List of top Mathematics Questions asked in AP EAPCET

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

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

The shortest distance between the lines \[ \vec r=\vec a+t\vec b \] and \[ \vec r=\vec c+s\vec d \] where \[ \vec a=\hat i-2\hat j+2\hat k, \quad \vec b=3\hat i-2\hat j-2\hat k, \] \[ \vec c=6\hat i+2\hat j+2\hat k, \quad \vec d=-4\hat i-\hat k, \] is

Given that \[ \vec a=2\hat i-\hat j+2\hat k,\qquad \vec b=\hat i-2\hat j+2\hat k,\qquad \vec c=2\hat i-2\hat j-\hat k, \] if \(\vec d\) is a vector perpendicular to the plane containing \(\vec a,\vec b,\vec c\) and \[ |\vec d-\vec c|=2, \] then \[ |(\vec d-\vec c)\times(\vec a\times\vec b)|= \]

The variance of the following frequency distribution is

If \[ \vec a=2\hat i+\hat j-\hat k \] and \[ \vec b=\hat i-2\hat j+3\hat k, \] then the value of \[ \vec a+\vec b \] is:

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 \(x+5y=\)

The ratio in which the point \[ (3,4) \] divides the line segment joining \[ (1,2) \] and \[ (5,6) \] is:

If \[ A= \begin{bmatrix} 1&2\\ 3&4 \end{bmatrix}, \] then \(\det(A)\) is equal to:

If \[ x+\frac1x=3, \] then the value of \[ x^2+\frac1{x^2} \] is:

If the arithmetic mean of the numbers \[ 2,4,6,\ldots,2n \] is \(\frac{7}{4}\), then \(n\) is equal to:

The distance between the points \[ (1,2) \quad \text{and} \quad (4,6) \] is:

If \[ z=\cos\theta+i\sin\theta, \] then \(|z|\) is equal to:

If \[ \log_a 2+\log_a 5=1, \] then the value of \(a\) is:

If \[ \sin\theta+\cos\theta=1, \] then the value of \[ \sin\theta\cos\theta \] is:

If \[ f(x)=|x-2|+|x+1|, \] then the minimum value of \(f(x)\) is:

If \(\alpha,\beta\) are the roots of the quadratic equation \[ x^2-3x+1=0, \] then the value of \(\alpha^3+\beta^3\) is:

If the coefficients of the first, second, and third terms in the expansion of \( (1+x)^n \) are in the ratio \(1:20:190\), then \(n\) is equal to:

If the coefficient of \(x^2\) in the expansion of \[ (1+x)^5(1-x)^4 \] is \(k\), then \(k\) is equal to:

If \[ \log_2(x-1)+\log_2(x+1)=3, \] then \(x\) is equal to:

If \(5\) is the remainder when \[ 2x^5+kx^4+5x^3-3x^2+2x-1 \] is divided by \[ x^2+x+1, \] then the quotient is:

The number of arrangements of the letters of the word SEARCH such that no letter remains in its original position is:

The number of integers that satisfy both the inequalities \[ x^2-2x+8>0 \] and \[ x^2-3x+2\le 0 \] is:

2 is a zero of the polynomial function \[ f(x)=x^4+kx^3+22x^2-6x-20. \] If \(-2,\alpha,\beta\) are the roots of the equation \[ x^3+3x^2+2kx-40=0 \] and \(\alpha<\beta\), then \(2\alpha+3\beta=\)

If \[ {}^{n}P_{4}=5040 \] and \[ {}^{15}P_{r}=2730, \] then the value of \(n+r\) is: