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?
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