ClearStepsCLEARSTEPS AI
TGBIE · 2nd Year · MPC

Maths IIB — Important Questions

Chapter-wise important questions for TS Intermediate 2nd Year Mathematics IIB — organised by VSAQ, SAQ, and LAQ as per the TGBIE exam pattern. Paper: 75 marks · 3 hours.

VSAQ(2 marks each)

Answer in 2–3 lines. Expect 10 questions — attempt all.

  1. 1.
    [Circle]Find the centre and radius of the circle x² + y² − 4x + 6y − 3 = 0.
  2. 2.
    [Circle]Find the length of the tangent from (1, 3) to the circle x² + y² − 2x + 4y − 11 = 0.
  3. 3.
    [System of Circles]Find the equation of the radical axis of x² + y² + 2x + 4y − 1 = 0 and x² + y² − 4x + 6y − 4 = 0.
  4. 4.
    [Parabola]Find the equation of the parabola with vertex at origin, axis along x-axis and passing through (3, 6).
  5. 5.
    [Ellipse]Find the eccentricity and foci of the ellipse 9x² + 16y² = 144.
  6. 6.
    [Hyperbola]Write the asymptotes of the hyperbola x²/9 − y²/16 = 1.
  7. 7.
    [Integration]Evaluate: ∫(3x² − 2x + 1) dx.
  8. 8.
    [Integration]Evaluate: ∫ sin x · eˣ dx using integration by parts.
  9. 9.
    [Definite Integrals]Evaluate: ∫₀¹ x²/(1+x²) dx.
  10. 10.
    [Differential Equations]Find the order and degree of (d²y/dx²)³ + (dy/dx)² + y = 0.
SAQ(4 marks each)

Answer in 5–7 lines with working. Choose 5 from 7 questions.

  1. 1.
    [Circle]Find the equation of the circle passing through (1, 2), (3, −4), and (5, −6).
  2. 2.
    [Parabola]Find the equations of tangent and normal to the parabola y² = 8x at the point (2, 4).
  3. 3.
    [Ellipse]Show that the tangent to the ellipse x²/a² + y²/b² = 1 at (x₁, y₁) is xx₁/a² + yy₁/b² = 1.
  4. 4.
    [Integration]Evaluate: ∫ x²/√(1 − x⁶) dx using substitution u = x³.
  5. 5.
    [Integration]Evaluate: ∫ 1/(5 + 4 cos x) dx.
  6. 6.
    [Definite Integrals]Evaluate ∫₀^(π/2) sin²x dx using the reduction formula.
  7. 7.
    [Differential Equations]Solve: (1 + x²)dy + 2xy dx = cot x dx.
LAQ(7 marks each)

Full working required. Choose 5 from 7. Each carries 7 marks.

  1. 1.
    [Circle]Find the equation of the circle passing through the intersection of 2x² + 2y² − 3x + 6y − 8 = 0, 3x − 2y − 1 = 0 and passing through (1, 2).
  2. 2.
    [System of Circles]Find the radical centre of three circles and show that it lies at the point where the three radical axes of pairs of circles meet.
  3. 3.
    [Integration]Evaluate ∫(x + 1)/[(x − 1)(x + 2)] dx using partial fractions.
  4. 4.
    [Integration (Reduction)]Derive the reduction formula for ∫ xⁿeˣ dx and hence find ∫ x³eˣ dx.
  5. 5.
    [Definite Integrals (Area)]Find the area bounded by y = x² − 4x + 3, the x-axis, and the lines x = 1 and x = 4.
  6. 6.
    [Differential Equations]Solve: dy/dx + (y/x) = x³y⁶ (Bernoulli equation).
  7. 7.
    [Definite Integrals]State and prove: ∫₀ᵃ f(x)dx = ∫₀ᵃ f(a−x)dx and use it to evaluate ∫₀^π x·sin x/(1+cos²x) dx.
Formula Sheet →Model Paper →