List of top Mathematics Questions asked in AP EAPCET

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

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

The standard deviation of the first \(10\) multiples of \(4\) 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 \(\vec{x}=\)

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 \(\dfrac{xy}{z^2}=\)

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

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:

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

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

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

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

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

Factorize \[ 2\cot^2\theta-\cot\theta-3 \]

Evaluate \[ \frac{\sin x}{1+\cos x}+\frac{1+\cos x}{\sin x} \]

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

If \[ {}^{\,n-1}P_r = {}^{\,n-1}P_{\,r} + x\cdot {}^{\,n-1}P_{(r+1)} \] for \(n,r\in \mathbb{N}\) and \(r\leq n\), then \(x=\)

The value of \[ \sin\left(\frac{5\pi}{24}\right)\cos\left(\frac{\pi}{24}\right) \] is

In a plane there are \(37\) straight lines of which \(13\) pass through point \(A\) and \(11\) pass through point \(B\). Moreover, no three lines apart from the lines passing through \(A\) and \(B\) pass through the same point and no two are parallel. What is the number of points of intersection of the straight lines?

The English alphabets have 5 vowels and 21 consonants. How many words with two different vowels and two different consonants can be formed from the alphabet?

The sum of all possible numbers that can be formed by using the digits \(2,3,5,7\) without repetition of digits is:

If \(2,3,6\) are the roots of the polynomial \[ f(x)=x^3+ax^2+bx+c, \] where \(a,b,c\in \mathbb{C}\), then the value of \(a-c\) is

If \(y^2+z^2=3yz,\ z^2+x^2=8zx,\ x^2+y^2=4xy\), then the value of \(\dfrac{y^2}{xz}+\dfrac{xz}{y^2}\) is:

If \(1,\omega,\omega^2\) denote the cube roots of unity, then the value of \[ (1-\omega+\omega^2)^5+(1+\omega-\omega^2)^5 \] is