List of top Mathematics Questions asked in AP EAPCET

An angle between the plane \[ x+y+z=5 \] and the line \[ \frac{x-16}{0} = \frac{y-0}{-1} = \frac{z+47}{4} \] is
If \(C\) is the centre of the hyperbola \[ \frac{x^2}{a^2}-\frac{y^2}{b^2}=1 \] and the tangent drawn at any point \(P\) on the hyperbola meets the lines \[ bx-ay=0 \] and \[ bx+ay=0 \] at \(Q\) and \(R\) respectively, then \[ CQ\cdot CR= \]
The direction ratios of a line \(L\) are \((ab,b,b)\) \((b\gt 0)\) and the line \(L\) passes through \[ P(b,b,b). \] If \(Q(x,y,z)\) is a point on the line at a distance of \(b\) units from \(P\), then \[ x+y+z= \]
The equation of the line that is a tangent to the circle \[ x^2+y^2-6x+4y+12=0 \] is
If the centre of a circle \(S\) is \((2,4)\) and the length of the chord made by the secant \[ x+y+2=0 \] on \(S\) is \(6\) units, then the equation of the circle \(S\) is
If \(a\neq 0\) and the line \[ 2bx+3cy+4d=0 \] passes through the points of intersection of the parabolas \[ y^2=4ax \] and \[ x^2=4ay, \] then
For all real values of \(\lambda\), the point that lies on the polar of \[ (2\lambda,\lambda-4) \] with respect to the circle \[ x^2+y^2-4x-6y+1=0 \] is
The equation of the circle passing through the points of intersection of the circles \[ x^2+y^2-2x-4y+1=0, \] \[ x^2+y^2-4x-2y+4=0 \] and having its centre on the line \[ x-2y-3=0 \] is
If the points \[ (2,0),\ (0,1),\ (4,0),\ (0,k) \] are concyclic, then \(k=\)
If the equation \[ \lambda x^2-5xy+6y^2+x-3y=0 \] represents a pair of straight lines, then the point of intersection of these straight lines is
If the slope of one of the lines is twice the slope of the other in the pair of straight lines \[ 6x^2+2hxy+y^2=0, \] then \[ |h|= \]
If the coordinate axes are rotated about the origin through an angle \[ \frac{\pi}{8} \] in the positive direction to remove the \(xy\)-term from the equation \[ ax^2+bxy+y^2=0, \] then
Consider the lines \[ L_1: 2x+3y+1=0 \] and \[ L_2: 3x-2y+1=0. \] The locus of a variable point that is equidistant from the two lines \(L_1=0\) and \(L_2=0\) is
The lines \[ L_1:2x+y+1=0 \] and \[ L_2:x-2y+4=0 \] intersect at \(A\). Let \(P\) be a point at a distance \(5\) units from \(L_1=0\) and \(\alpha\) units from \(L_2=0\). If \(M\) and \(N\) are the feet of the perpendiculars from \(P\) on the lines \(L_1=0\) and \(L_2=0\) respectively, and the area of the quadrilateral \(AMPN\) is \(25\) sq. units, then the point \(P\) lies on the line
If \(P(\alpha,\alpha+1)\) is the foot of the perpendicular drawn from the origin to the line \(L\) and the \(x\)-intercept of \(L\) is \[ \left(-\frac52,0\right), \] then the sum of the squares of the distances from the origin to all such possible points \(P\) is
5 letters are randomly selected from English alphabets and they are arranged in alphabetical order. The probability that the 5 letters selected and arranged has \(M\) in the middle place is
In a pack of 6 cards, two cards are marked with \(5\), two cards are marked with \(6\), one card is marked with \(7\) and another card is marked with \(8\). In another pack of 6 cards, one card is marked with \(5\), two cards are marked with \(6\), two cards are marked with \(7\) and one card is marked with \(8\). If one card from each pack is drawn at random, the probability that the sum of the numbers on the cards is \(12\) or \(13\) is
Two balls are drawn at random from a box containing 4 white and 6 black balls one after the other without replacement. If it is known that the second ball drawn is black, then the probability that the first ball drawn is also black is
Let \(S\) be the set of all words formed by arranging all the letters of the word HOMOGENEOUS. If a word is randomly chosen from the set \(S\), then the probability that the word selected has all the consonants together is
The following is the probability distribution of a discrete random variable. If its mean is \(2.81\), then \(\alpha\beta=\) \[ \begin{array}{|c|c|c|c|c|c|} \hline X=x & -1 & -2 & 1 & \alpha & 3\\ \hline P(X=x) & \frac{1}{25} & \beta & \frac14 & \frac{9}{25} & \frac{3}{10}\\ \hline \end{array} \]
A box \(P\) contains 3 white and 7 red balls. A bag \(Q\) contains 4 green and 5 blue balls. Two balls are randomly drawn from box \(P\). If both are of the same color, one ball is drawn from bag \(Q\), and if the two balls are of different colors, 2 balls are drawn from bag \(Q\). If it is known that there is exactly one green ball among the balls drawn from bag \(Q\), then the probability that the two balls drawn from box \(P\) are of different colors is
The position vectors of the vertices \(A\) and \(B\) of a triangle \(ABC\) are \[ \hat{i}+3\hat{j}+4\hat{k} \] and \[ 2\hat{i}+\hat{j}+2\hat{k} \] respectively. If \[ |AC|=5 \] and \[ \angle A=\frac{\pi}{3}, \] then \[ |BC|= \]
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 \[ |\vec a|^2= \]
If \[ \vec a=\hat i-\hat j+2\hat k,\qquad \vec b=-\hat i+2\hat j \] and \(\vec c\) are three vectors such that \(\vec a+\vec b\) is parallel to \(\vec c\) and \[ (\vec c+\vec a)\cdot(\vec c+\vec b)=7, \] then the vector \(\vec c\) having minimum length 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 \(a+3b+c=\)