List of top Mathematics Questions asked in AP EAPCET

If \[ y=a\log|x|+bx^2+x \] has its extremum values at \[ x=-1 \quad\text{and}\quad x=2, \] then \((a,b)=\)

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 set of all values of \( \theta \) satisfying \(0<\theta<\frac{\pi}{2}\) and \[ \begin{vmatrix} 1+\sin^2\theta & \cos^2\theta & 4\sin4\theta
\sin^2\theta & 1+\cos^2\theta & 4\sin4\theta
\sin^2\theta & \cos^2\theta & 1+4\sin4\theta \end{vmatrix} =0 \] is

A random variable $X$ has the following probability distribution:
$X = x$: 0, 1, 2, 3, 4, 5
$P(X=x)$: $k$, $3k$, $5k$, $7k$, $9k$, $11k$
Then the value of $k$ is:

The value of $\lim_{x \to \infty} \left(\frac{x+6}{x+1}\right)^{x+4}$ is:

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

The value of the limit $\lim_{x \to 0} \frac{e^{3x} - e^{-2x}}{\sin 4x}$ is:

If $\frac{3x + 4}{(x-1)(x-2)^2} = \frac{A}{x-1} + \frac{B}{x-2} + \frac{C}{(x-2)^2}$, then $A + B + C =$

If \(I = \int \frac{\sin x + \sin^3 x}{\cos 2x} dx = P \cos x + Q \log \left| \frac{\sqrt{2} \cos x - 1}{\sqrt{2} \cos x + 1} \right|\) (where \(c\) is a constant of integration), then values of \(P\) and \(Q\) are respectively

If the mean and variance of a random variable X having binomial distribution are 4 and 2 respectively, then \( P(X=2)= \)

One of the partial fractions of \[ \frac{2x^2+x-3}{(x^2+2)(3x-1)} \] is

The acute angle between the planes $2x - y + z = 6$ and $x + y + 2z = 3$ is:

The set of all the points at which \[ f(x)=|2-|x|| \] is continuous but not differentiable is:

Evaluate: \[ \lim_{x\to e}\frac{\log x-1}{x-e} \]

The locus of the point \(z=x+iy\) satisfying \[ \left|\frac{z-(2+i)}{z+(2-i)}\right|=2 \] is:

The order and degree of the differential equation $\left[1 + \left(\frac{dy}{dx}\right)^2\right]^{3/2} = \frac{d^2y}{dx^2}$ are respectively:

The locus of the point which forms a right-angled triangle with the fixed points \((2,3)\) and \((5,1)\) is

If $\omega$ is a complex cube root of unity, then $(1 - \omega + \omega^2)^5 + (1 + \omega - \omega^2)^5 =$

If a tangent drawn to the parabola \( y^{2}=16x \) meets the curve \( xy=4 \) at the points P and Q, then the locus of midpoint of PQ is

Evaluate \[ \int_{1/e}^{e^2} \left| \frac{\log_e x}{x} \right| \,dx \]

If \[ f(x)=\frac1{x^2}\int_{3}^{x}\left(2t-3f'(t)\right)\,dt, \] then \[ f'(3)= \]

The area of the region enclosed between the curve \[ y=\log_e(x+e) \] and the coordinate axes is

If \[ y= \tan^{-1}\!\left(\frac{1}{1+x+x^2}\right) + \tan^{-1}\!\left(\frac{1}{x^2+3x+3}\right) + \tan^{-1}\!\left(\frac{1}{x^2+5x+7}\right), \] then \[ y'(0)= \]

PSQ is a focal chord of the parabola \[ y^2=12x. \] \(A\) and \(B\) are respectively the feet of the perpendiculars drawn from \(P\) and \(Q\) on the directrix of the parabola. If the length of \(AB\) is \(7\sqrt3\) and \[ P=(3t^2,6t), \qquad (0<t<1), \] then \(t=\)

The acute angle between the lines whose direction cosines satisfy \[ l^2-5m^2+n^2=0 \] and \[ l+m-n=0 \] is