Question
The direction cosines of vector $\hat{i}+\hat{j}+\hat{k}$ will be ___________ .
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Answer
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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.
- $3\pi\text{ sq.units}$
- $2\pi\text{ sq.units}$
- $5\pi\text{ sq.units}$
- $4\pi\text{ sq.units}$
The values of a for which the function f(x) = sinx - ax + b increases on R are ______.
In the first quadrant the area of the region bounded by the circle $x^2+y^2=(2)^2$ and lines $x=0, x=2$ will be ___________ .
→The area of the region bounded by the curve $x=\phi(y)$, $y$-axis and abscissae $y=c$ and $y=d$ will be ______________ .
→Fill in the blank.
The value of $\cos(\sin^{-1}\text{x}+\cos^{-1}\text{x}),$ where $|\text{x}|\leq1,$ is ______.
→The value of $\cos(\sin^{-1}\text{x}+\cos^{-1}\text{x}),$ where $|\text{x}|\leq1,$ is ______.
Fill in the blanks.
Let X be a random variable taking values $x_1, x_2, ......, x_n$ with probabilities $p_1, p_2, ..., p_n$, respectively. Then var (X) = ________.
→Let X be a random variable taking values $x_1, x_2, ......, x_n$ with probabilities $p_1, p_2, ..., p_n$, respectively. Then var (X) = ________.
If $\vec{a}=2 \hat{i}+\hat{j}+3 \hat{k}$ and $\vec{b}=3 \hat{i}+5 \hat{j}-2 \hat{k}$, then the value of $|\vec{a} \times \vec{b}|$ will be ___________ .
→The value of $\cos ^{-1}\left\{\sin \left(\cos ^{-1} \frac{1}{2}\right)\right\}$ is. _________
→The maximum value of function $f(x)=\sin x+\cos x$ is _________ .
→The position vectors of two points A and B are $\overrightarrow{\text{OA}}=2\hat{\text{i}}-\hat{\text{j}}-\hat{\text{k}}$ and $\overrightarrow{\text{OB}}=2\hat{\text{i}}-\hat{\text{j}}-2\hat{\text{k}},$ respectively. The position vector of a point P which divides the line segment joining A and B in the ratio 2 : 1 is ___________.
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