Mathematics Tes...

Find the equation of the line through the point \((-1,5)\) and making an intercept of \(-2\) on the \(y\)-axis?

Find the mean deviation for the given data is p, 6, 6, 7, 8, 11, 15, 16, if value of mean of the data is 3 times of the ‘p’.

Let \(f: R \rightarrow R\) be defined as \(f(x)=e^{-x} \sin x\). If \(F:[0,1] \rightarrow R\) is a differentiable function, such that \(F(x)=\int_0^x f(t) d t\), then the value of \(\int_0^1\left[F^{\prime}(x)+f(x)\right] e^x d x\) lies in the interval:

If \(5 \times{ }^{{n}} {P}_{4}=7 \times{ }^{({n}-1)} {P}_{4}\), then find the value of \({n}\).

The equation \(\tan ^{-1}(1+x)+\tan ^{-1}(1-x)=\frac{\pi}{2}\) is satisfied by:

Let \(\mathrm{A}\) and \(\mathrm{B}\) be two events such that \(\mathrm{P}(\mathrm{B} \mid \mathrm{A})=\frac{2}{5}, \mathrm{P}(\mathrm{A} \mid \mathrm{B})=\frac{1}{7}\) and \(\mathrm{P}(\mathrm{A} \cap \mathrm{B})=\frac{1}{9} \cdot\) Consider

(S1) \(\mathrm{P}\left(\mathrm{A}^{\prime} \cup \mathrm{B}\right)=\frac{5}{6}\),

(S2) \(\mathrm{P}\left(\mathrm{A}^{\prime} \cap \mathrm{B}^{\prime}\right)=\frac{1}{18}\)

Then

If \(p\) is a natural number, then prove that \(p^{n+1}+(p+1) 2^{n-1}\) is divisible by \(p^{2}+p+1\) for every ________ \(n\).

If \(f(x)=\frac{\left(\tan 1^{\circ}\right) x+\log _e(123)}{x \log _e(1234)-\left(\tan 1^{\circ}\right)}, x>0\), then the least value of \(\mathrm{f}(\mathrm{f}(\mathrm{x}))+\mathrm{f}\left(\mathrm{f}\left(\frac{4}{\mathrm{x}}\right)\right)\) is:

The equation of tangents to the curve \(y\left(1+x^{2}\right)=2-x\), where it crosses \(x\)-axis is: