Mathematics Tes...

Let P(3,3) be a point on the hyperbola, \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\). If the normal to it at P intersects the x-axis at (9,0) and e is its eccentricity, then the ordered pair (a²,e²) is equal to :

There are 20 cricket players, out of which 5 players can bowl. In how many ways can a team of 11 players be selected so, to include 4 bowlers?

Solve: |x – 1| ≤ 5, |x| ≥ 2

If \(\sec ^{2} \theta+\tan ^{2} \theta=3\) then find the value of \(\cot \theta\).

If \(\mathrm{f}(\mathrm{x}), \mathrm{g}(\mathrm{x})\) be twice differential functions on \([0,~2]\) satisfying \(\mathrm{f}^{\prime \prime}(\mathrm{x})=\mathrm{g}^{\prime \prime}(\mathrm{x}), \mathrm{f}^{\prime}(1)\) \(=2 g^{\prime}(1)=4\) and \(f(2)=3 g(2)=9,\) then:

Let the image of the point \((1,0,7)\) in the line \(\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}\) be the point \((\alpha, \beta, \gamma)\). Then which one of the following points lies on the line passing through \((\alpha, \beta, \gamma)\) and making angles \(\frac{2 \pi}{3}\) and \(\frac{3 \pi}{4}\) with \(\mathrm{y}\)-axis and \(\mathrm{z}\)-axis respectively and an acute angle with \(\mathrm{x}\)-axis?

The value of \(\sin ^{-1}\left(\frac{4}{5}\right)-\sin ^{-1}\left(\frac{3}{5}\right)\) is equal to:

Find the standard deviation of the given set: \(\{12,15,16,14,18\}\)

The value of \(\left|\begin{array}{ccc}a & b & c \\ b+c & c+a & a+b \\ a^{2} & b^{2} & c^{2}\end{array}\right|\) is: