Mathematics Tes...

If \(\alpha, \beta\) are the roots of the equation, \(x^2-x-1=0\) and \(\mathrm{S}_{\mathrm{n}}=2023 \alpha^{\mathrm{n}}+2024 \beta^{\mathrm{n}}\), then

Solve the following LPP by:

Mininize \(z=8 x+10 y\)

Subject to \(2 \mathrm{x}+\mathrm{y} \geq 7,2 \mathrm{x}+3 \mathrm{y} \geq 15, \mathrm{y} \geq 2, \mathrm{x} \geq 0, \mathrm{y} \geq 0\)

If \(f: R \rightarrow R\) and \(g: R \rightarrow R\) are two mappings defined as \(f(x)=2 x\) and \(g(x)=x^{2}+2\), then the value of \((f+g)(2)\) is:

What is the value of \(\lim _{{x} \rightarrow \infty} \frac{{x}^{3}+3 {x}^{2}+6 {x}+5}{{x}^{3}+2 {x}+6}\)?

For the vectors \(\overrightarrow{\mathrm{a}}=-4 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}, \overrightarrow{\mathrm{b}}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}\) and \(\overrightarrow{\mathrm{c}}=2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}},\) if\(\overrightarrow{\mathrm{c}}=\mathrm{m} \overrightarrow{\mathrm{a}}+\mathrm{n} \overrightarrow{\mathrm{b}},\) then the value of \(\mathrm{m}+\mathrm{n}\) is:

The longest period of 3sin x - 4sin³ x is?

The area bounded by \(y=\log x, x\)-axis and ordinates \(x=1, x=2\) is:

If \({ }^{10} {P}_{{r}}=5040\), then \({r}=?\)

If f(x) = tan^-1$\left[\frac{\sin x}{1+\cos x}\right]$, then what is the first derivative of f(x)?

If \(f(x)=\left\{\begin{array}{ll}\frac{\sin 3 x}{e^{2 x}-1}, & x \neq 0 \\ k-2, & x=0\end{array}\right.\) is continuous at \(x=0\), then \(k=\)?