List of top Mathematics Questions asked in TS EAMCET

The position vector of the point of intersection of the line joining the points \( \mathbf{i} - \mathbf{j} + \mathbf{k} \) and the line joining the points \( 2\mathbf{i} + \mathbf{j} - 6\mathbf{k} \), \( 3\mathbf{i} - \mathbf{j} - 7\mathbf{k} \) is:
If \[ 2x^2 - 3xy + 4y^2 + 2x - 3y + 4 = 0 \] then \[ \left( \frac{dy}{dx} \right)_{(3,2)} = \]
If \[ x = \frac{9t^2}{1 + t^4}, \quad y = \frac{16t^2}{1 - t^4} \] then \[ \frac{dy}{dx} = \]
A plane \(\pi\) passes through the points \( (5,1,2) \), \( (3,-4,6) \), and \( (7,0,-1) \). If \( p \) is the perpendicular distance from the origin to the plane \(\pi\) and \([l, m, n]\) are the direction cosines of a normal to the plane \(\pi\), then \([3l + 2m + 5n] =\)
If \(y = \sin ax + \cos bx\) then \(y'' + b^2y =\)
The radius of a sphere is 7 cm. If an error of 0.08 sq.cm. is made in measuring its surface area, then the approximate error (in cubic cm) found in its volume is:
If \( f(x) = (2x-1)(3x+2)(4x-3) \) is a real-valued function defined on \(\left[\frac{1}{2}, \frac{3}{4}\right]\), then the value(s) of 'c' as defined in the statement of Rolle's theorem is:
If the slope of the tangent drawn at any point \((x, y)\) on the curve \(y = f(x)\) is \(y = 6x^2 + 10x - 9\) and \(f(2) = 0\), then \(f(-2) = \)?
The general solution of the differential equation \((3x^2 - 2xy)dy + (y^2 - 2xy)dx = 0\) is
The curve \(y = x^3 - 2x^2 + 3x - 4\) intersects the horizontal line \(y = -2\) at the point \(P(h,k)\). If the tangent drawn to this curve at \(P\) meets the X-axis at \((x_1, y_1)\), then \(x_1 =\)
A particle moving from a fixed point on a straight line travels a distance \(S\) meters in \(t\) sec. If \(S = t^3 - t^2 + t + 3\), then the distance (in mts) travelled by the particle when it comes to rest is:
The direction cosines of two lines are connected by the relations \[ l - m + n = 0, \quad 2lm - 3mn + nl = 0. \] If \( \theta \) is the angle between these two lines, then \( \cos \theta \) is:
If the ratio of the perpendicular distances of a variable point \( P(x,y,z) \) from the X-axis and from the YZ-plane is 2:3, then the equation of the locus of \( P \) is:
The point of intersection of two tangents drawn to the hyperbola \[ \frac{x^2}{a^2} - \frac{y^2}{4} = 1 \] lie on the circle \[ x^2 + y^2 = 5. \] If these tangents are perpendicular to each other, then \( a \) is:
\(\lim_{x \to 0}\) \(\frac{3^{\sin x} - 2^{\tan x}}{\sin x}\) =

The variance of the following continuous frequency distribution is:

class intervalFrequency
0 -- 42
4 -- 83
8 -- 122
12 -- 161

 

Evaluate the limit: \[ \lim_{\theta \to \frac{\pi}{2}} \frac{8\tan^4\theta + 4\tan^2\theta + 5}{(3 - 2\tan\theta)^4} \]
If \(\mathbf{i} + \mathbf{j},\; \mathbf{j} + \mathbf{k},\; \mathbf{k} + \mathbf{i},\; \mathbf{i} - \mathbf{j},\; \mathbf{j} - \mathbf{k}\) are the position vectors of the points \(A, B, C, D, E\) respectively, then the point of intersection of the line \(AB\) and the plane passing through \(C, D, E\) is:
Length of the common chord of the circles \(x^2 + y^2 - 6x + 5 = 0\) and \(x^2 + y^2 + 4y - 5 = 0\) is:

In a triangle \(ABC\), \(\displaystyle \frac{a(rr_1+r_2r_3)}{r_1-r+r_2r_3} =\;?\)

Among the 5 married couples, if the names of 5 men are matched with the names of their wives randomly, then the probability that no man is matched with the name of his own wife is ?

P and Q are the extremities of a focal chord of the parabola \( y^2 = 4ax \). If \( P = (9,9) \) and \( Q = (p, q) \), then \( p - q \) is:
If \(\vec{a},\vec{b}\) are two vectors such that \(\lvert \vec{a}\rvert =3,\;\lvert \vec{b}\rvert =4,\;\lvert \vec{a}+\vec{b}\rvert =\sqrt{37},\;\lvert \vec{a}-\vec{b}\rvert = k,\) and the angle between \(\vec{a}\) and \(\vec{b}\) is \(\theta,\) then \(\frac{4}{13}\,(k \sin \theta)^2 =\,?\)
\(\vec{r}\) is a vector perpendicular to the plane determined by \(\vec{r_1}=2\mathbf{i}-\mathbf{j}\) and \(\vec{r_2}=\mathbf{j}+2\mathbf{k}\). If the magnitude of the projection of \(\vec{r}\) on the vector \(2\mathbf{i}+\mathbf{j}+2\mathbf{k}\) is 1, then \(\lvert \vec{r}\rvert =\,?\)
If \( \vec{b} = \mathbf{i}-\mathbf{j} +2\mathbf{k},\;\vec{c} = \mathbf{i} +2\mathbf{j} -\mathbf{k} \) are two vectors and \( \vec{a} \) is a vector such that \( \cos\angle(\vec{a},\vec{b}\times \vec{c}) = \frac{2}{\sqrt{3}} \). If \( \vec{a} \) is a unit vector, then \( \lvert \vec{a}\times(\vec{b}\times \vec{c})\rvert =\,? \)