1
JEE Main 2024 (Online) 27th January Morning Shift
Numerical
+4
-1
Let $f(x)=x^3+x^2 f^{\prime}(1)+x f^{\prime \prime}(2)+f^{\prime \prime \prime}(3), x \in \mathbf{R}$. Then $f^{\prime}(10)$ is equal to ____________.
2
JEE Main 2023 (Online) 13th April Evening Shift
Numerical
+4
-1

Let $$f(x)=\sum_\limits{k=1}^{10} k x^{k}, x \in \mathbb{R}$$. If $$2 f(2)+f^{\prime}(2)=119(2)^{\mathrm{n}}+1$$ then $$\mathrm{n}$$ is equal to ___________

3
JEE Main 2023 (Online) 1st February Morning Shift
Numerical
+4
-1

If $$f(x)=x^{2}+g^{\prime}(1) x+g^{\prime \prime}(2)$$ and $$g(x)=f(1) x^{2}+x f^{\prime}(x)+f^{\prime \prime}(x)$$, then the value of $$f(4)-g(4)$$ is equal to ____________.

4
JEE Main 2023 (Online) 30th January Morning Shift
Numerical
+4
-1

Let $$f^{1}(x)=\frac{3 x+2}{2 x+3}, x \in \mathbf{R}-\left\{\frac{-3}{2}\right\}$$ For $$\mathrm{n} \geq 2$$, define $$f^{\mathrm{n}}(x)=f^{1} \mathrm{o} f^{\mathrm{n}-1}(x)$$. If $$f^{5}(x)=\frac{\mathrm{a} x+\mathrm{b}}{\mathrm{b} x+\mathrm{a}}, \operatorname{gcd}(\mathrm{a}, \mathrm{b})=1$$, then $$\mathrm{a}+\mathrm{b}$$ is equal to ____________.