English Medium
Academic Year: 2021-2022
Date & Time: 5th May 2022, 10:30 am
Duration: 2h
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General Instructions :
- This question paper contains of 14 questions. All questions are compulsory.
- This question paper is divided into four sections -A, B, C, and D.
- Section A contains 6 questions (Q No.1 to 6) of 2 marks each. Internal choice has been provided in two questions.
- Section B contains 4 questions (Q No. 7 to 10) of 3 marks each. Internal choice has been provided in one question.
- Section C contains 4 questions (Q No. 11 to 14) of 4 marks each. An internal choice has been provided in one question. It also contains two case study board questions.
- Use of calculator is not permitted.
Solve the quadratic equation: `x^2 + 2sqrt(2)x - 6` = 0 for x.
Chapter: [0.023] Quadratic Equations
Which term of the A.P. `-11/2, -3, -1/2`.... is `49/2`?
Chapter: [0.024] Arithmetic Progressions
Find a and b so that the numbers a, 7, b, 23 are in A.P.
Chapter: [0.024] Arithmetic Progressions
A solid piece of metal in the form of a cuboid of dimensions 11 cm × 7 cm × 7 cm is melted to form 'n' number of solid spheres of radii `7/2` cm each. Find the value of n.
Chapter: [0.062] Surface Areas and Volumes
In the given figure, AB is diameter of a circle centered at O. BC is tangent to the circle at B. If OP bisects the chord AD and ∠AOP = 60°, then find ∠C.
Chapter: [0.042] Circles
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In the given figure, XAY is a tangent to the circle centered at O. If ∠ABO = 40°, then find ∠BAY and ∠AOB.
Chapter: [0.042] Circles
If mode of the following frequency distribution is 55, then find the value of x.
| Class | 0 – 15 | 15 – 30 | 30 – 45 | 45 – 60 | 60 – 75 | 75 – 90 |
| Frequency | 10 | 7 | x | 15 | 10 | 12 |
Chapter: [0.071] Statistics
Find the sum of first 20 terms of an A.P. whose nth term is given as an = 5 – 2n.
Chapter: [0.024] Arithmetic Progressions
Draw two concentric circles of radii 2 cm and 3 cm. From a point on the outer circle, construct a pair of tangents to the inner circle.
Chapter: [0.042] Circles
In the given figure, AB is tower of height 50 m. A man standing on its top, observes two car on the opposite sides of the tower with angles of depression 30° and 45° respectively. Find the distance between the two cars.
Chapter: [0.053] Some Applications of Trigonometry
The mean of the following frequency distribution is 25. Find the value of f.
| Class | 0 – 10 | 10 – 20 | 20 – 30 | 30 – 40 | 40 – 50 |
| Frequency | 5 | 18 | 15 | f | 6 |
Chapter: [0.071] Statistics
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Find the mean of the following data using assumed mean method:
| Class | 0 – 5 | 5 – 10 | 10 – 15 | 15 – 20 | 20 – 25 |
| Frequency | 8 | 7 | 10 | 13 | 12 |
Chapter: [0.071] Statistics
Heights of 50 students of class X of a school are recorded and following data is obtained:
| Height (in cm) | 130 – 135 | 135 – 140 | 140 – 145 | 145 – 150 | 150 – 155 | 155 – 160 |
| Number of students | 4 | 11 | 12 | 7 | 10 | 6 |
Find the median height of the students.
Chapter: [0.071] Statistics
In the given figure, PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q meet at a point T. Find the length of TP.
Chapter: [0.042] Circles
A 2-digit number is such that the product of its digits is 24. If 18 is subtracted from the number, the digits interchange their places. Find the number.
Chapter: [0.022000000000000002] Pair of Linear Equations in Two Variables
The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find two numbers.
Chapter: [0.023] Quadratic Equations
Read the following passage and answer the questions given below.
|
Kite Festival Kite festival is celebrated in many countries at different times of the year. In India, every year 14th January is celebrated as International Kite Day. On this day many people visit India and participate in the festival by flying various kinds of kites. The picture given below, show three kites flying together.
In the given figure, the angles of elevation of two kites (Points A and B) from the hands of a man (Point C) are found to be 30° and 60° respectively. Taking AD = 50 m and BE = 60 m, find. |
- the lengths of strings used (take them straight) for kites A and B as shown in the figure.
- the distance 'd' between these two kites.
Chapter: [0.053] Some Applications of Trigonometry
Read the following passage and answer the questions given below.
|
A 'circus' is a company of performers who put on shows of acrobats, clowns etc. to entertain people started around 250 years back, in open fields, now generally performed in tents. One such 'Circus Tent' is shown below. The tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of cylindrical part are 9 m and 30 m respectively and height of conical part is 8 m with same diameter as that of the cylindrical part, then find |
- the area of the canvas used in making the tent;
- the cost of the canvas bought for the tent at the rate ₹ 200 per sq m, if 30 sq m canvas was wasted during stitching.
Chapter: [0.062] Surface Areas and Volumes
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