Choose the correct answer from the given four option. The general solution of e^ x -e^x =0 is: 1. e^ x =k 2. e^ x =k 3. e^ x =k 4. e^ x =k

1. e^ x =k Solution: Given is, e^ x -e^x =0 ^ x =e^x dy dx = = On integrating both sides, we get x= +C -C= =e^ x-c 1 = e^x e^c ^ x =k [where,K=e^c]

Choose the correct answer from the given four option. The general…

If from Lagrange's mean value theorem, we have
$\text{f}'(\text{x}_1)=\frac{\text{f}(\text{b})-\text{f}(\text{a})}{\text{b}-\text{a}},$ then:

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If $\frac{\text{dy}}{\text{dx}}=\frac{1}{\text{x}}$ then y =

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If $\text{A} = \displaystyle \left[ \begin{matrix} 1 &\text{amp ; 2} \\ 3&\text{amp; 4} \end{matrix} \right],$ then number of elements in A are:

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The normal to the curve $x^2 = 4y$ passing through $(1, 2)$ is:

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The sine of the angle between the straight line $\frac{\text{x}-2}{3}=\frac{\text{y}-3}{4}=\frac{\text{z}-4}{5}$ and the plane 2x - 2y + z = 5 is:

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If A is any skew-symmetric matrix of odd order then ∣A∣ equals

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Let $\text{f(x)}=|\cos\text{x}|.$ Then,

f(x) is everywhere differentiable.
f(x) is everywhere continuous but not differentiable at $\text{x}=\text{n}\pi,\text{n}\in\text{Z}$
f(x) is everywhere continuous but not differentiable at $\text{x}=(2\text{n}+1)\frac{\pi}{2},\text{n}\in\text{Z}.$
None of these.

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Let A = {x : -1 ≤ x ≤ 1} and f : A → A is a function defined by f(x) = x |x| then f is:

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The equation of tangent to the curve $y (1 + x^2) = 2 - x,$ where it crosses $x-$axis is:

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If $A=\left[\begin{array}{ll}0 & 2 \\ 2 & 0\end{array}\right]$, then $A^2$ is equal to

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