A pair of fair dice is thrown independently three times. The probability of getting a score of exactly 9 twice is

If ${\sin }^{-1}\left(\frac{x}{5}\right)+\cos e{c}^{-1}\left(\frac{5}{4}\right)=\frac{\pi }{2}$ then the value of x is:

In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then the common ratio of this progression equals

The differential equation of all circles passing through the origin and having their centres on the x-axis is

Let L be the line of intersection of the planes $2x+3y+z=1$ and $x+3y+2z=2$. If L makes an angles $\alpha$with the positive x-axis, then cos$\alpha$ equals

The set $S=\left\{1,2,3,,12\right)$is to be partitioned into three sets A, B, C of equal size. Thus, $A\cup B\cup C=S,A\cap B=B\cap C=A\cap C=\phi$. The number of ways to partition S is

Consider a family of circles which are passing through the point $\left(-1,1\right)$and are tangent to x-axis. If (h, k) are the co-ordinates of the centre of the circles, then the set of values of k is given by the interval

The largest interval lying in $\left(-\frac{\pi }{2},\frac{\pi }{2}\right)$for which the function \displaystyle{\left[{f{{\left({x}\right)}}}={4}^{{-{{x}}}}^{2}+{{\cos}^{{-{1}}}{\left(\frac{{x}}{{2}}-{1}\right)}}+{\log{{\left({\cos{{x}}}\right)}}}\right]} is defined, is

If p and q are positive real numbers such that $p^2+q^2=1$, then the maximum value of $\left(p+q\right)$ is

Two aeroplanes I and II bomb a target in succession. The probabilities of I and II scoring a hit correctly are 0.3 and 0.2, respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane is