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. Which of the following can be the probability of an event?
a) -0.04
b) 1.004
c) 18/23
d) 8/7
2. What is the mode of the observation 5, 7, 8, 5, 7, 6, 9, 5, 10, 6.
3. If the circumference of two circles are equal , then what is the ratio between their areas?
4. In the given figure, ABC is circumscribing a circle , then find the length of BC.
5. Write the statement of Pythagoras theorem.
6. If k, 2k-1 and 2k+1 are in A.P. then the value of k is .......
7. If discriminant of 6x2 - bx+2= 0 is 1 ,then the value of b is
8. The mean and mode of the data are 24 and 12 respectively. Find the median.
9. Does the point (2,3) lie on line of graph of 3x-2y =5.
10. If one of zeros of quadratic polynomial (k-1)x2 + Kx +1 is -3 , then the value of K is
11. If the area of circle is 616 cm2, what is its circumference?
12. What can you say about the product of a non zero rational and irrational number?
13. What cross section is made by a cone when it is cut parallel to its base?
14. Write the statement of Basic proportionality theorem.
15. From the external point P tangents PA and PB are drawn to a circle with center O. If ∠PAB = 50° , then find ∠AOB.
16. For what value of k system of equations x+ 2y = 3 and 5x+ ky+7= 0 has a unique solution.
17. If α and β are zeros of x2-x-1, find the value of 1/α + 1/β.
18. After how many places the decimal expansion of 13497/1250 will terminate?
19. A quadratic polynomial , whose zeros are -3 and 4 , is
a) x2-x+12
b) x2+ x+ 12
c) x2/2 - x/2 -6
d) 2x2 + 2x -24.
20. (x-1)3 = x3+1 is quadratic equation (T/F)
a) -0.04
b) 1.004
c) 18/23
d) 8/7
2. What is the mode of the observation 5, 7, 8, 5, 7, 6, 9, 5, 10, 6.
3. If the circumference of two circles are equal , then what is the ratio between their areas?
4. In the given figure, ABC is circumscribing a circle , then find the length of BC.
6. If k, 2k-1 and 2k+1 are in A.P. then the value of k is .......
7. If discriminant of 6x2 - bx+2= 0 is 1 ,then the value of b is
8. The mean and mode of the data are 24 and 12 respectively. Find the median.
9. Does the point (2,3) lie on line of graph of 3x-2y =5.
10. If one of zeros of quadratic polynomial (k-1)x2 + Kx +1 is -3 , then the value of K is
11. If the area of circle is 616 cm2, what is its circumference?
12. What can you say about the product of a non zero rational and irrational number?
13. What cross section is made by a cone when it is cut parallel to its base?
14. Write the statement of Basic proportionality theorem.
15. From the external point P tangents PA and PB are drawn to a circle with center O. If ∠PAB = 50° , then find ∠AOB.
16. For what value of k system of equations x+ 2y = 3 and 5x+ ky+7= 0 has a unique solution.
17. If α and β are zeros of x2-x-1, find the value of 1/α + 1/β.
18. After how many places the decimal expansion of 13497/1250 will terminate?
19. A quadratic polynomial , whose zeros are -3 and 4 , is
a) x2-x+12
b) x2+ x+ 12
c) x2/2 - x/2 -6
d) 2x2 + 2x -24.
20. (x-1)3 = x3+1 is quadratic equation (T/F)
Section B
21. A card is drawn at random from a well shuffled pack of 52 playing cards. Find probability of getting neither a red card nor a queen.
22. Find the mean of following distribution
23. Find the height of largest right circular cone that can be cut out of a cube whose volume is 729 cm3.
24. If x= psecθ + qtanθ & y= ptanθ + qsecθ then prove that x2- y2= p2-q2.
25. E is a point on the side AD produced of a parallelogram ABCD and BE intersect CD at F. Show that ∆ABE ∼ ∆DCB.
26. Solve using quadratic formula
4√3x2 + 5x- 2√3=0
22. Find the mean of following distribution
24. If x= psecθ + qtanθ & y= ptanθ + qsecθ then prove that x2- y2= p2-q2.
25. E is a point on the side AD produced of a parallelogram ABCD and BE intersect CD at F. Show that ∆ABE ∼ ∆DCB.
26. Solve using quadratic formula
4√3x2 + 5x- 2√3=0
Section C
27. Area of a sector of a circle of radius 36 cm is 54π cm2. Find the length of the corresponding arc of the sector.
28. In the given figure,AB is a tangent to a circle with center O. Prove that ∠BPQ= ∠PRQ.
29. In the given figure, AB is a tangent to a circle with center O. Prove BPQ= PRQ.
30. If acosθ + b sinθ= m and asinθ - b cosθ= n , Prove that a2 + b2 = m2 + n2
31. Show that the points A(-3,2) B (-5,-5) C(2,-3) and D (4,4) are the verticles of a rhombus.
32. Find the middle term of an A.P. 20,16, 12,.......,-176.
33. Prove that (tanθ - cotθ)/ sinθ cosθ = tan2θ - cot2θ.
34. Find the ratio in which the point (2,y) divides the lines segment joining the points A( -2, 2) and B(3, 7). Also find the value of y.
Section D
35. If the median of the distribution given below is 28.5 , find the values of x and y (given total frequency is 60) .
36. A container opened at the top and made up of a metal sheet , is in the form of a frustum of a cone of height 16 cm with radio of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of milk which can completely fill the container , at the rate of ₹ 50 per litre. Also find the cost of metal sheet used to make the container, if it costs ₹ 10 per 100 cm
37. From the top of a tower h metre high, the angles of depression of two objects , which are in the line with the foot of the tower are α and β. Find the distance the two objects.
38. Construct a ∆ABC of sides AB= 4cm ,BC= 5 cm and AC= 7 cm, construct another triangle similar to ∆ABC such that each of its sides is 5/7 of the corresponding side of ∆ABC.
39. The area of a rectangle gets reduced by a 9 sq. Units, if its length is reduced by 5 units and the breadth is increased by 3 units. The area is increased by 67 sq. Unit if length is increased by 3 units and breadth is increased by 2 units. Find the perimeter of the rectangle.
40. Prove that in a right angle triangle , the square of the hypotenuse is equal the sum of the squares of other two sides
37. From the top of a tower h metre high, the angles of depression of two objects , which are in the line with the foot of the tower are α and β. Find the distance the two objects.
38. Construct a ∆ABC of sides AB= 4cm ,BC= 5 cm and AC= 7 cm, construct another triangle similar to ∆ABC such that each of its sides is 5/7 of the corresponding side of ∆ABC.
39. The area of a rectangle gets reduced by a 9 sq. Units, if its length is reduced by 5 units and the breadth is increased by 3 units. The area is increased by 67 sq. Unit if length is increased by 3 units and breadth is increased by 2 units. Find the perimeter of the rectangle.
40. Prove that in a right angle triangle , the square of the hypotenuse is equal the sum of the squares of other two sides
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