Question
The value of $\int \sec ^2(2 x+1) d x$ is

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If $\text{y}=\log\sqrt{\tan\text{x}},$ then the value of $\frac{\text{dy}}{\text{dx}}$ at $\text{x}=\frac{\pi}{4}$ is givne by:
  1. $\infty$
  2. $1$
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  4. $\frac{1}{2}$
Evaluate $\begin{bmatrix}8\text{x}+1&2\text{x}-2\\\text{x}^2-1&3\text{x}+5\end{bmatrix}$ is:
If $A = [a_{ij}]$ is a square matrix of even order such that $a_{ij} = i^2 - j^2,$ then
The area bounded by the curve $\text{y}=\sec^2\text{x},\text{y}$ and $\text{x}=\frac{\pi}{3}$ is:
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  2. $\sqrt{2}\text{ sq.}\text{ units}$
  3. $2\sqrt{3}\text{ sq.}\text{ units}$
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The distance of the plane through the intersection of the planes ax + by + cz +d = 0 and lx + my + nz + P = 0 and parallel to the line y = 0, z = 0
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The area bounded by the curve $\text{y}=\sin\text{x}$ between the ordinates $\text{x}=0,\text{x}=\pi$ and the x-axis is:
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If $\left[\begin{array}{cc}2 x+y & 4 x \\ 5 x-7 & 4 x\end{array}\right]=\left[\begin{array}{cc}7 & 7 y-13 \\ y & x+6\end{array}\right]$, then the values of $x, y$ respectively are
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