Question
The value of $\int \sin ^2 x d x$ is ___________
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If A and B are such that $\text{P}(\text{A}'\cup\text{B}')=\frac{2}{3}$ and $\text{P}(\text{A}\cup\text{B})=\frac{5}{9},$ then $\text{P}(\text{A}')+\text{P}(\text{B}')=$ ________.
→If A and B are such that $\text{P}(\text{A}'\cup\text{B}')=\frac{2}{3}$ and $\text{P}(\text{A}\cup\text{B})=\frac{5}{9},$ then $\text{P}(\text{A}')+\text{P}(\text{B}')=$ ________.
Fill in the blanks.
$\frac{\text{dy}}{\text{dx}}+\frac{\text{y}}{\text{x}\log\text{x}}=\frac{1}{\text{x}}$ is an equation of the type _________.
→$\frac{\text{dy}}{\text{dx}}+\frac{\text{y}}{\text{x}\log\text{x}}=\frac{1}{\text{x}}$ is an equation of the type _________.
If $f(x)=\left\{\begin{array}{cc}\frac{\sin ^2 a x}{x^2} & , x \neq 0 \\ 1 & , x=0\end{array}\right.$ is continuous function at _________ .
→Two dice are thrown, the probability of getting the sum of numbers on two dice as 9 will be ___________ .
If A has skew symmetric matrix having order $3 \times 3$, $|A|=$ __________ .
→Those problems in which an attempt is made to discover maximization of profit and minimization of cost are called _________ .
Fill in the blanks:
The value of $\int\limits^\pi_{-\pi}\sin^3\text{x}\cos^2\text{x dx}$ is _______.
→The value of $\int\limits^\pi_{-\pi}\sin^3\text{x}\cos^2\text{x dx}$ is _______.
The numbers $l r, m r$ and $n r$ proportional to direction cosines are called __________ of $\vec{r}$.
→Fill in the blanks:
If A is a matrix of order 3 × 3, then |3A| = _______.
If A is a matrix of order 3 × 3, then |3A| = _______.
A child cut a pizza with a knife. Pizza is circular in shape which is represented by $x^2+y^2=4$ and sharp edge of knife represents a straight line given by $\text{x}=\sqrt{3\text{y}}$ Based on the above information, answer the following questions. 
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- The point(s) of intersection of the edge of knife (line) and pizza shown in the figure is (are).
- $(1, \sqrt{3}),(-1,-\sqrt{3})$
- $(\sqrt{3},1),(-\sqrt{3,}-1)$
- $(\sqrt{2,}0),(0,\sqrt{3})$
- $(-\sqrt{3,}),(1,-\sqrt{3})$
- Which of the following shaded portion represent the smaller area bounded by pizza and edge of knife in first quadrant?
- Value of area of the region bounded by circular pizza and edge of knife in first quadrant is.
- $\frac{\pi}{2}\text{ sq.units}$
- $\frac{\pi}{3}\text{ sq.units}$
- $\frac{\pi}{5}\text{ sq.units}$
- $\pi\text{ sq.units}$
- Area of each slice of pizza when child cut the pizza into $4$ equal pieces is.
- $\pi\text{ sq.units}$
- $\frac{\pi}{2}\text{ sq.units}$
- $3\pi\text{ sq.units}$
- $2\pi\text{ sq.units}$
- Area of whole pizza is.
- $3\pi\text{ sq.units}$
- $2\pi\text{ sq.units}$
- $5\pi\text{ sq.units}$
- $4\pi\text{ sq.units}$