List of top Questions asked in AP EAPCET

The straight line touching the circle \[ x^2+y^2-2x-3=0 \] and remaining normal to the circle \[ x^2+y^2-4y-6=0 \] is

If \[ ax^2-34xy-5y^2+2x+26y-5=0 \] represents a pair of straight lines, then the value of \(a\) is:

If \(X\) is a Poisson random variable with mean \(3\), then \[ P(|X-3|\lt 2) = \] is equal to:

A point \(P(x,y)\) is such that the sum of squares of its distances from \((a,0)\) and \((-a,0)\) is \(2b^2\). The equation representing the locus of \(P\) is:

Suppose the hypotenuse and its opposite vertex of an isosceles right angled triangle are \(3x+4y-4=0\) and \((2,2)\) respectively. Then, which of the following is another side of the triangle?

A point \(P\) on a line is at a distance of \(4\) units from the origin \((0,0)\). If the line makes \(60^\circ\) with the negative direction of the \(x\)-axis, then \(P\) is

Suppose \(ABOC\) is a rhombus in the first quadrant with \(O\) being the origin. If the vertices \(B\) and \(C\) of \(\triangle ABC\) lie respectively on \[ y=\frac{4}{3}x \] and \[ y=0, \] and the side \(BC\) passes through \[ \left(\frac23,\frac23\right), \] then the midpoint of \(BC\) is

From a well shuffled pack of \(52\) cards, two cards are drawn at random. Then, the probability of both the cards being kings is:

Person A can solve \(90\%\) of the problems given in the book and Person B can solve \(70\%\). Then the probability that at least one of them will solve the problem selected at random from the book is:

A bag contains \(3\) white, \(2\) blue and \(5\) red balls. One ball is drawn at random from this bag. Then, the probability that the ball drawn is not red is

A person \(P\) speaks truth in \(75\%\) cases and another person \(R\) in \(80\%\) cases. Then the probability that they are likely to contradict each other in narrating the same event is

During the winter months in a certain village in Scotland, the probability of a day having severe fog is \(0.6\). The probability that in a given week there will be exactly two days with severe fog is:

The set of real values of \(\lambda\) for which the vectors \[ \lambda \hat{i}-3\hat{j}+5\hat{k} \] and \[ 2\lambda \hat{i}-\lambda \hat{j}+\hat{k} \] are perpendicular to each other is

\(\vec{a},\vec{b}\) are two vectors such that \(|\vec{a}|=\sqrt{3}\), \(|\vec{b}|=\sqrt{2}\). If \(\vec{x}\) is a unit vector satisfying \(\vec{x}\times \vec{a}=\vec{b}\), then \(\vec{x}=\)

The vector \(\vec{x}\) is perpendicular to the vectors \(\vec{a}=3\hat{i}+2\hat{j}+2\hat{k}\), \(\vec{b}=18\hat{i}-22\hat{j}-5\hat{k}\) and makes an obtuse angle with \(\hat{j}\). If \(|\vec{x}|=14\), then \(\vec{x}=\)

The standard deviation of the first \(10\) multiples of \(4\) is

Let \[ \vec{a}=\hat{i}+x\hat{j}+\hat{k}, \qquad \vec{b}=\hat{i}+\hat{j}+\hat{k} \] and \[ |\vec{a}+\vec{b}|=|\vec{a}|+|\vec{b}|. \] Then

If \(\vec{a}=\vec{i}+2\vec{j}+3\vec{k}\), \(\vec{b}=2\vec{i}+3\vec{j}+\vec{k}\), \(\vec{c}=8\vec{i}+13\vec{j}+9\vec{k}\) and \(x\vec{a}+y\vec{b}+z\vec{c}=0\), then \(\dfrac{xy}{z^2}=\)

In a triangle \(ABC\), let \(\angle C=\dfrac{\pi}{2}\). If \(r\) and \(R\) are respectively the inradius and circumradius of \(ABC\), then \(R+r=\)

In any triangle \(ABC\), \[ \frac{\cos 2A}{a^2}-\frac{\cos 2B}{b^2} = \] is equal to:

In a triangle \(ABC\), if \[ a=4,\quad b=5,\quad c=7, \] then \[ \sin\left(\frac{A}{2}\right) \] is

Let \(ABC\) be an acute-angled triangle with circumradius \(R\). Then \[ \sqrt{a^2b^2-4R^2} + \sqrt{b^2c^2-4R^2} + \sqrt{c^2a^2-4R^2} = \] is equal to:

Evaluate \[ \cos\theta(\cosec\theta-\sec\theta)-\cot\theta \]

The value of \[ \tanh(\log x) \] is

The expression \[ \frac{x^4}{(x^2+1)(x^2+3)} \] is equal to