JEE Main · 2023 · 24 Jan 2023 · Shift 1 · Differentiation

More JEE Main questions on Differentiation

1. Let $f(x)=x^3+x^2{f}^{\prime }(1)+2x{f}^{\prime \prime }(2)+f^{\prime \prime \prime }(3)$, $x\in \mathbf{R}$. Then the value of $f^{\prime }(5)$ is :
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2. If $y(x)=\left|\begin{array}{ccc}\sin x& \cos x& \sin x+\cos x+1\\ 27& 28& 27\\ 1& 1& 1\end{array}\right|$, $x\in \mathbb{R}$, then $\frac{d^{2}y}{d{x}^2}+y$ is equal to
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3. Let $f(x)=x^5+2e^{x/4}$ for all $x\in R$. Consider a function $g(x)$ such that $(g\circ f)(x)=x$ for all $x\in R$. Then the value of $8g^{\prime }(2)$ is
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4. Let $f(x)=x^5+2x^3+3x+1,x\in R$, and $g(x)$ be a function such that $f(g(x))=x$ for all $x\in R$. Then $\frac{g(7)}{g^{\prime }(7)}$ is equal to:
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5. If $y(\theta )=\frac{2\cos \theta +\cos 2\theta }{\cos 3\theta +4\cos 2\theta +5\cos \theta +2}$, then at $\theta =\frac{\pi }{2}$, $y^{\prime \prime }+y^{\prime }+y$ is equal to
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6. Suppose for a function $h,h(0)=0,h(1)=1$ and $h^{\prime }(0)=h^{\prime }(1)=2$. If $g(x)=h\left(e^x\right)e^{h(x)}$, then $g^{\prime }(0)$ is equal to
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