Question
Given an arbitrary equivalence relation $R$ is an arbitrary set $X , R$ divides X into mutually disjoint subsets $A _i$ called _________ of X .
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The value of $\sec ^2\left(\tan ^{-1} 2\right)+\operatorname{cosec}^2\left(\cot ^{-1} 3\right)$ is _______
→The value of $\int \cot x d x=$ ____________
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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 _________.
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If A is invertible matrix of order $3 × 3,$ then $|A^{-1}| \_\_\_\_\_\_\_ .$
→If A is invertible matrix of order $3 × 3,$ then $|A^{-1}| \_\_\_\_\_\_\_ .$
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If x = -9 is a root of $\begin{vmatrix}\text{x}&3&7\\2&\text{x}&2\\7&6&\text{x}\end{vmatrix}=0,$ then other two roots are __________.
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The general solution of the differential equation $\frac{d y}{d x}=\frac{1+y^2}{1+x^2}$ will be ___________ .
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$\begin{vmatrix}0&\text{xyz}&\text{x}-\text{z}\\\text{y}-\text{x}&0&\text{y}-\text{z}\\\text{z}-\text{x}&\text{z}-\text{y}&0\end{vmatrix}=$ ________.
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If $\text{f(x)}=|\cos\text{x}|,$ then $\text{f}'\Big(\frac{\pi}{4}\Big)=$ _______.
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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