List of top Mathematics Questions asked in TS EAMCET

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:
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 \(x_1 =\)
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

 

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 \(\lvert \vec{r}\rvert =\,?\)
A plane \( (\pi) \) passing through the point \( (1,2,-3) \) is perpendicular to the planes \( x + y - z + 4 = 0 \) and \( 2x - y + z + 1 = 0 \). If the equation of the plane \( (\pi) \) is \( ax + by + cz + 1 = 0 \), then \( a^2 + b^2 + c^2 \) is equal to:
In a triangle \(ABC\), if \(\tan\tfrac{A}{2} : \tan\tfrac{B}{2} : \tan\tfrac{C}{2} = 15 : 10 : 6\), then \(\frac{a}{b - c} = \,?\)
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:
A, B, C are the vertices of a triangle ABC. If the bisector of \( \angle BAC \) intersects the side BC at D\((p,q,r)\), then \( \sqrt{2p+q+r} = ? \)
Evaluate the integral: \[ I = \int_{\frac{-3\pi}{4}}^{\frac{\pi}{6}} \log(\sin(4x+3)) \,dx \]
Evaluate the integral: \[ \int_0^{16} \frac{\sqrt{x}}{1 + \sqrt{x}} dx. \]
Evaluate the integral: \[ I = \int_{0}^{32\pi} \sqrt{1 - \cos 4x} \,dx \]
The vertical angle of a right circular cone is \( 60^\circ \). If water is being poured into the cone at the rate of \( \frac{1}{\sqrt{3}} \) m\(^3\)/min, then the rate (m/min) at which the radius of the water level is increasing when the height of the water level is 3m is:
Among the following four statements, the statement which is not true, for all \( n \in N \) is:
The mean of a binomial variate \( X \sim B(n, p) \) is 1. If \( n>2 \) and \( P(X = 2) = \frac{27}{128} \), then the variance of the distribution is:}
Bag \( P \) contains 3 white, 2 red, 5 blue balls and bag \( Q \) contains 2 white, 3 red, 5 blue balls. A ball is chosen at random from \( P \) and is placed in \( Q \). If a ball is chosen from bag \( Q \) at random, then the probability that it is a red ball is:
If the distance from a variable point \( P \) to the point \( (4,3) \) is equal to the perpendicular distance from \( P \) to the line \( x + 2y - 1 = 0 \), then the equation of the locus of the point \( P \) is:
If \( \beta \) is the angle made by the perpendicular drawn from origin to the line \( L = x + y - 2 = 0 \) with the positive X-axis in the anticlockwise direction. If \( a \) is the X-intercept of the line \( L = 0 \) and \( p \) is the perpendicular distance from the origin to the line \( L = 0 \), then \( \tan \beta + p^2 = \):
If \( (l, k) \) is a point on the circle passing through the points \( (-1, 1) \), \( (0, -1) \), and \( (1, 0) \), and if \( k \neq 0 \), then find \( k \).

If (h,k) is the image of the point (3,4) with respect to the line 2x - 3y -5 = 0 and (l,m) is the foot of the perpendicular from (h,k) on the line 3x + 2y + 12 = 0, then lh + mk + 1 = 2x - 3y - 5 = 0.