List of top Questions asked in AP EAPCET- 2026

The value of \( \lim_{x\rightarrow0}\frac{e^{2x^{2}}-\cos 2x}{x^{2}} = \)

If the angle between the planes \( \lambda x-2y+3z+1=0 \) and \( 2x+3y-\lambda z+\lambda=0 \) is \( \cos^{-1}(\frac{12}{49}) \) and \( \lambda\in\mathbb{Z} \), then the sum of the perpendicular distances from the origin to these planes is

The value of \( \lim_{x\rightarrow\infty}\frac{x^{3}+2x^{2}\sin x-4x \cos x}{\sqrt{(3x^{2}+2x \cos x)^{3}}} = \)

A normal is drawn to the hyperbola \( 9x^{2}-16y^{2}=144 \) at one of the ends of its latus rectum. If that end lies in the third quadrant and the equation of the normal is \( ax+by+c=0 \) then \( \frac{b+c}{a} = \)

If a tangent drawn to the parabola \( y^{2}=16x \) meets the curve \( xy=4 \) at the points P and Q, then the locus of midpoint of PQ is

If the distance of a point P on an ellipse from its focus (1, 2) is half of the distance of P from its corresponding directrix \( x+y=0 \), then the point of intersection of the given directrix and its major axis, is

Let S be the focus of the parabola \( y^{2}=36x \) and let the line \( x+by+c=0 \) intersect the parabola at the points Q and R. If the centroid of \( \triangle QRS \) is (57,0), then -c is

Let \( \theta \) be the angle between the circles \( x^{2}+y^{2}-4x+2fy-f=0 \) and \( x^{2}+y^{2}+2fx-4y-f=0 \). If \( \cos\theta=\frac{9}{16} \) and \( f\in\mathbb{Z} \), then the distance between the centres of these circles is

The perpendicular distance from origin to the tangent drawn at the point \( P(\frac{\pi}{4}) \) to the circle \( x^{2}+y^{2}-4x-4y+6=0 \) is

The line \( 5x-12y-4=0 \) cuts the circle \( x^{2}+y^{2}-2x+2y+c=0 \) at two points A, B. If \( AB=2\sqrt{3} \), then the length of the tangent drawn from the point (2, 1) to the given circle is

If \( 2x+y-2=0 \) and \( 6x-4y+1=0 \) are two normals of a circle S and the length of the perpendicular drawn from (2, 3) to the line \( 3x+4y-3=0 \) is the radius of S, then the interior point of the circle S among the following options is

The sum of the slopes of the common tangents drawn to the circles \( x^{2}+y^{2}+4x-2y-11=0 \) and \( x^{2}+y^{2}-2x+6y+6=0 \) is

Let A be the resulting point after the point (4, 1) undergoes the following transformations successively:
i. reflection in the line \( y=x \)
ii. translation through a distance of 2 units along the positive direction of X-axis.
If the axes are rotated through an angle of \( \frac{\pi}{4} \) about origin in the positive direction, then the coordinates of the point A are

In \( \triangle ABC \), coordinates of A are (1, 2). If the equations of the medians through B and C are \( x+y=5 \) and \( x=4 \) respectively, then the area of \( \triangle ABC \) (in sq. units) is

The straight line which is parallel to X-axis and passing through the intersection of the lines \( ax+2by+3b=0 \) and \( bx-2ay-3a=0 \), \( (a,b)\neq(0,0) \) is

If the slope of one of the lines \( 2x^{2}-17xy+by^{2}=0 \) is 16 times the slope of another line, then the angle between this pair of lines is

The square of the distance from the origin to the point of intersection of the pair of lines \( ax^{2}-xy-3y^{2}-5x+20y-25=0 \) is

If the mean and variance of a random variable X having binomial distribution are 4 and 2 respectively, then \( P(X=2)= \)

Three numbers are chosen at random from \{1, 2, ..., 10\}. The probability that the minimum of the chosen numbers is 3 or their maximum is 7, is

From a set containing four positive numbers and four negative numbers, four numbers are chosen at random and they are multiplied. The probability that the obtained product is positive is:

From a pack of 52 playing cards, one card was found missing. From the remaining cards, two cards are drawn at random and found to be spade cards. The probability that the missing card is a spade card is

From a group of 10 men and 5 women, a four-member committee which includes at least one woman is to be formed. Then the probability for the committee thus formed to have more women than men is:

A dice is thrown twice. If getting a number greater than four is considered a success, the variance of the probability distribution of the number of successes is

Consider the following statements:
Statement - I: The variance of the first n even natural numbers is \( \frac{n^{2}-1}{4} \)
Statement - II: The difference between the variance of the first 20 even natural numbers and their mean is 112
Which of the following is correct?

If M is the foot of the perpendicular drawn from \( P(1,2,-1) \) to the plane passing through the point \( A(3,-2,1) \) and perpendicular to the vector \( 4\overline{i}+7\overline{j}-4\overline{k} \) then the length of PM is