If the both the root of the quadratic equation χ² - 2kχ + k² + k - 5 = 0 are less than 5, then k lies in the interval

1) (4, 5)
2) (- ∞, 4)
3) (6, ∞)
4) (5, 6)

The value of cot (cosec^-1 5/3 + tan^-1 2/3) is

1) 4/17
2) 5/17
3) 6/17
4) 3/17

The number of ways in which 52 cards can be divided into 4 sets, three of them having 17 cards each and the fourth one having just one card

1) $$\dfrac {52!}{(17!)^3}$$
2) $$\dfrac {52!}{(17!)^33!}$$
3) $$\dfrac {51!}{(17!)^3}$$
4) $$\dfrac {51!}{(17!)^33!}$$

The shortest distance between the line y = x and the curve y² = x - 2 is :

The equation |z+1−i|=|z−1+i| represents a
1) straight line
2) circle
3) parabola
4) hyperbola

If the functions f(x)=sin(x+a) and g(x)=bsinx+ccosx satisfy f(0)=g(0) and f′(0)=g′(0) then

1) b=π / 2?
2) b=cosa
3) c=sina
4) c=cosa

Let f (x) =    and g (x) be the inverse of f(x), then which one of the following holds good?

1) 2g'' = g2 
2) 2g'' = 3g²
3) 3g'' = 2g²
4) 3g'' = g²

An aircraft gun can take a maximum of four shots at an enemys plane moving away from it. The probability of hitting the plane at first, second, third & fourth shots are $$0.4, 0.3, 0.2$$ & $$0.1$$ respectively. What is the probability that the gun hits the plane?

1) $$0.6976$$
2) $$0.64$$
3) $$0.775$$
4) none of these

If m₁ , m₂ , m₃ and m₄ respectively denote the moduli of the complex numbers 1 + 4i, 3 + i,1- i and 2 - 3i , then the correct one, among the following is
1)  m₁ < m₂ < m₃ < m₄
2) m₄ < m₃ < m₂ < m₁
3) m₃ < m₂ < m₄ < m₁
4) m₃ < m₁ < m₂ < m₄

$$A$$ and $$B$$ are two events where $$P(A) = 0.25$$ and $$P(B) = 0.5$$. The probability of both happening together is $$0.14$$. The probability of both $$A$$ and $$B$$ not happening is

1) $$\displaystyle 0.39$$
2) $$\displaystyle 0.25$$
3) $$\displaystyle 0.11$$
4) none of these