List of top Questions asked in AP EAPCET- 2022

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 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 \[ x^2+y^2=16 \] 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 length of the latus rectum of the parabola \[ (x-2)^2+(y-3)^2=\frac{1}{25}(3x-4y+7)^2 \] is

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

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

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 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

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

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?

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

A bag contains \(19\) red balls and \(19\) black balls. Two balls are chosen at a time repeatedly and discarded if they are of the same color, but if they are different, black ball is discarded and red ball is returned to the bag. The probability that this process will terminate with one red ball is

An unbiased dice with faces marked \(1,2,3,4,5,6\) is rolled four times. Out of four face values obtained, the probability that the minimum face value is not less than \(2\) and the maximum face value is not greater than \(5\) is

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

Let \(P\) be a real number and \(|P|\geq 2\). If \(A\), \(B\), \(C\) are variable angles such that \[ \sqrt{P^2-4}\tan A+P\tan B+\sqrt{P^2+4}\tan C=6P, \] then the minimum value of \[ \tan^2 A+\tan^2 B+\tan^2 C \] is

If \[ \vec{a}=\hat{i}+\hat{j}+\hat{k},\quad \vec{c}=\hat{j}-\hat{k}, \] \[ \vec{a}\times \vec{b}=\vec{c} \] and \[ \vec{a}\cdot \vec{b}=3, \] then \(\vec{b}=\)