List of top Mathematics Questions asked in AP EAPCET

The probability of getting a sum \(9\) when two dice are thrown is

Two brothers \(X\) and \(Y\) appeared for an exam. Let \(A\) be the event that \(X\) has passed the exam and \(B\) be the event that \(Y\) has passed. The probability of \(A\) is \[ \frac17 \] and of \(B\) is \[ \frac29. \] Then, the probability that both of them pass the exam is

Let \(\vec a,\vec b,\vec c\) be unit vectors such that \(\vec a\) is perpendicular to the plane containing \(\vec b\) and \(\vec c\), and angle between \(\vec b\) and \(\vec c\) is \(\frac{\pi}{3}\). Then \[ |\vec a+\vec b+\vec c|= \]

Let \[ \vec F=2\hat i+2\hat j+5\hat k,\quad A=(1,2,5),\quad B=(-1,-2,-3) \] and \[ \overrightarrow{BA}\times \vec F=4\hat i+6\hat j+2\lambda\hat k, \] then \[ \lambda= \]

\(\vec a,\vec b,\vec c\) are non-coplanar vectors. If \[ \vec a+3\vec b+4\vec c = x(\vec a-2\vec b+3\vec c) +y(\vec a+5\vec b-2\vec c) +z(6\vec a+14\vec b+4\vec c), \] then \[ x+y+z= \]

Three vectors of magnitudes \(a\), \(2a\), \(3a\) are along the directions of the diagonals of \(3\) adjacent faces of a cube that meet in a point. Then the magnitude of the sum of these vectors is

In a triangle \(ABC\), if \[ a=6,\quad b=5 \quad \text{and} \quad c=4, \] then \[ \cos2A= \]

In a triangle \(ABC\), if \[ r_1=36,\quad r_2=18 \quad \text{and} \quad r_3=12, \] then \[ s= \]

In any triangle \(ABC\), \[ \frac{\cos A}{a}+\frac{\cos B}{b}+\frac{\cos C}{c} = \]

If \(\vec a\) is collinear with \[ \vec b=3\hat i+6\hat j+6\hat k \] and \[ \vec a\cdot \vec b=27, \] then \[ |\vec a|= \]

If \[ \sin\theta+\cosec\theta=4, \] then \[ \sin^2\theta+\cosec^2\theta= \]

If \[ \sin\theta=-\frac{3}{4}, \] then \[ \sin2\theta= \]

If \[ \frac{1}{\sin1^\circ\sin2^\circ} + \frac{1}{\sin2^\circ\sin3^\circ} +\cdots+ \frac{1}{\sin89^\circ\sin90^\circ} = \] then its value is

Which of the following trigonometric values are negative?
\[ \text{I) } \sin(-292^\circ) \] \[ \text{II) } \tan(-193^\circ) \] \[ \text{III) } \cos(-207^\circ) \] \[ \text{IV) } \cot(-222^\circ) \]

Find the value of \[ \sin^2\frac{2\pi}{3}+\cos^2\frac{5\pi}{6}-\tan^2\frac{3\pi}{4} \]

If \[ 2\cosh2x+10\sinh2x=5, \] then \(x=\)

If \[ {}^{10}C_2=3\cdot {}^{n+1}C_3, \] then the value of \(n\) is

There are \(10\) points in a plane, out of these \(6\) are collinear. If \(N\) is the total number of triangles formed by joining these points, then \[ N= \]

If one root of the cubic equation \[ x^3+36=7x^2 \] is double of another, then the number of negative roots is

In an examination, the maximum marks for each of three subjects is \(n\) and that for the fourth subject is \(2n\). The number of ways in which candidates can get \(3n\) marks is

If \[ \frac{2x^2+1}{x^3-1} = \frac{A}{x-1} + \frac{Bx+C}{x^2+x+1}, \] then \[ 7A+2B+C= \]

205 students take an examination of whom \(105\) pass in English, \(70\) students pass in mathematics and \(30\) students fail in both. How many students pass in both subjects?

If \[ \sin^4\theta \cos^2\theta=\sum_{n=0}^{\infty} a_{2n}\cos 2n\theta, \] then the least \(n\) for which \[ a_{2n}=0 \] is

The sum of the real roots of the equation \[ x^4-2x^3+x-380=0 \] is

If \[ S=\{m\in \mathbb{R}:x^2-2(1+3m)x+7(3+2m)=0 \text{ has distinct roots}\}, \] then the number of elements in \(S\) is