List of top Questions asked in AP EAPCET- 2022

If a set $A$ has $m$ elements and the set $B$ has $n$ elements, then the number of injections from $A$ to $B$ is
What is the sum of the first \( n \) terms of the series, whose \( k \)-term is \( k! \cdot k \)?
In a plane there are 37 straight lines of which 13 pass through point A and 11 pass through point B. Moreover, no three lines (apart from the lines passing through A and B) pass through same point and no two lines are parallel. What is the number of points of intersection of the straight lines?
The sum of all possible numbers that can be formed by using the digits 2,3,5,7 without repetition of digits is
A natural number $n$ such that $n!$ ends in exactly 1000 zeros is
If \( {}^n P_r = {}^{n-1}P_r + x \cdot {}^{n-1}P_{r-1} \quad \forall n,r \in N \text{ and } r \le n \), then x = .
How many chords can be drawn through 21 points on a circle?
The number of real values of \( m \) such that the equation \[ x^2 + (2m + 1)x + m = 0 \] has equal roots is:
If $$ S = \left\{ m \in \mathbb{R} : x^2 - 2(1 + 3m)x + 7(3 + 2m) = 0 \text{ has distinct roots} \right\} $$ then the number of elements in $ S $ is:
The triangle formed by \( x^2 - 4xy + y^2 = 0 \) and \( x + y + 4\sqrt{6} = 0 \) is:
If $ e_1 $ and $ e_2 $ are the eccentricities of the hyperbola $$ 16x^2 - 9y^2 = 1 $$ and its conjugate respectively, then find $ 3e_1 $ in terms of $ e_2 $.
If the angle between the lines joining the foci and the ends of the minor axis of the ellipse $$ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 $$ is $ 90^\circ $, then its **eccentricity** is:
The eccentric angle of a point on the ellipse $x^2 + 3y^2 = 6$ lying at a distance of 2 units from its centre is
If the product of the perpendicular distances from any point on the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \) to its asymptotes is 6, and the eccentricity of the hyperbola is \( \sqrt{3} \), then the length of the conjugate axis is:
If the lines represented by $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$ intersect on the x-axis, which of the following is in general incorrect
If \( ax + by = 1 \) is a normal to the parabola \( y^2 = 4px \), then the condition is
If the pair of straight lines $9x^2 + axy + 4y^2 + 6x + by - 3 = 0$ represents two parallel lines then
The locus of a variable point whose chord of contact w.r.t. the hyperbola $\dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1$ subtends a right angle at the origin is
For the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \), if the length of the transverse axis is 8 and the distance between the foci is \( 2\sqrt{41} \), then the length of its latus rectum is:
The curves \( y = x^2 - 1 \) and \( y = 8x - x^2 - 9 \)
Suppose a parabola passes through $(0, 4)$, $(1, 9)$ and $(4, 5)$ and has its axis parallel to the $y$-axis. Then the equation of the parabola is
If the normal to the rectangular hyperbola $x^2 - y^2 = 1$ at the point $P(\tfrac{\pi}{4})$ meets the curve again at $Q(\theta)$, then $\sec^2\theta + \tan\theta =$
If the straight line \( x\cos\alpha + y\sin\alpha = p \) touches the curve \( \left( \frac{x}{a} \right)^n + \left( \frac{y}{b} \right)^n = 2 \) at the point (a, b), and \( \frac{1}{a^2} + \frac{1}{b^2} = \frac{k}{p^2} \), then \( k = \):
Which of the following equations represents a **parabola**?
Find the locus of the point of intersection of tangents drawn at the ends of a **normal chord** of the hyperbola: $$ x^2 - y^2 = a^2 $$