List of top Mathematics Questions asked in AP EAPCET

If \[ \frac34+\frac{15}{16}+\frac{63}{64}+\cdots+n \text{ terms} =\frac{939}{256}, \] then $5n=$

A $\subseteq \mathbb{R}$ and $f:A \to \mathbb{R}$ is a function defined by $f(x)=\dfrac{x-1}{x+1}$. If the domain of the function $f(2x)$ is $B$, then $A \cap B =$

If the point P which divides the line segment joining $A(1,1,1)$ and $B(2,2,2)$ in the ratio 1: m lies on the plane $x+2y+3z-1=0$, then $m=$

If $I_{n}=\int\sin^{n}x dx$, then $I_{6}-\frac{5}{6}I_{4}=$

If $X\sim B(n,p)$ is a binomial variate, $8p^2+15p-2=0$ and the product of the mean and variance of $X$ is $\dfrac78$, then $P(X=4)=$

Consider the random experiment of throwing a die and tossing a coin. Let \[ \{(a,b)\mid a\in\{H,T\},\ b\in\{1,2,\ldots,6\}\} \] denote the outcomes of the experiment. If $X$ is a random variable defined by \[ X(a,b)=b, \] then the variance of $X$ is

Let $[y]$ represent the greatest integer less than or equal to $y$. Then the set of all $x$ at which $f(x)=\cos^{-1}[4x+3]$ is differentiable is

If the function $f(x)=\begin{cases}\frac{2h(x)-g(x)}{(h(x)+7)^{2/3}}, & x\ne0 \\ \frac{7}{4}, & x=0\end{cases}$ is continuous at $x=0$ and $\lim_{x\rightarrow0}h(x)=1$, then $\lim_{x\rightarrow0}g(x)=$

Let $f:\mathbb{R}^{+}\rightarrow\mathbb{R}$ be such that $f(e)=\frac{7}{4}$ and $f^{\prime}(x^{2})=\frac{3\log x}{x^{2}}$, then $f(e^{2})=$

If $\lim_{n\rightarrow5}(\frac{[n]}{2})^{3}-(\frac{[n]^{3}}{2^{4}})=k$, then $\lim_{n\rightarrow k^{+}}(\frac{[n]}{2})^{3}-(\frac{[n]^{3}}{2^{4}})=$

$\lim_{x\rightarrow1}\frac{(9x-1)(\sqrt{x}-1)}{3x^{2}+2x-5}=$

The area of the region bounded by the curve $y=x^{2}+x$, the lines $y=x$, $x=1$ and $y=2$ is

The mean deviation about the mean for the following data is \[ \begin{array}{c|cccc} x_i & 1 & 2 & 4 & 7\\ \hline f_i & 3 & 2 & 4 & 1 \end{array} \]

If $\int\frac{1}{x^{2}+4x+\alpha}dx=\frac{1}{2\sqrt{2}}\tan^{-1}\left(\frac{x+2}{2\sqrt{2}}\right)+c$, then $\int\frac{1}{x^{2}+4x-\alpha}dx=$

If \[ \frac{x}{(x^2+1)^2(x-1)} = \frac{Ax+B}{x^2+1} + \frac{Cx+D}{(x^2+1)^2} + \frac{E}{x-1}, \] then \[ A+B-C+2D= \]

If the acute angle between the parabolas $y=8x-x^{2}$ and $y=x^{2}-4x$ is $\theta$, then $\tan\theta=$

If $(h, k)$ is the pole of the line $2x-3y+4=0$ with respect to the circle $x^{2}+y^{2}-4x+6y-3=0$, then $10h+k=$

When the origin is shifted to the point \[ \left(\frac74,-\frac14\right) \] by translation of axes, the transformed equation of \[ x^2-2xy+3y^2+2gx+2fy-6=0 \] is \[ 8X^2-16XY+24Y^2+k=0. \] Then \[ -27(2f+g)= \]

The shortest distance between the two lines \[ \vec r=(\hat i-\hat j)+s(\hat j+2\hat k) \] and \[ \vec r=(2\hat i+\hat k)+t(\hat i-\hat j+\hat k) \] is

Assertion (A): If each of the angles $A,B,C$ is not a multiple of $\pi$, then the vectors \[ \vec r_1=(\sec^2A)\hat i+\hat j+\hat k, \] \[ \vec r_2=\hat i+(\sec^2B)\hat j+\hat k, \] \[ \vec r_3=\hat i+\hat j+(\sec^2C)\hat k \] are coplanar. Reason (R): The three vectors \[ \vec a=a_1\hat i+a_2\hat j+a_3\hat k, \] \[ \vec b=b_1\hat i+b_2\hat j+b_3\hat k, \] \[ \vec c=c_1\hat i+c_2\hat j+c_3\hat k \] are coplanar if and only if \[ \begin{vmatrix} a_1&a_2&a_3\\ b_1&b_2&b_3\\ c_1&c_2&c_3 \end{vmatrix}=0. \] Which of the following is true?

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

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 \( \lambda+\mu = \)

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 \( (\frac{x_n}{n-1})^2 = \)

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

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