Mathematics Tes...

What is the area bounded by \(y=\tan x, y=0\) and \(x=\frac{\pi}{4}?\)

What is the distance of the point whose position vector is \(2 \vec{i}-\vec{j}-3 \vec{k}\) from the plane \(\vec{r} \cdot(\vec{i}+2 \vec{j}-4 \vec{k})=9\)?

If \(\lambda\) be the ratio of the roots of the quadratic equation in \(x\), \(3 m^2 x^2+m(m-4) x+2=0\), then the least value of \(m\) for which \(\lambda+\frac{1}{\lambda}=1\), is:

The relation 'has the same father as' over the set of children is:

The value of \(2 \tan ^{-1}\left[\operatorname{cosec}\left(\tan ^{-1} x\right)-\tan \left(\cot ^{-1} x\right)\right]\) is:

Which of the following is true regarding the function \(f(x)=\log (\sin x)\)?

The coordinate of foot of perpendicular drawn from the point \(A(1,0,3)\) to the join of the point \(B(4,7,1)\) and \(C(3,5,3)\) are:

If the shortest distance between the lines \(\frac{x-4}{1}=\frac{y+1}{2}=\frac{z}{-3}\) and \(\frac{x-\lambda}{2}=\frac{y+1}{4}=\frac{z-2}{-5}\) is \(\frac{6}{\sqrt{5}}\), then the sum of all possible values of \(\lambda\) is :