List of top Mathematics Questions asked in AP EAPCET

A chord is drawn through the focus of the parabola \(y^2=6x\) such that its perpendicular distance from the vertex is \(\frac{\sqrt5}{2}\). Then its slope can be:

If \((K,3,5)\), \((2,-1,2)\) are direction ratios of two lines and the angle between them is \(45^\circ\), then a value of \(K\) is:

A perpendicular is drawn through the vertex \(O\) of the parabola \(y^2=8x\) to any non-vertical tangent meeting the parabola at \(P\). Then \(OP.OQ=\)

The tangents drawn at the points \(P_1\) and \(P_2\) lying on the ellipse \(\frac{x^2}{4}+y^2=1\) are parallel to the chord joining the points \((0,1)\) and \((2,0)\), then the distance between \(P_1\) and \(P_2\) is:

The tangent to the circle \(C_1:x^2+y^2-2x-1=0\) at the point \((2,1)\) cuts off a chord of length \(4\) units from a circle \(C_2\) whose centre is \((3,-2)\). The radius of circle \(C_2\) is:

The radical axis of two orthogonal circles is \(x+1=0\). If one of those circles is \(x^2+y^2=4\), then the equation of the other circle is:

If the radical axis of the circles \(x^2+y^2+2gx+2fy+c=0\) and \(2x^2+2y^2+3x+8y+2c=0\) touches the circle \(x^2+y^2+2x+2y+1=0\), then:

Equation of the circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length \(3\) is:

The circumcenter of a triangle lies at the origin and its centroid is the midpoint of the line segment joining the points \((a^2+1,a^2+1)\) and \((2a,-2a)\), where \(a\neq0\). Then the equation of the parabola passing through the orthocentre is

If the chord \(y=mx+1\) of the circle \(x^2+y^2=1\) subtends an angle \(45^\circ\) at the major segment of the circle, then the value of \(m\) is:

The following table gives the probability distribution of a random variable \(X\): \[ \begin{array}{|c|c|c|c|c|} \hline x_i & 0 & 1 & 2 & 3 \\ \hline P(X=x_i) & 0.1 & 0.3 & 0.5 & 0.1 \\ \hline \end{array} \] The standard deviation of \(X\) is:

The equations of the pairs of opposite sides of a parallelogram are \[ x^2-5x+6=0 \] and \[ y^2-6y+5=0. \] Then the equations of its diagonals are

If a non-horizontal line \(L\) passes through the point \((4,-2)\) and the distance of \(L\) from the origin is \(2\) units, then the equation of the line \(L\) is

If the equation of the line passing through the orthocentre and circumcentre of triangle \(ABC\), whose vertices are \(A(3,1)\), \(B(3,3)\), \(C(6,1)\), is \(2x+by+c=0\), then \(b+c=\)

If the axes are rotated about the origin in positive direction through an angle of \(30^\circ\), then the transformed equation of \[ x^2+2\sqrt{3}xy-y^2=2a^2 \] is

If \(O\) is the origin and \(P\) is a point moving on the straight line \(lx + my + n = 0 \; (n \neq 0)\). If \(Q\) is a point on the segment \(OP\) such that \(OP \cdot OQ = k^2\), where \(k \neq 0\), then the locus of \(Q\) is

Let \( E_1, E_2 \) and \( E_3 \) be mutually independent events. Statement I: \( E_1 \) and \( E_2 \cup E_3 \) are independent. Statement II: \( E_1 \) and \( E_2 \cap E_3 \) are independent. Which one of the following options is correct?

If \( b \) and \( c \) are numbers chosen at random from the set \( \{1,2,3,\ldots,10\} \) with replacement, then the probability that the quadratic equation \[ x^2 + bx + c = 0 \] has real roots is:

A pair of dice is thrown independently \(3\) times. The probability of getting a total score of at least \(9\) twice, is:

If the mean of the set of values \( (3,6,9,10,n) \) is \( 9 \), then the variance of the given set of values is:

If \(E_1\) and \(E_2\) are two events of a sample space such that \(P(E_1)=0.8\), \(P(E_2)=0.7\) and \(P(E_1\cap E_2)\geq c\), then \(c=\)

In a bolt factory, machines \(A\), \(B\), and \(C\) manufacture \(25\%\), \(35\%\), and \(40\%\) of the total output respectively. There is a chance of having \(5\%\), \(4\%\), and \(2\%\) defective bolts manufactured by \(A\), \(B\), and \(C\) respectively. If a bolt is drawn at random from the output, then the probability that it is defective is:

In a triangle \(ABC\), if \(r_1=\dfrac{5}{\sqrt2},\ r_2=2\sqrt2,\ r=r\sqrt2\), then \(\dfrac{a+c}{b}=\)

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 \( \vec{a} = \hat{i} - \hat{j} + 3\hat{k} \) 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: