Types of Differential Equations is an important topic in the Mathematics section in TS EAMCET exam. Practising this topic will increase your score overall and make your conceptual grip on TS EAMCET exam stronger.
This article gives you a full set of TS EAMCET PYQs for Types of Differential Equations with explanations for effective preparation. Practice of TS EAMCET Mathematics PYQs including Types of Differential Equations questions regularly will improve accuracy, speed, and confidence in the TS EAMCET 2026 exam.
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TS EAMCET PYQs for Types of Differential Equations with Solutions
1.
If \( m_1 \) and \( m_2 \) are the slopes of the direct common tangents drawn to the circles \[ x^2 + y^2 - 2x - 8y + 8 = 0 \quad \text{and} \quad x^2 + y^2 - 8x + 15 = 0 \] then \( m_1 + m_2 \) is:- \( \frac{-24}{5} \)
- \( \frac{12}{5} \)
- \( \frac{24}{5} \)
- \( \frac{-12}{5} \)
2.
If the normal drawn at the point \((2, -1)\) to the ellipse \(x^2 + 4y^2 = 8\) meets the ellipse again at \((a, b)\), then \(17a\) is:- 23
- 14
- 37
9
3.
Consider the parabola \(25[(x-2)^2 + (y+5)^2] = (3x+4y-1)^2\), match the characteristic of this parabola given in List-I with its corresponding item in List-II.
- I-B, II-E, III-C, IV-D
- I-D, II-A, III-C, IV-B
- I-B, II-A, III-C, IV-D
- I-D, II-B, III-C, IV-A
4.
A circle \( S \) passes through the points of intersection of the circles \( x^2 + y^2 - 2x - 3 = 0 \) and \( x^2 + y^2 - 2y = 0 \). If \( x + y + 1 = 0 \) is a tangent to the circle \( S \), then the equation of \( S \) is:- \( 2x^2 + 2y^2 + 2x + 2y + 3 = 0 \)
- \( 2x^2 + 2y^2 - 2x - 2y + 3 = 0 \)
- \( x^2 + y^2 - 2x - 2y + 3 = 0 \)
\( 2x^2 + 2y^2 - 2x - 2y - 3 = 0 \)
5.
The point of intersection of two tangents drawn to the hyperbola \[ \frac{x^2}{a^2} - \frac{y^2}{4} = 1 \] lie on the circle \[ x^2 + y^2 = 5. \] If these tangents are perpendicular to each other, then \( a \) is:- \( 25 \)
- \( 5 \)
- \( 9 \)
- \( 3 \)
6.
P(\( \theta \)) is a point on the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{9} = 1 \), S is its focus lying on the positive X-axis and Q = (0,1). If SQ = \( \sqrt{26} \) and SP = 6, then \( \theta \) is:- \( \frac{\pi}{6} \)
- \( \frac{\pi}{4} \)
- \( \frac{\pi}{3} \)
- \( \cos^{-1}\left(\frac{2}{3}\right) \) \vspace{0.5cm}
7.
A circle \( S \equiv x^2 + y^2 + 2gx + 2fy + 6 = 0 \) cuts another circle \[ x^2 + y^2 - 6x - 6y - 6 = 0 \] orthogonally. If the angle between the circles \( S = 0 \) and \[ x^2 + y^2 + 6x + 6y + 2 = 0 \] is 60°, then the radius of the circle \( S = 0 \) is:- \(2\)
- \(1\)
- \(4\)
- \(5\)
8.
If \( (2,3) \) is the focus and \( x - y + 3 = 0 \) is the directrix of a parabola, then the equation of the tangent drawn at the vertex of the parabola is:- \( x - y - 2 = 0 \)
- \( x - y + 2 = 0 \)
- \( x - y + 5 = 0 \)
- \( x - y - 5 = 0 \)
9.
The axis of a parabola is parallel to Y-axis. If this parabola passes through the points \( (1,0), (0,2), (-1,-1) \) and its equation is \( ax^2 + bx + cy + d = 0 \), then \( \frac{ad}{bc} \) is:- \(\frac{5}{8}\)
- \(\frac{5}{2}\)
- -10
10
10.
If the focus of an ellipse is \((-1,-1)\), equation of its directrix corresponding to this focus is \(x + y + 1 = 0\) and its eccentricity is \(\frac{1}{\sqrt{2}}\), then the length of its major axis is:- 2
- 1
- 4
3
11.
If the common chord of the circles \( x^2 + y^2 - 2x + 2y + 1 = 0 \) and \( x^2 + y^2 - 2x - 2y - 2 = 0 \) is the diameter of a circle \( S \), then the centre of the circle \( S \) is:- \( \left( \frac{1}{2}, -\frac{3}{4} \right) \)
- \( \left( 1, -\frac{3}{4} \right) \)
- \( \left( 1, \frac{3}{4} \right) \)
\( \left( \frac{1}{2}, -\frac{3}{4} \right) \)
12.
If \( (1,1) \) is the vertex and \( x + y + 1 = 0 \) is the directrix of a parabola. If \( (a, b) \) is its focus and \( (c, d) \) is the point of intersection of the directrix and the axis of the parabola, then \( a + b + c + d \) is:- 6
- 5
- 4
3
13.
If \(6x-5y-20=0\) is a normal to the ellipse \(x^2 + 3y^2 = k\), then \(k =\)- 9
- 17
- 25
- 37
14.
The equation of the common tangent to the parabola \(y^2 = 8x\) and the circle \(x^2 + y^2 = 2\) is \(ax + by + 2 = 0\). If \(-\frac{a}{b}>0\), then \(3a^2 + 2b + 1 =\)- 5
- 4
- 3
- 2
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