# Class 10 Maths Sample Paper Term 2 With Solutions Set B

Please refer to Class 10 Maths Sample Paper Term 2 With Solutions Set B provided below. The Sample Papers for Class 10 Maths have been prepared based on the latest pattern issued by CBSE. Students should practice these guess papers for class 10 Maths to gain more practice and get better marks in examinations. The Term 2 Sample Papers for Maths Standard 10 will help you to understand the type of questions which can be asked in upcoming examinations.

## Term 2 Sample Paper for Class 10 Maths With Solutions Set B

SECTION – A

1. If (x – a) is one of the factors of the polynomial ax2 + bx + c, then one of the roots of ax2 + bx + c = 0 is
(a) 1
(b) c
(c) a
(d) none of these

2. If the roots of ax2 + bx + c = 0 are equal in magnitude but opposite in sign, then
(a) a = 0
(b) b = 0
(c) c = 0
(d) none of these

3. The list of numbers –10, – 6, –2, 2, … is
(a) an AP with d = –16
(b) an AP with d = 4
(c) an AP with d = – 4
(d) not an AP

Answer : (b) an AP with d = 4

4. If the common difference of an AP is 3, then a20 – a15 is
(a) 5
(b) 3
(c) 15
(d) 20

5. The angle of elevation of the top of a tower from a point 20 metres away from its base is 45°.The height of the tower is
(a) 10 m
(b) 20 m
(c) 30 m
(d) 20√3m

6. The angle of elevation of the top of a 15 m high tower at a point 15 m away from the base of the tower is ________.
(a) 45°
(b) 30°
(c) 60°
(d) 90°

SECTION – B

7. Find the value of k for which the roots of the quadratic equation:
(k – 4)x2 + 2(k – 4)x + 2 = 0 are equal.

8. If 5 times the 5th term of an AP is equal to 10 times the 10th term, show that its 15th term is zero.

SECTION – C

9. Solve the following equation for x: 1/(x+1) + 2/(x+2) = 5/(x+4) ; x ≠ -1, -2, -4

10. The sum of n terms of an AP is 5n2 – 3n. Find the AP and also its 10th term.

11. In an AP, the sum of first ten terms is –150 and the sum of its next ten terms is –550. Find the AP.

12. As observed from the top of a light-house, 100 m high above sea level, the angle of depression of a ship, sailing directly towards it, changes from 30° to 60°. Determine the distance travelled by the ship during the period of observation. (Use √3 = 1.732)

SECTION – D
CASE STUDY QUESTIONS

13. Your friend Veer wants to participate in a 200 m race. He can currently run that distance in 51 seconds and with each day of practice it takes him 2 seconds less. He wants to do in 31 seconds.

(a) Which of the following terms are in AP for the given situation
(i) 51, 53, 55….
(ii) 51, 49, 47….
(iii) –51, –53, –55….
(iv) 51, 55, 59…

Answer : (ii) 51, 49, 47….

(b) What is the minimum number of days he needs to practice till his goal is achieved
(i) 10
(ii) 12
(iii) 11
(iv) 9

(c) Which of the following term is not in the AP of the above given situation
(i) 41
(ii) 30
(iii) 37
(iv) 39

(d) If nth term of an AP is given by an = 2n + 3 then common difference of an AP is
(i) 2
(ii) 3
(iii) 5
(iv) 1

(e) The value of x, for which 2x, x + 10, 3x + 2 are three consecutive terms of an AP
(i) 6
(ii) –6
(iii) 18
(iv) –18

14. A group of students of class X visited India Gate on an education trip. The teacher and students had interest in history as well. The teacher narrated that India Gate, official name Delhi Memorial, originally called All- India War Memorial, monumental sandstone arch in New Delhi, dedicated to the troops of British India who died in wars fought between 1914 and 1919. The teacher also said that India Gate, which is located at the eastern end of the Rajpath (formerly called the Kingsway), is about 138 feet (42 metres) in height.

(a) What is the angle of elevation if they are standing at a distance of 42 m away from the monument?
(i) 30°
(ii) 45°
(iii) 60°
(iv) 0°

(b) They want to see the tower at an angle of 60°. So, they want to know the distance where they should stand and hence find the distance.
(i) 25.24 m
(ii) 20.12 m
(iii) 42 m
(iv) 24.64 m

(c) If the altitude of the Sun is at 60°, then the height of the vertical tower that will cast a shadow of length 20 m is
(i) 20√3
(ii) 20√3
(iii) 15√3
(iv) 15√3

(d) The ratio of the length of a rod and its shadow is 1 : 1. The angle of elevation of the Sun is
(i) 30°
(ii) 45°
(iii) 60°
(iv) 90°