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A bag X contains 4 white balls and 2 black balls, while another bag Y contains 3 white balls and 3 black balls. Two balls are drawn (without replacement) at random from one of the bags and were found to be one white and one black. Find the probability that balls were drawn from bag Y.

OR A and B throw a pair of dice alternatively, till one of them gets a total of 10 and wins the game, Find their respective probabilities of winning, if A starts first.

A manufacturer make two types of toys A and B. Three machines are needed for this purpose and the time (in minutes) required for each toy on the machines is given below.
$\begin{array}{cccc}Types& & Machines& \\ & I& II& III\\ A& 12& 18& 6\\ B& 6& 0& 9\end{array}$
Each machine is available for a maximum of 6 h per day. If the profit on each toy of type A is Rs.7.50 and that the each toy of type B is Rs. 5, show that 15 toys of type A and 30 of type B should be manufactured in a day to get maximum profit.

The value of the integral $\underset{-2}{\overset{2}{\int }}\left(\right[x]+\log \left(\frac{1+x}{1-x}\right)+\sin \left(\log \left(\frac{2+x}{2-x}\right)\right)+x^{2011})dx$ is

(where [.] denotes greatest integer function)

Show that the matrix B' AB is symmetric or skew-symmetric according to A which is symmetric or skew -symmetric.

Find
the 13^th
term in the expansion of.

If $x=2+2^{2/3}+2^{1/3}$, then the value of $x^3-6x^2+6x$ is

Locus of mid points of normal chords of the parabola $y^2=4ax$ is :

Solve the following system of inequalities graphically: x ≥ 3, y ≥ 2

Out of the given equations, is not a quadratic equation.

Solution of the differential equation $2xy\frac{dy}{dx}=x^2+3y^2$ is :

(where $c$ is integration constant)

The solution of the differential equation x dx + y dy = 0 is:

What is the least value of x possible if -1 < x ≤ 1 and x is a real number?

Let $A$ be a non-empty set such that $A\times A$ has $16$ elements among which three elements are found to be $(a,b),(b,c)$ and $(c,d)$ and $I_A$ be the identity relation on $A,$ then

Let $\overrightarrow{a}=i+2j+3k$ if $\overrightarrow{b}$ is a vector such that $\overrightarrow{a},\overrightarrow{b}=|\overrightarrow{b}|$ and $|\overrightarrow{a}-\overrightarrow{b}|=\sqrt{7}$, then $|\overrightarrow{b}|=$ ____________

Find the discriminant for the quadratic equation represented by $\left(\frac{m+n}{2}\right)x^2+(m+n)x+\left(\frac{m+n}{2}\right)=0$ and determine the nature of roots. $(m,n>0)$

If $A=\left\{\right(x,y):x^2+y^2\le 1;x,y\in R\}$ and $B=\left\{\right(x,y):x^2+y^2\ge 4;x,y\in R\}$, then

Let $A=\{a,b,c,d,e\}$ and $B=\{1,2,3,4,5\}$. The number of relations which are not functions from $A$ to $B$ is

A function F(A,B,C) defined by three Boolean variables A, B and C when expressed as sum of products is given by

$F=\overline{A}.\overline{B}.\overline{C}+\overline{A}.B.\overline{C}+A.\overline{B}.\overline{C}$

where, $\overline{A},\overline{B},and\overline{C}$ are the complements of the respective variables. The product of sums (POS) form of the function F is

If $1,z_1,z_2,z_3,\cdots z_{n-1}$ are $n$ roots of unity, then the value of $\frac{1}{3-z_1}+\frac{1}{3-z_2}+\cdots +\frac{1}{3-z_{n-1}}$ is equal to :

If$f\left(x\right)=\frac{\alpha x}{x+1},x\ne -1$ then , for what value of $\alpha$ is $f\left(f\right(x\left)\right)=x$

Find the range of $x\in (0,4\pi )$

for which $\tan x\ge 0?$

A man starts repaying a
loan as first installment of Rs. 100. If he increases the installment
by Rs 5 every month, what amount he will pay in the 30^th
installment?

Solve the inequality

If $\int \frac{(1-\cos \theta {)}^{\frac{2}{7}}}{(1+\cos \theta {)}^{\frac{9}{7}}}d\theta =A{\left(\tan \frac{\theta }{2}\right)}^B+C,$ then $AB$ is equal to

What is the period of f(x)= 2tanx +3 ?

The value of the integral $\underset{0}{\overset{\frac{\pi }{2}}{\int }}\frac{3\sqrt{\cos \theta }}{{(\sqrt{\cos \theta }+\sqrt{\sin \theta })}^5}d\theta$ equals to

The value of $2\cos \frac{\pi }{13}\cos \frac{9\pi }{13}+\cos \frac{3\pi }{13}+\cos \frac{5\pi }{13}$ is

If the power of point $(1,-2)$ with respect to $x^2+y^2=1$ is equal to the radius of a circle and $(3,2)$ is the centre of that circle, then the equation of that circle is

1. 6

1. 0.0988

Solve the equation

If $p\left(x\right)=x^2-4x+3$, then the value of $p\left(2\right)+p\left(1\right)$ is.