List of top Questions asked in AP EAMCET- 2024

The rank of the word "TABLE" counted from the rank of the word "BLATE" in dictionary order is:
Find the sum of the sequence: \( 2 + 3 + 5 + 6 + 8 + 9 + \dots + 2n \) terms.
In \( \triangle PQR \), \((4\overline{i} + 3\overline{j} + 6\overline{k} )\) and \((3\overline{i} + \overline{j} + 3\overline{k} )\) are the position vectors of the vertices P, Q, R respectively. Then the position vector of the point of intersection of the angle bisector of \( P \) with \( QR \).
Equation of the normal to the curve \( y = x^2 + x \) at the point \( (1,2) \) is:
If the slope of one of the pair of lines represented by \( 2x^2 + 3xy + Ky^2 = 0 \) is 2, then the angle between the pair of lines is:
The length of x-intercept made by the pair of lines \( 2x^2 + xy - 6y^2 - 2x + 17y - 12 = 0 \) is:
If \( M_1 \) and \( M_2 \) are the maximum values of \( \frac{1}{11 \cos 2x + 60 \sin 2x + 69} \) and \( 3 \cos^2 5x + 4\sin^2 5x \) respectively, then \( \frac{M_1}{M_2} = \):
Displacement \( s \) of a particle at time \( t \) is expressed as \( s = 2t^3 - 9t \). Find the acceleration at the time when the velocity vanishes.
The value \( c \) of Lagrange’s Mean Value Theorem for \( f(x) = e^x + 24 \) in \( [0,1] \) is:
The area (in square units) bounded by the curves \( x = y^2 \) and \( x = 3 - 2y^2 \) is:
In a Binomial distribution, the difference between the mean and standard deviation is 3, and the difference between their squares is 21. Then, the ratio \( P(x = 1) : P(x = 2) \) is:
Evaluate: \[ \lim_{x \to 0} \left[ \frac{1}{x} - \frac{1}{e^x - 1} \right] \]
Let \( f(x) \) be defined as: \[ f(x) = \begin{cases} 0, & x = 0 \\ 2 - x, & 0 < x < 1 \\ 2, & x = 1 \\ 1 - x, & 1 < x < 2 \\ -\frac{3}{2}, & x \geq 2 \end{cases} \] Then which of the following is true?
If \( f(x) = \left(\frac{1+x}{1-x}\right)^{\frac{1}{x}} \) is continuous at \( x = 0 \), then \( f(0) \) is:
The domain of the real-valued function \( f(x) = \sqrt{9 - \sqrt{x^2 - 144}} \) is
The function \( f(x) = |x - 24| \) is:
If set A has 5 elements, and set B has 7 elements, then the number of one-one functions that can be defined from A to B is
If \( |x| < 1 \), then the number of terms in the expansion of \( \left[ \frac{1}{2} (1.2 + 2.3x + 3.4x^2 + \dots) \right]^{-25} \) is:
If \( |x| < 1 \), the coefficient of \( x^2 \) in the power series expansion of \( \frac{x^4}{(x+1)(x-2)} \) is:
A bag contains 6 balls. If three balls are drawn at a time and all of them are found to be green, then the probability that exactly 5 of the balls in the bag are green is:
If \( f(x) = x^x \), then the interval in which \( f(x) \) decreases is:
The area of the region under the curve \( y = |\sin x - \cos x| \) in the interval \( 0 \leq x \leq \frac{\pi}{2} \), above the x-axis, is (in square units):
7 coins are tossed simultaneously and the number of heads turned up is denoted by the random variable \( X \). If \( \mu \) is the mean and \( \sigma^2 \) is the variance of \( X \), then \( \frac{\mu^2}{P(X = 3)} \) is:
If \( P(2, \beta, \alpha) \) lies on the plane \( x + 2y - z - 2 = 0 \) and \( Q (\alpha, -1, \beta) \) lies on the plane \( 2x - y + 3z + 6 = 0 \), then the direction cosines of the line \( PQ \) are:
Let \( \pi \) be the plane that passes through the point \( (-2,1,-1) \) and is parallel to the plane \( 2x - y + 2z = 0 \). Then the foot of the perpendicular drawn from the point \( (1,2,1) \) to the plane \( \pi \) is: