MCQsClass 11 Maths Chapter 11 Conic Sections MCQs

Class 11 Maths Chapter 11 Conic Sections MCQs

Class 11 students can access MCQs for Maths Chapter 11 – Conic Sections online, designed to help them perform well in exams. These multiple-choice questions follow NCERT guidelines and align with the CBSE syllabus (2024-2025). Detailed answers and explanations are provided for each question. Explore chapter-wise MCQs for Class 11 Maths by clicking here.

MCQs on Class 11 Maths Chapter 11 Conic Sections

1. What is the equation of a circle with center (0, 0) and radius 5?

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    a) \(x^2 + y^2 = 25\)

    b) \(x^2 + y^2 = 5\)

    c) \(x^2 + y^2 – 25 = 0\)

    d) Both a and c

    Answer: d) Both a and c

    2. What is the standard form of a parabola opening upwards?

    a) \(y^2 = 4ax\)

    b) \(x^2 = 4ay\)

    c) \(y^2 + x^2 = 1\)

    d) None of these

    Answer: b) \(x^2 = 4ay\)

    3. Which conic section is represented by \(x^2 + y^2 = 1\)?

    a) Circle

    b) Ellipse

    c) Parabola

    d) Hyperbola

    Answer: a) Circle

    4. What is the eccentricity (\(e\)) of a circle?

    a) 0

    b) 1

    c) 2

    d) Infinite

    Answer: a) 0

    5. What is the general equation of a hyperbola?

    a) \(x^2 – y^2 = 1\)

    b) \(\frac{x^2}{a^2} – \frac{y^2}{b^2} = 1\)

    c) \(x^2 + y^2 = 1\)

    d) None of these

    Answer: b) \(\frac{x^2}{a^2} – \frac{y^2}{b^2} = 1\)

    6. If the focus of a parabola is (0, 3), what is the directrix?

    a) \(y = 3\)

    b) \(y = -3\)

    c) \(x = 3\)

    d) \(x = -3\)

    Answer: b) \(y = -3\)

    7. What is the eccentricity of an ellipse?

    a) Always less than 1

    b) Always 1

    c) Always greater than 1

    d) None of these

    Answer: a) Always less than 1

    8. In the equation of an ellipse \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\), if \(a > b\), the ellipse is:

    a) Vertical

    b) Horizontal

    c) Circle

    d) Hyperbola

    Answer: b) Horizontal

    9. The latus rectum of a parabola is:

    a) The longest chord

    b) A line parallel to the directrix

    c) A line through the focus perpendicular to the axis

    d) None of these

    Answer: c) A line through the focus perpendicular to the axis

    10. What is the shape of the path of a projectile under gravity (neglecting air resistance)?

    a) Circle

    b) Ellipse

    c) Parabola

    d) Hyperbola

    Answer: c) Parabola

    11. For a hyperbola, the difference between the distances to the two foci is:

    a) Constant

    b) Variable

    c) Zero

    d) Infinite

    Answer: a) Constant

    12. Which conic section has an eccentricity \(e = 1\)?

    a) Circle

    b) Ellipse

    c) Parabola

    d) Hyperbola

    Answer: c) Parabola

    13. The distance between the foci of an ellipse is given by:

    a) \(2a\)

    b) \(2b\)

    c) \(2\sqrt{a^2 – b^2}\)

    d) None of these

    Answer: c) \(2\sqrt{a^2 – b^2}\)

    14. What is the length of the latus rectum of a parabola \(y^2 = 4ax\)?

    a) \(a\)

    b) \(4a\)

    c) \(2a\)

    d) None of these

    Answer: b) \(4a\)

    15. Which term represents the distance from the center to a focus of an ellipse?

    a) Major axis

    b) Minor axis

    c) Semi-major axis

    d) None of these

    Answer: d) None of these

    16. In the equation of a hyperbola \(\frac{x^2}{a^2} – \frac{y^2}{b^2} = 1\), the transverse axis is:

    a) Horizontal

    b) Vertical

    c) Circular

    d) None of these

    Answer: a) Horizontal

    17. If the eccentricity of an ellipse is 0.8, then the shape is:

    a) Nearly circular

    b) Narrow ellipse

    c) Parabola

    d) Hyperbola

    Answer: a) Nearly circular

    18. For the parabola \(x^2 = 4ay\), the focus is at:

    a) (0, 0)

    b) (0, a)

    c) (a, 0)

    d) (0, -a)

    Answer: b) (0, a)

    19. What is the directrix of the parabola \(y^2 = 4ax\)?

    a) \(x = -a\)

    b) \(x = a\)

    c) \(y = a\)

    d) \(y = -a\)

    Answer: a) \(x = -a\)

    20. Which conic section has two branches?

    a) Circle

    b) Ellipse

    c) Parabola

    d) Hyperbola

    Answer: d) Hyperbola

    21. The length of the latus rectum for an ellipse \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\) is:

    a) \(\frac{2b^2}{a}\)

    b) \(\frac{2a^2}{b}\)

    c) \(a + b\)

    d) None of these

    Answer: a) \(\frac{2b^2}{a}\)

    22. For the equation of a circle \((x – h)^2 + (y – k)^2 = r^2\), \((h, k)\) is:

    a) Radius

    b) Center

    <p)c) Diameter

    d) None of these

    Answer: b) Center

    23. The general equation of a parabola is:

    a) \(Ax^2 + By^2 = C\)

    b) \(Ax^2 + Bx + C = 0\)

    c) \(y^2 = 4ax\)

    d) None of these

    Answer: c) \(y^2 = 4ax\)

    24. The foci of a hyperbola are:

    a) Inside the ellipse

    b) On the major axis

    c) Outside the branches

    d) None of these

    Answer: c) Outside the branches

    25. For an ellipse, if \(b = a\), the ellipse becomes:

    a) A circle

    b) A parabola

    c) A hyperbola

    d) None of these

    Answer: a) A circle

     

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