Phrases Previous Year Questions (PYQs) – 2014 – Page 1 of 5

An equilateral triangle is inscribed in the parabola $y^2=4ax$, such that one of the vertices of the triangle coincides with the vertex of the parabola. The length of the side of the triangle is:

A chain of video stores sells three different brands of DVD players. Of its DVD player sales, 50% are brand 1, 30% are brand 2 and 20% are brand 3. Each manufacturer offers one year warranty on parts and labor. It is known that 25% of brand 1 DVD players require warranty repair work whereas the corresponding percentage for brands 2 and 3 are 20% and 10% respectively. The probability that a randomly selected purchaser has a DVD player that will need repair while under warranty, is:

The locus of the intersection of the two lines $\sqrt{3}x-y=4k\sqrt{3}$ and $k(\sqrt{3}x+y)=4\sqrt{3}$, for different values of k, is a hyperbola. The eccentricity of the hyperbola is:

Constant forces $\overrightarrow{P}=2\hat{i}-5\hat{j}+6\hat{k}$ and $\overrightarrow{Q}=-\hat{i}+2\hat{j}-\hat{k}$  act on a particle. The work done when the particle is displaced from A whose position vector is $4\hat{i}-3\hat{j}-2\hat{k}$, to B whose position vector is $6\hat{i}+\hat{j}-3k\hat{k}$ , is:

The value of $\int \sqrt{x}{e}^{\sqrt{x}}dx$ is equal to:

For the vectors $\overrightarrow{a}=-4\hat{i}+2\hat{j},\overrightarrow{b}=2\hat{i}+\hat{j}$ and $\overrightarrow{c}=2\hat{i}+3\hat{j}$, if $\overrightarrow{c}=m\overrightarrow{a}+n\overrightarrow{b}$ then the value of m + n is

The value of ${\int }_0^{\pi /4}log(1+tanx)dx$ is equal to:

The number of ways in which 5 days can be chosen in each of the 12 months of a non-leap year, is:

If [x] represents the greatest integer not exceeding x, then ${\int }_0^9[x]dx$ is