Read and download free pdf of CBSE Class 11 Conic Section Worksheet A. Download printable Mathematics Class 11 Worksheets in pdf format, CBSE Class 11 Mathematics Chapter 11 Conic Sections Worksheet has been prepared as per the latest syllabus and exam pattern issued by CBSE, NCERT and KVS. Also download free pdf Mathematics Class 11 Assignments and practice them daily to get better marks in tests and exams for Class 11. Free chapter wise worksheets with answers have been designed by Class 11 teachers as per latest examination pattern

## Chapter 11 Conic Sections Mathematics Worksheet for Class 11

Class 11 Mathematics students should refer to the following printable worksheet in Pdf in Class 11. This test paper with questions and solutions for Class 11 Mathematics will be very useful for tests and exams and help you to score better marks

### Class 11 Mathematics Chapter 11 Conic Sections Worksheet Pdf

**Question. The largest value of r for which the region represented by ****the set {ω ∈ C|ω – 4 – i| ≤ r} is contained in the region ****represented by the set (z ≤ c / | z -1|≤| z + i |), is equal ****to: **

(a) 5/2 √2

(b) 2√2

(c) 3/2 √2

(d) √17

**Answer : A**

**Question. Equation of a common tangent to the circle, x^{2} + y^{2} – 6x = 0 **

**and the parabola, y**

^{2}= 4x, is :(a) 2√3y = 12x + 1

(b) √3y = x + 3

(c) 2√3y = – x – 12

(d) √3y = 3x + 1

**Answer : B**

**Question. If y = mx + c is the normal at a point on the parabola y ^{2} = 8x **

**whose focal distance is 8 units, then |c| is equal to :**

(a) 2√3

(b) 8√3

(c) 10√3

(d) 16√3

**Answer : C**

**Question. Let O be the vertex and Q be any point on the parabola, ****x ^{2} = 8y. If the point P divides the line segment OQ internally **

**in the ratio 1 : 3, then locus of P is :**

(a) y

^{2}= 2x

(b) x

^{2}= 2y

(c) x

^{2}= y

(d) y

^{2}= x

**Answer : B**

**Question. A chord is drawn through the focus of the parabola y ^{2} = 6x **

**such that its distance from the vertex of this parabola is √5/**

**2**

**, then its slope can be:**

(a) √5/2

(b) √3/2

(c) 2/√5

(d) 2/√3

**Answer : A**

**Question. Two tangents are drawn from a point (– 2, – 1) to the curve, ****y ^{2} = 4x. If a is the angle between them, then |tan a| is equal **

**to:**

(a) 1/3

(b) 1/√3

(c) √3

(d) 3

**Answer : D**

**Question. If the common tangents to the parabola, x ^{2} = 4y and the **

**circle,**

**x**= 4 intersect at the point P, then the distance^{2}+ y^{2}**of P from the origin, is :**

(a) √2+1

(b) 2(3 + 2√2)

(c) 2(√2 +1)

(d) 3 + 2√2

**Answer : C**

**Question. Let A (4, – 4) and B (9, 6) be points on the parabola, ****y ^{2} = 4x. Let C be chosen on the arc AOB of the parabola, **

**where O is the origin, such that the area of ΔACB is**

**maximum. Then, the area (in sq. units) of ΔACB, is:**

(a) 31(1/4)

(b) 30(1/2)

(c) 32

(d) 31(3/4)

**Answer : A**

**Question. The shortest distance between the line y = x and the curve ****y ^{2} = x – 2 is : **

(a) 2

(b) 7/8

(c) 7/4√2

(d) 11/4√2

**Answer : C**

**Question. The equation of a tangent to the parabola, x ^{2} = 8y, which **

**makes an angle q with the positive direction of x-axis, is :**

(a) y = x tanθ + 2 cotθ

(b) y = x tanθ – 2 cotθ

(c) x = y cotθ + 2 tanθ

(d) x = y cotθ – 2 tanθ

**Answer : C**

**Question. The length of the chord of the parabola x ^{2} = 4y having **

**equation x - √2y + 4√2 = 0 is:**

(a) 3

**√**2

(b) 2

**√**11

(c) 8

**√**2

(d) 6

**√**3

**Answer : D**

**Question. Tangent and normal are drawn at P(16, 16) on the parabola ****y ^{2} = 16x , which intersect the axis of the parabola at A and **

**B, respectively. If C is the centre of the circle through the**

**points P, A and B and ∠CPB = θ , then a value of tan θ is:**

(a) 2

(b) 3

(c) 4/3

(d) 1/2

**Answer : A**

**Question. Let PQ be a double ordinate of the parabola, y ^{2} = – 4x, **

**where P lies in the second quadrant. If R divides PQ in**

**the ratio 2 : 1 then the locus of R is :**

(a) 3y

^{2}= – 2x

(b) 3y

^{2}= 2x

(c) 9y

^{2}= 4x

(d) 9y

^{2}= – 4x

**Answer : D**

**Question. The slope of the line touching both the parabolas y ^{2} = 4x **

**and x**

^{2}= -32y is(a) 1/8

(b) 2/3

(c) 1/2

(d) 3/2

**Answer : C**

**Question. P and Q are two distinct points on the parabola, y ^{2} = 4x, **

**with parameters t and t1 respectively. If the normal at P**

**passes through Q, then the minimum value of 2**

**t1 is :**

(a) 8

(b) 4

(c) 6

(d) 2

**Answer : A**

**Question. Let L_{1} be the length of the common chord of the curves **

**x**

^{2}+ y^{2}= 9 and y^{2}= 8x, and L_{2}be the length of the latus**rectum of y**

^{2}= 8x, then:(a) L

_{1}> L

_{2}

(b) L

_{1}= L

_{1}

(c) L

_{1}< L

_{2}

(d) L

_{1 / }L

_{2 }√2

**Answer : C**

**Question. The normal at (2, ****3/2) ****to the ellipse, x**^{2}/16 + y^{2}/3 = **1 ****touches ****a parabola, whose equation is **

(a) y^{2} = – 104 x

(b) y^{2} = 14 x

(c) y^{2} = 26x

(d) y^{2} = – 14x

**Answer : A**

**Question. The chord PQ of the parabola y ^{2} = x, where one end P of **

**the chord is at point (4, – 2), is perpendicular to the axis of**

**the parabola. Then the slope of the normal at Q is**

(a) – 4

(b) - 1/4

(c) 4

(d) 1/4

**Answer : A**

**Question. Statement-1: The line x – 2y = 2 meets the parabola, ****y ^{2} + 2x = 0 only at the point (– 2, – 2).**

**Statement-2: The line mx - 1/2m (m ≠ 0)**

**is tangent to**

**the parabola, y**.

^{2}= – 2x at the point (- 1/2m^{2}, - 1/m)(a) Statement-1 is true; Statement-2 is false.

(b) Statement-1 is true; Statement-2 is true; Statement-2 is a correct explanation for statement-1.

(c) Statement-1 is false; Statement-2 is true.

(d) Statement-1 a true; Statement-2 is true; Statement-2 is not a correct explanation for statement-1.

**Answer : B**

**Question. If two tangents drawn from a point P to the parabola ****y ^{2} = 4x are at right angles, then the locus of P is **

(a) 2x + 1 = 0

(b) x = – 1

(c) 2x – 1 = 0

(d) x = 1

**Answer : B**

**Question. A hyperbola having the transverse axis of length 2 has ****the same foci as that of the ellipse 3x ^{2} + 4y^{2} = 12, then this **

**hyperbola does not pass through which of the following**

**points?**

(a) (1/√2, 0)

(b) (-√3/2, 1)

(c) (1,- 1/√2)

(d) (3/2, - 1/√2)

**Answer : D**

**Question. If the point (1, 4) lies inside the circle x ^{2} + y^{2} – 6x – 10y + P = 0 and the circle does not touch or **

**intersect the coordinate axes, then the set of all possible**

**values of P is the interval:**

(a) (0, 25)

(b) (25, 39)

(c) (9, 25)

(d) (25, 29)

**Answer : D**

**Question. Let a and b be any two numbers satisfying 1/a ^{2} + 1/b^{2} = 1/4 **

**Then, the foot of perpendicular from the origin on the**

**variable line,**

**x/a +**

**b/b = 1**

**, lies on:**

(a) a hyperbola with each semi-axis = √2

(b) a hyperbola with each semi-axis = 2

(c) a circle of radius = 2

(d) a circle of radius = √2

**Answer : C**

**Question. Let C be the circle with centre at (1, 1) and radius = 1. If T is the circle centred at (0, y), passing through origin and ****touching the circle C externally, then the radius of T is ****equal to **

(a) 1/2

(b) 1/4

(c) 3/2

(d) 3/2

**Answer : B**

**Question. The equation of circle described on the chord 3x + y + 5 = 0 of the circle x ^{2} + y^{2}= 16 as diameter is:**

(a) x

^{2}+ y

^{2}+ 3x + y – 11 = 0

(b) x

^{2}+ y

^{2}+ 3x + y + 1 = 0

(c) x

^{2}+ y

^{2}+ 3x + y – 2 = 0

(d) x

^{2}+ y

^{2}+ 3x + y – 22 = 0

**Answer : A**

**Question. For the two circles x ^{2} + y^{2} = 16 and x^{2} + y^{2} – 2y = 0, there is/are**

(a) one pair of common tangents

(b) two pair of common tangents

(c) three pair of common tangents

(d) no common tangent

**Answer : D**

**Question. If the incentre of an equilateral triangle is (1, 1) and the equation of its one side is 3x + 4y + 3 = 0, then the ****equation of the circumcircle of this triangle is :**

(a) x^{2} + y^{2} – 2x – 2y – 14 = 0

(b) x^{2} + y^{2} – 2x – 2y – 2 = 0

(c) x^{2} + y^{2} – 2x – 2y + 2 = 0

(d) x^{2} + y^{2} – 2x – 2y – 7 = 0

**Answer : A**

**Question. If a circle passing through the point (–1, 0) touches yaxis at (0, 2), then the length of the chord of the circle ****along the x-axis is : **

(a) 3/2

(b) 3

(c) 5/2

(d) 5

**Answer : B**

**Question. Let the tangents drawn to the circle, x ^{2} + y^{2} = 16 from the point P(0, h) meet the x-axis at point A and B. If the area of Δ**

**APB is minimum, then h is equal to :**

(a) 4√2

(b) 3√3

(c) 3√2

(d) 4√3

**Answer : A**

**Question. If y + 3x = 0 is the equation of a chord of the circle, x ^{2} + y^{2} – 30x = 0, then the equation of the circle with this **

**chord as diameter is :**

(a) x

^{2}+ y

^{2}+ 3x + 9y = 0

(b) x

^{2}+ y

^{2}+ 3x – 9y = 0

(c) x

^{2}+ y

^{2}– 3x – 9y = 0

(d) x

^{2}+ y

^{2}– 3x + 9y = 0

**Answer : D**

**Question. If the line y = mx + 1 meets the circle x ^{2} + y^{2} + 3x = 0 in two points equidistant from and on opposite sides of x-axis, **

**then**

(a) 3m + 2 = 0

(b) 3m – 2 = 0

(c) 2m + 3 = 0

(d) 2m – 3 = 0

**Answer : B**

**Question. If three distinct points A, B, C are given in the 2-dimensional coordinate plane such that the ratio of the distance of ****each one of them from the point (1, 0) to the distance from ****(– 1, 0) is equal to ****1/****2****, then the circumcentre of the triangle ****ABC is at the point**

(a) (5/3, 0)

(b) (0, 0)

(c) (1/3, 0)

(d) (3, 0)

**Answer : A**

**Question. If a circle of unit radius is divided into two parts by an arc of another circle subtending an angle 60 on the ****circumference of the first circle, then the radius of the arc ****is:**

(a) √3

(b) 1/2

(c) 1

(d) √2

**Answer : A**

**Question. Statement 1: The only circle having radius √10 and a diameter along line 2x + y = 5 is x ^{2} + y^{2} – 6x + 2y = 0.**

**Statement 2 : 2x + y = 5 is a normal to the circle**

**x**

^{2}+ y^{2}– 6x + 2y = 0.(a) Statement 1 is false; Statement 2 is true.

(b) Statement 1 is true; Statement 2 is true, Statement 2 is a correct explanation for Statement 1.

(c) Statement 1 is true; Statement 2 is false.

(d) Statement 1 is true; Statement 2 is true; Statement 2 is not a correct explanation for Statement 1.

**Answer : A**

**Question. The set of all real values of λ for which exactly two common tangents can be drawn to the circles**

**x ^{2} + y^{2} – 4x – 4y + 6 = 0 and**

**x**

^{2}+ y^{2}– 10x – 10y + l = 0 is the interval:(a) (12, 32)

(b) (18, 42)

(c) (12, 24)

(d) (18, 48)

**Answer : B**

**Question. The circle passing through (1, –2) and touching the axis of x at (3, 0) also passes through the point **

(a) (–5, 2)

(b) (2, –5)

(c) (5, –2)

(d) (–2, 5)

**Answer : C**

**Question. If the circle x ^{2} + y^{2} – 6x – 8y + (25 – a^{2}) = 0 touches the axis of x, then a equals.**

(a) 0

(b) ±4

(c) ±2

(d) ±3

**Answer : B**

**Question. If each of the lines 5x + 8y = 13 and 4x – y = 3 contains a diameter of the circle ****x ^{2} + y^{2} – 2(a^{2} – 7a + 11) x – 2 (a^{2} – 6a + 6) y + b^{3} + 1 = 0, **

**then**

(a) a = 5 and b ∉ (-1,1)

(b) a = 1 and b ∉ (-1,1)

(c) a = 2 and b ∉ (-∞,1)

(d) a = 5 and b ∈ (-∞,1)

**Answer : D**

**Question. The equation of the circle passing through the point (1, 2) and through the points of intersection of ****x ^{2} + y^{2} – 4x – 6y – 21 = 0 and 3x + 4y + 5 = 0 is given by**

(a) x

^{2}+ y

^{2}+ 2x + 2y + 11 = 0

(b) x

^{2}+ y

^{2}– 2x + 2y – 7 = 0

(c) x

^{2}+ y

^{2}+ 2x – 2y – 3 = 0

(d) x

^{2}+ y

^{2}+ 2x + 2y – 11 = 0

**Answer : D**

**Question. The equation of the circle passing through the point (1, 0) and (0, 1) and having the smallest radius is -**

(a) x^{2} + y^{2} - 2x - 2y +1 = 0

(b) x^{2} + y^{2} – x – y = 0

(c) x^{2} + y^{2} + 2x + 2y – 7= 0

(d) x^{2} + y^{2} + x + y – 2 = 0

**Answer : B**

**Question. Three distinct points A, B and C are given in the 2-dimensional coordinates plane such that the ratio of the ****distance of any one of them from the point (1, 0) to the ****distance from the point (–1, 0) is equal to ****1/****3****. Then the ****circumcentre of the triangle ABC is at the point: **

(a) (5/4, 0)

(b) (5/2, 0)

(c) (5/3, 0)

(d) (3, 0)

**Answer : A**

**Question. If a circle C passing through (4, 0) touches the circle x ^{2} + y^{2} + 4x – 6y – 12 = 0 externally at a point (1, –1), then **

**the radius of the circle C is :**

(a) 5

(b) 2√5

(c) 4

(d) √57

**Answer : A**

**Click on link below to download ****CBSE Class 11 Conic Section Worksheet A.**

CBSE Class 11 Maths Discrete Frequency Distribution Worksheet Set A |

#### CBSE Class 11 Mathematics Chapter 11 Conic Sections Worksheet

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