General Instruction
1. All the questions are compulsory
2. The question paper consists of 40 question and it is divided into four sections A,B , C and D. SECTION A Comprises of 20 questions carrying 1 mark each. Section B comprises of 6 questions carrying 2 marks each, Second C comprises of 8 questions carrying 3 marks each. Section D comprises of 6 questions carrying 4 marks each.
3. There is no overall choice
4. Use of calculator is not permitted.
2. The question paper consists of 40 question and it is divided into four sections A,B , C and D. SECTION A Comprises of 20 questions carrying 1 mark each. Section B comprises of 6 questions carrying 2 marks each, Second C comprises of 8 questions carrying 3 marks each. Section D comprises of 6 questions carrying 4 marks each.
3. There is no overall choice
4. Use of calculator is not permitted.
Section A
1. In a family of 3 children, the probability of having atleast one boy is
a ) 7/8
b) 1/8
c) 5/8
d) 3/4
2. The mean of 20 numbers is 18. If 2 is added to each number , what is the new mean?
3. Find the area of quadrant of a circle whose circumference is 22 cm.
4. The number 525 and 3000 are divisible by 3 ,5 , 15, 25 and 75. What is the HCF of 525 and 3000?
5. What should be added to the polynomial x2 -5x +4 ,so that 3 is the zero of the resulting polynomial:
a) 1
b) 2
c) 4
d) 5.
6. What is the point of intersection of the line represented by 3x - 2y = 6 and the y axis?
7. If px2+qx+r = 0 has equal roots then value of r will be ________
8. Write the nth term of odd numbers.
9. If the corresponding medians of two similar triangles are in the ratio 5:7 . Then find the ratio of their sides.
10. What will be the digit at unit's place of 9n?
11. If a and b are the roots of the polynomial f(x) = x2+x+1 , then 1/a +1/b =
12.the quadratic equation x2-5x-6 =0 if expressed as (x+p)(x+q)=0 then the value of p and q respectively are _____ and ______.
13. Write the sum of first n natural numbers.
14. If two tangents inclined at an angle 60° are drawn to a circle of radius 3 cm , then find the length of each tangent.
15. In the given figure, find the value of x which will make DE|| AB?
16. If radii of two concentric circles are 4 cm and 5cm , then find the length of the chord of one circle which is tangent to other circle.
17. Write the sum of first n even numbers.
18. For what value of p, system of equations 2x + py = 8 and x+y = 6 has no solution.
19. If a quadratic polynomial f(x) is not factorize into linear factors, then it has no real zero (T/F).
20. The mean of 5 observation 3,5,7,x and 11 is 7 , find the value of x.
a ) 7/8
b) 1/8
c) 5/8
d) 3/4
2. The mean of 20 numbers is 18. If 2 is added to each number , what is the new mean?
3. Find the area of quadrant of a circle whose circumference is 22 cm.
4. The number 525 and 3000 are divisible by 3 ,5 , 15, 25 and 75. What is the HCF of 525 and 3000?
5. What should be added to the polynomial x2 -5x +4 ,so that 3 is the zero of the resulting polynomial:
a) 1
b) 2
c) 4
d) 5.
6. What is the point of intersection of the line represented by 3x - 2y = 6 and the y axis?
7. If px2+qx+r = 0 has equal roots then value of r will be ________
8. Write the nth term of odd numbers.
9. If the corresponding medians of two similar triangles are in the ratio 5:7 . Then find the ratio of their sides.
10. What will be the digit at unit's place of 9n?
11. If a and b are the roots of the polynomial f(x) = x2+x+1 , then 1/a +1/b =
12.the quadratic equation x2-5x-6 =0 if expressed as (x+p)(x+q)=0 then the value of p and q respectively are _____ and ______.
13. Write the sum of first n natural numbers.
14. If two tangents inclined at an angle 60° are drawn to a circle of radius 3 cm , then find the length of each tangent.
15. In the given figure, find the value of x which will make DE|| AB?
17. Write the sum of first n even numbers.
18. For what value of p, system of equations 2x + py = 8 and x+y = 6 has no solution.
19. If a quadratic polynomial f(x) is not factorize into linear factors, then it has no real zero (T/F).
20. The mean of 5 observation 3,5,7,x and 11 is 7 , find the value of x.
Section B
21. Two different dice are rolled together. Find the probability
a) of getting a doublet
b) of getting a sum of 10 of the number on the two dice.
22. Find the mode of the following frequency distribution (click on image to zoom)
23. Use Euclid's division algorithm to find the HCF of 16 and 28.
24. Find the value of (cos220° + cos270° ) / (sin259° + sin231°)
25.Determine the A.P. where 6th term is 18 and the difference of 10th term from the 15 th term is 30.
26. If n is an odd integer then show that n2-1 is divisible by 8.
a) of getting a doublet
b) of getting a sum of 10 of the number on the two dice.
22. Find the mode of the following frequency distribution (click on image to zoom)
24. Find the value of (cos220° + cos270° ) / (sin259° + sin231°)
25.Determine the A.P. where 6th term is 18 and the difference of 10th term from the 15 th term is 30.
26. If n is an odd integer then show that n2-1 is divisible by 8.
Section C
27. In figure ABCD is a quadrant of a circle of a radius 28 cm and a semi circles BEC is drawn with BC as diameter, find the area of shaded region.
29. If A(-3,2),B(x,y) and C (1,4) are the vertices of an isosceles triangle with AB= BC . Find the value of (2x+y).
30. Prove that 1/(secθ - tanθ) -1/cosθ = 1/cosθ - 1/(secθ + tanθ)
31. In the given figure, find AD, BE, CF where AB = 12 cm ,BC= 8 cm and AC = 10 cm.
32. Prove that tanθ/(1-cotθ) + cotθ/(1-tanθ) = 1 + tanθ + cotθ .
33. If the points P(3,4) is equidistant from the point A(a+b,b-a) and B(a-b, a+b),then prove that 3b- 4a=0.
34. Find the middle terms of the A.P. 7,13,19 .....241.
Section D
35. A boat covers 32 km upstream and 36 km downstream in 7 hours. Also it covers 40 km upstream and 48 km downstream in 9 hours. Find the speed of boat in still water and that of the stream.
36. Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.
37. The pillars of equal heights stand on either side of a roadway 150 m wide from a joint on the roadway between the pillars, the angles of elevation of the top of the pillars are 60° and 30° . Find the height of pillars and the position of the point.
38. construct a ABC in which BC= 5 cm,CA= 6 cm and AB=7 cm. Construct a similar triangle to ABC , each of whose side are times 7/5 the corresponding sides of ABC.
39. A tent is in the shape of a right circular cylinder upto a height of 3m and conical above it . The total height of the tent is 13.5 m and radius of base is 14 m . Find the cost of cloth required to make the tent at the rate of ₹ 80 per sq. m.
40. The rainfall recorded in a city for 60 days is given in the following table :(click on image to zoom)
Calculate the median rainfall using a more than ogive.
36. Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.
37. The pillars of equal heights stand on either side of a roadway 150 m wide from a joint on the roadway between the pillars, the angles of elevation of the top of the pillars are 60° and 30° . Find the height of pillars and the position of the point.
38. construct a ABC in which BC= 5 cm,CA= 6 cm and AB=7 cm. Construct a similar triangle to ABC , each of whose side are times 7/5 the corresponding sides of ABC.
39. A tent is in the shape of a right circular cylinder upto a height of 3m and conical above it . The total height of the tent is 13.5 m and radius of base is 14 m . Find the cost of cloth required to make the tent at the rate of ₹ 80 per sq. m.
40. The rainfall recorded in a city for 60 days is given in the following table :(click on image to zoom)
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