List of top Questions asked in AP EAPCET- 2022

\(\vec a,\vec b,\vec c\) 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 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 \[ 2\cosh2x+10\sinh2x=5, \] then \(x=\)

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

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

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

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

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

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

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 \[ {}^{10}C_2=3\cdot {}^{n+1}C_3, \] 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 \[ N= \]

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

If \[ 4^x-3^{x-\frac{1}{2}}=3^{x+\frac{1}{2}}-2^{2x-1}, \] then \[ x= \]

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

If \[ A= \begin{bmatrix} 1 & 0 \\ 2 & 1 \end{bmatrix}, \quad B= \begin{bmatrix} 1 & 3 \\ 0 & 1 \end{bmatrix}, \] then \[ \det(A^4+B^6)= \]

By simplifying \[ i^{18}-3i^7+i^2(1+i^4)(i)^{22} \] we get

The values of \(x\) for which \[ \sin x+i\cos 2x \] and \[ \cos x-i\sin 2x \] are conjugate to each other are

Let \[ G(x)= \begin{bmatrix} \cos x & -\sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1 \end{bmatrix}. \] If \(x+y=0\), then \(G(x)G(y)=\)

The locus of a point \(z\) satisfying \[ |z|^2=\operatorname{Re}(z) \] is a circle with centre