List of top Questions asked in AP EAPCET- 2022

If \[ f(x)=\frac{1-\sin x}{\log(1+\pi^2-4\pi x+4x^2)} \] is continuous at \(x=\frac{\pi}{2}\), then \(f\left(\frac{\pi}{2}\right)=\)

If \(a,b,c\) are the intercepts made by the plane passing through the point \((1,2,3)\) parallel to the plane \(3x+4y-5z=0\) on \(X,Y,Z\)-axes respectively, then \(3a+b+5c=\)

If \(a\gt 0,\ b\gt 0\), then \[ \lim_{n\to\infty} \left( \frac{a+b^{1/n}-1}{a} \right)^n = \] is equal to:

If \(a,b,c\) are the direction ratios of a line \(L\) and \(\ell,m,n\) are its direction cosines, then \[ \frac{a^2}{b^2+c^2}= \] is equal to:

The parabola with focus at \((4,-3)\) and vertex at \((4,-1)\) is

If the line \(3x-my+5=0\) is a tangent to the hyperbola \(3x^2-4y^2=300\), then the square of the \(Y\)-intercept made by this tangent line is

Let \(L(x_1,4)\) be the end of the latus rectum of the hyperbola \[ \frac{x^2}{a^2}-\frac{y^2}{b^2}=1 \] lying in the first quadrant and let \(S(8,y_1)\) be the focus of the given hyperbola. Then the length of its transverse axis is:

If the vertices of a triangle \(ABC\) are \(A(1,2,3)\), \(B(h,-3,0)\) and \(C(-4,k,-1)\) and the centroid of the triangle is \(\left(5,-1,\dfrac{2}{3}\right)\), then triangle \(ABC\) is:

If the latus rectum of an ellipse is equal to half of the minor axis, then its eccentricity is:

Suppose the tangents drawn to the circle \(x^2+y^2-6x-4y-11=0\) from \(P(1,8)\) touch the circle at \(A\) and \(B\). Then the centre of the circle passing through \(P,A\) and \(B\) is

The circle possessing \(y\)-axis as its tangent at \((0,2)\) and passing through \((-1,0)\), also passes through

The midpoint of the diagonal of a rectangle formed by \(x^2+5x-6=0\) and \(y^2-8y-20=0\) is

The slope of the normal to the circle \(x^2+y^2+2gx+2fy+c=0\) at \((x_1,y_1)\) is

Suppose two tangents \(PA\) and \(PB\) are drawn to the circle centered at \(C(1,2)\) from the point \(P(16,7)\). If the area of the quadrilateral \(PACB\) is \(75\) square units, then the radius of the circle is

The centre of the circle that passes through the point \((0,1)\) and touches the curve \(y=x^2\) at \((2,4)\) is

If a point \((\alpha,\beta)\) of \(3x+y=0\) and \((3,4)\) lie on the opposite sides of \(3x-4y-8=0\), then which of the following is correct?

The family of lines, forming an isosceles triangle with the lines \(3x-4y-2=0\) and \(12x-5y+6=0\), is

The straight line passing through \((-1,1)\) and remaining parallel to the line common to the pairs of lines provided by \(6x^2-xy-12y^2=0\) and \(15x^2+14xy-8y^2=0\), is

If a particle moving along \[ x-2y-3=0 \] gets reflected in a perpendicular direction upon hitting the line \[ 3x-2y-5=0, \] then the line of movement of the particle after reflection is

A multiple choice test consists of \(5\) questions, each question having \(4\) responses. There is only one correct response and the remaining \(3\) are incorrect responses. If a candidate attempts all the \(5\) questions, then the probability that he answers at least \(3\) questions incorrectly is

A point \(P(x,y)\) is such that its distances from \((-1,0)\) and \((0,2)\) are in the ratio of \[ \sqrt{2}:1 \] Then the locus of \(P\) is

The random variable \(X\) has Binomial distribution \[ B(20,0.4) \] Then \[ 5-5P(X\geq 2)= \] is equal to:

If the total number of observations is \(20\), \[ \sum x_i=1000 \] and \[ \sum x_i^2=84000, \] then the variance of the distribution is

A bag contains \(21\) toys numbered \(1\) to \(21\). A toy is drawn and then another toy is drawn without replacement. The probability that both toys will show even numbers is

A bag contains \(2\) red, \(3\) green and \(2\) blue balls. Two balls are drawn at random. Then, the probability that none of the balls drawn is blue is