Mathematics Tes...

Find the values of \(k\) for which the length of the perpendicular from the point \((4,1)\) on the line \(3 x-4 y+k=0\) is 2 units?

The number of ways in which 5 boys and 4 girls to sit around a table, so that, all the boys sit together is:

If \(|x|<-5\) then the value of \(x\) lies in the interval:

The tangent to the curve \(y^{2}=16 x\) and touches the curve at a point (1,4). Find the distance of origin from the tangent.

Find the value of \(\cos ^{-1}\left(4 x^3-3 x\right), x \in[-1,1]\).

Find the value of \(\int \frac{\mathrm{dx}}{1+\mathrm{e}^{-\mathrm{x}}}\), where \(c\) is the constant of integration.

If a curve \(y=f(x)\) passes through the point \((1,2)\) and satisfies \(x \frac{d y}{d x}+y=b x^4\), then for what value of \(b, \int_1^2 f(x) d x=\frac{62}{5} ?\)

A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade, is:

Let \(\vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{c}=\hat{j}-\hat{k}\) and a vector \(\vec{b}\) be such that \(\vec{a} \times \vec{b}=\vec{c}\) and \(\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{b}}=3\). Then \(|\overrightarrow{\mathrm{b}}|\) equals?

One of the roots of \(\left|\begin{array}{ccc}x+a & b & c \\ a & x+b & c \\ a & b & x+c\end{array}\right|=0\) is