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 cach. 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 cach. 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. LCM of 14 and 122.
2.If one of zeros of quadratic polynomial x2 + 3x + k is 2 , then the value of k is .......
A) 10
b) -10
c) 5
d) -5
3. The pair of equations x=a and y=b graphically represents lines which are :
a) Parallel
b) intersecting at ( b,a)
c) coincident.
d) intersecting at ( a,b)
4. For what value of K , do the equation 3x-y +8 =0 and 6x- Ky = -16 represent coincident lives?
a) 1/2
b) -1/2
c) 2
d) -2
5. If k, 2k -1 and 2k+1 are in A.P. , then value of k is....
6. The median of 1st ten prime number is____.
7. The distance of P (3,-2) from y axis is ___.
8. Write the general form of an even integer.
9. Write the form in which every odd integer can be written taking t as variable.
10.If one zero of the quadratic polynomial x2 + 3x + k is 2 , then the value of k is
11. Mode = 3________ -2 _________.
12. The total surface area of a solid hemisphere of radius r is
a) πr2
b) 2πr2
c) 3πr2
d) 4πr2
14. If a and b are the zeros of the quadratic polynomial p(x) = x2 - p(x+1) -c such that (a+1)(1+b) =0 ,then c=
15. If the diameter of a protractor is 21 cm, then find its perimeter.
16. The 10th term from the end of the A.P. 8 , 10 ,12.......126 is ...............
17. Every quadratic equation can have at most
a) three roots
b) one root
c) two roots
d) any number of roots.
18. Roots of quadratic equation x2- 7x= 0 will be
a) 7
b) 0,-7
c) 0,5
d) 0,7
19. The length of the tangent to a circle from a point P , which is 25 cm away from the centre is 24 cm. What is the radius of the circle?
20. Is the triangle with sides 12 cm , 16 cm and 18 cm a right triangle?
2.If one of zeros of quadratic polynomial x2 + 3x + k is 2 , then the value of k is .......
A) 10
b) -10
c) 5
d) -5
3. The pair of equations x=a and y=b graphically represents lines which are :
a) Parallel
b) intersecting at ( b,a)
c) coincident.
d) intersecting at ( a,b)
4. For what value of K , do the equation 3x-y +8 =0 and 6x- Ky = -16 represent coincident lives?
a) 1/2
b) -1/2
c) 2
d) -2
5. If k, 2k -1 and 2k+1 are in A.P. , then value of k is....
6. The median of 1st ten prime number is____.
7. The distance of P (3,-2) from y axis is ___.
8. Write the general form of an even integer.
9. Write the form in which every odd integer can be written taking t as variable.
10.If one zero of the quadratic polynomial x2 + 3x + k is 2 , then the value of k is
11. Mode = 3________ -2 _________.
12. The total surface area of a solid hemisphere of radius r is
a) πr2
b) 2πr2
c) 3πr2
d) 4πr2
14. If a and b are the zeros of the quadratic polynomial p(x) = x2 - p(x+1) -c such that (a+1)(1+b) =0 ,then c=
15. If the diameter of a protractor is 21 cm, then find its perimeter.
16. The 10th term from the end of the A.P. 8 , 10 ,12.......126 is ...............
17. Every quadratic equation can have at most
a) three roots
b) one root
c) two roots
d) any number of roots.
18. Roots of quadratic equation x2- 7x= 0 will be
a) 7
b) 0,-7
c) 0,5
d) 0,7
19. The length of the tangent to a circle from a point P , which is 25 cm away from the centre is 24 cm. What is the radius of the circle?
20. Is the triangle with sides 12 cm , 16 cm and 18 cm a right triangle?
Section B
21.The sum of n terms of an A.P. is 3n +n2 , find its 20th term.
22. Two concentric circle with centre O are of radii 6 cm and 3cm, from an external point P , tangents PA and PB are drawn to these circle as shown in figure. If AP= 10 cm . Find BP.
23. For what value of p, the points (-3,9) , (2,p) and (4,-5 ) are collinear.
24. In ABC , right angled at B , AB= 5 cm and ACB= 30° . Find BC and AC.
25. How many cubes of 2 cm can be cut from a cuboid measuring ( 16cm 12cm 10cm)
26.Find the area of a quadrant of a circle whose circumference is 44 cm.
22. Two concentric circle with centre O are of radii 6 cm and 3cm, from an external point P , tangents PA and PB are drawn to these circle as shown in figure. If AP= 10 cm . Find BP.
24. In ABC , right angled at B , AB= 5 cm and ACB= 30° . Find BC and AC.
25. How many cubes of 2 cm can be cut from a cuboid measuring ( 16cm 12cm 10cm)
26.Find the area of a quadrant of a circle whose circumference is 44 cm.
Section C
27. In a single throw of a pair of different dice, what is the probability of getting
a) a prime number on each dice
b) a total of 9 or 11.
28. In the given figure ABC is drawn to circumscribe a circle of radius 3 cm, such that the segment BD and DC into which BC is divided by the point of contact D are of length 6 cm and 8 cm respectively. Find side AB if the ar(ABC) = 63 cm2.
30. A man goes 24 m towards West and then 10 m towards North . How far is he from the starting point?
31. For what value of k , ( 4-k) x2 + (2k+4) x + (8k+1)= 0 is a perfect square.
32. Solve for x and y by cross multiplication method x+ y = a+b , ax-by= a2- b2
33. The sum of three numbers in A.P. is 24 and their product is 440 . Find the numbers.
34. If secθ = x + 1/4x , prove that secθ + tanθ = 2x or 1/2x.
Section D
35. Once a sports organization organized a campaign "Run to live" to spread awareness about benefits of walking. In that Sachin and Anuradha participated. There was a circular path around a sports field. Sachin took 12 minutes to drive one round of the field, while Anuradha took 18 minutes for the same. Suppose they started at the same point and at the same time and went in the same direction. After how many minutes have they met again at the starting point?
36. Find the mean , median and mode of the following data :(click on image to zoom)
37. An open metallic bucket is in the shape of frustum of a cone. If the diameter of the two circular ends of the busket are 45 cm and 25 cm and the vertical height of the bucket is 24 cm. Find the area of the metallic sheet used to make the busket. Also find the volume of the water it can hold.
38. A window of a house is h metres above the ground. From the window the angles of elevation and depression of the top and bottom of another house situated on the opposite side of the lane are found to be a and b respectively. Prove that the height of house is h(1+ tan(a).tan(b)) metres.
39. If A(-5,7) , B(-4,-5) , C (-1,-6) and D (4,5) are vertices of a quadrilateral ABCD. Find the area of quadrilateral ABCD.
40. Construct a triangle ABC with sides AB= 7 cm , BC= 7.5 cm and CA = 6.5 cm. Construct a triangle similar to ABC whose side are 3/2 of the corresponding sides of ABC.
36. Find the mean , median and mode of the following data :(click on image to zoom)
38. A window of a house is h metres above the ground. From the window the angles of elevation and depression of the top and bottom of another house situated on the opposite side of the lane are found to be a and b respectively. Prove that the height of house is h(1+ tan(a).tan(b)) metres.
39. If A(-5,7) , B(-4,-5) , C (-1,-6) and D (4,5) are vertices of a quadrilateral ABCD. Find the area of quadrilateral ABCD.
40. Construct a triangle ABC with sides AB= 7 cm , BC= 7.5 cm and CA = 6.5 cm. Construct a triangle similar to ABC whose side are 3/2 of the corresponding sides of ABC.
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