List of top Mathematics Questions asked in AP EAPCET

If \((l_1,m_1,n_1)\) and \((l_2,m_2,n_2)\) are the direction cosines of two lines satisfying the relations \[ l^2+mn-6n^2=0 \] and \[ 2l-m+3n=0, \] then \[ |l_1l_2|+|m_1m_2|= \]

The value of \[ \lim_{x\to 0}\left(\frac{e^x-1}{x}\right)^{\frac{1+x-e^x}{x}} \] is

If \((3,4,-7)\) is the foot of the perpendicular drawn from the point \((-2,3,6)\) to the plane \(\pi\), then the sum of the intercepts made by the plane \(\pi\) on the \(x\)- and \(y\)-axes is

The value of \[ \lim_{n\to \infty}\sum_{r=1}^{n}\cot^{-1}\left(r^2+\frac{3}{4}\right) \] is

The length of the latus rectum of the parabola \[ (x-2)^2+(y-3)^2=\frac{1}{25}(3x-4y+7)^2 \] is

Let \[ x^2+y^2=16 \] be the equation of the auxiliary circle of a hyperbola \[ \frac{x^2}{a^2}-\frac{y^2}{b^2}=1 \] and let \((4\sqrt{2},3)\) be a point on the hyperbola. Then the eccentricity of the hyperbola is

The distance between the tangent lines to the hyperbola \[ x^2-2y^2=18 \] which are perpendicular to the line \(y=x\) is

The radical centre of the circles \[ x^2+y^2+3x+2y+1=0, \] \[ x^2+y^2-x+6y+5=0 \] and \[ x^2+y^2+5x-8y+15=0 \] is

Let the centroid of a triangle formed by the points \(A(4,x,1)\), \(B(y,-5,2)\), and \(C(7,8,3)\) be \(G(3,5,2)\), and \(CG\) meet \(AB\) in \(F\). Then \(F=\)

The values of \(\lambda\), for which \((\lambda,\lambda-2)\) lies inside the ellipse \[ 4x^2+9y^2=36 \] and outside the parabola \[ y^2=x, \] satisfy

If the equation \[ ax^2+by^2+2hxy+2gx+2fy+c=0 \] represents a circle passing through the origin, then

If the circle \[ x^2+y^2+2ax+c=0 \] lies completely inside the circle \[ x^2+y^2+2bx+c=0, \] then which of the following holds?

If the line \[ 3x-4y=1 \] touches the circle \[ (x-1)^2+(y+2)^2=4 \] at \((\alpha,\beta)\), the values of \(\alpha\) and \(\beta\) are

Number of triangles formed by the lines \[ x-y+3=0,\quad 2x-y+3=0,\quad 3x-y+2=0 \] and \[ x+y-3=0 \] is

The two pairs of straight lines \[ 12x^2+7xy-12y^2=0 \] and \[ 12x^2+7xy-12y^2-x+7y-1=0 \] constitute a

The equation of a tangent to the circle \[ x^2+y^2=1, \] which is perpendicular to the line \[ y=mx+1, \] is

The distance between the lines represented by \[ 4x^2+20xy+25y^2+2x+5y-12=0 \] is equal to

A variable line passing through \((l,m)\) intersects the coordinate axes at the points \(A\) and \(B\). If the lines drawn parallel to \(y\)-axis through \(A\) and parallel to \(x\)-axis through \(B\) meet at \(P\), then the locus of \(P\) is

A discrete random variable \(X\) has the distribution \(B(15,p)\). Given that \[ \operatorname{Var}(X)=3.15, \] then the two possible values of \(p\) are

When success is not an impossible event, then the mean of Binomial distribution is

The triangle with vertices at \[ (-2,2),\ (2,-2)\ \text{and}\ (1,1) \] is

For the three points \(A(2,0)\), \(B(0,2)\) and \(P(1,1)\), suppose \(d\) is the algebraic sum of the distances of \(A\) and \(B\) from a line that passes through \(P\). Then which of the following is correct?

If the variance of four numbers \(w,x,y,z\) is \(9\), then the variance of \[ 5w,5x,5y,5z \] is

An unbiased coin is tossed \(3\) times. If the third toss gets head, then the probability of getting at least one more head is

Two dice are rolled. Then, the probability that the total score is a prime number is