List of top Mathematics Questions asked in AP EAPCET

If standard deviation of the data \[ 1,15,35,53,72,64 \] is \(x\), then the variance of the data \[ 62,70,51,33,13,-1 \] is

If the equation of the plane containing the line \[ \vec r=\hat i+2\hat j+\hat k+t(\hat i-\hat j+2\hat k) \] and parallel to the line \[ \vec r=-\hat i+2\hat j+s(-\hat i+2\hat j+\hat k) \] in Cartesian coordinates is \[ \frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1, \] then \(a+3b+c=\)

If the sides of a triangle \(ABC\) are in arithmetic progression, then \[ b\cos\left(\frac{A-C}{2}\right)= \]

If \[ \sinh x=-\frac12,\qquad \cosh y=2, \] and \[ x+y=\log p, \] then \(p=\)

In a \(\triangle ABC\), if \[ \cot\frac{A}{2}:\cot\frac{B}{2}:\cot\frac{C}{2} = 3:5:7, \] then \[ \cos A:\cos B:\cos C= \]

If \[ \tan^{-1}\left(\frac{1}{2\sqrt2}\right) - \cos^{-1}\left(\frac{1}{\sqrt3}\right) + \sin^{-1}(x) = 0, \] then \(x=\)

The sum of all the values of \(\theta\in(0,2\pi)\) satisfying the equation \[ \sin\theta+3\cos2\theta+\sin3\theta = \cos\theta+3\sin2\theta+\cos3\theta \] is

In \(\triangle ABC\), if \[ r_1=\frac{21}{2},\qquad r_2=12,\qquad r_3=14, \] then \(\Delta=\)

The coefficient of \(x^{12}\) in the expansion of \[ (x^2+x+2)^8 \] is

The period of the function \[ f(x)=\log(\cos x)+\cot^4\left(\frac{x}{2}\right)+\sin(3x+7) \] is

The coefficient of \(x^3\) in the power series expansion of \[ \frac{x}{x^2-x-2} \] is

Find the sum of the infinite series \[ -1+\frac{7}{10}\cdot 2^2-\frac{7\cdot 9}{10\cdot 15}\cdot 2^3+\frac{7\cdot 9\cdot 11}{10\cdot 15\cdot 20}\cdot 2^4-\cdots\infty \]

If \(A\) and \(B\) are the minimum and maximum values of \[ \sin^6 x+\cos^6 x, \] then \(A+B=\)

If \[ \tan\alpha=-\frac{7}{24}, \qquad \sec\beta=\frac{61}{60} \] and both \(\alpha,\beta\) lie in the same quadrant, then \[ \cos(\alpha+\beta)= \]

All possible 3 digit numbers are formed using all the digits \(2,3,5,7,9\) without using any digit more than once. Among these 3 digit numbers, the number of numbers which are divisible by \(3\) but not divisible by \(5\) is

If \(\alpha,\beta,\gamma\) are the roots of the equation \[ 24x^3-10x^2-3x+1=0, \] then \[ \frac{1}{\alpha^2}+\frac{1}{\beta^2}+\frac{1}{\gamma^2} = \]

A positive root of the equation \[ 18x^3-9x^2-5x+2=0 \] is twice another root of it. If among its three roots, the least value is \(a\) and the greatest value is \(b\), then \(2a+3b=\)

The interval containing all the solutions of the inequality \[ \sqrt{x^2-12x+48}\lt 2x+3 \] only is

There are 10 cards numbered \(1\) to \(10\). The number of ways in which at least 3 cards can be chosen from these 10 cards is

There are 15 identical balls for sale among which 4 are red, 5 are black and 6 are white. If a person buys at least one ball out of these 15 balls, then the total number of ways in which that person can buy the balls is

If \(1,i\in\mathbb{C}\), the set of complex numbers, then the value of \[ \sqrt{1+\sqrt{i}} \] cannot be

If the quadratic equations \[ x^2+2x-4k=0 \] and \[ x^2+9x+3k=0 \] have exactly one common root and \(k\neq 0\), then the equation having \(k\) as a root is

One of the values of the square root of \[ \left(\frac{1}{2}+\frac{\sqrt{3}}{2}i\right) \] is

Let a point \(P\) in the Argand plane represent the complex number \(z\). If \[ \operatorname{Arg}\left(\frac{2z-i}{z-2}\right)=\frac{\pi}{4}, \] then the locus of \(P\) is

If \[ A= \begin{bmatrix} 2 & -3 & 1\\ -3 & 1 & -2\\ 1 & -2 & 3 \end{bmatrix}, \] then \(\operatorname{Adj}(A)=\)