Question
The linear inequalities or equations or restrictions on the variables of a linear programming problem are called:

Answer

  1. A constraint

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If $\begin{bmatrix} 1 & -\tan\theta \\ \tan\theta & 1 \end{bmatrix}\begin{bmatrix} 1 & \tan\theta \\ -\tan\theta & 1 \end{bmatrix}-1=\begin{bmatrix} \text{a} & -\text{b} \\ \text{b} & \text{a} \end{bmatrix},$ then:
  1. $\text{a}=1,\text{b}=1$
  2. $\text{a}=\cos2\theta,\text{b}=\sin2\theta$
  3. $\text{a}=\sin2\theta,\text{b}=\cos2\theta$
  4. None of these.
The order and degree of the differential equation, $\frac{\text{d}^2\text{y}}{\text{dx}^2}+\Big(\frac{\text{dy}}{\text{dx}}\Big)^{\frac{1}{4}}+\text{x}^{\frac{1}{5}}=0$ respectively are:
  1. 2 and not defined
  2. 2 and 2
  3. 2 and 3
  4. 3 and 3
 
Choose the correct answer from the given four options.The order and degree of the differential equation $\Big[1+\Big(\frac{\text{dy}}{\text{dx}}\Big)^2\Big]=\frac{\text{d}^2\text{y}}{\text{d}\text{x}^2}$ are:
  1. $2,\frac{3}{2}$
  2. 2, 3
  3. 2, 1
  4. 3, 4
The feasible solution for a LPP is shown in the following figure. Let Z = 3x - 4y be the objective function.
Minimum of Z occurs at:
If the matrix AB is zero, then:
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  2. A = 0 or B = 0
  3. A = 0 and B = 0
  4. All the above statements are wrong
$\int\limits^1_0\sqrt{\text{x}(1-\text{x})}\text{ dx}$ equals:
  1. $\frac{\pi}{2}$
  2. $\frac{\pi}{4}$
  3. $\frac{\pi}{6}$
  4. $\frac{\pi}{8}$
If $\text{A} = \begin{bmatrix} 2 &\text{amp; } 3\\ 6 &\text{amp; x} \end{bmatrix}, \text{B} = \begin{bmatrix} 2 &\text{amp; 3}\\ \text{p} &\text{amp; }2 \end{bmatrix}$ and $\text{A} = \text{B}, $ then$\text{p}$ and $ \text{x} $ are:
  1. p = 6, x = 4
  2. p = 3, x = 4
  3. p = 4, x = 3
  4. p = 6, x = 2
Choose the correct answer from the given four options.Eight coins are tossed together. The probability of getting exactly 3 heads is:
$\frac{d}{d x}\left[\sin ^{-1} x-\sin ^{-1} \sqrt{x}\right]$ is equal to
If $f(x)=\frac{1-\cos x}{x^2}$, is continuous at $x=0$, then $f(0)$ equals to: