If | , * 20 c - a^2 & ab & ac ab & - b^2 & bc ac & bc & - c^2 , | = K a^2 b^2 c^2 , then K =

If | , * 20 c - a^2 & ab & ac ab & - b^2 & bc ac & bc & - c^2 , |…

The determinant $\left|\begin{array}{ccc}y+k & y & y \\ y & y+k & y \\ y & y & y+k\end{array}\right|$ is equal to

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Let $f(x + y) = f(x)f(y)$ and $f(x) = 1 + \sin (3x)g(x)$ where $g(x)$ is continuous then $f'(x)$ is

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The transpose of a row matrix is:

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Derivative of ${x^6} + {6^x}$ with respect to $x $ is

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The antiderivative of every odd function is:

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The value of $x$ that maximises the value of the integral $\int\limits_x^{x + 3} {t(5 - t)\,dt}$ is

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Let a vector $\vec{\text{r}}$ make angles 60°, 30° with it and y-axes respectively. Find the angle $\vec{\text{r}}$ make with z-axis:

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If $\left| {\,\begin{array}{*{20}{c}}{x + 1}&3&5\\2&{x + 2}&5\\2&3&{x + 4}\end{array}\,} \right| = 0$, then $ x =$

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If x = – 4 is a root of $\triangle=\begin{bmatrix}\text{x}&2&3\\1&\text{x}&1\\3&2&\text{x}\end{bmatrix}=0,$ then the other roots are:

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The matrix $\begin{bmatrix} 5 & 10 & 3 \\ -2 & -4 & 6 \\ -1 & -2 & \text{b} \end{bmatrix}$ is a singular matrix, if the value of b is:

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