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Solution of $\int \sin 3 x d x$ is

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Refer to Question 18 (Maximum value of Z+ Minimum value of Z) is equal to:
  1. 13
  2. 1
  3. -13
  4. -17
If $\text{A}=\begin{bmatrix}1&2&\text{x}\\0&1&0\\0&0&1\end{bmatrix}$ and $\text{B}=\begin{bmatrix}1&-2&\text{y}\\0&1&0\\0&0&1\end{bmatrix}$ and $AB = I_3, $ then $x + y$ equals:
If $\text{x}=2\text{ at},\text{y}=\text{at}^2,$ where a is a constant, then $\frac{\text{d}^2\text{y}}{\text{dx}^2}\text{ at}\ \text{x}=\frac{1}{2}$ is:
  1. $\frac{1}{2}\text{a}$
  2. 1
  3. 2a
  4. None of these
The solution of the differential equation $\frac{\text{dy}}{\text{dx}}-\text{Ky}=0, \text{y}(0)=1$ approaches to zero when $\text{x}\rightarrow\propto$ if,
  1. K = 0
  2. K > 0
  3. K < 0
  4. None of these.
If $\text{y}=\tan^{-1}\Big(\frac{\sin\text{x}+\cos\text{x}}{\cos\text{x}-\sin\text{x}}\Big),$ then $\frac{\text{dy}}{\text{dx}}$ is equals to:
  1. $\frac{1}{2}$
  2. 0
  3. 1
  4. None of these.
If $B$ is a non$-$singular matrix and $A$ is a square matrix, then det $(B^{-1} AB)$ is equal to:
Which of the following transformation reduce the differential quation  into the form $\frac{\text{du}}{\text{dx}}+\text{P}(\text{x})\text{u}=\text{Q}(\text{x})$ into the from $\frac{\text{dz}}{\text{dx}}+\frac{\text{z}}{\text{x}}\log\text{z}=\frac{\text{z}}{\text{x}^{2}}(\log\text{z})^{2}$
  1. $\text{u}=\log\text{x}$
  2. $\text{u}=\text{e}^{\text{z}}$
  3. $\text{u}=(\log\text{z})^{-1}$
  4. $\text{u}=(\log\text{z})^{2}$ 
If the function f : R → A given by $\text{f(x)}=\frac{\text{x}^2}{\text{x}^2+1}$ is a surjection, then A =
  1. R
  2. [0, 1]
  3. [0, 1)
  4. [0, 1)
If $f : R \rightarrow (-1, 1)$ is defined by $\text{f(x)}=\frac{-\text{x}|\text{x}|}{1+\text{x}^2},$ then $f^{-1}(x)$ equals,
Evaluate: $\int 2^{2^{2^x}} 2^{2^x} 2^x d x$