SAMPLE QUESTION PAPER 2021-22
TERM II
CLASS X
MATHEMATICS (STANDARD) – 041
Time Allowed: 2 Hours Maximum Marks: 40
General Instructions:
1. The question paper consists of 14 questions divided into 3 sections A, B, C
2. All questions are compulsory
3. Section A comprises of 6 questions of 2 marks each. Internal choice as been provided in two questions.
4. Section B comprises of 4 questions of 3 marks each. Internal choice as been provided in one questions.
5. Section C comprises of 4 questions of 4 marks each. Internal choice as been provided in one questions.
It contains two case study based questions.
SECTION A
1. The length of a string between a kite and a point on the ground is 85 m. If the string makes an angle θ with level ground such that tan θ = 15/8, how high is the kite?
2. Solve for x: 25x2 – 10a2x + (a4 – b4) = 0
OR
Is the following situation possible? The sum of ages of a mother and her daughter is 25 years. Five years ago the product of their ages was 58.
3. Find the mean age (in years) from the frequency distribution given below:
4. The top of two poles of height 20 m and 14 m are connected by a wire. If the wire makes an angle of 300 with the horizontal, then find the length of the wire.
OR
The ratio of the length of a rod and its shadow is 1 : √3. Find the altitude of the sun.
5. Divide a line segment of length 9 cm internally in the ratio 4 : 3
6. From the following data find the median age of 100 residents of a colony who took part in swachch bharat abhiyan.
SECTION B
7. A toy is in the form of a cone mounted on a hemisphere of radius 7 cm. The total height of the toy is 14.5 cm. Find the volume of the toy. (Take π = 22/7)
8. In a violent storm, a tree got bent by the wind. The top of the tree meets the ground at an angle of 300, at a distance of 30 m from the root. At what height from the bottom did the tree get bend? What was the original height of the tree? (use √3 = 1.73)
9. A medicine-capsule is in the shape of a cylinder of diameter 0.5 cm with two hemispheres stuck to each oth its ends. The length of entire capsule is 2 cm. Find the capacity of the capsule.
OR
A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The radius and height of the cylindrical part are 5 cm and 12 cm respectively. The radii of the hemispherical and conical parts are the same as that of the cylindrical part. Find the surface area of the toy, if the total height of the toy is 30 cm.
10. ABC is right angled triangle, right angled at A. A circle is inscribed in it. The length of two sides containing the right angles are 5 cm and 12 cm. Find the radius of the circle.
SECTION C
11. Jaspal Singh repays his total loan of ₹118000 by paying every month starting with the first instalment of ₹1000. If he increases the instalment by ₹100 every month, what amount will be paid by him in the 30th instalment?
OR
In an A.P. show that the sum of the terms equidistant from the beginning and the end is the same and is equal to the sum of first and last terms.
12. The sum of the areas of two squares is 452m2. If the difference of their perimeters is 8 m, then find the sides of the two squares.
13. Prem did an activity on tangents drawn to a circle from an external point using 2 straws and a nail for maths project as shown in figure.
Based on the above information, answer the following questions.
(i) On the basis of which of the following congruency criterion, ΔOAP ≅ ΔOBP?
(ii) If ∠AOB = 1500 , then find measure of ∠APB.
14. As the demand for the products grew, a manufacturing company decided to hire more employees. For which they want to know the mean time required to complete the work for a worker.
The following table shows the frequency distribution of the time required for each worker to complete a work.
Based on the above information, answer the following questions.
(i) If xi’s denotes the class marks and fi’s denotes the corresponding frequencies for the given data, then find the value of
(ii) Find the mean time (in hrs) required to complete the work for a worker.
