CLASS X TH CBSE Math SA-1 ASSIGNMENT2019

Time Allowed : 3 to 3¹/ ₂ hours                                                       [Maximum Marks: 80 General Instructions :

(i)All questions are compulsory.

(ii) The question paper consists of 34 questions divided into four sections A, B, C and D. Section A comprises of 10 questions of 1 mark each, Section B comprises of8 questions of 2 marks each, Section C comprises of 10 questions of 3 marks each and Section D comprises of 6 questions of 4 marks each.

(iii) Question numbers 1 to 10 in Section A are multiple choice questions where you are to select one correct option out of the given four.

(iv) There is no overall choice. However, internal choice has been provided in 1 question of two marks, 3 questions of three marks each and 2 questions of four marks each. You have to attempt only one of the alternatives in all such questions.

(v) Use of calculators is not permitted. –

(vi) An additional 15 minutes time has been allotted to read this question paper only

Section ‘A’

1. The value of P for which the polynomial x³+4x² -px +8 is exactly divisible by (x-2) is

(a) 0                                                    (b)3

(c)5                                                     (d)16

2.If HCF and LCM of two numbers are 4 and 9696 then the product of the number is

(a)9696                                       (b)24242

(c)38784                                     (d)4848

3.The pair of linear equations 2x +7y = k, kx +21y = 18 has infinitely many solution if

(a)3                                                (b)6

(c)9                                                 (d)18

4. If cosecθ=4 and cotθ=√3k then k =

(a)1                                                (b)2

(c)√5                                            (d)5

Section B

5. Can two numbers have 18 as their HCF and 380 as their LCM? Give reason.

Class 10 maths ncert solutions chapter 1: Real numbers

6. The cost of 2 kg of apples and 1 kg of grapes on a day was found to be Rs. 160. Also, the cost of 4 kg of apples and 2 kg of grapes is Rs 300. Represent this situation algebraically.

7. Write three rational numbers between √2 and √3.

8.Express 43 in the form of 7q + 8.

9. Use Euclid’s division algorithm to find HCF of 456 and  84.

10-If one zero of the polynomial p(x) = (a²+9)x²+45x +6a is reciprocal of other, find the value of a.

SectionC

11. For which value of p does the equations 4x +py +8 = 0 and x + y +1=0 have unique solution.

12. If 7sin²θ + 3cos²θ = 4 then prove that

13. What must be subtracted from the polynomial 4x³+ 5x²–10x +7 so that resulting polynomial is exactly divisible by 2x +5.

14. Find the value of a and b if the following pair of the linear equation has infinite number of solutions.

4x–(a +2)y =b+2, 6x + (1 – 3a)y = b

15. If the sum of the square of the zeroes of the polynomial is 6x² + x +k is 25/36.find the value of k.

16.The altitude AD of ΔABC is drown from the vertex A on BC where ∠A is obtuse . If AD = 10cm, BD =10 cm and CD =10√3cm, find ∠A.

17. State and prove Pythagoras theorem. Also, prove thatΔ ABC is an isosceles triangle with AC =BC, if AB² = 2AC² then ABC is a right triangle.

18. If A,B and C are interior angles of a triangle ABC,prove that

19. Find the mean of the following distribution.

20. Find the mode of the following data.

Section D

21. Find the largest positive integer that will divide 100,245 and 343 leaving reminders 4,5 and 7 respectively.

22. Solve the following equations graphically also find the points where the lines meet the x-axis .

x +2y =5

2x + 3y = 4

23.Find all the zeroes  of the polynomial 4x⁴–2oxᶾ +23x² +5x –6, if two of its zeroes are 2 and 3.

24.In an equilateral ABC, AD is the altitude drawn from A on side BC, Prove that 3AB² = 4AD².

25. For the f0llowing frequency distribution draw a more than type ogive and then determine the median.

26. If the median of the following frequency distribution is 28.5, find values of x and y.

Q27.Sum of the areas of two squares is 468 sq.m, if the difference of their perimeter is 24 m, find the sides of two square.

Q28. If in Δ ABC  AD is median and AM  ⊥BC, then prove that AB² +AC² =2AD²+1/2BC².

Q30. Prove that:

Q31. Prove that √3 is an irrational number, Hence show that 7 + 2√3 is also an irrational number.