Question
Maximum value of $f(x)=x e^{-x}$ is _________ .
✓
Answer
$\frac{1}{e}$
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If A and B are two events such that $\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)=\text{p},\text{P}(\text{A})=\text{p},\text{P}(\text{B})=\frac{1}{3}$ and $\text{P}(\text{A}\cap\text{B})=\frac{5}{9},$ then p = __________.
→If A and B are two events such that $\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)=\text{p},\text{P}(\text{A})=\text{p},\text{P}(\text{B})=\frac{1}{3}$ and $\text{P}(\text{A}\cap\text{B})=\frac{5}{9},$ then p = __________.
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A matrix which is not a square matrix is called a _________ matrix.
A matrix which is not a square matrix is called a _________ matrix.
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The vectors $\vec{\text{a}}=3\hat{\text{i}}-2\hat{\text{j}}+2\hat{\text{k}}$ and $\vec{\text{b}}=-\hat{\text{i}}-2\hat{\text{k}}$ are the adjacent sides of a parallelogram. The angle between its diagonals is _________.
→The vectors $\vec{\text{a}}=3\hat{\text{i}}-2\hat{\text{j}}+2\hat{\text{k}}$ and $\vec{\text{b}}=-\hat{\text{i}}-2\hat{\text{k}}$ are the adjacent sides of a parallelogram. The angle between its diagonals is _________.
The value of $\int \tan ^2 x d x=$ ____________
→The value of $\sin ^{-1}\left(\cos \frac{33 \pi}{5}\right)$ is. ________
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The solution of differential equation $\cot\text{y dx}=\text{x dy} $ is _________.
→The solution of differential equation $\cot\text{y dx}=\text{x dy} $ is _________.
If $\left[\begin{array}{lll}3 & -2 & 0\end{array}\right]\left[\begin{array}{c}2 \\ k \\ -5\end{array}\right]=0$, then value of $k$ is _________
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If A and B are symmetric matrices of same order, then AB is symmetric if and only if _________.
If A and B are symmetric matrices of same order, then AB is symmetric if and only if _________.
In a classroom, teacher explains the properties of a particular curve by saying that this particular curve has beautiful up and downs. It starts at 1 and heads down until $\pi$ radian, and then heads up again and closely related to sine function and both follow each other, exactly $\frac{\pi}{2}$ radians apart as shown in figure.
Based on the above information, answer the following questions.
→Based on the above information, answer the following questions.
- Name the curve, about which teacher explained in the classroom.
- Cosine
- Sine
- Tangent
- Cotangent
- Area of curve explained in the passage from 0 to $\frac{\pi}{2}$ is.
- $\frac{1}{3}\text{ sq.unit}$
- $\frac{1}{2}\text{ sq.unit}$
- ${1}\text{ sq.unit}$
- ${2}\text{ sq.units}$
- Area of curve discussed in classroom from $\frac{\pi}{2}$ to $\frac{3\pi}{2}$ is.
- -2 sq. units
- 2 sq. units
- 3 sq. units
- -3 sq. units
- Area of curve discussed in classroom from $\frac{3\pi}{2}$ to $2\pi$ is.
- 1 sq. unit
- 2 sq. units
- 3 sq. units
- 4 sq. units
- Area of explained curve from 0 to $2\pi$ is.
- 1 sq. unit
- 2 sq. units
- 3 sq. units
- 4 sq. units
If $P ( B )=0.5$ and $P ( A \cap B )=0.32$ then the value of $P ( A \mid B )$ will be ____________ .
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