NDA MATHEMATICS QUIZ-4

The probability of seeing 6 at least once in 4 Throws with a single die is.

The term independent of a in the expansion of $\left(\sqrt{\frac{a}{3}}+\frac{3}{2 a^{2}}\right)^{10}$ is:

The derivative of $\sec ^{-1} \frac{1}{\left(2 x^{2}-1\right)}$  with respect to $\sqrt{1-x^{2}}$ at $x=\frac{1}{4}$ will be

If $\frac{1}{1+\log x}, \frac{1}{1+\log y}, \frac{1}{1+\log z}$ are in H.P then $x, y, z$ are in. where $x>1$, $y>1$, $z>1$

The Number of ways in which 12 examination papers be arranged so that the best and the worst paper never come together is:

The shortest distance between the lines $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ and $\frac{x-2}{1}=\frac{y-4}{1}=\frac{z-5}{5}$ is.

Value of the integal $\int_{0}^{\frac{\pi}{2}} \frac{\sin ^{\frac{n}{2}} x}{\sin ^{\frac{n}{2}} x+\cos ^{\frac{n}{2}} x} d x$ will be

If $x^{a} y^{b}=(x+y)^{a+b}$, then $x d y-y d x=k$ where k equals:

$If \log _{\frac{1}{2}} x>\log _{\frac{1}{3}} x$ then

Domain of the function $y=\frac{x}{\sqrt{x^{2}-5 x+6}}$ is