List of top Mathematics Questions asked in TS EAMCET

If \(f(x)\) is a real valued bijective function and twice differentiable function. If \(g(x)\) is inverse of \(f(x)\) and \(f(0)=a\), then \(g''(a)=\)

If \[ y=\frac{x^4+x^2+1}{x^2+x+1}, \] \[ \frac{dy}{dx}=y_1 \] and \[ \frac{d^2y}{dx^2}=y_2, \] then the value of \[ \left| \frac{(1+y_1^2)^{3/2}}{y_2} \right| \] at \[ x=\left(\frac12+\sqrt2\right) \] is

Evaluate \[ \frac{d}{dx}\left(\sin^{-1}(\tan x)+\tan^{-1}(\sin x)\right). \]

Let \[ f(x)= \begin{cases} -150-25x, & -10\le x\le -5,[2mm] x|x|, & -5\le x\le 5,[2mm] 150-25x, & 5\le x\le 10. \end{cases} \] Which of the following is correct?

If \[ \lim_{x\to0}\frac{2^{\tan x}-2^{\sin x}}{x^2\sin x}=k, \] then \(e^{2k}=\)

If the direction cosines of two lines satisfy the relations \[ l+m-n=0, \] \[ 3l^2+m^2+6nl=0, \] then those lines are

If \[ \frac{x+3}{a}=\frac{y-1}{b}=\frac{z}{c} \] is the common line of the two perpendicular planes \[ 2x+3y+4z+d=0 \] and \[ x+py+z+5=0, \] then \(p+d=\)

The foci of the ellipse \[ \frac{x^2}{25}+\frac{y^2}{16}=1 \] and that of the hyperbola \[ \frac{x^2}{a^2}-\frac{y^2}{b^2}=1 \] are same. The greatest length of the transverse axis of the hyperbola such that the difference of the squares of their eccentricities is at least one is

A\((3,5,-4)\), B\((-5,-5,-2)\), C\((-1,1,2)\) are the vertices of a triangle. \(P\) is a point on \(AB\) and \(CP\) is an angle bisector of \(\triangle ABC\). \(G\) is the centroid of the triangle \(ABC\). If the point which divides \(GP\) in the ratio \(1:3\) is \((\alpha,\beta,\gamma)\), then \(\alpha+\beta-\gamma=\)

If the length of minor axis of an ellipse is \[ \frac13 \] times the sum of the distances of any point on the ellipse from its foci, then the eccentricity of the ellipse is

If the latus rectum of the ellipse \[ \frac{x^2}{16}+\frac{y^2}{b^2}=1 \] subtends an angle \[ \frac{\pi}{3} \] at the centre of the ellipse, then \(b^2=\)

Let \(L=0\) be the chord of contact of \((5,1)\) with respect to the circle \[ S\equiv x^2+y^2+8x+10y-8=0. \] If the pole of \(L=0\) with respect to the circle \[ S'\equiv x^2+y^2+4y-21=0 \] is \((-k,-h)\), then \(k+h=\)

If \[ P\equiv y^2+2y-x+6=0 \] is a parabola. \(S=0\) is another parabola such that the axes of \(S=0\) and \(P=0\) are same and the distance between their foci is \[ \frac54. \] If the foci of these parabolas are on either side of the vertex of \(S=0\) and the vertex of \(S=0\) is on the directrix of \(P=0\), then the length of latus rectum of \(S=0\) is

Let \[ S\equiv x^2+y^2-6x+4y+c=0,\qquad S'\equiv x^2+y^2-4x+6y+9=0, \] \[ S''\equiv x^2+y^2+5x+3y+k=0 \] be three circles. If the angles of intersection of the circle \(S'=0\) with the circles \(S=0\) and \(S''=0\) are respectively \[ \frac{\pi}{4} \quad\text{and}\quad \frac{\pi}{2}, \] then \(c+k=\)

If a normal drawn at the point \(t=1\) on the parabola \[ x^2+4y+2x-8=0 \] intersects the parabola again at a point \(A(\alpha,\beta)\), then \(4\alpha\beta=\)

The radical axis of the circles \[ x^2+y^2+4x+6y+7=0 \] and \[ 4x^2+4y^2+8x+12y-24=0 \] is a tangent to the circle \[ x^2+y^2=13 \] at a point \((\alpha,\beta)\), then \(\alpha+\beta=\)

If the locus of midpoints of the chords of the circle \[ S\equiv x^2+y^2-6x-8y-11=0 \] which subtend a right angle at \(A(1,2)\) is another circle \(S'=0\), then the centre of \(S'=0\)

If the equation of the line joining the points \(A(x_1,y_1)\) and \(B(x_2,y_2)\) is \[ ax+by=c \] and the distance between \(A\) and \(B\) is \(\sqrt{a^2+b^2}\), then \(c^2=\)

The line common to the two families of concurrent lines \[ x+y+\lambda(4x+3y-1)=0 \] and \[ 2x-3y+k(x+y-5)=0 \] is along the base of a triangle. If \((1,1)\) is the vertex of the triangle, then the perpendicular distance from that vertex to its base is

The locus of the centre of a circle touching the lines \[ x+2y=0 \] and \[ x-2y=0 \] is

Two diagonal sides of a parallelogram \(ABCD\) are \[ x-y+1=0 \] and \[ 3x-y=9. \] If one of its diagonals is \[ 7x-5y+3=0, \] then the equation of the other diagonal is

The locus of midpoints of the chords of the circle \[ x^2+y^2-2x-2y+1=0 \] which are parallel to the line \[ x+y+2=0 \] is

Equation of the image of the pair of lines \[ ax^2+2hxy+by^2=0 \] with respect to \(y=0\) is

Let \(E\) and \(F\) be two events such that \[ P(\bar E)=\frac13,\qquad P(E\cap F)=\frac13,\qquad P(\overline{E\cup F})=\frac16. \] Which of the following is correct?

Let \(X\) be a discrete random variable. If \[ P(X=r)=\frac{3}{7}a^r,\qquad r=0,1,2,\ldots,\infty,\quad 0<a<1, \] then \(aP(X=2)=\)