PGDBA 2017

Instructions

For the following questions answer them individually

Question 41

If $$\alpha$$ and $$\beta$$ are two roots of the equation $$x^2 + x + 1 = 0$$, then the value of $$\alpha^{2017} + \beta^{2017}$$ is

Question 42

The number of different solutions $$(x,y,z)$$ of the equation $$x + y + z = 10$$, where $$x, y$$ and $$z$$ are positive integers, is

Question 43

In the $$xy$$-plane, the equation $$x^2 - y^2 = 2y + 1$$ represents a


Question 44

There are 100 students in a class. in an examination, 50 of them failed in Mathematics, 45 failed in Physics and 40 failed in Biology. 32 failed in exactly two of the three subjects. Only one student passed in all the subjects. The number of students failing in all the three subjects is

Question 45

The point $$R (4,10)$$ lies on the curve $$C: y = x^2 - 6x + 18.$$ The tangent and normal to $$C$$ at $$R$$ meets the Y-axis at points $$P$$ and $$Q$$ respectively. A circle passes through the points $$P,Q$$ and $$R$$. The radius of this circle is

Question 46

An equilateral triangle, having each side as a , has its corners cut away so as to form a regular hexagon. The area of the hexagon is


Question 47

Let $$f(x) = a_0 + a_1 \mid x\mid +  a_2 \mid x\mid^2 + a_3 \mid x\mid^3$$, where $$a_0, a_1, a_2$$ and $$a_3$$ are constants. Which of the following statements is correct?

Question 48

If $$P = \begin{bmatrix}a & b & c\\x & y & z\\p & q & r \end{bmatrix}$$ and  $$Q = \begin{bmatrix}-x & a & -p \\y & -b & q\\z & -c & r \end{bmatrix}$$ then

Question 49

Let S = {1,2,...,100}. The number of nonempty subsets T of S such that the, product of numbers in T is even is


Question 50

What is the sum of the interior angles at the vertices of a 5-pointed star as shown below? The star need not have sides of the same length.

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