List of top Mathematics Questions asked in AP EAMCET

Among the 4-digit numbers formed using the digits \( 0, 1, 2, 3, 4 \) when repetition of digits is allowed, the number of numbers which are divisible by 4 is:

If

 
and \( AA^T = I \), then \( \frac{a}{b} + \frac{b}{a} = \):

If a direct common tangent is drawn to the circles \( x^2 + y^2 - 6x + 4y + 9 = 0 \) and \( x^2 + y^2 + 2x - 2y + 1 = 0 \) that touches the circles at points \( A \) and \( B \), then \( AB = \):
In the expansion of \( \frac{2x+1}{(1+x)(1-2x)} \), the sum of the coefficients of the first 5 odd powers of \( x \) is:
The number of ways a committee of 8 members can be formed from a group of 10 men and 8 women such that the committee contains at most 5 men and at least 5 women is:
There were two women participating with some men in a chess tournament. Each participant played two games with the other. The number of games that the men played among themselves is 66 more than the number of games the men played with the women. Then the total number of participants in the tournament is:
If the probability distribution of a random variable \( X \) is given as follows, then find \( k \):
probability distribution of a random variable X
In \( \triangle ABC \), if \( (a+c)^2 = b^2 + 3ca \), then \( \frac{a+c}{2R} \) is:
The probability that A speaks truth is 75\% and the probability that B speaks truth is 80\%. The probability that they contradict each other when asked to speak on a fact is:
If \[ y = \tan^{-1} \left( \frac{2 - 3\sin x}{3 - 2\sin x} \right), \] then find \( \frac{dy}{dx} \).
The equations of the perpendicular bisectors of the sides AB and AC of \( \triangle ABC \) are \( x - y + 5 = 0 \) and \( x + 2y = 0 \) respectively. If the coordinates of \( A \) are \( (1, -2) \), then the equation of the line BC is:
If \( x_1, x_2, x_3, \dots, x_n \) are \( n \) observations such that \( \sum (x_i + 2)^2 = 28n \) and \( \sum (x_i - 2)^2 = 12n \), then the variance is:
If \(\int \frac{\log(1+x^4)}{x^3} dx = f(x) \log(\frac{1}{g(x)}) + \tan^{-1}(h(x)) + c\), then \(h(x) [f(x) + f(\frac{1}{x})] =\)
The triangle \( PQR \) is inscribed in the circle \[ x^2 + y^2 = 25. \] If \( Q = (3,4) \) and \( R = (-4,3) \), then \( \angle QPR \) is:
If \( A(1,2,0), B(2,0,1), C(-3,0,2) \) are the vertices of \( \triangle ABC \), then the length of the internal bisector of \( \angle BAC \) is:
If \( z_1 = 10 + 6i \), \( z_2 = 4 + 6i \) and \( z \) is any complex number such that the argument of \( \frac{z-z_1}{z-z_2} \) is \( \frac{\pi}{4} \), then the value of \( |z - 7 - 9i| \) is:
There are 6 different novels and 3 different poetry books on a table. If 4 novels and 1 poetry book are to be selected and arranged in a row on a shelf such that the poetry book is always in the middle, then the number of such possible arrangements is:
The sum of the series \( 1 - \frac{2}{3} + \frac{2.4}{3.6} - \frac{2.4.6}{3.6.9} + \cdots \infty \) is:
The circumference of a circle passing through the point \( (4, 6) \) with two normals represented by \( 2x - 3y + 4 = 0 \) and \( x + y - 3 = 0 \) is:
If \( z = x+iy \), \( x^2+y^2 = 1 \) and \( z_1 = e^{i\theta} \), then the expression \( \frac{z_1^{2n-1} - 1}{z_1^{2^n-1} + 1} \) simplifies to:
If \(2.4^{2n+1} + 3^{3n+1}\) is divisible by \(k\) for all \(n \in \mathbb{N}\), then \(k\) is:
If \((\alpha + \beta)\) is not a multiple of \(\frac{\pi}{2}\) and \(3 \sin(\alpha - \beta) = 5 \cos(\alpha + \beta)\), then \[ \tan\left(\frac{\pi}{4} + \alpha\right) + 4\tan\left(\frac{\pi}{4} + \beta\right) = \]
If \([x]\) is the greatest integer function, then evaluate the integral \( \int_{0}^{5} [x] \, dx \):
If \( L_1 \) and \( L_2 \) are two lines which pass through origin and have direction ratios \( (3, 1, -5) \) and \( (2, 3, -1) \) respectively, then the equation of the plane containing \( L_1 \) and \( L_2 \) is:
The largest among the distances from the point \(P(15,9)\) to the points on the circle \(x^2 + y^2 - 6x - 8y - 11 = 0\) is: