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. After how many decimal places the decimal expansion of 54/150 will terminate.
2. Which of the following can't be the probability of an event?
a) 0.7
b) 2/3
c) -1.5
d) 15%
3. What is the median of first 5 natural numbers?
4. In the given figure, find x , where ST is the tangent.
5. If sinθ = cosθ, find the value of θ.
6.Find the value of m in which the points (3,5) , (m,6) and (1/2, 15/2) are collinear.
7.If sides of two similar triangles are in the ratio of 8:10, then areas of these triangles are in the ratio....
8. ABC is an isosceles right triangle , right angled at C , then AB2=
A) AC2
B) 2 AC2
c) 4AC2
d) 3AC2
9. What is the common difference of an A.P. -3, -1/2 ,....
10. In the given if AC= 9 , find BD.
11. Find the sum of first 10 natural numbers.
12. In Euclid's Division Lemma, when a= bq+r where a,b are positive integers then what values r can take?
13. If in two triangles ∆ABC and ∆PQR , AB/QR= BC/RP = CA/PQ, then
A) ∆PQR ∼ ∆CAB
b) ∆PQR ∼ ∆ABC
c)∆CBA ∼ ∆PQR
d)∆BCA ∼ ∆PQR
14. The value of k is ..... If x= 3 is one root of x2 -2kx -6 = 0.
15. If a and b are zeros of a quadratic polynomial p(x) , then factorize p(x).
16. HCF of x4y4 and x8y2
17. A line DE is drawn parallel to base BC of ABC , meeting AB in D and AC at E. If AB/BD = 4 and CE= 2 cm , find the length of AE.
18. What is the distance between the points A(c,0) and B ( 0, -c)
19. If the discriminant of 3x2 + 2x +a = 0 is double the discriminant of x2-4x +2=0 , then the value of a is.
20. If the diameter of a semi circular protractor is 14 cm, then find its perimeter.
2. Which of the following can't be the probability of an event?
a) 0.7
b) 2/3
c) -1.5
d) 15%
3. What is the median of first 5 natural numbers?
4. In the given figure, find x , where ST is the tangent.
6.Find the value of m in which the points (3,5) , (m,6) and (1/2, 15/2) are collinear.
7.If sides of two similar triangles are in the ratio of 8:10, then areas of these triangles are in the ratio....
8. ABC is an isosceles right triangle , right angled at C , then AB2=
A) AC2
B) 2 AC2
c) 4AC2
d) 3AC2
9. What is the common difference of an A.P. -3, -1/2 ,....
10. In the given if AC= 9 , find BD.
11. Find the sum of first 10 natural numbers.
12. In Euclid's Division Lemma, when a= bq+r where a,b are positive integers then what values r can take?
13. If in two triangles ∆ABC and ∆PQR , AB/QR= BC/RP = CA/PQ, then
A) ∆PQR ∼ ∆CAB
b) ∆PQR ∼ ∆ABC
c)∆CBA ∼ ∆PQR
d)∆BCA ∼ ∆PQR
14. The value of k is ..... If x= 3 is one root of x2 -2kx -6 = 0.
15. If a and b are zeros of a quadratic polynomial p(x) , then factorize p(x).
16. HCF of x4y4 and x8y2
17. A line DE is drawn parallel to base BC of ABC , meeting AB in D and AC at E. If AB/BD = 4 and CE= 2 cm , find the length of AE.
18. What is the distance between the points A(c,0) and B ( 0, -c)
19. If the discriminant of 3x2 + 2x +a = 0 is double the discriminant of x2-4x +2=0 , then the value of a is.
20. If the diameter of a semi circular protractor is 14 cm, then find its perimeter.
Section B
21. If the angle between two tangents drawn from an external point P to a circle of radius a and center O is 60°, then find the length of OP.
22. Prove that :
sec4θ - sec2θ = tan4θ + tan2θ
23. How many 2 digit number are there in between 6 and 102 which are divisible by 6.
24. If roots of x2 + Kx +12= 0 are in the ratio 1:3, find k.
25. If the system of equations 6x + 2y = 3 and Kx+ y = 2 has a unique solution, find the value of K.
26. Prove that :
√(1 +sinθ) / √ ( 1-sinθ) = tanθ + secθ
22. Prove that :
sec4θ - sec2θ = tan4θ + tan2θ
23. How many 2 digit number are there in between 6 and 102 which are divisible by 6.
24. If roots of x2 + Kx +12= 0 are in the ratio 1:3, find k.
25. If the system of equations 6x + 2y = 3 and Kx+ y = 2 has a unique solution, find the value of K.
26. Prove that :
√(1 +sinθ) / √ ( 1-sinθ) = tanθ + secθ
Section C
27. A number x is selected at random from the numbers 1, 2,3 and 4. Another number y is selected at random from the numbers 1,4,9 and 16. Find the probability that the product of x and y is less than 16.
28. A horse is tied to a pole with 28 cm long string. Find the area where the horse can graze.
29. In fig. Two concentric circles with center O , have radii 21 cm and 42 cm. If AOB = 60°, find the area of the shaded region.
30. Draw two tangents to a circle of radius 3.5 cm from a point P at a distance of 5.5 from its centre. Measure its length.
31. Prove that:
If sinθ + sin2θ = 1 , prove that cos2 + cos4 =1
32. Find the fives terms of A.P. whose sum is 25/2 and first and last term ratio is 2:3.
33. If α and β are zeros of the polynomial px2+ qx+ r and zeros are reciprocal to each other , find the relation between p and r.
34. prove that 3-√5 is an irrational number.
Section D
35. The mean of the following data is 53, find the value of f1 and f2.(given total frequency is 100)
36. A right cylindrical container of radius 6 cm and height 15 cm is full of ice cream, which has to be distributed to 10 children in equal cones having hemispherical shape on the top. If the height of the conical portion is four times its base radius, find radius of the ice cream.
37. From the top of a 120 m of high tower a man observes two cars on the opposite sides of the tower and in straight line with the base of tower with angles of depression as 60° and 45° . Find the distance between the cars.
38. If the point P divides the line segment joining the points A ( -2,-2) and B ( 2, -4) such that AP/ AB = 3/7 , then find the coordinate of P.
39. State and prove Basic proportionality theorem.
40. Solve the following pair of equation graphically :
3x+ 5y = 12 and 3x-5y = -18
Also shade the region enclosed by these two lines and x-axis.
36. A right cylindrical container of radius 6 cm and height 15 cm is full of ice cream, which has to be distributed to 10 children in equal cones having hemispherical shape on the top. If the height of the conical portion is four times its base radius, find radius of the ice cream.
37. From the top of a 120 m of high tower a man observes two cars on the opposite sides of the tower and in straight line with the base of tower with angles of depression as 60° and 45° . Find the distance between the cars.
38. If the point P divides the line segment joining the points A ( -2,-2) and B ( 2, -4) such that AP/ AB = 3/7 , then find the coordinate of P.
39. State and prove Basic proportionality theorem.
40. Solve the following pair of equation graphically :
3x+ 5y = 12 and 3x-5y = -18
Also shade the region enclosed by these two lines and x-axis.
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