Reference no: EM131574604

Q1. If M is a 7 × 5 matrix of rank 3 and N is a 5 × 7 matrix of rank 5 then rank(MN ) is -

Q2. If

x = a (t + sin t)

y = a (1 - cos t)

then the value of dy/dx|_t=π/2 is

Q3. Which of the following functions is not differentiable in the domain [-1, 1]?

Q4. The value of lim_x→∞[1/sinx -1/tanx] is -

Q5. The general solution of the partial differential equation ∂²z/∂x∂y = x + y is of the form -

Q6. Real and imaginary parts of Log(x + iy)

Q7. The value of the integral

_C dz/z² - 1, C : |z| = 4

Q8. The particular integral of the given differential equation

d²y/dx² + dy/dx + y = cos 2x

Q9. If a function f(x) = x³ - 12x² + 36x + 17, which is continuous and differentiable for all x ∈ R,the interval in which the given function strictly decreasing is

Q10. The value of directional derivative of

f (x, y, z) = 2x² + 3y² + z²

at the point (2, 3, 4) in the direction of the vector A^→ = i^{^} + 2^{^}k.

Q11. Simpson's 3/8th rule is the degree of polynomial:

Q12. Using Euler's method taking the step size = 0.1 obtain the approximate value of y corresponding to x = 0.2 for the initial valued problem

dy/dx = x² + y² and y(0) = 1

is

Q13. A continuous random variable X has a probability density function

f(x) = 3/5e^-3x/5, x > 0

          0         ,  x ≤ 0

the probability density function of Y = 3X + 2 is

Q14. If X is a continuous random variable with probability density function

f (x) = k(5x - 2x ),     0 ≤ x ≤ 2
                0,            otherwise

then the value of k is

Q15. Seven different objects must be divided among three peopl. There are "____ "ways,this can be done if one or two of them must get no objects.

Q16. If A is a nonsingular matrix of order n the |Adj (AdjA)| is.