Let f be defined on [-5,5] as f(x)= l x if x is rational -x if x is irrational . Then f(x) is

As x 0 both x and -x tend to zero, f(0)=0 f(x) is continuous at x=0. For x 0, x -x, f(x) is discontinuous.

Let f be defined on [-5,5] as f(x)= l x if x is rational -x if x …

The solution of the set of constraints of a linear programming problem is a convex (open or closed) is called ______ region.

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The value of $\sin\big(2\big(\tan^{-1}0.75\big)\big)$ is equal to:

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If $u=x^2+y^2$ and $x=s+3 t, y=2 s-t,$ then $\frac{d^2 u}{d s^2}$ is equal to

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If $\text{y}=\text{a}+\text{bx}^2,\text{a,b}$ arbitrary constants, then

$\frac{\text{d}^2\text{y}}{\text{dx}^2}=2\text{xy}$
$\text{x}\frac{\text{d}^2\text{y}}{\text{dx}^2}=\text{y}_1$
$\text{x}\frac{\text{d}^2\text{y}}{\text{dx}^2}-\frac{\text{dy}}{\text{dx}}+\text{y}=0$
$\text{x}\frac{\text{d}^2\text{y}}{\text{dx}^2}=2\text{xy}$

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For the matrix $A=\left[\begin{array}{ccc}2 & -1 & 1 \\ \lambda & 2 & 0 \\ 1 & -2 & 3\end{array}\right]$ to be invertible, the value of $\lambda$ is

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Choose the correct answer from the given four options. On using elementary column operations $C_2 \rightarrow C_2 – 2C_1$ in the following matrix equation $\begin{bmatrix}1&-3\\2&4\end{bmatrix}=\begin{bmatrix}1&-1\\0&1\end{bmatrix}\begin{bmatrix}3&1\\2&4\end{bmatrix},$ we have$:$

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A line makes angles $\alpha, \beta$ and $\gamma$ with the co-ordinate axes. If $\alpha+\beta=90^{\circ}$, then the value of angle $\gamma$ is

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Let $f: R \rightarrow R$ be defined as $f(x)=x^3$. Choose the correct answer.

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For the binary operation * defined on R − {1} by the rule a * b = a + b + ab for all a, b ∈ R − {1}, the inverse of a is:

$-\text{a}$
$-\frac{\text{a}}{\text{a}-1}$
$\frac{1}{\text{a}}$
$\text{a}^2$

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$\cot ^{-1} \frac{\sqrt{1-x^2}}{x}$ equal to :

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Continuity and Differentiability — MATHS STD 12 Science — Question

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