When a + b + c = 0, then the quadratic equation $3ax^{2}+2bx+c=0$ has :
1). Imaginary roots
2). At least one root in [0, 1]
3). One root in [-2,-1] and other root in [2, 3]
4). One root in [-2, -1] and other root in [1, 2]
If $ f(z)=(x^{2}+axy+by^{2})+i(cx^{2}+dxy+y^{2})$ is an analytic function of z. then the values of a, b, c and d are :
1). a = 2, b = -1, c = -1, d = 4
2). a = -2, b = 1, c = -1, d = 2
3). a = 2, b = 1, c = -1, d = -2
4). a = 2, b = -1, c = -1, d = 2
The polar form ot the complex number $\left(\frac{2+i}{3-i}\right)^{2}$ is :
1). $\frac{1}{2}\left(cos \frac{\pi}{4}-i sin\frac{\pi}{4}\right)$
2). $\frac{1}{2}\left(cos \frac{\pi}{2}-i sin\frac{\pi}{2}\right)$
3). $\frac{1}{2}\left(cos \frac{\pi}{4}+i sin\frac{\pi}{4}\right)$
4). $\frac{1}{2}\left(cos \frac{\pi}{2}+i sin\frac{\pi}{2}\right)$
The number of permutations can be made out of the letters word “COMPUTER" as :
1). 720
2). 10,080
3). 5,040
4). 40,320
If A and B are mutually exclusive events such that P(A) = 0.29 and P(B) = 0.43. then $P(A\cap\overline{B})$ is equal to:
1). 0.29
2). 0.85
3). 0.50
4). 0.37