Seven balls are drawn simultaneously from bag containing 5 white and 6 green balls. The probability of drawing 3 white and 4 green balls is :

If \(4 \cos x+3 \sin x=5\), then find the value of \(\tan x=\)

If the image of the point \((3,8)\) in the line \(x+3 y=7\) is \((\alpha, \beta)\), then \(\alpha+\beta=\)

Let \(a_0, a_1, a_2, \ldots a_n \in R\) be in an arithmetic progression and let \(C_0, C_1, C_2, \ldots, C_n\) be the binomial coefficients. Then \(\sum_{k=0}^n a_k \cdot C_k=\)

In a city, 10 accidents take place in a span of 50 days.Assuming that the number of accidents follow the Poisson distribution,the probability that three or more accidents occur in a day, is

In triangle \(A B C\), if \(r_1=36, r_2=18\) and \(r_3=12\), then \(a+b=\)

The equation of the locus of a point \((2 \cos \theta-3,3 \sin \theta-4)\) is

If \(E_1\) and \(E_2\) are two events of a random experiment such that \(P\left(E_1\right)=\frac{1}{8}, P\left(E_1 \mid E_2\right)=\frac{1}{3}\), \(P\left(E_2 \mid E_1\right)=\frac{1}{4}\), then match the items of List-I with the items of List-II.
\(\begin{array}{lllc}
\hline & \text { List-I } & & \text { List-II } \\
\hline \text { (A) } & P\left(E_2\right) & \text { I. } & \frac{3}{16} \\
\hline \text { (B) } & P\left(E_1 \cup E_2\right) & \text { II. } & \frac{3}{29} \\
\hline \text { (C) } & P\left(\bar{E}_1 \mid \bar{E}_2\right) & \text { III. } & \frac{3}{32} \\
\hline \text { (D) } & P\left(E_1 \mid \bar{E}_2\right) & \text { IV. } & \frac{26}{29} \\
\hline & & \text { V. } & \frac{13}{32} \\
\hline
\end{array}\)
The correct match is

Let \(a, b, c\) be real numbers. A set formed with \(a, b, c\) whose order of occurrence is preassigned is called

The asymptotes of a hyperbola are parallel to \(2 x+3 y=0\) and \(3 x+2 y=0\). The equation of that hyperbola whose centre is at \((1,2)\) and passing through \((5,3)\) is

If the vectors \(2 \overline{\mathrm{i}}+4 \overline{\mathrm{j}}-3 \overline{\mathrm{k}},-\overline{\mathrm{i}}+2 \overline{\mathrm{j}}+3 \overline{\mathrm{k}}\) and \(\mathrm{p} \overline{\mathrm{i}}-2 \overline{\mathrm{j}}+\overline{\mathrm{k}}\) are coplanar, then the unit vector in the direction of the vector \(9 p \bar{i}-4 \bar{j}+4 \bar{k}\) is

A body of mass \(10 \mathrm{~g}\) is tied to a string of length \(0.4 \mathrm{~m}\) and it is whirled in a horizontal plane with a speed of \(6 \mathrm{~ms}^{-1}\). Then the tension in the string is

If the inverse point of the point \((-1,1)\) with respect to the circle \(x^2+y^2-2 x+2 y-1=0\) is \((p, q)\), then \(p^2+q^2=\)