TS Inter 2nd Year Mathematics 2B Guess Paper 2025: Important Questions & Exam Preparation Guide

The Telangana Board of Intermediate Education (TSBIE) has scheduled the TS Inter 2nd Year Mathematics 2B exam for March 15, 2025. To help students with their preparation, we provide a comprehensive guess paper that includes important questions and answers based on an analysis of previous years’ question papers. This guide will help students understand the exam pattern, question types, and weightage of different topics.

TS Inter 2nd Year Mathematics 2B Exam Pattern 2025

The exam consists of three sections:

Section A: Very Short Answer Type Questions (2 marks each)
Section B: Short Answer Type Questions (4 marks each)
Section C: Long Answer Type Questions (8 marks each)

Candidates must answer questions worth a total of 80 marks within the given time limit.

TS Inter 2nd Year Mathematics 2B Section-Wise Guess Paper 2025

Section A: Very Short Answer Type Questions (2 Marks Each)

If the equation x2+y2+2gx+2fy−12=0x^2 + y^2 + 2gx + 2fy – 12 = 0 represents a circle with centre (2,3), find g,fg, f and its radius.
- Answer: Comparing with the standard equation (x−h)2+(y−k)2=r2(x – h)^2 + (y – k)^2 = r^2, we get g=−2,f=−3g = -2, f = -3, and the radius r=g2+f2−c=5r = \sqrt{g^2 + f^2 – c} = 5.
Find the value of kk if the points (1,3) and (2,k) are conjugate with respect to the circle x2+y2=35x^2 + y^2 = 35.
- Answer: Using the conjugate condition formula, we find k=4k = 4.
If the eccentricity of a hyperbola is 54\frac{5}{4}, then find the eccentricity of its conjugate hyperbola.
- Answer: The eccentricity of the conjugate hyperbola is 45\frac{4}{5}.
Find the value of kk if the line 2y=5x+k2y = 5x + k is a tangent to the parabola y2=6xy^2 = 6x.
- Answer: Using the tangent condition, we find k=±30k = \pm \sqrt{30}.
Find the angle between the circles x2+y2+4x−14y+28=0x^2 + y^2 + 4x – 14y + 28 = 0 and x2+y2+4x−5=0x^2 + y^2 + 4x – 5 = 0.
- Answer: The angle between the two circles is 90 degrees.

Section B: Short Answer Type Questions (4 Marks Each)

Find the length of the chord intercepted by the circle x2+y2−x+3y−22=0x^2 + y^2 – x + 3y – 22 = 0 on the line y=x−3y = x – 3.
- Answer: Using chord length formula, the length is 6 units.
Find the equation of the tangent and normal to the ellipse x2+8y2=33x^2 + 8y^2 = 33 at (-1,2).
- Answer: Tangent equation is −x+83y=333-x + \frac{8}{3}y = \frac{33}{3} and normal equation is x+83y=−333x + \frac{8}{3}y = -\frac{33}{3}.
Find equations of the tangents to the hyperbola x2−4y2=4x^2 – 4y^2 = 4 which are:
- (i) Parallel to the line x+2y=0x + 2y = 0
- (ii) Perpendicular to the line x+2y=0x + 2y = 0
- Answer: Solving for slopes, the equations are obtained as x−2y=4x – 2y = 4 and x+2y=−4x + 2y = -4.
Find the length of the major axis, minor axis, latus rectum, eccentricity, coordinates of centre, foci, and equation of the directrix for the ellipse x2+2y2−4x+12y+14=0x^2 + 2y^2 – 4x + 12y + 14 = 0.
- Answer: Major axis = 6 units, Minor axis = 4 units, Eccentricity = 0.866, Foci = (3,0) and (-3,0), Directrix equation = x = \pm 4.

Section C: Long Answer Type Questions (8 Marks Each)

If the points (2,0), (0,1), (4,5), and (0,C) are concyclic, find C.
- Answer: Using the determinant method for concyclic points, C=7C = 7.
Find the equation of the parabola whose axis is parallel to the Y-axis and which passes through the points (4,5), (-2,11), and (-4,21).
- Answer: Using the general form y=ax2+bx+cy = ax^2 + bx + c, solving for coefficients gives y=12×2−2x+5y = \frac{1}{2}x^2 – 2x + 5.
Find the coordinates of the vertex and focus, the equation of the directrix and axis for the parabola y2+4x+4y−3=0y^2 + 4x + 4y – 3 = 0.
- Answer: Vertex = (-1, -2), Focus = (0, -2), Directrix equation = x = -2, Axis equation = y = -2.

Conclusion

This TS Inter 2nd Year Mathematics 2B Guess Paper 2025 aims to provide students with a structured revision plan before their exam on March 15, 2025. By practicing these questions and their solutions, students can boost their confidence, improve problem-solving skills, and maximize their scores in the final exam.

Stay consistent with your preparation, and best of luck for your exams!

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