Which of the following functions is discontinuous function? - Vidyadip

Question

Which of the following functions is discontinuous function?

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Answer

self

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If $\text{A} = \begin{bmatrix}1\end{bmatrix}$ then the order of the matrix is:

1 × 1
2 × 1
1 × 2
None of these

The number of real values of x satisfying the equation $ \tan^{-1}\left(\frac{\text{x}}{1-\text{x}^2}\right)+\tan^{-1}\left(\frac{1}{\text{x}^3}\right)=\frac{3\pi}{4}$, is?

0
1
2
Infinitely many

The angle between the vectors $\vec{a} \times \vec{b}$ and $\vec{b} \times \vec{a}$ is

Let $\text{U}=\sin^{-1}\Big(\frac{2\text{x}}{1+\text{x}^2}\Big)$ and $\text{V}=\tan^{-1}\Big(\frac{2\text{x}}{1-\text{x}^2}\Big),$ then $\frac{\text{dU}}{\text{dV}}=$

$\frac{1}{2}$
$\text{x}$
$\frac{1-\text{x}^2}{\text{x}^2-4}$
$1$

If $y=\cos ^2 x$, then the value of $\frac{d y}{d x}$ is

If $\text{f(x)}=\begin{cases}\frac{1-\sin^2\text{x}}{3\cos^2\text{x}},&\text{if}\text{ x}<\frac{\pi}{2}\\\text{a},&\text{if}\text{ x}=\frac{\pi}{2}\\\frac{\text{b}(1-\sin\text{x})}{(\pi-2\text{x})^2},&\text{if}\text{ x }>\frac{\pi}{2}\end{cases}$ Then f(x) is continuous at $\text{x}=\frac{\pi}{2},$ if:

$\text{a}=\frac{1}{3},\text{ b}=2$
$\text{a}=\frac{1}{3},\text{ b}=\frac{8}{3}$
$\text{a}=\frac{2}{3},\text{ b}=\frac{8}{3}$
none of these

If $\vec{\text{a}}$ and $\vec{\text{b}}$ are unit vectors, then which of the following values of $\vec{\text{a}}.\vec{\text{b}}$ is not possible?

$\sqrt{3}$
$\frac{\sqrt{3}}{2}$
$\frac{1}{\sqrt{2}}$
$\frac{-1}{2}$

If $\hat{\text{i}},\hat{\text{j}},\hat{\text{k}}$ are unit vectors, then

$\hat{\text{i}}.\hat{\text{j}}=1$
$\hat{\text{i}}.\hat{\text{i}}=1$
$\hat{\text{i}}\times\hat{\text{j}}=1$
$\hat{\text{i}}\times\big(\hat{\text{j}}\times\hat{\text{k}}\big)=1$

The order the matrix is $\begin{bmatrix}2&\text{amp; }3&\text{amp; }4\\9&\text{amp; }8&\text{amp; }7\end{bmatrix}$ is:

4 × 3
3 × 2
2 × 3
3 × 1

$\int_0^{\frac{\pi}{6}} \sec ^2\left(x-\frac{\pi}{6}\right) d x$ is equal to :