Question
Optimization of the objective function is a process of

Answer

(b)

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If the position vectors of the points A and B are $\vec{a}$ and $\vec{b}$ respectively, then the position vector of the mid-point of the line $A B$ will be :
If $\int\frac{\cos8\text{x}+1}{\tan2\text{x}-\cot2\text{x}}\text{ dx}=\text{a}\cos8\text{x}+\text{C},$ then a =
  1. $-\frac{1}{16}$
  2. $\frac{1}{8}$
  3. $\frac{1}{16}$
  4. $-\frac{1}{8}$
The number of arbitrary constants in the particular solution of a differential equation of third order is:
  1. 3
  2. 2
  3. 1
  4. 0
Choose the correct answer from the given four option.
The differential equation for $\text{y}=\text{A}\cos\alpha\text{x}+\text{B}\sin\alpha\text{x},$ where A and B are arbitrary constants is:
  1. $\frac{\text{d}^2\text{y}}{\text{d}\text{x}^2}-\alpha^2\text{y}=0$
  2. $\frac{\text{d}^2\text{y}}{\text{d}\text{x}^2}+\alpha^2\text{y}=0$
  3. $\frac{\text{d}^2\text{y}}{\text{d}\text{x}^2}+\alpha\text{y}=0$
  4. $\frac{\text{d}^2\text{y}}{\text{d}\text{x}^2}-\alpha\text{y}=0$
Find the maximum value of $f(x)=\sin (\sin x)$ for all $x \in R$.
Find the shortest distance between the given two lines :
$\frac{x+1}{1}=\frac{y+1}{-1}=\frac{z+1}{1}$ and $\frac{x-2}{2}=\frac{y-3}{3}=\frac{z-4}{4}$.
Area of the region between the curves $\text{x}^2+\text{y}^2=\pi,\text{y}=\sin\text{x}$ and y-axis in first quadrant is:
  1. $\frac{\pi^3-8}{4\text{ sq.}\text{ units}}$
  2. $\frac{\pi^3-4}{4\text{ sq.}\text{ units}}$
  3. $\frac{\pi^3-8}{4\text{ sq.}\text{ units}}$
  4. $\frac{\pi^3-4}{4\text{ sq.}\text{ units}}$
The diameter of a circle is increasing at the rate of 1cm/sec. When its radius is $\pi$ the rate of increase of its area is:
  1. $\pi\text{cm}^{2}/\text{sec}.$
  2. $2\pi\text{cm}^{2}/\text{sec}.$
  3. $\pi^{2}\text{cm}^{2}/\text{sec}.$
  4. $2\pi^{2}\text{cm}^{2}/\text{sec}^{2}.$ 
If $\alpha,\beta,\gamma$ are the angles which a directed line makes with the positive directions of the coordinate axes, then $\sin^2\alpha+\sin^2\beta+\sin^2\gamma$ is equal to:
  1. 1
  2. 4
  3. 3
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Choose the correct answer from the given four options.
$A$ and $B$ are two students. Their chances of solving a problem correctly are $\frac{1}{3}$ and $\frac{1}{4},$ respectively. If the probability of their making a common error is, $\frac{1}{20}$ and they obtain the same answer, then the probability of their answer to be correct is: