List of top Questions asked in AP EAPCET- 2026

If \[ \log_2(x-1)+\log_2(x-3)=3, \] then the value of \(x\) is

If the equation \[ 2x^2-5x+k=0 \] has equal roots, then the value of \(k\) is

If \[ y=mx+\frac{3}{m} \] is a tangent to the parabola \[ y^2=4ax \] at the point \(P(3,\beta)\), where \(\beta<0\), then the value of \[ 3m-\beta \] is:

The centre of the circle which intersects the circles \[ x^2+y^2-8x+10y+5=0 \] and \[ x^2+y^2-2x+2y+1=0 \] orthogonally is:

If the pole of the line \[ 2x+3y-20=0 \] with respect to the circle \[ x^2+y^2-4x+6y-12=0 \] is \((\alpha,\beta)\), then the number of tangents that can be drawn from \((\alpha,\beta)\) to the given circle is:

If the equation \[ x^2-6x+y^2+8y+9=0 \] represents a circle, then its radius is:

The equation of the tangent to the ellipse \[ \frac{x^2}{16}+\frac{y^2}{9}=1 \] which is parallel to the line \[ 3x+4y+5=0 \] is

If \[ \int_0^1 (3x^2+2x+1)\,dx=k, \] then the value of \(k\) is

The equation of the normal to the parabola \[ y^2=12x \] at the point \((3\lambda^2,6\lambda)\) is

The eccentricity of the hyperbola \[ 16x^2-9y^2=144 \] is

The locus of the point which forms a right-angled triangle with the fixed points \((2,3)\) and \((5,1)\) is

If it is known that a woman has two children and she has at least one girl child, then the probability that both children are girls is

If the probability function of a random variable \(X\) is \[ P(X=x)=ak^x,\qquad x=0,1,2,\ldots, \] then the value of \(k\) is

A bag \(P\) contains \(5\) white and \(4\) blue balls. Another bag \(Q\) contains \(4\) white and \(5\) blue balls. One ball is drawn at random from bag \(P\) and transferred to another bag. Then one ball is drawn from bag \(Q\). Find the probability that the ball drawn from bag \(Q\) has the same colour as the ball transferred from bag \(P\).

If \[ X\sim B\!\left(n,\frac14\right), \] \[ P(X=2)=P(X=3) \] and \[ \sum_{k=0}^{2}P(X=k)=\frac{39}{411}, \] then \(n=\)

In a sample space, \(E\) is an event associated with the events \(A\) and \(B\). If \[ P(A|E)=l \] and \[ P(E|B)=m, \] then \(P(B|E)\) is

From the set of numbers \[ \{1,2,3,4,5,6,7,8,9,10,11,12\}, \] two numbers are selected at random. The probability that the two numbers selected differ by a prime number is

The variance of the following frequency distribution is

The shortest distance between the lines \[ \vec r=\vec a+t\vec b \] and \[ \vec r=\vec c+s\vec d \] where \[ \vec a=\hat i-2\hat j+2\hat k, \quad \vec b=3\hat i-2\hat j-2\hat k, \] \[ \vec c=6\hat i+2\hat j+2\hat k, \quad \vec d=-4\hat i-\hat k, \] is

Given that \[ \vec a=2\hat i-\hat j+2\hat k,\qquad \vec b=\hat i-2\hat j+2\hat k,\qquad \vec c=2\hat i-2\hat j-\hat k, \] if \(\vec d\) is a vector perpendicular to the plane containing \(\vec a,\vec b,\vec c\) and \[ |\vec d-\vec c|=2, \] then \[ |(\vec d-\vec c)\times(\vec a\times\vec b)|= \]

If \[ |\vec a|=2k, \qquad |\vec b|=k \] and \[ |\vec a-\vec b|^2=20k^2-|2\vec a+\vec b|^2, \] then \[ |\vec a\times\vec b| = \ ? \]

Let \(\vec a,\vec b\) be two non-collinear vectors. If \[ \vec r=(x+2y-3)\vec a+(2x-y+1)\vec b \] and \[ \vec R=(3x-y-2)\vec a+(x+3y+2)\vec b \] are vectors such that \[ 2\vec r=m\vec R, \] then \(x+5y=\)

If \[ \vec a=2\hat i+\hat j-\hat k \] and \[ \vec b=\hat i-2\hat j+3\hat k, \] then the value of \[ \vec a+\vec b \] is:

The ratio in which the point \[ (3,4) \] divides the line segment joining \[ (1,2) \] and \[ (5,6) \] is:

If \[ x+\frac1x=3, \] then the value of \[ x^2+\frac1{x^2} \] is: