List of top Questions asked in AP EAMCET

The angle made by the resultant vector of two vectors \( 2\hat{i} + 3\hat{j} + 4\hat{k} \) and \( 2\hat{i} - 7\hat{j} - 4\hat{k} \) with the x-axis is:
Evaluate the limit: \[ \lim_{n \to \infty} \left( \frac{1}{\sqrt{n^2}} + \frac{1}{\sqrt{n^2 - 1}} + \dots + \frac{1}{\sqrt{n^2 - (n-1)^2}} \right). \]
The area (in square units) bounded by the curves \( x = y^2 \) and \( x = 3 - 2y^2 \) is:
Evaluate the integral: \[ I = \int_0^{\frac{\pi}{4}} \log(1 + \tan x) \,dx. \]
Evaluate the integral: \[ I = \int \frac{1}{x^2\sqrt{1 + x^2}} \,dx. \]
Evaluate the integral: \[ I = \int \frac{\sin 7x}{\sin 2x \sin 5x} \,dx. \]
Evaluate the integral: \[ I = \int_{-\pi}^{\pi} \frac{x \sin x}{1 + \cos^2 x} \,dx. \]
Evaluate the integral: \[ \int \frac{x^2 - 1}{x^3\sqrt{2x^4 - 2x^2 + 1}} \,dx. \]
The value \( c \) of Lagrange’s Mean Value Theorem for \( f(x) = e^x + 24 \) in \( [0,1] \) is:
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.
Equation of the normal to the curve \( y = x^2 + x \) at the point \( (1,2) \) is:
Evaluate: \[ \lim_{x \to 0} \left[ \frac{1}{x} - \frac{1}{e^x - 1} \right] \]
If \( P = (0,1,2) \), \( Q = (4,-2,-1) \) and \( O = (0,0,0) \), then \( \angle POQ \) is:
If the perpendicular distance from \( (1,2,4) \) to the plane \( 2x + 2y - z + k = 0 \) is 3, then \( k \) is:
The orthocentre of triangle formed by points: \( (2,1,5) \), \( (3,2,3) \) and \( (4,0,4) \) is:
The length of x-intercept made by the pair of lines \( 2x^2 + xy - 6y^2 - 2x + 17y - 12 = 0 \) is:
The transformed equation of \( x^2 - y^2 + 2x + 4y = 0 \) when the origin is shifted to the point \( (-1,2) \) is:
The orthocentre of the triangle formed by lines \( x + y + 1 = 0 \), \( x - y - 1 = 0 \) and \( 3x + 4y + 5 = 0 \) is:
The equation of one side of an equilateral triangle is \( x + y = 2 \), and one vertex is \( (2,-1) \). The length of the side 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:
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:
When an unfair dice is thrown, the probability of getting a number \( k \) on it is \( P(X = k) = k^2 P \), where \( k = 1, 2, 3, 4, 5, 6 \) and \( X \) is the random variable denoting a number on the dice. Then, the mean of \( X \) is:
Two persons A and B throw three unbiased dice one after the other. If A gets the sum 13, then the probability that B gets a higher sum is:
8 teachers and 4 students are sitting around a circular table at random. The probability that no two students sit together is:
The equation of the locus of points that are equidistant from the points \( (2,3) \) and \( (4,5) \) is: