Date: April 2022

Duration: 1h30m

**Note :**

- Answers to this Paper must be written on the paper provided separately.
- You will not be allowed to write during the first 10 minutes.
- This time is to be spent in reading the question paper.
- The time given at the head of this Paper is the time allowed for writing the answers.
- Attempt all questions from Section A and any three questions from Section B.
- The intended marks for questions or parts of questions are given in brackets [ ].

The point (3, 0) is invariant under reflection in:

The origin

x-axis

y-axis

both x and y axes

Chapter: [0.09] Reflection

In the given figure, AB is a diameter of the circle with centre ‘O’. If ∠COB = 55⁰ then the value of x is:

27.5°

55°

110°

125°

Chapter: [0.02] Circles

If a rectangular sheet having dimensions 22 cm x 11 cm is rolled along its shorter side to form a cylinder. Then the curved surface area of the cylinder so formed is:

968 cm^{2}

424 cm^{2}

121 cm^{2}

242 cm^{2}

Chapter: [0.04] Mensuration

If the vertices of a triangle are (1, 3), (2, - 4) and (-3, 1). Then the co-ordinate of its centroid is:

(0, 0)

(0, 1)

(1, 0)

(1, 1)

Chapter: [0.01] Co-ordinate Geometry Distance and Section Formula

tan θ × `sqrt(1 - sin^2 θ)` is equal to:

cos θ

sin θ

tan θ

cot θ

Chapter: [0.05] Trigonometry

The median class for the given distribution is:

Class Interval | 1 - 5 | 6 - 10 | 11 - 15 | 16 - 20 |

Cumulative Frequency | 2 | 6 | 11 | 18 |

1 – 5

6 – 10

11 – 15

11 – 20

Chapter: [0.06] Statistics

If the lines 7y = ax + 4 and 2y = 3 − x, are parallel to each other, then the value of ‘a’ is:

- 1

`(-7)/2`

`(-2)/7`

14

Chapter: [0.1] Co-ordinate Geometry Equation of a Line

Volume of a cylinder is 330 cm^{3}. The volume of the cone having same radius and height as that of the given cylinder is:

330 cm^{3}

165 cm^{3}

110 cm^{3}

220 cm^{3}

Chapter: [0.04] Mensuration

In the given graph, the modal class is the class with frequency:

72

21

48

36

Chapter: [0.06] Statistics

If the probability of a player winning a game is 0.56. The probability of his losing this game is:

0.56

1

0.44

0

Chapter: [0.07] Probability

Find the ratio in which the x-axis divides internally the line joining points A (6, -4) and B ( -3, 8).

Chapter: [0.01] Co-ordinate Geometry Distance and Section Formula

Three rotten apples are accidentally mixed with twelve good ones. One apple is picked at random. What is the probability that it is a good one?

Chapter: [0.07] Probability

In the given figure, AC is a tangent to circle at point B. ∆EFD is an equilateral triangle and ∠CBD = 40°. Find:

- ∠BFD
- ∠FBD
- ∠ABF

Chapter: [0.02] Circles

A drone camera is used to shoot an object P from two different positions R and S along the same vertical line QRS. The angle of depression of the object P from these two positions is 35° and 60° respectively as shown in the diagram. If the distance of the object P from point Q is 50 metres, then find the distance between R and S correct to the nearest meter.

Chapter: [0.05] Trigonometry

In the given figure, PT is a tangent to the circle at T, chord BA is produced to meet the tangent at P. Perpendicular BC bisects the chord TA at C. If PA = 9 cm and TB = 7 cm, find the lengths of:

- AB
- PT

Chapter: [0.02] Circles

How many solid right circular cylinders of radius 2 cm and height 3 cm can be made by melting a solid right circular cylinder of diameter 12 cm and height 15 cm?

Chapter: [0.04] Mensuration

Prove that:

`(cos^2 "A")/(cos "A" - sin "A") + (sin "A")/(1 - cot "A")` = sin A + cos A

Chapter: [0.05] Trigonometry

Use graph paper for this question, take 2 cm = 10 marks along one axis and 2 cm = 10 students along the other axis.

The following table shows the distribution of marks in a 50 marks test in Mathematics:

Marks | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 |

No. of. Students | 6 | 10 | 13 | 7 | 4 |

Draw the ogive for the above distribution and hence estimate the median marks.

Chapter: [0.06] Statistics

Find the equation of the perpendicular dropped from the point (−1, 2) onto the line joining the points (1, 4) and (2, 3)

Chapter: [0.1] Co-ordinate Geometry Equation of a Line

Find the mean for the following distribution:

Class Interval |
20 - 40 | 40 - 60 | 60 - 80 | 80 - 100 |

Frequency |
4 | 7 | 6 | 3 |

Chapter: [0.06] Statistics

A solid piece of wooden cone is of radius OP = 7 cm and height OQ = 12 cm. A cylinder whose radius and height equal to half of that of the cone is drilled out from this piece of wooden cone. Find the volume of the remaining piece of wood. (Use, `pi = 22/7`)

Chapter: [0.04] Mensuration

Use a graph sheet for this question, take 2 cm = 1 unit along both x and y-axis:

- Plot the points A (3, 2) and B (5, 0). Reflect point A on the y-axis to A΄. Write co-ordinates of A΄.
- Reflect point B on the line AA΄ to B΄. Write the co-ordinates of B΄.
- Name the closed figure A’B’AB.

Chapter: [0.1] Co-ordinate Geometry Equation of a Line

In the given figure, the sides of the quadrilateral PQRS touches the circle at A, B, C and D. If RC = 4 cm, RQ = 7 cm and PD = 5 cm. Find the length of PQ:

Chapter: [0.02] Circles

Prove that:

`(sin^3 theta + cos^3 theta)/(sin theta + cos theta) = 1 - sin theta cos theta`

Chapter: [0.05] Trigonometry

In the given diagram, OA = OB, ∠OAB = 𝜃 and the line AB passes through point P (-3, 4).

Find:

- Slope and inclination (𝜃) of the line AB
- Equation of the line AB

Chapter: [0.1] Co-ordinate Geometry Equation of a Line

Use graph paper for this question. Estimate the mode of the given distribution by plotting a histogram. [Take 2 cm = 10 marks along one axis and 2 cm = 5 students along the other axis]

Daily wages (in ₹) |
30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 | 70 - 80 |

No. of Workers |
6 | 12 | 20 | 15 | 9 |

Chapter: [0.06] Statistics [0.06] Statistics

A box contains tokens numbered 5 to 16. A token is drawn at random. Find the probability that the token drawn bears a number divisible by:

- 5
- Neither by 2 nor by 3

Chapter: [0.07] Probability

Point M (2, b) is the mid-point of the line segment joining points P (a, 7) and Q (6, 5). Find the values of ‘a’ and ‘b’.

Chapter: [0.01] Co-ordinate Geometry Distance and Section Formula

An aeroplane is flying horizontally along a straight line at a height of 3000 m from the ground at a speed of 160 m/s. Find the time it would take for the angle of elevation of the plane as seen from a particular point on the ground to change from 60⁰ to 45⁰. Give your answer correct to the nearest second.

Chapter: [0.05] Trigonometry

Given that the mean of the following frequency distribution is 30, find the missing frequency ‘f’.

Class Interval |
0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 |

Frequency |
4 | 6 | 10 | f | 6 | 4 |

Chapter: [0.06] Statistics

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