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AP EAPCET
List of top Questions asked in AP EAPCET
If \( P(X = x) = k \left( \frac{3}{8} \right)^x \), where \( x = 1, 2, 3, \dots \) is the probability distribution function of a discrete random variable X, then \( k = \)
AP EAPCET - 2023
AP EAPCET
Mathematics
Probability
The diagonals AC and BD of a rhombus ABCD intersect at the point (3, 4). If \( BD = \frac{2}{\sqrt{2}} \), \( A = (1, 2) \), \( A = (\alpha, \beta) \), \( D = (\gamma, \delta) \), and \( \alpha<\delta<\gamma<\beta \), then \( \beta + \gamma - \delta = \dots \)
AP EAPCET - 2023
AP EAPCET
Mathematics
Geometry
The lines \( p(x^2 + 1) + x - y + q = 0 \) and \( (p^2 + 1)x^2 + (p^2 + 1)y + 2q = 0 \) are perpendicular to a line L. Then the equation of the line L is:
AP EAPCET - 2023
AP EAPCET
Mathematics
Geometry
If \( 2x^2 - 3xy + y^2 = 0 \) represents two sides of a triangle and \( x + y - 1 = 0 \) is its third side, then the distance between the orthocenter and the circumcenter of that triangle is:
AP EAPCET - 2023
AP EAPCET
Mathematics
Geometry
Assertion (A): The difference of the slopes of the lines represented by \( y^2 - 2xy \sec^2 \alpha + (3 + \tan^2 \alpha) \left( 1 + \tan^2 \alpha \right) \cos^2 \theta = 0 \) is 4.
Reason (R): The difference of the slopes represented by \( ax^2 + 2hxy + by^2 = 0 \) is \( \frac{2\sqrt{h^2 - ab}}{|b|} \).
AP EAPCET - 2023
AP EAPCET
Mathematics
Geometry
If \( A(3, -1, 1), B(0, 2, 3), C(4, 8, 11) \) are three points, then the coordinates of the foot of the perpendicular drawn from the point A to the line joining the points B and C is:
AP EAPCET - 2023
AP EAPCET
Mathematics
Geometry
If \( S \) is the set of all real values of \( a \) such that a plane passing through the points \( (-a^2, 1, 1), (1, -a^2, 1), (1, 1, -a^2) \) also passes through the point \( (-1, -1, 1) \), then \( S = \dots \)
AP EAPCET - 2023
AP EAPCET
Mathematics
Geometry
The distance between the centres of similitude of the circles \( x^2 + y^2 + 6x - 8y + 16 = 0 \) and \( x^2 + y^2 - 2x - 2y + 1 = 0 \) is:
AP EAPCET - 2023
AP EAPCET
Mathematics
Geometry
Let P and Q be the inverse points with respect to the circle \( S = x^2 + y^2 - 4x - 6y + k = 0 \), and C be the center of the circle. If \( CP.CQ = 4 \), and \( P = (1, 2) \), then \( Q = (a, b) \) and \( 2a = \dots \)
AP EAPCET - 2023
AP EAPCET
Mathematics
Geometry
Let \( A(2, 3) \), \( B(3, -1) \), and \( C(-3, 2) \) be three points. If the centre of the circle passing through A, B, and C is \( (h, k) \), then \( 2k - 4 = \):
AP EAPCET - 2023
AP EAPCET
Mathematics
Geometry
If \( P \left( \frac{\pi}{3} \right) \) and \( Q \left( \frac{2\pi}{3} \right) \) represent two points on the circle \( x^2 + y^2 - 4x - 6y - 12 = 0 \) in parametric form, then the length of the chord PQ is:
AP EAPCET - 2023
AP EAPCET
Mathematics
Geometry
Let \( A(1,2) \) be the centre and 3 be the radius of a circle \( S \). Let \( B(-1, -1) \) be the centre and \( r \) be the radius of another circle \( S_1 \). If \( \frac{\pi}{3} \) is the angle between the circles \( S \) and \( S_1 \), then the number of possible values of \( r \) is:
AP EAPCET - 2023
AP EAPCET
Mathematics
Geometry
The perpendicular distance from the origin to the focal chord drawn through the point \( (4, 5) \) to the parabola \( y^2 - 4y - 3x + 7 = 0 \) is:
AP EAPCET - 2023
AP EAPCET
Mathematics
Geometry
Let the length of the latus rectum of an ellipse \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \) be equal to the length of its semi-major axis. If the radius of its director circle is \( \sqrt{3} \) and \( e \) is its eccentricity, then the length of its latus rectum is:
AP EAPCET - 2023
AP EAPCET
Mathematics
Geometry
Let \( (1, 2) \) be the focus and \( x + y + 1 = 0 \) be the directrix of a hyperbola. If \( \sqrt{3} \) is the eccentricity of the hyperbola, then its equation is:
AP EAPCET - 2023
AP EAPCET
Mathematics
Geometry
If \( S = \frac{x^2}{k - 7} - \frac{y^2}{11 - k} = 0, k \in \mathbb{R}, k \neq 7,11 \), then which one of the following statements is incorrect?
AP EAPCET - 2023
AP EAPCET
Mathematics
Conic sections
The function \( f(x) = \frac{\sqrt{3x^2 - 5x - 2}}{2x^2 - 7x + 5} \) has discontinuous points at \( x = \dots \)
AP EAPCET - 2023
AP EAPCET
Mathematics
Rational Numbers
If \( f(x) \) is defined as follows:
\[ f(x) = \begin{cases} \frac{x - \lfloor x \rfloor}{x - 2} & \text{if } x = 2 \\ \frac{|x - \lfloor x \rfloor|}{a^2 + (x - \lfloor x \rfloor)^2} & \text{if } 1 < x < 2 \\ 2a - b & \text{if } x = 1 \end{cases} \]
Then the limit \( \displaystyle \lim_{x \to 0} \frac{\sin(ax) + x \tan(bx)}{x^2} \) is:
AP EAPCET - 2023
AP EAPCET
Mathematics
limits of trigonometric functions
Let \( [x] \) represent the greatest integer not more than \( x \). The discontinuous points of the function
\[ f(x) = \frac{5 + [x]}{\sqrt{11 + [x]} - 6x + 2 + [x]} \]
lie in the interval:
AP EAPCET - 2023
AP EAPCET
Mathematics
limits of trigonometric functions
If \( x^x y^y = e^e \), then \( \left( \frac{d^2 y}{dx^2} \right)_{(e, e)} = \):
AP EAPCET - 2023
AP EAPCET
Mathematics
Differentiation
A body 'A' of mass $ m_1 $ moving with a velocity of 6 m/s collides with another body 'B' of mass $ m_2 $ which is at rest. After collision if 'A' moves with 2 m/s and 'B' moves with 3 m/s in the initial direction of A, then the ratio of $ \frac{m_1}{m_2} $ is
AP EAPCET - 2023
AP EAPCET
Physics
Momentum and Force
If \( f(x) = |x - 5| + |x + 5| + |x - 4| + |x + 4| \), then
\[ \frac{f'(1) - f'(-6)}{f'(1) + f'(-6)} \]
AP EAPCET - 2023
AP EAPCET
Mathematics
Differentiation
If \( f(x + ay) + g(x - ay) = 0 \), then \( \frac{dy}{dx} = \):
AP EAPCET - 2023
AP EAPCET
Mathematics
Differentiation
If the angle between the curves \( y = e^{(x+4)} \) and \( x^2 y = 1 \) at the point \( (1, 1) \) is \( \theta \), then
\[ \sin \theta + \cos \theta = \dots \]
AP EAPCET - 2023
AP EAPCET
Mathematics
Geometry
If a line is moving between the coordinate axes such that the sum of the intercepts made by it on the coordinate axes is always 12, then the equation of that line which forms a triangle of maximum area with the coordinate axes is:
AP EAPCET - 2023
AP EAPCET
Mathematics
Geometry
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