A parabola has the origin as its focus and the line $x=2$as the directrix. Then the vertex of the parabola is at

It is given that the events A and B are such that $P\left(A\right)=\frac{1}{4},P\left(\frac{A}{B}\right)=\frac{1}{2}\text{and}p\left(\frac{B}{A}\right)=\frac{2}{3}\dot{}$ Then P(B) is:

The first two terms of a geometric progression add up to 12. The sum of the third and the fourth terms is 48. If the terms of the geometric progression are alternately positive and negative, then the first term is

A die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then $P\left(A\cup B\right)$is

In a shop there are five types of ice-creams available. A child buys six ice-creams.Statement -1: The number of different ways the child can buy the six ice-creams is ${}^{10}{C}_5$.Statement -2: The number of different ways the child can buy the six ice-creams is equal to thenumber of different ways of arranging 6 As and 4 Bs in a row.

Let R be the real line. Consider the following subsets of the plane $R\times R$.$S=\left\{\left(x,y\right):y=x+1and0<x<2\right\},T=\{\left(x,y\right):x-y$is an integer }. Which one of the following is true?

The nonzero verctors $\vec{a}$, $\vec{b}$and $\vec{c}$are related by $\vec{a}=8\vec{b}\text{and}\vec{c}=-7\vec{b}$. Then the angle between $\vec{a}$and $\vec{c}$is

The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the followinggives possible values of a and b?

The line passing through the points (5, 1, a) and (3, b, 1) crosses the yzplane at the point $\left(0,\frac{17}{2},\frac{-13}{2}\right)$.Then

A focus of an ellipse is at the origin. The directrix is the line $x=4$and the eccentricity is 1/2. Then the length of the semimajor axis is