### Multiple Choice Questions (MCQ) On Mathematics

MCQ in Mathematics  For IX, X, XI and XII Classes Multiple Choice Questions (MCQ) in Mathematics for 9th, 10th, 11th and 12th standard and case study based questions with answers. Chapter-wise important MCQ in mathematics. Multiple Choice Questions (MCQ)  in Mathematics For Class 09 Mathematics MCQ Class 09   Case Study Based Questions Class 09 : Mathematics   Mathematics MCQ  (Chapter -1) Class 09 : Real Numbers Mathematics MCQ  (Chapter -2) Class 09 : Polynomials Mathematics MCQ (Chapter - 4) Class 09 : Linear Equations in Two Variables Mathematics MCQ (Chapter -6) Class 09 : Lines & Angles Mathematics MCQ (Chapter -7) Class 09 : Triangles Mathematics MCQ (Chapter -8) Class 09 : Quadrilaterals Mathematics MCQ (Chapter -10) Class 09 : Circle Mathematics MCQ (Chapter - 13) Class 09 : Surface Area & Volume Mathematics MCQ (Chapter - 14) Class 09 : Statistics Mathematics MCQ (Chapter - 15) Class 09 : Probability Multiple Choice Questi

## Conic Section

MCQ based on conic sections like circle Parabola, Ellipse, Hyperbola. Multiple Choice Questions on conic section chapter 11 class XI strictly according to the CBSE syllabus and pattern.

## MCQ BASED ON CIRCLE CLASS XI

Question 1

Find the equation of circle with centre at origin and radius 5 units.
a) x2 + y2 = 25
b) x2 + y2 = 5
c) x2 = 25
d) y2 = 25

Answer a

Question 2

The point (6, 2) lie ___________ the circle x2 + y- 2x -4y – 36 = 0.
a) inside circle
b) outside circle
c) on the circle
d) either inside or outside

Answer c

Question 3

Find the equation of circle with centre at (2, 5) and radius 5 units.
a) x2 + y2   + 4x - 10y + 4 = 0
b) x2 + y2  - 4x - 10y + 4 = 0
c) x2 + y2  + 4x + 10y + 4 = 0
d) x2 + y2  + 4x - 10y – 4 = 0

Answer b

Question 4

Find the centre of the circle with equation x2 + y2 - 4x - 10y + 4 = 0.
a) (-2, 5)
b) (-2, -5)
c) (2, -5)
d) (2, 5)

Answer: d
Explanation: Comparing the equation with general form x2 + y2 + 2gx + 2fy + c = 0, we get
2g = - 4 ⇒ g = - 2
2f = -10
f = - 5
c = 4
Centre is at (-g, -f) i.e. (2, 5).

Question 5

Find the radius of the circle with equation x2 + y2 - 4x - 10y + 4 = 0.
a) 25 units
b) 20 units
c) 5 units
d) 10 units

Answer: c

Question 6

The centre of the circle 4x2 + 4y2 – 8x + 12y – 25 = 0 is

a) (-2, 3)

b) (1, -3/2)

c) (-4, 6)

d) (4, -6)

Answer: (b) (1, -3/2)

Explanation:

Given circle equation: 4x2 + 4y2 – 8x + 12y – 25 = 0

x2 + y2 – (8x/4) + (12y/4) – (25/4) = 0

x2 +y2 -2x +3y -(25/4) = 0 …(1)

As we know that the general equation of a circle is x+ y+ 2gx + 2fy + c = 0, and the centre of the circle = (-g, -f)

Hence, by comparing equation (1) and the general equation,

2g = -2,   g = -1

2f = 3,     f = 3/2

Now, substitute the values in the centre of the circle (-g, -f), we get,

Centre = (1, -3/2).

Question 7

If a circle pass through (2, 0) and (0, 4) and centre at x-axis then find the radius of the circle.
a) 25 units
b) 20 units
c) 5 units
d) 10 units

Answer: c
Explanation: Equation of circle with centre at x-axis (a, 0) and radius r units is
(x - a)2 + (y)2 = r2
⇒ (2 - a)2 + (0)2 = r2
And (0 - a)2 + (4)2 = r2
⇒ (a - 2)2 = a2 + 42  (- 2)(2a - 2) =16  a – 1 = - 4  a = - 3

So, r2 = (2 + 3)2 = 5 2  ⇒ r = 5 units.

Question 8
The center of the circle 4x² + 4y² – 8x + 12y – 25 = 0 is?
(a) (2,-3)
(b) (-2,3)
(c) (-4,6)
(d) (4,-6)

Answer a

Question 9

If a circle pass through (4, 0) and (0, 2) and centre at y-axis then find the radius of the circle.
a) 25 units
b) 20 units
c) 5 units
d) 10 units

Answer: c

Question 10

The point (1, 4) lie ___________ the circle x2 + y2 - 2x - 4y + 2 = 0.
a) inside circle
b) outside circle
c) on the circle
d) either inside or outside

Answer b

Question 11
The radius of the circle 4x² + 4y² – 8x + 12y – 25 = 0 is?
(a) √57/4
(b) √77/4
(c) √77/2
(d) √87/4

Answer c

## MCQ BASED ON PARABOLA CLASS XI

Question 1

Find the focus of parabola with equation y2 = 100x.
a) (0, 25)
b) (0, -25)
c) (25, 0)
d) (-25, 0)

Answer c

Question 2

Find the focus of parabola with equation y2 = - 100x.
a) (0, 25)
b) (0, -25)
c) (25, 0)
d) (-25, 0)

Answer d

Question 3

Find the focus of parabola with equation x2 = 100y.
a) (0, 25)
b) (0, -25)
c) (25, 0)
d) (-25, 0)

Answer a

Question 4

The focus of the parabola y2 = 8x is

a) (0, 2)

b) (2, 0)

c) (0, -2)

d) (-2, 0)

Answer: (b) (2, 0)

Explanation:

Given parabola equation y2 = 8x …(1)

Here, the coefficient of x is positive and the standard form of parabola is y2 = 4ax …(2)

Comparing (1) and (2), we get

4a = 8

a = 8/4 = 2

We know that the focus of parabolic equation y2 = 4ax is (a, 0).

Therefore, the focus of the parabola y2 =8x is (2, 0).

Question 5

The length of the latus rectum of x2 = -9y is equal to

a)  3 units

b) - 3 units

c)  9/4 units

d)  9 units

Answer: (d) 9 units

Explanation:

Given parabola equation: x2 = - 9y …(1)

Since the coefficient of y is negative, the parabola opens downwards.

The general equation of parabola is x= - 4ay…(2)

Comparing (1) and (2), we get

-4a = -9

a = 9/4

We know that the length of latus rectum = 4a = 4(9/4) = 9.

Therefore, the length of the latus rectum of x2 = -9y is equal to 9 units.

Question 6

The parametric equation of the parabola y2 = 4ax is

a) x = at; y = 2at

b) x = at2; y = 2at

c) x = at2; y= at3

d) x = at2; y = 4at

Answer: (b) x = at2; y = 2at

Question 7

Find the equation of latus rectum of parabola y2 = 100x.

a) x = 25
b) x = - 25
c) y = 25
d) y = - 25

Answer a

Question 8

Find the equation of latus rectum of parabola x2 = - 100y.
a) x = 25
b) x = - 25
c) y = - 25
d) y = 25

Answer c

Question 9

Find the equation of directrix of parabola y2=-100x.
a) x = 25
b) x = - 25
c) y = - 25
d) y = 25

Answer a

Question 10
If a parabolic reflector is 20 cm in diameter and 5 cm deep then the focus of parabolic reflector is
(a) (0 0)
(b) (0, 5)
(c) (5, 0)
(d) (5, 5)

Answer c

Question 11

The equation of parabola with vertex at origin the axis is along x-axis and passing through the point (2, 3) is
(a) y² = 9x
(b) y² = 9x/2
(c) y² = 2x
(d) y² = 2x/9

Answer b

Question 12

Find the vertex of the parabola y2 = 4ax.
a) (0, 4)
b) (0, 0)
c) (4, 0)
d) (0, -4)

Answer b

Question 13

Find the equation of axis of the parabola y2 = 24x.
a) x = 0
b) x = 6
c) y = 6
d) y = 0

Answer d

Question 14

Find the equation of axis of the parabola x2 = 24y.
a) x = 0
b) x = 6
c) y = 6
d) y = 0

Answer a

Question 15

Find the length of latus rectum of the parabola y= 40x.

a) 4 units
b) 10 units
c) 40 units
d) 80 units

Answer c

Question 16

At what point of the parabola x² = 9y is the abscissa three times that of ordinate
(a) (1, 1)
(b) (3, 1)
(c) (-3, 1)
(d) (-3, -3)

Answer b

## MCQ BASED ON ELLIPSE CLASS - XI

Question 1

An ellipse has ___________ vertices and ____________ foci.
a) two, one
b) one, one
c) one, two
d) two, two

Answer d

Question 2

Find the coordinates of foci of ellipse (x/25)+ (y/16)= 1.
a) (±3, 0)
b) (±4, 0)
c) (0, ±3)
d) (0, ±4)

Answer a

Question 3
In an ellipse, the distance between its foci is 6 and its minor axis is 8 then its eccentricity is
(a) 4/5
(b) 1/√52
(c) 3/5
(d) 1/ 2

Answer c

Question 4
A rod of length 12 CM moves with its and always touching the co-ordinate Axes. Then the equation of the locus of a point P on the road which is 3 cm from the end in contact with the x-axis is
(a) x²/81 + y²/9 = 1
(b) x²/9 + y²/81 = 1
(c) x²/169 + y²/9 = 1
(d) x²/9 + y²/169 = 1

Answer a

Question 5

Find the coordinates of foci of ellipse (x/16)+ (y/25)= 1.
a) (±3, 0)
b) (±4, 0)
c) (0, ±3)
d) (0, ±4)

Answer c

Question 6

What is major axis length for ellipse (x/25)+ (y/16)= 1?
a) 5 units
b) 4 units
c) 8 units
d) 10 units

Answer d

Question 7

For the ellipse 3x+ 4y2 = 12, the length of the latus rectum is:

a)  2/5
b)  3/5
c)  3
d) 4

Answer: (c) 3

Explanation:

Given ellipse equation: 3x+ 4y2 = 12

The given equation can be written as (x2/4) + (y2/3) = 1…(1)

Now, compare the given equation with the standard ellipse equation: (x2/a2) + (y2/b2) = 1, we get

a = 2 and b = √3

Therefore, a > b.

If a>b, then the length of latus rectum is 2b2/a

Substituting the values in the formula, we get

Length of latus rectum = [2(√3)2] /2 = 3

Question 8

What is minor axis length for ellipse (x/25)+ (y/16)= 1?
a) 5 units
b) 4 units
c) 8 units
d) 10 units

Answer c

Question 9

What is equation of latus rectums of ellipse (x/25)+ (y/16)= 1?

a) x = ±3
b) y = ±3
c) x = ±2
d) y = ±2

Answer a

Question 10

In an ellipse, the distance between its foci is 6 and the minor axis is 8, then its eccentricity is

a) 1/2

b)  1/5

c)   3/5

d)   4/5

Answer: (c) 3/5

Explanation:

Given that the minor axis of ellipse is 8.(i. e) 2b = 8. So, b=4.

Also, the distance between its foci is 6. (i. e) 2ae = 6

Therefore, ae = 6/2 = 3

We know that b2 = a2(1-e2)

b2 = a2 – a2e2

b2 = a2 – (ae)2

Now, substitute the values to find the value of a.

(4)2 = a2 -(3)2

16 = a2 – 9

a2 = 16+9 = 25.

So, a = 5.

The formula to calculate the eccentricity of ellipse is e = √[1-(b2/a2)]

e = √[1-(42/52)]

e = √[(25-16)/25]

e = √(9/25) = 3/5.

Question 11

A man running a race course notes that the sum of the distances from the two flag posts from him is always 10 meter and the distance between the flag posts is 8 meter. The equation of posts traced by the man is
(a) x²/9 + y²/5 = 1
(b) x²/9 + y2 /25 = 1
(c) x²/5 + y²/9 = 1
(d) x²/25 + y²/9 = 1

Answer d

## MCQ BASED ON HYPERBOLA CLASS XI

Question 1

A hyperbola has ___________ vertices and ____________ foci.
a) two, one
b) one, one
c) one, two
d) two, two

Answer d

Question 2

Find the coordinates of foci of hyperbola (x/9)2(y/16)2=1.
a) (±5,0)
b) (±4,0)
c) (0,±5)
d) (0,±4)

Answer a

Question 3
The equation of a hyperbola with foci on the x-axis is
(a) x²/a² + y²/b² = 1
(b) x²/a² – y²/b² = 1
(c) x² + y² = (a² + b²)
(d) x² – y² = (a² + b²)

Answer b

Question 4
The eccentricity of hyperbola is
a. e =1
b. e > 1
c. e < 1
d. 0 < e < 1
Answer: (b) e > 1

Question 5

Find the coordinates of foci of hyperbola (y/16)2(/x9)2=1.
a) (±5,0)
b) (±4,0)
c) (0,±5)
d) (0,±4)

Answer c

Question 6

What is transverse axis length for hyperbola (x/9)2(y/16)2=1?
a) 5 units
b) 4 units
c) 8 units
d) 6 units

Answer d

Question 7

What is conjugate axis length for hyperbola (x/9)2(y/16)2=1?
a) 5 units
b) 4 units
c) 8 units
d) 10 units

Answer c

Question 8

What is equation of latus rectums of hyperbola (x/9)2(y/16)2=1?
a) x = ±5
b) y = ±5
c) x = ±2
d) y = ±2

Answer a

Question 9

The length of the transverse axis is the distance between the ____.

a)   Two vertices

b)   Two Foci

c)   Vertex and the origin

d)   Focus and the vertex

Answer: (a) Two vertices

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