List of top Mathematics Questions asked in AP EAPCET

Let \(A\) be a \(3\times3\) matrix such that \[ AA^{T}=I_3. \] Then \(A\) is:

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

If $\vec a,\vec b,\vec c$ are $3$ vectors such that \[ \vec b=2\hat i-\hat j,\qquad \vec c=\hat j+2\hat k, \] \[ |\vec a+\vec b|=3,\qquad |\vec a\times(\vec b\times\vec c)|=3\sqrt2 \] and \[ (\vec a,\vec b\times\vec c)=\frac{\pi}{3}, \] then $\vec a\cdot\vec b=$

$\overline{V}=2\overline{i}+\overline{j}-\overline{k}$ and $\overline{W}=\overline{i}+3\overline{k}$. If $\overline{U}$ is a unit vector, then the maximum value of the scalar triple product $[\overline{U}\overline{V}\overline{W}]$ is

If $\vec{a} = \vec{i} + \vec{j} + \vec{k}$, $\vec{b} = 4\vec{i} + 3\vec{j} + 4\vec{k}$ and $\vec{c} = \vec{i} + \alpha\vec{j} + \beta\vec{k}$ are linearly dependent vectors and $|\vec{c}| = \sqrt{3}$, then:

Let $\vec{a}$ and $\vec{b}$ be two unit vectors. If the angle between them is $\theta$, then $\cos(\theta/2) =$

If \( \overline{a}=\overline{i}+\overline{j}+\overline{k} \), \( \overline{a}.\overline{b}=1 \) and \( \overline{a}\times\overline{b}=\overline{j}-\overline{k} \), then \( \overline{b}= \)

If $\vec{a}$, $\vec{b}$, and $\vec{c}$ are three unit vectors such that $\vec{a} + \vec{b} + \vec{c} = \vec{0}$, then the value of $\vec{a} \cdot \vec{b} + \vec{b} \cdot \vec{c} + \vec{c} \cdot \vec{a}$ is:

OABCD is a pentagon in which \(OA\) and \(CB\) are parallel and \(OD\) and \(AB\) are parallel. If \[ \overrightarrow{OA}=\overrightarrow{a}, \qquad \overrightarrow{OD}=\overrightarrow{d}, \] and \[ \frac{OA}{CB}=2, \qquad \frac{OD}{AB}=\frac13, \] then \[ \overrightarrow{AD}+\overrightarrow{OC}+\overrightarrow{DC} \] is equal to:

Let \( \vec{a} = 3\hat{i} - \hat{j} - \hat{k}, \vec{b} = \hat{i} + \hat{j} - 2\hat{k} \) and \( \vec{c} = 2\hat{i} + 2\hat{j} + \hat{k} \). Let \( \vec{d} \) be a vector such that \( |\vec{d}| = \sqrt{2} \) units. If the vector \( \vec{d} \) is coplanar with \( \vec{a}, \vec{b} \) and perpendicular to \( \vec{c} \), then \( \vec{d} = \)

If $\vec{a} = 2\vec{i} + 3\vec{j} - \vec{k}$, $\vec{b} = -\vec{i} + 2\vec{j} - 4\vec{k}$ and $\vec{c} = \vec{i} + \vec{j} + \vec{k}$, then $(\vec{a} \times \vec{b}) \cdot (\vec{a} \times \vec{c}) =$

$\overline{b}$ and $\overline{c}$ are non-collinear vectors and $\overline{a}$ is a vector such that $(\overline{c}\cdot\overline{c})\overline{a}=\overline{c}$. If $\overline{a}\times(\overline{b}\times\overline{c})+(\overline{a}\cdot\overline{b})\overline{b}=(4-2\beta-sin~\alpha)\overline{b}+(\beta^{2}-1)\overline{c}$, then the values of the scalars $\alpha$ and $\beta$ are

O is the origin, \( \overline{OP} \) and \( \overline{OR} \) are vectors making angles \( 45^{\circ} \) and \( 135^{\circ} \) respectively with the positive direction of x-axis, \( |\overline{OP}|=3 \) and \( |\overline{OR}|=4 \). M is the midpoint of PQ in the rectangle OPQR. If OM meets the diagonal PR at T, then \( \overline{OT}= \)

If \( \vec{a} = \hat{i} - \hat{j} + 3\hat{k} \) and \( \vec{b} = 3\hat{i} - 5\hat{j} + 6\hat{k} \), then the magnitude of the projection of \( 2\vec{a} - \vec{b} \) on \( \vec{a} + \vec{b} \) is:

Let \( \overline{a}=4\overline{i}+3\overline{j} \) and \( \overline{b} \) be two vectors in XOY plane, and let \( \overline{a} \) be perpendicular to \( \overline{b} \). Then a vector \( \overline{c} \) in the same plane having projections 1 and 2 respectively on \( \overline{a} \) and \( \overline{b} \) is:

Let $\overline{a}=x\overline{i}-2\overline{j}+3\overline{k}$, $\overline{b}=-2\overline{i}+x\overline{j}-\overline{k}$ and $\overline{c}=7\overline{i}-2\overline{j}+x\overline{k}$. If $x=x_0$ is the point of the local maxima of $f(x)=\overline{a}\cdot(\overline{b}\times\overline{c})$, then at $x=x_0$, $\overline{a}\cdot\overline{b}+\overline{b}\cdot\overline{c}+\overline{c}\cdot\overline{a}=$

If the median AD of \(\Delta ABC\) is bisected at the point E and BE is produced to meet the side AC at F. Then the vector \( \overline{BF} = \)

Let \[ \vec a=4\hat i-\hat j+\alpha\hat k \] and \[ \vec b=\hat i+\alpha\hat j-4\hat k \] be two vectors. If $\alpha_1,\alpha_2$ ($\alpha_1<\alpha_2$) are two different values of $\alpha$ such that \[ (\vec a,\vec b)=\cos^{-1}\left(-\frac{2}{7}\right), \] then \[ \alpha_1+2\alpha_2= \]

Let $\vec a,\vec b$ and $\vec c$ be three non-zero vectors such that no two of them are collinear. If the vector $\vec a+\vec b$ is collinear with $\vec c$ and $\vec b+\vec c$ is collinear with $\vec a$, then \[ \vec a+\vec b+\vec c= \]

If \(\hat i+2\hat j+\hat k,\ a\hat i+3\hat j+2\hat k,\ -\hat i+4\hat j+\beta\hat k\) are the position vectors of three points \(A,B,C\), then the position vector of a point which divides \(BC\) in the ratio \(a+1:\beta\) is

If \( \vec{a} = \hat{i}+\hat{j}+\hat{k} \), \( \vec{b} = \hat{i}-\hat{j}+\hat{k} \) and \( \vec{c} = \hat{i}+\hat{j}-\hat{k} \), then match the following: \[ \begin{array}{|c|c|c|} \hline \text{List-I} & & \text{List-II} \\ \hline A & [\vec{a}\ \vec{b}\ \vec{c}] & I: 4 \\ \hline B & |\vec{a}+\vec{b}+\vec{c}|^2 & II: 11 \\ \hline C & \text{Volume of tetrahedron} & III: \dfrac{2}{3} \\ \hline D & |(\vec{a}\times\vec{b})\times(\vec{a}\times\vec{c})| & IV: 4\sqrt{3} \\ \hline & & V: 12 \\ \hline \end{array} \]

If the vector components of a vector \(\vec a\) along a vector \[ \vec b=4\hat i+5\hat j+3\hat k \] and perpendicular to \(\vec b\) are respectively \[ \frac{7}{25}(4\hat i+5\hat j+3\hat k) \] and \[ \frac{1}{25}(47\hat i-10\hat j-46\hat k), \] then \[ |\vec a|^2= \]

Identify the correct set of molecules with zero dipole moment:

The maximum value of $3 \sin x + 4 \cos x + 5$ is:

The value of \[ \tan81^\circ-\tan63^\circ-\tan27^\circ+\tan9^\circ \] is