If ,  where  , then α -β is equal to :
 

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)

Let  S _k be the sum of an infinite GP series whose first term k is k and common  ratio is k/(k + 1) (k> 0). Then, the value of

1) log_e 4
2) log_e 2 – 1
3) 1 - log_e 2
4) 1 - log_e 4

The converse of "If in a triangle ABC,AB=AC, then ∠B=∠C", is

1) lf in a triangle $$ABC, \angle B\neq\angle C$$, then $$AB\neq AC$$.

2) lf in a triangle$$ABC, AB\neq AC$$, then $$\angle B\neq\angle C$$.

3) lf in a triangle $$ABC, \angle B=\angle C$$, then $$AB=AC$$

4) lf in a triangle $$ABC, \angle B\neq\angle C$$, then $$AB=AC$$ .

A room has three electric lamps. From a collection of 10 electric bulbs of which 6 are good 3 are selected at random & put in the lamps. Find the probability that the room is lighted

1)$$\displaystyle \frac {29}{30}$$

2)$$\displaystyle \frac {1}{30}$$

3)$$\displaystyle \frac {23}{30}$$

4)$$\displaystyle \frac {7}{30}$$

If ax²  + 2hxy + by²   = 1, then d²y/ dx2  is equal to

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

In a family the husband tells a lie in $$30\%$$ and the wife in $$35\%$$ cases. Find the probability that both contradict each other.

1) $$ = 34\% $$
2) $$ = 44\% $$
3) $$ = 25\% $$
4) $$ = 35\% $$

The locus represented by the complex equation $$ \left| z-2-i \right|=\left| z \right|\,sin\left( \cfrac{\pi }{4}-\arg z \right) $$ is the part of

1) A circle
2) A parabola
3) A pair of straight lines
4) A rectangle hyperbola

?ABC is right angled at B. BD is an altitude. AD=3cm and DC=9cm. What is the value of AB (in cm)?

1) 6

2) 5

3) 4.5

4) 5.5