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
- The value of P for which the polynomial x³+4x² -px +8 is exactly divisible by (x-2) is
(a) 0 (b)3
2.If HCF and LCM of two numbers are 4 and 9696 then the product of the number is
3.The pair of linear equations 2x +7y = k, kx +21y = 18 has infinitely many solution if
4. If cosecθ=4 and cotθ=√3k then k =
5. Can two numbers have 18 as their HCF and 380 as their LCM? Give reason.
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.
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.
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.