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NCERT MATHS TEST 01 Class: 10 (CBSE)
Time: 2 Hours
Max. Marks: 80
General Instructions: All questions are compulsory. Questions are strictly from Odd Chapters (1, 3, 5, 7, 9, 11, 13).
SECTION A (Multiple Choice Questions) - 1 Mark Each
1.
The HCF of two numbers is 27 and their LCM is 162. If one of the numbers is 54, what is the other number?
(a) 36
(b) 81
(c) 9
(d) 45
[1]
2.
The pair of equations x + 2y - 5 = 0 and -3x - 6y + 15 = 0 have:
(a) A unique solution
(b) Exactly two solutions
(c) Infinitely many solutions
(d) No solution
[1]
3.
The 10th term of the AP: 2, 7, 12, ... is:
(a) 47
(b) 52
(c) 57
(d) 37
[1]
4.
The distance of point P(2, 3) from the x-axis is:
(a) 2
(b) 3
(c) 1
(d) 5
[1]
5.
If the length of the shadow of a tower is increasing, then the angle of elevation of the sun:
(a) Is also increasing
(b) Is decreasing
(c) Remains unchanged
(d) None of these
[1]
6.
Area of a sector of a circle with radius R and angle P (in degrees) is:
(a) (P/180) × 2πR
(b) (P/180) × πR²
(c) (P/360) × 2πR
(d) (P/720) × 2πR²
[1]
7.
For the following distribution, the sum of lower limits of the median class and modal class is:
Class 0-5 5-10 10-15 15-20 20-25
Frequency 10 15 12 20 9
(a) 15
(b) 25
(c) 30
(d) 35
[1]
8.
Which of the following numbers is irrational?
(a) √4
(b) 3.1414... (terminating)
(c) √7
(d) 22/7
[1]
9.
The value of k for which the system of equations x + 2y - 3 = 0 and 5x + ky + 7 = 0 has no solution, is:
(a) 10
(b) 6
(c) 3
(d) 1
[1]
10.
The common difference of the AP: 1/p, (1-p)/p, (1-2p)/p, ... is:
(a) p
(b) -p
(c) -1
(d) 1
[1]
11.
The distance between the points (a, b) and (-a, -b) is:
(a) 2√(a²+b²)
(b) √(a²+b²)
(c) 4√(a²+b²)
(d) 0
[1]
12.
A pole 6 m high casts a shadow 2√3 m long on the ground, then the Sun's elevation is:
(a) 60°
(b) 45°
(c) 30°
(d) 90°
[1]
13.
If the perimeter and the area of a circle are numerically equal, then the radius of the circle is:
(a) 2 units
(b) π units
(c) 4 units
(d) 7 units
[1]
14.
The empirical relationship between the three measures of central tendency is:
(a) 3 Median = Mode + 2 Mean
(b) 2 Median = Mode + 2 Mean
(c) 3 Mean = Mode + 2 Median
(d) 3 Mode = Median + 2 Mean
[1]
15.
Prime factorization of 140 is:
(a) 2 × 2 × 5 × 7
(b) 2 × 5 × 7
(c) 2 × 2 × 2 × 5 × 7
(d) 2 × 7 × 10
[1]
16.
One equation of a pair of dependent linear equations is -5x + 7y = 2. The second equation can be:
(a) 10x + 14y + 4 = 0
(b) -10x - 14y + 4 = 0
(c) -10x + 14y + 4 = 0
(d) 10x - 14y = -4
[1]
17.
Find the coordinates of the point which divides the join of (-1, 7) and (4, -3) in the ratio 2:3.
(a) (1, 3)
(b) (2, 3)
(c) (3, 1)
(d) (1, 1)
[1]
18.
The minute hand of a watch is 14 cm long. The area swept by the minute hand in 5 minutes is:
(a) 154 cm²
(b) 44 cm²
(c) 51.33 cm²
(d) 616 cm²
[1]
19.
If the mean of 6, 7, x, 8, y, 14 is 9, then:
(a) x + y = 21
(b) x + y = 19
(c) x - y = 19
(d) x + y = 12
[1]
20.
Which term of the AP: 21, 18, 15, ... is -81?
(a) 34
(b) 35
(c) 36
(d) 33
[1]
SECTION B (Very Short Answer Questions) - 2 Marks Each
21.
Given that HCF (306, 657) = 9, find LCM (306, 657).
[2]
22.
Solve 2x + 3y = 11 and 2x – 4y = – 24 and hence find the value of ‘m’ for which y = mx + 3.
[2]
23.
Find the point on the x-axis which is equidistant from (2, –5) and (–2, 9).
[2]
24.
A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30°. (Refer to the given figure) Question 24 Figure
[2]
25.
Find the area of a quadrant of a circle whose circumference is 22 cm.
[2]
SECTION C (Short Answer Questions) - 3 Marks Each
26.
Prove that 3 + 2√5 is irrational.
[3]
27.
The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is ₹ 105 and for a journey of 15 km, the charge paid is ₹ 155. What are the fixed charges and the charge per km?
[3]
28.
How many two-digit numbers are divisible by 3?
[3]
29.
Find the ratio in which the line segment joining A(1, – 5) and B(– 4, 5) is divided by the x-axis. Also find the coordinates of the point of division.
[3]
30.
The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.
Literacy rate (in %) 45-55 55-65 65-75 75-85 85-95
Number of cities 3 10 11 8 3
[3]
31.
Find the sum of the first 15 multiples of 8.
[3]
SECTION D (Long Answer Questions) - 5 Marks Each
32.
A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km downstream. Determine the speed of the stream and that of the boat in still water.
[5]
33.
A spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre at A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, . . . as shown in the figure. What is the total length of such a spiral made up of thirteen consecutive semicircles? (Take π = 22/7) Question 33 Figure
[5]
34.
From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower.
[5]
35.
If the median of the distribution given below is 28.5, find the values of x and y.
Class Interval 0-10 10-20 20-30 30-40 40-50 50-60
Frequency 5 x 20 15 y 5
Total Frequency: 60
[5]
SECTION E (Case Study Based Questions) - 4 Marks Each
36.
Case Study 1 (Coordinate Geometry): To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1m each. 100 flower pots have been placed at a distance of 1m from each other along AD. Question 36 Figure (i) What are the coordinates of Niharika if she runs 1/4th the distance AD on the 2nd line? [1]
(ii) What are the coordinates of Preet if she runs 1/5th the distance AD on the 8th line? [1]
(iii) What is the distance between both the flags? [2]
[4]
37.
Case Study 2 (Areas Related to Circles): A round table cover has six equal designs as shown in the figure. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of ₹ 0.35 per cm². (Use √3 = 1.7) Question 37 Figure (i) Find the area of the circle. [1]
(ii) Find the area of one sector (Design sector). [1]
(iii) Find the total area of the 6 designs. [2]
[4]
38.
Case Study 3 (Arithmetic Progressions): In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato, and the other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line. Question 38 Figure (i) What is the distance run to pick up the first potato and return? [1]
(ii) What is the distance run to pick up the second potato and return? [1]
(iii) What is the total distance the competitor has to run? [2]
[4]
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