MATHS II (A)

Time: 3 hrs Max. marks: 75

I Answer all questions

1) Z=(cos, sin) find (Z-)2) If (3 + )100=299(a+ib) show a2+b2=4

3) Find all values of (3 + )4) Find the quadratic equation whose roots are -35i

5) are roots of 10+ 6 8find + + 6) nP7=42np5 find n.7) Find the number ways selecting 3 girls and 3 boys out of 7 girls and 6 boys.8) 22c8 is the largest binomial co-efficient 11th expansion of (1+x)22 find the value of 13c89) The variance of 20 observations is 5. If each of the observation is multiplied by 2. Find the

variance of the resulting observation.

10) If the mean and variance of a binomial variable x are 2.4 and 1.44 respectively find P(1

Find the probability of the problem being solved if both of them try independently.

16) A problem in calicoes is given to two statements a, and b whose chances of solving are

into partial functions.)(( ) 15) Resolve

without separators.

14) Find the sum of all 4 digited numbers that can be formed using the digits 1,2,3,4,5,6 ii) Persons of same rationality sit togetheri) All Indians sit together so that

13) Find the number of ways seating 5 Indians ,4 Americans and 3 Russians at a round table do not lies between 5 and 9.

12) If x is the real show that the values of the expression4+3i,2+5i,3i are vertices a square..

11) Show that four points in argand plane represented by the complex numbers 2+i,

II Answer any FIVE of the following 5x4=10

P(A),P(B),P(C) 17) A ,B and c are independent events such that P(ABC)= , P(ABC)= ,P(ABC)= find

manabadi.com is not responsible for any inadvertent error that may have crept in the guess paper being published on NET. Theguess paper published on net is for the information to the examines. this does not constitute to be a Main Question paper andshould NOT follow the same. While all efforts have been made to make the guess paper available on this website as authentic aspossible. manabadi or any staff persons will not be responsible for any loss to persons caused by any shortcoming, defect or

inaccuracy in the Guess papers provided by Manabadi.com website.

III Answer any FIVE of the following

18) Show that one value of = -119) Solve 4 + 3 162 4 + 48 = 0given that product of two roots is 620) If =..+ ....+ ......+ p.t 9x2+2x=1121) If the co-efficient of 4 consecutive terms of expansion of (1+X)n are a1,a2,a3,a4

respectively, then show that + = 22) Find the mean deviation about the median for the following continuous distribution.

Class interval

0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80

Frequency 5 8 7 12 28 20 10 10

23) Define conditional probability, state and prove multiplication theorem on probability.24) A random variable x has the following probability distribution

X=x 0 1 2 3 4 5 6 7

P(X=x) 0 K 2k 2k 3k K2 2k2 7k2+K

Find i) K ii) the mean of x iii) P (0