List of top Mathematics Questions asked in TS EAMCET

If \[ x=\sin2\theta+\sin3\theta,\qquad y=\cos2\theta-\cos3\theta \] then \[ \frac{d^2y}{dx^2} = \]

The probability distribution of a random variable \(X\) is given below. Then, the mean of \(X\) is 

\(X=x_i\)\(0\)\(1\)\(2\)
\(P(X=x_i)\)\(3k^2\)\(2k^2\)\(k^2+k\)

Consider the following:

Assertion (A): \(1^2 + 3^2 + 5^2 + \cdots + 39^2 = 10760\)

Reason (R): The sum of the squares of the first \(n\) odd numbers is \[ \frac{n(4n^2-1)}{3}. \]

The correct answer is:

If \(A\) and \(B\) are the entire domain and range, respectively, of the real-valued function \[ f(x)=\cos^{-1}\!\left(\frac{2-x^2}{2+x^2}\right), \] then \(A\cap B=\)
One of the values of \[ (\sqrt{3}-i)^{5/3} \] is:

If \(|x|\) is so small that \(x^2\) and higher powers of \(x\) may be neglected, and hence \[ \frac{(8-3x)^{1/3}}{(2+3x)^3} \approx \frac{1}{a}(1+bx), \] then \(2ab=\) 

The coefficient of \(x^2\) in the power series expansion of \[ \frac{2x}{(x-1)(x+2)^2} \] when \(|x|<1\) is 

If both \( \alpha \) and \( \beta \) lie in \( \left(-\dfrac{\pi}{4},\,0\right] \), \( \sin(\alpha+\beta) = -\dfrac{33}{65} \), and \( \sin\alpha = -\dfrac{3}{5} \), then \( \tan(2\alpha+\beta) \) is

The variance of the following continuous frequency distribution is 

Class Interval\(0\!-\!10\)\(10\!-\!20\)\(20\!-\!30\)
Frequency\(3\)\(4\)\(3\)
In the binomial expansion of \((1+x)^n\), the coefficients of \(x^{k-1}\), \(x^k\), \(x^{k+1}\) and also the coefficients of \(x^{l-1}\), \(x^l\), \(x^{l+1}\) are in A.P.

Then, the numerically greatest term in the expansion of \((1+x)^{14}\) when \(x=\dfrac{2}{3}\) is
If the general solution of the differential equation \[ \frac{dy}{dx} + \frac{2x+2y-1}{x+y-5} = 0 \] is \[ ax+by-9\log(x+y+p)=c, \] and \(b,a,p\) are in G.P., then the common ratio of this G.P. is
Evaluate \[ \int \frac{x^7-1} {x^8\sqrt{\,1-2x^7+7x^{14}\,}} \,dx. \]
Evaluate \[ \int \frac{\sin^2x\tan x} {\cos^6x+\sin^4x\cos^2x+\cos^4x\sin^2x+\sin^6x}\,dx. \]
Let \(f:\mathbb{R}\rightarrow\mathbb{R}\) be an odd function and \[ \int_{-1}^{1}x^3f''(x)\,dx=\frac85. \] If \[ g(x)=xf(x), \] \[ g'(1)=\frac83 \] and \[ \int_0^1g(x)\,dx=\frac{2}{15}, \] then \(f(1)=\)
The area of the region bounded by the curves \[ y=x^2+1,\qquad x=y^2+1, \] \(X\)-axis, \(Y\)-axis and \(x=2\) (in sq. units) is
If \[ f(x)=\frac{x^3}{1-3x+3x^2}, \] then \[ \lim_{n\to\infty} \frac{2}{n} \sum_{r=1}^{n} f\!\left(\frac{r}{n}\right) = \]
The integrating factor of the linear differential equation in \(x\) given by \[ \frac{dy}{dx}=\frac{1}{3x+y+2} \] is
If the line \[ 2x+y=7 \] touches the curve \[ y=f(x) \] at \[ x=\frac12, \] then the sum of the lengths of the normal and subnormal is
If the local maximum value of the real valued function \[ f(x)=2(x^3-1)-3ax(x+4a),\qquad a>0 \] is \(54\), then \(a=\)
If \[ \int \frac{\cos\left(\frac{7x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\,dx = a\sin x+b\sin2x+c\sin^3x-dx+k, \] then \(a+b+c+d=\)
If \[ \int \frac{e^{\cos x}\sin x}{e^{\cos x}+e^{-\cos x}}\,dx = -\frac12\left[f(x)+\log\!\left(e^{\cos x}+e^{-\cos x}\right)\right]+c \] and \[ f\!\left(\frac{\pi}{3}\right)=\frac12, \] then the number of points at which \(f(x)\) attains the maximum value in \[ [-2\pi,2\pi] \] is
\(f(x)\) is a cubic polynomial and the curve represented by \(y=f(x)\) passes through the origin. The function \(y=f(x)\) is an increasing function in \[ (-\infty,0)\cup(1,\infty) \] and a decreasing function in \[ (0,1). \] If \[ f'(2)=6, \] then the \(c\) of Lagrange's Mean Value Theorem on the interval \([0,2]\) satisfies the equation
If \(P\) is any point on the curve \[ y^2=4ax, \] other than the origin, then the length of the subtangent at \(P\), \(y\)-coordinate of \(P\) and the length of the subnormal at \(P\) are in
The edges of a cuboid are measured with a scale having an error of \(0.01\) cm per cm. If the dimensions of the cuboid are \[ (l,b,h)=(12,5,7), \] then the percentage error in the volume of the cuboid is
Evaluate \[ \frac{d}{dx}\left(\sin^{-1}(\tan x)+\tan^{-1}(\sin x)\right). \]