List of top Mathematics Questions asked in AP EAPCET

If \( \alpha, \beta, \gamma \) are the roots of the equation \( x^3 - 3x + 1 = 0 \), then \( \frac{\alpha}{1-\alpha} + \frac{\beta}{1-\beta} + \frac{\gamma}{1-\gamma} = \)

If the two systems of equations \( x+y-2z=0, 4x+4y-8z=0, 3x+3y-6z=0 \) and \( x+y+z=3, 2x+2y-z=\lambda, x+y-\mu z=1 \) have the same set of solutions, then \( \lambda+\mu = \)

A random variable X takes values 0, 1, 2, 3 and its mean is 1.3. If $P(X=3)=2P(X=1)$ and $P(X=2)=0.3$, then find $P(X=0)$.

In a binomial distribution with 5 trials, the probabilities of 1 success and 2 successes are 0.4096 and 0.2048 respectively. Find the variance of the distribution.

A circle passes through the ends of the latus rectum of parabola \( y^2=12x \) and has its centre at the vertex. The area inside the circle and outside the parabola in the \( 1^{st} \) quadrant is:

The complete range of the function \( f(x) = [x]^2 + 5[x] + 6 \), where \([x]\) is the greatest integer function, is:

Evaluate \(\lim_{x\rightarrow2}(x^{2}-3x+3)^{\frac{1}{x^{2}-4}}\).

The mean of 5 observations is 5. If three of the observations are 1, 2, 6 and the other two observations are such that each is greater than 5, then the mean deviation from the mean of the observations is

Points \((h,k)\), \((1,2)\), \((-3,4)\) lie on \(L_1\). Line \(L_2\) through \((h,k)\) and \((4,3)\) is perpendicular to \(L_1\). Find \(\frac{k}{h}\).

If \[ f(x)= \begin{cases} \dfrac{x^{2}-4}{\sqrt{2-x}}, & x<2\\ a, & x=2\\ \log(x-2), & x>2 \end{cases} \] is a real valued function, then:

If \( x_1+x_2+x_3+\dots+x_n=pn(n-1) \forall n \in \mathbb{N} \) and \( x_{j+1}-x_j = \text{constant} \, (j=1,2,\dots,n-1) \), then \( (\frac{x_n}{n-1})^2 = \)

If a real valued function \( f:(1, 2] \rightarrow B \) defined by \( f(x) = \log_{10}(x-1) \) is a bijection, then \( B = \)

If \(a\neq 0\) and the line \[ 2bx+3cy+4d=0 \] passes through the points of intersection of the parabolas \[ y^2=4ax \] and \[ x^2=4ay, \] then

The normal drawn to the parabola \[ y^2=8x \] at \((2,4)\) meets the parabola again at the point

The interval containing all the solutions of the inequality \[ \sqrt{x^2-12x+48}\lt 2x+3 \] only is

Two balls are drawn at random from a box containing 4 white and 6 black balls one after the other without replacement. If it is known that the second ball drawn is black, then the probability that the first ball drawn is also black is

The position vectors of the vertices \(A\) and \(B\) of a triangle \(ABC\) are \[ \hat{i}+3\hat{j}+4\hat{k} \] and \[ 2\hat{i}+\hat{j}+2\hat{k} \] respectively. If \[ |AC|=5 \] and \[ \angle A=\frac{\pi}{3}, \] then \[ |BC|= \]

There are 15 identical balls for sale among which 4 are red, 5 are black and 6 are white. If a person buys at least one ball out of these 15 balls, then the total number of ways in which that person can buy the balls is

There are 10 cards numbered \(1\) to \(10\). The number of ways in which at least 3 cards can be chosen from these 10 cards is

At any point on the curve \[ by^2=(x+a)^3, \] if the length of the sub-tangent (ST) and the length of the sub-normal (SN) are such that \[ p(\text{SN})=q(\text{ST})^2, \] then \[ \frac{p}{q}= \]

If the equation of the plane containing the line \[ \vec r=\hat i+2\hat j+\hat k+t(\hat i-\hat j+2\hat k) \] and parallel to the line \[ \vec r=-\hat i+2\hat j+s(-\hat i+2\hat j+\hat k) \] in Cartesian coordinates is \[ \frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1, \] then \(a+3b+c=\)

If \[ \int \frac{\tan x}{1+\tan x+\tan^2x}\,dx = x-\frac{K}{\sqrt A} \tan^{-1} \left( \frac{K\tan x+1}{\sqrt A} \right) +C, \] then the ordered pair \((K,A)\) is

Evaluate \[ \int \frac{dx}{(1+\sqrt{x})\sqrt{x-x^2}}. \]

If \[ u=\sqrt{a^2\cos^2\theta+b^2\sin^2\theta} + \sqrt{a^2\sin^2\theta+b^2\cos^2\theta}, \] then the difference between the maximum and minimum values of \(u^2\) is

The maximum volume (in cu. m) of a right circular cone having slant height \(3\) m is