Mathematics Tes...

How many three- digits numbers are there which are divisible by 9.

The domain of the function \(f(x)=\sqrt{1-\sqrt{1-\sqrt{1-x^{2}}}}\) is:

Statement - 1: If $\frac{1}{5}(1+5p),\frac{1}{3}(1+2p),\frac{1}{3}(1-p)and\frac{1}{5}(1-3p)$ are the probabilities of four mutually exclusive events, then $p$ can take infinite number of values.

Statement - 2: If $A, B, C$ and $D$ are four mutually exclusive events, then $P\left(A\right), P\left(B\right), P\left(C\right), P\left(D\right)\ge 0$ and $P\left(A\right) + P\left(B\right) + P\left(C\right) + P\left(D\right)\le 1$.

If \(a=\lim _{n \rightarrow \infty} \sum_{k=1}^n \frac{2 n}{n^2+k^2}\) and \(f(x)=\sqrt{\frac{1-\cos x}{1+\cos x}}, x \in(0,1)\), then

\(\mathrm{n}(\mathrm{n}+1)(\mathrm{n}+5)\) is a multiple of 3 is true for:

XY-plane divides the line joining the points \(A(2,3,-5)\) and \(B(-1,-2,-3)\) in the ratio:

If \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\), then \(\frac{d y}{d x}=?\)

Find the equation of tangent to the curve \(y=\sqrt{5 x-3}-2\), which is parallel to the line \(4 x-2 y+3=0\)?

The solution of the differential equation \(y d x+\left(x+x^{2} y\right) d y=0\) is: