For any two vectors a and b write the value of ( a . b )^2+

( a . b )^2+ | a b |^2 = (| a | | b | )^2+ (| a | | b | )^2 =| a |^2 | b |^2 ( ^2 + ^2 ) =| a |^2 | b |^2 (1) =| a |^2 | b |^2

Write the general equation of a plane parallel to X-axis.

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Write the domain of the relation $R$ defined on the set $Z$ of integers as follows$: (a, b) \in R ⇔ a^2 + b^2 = 25$

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If f'(1) = 2 and $\text{y}=\text{f}(\log_\text{e}\text{x}),$ find $\frac{\text{d}}{\text{dx}}\text{at x}=\text{e}.$

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If $f : R \rightarrow R, g : R \rightarrow R$ are given by $f(x) = (x + 1)^2$ and $g(x) = x^2 + 1,$ then write the value of $fog \ (-3).$

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Find the principal values:
$\text{cosec}^{-1}(2)$

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Let $A = \left[\begin{array}{ccc} {1} & {2} & {1} \\ {2} & {3} & {1} \\ {1} & {1} & {5} \end{array}\right]$. verify that $(A^{–1})^{–1} = A$

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Examine the following functions for continuity.
$f(x) = \frac{1}{\text{x}-5}$

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Show that the vector $\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}}$ is equally inclined with the axes OX, OY and OZ.

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Write rthe value of the determinant $\begin{vmatrix}\text{p}&\text{p}+1\\\text{p}-1&\text{p}\ \end{vmatrix}$

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Differentiate the function $\cos \left( {a\cos x + b\sin x} \right)$ w.r.t x for some constant a and b.

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Answer