \times \vec c} \right| = 3\) and the angle between \(\vec c\) and \(\vec a \times \vec b\) be \(30^\circ \) . Then \(\vec a \cdot \vec c\) is equal to :JEE Mains 2017 Hard
- The set of all real values of \(\lambda \) for which exactly two common tangents can be drawn to the circles \(x^2 + y^2 - 4x - 4y+ 6\, = 0\) and \(x^2 + y^2 - 10x - 10y + \lambda \, = 0\) is the interval:JEE Mains 2014 Hard
- If \(\lambda \in R\) is such that the sum of the cubes of the roots of the equation, \(x^2 +(2 - \lambda ) x+ (10 - \lambda ) = 0\) is minimum, then the magnitude of the difference of the roots of this equation isJEE Mains 2018 Hard
More PYQs from JEE Mains
- Let \(A=\{z\in\mathbb{C}:|z-2|\le4\}\) and
\(B=\{z\in\mathbb{C}:|z-2|+|z+2|=5\}\).
Then the max \(\left\{\left| z _1- z _2\right|: z _1 \in A\right.\) and \(\left.z _2 \in B\right\}\) isJEE Mains 2026 Medium - If \(\alpha=1\) and \(\beta=1+i\sqrt{2}\), where \(i=\sqrt{-1}\) are two roots of the equation \(x^3+ax^2+bx+c=0\), \(a,b,c \in \mathbb{R}\), then \(\int_{-1}^{1}(x^3+ax^2+bx+c)dx\) is equal to:JEE Mains 2026 Medium
- The mean and standard deviation of \(40\) observations are \(30\) and \(5\) respectively. It was noticed that two of these observations \(12\) and \(10\) were wrongly recorded. If \(\sigma\) is the standard deviation of the data after omitting the two wrong observations from the data, then \(38 \sigma^{2}\) is equal to\(.........\)JEE Mains 2022 Hard
- If \({e^y} + xy = e\), the ordered pair \(\left( {\frac{{dy}}{{dx}},\frac{{{d^2}y}}{{d{x^2}}}} \right)\) at \(x = 0\) is equal toJEE Mains 2019 Hard
- Let \(\alpha, \beta\) be the roots of the equation \(x^2-\sqrt{6} x+3=0\) such that \(\operatorname{Im}(\alpha)>\operatorname{Im}(\beta)\). Let \(a, b\) be integers not divisible by \(3\) and \(n\) be a natural number such that \(\frac{\alpha^{99}}{\beta}+\alpha^{98}=3^n(a+i b), i=\sqrt{-1}\). Then \(\mathrm{n}+\mathrm{a}+\mathrm{b}\) is equal to ...........JEE Mains 2024 Hard
- Consider an A. P. of positive integers, whose sum of the first three terms is 54 and the sum of the first twenty terms lies between 1600 and 1800. Then its \(11^{\text {th }}\) term is :JEE Mains 2025 Medium