List of top Mathematics Questions asked in TS EAMCET

Find the value of \( k \) such that \( 5 \cdot 2^n - 48n + k \) is divisible by 24.
If \( g \circ f \) is a bijective function, then:
If the roots of the quadratic equation \( ax^2 + bx + c = 0 \) are real and distinct, then which of the following conditions must be true?
The value of the integral \( \int_0^1 x^2 \, dx \) is:
If \( \theta \) is an acute angle and \( 2\sin^2 \theta = \cos^4 \frac{\pi}{8} + \sin^4 \frac{3\pi}{8} + \cos^4 \frac{5\pi}{8} + \sin^4 \frac{7\pi}{8} \), then \( \theta \) is:
If \( f(x) = ax^2 + bx + c \) is an even function and \( g(x) = px^3 + qx^2 + rx \) is an odd function, and if \( h(x) = f(x) + g(x) \) and \( h(-2) = 0 \), then \( 8p + 4q + 2r = \)?
Evaluate the integral: \[ \int \frac{dx}{9\cos^2 2x + 16\sin^2 2x} \]

Evaluate the integral: \[ \int \frac{\sec x}{3(\sec x + \tan x) + 2} \,dx \]

In a triangle ABC, if \( r_1 = 6 \), \( r_2 = 9 \), \( r_3 = 18 \), then \( \cos A \) is:
The mean and variance of a binomial variate \(X\) are \(\frac{16}{5}\) and \(\frac{48}{25}\) respectively. Given that \(P(X \geq 1) = 1 - K \left(\frac{3}{5}\right)^7\), find \(5K\):
If \( (2, -1) \) is the point of intersection of the pair of lines \[ 2x^2 + axy + 3y^2 + bx + cy - 3 = 0 \quad \text{then} \quad 3a + 2b + c = \]
The combined equation of a possible pair of adjacent sides of a square with area 16 square units whose centre is the point of intersection of the lines \[ x + 2y - 3 = 0 \quad \text{and} \quad 2x - y - 1 = 0 \] is: \
The slope of a common tangent to the circles \( x^2 + y^2 - 4x - 8y + 16 = 0 \) and \( x^2 + y^2 - 6x - 16y + 64 = 0 \) is:
If 4 letters are selected at random from the letters of the word PROBABILITY, compute the probability that at least one letter is repeated in the selection.
If \( x - 2y - 6 = 0 \) is a normal to the circle \( x^2 + y^2 + 2gx + 2fy - 8 = 0 \) and the line \( y = 2 \) touches this circle, then the radius of the circle can be:
The sum of all the 4-digit numbers formed by taking all the digits from \(2, 3, 5, 7\) without repetition is
If \(A + B + C = 2S\), then \[ \sin(S - A)\,\cos(S - B)\;-\;\sin(S - C)\,\cos S \;=\;? \]
If \(4+3x-7x^2\) attains its maximum value \(M\) at \(x=\alpha\) and \(5x^2-2x+1\) attains its minimum value at \(x=\beta\), then \[ \frac{28\,(M - \alpha)}{5\,(m + \beta)} =\,? \] \textit{(Assume \(m\) is that minimum value of \(5x^2 -2x +1\) at \(x=\beta\))}
If \( z = x + iy \) and the point \( P \) represents \( z \) in the Argand plane, then the locus of \( z \) satisfying the equation \( |z-1| + |z+i| = 2 \) is:

The numerically greatest term in the expansion of (3x - 16y)15 when x = 2⁄3 and y = 3⁄2 is ?

If the coefficients of three consecutive terms in the expansion of (1 + x)23 are in arithmetic progression, then those terms are ?
The general solution of the differential equation \[ \frac{dy}{dx} + \frac{\sin(2x + y)}{\cos x} + 2 = 0 \] is:

If \( A = \begin{pmatrix} 9 & 3 & 0 \\ 1 & 5 & 8 \\ 7 & 6 & 2 \end{pmatrix} \) and

\[ A^T A^{-2} = \begin{pmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{pmatrix} \]

then

\[ \sum_{1 \leq i \leq 3} \sum_{1 \leq j \leq 3} a_{ij} \]

is:

Given a square matrix \(A\) where \(A^2 + I = 2A\), find \(A^9\).
All the letters of the word 'COLLEGE' are arranged in all possible ways and all the seven letter words (with or without meaning) thus formed are arranged in the dictionary order. Then the rank of the word 'COLLEGE' is: