Vinod Singh and Shweta Pawar Solutions for Chapter: Model Question Paper, Exercise 1: MODEL QUESTION PAPER

$y=a+\frac{b}{x}$ is a solution of the differential equation

The line $\frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{0}$ is parallel to

${\int }_{\frac{-\pi }{4}}^{\frac{\pi }{4}}{x}^3{\sin }^{4}xdx=$

If $A$ is an obtuse angle, then $\frac{{\sin }^{3}A-{\cos }^{3}A}{\sin A-\cos A}+\frac{\sin A}{\sqrt{1+{\tan }^{2}A}}-2\tan A\cot A$ is equal to

$\int \frac{{\log }_{e}x}{x^3}dx=$

If $5^{\mathrm{th}}$ term of a $\mathrm{HP}$ is $\frac{1}{45}$ and ${11}^{\mathrm{th}}$ term is $\frac{1}{69}$, then its ${16}^{\mathrm{th}}$ term will be

Cosine of the angle between the lines $\overrightarrow{r}=5\hat{i}-\hat{j}+4\hat{k}+\lambda \left(\hat{i}+2\hat{j}+2\hat{k}\right)$ and $\overrightarrow{r}=7\hat{i}+2\hat{j}+2\hat{k}+\mu \left(3\hat{i}+2\hat{j}+6\hat{k}\right)$ is

If the distance between a focus and corresponding directrix of an ellipse be $8$ and the eccentricity be $\frac{1}{2}$, then length of the minor axis is