ISRO Scientist or Engineer Electrical 2014

A function f from the set of natural numbers to integers defined by
$$f(n) = \begin{cases}\frac{n - 1}{2}, & when  n  is  odd\\-\frac{n}{2}, & when  n  is  even\end{cases}$$ is

lf the sum of the roots of the quadratic equation $$ax^2 + bx + c = 0$$ is equal to the sum of the squares of their reciprocals, then $$\frac{a}{c}, \frac{b}{a}$$ and $$\frac{c}{b}$$ are in

If $$\left(\frac{1 + i}{1 - i}\right) = 1$$, then

If a vertex of a triangle is (1, 1) and the mid-points of two sides through this vertex are (-1, 2) and (3, 2), then the centroid of the triangle is

Let $$A = \begin{bmatrix}0 & 0 & -1 \\0 & -1 & 0 \\-1 & 0 & 0 \end{bmatrix}$$. The only correct statement about the matrix A is

If one root of the equation $$x^2 + px + 12 = 0$$ is 4, while the equation $$x^2 + px + q = 0$$ has equal roots, then the value of 'q' is

A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is $$60^\circ$$ and when he retires 40 meter away from the tree the angle of elevation becomes $$30^\circ$$. The breadth of the river is

A particle moves towards east from a point A to a point B at the rate of 4 km/h and then towards north from B to C atthe rate of 5 km/h. If AB = 12 km and BC = 5 km, then its
average speedfor its journey from A to C and resultant average velocity direct from A to C are respectively

If $$\tan \theta = \frac{8}{15}$$ and $$\theta$$ is acute, then $$\cosec \theta$$

A student is to answer 10 out of 13 questions in an examination such that he must chooseat least 4 from thefirst five questions. The numberof choices available to him is