List of top Mathematics Questions asked in AP EAPCET

If \[ \sin\theta+\cos\theta=\sqrt{2}\cos\alpha, \] where \(0<\theta<\frac{\pi}{2}\), then the value of \[ \sin2\theta \] is:

Let \[ A= \begin{bmatrix} 1 & 2\\ 2 & 1 \end{bmatrix}. \] Then the determinant of \(A^2\) is:

If \[ \tan\theta+\cot\theta=4, \] then the value of \[ \sec^2\theta+\csc^2\theta \] is:

If the ends of the major axis \(A'\) and \(A\) of the ellipse \[ \frac{(x-2)^2}{a^2}+\frac{(y-3)^2}{b^2}=1 \] are respectively at distances \(9\) and \(3\) units from a directrix \(L\), then the foci of the ellipse are:

Consider the hyperbola \[ S \equiv \frac{x^2}{25}-\frac{y^2}{16}-1=0. \] Let \(B,B'\) be the ends of the transverse axis of the conjugate hyperbola of \(S=0\). If \(C\) is the circle with \(B,B'\) as ends of a diameter, then the slope of a common tangent to \(C\) and the given hyperbola is:

If the feet of the perpendiculars drawn from the point \[ (3,4,5) \] to the \(X\)-, \(Y\)- and \(Z\)-coordinate axes are \(A,B,C\) respectively and the angle between \(AB\) and \(AC\) is \[ \cos^{-1}\left(\frac{9}{a}\right), \] then the value of \(a\) is:

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

Let \[ O(0,0,0) \] and \[ A(2,1,-3) \] be vertices of a triangle \(OAB\). If \[ (-1,2,1) \] is the midpoint of side \(AB\), and the perimeter of the triangle is \[ \sqrt2\,(k+l\sqrt7+m\sqrt{13}), \] then the value of \[ k+l+m \] is:

The value of \[ \sin^2 15^\circ+\cos^2 15^\circ \] is

If \[ \log_2(x-1)+\log_2(x-3)=3, \] then the value of \(x\) is

The centre of the circle which intersects the circles \[ x^2+y^2-8x+10y+5=0 \] and \[ x^2+y^2-2x+2y+1=0 \] orthogonally 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 equation \[ 2x^2-5x+k=0 \] has equal roots, then the value of \(k\) 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:

If the equation \[ x^2-6x+y^2+8y+9=0 \] represents a circle, then its radius is:

The eccentricity of the hyperbola \[ 16x^2-9y^2=144 \] is

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

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

The equation of the tangent to the ellipse \[ \frac{x^2}{16}+\frac{y^2}{9}=1 \] which is parallel to the line \[ 3x+4y+5=0 \] is

If \[ \int_0^1 (3x^2+2x+1)\,dx=k, \] then the value of \(k\) is

A bag \(P\) contains \(5\) white and \(4\) blue balls. Another bag \(Q\) contains \(4\) white and \(5\) blue balls. One ball is drawn at random from bag \(P\) and transferred to another bag. Then one ball is drawn from bag \(Q\). Find the probability that the ball drawn from bag \(Q\) has the same colour as the ball transferred from bag \(P\).

If the probability function of a random variable \(X\) is \[ P(X=x)=ak^x,\qquad x=0,1,2,\ldots, \] then the value of \(k\) 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

From the set of numbers \[ \{1,2,3,4,5,6,7,8,9,10,11,12\}, \] two numbers are selected at random. The probability that the two numbers selected differ by a prime number is