List of top Questions asked in AP EAPCET- 2022

Equation of tangent to the curve \[ y=x+\frac{4}{x^2} \] which is parallel to \(x\)-axis is

Evaluate \[ \lim_{x\to \frac{\pi}{2}} \frac{1-\tan \frac{x}{2}}{1+\tan \frac{x}{2}} \cdot \frac{1-\sin x}{(\pi-2x)^3} \]

Let \[ f(x)= \begin{cases} 4, & -\infty\lt x\lt -\sqrt5 \\ x^2-1, & -\sqrt5\leq x\leq \sqrt5 \\ 4, & \sqrt5\lt x\lt \infty \end{cases} \] If \(k\) is the number of points where \(f(x)\) is not differentiable, then \(k-2=\)

Evaluate \[ \lim_{x\to \infty}x^3\left\{\sqrt{x^2+\sqrt{x^4+1}}-\sqrt2x\right\} \]

If \[ \lim_{x\to -a}\frac{x^7+a^7}{x+a}=7, \] then \(a=\)

A plane meets the \(X, Y, Z\)-axes in \(A, B, C\) respectively. If the centroid of the triangle \(ABC\) is \((2,-3,5)\), then the perpendicular distance from origin to the given plane is

A ray makes angles \(\frac{\pi}{3}\) and \(\frac{\pi}{4}\) with \(Y\)-axis and \(Z\)-axis respectively. Then the value of the sine of the angle made by the ray with \(X\)-axis is

The foci of the ellipse \[ 9x^2+25y^2=225 \] are

If the centroid of a triangle with vertices \[ (4,p,-3),\quad (-1,-1,2),\quad (3,5,-8) \] is given by the midpoint of \[ (1,4,-2) \] and \[ (q,2,-4), \] then \(p^2+q^2=\)

If \((1,2)\) is the focus, \(x+2y=0\) is the directrix and \(\sqrt{2}\) is the eccentricity of a hyperbola, then the equation of the hyperbola is

The locus of the point of intersection of the lines \[ \sqrt3x-y-4\sqrt3k=0 \] and \[ \sqrt3kx+ky-4\sqrt3=0 \] for different real values of \(k\) is a hyperbola \(H\). If \(e\) is the eccentricity of \(H\), then \(4e^2=\)

Suppose \(A(2,3)\) and \(B\) are the points of intersections of two circles. The points \(P\) lying on one circle and \(Q\) lying on the other circle are such that \(BP\) and \(BQ\) constitute the diameters of the circles respectively. If the slopes of the radical axis and \(PQ\) are \(\frac{3}{4}\) and \(\frac{a}{b}\) respectively, then the value of \(3a+4b\) is

If the directrix of the parabola \[ x^2+4y-6x+\lambda=0 \] is \(y+1=0\), then which of the following is correct?

The equations of the lines perpendicular to \[ x^2-5xy+4y^2=0 \] and passing through \((2,1)\) is:

The straight line touching the circle \[ x^2+y^2-2x-3=0 \] and remaining normal to the circle \[ x^2+y^2-4y-6=0 \] is

The equation of circle with centre \((2,-3)\) and touching \(x\)-axis is

In a square \(ABCD\) of side length \(a\), suppose \(AB\) and \(AD\) are along the coordinate axes. Then the circle that circumscribes the square is

The ratio of the areas of the greatest and the smallest circles touching \[ (x\pm 1)^2+(y\pm 1)^2=1 \] is

Suppose \(ABOC\) is a rhombus in the first quadrant with \(O\) being the origin. If the vertices \(B\) and \(C\) of \(\triangle ABC\) lie respectively on \[ y=\frac{4}{3}x \] and \[ y=0, \] and the side \(BC\) passes through \[ \left(\frac23,\frac23\right), \] then the midpoint of \(BC\) is

Suppose the hypotenuse and its opposite vertex of an isosceles right angled triangle are \(3x+4y-4=0\) and \((2,2)\) respectively. Then, which of the following is another side of the triangle?

If \(X\) is a Poisson random variable with mean \(3\), then \[ P(|X-3|\lt 2) = \] is equal to:

A point \(P(x,y)\) is such that the sum of squares of its distances from \((a,0)\) and \((-a,0)\) is \(2b^2\). The equation representing the locus of \(P\) is:

If \[ ax^2-34xy-5y^2+2x+26y-5=0 \] represents a pair of straight lines, then the value of \(a\) is:

A point \(P\) on a line is at a distance of \(4\) units from the origin \((0,0)\). If the line makes \(60^\circ\) with the negative direction of the \(x\)-axis, then \(P\) is

A bag contains \(3\) white, \(2\) blue and \(5\) red balls. One ball is drawn at random from this bag. Then, the probability that the ball drawn is not red is