In this Question

If the length of sub-normal at any point P(x, y) on the curve passing through M(0, 1) is unity, then the area bounded by the curves equals

1) 1/3
2) 2/3
3) 4/3
4) 8/3 

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)

 If the two circles x² + 2y² - 2x + 22y + 5 = 0 and x² + y² + 14x + 6y + k = 0 intersect orthogonally, then k is equal to

1) -49
2) – 47
3) 49
4) 47

If a and b be the roots of the equation x² - 2x + 2 = 0, then the least value of n for which 
$$\left(\frac{\alpha}{\beta}\right)^{n}=1$$  is

1) 5
2) 2
3) 4
4) 3

An urn contain 20 tickets numbered 1 to 20. A ticket is drawn and then another ticket is drawn without replacement. The probability that both the tickets show even number is

1) 9/38
2) 1/8
3) 1/4
4) 5/8 

Let f(x) be a polynomial function of second degree.If f(1)=f(−1) and  a,b,c are in A.P f′(a),f′(b),f′(c) are in 

1) G.P.
2) H.P.
3) A.G.P
4) A.P.

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 $$AB=AC$$ .

For a biased die the probabilities for different faces to turn up are given below: The die is tossed and you are told that either face 1 or 2 has turned up. Then the probability that it is face 1 is .....

1) $$\displaystyle \frac{5}{42}$$
2) $$\displaystyle \frac{16}{21}$$
3) $$\displaystyle \frac{5}{21}$$
4) $$\displaystyle \frac{16}{42}$$

In a college, 25% boys and 10% girls offer mathematics. There are 60% girls in the college. If a Mathematics student is chosen at random, then the probability that the student is a girl, will be

1) 1/6
2) 3/8
3) 5/8
4) 5/6