Mathematics Sample paper 11, Part- A for class 10th

 Mathematics Sample paper 

Part- A

Section- I

Directions (Q.nos. 1-16 are of 1 marks each)

1. Find the real roots of the quadratic equation 3x²-5x-2 =0.

2. What is the maximum sum of the following AP series 20 + 19 ⅓ + 18 1 + 18......

3. Prove that cos⁴x - sin⁴x= 2cos²x -1.

Or

Show that cos ∅(1/1-sin∅ - 1/1+sin∅) can be written in the form ktan∅ and find the value of k.

4. AB and CD are two common tangents to circles which touch each other at point C. If D lies on AB such that CD=4 cm, find AB.

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5. In ∆ABC, AB/AC=BD/DC, angle B=70°

and angle C = 50°.

Determine the value of angle BAD.

6. A metallic sphere of radius 10.5cm is melted and then recast into small cones each of radius 3.5cm and height 3 cm. Find the number of such cones.

7. In the given figure, if angle ADE = angle ABC, then find CE.

Or

In the given figure, DE\\AB. If AD=2x, DC=x+3, BE =2x-1 and CE =x, then find the value of x.

8. In the given figure, if AP=PB, then prove that AC=BC.

9. The probability of guessing the correct answer to a certain test question is x/12. If the probability of not guessing the correct answer to this question is 2/3, then find the value of x.

10. If the distance between the points (4,p) and (1,0) is 5, what is the value of p.

11. What is the positive minimum value of sec∅?

12. Find the sum of the zeroes of 2x² -8x +6.

Or

If 2 is a zero of a polynomial p(x) =3x² +2kx +5, determine the value of k.

13. What is the perimeter of a square whose diagonal is 20cm?

Or

If the area of a sector of a circle is 7/20 of the area of the circle, then find the sector angle.

14. If the mean of a frequency distribution is 8.1 and sigma fixi = 132 + 5kf, sigma fi =20, the ln find the value of k.

15. The 8th term of an AP is 17 and it's 14th term is 29. Find it's common difference.

Or

Determine k, so that 2/3,k and 5/8k are the three consecutive terms of an AP.

16. A solid ball is exactly fitted inside the cubical box of side a. Find the volume of ball.

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Section-II

Directions (Q.nos 17-20 are of 4 marks each)

17. Case Study I

Labour suffer from Literacy

India's literacy rate has increased six times since the end of the British rule in 1947. From 12% to 74% in recent times. Yet India has the world's largest population of illiterate people according to a report of Oxfam.

Ram asks the labour to dig a well up to a depth of 10m. Labour changes Rs 150 for first metre and Rs 50 for each subsequent metres. As labour was uneducated, he claims Rs 550 for the whole work.

a) What type of series is formed from the given statement?

i. AP

ii. None AP

iii. Don't say anything

iv. None of the above

b) What should be the actual amount to be paid to the labour?

i. Rs 665

ii. Rs 600

iii. Rs 645

iv. Rs 640

c) How much money did Ram will save, if he agree with Rs 550?

i. Rs 50

ii. Rs 40

iii. Rs 45

iv. Rs 55

d) In AP sequence if each term is multiplied by constant k, then the new sequence will be 

i. AP

ii. Non AP

iii. Don't say anything

iv. None of the above

e) If AP sequence has n terms then the third term from the last is given by ( where l is the last term of a sequence)

i. l-2d

ii. l-d

iii. l-3d

iv. l-4d

18. Case Study III

Old age House

Old age homes are mean for senior citizens who are unable to stay with their families or destitute . These old age homes have special medical facilities for senior citizens such as mobile health care system, ambulances nurses and provision of well balanced meals.

Amita, Suneha and Raghav start preparing cards for greeting each person of an old age home on new year. In order to complete one card, they take 10,16 and 20 min respectively.

a) If all of them started together,after what time will they start preparing a new card together.

i. 85 min

ii. 80 min

iii. 60 min

iv. 90 min

b) What is the common time to make a one card?

i. 1 min

ii. 2 min

iii. 4 min

iv. None of these

c) The smallest prime even number is

i. 1

ii. 2

iii. 3 

iv. 4

d) A largest positive integer that divides given two positive integers is called the 

i. LCM

ii. HCF

iii. Can't say

iv. None of the above

e) Coprime number are those numbers which donot have any common factor other then 

i. 0

ii. 1

iii. 2

iv. None of these

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Posted by:- Anuranjan Gadekar

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