List of top Questions asked in AP EAMCET

The distance of a point \( (2,3,-5) \) from the plane \( \vec{r} \cdot (4i - 3j + 2k) = 4 \) is:
There were two women participating with some men in a chess tournament. Each participant played two games with the other. The number of games that the men played among themselves is 66 more than the number of games the men played with the women. Then the total number of participants in the tournament is:
The number of ways a committee of 8 members can be formed from a group of 10 men and 8 women such that the committee contains at most 5 men and at least 5 women is:
The number of ways of distributing 15 apples to three persons A, B, C such that A and C each get at least 2 apples and B gets at most 5 apples is:
5 boys and 6 girls are arranged in all possible ways. Let \(X\) denote the number of linear arrangements in which no two boys sit together, and \(Y\) denote the number of linear arrangements in which no two girls sit together. If \(Z\) denotes the number of ways of arranging all of them around a circular table such that no two boys sit together, then \(X:Y:Z\) = ?
The number of different permutations that can be formed by taking 4 letters at a time from the letters of the word "REPETITION" is:
The number of different ways of preparing a garland using 6 distinct white roses and 6 distinct red roses such that no two red roses come together is:
If all the letters of the word CRICKET are permuted in all possible ways and the words (with or without meaning) thus formed are arranged in dictionary order, then the rank of the word CRICKET is:
If set \( A \) contains 8 elements, then the number of subsets of \( A \) which contain at least 6 elements is:
If all the letters of the word MASTER are permuted in all possible ways and words (with or without meaning) thus formed are arranged in dictionary order, then the rank of the word MASTER is:
The number of ways of selecting 3 numbers that are in GP from the set \( \{1, 2, 3, \dots, 100\} \) is:
The number of ways of arranging 9 men and 5 women around a circular table so that no two women come together are:
If the roots of the quadratic equation \( x^2 - 35x + c = 0 \) are in the ratio 2:3 and \( c = 6K \), then \( K \) is:
If \( a \) is a rational number, then the roots of the equation \( x^2 - 3ax + a^2 - 2a - 4 = 0 \) are:
Simplify the expression: \( 4 + \frac{1}{4 + \frac{1}{4 + \frac{1}{4 + \cdots}}} \)
The set of all real values \( a \) for which \[ -1<\frac{2x^2 + ax + 2}{x^2 + x + 1}<3 \] holds for all real values of \( x \) is:
If both the roots of the equation \( x^2 - 6ax + 2 - 2a + 9a^2 = 0 \) exceed 3, then:
If \[ y = \tan^{-1} \left( \frac{2 - 3\sin x}{3 - 2\sin x} \right), \] then find \( \frac{dy}{dx} \).
If \[ x = 3 \left[ \sin t - \log \left( \cot \frac{t}{2} \right) \right], \quad y = 6 \left[ \cos t + \log \left( \tan \frac{t}{2} \right) \right] \] then find \( \frac{dy}{dx} \).
If \( f(0) = 0 \), \( f'(0) = 3 \), then the derivative of \( y = f(f(f(f(f(x))))) \) at \( x = 0 \) is:
If $$ f(x) = \min \{ x, x^2 \} $$ Which of the following is true? 
If $y = \tan^{-1} \frac{x}{1+2x^2} + \tan^{-1} \frac{x}{1+6x^2} + \tan^{-1} \frac{x}{1+12x^2}$, then $\left(\frac{dy}{dx}\right)_{x=\frac{1}{2}} =$
If \( y = \sinh^{-1} \left(\frac{1 - x}{1 + x} \right) \), then \( \frac{dy}{dx} \) is given by:
If $$ y = 1 + x + x^2 + x^3 + \dots \quad \text{and} \quad |x| < 1, \text{ then } y'' = $$

If the curves $$ 2x^2 + ky^2 = 30 \quad \text{and} \quad 3y^2 = 28x $$ cut each other orthogonally, then \( k = \)