Q1. The Eigen values and the corresponding Eigen vectors of a 2 × 2 matrix is given by: Eigen values 1, 2; Eigen vectors

Q2. Let A = [2a_ij], 1 ≤ i & j ≤ n with n ≥ 3 and a_ij = ij/2. Then the rank of A is -

Q3. If

the top row of A^-1 is

Q4. In a game of chess, in how many ways can a pawn initially at a3 can reach e8.

Q5. The probability that Indian Women Cricket Team winning the next game after losing the previous one is 0.8 and the probability of losing the next game after winning the previous one is 0.2. In a 7 matches ODI Series,what is the probability that India wins the 7^th game given that India won the first three games.(We are supposed to assume that in all matches India either win or lose.)

Q6. In two fair coins care flipped and atleast one of the outcomes is known to be tail, what is the probability that other outcome is tail?

Q7. Production of sugar in a sugar company for each year is given below

(in metric tonnes)

The production for the year 1975 will be -

Q8. The values of a function f (x) are tabulated below

  x  :  0 1 2 3
f (x) : 1 2 1 9

Degree of the given function f(x) is -

Q9. The complete solution of

d²y/dx² + y = cos x

is -

Q10. The general solution of the equation

d⁴y/dx⁴ - 6d³y/dx³ + 12d²y/dx² - 8dx/dy = 0 is

Q11. Solution of the equation

d³y/dx³ + y = 0 is

Q12. The integral

lim    ₀∫^ax^-3dx
a→∞

Q13.

₀∫⁶₀∫^x₁∫^√(x+y)zdxdydz is

Q14. Divide 24 into three equal parts a, b, c so that a³b²c is a maximum.

Q15.

lim  x^x = ?
x→0

Q16.

lim (8x² + 10x³ sin(1/x) + 7x)/(18x² + 9cosx +8) = ?
x→∞