List of top Mathematics Questions asked in AP EAPCET

An ellipse has \(6\) and \(2\) as lengths of major and minor axes respectively. If the centre is at \((5,6)\) and the major axis is along \[ x-y+1=0, \] then the ellipse is:

For a hyperbola \[ \frac{x^2}{a^2}-\frac{y^2}{b^2}=1, \] if the length of the transverse axis is \(8\) and the distance between the foci is \(2\sqrt{41}\), then the length of its latus rectum is:

If the product of the perpendicular distances from any point on the hyperbola \[ \frac{x^2}{a^2}-\frac{y^2}{b^2}=1 \] to its asymptotes is \(6\) and eccentricity of the hyperbola is \(\sqrt3\), then the length of the conjugate axis of the hyperbola is:

If the point \((3,4,5)\) divides the line segment joining the points \((1,2,3)\) and \((4,5,6)\) in the ratio \(\lambda:1\), then the point which divides the line segment joining the points \((3,4,5)\) and \((1,2,3)\) in the ratio \(-1:\lambda\) is:

Suppose \(d_1\) and \(d_2\) are respectively the lengths of intercepts of the circles \(x^2+y^2=4\) and \(x^2+y^2-10x-14y+65=0\) on the line \(2x-2y-3=0\). Then which of the following is true?

The equation of bisectors of the angle between the lines given by \[ 3x^2+5xy+4y^2=0 \] is:

If the point \((2,\lambda)\) lies inside the circles \(x^2+y^2=13\) and \(x^2+y^2+x-2y=14\), then \(\lambda\) lies in the set:

For different real non-zero numbers \(x_1,x_2,x_3\) and \(x_4\), suppose the points \[ \left(x_1,\frac{1}{x_1}\right),\left(x_2,\frac{1}{x_2}\right),\left(x_3,\frac{1}{x_3}\right) \textbf{ and } \left(x_4,\frac{1}{x_4}\right) \] lie on the boundary of a circle of radius \(4\). Then the value of \(x_1x_2x_3x_4\) is:

The equation of the tangent to the circle \[ x^2+y^2-9=0 \] making an angle \(60^\circ\) with the \(x\)-axis is:

The equation of the circle passing through \((0,0)\) and cutting orthogonally the circles \[ x^2+y^2+6x-15=0 \] and \[ x^2+y^2-8y-10=0 \] is:

On the locus of the point \(P(x,y)\) equidistant from \((3,0)\) and \((0,4)\), if \(A\) and \(B\) are two points that satisfy \(4x=3y\) and \(x=y\) respectively, then the distance between \(A\) and \(B\) is:

If one side of an isosceles triangle is given by \(y=2\) and the base is provided by the points \((2,0)\) and \((0,2)\), then its area (in sq. units) is:

The straight line passing through \((0,0)\) and the foot of perpendicular from \((2,4)\) onto \[ x+y-1=0 \] is:

If \(P(\sin\alpha,\cos\alpha)\) lies inside the triangle formed by the vertices \[ (0,0),\left(\frac{\sqrt3}{2},0\right),\left(0,\frac{\sqrt3}{2}\right), \] then \(\alpha\) lies in the interval:

The triangle formed by \[ x^2-4xy+y^2=0 \] and \[ x+y+4\sqrt6=0 \] is:

Suppose that a book of 600 pages contains 40 print mistakes. Assume that these errors are randomly distributed throughout the book and the number of errors per page follows a Poisson distribution. The probability that all the 10 pages selected at random will have no print mistakes is:

The maximum value of the variance of Binomial distribution with parameters \(n\) and \(p\) is:

If \(A\) and \(B\) are two independent events such that \(P(A)=0.3\), \(P(B)=x\), and \(P(A\cup B)=0.44\), then \(x=\)

In a set of \(30\) game cards, \(17\) are white and the rest are green. Out of \(30\), \(4\) white and \(5\) green are marked IMPORTANT. If a card is chosen randomly from this set, the possibility of choosing a green card or an IMPORTANT card is:

In a toy factory, the machines \(A\), \(B\), and \(C\) are used to manufacture \(30\%\), \(40\%\), and \(30\%\) of the output, respectively. The probabilities of toys made by machines \(A\), \(B\), and \(C\) to be defective are respectively \(2\%\), \(3\%\), and \(1\%\). A toy is taken from the factory and is found to be defective. The probability that it was manufactured by machine \(B\) is

If a number is chosen at random from the set \[ \{1,2,3,\ldots,100\}, \] then the probability that the chosen number is a perfect cube is:

The range of the data \(35, 12, 21, 24, 15, 7, 16, 12, 30, 32, 13, 17\) is:

Two vertices of a triangle are at \(-\hat{i}+3\hat{j}\) and \(2\hat{i}+5\hat{j}\), and its orthocenter is at \(\hat{i}+2\hat{j}\). If the position vector of the \(3^{rd}\) vertex is \(a\hat{i}+b\hat{j}\), then \((a,b)=\)

\(\overline{a}\), \(\overline{b}\) are non-collinear vectors, \(|\overline{a}|=2\sqrt{2}\), \(|\overline{b}|=3\), and the angle between \(\overline{a}\) and \(\overline{b}\) is \(45^\circ\). Then the lengths of the diagonals of the parallelogram whose adjacent sides are represented by the vectors \(5\overline{a}+2\overline{b}\) and \(\overline{a}-3\overline{b}\) are

If \(C\) is the midpoint of the line segment \(AB\) and \(P\) is any point outside the line \(AB\), then: