For the following questions answer them individually
Let z be a complex number such that |z - 6| = 5 and |z + 2 - 6i| = 5. Then the value of $$z^{3}+3z^{2}-15z+141$$ is equal to
If $$g(x)=3x^{2}+2x-3, f(0)=-3$$ and $$4g(f(x))=3x^{2}-32x+72$$, then f(g(2)) is equal to:
If the distances of the point (1 , 2, a) from the line $$\frac{x-1}{1}=\frac{y}{2}=\frac{z-1}{1}$$ along the lines $$L_{1}:\frac{x-1}{3}=\frac{y-2}{4}=\frac{z-a}{b}$$ and $$L_{2}:\frac{x-1}{1}=\frac{y-2}{4}=\frac{z-a}{c}$$ are equal, then a + b + c is equal to
The area of the region $$R=\left\{(x,y):xy\leq 8,1\leq y\leq x^{2},x\geq 0\right\}$$ is
A bag contains 1O balls out of which k are red and (10 - k) are black, where $$0\leq k\leq 10$$. If three balls are drawn at random without replacement and all of them are found to be black, then the probability that the bag contains 1 red and 9 black balls is:
Let ABC be an equilateral triangle with orthocenter at the origin and the side BC on the line $$x+2\sqrt{2}y=4$$. If the co-ordinates of the vertex A are $$(\alpha, \beta)$$, then the greatest integer less than or equal to $$|\alpha + \sqrt{5}\beta |$$ is
Let S = { l, 2, 3, 4, 5, 6, 7, 8, 9}. Let x be the number of 9-digit numbers formed using the digits of the set S such that only one digit is repeated and it is repeated exactly twice. Let y be the number of 9-digit numbers formed using the digits of the set S such that only two digits are repeated and each of these is repeated exactly twice. Then,
Let $$y=y(x)$$ be the solution of the differential equation $$x\frac{dy}{dx}-\sin 2y=x^{3}\left(2-x^{3}\right)\cos^{2}y,y\neq 0$$. If y(2) = 0, then tan(y(l)) is equal to
If $$\frac{\tan (A-B)}{\tan A}+\frac{\sin^{2}C}{\sin^{2}A}=1,A,B,C \in \left(0,\frac{\pi}{2}\right)$$, Then
If $$\int_{}^{}\left(\frac{1-5\cos^{2} x}{\sin^{5} x \cos^{2} x}\right)dx=f(x)+C$$, where C is the constant of integration, then $$f\left(\frac{\pi}{6}\right)-f\left(\frac{\pi}{4}\right)$$ is equal to
