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 ${(\sqrt{\frac{a}{3}}+\frac{3}{2a^2})}^{10}$ is:

The derivative of ${\sec }^{-1}\frac{1}{(2x^2-1)}$  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 ${\int }_0^{\frac{\pi }{2}}\frac{{\sin }^{\frac{n}{2}}x}{{\sin }^{\frac{n}{2}}x+{\cos }^{\frac{n}{2}}x}dx$ will be

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

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

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