List of top Questions asked in TS EAMCET

The area of a triangle is obtained with lengths of two sides and included angle between them. If the angle is measured as $60^{\circ}20^{\prime}$ instead of $60^{\circ}$, then the percentage error in its area is}

Plane through (3,5,7), (7,-5,3) parallel to line joining (1,-2,-4) and (4,2,-1) is \(ax+by+cz+80=0\). Then \(a+b+c=\)

If $f(x)=\begin{cases}\frac{x}{|x|}when~x\ne0\\ |x|when~x=0\end{cases}$ is a real valued function, then}

If the function $\Gamma(x)=\begin{cases}\frac{sin^{2}ax-sin^{2}bx}{x^{2}} & x<0 \\ x & x=0 \\ \frac{(s+2x^{2})^{\frac{1}{2}}-x^{\frac{3}{2}}}{sin^{2}x} & 0<x<\pi\end{cases}$ is continuous at $x=0$, then $a^{2}+b=$}

Direction cosines satisfy \(l-2m+n=0\), \(2l^2-3m^2+n^2=0\). Angle between lines is

If A(1,2,-3), B(2,3,-1), C(3,1,-2) are vertices of triangle ABC, then area is

For an ellipse, distance between centre and focus is \(\sqrt7\) and semi-latus rectum is \(\frac{9}{4}\). Area of triangle formed by foci and one end of minor axis is

Line \(x+y+k=0\) touches hyperbola \(x^2-5y^2=5\). Point of contact is

Common tangent to circle \(x^2+y^2=4\) and parabola \(y^2=8\sqrt2 x\) is \(y=mx+c\). Then \(\sqrt{m+c^2}=\)

For ellipse \(9x^2+25y^2=225\), focal chord \(L_1\) makes equal intercepts on axes. Intersection with tangent at end of latus rectum lies in

For parabola \(y^2=5x\), normal at P meets x-axis at Q. If PQ subtends \(60^\circ\) at vertex, slope of normal is

If \((h,k)\) is the centre of a circle cutting three circles orthogonally, then \(\frac{3}{h}+\frac{1}{k}=\)

If \((h,k)\) is external centre of similitude of circles \[ x^2+y^2-6x-10y+9=0 \] and \[ x^2+y^2+6x+6y+2=0, \] then \(k-h=\)

If \(\theta\) is the angle between the circles \[ x^{2}+y^{2}+2x-4y-4=0,\quad x^{2}+y^{2}-4x-6y-3=0 \] then \(\cos\theta=\)

For circle \(x^2+y^2+12x-4y-9=0\), line \(x+2y-3=0\) represents

Tangent to circle \(x^2+y^2-4x-8y-5=0\) equally inclined to axes is \(x+by+c=0\), \(b0\). Find \(2b+c\).

If line \(2y-3=0\) bisects angle between \(x+2y-k=0\) and \(x-2y+k=0\), then a point on the bisector of other angle is

A circle makes intercepts \(2\sqrt7\) and \(2\sqrt{12}\) on axes and diameter lies on \(3x+2y=0\). Find a point on circle.

If the image of the point (2,6) in the line \(x-3y+10=0\) is (h,k), then \(2h-k=\)

Let P be a variable point such that it forms a triangle of area 14 square units with two fixed points \((-3,4)\) and \((4,-3)\). Then the locus of P represents a pair of parallel lines. The distance between these two parallel lines is

Point \((a,2a)\), \(a>0\), lies in region between lines \(3x-y-3=0\) and \(6x-y-6=0\). Then \(a\in\)

If an acute angle \(\theta\) is used to rotate axes to remove the \(xy\)-term from \[ 4x^{2}+3xy+y^{2}+1=0, \] then \((1+\tan\theta)^2=\)

If sum of reciprocals of intercepts of a line equals A.M. of \(\frac{2}{3}\) and \(\frac{4}{5}\), then point of concurrence is

If \(P(X=k)=c\left(\frac{2}{7}\right)^k,\ k=0,1,2,\dots\), then \(P(X=2)=\)

A card is drawn from 52 cards. If A = diamond, B = ace, probability that exactly one occurs is