List of top Mathematics Questions asked in AP EAPCET

If the angular bisectors of the lines \[ 3x-4y-5=0 \] and \[ 8x-6y+1=0 \] are \[ x+y+c=0 \] and \[ x-y+k=0, \] then \[ 7(c+k)= \]

In a binomial distribution \[ P(X=2)\div P(X=23)=\left(\frac{2}{3}\right)^{21}, \] then the mean of the binomial distribution is

In \(\triangle ABC\), if \[ c=9,\qquad s=10,\qquad \Delta=10\sqrt2, \] then \[ \sin\frac{C}{2} = \]

If \(|x|\) is so small that \(x^2\) and higher powers of \(x\) may be neglected, then the approximate value of \[ \left(\frac{3x+64}{3x+8}\right)^{\frac{2}{3}} \] is

Find the area of the region bounded by the curve \[ y=x^2-4, \] the \(x\)-axis and the lines \(x=-2\) and \(x=3\).

If a non-horizontal line \(L\) passes through the point \((4,-2)\) and the distance of \(L\) from the origin is \(2\) units, then the equation of the line \(L\) is

If the equation of the line passing through the orthocentre and circumcentre of triangle \(ABC\), whose vertices are \(A(3,1)\), \(B(3,3)\), \(C(6,1)\), is \(2x+by+c=0\), then \(b+c=\)

The following table gives the probability distribution of a random variable \(X\): \[ \begin{array}{|c|c|c|c|c|} \hline x_i & 0 & 1 & 2 & 3 \\ \hline P(X=x_i) & 0.1 & 0.3 & 0.5 & 0.1 \\ \hline \end{array} \] The standard deviation of \(X\) is:

If the mean of the set of values \( (3,6,9,10,n) \) is \( 9 \), then the variance of the given set of values is:

In a triangle \(ABC\), \(\dfrac{r_3+r_2}{r_2+r_1}=\)

If \[ \frac{f(x)}{(x-1)(x-2)} = \frac{2}{x-2} - \frac{1}{x-1} \] and \[ f(x)+\frac{xf(x)}{(x-1)(x-2)} = g(x)+\frac{A}{x-2}+\frac{B}{x-1}, \] then $g(A+B)=$

Evaluate $\int_{-\pi}^{\pi} \frac{\cos^2 x}{1+a^x} dx$

Area between $y^2=x$ and $y=|x|$ is:

Let \(\theta\) be the angle between the line \[ \frac{x+1}{1}=\frac{y-1}{2}=\frac{z-2}{2} \] and the plane \[ 2x-y+\sqrt{\lambda}\,z+4=0. \] If \[ \sin\theta=\frac13, \] then the value of \(\lambda\) is:

Let \[ \vec a=\hat i+2\hat j+2\hat k, \qquad \vec b=2\hat i+\hat j+2\hat k. \] If \(\theta\) is the angle between \(\vec a\) and \(\vec b\), then the value of \[ \cos\theta \] is:

The product of the slopes of the non-horizontal normals drawn through the point \[ (6,0) \] to the parabola \[ y^2=8x \] is:

If \[ y=mx+\frac{3}{m} \] is a tangent to the parabola \[ y^2=4ax \] at the point \(P(3,\beta)\), where \(\beta<0\), then the value of \[ 3m-\beta \] is:

If the pole of the line \[ 2x+3y-20=0 \] with respect to the circle \[ x^2+y^2-4x+6y-12=0 \] is \((\alpha,\beta)\), then the number of tangents that can be drawn from \((\alpha,\beta)\) to the given circle is:

The equation of the normal to the parabola \[ y^2=12x \] at the point \((3\lambda^2,6\lambda)\) is

If \[ X\sim B\!\left(n,\frac14\right), \] \[ P(X=2)=P(X=3) \] and \[ \sum_{k=0}^{2}P(X=k)=\frac{39}{411}, \] then \(n=\)

In a sample space, \(E\) is an event associated with the events \(A\) and \(B\). If \[ P(A|E)=l \] and \[ P(E|B)=m, \] then \(P(B|E)\) is

The variance of the following frequency distribution is

If \[ |\vec a|=2k, \qquad |\vec b|=k \] and \[ |\vec a-\vec b|^2=20k^2-|2\vec a+\vec b|^2, \] then \[ |\vec a\times\vec b| = \ ? \]

Let \(\vec a,\vec b\) be two non-collinear vectors. If \[ \vec r=(x+2y-3)\vec a+(2x-y+1)\vec b \] and \[ \vec R=(3x-y-2)\vec a+(x+3y+2)\vec b \] are vectors such that \[ 2\vec r=m\vec R, \] then \(x+5y=\)