Question
For a binomial variate X, if $\text{n}=3$ and $\text{P(X}=1)=8\text{ P(X = 3}),$ then p =

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The value of $ \left( {{{\tan }^{ - 1}}\pi + {{\tan }^{ - 1}}\left( {\frac{1}{\pi }} \right)} \right) + {\tan ^{ - 1}}\sqrt 3 - {\sec ^{ - 1}}( - 2)$ is equal to
  1. $ \frac{{ - \pi }}{3}$
  2. $ \frac{{ \pi }}{6}$
  3. $ \frac{{ 2 \pi }}{3}$
  4. $ \pi$
The value of the determinant $\left|\begin{array}{ccc}2 & 7 & 1 \\ 1 & 1 & 1 \\ 10 & 8 & 1\end{array}\right|$ is
$\int\limits^\text{e}_1\log\text{x}\text{ dx}=$
  1. 1
  2. e - 1
  3. e + 1
  4. 0
Choose the correct answer from the given four options. On using elementary row operation $R_1 \rightarrow R_1 – 3R_2$ in the following matrix equation $\begin{bmatrix}4&2\\3&3\end{bmatrix}=\begin{bmatrix}1&2\\0&3\end{bmatrix}\begin{bmatrix}2&0\\1&1\end{bmatrix},$ we have:
If $\tan^{-1}(\text{x}-1)+\tan^{-1}\text{x}+\tan^{-1}(\text{x}+1)=\tan^{-1}3\text{x},$ then the values of x are:
  1. $\pm\frac{1}{2}$
  2. $0,\frac{1}{2}$
  3. $0,-\frac{1}{2}$
  4. $0,\pm\frac{1}{2}$
Choose the correct answer from the given four options.The general solution of the differential equation $(\text{e}^{\text{x}}+1)\text{ydy}=(\text{y}+1)\text{e}^{\text{x}}$ is:
  1. $(\text{y}+1)=\text{k}(\text{e}^{\text{x}}+1)$
  2. $\text{y}+1=\text{e}^{\text{x}}+1+\text{k}$
  3. $\text{y}=\log\left\{\text{k}(\text{y}+1)(\text{e}^{\text{x}}+1)\right\}$
  4. $\text{y}=\log\left\{\frac{\text{e}^{\text{x}}+1}{\text{y}+1}\right\}+\text{k}$
The solution set of the inequation 3x + 2y > 3 is:
$\int\frac{2}{(\text{e}^{\text{x}}+\text{e}^{-\text{x}})^2}\text{ dx}=$
  1. $\frac{-\text{e}^{-\text{x}}}{\text{e}^{\text{x}}+\text{e}^{-\text{x}}}+\text{C}$
  2. $-\frac{1}{\text{e}^{\text{x}}+\text{e}^{-\text{x}}}+\text{C}$
  3. $\frac{-1}{(\text{e}^{\text{x}}+1)^2}+\text{C}$
  4. $\frac{1}{\text{e}^{\text{x}}-\text{e}^{-\text{x}}}+\text{C}$
The maximum value of Z = 4x + 3y subjected to the constraints $2\text{x}+3\text{y}\leq18,$ $\text{x}+\text{y}\geq10;\text{x},\text{y}\geq0$ is:
  1. 36
  2. 40
  3. 20
  4. None of these
The straigth line $\frac{\text{x}-3}{3}=\frac{\text{y}-2}{1}=\frac{\text{z}-1}{0}$ is:
  1. parallel to x-axis
  2. parallel to y-axis
  3. parallel to z-axis
  4. perpendicular to z-axis